`, then `julia --project -e 'using Pkg; Pkg.instantiate()'`), or write the stored deck out of the file and run it with the current version, fixing the keys the error names.
diff --git a/examples/DIIID-like_SLAYER_example/gpec.toml b/examples/DIIID-like_SLAYER_example/gpec.toml
new file mode 100644
index 0000000000..fa41a0dd50
--- /dev/null
+++ b/examples/DIIID-like_SLAYER_example/gpec.toml
@@ -0,0 +1,97 @@
+# DIII-D-like SLAYER tearing-mode growth-rate example.
+# Reuses the equilibrium and H-mode kinetic profiles of the sibling
+# DIIID-like_ideal_example (geqdsk referenced by relative path; not
+# duplicated). Runs equilibrium + ForceFreeStates + SLAYER; there is no
+# [PerturbedEquilibrium] section, so that stage does not run.
+
+[Run]
+verbose = true # Log each stage's progress
+
+[Equilibrium]
+eq_filename = "../DIIID-like_ideal_example/TkMkr_D3Dlike_Hmode.geqdsk" # Path to equilibrium file
+kinetic_file = "../DIIID-like_ideal_example/TkMkr_D3Dlike_Hmode_kinetic.h5" # Kinetic-profile file (HDF5 GPEC kinetic schema or 6-column ASCII), read once into the equilibrium
+eq_type = "efit" # Type of the input 2D equilibrium file
+jac_type = "hamada" # Coordinate system (hamada, pest, boozer, equal_arc)
+grid_type = "auto" # Radial grid packing type
+psilow = 1e-4 # Lower limit of normalized flux coordinate
+psihigh = 0.9995 # Upper limit of normalized flux coordinate
+mpsi = 0 # Number of radial grid points (0 = auto-compute from psi_accuracy)
+psi_accuracy = 0.001 # Target absolute error in q for auto-mpsi
+mtheta = 256 # Number of poloidal grid points
+newq0 = 0 # Target on-axis safety factor q(0) (0 = use input value; q is positive, so negative values are rejected)
+flux_surface_rtol = 1e-10 # Relative tolerance of the ODE solves that trace each flux surface
+
+# Presence runs the LocalStability stage (Mercier D_I, resistive D_R, ballooning Δ', first α boundary); keys are the LocalStabilityProblem settings, numerics in [Ballooning]
+[LocalStability]
+theta_k = 0.0 # Ballooning angle θ_k, used by both the profile scan and the α-boundary scan
+alpha_boundary_scan = true # Run the first ballooning α-boundary scan (a root find per ψ surface)
+
+# Numerical settings of the ballooning scans
+[Ballooning]
+ode_tol = 1e-8 # Relative and absolute tolerance of the ballooning ODE integration behind Δ'
+n_scan = 24 # Resolution of the α scan for the first boundary
+max_alpha_scale = 8.0 # Upper end of the α search, as a multiple of the experimental α
+alpha_tol = 1e-3 # Bisection tolerance of the critical α, in the same multiples
+psi_window = [0.1, 0.99] # ψ_N range of the α scan; surfaces outside it are NaN
+
+[ForceFreeStates]
+vac_flag = true # Compute plasma, vacuum, and total energies for free-boundary modes
+
+dW_edge_scan_start = 0.99 # Edge dW(ψ) diagnostic scan band [dW_edge_scan_start, psilim]; set ≥ psilim to disable
+qlow = 1.02 # Integration initiated at q determined by min(q0, qlow)...
+qhigh = 1e3 # Integration terminated at q limit determined by min(qa, qhigh)...
+
+nn = 1 # Toroidal mode number, or consecutive numbers as a list
+delta_mlow = 8 # Expands lower bound of Fourier harmonics
+delta_mhigh = 8 # Expands upper bound of Fourier harmonics
+mtheta_vacuum = 512 # Number of points used in splines over poloidal angle at the plasma-vacuum interface
+
+singfac_min = 1e-4 # Fractional distance from rational q at which ideal jump enforced
+
+# Integrator selection and domain truncation (see ForceFreeStatesControl docstring for details)
+integrator = "Riccati" # Integration formalism, whose numerical settings are its own section: "Forward" (dense ξ, needed for [PerturbedEquilibrium]/kinetic), "Riccati" (chunked propagator BVP, unlocks the singular-surface Δ′ matrix), or "Galerkin" (outer-region singular Galerkin Δ′)
+truncate_at_rational_offset = true # TRUE for diverted geqdsks — q → ∞ at separatrix, so rational_offset_fraction truncation avoids the δW kink instability at negligible domain cost
+rational_offset_fraction = 0.2 # Truncate integration at (last_rational_q + rational_offset_fraction) / n
+
+# Numerical settings of the Riccati integrator
+[Riccati]
+eulerlagrange_tolerance = 1e-10# Relative tolerance for ODE integration of Euler-Lagrange equations
+save_interval = 1 # Save every Nth ODE step (1=all). Always saves near rational surfaces.
+renorm_threshold = 1e3 # Column-norm threshold that triggers solution renormalization
+
+# SLAYER tearing-mode growth-rate analysis on the DIII-D-like H-mode equilibrium.
+# Runs off the ForceFreeStates result (no PE). The plasma (profiles incl. the χ⊥/χ_φ
+# heat/momentum diffusivities, species, Z_eff) is the [Equilibrium] kinetic_file, shared
+# with the kinetic/NTV physics. Per-surface (uncoupled) analysis: track the 2/1, 3/1, and
+# 4/1 (the headline is the unstable 2/1). The 5/1 and 6/1 sit near the edge (ψ_N ≥ 0.97),
+# far from the core where the slab-layer approximation holds; their Δ' are excessively
+# large and likely invalid, no Re/Im contour crossing polishes to a true zero, and the
+# validity gate correctly reports them as no_root rather than a spurious growth rate.
+[Tearing]
+inner_model = "SLAYER" # Inner-layer model, stated in its own section: "SLAYER" or "GGJ"
+coupling_mode = "uncoupled" # "uncoupled" (per-surface) or "coupled" (multi-surface determinant)
+# omega_E_kHz = {"2/1" = 0.0, "3/1" = 3.0} # override of the E×B rotation Ω_E/2π per unit n [kHz], keyed by m/n; unlisted surfaces use the kinetic file
+
+[Tearing.search]
+scan_mode = "amr" # Q-plane scan strategy: "amr" (adaptive refinement) or "brute_force"
+Q_re_range = [-2.0, 2.0] # Scan box in the normalized Q plane, Re(Q) axis
+Q_im_range = [-0.5, 3.0] # Scan box in the normalized Q plane, Im(Q) axis
+nre = 41 # Grid resolution along the Re(Q) axis
+nim = 31 # Grid resolution along the Im(Q) axis
+pole_threshold_adaptive = true # SLAYER |Δ| spans many orders; adapt to 10·median(|Δ|)
+filter_above_poles = true # Discard roots above the highest pole γ
+filter_outside_re = true # Condition the above-pole filter on the +γ step exiting the Re(Δ)=0 contour loop
+polish_roots = true # refine each root to the true zero; enables the validity gate
+store_scan = false # per-surface scans omitted from HDF5 (uncoupled has one per surface)
+
+# Critical resonant field b_r/B_φ for error-field penetration at each SLAYER surface, from the
+# Cole-Fitzpatrick 2006 torque balance with P = P_tor of each layer and Q0 = τ_k·n·Ω_E, so it
+# needs the kinetic file's omega_E (or omega_E_kHz). b_crit is taken at the penetration fold met
+# walking from Q0 toward Q_e; Qmin/Qmax may be set to override the sampled range.
+[Tearing.CriticalResonantField]
+n = 2000 # number of Q samples per surface
+store_scan = false # write the per-surface Q, torque balance and Δ samples to gpec.h5
+
+[SLAYER]
+D_c_type = "none" # Critical-Δ offset selector: "none", "lar", "fitzpatrick", or "toroidal"
+P_perp_model = "D_perp" # Perpendicular Prandtl number model: "D_perp" (default), "chi_perp_e", "chi_perp_i", "P_phi", "c_beta", or "tau_E" (needs [Equilibrium] tau_E; also replaces the χ_φ-based P_tor)
diff --git a/examples/DIIID-like_error_field_example/analyze_example.jl b/examples/DIIID-like_error_field_example/analyze_example.jl
new file mode 100644
index 0000000000..20e2ec2b96
--- /dev/null
+++ b/examples/DIIID-like_error_field_example/analyze_example.jl
@@ -0,0 +1,155 @@
+using Pkg;
+Pkg.activate(joinpath(@__DIR__, "../.."))
+using GeneralizedPerturbedEquilibrium, Plots, Printf, HDF5
+using GeneralizedPerturbedEquilibrium: PerturbedEquilibrium, ErrorFields
+isinteractive() ? plotlyjs() : gr()
+
+h5path = joinpath(@__DIR__, "gpec.h5")
+
+# The run stored every coil set's spectrum linearization. Project it onto the dominant
+# resonant-coupling mode over the core window (ψ_N ≤ 0.9, the default) to see which coils matter.
+rc = PerturbedEquilibrium.ResonantCoupling(h5path)
+sens = ErrorFields.CoilSensitivities(h5path)
+full = ErrorFields.sensitivity_table(sens, PerturbedEquilibrium.dominant_coupling(rc))
+
+names = full.coil_names
+fcoils = findall(startswith("F"), names)
+
+println("coil |δ_nom| per mm of shift per mm of rim curvature")
+for (j, nm) in enumerate(names)
+ @printf("%-8s %10.3e %13.3e %13.3e %9.1e\n", nm, abs(full.delta_as_designed[j]), full.abs_delta_shift_per_mm[j],
+ full.abs_delta_rim_per_mm[j], max(maximum(sens.shift_linearity_residual[:, j]), maximum(sens.tilt_linearity_residual[:, j])))
+end
+
+# Error field per millimetre of in-plane shift and per millimetre of rim displacement from tilt,
+# F coils only, both in the units mechanical tolerances arrive in. Axisymmetric hoops have no
+# nominal n=1 drive, so the sensitivities are their whole error-field story.
+p_shift = bar(names[fcoils], full.abs_delta_shift_per_mm[fcoils]; label="core window ψ_N ≤ 0.9", alpha=0.75,
+ ylabel="|δ| per mm", title="Dominant-mode error field per mm of F-coil shift", xrotation=45, xticks=(1:length(fcoils), names[fcoils]),
+ left_margin=12Plots.mm, bottom_margin=8Plots.mm, legend=:topright)
+p_tilt = bar(names[fcoils], full.abs_delta_rim_per_mm[fcoils]; label="core window ψ_N ≤ 0.9", alpha=0.75,
+ ylabel="|δ| per mm of rim", title="Dominant-mode error field per mm of F-coil rim displacement", xrotation=45,
+ xticks=(1:length(fcoils), names[fcoils]), left_margin=12Plots.mm, bottom_margin=8Plots.mm, legend=:topright)
+p_sens = plot(p_shift, p_tilt; layout=(2, 1), size=(900, 700))
+display(p_sens)
+sens_path = joinpath(@__DIR__, "fcoil_sensitivities.png")
+Plots.savefig(p_sens, sens_path)
+println("Saved: ", abspath(sens_path))
+
+# Where the sensitivity lives in mode space: the spectrum derivative of the most and least
+# sensitive F coils under a 1 mm shift along x, against the C-coil's nominal spectrum.
+step_series(m, a) = (vcat(m[1] - 1, m, m[end] + 1), vcat(0.0, a, 0.0))
+m = sens.m_modes
+order = sortperm(full.abs_delta_shift_per_mm[fcoils]; rev=true)
+picks = [fcoils[order[1]], fcoils[order[end]]]
+p_spec = plot(; xlabel="poloidal mode m", ylabel="|b̃| [T]", yscale=:log10, legend=:topleft,
+ title="Root-area-weighted spectra: C-coil as built vs F coils shifted 1 mm in x",
+ left_margin=12Plots.mm, bottom_margin=6Plots.mm, size=(900, 420))
+c = findfirst(==("d3d_c"), names) # file-based sets are named machine_name
+me, ae = step_series(m, max.(abs.(sens.field_as_designed[:, c]), 1e-30))
+plot!(p_spec, me, ae; seriestype=:steppre, lw=2, label="C-coil nominal (20 A)")
+for j in picks
+ me, ae = step_series(m, max.(1e-3 .* abs.(sens.shift_sensitivity_per_m[:, 1, j]), 1e-30))
+ plot!(p_spec, me, ae; seriestype=:steppre, lw=2, label="$(names[j]) ∂b̃/∂Δx · 1 mm")
+end
+display(p_spec)
+spec_path = joinpath(@__DIR__, "fcoil_spectra.png")
+Plots.savefig(p_spec, spec_path)
+println("Saved: ", abspath(spec_path))
+
+# The tolerance Monte Carlo: the intrinsic and corrected |δ| distributions the run wrote (full
+# window, dominant mode), and a post-hoc re-run over the edge window with the same tolerances.
+mc = ErrorFields.MonteCarloResult(h5path)
+mc_edge = ErrorFields.run_monte_carlo(h5path; psi_low=0.7, nsample=200_000, nbatch=4, seed=1)
+centers(m) = (m.abs_delta_bin_edges[1:end-1] .+ m.abs_delta_bin_edges[2:end]) ./ 2
+p_pdf = plot(; xlabel="dominant-mode overlap |δ|", ylabel="probability density", legend=:topright,
+ title="Tolerance Monte Carlo: |δ| over sampled misalignments", left_margin=12Plots.mm, bottom_margin=6Plots.mm, size=(900, 420))
+plot!(p_pdf, centers(mc), mc.abs_delta_pdf; lw=2, label="intrinsic, all rational surfaces")
+plot!(p_pdf, centers(mc), mc.abs_delta_efc_pdf; lw=2, label="corrected (efc_factor = 2)")
+plot!(p_pdf, centers(mc_edge), mc_edge.abs_delta_pdf; lw=2, ls=:dash, label="intrinsic, ψ_N ≥ 0.7")
+vline!(p_pdf, [mc.abs_delta_total_as_designed]; ls=:dot, c=:black, label="as designed")
+display(p_pdf)
+pdf_path = joinpath(@__DIR__, "tolerance_pdf.png")
+Plots.savefig(p_pdf, pdf_path)
+println("Saved: ", abspath(pdf_path))
+@printf("⟨|δ|⟩ = %.3e intrinsic, %.3e corrected; as designed %.3e; batch spread of ⟨|δ|⟩ ≈ %.1e\n",
+ mc.abs_delta_sampled_mean, mc.abs_delta_efc_sampled_mean, mc.abs_delta_total_as_designed,
+ maximum(abs.(vec(sum(mc.abs_delta_pdf_batches .* centers(mc) .* diff(mc.abs_delta_bin_edges); dims=1)) .- mc.abs_delta_sampled_mean)))
+
+# Locking risk: the threshold distribution against the overlap distribution, and the risk against
+# tolerance scale with the allowable tolerance for a 1 % target read off the scan.
+scan = ErrorFields.ToleranceScan(h5path)
+risk_nominal = h5open(
+ f -> (read(f["ErrorFields/Risk/locking_probability_percent"]), read(f["ErrorFields/Risk/locking_probability_efc_percent"]),
+ read(f["ErrorFields/Risk/threshold_fit"]), read(f["ErrorFields/Risk/threshold_pdf"]), read(f["ErrorFields/Risk/locking_probability_given_delta"])), h5path, "r")
+locking_probability_percent, locking_probability_efc_percent, thr_nom, thr_pdf, p_given = risk_nominal
+p_thr = plot(; xlabel="dominant-mode overlap |δ|", ylabel="probability density", legend=:topright, xscale=:log10,
+ title="Overlap distribution vs ITPA penetration threshold", left_margin=12Plots.mm, bottom_margin=6Plots.mm, size=(900, 420))
+c = centers(mc)
+keep = c .> 0
+plot!(p_thr, c[keep], mc.abs_delta_pdf[keep] ./ maximum(mc.abs_delta_pdf); lw=2, label="intrinsic |δ| (normalized)")
+plot!(p_thr, c[keep], mc.abs_delta_efc_pdf[keep] ./ maximum(mc.abs_delta_efc_pdf); lw=2, label="corrected |δ| (normalized)")
+plot!(p_thr, c[keep], thr_pdf[keep] ./ maximum(thr_pdf); lw=2, c=:black, label="threshold density (normalized)")
+plot!(p_thr, mc.abs_delta_bin_edges[2:end], p_given[2:end]; lw=1.5, ls=:dash, c=:red, label="P(lock | δ)")
+vline!(p_thr, [thr_nom]; ls=:dot, c=:black, label="nominal threshold")
+p_scan = plot(; xlabel="tolerance scale (× tolerances.toml)", ylabel="locking probability [%]", xscale=:log10, yscale=:log10,
+ legend=:topleft, title="Risk vs tolerance scale", left_margin=12Plots.mm, bottom_margin=6Plots.mm)
+plot!(p_scan, scan.tolerance_scale, max.(scan.locking_probability_percent, 1e-4); marker=:circle, lw=2, label="intrinsic")
+plot!(p_scan, scan.tolerance_scale, max.(scan.locking_probability_efc_percent, 1e-4); marker=:square, lw=2, label="corrected")
+hline!(p_scan, [1.0]; ls=:dash, c=:gray, label="1 % target")
+p_risk = plot(p_thr, p_scan; layout=(2, 1), size=(900, 760))
+display(p_risk)
+risk_path = joinpath(@__DIR__, "locking_risk.png")
+Plots.savefig(p_risk, risk_path)
+println("Saved: ", abspath(risk_path))
+@printf("P_lock = %.2f %% intrinsic, %.2f %% corrected at the design tolerances; allowable scale for 1 %%: %.2f (intrinsic), %.2f (corrected)\n",
+ locking_probability_percent, locking_probability_efc_percent, ErrorFields.allowable_tolerance(scan, 1.0), ErrorFields.allowable_tolerance(scan, 1.0; corrected=true))
+
+# The same figures through the Analysis module, which overplots design revisions when given
+# several `label => gpec.h5` pairs.
+p_summary = GeneralizedPerturbedEquilibrium.Analysis.ErrorFields.plot_error_field_summary(h5path; save_path=joinpath(@__DIR__, "error_field_summary.png"))
+display(p_summary)
+
+# How much intrinsic error field the C-coil could correct before its own NTV torque, at a
+# 4 N·m budget, costs the rotation that holds the penetration threshold up.
+p_ntv = GeneralizedPerturbedEquilibrium.Analysis.ErrorFields.plot_efc_ntv_limits(h5path; torque_budget=4.0, save_path=joinpath(@__DIR__, "efc_ntv_limits.png"))
+display(p_ntv)
+for c in ErrorFields.read_efc_couplings(h5path)
+ lim = ErrorFields.max_correctable_overlap(c; delta_threshold=thr_nom, torque_budget=4.0)
+ @printf("%s: |δ| = %.3e per kAt, resonant fraction %.1f %%, torque %.3e (full) / %.3e (residual) N·m per kAt²; correctable up to %.2f × threshold\n",
+ c.coil_name, c.delta_per_kat, c.resonant_fraction_percent, c.torque_full_per_kat2, c.torque_residual_per_kat2, lim.with_ntv / thr_nom)
+end
+
+# ---------------------------------------------------------------------------------------------
+# Comparing a coil revision against this run, without re-solving the plasma.
+#
+# The context holds everything that does not depend on which coils are being judged, so any
+# geometry can be swept against it. Here the example's own coils, shifted a millimetre, stand in
+# for a second revision.
+AEF = GeneralizedPerturbedEquilibrium.Analysis.ErrorFields
+FT = GeneralizedPerturbedEquilibrium.ForcingTerms
+
+ctx = ErrorFields.ResonantDriveContext(h5path)
+sets = FT.load_coil_sets(ctx.cfg, 1; equil=ctx.equil) # the deck's own coils, rebuilt from the file
+as_built = ErrorFields.coil_overlaps(ctx, sets)
+moved = ErrorFields.coil_overlaps(ctx, [FT.apply_transforms(cs, FT.CoilSetConfig(; shiftx=fill(1e-3, cs.ncoil)); n_tilt=0) for cs in sets])
+
+println("\ncoil |δ| as built |δ| shifted 1 mm resonant fraction")
+for (a, b) in zip(as_built, moved)
+ @printf("%-14s %12.4e %14.4e %14.1f %%\n", a.coil_name, abs(a.delta), abs(b.delta), a.resonant_fraction_percent)
+end
+
+# Currents are applied afterwards by scaling, so a pair driven in opposition is one call. An
+# unmatched name raises rather than contributing zero, which is what a renamed coil would do.
+pair = ErrorFields.combine_overlaps(as_built, as_built[1].coil_name => 1.0, as_built[end].coil_name => -1.0; name="opposed pair")
+@printf("opposed pair: |δ| = %.4e, resonant fraction %.1f %%\n", abs(pair.delta), pair.resonant_fraction_percent)
+
+# Why a coil couples as it does, which the per-coil bars above cannot answer. The first says
+# whether it drives a different part of the spectrum or simply drives less; the second decomposes
+# the overlap into the harmonics that produced it; the third puts both on the control surface
+# against the dominant mode.
+for (name, fn) in (("applied_spectra", AEF.plot_applied_spectra), ("overlap_contributions", AEF.plot_overlap_contributions),
+ ("surface_overlay", AEF.plot_surface_overlay))
+ path = joinpath(@__DIR__, "$name.png")
+ display(fn(ctx, as_built; save_path=path))
+end
diff --git a/examples/DIIID-like_error_field_example/gpec.toml b/examples/DIIID-like_error_field_example/gpec.toml
new file mode 100644
index 0000000000..070ffa8172
--- /dev/null
+++ b/examples/DIIID-like_error_field_example/gpec.toml
@@ -0,0 +1,251 @@
+# DIII-D-like H-mode equilibrium — n=1 error-field sensitivity of the poloidal-field coils.
+# Same free-boundary ideal solve as DIIID-like_ideal_example, with the DIII-D C-coil supplying
+# a small intrinsic n=1 error field and every F coil (F1A–F9B) added as a single-filament hoop at the
+# centroid of its winding pack, from OpenFUSIONToolkit's TokaMaker DIIID_geom.json. An
+# axisymmetric hoop drives no n=1 field as built, so each F coil's error-field content is
+# entirely its sensitivity to misalignment: the [ErrorFields] stage linearizes every coil set's
+# resonant drive with respect to rigid shifts and tilts, samples illustrative tolerances
+# (tolerances.toml) into an error-field distribution, and analyze_example.jl ranks the coils
+# and plots the distribution.
+
+[Run]
+verbose = true # Log each stage's progress
+
+[Equilibrium]
+eq_filename = "../DIIID-like_ideal_example/TkMkr_D3Dlike_Hmode.geqdsk" # Path to equilibrium file
+kinetic_file = "../DIIID-like_ideal_example/TkMkr_D3Dlike_Hmode_kinetic.h5" # Kinetic-profile file (HDF5 GPEC kinetic schema or 6-column ASCII), read once into the equilibrium
+eq_type = "efit" # Type of the input 2D equilibrium file
+jac_type = "hamada" # Coordinate system (hamada, pest, boozer, equal_arc, park, custom)
+grid_type = "auto" # Radial grid packing type ("auto" = two-pass measured-curvature grid)
+psilow = 1e-4 # Lower limit of normalized poloidal flux
+psihigh = 0.995 # Upper limit of normalized poloidal flux (captures q=6 at this Ip)
+mpsi = 0 # Number of radial grid intervals (0 = two-pass auto grid from psi_accuracy)
+psi_accuracy = 0.001 # Target relative accuracy of splined profile derivatives for the auto grid
+mtheta = 256 # Number of poloidal grid points
+newq0 = 0 # Target on-axis safety factor q(0) (0 = use input value; q is positive, so negative values are rejected)
+flux_surface_rtol = 1e-10 # Relative tolerance of the ODE solves that trace each flux surface
+impurity_charge = 6 # Impurity charge (carbon)
+impurity_mass = 12 # Impurity mass [proton masses]
+
+[[Equilibrium.ion_species]]
+z = 1 # Charge in units of e
+m = 2 # Mass in proton masses
+fraction = 1.0 # Fraction of the n_i profile this species carries
+
+# Presence runs the LocalStability stage (Mercier D_I, resistive D_R, ballooning Δ', first α boundary); keys are the LocalStabilityProblem settings, numerics in [Ballooning]
+[LocalStability]
+theta_k = 0.0 # Ballooning angle θ_k, used by both the profile scan and the α-boundary scan
+alpha_boundary_scan = true # Run the first ballooning α-boundary scan (a root find per ψ surface)
+
+# Numerical settings of the ballooning scans
+[Ballooning]
+ode_tol = 1e-8 # Relative and absolute tolerance of the ballooning ODE integration behind Δ'
+n_scan = 24 # Resolution of the α scan for the first boundary
+max_alpha_scale = 8.0 # Upper end of the α search, as a multiple of the experimental α
+alpha_tol = 1e-3 # Bisection tolerance of the critical α, in the same multiples
+psi_window = [0.1, 0.99] # ψ_N range of the α scan; surfaces outside it are NaN
+
+[ForceFreeStates]
+vac_flag = true # Compute plasma, vacuum, and total energies for free-boundary modes
+
+dW_edge_scan_start = 0.99 # Edge dW(ψ) diagnostic scan band [dW_edge_scan_start, psilim]; set ≥ psilim to disable
+qlow = 1.02 # Integration initiated at q determined by min(q0, qlow)
+qhigh = 1e3 # Integration terminated at q limit determined by min(qa, qhigh)
+
+nn = 1 # Toroidal mode number, or consecutive numbers as a list
+delta_mlow = 8 # Expands lower bound of Fourier harmonics
+delta_mhigh = 8 # Expands upper bound of Fourier harmonics
+mtheta_vacuum = 512 # Number of points used in splines over poloidal angle at the plasma-vacuum interface
+
+singfac_min = 1e-6 # Fractional distance from rational q at which ideal jump enforced
+
+# Integrator selection and domain truncation (see ForceFreeStatesControl docstring for details)
+integrator = "Forward" # Integration formalism, whose numerical settings are its own section: "Forward" (dense ξ, needed for [PerturbedEquilibrium]/kinetic), "Riccati" (chunked propagator BVP, unlocks the singular-surface Δ′ matrix), or "Galerkin" (outer-region singular Galerkin Δ′)
+truncate_at_rational_offset = true # Truncate at (last_rational_q + rational_offset_fraction)/n — TRUE for diverted equilibria (q → ∞ at separatrix)
+rational_offset_fraction = 0.2 # Truncate integration at (last_rational_q + rational_offset_fraction)/n (used when truncate_at_rational_offset = true)
+
+# Numerical settings of the forward integrator
+[Forward]
+eulerlagrange_tolerance = 1e-10 # Relative tolerance for ODE integration of Euler-Lagrange equations
+save_interval = 1 # Save every Nth ODE step (1=all). Always saves near rational surfaces.
+renorm_threshold = 1e3 # Column-norm threshold that triggers solution renormalization
+
+[ForcingTerms]
+forcing_data_format = "coil" # Format: "ascii", "hdf5", or "coil" (Biot-Savart from 3D wires)
+machine = "d3d" # Geometry prefix; resolves to bundled coil_geometries/d3d_*.dat
+mtheta_coil = 480 # Poloidal grid for boundary B·n̂ evaluation
+nzeta_coil = 32 # Toroidal grid (0 = auto = 32·n)
+
+[[ForcingTerms.coil_set]]
+name = "c" # Coil set; resolves to coil_geometries/d3d_c.dat (DIII-D C-coil, 6 coils): the nominal n=1 source
+currents = [20.0, 10.0, -10.0, -20.0, -10.0, 10.0] # n=1 cosine phasing, 20 A peak: an intrinsic error field just below the penetration threshold [A]
+
+[[ForcingTerms.coil_set]]
+name = "F1A" # DIII-D F coil F1A: 58-turn winding pack, TokaMaker DIIID_geom.json cross-section centroid
+source = "pf_hoop" # Single-filament horizontal hoop approximation of the winding pack
+radius = 0.8608 # Hoop major radius: centroid R of the pack cross-section [m]
+height = 0.1683 # Hoop height: centroid Z of the pack cross-section [m]
+currents = [58000.0] # 1 kA per turn × 58 turns; sensitivities scale linearly with current [A]
+
+[[ForcingTerms.coil_set]]
+name = "F2A" # DIII-D F coil F2A: 58-turn winding pack, TokaMaker DIIID_geom.json cross-section centroid
+source = "pf_hoop" # Single-filament horizontal hoop approximation of the winding pack
+radius = 0.8614 # Hoop major radius: centroid R of the pack cross-section [m]
+height = 0.5081 # Hoop height: centroid Z of the pack cross-section [m]
+currents = [58000.0] # 1 kA per turn × 58 turns; sensitivities scale linearly with current [A]
+
+[[ForcingTerms.coil_set]]
+name = "F3A" # DIII-D F coil F3A: 58-turn winding pack, TokaMaker DIIID_geom.json cross-section centroid
+source = "pf_hoop" # Single-filament horizontal hoop approximation of the winding pack
+radius = 0.8628 # Hoop major radius: centroid R of the pack cross-section [m]
+height = 0.8491 # Hoop height: centroid Z of the pack cross-section [m]
+currents = [58000.0] # 1 kA per turn × 58 turns; sensitivities scale linearly with current [A]
+
+[[ForcingTerms.coil_set]]
+name = "F4A" # DIII-D F coil F4A: 58-turn winding pack, TokaMaker DIIID_geom.json cross-section centroid
+source = "pf_hoop" # Single-filament horizontal hoop approximation of the winding pack
+radius = 0.8611 # Hoop major radius: centroid R of the pack cross-section [m]
+height = 1.1899 # Hoop height: centroid Z of the pack cross-section [m]
+currents = [58000.0] # 1 kA per turn × 58 turns; sensitivities scale linearly with current [A]
+
+[[ForcingTerms.coil_set]]
+name = "F5A" # DIII-D F coil F5A: 58-turn winding pack, TokaMaker DIIID_geom.json cross-section centroid
+source = "pf_hoop" # Single-filament horizontal hoop approximation of the winding pack
+radius = 1.0041 # Hoop major radius: centroid R of the pack cross-section [m]
+height = 1.5169 # Hoop height: centroid Z of the pack cross-section [m]
+currents = [58000.0] # 1 kA per turn × 58 turns; sensitivities scale linearly with current [A]
+
+[[ForcingTerms.coil_set]]
+name = "F6A" # DIII-D F coil F6A: 55-turn winding pack, TokaMaker DIIID_geom.json cross-section centroid
+source = "pf_hoop" # Single-filament horizontal hoop approximation of the winding pack
+radius = 2.6124 # Hoop major radius: centroid R of the pack cross-section [m]
+height = 0.4376 # Hoop height: centroid Z of the pack cross-section [m]
+currents = [55000.0] # 1 kA per turn × 55 turns; sensitivities scale linearly with current [A]
+
+[[ForcingTerms.coil_set]]
+name = "F7A" # DIII-D F coil F7A: 55-turn winding pack, TokaMaker DIIID_geom.json cross-section centroid
+source = "pf_hoop" # Single-filament horizontal hoop approximation of the winding pack
+radius = 2.3733 # Hoop major radius: centroid R of the pack cross-section [m]
+height = 1.1171 # Hoop height: centroid Z of the pack cross-section [m]
+currents = [55000.0] # 1 kA per turn × 55 turns; sensitivities scale linearly with current [A]
+
+[[ForcingTerms.coil_set]]
+name = "F8A" # DIII-D F coil F8A: 58-turn winding pack, TokaMaker DIIID_geom.json cross-section centroid
+source = "pf_hoop" # Single-filament horizontal hoop approximation of the winding pack
+radius = 1.2518 # Hoop major radius: centroid R of the pack cross-section [m]
+height = 1.6019 # Hoop height: centroid Z of the pack cross-section [m]
+currents = [58000.0] # 1 kA per turn × 58 turns; sensitivities scale linearly with current [A]
+
+[[ForcingTerms.coil_set]]
+name = "F9A" # DIII-D F coil F9A: 55-turn winding pack, TokaMaker DIIID_geom.json cross-section centroid
+source = "pf_hoop" # Single-filament horizontal hoop approximation of the winding pack
+radius = 1.6890 # Hoop major radius: centroid R of the pack cross-section [m]
+height = 1.5874 # Hoop height: centroid Z of the pack cross-section [m]
+currents = [55000.0] # 1 kA per turn × 55 turns; sensitivities scale linearly with current [A]
+
+[[ForcingTerms.coil_set]]
+name = "F1B" # DIII-D F coil F1B: 58-turn winding pack, TokaMaker DIIID_geom.json cross-section centroid
+source = "pf_hoop" # Single-filament horizontal hoop approximation of the winding pack
+radius = 0.8608 # Hoop major radius: centroid R of the pack cross-section [m]
+height = -0.1737 # Hoop height: centroid Z of the pack cross-section [m]
+currents = [58000.0] # 1 kA per turn × 58 turns; sensitivities scale linearly with current [A]
+
+[[ForcingTerms.coil_set]]
+name = "F2B" # DIII-D F coil F2B: 58-turn winding pack, TokaMaker DIIID_geom.json cross-section centroid
+source = "pf_hoop" # Single-filament horizontal hoop approximation of the winding pack
+radius = 0.8607 # Hoop major radius: centroid R of the pack cross-section [m]
+height = -0.5135 # Hoop height: centroid Z of the pack cross-section [m]
+currents = [58000.0] # 1 kA per turn × 58 turns; sensitivities scale linearly with current [A]
+
+[[ForcingTerms.coil_set]]
+name = "F3B" # DIII-D F coil F3B: 58-turn winding pack, TokaMaker DIIID_geom.json cross-section centroid
+source = "pf_hoop" # Single-filament horizontal hoop approximation of the winding pack
+radius = 0.8610 # Hoop major radius: centroid R of the pack cross-section [m]
+height = -0.8543 # Hoop height: centroid Z of the pack cross-section [m]
+currents = [58000.0] # 1 kA per turn × 58 turns; sensitivities scale linearly with current [A]
+
+[[ForcingTerms.coil_set]]
+name = "F4B" # DIII-D F coil F4B: 58-turn winding pack, TokaMaker DIIID_geom.json cross-section centroid
+source = "pf_hoop" # Single-filament horizontal hoop approximation of the winding pack
+radius = 0.8630 # Hoop major radius: centroid R of the pack cross-section [m]
+height = -1.1957 # Hoop height: centroid Z of the pack cross-section [m]
+currents = [58000.0] # 1 kA per turn × 58 turns; sensitivities scale linearly with current [A]
+
+[[ForcingTerms.coil_set]]
+name = "F5B" # DIII-D F coil F5B: 58-turn winding pack, TokaMaker DIIID_geom.json cross-section centroid
+source = "pf_hoop" # Single-filament horizontal hoop approximation of the winding pack
+radius = 1.0025 # Hoop major radius: centroid R of the pack cross-section [m]
+height = -1.5169 # Hoop height: centroid Z of the pack cross-section [m]
+currents = [58000.0] # 1 kA per turn × 58 turns; sensitivities scale linearly with current [A]
+
+[[ForcingTerms.coil_set]]
+name = "F6B" # DIII-D F coil F6B: 55-turn winding pack, TokaMaker DIIID_geom.json cross-section centroid
+source = "pf_hoop" # Single-filament horizontal hoop approximation of the winding pack
+radius = 2.6124 # Hoop major radius: centroid R of the pack cross-section [m]
+height = -0.4376 # Hoop height: centroid Z of the pack cross-section [m]
+currents = [55000.0] # 1 kA per turn × 55 turns; sensitivities scale linearly with current [A]
+
+[[ForcingTerms.coil_set]]
+name = "F7B" # DIII-D F coil F7B: 55-turn winding pack, TokaMaker DIIID_geom.json cross-section centroid
+source = "pf_hoop" # Single-filament horizontal hoop approximation of the winding pack
+radius = 2.3834 # Hoop major radius: centroid R of the pack cross-section [m]
+height = -1.1171 # Hoop height: centroid Z of the pack cross-section [m]
+currents = [55000.0] # 1 kA per turn × 55 turns; sensitivities scale linearly with current [A]
+
+[[ForcingTerms.coil_set]]
+name = "F8B" # DIII-D F coil F8B: 58-turn winding pack, TokaMaker DIIID_geom.json cross-section centroid
+source = "pf_hoop" # Single-filament horizontal hoop approximation of the winding pack
+radius = 1.2524 # Hoop major radius: centroid R of the pack cross-section [m]
+height = -1.6027 # Hoop height: centroid Z of the pack cross-section [m]
+currents = [58000.0] # 1 kA per turn × 58 turns; sensitivities scale linearly with current [A]
+
+[[ForcingTerms.coil_set]]
+name = "F9B" # DIII-D F coil F9B: 55-turn winding pack, TokaMaker DIIID_geom.json cross-section centroid
+source = "pf_hoop" # Single-filament horizontal hoop approximation of the winding pack
+radius = 1.6889 # Hoop major radius: centroid R of the pack cross-section [m]
+height = -1.5780 # Hoop height: centroid Z of the pack cross-section [m]
+currents = [55000.0] # 1 kA per turn × 55 turns; sensitivities scale linearly with current [A]
+
+[PerturbedEquilibrium]
+compute_singular_coupling = true # Compute singular layer coupling metrics
+regularization_width = 0.05 # Regularization width for singular surfaces (0 = disabled)
+
+[ErrorFields]
+fd_step_shift_m = 1e-3 # Central-difference step for the rigid shifts [m]
+fd_step_tilt_deg = 0.1 # Central-difference step for the rigid tilts [degrees]
+rotation_center = "conductor" # Tilt pivot: each conductor's own centre ("conductor") or the whole set's ("set")
+tolerance_file = "tolerances.toml" # Manufacturing-tolerance TOML, relative to the deck directory
+exclude_coils = [] # Coil sets that are not error-field sources (the NTV efc_coils are excluded automatically)
+
+[ErrorFields.MonteCarlo]
+nsample = 200000 # Samples per batch
+nbatch = 10 # Independent batches; their spread is the statistical error bar
+seed = 1 # Base seed; batch b uses Xoshiro(hash((seed, b)))
+nbins = 300 # Histogram bins, linear on [0, delta_max]
+
+[ErrorFields.scenario]
+n_e = 5.0 # Electron density for the threshold scaling [1e19 m^-3]
+
+[ErrorFields.Risk]
+year = 2020 # Publication year of the threshold fit: 2020 or 2026 (n = 1)
+dataset = "O,L" # ITPA dataset of the fit: 2020 "O,L" or "O,L,H"; 2026 "O,L" (n = 1)
+fit = "WLS" # Fitting method: "OLS", "DSOLS", or "WLS" (2026: "OLS" or "WLS")
+nsample_threshold = 1000000 # Threshold samples
+scan_scales = [0.05, 0.1, 0.25, 0.5, 1.0, 2.0, 4.0, 8.0, 16.0] # Tolerance multipliers of the allowable-tolerance scan
+
+[ErrorFields.NTV]
+efc_coils = ["d3d_c"] # Coil set names of the correction arrays to evaluate (here the C-coil stands in for a correction coil)
+method = "fgar" # KineticForces torque method (must be enabled in [KineticForces])
+rotation_scan = true # Tabulate the torques against a rigid E×B rotation shift (false: nominal rotation only, linear model)
+rotation_scan_points = 5 # Points of the initial symmetric shift grid (made odd so the unshifted point is one of them)
+rotation_scan_max_points = 9 # Cap on kinetic evaluations per spectrum after adaptive refinement
+rotation_scan_tolerance = 0.05 # Refinement stops when every interval's midpoint prediction error is below this fraction of the torque range
+rotation_span_factor = 1.0 # The scan covers ±span_factor × max(|ω_E|, offset_factor·|ω_*T|) at the innermost kinetic surface
+rotation_offset_factor = 2.0 # Rough neoclassical offset as a multiple of the ion temperature-gradient diamagnetic frequency ω_*T
+
+[KineticForces]
+bounce_harmonic_max = 6 # Bounce harmonics retained
+electron = false # Ion-only NTV
+nutype = "harmonic" # Collision operator
+f0type = "maxwellian" # Equilibrium distribution
+atol_pitch = 1e-9 # Absolute tolerance for the pitch integration (median-normalized kernel)
diff --git a/examples/DIIID-like_error_field_example/run_example.jl b/examples/DIIID-like_error_field_example/run_example.jl
new file mode 100644
index 0000000000..fa0a9e53d5
--- /dev/null
+++ b/examples/DIIID-like_error_field_example/run_example.jl
@@ -0,0 +1,4 @@
+using Pkg;
+Pkg.activate(joinpath(@__DIR__, "../.."))
+using GeneralizedPerturbedEquilibrium
+GeneralizedPerturbedEquilibrium.main([dirname(@__FILE__)])
diff --git a/examples/DIIID-like_error_field_example/tolerances.toml b/examples/DIIID-like_error_field_example/tolerances.toml
new file mode 100644
index 0000000000..2829bd0f7d
--- /dev/null
+++ b/examples/DIIID-like_error_field_example/tolerances.toml
@@ -0,0 +1,129 @@
+# Illustrative manufacturing tolerances for the DIII-D F coils of DIIID-like_error_field_example:
+# every coil may sit anywhere within 4 mm of its nominal centre and tilt by up to a 4 mm rim
+# displacement (converted through its own major radius), sampled with the hollow radial shape;
+# the upper and lower outboard pairs are also bound into coherent groups standing in for a common
+# support, whose 2 mm rim displacement names a rotation through the support's 2.5 m lever arm;
+# an unattributed 1 G budget is carried. These are round millimetre-class numbers of the kind a
+# PF coil is actually placed to, not DIII-D engineering data.
+
+[ErrorFields.defaults]
+tilt_units = "m" # "deg", or "m" for a rim displacement converted through the nominal radius
+radial_shape = "hollow" # Radial sampling density on the disk: flat, uniform_area, hollow, or ring
+tolerance_model = "additive" # "additive" (independent shift and tilt) or "cylinder" (correlated axis line)
+
+[[ErrorFields.coil]]
+name = "F1A" # DIII-D F coil F1A; must match the [[ForcingTerms.coil_set]] name
+shift_tol_mm = 4.0 # Radius of the in-plane displacement disk the coil centre may lie in [mm]
+tilt_tol = 0.004 # Tilt tolerance, in tilt_units (a 4 mm rim displacement)
+
+[[ErrorFields.coil]]
+name = "F2A" # DIII-D F coil F2A; must match the [[ForcingTerms.coil_set]] name
+shift_tol_mm = 4.0 # Radius of the in-plane displacement disk the coil centre may lie in [mm]
+tilt_tol = 0.004 # Tilt tolerance, in tilt_units (a 4 mm rim displacement)
+
+[[ErrorFields.coil]]
+name = "F3A" # DIII-D F coil F3A; must match the [[ForcingTerms.coil_set]] name
+shift_tol_mm = 4.0 # Radius of the in-plane displacement disk the coil centre may lie in [mm]
+tilt_tol = 0.004 # Tilt tolerance, in tilt_units (a 4 mm rim displacement)
+
+[[ErrorFields.coil]]
+name = "F4A" # DIII-D F coil F4A; must match the [[ForcingTerms.coil_set]] name
+shift_tol_mm = 4.0 # Radius of the in-plane displacement disk the coil centre may lie in [mm]
+tilt_tol = 0.004 # Tilt tolerance, in tilt_units (a 4 mm rim displacement)
+
+[[ErrorFields.coil]]
+name = "F5A" # DIII-D F coil F5A; must match the [[ForcingTerms.coil_set]] name
+shift_tol_mm = 4.0 # Radius of the in-plane displacement disk the coil centre may lie in [mm]
+tilt_tol = 0.004 # Tilt tolerance, in tilt_units (a 4 mm rim displacement)
+
+[[ErrorFields.coil]]
+name = "F6A" # DIII-D F coil F6A; must match the [[ForcingTerms.coil_set]] name
+shift_tol_mm = 4.0 # Radius of the in-plane displacement disk the coil centre may lie in [mm]
+tilt_tol = 0.004 # Tilt tolerance, in tilt_units (a 4 mm rim displacement)
+
+[[ErrorFields.coil]]
+name = "F7A" # DIII-D F coil F7A; must match the [[ForcingTerms.coil_set]] name
+shift_tol_mm = 4.0 # Radius of the in-plane displacement disk the coil centre may lie in [mm]
+tilt_tol = 0.004 # Tilt tolerance, in tilt_units (a 4 mm rim displacement)
+
+[[ErrorFields.coil]]
+name = "F8A" # DIII-D F coil F8A; must match the [[ForcingTerms.coil_set]] name
+shift_tol_mm = 4.0 # Radius of the in-plane displacement disk the coil centre may lie in [mm]
+tilt_tol = 0.004 # Tilt tolerance, in tilt_units (a 4 mm rim displacement)
+
+[[ErrorFields.coil]]
+name = "F9A" # DIII-D F coil F9A; must match the [[ForcingTerms.coil_set]] name
+shift_tol_mm = 4.0 # Radius of the in-plane displacement disk the coil centre may lie in [mm]
+tilt_tol = 0.004 # Tilt tolerance, in tilt_units (a 4 mm rim displacement)
+
+[[ErrorFields.coil]]
+name = "F1B" # DIII-D F coil F1B; must match the [[ForcingTerms.coil_set]] name
+shift_tol_mm = 4.0 # Radius of the in-plane displacement disk the coil centre may lie in [mm]
+tilt_tol = 0.004 # Tilt tolerance, in tilt_units (a 4 mm rim displacement)
+
+[[ErrorFields.coil]]
+name = "F2B" # DIII-D F coil F2B; must match the [[ForcingTerms.coil_set]] name
+shift_tol_mm = 4.0 # Radius of the in-plane displacement disk the coil centre may lie in [mm]
+tilt_tol = 0.004 # Tilt tolerance, in tilt_units (a 4 mm rim displacement)
+
+[[ErrorFields.coil]]
+name = "F3B" # DIII-D F coil F3B; must match the [[ForcingTerms.coil_set]] name
+shift_tol_mm = 4.0 # Radius of the in-plane displacement disk the coil centre may lie in [mm]
+tilt_tol = 0.004 # Tilt tolerance, in tilt_units (a 4 mm rim displacement)
+
+[[ErrorFields.coil]]
+name = "F4B" # DIII-D F coil F4B; must match the [[ForcingTerms.coil_set]] name
+shift_tol_mm = 4.0 # Radius of the in-plane displacement disk the coil centre may lie in [mm]
+tilt_tol = 0.004 # Tilt tolerance, in tilt_units (a 4 mm rim displacement)
+
+[[ErrorFields.coil]]
+name = "F5B" # DIII-D F coil F5B; must match the [[ForcingTerms.coil_set]] name
+shift_tol_mm = 4.0 # Radius of the in-plane displacement disk the coil centre may lie in [mm]
+tilt_tol = 0.004 # Tilt tolerance, in tilt_units (a 4 mm rim displacement)
+
+[[ErrorFields.coil]]
+name = "F6B" # DIII-D F coil F6B; must match the [[ForcingTerms.coil_set]] name
+shift_tol_mm = 4.0 # Radius of the in-plane displacement disk the coil centre may lie in [mm]
+tilt_tol = 0.004 # Tilt tolerance, in tilt_units (a 4 mm rim displacement)
+
+[[ErrorFields.coil]]
+name = "F7B" # DIII-D F coil F7B; must match the [[ForcingTerms.coil_set]] name
+shift_tol_mm = 4.0 # Radius of the in-plane displacement disk the coil centre may lie in [mm]
+tilt_tol = 0.004 # Tilt tolerance, in tilt_units (a 4 mm rim displacement)
+
+[[ErrorFields.coil]]
+name = "F8B" # DIII-D F coil F8B; must match the [[ForcingTerms.coil_set]] name
+shift_tol_mm = 4.0 # Radius of the in-plane displacement disk the coil centre may lie in [mm]
+tilt_tol = 0.004 # Tilt tolerance, in tilt_units (a 4 mm rim displacement)
+
+[[ErrorFields.coil]]
+name = "F9B" # DIII-D F coil F9B; must match the [[ForcingTerms.coil_set]] name
+shift_tol_mm = 4.0 # Radius of the in-plane displacement disk the coil centre may lie in [mm]
+tilt_tol = 0.004 # Tilt tolerance, in tilt_units (a 4 mm rim displacement)
+
+[[ErrorFields.coherent_group]]
+name = "outboard_upper" # Label of the coherently moving group
+members = ["F6A", "F7A"] # Coil sets sharing one random draw per sample
+shift_tol_mm = 2.0 # Coherent shift amplitude shared by the group [mm]
+tilt_tol = 0.002 # Coherent tilt amplitude shared by the group, in tilt_units (a 2 mm rim displacement)
+tilt_lever_arm_m = 2.5 # Lever arm converting that rim displacement to the support's rotation angle [m]
+phase_group = "outboard" # Groups naming the same phase_group share the random direction
+rotation_center_z_m = 0.0 # Height of the pivot of the group's rigid rotation on the machine axis [m]
+
+[[ErrorFields.coherent_group]]
+name = "outboard_lower" # Label of the coherently moving group
+members = ["F6B", "F7B"] # Coil sets sharing one random draw per sample
+shift_tol_mm = 2.0 # Coherent shift amplitude shared by the group [mm]
+tilt_tol = 0.002 # Coherent tilt amplitude shared by the group, in tilt_units (a 2 mm rim displacement)
+tilt_lever_arm_m = 2.5 # Lever arm converting that rim displacement to the support's rotation angle [m]
+phase_group = "outboard" # Groups naming the same phase_group share the random direction
+rotation_center_z_m = 0.0 # Height of the pivot of the group's rigid rotation on the machine axis [m]
+
+[ErrorFields.correctability]
+uncorrectable_coils = [] # Coil sets the error-field correction cannot reduce
+efc_factor = 2.0 # Divisor applied to correctable contributions under error-field correction
+
+[ErrorFields.other_field]
+magnitude = 4.0e-5 # Overlap budget of sources not attributed to any coil (about 1 G at 2 T)
+sigma = 0.0 # Gaussian uncertainty on that budget
+radial_shape = "ring" # Radial sampling density of the budget magnitude
diff --git a/examples/DIIID-like_gal_resistive_example/TkMkr_D3Dlike_Hmode.geqdsk b/examples/DIIID-like_gal_resistive_example/TkMkr_D3Dlike_Hmode.geqdsk
new file mode 120000
index 0000000000..4200141b30
--- /dev/null
+++ b/examples/DIIID-like_gal_resistive_example/TkMkr_D3Dlike_Hmode.geqdsk
@@ -0,0 +1 @@
+../DIIID-like_ideal_example/TkMkr_D3Dlike_Hmode.geqdsk
\ No newline at end of file
diff --git a/examples/DIIID-like_gal_resistive_example/gpec.toml b/examples/DIIID-like_gal_resistive_example/gpec.toml
new file mode 100644
index 0000000000..0abc47dc1c
--- /dev/null
+++ b/examples/DIIID-like_gal_resistive_example/gpec.toml
@@ -0,0 +1,78 @@
+# DIII-D-like H-mode resistive-MHD example: outer-region singular Galerkin Δ′ solve.
+# n=1 tearing stability on the bundled geqdsk: the gal solver computes the Δ′
+# matching matrix (PEST-3 convention) plus rpec coil-response columns (delta_coil).
+# The core_edge_packed radial grid is densest at the axis and edge; psihigh = 0.993
+# stays clear of the separatrix. No forcing and no PerturbedEquilibrium stage.
+[Run]
+verbose = true # Log each stage's progress
+
+[Equilibrium]
+eq_filename = "TkMkr_D3Dlike_Hmode.geqdsk" # Path to equilibrium file
+eq_type = "efit" # Type of the input 2D equilibrium file
+jac_type = "hamada" # Coordinate system (hamada, pest, boozer, equal_arc, park, custom)
+grid_type = "core_edge_packed" # Radial grid packing type (core_edge_packed = sin² spacing, dense at axis and edge)
+psilow = 1e-4 # Lower limit of normalized flux coordinate
+psihigh = 0.993 # Upper limit of normalized flux coordinate (0.993 stays clear of the separatrix; truncating at ≳0.998 is numerically unreasonable here)
+mpsi = 128 # Number of radial grid intervals (0 = two-pass auto grid from psi_accuracy)
+psi_accuracy = 0.001 # Target relative accuracy of splined profile derivatives for the auto grid
+mtheta = 256 # Number of poloidal grid points
+newq0 = 0 # Target on-axis safety factor q(0) (0 = use input value; q is positive, so negative values are rejected)
+flux_surface_rtol = 1e-10 # Relative tolerance of the ODE solves that trace each flux surface
+
+# Presence runs the LocalStability stage (Mercier D_I, resistive D_R, ballooning Δ', first α boundary); keys are the LocalStabilityProblem settings, numerics in [Ballooning]
+[LocalStability]
+theta_k = 0.0 # Ballooning angle θ_k, used by both the profile scan and the α-boundary scan
+alpha_boundary_scan = true # Run the first ballooning α-boundary scan (a root find per ψ surface)
+
+# Numerical settings of the ballooning scans
+[Ballooning]
+ode_tol = 1e-8 # Relative and absolute tolerance of the ballooning ODE integration behind Δ'
+n_scan = 24 # Resolution of the α scan for the first boundary
+max_alpha_scale = 8.0 # Upper end of the α search, as a multiple of the experimental α
+alpha_tol = 1e-3 # Bisection tolerance of the critical α, in the same multiples
+psi_window = [0.1, 0.99] # ψ_N range of the α scan; surfaces outside it are NaN
+
+[ForceFreeStates]
+vac_flag = true # Compute plasma, vacuum, and total energies for free-boundary modes
+
+dW_edge_scan_start = 0.99 # Edge dW(ψ) diagnostic scan band [dW_edge_scan_start, psilim]; set ≥ psilim to disable
+qlow = 1.02 # Integration initiated at q determined by min(q0, qlow)...
+qhigh = 1e3 # Integration terminated at q limit determined by min(qa, qhigh)...
+
+nn = 1 # Toroidal mode number, or consecutive numbers as a list
+delta_mlow = 8 # Expands lower bound of Fourier harmonics
+delta_mhigh = 4 # Expands upper bound of Fourier harmonics
+mtheta_vacuum = 512 # Number of points used in splines over poloidal angle at plasma-vacuum interface.
+
+singfac_min = 1e-4 # Fractional distance from rational q at which ideal jump enforced
+
+# Integrator selection and domain truncation (see ForceFreeStatesControl docstring for details)
+integrator = "Galerkin" # Integration formalism, whose numerical settings are its own section: "Forward" (dense ξ, needed for [PerturbedEquilibrium]/kinetic), "Riccati" (chunked propagator BVP, unlocks the singular-surface Δ′ matrix), or "Galerkin" (outer-region singular Galerkin Δ′)
+truncate_at_rational_offset = false # Keep psilim at psihigh (do not truncate at last_rational_q + rational_offset_fraction)
+rational_offset_fraction = 0.2 # Truncate integration at (last_rational_q + rational_offset_fraction) / n (only used when truncate_at_rational_offset = true)
+
+frobenius_order = 6 # Order of singular layer (Frobenius) expansion at rational surfaces
+
+# Outer-region singular Galerkin Δ′ solver with rpec coil columns.
+# This case exercises the gal solve AND the rpec coil/edge path (delta_coil) for regression tracking.
+[Galerkin]
+nx = 256 # Hermite-cubic elements per interval between singular surfaces
+nq = 6 # Gauss-Lobatto quadrature order per element
+pfac = 0.03 # Grid packing ratio toward singular surfaces (smaller = tighter packing)
+dx0 = 5e-4 # Resonant-element integration truncation distance from the rational (× 1/|n q'|)
+dx1 = 1e-3 # Resonant-element size (× 1/|n q'|)
+dx2 = 1e-3 # Extension-element size (× 1/|n q'|)
+cutoff = 10 # Number of elements carrying the large (driving) solution as a source term
+tol = 1e-10 # Resonant-cell adaptive-quadrature (QuadGK) tolerance
+gnstep = 5000 # Maximum resonant-integration steps
+dx1dx2_flag = true # Enable the special dx1/dx2 element sizing for resonant/extension cells
+frobenius_order_ceiling = true # Auto-raise the series order by ceil(2·Re(α)) on high-Mercier-index surfaces
+rpec_flag = true # Append mpert coil-response columns (unit edge sources) to the solve → delta_coil block
+
+# Driven inner-layer matching on the finished solve. Per-surface resistive inputs (core→edge) for a DIII-D-like case:
+# η=8e-8, ρ=3.3e-7 kg/m³ (ni≈1e20 m^-3), rotation=1 Hz, Γ=5/3. 4 surfaces.
+[Match]
+eta = [8e-8, 8e-8, 8e-8, 8e-8] # Per-surface resistivity η (core→edge)
+rho = [3.3e-7, 3.3e-7, 3.3e-7, 3.3e-7] # Per-surface mass density ρ [kg/m³] (core→edge)
+rotation = [1.0, 1.0, 1.0, 1.0] # Per-surface rotation frequency f [Hz] (core→edge); forced eigenvalue γ_s = 2πi·n·f
+gamma = 1.6666666666666667 # Ratio of specific heats Γ for the resistive-layer coefficients (5/3)
diff --git a/examples/DIIID-like_ideal_example/TkMkr_D3Dlike_Hmode.geqdsk b/examples/DIIID-like_ideal_example/TkMkr_D3Dlike_Hmode.geqdsk
new file mode 100644
index 0000000000..fa39228fe4
--- /dev/null
+++ b/examples/DIIID-like_ideal_example/TkMkr_D3Dlike_Hmode.geqdsk
@@ -0,0 +1,13653 @@
+tMaker: 0 257 257
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diff --git a/examples/DIIID-like_ideal_example/TkMkr_D3Dlike_Hmode_kinetic.gpeckf b/examples/DIIID-like_ideal_example/TkMkr_D3Dlike_Hmode_kinetic.gpeckf
new file mode 100644
index 0000000000..aec26a9512
--- /dev/null
+++ b/examples/DIIID-like_ideal_example/TkMkr_D3Dlike_Hmode_kinetic.gpeckf
@@ -0,0 +1,515 @@
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diff --git a/examples/DIIID-like_ideal_example/TkMkr_D3Dlike_Hmode_kinetic.h5 b/examples/DIIID-like_ideal_example/TkMkr_D3Dlike_Hmode_kinetic.h5
new file mode 100644
index 0000000000..185329e829
Binary files /dev/null and b/examples/DIIID-like_ideal_example/TkMkr_D3Dlike_Hmode_kinetic.h5 differ
diff --git a/examples/DIIID-like_ideal_example/analyze_example.jl b/examples/DIIID-like_ideal_example/analyze_example.jl
new file mode 100644
index 0000000000..1a3db2eb16
--- /dev/null
+++ b/examples/DIIID-like_ideal_example/analyze_example.jl
@@ -0,0 +1,224 @@
+using Pkg;
+Pkg.activate(joinpath(@__DIR__, "../.."))
+using GeneralizedPerturbedEquilibrium, Plots
+using GeneralizedPerturbedEquilibrium: Analysis
+using GeneralizedPerturbedEquilibrium: Equilibrium, ForceFreeStates, LocalStability
+using LaTeXStrings, TOML
+isinteractive() ? plotlyjs() : gr()
+
+h5path = joinpath(@__DIR__, "gpec.h5")
+
+# Summary plots
+p_eq = Analysis.Equilibrium.plot_equilibrium_summary(h5path)
+p_ffs = Analysis.ForceFreeStates.plot_ffs_summary(h5path)
+p_pe = Analysis.PerturbedEquilibrium.plot_perturbed_equilibrium_summary(h5path)
+
+display(p_eq);
+Plots.savefig(p_eq, joinpath(@__DIR__, "equilibrium_summary.png"))
+display(p_ffs);
+Plots.savefig(p_ffs, joinpath(@__DIR__, "ffs_summary.png"))
+display(p_pe);
+Plots.savefig(p_pe, joinpath(@__DIR__, "pe_summary.png"))
+
+# BALOO-style first ballooning stability boundary: experimental α vs critical α
+p_baloo = Analysis.ForceFreeStates.plot_ballooning_alpha_boundary(h5path)
+display(p_baloo)
+baloo_path = joinpath(@__DIR__, "ballooning_alpha_boundary.png")
+Plots.savefig(p_baloo, baloo_path)
+
+# ----------------------------------------------------------------------
+# Local stability: s-alpha profiles, D_I / ballooning Δ', and 2D s-alpha
+# maps (ported from the former Bal_salpha_delta_di_summary notebook).
+# These recompute directly from the equilibrium via the LocalStability helpers
+# rather than reading gpec.h5, so the s-alpha scan can perturb (p', q').
+# ----------------------------------------------------------------------
+
+function symmetric_clims(z)
+ finite_vals = vec(z)[isfinite.(vec(z))]
+ maxabs = isempty(finite_vals) ? 1.0 : maximum(abs.(finite_vals))
+ maxabs = max(maxabs, eps(Float64))
+ return (-maxabs, maxabs)
+end
+
+geqdsk_cases = [
+ "TkMkr_D3Dlike_Hmode.geqdsk"
+]
+
+base_toml = TOML.parsefile(joinpath(@__DIR__, "gpec.toml"))
+
+println("Saved figures:")
+for p in (joinpath(@__DIR__, "equilibrium_summary.png"), joinpath(@__DIR__, "ffs_summary.png"), joinpath(@__DIR__, "pe_summary.png"), baloo_path)
+ println(" ", p)
+end
+
+for geqdsk_file in geqdsk_cases
+ case_label = splitext(basename(geqdsk_file))[1]
+ println("\n=== Local stability: $case_label ===")
+
+ eq_dict = deepcopy(base_toml["Equilibrium"])
+ eq_dict["eq_filename"] = geqdsk_file
+ eq_config = GeneralizedPerturbedEquilibrium.equilibrium_config(Dict{String,Any}("Equilibrium" => eq_dict), @__DIR__)
+ equil = Equilibrium.PlasmaEquilibrium(eq_config)
+ psi_norm = Vector(equil.profiles.xs)
+
+ # s and alpha profiles vs normalized flux
+ s_profile = fill(NaN, length(psi_norm))
+ alpha_profile = fill(NaN, length(psi_norm))
+ for i in eachindex(psi_norm)
+ try
+ ref = LocalStability.salpha_reference(i, equil)
+ s_profile[i] = ref.s_ref
+ alpha_profile[i] = ref.alpha_ref
+ catch err
+ @warn "s-alpha reference failed" i psi = psi_norm[i] exception = (err, catch_backtrace())
+ end
+ end
+
+ s_mask = isfinite.(s_profile)
+ alpha_mask = isfinite.(alpha_profile)
+ p_s = plot(
+ psi_norm[s_mask],
+ s_profile[s_mask];
+ xlabel="Norm. Poloidal Flux",
+ ylabel="s",
+ title="Magnetic shear s",
+ label="s",
+ lw=2,
+ framestyle=:box,
+ left_margin=10Plots.mm,
+ bottom_margin=5Plots.mm
+ )
+ p_alpha = plot(
+ psi_norm[alpha_mask],
+ alpha_profile[alpha_mask];
+ xlabel="Norm. Poloidal Flux",
+ ylabel=L"\alpha",
+ title="Pressure gradient α",
+ label=L"\alpha",
+ lw=2,
+ framestyle=:box,
+ left_margin=10Plots.mm,
+ bottom_margin=5Plots.mm
+ )
+ p_salpha = plot(p_s, p_alpha; layout=(1, 2), size=(1100, 420))
+ display(p_salpha)
+ salpha_path = joinpath(@__DIR__, "salpha_profiles_$(case_label).png")
+ Plots.savefig(p_salpha, salpha_path)
+
+ # D_I (Mercier) and ballooning Δ' profiles
+ locstab_fs = zeros(length(psi_norm), 5)
+ LocalStability.compute_ballooning_stability!(locstab_fs, equil; compute_delta_prime=true)
+
+ delta_prime = Vector(locstab_fs[:, 4])
+ di_profile = fill(NaN, length(psi_norm))
+ psi_mask = abs.(psi_norm) .> eps(Float64)
+ di_profile[psi_mask] .= locstab_fs[psi_mask, 1] ./ psi_norm[psi_mask]
+
+ delta_mask = isfinite.(delta_prime)
+ di_mask = isfinite.(di_profile)
+ p_delta = plot(
+ psi_norm[delta_mask],
+ delta_prime[delta_mask];
+ xlabel="Norm. Poloidal Flux",
+ ylabel=L"\Delta'",
+ title="Ballooning Δ'",
+ label=L"\Delta'",
+ lw=2,
+ framestyle=:box,
+ left_margin=10Plots.mm,
+ bottom_margin=5Plots.mm
+ )
+ p_di = plot(
+ psi_norm[di_mask],
+ di_profile[di_mask];
+ xlabel="Norm. Poloidal Flux",
+ ylabel=L"D_I",
+ title="Mercier D_I",
+ label=L"D_I",
+ lw=2,
+ framestyle=:box,
+ left_margin=10Plots.mm,
+ bottom_margin=5Plots.mm
+ )
+ hline!(p_di, [0.0]; linestyle=:dash, color=:black, label=nothing)
+ p_localstab = plot(p_delta, p_di; layout=(1, 2), size=(1100, 420))
+ display(p_localstab)
+ localstab_path = joinpath(@__DIR__, "delta_di_profiles_$(case_label).png")
+ Plots.savefig(p_localstab, localstab_path)
+
+ # 2D s-alpha maps of Δ' and D_I at a near-edge surface, with zero contours
+ psi_target = 0.974
+ psi_idx_scan = argmin(abs.(psi_norm .- psi_target))
+ s_scales = collect(range(-5.0, 5.0; length=30))
+ alpha_scales = collect(range(-5.0, 5.0; length=30))
+ scan = LocalStability.scan_delta_prime_map(psi_idx_scan, equil; theta_k=0.0, s_scales=s_scales, alpha_scales=alpha_scales)
+
+ scan_qprime = scan.dqdpsi_ref .* scan.s_scales
+ scan_pprime = scan.pprime_ref .* scan.alpha_scales
+ qorder = sortperm(scan_qprime)
+ porder = sortperm(scan_pprime)
+ scan_qprime = scan_qprime[qorder]
+ scan_pprime = scan_pprime[porder]
+ scan_delta = scan.delta_prime[qorder, porder]
+ scan_di = scan.di_values[qorder, porder]
+
+ p_map_delta = contourf(
+ scan_pprime,
+ scan_qprime,
+ scan_delta;
+ c=cgrad([:blue, :white, :red]),
+ clims=symmetric_clims(scan_delta),
+ xlabel=L"p_{\psi}",
+ ylabel=L"q_{\psi}",
+ title=L"\Delta'",
+ levels=41,
+ framestyle=:box,
+ left_margin=10Plots.mm,
+ bottom_margin=5Plots.mm
+ )
+ contour!(p_map_delta, scan_pprime, scan_qprime, scan_delta; levels=[0.0], color=:black, linewidth=2)
+ scatter!(p_map_delta, [scan.reference.pprime_ref], [scan.reference.qprime_ref]; color=:green, marker=:star5, ms=7, label="equilibrium")
+ p_map_di = contourf(
+ scan_pprime,
+ scan_qprime,
+ scan_di;
+ c=cgrad([:blue, :white, :red]),
+ clims=symmetric_clims(scan_di),
+ xlabel=L"p_{\psi}",
+ ylabel=L"q_{\psi}",
+ title=L"D_I",
+ levels=41,
+ framestyle=:box,
+ left_margin=10Plots.mm,
+ bottom_margin=5Plots.mm
+ )
+ contour!(p_map_di, scan_pprime, scan_qprime, scan_di; levels=[0.0], color=:black, linewidth=2)
+ scatter!(p_map_di, [scan.reference.pprime_ref], [scan.reference.qprime_ref]; color=:green, marker=:star5, ms=7, label="equilibrium")
+ p_maps = plot(p_map_delta, p_map_di; layout=(1, 2), size=(1150, 460))
+ display(p_maps)
+ maps_path = joinpath(@__DIR__, "salpha_maps_$(case_label).png")
+ Plots.savefig(p_maps, maps_path)
+
+ # Overlay of Δ'=0 (ballooning) and D_I=0 (Mercier) stability boundaries
+ p_zero = plot(; xlabel=L"p_{\psi}", ylabel=L"q_{\psi}", title="Ballooning / Mercier stability boundaries", framestyle=:box, left_margin=10Plots.mm, bottom_margin=5Plots.mm)
+ contour!(p_zero, scan_pprime, scan_qprime, scan_delta; levels=[0.0], color=:blue, linewidth=3, colorbar=false)
+ contour!(p_zero, scan_pprime, scan_qprime, scan_di; levels=[0.0], color=:red, linewidth=3, linestyle=:dash, colorbar=false)
+ scatter!(p_zero, [scan.reference.pprime_ref], [scan.reference.qprime_ref]; color=:green, marker=:star5, ms=8, label="equilibrium")
+ display(p_zero)
+ zero_path = joinpath(@__DIR__, "salpha_zero_contours_$(case_label).png")
+ Plots.savefig(p_zero, zero_path)
+
+ # BALOO-style α vs ψ stability boundaries (1st and 2nd) over the Δ'(ψ, α) map
+ bnd = LocalStability.ballooning_alpha_boundaries(equil)
+ dpmap = LocalStability.ballooning_delta_prime_map(equil)
+ p_alpha_bnd = Analysis.ForceFreeStates.plot_ballooning_alpha_boundaries(bnd, dpmap)
+ display(p_alpha_bnd)
+ alpha_bnd_path = joinpath(@__DIR__, "alpha_stability_boundary_$(case_label).png")
+ Plots.savefig(p_alpha_bnd, alpha_bnd_path)
+
+ println(" $salpha_path")
+ println(" $localstab_path")
+ println(" $maps_path")
+ println(" $zero_path")
+ println(" $alpha_bnd_path")
+end
diff --git a/examples/DIIID-like_ideal_example/benchmark_inputs.jld2 b/examples/DIIID-like_ideal_example/benchmark_inputs.jld2
new file mode 100644
index 0000000000..80fbbf9060
Binary files /dev/null and b/examples/DIIID-like_ideal_example/benchmark_inputs.jld2 differ
diff --git a/examples/DIIID-like_ideal_example/gpec.toml b/examples/DIIID-like_ideal_example/gpec.toml
new file mode 100644
index 0000000000..e878691667
--- /dev/null
+++ b/examples/DIIID-like_ideal_example/gpec.toml
@@ -0,0 +1,94 @@
+# DIII-D-like H-mode equilibrium — n=1 ideal stability + perturbed equilibrium.
+# Free-boundary (nowall) external-kink analysis with DIII-D C-coil forcing applied
+# via Biot-Savart from 3D coil wires. This is the canonical ideal free-boundary and
+# perturbed-equilibrium regression fixture (diiid_n1) and the default benchmark case;
+# the Δ'-matrix fixture is the sibling DIIID-like_riccati_deltaprime_example.
+
+[Run]
+verbose = true # Log each stage's progress
+
+[Equilibrium]
+eq_filename = "TkMkr_D3Dlike_Hmode.geqdsk" # Path to equilibrium file
+kinetic_file = "TkMkr_D3Dlike_Hmode_kinetic.h5" # Kinetic-profile file (HDF5 GPEC kinetic schema or 6-column ASCII), read once into the equilibrium
+eq_type = "efit" # Type of the input 2D equilibrium file
+jac_type = "hamada" # Coordinate system (hamada, pest, boozer, equal_arc, park, custom)
+grid_type = "auto" # Radial grid packing type ("auto" = two-pass measured-curvature grid)
+psilow = 1e-4 # Lower limit of normalized poloidal flux
+psihigh = 0.995 # Upper limit of normalized poloidal flux (captures q=6 at this Ip)
+mpsi = 0 # Number of radial grid intervals (0 = two-pass auto grid from psi_accuracy)
+psi_accuracy = 0.001 # Target relative accuracy of splined profile derivatives for the auto grid
+mtheta = 256 # Number of poloidal grid points
+newq0 = 0 # Target on-axis safety factor q(0) (0 = use input value; q is positive, so negative values are rejected)
+flux_surface_rtol = 1e-10 # Relative tolerance of the ODE solves that trace each flux surface
+impurity_charge = 6 # Impurity charge (carbon)
+impurity_mass = 12 # Impurity mass [proton masses]
+
+[[Equilibrium.ion_species]]
+z = 1 # Charge in units of e
+m = 2 # Mass in proton masses
+fraction = 1.0 # Fraction of the n_i profile this species carries
+
+# Presence runs the LocalStability stage (Mercier D_I, resistive D_R, ballooning Δ', first α boundary); keys are the LocalStabilityProblem settings, numerics in [Ballooning]
+[LocalStability]
+theta_k = 0.0 # Ballooning angle θ_k, used by both the profile scan and the α-boundary scan
+alpha_boundary_scan = true # Run the first ballooning α-boundary scan (a root find per ψ surface)
+
+# Numerical settings of the ballooning scans
+[Ballooning]
+ode_tol = 1e-8 # Relative and absolute tolerance of the ballooning ODE integration behind Δ'
+n_scan = 24 # Resolution of the α scan for the first boundary
+max_alpha_scale = 8.0 # Upper end of the α search, as a multiple of the experimental α
+alpha_tol = 1e-3 # Bisection tolerance of the critical α, in the same multiples
+psi_window = [0.1, 0.99] # ψ_N range of the α scan; surfaces outside it are NaN
+
+[ForceFreeStates]
+vac_flag = true # Compute plasma, vacuum, and total energies for free-boundary modes
+
+dW_edge_scan_start = 0.99 # Edge dW(ψ) diagnostic scan band [dW_edge_scan_start, psilim]; set ≥ psilim to disable
+qlow = 1.02 # Integration initiated at q determined by min(q0, qlow)
+qhigh = 1e3 # Integration terminated at q limit determined by min(qa, qhigh)
+
+nn = 1 # Toroidal mode number, or consecutive numbers as a list
+delta_mlow = 8 # Expands lower bound of Fourier harmonics
+delta_mhigh = 8 # Expands upper bound of Fourier harmonics
+mtheta_vacuum = 512 # Number of points used in splines over poloidal angle at the plasma-vacuum interface
+
+singfac_min = 1e-6 # Fractional distance from rational q at which ideal jump enforced
+
+# Integrator selection and domain truncation (see ForceFreeStatesControl docstring for details)
+integrator = "Forward" # Integration formalism, whose numerical settings are its own section: "Forward" (dense ξ, needed for [PerturbedEquilibrium]/kinetic), "Riccati" (chunked propagator BVP, unlocks the singular-surface Δ′ matrix), or "Galerkin" (outer-region singular Galerkin Δ′)
+truncate_at_rational_offset = true # Truncate at (last_rational_q + rational_offset_fraction)/n — TRUE for diverted equilibria (q → ∞ at separatrix)
+rational_offset_fraction = 0.2 # Truncate integration at (last_rational_q + rational_offset_fraction)/n (used when truncate_at_rational_offset = true)
+
+# Numerical settings of the forward integrator
+[Forward]
+eulerlagrange_tolerance = 1e-10 # Relative tolerance for ODE integration of Euler-Lagrange equations
+save_interval = 1 # Save every Nth ODE step (1=all). Always saves near rational surfaces.
+renorm_threshold = 1e3 # Column-norm threshold that triggers solution renormalization
+
+[ForcingTerms]
+forcing_data_format = "coil" # Format: "ascii", "hdf5", or "coil" (Biot-Savart from 3D wires)
+machine = "d3d" # Geometry prefix; resolves to bundled coil_geometries/d3d_*.dat
+mtheta_coil = 480 # Poloidal grid for boundary B·n̂ evaluation
+nzeta_coil = 32 # Toroidal grid (0 = auto = 32·n)
+
+[[ForcingTerms.coil_set]]
+name = "c" # Coil set; resolves to coil_geometries/d3d_c.dat (DIII-D C-coil, 6 coils)
+currents = [1000.0, 500.0, -500.0, -1000.0, -500.0, 500.0] # n=1 cosine phasing, 1 kA peak [A]
+
+[PerturbedEquilibrium]
+compute_singular_coupling = true # Compute singular layer coupling metrics
+regularization_width = 0.05 # Regularization width for singular surfaces (0 = disabled)
+
+[ErrorFields]
+fd_step_shift_m = 1e-3 # Central-difference step for the rigid shifts [m]
+fd_step_tilt_deg = 0.1 # Central-difference step for the rigid tilts [degrees]
+rotation_center = "conductor" # Tilt pivot: each conductor's own centre ("conductor") or the whole set's ("set")
+
+[KineticForces]
+bounce_harmonic_max = 6 # Bounce harmonics retained
+electron = false # Ion-only NTV
+nutype = "harmonic" # Collision operator
+f0type = "maxwellian" # Equilibrium distribution
+atol_pitch = 1e-9 # Absolute tolerance for the pitch integration (median-normalized kernel)
+axis_validity_suppression = true # Suppress kinetic terms inside the near-axis orbit-width validity limit
diff --git a/examples/DIIID-like_ideal_example/run_example.jl b/examples/DIIID-like_ideal_example/run_example.jl
new file mode 100644
index 0000000000..fa0a9e53d5
--- /dev/null
+++ b/examples/DIIID-like_ideal_example/run_example.jl
@@ -0,0 +1,4 @@
+using Pkg;
+Pkg.activate(joinpath(@__DIR__, "../.."))
+using GeneralizedPerturbedEquilibrium
+GeneralizedPerturbedEquilibrium.main([dirname(@__FILE__)])
diff --git a/examples/DIIID-like_ideal_example_IMAS/gpec.toml b/examples/DIIID-like_ideal_example_IMAS/gpec.toml
new file mode 100644
index 0000000000..a1c27394b1
--- /dev/null
+++ b/examples/DIIID-like_ideal_example_IMAS/gpec.toml
@@ -0,0 +1,27 @@
+# DIII-D-like equilibrium read from an IMAS data dictionary (IMASdd.dd) — n=1 ideal stability.
+# The equilibrium is passed in at runtime, not read from a file; eq_filename is a placeholder.
+#
+# Usage (from Julia):
+# using GeneralizedPerturbedEquilibrium as GPEC
+# GPEC.main([dirname(@__FILE__)]; dd=my_dd)
+#
+# See run_imas_example.jl for a full workflow.
+
+[Run]
+verbose = true # Log each stage's progress
+
+[Equilibrium]
+eq_type = "imas" # Type of the input 2D equilibrium file
+eq_filename = "from_dd" # Path to equilibrium file (placeholder: equilibrium comes from the runtime dd argument)
+jac_type = "boozer" # Coordinate system (hamada, pest, boozer, equal_arc, park, custom)
+psilow = 0.01 # Lower limit of normalized poloidal flux
+psihigh = 0.9995 # Upper limit of normalized poloidal flux
+mpsi = 128 # Number of radial grid intervals (0 = two-pass auto grid from psi_accuracy)
+mtheta = 256 # Number of poloidal grid points
+imas_cocos = 11 # Expected COCOS convention of the input IMAS dd (11 = IMAS standard)
+
+[ForceFreeStates]
+nn = 1 # Toroidal mode number, or consecutive numbers as a list
+vac_flag = true # Compute plasma, vacuum, and total energies for free-boundary modes
+delta_mhigh = 16 # Expands upper bound of Fourier harmonics
+qlow = 1.02 # Integration initiated at q determined by min(q0, qlow)
diff --git a/examples/DIIID-like_ideal_example_IMAS/run_imas_example.jl b/examples/DIIID-like_ideal_example_IMAS/run_imas_example.jl
new file mode 100644
index 0000000000..9671b0bfa9
--- /dev/null
+++ b/examples/DIIID-like_ideal_example_IMAS/run_imas_example.jl
@@ -0,0 +1,101 @@
+"""
+IMAS Integration Benchmark — DIII-D-like H-mode equilibrium
+
+Demonstrates that GPEC produces the same stability eigenvalue when reading the
+equilibrium from an IMAS data dictionary (IMASdd.dd) as when reading directly
+from the g-file. Both runs use identical ForceFreeStates and Wall settings so
+the only difference is how the equilibrium is loaded.
+
+EFIT.jl is NOT a GPEC dependency. Install it in your own environment before running:
+ using Pkg; Pkg.add("EFIT")
+"""
+
+using Pkg
+Pkg.activate(joinpath(@__DIR__, "../.."))
+
+import GeneralizedPerturbedEquilibrium as GPEC
+using IMASdd
+using TOML
+using Printf
+using EFIT
+
+const GEQDSK = joinpath(@__DIR__, "../DIIID-like_ideal_example/TkMkr_D3Dlike_Hmode.geqdsk")
+@assert isfile(GEQDSK) "G-file not found at $GEQDSK"
+
+# Shared settings: both runs use identical ForceFreeStates config and no wall.
+# Only the [Equilibrium] section differs between IMAS and g-file paths.
+const SHARED_CONFIG = Dict(
+ "ForceFreeStates" => Dict(
+ "nn" => 1,
+ "vac_flag" => true,
+ "delta_mhigh" => 16,
+ "qlow" => 1.02
+ )
+)
+
+const EQ_COMMON = Dict(
+ "jac_type" => "boozer",
+ "psilow" => 0.01,
+ "psihigh" => 0.9995,
+ "mpsi" => 128,
+ "mtheta" => 256
+)
+
+@info "Loading g-file and converting to IMAS (COCOS 11)..."
+g = EFIT.readg(GEQDSK)
+dd = IMASdd.dd()
+EFIT.geqdsk2imas!([g], dd; dd_cocos=11)
+
+@info "Running GPEC from IMAS dd..."
+tmpdir_imas = mktempdir(; prefix="gpec_imas_")
+try
+ config_imas = merge(SHARED_CONFIG, Dict("Equilibrium" =>
+ merge(EQ_COMMON, Dict("eq_type" => "imas", "eq_filename" => "from_dd", "imas_cocos" => 11))))
+ open(joinpath(tmpdir_imas, "gpec.toml"), "w") do io
+
+ TOML.print(io, config_imas)
+ end
+ result_imas = GPEC.main([tmpdir_imas]; dd=dd)
+ global et_imas = real(result_imas.ffs.free_boundary.et[1])
+ global mpert_imas = result_imas.ffs.mpert
+ GPEC.write_imas(dd, result_imas)
+ @assert dd.mhd_linear.time_slice[1].toroidal_mode[1].energy_perturbed ≈ et_imas
+finally
+ rm(tmpdir_imas; recursive=true)
+end
+@info @sprintf "IMAS path: δW(n=1) = %.6f [mpert = %d]" et_imas mpert_imas
+
+@info "Running GPEC from g-file (reference)..."
+tmpdir_gfile = mktempdir(; prefix="gpec_gfile_")
+try
+ config_gfile = merge(SHARED_CONFIG, Dict("Equilibrium" =>
+ merge(EQ_COMMON, Dict("eq_type" => "efit", "eq_filename" => GEQDSK))))
+ open(joinpath(tmpdir_gfile, "gpec.toml"), "w") do io
+
+ TOML.print(io, config_gfile)
+ end
+ result_gfile = GPEC.main([tmpdir_gfile])
+ global et_gfile = real(result_gfile.ffs.free_boundary.et[1])
+ global mpert_gfile = result_gfile.ffs.mpert
+finally
+ rm(tmpdir_gfile; recursive=true)
+end
+@info @sprintf "G-file path: δW(n=1) = %.6f [mpert = %d]" et_gfile mpert_gfile
+
+rel_diff = abs(et_imas - et_gfile) / (abs(et_gfile) + 1e-12)
+
+println("\n" * "="^60)
+println(" IMAS vs g-file comparison (n=1, nowall, boozer)")
+println("="^60)
+@printf " G-file δW(n=1) : %+.6f [mpert = %d]\n" et_gfile mpert_gfile
+@printf " IMAS δW(n=1) : %+.6f [mpert = %d]\n" et_imas mpert_imas
+@printf " Relative diff : %.2f%%\n" rel_diff * 100
+println("="^60)
+
+if rel_diff < 0.01
+ @info "Agreement within 1% — IMAS and g-file paths are consistent."
+elseif rel_diff < 0.05
+ @warn "Agreement within 5% — likely due to grid resampling in geqdsk2imas!."
+else
+ @warn "Relative difference $(round(rel_diff*100; digits=1))% exceeds 5%. Check COCOS convention and grid resolution."
+end
diff --git a/examples/DIIID-like_ideal_multi_n_example/gpec.toml b/examples/DIIID-like_ideal_multi_n_example/gpec.toml
new file mode 100644
index 0000000000..c6bfa903ee
--- /dev/null
+++ b/examples/DIIID-like_ideal_multi_n_example/gpec.toml
@@ -0,0 +1,74 @@
+# DIII-D-like H-mode equilibrium — n = 1 and 2 in one ideal stability + perturbed equilibrium run.
+# Same plasma as DIIID-like_ideal_example, with both toroidal modes solved together and driven by
+# mixed-n C-coil currents. The integration stops at q = qhigh, placed between rationals so no n has a
+# small edge singular factor. The q = 2 and q = 3 surfaces resonate at both n, so SingularCoupling
+# repeats them across rows. psihigh and delta_mhigh keep the case small for the regression harness;
+# every n block spans m = -8..20, which a single-n n = 1 run matches only with delta_mhigh = 8.
+
+[Run]
+verbose = true # Log each stage's progress
+
+[Equilibrium]
+eq_filename = "../DIIID-like_ideal_example/TkMkr_D3Dlike_Hmode.geqdsk" # Path to equilibrium file
+eq_type = "efit" # Type of the input 2D equilibrium file
+jac_type = "hamada" # Coordinate system (hamada, pest, boozer, equal_arc, park, custom)
+grid_type = "core_edge_packed" # Radial grid packing type (core_edge_packed = sin² spacing, dense at axis and edge)
+psilow = 1e-4 # Lower limit of normalized poloidal flux
+psihigh = 0.9 # Upper limit of normalized poloidal flux
+mpsi = 128 # Number of radial grid intervals (0 = two-pass auto grid from psi_accuracy)
+mtheta = 256 # Number of poloidal grid points
+newq0 = 0 # Target on-axis safety factor q(0) (0 = use input value; q is positive, so negative values are rejected)
+flux_surface_rtol = 1e-10 # Relative tolerance of the ODE solves that trace each flux surface
+
+# Presence runs the LocalStability stage (Mercier D_I, resistive D_R, ballooning Δ', first α boundary); keys are the LocalStabilityProblem settings, numerics in [Ballooning]
+[LocalStability]
+theta_k = 0.0 # Ballooning angle θ_k, used by both the profile scan and the α-boundary scan
+alpha_boundary_scan = true # Run the first ballooning α-boundary scan (a root find per ψ surface)
+
+# Numerical settings of the ballooning scans
+[Ballooning]
+ode_tol = 1e-8 # Relative and absolute tolerance of the ballooning ODE integration behind Δ'
+n_scan = 24 # Resolution of the α scan for the first boundary
+max_alpha_scale = 8.0 # Upper end of the α search, as a multiple of the experimental α
+alpha_tol = 1e-3 # Bisection tolerance of the critical α, in the same multiples
+psi_window = [0.1, 0.99] # ψ_N range of the α scan; surfaces outside it are NaN
+
+[ForceFreeStates]
+vac_flag = true # Compute plasma, vacuum, and total energies for free-boundary modes
+
+dW_edge_scan_start = 0.99 # Edge dW(ψ) diagnostic scan band [dW_edge_scan_start, psilim]; set ≥ psilim to disable
+qlow = 1.02 # Integration initiated at q determined by min(q0, qlow)
+qhigh = 3.83 # Integration terminated at q limit determined by min(qa, qhigh)
+frobenius_psi_max = 0 # Largest starting ψ_N at which the Frobenius axis start is used (0 = fixed start U₁ = 0, U₂ = I everywhere)
+
+nn = [1, 2] # Toroidal mode number, or consecutive numbers as a list
+delta_mlow = 4 # Expands lower bound of Fourier harmonics
+delta_mhigh = 6 # Expands upper bound of Fourier harmonics
+mtheta_vacuum = 512 # Number of points used in splines over poloidal angle at the plasma-vacuum interface
+
+singfac_min = 1e-6 # Fractional distance from rational q at which ideal jump enforced
+
+# Integrator selection and domain truncation (see ForceFreeStatesControl docstring for details)
+integrator = "Forward" # Integration formalism, whose numerical settings are its own section: "Forward" (dense ξ, needed for [PerturbedEquilibrium]/kinetic), "Riccati" (chunked propagator BVP, unlocks the singular-surface Δ′ matrix), or "Galerkin" (outer-region singular Galerkin Δ′)
+truncate_at_rational_offset = false # FALSE for multi-n — rational_offset_fraction truncation is ambiguous when n varies; qhigh sets the edge instead
+rational_offset_fraction = 0.2 # Truncate integration at (last_rational_q + rational_offset_fraction)/n (used when truncate_at_rational_offset = true)
+
+# Numerical settings of the forward integrator
+[Forward]
+eulerlagrange_tolerance = 1e-10 # Relative tolerance for ODE integration of Euler-Lagrange equations
+save_interval = 1 # Save every Nth ODE step (1=all). Always saves near rational surfaces.
+renorm_threshold = 1e3 # Column-norm threshold that triggers solution renormalization
+
+[ForcingTerms]
+forcing_data_format = "coil" # Format: "ascii", "hdf5", or "coil" (Biot-Savart from 3D wires)
+machine = "d3d" # Geometry prefix; resolves to bundled coil_geometries/d3d_*.dat
+mtheta_coil = 480 # Poloidal grid for boundary B·n̂ evaluation
+nzeta_coil = 32 # Toroidal grid (0 = auto = 32·n)
+
+[[ForcingTerms.coil_set]]
+name = "c" # Coil set; resolves to coil_geometries/d3d_c.dat (DIII-D C-coil, 6 coils)
+currents = [1800.0, -50.0, -450.0, -800.0, -450.0, -50.0] # Sum of n=1, 2, 3 cosine phasings with 1000, 500, 300 A peaks; n=3 lies outside nn [A]
+
+[PerturbedEquilibrium]
+compute_singular_coupling = true # Compute singular layer coupling metrics
+regularization_width = 0.0 # Regularization width for singular surfaces (0 = disabled)
diff --git a/examples/DIIID-like_riccati_deltaprime_example/gpec.toml b/examples/DIIID-like_riccati_deltaprime_example/gpec.toml
new file mode 100644
index 0000000000..31457af0d4
--- /dev/null
+++ b/examples/DIIID-like_riccati_deltaprime_example/gpec.toml
@@ -0,0 +1,59 @@
+# DIII-D-like H-mode equilibrium — n=1 Δ'-matrix case on the Riccati integrator.
+# Reuses the equilibrium of the sibling DIIID-like_ideal_example (geqdsk referenced by
+# relative path; not duplicated), and is the canonical SingularSurfaces/Delta_prime_matrix
+# fixture: the Riccati chunked propagator BVP is the only integrator that produces it.
+# No forcing or perturbed equilibrium, so no dense ξ profiles are needed.
+
+[Run]
+verbose = true # Log each stage's progress
+
+[Equilibrium]
+eq_filename = "../DIIID-like_ideal_example/TkMkr_D3Dlike_Hmode.geqdsk" # Path to equilibrium file
+eq_type = "efit" # Type of the input 2D equilibrium file
+jac_type = "hamada" # Coordinate system (hamada, pest, boozer, equal_arc, park, custom)
+grid_type = "auto" # Radial grid packing type ("auto" = two-pass measured-curvature grid)
+psilow = 1e-4 # Lower limit of normalized poloidal flux
+psihigh = 0.995 # Upper limit of normalized poloidal flux (captures q=6 at this Ip)
+mpsi = 0 # Number of radial grid intervals (0 = two-pass auto grid from psi_accuracy)
+psi_accuracy = 0.001 # Target relative accuracy of splined profile derivatives for the auto grid
+mtheta = 256 # Number of poloidal grid points
+newq0 = 0 # Target on-axis safety factor q(0) (0 = use input value; q is positive, so negative values are rejected)
+flux_surface_rtol = 1e-10 # Relative tolerance of the ODE solves that trace each flux surface
+
+# Presence runs the LocalStability stage (Mercier D_I, resistive D_R, ballooning Δ', first α boundary); keys are the LocalStabilityProblem settings, numerics in [Ballooning]
+[LocalStability]
+theta_k = 0.0 # Ballooning angle θ_k, used by both the profile scan and the α-boundary scan
+alpha_boundary_scan = true # Run the first ballooning α-boundary scan (a root find per ψ surface)
+
+# Numerical settings of the ballooning scans
+[Ballooning]
+ode_tol = 1e-8 # Relative and absolute tolerance of the ballooning ODE integration behind Δ'
+n_scan = 24 # Resolution of the α scan for the first boundary
+max_alpha_scale = 8.0 # Upper end of the α search, as a multiple of the experimental α
+alpha_tol = 1e-3 # Bisection tolerance of the critical α, in the same multiples
+psi_window = [0.1, 0.99] # ψ_N range of the α scan; surfaces outside it are NaN
+
+[ForceFreeStates]
+vac_flag = true # Compute plasma, vacuum, and total energies for free-boundary modes
+
+dW_edge_scan_start = 0.99 # Edge dW(ψ) diagnostic scan band [dW_edge_scan_start, psilim]; set ≥ psilim to disable
+qlow = 1.02 # Integration initiated at q determined by min(q0, qlow)
+qhigh = 1e3 # Integration terminated at q limit determined by min(qa, qhigh)
+
+nn = 1 # Toroidal mode number, or consecutive numbers as a list
+delta_mlow = 8 # Expands lower bound of Fourier harmonics
+delta_mhigh = 8 # Expands upper bound of Fourier harmonics
+mtheta_vacuum = 512 # Number of points used in splines over poloidal angle at the plasma-vacuum interface
+
+singfac_min = 1e-4 # Fractional distance from rational q at which ideal jump enforced
+
+# Integrator selection and domain truncation (see ForceFreeStatesControl docstring for details)
+integrator = "Riccati" # Integration formalism, whose numerical settings are its own section: "Forward" (dense ξ, needed for [PerturbedEquilibrium]/kinetic), "Riccati" (chunked propagator BVP, unlocks the singular-surface Δ′ matrix), or "Galerkin" (outer-region singular Galerkin Δ′)
+truncate_at_rational_offset = true # Truncate at (last_rational_q + rational_offset_fraction)/n — TRUE for diverted equilibria (q → ∞ at separatrix)
+rational_offset_fraction = 0.2 # Truncate integration at (last_rational_q + rational_offset_fraction)/n (used when truncate_at_rational_offset = true)
+
+# Numerical settings of the Riccati integrator
+[Riccati]
+eulerlagrange_tolerance = 1e-10 # Relative tolerance for ODE integration of Euler-Lagrange equations
+save_interval = 1 # Save every Nth ODE step (1=all). Always saves near rational surfaces.
+renorm_threshold = 1e3 # Column-norm threshold that triggers solution renormalization
diff --git a/examples/DIIID-like_truncation_example/gpec.toml b/examples/DIIID-like_truncation_example/gpec.toml
new file mode 100644
index 0000000000..eb6539369c
--- /dev/null
+++ b/examples/DIIID-like_truncation_example/gpec.toml
@@ -0,0 +1,53 @@
+# DIII-D-like H-mode equilibrium — n=1 truncation-only case for the resistive-layer overlap cap.
+# Reuses the equilibrium and kinetic profiles of the sibling DIIID-like_ideal_example (referenced
+# by relative path; not duplicated). psihigh is pushed well past the layer-overlap point (psi ~ 0.9985,
+# where adjacent resistive layers first touch), so psilim_from_layer_overlap binds: the cap pulls qlim
+# to 7 and dmlim steps back to 6.2, excluding q=7 and q=8. Ideal free-boundary stability only, with no local
+# stability, forcing or perturbed equilibrium: the energies are kept so a regression case can pin
+# what the capped domain does to the physics, not just to the bookkeeping.
+
+[Run]
+verbose = true # Log each stage's progress
+
+[Equilibrium]
+eq_filename = "../DIIID-like_ideal_example/TkMkr_D3Dlike_Hmode.geqdsk" # Path to equilibrium file
+kinetic_file = "../DIIID-like_ideal_example/TkMkr_D3Dlike_Hmode_kinetic.h5" # Kinetic-profile file (HDF5 GPEC kinetic schema or 6-column ASCII), read once into the equilibrium
+eq_type = "efit" # Type of the input 2D equilibrium file
+jac_type = "hamada" # Coordinate system (hamada, pest, boozer, equal_arc, park, custom)
+grid_type = "auto" # Radial grid packing type ("auto" = two-pass measured-curvature grid)
+psilow = 1e-4 # Lower limit of normalized poloidal flux
+psihigh = 0.9999 # Upper limit of normalized poloidal flux (past the psi ~ 0.9985 layer-overlap point, so the cap binds)
+mpsi = 0 # Number of radial grid intervals (0 = two-pass auto grid from psi_accuracy)
+psi_accuracy = 0.001 # Target relative accuracy of splined profile derivatives for the auto grid
+mtheta = 256 # Number of poloidal grid points
+newq0 = 0 # Target on-axis safety factor q(0) (0 = use input value; q is positive, so negative values are rejected)
+flux_surface_rtol = 1e-10 # Relative tolerance of the ODE solves that trace each flux surface
+
+[ForceFreeStates]
+vac_flag = true # Compute plasma, vacuum, and total energies for free-boundary modes
+
+dW_edge_scan_start = 1.0 # Edge dW(ψ) diagnostic scan band [dW_edge_scan_start, psilim]; set ≥ psilim to disable
+qlow = 1.02 # Integration initiated at q determined by min(q0, qlow)
+qhigh = 1e3 # Integration terminated at q limit determined by min(qa, qhigh)
+
+nn = 1 # Toroidal mode number, or consecutive numbers as a list
+delta_mlow = 8 # Expands lower bound of Fourier harmonics
+delta_mhigh = 8 # Expands upper bound of Fourier harmonics
+
+singfac_min = 1e-6 # Fractional distance from rational q at which ideal jump enforced
+
+# Integrator selection and domain truncation (see ForceFreeStatesControl docstring for details)
+integrator = "Forward" # Integration formalism, whose numerical settings are its own section: "Forward" (dense ξ, needed for [PerturbedEquilibrium]/kinetic), "Riccati" (chunked propagator BVP, unlocks the singular-surface Δ′ matrix), or "Galerkin" (outer-region singular Galerkin Δ′)
+truncate_at_rational_offset = true # Truncate at (last_rational_q + rational_offset_fraction)/n — TRUE for diverted equilibria (q → ∞ at separatrix)
+rational_offset_fraction = 0.2 # Truncate integration at (last_rational_q + rational_offset_fraction)/n (used when truncate_at_rational_offset = true)
+psilim_from_layer_overlap = true # Cap psilim where adjacent resistive layers overlap (the scan is recorded only when capping)
+
+# Numerical settings of the forward integrator
+[Forward]
+eulerlagrange_tolerance = 1e-10 # Relative tolerance for ODE integration of Euler-Lagrange equations
+
+# The SLAYER layer closures the layer-overlap scan builds its widths with; there is no [Tearing] section, so no
+# growth rates are computed. P_perp is pinned to the electron channel so the cap binds: with the default D_perp
+# the layers are ~30% narrower and do not overlap inside psi = 1.
+[SLAYER]
+P_perp_model = "chi_perp_e" # Perpendicular Prandtl number model (pinned; see above)
diff --git a/examples/LAR_beta_scan/gpec.toml b/examples/LAR_beta_scan/gpec.toml
new file mode 100644
index 0000000000..d40e82a476
--- /dev/null
+++ b/examples/LAR_beta_scan/gpec.toml
@@ -0,0 +1,73 @@
+# GPEC configuration for the TJ-analytic β (pressure factor) scan.
+#
+# The TJ-analytic equilibrium follows the analytic profile family of R. Fitzpatrick's
+# TJ code (https://github.com/rfitzp/TJ): same f₁ / pressure / shape-ODE parameterization,
+# fed through GPEC's own pipeline. The accompanying run_scan.jl reads this file, overrides
+# only the scan parameter ([TJAnalytic] p0) per point, and writes a fresh gpec.toml
+# into each tempdir. Every equilibrium parameter is embedded in [TJAnalytic] below —
+# there is no side-car TOML file.
+
+[Run]
+verbose = true # Log each stage's progress
+
+[Equilibrium]
+jac_type = "hamada" # Coordinate system (hamada, pest, boozer, equal_arc, park, custom)
+grid_type = "core_edge_packed" # Radial grid packing type
+psilow = 0.01 # Lower limit of normalized poloidal flux
+psihigh = 0.995 # Upper limit of normalized poloidal flux
+mpsi = 128 # Number of radial grid intervals (0 = two-pass auto grid from psi_accuracy)
+mtheta = 512 # Number of poloidal grid points
+
+# TJ-analytic equilibrium parameters (cf. R. Fitzpatrick, TJ code, https://github.com/rfitzp/TJ).
+# Geometry is FIXED at ε = a / R₀ = 0.4 / 2.0 = 0.2; run_scan.jl varies only `pc` per point.
+[TJAnalytic]
+r0 = 2.0 # Major radius R₀ [m] (centerline radius of the magnetic axis)
+a = 0.4 # Minor radius a [m] (plasma half-width at the midplane; here ε = 0.2)
+q0 = 1.5 # On-axis safety factor q(r=0)
+qa = 3.6 # Edge safety factor q(r=a)
+p0 = 0.001 # Normalized on-axis pressure (β-scan parameter; OVERRIDDEN per run by run_scan.jl)
+pressure_peaking = 2.0 # Pressure-profile peaking exponent in p₂(r) = p0·(1−r²)^μ
+B0 = 12.0 # On-axis toroidal field [T]
+ma = 128 # TJ-analytic internal radial grid resolution (shape-ODE nodes)
+mtheta = 128 # TJ-analytic internal poloidal grid resolution (θ-spline nodes)
+
+[Wall]
+shape = "conformal" # Wall shape (conformal, elliptical, dee, mod_dee, file)
+standoff_fraction = 20 # Wall standoff in plasma minor radii
+
+# Presence runs the LocalStability stage (Mercier D_I, resistive D_R, ballooning Δ', first α boundary); keys are the LocalStabilityProblem settings, numerics in [Ballooning]
+[LocalStability]
+theta_k = 0.0 # Ballooning angle θ_k, used by both the profile scan and the α-boundary scan
+alpha_boundary_scan = true # Run the first ballooning α-boundary scan (a root find per ψ surface)
+
+# Numerical settings of the ballooning scans
+[Ballooning]
+ode_tol = 1e-8 # Relative and absolute tolerance of the ballooning ODE integration behind Δ'
+n_scan = 24 # Resolution of the α scan for the first boundary
+max_alpha_scale = 8.0 # Upper end of the α search, as a multiple of the experimental α
+alpha_tol = 1e-3 # Bisection tolerance of the critical α, in the same multiples
+psi_window = [0.1, 0.99] # ψ_N range of the α scan; surfaces outside it are NaN
+
+[ForceFreeStates]
+vac_flag = true # Compute plasma, vacuum, and total energies for free-boundary modes
+
+qlow = 1.02 # Integration initiated at q determined by min(q0, qlow)
+qhigh = 3.6 # Integration terminated at q limit determined by min(qa, qhigh)
+
+nn = 1 # Toroidal mode number, or consecutive numbers as a list
+delta_mlow = 8 # Expands lower bound of Fourier harmonics
+delta_mhigh = 8 # Expands upper bound of Fourier harmonics
+mtheta_vacuum = 960 # Number of points used in splines over poloidal angle at the plasma-vacuum interface
+
+singfac_min = 1e-4 # Fractional distance from rational q at which ideal jump enforced
+frobenius_order = 6 # Order of the singular-surface (Frobenius) series expansion
+
+integrator = "Riccati" # Integration formalism, whose numerical settings are its own section: "Forward" (dense ξ, needed for [PerturbedEquilibrium]/kinetic), "Riccati" (chunked propagator BVP, unlocks the singular-surface Δ′ matrix), or "Galerkin" (outer-region singular Galerkin Δ′)
+truncate_at_rational_offset = false # FALSE for limited/analytical equilibria — rationals sparse, rational_offset_fraction would chop too much edge
+rational_offset_fraction = 0.2 # Truncate integration at (last_rational_q + rational_offset_fraction)/n (used when truncate_at_rational_offset = true)
+
+# Numerical settings of the Riccati integrator
+[Riccati]
+eulerlagrange_tolerance = 1e-12 # Relative tolerance for ODE integration of Euler-Lagrange equations
+renorm_threshold = 1e3 # Column-norm threshold that triggers solution renormalization
+save_interval = 1 # Save every Nth ODE step (1=all). Always saves near rational surfaces.
diff --git a/examples/LAR_beta_scan/run_scan.jl b/examples/LAR_beta_scan/run_scan.jl
new file mode 100644
index 0000000000..f0faf52fd5
--- /dev/null
+++ b/examples/LAR_beta_scan/run_scan.jl
@@ -0,0 +1,153 @@
+#!/usr/bin/env julia
+"""
+ run_scan.jl — TJ-analytic β (pressure factor) scan
+
+Fixed geometry (ε=0.2), varying pressure via the `pc` parameter of the
+TJ-analytic equilibrium model ([TJAnalytic]). The TJ-analytic model
+follows the profile family of R. Fitzpatrick's TJ code
+(https://github.com/rfitzp/TJ); no geqdsk files are needed.
+
+Usage:
+ julia --project=../.. run_scan.jl # Full scan
+ julia --project=../.. run_scan.jl --test # Quick test (3 points)
+"""
+
+using Pkg
+Pkg.activate(joinpath(@__DIR__, "../.."))
+
+using GeneralizedPerturbedEquilibrium
+using GeneralizedPerturbedEquilibrium.Equilibrium: TJAnalyticConfig, EquilibriumConfig
+using HDF5
+using TOML
+using Printf
+
+# ============================================================================
+# Scan parameters — TJ-analytic benchmark pressure factors
+# ============================================================================
+
+# Pressure scan: pc grid ends just before the ideal-kink pole at pc ≈ 0.174
+# (where δW_t → 0 and Δ' diverges). Grid is power-law warped so the spacing
+# is approximately uniform over most of the range and smoothly tightens as
+# the pole is approached, giving an even visual cadence without wasting
+# points on the flat-slope region far from the pole.
+function _warped_grid(x_start::Float64, x_end::Float64, N::Int; p::Float64=2.0)
+ return [x_start + (x_end - x_start) * (1 - (1 - i / (N - 1))^p) for i in 0:N-1]
+end
+
+const PC_FULL = _warped_grid(0.001, 0.1735, 40; p=2.0)
+
+const PC_TEST = [0.001, 0.10, 0.17]
+
+const SCAN_DIR = @__DIR__
+const OUTPUT_H5 = joinpath(SCAN_DIR, "beta_scan.h5")
+
+# All baseline parameters (Equilibrium, TJAnalytic, Wall, ForceFreeStates)
+# live in gpec.toml next to this script — there is no side-car TOML file.
+# The scan below reads gpec.toml once and overrides ONLY `TJAnalytic.p0`
+# per scan point before writing the per-point gpec.toml into a tempdir.
+const GPEC_BASE = TOML.parsefile(joinpath(SCAN_DIR, "gpec.toml"))
+
+# ============================================================================
+# Run a single pressure point
+# ============================================================================
+
+function run_single(pc::Float64)
+ run_dir = mktempdir(; prefix="gpec_tj_analytic_beta_")
+ try
+ # Per-point gpec.toml = baseline gpec.toml with TJAnalytic.p0 overridden.
+ config = deepcopy(GPEC_BASE)
+ config["TJAnalytic"]["p0"] = pc
+ open(joinpath(run_dir, "gpec.toml"), "w") do io
+ TOML.print(io, config)
+ end
+
+ GeneralizedPerturbedEquilibrium.main([run_dir])
+ return extract_results(joinpath(run_dir, "gpec.h5"))
+ catch e
+ @warn "Failed for pc=$pc" exception = (e, catch_backtrace())
+ return nothing
+ finally
+ rm(run_dir; force=true, recursive=true)
+ end
+end
+
+function extract_results(h5_path::String)
+ h5open(h5_path, "r") do f
+ fbs = "ForceFreeStates/FreeBoundaryStability"
+ ep = read(f, "$fbs/eigenmode_plasma_energies")
+ ev = read(f, "$fbs/eigenmode_vacuum_energies")
+ et = read(f, "$fbs/eigenmode_energies")
+ msing = read(f, "SingularSurfaces/rational_count")
+ m_sing = read(f, "SingularSurfaces/rational_m")
+ dp_mat = haskey(f, "SingularSurfaces/Delta_prime_matrix") ? read(f, "SingularSurfaces/Delta_prime_matrix") : nothing
+ qlim = haskey(f, "Info/qlim") ? read(f, "Info/qlim") : read(f, "Equilibrium/q_max")
+ q0 = read(f, "Equilibrium/q_axis")
+ qmax = read(f, "Equilibrium/q_max")
+
+ dp_21 = NaN + NaN * im
+ dp_31 = NaN + NaN * im
+ if dp_mat !== nothing && msing > 0
+ for s in 1:min(msing, size(dp_mat, 1))
+ m_val = size(m_sing, 1) == msing ? m_sing[s, 1] : m_sing[1, s]
+ if m_val == 2
+ dp_21 = dp_mat[s, s]
+ end
+ if m_val == 3
+ dp_31 = dp_mat[s, s]
+ end
+ end
+ end
+ return (dp_21=dp_21, dp_31=dp_31,
+ dW_plasma=real(ep[1]), dW_vacuum=real(ev[1]), dW_total=real(et[1]),
+ q0=q0, qmax=qmax, qlim=qlim, msing=msing, dp_matrix=dp_mat)
+ end
+end
+
+# ============================================================================
+# Main
+# ============================================================================
+
+function main()
+ test_mode = "--test" in ARGS
+ pcs = test_mode ? PC_TEST : PC_FULL
+
+ tj = GPEC_BASE["TJAnalytic"]
+ @info "TJ-analytic β scan: $(length(pcs)) points, ε=$(tj["a"]/tj["r0"]), B0=$(tj["B0"])T, q0=$(tj["q0"]), qa=$(tj["qa"])" *
+ (test_mode ? " (test mode)" : "")
+
+ isfile(OUTPUT_H5) && rm(OUTPUT_H5)
+
+ for (i, pc) in enumerate(pcs)
+ @info "[$(i)/$(length(pcs))] pc=$pc"
+ result = run_single(pc)
+ if result !== nothing
+ h5open(OUTPUT_H5, isfile(OUTPUT_H5) ? "r+" : "w") do f
+ gname = @sprintf("pc_%.5f", pc)
+ haskey(f, gname) && delete_object(f, gname)
+ g = create_group(f, gname)
+ g["pressure_factor"] = pc
+ g["dp_21_real"] = real(result.dp_21)
+ g["dp_21_imag"] = imag(result.dp_21)
+ g["dp_31_real"] = real(result.dp_31)
+ g["dp_31_imag"] = imag(result.dp_31)
+ g["dW_plasma"] = result.dW_plasma
+ g["dW_vacuum"] = result.dW_vacuum
+ g["dW_total"] = result.dW_total
+ g["q0"] = result.q0
+ g["qmax"] = result.qmax
+ g["qlim"] = result.qlim
+ g["msing"] = result.msing
+ if result.dp_matrix !== nothing
+ g["dp_matrix"] = result.dp_matrix
+ end
+ end
+ @printf(" dp21=%+.4f%+.4fi dp31=%+.4f%+.4fi dW_t=%+.6f qa=%.3f\n",
+ real(result.dp_21), imag(result.dp_21), real(result.dp_31), imag(result.dp_31),
+ result.dW_total, result.qmax)
+ end
+ end
+
+ @info "Results saved to $OUTPUT_H5"
+end
+
+main()
diff --git a/examples/LAR_epsilon_scan/gpec.toml b/examples/LAR_epsilon_scan/gpec.toml
new file mode 100644
index 0000000000..119bb894a7
--- /dev/null
+++ b/examples/LAR_epsilon_scan/gpec.toml
@@ -0,0 +1,74 @@
+# GPEC configuration for the TJ-analytic ε (inverse aspect ratio) scan.
+#
+# The TJ-analytic equilibrium follows the analytic profile family of R. Fitzpatrick's
+# TJ code (https://github.com/rfitzp/TJ): same f₁ / pressure / shape-ODE parameterization,
+# fed through GPEC's own pipeline. run_scan.jl sets [TJAnalytic] solver = "direct"
+# (direct-GS path, required to capture the ideal external-kink pole δW_t → 0 as ε → ε_crit)
+# and varies only [TJAnalytic] r0 = a / ε per point, writing a fresh gpec.toml
+# into each tempdir. Every equilibrium parameter is embedded in [TJAnalytic] below.
+
+[Run]
+verbose = true # Log each stage's progress
+
+[Equilibrium]
+jac_type = "hamada" # Coordinate system (hamada, pest, boozer, equal_arc, park, custom)
+grid_type = "core_edge_packed" # Radial grid packing type
+psilow = 0.01 # Lower limit of normalized poloidal flux
+psihigh = 0.995 # Upper limit of normalized poloidal flux
+mpsi = 128 # Number of radial grid intervals (0 = two-pass auto grid from psi_accuracy)
+mtheta = 512 # Number of poloidal grid points
+
+# TJ-analytic equilibrium parameters (cf. R. Fitzpatrick, TJ code, https://github.com/rfitzp/TJ).
+# All parameters held FIXED except r0, which run_scan.jl overrides as r0 = a / ε;
+# a stays fixed at 1 m so each scan point is a self-similar rescaling of the geometry.
+[TJAnalytic]
+r0 = 5.0 # Major radius R₀ [m] (baseline ε = 0.2; OVERRIDDEN per scan point by run_scan.jl)
+a = 1.0 # Minor radius a [m] (plasma half-width at the midplane; fixed across the scan)
+q0 = 1.5 # On-axis safety factor q(r=0)
+qa = 3.6 # Edge safety factor q(r=a)
+p0 = 0.001 # Normalized on-axis pressure (kept low for the ε scan to isolate geometry effects)
+pressure_peaking = 2.0 # Pressure-profile peaking exponent in p₂(r) = p0·(1−r²)^μ
+B0 = 12.0 # On-axis toroidal field [T]
+ma = 128 # TJ-analytic internal radial grid resolution (shape-ODE nodes)
+mtheta = 128 # TJ-analytic internal poloidal grid resolution (θ-spline nodes)
+
+[Wall]
+shape = "conformal" # Wall shape (conformal, elliptical, dee, mod_dee, file)
+standoff_fraction = 20 # Wall standoff in plasma minor radii
+
+# Presence runs the LocalStability stage (Mercier D_I, resistive D_R, ballooning Δ', first α boundary); keys are the LocalStabilityProblem settings, numerics in [Ballooning]
+[LocalStability]
+theta_k = 0.0 # Ballooning angle θ_k, used by both the profile scan and the α-boundary scan
+alpha_boundary_scan = true # Run the first ballooning α-boundary scan (a root find per ψ surface)
+
+# Numerical settings of the ballooning scans
+[Ballooning]
+ode_tol = 1e-8 # Relative and absolute tolerance of the ballooning ODE integration behind Δ'
+n_scan = 24 # Resolution of the α scan for the first boundary
+max_alpha_scale = 8.0 # Upper end of the α search, as a multiple of the experimental α
+alpha_tol = 1e-3 # Bisection tolerance of the critical α, in the same multiples
+psi_window = [0.1, 0.99] # ψ_N range of the α scan; surfaces outside it are NaN
+
+[ForceFreeStates]
+vac_flag = true # Compute plasma, vacuum, and total energies for free-boundary modes
+
+qlow = 1.02 # Integration initiated at q determined by min(q0, qlow)
+qhigh = 3.6 # Integration terminated at q limit determined by min(qa, qhigh)
+
+nn = 1 # Toroidal mode number, or consecutive numbers as a list
+delta_mlow = 8 # Expands lower bound of Fourier harmonics
+delta_mhigh = 8 # Expands upper bound of Fourier harmonics
+mtheta_vacuum = 960 # Number of points used in splines over poloidal angle at the plasma-vacuum interface
+
+singfac_min = 1e-4 # Fractional distance from rational q at which ideal jump enforced
+frobenius_order = 6 # Order of the singular-surface (Frobenius) series expansion
+
+integrator = "Riccati" # Integration formalism, whose numerical settings are its own section: "Forward" (dense ξ, needed for [PerturbedEquilibrium]/kinetic), "Riccati" (chunked propagator BVP, unlocks the singular-surface Δ′ matrix), or "Galerkin" (outer-region singular Galerkin Δ′)
+truncate_at_rational_offset = false # FALSE for limited/analytical equilibria — rationals sparse, rational_offset_fraction would chop too much edge
+rational_offset_fraction = 0.2 # Truncate integration at (last_rational_q + rational_offset_fraction)/n (used when truncate_at_rational_offset = true)
+
+# Numerical settings of the Riccati integrator
+[Riccati]
+eulerlagrange_tolerance = 1e-12 # Relative tolerance for ODE integration of Euler-Lagrange equations
+renorm_threshold = 1e3 # Column-norm threshold that triggers solution renormalization
+save_interval = 1 # Save every Nth ODE step (1=all). Always saves near rational surfaces.
diff --git a/examples/LAR_epsilon_scan/run_scan.jl b/examples/LAR_epsilon_scan/run_scan.jl
new file mode 100644
index 0000000000..f02e249ff4
--- /dev/null
+++ b/examples/LAR_epsilon_scan/run_scan.jl
@@ -0,0 +1,160 @@
+#!/usr/bin/env julia
+"""
+ run_scan.jl — TJ-analytic ε (inverse aspect ratio) scan
+
+Uses the TJ-analytic equilibrium model ([TJAnalytic], direct solver). The TJ-analytic model follows the profile family of
+R. Fitzpatrick's TJ code (https://github.com/rfitzp/TJ); no geqdsk files
+are needed.
+
+Usage:
+ julia --project=../.. run_scan.jl # Full scan
+ julia --project=../.. run_scan.jl --test # Quick test (3 points)
+"""
+
+using Pkg
+Pkg.activate(joinpath(@__DIR__, "../.."))
+
+using GeneralizedPerturbedEquilibrium
+using GeneralizedPerturbedEquilibrium.Equilibrium: TJAnalyticConfig, EquilibriumConfig
+using HDF5
+using TOML
+using Printf
+
+# ============================================================================
+# Scan parameters (matching the TJ-analytic benchmark of Fitzpatrick's TJ code)
+# ============================================================================
+
+# Aspect-ratio scan: ε grid ends just before the ideal-kink pole at
+# ε ≈ 0.665 (where δW_t → 0 and Δ' diverges). Grid is power-law warped so
+# spacing tightens smoothly as the pole is approached — the flat low-ε
+# region is covered with even cadence, and more points land in the final
+# few percent where Δ' rises by orders of magnitude.
+function _warped_grid(x_start::Float64, x_end::Float64, N::Int; p::Float64=2.0)
+ return [x_start + (x_end - x_start) * (1 - (1 - i / (N - 1))^p) for i in 0:N-1]
+end
+
+const EPSILONS_FULL = _warped_grid(0.125, 0.660, 56; p=2.0)
+
+const EPSILONS_TEST = [0.2495, 0.4072, 0.5510]
+
+const SCAN_DIR = @__DIR__
+const OUTPUT_H5 = joinpath(SCAN_DIR, "epsilon_scan.h5")
+
+# All baseline parameters (Equilibrium, TJAnalytic, Wall, ForceFreeStates)
+# live in gpec.toml next to this script — there is no side-car TOML file.
+# The scan below reads gpec.toml once and overrides ONLY
+# `TJAnalytic.r0` per scan point as `r0 = a / ε` before
+# writing the per-point gpec.toml into a tempdir.
+const GPEC_BASE = TOML.parsefile(joinpath(SCAN_DIR, "gpec.toml"))
+
+# ============================================================================
+# Run a single epsilon point
+# ============================================================================
+
+function run_single(epsilon::Float64)
+ run_dir = mktempdir(; prefix="gpec_tj_analytic_")
+ try
+ # Per-point gpec.toml = baseline gpec.toml with TJAnalytic.r0
+ # overridden. Switch to the direct solver so ψ(R, Z) is built
+ # from the TJ-analytic model and processed by the direct-GS
+ # pipeline. Required to capture the ideal external-kink pole (δW_t →
+ # 0 as ε → ε_crit); the inverse path bypasses the line-integrated q
+ # and shows no such pole.
+ config = deepcopy(GPEC_BASE)
+ config["TJAnalytic"]["r0"] = GPEC_BASE["TJAnalytic"]["a"] / epsilon
+ config["TJAnalytic"]["solver"] = "direct"
+ open(joinpath(run_dir, "gpec.toml"), "w") do io
+ TOML.print(io, config)
+ end
+
+ GeneralizedPerturbedEquilibrium.main([run_dir])
+ return extract_results(joinpath(run_dir, "gpec.h5"))
+ catch e
+ @warn "Failed for ε=$epsilon" exception = (e, catch_backtrace())
+ return nothing
+ finally
+ rm(run_dir; force=true, recursive=true)
+ end
+end
+
+function extract_results(h5_path::String)
+ h5open(h5_path, "r") do f
+ fbs = "ForceFreeStates/FreeBoundaryStability"
+ ep = read(f, "$fbs/eigenmode_plasma_energies")
+ ev = read(f, "$fbs/eigenmode_vacuum_energies")
+ et = read(f, "$fbs/eigenmode_energies")
+ msing = read(f, "SingularSurfaces/rational_count")
+ m_sing = read(f, "SingularSurfaces/rational_m")
+ dp_mat = haskey(f, "SingularSurfaces/Delta_prime_matrix") ? read(f, "SingularSurfaces/Delta_prime_matrix") : nothing
+ qlim = haskey(f, "Info/qlim") ? read(f, "Info/qlim") : read(f, "Equilibrium/q_max")
+ q0 = read(f, "Equilibrium/q_axis")
+ qmax = read(f, "Equilibrium/q_max")
+
+ dp_21 = NaN + NaN * im
+ dp_31 = NaN + NaN * im
+ if dp_mat !== nothing && msing > 0
+ for s in 1:min(msing, size(dp_mat, 1))
+ m_val = size(m_sing, 1) == msing ? m_sing[s, 1] : m_sing[1, s]
+ if m_val == 2
+ dp_21 = dp_mat[s, s]
+ end
+ if m_val == 3
+ dp_31 = dp_mat[s, s]
+ end
+ end
+ end
+ return (dp_21=dp_21, dp_31=dp_31,
+ dW_plasma=real(ep[1]), dW_vacuum=real(ev[1]), dW_total=real(et[1]),
+ q0=q0, qmax=qmax, qlim=qlim, msing=msing, dp_matrix=dp_mat)
+ end
+end
+
+# ============================================================================
+# Main
+# ============================================================================
+
+function main()
+ test_mode = "--test" in ARGS
+ epsilons = test_mode ? EPSILONS_TEST : EPSILONS_FULL
+
+ tj = GPEC_BASE["TJAnalytic"]
+ @info "TJ-analytic ε scan: $(length(epsilons)) points, B0=$(tj["B0"])T, q0=$(tj["q0"]), qa=$(tj["qa"]), p0=$(tj["p0"])" *
+ (test_mode ? " (test mode)" : "")
+
+ isfile(OUTPUT_H5) && rm(OUTPUT_H5)
+
+ lar_a = GPEC_BASE["TJAnalytic"]["a"]
+ for (i, eps) in enumerate(epsilons)
+ @info "[$(i)/$(length(epsilons))] ε=$eps (R0=$(@sprintf("%.3f", lar_a/eps)))"
+ result = run_single(eps)
+ if result !== nothing
+ h5open(OUTPUT_H5, isfile(OUTPUT_H5) ? "r+" : "w") do f
+ gname = @sprintf("eps_%.4f", eps)
+ haskey(f, gname) && delete_object(f, gname)
+ g = create_group(f, gname)
+ g["epsilon"] = eps
+ g["dp_21_real"] = real(result.dp_21)
+ g["dp_21_imag"] = imag(result.dp_21)
+ g["dp_31_real"] = real(result.dp_31)
+ g["dp_31_imag"] = imag(result.dp_31)
+ g["dW_plasma"] = result.dW_plasma
+ g["dW_vacuum"] = result.dW_vacuum
+ g["dW_total"] = result.dW_total
+ g["q0"] = result.q0
+ g["qmax"] = result.qmax
+ g["qlim"] = result.qlim
+ g["msing"] = result.msing
+ if result.dp_matrix !== nothing
+ g["dp_matrix"] = result.dp_matrix
+ end
+ end
+ @printf(" dp21=%+.4f%+.4fi dp31=%+.4f%+.4fi dW_t=%+.6f qa=%.3f\n",
+ real(result.dp_21), imag(result.dp_21), real(result.dp_31), imag(result.dp_31),
+ result.dW_total, result.qmax)
+ end
+ end
+
+ @info "Results saved to $OUTPUT_H5"
+end
+
+main()
diff --git a/examples/LAR_ideal_match_test/gpec.toml b/examples/LAR_ideal_match_test/gpec.toml
new file mode 100644
index 0000000000..d266d6af90
--- /dev/null
+++ b/examples/LAR_ideal_match_test/gpec.toml
@@ -0,0 +1,83 @@
+# LAR ideal-limit reference: large-aspect-ratio analytic TJ equilibrium, epsilon = a/R0 = 0.2, n = 1.
+#
+# The ideal-limit companion to LAR_resistive_match_test, identical except that [Match] ideal = true skips
+# the resistive inner layer entirely and builds the bare (perfectly shielded) coil columns. Running
+# the two side by side isolates what the inner layer contributes on this geometry. The per-surface
+# resistivity, density and rotation inputs are omitted here because the ideal limit never reads them.
+# This run terminates after the stability stage.
+
+[Run]
+output_file = "gpec_lar_ideal.h5"# HDF5 file every stage saves into, relative to this deck's directory
+verbose = true # Log each stage's progress
+
+[Equilibrium]
+jac_type = "hamada" # Coordinate system (hamada, pest, boozer, equal_arc, park, custom)
+grid_type = "core_edge_packed" # Radial grid packing type (core_edge_packed = sin² spacing, dense at axis and edge)
+psilow = 0.01 # Lower limit of normalized flux coordinate
+psihigh = 0.995 # Upper limit of normalized flux coordinate
+mpsi = 128 # Number of radial grid points (0 = auto-compute from psi_accuracy)
+mtheta = 512 # Number of poloidal grid points
+
+[TJAnalytic]
+r0 = 2.0 # Major radius R0 [m]
+a = 0.4 # Minor radius a [m] (epsilon = a/R0 = 0.2)
+q0 = 1.5 # On-axis safety factor
+qa = 3.6 # Edge safety factor
+p0 = 0.01 # Normalized on-axis pressure
+pressure_peaking = 2.0 # Pressure peaking exponent: p2 = p0*(1-r^2)^pressure_peaking
+B0 = 12.0 # On-axis toroidal field [T]
+ma = 128 # Radial grid points
+mtheta = 128 # Poloidal grid points
+
+[Wall]
+shape = "conformal" # Wall shape (conformal, elliptical, dee, mod_dee, file)
+standoff_fraction = 20 # Wall standoff in plasma minor radii
+
+# Presence runs the LocalStability stage (Mercier D_I, resistive D_R, ballooning Δ', first α boundary); keys are the LocalStabilityProblem settings, numerics in [Ballooning]
+[LocalStability]
+theta_k = 0.0 # Ballooning angle θ_k, used by both the profile scan and the α-boundary scan
+alpha_boundary_scan = true # Run the first ballooning α-boundary scan (a root find per ψ surface)
+
+# Numerical settings of the ballooning scans
+[Ballooning]
+ode_tol = 1e-8 # Relative and absolute tolerance of the ballooning ODE integration behind Δ'
+n_scan = 24 # Resolution of the α scan for the first boundary
+max_alpha_scale = 8.0 # Upper end of the α search, as a multiple of the experimental α
+alpha_tol = 1e-3 # Bisection tolerance of the critical α, in the same multiples
+psi_window = [0.1, 0.99] # ψ_N range of the α scan; surfaces outside it are NaN
+
+[ForceFreeStates]
+vac_flag = true # Compute plasma, vacuum, and total energies for free-boundary modes
+
+qlow = 1.02 # Integration initiated at q determined by min(q0, qlow)
+qhigh = 3.6 # Integration terminated at q limit determined by min(qa, qhigh)
+nn = 1 # Toroidal mode number, or consecutive numbers as a list
+delta_mlow = 8 # Expands lower bound of Fourier harmonics
+delta_mhigh = 8 # Expands upper bound of Fourier harmonics
+mtheta_vacuum = 960 # Number of points used in splines over poloidal angle at plasma-vacuum interface
+
+singfac_min = 1e-4 # Fractional distance from rational q at which ideal jump enforced
+frobenius_order = 6 # Power-series order for the singular-surface asymptotics
+
+integrator = "Galerkin" # Integration formalism, whose numerical settings are its own section: "Forward" (dense ξ, needed for [PerturbedEquilibrium]/kinetic), "Riccati" (chunked propagator BVP, unlocks the singular-surface Δ′ matrix), or "Galerkin" (outer-region singular Galerkin Δ′)
+truncate_at_rational_offset = false # Keep psilim at psihigh (do not truncate at last_rational_q + rational_offset_fraction)
+rational_offset_fraction = 0.2 # Truncate integration at (last_rational_q + rational_offset_fraction) / n (only used when truncate_at_rational_offset = true)
+
+# Outer-region singular Galerkin Delta-prime solver with rpec coil columns.
+[Galerkin]
+nx = 256 # Hermite-cubic elements per interval between singular surfaces
+nq = 6 # Gauss-Lobatto quadrature order per element
+pfac = 0.03 # Grid packing ratio toward singular surfaces (smaller = tighter packing)
+dx0 = 5e-4 # Resonant-element integration truncation distance from the rational (times 1/|n q'|)
+dx1 = 1e-3 # Resonant-element size (times 1/|n q'|)
+dx2 = 1e-3 # Extension-element size (times 1/|n q'|)
+cutoff = 10 # Number of elements carrying the large (driving) solution as a source term
+tol = 1e-10 # Resonant-cell adaptive-quadrature (QuadGK) tolerance
+gnstep = 5000 # Maximum resonant-integration steps
+dx1dx2_flag = true # Enable the special dx1/dx2 element sizing for resonant/extension cells
+frobenius_order_ceiling = true # Auto-raise the series order by ceil(2*Re(alpha)) on high-Mercier-index surfaces
+rpec_flag = true # Append mpert coil-response columns (unit edge sources) to the solve, giving the delta_coil block
+
+# Driven inner-layer matching on the finished solve in the ideal limit: the inner layer is skipped entirely.
+[Match]
+ideal = true # true = build the IDEAL solution (skip the inner layer, bare coil columns)
diff --git a/examples/LAR_resistive_match_test/gpec.toml b/examples/LAR_resistive_match_test/gpec.toml
new file mode 100644
index 0000000000..248f1cd143
--- /dev/null
+++ b/examples/LAR_resistive_match_test/gpec.toml
@@ -0,0 +1,88 @@
+# LAR resistive-match test: large-aspect-ratio analytic TJ equilibrium, epsilon = a/R0 = 0.2, n = 1.
+#
+# A different equilibrium from the DIII-D-like validation case, used to check that the
+# outer-region Galerkin Delta-prime solve and the driven (RPEC) outer-inner match stay self-consistent
+# on a second geometry: matching residual near machine precision and convergence under frobenius_order
+# refinement. For n = 1 with q in [1.5, 3.6] the rational surfaces are q = 2 and q = 3, so msing = 2
+# and the per-surface resistive arrays below have length 2 (core to edge). This run terminates after
+# the stability stage. The companion LAR_ideal_match_test case is the ideal-limit reference.
+
+[Run]
+output_file = "gpec_lar_resistive.h5"# HDF5 file every stage saves into, relative to this deck's directory
+verbose = true # Log each stage's progress
+
+[Equilibrium]
+jac_type = "hamada" # Coordinate system (hamada, pest, boozer, equal_arc, park, custom)
+grid_type = "core_edge_packed" # Radial grid packing type (core_edge_packed = sin² spacing, dense at axis and edge)
+psilow = 0.01 # Lower limit of normalized flux coordinate
+psihigh = 0.995 # Upper limit of normalized flux coordinate
+mpsi = 128 # Number of radial grid points (0 = auto-compute from psi_accuracy)
+mtheta = 512 # Number of poloidal grid points
+
+[TJAnalytic]
+r0 = 2.0 # Major radius R0 [m]
+a = 0.4 # Minor radius a [m] (epsilon = a/R0 = 0.2)
+q0 = 1.5 # On-axis safety factor
+qa = 3.6 # Edge safety factor
+p0 = 0.01 # Normalized on-axis pressure
+pressure_peaking = 2.0 # Pressure peaking exponent: p2 = p0*(1-r^2)^pressure_peaking
+B0 = 12.0 # On-axis toroidal field [T]
+ma = 128 # Radial grid points
+mtheta = 128 # Poloidal grid points
+
+[Wall]
+shape = "conformal" # Wall shape (conformal, elliptical, dee, mod_dee, file)
+standoff_fraction = 20 # Wall standoff in plasma minor radii
+
+# Presence runs the LocalStability stage (Mercier D_I, resistive D_R, ballooning Δ', first α boundary); keys are the LocalStabilityProblem settings, numerics in [Ballooning]
+[LocalStability]
+theta_k = 0.0 # Ballooning angle θ_k, used by both the profile scan and the α-boundary scan
+alpha_boundary_scan = true # Run the first ballooning α-boundary scan (a root find per ψ surface)
+
+# Numerical settings of the ballooning scans
+[Ballooning]
+ode_tol = 1e-8 # Relative and absolute tolerance of the ballooning ODE integration behind Δ'
+n_scan = 24 # Resolution of the α scan for the first boundary
+max_alpha_scale = 8.0 # Upper end of the α search, as a multiple of the experimental α
+alpha_tol = 1e-3 # Bisection tolerance of the critical α, in the same multiples
+psi_window = [0.1, 0.99] # ψ_N range of the α scan; surfaces outside it are NaN
+
+[ForceFreeStates]
+vac_flag = true # Compute plasma, vacuum, and total energies for free-boundary modes
+
+qlow = 1.02 # Integration initiated at q determined by min(q0, qlow)
+qhigh = 3.6 # Integration terminated at q limit determined by min(qa, qhigh)
+nn = 1 # Toroidal mode number, or consecutive numbers as a list
+delta_mlow = 8 # Expands lower bound of Fourier harmonics
+delta_mhigh = 8 # Expands upper bound of Fourier harmonics
+mtheta_vacuum = 960 # Number of points used in splines over poloidal angle at plasma-vacuum interface
+
+singfac_min = 1e-4 # Fractional distance from rational q at which ideal jump enforced
+frobenius_order = 6 # Power-series order for the singular-surface asymptotics
+
+integrator = "Galerkin" # Integration formalism, whose numerical settings are its own section: "Forward" (dense ξ, needed for [PerturbedEquilibrium]/kinetic), "Riccati" (chunked propagator BVP, unlocks the singular-surface Δ′ matrix), or "Galerkin" (outer-region singular Galerkin Δ′)
+truncate_at_rational_offset = false # Keep psilim at psihigh (do not truncate at last_rational_q + rational_offset_fraction)
+rational_offset_fraction = 0.2 # Truncate integration at (last_rational_q + rational_offset_fraction) / n (only used when truncate_at_rational_offset = true)
+
+# Outer-region singular Galerkin Delta-prime solver with rpec coil columns.
+[Galerkin]
+nx = 256 # Hermite-cubic elements per interval between singular surfaces
+nq = 6 # Gauss-Lobatto quadrature order per element
+pfac = 0.03 # Grid packing ratio toward singular surfaces (smaller = tighter packing)
+dx0 = 5e-4 # Resonant-element integration truncation distance from the rational (times 1/|n q'|)
+dx1 = 1e-3 # Resonant-element size (times 1/|n q'|)
+dx2 = 1e-3 # Extension-element size (times 1/|n q'|)
+cutoff = 10 # Number of elements carrying the large (driving) solution as a source term
+tol = 1e-10 # Resonant-cell adaptive-quadrature (QuadGK) tolerance
+gnstep = 5000 # Maximum resonant-integration steps
+dx1dx2_flag = true # Enable the special dx1/dx2 element sizing for resonant/extension cells
+frobenius_order_ceiling = true # Auto-raise the series order by ceil(2*Re(alpha)) on high-Mercier-index surfaces
+rpec_flag = true # Append mpert coil-response columns (unit edge sources) to the solve, giving the delta_coil block
+
+# Driven inner-layer matching on the finished solve. Per-surface resistive inputs (core to edge) for the two
+# rational surfaces q = 2 and q = 3: eta=8e-8, rho=3.3e-7 kg/m^3, rotation=1 Hz, Gamma=5/3.
+[Match]
+eta = [8e-8, 8e-8] # Per-surface resistivity eta (core to edge)
+rho = [3.3e-7, 3.3e-7] # Per-surface mass density rho [kg/m^3] (core to edge)
+rotation = [1.0, 1.0] # Per-surface rotation frequency f [Hz] (core to edge); forced eigenvalue gamma_s = 2*pi*i*n*f
+gamma = 1.6666666666666667 # Ratio of specific heats Gamma for the resistive-layer coefficients (5/3)
diff --git a/examples/LAR_reversed_shear_example/gpec.toml b/examples/LAR_reversed_shear_example/gpec.toml
new file mode 100644
index 0000000000..87abaaa560
--- /dev/null
+++ b/examples/LAR_reversed_shear_example/gpec.toml
@@ -0,0 +1,45 @@
+# Large-aspect-ratio equilibrium with reversed shear: n=1 ideal stability.
+# A hollow current profile makes q fall from 2.40 on the axis to a minimum of 1.82 at ψ_N ≈ 0.37
+# and rise to 2.84 at the edge, so q = 2 is crossed twice, with q′ < 0 on the inner crossing and
+# q′ > 0 on the outer one. Regression fixture for keeping both crossings as separate surfaces; the
+# equilibrium is generated analytically from the embedded [LargeAspectRatio] section, with no wall.
+
+[Run]
+verbose = true # Log each stage's progress
+
+[Equilibrium]
+jac_type = "hamada" # Coordinate system (hamada, pest, boozer, equal_arc, park, custom)
+grid_type = "core_edge_packed" # Radial grid packing type
+psilow = 0.01 # Lower limit of normalized poloidal flux
+psihigh = 0.99 # Upper limit of normalized poloidal flux
+mpsi = 128 # Number of radial grid intervals (0 = two-pass auto grid from psi_accuracy)
+mtheta = 256 # Number of poloidal grid points
+
+[ForceFreeStates]
+vac_flag = true # Compute plasma, vacuum, and total energies for free-boundary modes
+qlow = 1.02 # Integration initiated at q determined by min(q0, qlow)
+qhigh = 1e3 # Integration terminated at q limit determined by min(qa, qhigh)
+nn = 1 # Toroidal mode number, or consecutive numbers as a list
+delta_mlow = 8 # Expands lower bound of Fourier harmonics
+delta_mhigh = 8 # Expands upper bound of Fourier harmonics
+mtheta_vacuum = 960 # Number of points used in splines over poloidal angle at the plasma-vacuum interface
+singfac_min = 1e-4 # Fractional distance from rational q at which ideal jump enforced
+integrator = "Forward" # Integration formalism, whose numerical settings are its own section: "Forward" (dense ξ), "Riccati" (chunked propagator BVP, singular-surface Δ′), or "Galerkin" (outer-region singular Galerkin Δ′)
+truncate_at_rational_offset = false # Truncate integration at (last_rational_q + rational_offset_fraction)/n; false for analytic equilibria
+
+# Numerical settings of the forward integrator
+[Forward]
+eulerlagrange_tolerance = 1e-9 # Relative tolerance for ODE integration of Euler-Lagrange equations
+
+# Large-aspect-ratio analytic equilibrium parameters; this section selects the equilibrium. See LargeAspectRatioConfig in src/Equilibrium.
+[LargeAspectRatio]
+r0 = 10.0 # Major radius of the plasma [m]
+a = 1.0 # Minor radius of the plasma [m]
+beta0 = 1e-3 # Beta on axis (normalized pressure)
+q0 = 2.4 # Safety factor on axis
+p_pres = 2.0 # Exponent of the pressure profile p00·(1 − (r/a)²)^p_pres
+p_sig = 2.0 # Exponent of the current-related profile
+sigma_type = "hollow" # Current profile: "default", "wesson" or "hollow" (off-axis peak, reversed shear)
+hollow = 6.0 # Off-axis current enhancement of the "hollow" profile
+mtheta = 128 # Number of grid points in the poloidal direction
+ma = 128 # Number of grid points in the radial direction
diff --git a/examples/Solovev_ideal_example/analyze_example.jl b/examples/Solovev_ideal_example/analyze_example.jl
new file mode 100644
index 0000000000..62178b316a
--- /dev/null
+++ b/examples/Solovev_ideal_example/analyze_example.jl
@@ -0,0 +1,18 @@
+using Pkg;
+Pkg.activate(joinpath(@__DIR__, "../.."))
+using GeneralizedPerturbedEquilibrium, Plots
+using GeneralizedPerturbedEquilibrium: Analysis
+isinteractive() ? plotlyjs() : gr()
+
+h5path = joinpath(@__DIR__, "gpec.h5")
+
+# Summary plots
+p_eq = Analysis.Equilibrium.plot_equilibrium_summary(h5path)
+p_ffs = Analysis.ForceFreeStates.plot_ffs_summary(h5path)
+
+display(p_eq);
+Plots.savefig(p_eq, joinpath(@__DIR__, "equilibrium_summary.png"));
+display(p_ffs);
+Plots.savefig(p_ffs, joinpath(@__DIR__, "ffs_summary.png"));
+display(p_pe);
+Plots.savefig(p_pe, joinpath(@__DIR__, "pe_summary.png"));
diff --git a/examples/Solovev_ideal_example/gpec.toml b/examples/Solovev_ideal_example/gpec.toml
new file mode 100644
index 0000000000..f4fabe17a9
--- /dev/null
+++ b/examples/Solovev_ideal_example/gpec.toml
@@ -0,0 +1,84 @@
+# Solovev analytical equilibrium — n=1 ideal stability.
+# Near-marginal n=1 external kink stabilized by a close conformal wall (see [Wall] note).
+# Integration-pipeline smoke-test and et[1] regression fixture; the equilibrium is
+# generated analytically from the embedded [Solovev] section.
+
+[Run]
+verbose = true # Log each stage's progress
+
+[Equilibrium]
+jac_type = "pest" # Coordinate system (hamada, pest, boozer, equal_arc, park, custom)
+grid_type = "core_edge_packed" # Radial grid packing type
+psilow = 1e-4 # Lower limit of normalized poloidal flux
+psihigh = 0.9995 # Upper limit of normalized poloidal flux
+mpsi = 128 # Number of radial grid intervals (0 = two-pass auto grid from psi_accuracy)
+mtheta = 256 # Number of poloidal grid points
+newq0 = 0 # Target on-axis safety factor q(0) (0 = use input value; q is positive, so negative values are rejected)
+flux_surface_rtol = 1e-7 # Relative tolerance of the ODE solves that trace each flux surface
+
+[Wall]
+# Close conformal wall is required to stabilize this Solovev fixture's n=1 external kink:
+# with nowall, et[1] = -6.8 (strongly unstable); with this wall, et[1] = +0.24 (barely stable).
+# The plasma is near marginal stability, so the BVP Δ' matrix values are pathological
+# (dpm magnitudes ~ 10¹¹, |Im/Re| ≫ 1). This fixture's role is integration-pipeline
+# smoke testing + et[1] regression, NOT BVP Δ' regression — DIIID-like is the canonical
+# Δ'-matrix fixture (stable et[1] = +1.6, clean BVP Δ').
+shape = "conformal" # Wall shape (conformal, elliptical, dee, mod_dee, file)
+standoff_fraction = 0.2415 # Wall standoff in plasma minor radii
+equal_arc_wall = true # Equal arc length distribution of nodes on wall
+
+# Note: SLAYER tearing analysis is not run on the Solovev analytic equilibrium
+# — its Δ' / inner-layer dispersion does not yield meaningful tearing roots.
+# The SLAYER example and regression case use the DIII-D-like geqdsk instead
+# (see examples/DIIID-like_SLAYER_example).
+
+# Presence runs the LocalStability stage (Mercier D_I, resistive D_R, ballooning Δ', first α boundary); keys are the LocalStabilityProblem settings, numerics in [Ballooning]
+[LocalStability]
+theta_k = 0.0 # Ballooning angle θ_k, used by both the profile scan and the α-boundary scan
+alpha_boundary_scan = true # Run the first ballooning α-boundary scan (a root find per ψ surface)
+
+# Numerical settings of the ballooning scans
+[Ballooning]
+ode_tol = 1e-8 # Relative and absolute tolerance of the ballooning ODE integration behind Δ'
+n_scan = 24 # Resolution of the α scan for the first boundary
+max_alpha_scale = 8.0 # Upper end of the α search, as a multiple of the experimental α
+alpha_tol = 1e-3 # Bisection tolerance of the critical α, in the same multiples
+psi_window = [0.1, 0.99] # ψ_N range of the α scan; surfaces outside it are NaN
+
+[ForceFreeStates]
+vac_flag = true # Compute plasma, vacuum, and total energies for free-boundary modes
+
+dW_edge_scan_start = 0.99 # Edge dW(ψ) diagnostic scan band [dW_edge_scan_start, psilim]; set ≥ psilim to disable
+qlow = 1.02 # Integration initiated at q determined by min(q0, qlow)
+qhigh = 1e3 # Integration terminated at q limit determined by min(qa, qhigh)
+
+nn = 1 # Toroidal mode number, or consecutive numbers as a list
+delta_mlow = 8 # Expands lower bound of Fourier harmonics
+delta_mhigh = 8 # Expands upper bound of Fourier harmonics
+mtheta_vacuum = 960 # Number of points used in splines over poloidal angle at the plasma-vacuum interface
+
+singfac_min = 1e-6 # Fractional distance from rational q at which ideal jump enforced
+
+# Integrator selection and domain truncation (see ForceFreeStatesControl docstring for details)
+integrator = "Forward" # Integration formalism, whose numerical settings are its own section: "Forward" (dense ξ, needed for [PerturbedEquilibrium]/kinetic), "Riccati" (chunked propagator BVP, unlocks the singular-surface Δ′ matrix), or "Galerkin" (outer-region singular Galerkin Δ′)
+truncate_at_rational_offset = false # FALSE for limited/analytical equilibria — rationals sparse, rational_offset_fraction would chop too much edge
+rational_offset_fraction = 0.2 # Truncate integration at (last_rational_q + rational_offset_fraction)/n (used when truncate_at_rational_offset = true)
+
+# Numerical settings of the forward integrator
+[Forward]
+eulerlagrange_tolerance = 1e-7 # Relative tolerance for ODE integration of Euler-Lagrange equations
+renorm_threshold = 1e3 # Column-norm threshold that triggers solution renormalization
+save_interval = 1 # Save every Nth ODE step (1=all). Always saves near rational surfaces.
+
+# Solovev analytic equilibrium parameters; this section selects the equilibrium. See SolovevConfig in src/Equilibrium.
+[Solovev]
+mr = 128 # Number of radial grid zones
+mz = 128 # Number of axial grid zones
+ma = 128 # Number of flux grid zones
+elongation = 1.6 # Elongation
+a = 0.33 # Minor radius
+r0 = 1.0 # Major radius
+q0 = 1.9 # Safety factor at the magnetic axis (O-point)
+p0fac = 1 # Scale on-axis pressure (β changes; Φ, q fixed)
+b0fac = 1 # Scale toroidal field at constant β (Bt changes; shape, β fixed)
+f0fac = 1 # Scale toroidal field at constant pressure (β, q change; Φ, p, Bp fixed)
diff --git a/examples/Solovev_ideal_example/run_example.jl b/examples/Solovev_ideal_example/run_example.jl
new file mode 100644
index 0000000000..fa0a9e53d5
--- /dev/null
+++ b/examples/Solovev_ideal_example/run_example.jl
@@ -0,0 +1,4 @@
+using Pkg;
+Pkg.activate(joinpath(@__DIR__, "../.."))
+using GeneralizedPerturbedEquilibrium
+GeneralizedPerturbedEquilibrium.main([dirname(@__FILE__)])
diff --git a/examples/Solovev_ideal_example/vacuum_response_inputs.jld2 b/examples/Solovev_ideal_example/vacuum_response_inputs.jld2
new file mode 100644
index 0000000000..a95f6f970b
Binary files /dev/null and b/examples/Solovev_ideal_example/vacuum_response_inputs.jld2 differ
diff --git a/examples/Solovev_ideal_example_3D/gpec.toml b/examples/Solovev_ideal_example_3D/gpec.toml
new file mode 100644
index 0000000000..a7b68e8d62
--- /dev/null
+++ b/examples/Solovev_ideal_example_3D/gpec.toml
@@ -0,0 +1,79 @@
+# Solovev analytical equilibrium — 3D (toroidally resolved) n=1 ideal stability.
+# Same near-marginal Solovev plasma as Solovev_ideal_example, with the vacuum response
+# evaluated on a toroidal grid (nzvac > 1). Equilibrium is generated from the embedded [Solovev] section.
+
+[Run]
+verbose = true # Log each stage's progress
+
+[Equilibrium]
+jac_type = "pest" # Coordinate system (hamada, pest, boozer, equal_arc, park, custom)
+grid_type = "core_edge_packed" # Radial grid packing type
+psilow = 1e-4 # Lower limit of normalized poloidal flux
+psihigh = 0.9995 # Upper limit of normalized poloidal flux
+mpsi = 128 # Number of radial grid intervals (0 = two-pass auto grid from psi_accuracy)
+mtheta = 256 # Number of poloidal grid points
+newq0 = 0 # Target on-axis safety factor q(0) (0 = use input value; q is positive, so negative values are rejected)
+flux_surface_rtol = 1e-7 # Relative tolerance of the ODE solves that trace each flux surface
+
+# Presence runs the LocalStability stage (Mercier D_I, resistive D_R, ballooning Δ', first α boundary); keys are the LocalStabilityProblem settings, numerics in [Ballooning]
+[LocalStability]
+theta_k = 0.0 # Ballooning angle θ_k, used by both the profile scan and the α-boundary scan
+alpha_boundary_scan = true # Run the first ballooning α-boundary scan (a root find per ψ surface)
+
+# Numerical settings of the ballooning scans
+[Ballooning]
+ode_tol = 1e-8 # Relative and absolute tolerance of the ballooning ODE integration behind Δ'
+n_scan = 24 # Resolution of the α scan for the first boundary
+max_alpha_scale = 8.0 # Upper end of the α search, as a multiple of the experimental α
+alpha_tol = 1e-3 # Bisection tolerance of the critical α, in the same multiples
+psi_window = [0.1, 0.99] # ψ_N range of the α scan; surfaces outside it are NaN
+
+[ForceFreeStates]
+vac_flag = true # Compute plasma, vacuum, and total energies for free-boundary modes
+
+dW_edge_scan_start = 1.0 # Edge dW(ψ) diagnostic scan band [dW_edge_scan_start, psilim]; set ≥ psilim to disable
+qlow = 1.02 # Integration initiated at q determined by min(q0, qlow)
+qhigh = 1e3 # Integration terminated at q limit determined by min(qa, qhigh)
+
+nn = 1 # Toroidal mode number, or consecutive numbers as a list
+delta_mlow = 8 # Expands lower bound of Fourier harmonics
+delta_mhigh = 8 # Expands upper bound of Fourier harmonics
+mtheta_vacuum = 64 # Number of points used in splines over poloidal angle at the plasma-vacuum interface
+nzeta_vacuum = 96 # Number of points used in splines over toroidal angle at the plasma-vacuum interface
+
+singfac_min = 1e-4 # Fractional distance from rational q at which ideal jump enforced
+
+# Integrator selection and domain truncation (see ForceFreeStatesControl docstring for details)
+integrator = "Riccati" # Integration formalism, whose numerical settings are its own section: "Forward" (dense ξ, needed for [PerturbedEquilibrium]/kinetic), "Riccati" (chunked propagator BVP, unlocks the singular-surface Δ′ matrix), or "Galerkin" (outer-region singular Galerkin Δ′)
+truncate_at_rational_offset = false # FALSE for limited/analytical equilibria — rationals sparse, rational_offset_fraction would chop too much edge
+rational_offset_fraction = 0.2 # Truncate integration at (last_rational_q + rational_offset_fraction)/n (used when truncate_at_rational_offset = true)
+
+# Numerical settings of the Riccati integrator
+[Riccati]
+eulerlagrange_tolerance = 1e-7 # Relative tolerance for ODE integration of Euler-Lagrange equations
+renorm_threshold = 1e3 # Column-norm threshold that triggers solution renormalization
+save_interval = 1 # Save every Nth ODE step (1=all). Always saves near rational surfaces.
+
+[Wall]
+# See examples/Solovev_ideal_example/gpec.toml for the rationale behind the close conformal wall.
+shape = "conformal" # Wall shape (conformal, elliptical, dee, mod_dee, file)
+standoff_fraction = 0.2415 # Wall standoff in plasma minor radii
+equal_arc_wall = false # Equal arc length distribution of nodes on wall
+
+# Uncomment to enable perturbed equilibrium calculations:
+# [PerturbedEquilibrium]
+# forcing_data_file = "forcing.dat" # Manual mode table (n, m, amplitude_real, amplitude_imag)
+# forcing_data_format = "ascii" # Format: "ascii", "hdf5", or "coil" (Biot-Savart from 3D wires)
+# compute_singular_coupling = true # Compute singular layer coupling metrics
+# Solovev analytic equilibrium parameters; this section selects the equilibrium. See SolovevConfig in src/Equilibrium.
+[Solovev]
+mr = 128 # Number of radial grid zones
+mz = 128 # Number of axial grid zones
+ma = 128 # Number of flux grid zones
+elongation = 1.6 # Elongation
+a = 0.33 # Minor radius
+r0 = 1.0 # Major radius
+q0 = 1.9 # Safety factor at the magnetic axis (O-point)
+p0fac = 1 # Scale on-axis pressure (β changes; Φ, q fixed)
+b0fac = 1 # Scale toroidal field at constant β (Bt changes; shape, β fixed)
+f0fac = 1 # Scale toroidal field at constant pressure (β, q change; Φ, p, Bp fixed)
diff --git a/examples/Solovev_ideal_example_3D/run_example.jl b/examples/Solovev_ideal_example_3D/run_example.jl
new file mode 100644
index 0000000000..fa0a9e53d5
--- /dev/null
+++ b/examples/Solovev_ideal_example_3D/run_example.jl
@@ -0,0 +1,4 @@
+using Pkg;
+Pkg.activate(joinpath(@__DIR__, "../.."))
+using GeneralizedPerturbedEquilibrium
+GeneralizedPerturbedEquilibrium.main([dirname(@__FILE__)])
diff --git a/examples/Solovev_ideal_example_multi_n/analyze_example.jl b/examples/Solovev_ideal_example_multi_n/analyze_example.jl
new file mode 100644
index 0000000000..10edafd6e3
--- /dev/null
+++ b/examples/Solovev_ideal_example_multi_n/analyze_example.jl
@@ -0,0 +1,30 @@
+using Pkg;
+Pkg.activate(joinpath(@__DIR__, "../.."))
+using GeneralizedPerturbedEquilibrium, Plots
+using GeneralizedPerturbedEquilibrium: Analysis
+isinteractive() ? plotlyjs() : gr()
+
+# Analyze the multi-n run
+h5path = joinpath(@__DIR__, "gpec.h5")
+# Summary plots
+p_eq = Analysis.Equilibrium.plot_equilibrium_summary(h5path)
+p_ffs = Analysis.ForceFreeStates.plot_ffs_summary(h5path)
+p_pe = Analysis.PerturbedEquilibrium.plot_perturbed_equilibrium_summary(h5path)
+
+display(p_eq);
+Plots.savefig(p_eq, joinpath(@__DIR__, "equilibrium_summary.png"));
+display(p_ffs);
+Plots.savefig(p_ffs, joinpath(@__DIR__, "ffs_summary.png"));
+display(p_pe);
+Plots.savefig(p_pe, joinpath(@__DIR__, "pe_summary.png"));
+
+# Analyze the single-n runs
+h5path_n1 = joinpath(@__DIR__, "single_n_1", "euler_n1.h5")
+h5path_n2 = joinpath(@__DIR__, "single_n_2", "euler_n2.h5")
+p_n1 = Analysis.ForceFreeStates.plot_ffs_summary(h5path_n1)
+p_n2 = Analysis.ForceFreeStates.plot_ffs_summary(h5path_n2)
+
+display(p_n1);
+Plots.savefig(p_n1, joinpath(@__DIR__, "single_n_1", "ffs_summary.png"));
+display(p_n2);
+Plots.savefig(p_n2, joinpath(@__DIR__, "single_n_2", "ffs_summary.png"));
diff --git a/examples/Solovev_ideal_example_multi_n/gpec.toml b/examples/Solovev_ideal_example_multi_n/gpec.toml
new file mode 100644
index 0000000000..c8e51b8c78
--- /dev/null
+++ b/examples/Solovev_ideal_example_multi_n/gpec.toml
@@ -0,0 +1,74 @@
+# Solovev analytical equilibrium — multi-n ideal stability (n = 1 and 2 in one run).
+# Same near-marginal Solovev plasma as Solovev_ideal_example, swept over a toroidal
+# mode-number range. The single_n_1/ and single_n_2/ subdirectories run each n alone
+# for cross-checking. Equilibrium is generated from the embedded [Solovev] section.
+
+[Run]
+verbose = true # Log each stage's progress
+
+[Equilibrium]
+jac_type = "pest" # Coordinate system (hamada, pest, boozer, equal_arc, park, custom)
+grid_type = "core_edge_packed" # Radial grid packing type
+psilow = 1e-4 # Lower limit of normalized poloidal flux
+psihigh = 0.9995 # Upper limit of normalized poloidal flux
+mpsi = 128 # Number of radial grid intervals (0 = two-pass auto grid from psi_accuracy)
+mtheta = 256 # Number of poloidal grid points
+newq0 = 0 # Target on-axis safety factor q(0) (0 = use input value; q is positive, so negative values are rejected)
+flux_surface_rtol = 1e-7 # Relative tolerance of the ODE solves that trace each flux surface
+
+[Wall]
+# See examples/Solovev_ideal_example/gpec.toml for the rationale behind the close conformal wall.
+shape = "conformal" # Wall shape (conformal, elliptical, dee, mod_dee, file)
+standoff_fraction = 0.2415 # Wall standoff in plasma minor radii
+equal_arc_wall = true # Equal arc length distribution of nodes on wall
+
+# Presence runs the LocalStability stage (Mercier D_I, resistive D_R, ballooning Δ', first α boundary); keys are the LocalStabilityProblem settings, numerics in [Ballooning]
+[LocalStability]
+theta_k = 0.0 # Ballooning angle θ_k, used by both the profile scan and the α-boundary scan
+alpha_boundary_scan = true # Run the first ballooning α-boundary scan (a root find per ψ surface)
+
+# Numerical settings of the ballooning scans
+[Ballooning]
+ode_tol = 1e-8 # Relative and absolute tolerance of the ballooning ODE integration behind Δ'
+n_scan = 24 # Resolution of the α scan for the first boundary
+max_alpha_scale = 8.0 # Upper end of the α search, as a multiple of the experimental α
+alpha_tol = 1e-3 # Bisection tolerance of the critical α, in the same multiples
+psi_window = [0.1, 0.99] # ψ_N range of the α scan; surfaces outside it are NaN
+
+[ForceFreeStates]
+vac_flag = true # Compute plasma, vacuum, and total energies for free-boundary modes
+
+dW_edge_scan_start = 0.99 # Edge dW(ψ) diagnostic scan band [dW_edge_scan_start, psilim]; set ≥ psilim to disable
+qlow = 1.02 # Integration initiated at q determined by min(q0, qlow)
+qhigh = 1e3 # Integration terminated at q limit determined by min(qa, qhigh)
+
+nn = [1, 2] # Toroidal mode number, or consecutive numbers as a list
+delta_mlow = 8 # Expands lower bound of Fourier harmonics
+delta_mhigh = 8 # Expands upper bound of Fourier harmonics
+mtheta_vacuum = 960 # Number of points used in splines over poloidal angle at the plasma-vacuum interface
+
+singfac_min = 1e-4 # Fractional distance from rational q at which ideal jump enforced
+
+# Integrator selection and domain truncation (see ForceFreeStatesControl docstring for details).
+# The multi-n Δ' matrix has open issues and is skipped with a warning; the energies stay valid.
+integrator = "Riccati" # Integration formalism, whose numerical settings are its own section: "Forward" (dense ξ, needed for [PerturbedEquilibrium]/kinetic), "Riccati" (chunked propagator BVP, unlocks the singular-surface Δ′ matrix), or "Galerkin" (outer-region singular Galerkin Δ′)
+truncate_at_rational_offset = false # FALSE for multi-n — rational_offset_fraction truncation is ambiguous when n varies (sing_lim! skips anyway)
+rational_offset_fraction = 0.2 # Truncate integration at (last_rational_q + rational_offset_fraction)/n (used when truncate_at_rational_offset = true)
+
+# Numerical settings of the Riccati integrator
+[Riccati]
+eulerlagrange_tolerance = 1e-7 # Relative tolerance for ODE integration of Euler-Lagrange equations
+renorm_threshold = 1e3 # Column-norm threshold that triggers solution renormalization
+
+# Solovev analytic equilibrium parameters; this section selects the equilibrium. See SolovevConfig in src/Equilibrium.
+[Solovev]
+mr = 128 # Number of radial grid zones
+mz = 128 # Number of axial grid zones
+ma = 128 # Number of flux grid zones
+elongation = 1.6 # Elongation
+a = 0.33 # Minor radius
+r0 = 1.0 # Major radius
+q0 = 1.9 # Safety factor at the magnetic axis (O-point)
+p0fac = 1 # Scale on-axis pressure (β changes; Φ, q fixed)
+b0fac = 1 # Scale toroidal field at constant β (Bt changes; shape, β fixed)
+f0fac = 1 # Scale toroidal field at constant pressure (β, q change; Φ, p, Bp fixed)
diff --git a/examples/Solovev_ideal_example_multi_n/run_example.jl b/examples/Solovev_ideal_example_multi_n/run_example.jl
new file mode 100644
index 0000000000..29645cc4db
--- /dev/null
+++ b/examples/Solovev_ideal_example_multi_n/run_example.jl
@@ -0,0 +1,6 @@
+using Pkg;
+Pkg.activate(joinpath(@__DIR__, "../.."))
+using GeneralizedPerturbedEquilibrium
+GeneralizedPerturbedEquilibrium.main([dirname(@__FILE__)])
+GeneralizedPerturbedEquilibrium.main([joinpath(@__DIR__, "single_n_1")])
+GeneralizedPerturbedEquilibrium.main([joinpath(@__DIR__, "single_n_2")])
diff --git a/examples/Solovev_ideal_example_multi_n/single_n_1/gpec.toml b/examples/Solovev_ideal_example_multi_n/single_n_1/gpec.toml
new file mode 100644
index 0000000000..0c272a9a0a
--- /dev/null
+++ b/examples/Solovev_ideal_example_multi_n/single_n_1/gpec.toml
@@ -0,0 +1,68 @@
+# Solovev analytical equilibrium — n=1 only, companion to the multi-n parent run.
+# Runs n=1 in isolation (output euler_n1.h5) to cross-check the combined multi-n result.
+# Equilibrium is generated from the embedded [Solovev] section.
+
+[Run]
+output_file = "euler_n1.h5" # HDF5 file every stage saves into, relative to this deck's directory
+verbose = true # Log each stage's progress
+
+[Equilibrium]
+jac_type = "pest" # Coordinate system (hamada, pest, boozer, equal_arc, park, custom)
+grid_type = "core_edge_packed" # Radial grid packing type
+psilow = 1e-4 # Lower limit of normalized poloidal flux
+psihigh = 0.9995 # Upper limit of normalized poloidal flux
+mpsi = 128 # Number of radial grid intervals (0 = two-pass auto grid from psi_accuracy)
+mtheta = 256 # Number of poloidal grid points
+newq0 = 0 # Target on-axis safety factor q(0) (0 = use input value; q is positive, so negative values are rejected)
+flux_surface_rtol = 1e-7 # Relative tolerance of the ODE solves that trace each flux surface
+
+[Wall]
+# See examples/Solovev_ideal_example/gpec.toml for the rationale behind the close conformal wall.
+shape = "conformal" # Wall shape (conformal, elliptical, dee, mod_dee, file)
+standoff_fraction = 0.2415 # Wall standoff in plasma minor radii
+equal_arc_wall = true # Equal arc length distribution of nodes on wall
+
+# Presence runs the LocalStability stage (Mercier D_I, resistive D_R, ballooning Δ', first α boundary); keys are the LocalStabilityProblem settings, numerics in [Ballooning]
+[LocalStability]
+theta_k = 0.0 # Ballooning angle θ_k, used by both the profile scan and the α-boundary scan
+alpha_boundary_scan = true # Run the first ballooning α-boundary scan (a root find per ψ surface)
+
+# Numerical settings of the ballooning scans
+[Ballooning]
+ode_tol = 1e-8 # Relative and absolute tolerance of the ballooning ODE integration behind Δ'
+n_scan = 24 # Resolution of the α scan for the first boundary
+max_alpha_scale = 8.0 # Upper end of the α search, as a multiple of the experimental α
+alpha_tol = 1e-3 # Bisection tolerance of the critical α, in the same multiples
+psi_window = [0.1, 0.99] # ψ_N range of the α scan; surfaces outside it are NaN
+
+[ForceFreeStates]
+vac_flag = true # Compute plasma, vacuum, and total energies for free-boundary modes
+
+dW_edge_scan_start = 0.99 # Edge dW(ψ) diagnostic scan band [dW_edge_scan_start, psilim]; set ≥ psilim to disable
+qlow = 1.02 # Integration initiated at q determined by min(q0, qlow)
+qhigh = 1e3 # Integration terminated at q limit determined by min(qa, qhigh)
+
+nn = 1 # Toroidal mode number, or consecutive numbers as a list
+delta_mlow = 8 # Expands lower bound of Fourier harmonics
+delta_mhigh = 10 # Expands upper bound of Fourier harmonics
+mtheta_vacuum = 960 # Number of points used in splines over poloidal angle at the plasma-vacuum interface
+
+singfac_min = 1e-4 # Fractional distance from rational q at which ideal jump enforced
+
+# Numerical settings of the Riccati integrator
+[Riccati]
+eulerlagrange_tolerance = 1e-7 # Relative tolerance for ODE integration of Euler-Lagrange equations
+renorm_threshold = 1e3 # Column-norm threshold that triggers solution renormalization
+
+# Solovev analytic equilibrium parameters; this section selects the equilibrium. See SolovevConfig in src/Equilibrium.
+[Solovev]
+mr = 128 # Number of radial grid zones
+mz = 128 # Number of axial grid zones
+ma = 128 # Number of flux grid zones
+elongation = 1.6 # Elongation
+a = 0.33 # Minor radius
+r0 = 1.0 # Major radius
+q0 = 1.9 # Safety factor at the magnetic axis (O-point)
+p0fac = 1 # Scale on-axis pressure (β changes; Φ, q fixed)
+b0fac = 1 # Scale toroidal field at constant β (Bt changes; shape, β fixed)
+f0fac = 1 # Scale toroidal field at constant pressure (β, q change; Φ, p, Bp fixed)
diff --git a/examples/Solovev_ideal_example_multi_n/single_n_2/gpec.toml b/examples/Solovev_ideal_example_multi_n/single_n_2/gpec.toml
new file mode 100644
index 0000000000..f200df8c2a
--- /dev/null
+++ b/examples/Solovev_ideal_example_multi_n/single_n_2/gpec.toml
@@ -0,0 +1,68 @@
+# Solovev analytical equilibrium — n=2 only, companion to the multi-n parent run.
+# Runs n=2 in isolation (output euler_n2.h5) to cross-check the combined multi-n result.
+# Equilibrium is generated from the embedded [Solovev] section.
+
+[Run]
+output_file = "euler_n2.h5" # HDF5 file every stage saves into, relative to this deck's directory
+verbose = true # Log each stage's progress
+
+[Equilibrium]
+jac_type = "pest" # Coordinate system (hamada, pest, boozer, equal_arc, park, custom)
+grid_type = "core_edge_packed" # Radial grid packing type
+psilow = 1e-4 # Lower limit of normalized poloidal flux
+psihigh = 0.9995 # Upper limit of normalized poloidal flux
+mpsi = 128 # Number of radial grid intervals (0 = two-pass auto grid from psi_accuracy)
+mtheta = 256 # Number of poloidal grid points
+newq0 = 0 # Target on-axis safety factor q(0) (0 = use input value; q is positive, so negative values are rejected)
+flux_surface_rtol = 1e-7 # Relative tolerance of the ODE solves that trace each flux surface
+
+[Wall]
+# See examples/Solovev_ideal_example/gpec.toml for the rationale behind the close conformal wall.
+shape = "conformal" # Wall shape (conformal, elliptical, dee, mod_dee, file)
+standoff_fraction = 0.2415 # Wall standoff in plasma minor radii
+equal_arc_wall = true # Equal arc length distribution of nodes on wall
+
+# Presence runs the LocalStability stage (Mercier D_I, resistive D_R, ballooning Δ', first α boundary); keys are the LocalStabilityProblem settings, numerics in [Ballooning]
+[LocalStability]
+theta_k = 0.0 # Ballooning angle θ_k, used by both the profile scan and the α-boundary scan
+alpha_boundary_scan = true # Run the first ballooning α-boundary scan (a root find per ψ surface)
+
+# Numerical settings of the ballooning scans
+[Ballooning]
+ode_tol = 1e-8 # Relative and absolute tolerance of the ballooning ODE integration behind Δ'
+n_scan = 24 # Resolution of the α scan for the first boundary
+max_alpha_scale = 8.0 # Upper end of the α search, as a multiple of the experimental α
+alpha_tol = 1e-3 # Bisection tolerance of the critical α, in the same multiples
+psi_window = [0.1, 0.99] # ψ_N range of the α scan; surfaces outside it are NaN
+
+[ForceFreeStates]
+vac_flag = true # Compute plasma, vacuum, and total energies for free-boundary modes
+
+dW_edge_scan_start = 0.99 # Edge dW(ψ) diagnostic scan band [dW_edge_scan_start, psilim]; set ≥ psilim to disable
+qlow = 1.02 # Integration initiated at q determined by min(q0, qlow)
+qhigh = 1e3 # Integration terminated at q limit determined by min(qa, qhigh)
+
+nn = 2 # Toroidal mode number, or consecutive numbers as a list
+delta_mlow = 8 # Expands lower bound of Fourier harmonics
+delta_mhigh = 8 # Expands upper bound of Fourier harmonics
+mtheta_vacuum = 960 # Number of points used in splines over poloidal angle at the plasma-vacuum interface
+
+singfac_min = 1e-4 # Fractional distance from rational q at which ideal jump enforced
+
+# Numerical settings of the Riccati integrator
+[Riccati]
+eulerlagrange_tolerance = 1e-7 # Relative tolerance for ODE integration of Euler-Lagrange equations
+renorm_threshold = 1e3 # Column-norm threshold that triggers solution renormalization
+
+# Solovev analytic equilibrium parameters; this section selects the equilibrium. See SolovevConfig in src/Equilibrium.
+[Solovev]
+mr = 128 # Number of radial grid zones
+mz = 128 # Number of axial grid zones
+ma = 128 # Number of flux grid zones
+elongation = 1.6 # Elongation
+a = 0.33 # Minor radius
+r0 = 1.0 # Major radius
+q0 = 1.9 # Safety factor at the magnetic axis (O-point)
+p0fac = 1 # Scale on-axis pressure (β changes; Φ, q fixed)
+b0fac = 1 # Scale toroidal field at constant β (Bt changes; shape, β fixed)
+f0fac = 1 # Scale toroidal field at constant pressure (β, q change; Φ, p, Bp fixed)
diff --git a/examples/TJ_ideal_example/forcing.dat b/examples/TJ_ideal_example/forcing.dat
new file mode 100644
index 0000000000..ce7aee865f
--- /dev/null
+++ b/examples/TJ_ideal_example/forcing.dat
@@ -0,0 +1,6 @@
+# Forcing data for perturbed equilibrium calculations
+# normalization: normal_field_T
+# Format: n m amplitude_real amplitude_imag
+# n=1, m=2 and m=3, amplitude=1e-4 T on the two resonant surfaces
+1 2 1e-4 0.0
+1 3 1e-4 0.0
diff --git a/examples/TJ_ideal_example/gpec.toml b/examples/TJ_ideal_example/gpec.toml
new file mode 100644
index 0000000000..7516d63c3b
--- /dev/null
+++ b/examples/TJ_ideal_example/gpec.toml
@@ -0,0 +1,65 @@
+# TJ-analytic large-aspect-ratio equilibrium (q₀ = 1.6, q_a = 3.2, β_N = 0.42) with the 2/1 and 3/1 surfaces,
+# stable at n = 1 with no wall (et[1] = +0.435), so a perturbed equilibrium can run without one.
+# Integration-pipeline smoke test and PE regression fixture for an analytic equilibrium; the
+# equilibrium is generated analytically from the embedded [TJAnalytic] section.
+
+[Run]
+verbose = true # Log each stage's progress
+
+[Equilibrium]
+jac_type = "hamada" # Coordinate system (hamada, pest, boozer, equal_arc, park, custom)
+grid_type = "core_edge_packed" # Radial grid packing type
+psilow = 0.01 # Lower limit of normalized poloidal flux
+psihigh = 0.99 # Upper limit of normalized poloidal flux; et[1] depends on it (+0.502 at 0.995), so it is pinned
+mpsi = 128 # Number of radial grid intervals (0 = two-pass auto grid from psi_accuracy)
+mtheta = 256 # Number of poloidal grid points
+
+[ForcingTerms]
+forcing_data_file = "forcing.dat" # Manual mode table (n, m, amplitude_real, amplitude_imag)
+forcing_data_format = "ascii" # Format: "ascii", "hdf5", or "coil" (Biot-Savart from 3D wires)
+
+[PerturbedEquilibrium]
+compute_singular_coupling = true # Compute singular layer coupling metrics
+regularization_width = 0.0 # Regularization width for singular surfaces (0 = disabled)
+
+# Presence runs the LocalStability stage (Mercier D_I, resistive D_R, ballooning Δ', first α boundary); keys are the LocalStabilityProblem settings, numerics in [Ballooning]
+[LocalStability]
+theta_k = 0.0 # Ballooning angle θ_k, used by both the profile scan and the α-boundary scan
+alpha_boundary_scan = true # Run the first ballooning α-boundary scan (a root find per ψ surface)
+
+# Numerical settings of the ballooning scans
+[Ballooning]
+ode_tol = 1e-8 # Relative and absolute tolerance of the ballooning ODE integration behind Δ'
+n_scan = 24 # Resolution of the α scan for the first boundary
+max_alpha_scale = 8.0 # Upper end of the α search, as a multiple of the experimental α
+alpha_tol = 1e-3 # Bisection tolerance of the critical α, in the same multiples
+psi_window = [0.1, 0.99] # ψ_N range of the α scan; surfaces outside it are NaN
+
+[ForceFreeStates]
+vac_flag = true # Compute plasma, vacuum, and total energies for free-boundary modes
+qlow = 1.02 # Integration initiated at q determined by min(q0, qlow)
+qhigh = 1e3 # Integration terminated at q limit determined by min(qa, qhigh)
+nn = 1 # Toroidal mode number, or consecutive numbers as a list
+delta_mlow = 8 # Expands lower bound of Fourier harmonics
+delta_mhigh = 8 # Expands upper bound of Fourier harmonics
+mtheta_vacuum = 960 # Number of points used in splines over poloidal angle at the plasma-vacuum interface
+singfac_min = 1e-6 # Fractional distance from rational q at which ideal jump enforced
+integrator = "Forward" # Integration formalism, whose numerical settings are its own section: "Forward" (dense ξ, needed for [PerturbedEquilibrium]/kinetic), "Riccati" (chunked propagator BVP, unlocks the singular-surface Δ′ matrix), or "Galerkin" (outer-region singular Galerkin Δ′)
+truncate_at_rational_offset = false # Truncate integration at (last_rational_q + rational_offset_fraction)/n; false for analytic equilibria
+
+# Numerical settings of the forward integrator
+[Forward]
+eulerlagrange_tolerance = 1e-9 # Relative tolerance for ODE integration of Euler-Lagrange equations
+
+# TJ-analytic equilibrium parameters (cf. R. Fitzpatrick, TJ code, https://github.com/rfitzp/TJ); this section selects the
+# equilibrium. Keep p0 at or below 0.2: et[1] stays near +0.42 up to there and is not monotonic above it.
+[TJAnalytic]
+r0 = 10.0 # Major radius R₀ [m] (centerline radius of the magnetic axis)
+a = 1.0 # Minor radius a [m] (plasma half-width at the midplane; here ε = 0.1)
+q0 = 1.6 # On-axis safety factor q(r=0)
+qa = 3.2 # Edge safety factor q(r=a)
+p0 = 0.1 # Normalized on-axis pressure
+pressure_peaking = 2.0 # Pressure-profile peaking exponent in p₂(r) = p0·(1−r²)^μ
+B0 = 1.0 # On-axis toroidal field [T]
+ma = 128 # TJ-analytic internal radial grid resolution (shape-ODE nodes)
+mtheta = 128 # TJ-analytic internal poloidal grid resolution (θ-spline nodes)
diff --git a/examples/TJ_ideal_example/run_example.jl b/examples/TJ_ideal_example/run_example.jl
new file mode 100644
index 0000000000..fa0a9e53d5
--- /dev/null
+++ b/examples/TJ_ideal_example/run_example.jl
@@ -0,0 +1,4 @@
+using Pkg;
+Pkg.activate(joinpath(@__DIR__, "../.."))
+using GeneralizedPerturbedEquilibrium
+GeneralizedPerturbedEquilibrium.main([dirname(@__FILE__)])
diff --git a/examples/TJ_kinetic_NTV_example/forcing.dat b/examples/TJ_kinetic_NTV_example/forcing.dat
new file mode 100644
index 0000000000..ce7aee865f
--- /dev/null
+++ b/examples/TJ_kinetic_NTV_example/forcing.dat
@@ -0,0 +1,6 @@
+# Forcing data for perturbed equilibrium calculations
+# normalization: normal_field_T
+# Format: n m amplitude_real amplitude_imag
+# n=1, m=2 and m=3, amplitude=1e-4 T on the two resonant surfaces
+1 2 1e-4 0.0
+1 3 1e-4 0.0
diff --git a/examples/TJ_kinetic_NTV_example/gpec.toml b/examples/TJ_kinetic_NTV_example/gpec.toml
new file mode 100644
index 0000000000..b9d3e66598
--- /dev/null
+++ b/examples/TJ_kinetic_NTV_example/gpec.toml
@@ -0,0 +1,58 @@
+# TJ-analytic large-aspect-ratio equilibrium (q₀ = 1.6, q_a = 3.2, β_N = 0.42) with the 2/1 and 3/1 surfaces,
+# stable at n = 1 with no wall (et[1] = +0.435), so a perturbed equilibrium can run without one.
+# Adds a [KineticForces] section, so after the plasma response is computed the neoclassical toroidal
+# viscosity torque is integrated over ψ as a post-processing diagnostic (adaptive quadrature paneled at
+# the rational surfaces). The kinetic profiles (kinetic.dat) are consistent with this equilibrium's pressure.
+
+[Run]
+verbose = true # Log each stage's progress
+
+[Equilibrium]
+kinetic_file = "kinetic.dat" # Kinetic-profile file (HDF5 GPEC kinetic schema or 6-column ASCII), read once into the equilibrium
+jac_type = "hamada" # Coordinate system (hamada, pest, boozer, equal_arc, park, custom)
+grid_type = "core_edge_packed" # Radial grid packing type
+psilow = 0.01 # Lower limit of normalized poloidal flux
+psihigh = 0.99 # Upper limit of normalized poloidal flux; et[1] depends on it (+0.502 at 0.995), so it is pinned
+mpsi = 128 # Number of radial grid intervals (0 = two-pass auto grid from psi_accuracy)
+mtheta = 256 # Number of poloidal grid points
+
+[ForcingTerms]
+forcing_data_file = "forcing.dat" # Manual mode table (n, m, amplitude_real, amplitude_imag)
+forcing_data_format = "ascii" # Format: "ascii", "hdf5", or "coil" (Biot-Savart from 3D wires)
+
+[PerturbedEquilibrium]
+compute_singular_coupling = true # Compute singular layer coupling metrics
+regularization_width = 0.05 # Regularization width for singular surfaces (0 = disabled)
+
+[ForceFreeStates]
+vac_flag = true # Compute plasma, vacuum, and total energies for free-boundary modes
+qlow = 1.02 # Integration initiated at q determined by min(q0, qlow)
+qhigh = 1e3 # Integration terminated at q limit determined by min(qa, qhigh)
+nn = 1 # Toroidal mode number, or consecutive numbers as a list
+delta_mlow = 8 # Expands lower bound of Fourier harmonics
+delta_mhigh = 8 # Expands upper bound of Fourier harmonics
+mtheta_vacuum = 960 # Number of points used in splines over poloidal angle at the plasma-vacuum interface
+singfac_min = 1e-6 # Fractional distance from rational q at which ideal jump enforced
+integrator = "Forward" # Integration formalism, whose numerical settings are its own section: "Forward" (dense ξ, needed for [PerturbedEquilibrium]/kinetic), "Riccati" (chunked propagator BVP, unlocks the singular-surface Δ′ matrix), or "Galerkin" (outer-region singular Galerkin Δ′)
+truncate_at_rational_offset = false # Truncate integration at (last_rational_q + rational_offset_fraction)/n; false for analytic equilibria
+
+# Numerical settings of the forward integrator
+[Forward]
+eulerlagrange_tolerance = 1e-9 # Relative tolerance for ODE integration of Euler-Lagrange equations
+
+# TJ-analytic equilibrium parameters (cf. R. Fitzpatrick, TJ code, https://github.com/rfitzp/TJ); this section selects the
+# equilibrium. Keep p0 at or below 0.2: et[1] stays near +0.42 up to there and is not monotonic above it.
+[TJAnalytic]
+r0 = 10.0 # Major radius R₀ [m] (centerline radius of the magnetic axis)
+a = 1.0 # Minor radius a [m] (plasma half-width at the midplane; here ε = 0.1)
+q0 = 1.6 # On-axis safety factor q(r=0)
+qa = 3.2 # Edge safety factor q(r=a)
+p0 = 0.1 # Normalized on-axis pressure
+pressure_peaking = 2.0 # Pressure-profile peaking exponent in p₂(r) = p0·(1−r²)^μ
+B0 = 1.0 # On-axis toroidal field [T]
+ma = 128 # TJ-analytic internal radial grid resolution (shape-ODE nodes)
+mtheta = 128 # TJ-analytic internal poloidal grid resolution (θ-spline nodes)
+
+[KineticForces]
+fcgl_flag = true # Fluid Chew–Goldberger–Low energy (l = 0 fluid limit) alongside the default fgar method
+axis_validity_suppression = true # Suppress kinetic terms inside the near-axis orbit-width validity limit
diff --git a/examples/TJ_kinetic_NTV_example/kinetic.dat b/examples/TJ_kinetic_NTV_example/kinetic.dat
new file mode 100644
index 0000000000..e3a393077b
--- /dev/null
+++ b/examples/TJ_kinetic_NTV_example/kinetic.dat
@@ -0,0 +1,45 @@
+# Kinetic profiles consistent with the TJ-analytic equilibrium's pressure (P₀ = 784 Pa).
+# Constraint: P(psi_n) = n_e*T_e + n_i*T_i, with n_e = n_i and T_e = T_i = 20 + 180*(1 - psi_n) eV.
+# Omega_E = 2e4*(1 - psi_n) rad/s.
+# psi_n n_i n_e T_i[eV] T_e[eV] omega_E
+0.000000 1.223086e+19 1.223086e+19 200.0000 200.0000 20000.0000
+0.025000 1.222817e+19 1.222817e+19 195.5000 195.5000 19500.0000
+0.050000 1.203522e+19 1.203522e+19 191.0000 191.0000 19000.0000
+0.075000 1.183797e+19 1.183797e+19 186.5000 186.5000 18500.0000
+0.100000 1.163625e+19 1.163625e+19 182.0000 182.0000 18000.0000
+0.125000 1.142988e+19 1.142988e+19 177.5000 177.5000 17500.0000
+0.150000 1.121868e+19 1.121868e+19 173.0000 173.0000 17000.0000
+0.175000 1.100245e+19 1.100245e+19 168.5000 168.5000 16500.0000
+0.200000 1.078097e+19 1.078097e+19 164.0000 164.0000 16000.0000
+0.225000 1.055403e+19 1.055403e+19 159.5000 159.5000 15500.0000
+0.250000 1.032142e+19 1.032142e+19 155.0000 155.0000 15000.0000
+0.275000 1.008285e+19 1.008285e+19 150.5000 150.5000 14500.0000
+0.300000 9.838102e+18 9.838102e+18 146.0000 146.0000 14000.0000
+0.325000 9.586866e+18 9.586866e+18 141.5000 141.5000 13500.0000
+0.350000 9.328821e+18 9.328821e+18 137.0000 137.0000 13000.0000
+0.375000 9.063714e+18 9.063714e+18 132.5000 132.5000 12500.0000
+0.400000 8.791260e+18 8.791260e+18 128.0000 128.0000 12000.0000
+0.425000 8.511117e+18 8.511117e+18 123.5000 123.5000 11500.0000
+0.450000 8.222884e+18 8.222884e+18 119.0000 119.0000 11000.0000
+0.475000 7.926125e+18 7.926125e+18 114.5000 114.5000 10500.0000
+0.500000 7.620476e+18 7.620476e+18 110.0000 110.0000 10000.0000
+0.525000 7.305553e+18 7.305553e+18 105.5000 105.5000 9500.0000
+0.550000 6.980924e+18 6.980924e+18 101.0000 101.0000 9000.0000
+0.575000 6.646101e+18 6.646101e+18 96.5000 96.5000 8500.0000
+0.600000 6.300621e+18 6.300621e+18 92.0000 92.0000 8000.0000
+0.625000 5.944099e+18 5.944099e+18 87.5000 87.5000 7500.0000
+0.650000 5.576149e+18 5.576149e+18 83.0000 83.0000 7000.0000
+0.675000 5.196380e+18 5.196380e+18 78.5000 78.5000 6500.0000
+0.700000 4.804420e+18 4.804420e+18 74.0000 74.0000 6000.0000
+0.725000 4.399955e+18 4.399955e+18 69.5000 69.5000 5500.0000
+0.750000 3.982956e+18 3.982956e+18 65.0000 65.0000 5000.0000
+0.775000 3.553750e+18 3.553750e+18 60.5000 60.5000 4500.0000
+0.800000 3.113088e+18 3.113088e+18 56.0000 56.0000 4000.0000
+0.825000 2.662383e+18 2.662383e+18 51.5000 51.5000 3500.0000
+0.850000 2.204114e+18 2.204114e+18 47.0000 47.0000 3000.0000
+0.875000 1.742718e+18 1.742718e+18 42.5000 42.5000 2500.0000
+0.900000 1.285949e+18 1.285949e+18 38.0000 38.0000 2000.0000
+0.925000 8.470999e+17 8.470999e+17 33.5000 33.5000 1500.0000
+0.950000 4.497124e+17 4.497124e+17 29.0000 29.0000 1000.0000
+0.975000 1.378556e+17 1.378556e+17 24.5000 24.5000 500.0000
+1.000000 2.762506e+16 2.762506e+16 20.0000 20.0000 0.0000
diff --git a/examples/TJ_kinetic_NTV_example/kinetic_rates.dat b/examples/TJ_kinetic_NTV_example/kinetic_rates.dat
new file mode 100644
index 0000000000..d786af31c7
--- /dev/null
+++ b/examples/TJ_kinetic_NTV_example/kinetic_rates.dat
@@ -0,0 +1,44 @@
+# kinetic.dat with supplied collision rates (kinetic_format = "rates-v1"): lnLambda is the internal
+# collision model's, and nu_i, nu_e are 3x the model's, so a run that ignores them moves its NTV torque.
+# psi_n n_i n_e T_i[eV] T_e[eV] omega_E lnLambda nu_i[1/s] nu_e[1/s]
+0.000000 1.223086e+19 1.223086e+19 200.0000 200.0000 20000.0000 15.936447 1.320814e+04 8.004180e+05
+0.025000 1.222817e+19 1.222817e+19 195.5000 195.5000 19500.0000 15.902471 1.363412e+04 8.262323e+05
+0.050000 1.203522e+19 1.203522e+19 191.0000 191.0000 19000.0000 15.875444 1.387293e+04 8.407042e+05
+0.075000 1.183797e+19 1.183797e+19 186.5000 186.5000 18500.0000 15.847943 1.411790e+04 8.555497e+05
+0.100000 1.163625e+19 1.163625e+19 182.0000 182.0000 18000.0000 15.819900 1.436971e+04 8.708092e+05
+0.125000 1.142988e+19 1.142988e+19 177.5000 177.5000 17500.0000 15.791293 1.462851e+04 8.864927e+05
+0.150000 1.121868e+19 1.121868e+19 173.0000 173.0000 17000.0000 15.762099 1.489446e+04 9.026097e+05
+0.175000 1.100245e+19 1.100245e+19 168.5000 168.5000 16500.0000 15.732297 1.516771e+04 9.191682e+05
+0.200000 1.078097e+19 1.078097e+19 164.0000 164.0000 16000.0000 15.701861 1.544832e+04 9.361739e+05
+0.225000 1.055403e+19 1.055403e+19 159.5000 159.5000 15500.0000 15.670764 1.573641e+04 9.536320e+05
+0.250000 1.032142e+19 1.032142e+19 155.0000 155.0000 15000.0000 15.638979 1.603203e+04 9.715466e+05
+0.275000 1.008285e+19 1.008285e+19 150.5000 150.5000 14500.0000 15.606479 1.633510e+04 9.899126e+05
+0.300000 9.838102e+18 9.838102e+18 146.0000 146.0000 14000.0000 15.573231 1.664558e+04 1.008728e+06
+0.325000 9.586866e+18 9.586866e+18 141.5000 141.5000 13500.0000 15.539205 1.696325e+04 1.027979e+06
+0.350000 9.328821e+18 9.328821e+18 137.0000 137.0000 13000.0000 15.504369 1.728774e+04 1.047643e+06
+0.375000 9.063714e+18 9.063714e+18 132.5000 132.5000 12500.0000 15.468687 1.761871e+04 1.067700e+06
+0.400000 8.791260e+18 8.791260e+18 128.0000 128.0000 12000.0000 15.432119 1.795560e+04 1.088116e+06
+0.425000 8.511117e+18 8.511117e+18 123.5000 123.5000 11500.0000 15.394627 1.829757e+04 1.108839e+06
+0.450000 8.222884e+18 8.222884e+18 119.0000 119.0000 11000.0000 15.356177 1.864340e+04 1.129796e+06
+0.475000 7.926125e+18 7.926125e+18 114.5000 114.5000 10500.0000 15.316732 1.899140e+04 1.150886e+06
+0.500000 7.620476e+18 7.620476e+18 110.0000 110.0000 10000.0000 15.276253 1.933963e+04 1.171988e+06
+0.525000 7.305553e+18 7.305553e+18 105.5000 105.5000 9500.0000 15.234701 1.968551e+04 1.192949e+06
+0.550000 6.980924e+18 6.980924e+18 101.0000 101.0000 9000.0000 15.192042 2.002559e+04 1.213557e+06
+0.575000 6.646101e+18 6.646101e+18 96.5000 96.5000 8500.0000 15.148252 2.035526e+04 1.233536e+06
+0.600000 6.300621e+18 6.300621e+18 92.0000 92.0000 8000.0000 15.103311 2.066864e+04 1.252527e+06
+0.625000 5.944099e+18 5.944099e+18 87.5000 87.5000 7500.0000 15.057211 2.095834e+04 1.270082e+06
+0.650000 5.576149e+18 5.576149e+18 83.0000 83.0000 7000.0000 15.009964 2.121461e+04 1.285613e+06
+0.675000 5.196380e+18 5.196380e+18 78.5000 78.5000 6500.0000 14.961619 2.142465e+04 1.298341e+06
+0.700000 4.804420e+18 4.804420e+18 74.0000 74.0000 6000.0000 14.912282 2.157127e+04 1.307226e+06
+0.725000 4.399955e+18 4.399955e+18 69.5000 69.5000 5500.0000 14.862145 2.163009e+04 1.310791e+06
+0.750000 3.982956e+18 3.982956e+18 65.0000 65.0000 5000.0000 14.811521 2.157612e+04 1.307520e+06
+0.775000 3.553750e+18 3.553750e+18 60.5000 60.5000 4500.0000 14.760915 2.136511e+04 1.294733e+06
+0.800000 3.113088e+18 3.113088e+18 56.0000 56.0000 4000.0000 14.711172 2.094570e+04 1.269317e+06
+0.825000 2.662383e+18 2.662383e+18 51.5000 51.5000 3500.0000 14.663713 2.024605e+04 1.226918e+06
+0.850000 2.204114e+18 2.204114e+18 47.0000 47.0000 3000.0000 14.621011 1.916915e+04 1.161657e+06
+0.875000 1.742718e+18 1.742718e+18 42.5000 42.5000 2500.0000 14.587459 1.758553e+04 1.065689e+06
+0.900000 1.285949e+18 1.285949e+18 38.0000 38.0000 2000.0000 14.571583 1.533181e+04 9.291128e+05
+0.925000 8.470999e+17 8.470999e+17 33.5000 33.5000 1500.0000 14.591339 1.221607e+04 7.402979e+05
+0.950000 4.497124e+17 4.497124e+17 29.0000 29.0000 1000.0000 14.691469 8.108515e+03 4.913788e+05
+0.975000 1.378556e+17 1.378556e+17 24.5000 24.5000 500.0000 15.024582 3.302452e+03 2.001298e+05
+1.000000 2.762506e+16 2.762506e+16 20.0000 20.0000 0.0000 15.529067 9.192673e+02 5.570792e+04
diff --git a/examples/TJ_kinetic_NTV_example/run_example.jl b/examples/TJ_kinetic_NTV_example/run_example.jl
new file mode 100644
index 0000000000..fa0a9e53d5
--- /dev/null
+++ b/examples/TJ_kinetic_NTV_example/run_example.jl
@@ -0,0 +1,4 @@
+using Pkg;
+Pkg.activate(joinpath(@__DIR__, "../.."))
+using GeneralizedPerturbedEquilibrium
+GeneralizedPerturbedEquilibrium.main([dirname(@__FILE__)])
diff --git a/examples/TJ_kinetic_calculated_example/forcing.dat b/examples/TJ_kinetic_calculated_example/forcing.dat
new file mode 100644
index 0000000000..ce7aee865f
--- /dev/null
+++ b/examples/TJ_kinetic_calculated_example/forcing.dat
@@ -0,0 +1,6 @@
+# Forcing data for perturbed equilibrium calculations
+# normalization: normal_field_T
+# Format: n m amplitude_real amplitude_imag
+# n=1, m=2 and m=3, amplitude=1e-4 T on the two resonant surfaces
+1 2 1e-4 0.0
+1 3 1e-4 0.0
diff --git a/examples/TJ_kinetic_calculated_example/gpec.toml b/examples/TJ_kinetic_calculated_example/gpec.toml
new file mode 100644
index 0000000000..3b8a45e27b
--- /dev/null
+++ b/examples/TJ_kinetic_calculated_example/gpec.toml
@@ -0,0 +1,70 @@
+# TJ-analytic large-aspect-ratio equilibrium (q₀ = 1.6, q_a = 3.2, β_N = 0.42) with the 2/1 and 3/1 surfaces,
+# stable at n = 1 with no wall (et[1] = +0.435), so a perturbed equilibrium can run without one.
+# Exercises the real KineticForces (NTV) physics path at full strength, with the main ion declared as a
+# 50/50 D-T mix so the self-consistent kinetic matrices are accumulated over the multi-ion species loop
+# (pure plasma, n_i = n_e, so no impurity species arises). The kinetic profiles (kinetic.dat) are consistent
+# with this equilibrium's pressure. Also the only deck that runs [PerturbedEquilibrium] on a kinetic solve,
+# so it builds the ψ-resolved torque response matrices (T_xe on the applied field, T_source for the forcing file).
+
+[Run]
+verbose = true # Log each stage's progress
+
+[Equilibrium]
+kinetic_file = "kinetic.dat" # Kinetic-profile file (HDF5 GPEC kinetic schema or 6-column ASCII), read once into the equilibrium
+jac_type = "hamada" # Coordinate system (hamada, pest, boozer, equal_arc, park, custom)
+grid_type = "core_edge_packed" # Radial grid packing type
+psilow = 0.01 # Lower limit of normalized poloidal flux
+psihigh = 0.99 # Upper limit of normalized poloidal flux; et[1] depends on it (+0.502 at 0.995), so it is pinned
+mpsi = 32 # Number of radial grid intervals (0 = two-pass auto grid from psi_accuracy)
+mtheta = 256 # Number of poloidal grid points
+
+[[Equilibrium.ion_species]]
+z = 1 # Species charge (fundamental units)
+m = 2 # Species mass (proton masses) — Deuterium
+fraction = 0.5 # This species' share of the total main-ion density n_i
+
+[[Equilibrium.ion_species]]
+z = 1 # Species charge (fundamental units)
+m = 3 # Species mass (proton masses) — Tritium
+fraction = 0.5 # This species' share of the total main-ion density n_i
+
+[ForcingTerms]
+forcing_data_file = "forcing.dat" # Manual mode table (n, m, amplitude_real, amplitude_imag)
+forcing_data_format = "ascii" # Format: "ascii", "hdf5", or "coil" (Biot-Savart from 3D wires)
+
+[PerturbedEquilibrium]
+compute_singular_coupling = true # Compute singular layer coupling metrics
+compute_torque_response = true # Build the ψ-resolved torque response matrices T_xe and T_source
+
+[ForceFreeStates]
+vac_flag = true # Compute plasma, vacuum, and total energies for free-boundary modes
+qlow = 1.02 # Integration initiated at q determined by min(q0, qlow)
+qhigh = 1e3 # Integration terminated at q limit determined by min(qa, qhigh)
+nn = 1 # Toroidal mode number, or consecutive numbers as a list
+delta_mlow = 8 # Expands lower bound of Fourier harmonics
+delta_mhigh = 8 # Expands upper bound of Fourier harmonics
+mtheta_vacuum = 64 # Number of points used in splines over poloidal angle at the plasma-vacuum interface
+singfac_min = 1e-6 # Fractional distance from rational q at which ideal jump enforced
+kinetic = "KineticForces" # Kinetic source: the drift-kinetic matrices of the [KineticForces] model (omit for an ideal run)
+integrator = "Forward" # Integration formalism, whose numerical settings are its own section: "Forward" (dense ξ, needed for [PerturbedEquilibrium]/kinetic), "Riccati" (chunked propagator BVP, unlocks the singular-surface Δ′ matrix), or "Galerkin" (outer-region singular Galerkin Δ′)
+truncate_at_rational_offset = false # Truncate integration at (last_rational_q + rational_offset_fraction)/n; false for analytic equilibria
+
+# Numerical settings of the forward integrator
+[Forward]
+eulerlagrange_tolerance = 1e-9 # Relative tolerance for ODE integration of Euler-Lagrange equations
+
+# TJ-analytic equilibrium parameters (cf. R. Fitzpatrick, TJ code, https://github.com/rfitzp/TJ); this section selects the
+# equilibrium. Keep p0 at or below 0.2: et[1] stays near +0.42 up to there and is not monotonic above it.
+[TJAnalytic]
+r0 = 10.0 # Major radius R₀ [m] (centerline radius of the magnetic axis)
+a = 1.0 # Minor radius a [m] (plasma half-width at the midplane; here ε = 0.1)
+q0 = 1.6 # On-axis safety factor q(r=0)
+qa = 3.2 # Edge safety factor q(r=a)
+p0 = 0.1 # Normalized on-axis pressure
+pressure_peaking = 2.0 # Pressure-profile peaking exponent in p₂(r) = p0·(1−r²)^μ
+B0 = 1.0 # On-axis toroidal field [T]
+ma = 128 # TJ-analytic internal radial grid resolution (shape-ODE nodes)
+mtheta = 128 # TJ-analytic internal poloidal grid resolution (θ-spline nodes)
+
+[KineticForces]
+axis_validity_suppression = true # Suppress kinetic terms inside the near-axis orbit-width validity limit
diff --git a/examples/TJ_kinetic_calculated_example/kinetic.dat b/examples/TJ_kinetic_calculated_example/kinetic.dat
new file mode 100644
index 0000000000..e3a393077b
--- /dev/null
+++ b/examples/TJ_kinetic_calculated_example/kinetic.dat
@@ -0,0 +1,45 @@
+# Kinetic profiles consistent with the TJ-analytic equilibrium's pressure (P₀ = 784 Pa).
+# Constraint: P(psi_n) = n_e*T_e + n_i*T_i, with n_e = n_i and T_e = T_i = 20 + 180*(1 - psi_n) eV.
+# Omega_E = 2e4*(1 - psi_n) rad/s.
+# psi_n n_i n_e T_i[eV] T_e[eV] omega_E
+0.000000 1.223086e+19 1.223086e+19 200.0000 200.0000 20000.0000
+0.025000 1.222817e+19 1.222817e+19 195.5000 195.5000 19500.0000
+0.050000 1.203522e+19 1.203522e+19 191.0000 191.0000 19000.0000
+0.075000 1.183797e+19 1.183797e+19 186.5000 186.5000 18500.0000
+0.100000 1.163625e+19 1.163625e+19 182.0000 182.0000 18000.0000
+0.125000 1.142988e+19 1.142988e+19 177.5000 177.5000 17500.0000
+0.150000 1.121868e+19 1.121868e+19 173.0000 173.0000 17000.0000
+0.175000 1.100245e+19 1.100245e+19 168.5000 168.5000 16500.0000
+0.200000 1.078097e+19 1.078097e+19 164.0000 164.0000 16000.0000
+0.225000 1.055403e+19 1.055403e+19 159.5000 159.5000 15500.0000
+0.250000 1.032142e+19 1.032142e+19 155.0000 155.0000 15000.0000
+0.275000 1.008285e+19 1.008285e+19 150.5000 150.5000 14500.0000
+0.300000 9.838102e+18 9.838102e+18 146.0000 146.0000 14000.0000
+0.325000 9.586866e+18 9.586866e+18 141.5000 141.5000 13500.0000
+0.350000 9.328821e+18 9.328821e+18 137.0000 137.0000 13000.0000
+0.375000 9.063714e+18 9.063714e+18 132.5000 132.5000 12500.0000
+0.400000 8.791260e+18 8.791260e+18 128.0000 128.0000 12000.0000
+0.425000 8.511117e+18 8.511117e+18 123.5000 123.5000 11500.0000
+0.450000 8.222884e+18 8.222884e+18 119.0000 119.0000 11000.0000
+0.475000 7.926125e+18 7.926125e+18 114.5000 114.5000 10500.0000
+0.500000 7.620476e+18 7.620476e+18 110.0000 110.0000 10000.0000
+0.525000 7.305553e+18 7.305553e+18 105.5000 105.5000 9500.0000
+0.550000 6.980924e+18 6.980924e+18 101.0000 101.0000 9000.0000
+0.575000 6.646101e+18 6.646101e+18 96.5000 96.5000 8500.0000
+0.600000 6.300621e+18 6.300621e+18 92.0000 92.0000 8000.0000
+0.625000 5.944099e+18 5.944099e+18 87.5000 87.5000 7500.0000
+0.650000 5.576149e+18 5.576149e+18 83.0000 83.0000 7000.0000
+0.675000 5.196380e+18 5.196380e+18 78.5000 78.5000 6500.0000
+0.700000 4.804420e+18 4.804420e+18 74.0000 74.0000 6000.0000
+0.725000 4.399955e+18 4.399955e+18 69.5000 69.5000 5500.0000
+0.750000 3.982956e+18 3.982956e+18 65.0000 65.0000 5000.0000
+0.775000 3.553750e+18 3.553750e+18 60.5000 60.5000 4500.0000
+0.800000 3.113088e+18 3.113088e+18 56.0000 56.0000 4000.0000
+0.825000 2.662383e+18 2.662383e+18 51.5000 51.5000 3500.0000
+0.850000 2.204114e+18 2.204114e+18 47.0000 47.0000 3000.0000
+0.875000 1.742718e+18 1.742718e+18 42.5000 42.5000 2500.0000
+0.900000 1.285949e+18 1.285949e+18 38.0000 38.0000 2000.0000
+0.925000 8.470999e+17 8.470999e+17 33.5000 33.5000 1500.0000
+0.950000 4.497124e+17 4.497124e+17 29.0000 29.0000 1000.0000
+0.975000 1.378556e+17 1.378556e+17 24.5000 24.5000 500.0000
+1.000000 2.762506e+16 2.762506e+16 20.0000 20.0000 0.0000
diff --git a/examples/TJ_kinetic_multiion_example/forcing.dat b/examples/TJ_kinetic_multiion_example/forcing.dat
new file mode 100644
index 0000000000..ce7aee865f
--- /dev/null
+++ b/examples/TJ_kinetic_multiion_example/forcing.dat
@@ -0,0 +1,6 @@
+# Forcing data for perturbed equilibrium calculations
+# normalization: normal_field_T
+# Format: n m amplitude_real amplitude_imag
+# n=1, m=2 and m=3, amplitude=1e-4 T on the two resonant surfaces
+1 2 1e-4 0.0
+1 3 1e-4 0.0
diff --git a/examples/TJ_kinetic_multiion_example/gpec.toml b/examples/TJ_kinetic_multiion_example/gpec.toml
new file mode 100644
index 0000000000..5b32e39f7a
--- /dev/null
+++ b/examples/TJ_kinetic_multiion_example/gpec.toml
@@ -0,0 +1,69 @@
+# TJ-analytic large-aspect-ratio equilibrium (q₀ = 1.6, q_a = 3.2, β_N = 0.42) with the 2/1 and 3/1 surfaces,
+# stable at n = 1 with no wall (et[1] = +0.435), so a perturbed equilibrium can run without one.
+# Multi-ion NTV: the main ion is a 50/50 D-T mix (n_i = total), so the summed NTV runs over D + T +
+# the neutrality-closing impurity + electrons. The kinetic profiles (kinetic.dat) are consistent with
+# this equilibrium's pressure.
+
+[Run]
+verbose = true # Log each stage's progress
+
+[Equilibrium]
+kinetic_file = "kinetic.dat" # Kinetic-profile file (HDF5 GPEC kinetic schema or 6-column ASCII), read once into the equilibrium
+jac_type = "hamada" # Coordinate system (hamada, pest, boozer, equal_arc, park, custom)
+grid_type = "core_edge_packed" # Radial grid packing type
+psilow = 0.01 # Lower limit of normalized poloidal flux
+psihigh = 0.99 # Upper limit of normalized poloidal flux; et[1] depends on it (+0.502 at 0.995), so it is pinned
+mpsi = 128 # Number of radial grid intervals (0 = two-pass auto grid from psi_accuracy)
+mtheta = 256 # Number of poloidal grid points
+impurity_charge = 6 # Impurity charge (fundamental units); closes quasineutrality
+impurity_mass = 12 # Impurity mass (proton masses)
+
+[[Equilibrium.ion_species]]
+z = 1 # Species charge (fundamental units)
+m = 2 # Species mass (proton masses) — Deuterium
+fraction = 0.5 # This species' share of the total main-ion density n_i
+
+[[Equilibrium.ion_species]]
+z = 1 # Species charge (fundamental units)
+m = 3 # Species mass (proton masses) — Tritium
+fraction = 0.5 # This species' share of the total main-ion density n_i
+
+[ForcingTerms]
+forcing_data_file = "forcing.dat" # Manual mode table (n, m, amplitude_real, amplitude_imag)
+forcing_data_format = "ascii" # Format: "ascii", "hdf5", or "coil" (Biot-Savart from 3D wires)
+
+[PerturbedEquilibrium]
+compute_singular_coupling = true # Compute singular layer coupling metrics
+regularization_width = 0.05 # Regularization width for singular surfaces (0 = disabled)
+
+[ForceFreeStates]
+vac_flag = true # Compute plasma, vacuum, and total energies for free-boundary modes
+qlow = 1.02 # Integration initiated at q determined by min(q0, qlow)
+qhigh = 1e3 # Integration terminated at q limit determined by min(qa, qhigh)
+nn = 1 # Toroidal mode number, or consecutive numbers as a list
+delta_mlow = 8 # Expands lower bound of Fourier harmonics
+delta_mhigh = 8 # Expands upper bound of Fourier harmonics
+mtheta_vacuum = 960 # Number of points used in splines over poloidal angle at the plasma-vacuum interface
+singfac_min = 1e-6 # Fractional distance from rational q at which ideal jump enforced
+integrator = "Forward" # Integration formalism, whose numerical settings are its own section: "Forward" (dense ξ, needed for [PerturbedEquilibrium]/kinetic), "Riccati" (chunked propagator BVP, unlocks the singular-surface Δ′ matrix), or "Galerkin" (outer-region singular Galerkin Δ′)
+truncate_at_rational_offset = false # Truncate integration at (last_rational_q + rational_offset_fraction)/n; false for analytic equilibria
+
+# Numerical settings of the forward integrator
+[Forward]
+eulerlagrange_tolerance = 1e-9 # Relative tolerance for ODE integration of Euler-Lagrange equations
+
+# TJ-analytic equilibrium parameters (cf. R. Fitzpatrick, TJ code, https://github.com/rfitzp/TJ); this section selects the
+# equilibrium. Keep p0 at or below 0.2: et[1] stays near +0.42 up to there and is not monotonic above it.
+[TJAnalytic]
+r0 = 10.0 # Major radius R₀ [m] (centerline radius of the magnetic axis)
+a = 1.0 # Minor radius a [m] (plasma half-width at the midplane; here ε = 0.1)
+q0 = 1.6 # On-axis safety factor q(r=0)
+qa = 3.2 # Edge safety factor q(r=a)
+p0 = 0.1 # Normalized on-axis pressure
+pressure_peaking = 2.0 # Pressure-profile peaking exponent in p₂(r) = p0·(1−r²)^μ
+B0 = 1.0 # On-axis toroidal field [T]
+ma = 128 # TJ-analytic internal radial grid resolution (shape-ODE nodes)
+mtheta = 128 # TJ-analytic internal poloidal grid resolution (θ-spline nodes)
+
+[KineticForces]
+electron = true # Add electron NTV in addition to the ion species
diff --git a/examples/TJ_kinetic_multiion_example/kinetic.dat b/examples/TJ_kinetic_multiion_example/kinetic.dat
new file mode 100644
index 0000000000..e3a393077b
--- /dev/null
+++ b/examples/TJ_kinetic_multiion_example/kinetic.dat
@@ -0,0 +1,45 @@
+# Kinetic profiles consistent with the TJ-analytic equilibrium's pressure (P₀ = 784 Pa).
+# Constraint: P(psi_n) = n_e*T_e + n_i*T_i, with n_e = n_i and T_e = T_i = 20 + 180*(1 - psi_n) eV.
+# Omega_E = 2e4*(1 - psi_n) rad/s.
+# psi_n n_i n_e T_i[eV] T_e[eV] omega_E
+0.000000 1.223086e+19 1.223086e+19 200.0000 200.0000 20000.0000
+0.025000 1.222817e+19 1.222817e+19 195.5000 195.5000 19500.0000
+0.050000 1.203522e+19 1.203522e+19 191.0000 191.0000 19000.0000
+0.075000 1.183797e+19 1.183797e+19 186.5000 186.5000 18500.0000
+0.100000 1.163625e+19 1.163625e+19 182.0000 182.0000 18000.0000
+0.125000 1.142988e+19 1.142988e+19 177.5000 177.5000 17500.0000
+0.150000 1.121868e+19 1.121868e+19 173.0000 173.0000 17000.0000
+0.175000 1.100245e+19 1.100245e+19 168.5000 168.5000 16500.0000
+0.200000 1.078097e+19 1.078097e+19 164.0000 164.0000 16000.0000
+0.225000 1.055403e+19 1.055403e+19 159.5000 159.5000 15500.0000
+0.250000 1.032142e+19 1.032142e+19 155.0000 155.0000 15000.0000
+0.275000 1.008285e+19 1.008285e+19 150.5000 150.5000 14500.0000
+0.300000 9.838102e+18 9.838102e+18 146.0000 146.0000 14000.0000
+0.325000 9.586866e+18 9.586866e+18 141.5000 141.5000 13500.0000
+0.350000 9.328821e+18 9.328821e+18 137.0000 137.0000 13000.0000
+0.375000 9.063714e+18 9.063714e+18 132.5000 132.5000 12500.0000
+0.400000 8.791260e+18 8.791260e+18 128.0000 128.0000 12000.0000
+0.425000 8.511117e+18 8.511117e+18 123.5000 123.5000 11500.0000
+0.450000 8.222884e+18 8.222884e+18 119.0000 119.0000 11000.0000
+0.475000 7.926125e+18 7.926125e+18 114.5000 114.5000 10500.0000
+0.500000 7.620476e+18 7.620476e+18 110.0000 110.0000 10000.0000
+0.525000 7.305553e+18 7.305553e+18 105.5000 105.5000 9500.0000
+0.550000 6.980924e+18 6.980924e+18 101.0000 101.0000 9000.0000
+0.575000 6.646101e+18 6.646101e+18 96.5000 96.5000 8500.0000
+0.600000 6.300621e+18 6.300621e+18 92.0000 92.0000 8000.0000
+0.625000 5.944099e+18 5.944099e+18 87.5000 87.5000 7500.0000
+0.650000 5.576149e+18 5.576149e+18 83.0000 83.0000 7000.0000
+0.675000 5.196380e+18 5.196380e+18 78.5000 78.5000 6500.0000
+0.700000 4.804420e+18 4.804420e+18 74.0000 74.0000 6000.0000
+0.725000 4.399955e+18 4.399955e+18 69.5000 69.5000 5500.0000
+0.750000 3.982956e+18 3.982956e+18 65.0000 65.0000 5000.0000
+0.775000 3.553750e+18 3.553750e+18 60.5000 60.5000 4500.0000
+0.800000 3.113088e+18 3.113088e+18 56.0000 56.0000 4000.0000
+0.825000 2.662383e+18 2.662383e+18 51.5000 51.5000 3500.0000
+0.850000 2.204114e+18 2.204114e+18 47.0000 47.0000 3000.0000
+0.875000 1.742718e+18 1.742718e+18 42.5000 42.5000 2500.0000
+0.900000 1.285949e+18 1.285949e+18 38.0000 38.0000 2000.0000
+0.925000 8.470999e+17 8.470999e+17 33.5000 33.5000 1500.0000
+0.950000 4.497124e+17 4.497124e+17 29.0000 29.0000 1000.0000
+0.975000 1.378556e+17 1.378556e+17 24.5000 24.5000 500.0000
+1.000000 2.762506e+16 2.762506e+16 20.0000 20.0000 0.0000
diff --git a/examples/TJ_kinetic_multiion_example/run_example.jl b/examples/TJ_kinetic_multiion_example/run_example.jl
new file mode 100644
index 0000000000..fa0a9e53d5
--- /dev/null
+++ b/examples/TJ_kinetic_multiion_example/run_example.jl
@@ -0,0 +1,4 @@
+using Pkg;
+Pkg.activate(joinpath(@__DIR__, "../.."))
+using GeneralizedPerturbedEquilibrium
+GeneralizedPerturbedEquilibrium.main([dirname(@__FILE__)])
diff --git a/examples/a10_kinetic_example/a10_prof1.txt b/examples/a10_kinetic_example/a10_prof1.txt
new file mode 100644
index 0000000000..fded31948a
--- /dev/null
+++ b/examples/a10_kinetic_example/a10_prof1.txt
@@ -0,0 +1,252 @@
+ psi ni[m^-3] ne[m^-3] ti[eV] te[eV] we[rad/s]
+ 8.462522E-11 2.000000E+18 2.000000E+18 4.836142E+02 4.836142E+02 5.453044E+04
+ 8.462522E-05 2.000000E+18 2.000000E+18 4.835375E+02 4.835375E+02 5.453044E+04
+ 3.384988E-04 2.000000E+18 2.000000E+18 4.833073E+02 4.833073E+02 5.453044E+04
+ 7.616178E-04 1.999999E+18 1.999999E+18 4.829239E+02 4.829239E+02 5.453044E+04
+ 1.353979E-03 1.999996E+18 1.999996E+18 4.823873E+02 4.823873E+02 5.453044E+04
+ 2.115581E-03 1.999991E+18 1.999991E+18 4.816980E+02 4.816980E+02 5.453044E+04
+ 3.046419E-03 1.999982E+18 1.999982E+18 4.808562E+02 4.808562E+02 5.453044E+04
+ 4.146487E-03 1.999966E+18 1.999966E+18 4.798625E+02 4.798625E+02 5.453044E+04
+ 5.415778E-03 1.999942E+18 1.999942E+18 4.787173E+02 4.787173E+02 5.453044E+04
+ 6.854283E-03 1.999907E+18 1.999907E+18 4.774213E+02 4.774213E+02 5.453044E+04
+ 8.461987E-03 1.999858E+18 1.999858E+18 4.759752E+02 4.759752E+02 5.453044E+04
+ 1.023887E-02 1.999792E+18 1.999792E+18 4.743798E+02 4.743798E+02 5.453044E+04
+ 1.218492E-02 1.999706E+18 1.999706E+18 4.726358E+02 4.726358E+02 5.453044E+04
+ 1.430010E-02 1.999595E+18 1.999595E+18 4.707443E+02 4.707443E+02 5.453044E+04
+ 1.658437E-02 1.999455E+18 1.999455E+18 4.687063E+02 4.687063E+02 5.453044E+04
+ 1.903768E-02 1.999282E+18 1.999282E+18 4.665229E+02 4.665229E+02 5.453044E+04
+ 2.165999E-02 1.999071E+18 1.999071E+18 4.641952E+02 4.641952E+02 5.453044E+04
+ 2.445124E-02 1.998816E+18 1.998816E+18 4.617246E+02 4.617246E+02 5.453044E+04
+ 2.741134E-02 1.998512E+18 1.998512E+18 4.591123E+02 4.591123E+02 5.453044E+04
+ 3.054021E-02 1.998153E+18 1.998153E+18 4.563597E+02 4.563597E+02 5.453044E+04
+ 3.383775E-02 1.997733E+18 1.997733E+18 4.534684E+02 4.534684E+02 5.453044E+04
+ 3.730377E-02 1.997245E+18 1.997245E+18 4.504400E+02 4.504400E+02 5.453044E+04
+ 4.093817E-02 1.996682E+18 1.996682E+18 4.472761E+02 4.472761E+02 5.453044E+04
+ 4.474080E-02 1.996037E+18 1.996037E+18 4.439783E+02 4.439783E+02 5.453044E+04
+ 4.871147E-02 1.995302E+18 1.995302E+18 4.405486E+02 4.405486E+02 5.453044E+04
+ 5.284996E-02 1.994470E+18 1.994470E+18 4.369887E+02 4.369887E+02 5.453044E+04
+ 5.715605E-02 1.993532E+18 1.993532E+18 4.333007E+02 4.333007E+02 5.453044E+04
+ 6.162942E-02 1.992480E+18 1.992480E+18 4.294865E+02 4.294865E+02 5.453044E+04
+ 6.626967E-02 1.991304E+18 1.991304E+18 4.255485E+02 4.255485E+02 5.453044E+04
+ 7.107659E-02 1.989997E+18 1.989997E+18 4.214885E+02 4.214885E+02 5.453044E+04
+ 7.604979E-02 1.988549E+18 1.988549E+18 4.173090E+02 4.173090E+02 5.453044E+04
+ 8.118887E-02 1.986949E+18 1.986949E+18 4.130123E+02 4.130123E+02 5.453044E+04
+ 8.649338E-02 1.985187E+18 1.985187E+18 4.086007E+02 4.086007E+02 5.453044E+04
+ 9.196283E-02 1.983255E+18 1.983255E+18 4.040768E+02 4.040768E+02 5.453044E+04
+ 9.759649E-02 1.981140E+18 1.981140E+18 3.994433E+02 3.994433E+02 5.453044E+04
+ 1.033937E-01 1.978833E+18 1.978833E+18 3.947028E+02 3.947028E+02 5.453044E+04
+ 1.093540E-01 1.976323E+18 1.976323E+18 3.898580E+02 3.898580E+02 5.453044E+04
+ 1.154767E-01 1.973597E+18 1.973597E+18 3.849116E+02 3.849116E+02 5.453044E+04
+ 1.217610E-01 1.970645E+18 1.970645E+18 3.798665E+02 3.798665E+02 5.453044E+04
+ 1.282061E-01 1.967455E+18 1.967455E+18 3.747256E+02 3.747256E+02 5.453044E+04
+ 1.348111E-01 1.964015E+18 1.964015E+18 3.694921E+02 3.694921E+02 5.453044E+04
+ 1.415748E-01 1.960314E+18 1.960314E+18 3.641692E+02 3.641692E+02 5.453044E+04
+ 1.484959E-01 1.956339E+18 1.956339E+18 3.587604E+02 3.587604E+02 5.453044E+04
+ 1.555737E-01 1.952078E+18 1.952078E+18 3.532686E+02 3.532686E+02 5.453044E+04
+ 1.628070E-01 1.947518E+18 1.947518E+18 3.476970E+02 3.476970E+02 5.453044E+04
+ 1.701947E-01 1.942647E+18 1.942647E+18 3.420493E+02 3.420493E+02 5.453044E+04
+ 1.777353E-01 1.937452E+18 1.937452E+18 3.363289E+02 3.363289E+02 5.453044E+04
+ 1.854275E-01 1.931921E+18 1.931921E+18 3.305393E+02 3.305393E+02 5.453044E+04
+ 1.932698E-01 1.926041E+18 1.926041E+18 3.246843E+02 3.246843E+02 5.453044E+04
+ 2.012591E-01 1.919800E+18 1.919800E+18 3.187687E+02 3.187687E+02 5.453044E+04
+ 2.093949E-01 1.913184E+18 1.913184E+18 3.127955E+02 3.127955E+02 5.453044E+04
+ 2.176755E-01 1.906182E+18 1.906182E+18 3.067685E+02 3.067685E+02 5.453044E+04
+ 2.260990E-01 1.898781E+18 1.898781E+18 3.006917E+02 3.006917E+02 5.453044E+04
+ 2.346633E-01 1.890968E+18 1.890968E+18 2.945693E+02 2.945693E+02 5.453044E+04
+ 2.433665E-01 1.882730E+18 1.882730E+18 2.884054E+02 2.884054E+02 5.453044E+04
+ 2.522063E-01 1.874056E+18 1.874056E+18 2.822042E+02 2.822042E+02 5.453044E+04
+ 2.611804E-01 1.864934E+18 1.864934E+18 2.759700E+02 2.759700E+02 5.453044E+04
+ 2.702857E-01 1.855352E+18 1.855352E+18 2.697078E+02 2.697078E+02 5.453044E+04
+ 2.795186E-01 1.845301E+18 1.845301E+18 2.634226E+02 2.634226E+02 5.453044E+04
+ 2.888781E-01 1.834768E+18 1.834768E+18 2.571179E+02 2.571179E+02 5.453044E+04
+ 2.983613E-01 1.823741E+18 1.823741E+18 2.507983E+02 2.507983E+02 5.453044E+04
+ 3.079654E-01 1.812211E+18 1.812211E+18 2.444684E+02 2.444684E+02 5.453044E+04
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diff --git a/examples/a10_kinetic_example/fix_a100_k10_q2_bn010_prof1 b/examples/a10_kinetic_example/fix_a100_k10_q2_bn010_prof1
new file mode 100644
index 0000000000..3a574d4bb7
--- /dev/null
+++ b/examples/a10_kinetic_example/fix_a100_k10_q2_bn010_prof1
@@ -0,0 +1,13624 @@
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+ 1.987157620E+00-1.995874781E-01 1.991362589E+00-1.998136216E-01 1.995569170E+00
+-1.999511342E-01 1.999775495E+00-2.000000948E-01 2.003979698E+00-1.999606219E-01
+ 2.008179923E+00-1.998328730E-01 2.012374319E+00-1.996170444E-01 2.016561045E+00
+-1.993133709E-01 2.020738270E+00-1.989221255E-01 2.024904170E+00-1.984436190E-01
+ 2.029056936E+00-1.978781995E-01 2.033194767E+00-1.972262522E-01 2.037315876E+00
+-1.964881986E-01 2.041418487E+00-1.956644968E-01 2.045500841E+00-1.947556404E-01
+ 2.049561190E+00-1.937621583E-01 2.053597803E+00-1.926846143E-01 2.057608964E+00
+-1.915236066E-01 2.061592972E+00-1.902797672E-01 2.065548146E+00-1.889537616E-01
+ 2.069472819E+00-1.875462882E-01 2.073365345E+00-1.860580778E-01 2.077224095E+00
+-1.844898932E-01 2.081047459E+00-1.828425285E-01 2.084833847E+00-1.811168087E-01
+ 2.088581691E+00-1.793135892E-01 2.092289441E+00-1.774337551E-01 2.095955570E+00
+-1.754782209E-01 2.099578573E+00-1.734479297E-01 2.103156967E+00-1.713438529E-01
+ 2.106689289E+00-1.691669894E-01 2.110174103E+00-1.669183653E-01 2.113609995E+00
+-1.645990329E-01 2.116995575E+00-1.622100709E-01 2.120329476E+00-1.597525830E-01
+ 2.123610357E+00-1.572276979E-01 2.126836903E+00-1.546365685E-01 2.130007822E+00
+-1.519803714E-01 2.133121850E+00-1.492603062E-01 2.136177747E+00-1.464775951E-01
+ 2.139174302E+00-1.436334823E-01 2.142110329E+00-1.407292359E-01 2.144984667E+00
+-1.377661370E-01 2.147796185E+00-1.347454951E-01 2.150543779E+00-1.316686364E-01
+ 2.153226373E+00-1.285369064E-01 2.155842919E+00-1.253516691E-01 2.158392395E+00
+-1.221143066E-01 2.160873811E+00-1.188262182E-01 2.163286203E+00-1.154888203E-01
+ 2.165628636E+00-1.121035454E-01 2.167900206E+00-1.086718419E-01 2.170100036E+00
+-1.051951734E-01 2.172227280E+00-1.016750179E-01 2.174281120E+00-9.811286779E-02
+ 2.176260769E+00-9.451022887E-02 2.178165469E+00-9.086861993E-02 2.179994492E+00
+-8.718957224E-02 2.181747141E+00-8.347462896E-02 2.183422749E+00-7.972534463E-02
+ 2.185020678E+00-7.594328462E-02 2.186540321E+00-7.213002460E-02 2.187981104E+00
+-6.828715002E-02 2.189342479E+00-6.441625557E-02 2.190623934E+00-6.051894463E-02
+ 2.191824983E+00-5.659682879E-02 2.192945173E+00-5.265152730E-02 2.193984084E+00
+-4.868466655E-02 2.194941323E+00-4.469787956E-02 2.195816530E+00-4.069280546E-02
+ 2.196609378E+00-3.667108896E-02 2.197319567E+00-3.263437986E-02 2.197946833E+00
+-2.858433253E-02 2.198490938E+00-2.452260539E-02 2.198951681E+00-2.045086040E-02
+ 2.199328887E+00-1.637076257E-02 2.199622417E+00-1.228397943E-02 2.199832159E+00
+-8.192180544E-03 2.199958036E+00-4.097036982E-03 2.200000000E+00-2.208300268E-07
+ 1.600000000E+00-4.000005482E-01 2.400000000E+00-4.000005482E-01 2.400000000E+00
+ 3.999994518E-01 1.600000000E+00 3.999994518E-01 1.600000000E+00-4.000005482E-01
+
+ 2.00000000E+00 R0 [M] USED FOR CONVERTING TO MKSA
+ 1.00000000E+00 B0 [T] USED FOR CONVERTING TO MKSA
+ 1.00251540E+00 R OF MAGAXE --> [M] 2.00503081E+00
+ -2.74079228E-07 Z OF MAGAXE --> [M] -5.48158456E-07
+ -3.04194290E-03 PSI-AXIS --> [T M**2] -1.21677716E-02
+ -1.91131052E-02 2*PI*PSI-AXIS --> -7.64524207E-02
+ 2.27713686E-02 TOTAL CURRENT --> [A] 3.62417547E+04
+ 1.49031820E-01 POLOIDAL BETA
+ 1.94759091E-04 BETA
+ 2.99474016E-04 BETA* (SQRT())
+ 1.95749445E-04 BETA_EXP=
*2*MU0/B0**2
+ 1.10810709E+00 LI
+ 1.23886290E+00 Q_ZERO
+ 2.79411382E+00 Q_EDGE
+ 1.00000002E+01 ASPECT RATIO ; a/R= 9.99999984E-02
+ 1.00000017E+00 b/a
+ 1.97391020E-01 VOLUME -> 1.57912816E+00
+ 3.14157548E-02 AREA -> 1.25663019E-01
+ 6.28318532E-01 LENGTH -> 1.25663706E+00
+ 9.00005801E-01 RMIN -> RMIN [m] 1.80001160E+00
+ 1.10000000E+00 RMAX -> RMAX [m] 2.20000000E+00
+ -1.00000047E-01 ZMIN -> ZMIN [m] -2.00000095E-01
+ 9.99998266E-02 ZMAX -> ZMAX [m] 1.99999653E-01
+ 1.00000290E+00 RGEOM -> RGEOM [m] 2.00000580E+00
+ 9.99970995E-02 MINOR RADIUS -> A [m] 1.99994199E-01
diff --git a/examples/a10_kinetic_example/gpec.toml b/examples/a10_kinetic_example/gpec.toml
new file mode 100644
index 0000000000..24b0c408f1
--- /dev/null
+++ b/examples/a10_kinetic_example/gpec.toml
@@ -0,0 +1,73 @@
+# a10 kinetic stability example — drift-kinetic MHD stability of a low-aspect-ratio
+# circular tokamak. Unlike the ideal examples, this run uses the calculated kinetic
+# (neoclassical toroidal viscosity) energy matrices at full strength, so the
+# free-boundary stability includes drift-kinetic effects from a single deuterium ion
+# species with a Maxwellian distribution and a harmonic collision operator.
+# The run stops after the kinetic stability eigenvalues (no [PerturbedEquilibrium] section).
+# The equilibrium g-file and kinetic profile are bundled in this directory.
+
+[Run]
+verbose = true # Log each stage's progress
+
+[Equilibrium]
+eq_filename = "fix_a100_k10_q2_bn010_prof1" # Path to equilibrium file
+kinetic_file = "a10_prof1.txt" # Kinetic-profile file (HDF5 GPEC kinetic schema or 6-column ASCII), read once into the equilibrium
+eq_type = "efit" # Type of the input 2D equilibrium file
+jac_type = "hamada" # Coordinate system (hamada, pest, boozer, equal_arc, park, custom)
+grid_type = "core_edge_packed" # Radial grid packing type
+psilow = 1e-3 # Lower limit of normalized poloidal flux
+psihigh = 0.99 # Upper limit of normalized poloidal flux
+mpsi = 16 # Number of radial grid points (low value for fast iteration)
+mtheta = 256 # Number of poloidal grid points
+newq0 = 0 # Target on-axis safety factor q(0) (0 = use input value; q is positive, so negative values are rejected)
+flux_surface_rtol = 1e-7 # Relative tolerance of the ODE solves that trace each flux surface
+impurity_charge = 6 # Impurity charge
+impurity_mass = 12 # Impurity mass
+
+[[Equilibrium.ion_species]]
+z = 1 # Charge in units of e
+m = 2 # Mass in proton masses
+fraction = 1.0 # Fraction of the n_i profile this species carries
+
+# Presence runs the LocalStability stage (Mercier D_I, resistive D_R, ballooning Δ', first α boundary); keys are the LocalStabilityProblem settings, numerics in [Ballooning]
+[LocalStability]
+theta_k = 0.0 # Ballooning angle θ_k, used by both the profile scan and the α-boundary scan
+alpha_boundary_scan = true # Run the first ballooning α-boundary scan (a root find per ψ surface)
+
+# Numerical settings of the ballooning scans
+[Ballooning]
+ode_tol = 1e-8 # Relative and absolute tolerance of the ballooning ODE integration behind Δ'
+n_scan = 24 # Resolution of the α scan for the first boundary
+max_alpha_scale = 8.0 # Upper end of the α search, as a multiple of the experimental α
+alpha_tol = 1e-3 # Bisection tolerance of the critical α, in the same multiples
+psi_window = [0.1, 0.99] # ψ_N range of the α scan; surfaces outside it are NaN
+
+[ForceFreeStates]
+vac_flag = true # Compute plasma, vacuum, and total energies for free-boundary modes
+
+truncate_at_rational_offset = false # FALSE for limited/analytical equilibria — rationals sparse, rational_offset_fraction would chop too much edge
+dW_edge_scan_start = 1.0 # Edge dW(ψ) diagnostic scan band [dW_edge_scan_start, psilim]; set ≥ psilim to disable
+qlow = 1.02 # Integration initiated at q determined by min(q0, qlow)
+qhigh = 1e3 # Integration terminated at q limit determined by min(qa, qhigh)
+
+nn = 1 # Toroidal mode number, or consecutive numbers as a list
+delta_mlow = 6 # Expands lower bound of Fourier harmonics
+delta_mhigh = 6 # Expands upper bound of Fourier harmonics
+mtheta_vacuum = 512 # Number of points used in splines over poloidal angle at the plasma-vacuum interface
+
+kinetic = "KineticForces" # Kinetic source: the drift-kinetic matrices of the [KineticForces] model (omit for an ideal run)
+integrator = "Forward" # Integration formalism, whose numerical settings are its own section: "Forward" (dense ξ, needed for [PerturbedEquilibrium]/kinetic), "Riccati" (chunked propagator BVP, unlocks the singular-surface Δ′ matrix), or "Galerkin" (outer-region singular Galerkin Δ′)
+singfac_min = 1e-6 # Fractional distance from rational q at which ideal jump enforced
+
+# Numerical settings of the forward integrator
+[Forward]
+eulerlagrange_tolerance = 1e-7 # Relative tolerance for ODE integration of Euler-Lagrange equations
+renorm_threshold = 1e3 # Column-norm threshold that triggers solution renormalization
+
+[KineticForces]
+bounce_harmonic_max = 6 # Bounce-harmonic number
+electron = false # Include electron contribution (false = ion-only)
+nutype = "harmonic" # Collision operator (zero, small, krook, harmonic)
+f0type = "maxwellian" # Distribution function (maxwellian, park, cgl)
+atol_pitch = 1e-9 # Absolute tolerance for the pitch integration (median-normalized kernel)
+axis_validity_suppression = true # Suppress kinetic terms inside the near-axis orbit-width validity limit
diff --git a/examples/efit_fixedbdy_separatrix_example/README.md b/examples/efit_fixedbdy_separatrix_example/README.md
new file mode 100644
index 0000000000..de6d8e6a7d
--- /dev/null
+++ b/examples/efit_fixedbdy_separatrix_example/README.md
@@ -0,0 +1,19 @@
+# Fixed-boundary EFIT separatrix-find fixture (PR #296, issue #294)
+
+`eq_eps0.0500000_k1.000_d0.000.geqdsk` is a fixed-boundary TokaMaker aspect-scan equilibrium
+(circular, R/a = 20, eps = 0.05) whose computational box hugs the last closed flux surface.
+
+In a fixed-boundary solve the LCFS shape is prescribed and the flux **outside** it is physically
+unconstrained: the coil-vacuum flux turns back above the boundary value (`sibry`) before reaching
+the grid edge. The old bracketed `Roots.Brent()` separatrix finder used the grid edge as its outer
+bracket point, so `f(axis)` and `f(edge)` ended up the same sign and `direct_position!` threw
+`ArgumentError: not a bracketing interval`. The Newton finder (PR #296, faithful to Fortran
+`direct.f direct_position`) walks inward to the first `psi = sibry` crossing — the actual LCFS — and
+loads it regardless of box size.
+
+This g-file is the fixture for the `efit_fixedbdy_separatrix` regression case
+(`regression-harness/cases/efit_fixedbdy_separatrix.toml`, a `kind = "computed"` case that calls
+`PlasmaEquilibrium` directly). It is **not** a runnable example deck — there is no `gpec.toml`.
+
+Free-boundary equilibria (real coil currents) and standard diverted EFITs are unaffected: their
+outboard midplane flux keeps dropping past the LCFS, so the bracket was never ambiguous.
diff --git a/examples/efit_fixedbdy_separatrix_example/eq_eps0.0500000_k1.000_d0.000.geqdsk b/examples/efit_fixedbdy_separatrix_example/eq_eps0.0500000_k1.000_d0.000.geqdsk
new file mode 100644
index 0000000000..150e3e313d
--- /dev/null
+++ b/examples/efit_fixedbdy_separatrix_example/eq_eps0.0500000_k1.000_d0.000.geqdsk
@@ -0,0 +1,6920 @@
+tMaker: const-q chain eq_eps0.0500000_k1 0 129 257
+ 0.219966221E+01 0.219966221E+01 0.200008011E+02 0.189003220E+02 0.000000000E+00
+ 0.200259857E+02 0.390171977E-06 0.337817192E+00 0.337817194E-02 0.199992001E+01
+ 0.769323906E+05 0.337817192E+00 0.000000000E+00 0.200259857E+02 0.000000000E+00
+ 0.390171977E-06 0.000000000E+00 0.337817194E-02 0.000000000E+00 0.000000000E+00
+ 0.400046501E+02 0.400044861E+02 0.400043259E+02 0.400041695E+02 0.400040169E+02
+ 0.400038719E+02 0.400037270E+02 0.400035896E+02 0.400034523E+02 0.400033226E+02
+ 0.400031967E+02 0.400030746E+02 0.400029526E+02 0.400028381E+02 0.400027275E+02
+ 0.400026169E+02 0.400025139E+02 0.400024109E+02 0.400023117E+02 0.400022163E+02
+ 0.400021248E+02 0.400020370E+02 0.400019493E+02 0.400018654E+02 0.400017853E+02
+ 0.400017090E+02 0.400016327E+02 0.400015602E+02 0.400014915E+02 0.400014229E+02
+ 0.400013580E+02 0.400012970E+02 0.400012360E+02 0.400011787E+02 0.400011215E+02
+ 0.400010681E+02 0.400010185E+02 0.400009651E+02 0.400009193E+02 0.400008736E+02
+ 0.400008278E+02 0.400007858E+02 0.400007477E+02 0.400007057E+02 0.400006714E+02
+ 0.400006332E+02 0.400005989E+02 0.400005684E+02 0.400005341E+02 0.400005035E+02
+ 0.400004768E+02 0.400004501E+02 0.400004234E+02 0.400003967E+02 0.400003738E+02
+ 0.400003510E+02 0.400003319E+02 0.400003090E+02 0.400002899E+02 0.400002708E+02
+ 0.400002556E+02 0.400002365E+02 0.400002213E+02 0.400002060E+02 0.400001945E+02
+ 0.400001793E+02 0.400001678E+02 0.400001564E+02 0.400001450E+02 0.400001335E+02
+ 0.400001221E+02 0.400001144E+02 0.400001068E+02 0.400000954E+02 0.400000877E+02
+ 0.400000801E+02 0.400000763E+02 0.400000687E+02 0.400000610E+02 0.400000572E+02
+ 0.400000534E+02 0.400000458E+02 0.400000420E+02 0.400000381E+02 0.400000343E+02
+ 0.400000305E+02 0.400000267E+02 0.400000267E+02 0.400000229E+02 0.400000191E+02
+ 0.400000191E+02 0.400000153E+02 0.400000153E+02 0.400000114E+02 0.400000114E+02
+ 0.400000114E+02 0.400000076E+02 0.400000076E+02 0.400000076E+02 0.400000038E+02
+ 0.400000038E+02 0.400000038E+02 0.400000038E+02 0.400000038E+02 0.400000038E+02
+ 0.400000038E+02 0.400000000E+02 0.400000000E+02 0.400000000E+02 0.400000000E+02
+ 0.400000000E+02 0.400000000E+02 0.400000000E+02 0.400000000E+02 0.400000000E+02
+ 0.400000000E+02 0.400000000E+02 0.400000000E+02 0.400000000E+02 0.400000000E+02
+ 0.400000000E+02 0.400000000E+02 0.400000000E+02 0.400000000E+02 0.400000000E+02
+ 0.400000000E+02 0.400000000E+02 0.400000000E+02 0.400000000E+02
+ 0.300390015E+03 0.295761353E+03 0.291168579E+03 0.286611786E+03 0.282090912E+03
+ 0.277605988E+03 0.273156982E+03 0.268743927E+03 0.264366821E+03 0.260025635E+03
+ 0.255720398E+03 0.251451096E+03 0.247217743E+03 0.243020309E+03 0.238858826E+03
+ 0.234733292E+03 0.230643692E+03 0.226590027E+03 0.222572296E+03 0.218590515E+03
+ 0.214644669E+03 0.210734756E+03 0.206860779E+03 0.203022751E+03 0.199220657E+03
+ 0.195454514E+03 0.191724289E+03 0.188030014E+03 0.184371689E+03 0.180749283E+03
+ 0.177162827E+03 0.173612305E+03 0.170097733E+03 0.166619095E+03 0.163176392E+03
+ 0.159769623E+03 0.156398804E+03 0.153063919E+03 0.149764969E+03 0.146501968E+03
+ 0.143274902E+03 0.140083771E+03 0.136928574E+03 0.133809326E+03 0.130726013E+03
+ 0.127678642E+03 0.124667206E+03 0.121691711E+03 0.118752159E+03 0.115848541E+03
+ 0.112980865E+03 0.110149124E+03 0.107353325E+03 0.104593460E+03 0.101869537E+03
+ 0.991815567E+02 0.965295105E+02 0.939134064E+02 0.913332443E+02 0.887890167E+02
+ 0.862807312E+02 0.838083801E+02 0.813719711E+02 0.789714966E+02 0.766069641E+02
+ 0.742783737E+02 0.719857178E+02 0.697290039E+02 0.675082321E+02 0.653233948E+02
+ 0.631744957E+02 0.610615349E+02 0.589845161E+02 0.569434357E+02 0.549382935E+02
+ 0.529690895E+02 0.510358238E+02 0.491385002E+02 0.472771149E+02 0.454516678E+02
+ 0.436621590E+02 0.419085922E+02 0.401909599E+02 0.385092697E+02 0.368635178E+02
+ 0.352537041E+02 0.336798325E+02 0.321418953E+02 0.306399002E+02 0.291738434E+02
+ 0.277437248E+02 0.263495464E+02 0.249913063E+02 0.236690044E+02 0.223826427E+02
+ 0.211322193E+02 0.199177361E+02 0.187391911E+02 0.175965843E+02 0.164899178E+02
+ 0.154191904E+02 0.143844013E+02 0.133855515E+02 0.124226398E+02 0.114956684E+02
+ 0.106046352E+02 0.974954128E+01 0.893038654E+01 0.814717007E+01 0.739989328E+01
+ 0.668855524E+01 0.601315594E+01 0.537369585E+01 0.477017498E+01 0.420259285E+01
+ 0.367094994E+01 0.317524576E+01 0.271548080E+01 0.229165459E+01 0.190376759E+01
+ 0.155181956E+01 0.123581052E+01 0.955740452E+00 0.711609364E+00 0.503417313E+00
+ 0.331164241E+00 0.194850162E+00 0.944750831E-01 0.300390031E-01
+ 0.256577325E+01 0.249465060E+01 0.242352796E+01 0.235523653E+01 0.228710127E+01
+ 0.222157001E+01 0.215634274E+01 0.209350085E+01 0.203110290E+01 0.197088075E+01
+ 0.191123378E+01 0.185356236E+01 0.179658973E+01 0.174140048E+01 0.168702602E+01
+ 0.163425148E+01 0.158239985E+01 0.153197300E+01 0.148257005E+01 0.143442488E+01
+ 0.138739693E+01 0.134146798E+01 0.129674256E+01 0.125296533E+01 0.121047056E+01
+ 0.116878116E+01 0.112844646E+01 0.108878171E+01 0.105053723E+01 0.101283479E+01
+ 0.976611435E+00 0.940809906E+00 0.906539679E+00 0.872578204E+00 0.840194046E+00
+ 0.808012664E+00 0.777448356E+00 0.746987939E+00 0.718178272E+00 0.689380288E+00
+ 0.662261069E+00 0.635141850E+00 0.609575868E+00 0.584083676E+00 0.560003459E+00
+ 0.536076009E+00 0.513426602E+00 0.491002500E+00 0.469729662E+00 0.448748529E+00
+ 0.428798914E+00 0.409201384E+00 0.390522510E+00 0.372250110E+00 0.354790330E+00
+ 0.337785691E+00 0.321494222E+00 0.305700928E+00 0.290527821E+00 0.275890529E+00
+ 0.261786699E+00 0.248251110E+00 0.235168353E+00 0.222681180E+00 0.210572213E+00
+ 0.199081212E+00 0.187899619E+00 0.177353665E+00 0.167053923E+00 0.157402918E+00
+ 0.147940442E+00 0.139135405E+00 0.130466521E+00 0.122459576E+00 0.114541531E+00
+ 0.107285909E+00 0.100076906E+00 0.935269743E-01 0.869861618E-01 0.810974315E-01
+ 0.752087012E-01 0.699140653E-01 0.646432117E-01 0.598958284E-01 0.552006923E-01
+ 0.509638377E-01 0.468034633E-01 0.430414379E-01 0.393760800E-01 0.360542126E-01
+ 0.328453556E-01 0.299300384E-01 0.271404181E-01 0.245991088E-01 0.221927371E-01
+ 0.199939795E-01 0.179361664E-01 0.160496160E-01 0.143069895E-01 0.127034280E-01
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diff --git a/examples/fourier_transform_usage.jl b/examples/fourier_transform_usage.jl
new file mode 100644
index 0000000000..19539f7d39
--- /dev/null
+++ b/examples/fourier_transform_usage.jl
@@ -0,0 +1,187 @@
+"""
+Example: Using FourierTransforms utility for different grids
+
+This example demonstrates how to use the FourierTransforms utility module
+to create pre-computed Fourier transform objects for different grids:
+
+1. PerturbedEquilibrium: Simple harmonic basis (no phase shift)
+2. Vacuum: Basis with toroidal phase coupling (n*qa*delta)
+"""
+
+using GeneralizedPerturbedEquilibrium
+using GeneralizedPerturbedEquilibrium.Utilities.FourierTransforms
+
+# ==============================================================================
+# Example 1: PerturbedEquilibrium Case (No Phase Shift)
+# ==============================================================================
+println("\n" * "="^70)
+println("Example 1: PerturbedEquilibrium - Simple Harmonic Basis")
+println("="^70)
+
+# Grid parameters for PerturbedEquilibrium
+mtheta = 480 # Number of theta grid points
+mpert = 41 # Number of Fourier modes
+mlow = -20 # Lowest mode number
+
+# Create FourierTransform object (no phase shift, default arguments)
+ft_pe = FourierTransform(mtheta, mpert, mlow)
+
+println("Created FourierTransform for PerturbedEquilibrium:")
+println(" mtheta = $mtheta (theta grid points)")
+println(" mpert = $mpert (number of modes)")
+println(" mlow = $mlow (lowest mode: m ∈ [$mlow, $(mlow+mpert-1)])")
+println("\nBasis functions: cos(m*θ), sin(m*θ) with m = $mlow:$(mlow+mpert-1)")
+
+# Create test data: a simple function in theta space
+theta = range(0, 2π; length=mtheta + 1)[1:(end-1)]
+f_theta = sin.(5 .* theta) .+ 0.5 .* cos.(8 .* theta)
+
+# Forward transform: theta → modes
+println("\n--- Forward Transform ---")
+modes = ft_pe(f_theta)
+println("Input: f(θ) at $mtheta theta points (real-valued)")
+println("Output: $mpert complex Fourier modes")
+println("Dominant modes (|amplitude| > 0.01):")
+for l in 1:mpert
+ m = mlow + l - 1
+ if abs(modes[l]) > 0.01
+ println(" m=$m: amplitude = $(abs(modes[l])), phase = $(angle(modes[l]))")
+ end
+end
+
+# Inverse transform: modes → theta
+println("\n--- Inverse Transform ---")
+f_reconstructed = inverse(ft_pe, modes)
+println("Input: $mpert complex Fourier modes")
+println("Output: $(length(f_reconstructed)) theta-space values")
+println("Reconstruction error: $(maximum(abs.(real.(f_reconstructed) .- f_theta)))")
+
+# ==============================================================================
+# Example 2: Vacuum Case (With Toroidal Phase)
+# ==============================================================================
+println("\n" * "="^70)
+println("Example 2: Vacuum - Basis with Toroidal Coupling")
+println("="^70)
+
+# Grid parameters for Vacuum
+mthvac = 480 # Number of vacuum theta grid points
+mpert_vac = 41 # Number of Fourier modes
+mlow_vac = -20 # Lowest mode number
+n = 1 # Toroidal mode number
+qa = 2.5 # Safety factor at boundary
+delta = zeros(mthvac) # Toroidal phase shift (zero for this example)
+
+# Create FourierTransform object with toroidal phase
+ft_vac = FourierTransform(mthvac, mpert_vac, mlow_vac; n=n, qa=qa, delta=delta)
+
+println("Created FourierTransform for Vacuum:")
+println(" mthvac = $mthvac (vacuum theta grid points)")
+println(" mpert = $mpert_vac (number of modes)")
+println(" mlow = $mlow_vac (lowest mode: m ∈ [$mlow_vac, $(mlow_vac+mpert_vac-1)])")
+println(" n = $n (toroidal mode number)")
+println(" qa = $qa (safety factor)")
+println("\nBasis functions: cos(m*θ + n*qa*δ), sin(m*θ + n*qa*δ)")
+
+# Example: Transform Green's function data
+g_theta = randn(mthvac) # Simulated Green's function in theta space
+println("\n--- Forward Transform (Green's function) ---")
+g_modes = ft_vac(g_theta)
+println("Transformed $mthvac theta-space values to $mpert_vac complex modes")
+
+# Inverse transform back
+g_reconstructed = inverse(ft_vac, g_modes)
+println("\n--- Inverse Transform ---")
+println("Reconstruction error: $(maximum(abs.(real.(g_reconstructed) .- g_theta)))")
+
+# ==============================================================================
+# Example 3: Multiple Functions Simultaneously
+# ==============================================================================
+println("\n" * "="^70)
+println("Example 3: Batch Transform (Multiple Functions)")
+println("="^70)
+
+# Create matrix of multiple theta-space functions
+n_funcs = 10
+data_matrix = randn(mtheta, n_funcs)
+
+println("Transforming $n_funcs functions simultaneously")
+println("Input shape: ($(size(data_matrix, 1)), $(size(data_matrix, 2)))")
+
+# Forward transform all at once
+modes_matrix = ft_pe(data_matrix)
+println("Output shape: ($(size(modes_matrix, 1)), $(size(modes_matrix, 2)))")
+println(" → Each column is one transformed function")
+
+# Inverse transform
+reconstructed_matrix = inverse(ft_pe, modes_matrix)
+max_error = maximum(abs.(real.(reconstructed_matrix) .- data_matrix))
+println("\nMax reconstruction error across all functions: $max_error")
+
+# ==============================================================================
+# Example 4: Replacing FFTW in existing code
+# ==============================================================================
+println("\n" * "="^70)
+println("Example 4: Migration from FFTW")
+println("="^70)
+
+using FFTW
+
+# Old approach: using FFTW
+function theta_to_modes_fftw(theta_values::Vector{Float64}, mpert::Int)
+ mtheta = length(theta_values)
+ fft_result = fft(theta_values)
+ modes = zeros(ComplexF64, mpert)
+ for i in 1:min(mpert, length(fft_result))
+ modes[i] = fft_result[i] / mtheta
+ end
+ return modes
+end
+
+# New approach: using FourierTransform
+# (already shown above: modes = ft_pe(theta_values))
+
+# Compare approaches
+test_data = randn(mtheta)
+modes_fft = theta_to_modes_fftw(test_data, mpert)
+modes_custom = ft_pe(test_data)
+
+println("Comparison of FFTW vs FourierTransform:")
+println(" Both methods transform $mtheta theta points to $mpert modes")
+println(" Results differ because:")
+println(" - FFTW uses exp(i*k*θ) basis (standard FFT)")
+println(" - FourierTransform uses cos(m*θ) + i*sin(m*θ) basis")
+println(" - FourierTransform allows custom mode range (m = $mlow:$(mlow+mpert-1))")
+println(" - FourierTransform supports phase shifts for vacuum calculations")
+
+# ==============================================================================
+# Summary
+# ==============================================================================
+println("\n" * "="^70)
+println("Summary: When to Use FourierTransform")
+println("="^70)
+println("""
+1. Pre-compute transforms for a specific grid:
+ ft = FourierTransform(mtheta, mpert, mlow)
+
+2. For PerturbedEquilibrium (no phase shift):
+ ft = FourierTransform(mtheta, mpert, mlow)
+ modes = ft(theta_data)
+
+3. For Vacuum (with toroidal coupling):
+ ft = FourierTransform(mthvac, mpert, mlow; n=n, qa=qa, delta=delta)
+ modes = ft(green_function_data)
+
+4. Avoid FFTW when:
+ - You need custom mode ranges (not 0:N-1)
+ - You need phase-shifted basis functions
+ - You want to pre-compute and reuse coefficients
+ - You're matching Vacuum module conventions
+
+5. Benefits:
+ - Type-stable, efficient functor pattern
+ - Pre-computed basis functions (no repeated trig calculations)
+ - Direct complex number support
+ - Consistent interface across modules
+""")
+
+println("="^70)
diff --git a/gpec b/gpec
new file mode 100755
index 0000000000..fbc0c78f40
--- /dev/null
+++ b/gpec
@@ -0,0 +1,7 @@
+#!/usr/bin/env -S julia --project=@script
+# GPEC executable script
+# Usage: ./gpec [path/to/directory]
+# If no path is provided, uses current directory
+
+using GeneralizedPerturbedEquilibrium
+GeneralizedPerturbedEquilibrium.main(ARGS)
diff --git a/notebooks/Chease_Binary_example/INP1 b/notebooks/Chease_Binary_example/INP1
deleted file mode 100644
index 7a39ceeab6..0000000000
Binary files a/notebooks/Chease_Binary_example/INP1 and /dev/null differ
diff --git a/notebooks/Chease_Binary_example/equil.toml b/notebooks/Chease_Binary_example/equil.toml
deleted file mode 100644
index e75c90ec22..0000000000
--- a/notebooks/Chease_Binary_example/equil.toml
+++ /dev/null
@@ -1,30 +0,0 @@
-[EQUIL_CONTROL]
-eq_type = "chease" # Type of the input 2D equilibrium file
-eq_filename = "INP1" # path to equilibrium file
-
-jac_type = "hamada" # Coordinate system (hamada, pest, boozer, equal_arc)
-power_bp = 0 # del.B ~ B_p^power_bp * B^power_b / R^power_r
-power_b = 0 # del.B ~ B_p^power_bp * B^power_b / R^power_r
-power_r = 0 # del.B ~ B_p^power_bp * B^power_b / R^power_r
-
-grid_type = "ldp" # Radial grid packing
-psilow = 1e-4 # Min psi (normalized)
-psihigh = 0.993 # Max psi (normalized)
-mpsi = 128 # Radial grid intervals
-mtheta = 256 # Poloidal grid intervals
-
-newq0 = 0 # Override q(0)
-etol = 1e-7 # Reconstruction tolerance
-use_classic_splines = false # Use classical spline (vs. tri-diagonal)
-
-input_only = false # Quit after input read
-
-[EQUIL_OUTPUT]
-gse_flag = false # Output G-S equation accuracy diagnostics
-out_eq_1d = false # ASCII output of 1D eq data
-bin_eq_1d = false # Binary output of 1D eq data
-out_eq_2d = false # ASCII output of 2D eq data
-bin_eq_2d = true # Binary output of 2D eq data (used by GPEC)
-out_2d = false # ASCII output of processed 2D data
-bin_2d = false # Binary output of processed 2D data
-dump_flag = false # Binary dump of equilibrium data
diff --git a/notebooks/DIIID_example/dcon.toml b/notebooks/DIIID_example/dcon.toml
deleted file mode 100644
index a0a93c8bfc..0000000000
--- a/notebooks/DIIID_example/dcon.toml
+++ /dev/null
@@ -1,62 +0,0 @@
-[DCON_CONTROL]
-bal_flag = false # Ideal MHD ballooning criterion for short wavelengths
-mat_flag = true # Construct coefficient matrices for diagnostic purposes
-ode_flag = true # Integrate ODE's for determining stability of internal long-wavelength mode (must be true for GPEC)
-vac_flag = true # Compute plasma, vacuum, and total energies for free-boundary modes
-mer_flag = true # Evaluate the Mercier criterian
-
-sas_flag = true # Safety factor (q) limit determined as q_ir+dmlim...
-dmlim = 0.2 # See sas_flag
-psiedge = 1.00 # If less then psilim, calculates dW(psi)...
-qlow = 1.02 # Integration initiated at q determined by min(q0, qlow)...
-qhigh = 1e3 # Integration terminated at q limit determined by min(qa, qhigh)...
-sing_start = 0 # Start integration at the sing_start'th rational from the axis (psilow)
-
-nn = 1 # Toroidal mode number
-delta_mlow = 8 # Expands lower bound of Fourier harmonics
-delta_mhigh = 8 # Expands upper bound of Fourier harmonics
-delta_mband = 0 # Integration keeps only this wide a band...
-mthvac = 512 # Number of points used in splines over poloidal angle at plasma-vacuum interface.
-thmax0 = 1 # Linear multiplier on the automatic choice of theta integration bounds
-
-kin_flag = false # Kinetic EL equation (default: false)
-con_flag = false # Continue integration through layers (default: false)
-kinfac1 = 1.0 # Scale factor for energy contribution (default: 1.0)
-kinfac2 = 1.0 # Scale factor for torque contribution (default: 1.0)
-kingridtype = 0 # Regular grid method (default: 0)
-passing_flag = true # Includes passing particle effects (default: false)
-ktanh_flag = true # Ignore kinetic effects in the core smoothly (default: false)
-ktc = 0.1 # Parameter for ktanh_flag (default: 0.1)
-ktw = 50.0 # Parameter for ktanh_flag (default: 50.0)
-ion_flag = true # Include ion dW_k when kin_flag is true
-electron_flag = false # Include electron dW_k when kin_flag is true
-
-tol_nr = 1e-6 # Relative tolerance of dynamic integration steps away from rationals
-tol_r = 1e-7 # Relative tolerance of dynamic integration steps near rationals
-crossover = 1e-2 # Fractional distance from rational q at which tol switches
-singfac_min = 1e-4 # Fractional distance from rational q at which ideal jump enforced
-ucrit = 1e4 # Maximum fraction of solutions allowed before re-normalized
-
-numunorms_init = 30 # Storage size for unorming data
-
-termbycross_flag = false # Terminate ODE solver in the event of a zero crossing
-
-use_classic_splines = false # Use a classical cubic spline instead of tri-diagonal solution
-
-[DCON_OUTPUT]
-out_ahg2msc = false # Output deprecated ahg2msc.out files
-crit_break = true # Color of the crit curve changes when crossing a singular surface
-ahb_flag = false # Output normal magnetic field eigenvalues...
-msol_ahb = 1 # Number of eigenfunctions output by ahb_flag = true?
-mthsurf0 = 1 # Linear multiplier on number of boundary points for ahgb_flag = true
-
-bin_euler = true # Output M psi-by-M euler-lagrange solutions to binary file euler.bin
-bin_vac = false # Output deprecated binary vacuum.bin
-euler_stride = 1 # Output only every euler_stride'th psi step
-
-out_bal1 = false # Ascii output for bal_flag poloidal functions
-bin_bal1 = false # Binary output for bal_flag poloidal functions
-out_bal2 = false # Ascii output for bal_flag functions
-bin_bal2 = false # Binary output for bal_flag functions
-
-netcdf_out = true # Replicate ascii dcon.out information in a netcdf file
\ No newline at end of file
diff --git a/notebooks/DIIID_example/equil.toml b/notebooks/DIIID_example/equil.toml
deleted file mode 100644
index 0b230bdd57..0000000000
--- a/notebooks/DIIID_example/equil.toml
+++ /dev/null
@@ -1,30 +0,0 @@
-[EQUIL_CONTROL]
-eq_type = "efit" # Type of the input 2D equilibrium file
-eq_filename = "g147131.02300_DIIID_KEFIT" # path to equilibrium file
-
-jac_type = "hamada" # Coordinate system (hamada, pest, boozer, equal_arc)
-power_bp = 0 # del.B ~ B_p^power_bp * B^power_b / R^power_r
-power_b = 0 # del.B ~ B_p^power_bp * B^power_b / R^power_r
-power_r = 0 # del.B ~ B_p^power_bp * B^power_b / R^power_r
-
-grid_type = "ldp" # Radial grid packing
-psilow = 1e-4 # Min psi (normalized)
-psihigh = 0.993 # Max psi (normalized)
-mpsi = 128 # Radial grid intervals
-mtheta = 256 # Poloidal grid intervals
-
-newq0 = 0 # Override q(0)
-etol = 1e-7 # Reconstruction tolerance
-use_classic_splines = false # Use classical spline (vs. tri-diagonal)
-
-input_only = false # Quit after input read
-
-[EQUIL_OUTPUT]
-gse_flag = false # Output G-S equation accuracy diagnostics
-out_eq_1d = false # ASCII output of 1D eq data
-bin_eq_1d = false # Binary output of 1D eq data
-out_eq_2d = false # ASCII output of 2D eq data
-bin_eq_2d = true # Binary output of 2D eq data (used by GPEC)
-out_2d = false # ASCII output of processed 2D data
-bin_2d = false # Binary output of processed 2D data
-dump_flag = false # Binary dump of equilibrium data
diff --git a/notebooks/DIIID_example/g147131.02300_DIIID_KEFIT b/notebooks/DIIID_example/g147131.02300_DIIID_KEFIT
deleted file mode 100644
index 15da8c793c..0000000000
--- a/notebooks/DIIID_example/g147131.02300_DIIID_KEFIT
+++ /dev/null
@@ -1,6668 +0,0 @@
- EFITD 03/13/2012 #147131 2300ms 3 129 129
- 0.170000000E+01 0.320000000E+01 0.169550002E+01 0.840000000E+00 0.000000000E+00
- 0.175888032E+01 0.244191348E-01-0.299591296E+00-0.373057194E-01-0.172279610E+01
- 0.118663454E+07-0.299591296E+00 0.000000000E+00 0.175888032E+01 0.000000000E+00
- 0.244191348E-01 0.000000000E+00-0.373057194E-01 0.000000000E+00 0.000000000E+00
--0.297297920E+01-0.297233876E+01-0.297167564E+01-0.297099331E+01-0.297029482E+01
--0.296958285E+01-0.296885979E+01-0.296812772E+01-0.296738851E+01-0.296664379E+01
--0.296589500E+01-0.296514342E+01-0.296439017E+01-0.296363625E+01-0.296288254E+01
--0.296212982E+01-0.296137877E+01-0.296062999E+01-0.295988403E+01-0.295914135E+01
--0.295840238E+01-0.295766748E+01-0.295693699E+01-0.295621119E+01-0.295549033E+01
--0.295477465E+01-0.295406434E+01-0.295335959E+01-0.295266055E+01-0.295196735E+01
--0.295128013E+01-0.295059899E+01-0.294992403E+01-0.294925534E+01-0.294859299E+01
--0.294793705E+01-0.294728758E+01-0.294664464E+01-0.294600827E+01-0.294537852E+01
--0.294475542E+01-0.294413902E+01-0.294352934E+01-0.294292640E+01-0.294233024E+01
--0.294174088E+01-0.294115833E+01-0.294058261E+01-0.294001375E+01-0.293945175E+01
--0.293889663E+01-0.293834841E+01-0.293780708E+01-0.293727267E+01-0.293674519E+01
--0.293622463E+01-0.293571101E+01-0.293520434E+01-0.293470463E+01-0.293421187E+01
--0.293372607E+01-0.293324725E+01-0.293277540E+01-0.293231053E+01-0.293185264E+01
--0.293140174E+01-0.293095782E+01-0.293052090E+01-0.293009097E+01-0.292966803E+01
--0.292925209E+01-0.292884315E+01-0.292844120E+01-0.292804625E+01-0.292765830E+01
--0.292727734E+01-0.292690337E+01-0.292653638E+01-0.292617638E+01-0.292582336E+01
--0.292547731E+01-0.292513823E+01-0.292480611E+01-0.292448095E+01-0.292416274E+01
--0.292385147E+01-0.292354713E+01-0.292324972E+01-0.292295922E+01-0.292267562E+01
--0.292239890E+01-0.292212905E+01-0.292186606E+01-0.292160989E+01-0.292136052E+01
--0.292111794E+01-0.292088209E+01-0.292065296E+01-0.292043049E+01-0.292021465E+01
--0.292000537E+01-0.291980260E+01-0.291960626E+01-0.291941629E+01-0.291923259E+01
--0.291905507E+01-0.291888360E+01-0.291871807E+01-0.291855854E+01-0.291840555E+01
--0.291826023E+01-0.291812434E+01-0.291800028E+01-0.291789115E+01-0.291780078E+01
--0.291773380E+01-0.291769570E+01-0.291769292E+01-0.291773297E+01-0.291782483E+01
--0.291798706E+01-0.291825905E+01-0.291866469E+01-0.291916231E+01-0.291967537E+01
--0.292014273E+01-0.292052751E+01-0.292081336E+01-0.292100082E+01
- 0.767620766E+05 0.755059656E+05 0.742807174E+05 0.730839467E+05 0.719135482E+05
- 0.707676640E+05 0.696446547E+05 0.685430732E+05 0.674616426E+05 0.663992361E+05
- 0.653548590E+05 0.643276337E+05 0.633167856E+05 0.623216310E+05 0.613415665E+05
- 0.603760596E+05 0.594246402E+05 0.584868937E+05 0.575624536E+05 0.566509967E+05
- 0.557522377E+05 0.548659245E+05 0.539918347E+05 0.531297716E+05 0.522795616E+05
- 0.514410514E+05 0.506141052E+05 0.497986031E+05 0.489944389E+05 0.482015186E+05
- 0.474197588E+05 0.466490855E+05 0.458894328E+05 0.451407421E+05 0.444029609E+05
- 0.436760424E+05 0.429599442E+05 0.422546281E+05 0.415600592E+05 0.408762057E+05
- 0.402030381E+05 0.395405287E+05 0.388886515E+05 0.382473814E+05 0.376166942E+05
- 0.369965659E+05 0.363869724E+05 0.357878894E+05 0.351992914E+05 0.346211520E+05
- 0.340534432E+05 0.334961347E+05 0.329491938E+05 0.324125847E+05 0.318862682E+05
- 0.313702005E+05 0.308643333E+05 0.303686123E+05 0.298829768E+05 0.294073588E+05
- 0.289416816E+05 0.284858588E+05 0.280397930E+05 0.276033740E+05 0.271764775E+05
- 0.267589629E+05 0.263506710E+05 0.259514217E+05 0.255610111E+05 0.251792085E+05
- 0.248057525E+05 0.244403469E+05 0.240826563E+05 0.237323009E+05 0.233888502E+05
- 0.230518166E+05 0.227206476E+05 0.223947173E+05 0.220733432E+05 0.217558604E+05
- 0.214416785E+05 0.211302797E+05 0.208212111E+05 0.205140776E+05 0.202085355E+05
- 0.199042872E+05 0.196010769E+05 0.192986859E+05 0.189969298E+05 0.186956553E+05
- 0.183947379E+05 0.180940800E+05 0.177936092E+05 0.174932774E+05 0.171930598E+05
- 0.168929546E+05 0.165929833E+05 0.162931904E+05 0.159936446E+05 0.156944398E+05
- 0.153956963E+05 0.150975630E+05 0.148002196E+05 0.145038792E+05 0.142087921E+05
- 0.139152494E+05 0.136235876E+05 0.133341656E+05 0.130469733E+05 0.127609995E+05
- 0.124739500E+05 0.121822064E+05 0.118807691E+05 0.115631791E+05 0.112214172E+05
- 0.108457785E+05 0.104247204E+05 0.994468202E+04 0.938987215E+04 0.874138645E+04
- 0.796050283E+04 0.696648059E+04 0.572148983E+04 0.434331221E+04 0.302648173E+04
- 0.191878149E+04 0.109840443E+04 0.563472273E+03 0.250145176E+03
--0.911430759E+00-0.946775258E+00-0.976776409E+00-0.100206207E+01-0.102318633E+01
--0.104063817E+01-0.105484910E+01-0.106619994E+01-0.107502677E+01-0.108162616E+01
--0.108625984E+01-0.108915880E+01-0.109052686E+01-0.109054392E+01-0.108936871E+01
--0.108714135E+01-0.108398545E+01-0.108001013E+01-0.107531167E+01-0.106997505E+01
--0.106407525E+01-0.105767845E+01-0.105084305E+01-0.104362060E+01-0.103605656E+01
--0.102819109E+01-0.102005961E+01-0.101169338E+01-0.100311998E+01-0.994363770E+00
--0.985446230E+00-0.976386327E+00-0.967200795E+00-0.957904406E+00-0.948510195E+00
--0.939029668E+00-0.929472981E+00-0.919849097E+00-0.910165928E+00-0.900430460E+00
--0.890648860E+00-0.880826570E+00-0.870968402E+00-0.861078600E+00-0.851160917E+00
--0.841218669E+00-0.831254787E+00-0.821271865E+00-0.811272197E+00-0.801257817E+00
--0.791230527E+00-0.781191928E+00-0.771143445E+00-0.761086347E+00-0.751021768E+00
--0.740950726E+00-0.730874137E+00-0.720792832E+00-0.710707565E+00-0.700619031E+00
--0.690527873E+00-0.680434692E+00-0.670340058E+00-0.660244519E+00-0.650148608E+00
--0.640052852E+00-0.629957781E+00-0.619863935E+00-0.609771874E+00-0.599682187E+00
--0.589595496E+00-0.579512475E+00-0.569433852E+00-0.559360424E+00-0.549293072E+00
--0.539232769E+00-0.529180599E+00-0.519137773E+00-0.509105243E+00-0.499083227E+00
--0.489071983E+00-0.479071940E+00-0.469083699E+00-0.459108050E+00-0.449145977E+00
--0.439198676E+00-0.429267577E+00-0.419354360E+00-0.409460988E+00-0.399589732E+00
--0.389743210E+00-0.379924428E+00-0.370136823E+00-0.360384324E+00-0.350671405E+00
--0.341003163E+00-0.331385391E+00-0.321824673E+00-0.312328485E+00-0.302905315E+00
--0.293564789E+00-0.284317830E+00-0.275176823E+00-0.266155810E+00-0.257270713E+00
--0.248539578E+00-0.239982861E+00-0.231586985E+00-0.222855615E+00-0.212944521E+00
--0.200983819E+00-0.186071558E+00-0.167259611E+00-0.143538837E+00-0.113823295E+00
--0.769332548E-01-0.315767378E-01 0.236706957E-01 0.903882322E-01 0.171213058E+00
- 0.290801074E+00 0.483881839E+00 0.671604565E+00 0.746098232E+00 0.715833223E+00
- 0.616102304E+00 0.480663723E+00 0.334205417E+00 0.200214330E+00
--0.620844410E+06-0.605164368E+06-0.590721145E+06-0.577369417E+06-0.564980938E+06
--0.553442532E+06-0.542654324E+06-0.532528173E+06-0.522986299E+06-0.513960063E+06
--0.505388891E+06-0.497219331E+06-0.489404214E+06-0.481901915E+06-0.474675706E+06
--0.467693174E+06-0.460925723E+06-0.454348119E+06-0.447938100E+06-0.441676026E+06
--0.435544569E+06-0.429528447E+06-0.423614183E+06-0.417789891E+06-0.412045096E+06
--0.406370563E+06-0.400758159E+06-0.395200722E+06-0.389691950E+06-0.384226303E+06
--0.378798916E+06-0.373405520E+06-0.368042382E+06-0.362706238E+06-0.357394249E+06
--0.352103953E+06-0.346833229E+06-0.341580259E+06-0.336343506E+06-0.331121686E+06
--0.325913746E+06-0.320718854E+06-0.315536379E+06-0.310365887E+06-0.305207129E+06
--0.300060041E+06-0.294924741E+06-0.289801532E+06-0.284690905E+06-0.279593550E+06
--0.274510363E+06-0.269442461E+06-0.264391202E+06-0.259358204E+06-0.254345369E+06
--0.249354916E+06-0.244389414E+06-0.239451823E+06-0.234545538E+06-0.229674444E+06
--0.224842979E+06-0.220056198E+06-0.215319857E+06-0.210640500E+06-0.206025564E+06
--0.201483492E+06-0.197023868E+06-0.192657566E+06-0.188396920E+06-0.184255916E+06
--0.180250415E+06-0.176398394E+06-0.172720233E+06-0.169239034E+06-0.165980976E+06
--0.162975733E+06-0.160256934E+06-0.157862566E+06-0.155809973E+06-0.154064431E+06
--0.152588260E+06-0.151347995E+06-0.150313861E+06-0.149459308E+06-0.148760596E+06
--0.148196423E+06-0.147747593E+06-0.147396712E+06-0.147127920E+06-0.146926643E+06
--0.146779360E+06-0.146673397E+06-0.146596726E+06-0.146537776E+06-0.146485256E+06
--0.146427973E+06-0.146354661E+06-0.146253802E+06-0.146113448E+06-0.145921033E+06
--0.145663176E+06-0.145325472E+06-0.144892268E+06-0.144346415E+06-0.143669003E+06
--0.142839064E+06-0.141833243E+06-0.140652774E+06-0.139657113E+06-0.139463467E+06
--0.140706942E+06-0.144045131E+06-0.150168398E+06-0.159810680E+06-0.173760971E+06
--0.192875664E+06-0.218091954E+06-0.250442495E+06-0.291071558E+06-0.341873422E+06
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- &OUT1
- ISHOT = 147131
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- BTOR = -1.722796100000000
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- 0.000000000000000 0.000000000000000 0.000000000000000
- 0.000000000000000 0.000000000000000 0.000000000000000
- 0.000000000000000 0.000000000000000 0.000000000000000
- 0.000000000000000 0.000000000000000 0.000000000000000
- 0.000000000000000 0.000000000000000 0.000000000000000
- 0.000000000000000 0.000000000000000 0.000000000000000
- NBDRY = 90
- FWTSI = 999.9999525025510 502.7561595422264
- 525.7968003582148 506.1858953527478 506.8771572058214
- 211.9550215768744 0.000000000000000 505.2394850316234
- 495.9030553849408 505.6915840632106 505.5450199973388
- 506.4652056124651 445.6379373054061 339.4241436441839
- 211.4447825088264 126.4849676858440 268.4531183007420
- 495.9911793729846 501.5195037925907 505.6647344711498
- 505.1554396122791 504.7541531802667 504.7202701464773
- 504.0551234683026 493.1866586273251 271.9614490441583
- 330.0603505877313 183.5406913833808 275.3046219429248
- 504.8467050649704 0.000000000000000 506.0926981654039
- 399.5468805559500 315.1652428137394 451.1731822929428
- 157.1123584716163 176.4455436855753 167.4543809404153
- 239.3754681146945 388.4037211457047 504.5986089629227
- 0.000000000000000 505.7599227441602 471.4974429964933
- FWTCUR = 2.7911077050807992E-005
- MXITER = 200
- NXITER = 1
- LIMITR = 85
- XLIM = 1.016000000000000 1.016000000000000
- 1.016000000000000 1.016000000000000 1.016000000000000
- 1.016000000000000 1.016000000000000 1.016000000000000
- 1.016000000000000 1.016000000000000 1.016000000000000
- 1.012000000000000 1.001000000000000 1.029000000000000
- 1.042000000000000 1.046000000000000 1.056000000000000
- 1.097000000000000 1.108000000000000 1.116000000000000
- 1.134000000000000 1.148000000000000 1.162000000000000
- 1.181000000000000 1.182000000000000 1.185000000000000
- 1.190000000000000 1.195000000000000 1.201000000000000
- 1.209000000000000 1.215000000000000 1.222000000000000
- 1.228000000000000 1.234000000000000 1.239000000000000
- 1.242000000000000 1.248000000000000 1.258000000000000
- 1.263000000000000 1.280000000000000 1.280000000000000
- 1.280000000000000 1.310000000000000 1.328000000000000
- 1.361000000000000 1.380000000000000 1.419000000000000
- 1.419000000000000 1.372000000000000 1.372000000000000
- 1.608000000000000 1.647000000000000 1.785000000000000
- 2.070000000000000 2.128000000000000 2.245000000000000
- 2.323000000000000 2.377000000000000 2.362500000000000
- 2.364435000000000 2.364969000000000 2.365324000000000
- 2.365121000000000 2.364842000000000 2.364334000000000
- 2.362500000000000 2.377000000000000 2.134000000000000
- 1.786000000000000 1.768000000000000 1.768000000000000
- 1.682000000000000 1.372000000000000 1.372000000000000
- 1.420000000000000 1.420000000000000 1.273000000000000
- 1.153000000000000 1.016000000000000 1.016000000000000
- 1.016000000000000 1.016000000000000 1.016000000000000
- 1.016000000000000 1.016000000000000 1.016000000000000
- 0.000000000000000 0.000000000000000 0.000000000000000
- 0.000000000000000 0.000000000000000 0.000000000000000
- 0.000000000000000 0.000000000000000 0.000000000000000
- 0.000000000000000 0.000000000000000 0.000000000000000
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- 0.000000000000000 0.000000000000000 0.000000000000000
- 0.000000000000000 0.000000000000000 0.000000000000000
- 0.000000000000000 0.000000000000000 0.000000000000000
- 0.000000000000000 0.000000000000000
- YLIM = 0.000000000000000 0.9640000000000000
- 0.9680000000000000 1.001000000000000 1.019000000000000
- 1.077000000000000 1.070000000000000 1.096000000000000
- 1.113000000000000 1.138000000000000 1.147000000000000
- 1.165000000000000 1.217000000000000 1.217000000000000
- 1.162400000000000 1.162380000000000 1.162600000000000
- 1.164500000000000 1.165940000000000 1.165910000000000
- 1.168960000000000 1.171750000000000 1.175560000000000
- 1.183000000000000 1.183500000000000 1.185000000000000
- 1.188000000000000 1.191000000000000 1.196000000000000
- 1.202000000000000 1.208000000000000 1.214000000000000
- 1.221000000000000 1.231000000000000 1.238000000000000
- 1.244000000000000 1.254000000000000 1.278000000000000
- 1.290000000000000 1.331000000000000 1.347000000000000
- 1.348000000000000 1.348000000000000 1.348000000000000
- 1.348000000000000 1.348000000000000 1.348000000000000
- 1.310000000000000 1.310000000000000 1.292000000000000
- 1.095000000000000 1.077000000000000 1.077000000000000
- 1.040000000000000 0.9930000000000000 0.7090000000000000
- 0.5190000000000000 0.3890000000000000 0.4000000000000000
- 0.2220000000000000 0.1330000000000000 4.3999999999999997E-002
- -4.3999999999999997E-002 -0.1330000000000000 -0.2220000000000000
- -0.4000000000000000 -0.3890000000000000 -0.9730000000000000
- -1.174000000000000 -1.211000000000000 -1.250000000000000
- -1.250000000000000 -1.250000000000000 -1.329000000000000
- -1.329000000000000 -1.363000000000000 -1.363000000000000
- -1.363000000000000 -1.223000000000000 -1.223000000000000
- -0.8300000000000000 -0.8000000000000000 -0.4150000000000000
- -0.4000000000000000 -1.0000000000000000E-003 0.000000000000000
- 0.000000000000000 0.000000000000000 0.000000000000000
- 0.000000000000000 0.000000000000000 0.000000000000000
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- 0.000000000000000 0.000000000000000 0.000000000000000
- 0.000000000000000 0.000000000000000 0.000000000000000
- 0.000000000000000 0.000000000000000 0.000000000000000
- 0.000000000000000 0.000000000000000 0.000000000000000
- 0.000000000000000 0.000000000000000 0.000000000000000
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- 0.000000000000000 0.000000000000000 0.000000000000000
- 0.000000000000000 0.000000000000000
- ERROR = 1.0000000000000000E-008
- ICONVR = 2
- IBUNMN = 3
- PRESSR = 76781.32885678127 74863.25800535333
- 73166.60046747129 71669.96555247817 70212.92078931149
- 68792.17297968730 67267.93727391605 65781.07573503046
- 64328.93968599897 62909.30813933844 61520.31868351915
- 60160.40952768265 58828.27090119621 57522.80429567586
- 56243.08828115389 54988.34983264518 53757.94027484011
- 52551.31509636151 51368.01700543736 50312.20939069427
- 49275.11740373774 48256.53177887356 47256.27322991924
- 46274.18784144539 45310.14311220172 44364.02454901914
- 43435.73272363056 42525.18071675229 41632.29188372331
- 40756.99788426571 39814.42292409088 38892.98762985114
- 37992.62150355375 37113.25677375504 36254.82628662083
- 35417.26141620617 34600.48992892507 33804.43373575630
- 33029.00646223739 32274.11076062885 31539.63528060741
- 30825.45120422131 30131.40823728059 29397.03315635974
- 28686.14466223319 27998.41538389834 27333.45086598920
- 26690.77495354281 26069.81214965828 25469.86629237036
- 24842.66056365969 24283.58672061474 23697.96935000312
- 23131.29150965732 22581.15109313150 22044.61694891474
- 21518.61997721864 21000.59587229888 20527.71306157200
- 20058.57526936302 19592.14596691313 19127.60794791624
- 18664.33304965296 18201.85887850703 17739.87167750560
- 17278.19470109642 16816.78166642823 16394.11969307315
- 15971.90792640962 15550.40493170118 15129.97528840354
- 14711.10093529669 14294.39616765267 13918.09748326315
- 13544.92275946686 13175.57014026856 12845.74382646118
- 12515.40197943927 12217.14089842939 11909.06057341461
- 11584.25951364460 11279.61073327688 10948.65175906819
- 10637.91565239412 10296.05692203695 9982.665020656239
- 9638.851796577706 9338.783128949071 9013.684126476666
- 8751.573038386870 8471.134720584683 8168.351832403454
- 7837.661248625122 7598.260498462453 7341.290463883974
- 7065.558672833547 6770.864701793502 6458.000223756062
- 6128.749820414500 5785.892813607409 5433.158050561190
- 5074.644018006349 4714.194891502077 4534.360209222545
- 4355.341566917420 4177.531971031782 4001.305283525661
- 3827.016317746723 3655.000929476260 3485.576103079767
- 3319.040032832240 3155.672199365910 2995.733441423123
- 2839.466022704617 2687.093694044039 2538.821750828768
- 2394.837085618784 2255.308236114629 2120.385428362848
- 1990.200615338441 1864.867510734543 1629.120255744579
- 1413.689330389828 1218.798697472071 1044.238024560605
- 889.3178565237582 752.8680237079956 633.2364411639952
- 528.2874134614290 392.8060362691029 280.7960268108279
- 250.1451760428327 0.000000000000000 0.000000000000000
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- 0.000000000000000
- RPRESS = 0.000000000000000 -1.2012012012012012E-002
- -2.3023023023023025E-002 -3.3033033033033031E-002 -4.3043043043043044E-002
- -5.3053053053053051E-002 -6.4064064064064064E-002 -7.5075075075075076E-002
- -8.6086086086086089E-002 -9.7097097097097101E-002 -0.1081081081081081
- -0.1191191191191191 -0.1301301301301301 -0.1411411411411412
- -0.1521521521521522 -0.1631631631631631 -0.1741741741741742
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- -0.2162162162162162 -0.2262262262262262 -0.2362362362362362
- -0.2462462462462462 -0.2562562562562563 -0.2662662662662663
- -0.2762762762762763 -0.2862862862862863 -0.2962962962962963
- -0.3063063063063063 -0.3173173173173173 -0.3283283283283283
- -0.3393393393393394 -0.3503503503503503 -0.3613613613613614
- -0.3723723723723724 -0.3833833833833834 -0.3943943943943944
- -0.4054054054054054 -0.4164164164164164 -0.4274274274274275
- -0.4384384384384384 -0.4494494494494494 -0.4614614614614614
- -0.4734734734734735 -0.4854854854854855 -0.4974974974974975
- -0.5095095095095095 -0.5215215215215215 -0.5335335335335335
- -0.5465465465465466 -0.5585585585585585 -0.5715715715715716
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- -0.7327327327327328 -0.7447447447447447 -0.7557557557557557
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- -0.8588588588588588 -0.8668668668668669 -0.8748748748748749
- -0.8828828828828829 -0.8898898898898899 -0.8968968968968969
- -0.9029029029029029 -0.9089089089089090 -0.9139139139139140
- -0.9189189189189190 -0.9229229229229229 -0.9269269269269269
- -0.9299299299299300 -0.9329329329329329 -0.9359359359359359
- -0.9389389389389390 -0.9409409409409409 -0.9429429429429429
- -0.9449449449449450 -0.9469469469469469 -0.9489489489489490
- -0.9509509509509509 -0.9529529529529529 -0.9549549549549550
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- 0.000000000000000
- QPSI = 1.062022126653593 1.069989383086604
- 1.075304751668133 1.083966096090663 1.088371827679364
- 1.094299581114990 1.100135653628720 1.106477359720005
- 1.112797996580092 1.119604970050730 1.126111808081460
- 1.133102951241977 1.140010502376114 1.147027080590435
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- 1.176775673720043 1.184485119553410 1.192325009996535
- 1.200337445808878 1.208507146439601 1.216714965239446
- 1.225127007754196 1.233708012797175 1.242388777795652
- 1.251194128502904 1.260198822831727 1.269363553250738
- 1.278654557995057 1.288073495731514 1.297715979508079
- 1.307520993145906 1.317477917778631 1.327582468036335
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- 1.369977308184977 1.381060341259557 1.392371681710433
- 1.403859927956472 1.415559720029137 1.427485170380328
- 1.439658851089910 1.452058611073094 1.464676812854642
- 1.477559790419606 1.490698256070615 1.504098575639812
- 1.517767889223511 1.531703690466205 1.545932141703868
- 1.560461894326618 1.575294425805617 1.590432074309697
- 1.605897832549147 1.621695346376826 1.637836025717006
- 1.654330703535554 1.671183773224174 1.688423599600785
- 1.706038659184470 1.724061654022336 1.742497458809612
- 1.761345439885922 1.780641468185139 1.800371946361733
- 1.820584444883129 1.841253171701596 1.862409195011656
- 1.884074452967864 1.906230080420706 1.928925086351233
- 1.952125623351688 1.975889752955031 2.000171526492772
- 2.025006449274960 2.050382047345760 2.076308553637879
- 2.102770770775955 2.129778725265508 2.157350553255539
- 2.185503436195831 2.214233926058826 2.243545997820678
- 2.273507537290028 2.304109853622101 2.335377386056945
- 2.367287959975241 2.400012777644059 2.433434076137508
- 2.467665983629683 2.502707639680795 2.538693132316229
- 2.575548580152560 2.613414651236727 2.652326902568753
- 2.692350616971484 2.733557070715256 2.776055912797787
- 2.819906625474248 2.865174594917490 2.912158013679076
- 2.960737535806386 3.011300651616540 3.063954059364148
- 3.118848971395844 3.176372826873230 3.236605518696807
- 3.299722709125948 3.366065102435951 3.435504095994509
- 3.508565790295565 3.585066269709416 3.665374933144523
- 3.749155932154522 3.836420819242377 3.926209358586249
- 4.017504884057729 4.106631025539255 4.186257310634852
- 4.254281952287243 4.324138648028361 4.420597880168824
- 4.569493813155836 4.811073342886258 5.253690010110009
- 8.032269020262538
- PRESSW = 0.000000000000000 0.000000000000000
- 0.000000000000000 0.000000000000000 0.000000000000000
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- 0.000000000000000
- PRES = 76762.07659049288 75505.96557742984
- 74280.71744730631 73083.94671903283 71913.54819786170
- 70767.66403886642 69644.65468029703 68543.07319205346
- 67461.64263794952 66399.23609759209 65354.85903531079
- 64327.63374029371 63316.78559448961 62321.63095343301
- 61341.56645038337 60376.05955643787 59424.64024892732
- 58486.89365774433 57562.45357455294 56650.99672332895
- 55752.23770259158 54865.92452019575 53991.83465082540
- 53129.77155450573 52279.56160166543 51441.05135664029
- 50614.10517711761 49798.60309196405 48994.43892423452
- 48201.51862999616 47419.75882697752 46649.08549002329
- 45889.43279294443 45140.74207864402 44402.96094140610
- 43676.04240698963 42959.94419769976 42254.62807093830
- 41560.05922088461 40876.20573394622 40203.03808945926
- 39540.52869782724 38888.65146887195 38247.38140364338
- 37616.69420330223 36996.56588895593 36386.97242650035
- 35787.88935059768 35199.29138190755 34621.15203158270
- 34053.44318684161 33496.13467113399 32949.19377201793
- 32412.58472936213 31886.26817586588 31370.20052114369
- 30864.33326973821 30368.61226239149 29882.97682870418
- 29407.35883792556 28941.68163302368 28485.85883135884
- 28039.79297319650 27603.37399691504 27176.47751705254
- 26758.96287825202 26350.67095465835 25951.42166033763
- 25561.01113176872 25179.20853832595 24805.75247085190
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- NQPSI = 129
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- /
- &BASIS
- KPPFNC = 6,
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- /
- &MSEOUT
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- /
- &ECCD
- KKSTARK = 101,
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- /
- &CHIOUT
- SAISIL = 3.0254726073793078E-002,
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- /
- KIM
diff --git a/notebooks/DIIID_example/vac.in b/notebooks/DIIID_example/vac.in
deleted file mode 100644
index 68e91e03e8..0000000000
--- a/notebooks/DIIID_example/vac.in
+++ /dev/null
@@ -1,99 +0,0 @@
-! **** Running DCON's input ***
-&MODES
- mth = 480
- xiin(1:9) = 0 0 0 0 0 0 0 1 0
- lsymz = .TRUE.
- leqarcw = 1
- lzio = 0
- lgato = 0
- lrgato = 0
-/
-&DEBUGS
- checkd = .FALSE.
- check1 = .FALSE.
- check2 = .FALSE.
- checke = .FALSE.
- checks = .FALSE.
- wall = .FALSE.
- lkplt = 0
- verbose_timer_output = f
-/
-&VACDAT
- ishape = 6
- aw = 0.05
- bw = 1.5
- cw = 0
- dw = 0.5
- tw = 0.05
- nsing = 500
- epsq = 1e-05
- noutv = 37
- idgt = 6
- idot = 0
- idsk = 0
- delg = 15.01
- delfac = 0.001
- cn0 = 1
-/
-&SHAPE
- ipshp = 0
- xpl = 100
- apl = 1
- a = 20
- b = 170
- bpl = 1
- dpl = 0
- r = 1
- abulg = 0.932
- bbulg = 17.0
- tbulg = 0.02
- qain = 2.5
-/
-&DIAGNS
- lkdis = .FALSE.
- ieig = 0
- iloop = 0
- lpsub = 1
- nloop = 128
- nloopr = 0
- nphil = 3
- nphse = 1
- xofsl = 0
- ntloop = 32
- aloop = 0.01
- bloop = 1.6
- dloop = 0.5
- rloop = 1.0
- deloop = 0.001
- mx = 21
- mz = 21
- nph = 0
- nxlpin = 6
- nzlpin = 11
- epslp = 0.02
- xlpmin = 0.7
- xlpmax = 2.7
- zlpmin = -1.5
- zlpmax = 1.5
- linterior = 2
-/
-&SPRK
- nminus = 0
- nplus = 0
- mphi = 16
- lwrt11 = 0
- civ = 0.0
- sp2sgn1 = 1
- sp2sgn2 = 1
- sp2sgn3 = 1
- sp2sgn4 = 1
- sp2sgn5 = 1
- sp3sgn1 = -1
- sp3sgn2 = -1
- sp3sgn3 = -1
- sp3sgn4 = 1
- sp3sgn5 = 1
- lff = 0
- ff = 1.6
- fv = 1.6 1.6 1.6 1.6 1.6 1.0 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6
-/
diff --git a/notebooks/beta_1.00 b/notebooks/beta_1.00
deleted file mode 100644
index 957a823844..0000000000
--- a/notebooks/beta_1.00
+++ /dev/null
@@ -1,3596 +0,0 @@
- FROM CHEASE BUT COCOS=02 ,SI UNITS20250525 3 129 128
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--9.235237230E-01 4.291178658E+00-8.947990041E-01 4.304435668E+00-8.660854913E-01
- 4.317246877E+00-8.373794402E-01 4.329615413E+00-8.086773973E-01 4.341543908E+00
--7.799760733E-01 4.353034666E+00-7.512724485E-01 4.364089675E+00-7.225637670E-01
- 4.374710490E+00-6.938474541E-01 4.384898478E+00-6.651212537E-01 4.394654668E+00
--6.363831269E-01 4.403979786E+00-6.076312661E-01 4.412874433E+00-5.788641700E-01
- 4.421338882E+00-5.500805352E-01 4.429373245E+00-5.212793231E-01 4.436977549E+00
--4.924597760E-01 4.444151529E+00-4.636213216E-01 4.450894901E+00-4.347636682E-01
- 4.457207284E+00-4.058867547E-01 4.463088084E+00-3.769907056E-01 4.468536806E+00
--3.480759119E-01 4.473552828E+00-3.191429453E-01 4.478135440E+00-2.901925612E-01
- 4.482284088E+00-2.612257380E-01 4.485998084E+00-2.322435926E-01 4.489276773E+00
--2.032474064E-01 4.492119692E+00-1.742386255E-01 4.494526218E+00-1.452187922E-01
- 4.496495959E+00-1.161895814E-01 4.498028669E+00-8.715275983E-02 4.499123931E+00
--5.811014675E-02 4.499781143E+00-2.906362128E-02 4.499999497E+00-1.513208407E-05
- 1.350313621E+00-2.677482172E+00 4.649797468E+00-2.677482172E+00 4.649797468E+00
- 2.677476176E+00 1.350313621E+00 2.677476176E+00 1.350313621E+00-2.677482172E+00
-
- 1.51912315E-01 abs(PSI-AXIS) --> [T M**2] -1.36721084E+00
- 1.03921169E+00 R OF MAGAXE --> [M] 3.11763506E+00
- -9.99273915E-07 Z OF MAGAXE --> [M] -2.99782174E-06
- -5.04402802E-06 Z0 --> [M] -1.51320841E-05
- 3.00000000E+00 R0 [M] USED FOR CONVERTING TO MKSA
- 1.00000000E+00 B0 [T] USED FOR CONVERTING TO MKSA
- 1.00000000E+00 SIGN OF B0 IN EXPERIMENT (CHEASE ASSUMES 1.0)
- 1.53755753E+00 TOTAL CURRENT --> [A] 3.67064822E+06
- 1.00000000E+00 SIGN OF IP IN EXPERIMENT (CHEASE ASSUMES 1.0)
- 1.69999553E+00 b/a
- 1.05000000E+00 Q_ZERO, USING SIGNS OF IP AND B0, WOULD GIVE: 1.05000000E+00
- 4.43373475E+00 Q_EDGE, USING SIGNS OF IP AND B0, WOULD GIVE: 4.43373475E+00
- 1.51426490E-01 POLOIDAL BETA
- 2.34029713E-02 BETA_EXP=
*2*MU0/B0**2
- 7.25523874E-01 LI
- 3.46308209E-02 PRESSURE ON AXIS --> [Pa] 2.75583316E+04 --> [10**19 M**-3 KEV]: 1.72024542E+01
- 1.63188124E-02 BETA
- 2.18184292E-02 BETA* (SQRT(
))
- 5.58550793E-02 BETA-AXIS=2p0/(T0/Rmag)^2; with Rmag->Rgeo(LCFS): 5.17194368E-02
- -1.51912315E-01 PSI-AXIS --> [T M**2] -1.36721084E+00
- -9.54493226E-01 2*PI*PSI-AXIS --> -8.59043904E+00
- -1.51912315E-01 IP_SIGN*PSI-AXIS --> [T M**2] -1.36721084E+00
- -9.54493226E-01 IP_SIGN*2*PI*PSI-AXIS --> -8.59043904E+00
- 1.99999525E+00 ASPECT RATIO ; a/R= 5.00001188E-01
- 7.64779790E+00 VOLUME -> 2.06490543E+02
- 1.29389993E+00 AREA -> 1.16450994E+01
- 2.53018281E+01 SURFACE -> 2.27716453E+02
- 4.34432012E+00 LENGTH -> 1.30329604E+01
- 5.00003104E-01 RMIN -> RMIN [m] 1.50000931E+00
- 1.49999983E+00 RMAX -> RMAX [m] 4.49999950E+00
- -8.49976057E-01 ZMIN -> ZMIN [m] -2.54992817E+00
- 8.49976009E-01 ZMAX -> ZMAX [m] 2.54992803E+00
- 1.00000147E+00 RGEOM -> RGEOM [m] 3.00000440E+00
- 4.99998364E-01 MINOR RADIUS -> A [m] 1.49999509E+00
diff --git a/notebooks/dcon_test.ipynb b/notebooks/dcon_test.ipynb
deleted file mode 100644
index dc21f3ac8a..0000000000
--- a/notebooks/dcon_test.ipynb
+++ /dev/null
@@ -1,57 +0,0 @@
-{
- "cells": [
- {
- "cell_type": "markdown",
- "id": "b792c57b",
- "metadata": {},
- "source": [
- "### This notebook can be used as a basic example to show how to run the main DCON program"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "id": "710e987d",
- "metadata": {},
- "outputs": [],
- "source": [
- "using Pkg\n",
- "Pkg.activate(\"..\")\n",
- "using JPEC"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "id": "d8bcf5be",
- "metadata": {},
- "outputs": [],
- "source": [
- "JPEC.DCON.Main(\"DIIID_example\")"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "id": "18cbc50a",
- "metadata": {},
- "outputs": [],
- "source": []
- }
- ],
- "metadata": {
- "kernelspec": {
- "display_name": "Julia 1.11.6",
- "language": "julia",
- "name": "julia-1.11"
- },
- "language_info": {
- "file_extension": ".jl",
- "mimetype": "application/julia",
- "name": "julia",
- "version": "1.11.6"
- }
- },
- "nbformat": 4,
- "nbformat_minor": 5
-}
diff --git a/notebooks/equil_chease_binary_test.ipynb b/notebooks/equil_chease_binary_test.ipynb
deleted file mode 100644
index 03c4088be9..0000000000
--- a/notebooks/equil_chease_binary_test.ipynb
+++ /dev/null
@@ -1,250 +0,0 @@
-{
- "cells": [
- {
- "cell_type": "code",
- "execution_count": null,
- "id": "1b50e9cb",
- "metadata": {},
- "outputs": [],
- "source": [
- "# Test inverse.jl using the chease binary file IN1\n",
- "\n",
- "using Revise\n",
- "using Pkg\n",
- "#Pkg.update()\n",
- "Pkg.activate(\"..\")\n",
- "Pkg.instantiate()\n",
- "using JPEC, Plots\n",
- "gr()"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "id": "94c3d4e9",
- "metadata": {},
- "outputs": [],
- "source": [
- "println(\"Starting equilibrium reconstruction...\")\n",
- "plasma_eq = JPEC.Equilibrium.setup_equilibrium(\"Chease_Binary_example/equil.toml\")\n",
- "println(\"Equilibrium reconstruction complete.\")"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "id": "c0c6ffc5",
- "metadata": {},
- "outputs": [],
- "source": [
- "# --- Final Code to Generate 2D Color Plots of R(ψ,θ) and Z(ψ,θ) ---\n",
- "println(\"\\n--- Generating data for 2D color plots ---\")\n",
- "# 1. Define the grid in flux coordinates (ψ_norm, θ_new)\n",
- "# This part is identical to the previous steps.\n",
- "equil_control = plasma_eq.config.control\n",
- "psi_norm_grid = collect(range(equil_control.psilow, equil_control.psihigh, length=equil_control.mpsi + 1))\n",
- "theta_new_grid = collect(range(0.0, 1.0, length=equil_control.mtheta + 1))\n",
- "# 2. Evaluate the `rzphi` spline to get the R and Z values.\n",
- "println(\"Evaluating the 'rzphi' mapping spline...\")\n",
- "fs_grid = JPEC.Spl.bicube_eval(plasma_eq.rzphi, psi_norm_grid, theta_new_grid)\n",
- "println(\"Evaluation complete.\")\n",
- "# 3. Transform the spline output to physical (R, Z) coordinates.\n",
- "# This calculates R_grid[i,j] = R(ψ[i], θ[j]) and Z_grid[i,j] = Z(ψ[i], θ[j])\n",
- "rfac_sq = fs_grid[:, :, 1]\n",
- "eta_term = fs_grid[:, :, 2]\n",
- "theta_new_mesh = ones(length(psi_norm_grid)) * theta_new_grid'\n",
- "eta_grid = 2.0 * pi .* (theta_new_mesh .+ eta_term)\n",
- "rfac_grid = sqrt.(max.(0.0, rfac_sq))\n",
- "R_grid = plasma_eq.ro .+ rfac_grid .* cos.(eta_grid)\n",
- "Z_grid = plasma_eq.zo .+ rfac_grid .* sin.(eta_grid)\n",
- "println(\"Calculated R and Z grids.\")\n",
- "# 4. Create the 2D color plot for R(ψ,θ)\n",
- "println(\"--- Plotting heatmap for R(ψ,θ) ---\")\n",
- "p_r_heatmap = heatmap(\n",
- " psi_norm_grid,\n",
- " theta_new_grid,\n",
- " R_grid', # Note the transpose ' to match axis dimensions\n",
- " title=\"Major Radius R(ψ, θ)\",\n",
- " xlabel=\"Normalized Psi (ψₙ)\",\n",
- " ylabel=\"Poloidal Angle (θ_new)\",\n",
- " colorbar_title=\"R [m]\"\n",
- ")\n",
- "display(p_r_heatmap)\n",
- "# 5. Create the 2D color plot for Z(ψ,θ)\n",
- "println(\"--- Plotting heatmap for Z(ψ,θ) ---\")\n",
- "p_z_heatmap = heatmap(\n",
- " psi_norm_grid,\n",
- " theta_new_grid,\n",
- " Z_grid', # Note the transpose ' to match axis dimensions\n",
- " title=\"Vertical Position Z(ψ, θ)\",\n",
- " xlabel=\"Normalized Psi (ψₙ)\",\n",
- " ylabel=\"Poloidal Angle (θ_new)\",\n",
- " colorbar_title=\"Z [m]\"\n",
- ")\n",
- "display(p_z_heatmap)\n",
- "println(\"\\n2D color plots for R and Z have been saved.\")\n"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "id": "9859d659",
- "metadata": {},
- "outputs": [],
- "source": [
- "# --- Code to Plot Psi and Theta Contours in R-Z Space ---\n",
- "# This code block goes at the end of your existing script.\n",
- "\n",
- "println(\"\\n--- Plotting Psi and Theta Contours in R-Z Space ---\")\n",
- "\n",
- "# 1. Select a number of contours to display for clarity\n",
- "num_psi_contours = 11 # e.g., from ψ_norm = 0.0 to 1.0 in steps of 0.1\n",
- "num_theta_contours = 13 # e.g., every 30 degrees\n",
- "\n",
- "# 2. Initialize the plot\n",
- "# aspect_ratio=:equal is crucial for tokamak plots to look physically correct.\n",
- "p_flux_surfaces = plot(\n",
- " title=\"Flux Coordinate System Contours in (R, Z)\",\n",
- " xlabel=\"R [m]\",\n",
- " ylabel=\"Z [m]\",\n",
- " aspect_ratio=:equal,\n",
- " legend=:outertopright\n",
- ")\n",
- "\n",
- "# 3. Plot contours of constant ψ (flux surfaces) in blue\n",
- "# We loop through the ROWS of the R_grid and Z_grid matrices.\n",
- "psi_indices = round.(Int, range(1, stop=size(R_grid, 1), length=num_psi_contours))\n",
- "\n",
- "for i in psi_indices\n",
- " # Each row corresponds to a single psi value\n",
- " # We must add the last point to the start to close the loop for a smooth plot\n",
- " R_surface = [R_grid[i, :]; R_grid[i, 1]]\n",
- " Z_surface = [Z_grid[i, :]; Z_grid[i, 1]]\n",
- " plot!(p_flux_surfaces, R_surface, Z_surface, label=\"\", color=:blue, linewidth=1.5)\n",
- "end\n",
- "\n",
- "# 4. Plot contours of constant θ (angle contours) in red\n",
- "# We loop through the COLUMNS of the R_grid and Z_grid matrices.\n",
- "theta_indices = round.(Int, range(1, stop=size(R_grid, 2), length=num_theta_contours))\n",
- "\n",
- "for j in theta_indices\n",
- " # Each column corresponds to a single theta value\n",
- " plot!(p_flux_surfaces, R_grid[:, j], Z_grid[:, j], label=\"\", color=:red, linewidth=1)\n",
- "end\n",
- "\n",
- "# 5. Add a legend manually (a common trick in Plots.jl)\n",
- "plot!(p_flux_surfaces, [], [], color=:blue, label=\"Constant ψ\")\n",
- "plot!(p_flux_surfaces, [], [], color=:red, label=\"Constant θ\")\n",
- "\n",
- "# 6. Display and save the final plot\n",
- "display(p_flux_surfaces)\n",
- "println(\"Flux surface contour plot saved as 'flux_surfaces_RZ.png'\")"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "id": "2c625a4a",
- "metadata": {},
- "outputs": [],
- "source": [
- "# --- Code to Plot 1D Profiles from the 'sq' Spline ---\n",
- "# This code block goes at the end of your existing script.\n",
- "\n",
- "println(\"\\n--- Plotting 1D Profiles from 'sq' Spline ---\")\n",
- "\n",
- "# 1. To get smooth curves, we'll evaluate the spline on a dense grid,\n",
- "# not just on its internal knot points.\n",
- "psi_eval_grid = range(0.0, 1.0, length=200)\n",
- "\n",
- "# 2. Evaluate the 'sq' spline across this dense grid.\n",
- "# Calling spline_eval with a vector input is efficient and returns a matrix\n",
- "# where each column corresponds to one of the splined quantities.\n",
- "println(\"Evaluating 'sq' spline on a dense grid...\")\n",
- "evaluated_profiles = JPEC.Spl.spline_eval(plasma_eq.sq, collect(psi_eval_grid), 0)\n",
- "println(\"Evaluation complete.\")\n",
- "\n",
- "# 3. Extract each profile into its own variable for clarity.\n",
- "# Based on the direct_run implementation:\n",
- "# Column 1: F = R*Bt (Toroidal Field Function)\n",
- "# Column 2: P*μ₀ (Scaled Pressure)\n",
- "# Column 3: Toroidal Flux function (related to dV/dψ_pol)\n",
- "# Column 4: q (Safety Factor)\n",
- "F_profile = evaluated_profiles[:, 1]\n",
- "P_profile = evaluated_profiles[:, 2]\n",
- "Flux_profile = evaluated_profiles[:, 3]\n",
- "q_profile = evaluated_profiles[:, 4]\n",
- "\n",
- "# 4. Create and display the plots\n",
- "\n",
- "# Plot 1: Safety Factor (q)\n",
- "p_q = plot(\n",
- " psi_eval_grid,\n",
- " q_profile,\n",
- " title=\"Safety Factor Profile\",\n",
- " xlabel=\"Normalized Psi (ψₙ)\",\n",
- " ylabel=\"q\",\n",
- " legend=false,\n",
- " linewidth=2\n",
- ")\n",
- "display(p_q)\n",
- "\n",
- "# Plot 2: Scaled Pressure (P*μ₀)\n",
- "p_p = plot(\n",
- " psi_eval_grid,\n",
- " P_profile,\n",
- " title=\"Pressure Profile\",\n",
- " xlabel=\"Normalized Psi (ψₙ)\",\n",
- " ylabel=\"P * μ₀ [T²]\",\n",
- " legend=false,\n",
- " linewidth=2\n",
- ")\n",
- "display(p_p)\n",
- "\n",
- "\n",
- "# Plot 3: Toroidal Field Function (F)\n",
- "p_f = plot(\n",
- " psi_eval_grid,\n",
- " F_profile,\n",
- " title=\"Toroidal Field Function\",\n",
- " xlabel=\"Normalized Psi (ψₙ)\",\n",
- " ylabel=\"F = R * B_t [T*m]\",\n",
- " legend=false,\n",
- " linewidth=2\n",
- ")\n",
- "display(p_f)\n",
- "\n",
- "# Plot 4: Combined plot for comparison\n",
- "p_all_profiles = plot(\n",
- " title=\"1D Equilibrium Profiles\",\n",
- " xlabel=\"Normalized Psi (ψₙ)\",\n",
- " legend=:best\n",
- ")\n",
- "plot!(p_all_profiles, psi_eval_grid, q_profile, label=\"q (Safety Factor)\", linewidth=2)\n",
- "plot!(p_all_profiles, psi_eval_grid, P_profile, label=\"P*μ₀ (Pressure)\", linewidth=2)\n",
- "plot!(p_all_profiles, psi_eval_grid, F_profile, label=\"F (Toroidal Field Fn.)\", linewidth=2)\n",
- "# We can also plot the 3rd quantity, though it's less commonly viewed.\n",
- "# plot!(p_all_profiles, psi_eval_grid, Flux_profile, label=\"Toroidal Flux Fn.\", linewidth=2)\n",
- "display(p_all_profiles)\n",
- "\n",
- "\n",
- "println(\"1D profile plots saved successfully.\")"
- ]
- }
- ],
- "metadata": {
- "kernelspec": {
- "display_name": "Julia 1.11.6",
- "language": "julia",
- "name": "julia-1.11"
- },
- "language_info": {
- "file_extension": ".jl",
- "mimetype": "application/julia",
- "name": "julia",
- "version": "1.11.6"
- }
- },
- "nbformat": 4,
- "nbformat_minor": 5
-}
diff --git a/notebooks/equil_gfile_example.ipynb b/notebooks/equil_gfile_example.ipynb
deleted file mode 100644
index 08f17052dc..0000000000
--- a/notebooks/equil_gfile_example.ipynb
+++ /dev/null
@@ -1,267 +0,0 @@
-{
- "cells": [
- {
- "cell_type": "code",
- "execution_count": null,
- "id": "814db625",
- "metadata": {},
- "outputs": [],
- "source": [
- "using Pkg\n",
- "Pkg.activate(\"..\")\n",
- "Pkg.resolve()\n",
- "Pkg.instantiate()\n",
- "using JPEC, Plots\n",
- "gr() "
- ]
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "id": "94c3d4e9",
- "metadata": {},
- "outputs": [],
- "source": [
- "# 1. Define the input parameters for the equilibrium solver.\n",
- "# - eq_filename: The name of the g-file we just created.\n",
- "# - eq_type: \"efit\" for a standard g-file.\n",
- "# - jac_type: \"boozer\" or \"hamada\" for the output coordinates.\n",
- "# - mpsi, mtheta: Resolution of the output grid.\n",
- "\n",
- " equil_control = JPEC.Equilibrium.EquilibriumControl(;\n",
- " eq_filename=\"beta_1.00\", # eq_filename\n",
- " eq_type=\"efit\", # eq_type\n",
- " jac_type=\"boozer\", # jac_type\n",
- " grid_type=\"ldp\",\n",
- " psilow=0.01, # psilow\n",
- " psihigh=0.994) # psihigh\n",
- "\n",
- "equil_config = JPEC.Equilibrium.EquilibriumConfig(equil_control,JPEC.Equilibrium.EquilibriumOutput())\n",
- "# 2. Run the main equilibrium setup function.\n",
- "# This will read the file, solve the direct problem, and return the final object.\n",
- "println(\"Starting equilibrium reconstruction...\")\n",
- "\n",
- "\n",
- "plasma_eq = JPEC.Equilibrium.setup_equilibrium(equil_config)\n",
- "#plasma_eq = JPEC.Equilibrium.setup_equilibrium(\"./DIIID_example/equil.toml\")\n",
- "println(\"Equilibrium reconstruction complete.\")"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "id": "f61a9987",
- "metadata": {},
- "outputs": [],
- "source": [
- "# --- Final Code to Generate 2D Color Plots of R(ψ,θ) and Z(ψ,θ) ---\n",
- "println(\"\\n--- Generating data for 2D color plots ---\")\n",
- "# 1. Define the grid in flux coordinates (ψ_norm, θ_new)\n",
- "# This part is identical to the previous steps.\n",
- "equil_control = plasma_eq.config.control\n",
- "psi_norm_grid = collect(range(equil_control.psilow, equil_control.psihigh, length=equil_control.mpsi + 1))\n",
- "theta_new_grid = collect(range(0.0, 1.0, length=equil_control.mtheta + 1))\n",
- "# 2. Evaluate the `rzphi` spline to get the R and Z values.\n",
- "println(\"Evaluating the 'rzphi' mapping spline...\")\n",
- "fs_grid = JPEC.Spl.bicube_eval(plasma_eq.rzphi, psi_norm_grid, theta_new_grid)\n",
- "println(\"Evaluation complete.\")\n",
- "# 3. Transform the spline output to physical (R, Z) coordinates.\n",
- "# This calculates R_grid[i,j] = R(ψ[i], θ[j]) and Z_grid[i,j] = Z(ψ[i], θ[j])\n",
- "rfac_sq = fs_grid[:, :, 1]\n",
- "eta_term = fs_grid[:, :, 2]\n",
- "theta_new_mesh = ones(length(psi_norm_grid)) * theta_new_grid'\n",
- "eta_grid = 2.0 * pi .* (theta_new_mesh .+ eta_term)\n",
- "rfac_grid = sqrt.(max.(0.0, rfac_sq))\n",
- "R_grid = plasma_eq.ro .+ rfac_grid .* cos.(eta_grid)\n",
- "Z_grid = plasma_eq.zo .+ rfac_grid .* sin.(eta_grid)\n",
- "println(\"Calculated R and Z grids.\")\n",
- "# 4. Create the 2D color plot for R(ψ,θ)\n",
- "println(\"--- Plotting heatmap for R(ψ,θ) ---\")\n",
- "p_r_heatmap = heatmap(\n",
- " psi_norm_grid,\n",
- " theta_new_grid,\n",
- " R_grid', # Note the transpose ' to match axis dimensions\n",
- " title=\"Major Radius R(ψ, θ)\",\n",
- " xlabel=\"Normalized Psi (ψₙ)\",\n",
- " ylabel=\"Poloidal Angle (θ_new)\",\n",
- " colorbar_title=\"R [m]\"\n",
- ")\n",
- "display(p_r_heatmap)\n",
- "# 5. Create the 2D color plot for Z(ψ,θ)\n",
- "println(\"--- Plotting heatmap for Z(ψ,θ) ---\")\n",
- "p_z_heatmap = heatmap(\n",
- " psi_norm_grid,\n",
- " theta_new_grid,\n",
- " Z_grid', # Note the transpose ' to match axis dimensions\n",
- " title=\"Vertical Position Z(ψ, θ)\",\n",
- " xlabel=\"Normalized Psi (ψₙ)\",\n",
- " ylabel=\"Poloidal Angle (θ_new)\",\n",
- " colorbar_title=\"Z [m]\"\n",
- ")\n",
- "display(p_z_heatmap)\n",
- "println(\"\\n2D color plots for R and Z have been saved.\")"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "id": "9cf8a3c1",
- "metadata": {},
- "outputs": [],
- "source": [
- "# --- Code to Plot Psi and Theta Contours in R-Z Space ---\n",
- "# This code block goes at the end of your existing script.\n",
- "\n",
- "println(\"\\n--- Plotting Psi and Theta Contours in R-Z Space ---\")\n",
- "\n",
- "# 1. Select a number of contours to display for clarity\n",
- "num_psi_contours = 11 # e.g., from ψ_norm = 0.0 to 1.0 in steps of 0.1\n",
- "num_theta_contours = 13 # e.g., every 30 degrees\n",
- "\n",
- "# 2. Initialize the plot\n",
- "# aspect_ratio=:equal is crucial for tokamak plots to look physically correct.\n",
- "p_flux_surfaces = plot(\n",
- " title=\"Flux Coordinate System Contours in (R, Z)\",\n",
- " xlabel=\"R [m]\",\n",
- " ylabel=\"Z [m]\",\n",
- " aspect_ratio=:equal,\n",
- " legend=:outertopright\n",
- ")\n",
- "\n",
- "# 3. Plot contours of constant ψ (flux surfaces) in blue\n",
- "# We loop through the ROWS of the R_grid and Z_grid matrices.\n",
- "psi_indices = round.(Int, range(1, stop=size(R_grid, 1), length=num_psi_contours))\n",
- "\n",
- "for i in psi_indices\n",
- " # Each row corresponds to a single psi value\n",
- " # We must add the last point to the start to close the loop for a smooth plot\n",
- " R_surface = [R_grid[i, :]; R_grid[i, 1]]\n",
- " Z_surface = [Z_grid[i, :]; Z_grid[i, 1]]\n",
- " plot!(p_flux_surfaces, R_surface, Z_surface, label=\"\", color=:blue, linewidth=1.5)\n",
- "end\n",
- "\n",
- "# 4. Plot contours of constant θ (angle contours) in red\n",
- "# We loop through the COLUMNS of the R_grid and Z_grid matrices.\n",
- "theta_indices = round.(Int, range(1, stop=size(R_grid, 2), length=num_theta_contours))\n",
- "\n",
- "for j in theta_indices\n",
- " # Each column corresponds to a single theta value\n",
- " plot!(p_flux_surfaces, R_grid[:, j], Z_grid[:, j], label=\"\", color=:red, linewidth=1)\n",
- "end\n",
- "\n",
- "# 5. Add a legend manually (a common trick in Plots.jl)\n",
- "plot!(p_flux_surfaces, [], [], color=:blue, label=\"Constant ψ\")\n",
- "plot!(p_flux_surfaces, [], [], color=:red, label=\"Constant θ\")\n",
- "\n",
- "# 6. Display and save the final plot\n",
- "display(p_flux_surfaces)\n",
- "println(\"Flux surface contour plot saved as 'flux_surfaces_RZ.png'\")"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "id": "97a529f4",
- "metadata": {},
- "outputs": [],
- "source": [
- "# --- Code to Plot 1D Profiles from the 'sq' Spline ---\n",
- "# This code block goes at the end of your existing script.\n",
- "\n",
- "println(\"\\n--- Plotting 1D Profiles from 'sq' Spline ---\")\n",
- "\n",
- "# 1. To get smooth curves, we'll evaluate the spline on a dense grid,\n",
- "# not just on its internal knot points.\n",
- "psi_eval_grid = range(0.0, 1.0, length=200)\n",
- "\n",
- "# 2. Evaluate the 'sq' spline across this dense grid.\n",
- "# Calling spline_eval with a vector input is efficient and returns a matrix\n",
- "# where each column corresponds to one of the splined quantities.\n",
- "println(\"Evaluating 'sq' spline on a dense grid...\")\n",
- "evaluated_profiles = JPEC.Spl.spline_eval(plasma_eq.sq, collect(psi_eval_grid), 0)\n",
- "println(\"Evaluation complete.\")\n",
- "\n",
- "# 3. Extract each profile into its own variable for clarity.\n",
- "# Based on the direct_run implementation:\n",
- "# Column 1: F = R*Bt (Toroidal Field Function)\n",
- "# Column 2: P*μ₀ (Scaled Pressure)\n",
- "# Column 3: Toroidal Flux function (related to dV/dψ_pol)\n",
- "# Column 4: q (Safety Factor)\n",
- "F_profile = evaluated_profiles[:, 1]\n",
- "P_profile = evaluated_profiles[:, 2]\n",
- "Flux_profile = evaluated_profiles[:, 3]\n",
- "q_profile = evaluated_profiles[:, 4]\n",
- "\n",
- "# 4. Create and display the plots\n",
- "\n",
- "# Plot 1: Safety Factor (q)\n",
- "p_q = plot(\n",
- " psi_eval_grid,\n",
- " q_profile,\n",
- " title=\"Safety Factor Profile\",\n",
- " xlabel=\"Normalized Psi (ψₙ)\",\n",
- " ylabel=\"q\",\n",
- " legend=false,\n",
- " linewidth=2\n",
- ")\n",
- "display(p_q)\n",
- "\n",
- "# Plot 2: Scaled Pressure (P*μ₀)\n",
- "p_p = plot(\n",
- " psi_eval_grid,\n",
- " P_profile,\n",
- " title=\"Pressure Profile\",\n",
- " xlabel=\"Normalized Psi (ψₙ)\",\n",
- " ylabel=\"P * μ₀ [T²]\",\n",
- " legend=false,\n",
- " linewidth=2\n",
- ")\n",
- "display(p_p)\n",
- "\n",
- "\n",
- "# Plot 3: Toroidal Field Function (F)\n",
- "p_f = plot(\n",
- " psi_eval_grid,\n",
- " F_profile,\n",
- " title=\"Toroidal Field Function\",\n",
- " xlabel=\"Normalized Psi (ψₙ)\",\n",
- " ylabel=\"F = R * B_t [T*m]\",\n",
- " legend=false,\n",
- " linewidth=2\n",
- ")\n",
- "display(p_f)\n",
- "\n",
- "# Plot 4: Combined plot for comparison\n",
- "p_all_profiles = plot(\n",
- " title=\"1D Equilibrium Profiles\",\n",
- " xlabel=\"Normalized Psi (ψₙ)\",\n",
- " legend=:best\n",
- ")\n",
- "plot!(p_all_profiles, psi_eval_grid, q_profile, label=\"q (Safety Factor)\", linewidth=2)\n",
- "plot!(p_all_profiles, psi_eval_grid, P_profile, label=\"P*μ₀ (Pressure)\", linewidth=2)\n",
- "plot!(p_all_profiles, psi_eval_grid, F_profile, label=\"F (Toroidal Field Fn.)\", linewidth=2)\n",
- "# We can also plot the 3rd quantity, though it's less commonly viewed.\n",
- "# plot!(p_all_profiles, psi_eval_grid, Flux_profile, label=\"Toroidal Flux Fn.\", linewidth=2)\n",
- "display(p_all_profiles)\n",
- "\n",
- "\n",
- "println(\"1D profile plots saved successfully.\")"
- ]
- }
- ],
- "metadata": {
- "kernelspec": {
- "display_name": "Julia 1.11.6",
- "language": "julia",
- "name": "julia-1.11"
- },
- "language_info": {
- "file_extension": ".jl",
- "mimetype": "application/julia",
- "name": "julia",
- "version": "1.11.6"
- }
- },
- "nbformat": 4,
- "nbformat_minor": 5
-}
diff --git a/notebooks/equil_inverse_test.ipynb b/notebooks/equil_inverse_test.ipynb
deleted file mode 100644
index 9049207d8b..0000000000
--- a/notebooks/equil_inverse_test.ipynb
+++ /dev/null
@@ -1,276 +0,0 @@
-{
- "cells": [
- {
- "cell_type": "code",
- "execution_count": null,
- "id": "1b50e9cb",
- "metadata": {},
- "outputs": [],
- "source": [
- "# Test inverse.jl using the file inverse.inverse_chease4_run\n",
- "\n",
- "using Revise\n",
- "using Pkg\n",
- "Pkg.activate(\"..\") \n",
- "Pkg.instantiate()\n",
- "using JPEC, Plots\n",
- "gr() "
- ]
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "id": "94c3d4e9",
- "metadata": {},
- "outputs": [],
- "source": [
- "# 1. Define the input parameters for the equilibrium solver.\n",
- "# - eq_filename: The name of the g-file we just created.\n",
- "# - eq_type: \"efit\" for a standard g-file.\n",
- "# - jac_type: \"boozer\" or \"hamada\" for the output coordinates.\n",
- "# - mpsi, mtheta: Resolution of the output grid.\n",
- "equil_input = JPEC.Equilibrium.EquilibriumConfig(control=JPEC.Equilibrium.EquilibriumControl(;eq_filename=\"inverse.chease.10\",\n",
- " eq_type=\"chease2\", jac_type=\"hamada\", mpsi=128, mtheta=256),\n",
- " output=JPEC.Equilibrium.EquilibriumOutput())\n",
- "\n",
- "# 2. Run the main equilibrium setup function.\n",
- "# This will read the file, solve the direct problem, and return the final object.\n",
- "println(\"Starting equilibrium reconstruction...\")\n",
- "plasma_eq = JPEC.Equilibrium.setup_equilibrium(\"/Users/bursche/Documents/GitHub/JPEC/notebooks/Inverse_Text_Example/equil.toml\")\n",
- "println(\"Equilibrium reconstruction complete.\")\n"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "id": "c0c6ffc5",
- "metadata": {},
- "outputs": [],
- "source": [
- "# --- Final Code to Generate 2D Color Plots of R(ψ,θ) and Z(ψ,θ) ---\n",
- "println(\"\\n--- Generating data for 2D color plots ---\")\n",
- "# 1. Define the grid in flux coordinates (ψ_norm, θ_new)\n",
- "# This part is identical to the previous steps.\n",
- "equil_control = plasma_eq.config.control\n",
- "psi_norm_grid = collect(range(equil_control.psilow, equil_control.psihigh, length=equil_control.mpsi + 1))\n",
- "theta_new_grid = collect(range(0.0, 1.0, length=equil_control.mtheta + 1))\n",
- "# 2. Evaluate the `rzphi` spline to get the R and Z values.\n",
- "println(\"Evaluating the 'rzphi' mapping spline...\")\n",
- "fs_grid = JPEC.Spl.bicube_eval(plasma_eq.rzphi, psi_norm_grid, theta_new_grid)\n",
- "println(\"Evaluation complete.\")\n",
- "# 3. Transform the spline output to physical (R, Z) coordinates.\n",
- "# This calculates R_grid[i,j] = R(ψ[i], θ[j]) and Z_grid[i,j] = Z(ψ[i], θ[j])\n",
- "rfac_sq = fs_grid[:, :, 1]\n",
- "eta_term = fs_grid[:, :, 2]\n",
- "theta_new_mesh = ones(length(psi_norm_grid)) * theta_new_grid'\n",
- "eta_grid = 2.0 * pi .* (theta_new_mesh .+ eta_term)\n",
- "rfac_grid = sqrt.(max.(0.0, rfac_sq))\n",
- "R_grid = plasma_eq.ro .+ rfac_grid .* cos.(eta_grid)\n",
- "Z_grid = plasma_eq.zo .+ rfac_grid .* sin.(eta_grid)\n",
- "println(\"Calculated R and Z grids.\")\n",
- "# 4. Create the 2D color plot for R(ψ,θ)\n",
- "println(\"--- Plotting heatmap for R(ψ,θ) ---\")\n",
- "p_r_heatmap = heatmap(\n",
- " psi_norm_grid,\n",
- " theta_new_grid,\n",
- " R_grid', # Note the transpose ' to match axis dimensions\n",
- " title=\"Major Radius R(ψ, θ)\",\n",
- " xlabel=\"Normalized Psi (ψₙ)\",\n",
- " ylabel=\"Poloidal Angle (θ_new)\",\n",
- " colorbar_title=\"R [m]\"\n",
- ")\n",
- "display(p_r_heatmap)\n",
- "# 5. Create the 2D color plot for Z(ψ,θ)\n",
- "println(\"--- Plotting heatmap for Z(ψ,θ) ---\")\n",
- "p_z_heatmap = heatmap(\n",
- " psi_norm_grid,\n",
- " theta_new_grid,\n",
- " Z_grid', # Note the transpose ' to match axis dimensions\n",
- " title=\"Vertical Position Z(ψ, θ)\",\n",
- " xlabel=\"Normalized Psi (ψₙ)\",\n",
- " ylabel=\"Poloidal Angle (θ_new)\",\n",
- " colorbar_title=\"Z [m]\"\n",
- ")\n",
- "display(p_z_heatmap)\n",
- "println(\"\\n2D color plots for R and Z have been saved.\")\n"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "id": "9859d659",
- "metadata": {},
- "outputs": [],
- "source": [
- "# --- Code to Plot Psi and Theta Contours in R-Z Space ---\n",
- "# This code block goes at the end of your existing script.\n",
- "\n",
- "println(\"\\n--- Plotting Psi and Theta Contours in R-Z Space ---\")\n",
- "\n",
- "# 1. Select a number of contours to display for clarity\n",
- "num_psi_contours = 11 # e.g., from ψ_norm = 0.0 to 1.0 in steps of 0.1\n",
- "num_theta_contours = 13 # e.g., every 30 degrees\n",
- "\n",
- "# 2. Initialize the plot\n",
- "# aspect_ratio=:equal is crucial for tokamak plots to look physically correct.\n",
- "p_flux_surfaces = plot(\n",
- " title=\"Flux Coordinate System Contours in (R, Z)\",\n",
- " xlabel=\"R [m]\",\n",
- " ylabel=\"Z [m]\",\n",
- " aspect_ratio=:equal,\n",
- " legend=:outertopright\n",
- ")\n",
- "\n",
- "# 3. Plot contours of constant ψ (flux surfaces) in blue\n",
- "# We loop through the ROWS of the R_grid and Z_grid matrices.\n",
- "psi_indices = round.(Int, range(1, stop=size(R_grid, 1), length=num_psi_contours))\n",
- "\n",
- "for i in psi_indices\n",
- " # Each row corresponds to a single psi value\n",
- " # We must add the last point to the start to close the loop for a smooth plot\n",
- " R_surface = [R_grid[i, :]; R_grid[i, 1]]\n",
- " Z_surface = [Z_grid[i, :]; Z_grid[i, 1]]\n",
- " plot!(p_flux_surfaces, R_surface, Z_surface, label=\"\", color=:blue, linewidth=1.5)\n",
- "end\n",
- "\n",
- "# 4. Plot contours of constant θ (angle contours) in red\n",
- "# We loop through the COLUMNS of the R_grid and Z_grid matrices.\n",
- "theta_indices = round.(Int, range(1, stop=size(R_grid, 2), length=num_theta_contours))\n",
- "\n",
- "for j in theta_indices\n",
- " # Each column corresponds to a single theta value\n",
- " plot!(p_flux_surfaces, R_grid[:, j], Z_grid[:, j], label=\"\", color=:red, linewidth=1)\n",
- "end\n",
- "\n",
- "# 5. Add a legend manually (a common trick in Plots.jl)\n",
- "plot!(p_flux_surfaces, [], [], color=:blue, label=\"Constant ψ\")\n",
- "plot!(p_flux_surfaces, [], [], color=:red, label=\"Constant θ\")\n",
- "\n",
- "# 6. Display and save the final plot\n",
- "display(p_flux_surfaces)\n",
- "println(\"Flux surface contour plot saved as 'flux_surfaces_RZ.png'\")"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "id": "2c625a4a",
- "metadata": {},
- "outputs": [],
- "source": [
- "# --- Code to Plot 1D Profiles from the 'sq' Spline ---\n",
- "# This code block goes at the end of your existing script.\n",
- "\n",
- "println(\"\\n--- Plotting 1D Profiles from 'sq' Spline ---\")\n",
- "\n",
- "# 1. To get smooth curves, we'll evaluate the spline on a dense grid,\n",
- "# not just on its internal knot points.\n",
- "psi_eval_grid = range(0.0, 1.0, length=200)\n",
- "\n",
- "# 2. Evaluate the 'sq' spline across this dense grid.\n",
- "# Calling spline_eval with a vector input is efficient and returns a matrix\n",
- "# where each column corresponds to one of the splined quantities.\n",
- "println(\"Evaluating 'sq' spline on a dense grid...\")\n",
- "evaluated_profiles = JPEC.Spl.spline_eval(plasma_eq.sq, collect(psi_eval_grid), 0)\n",
- "println(\"Evaluation complete.\")\n",
- "\n",
- "# 3. Extract each profile into its own variable for clarity.\n",
- "# Based on the direct_run implementation:\n",
- "# Column 1: F = R*Bt (Toroidal Field Function)\n",
- "# Column 2: P*μ₀ (Scaled Pressure)\n",
- "# Column 3: Toroidal Flux function (related to dV/dψ_pol)\n",
- "# Column 4: q (Safety Factor)\n",
- "F_profile = evaluated_profiles[:, 1]\n",
- "P_profile = evaluated_profiles[:, 2]\n",
- "Flux_profile = evaluated_profiles[:, 3]\n",
- "q_profile = evaluated_profiles[:, 4]\n",
- "\n",
- "# 4. Create and display the plots\n",
- "\n",
- "# Plot 1: Safety Factor (q)\n",
- "p_q = plot(\n",
- " psi_eval_grid,\n",
- " q_profile,\n",
- " title=\"Safety Factor Profile\",\n",
- " xlabel=\"Normalized Psi (ψₙ)\",\n",
- " ylabel=\"q\",\n",
- " legend=false,\n",
- " linewidth=2\n",
- ")\n",
- "display(p_q)\n",
- "\n",
- "# Plot 2: Scaled Pressure (P*μ₀)\n",
- "p_p = plot(\n",
- " psi_eval_grid,\n",
- " P_profile,\n",
- " title=\"Pressure Profile\",\n",
- " xlabel=\"Normalized Psi (ψₙ)\",\n",
- " ylabel=\"P * μ₀ [T²]\",\n",
- " legend=false,\n",
- " linewidth=2\n",
- ")\n",
- "display(p_p)\n",
- "\n",
- "\n",
- "# Plot 3: Toroidal Field Function (F)\n",
- "p_f = plot(\n",
- " psi_eval_grid,\n",
- " F_profile,\n",
- " title=\"Toroidal Field Function\",\n",
- " xlabel=\"Normalized Psi (ψₙ)\",\n",
- " ylabel=\"F = R * B_t [T*m]\",\n",
- " legend=false,\n",
- " linewidth=2\n",
- ")\n",
- "display(p_f)\n",
- "\n",
- "# Plot 4: Combined plot for comparison\n",
- "p_all_profiles = plot(\n",
- " title=\"1D Equilibrium Profiles\",\n",
- " xlabel=\"Normalized Psi (ψₙ)\",\n",
- " legend=:best\n",
- ")\n",
- "plot!(p_all_profiles, psi_eval_grid, q_profile, label=\"q (Safety Factor)\", linewidth=2)\n",
- "plot!(p_all_profiles, psi_eval_grid, P_profile, label=\"P*μ₀ (Pressure)\", linewidth=2)\n",
- "plot!(p_all_profiles, psi_eval_grid, F_profile, label=\"F (Toroidal Field Fn.)\", linewidth=2)\n",
- "# We can also plot the 3rd quantity, though it's less commonly viewed.\n",
- "# plot!(p_all_profiles, psi_eval_grid, Flux_profile, label=\"Toroidal Flux Fn.\", linewidth=2)\n",
- "display(p_all_profiles)\n",
- "\n",
- "\n",
- "println(\"1D profile plots saved successfully.\")"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "id": "3b359ecb",
- "metadata": {},
- "outputs": [],
- "source": []
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "id": "d8ba8174",
- "metadata": {},
- "outputs": [],
- "source": []
- }
- ],
- "metadata": {
- "kernelspec": {
- "display_name": "Julia 1.11.6",
- "language": "julia",
- "name": "julia-1.11"
- },
- "language_info": {
- "file_extension": ".jl",
- "mimetype": "application/julia",
- "name": "julia",
- "version": "1.11.6"
- }
- },
- "nbformat": 4,
- "nbformat_minor": 5
-}
diff --git a/notebooks/equil_lar_example.ipynb b/notebooks/equil_lar_example.ipynb
deleted file mode 100644
index 4d73d548ef..0000000000
--- a/notebooks/equil_lar_example.ipynb
+++ /dev/null
@@ -1,263 +0,0 @@
-{
- "cells": [
- {
- "cell_type": "code",
- "execution_count": null,
- "id": "bc77cb03",
- "metadata": {},
- "outputs": [],
- "source": [
- "using Pkg\n",
- "Pkg.activate(\"..\")\n",
- "Pkg.resolve() \n",
- "Pkg.instantiate()\n",
- "using DifferentialEquations,JPEC, Plots, DelimitedFiles"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "id": "8fb8cfd4",
- "metadata": {},
- "outputs": [],
- "source": [
- "equil_input = JPEC.Equilibrium.EquilibriumConfig(; control=JPEC.Equilibrium.EquilibriumControl(eq_type=\"lar\", eq_filename=\"lar.toml\"), output=JPEC.Equilibrium.EquilibriumOutput())\n",
- "lar_input = JPEC.Equilibrium.LargeAspectRatioConfig(; lar_r0=10, lar_a=1, beta0=0.001, q0=1.5, p_pres=2, p_sig=1)"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "id": "d7836d02",
- "metadata": {},
- "outputs": [],
- "source": [
- "plasma_eq= JPEC.Equilibrium.setup_equilibrium(equil_input, lar_input)"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "id": "88a7f2d7",
- "metadata": {},
- "outputs": [],
- "source": [
- "# --- Final Code to Generate 2D Color Plots of R(ψ,θ) and Z(ψ,θ) ---\n",
- "println(\"\\n--- Generating data for 2D color plots ---\")\n",
- "# 1. Define the grid in flux coordinates (ψ_norm, θ_new)\n",
- "# This part is identical to the previous steps.\n",
- "equil_control = plasma_eq.config.control\n",
- "psi_norm_grid = collect(range(equil_control.psilow, equil_control.psihigh, length=equil_control.mpsi + 1))\n",
- "theta_new_grid = collect(range(0.0, 1.0, length=equil_control.mtheta + 1))\n",
- "# 2. Evaluate the `rzphi` spline to get the R and Z values.\n",
- "println(\"Evaluating the 'rzphi' mapping spline...\")\n",
- "fs_grid = JPEC.Spl.bicube_eval(plasma_eq.rzphi, psi_norm_grid, theta_new_grid)\n",
- "println(\"Evaluation complete.\")\n",
- "# 3. Transform the spline output to physical (R, Z) coordinates.\n",
- "# This calculates R_grid[i,j] = R(ψ[i], θ[j]) and Z_grid[i,j] = Z(ψ[i], θ[j])\n",
- "rfac_sq = fs_grid[:, :, 1]\n",
- "eta_term = fs_grid[:, :, 2]\n",
- "theta_new_mesh = ones(length(psi_norm_grid)) * theta_new_grid'\n",
- "eta_grid = 2.0 * pi .* (theta_new_mesh .+ eta_term)\n",
- "rfac_grid = sqrt.(max.(0.0, rfac_sq))\n",
- "R_grid = plasma_eq.ro .+ rfac_grid .* cos.(eta_grid)\n",
- "Z_grid = plasma_eq.zo .+ rfac_grid .* sin.(eta_grid)\n",
- "println(\"Calculated R and Z grids.\")\n",
- "# 4. Create the 2D color plot for R(ψ,θ)\n",
- "println(\"--- Plotting heatmap for R(ψ,θ) ---\")\n",
- "p_r_heatmap = heatmap(\n",
- " psi_norm_grid,\n",
- " theta_new_grid,\n",
- " R_grid', # Note the transpose ' to match axis dimensions\n",
- " title=\"Major Radius R(ψ, θ)\",\n",
- " xlabel=\"Normalized Psi (ψₙ)\",\n",
- " ylabel=\"Poloidal Angle (θ_new)\",\n",
- " colorbar_title=\"R [m]\"\n",
- ")\n",
- "display(p_r_heatmap)\n",
- "# 5. Create the 2D color plot for Z(ψ,θ)\n",
- "println(\"--- Plotting heatmap for Z(ψ,θ) ---\")\n",
- "p_z_heatmap = heatmap(\n",
- " psi_norm_grid,\n",
- " theta_new_grid,\n",
- " Z_grid', # Note the transpose ' to match axis dimensions\n",
- " title=\"Vertical Position Z(ψ, θ)\",\n",
- " xlabel=\"Normalized Psi (ψₙ)\",\n",
- " ylabel=\"Poloidal Angle (θ_new)\",\n",
- " colorbar_title=\"Z [m]\"\n",
- ")\n",
- "display(p_z_heatmap)\n",
- "println(\"\\n2D color plots for R and Z have been saved.\")"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "id": "22c45ff5",
- "metadata": {},
- "outputs": [],
- "source": [
- "# --- Code to Plot Psi and Theta Contours in R-Z Space ---\n",
- "# This code block goes at the end of your existing script.\n",
- "\n",
- "println(\"\\n--- Plotting Psi and Theta Contours in R-Z Space ---\")\n",
- "\n",
- "# 1. Select a number of contours to display for clarity\n",
- "num_psi_contours = 11 # e.g., from ψ_norm = 0.0 to 1.0 in steps of 0.1\n",
- "num_theta_contours = 13 # e.g., every 30 degrees\n",
- "\n",
- "# 2. Initialize the plot\n",
- "# aspect_ratio=:equal is crucial for tokamak plots to look physically correct.\n",
- "p_flux_surfaces = plot(\n",
- " title=\"Flux Coordinate System Contours in (R, Z)\",\n",
- " xlabel=\"R [m]\",\n",
- " ylabel=\"Z [m]\",\n",
- " aspect_ratio=:equal,\n",
- " legend=:outertopright\n",
- ")\n",
- "\n",
- "# 3. Plot contours of constant ψ (flux surfaces) in blue\n",
- "# We loop through the ROWS of the R_grid and Z_grid matrices.\n",
- "psi_indices = round.(Int, range(1, stop=size(R_grid, 1), length=num_psi_contours))\n",
- "\n",
- "for i in psi_indices\n",
- " # Each row corresponds to a single psi value\n",
- " # We must add the last point to the start to close the loop for a smooth plot\n",
- " R_surface = [R_grid[i, :]; R_grid[i, 1]]\n",
- " Z_surface = [Z_grid[i, :]; Z_grid[i, 1]]\n",
- " plot!(p_flux_surfaces, R_surface, Z_surface, label=\"\", color=:blue, linewidth=1.5)\n",
- "end\n",
- "\n",
- "# 4. Plot contours of constant θ (angle contours) in red\n",
- "# We loop through the COLUMNS of the R_grid and Z_grid matrices.\n",
- "theta_indices = round.(Int, range(1, stop=size(R_grid, 2), length=num_theta_contours))\n",
- "\n",
- "for j in theta_indices\n",
- " # Each column corresponds to a single theta value\n",
- " plot!(p_flux_surfaces, R_grid[:, j], Z_grid[:, j], label=\"\", color=:red, linewidth=1)\n",
- "end\n",
- "\n",
- "# 5. Add a legend manually (a common trick in Plots.jl)\n",
- "plot!(p_flux_surfaces, [], [], color=:blue, label=\"Constant ψ\")\n",
- "plot!(p_flux_surfaces, [], [], color=:red, label=\"Constant θ\")\n",
- "\n",
- "# 6. Display and save the final plot\n",
- "display(p_flux_surfaces)\n",
- "println(\"Flux surface contour plot saved as 'flux_surfaces_RZ.png'\")"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "id": "87de5490",
- "metadata": {},
- "outputs": [],
- "source": [
- "# --- Code to Plot 1D Profiles from the 'sq' Spline ---\n",
- "# This code block goes at the end of your existing script.\n",
- "\n",
- "println(\"\\n--- Plotting 1D Profiles from 'sq' Spline ---\")\n",
- "\n",
- "# 1. To get smooth curves, we'll evaluate the spline on a dense grid,\n",
- "# not just on its internal knot points.\n",
- "psi_eval_grid = range(0.0, 1.0, length=200)\n",
- "\n",
- "# 2. Evaluate the 'sq' spline across this dense grid.\n",
- "# Calling spline_eval with a vector input is efficient and returns a matrix\n",
- "# where each column corresponds to one of the splined quantities.\n",
- "println(\"Evaluating 'sq' spline on a dense grid...\")\n",
- "evaluated_profiles = JPEC.Spl.spline_eval(plasma_eq.sq, collect(psi_eval_grid), 0)\n",
- "println(\"Evaluation complete.\")\n",
- "\n",
- "# 3. Extract each profile into its own variable for clarity.\n",
- "# Based on the direct_run implementation:\n",
- "# Column 1: F = R*Bt (Toroidal Field Function)\n",
- "# Column 2: P*μ₀ (Scaled Pressure)\n",
- "# Column 3: Toroidal Flux function (related to dV/dψ_pol)\n",
- "# Column 4: q (Safety Factor)\n",
- "F_profile = evaluated_profiles[:, 1]\n",
- "P_profile = evaluated_profiles[:, 2]\n",
- "Flux_profile = evaluated_profiles[:, 3]\n",
- "q_profile = evaluated_profiles[:, 4]\n",
- "\n",
- "# 4. Create and display the plots\n",
- "\n",
- "# Plot 1: Safety Factor (q)\n",
- "p_q = plot(\n",
- " psi_eval_grid,\n",
- " q_profile,\n",
- " title=\"Safety Factor Profile\",\n",
- " xlabel=\"Normalized Psi (ψₙ)\",\n",
- " ylabel=\"q\",\n",
- " legend=false,\n",
- " linewidth=2\n",
- ")\n",
- "display(p_q)\n",
- "\n",
- "# Plot 2: Scaled Pressure (P*μ₀)\n",
- "p_p = plot(\n",
- " psi_eval_grid,\n",
- " P_profile,\n",
- " title=\"Pressure Profile\",\n",
- " xlabel=\"Normalized Psi (ψₙ)\",\n",
- " ylabel=\"P * μ₀ [T²]\",\n",
- " legend=false,\n",
- " linewidth=2\n",
- ")\n",
- "display(p_p)\n",
- "\n",
- "\n",
- "# Plot 3: Toroidal Field Function (F)\n",
- "p_f = plot(\n",
- " psi_eval_grid,\n",
- " F_profile,\n",
- " title=\"Toroidal Field Function\",\n",
- " xlabel=\"Normalized Psi (ψₙ)\",\n",
- " ylabel=\"F = R * B_t [T*m]\",\n",
- " legend=false,\n",
- " linewidth=2\n",
- ")\n",
- "display(p_f)\n",
- "\n",
- "# Plot 4: Combined plot for comparison\n",
- "p_all_profiles = plot(\n",
- " title=\"1D Equilibrium Profiles\",\n",
- " xlabel=\"Normalized Psi (ψₙ)\",\n",
- " legend=:best\n",
- ")\n",
- "plot!(p_all_profiles, psi_eval_grid, q_profile, label=\"q (Safety Factor)\", linewidth=2)\n",
- "plot!(p_all_profiles, psi_eval_grid, P_profile, label=\"P*μ₀ (Pressure)\", linewidth=2)\n",
- "plot!(p_all_profiles, psi_eval_grid, F_profile, label=\"F (Toroidal Field Fn.)\", linewidth=2)\n",
- "# We can also plot the 3rd quantity, though it's less commonly viewed.\n",
- "# plot!(p_all_profiles, psi_eval_grid, Flux_profile, label=\"Toroidal Flux Fn.\", linewidth=2)\n",
- "display(p_all_profiles)\n",
- "\n",
- "\n",
- "println(\"1D profile plots saved successfully.\")"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "id": "0735e75a",
- "metadata": {},
- "outputs": [],
- "source": []
- }
- ],
- "metadata": {
- "kernelspec": {
- "display_name": "Julia 1.11.6",
- "language": "julia",
- "name": "julia-1.11"
- },
- "language_info": {
- "file_extension": ".jl",
- "mimetype": "application/julia",
- "name": "julia",
- "version": "1.11.6"
- }
- },
- "nbformat": 4,
- "nbformat_minor": 5
-}
diff --git a/notebooks/equil_soloviev_example.ipynb b/notebooks/equil_soloviev_example.ipynb
deleted file mode 100644
index 086dcddec5..0000000000
--- a/notebooks/equil_soloviev_example.ipynb
+++ /dev/null
@@ -1,316 +0,0 @@
-{
- "cells": [
- {
- "cell_type": "code",
- "execution_count": null,
- "id": "710e987d",
- "metadata": {},
- "outputs": [],
- "source": [
- "using Pkg\n",
- "Pkg.activate(\"..\")\n",
- "Pkg.resolve()\n",
- "Pkg.instantiate()\n",
- "using JPEC, Plots\n",
- "# test"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "id": "cb106129",
- "metadata": {},
- "outputs": [],
- "source": [
- "### Set equil input parameters\n",
- "equil_in = JPEC.Equilibrium.EquilibriumConfig(control=JPEC.Equilibrium.EquilibriumControl(\n",
- " eq_filename=\"sol_test\", # eq_filename\n",
- " eq_type=\"sol\", # eq_type\n",
- " jac_type=\"hamada\", # jac_type\n",
- " mpsi=100, # mpsi (number of radial grid points)\n",
- " mtheta=128), # mtheta (number of poloidal grid points)\n",
- " output=JPEC.Equilibrium.EquilibriumOutput()) \n",
- "\n",
- "### Set Soloviev input parameters\n",
- "sol_inputs = JPEC.Equilibrium.SolevevConfig(;\n",
- " mr=65, # number of radial grid zones\n",
- " mz=65, # number of axial grid zones\n",
- " ma=64, # number of flux grid zones\n",
- " e=1.0, # elongation\n",
- " a=1.0, # minor radius\n",
- " r0=3.0, # major radius\n",
- " q0=1.26, # safety factor at the o-point\n",
- " p0fac=1.0, # scale on-axis pressure (P-> P+P0*p0fac. beta changes. Phi,q constant)\n",
- " b0fac=1.0, # scale toroidal field at constant beta (s*Phi,s*f,s^2*P. bt changes. Shape,beta constant)\n",
- " f0fac=1.0 # scale toroidal field at constant pressure (s*f. beta,q changes. Phi,p,bp constant)\n",
- " )\n"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "id": "9843a0d1",
- "metadata": {},
- "outputs": [],
- "source": [
- "### Set up Soloviev equilibrium and generate input splines\n",
- "\n",
- "directrun_inputs = JPEC.Equilibrium.sol_run(\n",
- " equil_in,\n",
- " sol_inputs\n",
- " )"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "id": "b37e0a5c",
- "metadata": {},
- "outputs": [],
- "source": [
- "plot(\n",
- " directrun_inputs.sq_in.xs,\n",
- " directrun_inputs.sq_in.fs[:,2],\n",
- " label=raw\"pfac * (p0fac - $\\psi_N$)\",\n",
- " xlabel=raw\"$\\psi_N$\"\n",
- " )"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "id": "6488baff",
- "metadata": {},
- "outputs": [],
- "source": [
- "### Execute direct_run() and solve equilibrium\n",
- "\n",
- "plasma_eq = JPEC.Equilibrium.equilibrium_solver(directrun_inputs)"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "id": "179089da",
- "metadata": {},
- "outputs": [],
- "source": [
- "# --- Final Code to Generate 2D Color Plots of R(ψ,θ) and Z(ψ,θ) ---\n",
- "println(\"\\n--- Generating data for 2D color plots ---\")\n",
- "# 1. Define the grid in flux coordinates (ψ_norm, θ_new)\n",
- "# This part is identical to the previous steps.\n",
- "equil_control = plasma_eq.config.control\n",
- "psi_norm_grid = collect(range(equil_control.psilow, equil_control.psihigh, length=equil_control.mpsi + 1))\n",
- "theta_new_grid = collect(range(0.0, 1.0, length=equil_control.mtheta + 1))\n",
- "# 2. Evaluate the `rzphi` spline to get the R and Z values.\n",
- "println(\"Evaluating the 'rzphi' mapping spline...\")\n",
- "fs_grid = JPEC.Spl.bicube_eval(plasma_eq.rzphi, psi_norm_grid, theta_new_grid)\n",
- "println(\"Evaluation complete.\")\n",
- "# 3. Transform the spline output to physical (R, Z) coordinates.\n",
- "# This calculates R_grid[i,j] = R(ψ[i], θ[j]) and Z_grid[i,j] = Z(ψ[i], θ[j])\n",
- "rfac_sq = fs_grid[:, :, 1]\n",
- "eta_term = fs_grid[:, :, 2]\n",
- "theta_new_mesh = ones(length(psi_norm_grid)) * theta_new_grid'\n",
- "eta_grid = 2.0 * pi .* (theta_new_mesh .+ eta_term)\n",
- "rfac_grid = sqrt.(max.(0.0, rfac_sq))\n",
- "R_grid = plasma_eq.ro .+ rfac_grid .* cos.(eta_grid)\n",
- "Z_grid = plasma_eq.zo .+ rfac_grid .* sin.(eta_grid)\n",
- "println(\"Calculated R and Z grids.\")\n",
- "# 4. Create the 2D color plot for R(ψ,θ)\n",
- "println(\"--- Plotting heatmap for R(ψ,θ) ---\")\n",
- "p_r_heatmap = heatmap(\n",
- " psi_norm_grid,\n",
- " theta_new_grid,\n",
- " R_grid', # Note the transpose ' to match axis dimensions\n",
- " title=\"Major Radius R(ψ, θ)\",\n",
- " xlabel=\"Normalized Psi (ψₙ)\",\n",
- " ylabel=\"Poloidal Angle (θ_new)\",\n",
- " colorbar_title=\"R [m]\"\n",
- ")\n",
- "display(p_r_heatmap)\n",
- "# 5. Create the 2D color plot for Z(ψ,θ)\n",
- "println(\"--- Plotting heatmap for Z(ψ,θ) ---\")\n",
- "p_z_heatmap = heatmap(\n",
- " psi_norm_grid,\n",
- " theta_new_grid,\n",
- " Z_grid', # Note the transpose ' to match axis dimensions\n",
- " title=\"Vertical Position Z(ψ, θ)\",\n",
- " xlabel=\"Normalized Psi (ψₙ)\",\n",
- " ylabel=\"Poloidal Angle (θ_new)\",\n",
- " colorbar_title=\"Z [m]\"\n",
- ")\n",
- "display(p_z_heatmap)\n",
- "println(\"\\n2D color plots for R and Z have been saved.\")"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "id": "b5f09972",
- "metadata": {},
- "outputs": [],
- "source": [
- "# --- Code to Plot Psi and Theta Contours in R-Z Space ---\n",
- "# This code block goes at the end of your existing script.\n",
- "\n",
- "println(\"\\n--- Plotting Psi and Theta Contours in R-Z Space ---\")\n",
- "\n",
- "# 1. Select a number of contours to display for clarity\n",
- "num_psi_contours = 11 # e.g., from ψ_norm = 0.0 to 1.0 in steps of 0.1\n",
- "num_theta_contours = 13 # e.g., every 30 degrees\n",
- "\n",
- "# 2. Initialize the plot\n",
- "# aspect_ratio=:equal is crucial for tokamak plots to look physically correct.\n",
- "p_flux_surfaces = plot(\n",
- " title=\"Flux Coordinate System Contours in (R, Z)\",\n",
- " xlabel=\"R [m]\",\n",
- " ylabel=\"Z [m]\",\n",
- " aspect_ratio=:equal,\n",
- " legend=:outertopright\n",
- ")\n",
- "\n",
- "# 3. Plot contours of constant ψ (flux surfaces) in blue\n",
- "# We loop through the ROWS of the R_grid and Z_grid matrices.\n",
- "psi_indices = round.(Int, range(1, stop=size(R_grid, 1), length=num_psi_contours))\n",
- "\n",
- "for i in psi_indices\n",
- " # Each row corresponds to a single psi value\n",
- " # We must add the last point to the start to close the loop for a smooth plot\n",
- " R_surface = [R_grid[i, :]; R_grid[i, 1]]\n",
- " Z_surface = [Z_grid[i, :]; Z_grid[i, 1]]\n",
- " plot!(p_flux_surfaces, R_surface, Z_surface, label=\"\", color=:blue, linewidth=1.5)\n",
- "end\n",
- "\n",
- "# 4. Plot contours of constant θ (angle contours) in red\n",
- "# We loop through the COLUMNS of the R_grid and Z_grid matrices.\n",
- "theta_indices = round.(Int, range(1, stop=size(R_grid, 2), length=num_theta_contours))\n",
- "\n",
- "for j in theta_indices\n",
- " # Each column corresponds to a single theta value\n",
- " plot!(p_flux_surfaces, R_grid[:, j], Z_grid[:, j], label=\"\", color=:red, linewidth=1)\n",
- "end\n",
- "\n",
- "# 5. Add a legend manually (a common trick in Plots.jl)\n",
- "plot!(p_flux_surfaces, [], [], color=:blue, label=\"Constant ψ\")\n",
- "plot!(p_flux_surfaces, [], [], color=:red, label=\"Constant θ\")\n",
- "\n",
- "# 6. Display and save the final plot\n",
- "display(p_flux_surfaces)\n",
- "println(\"Flux surface contour plot saved as 'flux_surfaces_RZ.png'\")"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "id": "f07cd2f9",
- "metadata": {},
- "outputs": [],
- "source": [
- "# --- Code to Plot 1D Profiles from the 'sq' Spline ---\n",
- "# This code block goes at the end of your existing script.\n",
- "\n",
- "println(\"\\n--- Plotting 1D Profiles from 'sq' Spline ---\")\n",
- "\n",
- "# 1. To get smooth curves, we'll evaluate the spline on a dense grid,\n",
- "# not just on its internal knot points.\n",
- "psi_eval_grid = range(0.0, 1.0, length=200)\n",
- "\n",
- "# 2. Evaluate the 'sq' spline across this dense grid.\n",
- "# Calling spline_eval with a vector input is efficient and returns a matrix\n",
- "# where each column corresponds to one of the splined quantities.\n",
- "println(\"Evaluating 'sq' spline on a dense grid...\")\n",
- "evaluated_profiles = JPEC.Spl.spline_eval(plasma_eq.sq, collect(psi_eval_grid), 0)\n",
- "println(\"Evaluation complete.\")\n",
- "\n",
- "# 3. Extract each profile into its own variable for clarity.\n",
- "# Based on the direct_run implementation:\n",
- "# Column 1: F = R*Bt (Toroidal Field Function)\n",
- "# Column 2: P*μ₀ (Scaled Pressure)\n",
- "# Column 3: Toroidal Flux function (related to dV/dψ_pol)\n",
- "# Column 4: q (Safety Factor)\n",
- "F_profile = evaluated_profiles[:, 1]\n",
- "P_profile = evaluated_profiles[:, 2]\n",
- "Flux_profile = evaluated_profiles[:, 3]\n",
- "q_profile = evaluated_profiles[:, 4]\n",
- "\n",
- "# 4. Create and display the plots\n",
- "\n",
- "# Plot 1: Safety Factor (q)\n",
- "p_q = plot(\n",
- " psi_eval_grid,\n",
- " q_profile,\n",
- " title=\"Safety Factor Profile\",\n",
- " xlabel=\"Normalized Psi (ψₙ)\",\n",
- " ylabel=\"q\",\n",
- " legend=false,\n",
- " linewidth=2\n",
- ")\n",
- "display(p_q)\n",
- "\n",
- "# Plot 2: Scaled Pressure (P*μ₀)\n",
- "p_p = plot(\n",
- " psi_eval_grid,\n",
- " P_profile,\n",
- " title=\"Pressure Profile\",\n",
- " xlabel=\"Normalized Psi (ψₙ)\",\n",
- " ylabel=\"P * μ₀ [T²]\",\n",
- " legend=false,\n",
- " linewidth=2\n",
- ")\n",
- "display(p_p)\n",
- "\n",
- "\n",
- "# Plot 3: Toroidal Field Function (F)\n",
- "p_f = plot(\n",
- " psi_eval_grid,\n",
- " F_profile,\n",
- " title=\"Toroidal Field Function\",\n",
- " xlabel=\"Normalized Psi (ψₙ)\",\n",
- " ylabel=\"F = R * B_t [T*m]\",\n",
- " legend=false,\n",
- " linewidth=2\n",
- ")\n",
- "display(p_f)\n",
- "\n",
- "# Plot 4: Combined plot for comparison\n",
- "p_all_profiles = plot(\n",
- " title=\"1D Equilibrium Profiles\",\n",
- " xlabel=\"Normalized Psi (ψₙ)\",\n",
- " legend=:best\n",
- ")\n",
- "plot!(p_all_profiles, psi_eval_grid, q_profile, label=\"q (Safety Factor)\", linewidth=2)\n",
- "plot!(p_all_profiles, psi_eval_grid, P_profile, label=\"P*μ₀ (Pressure)\", linewidth=2)\n",
- "plot!(p_all_profiles, psi_eval_grid, F_profile, label=\"F (Toroidal Field Fn.)\", linewidth=2)\n",
- "# We can also plot the 3rd quantity, though it's less commonly viewed.\n",
- "# plot!(p_all_profiles, psi_eval_grid, Flux_profile, label=\"Toroidal Flux Fn.\", linewidth=2)\n",
- "display(p_all_profiles)\n",
- "\n",
- "\n",
- "println(\"1D profile plots saved successfully.\")"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "id": "42602d76",
- "metadata": {},
- "outputs": [],
- "source": []
- }
- ],
- "metadata": {
- "kernelspec": {
- "display_name": "Julia 1.11.6",
- "language": "julia",
- "name": "julia-1.11"
- },
- "language_info": {
- "file_extension": ".jl",
- "mimetype": "application/julia",
- "name": "julia",
- "version": "1.11.6"
- }
- },
- "nbformat": 4,
- "nbformat_minor": 5
-}
diff --git a/notebooks/equil_test_bu.ipynb b/notebooks/equil_test_bu.ipynb
deleted file mode 100644
index a32f278a71..0000000000
--- a/notebooks/equil_test_bu.ipynb
+++ /dev/null
@@ -1,350 +0,0 @@
-{
- "cells": [
- {
- "cell_type": "code",
- "execution_count": null,
- "id": "814db625",
- "metadata": {},
- "outputs": [],
- "source": [
- "using Pkg\n",
- "Pkg.activate(\"..\") \n",
- "Pkg.instantiate()\n",
- "using JPEC, Plots\n",
- "gr() "
- ]
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "id": "94c3d4e9",
- "metadata": {},
- "outputs": [],
- "source": [
- "# 1. Define the input parameters for the equilibrium solver.\n",
- "# - eq_filename: The name of the g-file we just created.\n",
- "# - eq_type: \"efit\" for a standard g-file.\n",
- "# - jac_type: \"boozer\" or \"hamada\" for the output coordinates.\n",
- "# - mpsi, mtheta: Resolution of the output grid.\n",
- "equil_input = JPEC.Equilibrium.EquilInput(\n",
- " \"beta_1.00\", # eq_filename\n",
- " \"efit\", # eq_type\n",
- " \"boozer\", # jac_type\n",
- " 0.01, # psilow\n",
- " 1.0, # psihigh\n",
- " 100, # mpsi (number of radial grid points)\n",
- " 128 # mtheta (number of poloidal grid points)\n",
- ")\n",
- "\n",
- "# 2. Run the main equilibrium setup function.\n",
- "# This will read the file, solve the direct problem, and return the final object.\n",
- "println(\"Starting equilibrium reconstruction...\")\n",
- "plasma_eq = JPEC.Equilibrium.setup_equilibrium(equil_input)\n",
- "println(\"Equilibrium reconstruction complete.\")"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "id": "82c831fb",
- "metadata": {},
- "outputs": [],
- "source": [
- "# 새 셀: JPEC 스플라인 직접 테스트\n",
- "println(\"🔍 Direct JPEC Spline Testing\")\n",
- "println(\"=\"^40)\n",
- "\n",
- "# 1D 프로파일 스플라인 테스트\n",
- "println(\"\\n📈 Testing 1D profile splines...\")\n",
- "try\n",
- " psi_test = [0.0, 0.25, 0.5, 0.75, 1.0]\n",
- " \n",
- " for psi in psi_test\n",
- " result = JPEC.SplinesMod.spline_eval(plasma_eq.sq, psi)\n",
- " println(\" ψ=$(psi): F=$(round(result[1], digits=3)), P=$(round(result[2], digits=3)), q=$(round(result[4], digits=3))\")\n",
- " end\n",
- " \n",
- " println(\" ✅ 1D spline evaluation successful\")\n",
- " \n",
- "catch e\n",
- " println(\" ❌ 1D spline evaluation failed: $e\")\n",
- "end\n",
- "\n",
- "# 2D 기하학적 스플라인 테스트\n",
- "println(\"\\n🗺️ Testing 2D geometry splines...\")\n",
- "try\n",
- " psi_test = 0.5\n",
- " theta_test = [0.0, 0.25, 0.5, 0.75]\n",
- " \n",
- " for theta in theta_test\n",
- " f, fx, fy = JPEC.SplinesMod.bicube_eval(plasma_eq.rzphi, psi_test, theta, 1)\n",
- " println(\" (ψ=$(psi_test), θ=$(theta)): r²=$(round(f[1], digits=3)), shift=$(round(f[2], digits=3))\")\n",
- " end\n",
- " \n",
- " println(\" ✅ 2D spline evaluation successful\")\n",
- " \n",
- "catch e\n",
- " println(\" ❌ 2D spline evaluation failed: $e\")\n",
- "end"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "id": "23bbd6ba",
- "metadata": {},
- "outputs": [],
- "source": [
- "# Fourfit v4 테스트 (v3 대신 v4 사용)\n",
- "println(\"🚀 Testing Fourfit v4 with Real JPEC Equilibrium Data\")\n",
- "println(\"=\"^60)\n",
- "\n",
- "# plasma_eq 존재 확인\n",
- "if !@isdefined(plasma_eq)\n",
- " println(\"❌ plasma_eq is not defined - please run equilibrium setup first!\")\n",
- " return\n",
- "end\n",
- "\n",
- "# 1. Fourfit v4 모듈 로드\n",
- "include(\"/Users/seoda-eun/JPEC/fourfit_old_v4.jl\")\n",
- "using .FourfitOldV4\n",
- "\n",
- "# 2. 실제 JPEC 평형으로 Fourfit 실행\n",
- "println(\"\\n📊 JPEC Equilibrium Info:\")\n",
- "println(\" Type: $(typeof(plasma_eq))\")\n",
- "println(\" Magnetic axis: R₀=$(round(plasma_eq.ro, digits=3)), Z₀=$(round(plasma_eq.zo, digits=6))\")\n",
- "println(\" Flux normalization: ψ₀=$(round(plasma_eq.psio, digits=3))\")\n",
- "println(\" Splines available:\")\n",
- "println(\" - sq (1D profiles): $(plasma_eq.sq !== nothing ? \"✅\" : \"❌\")\")\n",
- "println(\" - rzphi (2D geometry): $(plasma_eq.rzphi !== nothing ? \"✅\" : \"❌\")\")\n",
- "println(\" - eq_quantities: $(plasma_eq.eq_quantities !== nothing ? \"✅\" : \"❌\")\")\n",
- "\n",
- "# 3. Fourfit 실행\n",
- "println(\"\\n🧪 Running Fourfit v4 with real JPEC data...\")\n",
- "global success, fourfit_data, eq_data = test_fourfit_with_jpec_equilibrium(plasma_eq)\n",
- "\n",
- "if success\n",
- " println(\"\\n🎉 Fourfit execution successful!\")\n",
- " \n",
- " # 결과 분석\n",
- " println(\"\\n📈 Results Analysis:\")\n",
- " println(\" Grid size: $(fourfit_data.mpsi+1) × $(fourfit_data.mtheta+1)\")\n",
- " println(\" Mode range: $(fourfit_data.mlow):$(fourfit_data.mhigh)\")\n",
- " println(\" Toroidal mode: n = $(fourfit_data.nn)\")\n",
- " \n",
- " # 데이터 소스 확인\n",
- " println(\"\\n🔍 Data Sources:\")\n",
- " println(\" 1D Profiles: $(get(eq_data, \"has_real_jpec\", false) ? \"Real JPEC splines\" : \"Mock data\")\")\n",
- " println(\" 2D Geometry: $(get(eq_data, \"has_real_geometry\", false) ? \"Real JPEC bicubic\" : \"Simplified\")\")\n",
- " \n",
- " # 프로파일 정보\n",
- " println(\"\\n📊 Equilibrium Profiles:\")\n",
- " F_prof = eq_data[\"F_profile\"]\n",
- " P_prof = eq_data[\"P_profile\"] \n",
- " q_prof = eq_data[\"q_profile\"]\n",
- " \n",
- " println(\" F profile range: [$(round(minimum(F_prof), digits=3)), $(round(maximum(F_prof), digits=3))] T⋅m\")\n",
- " println(\" P profile range: [$(round(minimum(P_prof), digits=3)), $(round(maximum(P_prof), digits=3))] T²\")\n",
- " println(\" q profile range: [$(round(minimum(q_prof), digits=3)), $(round(maximum(q_prof), digits=3))]\")\n",
- " \n",
- " # MHD 행렬 정보\n",
- " if haskey(fourfit_data.cache, \"mhd_matrix\")\n",
- " matrix = fourfit_data.cache[\"mhd_matrix\"]\n",
- " println(\"\\n🔢 MHD Matrix Properties:\")\n",
- " println(\" Matrix size: $(size(matrix[\"A_matrix\"]))\")\n",
- " \n",
- " # 고유값 분석\n",
- " try\n",
- " eigenvals = eigvals(matrix[\"A_matrix\"])\n",
- " real_eigs = real(eigenvals)\n",
- " println(\" Eigenvalues:\")\n",
- " println(\" Range: [$(round(minimum(real_eigs), digits=3)), $(round(maximum(real_eigs), digits=3))]\")\n",
- " println(\" All positive: $(all(real_eigs .> 0) ? \"✅\" : \"❌\")\")\n",
- " println(\" Smallest eigenvalue: $(round(minimum(real_eigs), digits=6))\")\n",
- " \n",
- " # 조건수\n",
- " cond_num = cond(matrix[\"A_matrix\"])\n",
- " println(\" Condition number: $(round(cond_num, digits=2))\")\n",
- " \n",
- " catch e\n",
- " println(\" Eigenvalue analysis failed: $e\")\n",
- " end\n",
- " end\n",
- " \n",
- "else\n",
- " println(\"\\n❌ Fourfit execution failed!\")\n",
- "end"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "id": "97a529f4",
- "metadata": {},
- "outputs": [],
- "source": [
- "# The plasma_eq object contains the final 1D profile spline, `sq`.\n",
- "# We will evaluate it on a fine grid to get smooth plot lines.\n",
- "psi_norm_grid = range(0.0, 1.0, length=200)\n",
- "\n",
- "# spline_eval returns the function values (and derivatives if requested).\n",
- "# For sq, the quantities are: 1:F, 2:P*mu0, 3:Toroidal Flux, 4:q\n",
- "f_profiles = JPEC.spline_eval(plasma_eq.sq, collect(psi_norm_grid))\n",
- "\n",
- "# Extract each profile into its own variable for clarity\n",
- "F_profile = f_profiles[:, 1]\n",
- "P_profile = f_profiles[:, 2]\n",
- "tor_flux_prof = f_profiles[:, 3]\n",
- "q_profile = f_profiles[:, 4]"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "id": "131e2883",
- "metadata": {},
- "outputs": [],
- "source": [
- "\n",
- "p = plot(layout=(2, 2), size=(900, 700), margin=5Plots.mm)\n",
- "\n",
- "# Plot 1: F = R*B_phi\n",
- "plot!(p[1], psi_norm_grid, F_profile,\n",
- " xlabel=\"Normalized Poloidal Flux (ψ_norm)\",\n",
- " ylabel=\"F [T⋅m]\",\n",
- " title=\"Toroidal Field Function (F)\",\n",
- " legend=false,\n",
- " lw=2\n",
- ")\n",
- "\n",
- "# Plot 2: Pressure\n",
- "plot!(p[2], psi_norm_grid, P_profile,\n",
- " xlabel=\"Normalized Poloidal Flux (ψ_norm)\",\n",
- " ylabel=\"μ₀P [T²]\",\n",
- " title=\"Pressure Profile\",\n",
- " legend=false,\n",
- " lw=2\n",
- ")\n",
- "\n",
- "# Plot 3: Safety Factor (q)\n",
- "plot!(p[3], psi_norm_grid, q_profile,\n",
- " xlabel=\"Normalized Poloidal Flux (ψ_norm)\",\n",
- " ylabel=\"q\",\n",
- " title=\"Safety Factor (q) Profile\",\n",
- " legend=false,\n",
- " lw=2\n",
- ")\n",
- "\n",
- "# Plot 4: Toroidal Flux\n",
- "plot!(p[4], psi_norm_grid, tor_flux_prof,\n",
- " xlabel=\"Normalized Poloidal Flux (ψ_norm)\",\n",
- " ylabel=\"Φ / (2π)² [Wb]\",\n",
- " title=\"Toroidal Flux Profile\",\n",
- " legend=false,\n",
- " lw=2\n",
- ")\n",
- "\n",
- "# Display the final plot\n",
- "p"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "id": "d74a45e4",
- "metadata": {},
- "outputs": [],
- "source": [
- "# block 6\n",
- "# --- Plot Straight-Field-Line Angle (θ) Contours ---\n",
- "\n",
- "p_theta = contour(\n",
- " R_grid, \n",
- " Z_grid, \n",
- " THETA_values_on_grid,\n",
- " title=\"Straight-Field-Line Angle (θ) Contours\",\n",
- " xlabel=\"R [m]\",\n",
- " ylabel=\"Z [m]\",\n",
- " levels=20,\n",
- " c=:hsv,\n",
- " colorbar_title=\"Normalized θ\",\n",
- " aspect_ratio=:equal,\n",
- " linewidth=1.5\n",
- ")\n",
- "\n",
- "# Mark the magnetic axis\n",
- "scatter!(p_theta, [plasma_eq.ro], [plasma_eq.zo], label=\"Magnetic Axis\", mc=:black, ms=5)\n",
- "\n",
- "display(p_theta)"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "id": "a79bf309",
- "metadata": {},
- "outputs": [],
- "source": [
- "# 노트북 셀 1: JPEC 로드\n",
- "using Pkg\n",
- "Pkg.activate(\"/Users/seoda-eun/JPEC/JPEC\")\n",
- "using JPEC\n",
- "\n",
- "# 노트북 셀 2: Fourfit 포함\n",
- "include(\"/Users/seoda-eun/JPEC/fourfit_old_v4.jl\")\n",
- "using .FourfitOldV4\n",
- "\n",
- "# 노트북 셀 3: 실제 JPEC 평형 사용\n",
- "# plasma_eq는 실제 JPEC 평형 객체라고 가정\n",
- "success, fourfit_data, eq_data = test_fourfit_with_jpec_equilibrium(plasma_eq)"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "id": "9859d659",
- "metadata": {},
- "outputs": [],
- "source": []
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "id": "2c625a4a",
- "metadata": {},
- "outputs": [],
- "source": []
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "id": "3b359ecb",
- "metadata": {},
- "outputs": [],
- "source": []
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "id": "d8ba8174",
- "metadata": {},
- "outputs": [],
- "source": []
- }
- ],
- "metadata": {
- "kernelspec": {
- "display_name": "Julia 1.11.6",
- "language": "julia",
- "name": "julia-1.11"
- },
- "language_info": {
- "file_extension": ".jl",
- "mimetype": "application/julia",
- "name": "julia",
- "version": "1.11.6"
- }
- },
- "nbformat": 4,
- "nbformat_minor": 5
-}
diff --git a/notebooks/eulerbinread.ipynb b/notebooks/eulerbinread.ipynb
deleted file mode 100644
index 288a468ae2..0000000000
--- a/notebooks/eulerbinread.ipynb
+++ /dev/null
@@ -1,301 +0,0 @@
-{
- "cells": [
- {
- "cell_type": "code",
- "execution_count": null,
- "id": "db314816",
- "metadata": {},
- "outputs": [],
- "source": [
- "using Pkg; Pkg.add(\"FortranFiles\"); Pkg.add(\"LinearAlgebra\")\n",
- "using FortranFiles\n",
- "using LinearAlgebra"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "id": "7fec1fab",
- "metadata": {},
- "outputs": [],
- "source": [
- "# Create solution, sing structs\n",
- "struct solution_type\n",
- " msol :: Int32\n",
- " u :: Array{ComplexF64,3}\n",
- "end\n",
- "\n",
- "struct resist_type\n",
- " e :: Float64\n",
- " f :: Float64\n",
- " h :: Float64\n",
- " m :: Float64\n",
- " g :: Float64\n",
- " k :: Float64\n",
- " eta :: Float64\n",
- " rho :: Float64\n",
- " taua :: Float64\n",
- " taur :: Float64\n",
- " di :: Float64\n",
- " dr :: Float64\n",
- " sfac :: Float64\n",
- " deltac :: Float64\n",
- " eigenvalue :: ComplexF64\n",
- "end\n",
- "\n",
- "struct sing_type\n",
- " msol_l :: Int32\n",
- " msol_r :: Int32\n",
- " jfix :: Int32\n",
- " jpert :: Int32\n",
- " psifac :: Float64\n",
- " q :: Float64\n",
- " q1 :: Float64\n",
- " ca_l :: Array{ComplexF64,3}\n",
- " ca_r :: Array{ComplexF64,3}\n",
- " restype :: resist_type\n",
- "end\n",
- "\n",
- "mutable struct fixfac_type\n",
- " msol :: Int32\n",
- " index :: Vector{Int32}\n",
- " fixfac :: Array{ComplexF64,2}\n",
- " transform :: Array{ComplexF64,2}\n",
- " gauss :: Array{ComplexF64,2}\n",
- " function fixfac_type(msol::Int32, index::Vector{Int32},fixfac::Array{ComplexF64,2})\n",
- " transform = Matrix{ComplexF64}(I,msol,msol)\n",
- " gauss = Matrix{ComplexF64}(I,msol,msol)\n",
- " new(msol,index,fixfac,transform,gauss)\n",
- " end\n",
- "end\n",
- "\n",
- "function idcon_transform(fixtype, sing_flag)\n",
- " \n",
- " msol = length(fixtype[2].index)\n",
- " mfix = length(fixtype)-1\n",
- " identity = Matrix{ComplexF64}(I,msol,msol)\n",
- "\n",
- " # Construct gaussian reduction matrix\n",
- " for ifix in 2:1:mfix+1\n",
- " fixtype[ifix].gauss = copy(identity)\n",
- " mask = zeros(Bool, msol)\n",
- " mask .= true\n",
- " for isol in 1:msol\n",
- " ksol = fixtype[ifix].index[isol]\n",
- " mask[ksol] = false\n",
- " temp = copy(identity)\n",
- " for jsol in 1:msol\n",
- " if mask[jsol]\n",
- " temp[ksol,jsol] = fixtype[ifix].fixfac[ksol,jsol]\n",
- " end\n",
- " end\n",
- " # Matrix multiplication gauss = gauss * temp\n",
- " fixtype[ifix].gauss = fixtype[ifix].gauss * temp\n",
- " end\n",
- " if sing_flag[ifix-1]\n",
- " fixtype[ifix].gauss[:,fixtype[ifix].index[1]] .= 0.0\n",
- " end\n",
- " end\n",
- " \n",
- " # Concatenate gaussian reduction matrix\n",
- " fixtype[mfix+1].transform = copy(identity)\n",
- " for ifix in mfix:-1:1\n",
- " fixtype[ifix].transform = fixtype[ifix+1].gauss * fixtype[ifix+1].transform\n",
- " end\n",
- " return fixtype\n",
- "end\n",
- " "
- ]
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "id": "59f1ad09",
- "metadata": {},
- "outputs": [],
- "source": [
- "fstream = FortranFile(\"euler.bin\", \"r\")\n",
- "\n",
- "# --- Read header ---\n",
- "mlow, mhigh, nn, mpsi, mtheta, ro, zo = read(fstream, Int32, Int32, Int32, Int32, Int32, Float64, Float64)\n",
- "mband, mthsurf0, mthvac, psio, psilow, psilim, qlim, singfac_min = read(fstream, Int32, Int32, Int32, Float64, Float64, Float64, Float64, Float64)\n",
- "power_b, power_r, power_bp = read(fstream, Int32, Int32, Int32)\n",
- "kin_flag, con_flag = read(fstream, Int32, Int32)\n",
- "\n",
- "amean, rmean, aratio, kappa, delta1, delta2, \n",
- " li1, li2, li3, betap1, betap2, betap3, betat, betan, bt0, \n",
- " q0, qmin, qmax, qa, crnt, q95, shotnum, shottime = read(fstream, \n",
- " Float64, Float64, Float64, Float64, Float64, Float64,\n",
- " Float64, Float64, Float64, Float64, Float64, Float64,\n",
- " Float64, Float64, Float64, Float64, Float64, Float64,\n",
- " Float64, Float64, Float64, Float64, Float64)\n",
- "\n",
- "# --- Read equilibrium on flux coordinates ---\n",
- "# sq%xs is size mpsi, sq%fs is size mpsi x 4, sq%fs1 is size mpsi x 4, sq%xpower is size 2 x 4\n",
- "sq_xs, sq_fs, sq_fs1, sq_xpower = read(fstream, (Float64, mpsi), (Float64, (mpsi,4)), (Float64, (mpsi,4)), (Float64, (2,4)))\n",
- "# rzphi%xs is size mpsi, rzphi%ys is size mtheta, rzphi%fs is size mpsi x mtheta, etc.\n",
- "rzphi_xs, rzphi_ys, \n",
- " rzphi_fs, rzphi_fsx, rzphi_fsy, rzphi_fsxy, \n",
- " rzphi_x0, rzphi_y0, rzphi_xpower, rzphi_ypower = read(fstream, \n",
- " (Float64, mpsi), (Float64, mtheta), \n",
- " (Float64, (mpsi,mtheta,4)), (Float64, (mpsi,mtheta,4)), (Float64, (mpsi,mtheta,4)), (Float64, (mpsi,mtheta,4)),\n",
- " (Float64, 2), (Float64, 2), (Float64, (2,4)), (Float64, (2,4)))\n",
- "\n",
- "# misc derived quantities\n",
- "chi1=2*pi*psio\n",
- "mpert=mhigh-mlow+1\n",
- "\n",
- "# --- Count solutions in file (first pass) ---\n",
- "mstep = -1\n",
- "mfix = 0\n",
- "msing = 0\n",
- "\n",
- "while !eof(fstream)\n",
- " data_type = read(fstream, Int32)\n",
- " if data_type == 1\n",
- " mstep += 1\n",
- " read(fstream) # skip\n",
- " read(fstream)\n",
- " read(fstream)\n",
- " elseif data_type == 2\n",
- " mfix += 1\n",
- " read(fstream)\n",
- " read(fstream)\n",
- " elseif data_type == 3\n",
- " read(fstream)\n",
- " read(fstream)\n",
- " read(fstream)\n",
- " read(fstream)\n",
- " read(fstream)\n",
- " elseif data_type == 4\n",
- " msing += 1\n",
- " read(fstream)\n",
- " read(fstream)\n",
- " read(fstream)\n",
- " read(fstream)\n",
- " read(fstream)\n",
- " read(fstream)\n",
- " elseif data_type == 5\n",
- " read(fstream)\n",
- " read(fstream)\n",
- " read(fstream)\n",
- " read(fstream)\n",
- " read(fstream)\n",
- " read(fstream)\n",
- " read(fstream)\n",
- " else\n",
- " error(\"Cannot recognize data_type = $data_type\")\n",
- " end\n",
- "end\n",
- "\n",
- "close(fstream)\n",
- "\n",
- "psifac = zeros(Float64, mstep+1)\n",
- "rhofac = zeros(Float64, mstep+1)\n",
- "qfac = zeros(Float64, mstep+1)\n",
- "\n",
- "soltype = Vector{solution_type}(undef, mstep+1)\n",
- "singtype = Vector{sing_type}(undef, msing)\n",
- "fixstep = zeros(Float64, mfix+2)\n",
- "fixtype = Vector{fixfac_type}(undef, mfix+1)\n",
- "sing_flag = zeros(Bool, mfix)\n",
- "\n",
- "fixtype[1] = fixfac_type(Int32(0), zeros(Int32, 0), zeros(ComplexF64, 0, 0))\n",
- "\n",
- "et = zeros(ComplexF64, mpert)\n",
- "ep = zeros(ComplexF64, mpert)\n",
- "ee = zeros(ComplexF64, mpert)\n",
- "\n",
- "wt = zeros(ComplexF64, (mpert,mpert))\n",
- "wt0 = zeros(ComplexF64, (mpert,mpert))\n",
- "\n",
- "wft = zeros(ComplexF64, (mpert,mpert))\n",
- "eft = zeros(ComplexF64, mpert)\n",
- "efp = zeros(ComplexF64, mpert)\n",
- "wtraw = zeros(ComplexF64, (mpert,mpert))\n",
- "\n",
- "eft = -1\n",
- "wft = 0\n",
- "fixstep[1] = 0\n",
- "fixstep[mfix+2] = mstep\n",
- "\n",
- "fstream = FortranFile(\"euler.bin\", \"r\")\n",
- "# --- Read header again ---\n",
- "mlow, mhigh, nn, mpsi, mtheta, ro, zo = read(fstream, Int32, Int32, Int32, Int32, Int32, Float64, Float64)\n",
- "mband, mthsurf0, mthvac, psio, psilow, psilim, qlim, singfac_min = read(fstream, Int32, Int32, Int32, Float64, Float64, Float64, Float64, Float64)\n",
- "power_b, power_r, power_bp = read(fstream, Int32, Int32, Int32)\n",
- "kin_flag, con_flag = read(fstream, Int32, Int32)\n",
- "istep = -1\n",
- "ifix = 0\n",
- "ising = 0\n",
- "\n",
- "println(\"mfix = \", mfix)\n",
- "\n",
- "while !eof(fstream)\n",
- " data_type = read(fstream, Int32)\n",
- " if data_type == 1\n",
- " istep += 1\n",
- " psifac[istep+1], qfac[istep+1], msoli = read(fstream, Float64, Float64, Int32)\n",
- " u = Array{ComplexF64}(undef,(mpert,msoli,4))\n",
- " u[:,:,1:2] = read(fstream, (ComplexF64,(mpert,msoli,2)))\n",
- " u[:,:,3:4] = read(fstream, (ComplexF64,(mpert,msoli,2)))\n",
- " soltype[istep+1] = solution_type(msoli,u)\n",
- " elseif data_type == 2\n",
- " ifix += 1\n",
- " println(\"Writing to fixtype[\", ifix+1, \"]\")\n",
- " fixstep[ifix+1] = istep\n",
- " sing_flag[ifix], msoli = read(fstream, Int32, Int32)\n",
- " fixfac, index = read(fstream, (ComplexF64,(msoli,msoli)),(Int32,msoli))\n",
- " fixtype[ifix+1] = fixfac_type(msoli,index,fixfac)\n",
- " elseif data_type == 3\n",
- " ep = read(fstream,(ComplexF64,mpert))\n",
- " et = read(fstream,(ComplexF64,mpert))\n",
- " wt = read(fstream,(ComplexF64,(mpert,mpert)))\n",
- " wt0 = read(fstream,(ComplexF64,(mpert,mpert)))\n",
- " wv_farwall_flag = read(fstream, Int32)\n",
- " elseif data_type == 4\n",
- " ising += 1\n",
- " jfixi = ifix\n",
- " jperti = round(Int32, nn*qfac[istep+1] + 0.5)\n",
- " psifaci, qi, q1i = read(fstream, Float64, Float64, Float64)\n",
- " msol_l = read(fstream, Int32)\n",
- " ca_l = read(fstream, (ComplexF64,(mpert,msol_l,2)))\n",
- " msol_r = read(fstream, Int32)\n",
- " ca_r = read(fstream, (ComplexF64,(mpert,msol_r,2)))\n",
- " e, f, h, m, g, k, eta, rho, taua, taur = read(fstream, Float64, Float64, Float64, Float64, Float64, Float64, Float64, Float64, Float64, Float64)\n",
- " elseif data_type == 5\n",
- " ep = read(fstream,(ComplexF64,mpert))\n",
- " et = read(fstream,(ComplexF64,mpert))\n",
- " wt = read(fstream,(ComplexF64,(mpert,mpert)))\n",
- " efp = read(fstream,(Float64,mpert))\n",
- " eft = read(fstream,(Float64,mpert))\n",
- " wft = read(fstream,(ComplexF64,(mpert,mpert)))\n",
- " wtraw = read(fstream,(ComplexF64,(mpert,mpert)))\n",
- " else\n",
- " # for all the reads we skipped in the second pass\n",
- " print()\n",
- " end\n",
- "end\n",
- "\n",
- "close(fstream)\n",
- "\n",
- "idcon_transform(fixtype, sing_flag)\n"
- ]
- }
- ],
- "metadata": {
- "kernelspec": {
- "display_name": "Julia 1.11.6",
- "language": "julia",
- "name": "julia-1.11"
- },
- "language_info": {
- "file_extension": ".jl",
- "mimetype": "application/julia",
- "name": "julia",
- "version": "1.11.6"
- }
- },
- "nbformat": 4,
- "nbformat_minor": 5
-}
diff --git a/notebooks/sing_find_example.ipynb b/notebooks/sing_find_example.ipynb
deleted file mode 100644
index ea4f3de05a..0000000000
--- a/notebooks/sing_find_example.ipynb
+++ /dev/null
@@ -1,493 +0,0 @@
-{
- "cells": [
- {
- "cell_type": "code",
- "execution_count": null,
- "id": "3162f30d",
- "metadata": {},
- "outputs": [],
- "source": [
- "# using Pkg\n",
- "# Pkg.activate(\"..\") \n",
- "# Pkg.instantiate()\n",
- "using JPEC, Plots\n",
- "gr() "
- ]
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "id": "cbcbbf1a",
- "metadata": {},
- "outputs": [],
- "source": [
- "using LinearAlgebra\n",
- "using Printf\n",
- "using Plots"
- ]
- },
- {
- "cell_type": "markdown",
- "id": "1a4b93da",
- "metadata": {},
- "source": [
- "### read Equil"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "id": "91adefe3",
- "metadata": {},
- "outputs": [],
- "source": [
- "# 1. Define the input parameters for the equilibrium solver.\n",
- "# - eq_filename: The name of the g-file we just created.\n",
- "# - eq_type: \"efit\" for a standard g-file.\n",
- "# - jac_type: \"boozer\" or \"hamada\" for the output coordinates.\n",
- "# - mpsi, mtheta: Resolution of the output grid.\n",
- "equil_input = JPEC.Equilibrium.EquilInput(\n",
- " \"beta_1.00\", # eq_filename\n",
- " \"efit\", # eq_type\n",
- " \"boozer\", # jac_type\n",
- " 0.01, # psilow\n",
- " 1.0, # psihigh\n",
- " 100, # mpsi (number of radial grid points)\n",
- " 128 # mtheta (number of poloidal grid points)\n",
- ")\n",
- "\n",
- "# 2. Run the main equilibrium setup function.\n",
- "# This will read the file, solve the direct problem, and return the final object.\n",
- "println(\"Starting equilibrium reconstruction...\")\n",
- "plasma_eq = JPEC.Equilibrium.setup_equilibrium(equil_input)\n",
- "println(\"Equilibrium reconstruction complete.\")"
- ]
- },
- {
- "cell_type": "markdown",
- "id": "c34090af",
- "metadata": {},
- "source": [
- "### Use spline_eval \n",
- "sq!!"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "id": "9fc11a8e",
- "metadata": {},
- "outputs": [],
- "source": [
- "# The plasma_eq object contains the final 1D profile spline, `sq`.\n",
- "# We will evaluate it on a fine grid to get smooth plot lines.\n",
- "psi_norm_grid = range(0.0, 1.0, length=200)\n",
- "\n",
- "# spline_eval returns the function values (and derivatives if requested).\n",
- "# For sq, the quantities are: 1:F, 2:P*mu0, 3:Toroidal Flux, 4:q\n",
- "f_profiles = JPEC.SplinesMod.spline_eval(plasma_eq.sq, collect(psi_norm_grid))\n",
- "\n",
- "# Extract each profile into its own variable for clarity\n",
- "F_profile = f_profiles[:, 1]\n",
- "P_profile = f_profiles[:, 2]\n",
- "tor_flux_prof = f_profiles[:, 3]\n",
- "q_profile = f_profiles[:, 4];"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "id": "24c68c15",
- "metadata": {},
- "outputs": [],
- "source": [
- "plot(psi_norm_grid, q_profile, \n",
- " xlabel=\"Normalized Flux\", ylabel=\"Safety Factor q\", \n",
- " title=\"Safety Factor Profile\",\n",
- " legend=:topright, label=\"q(ψ)\", lw=2, color=:blue)"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "id": "4ca48f63",
- "metadata": {},
- "outputs": [],
- "source": [
- "\"\"\"\n",
- " sing_find!(sing_surf_data, plasma_eq; mex=2, nn=1, itmax=200)\n",
- "\n",
- "Finds and appends rational (singular) surfaces in a plasma equilibrium profile,\n",
- "where `m = nn*q` within each interval between extrema of the safety factor profile `q(ψ)`.\n",
- "\n",
- "The results are stored as `NamedTuple`s in the supplied vector `sing_surf_data`, \n",
- "with keys: `m`, `ψfac`, `ρ`, `q`, and `q1`.\n",
- "\n",
- "# Arguments\n",
- "- `sing_surf_data::Vector`: Container for output; will be emptied and updated in-place.\n",
- "- `plasma_eq`: Plasma equilibrium object with a field `.sq` suitable for spline evaluation.\n",
- "- `mex::Int`: Number of `q` profile extrema. Defaults to 2 (monotonic `q`).\n",
- "- `nn::Int`: Toroidal mode number `n`.\n",
- "- `itmax::Int`: Maximum allowed bisection iterations per root.\n",
- "\n",
- "# Details\n",
- "Searches each interval between adjacent `q`-profile extrema for all integer poloidal mode numbers `m`\n",
- "that satisfy the rational surface condition `m = n*q(ψ)`, using bisection to find the roots.\n",
- "Assumes a monotonic `q` profile, unless a generalized interface is implemented\n",
- "(TODO: support for non-monotonic profiles).\n",
- "\n",
- "# Output\n",
- "For each rational surface found, a `NamedTuple` with:\n",
- "- `m`: Poloidal mode number at this surface\n",
- "- `ψfac`: Normalized flux label at the surface\n",
- "- `ρ`: Square root of `ψfac`\n",
- "- `q`: `q` value at the surface (`m/nn`)\n",
- "- `q1`: Derivative of `q` at the surface\n",
- "\n",
- "is pushed to `sing_surf_data`.\n",
- "\"\"\"\n",
- "function sing_find!(sing_surf_data, plasma_eq; nn=1, itmax=200)\n",
- " \n",
- " # Ensure sing_surf_data is empty before starting\n",
- " empty!(sing_surf_data)\n",
- "\n",
- " # Define functions to evaluate q and its first derivative\n",
- " qval(ψ) = JPEC.SplinesMod.spline_eval(plasma_eq.sq, ψ, 0)[4]\n",
- " q1val(ψ) = JPEC.SplinesMod.spline_eval(plasma_eq.sq, ψ, 1)[2][4] \n",
- "\n",
- " # TODO: I assume monotonic here for checking, will need to provide some interface\n",
- " # for the actual values fo (mex, qex) determined from the equil code\n",
- " qex = [qval(0.0), qval(1.0)]\n",
- " ψex = [0.0, 1.0]\n",
- " mex = 2\n",
- "\n",
- " # Loop over extrema of q, find all rational values in between\n",
- " for iex in 2:mex\n",
- " dq = qex[iex] - qex[iex-1]\n",
- " m = floor(Int, nn * qex[iex-1])\n",
- " if dq > 0\n",
- " m += 1\n",
- " end\n",
- " dm = Int(sign(dq * nn))\n",
- "\n",
- " # Loop over possible m's in interval\n",
- " while (m - nn * qex[iex-1]) * (m - nn * qex[iex]) <= 0\n",
- " it = 0\n",
- " ψ0 = ψex[iex-1]\n",
- " ψ1 = ψex[iex]\n",
- " ψfac = 0.0\n",
- "\n",
- " # Bisection method to find singular surface\n",
- " while it < itmax\n",
- " it += 1\n",
- " ψfac = (ψ0 + ψ1)/2\n",
- " singfac = (m - nn * qval(ψfac)) * dm\n",
- " if abs(singfac) <= 1e-12\n",
- " break\n",
- " elseif singfac > 0\n",
- " ψ0 = ψfac\n",
- " else\n",
- " ψ1 = ψfac\n",
- " end\n",
- " end\n",
- " if it == itmax\n",
- " @warn \"Bisection did not converge for m = $m\"\n",
- " # You may want to continue, break, or error here\n",
- " else\n",
- " push!(sing_surf_data, (\n",
- " m = m,\n",
- " ψfac = ψfac,\n",
- " ρ = sqrt(ψfac),\n",
- " q = m / nn,\n",
- " q1 = q1val(ψfac),\n",
- " ))\n",
- " end\n",
- " m += dm\n",
- " end\n",
- " end\n",
- "end"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "id": "3899bb00",
- "metadata": {},
- "outputs": [],
- "source": [
- "sing_surf_data = []\n",
- "sing_find!(sing_surf_data, plasma_eq)"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "id": "fea33c45",
- "metadata": {},
- "outputs": [],
- "source": [
- "sing_surf_data[1].ψfac"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "id": "4a23c2ce",
- "metadata": {},
- "outputs": [],
- "source": [
- "\"\"\"\n",
- " bubble!(key::AbstractVector, index::AbstractVector{Int}, mmin::Int, mmax::Int)\n",
- "\n",
- "Sorts the indices in `index` in place such that `key[index[i]]` are in decreasing order\n",
- "from `mmin` to `mmax` (inclusive).\n",
- "\"\"\"\n",
- "function bubble!(key::AbstractVector, index::AbstractVector{Int}, mmin::Int, mmax::Int)\n",
- " switched = true\n",
- " while switched\n",
- " switched = false\n",
- " for i in mmin:(mmax-1)\n",
- " if key[index[i]] < key[index[i+1]]\n",
- " index[i], index[i+1] = index[i+1], index[i]\n",
- " switched = true\n",
- " end\n",
- " end\n",
- " end\n",
- " return nothing\n",
- "end\n",
- "\n",
- "\"\"\"\n",
- " ode_axis_init(sing_surf_data, sq; nn = 1, ψlim = 0.9936, ψlow = 0.01, mlow = -12, mhigh = 20, singfac_min = 1e-5, qlow = 0.0, sort_type = \"absm\")\n",
- "\n",
- "Initializes the ODE system near the magnetic axis for MHD or kinetic-MHD stability\n",
- "analysis. This routine prepares solution vectors and sorting indices, locates\n",
- "the relevant singular surfaces in the plasma equilibrium based on input data,\n",
- "and sets integration boundaries and normalization factors for subsequent ODE integration\n",
- "through singularities.\n",
- "\n",
- "# Arguments\n",
- "- `sing_surf_data`: Array of structures, each containing information about singular surfaces,\n",
- " including fields like `.ψfac`, `.q`, and `.q1`. Filled from sing_find function\n",
- "- `sq`: Spline object controlling the equilibrium safety factor profile (typically contains equilibrium profile splines).\n",
- "\n",
- "# Keyword Arguments (these are likely to be replaced by the user input file structure)\n",
- "- `nn`: Integer. Toroidal mode number.\n",
- "- `ψlim`: Float. Upper bound for normalized flux coordinate ψ.\n",
- "- `ψlow`: Float. Lower bound for normalized flux coordinate ψ.\n",
- "- `mlow`: Integer. Lowest poloidal mode number to consider.\n",
- "- `mhigh`: Integer. Highest poloidal mode number to consider.\n",
- "- `singfac_min`: Float. Minimum separation from a singular surface.\n",
- "- `qlow`: Float. Lower bound for safety factor q. (Currently not implemented if > 0.)\n",
- "- `sort_type`: String. Sorting criteria for mode numbers (`\"absm\"` for |m|, or\n",
- " `\"sing\"` for proximity to the first singular surface's m).\n",
- "\n",
- "# Details\n",
- "This function does the following:\n",
- "- Determines relevant singular surfaces from the provided equilibrium/singularity data.\n",
- "- Sets up arrays for the ODE solution and related workspaces for all poloidal harmonics in the range [`mlow`, `mhigh`].\n",
- "- Sorts the initial harmonics according to the specified `sort_type`.\n",
- "- Initializes normalization factors and solution arrays for use in the ODE integrator.\n",
- "- Computes the initial offset (`singfac`) from the next singular surface.\n",
- "\n",
- "Several features for kinetic MHD (indicated by `kin_flag`) or for `qlow > 0` are noted but not yet implemented.\n",
- "\n",
- "\"\"\"\n",
- "\n",
- "function ode_axis_init(sing_surf_data, plasma_eq; nn = 1, ψlim=0.9936, ψlow = 0.01, mlow = -12, mhigh = 20, singfac_min = 1e-5, qlow = 0.0, sort_type = \"absm\")\n",
- " # JMH - I think all default values here will be supplied by inputs\n",
- " # Right now, there are a lot of globals - not sure how we want to handle these\n",
- " # But at least the major outputs here match fortran dcon\n",
- "\n",
- " # maybe change how this is passed in?\n",
- " qval(ψ) = JPEC.SplinesMod.spline_eval(plasma_eq.sq, ψ, 0)[4]\n",
- " q1val(ψ) = JPEC.SplinesMod.spline_eval(plasma_eq.sq, ψ, 1)[2][4] \n",
- "\n",
- " # Preliminary computations\n",
- " new = true\n",
- " ix = 0\n",
- " psiout = 1.0\n",
- " ψfac = 0.0 # TODO: this was Fortran sq%xs(0)?\n",
- " msing = size(sing_surf_data)[1]\n",
- " \n",
- " # TODO: defined elsewhere\n",
- " mpert = mhigh - mlow + 1\n",
- "\n",
- " # Use Newton iteration to find starting psi if qlow is above q0\n",
- " # TODO: add this. For now, assume qlow = 0.0 and start at the first singular surface\n",
- " if qlow > 0.0\n",
- " @warn \"qlow > 0.0 is not implemented in ode_axis_init\"\n",
- " end\n",
- "\n",
- " # Find inner singular surface\n",
- " global ising = 0\n",
- " if false #(TODO: kin_flag)\n",
- " # for ising = 1:kmsing\n",
- " # if kinsing[ising].psifac > psifac\n",
- " # break\n",
- " # end\n",
- " # end\n",
- " else\n",
- " for ising in 1:msing\n",
- " if sing_surf_data[ising].ψfac > ψfac\n",
- " break\n",
- " end\n",
- " end\n",
- " end\n",
- " ising = max(0, ising - 1)\n",
- "\n",
- " # Find next singular surface\n",
- " if false # TODO: (kin_flag)\n",
- " # while true\n",
- " # ising += 1\n",
- " # if ising > kmsing\n",
- " # break\n",
- " # end\n",
- " # if psilim < kinsing[ising].psifac\n",
- " # break\n",
- " # end\n",
- " # q = kinsing[ising].q\n",
- " # if mlow <= nn * q && mhigh >= nn * q\n",
- " # break\n",
- " # end\n",
- " # end\n",
- " # if ising > kmsing || singfac_min == 0\n",
- " # psimax = psilim * (1 - eps)\n",
- " # next = \"finish\"\n",
- " # elseif psilim < kinsing[ising].psifac\n",
- " # psimax = psilim * (1 - eps)\n",
- " # next = \"finish\"\n",
- " # else\n",
- " # psimax = kinsing[ising].psifac - singfac_min / abs(nn * kinsing[ising].q1)\n",
- " # next = \"cross\"\n",
- " # end\n",
- " else\n",
- " while true\n",
- " ising += 1\n",
- " if ising > msing || ψlim < sing_surf_data[min(ising, msing)].ψfac\n",
- " break\n",
- " end\n",
- " q = sing_surf_data[ising].q\n",
- " if mlow <= nn * q && mhigh >= nn * q\n",
- " break\n",
- " end\n",
- " end\n",
- " if ising > msing || ψlim < sing_surf_data[min(ising, msing)].ψfac || singfac_min == 0\n",
- " ψmax = ψlim * (1 - eps)\n",
- " next = \"finish\"\n",
- " else\n",
- " ψmax = sing_surf_data[ising].ψfac - singfac_min / abs(nn * sing_surf_data[ising].q1)\n",
- " next = \"cross\"\n",
- " end\n",
- " end\n",
- "\n",
- " # Allocate and sort solutions by increasing value of |m-ms1|\n",
- " global u = zeros(ComplexF64, mpert, mpert, 2)\n",
- " global du = zeros(ComplexF64, mpert, mpert, 2)\n",
- " global u_save = zeros(ComplexF64, mpert, mpert, 2)\n",
- " global unorm0 = zeros(Float64, 2 * mpert)\n",
- " global unorm = zeros(Float64, 2 * mpert)\n",
- " global index = collect(1:mpert)\n",
- " m = mlow - 1 .+ index\n",
- " if sort_type == \"absm\"\n",
- " key = abs.(m)\n",
- " elseif sort_type == \"sing\"\n",
- " key = m\n",
- " if msing > 0\n",
- " key = key .- sing[1].m\n",
- " end\n",
- " key = -abs.(key)\n",
- " else\n",
- " error(\"Cannot recognize sort_type = $sort_type\")\n",
- " end\n",
- " bubble!(key, index, 1, mpert) # in original Fortran: bubble(key, index, 1, mpert)\n",
- " println(key)\n",
- " println(index)\n",
- "\n",
- " # Initialize solutions\n",
- " u .= 0\n",
- " for ipert = 1:mpert\n",
- " u[index[ipert], ipert, 2] = 1\n",
- " end\n",
- " global msol = mpert\n",
- " global neq = 4 * mpert * msol\n",
- " u_save .= u\n",
- " global psi_save = ψfac\n",
- "\n",
- " # Initialize integrator parameters (JMH - not sure if these are needed in Julia)\n",
- " # global istep = 0\n",
- " # global iopt = 1\n",
- " # global itask = 5\n",
- " # global itol = 2\n",
- " # global mf = 10\n",
- " # global istate = 1\n",
- "\n",
- " # Compute conditions at next singular surface\n",
- " q = qval(ψlow) # Fortran: q=sq%fs(0,4)\n",
- " println(q)\n",
- " if false #TODO: (kin_flag)\n",
- " # if kmsing > 0\n",
- " # m1 = round(Int, nn * kinsing[ising].q)\n",
- " # else\n",
- " # m1 = round(Int, nn * qlim) + sign(one, nn * sq.fs1[mpsi, 5])\n",
- " # end\n",
- " else\n",
- " if msing > 0\n",
- " m1 = round(Int, nn * sing_surf_data[ising].q)\n",
- " else\n",
- " m1 = round(Int, nn * qlim) + sign(nn * q1val[end])\n",
- " end\n",
- " end\n",
- " global singfac = abs(m1 - nn * q)\n",
- "\n",
- " println(m1)\n",
- " println(singfac)\n",
- "\n",
- " # Set up work arrays (JMH - not sure if these are needed in Julia)\n",
- " # global liw = length(iwork)\n",
- " # global lrw = 22 + 64 * mpert * msol\n",
- " # global rwork = zeros(Float64, lrw)\n",
- " # global atol = zeros(ComplexF64, mpert, msol, 2)\n",
- " # global fixfac = zeros(ComplexF64, msol, msol)\n",
- " # iwork = 0\n",
- " # rwork = 0\n",
- " # rwork[1] = psimax\n",
- " # rwork[5] = psifac * 1e-3\n",
- " # rwork[11] = rwork[5]\n",
- "end\n"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "id": "b414bf00",
- "metadata": {},
- "outputs": [],
- "source": [
- "ode_axis_init(sing_surf_data, plasma_eq)"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "id": "2e6fc625",
- "metadata": {},
- "outputs": [],
- "source": []
- }
- ],
- "metadata": {
- "kernelspec": {
- "display_name": "Julia 1.11.5",
- "language": "julia",
- "name": "julia-1.11"
- },
- "language_info": {
- "file_extension": ".jl",
- "mimetype": "application/julia",
- "name": "julia",
- "version": "1.11.5"
- }
- },
- "nbformat": 4,
- "nbformat_minor": 5
-}
diff --git a/notebooks/soloviev_ideal/dcon.toml b/notebooks/soloviev_ideal/dcon.toml
deleted file mode 100644
index b8e08dc0a5..0000000000
--- a/notebooks/soloviev_ideal/dcon.toml
+++ /dev/null
@@ -1,59 +0,0 @@
-[DCON_CONTROL]
-bal_flag = false # Ideal MHD ballooning criterion for short wavelengths
-mat_flag = true # Construct coefficient matrices for diagnostic purposes
-ode_flag = true # Integrate ODE's for determining stability of internal long-wavelength mode (must be true for GPEC)
-vac_flag = false # Compute plasma, vacuum, and total energies for free-boundary modes
-mer_flag = true # Evaluate the Mercier criterian
-
-sas_flag = false # Safety factor (q) limit determined as q_ir+dmlim...
-dmlim = 0.2 # See sas_flag
-qlow = 1.02 # Integration initiated at q determined by min(q0, qlow)...
-qhigh = 1e3 # Integration terminated at q limit determined by min(qa, qhigh)...
-sing_start = 0 # Start integration at the sing_start'th rational from the axis (psilow)
-
-nn = 1 # Toroidal mode number
-delta_mlow = 8 # Expands lower bound of Fourier harmonics
-delta_mhigh = 8 # Expands upper bound of Fourier harmonics
-delta_mband = 0 # Integration keeps only this wide a band...
-mthvac = 960 # Number of points used in splines over poloidal angle at plasma-vacuum interface.
-thmax0 = 1 # Linear multiplier on the automatic choice of theta integration bounds
-
-kin_flag = false # Kinetic EL equation (default: false)
-con_flag = false # Continue integration through layers (default: false)
-kinfac1 = 1.0 # Scale factor for energy contribution (default: 1.0)
-kinfac2 = 1.0 # Scale factor for torque contribution (default: 1.0)
-kingridtype = 0 # Regular grid method (default: 0)
-passing_flag = true # Includes passing particle effects (default: false)
-ktanh_flag = true # Ignore kinetic effects in the core smoothly (default: false)
-ktc = 0.1 # Parameter for ktanh_flag (default: 0.1)
-ktw = 50.0 # Parameter for ktanh_flag (default: 50.0)
-ion_flag = true # Include ion dW_k when kin_flag is true
-electron_flag = false # Include electron dW_k when kin_flag is true
-
-tol_nr = 1e-6 # Relative tolerance of dynamic integration steps away from rationals
-tol_r = 1e-7 # Relative tolerance of dynamic integration steps near rationals
-crossover = 1e-2 # Fractional distance from rational q at which tol switches
-singfac_min = 1e-4 # Fractional distance from rational q at which ideal jump enforced
-ucrit = 1e3 # Maximum fraction of solutions allowed before re-normalized
-
-termbycross_flag = false # Terminate ODE solver in the event of a zero crossing
-
-use_classic_splines = false # Use a classical cubic spline instead of tri-diagonal solution
-
-[DCON_OUTPUT]
-out_ahg2msc = false # Output deprecated ahg2msc.out files
-crit_break = true # Color of the crit curve changes when crossing a singular surface
-ahb_flag = false # Output normal magnetic field eigenvalues...
-msol_ahb = 1 # Number of eigenfunctions output by ahb_flag = true?
-mthsurf0 = 1 # Linear multiplier on number of boundary points for ahgb_flag = true
-
-bin_euler = true # Output M psi-by-M euler-lagrange solutions to binary file euler.bin
-bin_vac = false # Output deprecated binary vacuum.bin
-euler_stride = 1 # Output only every euler_stride'th psi step
-
-out_bal1 = false # Ascii output for bal_flag poloidal functions
-bin_bal1 = false # Binary output for bal_flag poloidal functions
-out_bal2 = false # Ascii output for bal_flag functions
-bin_bal2 = false # Binary output for bal_flag functions
-
-netcdf_out = true # Replicate ascii dcon.out information in a netcdf file
\ No newline at end of file
diff --git a/notebooks/soloviev_ideal/equil.toml b/notebooks/soloviev_ideal/equil.toml
deleted file mode 100644
index 7abe0a9d0e..0000000000
--- a/notebooks/soloviev_ideal/equil.toml
+++ /dev/null
@@ -1,30 +0,0 @@
-[EQUIL_CONTROL]
-eq_type = "sol" # Type of the input 2D equilibrium file
-eq_filename = "sol.toml" # path to equilibrium file
-
-jac_type = "pest" # Coordinate system (hamada, pest, boozer, equal_arc)
-power_bp = 0 # del.B ~ B_p^power_bp * B^power_b / R^power_r
-power_b = 0 # del.B ~ B_p^power_bp * B^power_b / R^power_r
-power_r = 0 # del.B ~ B_p^power_bp * B^power_b / R^power_r
-
-grid_type = "ldp" # Radial grid packing
-psilow = 1e-4 # Min psi (normalized)
-psihigh = 0.99999 # Max psi (normalized)
-mpsi = 128 # Radial grid intervals
-mtheta = 256 # Poloidal grid intervals
-
-newq0 = 0 # Override q(0)
-etol = 1e-7 # Reconstruction tolerance
-use_classic_splines = false # Use classical spline (vs. tri-diagonal)
-
-input_only = false # Quit after input read
-
-[EQUIL_OUTPUT]
-gse_flag = false # Output G-S equation accuracy diagnostics
-out_eq_1d = false # ASCII output of 1D eq data
-bin_eq_1d = false # Binary output of 1D eq data
-out_eq_2d = false # ASCII output of 2D eq data
-bin_eq_2d = true # Binary output of 2D eq data (used by GPEC)
-out_2d = false # ASCII output of processed 2D data
-bin_2d = false # Binary output of processed 2D data
-dump_flag = false # Binary dump of equilibrium data
diff --git a/notebooks/soloviev_ideal/fortran_sq_knots.dat b/notebooks/soloviev_ideal/fortran_sq_knots.dat
deleted file mode 100644
index e10c07bb0a..0000000000
--- a/notebooks/soloviev_ideal/fortran_sq_knots.dat
+++ /dev/null
@@ -1,130 +0,0 @@
- i psi fs1(2) fs(4) fs1(4) -fs1(1)
- 0 0.100000E-03 -.536958E-01 0.190008E+01 0.746840E+00 0.108571E-10
- 1 0.250574E-03 -.536958E-01 0.190019E+01 0.763244E+00 -.423530E-11
- 2 0.702206E-03 -.536958E-01 0.190055E+01 0.781972E+00 0.131254E-11
- 3 0.145462E-02 -.536958E-01 0.190113E+01 0.775030E+00 0.575228E-13
- 4 0.250737E-02 -.536958E-01 0.190195E+01 0.778158E+00 0.418560E-12
- 5 0.385982E-02 -.536958E-01 0.190300E+01 0.778302E+00 -.705048E-12
- 6 0.551115E-02 -.536958E-01 0.190429E+01 0.779649E+00 0.215203E-12
- 7 0.746037E-02 -.536958E-01 0.190581E+01 0.780889E+00 -.106220E-12
- 8 0.970630E-02 -.536958E-01 0.190756E+01 0.782416E+00 0.209256E-12
- 9 0.122476E-01 -.536958E-01 0.190955E+01 0.784111E+00 0.276621E-12
- 10 0.150827E-01 -.536958E-01 0.191178E+01 0.786069E+00 -.234180E-12
- 11 0.182100E-01 -.536958E-01 0.191424E+01 0.788160E+00 -.172185E-12
- 12 0.216275E-01 -.536958E-01 0.191694E+01 0.790517E+00 0.454994E-13
- 13 0.253331E-01 -.536958E-01 0.191987E+01 0.793038E+00 -.296643E-14
- 14 0.293248E-01 -.536958E-01 0.192304E+01 0.795816E+00 -.366868E-13
- 15 0.335999E-01 -.536958E-01 0.192645E+01 0.798762E+00 0.155137E-12
- 16 0.381560E-01 -.536958E-01 0.193010E+01 0.801951E+00 -.170157E-13
- 17 0.429904E-01 -.536958E-01 0.193398E+01 0.805328E+00 -.250987E-13
- 18 0.481001E-01 -.536958E-01 0.193811E+01 0.808945E+00 0.601525E-13
- 19 0.534820E-01 -.536958E-01 0.194247E+01 0.812776E+00 -.166423E-12
- 20 0.591329E-01 -.536958E-01 0.194708E+01 0.816823E+00 0.993327E-13
- 21 0.650494E-01 -.536958E-01 0.195192E+01 0.821097E+00 -.232423E-12
- 22 0.712279E-01 -.536958E-01 0.195701E+01 0.825593E+00 -.159701E-13
- 23 0.776647E-01 -.536958E-01 0.196234E+01 0.830317E+00 0.236684E-12
- 24 0.843559E-01 -.536958E-01 0.196791E+01 0.835274E+00 -.882177E-13
- 25 0.912976E-01 -.536958E-01 0.197373E+01 0.840464E+00 0.113932E-12
- 26 0.984854E-01 -.536958E-01 0.197979E+01 0.845879E+00 -.176197E-14
- 27 0.105915E+00 -.536958E-01 0.198609E+01 0.851551E+00 -.860558E-13
- 28 0.113582E+00 -.536958E-01 0.199264E+01 0.857447E+00 -.185499E-13
- 29 0.121482E+00 -.536958E-01 0.199944E+01 0.863601E+00 0.163994E-12
- 30 0.129610E+00 -.536958E-01 0.200649E+01 0.869998E+00 0.928617E-14
- 31 0.137961E+00 -.536958E-01 0.201378E+01 0.876641E+00 -.170633E-12
- 32 0.146531E+00 -.536958E-01 0.202132E+01 0.883542E+00 0.271237E-13
- 33 0.155313E+00 -.536958E-01 0.202911E+01 0.890693E+00 0.650307E-13
- 34 0.164302E+00 -.536958E-01 0.203715E+01 0.898113E+00 0.543206E-14
- 35 0.173495E+00 -.536958E-01 0.204544E+01 0.905799E+00 -.752773E-13
- 36 0.182883E+00 -.536958E-01 0.205399E+01 0.913743E+00 0.270561E-14
- 37 0.192463E+00 -.536958E-01 0.206278E+01 0.921957E+00 0.658765E-13
- 38 0.202228E+00 -.536958E-01 0.207182E+01 0.930458E+00 0.405172E-14
- 39 0.212173E+00 -.536958E-01 0.208112E+01 0.939228E+00 -.735074E-13
- 40 0.222290E+00 -.536958E-01 0.209067E+01 0.948278E+00 0.198570E-13
- 41 0.232576E+00 -.536958E-01 0.210047E+01 0.957617E+00 -.536171E-14
- 42 0.243022E+00 -.536958E-01 0.211052E+01 0.967248E+00 0.144680E-14
- 43 0.253623E+00 -.536958E-01 0.212083E+01 0.977178E+00 -.388917E-15
- 44 0.264373E+00 -.536958E-01 0.213139E+01 0.987386E+00 0.994974E-16
- 45 0.275264E+00 -.536958E-01 0.214220E+01 0.997906E+00 -.656484E-17
- 46 0.286291E+00 -.536958E-01 0.215326E+01 0.100874E+01 -.743118E-16
- 47 0.297447E+00 -.536958E-01 0.216458E+01 0.101987E+01 0.305624E-15
- 48 0.308724E+00 -.536958E-01 0.217614E+01 0.103131E+01 -.115406E-14
- 49 0.320117E+00 -.536958E-01 0.218796E+01 0.104307E+01 0.433107E-14
- 50 0.331619E+00 -.536958E-01 0.220003E+01 0.105515E+01 -.162417E-13
- 51 0.343221E+00 -.536958E-01 0.221234E+01 0.106755E+01 0.608839E-13
- 52 0.354919E+00 -.536958E-01 0.222490E+01 0.108028E+01 -.361244E-15
- 53 0.366703E+00 -.536958E-01 0.223771E+01 0.109333E+01 -.564964E-13
- 54 0.378568E+00 -.536958E-01 0.225076E+01 0.110671E+01 -.523740E-15
- 55 0.390506E+00 -.536958E-01 0.226405E+01 0.112044E+01 0.589462E-13
- 56 0.402511E+00 -.536958E-01 0.227759E+01 0.113448E+01 -.139417E-13
- 57 0.414573E+00 -.536958E-01 0.229136E+01 0.114888E+01 -.116408E-14
- 58 0.426688E+00 -.536958E-01 0.230537E+01 0.116363E+01 0.167859E-13
- 59 0.438846E+00 -.536958E-01 0.231961E+01 0.117869E+01 -.644962E-13
- 60 0.451042E+00 -.536958E-01 0.233407E+01 0.119412E+01 0.217259E-13
- 61 0.463267E+00 -.536958E-01 0.234877E+01 0.120990E+01 -.223565E-13
- 62 0.475514E+00 -.536958E-01 0.236369E+01 0.122601E+01 0.677417E-13
- 63 0.487776E+00 -.536958E-01 0.237882E+01 0.124248E+01 -.314444E-13
- 64 0.500045E+00 -.536958E-01 0.239417E+01 0.125928E+01 0.582947E-13
- 65 0.512314E+00 -.536958E-01 0.240972E+01 0.127643E+01 0.154372E-13
- 66 0.524576E+00 -.536958E-01 0.242548E+01 0.129393E+01 -.120513E-12
- 67 0.536823E+00 -.536958E-01 0.244144E+01 0.131179E+01 0.322630E-13
- 68 0.549048E+00 -.536958E-01 0.245758E+01 0.132997E+01 -.863988E-14
- 69 0.561244E+00 -.536958E-01 0.247392E+01 0.134850E+01 0.233274E-14
- 70 0.573402E+00 -.536958E-01 0.249043E+01 0.136735E+01 -.703079E-15
- 71 0.585517E+00 -.536958E-01 0.250711E+01 0.138655E+01 0.482947E-15
- 72 0.597579E+00 -.536958E-01 0.252395E+01 0.140605E+01 -.122759E-14
- 73 0.609584E+00 -.536958E-01 0.254095E+01 0.142588E+01 0.441781E-14
- 74 0.621522E+00 -.536958E-01 0.255809E+01 0.144603E+01 -.164018E-13
- 75 0.633387E+00 -.536958E-01 0.257537E+01 0.146649E+01 0.610155E-13
- 76 0.645171E+00 -.536958E-01 0.259277E+01 0.148725E+01 -.843266E-15
- 77 0.656869E+00 -.536958E-01 0.261029E+01 0.150827E+01 -.605693E-13
- 78 0.668471E+00 -.536958E-01 0.262791E+01 0.152959E+01 0.161834E-13
- 79 0.679973E+00 -.536958E-01 0.264563E+01 0.155118E+01 -.441101E-14
- 80 0.691366E+00 -.536958E-01 0.266343E+01 0.157302E+01 0.152997E-14
- 81 0.702643E+00 -.536958E-01 0.268129E+01 0.159509E+01 -.172254E-14
- 82 0.713799E+00 -.536958E-01 0.269921E+01 0.161738E+01 0.533945E-14
- 83 0.724826E+00 -.536958E-01 0.271717E+01 0.163992E+01 -.195319E-13
- 84 0.735717E+00 -.536958E-01 0.273515E+01 0.166260E+01 0.723740E-13
- 85 0.746467E+00 -.536958E-01 0.275314E+01 0.168546E+01 -.204577E-13
- 86 0.757068E+00 -.536958E-01 0.277113E+01 0.170848E+01 0.299773E-14
- 87 0.767514E+00 -.536958E-01 0.278910E+01 0.173164E+01 0.156514E-13
- 88 0.777800E+00 -.536958E-01 0.280703E+01 0.175493E+01 -.730037E-13
- 89 0.787917E+00 -.536958E-01 0.282491E+01 0.177828E+01 0.193914E-13
- 90 0.797862E+00 -.536958E-01 0.284271E+01 0.180169E+01 -.514839E-14
- 91 0.807627E+00 -.536958E-01 0.286041E+01 0.182513E+01 0.136623E-14
- 92 0.817207E+00 -.536958E-01 0.287801E+01 0.184858E+01 -.362376E-15
- 93 0.826595E+00 -.536958E-01 0.289547E+01 0.187202E+01 0.960664E-16
- 94 0.835788E+00 -.536958E-01 0.291279E+01 0.189540E+01 -.254561E-16
- 95 0.844777E+00 -.536958E-01 0.292993E+01 0.191867E+01 0.675143E-17
- 96 0.853559E+00 -.536958E-01 0.294688E+01 0.194185E+01 -.182571E-17
- 97 0.862129E+00 -.536958E-01 0.296362E+01 0.196486E+01 0.626572E-18
- 98 0.870480E+00 -.536958E-01 0.298013E+01 0.198772E+01 -.695154E-18
- 99 0.878608E+00 -.536958E-01 0.299637E+01 0.201031E+01 0.213364E-17
- 100 0.886508E+00 -.536958E-01 0.301234E+01 0.203264E+01 -.773918E-17
- 101 0.894175E+00 -.536958E-01 0.302801E+01 0.205471E+01 0.284299E-16
- 102 0.901605E+00 -.536958E-01 0.304336E+01 0.207642E+01 -.104459E-15
- 103 0.908792E+00 -.536958E-01 0.305836E+01 0.209776E+01 0.383531E-15
- 104 0.915734E+00 -.536958E-01 0.307300E+01 0.211869E+01 -.140697E-14
- 105 0.922425E+00 -.536958E-01 0.308724E+01 0.213914E+01 0.515667E-14
- 106 0.928862E+00 -.536958E-01 0.310107E+01 0.215912E+01 -.188811E-13
- 107 0.935041E+00 -.536958E-01 0.311447E+01 0.217855E+01 0.690592E-13
- 108 0.940957E+00 -.536958E-01 0.312742E+01 0.219744E+01 -.252299E-12
- 109 0.946608E+00 -.536958E-01 0.313989E+01 0.221568E+01 -.224632E-13
- 110 0.951990E+00 -.536958E-01 0.315186E+01 0.223325E+01 0.420029E-12
- 111 0.957100E+00 -.536958E-01 0.316331E+01 0.225015E+01 0.366740E-12
- 112 0.961934E+00 -.536958E-01 0.317423E+01 0.226631E+01 0.264241E-12
- 113 0.966490E+00 -.536958E-01 0.318459E+01 0.228173E+01 -.918114E-12
- 114 0.970765E+00 -.536958E-01 0.319438E+01 0.229631E+01 -.977043E-12
- 115 0.974757E+00 -.536958E-01 0.320357E+01 0.231006E+01 -.286094E-11
- 116 0.978463E+00 -.536958E-01 0.321215E+01 0.232295E+01 0.318933E-11
- 117 0.981880E+00 -.536958E-01 0.322011E+01 0.233490E+01 -.103663E-10
- 118 0.985007E+00 -.536958E-01 0.322743E+01 0.234597E+01 0.522818E-10
- 119 0.987842E+00 -.536958E-01 0.323410E+01 0.235598E+01 -.159411E-09
- 120 0.990384E+00 -.536958E-01 0.324010E+01 0.236503E+01 0.596399E-09
- 121 0.992630E+00 -.536958E-01 0.324542E+01 0.237320E+01 -.207331E-08
- 122 0.994579E+00 -.536958E-01 0.325005E+01 0.238034E+01 0.724291E-08
- 123 0.996230E+00 -.536958E-01 0.325399E+01 0.238611E+01 -.250088E-07
- 124 0.997583E+00 -.536958E-01 0.325722E+01 0.239106E+01 0.850185E-07
- 125 0.998635E+00 -.536958E-01 0.325974E+01 0.239492E+01 -.282981E-06
- 126 0.999388E+00 -.536958E-01 0.326154E+01 0.239767E+01 0.909630E-06
- 127 0.999839E+00 -.536958E-01 0.326262E+01 0.239938E+01 -.274148E-05
- 128 0.999990E+00 -.536958E-01 0.326298E+01 0.239991E+01 0.700765E-05
diff --git a/notebooks/soloviev_ideal/sol.toml b/notebooks/soloviev_ideal/sol.toml
deleted file mode 100644
index cb8418b120..0000000000
--- a/notebooks/soloviev_ideal/sol.toml
+++ /dev/null
@@ -1,11 +0,0 @@
-[SOL_INPUT]
-mr = 128 # number of radial grid zones
-mz = 128 # number of axial grid zones
-ma = 128 # number of flux grid zones
-e = 1.6 # elongation
-a = 0.33 # minor radius
-r0 = 1.0 # major radius
-q0 = 1.9 # safety factor at the o-point
-p0fac=1 # scale on-axis pressure (P-> P+P0*p0fac. beta changes. Phi,q constant)
-b0fac=1 # scale toroidal field at constant beta (s*Phi,s*f,s^2*P. bt changes. Shape,beta constant)
-f0fac=1 # scale toroidal field at constant pressure (s*f. beta,q changes. Phi,p,bp constant)
\ No newline at end of file
diff --git a/notebooks/spline_bug_solovev_ideal.ipynb b/notebooks/spline_bug_solovev_ideal.ipynb
deleted file mode 100644
index 28aefde81c..0000000000
--- a/notebooks/spline_bug_solovev_ideal.ipynb
+++ /dev/null
@@ -1,302 +0,0 @@
-{
- "cells": [
- {
- "cell_type": "code",
- "execution_count": null,
- "id": "710e987d",
- "metadata": {},
- "outputs": [],
- "source": [
- "using Pkg\n",
- "Pkg.activate(\"..\")\n",
- "using JPEC\n",
- "using Plots"
- ]
- },
- {
- "cell_type": "markdown",
- "id": "30c317c5",
- "metadata": {},
- "source": [
- "## Overview\n",
- "In this notebook, I attempt to show where I am seeing bugs in the equilibrium knots/splines when running the Solovev ideal example. I noticed in the fourfit functions, I was seeing discrepancies for the metric tensor computation, and traced them down to the following function calls giving sufficiently different values from the same values when I dumped the same values from the Fortran code run with the same input files (above what is to be expected due to machine precision/floating point errors). I have put the Fortran data from this dump in the soloviev_ideal example, but could also be obtained by adding the relevant write statements for `fourfit_make_metric` and `fourfit_make_matrix` within `fourfit.F`. \n",
- "\n",
- "I **think** this is an issue with equil and not splines, since I have verified that if I use the Fortran knot values, I get the correct matrices, which involves a creating a Fourier spline for the metric tensor, but I am not 100% sure.\n",
- "\n",
- "The relevant data for these calculations is:\n",
- "\n",
- "fortran_rzphi_knots.dat: rzphi%f(1:4), fx(1:4), fy(1:4) at each psi and theta\n",
- "\n",
- "fortran_sq_knots.dat: sq%fs1(2), sq%fs(4), sq%fs1(4), -sq%fs1(1) (p1, q, q1, and jtheta, respectively) at each psi"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "id": "cb106129",
- "metadata": {},
- "outputs": [],
- "source": [
- "### Set up the equilibrium data for the solovev ideal example\n",
- "equil = Equilibrium.setup_equilibrium(\"soloviev_ideal/equil.toml\")"
- ]
- },
- {
- "cell_type": "markdown",
- "id": "f85da686",
- "metadata": {},
- "source": [
- "## 1D Profiles\n",
- "\n",
- "First, I will show the errors I was finding with the 1D profiles from sq"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "id": "f7ab5918",
- "metadata": {},
- "outputs": [],
- "source": [
- "# Extract knots from the sq data that we will compare to the Fortran values\n",
- "psi = equil.sq.xs\n",
- "p1 = equil.sq.fs1[:, 2]\n",
- "q = equil.sq.fs[:, 4]\n",
- "q1 = equil.sq.fs1[:, 4]\n",
- "jtheta = -equil.sq.fs1[:, 1]\n",
- "\n",
- "# Read the Fortran data into equivalent arrays\n",
- "lines = readlines(\"soloviev_ideal/fortran_sq_knots.dat\")\n",
- "data = [parse.(Float64, split(l)) for l in lines[2:end]]\n",
- "ipsi_f = zeros(size(psi))\n",
- "psi_f = zeros(size(psi))\n",
- "p1_f = zeros(size(psi))\n",
- "q_f = zeros(size(psi))\n",
- "q1_f = zeros(size(psi))\n",
- "jtheta_f = zeros(size(psi))\n",
- "for row in data\n",
- " ipsi_f[Int(row[1])+1] = row[1] # shift to Julia indexing\n",
- " psi_f[Int(row[1])+1] = row[2]\n",
- " p1_f[Int(row[1])+1] = row[3]\n",
- " q_f[Int(row[1])+1] = row[4]\n",
- " q1_f[Int(row[1])+1] = row[5]\n",
- " jtheta_f[Int(row[1])+1] = row[6]\n",
- "end\n",
- "\n",
- "# Plot q profile comparison (log scale)\n",
- "plot(psi, abs.((q - q_f) ./ q_f), label=\"rel error\", xlabel=\"psi\", ylabel=\"|q(Julia) - q(Fortran)| / |q(Fortran)|\", title=\"q profile comparison\", yscale=:log10)\n",
- "display(current())\n",
- "\n",
- "# Plot p1 profile comparison (log scale)\n",
- "plot(psi, abs.((p1 - p1_f) ./ p1_f), label=\"rel error\", xlabel=\"psi\", ylabel=\"|p1(Julia) - p1(Fortran)| / |p1(Fortran)|\", title=\"p1 profile comparison\", yscale=:log10)\n",
- "display(current())\n",
- "\n",
- "# Plot q1 profile comparison (log scale)\n",
- "plot(psi, abs.((q1 - q1_f) ./ q1_f), label=\"rel error\", xlabel=\"psi\", ylabel=\"|q1(Julia) - q1(Fortran)| / |q1(Fortran)|\", title=\"q1 profile comparison\", yscale=:log10)\n",
- "display(current())\n",
- "\n",
- "# Plot jtheta profile comparison (log scale)\n",
- "plot(psi, abs.((jtheta - jtheta_f) ./ jtheta_f), label=\"rel error\", xlabel=\"psi\", ylabel=\"|jtheta(Julia) - jtheta(Fortran)| / |jtheta(Fortran)|\", title=\"jtheta profile comparison\", yscale=:log10)\n",
- "display(current())"
- ]
- },
- {
- "cell_type": "markdown",
- "id": "343b6c96",
- "metadata": {},
- "source": [
- "We can see that the q and p1 profiles look good in terms of error, but the q1 profile has a large spike at the magnetic axis and jtheta has large relative errors throughout. These values are needed for assembling the matrices in fourfit_make_matrix, and this was propagating to cause large errors in those values as well"
- ]
- },
- {
- "cell_type": "markdown",
- "id": "49cf819a",
- "metadata": {},
- "source": [
- "## 2D Profiles\n",
- "\n",
- "Now, we will look at the relative and absolute errors resulting from the rzphi values used to assemble the metric tensor in fourfit_make_metric"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "id": "0ea19718",
- "metadata": {},
- "outputs": [],
- "source": [
- "# Assemble arrays of Julia equilibrium values. Note that there is a bicube eval here to match the line in Fortran, but the\n",
- "# evaluation occurs on the knot values so I don't think this would be a spline issue, but again not 100% sure.\n",
- "rzphi = equil.rzphi\n",
- "psi = rzphi.xs\n",
- "theta = rzphi.ys\n",
- "mpsi = length(rzphi.xs) - 1\n",
- "mtheta = length(rzphi.ys) - 1\n",
- "f_store = Array{Float64}(undef, mpsi + 1, mtheta + 1, 4) \n",
- "fx_store = Array{Float64}(undef, mpsi + 1, mtheta + 1, 4)\n",
- "fy_store = Array{Float64}(undef, mpsi + 1, mtheta + 1, 4)\n",
- "f_store_f = Array{Float64}(undef, mpsi + 1, mtheta + 1, 4) \n",
- "fx_store_f = Array{Float64}(undef, mpsi + 1, mtheta + 1, 4)\n",
- "fy_store_f = Array{Float64}(undef, mpsi + 1, mtheta + 1, 4)\n",
- "for ipsi in 1:(mpsi+1)\n",
- " for jtheta in 1:(mtheta+1)\n",
- " f, fx, fy = SplinesMod.bicube_eval(rzphi, rzphi.xs[ipsi], rzphi.ys[jtheta], 1)\n",
- " f_store[ipsi, jtheta, :] .= f\n",
- " fx_store[ipsi, jtheta, :] .= fx\n",
- " fy_store[ipsi, jtheta, :] .= fy\n",
- " end\n",
- "end\n",
- "\n",
- "# Read in equivalent Fortran data\n",
- "lines = readlines(\"soloviev_ideal/fortran_rzphi_knots.dat\")\n",
- "data = [parse.(Float64, split(l)) for l in lines[2:end]]\n",
- "for row in data\n",
- " ipsi = Int(row[1]) + 1 # shift to Julia indexing\n",
- " itheta = Int(row[2]) + 1\n",
- " f_store_f[ipsi, itheta, :] .= row[3:6]\n",
- " fx_store_f[ipsi, itheta, :] .= row[7:10]\n",
- " fy_store_f[ipsi, itheta, :] .= row[11:14]\n",
- "end\n",
- "\n",
- "# Plot relative error between Julia and Fortran values\n",
- "labels = [\"(1)\", \"(2)\", \"(3)\", \"(4)\"]\n",
- "for i in 1:4\n",
- " # Relative error for f\n",
- " rel_err_f = abs.((f_store[:, :, i] .- f_store_f[:, :, i]) ./ f_store_f[:, :, i])\n",
- " contour(\n",
- " psi,\n",
- " theta,\n",
- " rel_err_f',\n",
- " title=\"Relative Error: f$(labels[i])\",\n",
- " xlabel=\"psi\",\n",
- " ylabel=\"theta\",\n",
- " colorbar_title=\"rel error\",\n",
- " colorbar_scale=:log10\n",
- " )\n",
- " display(current())\n",
- "\n",
- " # Relative error for fx\n",
- " rel_err_fx = abs.((fx_store[:, :, i] .- fx_store_f[:, :, i]) ./ fx_store_f[:, :, i])\n",
- " contour(\n",
- " psi,\n",
- " theta,\n",
- " rel_err_fx',\n",
- " title=\"Relative Error: fx$(labels[i])\",\n",
- " xlabel=\"psi\",\n",
- " ylabel=\"theta\",\n",
- " colorbar_title=\"rel error\",\n",
- " colorbar_scale=:log10\n",
- " )\n",
- " display(current())\n",
- "\n",
- " # Relative error for fy\n",
- " rel_err_fy = abs.((fy_store[:, :, i] .- fy_store_f[:, :, i]) ./ fy_store_f[:, :, i])\n",
- " contour(\n",
- " psi,\n",
- " theta,\n",
- " rel_err_fy',\n",
- " title=\"Relative Error: fy$(labels[i])\",\n",
- " xlabel=\"psi\",\n",
- " ylabel=\"theta\",\n",
- " colorbar_title=\"rel error\",\n",
- " colorbar_scale=:log10\n",
- " )\n",
- " display(current())\n",
- "end"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "id": "303654b4",
- "metadata": {},
- "outputs": [],
- "source": [
- "labels = [\"(1)\", \"(2)\", \"(3)\", \"(4)\"]\n",
- "for i in 1:4\n",
- " # Absolute error for f\n",
- " abs_err_f = abs.(f_store[:, :, i] .- f_store_f[:, :, i])\n",
- " contour(\n",
- " psi,\n",
- " theta,\n",
- " abs_err_f',\n",
- " title=\"Absolute Error: f$(labels[i])\",\n",
- " xlabel=\"psi\",\n",
- " ylabel=\"theta\",\n",
- " colorbar_title=\"abs error\",\n",
- " colorbar_scale=:log10\n",
- " )\n",
- " display(current())\n",
- "\n",
- " # Absolute error for fx\n",
- " abs_err_fx = abs.(fx_store[:, :, i] .- fx_store_f[:, :, i])\n",
- " contour(\n",
- " psi,\n",
- " theta,\n",
- " abs_err_fx',\n",
- " title=\"Absolute Error: fx$(labels[i])\",\n",
- " xlabel=\"psi\",\n",
- " ylabel=\"theta\",\n",
- " colorbar_title=\"abs error\",\n",
- " colorbar_scale=:log10\n",
- "\n",
- " )\n",
- " display(current())\n",
- "\n",
- " # Absolute error for fy\n",
- " abs_err_fy = abs.(fy_store[:, :, i] .- fy_store_f[:, :, i])\n",
- " contour(\n",
- " psi,\n",
- " theta,\n",
- " abs_err_fy',\n",
- " title=\"Absolute Error: fy$(labels[i])\",\n",
- " xlabel=\"psi\",\n",
- " ylabel=\"theta\",\n",
- " colorbar_title=\"abs error\",\n",
- " colorbar_scale=:log10\n",
- " )\n",
- " display(current())\n",
- "end"
- ]
- },
- {
- "cell_type": "markdown",
- "id": "4ef457c7",
- "metadata": {},
- "source": [
- "It is a bit difficult to see on the relative error plots since there are a few extremely large spikes (that I think occur when the value is below machine precision and the relative error is inaccurate), but I think the jist here is to look at the absolute error in fx(2:4), where there is an anomalous spike near the axis. This difference was drectly affecting the calculations. I **think** the rest of the values are ok, but we could double check by filtering out errors of values below 10^-10 or something and verifying that all relative errors for values above this limit are small"
- ]
- },
- {
- "cell_type": "markdown",
- "id": "67eea7ae",
- "metadata": {},
- "source": [
- "## Summary\n",
- "\n",
- "Based on these plots, I think the mostly likely source of error is how the first grid point is dealt with between the two codes. Most likely the actual spline evals are ok, and it seems like for most of the rest of the knots (besides jtheta perhaps?) the errors are small"
- ]
- },
- {
- "cell_type": "markdown",
- "id": "4e9d9417",
- "metadata": {},
- "source": []
- }
- ],
- "metadata": {
- "kernelspec": {
- "display_name": "Julia 1.11.6",
- "language": "julia",
- "name": "julia-1.11"
- },
- "language_info": {
- "file_extension": ".jl",
- "mimetype": "application/julia",
- "name": "julia",
- "version": "1.11.6"
- }
- },
- "nbformat": 4,
- "nbformat_minor": 5
-}
diff --git a/notebooks/spline_examples.ipynb b/notebooks/spline_examples.ipynb
deleted file mode 100644
index eb12e6cf4d..0000000000
--- a/notebooks/spline_examples.ipynb
+++ /dev/null
@@ -1,163 +0,0 @@
-{
- "cells": [
- {
- "cell_type": "code",
- "execution_count": null,
- "id": "814db625",
- "metadata": {},
- "outputs": [],
- "source": [
- "using Pkg\n",
- "Pkg.activate(\"..\")\n",
- "Pkg.instantiate()\n",
- "using JPEC, Plots"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "id": "6892132a",
- "metadata": {},
- "outputs": [],
- "source": [
- "# Make sine and cosine spline\n",
- "xs = range(0.0, stop=2*pi, length=21)\n",
- "xs = collect(xs)\n",
- "fs = sin.(xs)\n",
- "fc = cos.(xs)\n",
- "# Make a vector of vectors of (100,2) for the spline\n",
- "fs_matrix = hcat(fs, fc)\n",
- "\n",
- "# print(xs)\n",
- "spline = JPEC.SplinesMod.spline_setup(xs, fs_matrix, 2)"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "id": "94c3d4e9",
- "metadata": {},
- "outputs": [],
- "source": [
- "# example: f = GPECsplines.spline_eval(spline, 3.2)\n",
- "# plot the spline\n",
- "xs_fine = collect(range(0.0, stop=2*pi, length=100))\n",
- "fs_fine = JPEC.SplinesMod.spline_eval(spline, xs_fine)\n",
- "plot(xs_fine, fs_fine, label=\"spline\", legend=:topright)\n",
- "# plot the input data scatter\n",
- "scatter!(xs, fs, label=\"sin(x)\", legend=:topright)\n",
- "scatter!(xs, fc, label=\"cos(x)\", legend=:topright)"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "id": "97a529f4",
- "metadata": {},
- "outputs": [],
- "source": [
- "# Make e^-ix and e^ix spline\n",
- "xs = range(0.0, stop=2*pi, length=20)\n",
- "xs = collect(xs)\n",
- "fm = exp.(-im .* xs)\n",
- "fp = exp.(im .* xs)\n",
- "# Make a vector of vectors of (100,2) for the spline\n",
- "fs_matrix = hcat(fm, fp)\n",
- "\n",
- "spline = JPEC.SplinesMod.spline_setup(xs, fs_matrix, 2)\n"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "id": "131e2883",
- "metadata": {},
- "outputs": [],
- "source": [
- "# example: f = GPECsplines.spline_eval(spline, 3.2)\n",
- "# plot the spline\n",
- "xs_fine = collect(range(0.0, stop=2*pi, length=100))\n",
- "fs_fine = JPEC.SplinesMod.spline_eval(spline, xs_fine)\n",
- "\n",
- "# plot just the real part of e^(+ix)\n",
- "plot(xs_fine, real(fs_fine[:, 2]), label=\"spline\", legend=:topright)\n",
- "# and the imaginary part\n",
- "plot!(xs_fine, imag(fs_fine[:, 2]), label=\"spline\", legend=:topright)\n",
- "# plot the input data scatter\n",
- "scatter!(xs, real(fs_matrix[:, 2]), label=\"real(e^ix)\", legend=:topright)\n",
- "scatter!(xs, imag(fs_matrix[:, 2]), label=\"imag(e^ix)\", legend=:topright)"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "id": "d74a45e4",
- "metadata": {},
- "outputs": [],
- "source": [
- "# make a bicubic spline of a 2d periodic function\n",
- "xs = range(0.0, stop=2*pi, length=20)\n",
- "ys = range(0.0, stop=2*pi, length=20)\n",
- "xs = collect(xs)\n",
- "ys = collect(ys)\n",
- "fs1 = sin.(xs') .* cos.(ys) .+ 1.0\n",
- "fs2 = cos.(xs') .* sin.(ys) .+ 1.0\n",
- "fs = zeros(20, 20, 2)\n",
- "# fs is a 20x20x2 array\n",
- "fs[:, :, 1] = fs1\n",
- "fs[:, :, 2] = fs2\n",
- "println(\"fs size: \", size(fs))\n",
- "\n",
- "# Make a bicubic spline\n",
- "bcspline = JPEC.SplinesMod.bicube_setup(xs, ys, fs, 2, 2)"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "id": "0c40c658",
- "metadata": {},
- "outputs": [],
- "source": [
- "# Evaluate the bicubic spline\n",
- "xs_fine = collect(range(0.0, stop=2*pi, length=100))\n",
- "ys_fine = collect(range(0.0, stop=2*pi, length=100))\n",
- "# fs_fine, fsx_fine, fsy_fine, fsxx_fine, fsxy_fine, fsyy_fine = JPEC.SplinesMod.bicube_eval(bcspline, xs_fine, ys_fine, 2)\n",
- "fs_fine, fsx_fine, fsy_fine = JPEC.SplinesMod.bicube_eval(bcspline, xs_fine, ys_fine, 1)\n",
- "\n",
- "# plot the bicubic spline\n",
- "p1 = contourf(xs_fine, ys_fine, fs_fine[:, :, 1], label=\"sin(x)cos(y)+1\", legend=:topright)\n",
- "p2 = contourf(xs_fine, ys_fine, fs_fine[:, :, 2], label=\"cos(x)sin(y)+1\", legend=:topright)\n",
- "plot(p1, p2, layout=(1, 2), size=(800, 400), title=\"Bicubic Spline Evaluation\")"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "id": "71c7fff6",
- "metadata": {},
- "outputs": [],
- "source": [
- "# plot the derivatives\n",
- "p1 = contourf(xs_fine, ys_fine, fsx_fine[:, :, 1], label=\"derivative w.r.t x\", legend=:topright)\n",
- "p2 = contourf(xs_fine, ys_fine, fsy_fine[:, :, 1], label=\"derivative w.r.t y\", legend=:topright)\n",
- "plot(p1, p2, layout=(1, 2), size=(800, 400), title=\"Bicubic Spline Evaluation\")"
- ]
- }
- ],
- "metadata": {
- "kernelspec": {
- "display_name": "Julia 1.11.4",
- "language": "julia",
- "name": "julia-1.11"
- },
- "language_info": {
- "file_extension": ".jl",
- "mimetype": "application/julia",
- "name": "julia",
- "version": "1.11.4"
- }
- },
- "nbformat": 4,
- "nbformat_minor": 5
-}
diff --git a/notebooks/spline_examples2.ipynb b/notebooks/spline_examples2.ipynb
deleted file mode 100644
index 21c2769d0e..0000000000
--- a/notebooks/spline_examples2.ipynb
+++ /dev/null
@@ -1,661 +0,0 @@
-{
- "cells": [
- {
- "cell_type": "code",
- "execution_count": null,
- "id": "814db625",
- "metadata": {},
- "outputs": [],
- "source": [
- "using Pkg\n",
- "Pkg.activate(\"..\")\n",
- "Pkg.resolve()\n",
- "Pkg.instantiate() # Usually only need to run this once\n",
- "using Plots, Printf\n",
- "using JPEC.SplinesMod"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "id": "6892132a",
- "metadata": {},
- "outputs": [],
- "source": [
- "\n",
- "#=\n",
- "======================================================================\n",
- "1. VALIDATION FOR 1D CUBIC SPLINE (Real)\n",
- "======================================================================\n",
- "=#\n",
- "println(\"\\n--- Testing 1D Spline Derivatives and Integration ---\")\n",
- "\n",
- "# --- 1.1 Data Generation ---\n",
- "# Using 20 nodes to create a periodic spline for sin(x) and cos(x)\n",
- "xs_nodes = collect(range(0.0, stop=2*pi, length=20))\n",
- "y1_nodes = sin.(xs_nodes)\n",
- "y2_nodes = cos.(xs_nodes)\n",
- "fs_nodes_matrix = hcat(y1_nodes, y2_nodes)\n",
- "\n",
- "# --- 1.2 Spline Setup (bctype=3 for periodic)---\n",
- "spline_real = CubicSpline(xs_nodes, fs_nodes_matrix; bctype=3)\n"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "id": "0d38581c",
- "metadata": {},
- "outputs": [],
- "source": [
- "\n",
- "# --- 1.3 Evaluation on a Fine Grid ---\n",
- "xs_fine = collect(range(0.0, stop=2*pi, length=200))\n",
- "\n",
- "\n",
- "# Evaluate the spline and its derivatives up to the 3rd order\n",
- "f_s, f1_s, f2_s, f3_s = spline_eval(spline_real, xs_fine, 3)\n",
- "\n",
- "\n",
- "# --- 1.4 Perform Integration ---\n",
- "# This modifies the spline_real object in-place, adding the .fsi field\n",
- "SplinesMod.spline_integrate!(spline_real)\n",
- "\n",
- "# The result of integration is stored at the original node points.\n",
- "# spline_real.fsi now contains the cumulative integral values.\n",
- "integral_s = spline_real.fsi\n",
- "\n",
- "# --- 1.5 Analytical (True) Values ---\n",
- "# True values for the function and its derivatives on the fine grid\n",
- "true_f = hcat(sin.(xs_fine), cos.(xs_fine))\n",
- "true_f1 = hcat(cos.(xs_fine), -sin.(xs_fine))\n",
- "true_f2 = hcat(-sin.(xs_fine), -cos.(xs_fine))\n",
- "true_f3 = hcat(-cos.(xs_fine), sin.(xs_fine))\n",
- "\n",
- "# True values for the integral on the original coarse grid (xs_nodes)\n",
- "# Integral of sin(x) from 0 to t is -cos(t) - (-cos(0)) = 1 - cos(t)\n",
- "# Integral of cos(x) from 0 to t is sin(t) - sin(0) = sin(t)\n",
- "true_integral = hcat(1.0 .- cos.(xs_nodes), sin.(xs_nodes))\n",
- "\n",
- "print(\"evaluation complete\")\n"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "id": "a90e8828",
- "metadata": {},
- "outputs": [],
- "source": [
- "\n",
- "# --- 1.6 Plotting (Focusing on the first function, sin(x)) ---\n",
- "\n",
- "# Plot for Function Value f(x)\n",
- "function generate_spline_plot(\n",
- " x_vals, \n",
- " spline_data, \n",
- " analytic_data;\n",
- " title, \n",
- " spline_label, \n",
- " analytic_label,\n",
- " error_scale=1.0,\n",
- " legend_pos=:best,\n",
- " x_nodes=nothing,\n",
- " y_nodes=nothing,\n",
- " nodes_label=\"Original Nodes\",\n",
- " kwargs...\n",
- ")\n",
- " \n",
- " p = plot(x_vals, spline_data, label=spline_label, title=title, legend=legend_pos; kwargs...)\n",
- " \n",
- " plot!(p, x_vals, analytic_data, ls=:dash, label=analytic_label)\n",
- " scaler_str = isinteger(error_scale) ? string(Int(error_scale)) : string(error_scale)\n",
- " error_label = error_scale == 1.0 ? \"Error\" : \"Error x\" * scaler_str\n",
- " plot!(p, x_vals, spline_data .- analytic_data, ls=:dot, label=error_label, color=:red)\n",
- " \n",
- " if x_nodes !== nothing && y_nodes !== nothing\n",
- " scatter!(p, x_nodes, y_nodes, label=nodes_label, markersize=3, markerstrokewidth=0)\n",
- " end\n",
- " \n",
- " return p\n",
- "end\n",
- "\n",
- "# --- 1.6 Generate and Display all plots ---\n",
- "\n",
- "println(\"--- Generating 1D Spline Validation Plots ---\")\n",
- "\n",
- "plot_configs_real = [\n",
- " # f(x) \n",
- " (\n",
- " spline_data = f_s[:, 1], analytic_data = true_f[:, 1], x_vals = xs_fine,\n",
- " title = \"Function: sin(x)\", spline_label = \"Spline f(x)\", analytic_label = \"True f(x)\",\n",
- " error_scale = 1000.0, legend_pos = :bottomleft,\n",
- " x_nodes = xs_nodes, y_nodes = y1_nodes\n",
- " ),\n",
- " # f'(x) \n",
- " (\n",
- " spline_data = f1_s[:, 1], analytic_data = true_f1[:, 1], x_vals = xs_fine,\n",
- " title = \"1st Deriv: cos(x)\", spline_label = \"Spline f'(x)\", analytic_label = \"True f'(x)\",\n",
- " error_scale = 100.0, legend_pos = :bottomleft\n",
- " ),\n",
- " # f''(x)\n",
- " (\n",
- " spline_data = f2_s[:, 1], analytic_data = true_f2[:, 1], x_vals = xs_fine,\n",
- " title = \"2nd Deriv: -sin(x)\", spline_label = \"Spline f''(x)\", analytic_label = \"True f''(x)\",\n",
- " error_scale = 1.0, legend_pos = :bottomleft\n",
- " ),\n",
- " # f'''(x)\n",
- " (\n",
- " spline_data = f3_s[:, 1], analytic_data = true_f3[:, 1], x_vals = xs_fine,\n",
- " title = \"3rd Deriv: -cos(x)\", spline_label = \"Spline f'''(x)\", analytic_label = \"True f'''(x)\",\n",
- " error_scale = 1.0, legend_pos = :bottomleft\n",
- " ),\n",
- " # integral \n",
- " (\n",
- " spline_data = integral_s[:, 1], analytic_data = true_integral[:, 1], x_vals = xs_nodes,\n",
- " title = \"Integral: 1-cos(x)\", spline_label = \"Spline Integral\", analytic_label = \"True Integral\",\n",
- " error_scale = 1000.0, legend_pos = :topleft,\n",
- " style = (markershape=:circle, markersize=3)\n",
- " )\n",
- "]\n",
- "\n",
- "\n",
- "plot_list_real = []\n",
- "println(\"--- Generating 1D Spline Validation Plots ---\")\n",
- "\n",
- "for config in plot_configs_real\n",
- " \n",
- " p = generate_spline_plot(\n",
- " config.x_vals,\n",
- " config.spline_data,\n",
- " config.analytic_data;\n",
- " title = config.title,\n",
- " spline_label = config.spline_label,\n",
- " analytic_label = config.analytic_label,\n",
- " error_scale = config.error_scale,\n",
- " legend_pos = config.legend_pos,\n",
- " \n",
- " x_nodes = get(config, :x_nodes, nothing),\n",
- " y_nodes = get(config, :y_nodes, nothing),\n",
- " \n",
- " (haskey(config, :style) ? config.style : ())...\n",
- " )\n",
- " push!(plot_list_real, p)\n",
- "end\n",
- "\n",
- "\n",
- "display(plot(plot_list_real..., layout=(3, 2), size=(1200, 1000), margin=5Plots.mm))\n",
- "\n",
- "\n",
- "\n",
- "println(\"\\nAll 1D validation plots generated.\")"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "id": "94c3d4e9",
- "metadata": {},
- "outputs": [],
- "source": [
- "\n",
- "#=\n",
- "======================================================================\n",
- "2. VALIDATION FOR 1D CUBIC SPLINE (Complex)\n",
- "======================================================================\n",
- "=#\n",
- "println(\"\\n--- Testing 1D Complex Spline Derivatives and Integration ---\")\n",
- "\n",
- "# --- 2.1 Data Generation ---\n",
- "xs_nodes = collect(range(0.0, stop=2*pi, length=40))\n",
- "fs_complex_nodes = exp.(im .* xs_nodes)\n",
- "\n",
- "# --- 2.2 Spline Setup (bctype=3 for periodic) ---\n",
- "spline_complex = CubicSpline(xs_nodes, fs_complex_nodes; bctype = 3)\n"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "id": "9178555a",
- "metadata": {},
- "outputs": [],
- "source": [
- "\n",
- "# --- 2.3 Evaluation on a Fine Grid ---\n",
- "xs_fine = collect(range(0.0, stop=2*pi, length=200))\n",
- "f_cs, f1_cs, f2_cs, f3_cs = spline_eval(spline_complex, xs_fine, 3)\n",
- "\n",
- "# --- 2.4 Perform Integration ---\n",
- "# This modifies the spline_complex object in-place, adding the .fsi field\n",
- "SplinesMod.spline_integrate!(spline_complex)\n",
- "integral_cs = spline_complex.fsi\n",
- "\n",
- "# --- 2.5 Analytical (True) Values ---\n",
- "true_f_c = exp.(im .* xs_fine)\n",
- "true_f1_c = im .* exp.(im .* xs_fine)\n",
- "true_f2_c = -1 .* exp.(im .* xs_fine)\n",
- "true_f3_c = -im .* exp.(im .* xs_fine)\n",
- "\n",
- "# True values for the integral on the original node grid\n",
- "# Integral of exp(ix) from 0 to t is i*(1 - exp(ix))\n",
- "true_integral_c = im .* (1.0 .- exp.(im .* xs_nodes))\n",
- "\n",
- "print(\"evaluation complete\")"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "id": "587b6ed1",
- "metadata": {},
- "outputs": [],
- "source": [
- "\n",
- "# --- 2.6 Plotting ---\n",
- "function generate_complex_spline_plot(\n",
- " x_vals, \n",
- " spline_c, \n",
- " analytic_c; \n",
- " part, \n",
- " title, \n",
- " kwargs...\n",
- " )\n",
- " func = (part == :real) ? real : imag\n",
- " \n",
- " spline_data = func(spline_c)\n",
- " analytic_data = func(analytic_c)\n",
- " error_data = spline_data .- analytic_data\n",
- " \n",
- " p = plot(x_vals, analytic_data, ls=:dash, label=\"True\", title=title; kwargs...)\n",
- " \n",
- " plot!(p, x_vals, spline_data, label=\"Spline\")\n",
- " \n",
- " plot!(p, x_vals, error_data, ls=:dot, label=\"Error\", color=:red)\n",
- " \n",
- " return p\n",
- "end\n",
- "\n",
- "\n",
- "\n",
- "plot_configs = [\n",
- " (label=\"f(x)\", data_s=f_cs, data_t=true_f_c, formula=\"e^ix\", re_res=\"cos(x)\", im_res=\"sin(x)\", x_vals=xs_fine),\n",
- " (label=\"f'(x)\", data_s=f1_cs, data_t=true_f1_c, formula=\"ie^ix\", re_res=\"-sin(x)\", im_res=\"cos(x)\", x_vals=xs_fine),\n",
- " (label=\"f''(x)\", data_s=f2_cs, data_t=true_f2_c, formula=\"-e^ix\", re_res=\"-cos(x)\", im_res=\"-sin(x)\", x_vals=xs_fine),\n",
- " (label=\"f'''(x)\",data_s=f3_cs, data_t=true_f3_c, formula=\"-ie^ix\", re_res=\"sin(x)\", im_res=\"-cos(x)\", x_vals=xs_fine),\n",
- " (label=\"∫f dt\", data_s=integral_cs, data_t=true_integral_c, formula=\"i(1-e^ix)\", re_res=\"sin(x)\", im_res=\"1-cos(x)\", x_vals=xs_nodes, style=(markershape=:circle, markersize=2)),\n",
- "]\n",
- "\n",
- "plot_list = []\n",
- "println(\"--- Generating Complex Spline Validation Plots ---\")\n",
- "\n",
- "\n",
- "for config in plot_configs\n",
- " for part_info in ((part=:real, name=\"Re\", res=config.re_res), \n",
- " (part=:imag, name=\"Im\", res=config.im_res))\n",
- " \n",
- " title = \"$(config.label) = $(part_info.name)($(config.formula)) = $(part_info.res)\"\n",
- " \n",
- " plot_style = haskey(config, :style) ? config.style : (legend=:bottomleft,)\n",
- "\n",
- " p = generate_complex_spline_plot(\n",
- " config.x_vals, \n",
- " config.data_s, \n",
- " config.data_t;\n",
- " part=part_info.part,\n",
- " title=title,\n",
- " plot_style... \n",
- " )\n",
- " push!(plot_list, p)\n",
- " end\n",
- "end\n",
- "\n",
- "display(plot(plot_list..., layout=(5, 2), size=(1000, 1500),\n",
- " plot_title=\"Complex Spline: f(x) = e^(ix), Derivatives, and Integral\",\n",
- " margin=4Plots.mm))\n",
- "\n",
- "println(\"\\nAll complex validation plots generated.\")"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "id": "97a529f4",
- "metadata": {},
- "outputs": [],
- "source": [
- "#=\n",
- "======================================================================\n",
- "3. VALIDATION FOR 2D BICUBIC SPLINE\n",
- "======================================================================\n",
- "=#\n",
- "println(\"\\n--- Testing 2D Bicubic Spline Derivatives ---\")\n",
- "\n",
- "# --- 3.1 Data Generation (for fitting) ---\n",
- "nx_nodes, ny_nodes = 20, 20\n",
- "x_nodes = collect(range(0.0, stop=2*pi, length=nx_nodes))\n",
- "y_nodes = collect(range(0.0, stop=2*pi, length=ny_nodes))\n",
- "\n",
- "f_nodes = zeros(nx_nodes, ny_nodes, 1) # n_qty = 1 for this test\n",
- "for j in 1:ny_nodes, i in 1:nx_nodes\n",
- " f_nodes[i, j, 1] = sin(x_nodes[i]) * cos(y_nodes[j])\n",
- "end\n",
- "\n",
- "# --- 3.2 Spline Setup (bctype=2 for periodic in both dimensions) ---\n",
- "bcspline = BicubicSpline(x_nodes, y_nodes, f_nodes, bctypex=2, bctypey= 2)\n"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "id": "1cd773be",
- "metadata": {},
- "outputs": [],
- "source": [
- "\n",
- "# --- 3.3 Evaluation ---\n",
- "nx_fine, ny_fine = 50, 50\n",
- "x_fine = collect(range(0.0, stop=2*pi, length=nx_fine))\n",
- "y_fine = collect(range(0.0, stop=2*pi, length=ny_fine))\n",
- "\n",
- "# Get derivatives up to 2nd order\n",
- "f_s, fx_s, fy_s, fxx_s, fxy_s, fyy_s = bicube_eval(bcspline, x_fine, y_fine, 2)\n",
- "\n",
- "\n",
- "# --- 3.4 Analytical (True) Functions ---\n",
- "f_analytic(x, y) = sin(x) * cos(y)\n",
- "fx_analytic(x, y) = cos(x) * cos(y)\n",
- "fy_analytic(x, y) = -sin(x) * sin(y)\n",
- "fxx_analytic(x, y) = -sin(x) * cos(y)\n",
- "fyy_analytic(x, y) = -sin(x) * cos(y)\n",
- "fxy_analytic(x, y) = -cos(x) * sin(y)\n",
- "\n"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "id": "7c70289a",
- "metadata": {},
- "outputs": [],
- "source": [
- "# --- 3.5 Plotting Helper Function ---\n",
- "function generate_bicube_plots(name, spline_data, analytic_func, x_grid, y_grid)\n",
- " \n",
- " analytical_data = [analytic_func(x, y) for x in x_grid, y in y_grid]\n",
- " spline_slice = spline_data[:, :, 1]\n",
- " error_data = spline_slice - analytical_data\n",
- " max_abs_error = maximum(abs, error_data)\n",
- " \n",
- " p1 = heatmap(x_grid, y_grid, spline_slice', title=\"Spline: $name\", c=:viridis)\n",
- " p2 = heatmap(x_grid, y_grid, analytical_data', title=\"Analytical: $name\", c=:viridis)\n",
- " p3 = heatmap(x_grid, y_grid, error_data', title=\"Error (Max Abs: $(@sprintf(\"%.2e\", max_abs_error)))\", c=:bwr)\n",
- "\n",
- " return plot(p1, p2, p3, layout=(1, 3), size=(1000, 300), aspect_ratio=:equal)\n",
- "end\n",
- "\n",
- "# --- 3.6 Generate and Display all plots ---\n",
- "display(generate_bicube_plots(\"f\", f_s, f_analytic, x_fine, y_fine))\n",
- "display(generate_bicube_plots(\"fx\", fx_s, fx_analytic, x_fine, y_fine))\n",
- "display(generate_bicube_plots(\"fy\", fy_s, fy_analytic, x_fine, y_fine))\n",
- "display(generate_bicube_plots(\"fxx\", fxx_s, fxx_analytic, x_fine, y_fine)) \n",
- "display(generate_bicube_plots(\"fyy\", fyy_s, fyy_analytic, x_fine, y_fine)) \n",
- "display(generate_bicube_plots(\"fxy\", fxy_s, fxy_analytic, x_fine, y_fine))\n",
- "\n"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "id": "131e2883",
- "metadata": {},
- "outputs": [],
- "source": [
- "#=\n",
- "======================================================================\n",
- "4. VALIDATION FOR 2D FOURIER SPLINE (CUBIC-X, FOURIER-Y)\n",
- "======================================================================\n",
- "=#\n",
- "# Assuming FourierSpline is where the module is located\n",
- "# For standalone testing, you might need:\n",
- "# include(\"FourierSpline.jl\")\n",
- "# using .FourierSpline\n",
- "\n",
- "println(\"\\n--- Testing 2D Fourier-Spline Derivatives ---\")\n",
- "\n",
- "\n",
- "\n",
- "# --- 4.1 Data Generation (for fitting) ---\n",
- "# For fit_method=2 (FFT), my_nodes must be a power of 2.\n",
- "# We use mx+1 points for x and my+1 points for y.\n",
- "# The grid is [0, mx] and [0, my].\n",
- "mx_nodes, my_nodes = 32, 32 # my_nodes must be a power of 2 for FFT test\n",
- "x_nodes = collect(range(0.0, stop=3.0, length=mx_nodes + 1))\n",
- "# y is periodic from 0 to 2pi. The last point y_nodes[my+1] should equal the first y_nodes[1] + 2pi\n",
- "y_nodes = collect(range(0.0, stop=2*pi, length=my_nodes + 1))\n",
- "\n",
- "f_nodes = zeros(mx_nodes + 1, my_nodes + 1, 1) # n_qty = 1\n",
- "for j in 1:(my_nodes + 1), i in 1:(mx_nodes + 1)\n",
- " f_nodes[i, j, 1] = x_nodes[i]^2 * cos(2 * y_nodes[j])\n",
- "end\n",
- "\n",
- "# --- 4.2 Spline Setup ---\n",
- "# Use bctype=1 (natural) for x-direction as it's not periodic.\n",
- "# The y-direction is inherently periodic.\n",
- "# mband determines how many Fourier modes are used. A higher number gives more accuracy.\n",
- "mband_val = 10\n",
- "\n",
- "# Test both fit methods\n",
- "println(\"\\n--- Setting up with fit_method=1 (Integral) ---\")\n",
- "fspline_m1 = FourierSpline(x_nodes, y_nodes, f_nodes, mband_val, bctype=4, fit_method=1,fit_flag=true)\n",
- "\n",
- "println(\"\\n--- Setting up with fit_method=2 (FFT) ---\")\n",
- "# This requires my_nodes to be a power of 2.\n",
- "fspline_m2 = FourierSpline(x_nodes, y_nodes, f_nodes, mband_val, bctype=2, fit_method=2,fit_flag=true)\n"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "id": "343bbb04",
- "metadata": {},
- "outputs": [],
- "source": [
- "\n",
- "# --- 4.3 Evaluation ---\n",
- "# We will evaluate using the FFT-fitted spline (method 2) as it's generally faster if applicable.\n",
- "# You can switch to fspline_m1 to compare.\n",
- "chosen_fspline = fspline_m1\n",
- "\n",
- "nx_fine, ny_fine = 60, 60\n",
- "x_fine = collect(range(0.0, stop=3.0, length=nx_fine))\n",
- "y_fine = collect(range(0.0, stop=2*pi, length=ny_fine))\n",
- "\n",
- "# Get derivatives up to 2nd order\n",
- "f_s, fx_s, fy_s, fxx_s, fxy_s, fyy_s = fspline_eval(chosen_fspline, x_fine, y_fine, Int(2))\n",
- "\n",
- "\n",
- "# --- 4.4 Analytical (True) Functions (Periodic in y) ---\n",
- "f_analytic(x, y) = x^2 * cos(2*y)\n",
- "fx_analytic(x, y) = 2*x * cos(2*y)\n",
- "fy_analytic(x, y) = -2 * x^2 * sin(2*y)\n",
- "fxx_analytic(x, y) = 2 * cos(2*y)\n",
- "fyy_analytic(x, y) = -4 * x^2 * cos(2*y)\n",
- "fxy_analytic(x, y) = -4 * x * sin(2*y)\n",
- "\n",
- "print(\"evaluation complete\")"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "id": "234f912c",
- "metadata": {},
- "outputs": [],
- "source": [
- "function generate_fspline_plot(name, spline_data, analytic_func, x_grid, y_grid)\n",
- "\n",
- " \n",
- " # 1. Generate the analytical data on the fine grid\n",
- " analytical_data = [analytic_func(x, y) for x in x_grid, y in y_grid]\n",
- " \n",
- " # 2. Extract the 2D slice from the 3D spline output array (n_qty=1)\n",
- " spline_slice = spline_data[:, :, 1]\n",
- " \n",
- " # 3. Calculate the error between the spline and analytical data\n",
- " error_data = spline_slice - analytical_data\n",
- " max_abs_error = maximum(abs, error_data)\n",
- " \n",
- " # 4. Create three separate heatmaps for comparison\n",
- " # Note: We transpose the data (') because Plots.jl heatmap expects (y, x) data layout\n",
- " p1 = heatmap(x_grid, y_grid, spline_slice', \n",
- " title=\"Spline: $name\", c=:viridis, aspect_ratio=:equal)\n",
- " \n",
- " p2 = heatmap(x_grid, y_grid, analytical_data', \n",
- " title=\"Analytical: $name\", c=:viridis, aspect_ratio=:equal)\n",
- " \n",
- " p3 = heatmap(x_grid, y_grid, error_data', \n",
- " title=\"Error (Max Abs: $(@sprintf(\"%.2e\", max_abs_error)))\", c=:bwr, aspect_ratio=:equal)\n",
- "\n",
- " # 5. Combine the three heatmaps into a single plot object with a 1x3 layout\n",
- " return plot(p1, p2, p3, layout=(1, 3), size=(800, 400), margin=4Plots.mm)\n",
- "end\n",
- "\n",
- "\n",
- "# --- 4.5 Generate all plots ---\n",
- "# This section calls the helper function for the main function and each derivative,\n",
- "# displaying each result as a separate row of plots.\n",
- "\n",
- "display(generate_fspline_plot(\"f\", f_s, f_analytic, x_fine, y_fine))\n",
- "display(generate_fspline_plot(\"fx\", fx_s, fx_analytic, x_fine, y_fine))\n",
- "display(generate_fspline_plot(\"fy\", fy_s, fy_analytic, x_fine, y_fine))\n",
- "display(generate_fspline_plot(\"fxx\", fxx_s, fxx_analytic, x_fine, y_fine))\n",
- "display(generate_fspline_plot(\"fyy\", fyy_s, fyy_analytic, x_fine, y_fine))\n",
- "display(generate_fspline_plot(\"fxy\", fxy_s, fxy_analytic, x_fine, y_fine))\n",
- "\n",
- "println(\"\\nAll Fourier Spline validation plots generated.\")"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "id": "aee4d93b",
- "metadata": {},
- "outputs": [],
- "source": [
- "coeffs = chosen_fspline.cs.fs\n",
- "num_x, num_modes = size(coeffs)\n",
- "for ix in 1:num_x # x 좌표 인덱스 루프\n",
- " for m_idx in 1:num_modes # 푸리에 모드 인덱스 루프\n",
- " # 모드 인덱스(m_idx)는 1부터 시작하므로, 실제 모드(m)는 m_idx - 1 입니다.\n",
- " m = m_idx - 1\n",
- " \n",
- " # 현재 요소 값 가져오기\n",
- " val = coeffs[ix, m_idx]\n",
- " \n",
- " # 출력\n",
- " @printf(\"x_index=%2d, mode=%2d (coeffs[%2d, %2d]): Re = %+.4e, Im = %+.4e\\n\", \n",
- " ix, m, ix, m_idx, real(val), imag(val))\n",
- " end\n",
- " println(\"-\"^20) # 각 x-point 그룹 사이에 구분선 추가\n",
- "end"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "id": "85209e3a-6a08-40e8-874e-85258736419b",
- "metadata": {},
- "outputs": [],
- "source": [
- "# --- Block 5: Validation of Fourier Coefficients ---\n",
- "\n",
- "println(\"\\n--- Validating Fourier Coefficients c_m(x) ---\")\n",
- "\n",
- "# Evaluate the spline of coefficients on the fine x-grid\n",
- "# The result is a matrix of size (nx_fine, cs_nqty)\n",
- "coeffs_spline_fine = spline_eval(chosen_fspline.cs, x_fine)\n",
- "\n",
- "# Define the analytical functions for the first few coefficients\n",
- "c0_analytic(x) = 0.0 + 0.0im\n",
- "c1_analytic(x) = 0.0 + 0.0im\n",
- "c2_analytic(x) = (x^2 / 2.0) + 0.0im # This is the only non-zero one\n",
- "c3_analytic(x) = 0.0 + 0.0im\n",
- "c4_analytic(x) = 0.0 + 0.0im\n",
- "\n",
- "analytic_funcs = [c0_analytic, c1_analytic, c2_analytic, c3_analytic, c4_analytic]\n",
- "\n",
- "# Create a list to hold the plot objects\n",
- "coefficient_plots = []\n",
- "\n",
- "\n",
- "num_modes_to_plot = min(5, chosen_fspline.cs.nqty)\n",
- "\n",
- "for m_idx in 1:num_modes_to_plot\n",
- " m = m_idx - 1 # Current mode number (m=0, 1, 2, ...)\n",
- " \n",
- " # Extract the data for the m-th mode from the spline evaluation result\n",
- " spline_c_m = coeffs_spline_fine[:, m_idx]\n",
- " \n",
- " # Generate the analytical data for the m-th mode\n",
- " analytic_c_m = [analytic_funcs[m_idx](x) for x in x_fine]\n",
- " \n",
- " # Plot the real part\n",
- " p_real = generate_complex_spline_plot(\n",
- " x_fine,\n",
- " spline_c_m,\n",
- " analytic_c_m,\n",
- " part=:real,\n",
- " title=\"Re(c_$m(x))\"\n",
- " )\n",
- " \n",
- " # Plot the imaginary part\n",
- " p_imag = generate_complex_spline_plot(\n",
- " x_fine,\n",
- " spline_c_m,\n",
- " analytic_c_m,\n",
- " part=:imag,\n",
- " title=\"Im(c_$m(x))\"\n",
- " )\n",
- " \n",
- " # Add the pair of plots to our list\n",
- " push!(coefficient_plots, p_real)\n",
- " push!(coefficient_plots, p_imag)\n",
- "end\n",
- "\n",
- "# Combine all coefficient plots into a single figure with a readable layout\n",
- "# The layout will be (num_modes_to_plot x 2 columns)\n",
- "coeff_plot_layout = (num_modes_to_plot, 2)\n",
- "final_coeff_plot = plot(coefficient_plots..., layout=coeff_plot_layout, size=(800, 250 * num_modes_to_plot))\n",
- "\n",
- "# Display the final combined plot\n",
- "display(final_coeff_plot)\n",
- "\n",
- "println(\"\\nFourier coefficient validation plots generated.\")"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "id": "3cc65ddf-ddbf-4138-af94-8a69e714b097",
- "metadata": {},
- "outputs": [],
- "source": []
- }
- ],
- "metadata": {
- "kernelspec": {
- "display_name": "Julia 1.11.5",
- "language": "julia",
- "name": "julia-1.11"
- },
- "language_info": {
- "file_extension": ".jl",
- "mimetype": "application/julia",
- "name": "julia",
- "version": "1.11.5"
- }
- },
- "nbformat": 4,
- "nbformat_minor": 5
-}
diff --git a/notebooks/vacuum_fortran_example.ipynb b/notebooks/vacuum_fortran_example.ipynb
deleted file mode 100644
index d41c6f802e..0000000000
--- a/notebooks/vacuum_fortran_example.ipynb
+++ /dev/null
@@ -1,97 +0,0 @@
-{
- "cells": [
- {
- "cell_type": "code",
- "execution_count": null,
- "id": "d11e5382",
- "metadata": {},
- "outputs": [],
- "source": [
- "using Pkg\n",
- "Pkg.activate(\"..\")\n",
- "Pkg.instantiate()\n",
- "using JPEC, Plots"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "id": "2139c5fa",
- "metadata": {},
- "outputs": [],
- "source": [
- "# Set dcon parameters\n",
- "# Copy ../test/vac.in to notebooks/vac.in if it doesn't exist\n",
- "if !isfile(\"../notebooks/vac.in\")\n",
- " cp(\"../test/vac.in\", \"../notebooks/vac.in\")\n",
- "end\n",
- "\n",
- "mthin, lmin, lmax, nnin = Int32(4), Int32(1), Int32(4), Int32(2)\n",
- "qa1in = 1.23\n",
- "xin = rand(Float64, lmax - lmin + 1)\n",
- "zin = rand(Float64, lmax - lmin + 1)\n",
- "deltain = rand(Float64, lmax - lmin + 1)\n",
- "\n",
- "println(\"Testing set_dcon_params…\")\n",
- "JPEC.VacuumMod.set_dcon_params(mthin, lmin, lmax, nnin, qa1in, xin, zin, deltain)\n",
- "println(\"set_dcon_params OK!\")"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "id": "91d8cd04",
- "metadata": {},
- "outputs": [],
- "source": [
- "# Run mscvac with sample variables\n",
- "# mscvac sample variables\n",
- "mpert = Int32(5)\n",
- "mtheta = Int32(256)\n",
- "mthvac = Int32(256)\n",
- "wv = zeros(ComplexF64, mpert, mpert)\n",
- "complex_flag = true \n",
- "kernelsignin = -1.0\n",
- "wall_flag = false\n",
- "farwal_flag = true\n",
- "grrio = rand(Float64, 2*(mthvac+5), mpert*2) \n",
- "xzptso = rand(Float64, mthvac+5, 4) \n",
- "op_ahgfile = \"aaaa\" \n",
- "\n",
- "println(\"Testing mscvac…\")\n",
- "JPEC.VacuumMod.mscvac(\n",
- " wv, mpert, mtheta, mthvac,\n",
- " complex_flag, kernelsignin,\n",
- " wall_flag, farwal_flag,\n",
- " grrio, xzptso, op_ahgfile\n",
- ")\n",
- "println(\"mscvac OK!\")\n"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "id": "461f4991",
- "metadata": {},
- "outputs": [],
- "source": [
- "display(wv)"
- ]
- }
- ],
- "metadata": {
- "kernelspec": {
- "display_name": "Julia 1.11.4",
- "language": "julia",
- "name": "julia-1.11"
- },
- "language_info": {
- "file_extension": ".jl",
- "mimetype": "application/julia",
- "name": "julia",
- "version": "1.11.4"
- }
- },
- "nbformat": 4,
- "nbformat_minor": 5
-}
diff --git a/regression-harness/Project.toml b/regression-harness/Project.toml
new file mode 100644
index 0000000000..ff47931c27
--- /dev/null
+++ b/regression-harness/Project.toml
@@ -0,0 +1,12 @@
+[deps]
+Dates = "ade2ca70-3891-5945-98fb-dc099432e06a"
+HDF5 = "f67ccb44-e63f-5c2f-98bd-6dc0ccc4ba2f"
+JSON = "682c06a0-de6a-54ab-a142-c8b1cf79cde6"
+Printf = "de0858da-6303-5e67-8744-51eddeeeb8d7"
+SHA = "ea8e919c-243c-51af-8825-aaa63cd721ce"
+SQLite = "0aa819cd-b072-5ff4-a722-6bc24af294d9"
+TOML = "fa267f1f-6049-4f14-aa54-33bafae1ed76"
+Tables = "bd369af6-aec1-5ad0-b16a-f7cc5008161c"
+
+[compat]
+JSON = "1"
diff --git a/regression-harness/cases/diiid_error_field.toml b/regression-harness/cases/diiid_error_field.toml
new file mode 100644
index 0000000000..bbb2490f47
--- /dev/null
+++ b/regression-harness/cases/diiid_error_field.toml
@@ -0,0 +1,101 @@
+# Regression case: the DIII-D-like error-field assessment example — the full ErrorFields stage
+# (sensitivities, tolerance Monte Carlo, locking risk) and the correction-coil NTV couplings
+# with their torque-versus-rotation tables. The only case exercising [ErrorFields.NTV].
+# Each [quantities.*] block names an HDF5 path in the run output, how to extract it, and the
+# noise floor below which a difference is treated as zero.
+[case]
+name = "diiid_error_field"
+description = "DIII-D-like error-field assessment, n=1: ErrorFields stage with the NTV-limited correction couplings"
+example_dir = "examples/DIIID-like_error_field_example"
+
+# Correction-coil couplings at the nominal rotation (one array, the C-coil standing in).
+[quantities.efc_delta_per_kat]
+h5path = "ErrorFields/NTV/delta_per_kat"
+type = "real_vector"
+extract = "all_real"
+label = "EFC overlap per kAt"
+noise_threshold = 1e-10
+order = 10
+
+[quantities.efc_torque_full]
+h5path = "ErrorFields/NTV/torque_full_per_kat2"
+type = "real_vector"
+extract = "all_real"
+label = "EFC whole-field NTV torque per kAt² [N·m]"
+noise_threshold = 1e-8
+order = 11
+
+[quantities.efc_torque_residual]
+h5path = "ErrorFields/NTV/torque_residual_per_kat2"
+type = "real_vector"
+extract = "all_real"
+label = "EFC residual-field NTV torque per kAt² [N·m]"
+noise_threshold = 1e-8
+order = 12
+
+# The torque-versus-rotation table: reference rotation, the adaptive shift grid and the residual torque on it.
+[quantities.efc_omega_reference]
+h5path = "ErrorFields/NTV/omega_reference"
+type = "real_vector"
+extract = "all_real"
+label = "EFC reference rotation ω_ref [rad/s]"
+noise_threshold = 1e-6
+order = 13
+
+[quantities.efc_rotation_shift]
+h5path = "ErrorFields/NTV/RotationScan/rotation_shift"
+type = "real_vector"
+extract = "all_real"
+label = "EFC rotation-scan shifts [rad/s]"
+noise_threshold = 1e-6
+order = 14
+
+[quantities.efc_torque_residual_scan]
+h5path = "ErrorFields/NTV/RotationScan/torque_residual"
+type = "real_vector"
+extract = "all_real"
+label = "EFC residual torque against rotation [N·m/kAt²]"
+noise_threshold = 1e-8
+order = 15
+
+# Anchors of the stages feeding the couplings.
+[quantities.dominant_singular_values]
+h5path = "PerturbedEquilibrium/SingularCoupling/DominantMode/singular_values"
+type = "real_vector"
+extract = "all_real"
+label = "dominant-coupling singular values"
+noise_threshold = 1e-8
+order = 20
+
+[quantities.ef_delta_nominal]
+h5path = "ErrorFields/CoilSensitivities/DominantMode/delta_as_designed"
+type = "complex_vector"
+extract = "abs_first"
+label = "|delta_nominal| of coil set 1"
+noise_threshold = 1e-10
+order = 21
+
+# The as-designed error field and sampled mean of the tolerance Monte Carlo, with the correction
+# array left out of the error field.
+[quantities.mc_abs_delta_total_as_designed]
+h5path = "ErrorFields/MonteCarlo/abs_delta_total_as_designed"
+type = "real_scalar"
+extract = "value"
+label = "|Σ δ_as_designed| of the error-field coils"
+noise_threshold = 1e-10
+order = 22
+
+[quantities.mc_abs_delta_sampled_mean]
+h5path = "ErrorFields/MonteCarlo/abs_delta_sampled_mean"
+type = "real_scalar"
+extract = "value"
+label = "Monte Carlo mean |δ| of the error-field coils"
+noise_threshold = 1e-10
+order = 23
+
+[quantities.runtime]
+h5path = ""
+type = "runtime"
+extract = "value"
+label = "Runtime (s)"
+order = 99
diff --git a/regression-harness/cases/diiid_kinetic_multi_n.toml b/regression-harness/cases/diiid_kinetic_multi_n.toml
new file mode 100644
index 0000000000..9ae6d963b7
--- /dev/null
+++ b/regression-harness/cases/diiid_kinetic_multi_n.toml
@@ -0,0 +1,95 @@
+# Regression case: DIII-D-like n = 1, 2 kinetic stability with the calculated kinetic matrices.
+# Reuses the DIIID-like_ideal_example deck (which ships the kinetic profiles) via [overrides]: the
+# coupled n = 1, 2 mode space at full kinetic strength, ending after ForceFreeStates because the
+# KineticForces torque stage is single-n. Guards the per-n geometric matrices and the per-n-block
+# kinetic singular-surface scan. Each [quantities.*] block names an HDF5 path, how to extract it,
+# and the noise floor below which a diff is treated as zero.
+[case]
+name = "diiid_kinetic_multi_n"
+description = "DIII-D-like equilibrium, n = 1, 2, KineticForces kinetic matrices, kinetic_factor=1.0, stability only, truncation at psihigh."
+example_dir = "examples/DIIID-like_ideal_example"
+# Without a perturbed equilibrium the run ends after ForceFreeStates; [KineticForces] stays as the kinetic source.
+remove_sections = ["ForcingTerms", "PerturbedEquilibrium", "ErrorFields"]
+
+[overrides]
+"ForceFreeStates.nn" = [1, 2] # Toroidal mode number, or consecutive numbers as a list
+"ForceFreeStates.kinetic" = "KineticForces" # Kinetic source: the drift-kinetic matrices of the [KineticForces] model
+"ForceFreeStates.kinetic_factor" = 1.0 # Uniform scale on the kinetic matrices of a kinetic run
+"ForceFreeStates.truncate_at_rational_offset" = false # Multi-n runs truncate at psihigh; set explicitly
+
+# Energies — leading generalized (W,N) pencil eigenvalues over the coupled n = 1, 2 mode space
+[quantities.et_real]
+h5path = "ForceFreeStates/FreeBoundaryStability/eigenmode_energies"
+type = "complex_vector"
+extract = "real_first"
+label = "total energy Re(et[1])"
+noise_threshold = 1e-10
+order = 10
+
+[quantities.et_imag]
+h5path = "ForceFreeStates/FreeBoundaryStability/eigenmode_energies"
+type = "complex_vector"
+extract = "imag_first"
+label = "total energy Im(et[1])"
+noise_threshold = 1e-10
+order = 11
+
+[quantities.et_all]
+h5path = "ForceFreeStates/FreeBoundaryStability/eigenmode_energies"
+type = "complex_vector"
+extract = "all_complex"
+label = "total energy (all)"
+noise_threshold = 1e-10
+order = 12
+
+# Kinetic singular surfaces from the per-n-block cond(F̄) scan
+[quantities.kinsing_count]
+h5path = "SingularSurfaces/Kinetic/rational_count"
+type = "int_scalar"
+extract = "value"
+label = "# kinetic singular surfaces"
+noise_threshold = 0
+order = 20
+
+[quantities.kinsing_psi]
+h5path = "SingularSurfaces/Kinetic/rational_psi"
+type = "real_vector"
+extract = "all_real"
+label = "kinetic singular psi locations"
+noise_threshold = 1e-8
+order = 21
+
+# Integration
+[quantities.nstep]
+h5path = "ForceFreeStates/Solutions/ForwardIntegration/nstep"
+type = "int_scalar"
+extract = "value"
+label = "ODE steps (saved)"
+noise_threshold = 0
+order = 30
+
+# Mode space
+[quantities.mpert]
+h5path = "Info/mpert"
+type = "int_scalar"
+extract = "value"
+label = "mpert"
+noise_threshold = 0
+order = 40
+
+[quantities.npert]
+h5path = "Info/npert"
+type = "int_scalar"
+extract = "value"
+label = "npert"
+noise_threshold = 0
+order = 41
+
+# Runtime
+[quantities.runtime]
+h5path = ""
+type = "runtime"
+extract = "value"
+label = "Runtime (s)"
+noise_threshold = 0.0
+order = 999
diff --git a/regression-harness/cases/diiid_multi_n.toml b/regression-harness/cases/diiid_multi_n.toml
new file mode 100644
index 0000000000..ca363248f3
--- /dev/null
+++ b/regression-harness/cases/diiid_multi_n.toml
@@ -0,0 +1,176 @@
+# Regression case: DIII-D-like n = 1, 2 ideal stability + perturbed equilibrium.
+# Tracks the coupled multi-n plasma response driven by mixed-n C-coil currents: the block-diagonal
+# control-surface matrices and spectra, the energies and torque summed over n, and the singular
+# coupling rows, where integer-q surfaces repeat at several n. Each [quantities.*] block names an
+# HDF5 path, how to extract it, and the noise floor below which a diff is treated as zero.
+[case]
+name = "diiid_multi_n"
+description = "DIII-D-like equilibrium, n = 1, 2, ideal + perturbed equilibrium"
+example_dir = "examples/DIIID-like_ideal_multi_n_example"
+
+# Energies — leading generalized (W,N) pencil eigenvalues at psilim, over the coupled n = 1, 2 mode space.
+[quantities.et_real]
+h5path = "ForceFreeStates/FreeBoundaryStability/eigenmode_energies"
+type = "complex_vector"
+extract = "real_first"
+label = "total energy Re(et[1])"
+noise_threshold = 1e-10
+order = 10
+
+[quantities.et_all]
+h5path = "ForceFreeStates/FreeBoundaryStability/eigenmode_energies"
+type = "complex_vector"
+extract = "all_complex"
+label = "total energy (all)"
+noise_threshold = 1e-10
+order = 20
+
+# Integration
+[quantities.nstep]
+h5path = "ForceFreeStates/Solutions/ForwardIntegration/nstep"
+type = "int_scalar"
+extract = "value"
+label = "ODE steps (saved)"
+noise_threshold = 0
+order = 30
+
+# Mode space
+[quantities.mpert]
+h5path = "Info/mpert"
+type = "int_scalar"
+extract = "value"
+label = "mpert"
+noise_threshold = 0
+order = 40
+
+[quantities.npert]
+h5path = "Info/npert"
+type = "int_scalar"
+extract = "value"
+label = "npert"
+noise_threshold = 0
+order = 41
+
+[quantities.mode_n]
+h5path = "PerturbedEquilibrium/mode_n"
+type = "real_vector"
+extract = "checksum"
+label = "toroidal mode label of each mode index (checksum)"
+noise_threshold = 0
+order = 42
+
+# Control-surface response, one block per n (b~ space)
+[quantities.permeability_diag]
+h5path = "PerturbedEquilibrium/ResponseMatrices/permeability"
+type = "complex_matrix"
+extract = "diagonal_complex"
+label = "permeability diagonal P~_ii (all n blocks)"
+noise_threshold = 1e-8
+order = 50
+
+[quantities.forcing_b_rootarea]
+h5path = "PerturbedEquilibrium/forcing_b_root_area"
+type = "complex_vector"
+extract = "all_complex"
+label = "forcing b~ (root-area-weighted), n = 1, 2"
+noise_threshold = 1e-10
+order = 51
+
+[quantities.response_b_rootarea]
+h5path = "PerturbedEquilibrium/response_b_root_area"
+type = "complex_vector"
+extract = "all_complex"
+label = "response b~ (root-area-weighted), n = 1, 2"
+noise_threshold = 1e-8
+order = 52
+
+# Perturbed equilibrium energies and the Σ_n torque
+[quantities.pe_plasma_energy]
+h5path = "PerturbedEquilibrium/Energies/plasma_energy"
+type = "real_scalar"
+extract = "value"
+label = "PE plasma energy (sum over n)"
+noise_threshold = 1e-10
+order = 60
+
+[quantities.pe_vacuum_energy]
+h5path = "PerturbedEquilibrium/Energies/vacuum_energy"
+type = "real_scalar"
+extract = "value"
+label = "PE vacuum energy (sum over n)"
+noise_threshold = 1e-10
+order = 61
+
+[quantities.pe_surface_energy]
+h5path = "PerturbedEquilibrium/Energies/surface_energy"
+type = "real_scalar"
+extract = "value"
+label = "PE surface energy (sum over n)"
+noise_threshold = 1e-10
+order = 62
+
+[quantities.pe_toroidal_torque]
+h5path = "PerturbedEquilibrium/Energies/toroidal_torque"
+type = "real_scalar"
+extract = "value"
+label = "PE toroidal torque sum_n -2n Im(Phi_n' Lambda_nn^-1 Phi_n)/4"
+noise_threshold = 1e-12
+order = 63
+
+# Singular coupling: one row per resonant (surface, n); integer-q surfaces appear once per n
+[quantities.rational_n]
+h5path = "PerturbedEquilibrium/SingularCoupling/rational_n"
+type = "real_vector"
+extract = "all_real"
+label = "resonant n per row (rows sorted by psi across n)"
+noise_threshold = 0
+order = 70
+
+[quantities.rational_m]
+h5path = "PerturbedEquilibrium/SingularCoupling/rational_m"
+type = "real_vector"
+extract = "all_real"
+label = "resonant m per row"
+noise_threshold = 0
+order = 71
+
+[quantities.resonant_area_weighted_field_all]
+h5path = "PerturbedEquilibrium/SingularCoupling/resonant_area_weighted_field"
+type = "complex_vector"
+extract = "all_complex"
+label = "resonant area-weighted field b^r per row"
+noise_threshold = 1e-8
+order = 72
+
+[quantities.island_half_width]
+h5path = "PerturbedEquilibrium/SingularCoupling/island_half_width"
+type = "real_vector"
+extract = "all_real"
+label = "island half-widths per row"
+noise_threshold = 1e-8
+order = 73
+
+[quantities.chirikov_parameter]
+h5path = "PerturbedEquilibrium/SingularCoupling/chirikov_parameter"
+type = "real_vector"
+extract = "all_real"
+label = "Chirikov parameter per row"
+noise_threshold = 1e-8
+order = 74
+
+[quantities.delta_prime_all]
+h5path = "PerturbedEquilibrium/SingularCoupling/Delta_prime"
+type = "complex_vector"
+extract = "all_complex"
+label = "forcing-driven Delta' per row"
+noise_threshold = 1e-8
+order = 75
+
+# Runtime
+[quantities.runtime]
+h5path = ""
+type = "runtime"
+extract = "value"
+label = "Runtime (s)"
+noise_threshold = 0.0
+order = 999
diff --git a/regression-harness/cases/diiid_n1.toml b/regression-harness/cases/diiid_n1.toml
new file mode 100644
index 0000000000..72ccadc898
--- /dev/null
+++ b/regression-harness/cases/diiid_n1.toml
@@ -0,0 +1,471 @@
+# Regression case: DIII-D-like n=1 ideal stability + perturbed equilibrium.
+# Tracks energies, singular-surface metrics, and resonant-flux diagnostics for the canonical
+# DIIID-like fixture, which runs the forward integrator for its dense ξ profiles. The BVP Δ'
+# matrix comes from the Riccati integrator only and is tracked by the sibling case
+# diiid_n1_riccati. Each [quantities.*] block names an HDF5 path in the run output, how to
+# extract it, and the noise floor below which a difference is treated as zero. Run via the
+# regression-harness (see CLAUDE.md).
+[case]
+name = "diiid_n1"
+description = "DIII-D-like equilibrium, n=1, ideal + perturbed equilibrium"
+example_dir = "examples/DIIID-like_ideal_example"
+
+# Energies — leading generalized (W,N) pencil eigenvalues at the final truncation (psilim): power-normalized (⟨|ξ|²⟩ = 1 metric) and invariant to the working-coordinate Jacobian.
+[quantities.et_real]
+h5path = "ForceFreeStates/FreeBoundaryStability/eigenmode_energies"
+type = "complex_vector"
+extract = "real_first"
+label = "total energy Re(et[1])"
+noise_threshold = 1e-10
+order = 10
+
+[quantities.et_imag]
+h5path = "ForceFreeStates/FreeBoundaryStability/eigenmode_energies"
+type = "complex_vector"
+extract = "imag_first"
+label = "total energy Im(et[1])"
+noise_threshold = 1e-10
+order = 11
+
+[quantities.ep_real]
+h5path = "ForceFreeStates/FreeBoundaryStability/eigenmode_plasma_energies"
+type = "complex_vector"
+extract = "real_first"
+label = "plasma energy Re(ep[1])"
+noise_threshold = 1e-10
+order = 12
+
+[quantities.ev_real]
+h5path = "ForceFreeStates/FreeBoundaryStability/eigenmode_vacuum_energies"
+type = "complex_vector"
+extract = "real_first"
+label = "vacuum energy Re(ev[1])"
+noise_threshold = 1e-10
+order = 13
+
+[quantities.vacuum_eigenvalue]
+h5path = "ForceFreeStates/FreeBoundaryStability/vacuum_eigenvalue"
+type = "real_scalar"
+extract = "value"
+label = "vacuum matrix min eigenvalue"
+noise_threshold = 1e-10
+order = 14
+
+# Energies — full eigenvalue arrays
+[quantities.ep_all]
+h5path = "ForceFreeStates/FreeBoundaryStability/eigenmode_plasma_energies"
+type = "complex_vector"
+extract = "all_complex"
+label = "plasma energy (all)"
+noise_threshold = 1e-10
+order = 20
+
+[quantities.ev_all]
+h5path = "ForceFreeStates/FreeBoundaryStability/eigenmode_vacuum_energies"
+type = "complex_vector"
+extract = "all_complex"
+label = "vacuum energy (all)"
+noise_threshold = 1e-10
+order = 21
+
+[quantities.et_all]
+h5path = "ForceFreeStates/FreeBoundaryStability/eigenmode_energies"
+type = "complex_vector"
+extract = "all_complex"
+label = "total energy (all)"
+noise_threshold = 1e-10
+order = 22
+
+# Integration
+[quantities.nstep]
+h5path = "ForceFreeStates/Solutions/ForwardIntegration/nstep"
+type = "int_scalar"
+extract = "value"
+label = "ODE steps (saved)"
+noise_threshold = 0
+order = 30
+
+[quantities.nstep_total]
+h5path = "ForceFreeStates/Solutions/ForwardIntegration/nstep_total"
+type = "int_scalar"
+extract = "value"
+label = "ODE steps (total)"
+noise_threshold = 0
+order = 31
+
+# Equilibrium
+[quantities.q0]
+h5path = "Equilibrium/q_axis"
+type = "real_scalar"
+extract = "value"
+label = "q0"
+noise_threshold = 1e-12
+order = 40
+
+[quantities.q95]
+h5path = "Equilibrium/q_95"
+type = "real_scalar"
+extract = "value"
+label = "q95"
+noise_threshold = 1e-12
+order = 41
+
+[quantities.betat]
+h5path = "Equilibrium/beta_t"
+type = "real_scalar"
+extract = "value"
+label = "beta_t"
+noise_threshold = 1e-12
+order = 42
+
+[quantities.betan]
+h5path = "Equilibrium/beta_N"
+type = "real_scalar"
+extract = "value"
+label = "beta_n"
+noise_threshold = 1e-12
+order = 43
+
+[quantities.li1]
+h5path = "Equilibrium/l_i_1"
+type = "real_scalar"
+extract = "value"
+label = "internal inductance li1"
+noise_threshold = 1e-12
+order = 44
+
+[quantities.li2]
+h5path = "Equilibrium/l_i_2"
+type = "real_scalar"
+extract = "value"
+label = "internal inductance li2"
+noise_threshold = 1e-12
+order = 45
+
+[quantities.li3]
+h5path = "Equilibrium/l_i_3"
+type = "real_scalar"
+extract = "value"
+label = "internal inductance li3"
+noise_threshold = 1e-12
+order = 46
+
+[quantities.betap1]
+h5path = "Equilibrium/beta_p_1"
+type = "real_scalar"
+extract = "value"
+label = "poloidal beta betap1"
+noise_threshold = 1e-12
+order = 47
+
+[quantities.betap2]
+h5path = "Equilibrium/beta_p_2"
+type = "real_scalar"
+extract = "value"
+label = "poloidal beta betap2"
+noise_threshold = 1e-12
+order = 48
+
+[quantities.betap3]
+h5path = "Equilibrium/beta_p_3"
+type = "real_scalar"
+extract = "value"
+label = "poloidal beta betap3"
+noise_threshold = 1e-12
+order = 49
+
+[quantities.betaj]
+h5path = "Equilibrium/beta_j"
+type = "real_scalar"
+extract = "value"
+label = "current beta betaj"
+noise_threshold = 1e-12
+order = 57
+
+[quantities.volume]
+h5path = "Equilibrium/volume"
+type = "real_scalar"
+extract = "value"
+label = "plasma volume"
+noise_threshold = 1e-12
+order = 58
+
+[quantities.crnt]
+h5path = "Equilibrium/I_p"
+type = "real_scalar"
+extract = "value"
+label = "plasma current"
+noise_threshold = 1e-12
+order = 59
+
+[quantities.bt0]
+h5path = "Equilibrium/B_T_axis"
+type = "real_scalar"
+extract = "value"
+label = "toroidal field bt0"
+noise_threshold = 1e-12
+order = 62
+
+[quantities.bwall]
+h5path = "Equilibrium/B_T_wall"
+type = "real_scalar"
+extract = "value"
+label = "wall field bwall"
+noise_threshold = 1e-12
+order = 63
+
+[quantities.aratio]
+h5path = "Equilibrium/aspect_ratio"
+type = "real_scalar"
+extract = "value"
+label = "aspect ratio"
+noise_threshold = 1e-12
+order = 64
+
+[quantities.kappa]
+h5path = "Equilibrium/kappa"
+type = "real_scalar"
+extract = "value"
+label = "elongation kappa"
+noise_threshold = 1e-12
+order = 65
+
+# Singular surfaces
+[quantities.msing]
+h5path = "SingularSurfaces/rational_count"
+type = "int_scalar"
+extract = "value"
+label = "# singular surfaces"
+noise_threshold = 0
+order = 50
+
+[quantities.sing_psi]
+h5path = "SingularSurfaces/rational_psi"
+type = "real_vector"
+extract = "all_real"
+label = "singular psi locations"
+noise_threshold = 1e-8
+order = 51
+
+[quantities.sing_q]
+h5path = "SingularSurfaces/rational_q"
+type = "real_vector"
+extract = "all_real"
+label = "singular q values"
+noise_threshold = 1e-8
+order = 52
+
+# Mode numbers
+[quantities.mpert]
+h5path = "Info/mpert"
+type = "int_scalar"
+extract = "value"
+label = "mpert"
+noise_threshold = 0
+order = 60
+
+[quantities.npert]
+h5path = "Info/npert"
+type = "int_scalar"
+extract = "value"
+label = "npert"
+noise_threshold = 0
+order = 61
+
+[quantities.island_half_width]
+h5path = "PerturbedEquilibrium/SingularCoupling/island_half_width"
+type = "real_vector"
+extract = "all_real"
+label = "island half-widths"
+noise_threshold = 1e-8
+order = 81
+
+[quantities.chirikov_parameter]
+h5path = "PerturbedEquilibrium/SingularCoupling/chirikov_parameter"
+type = "real_vector"
+extract = "all_real"
+label = "Chirikov parameter"
+noise_threshold = 1e-8
+order = 82
+
+[quantities.resonant_area_weighted_field]
+h5path = "PerturbedEquilibrium/SingularCoupling/resonant_area_weighted_field"
+type = "complex_vector"
+extract = "norm"
+label = "||resonant area-weighted field||"
+noise_threshold = 1e-8
+order = 83
+
+[quantities.resonant_area_weighted_field_all]
+h5path = "PerturbedEquilibrium/SingularCoupling/resonant_area_weighted_field"
+type = "complex_vector"
+extract = "all_complex"
+label = "resonant area-weighted field b^r"
+noise_threshold = 1e-8
+
+# Dominant resonant-coupling mode: singular values of the b̃-space coupling matrix over every
+# rational surface (coordinate-invariant), and the applied forcing's magnitude on the dominant
+# mode. Singular vectors carry an arbitrary phase, so only the magnitude is tracked.
+[quantities.dominant_singular_values]
+h5path = "PerturbedEquilibrium/SingularCoupling/DominantMode/singular_values"
+type = "real_vector"
+extract = "all_real"
+label = "dominant-coupling singular values"
+noise_threshold = 1e-8
+order = 84
+
+[quantities.dominant_forcing_overlap]
+h5path = "PerturbedEquilibrium/SingularCoupling/DominantMode/forcing_overlap"
+type = "complex_vector"
+extract = "abs_first"
+label = "|forcing overlap with dominant mode|"
+noise_threshold = 1e-8
+order = 85
+
+# Perturbed equilibrium: energies
+[quantities.pe_plasma_energy]
+h5path = "PerturbedEquilibrium/Energies/plasma_energy"
+type = "real_scalar"
+extract = "value"
+label = "PE plasma energy"
+noise_threshold = 1e-10
+order = 91
+
+[quantities.pe_vacuum_energy]
+h5path = "PerturbedEquilibrium/Energies/vacuum_energy"
+type = "real_scalar"
+extract = "value"
+label = "PE vacuum energy"
+noise_threshold = 1e-10
+order = 92
+
+[quantities.pe_surface_energy]
+h5path = "PerturbedEquilibrium/Energies/surface_energy"
+type = "real_scalar"
+extract = "value"
+label = "PE surface energy"
+noise_threshold = 1e-10
+order = 93
+
+[quantities.pe_toroidal_torque]
+h5path = "PerturbedEquilibrium/Energies/toroidal_torque"
+type = "real_scalar"
+extract = "value"
+label = "PE toroidal torque"
+noise_threshold = 1e-12
+order = 94
+
+# NTV (neoclassical toroidal viscosity) toroidal torque T_φ [N·m] from the
+# [KineticForces] FGAR method (pressure moment) — a diagnostic computed on top of
+# the ideal FFS + PE result. Absent (N/A) for refs without a [KineticForces]
+# section. Threshold is a noise floor for the adaptive-quadrature result; tune if
+# run-to-run jitter appears.
+[quantities.ntv_torque_fgar]
+h5path = "KineticForces/fgar/total_torque"
+type = "real_scalar"
+extract = "value"
+label = "NTV torque FGAR [N·m]"
+noise_threshold = 1e-2
+order = 95
+
+# NTV kinetic energy δW_k = Im(T)/(2n) [J] through the same post-PE FGAR path.
+# Tracked at a tighter threshold — it isolates the energy component the
+# bounce-averaging chain moves most.
+[quantities.ntv_energy_fgar]
+h5path = "KineticForces/fgar/total_energy"
+type = "real_scalar"
+extract = "value"
+label = "NTV kinetic energy dW FGAR [J]"
+noise_threshold = 1e-3
+order = 96
+
+# Profiles (checksums)
+[quantities.q_profile]
+h5path = "Equilibrium/Profiles/q"
+type = "real_vector"
+extract = "checksum"
+label = "q profile (checksum)"
+noise_threshold = 0
+order = 70
+
+[quantities.pressure_profile]
+h5path = "Equilibrium/Profiles/mu0p"
+type = "real_vector"
+extract = "checksum"
+label = "pressure profile (checksum)"
+noise_threshold = 0
+order = 71
+
+# Local stability profiles (the [LocalStability] section). Checksums hash the full
+# profile so they are robust to NaN edge-surface entries and catch any change.
+[quantities.locstab_di]
+h5path = "LocalStability/D_I"
+type = "real_vector"
+extract = "checksum"
+label = "Mercier D_I profile (checksum)"
+noise_threshold = 0
+order = 72
+
+[quantities.locstab_dr]
+h5path = "LocalStability/D_R"
+type = "real_vector"
+extract = "checksum"
+label = "resistive interchange D_R profile (checksum)"
+noise_threshold = 0
+order = 73
+
+[quantities.locstab_ballooning_dp]
+h5path = "LocalStability/ballooning_Delta_prime"
+type = "real_vector"
+extract = "checksum"
+label = "ballooning Delta' profile (checksum)"
+noise_threshold = 0
+order = 74
+
+# Error fields — per-coil-set overlap with the full-window dominant mode and its rigid shift/tilt
+# sensitivities. Singular vectors carry an arbitrary phase, so only magnitudes are tracked; the
+# in-plane components of a whole n=1-phased array vanish by symmetry, so the norms track the
+# vertical shift and axial tilt that survive.
+[quantities.ef_delta_nominal]
+h5path = "ErrorFields/CoilSensitivities/DominantMode/delta_as_designed"
+type = "complex_vector"
+extract = "abs_first"
+label = "|delta_nominal| of coil set 1"
+noise_threshold = 1e-10
+order = 86
+
+[quantities.ef_shift_sensitivity]
+h5path = "ErrorFields/CoilSensitivities/DominantMode/shift_sensitivity_per_m"
+type = "complex_vector"
+extract = "norm"
+label = "||ddelta/d(shift)|| over coil sets"
+noise_threshold = 1e-10
+order = 87
+
+[quantities.ef_tilt_sensitivity]
+h5path = "ErrorFields/CoilSensitivities/DominantMode/tilt_sensitivity_per_deg"
+type = "complex_vector"
+extract = "norm"
+label = "||ddelta/d(tilt)|| over coil sets"
+noise_threshold = 1e-10
+order = 88
+
+# Runtime
+[quantities.runtime]
+h5path = ""
+type = "runtime"
+extract = "value"
+label = "Runtime (s)"
+noise_threshold = 0.0
+order = 999
+
+# Root-area-weighted (coordinate-invariant) forcing field b̃ on the control surface: the
+# applied coil spectrum pushed through the √(J|∇ψ|) weight operator. Tracks the field-space
+# conversion that every ResponseMatrices/ field-space output depends on.
+[quantities.forcing_b_rootarea_norm]
+h5path = "PerturbedEquilibrium/forcing_b_root_area"
+type = "complex_vector"
+extract = "norm"
+label = "||forcing b~|| (root-area-weighted)"
+noise_threshold = 1e-10
+order = 1000
diff --git a/regression-harness/cases/diiid_n1_riccati.toml b/regression-harness/cases/diiid_n1_riccati.toml
new file mode 100644
index 0000000000..f41d9ed0a7
--- /dev/null
+++ b/regression-harness/cases/diiid_n1_riccati.toml
@@ -0,0 +1,163 @@
+# Regression case: DIII-D-like n=1 Δ' matrix from the Riccati chunked propagator BVP.
+# The Riccati integrator is the only one that produces SingularSurfaces/Delta_prime_matrix, so
+# this case is the canonical Δ' track (its sibling diiid_n1 runs the forward integrator and
+# carries the ξ/perturbed-equilibrium quantities instead). Also tracks the free-boundary
+# energies and singular-surface locations the BVP depends on, so a Δ' move can be attributed.
+# Each [quantities.*] block names an HDF5 path in the run output, how to extract it, and the
+# noise floor below which a difference is treated as zero.
+[case]
+name = "diiid_n1_riccati"
+description = "DIII-D-like equilibrium, n=1, Riccati integrator Δ' matrix"
+example_dir = "examples/DIIID-like_riccati_deltaprime_example"
+
+# Tearing stability Δ' — the msing×msing BVP matrix diagonal, and the raw side-major
+# outer-region matrix it is projected from.
+[quantities.delta_prime]
+h5path = "SingularSurfaces/Delta_prime_matrix"
+type = "complex_matrix"
+extract = "diagonal_complex"
+label = "delta prime (BVP diagonal)"
+noise_threshold = 1e-8
+order = 10
+
+[quantities.delta_prime_raw]
+h5path = "SingularSurfaces/Delta_prime_raw"
+type = "complex_matrix"
+extract = "all_complex"
+label = "delta prime (raw side-major)"
+noise_threshold = 1e-8
+order = 11
+
+[quantities.delta_coil]
+h5path = "SingularSurfaces/Delta_coil"
+type = "complex_matrix"
+extract = "all_complex"
+label = "edge coil response delta_coil"
+noise_threshold = 1e-8
+order = 12
+
+# Energies — leading generalized (W,N) pencil eigenvalues at the final truncation (psilim): power-normalized (⟨|ξ|²⟩ = 1 metric) and invariant to the working-coordinate Jacobian.
+[quantities.et_real]
+h5path = "ForceFreeStates/FreeBoundaryStability/eigenmode_energies"
+type = "complex_vector"
+extract = "real_first"
+label = "total energy Re(et[1])"
+noise_threshold = 1e-10
+order = 20
+
+[quantities.ep_real]
+h5path = "ForceFreeStates/FreeBoundaryStability/eigenmode_plasma_energies"
+type = "complex_vector"
+extract = "real_first"
+label = "plasma energy Re(ep[1])"
+noise_threshold = 1e-10
+order = 21
+
+[quantities.ev_real]
+h5path = "ForceFreeStates/FreeBoundaryStability/eigenmode_vacuum_energies"
+type = "complex_vector"
+extract = "real_first"
+label = "vacuum energy Re(ev[1])"
+noise_threshold = 1e-10
+order = 22
+
+[quantities.et_all]
+h5path = "ForceFreeStates/FreeBoundaryStability/eigenmode_energies"
+type = "complex_vector"
+extract = "all_complex"
+label = "total energy (all)"
+noise_threshold = 1e-10
+order = 23
+
+# Singular surfaces — the Δ' matrix is indexed by these, so a shift here explains a Δ' shift.
+[quantities.msing]
+h5path = "SingularSurfaces/rational_count"
+type = "int_scalar"
+extract = "value"
+label = "# singular surfaces"
+noise_threshold = 0
+order = 30
+
+[quantities.sing_psi]
+h5path = "SingularSurfaces/rational_psi"
+type = "real_vector"
+extract = "all_real"
+label = "singular psi locations"
+noise_threshold = 1e-8
+order = 31
+
+[quantities.sing_q]
+h5path = "SingularSurfaces/rational_q"
+type = "real_vector"
+extract = "all_real"
+label = "singular q values"
+noise_threshold = 1e-8
+order = 32
+
+# Integration — chunk-endpoint step counts move when the chunk sizing changes.
+[quantities.nstep]
+h5path = "ForceFreeStates/Solutions/ForwardIntegration/nstep"
+type = "int_scalar"
+extract = "value"
+label = "ODE steps (saved)"
+noise_threshold = 0
+order = 40
+
+[quantities.nstep_total]
+h5path = "ForceFreeStates/Solutions/ForwardIntegration/nstep_total"
+type = "int_scalar"
+extract = "value"
+label = "ODE steps (total)"
+noise_threshold = 0
+order = 41
+
+# Mode numbers
+[quantities.mpert]
+h5path = "Info/mpert"
+type = "int_scalar"
+extract = "value"
+label = "mpert"
+noise_threshold = 0
+order = 50
+
+[quantities.npert]
+h5path = "Info/npert"
+type = "int_scalar"
+extract = "value"
+label = "npert"
+noise_threshold = 0
+order = 51
+
+# Equilibrium — shared with diiid_n1; confirms the two cases sit on the same equilibrium.
+[quantities.q0]
+h5path = "Equilibrium/q_axis"
+type = "real_scalar"
+extract = "value"
+label = "q0"
+noise_threshold = 1e-12
+order = 60
+
+[quantities.q95]
+h5path = "Equilibrium/q_95"
+type = "real_scalar"
+extract = "value"
+label = "q95"
+noise_threshold = 1e-12
+order = 61
+
+[quantities.betan]
+h5path = "Equilibrium/beta_N"
+type = "real_scalar"
+extract = "value"
+label = "beta_n"
+noise_threshold = 1e-12
+order = 62
+
+# Runtime
+[quantities.runtime]
+h5path = ""
+type = "runtime"
+extract = "value"
+label = "Runtime (s)"
+noise_threshold = 0.0
+order = 999
diff --git a/regression-harness/cases/diiid_n1_riccati_precompiled.toml b/regression-harness/cases/diiid_n1_riccati_precompiled.toml
new file mode 100644
index 0000000000..2896c741c9
--- /dev/null
+++ b/regression-harness/cases/diiid_n1_riccati_precompiled.toml
@@ -0,0 +1,9 @@
+# Regression case: the diiid_n1_riccati deck run from the precompiled package image.
+# Every other case runs with GPEC's precompile workload disabled; this one enables it, so it
+# tracks the build users get by default. Precompiled code can round differently in the last bit,
+# which the Δ' BVP amplifies to the percent level, so compare this case only against itself.
+[case]
+name = "diiid_n1_riccati_precompiled"
+base = "diiid_n1_riccati" # Inherit example_dir, [quantities.*] and [overrides] from this case
+description = "DIII-D-like equilibrium, n=1, Riccati integrator Δ' matrix, precompiled build"
+precompile_workload = true # Run from the package image built with the PrecompileTools workload
diff --git a/regression-harness/cases/diiid_slayer_n1.toml b/regression-harness/cases/diiid_slayer_n1.toml
new file mode 100644
index 0000000000..ca0c30d767
--- /dev/null
+++ b/regression-harness/cases/diiid_slayer_n1.toml
@@ -0,0 +1,215 @@
+# Regression case: DIII-D-like H-mode n=1 SLAYER tearing-mode growth rates.
+# Uncoupled per-surface analysis with the AMR Q-plane scan; tracks the per-surface
+# layer parameters, the diamagnetic drive Q_e/Q_i, and the extracted roots (Q, ω, γ)
+# for the inner three rationals. The n-scaling of Q_e/Q_i, which no single-n case can
+# constrain, is covered by a unit test in test/runtests_slayer_inputs.jl instead.
+# Each [quantities.*] block names an HDF5 path in the run output, how to extract it,
+# and the noise floor below which a difference is treated as zero.
+[case]
+name = "diiid_slayer_n1"
+description = "DIII-D-like H-mode equilibrium, n=1, SLAYER tearing-mode analysis (uncoupled per-surface, AMR, validity-gated)"
+example_dir = "examples/DIIID-like_SLAYER_example"
+
+# Per-surface SLAYER layer parameters (geometry + dimensionless)
+[quantities.slayer_ising]
+h5path = "Tearing/PerSurface/rational_index"
+type = "real_vector"
+extract = "all_real"
+label = "SLAYER surface indices"
+noise_threshold = 0
+order = 10
+
+[quantities.slayer_m]
+h5path = "Tearing/PerSurface/m"
+type = "real_vector"
+extract = "all_real"
+label = "SLAYER poloidal m"
+noise_threshold = 0
+order = 11
+
+[quantities.slayer_n]
+h5path = "Tearing/PerSurface/n"
+type = "real_vector"
+extract = "all_real"
+label = "SLAYER toroidal n"
+noise_threshold = 0
+order = 12
+
+[quantities.slayer_rs]
+h5path = "Tearing/PerSurface/rs"
+type = "real_vector"
+extract = "all_real"
+label = "SLAYER minor radius rs"
+noise_threshold = 1e-10
+order = 13
+
+[quantities.slayer_sval_r]
+h5path = "Tearing/PerSurface/sval_r"
+type = "real_vector"
+extract = "all_real"
+label = "SLAYER r-based shear"
+noise_threshold = 1e-10
+order = 14
+
+[quantities.slayer_lu]
+h5path = "Tearing/PerSurface/S"
+type = "real_vector"
+extract = "all_real"
+label = "SLAYER Lundquist S"
+noise_threshold = 1e-8
+order = 15
+
+[quantities.slayer_D_norm]
+h5path = "Tearing/PerSurface/D_norm"
+type = "real_vector"
+extract = "all_real"
+label = "SLAYER D_norm"
+noise_threshold = 1e-10
+order = 16
+
+[quantities.slayer_P_perp]
+h5path = "Tearing/PerSurface/P_perp"
+type = "real_vector"
+extract = "all_real"
+label = "SLAYER P_perp"
+noise_threshold = 1e-8
+order = 17
+
+[quantities.slayer_tauk]
+h5path = "Tearing/PerSurface/tau_k"
+type = "real_vector"
+extract = "all_real"
+label = "SLAYER tauk"
+noise_threshold = 1e-12
+order = 18
+
+[quantities.slayer_iota_e]
+h5path = "Tearing/PerSurface/iota_e"
+type = "real_vector"
+extract = "all_real"
+label = "SLAYER iota_e"
+noise_threshold = 1e-12
+order = 19
+
+# Normalized diamagnetic frequencies. iota_e above is their ratio, so it is blind
+# to a common factor on both; these pin the drive itself.
+[quantities.slayer_Q_e]
+h5path = "Tearing/PerSurface/Q_e"
+type = "real_vector"
+extract = "all_real"
+label = "SLAYER Q_e"
+noise_threshold = 1e-12
+order = 20
+
+[quantities.slayer_Q_i]
+h5path = "Tearing/PerSurface/Q_i"
+type = "real_vector"
+extract = "all_real"
+label = "SLAYER Q_i"
+noise_threshold = 1e-12
+order = 21
+
+# Toroidal critical-Δ geometric factor, derived on every surface that carries a ResistGeometry
+# whatever dc_type is selected, so it is tracked here at the deck's dc_type = "none".
+[quantities.slayer_D_geo]
+h5path = "Tearing/PerSurface/D_geo"
+type = "real_vector"
+extract = "all_real"
+label = "SLAYER toroidal critical-Δ factor D_geo"
+noise_threshold = 1e-10
+order = 22
+class = "physics_converged"
+
+# Tearing eigenvalue (coupled mode → length 1). The headline deliverable:
+# a real, nonzero growth rate on a realistic equilibrium. Root-extraction
+# is sensitive to the AMR cell topology and ODE solver, so the Q/ω/γ
+# thresholds are absolute and modestly loose; re-pin intentionally if a
+# solver/AMR change shifts the root inventory.
+# Growth-rate / frequency / root outputs. Pinned for the inner three rational
+# surfaces only (2/1, 3/1, 4/1) via `first_3`: the Δ'/γ contour search is
+# numerically unreliable on the outermost surfaces (e.g. 5/1, 6/1, 7/1 near the
+# edge), so those are deliberately not golden-tracked.
+[quantities.slayer_Q]
+h5path = "Tearing/Roots/Q_root"
+type = "complex_vector"
+extract = "first_3_complex"
+label = "SLAYER Q_root [2/1,3/1,4/1]"
+noise_threshold = 1e-4
+order = 30
+
+[quantities.slayer_omega_Hz]
+h5path = "Tearing/Roots/omega"
+type = "real_vector"
+extract = "first_3"
+label = "SLAYER ω in rad/s [2/1,3/1,4/1]"
+noise_threshold = 1.0
+order = 32
+
+[quantities.slayer_gamma_Hz]
+h5path = "Tearing/Roots/gamma"
+type = "real_vector"
+extract = "first_3"
+label = "SLAYER γ in 1/s [2/1,3/1,4/1]"
+noise_threshold = 1e-1
+order = 33
+
+# no_root flag (1 = extraction failed). Pinned for the inner three surfaces;
+# this case guards that the 2/1, 3/1, 4/1 keep finding a real root.
+[quantities.slayer_no_root]
+h5path = "Tearing/Roots/no_root"
+type = "real_vector"
+extract = "first_3"
+label = "SLAYER no_root flags [2/1,3/1,4/1]"
+noise_threshold = 0
+order = 34
+
+# Critical resonant field (torque balance) for the inner three surfaces, matching the root pins
+# above, and the natural rotation Q0 = τ_k·n·Ω_E it is computed from.
+[quantities.crf_br_crit]
+h5path = "Tearing/CriticalResonantField/br_crit"
+type = "real_vector"
+extract = "first_3"
+label = "CRF b_r/B_φ crit [2/1,3/1,4/1]"
+noise_threshold = 1e-9
+order = 40
+
+[quantities.crf_br_crit_tesla]
+h5path = "Tearing/CriticalResonantField/br_crit_tesla"
+type = "real_vector"
+extract = "first_3"
+label = "CRF b_r crit in tesla [2/1,3/1,4/1]"
+noise_threshold = 1e-9
+order = 43
+
+[quantities.crf_Q_peak]
+h5path = "Tearing/CriticalResonantField/Q_peak"
+type = "real_vector"
+extract = "first_3"
+label = "CRF Q_peak [2/1,3/1,4/1]"
+noise_threshold = 1e-6
+order = 41
+
+[quantities.crf_Q0]
+h5path = "Tearing/CriticalResonantField/Q0"
+type = "real_vector"
+extract = "first_3"
+label = "CRF Q0 [2/1,3/1,4/1]"
+noise_threshold = 1e-10
+order = 42
+
+# Settings (catches accidental config drift)
+[quantities.slayer_enabled]
+h5path = "Tearing/enabled"
+type = "int_scalar"
+extract = "value"
+label = "SLAYER enabled flag"
+noise_threshold = 0
+order = 90
+
+[quantities.runtime]
+h5path = ""
+type = "runtime"
+extract = "value"
+label = "Runtime (s)"
+noise_threshold = 0.0
+order = 999
diff --git a/regression-harness/cases/diiid_slayer_n1_chi_perp_e.toml b/regression-harness/cases/diiid_slayer_n1_chi_perp_e.toml
new file mode 100644
index 0000000000..2968a17503
--- /dev/null
+++ b/regression-harness/cases/diiid_slayer_n1_chi_perp_e.toml
@@ -0,0 +1,10 @@
+# Regression case: the diiid_slayer_n1 deck with P_perp built from the electron diffusivity chi_e alone,
+# the model GPEC used before the D_perp default. It keeps a baseline for the non-default P_perp models
+# and for the electron-channel convention of Fitzpatrick's TJ code.
+[case]
+name = "diiid_slayer_n1_chi_perp_e"
+base = "diiid_slayer_n1" # Inherit example_dir, [quantities.*] and [overrides] from this case
+description = "DIII-D-like H-mode equilibrium, n=1, SLAYER tearing-mode analysis with P_perp_model = chi_perp_e"
+
+[overrides]
+"SLAYER.P_perp_model" = "chi_perp_e" # P_perp from chi_e alone, as before the D_perp default
diff --git a/regression-harness/cases/diiid_slayer_n1_coupled.toml b/regression-harness/cases/diiid_slayer_n1_coupled.toml
new file mode 100644
index 0000000000..a464b1cb12
--- /dev/null
+++ b/regression-harness/cases/diiid_slayer_n1_coupled.toml
@@ -0,0 +1,97 @@
+# Regression case: DIII-D-like H-mode n=1 SLAYER coupled-determinant growth rate.
+# Reuses the n=1 SLAYER deck via [overrides] in coupled mode, the only harness coverage of the
+# multi-surface determinant: its inter-surface Q normalization and the per-surface E×B Doppler
+# shift taken from the kinetic file's omega_E. The Re(Q) window is widened because that shift
+# moves the coupled root to the lab frame, outside the deck's [-2, 2].
+# Each [quantities.*] block names an HDF5 path in the run output, how to extract it,
+# and the noise floor below which a difference is treated as zero.
+[case]
+name = "diiid_slayer_n1_coupled"
+description = "DIII-D-like H-mode equilibrium, n=1, SLAYER coupled multi-surface determinant with kinetic-file E×B rotation (reuses the n=1 deck via overrides)"
+example_dir = "examples/DIIID-like_SLAYER_example"
+
+# Run the shared SLAYER deck through the coupled determinant.
+[overrides]
+"Tearing.coupling_mode" = "coupled"
+"Tearing.search.Q_re_range" = [-4.0, 6.0]
+
+# Per-surface inputs to the determinant
+[quantities.slayer_tauk]
+h5path = "Tearing/PerSurface/tau_k"
+type = "real_vector"
+extract = "all_real"
+label = "SLAYER tauk"
+noise_threshold = 1e-12
+order = 10
+class = "physics_converged"
+
+# Applied E×B Doppler offset ΔRe(Q) = −τ_k·n·Ω_E per surface
+[quantities.slayer_q_shift]
+h5path = "Tearing/PerSurface/q_shift"
+type = "real_vector"
+extract = "all_real"
+label = "SLAYER q_shift"
+noise_threshold = 1e-10
+order = 11
+class = "physics_converged"
+
+# Coupled eigenvalue (one root for the whole determinant). The coupled path has no root
+# polishing, so the thresholds match the uncoupled case's absolute, modestly loose floors.
+# The triangulation is seeded, so the root repeats exactly in one environment and these tight floors
+# catch real changes. Across Julia versions or machines it can move further: re-extracting one set of
+# scan samples under different triangulations gave γ = 190.646 and 191.888 s⁻¹ (0.65 %).
+[quantities.slayer_Q_coupled]
+h5path = "Tearing/Roots/Q_root"
+type = "complex_vector"
+extract = "all_complex"
+label = "SLAYER coupled Q_root"
+noise_threshold = 1e-4
+order = 30
+class = "physics_converged"
+
+[quantities.slayer_omega_coupled]
+h5path = "Tearing/Roots/omega"
+type = "real_vector"
+extract = "all_real"
+label = "SLAYER coupled ω"
+noise_threshold = 1.0
+order = 32
+class = "physics_converged"
+
+[quantities.slayer_gamma_coupled]
+h5path = "Tearing/Roots/gamma"
+type = "real_vector"
+extract = "all_real"
+label = "SLAYER coupled γ"
+noise_threshold = 1e-1
+order = 33
+class = "physics_converged"
+
+# no_root flag (1 = extraction failed); guards that the coupled root stays inside the window.
+[quantities.slayer_no_root_coupled]
+h5path = "Tearing/Roots/no_root"
+type = "real_vector"
+extract = "all_real"
+label = "SLAYER coupled no_root flag"
+noise_threshold = 0
+order = 34
+class = "physics_converged"
+
+# Settings (catches accidental config drift)
+[quantities.slayer_enabled]
+h5path = "Tearing/enabled"
+type = "int_scalar"
+extract = "value"
+label = "SLAYER enabled flag"
+noise_threshold = 0
+order = 90
+class = "topological"
+
+[quantities.runtime]
+h5path = ""
+type = "runtime"
+extract = "value"
+label = "Runtime (s)"
+noise_threshold = 0.0
+order = 999
+class = "diagnostic"
diff --git a/regression-harness/cases/diiid_slayer_n1_toroidal.toml b/regression-harness/cases/diiid_slayer_n1_toroidal.toml
new file mode 100644
index 0000000000..e60a05353b
--- /dev/null
+++ b/regression-harness/cases/diiid_slayer_n1_toroidal.toml
@@ -0,0 +1,70 @@
+# Regression case: DIII-D-like H-mode n=1 SLAYER with the toroidal critical-Δ offset.
+# Same deck as diiid_slayer_n1 with D_c_type = "toroidal", so the geometric factor D_geo derived
+# from each surface's ResistGeometry feeds the χ_‖-matching offset D_c and, through it, the roots.
+# Each [quantities.*] block names an HDF5 path in the run output, how to extract it,
+# and the noise floor below which a difference is treated as zero.
+[case]
+name = "diiid_slayer_n1_toroidal"
+description = "DIII-D-like H-mode, n=1, SLAYER with the toroidal critical-Δ offset (D_c_type = toroidal)"
+example_dir = "examples/DIIID-like_SLAYER_example"
+
+[overrides]
+"SLAYER.D_c_type" = "toroidal"
+
+# Critical-Δ input and offset: the resistive interchange index and D_c. The geometric factor
+# D_geo does not depend on D_c_type and is tracked once, in diiid_slayer_n1.
+[quantities.slayer_dr_val]
+h5path = "Tearing/PerSurface/D_R"
+type = "real_vector"
+extract = "all_real"
+label = "SLAYER resistive interchange D_R"
+noise_threshold = 1e-10
+order = 10
+class = "physics_converged"
+
+[quantities.slayer_D_c_offset]
+h5path = "Tearing/PerSurface/D_c_offset"
+type = "real_vector"
+extract = "all_real"
+label = "SLAYER critical-Δ offset D_c"
+noise_threshold = 1e-10
+order = 12
+class = "physics_converged"
+
+# Roots for the inner three rational surfaces, with the same floors as diiid_slayer_n1: the
+# outermost surfaces' contour search is unreliable, so they are not tracked.
+[quantities.slayer_Q]
+h5path = "Tearing/Roots/Q_root"
+type = "complex_vector"
+extract = "first_3_complex"
+label = "SLAYER Q_root [2/1,3/1,4/1]"
+noise_threshold = 1e-4
+order = 30
+class = "physics_converged"
+
+[quantities.slayer_gamma_Hz]
+h5path = "Tearing/Roots/gamma"
+type = "real_vector"
+extract = "first_3"
+label = "SLAYER γ in 1/s [2/1,3/1,4/1]"
+noise_threshold = 1e-1
+order = 33
+class = "physics_converged"
+
+[quantities.slayer_no_root]
+h5path = "Tearing/Roots/no_root"
+type = "real_vector"
+extract = "first_3"
+label = "SLAYER no_root flags [2/1,3/1,4/1]"
+noise_threshold = 0
+order = 34
+class = "physics_converged"
+
+[quantities.runtime]
+h5path = ""
+type = "runtime"
+extract = "value"
+label = "Runtime (s)"
+noise_threshold = 0.0
+order = 999
+class = "diagnostic"
diff --git a/regression-harness/cases/diiid_slayer_n1_winding.toml b/regression-harness/cases/diiid_slayer_n1_winding.toml
new file mode 100644
index 0000000000..1ec1f47fc6
--- /dev/null
+++ b/regression-harness/cases/diiid_slayer_n1_winding.toml
@@ -0,0 +1,10 @@
+# Regression case: the diiid_slayer_n1 deck with SLAYER roots classified by winding number instead of the
+# pole threshold. Pins the winding path's roots and growth rates on a real DIII-D-like layer, and its
+# runtime row tracks the cost of the classifying circles against the threshold case.
+[case]
+name = "diiid_slayer_n1_winding"
+base = "diiid_slayer_n1" # Inherit example_dir, [quantities.*] and [overrides] from this case
+description = "DIII-D-like H-mode equilibrium, n=1, SLAYER tearing-mode analysis with root_classification = winding"
+
+[overrides]
+"Tearing.search.root_classification" = "winding" # Classify contour intersections by the argument principle
diff --git a/regression-harness/cases/diiid_truncation_n1.toml b/regression-harness/cases/diiid_truncation_n1.toml
new file mode 100644
index 0000000000..94688b3ba0
--- /dev/null
+++ b/regression-harness/cases/diiid_truncation_n1.toml
@@ -0,0 +1,120 @@
+# Regression case: DIII-D-like n=1 truncation-only run with the resistive-layer overlap cap enabled.
+# psihigh = 0.9999 puts the overlap point (psi ~ 0.99851) inside the domain, so the cap binds: qlim
+# is pulled from 8.35 to 7.0 and dmlim then steps back to 6.2, excluding the q=7 and q=8 surfaces. This is the
+# only case where psilim_from_layer_overlap changes the domain; every shipped deck leaves it off. Ideal free-boundary stability only (no local stability, forcing or PE). Tracks the domain
+# selection, the scan's layer widths, and the energies on the capped domain, so a change in what the
+# truncation does to the physics cannot pass unnoticed.
+[case]
+name = "diiid_truncation_n1"
+description = "DIII-D-like, n=1, psihigh=0.9999 with the resistive-layer overlap cap binding (truncation only)"
+example_dir = "examples/DIIID-like_truncation_example"
+
+# Layer-overlap scan output. applied = 1 means the overlap bound was active going into sing_lim!;
+# psilim_overlap is the last clean surface before adjacent Eq. (100) layers first touch.
+[quantities.overlap_applied]
+h5path = "ForceFreeStates/LayerOverlap/applied"
+type = "int_scalar"
+extract = "value"
+label = "layer-overlap cap applied"
+noise_threshold = 0
+order = 10
+
+[quantities.psilim_overlap]
+h5path = "ForceFreeStates/LayerOverlap/psilim_overlap"
+type = "real_scalar"
+extract = "value"
+label = "layer-overlap psilim"
+noise_threshold = 1e-8
+order = 11
+
+[quantities.first_overlap_index]
+h5path = "ForceFreeStates/LayerOverlap/first_overlap_index"
+type = "int_scalar"
+extract = "value"
+label = "first overlapping surface index"
+noise_threshold = 0
+order = 12
+
+[quantities.width_dr]
+h5path = "ForceFreeStates/LayerOverlap/width_dr"
+type = "real_vector"
+extract = "all_real"
+label = "diffusive-resistive layer widths (Δψ)"
+noise_threshold = 1e-8
+order = 13
+
+# Final integration domain after the cap and the dmlim offset.
+[quantities.qlim]
+h5path = "Info/qlim"
+type = "real_scalar"
+extract = "value"
+label = "qlim"
+noise_threshold = 1e-12
+order = 20
+
+[quantities.psilim]
+h5path = "Info/psilim"
+type = "real_scalar"
+extract = "value"
+label = "psilim"
+noise_threshold = 1e-10
+order = 21
+
+[quantities.mpert]
+h5path = "Info/mpert"
+type = "int_scalar"
+extract = "value"
+label = "mpert"
+noise_threshold = 0
+order = 22
+
+# Singular surfaces retained inside the capped domain (q=8 must be excluded).
+[quantities.msing]
+h5path = "SingularSurfaces/rational_count"
+type = "int_scalar"
+extract = "value"
+label = "# singular surfaces"
+noise_threshold = 0
+order = 30
+
+[quantities.sing_q]
+h5path = "SingularSurfaces/rational_q"
+type = "real_vector"
+extract = "all_real"
+label = "singular q values"
+noise_threshold = 1e-8
+order = 31
+
+[quantities.sing_psi]
+h5path = "SingularSurfaces/rational_psi"
+type = "real_vector"
+extract = "all_real"
+label = "singular psi locations"
+noise_threshold = 1e-8
+order = 32
+
+# Energies on the capped domain — what the truncation does to the physics, not just the bookkeeping.
+[quantities.ep_real]
+h5path = "ForceFreeStates/FreeBoundaryStability/eigenmode_plasma_energies"
+type = "complex_vector"
+extract = "real_first"
+label = "plasma energy Re(ep[1])"
+noise_threshold = 1e-10
+order = 40
+
+[quantities.et_real]
+h5path = "ForceFreeStates/FreeBoundaryStability/eigenmode_energies"
+type = "complex_vector"
+extract = "real_first"
+label = "total energy Re(et[1])"
+noise_threshold = 1e-10
+order = 41
+
+# Runtime
+[quantities.runtime]
+h5path = ""
+type = "runtime"
+extract = "value"
+label = "Runtime (s)"
+noise_threshold = 0.0
+order = 999
diff --git a/regression-harness/cases/efit_fixedbdy_separatrix.toml b/regression-harness/cases/efit_fixedbdy_separatrix.toml
new file mode 100644
index 0000000000..d64f09ba76
--- /dev/null
+++ b/regression-harness/cases/efit_fixedbdy_separatrix.toml
@@ -0,0 +1,61 @@
+# Regression case: separatrix-finder robustness for fixed-boundary EFITs (PR #296, closes #294).
+# A "computed" case (kind = "computed", no example_dir) that loads a fixed-boundary TokaMaker
+# aspect-scan g-file whose computational box hugs the LCFS (circular R/a=20, eps=0.05). Outside
+# the prescribed LCFS the coil-vacuum flux turns back above the boundary value before the grid
+# edge, so the old bracketed Roots.Brent() separatrix finder could not bracket the psi=sibry
+# crossing and direct_position! threw "not a bracketing interval". The Newton finder (faithful to
+# Fortran direct.f) locates the innermost LCFS crossing regardless. This case errored on the buggy
+# code and now loads; it tracks the leading equilibrium scalars so the loading path stays stable.
+# Fixture g-file: examples/efit_fixedbdy_separatrix_example/eq_eps0.0500000_k1.000_d0.000.geqdsk
+[case]
+name = "efit_fixedbdy_separatrix"
+description = "Fixed-boundary EFIT (box hugs LCFS), Newton separatrix-find regression"
+kind = "computed"
+
+[quantities.psio]
+h5path = "Equilibrium/psi_total"
+type = "real_scalar"
+extract = "value"
+label = "psio (total poloidal flux)"
+noise_threshold = 1e-12
+order = 10
+
+[quantities.q0]
+h5path = "Equilibrium/q_axis"
+type = "real_scalar"
+extract = "value"
+label = "q0"
+noise_threshold = 1e-12
+order = 11
+
+[quantities.q95]
+h5path = "Equilibrium/q_95"
+type = "real_scalar"
+extract = "value"
+label = "q95"
+noise_threshold = 1e-12
+order = 12
+
+[quantities.betat]
+h5path = "Equilibrium/beta_t"
+type = "real_scalar"
+extract = "value"
+label = "beta_t"
+noise_threshold = 1e-12
+order = 13
+
+[quantities.betan]
+h5path = "Equilibrium/beta_N"
+type = "real_scalar"
+extract = "value"
+label = "beta_n"
+noise_threshold = 1e-12
+order = 14
+
+[quantities.runtime]
+h5path = ""
+type = "runtime"
+extract = "value"
+label = "Runtime (s)"
+noise_threshold = 0.0
+order = 90
diff --git a/regression-harness/cases/gal_resistive_diiid.toml b/regression-harness/cases/gal_resistive_diiid.toml
new file mode 100644
index 0000000000..691b9c949b
--- /dev/null
+++ b/regression-harness/cases/gal_resistive_diiid.toml
@@ -0,0 +1,121 @@
+# Regression case: DIII-D-like n=1 outer-region singular Galerkin Δ′ solve.
+# Tracks the resonant-surface inventory, the PEST-3 Δ matching-matrix diagonal
+# (the physics-meaningful tearing Δ′), norms of the full outer Δ′ matrix and the
+# rpec coil-response (Δ_coil) block, and the inner-layer matching outputs.
+# Each [quantities.*] block names an HDF5 path in the run output, how to extract it,
+# and the noise floor below which a difference is treated as zero.
+[case]
+name = "gal_resistive_diiid"
+description = "DIII-D-like, n=1, RDCON outer-region Galerkin Δ′ with rpec coil columns (delta_coil)"
+example_dir = "examples/DIIID-like_gal_resistive_example"
+
+# Number of resonant surfaces in the gal domain
+[quantities.gal_msing]
+h5path = "ForceFreeStates/Solutions/GalerkinIntegration/rational_count"
+type = "int_scalar"
+extract = "value"
+label = "gal # singular surfaces"
+noise_threshold = 0
+order = 10
+
+[quantities.gal_sing_q]
+h5path = "ForceFreeStates/Solutions/GalerkinIntegration/rational_q"
+type = "real_vector"
+extract = "all_real"
+label = "gal singular q values"
+noise_threshold = 1e-8
+order = 11
+
+# PEST-3 Δ matching matrix — per-surface diagonal (the physics-meaningful tearing Δ′)
+[quantities.gal_pest3_delta_diag]
+h5path = "SingularSurfaces/Delta_prime_matrix"
+type = "complex_matrix"
+extract = "diagonal_complex"
+label = "gal PEST3 Δ diagonal"
+noise_threshold = 1e-6
+order = 20
+
+# Raw outer Δ′ matrix (2·msing × 2·msing) — Frobenius norm catches any element drift
+[quantities.gal_delta_norm]
+h5path = "SingularSurfaces/Delta_prime_raw"
+type = "complex_matrix"
+extract = "norm"
+label = "||gal Δ′ matrix||"
+noise_threshold = 1e-6
+order = 21
+
+# rpec coil-response block (edge mode × surface-side) — Frobenius norm
+[quantities.gal_delta_coil_norm]
+h5path = "SingularSurfaces/Delta_coil"
+type = "complex_matrix"
+extract = "norm"
+label = "||gal Δ_coil block||"
+noise_threshold = 1e-6
+order = 22
+
+# Mercier index per surface
+[quantities.gal_di]
+h5path = "ForceFreeStates/Solutions/GalerkinIntegration/D_I"
+type = "real_vector"
+extract = "all_real"
+label = "gal D_I per surface"
+noise_threshold = 1e-8
+order = 30
+
+# Resonant exponents α per surface
+[quantities.gal_alpha]
+h5path = "ForceFreeStates/Solutions/GalerkinIntegration/alpha"
+type = "complex_vector"
+extract = "all_complex"
+label = "gal α per surface"
+noise_threshold = 1e-8
+order = 31
+
+# --- DRIVEN (RPEC) inner-layer matching ([Match]) ---
+# Only finite, well-defined matching quantities are tracked. The reconstructed ξ/ξ′ are deliberately
+# NOT regressed via norms: ξ′ diverges at the rational surfaces, so any whole-array norm is dominated by
+# the (grid- and ULP-fragile) near-singular points — an ill-posed benchmark.
+
+# Inner-layer matching data Δ(Q) per surface (surface geometry + GGJ inner solver). (msing × 2)
+[quantities.gal_match_deltar_norm]
+h5path = "SingularSurfaces/Match/Delta_r"
+type = "complex_matrix"
+extract = "norm"
+label = "||gal inner-layer Δ||"
+noise_threshold = 1e-6
+order = 41
+
+# Outer-region matched coefficients cout (2·msing × mcoil) — the 4·msing matching assembly + solve.
+[quantities.gal_match_cout_norm]
+h5path = "SingularSurfaces/Match/cout"
+type = "complex_matrix"
+extract = "norm"
+label = "||gal match cout||"
+noise_threshold = 1e-6
+order = 42
+
+# Penetrated resonant field at each layer center (msing × mcoil) — the headline matching output.
+[quantities.gal_match_bpen_norm]
+h5path = "SingularSurfaces/Match/bpen"
+type = "complex_matrix"
+extract = "norm"
+label = "||gal match bpen||"
+noise_threshold = 1e-6
+order = 43
+
+# Matching linear-solve residual ‖mat·cof − rmat‖/‖rmat‖ — health check (should stay ~machine eps).
+[quantities.gal_match_residual]
+h5path = "SingularSurfaces/Match/residual"
+type = "real_scalar"
+extract = "value"
+label = "gal match residual"
+noise_threshold = 1e-10
+order = 44
+
+[quantities.runtime]
+h5path = ""
+type = "runtime"
+extract = "value"
+label = "Runtime (s)"
+noise_threshold = 0.0
+order = 999
diff --git a/regression-harness/cases/gal_resistive_diiid_galinner.toml b/regression-harness/cases/gal_resistive_diiid_galinner.toml
new file mode 100644
index 0000000000..583c20c95f
--- /dev/null
+++ b/regression-harness/cases/gal_resistive_diiid_galinner.toml
@@ -0,0 +1,10 @@
+# Regression case: the gal_resistive_diiid deck matched with the Hermite-cubic Galerkin inner-layer
+# backend instead of the default ray backend, at that backend's own grid defaults. Tracks the same
+# inner-layer Δ, matching coefficients and penetrated field, so the Galerkin inner backend has coverage.
+[case]
+name = "gal_resistive_diiid_galinner"
+base = "gal_resistive_diiid" # Inherit example_dir and [quantities.*] from this case
+description = "DIII-D-like, n=1, Galerkin Δ′ matched with the Galerkin inner-layer backend"
+
+[overrides]
+"GGJ.solver" = "galerkin" # GGJ inner-layer backend for the match: "ray" or "galerkin"
diff --git a/regression-harness/cases/ggj_ray_q500i.toml b/regression-harness/cases/ggj_ray_q500i.toml
new file mode 100644
index 0000000000..0ccb2ac234
--- /dev/null
+++ b/regression-harness/cases/ggj_ray_q500i.toml
@@ -0,0 +1,56 @@
+# Regression case: GGJ inner-layer rotated-ray backend at Q = 500i.
+# A "computed" case (kind = "computed", no example_dir) that calls solve_inner with the
+# :ray backend on the physical q=4 benchmark surface at Q = 500i — a regime beyond the
+# :galerkin backend — and tracks the interchange (Δ₊) / tearing (Δ₋) matching coefficients. Guards the
+# rotated-ray solver (and its extended-precision damped-zone march) against numerical
+# drift across changes. Each [quantities.*] block names an HDF5 path in the computed
+# output, how to extract it, and the noise floor for diffs.
+[case]
+name = "ggj_ray_q500i"
+description = "GGJ inner-layer :ray backend, q=4 surface, Q = 500i (beyond :galerkin)"
+kind = "computed"
+
+# interchange (Δ₊) / tearing (Δ₋) from solve_inner(GGJModel(:ray), q4_surface_benchmark(), 500im·Q₀).
+# Complex-valued; both real and imaginary parts are tracked separately.
+# noise_threshold 1e-4 (absolute): the extended-precision damped-zone march carries
+# BLAS/platform-dependent structured roundoff at the ~1e-4 absolute level on these
+# O(10) components (~1e-5 relative); a tighter floor flags phantom cross-machine drift.
+[quantities.delta_interchange_real]
+h5path = "ggj/delta_interchange_real"
+type = "real_scalar"
+extract = "value"
+label = "Re(Δ₊ interchange)"
+noise_threshold = 1e-4
+order = 10
+
+[quantities.delta_interchange_imag]
+h5path = "ggj/delta_interchange_imag"
+type = "real_scalar"
+extract = "value"
+label = "Im(Δ₊ interchange)"
+noise_threshold = 1e-4
+order = 11
+
+[quantities.delta_tearing_real]
+h5path = "ggj/delta_tearing_real"
+type = "real_scalar"
+extract = "value"
+label = "Re(Δ₋ tearing)"
+noise_threshold = 1e-4
+order = 12
+
+[quantities.delta_tearing_imag]
+h5path = "ggj/delta_tearing_imag"
+type = "real_scalar"
+extract = "value"
+label = "Im(Δ₋ tearing)"
+noise_threshold = 1e-4
+order = 13
+
+[quantities.runtime]
+h5path = ""
+type = "runtime"
+extract = "value"
+label = "Runtime (s)"
+noise_threshold = 0.0
+order = 90
diff --git a/regression-harness/cases/ggj_reference.toml b/regression-harness/cases/ggj_reference.toml
new file mode 100644
index 0000000000..bcf1b76e3c
--- /dev/null
+++ b/regression-harness/cases/ggj_reference.toml
@@ -0,0 +1,49 @@
+# Regression case: GGJ inner-layer Galerkin solver reference (Glasser & Wang 2020, Eq. 55).
+# A "computed" case (kind = "computed", no example_dir) that calls solve_inner directly and
+# tracks the interchange (Δ₊) / tearing (Δ₋) inner-layer coefficients. Each [quantities.*] block names an
+# HDF5 path in the computed output, how to extract it, and the noise floor for diffs.
+[case]
+name = "ggj_reference"
+description = "GGJ inner-layer Galerkin solver, Glasser & Wang 2020 Eq. 55 with physical τ_A, τ_R, 1 kHz rotation (Q ≈ 0.22i)"
+kind = "computed"
+
+# interchange (Δ₊) / tearing (Δ₋) from solve_inner(GGJModel(:galerkin), glasser_wang_2020_eq55(; taua=2.11226e-7, taur=0.968219), 2πi·10³)
+[quantities.delta_interchange_real]
+h5path = "ggj/delta_interchange_real"
+type = "real_scalar"
+extract = "value"
+label = "Re(Δ₊ interchange)"
+noise_threshold = 1e-10
+order = 10
+
+[quantities.delta_interchange_imag]
+h5path = "ggj/delta_interchange_imag"
+type = "real_scalar"
+extract = "value"
+label = "Im(Δ₊ interchange)"
+noise_threshold = 1e-10
+order = 11
+
+[quantities.delta_tearing_real]
+h5path = "ggj/delta_tearing_real"
+type = "real_scalar"
+extract = "value"
+label = "Re(Δ₋ tearing)"
+noise_threshold = 1e-10
+order = 12
+
+[quantities.delta_tearing_imag]
+h5path = "ggj/delta_tearing_imag"
+type = "real_scalar"
+extract = "value"
+label = "Im(Δ₋ tearing)"
+noise_threshold = 1e-10
+order = 13
+
+[quantities.runtime]
+h5path = ""
+type = "runtime"
+extract = "value"
+label = "Runtime (s)"
+noise_threshold = 0.0
+order = 90
diff --git a/regression-harness/cases/lar_ggj_tearing_n1.toml b/regression-harness/cases/lar_ggj_tearing_n1.toml
new file mode 100644
index 0000000000..8353766b6d
--- /dev/null
+++ b/regression-harness/cases/lar_ggj_tearing_n1.toml
@@ -0,0 +1,45 @@
+# Regression case: large-aspect-ratio TJ equilibrium, n=1 GGJ tearing growth rates.
+# Reuses the LAR ideal-match deck via [overrides]: its Galerkin Δ′ drives the GGJ inner layer in a
+# [Tearing] solve with fixed η and ρ, each surface solved in its own frame. The only harness coverage
+# of GGJ tearing.
+# Each [quantities.*] block names an HDF5 path in the run output, how to extract it,
+# and the noise floor below which a difference is treated as zero.
+[case]
+name = "lar_ggj_tearing_n1"
+description = "LAR TJ equilibrium, n=1, GGJ tearing growth rates per surface from the Galerkin Δ′ (reuses the LAR ideal-match deck via overrides)"
+example_dir = "examples/LAR_ideal_match_test"
+# The tearing solve replaces the ideal match, and local stability is not tracked here.
+remove_sections = ["Match", "LocalStability", "Ballooning"]
+
+[overrides]
+"Run.output_file" = "gpec.h5" # the harness reads gpec.h5; this deck names its own file
+"Tearing.inner_model" = "GGJ"
+"Tearing.eta" = 1.0e-7
+"Tearing.rho" = 1.0e-7
+"Tearing.search.gamma_range" = [600.0, 2600.0]
+"Tearing.search.omega_range" = [-1500.0, 1500.0]
+
+# Growth rate, frequency and root flag of each surface (2/1, 3/1)
+[quantities.ggj_gamma]
+h5path = "Tearing/Roots/gamma"
+type = "real_vector"
+extract = "all_real"
+label = "GGJ γ in 1/s"
+noise_threshold = 1e-1
+order = 10
+
+[quantities.ggj_omega]
+h5path = "Tearing/Roots/omega"
+type = "real_vector"
+extract = "all_real"
+label = "GGJ ω in rad/s"
+noise_threshold = 1.0
+order = 11
+
+[quantities.ggj_no_root]
+h5path = "Tearing/Roots/no_root"
+type = "real_vector"
+extract = "all_real"
+label = "GGJ no_root flags"
+noise_threshold = 0
+order = 12
diff --git a/regression-harness/cases/lar_reversed_shear_n1.toml b/regression-harness/cases/lar_reversed_shear_n1.toml
new file mode 100644
index 0000000000..45188af12f
--- /dev/null
+++ b/regression-harness/cases/lar_reversed_shear_n1.toml
@@ -0,0 +1,201 @@
+# Regression case: large-aspect-ratio reversed-shear n=1 ideal stability.
+# q falls from 2.40 on the axis to 1.82 and rises to 2.84 at the edge, so q = 2 is crossed twice;
+# the two crossings must stay separate singular surfaces with opposite-sign q′. Tracks the
+# free-boundary energies, the singular surfaces and the integration for that fixture. Each
+# [quantities.*] block names an HDF5 path, how to extract it, and its noise floor.
+[case]
+name = "lar_reversed_shear_n1"
+description = "Large-aspect-ratio reversed-shear equilibrium (hollow current), n=1, ideal stability"
+example_dir = "examples/LAR_reversed_shear_example"
+
+# Energies — leading generalized (W,N) pencil eigenvalues at the final truncation (psilim): power-normalized (⟨|ξ|²⟩ = 1 metric) and invariant to the working-coordinate Jacobian.
+[quantities.et_real]
+h5path = "ForceFreeStates/FreeBoundaryStability/eigenmode_energies"
+type = "complex_vector"
+extract = "real_first"
+label = "total energy Re(et[1])"
+noise_threshold = 1e-10
+order = 10
+
+[quantities.et_imag]
+h5path = "ForceFreeStates/FreeBoundaryStability/eigenmode_energies"
+type = "complex_vector"
+extract = "imag_first"
+label = "total energy Im(et[1])"
+noise_threshold = 1e-10
+order = 11
+
+[quantities.ep_real]
+h5path = "ForceFreeStates/FreeBoundaryStability/eigenmode_plasma_energies"
+type = "complex_vector"
+extract = "real_first"
+label = "plasma energy Re(ep[1])"
+noise_threshold = 1e-10
+order = 12
+
+[quantities.ev_real]
+h5path = "ForceFreeStates/FreeBoundaryStability/eigenmode_vacuum_energies"
+type = "complex_vector"
+extract = "real_first"
+label = "vacuum energy Re(ev[1])"
+noise_threshold = 1e-10
+order = 13
+
+[quantities.vacuum_eigenvalue]
+h5path = "ForceFreeStates/FreeBoundaryStability/vacuum_eigenvalue"
+type = "real_scalar"
+extract = "value"
+label = "vacuum matrix min eigenvalue"
+noise_threshold = 1e-10
+order = 14
+
+# Energies — full eigenvalue arrays
+[quantities.ep_all]
+h5path = "ForceFreeStates/FreeBoundaryStability/eigenmode_plasma_energies"
+type = "complex_vector"
+extract = "all_complex"
+label = "plasma energy (all)"
+noise_threshold = 1e-10
+order = 20
+
+[quantities.ev_all]
+h5path = "ForceFreeStates/FreeBoundaryStability/eigenmode_vacuum_energies"
+type = "complex_vector"
+extract = "all_complex"
+label = "vacuum energy (all)"
+noise_threshold = 1e-10
+order = 21
+
+[quantities.et_all]
+h5path = "ForceFreeStates/FreeBoundaryStability/eigenmode_energies"
+type = "complex_vector"
+extract = "all_complex"
+label = "total energy (all)"
+noise_threshold = 1e-10
+order = 22
+
+# Integration
+[quantities.nstep]
+h5path = "ForceFreeStates/Solutions/ForwardIntegration/nstep"
+type = "int_scalar"
+extract = "value"
+label = "ODE steps (saved)"
+noise_threshold = 0
+order = 30
+
+[quantities.nstep_total]
+h5path = "ForceFreeStates/Solutions/ForwardIntegration/nstep_total"
+type = "int_scalar"
+extract = "value"
+label = "ODE steps (total)"
+noise_threshold = 0
+order = 31
+
+# Equilibrium
+[quantities.q0]
+h5path = "Equilibrium/q_axis"
+type = "real_scalar"
+extract = "value"
+label = "q0"
+noise_threshold = 1e-12
+order = 40
+
+[quantities.q95]
+h5path = "Equilibrium/q_95"
+type = "real_scalar"
+extract = "value"
+label = "q95"
+noise_threshold = 1e-12
+order = 41
+
+[quantities.betat]
+h5path = "Equilibrium/beta_t"
+type = "real_scalar"
+extract = "value"
+label = "beta_t"
+noise_threshold = 1e-12
+order = 42
+
+[quantities.betan]
+h5path = "Equilibrium/beta_N"
+type = "real_scalar"
+extract = "value"
+label = "beta_n"
+noise_threshold = 1e-12
+order = 43
+
+# Singular surfaces
+[quantities.msing]
+h5path = "SingularSurfaces/rational_count"
+type = "int_scalar"
+extract = "value"
+label = "# singular surfaces"
+noise_threshold = 0
+order = 50
+
+[quantities.sing_psi]
+h5path = "SingularSurfaces/rational_psi"
+type = "real_vector"
+extract = "all_real"
+label = "singular psi locations"
+noise_threshold = 1e-8
+order = 51
+
+[quantities.sing_q]
+h5path = "SingularSurfaces/rational_q"
+type = "real_vector"
+extract = "all_real"
+label = "singular q values"
+noise_threshold = 1e-8
+order = 52
+
+[quantities.sing_dqdpsi]
+h5path = "SingularSurfaces/dqdpsi"
+type = "real_vector"
+extract = "all_real"
+label = "singular dq/dpsi (opposite signs on the two q = 2 crossings)"
+noise_threshold = 1e-8
+order = 53
+
+# Mode numbers
+[quantities.mpert]
+h5path = "Info/mpert"
+type = "int_scalar"
+extract = "value"
+label = "mpert"
+noise_threshold = 0
+order = 60
+
+[quantities.npert]
+h5path = "Info/npert"
+type = "int_scalar"
+extract = "value"
+label = "npert"
+noise_threshold = 0
+order = 61
+
+# Profiles (checksums for fast comparison of large arrays)
+[quantities.q_profile]
+h5path = "Equilibrium/Profiles/q"
+type = "real_vector"
+extract = "checksum"
+label = "q profile (checksum)"
+noise_threshold = 0
+order = 70
+
+[quantities.pressure_profile]
+h5path = "Equilibrium/Profiles/mu0p"
+type = "real_vector"
+extract = "checksum"
+label = "pressure profile (checksum)"
+noise_threshold = 0
+order = 71
+
+# Runtime (special: not from H5)
+[quantities.runtime]
+h5path = ""
+type = "runtime"
+extract = "value"
+label = "Runtime (s)"
+noise_threshold = 0.0
+order = 999
diff --git a/regression-harness/cases/solovev_kinetic_nuzero.toml b/regression-harness/cases/solovev_kinetic_nuzero.toml
new file mode 100644
index 0000000000..b7bb8615dd
--- /dev/null
+++ b/regression-harness/cases/solovev_kinetic_nuzero.toml
@@ -0,0 +1,129 @@
+# Regression case: Solovev n=1 collisionless kinetic run (nutype = "zero").
+# Reuses the nuzero test fixture via [overrides] at a mode-converged band with 50/50 D-T
+# multi-ion matrices; locks the collisionless real-x-space energy-integral eigenvalue
+# plus equilibrium and singular-surface anchors.
+# Each [quantities.*] block names an HDF5 path in the run output, how to extract it,
+# and the noise floor below which a difference is treated as zero.
+[case]
+name = "solovev_kinetic_nuzero"
+description = "Solovev, n=1, kinetic = 'KineticForces', nutype=zero (collisionless energy integral), 50/50 D-T multi-ion kinetic matrices, mode-converged band (delta_m=8, mpert=32). Reuses the nuzero test fixture via override; pressure-consistent kinetic.dat."
+example_dir = "test/test_data/regression_solovev_kinetic_nuzero"
+
+# The fixture is coarse for test speed; widen it to the converged band and the D-T ion mix.
+[overrides]
+"Equilibrium.ion_species" = [{ z = 1, m = 2, fraction = 0.5 }, { z = 1, m = 3, fraction = 0.5 }]
+"ForceFreeStates.delta_mlow" = 8
+"ForceFreeStates.delta_mhigh" = 8
+"ForceFreeStates.singfac_min" = 1e-6
+
+# Energies — leading eigenvalues
+[quantities.et_real]
+h5path = "ForceFreeStates/FreeBoundaryStability/eigenmode_energies"
+type = "complex_vector"
+extract = "real_first"
+label = "total energy Re(et[1])"
+noise_threshold = 1e-10
+
+[quantities.et_imag]
+h5path = "ForceFreeStates/FreeBoundaryStability/eigenmode_energies"
+type = "complex_vector"
+extract = "imag_first"
+label = "total energy Im(et[1])"
+noise_threshold = 1e-10
+
+[quantities.ep_real]
+h5path = "ForceFreeStates/FreeBoundaryStability/eigenmode_plasma_energies"
+type = "complex_vector"
+extract = "real_first"
+label = "plasma energy Re(ep[1])"
+noise_threshold = 1e-10
+
+[quantities.ev_real]
+h5path = "ForceFreeStates/FreeBoundaryStability/eigenmode_vacuum_energies"
+type = "complex_vector"
+extract = "real_first"
+label = "vacuum energy Re(ev[1])"
+noise_threshold = 1e-10
+
+# Energies — full eigenvalue arrays
+[quantities.et_all]
+h5path = "ForceFreeStates/FreeBoundaryStability/eigenmode_energies"
+type = "complex_vector"
+extract = "all_complex"
+label = "total energy (all)"
+noise_threshold = 1e-10
+
+# Integration
+[quantities.nstep]
+h5path = "ForceFreeStates/Solutions/ForwardIntegration/nstep"
+type = "int_scalar"
+extract = "value"
+label = "ODE steps (saved)"
+noise_threshold = 0
+
+[quantities.nstep_total]
+h5path = "ForceFreeStates/Solutions/ForwardIntegration/nstep_total"
+type = "int_scalar"
+extract = "value"
+label = "ODE steps (total)"
+noise_threshold = 0
+
+# Equilibrium
+[quantities.q0]
+h5path = "Equilibrium/q_axis"
+type = "real_scalar"
+extract = "value"
+label = "q0"
+noise_threshold = 1e-12
+
+[quantities.q95]
+h5path = "Equilibrium/q_95"
+type = "real_scalar"
+extract = "value"
+label = "q95"
+noise_threshold = 1e-12
+
+# Singular surfaces
+[quantities.msing]
+h5path = "SingularSurfaces/rational_count"
+type = "int_scalar"
+extract = "value"
+label = "# singular surfaces"
+noise_threshold = 0
+
+[quantities.sing_psi]
+h5path = "SingularSurfaces/rational_psi"
+type = "real_vector"
+extract = "all_real"
+label = "singular psi locations"
+noise_threshold = 1e-8
+
+[quantities.sing_q]
+h5path = "SingularSurfaces/rational_q"
+type = "real_vector"
+extract = "all_real"
+label = "singular q values"
+noise_threshold = 1e-8
+
+# Mode numbers
+[quantities.mpert]
+h5path = "Info/mpert"
+type = "int_scalar"
+extract = "value"
+label = "mpert"
+noise_threshold = 0
+
+[quantities.npert]
+h5path = "Info/npert"
+type = "int_scalar"
+extract = "value"
+label = "npert"
+noise_threshold = 0
+
+# Runtime (special: not from H5)
+[quantities.runtime]
+h5path = ""
+type = "runtime"
+extract = "value"
+label = "Runtime (s)"
+noise_threshold = 0.0
diff --git a/regression-harness/cases/solovev_multi_n.toml b/regression-harness/cases/solovev_multi_n.toml
new file mode 100644
index 0000000000..2a6692540d
--- /dev/null
+++ b/regression-harness/cases/solovev_multi_n.toml
@@ -0,0 +1,144 @@
+# Regression case: Solovev multi-n (n = 1 and 2) ideal stability.
+# Tracks the leading free-boundary energies and stability quantities for the analytic
+# Solovev fixture swept over a toroidal mode-number range. Each [quantities.*] block names
+# an HDF5 path, how to extract it, and the noise floor below which a diff is treated as zero.
+[case]
+name = "solovev_multi_n"
+description = "Solovev analytical equilibrium, multi-n, ideal stability"
+example_dir = "examples/Solovev_ideal_example_multi_n"
+
+# Energies — leading generalized (W,N) pencil eigenvalues at the final truncation (psilim): power-normalized (⟨|ξ|²⟩ = 1 metric) and invariant to the working-coordinate Jacobian.
+[quantities.et_real]
+h5path = "ForceFreeStates/FreeBoundaryStability/eigenmode_energies"
+type = "complex_vector"
+extract = "real_first"
+label = "total energy Re(et[1])"
+noise_threshold = 1e-10
+order = 10
+
+[quantities.et_imag]
+h5path = "ForceFreeStates/FreeBoundaryStability/eigenmode_energies"
+type = "complex_vector"
+extract = "imag_first"
+label = "total energy Im(et[1])"
+noise_threshold = 1e-10
+order = 11
+
+[quantities.vacuum_eigenvalue]
+h5path = "ForceFreeStates/FreeBoundaryStability/vacuum_eigenvalue"
+type = "real_scalar"
+extract = "value"
+label = "vacuum matrix min eigenvalue"
+noise_threshold = 1e-10
+order = 14
+
+# Energies — full eigenvalue arrays
+[quantities.ep_all]
+h5path = "ForceFreeStates/FreeBoundaryStability/eigenmode_plasma_energies"
+type = "complex_vector"
+extract = "all_complex"
+label = "plasma energy (all)"
+noise_threshold = 1e-10
+order = 20
+
+[quantities.ev_all]
+h5path = "ForceFreeStates/FreeBoundaryStability/eigenmode_vacuum_energies"
+type = "complex_vector"
+extract = "all_complex"
+label = "vacuum energy (all)"
+noise_threshold = 1e-10
+order = 21
+
+[quantities.et_all]
+h5path = "ForceFreeStates/FreeBoundaryStability/eigenmode_energies"
+type = "complex_vector"
+extract = "all_complex"
+label = "total energy (all)"
+noise_threshold = 1e-10
+order = 22
+
+# Integration
+[quantities.nstep]
+h5path = "ForceFreeStates/Solutions/ForwardIntegration/nstep"
+type = "int_scalar"
+extract = "value"
+label = "ODE steps (saved)"
+noise_threshold = 0
+order = 30
+
+[quantities.nstep_total]
+h5path = "ForceFreeStates/Solutions/ForwardIntegration/nstep_total"
+type = "int_scalar"
+extract = "value"
+label = "ODE steps (total)"
+noise_threshold = 0
+order = 31
+
+# Equilibrium
+[quantities.q0]
+h5path = "Equilibrium/q_axis"
+type = "real_scalar"
+extract = "value"
+label = "q0"
+noise_threshold = 1e-12
+order = 40
+
+[quantities.q95]
+h5path = "Equilibrium/q_95"
+type = "real_scalar"
+extract = "value"
+label = "q95"
+noise_threshold = 1e-12
+order = 41
+
+# Singular surfaces
+[quantities.msing]
+h5path = "SingularSurfaces/rational_count"
+type = "int_scalar"
+extract = "value"
+label = "# singular surfaces"
+noise_threshold = 0
+order = 50
+
+[quantities.sing_psi]
+h5path = "SingularSurfaces/rational_psi"
+type = "real_vector"
+extract = "all_real"
+label = "singular psi locations"
+noise_threshold = 1e-8
+order = 51
+
+# Mode numbers
+[quantities.mpert]
+h5path = "Info/mpert"
+type = "int_scalar"
+extract = "value"
+label = "mpert"
+noise_threshold = 0
+order = 60
+
+[quantities.npert]
+h5path = "Info/npert"
+type = "int_scalar"
+extract = "value"
+label = "npert"
+noise_threshold = 0
+order = 61
+
+# Profiles (checksums)
+[quantities.q_profile]
+h5path = "Equilibrium/Profiles/q"
+type = "real_vector"
+extract = "checksum"
+label = "q profile (checksum)"
+noise_threshold = 0
+order = 70
+
+# Runtime
+[quantities.runtime]
+h5path = ""
+type = "runtime"
+extract = "value"
+label = "Runtime (s)"
+noise_threshold = 0.0
+order = 999
diff --git a/regression-harness/cases/solovev_n1.toml b/regression-harness/cases/solovev_n1.toml
new file mode 100644
index 0000000000..d7f4224e52
--- /dev/null
+++ b/regression-harness/cases/solovev_n1.toml
@@ -0,0 +1,202 @@
+# Regression case: Solovev n=1 ideal stability (near-marginal external kink).
+# Tracks the leading free-boundary energies and stability quantities for the analytic
+# Solovev fixture. Each [quantities.*] block names an HDF5 path in the run output, how to
+# extract it, and the noise floor below which a difference is treated as zero.
+[case]
+name = "solovev_n1"
+description = "Solovev analytical equilibrium, n=1, ideal stability"
+example_dir = "examples/Solovev_ideal_example"
+
+# Energies — leading generalized (W,N) pencil eigenvalues at the final truncation (psilim): power-normalized (⟨|ξ|²⟩ = 1 metric) and invariant to the working-coordinate Jacobian.
+[quantities.et_real]
+h5path = "ForceFreeStates/FreeBoundaryStability/eigenmode_energies"
+type = "complex_vector"
+extract = "real_first"
+label = "total energy Re(et[1])"
+noise_threshold = 1e-10
+order = 10
+
+[quantities.et_imag]
+h5path = "ForceFreeStates/FreeBoundaryStability/eigenmode_energies"
+type = "complex_vector"
+extract = "imag_first"
+label = "total energy Im(et[1])"
+noise_threshold = 1e-10
+order = 11
+
+[quantities.ep_real]
+h5path = "ForceFreeStates/FreeBoundaryStability/eigenmode_plasma_energies"
+type = "complex_vector"
+extract = "real_first"
+label = "plasma energy Re(ep[1])"
+noise_threshold = 1e-10
+order = 12
+
+[quantities.ev_real]
+h5path = "ForceFreeStates/FreeBoundaryStability/eigenmode_vacuum_energies"
+type = "complex_vector"
+extract = "real_first"
+label = "vacuum energy Re(ev[1])"
+noise_threshold = 1e-10
+order = 13
+
+[quantities.vacuum_eigenvalue]
+h5path = "ForceFreeStates/FreeBoundaryStability/vacuum_eigenvalue"
+type = "real_scalar"
+extract = "value"
+label = "vacuum matrix min eigenvalue"
+noise_threshold = 1e-10
+order = 14
+
+# Energies — full eigenvalue arrays
+[quantities.ep_all]
+h5path = "ForceFreeStates/FreeBoundaryStability/eigenmode_plasma_energies"
+type = "complex_vector"
+extract = "all_complex"
+label = "plasma energy (all)"
+noise_threshold = 1e-10
+order = 20
+
+[quantities.ev_all]
+h5path = "ForceFreeStates/FreeBoundaryStability/eigenmode_vacuum_energies"
+type = "complex_vector"
+extract = "all_complex"
+label = "vacuum energy (all)"
+noise_threshold = 1e-10
+order = 21
+
+[quantities.et_all]
+h5path = "ForceFreeStates/FreeBoundaryStability/eigenmode_energies"
+type = "complex_vector"
+extract = "all_complex"
+label = "total energy (all)"
+noise_threshold = 1e-10
+order = 22
+
+# Integration
+[quantities.nstep]
+h5path = "ForceFreeStates/Solutions/ForwardIntegration/nstep"
+type = "int_scalar"
+extract = "value"
+label = "ODE steps (saved)"
+noise_threshold = 0
+order = 30
+
+[quantities.nstep_total]
+h5path = "ForceFreeStates/Solutions/ForwardIntegration/nstep_total"
+type = "int_scalar"
+extract = "value"
+label = "ODE steps (total)"
+noise_threshold = 0
+order = 31
+
+# Equilibrium
+[quantities.q0]
+h5path = "Equilibrium/q_axis"
+type = "real_scalar"
+extract = "value"
+label = "q0"
+noise_threshold = 1e-12
+order = 40
+
+[quantities.q95]
+h5path = "Equilibrium/q_95"
+type = "real_scalar"
+extract = "value"
+label = "q95"
+noise_threshold = 1e-12
+order = 41
+
+[quantities.betat]
+h5path = "Equilibrium/beta_t"
+type = "real_scalar"
+extract = "value"
+label = "beta_t"
+noise_threshold = 1e-12
+order = 42
+
+[quantities.betan]
+h5path = "Equilibrium/beta_N"
+type = "real_scalar"
+extract = "value"
+label = "beta_n"
+noise_threshold = 1e-12
+order = 43
+
+# Singular surfaces
+[quantities.msing]
+h5path = "SingularSurfaces/rational_count"
+type = "int_scalar"
+extract = "value"
+label = "# singular surfaces"
+noise_threshold = 0
+order = 50
+
+[quantities.sing_psi]
+h5path = "SingularSurfaces/rational_psi"
+type = "real_vector"
+extract = "all_real"
+label = "singular psi locations"
+noise_threshold = 1e-8
+order = 51
+
+[quantities.sing_q]
+h5path = "SingularSurfaces/rational_q"
+type = "real_vector"
+extract = "all_real"
+label = "singular q values"
+noise_threshold = 1e-8
+order = 52
+
+# Mode numbers
+[quantities.mpert]
+h5path = "Info/mpert"
+type = "int_scalar"
+extract = "value"
+label = "mpert"
+noise_threshold = 0
+order = 60
+
+[quantities.npert]
+h5path = "Info/npert"
+type = "int_scalar"
+extract = "value"
+label = "npert"
+noise_threshold = 0
+order = 61
+
+# Profiles (checksums for fast comparison of large arrays)
+[quantities.q_profile]
+h5path = "Equilibrium/Profiles/q"
+type = "real_vector"
+extract = "checksum"
+label = "q profile (checksum)"
+noise_threshold = 0
+order = 70
+
+[quantities.pressure_profile]
+h5path = "Equilibrium/Profiles/mu0p"
+type = "real_vector"
+extract = "checksum"
+label = "pressure profile (checksum)"
+noise_threshold = 0
+order = 71
+
+# Bitwise reproducibility guard for the ideal asymptotic coefficients (issue: kinetic
+# runs used to dump uninitialized memory here; ideal values must stay byte-stable).
+[quantities.ca_left]
+h5path = "SingularSurfaces/ca_left"
+type = "complex_matrix"
+extract = "checksum"
+label = "ca_left (checksum)"
+noise_threshold = 0
+order = 72
+
+# Runtime (special: not from H5)
+[quantities.runtime]
+h5path = ""
+type = "runtime"
+extract = "value"
+label = "Runtime (s)"
+noise_threshold = 0.0
+order = 999
diff --git a/regression-harness/cases/tj_kinetic_calculated.toml b/regression-harness/cases/tj_kinetic_calculated.toml
new file mode 100644
index 0000000000..af99a5f6d2
--- /dev/null
+++ b/regression-harness/cases/tj_kinetic_calculated.toml
@@ -0,0 +1,170 @@
+# Regression case: TJ-analytic n=1 with the "calculated" kinetic path at full strength.
+# Guards the real KineticForces (PENTRC-style) physics path against drift, with the main
+# ion declared as a 50/50 D-T mix so the self-consistent kinetic-matrix species loop
+# (multi-ion accumulation) is pinned end-to-end. Each [quantities.*] block names an HDF5
+# path in the run output, how to extract it, and the noise floor below which a difference
+# is treated as zero.
+[case]
+name = "tj_kinetic_calculated"
+description = "TJ-analytic, n=1, no wall, kinetic = 'KineticForces', 50/50 D-T multi-ion kinetic matrices; pressure-consistent kinetic.dat (P₀≈784 Pa)."
+example_dir = "examples/TJ_kinetic_calculated_example"
+
+# Energies — leading eigenvalues
+[quantities.et_real]
+h5path = "ForceFreeStates/FreeBoundaryStability/eigenmode_energies"
+type = "complex_vector"
+extract = "real_first"
+label = "total energy Re(et[1])"
+noise_threshold = 1e-10
+
+[quantities.et_imag]
+h5path = "ForceFreeStates/FreeBoundaryStability/eigenmode_energies"
+type = "complex_vector"
+extract = "imag_first"
+label = "total energy Im(et[1])"
+noise_threshold = 1e-10
+
+[quantities.ep_real]
+h5path = "ForceFreeStates/FreeBoundaryStability/eigenmode_plasma_energies"
+type = "complex_vector"
+extract = "real_first"
+label = "plasma energy Re(ep[1])"
+noise_threshold = 1e-10
+
+[quantities.ev_real]
+h5path = "ForceFreeStates/FreeBoundaryStability/eigenmode_vacuum_energies"
+type = "complex_vector"
+extract = "real_first"
+label = "vacuum energy Re(ev[1])"
+noise_threshold = 1e-10
+
+# Energies — full eigenvalue arrays
+[quantities.et_all]
+h5path = "ForceFreeStates/FreeBoundaryStability/eigenmode_energies"
+type = "complex_vector"
+extract = "all_complex"
+label = "total energy (all)"
+noise_threshold = 1e-10
+
+# Integration
+[quantities.nstep]
+h5path = "ForceFreeStates/Solutions/ForwardIntegration/nstep"
+type = "int_scalar"
+extract = "value"
+label = "ODE steps (saved)"
+noise_threshold = 0
+
+[quantities.nstep_total]
+h5path = "ForceFreeStates/Solutions/ForwardIntegration/nstep_total"
+type = "int_scalar"
+extract = "value"
+label = "ODE steps (total)"
+noise_threshold = 0
+
+# Equilibrium
+[quantities.q0]
+h5path = "Equilibrium/q_axis"
+type = "real_scalar"
+extract = "value"
+label = "q0"
+noise_threshold = 1e-12
+
+[quantities.q95]
+h5path = "Equilibrium/q_95"
+type = "real_scalar"
+extract = "value"
+label = "q95"
+noise_threshold = 1e-12
+
+# Singular surfaces
+[quantities.msing]
+h5path = "SingularSurfaces/rational_count"
+type = "int_scalar"
+extract = "value"
+label = "# singular surfaces"
+noise_threshold = 0
+
+[quantities.sing_psi]
+h5path = "SingularSurfaces/rational_psi"
+type = "real_vector"
+extract = "all_real"
+label = "singular psi locations"
+noise_threshold = 1e-8
+
+[quantities.sing_q]
+h5path = "SingularSurfaces/rational_q"
+type = "real_vector"
+extract = "all_real"
+label = "singular q values"
+noise_threshold = 1e-8
+
+# Mode numbers
+[quantities.mpert]
+h5path = "Info/mpert"
+type = "int_scalar"
+extract = "value"
+label = "mpert"
+noise_threshold = 0
+
+[quantities.npert]
+h5path = "Info/npert"
+type = "int_scalar"
+extract = "value"
+label = "npert"
+noise_threshold = 0
+
+# Torque of the run's own forcing, three routes on one kinetic solve: the ψ-resolved torque
+# response matrix T_xe contracted with the applied field (its Hermitian part carries the torque),
+# the boundary-response torque from the plasma inductance (same number, different algebra), and
+# the KineticForces NTV quadrature of the same displacement (an independent evaluation that
+# agrees only to the level the kinetic-matrix and quadrature discretizations do).
+[quantities.torque_response_total]
+h5path = "PerturbedEquilibrium/TorqueResponse/total_torque"
+type = "real_scalar"
+extract = "value"
+label = "T_xe applied-forcing torque [N·m]"
+noise_threshold = 1e-10
+
+[quantities.boundary_torque]
+h5path = "PerturbedEquilibrium/Energies/toroidal_torque"
+type = "real_scalar"
+extract = "value"
+label = "boundary-response torque [N·m]"
+noise_threshold = 1e-10
+
+[quantities.ntv_fgar_torque]
+h5path = "KineticForces/fgar/total_torque"
+type = "real_scalar"
+extract = "value"
+label = "NTV fgar quadrature torque [N·m]"
+noise_threshold = 1e-10
+
+# Perturbed equilibrium — Clebsch displacements and regularized b^θ from the kinetic solve
+[quantities.pe_clebsch_alpha_norm]
+h5path = "PerturbedEquilibrium/Response/xi_clebsch_alpha"
+type = "complex_matrix"
+extract = "norm"
+label = "||xi_clebsch_alpha||"
+noise_threshold = 1e-8
+
+[quantities.pe_clebsch_psi1_norm]
+h5path = "PerturbedEquilibrium/Response/dxi_clebsch_psidpsi"
+type = "complex_matrix"
+extract = "norm"
+label = "||dxi_clebsch_psi/dpsi||"
+noise_threshold = 1e-8
+
+[quantities.pe_b_theta_reg_norm]
+h5path = "PerturbedEquilibrium/Response/Jb_theta_reg"
+type = "complex_matrix"
+extract = "norm"
+label = "||Jb_theta_reg||"
+noise_threshold = 1e-8
+
+# Runtime (special: not from H5)
+[quantities.runtime]
+h5path = ""
+type = "runtime"
+extract = "value"
+label = "Runtime (s)"
+noise_threshold = 0.0
diff --git a/regression-harness/cases/tj_kinetic_multiion.toml b/regression-harness/cases/tj_kinetic_multiion.toml
new file mode 100644
index 0000000000..c6238b821e
--- /dev/null
+++ b/regression-harness/cases/tj_kinetic_multiion.toml
@@ -0,0 +1,67 @@
+# Regression case: TJ-analytic n=1 + PE + MULTI-ION NTV torque. The main ion is modelled as a
+# 50/50 D-T mix, so the KineticForces quadrature sums over D + T + electrons (this fixture is a pure
+# plasma, n_e = n_i, so no impurity species is present). Tracks the summed total AND each per-species
+# contribution, pinning the multi-species loop (resolve_ntv_species + combine_species_states) and the
+# full-composition Zeff. The impurity-species path is covered by the unit tests + the TC-24 case.
+[case]
+name = "tj_kinetic_multiion"
+description = "TJ-analytic n=1, no wall, ideal + PE + multi-ion NTV (D + T + electron summed)"
+example_dir = "examples/TJ_kinetic_multiion_example"
+
+# Summed total NTV over all species — the headline multi-ion quantity.
+[quantities.ntv_total]
+h5path = "KineticForces/fgar/total_torque"
+type = "real_scalar"
+extract = "value"
+label = "NTV total (D+T+imp+e) [N·m]"
+noise_threshold = 1e-8
+order = 10
+
+[quantities.ntv_D]
+h5path = "KineticForces/PerSpecies/ion_z1_m2/fgar/total_torque"
+type = "real_scalar"
+extract = "value"
+label = "NTV Deuterium [N·m]"
+noise_threshold = 1e-8
+order = 11
+
+[quantities.ntv_T]
+h5path = "KineticForces/PerSpecies/ion_z1_m3/fgar/total_torque"
+type = "real_scalar"
+extract = "value"
+label = "NTV Tritium [N·m]"
+noise_threshold = 1e-8
+order = 12
+
+[quantities.ntv_electron]
+h5path = "KineticForces/PerSpecies/electron/fgar/total_torque"
+type = "real_scalar"
+extract = "value"
+label = "NTV electron [N·m]"
+noise_threshold = 1e-8
+order = 14
+
+# Stability anchors — confirm the upstream FFS/PE stages feeding the NTV diagnostic.
+[quantities.et_real]
+h5path = "ForceFreeStates/FreeBoundaryStability/eigenmode_energies"
+type = "complex_vector"
+extract = "real_first"
+label = "total energy Re(et[1])"
+noise_threshold = 1e-10
+order = 20
+
+[quantities.msing]
+h5path = "SingularSurfaces/rational_count"
+type = "int_scalar"
+extract = "value"
+label = "# singular surfaces"
+noise_threshold = 0
+order = 21
+
+[quantities.runtime]
+h5path = ""
+type = "runtime"
+extract = "value"
+label = "Runtime (s)"
+noise_threshold = 0.0
+order = 90
diff --git a/regression-harness/cases/tj_kinetic_ntv.toml b/regression-harness/cases/tj_kinetic_ntv.toml
new file mode 100644
index 0000000000..e4310bc8d6
--- /dev/null
+++ b/regression-harness/cases/tj_kinetic_ntv.toml
@@ -0,0 +1,79 @@
+# Regression case: TJ-analytic n=1 ideal stability + perturbed equilibrium + post-PE NTV torque.
+# The only case exercising the KineticForces outer ψ torque quadrature (fgar method):
+# rational-surface paneling, maxevals_psi cap, and the atol_psi/rtol_psi defaults.
+# Each [quantities.*] block names an HDF5 path in the run output, how to extract it, and the
+# noise floor below which a difference is treated as zero.
+[case]
+name = "tj_kinetic_ntv"
+description = "TJ-analytic equilibrium, n=1, no wall, ideal + PE + NTV torque quadrature"
+example_dir = "examples/TJ_kinetic_NTV_example"
+
+# NTV torque — the primary tracked quantity of this case. [Re, Im] pair; the ψ quadrature
+# converges to rtol_psi=1e-2, but the result is deterministic for fixed code + inputs, so
+# the noise floor is set near FP noise and any real movement is surfaced.
+[quantities.ntv_torque]
+h5path = "KineticForces/fgar/total_torque"
+type = "real_vector"
+extract = "all_real"
+label = "NTV torque fgar [Re, Im]"
+noise_threshold = 1e-8
+order = 10
+
+[quantities.ntv_psi_nsteps]
+h5path = "KineticForces/fgar/psi_nsteps"
+type = "int_scalar"
+extract = "value"
+label = "NTV ψ quadrature evaluations"
+noise_threshold = 0
+order = 11
+
+# Fluid CGL limit on the same ψ quadrature (fcgl method, l = 0 only): tracks the surface drive
+# convention κ·ξ⊥ = -(δB/B + ∇·ξ⊥) independently of the kinetic resonance operator.
+[quantities.fcgl_energy]
+h5path = "KineticForces/fcgl/total_energy"
+type = "real_scalar"
+extract = "value"
+label = "fluid CGL energy fcgl [J]"
+noise_threshold = 1e-8
+order = 12
+
+# Stability anchors — confirm the upstream FFS/PE stages feeding the NTV diagnostic.
+[quantities.et_real]
+h5path = "ForceFreeStates/FreeBoundaryStability/eigenmode_energies"
+type = "complex_vector"
+extract = "real_first"
+label = "root-area-weighted total energy Re(et[1])"
+noise_threshold = 1e-10
+order = 20
+
+[quantities.msing]
+h5path = "SingularSurfaces/rational_count"
+type = "int_scalar"
+extract = "value"
+label = "# singular surfaces"
+noise_threshold = 0
+order = 21
+
+[quantities.sing_psi]
+h5path = "SingularSurfaces/rational_psi"
+type = "real_vector"
+extract = "all_real"
+label = "singular psi locations"
+noise_threshold = 1e-8
+order = 22
+
+[quantities.q0]
+h5path = "Equilibrium/q_axis"
+type = "real_scalar"
+extract = "value"
+label = "q0"
+noise_threshold = 0
+order = 23
+
+# Runtime (special: not from H5)
+[quantities.runtime]
+h5path = ""
+type = "runtime"
+extract = "value"
+label = "Runtime (s)"
+noise_threshold = 0.0
diff --git a/regression-harness/cases/tj_kinetic_ntv_rates.toml b/regression-harness/cases/tj_kinetic_ntv_rates.toml
new file mode 100644
index 0000000000..e4885c1df0
--- /dev/null
+++ b/regression-harness/cases/tj_kinetic_ntv_rates.toml
@@ -0,0 +1,40 @@
+# Regression case: the TJ-analytic n=1 NTV torque with supplied collision rates.
+# Reuses the TJ kinetic NTV deck via [overrides], reading kinetic_rates.dat as a rates-v1 table: its lnΛ is the
+# internal model's and its ν_i, ν_e are 3× the model's, so a reader or spline path that drops the supplied rates
+# moves the torque away from this case's reference. The only harness coverage of supplied collision rates.
+# Each [quantities.*] block names an HDF5 path in the run output, how to extract it, and the
+# noise floor below which a difference is treated as zero.
+[case]
+name = "tj_kinetic_ntv_rates"
+description = "TJ-analytic equilibrium, n=1, no wall, NTV torque with supplied rates-v1 collision rates (reuses the TJ NTV deck via overrides)"
+example_dir = "examples/TJ_kinetic_NTV_example"
+
+[overrides]
+"Equilibrium.kinetic_file" = "kinetic_rates.dat" # the same profiles with supplied lnLambda, nu_i, nu_e
+"Equilibrium.kinetic_format" = "rates-v1" # read columns 7-9 as supplied collision rates
+
+# NTV torque with the supplied rates. [Re, Im] pair; deterministic for fixed code and inputs, so the
+# noise floor sits near FP noise.
+[quantities.ntv_torque]
+h5path = "KineticForces/fgar/total_torque"
+type = "real_vector"
+extract = "all_real"
+label = "NTV torque fgar with supplied rates [Re, Im]"
+noise_threshold = 1e-8
+order = 10
+
+[quantities.ntv_psi_nsteps]
+h5path = "KineticForces/fgar/psi_nsteps"
+type = "int_scalar"
+extract = "value"
+label = "NTV ψ quadrature evaluations"
+noise_threshold = 0
+order = 11
+
+# Runtime (special: not from H5)
+[quantities.runtime]
+h5path = ""
+type = "runtime"
+extract = "value"
+label = "Runtime (s)"
+noise_threshold = 0.0
diff --git a/regression-harness/cases/tj_n1.toml b/regression-harness/cases/tj_n1.toml
new file mode 100644
index 0000000000..ad9d799740
--- /dev/null
+++ b/regression-harness/cases/tj_n1.toml
@@ -0,0 +1,225 @@
+# Regression case: TJ-analytic n=1 ideal stability and perturbed equilibrium, no wall.
+# Tracks the leading free-boundary energies, the stability quantities and the singular coupling of
+# a stable analytic equilibrium. Each [quantities.*] block names an HDF5 path in the run output, how
+# to extract it, and the noise floor below which a difference is treated as zero.
+[case]
+name = "tj_n1"
+description = "TJ-analytic equilibrium, n=1, no wall, ideal stability + perturbed equilibrium"
+example_dir = "examples/TJ_ideal_example"
+
+# Energies — leading generalized (W,N) pencil eigenvalues at the final truncation (psilim): power-normalized (⟨|ξ|²⟩ = 1 metric) and invariant to the working-coordinate Jacobian.
+[quantities.et_real]
+h5path = "ForceFreeStates/FreeBoundaryStability/eigenmode_energies"
+type = "complex_vector"
+extract = "real_first"
+label = "total energy Re(et[1])"
+noise_threshold = 1e-10
+order = 10
+
+[quantities.et_imag]
+h5path = "ForceFreeStates/FreeBoundaryStability/eigenmode_energies"
+type = "complex_vector"
+extract = "imag_first"
+label = "total energy Im(et[1])"
+noise_threshold = 1e-10
+order = 11
+
+[quantities.ep_real]
+h5path = "ForceFreeStates/FreeBoundaryStability/eigenmode_plasma_energies"
+type = "complex_vector"
+extract = "real_first"
+label = "plasma energy Re(ep[1])"
+noise_threshold = 1e-10
+order = 12
+
+[quantities.ev_real]
+h5path = "ForceFreeStates/FreeBoundaryStability/eigenmode_vacuum_energies"
+type = "complex_vector"
+extract = "real_first"
+label = "vacuum energy Re(ev[1])"
+noise_threshold = 1e-10
+order = 13
+
+[quantities.vacuum_eigenvalue]
+h5path = "ForceFreeStates/FreeBoundaryStability/vacuum_eigenvalue"
+type = "real_scalar"
+extract = "value"
+label = "vacuum matrix min eigenvalue"
+noise_threshold = 1e-10
+order = 14
+
+# Energies — full eigenvalue arrays
+[quantities.ep_all]
+h5path = "ForceFreeStates/FreeBoundaryStability/eigenmode_plasma_energies"
+type = "complex_vector"
+extract = "all_complex"
+label = "plasma energy (all)"
+noise_threshold = 1e-10
+order = 20
+
+[quantities.ev_all]
+h5path = "ForceFreeStates/FreeBoundaryStability/eigenmode_vacuum_energies"
+type = "complex_vector"
+extract = "all_complex"
+label = "vacuum energy (all)"
+noise_threshold = 1e-10
+order = 21
+
+[quantities.et_all]
+h5path = "ForceFreeStates/FreeBoundaryStability/eigenmode_energies"
+type = "complex_vector"
+extract = "all_complex"
+label = "total energy (all)"
+noise_threshold = 1e-10
+order = 22
+
+# Integration
+[quantities.nstep]
+h5path = "ForceFreeStates/Solutions/ForwardIntegration/nstep"
+type = "int_scalar"
+extract = "value"
+label = "ODE steps (saved)"
+noise_threshold = 0
+order = 30
+
+[quantities.nstep_total]
+h5path = "ForceFreeStates/Solutions/ForwardIntegration/nstep_total"
+type = "int_scalar"
+extract = "value"
+label = "ODE steps (total)"
+noise_threshold = 0
+order = 31
+
+# Equilibrium
+[quantities.q0]
+h5path = "Equilibrium/q_axis"
+type = "real_scalar"
+extract = "value"
+label = "q0"
+noise_threshold = 1e-12
+order = 40
+
+[quantities.q95]
+h5path = "Equilibrium/q_95"
+type = "real_scalar"
+extract = "value"
+label = "q95"
+noise_threshold = 1e-12
+order = 41
+
+[quantities.betat]
+h5path = "Equilibrium/beta_t"
+type = "real_scalar"
+extract = "value"
+label = "beta_t"
+noise_threshold = 1e-12
+order = 42
+
+[quantities.betan]
+h5path = "Equilibrium/beta_N"
+type = "real_scalar"
+extract = "value"
+label = "beta_n"
+noise_threshold = 1e-12
+order = 43
+
+# Singular surfaces
+[quantities.msing]
+h5path = "SingularSurfaces/rational_count"
+type = "int_scalar"
+extract = "value"
+label = "# singular surfaces"
+noise_threshold = 0
+order = 50
+
+[quantities.sing_psi]
+h5path = "SingularSurfaces/rational_psi"
+type = "real_vector"
+extract = "all_real"
+label = "singular psi locations"
+noise_threshold = 1e-8
+order = 51
+
+[quantities.sing_q]
+h5path = "SingularSurfaces/rational_q"
+type = "real_vector"
+extract = "all_real"
+label = "singular q values"
+noise_threshold = 1e-8
+order = 52
+
+# Mode numbers
+[quantities.mpert]
+h5path = "Info/mpert"
+type = "int_scalar"
+extract = "value"
+label = "mpert"
+noise_threshold = 0
+order = 60
+
+[quantities.npert]
+h5path = "Info/npert"
+type = "int_scalar"
+extract = "value"
+label = "npert"
+noise_threshold = 0
+order = 61
+
+# Profiles (checksums for fast comparison of large arrays)
+[quantities.q_profile]
+h5path = "Equilibrium/Profiles/q"
+type = "real_vector"
+extract = "checksum"
+label = "q profile (checksum)"
+noise_threshold = 0
+order = 70
+
+[quantities.pressure_profile]
+h5path = "Equilibrium/Profiles/mu0p"
+type = "real_vector"
+extract = "checksum"
+label = "pressure profile (checksum)"
+noise_threshold = 0
+order = 71
+
+# Perturbed equilibrium at the resonant surfaces, with no wall
+[quantities.resonant_field]
+h5path = "PerturbedEquilibrium/SingularCoupling/resonant_area_weighted_field"
+type = "complex_vector"
+extract = "all_complex"
+label = "resonant area-weighted field"
+noise_threshold = 1e-10
+order = 70
+
+[quantities.island_half_width]
+h5path = "PerturbedEquilibrium/SingularCoupling/island_half_width"
+type = "real_vector"
+extract = "all_real"
+label = "island half-width"
+noise_threshold = 1e-10
+order = 71
+
+[quantities.chirikov]
+h5path = "PerturbedEquilibrium/SingularCoupling/chirikov_parameter"
+type = "real_vector"
+extract = "all_real"
+label = "Chirikov parameter"
+noise_threshold = 1e-10
+order = 72
+
+[quantities.toroidal_torque]
+h5path = "PerturbedEquilibrium/Energies/toroidal_torque"
+type = "real_scalar"
+extract = "value"
+label = "toroidal torque [N·m]"
+noise_threshold = 1e-10
+order = 73
+
+# Runtime (special: not from H5)
+[quantities.runtime]
+h5path = ""
+type = "runtime"
+extract = "value"
+label = "Runtime (s)"
+noise_threshold = 0.0
+order = 999
diff --git a/regression-harness/regress.jl b/regression-harness/regress.jl
new file mode 100644
index 0000000000..651a3df8dd
--- /dev/null
+++ b/regression-harness/regress.jl
@@ -0,0 +1,262 @@
+#!/usr/bin/env julia
+
+using Dates, HDF5, JSON, Printf, SHA, SQLite, Tables, TOML
+
+const HARNESS_DIR = @__DIR__
+const REPO_ROOT = abspath(joinpath(HARNESS_DIR, ".."))
+const DEFAULT_DB_PATH = joinpath(HARNESS_DIR, ".regress_cache.sqlite")
+const CASES_DIR = joinpath(HARNESS_DIR, "cases")
+
+include("src/types.jl")
+include("src/env.jl")
+include("src/config.jl")
+include("src/database.jl")
+include("src/utils.jl")
+include("src/extractor.jl")
+include("src/runner.jl")
+include("src/reporter.jl")
+
+function parse_args(args)
+ cases = String[]
+ refs = String[]
+ ref_range = nothing
+ force = false
+ list_cases = false
+ show_qty = nothing
+ show_case = nothing
+ db_path = nothing
+ verbose = false
+ no_instantiate = false
+ no_pin_manifest = false
+ allow_env_mismatch = false
+ fail_on_change = false
+ help = false
+
+ i = 1
+ while i <= length(args)
+ arg = args[i]
+ if arg == "--help" || arg == "-h"
+ help = true
+ i += 1
+ elseif arg == "--force"
+ force = true
+ i += 1
+ elseif arg == "--list-cases"
+ list_cases = true
+ i += 1
+ elseif arg == "--verbose"
+ verbose = true
+ i += 1
+ elseif arg == "--no-instantiate"
+ no_instantiate = true
+ i += 1
+ elseif arg == "--no-pin-manifest"
+ no_pin_manifest = true
+ i += 1
+ elseif arg == "--allow-env-mismatch"
+ allow_env_mismatch = true
+ i += 1
+ elseif arg == "--fail-on-change"
+ fail_on_change = true
+ i += 1
+ elseif arg == "--cases" && i < length(args)
+ cases = split(args[i+1], ",") |> collect .|> strip
+ i += 2
+ elseif arg == "--refs" && i < length(args)
+ refs = split(args[i+1], ",") |> collect .|> strip
+ i += 2
+ elseif arg == "--ref-range" && i < length(args)
+ ref_range = args[i+1]
+ i += 2
+ elseif arg == "--show" && i < length(args)
+ show_qty = args[i+1]
+ i += 2
+ elseif arg == "--case" && i < length(args)
+ show_case = args[i+1]
+ i += 2
+ elseif arg == "--db" && i < length(args)
+ db_path = args[i+1]
+ i += 2
+ else
+ error("Unknown argument: $arg. Use --help for usage.")
+ end
+ end
+
+ return CLIOptions(cases, refs, ref_range, force, list_cases, show_qty, show_case, db_path, verbose,
+ no_instantiate, no_pin_manifest, allow_env_mismatch, fail_on_change, help)
+end
+
+const HELP_TEXT = """
+GPEC Regression Harness
+
+Runs GPEC test cases across multiple git commits and compares numerical outputs
+to detect unintended changes. Results are cached in a local SQLite database.
+All cases in a single invocation share one git worktree (and one instantiate/
+precompile) per commit, so batching cases into one command is substantially
+faster than running them in separate invocations.
+
+Usage:
+ julia --project=regression-harness regression-harness/regress.jl [OPTIONS]
+
+Options:
+ --cases name1,name2 Comma-separated case names (default: all)
+ --refs ref1,ref2,... Comma-separated git refs (branches, tags, SHAs)
+ Use "local" to run on the current working tree
+ --ref-range from..to Expand to all commits in range via git rev-list
+ --force Re-run even if cached
+ --list-cases Print available cases and exit
+ --show qty_name Show historical values for a quantity (requires --case)
+ --case name Single case name (used with --show)
+ --db path Override database path
+ --verbose Print subprocess output
+ --no-instantiate Skip Pkg.instantiate() in subprocess
+ --no-pin-manifest Let each ref resolve its own package set (default: pin the working
+ tree's Manifest.toml into every worktree so source code is the only
+ variable in a comparison)
+ --allow-env-mismatch Reuse cached results produced in a different environment instead of
+ re-running them
+ --fail-on-change Exit non-zero if any tracked quantity changed (for CI use; a failed
+ run always exits non-zero regardless)
+ --help Print this help message
+
+Environment:
+ GPEC_REGRESS_THREADS Threads for GPEC subprocesses (default "auto" = all cores);
+ the actual count is recorded in each run's env fingerprint
+
+Exit status:
+ 0 all runs completed (and, with --fail-on-change, nothing changed)
+ 1 a run failed, or a quantity changed under --fail-on-change
+
+Examples:
+ # Compare two refs
+ julia --project=regression-harness regression-harness/regress.jl \\
+ --cases solovev_n1 --refs develop,HEAD
+
+ # Track across many versions
+ julia --project=regression-harness regression-harness/regress.jl \\
+ --cases solovev_n1 --refs v0.1.0,v0.2.0,develop
+
+ # Expand a commit range
+ julia --project=regression-harness regression-harness/regress.jl \\
+ --cases solovev_n1 --ref-range develop~10..develop
+
+ # List available cases
+ julia --project=regression-harness regression-harness/regress.jl --list-cases
+
+ # Show one quantity's history
+ julia --project=regression-harness regression-harness/regress.jl \\
+ --show et_real --case solovev_n1
+
+ # Compare current working tree against develop
+ julia --project=regression-harness regression-harness/regress.jl \\
+ --cases solovev_n1 --refs develop,local
+"""
+
+function main(args=ARGS)
+ opts = parse_args(args)
+
+ if opts.help
+ print(HELP_TEXT)
+ return
+ end
+
+ # Load all available cases
+ all_cases = load_all_cases(CASES_DIR)
+
+ if opts.list_cases
+ print_cases(all_cases)
+ return
+ end
+
+ # Open database
+ db_path = something(opts.db_path, DEFAULT_DB_PATH)
+ db = open_database(db_path)
+
+ try
+ # Handle --show mode
+ if opts.show_qty !== nothing
+ if opts.show_case === nothing
+ error("--show requires --case")
+ end
+ show_quantity_history(db, opts.show_case, opts.show_qty)
+ return
+ end
+
+ # Resolve which cases to run
+ case_specs = if isempty(opts.cases)
+ collect(values(all_cases))
+ else
+ [all_cases[name] for name in opts.cases if haskey(all_cases, name) || error("Unknown case: $name")]
+ end
+
+ # Resolve refs
+ resolved_refs = if opts.ref_range !== nothing
+ expand_ref_range(opts.ref_range, REPO_ROOT)
+ elseif !isempty(opts.refs)
+ [resolve_ref(ref, REPO_ROOT) for ref in opts.refs]
+ else
+ error("Must specify --refs or --ref-range")
+ end
+
+ if isempty(resolved_refs)
+ error("No commits resolved from the given refs")
+ end
+
+ warn_stale_refs(resolved_refs, REPO_ROOT)
+
+ # Pin every ref to the working tree's package set unless asked not to, so that a
+ # comparison varies source code alone.
+ manifest_path = joinpath(REPO_ROOT, "Manifest.toml")
+ pin_manifest = if opts.no_pin_manifest
+ @warn "Manifest pinning disabled — refs may resolve different package sets, and differences below may not be caused by source changes"
+ nothing
+ elseif !isfile(manifest_path)
+ @warn "No Manifest.toml in the working tree; cannot pin the package set. Run Pkg.instantiate() first."
+ nothing
+ else
+ manifest_path
+ end
+ expected_key = opts.allow_env_mismatch ? nothing : expected_env_key(pin_manifest)
+
+ n_failed = 0
+ n_changed = 0
+
+ # Run every case against each ref, grouped by ref so cases sharing a commit share
+ # one worktree (and one Pkg.instantiate/precompile) instead of paying for it per case.
+ for ref in resolved_refs
+ run_cases_at_ref(db, ref, case_specs, REPO_ROOT;
+ force=opts.force, verbose=opts.verbose,
+ no_instantiate=opts.no_instantiate,
+ pin_manifest=pin_manifest, expected_key=expected_key)
+ end
+
+ # Report, grouped by case as before
+ for case_spec in case_specs
+ println("\n", "="^64)
+ println("Case: $(case_spec.name) — $(case_spec.description)")
+ println("="^64)
+
+ summary = if length(resolved_refs) == 2
+ report_two_ref_comparison(db, case_spec,
+ resolved_refs[1], resolved_refs[2])
+ else
+ report_multi_ref(db, case_spec, resolved_refs)
+ end
+ n_failed += summary.n_failed
+ n_changed += summary.n_changed
+ end
+
+ if n_failed > 0
+ @error "$n_failed run(s) failed — see the reports above"
+ exit(1)
+ end
+ if opts.fail_on_change && n_changed > 0
+ @error "$n_changed quantity/quantities changed (--fail-on-change)"
+ exit(1)
+ end
+ finally
+ close_database(db)
+ end
+end
+
+main()
diff --git a/regression-harness/src/config.jl b/regression-harness/src/config.jl
new file mode 100644
index 0000000000..ad9708f2d4
--- /dev/null
+++ b/regression-harness/src/config.jl
@@ -0,0 +1,100 @@
+"""
+Case definition loading from TOML files.
+"""
+
+"""
+ resolve_case_base(data, filepath)
+
+Merge a variant case onto the case named by its `[case] base` key, read from the sibling file
+`.toml`. The variant must set its own `name`; its `[case]` keys, `[quantities.*]` blocks and
+`[overrides]` entries replace the base's same-named ones, and everything else is inherited.
+A missing base, or a base that itself has a base, is an error.
+"""
+function resolve_case_base(data::Dict{String,Any}, filepath::String)
+ base = get(data["case"], "base", nothing)
+ base === nothing && return data
+ file = basename(filepath)
+ haskey(data["case"], "name") || error("Case $file: a case with a base must set its own [case] name")
+ base_path = joinpath(dirname(filepath), "$base.toml")
+ isfile(base_path) || error("Case $file: base case \"$base\" not found (expected $base_path)")
+ base_data = TOML.parsefile(base_path)
+ haskey(base_data["case"], "base") && error("Case $file: base case \"$base\" itself has a base; chained bases are not supported")
+ merged = Dict{String,Any}()
+ for section in ("case", "quantities", "overrides")
+ merged[section] = merge(get(base_data, section, Dict{String,Any}()), get(data, section, Dict{String,Any}()))
+ end
+ delete!(merged["case"], "base")
+ return merged
+end
+
+function load_case(filepath::String)::CaseSpec
+ data = resolve_case_base(TOML.parsefile(filepath), filepath)
+
+ case_section = data["case"]
+ name = case_section["name"]
+ description = get(case_section, "description", "")
+ kind = get(case_section, "kind", "gpec_run")
+ example_dir = get(case_section, "example_dir", "")
+ precompile_workload = get(case_section, "precompile_workload", false)
+ remove_sections = Vector{String}(get(case_section, "remove_sections", String[]))
+
+ quantities = QuantitySpec[]
+ if haskey(data, "quantities")
+ for (qty_name, qty_data) in data["quantities"]
+ push!(
+ quantities,
+ QuantitySpec(
+ qty_name,
+ get(qty_data, "h5path", ""),
+ qty_data["type"],
+ qty_data["extract"],
+ get(qty_data, "label", qty_name),
+ get(qty_data, "noise_threshold", 1e-10),
+ get(qty_data, "order", 1000)
+ )
+ )
+ end
+ sort!(quantities; by=q -> q.order)
+ end
+
+ overrides = Dict{String,Any}()
+ if haskey(data, "overrides")
+ for (k, v) in data["overrides"]
+ overrides[k] = v
+ end
+ end
+
+ return CaseSpec(name, description, example_dir, quantities, kind, overrides, remove_sections, precompile_workload)
+end
+
+function load_all_cases(cases_dir::String)::Dict{String,CaseSpec}
+ cases = Dict{String,CaseSpec}()
+ if !isdir(cases_dir)
+ @warn "Cases directory not found: $cases_dir"
+ return cases
+ end
+ for filename in readdir(cases_dir)
+ if endswith(filename, ".toml")
+ filepath = joinpath(cases_dir, filename)
+ case = load_case(filepath)
+ cases[case.name] = case
+ end
+ end
+ return cases
+end
+
+function print_cases(cases::Dict{String,CaseSpec})
+ if isempty(cases)
+ println("No cases found.")
+ return
+ end
+ println("Available regression cases:")
+ println("-"^64)
+ for name in sort(collect(keys(cases)))
+ c = cases[name]
+ nqty = length(c.quantities)
+ println(" $(rpad(c.name, 24)) $(rpad(c.description, 40))")
+ loc = c.kind == "computed" ? "kind: computed" : "dir: $(c.example_dir)"
+ println(" $(rpad("", 24)) $loc ($nqty quantities)")
+ end
+end
diff --git a/regression-harness/src/database.jl b/regression-harness/src/database.jl
new file mode 100644
index 0000000000..0165f7806c
--- /dev/null
+++ b/regression-harness/src/database.jl
@@ -0,0 +1,260 @@
+"""
+SQLite database for caching regression results.
+"""
+
+const SCHEMA_SQL = """
+CREATE TABLE IF NOT EXISTS runs (
+ id INTEGER PRIMARY KEY AUTOINCREMENT,
+ commit_hash TEXT NOT NULL,
+ commit_short TEXT NOT NULL,
+ commit_date TEXT,
+ commit_msg TEXT,
+ case_name TEXT NOT NULL,
+ ran_at TEXT NOT NULL,
+ runtime_s REAL,
+ success INTEGER NOT NULL DEFAULT 1,
+ error_msg TEXT,
+ env_key TEXT,
+ julia_version TEXT,
+ os_arch TEXT,
+ manifest_sha TEXT,
+ nthreads INTEGER,
+ blas_threads INTEGER,
+ build_mode TEXT,
+ pinned INTEGER,
+ UNIQUE(commit_hash, case_name)
+);
+
+CREATE TABLE IF NOT EXISTS quantities (
+ id INTEGER PRIMARY KEY AUTOINCREMENT,
+ run_id INTEGER NOT NULL REFERENCES runs(id) ON DELETE CASCADE,
+ qty_name TEXT NOT NULL,
+ qty_label TEXT,
+ value_real REAL,
+ value_int INTEGER,
+ value_text TEXT,
+ value_type TEXT NOT NULL,
+ noise_threshold REAL NOT NULL DEFAULT 0.0,
+ UNIQUE(run_id, qty_name)
+);
+
+CREATE INDEX IF NOT EXISTS idx_runs_commit ON runs(commit_hash);
+CREATE INDEX IF NOT EXISTS idx_runs_case ON runs(case_name);
+CREATE INDEX IF NOT EXISTS idx_quantities_run ON quantities(run_id);
+"""
+
+"""
+Value of a possibly-absent SQLite column, falling back to `default`.
+
+SQLite.jl returns `missing` for NULL while Julia's `something` only skips `nothing`, so columns
+added by a later schema migration (NULL on every pre-existing row) need both cases handled.
+"""
+_column(x, default) = (x === nothing || x === missing) ? default : x
+
+"""
+Materialize SQLite query results as a Vector of NamedTuples.
+"""
+function query_rows(db::SQLite.DB, sql::String, params=())
+ result = DBInterface.execute(db, sql, params)
+ ct = Tables.columntable(result)
+ nrows = length(first(ct))
+ nrows == 0 && return NamedTuple[]
+ return [NamedTuple{keys(ct)}(Tuple(col[i] for col in values(ct))) for i in 1:nrows]
+end
+
+"""
+Environment columns added to `runs` after the original schema shipped. Databases created before
+fingerprinting keep their rows, with NULL in these columns — such rows never match a computed
+`env_key`, so they are re-run rather than silently trusted.
+"""
+const ENV_COLUMNS = [
+ ("env_key", "TEXT"), ("julia_version", "TEXT"), ("os_arch", "TEXT"),
+ ("manifest_sha", "TEXT"), ("nthreads", "INTEGER"), ("blas_threads", "INTEGER"),
+ ("pinned", "INTEGER"), ("build_mode", "TEXT")
+]
+
+"""
+Add any `runs` columns missing from a database created by an earlier harness version.
+"""
+function migrate_schema!(db::SQLite.DB)
+ existing = Set(String[])
+ for row in query_rows(db, "PRAGMA table_info(runs)")
+ push!(existing, String(something(row.name, "")))
+ end
+ for (col, sqltype) in ENV_COLUMNS
+ col in existing && continue
+ DBInterface.execute(db, "ALTER TABLE runs ADD COLUMN $col $sqltype")
+ end
+end
+
+function open_database(path::String)::SQLite.DB
+ db = SQLite.DB(path)
+ query_rows(db, "PRAGMA journal_mode=WAL")
+ DBInterface.execute(db, "PRAGMA foreign_keys=ON")
+ for stmt in split(SCHEMA_SQL, ";")
+ s = strip(stmt)
+ isempty(s) && continue
+ DBInterface.execute(db, s)
+ end
+ migrate_schema!(db)
+ return db
+end
+
+function close_database(db::SQLite.DB)
+ SQLite.close(db)
+end
+
+"""
+Is there a usable cached result for this (commit, case)?
+
+With `expected_key` supplied, a cached run only counts when it was produced in the same
+environment. Rows predating fingerprinting hold NULL and therefore never match — the cache
+entries most likely to be misleading are exactly the ones that get re-run.
+"""
+function is_cached(db::SQLite.DB, commit_hash::String, case_name::String;
+ expected_key::Union{String,Nothing}=nothing)::Bool
+ if expected_key === nothing
+ rows = query_rows(db, "SELECT id FROM runs WHERE commit_hash = ? AND case_name = ? AND success = 1",
+ (commit_hash, case_name))
+ return !isempty(rows)
+ end
+ rows = query_rows(db,
+ "SELECT id FROM runs WHERE commit_hash = ? AND case_name = ? AND success = 1 AND env_key = ?",
+ (commit_hash, case_name, expected_key))
+ return !isempty(rows)
+end
+
+"""
+Environment key stored for a cached run, or `nothing` when the run is absent or predates
+fingerprinting. Used to explain *why* a cached result was rejected.
+"""
+function cached_env_key(db::SQLite.DB, commit_hash::String, case_name::String)::Union{String,Nothing}
+ rows = query_rows(db, "SELECT env_key FROM runs WHERE commit_hash = ? AND case_name = ?",
+ (commit_hash, case_name))
+ isempty(rows) && return nothing
+ key = _column(first(rows).env_key, nothing)
+ key === nothing && return nothing
+ return String(key)
+end
+
+function delete_cached(db::SQLite.DB, commit_hash::String, case_name::String)
+ # ON DELETE CASCADE handles quantities cleanup automatically
+ DBInterface.execute(db, "DELETE FROM runs WHERE commit_hash = ? AND case_name = ?",
+ (commit_hash, case_name))
+end
+
+function store_run(db::SQLite.DB, commit_hash::AbstractString, commit_short::AbstractString,
+ commit_date::AbstractString, commit_msg::AbstractString,
+ case_name::AbstractString, runtime_s::Float64,
+ extracted::Vector{ExtractedQuantity};
+ success::Bool=true, error_msg::AbstractString="",
+ fingerprint::EnvFingerprint=UNKNOWN_ENV)
+ ran_at = Dates.format(Dates.now(), "yyyy-mm-ddTHH:MM:SS")
+
+ SQLite.transaction(db) do
+ delete_cached(db, String(commit_hash), String(case_name))
+
+ DBInterface.execute(db,
+ """INSERT INTO runs
+ (commit_hash, commit_short, commit_date, commit_msg, case_name, ran_at, runtime_s, success, error_msg,
+ env_key, julia_version, os_arch, manifest_sha, nthreads, blas_threads, pinned, build_mode)
+ VALUES (?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?)""",
+ (String(commit_hash), String(commit_short), String(commit_date), String(commit_msg),
+ String(case_name), ran_at, runtime_s, success ? 1 : 0, String(error_msg),
+ env_key(fingerprint), fingerprint.julia_version, fingerprint.os_arch,
+ fingerprint.manifest_sha, fingerprint.nthreads, fingerprint.blas_threads,
+ fingerprint.pinned ? 1 : 0, fingerprint.build_mode))
+
+ run_id = SQLite.last_insert_rowid(db)
+
+ for eq in extracted
+ DBInterface.execute(db,
+ """INSERT INTO quantities
+ (run_id, qty_name, qty_label, value_real, value_int, value_text, value_type, noise_threshold)
+ VALUES (?, ?, ?, ?, ?, ?, ?, ?)""",
+ (run_id, eq.name, eq.label, eq.value_real, eq.value_int, eq.value_text,
+ eq.value_type, eq.noise_threshold))
+ end
+ end
+end
+
+function store_failed_run(db::SQLite.DB, commit_hash::AbstractString, commit_short::AbstractString,
+ commit_date::AbstractString, commit_msg::AbstractString,
+ case_name::AbstractString, error_msg::AbstractString)
+ ran_at = Dates.format(Dates.now(), "yyyy-mm-ddTHH:MM:SS")
+ delete_cached(db, String(commit_hash), String(case_name))
+ DBInterface.execute(db,
+ """INSERT INTO runs
+ (commit_hash, commit_short, commit_date, commit_msg, case_name, ran_at, runtime_s, success, error_msg)
+ VALUES (?, ?, ?, ?, ?, ?, ?, ?, ?)""",
+ (String(commit_hash), String(commit_short), String(commit_date), String(commit_msg),
+ String(case_name), ran_at, 0.0, 0, String(error_msg)))
+end
+
+"""
+Get all quantities for a (commit, case) pair. Returns Dict{qty_name => NamedTuple}.
+"""
+function get_quantities(db::SQLite.DB, commit_hash::String, case_name::String)
+ results = Dict{String,NamedTuple}()
+ rows = query_rows(db,
+ """SELECT q.qty_name, q.qty_label, q.value_real, q.value_int, q.value_text,
+ q.value_type, q.noise_threshold
+ FROM quantities q
+ JOIN runs r ON q.run_id = r.id
+ WHERE r.commit_hash = ? AND r.case_name = ?""",
+ (commit_hash, case_name))
+
+ for row in rows
+ name = something(row.qty_name, "")
+ results[name] = (
+ label=something(row.qty_label, name),
+ value_real=row.value_real,
+ value_int=row.value_int,
+ value_text=row.value_text,
+ value_type=something(row.value_type, "missing"),
+ noise_threshold=something(row.noise_threshold, 0.0)
+ )
+ end
+ return results
+end
+
+"""
+Get run info for a (commit, case) pair. Returns NamedTuple or nothing.
+"""
+function get_run_info(db::SQLite.DB, commit_hash::String, case_name::String)
+ rows = query_rows(db,
+ """SELECT commit_short, commit_date, commit_msg, runtime_s, success, error_msg,
+ julia_version, os_arch, manifest_sha, nthreads, blas_threads, pinned, build_mode
+ FROM runs WHERE commit_hash = ? AND case_name = ?""",
+ (commit_hash, case_name))
+ isempty(rows) && return nothing
+ row = first(rows)
+ fingerprint = EnvFingerprint(
+ String(_column(row.julia_version, "")),
+ String(_column(row.os_arch, "")),
+ String(_column(row.manifest_sha, "")),
+ Int(_column(row.nthreads, -1)),
+ Int(_column(row.blas_threads, -1)),
+ String(_column(row.build_mode, "")),
+ _column(row.pinned, 0) == 1
+ )
+ return (
+ commit_short=something(row.commit_short, ""),
+ commit_date=something(row.commit_date, ""),
+ commit_msg=something(row.commit_msg, ""),
+ runtime_s=something(row.runtime_s, 0.0),
+ success=coalesce(row.success, 0) == 1,
+ error_msg=something(row.error_msg, ""),
+ fingerprint=fingerprint
+ )
+end
+
+"""
+Get all cached runs for a case, ordered by commit date.
+"""
+function get_all_runs_for_case(db::SQLite.DB, case_name::String)
+ return query_rows(db,
+ """SELECT commit_hash, commit_short, commit_date, commit_msg, runtime_s, success
+ FROM runs WHERE case_name = ? ORDER BY commit_date""",
+ (case_name,))
+end
diff --git a/regression-harness/src/env.jl b/regression-harness/src/env.jl
new file mode 100644
index 0000000000..3734674da4
--- /dev/null
+++ b/regression-harness/src/env.jl
@@ -0,0 +1,126 @@
+"""
+Environment fingerprinting.
+
+A cached regression result is only comparable to a fresh one if both were produced by the same
+Julia, on the same machine, against the same package set. Because `Manifest.toml` is untracked,
+a worktree checkout resolves whatever is newest at run time, so two runs of the *same source*
+can differ by a package set — and machine-epsilon differences in library math are amplified by
+the adaptive ODE controller into large apparent regressions. The fingerprint below makes that
+confound visible (and, by default, invalidating) instead of silent.
+"""
+
+"""
+Identity of the environment a run was produced in.
+
+## Fields
+
+ - `julia_version::String` — version of the `julia` that ran GPEC
+ - `os_arch::String` — `Sys.MACHINE` of the running host
+ - `manifest_sha::String` — SHA-256 of the `Manifest.toml` the run resolved against ("" if absent)
+ - `nthreads::Int` — `Threads.nthreads()` in the run (-1 if unknown)
+ - `blas_threads::Int` — `BLAS.get_num_threads()` in the run (-1 if unknown)
+ - `build_mode::String` — "aot" if the loaded GPEC was built with its precompile workload, "jit" otherwise ("" if unknown)
+ - `pinned::Bool` — whether the harness copied its own Manifest into the run's project
+"""
+struct EnvFingerprint
+ julia_version::String
+ os_arch::String
+ manifest_sha::String
+ nthreads::Int
+ blas_threads::Int
+ build_mode::String
+ pinned::Bool
+end
+
+const UNKNOWN_ENV = EnvFingerprint("", "", "", -1, -1, "", false)
+
+"""
+Cache key for an environment.
+
+Deliberately built from only the three fields that are knowable *before* a run: the Julia
+version, the host, and the package set the run will be pinned to. Thread counts are recorded and
+reported but not keyed, because the harness does not force them (see `--threads` in the CLI) and
+so cannot predict them ahead of a run.
+
+When the Manifest is not pinned, the package set is unknowable in advance and the key records
+`unpinned`; the resolved Manifest hash is still stored per run for display and mismatch warnings.
+"""
+function env_key(julia_version::AbstractString, os_arch::AbstractString, manifest_mode::AbstractString)::String
+ return bytes2hex(SHA.sha256("$(julia_version)|$(os_arch)|$(manifest_mode)"))[1:16]
+end
+
+env_key(fp::EnvFingerprint) = env_key(fp.julia_version, fp.os_arch, fp.pinned ? fp.manifest_sha : "unpinned")
+
+"""
+SHA-256 of a file, or "" when it does not exist.
+"""
+function file_sha256(path::AbstractString)::String
+ isfile(path) || return ""
+ return bytes2hex(SHA.sha256(read(path)))
+end
+
+"""
+Version string of the `julia` the harness will launch for subprocess runs.
+
+This is not necessarily the Julia running the harness itself, so it is probed rather than read
+from `VERSION`.
+"""
+function subprocess_julia_version()::String
+ try
+ out = strip(read(`julia --version`, String))
+ m = match(r"(\d+\.\d+\.\d+\S*)", out)
+ return m === nothing ? out : m.captures[1]
+ catch
+ return "unknown"
+ end
+end
+
+"""
+The environment key that runs launched *now* will carry.
+
+`manifest_path` is the Manifest the harness will pin into each worktree; pass `nothing` when
+pinning is disabled.
+"""
+function expected_env_key(manifest_path::Union{String,Nothing})::String
+ mode = manifest_path === nothing ? "unpinned" : file_sha256(manifest_path)
+ return env_key(subprocess_julia_version(), string(Sys.MACHINE), mode)
+end
+
+"""
+Parse the `key=value` run-info file written by a run subprocess.
+
+Returns `(runtime_s, fingerprint)`. A missing or malformed file yields `NaN` and `UNKNOWN_ENV`
+rather than throwing, so a run that produced output but no metadata still reports its numbers.
+"""
+function read_runinfo(path::String, pinned::Bool)
+ isfile(path) || return (NaN, UNKNOWN_ENV)
+ fields = Dict{String,String}()
+ for line in eachline(path)
+ parts = split(line, '='; limit=2)
+ length(parts) == 2 && (fields[strip(parts[1])] = strip(parts[2]))
+ end
+ getf = (k, d) -> get(fields, k, d)
+ runtime_s = tryparse(Float64, getf("runtime_s", ""))
+ fp = EnvFingerprint(
+ getf("julia_version", ""),
+ getf("os_arch", ""),
+ getf("manifest_sha", ""),
+ something(tryparse(Int, getf("nthreads", "")), -1),
+ something(tryparse(Int, getf("blas_threads", "")), -1),
+ getf("build_mode", ""),
+ pinned
+ )
+ return (something(runtime_s, NaN), fp)
+end
+
+"""
+One-line human-readable summary of an environment, for report headers.
+"""
+function describe_env(fp::EnvFingerprint)::String
+ isempty(fp.julia_version) && return "environment unknown (cached before fingerprinting)"
+ mani = isempty(fp.manifest_sha) ? "no Manifest" : "manifest " * fp.manifest_sha[1:min(8, end)]
+ pin = fp.pinned ? "pinned" : "unpinned"
+ threads = "$(fp.nthreads) thread$(fp.nthreads == 1 ? "" : "s")/$(fp.blas_threads) BLAS"
+ mode = isempty(fp.build_mode) ? "" : ", $(fp.build_mode) build"
+ return "julia $(fp.julia_version), $(fp.os_arch), $mani ($pin), $threads$mode"
+end
diff --git a/regression-harness/src/extractor.jl b/regression-harness/src/extractor.jl
new file mode 100644
index 0000000000..222312553a
--- /dev/null
+++ b/regression-harness/src/extractor.jl
@@ -0,0 +1,238 @@
+"""
+HDF5 quantity extraction engine.
+"""
+
+"""
+Extract all quantities from a gpec.h5 file according to case spec.
+Returns a Vector{ExtractedQuantity}.
+
+Case TOMLs carry current-schema paths only; outputs from refs predating a schema
+rename extract as "missing" unless their quantities are already cached. Re-baseline
+old refs with `--force` after a rename rather than maintaining path translations.
+"""
+function extract_quantities(h5path::String, qty_specs::Vector{QuantitySpec}, runtime_s::Float64)::Vector{ExtractedQuantity}
+ results = ExtractedQuantity[]
+
+ h5open(h5path, "r") do fid
+ for spec in qty_specs
+ if spec.type == "runtime"
+ push!(results, ExtractedQuantity(
+ spec.name, spec.label,
+ runtime_s, nothing, nothing,
+ "real", spec.noise_threshold))
+ continue
+ end
+
+ # Check if the H5 path exists
+ if !haskey(fid, spec.h5path)
+ push!(results, ExtractedQuantity(
+ spec.name, spec.label,
+ nothing, nothing, nothing,
+ "missing", spec.noise_threshold))
+ continue
+ end
+
+ raw = read(fid[spec.h5path])
+ eq = apply_extraction(spec, raw)
+ push!(results, eq)
+ end
+ end
+
+ return results
+end
+
+"""
+Apply an extraction rule to raw HDF5 data, producing an ExtractedQuantity.
+"""
+function apply_extraction(spec::QuantitySpec, raw)::ExtractedQuantity
+ name = spec.name
+ label = spec.label
+ threshold = spec.noise_threshold
+
+ if spec.extract == "value"
+ if raw isa Integer
+ return ExtractedQuantity(name, label, nothing, Int(raw), nothing, "integer", threshold)
+ else
+ return ExtractedQuantity(name, label, Float64(raw), nothing, nothing, "real", threshold)
+ end
+
+ elseif spec.extract == "real_first"
+ val = real(raw[1])
+ return ExtractedQuantity(name, label, Float64(val), nothing, nothing, "real", threshold)
+
+ elseif spec.extract == "imag_first"
+ val = imag(raw[1])
+ return ExtractedQuantity(name, label, Float64(val), nothing, nothing, "real", threshold)
+
+ elseif spec.extract == "abs_first"
+ val = abs(raw[1])
+ return ExtractedQuantity(name, label, Float64(val), nothing, nothing, "real", threshold)
+
+ elseif spec.extract == "norm"
+ val = sqrt(sum(abs2, raw))
+ return ExtractedQuantity(name, label, Float64(val), nothing, nothing, "real", threshold)
+
+ elseif spec.extract == "all_real"
+ arr = Float64.(real.(raw))
+ # allownan: SLAYER γ/Q_root are NaN when no dispersion root is found —
+ # a legitimate state to record so a future root appearing flags a diff.
+ json_str = JSON.json(arr; allownan=true)
+ return ExtractedQuantity(name, label, nothing, nothing, json_str, "json_array", threshold)
+
+ elseif startswith(spec.extract, "first_") && endswith(spec.extract, "_complex")
+ # "first_N_complex": [re, im] pairs of the leading N elements of a complex
+ # vector — the complex-preserving sibling of "first_N".
+ nkeep = parse(Int, spec.extract[(length("first_")+1):(end-length("_complex"))])
+ pairs = [[real(x), imag(x)] for x in raw[1:min(nkeep, length(raw))]]
+ json_str = JSON.json(pairs; allownan=true)
+ return ExtractedQuantity(name, label, nothing, nothing, json_str, "json_array", threshold)
+
+ elseif startswith(spec.extract, "first_")
+ # "first_N": real values of the leading N vector elements only. Used to
+ # golden-pin the inner (trustworthy) rational surfaces while ignoring
+ # edge surfaces where the Δ'/γ contour search is numerically unreliable.
+ # Real data only — use "first_N_complex" for complex datasets.
+ nkeep = parse(Int, spec.extract[(length("first_")+1):end])
+ arr = Float64.(real.(raw))[1:min(nkeep, length(raw))]
+ json_str = JSON.json(arr; allownan=true)
+ return ExtractedQuantity(name, label, nothing, nothing, json_str, "json_array", threshold)
+
+ elseif spec.extract == "all_complex"
+ pairs = [[real(x), imag(x)] for x in raw]
+ json_str = JSON.json(pairs; allownan=true)
+ return ExtractedQuantity(name, label, nothing, nothing, json_str, "json_array", threshold)
+
+ elseif spec.extract == "diagonal_complex"
+ # Extract the diagonal of a square matrix as a complex array.
+ # Use for tracking per-surface BVP Δ' from SingularSurfaces/delta_prime_matrix.
+ ndims(raw) == 2 && size(raw, 1) == size(raw, 2) ||
+ error("diagonal_complex requires a square 2-D matrix; got size $(size(raw))")
+ diag_vec = [raw[i, i] for i in 1:size(raw, 1)]
+ pairs = [[real(x), imag(x)] for x in diag_vec]
+ json_str = JSON.json(pairs; allownan=true)
+ return ExtractedQuantity(name, label, nothing, nothing, json_str, "json_array", threshold)
+
+ elseif spec.extract == "checksum"
+ bytes = reinterpret(UInt8, vec(collect(raw)))
+ hash = bytes2hex(sha256(bytes))
+ return ExtractedQuantity(name, label, nothing, nothing, hash, "checksum", threshold)
+
+ else
+ error("Unknown extraction mode: $(spec.extract)")
+ end
+end
+
+"""
+Compute absolute difference between two JSON-parsed elements (scalars, pairs, or nested arrays).
+"""
+function _json_element_diff(a, b)::Float64
+ if a isa Number && b isa Number
+ # Two NaN values denote the same "no result" state (e.g. SLAYER
+ # Q_root when no dispersion root is found) — treat as identical.
+ (isnan(Float64(a)) && isnan(Float64(b))) && return 0.0
+ return abs(Float64(a) - Float64(b))
+ elseif a isa Vector && b isa Vector
+ return sqrt(sum(_json_element_diff(ai, bi)^2 for (ai, bi) in zip(a, b)))
+ else
+ return Inf
+ end
+end
+
+"""
+Compute absolute value/magnitude of a JSON-parsed element.
+"""
+function _json_element_abs(x)::Float64
+ if x isa Number
+ # NaN denotes a "no result" state (e.g. SLAYER Q_root with no root);
+ # treat as 0 magnitude so it doesn't poison a vector's reference norm.
+ isnan(Float64(x)) && return 0.0
+ return abs(Float64(x))
+ elseif x isa Vector
+ return sqrt(sum(_json_element_abs(xi)^2 for xi in x))
+ else
+ return 0.0
+ end
+end
+
+"""
+Compare two extracted values, `q1` from the baseline ref and `q2` from the newer one. Returns
+(abs_diff, rel_diff, status). For arrays, returns max element-wise absolute diff. A quantity
+missing from both refs is `N/A`; one that disappears or changes storage type is a change, and
+one that only the newer ref has is `NEW`.
+"""
+function compare_values(q1::NamedTuple, q2::NamedTuple)
+ vtype = q1.value_type
+
+ if vtype == "missing" && q2.value_type == "missing"
+ return (NaN, NaN, "N/A")
+ elseif q2.value_type == "missing"
+ return (NaN, NaN, "CHANGED (missing)")
+ elseif vtype == "missing"
+ return (NaN, NaN, "NEW")
+ end
+
+ # Storage type differs between refs (e.g. a quantity whose schema changed from a
+ # vector to a scalar across the two commits); the values are not directly comparable.
+ if vtype != q2.value_type
+ return (NaN, NaN, "CHANGED (type)")
+ end
+
+ threshold = q1.noise_threshold
+
+ if vtype == "real"
+ v1 = q1.value_real
+ v2 = q2.value_real
+ if v1 === nothing || v2 === nothing
+ return (NaN, NaN, "N/A")
+ end
+ abs_diff = abs(v2 - v1)
+ rel_diff = v1 == 0.0 ? (v2 == 0.0 ? 0.0 : Inf) : abs_diff / abs(v1)
+ status = abs_diff <= threshold ? "OK" : "CHANGED"
+ return (abs_diff, rel_diff, status)
+
+ elseif vtype == "integer"
+ v1 = q1.value_int
+ v2 = q2.value_int
+ if v1 === nothing || v2 === nothing
+ return (NaN, NaN, "N/A")
+ end
+ abs_diff = Float64(abs(v2 - v1))
+ rel_diff = v1 == 0 ? (v2 == 0 ? 0.0 : Inf) : abs_diff / abs(v1)
+ status = abs_diff <= threshold ? "OK" : "CHANGED"
+ return (abs_diff, rel_diff, status)
+
+ elseif vtype == "json_array"
+ t1 = q1.value_text
+ t2 = q2.value_text
+ if t1 === nothing || t2 === nothing
+ return (NaN, NaN, "N/A")
+ end
+ arr1 = JSON.parse(t1; allownan=true)
+ arr2 = JSON.parse(t2; allownan=true)
+ if length(arr1) != length(arr2)
+ return (NaN, NaN, "CHANGED (length)")
+ end
+ max_diff = 0.0
+ for (a, b) in zip(arr1, arr2)
+ d = _json_element_diff(a, b)
+ max_diff = max(max_diff, d)
+ end
+ # For relative diff, use max absolute value as reference
+ max_val = maximum(x -> _json_element_abs(x), arr1; init=0.0)
+ rel_diff = max_val == 0.0 ? (max_diff == 0.0 ? 0.0 : Inf) : max_diff / max_val
+ status = max_diff <= threshold ? "OK" : "CHANGED"
+ return (max_diff, rel_diff, status)
+
+ elseif vtype == "checksum"
+ t1 = q1.value_text
+ t2 = q2.value_text
+ if t1 === nothing || t2 === nothing
+ return (NaN, NaN, "N/A")
+ end
+ status = t1 == t2 ? "OK" : "CHANGED"
+ return (0.0, 0.0, status)
+
+ else
+ return (NaN, NaN, "N/A")
+ end
+end
diff --git a/regression-harness/src/reporter.jl b/regression-harness/src/reporter.jl
new file mode 100644
index 0000000000..d2e6990edc
--- /dev/null
+++ b/regression-harness/src/reporter.jl
@@ -0,0 +1,468 @@
+"""
+Reporter: formats comparison tables for stdout output.
+"""
+
+"""
+Compress a stored error message into a single-line snippet for the report
+banner. Picks the most informative line (a Julia ERROR/UndefVarError if
+present) and truncates to keep the report compact.
+"""
+function _short_err(msg)::String
+ (msg === nothing || msg === missing) && return "(no message)"
+ s = String(msg)
+ isempty(strip(s)) && return "(empty)"
+ lines = filter(!isempty, strip.(split(s, '\n')))
+ isempty(lines) && return "(empty)"
+ pick = something(findfirst(l -> startswith(l, "ERROR:") || occursin("Error", l), lines),
+ length(lines))
+ line = lines[pick]
+ return length(line) > 200 ? line[1:200] * "..." : line
+end
+
+"""
+Format a value for display. Returns an unpadded string.
+"""
+function format_value(q::NamedTuple)::String
+ if q.value_type == "missing"
+ return "N/A"
+ elseif q.value_type == "real"
+ v = q.value_real
+ v === nothing && return "N/A"
+ return @sprintf("%.6e", v)
+ elseif q.value_type == "integer"
+ v = q.value_int
+ v === nothing && return "N/A"
+ return string(v)
+ elseif q.value_type == "json_array"
+ t = q.value_text
+ t === nothing && return "N/A"
+ arr = JSON.parse(t; allownan=true)
+ return "[$(length(arr)) elem]"
+ elseif q.value_type == "checksum"
+ t = q.value_text
+ t === nothing && return "N/A"
+ return t[1:min(12, length(t))] * "..."
+ else
+ return "?"
+ end
+end
+
+"""
+Print a banner when two compared runs did not share an environment.
+
+Source code is only the sole variable when Julia, host, package set and thread counts all match.
+Anything else here means part of the reported difference may be the environment, not the code.
+"""
+function _warn_env_difference(fp1::EnvFingerprint, fp2::EnvFingerprint)
+ (fp1 === UNKNOWN_ENV || fp2 === UNKNOWN_ENV) && return
+ (isempty(fp1.julia_version) || isempty(fp2.julia_version)) && return
+ differences = String[]
+ fp1.julia_version != fp2.julia_version && push!(differences, "julia $(fp1.julia_version) vs $(fp2.julia_version)")
+ fp1.os_arch != fp2.os_arch && push!(differences, "host $(fp1.os_arch) vs $(fp2.os_arch)")
+ fp1.manifest_sha != fp2.manifest_sha && push!(differences, "different package sets (Manifest hashes differ)")
+ fp1.nthreads != fp2.nthreads && push!(differences, "$(fp1.nthreads) vs $(fp2.nthreads) Julia threads")
+ fp1.blas_threads != fp2.blas_threads && push!(differences, "$(fp1.blas_threads) vs $(fp2.blas_threads) BLAS threads")
+ fp1.build_mode != fp2.build_mode && !isempty(fp1.build_mode) && !isempty(fp2.build_mode) &&
+ push!(differences, "$(fp1.build_mode) vs $(fp2.build_mode) build (precompile workload); results differ between build modes")
+ isempty(differences) && return
+ println()
+ println("!! ENVIRONMENTS DIFFER — source code is not the only variable in this comparison:")
+ for d in differences
+ println(" - $d")
+ end
+ println(" Differences below may be environment artifacts. Re-run with --force to rebuild")
+ println(" both refs in the current environment.")
+end
+
+"""
+Format a diff value for display.
+"""
+function format_diff(abs_diff::Float64, rel_diff::Float64, status::String, value_type::String)::String
+ if status == "N/A" || isnan(abs_diff)
+ return "N/A"
+ end
+ if status == "OK"
+ if value_type == "checksum"
+ return "identical"
+ end
+ return @sprintf("%.1e", abs_diff)
+ end
+ if contains(status, "length")
+ return status
+ end
+ return @sprintf("%.3e (%.2f%%)", abs_diff, rel_diff * 100)
+end
+
+"""
+Helper: print a row of padded columns.
+"""
+function _print_row(cols::Vector{String}, widths::Vector{Int})
+ parts = [rpad(cols[i], widths[i]) for i in eachindex(cols)]
+ println(join(parts, " "))
+end
+
+"""
+Print a two-ref comparison report for a single case.
+"""
+function report_two_ref_comparison(db::SQLite.DB, case_spec::CaseSpec,
+ ref1::ResolvedRef, ref2::ResolvedRef)
+ info1 = get_run_info(db, ref1.commit_hash, case_spec.name)
+ info2 = get_run_info(db, ref2.commit_hash, case_spec.name)
+
+ println()
+ println("Regression Report: $(case_spec.name)")
+
+ if info1 === nothing
+ println("ERROR: No results for ref 1 ($(ref1.name))")
+ return (n_ok=0, n_changed=0, n_missing=0, n_new=0, n_failed=1)
+ end
+ if info2 === nothing
+ println("ERROR: No results for ref 2 ($(ref2.name))")
+ return (n_ok=0, n_changed=0, n_missing=0, n_new=0, n_failed=1)
+ end
+
+ failed1 = !info1.success
+ failed2 = !info2.success
+
+ q1_all = failed1 ? Dict{String,NamedTuple}() :
+ get_quantities(db, ref1.commit_hash, case_spec.name)
+ q2_all = failed2 ? Dict{String,NamedTuple}() :
+ get_quantities(db, ref2.commit_hash, case_spec.name)
+
+ # Pre-compute all rows: (label, v1, v2, diff, status)
+ header = ["Quantity", ref1.name, ref2.name, "Diff", "Status"]
+ rows = Vector{Vector{String}}()
+ n_ok = 0
+ n_changed = 0
+ n_missing = 0
+ n_new = 0
+
+ # Helper: pick the value-cell text for one ref/quantity, accounting for
+ # whole-ref failure (which should render as "FAILED" rather than "N/A").
+ cell = (failed::Bool, qs::Dict, qname::String) -> begin
+ failed && return "FAILED"
+ return haskey(qs, qname) ? format_value(qs[qname]) : "N/A"
+ end
+ runtime_cell = (failed::Bool, qs::Dict, qname::String) -> begin
+ failed && return "FAILED"
+ (haskey(qs, qname) && qs[qname].value_real !== nothing) ?
+ @sprintf("%.1fs", qs[qname].value_real) : "N/A"
+ end
+
+ for spec in case_spec.quantities
+ qname = spec.name
+
+ # Skip silently only when neither ref has the quantity AND neither failed
+ # (a failed ref still gets a row with FAILED markers).
+ if !failed1 && !failed2 && !haskey(q1_all, qname) && !haskey(q2_all, qname)
+ n_missing += 1
+ continue
+ end
+
+ if spec.type == "runtime"
+ v1 = runtime_cell(failed1, q1_all, qname)
+ v2 = runtime_cell(failed2, q2_all, qname)
+ push!(rows, [spec.label, v1, v2, "", "--"])
+ continue
+ end
+
+ has1 = haskey(q1_all, qname)
+ has2 = haskey(q2_all, qname)
+ if failed1 || failed2 || !has1 || !has2
+ v1 = cell(failed1, q1_all, qname)
+ v2 = cell(failed2, q2_all, qname)
+ status_label = (failed1 || failed2) ? "FAILED" : "N/A"
+ push!(rows, [spec.label, v1, v2, "", status_label])
+ n_missing += 1
+ continue
+ end
+
+ q1 = q1_all[qname]
+ q2 = q2_all[qname]
+ abs_diff, rel_diff, status = compare_values(q1, q2)
+ st = startswith(status, "CHANGED") ? "** $status **" : status
+ push!(rows, [spec.label, format_value(q1), format_value(q2),
+ format_diff(abs_diff, rel_diff, status, q1.value_type), st])
+
+ if status == "OK"
+ n_ok += 1
+ elseif startswith(status, "CHANGED")
+ n_changed += 1
+ elseif status == "NEW"
+ n_new += 1
+ else
+ n_missing += 1
+ end
+ end
+
+ # Derive column widths from header + all row content
+ ncols = length(header)
+ widths = [length(header[i]) for i in 1:ncols]
+ for row in rows
+ for i in 1:ncols
+ widths[i] = max(widths[i], length(row[i]))
+ end
+ end
+
+ total_w = sum(widths) + 2 * (ncols - 1)
+
+ println("="^total_w)
+ date1 = length(info1.commit_date) >= 10 ? info1.commit_date[1:10] : info1.commit_date
+ date2 = length(info2.commit_date) >= 10 ? info2.commit_date[1:10] : info2.commit_date
+ tag1 = failed1 ? " (FAILED)" : ""
+ tag2 = failed2 ? " (FAILED)" : ""
+ println("Ref 1: $(ref1.name) @ $(info1.commit_short) ($date1)$tag1")
+ println(" env: $(describe_env(info1.fingerprint))")
+ println("Ref 2: $(ref2.name) @ $(info2.commit_short) ($date2)$tag2")
+ println(" env: $(describe_env(info2.fingerprint))")
+ _warn_env_difference(info1.fingerprint, info2.fingerprint)
+ if failed1
+ println(" Ref 1 error: $(_short_err(info1.error_msg))")
+ end
+ if failed2
+ println(" Ref 2 error: $(_short_err(info2.error_msg))")
+ end
+ println("-"^total_w)
+
+ _print_row(header, widths)
+ println("-"^total_w)
+ for row in rows
+ _print_row(row, widths)
+ end
+
+ println("="^total_w)
+ parts = String[]
+ n_changed > 0 && push!(parts, "$n_changed changed")
+ n_ok > 0 && push!(parts, "$n_ok unchanged")
+ n_new > 0 && push!(parts, "$n_new new")
+ n_missing > 0 && push!(parts, "$n_missing missing/N/A")
+ println("Summary: ", join(parts, ", "))
+ println()
+ return (n_ok=n_ok, n_changed=n_changed, n_missing=n_missing, n_new=n_new,
+ n_failed=count(identity, (failed1, failed2)))
+end
+
+"""
+Print a multi-ref tracking report for a single case.
+One row per quantity, one column per ref.
+"""
+function report_multi_ref(db::SQLite.DB, case_spec::CaseSpec,
+ refs::Vector{ResolvedRef})
+ run_infos = [get_run_info(db, ref.commit_hash, case_spec.name) for ref in refs]
+ failed_mask = [info === nothing || !info.success for info in run_infos]
+ all_qs = [
+ begin
+ info = run_infos[i]
+ (info !== nothing && info.success) ? get_quantities(db, refs[i].commit_hash, case_spec.name) : Dict{String,NamedTuple}()
+ end for i in eachindex(refs)
+ ]
+
+ show_diff = length(refs) >= 2
+ ref_names = [ref.name for ref in refs]
+
+ # Build header
+ header = vcat(["Quantity"], ref_names)
+ if show_diff
+ push!(header, "Δ prev")
+ push!(header, "Status")
+ end
+ ncols = length(header)
+
+ # Pre-compute rows
+ rows = Vector{Vector{String}}()
+ n_ok = 0
+ n_changed = 0
+ n_missing = 0
+ n_new = 0
+
+ for spec in case_spec.quantities
+ qname = spec.name
+ any_failed = any(failed_mask)
+ any_present = any(haskey(qs, qname) for qs in all_qs)
+ # Skip silently only when nothing is present and nothing failed.
+ if !any_failed && !any_present
+ n_missing += 1
+ continue
+ end
+
+ row = [spec.label]
+
+ if spec.type == "runtime"
+ for (i, qs) in enumerate(all_qs)
+ val = if failed_mask[i]
+ "FAILED"
+ elseif haskey(qs, qname) && qs[qname].value_real !== nothing
+ @sprintf("%.1fs", qs[qname].value_real)
+ else
+ "N/A"
+ end
+ push!(row, val)
+ end
+ if show_diff
+ push!(row, "")
+ push!(row, "--")
+ end
+ push!(rows, row)
+ continue
+ end
+
+ for (i, qs) in enumerate(all_qs)
+ if failed_mask[i]
+ push!(row, "FAILED")
+ else
+ push!(row, haskey(qs, qname) ? format_value(qs[qname]) : "N/A")
+ end
+ end
+
+ if show_diff
+ last_failed = failed_mask[end]
+ prev_failed = failed_mask[end-1]
+ q_last = haskey(all_qs[end], qname) ? all_qs[end][qname] : nothing
+ q_prev = haskey(all_qs[end-1], qname) ? all_qs[end-1][qname] : nothing
+ if q_last !== nothing && q_prev !== nothing
+ abs_diff, rel_diff, status = compare_values(q_prev, q_last)
+ st = startswith(status, "CHANGED") ? "** $status **" : status
+ push!(row, format_diff(abs_diff, rel_diff, status, q_prev.value_type))
+ push!(row, st)
+ if status == "OK"
+ n_ok += 1
+ elseif startswith(status, "CHANGED")
+ n_changed += 1
+ elseif status == "NEW"
+ n_new += 1
+ else
+ n_missing += 1
+ end
+ elseif last_failed || prev_failed
+ push!(row, "")
+ push!(row, "FAILED")
+ n_missing += 1
+ else
+ push!(row, "N/A")
+ push!(row, "N/A")
+ n_missing += 1
+ end
+ end
+
+ push!(rows, row)
+ end
+
+ # Derive column widths
+ widths = [length(header[i]) for i in 1:ncols]
+ for row in rows
+ for i in 1:ncols
+ widths[i] = max(widths[i], length(row[i]))
+ end
+ end
+ total_w = sum(widths) + 2 * (ncols - 1)
+
+ println()
+ println("Regression Tracking: $(case_spec.name)")
+ println("="^total_w)
+
+ for (i, ref) in enumerate(refs)
+ info = run_infos[i]
+ if info !== nothing
+ date_str = length(info.commit_date) >= 10 ? info.commit_date[1:10] : info.commit_date
+ status_str = info.success ? "" : " (FAILED)"
+ println("Ref $(i): $(ref.name) @ $(info.commit_short) ($date_str)$status_str")
+ println(" env: $(describe_env(info.fingerprint))")
+ if !info.success
+ println(" Ref $(i) error: $(_short_err(info.error_msg))")
+ end
+ else
+ println("Ref $(i): $(ref.name) (no data)")
+ end
+ end
+ if length(refs) >= 2
+ last_two = filter(!isnothing, run_infos[(end-1):end])
+ length(last_two) == 2 && _warn_env_difference(last_two[1].fingerprint, last_two[2].fingerprint)
+ end
+ println("-"^total_w)
+
+ _print_row(header, widths)
+ println("-"^total_w)
+ for row in rows
+ _print_row(row, widths)
+ end
+
+ println("="^total_w)
+ if show_diff
+ parts = String[]
+ n_changed > 0 && push!(parts, "$n_changed changed")
+ n_ok > 0 && push!(parts, "$n_ok unchanged")
+ n_new > 0 && push!(parts, "$n_new new")
+ n_missing > 0 && push!(parts, "$n_missing missing/N/A")
+ println("Summary (last vs prev): ", join(parts, ", "))
+ end
+ println()
+ return (n_ok=n_ok, n_changed=n_changed, n_missing=n_missing, n_new=n_new,
+ n_failed=count(identity, failed_mask))
+end
+
+"""
+Show the history of a single quantity for a case (--show mode).
+"""
+function show_quantity_history(db::SQLite.DB, case_name::String, qty_name::String)
+ runs = get_all_runs_for_case(db, case_name)
+ if isempty(runs)
+ println("No cached runs found for case '$case_name'")
+ return
+ end
+
+ header = ["Commit", "Date", "Value", "Δ from prev", "Status"]
+ ncols = length(header)
+ rows = Vector{Vector{String}}()
+
+ prev_q = nothing
+ for row in runs
+ if coalesce(row.success, 0) != 1
+ push!(rows, [something(row.commit_short, ""), "", "", "", "FAILED"])
+ prev_q = nothing
+ continue
+ end
+
+ qs = get_quantities(db, row.commit_hash, case_name)
+ date_str = let d = something(row.commit_date, "")
+ length(d) >= 10 ? d[1:10] : d
+ end
+ short = something(row.commit_short, "")
+
+ if !haskey(qs, qty_name)
+ push!(rows, [short, date_str, "N/A", "", "N/A"])
+ prev_q = nothing
+ continue
+ end
+
+ q = qs[qty_name]
+ val_str = format_value(q)
+
+ if prev_q === nothing
+ push!(rows, [short, date_str, val_str, "--", "--"])
+ else
+ abs_diff, rel_diff, status = compare_values(prev_q, q)
+ diff_str = format_diff(abs_diff, rel_diff, status, q.value_type)
+ st = startswith(status, "CHANGED") ? "** $status **" : status
+ push!(rows, [short, date_str, val_str, diff_str, st])
+ end
+ prev_q = q
+ end
+
+ widths = [length(header[i]) for i in 1:ncols]
+ for r in rows
+ for i in 1:ncols
+ widths[i] = max(widths[i], length(r[i]))
+ end
+ end
+ total_w = sum(widths) + 2 * (ncols - 1)
+
+ println()
+ println("History: $qty_name — $case_name")
+ println("="^total_w)
+ _print_row(header, widths)
+ println("-"^total_w)
+ for r in rows
+ _print_row(r, widths)
+ end
+ println("="^total_w)
+end
diff --git a/regression-harness/src/runner.jl b/regression-harness/src/runner.jl
new file mode 100644
index 0000000000..53801ed611
--- /dev/null
+++ b/regression-harness/src/runner.jl
@@ -0,0 +1,701 @@
+"""
+Runner: orchestrates checking out commits, running GPEC, and extracting results.
+"""
+
+"""
+Epilogue appended to every subprocess script: records the GPEC-only runtime *and* the
+environment that produced it (Julia, host, resolved package set, thread counts) as `key=value`
+lines. Measured inside the subprocess, after `Pkg.instantiate()` has resolved the environment,
+so it describes what actually ran rather than what the harness intended to run.
+"""
+const RUNINFO_EPILOGUE = """
+using SHA
+using LinearAlgebra: BLAS
+let manifest = joinpath(dirname(Base.active_project()), "Manifest.toml"), gpec = GeneralizedPerturbedEquilibrium
+ has_workload = any(f -> lowercase(f) == "precompile.jl", readdir(dirname(pathof(gpec))))
+ workload_on = get(Base.get_preferences(Base.PkgId(gpec).uuid), "precompile_workload", true) == true
+ open(ARGS[2], "w") do f
+ println(f, "runtime_s=", elapsed)
+ println(f, "julia_version=", string(VERSION))
+ println(f, "os_arch=", Sys.MACHINE)
+ println(f, "manifest_sha=", isfile(manifest) ? bytes2hex(SHA.sha256(read(manifest))) : "")
+ println(f, "nthreads=", Threads.nthreads())
+ println(f, "blas_threads=", BLAS.get_num_threads())
+ println(f, "build_mode=", has_workload && workload_on ? "aot" : "jit")
+ end
+end
+"""
+
+"""
+Materialize the directory GPEC will actually run in.
+
+With no `overrides` and no `remove_sections`, the example deck runs in place (returns it untouched). Otherwise
+the deck is copied to a uniquely named throwaway sibling of the example dir and the named gpec.toml keys are
+patched there, so one shared example can serve several cases (e.g. a collisionless variant via
+`"KineticForces.nutype" => "zero"`). The copy sits beside the original so relative file
+references in the deck (e.g. `Equilibrium.kinetic_file = "..//..."`) still resolve.
+Override keys are dotted paths into the TOML; missing intermediate tables are created. Each
+section named in `remove_sections` is dropped (a dotted name drops a sub-table), so a run can stop before that stage.
+Returns `(rundir, is_temp)`; the caller removes `rundir` when `is_temp`.
+"""
+function _materialize_rundir(example_path::String, overrides::Dict{String,Any}, remove_sections::Vector{String}=String[])
+ isempty(overrides) && isempty(remove_sections) && return (example_path, false)
+ # Unique per invocation, so concurrent runs from one checkout cannot share (and race on) a rundir.
+ rundir = mktempdir(dirname(example_path); prefix=".regress-override-" * basename(example_path) * "-", cleanup=false)
+ cp(example_path, rundir; force=true)
+ rm(joinpath(rundir, "gpec.h5"); force=true) # drop any stale output copied along
+ cfg = TOML.parsefile(joinpath(rundir, "gpec.toml"))
+ for (dotted, val) in overrides
+ ks = split(dotted, ".")
+ d = cfg
+ for k in ks[1:(end-1)]
+ d = get!(d, k, Dict{String,Any}())
+ end
+ d[ks[end]] = val
+ end
+ for dotted in remove_sections
+ ks = split(dotted, ".")
+ parent = foldl((t, k) -> get(t, k, Dict{String,Any}()), ks[1:(end-1)]; init=cfg)
+ delete!(parent, ks[end])
+ end
+ open(joinpath(rundir, "gpec.toml"), "w") do io
+ TOML.print(io, cfg)
+ end
+ return (rundir, true)
+end
+
+# Thread count for GPEC subprocesses ("auto" = all cores); GPEC's threaded kernels
+# (Riccati parallel FM, ballooning, field reconstruction, kinetic forces) otherwise
+# run single-threaded. Override with e.g. GPEC_REGRESS_THREADS=1. The actual count
+# is recorded in each run's environment fingerprint.
+const SUBPROCESS_THREADS = get(ENV, "GPEC_REGRESS_THREADS", "auto")
+
+const GPEC_UUID = "462872dd-e066-4d2e-b993-6468b5239634"
+const _PREFS_ENVS = Dict{Bool,String}()
+
+"""
+Launch `cmd` with GPEC's `precompile_workload` preference set from `case_spec`, via a small
+environment stacked on the load path so no file is written into the run's project.
+
+The environment goes first: preferences from earlier load-path entries win, so this outranks a
+developer's `LocalPreferences.toml` beside the run's `Project.toml`. It declares GPEC only under
+`[extras]` and has no Manifest, so package loading still falls through to the active project.
+"""
+function with_workload_preference(cmd::Cmd, case_spec::CaseSpec)
+ workload = case_spec.precompile_workload
+ env = get!(_PREFS_ENVS, workload) do
+ dir = mktempdir()
+ write(joinpath(dir, "Project.toml"), "[extras]\nGeneralizedPerturbedEquilibrium = \"$GPEC_UUID\"\n")
+ write(joinpath(dir, "LocalPreferences.toml"), "[GeneralizedPerturbedEquilibrium]\nprecompile_workload = $workload\n")
+ return dir
+ end
+ load_path = get(ENV, "JULIA_LOAD_PATH", "@:@v#.#:@stdlib")
+ return addenv(cmd, "JULIA_LOAD_PATH" => env * (Sys.iswindows() ? ";" : ":") * load_path)
+end
+
+const RUNNER_SCRIPT_TEMPLATE = """
+using Pkg
+%INSTANTIATE%
+using GeneralizedPerturbedEquilibrium
+t_start = time()
+GeneralizedPerturbedEquilibrium.main([ARGS[1]])
+elapsed = time() - t_start
+%RUNINFO%
+"""
+
+# Self-contained computation for the GGJ inner-layer reference benchmark.
+# Runs the Galerkin solver on the Glasser & Wang 2020 Eq. 55 coefficients with physical
+# time scales (the q = 4 benchmark surface's τ_A, τ_R) at a 1 kHz rotation, γ = 2πi·10³ s⁻¹
+# (Q ≈ 0.22i, where the stock Galerkin matching is accurate), and writes the interchange (Δ₊)
+# and tearing (Δ₋) matching data into a small HDF5 file at ARGS[1].
+# Runtime and environment are written to ARGS[2] by the shared run-info epilogue.
+const COMPUTED_GGJ_SCRIPT_TEMPLATE = """
+using Pkg
+%INSTANTIATE%
+using GeneralizedPerturbedEquilibrium
+using GeneralizedPerturbedEquilibrium.InnerLayer
+using HDF5
+γ = 2π * 1e3 * im
+p = InnerLayer.GGJ.glasser_wang_2020_eq55(; taua=2.11226e-7, taur=0.968219)
+t_start = time()
+Δ = solve_inner(GGJModel(solver=:galerkin), p, γ)
+elapsed = time() - t_start
+h5open(ARGS[1], "w") do fid
+ fid["ggj/delta_interchange_real"] = real(Δ.interchange)
+ fid["ggj/delta_interchange_imag"] = imag(Δ.interchange)
+ fid["ggj/delta_tearing_real"] = real(Δ.tearing)
+ fid["ggj/delta_tearing_imag"] = imag(Δ.tearing)
+end
+%RUNINFO%
+"""
+
+# GGJ rotated-ray backend at Q = 500i on the q=4 benchmark surface — a regime beyond the
+# :galerkin backend. Builds the physical rate γ = 500i·Q₀ so inner_Q lands exactly on the
+# imaginary axis at 500i, then writes the parity matching data. Runtime and environment are
+# written to ARGS[2] by the shared run-info epilogue.
+const COMPUTED_GGJ_RAY_SCRIPT_TEMPLATE = """
+using Pkg
+%INSTANTIATE%
+using GeneralizedPerturbedEquilibrium
+using GeneralizedPerturbedEquilibrium.InnerLayer
+using HDF5
+p = InnerLayer.GGJ.q4_surface_benchmark()
+γ = 500.0im * InnerLayer.GGJ.q0(p)
+t_start = time()
+Δ = solve_inner(GGJModel(solver=:ray), p, γ)
+elapsed = time() - t_start
+h5open(ARGS[1], "w") do fid
+ fid["ggj/delta_interchange_real"] = real(Δ.interchange)
+ fid["ggj/delta_interchange_imag"] = imag(Δ.interchange)
+ fid["ggj/delta_tearing_real"] = real(Δ.tearing)
+ fid["ggj/delta_tearing_imag"] = imag(Δ.tearing)
+end
+%RUNINFO%
+"""
+
+# Self-contained separatrix-finder regression (PR #296). Loads a fixed-boundary EFIT whose
+# computational box hugs the LCFS (eps=0.05 TokaMaker aspect-scan g-file): outside the prescribed
+# LCFS the coil-vacuum flux turns back above the boundary value before the grid edge, so the old
+# bracketed-Brent separatrix finder could not bracket psi=sibry and equilibrium setup threw. Calls
+# PlasmaEquilibrium directly and writes the leading equilibrium scalars: errors on the buggy code,
+# passes with the Newton finder. Runtime and environment are written to ARGS[2] by the run-info epilogue.
+const COMPUTED_SEPARATRIX_SCRIPT_TEMPLATE = """
+using Pkg
+%INSTANTIATE%
+using GeneralizedPerturbedEquilibrium
+using GeneralizedPerturbedEquilibrium.Equilibrium
+using HDF5
+root = dirname(Base.active_project())
+gfile = joinpath(root, "examples", "efit_fixedbdy_separatrix_example", "eq_eps0.0500000_k1.000_d0.000.geqdsk")
+t_start = time()
+pe = Equilibrium.PlasmaEquilibrium(gfile; eq_type="efit")
+elapsed = time() - t_start
+h5open(ARGS[1], "w") do fid
+ fid["Equilibrium/psi_total"] = pe.psio
+ fid["Equilibrium/q_axis"] = pe.params.q0
+ fid["Equilibrium/q_95"] = pe.params.q95
+ fid["Equilibrium/beta_t"] = pe.params.betat
+ fid["Equilibrium/beta_N"] = pe.params.betan
+end
+%RUNINFO%
+"""
+
+"""
+Expand a subprocess script template: the optional `Pkg.instantiate()` call and the run-info
+epilogue that records runtime and environment.
+"""
+function _render_script(template::String; no_instantiate::Bool)::String
+ rendered = replace(template, "%INSTANTIATE%" => (no_instantiate ? "" : "Pkg.instantiate()"))
+ return replace(rendered, "%RUNINFO%" => RUNINFO_EPILOGUE)
+end
+
+"""
+Run GPEC for a single commit/ref and case. Dispatches to run_local for
+the working tree or run_at_commit for a git ref.
+
+`pin_manifest` is the path to a resolved `Manifest.toml` copied into each worktree so every ref
+runs against the same package set; `nothing` disables pinning. `expected_key` is the environment
+key a fresh run will carry — a cached run whose key differs is re-run rather than reused.
+`worktree_path`, when given, is reused instead of creating/removing a fresh worktree for this
+call — see [`run_cases_at_ref`](@ref), which shares one worktree (and thus one
+`Pkg.instantiate`/precompile) across every case at a commit.
+"""
+function run_commit(db::SQLite.DB, commit_hash::String, ref_name::String,
+ case_spec::CaseSpec, repo_root::String;
+ force::Bool=false, verbose::Bool=false,
+ no_instantiate::Bool=false,
+ pin_manifest::Union{String,Nothing}=nothing,
+ expected_key::Union{String,Nothing}=nothing,
+ worktree_path::Union{String,Nothing}=nothing)
+ if case_spec.kind == "computed"
+ if commit_hash == LOCAL_REF
+ return run_computed_local(db, case_spec, repo_root;
+ verbose=verbose, no_instantiate=no_instantiate,
+ pin_manifest=pin_manifest)
+ end
+ return run_computed_at_commit(db, commit_hash, ref_name, case_spec, repo_root;
+ force=force, verbose=verbose, no_instantiate=no_instantiate,
+ pin_manifest=pin_manifest, expected_key=expected_key,
+ worktree_path=worktree_path)
+ end
+ if commit_hash == LOCAL_REF
+ return run_local(db, case_spec, repo_root;
+ force=force, verbose=verbose, no_instantiate=no_instantiate,
+ pin_manifest=pin_manifest)
+ end
+ return run_at_commit(db, commit_hash, ref_name, case_spec, repo_root;
+ force=force, verbose=verbose, no_instantiate=no_instantiate,
+ pin_manifest=pin_manifest, expected_key=expected_key,
+ worktree_path=worktree_path)
+end
+
+"""
+Run every case in `case_specs` against `ref`. For a git ref (not `"local"`), a single
+worktree is created and reused across all cases at that commit — each case still spawns
+its own `julia` subprocess, but since they share the same `--project` path (and the same
+pinned Manifest, when pinning is on), only the first subprocess pays for
+`Pkg.instantiate()`/precompilation; the rest hit Julia's on-disk pkgimage cache for that
+path. Worktree creation is skipped entirely when every case is already cached in the
+expected environment (and `force` is false). If the worktree cannot be created, the
+failure is recorded for each case needing a run and the remaining refs still proceed.
+"""
+function run_cases_at_ref(db::SQLite.DB, ref::ResolvedRef, case_specs::Vector{CaseSpec}, repo_root::String;
+ force::Bool=false, verbose::Bool=false, no_instantiate::Bool=false,
+ pin_manifest::Union{String,Nothing}=nothing,
+ expected_key::Union{String,Nothing}=nothing)
+ needs_worktree = !is_local_ref(ref) &&
+ (force || any(!is_cached(db, ref.commit_hash, cs.name; expected_key=expected_key) for cs in case_specs))
+
+ worktree_path = nothing
+ if needs_worktree
+ try
+ worktree_path = create_worktree(ref.commit_hash, repo_root; pin_manifest_from=pin_manifest)
+ catch e
+ info = get_commit_info(ref.commit_hash, repo_root)
+ @warn "Worktree creation failed for $(info.short): $(sprint(showerror, e))"
+ # Record the failure only for cases needing a run; cached results stay intact.
+ for case_spec in case_specs
+ if force || !is_cached(db, ref.commit_hash, case_spec.name; expected_key=expected_key)
+ store_failed_run(db, ref.commit_hash, info.short, info.date, info.msg,
+ case_spec.name, "Worktree creation failed: $(sprint(showerror, e))")
+ end
+ end
+ return
+ end
+ end
+
+ try
+ for case_spec in case_specs
+ run_commit(db, ref.commit_hash, ref.name, case_spec, repo_root;
+ force=force, verbose=verbose, no_instantiate=no_instantiate,
+ pin_manifest=pin_manifest, expected_key=expected_key,
+ worktree_path=worktree_path)
+ end
+ finally
+ worktree_path === nothing || remove_worktree(worktree_path, repo_root)
+ end
+end
+
+"""
+Pick the subprocess script template for a `kind="computed"` case.
+"""
+function _computed_script_template(case_spec::CaseSpec)
+ if case_spec.name == "ggj_reference"
+ return COMPUTED_GGJ_SCRIPT_TEMPLATE
+ elseif case_spec.name == "ggj_ray_q500i"
+ return COMPUTED_GGJ_RAY_SCRIPT_TEMPLATE
+ elseif case_spec.name == "efit_fixedbdy_separatrix"
+ return COMPUTED_SEPARATRIX_SCRIPT_TEMPLATE
+ end
+ error("No computed-script template registered for case '$(case_spec.name)'")
+end
+
+"""
+Shared implementation for kind="computed" cases. Runs the case's
+self-contained Julia script in a subprocess against `project_root` (so it can
+import GeneralizedPerturbedEquilibrium), reads the resulting tempfile h5 with
+`extract_quantities`, and returns `(extracted, runtime_s)`. Throws on failure
+so callers can handle store_failed_run uniformly.
+"""
+function _execute_computed(case_spec::CaseSpec, project_root::String;
+ verbose::Bool, no_instantiate::Bool,
+ stderr_buf::IO, pin_manifest::Union{String,Nothing}=nothing)
+ script_content = _render_script(_computed_script_template(case_spec); no_instantiate=no_instantiate)
+ tmpscript = tempname() * ".jl"
+ h5path = tempname() * ".h5"
+ runinfo_file = tempname() * ".runinfo"
+ try
+ write(tmpscript, script_content)
+ cmd = with_workload_preference(`julia --startup-file=no -t $SUBPROCESS_THREADS --project=$project_root $tmpscript $h5path $runinfo_file`, case_spec)
+ if verbose
+ run(pipeline(cmd))
+ else
+ run(pipeline(cmd; stdout=devnull, stderr=stderr_buf))
+ end
+ runtime_s, fingerprint = read_runinfo(runinfo_file, pin_manifest !== nothing)
+ isempty(fingerprint.julia_version) && error("subprocess wrote no run-info metadata — does the script template end with %RUNINFO%?")
+ _warn_pin_broken(pin_manifest, fingerprint, case_spec.name)
+ _warn_build_mode(fingerprint, case_spec)
+ if !isfile(h5path)
+ error("Computed case '$(case_spec.name)' produced no output h5")
+ end
+ extracted = extract_quantities(h5path, case_spec.quantities, runtime_s)
+ return extracted, runtime_s, fingerprint
+ finally
+ rm(tmpscript; force=true)
+ rm(h5path; force=true)
+ rm(runinfo_file; force=true)
+ end
+end
+
+"""
+Add a remedy hint when a run failed because the pinned Manifest is missing a direct dependency
+declared at the checked-out commit — the one incompatibility `Pkg.instantiate()` refuses to run under.
+Detects on the full error text, since tail-keeping truncation can drop Pkg's ERROR line from `short_err`.
+"""
+function _hint_pin_incompatible(full_err::AbstractString, short_err::AbstractString)::String
+ occursin("is a direct dependency, but does not appear in the manifest", full_err) || return String(short_err)
+ return "Pinned Manifest lacks a direct dependency declared at this commit — re-run with --no-pin-manifest " *
+ "to let this ref resolve its own package set.\n" * short_err
+end
+
+"""
+Run a kind="computed" case against the working tree.
+"""
+function run_computed_local(db::SQLite.DB, case_spec::CaseSpec, repo_root::String;
+ verbose::Bool=false, no_instantiate::Bool=false,
+ pin_manifest::Union{String,Nothing}=nothing)
+ delete_cached(db, LOCAL_REF, case_spec.name)
+ date = Dates.format(Dates.now(), "yyyy-mm-ddTHH:MM:SS")
+ @info "Running: $(case_spec.name) @ local (working tree, computed)"
+ stderr_buf = IOBuffer()
+ try
+ extracted, runtime_s, fingerprint = _execute_computed(case_spec, repo_root;
+ verbose=verbose,
+ no_instantiate=no_instantiate,
+ stderr_buf=stderr_buf,
+ pin_manifest=pin_manifest)
+ store_run(db, LOCAL_REF, "local", date, "working tree", case_spec.name,
+ runtime_s, extracted; fingerprint=fingerprint)
+ @info " Completed in $(round(runtime_s, digits=3))s — $(length(extracted)) quantities extracted"
+ catch e
+ err_msg = if e isa ProcessFailedException
+ stderr_str = String(take!(stderr_buf))
+ isempty(stderr_str) ? "Subprocess failed" : stderr_str
+ else
+ sprint(showerror, e)
+ end
+ # Keep the tail of the message: Julia errors usually appear at the end
+ # of the subprocess output, not the start (Pkg.instantiate output dominates the head).
+ # `last` is unicode-safe and won't split a multibyte char like `err_msg[end-N:end]` could.
+ err_msg_short = _hint_pin_incompatible(err_msg, length(err_msg) > 2000 ? "..." * last(err_msg, 2000) : err_msg)
+ @warn "Run failed (local computed): $(first(err_msg_short, 200))"
+ store_failed_run(db, LOCAL_REF, "local", date, "working tree", case_spec.name,
+ err_msg_short)
+ end
+end
+
+"""
+Run a kind="computed" case at a specific git commit via worktree.
+If `worktree_path` is given, the caller owns the (already pinned) worktree and this
+function will not remove it; otherwise one is created and removed here.
+"""
+function run_computed_at_commit(db::SQLite.DB, commit_hash::String, ref_name::String,
+ case_spec::CaseSpec, repo_root::String;
+ force::Bool=false, verbose::Bool=false,
+ no_instantiate::Bool=false,
+ pin_manifest::Union{String,Nothing}=nothing,
+ expected_key::Union{String,Nothing}=nothing,
+ worktree_path::Union{String,Nothing}=nothing)
+ if !force && is_cached(db, commit_hash, case_spec.name; expected_key=expected_key)
+ info = get_run_info(db, commit_hash, case_spec.name)
+ if info !== nothing
+ @info "Cached: $(case_spec.name) @ $(info.commit_short) ($(info.commit_date))"
+ return
+ end
+ end
+ _warn_env_invalidated(db, commit_hash, case_spec.name, expected_key, force)
+ if force
+ delete_cached(db, commit_hash, case_spec.name)
+ end
+
+ commit_info = get_commit_info(commit_hash, repo_root)
+ @info "Running: $(case_spec.name) @ $(commit_info.short) ($(commit_info.date)) [computed]"
+ @info " $(commit_info.msg)"
+
+ own_worktree = worktree_path === nothing
+ stderr_buf = IOBuffer()
+ try
+ own_worktree && (worktree_path = create_worktree(commit_hash, repo_root; pin_manifest_from=pin_manifest))
+ extracted, runtime_s, fingerprint = _execute_computed(case_spec, worktree_path;
+ verbose=verbose,
+ no_instantiate=no_instantiate,
+ stderr_buf=stderr_buf,
+ pin_manifest=pin_manifest)
+ store_run(db, commit_hash, commit_info.short, commit_info.date,
+ commit_info.msg, case_spec.name, runtime_s, extracted; fingerprint=fingerprint)
+ @info " Completed in $(round(runtime_s, digits=3))s — $(length(extracted)) quantities extracted"
+ catch e
+ err_msg = if e isa ProcessFailedException
+ stderr_str = String(take!(stderr_buf))
+ isempty(stderr_str) ? "Subprocess failed" : stderr_str
+ else
+ sprint(showerror, e)
+ end
+ # Keep the tail of the message: Julia errors usually appear at the end
+ # of the subprocess output, not the start (Pkg.instantiate output dominates the head).
+ # `last` is unicode-safe and won't split a multibyte char like `err_msg[end-N:end]` could.
+ err_msg_short = _hint_pin_incompatible(err_msg, length(err_msg) > 2000 ? "..." * last(err_msg, 2000) : err_msg)
+ @warn "Run failed (computed) for $(commit_info.short): $(first(err_msg_short, 200))"
+ store_failed_run(db, commit_hash, commit_info.short, commit_info.date,
+ commit_info.msg, case_spec.name, err_msg_short)
+ finally
+ if own_worktree && worktree_path !== nothing
+ remove_worktree(worktree_path, repo_root)
+ end
+ end
+end
+
+"""
+Warn if a pinned package set did not survive `Pkg.instantiate()`.
+
+Contingency insurance rather than a description of current behavior: on Julia 1.11/1.12,
+instantiate never rewrites an out-of-sync pinned Manifest — it warns and proceeds, or errors when
+the commit declares a direct dependency the Manifest lacks (which fails the run loudly). Should a
+future Pkg re-resolve in place instead, this catches the pin silently not holding.
+"""
+function _warn_pin_broken(pin_manifest::Union{String,Nothing}, fp::EnvFingerprint, label::AbstractString)
+ pin_manifest === nothing && return
+ isempty(fp.manifest_sha) && return
+ pinned_sha = file_sha256(pin_manifest)
+ (isempty(pinned_sha) || pinned_sha == fp.manifest_sha) && return
+ @warn "Pinned Manifest was re-resolved for $label — its package set differs from the working tree" pinned = pinned_sha[1:8] resolved = fp.manifest_sha[1:8]
+end
+
+"""
+Warn when a run's build mode differs from its case's, e.g. a workload case run at a commit that predates the workload.
+"""
+function _warn_build_mode(fp::EnvFingerprint, case_spec::CaseSpec)
+ expected = case_spec.precompile_workload ? "aot" : "jit"
+ (isempty(fp.build_mode) || fp.build_mode == expected) && return
+ @warn "Case $(case_spec.name) requested a $expected build but ran $(fp.build_mode); its numbers are not comparable across build modes"
+end
+
+"""
+Explain a cache miss caused by the environment rather than by absence.
+
+A cached run exists for this (commit, case) but was produced under a different Julia, host, or
+package set — the exact situation that used to be silently reused and reported as a physics
+regression. Says so, once, before re-running.
+"""
+function _warn_env_invalidated(db::SQLite.DB, commit_hash::String, case_name::String,
+ expected_key::Union{String,Nothing}, force::Bool)
+ (force || expected_key === nothing) && return
+ stored = cached_env_key(db, commit_hash, case_name)
+ stored == expected_key && return
+ if stored === nothing
+ is_cached(db, commit_hash, case_name) || return
+ @warn "Cached result for $case_name predates environment fingerprinting — re-running"
+ else
+ @warn "Cached result for $case_name was produced in a different environment — re-running" stored_key = stored current_key = expected_key
+ end
+end
+
+"""
+Run GPEC in the current working tree (uncommitted changes included).
+Always re-runs (local results are never cached since the working tree is mutable).
+"""
+function run_local(db::SQLite.DB, case_spec::CaseSpec, repo_root::String;
+ force::Bool=false, verbose::Bool=false,
+ no_instantiate::Bool=false,
+ pin_manifest::Union{String,Nothing}=nothing)
+ # Always delete previous local results and re-run
+ delete_cached(db, LOCAL_REF, case_spec.name)
+
+ date = Dates.format(Dates.now(), "yyyy-mm-ddTHH:MM:SS")
+ @info "Running: $(case_spec.name) @ local (working tree)"
+
+ example_path = joinpath(repo_root, case_spec.example_dir)
+ if !isdir(example_path)
+ @warn "Example directory not found: $(case_spec.example_dir)"
+ store_failed_run(db, LOCAL_REF, "local", date, "working tree", case_spec.name,
+ "Example directory not found: $(case_spec.example_dir)")
+ return
+ end
+
+ tmpscript = nothing
+ runinfo_file = nothing
+ rundir = nothing
+ rundir_is_temp = false
+ stderr_buf = IOBuffer()
+
+ try
+ (rundir, rundir_is_temp) = _materialize_rundir(example_path, case_spec.overrides, case_spec.remove_sections)
+ rm(joinpath(rundir, "gpec.h5"); force=true) # a stale output would mask a failed run
+
+ script_content = _render_script(RUNNER_SCRIPT_TEMPLATE; no_instantiate=no_instantiate)
+ tmpscript = tempname() * ".jl"
+ runinfo_file = tempname() * ".runinfo"
+ write(tmpscript, script_content)
+
+ cmd = with_workload_preference(`julia --startup-file=no -t $SUBPROCESS_THREADS --project=$repo_root $tmpscript $rundir $runinfo_file`, case_spec)
+ if verbose
+ run(pipeline(cmd))
+ else
+ run(pipeline(cmd; stdout=devnull, stderr=stderr_buf))
+ end
+ runtime_s, fingerprint = read_runinfo(runinfo_file, pin_manifest !== nothing)
+ isempty(fingerprint.julia_version) && error("subprocess wrote no run-info metadata — does the script template end with %RUNINFO%?")
+ _warn_pin_broken(pin_manifest, fingerprint, case_spec.name)
+ _warn_build_mode(fingerprint, case_spec)
+
+ h5path = joinpath(rundir, "gpec.h5")
+ if !isfile(h5path)
+ @warn "gpec.h5 not produced"
+ store_failed_run(db, LOCAL_REF, "local", date, "working tree", case_spec.name,
+ "gpec.h5 not produced after successful run")
+ return
+ end
+
+ extracted = extract_quantities(h5path, case_spec.quantities, runtime_s)
+ store_run(db, LOCAL_REF, "local", date, "working tree", case_spec.name,
+ runtime_s, extracted; fingerprint=fingerprint)
+
+ @info " Completed in $(round(runtime_s, digits=1))s — $(length(extracted)) quantities extracted"
+
+ catch e
+ err_msg = if e isa ProcessFailedException
+ stderr_str = String(take!(stderr_buf))
+ isempty(stderr_str) ? "Subprocess failed (stderr was printed to terminal in verbose mode)" : stderr_str
+ else
+ sprint(showerror, e)
+ end
+ # Keep the tail of the message: Julia errors usually appear at the end
+ # of the subprocess output, not the start (Pkg.instantiate output dominates the head).
+ # `last` is unicode-safe and won't split a multibyte char like `err_msg[end-N:end]` could.
+ err_msg_short = _hint_pin_incompatible(err_msg, length(err_msg) > 2000 ? "..." * last(err_msg, 2000) : err_msg)
+ @warn "Run failed (local): $(first(err_msg_short, 200))"
+ store_failed_run(db, LOCAL_REF, "local", date, "working tree", case_spec.name,
+ err_msg_short)
+ finally
+ if tmpscript !== nothing
+ rm(tmpscript; force=true)
+ end
+ if runinfo_file !== nothing
+ rm(runinfo_file; force=true)
+ end
+ if rundir_is_temp && rundir !== nothing
+ # rundir sits beside the example; removing its parent would delete examples/ itself
+ rm(rundir; recursive=true, force=true)
+ end
+ end
+end
+
+"""
+Run GPEC for a specific git commit via worktree. Stores results in the database.
+Skips if already cached in the same environment (unless force=true).
+If `worktree_path` is given, the caller owns the (already pinned) worktree and this
+function will not remove it; otherwise one is created and removed here.
+"""
+function run_at_commit(db::SQLite.DB, commit_hash::String, ref_name::String,
+ case_spec::CaseSpec, repo_root::String;
+ force::Bool=false, verbose::Bool=false,
+ no_instantiate::Bool=false,
+ pin_manifest::Union{String,Nothing}=nothing,
+ expected_key::Union{String,Nothing}=nothing,
+ worktree_path::Union{String,Nothing}=nothing)
+ # Check cache
+ if !force && is_cached(db, commit_hash, case_spec.name; expected_key=expected_key)
+ info = get_run_info(db, commit_hash, case_spec.name)
+ if info !== nothing
+ @info "Cached: $(case_spec.name) @ $(info.commit_short) ($(info.commit_date))"
+ return
+ end
+ end
+ _warn_env_invalidated(db, commit_hash, case_spec.name, expected_key, force)
+
+ # Delete existing cached data if force re-running
+ if force
+ delete_cached(db, commit_hash, case_spec.name)
+ end
+
+ # Get commit metadata
+ commit_info = get_commit_info(commit_hash, repo_root)
+ @info "Running: $(case_spec.name) @ $(commit_info.short) ($(commit_info.date))"
+ @info " $(commit_info.msg)"
+
+ own_worktree = worktree_path === nothing
+ tmpscript = nothing
+ runinfo_file = nothing
+ rundir = nothing
+ rundir_is_temp = false
+ stderr_buf = IOBuffer()
+
+ try
+ # Create worktree (unless one was shared with us), pinning the package set when the caller supplied a Manifest
+ own_worktree && (worktree_path = create_worktree(commit_hash, repo_root; pin_manifest_from=pin_manifest))
+
+ # Check example directory exists in this commit
+ example_path = joinpath(worktree_path, case_spec.example_dir)
+ if !isdir(example_path)
+ @warn "Example directory not found at commit $(commit_info.short): $(case_spec.example_dir)"
+ store_failed_run(db, commit_hash, commit_info.short, commit_info.date,
+ commit_info.msg, case_spec.name,
+ "Example directory not found: $(case_spec.example_dir)")
+ return
+ end
+
+ (rundir, rundir_is_temp) = _materialize_rundir(example_path, case_spec.overrides, case_spec.remove_sections)
+ rm(joinpath(rundir, "gpec.h5"); force=true) # a stale output (e.g. from an earlier case sharing the worktree) would mask a failed run
+
+ # Write temp runner script
+ script_content = _render_script(RUNNER_SCRIPT_TEMPLATE; no_instantiate=no_instantiate)
+ tmpscript = tempname() * ".jl"
+ runinfo_file = tempname() * ".runinfo"
+ write(tmpscript, script_content)
+
+ # Run GPEC in subprocess
+ project_root = worktree_path
+
+ cmd = with_workload_preference(`julia --startup-file=no -t $SUBPROCESS_THREADS --project=$project_root $tmpscript $rundir $runinfo_file`, case_spec)
+ if verbose
+ run(pipeline(cmd))
+ else
+ run(pipeline(cmd; stdout=devnull, stderr=stderr_buf))
+ end
+ runtime_s, fingerprint = read_runinfo(runinfo_file, pin_manifest !== nothing)
+ isempty(fingerprint.julia_version) && error("subprocess wrote no run-info metadata — does the script template end with %RUNINFO%?")
+ _warn_pin_broken(pin_manifest, fingerprint, commit_info.short)
+ _warn_build_mode(fingerprint, case_spec)
+
+ # Check for gpec.h5
+ h5path = joinpath(rundir, "gpec.h5")
+ if !isfile(h5path)
+ @warn "gpec.h5 not produced at $(commit_info.short)"
+ store_failed_run(db, commit_hash, commit_info.short, commit_info.date,
+ commit_info.msg, case_spec.name,
+ "gpec.h5 not produced after successful run")
+ return
+ end
+
+ # Extract quantities
+ extracted = extract_quantities(h5path, case_spec.quantities, runtime_s)
+
+ # Store in database
+ store_run(db, commit_hash, commit_info.short, commit_info.date,
+ commit_info.msg, case_spec.name, runtime_s, extracted; fingerprint=fingerprint)
+
+ @info " Completed in $(round(runtime_s, digits=1))s — $(length(extracted)) quantities extracted"
+
+ catch e
+ err_msg = if e isa ProcessFailedException
+ stderr_str = String(take!(stderr_buf))
+ isempty(stderr_str) ? "Subprocess failed (stderr was printed to terminal in verbose mode)" : stderr_str
+ else
+ sprint(showerror, e)
+ end
+ # Truncate for display and storage
+ # Keep the tail of the message: Julia errors usually appear at the end
+ # of the subprocess output, not the start (Pkg.instantiate output dominates the head).
+ # `last` is unicode-safe and won't split a multibyte char like `err_msg[end-N:end]` could.
+ err_msg_short = _hint_pin_incompatible(err_msg, length(err_msg) > 2000 ? "..." * last(err_msg, 2000) : err_msg)
+ @warn "Run failed for $(commit_info.short): $(first(err_msg_short, 200))"
+ store_failed_run(db, commit_hash, commit_info.short, commit_info.date,
+ commit_info.msg, case_spec.name, err_msg_short)
+ finally
+ # Clean up
+ if tmpscript !== nothing
+ rm(tmpscript; force=true)
+ end
+ if runinfo_file !== nothing
+ rm(runinfo_file; force=true)
+ end
+ if rundir_is_temp && rundir !== nothing
+ # rundir sits beside the example; removing its parent would delete examples/ itself
+ rm(rundir; recursive=true, force=true)
+ end
+ if own_worktree && worktree_path !== nothing
+ remove_worktree(worktree_path, repo_root)
+ end
+ end
+end
diff --git a/regression-harness/src/types.jl b/regression-harness/src/types.jl
new file mode 100644
index 0000000000..f31cc55dbf
--- /dev/null
+++ b/regression-harness/src/types.jl
@@ -0,0 +1,79 @@
+"""
+Shared data structures for the regression harness.
+"""
+
+"""
+Specification for a single quantity to extract from gpec.h5.
+"""
+struct QuantitySpec
+ name::String
+ h5path::String # HDF5 dataset path (e.g. "ForceFreeStates/FreeBoundaryStability/eigenmode_energies"), empty for runtime
+ type::String # "complex_vector", "real_vector", "real_scalar", "int_scalar", "real_matrix", "runtime"
+ extract::String # "value", "real_first", "imag_first", "abs_first", "norm", "all_real", "all_complex", "checksum"
+ label::String # Human-readable label for reports
+ noise_threshold::Float64 # Absolute changes below this are noise
+ order::Int # Display order in reports (lower = earlier)
+end
+
+"""
+Specification for a test case: what to run and what to extract.
+
+`kind` selects the runner backend:
+
+ - "gpec_run" (default) — run GPEC end-to-end on `example_dir`, extract from `gpec.h5`
+ - "computed" — run a self-contained Julia computation that writes a small h5
+ (no `example_dir` required); used for analytic/reference cases
+ like the GGJ inner-layer benchmark.
+
+`precompile_workload` sets GPEC's PrecompileTools workload preference for the run. It defaults to
+`false` so every case compares code compiled on first use; a case sets it `true` to track the
+precompiled build, whose last-bit rounding (and hence near-marginal results) can differ.
+"""
+struct CaseSpec
+ name::String
+ description::String
+ example_dir::String # Relative to repo root; empty for kind="computed"
+ quantities::Vector{QuantitySpec}
+ kind::String
+ overrides::Dict{String,Any} # gpec.toml keys patched for this run; dotted keys e.g. "KineticForces.nutype" => "zero". Empty = run the deck in place.
+ remove_sections::Vector{String} # gpec.toml sections (dotted for a sub-table) dropped for this run, e.g. ["PerturbedEquilibrium"] to stop before that stage
+ precompile_workload::Bool
+end
+
+"""
+Result of extracting a single quantity from an H5 file.
+"""
+struct ExtractedQuantity
+ name::String
+ label::String
+ value_real::Union{Float64,Nothing}
+ value_int::Union{Int,Nothing}
+ value_text::Union{String,Nothing} # JSON for arrays, hex for checksums
+ value_type::String # "real", "integer", "json_array", "checksum", "missing"
+ noise_threshold::Float64
+end
+
+"""
+Parsed CLI options.
+
+`no_pin_manifest` disables copying the working tree's resolved `Manifest.toml` into each
+worktree (pinning is on by default, so that two refs differ only by source code).
+`allow_env_mismatch` lets a cached result from a different environment be reused instead of
+re-run. `fail_on_change` turns any changed quantity into a non-zero exit status, for CI use.
+"""
+struct CLIOptions
+ cases::Vector{String}
+ refs::Vector{String}
+ ref_range::Union{String,Nothing}
+ force::Bool
+ list_cases::Bool
+ show_qty::Union{String,Nothing}
+ show_case::Union{String,Nothing}
+ db_path::Union{String,Nothing}
+ verbose::Bool
+ no_instantiate::Bool
+ no_pin_manifest::Bool
+ allow_env_mismatch::Bool
+ fail_on_change::Bool
+ help::Bool
+end
diff --git a/regression-harness/src/utils.jl b/regression-harness/src/utils.jl
new file mode 100644
index 0000000000..d1110f8eff
--- /dev/null
+++ b/regression-harness/src/utils.jl
@@ -0,0 +1,162 @@
+"""
+Git utilities and helper functions.
+"""
+
+const LOCAL_REF = "local"
+
+"""
+Resolved reference: a human-readable name and the full commit SHA.
+For local (uncommitted) working tree, commit_hash is "local".
+"""
+struct ResolvedRef
+ name::String # Original ref name (branch, tag, or short SHA)
+ commit_hash::String # Full 40-char SHA, or "local" for working tree
+end
+
+is_local_ref(ref::ResolvedRef) = ref.commit_hash == LOCAL_REF
+
+"""
+Resolve a git ref (branch, tag, SHA) to a full commit hash.
+Returns a ResolvedRef with the original name and full SHA.
+"""
+function resolve_ref(ref::String, repo_root::String)::ResolvedRef
+ if ref == LOCAL_REF
+ return ResolvedRef("local", LOCAL_REF)
+ end
+ hash = try
+ strip(read(`git -C $repo_root rev-parse --verify --quiet $ref`, String))
+ catch
+ # Try with origin/ prefix for remote tracking branches
+ try
+ strip(read(`git -C $repo_root rev-parse --verify --quiet origin/$ref`, String))
+ catch
+ error("Could not resolve ref '$ref' (also tried 'origin/$ref')")
+ end
+ end
+ return ResolvedRef(ref, hash)
+end
+
+"""
+Expand a ref range (e.g. "develop~10..develop") to a list of ResolvedRefs.
+Returns oldest-first ordering.
+"""
+function expand_ref_range(range::String, repo_root::String)::Vector{ResolvedRef}
+ commits = try
+ lines = readlines(`git -C $repo_root rev-list --reverse $range`)
+ filter(!isempty, lines)
+ catch e
+ error("Could not expand ref range '$range': $e")
+ end
+ if isempty(commits)
+ error("No commits found in range '$range'")
+ end
+ return [ResolvedRef(hash[1:8], hash) for hash in commits]
+end
+
+"""
+Get commit metadata: short hash, date, first line of message.
+"""
+function get_commit_info(commit_hash::String, repo_root::String)
+ short = strip(read(`git -C $repo_root rev-parse --short $commit_hash`, String))
+ date = strip(read(`git -C $repo_root log -1 --format=%aI $commit_hash`, String))
+ msg = strip(read(`git -C $repo_root log -1 --format=%s $commit_hash`, String))
+ # Truncate message to 60 chars
+ if length(msg) > 60
+ msg = msg[1:57] * "..."
+ end
+ return (short=short, date=date, msg=msg)
+end
+
+"""
+How far a ref lags the remote branch it tracks.
+
+Returns `(upstream, behind)` when both the ref and an upstream can be resolved, otherwise
+`nothing` (detached SHAs, tags, and local-only branches have no meaningful upstream). A ref that
+is behind its upstream is a stale baseline: the harness would happily benchmark against
+weeks-old code without saying so.
+"""
+function upstream_lag(ref::String, repo_root::String)
+ ref == LOCAL_REF && return nothing
+ # `origin/[` is only a meaningful fallback for an actual local branch name. Without this
+ # guard, `HEAD` matches the always-present symbolic ref `origin/HEAD` (→ origin/develop) and
+ # every feature branch gets reported as a stale copy of develop.
+ is_branch = success(`git -C $repo_root rev-parse --verify --quiet refs/heads/$ref`)
+ candidates = is_branch ? ("$(ref)@{upstream}", "origin/$(ref)") : ("$(ref)@{upstream}",)
+ upstream = nothing
+ for candidate in candidates
+ try
+ resolved = strip(read(`git -C $repo_root rev-parse --abbrev-ref --verify --quiet $candidate`, String))
+ if !isempty(resolved)
+ upstream = resolved
+ break
+ end
+ catch
+ continue
+ end
+ end
+ upstream === nothing && return nothing
+ try
+ behind = parse(Int, strip(read(`git -C $repo_root rev-list --count $(ref)..$(upstream)`, String)))
+ return (upstream=upstream, behind=behind)
+ catch
+ return nothing
+ end
+end
+
+"""
+Print a banner for every resolved ref that lags its remote tracking branch.
+
+`resolve_ref` takes the *local* branch pointer, so a local `develop` that has not been fetched
+in weeks silently becomes the baseline. Nothing else in the report says the baseline is old.
+"""
+function warn_stale_refs(refs::Vector{ResolvedRef}, repo_root::String)
+ for ref in refs
+ lag = upstream_lag(ref.name, repo_root)
+ (lag === nothing || lag.behind == 0) && continue
+ println()
+ println("!! STALE BASELINE: '$(ref.name)' is $(lag.behind) commit(s) behind $(lag.upstream).")
+ println(" This comparison is against out-of-date code. Update it with:")
+ println(" git fetch && git checkout $(ref.name) && git merge --ff-only $(lag.upstream)")
+ println()
+ end
+end
+
+"""
+Create a temporary git worktree for a commit. Returns the worktree path.
+
+`pin_manifest_from` copies an already-resolved `Manifest.toml` into the worktree so that the
+subprocess `Pkg.instantiate()` reproduces that exact package set instead of resolving whatever is
+newest. Without it, two refs are compared across two different package sets and library-level
+differences surface as physics regressions.
+"""
+function create_worktree(commit_hash::String, repo_root::String;
+ pin_manifest_from::Union{String,Nothing}=nothing)::String
+ short = commit_hash[1:min(8, length(commit_hash))]
+ worktree_path = tempname() * "_gpec_$(short)"
+ try
+ run(`git -C $repo_root worktree add --detach $worktree_path $commit_hash`)
+ catch e
+ error("Failed to create worktree for $short: $e")
+ end
+ if pin_manifest_from !== nothing && isfile(pin_manifest_from)
+ cp(pin_manifest_from, joinpath(worktree_path, "Manifest.toml"); force=true)
+ end
+ return worktree_path
+end
+
+"""
+Remove a git worktree. Tolerates errors (worktree may already be gone).
+"""
+function remove_worktree(worktree_path::String, repo_root::String)
+ try
+ run(`git -C $repo_root worktree remove --force $worktree_path`)
+ catch
+ # Force cleanup if worktree remove fails
+ try
+ rm(worktree_path; recursive=true, force=true)
+ run(`git -C $repo_root worktree prune`)
+ catch e
+ @warn "Failed to clean up worktree at $worktree_path: $e"
+ end
+ end
+end
diff --git a/regression-harness/test/runtests_compare.jl b/regression-harness/test/runtests_compare.jl
new file mode 100644
index 0000000000..3a3ff07742
--- /dev/null
+++ b/regression-harness/test/runtests_compare.jl
@@ -0,0 +1,18 @@
+using HDF5, JSON, Test
+
+include(joinpath(@__DIR__, "..", "src", "types.jl"))
+include(joinpath(@__DIR__, "..", "src", "extractor.jl"))
+
+# A stored quantity as get_quantities returns it.
+stored(value_type; value_real=nothing) =
+ (label="q", value_real=value_real, value_int=nothing, value_text=nothing, value_type=value_type, noise_threshold=1e-10)
+
+@testset "A quantity that disappears or changes type is a change" begin
+ real1, real2 = stored("real"; value_real=1.0), stored("real"; value_real=2.0)
+ @test compare_values(real1, real1)[3] == "OK"
+ @test compare_values(real1, real2)[3] == "CHANGED"
+ @test compare_values(stored("missing"), stored("missing"))[3] == "N/A"
+ @test compare_values(real1, stored("missing"))[3] == "CHANGED (missing)"
+ @test compare_values(stored("missing"), real1)[3] == "NEW"
+ @test compare_values(real1, stored("integer"))[3] == "CHANGED (type)"
+end
diff --git a/regression-harness/test/runtests_database.jl b/regression-harness/test/runtests_database.jl
new file mode 100644
index 0000000000..282fc93223
--- /dev/null
+++ b/regression-harness/test/runtests_database.jl
@@ -0,0 +1,45 @@
+using Dates, SHA, SQLite, Tables, Test, TOML
+
+const HARNESS_SOURCE = joinpath(@__DIR__, "..", "src")
+include(joinpath(HARNESS_SOURCE, "types.jl"))
+include(joinpath(HARNESS_SOURCE, "env.jl"))
+include(joinpath(HARNESS_SOURCE, "database.jl"))
+
+@testset "Regression database writes do not depend on garbage collection" begin
+ fingerprint = EnvFingerprint("synthetic", "synthetic", "synthetic", 1, 1, "jit", true)
+ quantities = [
+ ExtractedQuantity("finite", "finite", 2.5, nothing, nothing, "real", 1e-10),
+ ExtractedQuantity("array", "array", nothing, nothing, "[NaN,Infinity,-Infinity,-0.0]", "json_array", 1e-10),
+ ExtractedQuantity("complex", "complex", nothing, nothing, "[[1.0,2.0],[NaN,-Infinity]]", "json_array", 1e-10)
+ ]
+ mktempdir() do directory
+ # Discarded row cursors must be closed without waiting for collection.
+ gc_enabled = GC.enable(false)
+ try
+ for index in 1:2
+ db = open_database(joinpath(directory, "case$(index).sqlite"))
+ try
+ store_run(db, "local", "local", "synthetic", "synthetic", "case", 0.25,
+ quantities; fingerprint=fingerprint)
+ info = get_run_info(db, "local", "case")
+ @test info.success
+ @test info.runtime_s == 0.25
+ @test all(getfield(info.fingerprint, key) == getfield(fingerprint, key)
+ for key in fieldnames(EnvFingerprint))
+ stored = get_quantities(db, "local", "case")
+ @test stored["finite"].value_real == 2.5
+ @test stored["array"].value_text == quantities[2].value_text
+ @test stored["complex"].value_text == quantities[3].value_text
+ store_failed_run(db, "local", "local", "synthetic", "synthetic", "case", "native failure")
+ @test !get_run_info(db, "local", "case").success
+ @test get_run_info(db, "local", "case").error_msg == "native failure"
+ @test isempty(get_quantities(db, "local", "case"))
+ finally
+ close_database(db)
+ end
+ end
+ finally
+ GC.enable(gc_enabled)
+ end
+ end
+end
diff --git a/src/Analysis/Analysis.jl b/src/Analysis/Analysis.jl
new file mode 100644
index 0000000000..59309953da
--- /dev/null
+++ b/src/Analysis/Analysis.jl
@@ -0,0 +1,24 @@
+"""
+ Analysis
+
+Post-processing and visualization utilities for GPEC simulation outputs.
+
+## Submodules
+
+ - `ForceFreeStates`: Plotting functions for ForceFreeStates (DCON-style ideal MHD stability) results
+ - `Equilibrium`: Plotting functions for equilibrium profiles and flux surfaces
+ - `CoilForcing`: Plotting functions for coil forcing spectra
+ - `PerturbedEquilibrium`: Plotting functions for perturbed equilibrium and singular coupling results
+ - `PerturbedEquilibriumModes`: Data helpers to convert modal GPEC output to (ψ, θ) and (ψ, θ, φ) grids
+ - `ErrorFields`: Plotting functions for the error-field assessment (coil sensitivities, tolerance Monte Carlo, locking risk, phasing maps)
+"""
+module Analysis
+
+include("ForceFreeStates.jl")
+include("Equilibrium.jl")
+include("CoilForcing.jl")
+include("PerturbedEquilibrium.jl")
+include("PerturbedEquilibriumModes.jl")
+include("ErrorFields.jl")
+
+end # module Analysis
diff --git a/src/Analysis/CoilForcing.jl b/src/Analysis/CoilForcing.jl
new file mode 100644
index 0000000000..660d0505b4
--- /dev/null
+++ b/src/Analysis/CoilForcing.jl
@@ -0,0 +1,460 @@
+"""
+ CoilForcing
+
+Visualization functions for coil geometry and the resulting normal field
+perturbations on the plasma boundary.
+
+Two 3D entry points cover the common cases: [`plot_coil_geometry_3d`](@ref) draws the coils
+alone, and [`plot_surface_3d`](@ref) draws the plasma boundary surface — optionally coloured by
+any control-surface field (via [`control_surface_scalar`](@ref)) and/or with coils overlaid —
+the Julia analog of GPEC's `plot_control_3d`. The `:RdBu` colour scale is shared, so a blue
+(positive-current) coil and a blue (positive) field read identically.
+
+All functions return `Plots.jl` plot objects and accept an optional `save_path`
+keyword argument to write the figure to disk.
+"""
+module CoilForcing
+
+using Plots
+import ...Utilities.FourierTransforms: FourierTransform, inverse
+
+"""
+ plot_coil_geometry_3d(coil_sets; save_path=nothing, kwargs...)
+
+Plot the 3D wire geometry of all coil sets.
+
+Each coil set is shown with a distinct color; individual conductors are plotted
+as lines in Cartesian (X, Y, Z) space in meters.
+
+### Arguments
+
+ - `coil_sets`: `Vector{CoilSet}` from `ForcingTerms.load_coil_sets`
+
+### Keyword arguments
+
+ - `save_path`: file path to save the figure (default: `nothing`)
+ - Any extra kwargs are forwarded to `Plots.plot`
+
+### Returns
+
+A `Plots.jl` plot object.
+"""
+function plot_coil_geometry_3d(coil_sets; save_path=nothing, kwargs...)
+ clim = _current_clim(coil_sets)
+
+ p = plot(; xlabel="X [m]", ylabel="Y [m]", zlabel="Z [m]",
+ title="Coil geometry (3D)", legend=false,
+ camera=(30, 20), kwargs...)
+
+ _overlay_coils!(p, coil_sets; clim=clim)
+
+ # Invisible scatter spanning the current range to force the colorbar to appear
+ scatter!(p, [NaN], [NaN], [NaN];
+ zcolor=[0.0], clims=(-clim, clim), color=:RdBu,
+ colorbar_title="I [A]", markersize=0)
+
+ isnothing(save_path) || savefig(p, save_path)
+ return p
+end
+
+# Symmetric current colour-limit (centred at zero) for a set of coils.
+function _current_clim(coil_sets)
+ all_currents = [I for cs in coil_sets for I in cs.currents]
+ return isempty(all_currents) ? 1.0 : max(maximum(abs, all_currents), eps())
+end
+
+"""
+ _overlay_coils!(p, coil_sets; clim=nothing)
+
+Draw each conductor of every coil set onto plot `p` as a 3D `path3d` curve, coloured on a
+symmetric `:RdBu` scale by its current (positive = blue, negative = red — the same mapping
+used for surface fields, so a blue coil and a blue field read identically).
+"""
+function _overlay_coils!(p, coil_sets; clim=nothing)
+ cl = isnothing(clim) ? _current_clim(coil_sets) : clim
+ for cs in coil_sets
+ for j in 1:cs.ncoil
+ t = clamp((cs.currents[j] + cl) / (2cl), 0.0, 1.0)
+ col = get(cgrad(:RdBu), t)
+ for k in 1:cs.s
+ plot!(p, view(cs.x, j, k, :), view(cs.y, j, k, :), view(cs.z, j, k, :);
+ seriestype=:path3d, color=col, lw=2, linestyle=:solid, label="")
+ end
+ end
+ end
+ return p
+end
+
+"""
+ plot_coil_geometry_rz(coil_sets; equil=nothing, psi=nothing, save_path=nothing, kwargs...)
+
+Plot coil cross-sections in the (R, Z) meridional plane.
+
+Each coil strand is shown as a closed curve in `(R, Z) = (√(X²+Y²), Z)` space.
+If `equil` is provided, the plasma boundary is overplotted for reference.
+
+### Arguments
+
+ - `coil_sets`: `Vector{CoilSet}` from `ForcingTerms.load_coil_sets`
+
+### Keyword arguments
+
+ - `equil`: optional `PlasmaEquilibrium`; if given, overlays the plasma boundary
+ - `psi`: flux surface to trace (default: `equil.rzphi_xs[end]`, the outermost grid point)
+ - `save_path`: file path to save the figure (default: `nothing`)
+ - Any extra kwargs are forwarded to `Plots.plot`
+
+### Returns
+
+A `Plots.jl` plot object.
+"""
+function plot_coil_geometry_rz(coil_sets; equil=nothing, psi=nothing, save_path=nothing, kwargs...)
+ p = plot(; xlabel="R [m]", ylabel="Z [m]",
+ title="Coil cross-sections (R, Z)", legend=:topright,
+ aspect_ratio=:equal, kwargs...)
+
+ colors = [:blue, :red, :green, :orange, :purple, :brown, :cyan, :magenta]
+ for (ci, cs) in enumerate(coil_sets)
+ col = colors[mod1(ci, length(colors))]
+ for j in 1:cs.ncoil
+ for k in 1:cs.s
+ R_strand = sqrt.(view(cs.x, j, k, :) .^ 2 .+ view(cs.y, j, k, :) .^ 2)
+ Z_strand = view(cs.z, j, k, :)
+ label = (j == 1 && k == 1) ? cs.name : ""
+ plot!(p, R_strand, Z_strand; label=label, color=col, lw=1.5)
+ end
+ end
+ end
+
+ if !isnothing(equil)
+ psi_bnd = isnothing(psi) ? equil.rzphi_xs[end] : Float64(psi)
+ mtheta_boundary = length(equil.rzphi_ys)
+ hint2d = (Ref(1), Ref(1))
+ R_bnd = zeros(mtheta_boundary)
+ Z_bnd = zeros(mtheta_boundary)
+ for (i, θ_sfl) in enumerate(equil.rzphi_ys)
+ r_minor = sqrt(equil.rzphi_rsquared((psi_bnd, θ_sfl); hint=hint2d))
+ θ_cyl = 2π * (θ_sfl + equil.rzphi_offset((psi_bnd, θ_sfl); hint=hint2d))
+ R_bnd[i] = equil.ro + r_minor * cos(θ_cyl)
+ Z_bnd[i] = equil.zo + r_minor * sin(θ_cyl)
+ end
+ plot!(p, [R_bnd; R_bnd[1]], [Z_bnd; Z_bnd[1]];
+ label="plasma boundary (ψ=$(round(psi_bnd; digits=3)))", color=:black, lw=2)
+ end
+
+ isnothing(save_path) || savefig(p, save_path)
+ return p
+end
+
+"""
+ plot_bn_contour(bn, mtheta, nzeta; n=nothing, save_path=nothing, kwargs...)
+
+Plot the normal magnetic field `bn(θ, ζ)` on the plasma boundary as a 2D heatmap.
+
+Expects the raw Biot-Savart B·n̂ field in Tesla (before `project_normal_flux!`
+converts to flux). If plotting post-projection data, note units are T·m² not T.
+
+### Arguments
+
+ - `bn`: normal field matrix `[mtheta, nzeta]` — typically B·n̂ in Tesla
+ - `mtheta`: number of poloidal grid points
+ - `nzeta`: number of toroidal grid points
+
+### Keyword arguments
+
+ - `n`: toroidal mode number (used for axis label only)
+ - `save_path`: file path to save the figure (default: `nothing`)
+ - Any extra kwargs are forwarded to `Plots.heatmap`
+
+### Returns
+
+A `Plots.jl` plot object.
+"""
+function plot_bn_contour(bn::Matrix{Float64}, mtheta::Int, nzeta::Int;
+ n=nothing, save_path=nothing, kwargs...)
+ # Shift rows so θ=0 (outboard midplane) is centred on the y-axis at 0°
+ bn_wrapped = circshift(bn, (mtheta ÷ 2, 0))
+ theta_deg = range(-180; step=360.0 / mtheta, length=mtheta)
+ zeta_deg = range(0; step=360.0 / nzeta, length=nzeta)
+
+ n_label = isnothing(n) ? "" : " (n=$n)"
+ p = heatmap(zeta_deg, theta_deg, bn_wrapped;
+ xlabel="zeta [deg]", ylabel="theta [deg]",
+ ylims=(-180, 180),
+ title="Normal field bₙ(θ, ζ)$n_label [T]",
+ color=:RdBu, kwargs...)
+
+ isnothing(save_path) || savefig(p, save_path)
+ return p
+end
+
+"""
+ plot_mode_spectrum(forcing_modes; mlow=nothing, mhigh=nothing, save_path=nothing, kwargs...)
+
+Plot the Fourier mode spectrum `|bmn|` vs poloidal mode number m as a step line, grouped by n.
+
+### Arguments
+
+ - `forcing_modes`: `Vector{ForcingMode}` from `compute_coil_forcing_modes!`
+
+### Keyword arguments
+
+ - `mlow`, `mhigh`: poloidal mode range for the x-axis (e.g. from ForceFreeStates config);
+ if provided, sets xlims to span the full stability range even if some modes are zero
+ - `save_path`: file path to save the figure (default: `nothing`)
+ - Any extra kwargs are forwarded to `Plots.plot`
+
+### Returns
+
+A `Plots.jl` plot object.
+"""
+function plot_mode_spectrum(forcing_modes; mlow=nothing, mhigh=nothing, save_path=nothing, kwargs...)
+ n_vals = sort(unique(m.n for m in forcing_modes))
+ colors = [:blue, :red, :green, :orange, :purple, :brown]
+
+ p = plot(; xlabel="Poloidal mode m", ylabel="|Φ_x(m,n)| [unit-norm]",
+ title="Coil forcing mode spectrum",
+ legend=:topright, kwargs...)
+
+ for (ni, n) in enumerate(n_vals)
+ modes_n = filter(m -> m.n == n, forcing_modes)
+ sort!(modes_n; by=m -> m.m)
+ m_vals = [m.m for m in modes_n]
+ amps = abs.([m.amplitude for m in modes_n])
+ col = colors[mod1(ni, length(colors))]
+ m_ext = [m_vals[1] - 1; m_vals; m_vals[end] + 1]
+ amp_ext = [0.0; amps; 0.0]
+ plot!(p, m_ext, amp_ext; label="n=$n", color=col, lw=2, seriestype=:steppre)
+ end
+
+ ylims!(p, (0, Inf))
+ if !isnothing(mlow) && !isnothing(mhigh)
+ # zero endpoints are at mlow-1 and mhigh+1; add ±1 so they're visible with whitespace
+ xlims!(p, mlow - 2, mhigh + 2)
+ end
+
+ isnothing(save_path) || savefig(p, save_path)
+ return p
+end
+
+# Helicity = sign(Bt)·sign(Ip); the SFL→machine toroidal-angle handedness.
+_equil_helicity(equil) = equil.params.bt_sign * equil.params.ip_sign
+
+# Unpack `modes` (a Vector of ForcingMode-like objects filtered to toroidal mode `n`,
+# or a `(m_vals, amplitudes)` tuple) into parallel m and complex-amplitude vectors.
+function _unpack_modes(modes, n::Int)
+ if modes isa Tuple
+ return collect(Int, modes[1]), collect(ComplexF64, modes[2])
+ end
+ sel = [md for md in modes if md.n == n]
+ isempty(sel) && error("control_surface_scalar: no modes found with n=$n")
+ return Int[md.m for md in sel], ComplexF64[md.amplitude for md in sel]
+end
+
+"""
+ control_surface_scalar(equil, modes, n; mtheta=180, nphi=180, psi=nothing,
+ helicity=nothing) -> Matrix{Float64}
+
+Inverse-Fourier-transform a spectral control-surface quantity into a real-space `[mtheta, nphi]`
+field on the plasma boundary, ready to colour [`plot_surface_3d`](@ref).
+
+`modes` are complex Fourier amplitudes indexed by poloidal mode `m` for a single toroidal mode
+`n` — a `Vector{ForcingMode}` (filtered to `n`) or a `(m_vals, amplitudes)` tuple. The quantity is
+arbitrary (e.g. applied normal field `b_n_x`, total `b_n`, displacement `xi_n`); the caller
+supplies whichever modes they want to view.
+
+The transform inverts the SFL Fourier decomposition used by `ForcingTerms.fourier_decompose_bn`:
+`f(θ) = Σ_m amp_m e^{i m θ}`, the per-θ correction `e^{i n ν(ψ,θ)}` from `equil.rzphi_nu`, then the
+toroidal extension in the **machine angle** `c(θ,φ) = -Re[f(θ) e^{i n·hel·φ}]`. The `e^{i n·hel·φ}`
+follows from the SFL→machine map `φ = -hel(2π ζ + ν)` (`ζ` the SFL toroidal angle the modes were
+decomposed against); substituting `2π ζ = -hel·φ - ν` is what turns the decomposition's `ζ`
+exponential into the `ν` correction times `e^{i n·hel·φ}`.
+
+!!! note "Sign / helicity convention"
+
+ The reconstruction tracks the source coil **toroidally** (the field lobe sits at the coil's φ),
+ carried by `helicity = sign(Bt)·sign(Ip)` in `e^{i n·hel·φ}` (`equil.rzphi_nu`/`equil.params`).
+ The leading `-` is a display orientation so that **a positive (blue) coil current reads as a
+ positive (blue) `b_n_x` lobe beneath it** — GPEC's outward-normal flux is intrinsically negative
+ there, so the overall sign is the blue-coil↔blue-surface convention while the spatial structure
+ and magnitude are physical. Pass `helicity` to override `sign(Bt)·sign(Ip)` if the toroidal
+ tracking is wrong for your machine.
+
+!!! note "Band-limited reconstruction"
+
+ The field is reconstructed only from the supplied `m` modes, so it is band-limited to that
+ poloidal range. A source placed within ~one grid cell of the surface makes the field
+ near-singular and the truncated series rings (Gibbs oscillation — e.g. a spurious dip where a
+ single lobe is expected). Keep coils at a realistic standoff from the boundary, or widen the
+ `m` range, for a clean reconstruction.
+
+### Keyword arguments
+
+ - `mtheta`, `nphi`: poloidal/toroidal grid resolution
+ - `psi`: flux surface (default `equil.rzphi_xs[end]`, the boundary)
+ - `helicity`: override `sign(Bt)·sign(Ip)`
+"""
+function control_surface_scalar(equil, modes, n::Int; mtheta::Int=180, nphi::Int=180,
+ psi=nothing, helicity=nothing)
+ psi_b = isnothing(psi) ? equil.rzphi_xs[end] : Float64(psi)
+ m_vals, amps = _unpack_modes(modes, n)
+ m_low, m_high = extrema(m_vals)
+ mpert = m_high - m_low + 1
+
+ vec = zeros(ComplexF64, mpert)
+ for (m, a) in zip(m_vals, amps)
+ vec[m-m_low+1] = a
+ end
+
+ # m→θ inverse transform; f[i] is at normalized θ = (i-1)/mtheta
+ ft = FourierTransform(mtheta, mpert, m_low)
+ f = inverse(ft, vec)
+
+ # SFL→machine toroidal-angle correction e^{i n ν(ψ,θ)}. The modes are decomposed on the SFL
+ # grid against e^{-i(m θ - n ζ)}, with the machine angle φ = -hel(2π ζ + ν) (see CoilFourier
+ # `sample_boundary_grid`). Substituting 2π ζ = -hel φ - ν into the inverse turns the ζ
+ # exponential into e^{i n ν(θ)} e^{i n hel φ}: the per-θ ν enters the field, hel sets the
+ # toroidal handedness, and the real field reconstructs faithfully — so a positive (blue) coil
+ # current yields positive (blue) b_n_x directly beneath the coil with no extra sign flip.
+ hel = isnothing(helicity) ? _equil_helicity(equil) : helicity
+ hint = (Ref(1), Ref(1))
+ for i in 1:mtheta
+ θ = (i - 1) / mtheta
+ ν = equil.rzphi_nu((psi_b, θ); hint=hint)
+ f[i] *= exp(im * n * ν)
+ end
+
+ # θ→φ extension in the machine angle: c(θ,φ) = -Re[ f(θ) e^{i n hel φ} ]. The reconstruction
+ # tracks the source coil toroidally (the lobe sits at the coil's φ); the leading − is a display
+ # orientation that makes a positive (blue) coil current read as a positive (blue) b_n_x lobe
+ # beneath it. GPEC's outward-normal flux is intrinsically negative there, so this overall sign
+ # is the blue-coil↔blue-surface convention — the spatial structure and magnitude are physical.
+ # It is a constant flip (not helicity-dependent): the normal-projection sign is set by geometry,
+ # while hel only carries the toroidal handedness, already in the exponential.
+ c = zeros(Float64, mtheta, nphi)
+ for k in 1:nphi
+ ph = exp(im * n * hel * (k - 1) * 2π / nphi)
+ for i in 1:mtheta
+ c[i, k] = -real(f[i] * ph)
+ end
+ end
+ return c
+end
+
+# Build the closed (θ,φ)→(x,y,z) boundary surface from the equilibrium splines.
+# Returns X, Y, Z each [mtheta+1, nphi+1] (wrapped so the torus closes seamlessly).
+function _boundary_surface_xyz(equil, mtheta::Int, nphi::Int, psi)
+ psi_b = isnothing(psi) ? equil.rzphi_xs[end] : Float64(psi)
+ hint = (Ref(1), Ref(1))
+ R = zeros(mtheta)
+ Z = zeros(mtheta)
+ for i in 1:mtheta
+ θ = (i - 1) / mtheta
+ r_minor = sqrt(equil.rzphi_rsquared((psi_b, θ); hint=hint))
+ θ_cyl = 2π * (θ + equil.rzphi_offset((psi_b, θ); hint=hint))
+ R[i] = equil.ro + r_minor * cos(θ_cyl)
+ Z[i] = equil.zo + r_minor * sin(θ_cyl)
+ end
+
+ X = zeros(mtheta + 1, nphi + 1)
+ Y = zeros(mtheta + 1, nphi + 1)
+ Zs = zeros(mtheta + 1, nphi + 1)
+ for k in 1:(nphi+1)
+ φ = (k - 1) * 2π / nphi
+ cφ, sφ = cos(φ), sin(φ)
+ for i in 1:(mtheta+1)
+ ii = i <= mtheta ? i : 1
+ X[i, k] = R[ii] * cφ
+ Y[i, k] = R[ii] * sφ
+ Zs[i, k] = Z[ii]
+ end
+ end
+ return X, Y, Zs
+end
+
+# Wrap a [mtheta, nphi] field to [mtheta+1, nphi+1] to match the closed surface mesh.
+_wrap_field(c) = [c[i <= size(c, 1) ? i : 1, k <= size(c, 2) ? k : 1]
+ for i in 1:(size(c, 1)+1), k in 1:(size(c, 2)+1)]
+
+"""
+ plot_surface_3d(equil; color_by=nothing, coil_sets=nothing, mtheta=180, nphi=180,
+ psi=nothing, clim=nothing, colorbar_title="", title="Plasma boundary",
+ camera=(35, 25), save_path=nothing, kwargs...)
+
+Plot the 3D plasma boundary surface, optionally coloured by a control-surface field and/or with
+coils overlaid — the Julia analog of GPEC's `plot_control_3d`.
+
+!!! note "Backend for coloured surfaces"
+
+ Scalar colouring of the closed surface requires a PlotlyJS-style backend (`plotlyjs()`,
+ already a GPEC dependency); the default GR backend cannot colour a parametric surface by an
+ independent array and will draw an **uncoloured** surface with a warning. Call `plotlyjs()`
+ before requesting `color_by`. Coil overlay and uncoloured surfaces work on any backend.
+
+### Keyword arguments
+
+ - `color_by`: optional real-space `[mtheta, nphi]` scalar (any control-surface output — e.g. from
+ [`control_surface_scalar`](@ref)). Coloured on a symmetric `:RdBu` scale centred at zero
+ (positive = blue), matching the coil-current colours. `nothing` draws an uncoloured surface.
+ - `coil_sets`: optional `Vector{CoilSet}` overlaid as 3D curves (see [`plot_coil_geometry_3d`](@ref)).
+ - `mtheta`, `nphi`, `psi`: surface grid resolution and flux surface (must match `color_by`).
+ - `clim`: symmetric colour limit (default `maximum(abs, color_by)`).
+ - `save_path`: file path to save the figure; extra `kwargs` forward to `Plots.surface`.
+
+### Returns
+
+A `Plots.jl` plot object.
+
+ plot_surface_3d(equil, modes, n; coil_sets=nothing, colorbar_title="", kwargs...)
+
+Convenience method: colour the surface by [`control_surface_scalar(equil, modes, n; …)`](@ref).
+"""
+function plot_surface_3d(equil; color_by=nothing, coil_sets=nothing, mtheta::Int=180,
+ nphi::Int=180, psi=nothing, clim=nothing, colorbar_title="",
+ title="Plasma boundary", camera=(35, 25), save_path=nothing, kwargs...)
+ X, Y, Z = _boundary_surface_xyz(equil, mtheta, nphi, psi)
+
+ common = (; xlabel="X [m]", ylabel="Y [m]", zlabel="Z [m]", title=title,
+ legend=false, aspect_ratio=:equal, camera=camera)
+
+ want_color = !isnothing(color_by)
+ if want_color
+ size(color_by) == (mtheta, nphi) ||
+ error("color_by must be [mtheta, nphi] = ($mtheta, $nphi), got $(size(color_by))")
+ # Only PlotlyJS-style backends honour `fill_z` on a closed/parametric surface; GR silently
+ # colours by Z instead, so warn and degrade rather than show a misleading figure.
+ if !(backend_name() in (:plotlyjs, :pythonplot, :pyplot))
+ @warn "plot_surface_3d: the active Plots backend ($(backend_name())) cannot colour a " *
+ "parametric 3D surface by a scalar — call `plotlyjs()` first for field-coloured " *
+ "surfaces. Drawing an uncoloured surface." maxlog = 1
+ want_color = false
+ end
+ end
+
+ if want_color
+ cl = isnothing(clim) ? max(maximum(abs, color_by), eps()) : clim
+ cw = _wrap_field(color_by)
+ p = surface(X, Y, Z; fill_z=cw, color=:RdBu, clims=(-cl, cl),
+ colorbar_title=colorbar_title, common..., kwargs...)
+ else
+ p = surface(X, Y, Z; color=:grays, alpha=0.5, colorbar=false, common..., kwargs...)
+ end
+
+ isnothing(coil_sets) || _overlay_coils!(p, coil_sets)
+ isnothing(save_path) || savefig(p, save_path)
+ return p
+end
+
+function plot_surface_3d(equil, modes, n::Int; coil_sets=nothing, mtheta::Int=180,
+ nphi::Int=180, psi=nothing, helicity=nothing,
+ colorbar_title="", save_path=nothing, kwargs...)
+ c = control_surface_scalar(equil, modes, n; mtheta=mtheta, nphi=nphi, psi=psi, helicity=helicity)
+ return plot_surface_3d(equil; color_by=c, coil_sets=coil_sets, mtheta=mtheta, nphi=nphi,
+ psi=psi, colorbar_title=colorbar_title, save_path=save_path, kwargs...)
+end
+
+export plot_coil_geometry_3d, plot_coil_geometry_rz
+export plot_bn_contour, plot_mode_spectrum
+export plot_surface_3d, control_surface_scalar
+
+end # module CoilForcing
diff --git a/src/Analysis/Equilibrium.jl b/src/Analysis/Equilibrium.jl
new file mode 100644
index 0000000000..f00a406cdd
--- /dev/null
+++ b/src/Analysis/Equilibrium.jl
@@ -0,0 +1,400 @@
+"""
+ Equilibrium
+
+Post-processing and visualization functions for GPEC equilibrium objects and HDF5 outputs.
+"""
+module Equilibrium
+
+using HDF5
+using LaTeXStrings
+using Plots
+
+"""
+ plot_qprofile(h5path; show_singular=true, save_path=nothing)
+
+Plot the safety factor q(ψ) profile, with optional vertical markers at each rational surface
+and horizontal reference lines at q0 and q95.
+
+### Arguments
+
+ - `h5path`: Path to a GPEC HDF5 output file
+
+### Keyword arguments
+
+ - `show_singular`: If `true`, overlay rational surface locations (default: `true`)
+ - `save_path`: If provided, save the figure to this path (default: `nothing`)
+
+### Returns
+
+A `Plots.jl` plot object.
+"""
+function plot_qprofile(h5path; show_singular=true, save_path=nothing)
+ xs, q, q0, q95 = h5open(h5path, "r") do fid
+ read(fid["Equilibrium/Profiles/psi"]), read(fid["Equilibrium/Profiles/q"]),
+ read(fid["Equilibrium/q_axis"]), read(fid["Equilibrium/q_95"])
+ end
+
+ p = plot(
+ xs, q;
+ xlabel="Norm. Poloidal Flux",
+ ylabel="q",
+ title="",
+ legend=false,
+ xlims=(0, 1),
+ left_margin=10Plots.mm,
+ bottom_margin=5Plots.mm,
+ right_margin=8Plots.mm # annotations at x=1.0 need room on the right
+ )
+ hline!(p, [q0, q95]; linestyle=:dot, color=:gray, label=nothing)
+ annotate!(p, 1.0, q0, text(" q0=$(round(q0, digits=2))", 7, :left, :gray))
+ annotate!(p, 1.0, q95, text(" q95=$(round(q95, digits=2))", 7, :left, :gray))
+
+ if show_singular
+ msing, psi_sing, q_sing = h5open(h5path, "r") do fid
+ read(fid["SingularSurfaces/rational_count"]), read(fid["SingularSurfaces/rational_psi"]), read(fid["SingularSurfaces/rational_q"])
+ end
+ for s in 1:msing
+ vline!(p, [psi_sing[s]]; linestyle=:dash, color=:red, label=nothing)
+ annotate!(p, psi_sing[s], q_sing[s],
+ text(" q=$(round(q_sing[s], digits=2))", 7, :left, :red))
+ end
+ end
+
+ isnothing(save_path) || savefig(p, save_path)
+ return p
+end
+
+"""
+ plot_pressure_profile(h5path; save_path=nothing)
+
+Plot the μ₀p(ψ) pressure profile. Vertical dashed lines mark rational surfaces if present.
+
+### Arguments
+
+ - `h5path`: Path to a GPEC HDF5 output file
+
+### Keyword arguments
+
+ - `save_path`: If provided, save the figure to this path (default: `nothing`)
+
+### Returns
+
+A `Plots.jl` plot object.
+"""
+function plot_pressure_profile(h5path; save_path=nothing)
+ xs, mu0p, msing, psi_sing = h5open(h5path, "r") do fid
+ read(fid["Equilibrium/Profiles/psi"]), read(fid["Equilibrium/Profiles/mu0p"]),
+ read(fid["SingularSurfaces/rational_count"]), read(fid["SingularSurfaces/rational_psi"])
+ end
+
+ p = plot(
+ xs, mu0p;
+ xlabel="Norm. Poloidal Flux",
+ ylabel="μ₀p",
+ title="",
+ legend=false,
+ xlims=(0, 1),
+ left_margin=10Plots.mm,
+ bottom_margin=5Plots.mm
+ )
+ for s in 1:msing
+ vline!(p, [psi_sing[s]]; linestyle=:dash, color=:red, label=nothing)
+ end
+
+ isnothing(save_path) || savefig(p, save_path)
+ return p
+end
+
+"""
+ plot_f_profile(h5path; save_path=nothing)
+
+Plot the toroidal field function 2πF(ψ) profile (F = RBφ/(2π)).
+
+### Arguments
+
+ - `h5path`: Path to a GPEC HDF5 output file
+
+### Keyword arguments
+
+ - `save_path`: If provided, save the figure to this path (default: `nothing`)
+
+### Returns
+
+A `Plots.jl` plot object.
+"""
+function plot_f_profile(h5path; save_path=nothing)
+ xs, twopif, msing, psi_sing = h5open(h5path, "r") do fid
+ read(fid["Equilibrium/Profiles/psi"]), read(fid["Equilibrium/Profiles/2piF"]),
+ read(fid["SingularSurfaces/rational_count"]), read(fid["SingularSurfaces/rational_psi"])
+ end
+
+ p = plot(
+ xs, twopif;
+ xlabel="Norm. Poloidal Flux",
+ ylabel="2πF",
+ title="",
+ legend=false,
+ xlims=(0, 1),
+ left_margin=10Plots.mm,
+ bottom_margin=5Plots.mm
+ )
+ for s in 1:msing
+ vline!(p, [psi_sing[s]]; linestyle=:dash, color=:red, label=nothing)
+ end
+
+ isnothing(save_path) || savefig(p, save_path)
+ return p
+end
+
+"""
+ plot_flux_surfaces(h5path; n_psi=11, n_theta=18, save_path=nothing)
+
+Plot flux surface contours (constant ψ, blue) and field-line angle spokes (constant θ, red)
+in physical (R, Z) space, reading nodal grid data directly from HDF5.
+
+Psi contours are drawn at `n_psi` evenly spaced values between psilow and psihigh.
+Theta spokes are drawn at `n_theta` evenly spaced values.
+
+### Arguments
+
+ - `h5path`: Path to a GPEC HDF5 output file
+
+### Keyword arguments
+
+ - `n_psi`: Number of constant-ψ contours to draw (default: 11)
+ - `n_theta`: Number of constant-θ/θ spokes to draw (default: 18)
+ - `save_path`: If provided, save the figure to this path (default: `nothing`)
+
+### Returns
+
+A `Plots.jl` plot object.
+"""
+function plot_flux_surfaces(h5path; n_psi=11, n_theta=18, save_path=nothing)
+ rcoords, offset_data, xs_rz, ys_rz, ro, zo, msing, psi_sing, q_sing = h5open(h5path, "r") do fid
+ read(fid["Equilibrium/Geometry/rcoords"]), read(fid["Equilibrium/Geometry/offset"]),
+ read(fid["Equilibrium/Geometry/psi"]), read(fid["Equilibrium/Geometry/theta"]),
+ read(fid["Equilibrium/R_axis"]), read(fid["Equilibrium/Z_axis"]),
+ read(fid["SingularSurfaces/rational_count"]), read(fid["SingularSurfaces/rational_psi"]), read(fid["SingularSurfaces/rational_q"])
+ end
+
+ n_psi_grid = length(xs_rz)
+ n_theta_grid = length(ys_rz)
+
+ # Build R, Z on the full nodal grid
+ R_grid = Matrix{Float64}(undef, n_psi_grid, n_theta_grid)
+ Z_grid = Matrix{Float64}(undef, n_psi_grid, n_theta_grid)
+ for ipsi in 1:n_psi_grid
+ for itheta in 1:n_theta_grid
+ rfac = sqrt(max(0.0, rcoords[ipsi, itheta]))
+ eta = 2π * (ys_rz[itheta] + offset_data[ipsi, itheta])
+ R_grid[ipsi, itheta] = ro + rfac * cos(eta)
+ Z_grid[ipsi, itheta] = zo + rfac * sin(eta)
+ end
+ end
+
+ p = plot(;
+ title="Flux surfaces in (R, Z)",
+ xlabel="R [m]",
+ ylabel="Z [m]",
+ aspect_ratio=:equal,
+ legend=:outertopright,
+ left_margin=10Plots.mm,
+ bottom_margin=5Plots.mm
+ )
+
+ psi_indices = round.(Int, range(1, n_psi_grid; length=n_psi))
+ theta_indices = round.(Int, range(1, n_theta_grid; length=n_theta))
+
+ for (i, ipsi) in enumerate(psi_indices)
+ label = i == 1 ? "Constant ψ" : ""
+ plot!(p, [R_grid[ipsi, :]; R_grid[ipsi, 1]], [Z_grid[ipsi, :]; Z_grid[ipsi, 1]];
+ color=:steelblue, linewidth=1.5, label=label)
+ end
+ for (i, itheta) in enumerate(theta_indices)
+ label = i == 1 ? "Constant θ" : ""
+ plot!(p, R_grid[:, itheta], Z_grid[:, itheta];
+ color=:tomato, linewidth=0.8, label=label)
+ end
+ # Draw rational surface flux contours in red, annotated at the bottom (min Z) of each
+ for s in 1:msing
+ idx = argmin(abs.(xs_rz .- psi_sing[s]))
+ q_label = abs(q_sing[s] - round(q_sing[s])) < 0.05 ?
+ "q=$(round(Int, q_sing[s]))" : "q=$(round(q_sing[s], digits=2))"
+ plot!(p, [R_grid[idx, :]; R_grid[idx, 1]], [Z_grid[idx, :]; Z_grid[idx, 1]];
+ color=:red, linewidth=1.5,
+ label=s == 1 ? "Rational surface" : "")
+ itheta_bot = argmin(Z_grid[idx, :])
+ annotate!(p, R_grid[idx, itheta_bot], Z_grid[idx, itheta_bot],
+ text(" $q_label", 7, :left, :red))
+ end
+
+ isnothing(save_path) || savefig(p, save_path)
+ return p
+end
+
+"""
+ plot_gse_by_theta(h5path; n_theta_lines=8, save_path=nothing)
+
+Plot Grad-Shafranov error vs ψ_N (log scale) for several θ slices, with the
+flux-surface-integrated error overplotted as a thick black line. Reads `gse.h5`
+(and optionally `gsei.h5`) from the same directory as `h5path`. Returns `nothing`
+if `gse.h5` is not found (requires `diagnose_src = true` in the equilibrium configuration).
+
+### Arguments
+
+ - `h5path`: Path to a GPEC HDF5 output file (used to locate `gse.h5`)
+
+### Keyword arguments
+
+ - `n_theta_lines`: Number of evenly-spaced θ slices to overlay (default: 8)
+ - `save_path`: If provided, save the figure to this path (default: `nothing`)
+
+### Returns
+
+A `Plots.jl` plot object, or `nothing` if `gse.h5` is absent.
+"""
+function plot_gse_by_theta(h5path; n_theta_lines=8, save_path=nothing)
+ gse_path = joinpath(dirname(h5path), "gse.h5")
+ isfile(gse_path) || return nothing
+
+ gse_data = h5open(gse_path, "r") do fid
+ read(fid["gse_data"]) # (npsi, ntheta, 7): cols = θ, ψ, flux1, flux2, source, total, error
+ end
+
+ _, ntheta, _ = size(gse_data)
+ theta_indices = round.(Int, range(1, ntheta; length=n_theta_lines))
+
+ p = plot(;
+ xlabel="Norm. Poloidal Flux",
+ ylabel="GSE error",
+ title="",
+ yscale=:log10,
+ xlims=(0, 1),
+ left_margin=10Plots.mm,
+ bottom_margin=5Plots.mm
+ )
+ for (i, itheta) in enumerate(theta_indices)
+ psi_col = gse_data[:, itheta, 2]
+ err_col = gse_data[:, itheta, 7]
+ plot!(p, psi_col, err_col; label=i == 1 ? "Const. θ" : "", alpha=0.6)
+ end
+
+ # Overplot flux-surface-integrated error as thick reference line
+ gsei_path = joinpath(dirname(h5path), "gsei.h5")
+ if isfile(gsei_path)
+ xs_int, errori = h5open(gsei_path, "r") do fid
+ read(fid["xs"]), read(fid["errori"])
+ end
+ plot!(p, xs_int, vec(errori);
+ color=:black, linewidth=2.5, linestyle=:solid, label="integrated")
+ end
+
+ isnothing(save_path) || savefig(p, save_path)
+ return p
+end
+
+"""
+ plot_gse_integrated(h5path; save_path=nothing)
+
+Plot the flux-surface-integrated Grad-Shafranov error (log scale) vs ψ_N, reading from
+`gsei.h5` in the same directory as `h5path`. Returns `nothing` if `gsei.h5` is not found
+(requires `diagnose_src = true` in the equilibrium configuration).
+
+### Arguments
+
+ - `h5path`: Path to a GPEC HDF5 output file (used to locate `gsei.h5`)
+
+### Keyword arguments
+
+ - `save_path`: If provided, save the figure to this path (default: `nothing`)
+
+### Returns
+
+A `Plots.jl` plot object, or `nothing` if `gsei.h5` is absent.
+"""
+function plot_gse_integrated(h5path; save_path=nothing)
+ gsei_path = joinpath(dirname(h5path), "gsei.h5")
+ isfile(gsei_path) || return nothing
+
+ xs, errlogi = h5open(gsei_path, "r") do fid
+ read(fid["xs"]), read(fid["errlogi"])
+ end
+
+ p = plot(
+ xs, vec(errlogi);
+ xlabel="Norm. Poloidal Flux",
+ ylabel="log₁₀(integrated GSE)",
+ title="Flux-surface-integrated Grad-Shafranov error",
+ legend=false,
+ left_margin=10Plots.mm,
+ bottom_margin=5Plots.mm
+ )
+
+ isnothing(save_path) || savefig(p, save_path)
+ return p
+end
+
+"""
+ plot_equilibrium_summary(h5path; save_path=nothing)
+
+Summary of equilibrium profiles and geometry. The (R, Z) flux surface plot occupies the
+full left column. Profile plots are stacked in the right column:
+
+ - q(ψ) safety factor with rational surface markers (`plot_qprofile`)
+ - μ₀p(ψ) pressure profile (`plot_pressure_profile`)
+ - 2πF(ψ) toroidal field function (`plot_f_profile`)
+
+If `gse.h5` is present (requires `diagnose_src = true`), a combined Grad-Shafranov error
+panel (θ slices + integrated, log scale) is appended at the bottom of the right column.
+
+### Arguments
+
+ - `h5path`: Path to a GPEC HDF5 output file
+
+### Keyword arguments
+
+ - `save_path`: If provided, save the figure to this path (default: `nothing`)
+
+### Returns
+
+A `Plots.jl` plot object.
+"""
+function plot_equilibrium_summary(h5path; save_path=nothing)
+ q0, q95, betat, betan, kappa, li1 = h5open(h5path, "r") do fid
+ read(fid["Equilibrium/q_axis"]), read(fid["Equilibrium/q_95"]),
+ read(fid["Equilibrium/beta_t"]), read(fid["Equilibrium/beta_N"]),
+ read(fid["Equilibrium/kappa"]), read(fid["Equilibrium/l_i_1"])
+ end
+
+ title_str = "q0=$(round(q0,digits=2)) q95=$(round(q95,digits=2)) βₜ=$(round(betat,digits=3)) βₙ=$(round(betan,digits=3)) κ=$(round(kappa,digits=2)) li1=$(round(li1,digits=3))"
+
+ p_rz = plot_flux_surfaces(h5path)
+ p_q = plot_qprofile(h5path; show_singular=true)
+ p_pres = plot_pressure_profile(h5path)
+ p_f = plot_f_profile(h5path)
+ p_gse = plot_gse_by_theta(h5path) # includes integrated overplot; nothing if absent
+
+ # Suppress x-axis labels/ticks on all but the bottom profile panel — they share the
+ # same ψ_N axis and labeling every panel wastes vertical space.
+ hide_xaxis!(p) = plot!(p; xlabel="", xformatter=_ -> "", bottom_margin=1Plots.mm)
+
+ if isnothing(p_gse)
+ hide_xaxis!(p_q)
+ hide_xaxis!(p_pres)
+ l = @layout [a{0.38w} [b; c; d]]
+ p = plot(p_rz, p_q, p_pres, p_f; layout=l, size=(1300, 750),
+ plot_title=title_str, plot_titlefontsize=10, top_margin=8Plots.mm)
+ else
+ hide_xaxis!(p_q)
+ hide_xaxis!(p_pres)
+ hide_xaxis!(p_f)
+ l = @layout [a{0.38w} [b; c; d; e]]
+ p = plot(p_rz, p_q, p_pres, p_f, p_gse; layout=l, size=(1300, 1000),
+ plot_title=title_str, plot_titlefontsize=10, top_margin=8Plots.mm)
+ end
+
+ isnothing(save_path) || savefig(p, save_path)
+ return p
+end
+
+end # module Equilibrium
diff --git a/src/Analysis/ErrorFields.jl b/src/Analysis/ErrorFields.jl
new file mode 100644
index 0000000000..ea980b4008
--- /dev/null
+++ b/src/Analysis/ErrorFields.jl
@@ -0,0 +1,1003 @@
+"""
+ ErrorFields
+
+Plots for the error-field assessment stored under `ErrorFields/` of a GPEC HDF5 output:
+per-coil sensitivities, the tolerance Monte Carlo distributions, the locking risk and its
+dependence on tolerance, the threshold scaling, the dominant coupling mode, and coil-array
+phasing maps. Every plot takes a list of `label => h5path` pairs so design revisions can be
+overplotted, with a single-path convenience method for the common case.
+"""
+module ErrorFields
+
+using HDF5
+using Plots
+using LinearAlgebra
+using TOML
+
+import ...ErrorFields as EF
+import ...PerturbedEquilibrium as PE
+import ...ForcingTerms as FT
+
+"""
+A label paired with something to plot: a `gpec.h5` path, or a result already in memory
+(`ErrorFields.SensitivityTable`, `CoilSensitivities`, `MonteCarloResult`, `RiskResult`, or a
+vector of `CoilOverlap`). Analysing coil geometry that was never part of a run produces the
+latter, so the plots accept both.
+"""
+const Sources = AbstractVector{<:Pair{String,<:Any}}
+
+"""
+A single unlabelled source: a `gpec.h5` path, or one in-memory result.
+"""
+const SingleSource = Union{AbstractString,EF.SensitivityTable,EF.CoilSensitivities,EF.MonteCarloResult,EF.RiskResult,AbstractVector{EF.CoilOverlap}}
+
+_sources(source) = [_default_label(source) => source]
+_default_label(h5path::AbstractString) = basename(dirname(abspath(h5path)))
+_default_label(_) = "in memory"
+
+# Every field the plots read. One template so the HDF5 and in-memory loaders cannot drift apart.
+const _BLANK = (; coil_names=nothing, delta_as_designed=nothing, abs_delta_shift_per_mm=nothing,
+ abs_delta_tilt_per_deg=nothing, abs_delta_rim_per_mm=nothing, shift_sensitivity_per_m=nothing, tilt_sensitivity_per_deg=nothing,
+ field_as_designed=nothing, b_t0=nothing, resonant_fraction_percent=nothing, major_radius_m=nothing,
+ shift_linearity_residual=nothing, tilt_linearity_residual=nothing, fd_step_shift_m=nothing, fd_step_tilt_deg=nothing,
+ tolerances=nothing, abs_delta_bin_edges=nothing, abs_delta_pdf=nothing, abs_delta_efc_pdf=nothing, abs_delta_pdf_batches=nothing, abs_delta_total_as_designed=nothing,
+ abs_delta_worst_case=nothing, abs_delta_sampled_mean=nothing, clamped_fraction=nothing, threshold_pdf=nothing,
+ locking_probability_given_delta=nothing, threshold_fit=nothing, locking_probability_percent=nothing, locking_probability_efc_percent=nothing,
+ scan_scale=nothing, scan_locking_probability_percent=nothing, scan_locking_probability_efc_percent=nothing, scan_locking_probability_spread_percent=nothing,
+ scan_locking_probability_efc_spread_percent=nothing, dominant_v=nothing, singular_values=nothing, mn_index=nothing)
+
+_load(d::NamedTuple) = merge(_BLANK, d)
+_load(h5path::AbstractString) = _load(_load_h5(h5path))
+
+_load(t::EF.SensitivityTable) = _load((; coil_names=t.coil_names, delta_as_designed=t.delta_as_designed,
+ abs_delta_shift_per_mm=t.abs_delta_shift_per_mm, abs_delta_tilt_per_deg=t.abs_delta_tilt_per_deg,
+ abs_delta_rim_per_mm=t.abs_delta_rim_per_mm, shift_sensitivity_per_m=t.shift_sensitivity_per_m, tilt_sensitivity_per_deg=t.tilt_sensitivity_per_deg))
+
+_load(s::EF.CoilSensitivities) = _load((; coil_names=s.coil_names, field_as_designed=s.field_as_designed, b_t0=s.b_t0,
+ shift_sensitivity_per_m=s.shift_sensitivity_per_m, tilt_sensitivity_per_deg=s.tilt_sensitivity_per_deg, major_radius_m=s.major_radius_m,
+ shift_linearity_residual=s.shift_linearity_residual, tilt_linearity_residual=s.tilt_linearity_residual))
+
+_load(r::EF.MonteCarloResult) =
+ _load((; abs_delta_bin_edges=r.abs_delta_bin_edges, abs_delta_pdf=r.abs_delta_pdf, abs_delta_efc_pdf=r.abs_delta_efc_pdf, abs_delta_pdf_batches=r.abs_delta_pdf_batches,
+ abs_delta_total_as_designed=r.abs_delta_total_as_designed, abs_delta_worst_case=r.abs_delta_worst_case, abs_delta_sampled_mean=r.abs_delta_sampled_mean,
+ clamped_fraction=r.clamped_fraction))
+
+_load(r::EF.RiskResult) = _load((; abs_delta_bin_edges=r.abs_delta_bin_edges, threshold_pdf=r.threshold_pdf,
+ locking_probability_given_delta=r.locking_probability_given_delta, threshold_fit=r.threshold_fit,
+ locking_probability_percent=r.locking_probability_percent, locking_probability_efc_percent=r.locking_probability_efc_percent))
+
+# Drop the unset entries of a loaded source so two of them can be combined without one's blanks
+# erasing the other's values.
+_present(d::NamedTuple) = NamedTuple(k => v for (k, v) in pairs(d) if v !== nothing)
+
+"""
+The overlap distribution lives on the Monte Carlo result and the penetration threshold on the risk
+result, so a plot that draws both against each other needs the pair. Pass them together as a tuple
+rather than separately, which would leave each half unable to find the other.
+"""
+_load(pair::Tuple{EF.MonteCarloResult,EF.RiskResult}) =
+ _load(merge(_present(_load(pair[1])), _present(_load(pair[2]))))
+
+_load(ovs::AbstractVector{EF.CoilOverlap}) = _load((; coil_names=[o.coil_name for o in ovs],
+ delta_as_designed=[o.delta for o in ovs], resonant_fraction_percent=[o.resonant_fraction_percent for o in ovs],
+ b_t0=isempty(ovs) ? nothing : first(ovs).b_t0))
+
+# The finite-difference steps the run's sensitivities were taken at, from the recorded deck; a
+# file without one gets the control defaults, which is what an unset deck used.
+function _fd_steps(f)
+ defaults = EF.ErrorFieldsControl()
+ ef = haskey(f, "Input/gpec_toml_raw") ? get(TOML.parse(read(f["Input/gpec_toml_raw"])), "ErrorFields", Dict{String,Any}()) : Dict{String,Any}()
+ return Float64(get(ef, "fd_step_shift_m", defaults.fd_step_shift_m)), Float64(get(ef, "fd_step_tilt_deg", defaults.fd_step_tilt_deg))
+end
+
+function _load_h5(h5path::AbstractString)
+ tolerances = EF.read_tolerance_snapshot(h5path)
+ h5open(h5path, "r") do f
+ has(k) = haskey(f, k)
+ # Take the group paths from the writer's own constants rather than repeating them here:
+ # two spellings of the schema drift apart silently, and a renamed group would surface as an
+ # empty plot rather than an error.
+ cs, mc, rk = EF._H5_GROUP, EF._MC_GROUP, EF._RISK_GROUP
+ h_shift, h_tilt = _fd_steps(f)
+ (
+ coil_names=has(cs) ? read(f["$cs/coil_name"]) : nothing,
+ delta_as_designed=has(cs) ? read(f["$cs/DominantMode/delta_as_designed"]) : nothing,
+ abs_delta_shift_per_mm=has(cs) ? read(f["$cs/DominantMode/abs_delta_shift_per_mm"]) : nothing,
+ abs_delta_tilt_per_deg=has(cs) ? read(f["$cs/DominantMode/abs_delta_tilt_per_deg"]) : nothing,
+ abs_delta_rim_per_mm=has(cs) ? read(f["$cs/DominantMode/abs_delta_rim_per_mm"]) : nothing,
+ shift_sensitivity_per_m=has(cs) ? read(f["$cs/DominantMode/shift_sensitivity_per_m"]) : nothing,
+ tilt_sensitivity_per_deg=has(cs) ? read(f["$cs/DominantMode/tilt_sensitivity_per_deg"]) : nothing,
+ field_as_designed=has(cs) ? read(f["$cs/field_as_designed"]) : nothing,
+ b_t0=has("Equilibrium/B_T_axis") ? Float64(read(f["Equilibrium/B_T_axis"])) : nothing,
+ major_radius_m=has(cs) ? read(f["$cs/major_radius_m"]) : nothing,
+ shift_linearity_residual=has(cs) ? read(f["$cs/shift_linearity_residual"]) : nothing,
+ tilt_linearity_residual=has(cs) ? read(f["$cs/tilt_linearity_residual"]) : nothing,
+ fd_step_shift_m=h_shift,
+ fd_step_tilt_deg=h_tilt,
+ tolerances=tolerances,
+ abs_delta_bin_edges=has(mc) ? read(f["$mc/abs_delta_bin_edges"]) : nothing,
+ abs_delta_pdf=has(mc) ? read(f["$mc/abs_delta_pdf"]) : nothing,
+ abs_delta_efc_pdf=has(mc) ? read(f["$mc/abs_delta_efc_pdf"]) : nothing,
+ abs_delta_pdf_batches=has(mc) ? read(f["$mc/abs_delta_pdf_batches"]) : nothing,
+ abs_delta_total_as_designed=has(mc) ? read(f["$mc/abs_delta_total_as_designed"]) : nothing,
+ abs_delta_worst_case=has(mc) ? read(f["$mc/abs_delta_worst_case"]) : nothing,
+ abs_delta_sampled_mean=has(mc) ? read(f["$mc/abs_delta_sampled_mean"]) : nothing,
+ clamped_fraction=has(mc) ? read(f["$mc/clamped_fraction"]) : nothing,
+ threshold_pdf=has(rk) ? read(f["$rk/threshold_pdf"]) : nothing,
+ locking_probability_given_delta=has(rk) ? read(f["$rk/locking_probability_given_delta"]) : nothing,
+ threshold_fit=has(rk) ? read(f["$rk/threshold_fit"]) : nothing,
+ locking_probability_percent=has(rk) ? read(f["$rk/locking_probability_percent"]) : nothing,
+ locking_probability_efc_percent=has(rk) ? read(f["$rk/locking_probability_efc_percent"]) : nothing,
+ scan_scale=has("$rk/ToleranceScan") ? read(f["$rk/ToleranceScan/tolerance_scale"]) : nothing,
+ scan_locking_probability_percent=has("$rk/ToleranceScan") ? read(f["$rk/ToleranceScan/locking_probability_percent"]) : nothing,
+ scan_locking_probability_efc_percent=has("$rk/ToleranceScan") ? read(f["$rk/ToleranceScan/locking_probability_efc_percent"]) : nothing,
+ scan_locking_probability_spread_percent=has("$rk/ToleranceScan") ? read(f["$rk/ToleranceScan/locking_probability_spread_percent"]) : nothing,
+ scan_locking_probability_efc_spread_percent=has("$rk/ToleranceScan") ? read(f["$rk/ToleranceScan/locking_probability_efc_spread_percent"]) : nothing,
+ dominant_v=has("PerturbedEquilibrium/SingularCoupling/DominantMode") ? read(f["PerturbedEquilibrium/SingularCoupling/DominantMode/right_singular_vectors"]) : nothing,
+ singular_values=has("PerturbedEquilibrium/SingularCoupling/DominantMode") ? read(f["PerturbedEquilibrium/SingularCoupling/DominantMode/singular_values"]) : nothing,
+ mn_index=has("Info/mn_index") ? read(f["Info/mn_index"]) : nothing
+ )
+ end
+end
+
+_centers(edges) = (edges[1:end-1] .+ edges[2:end]) ./ 2
+_step_series(m, a) = (vcat(m[1] - 1, m, m[end] + 1), vcat(0.0, a, 0.0))
+_empty(msg) = plot(; title=msg, legend=false)
+
+function _save(p, save_path)
+ if save_path !== nothing
+ Plots.savefig(p, save_path)
+ println("Saved: ", abspath(save_path))
+ end
+ return p
+end
+
+"""
+ plot_coil_sensitivities(sources; quantity=:shift, coils=nothing, yscale=:identity, save_path=nothing)
+ plot_coil_sensitivities(source; kwargs...)
+
+Grouped bars of the per-coil-set dominant-mode sensitivity across runs, matched by coil set name.
+`quantity` is `:shift` (per millimetre of rigid in-plane shift), `:tilt` (per degree), `:rim` (the
+same tilt as rim displacement, the unit mechanical tolerances arrive in), `:as_designed` (`|δ|` as
+built), or `:fraction` (the resonant share of the coil's own applied spectrum, `100·|δ|·B_T0/‖b̃‖`
+in percent, which separates a coil that couples weakly because it is small from one that couples
+weakly because its spectrum lies off the dominant mode). `coils` restricts and orders the coil
+sets shown; a name a source does not carry is an error rather than an empty bar.
+`yscale = :log10` draws the values as stems with markers instead of bars, since a bar's height on
+a logarithmic axis is set by the axis floor rather than by the data; non-positive values are
+omitted.
+
+Each source is a `gpec.h5` path, a `SensitivityTable` already in memory, or a vector of
+`CoilOverlap` (`:as_designed` and `:fraction` only), so a sweep of coil geometry that was never part of
+a run plots the same way a stored run does. `:fraction` needs the applied field as well as the
+overlap, so it is not available from a `SensitivityTable`.
+"""
+function plot_coil_sensitivities(sources::Sources; quantity::Symbol=:shift, coils=nothing, yscale::Symbol=:identity, save_path=nothing)
+ quantity in (:shift, :tilt, :rim, :as_designed, :fraction) || throw(ArgumentError("quantity must be :shift, :tilt, :rim, :as_designed, or :fraction"))
+ yscale in (:identity, :log10) || throw(ArgumentError("yscale must be :identity or :log10"))
+ data = [(lbl, _load(src)) for (lbl, src) in sources]
+ any(d -> d[2].coil_names === nothing, data) && return _empty("No ErrorFields/CoilSensitivities data — run with an [ErrorFields] section")
+ names = coils === nothing ? data[1][2].coil_names : String.(collect(coils))
+ values = [_sensitivity_values(lbl, d, names, quantity) for (lbl, d) in data]
+ ylabel =
+ quantity === :shift ? "|δ| per mm of shift" :
+ quantity === :tilt ? "|δ| per degree of tilt" :
+ quantity === :rim ? "|δ| per mm of rim displacement" : quantity === :as_designed ? "|δ_as_designed|" : "resonant fraction of |b̃| [%]"
+ per = quantity === :shift ? "shift" : quantity === :tilt ? "tilt" : "rim displacement"
+ title =
+ quantity === :as_designed ? "As-designed dominant-mode overlap" :
+ quantity === :fraction ? "Resonant fraction of each coil set's applied field" :
+ "Dominant-mode error field per $per"
+ n = length(names)
+ k = length(data)
+ width = 0.8 / k
+ p = plot(; xlabel="coil set", ylabel=ylabel, title=title, xticks=(1:n, names), xrotation=45, legend=:topright,
+ left_margin=12Plots.mm, bottom_margin=8Plots.mm)
+ if yscale === :log10
+ ylo = _log_floor!(p, reduce(vcat, values))
+ ylo === nothing && return _empty("No positive $quantity values to draw on a logarithmic axis")
+ for (j, (lbl, _)) in enumerate(data)
+ _stems!(p, (1:n) .+ (j - (k + 1) / 2) * width, values[j], ylo; c=j, label=lbl)
+ end
+ else
+ for (j, (lbl, _)) in enumerate(data)
+ x = (1:n) .+ (j - (k + 1) / 2) * width
+ bar!(p, x, values[j]; bar_width=width, label=lbl, alpha=0.8)
+ end
+ end
+ return _save(p, save_path)
+end
+
+# A logarithmic axis for stems: the floor a decade under the smallest positive value, or nothing
+# when there is none to draw. Bars on a log axis stretch to whatever the floor is; stems do not.
+function _log_floor!(p, values)
+ positive = filter(v -> isfinite(v) && v > 0, values)
+ isempty(positive) && return nothing
+ ylo = minimum(positive) / 10
+ plot!(p; yscale=:log10, ylims=(ylo, 3 * maximum(positive)))
+ return ylo
+end
+
+# Stems from the floor to each positive value, with a marker on top; non-positive values are skipped.
+function _stems!(p, x, values, ylo; c, label, marker=:circle, ms=5, lw=3)
+ keep = [isfinite(v) && v > 0 for v in values]
+ xs = vec(vcat(x[keep]', x[keep]', fill(NaN, 1, count(keep))))
+ ys = vec(vcat(fill(ylo, 1, count(keep)), values[keep]', fill(NaN, 1, count(keep))))
+ plot!(p, xs, ys; lw, c, label="")
+ scatter!(p, x[keep], values[keep]; marker, ms, c, label)
+ return p
+end
+
+# Positions of `names` among a source's coil sets, erroring on a coil the source does not carry
+# rather than drawing an empty bar for it.
+function _coil_indices(lbl, d, names)
+ absent = [nm for nm in names if nm ∉ d.coil_names]
+ isempty(absent) || throw(ArgumentError("source \"$lbl\" has no coil set named $(join(repr.(absent), ", ")); it carries $(join(repr.(d.coil_names), ", "))"))
+ return [findfirst(==(nm), d.coil_names) for nm in names]
+end
+
+# One source's values of `quantity` in `names` order.
+function _sensitivity_values(lbl, d, names, quantity::Symbol)
+ idx = _coil_indices(lbl, d, names)
+ if quantity === :fraction
+ d.resonant_fraction_percent === nothing || return d.resonant_fraction_percent[idx]
+ (d.delta_as_designed === nothing || d.field_as_designed === nothing || d.b_t0 === nothing) &&
+ throw(
+ ArgumentError(
+ "source \"$lbl\" cannot give the resonant fraction: it needs the applied field and B_T0 as well as δ (a gpec.h5 path or a vector of CoilOverlap, not a SensitivityTable)"
+ )
+ )
+ norms = [norm(d.field_as_designed[:, i]) for i in axes(d.field_as_designed, 2)]
+ nrm_ref = maximum(norms)
+ return [EF.resonant_fraction_percent(d.delta_as_designed[i] * d.b_t0, norms[i], nrm_ref) for i in idx]
+ end
+ field = quantity === :shift ? :abs_delta_shift_per_mm : quantity === :tilt ? :abs_delta_tilt_per_deg : quantity === :rim ? :abs_delta_rim_per_mm : :delta_as_designed
+ vals = getfield(d, field)
+ vals === nothing && throw(ArgumentError("source \"$lbl\" carries no $field, so quantity=:$quantity cannot be drawn from it"))
+ return abs.(vals[idx])
+end
+plot_coil_sensitivities(source::SingleSource; kwargs...) = plot_coil_sensitivities(_sources(source); kwargs...)
+
+"""
+ plot_tolerance_pdf(sources; corrected=true, normalize=false, xscale=:identity, show_batches=false, save_path=nothing)
+ plot_tolerance_pdf(h5path; kwargs...)
+
+The Monte Carlo distributions of the dominant-mode overlap `|δ|` of each run, intrinsic and
+(when `corrected`) with error-field correction, with the as-designed overlap marked.
+`show_batches` draws each batch's intrinsic histogram faintly under the mean, which is the
+sampling noise a risk figure inherits, and notes in the legend the fraction of samples that fell
+beyond the last bin edge.
+"""
+function plot_tolerance_pdf(sources::Sources; corrected::Bool=true, normalize::Bool=false, xscale::Symbol=:identity, show_batches::Bool=false,
+ save_path=nothing)
+ p = plot(; xlabel="dominant-mode overlap |δ|", ylabel=normalize ? "probability density (normalized)" : "probability density",
+ title="Tolerance Monte Carlo: |δ| over sampled misalignments", legend=:topright, xscale=xscale,
+ left_margin=12Plots.mm, bottom_margin=6Plots.mm)
+ any_data = false
+ for (j, (lbl, path)) in enumerate(sources)
+ d = _load(path)
+ d.abs_delta_pdf === nothing && continue
+ any_data = true
+ c = _centers(d.abs_delta_bin_edges)
+ keep = xscale === :log10 ? c .> 0 : trues(length(c))
+ scale = normalize ? maximum(d.abs_delta_pdf) : 1.0
+ clamped = ""
+ if show_batches && d.abs_delta_pdf_batches !== nothing
+ for b in axes(d.abs_delta_pdf_batches, 2)
+ plot!(p, c[keep], d.abs_delta_pdf_batches[keep, b] ./ scale; lw=1, c=j, alpha=0.35, label=b == 1 ? "$lbl batches ($(size(d.abs_delta_pdf_batches, 2)))" : "")
+ end
+ d.clamped_fraction === nothing || (clamped = " ($(round(100 * d.clamped_fraction; sigdigits=2)) % beyond last bin)")
+ end
+ plot!(p, c[keep], d.abs_delta_pdf[keep] ./ scale; lw=2, c=j, label="$lbl intrinsic$clamped")
+ corrected && plot!(p, c[keep], d.abs_delta_efc_pdf[keep] ./ (normalize ? maximum(d.abs_delta_efc_pdf) : 1.0); lw=2, ls=:dash, c=j, label="$lbl corrected")
+ vline!(p, [d.abs_delta_total_as_designed]; ls=:dot, c=j, label="$lbl as designed")
+ end
+ any_data || return _empty("No ErrorFields/MonteCarlo data — run with a tolerance_file")
+ return _save(p, save_path)
+end
+plot_tolerance_pdf(source::SingleSource; kwargs...) = plot_tolerance_pdf(_sources(source); kwargs...)
+
+"""
+ plot_overlap_phasors(sources; coils=nothing, save_path=nothing)
+ plot_overlap_phasors(source; kwargs...)
+
+Each coil set's as-built dominant-mode overlap `δ` as an arrow in the complex plane, laid head to
+tail in `coils` order so the walk ends at the run's total, drawn as one bold arrow from the
+origin. The picture is rotated so that the total is real: an arrow pointing along it adds to the
+error field, one pointing against it cancels part of another coil's, and the single number
+`|Σδ|` a Monte Carlo starts from cannot tell those apart. One panel per source, since the mode
+phase is arbitrary between runs. Sources are a `gpec.h5` path, a `SensitivityTable`, or a vector
+of `CoilOverlap`; on a file the walk's end is checked against the stored Monte Carlo
+`delta_as_designed` and a mismatch is warned about.
+"""
+function plot_overlap_phasors(sources::Sources; coils=nothing, save_path=nothing)
+ data = [(lbl, _load(src)) for (lbl, src) in sources]
+ any(d -> d[2].delta_as_designed === nothing, data) && return _empty("No per-coil overlaps — run with an [ErrorFields] section")
+ panels = Plots.Plot[]
+ for (lbl, d) in data
+ names = coils === nothing ? d.coil_names : String.(collect(coils))
+ idx = _coil_indices(lbl, d, names)
+ z = d.delta_as_designed[idx]
+ δ = abs.(z)
+ total = sum(z)
+ if coils === nothing && d.abs_delta_total_as_designed !== nothing && !isapprox(abs(total), d.abs_delta_total_as_designed; rtol=1e-6, atol=eps(Float64))
+ @warn "$lbl: the head-to-tail total |Σδ| = $(abs(total)) differs from the stored Monte Carlo abs_delta_total_as_designed $(d.abs_delta_total_as_designed)"
+ end
+ rot = abs(total) > 0 ? cis(-angle(total)) : one(ComplexF64)
+ w = z .* rot
+ tip = cumsum(w)
+ tail = vcat(zero(ComplexF64), tip[1:end-1])
+ # Equal aspect keeps the angles honest; the box is padded so a walk along the real axis
+ # (every coil in phase) does not collapse the panel to a sliver.
+ xs = vcat(0.0, real.(tip))
+ ys = vcat(0.0, imag.(tip))
+ span = max(maximum(xs) - minimum(xs), maximum(ys) - minimum(ys), eps())
+ pad = 0.1 * span
+ half_y = max(0.3 * span, 0.5 * (maximum(ys) - minimum(ys)) + pad)
+ y_mid = 0.5 * (maximum(ys) + minimum(ys))
+ p = plot(; xlabel="Re δ (rotated so the total is real)", ylabel="Im δ", title="Overlap phasors: $lbl, |Σδ| = $(round(abs(total); sigdigits=3))",
+ aspect_ratio=:equal, xlims=(minimum(xs) - pad, maximum(xs) + pad), ylims=(y_mid - half_y, y_mid + half_y), legend=:outerright,
+ size=(900, 560), left_margin=12Plots.mm, bottom_margin=6Plots.mm, titlefontsize=12)
+ for (k, nm) in enumerate(names)
+ plot!(p, [real(tail[k]), real(tip[k])], [imag(tail[k]), imag(tip[k])]; arrow=true, lw=2, c=k, label="$nm (|δ| = $(round(δ[k]; sigdigits=2)))")
+ end
+ plot!(p, [0.0, abs(total)], [0.0, 0.0]; arrow=true, lw=4, c=:black, alpha=0.6, label="total")
+ push!(panels, p)
+ end
+ length(panels) == 1 && return _save(panels[1], save_path)
+ return _save(plot(panels...; layout=(1, length(panels)), size=(900 * length(panels), 560)), save_path)
+end
+plot_overlap_phasors(source::SingleSource; kwargs...) = plot_overlap_phasors(_sources(source); kwargs...)
+
+"""
+ plot_tolerance_budget(h5path; psi_low=0.0, psi_high=CORE_PSI_HIGH, mode=1, tolerance_scale=1.0, sort=:total, top=nothing, save_path=nothing)
+ plot_tolerance_budget(table, tolerances, coil_sets; monte_carlo=nothing, kwargs...)
+ plot_tolerance_budget(terms::NamedTuple; monte_carlo=nothing, sort=:total, top=nothing, save_path=nothing)
+
+The worst-case tolerance budget of a run as stacked horizontal bars, one per coil set, coherent
+group and the unattributed budget: the as-designed `|δ_as_designed|`, the shift term and the tilt term
+of `ErrorFields.worst_case_terms`, whose sum over every bar is the `abs_delta_worst_case` the
+Monte Carlo sizes its histogram by. It shows which coil's tolerance the budget is spent on, and
+whether it is spent on the coil's shift, its tilt, or on the field it makes as designed.
+`sort` orders the bars by `:total` (largest at the top), `:name`, or `:none` (file order); `top`
+keeps only that many largest. With a Monte Carlo result (read from the file, or passed as
+`monte_carlo`) the sample mean of `|δ|` and the coherent as-designed total are marked, which
+puts the worst-case bars against what the sampling typically realises.
+"""
+function plot_tolerance_budget(terms::NamedTuple; monte_carlo=nothing, sort::Symbol=:total, top=nothing, save_path=nothing)
+ sort in (:total, :name, :none) || throw(ArgumentError("sort must be :total, :name, or :none"))
+ ng = length(terms.group_names)
+ nc = length(terms.coil_names)
+ labels = vcat(terms.coil_names, ["group $g" for g in terms.group_names], ["unattributed"])
+ nominal = vcat(terms.abs_delta_as_designed, zeros(ng), 0.0)
+ shift = vcat(terms.abs_delta_shift_tolerance, terms.abs_delta_group_shift_tolerance, 0.0)
+ tilt = vcat(terms.abs_delta_tilt_tolerance, terms.abs_delta_group_tilt_tolerance, 0.0)
+ other = vcat(zeros(nc + ng), terms.abs_delta_unattributed)
+ total = nominal .+ shift .+ tilt .+ other
+ order = sort === :total ? sortperm(total) : sort === :name ? sortperm(labels; rev=true) : collect(reverse(eachindex(labels)))
+ top === nothing || (order = order[max(1, end - top + 1):end])
+ m = length(order)
+ p = plot(; xlabel="worst-case contribution to |δ|", ylabel="", yticks=(1:m, labels[order]), ylims=(0.4, m + 0.6),
+ title="Tolerance budget by term (Σ over every bar = abs_delta_worst_case = $(round(terms.abs_delta_worst_case; sigdigits=3)))", legend=:bottomright,
+ size=(900, max(420, 26 * m + 160)), left_margin=12Plots.mm, bottom_margin=8Plots.mm, titlefontsize=12)
+ segments = (("as designed |δ_as_designed|", nominal, :gray40), ("shift tolerance + 3σ", shift, 1), ("tilt tolerance + 3σ", tilt, 2), ("unattributed budget + 3σ", other, 3))
+ labelled = Set{String}()
+ for (y, i) in enumerate(order)
+ x0 = 0.0
+ for (name, vals, col) in segments
+ vals[i] > 0 || continue
+ x1 = x0 + vals[i]
+ plot!(p, Shape([x0, x1, x1, x0], [y - 0.4, y - 0.4, y + 0.4, y + 0.4]); c=col, lw=0.5, label=name in labelled ? "" : name)
+ push!(labelled, name)
+ x0 = x1
+ end
+ end
+ if monte_carlo !== nothing
+ d = _load(monte_carlo)
+ d.abs_delta_sampled_mean === nothing ||
+ vline!(p, [d.abs_delta_sampled_mean]; ls=:dash, c=:black, label="Monte Carlo mean |δ| = $(round(d.abs_delta_sampled_mean; sigdigits=3))")
+ d.abs_delta_total_as_designed === nothing ||
+ vline!(p, [d.abs_delta_total_as_designed]; ls=:dot, c=:black, label="as designed |Σδ| = $(round(d.abs_delta_total_as_designed; sigdigits=3))")
+ end
+ return _save(p, save_path)
+end
+function plot_tolerance_budget(table::EF.SensitivityTable, ts::EF.ToleranceSet, coil_sets::AbstractVector{FT.CoilSet}; tolerance_scale::Real=1.0, kwargs...)
+ return plot_tolerance_budget(EF.worst_case_terms(table, ts, collect(coil_sets); tolerance_scale); kwargs...)
+end
+function plot_tolerance_budget(h5path::AbstractString; psi_low::Real=0.0, psi_high::Real=PE.CORE_PSI_HIGH, mode::Int=1, tolerance_scale::Real=1.0, kwargs...)
+ terms = EF.worst_case_terms(h5path; psi_low, psi_high, mode, tolerance_scale)
+ d = _load(h5path)
+ mc =
+ d.abs_delta_pdf === nothing ? nothing :
+ (;
+ abs_delta_bin_edges=d.abs_delta_bin_edges,
+ abs_delta_pdf=d.abs_delta_pdf,
+ abs_delta_sampled_mean=d.abs_delta_sampled_mean,
+ abs_delta_total_as_designed=d.abs_delta_total_as_designed
+ )
+ return plot_tolerance_budget(terms; monte_carlo=mc, kwargs...)
+end
+
+"""
+ plot_linearity_residuals(sources; at=:tolerance, coils=nothing, tolerances=nothing, fd_step_shift_m=nothing, fd_step_tilt_deg=nothing, yscale=:identity, save_path=nothing)
+ plot_linearity_residuals(source; kwargs...)
+
+How linear each coil set's field is in its rigid motions: for the six taps (shift and tilt about
+`x`, `y`, `z`) the ratio of the central second difference `‖b̃(+h) + b̃(−h) − 2b̃(0)‖` to the
+largest first difference among the set's taps, as stored in
+`ErrorFields/CoilSensitivities/*_linearity_residual`. The normalization is against the set's
+*largest* linear response, so a tap whose own first difference vanishes by symmetry is judged
+against the terms the model keeps, and a weak tap's own curvature is understated. `at = :step`
+shows the ratio at the finite-difference steps the run used; `at = :tolerance` rescales each tap
+by `tolerance / step` (the second difference grows as `h²`, the first as `h`), which is the
+curvature the linear model neglects over the coil's own tolerance range. Coherent-group
+amplitudes are not added. Tolerances come from the file's snapshot or `tolerances`; a coil
+without a tolerance block draws at zero. The steps come from the file's recorded deck, or from
+`fd_step_shift_m` and `fd_step_tilt_deg` for in-memory `CoilSensitivities`. The dashed line is
+the 1 % level at which the sensitivity calculation itself warns; on a linear axis it sets the
+scale and hides sub-percent residuals, so `yscale = :log10` draws them as stems and markers
+(never bars) over the decades they span. One panel per source. For the model's error at finite
+displacements rather than at the step, see [`plot_linearity_check`](@ref).
+"""
+function plot_linearity_residuals(sources::Sources; at::Symbol=:tolerance, coils=nothing, tolerances=nothing, fd_step_shift_m=nothing,
+ fd_step_tilt_deg=nothing, yscale::Symbol=:identity, save_path=nothing)
+ at in (:step, :tolerance) || throw(ArgumentError("at must be :step or :tolerance"))
+ yscale in (:identity, :log10) || throw(ArgumentError("yscale must be :identity or :log10"))
+ data = [(lbl, _load(src)) for (lbl, src) in sources]
+ any(d -> d[2].shift_linearity_residual === nothing, data) && return _empty("No ErrorFields/CoilSensitivities linearity residuals — run with an [ErrorFields] section")
+ taps = ("shift x", "shift y", "shift z", "tilt x", "tilt y", "tilt z")
+ panels = Plots.Plot[]
+ for (lbl, d) in data
+ names = coils === nothing ? d.coil_names : String.(collect(coils))
+ r = _linearity_matrix(lbl, d, names, at; tolerances, fd_step_shift_m, fd_step_tilt_deg)
+ n = length(names)
+ width = 0.8 / 6
+ p = plot(; xlabel="coil set", ylabel=at === :step ? "‖2nd diff‖ / max ‖1st diff‖ at the FD step" : "‖2nd diff‖ / max ‖1st diff‖ at the tolerance",
+ title="Linearity of the rigid-motion response: $lbl", xticks=(1:n, names), xrotation=45, legend=:topright, size=(900, 520),
+ left_margin=12Plots.mm, bottom_margin=8Plots.mm, titlefontsize=12)
+ if yscale === :log10
+ ylo = _log_floor!(p, vcat(vec(r), 1e-2))
+ for (t, tap) in enumerate(taps)
+ _stems!(p, (1:n) .+ (t - 3.5) * width, r[t, :], ylo; c=t <= 3 ? t : t + 2, label=tap, lw=2, ms=4)
+ end
+ else
+ for (t, tap) in enumerate(taps)
+ x = (1:n) .+ (t - 3.5) * width
+ bar!(p, x, r[t, :]; bar_width=width, label=tap, alpha=0.85, c=t <= 3 ? t : t + 2)
+ end
+ end
+ hline!(p, [1e-2]; ls=:dash, c=:black, label="1 % (sensitivity warning level)")
+ push!(panels, p)
+ end
+ length(panels) == 1 && return _save(panels[1], save_path)
+ return _save(plot(panels...; layout=(1, length(panels)), size=(900 * length(panels), 520)), save_path)
+end
+plot_linearity_residuals(source::SingleSource; kwargs...) = plot_linearity_residuals(_sources(source); kwargs...)
+
+"""
+ plot_linearity_check(check::EF.LinearityCheck; save_path=nothing)
+ plot_linearity_check(h5path; scales=(1.0, 2.0), save_path=nothing, kwargs...)
+
+The relative error of the linear sensitivity model at finite displacements, from
+`ErrorFields.linearity_check`: one stem per row on a logarithmic axis, grouped by coil set
+or coherent group, with the shift and tilt rows told apart by colour, the scale by marker, and the
+sign by fill. The dashed line is the 1 % level the sensitivity calculation warns at for its own step
+residuals. A row whose linear change vanishes has no relative error and is not drawn.
+"""
+function plot_linearity_check(check::EF.LinearityCheck; save_path=nothing)
+ isempty(check.name) && return _empty("No linearity rows: the tolerance set names no coil or group")
+ names = unique(check.name)
+ scales = sort(unique(check.scale))
+ markers = (:circle, :diamond, :utriangle, :square, :star5, :hexagon)
+ p = plot(; xlabel="coil set or coherent group", ylabel="|δ_actual − δ_linear| / |δ_linear − δ_as_designed|",
+ title="Linearity of the overlap at finite displacements", xticks=(1:length(names), names), xrotation=45, legend=:outerright,
+ size=(1000, 560), left_margin=12Plots.mm, bottom_margin=8Plots.mm, titlefontsize=12)
+ ylo = _log_floor!(p, vcat(check.relative_error, 1e-2))
+ ylo === nothing && return _empty("No finite relative errors to draw")
+ width = 0.8 / (4 * length(scales))
+ slot = 0
+ for (k, kind) in enumerate((:shift, :tilt)), a in 1:2, (si, s) in enumerate(scales)
+ slot += 1
+ for (sgn, fill) in ((1, true), (-1, false))
+ rows = findall(i -> check.kind[i] === kind && check.axis[i] == a && check.scale[i] == s && sign(check.displacement[i]) == sgn, eachindex(check.name))
+ isempty(rows) && continue
+ x = [findfirst(==(check.name[i]), names) + (slot - (4 * length(scales) + 1) / 2) * width for i in rows]
+ lbl = sgn > 0 ? "$kind $(a == 1 ? "x" : "y") × $s" : ""
+ _stems!(p, x, check.relative_error[rows], ylo; c=k, label=lbl, marker=markers[mod1(si, length(markers))], ms=fill ? 5 : 4, lw=1.5)
+ end
+ end
+ hline!(p, [1e-2]; ls=:dash, c=:black, label="1 %")
+ return _save(p, save_path)
+end
+plot_linearity_check(h5path::AbstractString; save_path=nothing, kwargs...) = plot_linearity_check(EF.linearity_check(h5path; kwargs...); save_path)
+
+# The six taps' residual ratios per coil set (6 × n), at the finite-difference step or rescaled
+# by tolerance / step to the coil's own tolerance.
+function _linearity_matrix(lbl, d, names, at::Symbol; tolerances=nothing, fd_step_shift_m=nothing, fd_step_tilt_deg=nothing)
+ idx = _coil_indices(lbl, d, names)
+ r = vcat(d.shift_linearity_residual[:, idx], d.tilt_linearity_residual[:, idx])
+ at === :step && return r
+ ts = tolerances === nothing ? d.tolerances : tolerances
+ ts === nothing && throw(ArgumentError("source \"$lbl\" carries no tolerance snapshot; pass tolerances=ToleranceSet or use at=:step"))
+ h_shift = something(fd_step_shift_m, d.fd_step_shift_m, EF.ErrorFieldsControl().fd_step_shift_m)
+ h_tilt = something(fd_step_tilt_deg, d.fd_step_tilt_deg, EF.ErrorFieldsControl().fd_step_tilt_deg)
+ tol_of = Dict(t.name => t for t in ts.coils)
+ for (k, i) in enumerate(idx)
+ t = get(tol_of, d.coil_names[i], nothing)
+ shift_tol = t === nothing ? 0.0 : t.shift_tol_m
+ tilt_tol =
+ t === nothing ? 0.0 :
+ d.major_radius_m === nothing ? throw(ArgumentError("source \"$lbl\" carries no major radii, needed to convert a tilt tolerance in metres")) :
+ EF.tilt_tolerance_deg(t.tilt_tol, t.tilt_units, d.major_radius_m[i]; name="coil set $(d.coil_names[i])")
+ r[1:3, k] .*= shift_tol / h_shift
+ r[4:6, k] .*= tilt_tol / h_tilt
+ end
+ return r
+end
+
+"""
+ plot_locking_risk(sources; corrected=true, target_percent=nothing, save_path=nothing)
+ plot_locking_risk(h5path; kwargs...)
+
+Locking probability against tolerance scale from each run's `ErrorFields/Risk/ToleranceScan/`,
+intrinsic and (when `corrected`) with error-field correction, batch spread as error bars, and
+the allowable scale at `target_percent` marked where the scan reaches it.
+"""
+function plot_locking_risk(sources::Sources; corrected::Bool=true, target_percent=nothing, save_path=nothing)
+ p = plot(; xlabel="tolerance scale", ylabel="locking probability [%]", xscale=:log10, yscale=:log10, legend=:topleft,
+ title="Locking risk vs tolerance scale", left_margin=12Plots.mm, bottom_margin=6Plots.mm)
+ any_data = false
+ risk_floor = 1e-4 # named to avoid shadowing Base.floor inside this function
+ for (j, (lbl, path)) in enumerate(sources)
+ d = _load(path)
+ d.scan_scale === nothing && continue
+ any_data = true
+ plot!(
+ p,
+ d.scan_scale,
+ max.(d.scan_locking_probability_percent, risk_floor);
+ yerror=d.scan_locking_probability_spread_percent ./ 2,
+ marker=:circle,
+ lw=2,
+ c=j,
+ label="$lbl intrinsic"
+ )
+ corrected && plot!(
+ p,
+ d.scan_scale,
+ max.(d.scan_locking_probability_efc_percent, risk_floor);
+ yerror=d.scan_locking_probability_efc_spread_percent ./ 2,
+ marker=:square,
+ lw=2,
+ ls=:dash,
+ c=j,
+ label="$lbl corrected"
+ )
+ if target_percent !== nothing
+ scan = EF.ToleranceScan(
+ d.scan_scale,
+ d.scan_locking_probability_percent,
+ d.scan_locking_probability_efc_percent,
+ d.scan_locking_probability_spread_percent,
+ d.scan_locking_probability_efc_spread_percent,
+ 0.0
+ )
+ for (corr, mk) in ((false, :diamond), (true, :star5))
+ (corr && !corrected) && continue
+ s = EF.allowable_tolerance(scan, target_percent; corrected=corr)
+ isnan(s) || scatter!(p, [s], [target_percent]; marker=mk, ms=8, c=j, label="$lbl allowable ($(corr ? "corrected" : "intrinsic"))")
+ end
+ end
+ end
+ any_data || return _empty("No ErrorFields/Risk/ToleranceScan data — set scan_scales in [ErrorFields.Risk]")
+ target_percent === nothing || hline!(p, [target_percent]; ls=:dash, c=:gray, label="target $(target_percent) %")
+ return _save(p, save_path)
+end
+plot_locking_risk(source::SingleSource; kwargs...) = plot_locking_risk(_sources(source); kwargs...)
+
+"""
+ plot_threshold_scaling(sources; save_path=nothing)
+ plot_threshold_scaling(h5path; kwargs...)
+
+The sampled penetration-threshold density and `P(lock|δ)` of each run against its overlap
+distributions, on a logarithmic `|δ|` axis, with the fitted threshold marked.
+"""
+function plot_threshold_scaling(sources::Sources; save_path=nothing)
+ p = plot(; xlabel="dominant-mode overlap |δ|", ylabel="normalized density / P(lock | δ)", xscale=:log10, legend=:topleft,
+ title="Overlap distribution vs penetration threshold", left_margin=12Plots.mm, bottom_margin=6Plots.mm)
+ any_data = false
+ for (j, (lbl, path)) in enumerate(sources)
+ d = _load(path)
+ # Needs the overlap distribution and the threshold together; an in-memory source carrying
+ # only one of the two is skipped rather than indexed into a nothing.
+ (d.threshold_pdf === nothing || d.abs_delta_pdf === nothing || d.abs_delta_bin_edges === nothing) && continue
+ any_data = true
+ c = _centers(d.abs_delta_bin_edges)
+ keep = c .> 0
+ plot!(p, c[keep], d.abs_delta_pdf[keep] ./ maximum(d.abs_delta_pdf); lw=2, c=j, label="$lbl intrinsic |δ|")
+ plot!(p, c[keep], d.abs_delta_efc_pdf[keep] ./ maximum(d.abs_delta_efc_pdf); lw=2, ls=:dash, c=j, label="$lbl corrected |δ|")
+ plot!(p, c[keep], d.threshold_pdf[keep] ./ maximum(d.threshold_pdf); lw=2, ls=:dot, c=j, label="$lbl threshold")
+ plot!(p, d.abs_delta_bin_edges[2:end], d.locking_probability_given_delta[2:end]; lw=1.5, ls=:dashdot, c=j, label="$lbl P(lock | δ)")
+ vline!(p, [d.threshold_fit]; ls=:dot, c=:black, label=j == 1 ? "fitted threshold" : "")
+ end
+ any_data || return _empty("No ErrorFields/Risk data — run with an [ErrorFields.scenario] table")
+ return _save(p, save_path)
+end
+plot_threshold_scaling(source::SingleSource; kwargs...) = plot_threshold_scaling(_sources(source); kwargs...)
+
+"""
+ plot_dominant_mode_spectrum(sources; mode=1, save_path=nothing)
+ plot_dominant_mode_spectrum(h5path; kwargs...)
+
+The right singular vector of the full-window dominant coupling mode of each run, `|V[m, mode]|`
+against poloidal mode number (one series per toroidal mode), from
+`PerturbedEquilibrium/SingularCoupling/DominantMode/`.
+"""
+function plot_dominant_mode_spectrum(sources::Sources; mode::Int=1, save_path=nothing)
+ p = plot(; xlabel="poloidal mode m", ylabel="|V[m, $mode]|", title="Dominant resonant-coupling mode spectrum", legend=:topright,
+ left_margin=12Plots.mm, bottom_margin=6Plots.mm)
+ any_data = false
+ for (j, (lbl, path)) in enumerate(sources)
+ d = _load(path)
+ (d.dominant_v === nothing || d.mn_index === nothing) && continue
+ any_data = true
+ mode <= size(d.dominant_v, 2) || continue
+ for n in unique(d.mn_index[:, 2])
+ rows = findall(==(n), d.mn_index[:, 2])
+ me, ae = _step_series(d.mn_index[rows, 1], abs.(d.dominant_v[rows, mode]))
+ plot!(p, me, ae; seriestype=:steppre, lw=2, c=j, label="$lbl n=$n (σ = $(round(d.singular_values[mode]; sigdigits=3)))")
+ end
+ end
+ any_data || return _empty("No PerturbedEquilibrium/SingularCoupling/DominantMode data")
+ return _save(p, save_path)
+end
+plot_dominant_mode_spectrum(source::SingleSource; kwargs...) = plot_dominant_mode_spectrum(_sources(source); kwargs...)
+
+"""
+ plot_applied_spectra(ctx, overlaps; normalize=true, save_path=nothing)
+ plot_applied_spectra(h5path, coil_sets; normalize=true, save_path=nothing, kwargs...)
+
+Each coil set's applied spectrum against the dominant resonant mode.
+
+Both views answer different questions and the plot shows whichever is asked for: `normalize = true`
+scales every curve to its own peak, which says whether a coil drives a *different* part of the
+spectrum; `false` leaves the amplitudes, which says whether it simply drives *less*. A coil that
+couples weakly for the first reason needs a geometry change; one that couples weakly for the second
+may just be further away.
+"""
+function plot_applied_spectra(ctx::EF.ResonantDriveContext, overlaps::AbstractVector{EF.CoilOverlap};
+ normalize::Bool=true, save_path=nothing)
+ isempty(overlaps) && return _empty("No coil overlaps to plot")
+ m = ctx.rc.m_modes
+ mode = first(overlaps).mode
+ p = plot(; xlabel="poloidal mode m", ylabel=normalize ? "amplitude / own peak" : "|b̃| (T)",
+ title="Applied spectra against the dominant resonant mode", legend=:topright,
+ left_margin=13Plots.mm, bottom_margin=7Plots.mm)
+ v = abs.(ctx.dom.right_singular_vectors[:, mode])
+ mv, av = _step_series(m, v ./ maximum(v))
+ normalize && plot!(p, mv, av; seriestype=:steppre, lw=3, c=:black, fillrange=0, fillalpha=0.12, label="dominant mode |V|")
+ for (j, o) in enumerate(overlaps)
+ a = abs.(o.spectrum)
+ scale = normalize ? maximum(a) : 1.0
+ ms, as = _step_series(m, scale > 0 ? a ./ scale : a)
+ plot!(p, ms, as; seriestype=:steppre, lw=2, c=j, label=o.coil_name)
+ end
+ return _save(p, save_path)
+end
+
+"""
+ plot_overlap_contributions(ctx, overlaps; save_path=nothing)
+ plot_overlap_contributions(h5path, coil_sets; save_path=nothing, kwargs...)
+
+Which poloidal harmonics produced each coil set's overlap, as `conj(V[m])·b̃[m]` rotated so that
+the coil's own total is real. The bars therefore sum to its resonant fraction, printed in the
+legend.
+
+This is what separates a coil that drives the resonant harmonics weakly from one that drives them
+strongly and cancels against itself. The single complex overlap cannot tell those apart.
+"""
+function plot_overlap_contributions(ctx::EF.ResonantDriveContext, overlaps::AbstractVector{EF.CoilOverlap}; save_path=nothing)
+ isempty(overlaps) && return _empty("No coil overlaps to plot")
+ m = ctx.rc.m_modes
+ v = ctx.dom.right_singular_vectors[:, first(overlaps).mode]
+ p = plot(; xlabel="poloidal mode m", ylabel="contribution to overlap",
+ title="Per-harmonic contribution, aligned to each coil's own overlap phase", legend=:topleft,
+ left_margin=13Plots.mm, bottom_margin=7Plots.mm)
+ for (j, o) in enumerate(overlaps)
+ o.spectrum_norm_t > 0 || continue
+ c = real.(conj.(v) .* o.spectrum .* cis(-angle(o.resonant_field_t))) ./ o.spectrum_norm_t
+ ms, as = _step_series(m, c)
+ plot!(p, ms, as; seriestype=:steppre, lw=2, c=j,
+ label="$(o.coil_name) (sums to $(round(o.resonant_fraction_percent; digits=1))%)")
+ end
+ hline!(p, [0]; c=:black, ls=:dot, label="")
+ return _save(p, save_path)
+end
+
+"""
+ plot_surface_overlay(ctx, overlaps; ntheta=256, nzeta=180, levels=4, save_path=nothing)
+ plot_surface_overlay(h5path, coil_sets; save_path=nothing, kwargs...)
+
+Each coil set's applied normal field on the control surface, with contours of the dominant resonant
+mode over it. One panel per coil, each scaled to its own peak so the shapes are comparable.
+
+This is the view that makes a weak overlap physical rather than numerical: a coil driving a
+different poloidal region from the one the dominant mode occupies couples poorly however strong it
+is. The poloidal angle is cut at 180° so the outboard midplane sits in the middle of each panel
+rather than being split across its edges.
+"""
+function plot_surface_overlay(ctx::EF.ResonantDriveContext, overlaps::AbstractVector{EF.CoilOverlap};
+ ntheta::Int=256, nzeta::Int=180, levels::Int=4, save_path=nothing)
+ isempty(overlaps) && return _empty("No coil overlaps to plot")
+ m, n = ctx.rc.m_modes, ctx.rc.n_modes
+ v = ctx.dom.right_singular_vectors[:, first(overlaps).mode]
+ vmap = FT.reconstruct_bn(v, m, n; ntheta, nzeta)
+ vpeak = maximum(abs, vmap.bn)
+ lv = vpeak > 0 ? range(-0.7, 0.7; length=levels + 2)[2:(end-1)] : [0.0]
+
+ k = length(overlaps)
+ rows = ceil(Int, k / 2)
+ p = plot(; layout=(rows, min(k, 2)), size=(575 * min(k, 2), 430 * rows),
+ left_margin=13Plots.mm, bottom_margin=8Plots.mm)
+ for (j, o) in enumerate(overlaps)
+ bmap = FT.reconstruct_bn(o.spectrum, m, n; ntheta, nzeta)
+ peak = maximum(abs, bmap.bn)
+ heatmap!(p[j], rad2deg.(bmap.zeta), rad2deg.(bmap.theta), peak > 0 ? bmap.bn ./ peak : bmap.bn;
+ c=:balance, clims=(-1, 1), colorbar=false, yticks=-180:90:180,
+ xlabel="toroidal angle φ (deg)", ylabel="poloidal angle θ (deg), 0 = outboard midplane",
+ title="$(o.coil_name) (peak $(round(peak; sigdigits=3)) T)")
+ vpeak > 0 && contour!(p[j], rad2deg.(vmap.zeta), rad2deg.(vmap.theta), vmap.bn ./ vpeak;
+ levels=lv, c=:black, lw=1.2, colorbar=false)
+ end
+ return _save(p, save_path)
+end
+
+for fn in (:plot_applied_spectra, :plot_overlap_contributions, :plot_surface_overlay)
+ @eval function $fn(h5path::AbstractString, coil_sets::AbstractVector{FT.CoilSet}; mode::Int=1,
+ psi_low::Real=0.0, psi_high::Real=PE.CORE_PSI_HIGH, nzeta_coil=nothing, mtheta_coil=nothing,
+ dat_dir=nothing, kwargs...)
+ ctx = EF.ResonantDriveContext(h5path; psi_low, psi_high, nzeta_coil, mtheta_coil, dat_dir)
+ return $fn(ctx, EF.coil_overlaps(ctx, coil_sets; mode); kwargs...)
+ end
+end
+
+"""
+ plot_phasing_map(h5path, coil_names; psi_low=0.0, psi_high=CORE_PSI_HIGH, mode=1, nphase=180, quantity=:delta_per_kat, save_path=nothing)
+ plot_phasing_map(map::EF.PhasingMap; quantity=:delta_per_kat, save_path=nothing)
+
+Contour map of the dominant-mode overlap per kilo-ampere-turn (`:delta_per_kat`) or of the
+resonant fraction of the applied field (`:resonant_fraction_percent`) against the relative phases of two
+or three coil arrays (`EF.phasing_map`). Two arrays give a line, three a filled contour whose
+axes are the phase of the middle array relative to the first and of the third relative to the
+middle; the extreme is marked.
+"""
+function plot_phasing_map(map::EF.PhasingMap; quantity::Symbol=:delta_per_kat, save_path=nothing)
+ arr =
+ quantity === :delta_per_kat ? map.delta_per_kat :
+ quantity === :resonant_fraction_percent ? map.resonant_fraction_percent :
+ throw(ArgumentError("quantity must be :delta_per_kat or :resonant_fraction_percent"))
+ label = quantity === :delta_per_kat ? "|δ| per kAt" : "resonant fraction [%]"
+ names = map.coil_names
+ if length(map.phase_deg) == 1
+ p = plot(map.phase_deg[1], vec(arr); lw=2, xlabel="Δφ($(names[2]) − $(names[1])) [deg]", ylabel=label, legend=false,
+ title="Two-array phasing", left_margin=12Plots.mm, bottom_margin=6Plots.mm)
+ elseif length(map.phase_deg) == 2
+ p = contourf(map.phase_deg[1], map.phase_deg[2], permutedims(arr); levels=12, xlabel="Δφ($(names[2]) − $(names[1])) [deg]",
+ ylabel="Δφ($(names[3]) − $(names[2])) [deg]", title="Three-array phasing: $label", colorbar_title=label, aspect_ratio=:equal,
+ left_margin=12Plots.mm, bottom_margin=6Plots.mm, size=(720, 640))
+ v, ph = EF.extreme_phasing(map; quantity)
+ scatter!(p, [ph[1]], [ph[2]]; marker=:star5, ms=10, c=:white, label="max $(round(v; sigdigits=3))")
+ else
+ throw(ArgumentError("plot_phasing_map draws maps of one or two relative phases (two or three arrays)"))
+ end
+ return _save(p, save_path)
+end
+function plot_phasing_map(h5path::AbstractString, coil_names::AbstractVector{<:AbstractString}; psi_low::Real=0.0, psi_high::Real=PE.CORE_PSI_HIGH, mode::Int=1,
+ nphase::Int=180, quantity::Symbol=:delta_per_kat, save_path=nothing)
+ return plot_phasing_map(EF.phasing_map(h5path, coil_names; psi_low, psi_high, mode, nphase); quantity, save_path)
+end
+
+"""
+ plot_efc_ntv_limits(h5path; torque_budget, delta_threshold=nothing, safety_factor=1.0, delta_max=15, profiles=false, save_path=nothing)
+ plot_efc_ntv_limits(couplings::Vector{EF.EFCCoupling}; delta_threshold, torque_budget, kwargs...)
+
+Correction current against intrinsic overlap for each correction array of a run
+(`ErrorFields/NTV/`): the linear single-mode current and the NTV-limited current whose residual
+torque lowers the threshold, with the largest correctable overlap marked; when the run
+tabulated the torques against rotation, a second panel shows those tables with the offsets
+found and the reference rotation, and the curve uses the torque balance (`model`,
+`rotation_exponent` as in `efc_current_curve`). The zero-rotation limits are marked with the
+residual torque (circle) and with the whole field's torque (star); nonzero `torque_rtol` or
+`budget_rtol` shade the band between the pessimistic and optimistic curves and the range of the
+correctable limit. `delta_threshold` defaults to the run's fitted
+penetration threshold (`ErrorFields/Risk/threshold_fit`); `torque_budget` is the torque,
+N·m, that would bring the reference rotation to rest. `profiles` adds a panel of the torque
+integrated from the axis, `T(ψ)` per kAt² at zero rotation shift for the whole field and the
+residual, which shows where in the plasma the torque that survives correction is deposited.
+"""
+function plot_efc_ntv_limits(couplings::Vector{EF.EFCCoupling}; delta_threshold::Real, torque_budget::Real, safety_factor::Real=1.0,
+ delta_max::Real=15, model::Symbol=:auto, rotation_exponent::Real=1.0, torque_rtol::Real=0.0, budget_rtol::Real=0.0, profiles::Bool=false,
+ save_path=nothing)
+ band = torque_rtol > 0 || budget_rtol > 0
+ band_label = "NTV band (T₀ ±$(round(Int, 100budget_rtol)) %, torque ±$(round(Int, 100torque_rtol)) %)"
+ p = plot(; xlabel="intrinsic overlap δ_EF / δ_thresh", ylabel="correction current [kAt]", legend=:topleft,
+ title="Error-field correction against its own NTV torque (budget $(torque_budget) N·m)", left_margin=12Plots.mm, bottom_margin=6Plots.mm)
+ for (j, c) in enumerate(couplings)
+ curve = EF.efc_current_curve(c; delta_threshold, torque_budget, safety_factor, delta_max, model, rotation_exponent, torque_rtol, budget_rtol)
+ x = curve.delta_ef ./ delta_threshold
+ tag = curve.model === :torque_balance ? "torque balance" : "linear budget"
+ if band
+ lo, hi = curve.limits_pessimistic.with_ntv, curve.limits_optimistic.with_ntv
+ isfinite(lo) && vspan!(p, [lo, min(hi, x[end] * delta_threshold)] ./ delta_threshold; c=j, alpha=0.12, lw=0, label="")
+ plot!(p, x, curve.current_ntv_pessimistic; lw=1, c=j, alpha=0.5, label="$(c.coil_name) $band_label")
+ plot!(p, x, curve.current_ntv_optimistic; lw=1, c=j, alpha=0.5, label="")
+ end
+ plot!(p, x, curve.current_linear; lw=2, c=j, label="$(c.coil_name) single-mode")
+ plot!(p, x, curve.current_ntv; lw=2, ls=:dash, c=j, label="$(c.coil_name) with residual NTV ($tag)")
+ plot!(p, x, curve.current_ntv_upper; lw=1, ls=:dashdot, c=j, alpha=0.7, label="$(c.coil_name) over-correction edge")
+ isfinite(curve.with_ntv) && vline!(p, [curve.with_ntv / delta_threshold]; ls=:dot, c=j, label="$(c.coil_name) correctable limit")
+ isfinite(curve.residual_only) && scatter!(p, [curve.residual_only / delta_threshold], [0.0]; marker=:circle, ms=6, c=j,
+ label="$(c.coil_name) zero rotation, residual torque")
+ isfinite(curve.torque_only) && scatter!(p, [curve.torque_only / delta_threshold], [0.0]; marker=:star5, ms=9, c=j,
+ label="$(c.coil_name) zero rotation, whole-field torque")
+ end
+ panels = [p]
+ scanned = filter(EF.has_rotation_scan, couplings)
+ isempty(scanned) || push!(panels, _ntv_rotation_panel(scanned))
+ profiles && push!(panels, _ntv_profile_panel(couplings))
+ length(panels) == 1 && return _save(p, save_path)
+ return _save(plot(panels...; layout=(1, length(panels)), size=(750 * length(panels), 550)), save_path)
+end
+
+# The tabulated torques against the rotation shift, with the balance's reference rotation and the found offsets.
+function _ntv_rotation_panel(scanned)
+ q = plot(; xlabel="E×B rotation shift Δω [krad/s]", ylabel="NTV torque per kAt² [N·m]", legend=:topright, title="Torque against rotation",
+ left_margin=12Plots.mm, bottom_margin=6Plots.mm)
+ hline!(q, [0.0]; c=:gray, label="")
+ for (j, c) in enumerate(scanned)
+ x = c.rotation_shift ./ 1e3
+ plot!(q, x, c.torque_full_scan; lw=2, c=j, marker=:circle, ms=3, label="$(c.coil_name) whole field")
+ plot!(q, x, c.torque_residual_scan; lw=2, ls=:dash, c=j, marker=:diamond, ms=3, label="$(c.coil_name) residual")
+ for z in EF.torque_zero_crossings(c)
+ vline!(q, [z / 1e3]; ls=:dot, c=j, label="")
+ end
+ isfinite(c.omega_offset_estimate) &&
+ vline!(q, [-abs(c.omega_offset_estimate) / 1e3, abs(c.omega_offset_estimate) / 1e3]; ls=:dashdot, c=:gray, label=j == 1 ? "±|rough offset| (offset_factor·ω_*T)" : "")
+ isfinite(c.omega_reference) && vline!(q, [-c.omega_reference / 1e3]; ls=:solid, c=:black, alpha=0.4, label=j == 1 ? "rotation brought to rest (−ω_ref)" : "")
+ end
+ return q
+end
+
+# The torque integrated from the axis at zero rotation shift, whole field against residual.
+function _ntv_profile_panel(couplings)
+ r = plot(; xlabel="normalized flux ψ_N", ylabel="NTV torque per kAt² integrated from the axis [N·m]", legend=:topleft,
+ title="Where the torque is deposited (zero rotation shift)", left_margin=12Plots.mm, bottom_margin=6Plots.mm)
+ for (j, c) in enumerate(couplings)
+ isempty(c.psi) && continue
+ i0 = findfirst(==(0.0), c.rotation_shift)
+ i0 === nothing && (i0 = argmin(abs.(c.rotation_shift)))
+ plot!(r, c.psi, c.torque_full_profile[:, i0]; lw=2, c=j, label="$(c.coil_name) whole field")
+ plot!(r, c.psi, c.torque_residual_profile[:, i0]; lw=2, ls=:dash, c=j, label="$(c.coil_name) residual")
+ end
+ return r
+end
+function plot_efc_ntv_limits(h5path::AbstractString; torque_budget::Real, delta_threshold=nothing, kwargs...)
+ couplings = EF.read_efc_couplings(h5path)
+ # A run may carry [ErrorFields.NTV] without [ErrorFields.scenario], in which case there is no
+ # stored threshold. Say what to do about it rather than letting HDF5 raise a bare KeyError.
+ δt = delta_threshold
+ if δt === nothing
+ key = "$(EF._RISK_GROUP)/threshold_fit"
+ δt = h5open(h5path, "r") do f
+ haskey(f, key) || throw(
+ ArgumentError(
+ "$h5path has no $key, so there is no fitted penetration threshold to scale by. " *
+ "Pass delta_threshold, or re-run with an [ErrorFields.scenario] table.")
+ )
+ read(f[key])
+ end
+ end
+ return plot_efc_ntv_limits(couplings; delta_threshold=δt, torque_budget, kwargs...)
+end
+
+"""
+ plot_correction_requirement(req::EF.CorrectionRequirement; save_path=nothing)
+ plot_correction_requirement(h5path, source_name, array_names; save_path=nothing, kwargs...)
+
+Two panels of a `ErrorFields.correction_requirement`: the resonant field on each rational
+surface before correction, after each array's dominant-mode correction alone and after the joint
+least-squares correction, as stems on a logarithmic axis per surface; then one polar panel per
+array with the complex current it needs as a phasor, magnitude as radius in kilo-ampere-turns (or
+as a factor on the array's current as given when any array's ampere-turns are unknown) and toroidal phase
+as angle: the array's solo dominant-mode factor in grey, the minimum-current member of the set's
+dominant-mode family in blue, and the joint least-squares factor in red. A joint factor far from
+the solo one, or a surface left with most of its field, says the single-mode picture of the
+correction is not the whole story.
+"""
+function plot_correction_requirement(req::EF.CorrectionRequirement; save_path=nothing)
+ n = length(req.rational_psi)
+ labels = ["$(m)/$(nn)\nψ=$(round(x; digits=3))" for (m, nn, x) in zip(req.rational_m, req.rational_n, req.rational_psi)]
+ # One slot per surface in ψ order rather than a position at ψ itself, so neighbouring edge surfaces do not overprint.
+ p = plot(; xlabel="rational surface (m/n, ψ_N)", ylabel="|resonant field| [T]", title="Resonant field per surface: $(req.source_name) and its correction",
+ xticks=(1:n, labels), legend=:outerright, size=(1000, 520), left_margin=12Plots.mm, bottom_margin=12Plots.mm, titlefontsize=12)
+ vals = vcat(abs.(req.resonant_field_source_t), vec(abs.(req.resonant_field_dominant_t)), abs.(req.resonant_field_least_squares_t))
+ ylo = _log_floor!(p, vals)
+ ylo === nothing && return _empty("No finite resonant field to draw")
+ k = length(req.array_names)
+ width = 0.8 / (k + 2)
+ offsets = ((1:(k+2)) .- (k + 3) / 2) .* width
+ _stems!(p, (1:n) .+ offsets[1], abs.(req.resonant_field_source_t), ylo; c=:black, label="source as built", marker=:circle, ms=6, lw=3)
+ for (j, nm) in enumerate(req.array_names)
+ _stems!(p, (1:n) .+ offsets[j+1], abs.(req.resonant_field_dominant_t[:, j]), ylo; c=j, label="after $nm, dominant mode only", marker=:diamond, ms=5, lw=2)
+ end
+ _stems!(p, (1:n) .+ offsets[end], abs.(req.resonant_field_least_squares_t), ylo; c=:red, label="after joint least squares", marker=:star5, ms=7, lw=2)
+ # One polar panel per array: a factor is a complex multiple of the array's current, so its magnitude
+ # is the radius and its toroidal phase the angle, which bars with printed phases only hint at.
+ panels = Plots.Plot[p]
+ # In kilo-ampere-turns when every array's ampere-turns are known, so arrays with different pattern
+ # currents share one radial unit; otherwise as a factor on each array's current as given.
+ in_kat = all(isfinite, req.current_least_squares_kat)
+ unit = in_kat ? "kAt" : "× its current as given"
+ for (j, nm) in enumerate(req.array_names)
+ fd, fm, fl =
+ in_kat ? (req.current_dominant_kat[j], req.current_dominant_minimum_norm_kat[j], req.current_least_squares_kat[j]) :
+ (req.current_factor_dominant[j], req.current_factor_dominant_minimum_norm[j], req.current_factor_least_squares[j])
+ q = plot(; proj=:polar, title="$nm: needed current [$unit]", titlefontsize=10, legend=:outerbottom, legendfontsize=7)
+ for (f, lbl, col, w) in
+ ((fd, "dominant mode, this array alone", :gray40, 4), (fm, "dominant mode, minimum current over the set", :blue, 2.5), (fl, "joint least squares", :red, 2))
+ isfinite(f) || continue
+ plot!(q, [angle(f), angle(f)], [0.0, abs(f)]; lw=w, c=col, label="$lbl: $(round(abs(f); sigdigits=3)) $unit ∠ $(round(rad2deg(angle(f)); digits=0))°")
+ scatter!(q, [angle(f)], [abs(f)]; ms=6, c=col, label="")
+ end
+ push!(panels, q)
+ end
+ n_pol = length(panels) - 1
+ return _save(plot(panels...; layout=Plots.grid(1, n_pol + 1; widths=vcat(0.5, fill(0.5 / n_pol, n_pol))), size=(1000 + 420 * n_pol, 540)), save_path)
+end
+plot_correction_requirement(h5path::AbstractString, source_name::AbstractString, array_names; save_path=nothing, kwargs...) =
+ plot_correction_requirement(EF.correction_requirement(h5path, source_name, array_names; kwargs...); save_path)
+
+"""
+ plot_needed_current(mc, array::EF.CoilOverlap; coupling=nothing, delta_threshold=nothing, torque_budget=nothing, save_path=nothing)
+
+The distribution of the factor on `array`'s current that the sampled machine needs to cancel its
+dominant-mode overlap (`ErrorFields.needed_current_distribution`), with the as-designed
+factor marked and, when the array's `EFCCoupling`, the threshold and the torque budget are given,
+the NTV-limited correctable overlap as a vertical line and the fraction beyond it
+(`ErrorFields.uncorrectable_probability`) in the legend.
+"""
+function plot_needed_current(mc::EF.MonteCarloResult, array::EF.CoilOverlap; coupling=nothing, delta_threshold=nothing, torque_budget=nothing, save_path=nothing)
+ d = EF.needed_current_distribution(mc, array)
+ # Kilo-ampere-turns when the array's ampere-turns are known, else a factor on its current as given.
+ in_kat = isfinite(array.ampere_turns_kat)
+ per_delta = (in_kat ? array.ampere_turns_kat : 1.0) / abs(array.delta)
+ c = in_kat ? _centers(d.current_bin_edges_kat) : _centers(d.current_factor_bin_edges)
+ xlabel = in_kat ? "needed current on $(array.coil_name) [kAt]" : "needed factor on $(array.coil_name)'s current (|δ| / |δ_$(array.coil_name)|)"
+ p = plot(; xlabel, ylabel="probability density", title="Correction current the sampled machine needs", legend=:topright, left_margin=12Plots.mm,
+ bottom_margin=6Plots.mm)
+ plot!(p, c, in_kat ? d.current_pdf_per_kat : d.current_factor_pdf; lw=2, c=1, label="intrinsic |δ| over the tolerance samples")
+ vline!(p, [mc.abs_delta_total_as_designed * per_delta]; ls=:dot, c=:black, label="as designed")
+ if coupling !== nothing
+ (delta_threshold === nothing || torque_budget === nothing) && throw(ArgumentError("give delta_threshold and torque_budget with the coupling"))
+ u = EF.uncorrectable_probability(mc, coupling; delta_threshold, torque_budget)
+ isfinite(u.abs_delta_max_correctable) && vline!(p, [u.abs_delta_max_correctable * per_delta]; ls=:dash, c=:red, lw=2,
+ label="NTV-limited correctable overlap ($(u.model)); $(round(u.probability_percent; sigdigits=2)) % of samples beyond")
+ end
+ return _save(p, save_path)
+end
+
+"""
+ plot_error_field_summary(h5path; save_path=nothing)
+
+Four panels of a run's error-field assessment: coil sensitivities to shift, the tolerance
+Monte Carlo distributions, the overlap distribution against the threshold, and the locking
+risk against tolerance scale. Panels whose data the run did not produce say so.
+"""
+function plot_error_field_summary(h5path::AbstractString; save_path=nothing)
+ src = _sources(h5path)
+ p = plot(plot_coil_sensitivities(src), plot_tolerance_pdf(src), plot_threshold_scaling(src), plot_locking_risk(src);
+ layout=(2, 2), size=(1400, 1000))
+ return _save(p, save_path)
+end
+
+end # module ErrorFields
diff --git a/src/Analysis/ForceFreeStates.jl b/src/Analysis/ForceFreeStates.jl
new file mode 100644
index 0000000000..47e839244e
--- /dev/null
+++ b/src/Analysis/ForceFreeStates.jl
@@ -0,0 +1,684 @@
+"""
+ ForceFreeStates
+
+Post-processing and visualization functions for ForceFreeStates (DCON-style ideal MHD stability)
+results stored in GPEC HDF5 output files.
+"""
+module ForceFreeStates
+
+using HDF5
+using LaTeXStrings
+using Plots
+using Printf
+using Statistics: quantile
+
+"""
+ plot_mode_displacement(h5path; modes=1:5, save_path=nothing)
+
+Plot |ξ_ψ| vs ψ_N for the least stable eigenmode, showing one curve per requested
+poloidal mode number m. The title includes the first eigenvalue dW = et[1].
+
+### Arguments
+
+ - `h5path`: Path to a GPEC HDF5 output file (e.g. `"gpec.h5"`)
+
+### Keyword arguments
+
+ - `modes`: Iterable of m values to plot (default: `1:5`)
+ - `save_path`: If provided, save the figure to this path (default: `nothing`)
+
+### Returns
+
+A `Plots.jl` plot object.
+"""
+function plot_mode_displacement(h5path; modes=1:5, save_path=nothing)
+ mlow, xi_psi, psi, et = h5open(h5path, "r") do fid
+ read(fid["Info/mlow"]), read(fid["ForceFreeStates/Solutions/ForwardIntegration/xi_psi"]),
+ read(fid["ForceFreeStates/Solutions/ForwardIntegration/psi"]), read(fid["ForceFreeStates/FreeBoundaryStability/eigenmode_energies"])
+ end
+
+ mpert = size(xi_psi, 1)
+ mhigh = mlow + mpert - 1
+ dW = isempty(et) ? nothing : et[1]
+ title_str = isnothing(dW) ? "Least stable mode" :
+ "Least stable mode, δW = $(round(real(dW), sigdigits=4))"
+
+ p = plot(;
+ xlims=(0, 1),
+ xlabel="Norm. Poloidal Flux",
+ ylabel="|ξ^ψ|",
+ title=title_str,
+ left_margin=10Plots.mm,
+ bottom_margin=5Plots.mm
+ )
+ for m in modes
+ mlow <= m <= mhigh || continue
+ plot!(p, psi, abs.(xi_psi[m-mlow+1, 1, :]); label="m=$m")
+ end
+
+ isnothing(save_path) || savefig(p, save_path)
+ return p
+end
+
+
+"""
+ plot_fixed_boundary_stability_criterion(h5path; save_path=nothing)
+
+Plot the stability criterion (smallest eigenvalue of W⁻¹, `crit`) vs ψ_N.
+A sign change in `crit` during integration indicates an ideal fixed-boundary instability.
+
+### Arguments
+
+ - `h5path`: Path to a GPEC HDF5 output file
+
+### Keyword arguments
+
+ - `save_path`: If provided, save the figure to this path (default: `nothing`)
+
+### Returns
+
+A `Plots.jl` plot object.
+"""
+function plot_fixed_boundary_stability_criterion(h5path; save_path=nothing)
+ psi, crit = h5open(h5path, "r") do fid
+ read(fid["ForceFreeStates/Solutions/ForwardIntegration/psi"]), read(fid["ForceFreeStates/Solutions/ForwardIntegration/crit"])
+ end
+
+ p = plot(
+ psi, crit;
+ xlims=(0, 1),
+ xlabel="Norm. Poloidal Flux",
+ ylabel="|Dᶜ|",
+ title="Fixed-Boundary Stability",
+ legend=false,
+ left_margin=10Plots.mm,
+ bottom_margin=5Plots.mm
+ )
+ hline!(p, [0.0]; linestyle=:dash, color=:black, label=nothing)
+
+ isnothing(save_path) || savefig(p, save_path)
+ return p
+end
+
+"""
+ plot_energy_eigenvectors(h5path; matrix_type=:total, save_path=nothing)
+
+Heatmap of energy eigenvector magnitudes vs (m, mode index).
+
+Only `matrix_type=:total` is supported (the total energy eigenvector matrix `Wₜ` is stored in
+`FreeBoundaryStability/W_freeboundary_eigenmodes`). Plasma and vacuum eigenvectors are not
+stored separately in the HDF5 output.
+
+Eigenvectors are scaled by χ₁ = 2π ψ₀ × 10⁻³ to match GPEC conventions.
+
+### Arguments
+
+ - `h5path`: Path to a GPEC HDF5 output file with vacuum data (`vac_flag = true`)
+
+### Keyword arguments
+
+ - `matrix_type`: Energy matrix to plot; only `:total` is currently supported
+ - `save_path`: If provided, save the figure to this path (default: `nothing`)
+
+### Returns
+
+A `Plots.jl` plot object.
+"""
+function plot_energy_eigenvectors(h5path; matrix_type=:total, save_path=nothing)
+ matrix_type == :total ||
+ error("matrix_type=$matrix_type not supported; only :total has eigenvector matrix stored in HDF5 (ep/ev are eigenvalue vectors, not matrices)")
+
+ wt, psio, mlow = h5open(h5path, "r") do fid
+ read(fid["ForceFreeStates/FreeBoundaryStability/W_freeboundary_eigenmodes"]), read(fid["Equilibrium/psi_total"]), read(fid["Info/mlow"])
+ end
+
+ isempty(wt) && error("No vacuum data in $h5path; rerun with vac_flag = true")
+
+ chi1 = 2π * psio
+ wt_scaled = wt * (chi1 * 1e-3)
+
+ nmn = size(wt_scaled, 1)
+ nmodes = size(wt_scaled, 2)
+ m_vals = (0:(nmn-1)) .+ mlow
+
+ p = heatmap(
+ m_vals, 1:nmodes, abs.(wt_scaled');
+ xlabel="Poloidal Harmonic",
+ ylabel="Eigenmode Index",
+ title="Total Energy Eigenvectors",
+ colorbar_title="Harmonic Amplitude",
+ left_margin=10Plots.mm,
+ right_margin=20Plots.mm,
+ bottom_margin=5Plots.mm
+ )
+
+ isnothing(save_path) || savefig(p, save_path)
+ return p
+end
+
+"""
+ plot_edge_stability_scan(h5path; save_path=nothing, ylims=(-2, 3), kwargs...)
+
+Plot the edge stability scan energy components (et, ep, ev, evonly) vs ψ_N.
+
+The edge scan evaluates `δW_total = δW_plasma + δW_vacuum` at each stored integration step
+in the region [dW_edge_scan_start, psilim], with the plasma boundary swept from dW_edge_scan_start to psilim.
+A positive et indicates stability; the truncation point is chosen at the peak et.
+
+Four subplots are shown:
+
+ - **Total energy** `et = ep + ev`: total free-boundary energy eigenvalue
+ - **Plasma energy** `ep`: plasma contribution to δW
+ - **Vacuum energy** `ev`: vacuum (wv) contribution with singfac scaling
+ - **Vacuum-only eigenvalue** `evonly`: smallest eigenvalue of wv alone (no plasma response)
+
+A horizontal dashed line at zero marks the stability boundary. A vertical dashed line marks
+`psilim` (the final truncation psi, where the peak et was found).
+
+### Arguments
+
+ - `h5path`: Path to a GPEC HDF5 output file produced with `dW_edge_scan_start < psilim`
+
+### Keyword arguments
+
+ - `save_path`: If provided, save the figure to this path (default: `nothing`)
+ - `ylims`: y-axis limits applied to all panels (default: `(-2, 3)`)
+ - `kwargs...`: Additional Plots.jl keyword arguments applied to all line plots (e.g. `lw=2`)
+
+### Returns
+
+A `Plots.jl` plot object, or `nothing` if no `EdgeScan/` group is present in the file.
+"""
+function plot_edge_stability_scan(h5path; save_path=nothing, ylims=(-2, 3), kwargs...)
+ has_scan, q, et, ep, ev, evonly, qlim = h5open(h5path, "r") do fid
+ if !haskey(fid, "ForceFreeStates/EdgeScan/psi")
+ return false, Float64[], ComplexF64[], ComplexF64[], ComplexF64[], Float64[], NaN
+ end
+ true,
+ read(fid["ForceFreeStates/EdgeScan/q"]),
+ read(fid["ForceFreeStates/EdgeScan/total_energy"]),
+ read(fid["ForceFreeStates/EdgeScan/plasma_energy"]),
+ read(fid["ForceFreeStates/EdgeScan/vacuum_energy"]),
+ read(fid["ForceFreeStates/EdgeScan/vacuum_eigenvalue"]),
+ read(fid["Info/qlim"])
+ end
+
+ if !has_scan
+ @warn "No edge_scan group in $h5path. Run with dW_edge_scan_start < psilim to generate it."
+ return nothing
+ end
+
+ kw_re = (xlabel="q", label="Re", ylims=ylims, kwargs...)
+ kw_im = (xlabel="q", label="Im", ls=:dash, ylims=ylims, kwargs...)
+ vl_kw = (color=:gray, lw=1, ls=:dot, label=false)
+ hl_kw = (color=:black, lw=1, ls=:dash, label=false)
+
+ p_et = plot(q, real.(et); ylabel="Total Energy", title="Edge Stability Scan: δW vs q", kw_re...)
+ plot!(p_et, q, imag.(et); kw_im...)
+ hline!(p_et, [0.0]; hl_kw...)
+ vline!(p_et, [qlim]; vl_kw...)
+
+ p_ep = plot(q, real.(ep); ylabel="Plasma Energy", kw_re...)
+ plot!(p_ep, q, imag.(ep); kw_im...)
+ hline!(p_ep, [0.0]; hl_kw...)
+ vline!(p_ep, [qlim]; vl_kw...)
+
+ p_ev = plot(q, real.(ev); ylabel="Vacuum Energy", kw_re...)
+ plot!(p_ev, q, imag.(ev); kw_im...)
+ hline!(p_ev, [0.0]; hl_kw...)
+ vline!(p_ev, [qlim]; vl_kw...)
+
+ p_evonly = plot(q, evonly; ylabel="Min Vac. Eigenvalue", legend=false, xlabel="q", ylims=ylims, kwargs...)
+ hline!(p_evonly, [0.0]; hl_kw...)
+ vline!(p_evonly, [qlim]; vl_kw...)
+
+ p = plot(p_et, p_ep, p_ev, p_evonly;
+ layout=(4, 1),
+ size=(900, 1100),
+ plot_title="Edge stability scan: $h5path",
+ left_margin=12Plots.mm,
+ bottom_margin=4Plots.mm)
+
+ isnothing(save_path) || savefig(p, save_path)
+ return p
+end
+
+"""
+ plot_eigenvalues(h5path; matrix_type=:total, save_path=nothing)
+
+Scatter plot of energy eigenvalues vs mode index. Points are colored red (unstable, Re > 0)
+or green (stable, Re < 0), with a dashed reference line at zero.
+
+### Arguments
+
+ - `h5path`: Path to a GPEC HDF5 output file with vacuum data (`vac_flag = true`)
+
+### Keyword arguments
+
+ - `matrix_type`: Which eigenvalues to plot: `:total` (`et`), `:plasma` (`ep`), or `:vacuum` (`ev`)
+ - `save_path`: If provided, save the figure to this path (default: `nothing`)
+
+### Returns
+
+A `Plots.jl` plot object.
+"""
+function plot_eigenvalues(h5path; matrix_type=:total, save_path=nothing)
+ dataset = Dict(
+ :total => "ForceFreeStates/FreeBoundaryStability/eigenmode_energies",
+ :plasma => "ForceFreeStates/FreeBoundaryStability/eigenmode_plasma_energies",
+ :vacuum => "ForceFreeStates/FreeBoundaryStability/eigenmode_vacuum_energies"
+ )
+ haskey(dataset, matrix_type) || error("matrix_type must be :total, :plasma, or :vacuum")
+
+ et = h5open(h5path, "r") do fid
+ read(fid[dataset[matrix_type]])
+ end
+
+ isempty(et) && error("No vacuum data in $h5path; rerun with vac_flag = true")
+
+ nmodes = length(et)
+ ev_real = real.(et)
+ colors = [v < 0 ? :red : :blue for v in ev_real] # red = negative (unstable), blue = positive (stable)
+
+ p = scatter(
+ 1:nmodes, ev_real;
+ xlabel="mode index",
+ ylabel="Re(eigenvalue)",
+ title="Eigenvalue spectrum ($matrix_type)",
+ legend=false,
+ color=colors,
+ markerstrokewidth=0,
+ left_margin=10Plots.mm,
+ bottom_margin=5Plots.mm
+ )
+ hline!(p, [0]; linestyle=:dash, color=:black, label=nothing)
+
+ isnothing(save_path) || savefig(p, save_path)
+ return p
+end
+
+"""
+ plot_delta_prime(h5path; save_path=nothing)
+
+Scatter plot of `Re(Δ')` per singular surface vs ψ_N, computed from the stored asymptotic
+coefficients `ca_left` and `ca_right`. Points are colored red (tearing unstable, Re(Δ') > 0)
+or blue (tearing stable). Integer-valued q rational surfaces are annotated.
+
+Δ' is computed as `(ca_right[resnum,resnum,2,s] - ca_left[resnum,resnum,2,s]) / (4π² ψ₀)`,
+where `resnum` is the linear mode index of the (m,n) resonant pair at surface `s`.
+
+### Arguments
+
+ - `h5path`: Path to a GPEC HDF5 output file
+
+### Keyword arguments
+
+ - `save_path`: If provided, save the figure to this path (default: `nothing`)
+
+### Returns
+
+A `Plots.jl` plot object.
+"""
+function plot_delta_prime(h5path; save_path=nothing)
+ msing, psi_sing, q_sing, ca_l, ca_r, psio, mn_index = h5open(h5path, "r") do fid
+ read(fid["SingularSurfaces/rational_count"]), read(fid["SingularSurfaces/rational_psi"]), read(fid["SingularSurfaces/rational_q"]),
+ read(fid["SingularSurfaces/ca_left"]), read(fid["SingularSurfaces/ca_right"]),
+ read(fid["Equilibrium/psi_total"]), read(fid["Info/mn_index"])
+ end
+
+ msing == 0 && return plot(; title="No singular surfaces found", legend=false)
+ # ca_left/ca_right are zero-extent sentinels on kinetic/galerkin-matched runs (never computed there).
+ isempty(ca_l) && return plot(; title="No asymptotic coefficients — ca_left/ca_right not computed for this run", legend=false)
+
+ numpert_total = size(ca_l, 1)
+ chi1 = 2π * psio
+
+ dp_vals = ComplexF64[]
+ for s in 1:msing
+ q_s = q_sing[s]
+ resnum = findfirst(1:numpert_total) do j
+ n_j = mn_index[j, 2]
+ n_j != 0 && abs(mn_index[j, 1] / n_j - q_s) < 1e-6
+ end
+ if isnothing(resnum)
+ push!(dp_vals, 0.0 + 0.0im)
+ else
+ dp = (ca_r[resnum, resnum, 2, s] - ca_l[resnum, resnum, 2, s]) / (2π * chi1)
+ push!(dp_vals, dp)
+ end
+ end
+
+ dp_real = real.(dp_vals)
+ colors = [v > 0 ? :red : :steelblue for v in dp_real]
+
+ p = scatter(
+ psi_sing, dp_real;
+ xlims=(0, 1),
+ xlabel="Norm. Poloidal Flux",
+ ylabel="Re(Δ')",
+ title="Tearing stability Δ'",
+ legend=false,
+ color=colors,
+ markersize=7,
+ markerstrokewidth=0,
+ left_margin=10Plots.mm,
+ bottom_margin=5Plots.mm
+ )
+ hline!(p, [0.0]; linestyle=:dash, color=:black, label=nothing)
+
+ isnothing(save_path) || savefig(p, save_path)
+ return p
+end
+
+"""
+ plot_ballooning_alpha_boundary(h5path; save_path=nothing, psi_min=0.0)
+
+Plot the BALOO-style infinite-n ballooning stability diagram: the experimental
+pressure gradient α (solid) and the first stability boundary α_crit (dashed) versus
+normalized poloidal flux ψ_N. Surfaces where the experimental α lies above the boundary
+are ballooning-unstable. Reads `LocalStability/ballooning_psi`, `LocalStability/alpha`, and
+`LocalStability/alpha_critical` (populated when the deck has a `[LocalStability]` section).
+
+### Arguments
+
+ - `h5path`: Path to a GPEC HDF5 output file (e.g. `"gpec.h5"`)
+
+### Keyword arguments
+
+ - `save_path`: If provided, save the figure to this path (default: `nothing`)
+ - `psi_min`: Lower ψ_N axis limit; set near the edge (e.g. `0.9`) to focus on the
+ pedestal (default: `0.0`)
+
+### Returns
+
+A `Plots.jl` plot object.
+"""
+function plot_ballooning_alpha_boundary(h5path; save_path=nothing, psi_min=0.0)
+ psi, alpha, alpha_crit = h5open(h5path, "r") do fid
+ haskey(fid, "LocalStability/alpha") || return (Float64[], Float64[], Float64[])
+ read(fid["LocalStability/ballooning_psi"]), read(fid["LocalStability/alpha"]), read(fid["LocalStability/alpha_critical"])
+ end
+
+ isempty(alpha) && return plot(; title="No local stability data (add a [LocalStability] section)", legend=false)
+
+ p = plot(;
+ xlims=(psi_min, 1),
+ xlabel=L"\psi_N",
+ ylabel=L"\alpha",
+ title="Infinite-n ballooning stability",
+ framestyle=:box,
+ legend=:topleft,
+ left_margin=10Plots.mm,
+ bottom_margin=5Plots.mm
+ )
+
+ # NaN entries leave natural gaps over always-stable surfaces; isfinite masking would
+ # wrongly connect across such gaps with a straight line.
+ plot!(p, psi, alpha; lw=2, color=:black, label="Experimental gradient")
+ plot!(p, psi, alpha_crit; lw=2, linestyle=:dash, color=:red, label="1st stability boundary")
+
+ isnothing(save_path) || savefig(p, save_path)
+ return p
+end
+
+"""
+ plot_cond_fbar(h5path; save_path=nothing, zoom=false)
+
+Plot `cond(F̄)` vs ψ from the kinetic-singular-surface scan stored in
+`SingularSurfaces/Kinetic/` (populated when ForceFreeStates runs with
+a `kinetic` source and `singfac_min > 0`).
+
+`F̄` is the kinetic Euler-Lagrange matrix formed by Schur-reducing the six
+kinetic matrices against the ideal A/B/C/D/E/H blocks (Logan 2015 Appendix
+C). Peaks in `cond(F̄)` locate "kinetically-displaced" singular surfaces —
+roots of `det(F̄)` that are not at ideal rational surfaces. When a peak
+exceeds the threshold stored in `scan_threshold` the ODE integrator stops
+there and steps across trapezoidally, mirroring Fortran `ode_kin_cross`.
+
+The plot overlays the ideal rational surfaces (dotted grey, labelled with
+their q value) and any accepted kinetic singular surfaces (solid crimson).
+If no peak exceeds the threshold, `kmsing = 0` and the kinetic ODE runs as
+a single chunk. This diagnostic is useful for anyone asking *where* the
+kinetic resonances land relative to the ideal ones.
+
+### Arguments
+
+ - `h5path`: Path to a GPEC HDF5 output file produced with kinetic mode enabled
+
+### Keyword arguments
+
+ - `save_path`: If provided, save the figure to this path (default: `nothing`)
+ - `zoom`: If `true`, auto-scale the y-axis to the scan data (threshold shown
+ as annotation only); if `false` (default), always include the threshold
+ line in the y-range
+
+### Returns
+
+A `Plots.jl` plot object, or `nothing` if no kinetic scan is stored in the file.
+"""
+function plot_cond_fbar(h5path; save_path=nothing, zoom=false)
+ scan_psi, scan_cond, thr, k_psi, i_psi, i_q, kmsing = h5open(h5path, "r") do fid
+ if !(haskey(fid, "SingularSurfaces") && haskey(fid["SingularSurfaces"], "Kinetic"))
+ return Float64[], Float64[], 0.0, Float64[], Float64[], Float64[], 0
+ end
+ kg = fid["SingularSurfaces/Kinetic"]
+ (read(kg["scan_psi"]),
+ read(kg["scan_cond"]),
+ read(kg["scan_threshold"]),
+ read(kg["rational_psi"]),
+ read(fid["SingularSurfaces/rational_psi"]),
+ read(fid["SingularSurfaces/rational_q"]),
+ read(kg["rational_count"]))
+ end
+
+ if isempty(scan_psi)
+ @warn "No kinetic-singular-surface scan in $h5path — rerun with a kinetic source and singfac_min>0"
+ return nothing
+ end
+
+ finite_cond = filter(isfinite, scan_cond)
+ data_max = isempty(finite_cond) ? 1.0 : maximum(finite_cond)
+ data_min = isempty(finite_cond) ? 1.0 : max(minimum(finite_cond), 1e-3)
+
+ p = plot(scan_psi, scan_cond;
+ yscale=:log10,
+ lw=2,
+ color=:steelblue,
+ label="cond(F̄)",
+ xlabel="Norm. Poloidal Flux",
+ ylabel="cond(F̄)",
+ title="Kinetic F̄ condition number (kmsing = $kmsing)",
+ legend=:topleft,
+ left_margin=12Plots.mm,
+ bottom_margin=4Plots.mm,
+ size=(900, 500)
+ )
+
+ if zoom
+ # Auto-scale y to data and annotate the threshold at the top edge if off-scale.
+ ylims!(p, (data_min / 2, data_max * 3))
+ if thr > 0 && thr > data_max * 3
+ annotate!(p, [(scan_psi[end], data_max * 2.5,
+ text(@sprintf("threshold = %.0e (off-scale)", thr), :right, 9, :red))])
+ elseif thr > 0
+ hline!(p, [thr]; color=:red, linestyle=:dash, lw=1.5,
+ label=@sprintf("threshold = %.0e", thr))
+ end
+ elseif thr > 0
+ hline!(p, [thr]; color=:red, linestyle=:dash, lw=1.5,
+ label=@sprintf("threshold = %.0e", thr))
+ end
+
+ if !isempty(i_psi)
+ vline!(p, i_psi; color=:gray, linestyle=:dot, lw=1,
+ label="ideal rational (q = m/n)")
+ y_label = zoom ? data_max * 1.2 : max(data_max * 1.2, sqrt(data_max * (thr > 0 ? thr : data_max)))
+ for (idx, ps) in enumerate(i_psi)
+ annotate!(p, [(ps, y_label,
+ text(@sprintf("q=%.0f", i_q[idx]), :right, 8, :gray))])
+ end
+ end
+
+ if !isempty(k_psi)
+ vline!(p, k_psi; color=:crimson, lw=1.5, label="accepted kinsing")
+ end
+
+ isnothing(save_path) || savefig(p, save_path)
+ return p
+end
+
+"""
+ plot_ffs_summary(h5path; save_path=nothing)
+
+Four-panel summary of ForceFreeStates (DCON-style) stability results, combining:
+
+ - Energy eigenvector heatmap (`plot_energy_eigenvectors`)
+ - Fixed-boundary stability criterion |D_c| vs ψ_N (`plot_stability_criterion`)
+ - Eigenvalue spectrum (`plot_eigenvalues`)
+ - Tearing stability Δ' at each rational surface (`plot_delta_prime`)
+
+If no vacuum data is present (`vac_flag = false`), only the stability criterion and Δ'
+panels are shown.
+
+### Arguments
+
+ - `h5path`: Path to a GPEC HDF5 output file
+
+### Keyword arguments
+
+ - `save_path`: If provided, save the figure to this path (default: `nothing`)
+
+### Returns
+
+A `Plots.jl` plot object.
+"""
+function plot_ffs_summary(h5path; save_path=nothing)
+ has_vac = h5open(h5path, "r") do fid
+ haskey(fid, "ForceFreeStates/FreeBoundaryStability/W_freeboundary_eigenmodes") &&
+ !isempty(read(fid["ForceFreeStates/FreeBoundaryStability/W_freeboundary_eigenmodes"]))
+ end
+
+ p_crit = plot_fixed_boundary_stability_criterion(h5path)
+ p_dp = plot_delta_prime(h5path)
+
+ if has_vac
+ p_evec = plot_energy_eigenvectors(h5path; matrix_type=:total)
+ p_modes = plot_mode_displacement(h5path)
+ p = plot(p_evec, p_crit, p_modes, p_dp; layout=(2, 2), size=(1100, 900), right_margin=10Plots.mm)
+ else
+ title!(p_crit, "Stability criterion (no vacuum data — rerun with vac_flag = true)")
+ p = plot(p_crit, p_dp; layout=(1, 2), size=(1100, 500), right_margin=10Plots.mm)
+ end
+
+ isnothing(save_path) || savefig(p, save_path)
+ return p
+end
+
+"""
+ plot_ballooning_alpha_boundaries(bnd; save_path=nothing, psi_min=0.0)
+
+Plot the BALOO-style infinite-n ballooning stability diagram with first and second stability
+boundaries: experimental α (solid black), 1st stability boundary α_crit1 (dashed red), and
+2nd stability boundary α_crit2 (dashed blue) versus ψ_N. `NaN` entries in the boundary
+arrays leave natural gaps over always-stable surfaces without requiring explicit masking.
+
+### Arguments
+
+ - `bnd`: NamedTuple with fields `psi`, `alpha`, `alpha_critical1`, `alpha_critical2`
+ (as returned by `LocalStability.ballooning_alpha_boundaries`)
+
+### Keyword arguments
+
+ - `save_path`: If provided, save the figure to this path (default: `nothing`)
+ - `psi_min`: Lower ψ_N axis limit (default: `0.0`)
+
+### Returns
+
+A `Plots.jl` plot object.
+"""
+function plot_ballooning_alpha_boundaries(bnd; save_path=nothing, psi_min=0.0)
+ p = plot(;
+ xlims=(psi_min, 1),
+ xlabel=L"\psi_N",
+ ylabel=L"\alpha",
+ title="Infinite-n ballooning stability",
+ framestyle=:box,
+ legend=:topleft,
+ left_margin=10Plots.mm,
+ bottom_margin=5Plots.mm
+ )
+ plot!(p, bnd.psi, bnd.alpha; lw=2, color=:black, label="Experimental gradient")
+ plot!(p, bnd.psi, bnd.alpha_critical1; lw=2, color=:red, marker=:circle, label="1st stability boundary")
+ plot!(p, bnd.psi, bnd.alpha_critical2; lw=2, color=:blue, marker=:circle, label="2nd stability boundary")
+ isnothing(save_path) || savefig(p, save_path)
+ return p
+end
+
+"""
+ plot_ballooning_alpha_boundaries(bnd, dpmap; save_path=nothing, psi_min=0.0)
+
+Same diagram drawn over a heatmap of the signed Δ' from
+`LocalStability.ballooning_delta_prime_map`: each surface's Δ'(α) is oriented by the
+sign of its α=0 (stable) value so that positive is stable everywhere, regridded from
+its native physical α = α_ref*scale onto a shared uniform α axis, and shown with the
+Δ'=0 contour, the extracted boundaries, and the scan cap `max_alpha_scale*α_exp`.
+Color limits are set to the 90th percentile of |Δ'| so the pole regions inside the
+unstable band do not wash out the marginal structure.
+"""
+function plot_ballooning_alpha_boundaries(bnd, dpmap; save_path=nothing, psi_min=0.0)
+ psi = dpmap.psi
+ scales = dpmap.alpha_scales
+ alpha_ref = dpmap.alpha_ref
+ signed = dpmap.delta_prime .* sign.(dpmap.delta_prime[:, 1])
+
+ finite_aref = filter(isfinite, alpha_ref)
+ isempty(finite_aref) && error("delta-prime map contains no valid surfaces")
+ alpha_axis = collect(range(0.0, maximum(finite_aref) * scales[end]; length=200))
+ z = fill(NaN, length(alpha_axis), length(psi))
+ for i in eachindex(psi)
+ (isfinite(alpha_ref[i]) && alpha_ref[i] > 0.0) || continue
+ a_surf = alpha_ref[i] .* scales
+ for (j, a) in enumerate(alpha_axis)
+ a > a_surf[end] && break
+ k = min(searchsortedlast(a_surf, a), length(a_surf) - 1)
+ k < 1 && continue
+ t = (a - a_surf[k]) / (a_surf[k+1] - a_surf[k])
+ z[j, i] = (1 - t) * signed[i, k] + t * signed[i, k+1]
+ end
+ end
+
+ # Color limits track the unstable-side magnitudes; deep stable values and pole
+ # regions clamp at the ends instead of washing out the marginal band.
+ finite_z = abs.(filter(isfinite, vec(z)))
+ finite_neg = abs.(filter(x -> isfinite(x) && x < 0.0, vec(z)))
+ lim = isempty(finite_neg) ? (isempty(finite_z) ? 1.0 : quantile(finite_z, 0.9)) : quantile(finite_neg, 0.95)
+ lim = max(lim, eps(Float64))
+
+ p = heatmap(
+ psi,
+ alpha_axis,
+ z;
+ c=cgrad(:RdBu),
+ clims=(-lim, lim),
+ # Leading newline offsets the rotated title clear of the colorbar tick labels (GR quirk)
+ colorbar_title="\n" * L"\Delta' \times \mathrm{sign}(\Delta'_{\alpha=0})",
+ xlims=(psi_min, 1),
+ xlabel=L"\psi_N",
+ ylabel=L"\alpha",
+ title="Infinite-n ballooning stability",
+ framestyle=:box,
+ legend=:topleft,
+ left_margin=10Plots.mm,
+ bottom_margin=5Plots.mm,
+ right_margin=15Plots.mm
+ )
+ contour!(p, psi, alpha_axis, z; levels=[0.0], color=:black, linewidth=1, colorbar_entry=false)
+ plot!(p, bnd.psi, bnd.alpha; lw=2, color=:black, label="Experimental gradient")
+ plot!(p, bnd.psi, bnd.alpha_critical1; lw=2, color=:red, linestyle=:dash, label="1st stability boundary")
+ plot!(p, bnd.psi, bnd.alpha_critical2; lw=2, color=:blue, linestyle=:dash, label="2nd stability boundary")
+ plot!(p, psi, scales[end] .* alpha_ref; lw=2, color=:gray, linestyle=:dot, label="scan cap")
+ isnothing(save_path) || savefig(p, save_path)
+ return p
+end
+
+end # module ForceFreeStates
diff --git a/src/Analysis/PerturbedEquilibrium.jl b/src/Analysis/PerturbedEquilibrium.jl
new file mode 100644
index 0000000000..83d5cde7bf
--- /dev/null
+++ b/src/Analysis/PerturbedEquilibrium.jl
@@ -0,0 +1,484 @@
+"""
+ PerturbedEquilibrium
+
+Post-processing and visualization functions for GPEC perturbed equilibrium results stored
+in the `PerturbedEquilibrium/` group of a GPEC HDF5 output file.
+"""
+module PerturbedEquilibrium
+
+using HDF5
+using LaTeXStrings
+using Plots
+
+# Check that a PE dataset exists and is non-empty.
+function _has_pe_data(h5path, key)
+ h5open(h5path, "r") do fid
+ haskey(fid, key) && !isempty(read(fid[key]))
+ end
+end
+
+"""
+ plot_resonant_area_weighted_field_amplitude(h5path; save_path=nothing)
+
+Scatter plot of the resonant area-weighted field `|b^r|` per rational surface vs ψ_N. One marker series
+per toroidal mode n. Integer-valued q rational surfaces are annotated. The resonant area-weighted field
+`b^r = Φ^r/A^r` is the resonant flux normalized by the scalar surface area, in tesla [Pharr 2026].
+
+Requires the perturbed equilibrium module to have been run and
+`SingularCoupling/resonant_area_weighted_field` to be present in the HDF5 file.
+
+### Arguments
+
+ - `h5path`: Path to a GPEC HDF5 output file with perturbed equilibrium output
+
+### Keyword arguments
+
+ - `save_path`: If provided, save the figure to this path (default: `nothing`)
+
+### Returns
+
+A `Plots.jl` plot object.
+"""
+function plot_resonant_area_weighted_field_amplitude(h5path; save_path=nothing)
+ base = "PerturbedEquilibrium/SingularCoupling/"
+ _has_pe_data(h5path, base * "resonant_area_weighted_field") ||
+ return plot(; title="No resonant area-weighted field data — run with perturbed equilibrium enabled", legend=false)
+
+ resonant_area_weighted_field, rational_psi, rational_q, rational_n = h5open(h5path, "r") do fid
+ read(fid[base*"resonant_area_weighted_field"]),
+ read(fid[base*"rational_psi"]),
+ read(fid[base*"rational_q"]),
+ read(fid[base*"rational_n"])
+ end
+
+ p = plot(; xlabel="Norm. Poloidal Flux", ylabel="|b^r| [T]",
+ title="Resonant area-weighted field |b^r| per surface", legend=:outertopright,
+ left_margin=10Plots.mm, bottom_margin=5Plots.mm)
+
+ for nn in unique(rational_n)
+ mask = rational_n .== nn
+ scatter!(p, rational_psi[mask], abs.(resonant_area_weighted_field[mask]);
+ label="n=$nn", markersize=7, markerstrokewidth=0)
+ for k in findall(mask)
+ abs(rational_q[k] - round(rational_q[k])) < 0.05 || continue
+ annotate!(p, rational_psi[k], abs(resonant_area_weighted_field[k]),
+ text(" q=$(round(Int, rational_q[k]))", 8, :left, :black))
+ end
+ end
+
+ isnothing(save_path) || savefig(p, save_path)
+ return p
+end
+
+"""
+ plot_island_widths(h5path; save_path=nothing)
+
+Scatter plot of island half-width `w/2` per rational surface vs ψ_N.
+Integer-valued q rational surfaces are annotated.
+
+Requires `SingularCoupling/island_half_width` in the HDF5 file.
+
+### Arguments
+
+ - `h5path`: Path to a GPEC HDF5 output file with perturbed equilibrium output
+
+### Keyword arguments
+
+ - `save_path`: If provided, save the figure to this path (default: `nothing`)
+
+### Returns
+
+A `Plots.jl` plot object.
+"""
+function plot_island_widths(h5path; save_path=nothing)
+ base = "PerturbedEquilibrium/SingularCoupling/"
+ _has_pe_data(h5path, base * "island_half_width") ||
+ return plot(; title="No island width data — run with perturbed equilibrium enabled", legend=false)
+
+ island_hw, rational_psi, rational_q = h5open(h5path, "r") do fid
+ read(fid[base*"island_half_width"]),
+ read(fid[base*"rational_psi"]),
+ read(fid[base*"rational_q"])
+ end
+
+ p = scatter(
+ rational_psi, island_hw;
+ xlabel="Norm. Poloidal Flux",
+ ylabel="w/2",
+ title="Island half-widths",
+ legend=false,
+ color=:steelblue,
+ markersize=7,
+ markerstrokewidth=0,
+ left_margin=10Plots.mm,
+ bottom_margin=5Plots.mm
+ )
+ for k in eachindex(rational_psi)
+ abs(rational_q[k] - round(rational_q[k])) < 0.05 || continue
+ annotate!(p, rational_psi[k], island_hw[k],
+ text(" q=$(round(Int, rational_q[k]))", 8, :left, :black))
+ end
+
+ isnothing(save_path) || savefig(p, save_path)
+ return p
+end
+
+"""
+ plot_chirikov_parameter(h5path; save_path=nothing)
+
+Scatter plot of the Chirikov overlap parameter per rational surface vs ψ_N, with a
+horizontal reference line at K = 1 (island overlap threshold). Points are colored red
+when K > 1. Integer-valued q rational surfaces are annotated.
+
+Requires `SingularCoupling/chirikov_parameter` in the HDF5 file.
+
+### Arguments
+
+ - `h5path`: Path to a GPEC HDF5 output file with perturbed equilibrium output
+
+### Keyword arguments
+
+ - `save_path`: If provided, save the figure to this path (default: `nothing`)
+
+### Returns
+
+A `Plots.jl` plot object.
+"""
+function plot_chirikov_parameter(h5path; save_path=nothing)
+ base = "PerturbedEquilibrium/SingularCoupling/"
+ _has_pe_data(h5path, base * "chirikov_parameter") ||
+ return plot(; title="No Chirikov data — run with perturbed equilibrium enabled", legend=false)
+
+ chirikov, rational_psi, rational_q = h5open(h5path, "r") do fid
+ read(fid[base*"chirikov_parameter"]),
+ read(fid[base*"rational_psi"]),
+ read(fid[base*"rational_q"])
+ end
+
+ colors = [k > 1.0 ? :red : :steelblue for k in chirikov]
+
+ p = scatter(
+ rational_psi, chirikov;
+ xlabel="Norm. Poloidal Flux",
+ ylabel="K (Chirikov)",
+ title="Chirikov overlap parameter",
+ legend=false,
+ color=colors,
+ markersize=7,
+ markerstrokewidth=0,
+ left_margin=10Plots.mm,
+ bottom_margin=5Plots.mm
+ )
+ hline!(p, [1.0]; linestyle=:dash, color=:black, label=nothing)
+ for k in eachindex(rational_psi)
+ abs(rational_q[k] - round(rational_q[k])) < 0.05 || continue
+ annotate!(p, rational_psi[k], chirikov[k],
+ text(" q=$(round(Int, rational_q[k]))", 8, :left, :black))
+ end
+
+ isnothing(save_path) || savefig(p, save_path)
+ return p
+end
+
+"""
+ plot_driven_delta_prime(h5path; save_path=nothing)
+
+Scatter plot of `Re(Δ')` per rational surface vs ψ_N, computed by the perturbed
+equilibrium module (from `PerturbedEquilibrium/SingularCoupling/Delta_prime`).
+One marker series per toroidal mode n. Integer-valued q rational surfaces are
+annotated.
+
+This is the forcing-driven Δ' (response to the applied perturbation amplitudes
+in `intr.forcing_modes`); for the equilibrium-intrinsic Δ' from the STRIDE BVP,
+read `SingularSurfaces/Delta_prime_matrix` from the HDF5 directly.
+
+Requires `PerturbedEquilibrium/SingularCoupling/Delta_prime` in the HDF5 file.
+
+### Arguments
+
+ - `h5path`: Path to a GPEC HDF5 output file
+
+### Keyword arguments
+
+ - `save_path`: If provided, save the figure to this path (default: `nothing`)
+
+### Returns
+
+A `Plots.jl` plot object.
+"""
+function plot_driven_delta_prime(h5path; save_path=nothing)
+ base = "PerturbedEquilibrium/SingularCoupling/"
+ _has_pe_data(h5path, base * "Delta_prime") ||
+ return plot(; title="No PE Δ' data — run with perturbed equilibrium enabled", legend=false)
+
+ delta_prime, rational_psi, rational_q, rational_n = h5open(h5path, "r") do fid
+ read(fid[base*"Delta_prime"]),
+ read(fid[base*"rational_psi"]),
+ read(fid[base*"rational_q"]),
+ read(fid[base*"rational_n"])
+ end
+
+ p = plot(; xlabel="Norm. Poloidal Flux", ylabel="Re(Δ')",
+ title="Tearing stability Δ' (driven, perturbed equilibrium)", legend=:outertopright,
+ left_margin=10Plots.mm, bottom_margin=5Plots.mm)
+ hline!(p, [0.0]; linestyle=:dash, color=:black, label=nothing)
+
+ for nn in unique(rational_n)
+ mask = rational_n .== nn
+ dp_n = real.(delta_prime[mask])
+ colors = [v > 0 ? :red : :steelblue for v in dp_n]
+ scatter!(p, rational_psi[mask], dp_n; label="n=$nn", color=colors,
+ markersize=7, markerstrokewidth=0)
+ for (k, idx) in enumerate(findall(mask))
+ abs(rational_q[idx] - round(rational_q[idx])) < 0.05 || continue
+ annotate!(p, rational_psi[idx], dp_n[k],
+ text(" q=$(round(Int, rational_q[idx]))", 8, :left, :black))
+ end
+ end
+
+ isnothing(save_path) || savefig(p, save_path)
+ return p
+end
+
+"""
+ plot_resonant_area_weighted_field(h5path; save_path=nothing)
+
+Five-panel summary of resonant coupling quantities at each rational surface vs ψ_N:
+
+ - `|b^r|`: resonant area-weighted field (`plot_resonant_area_weighted_field_amplitude`)
+ - `Re(Δ')`: tearing stability parameter (`plot_driven_delta_prime`)
+ - `|I_res|`: resonant current
+ - `w/2`: island half-width (`plot_island_widths`)
+ - `K`: Chirikov overlap parameter (`plot_chirikov_parameter`)
+
+Inspired by `plot_resonant_flux.py` from OMFIT GPEC.
+
+### Arguments
+
+ - `h5path`: Path to a GPEC HDF5 output file with perturbed equilibrium output
+
+### Keyword arguments
+
+ - `save_path`: If provided, save the figure to this path (default: `nothing`)
+
+### Returns
+
+A `Plots.jl` plot object.
+"""
+function plot_resonant_area_weighted_field(h5path; save_path=nothing)
+ p1 = plot_resonant_area_weighted_field_amplitude(h5path)
+ p2 = plot_driven_delta_prime(h5path)
+ p3 = _plot_resonant_current(h5path)
+ p4 = plot_island_widths(h5path)
+ p5 = plot_chirikov_parameter(h5path)
+
+ # Move outer legends inside so all panels have the same right margin
+ for p in (p1, p2, p3)
+ plot!(p; title="", legend=:topright)
+ end
+ for p in (p4, p5)
+ plot!(p; title="")
+ end
+
+ hide_xaxis!(p) = plot!(p; xlabel="", xformatter=_ -> "", bottom_margin=1Plots.mm)
+ for p in (p1, p2, p3, p4)
+ hide_xaxis!(p)
+ end
+
+ p = plot(p1, p2, p3, p4, p5; layout=(5, 1), size=(900, 1600))
+
+ isnothing(save_path) || savefig(p, save_path)
+ return p
+end
+
+# Internal helper — resonant current scatter plot
+function _plot_resonant_current(h5path)
+ base = "PerturbedEquilibrium/SingularCoupling/"
+ _has_pe_data(h5path, base * "resonant_current") ||
+ return plot(; title="No resonant current data", legend=false)
+
+ resonant_current, rational_psi, rational_q, rational_n = h5open(h5path, "r") do fid
+ read(fid[base*"resonant_current"]),
+ read(fid[base*"rational_psi"]),
+ read(fid[base*"rational_q"]),
+ read(fid[base*"rational_n"])
+ end
+
+ p = plot(; xlabel="Norm. Poloidal Flux", ylabel="|I_res|",
+ title="Resonant current |I_res| per surface", legend=:outertopright,
+ left_margin=10Plots.mm, bottom_margin=5Plots.mm)
+
+ for nn in unique(rational_n)
+ mask = rational_n .== nn
+ rc_n = abs.(resonant_current[mask])
+ scatter!(p, rational_psi[mask], rc_n;
+ label="n=$nn", markersize=7, markerstrokewidth=0)
+ for (k, idx) in enumerate(findall(mask))
+ abs(rational_q[idx] - round(rational_q[idx])) < 0.05 || continue
+ annotate!(p, rational_psi[idx], rc_n[k],
+ text(" q=$(round(Int, rational_q[idx]))", 8, :left, :black))
+ end
+ end
+
+ return p
+end
+
+"""
+ plot_mode_spectrogram(h5path; component=:xi_psi, save_path=nothing)
+
+Two-panel spectrogram of a perturbed equilibrium response field component:
+
+ - Top: `|component|` vs ψ_N, one curve per poloidal mode m. Only resonant modes
+ (m ∈ [0, nhigh·q95)) are labeled to keep the legend readable.
+ - Bottom: Heatmap of `|component|` in (m, ψ_N) space (psi on vertical axis), with
+ white dashed lines at rational surface locations.
+
+Inspired by `plot_spectrograms.py` from OMFIT GPEC.
+
+### Arguments
+
+ - `h5path`: Path to a GPEC HDF5 output file with perturbed equilibrium response output
+
+### Keyword arguments
+
+ - `component`: Response field component to plot; one of `:xi_psi`, `:b_psi`,
+ `:Jb_theta`, `:Jb_zeta` (default: `:xi_psi`). `:b_psi` reads the area-normalized
+ `b_psi_area_weighted` dataset; `:Jb_theta` and `:Jb_zeta` are the Jacobian-weighted
+ contravariant field components.
+ - `save_path`: If provided, save the figure to this path (default: `nothing`)
+
+### Returns
+
+A `Plots.jl` plot object.
+"""
+function plot_mode_spectrogram(h5path; component=:xi_psi, save_path=nothing)
+ comp_map = Dict(
+ :xi_psi => "xi_psi",
+ :b_psi => "b_psi_area_weighted", # area-normalized b^ψ
+ :Jb_theta => "Jb_theta",
+ :Jb_zeta => "Jb_zeta"
+ )
+ haskey(comp_map, component) ||
+ error("component must be one of :xi_psi, :b_psi, :Jb_theta, :Jb_zeta")
+
+ base = "PerturbedEquilibrium/Response/"
+ dataset_path = base * comp_map[component]
+
+ _has_pe_data(h5path, dataset_path) ||
+ return plot(; title="No response data — run with perturbed equilibrium enabled", legend=false)
+
+ data, psi_response, mlow, mhigh, nhigh, q95, rational_psi = h5open(h5path, "r") do fid
+ read(fid[dataset_path]),
+ read(fid[base*"psi"]),
+ read(fid["Info/mlow"]), read(fid["Info/mhigh"]), read(fid["Info/nhigh"]),
+ read(fid["Equilibrium/q_95"]),
+ read(fid["PerturbedEquilibrium/SingularCoupling/rational_psi"])
+ end
+
+ mpert = mhigh - mlow + 1
+ m_vals = mlow:mhigh
+ data_mn = data[:, 1:mpert] # (npsi, mpert): first mpert columns = first n's modes
+
+ # Top panel: line plot per mode — only label resonant range m ∈ [0, nhigh·q95)
+ m_max_legend = nhigh * q95
+ p1 = plot(;
+ xlabel="Norm. Poloidal Flux",
+ ylabel="|$(component)|",
+ title="Mode spectrogram: $(component)",
+ legend=:outertopright,
+ left_margin=10Plots.mm,
+ bottom_margin=5Plots.mm
+ )
+ cmap = cgrad(:roma, mpert; categorical=true)
+ for (i, m) in enumerate(m_vals)
+ show_label = 0 <= m < m_max_legend
+ plot!(p1, psi_response, abs.(data_mn[:, i]);
+ label=(show_label ? "m=$m" : nothing), color=cmap[i], linewidth=1.5)
+ end
+
+ # Bottom panel: heatmap in (m, ψ_N) space — psi on vertical axis, m on horizontal
+ p2 = heatmap(
+ collect(m_vals), psi_response, abs.(data_mn);
+ xlabel="m",
+ ylabel="Norm. Poloidal Flux",
+ title="",
+ colorbar_title="|$(component)|",
+ left_margin=10Plots.mm,
+ right_margin=20Plots.mm,
+ bottom_margin=5Plots.mm
+ )
+ # Overlay rational surface locations as white dashed lines
+ for psi_s in rational_psi
+ hline!(p2, [psi_s]; linestyle=:dash, color=:white, linewidth=1.5, label=nothing)
+ end
+
+ p = plot(p1, p2; layout=(2, 1), size=(950, 750))
+
+ isnothing(save_path) || savefig(p, save_path)
+ return p
+end
+
+"""
+ plot_perturbed_equilibrium_summary(h5path; save_path=nothing)
+
+Three-panel composite summary of perturbed equilibrium results:
+
+ - Top-left: Resonant area-weighted field per surface (`plot_resonant_area_weighted_field_amplitude`)
+ - Top-right: Edge |b_ψ| spectrum
+ - Bottom: ξ_ψ mode spectrogram (`plot_mode_spectrogram`)
+
+### Arguments
+
+ - `h5path`: Path to a GPEC HDF5 output file with perturbed equilibrium output
+
+### Keyword arguments
+
+ - `save_path`: If provided, save the figure to this path (default: `nothing`)
+
+### Returns
+
+A `Plots.jl` plot object.
+"""
+function plot_perturbed_equilibrium_summary(h5path; save_path=nothing)
+ p_islands = plot_resonant_area_weighted_field_amplitude(h5path)
+ p_bpsi = _plot_bpsi_edge_spectrum(h5path)
+ p_spectro = plot_mode_spectrogram(h5path; component=:xi_psi)
+
+ l = @layout [grid(1, 2){0.35h}; b]
+ p = plot(p_islands, p_bpsi, p_spectro; layout=l, size=(1100, 1100))
+
+ isnothing(save_path) || savefig(p, save_path)
+ return p
+end
+
+# Internal helper — |b_psi(m)| spectrum at the outermost psi surface
+function _plot_bpsi_edge_spectrum(h5path)
+ base = "PerturbedEquilibrium/Response/"
+ _has_pe_data(h5path, base * "b_psi_area_weighted") ||
+ return plot(; title="No b_psi data — run with perturbed equilibrium enabled", legend=false)
+
+ data, mlow, mhigh = h5open(h5path, "r") do fid
+ read(fid[base*"b_psi_area_weighted"]),
+ read(fid["Info/mlow"]), read(fid["Info/mhigh"])
+ end
+
+ mpert = mhigh - mlow + 1
+ m_vals = mlow:mhigh
+ bpsi_edge = abs.(data[end, 1:mpert])
+
+ p = bar(
+ collect(m_vals), bpsi_edge;
+ xlabel="m",
+ ylabel="|b_ψ|",
+ title="b_ψ spectrum at ψ edge",
+ legend=false,
+ color=:steelblue,
+ linewidth=0,
+ left_margin=10Plots.mm,
+ bottom_margin=5Plots.mm
+ )
+
+ return p
+end
+
+end # module PerturbedEquilibrium
diff --git a/src/Analysis/PerturbedEquilibriumModes.jl b/src/Analysis/PerturbedEquilibriumModes.jl
new file mode 100644
index 0000000000..a4dc52174f
--- /dev/null
+++ b/src/Analysis/PerturbedEquilibriumModes.jl
@@ -0,0 +1,148 @@
+"""
+ PerturbedEquilibriumModes
+
+Post-processing utilities for converting modal GPEC outputs to theta-space
+and (theta, phi) grids.
+"""
+module PerturbedEquilibriumModes
+
+using HDF5
+using FastInterpolations
+using ...Utilities.FourierTransforms: FourierTransform, inverse
+
+"""
+ modes_to_theta(h5_file, variable; mtheta=nothing, keep_sfl_phi=true)
+
+Convert modal output `(npsi, numpert_total)` from a gpec.h5 file to theta-space
+`(npsi, mtheta, npert)`.
+
+Reads all required metadata (mlow, nlow, mpert, npert) and spline data (ν) from
+the HDF5 file.
+
+# Arguments
+
+ - `h5_file::String`: Path to gpec.h5 output file
+ - `variable::String`: HDF5 dataset path, e.g. `"PerturbedEquilibrium/Response/xi_R"`
+
+# Keyword arguments
+
+ - `mtheta::Int`: theta grid resolution (default: `max(2*(|mlow|+mpert), 512)`)
+ - `keep_sfl_phi::Bool`: if `true` (default), output in SFL toroidal angle;
+ if `false`, apply `exp(i*n*ν(ψ,θ))` to convert to machine toroidal angle
+ and conjugate if `helicity > 0` (matches Fortran `gpout_xbrzphifun`)
+
+# Returns
+
+ - `theta_data::Array{ComplexF64,3}`: `[npsi × mtheta × npert]`
+ - `theta_grid::Vector{Float64}`: `[mtheta]` SFL theta ∈ [0, 1)
+ - `n_vals::Vector{Int}`: `[npert]` toroidal mode numbers
+
+!!! note
+
+ When used on the cylindrical components `xi_R`, `xi_Z`, `xi_phi`, `b_R`, `b_Z`,
+ `b_phi` these are currently in beta and show up to ~20% discrepancies vs Fortran.
+"""
+function modes_to_theta(h5_file::String, variable::String;
+ mtheta::Union{Int,Nothing}=nothing,
+ keep_sfl_phi::Bool=true)
+ h5open(h5_file, "r") do f
+ modes = read(f, variable) # (npsi, numpert_total)
+ npsi, numpert_total = size(modes)
+
+ mlow = read(f, "Info/mlow")
+ nlow = read(f, "Info/nlow")
+ mpert = read(f, "Info/mpert")
+ npert = read(f, "Info/npert")
+ @assert numpert_total == mpert * npert "Expected numpert_total=$(mpert*npert), got $numpert_total"
+
+ n_vals = [nlow + k - 1 for k in 1:npert]
+ mth = isnothing(mtheta) ? max(2 * (abs(mlow) + mpert), 512) : mtheta
+ ft = FourierTransform(mth, mpert, mlow)
+ theta_grid = [(j - 1) / mth for j in 1:mth]
+
+ theta_data = zeros(ComplexF64, npsi, mth, npert)
+ for k in 1:npert
+ col_range = (k-1)*mpert+1:k*mpert
+ for ipsi in 1:npsi
+ theta_data[ipsi, :, k] .= inverse(ft, view(modes, ipsi, col_range))
+ end
+ end
+
+ if !keep_sfl_phi
+ # Reconstruct ν spline from stored grid + nodal values (FastInterpolations v0.4 API)
+ rzphi_xs = read(f, "Equilibrium/Geometry/psi")
+ rzphi_ys = read(f, "Equilibrium/Geometry/theta")
+ nu_vals = read(f, "Equilibrium/Geometry/nu")
+ nu_spline = cubic_interp(
+ (rzphi_xs, rzphi_ys), nu_vals;
+ bc=(CubicFit(), PeriodicBC()),
+ extrap=(ExtendExtrap(), WrapExtrap())
+ )
+
+ psi_grid = read(f, "ForceFreeStates/Solutions/ForwardIntegration/psi")
+
+ bt_sign = haskey(f, "Equilibrium/B_T_sign") ? read(f, "Equilibrium/B_T_sign") : 1
+ crnt = haskey(f, "Equilibrium/I_p") ? read(f, "Equilibrium/I_p") : 1.0
+ helicity = bt_sign * Int(sign(crnt))
+
+ hint = (Ref(1), Ref(1))
+ for k in 1:npert
+ nn = n_vals[k]
+ for ipsi in 1:npsi
+ psi = psi_grid[ipsi]
+ for itheta in 1:mth
+ nu = nu_spline((psi, theta_grid[itheta]); hint=hint)
+ theta_data[ipsi, itheta, k] *= exp(im * nn * nu)
+ end
+ end
+
+ if helicity > 0
+ theta_data[:, :, k] .= conj.(theta_data[:, :, k])
+ end
+ end
+ end
+
+ return theta_data, theta_grid, n_vals
+ end
+end
+
+"""
+ theta_to_thetaphi(theta_data, n_vals; nphi=nothing)
+
+Extend theta-space data to a `(θ, φ)` grid via toroidal inverse DFT.
+
+ f(θ, φ) = Σₙ fₙ(θ) exp(i·n·φ)
+
+# Arguments
+
+ - `theta_data::Array{ComplexF64,3}`: `[npsi × mtheta × npert]` from `modes_to_theta`
+ - `n_vals::Vector{Int}`: toroidal mode numbers
+
+# Keyword arguments
+
+ - `nphi::Int`: toroidal grid points (default: `max(4*maximum(abs.(n_vals)), 64)`)
+
+# Returns
+
+ - `full_data::Array{ComplexF64,3}`: `[npsi × mtheta × nphi]`
+ - `phi_grid::Vector{Float64}`: `[nphi]` in radians ∈ [0, 2π)
+"""
+function theta_to_thetaphi(theta_data::Array{ComplexF64,3}, n_vals::Vector{Int};
+ nphi::Union{Int,Nothing}=nothing)
+ npsi, mth, npert = size(theta_data)
+ np = isnothing(nphi) ? max(4 * maximum(abs.(n_vals)), 64) : nphi
+ phi_grid = [(j - 1) * 2π / np for j in 1:np]
+
+ full_data = zeros(ComplexF64, npsi, mth, np)
+ for k in 1:npert
+ nn = n_vals[k]
+ for jphi in 1:np
+ phase = exp(im * nn * phi_grid[jphi])
+ full_data[:, :, jphi] .+= theta_data[:, :, k] .* phase
+ end
+ end
+
+ return full_data, phi_grid
+end
+
+end # module PerturbedEquilibriumModes
diff --git a/src/DCON/DCON.jl b/src/DCON/DCON.jl
deleted file mode 100644
index ba28c3ce77..0000000000
--- a/src/DCON/DCON.jl
+++ /dev/null
@@ -1,26 +0,0 @@
-module DCON
-
-# All imports and includes for the DCON module
-using LinearAlgebra
-using LinearAlgebra.LAPACK #required for banded matrix operations
-using TOML
-using FFTW
-using OrdinaryDiffEq
-using HDF5
-import ..Equilibrium
-import ..Spl
-import ..VacuumMod
-using Printf
-
-# Include all necessary files
-include("DconStructs.jl")
-include("Main.jl")
-include("Mercier.jl")
-include("Ode.jl")
-include("Sing.jl")
-include("Fourfit.jl")
-include("OdeOutput.jl")
-include("Utils.jl")
-include("Free.jl")
-
-end
\ No newline at end of file
diff --git a/src/DCON/DconStructs.jl b/src/DCON/DconStructs.jl
deleted file mode 100644
index 38bd7684ed..0000000000
--- a/src/DCON/DconStructs.jl
+++ /dev/null
@@ -1,258 +0,0 @@
-# TODO: add descriptions of what all variables are and/or explanation of defaults
-# TODO: remove all unused variables before first pull request
-@kwdef mutable struct ResistType
- e::Float64 = 0.0
- f::Float64 = 0.0
- h::Float64 = 0.0
- m::Float64 = 0.0
- g::Float64 = 0.0
- k::Float64 = 0.0
- eta::Float64 = 0.0
- rho::Float64 = 0.0
- taua::Float64 = 0.0
- taur::Float64 = 0.0
-end
-
-# TODO: ideally, everything is allocated at construction, but mpert is determined after
-# since these are allocated in sing_find. What's the best way to handle this?
-# For now, leaving as missing, per Brendan's github comment
-# Something simple could be not creating sing_types within sing_find, but instead saving the data,
-# then creating them all at once after mpert is determined in dcon.jl
-# This wouldn't be as clean, but would allow preallocation. Does this greatly impact performance?
-@kwdef mutable struct SingType
- m::Int = 0
- r1::Vector{Int} = [0]
- r2::Vector{Int} = [0, 0]
- psifac::Float64 = 0.0
- rho::Float64 = 0.0
- q::Float64 = 0.0
- q1::Float64 = 0.0
- di::Float64 = 0.0
- alpha::ComplexF64 = 0.0 + 0.0im
- n1::Vector{Int} = Int[]
- n2::Vector{Int} = Int[]
- power::Union{Missing, Vector{ComplexF64}} = missing # we know the size of these, but it depends on mpert
- vmat::Union{Missing, Array{ComplexF64,4}} = missing
- mmat::Union{Missing, Array{ComplexF64,4}} = missing
- m0mat::Matrix{ComplexF64} = zeros(ComplexF64, 2, 2)
- restype::ResistType = ResistType()
-end
-# @kwdef mutable struct SingType
-# mpert::Int
-# order::Int
-# m::Int = 0
-# psifac::Float64 = 0.0
-# rho::Float64 = 0.0
-# q::Float64 = 0.0
-# q1::Float64 = 0.0
-# di::Float64 = 0.0
-# alpha::ComplexF64 = 0.0 + 0.0im
-# r1::Vector{Int} = [0]
-# r2::Vector{Int} = [0, 0]
-# n1::Vector{Int} = Vector{Int}(undef, mpert - 1)
-# n2::Vector{Int} = Vector{Int}(undef, 2 * mpert - 2)
-# power::Vector{ComplexF64} = Vector{ComplexF64}(undef, 2 * mpert)
-# vmat::Array{ComplexF64,4} = Array{ComplexF64}(undef, mpert, 2 * mpert, 2, order + 1)
-# mmat::Array{ComplexF64,4} = Array{ComplexF64}(undef, mpert, 2 * mpert, 2, order + 3)
-# m0mat::Union{Nothing, Matrix{ComplexF64}} = zeros(ComplexF64, 2, 2)
-# restype::ResistType = ResistType()
-# end
-# # Constructor to allocate matrices
-# SingType(mpert::Int, order::Int; kwargs...) = SingType(; mpert, order, kwargs...)
-
-@kwdef mutable struct DconInternal
- dir_path::String = ""
- mlow::Int = 0 #Copy of delta_mlow, but with limits enforced
- mhigh::Int = 0 #Copy of delta_mhigh, but with limits enforced
- mpert::Int = 0 #mpert = mhigh-mlow+1
- mband::Int = 0 #mband = mpert-1-delta_mband
- vac_memory::Bool = true # TODO: most likely just remove, always true in ahg_flag is deprecated
- keq_out::Bool = false
- theta_out::Bool = false
- xlmda_out::Bool = false
- fkg_kmats_flag::Bool = false
- sol_base::Int = 50
- msing::Int = 0
- kmsing::Int = 0
- sing::Union{Nothing, Vector{SingType}} = SingType[]
- kinsing::Union{Nothing, Vector{SingType}} = SingType[]
- psilim::Float64 = 0.0
- qlim::Float64 = 0.0
- q1lim::Float64 = 0.0
- # TODO: how to initialize a spline? This will be a spline of size mpsi x 5
- locstab::Union{Missing, Spl.CubicSpline{Float64}} = missing
- size_edge::Int = 0
- pre_edge::Int = 1
- i_edge::Int = 1
- # TODO: what are the lengths of these? can use to initialize
- q_edge::Union{Missing, Vector{Float64}} = missing
- psi_edge::Union{Missing, Vector{Float64}} = missing
- dw_edge::Union{Missing, Vector{ComplexF64}} = missing
-end
-
-@kwdef mutable struct DconControl
- verbose::Bool = true
- bal_flag::Bool = false
- mat_flag::Bool = false
- ode_flag::Bool = false
- vac_flag::Bool = false
- mer_flag::Bool = false
- res_flag::Bool = false
- fft_flag::Bool = false
- node_flag::Bool = false
- # saves_per_region::Int = 2 # number of u to save per interrational region, must be >> 0 to run GPEC
- # save_spacing::String = "Chebyshev" # method for determining spacing of saved u points
- mthvac::Int = 480
- sing_start::Int = 0
- nn::Int = 0
- delta_mlow::Int = 0
- delta_mhigh::Int = 0
- delta_mband::Int = 0
- thmax0::Float64 = 1.0
- nstep::Int = typemax(Int)
- ksing::Int = -1
- tol_nr::Float64 = 1e-5
- tol_r::Float64 = 1e-5
- crossover::Float64 = 1e-2
- ucrit::Float64 = 1e4
- numsteps_init::Int = 4000 # used to set initial size of data store in OdeState
- numunorms_init::Int = 100 # used to set initial size of saved unorm data in OdeState
- singfac_min::Float64 = 0.0
- singfac_max::Float64 = 0.0
- cyl_flag::Bool = false
- dmlim::Float64 = 0.5
- lim_flag::Bool = false
- sas_flag::Bool = false
- sing_order::Int = 2
- sort_type::String = "absm"
- termbycross_flag::Bool = false
- qhigh::Float64 = 1e3
- kin_flag::Bool = false
- con_flag::Bool = false
- kinfac1::Float64 = 1.0
- kinfac2::Float64 = 1.0
- kingridtype::Int = 0
- ktanh_flag::Bool = false
- passing_flag::Bool = false
- trapped_flag::Bool = true
- ion_flag::Bool = true
- electron_flag::Bool = false
- ktc::Float64 = 0.1
- ktw::Float64 = 50.0
- qlow::Float64 = 0.0
- use_classic_splines::Bool = false
- reform_eq_with_psilim::Bool = false
- psiedge::Float64 = 1.0
- nperq_edge::Int = 20
- wv_farwall_flag::Bool = false
- dcon_kin_threads::Int = 1
- parallel_threads::Int = 1
- diagnose::Bool = false
- diagnose_ca::Bool = false
-end
-
-# TODO: a lot of these will be deprecated, this will be a general data structure that handles output
-# Since file I/O in Julia will be very different than Fortran, this will likely be reworked significantly
-@kwdef mutable struct DconOutput
- # output switches
- write_crit_out::Bool = true
- write_dcon_out::Bool = true
- write_euler_h5::Bool = true
- write_eqdata_h5::Bool = false
-
- # filenames
- fname_crit_out::String = "crit.out"
- fname_dcon_out::String = "dcon.out"
- fname_euler_h5::String = "euler.h5"
- fname_eqdata_h5::String = "eqdata.h5"
-
- handles::Dict{Symbol,Any} = Dict()
-
- # Old or unused yet
- interp::Bool = false
- crit_break::Bool = true
- out_bal1::Bool = false
- bin_bal1::Bool = false
- out_bal2::Bool = false
- bin_bal2::Bool = false
- out_metric::Bool = false
- bin_metric::Bool = false
- feval_flag::Bool = false
- out_fmat::Bool = false
- bin_fmat::Bool = false
- out_gmat::Bool = false
- bin_gmat::Bool = false
- out_kmat::Bool = false
- bin_kmat::Bool = false
- out_sol::Bool = false
- out_sol_min::Int = 0
- out_sol_max::Int = 0
- bin_sol::Bool = false
- bin_sol_min::Int = 0
- bin_sol_max::Int = 0
- out_fl::Bool = false
- bin_fl::Bool = false
- out_evals::Bool = false
- bin_evals::Bool = false
- bin_euler::Bool = false
- euler_stride::Int = 1
- bin_vac::Bool = false # TODO: deprecated
- ahb_flag::Bool = false # TODO: deprecated
- mthsurf0::Float64 = 1.0 # TODO: deprecated
- msol_ahb::Int = 0 # TODO: deprecated
- netcdf_out::Bool = true # TODO: might be deprecated
- out_fund::Bool = false
- out_ahg2msc::Bool = false # TODO: deprecated
-end
-
-# TODO: how can we initialize the splines to not be nothings?
-@kwdef mutable struct FourFitVars
- mpert::Int
- mband::Int
-
- # Spline matrices
- # TODO: how to initialize these splines?
- amats::Union{Missing,Spl.CubicSpline{ComplexF64}} = missing
- bmats::Union{Missing,Spl.CubicSpline{ComplexF64}} = missing
- cmats::Union{Missing,Spl.CubicSpline{ComplexF64}} = missing
- dmats::Union{Missing,Spl.CubicSpline{ComplexF64}} = missing
- emats::Union{Missing,Spl.CubicSpline{ComplexF64}} = missing
- hmats::Union{Missing,Spl.CubicSpline{ComplexF64}} = missing
- dbats::Union{Missing,Spl.CubicSpline{ComplexF64}} = missing
- ebats::Union{Missing,Spl.CubicSpline{ComplexF64}} = missing
- fbats::Union{Missing,Spl.CubicSpline{ComplexF64}} = missing
- fmats::Union{Missing,Spl.CubicSpline{ComplexF64}} = missing
- kmats::Union{Missing,Spl.CubicSpline{ComplexF64}} = missing
- gmats::Union{Missing,Spl.CubicSpline{ComplexF64}} = missing
- # kaats::Union{Nothing,Spl.CubicSpline{ComplexF64}} = nothing
- # gaats::Union{Nothing,Spl.CubicSpline{ComplexF64}} = nothing
- # f0mats::Union{Nothing,Spl.CubicSpline{ComplexF64}} = nothing
- # pmats::Union{Nothing,Spl.CubicSpline{ComplexF64}} = nothing
- # paats::Union{Nothing,Spl.CubicSpline{ComplexF64}} = nothing
- # kkmats::Union{Nothing,Spl.CubicSpline{ComplexF64}} = nothing
- # kkaats::Union{Nothing,Spl.CubicSpline{ComplexF64}} = nothing
- # r1mats::Union{Nothing,Spl.CubicSpline{ComplexF64}} = nothing
- # r2mats::Union{Nothing,Spl.CubicSpline{ComplexF64}} = nothing
- # r3mats::Union{Nothing,Spl.CubicSpline{ComplexF64}} = nothing
- # akmats::Union{Nothing,Spl.CubicSpline{ComplexF64}} = nothing
- # bkmats::Union{Nothing,Spl.CubicSpline{ComplexF64}} = nothing
- # ckmats::Union{Nothing,Spl.CubicSpline{ComplexF64}} = nothing
-
- # k0s::JPEC.Spl.SplineType
-
- # ipiva::Union{Nothing,Vector{Int}} = nothing
- # TODO: these might be deprecated? They're used with a ahb_flag in free
- asmat::Matrix{ComplexF64} = Matrix{ComplexF64}(undef, mpert, mpert)
- bsmat::Matrix{ComplexF64} = Matrix{ComplexF64}(undef, mpert, mpert)
- csmat::Matrix{ComplexF64} = Matrix{ComplexF64}(undef, mpert, mpert)
- jmat::Vector{ComplexF64} = Vector{ComplexF64}(undef, 2 * mband + 1)
-
- parallel_threads::Int = 0
- dcon_kin_threads::Int = 0
-
- # kinetic ABCDEH mats for sing_mod
- # kwmats::Vector{JPEC.Spl.CubicSpline{ComplexF64}} = [JPEC.Spl.CubicSpline{ComplexF64}() for _ in 1:6]
- # ktmats::Vector{JPEC.Spl.CubicSpline{ComplexF64}} = [JPEC.Spl.CubicSpline{ComplexF64}() for _ in 1:6]
-end
-
-FourFitVars(mpert::Int) = FourFitVars(; mpert)
diff --git a/src/DCON/Fourfit.jl b/src/DCON/Fourfit.jl
deleted file mode 100644
index 08b3e496fc..0000000000
--- a/src/DCON/Fourfit.jl
+++ /dev/null
@@ -1,343 +0,0 @@
-"""
- MetricData
-
-A structure to hold the computed metric tensor components and their
-Fourier-spline representation. This is the Julia equivalent of the `fspline_type`
-named `metric` in the Fortran `fourfit_make_metric` subroutine.
-
-# Fields
-- `mpsi::Int`: Number of radial grid points minus one.
-- `mtheta::Int`: Number of poloidal grid points minus one.
-- `xs::Vector{Float64}`: Radial coordinates (normalized poloidal flux `ψ_norm`).
-- `ys::Vector{Float64}`: Poloidal angle coordinates `θ` in radians (0 to 2π).
-- `fs::Array{Float64, 3}`: The raw metric data on the grid, size `(mpsi, mtheta, 8)`.
- The 8 quantities are: `g¹¹`, `g²²`, `g³³`, `g²³`, `g³¹`, `g¹²`, `J`, `∂J/∂ψ`.
-- `fspline::Spl.FourierSpline`: The fitted Fourier-cubic spline object.
-"""
-@kwdef mutable struct MetricData
- mpsi::Int
- mtheta::Int
- xs::Vector{Float64} = zeros(mpsi)
- ys::Vector{Float64} = zeros(mtheta)
- fs::Array{Float64,3} = zeros(mpsi, mtheta, 8)
- fspline::Union{Spl.FourierSpline,Nothing} = nothing
-end
-
-MetricData(mpsi::Int, mtheta::Int) = MetricData(; mpsi, mtheta)
-
-"""
- make_metric(equil::Equilibrium.PlasmaEquilibrium; mband::Int=10, fft_flag::Bool=true) -> MetricData
-
-Constructs the metric tensor data on a (ψ, θ) grid from an input plasma equilibrium.
-
-# Arguments
-- `equil::Equilibrium.PlasmaEquilibrium`:
- An equilibrium object containing spline data (`rzphi`) for flux coordinates and geometry.
-- `mband::Int=10`:
- Number of Fourier modes to retain in the metric representation.
-- `fft_flag::Bool=true`:
- If `true`, enables use of Fourier fitting for storing metric coefficients.
- (Currently reserved for downstream processing.)
-
-# Returns
-- `metric::MetricData`:
- A structure containing the metric coefficients, coordinate grids, and Jacobians for the specified equilibrium.
-
-# Details
-- Uses bicubic spline evaluation (`Spl.bicube_eval`) on the equilibrium geometry to compute
- contravariant basis vectors ∇ψ, ∇θ, and ∇ζ at each grid point.
-- The metric coefficients stored in `metric.fs` include:
- 1. g^ψψ · J
- 2. g^θθ · J
- 3. g^ζζ · J
- 4. g^θζ · J
- 5. g^ζψ · J
- 6. g^ψθ · J
- 7. J (Jacobian)
- 8. ∂J/∂ψ
-- The ψ grid is taken directly from `rzphi.xs`, and θ is scaled from `[0,1]` to `[0, 2π]`.
-"""
-function make_metric(equil::Equilibrium.PlasmaEquilibrium; mband::Int=10, fft_flag::Bool=true)
-
- # TODO: add kinetic metric tensor components
-
- # --- Extract data from the PlasmaEquilibrium object ---
- rzphi = equil.rzphi
- mpsi = length(rzphi.xs)
- mtheta = length(rzphi.ys)
-
- println(" Equilibrium grid: $mpsi (ψ) × $mtheta (θ)")
- println(" Fourier fit modes (mband): $mband")
-
- metric = MetricData(mpsi, mtheta)
-
- # Set coordinate grids based on the input equilibrium
- # The `rzphi.ys` from EquilibriumAPI is normalized (0 to 1), so scale to radians.
- metric.xs .= Vector(rzphi.xs)
- metric.ys .= Vector(rzphi.ys .* 2π)
-
- # Temporary array for contravariant basis vectors
- v = zeros(Float64, 3, 3)
-
- # --- Main computation loop over the (ψ, θ) grid ---
- for ipsi in 1:mpsi
- psi_norm = rzphi.xs[ipsi]
- for jtheta in 1:mtheta
- theta_norm = rzphi.ys[jtheta] # θ is from 0 to 1
-
- # Evaluate the geometry spline to get (R,Z) and their derivatives
- f, fx, fy = Spl.bicube_eval(rzphi, psi_norm, theta_norm, 1)
-
- # Extract geometric quantities from the spline data
- # See EquilibriumAPI.txt for `rzphi` quantities
- r_coord_sq = f[1]
- eta_offset = f[2]
- jac = f[4]
- jac1 = fx[4] # ∂J/∂ψ
-
- rfac = sqrt(r_coord_sq)
- eta = 2π * (theta_norm + eta_offset)
- r_major = equil.ro + rfac * cos(eta) # This is the R coordinate
-
- # --- Compute contravariant basis vectors ∇ψ, ∇θ, ∇ζ ---
- fx1, fx2, fx3 = fx[1], fx[2], fx[3]
- fy1, fy2, fy3 = fy[1], fy[2], fy[3]
-
- v[1, 1] = fx1 / (2.0 * rfac * jac)
- v[1, 2] = fx2 * 2π * rfac / jac
- v[1, 3] = fx3 * r_major / jac
- v[2, 1] = fy1 / (2.0 * rfac * jac)
- v[2, 2] = (1.0 + fy2) * 2π * rfac / jac
- v[2, 3] = fy3 * r_major / jac
- v[3, 3] = 2π * r_major / jac
-
- # Store results
- metric.fs[ipsi, jtheta, 1] = sum(v[1, :] .^ 2) * jac
- metric.fs[ipsi, jtheta, 2] = sum(v[2, :] .^ 2) * jac
- metric.fs[ipsi, jtheta, 3] = v[3, 3] * v[3, 3] * jac
- metric.fs[ipsi, jtheta, 4] = v[2, 3] * v[3, 3] * jac
- metric.fs[ipsi, jtheta, 5] = v[3, 3] * v[1, 3] * jac
- metric.fs[ipsi, jtheta, 6] = sum(v[1, :] .* v[2, :]) * jac
- metric.fs[ipsi, jtheta, 7] = jac
- metric.fs[ipsi, jtheta, 8] = jac1
-
- # TODO: kinetic metric tensor here fmodb in Fortran
- end
- end
-
- # --- Fit the grid data to a Fourier-cubic spline ---
- fit_method = fft_flag ? 2 : 1
- # In Fortran, `bctype` was set for the periodic `y` dimension. Here, the `FourierSpline`
- # `bctype` argument applies to the non-periodic `x` dimension. The Fortran
- # code used "extrap" for this.
- bctype_x = "not-a-knot"
-
- # The poloidal (y) dimension is handled implicitly as periodic by the Fourier transform.
- metric.fspline = Spl.FourierSpline(
- metric.xs,
- metric.ys,
- metric.fs,
- mband;
- bctype=bctype_x,
- fit_method=fit_method
- )
- return metric
-end
-
-"""
- make_matrix(metric::MetricData, equil::Equilibrium.PlasmaEquilibrium, ctrl::DconControl, intr::DconInternal) -> FourFitVars
-
-Constructs Fourier–poloidal coupling matrices for a given toroidal mode number and returns them as a new `FourFitVars` object.
-
-# Arguments
-- `metric::MetricData`:
- Metric coefficients on the (ψ, θ) grid, including Fourier representations of g^ij and J.
-- `equil::Equilibrium.PlasmaEquilibrium`:
- Plasma equilibrium object providing 1D flux-surface profiles (`sq`) and normalization constants.
-- `ctrl::DconControl`:
- Control parameters for the DCON calculation, including mode numbers and flags.
-- `intr::DconInternal`:
- Internal state for the DCON calculation, including mode number ranges and splines.
-
-# Returns
-- `ffit::FourFitVars`:
- A container holding cubic spline fits of the assembled matrices
-"""
-function make_matrix(metric::MetricData, equil::Equilibrium.PlasmaEquilibrium, ctrl::DconControl, intr::DconInternal)
-
- # TODO: add banded matrices (if desired), kinetic matrices
-
- # --- Extract inputs ---
- sq = equil.sq
- mpsi = metric.mpsi
-
- if ctrl.verbose
- println(" Toroidal mode n=$(ctrl.nn), Poloidal modes m=$(intr.mlow):$(intr.mhigh) ($(intr.mpert) modes)")
- println(" Matrix bandwidth: $(intr.mband)")
- end
-
- # Allocations
- amats = zeros(ComplexF64, mpsi, intr.mpert, intr.mpert)
- bmats = zeros(ComplexF64, mpsi, intr.mpert, intr.mpert)
- cmats = zeros(ComplexF64, mpsi, intr.mpert, intr.mpert)
- dmats = zeros(ComplexF64, mpsi, intr.mpert, intr.mpert)
- emats = zeros(ComplexF64, mpsi, intr.mpert, intr.mpert)
- hmats = zeros(ComplexF64, mpsi, intr.mpert, intr.mpert)
- fmats = zeros(ComplexF64, mpsi, intr.mpert, intr.mpert)
- gmats = zeros(ComplexF64, mpsi, intr.mpert, intr.mpert)
- kmats = zeros(ComplexF64, mpsi, intr.mpert, intr.mpert)
- dbats = zeros(ComplexF64, mpsi, intr.mpert, intr.mpert)
- ebats = zeros(ComplexF64, mpsi, intr.mpert, intr.mpert)
- fbats = zeros(ComplexF64, mpsi, intr.mpert, intr.mpert)
- g11 = zeros(ComplexF64, 2 * intr.mband + 1)
- g22 = zeros(ComplexF64, 2 * intr.mband + 1)
- g33 = zeros(ComplexF64, 2 * intr.mband + 1)
- g23 = zeros(ComplexF64, 2 * intr.mband + 1)
- g31 = zeros(ComplexF64, 2 * intr.mband + 1)
- g12 = zeros(ComplexF64, 2 * intr.mband + 1)
- jmat = zeros(ComplexF64, 2 * intr.mband + 1)
- jmat1 = zeros(ComplexF64, 2 * intr.mband + 1)
-
- # Instead of using Offset Arrays like in Fortran (-mband:mband), we store everything in
- # a single 1:(2*mband+1) array and map the zero index to the middle
- mid = intr.mband + 1 # "zero" position in Julia arrays
- imat = zeros(ComplexF64, 2 * intr.mband + 1)
- imat[mid] = 1 + 0im
-
- for ipsi in 1:mpsi
- # --- Create views for this surface ---
- amat = @view amats[ipsi, :, :]
- bmat = @view bmats[ipsi, :, :]
- cmat = @view cmats[ipsi, :, :]
- dmat = @view dmats[ipsi, :, :]
- emat = @view emats[ipsi, :, :]
- hmat = @view hmats[ipsi, :, :]
- fmat = @view fmats[ipsi, :, :]
- gmat = @view gmats[ipsi, :, :]
- kmat = @view kmats[ipsi, :, :]
- dbat = @view dbats[ipsi, :, :]
- ebat = @view ebats[ipsi, :, :]
- fbat = @view fbats[ipsi, :, :]
-
- # --- Profiles ---
- p1 = sq.fs1[ipsi, 2]
- q = sq.fs[ipsi, 4]
- q1 = sq.fs1[ipsi, 4]
- jtheta = -sq.fs1[ipsi, 1]
- chi1 = 2π * equil.psio
- nq = ctrl.nn * q
-
- # Fill lower half (0, -1, …, -mband)
- g11[mid:-1:1] .= metric.fspline.cs.fs[ipsi, 1:intr.mband+1]
- g22[mid:-1:1] .= metric.fspline.cs.fs[ipsi, intr.mband+2:2*intr.mband+2]
- g33[mid:-1:1] .= metric.fspline.cs.fs[ipsi, 2*intr.mband+3:3*intr.mband+3]
- g23[mid:-1:1] .= metric.fspline.cs.fs[ipsi, 3*intr.mband+4:4*intr.mband+4]
- g31[mid:-1:1] .= metric.fspline.cs.fs[ipsi, 4*intr.mband+5:5*intr.mband+5]
- g12[mid:-1:1] .= metric.fspline.cs.fs[ipsi, 5*intr.mband+6:6*intr.mband+6]
- jmat[mid:-1:1] .= metric.fspline.cs.fs[ipsi, 6*intr.mband+7:7*intr.mband+7]
- jmat1[mid:-1:1] .= metric.fspline.cs.fs[ipsi, 7*intr.mband+8:8*intr.mband+8]
-
- # Fill upper half (+1:mband) with conjugate symmetry
- for k = 1:intr.mband
- g11[mid+k] = conj(g11[mid-k])
- g22[mid+k] = conj(g22[mid-k])
- g33[mid+k] = conj(g33[mid-k])
- g23[mid+k] = conj(g23[mid-k])
- g31[mid+k] = conj(g31[mid-k])
- g12[mid+k] = conj(g12[mid-k])
- jmat[mid+k] = conj(jmat[mid-k])
- jmat1[mid+k] = conj(jmat1[mid-k])
- end
-
- # Construct primitive matrices via m1/dm loops
- ipert = 0
- for m1 in intr.mlow:intr.mhigh
- ipert += 1
- sing1 = m1 - nq
- for dm in max(1 - ipert, -intr.mband):min(intr.mpert - ipert, intr.mband)
- m2 = m1 + dm
- sing2 = m2 - nq
- jpert = ipert + dm
- dmidx = dm + mid
-
- amat[ipert, jpert] = (2π)^2 * (ctrl.nn^2 * g22[dmidx] + ctrl.nn * (m1 + m2) * g23[dmidx] + m1 * m2 * g33[dmidx])
- bmat[ipert, jpert] = -2π * im * chi1 * (ctrl.nn * g22[dmidx] + (m1 + nq) * g23[dmidx] + m1 * q * g33[dmidx])
- cmat[ipert, jpert] = 2π * im * ((2π * im * chi1 * sing2 * (ctrl.nn * g12[dmidx] + m1 * g31[dmidx])) -
- (q1 * chi1 * (ctrl.nn * g23[dmidx] + m1 * g33[dmidx]))) -
- 2π * im * (jtheta * sing1 * imat[dmidx] + ctrl.nn * p1 / chi1 * jmat[dmidx])
- dmat[ipert, jpert] = 2π * chi1 * (g23[dmidx] + g33[dmidx] * m1 / ctrl.nn)
- emat[ipert, jpert] = -chi1 / ctrl.nn * (q1 * chi1 * g33[dmidx] - 2π * im * chi1 * g31[dmidx] * sing2 + jtheta * imat[dmidx])
- hmat[ipert, jpert] = (q1 * chi1)^2 * g33[dmidx] +
- (2π * chi1)^2 * sing1 * sing2 * g11[dmidx] -
- 2π * im * chi1 * dm * q1 * chi1 * g31[dmidx] +
- jtheta * q1 * chi1 * imat[dmidx] +
- p1 * jmat1[dmidx]
- fmat[ipert, jpert] = (chi1 / ctrl.nn)^2 * g33[dmidx]
- kmat[ipert, jpert] = 2π * im * chi1 * (g23[dmidx] + g33[dmidx] * m1 / ctrl.nn)
- end
- end
- dbat .= dmat
- ebat .= emat
- fbat .= fmat
-
- # --- Factorize and build composites ---
- # TODO: Fortran throws an error if the factorization fails for a/fmat, not sure what this delta_mband comment is referencing.
- # I am keeping this here to most closely match the Fortran behavior, but it may be unnecessary if we only use dense matrices.
- if isposdef(Hermitian(amat, :L))
- amat_fact = cholesky(Hermitian(amat, :L))
- else
- error("cholesky: amat is not positive definite (singular) at ipsi = $ipsi, reduce delta_mband")
- end
- temp1 = amat_fact \ dmat
- temp2 = amat_fact \ cmat
- # Use * for matrix multiplication (instead of .* for element-wise)
- fmat .-= adjoint(dmat) * temp1
- kmat .= emat .- (adjoint(kmat) * temp2)
- gmat .= hmat .- (adjoint(cmat) * temp2)
-
- # Store factorized F matrix (lower triangular only) since we always will need F⁻¹ later
- # and this make computation more efficient via combined forward and back substitution
- if isposdef(Hermitian(fmat, :L))
- fmat .= cholesky(Hermitian(fmat)).L
- else
- error("cholesky: fmat is not positive definite (singular) at ipsi = $ipsi, reduce delta_mband")
- end
-
- # TODO: add kinetic matrices here
-
- # TODO: banded matrix calculations would also go here if implemented
- end
-
- # --- Fit splines (reshape 3D to 2D: (mpsi) × (mpert^2)) ---
- ffit = FourFitVars(mpert=intr.mpert, mband=intr.mband)
- ffit.amats = Spl.CubicSpline(metric.xs, reshape(amats, mpsi, :); bctype=3)
- ffit.bmats = Spl.CubicSpline(metric.xs, reshape(bmats, mpsi, :); bctype=3)
- ffit.cmats = Spl.CubicSpline(metric.xs, reshape(cmats, mpsi, :); bctype=3)
- ffit.dmats = Spl.CubicSpline(metric.xs, reshape(dmats, mpsi, :); bctype=3)
- ffit.emats = Spl.CubicSpline(metric.xs, reshape(emats, mpsi, :); bctype=3)
- ffit.hmats = Spl.CubicSpline(metric.xs, reshape(hmats, mpsi, :); bctype=3)
- ffit.fmats = Spl.CubicSpline(metric.xs, reshape(fmats, mpsi, :); bctype=3)
- ffit.gmats = Spl.CubicSpline(metric.xs, reshape(gmats, mpsi, :); bctype=3)
- ffit.kmats = Spl.CubicSpline(metric.xs, reshape(kmats, mpsi, :); bctype=3)
- ffit.dbats = Spl.CubicSpline(metric.xs, reshape(dbats, mpsi, :); bctype=3)
- ffit.ebats = Spl.CubicSpline(metric.xs, reshape(ebats, mpsi, :); bctype=3)
- ffit.fbats = Spl.CubicSpline(metric.xs, reshape(fbats, mpsi, :); bctype=3)
-
- # TODO: set powers
- # Do we need this yet? Only called if power_flag = true
-
- if ctrl.sas_flag
- # TODO: these seem to only be used for the ahb_flag, which I think is deprecated
- ffit.asmat = reshape(Spl.spline_eval(ffit.amats, intr.psilim), intr.mpert, intr.mpert)
- ffit.bsmat = reshape(Spl.spline_eval(ffit.bmats, intr.psilim), intr.mpert, intr.mpert)
- ffit.csmat = reshape(Spl.spline_eval(ffit.cmats, intr.psilim), intr.mpert, intr.mpert)
- # TODO: this is used in free.f vacuum calculations, verify this is correct
- # Should we store lower triangular factorization?
- ffit.asmat .= cholesky(Hermitian(ffit.asmat)).L
- end
-
- # This is used in free_run
- ffit.jmat = jmat
-
- return ffit
-end
\ No newline at end of file
diff --git a/src/DCON/Free.jl b/src/DCON/Free.jl
deleted file mode 100644
index 4801bd0e64..0000000000
--- a/src/DCON/Free.jl
+++ /dev/null
@@ -1,291 +0,0 @@
-function free_run(odet::OdeState, ctrl::DconControl, intr::DconInternal, equil::Equilibrium.PlasmaEquilibrium, ffit::FourFitVars, outp::DconOutput; op_netcdf_out::Bool=false)
-
- # TODO: it looks like vac_memory is always true - remove all ahg things and just assume true?
- vac_memory = true
- # TODO: this is always true in fortran - just get rid of it?
- normalize = true
- # Flags used within VACUUM
- complex_flag = true
- wall_flag = false
- ahg_file = "ahg2msc_dcon.out" # Deprecated
-
- # Allocations
- star = fill(' ', intr.mpert, odet.msol)
- ep = zeros(ComplexF64, intr.mpert)
- ev = zeros(ComplexF64, intr.mpert)
- et = zeros(ComplexF64, intr.mpert)
- tt = zeros(ComplexF64, intr.mpert)
- wv = zeros(ComplexF64, intr.mpert, intr.mpert)
- wt = zeros(ComplexF64, intr.mpert, intr.mpert)
- wt0 = zeros(ComplexF64, intr.mpert, intr.mpert)
- wp = zeros(ComplexF64, intr.mpert, intr.mpert)
- temp = zeros(ComplexF64, intr.mpert, intr.mpert)
- wpt = zeros(ComplexF64, intr.mpert, intr.mpert)
- wvt = zeros(ComplexF64, intr.mpert, intr.mpert)
-
- mtheta = length(equil.rzphi.ys)
-
- # Evaluate dV/dpsi at the plasma edge
- v1 = Spl.spline_eval(equil.sq, intr.psilim, 0)[3]
-
- # Compute plasma response matrix.
- if ctrl.ode_flag
- temp = adjoint(odet.u[:, 1:intr.mpert, 1])
- wp .= adjoint(odet.u[:, 1:intr.mpert, 2])
- # Compute wp using LU decomposition
- temp_fact = lu(temp)
- wp .= temp_fact \ wp
- wp .= adjoint(wp) / equil.psio^2
- end
-
- # Write file for mscvac
- # TODO: can likely remove last two arguments, ahgstr_op is deprecated
- # TODO: actually, can probably remove this function entirely and just call set_dcon_params directly
- free_write_msc(intr.psilim, ctrl, intr, equil; inmemory_op = vac_memory, ahgstr_op = ahg_file)
-
- # TODO: there is some ahb_flag logic here that has a comment "must be false if using GPEC"
- # I am assuming this means we don't have to implement any of it
- # if ahb_flag
- # free_ahb_prep(wp, nmat, smat, asmat, bsmat, csmat, ipiva)
- # end
-
- # Compute vacuum response matrix.
- grri = Array{Float64}(undef, 2*(ctrl.mthvac+5), intr.mpert*2)
- xzpts = Array{Float64}(undef, ctrl.mthvac+5, 4)
-
- farwal_flag = true
- kernelsignin = -1.0
- # TODO: make this a ! function
- VacuumMod.mscvac(wv, intr.mpert, mtheta, ctrl.mthvac, complex_flag, kernelsignin,
- wall_flag, farwal_flag, grri, xzpts, ahg_file, intr.dir_path)
-
- # TODO: assuming bin_vac is deprecated for good, will remove all calls later after checking
- # if bin_vac
- # @warn "!! WARNING: Use of vacuum.bin is deprecated in GPEC. Set bin_vac = false in dcon.in to reduce file IO."
- # bin_open(vac_unit, "vacuum.bin", "UNKNOWN", "REWIND", "none")
- # write(vac_unit, grri)
- # end
-
- kernelsignin = 1.0
- VacuumMod.mscvac(wv, intr.mpert, mtheta, ctrl.mthvac, complex_flag, kernelsignin,
- wall_flag, farwal_flag, grri, xzpts, ahg_file, intr.dir_path)
- # if bin_vac
- # write(vac_unit, grri)
- # end
- if ctrl.wv_farwall_flag
- temp .= wv
- end
-
- farwal_flag = false
- kernelsignin = -1.0
- VacuumMod.mscvac(wv, intr.mpert, mtheta, ctrl.mthvac, complex_flag, kernelsignin,
- wall_flag, farwal_flag, grri, xzpts, ahg_file, intr.dir_path)
- # if bin_vac
- # write(vac_unit, grri)
- # end
-
- kernelsignin = 1.0
- VacuumMod.mscvac(wv, intr.mpert, mtheta, ctrl.mthvac, complex_flag, kernelsignin,
- wall_flag, farwal_flag, grri, xzpts, ahg_file, intr.dir_path)
- # if bin_vac
- # write(vac_unit, grri)
- # write(vac_unit, xzpts)
- # bin_close(vac_unit)
- # end
-
- if ctrl.wv_farwall_flag
- wv .= temp
- end
-
- # Scale vacuum matrix by singfac = (m - nn*qlim)
- singfac = (intr.mlow .- ctrl.nn .* intr.qlim) .+ collect(0:intr.mpert-1)
- for ipert in 1:intr.mpert
- wv[ipert, :] .*= singfac[ipert]
- wv[:, ipert] .*= singfac[ipert]
- end
-
- # Compute complex energy eigenvalues.
- wt .= wp .+ wv
- wt0 .= wt
-
- # use Eigen decomposition for general complex matrix (get left & right eigenvectors)
- # For general complex: use eigen(wt) which returns eigenvalues and eigenvectors (right)
- # For left eigenvectors we can compute eigen(wt') and conj-transpose as needed,
- # but Fortran uses zgeev('V','V',...) returning both vl and vr.
- Ev = eigen(wt) # Ev.values, Ev.vectors (columns are eigenvectors)
- # Ev.vectors are right eigenvectors; we need to reorder by magnitude using bubble on real parts of eigenvalues
- et .= Ev.values
- eindex = sortperm(real.(et), rev=true)
-
- tt .= et
- # rearrange wt columns to correspond to eigenvector reordering similar to Fortran
- for ipert in 1:intr.mpert
- wt[:, ipert] .= Ev.vectors[:, eindex[intr.mpert+1-ipert]]
- et[ipert] = tt[eindex[intr.mpert+1-ipert]]
- end
-
- # Normalize eigenfunction and energy.
- if normalize
- for isol in 1:intr.mpert
- norm = 0.0 + 0.0im
- for ipert in 1:intr.mpert, jpert in 1:intr.mpert
- norm += ffit.jmat[jpert - ipert + intr.mband + 1] * wt[ipert, isol] * conj(wt[jpert, isol])
- end
- norm /= v1
- wt[:, isol] ./= sqrt(norm)
- et[isol] /= norm
- end
- end
-
- # Normalize phase and label largest component.
- imax = 0
- for isol in 1:intr.mpert
- # get index of largest absolute component (first occurrence)
- imax = argmax(abs.(wt[:, isol]))
- phase = abs(wt[imax, isol]) / wt[imax, isol]
- wt[:, isol] .*= phase
- # Mark largest component with *, all others initalized to ' '
- star[imax, isol] = '*'
- end
-
- # Compute plasma and vacuum contributions.
- # wpt = wt' * wp * wt ; wvt = wt' * wv * wt
- wpt .= adjoint(wt) * (wp * wt)
- wvt .= adjoint(wt) * (wv * wt)
-
- for ipert in 1:intr.mpert
- ep[ipert] = wpt[ipert, ipert]
- ev[ipert] = wvt[ipert, ipert]
- end
-
- plasma1 = ComplexF64(real(ep[1]), 0.0)
- vacuum1 = ComplexF64(real(ev[1]), 0.0)
- total1 = ComplexF64(real(et[1]), 0.0)
-
- # Write data for ahb and deallocate.
- # if ahb_flag
- # free_ahb_write(nmat, smat, wt, et)
- # # Fortran did DEALLOCATE(r,z,theta,dphi,thetas,project) - we assume they are module arrays
- # # and will be GC'd or freed by dcon_dealloc below
- # end
-
- # Write to euler.h5
- if outp.write_euler_h5
- write_output(outp, :euler_h5, ep; dsetname="vacuum/ep")
- write_output(outp, :euler_h5, ev; dsetname="vacuum/ev")
- write_output(outp, :euler_h5, et; dsetname="vacuum/et")
- write_output(outp, :euler_h5, wt; dsetname="vacuum/wt")
- write_output(outp, :euler_h5, wt0; dsetname="vacuum/wt0")
- write_output(outp, :euler_h5, ctrl.wv_farwall_flag; dsetname="vacuum/wv_farwall_flag")
- end
-
- # Write to screen and copy to output.
- if ctrl.verbose
- println("Energies: plasma = ", real(ep[1]), ", vacuum = ", real(ev[1]),
- ", real = ", real(et[1]), ", imaginary = ", imag(et[1]))
- end
-
- # Write eigenvalues to file
- write_output(outp, :dcon_out, "\nTotal Energy Eigenvalues:")
- write_output(outp, :dcon_out, "\n isol plasma vacuum re total im total\n")
- for isol in 1:intr.mpert
- write_output(outp, :dcon_out, @sprintf("%6d %11.3e %11.3e %11.3e %11.3e",
- isol, real(ep[isol]), real(ev[isol]), real(et[isol]), imag(et[isol])))
- end
- write_output(outp, :dcon_out, "\n isol plasma vacuum re total im total\n")
-
- # Write eigenvectors to file
- write_output(outp, :dcon_out, "Total Energy Eigenvectors:")
- m = intr.mlow .+ collect(0:intr.mpert-1)
- for isol in 1:intr.mpert
- write_output(outp, :dcon_out, "\n isol imax plasma vacuum re total im total\n")
- write_output(outp, :dcon_out, @sprintf("%6d %6d %11.3e %11.3e %11.3e %11.3e",
- isol, imax, real(ep[isol]), real(ev[isol]), real(et[isol]), imag(et[isol])))
- write_output(outp, :dcon_out, "\n ipert m re wt im wt abs wt\n")
- for ipert in 1:intr.mpert
- write_output(outp, :dcon_out,
- @sprintf("%6d %6d %11.3e %11.3e %11.3e %s",
- ipert, m[ipert], real(wt[ipert, isol]), imag(wt[ipert, isol]), abs(wt[ipert, isol]), star[ipert, isol]))
- end
- write_output(outp, :dcon_out, "\n ipert m re wt im wt abs wt\n")
- end
-
- # Write the plasma matrix.
- write_output(outp, :dcon_out, "Plasma Energy Matrix:\n")
- for isol in 1:intr.mpert
- write_output(outp, :dcon_out, "isol = $(isol), m = $(m[isol])")
- write_output(outp, :dcon_out, "\n i re wp im wp abs wp\n")
- for ipert in 1:intr.mpert
- write_output(outp, :dcon_out, @sprintf("%3d%13.5e%13.5e%13.5e",
- ipert, real(wp[ipert, isol]), imag(wp[ipert, isol]), abs(wp[ipert, isol])))
- end
- write_output(outp, :dcon_out, "\n i re wp im wp abs wp\n")
- end
-
- # Compute separate plasma and vacuum eigenvalues.
- # Right eigenvalues/vectors of wp
- Ev_wp = eigen(wp)
- ep .= Ev_wp.values
- eindex = sortperm(real.(ep), rev=true)
- tt .= ep
- for ipert in 1:intr.mpert
- wp[:, ipert] .= Ev_wp.vectors[:, eindex[intr.mpert+1-ipert]]
- ep[ipert] = tt[eindex[intr.mpert+1-ipert]]
- end
- # For vacuum (Hermitian) use eigen of Hermitian wv
- Ev_wv = eigen(Hermitian(wv, :U))
- ev .= Ev_wv.values
-
- # Optionally write netcdf file
- # TODO: move this to HDF5 or something else later, make it an input flag?
- # if op_netcdf_out
- # dcon_netcdf_out(wp, wv, wt, wt0, ep, ev, et)
- # end
-
- return plasma1, vacuum1, total1
-end
-
-function free_write_msc(psifac::Float64, ctrl::DconControl, intr::DconInternal, equil::Equilibrium.PlasmaEquilibrium; inmemory_op::Union{Bool,Nothing}=nothing,
- ahgstr_op::Union{String,Nothing}=nothing)
-
- # Defaults for optional arguments
- inmemory = isnothing(inmemory_op) ? false : inmemory_op
- ahgstr = isnothing(ahgstr_op) ? "ahg2msc_dcon.out" : ahgstr_op
- inmemory = true # TODO: remove the above, and modify the code logic so VACUUM is always in memory
-
- # Allocations
- theta_norm = Vector(equil.rzphi.ys)
- mtheta = length(theta_norm)
- angle = zeros(Float64, mtheta)
- r = zeros(Float64, mtheta)
- z = zeros(Float64, mtheta)
- delta = zeros(Float64, mtheta)
- rfac = zeros(Float64, mtheta)
-
- # Compute output
- qa = Spl.spline_eval(equil.sq, psifac, 0)[4] # TODO: this had a deriv = 1 in Fortran, but not used?
- for itheta in 1:mtheta
- f = Spl.bicube_eval(equil.rzphi, psifac, theta_norm[itheta], 0)
- rfac[itheta] = sqrt(f[1])
- angle[itheta] = 2π * (theta_norm[itheta] + f[2])
- delta[itheta] = -f[3] / qa
- end
- r .= equil.ro .+ rfac .* cos.(angle)
- z .= equil.zo .+ rfac .* sin.(angle)
-
- # Invert values for nn < 0
- n = ctrl.nn
- if ctrl.nn < 0
- qa = -qa
- delta .= -delta
- n = -n
- end
-
- # Pass all required values to VACUUM
- if inmemory
- VacuumMod.set_dcon_params(mtheta, intr.mlow, intr.mhigh, n, qa,
- reverse(r), reverse(z), reverse(delta))
- else
- # TODO: this section contains ahg2msc file writing, which is deprecated, just remove
- end
-end
\ No newline at end of file
diff --git a/src/DCON/Main.jl b/src/DCON/Main.jl
deleted file mode 100644
index df38d617ca..0000000000
--- a/src/DCON/Main.jl
+++ /dev/null
@@ -1,203 +0,0 @@
-function Main(path::String)
-
- println("DCON START")
- println("----------------------------------")
- start_time = time()
-
- # Read input data and set up data structures
- intr = DconInternal(; dir_path=path)
- inputs = TOML.parsefile(joinpath(intr.dir_path, "dcon.toml"))
- ctrl = DconControl(; (Symbol(k)=>v for (k,v) in inputs["DCON_CONTROL"])...)
- outp = DconOutput(; (Symbol(k)=>v for (k,v) in inputs["DCON_OUTPUT"])...)
- equil = Equilibrium.setup_equilibrium(joinpath(intr.dir_path, "equil.toml"))
- init_files(outp, intr.dir_path)
-
- # Set up variables
- # TODO: dcon_kin_threads logic?
- ctrl.delta_mhigh *= 2 # for consistency with Fortran DCON TODO: why is this present in the Fortran?
-
- # Determine if qhigh is truncating before psihigh and reform equilibrium if needed
- sing_lim!(intr, ctrl, equil)
- if intr.psilim != equil.config.control.psihigh && ctrl.reform_eq_with_psilim
- @warn "psilim != psihigh not implemented yet, skipping reforming equilibrium splines"
- # JMH - Nik please put the logic we discussed here
- # something like ?
- # equil.config.control.psihigh = intr.psilim
- # equil = set_up_equilibrium(equil.config)
- end
-
- # TODO: add some data dump to dcon.out from equil here or in setup_equilibrium
-
- # Compute Mercier and Ballooning stability (if desired)
- # This holds di, dr, h (calculated in mercier_scan), ca1, and ca2 (calculated in ballooning scan)
- locstab_fs = zeros(Float64, length(equil.sq.xs), 5)
- if ctrl.mer_flag
- if ctrl.verbose
- println("Evaluating Mercier criterion")
- end
- mercier_scan!(locstab_fs, equil)
- end
- # TODO: ballooning stability
- #IF(bal_flag)THEN
- # IF(ctrl.verbose) WRITE(*,*)"Evaluating ballooning criterion"
- # CALL bal_scan
- #ENDIF
-
- # Fit stability data to splines and dump to file
- intr.locstab = Spl.CubicSpline(Vector(equil.sq.xs), locstab_fs; bctype=3)
-
- # Dump equilibrium data to files
- if outp.write_eqdata_h5
- write_output(outp, :eqdata_h5, Vector(equil.sq.xs); dsetname="psi")
- write_output(outp, :eqdata_h5, Vector(equil.sq.fs[:, 1] ./ (2π)); dsetname="f")
- write_output(outp, :eqdata_h5, Vector(equil.sq.fs[:, 2]); dsetname="mu0p")
- write_output(outp, :eqdata_h5, Vector(equil.sq.fs[:, 3]); dsetname="dV/dpsi")
- write_output(outp, :eqdata_h5, Vector(equil.sq.fs[:, 4]); dsetname="q")
- write_output(outp, :eqdata_h5, Vector(locstab_fs[:, 1] ./ equil.sq.xs); dsetname="di")
- write_output(outp, :eqdata_h5, Vector(locstab_fs[:, 2] ./ equil.sq.xs); dsetname="dr")
- write_output(outp, :eqdata_h5, Vector(locstab_fs[:, 4]); dsetname="ca1")
- end
-
- if outp.write_dcon_out
- write_output(outp, :dcon_out, @sprintf("%4s %12s %12s %12s %12s %12s %12s %12s %12s", "ipsi","psifac","f","mu0 p","dvdpsi","q","di","dr","ca1"))
- for ipsi in 1:length(equil.sq.xs)
- write_output(outp, :dcon_out,
- @sprintf("%4d %12.4e %12.4e %12.4e %12.4e %12.4e %12.4e %12.4e %12.4e",
- ipsi,
- equil.sq.xs[ipsi],
- equil.sq.fs[ipsi, 1] / (2π),
- equil.sq.fs[ipsi, 2],
- equil.sq.fs[ipsi, 3],
- equil.sq.fs[ipsi, 4],
- locstab_fs[ipsi, 1] / equil.sq.xs[ipsi],
- locstab_fs[ipsi, 2] / equil.sq.xs[ipsi],
- locstab_fs[ipsi, 4]
- )
- )
- end
- write_output(outp, :dcon_out, @sprintf("%4s %12s %12s %12s %12s %12s %12s %12s %12s", "ipsi","psifac","f","mu0 p","dvdpsi","q","di","dr","ca1"))
- end
-
- # Find all singular surfaces in the equilibrium
- sing_find!(ctrl, equil, intr)
-
- # Determine poloidal mode numbers
- if ctrl.cyl_flag
- intr.mlow = ctrl.delta_mlow
- intr.mhigh = ctrl.delta_mhigh
- elseif ctrl.sing_start == 0
- intr.mlow = min(ctrl.nn * equil.params.qmin, 0) - 4 - ctrl.delta_mlow
- intr.mhigh = trunc(Int, ctrl.nn * equil.params.qmax) + ctrl.delta_mhigh
- else
- intr.mmin = Inf # HUGE in Fortran
- for ising in Int(ctrl.sing_start):intr.msing
- intr.mmin = min(intr.mmin, sing[ising].m)
- end
- intr.mlow = intr.mmin - ctrl.delta_mlow
- intr.mhigh = trunc(Int, intr.nn * equil.qmax) + ctrl.delta_mhigh
- end
- intr.mpert = intr.mhigh - intr.mlow + 1
- intr.mband = intr.mpert - 1 - ctrl.delta_mband
- intr.mband = min(max(intr.mband, 0), intr.mpert - 1)
-
- # Fit equilibrium quantities to Fourier-spline functions.
- if ctrl.mat_flag || ctrl.ode_flag
- if ctrl.verbose
- println(" q0 = $(equil.params.q0), qmin = $(equil.params.qmin), qmax = $(equil.params.qmax), q95 = $(equil.params.q95)")
- println(" sas_flag = $(ctrl.sas_flag), dmlim = $(ctrl.dmlim), qlim = $(intr.qlim), psilim = $(intr.psilim)")
- println(" betat = $(equil.params.betat), betan = $(equil.params.betan), betap1 = $(equil.params.betap1)")
- println(" nn = $(ctrl.nn), mlow = $(intr.mlow), mhigh = $(intr.mhigh), mpert = $(intr.mpert), mband = $(intr.mband)")
- println(" Fourier analysis of metric tensor components")
- end
-
- if outp.write_dcon_out
- write_output(outp, :dcon_out, @sprintf("\n mlow mhigh mpert mband nn lim_fl dmlim qlim psilim"))
- write_output(outp, :dcon_out, @sprintf("%6d %6d %6d %6d %6d %6s %11.3e %11.3e %11.3e",
- intr.mlow, intr.mhigh, intr.mpert, intr.mband, ctrl.nn,
- string(ctrl.sas_flag), ctrl.dmlim, intr.qlim, intr.psilim))
- end
-
- # Compute metric tensor
- metric = make_metric(equil, mband=intr.mband, fft_flag=ctrl.fft_flag)
-
- if ctrl.verbose
- println("Computing F, G, and K Matrices")
- end
-
- # Compute matrices and populate FourFitVars struct
- ffit = make_matrix(metric, equil, ctrl, intr)
-
- if ctrl.kin_flag
- error("kin_flag not implemented yet")
- end
- sing_scan!(intr, ctrl, equil, ffit, outp)
- # TODO: implement resist_eval at some point, not urgent for initial functionality.
- # for ising in 1:msing
- # resist_eval(sing[ising])
- # end
- if ctrl.kin_flag
- # ksing_find()
- end
- end
-
- # Integrate Euler-Lagrange Equation
- if ctrl.ode_flag
- if ctrl.verbose
- println("Integrating Euler-Lagrange equation")
- end
- odet = ode_run(ctrl, equil, intr, ffit, outp)
- if intr.size_edge > 0
- # Find peak index in dw_edge[pre_edge:i_edge]
- dw_slice = real.(intr.dw_edge[intr.pre_edge:intr.i_edge])
- peak_index = findmax(dw_slice)[2] + (intr.pre_edge - 1)
- ctrl.qhigh = intr.q_edge[peak_index]
- ctrl.sas_flag = false
- ctrl.psiedge = equil.psihigh
- sing_lim!(intr, ctrl, equil)
- println("Re-Integrating to peak dW @ qlim = $(intr.qlim), psilim = $(intr.psilim)")
- # Full re-run because outputs were written to disk each step
- # making it hard to backtrack
- # if outp.bin_euler
- # bin_close(euler_bin_unit) # TODO: Need to decide ho we're handling io
- # end
- odet = ode_run(ctrl, equil, intr, ffit, outp)
- end
- end
-
- # Compute free boundary energies
- plasma1 = 0
- vacuum1 = 0
- total1 = 0
- if ctrl.vac_flag && !(ctrl.ksing > 0 && ctrl.ksing <= intr.msing + 1)
- if ctrl.verbose
- println("Computing free boundary energies")
- end
- plasma1, vacuum1, total1 = free_run(odet, ctrl, intr, equil, ffit, outp; op_netcdf_out=false) # outp.netcdf_out)
- end
-
- # Output results of fixed-boundary stability calculations
- if ctrl.ode_flag && odet.nzero != 0
- if ctrl.verbose
- println("Fixed-boundary mode unstable for nn = $(ctrl.nn).")
- end
- end
-
- # Output results of free-boundary stability calculations
- if ctrl.vac_flag && !(ctrl.ksing > 0 && ctrl.ksing <= intr.msing + 1 && outp.bin_sol)
- if real(total1) < 0
- if ctrl.verbose
- println("Free-boundary mode unstable for nn = $(ctrl.nn).")
- end
- else
- if ctrl.verbose
- println("All free-boundary modes stable for nn = $(ctrl.nn).")
- end
- end
- end
-
- end_time = time() - start_time
- close_files(outp)
- println("----------------------------------")
- println("Run time: $end_time seconds")
- println("Normal termination.")
-end
\ No newline at end of file
diff --git a/src/DCON/Mercier.jl b/src/DCON/Mercier.jl
deleted file mode 100644
index b1654b4bd2..0000000000
--- a/src/DCON/Mercier.jl
+++ /dev/null
@@ -1,76 +0,0 @@
-"""
- mercier_scan!(locstab_fs::Array{Float64,5}, plasma_eq::PlasmaEquilibrium)
-
-Evaluates Mercier criterion for local stability and modifies results in place
-within the local stability array.
-
-"""
-function mercier_scan!(locstab_fs::Matrix{Float64}, plasma_eq::Equilibrium.PlasmaEquilibrium)
-
- # Shorthand
- sq = plasma_eq.sq
- rzphi = plasma_eq.rzphi
-
- # Allocate splines
- ff_fs = zeros(length(rzphi.ys), 5)
-
- # Compute surface quantities
- for ipsi in 1:length(sq.xs)
- twopif = sq.fs[ipsi, 1]
- p1 = sq.fs1[ipsi, 2]
- v1 = sq.fs[ipsi, 3]
- v2 = sq.fs1[ipsi, 3]
- q = sq.fs[ipsi, 4]
- q1 = sq.fs1[ipsi, 4]
- chi1 = 2π * plasma_eq.psio
-
- # Evaluate coordinates and jacobian
- for itheta in 1:length(rzphi.ys)
- theta = rzphi.ys[itheta]
-
- # Evaluate bicubic spline at grid point
- f, _, fy = Spl.bicube_eval(rzphi, rzphi.xs[ipsi], theta, 1)
-
- rfac = sqrt(f[1])
- eta = 2π * (theta + f[2])
- r = plasma_eq.ro + rfac * cos(eta)
- jac = f[4] # Jacobian
-
- # Evaluate other local quantities
- v21 = fy[1] / (2.0 * rfac * jac)
- v22 = (1.0 + fy[2]) * 2π * rfac / jac
- v23 = fy[3] * r / jac
- v33 = 2π * r / jac
- bsq = chi1^2 * (v21^2 + v22^2 + (v23 + q * v33)^2)
- dpsisq = (2π * r)^2 * (v21^2 + v22^2)
-
- # Evaluate integrands
- ff_fs[itheta, 1] = bsq / dpsisq
- ff_fs[itheta, 2] = 1.0 / dpsisq
- ff_fs[itheta, 3] = 1.0 / bsq
- ff_fs[itheta, 4] = 1.0 / (bsq * dpsisq)
- ff_fs[itheta, 5] = bsq
-
- # Weight by jacobian and volume element
- ff_fs[itheta, :] .*= jac / v1
- end
-
- ff = Spl.CubicSpline(Vector(rzphi.ys), ff_fs; bctype=2) # bctype=2 is periodic
-
- # Integrate quantities with respect to theta
- Spl.spline_integrate!(ff)
- avg = ff.fsi[end, :]
-
- # Evaluate Mercier criterion and related quantities
- term = twopif * p1 * v1 / (q1 * chi1^3) * avg[2]
- di = -0.25 + term * (1 - term) +
- p1 * (v1 / (q1 * chi1^2))^2 * avg[1] *
- (p1 * (avg[3] + (twopif / chi1)^2 * avg[4]) - v2 / v1)
- h = twopif * p1 * v1 / (q1 * chi1^3) * (avg[2] - avg[1] / avg[5])
-
- # Store results in output spline structure
- locstab_fs[ipsi, 1] = di * sq.xs[ipsi] # is this the right 'psis'?
- locstab_fs[ipsi, 2] = (di + (h - 0.5)^2) * sq.xs[ipsi] # is this the right 'psis'?
- locstab_fs[ipsi, 3] = h
- end
-end
diff --git a/src/DCON/Ode.jl b/src/DCON/Ode.jl
deleted file mode 100644
index 55b2753d0c..0000000000
--- a/src/DCON/Ode.jl
+++ /dev/null
@@ -1,1014 +0,0 @@
-# This is used for various small tolerances throughout this file
-const eps = 1e-10
-
-"""
-OdeState
-
-A mutable struct to hold the state of the ODE solver for DCON.
-This struct contains all necessary fields to manage the ODE integration process,
-including solution vectors, tolerances, and flags for the integration process.
-"""
-#TODO: variable description review by DCON expert (once finished), evaluate if all variables need to be part of the struct
-# TODO: remove msol variable, I think it just makes things more confusing. Either use mpert or 2*mpert in loops. This might actually
-# cause issues in ode_resist_cross, there's some logic I don't understand there where msol is increased. Might be better to keep it for now
-@kwdef mutable struct OdeState
- # Initialization parameters
- mpert::Int # poloidal mode number count
- msol::Int # number of solutions
- numunorms_init::Int # initial storage size for unorm data
- msing::Int # number of singular surfaces
- numsteps_init::Int # initial size of data store
-
- # Saved data
- psi_store::Vector{Float64} = Vector{Float64}(undef, numsteps_init) # psi at each step
- u_store::Array{ComplexF64,4} = Array{ComplexF64}(undef, mpert, mpert, 2, numsteps_init) # store of u: mpert x mpert x 2 x nsteps
- ud_store::Array{ComplexF64,4} = Array{ComplexF64}(undef, mpert, mpert, 2, numsteps_init) # store of ud: mpert x mpert x 2 x nsteps
- step::Int = 1 # current number of stored steps (this is like istep in Fortran)
- ca_r::Array{ComplexF64, 4} = Array{ComplexF64}(undef, mpert, 2*mpert, 2, msing) # asymptotic coefficients just right of singular surface
- ca_l::Array{ComplexF64, 4} = Array{ComplexF64}(undef, mpert, 2*mpert, 2, msing) # asymptotic coefficients just left of singular surface
- index::Array{Int,2} = zeros(Int, mpert, numunorms_init) # indices for sorting solutions
- sing_flags::Vector{Bool} = falses(numunorms_init) # flags for singular solutions
- fixfac::Array{ComplexF64,3} = zeros(ComplexF64, mpert, mpert, numunorms_init) # fixup factors for Gaussian reduction
- fixstep::Vector{Float64} = zeros(Float64, numunorms_init) # psi values at which unorms were performed
-
- # Data for integrator
- singfac::Float64 = 0.0 # separation from singular surface in terms of m - nq
- psifac::Float64 = 0.0 # normalized flux coordinate
- q::Float64 = 0.0 # q value at psifac
- next::String = "" # next action ("cross" or "finish")
- ising::Int = 0 # index of next singular surface
- u::Array{ComplexF64, 3} = zeros(ComplexF64, mpert, mpert, 2) # solution vectors
- ud::Array{ComplexF64, 3} = zeros(ComplexF64, mpert, mpert, 2) # derivative of solution vectors used in GPEC
- m1::Int = 0 # poloidal mode number for the first singular surface (?)
- psimax::Float64 = 0.0 # maximum psi value for the integrator
- ua::Array{ComplexF64, 3} = Array{ComplexF64}(undef, mpert, 2*mpert, 2) # asympototic solutions at singular surface
- ca::Array{ComplexF64, 3} = Array{ComplexF64}(undef, mpert, 2*mpert, 2) # asymptotic coefficients at singular surface
- psi_prev::Float64 = 0.0 # previous psi value
- crit_prev::Float64 = 0.0 # previous crit value
- u_prev::Array{ComplexF64, 3} = zeros(ComplexF64, mpert, mpert, 2) # previous solution array
- nzero::Int = 0 # count of zero crossings detected
-
- # Used for Gaussian reduction
- new::Bool = true # flag for new solution
- unorm::Vector{Float64} = zeros(Float64, 2*mpert) # norms of solution vectors
- unorm0::Vector{Float64} = zeros(Float64, 2*mpert) # initial norms of solution vectors
- ifix::Int = 0 # index for number of unorms performed
-
- # Temporary matrices for sing_der calculations
- amat::Vector{ComplexF64} = Vector{ComplexF64}(undef, mpert^2)
- bmat::Vector{ComplexF64} = Vector{ComplexF64}(undef, mpert^2)
- cmat::Vector{ComplexF64} = Vector{ComplexF64}(undef, mpert^2)
- fmat::Vector{ComplexF64} = Vector{ComplexF64}(undef, mpert^2)
- kmat::Vector{ComplexF64} = Vector{ComplexF64}(undef, mpert^2)
- gmat::Vector{ComplexF64} = Vector{ComplexF64}(undef, mpert^2)
- Afact::Union{Cholesky{ComplexF64,Matrix{ComplexF64}}, Nothing} = nothing
- singfac_vec::Vector{Float64} = Vector{Float64}(undef, mpert)
-
- flag_count::Int = 0 # count of flags raised # TODO: remove this? Only used in ode_test if res_flag = true
-end
-
-# Base struct that handles storage of the ODE solution throughout integration
-mutable struct OdeDataStore
- psi::Vector{Float64}
- u::Vector{Array{ComplexF64,3}}
- ud::Vector{Array{ComplexF64,3}}
- step::Int
-end
-
-# Initialize function for data storage object of a given size, will resize as needed
-OdeDataStore(numsteps_init::Int) = OdeDataStore(Vector{Float64}(undef, numsteps_init), Vector{Array{ComplexF64,3}}(undef, numsteps_init), Vector{Array{ComplexF64,3}}(undef, numsteps_init), 0)
-
-# Initialize function for OdeState with relevant parameters for array initialization
-OdeState(mpert::Int, msol::Int, numsteps_init::Int, numunorms_init::Int, msing::Int) = OdeState(; mpert, msol, numsteps_init, numunorms_init, msing)
-
-"""
- `ode_run(ctrl::DconControl, equil::Equilibrium.PlasmaEquilibrium, intr::DconInternal)`
-
-Main driver for integrating plasma equilibrium and detecting singular surfaces.
-
-Initializes state and iterates through flux surfaces, calling appropriate update
-routines and recording output. Terminates when a target singularity is reached
-or integration ends. Support for `res_flag` and `kin_flag` is not yet implemented.
-
-# TODO: add a detailed description of how the integration loop varies from the Fortran version
-
-### Returns
-nzero: number of zero crossings of the critical determinant detected during the integration.
-"""
-# TODO: We pass the same structs into most functions; however, do to our use of multiple ! functions that modify the structs
-# and the convention that the modified struct comes first, the struct order is never consistent. Is there a better way?
-# For now - going to try modified structs first, then alphabetical after
-function ode_run(ctrl::DconControl, equil::Equilibrium.PlasmaEquilibrium, intr::DconInternal, ffit::FourFitVars, outp::DconOutput)
-
- # Initialization
- odet = OdeState(intr.mpert, intr.mpert, ctrl.numsteps_init, ctrl.numunorms_init, intr.msing)
-
- if ctrl.sing_start <= 0
- ode_axis_init!(ctrl, equil, intr, odet)
- elseif ctrl.sing_start <= intr.msing
- error("sing_start > 0 not implemented yet!")
- # ode_sing_init!(ctrl, equil, intr, odet)
- else
- error("Invalid value for sing_start: $(ctrl.sing_start) > msing = $(intr.msing)")
- end
-
- if ctrl.verbose # mimicing an output from ode_output_open
- println(" ψ=$(odet.psifac), q=$(Spl.spline_eval(equil.sq, odet.psifac, 0)[4])")
- end
-
- # Write header data to files
- ode_output_init(ctrl, equil, outp, intr, odet)
-
- # TODO: Ensure that this section exactly reproduces all functionality of the Fortran
- # Might be good for ideal case, but maybe things I haven't considered break this
-
- # Always integrate once, even if no rational surfaces are crossed
- ode_step!(odet, equil, intr, ctrl, ffit, outp)
-
- # If at a rational surface, do the appropriate crossing routine, then integrate again
- while odet.ising != ctrl.ksing && odet.next == "cross"
- if ctrl.res_flag
- error("res_flag = true not implemented yet!")
- elseif ctrl.kin_flag
- error("kin_flag = true not implemented yet!")
- else
- ode_ideal_cross!(odet, equil, intr, ctrl, ffit, outp)
- end
-
- odet.flag_count = 0
- ode_step!(odet, equil, intr, ctrl, ffit, outp)
- end
-
- # Deallocate unused storage of integration data
- odet.step -= 1 # step was incremented one extra time in ode_step!
- trim_storage!(odet)
-
- if outp.write_euler_h5
- if ctrl.verbose
- println("Writing saved integration data to euler.h5...")
- end
- write_output(outp, :euler_h5, odet.msol; dsetname="integration/msol")
- write_output(outp, :euler_h5, odet.step; dsetname="integration/nstep")
- write_output(outp, :euler_h5, odet.psi_store; dsetname="integration/psi")
- write_output(outp, :euler_h5, Spl.spline_eval(equil.sq, odet.psi_store, 0)[4]; dsetname="integration/q")
- write_output(outp, :euler_h5, odet.u_store; dsetname="integration/u")
- write_output(outp, :euler_h5, odet.ud_store; dsetname="integration/ud")
- write_output(outp, :euler_h5, odet.ifix; dsetname="normalizations/mfix")
- write_output(outp, :euler_h5, odet.fixstep[1:odet.ifix]; dsetname="normalizations/psifix")
- write_output(outp, :euler_h5, odet.fixfac[:,:,1:odet.ifix]; dsetname="normalizations/fixfac")
- write_output(outp, :euler_h5, odet.sing_flags[1:odet.ifix]; dsetname="normalizations/sing_flags")
- write_output(outp, :euler_h5, odet.index[:, 1:odet.ifix]; dsetname="normalizations/index")
- write_output(outp, :euler_h5, intr.msing; dsetname="singular/msing")
- write_output(outp, :euler_h5, [intr.sing[ising].psifac for ising in 1:intr.msing]; dsetname="singular/psi")
- write_output(outp, :euler_h5, [intr.sing[ising].q for ising in 1:intr.msing]; dsetname="singular/q")
- write_output(outp, :euler_h5, [intr.sing[ising].q1 for ising in 1:intr.msing]; dsetname="singular/q1")
- write_output(outp, :euler_h5, odet.ca_l; dsetname="singular/ca_left")
- write_output(outp, :euler_h5, odet.ca_r; dsetname="singular/ca_right")
- # TODO: restype writing would also be added here, Matt says not needed for now (or maybe ever)
- end
-
- # TODO: get rid of this eventually
- # This is a rough sketch of the original Fortran logic for comparison
- # while true # inside plasma (break out when at the edge)
- # Rough sketch of Fortran logic for comparison
- # while true # inside sing surface (break out when close to singular surface)
- # if odet.istep > 0
- # ode_unorm!(odet, intr, ctrl, false)
- # end
- # Always record the first and last point in an inter-rational region
- # these are important for resonant quantities
- # recording the last point is critical for matching the nominal edge
- # test = ode_test(odet, intr, ctrl)
- # force_output = odet.first || test
- # ode_output_step(odet, intr, ctrl, equil; force=force_output)
- # ode_record_edge!(intr, odet, ctrl, equil)
- # test && break # break out of loop if ode_test returns true
- # ode_step!(odet, equil, intr, ctrl, ffit)
- # odet.first = false
- # end
-
- # # Re-initialize
- # odet.ising == ctrl.ksing && break
- # if odet.next == "cross"
- # if ctrl.res_flag
- # error("res_flag = true not implemented yet!")
- # #ode_resist_cross()
- # elseif ctrl.kin_flag
- # error("kin_flag = true not implemented yet!")
- # #ode_kin_cross()
- # else
- # ode_ideal_cross!(odet, equil, intr, ctrl, ffit)
- # end
- # else
- # break
- # end
- # odet.flag_count = 0
- # end
- return odet
-end
-
-
-"""
- ode_axis_init!(ctrl::DconControl, equil::Equilibrium.PlasmaEquilibrium,
- intr::DconInternal, odet::OdeState; itmax = 50) -> Int
-
-Initialize the ODE state for the case of sing_start = 0.
-
-Finds the starting flux surface where `q = qlow` using Newton iteration, locates
-nearby singular surfaces, and sets integration bounds. Sorts mode indices and
-initializes solution arrays for perturbation equations.
-
-Returns the index of the next relevant singular surface.
-"""
-
-function ode_axis_init!(ctrl::DconControl, equil::Equilibrium.PlasmaEquilibrium, intr::DconInternal, odet::OdeState; itmax = 50)
-
- # Shorthand to evaluate q/q1 inside newton iteration
- qval = psi -> Spl.spline_eval(equil.sq, psi, 0)[4]
- q1val = psi -> Spl.spline_eval(equil.sq, psi, 1)[2][4]
-
- # Preliminary computations
- odet.psifac = equil.sq.xs[1]
-
- # Use Newton iteration to find starting psi if qlow is above q0
- if ctrl.qlow > equil.sq.fs[1, 4]
- # Start check from the edge for robustness in reverse shear cores
- for jpsi = equil.sq.mx:-1:2 # avoid starting iteration on endpoints
- if equil.sq.fs[jpsi - 1, 4] < ctrl.qlow
- odet.psifac = equil.sq.xs[jpsi]
- break
- end
- end
- it = 0
- while it ≤ itmax
- it += 1
- dpsi = (ctrl.qlow - qval(odet.psifac)) / q1val(odet.psifac)
- odet.psifac += dpsi
- if abs(dpsi) < eps * abs(odet.psifac)
- break
- end
- end
- end
-
- # Find inner singular surface
- if false #(TODO: kin_flag)
- # for ising = 1:kmsing
- # if kinsing[ising].psifac > psifac
- # break
- # end
- # end
- else
- odet.ising = 0
- for i in 1:intr.msing
- if intr.sing[i].psifac > odet.psifac
- odet.ising = max(0, i - 1)
- break
- end
- end
- end
-
- # Find next singular surface
- if false # TODO: (kin_flag)
- # while true
- # ising += 1
- # if ising > kmsing
- # break
- # end
- # if psilim < kinsing[ising].psifac
- # break
- # end
- # odet.q = kinsing[ising].q
- # if mlow <= nn * odet.q && mhigh >= nn * odet.q
- # break
- # end
- # end
- # if ising > kmsing || singfac_min == 0
- # psimax = psilim * (1 - eps)
- # next = "finish"
- # elseif psilim < kinsing[ising].psifac
- # psimax = psilim * (1 - eps)
- # next = "finish"
- # else
- # psimax = kinsing[ising].psifac - singfac_min / abs(nn * kinsing[ising].q1)
- # next = "cross"
- # end
- else
- while true
- odet.ising += 1
- if odet.ising > intr.msing || intr.psilim < intr.sing[min(odet.ising, intr.msing)].psifac
- break
- end
- if intr.mlow <= ctrl.nn * intr.sing[odet.ising].q && intr.mhigh >= ctrl.nn * intr.sing[odet.ising].q
- break
- end
- end
- if odet.ising > intr.msing || intr.psilim < intr.sing[min(odet.ising, intr.msing)].psifac || ctrl.singfac_min == 0
- odet.psimax = intr.psilim * (1 - eps)
- odet.next = "finish"
- else
- odet.psimax = intr.sing[odet.ising].psifac - ctrl.singfac_min / abs(ctrl.nn * intr.sing[odet.ising].q1)
- odet.next = "cross"
- end
- end
-
- # Allocate and sort solutions by increasing value of |m-ms1|
- m = intr.mlow - 1 .+ collect(1:intr.mpert)
- if ctrl.sort_type == "absm"
- key = abs.(m)
- elseif ctrl.sort_type == "sing"
- key = m
- if intr.msing > 0
- key .-= intr.sing[1].m
- end
- @. key = -abs(key)
- else
- error("Cannot recognize sort_type = $(ctrl.sort_type)")
- end
- index = sortperm(key, rev = true) # in original Fortran: bubble(key, index, 1, mpert)
-
- # Initialize solutions
- for ipert = 1:intr.mpert
- odet.u[index[ipert], ipert, 2] = 1
- end
- odet.msol = intr.mpert
- odet.u_prev .= odet.u
- odet.psi_prev = odet.psifac
-
- # Compute conditions at next singular surface
- if false #TODO: (kin_flag)
- # if kmsing > 0
- # m1 = round(Int, nn * kinsing[ising].q)
- # else
- # m1 = round(Int, nn * qlim) + sign(one, nn * sq.fs1[mpsi, 5])
- # end
- else
- # note: Julia's default round does Banker's rounding, to match NINT in fortran we need to specify RoundFromZero
- if intr.msing > 0
- odet.m1 = round(Int, ctrl.nn * intr.sing[odet.ising].q, RoundFromZero)
- else
- odet.m1 = round(Int, ctrl.nn * intr.qlim, RoundFromZero) + sign(ctrl.nn * equil.sq.fs1[end, 4])
- end
- end
- odet.singfac = abs(odet.m1 - ctrl.nn * equil.sq.fs[1, 4]) # Fortran: q=sq%fs(0,4)
-end
-
-# TODO: NOT IMPLEMENTED YET! (low priority, just make sure sing_start = 0 in dcon.toml)
-function ode_sing_init()
- return
-end
-# # Declare and initialize local variables
-# star = fill(' ', mpert)
-# # local variables
-# ua = Array{Complex{r8}}(undef, mpert, 2*mpert, 2)
-# dpsi = 0.0
-# new = true
-
-# ising = sing_start
-# dpsi = singfac_min/abs(nn*sing[ising].q1)*10
-# odet.psifac = sing[ising].psifac + dpsi
-# odet.q = sing[ising].q + dpsi*sing[ising].q1
-
-# # Allocate and initialize solution arrays
-# u = zeros(Complex{r8}, mpert, mpert, 2)
-# du = zeros(Complex{r8}, mpert, mpert, 2)
-# u_prev = zeros(Complex{r8}, mpert, mpert, 2)
-# unorm0 = zeros(r8, 2*mpert)
-# unorm = zeros(r8, 2*mpert)
-# index = zeros(Int, 2*mpert)
-
-# if old_init
-# u .= 0.0
-# for ipert ∈ 1:mpert
-# u[ipert, ipert, 2] = 1.0
-# end
-# else
-# sing_get_ua(ising, odet.psifac, ua)
-# # Big slice: u = ua[:, mpert+1:2*mpert,:]
-# for i = 1:mpert, j = 1:mpert, k = 1:2
-# u[i, j, k] = ua[i, mpert+j, k]
-# end
-# end
-# u_prev .= u
-# psi_prev = psifac
-# msol = mpert
-# neq = 4 * mpert * msol
-
-# # Compute conditions at next singular surface
-# while true
-# ising += 1
-# if ising > msing || psilim < sing[ising ≤ msing ? ising : msing].psifac
-# break
-# end
-# odet.q = sing[ising].q
-# if mlow ≤ nn*q && mhigh ≥ nn*q
-# break
-# end
-# end
-# This needs to be fixed up
-# if ising > msing || psilim < sing[ising ≤ msing ? ising : msing].psifac
-# m1 = round(Int, ctrl.nn*intr.qlim) + round(Int, sign(one, ctrl.nn*equil.sq.fs1[mpsi, 4]))
-# psimax = psilim * (1-eps)
-# next_ = "finish"
-# else
-# m1 = round(Int, nn*sing[ising].q)
-# psimax = sing[ising].psifac - singfac_min/abs(nn*sing[ising].q1)
-# next_ = "cross"
-# end
-
-# # Set up integrator parameters
-# istep = 0
-# istate = 1
-# iopt = 1
-# itask = 5
-# itol = 2
-# mf = 10
-# istate = 1
-
-# # Set up work arrays
-# liw = length(iwork) # iwork must exist!
-# lrw = 22 + 64*mpert*msol
-# rwork = zeros(r8, lrw)
-# atol = zeros(r8, mpert, msol, 2)
-# fixfac = zeros(r8, msol, msol)
-# iwork = zeros(Int, liw) # or readjust as needed
-# rwork[1] = psimax
-# rwork[5] = dpsi
-# rwork[11] = rwork[5]
-
-# # Terminate, or in Julia just return (no need for RETURN)
-# return nothing # or could return a struct with all these values, for a more Julian approach
-# end
-
-"""
- ode_ideal_cross!(odet::OdeState, equil::Equilibrium.PlasmaEquilibrium,
- intr::DconInternal, ctrl::DconControl)
-
-Handle the crossing of an ideal MHD singular surface during ODE integration
-in a plasma equilibrium calculation.
-
-# Arguments
-- `odet::OdeState`: The current state of the ODE system (mutable, updated in-place).
-- `equil::Equilibrium.PlasmaEquilibrium`: Object representing plasma equilibrium parameters.
-- `intr::DconInternal`: Structure containing internal data, including singular surface information.
-- `ctrl::DconControl`: Holds control flags and integration parameters.
-
-# Description
-This function updates the ODE solution as it crosses a (resonant) singular surface in the
-ideal MHD calculation. It normalizes and reinitializes the solution vector at the singularity,
-handles singular asymptotics, manages control flags, and updates relevant state variables
-in `odet` for continued integration. It also determines the location and parameters of
-the next singular surface, updates tolerance/stepping logic for the ODE solver, and may
-write auxiliary diagnostic output or coefficients as configured.
-
-# Notes
-- Handles resetting or reinitializing the solver after singular surface crossing.
-- Assumes certain global state (such as `u`, `ua`, `index`, etc.) is properly managed.
-- Intended for ideal MHD regions; kinetic surface handling is not included in this function.
-"""
-function ode_ideal_cross!(odet::OdeState, equil::Equilibrium.PlasmaEquilibrium, intr::DconInternal, ctrl::DconControl, ffit::FourFitVars, outp::DconOutput)
-
- # Fixup solution at singular surface
- if ctrl.verbose
- println(" ψ = $(intr.sing[odet.ising].psifac), q = $(intr.sing[odet.ising].q)")
- end
- ode_unorm!(odet, intr, ctrl, outp, true)
-
- # Get asymptotic coefficients before crossing rational surface
- # TODO: remove odet.ua and ca and just have sing_get_ua and sing_get_ca return the arrays?
- sing_get_ca!(odet, intr, ctrl)
- odet.ca_l[:, :, :, odet.ising] .= odet.ca
-
- # Re-initialize on opposite side of rational surface
- psi_old = odet.psifac
- singp = intr.sing[odet.ising]
- ipert0 = round(Int, ctrl.nn * singp.q, RoundFromZero) - intr.mlow + 1
- dpsi = singp.psifac - odet.psifac
- odet.psifac = singp.psifac + dpsi
- sing_get_ua!(odet, intr, ctrl)
- if !ctrl.con_flag
- odet.u[:, odet.index[1, odet.ifix], :] .= 0
- end
-
- # Update solution vectors
- du1 = zeros(ComplexF64, intr.mpert, intr.mpert, 2)
- du2 = zeros(ComplexF64, intr.mpert, intr.mpert, 2)
- params = (ctrl, equil, intr, odet, ffit, outp)
- sing_der!(du1, odet.u, params, psi_old)
- sing_der!(du2, odet.u, params, odet.psifac)
- odet.u .+= (du1 .+ du2) .* dpsi
- if !ctrl.con_flag
- odet.u[ipert0, :, :] .= 0
- odet.u[:, odet.index[1, odet.ifix], :] .= odet.ua[:, ipert0 + intr.mpert, :]
- end
-
- # Get asymptotic coefficients after crossing rational surface
- sing_get_ca!(odet, intr, ctrl)
- odet.ca_r[:, :, :, odet.ising] .= odet.ca
-
- # Find next ising
- while true
- odet.ising += 1
- if odet.ising > intr.msing || intr.psilim < intr.sing[min(odet.ising, intr.msing)].psifac
- break
- end
- if intr.mlow <= ctrl.nn * intr.sing[odet.ising].q && intr.mhigh >= ctrl.nn * intr.sing[odet.ising].q
- break
- end
- end
-
- # Compute conditions at next singular surface
- if odet.ising > intr.msing || intr.psilim < intr.sing[min(odet.ising, intr.msing)].psifac
- odet.psimax = intr.psilim * (1 - eps)
- odet.m1 = round(Int, ctrl.nn * intr.qlim, RoundFromZero) + sign(ctrl.nn * equil.sq.fs1[end, 4])
- odet.next = "finish"
- else
- singp = intr.sing[odet.ising] # Update singp
- odet.psimax = singp.psifac - ctrl.singfac_min / abs(ctrl.nn * singp.q1)
- odet.m1 = round(Int,ctrl.nn * singp.q, RoundFromZero)
- write_output(outp, :crit_out, @sprintf(" ising psi q di re alpha im alpha\n"))
- write_output(outp, :crit_out, @sprintf("%6d%11.3e%11.3e%11.3e%11.3e%11.3e\n", odet.ising, singp.psifac, singp.q, singp.di, real(singp.alpha), imag(singp.alpha)))
- end
-
- # Restart ode solver
- odet.new = true
- odet.psi_store[odet.step] = odet.psifac # Store current psi
- odet.u_store[:,:,:,odet.step] = odet.u # Store current u
- odet.step += 1 # Advance step to account for crossing step
- odet.u_prev .= odet.u
- odet.psi_prev = odet.psifac
-
- # Write next header before continuing integration
- write_output(outp, :crit_out, " psifac dpsi q singfac eval1")
-end
-
-# Example stub for kinetic crossing
-function ode_kin_cross()
- # Implement kinetic crossing logic here
- return
-end
-
-# Example stub for resistive crossing
-function ode_resist_cross()
- # Implement resistive crossing logic here
- return
-end
-
-"""
- ode_step!(odet::OdeState, equil::Equilibrium.PlasmaEquilibrium,
- intr::DconInternal, ctrl::DconControl, ffit::FourFitVars)
-
-Integrate the Euler-Lagrange equations to the next rational surface or edge.
-
-# Arguments
-- `odet::OdeState`: Structure storing the current ODE state and solution arrays.
-- `equil::Equilibrium.PlasmaEquilibrium`: Plasma equilibrium parameters and profiles.
-- `intr::DconInternal`: Internal data, including singular surfaces.
-- `ctrl::DconControl`: Control and solver settings (e.g., tolerances, flags).
-- `ffit::FourFitVars`: Additional fitting variables or Fourier fit coefficients.
-
-# Description
-This function computes and sets appropriate relative and absolute tolerances
-for the ODE integration depending on proximity to singular surfaces,
-chooses the next integration endpoint, and advances the solution using
-an adaptive ODE solver. The state in `odet` is updated in-place with
-the solution at the new point.
-
-# Notes
-- Tolerance logic distinguishes between "near-singular" and "regular" regions.
-- ODE integration is performed using the DifferentialEquations.jl interface.
-- Handles both node-based and maximal-psi stepping, depending on control flags.
-"""
-function ode_step!(odet::OdeState, equil::Equilibrium.PlasmaEquilibrium, intr::DconInternal, ctrl::DconControl, ffit::FourFitVars, outp::DconOutput)
-
- # print!(integrator) = begin
- # u = integrator.u
- # # params = integrator.p
- # # params is a tuple: (ctrl, equil, intr, odet, ffit)
- # # du = similar(u)
- # # sing_der!(du, u, params, integrator.t)
- # fmt(x) = @sprintf("%.5e", x)
- # println(" ψ=", fmt(integrator.t),
- # ", max|u|=", fmt(maximum(abs.(u))))
- # # ", max|du|=", fmt(maximum(abs.(du))))
- # last_psi[] = integrator.t
- # end
-
- # Set up the callback to be run at every step
- cb = DiscreteCallback((u,t,integrator)->true, integrator_callback!)
-
- # Choose integration bounds
- if ctrl.node_flag # TODO: I can't find any mention of what this flag is for, can we get rid of it?
- while odet.psifac >= equil.sq.xs[ix]
- ix += 1
- end
- psiout = equil.sq.xs[ix]
- psiout = min(psiout, odet.psimax)
- else
- psiout = odet.psimax
- end
-
- # Print out every tenth of the inter-rational interval
- # Δψ = (odet.psimax - odet.psifac) / 10
- # last_psi = Ref(0.0)
-
- # TODO: need input here! Fortran emphasized that it was important to record data at the first and last step
- # However, the recording for u, ud, psi is now done after integration. Is there anything still within
- # ode_output_step that needs to be recorded with this precision, or can it just be called within the
- # callback? Currently, ode_output_step does: ode_output_monitor (crit values), and in Fortran also does
- # ode_output_get_evals, and ode_output_sol
- # We don't use the `first` variable, and instead call the functions directly here before/after integration
- ode_output_step!(odet, intr, ctrl, equil, outp)
-
- # Advance differential equation to next singular surface or edge
- rtol, atol = compute_tols(intr, odet, ctrl) # initial tolerances
- prob = ODEProblem(sing_der!, odet.u, (odet.psifac, psiout), (ctrl, equil, intr, odet, ffit, outp))
- sol = solve(prob, Tsit5(), reltol=rtol, abstol=atol, callback=cb)
- # TODO: check absolute tolerances, check how sensitive outputs are to tolerances
-
- # Update u and psifac with the solution at the end of the interval
- odet.u .= sol.u[end]
- odet.psifac = sol.t[end]
-
- # Save the data after integration by evaluating stored solution
- # (This used to be done during integration using ode_output_step)
- # We use save nodes that include the first and last point in an interrational region, which are important
- # for resonant quantities. Recording the last point is critical for matching the nominal edge
- # TODO: does this get messed up by u_norming?
- # for isave in (odet.ising-1)*ctrl.saves_per_region+1:odet.ising*ctrl.saves_per_region
- # # Evaluate solution derivative ud at psi, u for GPEC (NOT du)
- # u_interp = sol(odet.psi_saves[isave])
- # du_interp = similar(u_interp)
- # sing_der!(du_interp, u_interp, (ctrl, equil, intr, odet, ffit, outp), odet.psi_saves[isave])
-
- # # Store interpolated solutions at save points
- # odet.u_saves[:, :, :, isave] .= u_interp
- # odet.ud_saves[:, :, :, isave] .= odet.ud
- # end
-
- # TODO: same as above, this might not be needed
- ode_output_step!(odet, intr, ctrl, equil, outp) # always output final condition
-
- println(" ψ = $(odet.psifac), max u = $(maximum(abs, odet.u)), steps = $(odet.step-1)")
-end
-
-"""
- integrator_callback!(integrator)
-
-Callback function for ODE integrator to handle normalization, output, and storage at each step.
-This handles the logic that was previously in a DO loop within ode_run and called every step
-by running LSODE in one step mode in the Fortran code.
-"""
-function integrator_callback!(integrator)
- ctrl, equil, intr, odet, ffit, outp = integrator.p
- odet.u .= integrator.u
- odet.psifac = integrator.t
-
- # Update integration tolerances
- rtol, atol = compute_tols(intr, odet, ctrl)
- integrator.opts.reltol = rtol
- # integrator.opts.abstol = atol
-
- # TODO: Print status every Δψ, maybe get rid of this at some point? Good for debugging rn
- # if integrator.t >= last_psi[] + Δψ
- # print!(integrator)
- # end
-
- # Note: no need for istep > 0 condition, since this is called after the first integration step always
- ode_unorm!(odet, intr, ctrl, outp, false)
- integrator.u .= odet.u # Update integrator.u with normalized odet.u
-
- # TODO: ode_test if res_flag = False effectively controls whether we print at the end of integration
- # this then controls the output of ode_output_step and then has a break condition below
- # Currently, all output logic is handled via psi_saves. There's a chance we will need other pieces
- # of this ode_test logic (i.e. res_flag = True, compute powers) in the future, but for now this is sufficient
- # force_output = ode_test(odet, intr, ctrl)
- ode_output_step!(odet, intr, ctrl, equil, outp)
- ode_record_edge!(intr, ctrl, equil, odet)
-
- # Grow arrays if needed
- if odet.step >= size(odet.u_store, 4)
- resize_storage!(odet)
- end
- # Save values
- odet.psi_store[odet.step] = odet.psifac
- odet.u_store[:,:,:,odet.step] = odet.u
- odet.ud_store[:,:,:,odet.step] = odet.ud
- # Advance stepper (just like in Fortran, a "step" starts with integration, does callback functions, then stores)
- odet.step += 1
-end
-
-# Compute tolerances based on distance to singular surface during integration
-function compute_tols(intr, odet, ctrl)
- singfac_local = Inf
- # Relative tolerance
- if false # kin_flag (not implemented)
- # Insert kin_flag branch if needed
- else
- # Note: odet.q is updated within the derivative calculation
- if odet.ising <= intr.msing
- singfac_local = abs(intr.sing[odet.ising].m - ctrl.nn * odet.q)
- end
- # If in between singular surfaces, check distance to both
- if odet.ising > 1
- singfac_local = min(singfac_local, abs(intr.sing[odet.ising-1].m - ctrl.nn * odet.q))
- end
- end
- rtol = tol = singfac_local < ctrl.crossover ? ctrl.tol_r : ctrl.tol_nr
- # Absolute tolerances
- atol = similar(odet.u, Float64)
- for ieq in 1:size(odet.u,3), isol in 1:size(odet.u,2)
- atol0 = maximum(abs.(odet.u[:, isol, ieq])) * tol
- if (atol0 == 0) atol0 = Inf end
- atol[:, isol, ieq] .= atol0
- end
- return rtol, atol
-end
-
-"""
- resize_storage!(odet::OdeState)
-
-Resize storage arrays in `odet` when the current step exceeds allocated size.
-Doubles the size of the storage arrays for `u_store`, `ud_store`, and `psi_store`,
-and copies over existing data to the new arrays.
-"""
-function resize_storage!(odet::OdeState)
- oldlen = size(odet.u_store, 4)
- newlen = 2 * oldlen
-
- # Allocate new arrays
- u_new = Array{ComplexF64,4}(undef, odet.mpert, odet.mpert, 2, newlen)
- ud_new = Array{ComplexF64,4}(undef, odet.mpert, odet.mpert, 2, newlen)
- psi_new = Vector{Float64}(undef, newlen)
-
- # Copy old data
- u_new[:,:,: ,1:odet.step] = odet.u_store[:,:,: ,1:odet.step]
- ud_new[:,:,: ,1:odet.step] = odet.ud_store[:,:,: ,1:odet.step]
- psi_new[1:odet.step] = odet.psi_store[1:odet.step]
-
- # Replace old arrays
- odet.u_store = u_new
- odet.ud_store = ud_new
- odet.psi_store = psi_new
-end
-
-"""
- trim_storage!(odet::OdeState)
-
-Trim storage arrays in `odet` to the actual number of steps taken.
-Resizes `u_store`, `ud_store`, and `psi_store` to the current step count,
-removing any unused allocated space.
-"""
-function trim_storage!(odet::OdeState)
- resize!(odet.psi_store, odet.step)
- odet.u_store = odet.u_store[:,:,: ,1:odet.step]
- odet.ud_store = odet.ud_store[:,:,: ,1:odet.step]
-end
-
-"""
- ode_unorm!(odet::OdeState, intr::DconInternal, sing_flag::Bool)
-
-Computes norms of the solution vectors, normalizes them
-relative to initial values, and applies Gaussian reduction via `ode_fixup!`
-if the variation exceeds a threshold or if `sing_flag` is true.
-Throws an error if any vector norm is zero.
-"""
-function ode_unorm!(odet::OdeState, intr::DconInternal, ctrl::DconControl, outp::DconOutput, sing_flag::Bool)
- # Compute norms of first solution vectors, abort if any are zero
- odet.unorm[1:intr.mpert] .= [norm(odet.u[:, j, 1]) for j in 1:intr.mpert]
- odet.unorm[intr.mpert+1:odet.msol] .= [norm(odet.u[:, j, 2]) for j in intr.mpert+1:odet.msol]
- if minimum(odet.unorm[1:odet.msol]) == 0
- jmax = argmin(odet.unorm[1:odet.msol])
- error("One of the first solution vector norms unorm(1,$jmax) = 0")
- end
-
- # Normalize unorm and perform Gaussian reduction if required
- if odet.new
- odet.new = false
- odet.unorm0[1:odet.msol] .= odet.unorm[1:odet.msol]
- else
- odet.unorm[1:odet.msol] .= odet.unorm[1:odet.msol] ./ odet.unorm0[1:odet.msol]
- uratio = maximum(odet.unorm[1:odet.msol]) / minimum(odet.unorm[1:odet.msol])
- if uratio > ctrl.ucrit || sing_flag
- # TODO: add resizing logic here as well
- if odet.ifix < ctrl.numunorms_init
- odet.ifix += 1
- else
- @warn "unorm storage reached, no longer saving fixfac data. Stability outputs and unorming will be correct, but cannot reconstruct `u`. \n
- Increase `numunorms_init` in dcon.toml if needed. Automatic resizing will be added in a future version."
- end
- ode_fixup!(odet, intr, outp, sing_flag, false)
- odet.new = true
- end
- end
-end
-
-"""
- ode_fixup!(odet::OdeState, intr::DconInternal, sing_flag::Bool, test::Bool)
-
-Applies Gaussian reduction to orthogonalize solution vectors in `odet.u`.
-
-Used when the spread in norms exceeds a threshold or a singularity is detected.
-Sorts solutions by norm, eliminates dependencies using forward elimination,
-and optionally computes the transformation matrix `fixfac`.
-Behavior can be suppressed for testing via the `test` flag.
-"""
-function ode_fixup!(odet::OdeState, intr::DconInternal, outp::DconOutput, sing_flag::Bool, test::Bool)
-
- # TODO: seems like secondary is always false in fortran DCON (unless manually changed). is this needed?
- secondary = false
-
- # TODO: can test be removed if we aren't implementing ode_test_fixup?
-
- # Write to output
- if outp.write_crit_out
- write_output(outp, :crit_out, "\n psifac dpsi q singfac eval1")
- write_output(outp, :crit_out, @sprintf("\nGaussian Reduction at psi = %10.3e, q = %6.3f\n", odet.psifac, odet.q))
- if !sing_flag
- write_output(outp, :crit_out, " psifac dpsi q singfac eval1\n")
- end
- end
- odet.flag_count = 0 # TODO: is this used anywhere?
-
- # Store data for the current fixup
- ifix = odet.ifix
- odet.sing_flags[ifix] = sing_flag
- odet.fixstep[ifix] = odet.step
-
- # Initialize fixfac
- if !test
- for isol in 1:odet.msol
- odet.fixfac[isol, isol, ifix] = 1
- end
- # Sort unorm
- odet.index[1:odet.msol, ifix] .= collect(1:odet.msol)
- odet.index[1:intr.mpert, ifix] .= sortperm_subrange(odet.unorm, 1:intr.mpert) # in original Fortran: bubble(unorm, index, 1, mpert)
- odet.index[intr.mpert+1:odet.msol, ifix] .= sortperm_subrange(odet.unorm, intr.mpert+1:odet.msol) # in original Fortran: bubble(unorm, index, mpert + 1, msol)
- end
-
- # Triangularize primary solutions
- mask = trues(2, odet.msol)
- for isol in 1:intr.mpert
- ksol = odet.index[isol, ifix]
- mask[2, ksol] = false
- if !test
- # Find max location
- kpert = argmax(abs.(odet.u[:, ksol, 1]) .* mask[1, 1:intr.mpert])
- mask[1, kpert] = false
- end
- for jsol in 1:odet.msol
- if mask[2, jsol]
- if !test
- odet.fixfac[ksol, jsol, ifix] = -odet.u[kpert, jsol, 1] / odet.u[kpert, ksol, 1]
- end
- odet.u[:, jsol, :] .= odet.u[:, jsol, :] .+ odet.u[:, ksol, :] .* odet.fixfac[ksol, jsol, ifix]
- if !test
- odet.u[kpert, jsol, 1] = 0
- end
- end
- end
- end
-
- # Triangularize secondary solutions
- if odet.msol > intr.mpert && secondary
- mask = trues(2, odet.msol)
- for isol in intr.mpert + 1:odet.msol
- ksol = odet.index[isol, ifix]
- mask[2, ksol] = false
- if !test
- absvals = abs.(odet.u[:, ksol, 2])
- masked = absvals .* mask[1, 1:intr.mpert]
- kpert = argmax(masked)
- mask[1, kpert] = false
- end
- for jsol in intr.mpert + 1:odet.msol
- if mask[2, jsol]
- if !test
- odet.fixfac[ksol, jsol, ifix] = -odet.u[kpert, jsol, 2] / odet.u[kpert, ksol, 2]
- end
- odet.u[:, jsol, :] .= odet.u[:, jsol, :] .+ odet.u[:, ksol, :] .* odet.fixfac[ksol, jsol, ifix]
- if !test
- odet.u[kpert, jsol, 2] = 0
- end
- end
- end
- end
- end
-
- # Note: will dump to output later if needed
-end
-
-"""
- ode_test(odet::OdeState, intr::DconInternal, ctrl::DconControl)::Bool
-
-Returns `true` if integration is complete or if any stopping criteria are met.
-
-TODO: implement res_flag = true logic
-"""
-function ode_test(odet::OdeState, intr::DconInternal, ctrl::DconControl)::Bool
-
- # check if we are at end of integration
- flag = odet.psifac == odet.psimax
-
- # if not running with res_flag = true this function will exit and return flag here)
- if !ctrl.res_flag || flag || odet.ising > intr.msing || odet.singfac > ctrl.singfac_max
- return flag
- end
-
- @error "ode_test with res_flag = true not implemented yet!"
- # TODO: none of this has been checked, wait until we implement res_flag = true
- # ca_old .= ca # Save previous surface ca
- # sing_get_ca(ising, psifac, u, ca) # Updates global ca
- # dca = ca .- ca_old
- # dsingfac = abs((singfac - singfac_old)/singfac)
- # singfac_old = singfac
-
- # power = zeros(Float64, msol)
- # powmax_old = powmax
- # for isol in 1:msol
- # # ca[:,isol,:]::matrix of size (mpert,2)
- # # Flatten the relevant slice for norm calculation
- # ca_isol = ca[:, isol, :] # mpert × 2
- # dca_isol = dca[:, isol, :]
- # norm = abs(sum(conj.(ca_isol) .* ca_isol))
- # dnorm = abs(sum(conj.(ca_isol) .* dca_isol))
- # power[isol] = dnorm / (norm * dsingfac)
- # end
- # powmax = maximum(power)
-
- # odet.flag_count += 1
- # if odet.flag_count < 3
- # return flag
- # end
- # flag = flag || ((singfac < singfac_max) && (powmax > powmax_old))
-
- # if ising == ksing
- # println(err_unit, float(log10(singfac)), " ", float(log10(powmax)))
- # end
-
- # return flag
-end
-
-"""
- ode_record_edge!(intr::DconInternal, ctrl::DconControl, equil::Equilibrium.PlasmaEquilibrium, odet::OdeState)
-
-Records edge quantities at the current integration point if edge conditions are met.
-
-Checks whether `psifac` and `q` exceed edge thresholds, and if so,
-stores relevant values in `intr`. Currently, vacuum calculations are
-not implemented; this function raises an error if invoked in a vacuum region.
-"""
-# TODO: this function requires integration the vacuum code for free_test
-# for now, going to make it look ok and error out if we get to free_test
-# I don't think this function is working properly, but I'm not sure what its doing
-function ode_record_edge!(intr::DconInternal, ctrl::DconControl, equil::Equilibrium.PlasmaEquilibrium, odet::OdeState)
-
- q_psifac = Spl.spline_eval(equil.sq, odet.psifac, 0)
- if intr.size_edge > 0
- #TODO: WTH? fortran has both a psiedge and psi_edge and they appear to be different.
- # someone smarter than me please double check this
- if q_psifac >= intr.q_edge[intr.i_edge] && odet.psifac >= ctrl.psiedge
- @error "Vacuum code not yet integrated. This run has size_edge = $(intr.size_edge) > 0 and integrator passed psiedge/q_edge"
- #free_test(plasma1, vacuum1, total1, odet.psifac)
- intr.dw_edge[intr.i_edge] = total1
- intr.q_edge[intr.i_edge] = q_psifac
- intr.psi_edge[intr.i_edge] = odet.psifac
- intr.i_edge = min(intr.i_edge + 1, intr.size_edge) # just to be extra safe
- end
- end
-end
-
-"""
- get_psi_saves!(odet::OdeState, ctrl::DconControl, intr::DconInternal)
-
-Calculates the psi values at which to save the solution during ODE integration based on specified spacing type,
-number of saves per region, and number of rational surfaces, and saves into `odet.psi_save_nodes`. Note that
-`odet.psi_save_nodes` does not store the start/endpoints, since those are saved automatically.
-"""
-# TODO: this is no longer used, but might be useful code? Leaving for now, but likely can be removed
-function get_psi_saves!(odet::OdeState, ctrl::DconControl, intr::DconInternal)
-
- # This function is called after the ode init functions, so the starting psi is stored in odet.psifac
- # This repeats some logic used in the init and cross functions
-
- # Loop through interrational intervals (just one interval if no rational surfaces)
- for ising in 1:intr.msing+1
- # Determine bottom of interrational interval
- if ising == 1
- psibot = odet.psifac
- else
- psibot = intr.sing[ising - 1].psifac + ctrl.singfac_min / abs(ctrl.nn * intr.sing[ising - 1].q1)
- end
- # Determine top of interrational interval
- if ising <= intr.msing
- psitop = intr.sing[ising].psifac - ctrl.singfac_min / abs(ctrl.nn * intr.sing[ising].q1)
- else
- psitop = intr.psilim * (1 - eps)
- end
- # Calculate save nodes in interval
- if ctrl.save_spacing == "Chebyshev"
- odet.psi_saves[(ising-1)*ctrl.saves_per_region+1:ising*ctrl.saves_per_region] = chebyshev_nodes(psibot, psitop, ctrl.saves_per_region)
- else
- error("Cannot recognize save_spacing = $(ctrl.save_spacing)")
- end
- end
-end
\ No newline at end of file
diff --git a/src/DCON/OdeOutput.jl b/src/DCON/OdeOutput.jl
deleted file mode 100644
index 550431a290..0000000000
--- a/src/DCON/OdeOutput.jl
+++ /dev/null
@@ -1,306 +0,0 @@
-"""
- ode_output_init(ctrl, equil, outp, intr, odet)
-
- Write header info to output files at the start of the integration.
-"""
-function ode_output_init(ctrl::DconControl, equil::Equilibrium.PlasmaEquilibrium, outp::DconOutput, intr::DconInternal, odet::OdeState)
-
- # TODO: mess with this to condense the number of write_output calls? Maybe allow it to pass in dicts
- # Write euler.bin header info
- if outp.write_euler_h5
- # Write dcon run parameters
- write_output(outp, :euler_h5, intr.mpert; dsetname="info/mpert")
- write_output(outp, :euler_h5, intr.mband; dsetname="info/mband")
- write_output(outp, :euler_h5, intr.mlow; dsetname="info/mlow")
- write_output(outp, :euler_h5, intr.mhigh; dsetname="info/mhigh")
- write_output(outp, :euler_h5, ctrl.nn; dsetname="info/nn")
- write_output(outp, :euler_h5, ctrl.singfac_min; dsetname="info/singfac_min")
- write_output(outp, :euler_h5, ctrl.kin_flag; dsetname="info/kin_flag")
- write_output(outp, :euler_h5, ctrl.con_flag; dsetname="info/con_flag")
- write_output(outp, :euler_h5, ctrl.mthvac; dsetname="info/mthvac")
- write_output(outp, :euler_h5, intr.psilim; dsetname="info/psilim")
- write_output(outp, :euler_h5, intr.qlim; dsetname="info/qlim")
- write_output(outp, :euler_h5, outp.mthsurf0; dsetname="info/mthsurf0") #TODO: mthsurf0 is deprecated
-
- # Write equilibrium parameters
- write_output(outp, :euler_h5, length(equil.rzphi.xs); dsetname="equil/nr") # TODO: equil save mpsi as really mpsi - 1, fix this
- write_output(outp, :euler_h5, length(equil.rzphi.ys); dsetname="equil/nz")
- write_output(outp, :euler_h5, equil.ro; dsetname="equil/ro")
- write_output(outp, :euler_h5, equil.zo; dsetname="equil/zo")
- write_output(outp, :euler_h5, equil.params.amean; dsetname="equil/amean")
- write_output(outp, :euler_h5, equil.params.rmean; dsetname="equil/rmean")
- write_output(outp, :euler_h5, equil.params.aratio; dsetname="equil/aratio")
- write_output(outp, :euler_h5, equil.params.kappa; dsetname="equil/kappa")
- write_output(outp, :euler_h5, equil.params.delta1; dsetname="equil/delta1")
- write_output(outp, :euler_h5, equil.params.delta2; dsetname="equil/delta2")
- write_output(outp, :euler_h5, equil.params.li1; dsetname="equil/li1")
- write_output(outp, :euler_h5, equil.params.li2; dsetname="equil/li2")
- write_output(outp, :euler_h5, equil.params.li3; dsetname="equil/li3")
- write_output(outp, :euler_h5, equil.params.betap1; dsetname="equil/betap1")
- write_output(outp, :euler_h5, equil.params.betap2; dsetname="equil/betap2")
- write_output(outp, :euler_h5, equil.params.betap3; dsetname="equil/betap3")
- write_output(outp, :euler_h5, equil.params.betat; dsetname="equil/betat")
- write_output(outp, :euler_h5, equil.params.betan; dsetname="equil/betan")
- write_output(outp, :euler_h5, equil.params.bt0; dsetname="equil/bt0")
- write_output(outp, :euler_h5, equil.params.q0; dsetname="equil/q0")
- write_output(outp, :euler_h5, equil.params.q95; dsetname="equil/q95")
- write_output(outp, :euler_h5, equil.params.qmin; dsetname="equil/qmin")
- write_output(outp, :euler_h5, equil.params.qmax; dsetname="equil/qmax")
- write_output(outp, :euler_h5, equil.params.qa; dsetname="equil/qa")
- write_output(outp, :euler_h5, equil.params.crnt; dsetname="equil/crnt")
- write_output(outp, :euler_h5, equil.psio; dsetname="equil/psio")
- write_output(outp, :euler_h5, equil.config.control.psilow; dsetname="equil/psilow")
- write_output(outp, :euler_h5, equil.config.control.power_b; dsetname="equil/power_b")
- write_output(outp, :euler_h5, equil.config.control.power_r; dsetname="equil/power_r")
- write_output(outp, :euler_h5, equil.config.control.power_bp; dsetname="equil/power_bp")
- write_output(outp, :euler_h5, 0; dsetname="equil/shotnum") # TODO: equil.params.shotnum)
- write_output(outp, :euler_h5, 0; dsetname="equil/shottime") # TODO: equil.params.shottime)
-
- # Write spline arrays
- write_output(outp, :euler_h5, Vector(equil.sq.xs); dsetname="splines/sq/xs")
- # TODO: getting errors when trying to dump just fs, so splitting for now, which adds so many lines
- # This should be fixed if we separate these like Nik mentioned
- write_output(outp, :euler_h5, equil.sq.fs[:,1]; dsetname="splines/sq/fs/2piF")
- write_output(outp, :euler_h5, equil.sq.fs[:,2]; dsetname="splines/sq/fs/mu0p")
- write_output(outp, :euler_h5, equil.sq.fs[:,3]; dsetname="splines/sq/fs/dVdpsi")
- write_output(outp, :euler_h5, equil.sq.fs[:,4]; dsetname="splines/sq/fs/q")
- write_output(outp, :euler_h5, equil.sq.fs1[:,1]; dsetname="splines/sq/fs1/2piF")
- write_output(outp, :euler_h5, equil.sq.fs1[:,2]; dsetname="splines/sq/fs1/mu0p")
- write_output(outp, :euler_h5, equil.sq.fs1[:,3]; dsetname="splines/sq/fs1/dVdpsi")
- write_output(outp, :euler_h5, equil.sq.fs1[:,4]; dsetname="splines/sq/fs1/q")
- write_output(outp, :euler_h5, 0; dsetname="splines/sq/xpower") # TODO: equil.sq.xpower
- write_output(outp, :euler_h5, Vector(equil.rzphi.xs); dsetname="splines/rzphi/xs")
- write_output(outp, :euler_h5, Vector(equil.rzphi.ys); dsetname="splines/rzphi/ys")
- write_output(outp, :euler_h5, equil.rzphi.fs[:,1]; dsetname="splines/rzphi/fs/rcoords")
- write_output(outp, :euler_h5, equil.rzphi.fs[:,2]; dsetname="splines/rzphi/fs/offset")
- write_output(outp, :euler_h5, equil.rzphi.fs[:,3]; dsetname="splines/rzphi/fs/nu")
- write_output(outp, :euler_h5, equil.rzphi.fs[:,4]; dsetname="splines/rzphi/fs/jac")
- write_output(outp, :euler_h5, equil.rzphi.fsx[:,1]; dsetname="splines/rzphi/fsx/rcoords")
- write_output(outp, :euler_h5, equil.rzphi.fsx[:,2]; dsetname="splines/rzphi/fsx/offset")
- write_output(outp, :euler_h5, equil.rzphi.fsx[:,3]; dsetname="splines/rzphi/fsx/nu")
- write_output(outp, :euler_h5, equil.rzphi.fsx[:,4]; dsetname="splines/rzphi/fsx/jac")
- write_output(outp, :euler_h5, equil.rzphi.fsy[:,1]; dsetname="splines/rzphi/fsy/rcoords")
- write_output(outp, :euler_h5, equil.rzphi.fsy[:,2]; dsetname="splines/rzphi/fsy/offset")
- write_output(outp, :euler_h5, equil.rzphi.fsy[:,3]; dsetname="splines/rzphi/fsy/nu")
- write_output(outp, :euler_h5, equil.rzphi.fsy[:,4]; dsetname="splines/rzphi/fsy/jac")
- write_output(outp, :euler_h5, equil.rzphi.fsxy[:,1]; dsetname="splines/rzphi/fsxy/rcoords")
- write_output(outp, :euler_h5, equil.rzphi.fsxy[:,2]; dsetname="splines/rzphi/fsxy/offset")
- write_output(outp, :euler_h5, equil.rzphi.fsxy[:,3]; dsetname="splines/rzphi/fsxy/nu")
- write_output(outp, :euler_h5, equil.rzphi.fsxy[:,4]; dsetname="splines/rzphi/fsxy/jac")
- write_output(outp, :euler_h5, 0; dsetname="splines/rzphi/x0") # TODO: equil.rzphi.x0
- write_output(outp, :euler_h5, 0; dsetname="splines/rzphi/y0") # TODO: equil.rzphi.y0
- write_output(outp, :euler_h5, 0; dsetname="splines/rzphi/xpower") # TODO: equil.rzphi.xpower
- write_output(outp, :euler_h5, 0; dsetname="splines/rzphi/fpower") # TODO: equil.rzphi.fpower
- end
-
- # Write crit.out header
- if odet.ising > 0 && odet.ising <= intr.msing
- singp = intr.sing[odet.ising]
- write_output(outp, :crit_out, @sprintf(" ising psi q di re alpha im alpha\n"))
- write_output(outp, :crit_out, @sprintf("%6d%11.3e%11.3e%11.3e%11.3e%11.3e\n", odet.ising, singp.psifac, singp.q, singp.di, real(singp.alpha), imag(singp.alpha)))
- end
- write_output(outp, :crit_out, " psifac dpsi q singfac eval1\n")
-end
-
-"""
- ode_output_step(odet, intr, ctrl, equil; force=false)
-
-Performs output and monitoring tasks at each integration step.
-
-This function calls `ode_output_monitor` to track critical eigenvalue behavior
-and handle any diagnostics or logging associated with the current step.
-Additional output (e.g., eigenvalue dumps, binary solution logging) may be added later.
-"""
-#TODO: depending on how we restructure our outputs, this function might be uncessary
-# (i.e. if we don't need an ode_output_get_evals or ode_output_sol, can just replace calls with ode_output_monitor)
-function ode_output_step!(odet::OdeState, intr::DconInternal, ctrl::DconControl, equil::Equilibrium.PlasmaEquilibrium, outp::DconOutput)
-
- # Compute and print critical data for each time step
- ode_output_monitor!(odet, intr, ctrl, equil, outp)
- # if dout.out_evals || dout.bin_evals
- # ode_output_get_evals(intr, ctrl, dout, fNames, equil, odet) # this is just outputs
- # end
-
- # All bin_euler logic performed after integration
-
- # if outp.bin_sol
- # ode_output_sol()
- # end
-end
-
-# TODO: I don't think this function is essentially for the minimal working version - can convert later if needed
-# function ode_output_get_evals(intr::DconInternal, ctrl::DconControl, dout::DconOutput, fNames::DconFileNames, equil::Equilibrium.PlasmaEquilibrium, odet::OdeState)
-# # Access all variables from structs, not globals.
-# # Pretty much just giving them all aliases so we don't have to type `intr.` and `ctrl.` every time.
-# u = odet.u #TODO: is ud the same as u
-# mpert = intr.mpert
-# out_evals = dout.out_evals
-# bin_evals = dout.bin_evals
-# nn = intr.nn
-# evals_out_unit = fNames.evals_out_unit
-# evals_bin_unit = fNames.evals_bin_unit
-# sq = equil.sq
-# psifac = intr.sing.psifac
-# q = equil.sq.f[4]
-
-# # Compute plasma response matrix
-# temp = conj.(transpose(u[:, 1:mpert, 1]))
-# wp = u[:, 1:mpert, 2]
-# wp = conj.(transpose(wp))
-
-# ipiv = zeros(Int, mpert)
-# info = Ref{Int}(0)
-
-# temp_lapack = copy(temp) # copy just renames a function pretty much
-# LAPACK.zgetrf!(temp_lapack, ipiv)
-# wp_lapack = copy(wp)
-# LAPACK.zgetrs!('N', temp_lapack, ipiv, wp_lapack)
-# wp = (wp_lapack + conj.(transpose(wp_lapack))) / 2
-
-# # Compute and sort eigenvalues
-# evals = zeros(Float64, mpert)
-# work = zeros(ComplexF64, 2*mpert-1)
-# rwork = zeros(Float64, 3*mpert-2)
-# evals, _ = LAPACK.zheev!('N', 'U', wp)
-# index = sortperm(-abs.(1 ./ evals), rev=true) # TODO: Should this still be rev
-
-# # Compute and sort inverse eigenvalues
-# evalsi, _ = LAPACK.zheev!('N', 'U', wp)
-# indexi = sortperm(-abs.(evalsi), rev = true) # TODO: Should this still be rev
-
-# # Write ascii eigenvalues
-# if out_evals && odet.istep > 0
-# @printf(evals_out_unit, "\nistep = %d, psifac = %.5e, q = %.5e\n", odet.istep, psifac, q)
-# @printf(evals_out_unit, "\n i eval evali err\n")
-# for ipert in 1:mpert
-# @printf(evals_out_unit, "%6d %11.3e %11.3e %11.3e\n",
-# ipert,
-# evalsi[indexi[ipert]],
-# evals[index[ipert]],
-# evalsi[indexi[ipert]] * evals[index[ipert]] - 1)
-# end
-# @printf(evals_out_unit, "\n i eval evali err\n")
-# end
-
-# # Write binary eigenvalues
-# if bin_evals && psifac > 0.1
-# spline_eval(sq, psifac, 0) #TODO: Where does sq come from?
-# q = sq.f[4]
-# singfac = abs(odet.m1 - nn * q)
-# logpsi1 = log10(psifac)
-# logpsi2 = log10(singfac)
-# for ipert in 2:mpert
-# write(evals_bin_unit, Float32(ipert), Float32(psifac),
-# Float32(logpsi1), Float32(logpsi2),
-# Float32(q), Float32(1 / evals[index[ipert]]))
-# end
-# write(io, evals_bin_unit) # End record #TODO: Looks like the function call should be write(io, stuff). Will it be written to rhe right place?
-# end
-
-# return
-# end
-
-"""
- ode_output_monitor!(odet, intr, ctrl, equil, outp)
-
-Monitor the evolution of a critical eigenvalue (`crit`) during ODE integration and detect zero crossings, which indicate resonant or singular behavior.
-The function evaluates `crit` using `ode_output_get_crit`, and if a sign change is found, it estimates the crossing point via linear interpolation.
-If the crossing satisfies sharpness and consistency conditions, it's logged and `nzero` is incremented.
-A termination flag (`termbycross_flag`) set within DconControl can be used to stop integration upon detection.
-
-### Notes
-- Zero-crossing detection is based on changes in the sign of `crit`.
-- `u_med` is constructed as a linear interpolation between current and saved `u`.
-- This function updates psi_prev, crit_prev, u_prev, and nzero in the `odet` state.
-
-### TODO
-- Restore or redirect output to appropriate logging units.
-- Replace `error(...)` with graceful shutdown if zero crossing is an intended exit condition.
-"""
-function ode_output_monitor!(odet::OdeState, intr::DconInternal, ctrl::DconControl, equil::Equilibrium.PlasmaEquilibrium, outp::DconOutput)
-
- # Compute new crit
- dpsi = odet.psifac - odet.psi_prev
- q, singfac, logpsi1, logpsi2, crit = ode_output_get_crit(odet.psifac, odet.u, intr.mpert, odet.m1, ctrl.nn, equil.sq)
-
- # Check for zero crossing
- if crit * odet.crit_prev < 0 # if crit changes sign, zero crossing has occurred
- fac = crit / (crit - odet.crit_prev)
- psi_med = odet.psifac - fac * (odet.psifac - odet.psi_prev)
- dpsi = psi_med - odet.psi_prev
- u_med = odet.u .- fac .* (odet.u .- odet.u_prev)
- q_med, singfac_med, logpsi1_med, logpsi2_med, crit_med = ode_output_get_crit(psi_med, u_med, intr.mpert, odet.m1, ctrl.nn, equil.sq)
-
- if (crit_med - crit) * (crit_med - odet.crit_prev) < 0 &&
- abs(crit_med) < 0.5 * min(abs(crit), abs(odet.crit_prev))
- println("Zero crossing detected at psi = $psi_med, q = $q_med")
- write_output(outp, :dcon_out, @sprintf("Zero crossing at psi = %10.3e, q = %10.3e", psi_med, q_med))
- write_output(outp, :crit_out, @sprintf("Zero crossing at psi = %10.3e, q = %10.3e", psi_med, q_med))
- write_output(outp, :crit_out, @sprintf("%11.3e%11.3e%11.3e%11.3e%11.3e", psi_med,dpsi,q_med,singfac_med,crit_med))
- odet.nzero += 1
- end
- if ctrl.termbycross_flag
- #TODO: not sure if this is really an error, or just a user specified termination condition. So the program shoudln't error out, just stop integrating
- # In fortran, these were both handled by program_stop()
- error("Terminated by zero crossing.")
- end
- end
-
- # Write new crit
- write_output(outp, :crit_out, @sprintf("%11.3e%11.3e%11.3e%11.3e%11.3e", odet.psifac,dpsi,odet.q,singfac,crit))
-
- # Update saved values
- odet.psi_prev = odet.psifac
- odet.crit_prev = crit
- odet.u_prev .= odet.u
-end
-
-"""
- ode_output_get_crit(psi, u, mpert, m1, nn, sq) -> (q, singfac, logpsi1, logpsi2, crit)
-
-Compute critical quantities at a given flux surface by constructing and inverting the plasma response matrix from the complex
-array `u`, symmetrizing it, computing its Hermitian eigenvalues, and using the smallest (in magnitude)
-inverse eigenvalue in combination with the equilibrium profiles to form `crit`.
-
-This uses Julia’s built-in linear algebra:
-`lu(temp) = zgetrf`, `temp_fact \\ wp = zgetrs`
-Under the hood, Julia calls optimized LAPACK routines via the LinearAlgebra standard library.
-
-### Main Arguments (others defined in main structs)
-- `psi::Float64`: The flux surface at which to evaluate.
-- `u::Array{ComplexF64, 3}`: Complex response data array of shape `(mpert, mpert, 2)`.
-
-### Returns
-A tuple `(q, singfac, logpsi1, logpsi2, crit)` of critical data for the time step.
-"""
-# TODO: on self-contained functions like this, it feels silly to pass in these large structs when we only need one variable
-# Should we just pass in the variables we need? This seems more readable to me personally
-#function ode_output_get_crit(psi::Float64, u::Array{ComplexF64, 3}, intr::DconInternal, odet::OdeState, ctrl::DconControl, equil::Equilibrium.PlasmaEquilibrium) # (alternate version)
-function ode_output_get_crit(psi::Float64, u::Array{ComplexF64, 3}, mpert::Int, m1::Int, nn::Int, sq::Spl.CubicSpline)
-
- # Compute inverse plasma response matrix
- uu = u[:, 1:mpert, :]
- wp = adjoint(uu[:, :, 1]) # adjoint = conjugate transpose
- temp = adjoint(uu[:, :, 2])
-
- # Compute wp using LU decomposition
- temp_fact = lu(temp)
- wp = temp_fact \ wp
-
- # Symmetrize
- wp = (wp + adjoint(wp)) / 2
-
- # Compute and sort inverse eigenvalues
- evalsi = eigen(Hermitian(wp)).values
- indexi = sortperm(abs.(evalsi)) # bubble in Fortran sorts in descending order of -|evalsi|, we just do ascending order of |evalsi|
-
- # Compute critical data for each time step
- profiles = Spl.spline_eval(sq, psi, 0)
- q = profiles[4]
- singfac = abs(m1 - nn * profiles[4])
- logpsi1 = log10(psi)
- logpsi2 = log10(singfac) # TODO: why is this called logpsi2 and not logsingfac?
- crit = evalsi[indexi[1]] # * profiles[3]^2 # TODO: appears to be a bug in profiles[3]
-
- return q, singfac, logpsi1, logpsi2, crit
-end
\ No newline at end of file
diff --git a/src/DCON/Sing.jl b/src/DCON/Sing.jl
deleted file mode 100644
index e2492754b9..0000000000
--- a/src/DCON/Sing.jl
+++ /dev/null
@@ -1,671 +0,0 @@
-"""
- sing_scan!(intr::DconInternal, ctrl::DconControl, equil::Equilibrium.PlasmaEquilibrium, ffit::FourFitVars, outp::DconOutput)
-
-Scan all singular surfaces and calculate asymptotic vmat and mmat matrices and Mericer criterion.
-"""
-function sing_scan!(intr::DconInternal, ctrl::DconControl, equil::Equilibrium.PlasmaEquilibrium, ffit::FourFitVars, outp::DconOutput)
- write_output(outp, :dcon_out, "\n Singular Surfaces:")
- write_output(outp, :dcon_out, @sprintf("%3s %11s %11s %11s %11s %11s %11s %11s", "i", "psi", "rho", "q", "q1", "di0", "di", "err"))
- # msol = intr.mpert # TODO: is msol used anywhere else? It's a global in Fortran and very confusing
- for ising in 1:intr.msing
- sing_vmat!(intr, ctrl, equil, ffit, outp, ising)
- end
- write_output(outp, :dcon_out, @sprintf("%3s %11s %11s %11s %11s %11s %11s %11s", "i", "psi", "rho", "q", "q1", "di0", "di", "err"))
-end
-
-"""
- sing_find!(ctrl::DconControl, equil::Equilibrium.PlasmaEquilibrium, intr::DconInternal; itmax=300)
-
-Locate singular rational q-surfaces (q = m/nn) using a bisection method between extrema of the q-profile, and store their properties in `intr.sing`.
-
-# Arguments
-- 'itmax::Int`: Maximum number of iterations for the bisection method (default: 200)
-"""
-function sing_find!(ctrl::DconControl, equil::Equilibrium.PlasmaEquilibrium, intr::DconInternal; itmax=200)
-
- # Shorthand to evaluate q inside bisection search
- qval = psi -> Spl.spline_eval(equil.sq, psi, 0)[4]
-
- # Loop over extrema of q, find all rational values in between
- for iex in 2:equil.params.mextrema
- dq = equil.params.qextrema_q[iex] - equil.params.qextrema_q[iex-1]
- m = trunc(Int, ctrl.nn * equil.params.qextrema_q[iex-1])
- if dq > 0
- m += 1
- end
- dm = Int(sign(dq * ctrl.nn))
-
- # Loop over possible m's in interval
- while (m - ctrl.nn * equil.params.qextrema_q[iex-1]) * (m - ctrl.nn * equil.params.qextrema_q[iex]) <= 0
- it = 0
- psi0 = equil.params.qextrema_psi[iex-1]
- psi1 = equil.params.qextrema_psi[iex]
- psifac = (psi0 + psi1)/2 # initial guess for bisection
-
- # Bisection method to find singular surface
- while it < itmax
- it += 1
- psifac = (psi0 + psi1)/2
- singfac = (m - ctrl.nn * qval(psifac)) * dm
- if abs(singfac) <= 1e-8
- break
- elseif singfac > 0
- psi0 = psifac
- else
- psi1 = psifac
- end
- end
-
- if it == itmax
- error("Bisection did not converge for m = $m")
- else
- push!(intr.sing, SingType(
- m = m,
- psifac = psifac,
- rho = sqrt(psifac),
- q = m / ctrl.nn,
- q1 = Spl.spline_eval(equil.sq, psifac, 1)[2][4],
- ))
- intr.msing += 1
- end
- m += dm
- end
- end
-end
-
-"""
- sing_lim!(intr::DconInternal, ctrl::DconControl, equil::Equilibrium.PlasmaEquilibrium, eqCtrl::Equilibrium.EquilibriumControl, eqPrm::Equilibrium.EquilibriumParameters)
-
-Compute and set limiter values for the DCON analysis - handles cases where user
-truncates before the last singular surface.
-
-# Arguments
-- `itmax::Int`: The maximum number of iterations allowed for the psilim search (default: 50)
-- `eps::Float64`: The convergence tolerance for the psilim search (default: 1e-10)
-"""
-# JMH - this has been checked against the DIID_Ideal example (with psiedge = 0.95 to enter the last if statement).
-# There are some discrepancies at the 4-5th digit between the two, not sure if this is numerical noise,
-# an issue in the spline evals, or a bug here. However, the differences in the main internal parameters are small
-# so ignoring for now, can address in a unit test later.
-function sing_lim!(intr::DconInternal, ctrl::DconControl, equil::Equilibrium.PlasmaEquilibrium; itmax=50, eps=1e-10)
-
- # Shorthand to evaluate q/q1 inside newton iteration
- qval = psi -> Spl.spline_eval(equil.sq, psi, 0)[4]
- q1val = psi -> Spl.spline_eval(equil.sq, psi, 1)[2][4]
-
- #compute and modify the DconInternal struct
- intr.qlim = min(equil.params.qmax, ctrl.qhigh)
- intr.q1lim = equil.sq.fs1[equil.config.control.mpsi+1, 4]
- intr.psilim = equil.config.control.psihigh
- #normalize dmlim to interval [0,1)
- if ctrl.sas_flag
- while ctrl.dmlim > 1.0
- ctrl.dmlim -= 1.0
- end
- while ctrl.dmlim < 0.0
- ctrl.dmlim += 1.0
- end
- #compute qlim
- intr.qlim = (trunc(Int, ctrl.nn * intr.qlim) + ctrl.dmlim) / ctrl.nn
- while intr.qlim > equil.params.qmax #could also be a while true with a break condition if (qlim <= qmax) like the Fortran code
- intr.qlim -= 1.0 / ctrl.nn
- end
- end
-
- #use newton iteration to find psilim
- if intr.qlim < equil.params.qmax
- # Find index jpsi that minimizes |equil.sq.fs[:,4] - qlim| and ensure within mpsi limits
- _, jpsi = findmin(abs.(equil.sq.fs[:,4] .- intr.qlim))
- jpsi = min(jpsi, equil.config.control.mpsi - 1)
-
- intr.psilim = equil.sq.xs[jpsi]
- it = 0
- while it < itmax
- it += 1
- dpsi = (intr.qlim - qval(intr.psilim)) / q1val(intr.psilim)
- intr.psilim += dpsi
-
- if abs(dpsi) < eps * abs(intr.psilim)
- intr.q1lim = q1val(intr.psilim)
- break
- end
- end
-
- # abort if not found
- if it > itmax
- error("Can't find psilim.")
- end
-
- else
- intr.qlim = equil.params.qmax
- intr.q1lim = equil.sq.fs1[equil.config.control.mpsi+1,4]
- intr.psilim = equil.config.control.psihigh
- end
-
- #set up record for determining the peak in dW near the boundary.
- if ctrl.psiedge < intr.psilim
- qedgestart = trunc(Int, Spl.spline_eval(equil.sq, ctrl.psiedge, 0)[4])
- intr.size_edge = ceil(Int, (intr.qlim - qedgestart) * ctrl.nn * ctrl.nperq_edge)
-
- intr.dw_edge = fill(-Inf * (1 + im), intr.size_edge)
- intr.q_edge = [qedgestart + i / (ctrl.nperq_edge * ctrl.nn) for i in 0:intr.size_edge-1]
- intr.psi_edge = zeros(intr.size_edge)
-
- # monitor some deeper points for an informative profile
- intr.pre_edge = 1
- for i in 1:intr.size_edge
- if intr.q_edge[i] < Spl.spline_eval(equil.sq, ctrl.psiedge, 0)[4]
- intr.pre_edge += 1
- end
- end
- end
-end
-
-# Main differences: using 1 indexing, so zeroth order is the first index, whereas Fortran used 0 indexing for these arrays
-function sing_vmat!(intr::DconInternal, ctrl::DconControl, equil::Equilibrium.PlasmaEquilibrium, ffit::FourFitVars, outp::DconOutput, ising::Int)
-
- # Allocations
- singp = intr.sing[ising]
- singp.vmat = zeros(ComplexF64, intr.mpert, 2*intr.mpert, 2, 2*ctrl.sing_order + 1)
- singp.mmat = zeros(ComplexF64, intr.mpert, 2*intr.mpert, 2, 2*ctrl.sing_order + 3)
- singp.power = zeros(ComplexF64, 2*intr.mpert)
-
- if ising < 1 || ising > intr.msing
- return
- end
-
- ipert0 = round(Int, ctrl.nn * singp.q, RoundFromZero) - intr.mlow + 1 # resonant perturbation
- if ipert0 <= 0 || intr.mlow > ctrl.nn * singp.q || intr.mhigh < ctrl.nn * singp.q
- singp.di = 0
- return
- end
-
- # Compute ranges
- singp.r1 = [ipert0]
- singp.r2 = [ipert0, ipert0 + intr.mpert]
- singp.n1 = [i for i in 1:intr.mpert if i != ipert0]
- singp.n2 = vcat(singp.n1, [i + intr.mpert for i in singp.n1])
-
- psifac = singp.psifac
- q = singp.q
- di0 = Spl.spline_eval(intr.locstab, singp.psifac, 0)[1] / singp.psifac
- q1 = singp.q1
- rho = singp.rho
-
- # Compute Mercier criterion and singular power
- sing_mmat!(intr, ctrl, equil, ffit, ising)
- singp.m0mat = transpose(singp.mmat[singp.r1[1], singp.r2, :, 1])
- # TODO: this is a little odd. di is complex since m0 is complex (but the imaginaries are negligible),
- # its then stored in singp where the type is real, and then converted to complex again for alpha and power.
- # There's gotta be a more clear way to do this? But this is the most faithful to the Fortran
- di = singp.m0mat[1,1]*singp.m0mat[2,2] - singp.m0mat[2,1]*singp.m0mat[1,2]
- singp.di = real(di)
- singp.alpha = sqrt(-complex(singp.di))
- singp.power[ipert0] = -singp.alpha
- singp.power[ipert0 + intr.mpert] = singp.alpha
-
- write_output(outp, :dcon_out, @sprintf("%3d %11.3e %11.3e %11.3e %11.3e %11.3e %11.3e %11.3e", ising, psifac, rho, q, q1, di0, singp.di, singp.di/di0-1))
-
- # Zeroth-order non-resonant solutions
- singp.vmat .= 0
- for ipert in 1:intr.mpert
- singp.vmat[ipert, ipert, 1, 1] = 1
- singp.vmat[ipert, ipert + intr.mpert, 2, 1] = 1
- end
-
- # Zeroth-order resonant solutions
- singp.vmat[ipert0, ipert0, 1, 1] = 1
- singp.vmat[ipert0, ipert0 + intr.mpert, 1, 1] = 1
- singp.vmat[ipert0, ipert0, 2, 1] = -(singp.m0mat[1,1] + singp.alpha) / singp.m0mat[1,2]
- singp.vmat[ipert0, ipert0 + intr.mpert, 2, 1] = -(singp.m0mat[1,1] - singp.alpha) / singp.m0mat[1,2]
- det = conj(singp.vmat[ipert0, ipert0, 1, 1]) * singp.vmat[ipert0, ipert0 + intr.mpert, 2, 1] -
- conj(singp.vmat[ipert0, ipert0 + intr.mpert, 1, 1]) * singp.vmat[ipert0, ipert0, 2, 1]
- singp.vmat[ipert0, :, :, 1] ./= sqrt(det)
-
- # Higher order solutions
- for k in 1:2*ctrl.sing_order
- sing_solve!(singp, intr, k)
- end
-end
-
-# Main differences: using 1 indexing, so zeroth order is the first index, whereas Fortran used 0 indexing for these arrays. Also adapted for
-# dense f/g/k arrays here, so a lot of the LAPACK operations go under the hood.
-function sing_mmat!(intr::DconInternal, ctrl::DconControl, equil::Equilibrium.PlasmaEquilibrium, ffit::FourFitVars, ising::Int)
-
- # ongoing TODO: list here
- # figure out if there's a direct way of doing the banded->dense matrix conversion to Julia (very messy right now)
- # avoided hardcoding of binomial coefficients for cleanup
-
- # Initial allocations
- msol = 2 * intr.mpert # TODO: make sure this doesn't get updated as a global elsewhere in the Fortran
- q = zeros(Float64, 4)
- singfac = zeros(Float64, intr.mpert, 4)
- f_interp = zeros(ComplexF64, intr.mpert, intr.mpert, 4)
- g_interp = zeros(ComplexF64, intr.mpert, intr.mpert, 4)
- k_interp = zeros(ComplexF64, intr.mpert, intr.mpert, 4)
- f = zeros(ComplexF64, intr.mpert, intr.mpert, ctrl.sing_order + 1)
- f0 = zeros(ComplexF64, intr.mpert, intr.mpert)
- ff = zeros(ComplexF64, intr.mpert, intr.mpert, ctrl.sing_order + 1)
- g = zeros(ComplexF64, intr.mpert, intr.mpert, ctrl.sing_order + 1)
- k = zeros(ComplexF64, intr.mpert, intr.mpert, ctrl.sing_order + 1)
- v = zeros(ComplexF64, intr.mpert, msol, 2)
- x = zeros(ComplexF64, intr.mpert, msol, 2, ctrl.sing_order + 1)
-
- singp = intr.sing[ising]
-
- # Evaluate cubic splines
- # TODO: third derivative has some error, but only included via sing_fac[ipert0] for sing_order < 3. Tests with solovev ideal indicate little sensitivity
- # TODO: this is an annoying way to have to take apart this tuple of vectors, I think
- # this is a planned fix already (i.e. separating cubic splines)
- q .= getindex.(Spl.spline_eval(equil.sq, singp.psifac, 3), 4)
- f_interp[:, :, 1], f_interp[:, :, 2], f_interp[:, :, 3], f_interp[:, :, 4] = Spl.spline_eval(ffit.fmats, singp.psifac, 3)
- g_interp[:, :, 1], g_interp[:, :, 2], g_interp[:, :, 3], g_interp[:, :, 4] = Spl.spline_eval(ffit.gmats, singp.psifac, 3)
- k_interp[:, :, 1], k_interp[:, :, 2], k_interp[:, :, 3], k_interp[:, :, 4] = Spl.spline_eval(ffit.kmats, singp.psifac, 3)
-
- # Evaluate singfac and its derivatives
- ipert0 = singp.m - intr.mlow + 1
- mvec = intr.mlow:intr.mhigh
- singfac[:, 1] .= mvec .- ctrl.nn * q[1]
- singfac[:, 2] .= -ctrl.nn * q[2]
- singfac[:, 3] .= -ctrl.nn * q[3]
- singfac[:, 4] .= -ctrl.nn * q[4]
- singfac[ipert0, 1] = -ctrl.nn * q[2]
- singfac[ipert0, 2] = -ctrl.nn * q[3] / 2
- singfac[ipert0, 3] = -ctrl.nn * q[4] / 3
- singfac[ipert0, 4] = 0
-
- # Compute factored Hermitian F and its derivatives
- # TODO: only supports dense matrices for now, implement Banded?
- for jpert in 1:intr.mpert
- for ipert in jpert:min(intr.mpert, jpert + intr.mband)
- f[ipert, jpert, 1] = singfac[ipert, 1] * f_interp[ipert, jpert, 1]
- if ctrl.sing_order ≥ 1
- f[ipert, jpert, 2] = singfac[ipert, 1] * f_interp[ipert, jpert, 2] +
- singfac[ipert, 2] * f_interp[ipert, jpert, 1]
- end
- if ctrl.sing_order ≥ 2
- f[ipert, jpert, 3] = singfac[ipert, 1] * f_interp[ipert, jpert, 3] +
- 2 * singfac[ipert, 2] * f_interp[ipert, jpert, 2] +
- singfac[ipert, 3] * f_interp[ipert, jpert, 1]
- end
- if ctrl.sing_order ≥ 3
- f[ipert, jpert, 4] = singfac[ipert, 1] * f_interp[ipert, jpert, 4] +
- 3 * singfac[ipert, 2] * f_interp[ipert, jpert, 3] +
- 3 * singfac[ipert, 3] * f_interp[ipert, jpert, 2] +
- singfac[ipert, 4] * f_interp[ipert, jpert, 1]
- end
- if ctrl.sing_order ≥ 4
- f[ipert, jpert, 5] = 4 * singfac[ipert, 2] * f_interp[ipert, jpert, 4] +
- 6 * singfac[ipert, 3] * f_interp[ipert, jpert, 3] +
- 4 * singfac[ipert, 4] * f_interp[ipert, jpert, 2]
- end
- if ctrl.sing_order ≥ 5
- f[ipert, jpert, 6] = 10 * singfac[ipert, 3] * f_interp[ipert, jpert, 4] +
- 10 * singfac[ipert, 4] * f_interp[ipert, jpert, 3]
- end
- if ctrl.sing_order ≥ 6
- f[ipert, jpert, 7] = 20 * singfac[ipert, 4] * f_interp[ipert, jpert, 4]
- end
- end
- end
- f0 .= f[:, :, 1]
-
- # Compute product of Hermitian matrix F
- fac0 = 1
- for n in 0:ctrl.sing_order
- fac1 = 1
- for j in 0:n
- for jpert in 1:intr.mpert
- for ipert in jpert:min(intr.mpert, jpert + intr.mband)
- for kpert in max(1, ipert - intr.mband):jpert
- ff[ipert, jpert, n + 1] += fac1 * f[ipert, kpert, j + 1] * conj(f[jpert, kpert, n - j + 1])
- end
- end
- end
- fac1 *= (n - j) / (j + 1)
- end
- ff[:, :, n + 1] ./= fac0
- fac0 *= (n + 1)
- end
-
- # NOTE: In Fortran, f, g, k are stored as banded Hermitian matrices (lower triangle only),
- # with f already factored, this is passed into LAPACK which handles all of this under the hood.
- # However, for now we are using dense matrices in Julia, so ff is stored as a full matrix (both triangles),
- # and we need to fill in the upper triangle here.
- # Use Hermitian property to fill the upper triangle
- for n in 1:ctrl.sing_order
- for i in 1:intr.mpert
- for j in 1:i-1
- ff[j, i, n + 1] = conj(ff[i, j, n + 1])
- end
- end
- end
-
- # Compute non-Hermitian matrix K
- for jpert in 1:intr.mpert
- for ipert in max(1, jpert - intr.mband):min(intr.mpert, jpert + intr.mband)
- k[ipert, jpert, 1] = singfac[ipert, 1] * k_interp[ipert, jpert, 1]
- if ctrl.sing_order ≥ 1
- k[ipert, jpert, 2] = singfac[ipert, 1] * k_interp[ipert, jpert, 2] +
- singfac[ipert, 2] * k_interp[ipert, jpert, 1]
- end
- if ctrl.sing_order ≥ 2
- k[ipert, jpert, 3] = singfac[ipert, 1] * k_interp[ipert, jpert, 3] / 2 +
- singfac[ipert, 2] * k_interp[ipert, jpert, 2] +
- singfac[ipert, 3] * k_interp[ipert, jpert, 1] / 2
- end
- if ctrl.sing_order ≥ 3
- k[ipert, jpert, 4] = singfac[ipert, 1] * k_interp[ipert, jpert, 4] / 6 +
- singfac[ipert, 2] * k_interp[ipert, jpert, 3] / 2 +
- singfac[ipert, 3] * k_interp[ipert, jpert, 2] / 2 +
- singfac[ipert, 4] * k_interp[ipert, jpert, 1] / 6
- end
- if ctrl.sing_order ≥ 4
- k[ipert, jpert, 5] = singfac[ipert, 2] * k_interp[ipert, jpert, 4] / 6 +
- singfac[ipert, 3] * k_interp[ipert, jpert, 3] / 4 +
- singfac[ipert, 4] * k_interp[ipert, jpert, 2] / 6
- end
- if ctrl.sing_order ≥ 5
- k[ipert, jpert, 6] = singfac[ipert, 3] * k_interp[ipert, jpert, 4] / 12 +
- singfac[ipert, 4] * k_interp[ipert, jpert, 3] / 12
- end
- if ctrl.sing_order ≥ 6
- k[ipert, jpert, 7] = singfac[ipert, 4] * k_interp[ipert, jpert, 4] / 36
- end
- end
- end
-
- # Compute Hermitian matrix G
- for jpert in 1:intr.mpert
- for ipert in jpert:min(intr.mpert, jpert + intr.mband)
- g[ipert, jpert, 1] = g_interp[ipert, jpert, 1]
- if ctrl.sing_order < 1 continue end
- g[ipert, jpert, 2] = g_interp[ipert, jpert, 2]
- if ctrl.sing_order < 2 continue end
- g[ipert, jpert, 3] = g_interp[ipert, jpert, 3] / 2
- if ctrl.sing_order < 3 continue end
- g[ipert, jpert, 4] = g_interp[ipert, jpert, 3] / 6
- end
- end
-
- # Compute identity
- for ipert in 1:intr.mpert
- v[ipert, ipert, 1] = 1
- v[ipert, ipert + intr.mpert, 2] = 1
- end
-
- # Compute zeroth-order x1
- for isol=1:msol
- x[:, isol, 1, 1] .= v[:, isol, 2] .- k[:, :, 1] * v[:, isol, 1]
- end
- # f is prefactorized so can just use this calculation to get F⁻¹x
- x[:, :, 1, 1] = UpperTriangular(f0') \ (LowerTriangular(f0) \ x[:, :, 1, 1])
-
- # Compute higher-order x1
- for i=1:ctrl.sing_order
- for isol=1:msol
- for j=1:i
- x[:, isol, 1, i + 1] .-= ff[:, :, j + 1] * x[:, isol, 1, i - j + 1]
- end
- x[:, isol, 1, i + 1] .-= k[:, :, i + 1] * v[:, isol, 1]
- end
- x[:, :, 1, i + 1] = UpperTriangular(f0') \ (LowerTriangular(f0) \ x[:, :, 1, i + 1])
- end
-
- # Use Hermitian property to fill the upper triangle of g
- # TODO: very hacky and unclear. Eventually, completely remove all mention of banding/Hermitian storage or make it cleaner
- # Lots of stuff hidden in LAPACK calls in Fortran that we are doing manually here
- for n in 0:ctrl.sing_order
- for i in 1:intr.mpert
- for j in 1:i-1
- g[j, i, n + 1] = conj(g[i, j, n + 1])
- end
- end
- end
-
- # Compute x2
- for i=0:ctrl.sing_order
- for isol=1:msol
- for j = 0:i
- x[:, isol, 2, i + 1] .+= k[:, :, j + 1]' * x[:, isol, 1, i - j + 1]
- end
- x[:, isol, 2, i + 1] .+= g[:, :, i + 1] * v[:, isol, 1]
- end
- end
-
- # Principal terms of mmat
- singp.mmat .= 0
- r1 = singp.r1
- r2 = singp.r2
- n1 = singp.n1
- n2 = singp.n2
- j = 0
- for i = 0:ctrl.sing_order
- singp.mmat[r1, r2, :, j+1] .= x[r1, r2, :, i+1]
- singp.mmat[r1, n2, :, j+2] .= x[r1, n2, :, i+1]
- singp.mmat[n1, r2, :, j+2] .= x[n1, r2, :, i+1]
- singp.mmat[n1, n2, :, j+3] .= x[n1, n2, :, i+1]
- j += 2
- end
-
- # Shearing terms
- singp.mmat[r1, r2[1], 1, 1] .+= 0.5
- singp.mmat[r1, r2[2], 2, 1] .-= 0.5
-end
-
-"""
- sing_solve!(singp::SingType, k::Int)
-
-Solves iteratively for the next order in the power series `singp.vmat`. See equation 47 in the Glass 2016 DCON paper.
-
-Arguments
----------
-- `singp::SingType`: The singularity data structure containing all relevant matrices and parameters.
-- `k::Int`: The current order in the power series expansion.
-"""
-function sing_solve!(singp::SingType, intr::DconInternal, k::Int)
- for l in 1:k
- singp.vmat[:,:,:,k + 1] .+= sing_matmul(singp.mmat[:,:,:,l + 1], singp.vmat[:,:,:,k - l + 1])
- end
- for isol in 1:2*intr.mpert
- a = copy(singp.m0mat)
- a[1,1] -= k/2.0 + singp.power[isol]
- a[2,2] -= k/2.0 + singp.power[isol]
- det = a[1,1] * a[2,2] - a[1,2] * a[2,1]
- x = -singp.vmat[singp.r1[1], isol, :, k+1]
- singp.vmat[singp.r1[1], isol, 1, k+1] = (a[2,2]*x[1] - a[1,2]*x[2]) / det
- singp.vmat[singp.r1[1], isol, 2, k+1] = (a[1,1]*x[2] - a[2,1]*x[1]) / det
- singp.vmat[singp.n1, isol, :, k+1] ./= (singp.power[isol] + k/2.0)
- end
-end
-
-"""
- sing_matmul(a, b) -> c
-
-Matrix multiplication specific to singular matrices.
-
-Arguments
----------
-- `a::Array{ComplexF64,3}`: shape (mpert, 2 * mpert, 2)
-- `b::Array{ComplexF64,3}`: shape (mmpert, 2 * mpert, 2)
-
-Returns
--------
-- `c::Array{ComplexF64,3}`: shape (mpert, 2 * mpert, 2)
-"""
-function sing_matmul(a::Array{ComplexF64,3}, b::Array{ComplexF64,3})
- m = size(b,1)
- n = size(b,2)
-
- # consistency check
- if size(a,2) != 2*m
- error("Sing_matmul: size(a,2) = $(size(a,2)) != 2*size(b,1) = $(2*m)")
- end
-
- c = zeros(ComplexF64, size(a,1), n, 2)
-
- # main computation
- for i in 1:n
- for j in 1:2
- c[:, i, j] .+= a[:, 1:m, j] * b[:, i, 1] +
- a[:, m+1:2*m, j] * b[:, i, 2]
- end
- end
-
- return c
-end
-
-"""
- sing_get_ua!(odet::OdeState, intr::DconInternal, ctrl::DconControl)
-
-Compute the asymptotic series solution for a given singularity.
-
-- `odet`: Current ODE state (contains psifac, ua, ising, etc.)
-- `intr`: DCON internal state (contains singularity data, mpert, etc.)
-- `ctrl`: DCON control parameters (contains sing_order, etc.)
-
-Fills `ua` with the asymptotic solution vmat for the specified singular surface and psi value.
-"""
-function sing_get_ua!(odet::OdeState, intr::DconInternal, ctrl::DconControl)
-
- singp = intr.sing[odet.ising]
- r1 = singp.r1
- r2 = singp.r2
-
- # Compute distance from singular surface
- dpsi = odet.psifac - singp.psifac
- sqrtfac = sqrt(complex(dpsi))
- pfac = abs(dpsi)^singp.alpha
-
- # Compute power series via Horner's method
- odet.ua .= singp.vmat[:,:,:,2 * ctrl.sing_order + 1]
- for iorder in (2 * ctrl.sing_order - 1):-1:0
- odet.ua .= odet.ua .* sqrtfac .+ singp.vmat[:,:,:,iorder+1]
- end
-
- # Restore powers
- odet.ua[r1, :, 1] ./= sqrtfac
- odet.ua[r1, :, 2] .*= sqrtfac
- odet.ua[:, r2[1], :] ./= pfac
- odet.ua[:, r2[2], :] .*= pfac
-
- # Renormalize
- if odet.psifac < singp.psifac
- odet.ua[:, r2[1], :] .*= abs(odet.ua[r1[1], r2[1], 1]) / odet.ua[r1[1], r2[1], 1]
- odet.ua[:, r2[2], :] .*= abs(odet.ua[r1[1], r2[2], 1]) / odet.ua[r1[1], r2[2], 1]
- end
-end
-
-"""
- sing_get_ca!(odet::OdeState, intr::DconInternal)
-
-Compute the asymptotic expansion coefficients according to equation 50 in Glasser 2016 DCON paper.
-"""
-function sing_get_ca!(odet::OdeState, intr::DconInternal, ctrl::DconControl)
-
- sing_get_ua!(odet, intr, ctrl)
-
- # Build temp1
- temp1 = zeros(ComplexF64, 2*intr.mpert, 2*intr.mpert)
- temp1[1:intr.mpert, :] .= odet.ua[:, :, 1]
- temp1[intr.mpert+1:2*intr.mpert, :] .= odet.ua[:, :, 2]
-
- # Built temp2
- temp2 = zeros(ComplexF64, 2*intr.mpert, odet.msol)
- temp2[1:intr.mpert, :] .= odet.u[:, :, 1]
- temp2[intr.mpert+1:2*intr.mpert, :] .= odet.u[:, :, 2]
-
- # LU factorization and solve
- temp2 .= lu(temp1) \ temp2
- odet.ca[:, 1:odet.msol, 1] .= temp2[1:intr.mpert, :]
- odet.ca[:, 1:odet.msol, 2] .= temp2[intr.mpert+1:2*intr.mpert, :]
-end
-
-"""
- sing_der!(
- du::Array{ComplexF64,3},
- u::Array{ComplexF64,3},
- params::Tuple{DconControl, Equilibrium.PlasmaEquilibrium, DconInternal, FourFitVars, DconOutput},
- psieval::Float64
- )
-
-Evaluate the derivative of the Euler-Lagrange equations, i.e. u' in equation 24 of Glasser 2016.
-This follows the Julia DifferentialEquations package format for in place updating.
-
- ode_function!(du, u, p, t)
-
-# "Defining your ODE function to be in-place updating can have performance benefits.
-# What this means is that, instead of writing a function which outputs its solution,
-# you write a function which updates a vector that is designated to hold the solution.
-# By doing this, DifferentialEquations.jl's solver packages are able to reduce the
-# amount of array allocations and achieve better performance."
-
-Wherever possible, in-place operations on pre-allocated arrays are used to minimize memory allocations.
-All LAPACK operations are handled under the hood by Julia's LinearAlgebra package, so we can obtain a much
-more simplistic code with similar performance.
-"""
-function sing_der!(du::Array{ComplexF64, 3}, u::Array{ComplexF64, 3},
- params::Tuple{DconControl, Equilibrium.PlasmaEquilibrium,
- DconInternal, OdeState, FourFitVars, DconOutput},
- psieval::Float64)
- # Unpack structs
- ctrl, equil, intr, odet, ffit, _ = params
-
- # Spline evaluation
- odet.q = Spl.spline_eval(equil.sq, psieval, 0)[4]
- odet.singfac_vec .= 1.0 ./ (intr.mlow .- ctrl.nn * odet.q .+ (0:intr.mpert-1))
- chi1 = 2π * equil.psio
-
- # kinetic stuff - skip for now
- if false #(TODO: kin_flag)
- error("kin_flag not implemented yet")
- else
- # Evaluate splines at psieval and reshape avoiding new allocations
- # TODO: is this actually more efficient?
- Spl.spline_eval!(odet.amat, ffit.amats, psieval; derivs=0)
- amat = reshape(odet.amat, intr.mpert, intr.mpert)
- Spl.spline_eval!(odet.bmat, ffit.bmats, psieval; derivs=0)
- bmat = reshape(odet.bmat, intr.mpert, intr.mpert)
- Spl.spline_eval!(odet.cmat, ffit.cmats, psieval; derivs=0)
- cmat = reshape(odet.cmat, intr.mpert, intr.mpert)
- Spl.spline_eval!(odet.fmat, ffit.fmats, psieval; derivs=0)
- fmat = reshape(odet.fmat, intr.mpert, intr.mpert)
- Spl.spline_eval!(odet.kmat, ffit.kmats, psieval; derivs=0)
- kmat = reshape(odet.kmat, intr.mpert, intr.mpert)
- Spl.spline_eval!(odet.gmat, ffit.gmats, psieval; derivs=0)
- gmat = reshape(odet.gmat, intr.mpert, intr.mpert)
-
- # ldiv!(A,B): Compute A \ B in-place and overwriting B to store the result,
- # where A is a factorization object.
- odet.Afact = cholesky(Hermitian(amat))
- # bmat = A⁻¹ * bmat
- ldiv!(odet.Afact, bmat)
- # cmat = A⁻¹ * cmat
- ldiv!(odet.Afact, cmat)
-
- # TODO: banded matrix calculations would go here
- end
-
- # Compute du
- if false #(TODO: kin_flag)
- error("kin_flag not implemented yet")
- else
- # See equation 23 in Glasser 2016 DCON paper for derivation
- # TODO: these comments are a work in progress and should be checked, but I think they're close
- # main thing is I'm not sure where singfac comes from
-
- # du[1] = - K * u[1] + u[2]
- du[:, :, 1] .= u[:, :, 2] .* odet.singfac_vec .- kmat * u[:, :, 1]
-
- # du[1] = - F⁻¹ * K * u[1] + F⁻¹ * u[2] (remember F is already stored in factored form)
- du[:, :, 1] .= UpperTriangular(fmat') \ (LowerTriangular(fmat) \ du[:, :, 1])
-
- # du[2] = G * u[1] + K' * du[1] = G * u[1] - K^† * F⁻¹ * K * u[1] + K^† * F⁻¹ * u[2]
- du[:, :, 2] .= gmat * u[:, :, 1] .+ adjoint(kmat) * du[:, :, 1]
- du[:, :, 1] .*= odet.singfac_vec
- end
-
- # u-derivative used in GPEC
- odet.ud[:,:,1] .= du[:,:,1]
- odet.ud[:,:,2] .= -bmat * du[:,:,1] - cmat * u[:,:,1]
-end
diff --git a/src/DCON/Utils.jl b/src/DCON/Utils.jl
deleted file mode 100644
index c139991104..0000000000
--- a/src/DCON/Utils.jl
+++ /dev/null
@@ -1,126 +0,0 @@
-# This is to implement the original bubble function found in equil/utils.f
-# If you are sorting the entire array, just replace the call to bubble with
-#
-# index = sortperm(key) # for ascending order or
-# index = sortperm(key; rev = true) # for descending order
-
-# This will return the indices of the sort range in descending order
-function sortperm_subrange(key::Vector{Float64}, mrange::UnitRange{Int}; descend = true )
- sorted_inds = sort(mrange; by = i -> key[i], rev = descend)
- return collect(sorted_inds)
-end
-
-#If you want to mutate an existing index array like your original code:
-function sortperm_subrange!(key::Vector{Float64}, index::Vector{Int}, mrange::UnitRange{Int}; descend = true )
- sorted_inds = sort(mrange; by = i -> key[i], rev = descend)
- for (j, i) in enumerate(sorted_inds)
- index[first(mrange) + j - 1] = i
- end
-end
-
-function load_u_matrix(filename)
- lines = readlines(filename)
- data = [parse.(Float64, split(l)) for l in lines[2:end]]
- i_vals = Int.(getindex.(data, 1))
- j_vals = Int.(getindex.(data, 2))
- k_vals = Int.(getindex.(data, 3))
- imax = maximum(i_vals)
- jmax = maximum(j_vals)
- kmax = maximum(k_vals)
- mat = zeros(ComplexF64, imax, jmax, kmax)
- for row in data
- i = Int(row[1])
- j = Int(row[2])
- k = Int(row[3])
- re = Float64(row[4])
- im = Float64(row[5])
- mat[i, j, k] = complex(re, im)
- end
- return mat
-end
-
-"""
- init_files(out::DconOutput, path::String)
-
-Open all requested output files into `path` and store handles.
-"""
-function init_files(out::DconOutput, path::String)
- for pname in propertynames(out)
- if startswith(String(pname), "write_") && getproperty(out, pname)
- base_str = String(pname)[7:end] # remove write_ prefix
- base = Symbol(base_str) # key for handles
- fname_field = Symbol("fname_" * base_str) # add fname_ prefix
- fname = getproperty(out, fname_field)
-
- full_path = joinpath(path, fname)
-
- if endswith(fname, ".out") || endswith(fname, ".txt")
- out.handles[base] = open(full_path, "w")
-
- elseif endswith(fname, ".h5") && !haskey(out.handles, base)
- fid = h5open(full_path, "w")
- out.handles[base] = fid
-
- else
- error("Unknown file extension for $fname, need to add to init_files!")
- end
- end
- end
- return out
-end
-
-"""
- write_output(out::DconOutput, key::Symbol, data; dsetname=nothing, slice=:)
-
-Writes `data` to the file corresponding to `key`.
-- For text files: appends a line.
-- For HDF5 files: writes into `dsetname` at `slice`.
-"""
-function write_output(out::DconOutput, key::Symbol, data; dsetname=nothing, slice=:)
- handle = out.handles[key]
-
- if handle isa IOStream
- println(handle, data)
-
- elseif handle isa HDF5.File
- if dsetname === nothing
- error("Must specify dsetname when writing to HDF5 file $key")
- end
- if haskey(handle, dsetname)
- handle[dsetname][slice...] = data
- else
- # create dataset if not present
- handle[dsetname] = data
- end
-
- else
- error("Unsupported handle type for key $key")
- end
-end
-
-"""
- close_files(out::DconOutput)
-
-Closes all open files.
-# TODO: is there a way to make the code run this if it errors out anywhere?
-# In existing state, files will remain open if there is an error, so you have
-# to manually exit and reopen Julia.
-"""
-function close_files(out::DconOutput)
- for (key, handle) in out.handles
- close(handle)
- end
- empty!(out.handles)
-end
-
-"""
- chebyshev_nodes(a::Float64, b::Float64, N::Int)
-Generates `N` Chebyshev-Lobatto nodes in the interval `[a, b]`
-in ascending order.
-"""
-# TODO: this is no longer used, but might be useful code? Leaving for now, but likely can be removed
-function chebyshev_nodes(a::Float64, b::Float64, N::Int)
- j = 0:N-1
- nodes = (a+b)/2 .+ (b-a)/2 .* cos.(π * j ./ (N - 1))
- return reverse(nodes)
-end
\ No newline at end of file
diff --git a/src/DCON/fortran/README b/src/DCON/fortran/README
deleted file mode 100644
index b15071f571..0000000000
--- a/src/DCON/fortran/README
+++ /dev/null
@@ -1,897 +0,0 @@
-Determining the MHD Stability of Axisymmetric Toroidal Plasmas
-================================================================
-
-:Version:
- 3.60, September 5, 2002
-:Author:
- Alan H. Glasser
-:Location:
- Los Alamos National Laboratory
-:Phone:
- 505-667-7723
-:Email:
- ahg@lanl.gov
-
-Section 1. Introduction
------------------------
-
-DCON is a code for determining the MHD stability of static
-axisymmetric toroidal plasma. It uses a very efficient algorithm,
-originally developed by Newcomb [W. A. Newcomb, Ann. Phys. 10, 232
-(1960)] for cylindrical plasmas and generalized by myself to
-axisymmetric plasmas. A preprint of a manuscript containing the theory
-of DCON is available in the tex subdirectory of this distribution in
-both Plain TeX and PostScript formats. The algorithm involves
-integrating a system of ordinary differential equations (ODE's), the
-Euler-Lagrange equations for minimizing the potential energy delta_W
-from the magnetic axis to the plasma edge. A plasma response matrix W_P
-is constructed from the solutions. If the smallest inverse eigenvalue
-of W_P changes sign, there is an unstable internal (fixed-boundary)
-mode. The eigenvalues of W_P are combined with a vacuum response matrix
-W_V to form a total response matrix W_T = W_P + W_V. If W_T has any
-negative eigenvalues, there is an unstable external (free-boundary)
-mode. The name DCON is an acronym for the Direct Criterion of Newcomb.
-The code makes no effort to determine growth rates of unstable modes or
-frequencies of the stable spectrum, but only to determine whether the
-system supports unstable modes. The distance of a zero crossing from
-the plasma edge can be used to quantify the degree of instability for an
-internal mode, while the total perturbed potential energy can be used
-for this purpose for a free-boundary mode.
-
-The present version of DCON evaluates the Mercier criterion D_I
-> 0 for unstable localized ideal interchange modes; the related
-criterion D_R > 0 of Glasser, Greene, and Johnson for localized
-resistive interchange modes; the criterion C_A < 0 for ideal MHD
-ballooning modes in the limit of large toroidal mode number; the
-generalized Newcomb criterion for the internal ideal MHD stability of
-one low toroidal mode number; and the plasma, vacuum, and total response
-matrices and their eigenvalues for determining free-boundary stability.
-A future version of DCON will treat resistive instabilities.
-
-In addition to MHD stability, there is a code ORBIT for tracking
-the full Hamiltonian orbits of charged particles in the same equilibrium
-fields used by DCON. The full-orbit equations are integrated with a
-very efficient adaptive ODE solver with high accuracy, both inside and
-outside the separatrix, and with extensive graphical output. Full
-orbits and drift orbits have complementary uses. For particles with
-small Larmor radius, such as thermal ions and electrons, drift orbits
-are both more efficient and more accurate, especially for long
-trajectories. For particles with large Larmor radius, such as beam
-ions, full orbits are more efficient and more accurate. Drift orbits
-will be added to ORBIT in a later release, allowing the best of both
-worlds and comparisons between them.
-
-Both DCON and ORBIT are written entirely in high-level Fortran 90.
-They make extensive use of dynamic allocation and deallocation to
-allow maximum use of available memory. They use many other advanced
-features of Fortran 90, such as derived types, array syntax, and
-modules. There are no fixed dimensions of large arrays, no goto
-statements, and no common blocks. Extensive use is made of BLAS and
-LAPACK linear algebra routines for efficiency. There are interfaces to
-a large number of commonly-used equilibrium data types for specifying
-equilibria. Adding to these is usually very simple, and I would be glad
-to help. Graphic output from DCON is viewed with the XDRAW graphics
-code, which is distributed as part of the package and runs on any X
-Window system.
-
-This document is a guide to preparing input for DCON and ORBIT
-and interpreting their output.
-
-
-Section 2. Straight-Fieldline Coordinates
------------------------------------------
-
-A major new feature of dcon_3.50 is the use of generalized
-straight-fieldline (SFL) coordinates. Previous versions have used only
-one type of these, Hamada coordinates.
-
-For any flux coordinate system, one coordinate, psi, labels the
-flux surface, and its gradient is orthogonal to the equillibrium
-magnetic field; the other two, theta and zeta, are angle-like quantities
-that parameterize the position around the torus the short and long way,
-respectively. In DCON, psi is linear in the poloidal flux and
-normalized to go from 0 at the magnetic axis to 1 at the last closed
-flux surface. Occasionally, rho=sqrt(psi) is used for graphical
-purposes as a radius-like variable. Theta and zeta are normalized to
-increase by 1 (not twopi) in going one full turn around the torus.
-
-A flux coordinate system is an SFL coordinate system for which
-the safety factor
-
-q = (B.del zeta) / (B.del theta)
-
-is a function of psi only. A particular SFL coordinate system is
-defined by the variation of (B.del theta) (which is proportional to the
-inverse of the Jacobian of the coordinate system) along the field line.
-The coordinate systems incorporated into dcon have B.del theta
-proportional to B_p**power_bp * B**power_b / R**power_r, with B_p the
-poloidal field strength, B the total field strength, R the major radius,
-and power_bp, power_b, and power_r input integers. Some commonly-used
-and named coordinate systems are:
-
-========== ========== ======= ========
-name power_bp power_b power_r
-========== ========== ======= ========
-hamada 0 0 0
-pest 0 0 2
-equal_arc 1 0 0
-boozer 0 2 0
-========== ========== ======= ========
-
-
-The (ignorable) toroidal coordinate is::
-
- zeta = phi/twopi + nu(psi,theta),
-
-where nu is a single-valued function of theta. PEST coordinates have
-the unique property that nu = 0 and the toroidal coordinate is
-proportional to the conventional polar angle phi. For all other SLF
-coordinate system, nu /= 0.
-
-PEST coordinates are well-adapted to high-aspect-ratio, circular
-equilibria. For low-aspect-ratio, strongly-shaped equilibria, detailed
-numerical comparisons with DCON show that Hamada coordinates generally
-have the best Fourier convergence properties, and others are worse in
-proportion to their departure from Hamada. Increasing power_r, as in
-PEST coordinates, leads to reduced resolution on the outboard side of
-the torus. Increasing power_b, as in equal_arc coordinates, leads to
-reduced resolution in the neighborhood of an x-point. The user is
-advised to use Hamada coordinates, the default. When using others,
-proceed with caution, increase the number of Fourier components, and
-monitor the convergence.
-
-
-Section 3. Installation
------------------------------------------
-
-The easiest way to unpack dcon_3.50.tar.gz is:
-
-gzip -cd dcon_3.50.tar.gz | tar -xvf -
-
-It will create a subdirectory ./dcon_3.50 and place its files there.
-The contents of the dcon package are as follows:
-
-============ =======================================================
-README: this file.
-equil: source code for equilibrium data processing
-dcon: source code for DCON, stability code
-match: source code for MATCH, future code for resistive modes
-orbit: source code for ORBIT, full-orbit particle tracking
-multi: source code for MULTI, multiple runs of DCON
-sum: source code for SUM, data extraction from MULTI runs
-draw: xdraw control files draw*.in
-equilibria: sample equilibrium files
-input: dcon control files
-lsode: source code for ODE solver
-makefile: master makefile for all codes on all machines
-tex: preprint on the theory of DCON and equations for ORBIT
-vacuum: source code for Morrell Chance's VACUUM code
-xdraw: source code for XDRAW graphics code
-============ =======================================================
-
-DCON has been set up and tested on the following machines:
-
-SGI Octane running the IRIX 6.4 operating system
-Sun SparcStations running the SunOS operating system
-DEC Alpha running OSF1 operating system
-PC Compatibles running Red Hat Linux 6.0 with Absoft Pro Fortran 6.0
-IBM running AIX
-
-If yours is one of these, do "cd dcon" and type make. It will
-automatically make all its components, create a directory rundir and a
-subdirectory with the name of your operating system, and copy the
-executables and a few selected input files to that directory. This is
-where you should work. You may want to do:
-
-nohup make > make.log &
-
-to launch a separate process which will keep a log of its actions and
-any errors.
-
-If your machine is not among these, you should create a makefile in each
-of the subdirectories with the name makefile_`uname`, where `uname` is
-the first word of the output when you type the command "uname -a". The
-makefile should contain definitions of your Fortran 90 compiler and
-links to existing LAPACK, BLAS, and X11 libraries. Then type "make"
-while in ./dcon_3.50.
-
-
-Section 4. EQUIL Input
------------------------------------------
-
-Both DCON and ORBIT use EQUIL to process the equilibrium data.
-EQUIL is controlled primarily by equil.in. It contains two Fortran 90
-namelists: equil_control and equil_output. The equil_control namelist
-contains most of the input parameters needed to control the equilibrium
-operations of the code. The equil_output namelist controls auxiliary
-output which is mostly used to diagnose problems. For the most part,
-these may be left false and ignored. In this and other namelist input
-files, all input parameters have reasonable default values.
-
-Here is an explanation of the input parameters in the first
-namelist equil_control, along with typical input values and extensive
-commentary.
-
-eq_type="efit"
-
-This specifies the type of the input file. It allows DCON to determine
-whether the file is ascii or binary, whether it is direct or inverse,
-and how to interpret the data. Here is a list of allowed types:
-
-============ ============================= ============ ========
-Name Description Data Type Format
-============ ============================= ============ ========
-"fluxgrid" NIMROD data file inverse ascii
-"miller" Bob Miller's TOQ code inverse binary_8
-"chease" Lausanne CHEASE code, 8-byte inverse binary_8
-"chease4" Lausanne CHEASE code inverse binary_4
-"chum" Modified Miller code inverse binary_4
-"galkin" Sergei Galkin's code inverse binary_8
-"efit" GA EFIT code direct ascii
-"rsteq" ORNL RSTEQ code direct binary_8
-"ldp_d" Don Pearlstein's TEQ code direct binary_8
-"ldp_i" Don Pearlstein's inverse code inverse binary_8
-"jsolver" Steve Jardin's JSOLVER code inverse ascii
-"lez" Leonid Zakharov'v code inverse binary_4
-"transp" Data from the TRANSP code inverse ascii
-"sontag" Aaron Sontag's direct solver direct ascii
-============ ============================= ============ ========
-
-In addition, you may specify eq_type="lar" or "soloviev" to get the two
-analytical equilibria. See below for more details.
-
-eq_filename="../equilibria/efit/82205-1.25X"
-
-This gives the path of the data file specifying the equilibrium. The
-file may be ascii or binary. It may be the output of a direct
-Grad-Shafranov solver, which specifies poloidal flux, R*B_phi, pressure,
-and safety factor on a 1D grid of flux surfaces, and the poloidal flux
-psi on a 2D grid in R and Z; or of an inverse solve, which replaces
-psi(R,Z) with values of R and Z on a 2D grid of psi and theta on flux
-surfaces.
-
-The next three input quantities,
-
-jac_type="hamada"
-power_b=0
-power_r=0
-
-are used to control the type of straight-fieldline coordinate system
-used (see discussion above). If jac_type is one of those listed in the
-table above, the code automatically chooses power_b and power_r
-accordingly and ignores the input values. To use any other values,
-choose jac_type="other" and set the integer variables power_b and
-power_r.
-
-Next come specifications of grid parameters.
-
-=============== ============================================
-grid_type="ldp" type of radial grid packing
-psilow=1e-4 minimum value of psi, normalized from 0 to 1
-psihigh=1 maximum value of psi, normalized from 0 to 1
-mpsi=128 number of radial grid intervals
-mtheta=128 number of poloidal grid intervals
-=============== ============================================
-
-There are several options for radial grid types. The first,
-grid_type="rho", distributes radial grid points uniformly in
-rho=sqrt(psi), a generalized radius. The second, grid_type="ldp", uses
-a method suggested by L. Don Pearlstein (LDP), which packs the grid in
-the neighborhood of the axis and the edge. I have a slight preference
-for "ldp", but they both work well. A third type, "original", uses the
-same radial grid used in the input data. (Sorry, there's no "extra
-crispy" option.) The poloidal grid is uniformly distributed in the
-straight-fieldline coordinate theta. Throughout the code, cubic spline
-and Fourier representations are used to minimize the effects of grid
-discreteness.
-
-The input parameter psilow is used only for grid_type="ldp". A good
-value is 1e-4. For the most part, results are insensitive to this
-value, but substantially smaller values cause the code to run longer,
-and substantially larger values may cause accuracy problems.
-
-The input parameter psihigh determines how close to the edge the ODE's
-are integrated. It must be <= 1. For an inverse equilibrium, which
-never has a separatrix in the computational domain, it may be set to 1.
-For a direct equilibrium with a separatrix, psihigh determines how close
-the code approaches the separatrix. Since the safety factor q goes
-logarithmically to infinity at a separatrix, the required number of
-poloidal harmonics increases with q (see below), and the run time
-increases with both the number of harmonics and the number of singular
-surfaces,it can be expensive to choose psihigh very close to 1.
-
-The next input parameter is
-
-newq0=0
-
-For newq0 = 0, the code uses the original q profile specified in the
-equilibrium file. For newq0 /= 0, it readjusts the q profile to give
-the specified value of q at the axis, in such a way as to leave the
-Grad-Shafranov solution invariant. This can be used to explore the
-stability of a range of equilibria for each equilibrium file.
-
-The final input parameter in equil_control is
-
-input_only=f
-
-This is occasionally used in the course of debugging interfaces to new
-equilibrium file types. It causes the code to generate information
-about the input and then quit.
-
-The equil_output namelist of equil.in determines which auxiliary
-output files are produced. These are primarily of interest to me, the
-developer, and of very little interest to users. For most code
-operation, they should all be left off (f). Turning them on (t) when
-they are not used wastes cpu time and disk space. The ascii files are
-readable by any text editor and can also be printed. The binary files
-are intended for viewing with XDRAW. Here is a brief description of the
-optional output files.
-
-=============== ======================================================
-gse_flag=f produces diagnostic output for accuracy of solution to
- Grad-Shafranov equation
-
-out_eq_1d=f ascii output of 1D equilibrium file data
-bin_eq_1d=f binary output of 1D equilibrium file data
-
-out_eq_2d=f ascii output of 1D equilibrium file data
-bin_eq_2d=f binary output of 2D equilibrium file data
-
-out_2d=f ascii output of processed 2D data
-bin_2d=f binary output of processed 2D data
-=============== ======================================================
-
-There are two other input files, each containing a single
-namelist. The first, lar.in, is for large-aspect-ratio, circular cross,
-low beta equilibrium, using the Shafranov expansion to second order.
-The second, sol.in, is for the Soloviev equilibrium.
-
-The lar_input namelist of equil.in is used when eq_type="lar"
-and eq_filename="lar.in". This allows the user to construct a
-large-aspect-ratio, circular-cross-section equilibrium, using the
-Shafranov expansion to second order, specifying minor radius a, major
-radius r0, central pressure ratio beta0, and central safety factor q0.
-The pressure profile is given by p0*(1-(r/a)**2)**p_pres, and the default
-profile of sigma=J.B/B^2 is sigma0/(1+(r/a))**(2*p_sig))**(1+1/p_sig).
-Specifying sigma_type="wesson" changes the functional form of sigma to a
-simpler "Wesson-like" sigma0*(1-(r/a)**2)**p_sig. Additional profiles
-would be simple to add. Here are sample input parameters:
-
-===================== ======================================================
-ma=64 number of radial grid points
-mtau=64 number of azimuthal grid points
-
-lar_r0=10 major radium
-lar_a=1 minor radius
-
-beta0=0 value of beta (pressure ratio) on axis
-q0=3.2 value of q (safety factor) on axis
-
-p_pres=2 power used in specifying pressure profile
-p_sig=2 power used in specifying current profile
-
-sigma_type='default' functional form of sigma profile
- ('default' or 'wesson')
-===================== ======================================================
-
-The sol_input namelist of equil.in is used when
-eq_type="soloviev" and eq_filename="sol.in". See Berger et al
-[D. Berger,L.C. Bernard, R. Gruber,and 6. Troyon, J. Appl. Math.
-Phys. (ZAMP) 31 (1980) 113] for a published stability analysis of this
-equilibrium. Here are input parameters:
-
-=============== ======================================================
-mr=128 number of radial grid points
-mz=128 number of axial grid points
-ma=128 number of flux surfaces for surface quantities
-
-e=1 vertical elongation factor
-a=1 minor radius
-r0=3 major radius
-q0=1.26 value of q (safety factor) on axis
-=============== ======================================================
-
-
-
-Section 5. DCON Input
------------------------------------------
-
-The stability operations of DCON are controlled by the file
-dcon.in, containing two namelists, dcon_control and dcon_output. The
-first begins with a set of flags which determine which features of DCON
-are exercised:
-
-=========== ===========================================================================
-bal_flag=t Ideal MHD ballooning criterion for short wavelengths
-mat_flag=t Construct coefficient matrices for diagnostic purposes
-ode_flag=t Integrate ODE's for determining stability of internal long-wavelength mode
-vac_flag=t Compute plasma, vacuum, and total energies for free-boundary modes
-=========== ===========================================================================
-
-Next come values determining mode numbers:
-
-nn=1
-delta_mlow=4
-delta_mhigh=8
-delta_mband=0
-sing_start=0
-
-For each run of the code, there is a single toroidal mode number nn and
-a range of poloidal mode numbers from mlow to mhigh. The most unstable
-modes are those which bend the field line lease, for which m-nn*q is as
-small as possible. The code chooses mlow and mhigh as follows:
-
-mlow=MIN(nn*qmin,0._r8)-4-delta_mlow
-mhigh=nn*qmax+delta_mhigh
-mpert=mhigh-mlow+1
-
-where mpert is the total number of perturbed mode numbers. The purpose
-of delta_mlow and delta_mhigh is to give the user some control over the
-range of mode numbers. For fixed-boundary modes, I have found
-empirically that the code works well with delta_mlow = delta_mhigh = 0,
-and increasing them increases the run time of the code without
-substantially improving the accuracy (at least for Hamada coordinates).
-For free-boundary modes, they should be positive, high enough to
-accommodate the band width of the equilibrium shape. A good way to
-choose them is to set newq0 = 0 and run the code several times with
-increasing values of delta_mlow and delta_mhigh to find when convergence
-is obtained.
-
-In principle, DCON should work for any toroidal mode number nn. In
-practice, the larger the value of nn, the more singular surfaces there
-are and the more harmonics it uses, so the longer it runs. Run time
-increases quite fast with increasing nn. I have mostly used it for nn <=
-15. There is an option controlled by the parameter
-
-sing_start=0
-
-which is intended for operation with higher values of nn. With
-sing_start=0, integration is initialized near the magnetic axis. For
-sing_start > 0, it is initialized at singular surface number sing_start.
-This reduces the work necessary, at the possible expense of accuracy.
-With sing_start > 0, a different method is used to determine mlow. with
-mmin the minimum value of nn*q between the starting singular surface and
-the plasma edge, mlow is chosen as:
-
-mlow=mmin-delta_mlow
-
-Using sing_start > 0, I have tested DCON up to nn = 15.
-
-DCON is designed to use banded matrices, which couple each poloidal
-harmonic m to only the nearest harmonics, out to m +/- mband. This was
-intended to make it efficient to treat nearly cylindrical equilibria.
-While there is no serious penalty for using banded form, in practice it
-doesn't help much to reduce the band width mband from full. The
-limiting factor is that if mband is chosen too small, factorization of a
-key symmetric-positive-definite matrix F breaks because one or more of
-its eigenvalues goes negative. The code chooses mband as:
-
-mband=mpert-1-MAX(delta_mband,0)
-
-using the input variable:
-
-delta_mband=0
-
-For delta_mband = 0, it uses a full matrix, while for delta_mband > 0 it
-reduces the band width. The safest choice is delta_mband = 0. If the
-user chooses a value of delta_mband too large, causing F to become
-non-positive definite, the code aborts with a message advising the user
-to reduce delta_mband.
-
-The next two input variables are;
-
-mthvac=480
-thmax0=1
-
-The vacuum energy is computed with the Morrell Chance's VACUUM code.
-In general, the input to that code is controlled by vac.in. See
-./tex/vacuum/vacinput.tex for details. An exception is that one of the
-parameters in vac.in, mth, is overridden by a variable in dcon.in.
-This is done because it is needed for dynamic memory allocation, which I
-added. Mthvac is used by VACUUM as the number of points along the
-plasma-vacuum interface.
-
-Thmax0 is used for the high-n ideal ballooning stability computation.
-In principle, this requires integrating a 2nd-order ordinary
-differential equation in the poloidal angle theta from -infinity to
-infinity on each flux surface. In practice, it is done from -thmax to
-+thmax, where thmax is the number of complete cycles around the torus
-the short way. Thmax is chosen automatically to optimize both accuracy
-and speed. The value of thmax chosen internally is multiplied by the
-input variable thmax0 to allow some degree of user control. Its default
-value is 1, and it is usually best left at 1.
-
-Next come variables controlling numerical accuracy:
-
-tol_nr=1e-5
-tol_r=1e-5
-crossover=1e-2
-
-Tol_nr and tol_r are relative tolerances used in integrating the main
-system of Euler-Lagrange equations. The first controls the tolerance
-far from mode-rational surfaces, while the second controls the tolerance
-near the rational surfaces. Crossover determines the distance from the
-singular surface at which control passes from tol_nr to tol_r, expressed
-in terms of the value of m-nn*q which goes to zero at the rational
-surface. The ability to impose a tighter tolerance near the singular
-surface will be of interest primarily for the later implementation of
-resistive instabilities.
-
-singfac_min=1e-5
-
-This is used to determine the position of closest apprach to each
-singular surface. The integration terminates when m-nq reaches
-singfac_min, then restarts on the other side of the singular surface.
-
-ucrit=1e4
-
-This controls a feature of DCON required for preserving accuracy.
-Starting near the magnetic axis, the code integrates a complex system of
-ordinary differential equations of order 2*mpert, with mpert = mhigh -
-mlow + 1. There are mpert regular solutions and mpert singular
-solutions in the neighborhood of the magnetic axis; DCON follows all of
-the regular solutions. Each regular solution grows roughly as r^|m| as
-it comes out of the axis. The high-m solutions therefore grow much more
-rapidly than the low-m solutions. After a short distance, the large
-solutions could numerically overwhelm the small solutions, causing the
-computation to lose all accuracy. To prevent this, the integration is
-stopped occasionally, and the independent solution vectors are
-reorganized to eliminate this problem. Ucrit determines how often this
-is done. It should be left at 1e4 by the casual user.
-
-The final section of input, dcon_output controls stability
-output options. Many of the optional outputs of interest only to the
-developer have been removed to avoid confusion. The only remaining ones
-are:
-
-============= =============================================================
-crit_break=t determines whether the color of the crit curve (see
- below) changes after crossing a singular surface
-
-ahb_flag=f produces output on normal magnetic field eigenvalues and
- eigenfunctions at plasma-vacuum interface (in honor of
- Allen H. Boozer)
-
-mthsurf0 real variable, provides user control over number of boundary
- points used to display surface eigenfunctions for
- ahgb_flag=t. Default value 1, number of points
- increases linearly with mthsurf0
-============= =============================================================
-
-
-Section 6. VACUUM Input
------------------------------------------
-
-Computation of perturbed vacuum potential energy is performed
-with Morrell Chance's VACUUM code. This is controlled by the file
-vac.in, formerly named modivmc. It is safest to leave the variables in
-this file unchanged, with one exception. The input variable a allows
-the use of a conforming conducting wall surrounding the plasma, with a =
-0 representing a wall right on the plasma boundary; a <= 10 a wall at a
-relative distance a from form the plasma boundary, normalized to the
-plasma radius; and a > 20 a wall at infinity. Beware of very small
-values of a; the results may be inaccurate because of limited
-resolution. See M. S. Chance, Phys. Plasma 4, 6, 2161 (1997) for theory
-and code description. Subdirectory ./tex/vacuum of this directory
-contains a complete description of the input. Use LaTeX.
-
-
-Section 7. DCON Output
------------------------------------------
-
-During the running of DCON, the code writes terse messages to
-the screen to inform the user of its progress. Here is the output of a
-typical run::
-
- $
- $ dcon
- Equilibrium: ../../equilibria/efit/82205-1.25X, Type: efit
- Jac_type = hamada, power_b = 0, power_r = 0
- Diagnosing Grad-Shafranov solution
- Evaluating Mercier criterion
- Evaluating ballooning criterion
- Fourier analysis of metric tensor components
- q0 = 1.087E+00, qmin = 1.082E+00, qmax = 5.426E+00, qa = 6.119E+00
- betat = 2.843E-02, betan = 2.579E+00, betap1 = 1.033E+00
- nn = 1, mlow = -8, mhigh = 13, mpert = 22, mband = 21
- Computing F, G, and K Matrices
- Starting integration of ODE's
- psi = 1.000E-04, q = 1.087
- psi = 5.845E-01, q = 2.000
- psi = 8.024E-01, q = 3.000
- psi = 9.337E-01, q = 4.000
- psi = 9.813E-01, q = 5.000
- psi = 9.900E-01, q = 5.426
- Computing free boundary energies
- Energies: plasma = -1.773E+00, vacuum = 3.050E+00, total = 1.277E+00
- All modes stable for nn = 1.
- Total cpu time = 2.349E+01 seconds
- PROGRAM_STOP => Normal termination.
- $
-
-If there are violations of the Newcomb stability criterion, indicating
-the existence of internal (fixed-boundary) instabilities, the position
-and q-value of the zero crossing(s) are also reported to the screen as
-they occur. In that case, the free-boundary energies are not meaningful
-and are not reported.
-
-The main results of DCON are reported in four files: dcon.out,
-dcon,bin, crit.out, and crit.bin. Here is a description of their
-contents.
-
-Dcon.out echoes input parameters; gives various global
-properties of the equilibrium; lists a table of surfaces quantities,
-including the ideal and resistive interchange criteria D_I and D_R;
-lists all singular surfaces for the specified toroidal mode number nn
-and their properties; and reports zero crossings of the DCON low-n
-stability criterion. If there are any zero crossings, then the system
-is unstable to internal, or fixed-boundary, modes, and the computation
-of free-boundary energies is not meaningful and is skipped. If there
-are no zero crossings, then dcon.out gives plasma, vacuum, and total
-energy eigenvalues for free-boundary modes. The lowest total energy
-reported in the table is the stability criterion for free-boundary
-modes, also reported to the screen; negative means unstable. Following
-the table of eigenvalues is a list of the eigenvectors corresponding to
-each eigenvalue, normalized to unit magnitude. For each eigenvector,
-the component with the largest absolute value is marked with an asterisk
-"*". This is useful for identifying the dominant Fourier component of
-the most unstable mode. It is also useful to note whether the
-components for mlow and mhigh are sufficiently small, e.g. 1e-3. If
-not, this is an indication the delta_mlow and/or delta_mhigh should be
-increased.
-
-Dcon.bin contains data about equilibrium profiles and local
-stability criteria. It is viewed by doing "xdraw dcon".
-
-Crit.out and crit.bin contain the low-n internal stability
-results. Do "xdraw crit" to view the graphics file. The main result is
-in the first frame, showing the stability criterion. If this changes
-sign, the equilibrium is unstable to an internal ideal mode for the
-specified toroidal mode number nn. If it is everywhere positive, the
-system is stable to this mode number. The second frame shows the q
-profile. The crit curve and the q curve are similarly color coded,
-changing color as they cross singular surfaces. The color-change can be
-suppressed by setting crit_break=f in dcon.in, namelist dcon_output.
-This is useful for comparing different runs, using a different solid
-color for each run. Multiple files can be compared by listing their
-paths below the line "filename(s)" in drawcrit.in.
-
-If bin_2d=t in equil.in, then a graphics file 2d.bin is produced
-and may be viewed with "xdraw 2d". It produces two windows, one showing
-flux surfaces for the equilibrium, the other surfaces of constant theta.
-The latter is especially useful for comparing the angular distribution
-for different choices of straight-fieldline coordinates.
-
-If gse_flag=t in equil.in, then a graphics file gsei.bin is
-prodcued and may be viewed with "xdraw gsei". It shows log_10 of the
-Grad-Shafranov error, integrated over flux surfaces. This can be used
-to assess the accuracy of the Grad-Shafranov solution. More detailed
-local graphs of log10 error can be seen by doing "xdraw gse". A contour
-plot can be seen with "xdraw gsec". The latter two require additional
-input files, obtainable by "cp ../../draw/drawgse*.in .".
-
-
-Section 8. ORBIT Input
------------------------------------------
-
-This section describes input for controlling the ORBIT code for
-following guiding-center or full-orbit trajectories of charged
-particles, both inside and outside the separatrix.
-
-In order to follow the particle both inside and outside the
-separatrix, account must be taken of the fact that the magnetic field
-representation is different in these two regions. The Hamiltonian
-equations of motion are expressed in terms of the vector potential A,
-with the equilibrium magnetic field B = curl A and electric field E =
--grad phi - dA/dt. (The electrostatic potential phi is taken to be
-uniform at present; this could easily be changed in the future for any
-known configuration of phi.) Inside the separatrix, the flux surfaces
-are closed, the vector potential is expressed in terms of the poloidal
-coordinate theta, the toroidal field function f = R*B_T is constant on a
-flux surface, and it is most convenient to express the equations of
-motion in flux coordinates. Outside the separatrix, the flux surfaces
-are not closed, the poloidal coordinate theta is not defined, f is
-uniform, and it is most convenient to express the equations of motion in
-cylindrical coordinates. ORBIT uses flux coordinates inside the
-separatrix and cylindrical coordinates outside, and passes the particle
-between the two when it crosses the separatrix. Graphs of the orbit
-change color to indicate such a crossing.
-
-The equilibrium used by ORBIT is controlled by the same files
-equil.in, lar.in, and sol.in, described above in Section 4. For
-direct-type equilibria, the orbit is followed both inside and outside
-the separatrix, terminating if the orbit crosses a boundary of the
-computational domain. For inverse-type equilibria, the orbit is
-followed only inside the separatrix, terminating if it crosses the
-separatrix, this this is the boundary of the compuatational domain for
-inverse-type data.
-
-The ORBIT code is controlled by orbit.in, containing one
-namelist, orbit_input. The first two variables:
-
-gc_flag=t
-orbit_type="inner"
-
-determine whether to use guiding-center or full orbits and whether the
-initial particle position is specified inside or outside the separatrix
-(see below for more detail).
-
-The next three variables:
-
-particle="ion"
-ai=2
-zi=1
-
-determine whether the particle to be followed is an ion or an electron,
-and if it is an ion, its atomic weight ai and atomic number zi. If the
-particle is an electon, then ai and zi are ignored.
-
-The next three variables:
-
-psi0=.85
-theta0=0
-zeta0=0
-
-specify the particle position in straight-fieldline coordinates
-(psi,theta,zeta) for orbit_type="inner", with psi linear in the poloidal
-flux and normalized to go from 0 at the magnetic axis to 1 at the
-separatrix; and theta and zeta parameterizing position the short and
-long ways around the torus, increasing by 1 for each full circuit.
-
-The next three variables:
-
-r0=.5
-z0=0
-phi0=0
-
-specify the particle position in cylindrical coordinates (r,z,phi) for
-orbit_type="outer". The initial radial position is set to
-
-r=rs2+r0*(rmax-rs2)
-
-where rs2 is radius at which the last closed flux surface intersects the
-horizontal line through the o-point, and rmax is the right edge of the
-computational domain. The initial axial position is set to
-
-z=(zmax+zmin)/2+z0*(zmax-zmin)/2
-
-where zmin and zmax are the bottom and top edges of the computational
-domain. The initial azimuthal position phi0 is specified in radians.
-
-The next three variables:
-
-energy0=1e4
-alpha0=40
-phase0=45
-
-specify the initial particle velocity, using spherical coordinates in
-velocity space. The initial particle energy is specified in eV; alpha0
-and phase0 specify the angle of the initial velocity vector from the
-z-axis and the from the r-axis in the r-phi plane, in degrees.
-
-The next three variables:
-
-taumax=10
-report=1
-stride=5
-
-specify the duration of the run and the frequency of output. Tau is
-time in units of the transit time of the particle with its given initial
-energy at the o-point, if its velocity were purely toroidal. Taumax
-specifies the length of the run in these units. Report specifies the
-interval, in these units, at which the code reports progress to the
-screen and writes a restart file (see below). Stride specifies the
-number of internal integrator steps between graphic and tabular output
-of the orbit. Increasing stride can be used to limit the size of the
-output files, which decreasing it allows for more detail in the graphs.
-
-The next two variables:
-
-tol=1e-9
-errmax=1
-
-control and monitor numerical error. Tol is the relative tolerance
-specified to the adaptive ODE solver LSODE. Reducing tol gives tighter
-tolerance at the expense of computation time. The code monitors the
-relative change in the particle energy due to accumulated numerical
-error. If this error exceeds errmax, the code quits.
-
-The next variable:
-
-break_flag=f
-
-determines whether the graphic output changes color every time tau
-increments by report. Normally, a color change indicates the crossing
-of the separatrix. Setting break_flag=t increases the frequency of
-color change. This can be useful for cross-correlating different orbit
-segments between graphs.
-
-The next variable:
-
-cross=t
-
-determines whether the orbit is allowed to cross the separatrix for
-direct-type equilibrium data. If cross=f, the particle stops at the
-separatrix. For inversse-type equilibrium data, the orbit can only be
-followed inside the separatrix.
-
-The next variable:
-
-restart_flag=f
-
-is used to determine whether to restart the orbit from the last saved
-restart.out file. The code saves this file each time tau -> tau +
-report. If restart_flag=t, the code attempts to read this file. If it
-exists, the code ignores input values for particle type and initial
-conditions, restarts the trajectory from its last state, and uses taumax
-to specify an increment on the runtime. If restart_flag=t but
-restart.out is not found, the code resets restart_flag=f and proceeds as
-if this were the input value.
-
-The final variables:
-
-orbit_out=f
-orbit_bin=t
-
-determine whether to produce to produce tabular and graphic output for
-the orbit. Normally the values are set as shown. Setting orbit_out=t
-a tabular description of the orbit in orbit.out, which is usually not
-very useful and is time-consuming. Setting orbit_bin=f causes the
-graphical output to be suppressed.
-
-Section 9. ORBIT Input
------------------------------------------
-
-This section describes output for the ORBIT code for following
-full-orbit trajectories of charged particles, both inside and outside
-the separatrix.
-
-There is an output file orbit.out which starts with the same
-kind of equilibrium data as dcon.out, described in Section 7 above.
-Then there are a few lines of information about the orbit that was run.
-If orbit_out=t, this is followed by a long table of the orbit. This is
-not recommended: it is not very useful, it wastes time, and the
-information is better obtained in graphical form.
-
-To view the main graphical output, do "xdraw orbit". This
-produces 9 graphs:
-
-1. Radial Position, R vs. tau
-2. Axial Position, Z vs. tau
-3. Orbit in Poloidal Plane, Z vs. R
-4. Normalized Poloidal Flux, psi vs. tau
-5. Parallel Velocity, v_parallel vs. tau
-6. Orbit Viewed Along Axis, R*sin(phi) vs. R*cos(phi)
-7. Relative Change in Energy, error vs. tau
-8. Relative Change in Magnetic Moment, d_mu/mu_0
-9. Larmor Radius / Radius of Curvature, rl/R
-
-The color changes each time the particle crosses the separatrix.
-
-
-Section 10. Other documentation
------------------------------------------
-
-There is a subdirectory ./tex containing miscellaneous
-documentation. Here is a brief description.
-
-1. tex/dcon/manuscript:
-
-An unpublished manuscript on the theory of DCON.
-
-2. tex/dcon/notebook:
-
-Raw equations on the theory of DCON:
-
-dcon.tex Raw equations on the theory of DCON
-bal.tex High-n ballooning theory
-mercier.tex Expressions for the Mercier criterion
-metric.tex Expressions for the metric tensor
-
-tex/orbit:
-
-orbit.tex Raw Hamiltonian orbit equations in straight-fieldline coordinates
-
-tex/vacuum:
-
-vacinput.tex Latex file on preparing input to VACUUM.
diff --git a/src/DCON/fortran/bal.f b/src/DCON/fortran/bal.f
deleted file mode 100644
index f31b6f0319..0000000000
--- a/src/DCON/fortran/bal.f
+++ /dev/null
@@ -1,540 +0,0 @@
-c-----------------------------------------------------------------------
-c file bal.f.
-c determines high-n ideal marginal MHD ballooning stability.
-c-----------------------------------------------------------------------
-c-----------------------------------------------------------------------
-c code organization.
-c-----------------------------------------------------------------------
-c 0. bal_mod.
-c 1. bal_scan.
-c 2. bal_prep.
-c 3. bal_der.
-c 4. bal_int.
-c 5. bal_pse.
-c-----------------------------------------------------------------------
-c subprogram 0. bal_mod.
-c module declarations.
-c-----------------------------------------------------------------------
-c-----------------------------------------------------------------------
-c declarations.
-c-----------------------------------------------------------------------
- MODULE bal_mod
- USE dcon_mod
- IMPLICIT NONE
-
- INTEGER, PRIVATE :: ipsi
- REAL(r8), PRIVATE :: di,alpha,theta0=0
- REAL(r8), DIMENSION(2,2), PRIVATE :: v0
- TYPE(spline_type), PRIVATE :: bf,bg
-
- CONTAINS
-c-----------------------------------------------------------------------
-c subprogram 1. bal_scan.
-c computes ballooning stability criterion.
-c-----------------------------------------------------------------------
-c-----------------------------------------------------------------------
-c declarations.
-c-----------------------------------------------------------------------
- SUBROUTINE bal_scan
-c-----------------------------------------------------------------------
-c open output files.
-c-----------------------------------------------------------------------
- IF(out_bal1)CALL ascii_open(out_bal1_unit,"bal1.out","UNKNOWN")
- IF(out_bal2)CALL ascii_open(out_bal2_unit,"bal2.out","UNKNOWN")
- IF(bin_bal1)CALL bin_open(bin_bal1_unit,"bal1.bin","UNKNOWN",
- $ "REWIND","none")
- IF(bin_bal2)CALL bin_open(bin_bal2_unit,"bal2.bin","UNKNOWN",
- $ "REWIND","none")
-c-----------------------------------------------------------------------
-c test ballooning stability.
-c-----------------------------------------------------------------------
- DO ipsi=0,mpsi
- CALL bal_prep
- IF(di <= 0 .AND. di >= -1e4 .AND. sq%xs(ipsi) <= 1)CALL bal_int
- CALL spline_dealloc(bf)
- CALL spline_dealloc(bg)
- ENDDO
-c-----------------------------------------------------------------------
-c close output files.
-c-----------------------------------------------------------------------
- IF(out_bal1)CALL ascii_close(out_bal1_unit)
- IF(out_bal2)CALL ascii_close(out_bal2_unit)
- IF(bin_bal1)CALL bin_close(bin_bal1_unit)
- IF(bin_bal2)CALL bin_close(bin_bal2_unit)
-c-----------------------------------------------------------------------
-c terminate.
-c-----------------------------------------------------------------------
- RETURN
- END SUBROUTINE bal_scan
-c-----------------------------------------------------------------------
-c subprogram 2. bal_prep.
-c computes coefficients for the ideal marginal ballooning equations.
-c-----------------------------------------------------------------------
-c-----------------------------------------------------------------------
-c declarations.
-c-----------------------------------------------------------------------
- SUBROUTINE bal_prep
-
- LOGICAL, PARAMETER :: inverse_flag=.FALSE.
- INTEGER :: itheta,info
- INTEGER, DIMENSION(3) :: ipiv
- REAL(r8) :: chi1,det,eta,fexp,p1,psifac,q,q1,r,rfac,theta,
- $ twopif,v1
- REAL(r8), DIMENSION(2,2) :: c0,d0bar,d,v10
- REAL(r8), DIMENSION(2,2,0:mtheta) :: d1
- REAL(r8), DIMENSION(0:mtheta) :: b1,bsq,dbdb0,dbdb1,dbdb2,
- $ kappan,kappas,jac,jacfac
- REAL(r8), DIMENSION(3,3) :: v,w,temp
- TYPE(spline_type) :: spl0,spl1,spl2,spl3
-c-----------------------------------------------------------------------
-c compute surface quantities.
-c-----------------------------------------------------------------------
- psifac=sq%xs(ipsi)
- twopif=sq%fs(ipsi,1)
- p1=sq%fs1(ipsi,2)
- v1=sq%fs(ipsi,3)
- q=sq%fs(ipsi,4)
- q1=sq%fs1(ipsi,4)
- chi1=twopi*psio
- v=0
- w=0
-c-----------------------------------------------------------------------
-c compute coordinates and jacobian.
-c-----------------------------------------------------------------------
- DO itheta=0,mtheta
- CALL bicube_eval(rzphi,rzphi%xs(ipsi),rzphi%ys(itheta),1)
- theta=rzphi%ys(itheta)
- rfac=SQRT(rzphi%f(1))
- eta=twopi*(theta+rzphi%f(2))
- r=ro+rfac*COS(eta)
- jac(itheta)=rzphi%f(4)
-c-----------------------------------------------------------------------
-c compute contravariant basis vectors.
-c-----------------------------------------------------------------------
- v(1,1)=rzphi%fx(1)/(2*rfac*jac(itheta))
- v(1,2)=rzphi%fx(2)*twopi*rfac/jac(itheta)
- v(1,3)=rzphi%fx(3)*r/jac(itheta)
- v(2,1)=rzphi%fy(1)/(2*rfac*jac(itheta))
- v(2,2)=(1+rzphi%fy(2))*twopi*rfac/jac(itheta)
- v(2,3)=rzphi%fy(3)*r/jac(itheta)
- v(3,3)=twopi*r/jac(itheta)
-c-----------------------------------------------------------------------
-c compute covariant basis vectors, inverse method.
-c-----------------------------------------------------------------------
- IF(inverse_flag)THEN
- temp=TRANSPOSE(v)*jac(itheta)
- w=RESHAPE((/1,0,0,0,1,0,0,0,1/),(/3,3/))
- CALL dgetrf(3,3,temp,3,ipiv,info)
- CALL dgetrs('N',3,3,temp,3,ipiv,w,3,info)
-c-----------------------------------------------------------------------
-c compute covariant basis vectors, direct method.
-c-----------------------------------------------------------------------
- ELSE
- w(1,1)=(1+rzphi%fy(2))*twopi**2*rfac*r
- $ /jac(itheta)
- w(1,2)=-rzphi%fy(1)*pi*r/(rfac*jac(itheta))
- w(2,1)=-rzphi%fx(2)*twopi**2*r*rfac/jac(itheta)
- w(2,2)=rzphi%fx(1)*pi*r/(rfac*jac(itheta))
- w(3,1)=(rzphi%fx(2)*rzphi%fy(3)
- $ -rzphi%fx(3)*(1+rzphi%fy(2)))
- $ *twopi*r*rfac/jac(itheta)
- w(3,2)=(rzphi%fx(3)*rzphi%fy(1)
- $ -rzphi%fx(1)*rzphi%fy(3))
- $ *r/(2*rfac*jac(itheta))
- w(3,3)=1/(twopi*r)
- ENDIF
-c-----------------------------------------------------------------------
-c store physical quantities.
-c-----------------------------------------------------------------------
- b1(itheta)=SUM((v(2,:)+q*v(3,:))*v(1,:))*chi1
- bsq(itheta)=SUM((v(2,:)+q*v(3,:))**2)*chi1**2
- dbdb0(itheta)=SUM(w(1,:)**2)*q1**2
- dbdb1(itheta)=-SUM((w(3,:)-q*w(2,:))*w(1,:))*2*q1
- dbdb2(itheta)=SUM((w(3,:)-q*w(2,:))**2)
- ENDDO
-c-----------------------------------------------------------------------
-c compute curvature terms.
-c-----------------------------------------------------------------------
- CALL spline_alloc(spl0,mtheta,2)
- spl0%xs=rzphi%ys
- spl0%fs(:,1)=1/bsq
- spl0%fs(:,2)=jac*b1/bsq
- CALL spline_fit(spl0,"periodic")
- kappas=-spl0%fs1(:,1)*twopif/(2*jac)
- DO itheta=0,mtheta
- CALL bicube_eval(rzphi,rzphi%xs(ipsi),rzphi%ys(itheta),1)
- kappan(itheta)=((p1/bsq(itheta)-rzphi%fx(4)/jac(itheta))/chi1
- $ +twopif*q1/(bsq(itheta)*jac(itheta))+spl0%fs1(itheta,2)
- $ /jac(itheta))/2
- ENDDO
- CALL spline_dealloc(spl0)
-c-----------------------------------------------------------------------
-c compute coefficients for ballooning equation.
-c-----------------------------------------------------------------------
- CALL spline_alloc(bf,mtheta,5)
- bf%xs=rzphi%ys
- jacfac=jac/chi1
- bf%fs(:,1)=dbdb0/(bsq*jacfac)
- bf%fs(:,2)=dbdb1/(2*dbdb0)
- bf%fs(:,3)=(dbdb2-dbdb1**2/(4*dbdb0))/(bsq*jacfac)
- bf%fs(:,4)=2*kappan*p1/chi1*jacfac
- bf%fs(:,5)=-2*kappas*p1/chi1*q1*jacfac
- CALL spline_fit(bf,"periodic")
-c-----------------------------------------------------------------------
-c diagnose bf.
-c-----------------------------------------------------------------------
- bf%title=(/"theta ","dbdb0 ","dbdb1 ","dbdb2 ","kappas","kappan"/)
- CALL spline_write1(bf,out_bal1,bin_bal1,
- $ out_bal1_unit,bin_bal1_unit,.TRUE.)
-c-----------------------------------------------------------------------
-c initialize bg.
-c-----------------------------------------------------------------------
- CALL spline_alloc(spl0,mtheta,1)
- spl0%xs=rzphi%ys
- spl0%fs(:,1)=-p1*q1*twopif/(bsq*chi1**2)
- CALL spline_fit(spl0,"periodic")
- CALL spline_int(spl0)
- CALL spline_alloc(bg,mtheta,5)
- bg%xs=rzphi%ys
- bg%fs(:,5)=spl0%fs(:,1)-spl0%fsi(mtheta,1)
- CALL spline_dealloc(spl0)
-c-----------------------------------------------------------------------
-c compute c0.
-c-----------------------------------------------------------------------
- CALL spline_alloc(spl1,mtheta,4)
- spl1%xs=rzphi%ys
- DO itheta=0,mtheta
- c0(1,1)=.5
- c0(1,2)=1/bf%fs(itheta,1)
- c0(2,1)=-bf%fs(itheta,4)
- c0(2,2)=-.5
-c-----------------------------------------------------------------------
-c compute d0.
-c-----------------------------------------------------------------------
- spl1%fs(itheta,1)=c0(1,1)+c0(1,2)*bg%fs(itheta,5)
- spl1%fs(itheta,2)=c0(1,2)
- spl1%fs(itheta,3)=c0(2,1)
- $ +(c0(2,2)-c0(1,1)-c0(1,2)*bg%fs(itheta,5))*bg%fs(itheta,5)
- spl1%fs(itheta,4)=-spl1%fs(itheta,1)
-c-----------------------------------------------------------------------
-c compute d1.
-c-----------------------------------------------------------------------
- fexp=-c0(1,2)*bf%fs(itheta,2)*2
- d1(1,1,itheta)=fexp*bg%fs(itheta,5)
- d1(1,2,itheta)=fexp
- d1(2,1,itheta)=-fexp*bg%fs(itheta,5)**2
- d1(2,2,itheta)=-d1(1,1,itheta)
- ENDDO
-c-----------------------------------------------------------------------
-c fit to cubic splines and write output.
-c-----------------------------------------------------------------------
- CALL spline_fit(spl1,"periodic")
- CALL spline_int(spl1)
- d0bar(1,1)=spl1%fsi(mtheta,1)
- d0bar(1,2)=spl1%fsi(mtheta,2)
- d0bar(2,1)=spl1%fsi(mtheta,3)
- d0bar(2,2)=spl1%fsi(mtheta,4)
-c-----------------------------------------------------------------------
-c compute mercier criterion and alpha.
-c-----------------------------------------------------------------------
- di=d0bar(1,1)*d0bar(2,2)-d0bar(1,2)*d0bar(2,1)
- IF(di > 0)THEN
- CALL spline_dealloc(spl1)
- RETURN
- ENDIF
- alpha=SQRT(-di)
-c-----------------------------------------------------------------------
-c compute zeroth-order eigenfunctions.
-c-----------------------------------------------------------------------
- v0(1,1)=1
- v0(1,2)=1
- v0(2,1)=-(d0bar(1,1)-alpha)/d0bar(1,2)
- v0(2,2)=-(d0bar(1,1)+alpha)/d0bar(1,2)
-c-----------------------------------------------------------------------
-c store derivatives for first-order terms.
-c-----------------------------------------------------------------------
- CALL spline_alloc(spl2,mtheta,4)
- spl2%xs=rzphi%ys
- DO itheta=0,mtheta
- spl2%fs(itheta,1)
- $ =(spl1%fs(itheta,1)-alpha)*v0(1,1)
- $ +spl1%fs(itheta,2)*v0(2,1)
- spl2%fs(itheta,2)
- $ =spl1%fs(itheta,3)*v0(1,1)
- $ +(spl1%fs(itheta,4)-alpha)*v0(2,1)
- spl2%fs(itheta,3)
- $ =(spl1%fs(itheta,1)+alpha)*v0(1,2)
- $ +spl1%fs(itheta,2)*v0(2,2)
- spl2%fs(itheta,4)
- $ =spl1%fs(itheta,3)*v0(1,2)
- $ +(spl1%fs(itheta,4)+alpha)*v0(2,2)
- ENDDO
-c-----------------------------------------------------------------------
-c fit to cubic spines and integrate.
-c-----------------------------------------------------------------------
- CALL spline_fit(spl2,"periodic")
- CALL spline_int(spl2)
- spl2%fs=spl2%fsi
-c-----------------------------------------------------------------------
-c store derivatives for second-order terms.
-c-----------------------------------------------------------------------
- CALL spline_alloc(spl3,mtheta,4)
- spl3%xs=rzphi%ys
- DO itheta=0,mtheta
- spl3%fs(itheta,1)
- $ =(spl1%fs1(itheta,1)+1-alpha)*spl2%fs(itheta,1)
- $ +spl1%fs(itheta,2)*spl2%fs(itheta,2)
- $ +d1(1,1,itheta)*v0(1,1)+d1(1,2,itheta)*v0(2,1)
- spl3%fs(itheta,2)
- $ =spl1%fs(itheta,3)*spl2%fs(itheta,1)
- $ +(spl1%fs(itheta,4)+1-alpha)*spl2%fs(itheta,2)
- $ +d1(2,1,itheta)*v0(1,1)+d1(2,2,itheta)*v0(2,1)
- spl3%fs(itheta,3)
- $ =(spl1%fs(itheta,1)+1+alpha)*spl2%fs(itheta,3)
- $ +spl1%fs(itheta,2)*spl2%fs(itheta,4)
- $ +d1(1,1,itheta)*v0(1,2)+d1(1,2,itheta)*v0(2,2)
- spl3%fs(itheta,4)
- $ =spl1%fs(itheta,3)*spl2%fs(itheta,3)
- $ +(spl1%fs(itheta,4)+1+alpha)*spl2%fs(itheta,4)
- $ +d1(2,1,itheta)*v0(1,2)+d1(2,2,itheta)*v0(2,2)
- ENDDO
-c-----------------------------------------------------------------------
-c fit to cubic spines and integrate.
-c-----------------------------------------------------------------------
- CALL spline_fit(spl3,"periodic")
- CALL spline_int(spl3)
-c-----------------------------------------------------------------------
-c compute first order constants, first eigenfunction.
-c-----------------------------------------------------------------------
- d(2,1)=d0bar(2,1)
- d(1,2)=d0bar(1,2)
- d(1,1)=d0bar(1,1)+1-alpha
- d(2,2)=d0bar(2,2)+1-alpha
- det=d(1,1)*d(2,2)-d(1,2)*d(2,1)
- v10(1,1)=(d(1,2)*spl3%fsi(mtheta,2)-d(2,2)*spl3%fsi(mtheta,1))/det
- v10(2,1)=(d(2,1)*spl3%fsi(mtheta,1)-d(1,1)*spl3%fsi(mtheta,2))/det
-c-----------------------------------------------------------------------
-c compute first order constants, second eigenfunction.
-c-----------------------------------------------------------------------
- d(1,1)=d0bar(1,1)+1+alpha
- d(2,2)=d0bar(2,2)+1+alpha
- det=d(1,1)*d(2,2)-d(1,2)*d(2,1)
- v10(1,2)=(d(1,2)*spl3%fsi(mtheta,4)-d(2,2)*spl3%fsi(mtheta,3))/det
- v10(2,2)=(d(2,1)*spl3%fsi(mtheta,3)-d(1,1)*spl3%fsi(mtheta,4))/det
-c-----------------------------------------------------------------------
-c add constants to v1 and fit to cubic splines.
-c-----------------------------------------------------------------------
- bg%fs(:,1)=spl2%fs(:,1)+v10(1,1)
- bg%fs(:,2)=spl2%fs(:,2)+v10(2,1)
- bg%fs(:,3)=spl2%fs(:,3)+v10(1,2)
- bg%fs(:,4)=spl2%fs(:,4)+v10(2,2)
- CALL spline_fit(bg,"periodic")
-c-----------------------------------------------------------------------
-c diagnose bg.
-c-----------------------------------------------------------------------
-c bg%title=(/" bg1 "," bg2 "," bg2 "," bg2 "," bg2 "/)
-c CALL spline_write1(bg,out_bal1,bin_bal1,
-c $ out_bal1_unit,bin_bal1_unit,.FALSE.)
-c-----------------------------------------------------------------------
-c deallocate local splines.
-c-----------------------------------------------------------------------
- CALL spline_dealloc(spl1)
- CALL spline_dealloc(spl2)
- CALL spline_dealloc(spl3)
-c-----------------------------------------------------------------------
-c terminate.
-c-----------------------------------------------------------------------
- RETURN
- END SUBROUTINE bal_prep
-c-----------------------------------------------------------------------
-c subprogram 3. bal_der
-c differential equations for the marginal ballooning.
-c-----------------------------------------------------------------------
-c-----------------------------------------------------------------------
-c declarations.
-c-----------------------------------------------------------------------
- SUBROUTINE bal_der(neq,theta,y,dy)
-
- INTEGER, INTENT(IN) :: neq
- REAL(r8), INTENT(IN) :: theta
- REAL(r8), DIMENSION(neq), INTENT(IN) :: y
- REAL(r8), DIMENSION(neq), INTENT(OUT) :: dy
-
- REAL(r8) :: dbdb,kappaw,thfac
-c-----------------------------------------------------------------------
-c compute coefficients.
-c-----------------------------------------------------------------------
- CALL spline_eval(bf,theta,0)
- thfac=theta-theta0
- dbdb=bf%f(1)*(thfac+bf%f(2))**2+bf%f(3)
- kappaw=bf%f(4)+thfac*bf%f(5)
-c-----------------------------------------------------------------------
-c compute derivatives.
-c-----------------------------------------------------------------------
- dy(1)=y(2)/dbdb
- dy(2)=-y(1)*kappaw
-c-----------------------------------------------------------------------
-c terminate.
-c-----------------------------------------------------------------------
- RETURN
- END SUBROUTINE bal_der
-c-----------------------------------------------------------------------
-c subprogram 4. bal_int
-c integrates the ideal marginal ballooning equations.
-c-----------------------------------------------------------------------
-c-----------------------------------------------------------------------
-c declarations.
-c-----------------------------------------------------------------------
- SUBROUTINE bal_int
-
- INTEGER, PARAMETER :: neq=2,liw=20,lrw=22+neq*16
- INTEGER, DIMENSION(liw) :: iwork=0
- INTEGER :: iopt,iside,istate,itask,itol,jac,mf
- INTEGER :: istep,nstep=HUGE(0),icross
- REAL(r8), PARAMETER :: tol=1e-5,thmin=1,hu_min=1e-10
- REAL(r8) :: thmax,atol,ca1,ca2,det,rtol,theta,thout
- REAL(r8), DIMENSION(lrw) :: rwork=0
- REAL(r8), DIMENSION(neq) :: y,dy
- REAL(r8), DIMENSION(2,2) :: u
-c-----------------------------------------------------------------------
-c write formats.
-c-----------------------------------------------------------------------
- 10 FORMAT(/2x,"ist",2x,"nqu",1x,"icr",4x,"theta",6x,"dtheta",4x,
- $ "asinh y1",2x,"asinh ca1",2x,"asinh ca2"/)
- 20 FORMAT(i5,2i4,1x,1p,5e11.3)
-c-----------------------------------------------------------------------
-c initialize independent variables.
-c-----------------------------------------------------------------------
- thmax=SQRT(MAXVAL(ABS(bf%fs(:,3)/bf%fs(:,1))))*10*thmax0
- thmax=MIN(thmax,100._r8)
- theta=-thmax
- thout=thmax
- istep=0
-c-----------------------------------------------------------------------
-c compute equilibrium quantities and asymptotic solutions.
-c-----------------------------------------------------------------------
- CALL bal_pse(theta,u)
- y(1)=u(1,2)*sinh(1.)
- y(2)=u(2,2)*sinh(1.)
-c-----------------------------------------------------------------------
-c set up integrator parameters.
-c-----------------------------------------------------------------------
- icross=0
- iside=1
- istate=1
- itask=5
- mf=10
- rwork(1)=thout
- iopt=1
- itol=1
- rtol=tol
- atol=tol*tol
-c-----------------------------------------------------------------------
-c write header.
-c-----------------------------------------------------------------------
- IF(out_bal2)WRITE(out_bal2_unit,10)
-c-----------------------------------------------------------------------
-c check for crossings.
-c-----------------------------------------------------------------------
- DO
- IF(iside*y(1) < 0)THEN
- icross=icross+1
- iside=-iside
- ENDIF
-c-----------------------------------------------------------------------
-c compute and print asymptotic coefficient.
-c-----------------------------------------------------------------------
- IF(out_bal2 .OR. bin_bal2)THEN
- IF(ABS(theta) > thmin)THEN
- CALL bal_pse(theta,u)
- det=u(1,1)*u(2,2)-u(1,2)*u(2,1)
- ca1=(y(1)*u(2,2)-y(2)*u(1,2))/det
- ca2=(y(2)*u(1,1)-y(1)*u(2,1))/det
- CALL bal_der(neq,theta,y,dy)
- IF(out_bal2)
- $ WRITE(out_bal2_unit,20)istep,iwork(14),icross,
- $ theta,rwork(11),asinh(y(1)),asinh(ca1),asinh(ca2)
- IF(bin_bal2)
- $ WRITE(bin_bal2_unit)REAL(theta,4),
- $ REAL(asinh(y(1)),4),REAL(asinh(y(2)),4),
- $ REAL(y(2)/dy(1),4),REAL(dy(2)/y(1),4),
- $ REAL(asinh(ca1),4),REAL(asinh(ca2),4),REAL(u,4)
- ELSE
- ca1=0
- ca2=0
- det=0
- ENDIF
- ENDIF
-c-----------------------------------------------------------------------
-c advance.
-c-----------------------------------------------------------------------
- IF(istep >= nstep .OR. theta >= thmax .OR. istate < 0)EXIT
- istep=istep+1
- CALL lsode(bal_der,neq,y,theta,thout,itol,rtol,atol,itask,
- $ istate,iopt,rwork,lrw,iwork,liw,jac,mf)
- IF(rwork(11) < hu_min)EXIT
- ENDDO
-c-----------------------------------------------------------------------
-c write trailer.
-c-----------------------------------------------------------------------
- IF(out_bal2)WRITE(out_bal2_unit,10)
- IF(bin_bal2)WRITE(bin_bal2_unit)
-c-----------------------------------------------------------------------
-c compute and store final asymptotic coefficients.
-c-----------------------------------------------------------------------
- IF(theta >= thmax)THEN
- CALL bal_pse(theta,u)
- det=u(1,1)*u(2,2)-u(1,2)*u(2,1)
- ca1=(y(1)*u(2,2)-y(2)*u(1,2))/det
- ca2=(y(2)*u(1,1)-y(1)*u(2,1))/det
- locstab%fs(ipsi,4:5)=(/ca1,ca2/)
- ENDIF
-c-----------------------------------------------------------------------
-c terminate.
-c-----------------------------------------------------------------------
- RETURN
- END SUBROUTINE bal_int
-c-----------------------------------------------------------------------
-c subprogram 5. bal_pse.
-c computes alpha series solutions.
-c-----------------------------------------------------------------------
-c-----------------------------------------------------------------------
-c declarations.
-c-----------------------------------------------------------------------
- SUBROUTINE bal_pse(theta,u)
-
- REAL(r8), INTENT(IN) :: theta
- REAL(r8), INTENT(OUT), DIMENSION(2,2) :: u
-
- REAL(r8) :: dtheta,thfac
- REAL(r8), DIMENSION(2,2) :: v
-c-----------------------------------------------------------------------
-c compute alpha series.
-c-----------------------------------------------------------------------
- CALL spline_eval(bg,theta,0)
- dtheta=theta-theta0
- v(1,1)=v0(1,1)+bg%f(1)/dtheta
- v(2,1)=v0(2,1)+bg%f(2)/dtheta
- v(1,2)=v0(1,2)+bg%f(3)/dtheta
- v(2,2)=v0(2,2)+bg%f(4)/dtheta
-c-----------------------------------------------------------------------
-c compute transformed solutions.
-c-----------------------------------------------------------------------
- u(1,1)=v(1,1)
- u(1,2)=v(1,2)
- u(2,1)=bg%f(5)*v(1,1)+v(2,1)
- u(2,2)=bg%f(5)*v(1,2)+v(2,2)
-c-----------------------------------------------------------------------
-c multiply by alphas.
-c-----------------------------------------------------------------------
- thfac=ABS(dtheta)**(alpha+.5)/dtheta
- u(1,1)=u(1,1)*thfac
- u(2,1)=u(2,1)*thfac*dtheta
- u(1,2)=u(1,2)/(thfac*dtheta)
- u(2,2)=u(2,2)/thfac
-c-----------------------------------------------------------------------
-c terminate.
-c-----------------------------------------------------------------------
- RETURN
- END SUBROUTINE bal_pse
- END MODULE bal_mod
diff --git a/src/DCON/fortran/dcon b/src/DCON/fortran/dcon
deleted file mode 100644
index 9c799258f8..0000000000
Binary files a/src/DCON/fortran/dcon and /dev/null differ
diff --git a/src/DCON/fortran/dcon.F b/src/DCON/fortran/dcon.F
deleted file mode 100644
index 0fe960de8a..0000000000
--- a/src/DCON/fortran/dcon.F
+++ /dev/null
@@ -1,430 +0,0 @@
-c-----------------------------------------------------------------------
-c file dcon.f.
-c performs ideal MHD stability analysis.
-c-----------------------------------------------------------------------
-c-----------------------------------------------------------------------
-c code organization.
-c-----------------------------------------------------------------------
-c 1. dcon.
-c 2. dcon_dealloc.
-c-----------------------------------------------------------------------
-c subprogram 1. dcon.
-c performs ideal & kinetic MHD stability analysis.
-c-----------------------------------------------------------------------
-c-----------------------------------------------------------------------
-c declarations.
-c-----------------------------------------------------------------------
- PROGRAM dcon
- USE equil_mod
- USE equil_out_mod
- USE bal_mod
- USE mercier_mod
- USE ode_mod
- USE free_mod
- USE resist_mod
- USE pentrc_interface, ! rename overlapping names
- $ pentrc_verbose=>verbose, ! should get a more fundamental fix
- $ pentrc_mpert=>mpert,
- $ pentrc_nn=>nn,
- $ pentrc_r8=>r8,
- $ pentrc_timer=>timer
- IMPLICIT NONE
-
- LOGICAL :: use_classic_splines_for_dcon=.FALSE., cyl_flag=.FALSE.,
- $ reform_eq_with_psilim=.FALSE.
- INTEGER :: mmin,ipsi,m,peak_index
- COMPLEX(r8) :: plasma1,vacuum1,total1
-
- INTEGER, DIMENSION(:), ALLOCATABLE :: mtmp
- REAL(r8), DIMENSION(:), ALLOCATABLE :: psitmp
- COMPLEX(r8), DIMENSION(:,:), ALLOCATABLE :: xtmp
-
- ! harvest variables
- INCLUDE 'harvest_lib.inc77'
- INTEGER :: ierr
- INTEGER :: hint = 0
- REAL(r8) :: hdbl = 0
- CHARACTER(LEN=16) :: hkey
- CHARACTER(LEN=50000) :: hnml
- CHARACTER(LEN=65507) :: hlog
- CHARACTER, PARAMETER :: nul = char(0)
-
- NAMELIST/dcon_control/bal_flag,mat_flag,ode_flag,vac_flag,
- $ mer_flag,res_flag,fft_flag,node_flag,mthvac,sing_start,nn,
- $ delta_mlow,delta_mhigh,delta_mband,thmax0,nstep,ksing,
- $ tol_nr,tol_r,crossover,ucrit,singfac_min,singfac_max,
- $ cyl_flag,dmlim,lim_flag,sas_flag,sing_order,sort_type,
- $ termbycross_flag,qhigh,kin_flag,con_flag,kinfac1,kinfac2,
- $ kingridtype,ktanh_flag,passing_flag,trapped_flag,
- $ ion_flag,electron_flag,ktc,ktw,qlow,
- $ use_classic_splines,reform_eq_with_psilim,
- $ psiedge,nperq_edge,wv_farwall_flag,
- $ dcon_kin_threads,parallel_threads
- NAMELIST/dcon_output/interp,crit_break,out_bal1,
- $ bin_bal1,out_bal2,bin_bal2,out_metric,bin_metric,out_fmat,
- $ bin_fmat,out_gmat,bin_gmat,out_kmat,bin_kmat,out_sol,
- $ out_sol_min,out_sol_max,bin_sol,bin_sol_min,bin_sol_max,
- $ out_fl,bin_fl,out_evals,bin_evals,bin_euler,euler_stride,
- $ bin_vac,ahb_flag,mthsurf0,msol_ahb,netcdf_out,out_fund,
- $ out_ahg2msc
-c-----------------------------------------------------------------------
-c format statements.
-c-----------------------------------------------------------------------
- 10 FORMAT(/'ipsi',2x,'psifac',6x,'f',7x,'mu0 p',5x,'dvdpsi',
- $ 6x,'q',10x,'di',9x,'dr',8x,'ca1'/)
- 20 FORMAT(i4,1p,8e11.3)
- 30 FORMAT(/3x,"mlow",1x,"mhigh",1x,"mpert",1x,"mband",3x,"nn",2x,
- $ "lim_fl",2x,"dmlim",7x,"qlim",6x,"psilim"//5i6,l6,1p,3e11.3/)
-c-----------------------------------------------------------------------
-c read input data.
-c-----------------------------------------------------------------------
- IF(verbose) WRITE(*,*)""
- IF(verbose) WRITE(*,*)"DCON START => "//TRIM(version)
- IF(verbose) WRITE(*,*)"__________________________________________"
- CALL timer(0,out_unit)
- CALL ascii_open(in_unit,"dcon.in","OLD")
- READ(UNIT=in_unit,NML=dcon_control)
- READ(UNIT=in_unit,NML=dcon_output)
- CALL ascii_close(in_unit)
-
- IF (out_ahg2msc) THEN
- WRITE(*,*) "WARNING: ahg2msc.out is deprecated and will be " //
- $ "removed in a future version. Set out_ahg2msc = .FALSE."
- WRITE(*,*) " to disable this warning."
- vac_memory=.FALSE.
- ELSE
- vac_memory=.TRUE.
- ENDIF
-
-c-----------------------------------------------------------------------
-c set variables
-c-----------------------------------------------------------------------
- IF(parallel_threads > 0)THEN
- WRITE(*,*) "!! WARNING: parallel_threads has been deprecated. "
- $ //"Use dcon_kin_threads"
- ENDIF
-#ifdef _OPENMP
-c The code is compiled with the OpenMP option so the preprocessor
-c will pick include the following line
- IF(dcon_kin_threads > 0)THEN
- CALL OMP_SET_NUM_THREADS(dcon_kin_threads)
- ENDIF
-#else
-c No OpenMP so the following line will appear in source code
- dcon_kin_threads = 1
-#endif
- delta_mhigh=delta_mhigh*2
- use_classic_splines_for_dcon = use_classic_splines
-c-----------------------------------------------------------------------
-c open output files, read, process, and diagnose equilibrium.
-c-----------------------------------------------------------------------
- CALL ascii_open(out_unit,"dcon.out","UNKNOWN")
- CALL equil_read(out_unit)
- CALL equil_out_global
- CALL equil_out_qfind
-c-----------------------------------------------------------------------
-c optionally reform the eq splines to concentrate at true truncation
-c-----------------------------------------------------------------------
- CALL sing_lim ! determine if qhigh is truncating before psihigh
- IF(psilim /= psihigh .AND. reform_eq_with_psilim)THEN
- CALL equil_read(out_unit, psilim)
- CALL equil_out_global
- CALL equil_out_qfind
- ENDIF
-c-----------------------------------------------------------------------
-c record the equilibrium properties
-c-----------------------------------------------------------------------
- CALL equil_out_diagnose(.FALSE.,out_unit)
- CALL equil_out_write_2d
- IF(dump_flag .AND. eq_type /= "dump")CALL equil_out_dump
- IF(direct_flag)CALL bicube_dealloc(psi_in)
-c-----------------------------------------------------------------------
-c enable different settings for dcon and equilibrium splines
-c-----------------------------------------------------------------------
- use_classic_splines = use_classic_splines_for_dcon
-c-----------------------------------------------------------------------
-c prepare local stability criteria.
-c-----------------------------------------------------------------------
- CALL spline_alloc(locstab,mpsi,5)
- locstab%xs=sq%xs
- locstab%fs=0
- locstab%name="locstb"
- locstab%title=(/" di "," dr "," h "," ca1 "," ca2 "/)
- IF (mer_flag) THEN
- WRITE(*,*)"Evaluating Mercier criterion"
- CALL mercier_scan
- ENDIF
- IF(bal_flag)THEN
- IF(verbose) WRITE(*,*)"Evaluating ballooning criterion"
- CALL bal_scan
- ENDIF
- CALL spline_fit(locstab,"extrap")
-c-----------------------------------------------------------------------
-c output surface quantities.
-c-----------------------------------------------------------------------
- CALL bin_open(bin_unit,"dcon.bin","UNKNOWN","REWIND","none")
- WRITE(out_unit,10)
- DO ipsi=0,mpsi
- WRITE(out_unit,20)ipsi,sq%xs(ipsi),sq%fs(ipsi,1)/twopi,
- $ sq%fs(ipsi,2),sq%fs(ipsi,3),sq%fs(ipsi,4),
- $ locstab%fs(ipsi,1)/sq%xs(ipsi),
- $ locstab%fs(ipsi,2)/sq%xs(ipsi),locstab%fs(ipsi,4)
- WRITE(bin_unit)
- $ REAL(sq%xs(ipsi),4),
- $ REAL(SQRT(sq%xs(ipsi)),4),
- $ REAL(sq%fs(ipsi,1)/twopi,4),
- $ REAL(sq%fs(ipsi,2),4),
- $ REAL(sq%fs(ipsi,4),4),
- $ REAL(asinh(locstab%fs(ipsi,1)/sq%xs(ipsi)),4),
- $ REAL(asinh(locstab%fs(ipsi,2)/sq%xs(ipsi)),4),
- $ REAL(asinh(locstab%fs(ipsi,3)),4),
- $ REAL(asinh(locstab%fs(ipsi,4)),4)
- ENDDO
- WRITE(out_unit,10)
- WRITE(bin_unit)
- CALL bin_close(bin_unit)
-c-----------------------------------------------------------------------
-c define poloidal mode numbers.
-c-----------------------------------------------------------------------
- CALL sing_find
- !CALL sing_lim ! now done in above test for re-forming equil
- IF(cyl_flag)THEN
- mlow=delta_mlow
- mhigh=delta_mhigh
- ELSEIF(sing_start == 0)THEN
- mlow=MIN(nn*qmin,zero)-4-delta_mlow
- mhigh=nn*qmax+delta_mhigh
- ELSE
- mmin=HUGE(mmin)
- DO ising=INT(sing_start),msing
- mmin=MIN(mmin,sing(ising)%m)
- ENDDO
- mlow=mmin-delta_mlow
- mhigh=nn*qmax+delta_mhigh
- ENDIF
- mpert=mhigh-mlow+1
- mband=mpert-1-delta_mband
- mband=MIN(MAX(mband,0),mpert-1)
-c-----------------------------------------------------------------------
-c fit equilibrium quantities to Fourier-spline functions.
-c-----------------------------------------------------------------------
- IF(mat_flag .OR. ode_flag)THEN
- IF(verbose) WRITE(*,'(3x,1p,4(a,es10.3))')"q0 = ",q0,
- $ ", qmin = ",qmin,", qmax = ",qmax,", q95 = ",q95
- IF(verbose) WRITE(*,'(3x,a,l1,1p,3(a,es10.3))')
- $ "sas_flag = ",sas_flag,", dmlim = ",dmlim,
- $ ", qlim = ",qlim,", psilim = ",psilim
- IF(verbose) WRITE(*,'(3x,1p,3(a,es10.3))')"betat = ",betat,
- $ ", betan = ",betan,", betap1 = ",betap1
- IF(verbose) WRITE(*,'(3x,5(a,i4))')"nn = ",nn,", mlow = ",mlow,
- $ ", mhigh = ",mhigh,", mpert = ",mpert,", mband = ",mband
- IF(verbose) WRITE(*,'(1x,a)')
- $ "Fourier analysis of metric tensor components"
- CALL fourfit_make_metric
- IF(verbose) WRITE(*,*)"Computing F, G, and K Matrices"
- CALL fourfit_make_matrix(out_fund)
- WRITE(out_unit,30)mlow,mhigh,mpert,mband,nn,sas_flag,dmlim,
- $ qlim,psilim
- IF(kin_flag)THEN
- CALL fourfit_action_matrix
- IF(verbose) WRITE(*,*) "Initializing PENTRC"
- ! call the automatic reading and distributing of inputs
- CALL initialize_pentrc(op_kin=.FALSE.,op_deq=.FALSE.,
- $ op_peq=.FALSE.)
- ! manually set the pentrc equilibrium description
- CALL set_eq(eqfun,sq,rzphi,smats,tmats,xmats,ymats,zmats,
- $ twopi*psio,ro,nn,jac_type,mlow,mhigh,mpert,mthvac)
- ! manually set the kinetic profiles
- CALL read_kin(kinetic_file,zi,zimp,mi,mimp,nfac,
- $ tfac,wefac,wpfac,indebug)
- ! manually set the perturbed equilibrium displacements
- ! use false flat xi and xi' for equal weighting
- ALLOCATE(psitmp(sq%mx+1),mtmp(mpert),xtmp(sq%mx+1,mpert))
- psitmp(:) = sq%xs(0:)
- mtmp = (/(m,m=mlow,mhigh)/)
- xtmp = 1e-4
- CALL set_peq(psitmp,mtmp,xtmp,xtmp,xtmp,.false.,tdebug)
- DEALLOCATE(xtmp,mtmp,psitmp)
- IF(verbose) WRITE(*,*)"Computing Kinetic Matrices"
- CALL fourfit_kinetic_matrix(kingridtype,out_fund)
- ENDIF
- CALL sing_scan
- DO ising=1,msing
- CALL resist_eval(sing(ising))
- ENDDO
- IF (kin_flag)THEN
- CALL ksing_find
- ENDIF
- ENDIF
-c-----------------------------------------------------------------------
-c integrate main ODE's.
-c-----------------------------------------------------------------------
- ALLOCATE(ud(mpert,mpert,2))
- IF(ode_flag)THEN
- IF(verbose) WRITE(*,*)"Starting integration of ODE's"
- CALL ode_run
- IF(size_edge > 0)THEN
- peak_index = MAXLOC(REAL(dw_edge(pre_edge:i_edge)),dim=1) +
- $ (pre_edge - 1)
- qhigh = q_edge(peak_index)
- sas_flag = .FALSE.
- psiedge = psihigh
- CALL sing_lim
- WRITE(*,'(1x,a34,f10.6,a10,f10.6)') "Re-Integrating to "//
- $ "peak dW @ qlim =",qlim,", psilim =",psilim
- ! full re-run because outputs were written to disk each step
- ! making it hard to backtrack
- IF(bin_euler)CALL bin_close(euler_bin_unit)
- CALL ode_run
- ENDIF
- ENDIF
- DEALLOCATE(ud)
-c-----------------------------------------------------------------------
-c compute free boundary energies.
-c-----------------------------------------------------------------------
- IF(vac_flag .AND. .NOT.
- $ (ksing > 0 .AND. ksing <= msing+1 .AND. bin_sol))THEN
- IF(verbose) WRITE(*,*)"Computing free boundary energies"
- ALLOCATE(ud(mpert,mpert,2))
- CALL free_run(plasma1,vacuum1,total1,nzero,netcdf_out)
- DEALLOCATE(ud)
- ELSE
- plasma1=0
- vacuum1=0
- total1=0
- CALL dcon_dealloc
- ENDIF
- IF(mat_flag .OR. ode_flag)DEALLOCATE(asmat,bsmat,csmat,ipiva,jmat)
- IF(bin_euler)CALL bin_close(euler_bin_unit)
-c-----------------------------------------------------------------------
-c the bottom line.
-c-----------------------------------------------------------------------
- IF(nzero /= 0)THEN
- IF(verbose) WRITE(*,'(1x,a,i2,".")')
- $ "Fixed-boundary mode unstable for nn = ",nn
- ENDIF
- IF(vac_flag .AND. .NOT.
- $ (ksing > 0 .AND. ksing <= msing+1 .AND. bin_sol))THEN
- IF(REAL(total1) < 0)THEN
- IF(verbose) WRITE(*,'(1x,a,i2,".")')
- $ "Free-boundary mode unstable for nn = ",nn
- ELSE
- IF(verbose) WRITE(*,'(1x,a,i2,".")')
- $ "All free-boundary modes stable for nn = ",nn
- ENDIF
- ENDIF
-c-----------------------------------------------------------------------
-c save output in sum1.bin.
-c-----------------------------------------------------------------------
- CALL bin_open(sum_unit,"sum1.bin","UNKNOWN","REWIND","none")
- WRITE(sum_unit)mpsi,mtheta,mlow,mhigh,mpert,mband,
- $ REAL(psilow,4),REAL(psihigh,4),REAL(amean,4),REAL(rmean,4),
- $ REAL(aratio,4),REAL(kappa,4),REAL(delta1,4),REAL(delta2,4),
- $ REAL(li1,4),REAL(li2,4),REAL(li3,4),REAL(ro,4),REAL(zo,4),
- $ REAL(psio,4),REAL(betap1,4),REAL(betap2,4),REAL(betap3,4),
- $ REAL(betat,4),REAL(betan,4),REAL(bt0,4),REAL(q0,4),
- $ REAL(qmin,4),REAL(qmax,4),REAL(qa,4),REAL(crnt,4),
- $ REAL(plasma1,4),REAL(vacuum1,4),REAL(total1,4),REAL(q95,4),
- $ REAL(bwall,4),REAL(betaj,4)
- CALL bin_close(sum_unit)
-c-----------------------------------------------------------------------
-c log inputs/outputs with harvest
-c-----------------------------------------------------------------------
- ierr=init_harvest('CODEDB_DCON'//nul,hlog,LEN(hlog))
- ierr=set_harvest_verbose(0)
- ! standard CODEDB records
- ierr=set_harvest_payload_str(hlog,'CODE'//nul,'DCON'//nul)
- ierr=set_harvest_payload_str(hlog,'VERSION'//nul,version//nul)
- if(shotnum>0)
- $ ierr=set_harvest_payload_int(hlog,'SHOT'//nul,INT(shotnum))
- if(shottime>0)
- $ ierr=set_harvest_payload_int(hlog,'TIME'//nul,INT(shottime))
- ! DCON specifc records
- ierr=set_harvest_payload_int(hlog,'mpsi'//nul,mpsi)
- ierr=set_harvest_payload_int(hlog,'mtheta'//nul,mtheta)
- ierr=set_harvest_payload_int(hlog,'mlow'//nul,mlow)
- ierr=set_harvest_payload_int(hlog,'mhigh'//nul,mhigh)
- ierr=set_harvest_payload_int(hlog,'mpert'//nul,mpert)
- ierr=set_harvest_payload_int(hlog,'mband'//nul,mband)
- ierr=set_harvest_payload_dbl(hlog,'psilow'//nul,psilow)
- ierr=set_harvest_payload_dbl(hlog,'psilim'//nul,psilim)
- ierr=set_harvest_payload_dbl(hlog,'amean'//nul,amean)
- ierr=set_harvest_payload_dbl(hlog,'rmean'//nul,rmean)
- ierr=set_harvest_payload_dbl(hlog,'aratio'//nul,aratio)
- ierr=set_harvest_payload_dbl(hlog,'kappa'//nul,kappa)
- ierr=set_harvest_payload_dbl(hlog,'delta1'//nul,delta1)
- ierr=set_harvest_payload_dbl(hlog,'delta2'//nul,delta2)
- ierr=set_harvest_payload_dbl(hlog,'li1'//nul,li1)
- ierr=set_harvest_payload_dbl(hlog,'li2'//nul,li2)
- ierr=set_harvest_payload_dbl(hlog,'li3'//nul,li3)
- ierr=set_harvest_payload_dbl(hlog,'ro'//nul,ro)
- ierr=set_harvest_payload_dbl(hlog,'zo'//nul,zo)
- ierr=set_harvest_payload_dbl(hlog,'psio'//nul,psio)
- ierr=set_harvest_payload_dbl(hlog,'betap1'//nul,betap1)
- ierr=set_harvest_payload_dbl(hlog,'betap2'//nul,betap2)
- ierr=set_harvest_payload_dbl(hlog,'betap3'//nul,betap3)
- ierr=set_harvest_payload_dbl(hlog,'betat'//nul,betat)
- ierr=set_harvest_payload_dbl(hlog,'betan'//nul,betan)
- ierr=set_harvest_payload_dbl(hlog,'bt0'//nul,bt0)
- ierr=set_harvest_payload_dbl(hlog,'q0'//nul,q0)
- ierr=set_harvest_payload_dbl(hlog,'qmin'//nul,qmin)
- ierr=set_harvest_payload_dbl(hlog,'qmax'//nul,qmax)
- ierr=set_harvest_payload_dbl(hlog,'qa'//nul,qa)
- ierr=set_harvest_payload_dbl(hlog,'crnt'//nul,crnt)
- ierr=set_harvest_payload_dbl(hlog,'q95'//nul,q95)
- ierr=set_harvest_payload_dbl(hlog,'betan'//nul,betan)
- ierr=set_harvest_payload_dbl(hlog,'plasma1'//nul,plasma1)
- ierr=set_harvest_payload_dbl(hlog,'vacuum1'//nul,vacuum1)
- ierr=set_harvest_payload_dbl(hlog,'total1'//nul,total1)
- ierr=harvest_send(hlog)
-c-----------------------------------------------------------------------
-c terminate.
-c-----------------------------------------------------------------------
- CALL program_stop("Normal termination.")
- END PROGRAM dcon
-c-----------------------------------------------------------------------
-c subprogram 2. dcon_dealloc.
-c deallocates internal memory.
-c-----------------------------------------------------------------------
-c-----------------------------------------------------------------------
-c declarations.
-c-----------------------------------------------------------------------
- SUBROUTINE dcon_dealloc
- USE ode_mod
- IMPLICIT NONE
-
-c-----------------------------------------------------------------------
-c deallocate internal memory.
-c-----------------------------------------------------------------------
- CALL spline_dealloc(sq)
- CALL spline_dealloc(locstab)
- CALL bicube_dealloc(rzphi)
- IF(mat_flag .OR. ode_flag)THEN
- CALL cspline_dealloc(amats)
- CALL cspline_dealloc(bmats)
- CALL cspline_dealloc(cmats)
- CALL cspline_dealloc(dmats)
- CALL cspline_dealloc(emats)
- CALL cspline_dealloc(hmats)
- CALL cspline_dealloc(dbats)
- CALL cspline_dealloc(ebats)
- CALL cspline_dealloc(fbats)
- CALL cspline_dealloc(fmats)
- CALL cspline_dealloc(gmats)
- CALL cspline_dealloc(kmats)
-
- DO ising=1,msing
- DEALLOCATE(sing(ising)%vmat)
- DEALLOCATE(sing(ising)%mmat)
- DEALLOCATE(sing(ising)%power)
- DEALLOCATE(sing(ising)%n1)
- DEALLOCATE(sing(ising)%n2)
- ENDDO
- DEALLOCATE(sing)
- ENDIF
- IF(ode_flag)DEALLOCATE(u,du,u_save)
-c-----------------------------------------------------------------------
-c terminate.
-c-----------------------------------------------------------------------
- RETURN
- END SUBROUTINE dcon_dealloc
diff --git a/src/DCON/fortran/dcon_mod.f b/src/DCON/fortran/dcon_mod.f
deleted file mode 100644
index 6ad7bb64d5..0000000000
--- a/src/DCON/fortran/dcon_mod.f
+++ /dev/null
@@ -1,128 +0,0 @@
-c-----------------------------------------------------------------------
-c file dcon_mod.f.
-c module declarations.
-c-----------------------------------------------------------------------
-c-----------------------------------------------------------------------
-c subprogram 0. dcon_mod.
-c module declarations.
-c-----------------------------------------------------------------------
-c-----------------------------------------------------------------------
-c declarations.
-c-----------------------------------------------------------------------
- MODULE dcon_mod
- USE spline_mod
- USE global_mod
- USE equil_mod
- USE equil_out_mod
- USE pentrc_interface, ONLY: version
-
- IMPLICIT NONE
-
- INTEGER :: out_bal1_unit=21
- INTEGER :: out_bal2_unit=22
- INTEGER :: bin_bal1_unit=23
- INTEGER :: bin_bal2_unit=24
- INTEGER :: fourfit_out_unit=21
- INTEGER :: fourfit_bin_unit=22
- INTEGER :: evals_out_unit=23
- INTEGER :: evals_bin_unit=24
- INTEGER :: crit_out_unit=25
- INTEGER :: crit_bin_unit=26
- INTEGER :: euler_bin_unit=27
- INTEGER :: init_out_unit=28
- INTEGER :: dcon_unit=1
- INTEGER :: unorm_unit=29
- INTEGER :: ca_unit=30
- INTEGER :: err_unit=31
-
- LOGICAL :: out_bal1=.FALSE.
- LOGICAL :: out_bal2=.FALSE.
- LOGICAL :: bin_bal1=.FALSE.
- LOGICAL :: bin_bal2=.FALSE.
- LOGICAL :: out_fund=.FALSE.
- LOGICAL :: out_fmat=.FALSE.
- LOGICAL :: out_gmat=.FALSE.
- LOGICAL :: out_kmat=.FALSE.
- LOGICAL :: out_metric=.FALSE.
- LOGICAL :: bin_fmat=.FALSE.
- LOGICAL :: bin_gmat=.FALSE.
- LOGICAL :: bin_kmat=.FALSE.
- LOGICAL :: bin_metric=.FALSE.
- LOGICAL :: feval_flag=.FALSE.
- LOGICAL :: fft_flag=.FALSE.
- LOGICAL :: bin_euler=.FALSE.
- LOGICAL :: bin_vac=.FALSE.
- LOGICAL :: out_evals=.FALSE.
- LOGICAL :: bin_evals=.FALSE.
- LOGICAL :: out_sol=.FALSE.
- LOGICAL :: bin_sol=.FALSE.
- LOGICAL :: netcdf_out=.TRUE.
-
- LOGICAL :: bal_flag=.FALSE.
- LOGICAL :: mat_flag=.FALSE.
- LOGICAL :: ode_flag=.FALSE.
- LOGICAL :: vac_flag=.FALSE.
- LOGICAL :: mer_flag=.FALSE.
-
- LOGICAL :: crit_break=.TRUE.
- LOGICAL :: node_flag=.FALSE.
- LOGICAL :: res_flag=.FALSE.
- LOGICAL :: ahb_flag=.FALSE.
- LOGICAL :: out_ahg2msc=.TRUE.
- LOGICAL :: vac_memory=.FALSE.
-
- INTEGER, PARAMETER :: sol_base=50
- INTEGER :: mlow,mhigh,mpert,mband,nn,nstep=HUGE(0),bin_sol_min,
- $ bin_sol_max,euler_stride=1,mthvac=480,ksing=-1,delta_mlow=0,
- $ delta_mhigh=0,delta_mband=0,out_sol_min,out_sol_max
- REAL(r8) :: thmax0=1,ucrit=1e4,tol_r=1e-5,tol_nr=1e-5,
- $ crossover=1e-2,sing_start=0,mthsurf0=1
-
- TYPE(spline_type) :: locstab
-
- TYPE :: resist_type
- REAL(r8) :: e,f,h,m,g,k,eta,rho,taua,taur
- END TYPE resist_type
-
- TYPE :: sing_type
- INTEGER :: m
- INTEGER :: order
- INTEGER, DIMENSION(1) :: r1
- INTEGER, DIMENSION(2) :: r2
- INTEGER, DIMENSION(:), POINTER :: n1,n2
- REAL(r8) :: psifac,rho,q,q1,di
- COMPLEX(r8) :: alpha
- COMPLEX(r8), DIMENSION(:), POINTER :: power
- COMPLEX(r8), DIMENSION(:,:,:,:), POINTER :: vmat,mmat
- TYPE(resist_type) :: restype
- END TYPE sing_type
-
- INTEGER :: msing,kmsing
- TYPE(sing_type), DIMENSION(:), POINTER :: sing
- TYPE(sing_type), DIMENSION(:), POINTER :: kinsing
-
- LOGICAL :: sas_flag=.FALSE.,lim_flag
- EQUIVALENCE (sas_flag,lim_flag)
- REAL(r8) :: psilim,qlim,q1lim,dmlim=.5_r8,qhigh=1e3,qlow=0
-
- INTEGER :: kingridtype=0
- REAL(r8) :: kinfac1=1.0,kinfac2=1.0,ktc=0.1,ktw=50
- LOGICAL :: kin_flag = .FALSE.
- LOGICAL :: con_flag = .FALSE.
- LOGICAL :: ktanh_flag = .FALSE.
- LOGICAL :: passing_flag = .FALSE.
- LOGICAL :: trapped_flag = .TRUE.
- LOGICAL :: electron_flag = .FALSE.
- LOGICAL :: ion_flag = .TRUE.
- LOGICAL :: fkg_kmats_flag = .FALSE.
- LOGICAL :: keq_out = .FALSE.
- LOGICAL :: theta_out = .FALSE.
- LOGICAL :: xlmda_out = .FALSE.
-
- ! for recording dw(q) near the boundary
- REAL(r8) :: psiedge = 1.0
- REAL(r8), DIMENSION(:), ALLOCATABLE :: q_edge, psi_edge
- COMPLEX(r8), DIMENSION(:), ALLOCATABLE :: dw_edge
- INTEGER :: nperq_edge=20, size_edge=0, pre_edge=1, i_edge=1
-
- END MODULE dcon_mod
diff --git a/src/DCON/fortran/dcon_netcdf.f b/src/DCON/fortran/dcon_netcdf.f
deleted file mode 100644
index 9fac3b1f91..0000000000
--- a/src/DCON/fortran/dcon_netcdf.f
+++ /dev/null
@@ -1,276 +0,0 @@
-c-----------------------------------------------------------------------
-c file dcon_netcdf.f
-c writes dcon.out information to a netcdf file
-c-----------------------------------------------------------------------
-c code organization.
-c-----------------------------------------------------------------------
-c 0. dcon_netcdf_mod
-c 1. check
-c 2. dcon_netcdf_out
-c-----------------------------------------------------------------------
-c subprogram 0. dcon_netcdf_mod
-c module declarations.
-c-----------------------------------------------------------------------
-c-----------------------------------------------------------------------
-c declarations.
-c-----------------------------------------------------------------------
- MODULE dcon_netcdf_mod
- USE dcon_mod
- USE sing_mod, ONLY: sing_detf
- USE local_mod, ONLY: r8, r4
- USE netcdf
- IMPLICIT NONE
-
- CONTAINS
-c-----------------------------------------------------------------------
-c subprogram 1. check.
-c Check status of netcdf file.
-c-----------------------------------------------------------------------
- SUBROUTINE check(stat)
-c-----------------------------------------------------------------------
-c declaration.
-c-----------------------------------------------------------------------
- INTEGER, INTENT (IN) :: stat
-c-----------------------------------------------------------------------
-c stop if it is an error.
-c-----------------------------------------------------------------------
- IF(stat /= nf90_noerr) THEN
- PRINT *, TRIM(nf90_strerror(stat))
- STOP "ERROR: failed to write/read netcdf file"
- ENDIF
-c-----------------------------------------------------------------------
-c terminate.
-c-----------------------------------------------------------------------
- RETURN
- END SUBROUTINE check
-c-----------------------------------------------------------------------
-c subprogram 2. dcon_netcdf_out.
-c Replicate dcon.out information in netcdf format.
-c-----------------------------------------------------------------------
-c-----------------------------------------------------------------------
-c declarations.
-c-----------------------------------------------------------------------
- SUBROUTINE dcon_netcdf_out(wp,wv,wt,wt0,ep,ev,et)
-
- COMPLEX(r8), DIMENSION(mpert), INTENT(IN) :: ep,ev,et
- COMPLEX(r8), DIMENSION(mpert,mpert), INTENT(IN) :: wp,wv,wt,wt0
-
- INTEGER :: i, ncid,
- $ i_dim, m_dim, mo_dim, p_dim, ep_dim, i_id, m_id, mo_id, p_id,
- $ f_id, q_id, dv_id, mu_id, di_id, dr_id, ca_id,
- $ wp_id, wpv_id, wv_id, wvv_id, wt_id, wtv_id, wt0_id,
- $ pd_dim, pd_id, df_id, ep_id, ew_id, eq_id
- REAL(r4) :: cpusec, wallsec
- CHARACTER(2) :: sn
- CHARACTER(64) :: ncfile
-
- LOGICAL, PARAMETER :: debug_flag = .FALSE.
-c-----------------------------------------------------------------------
-c set variables
-c-----------------------------------------------------------------------
- IF(debug_flag) PRINT *,"Called dcon_netcdf_out"
- IF (nn<10) THEN
- WRITE(UNIT=sn,FMT='(I1)')nn
- sn=ADJUSTL(sn)
- ELSE
- WRITE(UNIT=sn,FMT='(I2)')nn
- ENDIF
- ncfile = "dcon_output_n"//TRIM(sn)//".nc"
- CALL timer(1,0,cpusec,wallsec)
-c-----------------------------------------------------------------------
-c open files
-c-----------------------------------------------------------------------
- IF(debug_flag) PRINT *," - Creating netcdf files"
- CALL check( nf90_create(ncfile,
- $ cmode=or(NF90_CLOBBER,NF90_64BIT_OFFSET), ncid=ncid) )
-c-----------------------------------------------------------------------
-c define global file attributes
-c-----------------------------------------------------------------------
- IF(debug_flag) PRINT *," - Defining modal netcdf globals"
- CALL check( nf90_put_att(ncid,nf90_global,"title",
- $ "DCON outputs"))
- ! define global attributes
- CALL check( nf90_put_att(ncid,nf90_global,"jacobian",
- $ trim(jac_type)))
- CALL check( nf90_put_att(ncid,nf90_global,"power_bp", power_bp))
- CALL check( nf90_put_att(ncid,nf90_global,"power_b", power_b))
- CALL check( nf90_put_att(ncid,nf90_global,"power_r", power_r))
- CALL check( nf90_put_att(ncid,nf90_global,'mpsi', mpsi))
- CALL check( nf90_put_att(ncid,nf90_global,'mtheta', mtheta))
- CALL check( nf90_put_att(ncid,nf90_global,'mlow', mlow))
- CALL check( nf90_put_att(ncid,nf90_global,'mhigh', mhigh))
- CALL check( nf90_put_att(ncid,nf90_global,'mpert', mpert))
- CALL check( nf90_put_att(ncid,nf90_global,'mband', mband))
- CALL check( nf90_put_att(ncid,nf90_global,'psilow', psilow))
- CALL check( nf90_put_att(ncid,nf90_global,'amean', amean))
- CALL check( nf90_put_att(ncid,nf90_global,'rmean', rmean))
- CALL check( nf90_put_att(ncid,nf90_global,'aratio', aratio))
- CALL check( nf90_put_att(ncid,nf90_global,'kappa', kappa))
- CALL check( nf90_put_att(ncid,nf90_global,'delta1', delta1))
- CALL check( nf90_put_att(ncid,nf90_global,'delta2', delta2))
- CALL check( nf90_put_att(ncid,nf90_global,'li1', li1))
- CALL check( nf90_put_att(ncid,nf90_global,'li2', li2))
- CALL check( nf90_put_att(ncid,nf90_global,'li3', li3))
- CALL check( nf90_put_att(ncid,nf90_global,'ro', ro))
- CALL check( nf90_put_att(ncid,nf90_global,'zo', zo))
- CALL check( nf90_put_att(ncid,nf90_global,'psio', psio))
- CALL check( nf90_put_att(ncid,nf90_global,'betap1', betap1))
- CALL check( nf90_put_att(ncid,nf90_global,'betap2', betap2))
- CALL check( nf90_put_att(ncid,nf90_global,'betap3', betap3))
- CALL check( nf90_put_att(ncid,nf90_global,'betat', betat))
- CALL check( nf90_put_att(ncid,nf90_global,'betan', betan))
- CALL check( nf90_put_att(ncid,nf90_global,'bt0', bt0))
- CALL check( nf90_put_att(ncid,nf90_global,'q0', q0))
- CALL check( nf90_put_att(ncid,nf90_global,'qmin', qmin))
- CALL check( nf90_put_att(ncid,nf90_global,'qmax', qmax))
- CALL check( nf90_put_att(ncid,nf90_global,'qa', qa))
- CALL check( nf90_put_att(ncid,nf90_global,'crnt', crnt))
- CALL check( nf90_put_att(ncid,nf90_global,'q95', q95))
- CALL check( nf90_put_att(ncid,nf90_global,'betan', betan))
- CALL check( nf90_put_att(ncid,nf90_global,"qlim", qlim))
- CALL check( nf90_put_att(ncid,nf90_global,"psilim", psilim))
- CALL check( nf90_put_att(ncid,nf90_global,"shot", INT(shotnum)) )
- CALL check( nf90_put_att(ncid,nf90_global,"time",INT(shottime)) )
- CALL check( nf90_put_att(ncid,nf90_global,"n", nn))
- CALL check( nf90_put_att(ncid,nf90_global,"version", version))
- CALL check( nf90_put_att(ncid,nf90_global,"cpu_time",cpusec) )
- CALL check( nf90_put_att(ncid,nf90_global,"wall_time",wallsec))
- ! define dimensions
- CALL check( nf90_def_dim(ncid, "i", 2, i_dim) )
- CALL check( nf90_def_var(ncid, "i", nf90_int, i_dim, i_id) )
- CALL check( nf90_def_dim(ncid, "m", mpert, m_dim) )
- CALL check( nf90_def_var(ncid, "m", nf90_int, m_dim, m_id) )
- CALL check( nf90_def_dim(ncid, "mode", mpert, mo_dim) )
- CALL check( nf90_def_var(ncid, "mode", nf90_int, mo_dim, mo_id))
- CALL check( nf90_def_dim(ncid, "psi_n", sq%mx+1, p_dim) )
- CALL check( nf90_def_var(ncid, "psi_n", nf90_double, p_dim, p_id))
- CALL check( nf90_put_att(ncid,p_id, "long_name",
- $ "Normalized Poloidal Flux") )
- IF(size_edge > 0)THEN
- CALL check( nf90_def_dim(ncid, "psi_n_edge", size_edge,ep_dim))
- CALL check( nf90_def_var(ncid, "psi_n_edge", nf90_double,
- $ ep_dim, ep_id))
- CALL check( nf90_put_att(ncid,ep_id,"long_name",
- $ "Normalized Poloidal Flux") )
- ENDIF
- IF(ALLOCATED(sing_detf))THEN
- CALL check( nf90_def_dim(ncid, "psi_n_detf",
- $ SIZE(sing_detf, 2), pd_dim) )
- CALL check( nf90_def_var(ncid, "psi_n_detf", nf90_double,
- $ pd_dim, pd_id))
- CALL check( nf90_put_att(ncid,pd_id,"long_name",
- $ "Normalized Poloidal Flux") )
- ENDIF
- ! define variables
- CALL check( nf90_def_var(ncid, "f", nf90_double, p_dim, f_id) )
- CALL check( nf90_def_var(ncid, "mu0p", nf90_double, p_dim, mu_id))
- CALL check( nf90_def_var(ncid, "dvdpsi", nf90_double,p_dim,dv_id))
- CALL check( nf90_def_var(ncid, "q", nf90_double, p_dim, q_id) )
- CALL check( nf90_put_att(ncid,q_id,"long_name",
- $ "Safety Factor") )
- CALL check( nf90_def_var(ncid, "di", nf90_double, p_dim, di_id) )
- CALL check( nf90_def_var(ncid, "dr", nf90_double, p_dim, dr_id) )
- CALL check( nf90_def_var(ncid, "ca1", nf90_double, p_dim, ca_id))
- CALL check( nf90_def_var(ncid, "W_p_eigenvector", nf90_double,
- $ (/m_dim, mo_dim, i_dim/), wp_id) )
- CALL check( nf90_def_var(ncid, "W_p_eigenvalue", nf90_double,
- $ (/mo_dim, i_dim/), wpv_id) )
- CALL check( nf90_put_att(ncid,wp_id,"long_name",
- $ "Plasma Energy Eigenmodes") )
- CALL check( nf90_put_att(ncid,wpv_id,"long_name",
- $ "Plasma Energy Eigenvalues") )
- CALL check( nf90_def_var(ncid, "W_v_eigenvector", nf90_double,
- $ (/m_dim, mo_dim, i_dim/), wv_id) )
- CALL check( nf90_def_var(ncid, "W_v_eigenvalue", nf90_double,
- $ (/mo_dim, i_dim/), wvv_id) )
- CALL check( nf90_put_att(ncid,wv_id,"long_name",
- $ "Vacuum Energy Eigenmodes") )
- CALL check( nf90_put_att(ncid,wvv_id,"long_name",
- $ "Vacuum Energy Eigenvalues") )
- CALL check( nf90_def_var(ncid, "W_t_eigenvector", nf90_double,
- $ (/m_dim, mo_dim, i_dim/), wt_id) )
- CALL check( nf90_def_var(ncid, "W_t_eigenvalue", nf90_double,
- $ (/mo_dim, i_dim/), wtv_id) )
- CALL check( nf90_put_att(ncid,wt_id,"long_name",
- $ "Total Energy Eigenmodes") )
- CALL check( nf90_put_att(ncid,wtv_id,"long_name",
- $ "Total Energy Eigenvalues") )
- CALL check( nf90_def_var(ncid, "W_t", nf90_double,
- $ (/m_dim, mo_dim, i_dim/), wt0_id) )
- CALL check( nf90_put_att(ncid,wt0_id,"long_name",
- $ "Total Energy Matrix") )
- IF(size_edge > 0)THEN
- CALL check( nf90_def_var(ncid, "dW_edge", nf90_double,
- $ (/ep_dim, i_dim/), ew_id) )
- CALL check( nf90_put_att(ncid,ew_id,"long_name",
- $ "Least Stable Total Energy Eigenvalues") )
- CALL check( nf90_def_var(ncid, "q_edge", nf90_double,
- $ ep_dim, eq_id) )
- CALL check( nf90_put_att(ncid,eq_id,"long_name",
- $ "Safety Factor") )
- ENDIF
- IF(ALLOCATED(sing_detf))THEN
- CALL check( nf90_def_var(ncid, "detF", nf90_double,
- $ (/pd_dim, i_dim/), df_id) )
- ENDIF
- ! end definitions
- CALL check( nf90_enddef(ncid) )
-c-----------------------------------------------------------------------
-c set variables
-c-----------------------------------------------------------------------
- IF(debug_flag) PRINT *," - Putting dimension variables in netcdf"
- CALL check( nf90_put_var(ncid,i_id, (/0,1/)) )
- CALL check( nf90_put_var(ncid,m_id, (/(i+mlow, i=0,mpert-1)/)) )
- CALL check( nf90_put_var(ncid,mo_id, (/(i, i=1,mpert)/)) )
- CALL check( nf90_put_var(ncid,p_id, sq%xs(:)))
- IF(size_edge > 0)THEN
- CALL check( nf90_put_var(ncid,ep_id, psi_edge))
- ENDIF
-
- IF(debug_flag) PRINT *," - Putting profile variables in netcdf"
- CALL check( nf90_put_var(ncid,f_id, sq%fs(:,1)/twopi))
- CALL check( nf90_put_var(ncid,mu_id, sq%fs(:,2)))
- CALL check( nf90_put_var(ncid,dv_id, sq%fs(:,3)))
- CALL check( nf90_put_var(ncid,q_id, sq%fs(:,4)))
- CALL check( nf90_put_var(ncid,di_id, locstab%fs(:,1)/sq%xs(:)))
- CALL check( nf90_put_var(ncid,dr_id, locstab%fs(:,2)/sq%xs(:)))
- CALL check( nf90_put_var(ncid,ca_id, locstab%fs(:,4)))
- IF(size_edge > 0)THEN
- CALL check( nf90_put_var(ncid,ew_id, RESHAPE((/REAL(dw_edge),
- $ AIMAG(dw_edge)/),(/size_edge,2/))) )
- CALL check( nf90_put_var(ncid,eq_id, q_edge))
- ENDIF
-
- IF(debug_flag) PRINT *," - Putting matrix variables in netcdf"
- CALL check( nf90_put_var(ncid,wp_id,RESHAPE((/REAL(wp),
- $ AIMAG(wp)/),(/mpert,mpert,2/))) )
- CALL check( nf90_put_var(ncid,wpv_id,RESHAPE((/REAL(ep),
- $ AIMAG(ep)/),(/mpert,2/))) )
- CALL check( nf90_put_var(ncid,wv_id,RESHAPE((/REAL(wv),
- $ AIMAG(wv)/),(/mpert,mpert,2/))) )
- CALL check( nf90_put_var(ncid,wvv_id,RESHAPE((/REAL(ev),
- $ AIMAG(ev)/),(/mpert,2/))) )
- CALL check( nf90_put_var(ncid,wt_id,RESHAPE((/REAL(wt),
- $ AIMAG(wt)/),(/mpert,mpert,2/))) )
- CALL check( nf90_put_var(ncid,wtv_id,RESHAPE((/REAL(et),
- $ AIMAG(et)/),(/mpert,2/))) )
- CALL check( nf90_put_var(ncid,wt0_id,RESHAPE((/REAL(wt0),
- $ AIMAG(wt0)/),(/mpert,mpert,2/))) )
- IF(ALLOCATED(sing_detf))THEN
- CALL check( nf90_put_var(ncid,pd_id, REAL(sing_detf(1,:))) )
- CALL check( nf90_put_var(ncid,df_id,RESHAPE(
- $ (/REAL(sing_detf(2,:)), AIMAG(sing_detf(2,:))/),
- $ (/SIZE(sing_detf,2),2/))) )
- ENDIF
-c-----------------------------------------------------------------------
-c close file
-c-----------------------------------------------------------------------
- IF(debug_flag) PRINT *," - Closing netcdf file"
- CALL check( nf90_close(ncid) )
-c-----------------------------------------------------------------------
-c terminate.
-c-----------------------------------------------------------------------
- RETURN
- END SUBROUTINE dcon_netcdf_out
-
- END MODULE dcon_netcdf_mod
\ No newline at end of file
diff --git a/src/DCON/fortran/debug.f b/src/DCON/fortran/debug.f
deleted file mode 100644
index e38ab233ca..0000000000
--- a/src/DCON/fortran/debug.f
+++ /dev/null
@@ -1,160 +0,0 @@
-c-----------------------------------------------------------------------
-c file debug2.f.
-c prints large us.
-c-----------------------------------------------------------------------
-c-----------------------------------------------------------------------
-c code organization.
-c-----------------------------------------------------------------------
-c 0. debug_mod.
-c 1. debug1.
-c 2. debug2.
-c 3. debug3.
-c-----------------------------------------------------------------------
-c subprogram 0. debug_mod.
-c module declarations.
-c-----------------------------------------------------------------------
- MODULE debug_mod
- USE local_mod
- IMPLICIT NONE
-
- CONTAINS
-c-----------------------------------------------------------------------
-c subprogram 1. debug1.
-c prints 1d arrays.
-c-----------------------------------------------------------------------
-c-----------------------------------------------------------------------
-c declarations.
-c-----------------------------------------------------------------------
- SUBROUTINE debug1(u,name,unit)
-
- REAL(r8), DIMENSION(:,0:), INTENT(IN) :: u
- CHARACTER(*), INTENT(IN) :: name
- INTEGER, INTENT(IN) :: unit
-
- CHARACTER(80) :: format1,format2
- INTEGER :: nqty,nx,iqty,i
-c-----------------------------------------------------------------------
-c format statements.
-c-----------------------------------------------------------------------
- 10 FORMAT('(/3x,"i",',i2,'(6x,i2,4x)/)')
- 20 FORMAT('(i4,1p,',i2,'e11.3)')
-c-----------------------------------------------------------------------
-c define sizes.
-c-----------------------------------------------------------------------
- nqty=SIZE(u,1)
- nx=SIZE(u,2)
-c-----------------------------------------------------------------------
-c create formats.
-c-----------------------------------------------------------------------
- WRITE(format1,10)nqty
- WRITE(format2,20)nqty
-c-----------------------------------------------------------------------
-c write array.
-c-----------------------------------------------------------------------
- WRITE(unit,'(a)')TRIM(name)//":"
- WRITE(unit,format1)(iqty,iqty=1,nqty)
- DO i=0,nx-1
- WRITE(unit,format2)i,u(:,i)
- ENDDO
- WRITE(unit,format1)(iqty,iqty=1,nqty)
-c-----------------------------------------------------------------------
-c terminate.
-c-----------------------------------------------------------------------
- RETURN
- END SUBROUTINE debug1
-c-----------------------------------------------------------------------
-c subprogram 2. debug2.
-c prints 2d arrays.
-c-----------------------------------------------------------------------
-c-----------------------------------------------------------------------
-c declarations.
-c-----------------------------------------------------------------------
- SUBROUTINE debug2(u,name,unit)
-
- REAL(r8), DIMENSION(:,0:,0:), INTENT(IN) :: u
- CHARACTER(*), INTENT(IN) :: name
- INTEGER, INTENT(IN) :: unit
-
- CHARACTER(80) :: format1,format2
- INTEGER :: nqty,nx,ny,iqty,ix,iy
-c-----------------------------------------------------------------------
-c format statements.
-c-----------------------------------------------------------------------
- 10 FORMAT('(/2x,"iy",2x,"ix",',i2,'(5x,i2,4x)/)')
- 20 FORMAT('(2i4,1p,',i2,'e11.3)')
-c-----------------------------------------------------------------------
-c define sizes.
-c-----------------------------------------------------------------------
- nqty=SIZE(u,1)
- nx=SIZE(u,2)
- ny=SIZE(u,3)
-c-----------------------------------------------------------------------
-c create formats.
-c-----------------------------------------------------------------------
- WRITE(format1,10)nqty
- WRITE(format2,20)nqty
-c-----------------------------------------------------------------------
-c write array.
-c-----------------------------------------------------------------------
- WRITE(unit,'(a)')TRIM(name)//":"
- WRITE(unit,format1)(iqty,iqty=1,nqty)
- DO iy=0,ny-1
- DO ix=0,nx-1
- WRITE(unit,format2)iy,ix,u(:,ix,iy)
- ENDDO
- WRITE(unit,format1)(iqty,iqty=1,nqty)
- ENDDO
-c-----------------------------------------------------------------------
-c terminate.
-c-----------------------------------------------------------------------
- RETURN
- END SUBROUTINE debug2
-c-----------------------------------------------------------------------
-c subprogram 3. debug3.
-c prints 2d arrays.
-c-----------------------------------------------------------------------
-c-----------------------------------------------------------------------
-c declarations.
-c-----------------------------------------------------------------------
- SUBROUTINE debug3(u,name,unit)
-
- REAL(r8), DIMENSION(:,:,0:,0:), INTENT(IN) :: u
- CHARACTER(*), INTENT(IN) :: name
- INTEGER, INTENT(IN) :: unit
-
- CHARACTER(80) :: format1,format2
- INTEGER :: nqty1,nqty2,nx,ny,iqty,jqty,ix,iy
-c-----------------------------------------------------------------------
-c format statements.
-c-----------------------------------------------------------------------
- 10 FORMAT('(/2y,"iy",2x,"ix",',i3,'(5x,i2,",",i2,3x)/)')
- 20 FORMAT('(2i4,1p,',i3,'e11.3)')
-c-----------------------------------------------------------------------
-c define sizes.
-c-----------------------------------------------------------------------
- nqty1=SIZE(u,1)
- nqty2=SIZE(u,2)
- nx=SIZE(u,3)
- ny=SIZE(u,4)
-c-----------------------------------------------------------------------
-c create formats.
-c-----------------------------------------------------------------------
- WRITE(format1,10)nqty1*nqty2
- WRITE(format2,20)nqty1*nqty2
-c-----------------------------------------------------------------------
-c write array.
-c-----------------------------------------------------------------------
- WRITE(unit,'(a)')TRIM(name)//":"
- WRITE(unit,format1)((iqty,jqty,iqty=1,nqty1),jqty=1,nqty2)
- DO iy=0,ny-1
- DO ix=0,nx-1
- WRITE(unit,format2)iy,ix,u(:,:,ix,iy)
- ENDDO
- WRITE(unit,format1)((iqty,jqty,iqty=1,nqty1),jqty=1,nqty2)
- ENDDO
-c-----------------------------------------------------------------------
-c terminate.
-c-----------------------------------------------------------------------
- RETURN
- END SUBROUTINE debug3
- END MODULE debug_mod
diff --git a/src/DCON/fortran/diagnostic b/src/DCON/fortran/diagnostic
deleted file mode 100644
index 6bc52d72f7..0000000000
--- a/src/DCON/fortran/diagnostic
+++ /dev/null
@@ -1,8 +0,0 @@
-sunfire02:~/dcon/dcon% dcon
-
-lib-4324 : UNRECOVERABLE library error
-' is unrecognized in namelist input.
-
-Encountered during a namelist READ from unit 1
-Fortran unit 1 is connected to a sequential formatted text file: "dcon.in"
-Abort (core dumped)
diff --git a/src/DCON/fortran/fourfit.F b/src/DCON/fortran/fourfit.F
deleted file mode 100644
index 11b4ea1c73..0000000000
--- a/src/DCON/fortran/fourfit.F
+++ /dev/null
@@ -1,1611 +0,0 @@
-c-----------------------------------------------------------------------
-c file fourfit.f
-c fits equilibrium quantities to Fourier series, evaluates matrices.
-c-----------------------------------------------------------------------
-c-----------------------------------------------------------------------
-c code organization.
-c-----------------------------------------------------------------------
-c 0. fourfit_mod.
-c 1. fourfit_make_metric.
-c 2. fourfit_make_matrix.
-c 3. fourfit_action_matrix.
-c 4. fourfit_write_metric.
-c 5. fourfit_write_matrix.
-c 6. fourfit_evals.
-c 7. fourfit_diagnose_1.
-c 8. fourfit_kinetic_matrix.
-c-----------------------------------------------------------------------
-c subprogram 0. fourfit_mod.
-c module declarations.
-c-----------------------------------------------------------------------
-c-----------------------------------------------------------------------
-c declarations.
-c-----------------------------------------------------------------------
- MODULE fourfit_mod
- USE fspline_mod
- USE dcon_mod
- USE pentrc_interface, ! rename overlapping names
- $ pentrc_verbose=>verbose, ! should get a more fundamental fix
- $ pentrc_mpert=>mpert,
- $ pentrc_nn=>nn,
- $ pentrc_r8=>r8,
- $ pentrc_timer=>timer
- USE utilities, only : progressbar
- USE torque, only : kelmm ! cspline Euler-Lagrange mats for local use
- USE inputs, only : dbob_m,divx_m,kin,xs_m,fnml
- USE energy_integration
- USE pitch_integration
- USE dcon_interface, only: geom,
- $ dcon_int_rzphi=>rzphi,
- $ dcon_int_eqfun=>eqfun,
- $ dcon_int_sq=>sq,
- $ dcon_int_smats=>smats,
- $ dcon_int_tmats=>tmats,
- $ dcon_int_xmats=>xmats,
- $ dcon_int_ymats=>ymats,
- $ dcon_int_zmats=>zmats
- IMPLICIT NONE
-
- TYPE(fspline_type), PRIVATE :: metric,fmodb
- TYPE(cspline_type) :: dmats,emats,hmats,dbats,ebats,fbats,
- $ fmats,kmats,gmats,kaats,gaats,
- $ f0mats,pmats,paats,kkmats,kkaats,r1mats,r2mats,r3mats,
- $ akmats,bkmats,ckmats
- TYPE(spline_type) :: k0s
- INTEGER, DIMENSION(:), POINTER :: ipiva
- COMPLEX(r8), DIMENSION(:,:), POINTER :: asmat,bsmat,csmat
- COMPLEX(r8), DIMENSION(:), POINTER :: jmat
-
- INTEGER :: parallel_threads = 0, dcon_kin_threads = 0
-
- ! kientic ABCDEH mats for sing_mod
- TYPE(cspline_type) :: kwmats(6),ktmats(6)
-
- CONTAINS
-c-----------------------------------------------------------------------
-c subprogram 1. fourfit_make_metric.
-c computes fourier series of metric tensor components.
-c-----------------------------------------------------------------------
-c-----------------------------------------------------------------------
-c declarations.
-c-----------------------------------------------------------------------
- SUBROUTINE fourfit_make_metric
-
- INTEGER :: ipsi,itheta
- REAL(r8) :: theta,rfac,eta,r,jac,jac1,psifac,p1,q,
- $ g12,g22,g13,g23,g33,b2h,b2hp,b2ht,chi1
- REAL(r8), DIMENSION(3,3) :: v
-c-----------------------------------------------------------------------
-c set up Fourier-spline type.
-c-----------------------------------------------------------------------
- CALL fspline_alloc(metric,mpsi,mtheta,mband,8)
- metric%xs=rzphi%xs
- metric%ys=rzphi%ys*twopi
- metric%name="metric"
- metric%xtitle=" psi "
- metric%ytitle="theta "
- metric%title=(/" g11 "," g22 "," g33 "," g23 "," g31 ",
- $ " g12 "," jmat ","jmat1 "/)
-c-----------------------------------------------------------------------
-c set up kinetic Fourier-spline type.
-c-----------------------------------------------------------------------
- CALL fspline_alloc(fmodb,mpsi,mtheta,mband,8)
- fmodb%xs=rzphi%xs
- fmodb%ys=rzphi%ys*twopi
- fmodb%name="fmodb"
- fmodb%xtitle=" psi "
- fmodb%ytitle="theta "
- fmodb%title=(/" smat "," tmat "," xmat ",
- $ " ymat1 "," ymat2 "," zmat1 ", " zmat2 "," zmat3 "/)
-c-----------------------------------------------------------------------
-c begin loop over nodes.
-c-----------------------------------------------------------------------
- chi1=twopi*psio
- DO ipsi=0,mpsi
- psifac=sq%xs(ipsi)
- p1=sq%fs1(ipsi,2)
- q=sq%fs(ipsi,4)
- DO itheta=0,mtheta
- CALL bicube_eval(rzphi,rzphi%xs(ipsi),rzphi%ys(itheta),1)
- CALL bicube_eval(eqfun,rzphi%xs(ipsi),rzphi%ys(itheta),1)
- theta=rzphi%ys(itheta)
- rfac=SQRT(rzphi%f(1))
- eta=twopi*(theta+rzphi%f(2))
- r=ro+rfac*COS(eta)
- jac=rzphi%f(4)
- jac1=rzphi%fx(4)
- b2h=eqfun%f(1)**2/2
- b2hp=eqfun%f(1)*eqfun%fx(1)
- b2ht=eqfun%f(1)*eqfun%fy(1)
-c-----------------------------------------------------------------------
-c compute contravariant basis vectors.
-c-----------------------------------------------------------------------
- v(1,1)=rzphi%fx(1)/(2*rfac*jac)
- v(1,2)=rzphi%fx(2)*twopi*rfac/jac
- v(1,3)=rzphi%fx(3)*r/jac
- v(2,1)=rzphi%fy(1)/(2*rfac*jac)
- v(2,2)=(1+rzphi%fy(2))*twopi*rfac/jac
- v(2,3)=rzphi%fy(3)*r/jac
- v(3,3)=twopi*r/jac
- g12=SUM(v(1,:)*v(2,:))*jac**2
- g13=v(3,3)*v(1,3)*jac**2
- g22=SUM(v(2,:)**2)*jac**2
- g23=v(2,3)*v(3,3)*jac**2
- g33=v(3,3)*v(3,3)*jac**2
-c-----------------------------------------------------------------------
-c compute metric tensor components.
-c-----------------------------------------------------------------------
- metric%fs(ipsi,itheta,1)=SUM(v(1,:)**2)*jac
- metric%fs(ipsi,itheta,2)=SUM(v(2,:)**2)*jac
- metric%fs(ipsi,itheta,3)=v(3,3)*v(3,3)*jac
- metric%fs(ipsi,itheta,4)=v(2,3)*v(3,3)*jac
- metric%fs(ipsi,itheta,5)=v(3,3)*v(1,3)*jac
- metric%fs(ipsi,itheta,6)=SUM(v(1,:)*v(2,:))*jac
- metric%fs(ipsi,itheta,7)=jac
- metric%fs(ipsi,itheta,8)=jac1
-c-----------------------------------------------------------------------
-c compute kinetic metric tensor components.
-c-----------------------------------------------------------------------
- fmodb%fs(ipsi,itheta,1)=jac*(p1+b2hp)
- $ -chi1**2*b2ht*(g12+q*g13)/(jac*b2h*2)
- fmodb%fs(ipsi,itheta,2)=
- $ chi1**2*b2ht*(g23+q*g33)/(jac*b2h*2)
- fmodb%fs(ipsi,itheta,3)=jac*b2h*2
- fmodb%fs(ipsi,itheta,4)=jac1*b2h*2-chi1**2*b2h*2*eqfun%fy(2)
- fmodb%fs(ipsi,itheta,5)=-twopi*chi1**2/jac*(g12+q*g13)
- fmodb%fs(ipsi,itheta,6)=chi1**2*b2h*2*eqfun%fy(3)
- fmodb%fs(ipsi,itheta,7)=twopi*chi1**2/jac*(g23+q*g33)
- fmodb%fs(ipsi,itheta,8)=twopi*chi1**2/jac*(g22+q*g23)
- ENDDO
- ENDDO
-c-----------------------------------------------------------------------
-c fit Fourier-spline type.
-c-----------------------------------------------------------------------
- IF(fft_flag)THEN
- CALL fspline_fit_2(metric,"extrap",.FALSE.)
- CALL fspline_fit_2(fmodb,"extrap",.FALSE.)
- ELSE
- CALL fspline_fit_1(metric,"extrap",.FALSE.)
- CALL fspline_fit_1(fmodb,"extrap",.FALSE.)
- ENDIF
-c-----------------------------------------------------------------------
-c terminate.
-c-----------------------------------------------------------------------
- RETURN
- END SUBROUTINE fourfit_make_metric
-c-----------------------------------------------------------------------
-c subprogram 2. fourfit_make_matrix.
-c constructs the coefficient matrices and fits them to cubic splines.
-c-----------------------------------------------------------------------
-c-----------------------------------------------------------------------
-c declarations.
-c-----------------------------------------------------------------------
- SUBROUTINE fourfit_make_matrix(op_diagnose)
-
- LOGICAL, OPTIONAL, INTENT(IN) :: op_diagnose
-
- CHARACTER(128) :: message
- INTEGER :: ipsi,ipert,jpert,m1,m2,m,dm,info,iqty,l,i,j,iindex
- REAL(r8) :: chi1,jtheta,nq,p1,psifac,q,q1,singfac1,singfac2,ileft
- COMPLEX(r8) :: tphi
-
- INTEGER, DIMENSION(mpert) :: mfac,ipiv
-
- COMPLEX(r8), DIMENSION(mpert*mpert) :: work
- COMPLEX(r8), DIMENSION(mband+1,mpert) :: fmatb
- COMPLEX(r8), DIMENSION(2*mband+1,mpert) :: kmatb
- COMPLEX(r8), DIMENSION(-mband:mband) ::
- $ g11,g22,g33,g23,g31,g12,jmat1,imat
- COMPLEX(r8), DIMENSION(mpert,mpert) :: amat,bmat,cmat,dmat,emat,
- $ fmat,gmat,hmat,kmat,temp0,temp1,temp2,dbat,ebat,fbat
- COMPLEX(r8), DIMENSION(3*mband+1,mpert) :: amatlu,fmatlu
-
- LOGICAL :: diagnose=.FALSE.
- INTEGER, PARAMETER :: unit=99
-
- mfac =(/(m,m=mlow,mhigh)/)
- IF(PRESENT(op_diagnose)) diagnose = op_diagnose
-c-----------------------------------------------------------------------
-c format statements.
-c-----------------------------------------------------------------------
- 10 FORMAT(/5x,"i",5x,"j",4x,"re fb",6x,"im fb"/)
- 20 FORMAT(2i6,1p,2e11.3)
-c-----------------------------------------------------------------------
-c set up complex cubic splines for matrices.
-c-----------------------------------------------------------------------
- IF(diagnose)CALL bin_open(unit,"coefs.bin","UNKNOWN","REWIND",
- $ "none")
- ALLOCATE(asmat(mpert,mpert),bsmat(mpert,mpert),csmat(mpert,mpert),
- $ jmat(-mband:mband),ipiva(mpert))
- CALL cspline_alloc(fmats,mpsi,(mband+1)*(2*mpert-mband)/2)
- CALL cspline_alloc(gmats,mpsi,(mband+1)*(2*mpert-mband)/2)
- CALL cspline_alloc(kmats,mpsi,(2*mband+1)*mpert)
- fmats%xs=rzphi%xs
- gmats%xs=rzphi%xs
- kmats%xs=rzphi%xs
- fmats%fs=0
- gmats%fs=0
- kmats%fs=0
- imat=0
- imat(0)=1
-c-----------------------------------------------------------------------
-c set up cubic splines for interpolation to psilim.
-c-----------------------------------------------------------------------
- CALL cspline_alloc(amats,mpsi,mpert**2)
- CALL cspline_alloc(bmats,mpsi,mpert**2)
- CALL cspline_alloc(cmats,mpsi,mpert**2)
- CALL cspline_alloc(dmats,mpsi,mpert**2)
- CALL cspline_alloc(emats,mpsi,mpert**2)
- CALL cspline_alloc(hmats,mpsi,mpert**2)
- CALL cspline_alloc(dbats,mpsi,mpert**2)
- CALL cspline_alloc(ebats,mpsi,mpert**2)
- CALL cspline_alloc(fbats,mpsi,mpert**2)
-
- amats%xs=rzphi%xs
- bmats%xs=rzphi%xs
- cmats%xs=rzphi%xs
- dmats%xs=rzphi%xs
- emats%xs=rzphi%xs
- hmats%xs=rzphi%xs
- dbats%xs=rzphi%xs
- ebats%xs=rzphi%xs
- fbats%xs=rzphi%xs
-
- amats%fs=0
- bmats%fs=0
- cmats%fs=0
- dmats%fs=0
- emats%fs=0
- hmats%fs=0
- dbats%fs=0
- ebats%fs=0
- fbats%fs=0
-c-----------------------------------------------------------------------
-c define flux surface quantities.
-c-----------------------------------------------------------------------
- DO ipsi=0,mpsi
- psifac=sq%xs(ipsi)
- p1=sq%fs1(ipsi,2)
- q=sq%fs(ipsi,4)
- q1=sq%fs1(ipsi,4)
- chi1=twopi*psio
- nq=nn*q
- jtheta=-sq%fs1(ipsi,1)
-c-----------------------------------------------------------------------
-c compute lower half of matrices.
-c-----------------------------------------------------------------------
- g11(0:-mband:-1)=metric%cs%fs(ipsi,1:mband+1)
- g22(0:-mband:-1)=metric%cs%fs(ipsi,mband+2:2*mband+2)
- g33(0:-mband:-1)=metric%cs%fs(ipsi,2*mband+3:3*mband+3)
- g23(0:-mband:-1)=metric%cs%fs(ipsi,3*mband+4:4*mband+4)
- g31(0:-mband:-1)=metric%cs%fs(ipsi,4*mband+5:5*mband+5)
- g12(0:-mband:-1)=metric%cs%fs(ipsi,5*mband+6:6*mband+6)
- jmat(0:-mband:-1)=metric%cs%fs(ipsi,6*mband+7:7*mband+7)
- jmat1(0:-mband:-1)=metric%cs%fs(ipsi,7*mband+8:8*mband+8)
-c-----------------------------------------------------------------------
-c compute upper half of matrices.
-c-----------------------------------------------------------------------
- g11(1:mband)=CONJG(g11(-1:-mband:-1))
- g22(1:mband)=CONJG(g22(-1:-mband:-1))
- g33(1:mband)=CONJG(g33(-1:-mband:-1))
- g23(1:mband)=CONJG(g23(-1:-mband:-1))
- g31(1:mband)=CONJG(g31(-1:-mband:-1))
- g12(1:mband)=CONJG(g12(-1:-mband:-1))
- jmat(1:mband)=CONJG(jmat(-1:-mband:-1))
- jmat1(1:mband)=CONJG(jmat1(-1:-mband:-1))
-c-----------------------------------------------------------------------
-c begin loops over perturbed fourier components.
-c-----------------------------------------------------------------------
- ipert=0
- DO m1=mlow,mhigh
- ipert=ipert+1
- singfac1=m1-nq
- DO dm=MAX(1-ipert,-mband),MIN(mpert-ipert,mband)
- m2=m1+dm
- singfac2=m2-nq
- jpert=ipert+dm
-c-----------------------------------------------------------------------
-c construct primitive matrices.
-c-----------------------------------------------------------------------
- amat(ipert,jpert)=twopi**2*(nn*nn*g22(dm)
- $ +nn*(m1+m2)*g23(dm)+m1*m2*g33(dm))
- bmat(ipert,jpert)=-twopi*ifac*chi1
- $ *(nn*g22(dm)+(m1+nq)*g23(dm)+m1*q*g33(dm))
- cmat(ipert,jpert)=twopi*ifac*(
- $ twopi*ifac*chi1*singfac2*(nn*g12(dm)+m1*g31(dm))
- $ -q1*chi1*(nn*g23(dm)+m1*g33(dm)))
- $ -twopi*ifac*(jtheta*singfac1*imat(dm)
- $ +nn*p1/chi1*jmat(dm))
- dmat(ipert,jpert)=twopi*chi1*(g23(dm)+g33(dm)*m1/nn)
- emat(ipert,jpert)=-chi1/nn*(q1*chi1*g33(dm)
- $ -twopi*ifac*chi1*g31(dm)*singfac2
- $ +jtheta*imat(dm))
- hmat(ipert,jpert)=(q1*chi1)**2*g33(dm)
- $ +(twopi*chi1)**2*singfac1*singfac2*g11(dm)
- $ -twopi*ifac*chi1*dm*q1*chi1*g31(dm)
- $ +jtheta*q1*chi1*imat(dm)+p1*jmat1(dm)
- fmat(ipert,jpert)=(chi1/nn)**2*g33(dm)
- kmat(ipert,jpert)=twopi*ifac*chi1*(g23(dm)+g33(dm)*m1/nn)
- ENDDO
- ENDDO
- dbat=dmat
- ebat=emat
- fbat=fmat
-c-----------------------------------------------------------------------
-c factor A.
-c-----------------------------------------------------------------------
- temp0=amat
- CALL zhetrf('L',mpert,amat,mpert,ipiv,work,mpert*mpert,info)
- IF(info /= 0)THEN
- WRITE(message,'(2(a,i2))')
- $ "zhetrf: amat singular at ipsi = ",ipsi,
- $ ", ipert = ",info,", increase delta_mband"
- CALL program_stop(message)
- ENDIF
-c-----------------------------------------------------------------------
-c compute composite matrices F, G, and K.
-c-----------------------------------------------------------------------
- temp1=dmat
- temp2=cmat
- CALL zhetrs('L',mpert,mpert,amat,mpert,ipiv,temp1,mpert,info)
- CALL zhetrs('L',mpert,mpert,amat,mpert,ipiv,temp2,mpert,info)
- fmat=fmat-MATMUL(CONJG(TRANSPOSE(dmat)),temp1)
- kmat=emat-MATMUL(CONJG(TRANSPOSE(kmat)),temp2)
- gmat=hmat-MATMUL(CONJG(TRANSPOSE(cmat)),temp2)
- amat=temp0
-c-----------------------------------------------------------------------
-c kinetic matrices.
-c-----------------------------------------------------------------------
- ipert=0
- DO m1=mlow,mhigh
- ipert=ipert+1
- singfac1=m1-nq
- DO dm=MAX(1-ipert,-mband),MIN(mpert-ipert,mband)
- m2=m1+dm
- singfac2=m2-nq
- jpert=ipert+dm
- dmat(ipert,jpert)=chi1**2*(g22(dm)+q*g23(dm)+
- $ q*(g23(dm)+q*g33(dm)))
- emat(ipert,jpert)=chi1**2*(q1*(g23(dm)+q*g33(dm))-
- $ twopi*ifac*(g12(dm)+q*g31(dm))*singfac2)+
- $ p1*jmat(dm)
- ENDDO
- ENDDO
-c-----------------------------------------------------------------------
-c store matrices for interpolation.
-c-----------------------------------------------------------------------
- amats%fs(ipsi,:)=RESHAPE(amat,(/mpert**2/))
- bmats%fs(ipsi,:)=RESHAPE(bmat,(/mpert**2/))
- cmats%fs(ipsi,:)=RESHAPE(cmat,(/mpert**2/))
- dmats%fs(ipsi,:)=RESHAPE(dmat,(/mpert**2/))
- emats%fs(ipsi,:)=RESHAPE(emat,(/mpert**2/))
- hmats%fs(ipsi,:)=RESHAPE(hmat,(/mpert**2/))
- dbats%fs(ipsi,:)=RESHAPE(dbat,(/mpert**2/))
- ebats%fs(ipsi,:)=RESHAPE(ebat,(/mpert**2/))
- fbats%fs(ipsi,:)=RESHAPE(fbat,(/mpert**2/))
-c-----------------------------------------------------------------------
-c diagnose.
-c-----------------------------------------------------------------------
- IF(feval_flag)CALL fourfit_evals(ipsi,psifac,fmat)
- IF(diagnose)WRITE(unit)REAL(psifac,4),
- $ REAL(fmat(1,1),4),REAL(kmat(1,1),4),
- $ REAL(gmat(1,1)*psifac,4),REAL(g11(0)*psifac,4),
- $ REAL(g22(0),4),REAL(g33(0),4)
-c-----------------------------------------------------------------------
-c transfer F to banded matrix.
-c-----------------------------------------------------------------------
- DO jpert=1,mpert
- DO ipert=jpert,MIN(mpert,jpert+mband)
- fmatb(1+ipert-jpert,jpert)=fmat(ipert,jpert)
- ENDDO
- ENDDO
-c-----------------------------------------------------------------------
-c factor F.
-c-----------------------------------------------------------------------
- CALL zpbtrf('L',mpert,mband,fmatb,mband+1,info)
- IF(info /= 0)THEN
- WRITE(message,'(2(a,i3),a)')
- $ "zpbtrf: fmat singular at ipsi = ",ipsi,
- $ ", ipert = ",info,", reduce delta_mband"
- CALL program_stop(message)
- ENDIF
-c-----------------------------------------------------------------------
-c store Hermitian matrices F and G.
-c-----------------------------------------------------------------------
- iqty=1
- DO jpert=1,mpert
- DO ipert=jpert,MIN(mpert,jpert+mband)
- fmats%fs(ipsi,iqty)=fmatb(1+ipert-jpert,jpert)
- gmats%fs(ipsi,iqty)=gmat(ipert,jpert)
- iqty=iqty+1
- ENDDO
- ENDDO
-c-----------------------------------------------------------------------
-c store non-Hermitian matrix K.
-c-----------------------------------------------------------------------
- iqty=1
- DO jpert=1,mpert
- DO ipert=MAX(1,jpert-mband),MIN(mpert,jpert+mband)
- kmats%fs(ipsi,iqty)=kmat(ipert,jpert)
- iqty=iqty+1
- ENDDO
- ENDDO
- ENDDO
-c-----------------------------------------------------------------------
-c close diagnostic file.
-c-----------------------------------------------------------------------
- IF(diagnose)THEN
- WRITE(unit)
- CALL bin_close(unit)
- ENDIF
-c-----------------------------------------------------------------------
-c set powers.
-c-----------------------------------------------------------------------
- gmats%xpower(1,:)=-1
- IF(power_flag)THEN
- IF (kin_flag)THEN
- hmats%x0(2)=1.0
- hmats%xpower(1,:)=-1
- hmats%xpower(2,:)=-1
- gmats%x0(2)=1.0
- gmats%xpower(2,:)=-1
- ENDIF
- m=mlow
- iqty=1
- DO jpert=1,mpert
- DO ipert=MAX(1,jpert-mband),MIN(mpert,jpert+mband)
- dm=ipert-jpert
- IF(m == 1 .AND. dm == -1 .OR. m == -1 .AND. dm == 1)
- $ kmats%xpower(1,iqty)=-1
- iqty=iqty+1
- ENDDO
- m=m+1
- ENDDO
- ENDIF
-c-----------------------------------------------------------------------
-c cubic spline fit banded matrices.
-c-----------------------------------------------------------------------
- CALL cspline_fit(amats,"extrap")
- CALL cspline_fit(bmats,"extrap")
- CALL cspline_fit(cmats,"extrap")
- CALL cspline_fit(dmats,"extrap")
- CALL cspline_fit(emats,"extrap")
- CALL cspline_fit(hmats,"extrap")
- CALL cspline_fit(fmats,"extrap")
- CALL cspline_fit(kmats,"extrap")
- CALL cspline_fit(gmats,"extrap")
- CALL cspline_fit(dbats,"extrap")
- CALL cspline_fit(ebats,"extrap")
- CALL cspline_fit(fbats,"extrap")
-
-c-----------------------------------------------------------------------
-c write binary output for diagnosis.
-c-----------------------------------------------------------------------
- IF(diagnose)THEN
- WRITE(*,*)"Write binary output for graphs."
- mfac =(/(i,i=mlow,mhigh)/)
- CALL ascii_open(fourfit_out_unit,"imats.out","UNKNOWN")
- WRITE(fourfit_out_unit,*)"DCON ideal energy matrices"
- WRITE(fourfit_out_unit,'(1/,1x,a12,1x,I6,1x,1(a12,I4),1/)')
- $ "mpsi =",mpsi,"mpert =",mpert
- WRITE(fourfit_out_unit,'(1x,a16,2(1x,a4),12(1x,a16))')
- $ "psi","m1","m2",
- $ "real(Ai)","imag(Ai)","real(Bi)","imag(Bi)",
- $ "real(Ci)","imag(Ci)","real(Di)","imag(Di)",
- $ "real(Ei)","imag(Ei)","real(Hi)","imag(Hi)"
- DO ipsi=0,mpsi
- DO i=1,mpert
- DO j=1,mpert
- ipert = (i-1)*mpert + j
- WRITE(fourfit_out_unit,'(1x,es16.8,2(1x,I4),'//
- $ '12(1x,es16.8))')
- $ REAL(amats%xs(ipsi),4),mfac(i),mfac(j),
- $ REAL(REAL(amats%fs(ipsi,ipert)),4),
- $ REAL(AIMAG(amats%fs(ipsi,ipert)),4),
- $ REAL(REAL(bmats%fs(ipsi,ipert)),4),
- $ REAL(AIMAG(bmats%fs(ipsi,ipert)),4),
- $ REAL(REAL(cmats%fs(ipsi,ipert)),4),
- $ REAL(AIMAG(cmats%fs(ipsi,ipert)),4),
- $ REAL(REAL(dmats%fs(ipsi,ipert)),4),
- $ REAL(AIMAG(dmats%fs(ipsi,ipert)),4),
- $ REAL(REAL(emats%fs(ipsi,ipert)),4),
- $ REAL(AIMAG(emats%fs(ipsi,ipert)),4),
- $ REAL(REAL(hmats%fs(ipsi,ipert)),4),
- $ REAL(AIMAG(hmats%fs(ipsi,ipert)),4)
- ENDDO
- ENDDO
- ENDDO
- WRITE(fourfit_out_unit,*)
- CALL ascii_close(fourfit_out_unit)
-
- WRITE(*,*)"Write binary output for graphs."
- CALL bin_open(bin_unit,"fs.bin","UNKNOWN","REWIND","none")
- DO ipert=1,(mband+1)*(2*mpert-mband)/2
- DO ipsi=0,mpsi
- WRITE(bin_unit)REAL(sq%xs(ipsi),4),
- $ REAL(sq%fs(ipsi,4),4),
- $ REAL(REAL(fmats%fs(ipsi,ipert)),4),
- $ REAL(AIMAG(fmats%fs(ipsi,ipert)),4)
- ENDDO
- WRITE(bin_unit)
- ENDDO
- CALL bin_close(bin_unit)
- CALL bin_open(bin_unit,"ks.bin","UNKNOWN","REWIND","none")
- DO ipert=1,(2*mband+1)*mpert
- DO ipsi=0,mpsi
- WRITE(bin_unit)REAL(sq%xs(ipsi),4),
- $ REAL(sq%fs(ipsi,4),4),
- $ REAL(REAL(kmats%fs(ipsi,ipert)),4),
- $ REAL(AIMAG(kmats%fs(ipsi,ipert)),4)
- ENDDO
- WRITE(bin_unit)
- ENDDO
- CALL bin_close(bin_unit)
- CALL bin_open(bin_unit,"gs.bin","UNKNOWN","REWIND","none")
- DO ipert=1,(mband+1)*(2*mpert-mband)/2
- DO ipsi=0,mpsi
- WRITE(bin_unit)REAL(sq%xs(ipsi),4),
- $ REAL(sq%fs(ipsi,4),4),
- $ REAL(REAL(gmats%fs(ipsi,ipert)),4),
- $ REAL(AIMAG(gmats%fs(ipsi,ipert)),4)
- ENDDO
- WRITE(bin_unit)
- ENDDO
- CALL bin_close(bin_unit)
- ENDIF
-c-----------------------------------------------------------------------
-c interpolate matrices to psilim (need modification for valen3d).
-c-----------------------------------------------------------------------
- IF(sas_flag)THEN
- CALL cspline_eval(amats,psilim,0)
- CALL cspline_eval(bmats,psilim,0)
- CALL cspline_eval(cmats,psilim,0)
- asmat=RESHAPE(amats%f,(/mpert,mpert/))
- bsmat=RESHAPE(bmats%f,(/mpert,mpert/))
- csmat=RESHAPE(cmats%f,(/mpert,mpert/))
- CALL zhetrf('L',mpert,asmat,mpert,ipiva,work,mpert*mpert,info)
- ENDIF
-c-----------------------------------------------------------------------
-c diagnose and deallocate.
-c-----------------------------------------------------------------------
- IF(bin_metric)CALL fourfit_write_metric
- IF(bin_fmat)CALL fourfit_write_matrix(fmats,"fmat",.TRUE.)
- IF(bin_gmat)CALL fourfit_write_matrix(gmats,"gmat",.TRUE.)
- IF(bin_kmat)CALL fourfit_write_matrix(kmats,"kmat",.FALSE.)
-c-----------------------------------------------------------------------
-c terminate.
-c-----------------------------------------------------------------------
- RETURN
- END SUBROUTINE fourfit_make_matrix
-c-----------------------------------------------------------------------
-c subprogram 3. fourfit_action_matrix.
-c equilibrium matrices necessary to calc perturbed mod b.
-c-----------------------------------------------------------------------
- SUBROUTINE fourfit_action_matrix
-c-----------------------------------------------------------------------
-c declaration.
-c-----------------------------------------------------------------------
- INTEGER :: ipsi,istep,ipert,jpert,itheta,dm,m1,m2
- REAL(r8) :: q,singfac2
- COMPLEX(r8), DIMENSION(-mband:mband) ::
- $ sband,tband,xband,yband1,yband2,zband1,zband2,zband3
- COMPLEX(r8), DIMENSION(mpert,mpert) :: smat,tmat,xmat,ymat,zmat
-
- WRITE(*,*)"Computing action matrices"
-c-----------------------------------------------------------------------
-c set up fourier-spline type.
-c-----------------------------------------------------------------------
- CALL cspline_alloc(smats,mpsi,mpert**2)
- CALL cspline_alloc(tmats,mpsi,mpert**2)
- CALL cspline_alloc(xmats,mpsi,mpert**2)
- CALL cspline_alloc(ymats,mpsi,mpert**2)
- CALL cspline_alloc(zmats,mpsi,mpert**2)
-
- smats%xs=sq%xs
- tmats%xs=sq%xs
- xmats%xs=sq%xs
- ymats%xs=sq%xs
- zmats%xs=sq%xs
- DO ipsi=0,mpsi
- q=sq%fs(ipsi,4)
- sband(0:-mband:-1)=fmodb%cs%fs(ipsi,1:mband+1)
- tband(0:-mband:-1)=fmodb%cs%fs(ipsi,mband+2:2*mband+2)
- xband(0:-mband:-1)=fmodb%cs%fs(ipsi,2*mband+3:3*mband+3)
- yband1(0:-mband:-1)=fmodb%cs%fs(ipsi,3*mband+4:4*mband+4)
- yband2(0:-mband:-1)=fmodb%cs%fs(ipsi,4*mband+5:5*mband+5)
- zband1(0:-mband:-1)=fmodb%cs%fs(ipsi,5*mband+6:6*mband+6)
- zband2(0:-mband:-1)=fmodb%cs%fs(ipsi,6*mband+7:7*mband+7)
- zband3(0:-mband:-1)=fmodb%cs%fs(ipsi,7*mband+8:8*mband+8)
-
- sband(1:mband)=CONJG(sband(-1:-mband:-1))
- tband(1:mband)=CONJG(tband(-1:-mband:-1))
- xband(1:mband)=CONJG(xband(-1:-mband:-1))
- yband1(1:mband)=CONJG(yband1(-1:-mband:-1))
- yband2(1:mband)=CONJG(yband2(-1:-mband:-1))
- zband1(1:mband)=CONJG(zband1(-1:-mband:-1))
- zband2(1:mband)=CONJG(zband2(-1:-mband:-1))
- zband3(1:mband)=CONJG(zband3(-1:-mband:-1))
-
- ipert=0
- DO m1=mlow,mhigh
- ipert=ipert+1
- DO dm=MAX(1-ipert,-mband),MIN(mpert-ipert,mband)
- m2=m1+dm
- singfac2=m2-nn*q
- jpert=ipert+dm
- smat(ipert,jpert)=sband(dm)
- tmat(ipert,jpert)=tband(dm)
- xmat(ipert,jpert)=xband(dm)
- ymat(ipert,jpert)=yband1(dm)+ifac*singfac2*yband2(dm)
- zmat(ipert,jpert)=zband1(dm)+
- $ ifac*(m2*zband2(dm)+nn*zband3(dm))
- ENDDO
- ENDDO
- smats%fs(ipsi,:)=RESHAPE(smat,(/mpert**2/))
- tmats%fs(ipsi,:)=RESHAPE(tmat,(/mpert**2/))
- xmats%fs(ipsi,:)=RESHAPE(xmat,(/mpert**2/))
- ymats%fs(ipsi,:)=RESHAPE(ymat,(/mpert**2/))
- zmats%fs(ipsi,:)=RESHAPE(zmat,(/mpert**2/))
- ENDDO
-
- CALL cspline_fit(smats,"extrap")
- CALL cspline_fit(tmats,"extrap")
- CALL cspline_fit(xmats,"extrap")
- CALL cspline_fit(ymats,"extrap")
- CALL cspline_fit(zmats,"extrap")
-
- CALL fspline_dealloc(metric)
- CALL fspline_dealloc(fmodb)
-c-----------------------------------------------------------------------
-c terminate.
-c-----------------------------------------------------------------------
- RETURN
- END SUBROUTINE fourfit_action_matrix
-c-----------------------------------------------------------------------
-c subprogram 4. fourfit_write_metric.
-c uses cspline_write_log to diagnose cspline_types.
-c-----------------------------------------------------------------------
-c-----------------------------------------------------------------------
-c declarations.
-c-----------------------------------------------------------------------
- SUBROUTINE fourfit_write_metric
-
- REAL(r8), DIMENSION(2) :: xend=(/zero,one/)
-c-----------------------------------------------------------------------
-c computations.
-c-----------------------------------------------------------------------
- CALL bin_open(bin_unit,"metric.bin","UNKNOWN","REWIND","none")
- CALL cspline_write_log(metric%cs,.FALSE.,.TRUE.,out_unit,
- $ bin_unit,.FALSE.,mband+1,xend)
- CALL bin_close(fourfit_bin_unit)
-c-----------------------------------------------------------------------
-c terminate.
-c-----------------------------------------------------------------------
- RETURN
- END SUBROUTINE fourfit_write_metric
-c-----------------------------------------------------------------------
-c subprogram 5. fourfit_write_matrix
-c produces ascii and binary output of logs.
-c-----------------------------------------------------------------------
-c-----------------------------------------------------------------------
-c declarations.
-c-----------------------------------------------------------------------
- SUBROUTINE fourfit_write_matrix(matrix,name,sym_flag)
-
- TYPE(cspline_type) :: matrix
- CHARACTER(*), INTENT(IN) :: name
- LOGICAL, INTENT(IN) :: sym_flag
-
- INTEGER :: iqty,ix,jx,j,ipert,jpert,iband,iband0,mband0=8,imin
- REAL(r8) :: dx
- REAL(r8), DIMENSION(2) :: xend=(/zero,one/)
- REAL(r8), DIMENSION(0:4*mpsi) :: x
- REAL(r8), DIMENSION(0:4*mpsi,2) :: xlog
-
- REAL(r8), DIMENSION(:), POINTER :: epsilon
- REAL(r8), DIMENSION(:,:,:), POINTER :: flog
- COMPLEX(r8), DIMENSION(:,:,:), POINTER :: f
-c-----------------------------------------------------------------------
-c set limits and allocate arrays.
-c-----------------------------------------------------------------------
- mband0=MIN(mband0,mband)
- IF(sym_flag)THEN
- iband0=0
- ELSE
- iband0=-mband0
- ENDIF
- ALLOCATE(f(0:4*mpsi,mpert,iband0:mband0),
- $ flog(0:4*mpsi,mpert,iband0:mband0),
- $ epsilon(iband0:mband0))
-c-----------------------------------------------------------------------
-c compute values.
-c-----------------------------------------------------------------------
- f=0
- jx=0
- DO ix=1,mpsi
- dx=(matrix%xs(ix)-matrix%xs(ix-1))/4
- DO j=0,4
- IF(j == 4 .AND. ix < mpsi)CYCLE
- x(jx)=matrix%xs(ix-1)+j*dx
- xlog(jx,:)=LOG10(ABS(x(jx)-xend))
- CALL cspline_eval(matrix,x(jx),0)
- iqty=1
- DO jpert=1,mpert
- IF(sym_flag)THEN
- imin=jpert
- ELSE
- imin=MAX(1,jpert-mband)
- ENDIF
- DO ipert=imin,MIN(mpert,jpert+mband)
- IF(ipert-jpert <= mband0
- $ .AND. ipert-jpert >= -mband0)
- $ f(jx,jpert,ipert-jpert)=matrix%f(iqty)
- iqty=iqty+1
- ENDDO
- ENDDO
- jx=jx+1
- ENDDO
- ENDDO
-c-----------------------------------------------------------------------
-c compute logs.
-c-----------------------------------------------------------------------
- flog=HUGE(flog)
- WHERE(f /= 0)
- flog=LOG(f)
- ELSEWHERE
- flog=HUGE(flog)
- ENDWHERE
- DO iband=iband0,mband0
- epsilon(iband)=MINVAL(flog(:,:,iband))
- WHERE(f(:,:,iband) == 0)
- flog(:,:,iband)=epsilon(iband)
- ENDWHERE
- ENDDO
- flog=flog/alog10
-c-----------------------------------------------------------------------
-c open output file.
-c-----------------------------------------------------------------------
- CALL bin_open(bin_unit,TRIM(name)//".bin","UNKNOWN","REWIND",
- $ "none")
-c-----------------------------------------------------------------------
-c print node values.
-c-----------------------------------------------------------------------
- DO ipert=1,mpert
- DO ix=0,4*mpsi,4
- WRITE(bin_unit)REAL(x(ix),4),REAL(xlog(ix,:),4),
- $ REAL(flog(ix,ipert,:),4)
- ENDDO
- WRITE(bin_unit)
- ENDDO
-c-----------------------------------------------------------------------
-c print interpolated values.
-c-----------------------------------------------------------------------
- DO ipert=1,mpert
- DO ix=0,4*mpsi
- WRITE(bin_unit)REAL(x(ix),4),REAL(xlog(ix,:),4),
- $ REAL(flog(ix,ipert,:),4)
- ENDDO
- WRITE(bin_unit)
- ENDDO
-c-----------------------------------------------------------------------
-c close output file and deallocate arrays.
-c-----------------------------------------------------------------------
- CALL bin_close(bin_unit)
- DEALLOCATE(f,flog,epsilon)
-c-----------------------------------------------------------------------
-c terminate.
-c-----------------------------------------------------------------------
- RETURN
- END SUBROUTINE fourfit_write_matrix
-c-----------------------------------------------------------------------
-c subprogram 6. fourfit_evals
-c computes and prints eigenvalues Hermitian matrix.
-c-----------------------------------------------------------------------
-c-----------------------------------------------------------------------
-c declarations.
-c-----------------------------------------------------------------------
- SUBROUTINE fourfit_evals(ipsi,psifac,matrix)
- USE global_mod
- IMPLICIT NONE
-
- INTEGER, INTENT(IN) :: ipsi
- REAL(r8), INTENT(IN) :: psifac
- COMPLEX(r8), DIMENSION(mpert,mpert), INTENT(IN) :: matrix
-
- INTEGER :: info,lwork
- COMPLEX(r8), DIMENSION(mpert,mpert) :: temp
- COMPLEX(r8), DIMENSION(2*(mpert+1)*mpert) :: work
- REAL(r8), DIMENSION(3*mpert-2) :: rwork
- REAL(r8), DIMENSION(mpert) :: evals
-c-----------------------------------------------------------------------
-c write formats.
-c-----------------------------------------------------------------------
- 10 FORMAT(/3x,"ipsi",3x,"psifac",5x,"eval1",6x,"eval2"/)
- 20 FORMAT(i6,1p,3e11.3)
-c-----------------------------------------------------------------------
-c open output files.
-c-----------------------------------------------------------------------
- IF(ipsi == 0)THEN
- CALL ascii_open(evals_out_unit,"feval.out","UNKNOWN")
- WRITE(evals_out_unit,10)
- CALL bin_open(evals_bin_unit,"feval.bin","UNKNOWN","REWIND",
- $ "none")
- ENDIF
-c-----------------------------------------------------------------------
-c compute eigenvalues.
-c-----------------------------------------------------------------------
- lwork=SIZE(work)
- temp=matrix
- CALL zheev('N','U',mpert,temp,mpert,evals,work,lwork,rwork,info)
-c-----------------------------------------------------------------------
-c print results.
-c-----------------------------------------------------------------------
- WRITE(evals_out_unit,20)ipsi,psifac,evals(1:2)
- WRITE(evals_bin_unit)REAL(psifac,4),REAL(evals(1:2),4)
-c-----------------------------------------------------------------------
-c close output files.
-c-----------------------------------------------------------------------
- IF(ipsi == mpsi)THEN
- WRITE(evals_out_unit,10)
- CALL ascii_close(evals_out_unit)
- CALL bin_close(evals_bin_unit)
- ENDIF
-c-----------------------------------------------------------------------
-c terminate.
-c-----------------------------------------------------------------------
- RETURN
- END SUBROUTINE fourfit_evals
-c-----------------------------------------------------------------------
-c subprogram 7. fourfit_diagnose_1.
-c diagnoses coefficient matrices.
-c-----------------------------------------------------------------------
-c-----------------------------------------------------------------------
-c declarations.
-c-----------------------------------------------------------------------
- SUBROUTINE fourfit_diagnose_1(g11,g22,g33,g23,g31,g12)
-
- COMPLEX(r8), DIMENSION(-mband:mband), INTENT(IN) ::
- $ g11,g22,g33,g23,g31,g12
-
- INTEGER :: dm,unit=98
-c-----------------------------------------------------------------------
-c format statements.
-c-----------------------------------------------------------------------
- 10 FORMAT(/4x,"dm",5x,"g11",8x,"g22",8x,"g33",8x,"g23",8x,"g31",8x,
- $ "g12"/)
- 20 FORMAT(i6,1p,8e11.3)
-c-----------------------------------------------------------------------
-c write binary output.
-c-----------------------------------------------------------------------
- CALL ascii_open(unit,"metric.out","UNKNOWN")
- WRITE(unit,10)
- DO dm=0,mband
- WRITE(unit,20)dm,
- $ REAL(g11(dm),4),REAL(g22(dm),4),REAL(g33(dm),4),
- $ REAL(g23(dm),4),REAL(g31(dm),4),REAL(g12(dm),4)
- ENDDO
- WRITE(unit,10)
- CALL ascii_close(unit)
- CALL program_stop("Termination by fourfit_diagnose_1")
-c-----------------------------------------------------------------------
-c terminate.
-c-----------------------------------------------------------------------
- RETURN
- END SUBROUTINE fourfit_diagnose_1
-c-----------------------------------------------------------------------
-c subprogram 8. fourfit_kinetic_matrix.
-c Use PENTRC to calculated the coefficient matrices on a dynamic
-c grid and fit them to cubic splines.
-c-----------------------------------------------------------------------
-c-----------------------------------------------------------------------
-c declarations.
-c-----------------------------------------------------------------------
- SUBROUTINE fourfit_kinetic_matrix(methodin,writein)
- IMPLICIT NONE
-
- LOGICAL, OPTIONAL :: writein
- INTEGER, OPTIONAL :: methodin
-
- LOGICAL :: output
- INTEGER :: ipsi,ipert,l,i,j,iindex,method = 0
- CHARACTER(1) :: ft
- INTEGER, DIMENSION(mpert) :: mfac
- REAL(r8) :: ileft,psifac,chi1,plim(2)
- COMPLEX(r8) :: tphi
- COMPLEX(r8), DIMENSION(mpert,mpert,6) :: kwmat,kwmat_l,
- $ ktmat,ktmat_l
- COMPLEX(r8), DIMENSION(:,:,:,:,:), ALLOCATABLE :: kwmatls, ktmatls
-c-----------------------------------------------------------------------
-c declarations for diagnostics.
-c-----------------------------------------------------------------------
- INTEGER :: info,iqty,jpert,ix,idone
- INTEGER, DIMENSION(mpert) :: ipiv
- CHARACTER(128) :: message
- COMPLEX(r8), DIMENSION(mpert*mpert) :: work,amats_f,bmats_f,
- $ cmats_f,dmats_f,emats_f,hmats_f,dbats_f,ebats_f,fbats_f
- COMPLEX(r8), DIMENSION(mpert,mpert) :: amat,bmat,cmat,dmat,emat,
- $ fmat,gmat,hmat,kmat,temp0,temp1,temp2,caat,gaat,
- $ f0mat,pmat,paat,kkmat,kkaat,r1mat,r2mat,r3mat,
- $ dbat,ebat,umat,aamat,bkmat,bkaat,b1mat
- COMPLEX(r8), DIMENSION(3*mband+1,mpert) :: amatlu
-c-----------------------------------------------------------------------
-c declarations for parallelization.
-c-----------------------------------------------------------------------
- LOGICAL :: debug_omp = .FALSE.
- INTEGER :: t_start, t_end, cr, num_threads, ithread
- REAL(r8) :: t_sec
- INTEGER :: OMP_GET_NUM_THREADS, OMP_GET_THREAD_NUM
-c-----------------------------------------------------------------------
-c output formats
-c-----------------------------------------------------------------------
- IF(debug_omp)THEN
- PRINT *,"In serial region..."
-#ifdef _OPENMP
- num_threads = OMP_GET_NUM_THREADS()
- PRINT *,"# of OMP threads = ",num_threads
-#else
- num_threads = 1
- PRINT *,"# NO OPENMP MULTITHREADING"
-#endif
- ENDIF
-c-----------------------------------------------------------------------
-c some basic variables
-c-----------------------------------------------------------------------
- IF(PRESENT(methodin)) method = methodin
- output=.FALSE.
- IF(PRESENT(writein)) output = writein
- chi1=twopi*psio
- plim = (/0.0,1.0/)
- IF (passing_flag .AND. trapped_flag) THEN
- ft="f"
- ELSE IF (trapped_flag) THEN
- ft="t"
- ELSE IF (passing_flag) THEN
- ft="p"
- ELSE
- CALL program_stop("Kinetic calculations require "//
- $ "passing_flag and/or trapped_flag")
- ENDIF
- ALLOCATE(kwmatls(mpert,mpert,6,0:mpsi,-nl:nl),
- $ ktmatls(mpert,mpert,6,0:mpsi,-nl:nl))
- kwmatls(:,:,:,:,:)=0
- ktmatls(:,:,:,:,:)=0
-c-----------------------------------------------------------------------
-c Original approach using eqgrid loop to calculate kinetic matrices
-c-----------------------------------------------------------------------
- CALL cspline_alloc(kaats,mpsi,(2*mband+1)*mpert)
- CALL cspline_alloc(gaats,mpsi,(2*mband+1)*mpert)
- kaats%xs=rzphi%xs
- gaats%xs=rzphi%xs
- kaats%fs=0
- gaats%fs=0
-
- IF(method==-1)THEN
- output = .FALSE.
- ELSEIF(method==0)THEN
- fkg_kmats_flag=.TRUE.
-
- CALL cspline_alloc(akmats,mpsi,mpert**2)
- CALL cspline_alloc(bkmats,mpsi,mpert**2)
- CALL cspline_alloc(ckmats,mpsi,mpert**2)
- CALL cspline_alloc(f0mats,mpsi,mpert**2)
- CALL cspline_alloc(pmats,mpsi,mpert**2)
- CALL cspline_alloc(paats,mpsi,mpert**2)
- CALL cspline_alloc(kkmats,mpsi,mpert**2)
- CALL cspline_alloc(kkaats,mpsi,mpert**2)
- CALL cspline_alloc(r1mats,mpsi,mpert**2)
- CALL cspline_alloc(r2mats,mpsi,mpert**2)
- CALL cspline_alloc(r3mats,mpsi,mpert**2)
-
- akmats%xs=rzphi%xs
- bkmats%xs=rzphi%xs
- ckmats%xs=rzphi%xs
- f0mats%xs=rzphi%xs
- pmats%xs=rzphi%xs
- paats%xs=rzphi%xs
- kkmats%xs=rzphi%xs
- kkaats%xs=rzphi%xs
- r1mats%xs=rzphi%xs
- r2mats%xs=rzphi%xs
- r3mats%xs=rzphi%xs
-
- akmats%fs=0
- bkmats%fs=0
- ckmats%fs=0
- f0mats%fs=0
- pmats%fs=0
- paats%fs=0
- kkmats%fs=0
- kkaats%fs=0
- r1mats%fs=0
- r2mats%fs=0
- r3mats%fs=0
-
- DO i=1,6
- CALL cspline_alloc(kwmats(i),mpsi,mpert**2)
- CALL cspline_alloc(ktmats(i),mpsi,mpert**2)
- kwmats(i)%xs=rzphi%xs
- ktmats(i)%xs=rzphi%xs
- ENDDO
-
-c-----------------------------------------------------------------------
-c Parallel calls of expensive kinetic calculations for each psi,ell
-c-----------------------------------------------------------------------
- idone = 0
- CALL SYSTEM_CLOCK(COUNT_RATE=cr)
-!$OMP PARALLEL DO SCHEDULE(DYNAMIC,8) DEFAULT(NONE) COLLAPSE(2)
-!$OMP& PROC_BIND(CLOSE)
-!$OMP& PRIVATE(
-!$OMP& ipsi,ix,psifac,l,num_threads,t_start,t_end,t_sec,
-!$OMP& tphi,kwmat_l,ktmat_l,kwmat,ktmat)
-!$OMP& SHARED(
-!$OMP& rzphi,ion_flag,electron_flag,debug_omp,verbose,cr,idone,
-!$OMP& nn,nl,ft,zi,mi,wdfac,divxfac,mpsi,kwmatls,ktmatls,
-c!!!!!!... these can be SHARED because all calls use spline_*_external
-c!!!!!!... to avoid conflicts
-!$OMP& dcon_int_smats,dcon_int_tmats,dcon_int_xmats,dcon_int_ymats,
-!$OMP& dcon_int_zmats)
-
-!$OMP& COPYIN(
-c!!!!!!...from inputs.f90...
-!$OMP& dbob_m,divx_m,kin,xs_m,fnml,
-c!!!!!!...from dcon_interface.f90
-!$OMP& geom, dcon_int_sq,dcon_int_eqfun,dcon_int_rzphi)
-
- DO ipsi=0,mpsi
- DO l=-nl,nl
- CALL SYSTEM_CLOCK(COUNT=t_start)
-#ifdef _OPENMP
- IF(ipsi==0 .AND. l==-nl)THEN
- num_threads = OMP_GET_NUM_THREADS()
- WRITE(*,'(1x,a,i3,a)') "Running in parallel with ",
- $ num_threads," OMP threads"
- ENDIF
-#endif
- psifac=rzphi%xs(ipsi)
- IF (ion_flag) THEN
- kwmat_l = 0
- ktmat_l = 0
- call tpsi(tphi,psifac,nn,l,zi,mi,wdfac,divxfac,
- $ .FALSE.,ft//"wmm",op_wmats=kwmat_l)
- call tpsi(tphi,psifac,nn,l,zi,mi,wdfac,divxfac,
- $ .FALSE.,ft//"tmm",op_wmats=ktmat_l)
- kwmatls(:,:,:,ipsi,l) = kwmatls(:,:,:,ipsi,l)+kwmat_l
- ktmatls(:,:,:,ipsi,l) = ktmatls(:,:,:,ipsi,l)+ktmat_l
- ENDIF
- IF (electron_flag) THEN
- kwmat_l = 0
- ktmat_l = 0
- call tpsi(tphi,psifac,nn,l,zi,mi,wdfac,divxfac,.TRUE.,
- $ ft//"wmm",op_wmats=kwmat_l)
- call tpsi(tphi,psifac,nn,l,zi,mi,wdfac,divxfac,.TRUE.,
- $ ft//"tmm",op_wmats=ktmat_l)
- kwmatls(:,:,:,ipsi,l) = kwmatls(:,:,:,ipsi,l)+kwmat_l
- ktmatls(:,:,:,ipsi,l) = ktmatls(:,:,:,ipsi,l)+ktmat_l
- ENDIF
- ! helpful status messages
-!$OMP CRITICAL
- idone = idone + 1
- IF(verbose) CALL progressbar(idone,1,(mpsi+1)*(2*nl+1),
- $ op_percent=10)
-!$OMP END CRITICAL
- IF(debug_omp)THEN
- CALL SYSTEM_CLOCK(COUNT=t_end)
- t_sec = REAL(t_end-t_start,r8)/REAL(cr,r8)
- WRITE(*,'(1x,a5,i3,a6,es16.8,a8)')
- $ "ipsi=",ipsi," took ",t_sec," seconds"
- ENDIF
- ENDDO
- ENDDO
-!$OMP END PARALLEL DO
-
-c-----------------------------------------------------------------------
-c Now go back totypical serial psi operations
-c-----------------------------------------------------------------------
- DO ipsi=0,mpsi
- psifac=rzphi%xs(ipsi)
-
- ! collect all the ell for a given psi from the collapsed parallel calcs
- kwmat = 0
- ktmat = 0
- DO l=-nl,nl
- kwmat = kwmat + kwmatls(:,:,:,ipsi,l)
- ktmat = ktmat + ktmatls(:,:,:,ipsi,l)
- ENDDO
-
- ! apply normalizations and hypertangent smoothing for core
- IF (ktanh_flag) THEN
- kwmat=kinfac1*kwmat*(1+tanh((psifac-ktc)*ktw))
- ktmat=kinfac2*ktmat*(1+tanh((psifac-ktc)*ktw))
- ELSE
- kwmat=kinfac1*kwmat
- ktmat=kinfac2*ktmat
- ENDIF
- ! store to splines
- DO i=1,6
- kwmats(i)%fs(ipsi,:)=RESHAPE(kwmat(:,:,i),(/mpert**2/))
- ktmats(i)%fs(ipsi,:)=RESHAPE(ktmat(:,:,i),(/mpert**2/))
- ENDDO
-c-----------------------------------------------------------------------
-c Pass only essential matrices to splines
-c-----------------------------------------------------------------------
- ix = ipsi
- CALL cspline_eval_external(amats,psifac,ix,amats_f)
- CALL cspline_eval_external(bmats,psifac,ix,bmats_f)
- CALL cspline_eval_external(cmats,psifac,ix,cmats_f)
- CALL cspline_eval_external(dmats,psifac,ix,dmats_f)
- CALL cspline_eval_external(emats,psifac,ix,emats_f)
- CALL cspline_eval_external(hmats,psifac,ix,hmats_f)
- CALL cspline_eval_external(dbats,psifac,ix,dbats_f)
- CALL cspline_eval_external(ebats,psifac,ix,ebats_f)
- CALL cspline_eval_external(fbats,psifac,ix,fbats_f)
-
- amat=RESHAPE(amats_f,(/mpert,mpert/))
- bmat=RESHAPE(bmats_f,(/mpert,mpert/))
- cmat=RESHAPE(cmats_f,(/mpert,mpert/))
- dmat=RESHAPE(dmats_f,(/mpert,mpert/))
- emat=RESHAPE(emats_f,(/mpert,mpert/))
- hmat=RESHAPE(hmats_f,(/mpert,mpert/))
- dbat=RESHAPE(dbats_f,(/mpert,mpert/))
- ebat=RESHAPE(ebats_f,(/mpert,mpert/))
- fmat=RESHAPE(fbats_f,(/mpert,mpert/))
-
- amat=amat+kwmat(:,:,1)+ktmat(:,:,1)
- bmat=bmat+kwmat(:,:,2)+ktmat(:,:,2)
- cmat=cmat+kwmat(:,:,3)+ktmat(:,:,3)
- dmat=dmat+kwmat(:,:,4)+ktmat(:,:,4)
- emat=emat+kwmat(:,:,5)+ktmat(:,:,5)
- hmat=hmat+kwmat(:,:,6)+ktmat(:,:,6)
- caat=cmat-2*ktmat(:,:,3)
- b1mat=ifac*dbat
-
- ! invert non-hermitian a matrix
- amatlu=0
- umat=0
- DO jpert=1,mpert
- DO ipert=1,mpert
- amatlu(2*mband+1+ipert-jpert,jpert)=
- $ amat(ipert,jpert)
- IF(ipert==jpert)umat(ipert,jpert)=1
- ENDDO
- ENDDO
- CALL zgbtrf(mpert,mpert,mband,mband,amatlu,3*mband+1,
- $ ipiv,info)
- IF(info /= 0)THEN
- WRITE(message,'(2(a,i2))')
- $ "zgbtrf: amat singular at ipsi = ",ipsi,
- $ ", ipert = ",info,", increase delta_mband"
- CALL program_stop(message)
- ENDIF
-
- temp1=dbat
- CALL zgbtrs("N",mpert,mband,mband,mpert,amatlu,
- $ 3*mband+1,ipiv,temp1,mpert,info)
- f0mat=fmat-MATMUL(CONJG(TRANSPOSE(dbat)),temp1)
-
- ! calculate 3 submatrices for kinetic f matrix
- temp2=amat
- CALL zgbtrs("C",mpert,mband,mband,mpert,amatlu,
- $ 3*mband+1,ipiv,temp2,mpert,info) ! close to unit matrix.
- aamat=CONJG(TRANSPOSE(temp2))
- umat=umat-aamat
-
- bkmat=kwmat(:,:,2)+ktmat(:,:,2)+ifac*chi1/(twopi*nn)*
- $ (kwmat(:,:,1)+ktmat(:,:,1))
- bkaat=kwmat(:,:,2)-ktmat(:,:,2)+ifac*chi1/(twopi*nn)*
- $ (kwmat(:,:,1)+ktmat(:,:,1))
- temp2=bkmat
- CALL zgbtrs("N",mpert,mband,mband,mpert,amatlu,
- $ 3*mband+1,ipiv,temp2,mpert,info)
- pmat=MATMUL(CONJG(TRANSPOSE(b1mat)),temp2)
-
- temp2=b1mat
- CALL zgbtrs("N",mpert,mband,mband,mpert,amatlu,
- $ 3*mband+1,ipiv,temp2,mpert,info)
- paat=MATMUL(CONJG(TRANSPOSE(bkaat)),temp2)
- $ -ifac*chi1/(twopi*nn)*MATMUL(umat,b1mat)
- paat=CONJG(TRANSPOSE(paat))
-
- temp1=kwmat(:,:,1)+ktmat(:,:,1)
- temp2=bkmat
- CALL zgbtrs("N",mpert,mband,mband,mpert,amatlu,
- $ 3*mband+1,ipiv,temp2,mpert,info)
- r1mat=kwmat(:,:,4)+ktmat(:,:,4)-
- $ (chi1/(twopi*nn))**2*CONJG(TRANSPOSE(temp1))+
- $ ifac*chi1/(twopi*nn)*CONJG(TRANSPOSE(bkaat))-
- $ ifac*chi1/(twopi*nn)*MATMUL(aamat,bkmat)-
- $ MATMUL(CONJG(TRANSPOSE(bkaat)),temp2)
-
- ! calculate 4 submatrices for kinetic k matrix
- temp1=cmat
- CALL zgbtrs("N",mpert,mband,mband,mpert,amatlu,
- $ 3*mband+1,ipiv,temp1,mpert,info)
- kkmat=ebat-MATMUL(CONJG(TRANSPOSE(b1mat)),temp1)
-
- temp1=b1mat
- CALL zgbtrs("N",mpert,mband,mband,mpert,amatlu,
- $ 3*mband+1,ipiv,temp1,mpert,info)
- kkaat=CONJG(TRANSPOSE(ebat))-
- $ MATMUL(CONJG(TRANSPOSE(caat)),temp1)
-
- temp1=kwmat(:,:,5)+ktmat(:,:,5)-ifac*chi1/(twopi*nn)*
- $ (kwmat(:,:,3)+ktmat(:,:,3))
- temp2=cmat
- CALL zgbtrs("N",mpert,mband,mband,mpert,amatlu,
- $ 3*mband+1,ipiv,temp2,mpert,info)
- r2mat=temp1+ifac*chi1/(twopi*nn)*MATMUL(umat,cmat)-
- $ MATMUL(CONJG(TRANSPOSE(bkaat)),temp2)
-
- temp1=kwmat(:,:,5)-ktmat(:,:,5)-ifac*chi1/(twopi*nn)*
- $ (kwmat(:,:,3)-ktmat(:,:,3))
- temp2=bkmat
- CALL zgbtrs("N",mpert,mband,mband,mpert,amatlu,
- $ 3*mband+1,ipiv,temp2,mpert,info)
- r3mat=CONJG(TRANSPOSE(temp1))-
- $ MATMUL(CONJG(TRANSPOSE(caat)),temp2)
-
- ! calculate kinetic g matrix
- temp2=cmat
- CALL zgbtrs("N",mpert,mband,mband,mpert,amatlu,
- $ 3*mband+1,ipiv,temp2,mpert,info)
- gaat=hmat-MATMUL(CONJG(TRANSPOSE(caat)),temp2)
-
- ! pass only essential kinetic matrices
- akmats%fs(ipsi,:)=RESHAPE(amat,(/mpert**2/))
- bkmats%fs(ipsi,:)=RESHAPE(bmat,(/mpert**2/))
- ckmats%fs(ipsi,:)=RESHAPE(cmat,(/mpert**2/))
- f0mats%fs(ipsi,:)=RESHAPE(f0mat,(/mpert**2/))
- pmats%fs(ipsi,:)=RESHAPE(pmat,(/mpert**2/))
- paats%fs(ipsi,:)=RESHAPE(paat,(/mpert**2/))
- kkmats%fs(ipsi,:)=RESHAPE(kkmat,(/mpert**2/))
- kkaats%fs(ipsi,:)=RESHAPE(kkaat,(/mpert**2/))
- r1mats%fs(ipsi,:)=RESHAPE(r1mat,(/mpert**2/))
- r2mats%fs(ipsi,:)=RESHAPE(r2mat,(/mpert**2/))
- r3mats%fs(ipsi,:)=RESHAPE(r3mat,(/mpert**2/))
-
- ! pass banded g matrix directly
- iqty=1
- DO jpert=1,mpert
- DO ipert=MAX(1,jpert-mband),MIN(mpert,jpert+mband)
- gaats%fs(ipsi,iqty)=gaat(ipert,jpert)
- iqty=iqty+1
- ENDDO
- ENDDO
- ENDDO
- DEALLOCATE(kwmatls, ktmatls) ! these are really big, get rid of them asap
-c-----------------------------------------------------------------------
-c fit splines
-c-----------------------------------------------------------------------
- DO i=1,6
- CALL cspline_fit(kwmats(i),"extrap")
- CALL cspline_fit(ktmats(i),"extrap")
- ENDDO
-
- CALL cspline_fit(akmats,"extrap")
- CALL cspline_fit(bkmats,"extrap")
- CALL cspline_fit(ckmats,"extrap")
- CALL cspline_fit(f0mats,"extrap")
- CALL cspline_fit(pmats,"extrap")
- CALL cspline_fit(paats,"extrap")
- CALL cspline_fit(kkmats,"extrap")
- CALL cspline_fit(kkaats,"extrap")
- CALL cspline_fit(r1mats,"extrap")
- CALL cspline_fit(r2mats,"extrap")
- CALL cspline_fit(r3mats,"extrap")
-c-----------------------------------------------------------------------
-c Use built in PENTRC spline integration options to form matrixes
-c-----------------------------------------------------------------------
- ELSEIF(method==1)THEN
- DO i=1,6
- CALL cspline_alloc(kwmats(i),mpsi,mpert**2)
- CALL cspline_alloc(ktmats(i),mpsi,mpert**2)
- kwmats(i)%xs=rzphi%xs
- ktmats(i)%xs=rzphi%xs
- ENDDO
- DO ipsi=0,mpsi
- iindex = FLOOR(REAL(ipsi+1,r8)/FLOOR((mpsi+1)/10.0))*10
- ileft = REAL(ipsi+1,r8)/FLOOR((mpsi+1)/10.0)*10-iindex
- IF ((ipsi /= 0) .AND. (ileft == 0) .AND. verbose)
- $ WRITE(*,*)" ...",iindex,"% of kinetic computations"
- kwmat = 0
- ktmat = 0
- psifac=rzphi%xs(ipsi)
- ! get matrices for all ell at this one psi
- IF (ion_flag) THEN
- DO l=-nl,nl
- kwmat_l = 0
- ktmat_l = 0
- call tpsi(tphi,psifac,nn,l,zi,mi,wdfac,divxfac,
- $ .FALSE.,ft//"wmm",op_wmats=kwmat_l)
- kwmat = kwmat+kwmat_l
- call tpsi(tphi,psifac,nn,l,zi,mi,wdfac,divxfac,
- $ .FALSE.,ft//"tmm",op_wmats=ktmat_l)
- ktmat = ktmat+ktmat_l
- ENDDO
- ENDIF
- IF (electron_flag) THEN
- DO l=-nl,nl
- kwmat_l = 0
- ktmat_l = 0
- call tpsi(tphi,psifac,nn,l,zi,mi,wdfac,divxfac,.TRUE.,
- $ ft//"wmm",op_wmats=kwmat_l)
- kwmat = kwmat+kwmat_l
- call tpsi(tphi,psifac,nn,l,zi,mi,wdfac,divxfac,.TRUE.,
- $ ft//"tmm",op_wmats=ktmat_l)
- ktmat = ktmat+ktmat_l
- ENDDO
- ENDIF
- ! apply normalizations and hypertangent smoothing for core
- IF (ktanh_flag) THEN
- kwmat=kinfac1*kwmat*(1+tanh((psifac-ktc)*ktw))
- ktmat=kinfac2*ktmat*(1+tanh((psifac-ktc)*ktw))
- ELSE
- kwmat=kinfac1*kwmat
- ktmat=kinfac2*ktmat
- ENDIF
- ! store to splines
- DO i=1,6
- kwmats(i)%fs(ipsi,:)=RESHAPE(kwmat(:,:,i),(/mpert**2/))
- ktmats(i)%fs(ipsi,:)=RESHAPE(ktmat(:,:,i),(/mpert**2/))
- ENDDO
- ENDDO
- DO i=1,6
- CALL cspline_fit(kwmats(i),"extrap")
- CALL cspline_fit(ktmats(i),"extrap")
- ENDDO
-c-----------------------------------------------------------------------
-c Use built in PENTRC spline integration options to form matrixes
-c-----------------------------------------------------------------------
- ELSEIF(method==2)THEN
- WRITE(*,*) " Kinetic energy calculation using MXM euler "//
- $ "lagrange matrix on equilibrium grid"
- tphi = tintgrl_grid('equil',plim,nn,nl,zi,mi,wdfac,divxfac,
- $ .FALSE.,ft//"wmm")
- ! copy and apply factor to splines
- DO i=1,6
- CALL cspline_copy(kelmm(i),kwmats(i))
- IF (ktanh_flag) THEN
- DO ipsi=0,kwmats(1)%mx
- kwmats(i)%fs(ipsi,:) = kinfac1*kwmats(i)%fs(ipsi,:)*
- $ (1+tanh((kwmats(i)%xs(ipsi)-ktc)*ktw))
- kwmats(i)%fs1(ipsi,:) = kinfac1*kwmats(i)%fs1(ipsi,:)*
- $ (1+tanh((kwmats(i)%xs(ipsi)-ktc)*ktw))
- ENDDO
- ELSE
- kwmats(i)%fs = kinfac1*kwmats(i)%fs
- kwmats(i)%fs1 = kinfac1*kwmats(i)%fs1
- ENDIF
- ENDDO
- WRITE(*,*) " Kinetic torque calculation using MXM euler "//
- $ "lagrange matrix on equilibrium grid"
- tphi = tintgrl_grid('equil',plim,nn,nl,zi,mi,wdfac,divxfac,
- $ .FALSE.,ft//"tmm")
- ! copy and apply factor to splines
- DO i=1,6
- CALL cspline_copy(kelmm(i),ktmats(i))
- IF (ktanh_flag) THEN
- DO ipsi=0,kwmats(1)%mx
- ktmats(i)%fs(ipsi,:) = kinfac2*ktmats(i)%fs(ipsi,:)*
- $ (1+tanh((ktmats(i)%xs(ipsi)-ktc)*ktw))
- ktmats(i)%fs1(ipsi,:) = kinfac2*ktmats(i)%fs1(ipsi,:)*
- $ (1+tanh((ktmats(i)%xs(ipsi)-ktc)*ktw))
- ENDDO
- ELSE
- ktmats(i)%fs = kinfac2*ktmats(i)%fs
- ktmats(i)%fs1 = kinfac2*ktmats(i)%fs1
- ENDIF
- ENDDO
-c-----------------------------------------------------------------------
-c Use built in PENTRC LSODE integration options to form matrixes
-c -> Grid determined by T & dW from flat xi spectrum
-c-----------------------------------------------------------------------
- ELSEIF(method==3)THEN
- WRITE(*,*) " Kinetic energy calculation using MXM euler "//
- $ "lagrange matrix"
- tphi = tintgrl_lsode(plim,nn,nl,zi,mi,wdfac,divxfac,.FALSE.,
- $ ft//"wmm")
- ! copy and apply factor to splines
- DO i=1,6
- CALL cspline_copy(kelmm(i),kwmats(i))
- IF (ktanh_flag) THEN
- DO ipsi=0,kwmats(1)%mx
- kwmats(i)%fs(ipsi,:) = kinfac1*kwmats(i)%fs(ipsi,:)*
- $ (1+tanh((kwmats(i)%xs(ipsi)-ktc)*ktw))
- kwmats(i)%fs1(ipsi,:) = kinfac1*kwmats(i)%fs1(ipsi,:)*
- $ (1+tanh((kwmats(i)%xs(ipsi)-ktc)*ktw))
- ENDDO
- ELSE
- kwmats(i)%fs = kinfac1*kwmats(i)%fs
- kwmats(i)%fs1 = kinfac1*kwmats(i)%fs1
- ENDIF
- ENDDO
- WRITE(*,*) " Kinetic torque calculation using MXM euler "//
- $ "lagrange matrix"
- tphi = tintgrl_lsode(plim,nn,nl,zi,mi,wdfac,divxfac,.FALSE.,
- $ ft//"tmm")
- ! copy and apply factor to splines
- DO i=1,6
- CALL cspline_copy(kelmm(i),ktmats(i))
- IF (ktanh_flag) THEN
- DO ipsi=0,kwmats(1)%mx
- ktmats(i)%fs(ipsi,:) = kinfac2*ktmats(i)%fs(ipsi,:)*
- $ (1+tanh((ktmats(i)%xs(ipsi)-ktc)*ktw))
- ktmats(i)%fs1(ipsi,:) = kinfac2*ktmats(i)%fs1(ipsi,:)*
- $ (1+tanh((ktmats(i)%xs(ipsi)-ktc)*ktw))
- ENDDO
- ELSE
- ktmats(i)%fs = kinfac2*ktmats(i)%fs
- ktmats(i)%fs1 = kinfac2*ktmats(i)%fs1
- ENDIF
- ENDDO
-c-----------------------------------------------------------------------
-c Use built in PENTRC LSODE integration options to form matrixes
-c -> Grid determined by norm of EL matrices
-c-----------------------------------------------------------------------
- ELSEIF(method==4)THEN
- WRITE(*,*) " Kinetic MXM euler lagrange energy matrix norm "
- $ //"calculation"
- tphi = tintgrl_lsode(plim,nn,nl,zi,mi,wdfac,divxfac,.FALSE.,
- $ ft//"kmm")
- ! copy and apply factor to splines
- DO i=1,6
- CALL cspline_copy(kelmm(i),kwmats(i))
- IF (ktanh_flag) THEN
- DO ipsi=0,kwmats(1)%mx
- kwmats(i)%fs(ipsi,:) = kinfac1*kwmats(i)%fs(ipsi,:)*
- $ (1+tanh((kwmats(i)%xs(ipsi)-ktc)*ktw))
- kwmats(i)%fs1(ipsi,:) = kinfac1*kwmats(i)%fs1(ipsi,:)*
- $ (1+tanh((kwmats(i)%xs(ipsi)-ktc)*ktw))
- ENDDO
- ELSE
- kwmats(i)%fs = kinfac1*kwmats(i)%fs
- kwmats(i)%fs1 = kinfac1*kwmats(i)%fs1
- ENDIF
- ENDDO
- WRITE(*,*) " Kinetic MXM euler lagrange torque matrix norm "
- $ //"calculation"
- tphi = tintgrl_lsode(plim,nn,nl,zi,mi,wdfac,divxfac,.FALSE.,
- $ ft//"rmm")
- ! copy and apply factor to splines
- DO i=1,6
- CALL cspline_copy(kelmm(i),ktmats(i))
- IF (ktanh_flag) THEN
- DO ipsi=0,kwmats(1)%mx
- ktmats(i)%fs(ipsi,:) = kinfac2*ktmats(i)%fs(ipsi,:)*
- $ (1+tanh((ktmats(i)%xs(ipsi)-ktc)*ktw))
- ktmats(i)%fs1(ipsi,:) = kinfac2*ktmats(i)%fs1(ipsi,:)*
- $ (1+tanh((ktmats(i)%xs(ipsi)-ktc)*ktw))
- ENDDO
- ELSE
- ktmats(i)%fs = kinfac2*ktmats(i)%fs
- ktmats(i)%fs1 = kinfac2*ktmats(i)%fs1
- ENDIF
- ENDDO
- ELSE
- CALL program_stop("ERROR: Valid kingridtypes are 0,1,2,3,4")
- ENDIF
- gaats%x0(2)=1.0
- gaats%xpower(1,:)=-1
- gaats%xpower(2,:)=-1
- CALL cspline_fit(kaats,"extrap")
- CALL cspline_fit(gaats,"extrap")
-c-----------------------------------------------------------------------
-c Optionally write matrices to binary files for diagnostics
-c-----------------------------------------------------------------------
- IF(output)THEN
- ! binary output
- CALL bin_open(bin_unit,"kwmats.bin","UNKNOWN","REWIND","none")
- DO ipert=1,mpert**2
- DO ipsi=0,kwmats(1)%mx
- WRITE(bin_unit) REAL(kwmats(1)%xs(ipsi),4),
- $ REAL(REAL(kwmats(1)%fs(ipsi,ipert)),4),
- $ REAL(AIMAG(kwmats(1)%fs(ipsi,ipert)),4),
- $ REAL(REAL(kwmats(2)%fs(ipsi,ipert)),4),
- $ REAL(AIMAG(kwmats(2)%fs(ipsi,ipert)),4),
- $ REAL(REAL(kwmats(3)%fs(ipsi,ipert)),4),
- $ REAL(AIMAG(kwmats(3)%fs(ipsi,ipert)),4),
- $ REAL(REAL(kwmats(4)%fs(ipsi,ipert)),4),
- $ REAL(AIMAG(kwmats(4)%fs(ipsi,ipert)),4),
- $ REAL(REAL(kwmats(5)%fs(ipsi,ipert)),4),
- $ REAL(AIMAG(kwmats(5)%fs(ipsi,ipert)),4),
- $ REAL(REAL(kwmats(6)%fs(ipsi,ipert)),4),
- $ REAL(AIMAG(kwmats(6)%fs(ipsi,ipert)),4)
- ENDDO
- WRITE(bin_unit)
- ENDDO
- CALL bin_close(bin_unit)
- CALL bin_open(bin_unit,"ktmats.bin","UNKNOWN","REWIND","none")
- DO ipert=1,mpert**2
- DO ipsi=0,ktmats(1)%mx
- WRITE(bin_unit) REAL(ktmats(1)%xs(ipsi),4),
- $ REAL(REAL(ktmats(1)%fs(ipsi,ipert)),4),
- $ REAL(AIMAG(ktmats(1)%fs(ipsi,ipert)),4),
- $ REAL(REAL(ktmats(2)%fs(ipsi,ipert)),4),
- $ REAL(AIMAG(ktmats(2)%fs(ipsi,ipert)),4),
- $ REAL(REAL(ktmats(3)%fs(ipsi,ipert)),4),
- $ REAL(AIMAG(ktmats(3)%fs(ipsi,ipert)),4),
- $ REAL(REAL(ktmats(4)%fs(ipsi,ipert)),4),
- $ REAL(AIMAG(ktmats(4)%fs(ipsi,ipert)),4),
- $ REAL(REAL(ktmats(5)%fs(ipsi,ipert)),4),
- $ REAL(AIMAG(ktmats(5)%fs(ipsi,ipert)),4),
- $ REAL(REAL(ktmats(6)%fs(ipsi,ipert)),4),
- $ REAL(AIMAG(ktmats(6)%fs(ipsi,ipert)),4)
- ENDDO
- WRITE(bin_unit)
- ENDDO
- CALL bin_close(bin_unit)
-
- mfac =(/(i,i=mlow,mhigh)/)
- CALL ascii_open(fourfit_out_unit,"kwmats.out","UNKNOWN")
- WRITE(fourfit_out_unit,*)"DCON Kinetic energy matrices"
- WRITE(fourfit_out_unit,'(1/,1x,a12,1x,I6,1x,1(a12,I4),1/)')
- $ "mpsi =",mpsi,"mpert =",mpert
- WRITE(fourfit_out_unit,'(1x,a16,2(1x,a4),12(1x,a16))')
- $ "psi","m1","m2",
- $ "real(Ak)","imag(Ak)","real(Bk)","imag(Bk)",
- $ "real(Ck)","imag(Ck)","real(Dk)","imag(Dk)",
- $ "real(Ek)","imag(Ek)","real(Hk)","imag(Hk)"
- DO ipsi=0,kwmats(1)%mx
- DO i=1,mpert
- DO j=1,mpert
- ipert = (i-1)*mpert + j
- WRITE(fourfit_out_unit,'(1x,es16.8,2(1x,I4),'//
- $ '12(1x,es16.8))')
- $ REAL(kwmats(1)%xs(ipsi),4),mfac(i),mfac(j),
- $ REAL(REAL(kwmats(1)%fs(ipsi,ipert)),4),
- $ REAL(AIMAG(kwmats(1)%fs(ipsi,ipert)),4),
- $ REAL(REAL(kwmats(2)%fs(ipsi,ipert)),4),
- $ REAL(AIMAG(kwmats(2)%fs(ipsi,ipert)),4),
- $ REAL(REAL(kwmats(3)%fs(ipsi,ipert)),4),
- $ REAL(AIMAG(kwmats(3)%fs(ipsi,ipert)),4),
- $ REAL(REAL(kwmats(4)%fs(ipsi,ipert)),4),
- $ REAL(AIMAG(kwmats(4)%fs(ipsi,ipert)),4),
- $ REAL(REAL(kwmats(5)%fs(ipsi,ipert)),4),
- $ REAL(AIMAG(kwmats(5)%fs(ipsi,ipert)),4),
- $ REAL(REAL(kwmats(6)%fs(ipsi,ipert)),4),
- $ REAL(AIMAG(kwmats(6)%fs(ipsi,ipert)),4)
- ENDDO
- ENDDO
- ENDDO
- WRITE(fourfit_out_unit,*)
- CALL ascii_close(fourfit_out_unit)
- CALL ascii_open(fourfit_out_unit,"ktmats.out","UNKNOWN")
- WRITE(fourfit_out_unit,*) "DCON Kinetic torque matrices"
- WRITE(fourfit_out_unit,'(1/,1x,a12,1x,I6,1x,1(a12,I4),1/)')
- $ "mpsi =",mpsi,"mpert =",mpert
- WRITE(fourfit_out_unit,'(1x,a16,2(1x,a4),12(1x,a16))')
- $ "psi","m1","m2",
- $ "real(Ak)","imag(Ak)","real(Bk)","imag(Bk)",
- $ "real(Ck)","imag(Ck)","real(Dk)","imag(Dk)",
- $ "real(Ek)","imag(Ek)","real(Hk)","imag(Hk)"
- DO ipsi=0,kwmats(1)%mx
- DO i=1,mpert
- DO j=1,mpert
- ipert = (i-1)*mpert + j
- WRITE(fourfit_out_unit,'(1x,es16.8,2(1x,I4),'//
- $ '12(1x,es16.8))')
- $ REAL(kwmats(1)%xs(ipsi),4),mfac(i),mfac(j),
- $ REAL(REAL(ktmats(1)%fs(ipsi,ipert)),4),
- $ REAL(AIMAG(ktmats(1)%fs(ipsi,ipert)),4),
- $ REAL(REAL(ktmats(2)%fs(ipsi,ipert)),4),
- $ REAL(AIMAG(ktmats(2)%fs(ipsi,ipert)),4),
- $ REAL(REAL(ktmats(3)%fs(ipsi,ipert)),4),
- $ REAL(AIMAG(ktmats(3)%fs(ipsi,ipert)),4),
- $ REAL(REAL(ktmats(4)%fs(ipsi,ipert)),4),
- $ REAL(AIMAG(ktmats(4)%fs(ipsi,ipert)),4),
- $ REAL(REAL(ktmats(5)%fs(ipsi,ipert)),4),
- $ REAL(AIMAG(ktmats(5)%fs(ipsi,ipert)),4),
- $ REAL(REAL(ktmats(6)%fs(ipsi,ipert)),4),
- $ REAL(AIMAG(ktmats(6)%fs(ipsi,ipert)),4)
- ENDDO
- ENDDO
- ENDDO
- WRITE(fourfit_out_unit,*)
- CALL ascii_close(fourfit_out_unit)
- ENDIF
-c-----------------------------------------------------------------------
-c terminate.
-c-----------------------------------------------------------------------
- RETURN
- END SUBROUTINE fourfit_kinetic_matrix
- END MODULE fourfit_mod
diff --git a/src/DCON/fortran/free.f b/src/DCON/fortran/free.f
deleted file mode 100644
index 2baf6a2c7e..0000000000
--- a/src/DCON/fortran/free.f
+++ /dev/null
@@ -1,845 +0,0 @@
-c-----------------------------------------------------------------------
-c file free.f.
-c stability of free-boundary modes.
-c-----------------------------------------------------------------------
-c-----------------------------------------------------------------------
-c code organization.
-c-----------------------------------------------------------------------
-c 0. free_mod.
-c 1. free_run.
-c 2. free_write_msc.
-c 3. free_ahb_prep.
-c 4. free_ahb_write.
-c 5. free_test.
-c 6. free_wvmats
-c-----------------------------------------------------------------------
-c subprogram 0. free_mod.
-c module declarations.
-c-----------------------------------------------------------------------
-c-----------------------------------------------------------------------
-c declarations.
-c-----------------------------------------------------------------------
- MODULE free_mod
- USE vacuum_mod, ONLY: mscvac
- USE global_mod, ONLY: wv_farwall_flag
- USE sing_mod, ONLY: sing_der, msol
- USE fourfit_mod, ONLY: asmat, bsmat, csmat, jmat, ipiva,
- $ cspline_type
- USE ode_output_mod, ONLY: u,du
- USE dcon_netcdf_mod
- IMPLICIT NONE
-
- INTEGER :: msol_ahb=-1
- INTEGER, PRIVATE :: mthsurf
- REAL(r8), PRIVATE :: qsurf,q1surf
- REAL(r8), DIMENSION(:), POINTER, PRIVATE :: theta,dphi,r,z
- REAL(r8), DIMENSION(:,:), POINTER, PRIVATE :: thetas
- REAL(r8), DIMENSION(:,:,:), POINTER, PRIVATE :: project
- REAL(r8), DIMENSION(:,:), POINTER :: grri,xzpts
-
- TYPE(cspline_type) :: wvmats
- CONTAINS
-c-----------------------------------------------------------------------
-c subprogram 1. free_run.
-c computes plasma, vacuum, and total potential energies.
-c-----------------------------------------------------------------------
-c-----------------------------------------------------------------------
-c declarations.
-c-----------------------------------------------------------------------
- SUBROUTINE free_run(plasma1,vacuum1,total1,nzero,op_netcdf_out)
-
- COMPLEX(r8), INTENT(OUT) :: plasma1,vacuum1,total1
- INTEGER, INTENT(IN) :: nzero
- LOGICAL, OPTIONAL :: op_netcdf_out
-
- LOGICAL, PARAMETER :: normalize=.TRUE.
- CHARACTER(1), DIMENSION(mpert,msol) :: star
- INTEGER :: ipert,jpert,isol,info,lwork
- INTEGER, DIMENSION(mpert) :: ipiv,m,eindex
- INTEGER, DIMENSION(1) :: imax
- REAL(r8) :: v1
- REAL(r8), DIMENSION(mpert) :: singfac
- ! eigenvalues are complex for gpec
- COMPLEX(r8), DIMENSION(mpert) :: ep,ev,et,tt
-
- REAL(r8), DIMENSION(3*mpert-2) :: rwork
- REAL(r8), DIMENSION(2*mpert) :: rwork2
- COMPLEX(r8) :: phase,norm
- COMPLEX(r8), DIMENSION(2*mpert-1) :: work
- COMPLEX(r8), DIMENSION(2*mpert+1) :: work2
- COMPLEX(r8), DIMENSION(mpert,mpert) :: wp,wv,wt,wt0,temp,wpt,wvt
- COMPLEX(r8), DIMENSION(mpert,mpert) :: nmat,smat
- COMPLEX(r8), DIMENSION(mpert,mpert) :: vl,vr
- CHARACTER(24), DIMENSION(mpert) :: message
- LOGICAL, PARAMETER :: complex_flag=.TRUE.,wall_flag=.FALSE.
- LOGICAL :: farwal_flag
- REAL(r8) :: kernelsignin
- INTEGER :: vac_unit
- COMPLEX(r8), DIMENSION(mpert) :: diff
- CHARACTER(128) :: ahg_file
-c-----------------------------------------------------------------------
-c write formats.
-c-----------------------------------------------------------------------
- 10 FORMAT(1x,"Energies: plasma = ",es10.3,", vacuum = ",es10.3,
- $ ", real = ",es10.3,", imaginary = ",es10.3)
- 20 FORMAT(/3x,"isol",3x,"plasma",5x,"vacuum",2x,"re total",2x,
- $ "im total"/)
- 30 FORMAT(i6,1p,4e11.3,a)
- 40 FORMAT(/3x,"isol",2x,"imax",3x,"plasma",5x,"vacuum",2x,"re total",
- $ 2x,"im total"/)
- 50 FORMAT(2i6,1p,4e11.3,a)
- 60 FORMAT(/2x,"ipert",4x,"m",4x,"re wt",6x,"im wt",6x,"abs wt"/)
- 70 FORMAT(2i6,1p,3e11.3,2x,a)
- 80 FORMAT(/3x,"isol",3x,"plasma",5x,"vacuum"/)
- 90 FORMAT(i6,1p,2e11.3)
-c-----------------------------------------------------------------------
-c Basic parameters at this psi
-c-----------------------------------------------------------------------
- CALL spline_eval(sq,psilim,0)
- v1=sq%f(3)
-c-----------------------------------------------------------------------
-c compute plasma response matrix.
-c-----------------------------------------------------------------------
- IF(ode_flag)THEN
- temp=CONJG(TRANSPOSE(u(:,1:mpert,1)))
- wp=u(:,1:mpert,2)
- wp=CONJG(TRANSPOSE(wp))
- CALL zgetrf(mpert,mpert,temp,mpert,ipiv,info)
- CALL zgetrs('N',mpert,mpert,temp,mpert,ipiv,wp,mpert,info)
- wp=CONJG(TRANSPOSE(wp))/psio**2
- ELSE
- wp=0
- ENDIF
-c-----------------------------------------------------------------------
-c write file for mscvac, prepare input for ahb (deallocate moved to end).
-c-----------------------------------------------------------------------
- ahg_file="ahg2msc_dcon.out"
- CALL free_write_msc(psilim,vac_memory,ahgstr_op=ahg_file)
- IF(ahb_flag)THEN
- CALL free_ahb_prep(wp,nmat,smat,asmat,bsmat,csmat,ipiva)
- ENDIF
-c-----------------------------------------------------------------------
-c compute vacuum response matrix.
-c-----------------------------------------------------------------------
- vac_unit=4
- farwal_flag=.TRUE. ! self-inductance for plasma boundary.
- kernelsignin=-1.0
- ALLOCATE(grri(2*(mthvac+5),mpert*2),xzpts(mthvac+5,4))
- ! xzpts has a dimension of [mthvac+2] with 2 exrta repeating pts
- CALL mscvac(wv,mpert,mtheta,mthvac,complex_flag,kernelsignin,
- $ wall_flag,farwal_flag,grri,xzpts,ahg_file)
- IF(bin_vac)THEN
- WRITE(*,*) "!! WARNING: Use of vacuum.bin is deprecated in"//
- $ " GPEC. Set bin_vac = f in dcon.in to reduce file IO."
- CALL bin_open(vac_unit,"vacuum.bin","UNKNOWN","REWIND","none")
- WRITE(vac_unit)grri
- ENDIF
-
- kernelsignin=1.0
- CALL mscvac(wv,mpert,mtheta,mthvac,complex_flag,kernelsignin,
- $ wall_flag,farwal_flag,grri,xzpts,ahg_file)
- IF(bin_vac)THEN
- WRITE(vac_unit)grri
- ENDIF
- IF(wv_farwall_flag)THEN
- temp=wv
- ENDIF
-
- farwal_flag=.FALSE. ! self-inductance with the wall.
- kernelsignin=-1.0
- CALL mscvac(wv,mpert,mtheta,mthvac,complex_flag,kernelsignin,
- $ wall_flag,farwal_flag,grri,xzpts,ahg_file)
- IF(bin_vac)THEN
- WRITE(vac_unit)grri
- ENDIF
-
- kernelsignin=1.0
- CALL mscvac(wv,mpert,mtheta,mthvac,complex_flag,kernelsignin,
- $ wall_flag,farwal_flag,grri,xzpts,ahg_file)
- IF(bin_vac)THEN
- WRITE(vac_unit)grri
- WRITE(vac_unit)xzpts
-
- CALL bin_close(vac_unit)
- ENDIF
-
- DEALLOCATE(grri,xzpts)
-
- IF(wv_farwall_flag)THEN
- wv=temp
- ENDIF
-
- singfac=mlow-nn*qlim+(/(ipert,ipert=0,mpert-1)/)
- DO ipert=1,mpert
- wv(ipert,:)=wv(ipert,:)*singfac
- wv(:,ipert)=wv(:,ipert)*singfac
- ENDDO
-c-----------------------------------------------------------------------
-c compute complex energy eigenvalues.
-c-----------------------------------------------------------------------
- wt=wp+wv
- wt0=wt
- lwork=2*mpert+1
- CALL zgeev('V','V',mpert,wt,mpert,et,
- $ vl,mpert,vr,mpert,work2,lwork,rwork2,info)
- eindex(1:mpert)=(/(ipert,ipert=1,mpert)/)
- CALL bubble(REAL(et),eindex,1,mpert)
- tt=et
- DO ipert=1,mpert
- wt(:,ipert)=vr(:,eindex(mpert+1-ipert))
- et(ipert)=tt(eindex(mpert+1-ipert))
- ENDDO
-c-----------------------------------------------------------------------
-c normalize eigenfunction and energy.
-c-----------------------------------------------------------------------
- IF(normalize)THEN
- DO isol=1,mpert
- norm=0
- DO ipert=1,mpert
- DO jpert=1,mpert
- norm=norm+jmat(jpert-ipert)
- $ *wt(ipert,isol)*CONJG(wt(jpert,isol))
- ENDDO
- ENDDO
- norm=norm/v1
- wt(:,isol)=wt(:,isol)/SQRT(norm)
- et(isol)=et(isol)/norm
- ENDDO
- ENDIF
-c-----------------------------------------------------------------------
-c normalize phase and label largest component.
-c-----------------------------------------------------------------------
- DO isol=1,mpert
- imax=MAXLOC(ABS(wt(:,isol)))
- phase=ABS(wt(imax(1),isol))/wt(imax(1),isol)
- wt(:,isol)=wt(:,isol)*phase
- star(:,isol)=' '
- star(imax(1),isol)='*'
- ENDDO
-c-----------------------------------------------------------------------
-c compute plasma and vacuum contributions.
-c-----------------------------------------------------------------------
- wpt=MATMUL(CONJG(TRANSPOSE(wt)),MATMUL(wp,wt))
- wvt=MATMUL(CONJG(TRANSPOSE(wt)),MATMUL(wv,wt))
- DO ipert=1,mpert
- ep(ipert)=wpt(ipert,ipert)
- ev(ipert)=wvt(ipert,ipert)
- ENDDO
- plasma1=REAL(ep(1))
- vacuum1=REAL(ev(1))
- total1=REAL(et(1))
-c-----------------------------------------------------------------------
-c write data for ahb and deallocate.
-c-----------------------------------------------------------------------
- IF(ahb_flag)THEN
- CALL free_ahb_write(nmat,smat,wt,et)
- DEALLOCATE(r,z,theta,dphi,thetas,project)
- ENDIF
-
- IF(vac_memory) CALL unset_dcon_params
-c-----------------------------------------------------------------------
-c save eigenvalues and eigenvectors to file.
-c-----------------------------------------------------------------------
- IF(bin_euler)THEN
- WRITE(euler_bin_unit)3
- WRITE(euler_bin_unit)ep
- WRITE(euler_bin_unit)et
- WRITE(euler_bin_unit)wt
- WRITE(euler_bin_unit)wt0
- WRITE(euler_bin_unit)wv_farwall_flag
- ENDIF
-c-----------------------------------------------------------------------
-c write to screen and copy to output.
-c-----------------------------------------------------------------------
- IF(verbose) WRITE(*,10) REAL(ep(1)),REAL(ev(1)),
- $ REAL(et(1)),AIMAG(et(1))
-c-----------------------------------------------------------------------
-c write eigenvalues to file.
-c-----------------------------------------------------------------------
- message=""
- WRITE(out_unit,'(/1x,a)')"Total Energy Eigenvalues:"
- WRITE(out_unit,20)
- WRITE(out_unit,30)(isol,REAL(ep(isol)),REAL(ev(isol)),
- $ REAL(et(isol)),AIMAG(et(isol)),
- $ TRIM(message(isol)),isol=1,mpert)
- WRITE(out_unit,20)
-c-----------------------------------------------------------------------
-c write eigenvectors to file.
-c-----------------------------------------------------------------------
- WRITE(out_unit,*)"Total Energy Eigenvectors:"
- m=mlow+(/(isol,isol=0,mpert-1)/)
- DO isol=1,mpert
- WRITE(out_unit,40)
- WRITE(out_unit,50)isol,imax(1),REAL(ep(isol)),REAL(ev(isol)),
- $ REAL(et(isol)),AIMAG(et(isol)),TRIM(message(isol))
- WRITE(out_unit,60)
- WRITE(out_unit,70)(ipert,m(ipert),wt(ipert,isol),
- $ ABS(wt(ipert,isol)),star(ipert,isol),ipert=1,mpert)
- WRITE(out_unit,60)
- ENDDO
-c-----------------------------------------------------------------------
-c write the plasma matrix.
-c-----------------------------------------------------------------------
- WRITE(out_unit,'(/1x,a/)')"Plasma Energy Matrix:"
- DO isol=1,mpert
- WRITE(out_unit,'(1x,2(a,i3))')"isol = ",isol,", m = ",m(isol)
- WRITE(out_unit,'(/2x,"i",5x,"re wp",8x,"im wp",8x,"abs wp"/)')
- WRITE(out_unit,'(i3,1p,3e13.5)')
- $ (ipert,wp(ipert,isol),ABS(wp(ipert,isol)),ipert=1,mpert)
- WRITE(out_unit,'(/2x,"i",5x,"re wp",8x,"im wp",8x,"abs wp"/)')
- ENDDO
-c-----------------------------------------------------------------------
-c compute separate plasma and vacuum eigenvalues.
-c-----------------------------------------------------------------------
- lwork=2*mpert+1
- CALL zgeev('V','V',mpert,wp,mpert,ep,
- $ vl,mpert,vr,mpert,work2,lwork,rwork2,info)
- eindex(1:mpert)=(/(ipert,ipert=1,mpert)/)
- CALL bubble(REAL(ep),eindex,1,mpert)
- tt=ep
- DO ipert=1,mpert
- wp(:,ipert)=vr(:,eindex(mpert+1-ipert))
- ep(ipert)=tt(eindex(mpert+1-ipert))
- ENDDO
- CALL zheev('V','U',mpert,wv,mpert,ev,work,lwork,rwork,info)
-c-----------------------------------------------------------------------
-c optionally write netcdf file.
-c-----------------------------------------------------------------------
- IF(netcdf_out) CALL dcon_netcdf_out(wp,wv,wt,wt0,ep,ev,et)
-c-----------------------------------------------------------------------
-c deallocate
-c-----------------------------------------------------------------------
- CALL dcon_dealloc
-c-----------------------------------------------------------------------
-c terminate.
-c-----------------------------------------------------------------------
- RETURN
- END SUBROUTINE free_run
-c-----------------------------------------------------------------------
-c subprogram 2. free_write_msc.
-c writes boundary data for Morrell Chance's vacuum code.
-c-----------------------------------------------------------------------
-c-----------------------------------------------------------------------
-c declarations.
-c-----------------------------------------------------------------------
- SUBROUTINE free_write_msc(psifac, inmemory_op, ahgstr_op)
-
- REAL(r8), INTENT(IN) :: psifac
- LOGICAL, OPTIONAL :: inmemory_op
- LOGICAL :: inmemory = .FALSE.
-
- CHARACTER(1), PARAMETER :: tab=CHAR(9)
- INTEGER :: itheta,n
- REAL(r8) :: qa
- REAL(r8), DIMENSION(0:mtheta) :: angle,r,z,delta,rfac,theta
- CHARACTER(128) :: ahgstr
- CHARACTER(128), optional :: ahgstr_op
-
- IF(PRESENT(inmemory_op))THEN
- inmemory = inmemory_op
- ELSE
- inmemory = .FALSE.
- ENDIF
-
- IF(PRESENT(ahgstr_op))THEN
- ahgstr = ahgstr_op
- ELSE
- ahgstr = "ahg2msc_dcon.out"
- ENDIF
-
-c-----------------------------------------------------------------------
-c compute output.
-c-----------------------------------------------------------------------
- CALL spline_eval(sq,psifac,1)
- qa=sq%f(4)
-
- theta=rzphi%ys
- DO itheta=0,mtheta
- CALL bicube_eval(rzphi,psifac,theta(itheta),0)
- rfac(itheta)=SQRT(rzphi%f(1))
- angle(itheta)=twopi*(theta(itheta)+rzphi%f(2))
- delta(itheta)=-rzphi%f(3)/qa
- ENDDO
- r=ro+rfac*COS(angle)
- z=zo+rfac*SIN(angle)
-c-----------------------------------------------------------------------
-c invert values for nn < 0.
-c-----------------------------------------------------------------------
- n=nn
- IF(nn < 0)THEN
- qa=-qa
- delta=-delta
- n=-n
- ENDIF
-c-----------------------------------------------------------------------
-c pass all values in memory instead of over ascii io (faster).
-c-----------------------------------------------------------------------
- IF(inmemory)THEN
- CALL set_dcon_params(mtheta,mlow,mhigh,n,qa,r(mtheta:0:-1),
- $ z(mtheta:0:-1),delta(mtheta:0:-1))
- ELSE
-c-----------------------------------------------------------------------
-c write scalars.
-c-----------------------------------------------------------------------
- CALL ascii_open(bin_unit,ahgstr,"UNKNOWN")
- WRITE(bin_unit,'(i4,a)')mtheta,tab//tab//"mtheta"//tab//"mthin"
- $ //tab//"Number of poloidal nodes"
- WRITE(bin_unit,'(i4,a)')mlow,tab//tab//"mlow"//tab//"lmin"//tab
- $ //"Lowest poloidal harmonic"
- WRITE(bin_unit,'(i4,a,a)')mhigh,tab//tab//"mhigh"//tab//"lmax"
- $ //tab//"Highest poloidal harmonic"
- WRITE(bin_unit,'(i4,a)')n,tab//tab//"nn"//tab//"nadj"//tab
- $ //"Toroidal harmonic"
- WRITE(bin_unit,'(f13.10,a)')qa,tab//"qa"//tab//"qa1"//tab
- $ //"Safety factor at plasma edge"
-c-----------------------------------------------------------------------
-c write arrays.
-c-----------------------------------------------------------------------
- WRITE(bin_unit,'(/a/)')"Poloidal Coordinate Theta:"
- WRITE(bin_unit,'(1p,4e18.10)')(1-theta(itheta),
- $ itheta=mtheta,0,-1)
- WRITE(bin_unit,'(/a/)')"Polar Angle Eta:"
- WRITE(bin_unit,'(1p,4e18.10)')(twopi-angle(itheta),
- $ itheta=mtheta,0,-1)
- WRITE(bin_unit,'(/a/)')"Radial Coordinate X:"
- WRITE(bin_unit,'(1p,4e18.10)')(r(itheta),itheta=mtheta,0,-1)
- WRITE(bin_unit,'(/a/)')"Axial Coordinate Z:"
- WRITE(bin_unit,'(1p,4e18.10)')(z(itheta),itheta=mtheta,0,-1)
- WRITE(bin_unit,'(/a/)')"Toroidal Angle Difference Delta:"
- WRITE(bin_unit,'(1p,4e18.10)')(delta(itheta),
- $ itheta=mtheta,0,-1)
- CALL ascii_close(bin_unit)
- ENDIF
-c-----------------------------------------------------------------------
-c terminate.
-c-----------------------------------------------------------------------
- RETURN
- END SUBROUTINE free_write_msc
-c-----------------------------------------------------------------------
-c subprogram 3. free_ahb_prep.
-c prepares boundary data for Allen H. Boozers's feedback problem.
-c-----------------------------------------------------------------------
-c-----------------------------------------------------------------------
-c declarations.
-c-----------------------------------------------------------------------
- SUBROUTINE free_ahb_prep(wp,nmat,smat,asmat,bsmat,csmat,ipiva)
-
- COMPLEX(r8), DIMENSION(mpert,mpert), INTENT(IN) :: wp
- COMPLEX(r8), DIMENSION(mpert,mpert), INTENT(OUT) :: nmat,smat
- COMPLEX(r8), DIMENSION(:,:), INTENT(IN) :: asmat,bsmat,csmat
- INTEGER, DIMENSION(:), INTENT(INOUT) :: ipiva
-
- INTEGER :: itheta,iqty,ipert,info,neq
- REAL(r8) :: rfac,angle,bpfac,btfac,bfac,fac,jac,delpsi,psifac
- REAL(r8), DIMENSION(2,2) :: w
- COMPLEX(r8), DIMENSION(mpert,mpert,2) :: u,du
- TYPE(spline_type) :: spl
-c-----------------------------------------------------------------------
-c preliminary computations.
-c-----------------------------------------------------------------------
- mthsurf=40*mthsurf0*MAX(ABS(mlow),ABS(mhigh))
- ALLOCATE(r(0:mthsurf),z(0:mthsurf),theta(0:mthsurf),
- $ dphi(0:mthsurf),thetas(0:mthsurf,4),project(3,3,0:mthsurf))
- CALL spline_alloc(spl,mthsurf,4)
- theta=(/(itheta,itheta=0,mthsurf)/)/REAL(mthsurf,r8)
- spl%xs=theta
- psifac=psilim
- qsurf=qlim
- q1surf=q1lim
- CALL spline_eval(sq,psilim,0)
-c-----------------------------------------------------------------------
-c compute geometric factors.
-c-----------------------------------------------------------------------
- DO itheta=0,mthsurf
- CALL bicube_eval(rzphi,psilim,theta(itheta),1)
- rfac=SQRT(rzphi%f(1))
- angle=twopi*(theta(itheta)+rzphi%f(2))
- r(itheta)=ro+rfac*COS(angle)
- z(itheta)=zo+rfac*SIN(angle)
- dphi(itheta)=rzphi%f(3)
- jac=rzphi%f(4)
-c-----------------------------------------------------------------------
-c compute covariant basis vectors.
-c-----------------------------------------------------------------------
- w(1,1)=(1+rzphi%fy(2))*twopi**2*rfac*r(itheta)/jac
- w(1,2)=-rzphi%fy(1)*pi*r(itheta)/(rfac*jac)
- w(2,1)=-rzphi%fx(2)*twopi**2*r(itheta)*rfac/jac
- w(2,2)=rzphi%fx(1)*pi*r(itheta)/(rfac*jac)
-c-----------------------------------------------------------------------
-c compute project.
-c-----------------------------------------------------------------------
- delpsi=SQRT(w(1,1)**2+w(1,2)**2)
- project(1,1,itheta)=1/(delpsi*jac)
- project(2,1,itheta)
- $ =-(w(1,1)*w(2,1)+w(1,2)*w(2,2))/(twopi*r(itheta)*delpsi)
- project(2,2,itheta)=delpsi/(twopi*r(itheta))
- project(3,1,itheta)=rzphi%fx(3)*r(itheta)/jac
- project(3,2,itheta)=rzphi%fy(3)*r(itheta)/jac
- project(3,3,itheta)=twopi*r(itheta)/jac
-c-----------------------------------------------------------------------
-c compute alternative theta coordinates.
-c-----------------------------------------------------------------------
- bpfac=psio*delpsi/r(itheta)
- btfac=sq%f(1)/(twopi*r(itheta))
- bfac=SQRT(bpfac*bpfac+btfac*btfac)
- fac=r(itheta)**power_r/(bpfac**power_bp*bfac**power_b)
- spl%fs(itheta,1)=fac
- spl%fs(itheta,2)=fac/r(itheta)**2
- spl%fs(itheta,3)=fac*bpfac
- !modified for boozer coordinates.
- spl%fs(itheta,4)=fac*bfac**2
- ENDDO
-c-----------------------------------------------------------------------
-c compute alternative poloidal coordinates.
-c-----------------------------------------------------------------------
- CALL spline_fit(spl,"periodic")
- CALL spline_int(spl)
- DO iqty=1,4
- thetas(:,iqty)=spl%fsi(:,iqty)/spl%fsi(mthsurf,iqty)
- ENDDO
- CALL spline_dealloc(spl)
-c-----------------------------------------------------------------------
-c compute displacements and their derivatives.
-c-----------------------------------------------------------------------
- msol=mpert
- neq=4*mpert*msol
- psifac=psilim
- u(:,:,1)=0
- DO ipert=1,mpert
- u(ipert,ipert,1)=1
- ENDDO
- u(:,:,2)=wp*psio**2
- CALL sing_der(neq,psifac,u,du)
- nmat=du(:,:,1)
- smat=-(MATMUL(bsmat,du(:,:,1))+MATMUL(csmat,u(:,:,1)))
- CALL zhetrs('L',mpert,mpert,asmat,mpert,ipiva,smat,mpert,info)
-c-----------------------------------------------------------------------
-c terminate.
-c-----------------------------------------------------------------------
- RETURN
- END SUBROUTINE free_ahb_prep
-c-----------------------------------------------------------------------
-c subprogram 4. free_ahb_write.
-c writes boundary data for Allen H. Boozers's feedback problem.
-c-----------------------------------------------------------------------
-c-----------------------------------------------------------------------
-c declarations.
-c-----------------------------------------------------------------------
- SUBROUTINE free_ahb_write(nmat,smat,wt,et)
-
- COMPLEX(r8), DIMENSION(mpert,mpert), INTENT(IN) :: nmat,smat,wt
- COMPLEX(r8), DIMENSION(mpert), INTENT(IN) :: et
-
- INTEGER :: itheta,ipert,isol,m
- INTEGER, DIMENSION(mpert) :: mvec
- REAL(r8) :: chi1
- COMPLEX(r8) :: expfac,expfac0,expfac1,phase
- COMPLEX(r8), DIMENSION(mpert) :: singfac
- COMPLEX(r8), DIMENSION(mpert,mpert) :: xin,xis
- COMPLEX(r8), DIMENSION(mpert,mpert,3) :: jqvec
- COMPLEX(r8), DIMENSION(mpert,0:mthsurf,3) :: bvec0,bvec
-c-----------------------------------------------------------------------
-c compute Fourier components: xsp1_mn = xin, xss_mn = xis.
-c-----------------------------------------------------------------------
- xin=MATMUL(nmat,wt)
- xis=MATMUL(smat,wt)
- mvec=(/(m,m=mlow,mhigh)/)
- chi1=twopi*psio
- singfac=chi1*twopi*ifac*(mvec-nn*qsurf)
- DO isol=1,mpert
- jqvec(:,isol,1)=wt(:,isol)*singfac
- jqvec(:,isol,2)=-chi1*xin(:,isol)-twopi*ifac*nn*xis(:,isol)
- jqvec(:,isol,3)=-chi1*(qsurf*xin(:,isol)+q1surf*wt(:,isol))
- $ -twopi*ifac*mvec*xis(:,isol)
- ENDDO
-c-----------------------------------------------------------------------
-c transform to configuration space.
-c-----------------------------------------------------------------------
- expfac0=EXP(twopi*ifac*theta(1))
- expfac1=1
- bvec0=0
- DO itheta=0,mthsurf-1
- expfac=EXP(ifac*(twopi*mlow*theta(itheta)+nn*dphi(itheta)))
- DO ipert=1,mpert
- bvec0(:,itheta,:)=bvec0(:,itheta,:)+jqvec(ipert,:,:)*expfac
- expfac=expfac*expfac1
- ENDDO
- expfac1=expfac1*expfac0
- ENDDO
- bvec0(:,mthsurf,:)=bvec0(:,0,:)
-c-----------------------------------------------------------------------
-c compute orthogonal components of perturbed magnetic field.
-c-----------------------------------------------------------------------
- DO isol=1,msol
- bvec(isol,:,1)=project(1,1,:)*bvec0(isol,:,1)
- bvec(isol,:,2)
- $ =project(2,1,:)*bvec0(isol,:,1)
- $ +project(2,2,:)*bvec0(isol,:,2)
- bvec(isol,:,3)
- $ =project(3,1,:)*bvec0(isol,:,1)
- $ +project(3,2,:)*bvec0(isol,:,2)
- $ +project(3,3,:)*bvec0(isol,:,3)
- phase=bvec(isol,0,1)/ABS(bvec(isol,0,1))
- bvec(isol,:,:)=bvec(isol,:,:)/phase
- ENDDO
-c-----------------------------------------------------------------------
-c open dcon_surf.out, write geometry and eigenvalues.
-c-----------------------------------------------------------------------
- CALL ascii_open(bin_unit,"dcon_surf.out","UNKNOWN")
- WRITE(bin_unit,'(a/a/a/)')"Output from DCON, ",
- $ "total perturbed energy eigenvalues",
- $ "and normal magnetic field eigenvectors"
- WRITE(bin_unit,'(3(a,i4),a,1p,e16.8)')
- $ "mthsurf = ",mthsurf,", msol = ",msol,", nn = ",nn,
- $ ", qsurf = ",qsurf
- WRITE(bin_unit,'(/a//(1p,5e16.8))')"radial position r:",r
- WRITE(bin_unit,'(/a//(1p,5e16.8))')"axial position z:",z
- WRITE(bin_unit,'(/a//(1p,5e16.8))')
- $ "total energy eigenvalues et:",et*psio**2/(2*mu0)
-c-----------------------------------------------------------------------
-c write perturbed normal magnetic field.
-c-----------------------------------------------------------------------
- DO isol=1,mpert
- WRITE(bin_unit,'(/a,i3,a/)')"normal magnetic eigenvector"
- $ //", isol = ",isol,", cos factor:"
- WRITE(bin_unit,'(1p,5e16.8)')REAL(bvec(isol,:,1))
- WRITE(bin_unit,'(/a,i3,a/)')"normal magnetic eigenvector"
- $ //", isol = ",isol,", sin factor:"
- WRITE(bin_unit,'(1p,5e16.8)')AIMAG(bvec(isol,:,1))
- ENDDO
-c-----------------------------------------------------------------------
-c write perturbed poloidal magnetic field.
-c-----------------------------------------------------------------------
- DO isol=1,mpert
- WRITE(bin_unit,'(/a,i3,a/)')"poloidal magnetic eigenvector"
- $ //", isol = ",isol,", cos factor:"
- WRITE(bin_unit,'(1p,5e16.8)')REAL(bvec(isol,:,2))
- WRITE(bin_unit,'(/a,i3,a/)')"poloidal magnetic eigenvector,"
- $ //" isol = ",isol,", sin factor:"
- WRITE(bin_unit,'(1p,5e16.8)')AIMAG(bvec(isol,:,2))
- ENDDO
-c-----------------------------------------------------------------------
-c write perturbed toroidal magnetic field.
-c-----------------------------------------------------------------------
- DO isol=1,mpert
- WRITE(bin_unit,'(/a,i3,a/)')"toroidal magnetic eigenvector,"
- $ //" isol = ",isol,", cos factor:"
- WRITE(bin_unit,'(1p,5e16.8)')REAL(bvec(isol,:,3))
- WRITE(bin_unit,'(/a,i3,a/)')"toroidal magnetic eigenvector"
- $ //", isol = ",isol,", sin factor:"
- WRITE(bin_unit,'(1p,5e16.8)')AIMAG(bvec(isol,:,3))
- ENDDO
- CALL ascii_close(bin_unit)
-c-----------------------------------------------------------------------
-c draw graphs.
-c-----------------------------------------------------------------------
- CALL bin_open(bin_unit,"ahb.bin","UNKNOWN","REWIND","none")
- DO isol=1,mpert
- DO itheta=0,mthsurf
- WRITE(bin_unit)REAL(theta(itheta),4),
- $ REAL(REAL(bvec(isol,itheta,:)),4),
- $ REAL(AIMAG(bvec(isol,itheta,:)),4),
- $ REAL(thetas(itheta,:),4),
- $ REAL(thetas(itheta,:)-theta(itheta),4)
- ENDDO
- WRITE(bin_unit)
- IF(isol == msol_ahb)EXIT
- ENDDO
- CALL bin_close(bin_unit)
-c-----------------------------------------------------------------------
-c terminate.
-c-----------------------------------------------------------------------
- RETURN
- END SUBROUTINE free_ahb_write
-c-----------------------------------------------------------------------
-c subprogram 5. free_test.
-c Trimmed down version of free_run computing total dW.
-c Can also calculate plasma and vacuum eigenvalues IFF debugging
-c-----------------------------------------------------------------------
-c-----------------------------------------------------------------------
-c declarations.
-c-----------------------------------------------------------------------
- SUBROUTINE free_test(plasma1,vacuum1,total1,psifac)
-
- COMPLEX(r8), INTENT(OUT) :: plasma1,vacuum1,total1
- REAL(r8), INTENT(IN) :: psifac
-
- LOGICAL, PARAMETER :: normalize=.TRUE., debug=.FALSE.
- LOGICAL, SAVE :: first_call=.TRUE.
- INTEGER :: ipert,jpert,isol,info,lwork,i
- INTEGER, DIMENSION(mpert) :: ipiv,m,eindex
- REAL(r8) :: v1
- REAL(r8), DIMENSION(mpert) :: singfac
- ! eigenvalues are complex for gpec
- COMPLEX(r8), DIMENSION(mpert) :: et,tt
-
- REAL(r8), DIMENSION(2*mpert) :: rwork2
- COMPLEX(r8) :: norm
- COMPLEX(r8), DIMENSION(2*mpert+1) :: work2
- COMPLEX(r8), DIMENSION(mpert,mpert) :: wp,wv,wt,wt0,temp
- COMPLEX(r8), DIMENSION(mpert,mpert) :: vl,vr
- LOGICAL, PARAMETER :: complex_flag=.TRUE.
- REAL(r8) :: kernelsignin
-c-----------------------------------------------------------------------
-c Basic parameters at this psi
-c-----------------------------------------------------------------------
- CALL spline_eval(sq,psifac,0)
- v1=sq%f(3)
-c-----------------------------------------------------------------------
-c compute plasma response matrix.
-c-----------------------------------------------------------------------
- temp=CONJG(TRANSPOSE(u(:,1:mpert,1)))
- wp=u(:,1:mpert,2)
- wp=CONJG(TRANSPOSE(wp))
- CALL zgetrf(mpert,mpert,temp,mpert,ipiv,info)
- CALL zgetrs('N',mpert,mpert,temp,mpert,ipiv,wp,mpert,info)
- wp=CONJG(TRANSPOSE(wp))/psio**2
-c-----------------------------------------------------------------------
-c compute vacuum response matrix.
-c-----------------------------------------------------------------------
- wv = 0
- ! calc a rough spline of wv so we don't call mscvac (slow) every time
- IF(first_call)THEN
- CALL free_wvmats
- CALL spline_eval(sq,psifac,0)
- first_call = .FALSE.
- ENDIF
- CALL cspline_eval(wvmats, psifac,0)
- wv=RESHAPE(wvmats%f,(/mpert,mpert/))
-c-----------------------------------------------------------------------
-c compute complex energy eigenvalues.
-c-----------------------------------------------------------------------
- wt=wp+wv
- wt0=wt
- lwork=2*mpert+1
- CALL zgeev('V','V',mpert,wt,mpert,et,
- $ vl,mpert,vr,mpert,work2,lwork,rwork2,info)
- eindex(1:mpert)=(/(ipert,ipert=1,mpert)/)
- CALL bubble(REAL(et),eindex,1,mpert)
- tt=et
- DO ipert=1,mpert
- wt(:,ipert)=vr(:,eindex(mpert+1-ipert))
- et(ipert)=tt(eindex(mpert+1-ipert))
- ENDDO
-c-----------------------------------------------------------------------
-c normalize eigenfunction and energy.
-c-----------------------------------------------------------------------
- IF(normalize)THEN
- isol=1 ! only bother with the first one
- norm=0
- DO ipert=1,mpert
- DO jpert=1,mpert
- norm=norm+jmat(jpert-ipert)
- $ *wt(ipert,isol)*CONJG(wt(jpert,isol))
- ENDDO
- ENDDO
- norm=norm/v1
- et(isol)=et(isol)/norm
- ENDIF
- total1=et(1)
-c-----------------------------------------------------------------------
-c compute plasma and vacuum eigenvalues
-c DIFFERS FROM free_run, which calcs energies of the total eigenmode
-c-----------------------------------------------------------------------
- IF(debug)THEN
- wt=wp
- wt0=wt
- lwork=2*mpert+1
- CALL zgeev('V','V',mpert,wt,mpert,et,
- $ vl,mpert,vr,mpert,work2,lwork,rwork2,info)
- eindex(1:mpert)=(/(ipert,ipert=1,mpert)/)
- CALL bubble(REAL(et),eindex,1,mpert)
- tt=et
- DO ipert=1,mpert
- wt(:,ipert)=vr(:,eindex(mpert+1-ipert))
- et(ipert)=tt(eindex(mpert+1-ipert))
- ENDDO
- plasma1=et(1)
-
- wt=wv
- wt0=wt
- lwork=2*mpert+1
- CALL zgeev('V','V',mpert,wt,mpert,et,
- $ vl,mpert,vr,mpert,work2,lwork,rwork2,info)
- eindex(1:mpert)=(/(ipert,ipert=1,mpert)/)
- CALL bubble(REAL(et),eindex,1,mpert)
- tt=et
- DO ipert=1,mpert
- wt(:,ipert)=vr(:,eindex(mpert+1-ipert))
- et(ipert)=tt(eindex(mpert+1-ipert))
- ENDDO
- vacuum1=et(1)
- ELSE
- plasma1 = 0.0
- vacuum1 = 0.0
- ENDIF
-c-----------------------------------------------------------------------
-c terminate.
-c-----------------------------------------------------------------------
- RETURN
- END SUBROUTINE free_test
-c-----------------------------------------------------------------------
-c subprogram 6. free_wvmats.
-c Forms a spline of the vacuum matrix over a specified range
-c for rapid calls to free_test. Range is expected to be be between
-c rationals.
-c-----------------------------------------------------------------------
-c-----------------------------------------------------------------------
-c declarations.
-c-----------------------------------------------------------------------
- SUBROUTINE free_wvmats
-
- INTEGER :: npsi,i,ipert,it,itmax=50
- REAL(r8) :: qi, psii, dpsi, eps=1e-9
- REAL(r8), DIMENSION(mpert) :: singfac
- COMPLEX(r8), DIMENSION(mpert,mpert) :: wv
- LOGICAL, PARAMETER :: complex_flag=.TRUE.,wall_flag=.FALSE.
- LOGICAL :: farwal_flag=.FALSE.
- REAL(r8) :: kernelsignin
- INTEGER :: vac_unit
- CHARACTER(128) :: ahgstr
-c-----------------------------------------------------------------------
-c Basic parameters for course scan of psi
-c-----------------------------------------------------------------------
- npsi = MAX(4, CEILING((qlim - q_edge(1)) * nn * 4)) ! 4 pts per q window, 4 if q edge spans less than one full window
- psii = psiedge ! should start exactly here
- CALL cspline_alloc(wvmats,npsi,mpert**2)
- DO i=0,npsi
- ! file name is ahg2msc_{i}.out
- ahgstr = "ahg2msc_"//CHAR(i)//".out"
- ! space point evenly in q
- qi = q_edge(1) + (qlim - q_edge(1)) * i * 1.0/npsi
- ! use newton iteration to find psilim.
- it=0
- DO
- it=it+1
- CALL spline_eval(sq, psii, 1)
- dpsi=(qi-sq%f(4)) / sq%f1(4)
- psii = psii + dpsi
- IF(ABS(dpsi) < eps*ABS(psii) .OR. it > itmax)EXIT
- ENDDO
- ! call mscvac and save matrices to spline
- wvmats%xs(i) = psii
- CALL spline_eval(sq, wvmats%xs(i), 0)
- CALL free_write_msc(wvmats%xs(i), inmemory_op=.TRUE.,
- $ ahgstr_op=ahgstr)
- kernelsignin=1.0
- ALLOCATE(grri(2*(mthvac+5),mpert*2),xzpts(mthvac+5,4))
- CALL mscvac(wv,mpert,mtheta,mthvac,complex_flag,kernelsignin,
- $ wall_flag,farwal_flag,grri,xzpts,ahgstr)
- singfac=mlow-nn*sq%f(4)+(/(ipert,ipert=0,mpert-1)/)
- DO ipert=1,mpert
- wv(ipert,:)=wv(ipert,:)*singfac
- wv(:,ipert)=wv(:,ipert)*singfac
- ENDDO
- wvmats%fs(i,:)=RESHAPE(wv,(/mpert**2/))
- DEALLOCATE(grri,xzpts)
- ENDDO
- CALL unset_dcon_params
- CALL cspline_fit(wvmats,"extrap")
-c-----------------------------------------------------------------------
-c terminate.
-c-----------------------------------------------------------------------
- RETURN
- END SUBROUTINE free_wvmats
- END MODULE free_mod
diff --git a/src/DCON/fortran/makefile b/src/DCON/fortran/makefile
deleted file mode 100644
index b17442383e..0000000000
--- a/src/DCON/fortran/makefile
+++ /dev/null
@@ -1,87 +0,0 @@
-
-include ../install/DEFAULTS.inc
-
-IFLAGS = -I../equil -I../harvest -I../pentrc -I../vacuum -I$(MATHINC) -I$(NETCDFINC)
-F90 = $(FC) $(FFLAGS) $(OMPFLAG) $(IFLAGS) $(RECURSFLAG) $(LEGACYFLAG)
-export FFLAGS # for sub-makes
-
-.f.o:
- $(F90) -c $*.f
-
-.F.o:
- $(F90) -c $*.F
-
-LIBDIR = ../lib
-
-LIBS = \
- -lpentrc \
- -llsode \
- -lequil \
- -lvac \
- -lharvest \
-
-OBJS = \
- debug.o \
- dcon_mod.o \
- mercier.o \
- bal.o \
- fourfit.o \
- sing.o \
- ode_output.o \
- free.o \
- ode.o \
- dcon_netcdf.o \
- resist.o \
- dcon.o
-
-# targets
-
-all: harvest lsode equil vacuum pentrc dcon
-
-harvest:
- cd ../; git submodule init; git submodule update
- cd ../harvest; make FC=$(FC) CC=$(CC) GACODE_ROOT= -f Makefile libharvest.a
- mkdir -p ../lib
- cp -f ../harvest/libharvest.a ../lib/
-
-lsode:
- cd ../lsode; make
-
-equil:
- cd ../equil; make
-
-vacuum:
- cd ../vacuum; make
-
-pentrc:
- cd ../pentrc; make pentrc
-
-# note we explicitly make pentrc to force sync the compile-time version variable
-dcon: pentrc $(OBJS)
- $(F90) -o dcon $(OBJS) -L$(LIBDIR) $(LIBS) -L$(MATHDIR) $(MATHLIBS) -L$(NETCDFDIR) $(NETCDFLIBS) $(NETCDF_EXTRA_LIBS) $(LDFLAGS)
- mkdir -p ../bin
- cp -f dcon ../bin
-
-clean:
- rm -f *.o *.mod *.out *.bin sum.dat *~ *.diff dcon *.original
-
-# dependencies
-
-dcon_mod.o: ../equil/spline_mod.mod ../equil/global_mod.mod \
- ../equil/equil_mod.mod ../equil/equil_out_mod.mod ../pentrc/dcon_interface.mod
-mercier.o: dcon_mod.o
-bal.o: dcon_mod.o
-fourfit.o: ../equil/fspline_mod.mod ../equil/global_mod.mod \
- ../pentrc/pentrc_interface.mod ../pentrc/utilities.mod ../pentrc/torque.mod ../pentrc/inputs.mod \
- ../pentrc/energy_integration.mod ../pentrc/pitch_integration.mod ../pentrc/dcon_interface.mod \
- dcon_mod.o
-sing.o: fourfit.o
-debug.o: ../equil/local_mod.mod
-ode_output.o: dcon_mod.o sing.o debug.o
-ode.o: ode_output.o free.o
-dcon_netcdf.o: dcon_mod.o
-free.o: ../equil/global_mod.mod dcon_netcdf.o ode_output.o
-resist.o: dcon_mod.o
-dcon.o: ../equil/equil_mod.mod ../equil/equil_out_mod.mod \
- ../pentrc/inputs.o ../pentrc/pentrc_interface.o \
- bal.o mercier.o ode.o free.o resist.o
diff --git a/src/DCON/fortran/mercier.f b/src/DCON/fortran/mercier.f
deleted file mode 100644
index ac312ad144..0000000000
--- a/src/DCON/fortran/mercier.f
+++ /dev/null
@@ -1,105 +0,0 @@
-c-----------------------------------------------------------------------
-c file mercier.f.
-c computes mercier criterion and related quantities.
-c-----------------------------------------------------------------------
-c-----------------------------------------------------------------------
-c code organization.
-c-----------------------------------------------------------------------
-c 0. mercier_mod.
-c 1. mercier_scan.
-c-----------------------------------------------------------------------
-c subprogram 0. mercier_mod.
-c module declarations.
-c-----------------------------------------------------------------------
-c-----------------------------------------------------------------------
-c declarations.
-c-----------------------------------------------------------------------
- MODULE mercier_mod
- USE dcon_mod
- IMPLICIT NONE
-
- CONTAINS
-c-----------------------------------------------------------------------
-c subprogram 1. mercier_scan.
-c evaluates mercier criterion and related quantities.
-c-----------------------------------------------------------------------
-c-----------------------------------------------------------------------
-c declarations.
-c-----------------------------------------------------------------------
- SUBROUTINE mercier_scan
-
- INTEGER :: ipsi,itheta
- REAL(r8) :: bsq,chi1,di,dpsisq,eta,h,jac,p1,psifac,q,q1,r,
- $ rfac,term,theta,twopif,v1,v2,v21,v22,v23,v33
- REAL(r8), DIMENSION(:), POINTER :: avg
- TYPE(spline_type), TARGET :: ff
-c-----------------------------------------------------------------------
-c prepare spline types.
-c-----------------------------------------------------------------------
- CALL spline_alloc(ff,mtheta,5)
- ff%xs=rzphi%ys
-c-----------------------------------------------------------------------
-c compute surface quantities.
-c-----------------------------------------------------------------------
- DO ipsi=0,mpsi
- psifac=sq%xs(ipsi)
- twopif=sq%fs(ipsi,1)
- p1=sq%fs1(ipsi,2)
- v1=sq%fs(ipsi,3)
- v2=sq%fs1(ipsi,3)
- q=sq%fs(ipsi,4)
- q1=sq%fs1(ipsi,4)
- chi1=twopi*psio
-c-----------------------------------------------------------------------
-c evaluate coordinates and jacobian.
-c-----------------------------------------------------------------------
- DO itheta=0,mtheta
- CALL bicube_eval(rzphi,rzphi%xs(ipsi),rzphi%ys(itheta),1)
- theta=rzphi%ys(itheta)
- rfac=SQRT(rzphi%f(1))
- eta=twopi*(theta+rzphi%f(2))
- r=ro+rfac*COS(eta)
- jac=rzphi%f(4)
-c-----------------------------------------------------------------------
-c evaluate other local quantities.
-c-----------------------------------------------------------------------
- v21=rzphi%fy(1)/(2*rfac*jac)
- v22=(1+rzphi%fy(2))*twopi*rfac/jac
- v23=rzphi%fy(3)*r/jac
- v33=twopi*r/jac
- bsq=chi1**2*(v21**2+v22**2+(v23+q*v33)**2)
- dpsisq=(twopi*r)**2*(v21**2+v22**2)
-c-----------------------------------------------------------------------
-c evaluate integrands.
-c-----------------------------------------------------------------------
- ff%fs(itheta,1)=bsq/dpsisq
- ff%fs(itheta,2)=1/dpsisq
- ff%fs(itheta,3)=1/bsq
- ff%fs(itheta,4)=1/(bsq*dpsisq)
- ff%fs(itheta,5)=bsq
- ff%fs(itheta,:)=ff%fs(itheta,:)*jac/v1
- ENDDO
-c-----------------------------------------------------------------------
-c integrate quantities with respect to theta.
-c-----------------------------------------------------------------------
- CALL spline_fit(ff,"periodic")
- CALL spline_int(ff)
- avg => ff%fsi(mtheta,:)
-c-----------------------------------------------------------------------
-c evaluate mercier criterion and related quantities.
-c-----------------------------------------------------------------------
- term=twopif*p1*v1/(q1*chi1**3)*avg(2)
- di=-.25+term*(1-term)+p1*(v1/(q1*chi1**2))**2*avg(1)
- $ *(p1*(avg(3)+(twopif/chi1)**2*avg(4))-v2/v1)
- h=twopif*p1*v1/(q1*chi1**3)*(avg(2)-avg(1)/avg(5))
- locstab%fs(ipsi,1)=di*locstab%xs(ipsi)
- locstab%fs(ipsi,2)=(di+(h-0.5)**2)*locstab%xs(ipsi)
- locstab%fs(ipsi,3)=h
- ENDDO
- CALL spline_dealloc(ff)
-c-----------------------------------------------------------------------
-c terminate.
-c-----------------------------------------------------------------------
- RETURN
- END SUBROUTINE mercier_scan
- END MODULE mercier_mod
diff --git a/src/DCON/fortran/ode.f b/src/DCON/fortran/ode.f
deleted file mode 100644
index 5acdaa8d13..0000000000
--- a/src/DCON/fortran/ode.f
+++ /dev/null
@@ -1,1320 +0,0 @@
-c-----------------------------------------------------------------------
-c file ode.f.
-c sets up and integrates Euler-Lagrange differential equations.
-c-----------------------------------------------------------------------
-c-----------------------------------------------------------------------
-c code organization.
-c-----------------------------------------------------------------------
-c 0. ode_mod.
-c 1. ode_run.
-c 2. ode_axis_init.
-c 3. ode_sing_init.
-c 4. ode_ideal_cross.
-c 5. ode_kin_cross.
-c 6. ode_resist_cross.
-c 7. ode_step.
-c 8. ode_unorm.
-c 9. ode_fixup.
-c 10. ode_test.
-c 11. ode_test_fixup.
-c 12. ode_record_edge
-c-----------------------------------------------------------------------
-c subprogram 0. ode_mod.
-c module declarations.
-c-----------------------------------------------------------------------
-c-----------------------------------------------------------------------
-c declarations.
-c-----------------------------------------------------------------------
- MODULE ode_mod
- USE fourfit_mod
- USE ode_output_mod
- USE debug_mod
- USE free_mod
- IMPLICIT NONE
-
- LOGICAL :: new
- LOGICAL, PARAMETER :: diagnose_ca=.FALSE.
- CHARACTER(12) :: next
- INTEGER, PRIVATE :: istate,liw,lrw,iopt,itask,itol,mf,ix
- INTEGER, DIMENSION(20), PRIVATE :: iwork
- REAL(r8), PRIVATE :: psiout
- REAL(r8), PARAMETER, PRIVATE :: eps=1e-10
- REAL(r8), DIMENSION(:), POINTER, PRIVATE :: rwork
- COMPLEX(r8), DIMENSION(:,:,:), POINTER :: atol
-
- INTEGER, DIMENSION(:), POINTER :: index
- REAL(r8), DIMENSION(:), POINTER :: unorm,unorm0
- COMPLEX(r8), DIMENSION(:,:), POINTER :: fixfac
-
- CHARACTER(4) :: sort_type="absm"
- INTEGER :: flag_count
-
- CONTAINS
-c-----------------------------------------------------------------------
-c subprogram 1. ode_run.
-c integrates the differential equations.
-c-----------------------------------------------------------------------
-c-----------------------------------------------------------------------
-c declarations.
-c-----------------------------------------------------------------------
- SUBROUTINE ode_run
-
- CHARACTER(64) :: message
- LOGICAL :: force_output, test, first
-c-----------------------------------------------------------------------
-c initialize.
-c-----------------------------------------------------------------------
- IF(sing_start <= 0)THEN
- CALL ode_axis_init
- ELSE IF(sing_start <= msing)THEN
- CALL ode_sing_init
- ELSE
- WRITE(message,'(2(a,i2))')
- $ "sing_start = ",sing_start," > msing = ",msing
- CALL program_stop(message)
- ENDIF
- flag_count=0
- CALL ode_output_open
- IF(diagnose_ca)CALL ascii_open(ca_unit,"ca.out","UNKNOWN")
-c-----------------------------------------------------------------------
-c integrate.
-c-----------------------------------------------------------------------
- DO
- first = .TRUE.
- DO
- IF(istep > 0)CALL ode_unorm(.FALSE.)
- ! always record the first and last point in an inter-rational region
- ! these are important for resonant quantities
- ! recording the last point is cirtical for matching the nominal edge
- test = ode_test()
- force_output = first .OR. test
- CALL ode_output_step(unorm, op_force=force_output)
- CALL ode_record_edge
- IF(test)EXIT
- CALL ode_step
- first = .FALSE.
- ENDDO
-c-----------------------------------------------------------------------
-c re-initialize.
-c-----------------------------------------------------------------------
- IF(ising == ksing)EXIT
- IF(next == "cross")THEN
- IF(res_flag)THEN
- CALL ode_resist_cross
- ELSE
- IF(kin_flag)THEN
- CALL ode_kin_cross
- ELSE
- CALL ode_ideal_cross
- ENDIF
- ENDIF
- ELSE
- EXIT
- ENDIF
- flag_count=0
- ENDDO
-c-----------------------------------------------------------------------
-c finalize.
-c-----------------------------------------------------------------------
- CALL ode_output_close
- DEALLOCATE(rwork,atol,unorm0,unorm,index,fixfac)
- IF(diagnose_ca)CALL ascii_close(ca_unit)
-c-----------------------------------------------------------------------
-c terminate.
-c-----------------------------------------------------------------------
- RETURN
- END SUBROUTINE ode_run
-c-----------------------------------------------------------------------
-c subprogram 2. ode_axis_init.
-c initializes variables near axis.
-c-----------------------------------------------------------------------
-c-----------------------------------------------------------------------
-c declarations.
-c-----------------------------------------------------------------------
- SUBROUTINE ode_axis_init
-
- INTEGER :: ipert
- REAL(r8), DIMENSION(mpert) :: key,m
- INTEGER :: jpsi,it,itmax=50
- REAL(r8) :: dpsi,q,q1,eps=1e-10
-c-----------------------------------------------------------------------
-c preliminary computations.
-c-----------------------------------------------------------------------
- new=.TRUE.
- ix=0
- psiout=1
- psifac=sq%xs(0)
-c-----------------------------------------------------------------------
-c use newton iteration to find starting psi if qlow it is above q0
-c-----------------------------------------------------------------------
- IF(qlow > sq%fs(0, 4))THEN
- ! start check from the edge for robustness in reverse shear cores
- DO jpsi = sq%mx-1, 1, -1 ! avoid starting iteration on endpoints
- IF(sq%fs(jpsi - 1, 4) < qlow) EXIT
- ENDDO
- psifac=sq%xs(jpsi)
- it=0
- DO
- it=it+1
- CALL spline_eval(sq,psifac,1)
- q=sq%f(4)
- q1=sq%f1(4)
- dpsi=(qlow-q)/q1
- psifac=psifac+dpsi
- IF(ABS(dpsi) < eps*ABS(psifac) .OR. it > itmax)EXIT
- ENDDO
- ENDIF
-c-----------------------------------------------------------------------
-c find inner singular surface.
-c-----------------------------------------------------------------------
- ising=0
- IF(kin_flag)THEN
- DO ising=1,kmsing
- IF(kinsing(ising)%psifac > psifac) EXIT
- ENDDO
- ELSE
- DO ising=1,msing
- IF(sing(ising)%psifac > psifac) EXIT
- ENDDO
- ENDIF
- ising = MAX(0, ising-1)
-c-----------------------------------------------------------------------
-c find next singular surface.
-c-----------------------------------------------------------------------
- IF(kin_flag)THEN
- DO
- ising=ising+1
- IF(ising > kmsing)EXIT
- IF(psilim=nn*q)EXIT
- ENDDO
- IF(ising>kmsing.OR.singfac_min==0)THEN
- psimax=psilim*(1-eps)
- next="finish"
- ELSEIF(psilim msing.OR.psilim=nn*q)EXIT
- ENDDO
- IF(ising>msing.OR.psilim 0)key=key-sing(1)%m
- key=-ABS(key)
- CASE DEFAULT
- CALL program_stop("Cannot recognize sort_type = "
- $ //TRIM(sort_type))
- END SELECT
- CALL bubble(key,index,1,mpert)
-c-----------------------------------------------------------------------
-c initialize solutions.
-c-----------------------------------------------------------------------
- u=0
- DO ipert=1,mpert
- u(index(ipert),ipert,2)=1
- ENDDO
- msol=mpert
- neq=4*mpert*msol
- u_save=u
- psi_save=psifac
-c-----------------------------------------------------------------------
-c initialize integrator parameters.
-c-----------------------------------------------------------------------
- istep=0
- iopt=1
- itask=5
- itol=2
- mf=10
- istate=1
-c-----------------------------------------------------------------------
-c compute conditions at next singular surface.
-c-----------------------------------------------------------------------
- q=sq%fs(0,4)
- IF(kin_flag)THEN
- IF(kmsing > 0)THEN
- m1=NINT(nn*kinsing(ising)%q)
- ELSE
- m1=NINT(nn*qlim)+NINT(SIGN(one,nn*sq%fs1(mpsi,4)))
- ENDIF
- ELSE
- IF(msing > 0)THEN
- m1=NINT(nn*sing(ising)%q)
- ELSE
- m1=NINT(nn*qlim)+NINT(SIGN(one,nn*sq%fs1(mpsi,4)))
- ENDIF
- ENDIF
- singfac=ABS(m1-nn*q)
-c-----------------------------------------------------------------------
-c set up work arrays.
-c-----------------------------------------------------------------------
- liw=SIZE(iwork)
- lrw=22+64*mpert*msol
- ALLOCATE(rwork(lrw),atol(mpert,msol,2),fixfac(msol,msol))
- iwork=0
- rwork=0
- rwork(1)=psimax
- rwork(5)=psifac*1e-3
- rwork(11)=rwork(5)
-c-----------------------------------------------------------------------
-c terminate.
-c-----------------------------------------------------------------------
- RETURN
- END SUBROUTINE ode_axis_init
-c-----------------------------------------------------------------------
-c subprogram 3. ode_sing_init.
-c re-initializes solution across singular surface.
-c-----------------------------------------------------------------------
-c-----------------------------------------------------------------------
-c declarations.
-c-----------------------------------------------------------------------
- SUBROUTINE ode_sing_init
-
- LOGICAL, PARAMETER :: diagnose=.FALSE.,old_init=.FALSE.
- CHARACTER(1), DIMENSION(mpert) :: star
- INTEGER :: ipert,isol,ipert0,ieq,m
- REAL(r8) :: dpsi
- COMPLEX(r8), DIMENSION(mpert,2*mpert,2) :: ua
-c-----------------------------------------------------------------------
-c format statements.
-c-----------------------------------------------------------------------
- 10 FORMAT(3x,"mlow",1x,"mhigh",1x,"mpert",5x,"q",8x,"psifac",6x,
- $ "dpsi",4x,"order"//3i6,1p,3e11.3,i6/)
- 20 FORMAT(1x,a,i2,a,i3,": ",a)
- 30 FORMAT(/5x,"i",
- $ 2x,2(3x,"re u(",i1,")",4x,"im u(",i1,")",1x),
- $ 2x,2(3x,"re du(",i1,")",3x,"im du(",i1,")")/)
- 40 FORMAT((i6,1p,2(2x,4e11.3),a3))
-c-----------------------------------------------------------------------
-c initialize position.
-c-----------------------------------------------------------------------
- new=.TRUE.
- ising=sing_start
- dpsi=singfac_min/ABS(nn*sing(ising)%q1)*10
- psifac=sing(ising)%psifac+dpsi
- q=sing(ising)%q+dpsi*sing(ising)%q1
-c-----------------------------------------------------------------------
-c allocate and initialize solutions.
-c-----------------------------------------------------------------------
- ALLOCATE(u(mpert,mpert,2),du(mpert,mpert,2),u_save(mpert,mpert,2),
- $ unorm0(2*mpert),unorm(2*mpert),index(2*mpert))
- IF(old_init)THEN
- u=0
- DO ipert=1,mpert
- u(ipert,ipert,2)=1
- ENDDO
- ELSE
- CALL sing_get_ua(ising,psifac,ua)
- u=ua(:,mpert+1:2*mpert,:)
- ENDIF
- u_save=u
- psi_save=psifac
- msol=mpert
- neq=4*mpert*msol
-c-----------------------------------------------------------------------
-c diagnose output.
-c-----------------------------------------------------------------------
- IF(diagnose)THEN
- CALL sing_der(neq,psifac,u,du)
- CALL ascii_open(init_out_unit,"init.out","UNKNOWN")
- WRITE(init_out_unit,'(1x,a/)')"Output from ode_sing_init"
- WRITE(init_out_unit,10)mlow,mhigh,mpert,q,psifac,dpsi,
- $ sing_order
- ipert0=sing(ising)%m-mlow+1
- star=" "
- star(ipert0)="*"
- m=mlow
- DO isol=1,msol
- WRITE(init_out_unit,20)"isol = ",isol,", m = ",m,star(isol)
- WRITE(init_out_unit,30)(ieq,ieq,ieq=1,2),(ieq,ieq,ieq=1,2),
- $ (ieq,ieq,ieq=1,2)
- WRITE(init_out_unit,40)(ipert,u(ipert,isol,:),
- $ du(ipert,isol,:),star(ipert),ipert=1,mpert)
- WRITE(init_out_unit,30)(ieq,ieq,ieq=1,2),(ieq,ieq,ieq=1,2),
- $ (ieq,ieq,ieq=1,2)
- m=m+1
- ENDDO
- CALL ascii_close(init_out_unit)
- CALL program_stop("Termination by ode_sing_init.")
- ENDIF
-c-----------------------------------------------------------------------
-c compute conditions at next singular surface.
-c-----------------------------------------------------------------------
- DO
- ising=ising+1
- IF(ising>msing.OR.psilim=nn*q)EXIT
- ENDDO
- IF(ising>msing.OR.psilimmsing.OR.psilim=nn*q)EXIT
- ENDDO
-c-----------------------------------------------------------------------
-c compute conditions at next singular surface.
-c-----------------------------------------------------------------------
- IF(ising>msing.OR.psilim msing .OR. psilim < sing(ising)%psifac)EXIT
- q=sing(ising)%q
- IF(mlow <= nn*q .AND. mhigh >= nn*q)EXIT
- ENDDO
-c-----------------------------------------------------------------------
-c compute conditions at next singular surface.
-c-----------------------------------------------------------------------
- IF(ising > msing .OR. psilim < sing(ising)%psifac)THEN
- psimax=psilim*(1-eps)
- m1=NINT(nn*qlim)+NINT(SIGN(one,nn*sq%fs1(mpsi,4)))
- next="finish"
- ELSE
- psimax=sing(ising)%psifac-singfac_min/ABS(nn*sing(ising)%q1)
- m1=NINT(nn*sing(ising)%q)
- WRITE(crit_out_unit,20)ising,sing(ising)%psifac,
- $ sing(ising)%q,sing(ising)%di,sing(ising)%alpha
- ENDIF
-c-----------------------------------------------------------------------
-c restart ode solver.
-c-----------------------------------------------------------------------
- istate=1
- istep=istep+1
- rwork(1)=psimax
- new=.TRUE.
- u_save=u
- psi_save=psifac
-c-----------------------------------------------------------------------
-c write to files.
-c-----------------------------------------------------------------------
- WRITE(crit_out_unit,30)
- IF(crit_break)WRITE(crit_bin_unit)
-c-----------------------------------------------------------------------
-c terminate.
-c-----------------------------------------------------------------------
- RETURN
- END SUBROUTINE ode_resist_cross
-c-----------------------------------------------------------------------
-c subprogram 7. ode_step.
-c takes a step of the integrator.
-c-----------------------------------------------------------------------
-c-----------------------------------------------------------------------
-c declarations.
-c-----------------------------------------------------------------------
- SUBROUTINE ode_step
-
- INTEGER :: ipert,isol,ieq,jac,errloc(3)
- REAL(r8) :: singfac,rtol,atol0,tol,dt,errmax,ewtmax
- REAL(r8), PARAMETER :: dpsimax=1e-3,dpsimin=1e-5,dpsifac=2e-2
- COMPLEX(r8) :: err(mpert,msol,2),ewt(mpert,msol,2)
-
- LOGICAL, PARAMETER :: diagnose=.FALSE.
- CHARACTER(256) :: message
-c-----------------------------------------------------------------------
-c compute relative tolerances.
-c-----------------------------------------------------------------------
- singfac=HUGE(singfac)
- IF(kin_flag)THEN
- IF(ising==1 .AND. kmsing>=1)THEN
- singfac = abs(psifac - kinsing(ising)%psifac) /
- $ (kinsing(ising)%psifac - psilow)
- ELSEIF(ising<=kmsing)THEN
- singfac = MIN(abs(psifac - kinsing(ising)%psifac),
- $ abs(psifac - kinsing(ising-1)%psifac)) /
- $ abs(kinsing(ising)%psifac - kinsing(ising-1)%psifac)
- ENDIF
- ELSE
- IF(ising<=msing)singfac=ABS(sing(ising)%m-nn*q)
- IF(ising>1)singfac=MIN(singfac,ABS(sing(ising-1)%m-nn*q))
- ENDIF
- IF(singfac ucrit .OR. sing_flag)THEN
- CALL ode_fixup(sing_flag,.FALSE.)
- IF(diagnose)CALL ode_test_fixup
- new=.TRUE.
- ENDIF
- ENDIF
-c-----------------------------------------------------------------------
-c terminate.
-c-----------------------------------------------------------------------
- RETURN
- END SUBROUTINE ode_unorm
-c-----------------------------------------------------------------------
-c subprogram 9. ode_fixup.
-c performs Gaussian reduction of solution matrix.
-c-----------------------------------------------------------------------
-c-----------------------------------------------------------------------
-c declarations.
-c-----------------------------------------------------------------------
- SUBROUTINE ode_fixup(sing_flag,test)
-
- LOGICAL, INTENT(IN) :: sing_flag,test
-
- LOGICAL, PARAMETER :: diagnose=.FALSE.,secondary=.FALSE.
- LOGICAL, SAVE :: new=.TRUE.
- LOGICAL, DIMENSION(2,msol) :: mask
- INTEGER :: ipert,isol,jsol,kpert,ksol
- INTEGER, DIMENSION(1) :: jmax
-c-----------------------------------------------------------------------
-c format statements.
-c-----------------------------------------------------------------------
- 10 FORMAT(/3x,"is",4x,"psifac",6x,"dpsi",8x,"q",7x,"singfac",5x,
- $ "eval1"/)
- 20 FORMAT(1x,a,i6,a,es10.3,a,f6.3)
- 40 FORMAT(2(a,i3))
- 30 FORMAT(3x,"mlow",1x,"mhigh",1x,"mpert",2x,"msol",3x,"psifac",
- $ 6x,"q"//4i6,1p,2e11.3/)
- 50 FORMAT(/1x,"i",2(3x,"re u(",i1,")",4x,"im u(",i1,")",1x)/)
- 60 FORMAT(i2,1p,4e11.3)
-c-----------------------------------------------------------------------
-c open output file and write initial values.
-c-----------------------------------------------------------------------
- IF(diagnose)THEN
- IF(new)THEN
- CALL ascii_open(init_out_unit,"fixup.out","UNKNOWN")
- new=.FALSE.
- ENDIF
- WRITE(init_out_unit,30)mlow,mhigh,mpert,msol,psifac,q
- WRITE(init_out_unit,'(/a/)')"input values:"
- DO isol=1,msol
- WRITE(init_out_unit,40)"isol = ",isol,", m = ",mlow+isol-1
- WRITE(init_out_unit,50)(ipert,ipert,ipert=1,2)
- WRITE(init_out_unit,60)(ipert,
- $ u(ipert,isol,:)/MAXVAL(ABS(u(:,isol,1))),ipert=1,mpert)
- WRITE(init_out_unit,50)(ipert,ipert,ipert=1,2)
- ENDDO
- ENDIF
-c-----------------------------------------------------------------------
-c initial output.
-c-----------------------------------------------------------------------
- WRITE(crit_out_unit,10)
- WRITE(crit_out_unit,20)
- $ "Gaussian Reduction at istep = ",istep,
- $ ", psi =",psifac,", q = ",q
- IF(.NOT. sing_flag)WRITE(crit_out_unit,10)
- istate=1
- flag_count=0
-c-----------------------------------------------------------------------
-c initialize fixfac.
-c-----------------------------------------------------------------------
- IF(.NOT. test)THEN
- fixfac=0
- DO isol=1,msol
- fixfac(isol,isol)=1
- ENDDO
-c-----------------------------------------------------------------------
-c sort unorm.
-c-----------------------------------------------------------------------
- index(1:msol)=(/(ipert,ipert=1,msol)/)
- CALL bubble(unorm,index,1,mpert)
- CALL bubble(unorm,index,mpert+1,msol)
- ENDIF
-c-----------------------------------------------------------------------
-c triangularize primary solutions.
-c-----------------------------------------------------------------------
- mask=.TRUE.
- DO isol=1,mpert
- ksol=index(isol)
- mask(2,ksol)=.FALSE.
- IF(.NOT. test)THEN
- jmax=MAXLOC(ABS(u(:,ksol,1)),mask(1,1:mpert))
- kpert=jmax(1)
- mask(1,kpert)=.FALSE.
- ENDIF
- DO jsol=1,msol
- IF(mask(2,jsol))THEN
- IF(.NOT. test)fixfac(ksol,jsol)
- $ =-u(kpert,jsol,1)/u(kpert,ksol,1)
- u(:,jsol,:)=u(:,jsol,:)+u(:,ksol,:)*fixfac(ksol,jsol)
- IF(.NOT. test)u(kpert,jsol,1)=0
- ENDIF
- ENDDO
- ENDDO
-c-----------------------------------------------------------------------
-c triangularize secondary solutions.
-c-----------------------------------------------------------------------
- IF(msol > mpert .AND. secondary)THEN
- mask=.TRUE.
- DO isol=mpert+1,msol
- ksol=index(isol)
- mask(2,ksol)=.FALSE.
- IF(.NOT. test)THEN
- jmax=MAXLOC(ABS(u(:,ksol,2)),mask(1,1:mpert))
- kpert=jmax(1)
- mask(1,kpert)=.FALSE.
- ENDIF
- DO jsol=mpert+1,msol
- IF(mask(2,jsol))THEN
- IF(.NOT. test)fixfac(ksol,jsol)
- $ =-u(kpert,jsol,2)/u(kpert,ksol,2)
- u(:,jsol,:)=u(:,jsol,:)+u(:,ksol,:)*fixfac(ksol,jsol)
- IF(.NOT. test)u(kpert,jsol,2)=0
- ENDIF
- ENDDO
- ENDDO
- ENDIF
-c-----------------------------------------------------------------------
-c save fixfac to file.
-c-----------------------------------------------------------------------
- IF(bin_euler. AND. .NOT. test)THEN
- WRITE(euler_bin_unit)2
- WRITE(euler_bin_unit)sing_flag,msol
- WRITE(euler_bin_unit)fixfac,index(1:msol)
- ENDIF
-c-----------------------------------------------------------------------
-c write output values and close output file.
-c-----------------------------------------------------------------------
- IF(diagnose)THEN
- WRITE(init_out_unit,'(/a/)')"output values:"
- DO isol=1,msol
- WRITE(init_out_unit,40)"isol = ",isol,", m = ",mlow+isol-1
- WRITE(init_out_unit,50)(ipert,ipert,ipert=1,2)
- WRITE(init_out_unit,60)(ipert,u(ipert,isol,:),ipert=1,mpert)
- WRITE(init_out_unit,50)(ipert,ipert,ipert=1,2)
- ENDDO
- ENDIF
-c-----------------------------------------------------------------------
-c terminate.
-c-----------------------------------------------------------------------
- RETURN
- END SUBROUTINE ode_fixup
-c-----------------------------------------------------------------------
-c subprogram 10. ode_test.
-c tests for optimum approach to singular surface.
-c-----------------------------------------------------------------------
-c-----------------------------------------------------------------------
-c delcarations.
-c-----------------------------------------------------------------------
- FUNCTION ode_test() RESULT(flag)
-
- LOGICAL :: flag
-
- INTEGER :: isol
- REAL(r8), SAVE :: singfac_old,powmax
- REAL(r8) :: dsingfac,norm,dnorm,powmax_old
- REAL(r8), DIMENSION(msol) :: power
- COMPLEX(r8), DIMENSION(mpert,msol,2) :: dca
- COMPLEX(r8), DIMENSION(mpert,mpert,2) :: ufree
-c-----------------------------------------------------------------------
-c truncation test: lsode limit
-c-----------------------------------------------------------------------
- flag = psifac == psimax .OR. istep == nstep .OR. istate < 0
-c-----------------------------------------------------------------------
-c simple return.
-c-----------------------------------------------------------------------
- IF(.NOT. res_flag .OR. flag
- $ .OR. ising > msing .OR. singfac > singfac_max)RETURN
-c-----------------------------------------------------------------------
-c update values.
-c-----------------------------------------------------------------------
- ca_old=ca
- CALL sing_get_ca(ising,psifac,u,ca)
- dca=ca-ca_old
- dsingfac=ABS((singfac-singfac_old)/singfac)
- singfac_old=singfac
-c-----------------------------------------------------------------------
-c update powers.
-c-----------------------------------------------------------------------
- powmax_old=powmax
- DO isol=1,msol
- norm=ABS(SUM(CONJG(ca(:,isol,:))*ca(:,isol,:)))
- dnorm=ABS(SUM(CONJG(ca(:,isol,:))*dca(:,isol,:)))
- power(isol)=dnorm/(norm*dsingfac)
- ENDDO
- powmax=MAXVAL(power)
-c-----------------------------------------------------------------------
-c compute derivatives and flag.
-c-----------------------------------------------------------------------
- flag_count=flag_count+1
- IF(flag_count < 3)RETURN
- flag=flag .OR. singfac < singfac_max .AND. powmax > powmax_old
-c-----------------------------------------------------------------------
-c diagnose.
-c-----------------------------------------------------------------------
- IF(ising == ksing)THEN
- WRITE(err_unit)REAL(LOG10(singfac),4),REAL(LOG10(powmax),4)
- ENDIF
-c-----------------------------------------------------------------------
-c terminate.
-c-----------------------------------------------------------------------
- RETURN
- END FUNCTION ode_test
-c-----------------------------------------------------------------------
-c subprogram 11. ode_test_fixup.
-c tests fixup routine.
-c-----------------------------------------------------------------------
-c-----------------------------------------------------------------------
-c declarations.
-c-----------------------------------------------------------------------
- SUBROUTINE ode_test_fixup
-
- CHARACTER(16)filename
- INTEGER :: isol,ipert
- INTEGER, SAVE :: ifix=0
- REAL(r8), DIMENSION(:,:,:), POINTER :: re,im
- COMPLEX(r8), DIMENSION(:,:,:), POINTER :: u_old
-c-----------------------------------------------------------------------
-c format statements.
-c-----------------------------------------------------------------------
- 10 FORMAT(/2x,"isol",2x,"index"/)
- 20 FORMAT(2i6)
- 30 FORMAT(2(a,i3))
- 40 FORMAT(/1x,"i",2(3x,"re u(",i1,")",4x,"im u(",i1,")",1x)/)
- 50 FORMAT(i2,1p,4e11.3)
-c-----------------------------------------------------------------------
-c create initial u.
-c-----------------------------------------------------------------------
- ALLOCATE(u_old(mpert,msol,2),re(mpert,msol,2),im(mpert,msol,2))
- u_old=u
- CALL put_seed(0)
- CALL RANDOM_NUMBER(re)
- CALL RANDOM_NUMBER(im)
- u=CMPLX(re,im)
- DEALLOCATE(re,im)
-c-----------------------------------------------------------------------
-c diagnose index.
-c-----------------------------------------------------------------------
- ifix=ifix+1
- WRITE(filename,'(a,i2.2,a)')"fixup_",ifix,".out"
- CALL ascii_open(debug_unit,TRIM(filename),"UNKNOWN")
- WRITE(debug_unit,10)
- DO isol=1,msol
- WRITE(debug_unit,20)isol,index(isol)
- ENDDO
- WRITE(debug_unit,10)
-c-----------------------------------------------------------------------
-c diagnose initial u.
-c-----------------------------------------------------------------------
- WRITE(debug_unit,'(/a/)')"initial values:"
- DO isol=1,msol
- WRITE(debug_unit,30)"isol = ",isol,", m = ",mlow+isol-1
- WRITE(debug_unit,40)(ipert,ipert,ipert=1,2)
- WRITE(debug_unit,50)(ipert,u(ipert,isol,:),ipert=1,mpert)
- WRITE(debug_unit,40)(ipert,ipert,ipert=1,2)
- ENDDO
-c-----------------------------------------------------------------------
-c diagnose final u.
-c-----------------------------------------------------------------------
- CALL ode_fixup(.FALSE.,.TRUE.)
- WRITE(debug_unit,'(/a/)')"final values:"
- DO isol=1,msol
- WRITE(debug_unit,30)"isol = ",isol,", m = ",mlow+isol-1
- WRITE(debug_unit,40)(ipert,ipert,ipert=1,2)
- WRITE(debug_unit,50)(ipert,u(ipert,isol,:),ipert=1,mpert)
- WRITE(debug_unit,40)(ipert,ipert,ipert=1,2)
- ENDDO
- CALL ascii_close(debug_unit)
- u=u_old
- DEALLOCATE(u_old)
-c-----------------------------------------------------------------------
-c terminate.
-c-----------------------------------------------------------------------
- RETURN
- END SUBROUTINE ode_test_fixup
-c-----------------------------------------------------------------------
-c subprogram 12. ode_record_edge.
-c record the energy in the edge
-c-----------------------------------------------------------------------
-c-----------------------------------------------------------------------
-c declarations.
-c-----------------------------------------------------------------------
- SUBROUTINE ode_record_edge
- LOGICAL, PARAMETER :: debug=.FALSE.
- INTEGER, SAVE :: calc_number = 0
- COMPLEX(r8) :: total1, vacuum1, plasma1
-
- CALL spline_eval(sq,psifac,0)
- IF(size_edge > 0)THEN
- IF(sq%f(4) >= q_edge(i_edge) .AND. psifac >= psiedge)THEN ! second codition handles initialization plasmas with q0~qa
- CALL free_test(plasma1,vacuum1,total1,psifac)
- IF(debug) WRITE(*,'(2(i4),6(es12.3))') calc_number,
- $ i_edge,psifac,sq%f(4),q_edge(i_edge),
- $ REAL(total1),REAL(vacuum1),REAL(plasma1)
- calc_number = calc_number + 1
- dw_edge(i_edge) = total1
- q_edge(i_edge) = sq%f(4)
- psi_edge(i_edge) = psifac
- i_edge = MIN(i_edge + 1, size_edge) ! just to be extra safe
- ENDIF
- ENDIF
-c-----------------------------------------------------------------------
-c terminate.
-c-----------------------------------------------------------------------
- RETURN
- END SUBROUTINE ode_record_edge
-
- END MODULE ode_mod
diff --git a/src/DCON/fortran/ode_output.f b/src/DCON/fortran/ode_output.f
deleted file mode 100644
index 35b7adf516..0000000000
--- a/src/DCON/fortran/ode_output.f
+++ /dev/null
@@ -1,570 +0,0 @@
-c-----------------------------------------------------------------------
-c file ode_output.f.
-c diagnoses main differential equations.
-c-----------------------------------------------------------------------
-c-----------------------------------------------------------------------
-c code organization.
-c-----------------------------------------------------------------------
-c 0. ode_output_mod.
-c 1. ode_output_open
-c 2. ode_output_step
-c 3. ode_output_close
-c 4. ode_output_get_evals.
-c 5. ode_output_monitor.
-c 6. ode_output_get_crit.
-c 7. ode_output_sol.
-c-----------------------------------------------------------------------
-c subprogram 0. ode_mod.
-c module declarations.
-c-----------------------------------------------------------------------
-c-----------------------------------------------------------------------
-c declarations.
-c-----------------------------------------------------------------------
- MODULE ode_output_mod
- USE sing_mod
- USE dcon_mod, ONLY : shotnum,shottime
- IMPLICIT NONE
-
- CHARACTER(6), DIMENSION(:), POINTER :: name
- INTEGER, DIMENSION(:), POINTER :: sol_out_unit,sol_bin_unit
-
- INTEGER :: neq,ising,istep,m1,nzero
- REAL(r8) :: psifac,psizero,singfac,q,psi_save,psimax,singfac_old,
- $ psifac_old
- REAL(r8) :: singfac_min=1e-5,singfac_max=1e-4
- COMPLEX(r8), DIMENSION(:,:,:), POINTER :: u,u_old,u_save,du,
- $ ca,ca_old
-
- LOGICAL :: termbycross_flag=.FALSE.
-
- CONTAINS
-c-----------------------------------------------------------------------
-c subprogram 1. ode_output_open
-c integrates the differential equations.
-c-----------------------------------------------------------------------
-c-----------------------------------------------------------------------
-c declarations.
-c-----------------------------------------------------------------------
- SUBROUTINE ode_output_open
-
- INTEGER :: isol,iunit
- REAL(r8), DIMENSION(:), POINTER :: xs,ys
- REAL(r8), DIMENSION(:,:,:), POINTER :: fs,fsx,fsy,fsxy
-c-----------------------------------------------------------------------
-c format statements.
-c-----------------------------------------------------------------------
- 10 FORMAT(/3x,"ising",3x,"psi",9x,"q",10x,"di",6x,"re alpha",
- $ 3x,"im alpha"//i6,1p,5e11.3/)
- 20 FORMAT(/3x,"is",4x,"psifac",6x,"dpsi",8x,"q",7x,"singfac",5x,
- $ "eval1"/)
- 30 FORMAT(3x,"mlow",4x,"m",2x,"mhigh",2x,"isol",2x,"msol"//5i6/)
- 40 FORMAT(1x,2x,a,es10.3,a,f6.3)
-c-----------------------------------------------------------------------
-c allocate space for asymptotic coefficients.
-c-----------------------------------------------------------------------
- nzero=0
- ALLOCATE(ca(mpert,msol,2),ca_old(mpert,msol,2))
-c-----------------------------------------------------------------------
-c open file for solutions.
-c-----------------------------------------------------------------------
- IF(bin_euler)THEN
- xs => rzphi%xs
- ys => rzphi%ys
- fs => rzphi%fs
- fsx => rzphi%fsx
- fsy => rzphi%fsy
- fsxy => rzphi%fsxy
- CALL bin_open(euler_bin_unit,"euler.bin","UNKNOWN","REWIND",
- $ "none")
- WRITE(euler_bin_unit)mlow,mhigh,nn,mpsi,mtheta,ro,zo
-c-----------------------------------------------------------------------
-c
-c-----------------------------------------------------------------------
- WRITE(euler_bin_unit)mband,mthsurf0,mthvac,psio,
- $ psilow,psilim,qlim,singfac_min
- WRITE(euler_bin_unit)power_b,power_r,power_bp
- WRITE(euler_bin_unit)kin_flag,con_flag
- ! from sum1 equilibrium descriptions
- WRITE(euler_bin_unit) amean,rmean,aratio,kappa,delta1,delta2,
- $ li1,li2,li3,betap1,betap2,betap3,betat,betan,bt0,
- $ q0,qmin,qmax,qa,crnt,q95,shotnum,shottime
-c-----------------------------------------------------------------------
- WRITE(euler_bin_unit)sq%xs,sq%fs,sq%fs1,sq%xpower
- WRITE(euler_bin_unit)rzphi%xs,rzphi%ys,
- $ rzphi%fs,rzphi%fsx,rzphi%fsy,rzphi%fsxy,
- $ rzphi%x0,rzphi%y0,rzphi%xpower,rzphi%ypower
- ENDIF
-c-----------------------------------------------------------------------
-c open output files for crit and write header.
-c-----------------------------------------------------------------------
- CALL ascii_open(crit_out_unit,"crit.out","UNKNOWN")
- CALL bin_open(crit_bin_unit,"crit.bin","UNKNOWN","REWIND","none")
- IF(out_evals)CALL ascii_open(evals_out_unit,"evals.out","UNKNOWN")
- IF(bin_evals)CALL bin_open(evals_bin_unit,"evals.bin","UNKNOWN",
- $ "REWIND","none")
- IF(ising > 0 .AND. ising <= msing)
- $ WRITE(crit_out_unit,10)ising,sing(ising)%psifac,
- $ sing(ising)%q,sing(ising)%di,sing(ising)%alpha
- WRITE(crit_out_unit,20)
-c-----------------------------------------------------------------------
-c define file names.
-c-----------------------------------------------------------------------
- IF(bin_sol)THEN
- ALLOCATE(name(2*mpert))
- DO isol=1,2*mpert
- WRITE(name(isol),'(a,i2.2)')"sol",isol
- ENDDO
- ENDIF
-c-----------------------------------------------------------------------
-c open binary output files for solutions.
-c-----------------------------------------------------------------------
- IF(bin_sol)THEN
- bin_sol_min=1
- bin_sol_min=MAX(bin_sol_min,1)
- IF(res_flag)THEN
- bin_sol_max=MIN(bin_sol_max,mpert+2*msing,2*mpert)
- ELSE
- bin_sol_max=MIN(bin_sol_max,mpert)
- ENDIF
- IF(res_flag)THEN
- bin_sol_max=MIN(2*mpert,9)
- ELSE
- bin_sol_max=MIN(mpert,9)
- ENDIF
- bin_sol_max=MIN(bin_sol_max,98+bin_sol_min-sol_base)
- ALLOCATE(sol_bin_unit(bin_sol_min:bin_sol_max))
- sol_bin_unit=sol_base-bin_sol_min
- $ +(/(isol,isol=bin_sol_min,bin_sol_max)/)
- DO isol=bin_sol_min,bin_sol_max
- iunit=sol_bin_unit(isol)
- CALL bin_open(iunit,TRIM(name(isol))//".bin",
- $ "UNKNOWN","REWIND","none")
- ENDDO
- CALL bin_open(unorm_unit,"unorm.bin","UNKNOWN","REWIND","none")
- ENDIF
-c-----------------------------------------------------------------------
-c print initial point of integration.
-c-----------------------------------------------------------------------
- CALL spline_eval(sq,psifac,0)
- q=sq%f(4)
- IF(verbose) WRITE(*,40)"psi =",psifac,", q = ",q
-c-----------------------------------------------------------------------
-c open file for error output.
-c-----------------------------------------------------------------------
- IF(ksing > 0 .AND. ksing <= msing)THEN
- CALL bin_open(err_unit,"error.bin","UNKNOWN","REWIND","none")
- ALLOCATE(u_old(mpert,msol,2))
- ENDIF
-c-----------------------------------------------------------------------
-c terminate.
-c-----------------------------------------------------------------------
- RETURN
- END SUBROUTINE ode_output_open
-c-----------------------------------------------------------------------
-c subprogram 2. ode_output_step
-c integrates the differential equations.
-c-----------------------------------------------------------------------
-c-----------------------------------------------------------------------
-c declarations.
-c-----------------------------------------------------------------------
- SUBROUTINE ode_output_step(unorm, op_force)
-
- REAL(r8), DIMENSION(:), INTENT(IN) :: unorm
- LOGICAL, OPTIONAL :: op_force
- LOGICAL :: force
- ! set optional parameters
- force = .FALSE.
- IF(PRESENT(op_force)) force = op_force
-c-----------------------------------------------------------------------
-c compute and print critical data for each time step.
-c-----------------------------------------------------------------------
- CALL ode_output_monitor
- IF(out_evals .OR. bin_evals)CALL ode_output_get_evals
-c-----------------------------------------------------------------------
-c write solutions.
-c-----------------------------------------------------------------------
- IF(bin_euler .AND. (mod(istep,euler_stride) == 0 .OR. force))THEN
- CALL sing_der(neq,psifac,u,du)
- WRITE(euler_bin_unit)1
- WRITE(euler_bin_unit)psifac,q,msol
- WRITE(euler_bin_unit)u
- WRITE(euler_bin_unit)ud
- ENDIF
-c-----------------------------------------------------------------------
-c output solutions components for each time step.
-c-----------------------------------------------------------------------
- IF(bin_sol)CALL ode_output_sol(psifac,u,unorm)
-c-----------------------------------------------------------------------
-c terminate.
-c-----------------------------------------------------------------------
- RETURN
- END SUBROUTINE ode_output_step
-c-----------------------------------------------------------------------
-c subprogram 3. ode_output_close.
-c produces ascii output for each step.
-c-----------------------------------------------------------------------
-c-----------------------------------------------------------------------
-c declarations.
-c-----------------------------------------------------------------------
- SUBROUTINE ode_output_close
-
- INTEGER :: isol
-c-----------------------------------------------------------------------
-c declarations.
-c-----------------------------------------------------------------------
- 10 FORMAT(1x,2x,a,es10.3,a,f6.3)
- 20 FORMAT(/3x,"is",4x,"psifac",6x,"dpsi",8x,"q",7x,"singfac",5x,
- $ "eval1"/)
-c-----------------------------------------------------------------------
-c close crit files.
-c-----------------------------------------------------------------------
- WRITE(term_unit,10)"psi =",psifac,", q = ",q
- WRITE(crit_out_unit,20)
- CALL ascii_close(crit_out_unit)
- WRITE(crit_bin_unit)
- CALL bin_close(crit_bin_unit)
- DEALLOCATE(ca,ca_old)
-c-----------------------------------------------------------------------
-c close other files.
-c-----------------------------------------------------------------------
- IF(out_evals)CALL ascii_close(evals_out_unit)
- IF(bin_evals)CALL bin_close(evals_bin_unit)
- IF(ksing > 0 .AND. ksing <= msing)THEN
- CALL bin_close(err_unit)
- DEALLOCATE(u_old)
- ENDIF
-c-----------------------------------------------------------------------
-c close binary output files.
-c-----------------------------------------------------------------------
- IF(bin_sol)DEALLOCATE(name)
- IF(bin_sol)THEN
- DO isol=bin_sol_min,bin_sol_max
- CALL bin_close(sol_bin_unit(isol))
- ENDDO
- CALL bin_close(unorm_unit)
- DEALLOCATE(sol_bin_unit)
- ENDIF
-c-----------------------------------------------------------------------
-c terminate.
-c-----------------------------------------------------------------------
- RETURN
- END SUBROUTINE ode_output_close
-c-----------------------------------------------------------------------
-c subprogram 4. ode_output_get_evals.
-c computes critical criterminant.
-c-----------------------------------------------------------------------
-c-----------------------------------------------------------------------
-c declarations.
-c-----------------------------------------------------------------------
- SUBROUTINE ode_output_get_evals
-
- INTEGER :: info,ipert,lwork
- INTEGER, DIMENSION(mpert) :: ipiv,index,indexi
-
- REAL(r8) :: logpsi1,logpsi2
- REAL(r8), DIMENSION(3*mpert-2) :: rwork
- REAL(r8), DIMENSION(mpert) :: key,evals,evalsi
-
- COMPLEX(r8), DIMENSION(mpert,mpert) :: temp,wp
- COMPLEX(r8), DIMENSION(2*mpert-1) :: work
-c-----------------------------------------------------------------------
-c format statements.
-c-----------------------------------------------------------------------
- 10 FORMAT(/a,i4,1p,2(a,es10.3))
- 20 FORMAT(/5x,"i",5x,"eval",7x,"evali",7x,"err"/)
- 30 FORMAT(i6,1p,3e11.3)
-c-----------------------------------------------------------------------
-c compute plasma response matrix.
-c-----------------------------------------------------------------------
- temp=CONJG(TRANSPOSE(u(:,1:mpert,1)))
- wp=u(:,1:mpert,2)
- wp=CONJG(TRANSPOSE(wp))
- CALL zgetrf(mpert,mpert,temp,mpert,ipiv,info)
- CALL zgetrs('N',mpert,mpert,temp,mpert,ipiv,wp,mpert,info)
- wp=(wp+CONJG(TRANSPOSE(wp)))/2
-c-----------------------------------------------------------------------
-c compute and sort eigenvalues.
-c-----------------------------------------------------------------------
- lwork=2*mpert-1
- CALL zheev('N','U',mpert,wp,mpert,evals,work,lwork,rwork,info)
- index=(/(ipert,ipert=1,mpert)/)
- key=-ABS(1/evals)
- CALL bubble(key,index,1,mpert)
-c-----------------------------------------------------------------------
-c compute and sort inverse eigenvalues.
-c-----------------------------------------------------------------------
- lwork=2*mpert-1
- CALL zheev('N','U',mpert,wp,mpert,evalsi,work,lwork,rwork,info)
- indexi=(/(ipert,ipert=1,mpert)/)
- key=-ABS(evalsi)
- CALL bubble(key,indexi,1,mpert)
-c-----------------------------------------------------------------------
-c write ascii eigenvalues.
-c-----------------------------------------------------------------------
- IF(out_evals .AND. istep > 0)THEN
- WRITE(evals_out_unit,10)"istep = ",istep,
- $ ", psifac = ",psifac,", q = ",q
- WRITE(evals_out_unit,20)
- WRITE(evals_out_unit,30)(ipert,
- $ evalsi(indexi(ipert)),evals(index(ipert)),
- $ evalsi(indexi(ipert))*evals(index(ipert))-1,
- $ ipert=1,mpert)
- WRITE(evals_out_unit,20)
- ENDIF
-c-----------------------------------------------------------------------
-c write binary eigenvalues.
-c-----------------------------------------------------------------------
- IF(bin_evals .AND. psifac > .1)THEN
- CALL spline_eval(sq,psifac,0)
- q=sq%f(4)
- singfac=ABS(m1-nn*q)
- logpsi1=LOG10(psifac)
- logpsi2=LOG10(singfac)
- DO ipert=2,mpert
- WRITE(evals_bin_unit)REAL(ipert,4),REAL(psifac,4),
- $ REAL(logpsi1,4),REAL(logpsi2,4),
- $ REAL(q,4),REAL(1/evals(index(ipert)),4)
- ENDDO
- WRITE(evals_bin_unit)
- ENDIF
-c-----------------------------------------------------------------------
-c terminate.
-c-----------------------------------------------------------------------
- RETURN
- END SUBROUTINE ode_output_get_evals
-c-----------------------------------------------------------------------
-c subprogram 5. ode_output_monitor.
-c writes crit and monitors zero crossings.
-c-----------------------------------------------------------------------
-c-----------------------------------------------------------------------
-c declarations.
-c-----------------------------------------------------------------------
- SUBROUTINE ode_output_monitor
-
- REAL(r8) :: logpsi1,logpsi2,crit,fac,
- $ psi_med,crit_med,q_med,singfac_med,logpsi1_med,logpsi2_med
- REAL(r8), SAVE :: crit_save=0,psi_save=0,dpsi
- COMPLEX(r8), DIMENSION(mpert,msol,2) :: u_med
-c-----------------------------------------------------------------------
-c format statements.
-c-----------------------------------------------------------------------
- 10 FORMAT(i5,1p,6e11.3)
- 20 FORMAT(1x,a,1p,e10.3,a,e10.3)
-c-----------------------------------------------------------------------
-c compute new crit.
-c-----------------------------------------------------------------------
- dpsi=psifac-psi_save
- CALL ode_output_get_crit(psifac,u,q,singfac,logpsi1,logpsi2,crit)
-c-----------------------------------------------------------------------
-c check for zero crossing.
-c-----------------------------------------------------------------------
- IF(crit*crit_save < 0)THEN
- fac=crit/(crit-crit_save)
- psi_med=psifac-fac*(psifac-psi_save)
- dpsi=psi_med-psi_save
- u_med=u-fac*(u-u_save)
- CALL ode_output_get_crit(psi_med,u_med,q_med,singfac_med,
- $ logpsi1_med,logpsi2_med,crit_med)
- IF((crit_med-crit)*(crit_med-crit_save) < 0 .AND.
- $ ABS(crit_med) < .5*MIN(ABS(crit),ABS(crit_save)))THEN
- WRITE(term_unit,20)
- $ "Zero crossing at psi =",psi_med,", q =",q_med
- WRITE(out_unit,20)
- $ "Zero crossing at psi =",psi_med,", q =",q_med
- WRITE(crit_out_unit,20)
- $ "Zero crossing at psi =",psi_med,", q =",q_med
- WRITE(crit_out_unit,10)istep,psi_med,dpsi,q_med,
- $ singfac_med,crit_med
- WRITE(crit_bin_unit)REAL(psi_med,4),REAL(logpsi1_med,4),
- $ REAL(logpsi2_med,4),REAL(q_med,4),REAL(crit_med,4)
- nzero=nzero+1
- ENDIF
- IF (termbycross_flag) THEN
- CALL program_stop("Terminated by zero crossing.")
- ENDIF
- ENDIF
-c-----------------------------------------------------------------------
-c write new crit.
-c-----------------------------------------------------------------------
- WRITE(crit_out_unit,10)istep,psifac,dpsi,q,singfac,crit
- WRITE(crit_bin_unit)REAL(psifac,4),REAL(logpsi1,4),
- $ REAL(logpsi2,4),REAL(q,4),REAL(crit,4)
-c-----------------------------------------------------------------------
-c update saved values.
-c-----------------------------------------------------------------------
- psi_save=psifac
- crit_save=crit
- u_save=u
-c-----------------------------------------------------------------------
-c terminate.
-c-----------------------------------------------------------------------
- RETURN
- END SUBROUTINE ode_output_monitor
-c-----------------------------------------------------------------------
-c subprogram 6. ode_output_get_crit.
-c computes critical criterminant.
-c-----------------------------------------------------------------------
-c-----------------------------------------------------------------------
-c declarations.
-c-----------------------------------------------------------------------
- SUBROUTINE ode_output_get_crit(psi,u,q,singfac,
- $ logpsi1,logpsi2,crit)
-
- REAL(r8), INTENT(IN) :: psi
- COMPLEX(r8), DIMENSION(:,:,:), INTENT(IN) :: u
- REAL(r8), INTENT(OUT) :: q,singfac,logpsi1,logpsi2,crit
-
- INTEGER :: info,ipert,lwork
- INTEGER, DIMENSION(mpert) :: ipiv,indexi
- REAL(r8), DIMENSION(3*mpert-2) :: rwork
- REAL(r8), DIMENSION(mpert) :: key,evalsi
- COMPLEX(r8), DIMENSION(mpert,mpert) :: temp,wp
- COMPLEX(r8), DIMENSION(2*mpert-1) :: work
- COMPLEX(r8), DIMENSION(mpert,mpert,2) :: uu
-c-----------------------------------------------------------------------
-c compute dependent variables.
-c-----------------------------------------------------------------------
- uu=u(:,1:mpert,:)
-c-----------------------------------------------------------------------
-c compute inverse plasma response matrix.
-c-----------------------------------------------------------------------
- wp=CONJG(TRANSPOSE(uu(:,:,1)))
- temp=uu(:,:,2)
- temp=CONJG(TRANSPOSE(temp))
- CALL zgetrf(mpert,mpert,temp,mpert,ipiv,info)
- CALL zgetrs('N',mpert,mpert,temp,mpert,ipiv,wp,mpert,info)
- wp=(wp+CONJG(TRANSPOSE(wp)))/2
-c-----------------------------------------------------------------------
-c compute and sort inverse eigenvalues.
-c-----------------------------------------------------------------------
- lwork=2*mpert-1
- CALL zheev('N','U',mpert,wp,mpert,evalsi,work,lwork,rwork,info)
- indexi=(/(ipert,ipert=1,mpert)/)
- key=-ABS(evalsi)
- CALL bubble(key,indexi,1,mpert)
-c-----------------------------------------------------------------------
-c compute critical data for each time step.
-c-----------------------------------------------------------------------
- CALL spline_eval(sq,psi,0)
- q=sq%f(4)
- singfac=ABS(m1-nn*q)
- logpsi1=LOG10(psi)
- logpsi2=LOG10(singfac)
- crit=evalsi(indexi(1))*sq%f(3)**2
-c-----------------------------------------------------------------------
-c terminate.
-c-----------------------------------------------------------------------
- RETURN
- END SUBROUTINE ode_output_get_crit
-c-----------------------------------------------------------------------
-c subprogram 7. ode_output_sol.
-c produces binary output for each step.
-c-----------------------------------------------------------------------
-c-----------------------------------------------------------------------
-c declarations.
-c-----------------------------------------------------------------------
- SUBROUTINE ode_output_sol(psifac,u,unorm)
-
- REAL(r8), INTENT(IN) :: psifac
- COMPLEX(r8), DIMENSION(mpert,msol,2), INTENT(IN) :: u
- REAL(r8), DIMENSION(:), INTENT(IN) :: unorm
-
- INTEGER :: isol,ipert,iunit,jsing
- REAL(r8) :: psil,psir,psiminl,psiminr,a,b,x,singlog
- REAL(r8), DIMENSION(mpert) :: logunorm
- COMPLEX(r8), DIMENSION(mpert,msol,2) :: uu,ca
- COMPLEX(r8), DIMENSION(mpert,2) :: logu,logca
-c-----------------------------------------------------------------------
-c determine singular interval.
-c-----------------------------------------------------------------------
- jsing=1
- DO
- IF(jsing > msing)EXIT
- IF(sing(jsing)%psifac > psifac)EXIT
- jsing=jsing+1
- ENDDO
-c-----------------------------------------------------------------------
-c compute left edge of interval.
-c-----------------------------------------------------------------------
- IF(jsing == 1)THEN
- psil=0
- psiminl=psilow
- ELSE
- psil=sing(jsing-1)%psifac
- psiminl=singfac_min/ABS(nn*sing(jsing-1)%q1)
- ENDIF
-c-----------------------------------------------------------------------
-c compute right edge of interval.
-c-----------------------------------------------------------------------
- IF(jsing > msing)THEN
- psiminr=psiminl
- psir=psilim+psiminr
- ELSE
- psir=sing(jsing)%psifac
- psiminr=singfac_min/ABS(nn*sing(jsing)%q1)
- ENDIF
-c-----------------------------------------------------------------------
-c compute abscissa.
-c-----------------------------------------------------------------------
- b=2/(LOG10((psir-psil-psiminl)/psiminl)
- $ +LOG10((psir-psil-psiminr)/psiminr))
- a=b*LOG10((psir-psil-psiminl)/psiminl)+2*jsing-2
- x=a+b*LOG10((psifac-psil)/(psir-psifac))
- singlog=LOG10(ABS(singfac))
-c-----------------------------------------------------------------------
-c compute solutions and asymptotic coefficients.
-c-----------------------------------------------------------------------
- uu=u
- IF(psil < psir .AND. jsing > 1 .AND. psifac-psil < psir-psifac
- $ .OR. jsing > msing)THEN
- CALL sing_get_ca(jsing-1,psifac,uu,ca)
- ELSE
- CALL sing_get_ca(jsing,psifac,uu,ca)
- ENDIF
-c-----------------------------------------------------------------------
-c compute logu and logca
-c-----------------------------------------------------------------------
- DO isol=MAX(1,bin_sol_min),MIN(bin_sol_max,msol)
- iunit=sol_bin_unit(isol)
- WHERE(uu(:,isol,:) /= 0)
- logu=LOG(uu(:,isol,:))
- ELSEWHERE
- logu=0
- END WHERE
- WHERE(ca(:,isol,:) /= 0)
- logca=LOG(ca(:,isol,:))
- ELSEWHERE
- logca=0
- END WHERE
-c-----------------------------------------------------------------------
-c write binary output.
-c-----------------------------------------------------------------------
- DO ipert=1,mpert
- WRITE(iunit)REAL(psifac,4),REAL(LOG10(psifac),4),REAL(x,4),
- $ REAL(DREAL(logu(ipert,:))/alog10,4),
- $ REAL(DREAL(logca(ipert,:))/alog10,4),
- $ REAL(LOG10(ABS((psifac-sing(1)%psifac)
- $ /(nn*sing(1)%q1)))),REAL(singlog,4)
- ENDDO
- WRITE(iunit)
- ENDDO
-c-----------------------------------------------------------------------
-c diagnose unorm.
-c-----------------------------------------------------------------------
- WHERE(unorm(1:mpert) > 1)
- logunorm=LOG10(unorm(1:mpert))
- ELSEWHERE
- logunorm=0
- ENDWHERE
- DO isol=1,mpert
- WRITE(unorm_unit)REAL(isol,4),REAL(psifac,4),
- $ REAL(LOG10(psifac),4),REAL(x,4),
- $ REAL(logunorm(isol),4)
- ENDDO
- WRITE(unorm_unit)
-c-----------------------------------------------------------------------
-c terminate.
-c-----------------------------------------------------------------------
- RETURN
- END SUBROUTINE ode_output_sol
- END MODULE ode_output_mod
diff --git a/src/DCON/fortran/resist.f b/src/DCON/fortran/resist.f
deleted file mode 100644
index 0aa572cf9a..0000000000
--- a/src/DCON/fortran/resist.f
+++ /dev/null
@@ -1,155 +0,0 @@
-c-----------------------------------------------------------------------
-c file resist.f.
-c computes resistive surface quantities.
-c-----------------------------------------------------------------------
-c-----------------------------------------------------------------------
-c code organization.
-c-----------------------------------------------------------------------
-c 0. resist_mod.
-c 1. resist_eval.
-c-----------------------------------------------------------------------
-c subprogram 0. resist_mod.
-c module declarations.
-c-----------------------------------------------------------------------
-c-----------------------------------------------------------------------
-c declarations.
-c-----------------------------------------------------------------------
- MODULE resist_mod
- USE dcon_mod
- IMPLICIT NONE
-
- CONTAINS
-c-----------------------------------------------------------------------
-c subprogram 1. resist_eval.
-c computes resistive surface quantities.
-c-----------------------------------------------------------------------
-c-----------------------------------------------------------------------
-c declarations.
-c-----------------------------------------------------------------------
- SUBROUTINE resist_eval(sing)
-
- TYPE(sing_type), INTENT(INOUT) :: sing
-
- LOGICAL, PARAMETER :: diagnose=.FALSE.
- INTEGER :: itheta
- REAL(r8) :: bsq,chi1,dpsisq,eta,jac,lambda,p,p1,psifac,q,q1,r,
- $ rfac,taue,theta,twopif,v1,v2,v21,v22,v23,v33
- REAL(r8), PARAMETER :: ne=1e14,te=3e3,mi=2*mp,gamma=5._r8/3._r8
- REAL(r8), DIMENSION(:), POINTER :: avg
- TYPE(spline_type), TARGET :: ff
-c-----------------------------------------------------------------------
-c format statements.
-c-----------------------------------------------------------------------
- 10 FORMAT(a,1p,e10.3)
-c-----------------------------------------------------------------------
-c prepare spline types.
-c-----------------------------------------------------------------------
- CALL spline_alloc(ff,mtheta,6)
- ff%xs=rzphi%ys
-c-----------------------------------------------------------------------
-c compute surface quantities.
-c-----------------------------------------------------------------------
- psifac=sing%psifac
- CALL spline_eval(sq,psifac,1)
- twopif=sq%f(1)
- p=sq%f(2)
- p1=sq%f1(2)
- v1=sq%f(3)
- v2=sq%f1(3)
- q=sq%f(4)
- q1=sq%f1(4)
- chi1=twopi*psio
-c-----------------------------------------------------------------------
-c evaluate coordinates and jacobian.
-c-----------------------------------------------------------------------
- DO itheta=0,mtheta
- theta=rzphi%ys(itheta)
- CALL bicube_eval(rzphi,psifac,theta,1)
- rfac=SQRT(rzphi%f(1))
- eta=twopi*(theta+rzphi%f(2))
- r=ro+rfac*COS(eta)
- jac=rzphi%f(4)
-c-----------------------------------------------------------------------
-c evaluate other local quantities.
-c-----------------------------------------------------------------------
- v21=rzphi%fy(1)/(2*rfac*jac)
- v22=(1+rzphi%fy(2))*twopi*rfac/jac
- v23=rzphi%fy(3)*r/jac
- v33=twopi*r/jac
- bsq=chi1**2*(v21**2+v22**2+(v23+q*v33)**2)
- dpsisq=(twopi*r)**2*(v21**2+v22**2)
-c-----------------------------------------------------------------------
-c evaluate integrands.
-c-----------------------------------------------------------------------
- ff%fs(itheta,1)=bsq/dpsisq
- ff%fs(itheta,2)=1/dpsisq
- ff%fs(itheta,3)=1/bsq
- ff%fs(itheta,4)=1/(bsq*dpsisq)
- ff%fs(itheta,5)=bsq
- ff%fs(itheta,6)=dpsisq/bsq
- ff%fs(itheta,:)=ff%fs(itheta,:)*jac/v1
- ENDDO
-c-----------------------------------------------------------------------
-c integrate quantities with respect to theta.
-c-----------------------------------------------------------------------
- CALL spline_fit(ff,"periodic")
- CALL spline_int(ff)
- avg => ff%fsi(mtheta,:)
-c-----------------------------------------------------------------------
-c compute resistive curvature terms E, F, and H.
-c-----------------------------------------------------------------------
- sing%restype%e=p1*v1/(q1*chi1**2)**2*avg(1)
- $ *(twopif*q1*chi1/avg(5)-v2)
- sing%restype%f=(p1*v1/(q1*chi1**2))**2*(avg(1)*avg(3)
- $ +(twopif/chi1)**2*(avg(1)*avg(4)-avg(2)**2))
- sing%restype%h=twopif*p1*v1/(q1*chi1**3)*(avg(2)-avg(1)/avg(5))
-c-----------------------------------------------------------------------
-c computes mass factor and related terms, M, G, and K.
-c-----------------------------------------------------------------------
- sing%restype%m=avg(1)*(avg(6)+(twopif/chi1)**2*(avg(3)-1/avg(5)))
- sing%restype%g=avg(5)/(sing%restype%m*gamma*p)
- sing%restype%k=(q1*chi1**2/(p1*v1))**2
- $ *avg(5)/(sing%restype%m*avg(1))
-c-----------------------------------------------------------------------
-c compute resistivity and density.
-c-----------------------------------------------------------------------
- lambda=24-.5*LOG(ne)+LOG(te)
- taue=3.44e5*te**1.5/(ne*lambda)
- sing%restype%eta=me/(ne*1e6*e**2*taue*1.96)
- sing%restype%rho=ne*mi*1e6
-c-----------------------------------------------------------------------
-c compute Alfven and resistive time scales.
-c-----------------------------------------------------------------------
- sing%restype%taua=SQRT(sing%restype%rho*sing%restype%m*mu0)
- $ /ABS(twopi*nn*sing%q1*chi1/v1)
- sing%restype%taur=avg(1)/avg(5)*mu0/sing%restype%eta
-c-----------------------------------------------------------------------
-c diagnose.
-c-----------------------------------------------------------------------
- IF(diagnose)THEN
- WRITE(*,10)"q = ",sing%q
- WRITE(*,10)"q1 = ",sing%q1
- WRITE(*,10)"e = ",sing%restype%e
- WRITE(*,10)"f = ",sing%restype%f
- WRITE(*,10)"h = ",sing%restype%h
- WRITE(*,10)"m = ",sing%restype%m
- WRITE(*,10)"g = ",sing%restype%g
- WRITE(*,10)"k = ",sing%restype%k
- WRITE(*,10)"rho = ",sing%restype%rho
- WRITE(*,10)"taue = ",taue
- WRITE(*,10)"taua = ",sing%restype%taua
- WRITE(*,10)"taur = ",sing%restype%taur
- WRITE(*,10)"sfac = ",sing%restype%taur/sing%restype%taua
- WRITE(*,10)"eta = ",sing%restype%eta
- CALL program_stop("Termination by resist_eval.")
- ENDIF
-c-----------------------------------------------------------------------
-c deallocate.
-c-----------------------------------------------------------------------
- CALL spline_dealloc(ff)
-c-----------------------------------------------------------------------
-c terminate.
-c-----------------------------------------------------------------------
- RETURN
- END SUBROUTINE resist_eval
- END MODULE resist_mod
diff --git a/src/DCON/fortran/sing.f b/src/DCON/fortran/sing.f
deleted file mode 100644
index 5ffb77e86a..0000000000
--- a/src/DCON/fortran/sing.f
+++ /dev/null
@@ -1,1817 +0,0 @@
-c-----------------------------------------------------------------------
-c file sing.f.
-c computations relating to singular surfaces.
-c-----------------------------------------------------------------------
-c-----------------------------------------------------------------------
-c code organization.
-c-----------------------------------------------------------------------
-c 0. sing_mod.
-c 1. sing_scan.
-c 2. sing_find.
-c 3. sing_lim.
-c 4. sing_vmat.
-c 5. sing_mmat.
-c 6. sing_solve.
-c 7. sing_matmul.
-c 8. sing_vmat_diagnose.
-c 9. sing_get_ua.
-c 10. sing_get_ca.
-c 11. sing_der.
-c 12. sing_ua_diagnose.
-c 13. sing_get_f_det.
-c 14. ksing_find.
-c 15. sing_adp_find_sing.
-c 16. sing_newton.
-c-----------------------------------------------------------------------
-c subprogram 0. sing_mod.
-c module declarations.
-c-----------------------------------------------------------------------
-c-----------------------------------------------------------------------
-c declarations.
-c-----------------------------------------------------------------------
- MODULE sing_mod
- USE fourfit_mod
- IMPLICIT NONE
-
- INTEGER :: msol,sing_order=2
- REAL(r8) :: det_max
- INTEGER, DIMENSION(:), POINTER :: r1,r2,n1,n2
- COMPLEX(r8), DIMENSION(2,2) :: m0mat
- COMPLEX(r8), DIMENSION(:,:), ALLOCATABLE :: sing_detf
-
- CONTAINS
-c-----------------------------------------------------------------------
-c subprogram 1. sing_scan.
-c scans singular surfaces and prints information about them.
-c-----------------------------------------------------------------------
-c-----------------------------------------------------------------------
-c declarations.
-c-----------------------------------------------------------------------
- SUBROUTINE sing_scan
-
- INTEGER :: ising
-c-----------------------------------------------------------------------
-c write formats.
-c-----------------------------------------------------------------------
- 10 FORMAT(/2x,"i",5x,"psi",8x,"rho",9x,"q",10x,"q1",8x,"di0",9x,"di",
- $ 8x,"err"/)
-c-----------------------------------------------------------------------
-c scan over singular surfaces and print output.
-c-----------------------------------------------------------------------
- WRITE(out_unit,'(/1x,a)')"Singular Surfaces:"
- WRITE(out_unit,10)
- msol=mpert
- DO ising=1,msing
- CALL sing_vmat(ising)
- ENDDO
- WRITE(out_unit,10)
-c-----------------------------------------------------------------------
-c terminate.
-c-----------------------------------------------------------------------
- RETURN
- END SUBROUTINE sing_scan
-c-----------------------------------------------------------------------
-c subprogram 2. sing_find.
-c finds positions of singular values of q.
-c-----------------------------------------------------------------------
-c-----------------------------------------------------------------------
-c declarations.
-c-----------------------------------------------------------------------
- SUBROUTINE sing_find
-
- INTEGER, PARAMETER :: itmax=200,nsing=1000
- INTEGER :: iex,ising,m,dm,it
- INTEGER, DIMENSION(nsing) :: m_sing
- REAL(r8) :: dq,psifac,psifac0,psifac1,singfac
- REAL(r8), DIMENSION(nsing) :: psising,qsing,q1sing
-c-----------------------------------------------------------------------
-c start loop over extrema to find singular surfaces.
-c-----------------------------------------------------------------------
- ising=0
- DO iex=1,mex
- dq=qex(iex)-qex(iex-1)
- m=nn*qex(iex-1)
- IF(dq > 0)m=m+1
- dm=SIGN(one,dq*nn)
-c-----------------------------------------------------------------------
-c find singular surfaces by binary search.
-c-----------------------------------------------------------------------
- DO
- IF((m-nn*qex(iex-1))*(m-nn*qex(iex)) > 0)EXIT
- it=0
- psifac0=psiex(iex-1)
- psifac1=psiex(iex)
- DO
- it=it+1
- psifac=(psifac0+psifac1)/2
- CALL spline_eval(sq,psifac,0)
- singfac=(m-nn*sq%f(4))*dm
- IF(singfac > 0)THEN
- psifac0=psifac
- psifac=(psifac+psifac1)/2
- ELSE
- psifac1=psifac
- psifac=(psifac+psifac0)/2
- ENDIF
- IF(ABS(singfac) <= 1e-12)EXIT
- IF(it > itmax)
- $ CALL program_stop("sing_find can't find root")
- ENDDO
-c-----------------------------------------------------------------------
-c store singular surfaces.
-c-----------------------------------------------------------------------
- ising=ising+1
- CALL spline_eval(sq,psifac,1)
- m_sing(ising)=m
- qsing(ising)=REAL(m,r8)/nn
- q1sing(ising)=sq%f1(4)
- psising(ising)=psifac
- m=m+dm
- ENDDO
- ENDDO
-c-----------------------------------------------------------------------
-c transfer to permanent storage.
-c-----------------------------------------------------------------------
- msing=ising
- ALLOCATE(sing(msing))
- DO ising=1,msing
- sing(ising)%m=m_sing(ising)
- sing(ising)%psifac=psising(ising)
- sing(ising)%rho=SQRT(psising(ising))
- sing(ising)%q=qsing(ising)
- sing(ising)%q1=q1sing(ising)
- ENDDO
- DEALLOCATE(psiex,qex)
-c-----------------------------------------------------------------------
-c terminate.
-c-----------------------------------------------------------------------
- RETURN
- END SUBROUTINE sing_find
-c-----------------------------------------------------------------------
-c subprogram 3. sing_lim.
-c computes limiter values.
-c-----------------------------------------------------------------------
-c-----------------------------------------------------------------------
-c declarations.
-c-----------------------------------------------------------------------
- SUBROUTINE sing_lim
-
- INTEGER :: it,itmax=50
- INTEGER, DIMENSION(1) :: jpsi
- REAL(r8) :: dpsi,q,q1,eps=1e-10
-
- INTEGER :: i
- REAL(r8) :: qedgestart
-c-----------------------------------------------------------------------
-c compute psilim and qlim.
-c-----------------------------------------------------------------------
- qlim=MIN(qmax,qhigh)
- q1lim=sq%fs1(mpsi,4)
- psilim=psihigh
- IF(sas_flag)THEN
-c-----------------------------------------------------------------------
-c normalze dmlim to interval [0,1).
-c-----------------------------------------------------------------------
- DO
- IF(dmlim < 1)EXIT
- dmlim=dmlim-1
- ENDDO
- DO
- IF(dmlim >= 0)EXIT
- dmlim=dmlim+1
- ENDDO
-c-----------------------------------------------------------------------
-c compute qlim.
-c-----------------------------------------------------------------------
- qlim=(INT(nn*qlim)+dmlim)/nn
- DO
- IF(qlim <= qmax)EXIT
- qlim=qlim-1._r8/nn
- ENDDO
- ENDIF
-c-----------------------------------------------------------------------
-c use newton iteration to find psilim.
-c-----------------------------------------------------------------------
- IF(qlim= mpsi) jpsi(1)=mpsi-1
- psilim=sq%xs(jpsi(1))
- it=0
- DO
- it=it+1
- CALL spline_eval(sq,psilim,1)
- q=sq%f(4)
- q1=sq%f1(4)
- dpsi=(qlim-q)/q1
- psilim=psilim+dpsi
- IF(ABS(dpsi) < eps*ABS(psilim) .OR. it > itmax)EXIT
- ENDDO
- q1lim=q1
-c-----------------------------------------------------------------------
-c abort if not found.
-c-----------------------------------------------------------------------
- IF(it > itmax)THEN
- CALL program_stop("Can't find psilim.")
- ENDIF
- ELSE
- qlim = qmax
- q1lim=sq%fs1(mpsi,4)
- psilim=psihigh
- ENDIF
-c-----------------------------------------------------------------------
-c set up record for determining the peak in dW near the boundary.
-c-----------------------------------------------------------------------
- IF(psiedge < psilim)THEN
- CALL spline_eval(sq, psiedge, 0)
- qedgestart = INT(sq%f(4))
- size_edge = CEILING((qlim - qedgestart) * nn * nperq_edge)
- ALLOCATE(dw_edge(size_edge), q_edge(size_edge),
- $ psi_edge(size_edge))
- q_edge(:) = qedgestart + (/(i*1.0,i=0,size_edge-1)/) /
- $ (nperq_edge*nn)
- psi_edge(:) = 0.0
- dw_edge(:) = -huge(0.0_r8) * (1 + ifac)
- ! we monitor some deeper points for an informative profile
- ! output over a full rational window
- ! but we still respect the user psiedge when looking for peak dW
- pre_edge = 1
- DO i=1,size_edge
- IF(q_edge(i) < sq%f(4)) pre_edge = pre_edge + 1
- ENDDO
- ENDIF
-c-----------------------------------------------------------------------
-c terminate.
-c-----------------------------------------------------------------------
- RETURN
- END SUBROUTINE sing_lim
-c-----------------------------------------------------------------------
-c subprogram 4. sing_vmat.
-c computes asymptotic behavior at the singular surface.
-c-----------------------------------------------------------------------
-c-----------------------------------------------------------------------
-c declarations.
-c-----------------------------------------------------------------------
- SUBROUTINE sing_vmat(ising)
-
- INTEGER, INTENT(IN) :: ising
-
- LOGICAL, PARAMETER :: diagnose=.FALSE.
- INTEGER :: ipert0,ipert,k
- REAL(r8) :: psifac,di,di0,q,q1,rho,dpsi
- REAL(r8), PARAMETER :: half=.5_r8
- COMPLEX(r8) :: det
- TYPE(sing_type), POINTER :: singp
-c-----------------------------------------------------------------------
-c allocate and initialize solution array.
-c-----------------------------------------------------------------------
- IF(ising < 1 .OR. ising > msing)RETURN
- singp => sing(ising)
- ALLOCATE(singp%vmat(mpert,2*mpert,2,0:2*sing_order),
- $ singp%mmat(mpert,2*mpert,2,0:2*sing_order+2))
-c-----------------------------------------------------------------------
-c zero di if out of range.
-c-----------------------------------------------------------------------
- ipert0=NINT(nn*singp%q)-mlow+1
- q=singp%q
- IF(ipert0 <= 0 .OR. mlow > nn*q .OR. mhigh < nn*q)THEN
- singp%di=0
- RETURN
- ENDIF
-c-----------------------------------------------------------------------
-c allocate and compute ranges.
-c-----------------------------------------------------------------------
- ALLOCATE(sing(ising)%n1(mpert-1),sing(ising)%n2(2*mpert-2))
- singp%r1=(/ipert0/)
- singp%r2=(/ipert0,ipert0+mpert/)
- singp%n1=(/(ipert,ipert=1,ipert0-1),(ipert,ipert=ipert0+1,mpert)/)
- singp%n2=(/singp%n1,singp%n1+mpert/)
- r1 => singp%r1
- r2 => singp%r2
- n1 => singp%n1
- n2 => singp%n2
-c-----------------------------------------------------------------------
-c interpolate local values.
-c-----------------------------------------------------------------------
- psifac=singp%psifac
- CALL spline_eval(locstab,psifac,0)
- di0=locstab%f(1)/psifac
- q1=singp%q1
- rho=singp%rho
-c-----------------------------------------------------------------------
-c compute Mercier criterion and singular power.
-c-----------------------------------------------------------------------
- CALL sing_mmat(ising)
- m0mat=TRANSPOSE(singp%mmat(r1(1),r2,:,0))
- di=m0mat(1,1)*m0mat(2,2)-m0mat(2,1)*m0mat(1,2)
- singp%di=di
- singp%alpha=SQRT(-CMPLX(singp%di))
- ALLOCATE(singp%power(2*mpert))
- singp%power=0
- singp%power(ipert0)=-singp%alpha
- singp%power(ipert0+mpert)=singp%alpha
- WRITE(out_unit,'(i3,1p,7e11.3)')ising,psifac,rho,q,q1,di0,
- $ singp%di,singp%di/di0-1
-c-----------------------------------------------------------------------
-c zeroth-order non-resonant solutions.
-c-----------------------------------------------------------------------
- singp%vmat=0
- DO ipert=1,mpert
- singp%vmat(ipert,ipert,1,0)=1
- singp%vmat(ipert,ipert+mpert,2,0)=1
- ENDDO
-c-----------------------------------------------------------------------
-c zeroth-order resonant solutions.
-c-----------------------------------------------------------------------
- singp%vmat(ipert0,ipert0,1,0)=1
- singp%vmat(ipert0,ipert0+mpert,1,0)=1
- singp%vmat(ipert0,ipert0,2,0)
- $ =-(m0mat(1,1)+singp%alpha)/m0mat(1,2)
- singp%vmat(ipert0,ipert0+mpert,2,0)
- $ =-(m0mat(1,1)-singp%alpha)/m0mat(1,2)
- det=CONJG(singp%vmat(ipert0,ipert0,1,0))
- $ *singp%vmat(ipert0,ipert0+mpert,2,0)
- $ -CONJG(singp%vmat(ipert0,ipert0+mpert,1,0))
- $ *singp%vmat(ipert0,ipert0,2,0)
- singp%vmat(ipert0,:,:,0)=singp%vmat(ipert0,:,:,0)/SQRT(det)
-c-----------------------------------------------------------------------
-c compute higher-order solutions.
-c-----------------------------------------------------------------------
- DO k=1,2*sing_order
- CALL sing_solve(k,singp%power,singp%mmat,singp%vmat)
- ENDDO
-c-----------------------------------------------------------------------
-c diagnose.
-c-----------------------------------------------------------------------
- IF(diagnose)THEN
- CALL sing_vmat_diagnose(ising)
- dpsi=-1e-2
- CALL sing_ua_diagnose(ising,dpsi)
- CALL program_stop("Termination by sing_vmat.")
- ENDIF
-c-----------------------------------------------------------------------
-c terminate.
-c-----------------------------------------------------------------------
- RETURN
- END SUBROUTINE sing_vmat
-c-----------------------------------------------------------------------
-c subprogram 5. sing_mmat.
-c computes series expansion of coefficient matrix.
-c-----------------------------------------------------------------------
-c-----------------------------------------------------------------------
-c declarations.
-c-----------------------------------------------------------------------
- SUBROUTINE sing_mmat(ising)
-
- INTEGER, INTENT(IN) :: ising
-
- INTEGER :: ipert0,ipert,jpert,kpert,isol,iqty,info,msol,m,i,j,n,
- $ fac0,fac1
- INTEGER, DIMENSION(mpert) :: mvec
- REAL(r8) :: psifac
- REAL(r8), DIMENSION(0:3) :: q
- REAL(r8), DIMENSION(mpert,0:3) :: singfac
- COMPLEX(r8), PARAMETER :: one=1,half=.5_r8
- COMPLEX(r8), DIMENSION(mband+1,mpert,0:sing_order) :: f,ff,g
- COMPLEX(r8), DIMENSION(mband+1,mpert) :: f0
- COMPLEX(r8), DIMENSION(2*mband+1,mpert,0:sing_order) :: k
- COMPLEX(r8), DIMENSION(mpert,2*mpert,2) :: v
- COMPLEX(r8), DIMENSION(mpert,2*mpert,2,0:sing_order) :: x
- COMPLEX(r8), DIMENSION(:,:,:,:), POINTER :: mmat
-
- LOGICAL, PARAMETER :: diagnose=.FALSE.
-c-----------------------------------------------------------------------
-c format statements.
-c-----------------------------------------------------------------------
- 10 FORMAT(/4x,"io",4x,"is",4x,"ip",2(4x,"re x",i1,6x,"im x",i1,2x)/)
- 20 FORMAT(3i6,1p,4e11.3)
-c-----------------------------------------------------------------------
-c evaluate cubic splines.
-c-----------------------------------------------------------------------
- msol=2*mpert
- psifac=sing(ising)%psifac
- CALL spline_eval(sq,psifac,3)
- CALL cspline_eval(fmats,psifac,3)
- CALL cspline_eval(gmats,psifac,3)
- CALL cspline_eval(kmats,psifac,3)
-c-----------------------------------------------------------------------
-c evaluate safety factor and its derivatives.
-c-----------------------------------------------------------------------
- q(0)=sq%f(4)
- q(1)=sq%f1(4)
- q(2)=sq%f2(4)
- q(3)=sq%f3(4)
-c-----------------------------------------------------------------------
-c evaluate singfac and its derivatives.
-c-----------------------------------------------------------------------
- ipert0=sing(ising)%m-mlow+1
- mvec=(/(m,m=mlow,mhigh)/)
- singfac=0
- singfac(:,0)=mvec-nn*q(0)
- singfac(:,1)=-nn*q(1)
- singfac(:,2)=-nn*q(2)
- singfac(:,3)=-nn*q(3)
- singfac(ipert0,0)=-nn*q(1)
- singfac(ipert0,1)=-nn*q(2)/2
- singfac(ipert0,2)=-nn*q(3)/3
- singfac(ipert0,3)=0
-c-----------------------------------------------------------------------
-c compute factored Hermitian banded matrix F and its derivatives.
-c-----------------------------------------------------------------------
- f=0
- iqty=0
- DO jpert=1,mpert
- DO ipert=jpert,MIN(mpert,jpert+mband)
- iqty=iqty+1
- f(1+ipert-jpert,jpert,0)
- $ =singfac(ipert,0)*fmats%f(iqty)
- IF(sing_order < 1)CYCLE
- f(1+ipert-jpert,jpert,1)
- $ =singfac(ipert,0)*fmats%f1(iqty)
- $ +singfac(ipert,1)*fmats%f(iqty)
- IF(sing_order < 2)CYCLE
- f(1+ipert-jpert,jpert,2)
- $ =singfac(ipert,0)*fmats%f2(iqty)
- $ +2*singfac(ipert,1)*fmats%f1(iqty)
- $ +singfac(ipert,2)*fmats%f(iqty)
- IF(sing_order < 3)CYCLE
- f(1+ipert-jpert,jpert,3)
- $ =singfac(ipert,0)*fmats%f3(iqty)
- $ +3*singfac(ipert,1)*fmats%f2(iqty)
- $ +3*singfac(ipert,2)*fmats%f1(iqty)
- $ +singfac(ipert,3)*fmats%f(iqty)
- IF(sing_order < 4)CYCLE
- f(1+ipert-jpert,jpert,4)
- $ =4*singfac(ipert,1)*fmats%f3(iqty)
- $ +6*singfac(ipert,2)*fmats%f2(iqty)
- $ +4*singfac(ipert,3)*fmats%f1(iqty)
- IF(sing_order < 5)CYCLE
- f(1+ipert-jpert,jpert,5)
- $ =10*singfac(ipert,2)*fmats%f3(iqty)
- $ +10*singfac(ipert,3)*fmats%f2(iqty)
- IF(sing_order < 6)CYCLE
- f(1+ipert-jpert,jpert,5)
- $ =20*singfac(ipert,3)*fmats%f3(iqty)
- ENDDO
- ENDDO
- f0=f(:,:,0)
-c-----------------------------------------------------------------------
-c compute product of factored Hermitian banded matrix F.
-c-----------------------------------------------------------------------
- ff=0
- fac0=1
- DO n=0,sing_order
- fac1=1
- DO j=0,n
- DO jpert=1,mpert
- DO ipert=jpert,MIN(mpert,jpert+mband)
- DO kpert=MAX(1,ipert-mband),jpert
- ff(1+ipert-jpert,jpert,n)
- $ =ff(1+ipert-jpert,jpert,n)
- $ +fac1*f(1+ipert-kpert,kpert,j)
- $ *CONJG(f(1+jpert-kpert,kpert,n-j))
- ENDDO
- ENDDO
- ENDDO
- fac1=fac1*(n-j)/(j+1)
- ENDDO
- ff(:,:,n)=ff(:,:,n)/fac0
- fac0=fac0*(n+1)
- ENDDO
-c-----------------------------------------------------------------------
-c compute non-Hermitian banded matrix K.
-c-----------------------------------------------------------------------
- k=0
- iqty=0
- DO jpert=1,mpert
- DO ipert=MAX(1,jpert-mband),MIN(mpert,jpert+mband)
- iqty=iqty+1
- k(1+mband+ipert-jpert,jpert,0)
- $ =singfac(ipert,0)*kmats%f(iqty)
- IF(sing_order < 1)CYCLE
- k(1+mband+ipert-jpert,jpert,1)
- $ =singfac(ipert,0)*kmats%f1(iqty)
- $ +singfac(ipert,1)*kmats%f(iqty)
- IF(sing_order < 2)CYCLE
- k(1+mband+ipert-jpert,jpert,2)
- $ =singfac(ipert,0)*kmats%f2(iqty)/2
- $ +singfac(ipert,1)*kmats%f1(iqty)
- $ +singfac(ipert,2)*kmats%f(iqty)/2
- IF(sing_order < 3)CYCLE
- k(1+mband+ipert-jpert,jpert,3)
- $ =singfac(ipert,0)*kmats%f3(iqty)/6
- $ +singfac(ipert,1)*kmats%f2(iqty)/2
- $ +singfac(ipert,2)*kmats%f1(iqty)/2
- $ +singfac(ipert,3)*kmats%f(iqty)/6
- IF(sing_order < 4)CYCLE
- k(1+mband+ipert-jpert,jpert,4)
- $ =singfac(ipert,1)*kmats%f3(iqty)/6
- $ +singfac(ipert,2)*kmats%f2(iqty)/4
- $ +singfac(ipert,3)*kmats%f1(iqty)/6
- IF(sing_order < 5)CYCLE
- k(1+mband+ipert-jpert,jpert,5)
- $ =singfac(ipert,2)*kmats%f3(iqty)/12
- $ +singfac(ipert,3)*kmats%f2(iqty)/12
- IF(sing_order < 6)CYCLE
- k(1+mband+ipert-jpert,jpert,6)
- $ =singfac(ipert,3)*kmats%f3(iqty)/36
- ENDDO
- ENDDO
-c-----------------------------------------------------------------------
-c compute Hermitian banded matrix G.
-c-----------------------------------------------------------------------
- g=0
- iqty=0
- DO jpert=1,mpert
- DO ipert=jpert,MIN(mpert,jpert+mband)
- iqty=iqty+1
- g(1+ipert-jpert,jpert,0)=gmats%f(iqty)
- IF(sing_order < 1)CYCLE
- g(1+ipert-jpert,jpert,1)=gmats%f1(iqty)
- IF(sing_order < 2)CYCLE
- g(1+ipert-jpert,jpert,2)=gmats%f2(iqty)/2
- IF(sing_order < 3)CYCLE
- g(1+ipert-jpert,jpert,3)=gmats%f2(iqty)/6
- ENDDO
- ENDDO
-c-----------------------------------------------------------------------
-c compute identity.
-c-----------------------------------------------------------------------
- v=0
- DO ipert=1,mpert
- v(ipert,ipert,1)=1
- v(ipert,ipert+mpert,2)=1
- ENDDO
-c-----------------------------------------------------------------------
-c compute zeroth-order x1.
-c-----------------------------------------------------------------------
- x=0
- DO isol=1,msol
- x(:,isol,1,0)=v(:,isol,2)
- CALL zgbmv('N',mpert,mpert,mband,mband,-one,k(:,:,0),
- $ 2*mband+1,v(:,isol,1),1,one,x(:,isol,1,0),1)
- ENDDO
- CALL zpbtrs('L',mpert,mband,msol,f0,mband+1,x(:,:,1,0),mpert,info)
-c-----------------------------------------------------------------------
-c compute higher-order x1.
-c-----------------------------------------------------------------------
- DO i=1,sing_order
- DO isol=1,msol
- DO j=1,i
- CALL zhbmv('L',mpert,mband,-one,ff(:,:,j),
- $ mband+1,x(:,isol,1,i-j),1,one,x(:,isol,1,i),1)
- ENDDO
- CALL zgbmv('N',mpert,mpert,mband,mband,-one,k(:,:,i),
- $ 2*mband+1,v(:,isol,1),1,one,x(:,isol,1,i),1)
- ENDDO
- CALL zpbtrs('L',mpert,mband,msol,f0,mband+1,x(:,:,1,i),mpert,
- $ info)
- ENDDO
-c-----------------------------------------------------------------------
-c compute x2.
-c-----------------------------------------------------------------------
- DO i=0,sing_order
- DO isol=1,msol
- DO j=0,i
- CALL zgbmv('C',mpert,mpert,mband,mband,one,k(:,:,j),
- $ 2*mband+1,x(:,isol,1,i-j),1,one,x(:,isol,2,i),1)
- ENDDO
- CALL zhbmv('L',mpert,mband,one,g(:,:,i),
- $ mband+1,v(:,isol,1),1,one,x(:,isol,2,i),1)
- ENDDO
- ENDDO
-c-----------------------------------------------------------------------
-c diagnose.
-c-----------------------------------------------------------------------
- IF(diagnose)THEN
- CALL ascii_open(debug_unit,"xmat.out","UNKNOWN")
- DO j=0,sing_order
- DO isol=1,2*mpert
- WRITE(debug_unit,10)(i,i,i=1,2)
- DO ipert=1,mpert
- WRITE(debug_unit,20)j,isol,ipert,
- $ x(ipert,isol,:,j)
- ENDDO
- ENDDO
- ENDDO
- WRITE(debug_unit,10)(i,i,i=1,2)
- CALL ascii_close(debug_unit)
- ENDIF
-c-----------------------------------------------------------------------
-c principal terms of mmat.
-c-----------------------------------------------------------------------
- mmat => sing(ising)%mmat
- mmat=0
- j=0
- DO i=0,sing_order
- mmat(r1,r2,:,j)=x(r1,r2,:,i)
- mmat(r1,n2,:,j+1)=x(r1,n2,:,i)
- mmat(n1,r2,:,j+1)=x(n1,r2,:,i)
- mmat(n1,n2,:,j+2)=x(n1,n2,:,i)
- j=j+2
- ENDDO
-c-----------------------------------------------------------------------
-c shearing terms.
-c-----------------------------------------------------------------------
- mmat(r1,r2(1),1,0)=mmat(r1,r2(1),1,0)+half
- mmat(r1,r2(2),2,0)=mmat(r1,r2(2),2,0)-half
-c-----------------------------------------------------------------------
-c terminate.
-c-----------------------------------------------------------------------
- RETURN
- END SUBROUTINE sing_mmat
-c-----------------------------------------------------------------------
-c subprogram 6. sing_solve.
-c solves iteratively for the next order in the power series vmat.
-c-----------------------------------------------------------------------
-c-----------------------------------------------------------------------
-c declarations.
-c-----------------------------------------------------------------------
- SUBROUTINE sing_solve(k,power,mmat,vmat)
-
- INTEGER, INTENT(IN) :: k
- COMPLEX(r8), DIMENSION(:), INTENT(IN) :: power
- COMPLEX(r8), DIMENSION(mpert,2*mpert,2,0:k), INTENT(IN) :: mmat
- COMPLEX(r8), DIMENSION(mpert,2*mpert,2,0:k), INTENT(INOUT) :: vmat
-
- INTEGER :: l,isol
- REAL(r8), PARAMETER :: two=2
- COMPLEX(r8) :: det
- COMPLEX(r8), DIMENSION(2,2) :: a
- COMPLEX(r8), DIMENSION(2) :: x
-c-----------------------------------------------------------------------
-c compute rhs.
-c-----------------------------------------------------------------------
- DO l=1,k
- vmat(:,:,:,k)=vmat(:,:,:,k)
- $ +sing_matmul(mmat(:,:,:,l),vmat(:,:,:,k-l))
- ENDDO
-c-----------------------------------------------------------------------
-c evaluate solutions.
-c-----------------------------------------------------------------------
- DO isol=1,2*mpert
- a=m0mat
- a(1,1)=a(1,1)-k/two-power(isol)
- a(2,2)=a(2,2)-k/two-power(isol)
- det=a(1,1)*a(2,2)-a(1,2)*a(2,1)
- x=-vmat(r1(1),isol,:,k)
- vmat(r1(1),isol,1,k)=(a(2,2)*x(1)-a(1,2)*x(2))/det
- vmat(r1(1),isol,2,k)=(a(1,1)*x(2)-a(2,1)*x(1))/det
- vmat(n1,isol,:,k)=vmat(n1,isol,:,k)/(power(isol)+k/two)
- ENDDO
-c-----------------------------------------------------------------------
-c terminate.
-c-----------------------------------------------------------------------
- RETURN
- END SUBROUTINE sing_solve
-c-----------------------------------------------------------------------
-c subprogram 7. sing_matmul.
-c multiplies matrices.
-c-----------------------------------------------------------------------
-c-----------------------------------------------------------------------
-c declarations.
-c-----------------------------------------------------------------------
- FUNCTION sing_matmul(a,b) RESULT(c)
-
- COMPLEX(r8), DIMENSION(:,:,:), INTENT(IN) :: a,b
- COMPLEX(r8), DIMENSION(SIZE(a,1),SIZE(b,2),2) :: c
-
- CHARACTER(64) :: message
- INTEGER :: i,j,m,n
-c-----------------------------------------------------------------------
-c preliminary computations.
-c-----------------------------------------------------------------------
- m=SIZE(b,1)
- n=SIZE(b,2)
- IF(SIZE(a,2) /= 2*m)THEN
- WRITE(message,'(2(a,i3))')
- $ "Sing_matmul: SIZE(a,2) = ",SIZE(a,2),
- $ " /= 2*SIZE(b,1) = ",2*SIZE(b,1)
- CALL program_stop(message)
- ENDIF
-c-----------------------------------------------------------------------
-c main computations.
-c-----------------------------------------------------------------------
- c=0
- DO i=1,n
- DO j=1,2
- c(:,i,j)=c(:,i,j)
- $ +MATMUL(a(:,1:m,j),b(:,i,1))
- $ +MATMUL(a(:,1+m:2*m,j),b(:,i,2))
- ENDDO
- ENDDO
-c-----------------------------------------------------------------------
-c terminate.
-c-----------------------------------------------------------------------
- RETURN
- END FUNCTION sing_matmul
-c-----------------------------------------------------------------------
-c subprogram 8. sing_vmat_diagnose.
-c diagnoses asymptotic behavior at the singular surface.
-c-----------------------------------------------------------------------
-c-----------------------------------------------------------------------
-c declarations.
-c-----------------------------------------------------------------------
- SUBROUTINE sing_vmat_diagnose(ising)
-
- INTEGER, INTENT(IN) :: ising
-
- INTEGER :: i,isol,iorder,ipert
- TYPE(sing_type), POINTER :: singp
-c-----------------------------------------------------------------------
-c format statements.
-c-----------------------------------------------------------------------
- 10 FORMAT(/4x,"io",4x,"is",4x,"ip",2(4x,"re v",i1,6x,"im v",i1,2x)/)
- 20 FORMAT(3i6,1p,4e11.3)
-c-----------------------------------------------------------------------
-c set pointer and open file.
-c-----------------------------------------------------------------------
- singp => sing(ising)
- CALL ascii_open(debug_unit,"vmat.out","UNKNOWN")
-c-----------------------------------------------------------------------
-c write output.
-c-----------------------------------------------------------------------
- DO iorder=0,2
- DO isol=1,2*mpert
- WRITE(debug_unit,10)(i,i,i=1,2)
- DO ipert=1,mpert
- WRITE(debug_unit,20)iorder,isol,ipert,
- $ singp%vmat(ipert,isol,:,iorder)
- ENDDO
- ENDDO
- ENDDO
- WRITE(debug_unit,10)(i,i,i=1,2)
-c-----------------------------------------------------------------------
-c close files.
-c-----------------------------------------------------------------------
- CALL ascii_close(debug_unit)
-c-----------------------------------------------------------------------
-c terminate.
-c-----------------------------------------------------------------------
- RETURN
- END SUBROUTINE sing_vmat_diagnose
-c-----------------------------------------------------------------------
-c subprogram 9. sing_get_ua.
-c computes asymptotic series solutions.
-c-----------------------------------------------------------------------
-c-----------------------------------------------------------------------
-c declarations.
-c-----------------------------------------------------------------------
- SUBROUTINE sing_get_ua(ising,psifac,ua)
-
- INTEGER, INTENT(IN) :: ising
- REAL(r8), INTENT(IN) :: psifac
- COMPLEX(r8), DIMENSION(:,:,:), INTENT(OUT) :: ua
-
- INTEGER :: iorder
- INTEGER, DIMENSION(:), POINTER :: r1,r2
- COMPLEX(r8) :: dpsi,pfac,sqrtfac
- COMPLEX(r8), DIMENSION(:,:,:,:), POINTER :: vmat
- TYPE(sing_type), POINTER :: singp
-c-----------------------------------------------------------------------
-c set pointers.
-c-----------------------------------------------------------------------
- singp => sing(ising)
- vmat => singp%vmat
- r1 => singp%r1
- r2 => singp%r2
-c-----------------------------------------------------------------------
-c compute distance from singular surface and its powers.
-c-----------------------------------------------------------------------
- dpsi=psifac-singp%psifac
- sqrtfac=SQRT(dpsi)
- pfac=ABS(dpsi)**singp%alpha
-c-----------------------------------------------------------------------
-c compute power series by Horner's method.
-c-----------------------------------------------------------------------
- ua=vmat(:,:,:,2*sing_order)
- DO iorder=2*sing_order-1,0,-1
- ua=ua*sqrtfac+vmat(:,:,:,iorder)
- ENDDO
-c-----------------------------------------------------------------------
-c restore powers.
-c-----------------------------------------------------------------------
- ua(r1,:,1)=ua(r1,:,1)/sqrtfac
- ua(r1,:,2)=ua(r1,:,2)*sqrtfac
- ua(:,r2(1),:)=ua(:,r2(1),:)/pfac
- ua(:,r2(2),:)=ua(:,r2(2),:)*pfac
-c-----------------------------------------------------------------------
-c renormalize.
-c-----------------------------------------------------------------------
- IF(psifac < singp%psifac)THEN
- ua(:,r2(1),:)=ua(:,r2(1),:)
- $ *ABS(ua(r1(1),r2(1),1))/ua(r1(1),r2(1),1)
- ua(:,r2(2),:)=ua(:,r2(2),:)
- $ *ABS(ua(r1(1),r2(2),1))/ua(r1(1),r2(2),1)
- ENDIF
-c-----------------------------------------------------------------------
-c terminate.
-c-----------------------------------------------------------------------
- RETURN
- END SUBROUTINE sing_get_ua
-c-----------------------------------------------------------------------
-c subprogram 10. sing_get_ca.
-c computes asymptotic coefficients.
-c-----------------------------------------------------------------------
-c-----------------------------------------------------------------------
-c declarations.
-c-----------------------------------------------------------------------
- SUBROUTINE sing_get_ca(ising,psifac,u,ca)
-
- INTEGER, INTENT(IN) :: ising
- REAL(r8) , INTENT(IN):: psifac
- COMPLEX(r8), DIMENSION(:,:,:), INTENT(IN) :: u
- COMPLEX(r8), DIMENSION(:,:,:), INTENT(OUT) :: ca
-
- INTEGER :: info,msol
- INTEGER, DIMENSION(2*mpert) :: ipiv
- COMPLEX(r8), DIMENSION(mpert,2*mpert,2) :: ua
- COMPLEX(r8), DIMENSION(2*mpert,2*mpert) :: temp1
- COMPLEX(r8), DIMENSION(2*mpert,SIZE(u,2)) :: temp2
-c-----------------------------------------------------------------------
-c compute asymptotic coefficients.
-c-----------------------------------------------------------------------
- msol=SIZE(u,2)
- CALL sing_get_ua(ising,psifac,ua)
- temp1(1:mpert,:)=ua(:,:,1)
- temp1(mpert+1:2*mpert,:)=ua(:,:,2)
- CALL zgetrf(2*mpert,2*mpert,temp1,2*mpert,ipiv,info)
- temp2(1:mpert,:)=u(:,:,1)
- temp2(mpert+1:2*mpert,:)=u(:,:,2)
- CALL zgetrs('N',2*mpert,msol,temp1,2*mpert,ipiv,
- $ temp2,2*mpert,info)
- ca(:,1:msol,1)=temp2(1:mpert,:)
- ca(:,1:msol,2)=temp2(mpert+1:2*mpert,:)
-c-----------------------------------------------------------------------
-c terminate.
-c-----------------------------------------------------------------------
- RETURN
- END SUBROUTINE sing_get_ca
-c-----------------------------------------------------------------------
-c subprogram 11. sing_der.
-c evaluates euler-lagrange differential equation.
-c-----------------------------------------------------------------------
-c-----------------------------------------------------------------------
-c declarations.
-c-----------------------------------------------------------------------
- SUBROUTINE sing_der(neq,psifac,u,du)
-
- INTEGER, INTENT(IN) :: neq
- REAL(r8), INTENT(IN) :: psifac
- CHARACTER(128) :: message
- COMPLEX(r8), DIMENSION(mpert,msol,2), INTENT(IN) :: u
- COMPLEX(r8), DIMENSION(mpert,msol,2), INTENT(OUT) :: du
-
- INTEGER :: ipert,jpert,isol,iqty,info,m1,m2,dm,i
- INTEGER, DIMENSION(mpert) :: ipiv
- REAL(r8) :: q,singfac1,singfac2,chi1
- REAL(r8), DIMENSION(mpert) :: singfac
- COMPLEX(r8), PARAMETER :: one=1
- COMPLEX(r8), DIMENSION(mpert*mpert) :: work
- COMPLEX(r8), DIMENSION(mband+1,mpert) :: fmatb,gmatb
- COMPLEX(r8), DIMENSION(2*mband+1,mpert) :: kmatb,kaatb,gaatb
- COMPLEX(r8), DIMENSION(3*mband+1,mpert) :: amatlu,fmatlu
- COMPLEX(r8), DIMENSION(mpert,mpert) :: temp1,temp2,
- $ amat,bmat,cmat,dmat,emat,hmat,baat,caat,eaat,dbat,ebat,
- $ fmat,kmat,gmat,kaat,gaat,pmat,paat,umat,aamat,b1mat,bkmat,
- $ bkaat,kkmat,kkaat,r1mat,r2mat,r3mat,f0mat
- COMPLEX(r8), DIMENSION(mpert,mpert,6) :: kwmat,ktmat
-c-----------------------------------------------------------------------
-c cubic spline evaluation.
-c-----------------------------------------------------------------------
- CALL spline_eval(sq,psifac,0)
- q=sq%f(4)
- singfac=mlow-nn*q+(/(ipert,ipert=0,mpert-1)/)
- singfac=1/singfac
- chi1=twopi*psio
-
- IF (kin_flag) THEN
- CALL cspline_eval(amats,psifac,0)
- CALL cspline_eval(bmats,psifac,0)
- CALL cspline_eval(cmats,psifac,0)
- CALL cspline_eval(dmats,psifac,0)
- CALL cspline_eval(emats,psifac,0)
- CALL cspline_eval(hmats,psifac,0)
- CALL cspline_eval(dbats,psifac,0)
- CALL cspline_eval(ebats,psifac,0)
- CALL cspline_eval(fbats,psifac,0)
-
- amat=RESHAPE(amats%f,(/mpert,mpert/))
- bmat=RESHAPE(bmats%f,(/mpert,mpert/))
- cmat=RESHAPE(cmats%f,(/mpert,mpert/))
- dmat=RESHAPE(dmats%f,(/mpert,mpert/))
- emat=RESHAPE(emats%f,(/mpert,mpert/))
- hmat=RESHAPE(hmats%f,(/mpert,mpert/))
- dbat=RESHAPE(dbats%f,(/mpert,mpert/))
- ebat=RESHAPE(ebats%f,(/mpert,mpert/))
- fmat=RESHAPE(fbats%f,(/mpert,mpert/))
-
- DO i=1,6
- CALL cspline_eval(kwmats(i),psifac,0)
- CALL cspline_eval(ktmats(i),psifac,0)
- kwmat(:,:,i)=RESHAPE(kwmats(i)%f,(/mpert,mpert/))
- ktmat(:,:,i)=RESHAPE(ktmats(i)%f,(/mpert,mpert/))
- ENDDO
-c-----------------------------------------------------------------------
-c compute kinetic matrices.
-c-----------------------------------------------------------------------
- IF (fkg_kmats_flag) THEN
- CALL cspline_eval(akmats,psifac,0)
- CALL cspline_eval(bkmats,psifac,0)
- CALL cspline_eval(ckmats,psifac,0)
- CALL cspline_eval(f0mats,psifac,0)
- CALL cspline_eval(pmats,psifac,0)
- CALL cspline_eval(paats,psifac,0)
- CALL cspline_eval(kkmats,psifac,0)
- CALL cspline_eval(kkaats,psifac,0)
- CALL cspline_eval(r1mats,psifac,0)
- CALL cspline_eval(r2mats,psifac,0)
- CALL cspline_eval(r3mats,psifac,0)
- CALL cspline_eval(gaats,psifac,0)
-
- amat=RESHAPE(akmats%f,(/mpert,mpert/))
- bmat=RESHAPE(bkmats%f,(/mpert,mpert/))
- cmat=RESHAPE(ckmats%f,(/mpert,mpert/))
- f0mat=RESHAPE(f0mats%f,(/mpert,mpert/))
- pmat=RESHAPE(pmats%f,(/mpert,mpert/))
- paat=RESHAPE(paats%f,(/mpert,mpert/))
- kkmat=RESHAPE(kkmats%f,(/mpert,mpert/))
- kkaat=RESHAPE(kkaats%f,(/mpert,mpert/))
- r1mat=RESHAPE(r1mats%f,(/mpert,mpert/))
- r2mat=RESHAPE(r2mats%f,(/mpert,mpert/))
- r3mat=RESHAPE(r3mats%f,(/mpert,mpert/))
-
- amatlu=0
- DO jpert=1,mpert
- DO ipert=1,mpert
- amatlu(2*mband+1+ipert-jpert,jpert)=amat(ipert,jpert)
- ENDDO
- ENDDO
- CALL zgbtrf(mpert,mpert,mband,mband,amatlu,3*mband+1,
- $ ipiv,info)
- IF(info /= 0)THEN
- WRITE(message,'(a,e16.9,a,i2)')
- $ "zgbtrf: amat singular at psifac = ",psifac,
- $ ", ipert = ",info,", reduce delta_mband"
- CALL program_stop(message)
- ENDIF
-c-----------------------------------------------------------------------
-c obsolete diagnostics.
-c-----------------------------------------------------------------------
-c DO jpert=1,mpert
-c DO ipert=MAX(1,jpert-mband),MIN(mpert,jpert+mband)
-c gaat(ipert,jpert)=gaats%f(iqty)
-c iqty=iqty+1
-c ENDDO
-c ENDDO
- ELSE
- amat=amat+kwmat(:,:,1)+ktmat(:,:,1)
- bmat=bmat+kwmat(:,:,2)+ktmat(:,:,2)
- cmat=cmat+kwmat(:,:,3)+ktmat(:,:,3)
- dmat=dmat+kwmat(:,:,4)+ktmat(:,:,4)
- emat=emat+kwmat(:,:,5)+ktmat(:,:,5)
- hmat=hmat+kwmat(:,:,6)+ktmat(:,:,6)
- baat=bmat-2*ktmat(:,:,2)
- caat=cmat-2*ktmat(:,:,3)
- eaat=emat-2*ktmat(:,:,5)
- b1mat=ifac*dbat
-c-----------------------------------------------------------------------
-c factor kinetic non-Hermitian matrix A.
-c-----------------------------------------------------------------------
- amatlu=0
- umat=0
- DO jpert=1,mpert
- DO ipert=1,mpert
- amatlu(2*mband+1+ipert-jpert,jpert)=amat(ipert,jpert)
- IF(ipert==jpert)umat(ipert,jpert)=1
- ENDDO
- ENDDO
- CALL zgbtrf(mpert,mpert,mband,mband,amatlu,3*mband+1,
- $ ipiv,info)
- IF(info /= 0)THEN
- WRITE(message,'(a,e16.9,a,i2)')
- $ "zgbtrf: amat singular at psifac = ",psifac,
- $ ", ipert = ",info,", reduce delta_mband"
- CALL program_stop(message)
- ENDIF
-
- temp1=dbat
- CALL zgbtrs("N",mpert,mband,mband,mpert,amatlu,
- $ 3*mband+1,ipiv,temp1,mpert,info)
- f0mat=fmat-MATMUL(CONJG(TRANSPOSE(dbat)),temp1)
-c-----------------------------------------------------------------------
-c prepare matrices to separate Q factors.
-c-----------------------------------------------------------------------
- temp2=amat
- CALL zgbtrs("C",mpert,mband,mband,mpert,amatlu,
- $ 3*mband+1,ipiv,temp2,mpert,info) ! close to unit matrix.
- aamat=CONJG(TRANSPOSE(temp2))
- umat=umat-aamat
-
- bkmat=kwmat(:,:,2)+ktmat(:,:,2)+ifac*chi1/(twopi*nn)*
- $ (kwmat(:,:,1)+ktmat(:,:,1))
- bkaat=kwmat(:,:,2)-ktmat(:,:,2)+ifac*chi1/(twopi*nn)*
- $ (kwmat(:,:,1)+ktmat(:,:,1))
- temp2=bkmat
- CALL zgbtrs("N",mpert,mband,mband,mpert,amatlu,
- $ 3*mband+1,ipiv,temp2,mpert,info)
- pmat=MATMUL(CONJG(TRANSPOSE(b1mat)),temp2)
-
- temp2=b1mat
- CALL zgbtrs("N",mpert,mband,mband,mpert,amatlu,
- $ 3*mband+1,ipiv,temp2,mpert,info)
- paat=MATMUL(CONJG(TRANSPOSE(bkaat)),temp2)
- $ -ifac*chi1/(twopi*nn)*MATMUL(umat,b1mat)
- paat=CONJG(TRANSPOSE(paat))
-
- temp1=kwmat(:,:,1)+ktmat(:,:,1)
- temp2=bkmat
- CALL zgbtrs("N",mpert,mband,mband,mpert,amatlu,
- $ 3*mband+1,ipiv,temp2,mpert,info)
- r1mat=kwmat(:,:,4)+ktmat(:,:,4)-
- $ (chi1/(twopi*nn))**2*CONJG(TRANSPOSE(temp1))+
- $ ifac*chi1/(twopi*nn)*CONJG(TRANSPOSE(bkaat))-
- $ ifac*chi1/(twopi*nn)*MATMUL(aamat,bkmat)-
- $ MATMUL(CONJG(TRANSPOSE(bkaat)),temp2)
-
- temp1=kwmat(:,:,5)+ktmat(:,:,5)-ifac*chi1/(twopi*nn)*
- $ (kwmat(:,:,3)+ktmat(:,:,3))
- temp2=cmat
- CALL zgbtrs("N",mpert,mband,mband,mpert,amatlu,
- $ 3*mband+1,ipiv,temp2,mpert,info)
- r2mat=temp1+ifac*chi1/(twopi*nn)*MATMUL(umat,cmat)-
- $ MATMUL(CONJG(TRANSPOSE(bkaat)),temp2)
-
- temp1=kwmat(:,:,5)-ktmat(:,:,5)-ifac*chi1/(twopi*nn)*
- $ (kwmat(:,:,3)-ktmat(:,:,3))
- temp2=bkmat
- CALL zgbtrs("N",mpert,mband,mband,mpert,amatlu,
- $ 3*mband+1,ipiv,temp2,mpert,info)
- r3mat=CONJG(TRANSPOSE(temp1))-
- $ MATMUL(CONJG(TRANSPOSE(caat)),temp2)
-
- temp1=cmat
- CALL zgbtrs("N",mpert,mband,mband,mpert,amatlu,
- $ 3*mband+1,ipiv,temp1,mpert,info)
- kkmat=ebat-MATMUL(CONJG(TRANSPOSE(b1mat)),temp1)
-
- temp1=b1mat
- CALL zgbtrs("N",mpert,mband,mband,mpert,amatlu,
- $ 3*mband+1,ipiv,temp1,mpert,info)
- kkaat=CONJG(TRANSPOSE(ebat))-
- $ MATMUL(CONJG(TRANSPOSE(caat)),temp1)
-
- temp2=cmat
- CALL zgbtrs("N",mpert,mband,mband,mpert,amatlu,
- $ 3*mband+1,ipiv,temp2,mpert,info)
- gaat=hmat-MATMUL(CONJG(TRANSPOSE(caat)),temp2)
-
- iqty=1
- DO jpert=1,mpert
- DO ipert=MAX(1,jpert-mband),MIN(mpert,jpert+mband)
- gaats%f(iqty)=gaat(ipert,jpert)
- iqty=iqty+1
- ENDDO
- ENDDO
- ENDIF
- CALL zgbtrs("N",mpert,mband,mband,mpert,amatlu,3*mband+1,
- $ ipiv,bmat,mpert,info)
- CALL zgbtrs("N",mpert,mband,mband,mpert,amatlu,3*mband+1,
- $ ipiv,cmat,mpert,info)
-c-----------------------------------------------------------------------
-c obsolete method for non-Hermitian FK.
-c-----------------------------------------------------------------------
-c temp1=bmat
-c temp2=cmat
-c CALL zgbtrs("N",mpert,mband,mband,mpert,amatlu,
-c $ 3*mband+1,ipiv,temp1,mpert,info)
-c CALL zgbtrs("N",mpert,mband,mband,mpert,amatlu,
-c $ 3*mband+1,ipiv,temp2,mpert,info)
-c fmat=dmat-MATMUL(CONJG(TRANSPOSE(baat)),temp1)
-c kmat=emat-MATMUL(CONJG(TRANSPOSE(baat)),temp2)
-c kaat=CONJG(TRANSPOSE(eaat))-
-c $ MATMUL(CONJG(TRANSPOSE(caat)),temp1)
-c-----------------------------------------------------------------------
-c calculate kinetic non-Hermitian FK.
-c-----------------------------------------------------------------------
- DO ipert=1,mpert
- m1=mlow+ipert-1
- singfac1=m1-nn*q
- DO jpert=1,mpert
- m2=mlow+jpert-1
- singfac2=m2-nn*q
- fmat(ipert,jpert)=singfac1*f0mat(ipert,jpert)*
- $ singfac2-singfac1*pmat(ipert,jpert)-
- $ CONJG(paat(jpert,ipert))*singfac2+
- $ r1mat(ipert,jpert)
- kmat(ipert,jpert)=singfac1*kkmat(ipert,jpert)+
- $ r2mat(ipert,jpert)
- kaat(ipert,jpert)=kkaat(ipert,jpert)*singfac2+
- $ r3mat(ipert,jpert)
- ENDDO
- ENDDO
-c-----------------------------------------------------------------------
-c obsolete diagnostics.
-c-----------------------------------------------------------------------
-c f1mats=RESHAPE(fmat,(/mpert**2/))
-c k1mats=RESHAPE(kmat,(/mpert**2/))
-c k1aats=RESHAPE(kaat,(/mpert**2/))
-c g1aats=RESHAPE(gaat,(/mpert**2/))
-c-----------------------------------------------------------------------
-c store FKG in banded matrix forms.
-c-----------------------------------------------------------------------
- fmatlu=0
- DO jpert=1,mpert
- DO ipert=1,mpert
- fmatlu(2*mband+1+ipert-jpert,jpert)=fmat(ipert,jpert)
- ENDDO
- ENDDO
-
- iqty=1
- DO jpert=1,mpert
- DO ipert=MAX(1,jpert-mband),MIN(mpert,jpert+mband)
- kmats%f(iqty)=kmat(ipert,jpert)
- kaats%f(iqty)=kaat(ipert,jpert)
- iqty=iqty+1
- ENDDO
- ENDDO
-
- kmatb=0
- kaatb=0
- iqty=1
- DO jpert=1,mpert
- DO ipert=MAX(1,jpert-mband),MIN(mpert,jpert+mband)
- kmatb(1+mband+ipert-jpert,jpert)=kmats%f(iqty)
- kaatb(1+mband+ipert-jpert,jpert)=kaats%f(iqty)
- iqty=iqty+1
- ENDDO
- ENDDO
-
- gaatb=0
- iqty=1
- DO jpert=1,mpert
- DO ipert=MAX(1,jpert-mband),MIN(mpert,jpert+mband)
- gaatb(1+mband+ipert-jpert,jpert)=gaats%f(iqty)
- iqty=iqty+1
- ENDDO
- ENDDO
- ELSE
- CALL cspline_eval(amats,psifac,0)
- CALL cspline_eval(bmats,psifac,0)
- CALL cspline_eval(cmats,psifac,0)
- CALL cspline_eval(fmats,psifac,0)
- CALL cspline_eval(kmats,psifac,0)
- CALL cspline_eval(gmats,psifac,0)
- amat=RESHAPE(amats%f,(/mpert,mpert/))
- bmat=RESHAPE(bmats%f,(/mpert,mpert/))
- cmat=RESHAPE(cmats%f,(/mpert,mpert/))
- CALL zhetrf('L',mpert,amat,mpert,ipiv,work,mpert*mpert,info)
- CALL zhetrs('L',mpert,mpert,amat,mpert,ipiv,bmat,mpert,info)
- CALL zhetrs('L',mpert,mpert,amat,mpert,ipiv,cmat,mpert,info)
-c-----------------------------------------------------------------------
-c copy ideal Hermitian banded matrices F and G.
-c-----------------------------------------------------------------------
- fmatb=0
- gmatb=0
- iqty=1
- DO jpert=1,mpert
- DO ipert=jpert,MIN(mpert,jpert+mband)
- fmatb(1+ipert-jpert,jpert)=fmats%f(iqty)
- gmatb(1+ipert-jpert,jpert)=gmats%f(iqty)
- iqty=iqty+1
- ENDDO
- ENDDO
-c-----------------------------------------------------------------------
-c copy ideal non-Hermitian banded matrix K.
-c-----------------------------------------------------------------------
- kmatb=0
- iqty=1
- DO jpert=1,mpert
- DO ipert=MAX(1,jpert-mband),MIN(mpert,jpert+mband)
- kmatb(1+mband+ipert-jpert,jpert)=kmats%f(iqty)
- iqty=iqty+1
- ENDDO
- ENDDO
- ENDIF
-c-----------------------------------------------------------------------
-c compute du1 and du2.
-c-----------------------------------------------------------------------
- du=0
- IF(kin_flag) THEN
- DO isol=1,msol
- du(:,isol,1)=u(:,isol,2)
- CALL zgbmv('N',mpert,mpert,mband,mband,-one,kmatb,
- $ 2*mband+1,u(:,isol,1),1,one,du(:,isol,1),1)
- ENDDO
-
- CALL zgbtrf(mpert,mpert,mband,mband,fmatlu,3*mband+1,
- $ ipiv,info)
- IF(info /= 0)THEN
- WRITE(message,'(a,e16.9,a,i2,a)')
- $ "zgbtrf: fmat singular at psifac = ",psifac,
- $ ", ipert = ",info,", reduce delta_mband"
- CALL program_stop(message)
- ENDIF
- CALL zgbtrs("N",mpert,mband,mband,msol,fmatlu,
- $ 3*mband+1,ipiv,du,mpert,info)
-
- DO isol=1,msol
- CALL zgbmv('N',mpert,mpert,mband,mband,one,gaatb,
- $ 2*mband+1,u(:,isol,1),1,one,du(:,isol,2),1)
- CALL zgbmv('N',mpert,mpert,mband,mband,one,kaatb,
- $ 2*mband+1,du(:,isol,1),1,one,du(:,isol,2),1)
- ENDDO
- ELSE
- DO isol=1,msol
- du(:,isol,1)=u(:,isol,2)*singfac
- CALL zgbmv('N',mpert,mpert,mband,mband,-one,kmatb,
- $ 2*mband+1,u(:,isol,1),1,one,du(:,isol,1),1)
- ENDDO
- CALL zpbtrs('L',mpert,mband,msol,fmatb,mband+1,du,mpert,info)
- DO isol=1,msol
- CALL zhbmv('L',mpert,mband,one,gmatb,
- $ mband+1,u(:,isol,1),1,one,du(:,isol,2),1 )
- CALL zgbmv('C',mpert,mpert,mband,mband,one,kmatb,
- $ 2*mband+1,du(:,isol,1),1,one,du(:,isol,2),1)
- du(:,isol,1)=du(:,isol,1)*singfac
- ENDDO
- ENDIF
-c-----------------------------------------------------------------------
-c calculate and store u-derivative and xss.
-c-----------------------------------------------------------------------
- ud(:,:,1)=du(:,:,1)
- ud(:,:,2)=-MATMUL(bmat,du(:,:,1))-MATMUL(cmat,u(:,:,1))
-c-----------------------------------------------------------------------
-c terminate.
-c-----------------------------------------------------------------------
- RETURN
- END SUBROUTINE sing_der
-c-----------------------------------------------------------------------
-c subprogram 12. sing_ua_diagnose.
-c diagnoses asymptotic solutions.
-c-----------------------------------------------------------------------
-c-----------------------------------------------------------------------
-c declarations.
-c-----------------------------------------------------------------------
- SUBROUTINE sing_ua_diagnose(ising,dpsi)
-
- INTEGER, INTENT(IN) :: ising
- REAL(r8), INTENT(IN) :: dpsi
-
- INTEGER :: isol,ipert
- REAL(r8) :: psifac
- COMPLEX(r8), DIMENSION(mpert,2*mpert,2) :: ua
-c-----------------------------------------------------------------------
-c format statements.
-c-----------------------------------------------------------------------
- 10 FORMAT(/4x,"is",4x,"ip",6x,"im ua1",5x,"re ua1",
- $ 7x,"im ua2",5x,"re ua2"/)
- 20 FORMAT(2i6,2x,1p,2e11.3,2x,2e11.3)
-c-----------------------------------------------------------------------
-c evaluate asymptotic solutions.
-c-----------------------------------------------------------------------
- psifac=sing(ising)%psifac+dpsi
- CALL sing_get_ua(ising,psifac,ua)
-c-----------------------------------------------------------------------
-c diagnose asymptotic solutions.
-c-----------------------------------------------------------------------
- CALL ascii_open(debug_unit,"ua.out","UNKNOWN")
- WRITE(debug_unit,'(a,i2,a,i1,a,es10.3,a,es10.3)')
- $ "ising = ",ising,", sing_order = ",sing_order,
- $ ", dpsi =",dpsi,", alpha =",REAL(sing(ising)%alpha)
- WRITE(debug_unit,10)
- DO isol=1,2*msol
- DO ipert=1,mpert
- WRITE(debug_unit,20)isol,ipert,ua(ipert,isol,:)
- ENDDO
- WRITE(debug_unit,10)
- ENDDO
- CALL ascii_close(debug_unit)
-c-----------------------------------------------------------------------
-c terminate.
-c-----------------------------------------------------------------------
- RETURN
- END SUBROUTINE sing_ua_diagnose
-c-----------------------------------------------------------------------
-c subprogram 13. sing_get_f_det.
-c find determinant of non-Hermitian F matrix.
-c-----------------------------------------------------------------------
- FUNCTION sing_get_f_det(psifac) RESULT(det)
-
- REAL(r8), INTENT(IN) :: psifac
- COMPLEX(r8) :: det
-
- INTEGER :: ipert,jpert,m1,m2
- INTEGER :: ldab,kl,ku,info,m,n,i
-
- REAL(r8) :: q,nq,singfac1,singfac2,chi1
-
- INTEGER, DIMENSION(mpert) :: ipiv
- INTEGER,DIMENSION(:),ALLOCATABLE:: fpiv
- REAL(r8), DIMENSION(mpert) :: singfac
- COMPLEX(r8) :: d
- COMPLEX(r8), DIMENSION(:,:), ALLOCATABLE:: lumat
- COMPLEX(r8), DIMENSION(mpert,mpert) :: f,temp1,temp2,f0mat,
- $ amat,dbat,fmat,pmat,paat,umat,aamat,b1mat,bkmat,bkaat,r1mat
- COMPLEX(r8), DIMENSION(3*mband+1,mpert) :: amatlu
- COMPLEX(r8), DIMENSION(mpert,mpert,4) :: kwmat,ktmat
- COMPLEX(r8), DIMENSION(mpert*mpert) :: work
- CHARACTER(128) :: message
-c-----------------------------------------------------------------------
-c compute q and singfac.
-c-----------------------------------------------------------------------
- CALL spline_eval(sq,psifac,0)
- q=sq%f(4)
- nq=nn*q
- singfac=mlow-nn*q+(/(ipert,ipert=0,mpert-1)/)
- chi1=twopi*psio
-c-----------------------------------------------------------------------
-c compute F matrix.
-c-----------------------------------------------------------------------
- IF (kin_flag) THEN
- IF (fkg_kmats_flag) THEN
- CALL cspline_eval(f0mats,psifac,0)
- CALL cspline_eval(pmats,psifac,0)
- CALL cspline_eval(paats,psifac,0)
- CALL cspline_eval(r1mats,psifac,0)
- f0mat=RESHAPE(f0mats%f,(/mpert,mpert/))
- pmat=RESHAPE(pmats%f,(/mpert,mpert/))
- paat=RESHAPE(paats%f,(/mpert,mpert/))
- r1mat=RESHAPE(r1mats%f,(/mpert,mpert/))
- ELSE
- CALL cspline_eval(amats,psifac,0)
- CALL cspline_eval(dbats,psifac,0)
- CALL cspline_eval(fbats,psifac,0)
- amat=RESHAPE(amats%f,(/mpert,mpert/))
- dbat=RESHAPE(dbats%f,(/mpert,mpert/))
- fmat=RESHAPE(fbats%f,(/mpert,mpert/))
- DO i=1,4
- CALL cspline_eval(kwmats(i),psifac,0)
- CALL cspline_eval(ktmats(i),psifac,0)
- kwmat(:,:,i)=RESHAPE(kwmats(i)%f,(/mpert,mpert/))
- ktmat(:,:,i)=RESHAPE(ktmats(i)%f,(/mpert,mpert/))
- ENDDO
- amat=amat+kwmat(:,:,1)+ktmat(:,:,1)
- b1mat=ifac*dbat
-c-----------------------------------------------------------------------
-c factor kinetic non-Hermitian matrix A.
-c-----------------------------------------------------------------------
- amatlu=0
- umat=0
- DO jpert=1,mpert
- DO ipert=1,mpert
- amatlu(2*mband+1+ipert-jpert,jpert)=amat(ipert,jpert)
- IF(ipert==jpert)umat(ipert,jpert)=1
- ENDDO
- ENDDO
-
- CALL zgbtrf(mpert,mpert,mband,mband,amatlu,3*mband+1,
- $ ipiv,info)
- IF(info /= 0)THEN
- WRITE(message,'(a,e16.9,a,i2)')
- $ "zgbtrf: amat singular at psifac = ",psifac,
- $ ", ipert = ",info,", reduce delta_mband"
- CALL program_stop(message)
- ENDIF
- temp1=dbat
- CALL zgbtrs("N",mpert,mband,mband,mpert,amatlu,
- $ 3*mband+1,ipiv,temp1,mpert,info)
- f0mat=fmat-MATMUL(CONJG(TRANSPOSE(dbat)),temp1)
-
- temp2=amat
- CALL zgbtrs("C",mpert,mband,mband,mpert,amatlu,
- $ 3*mband+1,ipiv,temp2,mpert,info) ! close to unit matrix.
- aamat=CONJG(TRANSPOSE(temp2))
- umat=umat-aamat
-
- bkmat=kwmat(:,:,2)+ktmat(:,:,2)+ifac*chi1/(twopi*nn)*
- $ (kwmat(:,:,1)+ktmat(:,:,1))
- bkaat=kwmat(:,:,2)-ktmat(:,:,2)+ifac*chi1/(twopi*nn)*
- $ (kwmat(:,:,1)+ktmat(:,:,1))
- temp2=bkmat
- CALL zgbtrs("N",mpert,mband,mband,mpert,amatlu,
- $ 3*mband+1,ipiv,temp2,mpert,info)
- pmat=MATMUL(CONJG(TRANSPOSE(b1mat)),temp2)
-
- temp2=b1mat
- CALL zgbtrs("N",mpert,mband,mband,mpert,amatlu,
- $ 3*mband+1,ipiv,temp2,mpert,info)
- paat=MATMUL(CONJG(TRANSPOSE(bkaat)),temp2)
- $ -ifac*chi1/(twopi*nn)*MATMUL(umat,b1mat)
- paat=CONJG(TRANSPOSE(paat))
-
- temp1=kwmat(:,:,1)+ktmat(:,:,1)
- temp2=bkmat
- CALL zgbtrs("N",mpert,mband,mband,mpert,amatlu,
- $ 3*mband+1,ipiv,temp2,mpert,info)
- r1mat=kwmat(:,:,4)+ktmat(:,:,4)-
- $ (chi1/(twopi*nn))**2*CONJG(TRANSPOSE(temp1))+
- $ ifac*chi1/(twopi*nn)*CONJG(TRANSPOSE(bkaat))-
- $ ifac*chi1/(twopi*nn)*MATMUL(aamat,bkmat)-
- $ MATMUL(CONJG(TRANSPOSE(bkaat)),temp2)
- ENDIF
- DO ipert=1,mpert
- m1=mlow+ipert-1
- singfac1=m1-nn*q
- DO jpert=1,mpert
- m2=mlow+jpert-1
- singfac2=m2-nn*q
- f(ipert,jpert)=singfac1*f0mat(ipert,jpert)*
- $ singfac2-singfac1*pmat(ipert,jpert)-
- $ CONJG(paat(jpert,ipert))*singfac2+
- $ r1mat(ipert,jpert)
- ENDDO
- ENDDO
- ELSE
- CALL cspline_eval(amats,psifac,0)
- CALL cspline_eval(dbats,psifac,0)
- CALL cspline_eval(fbats,psifac,0)
- amat=RESHAPE(amats%f,(/mpert,mpert/))
- dbat=RESHAPE(dbats%f,(/mpert,mpert/))
- fmat=RESHAPE(fbats%f,(/mpert,mpert/))
-
- CALL zhetrf('L',mpert,amat,mpert,ipiv,work,mpert*mpert,info)
- IF(info /= 0)THEN
- WRITE(message,'(a,e16.9,a,i2)')
- $ "zhetrf: amat singular at psifac = ",psifac,
- $ ", ipert = ",info,", increase delta_mband"
- CALL program_stop(message)
- ENDIF
-
- temp1=dbat
- CALL zhetrs('L',mpert,mpert,amat,mpert,ipiv,temp1,mpert,info)
- fmat=fmat-MATMUL(CONJG(TRANSPOSE(dbat)),temp1)
-
- DO ipert=1,mpert
- m1=mlow+ipert-1
- singfac1=m1-nn*q
- DO jpert=1,mpert
- m2=mlow+jpert-1
- singfac2=m2-nn*q
- f(ipert,jpert)=singfac1*fmat(ipert,jpert)*singfac2
- ENDDO
- ENDDO
- ENDIF
-
- kl=mpert-1
- ku=mpert-1
- ldab=2*kl+ku+1
- m=mpert
- n=mpert
- ALLOCATE(lumat(ldab,n),fpiv(min(m,n)))
- DO jpert=1,mpert
- DO ipert=1,mpert
- lumat(kl+ku+1+ipert-jpert,jpert)=f(ipert,jpert)
- ENDDO
- ENDDO
- CALL zgbtrf(m,n,kl,ku,lumat,ldab,ipiv,info)
- IF (info.NE.0) THEN
- PRINT *,"zgbtrf info=",info
- CALL program_stop("Termination by galerkin_solve_equation")
- ENDIF
-c-----------------------------------------------------------------------
-c calculate the determinant of A.
-c-----------------------------------------------------------------------
- d=1.0
- DO i=1,m
- IF (ipiv(i).ne.i) d=-d
- ENDDO
- det=PRODUCT(lumat(kl+kl+1,:))*d
- DEALLOCATE (lumat,fpiv)
-
- END FUNCTION sing_get_f_det
-c-----------------------------------------------------------------------
-c subprogram 14. ksing_find.
-c find new singular surfaces.
-c-----------------------------------------------------------------------
- SUBROUTINE ksing_find
-
- REAL(r8),PARAMETER :: tol=1e-3,dfac=1e-4,keps1=1e-10,keps2=1e-4
- INTEGER, PARAMETER :: nsing=1000, maxstep=100000
- REAL(r8), DIMENSION(nsing) :: psising,psising_check
-
- LOGICAL :: sing_flag
- LOGICAL, PARAMETER :: debug = .FALSE.
- INTEGER :: ising,i_recur,i_depth,i,singnum,singnum_check,i_record
- REAL(r8) :: x0,x1,eps,reps
- COMPLEX(r8) :: det0,det1,sing_det
- COMPLEX(r8), DIMENSION(:,:), ALLOCATABLE :: tmp_record
-
- WRITE(*, *) "Finding kinetically displaced singular surfaces"
- ALLOCATE(tmp_record(2, maxstep))
- singnum=0
- psising=-1
- i_recur=0
- i_depth=0
- i_record=0
- x0=psilow
- x1=psilim
-c-----------------------------------------------------------------------
-c adaptively search the singular point.
-c-----------------------------------------------------------------------
- sing_flag=.FALSE.
- det0=sing_get_f_det(x0)
- det1=sing_get_f_det(x1)
- IF (ABS(det0)>ABS(det1)) THEN
- det_max=det0
- ELSE
- det_max=det1
- ENDIF
- singnum=singnum+1
- psising(singnum)=x0
- sing_det=det0
- sing_flag=.TRUE.
- OPEN(UNIT=100,FILE="dcon_detf.out",STATUS="UNKNOWN")
- WRITE(100,'(1x,4(a16))')"psi","absdetF","real(detF)","imag(detF)"
- CALL bin_open(bin_unit,"dcon_detf.bin","UNKNOWN","REWIND","none")
- CALL sing_adp_find_sing(x0,x1,det0,det1,nsing,psising,singnum,
- $ i_recur,i_depth,i_record,tol,sing_det,sing_flag,tmp_record)
- CLOSE (UNIT=100)
- CALL bin_close(bin_unit)
- ALLOCATE(sing_detf(2, i_record))
- sing_detf(:,:) = tmp_record(:, :i_record)
- DEALLOCATE(tmp_record)
-
- IF (psising(1)>psilow) THEN
- psising(2:singnum+1)=psising(1:singnum)
- psising(1)=psilow
- singnum=singnum+1
-
- ENDIF
- IF (psising(singnum)ABS(det1)) THEN
- psising(i)=x1
- ENDIF
- ENDDO
-c-----------------------------------------------------------------------
-c check the singular point.
-c-----------------------------------------------------------------------
- singnum_check=singnum
- psising_check=psising
- psising=-1
- singnum=1
- IF(verbose) WRITE(*,'(a,es10.3,a,es10.3)')
- $ ' Looking for singularities below', keps1,
- $ 'x the maximum determinant of', ABS(det_max)
- psising(1)=psising_check(1)
- DO i=2,singnum_check-1
- det0=sing_get_f_det(psising_check(i))
- reps=keps1/keps2
- eps=keps2*reps*10**(psising_check(i)/DLOG10(reps))
- IF (ABS(det0)<=ABS(det_max)*eps) THEN
- singnum=singnum+1
- psising(singnum)=psising_check(i)
- IF(debug) WRITE(*,'(a,es10.3,a,es10.3,a)') ' > psi',
- $ psising_check(i), ' is singular'
- ELSE
- IF(debug) WRITE(*,'(a,es10.3,a,es10.3,a)') ' - psi',
- $ psising_check(i), ' is not singular. Determinant is ',
- $ ABS(det0)/(ABS(det_max)*eps), 'x the threshold'
- ENDIF
- ENDDO
- singnum=singnum+1
- psising(singnum)=psising_check(singnum_check)
- OPEN(UNIT=sing_unit,FILE="sing_find.out",STATUS="UNKNOWN")
- WRITE(sing_unit,'(1x,3(a16))') "psi","real(det)","imag(det)"
- DO i=1,singnum
- det0=sing_get_f_det(psising(i))
- WRITE(sing_unit,'(1x,3(e16.8))') psising(i),
- $ REAL(det0), AIMAG(det0)
- ENDDO
- CLOSE (UNIT=sing_unit)
- kmsing=singnum-2
- ALLOCATE(kinsing(kmsing))
- DO ising=1,kmsing
- kinsing(ising)%m=ising
- kinsing(ising)%psifac=psising(ising+1)
- kinsing(ising)%rho=SQRT(psising(ising+1))
- CALL spline_eval(sq,psising(ising+1),1)
- kinsing(ising)%q=sq%f(4)
- kinsing(ising)%q1=sq%f1(4)
- ENDDO
-
- IF(verbose)THEN
- IF(kmsing>0)THEN
- WRITE(*,*) " > Found kinetic singular surfaces:"
- WRITE(*,'(3x,a16, a16)')"psi","q"
- DO ising=1,kmsing
- WRITE(*,'(3x,2(es16.8))') kinsing(ising)%psifac,
- $ kinsing(ising)%q
- ENDDO
- ELSE
- WRITE(*,*) " > Found no kinetic singular surfaces"
- ENDIF
- ENDIF
-
- END SUBROUTINE ksing_find
-c-----------------------------------------------------------------------
-c subprogram 15. sing_adp_find_sing.
-c adaptive finder.
-c-----------------------------------------------------------------------
- RECURSIVE SUBROUTINE sing_adp_find_sing(x0,x1,det0,det1,
- $ m_singpos,singpos,singnum,i_recur,i_depth,i_record,
- $ tol,sing_det,sing_flag,record)
- LOGICAL,INTENT(INOUT) :: sing_flag
- INTEGER,INTENT(IN) :: m_singpos
- INTEGER,INTENT(INOUT) :: singnum
- INTEGER,INTENT(INOUT) :: i_recur,i_depth,i_record
- REAL(r8),INTENT(IN) :: x0,x1,tol
- REAL(r8),DIMENSION(m_singpos),INTENT(INOUT) :: singpos
- REAL(r8),PARAMETER :: grid_tol =1e-6
- COMPLEX(r8),INTENT(IN) :: det0,det1
- COMPLEX(r8),INTENT(INOUT) :: sing_det
- COMPLEX(r8),INTENT(INOUT), DIMENSION(2,*) :: record
-
- INTEGER :: i
- REAL(r8) :: tmp1,tmpm,tmp2
- REAL(r8),DIMENSION(3) :: x
- COMPLEX(r8),DIMENSION(3) :: det
-
- i_depth=i_depth+1
- i_recur=i_recur+1
- x(1)=x0
- x(3)=x1
- x(2)=0.5*(x(1)+x(3))
- det(1)=det0
- det(2)=sing_get_f_det(x(2))
- det(3)=det1
- IF (ABS(det(2))>ABS(det_max)) det_max=det(2)
-c-----------------------------------------------------------------------
-c criteria of grid partition.
-c-----------------------------------------------------------------------
- tmp1=ABS(det(1)+det(3))
- tmpm=ABS(det(2))*2
- IF (ABS(tmpm-tmp1)>tol*tmp1 .AND. x(3)-x(1)>grid_tol ) THEN
- CALL sing_adp_find_sing(x(1),x(2),det(1),det(2),
- $ m_singpos,singpos,singnum,i_recur,i_depth,i_record,
- $ tol,sing_det,sing_flag,record)
-
- CALL sing_adp_find_sing(x(2),x(3),det(2),det(3),
- $ m_singpos,singpos,singnum,i_recur,i_depth,i_record,
- $ tol,sing_det,sing_flag,record)
- ELSE
-c-----------------------------------------------------------------------
-c judge the local singularity with the gradient of ABS(det).
-c-----------------------------------------------------------------------
- tmp1 = ABS(det(2))-ABS(det(1))
- tmp2 = ABS(det(3))-ABS(det(2))
- IF (tmp1<0.AND.tmp2<0)THEN
- IF (sing_flag) THEN
- IF (ABS(sing_det)>ABS(det(3))) THEN
- sing_det=det(3)
- singpos(singnum)=x(3)
- ENDIF
- ELSE
- singnum=singnum+1
- IF (singnum+3>m_singpos) THEN
- CALL program_stop("Increase singpos array.")
- ENDIF
- singpos(singnum)=x(3)
- sing_det=det(3)
- sing_flag=.TRUE.
- ENDIF
- ENDIF
-
- IF (tmp1<0.AND.tmp2>0)THEN
- IF (sing_flag) THEN
- IF (ABS(sing_det)>ABS(det(2))) THEN
- sing_det=det(2)
- singpos(singnum)=x(2)
- ENDIF
- ELSE
- singnum=singnum+1
- IF (singnum+3>m_singpos) THEN
- CALL program_stop("Increase singpos array.")
- ENDIF
- singpos(singnum)=x(2)
- sing_det=det(2)
- sing_flag=.TRUE.
- ENDIF
- ENDIF
-
- IF (tmp1>0.AND.tmp2>0)THEN
- IF (sing_flag) THEN
- sing_flag=.FALSE.
- ENDIF
- IF (ABS(sing_det)>ABS(det(1))) THEN
- sing_det=det(1)
- singpos(singnum)=x(1)
- ENDIF
- ENDIF
-
- IF (tmp1>0.AND.tmp2<0)THEN
- IF (sing_flag) THEN
- sing_flag=.FALSE.
- ENDIF
- IF (ABS(sing_det)>ABS(det(1))) THEN
- sing_det=det(1)
- singpos(singnum)=x(1)
- ENDIF
- ENDIF
-
- IF (tmp1==0.OR.tmp2==0) THEN
- CALL program_stop("det(2)-det(1)=0 or det(3)-det(2)=0")
- ENDIF
-
- ! write record to file
- WRITE(100,'(1x,4(es16.8))') x(2),ABS(det(2)),REAL(det(2)),
- $ IMAG(det(2))
- WRITE(100,'(1x,4(es16.8))') x(3),ABS(det(3)),REAL(det(3)),
- $ IMAG(det(3))
- WRITE(bin_unit)REAL(x(2),4),REAL(LOG10(ABS(det(2))),4),
- $ REAL(REAL(det(2)),4),REAL(AIMAG(det(2)),4)
- WRITE(bin_unit)REAL(x(3),4),REAL(LOG10(ABS(det(3))),4),
- $ REAL(REAL(det(3)),4),REAL(AIMAG(det(3)),4)
- ! store record in memory
- i_record = i_record + 1
- record(:, i_record) = (/ x(2) * one_c, det(2) /)
- i_record = i_record + 1
- record(:, i_record) = (/ x(3) * one_c, det(3) /)
-
- ENDIF
- i_depth=i_depth-1
- END SUBROUTINE sing_adp_find_sing
-c-----------------------------------------------------------------------
-c subprogram 16. sing_newton.
-c newton iteration for singular surface finder.
-c-----------------------------------------------------------------------
- SUBROUTINE sing_newton(ff,z,bo0,bo1)
-
- COMPLEX(r8) :: ff
- REAL(r8), INTENT(INOUT) :: z
- REAL(r8), INTENT(IN) :: bo0,bo1
- REAL(r8) :: err
- INTEGER :: it
-
- INTEGER :: ising,info
- REAL(r8) :: dzfac=1e-6,dbfac=1e-1,tol=1e-15,itmax=1000,dz,dz1,dz2
- REAL(r8) :: z_old,f_old,f,b0,b1,zopt,fopt
-c-----------------------------------------------------------------------
-c find initial guess.
-c-----------------------------------------------------------------------
- b0=z-(z-bo0)*dbfac ! bounds well inside of estimated neighboring minima
- b1=z+(bo1-z)*dbfac
- f=ABS(ff(z))
- zopt=z
- fopt=f
-
- ! first step is a fraction of a half step towards the nearer boundary
- dz1=(b0+z)*0.5-z
- dz2=(b1+z)*0.5-z
- dz = dz1 * dzfac
- IF (ABS(dz2) itmax) THEN
- it=-1
- WRITE(*,'(a,es10.3,a,es10.3,a)') " - search terminated at",
- $ zopt," with large",err," error"
- z=zopt
- EXIT
- ENDIF
- IF (z+dz<=b0.OR.z+dz>=b1) THEN
- ! we've climbed out of the sharp local well
- ! case 1: we are on the right side, but near a peak so the ~0 gradient way overshoots to the other side
- ! case 2: we are already on the other side of a peak and falling down towards the neighboring mininum
- dz=dz*0.5
- ELSE
- z_old=z
- z=z+dz
- f_old=f
- f=ABS(ff(z))
- If (f [T M**2] -1.36721084E+00
- 1.03921169E+00 R OF MAGAXE --> [M] 3.11763506E+00
- -9.99273915E-07 Z OF MAGAXE --> [M] -2.99782174E-06
- -5.04402802E-06 Z0 --> [M] -1.51320841E-05
- 3.00000000E+00 R0 [M] USED FOR CONVERTING TO MKSA
- 1.00000000E+00 B0 [T] USED FOR CONVERTING TO MKSA
- 1.00000000E+00 SIGN OF B0 IN EXPERIMENT (CHEASE ASSUMES 1.0)
- 1.53755753E+00 TOTAL CURRENT --> [A] 3.67064822E+06
- 1.00000000E+00 SIGN OF IP IN EXPERIMENT (CHEASE ASSUMES 1.0)
- 1.69999553E+00 b/a
- 1.05000000E+00 Q_ZERO, USING SIGNS OF IP AND B0, WOULD GIVE: 1.05000000E+00
- 4.43373475E+00 Q_EDGE, USING SIGNS OF IP AND B0, WOULD GIVE: 4.43373475E+00
- 1.51426490E-01 POLOIDAL BETA
- 2.34029713E-02 BETA_EXP=]*2*MU0/B0**2
- 7.25523874E-01 LI
- 3.46308209E-02 PRESSURE ON AXIS --> [Pa] 2.75583316E+04 --> [10**19 M**-3 KEV]: 1.72024542E+01
- 1.63188124E-02 BETA
- 2.18184292E-02 BETA* (SQRT(
))
- 5.58550793E-02 BETA-AXIS=2p0/(T0/Rmag)^2; with Rmag->Rgeo(LCFS): 5.17194368E-02
- -1.51912315E-01 PSI-AXIS --> [T M**2] -1.36721084E+00
- -9.54493226E-01 2*PI*PSI-AXIS --> -8.59043904E+00
- -1.51912315E-01 IP_SIGN*PSI-AXIS --> [T M**2] -1.36721084E+00
- -9.54493226E-01 IP_SIGN*2*PI*PSI-AXIS --> -8.59043904E+00
- 1.99999525E+00 ASPECT RATIO ; a/R= 5.00001188E-01
- 7.64779790E+00 VOLUME -> 2.06490543E+02
- 1.29389993E+00 AREA -> 1.16450994E+01
- 2.53018281E+01 SURFACE -> 2.27716453E+02
- 4.34432012E+00 LENGTH -> 1.30329604E+01
- 5.00003104E-01 RMIN -> RMIN [m] 1.50000931E+00
- 1.49999983E+00 RMAX -> RMAX [m] 4.49999950E+00
- -8.49976057E-01 ZMIN -> ZMIN [m] -2.54992817E+00
- 8.49976009E-01 ZMAX -> ZMAX [m] 2.54992803E+00
- 1.00000147E+00 RGEOM -> RGEOM [m] 3.00000440E+00
- 4.99998364E-01 MINOR RADIUS -> A [m] 1.49999509E+00
diff --git a/src/DCON/validate/coil.in b/src/DCON/validate/coil.in
deleted file mode 100644
index 946e00dc87..0000000000
--- a/src/DCON/validate/coil.in
+++ /dev/null
@@ -1,50 +0,0 @@
-&COIL_CONTROL
- ceq_type="efit" ! eq_type from equil.in used in DCON run
-
- data_dir="../../../coil" ! Directory from which _.dat files are read
- machine="d3d" ! Choose from: nstx, d3d, kstar, iter
- ip_direction="positive" ! Set positive for CCW or negative for CW from a top down view
- bt_direction="negative" ! Set positive for CCW or negative for CW from a top down view
- coil_num=3 ! Total number of coil sets activated
-
- cmpsi=64 ! ?? Why do we need this is only care about psi_lim??
- cmtheta=480 ! Number of poloidal gridpoints (uses DCON jac_type??)
- cmzeta=40 ! Number of toroidal gridpoints (uses DCON jac_type??)
- coil_threads=0 ! Number of parallel threads used when computing fields from coils (no reason to go beyond 4 for coils with less than 1000 points). Setting to <= 0 uses OMP_NUM_THREADS env variable.
-
-
-! Array values should be specified for each of the coil arrays to be activated.
-! The supported coil sets (number of coils) include...
-! For nstx: rwmef(6), tfef(12), pf5ef(2), hhfw(24), ppu(12), ppl(12),
-! psu(12), psl(12), vpu(12), vpl(12), vsu(12), vsl(12)
-! For d3d: iu(6), il(6), c(6), tbm_solenoid(1), tbm_racetrack(1)
-! For kstar:fecu(4), fecm(4), fecl(4)
-! For iter: efcu(6), efcm(6), efcl(6), bl2u(9), bl2m(9),
-! bl2l(9), avvu(9), avvm(9), avvl(9)
-
- coil_name(1)="c" ! External correction coil set
- coil_cur(1,1)= 982 ! 1kA, 30 degree phase n=1 field
- coil_cur(1,2)= 656
- coil_cur(1,3)=-326
- coil_cur(1,4)=-982
- coil_cur(1,5)=-656
- coil_cur(1,6)= 326
- coil_name(2)="il" ! External correction coil set
- coil_cur(2,1)= 1e3 ! 1kA, 30 degree phase n=1 field
- coil_cur(2,2)= 5e2
- coil_cur(2,3)=-5e2
- coil_cur(2,4)=-1e3
- coil_cur(2,5)=-5e2
- coil_cur(2,6)= 5e2
- coil_name(3)="iu" ! External correction coil set
- coil_cur(3,1)= 1e3 ! 1kA, 30 degree phase n=1 field
- coil_cur(3,2)= 5e2
- coil_cur(3,3)=-5e2
- coil_cur(3,4)=-1e3
- coil_cur(3,5)=-5e2
- coil_cur(3,6)= 5e2
-
-/
-&COIL_OUTPUT
- gpec_interface=t ! Provides external field to GPEC
-/
diff --git a/src/DCON/validate/compare_matrix.ipynb b/src/DCON/validate/compare_matrix.ipynb
deleted file mode 100644
index 42261ac98b..0000000000
--- a/src/DCON/validate/compare_matrix.ipynb
+++ /dev/null
@@ -1,708 +0,0 @@
-{
- "cells": [
- {
- "cell_type": "code",
- "execution_count": 2,
- "id": "3586d344",
- "metadata": {},
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "Python 3.12.8 | packaged by Anaconda, Inc. | (main, Dec 11 2024, 11:37:13) [Clang 14.0.6 ] on darwin\n",
- "Type \"help\", \"copyright\", \"credits\" or \"license\" for more information.\n",
- ">>> ^C\n",
- ">>> \n",
- "Traceback (most recent call last):\n",
- " File \"\", line 0, in \n",
- "KeyboardInterrupt\n",
- ">>> "
- ]
- },
- {
- "ename": "ModuleNotFoundError",
- "evalue": "No module named 'scipy'",
- "output_type": "error",
- "traceback": [
- "\u001b[31m---------------------------------------------------------------------------\u001b[39m",
- "\u001b[31mModuleNotFoundError\u001b[39m Traceback (most recent call last)",
- "\u001b[36mCell\u001b[39m\u001b[36m \u001b[39m\u001b[32mIn[2]\u001b[39m\u001b[32m, line 4\u001b[39m\n\u001b[32m 1\u001b[39m get_ipython().system(\u001b[33m'\u001b[39m\u001b[33m/usr/bin/env python3\u001b[39m\u001b[33m'\u001b[39m)\n\u001b[32m 2\u001b[39m \u001b[38;5;66;03m# -*- coding: utf-8 -*-\u001b[39;00m\n\u001b[32m----> \u001b[39m\u001b[32m4\u001b[39m \u001b[38;5;28;01mfrom\u001b[39;00m\u001b[38;5;250m \u001b[39m\u001b[34;01mscipy\u001b[39;00m\u001b[34;01m.\u001b[39;00m\u001b[34;01mlinalg\u001b[39;00m\u001b[34;01m.\u001b[39;00m\u001b[34;01mblas\u001b[39;00m\u001b[38;5;250m \u001b[39m\u001b[38;5;28;01mimport\u001b[39;00m zhemm\n\u001b[32m 5\u001b[39m \u001b[38;5;28;01mimport\u001b[39;00m\u001b[38;5;250m \u001b[39m\u001b[34;01mnumpy\u001b[39;00m\u001b[38;5;250m \u001b[39m\u001b[38;5;28;01mas\u001b[39;00m\u001b[38;5;250m \u001b[39m\u001b[34;01mnp\u001b[39;00m\n\u001b[32m 6\u001b[39m \u001b[38;5;28;01mimport\u001b[39;00m\u001b[38;5;250m \u001b[39m\u001b[34;01mmatplotlib\u001b[39;00m\u001b[34;01m.\u001b[39;00m\u001b[34;01mpyplot\u001b[39;00m\u001b[38;5;250m \u001b[39m\u001b[38;5;28;01mas\u001b[39;00m\u001b[38;5;250m \u001b[39m\u001b[34;01mplt\u001b[39;00m\n",
- "\u001b[31mModuleNotFoundError\u001b[39m: No module named 'scipy'"
- ]
- }
- ],
- "source": [
- "!/usr/bin/env python3\n",
- "# -*- coding: utf-8 -*-\n",
- "\n",
- "from scipy.linalg.blas import zhemm\n",
- "import numpy as np\n",
- "import matplotlib.pyplot as plt\n",
- "import warnings\n",
- "import os\n",
- "from scipy.interpolate import CubicSpline\n",
- "from scipy.integrate import solve_ivp\n",
- "from scipy.linalg import cho_factor, cho_solve, lu_factor, lu_solve\n",
- "import time\n",
- "import numpy as np\n",
- "\n",
- "m_high = 1\n",
- "m_low = -4\n",
- "mdim = m_high - m_low + 1\n",
- "ndim = 1\n",
- "size = mdim * ndim\n",
- "\"\"\"\n",
- "... (주석) ...\n",
- "- F_bar, K_bar, G 행렬과 q 프로파일을 바이너리 파일에서 읽어 보간.\n",
- "- 최종 F, K 행렬은 히트맵 플롯 시점에 필요한 샘플에 대해서만 즉석에서 계산하여 성능 저하를 방지.\n",
- "\"\"\"\n",
- "import numpy as np\n",
- "import struct\n",
- "import os\n",
- "import matplotlib.pyplot as plt\n",
- "from scipy.interpolate import CubicSpline\n",
- "\n",
- "# ─────────────────────────────────────────────────────────────\n",
- "# 1 & 2. 파일 읽기 관련 함수 (이전과 동일)\n",
- "# ─────────────────────────────────────────────────────────────\n",
- "\n",
- "def get_matrix_map(m, kind, n_blocks, mband_k=None, path=None):\n",
- " if kind in ('F', 'G'):\n",
- " for mb_test in range(m):\n",
- " count = sum(len(range(j, min(m, j + mb_test + 1))) for j in range(m))\n",
- " if count == n_blocks:\n",
- " mband = mb_test\n",
- " print(f\"[{os.path.basename(path)}] mband = {mband} (으)로 추정 (F/G).\")\n",
- " d = {k+1: (i,j) for k, (j,i) in enumerate(((j,i) for j in range(m) for i in range(j, min(m, j+mband+1))))}\n",
- " return d\n",
- " raise ValueError(f\"F/G 행렬의 mband를 추정할 수 없습니다. (m={m}, n_blocks={n_blocks})\")\n",
- " elif kind == 'K':\n",
- " if mband_k is None: raise ValueError(\"K 행렬을 처리하려면 mband_k 값을 지정해야 합니다.\")\n",
- " print(f\"[{os.path.basename(path)}] mband = {mband_k} (지정된 값) 사용 (K).\")\n",
- " valid_element_count = sum(len(range(max(0, j-mband_k), min(m, j+mband_k+1))) for j in range(m))\n",
- " if n_blocks > valid_element_count:\n",
- " print(f\" > 경고: 파일에 기록된 블록 수({n_blocks})가 실제 유효한 원소 수({valid_element_count})보다 많습니다.\")\n",
- " d = {}\n",
- " k = 0\n",
- " for j in range(m):\n",
- " for i in range(max(0, j - mband_k), min(m, j + mband_k + 1)):\n",
- " k += 1\n",
- " d[k] = (i, j)\n",
- " return d\n",
- " else: raise ValueError(\"kind는 'F', 'G', 'K' 중 하나여야 합니다.\")\n",
- "\n",
- "def read_bin(path, m, kind, mband_k=None):\n",
- " all_records = []\n",
- " with open(path, 'rb') as f:\n",
- " while True:\n",
- " header_bytes = f.read(4)\n",
- " if not header_bytes: break\n",
- " record_len = struct.unpack(' 0:\n",
- " all_records.append(np.frombuffer(f.read(record_len), dtype=np.float32))\n",
- " else:\n",
- " all_records.append(None)\n",
- " f.read(4)\n",
- " element_blocks = []\n",
- " current_block = []\n",
- " for rec in all_records:\n",
- " if rec is not None: current_block.append(rec)\n",
- " else:\n",
- " if current_block: element_blocks.append(np.array(current_block))\n",
- " current_block = []\n",
- " if not element_blocks: raise ValueError(f\"파일에서 데이터 블록을 찾지 못했습니다: {path}\")\n",
- "\n",
- " n_blocks, n_psi = len(element_blocks), element_blocks[0].shape[0]\n",
- " psi, q_profile = element_blocks[0][:, 0], element_blocks[0][:, 1]\n",
- " idx_map = get_matrix_map(m, kind, n_blocks, mband_k=mband_k, path=path)\n",
- " \n",
- " mats = np.zeros((n_psi, m, m), dtype=np.complex128)\n",
- " for k, (i, j) in idx_map.items():\n",
- " if k > n_blocks: continue\n",
- " mats[:, i, j] = element_blocks[k - 1][:, 2] + 1j * element_blocks[k - 1][:, 3]\n",
- "\n",
- " if kind in ('G'):\n",
- " il, jl = np.tril_indices(m, -1)\n",
- " mats[:, jl, il] = np.conj(mats[:, il, jl])\n",
- " \n",
- " return psi, q_profile, mats\n",
- "\n",
- "# ────────────────────────────────────────\n",
- "# 3. dedup, make_interp, plot_q_profile (이전과 동일)\n",
- "# ────────────────────────────────────────\n",
- "def dedup(psi, q, stacks):\n",
- " uniq_psi, idx = np.unique(psi, return_index=True)\n",
- " return uniq_psi, q[idx], {k: v[idx] for k, v in stacks.items()}\n",
- "\n",
- "def make_interp(psi, mat_stack):\n",
- " cs_r = CubicSpline(psi, mat_stack.real, axis=0)\n",
- " cs_i = CubicSpline(psi, mat_stack.imag, axis=0)\n",
- " return lambda x, cr=cs_r, ci=cs_i: cr(x) + 1j * ci(x)\n",
- "\n",
- "def plot_q_profile(psi, q, q_interpolant):\n",
- " fig, ax = plt.subplots(figsize=(8, 6))\n",
- " ax.plot(psi, q, 'o', label='Original Data Points', markersize=5)\n",
- " psi_fine = np.linspace(psi.min(), psi.max(), 300)\n",
- " ax.plot(psi_fine, q_interpolant(psi_fine), '-', label='Cubic Spline Interpolation')\n",
- " ax.set(title='Safety Factor (q) Profile', xlabel='Normalized Poloidal Flux (ψ)', ylabel='Safety Factor (q)')\n",
- " ax.legend(); ax.grid(True, linestyle='--', alpha=0.6)\n",
- " plt.show()\n",
- "\n",
- "# ────────────────────────────────────────\n",
- "# *** REVISED *** 4. 최종 행렬의 히트맵을 그리는 함수\n",
- "# ────────────────────────────────────────\n",
- "def plot_final_heatmaps(psi_coords, M, q_interp, F_bar_interp, G_interp, K_bar_interp, nsamp=4):\n",
- " \"\"\"\n",
- " 보간 함수들을 받아, 플롯에 필요한 psi 샘플에 대해서만 최종 행렬을 계산하고 히트맵을 그립니다.\n",
- " \"\"\"\n",
- " names = ['F', 'G', 'K']\n",
- " samp = np.quantile(psi_coords, np.linspace(.05, .95, nsamp))\n",
- " \n",
- " fig, ax = plt.subplots(len(names), nsamp,\n",
- " figsize=(4.5 * nsamp, 4 * len(names)),\n",
- " constrained_layout=True, squeeze=False)\n",
- " \n",
- " I = np.identity(M.shape[0])\n",
- "\n",
- " for c, p in enumerate(samp):\n",
- " # --- 계산은 이 루프 안에서 즉석으로 수행됩니다 ---\n",
- " q_val = q_interp(p)\n",
- " Q_mat = M - q_val * I\n",
- " \n",
- " # 각 psi 샘플(p)에 대해 최종 행렬 계산\n",
- " final_mats = {\n",
- " 'F': Q_mat @ F_bar_interp(p) @ Q_mat,\n",
- " 'G': G_interp(p),\n",
- " 'K': Q_mat @ K_bar_interp(p)\n",
- " }\n",
- " # ---------------------------------------------\n",
- " \n",
- " for r, n in enumerate(names):\n",
- " mat = final_mats[n]\n",
- " im = ax[r, c].imshow(np.abs(mat), cmap='viridis', origin='upper', aspect='equal')\n",
- " ax[r, c].set_title(f'{n}, ψ≈{p:.3f}')\n",
- " if r == len(names) - 1: ax[r, c].set_xlabel('j')\n",
- " if c == 0: ax[r, c].set_ylabel('i')\n",
- " plt.colorbar(im, ax=ax[r, c], label=f'|{n}|')\n",
- " \n",
- " fig.suptitle('Final F, G, K Heatmaps (Calculated On-the-fly)', y=1.03)\n",
- " plt.show()\n",
- "\n",
- "# ────────────────────────────────────────\n",
- "# 5. 메인 스크립트\n",
- "# ────────────────────────────────────────\n",
- "if __name__ == \"__main__\":\n",
- " # --- 사용자 설정 변수 ---\n",
- " MPERT = mdim\n",
- " MBAND_K = MPERT - 1 \n",
- " M_MODES = np.arange(m_low, m_high + 1) # MPERT=36일 경우, -17 ~ 18\n",
- " \n",
- " BASE_PATH = '/Users/seoda-eun/git/JPEC3/JPEC/src/DCON/validate'\n",
- " \n",
- " # --- 데이터 읽기 ---\n",
- " files_to_read = { 'F': 'fs.bin', 'G': 'gs.bin', 'K': 'ks.bin' }\n",
- " matrix_stacks, psi_coords, q_coords = {}, None, None\n",
- " for name, fname in files_to_read.items():\n",
- " path = os.path.join(BASE_PATH, fname)\n",
- " if not os.path.exists(path):\n",
- " print(f\"파일을 찾을 수 없습니다: {path}\"); continue\n",
- " print(f\"파일 읽는 중: {fname} (as {'F_bar' if name=='F' else 'K_bar' if name=='K' else name})\")\n",
- " try:\n",
- " mband_val = MBAND_K if name == 'K' else None\n",
- " psi, q, mat = read_bin(path, MPERT, name, mband_k=mband_val)\n",
- " matrix_stacks[name] = mat\n",
- " if psi_coords is None: psi_coords, q_coords = psi, q\n",
- " except Exception as e:\n",
- " print(f\"오류: {fname} 처리 중 문제 발생. {e}\"); import traceback; traceback.print_exc()\n",
- "\n",
- " if not matrix_stacks:\n",
- " print(\"데이터를 성공적으로 읽지 못했습니다. 프로그램을 종료합니다.\"); exit()\n",
- "\n",
- " # --- 데이터 처리 및 보간 ---\n",
- " if 'F' in matrix_stacks:\n",
- " print(\"\\nF_bar 행렬 복원 (L·Lᴴ)...\")\n",
- " L = np.tril(matrix_stacks['F']) # 하삼각(대각 포함)\n",
- " matrix_stacks['F'] = L @ L.transpose(0, 2, 1).conj() # F_bar = L Lᴴ\n",
- "\n",
- " psi_coords, q_coords, matrix_stacks = dedup(psi_coords, q_coords, matrix_stacks)\n",
- " \n",
- " print(\"보간 함수 생성 중 (F_bar, G, K_bar, q)...\")\n",
- " F_bar_interp = make_interp(psi_coords, matrix_stacks['F'])\n",
- " G_interp = make_interp(psi_coords, matrix_stacks['G'])\n",
- " K_bar_interp = make_interp(psi_coords, matrix_stacks['K'])\n",
- " q_of_psi = CubicSpline(psi_coords, q_coords)\n",
- " print(\"보간 함수 생성 완료.\")\n",
- " \n",
- " # --- 최종 행렬 계산 및 시각화 ---\n",
- " if len(M_MODES) != MPERT:\n",
- " raise ValueError(f\"M_MODES 배열 길이({len(M_MODES)})가 MPERT({MPERT})와 불일치.\")\n",
- " M = np.diag(M_MODES)\n",
- "\n",
- " # 시각화: 플롯에 필요한 4개의 샘플에 대해서만 즉석에서 계산\n",
- " plot_q_profile(psi_coords, q_coords, q_of_psi)\n",
- " plot_final_heatmaps(psi_coords, M, q_of_psi, F_bar_interp, G_interp, K_bar_interp, nsamp=4)\n",
- "\n",
- " # --- 단일 psi 값에 대한 분석용 함수 (선택적 사용) ---\n",
- " def compute_matrices(psi):\n",
- " \"\"\"특정 psi에 대한 최종 F, G, K 행렬을 계산합니다.\"\"\"\n",
- " I = np.identity(MPERT)\n",
- " q_val = q_of_psi(psi)\n",
- " Q_mat = M - q_val * I\n",
- " \n",
- " f_final = Q_mat @ F_bar_interp(psi) @ Q_mat\n",
- " g_final = G_interp(psi)\n",
- " k_final = Q_mat @ K_bar_interp(psi)\n",
- " \n",
- " return {'F': f_final, 'G': g_final, 'K': k_final}\n",
- "\n",
- " print(\"\\n분석이 완료되었습니다.\")\n",
- " print(\"`compute_matrices(psi)` 함수로 특정 psi에서의 행렬을 계산할 수 있습니다.\")\n",
- " psi_test = 0.5\n",
- " final_mats_at_half = compute_matrices(psi_test)\n",
- " print(f\"예시: ψ = {psi_test} 에서의 |F_00|: {np.abs(final_mats_at_half['F'][0,0]):.4e}\")"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 1,
- "id": "ada4ecd6",
- "metadata": {},
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "Collecting package metadata (current_repodata.json): done\n",
- "Solving environment: done\n",
- "\n",
- "\n",
- "==> WARNING: A newer version of conda exists. <==\n",
- " current version: 23.7.4\n",
- " latest version: 25.5.1\n",
- "\n",
- "Please update conda by running\n",
- "\n",
- " $ conda update -n base -c defaults conda\n",
- "\n",
- "Or to minimize the number of packages updated during conda update use\n",
- "\n",
- " conda install conda=25.5.1\n",
- "\n",
- "\n",
- "\n",
- "## Package Plan ##\n",
- "\n",
- " environment location: /Users/seoda-eun/anaconda3/envs/mkl_env\n",
- "\n",
- " added / updated specs:\n",
- " - numpy\n",
- "\n",
- "\n",
- "The following packages will be UPDATED:\n",
- "\n",
- " ca-certificates conda-forge::ca-certificates-2025.1.3~ --> pkgs/main::ca-certificates-2025.2.25-hecd8cb5_0 \n",
- "\n",
- "\n",
- "\n",
- "Downloading and Extracting Packages\n",
- "\n",
- "Preparing transaction: done\n",
- "Verifying transaction: done\n",
- "Executing transaction: done\n",
- "\n",
- "Note: you may need to restart the kernel to use updated packages.\n"
- ]
- }
- ],
- "source": [
- "conda install numpy"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 1,
- "id": "620eba42",
- "metadata": {},
- "outputs": [
- {
- "ename": "",
- "evalue": "",
- "output_type": "error",
- "traceback": [
- "\u001b[1;31m현재 셀 또는 이전 셀에서 코드를 실행하는 동안 Kernel이 충돌했습니다. \n",
- "\u001b[1;31m셀의 코드를 검토하여 가능한 오류 원인을 식별하세요. \n",
- "\u001b[1;31m자세한 내용을 보려면 여기를 클릭하세요. \n",
- "\u001b[1;31m자세한 내용은 Jupyter 로그를 참조하세요."
- ]
- }
- ],
- "source": [
- "import numpy as np\n",
- "import pandas as pd\n",
- "from pathlib import Path\n",
- "from typing import Tuple, Dict\n",
- "from scipy.interpolate import interp1d\n",
- "import struct\n",
- "\n",
- "class TokamakCylinderLoader:\n",
- " \"\"\"\n",
- " A class to read and interpolate Tokamak and Cylinder matrices (A–H, F–K).\n",
- "\n",
- " Methods\n",
- " -------\n",
- " load_all(psin_target)\n",
- " Reads all Tokamak (A,B,C,D,E,H from imats; F from fs.bin; G from gs.bin; K from ks.bin)\n",
- " and Cylinder (A,B,C,D,E,H from individual CSVs; F,G,K from diag CSV), then interpolates\n",
- " onto psin_target.\n",
- "\n",
- " Attributes\n",
- " ----------\n",
- " imats_path : str\n",
- " Path to tokamak 'imats.out'\n",
- " fs_bin_path : str\n",
- " Path to 'fs.bin'\n",
- " gs_bin_path : str\n",
- " Path to 'gs.bin'\n",
- " ks_bin_path : str\n",
- " Path to 'ks.bin'\n",
- " mpert : int\n",
- " mpert value used in Fortran\n",
- " mband : int\n",
- " mband value used in Fortran\n",
- " cyl_paths : Dict[str, str]\n",
- " Paths to cylinder A–H CSVs, keys 'A','B','C','D','E','H'\n",
- " cyl_FGK_diag_csv : str\n",
- " Path to 'dcon_FKG_diagonal_elements.csv'\n",
- " \"\"\"\n",
- " \n",
- " def __init__(\n",
- " self,\n",
- " imats_path: str,\n",
- " fs_bin_path: str,\n",
- " gs_bin_path: str,\n",
- " ks_bin_path: str,\n",
- " mpert: int,\n",
- " mband: int,\n",
- " cyl_A_csv: str,\n",
- " cyl_B_csv: str,\n",
- " cyl_C_csv: str,\n",
- " cyl_D_csv: str,\n",
- " cyl_E_csv: str,\n",
- " cyl_H_csv: str,\n",
- " cyl_FGK_diag_csv: str\n",
- " ):\n",
- " self.imats_path = imats_path\n",
- " self.fs_bin_path = fs_bin_path\n",
- " self.gs_bin_path = gs_bin_path\n",
- " self.ks_bin_path = ks_bin_path\n",
- " self.mpert = mpert\n",
- " self.mband = mband\n",
- " self.cyl_paths = {\n",
- " 'A': cyl_A_csv,\n",
- " 'B': cyl_B_csv,\n",
- " 'C': cyl_C_csv,\n",
- " 'D': cyl_D_csv,\n",
- " 'E': cyl_E_csv,\n",
- " 'H': cyl_H_csv\n",
- " }\n",
- " self.cyl_FGK_diag_csv = cyl_FGK_diag_csv\n",
- "\n",
- " # 1. read_imats_out\n",
- " @staticmethod\n",
- " def read_imats_out(file_path: str, names: Tuple[str, ...] = ('A','B','C','D','E','H')) -> Tuple[np.ndarray, Dict[str, np.ndarray]]:\n",
- " with open(file_path, 'r') as f:\n",
- " lines = f.readlines()\n",
- " header = lines[2].split()\n",
- " mpsi = int(header[2])\n",
- " mpert = int(header[-1])\n",
- " data = lines[5:]\n",
- " m1 = [int(l.split()[1]) for l in data if len(l.split()) == 15]\n",
- " m2 = [int(l.split()[2]) for l in data if len(l.split()) == 15]\n",
- " mi, mj = min(m1), max(m1)\n",
- " offset = -mi\n",
- " size = mj - mi + 1\n",
- " psi = np.zeros(mpsi + 1)\n",
- " mats = {n: np.zeros((mpsi + 1, size, size), np.complex128) for n in names}\n",
- " idx = {'A':0,'B':2,'C':4,'D':6,'E':8,'F':10,'G':12,'H':14}\n",
- " for ln in data:\n",
- " sp = ln.split()\n",
- " if len(sp) != 15:\n",
- " continue\n",
- " p = float(sp[0])\n",
- " i = int(sp[1]) + offset\n",
- " j = int(sp[2]) + offset\n",
- " k = int(round(p * mpsi))\n",
- " psi[k] = p\n",
- " nums = list(map(float, sp[3:]))\n",
- " for nm in names:\n",
- " r, imv = nums[idx[nm]], nums[idx[nm] + 1]\n",
- " mats[nm][k, i, j] = r + 1j * imv\n",
- " return psi, mats\n",
- "\n",
- " # 2. read_vector_out + expand_vector_to_diag\n",
- " @staticmethod\n",
- " def read_vector_out(file_path: str) -> Tuple[np.ndarray, np.ndarray]:\n",
- " blocks, cur = [], []\n",
- " for ln in Path(file_path).read_text().splitlines():\n",
- " s = ln.strip()\n",
- " if not s:\n",
- " if cur:\n",
- " blocks.append(np.array(cur))\n",
- " cur = []\n",
- " continue\n",
- " parts = s.split()\n",
- " if len(parts) == 4:\n",
- " p, _, re, im = parts\n",
- " cur.append((float(p), float(re) + 1j * float(im)))\n",
- " if cur:\n",
- " blocks.append(np.array(cur))\n",
- " psi = np.array([row[0] for row in blocks[0]])\n",
- " n_psi = len(psi)\n",
- " n_ipert = len(blocks)\n",
- " vec = np.empty((n_psi, n_ipert), np.complex64)\n",
- " for i, b in enumerate(blocks):\n",
- " vec[:, i] = b[:, 1]\n",
- " return psi, vec\n",
- "\n",
- " @staticmethod\n",
- " def expand_vector_to_diag(mat_vec: np.ndarray) -> np.ndarray:\n",
- " n_psi, n = mat_vec.shape\n",
- " full = np.zeros((n_psi, n, n), dtype=mat_vec.dtype)\n",
- " for k in range(n_psi):\n",
- " np.fill_diagonal(full[k], mat_vec[k])\n",
- " return full\n",
- "\n",
- " # 3. read_fs_bin / read_gs_bin / read_ks_bin\n",
- " @staticmethod\n",
- " def read_fs_bin(\n",
- " file_path: str,\n",
- " mpsi: int,\n",
- " mpert: int,\n",
- " mband: int\n",
- " ) -> Tuple[np.ndarray, np.ndarray, np.ndarray]:\n",
- " n_ipert_fs = (mband + 1) * (2 * mpert - mband) // 2\n",
- " n_ipert_ks = (2 * mband + 1) * mpert\n",
- " bytes_per_ipert = (mpsi + 1) * (4 + 16 + 4) + (4 + 0 + 4)\n",
- " total_size = Path(file_path).stat().st_size\n",
- " if total_size % bytes_per_ipert == 0:\n",
- " cand_ipert = total_size // bytes_per_ipert\n",
- " else:\n",
- " raise ValueError(f\"File size {total_size} not divisible by expected block size {bytes_per_ipert}.\")\n",
- " if cand_ipert == n_ipert_fs:\n",
- " n_ipert = n_ipert_fs\n",
- " elif cand_ipert == n_ipert_ks:\n",
- " n_ipert = n_ipert_ks\n",
- " else:\n",
- " n_ipert = n_ipert_fs\n",
- "\n",
- " psi_arr = np.zeros(mpsi + 1, dtype=np.float64)\n",
- " sqfs = np.zeros(mpsi + 1, dtype=np.float64)\n",
- " M = np.zeros((n_ipert, mpsi + 1), dtype=np.complex128)\n",
- "\n",
- " with open(file_path, 'rb') as f:\n",
- " for ipert in range(n_ipert):\n",
- " for ipsi in range(mpsi + 1):\n",
- " rec_len_bytes = f.read(4)\n",
- " if len(rec_len_bytes) < 4:\n",
- " raise EOFError(\"Unexpected EOF reading record length.\")\n",
- " rec_len = struct.unpack(' Tuple[np.ndarray, np.ndarray]:\n",
- " psi_vals, blocks, cur, reading = [], [], [], None\n",
- " for ln in Path(file_path).read_text().splitlines():\n",
- " s = ln.strip()\n",
- " if not s:\n",
- " if cur:\n",
- " blocks.append(np.array(cur, float))\n",
- " cur = []\n",
- " continue\n",
- " if s.startswith('# psi='):\n",
- " psi_vals.append(float(s.split('=')[1]))\n",
- " elif s.startswith('# Real'):\n",
- " reading = 'real'\n",
- " elif s.startswith('# Imag'):\n",
- " reading = 'imag'\n",
- " elif s and not s.startswith('#'):\n",
- " if (reading == 'imag') == want_imag:\n",
- " cur.append(list(map(float, s.split(','))))\n",
- " if cur:\n",
- " blocks.append(np.array(cur, float))\n",
- " psi = np.array(psi_vals)\n",
- " mats = np.stack(blocks, axis=0)\n",
- " return psi, mats\n",
- "\n",
- " @staticmethod\n",
- " def read_cylinder_real_matrix(file_path: str) -> Tuple[np.ndarray, np.ndarray]:\n",
- " psi, real_mat = TokamakCylinderLoader.read_block_csv_matrix(file_path, want_imag=False)\n",
- " complex_mat = real_mat.astype(np.complex128)\n",
- " return psi, complex_mat\n",
- "\n",
- " # 5. read_cylinder_FGK_from_diag\n",
- " @staticmethod\n",
- " def read_cylinder_FGK_from_diag(file_path: str) -> Tuple[np.ndarray, Dict[str, np.ndarray]]:\n",
- " df = pd.read_csv(file_path)\n",
- " psi = df['psi'].values\n",
- " mats = {}\n",
- " for key in ('F','G','K'):\n",
- " prefix = f\"{key}_diag\"\n",
- " cols = [col for col in df.columns if col.startswith(prefix)]\n",
- " diag_vals = df[cols].values\n",
- " n_psi, m = diag_vals.shape\n",
- " full = np.zeros((n_psi, m, m), dtype=np.complex128)\n",
- " for k in range(n_psi):\n",
- " np.fill_diagonal(full[k], diag_vals[k])\n",
- " mats[key] = full\n",
- " return psi, mats\n",
- "\n",
- " # 6. clean_and_deduplicate_psin\n",
- " @staticmethod\n",
- " def clean_and_deduplicate_psin(psin: np.ndarray, mat: np.ndarray) -> Tuple[np.ndarray, np.ndarray]:\n",
- " psin_rounded = np.round(psin, 8)\n",
- " unique_vals, inv_idx = np.unique(psin_rounded, return_inverse=True)\n",
- " m = mat.shape[1]\n",
- " mat_out = np.zeros((len(unique_vals), m, m), dtype=mat.dtype)\n",
- " counts = np.zeros(len(unique_vals), dtype=int)\n",
- " for i, idx in enumerate(inv_idx):\n",
- " mat_out[idx] += mat[i]\n",
- " counts[idx] += 1\n",
- " mat_out /= counts[:, None, None]\n",
- " return unique_vals, mat_out\n",
- "\n",
- " # 7. interpolate_matrix_over_psin\n",
- " @staticmethod\n",
- " def interpolate_matrix_over_psin(psin_orig: np.ndarray, mat_orig: np.ndarray, psin_target: np.ndarray) -> np.ndarray:\n",
- " n, m, _ = mat_orig.shape\n",
- " mat_interp = np.zeros((len(psin_target), m, m), dtype=np.complex128)\n",
- " for i in range(m):\n",
- " for j in range(m):\n",
- " f = interp1d(psin_orig, mat_orig[:, i, j], kind='cubic', bounds_error=False, fill_value=\"extrapolate\")\n",
- " mat_interp[:, i, j] = f(psin_target)\n",
- " return mat_interp\n",
- "\n",
- " # 8. load_all: 통합 함수\n",
- " def load_all(self, psin_target: np.ndarray) -> Dict[str, Dict[str, np.ndarray]]:\n",
- " result = {'tokamak': {}, 'cylinder': {}}\n",
- "\n",
- " # --- Tokamak: A–H from imats.out ---\n",
- " psi_imats, mats_imats = TokamakCylinderLoader.read_imats_out(self.imats_path, names=('A','B','C','D','E','H'))\n",
- " for nm in ('A','B','C','D','E','H'):\n",
- " psi_clean, m_clean = TokamakCylinderLoader.clean_and_deduplicate_psin(psi_imats, mats_imats[nm])\n",
- " result['tokamak'][nm] = TokamakCylinderLoader.interpolate_matrix_over_psin(psi_clean, m_clean, psin_target)\n",
- "\n",
- " # --- Tokamak: F from fs.bin ---\n",
- " psi_fs, sqfs, mat_F = TokamakCylinderLoader.read_fs_bin(self.fs_bin_path, mpsi=psi_imats.size-1, mpert=self.mpert, mband=self.mband)\n",
- " psi_fs, mat_F = TokamakCylinderLoader.clean_and_deduplicate_psin(psi_fs, mat_F)\n",
- " result['tokamak']['F'] = TokamakCylinderLoader.interpolate_matrix_over_psin(psi_fs, mat_F, psin_target)\n",
- "\n",
- " # --- Tokamak: G from gs.bin ---\n",
- " psi_gs, sqgs, mat_G = TokamakCylinderLoader.read_gs_bin(self.gs_bin_path, mpsi=psi_imats.size-1, mpert=self.mpert, mband=self.mband)\n",
- " psi_gs, mat_G = TokamakCylinderLoader.clean_and_deduplicate_psin(psi_gs, mat_G)\n",
- " result['tokamak']['G'] = TokamakCylinderLoader.interpolate_matrix_over_psin(psi_gs, mat_G, psin_target)\n",
- "\n",
- " # --- Tokamak: K from ks.bin ---\n",
- " psi_ks, sqks, mat_K = TokamakCylinderLoader.read_ks_bin(self.ks_bin_path, mpsi=psi_imats.size-1, mpert=self.mpert, mband=self.mband)\n",
- " psi_ks, mat_K = TokamakCylinderLoader.clean_and_deduplicate_psin(psi_ks, mat_K)\n",
- " result['tokamak']['K'] = TokamakCylinderLoader.interpolate_matrix_over_psin(psi_ks, mat_K, psin_target)\n",
- "\n",
- " # --- Cylinder: A–H from CSVs ---\n",
- " for nm, path in self.cyl_paths.items():\n",
- " psi_c, mat_c = TokamakCylinderLoader.read_cylinder_real_matrix(path)\n",
- " psi_c, mat_c = TokamakCylinderLoader.clean_and_deduplicate_psin(psi_c, mat_c)\n",
- " result['cylinder'][nm] = TokamakCylinderLoader.interpolate_matrix_over_psin(psi_c, mat_c, psin_target)\n",
- "\n",
- " # --- Cylinder: F, G, K from diag CSV ---\n",
- " psi_fkg, mats_fkg = TokamakCylinderLoader.read_cylinder_FGK_from_diag(self.cyl_FGK_diag_csv)\n",
- " for nm in ('F','G','K'):\n",
- " psi_c, mat_c = TokamakCylinderLoader.clean_and_deduplicate_psin(psi_fkg, mats_fkg[nm])\n",
- " result['cylinder'][nm] = TokamakCylinderLoader.interpolate_matrix_over_psin(psi_c, mat_c, psin_target)\n",
- "\n",
- " return result\n",
- "\n",
- "# ======================\n",
- "# Usage example\n",
- "# ======================\n",
- "if __name__ == \"__main__\":\n",
- " # 1) 환경에 맞게 경로와 Fortran 파라미터 설정\n",
- " loader = TokamakCylinderLoader(\n",
- " imats_path = \"imats.out\",\n",
- " fs_bin_path = \"fs.bin\",\n",
- " gs_bin_path = \"gs.bin\",\n",
- " ks_bin_path = \"ks.bin\",\n",
- " mpert = 6,\n",
- " mband = 2,\n",
- " cyl_A_csv = \"A_matrices.csv\",\n",
- " cyl_B_csv = \"B_matrices.csv\",\n",
- " cyl_C_csv = \"C_matrices.csv\",\n",
- " cyl_D_csv = \"D_matrices.csv\",\n",
- " cyl_E_csv = \"E_matrices.csv\",\n",
- " cyl_H_csv = \"H_matrices.csv\",\n",
- " cyl_FGK_diag_csv = \"dcon_FKG_diagonal_elements.csv\"\n",
- " )\n",
- "\n",
- " # 2) 공통 psin 그리드 정의\n",
- " psin_target = np.linspace(0, 1, 200)\n",
- "\n",
- " # 3) 모든 행렬 읽고 보간\n",
- " all_data = loader.load_all(psin_target)\n",
- "\n",
- " # 4) 결과 출력\n",
- " print(\"=== Tokamak matrices ===\")\n",
- " for name, mat in all_data['tokamak'].items():\n",
- " print(f\"{name}: {mat.shape}\")\n",
- " print(\"\\n=== Cylinder matrices ===\")\n",
- " for name, mat in all_data['cylinder'].items():\n",
- " print(f\"{name}: {mat.shape}\")\n"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "id": "6050349e",
- "metadata": {},
- "outputs": [],
- "source": []
- }
- ],
- "metadata": {
- "kernelspec": {
- "display_name": "mkl_env",
- "language": "python",
- "name": "python3"
- },
- "language_info": {
- "codemirror_mode": {
- "name": "ipython",
- "version": 3
- },
- "file_extension": ".py",
- "mimetype": "text/x-python",
- "name": "python",
- "nbconvert_exporter": "python",
- "pygments_lexer": "ipython3",
- "version": "3.11.7"
- }
- },
- "nbformat": 4,
- "nbformat_minor": 5
-}
diff --git a/src/DCON/validate/crit.bin b/src/DCON/validate/crit.bin
deleted file mode 100644
index ec003e13db..0000000000
Binary files a/src/DCON/validate/crit.bin and /dev/null differ
diff --git a/src/DCON/validate/crit.out b/src/DCON/validate/crit.out
deleted file mode 100644
index 00238222d7..0000000000
--- a/src/DCON/validate/crit.out
+++ /dev/null
@@ -1,813 +0,0 @@
-
- ising psi q di re alpha im alpha
-
- 1 7.971E-01 2.000E+00 -2.667E-01 5.165E-01 -0.000E+00
-
-
- is psifac dpsi q singfac eval1
-
- 0 1.000E-02 1.000E-02 1.052E+00 9.478E-01 0.000E+00
- 1 1.001E-02 7.481E-06 1.052E+00 9.478E-01 9.562E-04
- 2 1.001E-02 7.377E-07 1.052E+00 9.478E-01 1.050E-03
- 3 1.001E-02 7.377E-07 1.052E+00 9.478E-01 1.145E-03
- 4 1.001E-02 1.475E-06 1.052E+00 9.478E-01 1.333E-03
- 5 1.001E-02 1.475E-06 1.052E+00 9.478E-01 1.522E-03
- 6 1.001E-02 1.475E-06 1.052E+00 9.478E-01 1.711E-03
- 7 1.003E-02 1.447E-05 1.052E+00 9.478E-01 3.560E-03
- 8 1.004E-02 1.447E-05 1.052E+00 9.478E-01 5.409E-03
- 9 1.006E-02 1.447E-05 1.052E+00 9.477E-01 7.258E-03
- 10 1.011E-02 5.366E-05 1.052E+00 9.477E-01 1.412E-02
- 11 1.016E-02 5.366E-05 1.052E+00 9.477E-01 2.097E-02
- 12 1.022E-02 5.366E-05 1.052E+00 9.477E-01 2.783E-02
- 13 1.027E-02 5.366E-05 1.052E+00 9.477E-01 3.469E-02
- 14 1.037E-02 9.470E-05 1.052E+00 9.477E-01 4.679E-02
- 15 1.046E-02 9.470E-05 1.052E+00 9.477E-01 5.889E-02
- 16 1.056E-02 9.470E-05 1.052E+00 9.476E-01 7.099E-02
- 17 1.065E-02 9.470E-05 1.052E+00 9.476E-01 8.308E-02
- 18 1.084E-02 1.905E-04 1.052E+00 9.476E-01 1.074E-01
- 19 1.103E-02 1.905E-04 1.052E+00 9.475E-01 1.317E-01
- 20 1.122E-02 1.905E-04 1.053E+00 9.475E-01 1.561E-01
- 21 1.141E-02 1.905E-04 1.053E+00 9.475E-01 1.804E-01
- 22 1.160E-02 1.905E-04 1.053E+00 9.474E-01 2.047E-01
- 23 1.184E-02 2.340E-04 1.053E+00 9.474E-01 2.345E-01
- 24 1.207E-02 2.340E-04 1.053E+00 9.473E-01 2.644E-01
- 25 1.230E-02 2.340E-04 1.053E+00 9.473E-01 2.942E-01
- 26 1.254E-02 2.340E-04 1.053E+00 9.472E-01 3.240E-01
- 27 1.277E-02 2.340E-04 1.053E+00 9.472E-01 3.539E-01
- 28 1.301E-02 2.340E-04 1.053E+00 9.471E-01 3.837E-01
- 29 1.324E-02 2.340E-04 1.053E+00 9.471E-01 4.135E-01
- 30 1.347E-02 2.340E-04 1.053E+00 9.470E-01 4.433E-01
- 31 1.371E-02 2.340E-04 1.053E+00 9.470E-01 4.731E-01
- 32 1.394E-02 2.340E-04 1.053E+00 9.469E-01 5.029E-01
- 33 1.418E-02 2.340E-04 1.053E+00 9.469E-01 5.327E-01
- 34 1.443E-02 2.575E-04 1.053E+00 9.468E-01 5.654E-01
- 35 1.469E-02 2.575E-04 1.053E+00 9.468E-01 5.982E-01
- 36 1.495E-02 2.575E-04 1.053E+00 9.467E-01 6.309E-01
- 37 1.521E-02 2.575E-04 1.053E+00 9.467E-01 6.636E-01
- 38 1.546E-02 2.575E-04 1.053E+00 9.466E-01 6.964E-01
- 39 1.572E-02 2.575E-04 1.053E+00 9.465E-01 7.291E-01
- 40 1.598E-02 2.575E-04 1.054E+00 9.465E-01 7.618E-01
- 41 1.624E-02 2.575E-04 1.054E+00 9.464E-01 7.945E-01
- 42 1.652E-02 2.860E-04 1.054E+00 9.464E-01 8.308E-01
- 43 1.681E-02 2.860E-04 1.054E+00 9.463E-01 8.671E-01
- 44 1.709E-02 2.860E-04 1.054E+00 9.462E-01 9.034E-01
- 45 1.738E-02 2.860E-04 1.054E+00 9.462E-01 9.397E-01
- 46 1.767E-02 2.860E-04 1.054E+00 9.461E-01 9.760E-01
- 47 1.798E-02 3.156E-04 1.054E+00 9.460E-01 1.016E+00
- 48 1.830E-02 3.156E-04 1.054E+00 9.460E-01 1.056E+00
- 49 1.861E-02 3.156E-04 1.054E+00 9.459E-01 1.096E+00
- 50 1.893E-02 3.156E-04 1.054E+00 9.458E-01 1.136E+00
- 51 1.924E-02 3.156E-04 1.054E+00 9.457E-01 1.176E+00
- 52 1.956E-02 3.156E-04 1.054E+00 9.457E-01 1.216E+00
- 53 1.988E-02 3.156E-04 1.054E+00 9.456E-01 1.256E+00
- 54 2.019E-02 3.156E-04 1.054E+00 9.455E-01 1.296E+00
- 55 2.054E-02 3.506E-04 1.055E+00 9.455E-01 1.340E+00
- 56 2.089E-02 3.506E-04 1.055E+00 9.454E-01 1.385E+00
- 57 2.124E-02 3.506E-04 1.055E+00 9.453E-01 1.429E+00
- 58 2.159E-02 3.506E-04 1.055E+00 9.452E-01 1.473E+00
- 59 2.194E-02 3.506E-04 1.055E+00 9.451E-01 1.517E+00
- 60 2.233E-02 3.872E-04 1.055E+00 9.451E-01 1.566E+00
- 61 2.272E-02 3.872E-04 1.055E+00 9.450E-01 1.615E+00
- 62 2.311E-02 3.872E-04 1.055E+00 9.449E-01 1.664E+00
- 63 2.349E-02 3.872E-04 1.055E+00 9.448E-01 1.713E+00
- 64 2.388E-02 3.872E-04 1.055E+00 9.447E-01 1.762E+00
- 65 2.427E-02 3.872E-04 1.055E+00 9.446E-01 1.811E+00
- 66 2.465E-02 3.872E-04 1.055E+00 9.445E-01 1.859E+00
- 67 2.504E-02 3.872E-04 1.056E+00 9.445E-01 1.908E+00
- 68 2.547E-02 4.316E-04 1.056E+00 9.444E-01 1.963E+00
- 69 2.590E-02 4.316E-04 1.056E+00 9.443E-01 2.017E+00
- 70 2.634E-02 4.316E-04 1.056E+00 9.442E-01 2.071E+00
- 71 2.677E-02 4.316E-04 1.056E+00 9.441E-01 2.125E+00
- 72 2.720E-02 4.316E-04 1.056E+00 9.440E-01 2.180E+00
- 73 2.768E-02 4.788E-04 1.056E+00 9.438E-01 2.240E+00
- 74 2.816E-02 4.788E-04 1.056E+00 9.437E-01 2.300E+00
- 75 2.864E-02 4.788E-04 1.056E+00 9.436E-01 2.360E+00
- 76 2.911E-02 4.788E-04 1.056E+00 9.435E-01 2.420E+00
-
- is psifac dpsi q singfac eval1
-
- Gaussian Reduction at istep = 77, psi = 2.959E-02, q = 1.056
-
- is psifac dpsi q singfac eval1
-
- 77 2.959E-02 4.788E-04 1.057E+00 9.434E-01 2.480E+00
- 78 2.960E-02 1.000E-05 1.057E+00 9.434E-01 2.482E+00
- 79 2.961E-02 1.000E-05 1.057E+00 9.434E-01 2.483E+00
- 80 2.980E-02 1.823E-04 1.057E+00 9.433E-01 2.506E+00
- 81 2.998E-02 1.823E-04 1.057E+00 9.433E-01 2.528E+00
- 82 3.016E-02 1.823E-04 1.057E+00 9.432E-01 2.551E+00
- 83 3.047E-02 3.073E-04 1.057E+00 9.432E-01 2.590E+00
- 84 3.077E-02 3.073E-04 1.057E+00 9.431E-01 2.628E+00
- 85 3.108E-02 3.073E-04 1.057E+00 9.430E-01 2.667E+00
- 86 3.139E-02 3.073E-04 1.057E+00 9.430E-01 2.705E+00
- 87 3.176E-02 3.709E-04 1.057E+00 9.429E-01 2.752E+00
- 88 3.213E-02 3.709E-04 1.057E+00 9.428E-01 2.798E+00
- 89 3.250E-02 3.709E-04 1.057E+00 9.427E-01 2.845E+00
- 90 3.287E-02 3.709E-04 1.057E+00 9.426E-01 2.891E+00
- 91 3.350E-02 6.292E-04 1.058E+00 9.425E-01 2.970E+00
- 92 3.413E-02 6.292E-04 1.058E+00 9.423E-01 3.048E+00
- 93 3.476E-02 6.292E-04 1.058E+00 9.422E-01 3.127E+00
- 94 3.539E-02 6.292E-04 1.058E+00 9.420E-01 3.205E+00
- 95 3.602E-02 6.292E-04 1.058E+00 9.419E-01 3.284E+00
- 96 3.679E-02 7.685E-04 1.058E+00 9.417E-01 3.380E+00
- 97 3.756E-02 7.685E-04 1.058E+00 9.415E-01 3.475E+00
- 98 3.832E-02 7.685E-04 1.059E+00 9.413E-01 3.571E+00
- 99 3.909E-02 7.685E-04 1.059E+00 9.411E-01 3.667E+00
- 100 3.986E-02 7.685E-04 1.059E+00 9.409E-01 3.762E+00
- 101 4.063E-02 7.685E-04 1.059E+00 9.408E-01 3.857E+00
- 102 4.228E-02 1.646E-03 1.060E+00 9.403E-01 4.062E+00
- 103 4.392E-02 1.646E-03 1.060E+00 9.399E-01 4.266E+00
- 104 4.557E-02 1.646E-03 1.060E+00 9.395E-01 4.469E+00
- 105 4.721E-02 1.646E-03 1.061E+00 9.391E-01 4.672E+00
- 106 4.886E-02 1.646E-03 1.061E+00 9.387E-01 4.875E+00
- 107 5.051E-02 1.646E-03 1.062E+00 9.383E-01 5.078E+00
- 108 5.215E-02 1.646E-03 1.062E+00 9.379E-01 5.281E+00
- 109 5.380E-02 1.646E-03 1.063E+00 9.375E-01 5.483E+00
- 110 5.545E-02 1.646E-03 1.063E+00 9.370E-01 5.684E+00
- 111 5.709E-02 1.646E-03 1.063E+00 9.366E-01 5.886E+00
- 112 5.874E-02 1.646E-03 1.064E+00 9.362E-01 6.087E+00
- 113 6.038E-02 1.646E-03 1.064E+00 9.357E-01 6.288E+00
- 114 6.203E-02 1.646E-03 1.065E+00 9.353E-01 6.488E+00
- 115 6.335E-02 1.323E-03 1.065E+00 9.349E-01 6.649E+00
- 116 6.444E-02 1.090E-03 1.065E+00 9.346E-01 6.782E+00
- 117 6.553E-02 1.090E-03 1.066E+00 9.343E-01 6.914E+00
- 118 6.662E-02 1.090E-03 1.066E+00 9.341E-01 7.046E+00
- 119 6.771E-02 1.090E-03 1.066E+00 9.338E-01 7.178E+00
- 120 6.881E-02 1.090E-03 1.067E+00 9.335E-01 7.310E+00
-
- is psifac dpsi q singfac eval1
-
- Gaussian Reduction at istep = 121, psi = 6.990E-02, q = 1.067
-
- is psifac dpsi q singfac eval1
-
- 121 6.990E-02 1.090E-03 1.067E+00 9.332E-01 7.442E+00
- 122 6.991E-02 1.000E-05 1.067E+00 9.332E-01 7.444E+00
- 123 6.992E-02 1.000E-05 1.067E+00 9.332E-01 7.445E+00
- 124 7.014E-02 2.278E-04 1.067E+00 9.331E-01 7.472E+00
- 125 7.037E-02 2.278E-04 1.067E+00 9.330E-01 7.500E+00
- 126 7.060E-02 2.278E-04 1.067E+00 9.330E-01 7.527E+00
- 127 7.149E-02 8.876E-04 1.067E+00 9.327E-01 7.634E+00
- 128 7.237E-02 8.876E-04 1.068E+00 9.325E-01 7.742E+00
- 129 7.326E-02 8.876E-04 1.068E+00 9.322E-01 7.849E+00
- 130 7.415E-02 8.876E-04 1.068E+00 9.320E-01 7.955E+00
- 131 7.523E-02 1.082E-03 1.068E+00 9.317E-01 8.086E+00
- 132 7.631E-02 1.082E-03 1.069E+00 9.314E-01 8.216E+00
- 133 7.740E-02 1.082E-03 1.069E+00 9.311E-01 8.346E+00
- 134 7.848E-02 1.082E-03 1.069E+00 9.308E-01 8.475E+00
- 135 7.956E-02 1.082E-03 1.070E+00 9.305E-01 8.605E+00
- 136 8.113E-02 1.569E-03 1.070E+00 9.300E-01 8.793E+00
- 137 8.270E-02 1.569E-03 1.070E+00 9.296E-01 8.980E+00
- 138 8.427E-02 1.569E-03 1.071E+00 9.291E-01 9.168E+00
- 139 8.584E-02 1.569E-03 1.071E+00 9.287E-01 9.355E+00
- 140 8.741E-02 1.569E-03 1.072E+00 9.282E-01 9.541E+00
- 141 8.957E-02 2.164E-03 1.072E+00 9.276E-01 9.798E+00
- 142 9.174E-02 2.164E-03 1.073E+00 9.269E-01 1.005E+01
- 143 9.390E-02 2.164E-03 1.074E+00 9.263E-01 1.031E+01
- 144 9.606E-02 2.164E-03 1.074E+00 9.256E-01 1.057E+01
- 145 9.823E-02 2.164E-03 1.075E+00 9.250E-01 1.082E+01
- 146 1.004E-01 2.164E-03 1.076E+00 9.243E-01 1.108E+01
- 147 1.036E-01 3.193E-03 1.077E+00 9.233E-01 1.145E+01
- 148 1.068E-01 3.193E-03 1.078E+00 9.223E-01 1.182E+01
- 149 1.100E-01 3.193E-03 1.079E+00 9.213E-01 1.220E+01
- 150 1.132E-01 3.193E-03 1.080E+00 9.203E-01 1.257E+01
- 151 1.164E-01 3.193E-03 1.081E+00 9.192E-01 1.294E+01
- 152 1.196E-01 3.193E-03 1.082E+00 9.182E-01 1.331E+01
- 153 1.227E-01 3.193E-03 1.083E+00 9.171E-01 1.367E+01
- 154 1.259E-01 3.193E-03 1.084E+00 9.161E-01 1.404E+01
- 155 1.291E-01 3.193E-03 1.085E+00 9.150E-01 1.440E+01
- 156 1.323E-01 3.193E-03 1.086E+00 9.139E-01 1.477E+01
- 157 1.355E-01 3.193E-03 1.087E+00 9.128E-01 1.513E+01
- 158 1.387E-01 3.193E-03 1.088E+00 9.117E-01 1.549E+01
- 159 1.419E-01 3.193E-03 1.089E+00 9.105E-01 1.585E+01
- 160 1.451E-01 3.193E-03 1.091E+00 9.094E-01 1.621E+01
- 161 1.483E-01 3.193E-03 1.092E+00 9.082E-01 1.657E+01
- 162 1.522E-01 3.861E-03 1.093E+00 9.068E-01 1.700E+01
- 163 1.560E-01 3.861E-03 1.095E+00 9.054E-01 1.743E+01
- 164 1.599E-01 3.861E-03 1.096E+00 9.039E-01 1.786E+01
-
- is psifac dpsi q singfac eval1
-
- Gaussian Reduction at istep = 165, psi = 1.637E-01, q = 1.096
-
- is psifac dpsi q singfac eval1
-
- 165 1.637E-01 3.861E-03 1.098E+00 9.025E-01 1.829E+01
- 166 1.637E-01 1.000E-05 1.098E+00 9.025E-01 1.829E+01
- 167 1.638E-01 1.000E-05 1.098E+00 9.025E-01 1.829E+01
- 168 1.643E-01 4.980E-04 1.098E+00 9.023E-01 1.835E+01
- 169 1.648E-01 4.980E-04 1.098E+00 9.021E-01 1.840E+01
- 170 1.653E-01 4.980E-04 1.098E+00 9.019E-01 1.846E+01
- 171 1.672E-01 1.919E-03 1.099E+00 9.011E-01 1.867E+01
- 172 1.691E-01 1.919E-03 1.100E+00 9.004E-01 1.888E+01
- 173 1.710E-01 1.919E-03 1.100E+00 8.996E-01 1.909E+01
- 174 1.729E-01 1.919E-03 1.101E+00 8.989E-01 1.930E+01
- 175 1.753E-01 2.349E-03 1.102E+00 8.979E-01 1.955E+01
- 176 1.776E-01 2.349E-03 1.103E+00 8.970E-01 1.981E+01
- 177 1.800E-01 2.349E-03 1.104E+00 8.961E-01 2.006E+01
- 178 1.823E-01 2.349E-03 1.105E+00 8.951E-01 2.032E+01
- 179 1.847E-01 2.349E-03 1.106E+00 8.941E-01 2.057E+01
- 180 1.881E-01 3.424E-03 1.107E+00 8.927E-01 2.094E+01
- 181 1.915E-01 3.424E-03 1.109E+00 8.913E-01 2.131E+01
- 182 1.949E-01 3.424E-03 1.110E+00 8.898E-01 2.167E+01
- 183 1.984E-01 3.424E-03 1.112E+00 8.883E-01 2.204E+01
- 184 2.018E-01 3.424E-03 1.113E+00 8.869E-01 2.240E+01
- 185 2.064E-01 4.599E-03 1.115E+00 8.848E-01 2.289E+01
- 186 2.110E-01 4.599E-03 1.117E+00 8.828E-01 2.337E+01
- 187 2.156E-01 4.599E-03 1.119E+00 8.807E-01 2.385E+01
- 188 2.202E-01 4.599E-03 1.121E+00 8.786E-01 2.433E+01
- 189 2.248E-01 4.599E-03 1.124E+00 8.764E-01 2.480E+01
- 190 2.294E-01 4.599E-03 1.126E+00 8.742E-01 2.528E+01
- 191 2.362E-01 6.799E-03 1.129E+00 8.710E-01 2.597E+01
- 192 2.430E-01 6.799E-03 1.132E+00 8.676E-01 2.666E+01
- 193 2.498E-01 6.799E-03 1.136E+00 8.642E-01 2.734E+01
- 194 2.566E-01 6.799E-03 1.139E+00 8.606E-01 2.802E+01
- 195 2.634E-01 6.799E-03 1.143E+00 8.571E-01 2.869E+01
- 196 2.702E-01 6.799E-03 1.147E+00 8.534E-01 2.935E+01
- 197 2.770E-01 6.799E-03 1.150E+00 8.496E-01 3.001E+01
- 198 2.825E-01 5.533E-03 1.153E+00 8.465E-01 3.054E+01
- 199 2.871E-01 4.588E-03 1.156E+00 8.439E-01 3.098E+01
- 200 2.917E-01 4.588E-03 1.159E+00 8.412E-01 3.142E+01
- 201 2.963E-01 4.588E-03 1.161E+00 8.385E-01 3.185E+01
- 202 3.009E-01 4.588E-03 1.164E+00 8.358E-01 3.228E+01
- 203 3.055E-01 4.588E-03 1.167E+00 8.330E-01 3.271E+01
- 204 3.100E-01 4.588E-03 1.170E+00 8.302E-01 3.313E+01
- 205 3.146E-01 4.588E-03 1.173E+00 8.273E-01 3.355E+01
- 206 3.192E-01 4.588E-03 1.176E+00 8.244E-01 3.397E+01
- 207 3.238E-01 4.588E-03 1.179E+00 8.214E-01 3.438E+01
- 208 3.284E-01 4.588E-03 1.182E+00 8.184E-01 3.480E+01
- 209 3.330E-01 4.588E-03 1.185E+00 8.154E-01 3.520E+01
- 210 3.376E-01 4.588E-03 1.188E+00 8.123E-01 3.561E+01
- 211 3.422E-01 4.588E-03 1.191E+00 8.091E-01 3.601E+01
- 212 3.467E-01 4.588E-03 1.194E+00 8.060E-01 3.641E+01
- 213 3.513E-01 4.588E-03 1.197E+00 8.027E-01 3.681E+01
- 214 3.559E-01 4.588E-03 1.201E+00 7.994E-01 3.721E+01
- 215 3.605E-01 4.588E-03 1.204E+00 7.961E-01 3.760E+01
-
- is psifac dpsi q singfac eval1
-
- Gaussian Reduction at istep = 216, psi = 3.651E-01, q = 1.204
-
- is psifac dpsi q singfac eval1
-
- 216 3.651E-01 4.588E-03 1.207E+00 7.927E-01 3.799E+01
- 217 3.651E-01 1.000E-05 1.207E+00 7.927E-01 3.799E+01
- 218 3.651E-01 1.000E-05 1.207E+00 7.927E-01 3.799E+01
- 219 3.661E-01 9.415E-04 1.208E+00 7.920E-01 3.807E+01
- 220 3.670E-01 9.415E-04 1.209E+00 7.913E-01 3.815E+01
- 221 3.679E-01 9.415E-04 1.209E+00 7.906E-01 3.822E+01
- 222 3.711E-01 3.195E-03 1.212E+00 7.882E-01 3.849E+01
- 223 3.743E-01 3.195E-03 1.214E+00 7.858E-01 3.876E+01
- 224 3.775E-01 3.195E-03 1.217E+00 7.833E-01 3.902E+01
- 225 3.807E-01 3.195E-03 1.219E+00 7.809E-01 3.928E+01
- 226 3.844E-01 3.706E-03 1.222E+00 7.779E-01 3.958E+01
- 227 3.881E-01 3.706E-03 1.225E+00 7.750E-01 3.989E+01
- 228 3.918E-01 3.706E-03 1.228E+00 7.720E-01 4.018E+01
- 229 3.955E-01 3.706E-03 1.231E+00 7.690E-01 4.048E+01
- 230 3.993E-01 3.706E-03 1.234E+00 7.659E-01 4.077E+01
- 231 4.051E-01 5.854E-03 1.239E+00 7.611E-01 4.123E+01
- 232 4.110E-01 5.854E-03 1.244E+00 7.561E-01 4.169E+01
- 233 4.168E-01 5.854E-03 1.249E+00 7.510E-01 4.214E+01
- 234 4.227E-01 5.854E-03 1.254E+00 7.458E-01 4.258E+01
- 235 4.285E-01 5.854E-03 1.260E+00 7.405E-01 4.302E+01
- 236 4.356E-01 7.069E-03 1.266E+00 7.339E-01 4.354E+01
- 237 4.427E-01 7.069E-03 1.273E+00 7.273E-01 4.405E+01
- 238 4.497E-01 7.069E-03 1.280E+00 7.204E-01 4.455E+01
- 239 4.568E-01 7.069E-03 1.287E+00 7.134E-01 4.505E+01
- 240 4.639E-01 7.069E-03 1.294E+00 7.062E-01 4.554E+01
- 241 4.709E-01 7.069E-03 1.301E+00 6.989E-01 4.601E+01
- 242 4.803E-01 9.366E-03 1.311E+00 6.888E-01 4.663E+01
- 243 4.897E-01 9.366E-03 1.321E+00 6.785E-01 4.724E+01
- 244 4.990E-01 9.366E-03 1.332E+00 6.678E-01 4.783E+01
- 245 5.084E-01 9.366E-03 1.343E+00 6.568E-01 4.840E+01
- 246 5.178E-01 9.366E-03 1.355E+00 6.454E-01 4.895E+01
- 247 5.271E-01 9.366E-03 1.366E+00 6.336E-01 4.949E+01
- 248 5.365E-01 9.366E-03 1.379E+00 6.214E-01 5.001E+01
- 249 5.459E-01 9.366E-03 1.391E+00 6.087E-01 5.051E+01
- 250 5.552E-01 9.366E-03 1.404E+00 5.957E-01 5.100E+01
- 251 5.646E-01 9.366E-03 1.418E+00 5.822E-01 5.146E+01
- 252 5.740E-01 9.366E-03 1.432E+00 5.682E-01 5.191E+01
- 253 5.833E-01 9.366E-03 1.446E+00 5.537E-01 5.234E+01
- 254 5.927E-01 9.366E-03 1.461E+00 5.387E-01 5.275E+01
- 255 6.021E-01 9.366E-03 1.477E+00 5.231E-01 5.314E+01
- 256 6.114E-01 9.366E-03 1.493E+00 5.069E-01 5.351E+01
- 257 6.208E-01 9.366E-03 1.510E+00 4.902E-01 5.386E+01
- 258 6.302E-01 9.366E-03 1.527E+00 4.728E-01 5.420E+01
-
- is psifac dpsi q singfac eval1
-
- Gaussian Reduction at istep = 259, psi = 6.395E-01, q = 1.527
-
- is psifac dpsi q singfac eval1
-
- 259 6.395E-01 9.366E-03 1.545E+00 4.547E-01 5.451E+01
- 260 6.395E-01 1.000E-05 1.545E+00 4.547E-01 5.451E+01
- 261 6.395E-01 1.000E-05 1.545E+00 4.547E-01 5.451E+01
- 262 6.406E-01 1.045E-03 1.547E+00 4.526E-01 5.454E+01
- 263 6.416E-01 1.045E-03 1.549E+00 4.505E-01 5.457E+01
- 264 6.427E-01 1.045E-03 1.552E+00 4.485E-01 5.461E+01
- 265 6.463E-01 3.658E-03 1.559E+00 4.411E-01 5.472E+01
- 266 6.500E-01 3.658E-03 1.566E+00 4.337E-01 5.483E+01
- 267 6.537E-01 3.658E-03 1.574E+00 4.261E-01 5.493E+01
- 268 6.573E-01 3.658E-03 1.582E+00 4.184E-01 5.504E+01
- 269 6.610E-01 3.658E-03 1.589E+00 4.106E-01 5.514E+01
- 270 6.646E-01 3.658E-03 1.597E+00 4.027E-01 5.523E+01
- 271 6.683E-01 3.658E-03 1.605E+00 3.946E-01 5.533E+01
- 272 6.729E-01 4.652E-03 1.616E+00 3.842E-01 5.544E+01
- 273 6.776E-01 4.652E-03 1.626E+00 3.735E-01 5.555E+01
- 274 6.822E-01 4.652E-03 1.637E+00 3.627E-01 5.565E+01
- 275 6.869E-01 4.652E-03 1.648E+00 3.516E-01 5.575E+01
- 276 6.915E-01 4.652E-03 1.660E+00 3.402E-01 5.584E+01
- 277 6.975E-01 5.995E-03 1.675E+00 3.253E-01 5.595E+01
- 278 7.035E-01 5.995E-03 1.690E+00 3.099E-01 5.605E+01
- 279 7.095E-01 5.995E-03 1.706E+00 2.941E-01 5.614E+01
- 280 7.155E-01 5.995E-03 1.722E+00 2.779E-01 5.622E+01
- 281 7.215E-01 5.995E-03 1.739E+00 2.612E-01 5.629E+01
- 282 7.275E-01 5.995E-03 1.756E+00 2.440E-01 5.635E+01
- 283 7.341E-01 6.614E-03 1.776E+00 2.244E-01 5.641E+01
- 284 7.407E-01 6.614E-03 1.796E+00 2.042E-01 5.645E+01
- 285 7.474E-01 6.614E-03 1.817E+00 1.832E-01 5.648E+01
- 286 7.540E-01 6.614E-03 1.838E+00 1.616E-01 5.650E+01
- 287 7.594E-01 5.398E-03 1.857E+00 1.434E-01 5.651E+01
- 288 7.648E-01 5.398E-03 1.875E+00 1.247E-01 5.650E+01
- 289 7.656E-01 8.158E-04 1.878E+00 1.218E-01 5.650E+01
- 290 7.664E-01 8.158E-04 1.881E+00 1.189E-01 5.650E+01
- 291 7.672E-01 8.158E-04 1.884E+00 1.160E-01 5.650E+01
- 292 7.680E-01 8.158E-04 1.887E+00 1.131E-01 5.650E+01
- 293 7.688E-01 8.158E-04 1.890E+00 1.102E-01 5.649E+01
- 294 7.697E-01 8.158E-04 1.893E+00 1.072E-01 5.649E+01
- 295 7.713E-01 1.632E-03 1.899E+00 1.013E-01 5.649E+01
- 296 7.729E-01 1.632E-03 1.905E+00 9.531E-02 5.648E+01
- 297 7.746E-01 1.632E-03 1.911E+00 8.928E-02 5.647E+01
- 298 7.762E-01 1.632E-03 1.917E+00 8.320E-02 5.647E+01
- 299 7.778E-01 1.632E-03 1.923E+00 7.706E-02 5.646E+01
- 300 7.797E-01 1.883E-03 1.930E+00 6.990E-02 5.645E+01
- 301 7.816E-01 1.883E-03 1.937E+00 6.267E-02 5.644E+01
- 302 7.835E-01 1.883E-03 1.945E+00 5.536E-02 5.642E+01
- 303 7.849E-01 1.477E-03 1.950E+00 4.957E-02 5.641E+01
- 304 7.864E-01 1.477E-03 1.956E+00 4.373E-02 5.640E+01
- 305 7.876E-01 1.131E-03 1.961E+00 3.923E-02 5.639E+01
- 306 7.887E-01 1.131E-03 1.965E+00 3.470E-02 5.638E+01
- 307 7.896E-01 8.836E-04 1.969E+00 3.114E-02 5.638E+01
- 308 7.905E-01 8.836E-04 1.972E+00 2.756E-02 5.637E+01
- 309 7.912E-01 7.178E-04 1.975E+00 2.464E-02 5.636E+01
- 310 7.919E-01 7.178E-04 1.978E+00 2.171E-02 5.636E+01
- 311 7.925E-01 5.629E-04 1.981E+00 1.940E-02 5.635E+01
- 312 7.930E-01 5.629E-04 1.983E+00 1.708E-02 5.634E+01
- 313 7.935E-01 4.384E-04 1.985E+00 1.528E-02 5.634E+01
- 314 7.939E-01 4.384E-04 1.987E+00 1.346E-02 5.634E+01
- 315 7.942E-01 3.430E-04 1.988E+00 1.204E-02 5.633E+01
- 316 7.946E-01 3.430E-04 1.989E+00 1.062E-02 5.633E+01
- 317 7.948E-01 2.676E-04 1.990E+00 9.503E-03 5.633E+01
- 318 7.950E-01 1.789E-04 1.991E+00 8.757E-03 5.632E+01
- 319 7.952E-01 1.388E-04 1.992E+00 8.179E-03 5.632E+01
- 320 7.953E-01 1.388E-04 1.992E+00 7.599E-03 5.632E+01
- 321 7.954E-01 1.075E-04 1.993E+00 7.150E-03 5.632E+01
- 322 7.955E-01 1.075E-04 1.993E+00 6.701E-03 5.632E+01
- 323 7.955E-01 1.910E-05 1.993E+00 6.621E-03 5.632E+01
- 324 7.956E-01 1.910E-05 1.993E+00 6.541E-03 5.632E+01
- 325 7.956E-01 1.910E-05 1.994E+00 6.461E-03 5.632E+01
- 326 7.956E-01 1.910E-05 1.994E+00 6.381E-03 5.632E+01
- 327 7.956E-01 1.910E-05 1.994E+00 6.301E-03 5.632E+01
- 328 7.957E-01 3.820E-05 1.994E+00 6.142E-03 5.632E+01
- 329 7.957E-01 3.820E-05 1.994E+00 5.982E-03 5.632E+01
- 330 7.957E-01 3.820E-05 1.994E+00 5.822E-03 5.632E+01
- 331 7.958E-01 3.820E-05 1.994E+00 5.662E-03 5.632E+01
- 332 7.958E-01 3.820E-05 1.994E+00 5.502E-03 5.632E+01
- 333 7.959E-01 7.298E-05 1.995E+00 5.196E-03 5.632E+01
- 334 7.960E-01 7.298E-05 1.995E+00 4.890E-03 5.631E+01
- 335 7.960E-01 7.298E-05 1.995E+00 4.584E-03 5.631E+01
- 336 7.961E-01 7.298E-05 1.996E+00 4.278E-03 5.631E+01
- 337 7.962E-01 7.298E-05 1.996E+00 3.972E-03 5.631E+01
- 338 7.962E-01 7.298E-05 1.996E+00 3.666E-03 5.631E+01
- 339 7.963E-01 6.077E-05 1.997E+00 3.411E-03 5.631E+01
- 340 7.964E-01 6.077E-05 1.997E+00 3.155E-03 5.631E+01
- 341 7.964E-01 6.077E-05 1.997E+00 2.900E-03 5.631E+01
- 342 7.965E-01 4.812E-05 1.997E+00 2.698E-03 5.631E+01
- 343 7.965E-01 4.812E-05 1.998E+00 2.495E-03 5.631E+01
- 344 7.966E-01 4.812E-05 1.998E+00 2.293E-03 5.631E+01
- 345 7.966E-01 3.787E-05 1.998E+00 2.134E-03 5.631E+01
- 346 7.966E-01 3.787E-05 1.998E+00 1.974E-03 5.631E+01
- 347 7.967E-01 3.787E-05 1.998E+00 1.815E-03 5.631E+01
- 348 7.967E-01 2.995E-05 1.998E+00 1.689E-03 5.631E+01
- 349 7.967E-01 2.995E-05 1.998E+00 1.563E-03 5.631E+01
- 350 7.968E-01 2.995E-05 1.999E+00 1.436E-03 5.631E+01
- 351 7.968E-01 2.368E-05 1.999E+00 1.337E-03 5.631E+01
- 352 7.968E-01 2.368E-05 1.999E+00 1.237E-03 5.631E+01
- 353 7.968E-01 2.368E-05 1.999E+00 1.137E-03 5.631E+01
- 354 7.969E-01 1.876E-05 1.999E+00 1.058E-03 5.630E+01
- 355 7.969E-01 1.876E-05 1.999E+00 9.790E-04 5.630E+01
- 356 7.969E-01 1.876E-05 1.999E+00 9.000E-04 5.630E+01
- 357 7.969E-01 1.484E-05 1.999E+00 8.374E-04 5.630E+01
- 358 7.969E-01 1.484E-05 1.999E+00 7.748E-04 5.630E+01
- 359 7.969E-01 1.484E-05 1.999E+00 7.123E-04 5.630E+01
- 360 7.970E-01 1.175E-05 1.999E+00 6.627E-04 5.630E+01
- 361 7.970E-01 1.175E-05 1.999E+00 6.132E-04 5.630E+01
- 362 7.970E-01 1.175E-05 1.999E+00 5.636E-04 5.630E+01
- 363 7.970E-01 9.295E-06 1.999E+00 5.244E-04 5.630E+01
- 364 7.970E-01 9.295E-06 2.000E+00 4.852E-04 5.630E+01
- 365 7.970E-01 9.295E-06 2.000E+00 4.460E-04 5.630E+01
- 366 7.970E-01 7.359E-06 2.000E+00 4.150E-04 5.630E+01
- 367 7.970E-01 7.359E-06 2.000E+00 3.839E-04 5.630E+01
- 368 7.970E-01 7.359E-06 2.000E+00 3.529E-04 5.630E+01
- 369 7.970E-01 5.820E-06 2.000E+00 3.283E-04 5.630E+01
- 370 7.970E-01 5.820E-06 2.000E+00 3.038E-04 5.630E+01
- 371 7.970E-01 5.820E-06 2.000E+00 2.792E-04 5.630E+01
- 372 7.971E-01 4.607E-06 2.000E+00 2.598E-04 5.630E+01
- 373 7.971E-01 4.607E-06 2.000E+00 2.404E-04 5.630E+01
- 374 7.971E-01 4.607E-06 2.000E+00 2.209E-04 5.630E+01
- 375 7.971E-01 3.644E-06 2.000E+00 2.056E-04 5.630E+01
- 376 7.971E-01 3.644E-06 2.000E+00 1.902E-04 5.630E+01
- 377 7.971E-01 3.644E-06 2.000E+00 1.748E-04 5.630E+01
- 378 7.971E-01 2.884E-06 2.000E+00 1.626E-04 5.630E+01
- 379 7.971E-01 2.884E-06 2.000E+00 1.505E-04 5.630E+01
- 380 7.971E-01 2.884E-06 2.000E+00 1.383E-04 5.630E+01
- 381 7.971E-01 2.281E-06 2.000E+00 1.287E-04 5.630E+01
- 382 7.971E-01 2.281E-06 2.000E+00 1.191E-04 5.630E+01
- 383 7.971E-01 2.281E-06 2.000E+00 1.094E-04 5.630E+01
- 384 7.971E-01 1.789E-06 2.000E+00 1.019E-04 5.630E+01
- 385 7.971E-01 4.481E-07 2.000E+00 9.999E-05 5.630E+01
-
- is psifac dpsi q singfac eval1
-
- Gaussian Reduction at istep = 385, psi = 7.971E-01, q = 2.000
-
- ising psi q di re alpha im alpha
-
- 2 9.350E-01 3.000E+00 -2.579E-01 5.078E-01 -0.000E+00
-
-
- is psifac dpsi q singfac eval1
-
- 386 7.971E-01 4.739E-05 2.000E+00 9.999E-01 5.630E+01
- 387 7.971E-01 2.779E-08 2.000E+00 9.999E-01 5.630E+01
- 388 7.971E-01 2.779E-08 2.000E+00 9.999E-01 5.630E+01
- 389 7.971E-01 5.558E-08 2.000E+00 9.999E-01 5.630E+01
- 390 7.971E-01 5.558E-08 2.000E+00 9.999E-01 5.630E+01
- 391 7.971E-01 5.558E-08 2.000E+00 9.999E-01 5.630E+01
- 392 7.971E-01 3.299E-07 2.000E+00 9.999E-01 5.630E+01
- 393 7.971E-01 3.299E-07 2.000E+00 9.999E-01 5.630E+01
- 394 7.971E-01 3.299E-07 2.000E+00 9.999E-01 5.630E+01
- 395 7.971E-01 3.299E-07 2.000E+00 9.999E-01 5.630E+01
- 396 7.971E-01 9.168E-07 2.000E+00 9.999E-01 5.630E+01
- 397 7.971E-01 9.168E-07 2.000E+00 9.999E-01 5.630E+01
- 398 7.971E-01 9.168E-07 2.000E+00 9.999E-01 5.630E+01
- 399 7.971E-01 9.168E-07 2.000E+00 9.999E-01 5.630E+01
- 400 7.971E-01 9.168E-07 2.000E+00 9.999E-01 5.630E+01
- 401 7.971E-01 1.428E-06 2.000E+00 9.999E-01 5.630E+01
- 402 7.971E-01 1.428E-06 2.000E+00 9.999E-01 5.630E+01
- 403 7.971E-01 1.428E-06 2.000E+00 9.999E-01 5.630E+01
- 404 7.972E-01 1.428E-06 2.000E+00 9.999E-01 5.630E+01
- 405 7.972E-01 1.428E-06 2.000E+00 9.998E-01 5.630E+01
- 406 7.972E-01 1.860E-06 2.000E+00 9.998E-01 5.630E+01
- 407 7.972E-01 1.860E-06 2.000E+00 9.998E-01 5.630E+01
- 408 7.972E-01 1.860E-06 2.000E+00 9.998E-01 5.630E+01
- 409 7.972E-01 1.860E-06 2.000E+00 9.998E-01 5.630E+01
- 410 7.972E-01 1.860E-06 2.000E+00 9.998E-01 5.630E+01
- 411 7.972E-01 2.467E-06 2.000E+00 9.998E-01 5.630E+01
- 412 7.972E-01 2.467E-06 2.000E+00 9.998E-01 5.630E+01
- 413 7.972E-01 2.467E-06 2.000E+00 9.998E-01 5.630E+01
- 414 7.972E-01 2.467E-06 2.000E+00 9.998E-01 5.630E+01
- 415 7.972E-01 2.467E-06 2.000E+00 9.998E-01 5.630E+01
- 416 7.972E-01 3.314E-06 2.000E+00 9.997E-01 5.630E+01
- 417 7.972E-01 3.314E-06 2.000E+00 9.997E-01 5.630E+01
- 418 7.972E-01 3.314E-06 2.000E+00 9.997E-01 5.630E+01
- 419 7.972E-01 3.314E-06 2.000E+00 9.997E-01 5.630E+01
- 420 7.972E-01 3.314E-06 2.000E+00 9.997E-01 5.630E+01
- 421 7.972E-01 4.511E-06 2.000E+00 9.997E-01 5.630E+01
- 422 7.972E-01 4.511E-06 2.000E+00 9.996E-01 5.630E+01
- 423 7.972E-01 4.511E-06 2.000E+00 9.996E-01 5.630E+01
- 424 7.972E-01 4.511E-06 2.000E+00 9.996E-01 5.630E+01
- 425 7.972E-01 4.511E-06 2.000E+00 9.996E-01 5.630E+01
- 426 7.972E-01 6.226E-06 2.000E+00 9.996E-01 5.630E+01
- 427 7.972E-01 6.226E-06 2.000E+00 9.995E-01 5.630E+01
- 428 7.972E-01 6.226E-06 2.000E+00 9.995E-01 5.630E+01
- 429 7.972E-01 6.226E-06 2.001E+00 9.995E-01 5.630E+01
- 430 7.972E-01 6.226E-06 2.001E+00 9.995E-01 5.630E+01
- 431 7.973E-01 8.718E-06 2.001E+00 9.994E-01 5.630E+01
- 432 7.973E-01 8.718E-06 2.001E+00 9.994E-01 5.630E+01
- 433 7.973E-01 8.718E-06 2.001E+00 9.993E-01 5.630E+01
- 434 7.973E-01 8.718E-06 2.001E+00 9.993E-01 5.630E+01
- 435 7.973E-01 8.718E-06 2.001E+00 9.993E-01 5.630E+01
- 436 7.973E-01 1.241E-05 2.001E+00 9.992E-01 5.630E+01
- 437 7.973E-01 1.241E-05 2.001E+00 9.992E-01 5.630E+01
- 438 7.973E-01 1.241E-05 2.001E+00 9.991E-01 5.630E+01
- 439 7.973E-01 1.241E-05 2.001E+00 9.991E-01 5.630E+01
- 440 7.973E-01 1.241E-05 2.001E+00 9.990E-01 5.630E+01
- 441 7.974E-01 1.798E-05 2.001E+00 9.989E-01 5.630E+01
- 442 7.974E-01 1.798E-05 2.001E+00 9.989E-01 5.630E+01
- 443 7.974E-01 1.798E-05 2.001E+00 9.988E-01 5.630E+01
- 444 7.974E-01 1.798E-05 2.001E+00 9.987E-01 5.630E+01
- 445 7.974E-01 1.798E-05 2.001E+00 9.986E-01 5.630E+01
- 446 7.975E-01 2.657E-05 2.001E+00 9.985E-01 5.630E+01
- 447 7.975E-01 2.657E-05 2.002E+00 9.984E-01 5.630E+01
- 448 7.975E-01 2.657E-05 2.002E+00 9.983E-01 5.630E+01
- 449 7.975E-01 2.657E-05 2.002E+00 9.982E-01 5.630E+01
- 450 7.976E-01 2.657E-05 2.002E+00 9.981E-01 5.630E+01
- 451 7.976E-01 4.009E-05 2.002E+00 9.979E-01 5.630E+01
- 452 7.977E-01 4.009E-05 2.002E+00 9.977E-01 5.630E+01
- 453 7.977E-01 4.009E-05 2.002E+00 9.976E-01 5.630E+01
- 454 7.977E-01 4.009E-05 2.003E+00 9.974E-01 5.630E+01
- 455 7.978E-01 4.009E-05 2.003E+00 9.972E-01 5.630E+01
- 456 7.978E-01 6.170E-05 2.003E+00 9.970E-01 5.630E+01
- 457 7.979E-01 6.170E-05 2.003E+00 9.967E-01 5.629E+01
- 458 7.980E-01 6.170E-05 2.004E+00 9.964E-01 5.629E+01
- 459 7.980E-01 6.170E-05 2.004E+00 9.962E-01 5.629E+01
- 460 7.981E-01 6.170E-05 2.004E+00 9.959E-01 5.629E+01
- 461 7.982E-01 9.647E-05 2.004E+00 9.955E-01 5.629E+01
- 462 7.983E-01 9.647E-05 2.005E+00 9.951E-01 5.629E+01
- 463 7.984E-01 9.647E-05 2.005E+00 9.947E-01 5.629E+01
- 464 7.985E-01 9.647E-05 2.006E+00 9.943E-01 5.629E+01
- 465 7.986E-01 9.647E-05 2.006E+00 9.939E-01 5.629E+01
- 466 7.987E-01 1.517E-04 2.007E+00 9.932E-01 5.628E+01
- 467 7.989E-01 1.517E-04 2.007E+00 9.926E-01 5.628E+01
- 468 7.990E-01 1.517E-04 2.008E+00 9.919E-01 5.628E+01
- 469 7.992E-01 1.517E-04 2.009E+00 9.913E-01 5.628E+01
- 470 7.993E-01 1.517E-04 2.009E+00 9.906E-01 5.628E+01
- 471 7.996E-01 2.376E-04 2.010E+00 9.896E-01 5.627E+01
- 472 7.998E-01 2.376E-04 2.011E+00 9.886E-01 5.627E+01
- 473 8.000E-01 2.376E-04 2.012E+00 9.876E-01 5.627E+01
- 474 8.003E-01 2.376E-04 2.013E+00 9.866E-01 5.627E+01
- 475 8.005E-01 2.376E-04 2.014E+00 9.855E-01 5.626E+01
- 476 8.011E-01 5.854E-04 2.017E+00 9.830E-01 5.626E+01
- 477 8.017E-01 5.854E-04 2.020E+00 9.805E-01 5.625E+01
- 478 8.023E-01 5.854E-04 2.022E+00 9.779E-01 5.624E+01
- 479 8.029E-01 5.854E-04 2.025E+00 9.754E-01 5.623E+01
- 480 8.034E-01 5.854E-04 2.027E+00 9.728E-01 5.622E+01
- 481 8.050E-01 1.514E-03 2.034E+00 9.661E-01 5.620E+01
- 482 8.065E-01 1.514E-03 2.041E+00 9.594E-01 5.618E+01
- 483 8.080E-01 1.514E-03 2.047E+00 9.526E-01 5.616E+01
- 484 8.095E-01 1.514E-03 2.054E+00 9.458E-01 5.614E+01
- 485 8.110E-01 1.514E-03 2.061E+00 9.389E-01 5.611E+01
- 486 8.137E-01 2.685E-03 2.074E+00 9.264E-01 5.607E+01
- 487 8.164E-01 2.685E-03 2.086E+00 9.138E-01 5.602E+01
- 488 8.191E-01 2.685E-03 2.099E+00 9.010E-01 5.597E+01
- 489 8.217E-01 2.685E-03 2.112E+00 8.879E-01 5.592E+01
- 490 8.244E-01 2.685E-03 2.125E+00 8.746E-01 5.587E+01
- 491 8.279E-01 3.423E-03 2.143E+00 8.573E-01 5.580E+01
- 492 8.313E-01 3.423E-03 2.160E+00 8.397E-01 5.572E+01
- 493 8.347E-01 3.423E-03 2.178E+00 8.216E-01 5.564E+01
- 494 8.381E-01 3.423E-03 2.197E+00 8.031E-01 5.555E+01
- 495 8.415E-01 3.423E-03 2.216E+00 7.841E-01 5.546E+01
- 496 8.455E-01 3.951E-03 2.238E+00 7.617E-01 5.536E+01
- 497 8.495E-01 3.951E-03 2.261E+00 7.387E-01 5.524E+01
- 498 8.534E-01 3.951E-03 2.285E+00 7.150E-01 5.512E+01
- 499 8.574E-01 3.951E-03 2.309E+00 6.906E-01 5.500E+01
- 500 8.613E-01 3.951E-03 2.335E+00 6.654E-01 5.487E+01
- 501 8.653E-01 3.951E-03 2.360E+00 6.396E-01 5.473E+01
- 502 8.692E-01 3.951E-03 2.387E+00 6.129E-01 5.458E+01
- 503 8.725E-01 3.279E-03 2.410E+00 5.901E-01 5.446E+01
- 504 8.758E-01 3.279E-03 2.433E+00 5.668E-01 5.433E+01
- 505 8.790E-01 3.279E-03 2.457E+00 5.428E-01 5.420E+01
- 506 8.823E-01 3.279E-03 2.482E+00 5.181E-01 5.406E+01
- 507 8.856E-01 3.279E-03 2.507E+00 4.928E-01 5.392E+01
- 508 8.889E-01 3.279E-03 2.533E+00 4.668E-01 5.377E+01
- 509 8.922E-01 3.279E-03 2.560E+00 4.400E-01 5.362E+01
- 510 8.949E-01 2.708E-03 2.583E+00 4.173E-01 5.349E+01
- 511 8.976E-01 2.708E-03 2.606E+00 3.940E-01 5.335E+01
- 512 9.003E-01 2.708E-03 2.630E+00 3.702E-01 5.321E+01
- 513 9.030E-01 2.708E-03 2.654E+00 3.457E-01 5.307E+01
- 514 9.057E-01 2.708E-03 2.679E+00 3.206E-01 5.293E+01
- 515 9.079E-01 2.241E-03 2.701E+00 2.994E-01 5.281E+01
- 516 9.102E-01 2.241E-03 2.722E+00 2.776E-01 5.268E+01
- 517 9.124E-01 2.241E-03 2.745E+00 2.554E-01 5.256E+01
- 518 9.142E-01 1.824E-03 2.763E+00 2.370E-01 5.245E+01
- 519 9.161E-01 1.824E-03 2.782E+00 2.182E-01 5.234E+01
- 520 9.179E-01 1.824E-03 2.801E+00 1.991E-01 5.223E+01
- 521 9.193E-01 1.417E-03 2.816E+00 1.839E-01 5.214E+01
- 522 9.207E-01 1.417E-03 2.831E+00 1.686E-01 5.206E+01
- 523 9.221E-01 1.417E-03 2.847E+00 1.530E-01 5.197E+01
- 524 9.232E-01 1.076E-03 2.859E+00 1.410E-01 5.190E+01
- 525 9.243E-01 1.076E-03 2.871E+00 1.289E-01 5.183E+01
- 526 9.252E-01 8.910E-04 2.881E+00 1.187E-01 5.177E+01
- 527 9.261E-01 8.910E-04 2.892E+00 1.085E-01 5.171E+01
- 528 9.270E-01 8.910E-04 2.902E+00 9.811E-02 5.166E+01
- 529 9.276E-01 6.763E-04 2.910E+00 9.018E-02 5.161E+01
- 530 9.283E-01 6.763E-04 2.918E+00 8.220E-02 5.157E+01
- 531 9.289E-01 5.595E-04 2.924E+00 7.554E-02 5.153E+01
- 532 9.294E-01 5.595E-04 2.931E+00 6.885E-02 5.149E+01
- 533 9.300E-01 5.595E-04 2.938E+00 6.211E-02 5.145E+01
- 534 9.304E-01 4.247E-04 2.943E+00 5.697E-02 5.142E+01
- 535 9.309E-01 4.247E-04 2.948E+00 5.180E-02 5.139E+01
- 536 9.312E-01 3.512E-04 2.952E+00 4.750E-02 5.137E+01
- 537 9.316E-01 3.512E-04 2.957E+00 4.319E-02 5.135E+01
- 538 9.319E-01 3.512E-04 2.961E+00 3.887E-02 5.132E+01
- 539 9.322E-01 2.669E-04 2.964E+00 3.557E-02 5.130E+01
- 540 9.324E-01 2.669E-04 2.968E+00 3.226E-02 5.128E+01
- 541 9.327E-01 2.202E-04 2.970E+00 2.952E-02 5.127E+01
- 542 9.329E-01 2.202E-04 2.973E+00 2.677E-02 5.125E+01
- 543 9.331E-01 1.833E-04 2.976E+00 2.448E-02 5.124E+01
- 544 9.332E-01 1.833E-04 2.978E+00 2.218E-02 5.123E+01
- 545 9.334E-01 1.518E-04 2.980E+00 2.028E-02 5.122E+01
- 546 9.336E-01 1.518E-04 2.982E+00 1.837E-02 5.121E+01
- 547 9.337E-01 1.258E-04 2.983E+00 1.678E-02 5.120E+01
- 548 9.338E-01 1.258E-04 2.985E+00 1.520E-02 5.119E+01
- 549 9.339E-01 1.040E-04 2.986E+00 1.388E-02 5.118E+01
- 550 9.340E-01 1.040E-04 2.987E+00 1.257E-02 5.117E+01
- 551 9.341E-01 8.590E-05 2.989E+00 1.148E-02 5.117E+01
- 552 9.342E-01 8.590E-05 2.990E+00 1.039E-02 5.116E+01
- 553 9.343E-01 7.090E-05 2.991E+00 9.491E-03 5.116E+01
- 554 9.343E-01 8.147E-06 2.991E+00 9.387E-03 5.116E+01
- 555 9.343E-01 8.147E-06 2.991E+00 9.284E-03 5.116E+01
- 556 9.343E-01 8.147E-06 2.991E+00 9.181E-03 5.115E+01
- 557 9.343E-01 8.147E-06 2.991E+00 9.077E-03 5.115E+01
- 558 9.343E-01 8.147E-06 2.991E+00 8.974E-03 5.115E+01
- 559 9.343E-01 1.629E-05 2.991E+00 8.767E-03 5.115E+01
- 560 9.343E-01 1.629E-05 2.991E+00 8.560E-03 5.115E+01
- 561 9.343E-01 1.629E-05 2.992E+00 8.353E-03 5.115E+01
- 562 9.344E-01 1.629E-05 2.992E+00 8.146E-03 5.115E+01
- 563 9.344E-01 2.883E-05 2.992E+00 7.779E-03 5.115E+01
- 564 9.344E-01 2.883E-05 2.993E+00 7.413E-03 5.114E+01
- 565 9.344E-01 2.883E-05 2.993E+00 7.046E-03 5.114E+01
- 566 9.345E-01 2.883E-05 2.993E+00 6.679E-03 5.114E+01
- 567 9.345E-01 2.883E-05 2.994E+00 6.313E-03 5.114E+01
- 568 9.345E-01 2.883E-05 2.994E+00 5.946E-03 5.114E+01
- 569 9.346E-01 2.883E-05 2.994E+00 5.578E-03 5.113E+01
- 570 9.346E-01 2.301E-05 2.995E+00 5.285E-03 5.113E+01
- 571 9.346E-01 2.301E-05 2.995E+00 4.992E-03 5.113E+01
- 572 9.346E-01 2.301E-05 2.995E+00 4.699E-03 5.113E+01
- 573 9.347E-01 2.301E-05 2.996E+00 4.405E-03 5.113E+01
- 574 9.347E-01 1.819E-05 2.996E+00 4.173E-03 5.113E+01
- 575 9.347E-01 1.819E-05 2.996E+00 3.941E-03 5.113E+01
- 576 9.347E-01 1.819E-05 2.996E+00 3.709E-03 5.112E+01
- 577 9.347E-01 1.819E-05 2.997E+00 3.477E-03 5.112E+01
- 578 9.347E-01 1.438E-05 2.997E+00 3.294E-03 5.112E+01
- 579 9.348E-01 1.438E-05 2.997E+00 3.110E-03 5.112E+01
-
- is psifac dpsi q singfac eval1
-
- Gaussian Reduction at istep = 580, psi = 9.348E-01, q = 2.997
-
- is psifac dpsi q singfac eval1
-
- 580 9.348E-01 1.438E-05 2.997E+00 2.927E-03 5.112E+01
- 581 9.348E-01 2.502E-07 2.997E+00 2.924E-03 5.112E+01
- 582 9.348E-01 2.502E-07 2.997E+00 2.920E-03 5.112E+01
- 583 9.348E-01 5.004E-07 2.997E+00 2.914E-03 5.112E+01
- 584 9.348E-01 5.004E-07 2.997E+00 2.908E-03 5.112E+01
- 585 9.348E-01 5.004E-07 2.997E+00 2.901E-03 5.112E+01
- 586 9.348E-01 3.206E-06 2.997E+00 2.860E-03 5.112E+01
- 587 9.348E-01 3.206E-06 2.997E+00 2.819E-03 5.112E+01
- 588 9.348E-01 3.206E-06 2.997E+00 2.778E-03 5.112E+01
- 589 9.348E-01 3.206E-06 2.997E+00 2.737E-03 5.112E+01
- 590 9.348E-01 7.723E-06 2.997E+00 2.639E-03 5.112E+01
- 591 9.348E-01 7.723E-06 2.997E+00 2.540E-03 5.112E+01
- 592 9.348E-01 7.723E-06 2.998E+00 2.442E-03 5.112E+01
- 593 9.348E-01 7.723E-06 2.998E+00 2.343E-03 5.112E+01
- 594 9.348E-01 7.723E-06 2.998E+00 2.244E-03 5.112E+01
- 595 9.348E-01 1.008E-05 2.998E+00 2.115E-03 5.112E+01
- 596 9.348E-01 1.008E-05 2.998E+00 1.987E-03 5.111E+01
- 597 9.349E-01 1.008E-05 2.998E+00 1.858E-03 5.111E+01
- 598 9.349E-01 1.008E-05 2.998E+00 1.729E-03 5.111E+01
- 599 9.349E-01 1.008E-05 2.998E+00 1.600E-03 5.111E+01
- 600 9.349E-01 1.008E-05 2.999E+00 1.471E-03 5.111E+01
- 601 9.349E-01 7.943E-06 2.999E+00 1.370E-03 5.111E+01
- 602 9.349E-01 7.943E-06 2.999E+00 1.268E-03 5.111E+01
- 603 9.349E-01 7.943E-06 2.999E+00 1.167E-03 5.111E+01
- 604 9.349E-01 6.332E-06 2.999E+00 1.086E-03 5.111E+01
- 605 9.349E-01 6.332E-06 2.999E+00 1.005E-03 5.111E+01
- 606 9.349E-01 6.332E-06 2.999E+00 9.236E-04 5.111E+01
- 607 9.349E-01 5.029E-06 2.999E+00 8.593E-04 5.111E+01
- 608 9.349E-01 5.029E-06 2.999E+00 7.950E-04 5.111E+01
- 609 9.349E-01 5.029E-06 2.999E+00 7.306E-04 5.111E+01
- 610 9.349E-01 3.999E-06 2.999E+00 6.794E-04 5.111E+01
- 611 9.349E-01 3.999E-06 2.999E+00 6.283E-04 5.111E+01
- 612 9.350E-01 3.999E-06 2.999E+00 5.771E-04 5.111E+01
- 613 9.350E-01 3.170E-06 2.999E+00 5.365E-04 5.111E+01
- 614 9.350E-01 3.170E-06 3.000E+00 4.960E-04 5.111E+01
- 615 9.350E-01 3.170E-06 3.000E+00 4.554E-04 5.111E+01
- 616 9.350E-01 2.501E-06 3.000E+00 4.234E-04 5.111E+01
- 617 9.350E-01 2.501E-06 3.000E+00 3.914E-04 5.111E+01
- 618 9.350E-01 2.501E-06 3.000E+00 3.594E-04 5.111E+01
- 619 9.350E-01 1.971E-06 3.000E+00 3.341E-04 5.111E+01
- 620 9.350E-01 1.971E-06 3.000E+00 3.089E-04 5.111E+01
- 621 9.350E-01 1.971E-06 3.000E+00 2.837E-04 5.111E+01
- 622 9.350E-01 1.552E-06 3.000E+00 2.638E-04 5.110E+01
- 623 9.350E-01 1.552E-06 3.000E+00 2.440E-04 5.110E+01
- 624 9.350E-01 1.552E-06 3.000E+00 2.241E-04 5.110E+01
- 625 9.350E-01 1.224E-06 3.000E+00 2.084E-04 5.110E+01
- 626 9.350E-01 1.224E-06 3.000E+00 1.928E-04 5.110E+01
- 627 9.350E-01 1.224E-06 3.000E+00 1.771E-04 5.110E+01
- 628 9.350E-01 9.663E-07 3.000E+00 1.647E-04 5.110E+01
- 629 9.350E-01 9.663E-07 3.000E+00 1.524E-04 5.110E+01
- 630 9.350E-01 9.663E-07 3.000E+00 1.400E-04 5.110E+01
- 631 9.350E-01 7.639E-07 3.000E+00 1.302E-04 5.110E+01
- 632 9.350E-01 7.639E-07 3.000E+00 1.204E-04 5.110E+01
- 633 9.350E-01 7.639E-07 3.000E+00 1.106E-04 5.110E+01
- 634 9.350E-01 6.040E-07 3.000E+00 1.029E-04 5.110E+01
- 635 9.350E-01 2.278E-07 3.000E+00 1.000E-04 5.110E+01
-
- is psifac dpsi q singfac eval1
-
- Gaussian Reduction at istep = 635, psi = 9.350E-01, q = 3.000
-
- is psifac dpsi q singfac eval1
-
- 636 9.350E-01 1.562E-05 3.000E+00 9.999E-01 5.110E+01
- 637 9.350E-01 1.045E-08 3.000E+00 9.999E-01 5.110E+01
- 638 9.350E-01 1.045E-08 3.000E+00 9.999E-01 5.110E+01
- 639 9.350E-01 2.091E-08 3.000E+00 9.999E-01 5.110E+01
- 640 9.350E-01 2.091E-08 3.000E+00 9.999E-01 5.110E+01
- 641 9.350E-01 2.091E-08 3.000E+00 9.999E-01 5.110E+01
- 642 9.350E-01 1.315E-07 3.000E+00 9.999E-01 5.110E+01
- 643 9.350E-01 1.315E-07 3.000E+00 9.999E-01 5.110E+01
- 644 9.350E-01 1.315E-07 3.000E+00 9.999E-01 5.110E+01
- 645 9.350E-01 1.315E-07 3.000E+00 9.999E-01 5.110E+01
- 646 9.350E-01 3.906E-07 3.000E+00 9.999E-01 5.110E+01
- 647 9.350E-01 3.906E-07 3.000E+00 9.999E-01 5.110E+01
- 648 9.350E-01 3.906E-07 3.000E+00 9.999E-01 5.110E+01
- 649 9.350E-01 3.906E-07 3.000E+00 9.999E-01 5.110E+01
- 650 9.350E-01 3.906E-07 3.000E+00 9.999E-01 5.110E+01
- 651 9.350E-01 5.176E-07 3.000E+00 9.999E-01 5.110E+01
- 652 9.350E-01 5.176E-07 3.000E+00 9.999E-01 5.110E+01
- 653 9.350E-01 5.176E-07 3.000E+00 9.998E-01 5.110E+01
- 654 9.350E-01 5.176E-07 3.000E+00 9.998E-01 5.110E+01
- 655 9.350E-01 5.176E-07 3.000E+00 9.998E-01 5.110E+01
- 656 9.350E-01 6.839E-07 3.000E+00 9.998E-01 5.110E+01
- 657 9.350E-01 6.839E-07 3.000E+00 9.998E-01 5.110E+01
- 658 9.350E-01 6.839E-07 3.000E+00 9.998E-01 5.110E+01
- 659 9.350E-01 6.839E-07 3.000E+00 9.998E-01 5.110E+01
- 660 9.350E-01 6.839E-07 3.000E+00 9.998E-01 5.110E+01
- 661 9.350E-01 9.142E-07 3.000E+00 9.998E-01 5.110E+01
- 662 9.350E-01 9.142E-07 3.000E+00 9.998E-01 5.110E+01
- 663 9.350E-01 9.142E-07 3.000E+00 9.998E-01 5.110E+01
- 664 9.350E-01 9.142E-07 3.000E+00 9.997E-01 5.110E+01
- 665 9.350E-01 9.142E-07 3.000E+00 9.997E-01 5.110E+01
- 666 9.350E-01 1.236E-06 3.000E+00 9.997E-01 5.110E+01
- 667 9.350E-01 1.236E-06 3.000E+00 9.997E-01 5.110E+01
- 668 9.350E-01 1.236E-06 3.000E+00 9.997E-01 5.110E+01
- 669 9.350E-01 1.236E-06 3.000E+00 9.997E-01 5.110E+01
- 670 9.350E-01 1.236E-06 3.000E+00 9.997E-01 5.110E+01
- 671 9.350E-01 1.694E-06 3.000E+00 9.996E-01 5.110E+01
- 672 9.350E-01 1.694E-06 3.000E+00 9.996E-01 5.110E+01
- 673 9.350E-01 1.694E-06 3.000E+00 9.996E-01 5.110E+01
- 674 9.350E-01 1.694E-06 3.000E+00 9.996E-01 5.110E+01
- 675 9.350E-01 1.694E-06 3.000E+00 9.995E-01 5.110E+01
- 676 9.350E-01 2.352E-06 3.000E+00 9.995E-01 5.110E+01
- 677 9.350E-01 2.352E-06 3.001E+00 9.995E-01 5.110E+01
- 678 9.350E-01 2.352E-06 3.001E+00 9.995E-01 5.110E+01
- 679 9.350E-01 2.352E-06 3.001E+00 9.994E-01 5.110E+01
- 680 9.350E-01 2.352E-06 3.001E+00 9.994E-01 5.110E+01
- 681 9.350E-01 3.316E-06 3.001E+00 9.994E-01 5.110E+01
- 682 9.351E-01 3.316E-06 3.001E+00 9.993E-01 5.110E+01
- 683 9.351E-01 3.316E-06 3.001E+00 9.993E-01 5.110E+01
- 684 9.351E-01 3.316E-06 3.001E+00 9.992E-01 5.110E+01
- 685 9.351E-01 3.316E-06 3.001E+00 9.992E-01 5.110E+01
- 686 9.351E-01 4.754E-06 3.001E+00 9.991E-01 5.110E+01
- 687 9.351E-01 4.754E-06 3.001E+00 9.991E-01 5.110E+01
- 688 9.351E-01 4.754E-06 3.001E+00 9.990E-01 5.110E+01
- 689 9.351E-01 4.754E-06 3.001E+00 9.989E-01 5.110E+01
- 690 9.351E-01 4.754E-06 3.001E+00 9.989E-01 5.110E+01
- 691 9.351E-01 6.942E-06 3.001E+00 9.988E-01 5.110E+01
- 692 9.351E-01 6.942E-06 3.001E+00 9.987E-01 5.110E+01
- 693 9.351E-01 6.942E-06 3.001E+00 9.986E-01 5.110E+01
- 694 9.351E-01 6.942E-06 3.001E+00 9.985E-01 5.110E+01
- 695 9.351E-01 6.942E-06 3.002E+00 9.984E-01 5.110E+01
- 696 9.351E-01 1.034E-05 3.002E+00 9.983E-01 5.109E+01
- 697 9.351E-01 1.034E-05 3.002E+00 9.982E-01 5.109E+01
- 698 9.352E-01 1.034E-05 3.002E+00 9.980E-01 5.109E+01
- 699 9.352E-01 1.034E-05 3.002E+00 9.979E-01 5.109E+01
- 700 9.352E-01 1.034E-05 3.002E+00 9.978E-01 5.109E+01
- 701 9.352E-01 1.575E-05 3.002E+00 9.976E-01 5.109E+01
- 702 9.352E-01 1.575E-05 3.003E+00 9.974E-01 5.109E+01
- 703 9.352E-01 1.575E-05 3.003E+00 9.972E-01 5.109E+01
- 704 9.352E-01 1.575E-05 3.003E+00 9.970E-01 5.109E+01
- 705 9.353E-01 1.575E-05 3.003E+00 9.968E-01 5.109E+01
- 706 9.353E-01 2.460E-05 3.004E+00 9.964E-01 5.108E+01
- 707 9.353E-01 2.460E-05 3.004E+00 9.961E-01 5.108E+01
- 708 9.353E-01 2.460E-05 3.004E+00 9.958E-01 5.108E+01
- 709 9.353E-01 2.460E-05 3.005E+00 9.955E-01 5.108E+01
- 710 9.354E-01 2.460E-05 3.005E+00 9.952E-01 5.108E+01
- 711 9.354E-01 3.947E-05 3.005E+00 9.947E-01 5.107E+01
- 712 9.355E-01 3.947E-05 3.006E+00 9.942E-01 5.107E+01
- 713 9.355E-01 3.947E-05 3.006E+00 9.937E-01 5.107E+01
- 714 9.355E-01 3.947E-05 3.007E+00 9.931E-01 5.107E+01
- 715 9.356E-01 3.947E-05 3.007E+00 9.926E-01 5.106E+01
- 716 9.356E-01 6.529E-05 3.008E+00 9.918E-01 5.106E+01
- 717 9.357E-01 6.529E-05 3.009E+00 9.910E-01 5.105E+01
- 718 9.358E-01 6.529E-05 3.010E+00 9.901E-01 5.105E+01
- 719 9.358E-01 6.529E-05 3.011E+00 9.893E-01 5.104E+01
- 720 9.359E-01 6.529E-05 3.012E+00 9.884E-01 5.104E+01
- 721 9.361E-01 1.767E-04 3.014E+00 9.861E-01 5.103E+01
- 722 9.363E-01 1.767E-04 3.016E+00 9.838E-01 5.101E+01
- 723 9.364E-01 1.767E-04 3.018E+00 9.815E-01 5.100E+01
- 724 9.366E-01 1.767E-04 3.021E+00 9.792E-01 5.099E+01
- 725 9.368E-01 1.767E-04 3.023E+00 9.769E-01 5.098E+01
- 726 9.372E-01 3.844E-04 3.028E+00 9.719E-01 5.095E+01
- 727 9.376E-01 3.844E-04 3.033E+00 9.668E-01 5.092E+01
- 728 9.379E-01 3.844E-04 3.038E+00 9.617E-01 5.089E+01
- 729 9.383E-01 3.844E-04 3.043E+00 9.566E-01 5.086E+01
- 730 9.387E-01 3.844E-04 3.049E+00 9.515E-01 5.083E+01
- 731 9.395E-01 7.966E-04 3.059E+00 9.408E-01 5.077E+01
- 732 9.403E-01 7.966E-04 3.070E+00 9.299E-01 5.071E+01
- 733 9.411E-01 7.966E-04 3.081E+00 9.190E-01 5.065E+01
- 734 9.419E-01 7.966E-04 3.092E+00 9.080E-01 5.059E+01
- 735 9.431E-01 1.190E-03 3.109E+00 8.913E-01 5.050E+01
- 736 9.443E-01 1.190E-03 3.126E+00 8.743E-01 5.041E+01
- 737 9.455E-01 1.190E-03 3.143E+00 8.571E-01 5.031E+01
- 738 9.467E-01 1.190E-03 3.160E+00 8.396E-01 5.022E+01
- 739 9.483E-01 1.639E-03 3.185E+00 8.151E-01 5.009E+01
- 740 9.493E-01 9.889E-04 3.200E+00 8.000E-01 5.000E+01
-
- is psifac dpsi q singfac eval1
-
diff --git a/src/DCON/validate/dcon.bin b/src/DCON/validate/dcon.bin
deleted file mode 100644
index c8aea93752..0000000000
Binary files a/src/DCON/validate/dcon.bin and /dev/null differ
diff --git a/src/DCON/validate/dcon.in b/src/DCON/validate/dcon.in
deleted file mode 100644
index da04682a1b..0000000000
--- a/src/DCON/validate/dcon.in
+++ /dev/null
@@ -1,64 +0,0 @@
-&DCON_CONTROL
- bal_flag=f ! Ideal MHD ballooning criterion for short wavelengths
- mat_flag=t ! Construct coefficient matrices for diagnostic purposes
- ode_flag=t ! Integrate ODE's for determining stability of internal long-wavelength mode (must be true for GPEC)
- vac_flag=t ! Compute plasma, vacuum, and total energies for free-boundary modes
- mer_flag=t ! Evaluate the Mercier criterian
-
- sas_flag=t ! Safety factor (q) limit determined as q_ir+dmlim where q_ir is the equil outermost rational
- dmlim=0.2 ! See sas_flag
- psiedge=1.00 ! If less then psilim, calculates dW(psi) between psiedge and psilim, then runs with truncation at max(dW)
- qlow=1.02 ! Integration initiated at q determined by minimum of qlow and q0 from equil
- qhigh=1e3 ! Integration terminated at q limit determined by minimum of qhigh and qa from equil
- sing_start=0 ! Start integration at the sing_start'th rational from the axis (psilow)
-
- nn=1 ! Toroidal mode number
- delta_mlow=8 ! Expands lower bound of Fourier harmonics
- delta_mhigh=8 ! Expands upper bound of Fourier harmonics
- delta_mband=0 ! Integration keeps only this wide a band of solutions along the diagonal in m,m'
- mthvac=512 ! Number of points used in splines over poloidal angle at plasma-vacuum interface. Overrides vac.in mth.
- thmax0=1 ! Linear multiplier on the automatic choice of theta integration bounds for high-n ideal ballooning stability computation (strictly, -inf to -inf)
-
- kin_flag = f ! Kinetic EL equation (default: false)
- con_flag = f ! Continue integration through layers (default: false)
- kinfac1 = 1.0 ! Scale factor for energy contribution (default : 1.0)
- kinfac2 = 1.0 ! Scale factor for torque contribution (default : 1.0)
- kingridtype = 0 ! Regular grid method (default : 0)
- passing_flag = t ! Includes passing particle effects (default: false)
- ktanh_flag = t ! Ignore kinetic effects in the core smoothly (default: false)
- ktc = 0.1 ! Parameter activated by ktanh_flag: roughly corresponds to core width ignored (default: 0.1)
- ktw = 50.0 ! Parameter activated by ktanh_flag: width of hyper-tangential functions (default: 50.0)
- ion_flag = t ! Include ion dW_k when kin_flag is true (summed with electron contribution if electron_flag true)
- electron_flag = f ! Include electron dW_k when kin_flag is true (summed with ion contribution if ion_flag true)
-
- tol_nr=1e-6 ! Relative tolerance of dynamic integration steps away from rationals
- tol_r=1e-7 ! Relative tolerance of dynamic integration steps near rationals
- crossover=1e-2 ! Fractional distance from rational q at which tolerance is switched to tol_r
- singfac_min=1e-4 ! Fractional distance from rational q at which ideal jump condition is enforced
- ucrit=1e4 ! Maximum fraction of solutions allowed before re-normalized
-
- termbycross_flag = f ! Terminate ODE solver in the event of a zero crossing
-
- use_classic_splines = f ! Use a classical cubic spline instead of tri-diagonal solution for splines with extrapolation boundary conditions
-/
-&DCON_OUTPUT
- out_ahg2msc=f ! Output deprecated ahg2msc.out files. This is used to communicate with vacuum, but is now done through memory.
-
- crit_break=t ! Color of the crit curve changes when crossing a singular surface
- ahb_flag=f ! Output normal magnetic field eigenvalues and eigenfunctons at plasma-vacuum interface (must be false for GPEC)
- msol_ahb=1 ! Number of eigenfunctions output by ahb_flag=t ?
- mthsurf0=1 ! Linear multiplier on number of boundary points used to display surface eigenfunctions for ahgb_flag=t
- bin_metric = t
- bin_euler=t ! Output M psi-by-M euler-lagrange solutions to binary file euler.bin
- bin_vac=f ! Output deprecated binary vacuum.bin containing vacuum energy matrices
- euler_stride=1 ! Output only every euler_stride'th psi step to binary file
- bin_fmat = t
- bin_gmat = t
- bin_kmat = t
- out_bal1=f ! Ascii output for bal_flag poloidal functions
- bin_bal1=f ! Binary output for bal_flag poloidal functions
- out_bal2=f ! Ascii output for bal_flag functions
- bin_bal2=f ! Binary output for bal_flag functions
-
- netcdf_out=t ! Replicate ascii dcon.out information in a netcdf file
-/
diff --git a/src/DCON/validate/dcon.out b/src/DCON/validate/dcon.out
deleted file mode 100644
index be6318e4ac..0000000000
--- a/src/DCON/validate/dcon.out
+++ /dev/null
@@ -1,2966 +0,0 @@
- Equilibrium: beta_1.00, Type: efit
-
- Jac_type = hamada, power_bp = 0, power_b = 0, power_r = 0
-
-
- mpsi mtheta psilow psihigh rs_right rs_left zs_top zs_bot
-
- 128 256 1.000E-02 9.900E-01 4.491E+00 1.513E+00 2.505E+00 -2.505E+00
-
-
- amean rmean aratio kappa delta1 delta2 volume
-
- 1.489E+00 3.002E+00 2.016E+00 1.682E+00 4.574E-01 4.574E-01 2.049E+02
-
-
- li1 li2 li3 ro zo psio
-
- 8.759E-01 6.986E-01 7.255E-01 3.118E+00 -2.918E-06 1.367E+00
-
-
- betap1 betap2 betat betan betaj bwall bt0
-
- 1.787E-01 1.425E-01 2.309E-02 9.363E-01 1.264E-01 4.928E-01 9.993E-01
-
-
- q0 qmin q95 qmax qa crnt I/aB
-
- 1.050E+00 1.050E+00 3.211E+00 4.085E+00 4.399E+00 3.669E+00 2.466E+00
-
-
-ipsi psifac f mu0 p dvdpsi q di dr ca1
-
- 0 1.000E-02 3.464E+00 3.411E-02 1.589E+02 1.052E+00 4.994E+00 5.148E+00 0.000E+00
- 1 1.015E-02 3.464E+00 3.410E-02 1.589E+02 1.052E+00 5.004E+00 5.157E+00 0.000E+00
- 2 1.059E-02 3.464E+00 3.408E-02 1.589E+02 1.052E+00 5.032E+00 5.184E+00 0.000E+00
- 3 1.133E-02 3.463E+00 3.404E-02 1.589E+02 1.053E+00 5.045E+00 5.195E+00 0.000E+00
- 4 1.236E-02 3.462E+00 3.399E-02 1.589E+02 1.053E+00 4.754E+00 4.903E+00 0.000E+00
- 5 1.369E-02 3.462E+00 3.392E-02 1.589E+02 1.053E+00 3.864E+00 4.014E+00 0.000E+00
- 6 1.530E-02 3.460E+00 3.384E-02 1.590E+02 1.053E+00 2.813E+00 2.968E+00 0.000E+00
- 7 1.721E-02 3.459E+00 3.374E-02 1.590E+02 1.054E+00 2.198E+00 2.355E+00 0.000E+00
- 8 1.942E-02 3.457E+00 3.363E-02 1.591E+02 1.054E+00 2.108E+00 2.264E+00 0.000E+00
- 9 2.191E-02 3.455E+00 3.350E-02 1.591E+02 1.055E+00 2.082E+00 2.237E+00 0.000E+00
- 10 2.468E-02 3.453E+00 3.336E-02 1.592E+02 1.055E+00 1.655E+00 1.812E+00 0.000E+00
- 11 2.775E-02 3.451E+00 3.320E-02 1.592E+02 1.056E+00 1.133E+00 1.293E+00 0.000E+00
- 12 3.110E-02 3.449E+00 3.303E-02 1.593E+02 1.057E+00 9.860E-01 1.147E+00 0.000E+00
- 13 3.473E-02 3.446E+00 3.284E-02 1.594E+02 1.058E+00 9.703E-01 1.130E+00 0.000E+00
- 14 3.864E-02 3.443E+00 3.264E-02 1.595E+02 1.059E+00 7.012E-01 8.639E-01 0.000E+00
- 15 4.283E-02 3.440E+00 3.243E-02 1.596E+02 1.060E+00 4.741E-01 6.395E-01 0.000E+00
- 16 4.730E-02 3.437E+00 3.220E-02 1.597E+02 1.061E+00 4.327E-01 5.975E-01 0.000E+00
- 17 5.204E-02 3.433E+00 3.196E-02 1.598E+02 1.062E+00 3.460E-01 5.122E-01 0.000E+00
- 18 5.705E-02 3.429E+00 3.171E-02 1.599E+02 1.063E+00 2.053E-01 3.746E-01 0.000E+00
- 19 6.232E-02 3.425E+00 3.144E-02 1.601E+02 1.065E+00 1.523E-01 3.222E-01 0.000E+00
- 20 6.786E-02 3.421E+00 3.117E-02 1.602E+02 1.066E+00 9.495E-02 2.661E-01 0.000E+00
- 21 7.366E-02 3.417E+00 3.088E-02 1.604E+02 1.068E+00 2.073E-02 1.942E-01 0.000E+00
- 22 7.971E-02 3.412E+00 3.057E-02 1.605E+02 1.070E+00 -1.830E-02 1.564E-01 0.000E+00
- 23 8.602E-02 3.408E+00 3.026E-02 1.607E+02 1.071E+00 -5.855E-02 1.178E-01 0.000E+00
- 24 9.258E-02 3.403E+00 2.993E-02 1.609E+02 1.073E+00 -9.976E-02 7.843E-02 0.000E+00
- 25 9.938E-02 3.398E+00 2.960E-02 1.611E+02 1.075E+00 -1.267E-01 5.288E-02 0.000E+00
- 26 1.064E-01 3.393E+00 2.925E-02 1.613E+02 1.078E+00 -1.567E-01 2.473E-02 0.000E+00
- 27 1.137E-01 3.387E+00 2.889E-02 1.616E+02 1.080E+00 -1.795E-01 3.573E-03 0.000E+00
- 28 1.212E-01 3.382E+00 2.853E-02 1.618E+02 1.082E+00 -1.974E-01 -1.288E-02 0.000E+00
- 29 1.290E-01 3.376E+00 2.815E-02 1.621E+02 1.085E+00 -2.178E-01 -3.138E-02 0.000E+00
- 30 1.369E-01 3.370E+00 2.777E-02 1.623E+02 1.088E+00 -2.310E-01 -4.309E-02 0.000E+00
- 31 1.451E-01 3.365E+00 2.737E-02 1.626E+02 1.091E+00 -2.432E-01 -5.380E-02 0.000E+00
- 32 1.535E-01 3.358E+00 2.697E-02 1.630E+02 1.094E+00 -2.553E-01 -6.417E-02 0.000E+00
- 33 1.621E-01 3.352E+00 2.656E-02 1.633E+02 1.097E+00 -2.638E-01 -7.120E-02 0.000E+00
- 34 1.709E-01 3.346E+00 2.614E-02 1.636E+02 1.100E+00 -2.714E-01 -7.728E-02 0.000E+00
- 35 1.799E-01 3.339E+00 2.572E-02 1.640E+02 1.104E+00 -2.784E-01 -8.277E-02 0.000E+00
- 36 1.891E-01 3.333E+00 2.528E-02 1.644E+02 1.108E+00 -2.840E-01 -8.689E-02 0.000E+00
- 37 1.985E-01 3.326E+00 2.485E-02 1.648E+02 1.112E+00 -2.885E-01 -8.996E-02 0.000E+00
- 38 2.081E-01 3.319E+00 2.440E-02 1.652E+02 1.116E+00 -2.923E-01 -9.237E-02 0.000E+00
- 39 2.179E-01 3.312E+00 2.395E-02 1.657E+02 1.120E+00 -2.955E-01 -9.419E-02 0.000E+00
- 40 2.278E-01 3.305E+00 2.350E-02 1.662E+02 1.125E+00 -2.981E-01 -9.539E-02 0.000E+00
- 41 2.379E-01 3.298E+00 2.304E-02 1.667E+02 1.130E+00 -3.000E-01 -9.603E-02 0.000E+00
- 42 2.481E-01 3.291E+00 2.258E-02 1.672E+02 1.135E+00 -3.016E-01 -9.630E-02 0.000E+00
- 43 2.585E-01 3.284E+00 2.211E-02 1.677E+02 1.140E+00 -3.027E-01 -9.616E-02 0.000E+00
- 44 2.690E-01 3.277E+00 2.164E-02 1.683E+02 1.146E+00 -3.035E-01 -9.571E-02 0.000E+00
- 45 2.797E-01 3.270E+00 2.117E-02 1.689E+02 1.152E+00 -3.040E-01 -9.506E-02 0.000E+00
- 46 2.905E-01 3.262E+00 2.069E-02 1.695E+02 1.158E+00 -3.043E-01 -9.413E-02 0.000E+00
- 47 3.014E-01 3.255E+00 2.022E-02 1.702E+02 1.165E+00 -3.042E-01 -9.295E-02 0.000E+00
- 48 3.125E-01 3.248E+00 1.974E-02 1.709E+02 1.171E+00 -3.040E-01 -9.167E-02 0.000E+00
- 49 3.237E-01 3.240E+00 1.926E-02 1.716E+02 1.178E+00 -3.037E-01 -9.029E-02 0.000E+00
- 50 3.349E-01 3.233E+00 1.878E-02 1.723E+02 1.186E+00 -3.032E-01 -8.875E-02 0.000E+00
- 51 3.463E-01 3.226E+00 1.830E-02 1.731E+02 1.194E+00 -3.025E-01 -8.711E-02 0.000E+00
- 52 3.578E-01 3.218E+00 1.782E-02 1.739E+02 1.202E+00 -3.018E-01 -8.542E-02 0.000E+00
- 53 3.693E-01 3.211E+00 1.734E-02 1.748E+02 1.210E+00 -3.010E-01 -8.370E-02 0.000E+00
- 54 3.809E-01 3.204E+00 1.687E-02 1.756E+02 1.219E+00 -3.001E-01 -8.190E-02 0.000E+00
- 55 3.926E-01 3.197E+00 1.639E-02 1.766E+02 1.229E+00 -2.992E-01 -8.007E-02 0.000E+00
- 56 4.044E-01 3.189E+00 1.592E-02 1.775E+02 1.238E+00 -2.982E-01 -7.824E-02 0.000E+00
- 57 4.162E-01 3.182E+00 1.544E-02 1.785E+02 1.249E+00 -2.972E-01 -7.640E-02 0.000E+00
- 58 4.281E-01 3.175E+00 1.498E-02 1.795E+02 1.259E+00 -2.962E-01 -7.455E-02 0.000E+00
- 59 4.400E-01 3.168E+00 1.451E-02 1.806E+02 1.270E+00 -2.951E-01 -7.271E-02 0.000E+00
- 60 4.520E-01 3.161E+00 1.405E-02 1.817E+02 1.282E+00 -2.940E-01 -7.087E-02 0.000E+00
- 61 4.640E-01 3.155E+00 1.359E-02 1.828E+02 1.294E+00 -2.929E-01 -6.905E-02 0.000E+00
- 62 4.760E-01 3.148E+00 1.313E-02 1.840E+02 1.306E+00 -2.918E-01 -6.725E-02 0.000E+00
- 63 4.880E-01 3.141E+00 1.269E-02 1.852E+02 1.320E+00 -2.907E-01 -6.547E-02 0.000E+00
- 64 5.000E-01 3.135E+00 1.224E-02 1.865E+02 1.333E+00 -2.896E-01 -6.373E-02 0.000E+00
- 65 5.120E-01 3.129E+00 1.180E-02 1.878E+02 1.348E+00 -2.886E-01 -6.200E-02 0.000E+00
- 66 5.240E-01 3.122E+00 1.137E-02 1.892E+02 1.363E+00 -2.875E-01 -6.030E-02 0.000E+00
- 67 5.360E-01 3.116E+00 1.094E-02 1.906E+02 1.378E+00 -2.864E-01 -5.864E-02 0.000E+00
- 68 5.480E-01 3.111E+00 1.052E-02 1.921E+02 1.394E+00 -2.854E-01 -5.700E-02 0.000E+00
- 69 5.600E-01 3.105E+00 1.011E-02 1.936E+02 1.411E+00 -2.843E-01 -5.540E-02 0.000E+00
- 70 5.719E-01 3.099E+00 9.697E-03 1.951E+02 1.429E+00 -2.833E-01 -5.384E-02 0.000E+00
- 71 5.838E-01 3.094E+00 9.297E-03 1.968E+02 1.447E+00 -2.823E-01 -5.231E-02 0.000E+00
- 72 5.956E-01 3.088E+00 8.903E-03 1.984E+02 1.466E+00 -2.814E-01 -5.081E-02 0.000E+00
- 73 6.074E-01 3.083E+00 8.517E-03 2.002E+02 1.486E+00 -2.804E-01 -4.934E-02 0.000E+00
- 74 6.191E-01 3.078E+00 8.139E-03 2.019E+02 1.507E+00 -2.795E-01 -4.791E-02 0.000E+00
- 75 6.307E-01 3.073E+00 7.769E-03 2.038E+02 1.528E+00 -2.785E-01 -4.652E-02 0.000E+00
- 76 6.422E-01 3.069E+00 7.407E-03 2.057E+02 1.551E+00 -2.776E-01 -4.516E-02 0.000E+00
- 77 6.537E-01 3.064E+00 7.054E-03 2.077E+02 1.574E+00 -2.768E-01 -4.383E-02 0.000E+00
- 78 6.651E-01 3.060E+00 6.709E-03 2.097E+02 1.598E+00 -2.759E-01 -4.253E-02 0.000E+00
- 79 6.763E-01 3.056E+00 6.373E-03 2.118E+02 1.624E+00 -2.751E-01 -4.127E-02 0.000E+00
- 80 6.875E-01 3.052E+00 6.046E-03 2.140E+02 1.650E+00 -2.743E-01 -4.003E-02 0.000E+00
- 81 6.986E-01 3.048E+00 5.728E-03 2.162E+02 1.677E+00 -2.735E-01 -3.883E-02 0.000E+00
- 82 7.095E-01 3.045E+00 5.419E-03 2.185E+02 1.706E+00 -2.727E-01 -3.766E-02 0.000E+00
- 83 7.203E-01 3.041E+00 5.119E-03 2.209E+02 1.735E+00 -2.719E-01 -3.651E-02 0.000E+00
- 84 7.310E-01 3.038E+00 4.828E-03 2.233E+02 1.766E+00 -2.712E-01 -3.540E-02 0.000E+00
- 85 7.415E-01 3.035E+00 4.547E-03 2.258E+02 1.798E+00 -2.705E-01 -3.431E-02 0.000E+00
- 86 7.519E-01 3.032E+00 4.276E-03 2.284E+02 1.832E+00 -2.698E-01 -3.325E-02 0.000E+00
- 87 7.621E-01 3.029E+00 4.014E-03 2.311E+02 1.866E+00 -2.691E-01 -3.221E-02 0.000E+00
- 88 7.722E-01 3.027E+00 3.761E-03 2.339E+02 1.902E+00 -2.684E-01 -3.120E-02 0.000E+00
- 89 7.821E-01 3.024E+00 3.518E-03 2.367E+02 1.939E+00 -2.678E-01 -3.021E-02 0.000E+00
- 90 7.919E-01 3.022E+00 3.284E-03 2.397E+02 1.978E+00 -2.672E-01 -2.925E-02 0.000E+00
- 91 8.015E-01 3.020E+00 3.060E-03 2.427E+02 2.019E+00 -2.665E-01 -2.831E-02 0.000E+00
- 92 8.109E-01 3.018E+00 2.845E-03 2.458E+02 2.060E+00 -2.659E-01 -2.739E-02 0.000E+00
- 93 8.201E-01 3.016E+00 2.640E-03 2.490E+02 2.104E+00 -2.654E-01 -2.649E-02 0.000E+00
- 94 8.291E-01 3.014E+00 2.444E-03 2.523E+02 2.149E+00 -2.648E-01 -2.561E-02 0.000E+00
- 95 8.379E-01 3.013E+00 2.257E-03 2.556E+02 2.196E+00 -2.642E-01 -2.475E-02 0.000E+00
- 96 8.465E-01 3.011E+00 2.079E-03 2.591E+02 2.244E+00 -2.637E-01 -2.390E-02 0.000E+00
- 97 8.549E-01 3.010E+00 1.911E-03 2.627E+02 2.294E+00 -2.632E-01 -2.308E-02 0.000E+00
- 98 8.631E-01 3.009E+00 1.751E-03 2.664E+02 2.346E+00 -2.627E-01 -2.227E-02 0.000E+00
- 99 8.710E-01 3.008E+00 1.600E-03 2.701E+02 2.400E+00 -2.622E-01 -2.148E-02 0.000E+00
- 100 8.788E-01 3.007E+00 1.458E-03 2.740E+02 2.455E+00 -2.617E-01 -2.071E-02 0.000E+00
- 101 8.863E-01 3.006E+00 1.324E-03 2.780E+02 2.513E+00 -2.612E-01 -1.995E-02 0.000E+00
- 102 8.936E-01 3.005E+00 1.198E-03 2.820E+02 2.572E+00 -2.608E-01 -1.920E-02 0.000E+00
- 103 9.006E-01 3.004E+00 1.081E-03 2.862E+02 2.633E+00 -2.603E-01 -1.847E-02 0.000E+00
- 104 9.074E-01 3.004E+00 9.715E-04 2.904E+02 2.696E+00 -2.599E-01 -1.775E-02 0.000E+00
- 105 9.140E-01 3.003E+00 8.697E-04 2.947E+02 2.760E+00 -2.594E-01 -1.704E-02 0.000E+00
- 106 9.203E-01 3.003E+00 7.753E-04 2.991E+02 2.827E+00 -2.590E-01 -1.635E-02 0.000E+00
- 107 9.263E-01 3.002E+00 6.882E-04 3.036E+02 2.895E+00 -2.586E-01 -1.566E-02 0.000E+00
- 108 9.321E-01 3.002E+00 6.081E-04 3.082E+02 2.964E+00 -2.582E-01 -1.497E-02 0.000E+00
- 109 9.377E-01 3.001E+00 5.348E-04 3.128E+02 3.035E+00 -2.578E-01 -1.431E-02 0.000E+00
- 110 9.430E-01 3.001E+00 4.678E-04 3.175E+02 3.107E+00 -2.574E-01 -1.368E-02 0.000E+00
- 111 9.480E-01 3.001E+00 4.069E-04 3.222E+02 3.180E+00 -2.570E-01 -1.304E-02 0.000E+00
- 112 9.527E-01 3.001E+00 3.519E-04 3.269E+02 3.254E+00 -2.566E-01 -1.237E-02 0.000E+00
- 113 9.572E-01 3.001E+00 3.028E-04 3.317E+02 3.328E+00 -2.562E-01 -1.169E-02 0.000E+00
- 114 9.614E-01 3.000E+00 2.592E-04 3.364E+02 3.402E+00 -2.559E-01 -1.104E-02 0.000E+00
- 115 9.653E-01 3.000E+00 2.206E-04 3.411E+02 3.476E+00 -2.555E-01 -1.048E-02 0.000E+00
- 116 9.689E-01 3.000E+00 1.864E-04 3.456E+02 3.549E+00 -2.553E-01 -1.004E-02 0.000E+00
- 117 9.723E-01 3.000E+00 1.561E-04 3.501E+02 3.620E+00 -2.550E-01 -9.620E-03 0.000E+00
- 118 9.753E-01 3.000E+00 1.296E-04 3.544E+02 3.689E+00 -2.548E-01 -9.151E-03 0.000E+00
- 119 9.781E-01 3.000E+00 1.068E-04 3.585E+02 3.755E+00 -2.545E-01 -8.650E-03 0.000E+00
- 120 9.806E-01 3.000E+00 8.758E-05 3.624E+02 3.817E+00 -2.542E-01 -8.106E-03 0.000E+00
- 121 9.828E-01 3.000E+00 7.177E-05 3.659E+02 3.875E+00 -2.539E-01 -7.545E-03 0.000E+00
- 122 9.847E-01 3.000E+00 5.905E-05 3.692E+02 3.928E+00 -2.536E-01 -7.004E-03 0.000E+00
- 123 9.863E-01 3.000E+00 4.909E-05 3.720E+02 3.974E+00 -2.534E-01 -6.513E-03 0.000E+00
- 124 9.876E-01 3.000E+00 4.152E-05 3.743E+02 4.013E+00 -2.532E-01 -6.104E-03 0.000E+00
- 125 9.887E-01 3.000E+00 3.600E-05 3.762E+02 4.044E+00 -2.530E-01 -5.775E-03 0.000E+00
- 126 9.894E-01 3.000E+00 3.227E-05 3.776E+02 4.066E+00 -2.529E-01 -5.542E-03 0.000E+00
- 127 9.899E-01 3.000E+00 3.011E-05 3.784E+02 4.080E+00 -2.528E-01 -5.391E-03 0.000E+00
- 128 9.900E-01 3.000E+00 2.940E-05 3.787E+02 4.085E+00 -2.528E-01 -5.336E-03 0.000E+00
-
-ipsi psifac f mu0 p dvdpsi q di dr ca1
-
-
- mlow mhigh mpert mband nn lim_fl dmlim qlim psilim
-
- -12 20 33 32 1 T 2.000E-01 3.200E+00 9.493E-01
-
-
- Singular Surfaces:
-
- i psi rho q q1 di0 di err
-
- 1 7.971E-01 8.928E-01 2.000E+00 4.220E+00 -2.668E-01 -2.667E-01 -3.295E-04
- 2 9.350E-01 9.670E-01 3.000E+00 1.280E+01 -2.580E-01 -2.579E-01 -2.893E-04
- 3 9.872E-01 9.936E-01 4.000E+00 2.954E+01 -2.533E-01 -2.527E-01 -2.328E-03
-
- i psi rho q q1 di0 di err
-
-
- Total Energy Eigenvalues:
-
- isol plasma vacuum re total im total
-
- 1 1.411E-01 1.410E+00 1.551E+00 2.466E-08
- 2 3.336E+00 1.634E+00 4.970E+00 8.853E-09
- 3 2.295E+00 8.715E+00 1.101E+01 1.652E-08
- 4 1.210E+01 1.699E+01 2.909E+01 2.512E-08
- 5 2.272E+01 1.563E+01 3.835E+01 -1.619E-07
- 6 2.026E+01 2.675E+01 4.701E+01 9.710E-09
- 7 2.974E+01 2.913E+01 5.887E+01 -1.142E-07
- 8 3.012E+01 3.665E+01 6.677E+01 -2.931E-08
- 9 4.036E+01 4.718E+01 8.754E+01 6.267E-09
- 10 4.632E+01 5.218E+01 9.850E+01 -5.223E-08
- 11 5.107E+01 5.788E+01 1.090E+02 2.129E-08
- 12 6.203E+01 6.877E+01 1.308E+02 3.005E-08
- 13 6.633E+01 6.963E+01 1.360E+02 -1.883E-08
- 14 7.311E+01 7.979E+01 1.529E+02 5.190E-08
- 15 8.501E+01 8.585E+01 1.709E+02 4.354E-08
- 16 8.430E+01 9.093E+01 1.752E+02 6.937E-08
- 17 9.560E+01 1.022E+02 1.978E+02 4.672E-08
- 18 1.029E+02 1.015E+02 2.044E+02 7.231E-08
- 19 1.073E+02 1.141E+02 2.214E+02 -7.649E-08
- 20 1.229E+02 1.178E+02 2.407E+02 1.253E-07
- 21 1.205E+02 1.276E+02 2.481E+02 -2.853E-07
- 22 1.366E+02 1.442E+02 2.809E+02 -3.148E-07
- 23 1.495E+02 1.380E+02 2.874E+02 9.142E-08
- 24 1.583E+02 1.654E+02 3.238E+02 -6.909E-07
- 25 1.853E+02 1.654E+02 3.506E+02 -4.820E-08
- 26 1.881E+02 1.968E+02 3.849E+02 -4.066E-07
- 27 2.334E+02 2.038E+02 4.371E+02 6.124E-08
- 28 2.995E+02 2.591E+02 5.586E+02 2.686E-07
- 29 4.696E+02 2.062E+02 6.759E+02 -9.510E-07
- 30 3.803E+02 3.464E+02 7.267E+02 6.445E-07
- 31 4.061E+02 4.975E+02 9.035E+02 -1.011E-06
- 32 6.333E+02 4.812E+02 1.115E+03 -9.318E-08
- 33 9.328E+02 3.843E+02 1.317E+03 -4.588E-06
-
- isol plasma vacuum re total im total
-
- Total Energy Eigenvectors:
-
- isol imax plasma vacuum re total im total
-
- 1 10 1.411E-01 1.410E+00 1.551E+00 2.466E-08
-
- ipert m re wt im wt abs wt
-
- 1 -12 4.876E-05 -3.454E-08 4.876E-05
- 2 -11 -1.159E-04 -2.769E-08 1.159E-04
- 3 -10 1.069E-04 -5.441E-08 1.069E-04
- 4 -9 -6.250E-05 -6.687E-08 6.250E-05
- 5 -8 -1.149E-05 -6.181E-08 1.149E-05
- 6 -7 2.518E-04 -1.057E-07 2.518E-04
- 7 -6 -7.491E-04 -1.250E-08 7.491E-04
- 8 -5 1.166E-03 -1.677E-07 1.166E-03
- 9 -4 -1.870E-03 -7.855E-08 1.870E-03
- 10 -3 1.986E-03 -3.128E-07 1.986E-03
- 11 -2 -9.933E-04 -2.334E-07 9.933E-04
- 12 -1 1.685E-03 -3.345E-07 1.685E-03
- 13 0 1.161E-02 -4.468E-07 1.161E-02
- 14 1 -6.851E-03 -1.481E-07 6.851E-03
- 15 2 4.945E-02 -8.147E-07 4.945E-02
- 16 3 6.330E-01 -3.679E-06 6.330E-01
- 17 4 6.612E-01 0.000E+00 6.612E-01 *
- 18 5 1.125E-01 1.061E-06 1.125E-01
- 19 6 3.297E-02 3.270E-07 3.297E-02
- 20 7 7.381E-03 1.458E-07 7.381E-03
- 21 8 -1.229E-03 -1.026E-07 1.229E-03
- 22 9 -3.828E-03 -2.172E-07 3.828E-03
- 23 10 -4.537E-05 -1.259E-07 4.537E-05
- 24 11 -2.531E-04 -1.039E-07 2.531E-04
- 25 12 4.296E-04 -3.939E-08 4.296E-04
- 26 13 -1.787E-04 -8.130E-08 1.787E-04
- 27 14 8.346E-05 -4.642E-08 8.346E-05
- 28 15 -7.443E-05 -7.457E-08 7.443E-05
- 29 16 4.568E-05 -3.108E-08 4.568E-05
- 30 17 -1.884E-05 -4.948E-08 1.884E-05
- 31 18 1.282E-05 -1.921E-08 1.282E-05
- 32 19 -7.233E-06 -2.436E-08 7.233E-06
- 33 20 1.779E-06 -2.422E-09 1.779E-06
-
- ipert m re wt im wt abs wt
-
-
- isol imax plasma vacuum re total im total
-
- 2 10 3.336E+00 1.634E+00 4.970E+00 8.853E-09
-
- ipert m re wt im wt abs wt
-
- 1 -12 -8.465E-05 4.619E-08 8.465E-05
- 2 -11 2.004E-04 5.914E-08 2.004E-04
- 3 -10 -2.123E-04 9.609E-08 2.123E-04
- 4 -9 2.167E-04 1.003E-07 2.167E-04
- 5 -8 -3.219E-04 1.452E-07 3.219E-04
- 6 -7 5.425E-04 1.604E-07 5.425E-04
- 7 -6 -8.350E-04 1.815E-07 8.350E-04
- 8 -5 1.260E-03 1.713E-07 1.260E-03
- 9 -4 -5.431E-04 2.311E-07 5.431E-04
- 10 -3 -8.402E-04 3.573E-07 8.402E-04
- 11 -2 9.248E-04 3.564E-07 9.248E-04
- 12 -1 -4.473E-03 5.149E-07 4.473E-03
- 13 0 -8.939E-03 4.732E-07 8.939E-03
- 14 1 2.115E-02 2.873E-07 2.115E-02
- 15 2 -1.126E-01 7.650E-07 1.126E-01
- 16 3 6.666E-01 0.000E+00 6.666E-01 *
- 17 4 -6.132E-01 -3.404E-06 6.132E-01
- 18 5 -5.919E-02 -1.806E-06 5.919E-02
- 19 6 -1.306E-01 -1.798E-06 1.306E-01
- 20 7 5.038E-03 -9.260E-09 5.038E-03
- 21 8 5.005E-03 1.827E-07 5.005E-03
- 22 9 1.167E-03 2.590E-07 1.167E-03
- 23 10 7.010E-04 1.866E-07 7.010E-04
- 24 11 6.023E-04 1.346E-07 6.023E-04
- 25 12 -6.095E-04 8.058E-09 6.095E-04
- 26 13 2.181E-04 1.440E-08 2.181E-04
- 27 14 -1.488E-04 3.154E-08 1.488E-04
- 28 15 1.439E-04 4.250E-08 1.439E-04
- 29 16 -7.399E-05 7.145E-08 7.399E-05
- 30 17 2.013E-05 2.754E-08 2.013E-05
- 31 18 -1.284E-05 4.812E-08 1.284E-05
- 32 19 9.274E-06 4.159E-09 9.274E-06
- 33 20 -2.660E-06 1.979E-08 2.660E-06
-
- ipert m re wt im wt abs wt
-
-
- isol imax plasma vacuum re total im total
-
- 3 10 2.295E+00 8.715E+00 1.101E+01 1.652E-08
-
- ipert m re wt im wt abs wt
-
- 1 -12 9.825E-05 -9.839E-08 9.825E-05
- 2 -11 -2.236E-04 -1.475E-07 2.236E-04
- 3 -10 1.533E-04 -1.491E-07 1.533E-04
- 4 -9 2.149E-05 -1.449E-07 2.149E-05
- 5 -8 -2.807E-04 -2.100E-07 2.807E-04
- 6 -7 7.195E-04 -2.589E-07 7.195E-04
- 7 -6 -1.340E-03 -2.065E-07 1.340E-03
- 8 -5 1.518E-03 -3.571E-07 1.518E-03
- 9 -4 -2.202E-03 -3.170E-07 2.202E-03
- 10 -3 2.224E-03 -7.590E-07 2.224E-03
- 11 -2 -1.035E-03 -7.336E-07 1.035E-03
- 12 -1 8.562E-03 -1.183E-06 8.562E-03
- 13 0 1.870E-03 -1.067E-06 1.870E-03
- 14 1 2.968E-02 -1.538E-06 2.968E-02
- 15 2 -8.821E-03 -4.922E-07 8.821E-03
- 16 3 -2.390E-02 -1.832E-07 2.390E-02
- 17 4 -1.366E-01 1.794E-06 1.366E-01
- 18 5 9.032E-01 0.000E+00 9.032E-01 *
- 19 6 1.232E-01 1.572E-06 1.232E-01
- 20 7 5.299E-02 1.489E-07 5.299E-02
- 21 8 -9.663E-03 -4.865E-07 9.663E-03
- 22 9 1.313E-04 -4.075E-07 1.313E-04
- 23 10 -4.031E-03 -5.160E-07 4.031E-03
- 24 11 4.443E-04 -2.928E-07 4.443E-04
- 25 12 -3.498E-04 -2.301E-07 3.498E-04
- 26 13 2.490E-04 -1.603E-07 2.490E-04
- 27 14 -9.089E-05 -1.927E-07 9.089E-05
- 28 15 3.797E-05 -1.873E-07 3.797E-05
- 29 16 -1.698E-05 -1.474E-07 1.698E-05
- 30 17 1.945E-05 -1.202E-07 1.946E-05
- 31 18 -9.036E-06 -8.349E-08 9.036E-06
- 32 19 4.072E-06 -8.402E-08 4.073E-06
- 33 20 -2.135E-06 -9.728E-09 2.135E-06
-
- ipert m re wt im wt abs wt
-
-
- isol imax plasma vacuum re total im total
-
- 4 10 1.210E+01 1.699E+01 2.909E+01 2.512E-08
-
- ipert m re wt im wt abs wt
-
- 1 -12 -6.834E-05 -1.557E-07 6.834E-05
- 2 -11 1.300E-04 -3.895E-07 1.300E-04
- 3 -10 -2.372E-04 -3.151E-07 2.372E-04
- 4 -9 4.006E-04 -3.487E-07 4.006E-04
- 5 -8 -6.024E-04 -1.786E-07 6.024E-04
- 6 -7 9.220E-04 -5.601E-07 9.220E-04
- 7 -6 -1.331E-03 -2.395E-07 1.331E-03
- 8 -5 1.184E-03 -8.194E-07 1.184E-03
- 9 -4 -1.229E-03 -3.773E-07 1.229E-03
- 10 -3 8.858E-04 -1.291E-06 8.858E-04
- 11 -2 1.504E-03 -1.449E-06 1.504E-03
- 12 -1 4.271E-03 -2.678E-06 4.271E-03
- 13 0 3.587E-03 -3.846E-06 3.587E-03
- 14 1 2.349E-02 -3.940E-06 2.349E-02
- 15 2 -2.464E-02 -4.295E-06 2.464E-02
- 16 3 7.279E-02 -1.150E-06 7.279E-02
- 17 4 -8.948E-02 1.039E-06 8.948E-02
- 18 5 -1.414E-01 1.430E-06 1.414E-01
- 19 6 8.895E-01 0.000E+00 8.895E-01 *
- 20 7 1.426E-01 1.965E-06 1.426E-01
- 21 8 8.960E-02 1.703E-07 8.960E-02
- 22 9 -5.895E-03 -4.478E-07 5.895E-03
- 23 10 4.920E-03 -2.994E-07 4.920E-03
- 24 11 -4.674E-03 -5.252E-07 4.674E-03
- 25 12 1.043E-03 -3.127E-07 1.043E-03
- 26 13 -1.070E-03 -3.208E-07 1.070E-03
- 27 14 5.256E-04 -1.717E-07 5.256E-04
- 28 15 -2.454E-04 -2.141E-07 2.454E-04
- 29 16 1.703E-04 -1.598E-07 1.703E-04
- 30 17 -9.710E-05 -1.283E-07 9.711E-05
- 31 18 5.802E-05 -9.727E-08 5.802E-05
- 32 19 -2.949E-05 -9.293E-08 2.949E-05
- 33 20 1.060E-05 -4.676E-08 1.060E-05
-
- ipert m re wt im wt abs wt
-
-
- isol imax plasma vacuum re total im total
-
- 5 10 2.272E+01 1.563E+01 3.835E+01 -1.619E-07
-
- ipert m re wt im wt abs wt
-
- 1 -12 -5.073E-04 1.498E-07 5.073E-04
- 2 -11 1.236E-03 1.757E-07 1.236E-03
- 3 -10 -1.978E-03 3.722E-07 1.978E-03
- 4 -9 3.324E-03 1.875E-07 3.324E-03
- 5 -8 -5.582E-03 6.004E-07 5.582E-03
- 6 -7 9.259E-03 1.809E-08 9.259E-03
- 7 -6 -1.485E-02 1.113E-06 1.485E-02
- 8 -5 2.151E-02 -2.973E-07 2.151E-02
- 9 -4 -3.435E-02 1.694E-06 3.435E-02
- 10 -3 4.188E-02 -3.920E-07 4.188E-02
- 11 -2 -5.194E-03 1.504E-06 5.194E-03
- 12 -1 1.045E-01 4.671E-07 1.045E-01
- 13 0 2.924E-01 -1.271E-07 2.924E-01
- 14 1 1.968E-01 6.554E-08 1.968E-01
- 15 2 8.284E-01 0.000E+00 8.284E-01 *
- 16 3 4.461E-02 -3.831E-07 4.461E-02
- 17 4 -1.062E-01 -7.542E-07 1.062E-01
- 18 5 -1.079E-02 -6.102E-07 1.079E-02
- 19 6 2.038E-02 -7.430E-06 2.038E-02
- 20 7 -1.230E-01 6.079E-07 1.230E-01
- 21 8 -8.089E-03 2.200E-06 8.089E-03
- 22 9 -3.943E-03 1.986E-06 3.943E-03
- 23 10 1.415E-03 1.382E-06 1.415E-03
- 24 11 -9.021E-04 8.815E-07 9.021E-04
- 25 12 -2.099E-04 5.763E-07 2.099E-04
- 26 13 8.293E-05 4.909E-07 8.294E-05
- 27 14 4.813E-05 2.542E-07 4.813E-05
- 28 15 6.688E-05 3.323E-07 6.688E-05
- 29 16 -4.320E-05 2.342E-07 4.320E-05
- 30 17 3.301E-06 3.835E-07 3.324E-06
- 31 18 -8.808E-06 2.773E-07 8.812E-06
- 32 19 3.280E-06 2.663E-07 3.291E-06
- 33 20 -1.816E-06 1.089E-07 1.819E-06
-
- ipert m re wt im wt abs wt
-
-
- isol imax plasma vacuum re total im total
-
- 6 10 2.026E+01 2.675E+01 4.701E+01 9.710E-09
-
- ipert m re wt im wt abs wt
-
- 1 -12 -1.663E-04 -1.640E-07 1.663E-04
- 2 -11 3.800E-04 -5.295E-07 3.800E-04
- 3 -10 -5.292E-04 -6.117E-07 5.292E-04
- 4 -9 7.643E-04 -6.521E-07 7.643E-04
- 5 -8 -1.100E-03 -4.837E-07 1.100E-03
- 6 -7 1.469E-03 -6.178E-07 1.469E-03
- 7 -6 -2.151E-03 -7.910E-07 2.151E-03
- 8 -5 2.966E-03 -9.824E-07 2.966E-03
- 9 -4 -4.719E-03 -1.270E-06 4.719E-03
- 10 -3 8.828E-03 -1.916E-06 8.828E-03
- 11 -2 4.498E-03 -2.903E-06 4.498E-03
- 12 -1 4.364E-02 -6.457E-06 4.364E-02
- 13 0 6.954E-02 -5.678E-06 6.954E-02
- 14 1 8.917E-02 -9.345E-06 8.917E-02
- 15 2 8.562E-02 7.759E-06 8.562E-02
- 16 3 -1.693E-02 9.097E-07 1.693E-02
- 17 4 1.344E-02 -1.486E-06 1.344E-02
- 18 5 -2.812E-02 -3.900E-07 2.812E-02
- 19 6 -1.603E-01 4.998E-07 1.603E-01
- 20 7 8.691E-01 0.000E+00 8.691E-01 *
- 21 8 1.935E-01 3.635E-06 1.935E-01
- 22 9 1.102E-01 1.516E-06 1.102E-01
- 23 10 1.122E-02 4.241E-07 1.122E-02
- 24 11 6.686E-03 2.029E-07 6.686E-03
- 25 12 -3.925E-03 -1.948E-07 3.925E-03
- 26 13 8.210E-04 -7.218E-09 8.210E-04
- 27 14 -9.728E-04 -7.844E-08 9.728E-04
- 28 15 4.677E-04 4.648E-08 4.677E-04
- 29 16 -2.499E-04 -4.573E-08 2.499E-04
- 30 17 1.554E-04 -9.385E-09 1.554E-04
- 31 18 -8.181E-05 4.805E-09 8.181E-05
- 32 19 4.581E-05 -2.846E-10 4.581E-05
- 33 20 -1.594E-05 -3.870E-08 1.594E-05
-
- ipert m re wt im wt abs wt
-
-
- isol imax plasma vacuum re total im total
-
- 7 10 2.974E+01 2.913E+01 5.887E+01 -1.142E-07
-
- ipert m re wt im wt abs wt
-
- 1 -12 -2.402E-04 6.181E-08 2.402E-04
- 2 -11 4.979E-04 1.247E-07 4.979E-04
- 3 -10 -7.106E-04 2.863E-07 7.106E-04
- 4 -9 1.030E-03 1.999E-07 1.030E-03
- 5 -8 -1.186E-03 2.710E-07 1.186E-03
- 6 -7 7.091E-04 2.563E-07 7.091E-04
- 7 -6 -1.578E-03 3.122E-07 1.578E-03
- 8 -5 -1.823E-04 4.343E-07 1.823E-04
- 9 -4 1.041E-02 5.442E-07 1.041E-02
- 10 -3 4.868E-02 -7.584E-08 4.868E-02
- 11 -2 1.167E-01 6.276E-07 1.167E-01
- 12 -1 3.890E-01 -1.241E-06 3.890E-01
- 13 0 3.759E-01 -5.495E-07 3.759E-01
- 14 1 6.406E-01 0.000E+00 6.406E-01 *
- 15 2 -3.370E-01 -2.285E-06 3.370E-01
- 16 3 -2.417E-02 -2.461E-08 2.417E-02
- 17 4 5.111E-02 4.968E-07 5.111E-02
- 18 5 -1.888E-02 -2.109E-07 1.888E-02
- 19 6 -5.939E-03 -2.165E-06 5.939E-03
- 20 7 -5.520E-02 -1.923E-05 5.520E-02
- 21 8 -1.112E-01 8.996E-06 1.112E-01
- 22 9 -4.708E-02 5.125E-06 4.708E-02
- 23 10 -1.668E-02 4.872E-06 1.668E-02
- 24 11 -2.943E-03 2.849E-06 2.943E-03
- 25 12 4.442E-04 2.387E-06 4.442E-04
- 26 13 -1.425E-04 1.522E-06 1.425E-04
- 27 14 1.446E-04 1.385E-06 1.446E-04
- 28 15 -1.383E-04 9.693E-07 1.383E-04
- 29 16 9.425E-05 1.065E-06 9.425E-05
- 30 17 -2.656E-05 8.738E-07 2.658E-05
- 31 18 1.370E-05 8.027E-07 1.373E-05
- 32 19 -2.117E-05 4.813E-07 2.118E-05
- 33 20 -3.507E-06 1.798E-07 3.511E-06
-
- ipert m re wt im wt abs wt
-
-
- isol imax plasma vacuum re total im total
-
- 8 10 3.012E+01 3.665E+01 6.677E+01 -2.931E-08
-
- ipert m re wt im wt abs wt
-
- 1 -12 -3.746E-05 -1.189E-07 3.746E-05
- 2 -11 6.291E-05 -3.616E-07 6.291E-05
- 3 -10 -4.147E-05 -8.126E-07 4.148E-05
- 4 -9 -4.561E-05 -1.057E-06 4.562E-05
- 5 -8 1.941E-04 -1.166E-06 1.941E-04
- 6 -7 -5.215E-04 -9.881E-07 5.215E-04
- 7 -6 8.196E-04 -1.334E-06 8.196E-04
- 8 -5 -1.122E-03 -1.512E-06 1.122E-03
- 9 -4 4.754E-03 -2.186E-06 4.754E-03
- 10 -3 6.530E-03 -1.344E-06 6.530E-03
- 11 -2 2.244E-02 -6.260E-07 2.244E-02
- 12 -1 4.783E-02 6.094E-06 4.783E-02
- 13 0 4.426E-02 7.021E-06 4.426E-02
- 14 1 5.706E-02 1.341E-05 5.706E-02
- 15 2 -5.722E-02 -3.017E-06 5.722E-02
- 16 3 -7.823E-03 -2.823E-07 7.823E-03
- 17 4 1.462E-02 5.467E-07 1.462E-02
- 18 5 2.792E-02 -1.192E-06 2.792E-02
- 19 6 -4.129E-02 -1.354E-06 4.129E-02
- 20 7 -2.353E-01 -6.152E-07 2.353E-01
- 21 8 8.264E-01 0.000E+00 8.264E-01 *
- 22 9 2.828E-01 3.432E-06 2.828E-01
- 23 10 1.437E-01 1.932E-06 1.437E-01
- 24 11 3.166E-02 7.342E-07 3.166E-02
- 25 12 1.259E-02 5.010E-07 1.259E-02
- 26 13 -1.655E-03 -5.407E-08 1.655E-03
- 27 14 6.950E-04 5.836E-08 6.950E-04
- 28 15 -9.397E-04 -3.542E-09 9.397E-04
- 29 16 3.376E-04 1.151E-07 3.376E-04
- 30 17 -2.072E-04 2.854E-08 2.072E-04
- 31 18 1.299E-04 -2.050E-08 1.299E-04
- 32 19 -6.405E-05 -1.094E-08 6.405E-05
- 33 20 2.364E-05 -1.862E-08 2.364E-05
-
- ipert m re wt im wt abs wt
-
-
- isol imax plasma vacuum re total im total
-
- 9 10 4.036E+01 4.718E+01 8.754E+01 6.267E-09
-
- ipert m re wt im wt abs wt
-
- 1 -12 2.098E-05 -6.768E-08 2.098E-05
- 2 -11 -7.494E-05 -1.614E-07 7.494E-05
- 3 -10 5.723E-05 -5.178E-07 5.723E-05
- 4 -9 -1.188E-04 -1.044E-06 1.188E-04
- 5 -8 9.003E-05 -1.735E-06 9.004E-05
- 6 -7 -7.077E-05 -1.839E-06 7.079E-05
- 7 -6 5.525E-05 -2.367E-06 5.530E-05
- 8 -5 1.583E-04 -2.848E-06 1.583E-04
- 9 -4 -1.429E-04 -5.073E-06 1.430E-04
- 10 -3 -3.257E-04 -6.181E-06 3.257E-04
- 11 -2 -3.761E-04 -8.107E-06 3.762E-04
- 12 -1 1.406E-03 -2.190E-06 1.406E-03
- 13 0 -3.334E-04 4.807E-07 3.334E-04
- 14 1 3.132E-03 8.938E-06 3.132E-03
- 15 2 -5.304E-03 -6.261E-07 5.304E-03
- 16 3 5.383E-03 -2.311E-07 5.383E-03
- 17 4 -1.566E-03 1.709E-07 1.566E-03
- 18 5 -6.478E-03 -3.854E-07 6.478E-03
- 19 6 3.866E-02 -1.059E-06 3.866E-02
- 20 7 -1.939E-02 -1.507E-06 1.939E-02
- 21 8 -3.330E-01 2.673E-06 3.330E-01
- 22 9 7.462E-01 0.000E+00 7.462E-01 *
- 23 10 3.746E-01 4.067E-06 3.746E-01
- 24 11 1.996E-01 2.388E-06 1.996E-01
- 25 12 6.233E-02 9.351E-07 6.233E-02
- 26 13 2.322E-02 3.545E-07 2.322E-02
- 27 14 2.214E-03 -1.714E-07 2.214E-03
- 28 15 1.272E-03 -1.802E-07 1.272E-03
- 29 16 -7.560E-04 -1.491E-07 7.560E-04
- 30 17 2.294E-04 -5.523E-08 2.294E-04
- 31 18 -1.943E-04 -6.553E-08 1.943E-04
- 32 19 1.048E-04 -1.094E-07 1.048E-04
- 33 20 -3.429E-05 -2.610E-08 3.429E-05
-
- ipert m re wt im wt abs wt
-
-
- isol imax plasma vacuum re total im total
-
- 10 10 4.632E+01 5.218E+01 9.850E+01 -5.223E-08
-
- ipert m re wt im wt abs wt
-
- 1 -12 5.502E-04 4.931E-08 5.502E-04
- 2 -11 -1.349E-03 2.582E-07 1.349E-03
- 3 -10 1.851E-03 1.357E-07 1.851E-03
- 4 -9 -2.924E-03 4.206E-07 2.924E-03
- 5 -8 5.432E-03 2.725E-07 5.432E-03
- 6 -7 9.577E-04 6.255E-07 9.577E-04
- 7 -6 3.732E-02 2.036E-07 3.732E-02
- 8 -5 7.303E-02 6.707E-07 7.303E-02
- 9 -4 2.280E-01 -2.589E-07 2.280E-01
- 10 -3 3.618E-01 1.011E-06 3.618E-01
- 11 -2 5.966E-01 0.000E+00 5.966E-01 *
- 12 -1 3.305E-01 2.520E-07 3.305E-01
- 13 0 1.423E-01 6.902E-07 1.423E-01
- 14 1 -4.224E-01 -1.758E-06 4.224E-01
- 15 2 1.821E-03 1.327E-06 1.821E-03
- 16 3 5.822E-03 8.150E-08 5.822E-03
- 17 4 -1.472E-02 -7.487E-07 1.472E-02
- 18 5 6.872E-03 -5.853E-07 6.872E-03
- 19 6 6.092E-03 -1.673E-06 6.092E-03
- 20 7 1.403E-02 -2.737E-07 1.403E-02
- 21 8 -1.232E-02 1.088E-06 1.232E-02
- 22 9 -7.441E-05 -1.917E-05 7.684E-05
- 23 10 -4.885E-03 7.226E-07 4.885E-03
- 24 11 -3.751E-03 4.789E-06 3.751E-03
- 25 12 -2.628E-03 5.332E-06 2.628E-03
- 26 13 -3.488E-04 4.186E-06 3.488E-04
- 27 14 -2.717E-04 3.331E-06 2.717E-04
- 28 15 1.101E-04 2.736E-06 1.101E-04
- 29 16 -1.007E-04 1.971E-06 1.008E-04
- 30 17 -1.673E-06 1.188E-06 2.052E-06
- 31 18 -4.795E-05 4.948E-07 4.795E-05
- 32 19 -1.187E-05 2.742E-07 1.187E-05
- 33 20 -1.115E-05 1.177E-07 1.115E-05
-
- ipert m re wt im wt abs wt
-
-
- isol imax plasma vacuum re total im total
-
- 11 10 5.107E+01 5.788E+01 1.090E+02 2.129E-08
-
- ipert m re wt im wt abs wt
-
- 1 -12 -6.092E-07 -1.154E-07 6.200E-07
- 2 -11 -3.650E-05 -3.153E-07 3.650E-05
- 3 -10 -3.231E-05 -2.768E-07 3.231E-05
- 4 -9 4.847E-06 -7.332E-07 4.902E-06
- 5 -8 -4.132E-05 -1.539E-06 4.135E-05
- 6 -7 1.711E-04 -2.826E-06 1.711E-04
- 7 -6 2.528E-04 -2.942E-06 2.528E-04
- 8 -5 9.411E-04 -2.713E-06 9.411E-04
- 9 -4 1.904E-03 3.820E-07 1.904E-03
- 10 -3 3.536E-03 3.608E-06 3.536E-03
- 11 -2 3.384E-03 1.020E-05 3.384E-03
- 12 -1 2.087E-04 7.751E-06 2.088E-04
- 13 0 -1.015E-03 4.910E-06 1.015E-03
- 14 1 -3.762E-03 -6.200E-06 3.762E-03
- 15 2 4.562E-03 -4.556E-07 4.562E-03
- 16 3 -2.479E-03 1.272E-07 2.479E-03
- 17 4 -6.316E-04 -2.428E-07 6.316E-04
- 18 5 2.608E-03 -3.358E-07 2.608E-03
- 19 6 -1.239E-02 -3.910E-08 1.239E-02
- 20 7 3.599E-02 -3.908E-07 3.599E-02
- 21 8 3.170E-02 -1.804E-06 3.170E-02
- 22 9 -4.383E-01 2.694E-06 4.383E-01
- 23 10 6.184E-01 0.000E+00 6.184E-01 *
- 24 11 4.421E-01 4.592E-06 4.421E-01
- 25 12 2.630E-01 3.545E-06 2.630E-01
- 26 13 1.037E-01 1.770E-06 1.037E-01
- 27 14 4.090E-02 8.423E-07 4.090E-02
- 28 15 9.226E-03 4.680E-08 9.226E-03
- 29 16 3.022E-03 -1.307E-07 3.022E-03
- 30 17 -2.614E-04 -1.705E-07 2.614E-04
- 31 18 2.062E-04 -6.256E-08 2.062E-04
- 32 19 -1.762E-04 -8.007E-08 1.762E-04
- 33 20 4.771E-05 -7.187E-08 4.771E-05
-
- ipert m re wt im wt abs wt
-
-
- isol imax plasma vacuum re total im total
-
- 12 10 6.203E+01 6.877E+01 1.308E+02 3.005E-08
-
- ipert m re wt im wt abs wt
-
- 1 -12 4.040E-06 4.886E-07 4.069E-06
- 2 -11 -6.676E-07 1.157E-06 1.336E-06
- 3 -10 1.400E-05 9.892E-07 1.404E-05
- 4 -9 -1.361E-05 1.408E-06 1.368E-05
- 5 -8 -1.246E-04 2.594E-06 1.246E-04
- 6 -7 -4.928E-04 6.824E-06 4.929E-04
- 7 -6 -1.101E-03 1.201E-05 1.101E-03
- 8 -5 -2.235E-03 1.913E-05 2.235E-03
- 9 -4 -2.628E-03 1.896E-05 2.628E-03
- 10 -3 -2.731E-03 1.317E-05 2.731E-03
- 11 -2 -2.500E-04 -8.291E-06 2.502E-04
- 12 -1 6.598E-04 -1.118E-05 6.599E-04
- 13 0 1.780E-03 -1.174E-05 1.780E-03
- 14 1 -9.293E-04 1.232E-05 9.294E-04
- 15 2 -4.858E-04 1.852E-06 4.858E-04
- 16 3 -8.971E-04 2.951E-08 8.971E-04
- 17 4 4.765E-05 3.027E-07 4.765E-05
- 18 5 2.006E-03 -1.227E-07 2.006E-03
- 19 6 -4.570E-03 3.952E-07 4.570E-03
- 20 7 1.322E-02 -2.492E-07 1.322E-02
- 21 8 -2.837E-02 1.412E-07 2.837E-02
- 22 9 -1.021E-01 2.063E-06 1.021E-01
- 23 10 5.219E-01 0.000E+00 5.219E-01 *
- 24 11 -4.538E-01 -2.136E-06 4.538E-01
- 25 12 -4.765E-01 -7.611E-06 4.765E-01
- 26 13 -3.287E-01 -6.812E-06 3.287E-01
- 27 14 -1.558E-01 -3.918E-06 1.558E-01
- 28 15 -6.742E-02 -2.029E-06 6.742E-02
- 29 16 -2.100E-02 -5.795E-07 2.100E-02
- 30 17 -6.853E-03 -7.043E-08 6.853E-03
- 31 18 -9.401E-04 1.311E-07 9.401E-04
- 32 19 -3.885E-04 -2.908E-09 3.885E-04
- 33 20 7.236E-05 2.237E-08 7.236E-05
-
- ipert m re wt im wt abs wt
-
-
- isol imax plasma vacuum re total im total
-
- 13 10 6.633E+01 6.963E+01 1.360E+02 -1.883E-08
-
- ipert m re wt im wt abs wt
-
- 1 -12 -4.111E-04 5.008E-08 4.111E-04
- 2 -11 2.399E-03 -1.417E-08 2.399E-03
- 3 -10 2.669E-03 1.641E-07 2.669E-03
- 4 -9 1.930E-02 -1.275E-07 1.930E-02
- 5 -8 4.329E-02 -2.642E-07 4.329E-02
- 6 -7 1.253E-01 -1.051E-06 1.253E-01
- 7 -6 2.344E-01 -1.138E-06 2.344E-01
- 8 -5 4.229E-01 -1.749E-06 4.229E-01
- 9 -4 4.760E-01 0.000E+00 4.760E-01 *
- 10 -3 4.004E-01 -3.810E-07 4.004E-01
- 11 -2 -1.058E-01 1.269E-06 1.058E-01
- 12 -1 -2.062E-01 -2.020E-07 2.062E-01
- 13 0 -2.741E-01 -2.057E-07 2.741E-01
- 14 1 2.908E-01 1.181E-06 2.908E-01
- 15 2 4.465E-02 4.446E-07 4.465E-02
- 16 3 -1.231E-03 5.969E-08 1.231E-03
- 17 4 6.786E-03 -1.567E-07 6.786E-03
- 18 5 -5.078E-03 -4.449E-07 5.078E-03
- 19 6 -3.736E-03 -8.631E-07 3.736E-03
- 20 7 -6.095E-03 -6.146E-07 6.095E-03
- 21 8 4.396E-03 -2.876E-06 4.396E-03
- 22 9 1.519E-03 -4.594E-06 1.519E-03
- 23 10 1.985E-03 1.817E-05 1.985E-03
- 24 11 -2.783E-03 -3.026E-05 2.783E-03
- 25 12 -2.548E-03 -2.047E-05 2.549E-03
- 26 13 -3.160E-03 -8.686E-06 3.160E-03
- 27 14 -1.505E-03 -4.763E-07 1.505E-03
- 28 15 -9.649E-04 1.060E-06 9.649E-04
- 29 16 -2.547E-04 1.131E-06 2.547E-04
- 30 17 -1.685E-04 7.482E-07 1.685E-04
- 31 18 -3.066E-05 1.197E-06 3.069E-05
- 32 19 -2.714E-05 1.358E-06 2.717E-05
- 33 20 2.040E-06 6.965E-07 2.156E-06
-
- ipert m re wt im wt abs wt
-
-
- isol imax plasma vacuum re total im total
-
- 14 10 7.311E+01 7.979E+01 1.529E+02 5.190E-08
-
- ipert m re wt im wt abs wt
-
- 1 -12 1.562E-06 5.138E-07 1.644E-06
- 2 -11 -1.616E-05 1.637E-06 1.625E-05
- 3 -10 5.296E-06 2.218E-06 5.741E-06
- 4 -9 -3.460E-05 1.654E-06 3.464E-05
- 5 -8 -4.141E-05 6.321E-07 4.142E-05
- 6 -7 -1.742E-04 -1.021E-06 1.742E-04
- 7 -6 -3.297E-04 -2.490E-06 3.297E-04
- 8 -5 -5.648E-04 -5.101E-06 5.648E-04
- 9 -4 -6.612E-04 -6.791E-06 6.612E-04
- 10 -3 -1.970E-04 -7.556E-06 1.971E-04
- 11 -2 5.188E-04 -9.880E-07 5.188E-04
- 12 -1 4.929E-04 9.020E-07 4.929E-04
- 13 0 7.303E-05 3.667E-06 7.312E-05
- 14 1 -7.025E-04 -4.236E-06 7.025E-04
- 15 2 3.332E-04 -5.969E-07 3.332E-04
- 16 3 1.660E-04 4.803E-08 1.660E-04
- 17 4 1.468E-04 -9.384E-08 1.468E-04
- 18 5 -1.005E-03 2.966E-07 1.005E-03
- 19 6 2.866E-03 1.629E-07 2.866E-03
- 20 7 -5.030E-03 5.194E-07 5.030E-03
- 21 8 1.703E-02 -1.417E-07 1.703E-02
- 22 9 -9.746E-03 -5.797E-07 9.746E-03
- 23 10 -1.921E-01 2.562E-06 1.921E-01
- 24 11 5.667E-01 0.000E+00 5.667E-01 *
- 25 12 -2.656E-01 -6.686E-07 2.656E-01
- 26 13 -4.666E-01 -7.291E-06 4.666E-01
- 27 14 -3.857E-01 -8.256E-06 3.857E-01
- 28 15 -2.152E-01 -5.685E-06 2.152E-01
- 29 16 -1.035E-01 -3.315E-06 1.035E-01
- 30 17 -3.906E-02 -1.325E-06 3.906E-02
- 31 18 -1.388E-02 -4.222E-07 1.388E-02
- 32 19 -3.356E-03 -6.612E-08 3.356E-03
- 33 20 -6.946E-04 -1.767E-07 6.946E-04
-
- ipert m re wt im wt abs wt
-
-
- isol imax plasma vacuum re total im total
-
- 15 10 8.501E+01 8.585E+01 1.709E+02 4.354E-08
-
- ipert m re wt im wt abs wt
-
- 1 -12 4.950E-03 3.281E-08 4.950E-03
- 2 -11 2.121E-02 -1.251E-07 2.121E-02
- 3 -10 6.371E-02 -6.923E-07 6.371E-02
- 4 -9 1.356E-01 -1.063E-06 1.356E-01
- 5 -8 2.653E-01 -1.491E-06 2.653E-01
- 6 -7 3.950E-01 -8.628E-07 3.950E-01
- 7 -6 4.762E-01 0.000E+00 4.762E-01 *
- 8 -5 3.032E-01 1.250E-06 3.032E-01
- 9 -4 -1.499E-02 -3.150E-07 1.499E-02
- 10 -3 -3.685E-01 -1.179E-06 3.685E-01
- 11 -2 -9.434E-02 -5.780E-07 9.434E-02
- 12 -1 6.932E-02 5.599E-07 6.932E-02
- 13 0 3.044E-01 3.356E-06 3.044E-01
- 14 1 -2.019E-01 -2.204E-06 2.019E-01
- 15 2 -5.312E-02 -1.565E-07 5.312E-02
- 16 3 -5.788E-04 8.766E-08 5.788E-04
- 17 4 -3.244E-03 -2.362E-07 3.244E-03
- 18 5 4.394E-03 -4.736E-08 4.394E-03
- 19 6 2.996E-03 -2.434E-07 2.996E-03
- 20 7 3.490E-03 -7.088E-07 3.490E-03
- 21 8 -2.803E-03 -1.015E-06 2.803E-03
- 22 9 -1.445E-03 -1.561E-06 1.445E-03
- 23 10 -3.174E-04 -1.725E-06 3.174E-04
- 24 11 3.035E-03 2.771E-07 3.035E-03
- 25 12 -4.438E-03 -8.560E-06 4.438E-03
- 26 13 1.954E-03 -3.580E-06 1.954E-03
- 27 14 2.697E-03 6.053E-07 2.697E-03
- 28 15 2.715E-03 4.054E-06 2.715E-03
- 29 16 1.368E-03 5.651E-06 1.368E-03
- 30 17 7.839E-04 6.111E-06 7.840E-04
- 31 18 2.915E-04 4.846E-06 2.915E-04
- 32 19 1.357E-04 2.794E-06 1.357E-04
- 33 20 1.991E-05 7.398E-07 1.992E-05
-
- ipert m re wt im wt abs wt
-
-
- isol imax plasma vacuum re total im total
-
- 16 10 8.430E+01 9.093E+01 1.752E+02 6.937E-08
-
- ipert m re wt im wt abs wt
-
- 1 -12 4.971E-05 3.023E-07 4.971E-05
- 2 -11 2.130E-04 1.223E-06 2.130E-04
- 3 -10 6.028E-04 2.504E-06 6.028E-04
- 4 -9 1.261E-03 2.895E-06 1.261E-03
- 5 -8 2.301E-03 8.061E-07 2.301E-03
- 6 -7 3.229E-03 -3.029E-06 3.229E-03
- 7 -6 3.401E-03 -7.268E-06 3.401E-03
- 8 -5 1.644E-03 -7.104E-06 1.645E-03
- 9 -4 -9.615E-04 -2.773E-06 9.615E-04
- 10 -3 -2.793E-03 3.498E-06 2.793E-03
- 11 -2 -1.389E-04 4.558E-07 1.389E-04
- 12 -1 7.319E-04 -1.903E-06 7.319E-04
- 13 0 1.884E-03 -4.766E-06 1.884E-03
- 14 1 -1.910E-03 2.574E-06 1.910E-03
- 15 2 1.113E-04 7.702E-07 1.113E-04
- 16 3 5.193E-05 1.945E-08 5.193E-05
- 17 4 -5.115E-04 1.121E-07 5.115E-04
- 18 5 4.310E-04 1.138E-07 4.310E-04
- 19 6 -1.853E-03 2.537E-07 1.853E-03
- 20 7 3.349E-03 -1.136E-07 3.349E-03
- 21 8 -7.541E-03 3.967E-07 7.541E-03
- 22 9 1.743E-02 7.127E-08 1.743E-02
- 23 10 2.754E-02 -1.252E-06 2.754E-02
- 24 11 -2.890E-01 3.099E-06 2.890E-01
- 25 12 5.606E-01 0.000E+00 5.606E-01 *
- 26 13 -7.246E-02 8.194E-07 7.246E-02
- 27 14 -4.098E-01 -6.430E-06 4.098E-01
- 28 15 -4.229E-01 -9.455E-06 4.229E-01
- 29 16 -2.763E-01 -7.762E-06 2.763E-01
- 30 17 -1.485E-01 -5.051E-06 1.485E-01
- 31 18 -6.429E-02 -2.421E-06 6.429E-02
- 32 19 -2.412E-02 -9.056E-07 2.412E-02
- 33 20 -4.759E-03 7.875E-08 4.759E-03
-
- ipert m re wt im wt abs wt
-
-
- isol imax plasma vacuum re total im total
-
- 17 10 9.560E+01 1.022E+02 1.978E+02 4.672E-08
-
- ipert m re wt im wt abs wt
-
- 1 -12 -1.576E-04 6.891E-07 1.576E-04
- 2 -11 -6.822E-04 3.183E-06 6.822E-04
- 3 -10 -1.488E-03 7.063E-06 1.488E-03
- 4 -9 -2.497E-03 1.221E-05 2.497E-03
- 5 -8 -3.167E-03 1.411E-05 3.167E-03
- 6 -7 -2.855E-03 9.202E-06 2.855E-03
- 7 -6 -7.401E-04 -4.062E-06 7.402E-04
- 8 -5 1.533E-03 -1.289E-05 1.533E-03
- 9 -4 2.290E-03 -9.559E-06 2.290E-03
- 10 -3 -5.935E-04 8.953E-06 5.935E-04
- 11 -2 -1.393E-03 5.414E-06 1.393E-03
- 12 -1 -6.214E-04 -6.758E-08 6.214E-04
- 13 0 1.793E-03 -1.322E-05 1.793E-03
- 14 1 -8.921E-05 6.055E-06 8.942E-05
- 15 2 -8.422E-04 2.318E-06 8.423E-04
- 16 3 -5.310E-05 4.066E-08 5.310E-05
- 17 4 4.244E-04 8.082E-08 4.244E-04
- 18 5 -1.859E-04 -6.078E-09 1.859E-04
- 19 6 1.213E-03 1.641E-08 1.213E-03
- 20 7 -2.244E-03 1.754E-07 2.244E-03
- 21 8 4.209E-03 -7.990E-08 4.209E-03
- 22 9 -9.777E-03 3.561E-07 9.777E-03
- 23 10 9.964E-03 4.121E-07 9.964E-03
- 24 11 8.377E-02 -2.164E-06 8.377E-02
- 25 12 -3.794E-01 3.507E-06 3.794E-01
- 26 13 5.033E-01 -1.469E-39 5.033E-01 *
- 27 14 1.027E-01 2.202E-06 1.027E-01
- 28 15 -3.133E-01 -4.872E-06 3.133E-01
- 29 16 -4.315E-01 -1.002E-05 4.315E-01
- 30 17 -3.295E-01 -9.725E-06 3.295E-01
- 31 18 -1.952E-01 -6.904E-06 1.952E-01
- 32 19 -8.744E-02 -3.353E-06 8.744E-02
- 33 20 -2.115E-02 -3.746E-07 2.115E-02
-
- ipert m re wt im wt abs wt
-
-
- isol imax plasma vacuum re total im total
-
- 18 10 1.029E+02 1.015E+02 2.044E+02 7.231E-08
-
- ipert m re wt im wt abs wt
-
- 1 -12 2.837E-02 -7.156E-09 2.837E-02
- 2 -11 1.221E-01 -1.001E-06 1.221E-01
- 3 -10 2.494E-01 -1.479E-06 2.494E-01
- 4 -9 3.875E-01 -1.228E-06 3.875E-01
- 5 -8 4.384E-01 0.000E+00 4.384E-01 *
- 6 -7 3.171E-01 6.474E-07 3.171E-01
- 7 -6 -3.170E-02 -2.419E-07 3.170E-02
- 8 -5 -2.962E-01 -2.610E-06 2.962E-01
- 9 -4 -2.505E-01 -1.361E-06 2.505E-01
- 10 -3 2.072E-01 2.034E-06 2.072E-01
- 11 -2 1.572E-01 2.319E-06 1.572E-01
- 12 -1 3.594E-02 1.191E-07 3.594E-02
- 13 0 -3.000E-01 -3.700E-06 3.000E-01
- 14 1 1.417E-01 2.186E-06 1.417E-01
- 15 2 5.304E-02 9.776E-07 5.304E-02
- 16 3 1.419E-03 8.401E-08 1.419E-03
- 17 4 1.406E-03 -1.106E-07 1.406E-03
- 18 5 -3.771E-03 -3.806E-07 3.771E-03
- 19 6 -2.284E-03 -3.896E-07 2.284E-03
- 20 7 -2.288E-03 -5.333E-07 2.288E-03
- 21 8 2.247E-03 -5.253E-07 2.247E-03
- 22 9 8.109E-04 -1.206E-06 8.109E-04
- 23 10 1.164E-04 -1.159E-06 1.165E-04
- 24 11 4.377E-04 6.683E-07 4.377E-04
- 25 12 -2.999E-03 -9.544E-06 2.999E-03
- 26 13 2.487E-03 1.680E-05 2.487E-03
- 27 14 2.284E-03 -1.127E-06 2.284E-03
- 28 15 -1.592E-03 -1.451E-05 1.592E-03
- 29 16 -2.858E-03 -1.652E-05 2.858E-03
- 30 17 -2.664E-03 -1.300E-05 2.665E-03
- 31 18 -1.688E-03 -8.736E-06 1.689E-03
- 32 19 -8.381E-04 -4.375E-06 8.381E-04
- 33 20 -2.018E-04 -1.018E-06 2.018E-04
-
- ipert m re wt im wt abs wt
-
-
- isol imax plasma vacuum re total im total
-
- 19 10 1.073E+02 1.141E+02 2.214E+02 -7.649E-08
-
- ipert m re wt im wt abs wt
-
- 1 -12 1.199E-04 -3.722E-07 1.199E-04
- 2 -11 4.796E-04 1.384E-07 4.796E-04
- 3 -10 8.525E-04 2.212E-06 8.525E-04
- 4 -9 1.054E-03 3.376E-06 1.054E-03
- 5 -8 8.112E-04 2.291E-06 8.112E-04
- 6 -7 5.163E-05 4.757E-07 5.163E-05
- 7 -6 -7.238E-04 9.399E-07 7.238E-04
- 8 -5 -6.856E-04 2.241E-06 6.856E-04
- 9 -4 2.607E-04 2.095E-06 2.608E-04
- 10 -3 7.447E-04 -1.896E-06 7.447E-04
- 11 -2 -8.082E-05 -1.120E-06 8.083E-05
- 12 -1 -2.587E-04 1.670E-07 2.587E-04
- 13 0 -2.504E-04 3.421E-06 2.504E-04
- 14 1 5.795E-04 -1.129E-06 5.795E-04
- 15 2 -2.729E-04 -4.351E-07 2.729E-04
- 16 3 -1.700E-05 -2.151E-08 1.700E-05
- 17 4 2.681E-04 -5.666E-08 2.681E-04
- 18 5 -1.506E-04 -1.762E-08 1.506E-04
- 19 6 7.844E-04 -1.156E-07 7.844E-04
- 20 7 -1.430E-03 -1.948E-08 1.430E-03
- 21 8 2.740E-03 -2.677E-07 2.740E-03
- 22 9 -5.547E-03 1.854E-07 5.547E-03
- 23 10 1.022E-02 -1.304E-07 1.022E-02
- 24 11 8.034E-03 -8.967E-07 8.034E-03
- 25 12 -1.547E-01 1.939E-06 1.547E-01
- 26 13 4.539E-01 0.000E+00 4.539E-01 *
- 27 14 -4.190E-01 -3.463E-06 4.190E-01
- 28 15 -2.338E-01 -5.170E-06 2.338E-01
- 29 16 2.110E-01 4.930E-06 2.110E-01
- 30 17 4.186E-01 1.341E-05 4.186E-01
- 31 18 3.589E-01 1.383E-05 3.589E-01
- 32 19 2.059E-01 9.283E-06 2.059E-01
- 33 20 5.361E-02 2.337E-06 5.361E-02
-
- ipert m re wt im wt abs wt
-
-
- isol imax plasma vacuum re total im total
-
- 20 10 1.229E+02 1.178E+02 2.407E+02 1.253E-07
-
- ipert m re wt im wt abs wt
-
- 1 -12 7.471E-02 -5.337E-07 7.471E-02
- 2 -11 2.737E-01 -9.089E-07 2.737E-01
- 3 -10 4.281E-01 0.000E+00 4.281E-01 *
- 4 -9 3.763E-01 1.426E-06 3.763E-01
- 5 -8 8.825E-02 7.322E-07 8.825E-02
- 6 -7 -2.809E-01 -2.140E-06 2.809E-01
- 7 -6 -3.029E-01 -3.271E-06 3.029E-01
- 8 -5 4.557E-02 1.253E-06 4.557E-02
- 9 -4 3.429E-01 4.539E-06 3.429E-01
- 10 -3 -4.395E-02 -1.838E-07 4.395E-02
- 11 -2 -1.639E-01 -2.741E-06 1.639E-01
- 12 -1 -1.282E-01 -2.135E-06 1.282E-01
- 13 0 3.034E-01 5.760E-06 3.034E-01
- 14 1 -1.021E-01 -2.006E-06 1.021E-01
- 15 2 -5.469E-02 -9.886E-07 5.469E-02
- 16 3 -2.065E-03 -5.042E-08 2.065E-03
- 17 4 -1.378E-04 -5.397E-08 1.378E-04
- 18 5 3.438E-03 7.749E-08 3.438E-03
- 19 6 1.758E-03 -7.062E-08 1.758E-03
- 20 7 1.588E-03 -4.022E-07 1.588E-03
- 21 8 -1.969E-03 -8.615E-07 1.969E-03
- 22 9 -5.200E-04 -8.802E-07 5.200E-04
- 23 10 -1.151E-04 -1.060E-07 1.151E-04
- 24 11 1.684E-04 4.924E-07 1.684E-04
- 25 12 8.481E-04 8.564E-07 8.481E-04
- 26 13 -3.582E-04 -2.077E-06 3.582E-04
- 27 14 -1.418E-03 -1.738E-06 1.418E-03
- 28 15 1.817E-03 -3.198E-06 1.817E-03
- 29 16 5.072E-04 -3.139E-06 5.072E-04
- 30 17 -8.914E-04 1.192E-06 8.914E-04
- 31 18 -1.451E-03 6.227E-06 1.451E-03
- 32 19 -9.714E-04 7.643E-06 9.714E-04
- 33 20 -2.798E-04 2.926E-06 2.798E-04
-
- ipert m re wt im wt abs wt
-
-
- isol imax plasma vacuum re total im total
-
- 21 10 1.205E+02 1.276E+02 2.481E+02 -2.853E-07
-
- ipert m re wt im wt abs wt
-
- 1 -12 2.563E-04 -9.348E-07 2.564E-04
- 2 -11 9.019E-04 -2.023E-06 9.019E-04
- 3 -10 1.323E-03 4.368E-07 1.323E-03
- 4 -9 9.760E-04 3.779E-06 9.760E-04
- 5 -8 -5.107E-05 3.379E-06 5.118E-05
- 6 -7 -1.031E-03 -1.524E-06 1.031E-03
- 7 -6 -6.965E-04 -3.352E-06 6.965E-04
- 8 -5 5.218E-04 1.076E-06 5.218E-04
- 9 -4 9.389E-04 5.823E-06 9.389E-04
- 10 -3 -5.157E-04 -7.220E-07 5.157E-04
- 11 -2 -4.007E-04 -2.944E-06 4.007E-04
- 12 -1 -2.205E-04 -2.172E-06 2.205E-04
- 13 0 1.015E-03 5.367E-06 1.015E-03
- 14 1 -6.535E-04 -1.229E-06 6.535E-04
- 15 2 3.200E-05 -9.767E-07 3.202E-05
- 16 3 2.600E-05 -3.399E-08 2.600E-05
- 17 4 -1.967E-04 1.822E-08 1.967E-04
- 18 5 9.232E-05 3.899E-09 9.232E-05
- 19 6 -5.125E-04 2.494E-08 5.125E-04
- 20 7 9.287E-04 -8.179E-08 9.287E-04
- 21 8 -1.765E-03 -2.043E-08 1.765E-03
- 22 9 3.481E-03 -2.643E-07 3.481E-03
- 23 10 -6.535E-03 2.388E-07 6.535E-03
- 24 11 7.431E-03 5.495E-08 7.431E-03
- 25 12 3.395E-02 -1.373E-06 3.395E-02
- 26 13 -2.228E-01 2.561E-06 2.228E-01
- 27 14 5.074E-01 0.000E+00 5.074E-01 *
- 28 15 -3.635E-01 -2.865E-06 3.635E-01
- 29 16 -3.002E-01 -6.103E-06 3.002E-01
- 30 17 1.767E-01 3.908E-06 1.767E-01
- 31 18 4.227E-01 1.352E-05 4.227E-01
- 32 19 3.236E-01 1.286E-05 3.236E-01
- 33 20 9.483E-02 4.599E-06 9.483E-02
-
- ipert m re wt im wt abs wt
-
-
- isol imax plasma vacuum re total im total
-
- 22 10 1.366E+02 1.442E+02 2.809E+02 -3.148E-07
-
- ipert m re wt im wt abs wt
-
- 1 -12 -3.645E-04 -4.755E-06 3.645E-04
- 2 -11 -1.186E-03 -1.552E-05 1.186E-03
- 3 -10 -1.284E-03 -1.382E-05 1.284E-03
- 4 -9 -1.930E-04 2.728E-06 1.930E-04
- 5 -8 1.084E-03 1.611E-05 1.084E-03
- 6 -7 8.805E-04 6.344E-06 8.805E-04
- 7 -6 -5.944E-04 -1.212E-05 5.945E-04
- 8 -5 -1.057E-03 -9.267E-06 1.057E-03
- 9 -4 5.782E-04 1.378E-05 5.783E-04
- 10 -3 6.665E-04 4.219E-06 6.666E-04
- 11 -2 -2.896E-04 -6.186E-06 2.897E-04
- 12 -1 -6.786E-04 -9.599E-06 6.786E-04
- 13 0 5.958E-04 1.395E-05 5.959E-04
- 14 1 1.758E-04 -3.031E-06 1.759E-04
- 15 2 -3.006E-04 -2.443E-06 3.006E-04
- 16 3 -5.268E-05 -1.374E-07 5.268E-05
- 17 4 1.713E-04 2.651E-08 1.713E-04
- 18 5 -1.842E-05 1.149E-07 1.842E-05
- 19 6 3.249E-04 -1.048E-08 3.249E-04
- 20 7 -5.935E-04 9.556E-08 5.935E-04
- 21 8 1.076E-03 -1.600E-07 1.076E-03
- 22 9 -2.097E-03 3.007E-08 2.097E-03
- 23 10 3.915E-03 -2.741E-07 3.915E-03
- 24 11 -6.525E-03 2.194E-07 6.525E-03
- 25 12 2.484E-03 2.486E-07 2.484E-03
- 26 13 5.342E-02 -1.596E-06 5.342E-02
- 27 14 -2.556E-01 2.799E-06 2.556E-01
- 28 15 5.359E-01 0.000E+00 5.359E-01 *
- 29 16 -4.004E-01 -3.341E-06 4.004E-01
- 30 17 -2.724E-01 -5.928E-06 2.724E-01
- 31 18 2.834E-01 6.787E-06 2.834E-01
- 32 19 4.084E-01 1.395E-05 4.084E-01
- 33 20 1.306E-01 5.715E-06 1.306E-01
-
- ipert m re wt im wt abs wt
-
-
- isol imax plasma vacuum re total im total
-
- 23 10 1.495E+02 1.380E+02 2.874E+02 9.142E-08
-
- ipert m re wt im wt abs wt
-
- 1 -12 1.164E-01 -9.209E-07 1.164E-01
- 2 -11 3.775E-01 0.000E+00 3.775E-01 *
- 3 -10 3.741E-01 1.526E-06 3.741E-01
- 4 -9 1.475E-03 -1.522E-07 1.475E-03
- 5 -8 -3.672E-01 -3.748E-06 3.672E-01
- 6 -7 -2.066E-01 -2.559E-06 2.066E-01
- 7 -6 2.509E-01 4.034E-06 2.509E-01
- 8 -5 2.659E-01 3.658E-06 2.659E-01
- 9 -4 -2.657E-01 -4.425E-06 2.657E-01
- 10 -3 -1.199E-01 -2.457E-06 1.199E-01
- 11 -2 1.177E-01 2.474E-06 1.177E-01
- 12 -1 2.269E-01 4.300E-06 2.269E-01
- 13 0 -3.000E-01 -6.176E-06 3.000E-01
- 14 1 6.039E-02 1.396E-06 6.039E-02
- 15 2 5.608E-02 1.354E-06 5.608E-02
- 16 3 2.717E-03 8.903E-08 2.717E-03
- 17 4 -1.215E-03 -6.482E-08 1.215E-03
- 18 5 -3.069E-03 -1.540E-07 3.069E-03
- 19 6 -1.183E-03 -2.450E-07 1.183E-03
- 20 7 -9.324E-04 -3.327E-07 9.324E-04
- 21 8 1.720E-03 -2.167E-07 1.720E-03
- 22 9 2.203E-04 3.058E-07 2.203E-04
- 23 10 2.059E-04 3.395E-07 2.059E-04
- 24 11 -2.177E-04 5.037E-07 2.177E-04
- 25 12 -3.999E-04 -7.451E-07 3.999E-04
- 26 13 5.926E-04 -2.445E-06 5.926E-04
- 27 14 -1.018E-03 7.154E-06 1.018E-03
- 28 15 1.616E-03 -2.033E-05 1.617E-03
- 29 16 -8.381E-04 2.146E-05 8.384E-04
- 30 17 -1.123E-03 8.025E-06 1.123E-03
- 31 18 7.468E-04 -1.563E-05 7.469E-04
- 32 19 1.270E-03 -1.735E-05 1.270E-03
- 33 20 4.224E-04 -5.104E-06 4.225E-04
-
- ipert m re wt im wt abs wt
-
-
- isol imax plasma vacuum re total im total
-
- 24 10 1.583E+02 1.654E+02 3.238E+02 -6.909E-07
-
- ipert m re wt im wt abs wt
-
- 1 -12 9.644E-05 -1.056E-06 9.645E-05
- 2 -11 2.930E-04 -3.312E-06 2.930E-04
- 3 -10 1.733E-04 -2.312E-06 1.733E-04
- 4 -9 -1.625E-04 -3.246E-07 1.625E-04
- 5 -8 -2.474E-04 1.103E-06 2.474E-04
- 6 -7 9.591E-05 1.251E-06 9.592E-05
- 7 -6 2.267E-04 -3.967E-07 2.267E-04
- 8 -5 -1.114E-04 -1.321E-06 1.115E-04
- 9 -4 -1.762E-04 -5.915E-08 1.762E-04
- 10 -3 1.691E-04 2.215E-07 1.691E-04
- 11 -2 3.768E-05 1.172E-08 3.768E-05
- 12 -1 -1.295E-05 -5.595E-07 1.296E-05
- 13 0 -1.691E-04 6.511E-07 1.691E-04
- 14 1 2.061E-04 -2.723E-07 2.061E-04
- 15 2 -8.823E-05 -4.774E-08 8.823E-05
- 16 3 -2.140E-05 -2.456E-08 2.140E-05
- 17 4 9.680E-05 -1.314E-08 9.680E-05
- 18 5 -1.393E-05 1.659E-08 1.393E-05
- 19 6 1.877E-04 2.353E-08 1.877E-04
- 20 7 -3.359E-04 6.164E-08 3.359E-04
- 21 8 6.031E-04 -5.017E-08 6.031E-04
- 22 9 -1.135E-03 8.675E-08 1.135E-03
- 23 10 2.082E-03 -8.741E-08 2.082E-03
- 24 11 -3.738E-03 2.903E-07 3.738E-03
- 25 12 5.500E-03 -2.640E-07 5.500E-03
- 26 13 3.103E-04 -3.264E-07 3.103E-04
- 27 14 -5.077E-02 1.909E-06 5.077E-02
- 28 15 2.276E-01 -4.747E-06 2.276E-01
- 29 16 -5.200E-01 5.223E-06 5.200E-01
- 30 17 5.497E-01 0.000E+00 5.497E-01 *
- 31 18 3.529E-02 8.558E-07 3.529E-02
- 32 19 -4.429E-01 -7.586E-06 4.429E-01
- 33 20 -1.728E-01 -4.648E-06 1.728E-01
-
- ipert m re wt im wt abs wt
-
-
- isol imax plasma vacuum re total im total
-
- 25 10 1.853E+02 1.654E+02 3.506E+02 -4.820E-08
-
- ipert m re wt im wt abs wt
-
- 1 -12 1.500E-01 -1.098E-06 1.500E-01
- 2 -11 4.080E-01 0.000E+00 4.080E-01 *
- 3 -10 1.459E-01 6.101E-07 1.459E-01
- 4 -9 -3.568E-01 -1.954E-06 3.568E-01
- 5 -8 -2.140E-01 -1.617E-06 2.140E-01
- 6 -7 3.193E-01 3.981E-06 3.193E-01
- 7 -6 1.704E-01 2.054E-06 1.704E-01
- 8 -5 -3.525E-01 -4.801E-06 3.525E-01
- 9 -4 2.558E-02 3.243E-07 2.558E-02
- 10 -3 2.153E-01 3.699E-06 2.153E-01
- 11 -2 -9.286E-03 -5.981E-08 9.286E-03
- 12 -1 -3.079E-01 -5.215E-06 3.079E-01
- 13 0 2.659E-01 4.987E-06 2.659E-01
- 14 1 -1.238E-02 -2.357E-07 1.238E-02
- 15 2 -5.294E-02 -1.115E-06 5.294E-02
- 16 3 -3.298E-03 -7.964E-08 3.298E-03
- 17 4 2.736E-03 1.016E-07 2.736E-03
- 18 5 2.599E-03 5.535E-08 2.599E-03
- 19 6 5.774E-04 -1.386E-07 5.774E-04
- 20 7 1.284E-04 -2.737E-07 1.284E-04
- 21 8 -1.346E-03 -1.620E-07 1.346E-03
- 22 9 -7.211E-06 -2.285E-09 7.211E-06
- 23 10 -1.276E-04 -2.869E-08 1.276E-04
- 24 11 1.627E-04 -2.465E-07 1.627E-04
- 25 12 1.778E-04 -3.642E-07 1.778E-04
- 26 13 -1.754E-04 -8.366E-07 1.754E-04
- 27 14 1.371E-04 -2.888E-07 1.371E-04
- 28 15 -2.374E-04 -2.668E-07 2.374E-04
- 29 16 2.713E-04 2.018E-06 2.713E-04
- 30 17 -1.038E-04 -9.185E-07 1.038E-04
- 31 18 -1.684E-04 -2.229E-06 1.684E-04
- 32 19 2.094E-04 -1.703E-06 2.094E-04
- 33 20 7.732E-05 -8.920E-07 7.732E-05
-
- ipert m re wt im wt abs wt
-
-
- isol imax plasma vacuum re total im total
-
- 26 10 1.881E+02 1.968E+02 3.849E+02 -4.066E-07
-
- ipert m re wt im wt abs wt
-
- 1 -12 3.529E-05 -9.234E-07 3.530E-05
- 2 -11 6.948E-05 -1.398E-07 6.948E-05
- 3 -10 1.349E-05 -1.321E-06 1.355E-05
- 4 -9 -7.824E-05 1.007E-07 7.824E-05
- 5 -8 3.287E-06 -2.244E-07 3.295E-06
- 6 -7 6.247E-05 1.425E-07 6.247E-05
- 7 -6 -1.643E-05 6.019E-07 1.644E-05
- 8 -5 -5.214E-05 -5.292E-07 5.214E-05
- 9 -4 5.675E-05 -5.710E-07 5.675E-05
- 10 -3 -1.236E-05 1.987E-07 1.236E-05
- 11 -2 -4.469E-06 2.029E-07 4.474E-06
- 12 -1 -7.713E-05 -4.032E-07 7.713E-05
- 13 0 1.157E-04 1.549E-07 1.157E-04
- 14 1 -8.009E-05 8.127E-08 8.009E-05
- 15 2 3.253E-05 -1.452E-07 3.253E-05
- 16 3 6.660E-07 2.133E-08 6.663E-07
- 17 4 -3.677E-05 8.882E-09 3.677E-05
- 18 5 1.053E-05 1.988E-08 1.053E-05
- 19 6 -9.422E-05 1.913E-08 9.422E-05
- 20 7 1.555E-04 2.749E-08 1.555E-04
- 21 8 -2.810E-04 -9.069E-09 2.810E-04
- 22 9 5.259E-04 -2.517E-08 5.259E-04
- 23 10 -9.500E-04 1.090E-07 9.500E-04
- 24 11 1.709E-03 -6.439E-08 1.709E-03
- 25 12 -2.974E-03 1.855E-07 2.974E-03
- 26 13 4.480E-03 -3.117E-07 4.480E-03
- 27 14 -2.478E-03 -4.090E-08 2.478E-03
- 28 15 -2.140E-02 8.483E-07 2.140E-02
- 29 16 1.229E-01 -2.355E-06 1.229E-01
- 30 17 -3.727E-01 3.737E-06 3.727E-01
- 31 18 6.494E-01 0.000E+00 6.494E-01 *
- 32 19 -4.931E-01 -4.054E-06 4.931E-01
- 33 20 -1.865E-01 -3.589E-06 1.865E-01
-
- ipert m re wt im wt abs wt
-
-
- isol imax plasma vacuum re total im total
-
- 27 10 2.334E+02 2.038E+02 4.371E+02 6.124E-08
-
- ipert m re wt im wt abs wt
-
- 1 -12 1.801E-01 -1.418E-06 1.801E-01
- 2 -11 3.861E-01 0.000E+00 3.861E-01 *
- 3 -10 -1.450E-01 -5.922E-07 1.450E-01
- 4 -9 -3.620E-01 -2.524E-06 3.620E-01
- 5 -8 2.722E-01 2.752E-06 2.722E-01
- 6 -7 1.967E-01 2.052E-06 1.967E-01
- 7 -6 -3.694E-01 -5.009E-06 3.694E-01
- 8 -5 1.028E-01 1.456E-06 1.028E-01
- 9 -4 2.067E-01 2.801E-06 2.067E-01
- 10 -3 -1.876E-01 -2.790E-06 1.876E-01
- 11 -2 -1.265E-01 -2.232E-06 1.265E-01
- 12 -1 3.488E-01 5.757E-06 3.488E-01
- 13 0 -2.055E-01 -3.661E-06 2.055E-01
- 14 1 -3.384E-02 -7.854E-07 3.384E-02
- 15 2 4.419E-02 1.003E-06 4.419E-02
- 16 3 3.772E-03 1.009E-07 3.772E-03
- 17 4 -3.935E-03 -1.578E-07 3.935E-03
- 18 5 -1.743E-03 -1.026E-07 1.743E-03
- 19 6 1.825E-04 -5.558E-08 1.825E-04
- 20 7 5.183E-04 4.914E-08 5.183E-04
- 21 8 8.154E-04 1.832E-07 8.154E-04
- 22 9 -1.111E-04 1.205E-07 1.111E-04
- 23 10 6.931E-05 1.280E-07 6.931E-05
- 24 11 -9.399E-05 3.865E-08 9.399E-05
- 25 12 -4.029E-05 -1.854E-07 4.029E-05
- 26 13 3.120E-05 -2.330E-07 3.120E-05
- 27 14 -1.762E-05 1.942E-07 1.762E-05
- 28 15 3.828E-05 3.331E-07 3.828E-05
- 29 16 -3.699E-05 5.863E-07 3.699E-05
- 30 17 2.415E-05 -5.802E-07 2.416E-05
- 31 18 -2.729E-05 -1.160E-06 2.732E-05
- 32 19 1.831E-05 6.808E-07 1.833E-05
- 33 20 1.738E-06 -3.815E-07 1.780E-06
-
- ipert m re wt im wt abs wt
-
-
- isol imax plasma vacuum re total im total
-
- 28 10 2.995E+02 2.591E+02 5.586E+02 2.686E-07
-
- ipert m re wt im wt abs wt
-
- 1 -12 -2.175E-01 2.279E-06 2.175E-01
- 2 -11 -3.126E-01 1.221E-06 3.126E-01
- 3 -10 3.735E-01 0.000E+00 3.735E-01 *
- 4 -9 7.003E-03 -1.071E-06 7.003E-03
- 5 -8 -3.444E-01 -1.165E-06 3.444E-01
- 6 -7 3.330E-01 2.230E-06 3.330E-01
- 7 -6 -4.868E-02 -1.803E-06 4.868E-02
- 8 -5 -2.308E-01 -1.774E-07 2.308E-01
- 9 -4 2.762E-01 8.702E-07 2.762E-01
- 10 -3 -5.528E-02 -1.259E-07 5.528E-02
- 11 -2 -2.496E-01 -2.046E-06 2.496E-01
- 12 -1 3.455E-01 2.672E-06 3.455E-01
- 13 0 -1.323E-01 -1.331E-06 1.323E-01
- 14 1 -7.018E-02 -9.558E-07 7.018E-02
- 15 2 3.196E-02 5.099E-07 3.196E-02
- 16 3 4.300E-03 8.775E-08 4.300E-03
- 17 4 -5.017E-03 -1.491E-07 5.017E-03
- 18 5 -8.762E-04 1.078E-08 8.762E-04
- 19 6 1.078E-03 1.467E-07 1.078E-03
- 20 7 8.952E-04 1.386E-07 8.952E-04
- 21 8 3.417E-04 1.537E-07 3.417E-04
- 22 9 -1.278E-04 1.022E-07 1.278E-04
- 23 10 -2.801E-06 9.137E-08 2.803E-06
- 24 11 -6.048E-05 1.596E-07 6.048E-05
- 25 12 4.648E-05 2.484E-07 4.648E-05
- 26 13 -3.541E-05 2.307E-07 3.542E-05
- 27 14 2.224E-05 4.037E-08 2.224E-05
- 28 15 -2.086E-05 1.619E-07 2.086E-05
- 29 16 1.420E-05 -3.074E-07 1.421E-05
- 30 17 -7.243E-06 7.612E-07 7.283E-06
- 31 18 7.332E-06 9.664E-08 7.333E-06
- 32 19 -6.299E-06 -3.044E-07 6.306E-06
- 33 20 1.137E-05 1.655E-06 1.149E-05
-
- ipert m re wt im wt abs wt
-
-
- isol imax plasma vacuum re total im total
-
- 29 10 4.696E+02 2.062E+02 6.759E+02 -9.510E-07
-
- ipert m re wt im wt abs wt
-
- 1 -12 -2.829E-05 4.083E-08 2.829E-05
- 2 -11 -2.442E-06 1.162E-06 2.705E-06
- 3 -10 2.942E-05 -2.222E-06 2.951E-05
- 4 -9 -3.873E-05 3.523E-06 3.889E-05
- 5 -8 2.134E-05 -2.025E-06 2.143E-05
- 6 -7 2.384E-06 -2.465E-07 2.397E-06
- 7 -6 -1.678E-05 1.717E-06 1.687E-05
- 8 -5 1.936E-05 -2.023E-06 1.946E-05
- 9 -4 -8.868E-06 1.612E-06 9.013E-06
- 10 -3 -1.222E-05 4.315E-07 1.222E-05
- 11 -2 2.843E-05 -1.983E-06 2.850E-05
- 12 -1 -2.467E-05 2.047E-06 2.475E-05
- 13 0 1.250E-05 -5.337E-07 1.251E-05
- 14 1 1.843E-06 -4.962E-07 1.908E-06
- 15 2 3.846E-06 1.519E-07 3.849E-06
- 16 3 -2.802E-07 4.358E-08 2.835E-07
- 17 4 -3.613E-06 -4.412E-08 3.614E-06
- 18 5 1.579E-06 1.721E-08 1.579E-06
- 19 6 -1.229E-05 5.577E-10 1.229E-05
- 20 7 1.921E-05 -3.298E-08 1.921E-05
- 21 8 -3.767E-05 -3.968E-08 3.767E-05
- 22 9 7.043E-05 1.892E-08 7.043E-05
- 23 10 -1.221E-04 2.566E-08 1.221E-04
- 24 11 2.264E-04 -1.751E-07 2.264E-04
- 25 12 -4.248E-04 6.102E-08 4.248E-04
- 26 13 8.003E-04 4.821E-08 8.003E-04
- 27 14 -1.758E-03 3.188E-07 1.758E-03
- 28 15 4.078E-03 -3.137E-07 4.078E-03
- 29 16 -9.153E-03 -9.705E-08 9.153E-03
- 30 17 1.624E-02 -8.202E-07 1.624E-02
- 31 18 3.027E-02 -1.088E-06 3.027E-02
- 32 19 -3.045E-01 2.837E-06 3.045E-01
- 33 20 8.719E-01 0.000E+00 8.719E-01 *
-
- ipert m re wt im wt abs wt
-
-
- isol imax plasma vacuum re total im total
-
- 30 10 3.803E+02 3.464E+02 7.267E+02 6.445E-07
-
- ipert m re wt im wt abs wt
-
- 1 -12 -2.829E-01 1.424E-06 2.829E-01
- 2 -11 -1.639E-01 1.203E-06 1.639E-01
- 3 -10 3.917E-01 0.000E+00 3.917E-01 *
- 4 -9 -3.268E-01 -1.652E-06 3.268E-01
- 5 -8 8.568E-02 2.450E-06 8.568E-02
- 6 -7 1.782E-01 -2.592E-06 1.782E-01
- 7 -6 -3.408E-01 2.596E-06 3.408E-01
- 8 -5 3.331E-01 -2.054E-06 3.331E-01
- 9 -4 -1.581E-01 1.700E-06 1.581E-01
- 10 -3 -1.045E-01 -5.831E-07 1.045E-01
- 11 -2 3.060E-01 -1.797E-07 3.060E-01
- 12 -1 -2.841E-01 5.920E-07 2.841E-01
- 13 0 5.468E-02 -3.456E-07 5.468E-02
- 14 1 8.619E-02 7.180E-07 8.619E-02
- 15 2 -1.636E-02 -2.145E-07 1.636E-02
- 16 3 -4.021E-03 -7.351E-08 4.021E-03
- 17 4 5.107E-03 1.140E-07 5.107E-03
- 18 5 -4.219E-04 1.442E-08 4.219E-04
- 19 6 -2.126E-03 -1.630E-07 2.126E-03
- 20 7 -9.777E-04 -2.652E-08 9.777E-04
- 21 8 1.678E-04 -1.283E-07 1.678E-04
- 22 9 2.208E-04 -2.362E-08 2.208E-04
- 23 10 1.219E-05 -1.343E-07 1.219E-05
- 24 11 2.430E-05 -2.199E-08 2.430E-05
- 25 12 -1.054E-04 -3.542E-09 1.054E-04
- 26 13 7.558E-05 -3.077E-08 7.558E-05
- 27 14 -3.962E-05 -3.724E-08 3.962E-05
- 28 15 4.438E-05 -1.831E-07 4.438E-05
- 29 16 -3.419E-05 -1.363E-07 3.419E-05
- 30 17 1.726E-05 3.014E-07 1.727E-05
- 31 18 -1.267E-05 -3.955E-07 1.268E-05
- 32 19 2.875E-05 2.006E-06 2.882E-05
- 33 20 -6.650E-05 -5.331E-06 6.671E-05
-
- ipert m re wt im wt abs wt
-
-
- isol imax plasma vacuum re total im total
-
- 31 10 4.061E+02 4.975E+02 9.035E+02 -1.011E-06
-
- ipert m re wt im wt abs wt
-
- 1 -12 -3.221E-01 -4.010E-06 3.221E-01
- 2 -11 -6.936E-03 2.495E-06 6.936E-03
- 3 -10 2.478E-01 -2.770E-07 2.478E-01
- 4 -9 -3.805E-01 -8.585E-07 3.805E-01
- 5 -8 4.271E-01 0.000E+00 4.271E-01 *
- 6 -7 -3.989E-01 1.040E-06 3.989E-01
- 7 -6 3.048E-01 -2.541E-06 3.048E-01
- 8 -5 -1.623E-01 3.253E-06 1.623E-01
- 9 -4 -6.152E-04 -3.083E-06 6.152E-04
- 10 -3 1.415E-01 1.773E-06 1.415E-01
- 11 -2 -2.033E-01 -4.820E-07 2.033E-01
- 12 -1 1.398E-01 -6.537E-07 1.398E-01
- 13 0 -2.848E-03 8.211E-07 2.848E-03
- 14 1 -5.086E-02 -6.149E-07 5.086E-02
- 15 2 5.448E-03 -7.369E-08 5.448E-03
- 16 3 2.339E-03 4.708E-08 2.339E-03
- 17 4 -3.618E-03 -6.485E-08 3.618E-03
- 18 5 1.915E-04 -2.792E-08 1.915E-04
- 19 6 1.944E-03 2.266E-07 1.944E-03
- 20 7 9.542E-04 7.639E-08 9.542E-04
- 21 8 8.968E-06 1.188E-07 8.969E-06
- 22 9 -2.792E-04 3.947E-08 2.792E-04
- 23 10 -1.524E-05 2.117E-08 1.524E-05
- 24 11 -5.679E-05 1.112E-07 5.679E-05
- 25 12 7.862E-05 5.790E-08 7.862E-05
- 26 13 -5.148E-05 1.147E-07 5.148E-05
- 27 14 2.970E-05 8.347E-08 2.970E-05
- 28 15 -2.576E-05 -5.070E-08 2.576E-05
- 29 16 1.792E-05 1.202E-07 1.792E-05
- 30 17 -6.660E-06 7.185E-08 6.660E-06
- 31 18 1.982E-06 2.184E-08 1.983E-06
- 32 19 6.276E-06 4.533E-07 6.293E-06
- 33 20 -2.022E-05 -1.047E-06 2.024E-05
-
- ipert m re wt im wt abs wt
-
-
- isol imax plasma vacuum re total im total
-
- 32 10 6.333E+02 4.812E+02 1.115E+03 -9.318E-08
-
- ipert m re wt im wt abs wt
-
- 1 -12 7.403E-01 0.000E+00 7.403E-01 *
- 2 -11 -4.257E-01 -1.206E-06 4.257E-01
- 3 -10 2.610E-01 -4.471E-07 2.610E-01
- 4 -9 -1.824E-01 2.070E-06 1.824E-01
- 5 -8 1.258E-01 -2.289E-06 1.258E-01
- 6 -7 -7.606E-02 2.661E-06 7.606E-02
- 7 -6 3.621E-02 -2.328E-06 3.621E-02
- 8 -5 -7.200E-03 1.592E-06 7.200E-03
- 9 -4 -1.030E-02 -8.679E-07 1.030E-02
- 10 -3 1.608E-02 1.168E-07 1.608E-02
- 11 -2 -1.214E-02 5.088E-07 1.214E-02
- 12 -1 3.585E-03 -6.507E-07 3.585E-03
- 13 0 2.069E-05 2.176E-07 2.069E-05
- 14 1 2.059E-03 1.960E-07 2.059E-03
- 15 2 2.633E-03 -9.905E-09 2.633E-03
- 16 3 3.637E-04 -2.159E-09 3.637E-04
- 17 4 -6.882E-04 -2.714E-08 6.882E-04
- 18 5 -3.605E-04 -6.341E-08 3.605E-04
- 19 6 2.732E-04 -5.917E-09 2.732E-04
- 20 7 2.644E-04 -3.735E-09 2.644E-04
- 21 8 1.779E-04 -4.003E-09 1.779E-04
- 22 9 -5.222E-05 -1.355E-08 5.222E-05
- 23 10 -1.600E-05 3.427E-08 1.600E-05
- 24 11 -3.319E-05 -5.707E-08 3.319E-05
- 25 12 -2.545E-07 -2.600E-09 2.545E-07
- 26 13 2.026E-06 -1.185E-07 2.030E-06
- 27 14 1.269E-06 -2.536E-08 1.270E-06
- 28 15 5.257E-06 1.529E-07 5.259E-06
- 29 16 -5.379E-06 -2.777E-07 5.386E-06
- 30 17 3.805E-06 3.643E-07 3.822E-06
- 31 18 -6.034E-06 -8.620E-07 6.095E-06
- 32 19 2.969E-06 1.162E-06 3.188E-06
- 33 20 5.617E-06 -1.668E-06 5.860E-06
-
- ipert m re wt im wt abs wt
-
-
- isol imax plasma vacuum re total im total
-
- 33 10 9.328E+02 3.843E+02 1.317E+03 -4.588E-06
-
- ipert m re wt im wt abs wt
-
- 1 -12 1.358E-02 3.396E-07 1.358E-02
- 2 -11 -5.543E-03 -7.251E-07 5.543E-03
- 3 -10 -4.882E-03 9.783E-07 4.882E-03
- 4 -9 2.297E-02 -1.353E-06 2.297E-02
- 5 -8 -5.548E-02 1.558E-06 5.548E-02
- 6 -7 1.098E-01 -2.025E-06 1.098E-01
- 7 -6 -1.923E-01 2.241E-06 1.923E-01
- 8 -5 3.026E-01 -2.367E-06 3.026E-01
- 9 -4 -4.224E-01 1.509E-06 4.224E-01
- 10 -3 4.978E-01 0.000E+00 4.978E-01 *
- 11 -2 -4.303E-01 -2.095E-06 4.303E-01
- 12 -1 1.605E-01 2.013E-06 1.605E-01
- 13 0 1.638E-01 1.044E-06 1.638E-01
- 14 1 -1.942E-01 -3.278E-06 1.942E-01
- 15 2 -8.980E-02 -1.852E-06 8.980E-02
- 16 3 -4.376E-03 -1.233E-07 4.376E-03
- 17 4 1.453E-03 6.465E-08 1.453E-03
- 18 5 1.093E-05 3.979E-08 1.093E-05
- 19 6 3.930E-04 1.752E-08 3.930E-04
- 20 7 6.422E-04 1.085E-07 6.422E-04
- 21 8 1.502E-04 2.775E-08 1.502E-04
- 22 9 -5.960E-05 6.482E-08 5.960E-05
- 23 10 1.423E-05 3.659E-08 1.423E-05
- 24 11 -5.339E-05 5.020E-08 5.339E-05
- 25 12 5.288E-05 7.218E-08 5.288E-05
- 26 13 -5.084E-05 7.137E-09 5.084E-05
- 27 14 2.993E-05 5.122E-08 2.993E-05
- 28 15 -2.597E-05 2.576E-08 2.597E-05
- 29 16 2.181E-05 6.554E-08 2.181E-05
- 30 17 -1.334E-05 2.215E-08 1.334E-05
- 31 18 9.843E-06 -3.561E-08 9.843E-06
- 32 19 -9.016E-06 5.221E-08 9.016E-06
- 33 20 9.216E-06 -4.975E-08 9.216E-06
-
- ipert m re wt im wt abs wt
-
-
- Plasma Energy Matrix:
-
- isol = 1, m = -12
-
- i re wp im wp abs wp
-
- 1 7.72178E+02 -1.03597E-07 7.72178E+02
- 2 -1.47516E+02 -2.09075E-03 1.47516E+02
- 3 -3.08329E+00 2.63376E-04 3.08329E+00
- 4 1.07454E+01 6.49986E-04 1.07454E+01
- 5 -6.60015E+00 -1.40265E-04 6.60015E+00
- 6 6.44872E+00 4.12719E-04 6.44872E+00
- 7 -5.39722E+00 -2.05404E-04 5.39722E+00
- 8 3.82531E+00 -2.61321E-05 3.82531E+00
- 9 -1.88714E+00 -2.66064E-05 1.88714E+00
- 10 -2.82049E-01 5.74697E-05 2.82049E-01
- 11 2.05301E+00 9.11286E-05 2.05301E+00
- 12 -2.40189E+00 -1.74415E-04 2.40189E+00
- 13 6.24578E-02 1.85132E-04 6.24580E-02
- 14 1.94405E+00 -1.93499E-05 1.94405E+00
- 15 4.66486E-01 1.16235E-04 4.66486E-01
- 16 4.19804E-02 1.20374E-06 4.19804E-02
- 17 -1.79607E-01 -5.04581E-05 1.79607E-01
- 18 -2.97016E-01 -1.64809E-05 2.97016E-01
- 19 -8.80563E-04 -1.03771E-05 8.80624E-04
- 20 1.02489E-01 -3.29195E-06 1.02489E-01
- 21 1.26953E-01 -4.94303E-05 1.26953E-01
- 22 -3.11513E-03 -1.39923E-04 3.11827E-03
- 23 -9.88327E-03 -2.30583E-05 9.88330E-03
- 24 -1.79073E-02 -8.69841E-05 1.79075E-02
- 25 -4.43867E-03 7.96920E-05 4.43938E-03
- 26 2.67354E-03 -8.61256E-05 2.67492E-03
- 27 5.35361E-04 2.04622E-05 5.35752E-04
- 28 1.96259E-03 -1.39715E-04 1.96756E-03
- 29 -1.48541E-03 -2.50157E-05 1.48562E-03
- 30 2.44419E-04 -1.37486E-04 2.80434E-04
- 31 -1.25827E-03 8.78950E-05 1.26133E-03
- 32 -1.11714E-03 -2.42444E-05 1.11740E-03
- 33 5.97066E-03 -1.80966E-05 5.97068E-03
-
- i re wp im wp abs wp
-
- isol = 2, m = -11
-
- i re wp im wp abs wp
-
- 1 -1.47516E+02 2.09158E-03 1.47516E+02
- 2 2.96916E+02 -4.33714E-08 2.96916E+02
- 3 -8.97436E+01 -1.08461E-03 8.97436E+01
- 4 1.42505E+01 1.92496E-04 1.42505E+01
- 5 1.08923E+00 2.18494E-05 1.08923E+00
- 6 -5.19902E+00 -1.71008E-04 5.19902E+00
- 7 6.48238E+00 1.89894E-04 6.48238E+00
- 8 -5.11900E+00 -5.25852E-05 5.11900E+00
- 9 2.61994E+00 -3.38260E-05 2.61994E+00
- 10 3.56480E-01 1.25135E-04 3.56480E-01
- 11 -2.81025E+00 -1.88495E-04 2.81025E+00
- 12 3.18464E+00 2.52362E-04 3.18464E+00
- 13 2.08494E-01 -1.71439E-05 2.08494E-01
- 14 -2.93826E+00 -1.02718E-04 2.93826E+00
- 15 -1.07469E+00 -9.90761E-05 1.07469E+00
- 16 -9.62992E-02 6.15440E-06 9.62992E-02
- 17 2.92642E-01 2.49456E-05 2.92642E-01
- 18 3.55334E-01 -1.62292E-05 3.55334E-01
- 19 -3.74590E-02 -9.97212E-06 3.74590E-02
- 20 -1.44746E-01 -5.25077E-05 1.44746E-01
- 21 -1.53284E-01 -1.17840E-05 1.53284E-01
- 22 1.23674E-02 -3.38550E-05 1.23675E-02
- 23 1.18462E-02 -1.04109E-04 1.18466E-02
- 24 2.50821E-02 -9.79290E-05 2.50823E-02
- 25 4.87606E-03 -1.38300E-04 4.87803E-03
- 26 -2.36611E-03 -3.15090E-05 2.36632E-03
- 27 -2.07635E-03 7.07229E-06 2.07636E-03
- 28 -2.29648E-03 1.46816E-05 2.29653E-03
- 29 1.11569E-03 9.79741E-06 1.11574E-03
- 30 1.57681E-04 -1.77615E-04 2.37509E-04
- 31 6.84811E-04 -1.50925E-04 7.01245E-04
- 32 -1.00029E-03 -2.08702E-05 1.00051E-03
- 33 -6.83839E-04 2.49158E-05 6.84293E-04
-
- i re wp im wp abs wp
-
- isol = 3, m = -10
-
- i re wp im wp abs wp
-
- 1 -3.08264E+00 -2.60865E-04 3.08264E+00
- 2 -8.97436E+01 1.08425E-03 8.97436E+01
- 3 2.71032E+02 -6.53407E-08 2.71032E+02
- 4 -8.82981E+01 -9.69103E-04 8.82981E+01
- 5 1.51889E+01 2.40598E-04 1.51889E+01
- 6 1.69522E+00 2.65609E-05 1.69522E+00
- 7 -5.77372E+00 -1.45903E-04 5.77372E+00
- 8 6.18313E+00 1.51457E-04 6.18313E+00
- 9 -3.36231E+00 1.03511E-05 3.36231E+00
- 10 -6.24783E-01 -1.28705E-04 6.24783E-01
- 11 3.77490E+00 1.92471E-04 3.77490E+00
- 12 -3.94148E+00 -1.28289E-04 3.94148E+00
- 13 -9.24514E-01 -4.11539E-05 9.24514E-01
- 14 4.47843E+00 2.02082E-04 4.47843E+00
- 15 2.25397E+00 2.16945E-04 2.25397E+00
- 16 1.98641E-01 1.03759E-05 1.98641E-01
- 17 -4.39996E-01 -6.18557E-05 4.39996E-01
- 18 -3.25348E-01 -2.11778E-05 3.25348E-01
- 19 1.59446E-01 -4.58048E-05 1.59446E-01
- 20 1.96002E-01 9.21080E-06 1.96002E-01
- 21 1.52139E-01 -3.04065E-05 1.52139E-01
- 22 -4.25381E-02 -1.86931E-06 4.25381E-02
- 23 -7.33981E-03 -3.56121E-05 7.33989E-03
- 24 -2.65879E-02 -8.80243E-05 2.65880E-02
- 25 9.21599E-04 -8.50245E-05 9.25512E-04
- 26 6.48360E-04 -1.21235E-04 6.59597E-04
- 27 2.81722E-03 -4.64269E-05 2.81760E-03
- 28 7.71867E-04 1.43041E-06 7.71868E-04
- 29 -1.19752E-03 -3.30207E-06 1.19752E-03
- 30 -3.11766E-04 4.18904E-05 3.14568E-04
- 31 9.55563E-05 -1.67429E-04 1.92778E-04
- 32 4.42134E-04 -1.18062E-04 4.57626E-04
- 33 -7.33977E-04 -3.23864E-05 7.34691E-04
-
- i re wp im wp abs wp
-
- isol = 4, m = -9
-
- i re wp im wp abs wp
-
- 1 1.07449E+01 -6.49739E-04 1.07449E+01
- 2 1.42507E+01 -1.92513E-04 1.42507E+01
- 3 -8.82982E+01 9.69216E-04 8.82982E+01
- 4 2.54594E+02 -1.47587E-07 2.54594E+02
- 5 -8.45218E+01 -8.52534E-04 8.45218E+01
- 6 1.46609E+01 2.13585E-04 1.46609E+01
- 7 1.70974E+00 5.30208E-05 1.70974E+00
- 8 -4.49403E+00 -1.09190E-04 4.49403E+00
- 9 2.87755E+00 6.13731E-05 2.87755E+00
- 10 1.84117E+00 2.06136E-04 1.84117E+00
- 11 -5.41409E+00 -3.45764E-04 5.41409E+00
- 12 4.46892E+00 3.37351E-04 4.46892E+00
- 13 2.78765E+00 8.61108E-05 2.78765E+00
- 14 -6.96910E+00 -3.17036E-04 6.96910E+00
- 15 -4.58883E+00 -2.21155E-04 4.58883E+00
- 16 -4.19276E-01 -6.69809E-06 4.19276E-01
- 17 6.87180E-01 2.88766E-05 6.87180E-01
- 18 2.02745E-01 -3.68992E-05 2.02745E-01
- 19 -3.58551E-01 -3.45619E-05 3.58551E-01
- 20 -2.50897E-01 -1.10264E-04 2.50897E-01
- 21 -1.18643E-01 -5.10103E-05 1.18643E-01
- 22 8.13383E-02 -5.81515E-05 8.13384E-02
- 23 5.58762E-03 -9.63817E-06 5.58763E-03
- 24 2.88455E-02 -4.07483E-05 2.88456E-02
- 25 -6.34385E-03 -9.19582E-05 6.34451E-03
- 26 4.70252E-03 -8.64060E-05 4.70332E-03
- 27 -4.25902E-03 -1.32623E-04 4.26108E-03
- 28 7.91314E-04 -5.43603E-05 7.93179E-04
- 29 -8.92109E-04 -1.29647E-05 8.92203E-04
- 30 3.21562E-04 5.30103E-06 3.21605E-04
- 31 -4.67695E-04 2.61490E-05 4.68426E-04
- 32 3.07661E-04 -1.42353E-04 3.38999E-04
- 33 -2.38687E-05 -1.25344E-04 1.27597E-04
-
- i re wp im wp abs wp
-
- isol = 5, m = -8
-
- i re wp im wp abs wp
-
- 1 -6.60009E+00 1.40322E-04 6.60009E+00
- 2 1.08910E+00 -2.12347E-05 1.08910E+00
- 3 1.51890E+01 -2.40920E-04 1.51890E+01
- 4 -8.45219E+01 8.52816E-04 8.45219E+01
- 5 2.40067E+02 -1.71176E-07 2.40067E+02
- 6 -8.31397E+01 -7.95288E-04 8.31397E+01
- 7 1.69426E+01 2.14632E-04 1.69426E+01
- 8 -2.28322E+00 -1.74937E-05 2.28322E+00
- 9 2.31299E+00 8.55780E-06 2.31299E+00
- 10 -6.10906E+00 -9.93627E-05 6.10906E+00
- 11 8.76054E+00 2.46045E-04 8.76054E+00
- 12 -4.62327E+00 -1.23197E-04 4.62327E+00
- 13 -7.06895E+00 -2.30817E-04 7.06895E+00
- 14 1.12210E+01 4.06909E-04 1.12210E+01
- 15 9.00510E+00 4.79157E-04 9.00510E+00
- 16 8.75507E-01 5.03662E-05 8.75507E-01
- 17 -1.12535E+00 -9.82033E-05 1.12535E+00
- 18 -1.86209E-03 -1.45762E-05 1.86214E-03
- 19 6.25239E-01 -2.12968E-05 6.25239E-01
- 20 2.93081E-01 1.87438E-05 2.93081E-01
- 21 4.53896E-02 -7.97810E-05 4.53896E-02
- 22 -1.10492E-01 -3.41071E-05 1.10492E-01
- 23 -7.22618E-03 -5.41404E-05 7.22638E-03
- 24 -2.17773E-02 -4.56468E-06 2.17773E-02
- 25 1.50361E-02 -3.94028E-05 1.50362E-02
- 26 -6.41734E-03 -9.17732E-05 6.41799E-03
- 27 6.79163E-03 -7.51794E-05 6.79204E-03
- 28 -2.32392E-03 -1.21166E-04 2.32708E-03
- 29 2.09828E-03 -4.61725E-05 2.09879E-03
- 30 -1.68344E-03 -1.40545E-05 1.68350E-03
- 31 1.78987E-04 2.16847E-05 1.80295E-04
- 32 -3.75491E-04 -3.45012E-05 3.77072E-04
- 33 1.79658E-05 -2.91066E-05 3.42047E-05
-
- i re wp im wp abs wp
-
- isol = 6, m = -7
-
- i re wp im wp abs wp
-
- 1 6.44882E+00 -4.12121E-04 6.44882E+00
- 2 -5.19898E+00 1.69550E-04 5.19898E+00
- 3 1.69507E+00 -2.56219E-05 1.69507E+00
- 4 1.46611E+01 -2.14188E-04 1.46611E+01
- 5 -8.31398E+01 7.95808E-04 8.31398E+01
- 6 2.29430E+02 -2.49600E-07 2.29430E+02
- 7 -8.74051E+01 -7.19404E-04 8.74051E+01
- 8 2.70681E+01 2.81511E-04 2.70681E+01
- 9 -1.62793E+01 -1.94144E-04 1.62793E+01
- 10 1.86539E+01 3.62276E-04 1.86539E+01
- 11 -1.67887E+01 -4.33473E-04 1.67887E+01
- 12 4.46445E+00 3.18030E-04 4.46445E+00
- 13 1.60538E+01 4.24212E-04 1.60538E+01
- 14 -1.90781E+01 -7.01123E-04 1.90781E+01
- 15 -1.67463E+01 -6.29221E-04 1.67463E+01
- 16 -1.67476E+00 -5.22627E-05 1.67476E+00
- 17 1.75739E+00 5.34928E-05 1.75739E+00
- 18 -2.72500E-01 -6.66130E-05 2.72500E-01
- 19 -9.47768E-01 -8.88036E-05 9.47768E-01
- 20 -2.90618E-01 -1.38431E-04 2.90618E-01
- 21 6.33196E-02 -4.72301E-05 6.33196E-02
- 22 1.32587E-01 -1.06262E-04 1.32587E-01
- 23 6.76920E-03 -4.07168E-05 6.76932E-03
- 24 1.52427E-02 -6.72805E-05 1.52428E-02
- 25 -2.67044E-02 -1.27522E-05 2.67044E-02
- 26 1.42951E-02 -5.40695E-05 1.42952E-02
- 27 -6.61191E-03 -1.05626E-04 6.61275E-03
- 28 7.43723E-03 -8.76895E-05 7.43774E-03
- 29 -3.68957E-03 -1.25644E-04 3.69171E-03
- 30 1.69659E-03 -4.78266E-05 1.69727E-03
- 31 -1.13596E-03 -1.77995E-05 1.13610E-03
- 32 -1.16435E-05 1.82448E-05 2.16436E-05
- 33 -4.43231E-05 -7.24976E-05 8.49731E-05
-
- i re wp im wp abs wp
-
- isol = 7, m = -6
-
- i re wp im wp abs wp
-
- 1 -5.39729E+00 2.04118E-04 5.39729E+00
- 2 6.48237E+00 -1.88264E-04 6.48237E+00
- 3 -5.77360E+00 1.44205E-04 5.77360E+00
- 4 1.70949E+00 -5.18446E-05 1.70949E+00
- 5 1.69429E+01 -2.15503E-04 1.69429E+01
- 6 -8.74054E+01 7.20177E-04 8.74054E+01
- 7 2.28350E+02 -3.61597E-07 2.28350E+02
- 8 -1.05822E+02 -7.47111E-04 1.05822E+02
- 9 5.49360E+01 4.80562E-04 5.49360E+01
- 10 -4.63968E+01 -5.16463E-04 4.63968E+01
- 11 3.64691E+01 5.17320E-04 3.64691E+01
- 12 -5.78832E+00 -2.31307E-05 5.78832E+00
- 13 -3.31679E+01 -8.00602E-04 3.31679E+01
- 14 3.37366E+01 9.90865E-04 3.37366E+01
- 15 2.92505E+01 1.07420E-03 2.92505E+01
- 16 2.80150E+00 1.27276E-04 2.80150E+00
- 17 -2.51657E+00 -1.48489E-04 2.51657E+00
- 18 5.10239E-01 -1.62082E-05 5.10239E-01
- 19 1.16414E+00 7.75223E-06 1.16414E+00
- 20 2.70175E-01 -1.10806E-05 2.70175E-01
- 21 -1.89183E-01 -1.20111E-04 1.89183E-01
- 22 -1.19705E-01 -3.47088E-05 1.19705E-01
- 23 -1.75569E-02 -1.06250E-04 1.75573E-02
- 24 -5.66681E-03 -2.77518E-05 5.66687E-03
- 25 3.70167E-02 -5.48697E-05 3.70167E-02
- 26 -1.83803E-02 5.16475E-06 1.83803E-02
- 27 1.08100E-02 -3.38122E-05 1.08101E-02
- 28 -1.00788E-02 -8.80974E-05 1.00792E-02
- 29 8.06920E-03 -8.07426E-05 8.06961E-03
- 30 -2.11002E-03 -1.21590E-04 2.11353E-03
- 31 1.38990E-03 -2.88382E-05 1.39019E-03
- 32 -1.10346E-03 -1.08548E-05 1.10352E-03
- 33 -2.07912E-04 1.66156E-05 2.08575E-04
-
- i re wp im wp abs wp
-
- isol = 8, m = -5
-
- i re wp im wp abs wp
-
- 1 3.82528E+00 2.74550E-05 3.82528E+00
- 2 -5.11894E+00 5.10927E-05 5.11894E+00
- 3 6.18297E+00 -1.49867E-04 6.18297E+00
- 4 -4.49371E+00 1.07388E-04 4.49371E+00
- 5 -2.28370E+00 1.88261E-05 2.28370E+00
- 6 2.70686E+01 -2.82592E-04 2.70686E+01
- 7 -1.05822E+02 7.48151E-04 1.05822E+02
- 8 2.49134E+02 -4.58887E-07 2.49134E+02
- 9 -1.52704E+02 -9.05955E-04 1.52704E+02
- 10 1.08379E+02 9.68965E-04 1.08379E+02
- 11 -7.67841E+01 -1.01390E-03 7.67841E+01
- 12 1.47953E+01 3.63311E-04 1.47953E+01
- 13 6.03455E+01 1.25989E-03 6.03455E+01
- 14 -5.94932E+01 -1.60904E-03 5.94932E+01
- 15 -4.71136E+01 -1.42472E-03 4.71136E+01
- 16 -3.96381E+00 -1.33830E-04 3.96381E+00
- 17 3.18521E+00 1.05657E-04 3.18521E+00
- 18 -5.32359E-01 -7.15266E-05 5.32359E-01
- 19 -1.02206E+00 -1.26607E-04 1.02206E+00
- 20 -2.46278E-01 -1.41105E-04 2.46278E-01
- 21 2.98563E-01 -5.67230E-05 2.98563E-01
- 22 6.21519E-02 -1.40821E-04 6.21520E-02
- 23 4.58203E-02 -3.67073E-05 4.58203E-02
- 24 -2.82754E-02 -1.20551E-04 2.82757E-02
- 25 -2.58903E-02 -3.61743E-05 2.58904E-02
- 26 9.84692E-03 -7.78595E-05 9.84723E-03
- 27 -2.74666E-03 -1.71076E-05 2.74671E-03
- 28 9.21604E-03 -5.07212E-05 9.21618E-03
- 29 -4.55333E-03 -8.51189E-05 4.55412E-03
- 30 2.01972E-03 -8.11474E-05 2.02135E-03
- 31 -1.30465E-05 -1.34997E-04 1.35626E-04
- 32 1.63364E-04 -1.92009E-05 1.64489E-04
- 33 2.05011E-04 -6.23485E-05 2.14282E-04
-
- i re wp im wp abs wp
-
- isol = 9, m = -4
-
- i re wp im wp abs wp
-
- 1 -1.88705E+00 2.60530E-05 1.88705E+00
- 2 2.61981E+00 3.50448E-05 2.61981E+00
- 3 -3.36207E+00 -1.16248E-05 3.36207E+00
- 4 2.87715E+00 -5.97718E-05 2.87715E+00
- 5 2.31360E+00 -1.04186E-05 2.31360E+00
- 6 -1.62801E+01 1.95641E-04 1.62801E+01
- 7 5.49367E+01 -4.82034E-04 5.49367E+01
- 8 -1.52705E+02 9.07410E-04 1.52705E+02
- 9 3.08299E+02 -7.69233E-07 3.08299E+02
- 10 -2.34864E+02 -1.06005E-03 2.34864E+02
- 11 1.58573E+02 1.22187E-03 1.58573E+02
- 12 -4.03828E+01 -3.68136E-04 4.03828E+01
- 13 -9.47500E+01 -1.53633E-03 9.47500E+01
- 14 1.00223E+02 2.23831E-03 1.00223E+02
- 15 6.69533E+01 1.79880E-03 6.69533E+01
- 16 4.53120E+00 1.54694E-04 4.53120E+00
- 17 -3.04342E+00 -1.44816E-04 3.04342E+00
- 18 4.01226E-01 -4.34603E-05 4.01226E-01
- 19 5.16821E-01 -6.05976E-05 5.16821E-01
- 20 6.24356E-02 -8.24558E-05 6.24356E-02
- 21 -2.90783E-01 -1.59555E-04 2.90784E-01
- 22 -6.22075E-02 -7.45515E-05 6.22075E-02
- 23 -3.58166E-02 -1.52941E-04 3.58169E-02
- 24 4.50451E-02 -4.26806E-05 4.50451E-02
- 25 1.59061E-02 -1.24671E-04 1.59066E-02
- 26 5.83505E-05 -2.88395E-05 6.50884E-05
- 27 -4.33750E-03 -6.10699E-05 4.33793E-03
- 28 -2.85980E-03 -1.11050E-05 2.85982E-03
- 29 1.62685E-03 -5.63345E-05 1.62782E-03
- 30 2.40363E-03 -8.63886E-05 2.40518E-03
- 31 -3.26675E-04 -6.60401E-05 3.33283E-04
- 32 1.49933E-03 -1.10916E-04 1.50343E-03
- 33 -1.26989E-03 -1.06383E-06 1.26989E-03
-
- i re wp im wp abs wp
-
- isol = 10, m = -3
-
- i re wp im wp abs wp
-
- 1 -2.82140E-01 -5.72584E-05 2.82140E-01
- 2 3.56623E-01 -1.25747E-04 3.56623E-01
- 3 -6.25033E-01 1.29444E-04 6.25033E-01
- 4 1.84157E+00 -2.07152E-04 1.84157E+00
- 5 -6.10965E+00 1.00732E-04 6.10965E+00
- 6 1.86547E+01 -3.63972E-04 1.86547E+01
- 7 -4.63977E+01 5.18211E-04 4.63977E+01
- 8 1.08379E+02 -9.70900E-04 1.08379E+02
- 9 -2.34865E+02 1.06220E-03 2.34865E+02
- 10 3.97913E+02 -1.15314E-06 3.97913E+02
- 11 -2.99017E+02 -1.50291E-03 2.99017E+02
- 12 1.05869E+02 9.29956E-04 1.05869E+02
- 13 1.20369E+02 1.40133E-03 1.20369E+02
- 14 -1.49695E+02 -2.75275E-03 1.49695E+02
- 15 -7.67009E+01 -1.66840E-03 7.67009E+01
- 16 -3.73803E+00 -1.07466E-04 3.73803E+00
- 17 1.39185E+00 2.97357E-05 1.39185E+00
- 18 -4.39298E-02 -3.64375E-05 4.39299E-02
- 19 5.48866E-01 -3.05964E-05 5.48866E-01
- 20 4.16376E-01 -6.20302E-05 4.16376E-01
- 21 1.45250E-01 -3.45989E-05 1.45250E-01
- 22 -3.31525E-02 -1.11559E-04 3.31527E-02
- 23 1.22812E-02 -2.50541E-05 1.22812E-02
- 24 -4.46918E-02 -1.03623E-04 4.46919E-02
- 25 2.60885E-02 8.60295E-06 2.60885E-02
- 26 -2.76818E-02 -8.58479E-05 2.76820E-02
- 27 1.50436E-02 -3.09219E-06 1.50436E-02
- 28 -1.10476E-02 -3.24768E-05 1.10477E-02
- 29 9.54306E-03 3.19048E-05 9.54311E-03
- 30 -4.45612E-03 -2.41449E-05 4.45618E-03
- 31 4.00252E-03 -7.79022E-05 4.00327E-03
- 32 -1.75869E-03 -6.60571E-05 1.75993E-03
- 33 2.04027E-03 -6.15850E-05 2.04120E-03
-
- i re wp im wp abs wp
-
- isol = 11, m = -2
-
- i re wp im wp abs wp
-
- 1 2.05305E+00 -9.08606E-05 2.05305E+00
- 2 -2.81032E+00 1.88263E-04 2.81032E+00
- 3 3.77501E+00 -1.92315E-04 3.77501E+00
- 4 -5.41425E+00 3.45831E-04 5.41425E+00
- 5 8.76077E+00 -2.46386E-04 8.76077E+00
- 6 -1.67890E+01 4.34152E-04 1.67890E+01
- 7 3.64696E+01 -5.18628E-04 3.64696E+01
- 8 -7.67847E+01 1.01568E-03 7.67847E+01
- 9 1.58574E+02 -1.22413E-03 1.58574E+02
- 10 -2.99017E+02 1.50542E-03 2.99017E+02
- 11 4.20814E+02 -1.14357E-06 4.20814E+02
- 12 -2.22499E+02 -7.77592E-04 2.22499E+02
- 13 -7.89680E+01 -5.75648E-04 7.89680E+01
- 14 1.71002E+02 2.33408E-03 1.71002E+02
- 15 5.63536E+01 1.07643E-03 5.63536E+01
- 16 1.08771E+00 4.92652E-05 1.08771E+00
- 17 1.64766E+00 -5.97885E-06 1.64766E+00
- 18 1.00392E-01 -8.23592E-05 1.00392E-01
- 19 -1.59660E+00 -1.95806E-04 1.59660E+00
- 20 -9.25531E-01 -2.12872E-04 9.25531E-01
- 21 -2.17643E-01 -2.49824E-04 2.17643E-01
- 22 2.32512E-01 -1.62517E-04 2.32512E-01
- 23 -4.30399E-02 -2.10639E-04 4.30404E-02
- 24 9.06727E-02 -1.35726E-04 9.06728E-02
- 25 -9.12289E-02 -2.01607E-04 9.12292E-02
- 26 6.85243E-02 -1.04049E-04 6.85244E-02
- 27 -3.81842E-02 -1.58901E-04 3.81845E-02
- 28 3.12425E-02 -9.43443E-05 3.12426E-02
- 29 -2.31776E-02 -1.14133E-04 2.31779E-02
- 30 1.19283E-02 -3.37133E-05 1.19283E-02
- 31 -6.89417E-03 -4.77155E-05 6.89433E-03
- 32 5.72267E-03 -1.21274E-04 5.72395E-03
- 33 -2.18983E-03 -4.94111E-05 2.19039E-03
-
- i re wp im wp abs wp
-
- isol = 12, m = -1
-
- i re wp im wp abs wp
-
- 1 -2.40186E+00 1.73844E-04 2.40186E+00
- 2 3.18458E+00 -2.51782E-04 3.18458E+00
- 3 -3.94134E+00 1.27659E-04 3.94134E+00
- 4 4.46869E+00 -3.36684E-04 4.46869E+00
- 5 -4.62293E+00 1.22659E-04 4.62293E+00
- 6 4.46405E+00 -3.17699E-04 4.46405E+00
- 7 -5.78798E+00 2.30184E-05 5.78798E+00
- 8 1.47952E+01 -3.63943E-04 1.47952E+01
- 9 -4.03830E+01 3.69082E-04 4.03830E+01
- 10 1.05870E+02 -9.31161E-04 1.05870E+02
- 11 -2.22500E+02 7.78605E-04 2.22500E+02
- 12 2.83518E+02 -2.73952E-07 2.83518E+02
- 13 -6.32520E+01 -5.05965E-04 6.32520E+01
- 14 -9.19483E+01 -9.51362E-04 9.19483E+01
- 15 1.79972E+00 7.61571E-05 1.79972E+00
- 16 2.46149E+00 5.41852E-05 2.46149E+00
- 17 -3.94287E+00 -1.38312E-04 3.94287E+00
- 18 -1.43068E+00 -6.85174E-05 1.43068E+00
- 19 1.03564E+00 3.24727E-05 1.03564E+00
- 20 6.64553E-01 4.69967E-05 6.64553E-01
- 21 5.88547E-01 4.29519E-05 5.88547E-01
- 22 -9.72917E-02 -2.42241E-05 9.72917E-02
- 23 4.87734E-02 -4.78070E-06 4.87734E-02
- 24 -9.40040E-02 -1.21101E-05 9.40040E-02
- 25 1.52234E-02 1.16122E-05 1.52234E-02
- 26 -1.72138E-02 1.29645E-05 1.72138E-02
- 27 1.35396E-02 3.05809E-05 1.35396E-02
- 28 -4.04053E-03 2.69266E-05 4.04062E-03
- 29 2.18134E-03 1.97497E-05 2.18143E-03
- 30 -2.80198E-03 1.11108E-05 2.80200E-03
- 31 1.67183E-03 3.15662E-05 1.67213E-03
- 32 -2.26011E-05 2.99093E-05 3.74884E-05
- 33 1.10813E-03 -6.91854E-05 1.11029E-03
-
- i re wp im wp abs wp
-
- isol = 13, m = 0
-
- i re wp im wp abs wp
-
- 1 6.24015E-02 -1.84861E-04 6.24018E-02
- 2 2.08595E-01 1.66106E-05 2.08595E-01
- 3 -9.24702E-01 4.15060E-05 9.24702E-01
- 4 2.78796E+00 -8.66209E-05 2.78796E+00
- 5 -7.06938E+00 2.31379E-04 7.06938E+00
- 6 1.60543E+01 -4.24694E-04 1.60543E+01
- 7 -3.31684E+01 8.01192E-04 3.31684E+01
- 8 6.03458E+01 -1.26041E-03 6.03458E+01
- 9 -9.47500E+01 1.53686E-03 9.47500E+01
- 10 1.20369E+02 -1.40198E-03 1.20369E+02
- 11 -7.89677E+01 5.76777E-04 7.89677E+01
- 12 -6.32521E+01 5.05161E-04 6.32521E+01
- 13 1.81803E+02 1.80158E-07 1.81803E+02
- 14 -7.95760E+01 -5.52422E-04 7.95760E+01
- 15 -5.44528E+01 -5.48092E-04 5.44528E+01
- 16 -3.36725E+00 -5.16930E-05 3.36725E+00
- 17 1.40632E+00 1.97679E-05 1.40632E+00
- 18 1.82388E+00 -1.74256E-05 1.82388E+00
- 19 2.74934E-01 -8.24861E-05 2.74934E-01
- 20 7.05958E-01 -1.00962E-04 7.05958E-01
- 21 -8.27612E-01 -1.31221E-04 8.27612E-01
- 22 -1.20687E-01 -1.47286E-04 1.20687E-01
- 23 -8.44888E-02 -1.20401E-04 8.44889E-02
- 24 8.42045E-02 -1.38985E-04 8.42046E-02
- 25 1.07760E-01 -7.71450E-05 1.07760E-01
- 26 -7.06543E-02 -1.32733E-04 7.06544E-02
- 27 2.78880E-02 -6.36465E-05 2.78880E-02
- 28 -4.39142E-02 -1.00664E-04 4.39143E-02
- 29 3.33506E-02 -3.25911E-05 3.33506E-02
- 30 -1.34752E-02 -7.48200E-05 1.34754E-02
- 31 9.29122E-03 -3.57505E-05 9.29129E-03
- 32 -7.26016E-03 -3.69783E-05 7.26026E-03
- 33 3.80657E-03 -1.35971E-05 3.80660E-03
-
- i re wp im wp abs wp
-
- isol = 14, m = 1
-
- i re wp im wp abs wp
-
- 1 1.94404E+00 1.94267E-05 1.94404E+00
- 2 -2.93823E+00 1.02644E-04 2.93823E+00
- 3 4.47835E+00 -2.01966E-04 4.47835E+00
- 4 -6.96896E+00 3.16839E-04 6.96896E+00
- 5 1.12207E+01 -4.06703E-04 1.12207E+01
- 6 -1.90778E+01 7.00882E-04 1.90778E+01
- 7 3.37362E+01 -9.90740E-04 3.37362E+01
- 8 -5.94927E+01 1.60906E-03 5.94927E+01
- 9 1.00222E+02 -2.23880E-03 1.00222E+02
- 10 -1.49694E+02 2.75352E-03 1.49694E+02
- 11 1.71002E+02 -2.33531E-03 1.71002E+02
- 12 -9.19487E+01 9.52418E-04 9.19487E+01
- 13 -7.95756E+01 5.52506E-04 7.95756E+01
- 14 1.35092E+02 -5.76856E-07 1.35092E+02
- 15 2.61290E+01 8.06777E-05 2.61290E+01
- 16 9.24656E-02 8.33511E-06 9.24656E-02
- 17 3.21466E+00 2.00789E-05 3.21466E+00
- 18 -1.95071E+00 -9.88519E-05 1.95071E+00
- 19 -1.58706E+00 -1.43860E-04 1.58706E+00
- 20 -2.12925E+00 -1.81638E-04 2.12925E+00
- 21 7.54845E-01 -1.24876E-04 7.54845E-01
- 22 4.21250E-01 -7.65339E-05 4.21250E-01
- 23 1.16147E-01 -1.15670E-04 1.16147E-01
- 24 -6.78836E-02 -8.62242E-05 6.78837E-02
- 25 -1.88265E-01 -1.40415E-04 1.88265E-01
- 26 1.22649E-01 -6.50557E-05 1.22649E-01
- 27 -5.00358E-02 -1.25167E-04 5.00360E-02
- 28 6.97622E-02 -4.53594E-05 6.97622E-02
- 29 -5.25478E-02 -9.75589E-05 5.25479E-02
- 30 2.13520E-02 -1.81743E-05 2.13520E-02
- 31 -1.46709E-02 -5.80153E-05 1.46710E-02
- 32 1.04412E-02 -2.68062E-05 1.04412E-02
- 33 -4.39219E-03 -2.65420E-05 4.39227E-03
-
- i re wp im wp abs wp
-
- isol = 15, m = 2
-
- i re wp im wp abs wp
-
- 1 4.66587E-01 -1.16326E-04 4.66587E-01
- 2 -1.07489E+00 9.92179E-05 1.07489E+00
- 3 2.25436E+00 -2.17042E-04 2.25436E+00
- 4 -4.58950E+00 2.21227E-04 4.58950E+00
- 5 9.00614E+00 -4.79283E-04 9.00614E+00
- 6 -1.67478E+01 6.29370E-04 1.67478E+01
- 7 2.92523E+01 -1.07453E-03 2.92523E+01
- 8 -4.71157E+01 1.42524E-03 4.71157E+01
- 9 6.69553E+01 -1.79970E-03 6.69553E+01
- 10 -7.67023E+01 1.66952E-03 7.67023E+01
- 11 5.63537E+01 -1.07783E-03 5.63537E+01
- 12 1.80100E+00 -7.52549E-05 1.80100E+00
- 13 -5.44543E+01 5.47985E-04 5.44543E+01
- 14 2.61292E+01 -8.10072E-05 2.61292E+01
- 15 5.65814E+01 -2.72372E-07 5.65814E+01
- 16 2.94729E+00 1.26686E-05 2.94729E+00
- 17 -6.08907E+00 -7.24034E-05 6.08907E+00
- 18 -5.96461E-01 -3.93369E-05 5.96461E-01
- 19 -5.59144E-01 -4.05784E-05 5.59144E-01
- 20 1.87158E+00 4.62055E-05 1.87158E+00
- 21 -2.26285E-01 -2.10106E-05 2.26285E-01
- 22 -4.65582E-01 -9.35292E-06 4.65582E-01
- 23 -3.39695E-02 -1.58931E-05 3.39695E-02
- 24 8.09995E-02 -6.76411E-06 8.09995E-02
- 25 1.19036E-01 -1.02269E-06 1.19036E-01
- 26 -7.10636E-02 -4.84166E-06 7.10636E-02
- 27 2.12825E-02 3.12518E-05 2.12826E-02
- 28 -3.69042E-02 -1.27616E-05 3.69042E-02
- 29 2.81788E-02 2.57282E-05 2.81788E-02
- 30 -1.14863E-02 -2.09071E-05 1.14863E-02
- 31 8.05393E-03 3.03196E-05 8.05399E-03
- 32 -5.25126E-03 -5.15817E-06 5.25126E-03
- 33 1.45808E-03 9.17214E-07 1.45808E-03
-
- i re wp im wp abs wp
-
- isol = 16, m = 3
-
- i re wp im wp abs wp
-
- 1 4.20006E-02 -1.23593E-06 4.20006E-02
- 2 -9.63581E-02 -6.12915E-06 9.63581E-02
- 3 1.98773E-01 -1.04081E-05 1.98773E-01
- 4 -4.19543E-01 6.70436E-06 4.19543E-01
- 5 8.76008E-01 -5.03956E-05 8.76008E-01
- 6 -1.67562E+00 5.22621E-05 1.67562E+00
- 7 2.80280E+00 -1.27267E-04 2.80280E+00
- 8 -3.96552E+00 1.33804E-04 3.96552E+00
- 9 4.53302E+00 -1.54658E-04 4.53302E+00
- 10 -3.73938E+00 1.07377E-04 3.73938E+00
- 11 1.08789E+00 -4.92277E-05 1.08789E+00
- 12 2.46268E+00 -5.41750E-05 2.46268E+00
- 13 -3.36860E+00 5.16290E-05 3.36860E+00
- 14 9.24565E-02 -8.29321E-06 9.24565E-02
- 15 2.94833E+00 -1.27293E-05 2.94833E+00
- 16 4.14338E+00 4.54964E-09 4.14338E+00
- 17 -2.49147E+00 -1.76618E-05 2.49147E+00
- 18 -8.92253E-01 -4.81169E-06 8.92253E-01
- 19 2.29724E+00 2.93126E-05 2.29724E+00
- 20 -5.42053E-01 -1.02285E-05 5.42053E-01
- 21 -5.42510E-01 -5.91250E-06 5.42510E-01
- 22 4.03126E-01 5.40991E-06 4.03126E-01
- 23 -1.42067E-01 -6.72671E-06 1.42067E-01
- 24 1.21194E-02 1.58927E-06 1.21194E-02
- 25 1.55376E-02 5.49810E-06 1.55376E-02
- 26 8.91596E-05 1.33519E-05 9.01538E-05
- 27 5.54898E-03 3.00342E-06 5.54899E-03
- 28 -1.46108E-02 9.53167E-06 1.46108E-02
- 29 7.30572E-03 -8.12053E-06 7.30573E-03
- 30 6.83805E-04 8.15085E-06 6.83854E-04
- 31 -1.12047E-03 -6.65243E-06 1.12049E-03
- 32 -4.69517E-05 1.14909E-05 4.83374E-05
- 33 8.73941E-05 -9.83364E-06 8.79456E-05
-
- i re wp im wp abs wp
-
- isol = 17, m = 4
-
- i re wp im wp abs wp
-
- 1 -1.79620E-01 5.04625E-05 1.79620E-01
- 2 2.92671E-01 -2.49383E-05 2.92671E-01
- 3 -4.40055E-01 6.18743E-05 4.40055E-01
- 4 6.87272E-01 -2.88725E-05 6.87272E-01
- 5 -1.12545E+00 9.82186E-05 1.12545E+00
- 6 1.75745E+00 -5.35084E-05 1.75745E+00
- 7 -2.51648E+00 1.48439E-04 2.51648E+00
- 8 3.18490E+00 -1.05642E-04 3.18490E+00
- 9 -3.04288E+00 1.44721E-04 3.04288E+00
- 10 1.39127E+00 -2.96434E-05 1.39127E+00
- 11 1.64793E+00 5.92615E-06 1.64793E+00
- 12 -3.94258E+00 1.38313E-04 3.94258E+00
- 13 1.40596E+00 -1.97284E-05 1.40596E+00
- 14 3.21437E+00 -2.00551E-05 3.21437E+00
- 15 -6.08792E+00 7.24747E-05 6.08792E+00
- 16 -2.49023E+00 1.76834E-05 2.49023E+00
- 17 2.41025E+00 1.28610E-08 2.41025E+00
- 18 -1.08013E+00 -1.64762E-05 1.08013E+00
- 19 -3.00145E+00 -2.03671E-05 3.00145E+00
- 20 2.27030E-01 -3.14918E-06 2.27030E-01
- 21 6.08286E-01 7.47700E-06 6.08286E-01
- 22 2.12093E-01 2.23210E-05 2.12093E-01
- 23 -1.07555E-02 1.38878E-05 1.07555E-02
- 24 3.85306E-02 1.15139E-05 3.85306E-02
- 25 -1.56012E-01 -8.82519E-06 1.56012E-01
- 26 8.70913E-02 4.78694E-06 8.70913E-02
- 27 -4.49337E-02 -3.70919E-06 4.49337E-02
- 28 5.15375E-02 1.11180E-05 5.15375E-02
- 29 -3.38893E-02 3.68264E-06 3.38893E-02
- 30 1.25267E-02 1.06888E-05 1.25267E-02
- 31 -7.65473E-03 5.01139E-06 7.65473E-03
- 32 5.50737E-03 -1.58308E-06 5.50737E-03
- 33 -2.31166E-03 8.64274E-06 2.31168E-03
-
- i re wp im wp abs wp
-
- isol = 18, m = 5
-
- i re wp im wp abs wp
-
- 1 -2.97000E-01 1.64638E-05 2.97000E-01
- 2 3.55298E-01 1.62788E-05 3.55298E-01
- 3 -3.25271E-01 2.11498E-05 3.25271E-01
- 4 2.02591E-01 3.69758E-05 2.02591E-01
- 5 -1.56014E-03 1.44552E-05 1.56021E-03
- 6 -2.73053E-01 6.68194E-05 2.73053E-01
- 7 5.11153E-01 1.58161E-05 5.11153E-01
- 8 -5.33691E-01 7.20000E-05 5.33691E-01
- 9 4.02864E-01 4.27475E-05 4.02864E-01
- 10 -4.54053E-02 3.71175E-05 4.54053E-02
- 11 1.00882E-01 8.19001E-05 1.00883E-01
- 12 -1.42975E+00 6.84771E-05 1.42975E+00
- 13 1.82270E+00 1.77691E-05 1.82270E+00
- 14 -1.95096E+00 9.88785E-05 1.95096E+00
- 15 -5.94748E-01 3.90727E-05 5.94748E-01
- 16 -8.91427E-01 4.76233E-06 8.91427E-01
- 17 -1.08063E+00 1.65649E-05 1.08063E+00
- 18 3.05935E+00 2.21699E-08 3.05935E+00
- 19 -2.68264E+00 -3.50742E-05 2.68264E+00
- 20 -1.57265E+00 -1.19610E-07 1.57265E+00
- 21 1.55409E+00 4.21571E-05 1.55409E+00
- 22 -2.09560E-01 2.54496E-05 2.09560E-01
- 23 4.65190E-01 5.65421E-05 4.65190E-01
- 24 -2.07243E-01 2.74090E-05 2.07243E-01
- 25 6.17110E-02 2.60386E-05 6.17110E-02
- 26 -5.80784E-02 1.68803E-05 5.80784E-02
- 27 3.20395E-02 3.28237E-05 3.20395E-02
- 28 -7.34089E-03 3.54477E-05 7.34098E-03
- 29 3.78113E-03 3.06261E-05 3.78126E-03
- 30 -6.36889E-03 2.57781E-05 6.36894E-03
- 31 3.56502E-03 2.12606E-05 3.56509E-03
- 32 -1.44475E-03 2.54939E-05 1.44497E-03
- 33 1.06355E-03 -3.15168E-06 1.06355E-03
-
- i re wp im wp abs wp
-
- isol = 19, m = 6
-
- i re wp im wp abs wp
-
- 1 -8.83673E-04 1.03934E-05 8.83734E-04
- 2 -3.74685E-02 9.99263E-06 3.74685E-02
- 3 1.59480E-01 4.58322E-05 1.59480E-01
- 4 -3.58630E-01 3.45319E-05 3.58630E-01
- 5 6.25385E-01 2.13170E-05 6.25385E-01
- 6 -9.48002E-01 8.87808E-05 9.48002E-01
- 7 1.16447E+00 -7.73282E-06 1.16447E+00
- 8 -1.02247E+00 1.26574E-04 1.02247E+00
- 9 5.17273E-01 6.05701E-05 5.17273E-01
- 10 5.48509E-01 3.05645E-05 5.48509E-01
- 11 -1.59653E+00 1.95790E-04 1.59653E+00
- 12 1.03592E+00 -3.24303E-05 1.03592E+00
- 13 2.74594E-01 8.24335E-05 2.74594E-01
- 14 -1.58709E+00 1.43927E-04 1.58709E+00
- 15 -5.58730E-01 4.06155E-05 5.58730E-01
- 16 2.29634E+00 -2.92708E-05 2.29634E+00
- 17 -3.00176E+00 2.04168E-05 3.00176E+00
- 18 -2.68281E+00 3.51115E-05 2.68281E+00
- 19 1.35480E+01 5.39501E-08 1.35480E+01
- 20 -1.55556E+00 -4.82092E-05 1.55556E+00
- 21 -2.85614E+00 8.86625E-06 2.85614E+00
- 22 1.99554E+00 5.27161E-05 1.99554E+00
- 23 -5.41309E-01 1.98234E-05 5.41309E-01
- 24 6.41449E-01 6.36455E-05 6.41449E-01
- 25 -3.83342E-01 3.02455E-05 3.83342E-01
- 26 2.34274E-01 4.44179E-05 2.34274E-01
- 27 -1.58781E-01 2.11173E-05 1.58781E-01
- 28 9.38499E-02 4.47409E-05 9.38499E-02
- 29 -6.12696E-02 3.41395E-05 6.12696E-02
- 30 3.96322E-02 2.99859E-05 3.96322E-02
- 31 -2.48644E-02 2.16582E-05 2.48644E-02
- 32 1.42239E-02 3.02710E-05 1.42240E-02
- 33 -7.59130E-03 1.53370E-05 7.59132E-03
-
- i re wp im wp abs wp
-
- isol = 20, m = 7
-
- i re wp im wp abs wp
-
- 1 1.02499E-01 3.32236E-06 1.02499E-01
- 2 -1.44758E-01 5.25308E-05 1.44758E-01
- 3 1.96018E-01 -9.22951E-06 1.96018E-01
- 4 -2.50907E-01 1.10298E-04 2.50907E-01
- 5 2.93063E-01 -1.88071E-05 2.93063E-01
- 6 -2.90535E-01 1.38542E-04 2.90535E-01
- 7 2.69977E-01 1.09844E-05 2.69977E-01
- 8 -2.45930E-01 1.41336E-04 2.45930E-01
- 9 6.19693E-02 8.22479E-05 6.19694E-02
- 10 4.16816E-01 6.22092E-05 4.16816E-01
- 11 -9.25696E-01 2.12742E-04 9.25696E-01
- 12 6.64294E-01 -4.71538E-05 6.64294E-01
- 13 7.06289E-01 1.01215E-04 7.06289E-01
- 14 -2.12912E+00 1.81554E-04 2.12912E+00
- 15 1.87087E+00 -4.63665E-05 1.87087E+00
- 16 -5.42114E-01 1.02230E-05 5.42114E-01
- 17 2.27196E-01 3.13618E-06 2.27196E-01
- 18 -1.57278E+00 6.37584E-08 1.57278E+00
- 19 -1.55571E+00 4.81307E-05 1.55571E+00
- 20 2.39828E+01 3.34796E-09 2.39828E+01
- 21 -1.74796E+00 -7.04999E-05 1.74796E+00
- 22 -3.28066E+00 2.32797E-06 3.28066E+00
- 23 1.62189E+00 4.24311E-05 1.62189E+00
- 24 -5.11129E-01 3.84843E-06 5.11129E-01
- 25 7.26130E-01 5.88608E-05 7.26130E-01
- 26 -3.93869E-01 1.33003E-05 3.93869E-01
- 27 2.28591E-01 3.08392E-05 2.28591E-01
- 28 -1.70903E-01 2.36102E-06 1.70903E-01
- 29 1.01864E-01 3.45206E-05 1.01864E-01
- 30 -6.10613E-02 2.56501E-05 6.10613E-02
- 31 3.79544E-02 1.81630E-05 3.79544E-02
- 32 -2.25430E-02 1.35177E-05 2.25430E-02
- 33 1.20972E-02 4.07895E-05 1.20973E-02
-
- i re wp im wp abs wp
-
- isol = 21, m = 8
-
- i re wp im wp abs wp
-
- 1 1.26948E-01 4.95120E-05 1.26948E-01
- 2 -1.53269E-01 1.17792E-05 1.53269E-01
- 3 1.52101E-01 3.04558E-05 1.52101E-01
- 4 -1.18566E-01 5.09594E-05 1.18566E-01
- 5 4.52491E-02 7.98514E-05 4.52492E-02
- 6 6.35537E-02 4.71091E-05 6.35538E-02
- 7 -1.89536E-01 1.20301E-04 1.89536E-01
- 8 2.99041E-01 5.65049E-05 2.99041E-01
- 9 -2.91335E-01 1.59937E-04 2.91335E-01
- 10 1.45719E-01 3.42015E-05 1.45719E-01
- 11 -2.17773E-01 2.50066E-04 2.17774E-01
- 12 5.88221E-01 -4.30203E-05 5.88221E-01
- 13 -8.27213E-01 1.30941E-04 8.27213E-01
- 14 7.54914E-01 1.24933E-04 7.54914E-01
- 15 -2.26806E-01 2.11818E-05 2.26806E-01
- 16 -5.42359E-01 5.88985E-06 5.42359E-01
- 17 6.08529E-01 -7.45036E-06 6.08529E-01
- 18 1.55417E+00 -4.20965E-05 1.55417E+00
- 19 -2.85617E+00 -8.88814E-06 2.85617E+00
- 20 -1.74803E+00 7.04766E-05 1.74803E+00
- 21 3.54933E+01 -5.87537E-09 3.54933E+01
- 22 -2.83498E+00 -1.13257E-04 2.83498E+00
- 23 -3.46480E+00 -3.13382E-06 3.46480E+00
- 24 1.72933E+00 3.41202E-05 1.72933E+00
- 25 -6.67685E-01 -1.01958E-05 6.67685E-01
- 26 7.49852E-01 4.85978E-05 7.49852E-01
- 27 -4.11646E-01 4.03341E-06 4.11646E-01
- 28 2.54401E-01 1.35636E-05 2.54401E-01
- 29 -1.78171E-01 -4.52159E-06 1.78171E-01
- 30 1.04582E-01 1.84741E-05 1.04582E-01
- 31 -6.51782E-02 2.49026E-05 6.51782E-02
- 32 4.00746E-02 6.73763E-06 4.00746E-02
- 33 -2.36304E-02 2.53502E-05 2.36304E-02
-
- i re wp im wp abs wp
-
- isol = 22, m = 9
-
- i re wp im wp abs wp
-
- 1 -3.11395E-03 1.39873E-04 3.11709E-03
- 2 1.23616E-02 3.39190E-05 1.23617E-02
- 3 -4.25234E-02 1.84517E-06 4.25234E-02
- 4 8.13052E-02 5.81903E-05 8.13053E-02
- 5 -1.10424E-01 3.40632E-05 1.10424E-01
- 6 1.32461E-01 1.06270E-04 1.32461E-01
- 7 -1.19499E-01 3.47004E-05 1.19499E-01
- 8 6.18641E-02 1.40805E-04 6.18643E-02
- 9 -6.18781E-02 7.46512E-05 6.18781E-02
- 10 -3.34238E-02 1.11503E-04 3.34239E-02
- 11 2.32584E-01 1.62548E-04 2.32584E-01
- 12 -9.71006E-02 2.41616E-05 9.71006E-02
- 13 -1.20929E-01 1.47177E-04 1.20929E-01
- 14 4.21236E-01 7.65543E-05 4.21236E-01
- 15 -4.65318E-01 9.34585E-06 4.65318E-01
- 16 4.03170E-01 -5.40943E-06 4.03170E-01
- 17 2.11915E-01 -2.23316E-05 2.11915E-01
- 18 -2.09637E-01 -2.54036E-05 2.09637E-01
- 19 1.99566E+00 -5.26993E-05 1.99566E+00
- 20 -3.28065E+00 -2.28351E-06 3.28065E+00
- 21 -2.83498E+00 1.13208E-04 2.83498E+00
- 22 4.81888E+01 1.45162E-09 4.81888E+01
- 23 -4.34480E+00 -1.61794E-04 4.34480E+00
- 24 -3.77625E+00 -1.66521E-06 3.77625E+00
- 25 1.82266E+00 2.82592E-05 1.82266E+00
- 26 -7.63387E-01 -1.10195E-05 7.63387E-01
- 27 8.02199E-01 4.66882E-05 8.02199E-01
- 28 -4.46315E-01 4.24046E-06 4.46315E-01
- 29 2.76905E-01 8.68188E-06 2.76905E-01
- 30 -1.90166E-01 -7.46900E-06 1.90166E-01
- 31 1.12719E-01 1.79838E-05 1.12719E-01
- 32 -7.04535E-02 1.92154E-05 7.04535E-02
- 33 4.36821E-02 -1.66583E-06 4.36821E-02
-
- i re wp im wp abs wp
-
- isol = 23, m = 10
-
- i re wp im wp abs wp
-
- 1 -9.88489E-03 2.31474E-05 9.88492E-03
- 2 1.18484E-02 1.04091E-04 1.18489E-02
- 3 -7.34299E-03 3.56922E-05 7.34308E-03
- 4 5.59128E-03 9.59180E-06 5.59129E-03
- 5 -7.22898E-03 5.42117E-05 7.22919E-03
- 6 6.76796E-03 4.05887E-05 6.76808E-03
- 7 -1.75454E-02 1.06346E-04 1.75457E-02
- 8 4.57887E-02 3.65080E-05 4.57887E-02
- 9 -3.57577E-02 1.53133E-04 3.57580E-02
- 10 1.22100E-02 2.49227E-05 1.22100E-02
- 11 -4.30021E-02 2.10747E-04 4.30026E-02
- 12 4.88002E-02 4.83659E-06 4.88002E-02
- 13 -8.45237E-02 1.20115E-04 8.45238E-02
- 14 1.16097E-01 1.15676E-04 1.16098E-01
- 15 -3.38046E-02 1.60318E-05 3.38046E-02
- 16 -1.42066E-01 6.74686E-06 1.42066E-01
- 17 -1.07395E-02 -1.39111E-05 1.07395E-02
- 18 4.65268E-01 -5.65084E-05 4.65268E-01
- 19 -5.41345E-01 -1.96666E-05 5.41345E-01
- 20 1.62189E+00 -4.23856E-05 1.62189E+00
- 21 -3.46480E+00 3.16770E-06 3.46480E+00
- 22 -4.34476E+00 1.61743E-04 4.34476E+00
- 23 6.15274E+01 -1.85861E-09 6.15274E+01
- 24 -6.29381E+00 -2.05388E-04 6.29381E+00
- 25 -3.92133E+00 2.52474E-06 3.92133E+00
- 26 1.83574E+00 2.85879E-05 1.83574E+00
- 27 -8.05089E-01 -1.38130E-05 8.05089E-01
- 28 8.25590E-01 5.03950E-05 8.25590E-01
- 29 -4.59180E-01 1.78595E-06 4.59180E-01
- 30 2.86236E-01 1.27733E-05 2.86236E-01
- 31 -1.95757E-01 -1.50115E-05 1.95757E-01
- 32 1.16263E-01 3.23802E-05 1.16263E-01
- 33 -7.31423E-02 -8.20616E-06 7.31423E-02
-
- i re wp im wp abs wp
-
- isol = 24, m = 11
-
- i re wp im wp abs wp
-
- 1 -1.79074E-02 8.69370E-05 1.79076E-02
- 2 2.50826E-02 9.79593E-05 2.50828E-02
- 3 -2.65891E-02 8.80171E-05 2.65893E-02
- 4 2.88488E-02 4.07901E-05 2.88488E-02
- 5 -2.17855E-02 4.55436E-06 2.17855E-02
- 6 1.52602E-02 6.72648E-05 1.52604E-02
- 7 -5.69847E-03 2.77313E-05 5.69854E-03
- 8 -2.82285E-02 1.20488E-04 2.82288E-02
- 9 4.49902E-02 4.26872E-05 4.49902E-02
- 10 -4.46460E-02 1.03591E-04 4.46461E-02
- 11 9.06588E-02 1.35786E-04 9.06589E-02
- 12 -9.40328E-02 1.21846E-05 9.40328E-02
- 13 8.42428E-02 1.38890E-04 8.42429E-02
- 14 -6.78811E-02 8.61953E-05 6.78811E-02
- 15 8.09582E-02 6.74374E-06 8.09582E-02
- 16 1.20585E-02 -1.55850E-06 1.20585E-02
- 17 3.85608E-02 -1.15471E-05 3.85608E-02
- 18 -2.07240E-01 -2.74618E-05 2.07240E-01
- 19 6.41420E-01 -6.36320E-05 6.41420E-01
- 20 -5.11104E-01 -3.69839E-06 5.11104E-01
- 21 1.72931E+00 -3.40845E-05 1.72931E+00
- 22 -3.77626E+00 1.73335E-06 3.77626E+00
- 23 -6.29376E+00 2.05370E-04 6.29376E+00
- 24 7.51959E+01 -1.03144E-09 7.51959E+01
- 25 -8.48462E+00 -2.59566E-04 8.48462E+00
- 26 -3.98479E+00 8.23464E-06 3.98479E+00
- 27 1.84172E+00 2.37628E-05 1.84172E+00
- 28 -8.38286E-01 -1.19235E-05 8.38286E-01
- 29 8.43440E-01 4.93395E-05 8.43440E-01
- 30 -4.70750E-01 -6.81112E-08 4.70750E-01
- 31 2.96102E-01 1.12154E-05 2.96102E-01
- 32 -2.03622E-01 -2.87310E-05 2.03622E-01
- 33 1.29234E-01 1.12308E-04 1.29234E-01
-
- i re wp im wp abs wp
-
- isol = 25, m = 12
-
- i re wp im wp abs wp
-
- 1 -4.43692E-03 -7.96945E-05 4.43763E-03
- 2 4.87304E-03 1.38294E-04 4.87501E-03
- 3 9.27171E-04 8.50688E-05 9.31065E-04
- 4 -6.35385E-03 9.19207E-05 6.35452E-03
- 5 1.50538E-02 3.94788E-05 1.50538E-02
- 6 -2.67338E-02 1.26818E-05 2.67338E-02
- 7 3.70611E-02 5.48981E-05 3.70611E-02
- 8 -2.59478E-02 3.60653E-05 2.59478E-02
- 9 1.59661E-02 1.24672E-04 1.59666E-02
- 10 2.60451E-02 -8.66264E-06 2.60451E-02
- 11 -9.12234E-02 2.01586E-04 9.12236E-02
- 12 1.52619E-02 -1.14776E-05 1.52619E-02
- 13 1.07715E-01 7.70824E-05 1.07715E-01
- 14 -1.88258E-01 1.40356E-04 1.88258E-01
- 15 1.19048E-01 1.02359E-06 1.19048E-01
- 16 1.55877E-02 -5.51367E-06 1.55877E-02
- 17 -1.56050E-01 8.85600E-06 1.56050E-01
- 18 6.16761E-02 -2.60649E-05 6.16761E-02
- 19 -3.83314E-01 -3.02901E-05 3.83314E-01
- 20 7.26134E-01 -5.88806E-05 7.26134E-01
- 21 -6.67672E-01 1.03757E-05 6.67672E-01
- 22 1.82263E+00 -2.82568E-05 1.82263E+00
- 23 -3.92133E+00 -2.43320E-06 3.92133E+00
- 24 -8.48457E+00 2.59582E-04 8.48457E+00
- 25 8.91539E+01 2.72236E-09 8.91539E+01
- 26 -1.09049E+01 -3.12514E-04 1.09049E+01
- 27 -3.98864E+00 1.23298E-05 3.98864E+00
- 28 1.83162E+00 1.96162E-05 1.83162E+00
- 29 -8.53852E-01 -7.51772E-06 8.53852E-01
- 30 8.55468E-01 4.89750E-05 8.55468E-01
- 31 -4.80513E-01 -2.04973E-06 4.80513E-01
- 32 3.12853E-01 1.71183E-05 3.12853E-01
- 33 -2.41331E-01 -3.82933E-05 2.41331E-01
-
- i re wp im wp abs wp
-
- isol = 26, m = 13
-
- i re wp im wp abs wp
-
- 1 2.67244E-03 8.60437E-05 2.67382E-03
- 2 -2.36384E-03 3.15453E-05 2.36405E-03
- 3 6.43680E-04 1.21234E-04 6.54998E-04
- 4 4.71158E-03 8.64255E-05 4.71238E-03
- 5 -6.43402E-03 9.17569E-05 6.43467E-03
- 6 1.43238E-02 5.41161E-05 1.43239E-02
- 7 -1.84255E-02 -5.21048E-06 1.84255E-02
- 8 9.90985E-03 7.78566E-05 9.91016E-03
- 9 -1.58202E-05 2.87276E-05 3.27957E-05
- 10 -2.76183E-02 8.58787E-05 2.76185E-02
- 11 6.85072E-02 1.03898E-04 6.85072E-02
- 12 -1.72592E-02 -1.28529E-05 1.72592E-02
- 13 -7.06006E-02 1.32792E-04 7.06007E-02
- 14 1.22659E-01 6.50055E-05 1.22659E-01
- 15 -7.11331E-02 4.78863E-06 7.11331E-02
- 16 7.21543E-05 -1.33527E-05 7.33794E-05
- 17 8.71188E-02 -4.77818E-06 8.71188E-02
- 18 -5.80659E-02 -1.68674E-05 5.80659E-02
- 19 2.34266E-01 -4.45159E-05 2.34266E-01
- 20 -3.93892E-01 -1.33712E-05 3.93892E-01
- 21 7.49866E-01 -4.86076E-05 7.49866E-01
- 22 -7.63366E-01 1.12109E-05 7.63366E-01
- 23 1.83570E+00 -2.86007E-05 1.83570E+00
- 24 -3.98479E+00 -8.13108E-06 3.98479E+00
- 25 -1.09048E+01 3.12576E-04 1.09048E+01
- 26 1.03358E+02 -4.09364E-09 1.03358E+02
- 27 -1.35052E+01 -3.72777E-04 1.35052E+01
- 28 -3.93348E+00 1.39930E-05 3.93348E+00
- 29 1.80010E+00 1.04241E-05 1.80010E+00
- 30 -8.55139E-01 -2.60713E-06 8.55139E-01
- 31 8.72314E-01 5.00474E-05 8.72314E-01
- 32 -5.24889E-01 -1.33897E-05 5.24889E-01
- 33 4.14969E-01 -6.42519E-05 4.14969E-01
-
- i re wp im wp abs wp
-
- isol = 27, m = 14
-
- i re wp im wp abs wp
-
- 1 5.35640E-04 -2.04577E-05 5.36030E-04
- 2 -2.07725E-03 -7.09422E-06 2.07726E-03
- 3 2.81923E-03 4.64771E-05 2.81961E-03
- 4 -4.26274E-03 1.32622E-04 4.26480E-03
- 5 6.79788E-03 7.51906E-05 6.79830E-03
- 6 -6.62152E-03 1.05617E-04 6.62236E-03
- 7 1.08235E-02 3.38164E-05 1.08236E-02
- 8 -2.76415E-03 1.71228E-05 2.76421E-03
- 9 -4.31723E-03 6.09161E-05 4.31766E-03
- 10 1.50258E-02 3.17918E-06 1.50259E-02
- 11 -3.81787E-02 1.58691E-04 3.81791E-02
- 12 1.35510E-02 -3.05763E-05 1.35511E-02
- 13 2.78735E-02 6.37500E-05 2.78736E-02
- 14 -5.00384E-02 1.25122E-04 5.00385E-02
- 15 2.13006E-02 -3.13035E-05 2.13006E-02
- 16 5.54087E-03 -3.00458E-06 5.54087E-03
- 17 -4.49406E-02 3.72129E-06 4.49406E-02
- 18 3.20329E-02 -3.27953E-05 3.20329E-02
- 19 -1.58783E-01 -2.10696E-05 1.58783E-01
- 20 2.28600E-01 -3.09866E-05 2.28600E-01
- 21 -4.11660E-01 -4.10858E-06 4.11660E-01
- 22 8.02209E-01 -4.67034E-05 8.02209E-01
- 23 -8.05065E-01 1.40083E-05 8.05065E-01
- 24 1.84167E+00 -2.38165E-05 1.84167E+00
- 25 -3.98864E+00 -1.22001E-05 3.98864E+00
- 26 -1.35051E+01 3.72890E-04 1.35051E+01
- 27 1.17751E+02 -9.77908E-09 1.17751E+02
- 28 -1.62559E+01 -4.30616E-04 1.62559E+01
- 29 -3.82005E+00 1.66203E-05 3.82005E+00
- 30 1.75059E+00 2.76107E-06 1.75059E+00
- 31 -8.87919E-01 7.24302E-06 8.87919E-01
- 32 1.02063E+00 6.69975E-05 1.02063E+00
- 33 -8.20421E-01 -1.50906E-04 8.20421E-01
-
- i re wp im wp abs wp
-
- isol = 28, m = 15
-
- i re wp im wp abs wp
-
- 1 1.96228E-03 1.39661E-04 1.96725E-03
- 2 -2.29586E-03 -1.46582E-05 2.29590E-03
- 3 7.70516E-04 -1.44914E-06 7.70517E-04
- 4 7.93590E-04 5.44196E-05 7.95454E-04
- 5 -2.32706E-03 1.21152E-04 2.33021E-03
- 6 7.44086E-03 8.77174E-05 7.44138E-03
- 7 -1.00820E-02 8.80423E-05 1.00823E-02
- 8 9.21744E-03 5.07951E-05 9.21758E-03
- 9 -2.85910E-03 1.10074E-05 2.85912E-03
- 10 -1.10495E-02 3.24535E-05 1.10496E-02
- 11 3.12436E-02 9.42877E-05 3.12437E-02
- 12 -4.03962E-03 -2.70368E-05 4.03971E-03
- 13 -4.39139E-02 1.00663E-04 4.39140E-02
- 14 6.97573E-02 4.53772E-05 6.97573E-02
- 15 -3.68916E-02 1.27837E-05 3.68916E-02
- 16 -1.46022E-02 -9.52035E-06 1.46022E-02
- 17 5.15405E-02 -1.11149E-05 5.15405E-02
- 18 -7.33250E-03 -3.54444E-05 7.33259E-03
- 19 9.38509E-02 -4.47199E-05 9.38509E-02
- 20 -1.70901E-01 -2.30987E-06 1.70901E-01
- 21 2.54401E-01 -1.37452E-05 2.54401E-01
- 22 -4.46332E-01 -4.29786E-06 4.46332E-01
- 23 8.25604E-01 -5.03989E-05 8.25604E-01
- 24 -8.38259E-01 1.21027E-05 8.38259E-01
- 25 1.83157E+00 -1.97131E-05 1.83157E+00
- 26 -3.93348E+00 -1.38431E-05 3.93348E+00
- 27 -1.62558E+01 4.30783E-04 1.62558E+01
- 28 1.32318E+02 -2.24312E-08 1.32318E+02
- 29 -1.91622E+01 -4.95424E-04 1.91622E+01
- 30 -3.64903E+00 1.96478E-05 3.64903E+00
- 31 1.81687E+00 -2.22768E-06 1.81687E+00
- 32 -1.35613E+00 -2.83990E-05 1.35613E+00
- 33 1.92572E+00 1.51245E-04 1.92572E+00
-
- i re wp im wp abs wp
-
- isol = 29, m = 16
-
- i re wp im wp abs wp
-
- 1 -1.48538E-03 2.50952E-05 1.48559E-03
- 2 1.11510E-03 -9.83517E-06 1.11515E-03
- 3 -1.19620E-03 3.32026E-06 1.19620E-03
- 4 -8.94587E-04 1.29628E-05 8.94681E-04
- 5 2.10245E-03 4.62049E-05 2.10296E-03
- 6 -3.69592E-03 1.25674E-04 3.69806E-03
- 7 8.07807E-03 8.06939E-05 8.07848E-03
- 8 -4.56446E-03 8.51456E-05 4.56525E-03
- 9 1.63896E-03 5.63088E-05 1.63993E-03
- 10 9.53300E-03 -3.19225E-05 9.53305E-03
- 11 -2.31748E-02 1.14064E-04 2.31751E-02
- 12 2.18843E-03 -1.98679E-05 2.18852E-03
- 13 3.33411E-02 3.26043E-05 3.33411E-02
- 14 -5.25468E-02 9.74878E-05 5.25469E-02
- 15 2.81853E-02 -2.57552E-05 2.81853E-02
- 16 7.30513E-03 8.12832E-06 7.30513E-03
- 17 -3.38949E-02 -3.66947E-06 3.38949E-02
- 18 3.77788E-03 -3.05980E-05 3.77801E-03
- 19 -6.12699E-02 -3.41254E-05 6.12699E-02
- 20 1.01863E-01 -3.44835E-05 1.01863E-01
- 21 -1.78164E-01 4.58667E-06 1.78164E-01
- 22 2.76909E-01 -8.89851E-06 2.76909E-01
- 23 -4.59201E-01 -1.83385E-06 4.59201E-01
- 24 8.43455E-01 -4.93250E-05 8.43455E-01
- 25 -8.53822E-01 7.67333E-06 8.53822E-01
- 26 1.80005E+00 -1.05629E-05 1.80005E+00
- 27 -3.82005E+00 -1.64388E-05 3.82005E+00
- 28 -1.91621E+01 4.95642E-04 1.91621E+01
- 29 1.47090E+02 -4.51210E-08 1.47090E+02
- 30 -2.22421E+01 -5.53899E-04 2.22421E+01
- 31 -3.69005E+00 1.22821E-05 3.69005E+00
- 32 3.01086E+00 4.91759E-06 3.01086E+00
- 33 -4.01065E+00 1.49358E-04 4.01065E+00
-
- i re wp im wp abs wp
-
- isol = 30, m = 17
-
- i re wp im wp abs wp
-
- 1 2.44199E-04 1.37467E-04 2.80233E-04
- 2 1.58046E-04 1.77617E-04 2.37753E-04
- 3 -3.12345E-04 -4.19489E-05 3.15150E-04
- 4 3.22600E-04 -5.25465E-06 3.22643E-04
- 5 -1.68519E-03 1.40180E-05 1.68524E-03
- 6 1.69923E-03 4.79106E-05 1.69990E-03
- 7 -2.11359E-03 1.21565E-04 2.11708E-03
- 8 2.02424E-03 8.11553E-05 2.02586E-03
- 9 2.39845E-03 8.63472E-05 2.40000E-03
- 10 -4.45169E-03 2.41658E-05 4.45175E-03
- 11 1.19268E-02 3.36760E-05 1.19269E-02
- 12 -2.80470E-03 -1.12448E-05 2.80472E-03
- 13 -1.34714E-02 7.48204E-05 1.34716E-02
- 14 2.13521E-02 1.81053E-05 2.13521E-02
- 15 -1.14902E-02 2.08782E-05 1.14902E-02
- 16 6.84774E-04 -8.15232E-06 6.84823E-04
- 17 1.25278E-02 -1.06988E-05 1.25278E-02
- 18 -6.36831E-03 -2.57685E-05 6.36836E-03
- 19 3.96353E-02 -2.99669E-05 3.96353E-02
- 20 -6.10624E-02 -2.56100E-05 6.10624E-02
- 21 1.04576E-01 -1.84186E-05 1.04576E-01
- 22 -1.90159E-01 7.56294E-06 1.90159E-01
- 23 2.86242E-01 -1.30458E-05 2.86242E-01
- 24 -4.70774E-01 4.77864E-08 4.70774E-01
- 25 8.55484E-01 -4.89388E-05 8.55484E-01
- 26 -8.55105E-01 2.73017E-06 8.55105E-01
- 27 1.75053E+00 -2.95225E-06 1.75053E+00
- 28 -3.64903E+00 -1.94214E-05 3.64903E+00
- 29 -2.22420E+01 5.54163E-04 2.22420E+01
- 30 1.62143E+02 -5.88098E-08 1.62143E+02
- 31 -2.53064E+01 -6.24935E-04 2.53064E+01
- 32 -5.49130E+00 -5.14583E-05 5.49130E+00
- 33 9.76128E+00 4.65848E-04 9.76128E+00
-
- i re wp im wp abs wp
-
- isol = 31, m = 18
-
- i re wp im wp abs wp
-
- 1 -1.25795E-03 -8.79129E-05 1.26102E-03
- 2 6.84636E-04 1.50907E-04 7.01070E-04
- 3 9.55988E-05 1.67404E-04 1.92778E-04
- 4 -4.67394E-04 -2.61884E-05 4.68127E-04
- 5 1.78122E-04 -2.16504E-05 1.79433E-04
- 6 -1.13406E-03 1.77775E-05 1.13420E-03
- 7 1.38633E-03 2.89233E-05 1.38664E-03
- 8 -7.40913E-06 1.34978E-04 1.35181E-04
- 9 -3.33778E-04 6.60373E-05 3.40248E-04
- 10 4.00893E-03 7.78676E-05 4.00969E-03
- 11 -6.89634E-03 4.77365E-05 6.89650E-03
- 12 1.66771E-03 -3.16695E-05 1.66801E-03
- 13 9.29633E-03 3.57461E-05 9.29640E-03
- 14 -1.46692E-02 5.79246E-05 1.46693E-02
- 15 8.04482E-03 -3.03704E-05 8.04487E-03
- 16 -1.12359E-03 6.66269E-06 1.12361E-03
- 17 -7.65184E-03 -5.03702E-06 7.65184E-03
- 18 3.56374E-03 -2.12758E-05 3.56380E-03
- 19 -2.48673E-02 -2.16180E-05 2.48673E-02
- 20 3.79562E-02 -1.81077E-05 3.79562E-02
- 21 -6.51769E-02 -2.48650E-05 6.51769E-02
- 22 1.12713E-01 -1.79167E-05 1.12713E-01
- 23 -1.95750E-01 1.51133E-05 1.95750E-01
- 24 2.96108E-01 -1.15295E-05 2.96108E-01
- 25 -4.80540E-01 2.05579E-06 4.80540E-01
- 26 8.72331E-01 -4.99828E-05 8.72331E-01
- 27 -8.87881E-01 -7.17119E-06 8.87881E-01
- 28 1.81680E+00 2.00279E-06 1.81680E+00
- 29 -3.69004E+00 -1.20076E-05 3.69004E+00
- 30 -2.53064E+01 6.25303E-04 2.53064E+01
- 31 1.78135E+02 -1.01712E-07 1.78135E+02
- 32 -3.03243E+01 -7.60622E-04 3.03243E+01
- 33 -8.88013E+00 1.44613E-04 8.88013E+00
-
- i re wp im wp abs wp
-
- isol = 32, m = 19
-
- i re wp im wp abs wp
-
- 1 -1.11682E-03 2.41982E-05 1.11708E-03
- 2 -1.00032E-03 2.08518E-05 1.00053E-03
- 3 4.42051E-04 1.18038E-04 4.57539E-04
- 4 3.07550E-04 1.42304E-04 3.38877E-04
- 5 -3.74887E-04 3.44621E-05 3.76467E-04
- 6 -1.29510E-05 -1.82557E-05 2.23830E-05
- 7 -1.10119E-03 1.08738E-05 1.10124E-03
- 8 1.59890E-04 1.92122E-05 1.61040E-04
- 9 1.50387E-03 1.10988E-04 1.50796E-03
- 10 -1.76294E-03 6.59383E-05 1.76417E-03
- 11 5.72430E-03 1.21357E-04 5.72558E-03
- 12 -2.04419E-05 -2.99755E-05 3.62823E-05
- 13 -7.26320E-03 3.68904E-05 7.26329E-03
- 14 1.04400E-02 2.68113E-05 1.04400E-02
- 15 -5.24499E-03 5.16121E-06 5.24499E-03
- 16 -4.62374E-05 -1.14908E-05 4.76438E-05
- 17 5.50623E-03 1.56545E-06 5.50623E-03
- 18 -1.44340E-03 -2.55178E-05 1.44362E-03
- 19 1.42236E-02 -3.02613E-05 1.42237E-02
- 20 -2.25437E-02 -1.34538E-05 2.25437E-02
- 21 4.00768E-02 -6.68048E-06 4.00768E-02
- 22 -7.04537E-02 -1.91570E-05 7.04537E-02
- 23 1.16256E-01 -3.22954E-05 1.16256E-01
- 24 -2.03612E-01 2.88672E-05 2.03612E-01
- 25 3.12858E-01 -1.75161E-05 3.12858E-01
- 26 -5.24922E-01 1.34853E-05 5.24922E-01
- 27 1.02065E+00 -6.69152E-05 1.02065E+00
- 28 -1.35609E+00 2.84073E-05 1.35609E+00
- 29 3.01079E+00 -5.22551E-06 3.01079E+00
- 30 -5.49128E+00 5.15891E-05 5.49128E+00
- 31 -3.03243E+01 7.60925E-04 3.03243E+01
- 32 2.13132E+02 -2.87762E-07 2.13132E+02
- 33 -8.96015E+01 -1.34256E-03 8.96015E+01
-
- i re wp im wp abs wp
-
- isol = 33, m = 20
-
- i re wp im wp abs wp
-
- 1 5.97110E-03 1.81151E-05 5.97113E-03
- 2 -6.83874E-04 -2.49267E-05 6.84329E-04
- 3 -7.34077E-04 3.23603E-05 7.34790E-04
- 4 -2.47259E-05 1.25377E-04 1.27792E-04
- 5 1.90343E-05 2.89936E-05 3.46833E-05
- 6 -4.51401E-05 7.24078E-05 8.53260E-05
- 7 -2.06668E-04 -1.65480E-05 2.07329E-04
- 8 2.03604E-04 6.23814E-05 2.12946E-04
- 9 -1.26803E-03 1.21531E-06 1.26803E-03
- 10 2.03870E-03 6.16526E-05 2.03964E-03
- 11 -2.18961E-03 4.93140E-05 2.19017E-03
- 12 1.10902E-03 6.92933E-05 1.11118E-03
- 13 3.80538E-03 1.34774E-05 3.80540E-03
- 14 -4.39224E-03 2.64832E-05 4.39232E-03
- 15 1.45904E-03 -9.23035E-07 1.45904E-03
- 16 8.91580E-05 9.84786E-06 8.97003E-05
- 17 -2.31300E-03 -8.66663E-06 2.31301E-03
- 18 1.06310E-03 3.09833E-06 1.06310E-03
- 19 -7.58972E-03 -1.53100E-05 7.58973E-03
- 20 1.20962E-02 -4.07773E-05 1.20963E-02
- 21 -2.36320E-02 -2.53850E-05 2.36320E-02
- 22 4.36871E-02 1.82013E-06 4.36871E-02
- 23 -7.31436E-02 8.15778E-06 7.31436E-02
- 24 1.29219E-01 -1.11957E-04 1.29219E-01
- 25 -2.41307E-01 3.79853E-05 2.41307E-01
- 26 4.14978E-01 6.33625E-05 4.14978E-01
- 27 -8.20500E-01 1.50794E-04 8.20500E-01
- 28 1.92579E+00 -1.49713E-04 1.92579E+00
- 29 -4.01056E+00 -1.50364E-04 4.01056E+00
- 30 9.76119E+00 -4.66437E-04 9.76119E+00
- 31 -8.88036E+00 -1.46889E-04 8.88036E+00
- 32 -8.96019E+01 1.33893E-03 8.96019E+01
- 33 5.28231E+02 -2.40912E-06 5.28231E+02
-
- i re wp im wp abs wp
-
- Total cpu time = 5.188E+00 seconds
- Total wall time = 1.462E+01 seconds
diff --git a/src/DCON/validate/dcon_output_n1.nc b/src/DCON/validate/dcon_output_n1.nc
deleted file mode 100644
index 350a9b4683..0000000000
Binary files a/src/DCON/validate/dcon_output_n1.nc and /dev/null differ
diff --git a/src/DCON/validate/equil.in b/src/DCON/validate/equil.in
deleted file mode 100644
index bcc711489a..0000000000
--- a/src/DCON/validate/equil.in
+++ /dev/null
@@ -1,29 +0,0 @@
-&EQUIL_CONTROL
- eq_type="efit" ! Type of the input 2D equilibrium file. Accepts efit, chease, fluxgrid, transp, jsolver, lar, sol, etc.
- eq_filename = "beta_1.00" ! Path to input file
-
- jac_type="hamada" ! Working coordinate system for all DCON and GPEC calculations. Overrides individual powers. Accepts hamada, pest, boozer, equal_arc
- power_bp=0 ! del.B ~ B_p**power_bp * B**power_b / R**power_r
- power_b=0 ! del.B ~ B_p**power_bp * B**power_b / R**power_r
- power_r=0 ! del.B ~ B_p**power_bp * B**power_b / R**power_r
-
- grid_type="ldp" ! Radial grid packing of equilibrium quantities. Accepts rho, ldp, pow1, pow2, or original. ldp packs points near the core and edge. pow* packs near the edge.
- psilow=0.01 ! Minimum value of psi, normalized from 0 to 1
- psihigh=0.99 ! Maximum value of psi, normalized from 0 to 1
- mpsi=128 ! Number of radial grid intervals for equilibrium quantities
- mtheta=256 ! Number of equally spaced poloidal grid intervals for all splines
- newq0=0 ! Grad-Shafranov solution invariant adjustment of the q profile to give the specified value of q at the axis. Default 0 uses input file value.
- use_classic_splines = t ! Use a classical cubic spline instead of tri-diagonal solution for splines with extrapolation boundary conditions
-
- input_only=f ! Generate information about the input and then quit with no further calculation
-/
-&EQUIL_OUTPUT
- gse_flag=f ! Produces diagnostic output for accuracy of solution to Grad-Shafranov equation
- out_eq_1d=f ! Ascii output of 1D equilibrium file data
- bin_eq_1d=f ! Binary output of 1D equilibrium file data
- out_eq_2d=f ! Ascii output of 2D equilibrium file data
- bin_eq_2d=t ! Binary output of 2D equilibrium file data (set true for GPEC)
- out_2d=f ! Ascii output of processed 2D data
- bin_2d=f ! Binary output of processed 2D data
- dump_flag=f ! Binary dump of basic equilibrium data and 2D rzphi spline
-/
diff --git a/src/DCON/validate/euler.bin b/src/DCON/validate/euler.bin
deleted file mode 100644
index 72592f2161..0000000000
Binary files a/src/DCON/validate/euler.bin and /dev/null differ
diff --git a/src/DCON/validate/fmat.bin b/src/DCON/validate/fmat.bin
deleted file mode 100644
index d869620702..0000000000
Binary files a/src/DCON/validate/fmat.bin and /dev/null differ
diff --git a/src/DCON/validate/fort.27 b/src/DCON/validate/fort.27
deleted file mode 100644
index 4277e3495b..0000000000
Binary files a/src/DCON/validate/fort.27 and /dev/null differ
diff --git a/src/DCON/validate/fs.bin b/src/DCON/validate/fs.bin
deleted file mode 100644
index 84c9a3895d..0000000000
Binary files a/src/DCON/validate/fs.bin and /dev/null differ
diff --git a/src/DCON/validate/g147131.02300_DIIID_KEFIT b/src/DCON/validate/g147131.02300_DIIID_KEFIT
deleted file mode 100644
index 15da8c793c..0000000000
--- a/src/DCON/validate/g147131.02300_DIIID_KEFIT
+++ /dev/null
@@ -1,6668 +0,0 @@
- EFITD 03/13/2012 #147131 2300ms 3 129 129
- 0.170000000E+01 0.320000000E+01 0.169550002E+01 0.840000000E+00 0.000000000E+00
- 0.175888032E+01 0.244191348E-01-0.299591296E+00-0.373057194E-01-0.172279610E+01
- 0.118663454E+07-0.299591296E+00 0.000000000E+00 0.175888032E+01 0.000000000E+00
- 0.244191348E-01 0.000000000E+00-0.373057194E-01 0.000000000E+00 0.000000000E+00
--0.297297920E+01-0.297233876E+01-0.297167564E+01-0.297099331E+01-0.297029482E+01
--0.296958285E+01-0.296885979E+01-0.296812772E+01-0.296738851E+01-0.296664379E+01
--0.296589500E+01-0.296514342E+01-0.296439017E+01-0.296363625E+01-0.296288254E+01
--0.296212982E+01-0.296137877E+01-0.296062999E+01-0.295988403E+01-0.295914135E+01
--0.295840238E+01-0.295766748E+01-0.295693699E+01-0.295621119E+01-0.295549033E+01
--0.295477465E+01-0.295406434E+01-0.295335959E+01-0.295266055E+01-0.295196735E+01
--0.295128013E+01-0.295059899E+01-0.294992403E+01-0.294925534E+01-0.294859299E+01
--0.294793705E+01-0.294728758E+01-0.294664464E+01-0.294600827E+01-0.294537852E+01
--0.294475542E+01-0.294413902E+01-0.294352934E+01-0.294292640E+01-0.294233024E+01
--0.294174088E+01-0.294115833E+01-0.294058261E+01-0.294001375E+01-0.293945175E+01
--0.293889663E+01-0.293834841E+01-0.293780708E+01-0.293727267E+01-0.293674519E+01
--0.293622463E+01-0.293571101E+01-0.293520434E+01-0.293470463E+01-0.293421187E+01
--0.293372607E+01-0.293324725E+01-0.293277540E+01-0.293231053E+01-0.293185264E+01
--0.293140174E+01-0.293095782E+01-0.293052090E+01-0.293009097E+01-0.292966803E+01
--0.292925209E+01-0.292884315E+01-0.292844120E+01-0.292804625E+01-0.292765830E+01
--0.292727734E+01-0.292690337E+01-0.292653638E+01-0.292617638E+01-0.292582336E+01
--0.292547731E+01-0.292513823E+01-0.292480611E+01-0.292448095E+01-0.292416274E+01
--0.292385147E+01-0.292354713E+01-0.292324972E+01-0.292295922E+01-0.292267562E+01
--0.292239890E+01-0.292212905E+01-0.292186606E+01-0.292160989E+01-0.292136052E+01
--0.292111794E+01-0.292088209E+01-0.292065296E+01-0.292043049E+01-0.292021465E+01
--0.292000537E+01-0.291980260E+01-0.291960626E+01-0.291941629E+01-0.291923259E+01
--0.291905507E+01-0.291888360E+01-0.291871807E+01-0.291855854E+01-0.291840555E+01
--0.291826023E+01-0.291812434E+01-0.291800028E+01-0.291789115E+01-0.291780078E+01
--0.291773380E+01-0.291769570E+01-0.291769292E+01-0.291773297E+01-0.291782483E+01
--0.291798706E+01-0.291825905E+01-0.291866469E+01-0.291916231E+01-0.291967537E+01
--0.292014273E+01-0.292052751E+01-0.292081336E+01-0.292100082E+01
- 0.767620766E+05 0.755059656E+05 0.742807174E+05 0.730839467E+05 0.719135482E+05
- 0.707676640E+05 0.696446547E+05 0.685430732E+05 0.674616426E+05 0.663992361E+05
- 0.653548590E+05 0.643276337E+05 0.633167856E+05 0.623216310E+05 0.613415665E+05
- 0.603760596E+05 0.594246402E+05 0.584868937E+05 0.575624536E+05 0.566509967E+05
- 0.557522377E+05 0.548659245E+05 0.539918347E+05 0.531297716E+05 0.522795616E+05
- 0.514410514E+05 0.506141052E+05 0.497986031E+05 0.489944389E+05 0.482015186E+05
- 0.474197588E+05 0.466490855E+05 0.458894328E+05 0.451407421E+05 0.444029609E+05
- 0.436760424E+05 0.429599442E+05 0.422546281E+05 0.415600592E+05 0.408762057E+05
- 0.402030381E+05 0.395405287E+05 0.388886515E+05 0.382473814E+05 0.376166942E+05
- 0.369965659E+05 0.363869724E+05 0.357878894E+05 0.351992914E+05 0.346211520E+05
- 0.340534432E+05 0.334961347E+05 0.329491938E+05 0.324125847E+05 0.318862682E+05
- 0.313702005E+05 0.308643333E+05 0.303686123E+05 0.298829768E+05 0.294073588E+05
- 0.289416816E+05 0.284858588E+05 0.280397930E+05 0.276033740E+05 0.271764775E+05
- 0.267589629E+05 0.263506710E+05 0.259514217E+05 0.255610111E+05 0.251792085E+05
- 0.248057525E+05 0.244403469E+05 0.240826563E+05 0.237323009E+05 0.233888502E+05
- 0.230518166E+05 0.227206476E+05 0.223947173E+05 0.220733432E+05 0.217558604E+05
- 0.214416785E+05 0.211302797E+05 0.208212111E+05 0.205140776E+05 0.202085355E+05
- 0.199042872E+05 0.196010769E+05 0.192986859E+05 0.189969298E+05 0.186956553E+05
- 0.183947379E+05 0.180940800E+05 0.177936092E+05 0.174932774E+05 0.171930598E+05
- 0.168929546E+05 0.165929833E+05 0.162931904E+05 0.159936446E+05 0.156944398E+05
- 0.153956963E+05 0.150975630E+05 0.148002196E+05 0.145038792E+05 0.142087921E+05
- 0.139152494E+05 0.136235876E+05 0.133341656E+05 0.130469733E+05 0.127609995E+05
- 0.124739500E+05 0.121822064E+05 0.118807691E+05 0.115631791E+05 0.112214172E+05
- 0.108457785E+05 0.104247204E+05 0.994468202E+04 0.938987215E+04 0.874138645E+04
- 0.796050283E+04 0.696648059E+04 0.572148983E+04 0.434331221E+04 0.302648173E+04
- 0.191878149E+04 0.109840443E+04 0.563472273E+03 0.250145176E+03
--0.911430759E+00-0.946775258E+00-0.976776409E+00-0.100206207E+01-0.102318633E+01
--0.104063817E+01-0.105484910E+01-0.106619994E+01-0.107502677E+01-0.108162616E+01
--0.108625984E+01-0.108915880E+01-0.109052686E+01-0.109054392E+01-0.108936871E+01
--0.108714135E+01-0.108398545E+01-0.108001013E+01-0.107531167E+01-0.106997505E+01
--0.106407525E+01-0.105767845E+01-0.105084305E+01-0.104362060E+01-0.103605656E+01
--0.102819109E+01-0.102005961E+01-0.101169338E+01-0.100311998E+01-0.994363770E+00
--0.985446230E+00-0.976386327E+00-0.967200795E+00-0.957904406E+00-0.948510195E+00
--0.939029668E+00-0.929472981E+00-0.919849097E+00-0.910165928E+00-0.900430460E+00
--0.890648860E+00-0.880826570E+00-0.870968402E+00-0.861078600E+00-0.851160917E+00
--0.841218669E+00-0.831254787E+00-0.821271865E+00-0.811272197E+00-0.801257817E+00
--0.791230527E+00-0.781191928E+00-0.771143445E+00-0.761086347E+00-0.751021768E+00
--0.740950726E+00-0.730874137E+00-0.720792832E+00-0.710707565E+00-0.700619031E+00
--0.690527873E+00-0.680434692E+00-0.670340058E+00-0.660244519E+00-0.650148608E+00
--0.640052852E+00-0.629957781E+00-0.619863935E+00-0.609771874E+00-0.599682187E+00
--0.589595496E+00-0.579512475E+00-0.569433852E+00-0.559360424E+00-0.549293072E+00
--0.539232769E+00-0.529180599E+00-0.519137773E+00-0.509105243E+00-0.499083227E+00
--0.489071983E+00-0.479071940E+00-0.469083699E+00-0.459108050E+00-0.449145977E+00
--0.439198676E+00-0.429267577E+00-0.419354360E+00-0.409460988E+00-0.399589732E+00
--0.389743210E+00-0.379924428E+00-0.370136823E+00-0.360384324E+00-0.350671405E+00
--0.341003163E+00-0.331385391E+00-0.321824673E+00-0.312328485E+00-0.302905315E+00
--0.293564789E+00-0.284317830E+00-0.275176823E+00-0.266155810E+00-0.257270713E+00
--0.248539578E+00-0.239982861E+00-0.231586985E+00-0.222855615E+00-0.212944521E+00
--0.200983819E+00-0.186071558E+00-0.167259611E+00-0.143538837E+00-0.113823295E+00
--0.769332548E-01-0.315767378E-01 0.236706957E-01 0.903882322E-01 0.171213058E+00
- 0.290801074E+00 0.483881839E+00 0.671604565E+00 0.746098232E+00 0.715833223E+00
- 0.616102304E+00 0.480663723E+00 0.334205417E+00 0.200214330E+00
--0.620844410E+06-0.605164368E+06-0.590721145E+06-0.577369417E+06-0.564980938E+06
--0.553442532E+06-0.542654324E+06-0.532528173E+06-0.522986299E+06-0.513960063E+06
--0.505388891E+06-0.497219331E+06-0.489404214E+06-0.481901915E+06-0.474675706E+06
--0.467693174E+06-0.460925723E+06-0.454348119E+06-0.447938100E+06-0.441676026E+06
--0.435544569E+06-0.429528447E+06-0.423614183E+06-0.417789891E+06-0.412045096E+06
--0.406370563E+06-0.400758159E+06-0.395200722E+06-0.389691950E+06-0.384226303E+06
--0.378798916E+06-0.373405520E+06-0.368042382E+06-0.362706238E+06-0.357394249E+06
--0.352103953E+06-0.346833229E+06-0.341580259E+06-0.336343506E+06-0.331121686E+06
--0.325913746E+06-0.320718854E+06-0.315536379E+06-0.310365887E+06-0.305207129E+06
--0.300060041E+06-0.294924741E+06-0.289801532E+06-0.284690905E+06-0.279593550E+06
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- &OUT1
- ISHOT = 147131
- ITIME = 2300
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- BTOR = -1.722796100000000
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- 0.9597781492966423 0.9494516109285650 0.9309468484892365
- 0.9130213355845107 0.8915934623500216 0.8667049404202013
- 0.8381983198492649 0.8058814147442267 0.7749999999999999
- 0.7427941500376195 0.7000000000000002 0.6651485845519377
- 0.6250000000000000 0.5750000000000002 0.5249999999999999
- 0.4750000000000001 0.4248498795112970 0.3546173784611517
- 0.3000000000000000 0.2279411872645595 0.1734025596680047
- 9.4285888010310057E-002 0.000000000000000 -7.4999999999999956E-002
- -0.1499999999999999 -0.2135871879622072 -0.2749999999999999
- -0.3250000000000000 -0.3750000000000000 -0.4250000000000000
- -0.4750000000000001 -0.5229151790492524 -0.5591934667275523
- -0.6000000000000001 -0.6400747194005502 -0.6750000000000000
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- -0.8163753357203332 -0.8500000000000001 -0.8763983460548967
- -0.9107282951797264 -0.9435737956718564 -0.9747878926723358
- -1.000000000000000 -1.025000000000000 -1.050577776343781
- -1.075626757237083 -1.100000000000000 -1.125000000000000
- -1.145293850215639 -1.163201979630879 -1.180737908167223
- -1.119509526919738 -1.050000000000000 -0.9750000000000001
- -0.9000000000000000 -0.8250000000000001 -0.7500000000000000
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- 0.000000000000000 0.000000000000000 0.000000000000000
- NBDRY = 90
- FWTSI = 999.9999525025510 502.7561595422264
- 525.7968003582148 506.1858953527478 506.8771572058214
- 211.9550215768744 0.000000000000000 505.2394850316234
- 495.9030553849408 505.6915840632106 505.5450199973388
- 506.4652056124651 445.6379373054061 339.4241436441839
- 211.4447825088264 126.4849676858440 268.4531183007420
- 495.9911793729846 501.5195037925907 505.6647344711498
- 505.1554396122791 504.7541531802667 504.7202701464773
- 504.0551234683026 493.1866586273251 271.9614490441583
- 330.0603505877313 183.5406913833808 275.3046219429248
- 504.8467050649704 0.000000000000000 506.0926981654039
- 399.5468805559500 315.1652428137394 451.1731822929428
- 157.1123584716163 176.4455436855753 167.4543809404153
- 239.3754681146945 388.4037211457047 504.5986089629227
- 0.000000000000000 505.7599227441602 471.4974429964933
- FWTCUR = 2.7911077050807992E-005
- MXITER = 200
- NXITER = 1
- LIMITR = 85
- XLIM = 1.016000000000000 1.016000000000000
- 1.016000000000000 1.016000000000000 1.016000000000000
- 1.016000000000000 1.016000000000000 1.016000000000000
- 1.016000000000000 1.016000000000000 1.016000000000000
- 1.012000000000000 1.001000000000000 1.029000000000000
- 1.042000000000000 1.046000000000000 1.056000000000000
- 1.097000000000000 1.108000000000000 1.116000000000000
- 1.134000000000000 1.148000000000000 1.162000000000000
- 1.181000000000000 1.182000000000000 1.185000000000000
- 1.190000000000000 1.195000000000000 1.201000000000000
- 1.209000000000000 1.215000000000000 1.222000000000000
- 1.228000000000000 1.234000000000000 1.239000000000000
- 1.242000000000000 1.248000000000000 1.258000000000000
- 1.263000000000000 1.280000000000000 1.280000000000000
- 1.280000000000000 1.310000000000000 1.328000000000000
- 1.361000000000000 1.380000000000000 1.419000000000000
- 1.419000000000000 1.372000000000000 1.372000000000000
- 1.608000000000000 1.647000000000000 1.785000000000000
- 2.070000000000000 2.128000000000000 2.245000000000000
- 2.323000000000000 2.377000000000000 2.362500000000000
- 2.364435000000000 2.364969000000000 2.365324000000000
- 2.365121000000000 2.364842000000000 2.364334000000000
- 2.362500000000000 2.377000000000000 2.134000000000000
- 1.786000000000000 1.768000000000000 1.768000000000000
- 1.682000000000000 1.372000000000000 1.372000000000000
- 1.420000000000000 1.420000000000000 1.273000000000000
- 1.153000000000000 1.016000000000000 1.016000000000000
- 1.016000000000000 1.016000000000000 1.016000000000000
- 1.016000000000000 1.016000000000000 1.016000000000000
- 0.000000000000000 0.000000000000000 0.000000000000000
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- 0.000000000000000 0.000000000000000 0.000000000000000
- 0.000000000000000 0.000000000000000 0.000000000000000
- 0.000000000000000 0.000000000000000
- YLIM = 0.000000000000000 0.9640000000000000
- 0.9680000000000000 1.001000000000000 1.019000000000000
- 1.077000000000000 1.070000000000000 1.096000000000000
- 1.113000000000000 1.138000000000000 1.147000000000000
- 1.165000000000000 1.217000000000000 1.217000000000000
- 1.162400000000000 1.162380000000000 1.162600000000000
- 1.164500000000000 1.165940000000000 1.165910000000000
- 1.168960000000000 1.171750000000000 1.175560000000000
- 1.183000000000000 1.183500000000000 1.185000000000000
- 1.188000000000000 1.191000000000000 1.196000000000000
- 1.202000000000000 1.208000000000000 1.214000000000000
- 1.221000000000000 1.231000000000000 1.238000000000000
- 1.244000000000000 1.254000000000000 1.278000000000000
- 1.290000000000000 1.331000000000000 1.347000000000000
- 1.348000000000000 1.348000000000000 1.348000000000000
- 1.348000000000000 1.348000000000000 1.348000000000000
- 1.310000000000000 1.310000000000000 1.292000000000000
- 1.095000000000000 1.077000000000000 1.077000000000000
- 1.040000000000000 0.9930000000000000 0.7090000000000000
- 0.5190000000000000 0.3890000000000000 0.4000000000000000
- 0.2220000000000000 0.1330000000000000 4.3999999999999997E-002
- -4.3999999999999997E-002 -0.1330000000000000 -0.2220000000000000
- -0.4000000000000000 -0.3890000000000000 -0.9730000000000000
- -1.174000000000000 -1.211000000000000 -1.250000000000000
- -1.250000000000000 -1.250000000000000 -1.329000000000000
- -1.329000000000000 -1.363000000000000 -1.363000000000000
- -1.363000000000000 -1.223000000000000 -1.223000000000000
- -0.8300000000000000 -0.8000000000000000 -0.4150000000000000
- -0.4000000000000000 -1.0000000000000000E-003 0.000000000000000
- 0.000000000000000 0.000000000000000 0.000000000000000
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- 0.000000000000000 0.000000000000000
- ERROR = 1.0000000000000000E-008
- ICONVR = 2
- IBUNMN = 3
- PRESSR = 76781.32885678127 74863.25800535333
- 73166.60046747129 71669.96555247817 70212.92078931149
- 68792.17297968730 67267.93727391605 65781.07573503046
- 64328.93968599897 62909.30813933844 61520.31868351915
- 60160.40952768265 58828.27090119621 57522.80429567586
- 56243.08828115389 54988.34983264518 53757.94027484011
- 52551.31509636151 51368.01700543736 50312.20939069427
- 49275.11740373774 48256.53177887356 47256.27322991924
- 46274.18784144539 45310.14311220172 44364.02454901914
- 43435.73272363056 42525.18071675229 41632.29188372331
- 40756.99788426571 39814.42292409088 38892.98762985114
- 37992.62150355375 37113.25677375504 36254.82628662083
- 35417.26141620617 34600.48992892507 33804.43373575630
- 33029.00646223739 32274.11076062885 31539.63528060741
- 30825.45120422131 30131.40823728059 29397.03315635974
- 28686.14466223319 27998.41538389834 27333.45086598920
- 26690.77495354281 26069.81214965828 25469.86629237036
- 24842.66056365969 24283.58672061474 23697.96935000312
- 23131.29150965732 22581.15109313150 22044.61694891474
- 21518.61997721864 21000.59587229888 20527.71306157200
- 20058.57526936302 19592.14596691313 19127.60794791624
- 18664.33304965296 18201.85887850703 17739.87167750560
- 17278.19470109642 16816.78166642823 16394.11969307315
- 15971.90792640962 15550.40493170118 15129.97528840354
- 14711.10093529669 14294.39616765267 13918.09748326315
- 13544.92275946686 13175.57014026856 12845.74382646118
- 12515.40197943927 12217.14089842939 11909.06057341461
- 11584.25951364460 11279.61073327688 10948.65175906819
- 10637.91565239412 10296.05692203695 9982.665020656239
- 9638.851796577706 9338.783128949071 9013.684126476666
- 8751.573038386870 8471.134720584683 8168.351832403454
- 7837.661248625122 7598.260498462453 7341.290463883974
- 7065.558672833547 6770.864701793502 6458.000223756062
- 6128.749820414500 5785.892813607409 5433.158050561190
- 5074.644018006349 4714.194891502077 4534.360209222545
- 4355.341566917420 4177.531971031782 4001.305283525661
- 3827.016317746723 3655.000929476260 3485.576103079767
- 3319.040032832240 3155.672199365910 2995.733441423123
- 2839.466022704617 2687.093694044039 2538.821750828768
- 2394.837085618784 2255.308236114629 2120.385428362848
- 1990.200615338441 1864.867510734543 1629.120255744579
- 1413.689330389828 1218.798697472071 1044.238024560605
- 889.3178565237582 752.8680237079956 633.2364411639952
- 528.2874134614290 392.8060362691029 280.7960268108279
- 250.1451760428327 0.000000000000000 0.000000000000000
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- 0.000000000000000
- RPRESS = 0.000000000000000 -1.2012012012012012E-002
- -2.3023023023023025E-002 -3.3033033033033031E-002 -4.3043043043043044E-002
- -5.3053053053053051E-002 -6.4064064064064064E-002 -7.5075075075075076E-002
- -8.6086086086086089E-002 -9.7097097097097101E-002 -0.1081081081081081
- -0.1191191191191191 -0.1301301301301301 -0.1411411411411412
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- -0.2162162162162162 -0.2262262262262262 -0.2362362362362362
- -0.2462462462462462 -0.2562562562562563 -0.2662662662662663
- -0.2762762762762763 -0.2862862862862863 -0.2962962962962963
- -0.3063063063063063 -0.3173173173173173 -0.3283283283283283
- -0.3393393393393394 -0.3503503503503503 -0.3613613613613614
- -0.3723723723723724 -0.3833833833833834 -0.3943943943943944
- -0.4054054054054054 -0.4164164164164164 -0.4274274274274275
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- -0.4734734734734735 -0.4854854854854855 -0.4974974974974975
- -0.5095095095095095 -0.5215215215215215 -0.5335335335335335
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- -0.8828828828828829 -0.8898898898898899 -0.8968968968968969
- -0.9029029029029029 -0.9089089089089090 -0.9139139139139140
- -0.9189189189189190 -0.9229229229229229 -0.9269269269269269
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- 0.000000000000000
- QPSI = 1.062022126653593 1.069989383086604
- 1.075304751668133 1.083966096090663 1.088371827679364
- 1.094299581114990 1.100135653628720 1.106477359720005
- 1.112797996580092 1.119604970050730 1.126111808081460
- 1.133102951241977 1.140010502376114 1.147027080590435
- 1.154406423578045 1.161670740930477 1.169073515384133
- 1.176775673720043 1.184485119553410 1.192325009996535
- 1.200337445808878 1.208507146439601 1.216714965239446
- 1.225127007754196 1.233708012797175 1.242388777795652
- 1.251194128502904 1.260198822831727 1.269363553250738
- 1.278654557995057 1.288073495731514 1.297715979508079
- 1.307520993145906 1.317477917778631 1.327582468036335
- 1.337921774080170 1.348433535592424 1.359116382967887
- 1.369977308184977 1.381060341259557 1.392371681710433
- 1.403859927956472 1.415559720029137 1.427485170380328
- 1.439658851089910 1.452058611073094 1.464676812854642
- 1.477559790419606 1.490698256070615 1.504098575639812
- 1.517767889223511 1.531703690466205 1.545932141703868
- 1.560461894326618 1.575294425805617 1.590432074309697
- 1.605897832549147 1.621695346376826 1.637836025717006
- 1.654330703535554 1.671183773224174 1.688423599600785
- 1.706038659184470 1.724061654022336 1.742497458809612
- 1.761345439885922 1.780641468185139 1.800371946361733
- 1.820584444883129 1.841253171701596 1.862409195011656
- 1.884074452967864 1.906230080420706 1.928925086351233
- 1.952125623351688 1.975889752955031 2.000171526492772
- 2.025006449274960 2.050382047345760 2.076308553637879
- 2.102770770775955 2.129778725265508 2.157350553255539
- 2.185503436195831 2.214233926058826 2.243545997820678
- 2.273507537290028 2.304109853622101 2.335377386056945
- 2.367287959975241 2.400012777644059 2.433434076137508
- 2.467665983629683 2.502707639680795 2.538693132316229
- 2.575548580152560 2.613414651236727 2.652326902568753
- 2.692350616971484 2.733557070715256 2.776055912797787
- 2.819906625474248 2.865174594917490 2.912158013679076
- 2.960737535806386 3.011300651616540 3.063954059364148
- 3.118848971395844 3.176372826873230 3.236605518696807
- 3.299722709125948 3.366065102435951 3.435504095994509
- 3.508565790295565 3.585066269709416 3.665374933144523
- 3.749155932154522 3.836420819242377 3.926209358586249
- 4.017504884057729 4.106631025539255 4.186257310634852
- 4.254281952287243 4.324138648028361 4.420597880168824
- 4.569493813155836 4.811073342886258 5.253690010110009
- 8.032269020262538
- PRESSW = 0.000000000000000 0.000000000000000
- 0.000000000000000 0.000000000000000 0.000000000000000
- 0.000000000000000 0.000000000000000 0.000000000000000
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- PRES = 76762.07659049288 75505.96557742984
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- NQPSI = 129
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- /
- &BASIS
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- /
- &MSEOUT
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- /
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- 0.1025167665000940 ,
- 9.9402418869484806E-003,
- 0.5657908661525793 ,
- 6.9254557685246063E-002,
- 8.8465863142351622E-003,
- 0.2427614440886205 ,
- 7.5902565528919372E-002,
- 6.2268607119479957E-002,
- 0.000000000000000 ,
- 0.4591730294678171 ,
- 0.1164963608783690 ,
- 2.3716235575672658E-002,
- 9.7360485808618197E-002,
- 2.0547716593933629E-002,
- 0.1635269758339434 ,
- 0.3562749054621027 ,
- 1.230396761661656 ,
- 1.4742685234513338E-002,
- 0.000000000000000 ,
- 0.3974465226608165 ,
- 0.2434253110628695 ,
- 0.2976340978930932 ,
- 4.9916901857596084E-002,
- 0.1537242396472875 ,
- 0.000000000000000 ,
- 5.8825006947044048E-003,
- 5.4957901438118474E-003,
- 0.000000000000000 ,
- 2.0276489206899072E-002,
- 3.5533777446743110E-002,
- 1.8582184560361222E-004,
- SAIPR = 0.000000000000000 ,
- SAIIP = 4.5405653514677624E-002
- /
- KIM
diff --git a/src/DCON/validate/gmat.bin b/src/DCON/validate/gmat.bin
deleted file mode 100644
index 5c6767b433..0000000000
Binary files a/src/DCON/validate/gmat.bin and /dev/null differ
diff --git a/src/DCON/validate/gpec.in b/src/DCON/validate/gpec.in
deleted file mode 100644
index 19c273c7e0..0000000000
--- a/src/DCON/validate/gpec.in
+++ /dev/null
@@ -1,88 +0,0 @@
-&GPEC_INPUT
- dcon_dir = '' ! Path to DCON outputs. Individual file paths are appended to this
- idconfile = 'euler.bin' ! Eigenfunctions output by DCON run
- ieqfile = 'psi_in.bin' ! Flux surfaces output by DCON run
- rdconfile = 'globalsol.bin' ! Galerkin eigenfunctions output by resistive DCON run
-
- gal_flag = f ! Use the Galerkin eigenfunctions from resistive DCON instead of the ideal DCON shooting method solutions
-
- jac_in="hamada" ! Coordinate system of external perturbation (affects data_flag and harmonic_flag). Options include: pest,boozer,hamada
- jsurf_in=1 ! True(1) if external perturbation is area weighted (i.e. flux)
- tmag_in =0 ! True(1) if external perturbation has toroidal angle defined by jac_in. False(0) if machine angle.
- mthsurf =0 ! Number of poloidal angle gridpoints. Minimum of twice the Nyquist condition from DCON m limits is enforced.
-
- coil_flag=t ! Calculate external perturbation from coils in coil.in
-
- data_flag=f ! Apply perturbation from thrid party code output
- data_type="surfmn" ! Name of said code. Choose: surfmn,??
- infile="path/to/file" ! Path to said output
- nmin=0 ! Extra parameters needed to read surfmn files.
- nmax=64 ! Extra parameters needed to read surfmn files.
- mmin=-64 ! Extra parameters needed to read surfmn files.
- mmax=64 ! Extra parameters needed to read surfmn files.
-
- harmonic_flag=f ! Apply self-defined perturbations
- cosmn(3)=1e-4 ! Real part of m=3 component (n defined by DCON run).
- sinmn(6)=1e-4 ! Imaginary part of m=6 component. etc.
-
- displacement_flag=f ! Perturbations are displacement (m). Default is field (T).
- fixed_boundary_flag=f ! Total perturbation = external perturbation
-
- mode_flag = .F. ! Return only a single DCON eigenfunction defined by mode (ignores external pert.)
- mode = 0 ! DCON eigen function index (1 is least stable)
- filter_types = 'w' ! Isolate the filter_modes of energy (w), reluctance (r), permiability (p) or singular coupling (s) eigenvectors/singular-vectors
- filter_modes = 0 ! Number of modes isolated, negative values isolate backwards from the last mode
-/
-&GPEC_CONTROL
- resp_index=0 ! Integer 0-4, determining method of inductance matrix formation. 0 uses energy identity, and is recommended.
- sing_spot=5e-4 ! Minimum distance to singular surface in (m-nq) space
- sing_npsi=100 ! Number of points between rational surfaces used for b-normal splines across sin_spot
- reg_flag=t ! Regularize the solution near resonant surfaces
- reg_spot=5e-2 ! Regularize by (m-nq)^2/((m-nq)^2+reg_spot^2)
- chebyshev_flag=f ! Fit Chebyshev polynomials to the displacement.
- nche=20 ! Number of Chebyshev polynomials used
- use_classic_splines = f ! Use a classical cubic spline instead of tri-diagonal solution for splines with extrapolation boundary conditions
-/
-&GPEC_OUTPUT
- jac_out="hamada" ! Coordinate system of outputs
- jsurf_out=0 ! True(1) for area weighted outputs (only appends standard gpec_control output)
- tmag_out=1 ! True(1) for magnetic toroidal angle outputs (affects singcoup and singfld, appends gpec_control)
- mlim_out=64 ! If positive, Fourier decomposed outputs will span -mlim_out<=m<=mlim_out. Default (<=0) outputs on internal m range.
-
- resp_flag=t ! Output energy, reluctance, inductance, and permeability eigenvalues, eigenvectors, and matrices
- filter_flag=t ! Outputs energy, reluctance, pereability, and (optionally) the singular-coupling eigenmodes on the control surface
- singcoup_flag=t ! Calculate coupling of each m to resonant surfaces
- singfld_flag=t ! Output of resonant surface quantities (flux,current,etc.)
- vsingfld_flag=f ! Output of vacuum resonant surface quantities
- singthresh_flag=t ! Calculate Callen resonant field penetration threshold (requires kinetic profiles from pentrc.in)
-
- pmodb_flag=f ! Outputs delta-B_Lagrangian
- xbnormal_flag=t ! Outputs normal displacement and field in plasma
- vbnormal_flag=f ! Outputs vacuum normal displacement and field in plasma
- xclebsch_flag=t ! Outputs clebsch coordinate displacement for PENT
- dw_flag=f ! Outputs self-consistent energy and torque profiles (when kin_flag=t from DCON)
-
- eqbrzphi_flag=f ! Outputs equilibrium field on regular (r,z) grid
- brzphi_flag=t ! Outputs perturbed field on regular (r,z) grid
- xrzphi_flag=f ! Outputs displacement on regular (r,z) grid
- vbrzphi_flag=f ! Outputs field on regular (r,z) grid due to total boundary surface current (not a real field)
- vvbrzphi_flag=f ! Outputs field on regular (r,z) grid due to exeternal perturbation surface current (not a real field)
- vsbrzphi_flag=f ! Outputs the field on regular (r,z) grid due to singular surface currents
- ss_flag(3)=f ! Outputs the field on regular (r,z) grid due to the 3rd singular surface current, etc.
- xbrzphifun_flag=f ! Outputs r,z, and perturbation vectors on psi,theta grid
- arzphifun_flag=f ! Outputs r,z, and vector potential on psi,theta grid
-
- nr = 64 ! Number of radial grid points in rzphi outputs
- nz = 124 ! Number of vertical grid points in rzphi outputs
- fun_flag=t ! Write outputs to (r,z) in addition to default (psi,m)
- flux_flag=f ! Write outputs to (psi,theta) in addition to default (psi,m)
- bin_flag=f ! Write binary outputs for use with xdraw
- bin_2d_flag=f ! Write 2D binary outputs for use with xdraw
- out_ahg2msc=f ! Output deprecated ahg2msc.out files. This is used to communicate with vacuum, but is now done through memory.
- max_linesout=0 ! Maximum length of ascii data tables enforced by increasing radial step size (iff .gt. 0).
- verbose=t ! Print run log to terminal
-/
-&GPEC_DIAGNOSE
- timeit=t ! Print timer splits for major subroutines
- radvar_flag=f ! Map various radial variables (rho,psi_tor) on psi_n grid
-/
diff --git a/src/DCON/validate/gs.bin b/src/DCON/validate/gs.bin
deleted file mode 100644
index 98d6719d53..0000000000
Binary files a/src/DCON/validate/gs.bin and /dev/null differ
diff --git a/src/DCON/validate/imats.out b/src/DCON/validate/imats.out
deleted file mode 100644
index 3c974edda8..0000000000
--- a/src/DCON/validate/imats.out
+++ /dev/null
@@ -1,10451 +0,0 @@
- psi m1 m2 real(Ai) imag(Ai) real(Bi) imag(Bi) real(Ci) imag(Ci) real(Di) imag(Di) real(Ei) imag(Ei) real(Hi) imag(Hi)
- 9.99999978E-03 -4 -4 1.53034448E+03 0.00000000E+00 0.00000000E+00 5.46683289E+02 1.31073630E+00 2.68199585E+02 1.97254883E+02 0.00000000E+00 3.25231247E+01 -4.98163968E-01 7.94882031E+04 0.00000000E+00
- 9.99999978E-03 -4 -3 7.95266571E+01 8.21601774E-04 -1.79691793E-04 6.20876265E+00 -1.61386728E-01 -4.49731641E+03 -8.49028587E+00 3.04707210E-05 -2.15340771E+03 1.22419536E-01 -1.32670276E+03 -1.09824486E+01
- 9.99999978E-03 -4 -2 6.53283000E-01 -5.93868790E-05 5.27763623E-05 -2.87145585E-01 5.43229543E-02 -1.04547943E+02 3.93550515E-01 -1.92076070E-04 9.99627380E+01 -5.08461222E-02 -1.75877617E+04 -7.14816928E-01
- 9.99999978E-03 -4 -1 -1.32050300E-02 -1.47257384E-03 6.29312708E-05 1.43852634E-02 -8.52921084E-02 3.77276540E+00 -1.85435154E-02 1.09118177E-03 -5.01378870E+00 1.27484947E-01 5.25369446E+02 -1.05634308E+00
- 9.99999978E-03 -4 0 2.42494815E-03 4.96316585E-04 -2.04345299E-04 1.94436710E-04 -1.39783481E-02 -1.49472788E-01 -1.18730927E-03 -5.26981079E-04 1.96781352E-01 -2.24918462E-02 -1.05999422E+01 5.51852226E-01
- 9.99999978E-03 -4 1 3.26090754E-04 4.12505615E-04 -3.32525058E-04 3.22039967E-04 2.48988830E-02 -2.87849107E-03 -4.51125059E-04 -4.67361184E-04 2.82145105E-03 3.56667414E-02 3.52541767E-02 5.01533598E-03
- 9.99999978E-03 -4 2 -1.06569054E-03 2.15151231E-04 -1.76715839E-04 -8.34397390E-04 2.11251341E-02 1.25824526E-01 7.19141332E-04 -1.44953825E-04 -9.18405131E-02 1.64540112E-02 -5.11345685E-01 -3.15250069E-01
- 9.99999978E-03 -4 3 -2.04464101E-04 6.27206609E-05 -2.91938573E-04 9.86074912E-04 -4.84599583E-02 9.17024761E-02 -7.84339441E-04 -2.12040293E-04 -4.83552590E-02 -2.15011407E-02 4.25852448E-01 -2.97798011E-02
- 9.99999978E-03 -4 4 -1.56646129E-03 9.75607254E-05 5.89437317E-04 -8.91860924E-04 1.94737893E-02 2.31909677E-02 4.19167744E-04 3.45013686E-04 -1.23969056E-02 9.64546204E-03 1.88307822E-01 8.88301134E-01
- 9.99999978E-03 -3 -4 7.95266571E+01 -8.21601774E-04 2.29535581E-04 6.20847368E+00 -1.78978458E-01 4.82020264E+03 -8.49028587E+00 -3.04707210E-05 1.72717847E+03 9.81619954E-02 -1.32670276E+03 1.09824486E+01
- 9.99999978E-03 -3 -3 8.61666626E+02 0.00000000E+00 0.00000000E+00 4.09920258E+02 7.85368264E-01 2.10405807E+02 1.97254883E+02 0.00000000E+00 3.25231247E+01 -3.99561197E-01 5.11415352E+04 0.00000000E+00
- 9.99999978E-03 -3 -2 4.62471695E+01 4.44330421E-04 -1.29848020E-04 6.20905113E+00 -7.97844902E-02 -2.40449805E+03 -8.49028587E+00 3.04707210E-05 -1.72717871E+03 9.81916860E-02 -8.36365417E+02 -6.63343859E+00
- 9.99999978E-03 -3 -1 4.49012041E-01 9.30939791E-07 -1.05425115E-05 -2.87376106E-01 1.95228085E-02 -7.55909119E+01 3.93550515E-01 -1.92076070E-04 8.01768951E+01 -4.07857634E-02 -9.48540918E+03 -3.87120724E-01
- 9.99999978E-03 -3 0 -1.19107310E-02 -8.33830738E-04 4.21163975E-04 1.39846085E-02 1.38351624E-03 2.98471737E+00 -1.85435154E-02 1.09118177E-03 -4.02137423E+00 1.02272674E-01 2.16058624E+02 -4.25352544E-01
- 9.99999978E-03 -3 1 1.29569834E-03 2.35150306E-04 -3.76452925E-04 8.34961247E-04 -1.31037179E-02 -1.15633816E-01 -1.18730927E-03 -5.26981079E-04 1.57794192E-01 -1.80501286E-02 -4.23218191E-01 2.14393903E-02
- 9.99999978E-03 -3 2 8.39889326E-05 1.97956848E-04 -5.10776707E-04 4.73674241E-04 3.82103771E-02 1.02100549E-02 -4.51125059E-04 -4.67361184E-04 2.25405488E-03 2.85966322E-02 -5.84609151E-01 3.13203558E-02
- 9.99999978E-03 -3 3 -8.96688027E-04 1.50625565E-04 -2.51306104E-04 -1.15979963E-03 2.46318597E-02 1.50528893E-01 7.19141332E-04 -1.44953825E-04 -7.36431256E-02 1.31928325E-02 -8.28677118E-01 -5.21838367E-01
- 9.99999978E-03 -3 4 -5.70991950E-04 -3.65024534E-05 -3.62197898E-04 1.19780248E-03 -5.23508266E-02 9.67539772E-02 -7.84339441E-04 -2.12040293E-04 -3.87966707E-02 -1.72495116E-02 5.19476235E-01 -3.46651934E-02
- 9.99999978E-03 -2 -4 6.53283000E-01 5.93868790E-05 -1.79414114E-04 -2.86684543E-01 6.90151900E-02 7.56740036E+01 3.93550515E-01 1.92076070E-04 -6.03909149E+01 -3.06876861E-02 -1.75877617E+04 7.14816928E-01
- 9.99999978E-03 -2 -3 4.62471695E+01 -4.44330421E-04 1.79691793E-04 6.20876265E+00 -9.74093005E-02 2.72493823E+03 -8.49028587E+00 -3.04707210E-05 1.30094958E+03 7.39341453E-02 -8.36365417E+02 6.63343859E+00
- 9.99999978E-03 -2 -2 3.83826843E+02 0.00000000E+00 0.00000000E+00 2.73157196E+02 3.91251862E-01 1.52612045E+02 1.97254883E+02 0.00000000E+00 3.25231247E+01 -3.00958455E-01 2.90218477E+04 0.00000000E+00
- 9.99999978E-03 -2 -1 2.11802082E+01 1.78154471E-04 -8.00042326E-05 6.20933962E+00 -2.26888284E-02 -9.05375488E+02 -8.49028587E+00 3.04707210E-05 -1.30094971E+03 7.39638433E-02 -4.67032318E+02 -3.35766697E+00
- 9.99999978E-03 -2 0 3.02340984E-01 1.81933756E-05 -7.38613817E-05 -2.87606627E-01 -3.41098546E-03 -5.07141113E+01 3.93550515E-01 -1.92076070E-04 6.03910522E+01 -3.07254065E-02 -3.66397559E+03 -1.51675284E-01
- 9.99999978E-03 -2 1 -1.08484607E-02 -2.32669612E-04 7.79396680E-04 1.35839535E-02 5.36181517E-02 2.21705294E+00 -1.85435154E-02 1.09118177E-03 -3.02895975E+00 7.70604014E-02 8.08704662E+00 -1.09288224E-03
- 9.99999978E-03 -2 2 2.41782502E-04 -2.23322404E-05 -5.48560522E-04 1.47548586E-03 -1.12986630E-02 -8.38849247E-02 -1.18730927E-03 -5.26981079E-04 1.18807048E-01 -1.36084128E-02 5.76612377E+00 -3.01150292E-01
- 9.99999978E-03 -2 3 -1.48227875E-04 -3.91056710E-05 -6.89028297E-04 6.25308545E-04 4.25140969E-02 1.71223897E-02 -4.51125059E-04 -4.67361184E-04 1.68665894E-03 2.15265211E-02 -9.02428985E-01 4.48076129E-02
- 9.99999978E-03 -2 4 -5.29901707E-04 5.73752077E-05 -3.25896370E-04 -1.48520188E-03 2.43400019E-02 1.50724232E-01 7.19141332E-04 -1.44953825E-04 -5.54457344E-02 9.93165467E-03 -9.41572964E-01 -5.95335543E-01
- 9.99999978E-03 -1 -4 -1.32050300E-02 1.47257384E-03 1.01176684E-03 1.55872302E-02 -1.40809938E-01 -1.59558165E+00 -1.85435154E-02 -1.09118177E-03 2.03678393E+00 5.16347289E-02 5.25369446E+02 1.05634308E+00
- 9.99999978E-03 -1 -3 4.49012041E-01 -9.30939791E-07 -1.16095238E-04 -2.86915064E-01 3.42278704E-02 4.66998100E+01 3.93550515E-01 1.92076070E-04 -4.06050720E+01 -2.06273273E-02 -9.48540918E+03 3.87120724E-01
- 9.99999978E-03 -1 -2 2.11802082E+01 -1.78154471E-04 1.29848020E-04 6.20905113E+00 -4.03467305E-02 1.22336951E+03 -8.49028587E+00 -3.04707210E-05 8.74720581E+02 4.97063063E-02 -4.67032318E+02 3.35766697E+00
- 9.99999978E-03 -1 -1 9.68251419E+01 0.00000000E+00 0.00000000E+00 1.36394119E+02 1.28387034E-01 9.48182755E+01 1.97254883E+02 0.00000000E+00 3.25231247E+01 -2.02355713E-01 1.31291426E+04 0.00000000E+00
- 9.99999978E-03 -1 0 4.32577562E+00 2.30739533E-05 -3.01604450E-05 6.20962811E+00 9.90025979E-03 5.16343154E-02 -8.49028587E+00 3.04707210E-05 -8.74720764E+02 4.97360043E-02 -2.18703506E+02 -1.15513349E+00
- 9.99999978E-03 -1 1 2.13269815E-01 -7.59957084E-06 -1.37180265E-04 -2.87837148E-01 -1.44784246E-02 -2.99175396E+01 3.93550515E-01 -1.92076070E-04 4.06052094E+01 -2.06650477E-02 -1.23460915E+02 -8.48065596E-03
- 9.99999978E-03 -1 2 -1.00182211E-02 3.30909621E-04 1.13762938E-03 1.31832976E-02 7.14117959E-02 1.46977162E+00 -1.85435154E-02 1.09118177E-03 -2.03654528E+00 5.18481322E-02 -9.85453186E+01 2.16435924E-01
- 9.99999978E-03 -1 3 -7.36799266E-04 -2.76131061E-04 -7.20668177E-04 2.11601029E-03 -8.56318232E-03 -5.42261042E-02 -1.18730927E-03 -5.26981079E-04 7.98198953E-02 -9.16669611E-03 7.96808386E+00 -4.15916860E-01
- 9.99999978E-03 -1 4 -3.70559690E-04 -2.98681960E-04 -8.67279945E-04 7.76942819E-04 3.78100462E-02 1.78585164E-02 -4.51125059E-04 -4.67361184E-04 1.11926300E-03 1.44564118E-02 -9.18205321E-01 4.54771072E-02
- 9.99999978E-03 0 -4 2.42494815E-03 -4.96316585E-04 -4.84085147E-04 -2.36766157E-03 -9.05037334E-04 3.57570387E-02 -1.18730927E-03 5.26981079E-04 -4.12143096E-02 -4.62245243E-03 -1.05999422E+01 -5.51852226E-01
- 9.99999978E-03 0 -3 -1.19107310E-02 8.33830738E-04 6.53534138E-04 1.51865743E-02 -5.41231222E-02 -8.07464719E-01 -1.85435154E-02 -1.09118177E-03 1.04436958E+00 2.64224559E-02 2.16058624E+02 4.25352544E-01
- 9.99999978E-03 0 -2 3.02340984E-01 -1.81933756E-05 -5.27763623E-05 -2.87145585E-01 1.13069005E-02 2.18058510E+01 3.93550515E-01 1.92076070E-04 -2.08192272E+01 -1.05669694E-02 -3.66397559E+03 1.51675284E-01
- 9.99999978E-03 0 -1 4.32577562E+00 -2.30739533E-05 8.00042326E-05 6.20933962E+00 -7.79073220E-03 3.15496216E+02 -8.49028587E+00 -3.04707210E-05 4.48491638E+02 2.54784618E-02 -2.18703506E+02 1.15513349E+00
- 9.99999978E-03 0 0 6.61558509E-01 0.00000000E+00 -0.00000000E+00 -3.68937165E-01 -3.22623202E-03 3.70245132E+01 1.97254883E+02 0.00000000E+00 3.25231247E+01 -1.03752963E-01 3.46342139E+03 0.00000000E+00
- 9.99999978E-03 0 1 -4.31613016E+00 -2.09111222E-05 1.96833389E-05 6.20991659E+00 1.79827716E-02 3.11783234E+02 -8.49028587E+00 3.04707210E-05 -4.48491791E+02 2.55081598E-02 -9.13789520E+01 -2.58379877E-02
- 9.99999978E-03 0 2 1.81798548E-01 -7.64478973E-05 -2.00499126E-04 -2.88067669E-01 -1.36795081E-02 -1.32011986E+01 3.93550515E-01 -1.92076070E-04 2.08193645E+01 -1.06046898E-02 1.13613513E+03 4.24631797E-02
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- 9.90000010E-01 2 0 9.07955475E+01 -1.57434158E-02 -9.72187333E-03 -6.26818314E+01 -4.07048218E+02 9.83003320E+03 8.57077408E+01 4.51522972E-03 -1.54233170E+02 -8.61851379E+02 -7.12056688E+05 -2.45526641E+04
- 9.90000010E-01 2 1 -5.53023796E+01 3.09056812E-03 1.82639398E-02 2.21131134E+02 5.83161011E+02 7.47616748E+03 -3.02332489E+02 4.12194021E-02 1.29608721E+04 1.14291577E+03 3.56497406E+05 1.06566963E+04
- 9.90000010E-01 2 2 1.66555023E+02 0.00000000E+00 -0.00000000E+00 -2.65845490E+02 -7.47394836E+02 -1.72780920E+03 7.02395203E+02 0.00000000E+00 1.53711797E+04 -1.29784192E+03 1.36373488E+06 0.00000000E+00
- 9.90000010E-01 2 3 -1.24125938E+02 -1.15472497E-02 -2.59487145E-02 2.21130951E+02 7.45694885E+02 8.15283203E+03 -3.02332489E+02 -4.12194021E-02 -1.29608486E+04 1.14191833E+03 1.70830766E+05 -4.77797943E+02
- 9.90000010E-01 2 4 4.68702278E+01 2.75785336E-03 -3.00650415E-03 -6.26878815E+01 -6.25911194E+02 -2.07232986E+02 8.57077408E+01 -4.51522972E-03 1.54625809E+02 -8.62677429E+02 -1.35003438E+05 -6.04121045E+03
- 9.90000010E-01 3 -4 -3.06308794E+00 2.45061945E-02 3.26908305E-02 3.97923255E+00 7.71125138E-01 -6.68254013E+01 -5.43863630E+00 2.51279138E-02 3.56267204E+01 4.13895302E+01 2.81433862E+03 -2.03917151E+03
- 9.90000010E-01 3 -3 3.82546997E+00 -1.43413097E-02 -2.53317896E-02 -5.68139791E+00 -4.74386215E+01 -1.71981869E+01 7.77571583E+00 -5.05545177E-02 -3.10776463E+01 -4.54780960E+01 -4.73329443E+03 -1.90225867E+03
- 9.90000010E-01 3 -2 -7.16548824E+00 1.82494782E-02 2.95106582E-02 1.02528248E+01 6.05781631E+01 1.15496986E+02 -1.39622622E+01 4.43392992E-02 5.78462601E+01 8.97526932E+01 -4.47826445E+04 1.00150928E+04
- 9.90000010E-01 3 -1 1.34670506E+01 -9.74147487E-03 -7.45317899E-03 -1.55613184E+01 -7.93978424E+01 8.53235657E+02 2.12343884E+01 -1.06623499E-02 -1.18266357E+02 -1.68107285E+02 -1.31071734E+05 -5.35659424E+03
- 9.90000010E-01 3 0 -1.20122833E+01 -3.56593169E-03 -3.00575746E-03 2.80558090E+01 1.59989304E+02 2.22606201E+03 -3.83649254E+01 -1.12736467E-02 9.90836563E+01 2.89571503E+02 -2.68136406E+05 6.19656006E+03
- 9.90000010E-01 3 1 6.35857239E+01 -8.81157815E-03 -6.53977878E-03 -6.26833458E+01 -2.40834564E+02 4.90004053E+03 8.57077408E+01 4.51522972E-03 -8.04501801E+01 -4.49880554E+02 -3.54604250E+05 -5.60145801E+03
- 9.90000010E-01 3 2 -1.24125938E+02 1.15472497E-02 2.21063271E-02 2.21131042E+02 3.47481903E+02 3.17538916E+03 -3.02332489E+02 4.12194021E-02 6.76846045E+03 5.97094238E+02 1.70830766E+05 4.77797943E+02
- 9.90000010E-01 3 3 2.28227371E+02 0.00000000E+00 -0.00000000E+00 -3.84285492E+02 -4.40673340E+02 -6.27382666E+03 7.02395203E+02 0.00000000E+00 1.53711797E+04 -6.77761780E+02 8.01028938E+05 0.00000000E+00
- 9.90000010E-01 3 4 -1.60067062E+02 -1.86489951E-02 -2.97911018E-02 2.21130859E+02 4.32012115E+02 4.98641211E+03 -3.02332489E+02 -4.12194021E-02 -6.76843604E+03 5.96096802E+02 7.38715156E+04 4.83784814E+03
- 9.90000010E-01 4 -4 1.91602159E+00 -6.06359495E-03 -8.19421280E-03 -2.63033247E+00 -1.94857037E+00 -1.08309078E+01 3.59488606E+00 -3.01652849E-02 -2.17122102E+00 -2.24264002E+00 2.14267480E+03 -1.19858582E+03
- 9.90000010E-01 4 -3 -2.92173958E+00 2.26764418E-02 3.09224110E-02 3.97906852E+00 3.00178021E-01 -1.97919197E+01 -5.43863630E+00 2.51279138E-02 3.05151176E+00 3.31250381E+00 2.09504248E+03 -2.96692676E+03
- 9.90000010E-01 4 -2 4.13193941E+00 -1.94070116E-02 -2.69734878E-02 -5.68222761E+00 -4.27807188E+00 -3.17919121E+01 7.77571583E+00 -5.05545177E-02 -2.54635763E+00 -4.06541395E+00 -9.32921509E+02 -1.42130420E+03
- 9.90000010E-01 4 -1 -7.47055006E+00 2.16924660E-02 2.99898647E-02 1.02461605E+01 5.53606462E+00 3.78245544E+01 -1.39622622E+01 4.43392992E-02 5.71437359E+00 7.69540834E+00 -1.30303262E+04 2.15026794E+02
- 9.90000010E-01 4 0 1.15201702E+01 -5.79350209E-03 -7.52100395E-03 -1.55553989E+01 -7.11170292E+00 2.41969910E+02 2.12343884E+01 -1.06623499E-02 -1.07680578E+01 -1.43150120E+01 -4.82510742E+04 3.36115552E+03
- 9.90000010E-01 4 1 -1.99741402E+01 -3.20149795E-03 -4.28597722E-03 2.80570087E+01 1.47784119E+01 8.40200745E+02 -3.83649254E+01 -1.12736467E-02 8.29002857E+00 2.44922791E+01 -9.21891719E+04 -3.85226709E+03
- 9.90000010E-01 4 2 4.68702278E+01 -2.75785336E-03 -3.35768471E-03 -6.26848564E+01 -2.25382767E+01 1.58783850E+03 8.57077408E+01 4.51522972E-03 -6.66718864E+00 -3.79097137E+01 -1.35003438E+05 6.04121045E+03
- 9.90000010E-01 4 3 -1.60067062E+02 1.86489951E-02 2.59487145E-02 2.21130951E+02 3.36232567E+01 2.07381714E+03 -3.02332489E+02 4.12194021E-02 5.76048462E+02 5.12726517E+01 7.38715156E+04 -4.83784814E+03
- 9.90000010E-01 4 4 3.59946136E+02 0.00000000E+00 -0.00000000E+00 -5.02725525E+02 -4.17905540E+01 -1.08198438E+04 7.02395203E+02 0.00000000E+00 1.53711797E+04 -5.76816750E+01 5.91554562E+05 0.00000000E+00
-
diff --git a/src/DCON/validate/imats.xlsx b/src/DCON/validate/imats.xlsx
deleted file mode 100644
index 90cd5f74c3..0000000000
--- a/src/DCON/validate/imats.xlsx
+++ /dev/null
@@ -1,10455 +0,0 @@
- DCON ideal energy matrices
-
- mpsi = 128 mpert = 9
-
- psi m1 m2 real(Ai) imag(Ai) real(Bi) imag(Bi) real(Ci) imag(Ci) real(Di) imag(Di) real(Ei) imag(Ei) real(Hi) imag(Hi)
- 9.99999978E-03 -4 -4 1.53034448E+03 0.00000000E+00 0.00000000E+00 5.46683289E+02 1.31073630E+00 2.68199585E+02 1.97254883E+02 0.00000000E+00 3.25231247E+01 -4.98163968E-01 7.94882031E+04 0.00000000E+00
- 9.99999978E-03 -4 -3 7.95266571E+01 8.21601774E-04 -1.79691793E-04 6.20876265E+00 -1.61386728E-01 -4.49731641E+03 -8.49028587E+00 3.04707210E-05 -2.15340771E+03 1.22419536E-01 -1.32670276E+03 -1.09824486E+01
- 9.99999978E-03 -4 -2 6.53283000E-01 -5.93868790E-05 5.27763623E-05 -2.87145585E-01 5.43229543E-02 -1.04547943E+02 3.93550515E-01 -1.92076070E-04 9.99627380E+01 -5.08461222E-02 -1.75877617E+04 -7.14816928E-01
- 9.99999978E-03 -4 -1 -1.32050300E-02 -1.47257384E-03 6.29312708E-05 1.43852634E-02 -8.52921084E-02 3.77276540E+00 -1.85435154E-02 1.09118177E-03 -5.01378870E+00 1.27484947E-01 5.25369446E+02 -1.05634308E+00
- 9.99999978E-03 -4 0 2.42494815E-03 4.96316585E-04 -2.04345299E-04 1.94436710E-04 -1.39783481E-02 -1.49472788E-01 -1.18730927E-03 -5.26981079E-04 1.96781352E-01 -2.24918462E-02 -1.05999422E+01 5.51852226E-01
- 9.99999978E-03 -4 1 3.26090754E-04 4.12505615E-04 -3.32525058E-04 3.22039967E-04 2.48988830E-02 -2.87849107E-03 -4.51125059E-04 -4.67361184E-04 2.82145105E-03 3.56667414E-02 3.52541767E-02 5.01533598E-03
- 9.99999978E-03 -4 2 -1.06569054E-03 2.15151231E-04 -1.76715839E-04 -8.34397390E-04 2.11251341E-02 1.25824526E-01 7.19141332E-04 -1.44953825E-04 -9.18405131E-02 1.64540112E-02 -5.11345685E-01 -3.15250069E-01
- 9.99999978E-03 -4 3 -2.04464101E-04 6.27206609E-05 -2.91938573E-04 9.86074912E-04 -4.84599583E-02 9.17024761E-02 -7.84339441E-04 -2.12040293E-04 -4.83552590E-02 -2.15011407E-02 4.25852448E-01 -2.97798011E-02
- 9.99999978E-03 -4 4 -1.56646129E-03 9.75607254E-05 5.89437317E-04 -8.91860924E-04 1.94737893E-02 2.31909677E-02 4.19167744E-04 3.45013686E-04 -1.23969056E-02 9.64546204E-03 1.88307822E-01 8.88301134E-01
- 9.99999978E-03 -3 -4 7.95266571E+01 -8.21601774E-04 2.29535581E-04 6.20847368E+00 -1.78978458E-01 4.82020264E+03 -8.49028587E+00 -3.04707210E-05 1.72717847E+03 9.81619954E-02 -1.32670276E+03 1.09824486E+01
- 9.99999978E-03 -3 -3 8.61666626E+02 0.00000000E+00 0.00000000E+00 4.09920258E+02 7.85368264E-01 2.10405807E+02 1.97254883E+02 0.00000000E+00 3.25231247E+01 -3.99561197E-01 5.11415352E+04 0.00000000E+00
- 9.99999978E-03 -3 -2 4.62471695E+01 4.44330421E-04 -1.29848020E-04 6.20905113E+00 -7.97844902E-02 -2.40449805E+03 -8.49028587E+00 3.04707210E-05 -1.72717871E+03 9.81916860E-02 -8.36365417E+02 -6.63343859E+00
- 9.99999978E-03 -3 -1 4.49012041E-01 9.30939791E-07 -1.05425115E-05 -2.87376106E-01 1.95228085E-02 -7.55909119E+01 3.93550515E-01 -1.92076070E-04 8.01768951E+01 -4.07857634E-02 -9.48540918E+03 -3.87120724E-01
- 9.99999978E-03 -3 0 -1.19107310E-02 -8.33830738E-04 4.21163975E-04 1.39846085E-02 1.38351624E-03 2.98471737E+00 -1.85435154E-02 1.09118177E-03 -4.02137423E+00 1.02272674E-01 2.16058624E+02 -4.25352544E-01
- 9.99999978E-03 -3 1 1.29569834E-03 2.35150306E-04 -3.76452925E-04 8.34961247E-04 -1.31037179E-02 -1.15633816E-01 -1.18730927E-03 -5.26981079E-04 1.57794192E-01 -1.80501286E-02 -4.23218191E-01 2.14393903E-02
- 9.99999978E-03 -3 2 8.39889326E-05 1.97956848E-04 -5.10776707E-04 4.73674241E-04 3.82103771E-02 1.02100549E-02 -4.51125059E-04 -4.67361184E-04 2.25405488E-03 2.85966322E-02 -5.84609151E-01 3.13203558E-02
- 9.99999978E-03 -3 3 -8.96688027E-04 1.50625565E-04 -2.51306104E-04 -1.15979963E-03 2.46318597E-02 1.50528893E-01 7.19141332E-04 -1.44953825E-04 -7.36431256E-02 1.31928325E-02 -8.28677118E-01 -5.21838367E-01
- 9.99999978E-03 -3 4 -5.70991950E-04 -3.65024534E-05 -3.62197898E-04 1.19780248E-03 -5.23508266E-02 9.67539772E-02 -7.84339441E-04 -2.12040293E-04 -3.87966707E-02 -1.72495116E-02 5.19476235E-01 -3.46651934E-02
- 9.99999978E-03 -2 -4 6.53283000E-01 5.93868790E-05 -1.79414114E-04 -2.86684543E-01 6.90151900E-02 7.56740036E+01 3.93550515E-01 1.92076070E-04 -6.03909149E+01 -3.06876861E-02 -1.75877617E+04 7.14816928E-01
- 9.99999978E-03 -2 -3 4.62471695E+01 -4.44330421E-04 1.79691793E-04 6.20876265E+00 -9.74093005E-02 2.72493823E+03 -8.49028587E+00 -3.04707210E-05 1.30094958E+03 7.39341453E-02 -8.36365417E+02 6.63343859E+00
- 9.99999978E-03 -2 -2 3.83826843E+02 0.00000000E+00 0.00000000E+00 2.73157196E+02 3.91251862E-01 1.52612045E+02 1.97254883E+02 0.00000000E+00 3.25231247E+01 -3.00958455E-01 2.90218477E+04 0.00000000E+00
- 9.99999978E-03 -2 -1 2.11802082E+01 1.78154471E-04 -8.00042326E-05 6.20933962E+00 -2.26888284E-02 -9.05375488E+02 -8.49028587E+00 3.04707210E-05 -1.30094971E+03 7.39638433E-02 -4.67032318E+02 -3.35766697E+00
- 9.99999978E-03 -2 0 3.02340984E-01 1.81933756E-05 -7.38613817E-05 -2.87606627E-01 -3.41098546E-03 -5.07141113E+01 3.93550515E-01 -1.92076070E-04 6.03910522E+01 -3.07254065E-02 -3.66397559E+03 -1.51675284E-01
- 9.99999978E-03 -2 1 -1.08484607E-02 -2.32669612E-04 7.79396680E-04 1.35839535E-02 5.36181517E-02 2.21705294E+00 -1.85435154E-02 1.09118177E-03 -3.02895975E+00 7.70604014E-02 8.08704662E+00 -1.09288224E-03
- 9.99999978E-03 -2 2 2.41782502E-04 -2.23322404E-05 -5.48560522E-04 1.47548586E-03 -1.12986630E-02 -8.38849247E-02 -1.18730927E-03 -5.26981079E-04 1.18807048E-01 -1.36084128E-02 5.76612377E+00 -3.01150292E-01
- 9.99999978E-03 -2 3 -1.48227875E-04 -3.91056710E-05 -6.89028297E-04 6.25308545E-04 4.25140969E-02 1.71223897E-02 -4.51125059E-04 -4.67361184E-04 1.68665894E-03 2.15265211E-02 -9.02428985E-01 4.48076129E-02
- 9.99999978E-03 -2 4 -5.29901707E-04 5.73752077E-05 -3.25896370E-04 -1.48520188E-03 2.43400019E-02 1.50724232E-01 7.19141332E-04 -1.44953825E-04 -5.54457344E-02 9.93165467E-03 -9.41572964E-01 -5.95335543E-01
- 9.99999978E-03 -1 -4 -1.32050300E-02 1.47257384E-03 1.01176684E-03 1.55872302E-02 -1.40809938E-01 -1.59558165E+00 -1.85435154E-02 -1.09118177E-03 2.03678393E+00 5.16347289E-02 5.25369446E+02 1.05634308E+00
- 9.99999978E-03 -1 -3 4.49012041E-01 -9.30939791E-07 -1.16095238E-04 -2.86915064E-01 3.42278704E-02 4.66998100E+01 3.93550515E-01 1.92076070E-04 -4.06050720E+01 -2.06273273E-02 -9.48540918E+03 3.87120724E-01
- 9.99999978E-03 -1 -2 2.11802082E+01 -1.78154471E-04 1.29848020E-04 6.20905113E+00 -4.03467305E-02 1.22336951E+03 -8.49028587E+00 -3.04707210E-05 8.74720581E+02 4.97063063E-02 -4.67032318E+02 3.35766697E+00
- 9.99999978E-03 -1 -1 9.68251419E+01 0.00000000E+00 0.00000000E+00 1.36394119E+02 1.28387034E-01 9.48182755E+01 1.97254883E+02 0.00000000E+00 3.25231247E+01 -2.02355713E-01 1.31291426E+04 0.00000000E+00
- 9.99999978E-03 -1 0 4.32577562E+00 2.30739533E-05 -3.01604450E-05 6.20962811E+00 9.90025979E-03 5.16343154E-02 -8.49028587E+00 3.04707210E-05 -8.74720764E+02 4.97360043E-02 -2.18703506E+02 -1.15513349E+00
- 9.99999978E-03 -1 1 2.13269815E-01 -7.59957084E-06 -1.37180265E-04 -2.87837148E-01 -1.44784246E-02 -2.99175396E+01 3.93550515E-01 -1.92076070E-04 4.06052094E+01 -2.06650477E-02 -1.23460915E+02 -8.48065596E-03
- 9.99999978E-03 -1 2 -1.00182211E-02 3.30909621E-04 1.13762938E-03 1.31832976E-02 7.14117959E-02 1.46977162E+00 -1.85435154E-02 1.09118177E-03 -2.03654528E+00 5.18481322E-02 -9.85453186E+01 2.16435924E-01
- 9.99999978E-03 -1 3 -7.36799266E-04 -2.76131061E-04 -7.20668177E-04 2.11601029E-03 -8.56318232E-03 -5.42261042E-02 -1.18730927E-03 -5.26981079E-04 7.98198953E-02 -9.16669611E-03 7.96808386E+00 -4.15916860E-01
- 9.99999978E-03 -1 4 -3.70559690E-04 -2.98681960E-04 -8.67279945E-04 7.76942819E-04 3.78100462E-02 1.78585164E-02 -4.51125059E-04 -4.67361184E-04 1.11926300E-03 1.44564118E-02 -9.18205321E-01 4.54771072E-02
- 9.99999978E-03 0 -4 2.42494815E-03 -4.96316585E-04 -4.84085147E-04 -2.36766157E-03 -9.05037334E-04 3.57570387E-02 -1.18730927E-03 5.26981079E-04 -4.12143096E-02 -4.62245243E-03 -1.05999422E+01 -5.51852226E-01
- 9.99999978E-03 0 -3 -1.19107310E-02 8.33830738E-04 6.53534138E-04 1.51865743E-02 -5.41231222E-02 -8.07464719E-01 -1.85435154E-02 -1.09118177E-03 1.04436958E+00 2.64224559E-02 2.16058624E+02 4.25352544E-01
- 9.99999978E-03 0 -2 3.02340984E-01 -1.81933756E-05 -5.27763623E-05 -2.87145585E-01 1.13069005E-02 2.18058510E+01 3.93550515E-01 1.92076070E-04 -2.08192272E+01 -1.05669694E-02 -3.66397559E+03 1.51675284E-01
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diff --git a/src/DCON/validate/kmat.bin b/src/DCON/validate/kmat.bin
deleted file mode 100644
index 0d490a3826..0000000000
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diff --git a/src/DCON/validate/ks.bin b/src/DCON/validate/ks.bin
deleted file mode 100644
index f87d763e49..0000000000
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diff --git a/src/DCON/validate/metric.bin b/src/DCON/validate/metric.bin
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index 62f0b35700..0000000000
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diff --git a/src/DCON/validate/mets.out b/src/DCON/validate/mets.out
deleted file mode 100644
index 6ab555e611..0000000000
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diff --git a/src/DCON/validate/mets_grid.out b/src/DCON/validate/mets_grid.out
deleted file mode 100644
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- 1.0000 0.9200 -1.77137E+05
- 1.0000 0.9200 -4.90275E+06
- 1.0000 0.9300 -7.18214E+04
- 1.0000 0.9300 -2.73131E+03
- 1.0000 0.9300 9.88285E+02
- 1.0000 0.9300 -4.93235E+02
- 1.0000 0.9300 8.68447E+03
- 1.0000 0.9300 -2.63518E+04
- 1.0000 0.9300 -1.77137E+05
- 1.0000 0.9300 -4.90275E+06
- 1.0000 0.9400 -7.19680E+04
- 1.0000 0.9400 -2.55460E+03
- 1.0000 0.9400 9.83930E+02
- 1.0000 0.9400 -5.11381E+02
- 1.0000 0.9400 8.62756E+03
- 1.0000 0.9400 -2.59363E+04
- 1.0000 0.9400 -1.77137E+05
- 1.0000 0.9400 -4.90275E+06
- 1.0000 0.9500 -7.20883E+04
- 1.0000 0.9500 -2.38335E+03
- 1.0000 0.9500 9.79430E+02
- 1.0000 0.9500 -5.28649E+02
- 1.0000 0.9500 8.56938E+03
- 1.0000 0.9500 -2.55164E+04
- 1.0000 0.9500 -1.77137E+05
- 1.0000 0.9500 -4.90275E+06
- 1.0000 0.9600 -7.21827E+04
- 1.0000 0.9600 -2.21754E+03
- 1.0000 0.9600 9.74790E+02
- 1.0000 0.9600 -5.45047E+02
- 1.0000 0.9600 8.51001E+03
- 1.0000 0.9600 -2.50925E+04
- 1.0000 0.9600 -1.77137E+05
- 1.0000 0.9600 -4.90275E+06
- 1.0000 0.9700 -7.22518E+04
- 1.0000 0.9700 -2.05712E+03
- 1.0000 0.9700 9.70014E+02
- 1.0000 0.9700 -5.60583E+02
- 1.0000 0.9700 8.44955E+03
- 1.0000 0.9700 -2.46650E+04
- 1.0000 0.9700 -1.77137E+05
- 1.0000 0.9700 -4.90275E+06
- 1.0000 0.9800 -7.22963E+04
- 1.0000 0.9800 -1.90205E+03
- 1.0000 0.9800 9.65106E+02
- 1.0000 0.9800 -5.75268E+02
- 1.0000 0.9800 8.38811E+03
- 1.0000 0.9800 -2.42343E+04
- 1.0000 0.9800 -1.77137E+05
- 1.0000 0.9800 -4.90275E+06
- 1.0000 0.9900 -7.23167E+04
- 1.0000 0.9900 -1.75230E+03
- 1.0000 0.9900 9.60071E+02
- 1.0000 0.9900 -5.89113E+02
- 1.0000 0.9900 8.32582E+03
- 1.0000 0.9900 -2.38009E+04
- 1.0000 0.9900 -1.77137E+05
- 1.0000 0.9900 -4.90275E+06
- 1.0000 1.0000 -7.23139E+04
- 1.0000 1.0000 -1.60785E+03
- 1.0000 1.0000 9.54916E+02
- 1.0000 1.0000 -6.02132E+02
- 1.0000 1.0000 8.26278E+03
- 1.0000 1.0000 -2.33654E+04
- 1.0000 1.0000 -1.77137E+05
- 1.0000 1.0000 -4.90275E+06
diff --git a/src/DCON/validate/pentrc.in b/src/DCON/validate/pentrc.in
deleted file mode 100644
index 9a2d6072e2..0000000000
--- a/src/DCON/validate/pentrc.in
+++ /dev/null
@@ -1,73 +0,0 @@
-&PENT_INPUT
- kinetic_file="g147131.02300_DIIID_KEFIT.kin" ! Ascii profiles. columns: psi_n, ni(m^-3), ne(m^-3), ti(eV), te(eV), omega_EXB(rad/s)
- peq_file = "gpec_xclebsch_n1.out" ! Ascii displacement. columns: psi_n, m, real(xi^psi), imag(xi^psi), real(xi^alpha), imag(xi^alpha)
- idconfile = "euler.bin" ! DCON output
- data_dir = "" ! Location of pre-formed fnml matrix used in rlar and clar methods (check release package)
-
- mi = 2 ! Main ion mass (u)
- zi = 1 ! Main ion charge (e)
- mimp = 12 ! Impurity mass (u)
- zimp = 6 ! Impurity charge (e)
- nl = 4 ! Bounce harmonic range (-nl to nl)
- electron = .false. ! Calculate all results for electrons INSTEAD OF ions (only one species per PENTRC run)
- nutype = "harmonic" ! Collision operator: "zero", "krook", "harmonic"
- f0type = "maxwellian" ! Distribution function: "maxwellian"
- jac_in = "hamada" ! Jacobian of peq_file harmonic decomposition. 'default' uses jac_type of idconfile.
- jsurf_in=0 ! True(1) if peq_file is area weighted
- tmag_in=1 ! True(1) if peq_file has toroidal angle defined by jac_in. False(0) if machine angle.
-/
-&PENT_CONTROL
- wefac = 1 ! Artificial factor applied to omega_EXB
- wdfac = 1 ! Artificial factor applied to omega_b
- wpfac = 1 ! Artificial factor applied to omega_phi
- nufac = 1 ! Artificial factor applied to collision operator
- divxfac = 1 ! Artificial factor applied to div xi_perp
-
- force_xialpha = .false. ! Calculates tangential displacement from radial displacement and toroidal force balance (overwrites peq_file values)
-
- atol_xlmda = 1e-9 ! Absolute tolerance in energy and pitch integration
- rtol_xlmda = 1e-6 ! Relative tolerance in energy and pitch integration
- atol_psi = 1e-4 ! Absolute tolerance in psi_n integration
- rtol_psi = 1e-4 ! Relative tolerance in psi_n integration
- ntheta = 128 ! Poloidal angle grid for bounce integration
- nlmda = 128 ! Pitch grid for omega_D, oemga_b, dJdJ
-
- xmax = 128 ! Upper bound of energy integral (x=E/T)
- ximag = 0.0 ! Step off real energy axis (use to avoid zero collisionality singularities)
- psilims = 0 1 ! Range in psi_n
-/
-&PENT_OUTPUT
- moment = "pressure" ! Use 'pressure' for torque and particle transport, 'heat' for heat transport
-
- fgar_flag = .true. ! Full general aspect ratio calculation
- tgar_flag = .true. ! Trapped general aspect ratio calculation
- pgar_flag = .false. ! Passing general aspect ratio calculation
- clar_flag = .false. ! Circular large aspect ratio calculation
- rlar_flag = .false. ! Reduced large aspect ratio calculation
- fcgl_flag = .false. ! Fluid Chew-Goldberger-Low limit
- wxyz_flag = .false. ! Euler-lagrange equation matrix output at psiout
- fkmm_flag = .false. ! Full euler-lagrange matrix calculation (t,p also available)
- ftmm_flag = .false. ! Full torque mxm matrix calculation (t,p also available)
- fwmm_flag = .false. ! Full dW mxm matrix calculation (t,p also available)
-
- xlmda_out = .false. ! Output energy and pitch integrands on psi_out
- theta_out = .false. ! Output bounce integrands on psi_out
- psi_out = 0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9,1.0 ! 10 surfaces for energy, pitch, and poloidal outputs
-
- dynamic_grid = .true. ! Calculate each requested method using dynamic radial integration controlled by atol_psi and rtol_psi
- equil_grid = .false. ! Recalculate each requested method on equilibrium grid from DCON
- input_grid = .false. ! Recalculate each requested method on input displacements' grid
-
- verbose = .true. ! Print progress to terminal
- clean = .false. ! Remove pentrc_*.out before running
-/
-&PENT_ADMIN
- fnml_flag = .false. ! Special function matrix [JKP PRL 2009]
- ellip_flag = .false. ! Elliptic integral functions
- diag_flag = .false. ! Diagnostic module
- indebug = .false. ! Debug input file parsing and manipulations
- tdebug = .false. ! Debug psi integration
- lambdadebug = .false. ! Debug pitch integration
- xdebug = .false. ! Debug energy integration
-/
-
diff --git a/src/DCON/validate/psi_in.bin b/src/DCON/validate/psi_in.bin
deleted file mode 100644
index abc7934008..0000000000
Binary files a/src/DCON/validate/psi_in.bin and /dev/null differ
diff --git a/src/DCON/validate/read_matrix.ipynb b/src/DCON/validate/read_matrix.ipynb
deleted file mode 100644
index 9f242a385f..0000000000
--- a/src/DCON/validate/read_matrix.ipynb
+++ /dev/null
@@ -1,919 +0,0 @@
-{
- "cells": [
- {
- "cell_type": "code",
- "execution_count": null,
- "id": "a96ad3ad",
- "metadata": {},
- "outputs": [],
- "source": [
- "conda install scipy"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "id": "4a435f5f",
- "metadata": {},
- "outputs": [],
- "source": [
- "#!/usr/bin/env python3\n",
- "# -*- coding: utf-8 -*-\n",
- "\n",
- "from scipy.linalg.blas import zhemm\n",
- "import numpy as np\n",
- "import matplotlib.pyplot as plt\n",
- "import warnings\n",
- "import os\n",
- "from scipy.interpolate import CubicSpline\n",
- "from scipy.integrate import solve_ivp\n",
- "from scipy.linalg import cho_factor, cho_solve, lu_factor, lu_solve\n",
- "import time\n",
- "\n",
- "m_high = 1\n",
- "m_low = -4\n",
- "mdim = m_high - m_low + 1\n",
- "ndim = 1\n",
- "matrix_size = mdim * ndim # 'size' 변수명 변경\n",
- "\"\"\"\n",
- "... (주석) ...\n",
- "- F_bar, K_bar, G 행렬과 q 프로파일을 바이너리 파일에서 읽어 보간.\n",
- "- 최종 F, K 행렬은 히트맵 플롯 시점에 필요한 샘플에 대해서만 즉석에서 계산하여 성능 저하를 방지.\n",
- "\"\"\"\n",
- "import numpy as np\n",
- "import struct\n",
- "import os\n",
- "import matplotlib.pyplot as plt\n",
- "from scipy.interpolate import CubicSpline\n",
- "\n",
- "# ─────────────────────────────────────────────────────────────\n",
- "# 1 & 2. 파일 읽기 관련 함수 (이전과 동일)\n",
- "# ─────────────────────────────────────────────────────────────\n",
- "\n",
- "def get_matrix_map(m, kind, n_blocks, mband_k=None, path=None):\n",
- " if kind in ('F', 'G'):\n",
- " for mb_test in range(m):\n",
- " count = sum(len(range(j, min(m, j + mb_test + 1))) for j in range(m))\n",
- " if count == n_blocks:\n",
- " mband = mb_test\n",
- " print(f\"[{os.path.basename(path)}] mband = {mband} (으)로 추정 (F/G).\")\n",
- " d = {k+1: (i,j) for k, (j,i) in enumerate(((j,i) for j in range(m) for i in range(j, min(m, j+mband+1))))}\n",
- " return d\n",
- " raise ValueError(f\"F/G 행렬의 mband를 추정할 수 없습니다. (m={m}, n_blocks={n_blocks})\")\n",
- " elif kind == 'K':\n",
- " if mband_k is None: raise ValueError(\"K 행렬을 처리하려면 mband_k 값을 지정해야 합니다.\")\n",
- " print(f\"[{os.path.basename(path)}] mband = {mband_k} (지정된 값) 사용 (K).\")\n",
- " valid_element_count = sum(len(range(max(0, j-mband_k), min(m, j+mband_k+1))) for j in range(m))\n",
- " if n_blocks > valid_element_count:\n",
- " print(f\" > 경고: 파일에 기록된 블록 수({n_blocks})가 실제 유효한 원소 수({valid_element_count})보다 많습니다.\")\n",
- " d = {}\n",
- " k = 0\n",
- " for j in range(m):\n",
- " for i in range(max(0, j - mband_k), min(m, j + mband_k + 1)):\n",
- " k += 1\n",
- " d[k] = (i, j)\n",
- " return d\n",
- " else: raise ValueError(\"kind는 'F', 'G', 'K' 중 하나여야 합니다.\")\n",
- "\n",
- "def read_bin(path, m, kind, mband_k=None):\n",
- " all_records = []\n",
- " with open(path, 'rb') as f:\n",
- " while True:\n",
- " header_bytes = f.read(4)\n",
- " if not header_bytes: break\n",
- " record_len = struct.unpack(' 0:\n",
- " all_records.append(np.frombuffer(f.read(record_len), dtype=np.float32))\n",
- " else:\n",
- " all_records.append(None)\n",
- " f.read(4)\n",
- " element_blocks = []\n",
- " current_block = []\n",
- " for rec in all_records:\n",
- " if rec is not None: current_block.append(rec)\n",
- " else:\n",
- " if current_block: element_blocks.append(np.array(current_block))\n",
- " current_block = []\n",
- " if not element_blocks: raise ValueError(f\"파일에서 데이터 블록을 찾지 못했습니다: {path}\")\n",
- "\n",
- " n_blocks, n_psi = len(element_blocks), element_blocks[0].shape[0]\n",
- " psi, q_profile = element_blocks[0][:, 0], element_blocks[0][:, 1]\n",
- " idx_map = get_matrix_map(m, kind, n_blocks, mband_k=mband_k, path=path)\n",
- " \n",
- " mats = np.zeros((n_psi, m, m), dtype=np.complex128)\n",
- " for k, (i, j) in idx_map.items():\n",
- " if k > n_blocks: continue\n",
- " mats[:, i, j] = element_blocks[k - 1][:, 2] + 1j * element_blocks[k - 1][:, 3]\n",
- "\n",
- " if kind in ('G'):\n",
- " il, jl = np.tril_indices(m, -1)\n",
- " mats[:, jl, il] = np.conj(mats[:, il, jl])\n",
- " \n",
- " return psi, q_profile, mats\n",
- "\n",
- "# ────────────────────────────────────────\n",
- "# 3. dedup, make_interp, plot_q_profile (이전과 동일)\n",
- "# ────────────────────────────────────────\n",
- "def dedup(psi, q, stacks):\n",
- " uniq_psi, idx = np.unique(psi, return_index=True)\n",
- " return uniq_psi, q[idx], {k: v[idx] for k, v in stacks.items()}\n",
- "\n",
- "def make_interp(psi, mat_stack):\n",
- " cs_r = CubicSpline(psi, mat_stack.real, axis=0)\n",
- " cs_i = CubicSpline(psi, mat_stack.imag, axis=0)\n",
- " return lambda x, cr=cs_r, ci=cs_i: cr(x) + 1j * ci(x)\n",
- "\n",
- "def plot_q_profile(psi, q, q_interpolant):\n",
- " fig, ax = plt.subplots(figsize=(8, 6))\n",
- " ax.plot(psi, q, 'o', label='Original Data Points', markersize=5)\n",
- " psi_fine = np.linspace(psi.min(), psi.max(), 300)\n",
- " ax.plot(psi_fine, q_interpolant(psi_fine), '-', label='Cubic Spline Interpolation')\n",
- " ax.set(title='Safety Factor (q) Profile', xlabel='Normalized Poloidal Flux (ψ)', ylabel='Safety Factor (q)')\n",
- " ax.legend(); ax.grid(True, linestyle='--', alpha=0.6)\n",
- " plt.show()\n",
- "\n",
- "# ────────────────────────────────────────\n",
- "# *** REVISED *** 4. 최종 행렬의 히트맵을 그리는 함수\n",
- "# ────────────────────────────────────────\n",
- "def plot_final_heatmaps(psi_coords, M, q_interp, F_bar_interp, G_interp, K_bar_interp, nsamp=4):\n",
- " \"\"\"\n",
- " 보간 함수들을 받아, 플롯에 필요한 psi 샘플에 대해서만 최종 행렬을 계산하고 히트맵을 그립니다.\n",
- " \"\"\"\n",
- " names = ['F', 'G', 'K']\n",
- " samp = np.quantile(psi_coords, np.linspace(.05, .95, nsamp))\n",
- " \n",
- " fig, ax = plt.subplots(len(names), nsamp,\n",
- " figsize=(4.5 * nsamp, 4 * len(names)),\n",
- " constrained_layout=True, squeeze=False)\n",
- " \n",
- " I = np.identity(M.shape[0])\n",
- "\n",
- " for c, p in enumerate(samp):\n",
- " # --- 계산은 이 루프 안에서 즉석으로 수행됩니다 ---\n",
- " q_val = q_interp(p)\n",
- " Q_mat = M - q_val * I\n",
- " \n",
- " # 각 psi 샘플(p)에 대해 최종 행렬 계산\n",
- " final_mats = {\n",
- " 'F': Q_mat @ F_bar_interp(p) @ Q_mat,\n",
- " 'G': G_interp(p),\n",
- " 'K': Q_mat @ K_bar_interp(p)\n",
- " }\n",
- " # ---------------------------------------------\n",
- " \n",
- " for r, n in enumerate(names):\n",
- " mat = final_mats[n]\n",
- " im = ax[r, c].imshow(np.abs(mat), cmap='viridis', origin='upper', aspect='equal')\n",
- " ax[r, c].set_title(f'{n}, ψ≈{p:.3f}')\n",
- " if r == len(names) - 1: ax[r, c].set_xlabel('j')\n",
- " if c == 0: ax[r, c].set_ylabel('i')\n",
- " plt.colorbar(im, ax=ax[r, c], label=f'|{n}|')\n",
- " \n",
- " fig.suptitle('Final F, G, K Heatmaps (Calculated On-the-fly)', y=1.03)\n",
- " plt.show()\n",
- "\n",
- "# ────────────────────────────────────────\n",
- "# 5. 메인 스크립트\n",
- "# ────────────────────────────────────────"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "id": "a0e636b8",
- "metadata": {},
- "outputs": [],
- "source": [
- "println(\"Starting matrix reading and processing...\")"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "id": "740e0928",
- "metadata": {},
- "outputs": [],
- "source": [
- "using LinearAlgebra\n",
- "using Plots\n",
- "using Interpolations\n",
- "using Printf\n",
- "\n",
- "# Global parameters\n",
- "m_high = 1\n",
- "m_low = -4\n",
- "mdim = m_high - m_low + 1\n",
- "ndim = 1\n",
- "matrix_size = mdim * ndim # 'size' 변수명 변경\n",
- "\n",
- "\"\"\"\n",
- "DCON matrix binary file reader and analyzer for Julia\n",
- "- Reads F_bar, K_bar, G matrices and q profile from binary files\n",
- "- Provides interpolation and visualization capabilities\n",
- "- Calculates final F, K matrices on-demand for performance\n",
- "\"\"\"\n",
- "\n",
- "# ─────────────────────────────────────────────────────────────\n",
- "# 1. Matrix mapping functions\n",
- "# ─────────────────────────────────────────────────────────────\n",
- "\n",
- "\"\"\"\n",
- " get_matrix_map(m::Int, kind::String, n_blocks::Int; mband_k=nothing, path=\"\")\n",
- "\n",
- "Determine matrix element mapping for band storage format\n",
- "\"\"\"\n",
- "function get_matrix_map(m::Int, kind::String, n_blocks::Int; mband_k=nothing, path=\"\")\n",
- " if kind in [\"F\", \"G\"]\n",
- " for mb_test in 0:(m-1)\n",
- " count = sum(length(j:min(m, j + mb_test)) for j in 1:m)\n",
- " if count == n_blocks\n",
- " mband = mb_test\n",
- " println(\"[$path] mband = $mband (estimated for $kind)\")\n",
- " \n",
- " # Create index mapping (1-based indexing)\n",
- " d = Dict{Int, Tuple{Int,Int}}()\n",
- " k = 1\n",
- " for j in 1:m\n",
- " for i in j:min(m, j + mband)\n",
- " d[k] = (i, j)\n",
- " k += 1\n",
- " end\n",
- " end\n",
- " return d\n",
- " end\n",
- " end\n",
- " error(\"Cannot estimate mband for $kind matrix (m=$m, n_blocks=$n_blocks)\")\n",
- " \n",
- " elseif kind == \"K\"\n",
- " if mband_k === nothing\n",
- " error(\"mband_k must be specified for K matrix\")\n",
- " end\n",
- " \n",
- " println(\"[$path] mband = $mband_k (specified value for K)\")\n",
- " \n",
- " valid_element_count = sum(length(max(1, j-mband_k):min(m, j+mband_k)) for j in 1:m)\n",
- " if n_blocks > valid_element_count\n",
- " println(\" Warning: File blocks ($n_blocks) > valid elements ($valid_element_count)\")\n",
- " end\n",
- " \n",
- " d = Dict{Int, Tuple{Int,Int}}()\n",
- " k = 1\n",
- " for j in 1:m\n",
- " for i in max(1, j - mband_k):min(m, j + mband_k)\n",
- " d[k] = (i, j)\n",
- " k += 1\n",
- " end\n",
- " end\n",
- " return d\n",
- " else\n",
- " error(\"kind must be 'F', 'G', or 'K'\")\n",
- " end\n",
- "end\n",
- "\n",
- "# ─────────────────────────────────────────────────────────────\n",
- "# 2. Binary file reading functions\n",
- "# ─────────────────────────────────────────────────────────────\n",
- "\n",
- "\"\"\"\n",
- " read_bin(path::String, m::Int, kind::String; mband_k=nothing)\n",
- "\n",
- "Read DCON matrix binary files with Fortran unformatted structure\n",
- "\"\"\"\n",
- "function read_bin(path::String, m::Int, kind::String; mband_k=nothing)\n",
- " println(\"📖 Reading $kind matrix from: $(basename(path))\")\n",
- " \n",
- " all_records = []\n",
- " \n",
- " try\n",
- " open(path, \"r\") do f\n",
- " while !eof(f)\n",
- " # Read Fortran record header (4 bytes)\n",
- " if eof(f) break end\n",
- " header_bytes = read(f, 4)\n",
- " if length(header_bytes) < 4 break end\n",
- " \n",
- " record_len = reinterpret(Int32, header_bytes)[1]\n",
- " \n",
- " if record_len > 0\n",
- " # Read data\n",
- " data_bytes = read(f, record_len)\n",
- " if length(data_bytes) == record_len\n",
- " # Convert to Float32 array\n",
- " data = reinterpret(Float32, data_bytes)\n",
- " push!(all_records, data)\n",
- " else\n",
- " push!(all_records, nothing)\n",
- " end\n",
- " else\n",
- " push!(all_records, nothing)\n",
- " end\n",
- " \n",
- " # Read Fortran record footer (4 bytes)\n",
- " if !eof(f)\n",
- " read(f, 4)\n",
- " end\n",
- " end\n",
- " end\n",
- " catch e\n",
- " println(\"❌ Error reading file: $e\")\n",
- " return nothing, nothing, nothing\n",
- " end\n",
- " \n",
- " # Process records into blocks\n",
- " element_blocks = []\n",
- " current_block = []\n",
- " \n",
- " for rec in all_records\n",
- " if rec !== nothing\n",
- " push!(current_block, rec)\n",
- " else\n",
- " if !isempty(current_block)\n",
- " # 🔧 FIX: deprecated .' 연산자를 transpose()로 변경\n",
- " push!(element_blocks, transpose(hcat(current_block...)))\n",
- " current_block = []\n",
- " end\n",
- " end\n",
- " end\n",
- " \n",
- " # 🔧 FIX: 마지막 블록 처리\n",
- " if !isempty(current_block)\n",
- " push!(element_blocks, transpose(hcat(current_block...)))\n",
- " end\n",
- " \n",
- " if isempty(element_blocks)\n",
- " error(\"No data blocks found in file: $path\")\n",
- " end\n",
- " \n",
- " n_blocks = length(element_blocks)\n",
- " n_psi = size(element_blocks[1], 1)\n",
- " \n",
- " println(\" Found $n_blocks data blocks with $n_psi psi points each\")\n",
- " \n",
- " # Extract psi and q profile from first block\n",
- " psi = element_blocks[1][:, 1]\n",
- " q_profile = element_blocks[1][:, 2]\n",
- " \n",
- " # Get matrix mapping\n",
- " idx_map = get_matrix_map(m, kind, n_blocks; mband_k=mband_k, path=basename(path))\n",
- " \n",
- " # Initialize matrix array\n",
- " mats = zeros(ComplexF64, n_psi, m, m)\n",
- " \n",
- " # Fill matrix elements\n",
- " for (k, (i, j)) in idx_map\n",
- " if k <= n_blocks && k <= length(element_blocks)\n",
- " # FIX: 안전한 배열 인덱싱\n",
- " block = element_blocks[k]\n",
- " if size(block, 2) >= 4\n",
- " real_part = block[:, 3]\n",
- " imag_part = block[:, 4]\n",
- " mats[:, i, j] = complex.(real_part, imag_part)\n",
- " end\n",
- " end\n",
- " end\n",
- " \n",
- " # Apply symmetry for Hermitian matrices\n",
- " if kind == \"G\"\n",
- " println(\" Applying Hermitian symmetry\")\n",
- " for ipsi in 1:n_psi\n",
- " for i in 1:m\n",
- " for j in 1:(i-1)\n",
- " mats[ipsi, j, i] = conj(mats[ipsi, i, j])\n",
- " end\n",
- " end\n",
- " end\n",
- " end\n",
- " \n",
- " println(\"✅ Successfully read $kind matrix ($(size(mats)))\")\n",
- " \n",
- " return psi, q_profile, mats\n",
- "end\n",
- "\n",
- "# ─────────────────────────────────────────────────────────────\n",
- "# 3. Data processing functions\n",
- "# ─────────────────────────────────────────────────────────────\n",
- "\n",
- "\"\"\"\n",
- " dedup(psi, q, stacks)\n",
- "\n",
- "Remove duplicate psi values and corresponding data\n",
- "\"\"\"\n",
- "function dedup(psi, q, stacks)\n",
- " # Find unique psi values\n",
- " unique_psi = unique(psi)\n",
- " unique_indices = [findfirst(==(p), psi) for p in unique_psi]\n",
- " \n",
- " deduped_q = q[unique_indices]\n",
- " deduped_stacks = Dict(k => v[unique_indices, :, :] for (k, v) in stacks)\n",
- " \n",
- " return unique_psi, deduped_q, deduped_stacks\n",
- "end\n",
- "\n",
- "\"\"\"\n",
- " make_interp(psi, mat_stack)\n",
- "\n",
- "Create interpolation functions for complex matrix data\n",
- "\"\"\"\n",
- "function make_interp(psi, mat_stack)\n",
- " # Separate real and imaginary parts\n",
- " real_parts = real.(mat_stack)\n",
- " imag_parts = imag.(mat_stack)\n",
- " \n",
- " # Create interpolation objects for each matrix element\n",
- " m1, m2 = size(mat_stack)[2:3]\n",
- " \n",
- " interp_real = [linear_interpolation(psi, real_parts[:, i, j]) for i in 1:m1, j in 1:m2]\n",
- " interp_imag = [linear_interpolation(psi, imag_parts[:, i, j]) for i in 1:m1, j in 1:m2]\n",
- " \n",
- " # Return function that evaluates at given psi\n",
- " function interpolated_matrix(psi_val)\n",
- " result = zeros(ComplexF64, m1, m2)\n",
- " for i in 1:m1, j in 1:m2\n",
- " real_val = interp_real[i, j](psi_val)\n",
- " imag_val = interp_imag[i, j](psi_val)\n",
- " result[i, j] = complex(real_val, imag_val)\n",
- " end\n",
- " return result\n",
- " end\n",
- " \n",
- " return interpolated_matrix\n",
- "end\n",
- "\n",
- "\"\"\"\n",
- " plot_q_profile(psi, q, q_interpolant)\n",
- "\n",
- "Plot safety factor profile with interpolation\n",
- "\"\"\"\n",
- "function plot_q_profile(psi, q, q_interpolant)\n",
- " psi_fine = range(minimum(psi), maximum(psi), length=300)\n",
- " q_fine = [q_interpolant(p) for p in psi_fine]\n",
- " \n",
- " p = plot(psi, q, seriestype=:scatter, label=\"Original Data Points\", \n",
- " markersize=5, xlabel=\"Normalized Poloidal Flux (ψ)\", \n",
- " ylabel=\"Safety Factor (q)\", title=\"Safety Factor (q) Profile\")\n",
- " \n",
- " plot!(p, psi_fine, q_fine, label=\"Linear Interpolation\", linewidth=2)\n",
- " plot!(p, grid=true, gridwidth=1, gridstyle=:dash, gridalpha=0.6)\n",
- " \n",
- " display(p)\n",
- " return p\n",
- "end\n",
- "\n",
- "# ─────────────────────────────────────────────────────────────\n",
- "# 4. Final matrix calculation and visualization\n",
- "# ─────────────────────────────────────────────────────────────\n",
- "\n",
- "\"\"\"\n",
- " plot_final_heatmaps(psi_coords, M, q_interp, F_bar_interp, G_interp, K_bar_interp; nsamp=4)\n",
- "\n",
- "Plot heatmaps of final F, G, K matrices calculated on-demand\n",
- "\"\"\"\n",
- "function plot_final_heatmaps(psi_coords, M, q_interp, F_bar_interp, G_interp, K_bar_interp; nsamp=4)\n",
- " println(\"🎨 Plotting final matrix heatmaps...\")\n",
- " \n",
- " names = [\"F\", \"G\", \"K\"]\n",
- " \n",
- " # Sample psi values\n",
- " quantiles = range(0.05, 0.95, length=nsamp)\n",
- " samp = [quantile(psi_coords, q) for q in quantiles]\n",
- " \n",
- " # Create identity matrix\n",
- " I_mat = Matrix{Float64}(LinearAlgebra.I, size(M)) # 🔧 FIX: 변수명 변경\n",
- " \n",
- " # Create subplot array\n",
- " plots_array = []\n",
- " \n",
- " for (c, p) in enumerate(samp)\n",
- " println(\" Computing matrices for ψ ≈ $(round(p, digits=3))\")\n",
- " \n",
- " # Calculate Q matrix\n",
- " q_val = q_interp(p)\n",
- " Q_mat = M - q_val * I_mat\n",
- " \n",
- " # Calculate final matrices on-demand\n",
- " final_mats = Dict(\n",
- " \"F\" => Q_mat * F_bar_interp(p) * Q_mat,\n",
- " \"G\" => G_interp(p),\n",
- " \"K\" => Q_mat * K_bar_interp(p)\n",
- " )\n",
- " \n",
- " # Create heatmaps for each matrix\n",
- " for (r, name) in enumerate(names)\n",
- " mat = final_mats[name]\n",
- " \n",
- " p_heat = heatmap(abs.(mat), \n",
- " title=\"$name, ψ≈$(round(p, digits=3))\",\n",
- " color=:viridis,\n",
- " aspect_ratio=:equal,\n",
- " xlabel=\"j\", ylabel=\"i\")\n",
- " \n",
- " push!(plots_array, p_heat)\n",
- " end\n",
- " end\n",
- " \n",
- " # Combine plots\n",
- " layout = (length(names), nsamp)\n",
- " combined_plot = plot(plots_array..., layout=layout, size=(300*nsamp, 250*length(names)))\n",
- " plot!(combined_plot, plot_title=\"Final F, G, K Heatmaps (Calculated On-the-fly)\")\n",
- " \n",
- " display(combined_plot)\n",
- " return combined_plot\n",
- "end\n",
- "\n",
- "# ─────────────────────────────────────────────────────────────\n",
- "# 5. Main analysis function\n",
- "# ─────────────────────────────────────────────────────────────\n",
- "\n",
- "\"\"\"\n",
- " analyze_dcon_matrices(; m=6, mband_k=2, files=[\"fmat.bin\", \"gmat.bin\", \"kmat.bin\"])\n",
- "\n",
- "Main function to read and analyze DCON matrix files\n",
- "\"\"\"\n",
- "function analyze_dcon_matrices(; m=6, mband_k=2, files=[\"fmat.bin\", \"gmat.bin\", \"kmat.bin\"])\n",
- " println(\"🔍 DCON Matrix Analysis\")\n",
- " println(\"=\"^50)\n",
- " \n",
- " # Read matrix files\n",
- " data = Dict()\n",
- " kinds = [\"F\", \"G\", \"K\"]\n",
- " \n",
- " for (file, kind) in zip(files, kinds)\n",
- " if isfile(file)\n",
- " if kind == \"K\"\n",
- " psi, q, mats = read_bin(file, m, kind; mband_k=mband_k)\n",
- " else\n",
- " psi, q, mats = read_bin(file, m, kind)\n",
- " end\n",
- " \n",
- " if psi !== nothing\n",
- " data[kind] = Dict(\"psi\" => psi, \"q\" => q, \"matrices\" => mats)\n",
- " end\n",
- " else\n",
- " println(\"⚠️ File $file not found\")\n",
- " end\n",
- " end\n",
- " \n",
- " if isempty(data)\n",
- " println(\"❌ No valid data files found\")\n",
- " return nothing\n",
- " end\n",
- " \n",
- " # Use first available dataset for psi coordinates\n",
- " first_key = first(keys(data))\n",
- " psi_coords = data[first_key][\"psi\"]\n",
- " q_profile = data[first_key][\"q\"]\n",
- " \n",
- " println(\"\\n📊 Data Summary:\")\n",
- " println(\" Psi range: [$(minimum(psi_coords)), $(maximum(psi_coords))]\")\n",
- " println(\" Number of psi points: $(length(psi_coords))\")\n",
- " println(\" Available matrices: $(collect(keys(data)))\")\n",
- " \n",
- " # Remove duplicates\n",
- " matrix_stacks = Dict(k => v[\"matrices\"] for (k, v) in data)\n",
- " psi_unique, q_unique, stacks_unique = dedup(psi_coords, q_profile, matrix_stacks)\n",
- " \n",
- " println(\" After deduplication: $(length(psi_unique)) unique psi points\")\n",
- " \n",
- " # Create interpolation functions\n",
- " interpolants = Dict()\n",
- " for (k, mats) in stacks_unique\n",
- " interpolants[k] = make_interp(psi_unique, mats)\n",
- " println(\" ✅ Created interpolant for $k matrix\")\n",
- " end\n",
- " \n",
- " # Create q profile interpolation\n",
- " q_interp = linear_interpolation(psi_unique, q_unique)\n",
- " \n",
- " # Plot q profile\n",
- " plot_q_profile(psi_unique, q_unique, q_interp)\n",
- " \n",
- " # Create mode number matrix M\n",
- " mode_numbers = collect(m_low:m_high)\n",
- " M = diagm(mode_numbers)\n",
- " println(\"\\n🔢 Mode number matrix M:\")\n",
- " println(\" Mode range: $m_low to $m_high\")\n",
- " println(\" Matrix size: $(size(M))\")\n",
- " \n",
- " # Plot final matrices if we have the required data\n",
- " if haskey(interpolants, \"F\") && haskey(interpolants, \"G\") && haskey(interpolants, \"K\")\n",
- " plot_final_heatmaps(psi_unique, M, q_interp, \n",
- " interpolants[\"F\"], interpolants[\"G\"], interpolants[\"K\"])\n",
- " else\n",
- " println(\"⚠️ Cannot create final plots - missing some matrix types\")\n",
- " println(\" Available: $(collect(keys(interpolants)))\")\n",
- " end\n",
- " \n",
- " # Return results\n",
- " return Dict(\n",
- " \"psi\" => psi_unique,\n",
- " \"q\" => q_unique,\n",
- " \"interpolants\" => interpolants,\n",
- " \"q_interp\" => q_interp,\n",
- " \"M\" => M,\n",
- " \"raw_data\" => data\n",
- " )\n",
- "end\n",
- "\n",
- "\"\"\"\n",
- " test_matrix_reading()\n",
- "\n",
- "Quick test function for matrix reading\n",
- "\"\"\"\n",
- "function test_matrix_reading()\n",
- " println(\"🧪 Testing DCON matrix reading...\")\n",
- " \n",
- " # Test with common parameters\n",
- " results = analyze_dcon_matrices(m=6, mband_k=2)\n",
- " \n",
- " if results !== nothing\n",
- " println(\"✅ Test completed successfully!\")\n",
- " return results\n",
- " else\n",
- " println(\"❌ Test failed - check file availability\")\n",
- " return nothing\n",
- " end\n",
- "end\n",
- "\n",
- "# Export main functions\n",
- "export analyze_dcon_matrices, test_matrix_reading, read_bin, plot_q_profile\n",
- "export get_matrix_map, dedup, make_interp, plot_final_heatmaps\n",
- "\n",
- "println(\"📦 DCON Matrix Analysis Module Loaded\")\n",
- "println(\"Usage: results = analyze_dcon_matrices() or test_matrix_reading()\")"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "id": "84a61707",
- "metadata": {},
- "outputs": [],
- "source": [
- "# ═══════════════════════════════════════════════════════════════\n",
- "# 📖 DCON Matrix Reader 사용방법 (Usage Guide)\n",
- "# ═══════════════════════════════════════════════════════════════\n",
- "\n",
- "println(\"🚀 DCON Matrix Reader 사용방법\")\n",
- "println(\"=\"^60)\n",
- "\n",
- "println(\"\\n1️⃣ 기본 사용법 (Basic Usage):\")\n",
- "println(\" # 모든 행렬 파일 자동 분석\")\n",
- "println(\" results = analyze_dcon_matrices()\")\n",
- "println(\" \")\n",
- "println(\" # 파라미터 조정\")\n",
- "println(\" results = analyze_dcon_matrices(m=6, mband_k=2)\")\n",
- "\n",
- "println(\"\\n2️⃣ 단일 파일 읽기 (Single File Reading):\")\n",
- "println(\" # F 행렬 읽기\")\n",
- "println(\" psi, q, F_matrices = read_bin(\\\"fmat.bin\\\", 6, \\\"F\\\")\")\n",
- "println(\" \")\n",
- "println(\" # K 행렬 읽기 (mband_k 필수)\")\n",
- "println(\" psi, q, K_matrices = read_bin(\\\"kmat.bin\\\", 6, \\\"K\\\"; mband_k=2)\")\n",
- "\n",
- "println(\"\\n3️⃣ 개별 기능 사용 (Individual Functions):\")\n",
- "println(\" # q 프로파일 플롯\")\n",
- "println(\" plot_q_profile(psi, q, q_interpolant)\")\n",
- "println(\" \")\n",
- "println(\" # 히트맵 플롯\")\n",
- "println(\" plot_final_heatmaps(psi, M, q_interp, F_interp, G_interp, K_interp)\")\n",
- "\n",
- "println(\"\\n4️⃣ 커스터마이징 (Customization):\")\n",
- "println(\" # 특정 파일들만 분석\")\n",
- "println(\" files = [\\\"fmat.bin\\\", \\\"gmat.bin\\\"]\")\n",
- "println(\" results = analyze_dcon_matrices(files=files)\")\n",
- "println(\" \")\n",
- "println(\" # 샘플링 수 조정\")\n",
- "println(\" plot_final_heatmaps(...; nsamp=6)\")\n",
- "\n",
- "println(\"\\n5️⃣ 반환값 활용 (Using Results):\")\n",
- "println(\" results = analyze_dcon_matrices()\")\n",
- "println(\" psi = results[\\\"psi\\\"] # ψ 좌표\")\n",
- "println(\" q = results[\\\"q\\\"] # q 프로파일\")\n",
- "println(\" interpolants = results[\\\"interpolants\\\"] # 보간 함수들\")\n",
- "println(\" q_interp = results[\\\"q_interp\\\"] # q 보간 함수\")\n",
- "println(\" M = results[\\\"M\\\"] # 모드 번호 행렬\")\n",
- "\n",
- "println(\"\\n6️⃣ 빠른 테스트 (Quick Test):\")\n",
- "println(\" test_matrix_reading()\")\n",
- "\n",
- "println(\"\\n📋 파일 요구사항 (File Requirements):\")\n",
- "println(\" • fmat.bin, gmat.bin, kmat.bin\")\n",
- "println(\" • Fortran unformatted binary format\")\n",
- "println(\" • 현재 작업 디렉토리에 위치\")\n",
- "\n",
- "println(\"\\n⚙️ 파라미터 설명 (Parameters):\")\n",
- "println(\" • m: 행렬 크기 (기본값: 6)\")\n",
- "println(\" • mband_k: K 행렬의 밴드폭 (기본값: 2)\")\n",
- "println(\" • nsamp: 히트맵 샘플 수 (기본값: 4)\")\n",
- "\n",
- "println(\"\\n🎯 예제 실행 (Example Execution):\")\n",
- "println(\" # 현재 디렉토리에 바이너리 파일이 있다면:\")\n",
- "println(\" results = test_matrix_reading()\")\n",
- "println(\" \")\n",
- "println(\" # 결과 확인:\")\n",
- "println(\" if results !== nothing\")\n",
- "println(\" println(\\\"성공! 데이터 포인트 수: \\\", length(results[\\\"psi\\\"]))\")\n",
- "println(\" end\")\n",
- "\n",
- "println(\"\\n\" * \"=\"^60)\n",
- "println(\"🏁 Ready to analyze DCON matrices!\")"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "id": "9179d53b",
- "metadata": {},
- "outputs": [],
- "source": [
- "# ═══════════════════════════════════════════════════════════════\n",
- "# 🚀 실제 실행 예제 (Actual Execution Examples)\n",
- "# ═══════════════════════════════════════════════════════════════\n",
- "\n",
- "println(\"🔥 DCON Matrix Reader - 실제 실행 예제\")\n",
- "println(\"=\"^60)\n",
- "\n",
- "# 1. 기본 테스트 실행\n",
- "println(\"\\n1️⃣ 기본 테스트 실행 중...\")\n",
- "try\n",
- " results = test_matrix_reading()\n",
- " \n",
- " if results !== nothing\n",
- " println(\"✅ 성공! 다음 데이터를 읽었습니다:\")\n",
- " println(\" - Psi 포인트 수: \", length(results[\"psi\"]))\n",
- " println(\" - 사용 가능한 행렬들: \", collect(keys(results[\"interpolants\"])))\n",
- " println(\" - Psi 범위: [\", minimum(results[\"psi\"]), \", \", maximum(results[\"psi\"]), \"]\")\n",
- " else\n",
- " println(\"❌ 테스트 실패 - 바이너리 파일을 확인하세요\")\n",
- " end\n",
- "catch e\n",
- " println(\"❌ 오류 발생: \", e)\n",
- " println(\"💡 해결 방법:\")\n",
- " println(\" 1. fmat.bin, gmat.bin, kmat.bin 파일이 현재 디렉토리에 있는지 확인\")\n",
- " println(\" 2. 파일들이 올바른 Fortran 바이너리 형식인지 확인\")\n",
- " println(\" 3. 파일 접근 권한 확인\")\n",
- "end\n",
- "\n",
- "println(\"\\n\" * \"=\"^60)\n",
- "\n",
- "# 2. 개별 파일 읽기 예제\n",
- "println(\"\\n2️⃣ 개별 파일 읽기 예제:\")\n",
- "\n",
- "# F 행렬 읽기 시도\n",
- "if isfile(\"fmat.bin\")\n",
- " println(\"📖 F 행렬 읽기 중...\")\n",
- " try\n",
- " psi_f, q_f, mats_f = read_bin(\"fmat.bin\", 6, \"F\")\n",
- " if psi_f !== nothing\n",
- " println(\"✅ F 행렬 성공적으로 읽음 - 크기: \", size(mats_f))\n",
- " end\n",
- " catch e\n",
- " println(\"❌ F 행렬 읽기 실패: \", e)\n",
- " end\n",
- "else\n",
- " println(\"⚠️ fmat.bin 파일이 없습니다\")\n",
- "end\n",
- "\n",
- "# G 행렬 읽기 시도\n",
- "if isfile(\"gmat.bin\")\n",
- " println(\"📖 G 행렬 읽기 중...\")\n",
- " try\n",
- " psi_g, q_g, mats_g = read_bin(\"gmat.bin\", 6, \"G\")\n",
- " if psi_g !== nothing\n",
- " println(\"✅ G 행렬 성공적으로 읽음 - 크기: \", size(mats_g))\n",
- " end\n",
- " catch e\n",
- " println(\"❌ G 행렬 읽기 실패: \", e)\n",
- " end\n",
- "else\n",
- " println(\"⚠️ gmat.bin 파일이 없습니다\")\n",
- "end\n",
- "\n",
- "# K 행렬 읽기 시도\n",
- "if isfile(\"kmat.bin\")\n",
- " println(\"📖 K 행렬 읽기 중...\")\n",
- " try\n",
- " psi_k, q_k, mats_k = read_bin(\"kmat.bin\", 6, \"K\"; mband_k=2)\n",
- " if psi_k !== nothing\n",
- " println(\"✅ K 행렬 성공적으로 읽음 - 크기: \", size(mats_k))\n",
- " end\n",
- " catch e\n",
- " println(\"❌ K 행렬 읽기 실패: \", e)\n",
- " end\n",
- "else\n",
- " println(\"⚠️ kmat.bin 파일이 없습니다\")\n",
- "end\n",
- "\n",
- "println(\"\\n\" * \"=\"^60)\n",
- "\n",
- "# 3. 파라미터 조정 예제\n",
- "println(\"\\n3️⃣ 파라미터 조정 예제:\")\n",
- "\n",
- "# 다른 행렬 크기로 시도\n",
- "println(\"📊 다른 파라미터로 분석 시도...\")\n",
- "try\n",
- " # 더 작은 행렬 크기로 시도\n",
- " results_small = analyze_dcon_matrices(m=4, mband_k=1)\n",
- " if results_small !== nothing\n",
- " println(\"✅ m=4, mband_k=1로 성공\")\n",
- " end\n",
- "catch e\n",
- " println(\"❌ 파라미터 조정 실패: \", e)\n",
- "end\n",
- "\n",
- "try\n",
- " # 더 큰 행렬 크기로 시도\n",
- " results_large = analyze_dcon_matrices(m=8, mband_k=3)\n",
- " if results_large !== nothing\n",
- " println(\"✅ m=8, mband_k=3으로 성공\")\n",
- " end\n",
- "catch e\n",
- " println(\"❌ 파라미터 조정 실패: \", e)\n",
- "end\n",
- "\n",
- "println(\"\\n\" * \"=\"^60)\n",
- "\n",
- "# 4. 결과 활용 예제\n",
- "println(\"\\n4️⃣ 결과 활용 예제:\")\n",
- "\n",
- "try\n",
- " # 전체 분석 실행\n",
- " full_results = analyze_dcon_matrices()\n",
- " \n",
- " if full_results !== nothing\n",
- " println(\"🎯 분석 완료! 결과 활용 예제:\")\n",
- " \n",
- " # 특정 psi 값에서 q 계산\n",
- " psi_test = 0.5\n",
- " if haskey(full_results, \"q_interp\")\n",
- " q_at_test = full_results[\"q_interp\"](psi_test)\n",
- " println(\" ψ = $psi_test 에서 q = $q_at_test\")\n",
- " end\n",
- " \n",
- " # 특정 psi에서 행렬 계산\n",
- " if haskey(full_results[\"interpolants\"], \"F\")\n",
- " F_at_test = full_results[\"interpolants\"][\"F\"](psi_test)\n",
- " println(\" ψ = $psi_test 에서 F 행렬 크기: \", size(F_at_test))\n",
- " println(\" F 행렬 최대값: \", maximum(abs.(F_at_test)))\n",
- " end\n",
- " \n",
- " # 모드 번호 정보\n",
- " if haskey(full_results, \"M\")\n",
- " M = full_results[\"M\"]\n",
- " println(\" 모드 번호 행렬 대각선: \", diag(M))\n",
- " end\n",
- " \n",
- " println(\"✅ 모든 분석이 성공적으로 완료되었습니다!\")\n",
- " \n",
- " else\n",
- " println(\"❌ 전체 분석 실패\")\n",
- " end\n",
- " \n",
- "catch e\n",
- " println(\"❌ 결과 활용 중 오류: \", e)\n",
- "end\n",
- "\n",
- "println(\"\\n\" * \"=\"^60)\n",
- "\n",
- "# 5. 파일 상태 체크\n",
- "println(\"\\n5️⃣ 파일 상태 체크:\")\n",
- "files_to_check = [\"fmat.bin\", \"gmat.bin\", \"kmat.bin\"]\n",
- "\n",
- "for file in files_to_check\n",
- " if isfile(file)\n",
- " filesize = stat(file).size\n",
- " println(\"✅ $file: $(filesize) bytes\")\n",
- " else\n",
- " println(\"❌ $file: 파일 없음\")\n",
- " end\n",
- "end\n",
- "\n",
- "println(\"\\n🎉 실행 완료! 위 결과를 참고하여 필요한 수정을 진행하세요.\")\n",
- "println(\"💡 팁: 바이너리 파일이 없다면 DCON 시뮬레이션을 먼저 실행하세요.\")"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "id": "3074b173",
- "metadata": {},
- "outputs": [],
- "source": []
- }
- ],
- "metadata": {
- "kernelspec": {
- "display_name": "Julia 1.11.6",
- "language": "julia",
- "name": "julia-1.11"
- },
- "language_info": {
- "file_extension": ".jl",
- "mimetype": "application/julia",
- "name": "julia",
- "version": "1.11.6"
- }
- },
- "nbformat": 4,
- "nbformat_minor": 5
-}
diff --git a/src/DCON/validate/sol.in b/src/DCON/validate/sol.in
deleted file mode 100644
index e7aba88fee..0000000000
--- a/src/DCON/validate/sol.in
+++ /dev/null
@@ -1,14 +0,0 @@
-! Construct Soloviev equilibrium
-&SOL_INPUT
- mr = 128 ! number of radial grid zones
- mz = 128 ! number of axial grid zones
- ma = 128 ! number of flux grid zones
- e = 1.6 ! elongation
- a = 0.33 ! minor radius
- r0 = 1.0 ! major radius
- q0 = 1.9 ! safety factor at the o-point
- p0fac=1 ! scale on-axis pressure (P-> P+P0*p0fac. beta changes. Phi,q constant)
- b0fac=1 ! scale toroidal field at constant beta (s*Phi,s*f,s^2*P. bt changes. Shape,beta constant)
- f0fac=1 ! scale toroidal field at constant pressure (s*f. beta,q changes. Phi,p,bp constant)
-/
-
diff --git a/src/DCON/validate/stride.in b/src/DCON/validate/stride.in
deleted file mode 100755
index 1a0e240a0b..0000000000
--- a/src/DCON/validate/stride.in
+++ /dev/null
@@ -1,75 +0,0 @@
-&stride_control
- bal_flag=t ! Ideal MHD ballooning criterion for short wavelengths
- mat_flag=t ! Construct coefficient matrices for diagnostic purposes
- ode_flag=t ! Integrate ODE's for determining stability of internal long-wavelength mode (must be true for GPEC)
- vac_flag=t ! Compute plasma, vacuum, and total energies for free-boundary modes
- mer_flag=t ! Evaluate the Mercier criterian
-
- sas_flag=t ! Safety factor (q) limit determined as q_ir+dmlim where q_ir is the equil outermost rational
- dmlim=0.2 ! See sas_flag
- qlow=1.02 ! Integration initiated at q determined by minimum of qlow and q0 from equil
- qhigh=1e3 ! Integration terminated at q limit determined by minimum of qhigh and qa from equil
- sing_start=0 ! Start integration at the sing_start'th rational from the axis (psilow)
-
- nn=1 ! Toroidal mode number
- delta_mlow=8 ! Expands lower bound of Fourier harmonics
- delta_mhigh=8 ! Expands upper bound of Fourier harmonics
- delta_mband=0 ! Integration keeps only this wide a band of solutions along the diagonal in m,m'
- mthvac=512 ! Number of points used in splines over poloidal angle at plasma-vacuum interface. Overrides vac.in mth.
- thmax0=1 ! Linear multiplier on the automatic choice of theta integration bounds for high-n ideal ballooning stability computation (strictly, -inf to -inf)
-
- tol_nr=1e-8 ! Relative tolerance of dynamic integration steps away from rationals.
- tol_r=1e-8 ! Relative tolerance of dynamic integration steps near rationals
- crossover=1e-2 ! Fractional distance from rational q at which tolerance is switched to tol_r
- singfac_min=1e-4 ! Fractional distance from rational q at which ideal jump condition is enforced
- ucrit=1e4 ! Maximum fraction of solutions allowed before re-normalized
- sing_order=6 ! The highest order of power series to be retained near singular surfaces
-
- use_classic_splines=f ! Use a classical cubic spline instead of tri-diagonal solution for splines with extrapolation boundary conditions
- use_notaknot_splines=f ! Use not-a-knot boundary instead of either "extrap" spline extrapolation
-/
-
-&stride_output
- out_ahg2msc=f ! Output deprecated ahg2msc.out files. This is used to communicate with vacuum, but is now done through memory.
-
- crit_break=t ! Color of the crit curve changes when crossing a singular surface
-
- ahb_flag=f ! Output normal magnetic field eigenvalues and eigenfunctons at plasma-vacuum interface (must be false for GPEC)
- msol_ahb=1 ! Number of eigenfunctions output by ahb_flag=t ?
- mthsurf0=1 ! Linear multiplier on number of boundary points used to display surface eigenfunctions for ahgb_flag=t
-
- bin_euler=f ! **DUMMY VARIABLE** Currently does nothing
- euler_stride=1 ! **DUMMY VARIABLE** Currently does nothing
-
- out_bal1=f ! Ascii output for bal_flag poloidal functions
- bin_bal1=f ! Binary output for bal_flag poloidal functions
- out_bal2=f ! Ascii output for bal_flag functions
- bin_bal2=f ! Binary output for bal_flag functions
-
- netcdf_out=t ! Replicate ascii stride.out and delta_prime.out information in a netcdf file
-/
-
-&stride_params
- nThreads=32 ! Number of threads used to calculate intervals in parallel
- fourfit_metric_parallel=f ! Compute equilibrium metric tensor components in parallel
- vac_parallel=t ! Doubles the number of main level threads, creating more threads than processors
-
- nIntervalsTot=33 ! Number of radial intervals calculated in separately and recombined at end
- grid_packing="singularities" ! Choose from "singularities" and "naive"
- axis_mid_pt_skew=12.0 ! Skews the distribution of intervals between psilow and psihigh
- asymp_at_sing=t ! Use asymptotic expansions at singular surfaces
- kill_big_soln_for_ideal_dW=f ! Explicitly remove the big solution
-
- calc_delta_prime=t ! When false, sing_order=2 is better for speed, (with less accuracy).
- calc_dp_with_vac=t ! When vac_flag=t, this will use vacuum edge conditions to calculate delta prime.
- big_soln_err_tol=1e-7 ! Threshold error for correct solution to the delta prime bvp.
-
- integrate_riccati=f ! Use Riccati integration for dW. Cannot calculate delta_prime.
- riccati_bounce=t ! Toggle integration mode to control growth of matrix
- riccati_match_hamiltonian_evals=f !
- verbose_riccati_output=t ! Creates peig and Psize output files
- ric_dt=1e-8 ! Initial step size of Riccati integration
- ric_tol=1e-6 ! Relative tolerance of Riccati integration
-
- verbose_performance_output=f ! Print detailed timing information to terminal
-/
diff --git a/src/DCON/validate/sum1.bin b/src/DCON/validate/sum1.bin
deleted file mode 100644
index 1ce96212ce..0000000000
Binary files a/src/DCON/validate/sum1.bin and /dev/null differ
diff --git a/src/DCON/validate/vac.in b/src/DCON/validate/vac.in
deleted file mode 100644
index 68e91e03e8..0000000000
--- a/src/DCON/validate/vac.in
+++ /dev/null
@@ -1,99 +0,0 @@
-! **** Running DCON's input ***
-&MODES
- mth = 480
- xiin(1:9) = 0 0 0 0 0 0 0 1 0
- lsymz = .TRUE.
- leqarcw = 1
- lzio = 0
- lgato = 0
- lrgato = 0
-/
-&DEBUGS
- checkd = .FALSE.
- check1 = .FALSE.
- check2 = .FALSE.
- checke = .FALSE.
- checks = .FALSE.
- wall = .FALSE.
- lkplt = 0
- verbose_timer_output = f
-/
-&VACDAT
- ishape = 6
- aw = 0.05
- bw = 1.5
- cw = 0
- dw = 0.5
- tw = 0.05
- nsing = 500
- epsq = 1e-05
- noutv = 37
- idgt = 6
- idot = 0
- idsk = 0
- delg = 15.01
- delfac = 0.001
- cn0 = 1
-/
-&SHAPE
- ipshp = 0
- xpl = 100
- apl = 1
- a = 20
- b = 170
- bpl = 1
- dpl = 0
- r = 1
- abulg = 0.932
- bbulg = 17.0
- tbulg = 0.02
- qain = 2.5
-/
-&DIAGNS
- lkdis = .FALSE.
- ieig = 0
- iloop = 0
- lpsub = 1
- nloop = 128
- nloopr = 0
- nphil = 3
- nphse = 1
- xofsl = 0
- ntloop = 32
- aloop = 0.01
- bloop = 1.6
- dloop = 0.5
- rloop = 1.0
- deloop = 0.001
- mx = 21
- mz = 21
- nph = 0
- nxlpin = 6
- nzlpin = 11
- epslp = 0.02
- xlpmin = 0.7
- xlpmax = 2.7
- zlpmin = -1.5
- zlpmax = 1.5
- linterior = 2
-/
-&SPRK
- nminus = 0
- nplus = 0
- mphi = 16
- lwrt11 = 0
- civ = 0.0
- sp2sgn1 = 1
- sp2sgn2 = 1
- sp2sgn3 = 1
- sp2sgn4 = 1
- sp2sgn5 = 1
- sp3sgn1 = -1
- sp3sgn2 = -1
- sp3sgn3 = -1
- sp3sgn4 = 1
- sp3sgn5 = 1
- lff = 0
- ff = 1.6
- fv = 1.6 1.6 1.6 1.6 1.6 1.0 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6
-/
diff --git a/src/Deck.jl b/src/Deck.jl
new file mode 100644
index 0000000000..ea0f4b17ce
--- /dev/null
+++ b/src/Deck.jl
@@ -0,0 +1,652 @@
+# Deck.jl: the gpec.toml -> API translation. Every section goes through `section_keywords`, so a deck states exactly
+# the keywords of the constructor it feeds and a stale or misspelled key stops the run.
+#
+# Included directly into the GeneralizedPerturbedEquilibrium module.
+
+import .Utilities: deck_sections
+
+const _DEPRECATED_FFS_KEYS = ("mer_flag", "force_wv_symmetry", "ode_flag", "cyl_flag", "mat_flag", "reform_eq_with_psilim",
+ "use_riccati", "use_parallel", "parallel_threads", "populate_dense_xi",
+ "gal_flag", "nstep", "diagnose_ca", "diagnose", "ksing", "local_stability_flag", "gal_solver", "gal_sing_order", "force_termination",
+ "kinetic_source", "sing_start")
+const _DEPRECATED_EQUIL_KEYS = ("power_bp", "power_b", "power_r", "power_rc", "use_galgrid", "force_termination")
+const _DEPRECATED_KF_KEYS = ("moment", "eq_out", "theta_out", "xlmda_out", "eqpsi_out", "save_records", "gpec_file",
+ "fnml_flag", "ellip_flag", "diag_flag", "force_xialpha")
+const _DEPRECATED_PE_KEYS = ("fixed_boundary", "output_eigenmodes", "filter_modes", "singular_point_method", "compute_response")
+const _DEPRECATED_KEYS = ("Equilibrium" => _DEPRECATED_EQUIL_KEYS, "ForceFreeStates" => _DEPRECATED_FFS_KEYS,
+ "KineticForces" => _DEPRECATED_KF_KEYS, "PerturbedEquilibrium" => _DEPRECATED_PE_KEYS)
+# Per-section output and verbosity keys, replaced by the run-wide [Run] output_file and verbose.
+const _RUN_SECTION_KEYS = ("verbose", "HDF5_filename", "output_filename", "write_outputs_to_HDF5")
+const _RUN_KEY_SECTIONS = ("Equilibrium", "LocalStability", "ForceFreeStates", "PerturbedEquilibrium", "KineticForces", "ErrorFields")
+
+# Keys that moved to another section, each with where it lives now.
+const _ODE_DECK_KEYS = ("eulerlagrange_tolerance", "renorm_threshold", "numsteps_init", "numunorms_init", "save_interval")
+const _SEARCH_DECK_KEYS = ("scan_mode", "Q_re_range", "Q_im_range", "nre", "nim", "amr_passes", "amr_max_cells", "boxes",
+ "multi_box_prescreen_n", "pole_threshold", "pole_threshold_adaptive", "filter_above_poles", "filter_outside_re",
+ "gamma_gap_threshold", "polish_roots", "validity_rtol", "root_classification", "store_scan")
+const _KINETIC_FILE_HOME = "name the kinetic-profile file once, as kinetic_file (and kinetic_group) in [Equilibrium]"
+const _MOVED_KEYS = Dict{String,Dict{String,String}}(
+ "ForceFreeStates" => Dict{String,String}(
+ "nn_low" => "set nn = n, or nn = [n1, n2, ...] for consecutive toroidal modes",
+ "nn_high" => "set nn = n, or nn = [n1, n2, ...] for consecutive toroidal modes",
+ "extended_precision_bvp" => "moved to [Riccati]",
+ "nchunks" => "moved to [Riccati]",
+ "gal_match_flag" => "add a [Match] section to match the inner layer",
+ "gal_ideal_flag" => "moved to [Match] as ideal",
+ "gal_inner_solver" => "moved to [GGJ] as solver",
+ (k => "moved to the integrator's section, [Forward] or [Riccati]" for k in _ODE_DECK_KEYS)...,
+ ("gal_$k" => "moved to [Match] as $k" for k in ("eta", "rho", "rotation", "gamma"))...,
+ ("gal_inner_$k" => "moved to [GGJ] as $k" for k in ("xfac", "nx", "nq", "cutoff", "kmax"))...,
+ ("gal_$k" => "moved to [Galerkin] as $k" for k in ("nx", "nq", "pfac", "dx0", "dx1", "dx2", "cutoff", "tol", "gnstep",
+ "dx1dx2_flag", "rpec_flag", "edge_onesided"))...,
+ "gal_sing_order_ceiling" => "moved to [Galerkin] as frobenius_order_ceiling"),
+ "LocalStability" => Dict{String,String}(
+ k => "moved to [Ballooning]" for k in ("ode_tol", "n_scan", "max_alpha_scale", "alpha_tol", "psi_window")),
+ "KineticForces" => Dict{String,String}(
+ "ion_species" => "moved to [[Equilibrium.ion_species]]",
+ "ion_charge" => "state the main ions as [[Equilibrium.ion_species]] with z and m",
+ "ion_mass" => "state the main ions as [[Equilibrium.ion_species]] with z and m",
+ "impurity_charge" => "moved to [Equilibrium]",
+ "impurity_mass" => "moved to [Equilibrium]",
+ "nn" => "removed; KineticForces takes the toroidal mode number from the run",
+ "rlar_flag" => "removed; the large-aspect-ratio methods are not ported, use fgar_flag or tgar_flag",
+ "clar_flag" => "removed; the large-aspect-ratio methods are not ported, use fgar_flag or tgar_flag",
+ "kinetic_file" => _KINETIC_FILE_HOME),
+ "SLAYER" => Dict{String,String}(
+ "enabled" => "a [Tearing] section with inner_model = \"SLAYER\" runs the tearing analysis",
+ "inner_model" => "moved to [Tearing]; the SLAYER variant is [SLAYER] variant",
+ "coupling_mode" => "moved to [Tearing]", "msing_max" => "moved to [Tearing]", "omega_E_kHz" => "moved to [Tearing]",
+ "scan_grid" => "its keys moved to [Tearing.search]",
+ "CriticalResonantField" => "moved to [Tearing.CriticalResonantField]",
+ "gap_kHz_threshold" => "set [Tearing.search] gamma_gap_threshold in 1/s",
+ (k => "moved to [Tearing.search]" for k in _SEARCH_DECK_KEYS)...,
+ "ion_mass" => "the plasma is the equilibrium's kinetic data: state the main ions as [[Equilibrium.ion_species]]",
+ "zeff" => "moved to [Equilibrium] as zeff_default",
+ "impurity_charge" => "moved to [Equilibrium]",
+ "chi_perp_e" => "moved to [Equilibrium] as chi_e_default",
+ "chi_perp_i" => "moved to [Equilibrium] as chi_i_default",
+ "chi_tor" => "moved to [Equilibrium] as chi_phi_default",
+ "tau_E" => "moved to [Equilibrium]",
+ "resistivity_model" => "moved to [Equilibrium]",
+ "lnLambda_form" => "moved to [Equilibrium]",
+ "bt" => "removed; B_T comes from the equilibrium's F",
+ "profile_file" => _KINETIC_FILE_HOME, "profile_group" => _KINETIC_FILE_HOME))
+const _ANALYTIC_HOME = "; an analytic deck sets no [Equilibrium] eq_type"
+const _RETIRED_SECTIONS = Dict("DEBUG" => "[DEBUG] is retired: output_benchmark_data was never read, and gal_basis_output is [Galerkin] basis_output",
+ "SOL_INPUT" => "[SOL_INPUT] is now [Solovev]" * _ANALYTIC_HOME, "LAR_INPUT" => "[LAR_INPUT] is now [LargeAspectRatio]" * _ANALYTIC_HOME,
+ "TJ_ANALYTIC_INPUT" => "[TJ_ANALYTIC_INPUT] is now [TJAnalytic], whose solver = \"direct\" replaces eq_type = \"tj_analytic_direct\"" * _ANALYTIC_HOME)
+
+# Every section a deck may hold, besides the analytic-equilibrium sections.
+const _DECK_SECTIONS = ("Run", "Equilibrium", "Wall", "LocalStability", "Ballooning", "ForceFreeStates", "Forward", "Riccati",
+ "Galerkin", "Match", "GGJ", "Tearing", "SLAYER", "ForcingTerms", "PerturbedEquilibrium", "KineticForces", "ErrorFields")
+const _INTEGRATORS = ("Forward" => Forward, "Riccati" => Riccati, "Galerkin" => Galerkin)
+
+# Stop the run when a parsed gpec.toml section sets keys that no longer exist, so the deck is updated.
+function _stop_on_deprecated_keys(table, deprecated_keys, section::String; remedy::String="remove from gpec.toml")
+ found = [k for k in deprecated_keys if haskey(table, k)]
+ isempty(found) && return nothing
+ listed = join(("`$k`" for k in found), ", ")
+ error(length(found) == 1 ? "[$section] sets $listed, which is no longer a key; $remedy" : "[$section] sets $listed, which are no longer keys; $remedy")
+end
+
+# Stop on every retired key or section of a parsed deck. `remedy` replaces the per-key advice, e.g. for a stored deck that cannot be edited.
+function _stop_on_deprecated_deck_keys(inputs::AbstractDict; remedy::Union{Nothing,String}=nothing)
+ for (section, message) in _RETIRED_SECTIONS
+ haskey(inputs, section) && error(something(remedy, message))
+ end
+ for (section, keys) in _DEPRECATED_KEYS
+ haskey(inputs, section) && _stop_on_deprecated_keys(inputs[section], keys, section; remedy=something(remedy, "remove from gpec.toml"))
+ end
+ run_remedy = something(remedy, "set [Run] output_file or verbose instead; a deck run always writes its output file")
+ for section in _RUN_KEY_SECTIONS
+ haskey(inputs, section) && _stop_on_deprecated_keys(inputs[section], _RUN_SECTION_KEYS, section; remedy=run_remedy)
+ end
+ ntv = get(get(inputs, "ErrorFields", Dict{String,Any}()), "NTV", nothing)
+ ntv === nothing || _stop_on_deprecated_keys(ntv, ("verbose",), "ErrorFields.NTV"; remedy=run_remedy)
+ for (section, moved) in _MOVED_KEYS
+ table = get(inputs, section, nothing)
+ table isa AbstractDict || continue
+ found = sort!([k for k in keys(table) if haskey(moved, k)])
+ isempty(found) && continue
+ error("[$section] sets keys that moved: " * join(("`$k` ($(something(remedy, moved[k])))" for k in found), "; "))
+ end
+ return nothing
+end
+
+# A deck value as the constructor field type `T` takes it: strings become Symbols, arrays become tuples.
+_deck_value(::Type, v) = v
+_deck_value(::Type{Any}, v) = v
+_deck_value(::Type{Symbol}, v::AbstractString) = Symbol(v)
+_deck_value(::Type{Float64}, v::Integer) = Float64(v)
+_deck_value(::Type{T}, v::AbstractVector) where {T<:Tuple} = T(Tuple(v))
+_deck_value(::Type{Union{Nothing,T}}, v) where {T} = _deck_value(T, v)
+_deck_value(::Type{Vector{T}}, v::AbstractVector) where {T} = convert(Vector{T}, [_deck_value(T, x) for x in v])
+
+# The keyword fields of struct `T` with their types (a type parameter becomes `Any`), less `exclude`.
+function _struct_fields(T::Type, exclude=())
+ S = Base.unwrap_unionall(T)
+ return Dict{Symbol,Any}(f => (t = fieldtype(S, f); t isa Type ? t : Any) for f in fieldnames(S) if !(f in exclude))
+end
+
+"""
+ section_keywords(table, section, fields) -> Dict{Symbol,Any}
+
+The constructor keywords a deck section states: Symbol keys, each value coerced to the type
+`fields` gives its key (a string to a Symbol, an array to a tuple, an integer to a float). A key
+`fields` does not list is an error naming the section and its allowed keys.
+"""
+function section_keywords(table::AbstractDict, section::AbstractString, fields::AbstractDict{Symbol})
+ kwargs = Dict{Symbol,Any}()
+ for (k, v) in table
+ key = Symbol(k)
+ haskey(fields, key) ||
+ throw(ArgumentError("unknown key \"$k\" in [$section] (allowed: $(join(sort!(String.(collect(keys(fields)))), ", ")))"))
+ kwargs[key] = _deck_value(fields[key], v)
+ end
+ return kwargs
+end
+
+# A section's table without its sub-tables `names`, which are parsed on their own.
+_without(table::AbstractDict, names...) = filter(p -> !(p.first in names), table)
+
+# A copy of a deck section with its relative path `keys` resolved against the deck directory `path`; absolute paths are kept.
+_deck_paths(::Nothing, path, keys) = nothing
+function _deck_paths(section::AbstractDict, path::AbstractString, keys)
+ resolved = Dict{String,Any}(section)
+ for k in keys
+ v = get(resolved, k, "")
+ isempty(v) || isabspath(v) || (resolved[k] = normpath(joinpath(path, v)))
+ end
+ return resolved
+end
+
+# The value a selector key names, checked against `choices`.
+function _selector(table::AbstractDict, section::String, key::String, choices, default=nothing)
+ name = get(table, key, default)
+ name === nothing && error("[$section] needs $key = $(join(("\"$c\"" for c in choices), " | "))")
+ name in choices || error("[$section] $key = \"$name\" is not one of $(join(("\"$c\"" for c in choices), ", "))")
+ return name
+end
+
+"""
+ run_settings(inputs, path) -> (; output_file, verbose)
+
+The run-wide `[Run]` settings of a parsed deck: the one output file every stage saves into,
+resolved against the deck directory `path` when relative, and the one verbosity of the run.
+Defaults are `output_file = "gpec.h5"` and `verbose = false`.
+"""
+function run_settings(inputs::AbstractDict, path::AbstractString)
+ kwargs = section_keywords(get(inputs, "Run", Dict{String,Any}()), "Run", Dict{Symbol,Any}(:output_file => String, :verbose => Bool))
+ file = get(kwargs, :output_file, "gpec.h5")
+ return (; output_file=isabspath(file) ? file : normpath(joinpath(path, file)), verbose=get(kwargs, :verbose, false))
+end
+
+# The eq_type => ANALYTIC_EQ row of the one analytic-equilibrium section a deck holds, `nothing` when it holds none.
+function _analytic_row(inputs::AbstractDict)
+ rows = [row for row in Equilibrium.ANALYTIC_EQ if haskey(inputs, row.second.section)]
+ length(rows) > 1 && error("gpec.toml holds more than one analytic equilibrium: " * join(sort!(["[$(row.second.section)]" for row in rows]), ", "))
+ return isempty(rows) ? nothing : only(rows)
+end
+
+"""
+ analytic_config(inputs) -> Union{Nothing,Equilibrium.AnalyticEquilibriumConfig}
+
+The analytic equilibrium a deck's `[Solovev]`, `[LargeAspectRatio]` or `[TJAnalytic]` section
+states, `nothing` when the deck holds none.
+"""
+function analytic_config(inputs::AbstractDict)
+ row = _analytic_row(inputs)
+ row === nothing && return nothing
+ spec = row.second
+ return spec.config_type(; section_keywords(inputs[spec.section], spec.section, _struct_fields(spec.config_type))...)
+end
+
+"""
+ equilibrium_config(inputs, path) -> Equilibrium.EquilibriumConfig
+
+The `[Equilibrium]` section as an `EquilibriumConfig`, its file paths resolved against the deck
+directory `path`. An analytic-equilibrium section implies `eq_type`; otherwise it is required.
+"""
+function equilibrium_config(inputs::AbstractDict, path::AbstractString)
+ table = get(inputs, "Equilibrium", nothing)
+ table === nothing && error("No [Equilibrium] section in gpec.toml")
+ row = _analytic_row(inputs)
+ eq_type = get(table, "eq_type", nothing)
+ if row !== nothing
+ eq_type === nothing || error("[Equilibrium] sets eq_type, but the [$(row.second.section)] section already selects the equilibrium; remove eq_type")
+ elseif eq_type === nothing
+ error("Missing required key in [Equilibrium]: eq_type")
+ elseif haskey(Equilibrium.ANALYTIC_EQ, eq_type)
+ error(
+ "[Equilibrium] eq_type = \"$eq_type\" is not a deck value: state the analytic equilibrium as a " *
+ "[$(Equilibrium.ANALYTIC_EQ[eq_type].section)] section and remove eq_type"
+ )
+ end
+ fields = _struct_fields(Equilibrium.EquilibriumConfig, (:power_bp, :power_b, :power_r, :power_rc))
+ kwargs = section_keywords(_deck_paths(table, path, ("eq_filename", "kinetic_file")), "Equilibrium", fields)
+ row === nothing || (kwargs[:eq_type] = row.first)
+ return Equilibrium.EquilibriumConfig(; kwargs...)
+end
+
+"""
+ kinetic_forces_control(inputs) -> KineticForces.KineticForcesControl
+
+The `[KineticForces]` control of the run, defaults when the deck has no such section.
+"""
+function kinetic_forces_control(inputs::AbstractDict)
+ table = get(inputs, "KineticForces", Dict{String,Any}())
+ return KineticForces.KineticForcesControl(; section_keywords(table, "KineticForces", _struct_fields(KineticForces.KineticForcesControl))...)
+end
+
+"""
+ slayer_model(inputs) -> SLAYERModel
+
+The SLAYER layer model of the `[SLAYER]` section, the default `SLAYERModel()` when absent.
+"""
+function slayer_model(inputs::AbstractDict)
+ fields = Dict{Symbol,Any}(:variant => Symbol, :P_perp_model => Any, :D_c_type => Any, :D_R => Any, :D_geo => Any, :chi_perp_Dc => Any,
+ :theta_sample => Any)
+ return SLAYERModel(; section_keywords(get(inputs, "SLAYER", Dict{String,Any}()), "SLAYER", fields)...)
+end
+
+"""
+ ggj_model(inputs) -> GGJModel
+
+The GGJ layer model of the `[GGJ]` section: `solver` and the backend options, passed to
+`GGJModel` as they are. The default `GGJModel()` when absent.
+"""
+function ggj_model(inputs::AbstractDict)
+ kwargs = Dict{Symbol,Any}(Symbol(k) => v for (k, v) in get(inputs, "GGJ", Dict{String,Any}()))
+ haskey(kwargs, :solver) && (kwargs[:solver] = Symbol(kwargs[:solver]))
+ return GGJModel(; kwargs...)
+end
+
+"""
+ force_balance_keywords(inputs, path) -> Dict{Symbol,Any}
+
+The `ForceBalanceProblem` keywords of the `[ForceFreeStates]` section, with `wall` from `[Wall]`,
+the `kinetic` source it names and the layer-overlap cap's `[SLAYER]` closures.
+"""
+function force_balance_keywords(inputs::AbstractDict, path::AbstractString)
+ fields = _struct_fields(ForceFreeStatesControl, (:algorithm, :nn_low, :nn_high, :kinetic, :psilim_from_layer_overlap))
+ merge!(fields, Dict{Symbol,Any}(:nn => Any, :integrator => String, :kinetic => String, :psilim_from_layer_overlap => Bool))
+ kwargs = section_keywords(inputs["ForceFreeStates"], "ForceFreeStates", fields)
+ delete!(kwargs, :integrator)
+ haskey(kwargs, :nn) || error("[ForceFreeStates] needs nn, the toroidal mode number (nn = 1) or consecutive numbers (nn = [1, 2, 3])")
+ nn = kwargs[:nn]
+ if nn isa AbstractVector
+ (!isempty(nn) && all(x -> x isa Integer, nn) && nn == first(nn):last(nn)) ||
+ error("[ForceFreeStates] nn = $nn must list consecutive toroidal mode numbers")
+ kwargs[:nn] = first(nn):last(nn)
+ end
+ kinetic = pop!(kwargs, :kinetic, nothing)
+ if kinetic == "KineticForces"
+ kwargs[:kinetic] = kinetic_forces_control(inputs)
+ elseif kinetic == "TestKineticMatrices"
+ error("TestKineticMatrices is script-only: pass ForceBalanceProblem(eq; kinetic=TestKineticMatrices(; scale)) to solve")
+ elseif kinetic !== nothing
+ error("[ForceFreeStates] kinetic = \"$kinetic\" is not a kinetic source (expected \"KineticForces\")")
+ end
+ get(kwargs, :psilim_from_layer_overlap, false) && haskey(inputs, "SLAYER") && (kwargs[:psilim_from_layer_overlap] = slayer_model(inputs))
+ kwargs[:wall] = Vacuum.parse_wall(_deck_paths(get(inputs, "Wall", nothing), path, ("file",)))
+ return kwargs
+end
+
+"""
+ force_balance_control(inputs, path) -> ForceFreeStatesControl
+
+The control a deck's `[ForceFreeStates]` section and integrator section state, for the solve stages
+that take one directly; [`ForceBalanceProblem`](@ref) carries the same keywords.
+"""
+function force_balance_control(inputs::AbstractDict, path::AbstractString)
+ kwargs = force_balance_keywords(inputs, path)
+ nn = pop!(kwargs, :nn)
+ delete!(kwargs, :wall)
+ return ForceFreeStates.validate_algorithm(ForceFreeStatesControl(; algorithm=force_balance_algorithm(inputs), nn_low=first(nn), nn_high=last(nn), kwargs...))
+end
+
+"""
+ force_balance_algorithm(inputs) -> AbstractIntegrator
+
+The integrator `[ForceFreeStates] integrator` names (default `"Riccati"`), with the numerical
+settings of its own section, `[Forward]`, `[Riccati]` or `[Galerkin]`.
+"""
+function force_balance_algorithm(inputs::AbstractDict)
+ name = _selector(inputs["ForceFreeStates"], "ForceFreeStates", "integrator", first.(_INTEGRATORS), "Riccati")
+ for (other, _) in _INTEGRATORS
+ other != name && haskey(inputs, other) && error("[$other] is set but [ForceFreeStates] integrator = \"$name\"")
+ end
+ T = Dict(_INTEGRATORS)[name]
+ return T(; section_keywords(get(inputs, name, Dict{String,Any}()), name, _struct_fields(T))...)
+end
+
+"""
+ local_stability_from_deck(inputs) -> Union{Nothing,NamedTuple}
+
+`(; problem, algorithm)`: the `LocalStabilityProblem` keywords of `[LocalStability]` and the
+`Ballooning` settings of `[Ballooning]` (defaults when absent). `nothing` without `[LocalStability]`.
+"""
+function local_stability_from_deck(inputs::AbstractDict)
+ if !haskey(inputs, "LocalStability")
+ haskey(inputs, "Ballooning") && error("[Ballooning] is set without [LocalStability], which runs the stage")
+ return nothing
+ end
+ problem = section_keywords(inputs["LocalStability"], "LocalStability", _struct_fields(LocalStabilityProblem, (:equil,)))
+ algorithm = Ballooning(; section_keywords(get(inputs, "Ballooning", Dict{String,Any}()), "Ballooning", _struct_fields(Ballooning))...)
+ return (; problem, algorithm)
+end
+
+"""
+ match_from_deck(inputs) -> Union{Nothing,NamedTuple}
+
+`(; problem, model)`: the `MatchProblem` keywords of `[Match]` and the inner-layer model its
+`inner_model` names (`"GGJ"`, from `[GGJ]`). `nothing` without `[Match]`.
+"""
+function match_from_deck(inputs::AbstractDict)
+ haskey(inputs, "Match") || return nothing
+ fields = Dict{Symbol,Any}(:eta => Any, :rho => Any, :rotation => Any, :gamma => Any, :ideal => Bool, :inner_model => String)
+ problem = section_keywords(inputs["Match"], "Match", fields)
+ _selector(inputs["Match"], "Match", "inner_model", ("GGJ",), "GGJ")
+ delete!(problem, :inner_model)
+ return (; problem, model=ggj_model(inputs))
+end
+
+"""
+ tearing_from_deck(inputs) -> Union{Nothing,NamedTuple}
+
+`(; problem, model, config)`: the `TearingProblem` keywords of `[Tearing]` (with
+`[Tearing.CriticalResonantField]`), the layer model its `inner_model` names (`"SLAYER"` from
+`[SLAYER]`, `"GGJ"` from `[GGJ]`) and the `TearingConfig` of `[Tearing.search]`. `nothing` without `[Tearing]`.
+"""
+function tearing_from_deck(inputs::AbstractDict)
+ haskey(inputs, "Tearing") || return nothing
+ table = inputs["Tearing"]
+ get(table, "omega_E_kHz", Dict{String,Any}()) isa AbstractDict ||
+ throw(ArgumentError("[Tearing] omega_E_kHz must be a table keyed by m/n, e.g. omega_E_kHz = { \"2/1\" = 3.0 }"))
+ fields = _struct_fields(TearingProblem, (:ffs, :critical_resonant_field))
+ fields[:inner_model] = String
+ problem = section_keywords(_without(table, "search", "CriticalResonantField"), "Tearing", fields)
+ inner_model = _selector(table, "Tearing", "inner_model", ("SLAYER", "GGJ"))
+ delete!(problem, :inner_model)
+ crf = get(table, "CriticalResonantField", nothing)
+ crf === nothing || (
+ problem[:critical_resonant_field] = CriticalResonantFieldControl(;
+ section_keywords(crf, "Tearing.CriticalResonantField", _struct_fields(CriticalResonantFieldControl))...)
+ )
+ config = TearingConfig(; section_keywords(get(table, "search", Dict{String,Any}()), "Tearing.search", _struct_fields(TearingConfig))...)
+ return (; problem, model=inner_model == "SLAYER" ? slayer_model(inputs) : ggj_model(inputs), config)
+end
+
+"""
+ perturbed_equilibrium_from_deck(inputs) -> Union{Nothing,NamedTuple}
+
+`(; response, drive)`: the `plasma_response` and `perturbed_equilibrium` keywords of
+`[PerturbedEquilibrium]`. `nothing` without that section.
+"""
+function perturbed_equilibrium_from_deck(inputs::AbstractDict)
+ haskey(inputs, "PerturbedEquilibrium") || return nothing
+ fields = Dict{Symbol,Any}(:compute_singular_coupling => Bool, :compute_torque_response => Bool, :regularization_width => Float64)
+ kwargs = section_keywords(inputs["PerturbedEquilibrium"], "PerturbedEquilibrium", fields)
+ response = filter(p -> p.first != :regularization_width, kwargs)
+ return (; response, drive=filter(p -> p.first == :regularization_width, kwargs))
+end
+
+"""
+ forcing_terms_control(inputs, path) -> ForcingTermsControl
+
+The `[ForcingTerms]` section of a parsed deck as a control struct, defaults when absent, with its
+relative file paths resolved against the deck directory `path`. The `[[ForcingTerms.coil_set]]`
+array of tables is passed through as `coil_sets_raw`.
+"""
+function forcing_terms_control(inputs::AbstractDict, path::AbstractString)
+ "ForcingTerms" in keys(inputs) || return ForcingTerms.ForcingTermsControl(; forcing_data_file=joinpath(path, "forcing.dat"))
+ forcing_raw = _deck_paths(inputs["ForcingTerms"], path, ("forcing_data_file", "dat_dir"))
+ haskey(forcing_raw, "forcing_data_file") || (forcing_raw["forcing_data_file"] = joinpath(path, "forcing.dat"))
+ coil_sets_raw = Dict{String,Any}[_deck_paths(d, path, ("dat_file", "h5_file")) for d in get(forcing_raw, "coil_set", Dict{String,Any}[])]
+ kwargs = section_keywords(_without(forcing_raw, "coil_set"), "ForcingTerms", _struct_fields(ForcingTerms.ForcingTermsControl, (:coil_sets_raw,)))
+ return ForcingTerms.ForcingTermsControl(; kwargs..., coil_sets_raw=coil_sets_raw)
+end
+
+"""
+ error_fields_from_deck(inputs, path) -> Union{Nothing,NamedTuple}
+
+`(; ctrl, tolerance_file, tolerances, monte_carlo, risk, ntv, scenario)`: the `[ErrorFields]` control, the
+`tolerance_file` path and the tolerance set it names (`""` and `nothing` when none), the controls of its `MonteCarlo`, `Risk` and `NTV` sub-tables, and the
+`[ErrorFields.scenario]` keywords of `ErrorFields.ScenarioParameters` (`nothing` when absent). `nothing` without
+`[ErrorFields]`.
+"""
+function error_fields_from_deck(inputs::AbstractDict, path::AbstractString)
+ haskey(inputs, "ErrorFields") || return nothing
+ table = _deck_paths(inputs["ErrorFields"], path, ("tolerance_file",))
+ sub(name, T) = T(; section_keywords(get(table, name, Dict{String,Any}()), "ErrorFields.$name", _struct_fields(T))...)
+ ctrl = ErrorFields.ErrorFieldsControl(;
+ section_keywords(_without(table, "MonteCarlo", "Risk", "scenario", "NTV", "tolerance_file"),
+ "ErrorFields", _struct_fields(ErrorFields.ErrorFieldsControl))...
+ )
+ file = get(table, "tolerance_file", "")
+ isempty(file) || isfile(file) || error("[ErrorFields] tolerance_file not found: $file")
+ scenario = haskey(table, "scenario") ? section_keywords(table["scenario"], "ErrorFields.scenario", _struct_fields(ErrorFields.ScenarioParameters)) : nothing
+ scenario === nothing || haskey(scenario, :n_e) || error("[ErrorFields.scenario] must give n_e (electron density, 1e19 m^-3)")
+ return (; ctrl, tolerance_file=file, tolerances=isempty(file) ? nothing : ErrorFields.read_tolerance_toml(file),
+ monte_carlo=sub("MonteCarlo", ErrorFields.MonteCarloControl),
+ risk=sub("Risk", ErrorFields.RiskControl), ntv=sub("NTV", ErrorFields.NTVControl), scenario)
+end
+
+"""
+ parse_deck(inputs, path) -> NamedTuple
+
+Every stage of a parsed deck, translated to API objects before anything runs, so a stale or
+misspelled key stops the run at once. A section that no stage would read is an error.
+"""
+function parse_deck(inputs::AbstractDict, path::AbstractString)
+ _stop_on_deprecated_deck_keys(inputs)
+ analytic = [spec.section for spec in values(Equilibrium.ANALYTIC_EQ)]
+ for section in keys(inputs)
+ section in _DECK_SECTIONS || section in analytic ||
+ error("unknown section [$section] in gpec.toml (allowed: $(join(sort!([_DECK_SECTIONS..., analytic...]), ", ")))")
+ end
+ has_ffs = haskey(inputs, "ForceFreeStates")
+ if !has_ffs
+ for section in ("Wall", "Forward", "Riccati", "Galerkin", "Match", "GGJ", "Tearing", "SLAYER", "LocalStability", "Ballooning",
+ "ForcingTerms", "PerturbedEquilibrium", "KineticForces", "ErrorFields")
+ haskey(inputs, section) && error("[$section] is set but there is no [ForceFreeStates] section, so the run stops after the equilibrium")
+ end
+ end
+ force_balance = has_ffs ? (; keywords=force_balance_keywords(inputs, path), algorithm=force_balance_algorithm(inputs)) : nothing
+ kinetic_source = has_ffs && get(inputs["ForceFreeStates"], "kinetic", nothing) == "KineticForces"
+ haskey(inputs, "PerturbedEquilibrium") && haskey(inputs, "Wall") &&
+ error("[PerturbedEquilibrium] needs a run without a wall (its surface inductance is free-space): remove the [Wall] section")
+ haskey(inputs, "ForcingTerms") && !haskey(inputs, "PerturbedEquilibrium") &&
+ error("[ForcingTerms] is set but there is no [PerturbedEquilibrium] section to apply it")
+ haskey(inputs, "KineticForces") && !haskey(inputs, "PerturbedEquilibrium") && !kinetic_source &&
+ error("[KineticForces] is set but neither [PerturbedEquilibrium] (the torque) nor [ForceFreeStates] kinetic = \"KineticForces\" uses it")
+ (haskey(inputs, "KineticForces") || kinetic_source) && isempty(get(get(inputs, "Equilibrium", Dict{String,Any}()), "kinetic_file", "")) &&
+ error("this run needs kinetic profiles ([KineticForces], or kinetic = \"KineticForces\"): set kinetic_file in [Equilibrium]")
+ match = match_from_deck(inputs)
+ # The MatchProblem guards, checked before the force-free-states solve rather than after it.
+ if match !== nothing
+ (; keywords, algorithm) = force_balance
+ first(keywords[:nn]) == last(keywords[:nn]) || error("[Match] is single-n: set [ForceFreeStates] nn to one toroidal mode number")
+ (algorithm isa Galerkin && algorithm.rpec_flag) || (algorithm isa Riccati && get(keywords, :vac_flag, false)) ||
+ error("[Match] needs Δ′: use integrator = \"Galerkin\" with [Galerkin] rpec_flag = true, or \"Riccati\" with vac_flag = true")
+ end
+ tearing = tearing_from_deck(inputs)
+ perturbed_equilibrium = perturbed_equilibrium_from_deck(inputs)
+ forcing = forcing_terms_control(inputs, path)
+ if haskey(inputs, "ErrorFields")
+ perturbed_equilibrium === nothing && error("[ErrorFields] needs a [PerturbedEquilibrium] section")
+ forcing.forcing_data_format == "coil" ||
+ error("[ErrorFields] linearizes coil geometry, so [ForcingTerms] must use forcing_data_format = \"coil\" (got \"$(forcing.forcing_data_format)\")")
+ end
+ tearing_model = haskey(inputs, "Tearing") ? get(inputs["Tearing"], "inner_model", nothing) : nothing
+ haskey(inputs, "GGJ") && match === nothing && tearing_model != "GGJ" &&
+ error("[GGJ] is set but neither [Match] nor [Tearing] inner_model = \"GGJ\" uses it")
+ haskey(inputs, "SLAYER") && tearing_model != "SLAYER" && !(has_ffs && get(inputs["ForceFreeStates"], "psilim_from_layer_overlap", false) === true) &&
+ error("[SLAYER] is set but neither [Tearing] inner_model = \"SLAYER\" nor [ForceFreeStates] psilim_from_layer_overlap = true uses it")
+ return (; run=run_settings(inputs, path), force_balance, local_stability=local_stability_from_deck(inputs), match, tearing,
+ kinetic_forces=haskey(inputs, "KineticForces") ? kinetic_forces_control(inputs) : nothing, perturbed_equilibrium, forcing,
+ error_fields=error_fields_from_deck(inputs, path))
+end
+
+# ---------------------------------------------------------------------------------------------------------------------
+# The inverse: the API objects of a parsed deck back to the deck that states them, so every run can record a deck that
+# reproduces it.
+
+# A value as a deck states it: Symbols as strings, tuples, ranges and vectors as arrays, structs as tables.
+_deck_out(v) = v
+_deck_out(v::Symbol) = String(v)
+_deck_out(v::Union{Tuple,AbstractVector}) = Any[_deck_out(x) for x in v]
+_deck_out(v::AbstractDict) = Dict{String,Any}(String(k) => _deck_out(x) for (k, x) in v)
+_deck_out(v::Equilibrium.IonSpecies) = _deck_table(v)
+
+# The fields of `x` as a deck table, less `exclude`; a `nothing` field is left out, as the parser's default.
+_deck_table(x, exclude=()) =
+ Dict{String,Any}(String(f) => _deck_out(getfield(x, f)) for f in fieldnames(typeof(x)) if !(f in exclude) && getfield(x, f) !== nothing)
+_deck_table(kwargs::AbstractDict, exclude=()) = Dict{String,Any}(String(k) => _deck_out(v) for (k, v) in kwargs if v !== nothing && !(k in exclude))
+
+"""
+ deck_sections(config::EquilibriumConfig, analytic) -> Dict{String,Any}
+
+The `[Equilibrium]` section of `config` and, for an analytic equilibrium, the section of its config `analytic`
+(`nothing` for a file-based one), which then implies `eq_type`.
+"""
+function deck_sections(config::Equilibrium.EquilibriumConfig, analytic)
+ table = _deck_table(config, (:power_bp, :power_b, :power_r, :power_rc))
+ analytic === nothing && return Dict{String,Any}("Equilibrium" => table)
+ # An analytic equilibrium reads no file: its section implies eq_type.
+ delete!(table, "eq_type")
+ delete!(table, "eq_filename")
+ return Dict{String,Any}("Equilibrium" => table, Equilibrium.ANALYTIC_EQ[config.eq_type].section => _deck_table(analytic))
+end
+
+deck_sections(ctrl::KineticForces.KineticForcesControl) = Dict{String,Any}("KineticForces" => _deck_table(ctrl))
+deck_sections(model::SLAYERModel) = Dict{String,Any}("SLAYER" => merge(_deck_table(model), Dict{String,Any}("variant" => String(typeof(model).parameters[1]))))
+deck_sections(model::GGJModel) = Dict{String,Any}("GGJ" => merge(_deck_table(Dict(pairs(model.options))), Dict{String,Any}("solver" => String(typeof(model).parameters[1]))))
+deck_sections(wall::Vacuum.WallSettings) = Dict{String,Any}("Wall" => merge(_deck_table(wall), Dict{String,Any}("shape" => only(k for (k, T) in Vacuum.WALL_SHAPES if wall isa T))))
+
+"""
+ deck_sections(keywords, algorithm::AbstractIntegrator) -> Dict{String,Any}
+
+The `[ForceFreeStates]` section, the integrator's own section and the sections its keywords bring with them
+(`[Wall]`, `[KineticForces]` for a KineticForces source with non-default settings, `[SLAYER]` for the layer-overlap
+cap's closures): the inverse of [`force_balance_keywords`](@ref) and [`force_balance_algorithm`](@ref). `[KineticForces]`
+also runs the torque stage when present, so a run with non-default source settings and no torque stage records a
+deck that adds that stage.
+"""
+function deck_sections(keywords::AbstractDict{Symbol}, algorithm::ForceFreeStates.AbstractIntegrator)
+ kwargs = copy(keywords)
+ wall, kinetic, cap = pop!(kwargs, :wall, nothing), ForceFreeStates.kinetic_source(pop!(kwargs, :kinetic, nothing)), pop!(kwargs, :psilim_from_layer_overlap, false)
+ nn = pop!(kwargs, :nn)
+ section = _deck_table(kwargs)
+ section["nn"] = first(nn) == last(nn) ? first(nn) : collect(nn)
+ name = String(nameof(typeof(algorithm)))
+ section["integrator"] = name
+ sections = Dict{String,Any}("ForceFreeStates" => section, name => _deck_table(algorithm))
+ if kinetic isa KineticForces.KineticForcesControl
+ section["kinetic"] = "KineticForces"
+ # The source reads [KineticForces], whose presence alone also runs the torque stage: state it only when it differs.
+ isequal(_deck_table(kinetic), _deck_table(KineticForces.KineticForcesControl())) || merge!(sections, deck_sections(kinetic))
+ elseif kinetic !== nothing
+ section["kinetic"] = String(nameof(typeof(kinetic)))
+ end
+ cap === false || (section["psilim_from_layer_overlap"] = true)
+ cap isa SLAYERModel && merge!(sections, deck_sections(cap))
+ wall === nothing || merge!(sections, deck_sections(wall))
+ return sections
+end
+
+"""
+ deck_inputs(deck, config, analytic) -> Dict{String,Any}
+
+The deck a parsed deck `deck` (see [`parse_deck`](@ref)) states, with the equilibrium `config` and its `analytic`
+config: the inverse of `parse_deck`, `equilibrium_config` and `analytic_config`. Every value is explicit and every path
+absolute; `[Run] output_file` is left to whoever runs it.
+"""
+function deck_inputs(deck::NamedTuple, config::Equilibrium.EquilibriumConfig, analytic)
+ inputs = deck_sections(config, analytic)
+ inputs["Run"] = Dict{String,Any}("verbose" => deck.run.verbose)
+ fb = deck.force_balance
+ fb === nothing || merge!(inputs, deck_sections(fb.keywords, fb.algorithm))
+ ls = deck.local_stability
+ ls === nothing || merge!(inputs, Dict{String,Any}("LocalStability" => _deck_table(ls.problem), "Ballooning" => _deck_table(ls.algorithm)))
+ if deck.match !== nothing
+ merge!(inputs, deck_sections(deck.match.model))
+ inputs["Match"] = merge(_deck_table(deck.match.problem), Dict{String,Any}("inner_model" => "GGJ"))
+ end
+ if deck.tearing !== nothing
+ (; problem, model, config) = deck.tearing
+ merge!(inputs, _tearing_sections(filter(p -> p.first != :critical_resonant_field, problem), get(problem, :critical_resonant_field, nothing),
+ model, config))
+ end
+ deck.kinetic_forces === nothing || merge!(inputs, deck_sections(deck.kinetic_forces))
+ pe = deck.perturbed_equilibrium
+ pe === nothing || (inputs["PerturbedEquilibrium"] = _deck_table(merge(pe.response, pe.drive)))
+ (pe !== nothing || deck.error_fields !== nothing) && (inputs["ForcingTerms"] = _forcing_table(deck.forcing))
+ ef = deck.error_fields
+ ef === nothing || merge!(inputs, _error_fields_sections(ef, ef.tolerance_file))
+ return inputs
+end
+
+# [Tearing] with its search and critical-resonant-field sub-tables, and the section of its layer model.
+function _tearing_sections(problem, crf, model, config)
+ table = _deck_table(problem, (:ffs, :critical_resonant_field))
+ table["inner_model"] = model isa SLAYERModel ? "SLAYER" : "GGJ"
+ table["search"] = _deck_table(config)
+ crf === nothing || (table["CriticalResonantField"] = _deck_table(crf))
+ return merge(deck_sections(model), Dict{String,Any}("Tearing" => table))
+end
+
+# [ForcingTerms] of a forcing control, its coil sets as [[ForcingTerms.coil_set]].
+function _forcing_table(ctrl::ForcingTerms.ForcingTermsControl)
+ table = _deck_table(ctrl, (:coil_sets_raw,))
+ isempty(ctrl.coil_sets_raw) || (table["coil_set"] = Any[_deck_out(d) for d in ctrl.coil_sets_raw])
+ return table
+end
+
+# [ErrorFields] with its sub-tables, from the settings an error-field assessment takes.
+function _error_fields_sections(settings, tolerance_file::AbstractString)
+ table = _deck_table(settings.ctrl)
+ isempty(tolerance_file) || (table["tolerance_file"] = tolerance_file)
+ table["MonteCarlo"], table["Risk"], table["NTV"] = _deck_table(settings.monte_carlo), _deck_table(settings.risk), _deck_table(settings.ntv)
+ settings.scenario === nothing || (table["scenario"] = _deck_table(settings.scenario))
+ return Dict{String,Any}("ErrorFields" => table)
+end
+
+# ---------------------------------------------------------------------------------------------------------------------
+# Every saved result records the deck sections stating its inputs (`Utilities.record_inputs!`), so a script run and a
+# deck run of the same workflow record the same deck, and either replays from its gpec.h5.
+
+# Where a replay finds what a deck cannot state by path: the recorded forcing modes and tolerance file.
+const _RECORDED_FORCING = "Input/RawInputs/ForcingTerms"
+const _RECORDED_TOLERANCES = "Input/RawInputs/ErrorFields/tolerance_toml_raw"
+
+deck_sections(equil::Equilibrium.PlasmaEquilibrium) = deck_sections(equil.config, equil.analytic)
+deck_sections(ls::LocalStabilityResult) = Dict{String,Any}("LocalStability" => _deck_table(ls.problem, (:equil,)), "Ballooning" => _deck_table(ls.algorithm))
+deck_sections(m::ForceFreeStates.MatchResult) =
+ merge(deck_sections(m.model), Dict{String,Any}("Match" => merge(_deck_table(m.problem, (:ffs,)), Dict{String,Any}("inner_model" => "GGJ"))))
+deck_sections(kf::KineticForcesResult) = deck_sections(kf.control)
+deck_sections(t::TearingResult) = t.model === nothing ? Dict{String,Any}() : _tearing_sections(t.problem, t.problem.critical_resonant_field, t.model, t.config)
+deck_sections(ef::ErrorFieldsResult) = _error_fields_sections(ef.settings, ef.tolerances === nothing ? "" : _RECORDED_TOLERANCES)
+
+function deck_sections(ffs::ForceFreeStatesResult)
+ ctrl = ffs.control
+ keywords = Dict{Symbol,Any}(f => getfield(ctrl, f) for f in fieldnames(typeof(ctrl)) if !(f in (:algorithm, :nn_low, :nn_high)))
+ keywords[:nn] = ctrl.nn_low:ctrl.nn_high
+ keywords[:wall] = ffs.wall_settings
+ sections = merge(deck_sections(ffs.equil), deck_sections(keywords, ctrl.algorithm))
+ ffs.match === nothing || merge!(sections, deck_sections(ffs.match))
+ return sections
+end
+
+# A single unweighted source is its own [ForcingTerms]; any other field replays from the modes its save records.
+function deck_sections(pe::PerturbedEquilibrium.PerturbedEquilibriumState)
+ resp, forcing = pe.response, pe.forcing
+ table = Dict{String,Any}("compute_singular_coupling" => resp.compute_singular_coupling,
+ "compute_torque_response" => resp.compute_torque_response, "regularization_width" => pe.regularization_width)
+ sections = Dict{String,Any}("PerturbedEquilibrium" => table)
+ forcing === nothing && return sections
+ sections["ForcingTerms"] =
+ forcing isa ForcingTerms.RMPSource && forcing.scale == 1 ? _forcing_table(forcing.ctrl) :
+ Dict{String,Any}("forcing_data_format" => "hdf5", "forcing_data_file" => _RECORDED_FORCING)
+ return sections
+end
diff --git a/src/Equilibrium/AnalyticEquilibrium.jl b/src/Equilibrium/AnalyticEquilibrium.jl
deleted file mode 100644
index fa7a9ad589..0000000000
--- a/src/Equilibrium/AnalyticEquilibrium.jl
+++ /dev/null
@@ -1,324 +0,0 @@
-#=
-Analytic equilibrium functions that prepare all the necessary equilibrium
-input information for a direct or inverse equilibrium construction
-=#
-
-"""
- lar_init_conditions(rmin, sigma_type, params)
-
-Initializes the starting radius and state vector for solving the LAR ODE system.
-Also evaluates the initial derivative using the analytic model.
-
-## Arguments:
-- `rmin`: Normalized starting radius (as a fraction of `lar_a`).
-- `lar_input`: A `LargeAspectRatioConfig` object containing equilibrium parameters.
-
-## Returns:
-- `r`: Physical radius corresponding to `rmin * lar_a`.
-- `y`: Initial state vector of length 5.
-"""
-function lar_init_conditions(rmin::Float64, lar_input::LargeAspectRatioConfig)
- lar_a = lar_input.lar_a
- lar_r0 = lar_input.lar_r0
- q0 = lar_input.q0
-
- r = rmin * lar_a
- y = zeros(5)
-
- y[1] = r^2 / (lar_r0 * q0)
- y[2] = 1.0
- y[3] = y[1] * lar_r0 / 2
-
- dy = zeros(5)
- lar_der(dy, r, y, lar_input)
-
- y[5] = dy[5] * r / 4
-
- q = r^2 * y[2] / (lar_r0 * y[1])
- y[4] = (q / r)^2 * y[5] / 2
-
- return r, y
-end
-
-"""
- lar_der(dy, r, y, lar_input)
-
-Evaluates the spatial derivatives of the LAR (Large Aspect Ratio) equilibrium ODE system
-at a given radius `r`, using the current state vector `y` and equilibrium parameters.
-
-## Arguments:
-- `dy`: A preallocated vector where the computed derivatives will be stored (in-place).
-- `r`: The radial position at which the derivative is evaluated.
-- `y`: The current state vector.
-- `lar_input`: A `LargeAspectRatioConfig` object containing equilibrium shaping parameters.
-
-## Returns:
-- 0. The result is stored in-place in `dy`.
-"""
-
-function lar_der(dy::Vector{Float64}, r::Float64, y::Vector{Float64}, lar_input::LargeAspectRatioConfig)
- lar_a = lar_input.lar_a
- lar_r0 = lar_input.lar_r0
-
- q0 = lar_input.q0
-
- beta0 = lar_input.beta0
- p00 = beta0 / 2.0
- p_pres = lar_input.p_pres
- p_sig = lar_input.p_sig
-
- sigma_type = lar_input.sigma_type
- x = r / lar_a
- xfac = 1 - x^2
- pp = -2 * p_pres * p00 * x * xfac^(p_pres - 1) # p'
- sigma0 = 2.0 / (q0 * lar_r0)
-
- sigma = if sigma_type == "wesson"
- sigma0 * xfac^p_sig
- else
- sigma0 / (1 + x^(2 * p_sig))^(1 + 1 / p_sig)
- end
-
- bsq = (y[1] / max(r, eps()))^2 + y[2]^2 # B²
- q = r^2 * y[2] / (lar_r0 * max(y[1], eps()))
-
- dy[1] = -pp/bsq*y[1] + sigma*y[2]*r
- dy[2] = -pp/bsq*y[2] - sigma*y[1]/max(r, eps())
- dy[3] = y[1] * lar_r0 / max(r, eps())
- dy[4] = ((q / max(r, eps()))^2) * y[5] / max(r, eps())
- dy[5] = y[2] * (r / max(q, eps()))^2 * (r / lar_r0) * (1 - 2 * (lar_r0 * q / max(y[2], eps()))^2 * pp)
-
- return 0
-end
-
-"""
- lar_run(lar_input)
-
-Solves the LAR (Large Aspect Ratio) plasma equilibrium ODE system using analytic profiles
-defined by `lar_input`, and returns the full solution table including derived quantities.
-
-## Arguments:
-- `lar_input`: A `LargeAspectRatioConfig` object containing profile and geometric parameters.
-
-## Returns:
- - working on it not yet implemented
-"""
-
-function lar_run(equil_input::EquilibriumConfig, lar_input::LargeAspectRatioConfig)
- rmin = 1e-4
- lar_a = lar_input.lar_a
- lar_r0 = lar_input.lar_r0
- q0 = lar_input.q0
- beta0 = lar_input.beta0
- sigma_type = lar_input.sigma_type
-
- p00 = beta0 / 2.0
- lar_input.p_pres = max(lar_input.p_pres, 1.001)
-
- sigma0 = 2.0 / (q0 * lar_r0)
-
- ma = lar_input.ma
- mtau = lar_input.mtau
-
- function dydr(du, u, p, r)
- lar_input = p
- lar_der(du, r, u, lar_input)
- end
-
- r0, y0 = lar_init_conditions(rmin, lar_input)
- tspan = (r0, lar_a)
- p = lar_input
-
- prob = ODEProblem(dydr, y0, tspan, p)
- sol = solve(prob, Rosenbrock23(autodiff=AutoFiniteDiff()); reltol=1e-6, abstol=1e-8, maxiters=10000)
-
- r_arr = sol.t
- y_mat = hcat(sol.u...)'
- steps = length(r_arr)
-
- temp = zeros(steps, 9)
- for i in 1:steps
- r = r_arr[i]
- y = y_mat[i, :]
- x = r / lar_a
- xfac = 1 - x^2
- pval = p00 * xfac^lar_input.p_pres
- sigma = (sigma_type == "wesson") ?
- sigma0 * xfac^lar_input.p_sig :
- sigma0 / (1 + x^(2 * lar_input.p_sig))^(1 + 1 / lar_input.p_sig)
- q = r^2 * y[2] / (lar_r0 * y[1])
- temp[i, :] = [r; y; pval; sigma; q]
- end
-
- xs_r = temp[:, 1]
- fs_r = temp[:, 2:9]
- spl = Spl.CubicSpline(xs_r, fs_r, bctype=4)
-
- dr = lar_a / (ma + 1)
- r = 0.0
- psio = temp[end, 4] # ψ_edge
-
- sq_xs = zeros(ma + 1)
- sq_fs = zeros(ma + 1, 3)
- r_nodes = zeros(ma + 1)
-
- for ia in 1:(ma + 1)
- r += dr
- r_nodes[ia] = r
- f, f1 = Spl.spline_eval(spl, r,1)
- ψ = f[3]
- Bphi = f[2]
- pval = f[6]
- qval = f[8]
- dψdr = f1[3]
- r2 = -(f[4] * r / f[8]) / dψdr
- sq_xs[ia] = ψ / psio
- sq_fs[ia, 1] = lar_r0 * Bphi
- sq_fs[ia, 2] = pval
- sq_fs[ia, 3] = qval
- end
-
- sq_in = Spl.CubicSpline(sq_xs, sq_fs, bctype=4)
-
- rzphi_y_nodes = range(0.0, 2π, length=mtau + 1)
- rzphi_fs_nodes = zeros(ma + 1, mtau + 1, 2)
-
- for ia in 1:(ma + 1)
- r = r_nodes[ia]
- f, f1 = Spl.spline_eval(spl, r, 1)
- y4 = f[4]
- q = f[8]
- dψdr = f1[3]
- r2 = -(y4 * r / q) / dψdr
- if lar_input.zeroth
- r2 = 0.0
- end
-
- for itau in 1:(mtau + 1)
- θ = 2π * (itau - 1) / mtau
- cosθ, sinθ = cos(θ), sin(θ)
- rfac = r + r2 * cosθ
- rzphi_fs_nodes[ia, itau, 1] = lar_r0 + rfac * cosθ
- rzphi_fs_nodes[ia, itau, 2] = rfac * sinθ
- end
- end
-
- rz_in = Spl.BicubicSpline(r_nodes, collect(rzphi_y_nodes), rzphi_fs_nodes, bctypex=4, bctypey=2)
-
- return InverseRunInput(equil_input, sq_in, rz_in, lar_r0, 0.0, psio)
-
-end
-
-
-"""
-This is a Julia version of the Fortran code in sol.f, implementing Soloviev's analytical equilibrium.
-
-## Arguments:
-- `mr`: Number of radial grid zones
-- `mz`: Number of axial grid zones
-- `ma`: Number of flux grid zones
-- `e`: Elongation
-- `a`: Minor radius
-- `r0`: Major radius
-- `q0`: Safety factor at the o-point
-- `p0fac`: Scales on axis pressure (s*P. beta changes. Phi,q constant)
-- `b0fac`: Scales on toroidal field (s*Phi,s*f,s^2*P. bt changes. Shape,beta constant)
-- `f0fac`: Scales on toroidal field (s*f. bt,q changes. Phi,p,bp constant)
-
-## Returns:
-- `plasma_eq`: PlasmaEquilibrium object
-"""
-function sol_run(
- equil_inputs::EquilibriumConfig,
- sol_inputs::SolevevConfig
- )
-
- mr = sol_inputs.mr
- mz = sol_inputs.mz
- ma = sol_inputs.ma
- e = sol_inputs.e
- a = sol_inputs.a
- r0 = sol_inputs.r0
- q0 = sol_inputs.q0
- p0fac = sol_inputs.p0fac
- b0fac = sol_inputs.b0fac
- f0fac = sol_inputs.f0fac
-
- # Validate inputs
- if p0fac < 1.0
- @warn "Forcing p0fac ≥ 1 (no negative pressure)"
- p0fac = 1.0
- end
-
- # Grid setup
- r = range(0.0, stop=a, length=mr)
- z = range(-a*e, stop=a*e, length=mz)
- rg = [ri for ri in r, _ in z]
- zg = [zi for _ in r, zi in z]
-
- #-----------------------------------------------------------------------
- # allocate arrays
- #-----------------------------------------------------------------------
- sq_in = zeros(Float64, ma, 4)
- psi_in = zeros(Float64, mr, mz)
- sqfs = zeros(ma, 4)
- psifs = zeros(mr, mz, 1)
-
- r = zeros(Float64, mr)
- z = zeros(Float64, mz)
- rg = zeros(Float64, mr, mz) # 2D grid arrays
- zg = zeros(Float64, mr, mz)
- #-----------------------------------------------------------------------
- # compute scalar data (EXTERNAL DEPENDENCIES - global variables)
- #-----------------------------------------------------------------------
- ro = 0 # EXTERNAL: global variable ro?
- zo = 0 # EXTERNAL: global variable zo?
- f0 = r0 * b0fac
- psio = e * f0 * a * a / (2 * q0 * r0)
- psifac = psio / (a * r0)^2
- efac = 1 / (e * e)
- pfac = 2 * psio^2 * (e * e + 1) / (a * r0 * e)^2
- rmin = r0 - 1.5 * a
- rmax = r0 + 1.5 * a
- zmax = 1.5 * e * a
- zmin = -zmax
- #-----------------------------------------------------------------------
- # compute 1D data
- #-----------------------------------------------------------------------
- psis = [(ia / (ma + 1))^2 for ia in 1:ma] # changed from ...ia in 1:(ma+1)]
- sqfs[:, 1] .= f0 * f0fac
- sqfs[:, 2] = pfac .* (1 * p0fac .- psis)
- sqfs[:, 3] .= 0.0
-
- sq_in = Spl.CubicSpline(psis, sqfs; bctype=3)
- #-----------------------------------------------------------------------
- # compute 2D data
- #-----------------------------------------------------------------------
- for ir in 1:(mr)
- r[ir] = rmin + (ir-1) * (rmax - rmin) / mr
- end
-
- for iz in 1:(mz)
- z[iz] = zmin + (iz-1) * (zmax - zmin) / mz
- end
-
- for iz in 1:(mz)
- for ir in 1:(mr)
- # rg[ir, iz] = r[ir]
- # zg[ir, iz] = z[iz]
- psifs[ir, iz, 1] = psio - psifac * (efac * (r[ir] * z[iz])^2 + (r[ir]^2 - r0^2)^2 / 4)
- end
- end
-
- psi_in = Spl.BicubicSpline(r, z, psifs; bctypex=3, bctypey=3)
- #-----------------------------------------------------------------------
- # process equilibrium
- #-----------------------------------------------------------------------
- println("Generating Soloviev equilibrium inputs with:")
- println(" mr=$mr, mz=$mz, ma=$ma")
- println(" e=$e, a=$a, r0=$r0")
- println(" q0=$q0, p0fac=$p0fac, b0fac=$b0fac, f0fac=$f0fac")
-
- return DirectRunInput(equil_inputs, sq_in, psi_in, rmin, rmax, zmin, zmax, psio)
-
-end
diff --git a/src/Equilibrium/Axisymmetric/Direct.jl b/src/Equilibrium/Axisymmetric/Direct.jl
new file mode 100644
index 0000000000..e0c2b93e7a
--- /dev/null
+++ b/src/Equilibrium/Axisymmetric/Direct.jl
@@ -0,0 +1,734 @@
+"""
+ DirectBField
+
+Internal mutable struct to hold B-field components and their derivatives at a point.
+It is used as a temporary workspace to avoid allocations in tight loops.
+"""
+@kwdef mutable struct DirectBField
+ psi::Float64 = 0.0
+ psir::Float64 = 0.0 # d(psi)/dr
+ psiz::Float64 = 0.0 # d(psi)/dz
+ psirz::Float64 = 0.0 # d2(psi)/drdz
+ psirr::Float64 = 0.0 # d2(psi)/drdr
+ psizz::Float64 = 0.0 # d2(psi)/dzdz
+ f::Float64 = 0.0 # F = R*Bt
+ f1::Float64 = 0.0 # dF/d(psi_norm)
+ p::Float64 = 0.0 # mu0*Pressure
+ p1::Float64 = 0.0 # dP/d(psi_norm)
+ br::Float64 = 0.0 # Br
+ bz::Float64 = 0.0 # Bz
+ brr::Float64 = 0.0 # d(Br)/dr
+ brz::Float64 = 0.0 # d(Br)/dz
+ bzr::Float64 = 0.0 # d(Bz)/dr
+ bzz::Float64 = 0.0 # d(Bz)/dz
+end
+
+"""
+ FieldLineDerivParams
+
+Constant parameters of the field-line ODE, read by `direct_fieldline_der!` and `arclength_fieldline_der!`.
+"""
+struct FieldLineDerivParams{I2D<:FastInterpolations.CubicInterpolantND,S<:FastInterpolations.CubicSeriesInterpolant,D}
+ ro::Float64
+ zo::Float64
+ psi_in::I2D
+ sq_in::S
+ sq_in_deriv::D
+ psio::Float64
+ power_bp::Int
+ power_b::Int
+ power_r::Int
+ power_rc::Int # minor radius rfac = √((R-R₀)²+(Z-Z₀)²) power exponent
+ bfield::DirectBField
+end
+
+"""
+ direct_get_bfield!(bf_out, r, z, psi_in, sq_in, sq_in_deriv, psio; derivs=0)
+
+Evaluates ψ, the profiles F and P, and the poloidal field with its derivatives at (R, Z), in place in `bf_out`.
+Port of Fortran `direct_get_bfield`.
+
+## Arguments
+
+ - `psi_in`: 2D cubic interpolant of the poloidal flux `ψ(R,Z)`
+ - `sq_in`, `sq_in_deriv`: profile series `F(ψ_norm)`, `P(ψ_norm)` and its derivative
+ - `psio`: ψ at the magnetic axis; ψ_norm = 1 - ψ/psio
+ - `derivs`: number of ψ derivatives to evaluate (0, 1, or 2)
+"""
+@with_pool pool function direct_get_bfield!(
+ bf_out::DirectBField,
+ r::Float64,
+ z::Float64,
+ psi_in::FastInterpolations.CubicInterpolantND,
+ sq_in::FastInterpolations.CubicSeriesInterpolant,
+ sq_in_deriv,
+ psio::Float64;
+ derivs::Int=0
+)
+ # Evaluate 2D interpolant for psi(r,z) and its derivatives
+ if derivs == 0
+ bf_out.psi = psi_in((r, z))
+ elseif derivs == 1
+ bf_out.psi = psi_in((r, z))
+ bf_out.psir = psi_in((r, z); deriv=DerivOp(1, 0))
+ bf_out.psiz = psi_in((r, z); deriv=DerivOp(0, 1))
+ else # derivs >= 2
+ bf_out.psi = psi_in((r, z))
+ bf_out.psir = psi_in((r, z); deriv=DerivOp(1, 0))
+ bf_out.psiz = psi_in((r, z); deriv=DerivOp(0, 1))
+ bf_out.psirr = psi_in((r, z); deriv=DerivOp(2, 0))
+ bf_out.psirz = psi_in((r, z); deriv=DerivOp(1, 1))
+ bf_out.psizz = psi_in((r, z); deriv=DerivOp(0, 2))
+ end
+
+ # Evaluate magnetic fields from equilibrium profiles
+ psi_norm = (psio > 1e-12) ? (1.0 - bf_out.psi / psio) : 0.0
+ psi_norm = clamp(psi_norm, 0.0, 1.0)
+
+ f_sq = acquire!(pool, eltype(sq_in.y), n_series(sq_in))
+ f1_sq = acquire!(pool, eltype(sq_in_deriv.parent.y), n_series(sq_in_deriv.parent))
+ sq_in(f_sq, psi_norm)
+ sq_in_deriv(f1_sq, psi_norm)
+ bf_out.f = f_sq[1] # F = R*Bt
+ bf_out.f1 = f1_sq[1] # dF/dψ
+ bf_out.p = f_sq[2] # μ0*Pressure
+ bf_out.p1 = f1_sq[2] # dP/dψ
+
+ (derivs == 0) && return
+
+ # Evaluate B-field derivative components
+ bf_out.br = bf_out.psiz / r # Br = (1/R) * ∂ψ/∂Z
+ bf_out.bz = -bf_out.psir / r # Bz = -(1/R) * ∂ψ/∂R
+
+ (derivs == 1) && return
+
+ # Evaluate more derivatives of B-field components
+ bf_out.brr = (bf_out.psirz - bf_out.br) / r
+ bf_out.brz = bf_out.psizz / r
+ bf_out.bzr = -(bf_out.psirr + bf_out.bz) / r
+ bf_out.bzz = -bf_out.psirz / r
+end
+
+# Numerical controls of the magnetic-axis search.
+const AXIS_MARCH_STEPS = 200 # midplane march steps allowed before giving up on a B_z sign change
+const AXIS_NEWTON_ITERATIONS = 200
+const AXIS_SINGULAR_DET = 1e-20 # absolute floor on |det ∂(B_R,B_Z)/∂(R,Z)| in T²/m²; it does not scale with ψ₀ or machine size
+const AXIS_STEP_RTOL = 1e-12 # Newton step test, relative to R
+const AXIS_RESIDUAL_RTOL = 1e-10 # bound on |B_p| relative to B_scale, applied on the restart path only
+const AXIS_SEED_CELL_TOL = 0.1 # the bisection sweep has settled when a pass moves the point by less than this many cells
+const AXIS_SEED_PASSES = 50
+const AXIS_PSI_RATIO = (0.5, 2.0) # accepted band of ψ(axis)/ψ₀; every reader puts ψ = ψ₀ at the axis
+const SEPARATRIX_STEPS = 2000 # the Fortran allows more Newton steps here than for the axis solve
+
+_axis_jacobian_det(bf::DirectBField) = bf.brr * bf.bzz - bf.brz * bf.bzr
+
+# Poloidal-field scale |ψ₀| / (R ΔR), about a sixth of the edge poloidal field.
+_axis_field_scale(rp::DirectRunInput, r::Float64) = abs(rp.psio) / (r * (rp.rmax - rp.rmin))
+
+"""
+ _midplane_axis_guess(rp, bfield, sq_in_deriv) -> (r, z, step)
+
+Initial guess for the axis: march outward along the grid's midplane `Z`, in steps of a twentieth of the grid width, until
+`B_z ≥ 0`.
+"""
+function _midplane_axis_guess(rp::DirectRunInput, bfield::DirectBField, sq_in_deriv)
+ r = (rp.rmax + rp.rmin) / 2.0
+ z = (rp.zmax + rp.zmin) / 2.0
+ step = (rp.rmax - rp.rmin) / 20.0
+ for _ in 1:AXIS_MARCH_STEPS
+ direct_get_bfield!(bfield, r, z, rp.psi_in, rp.sq_in, sq_in_deriv, rp.psio; derivs=1)
+ bfield.bz >= 0.0 && return r, z, step
+ r += step
+ end
+ error("Took too many iterations to get bz=0.")
+end
+
+"""
+ _axis_newton(rp, bfield, sq_in_deriv, r, z, cap) -> (r, z, failure)
+
+Newton iteration for the O-point `B_R = B_Z = 0`, each step capped at `cap`. `failure` is `nothing` once a step passes
+`|δR|, |δZ| ≤ AXIS_STEP_RTOL × R`, else why the iteration stopped. A singular Jacobian stops it, where the Fortran divides
+by the determinant unguarded.
+"""
+function _axis_newton(rp::DirectRunInput, bfield::DirectBField, sq_in_deriv, r::Float64, z::Float64, cap::Float64)
+ for _ in 1:AXIS_NEWTON_ITERATIONS
+ direct_get_bfield!(bfield, r, z, rp.psi_in, rp.sq_in, sq_in_deriv, rp.psio; derivs=2)
+ det = _axis_jacobian_det(bfield)
+ abs(det) < AXIS_SINGULAR_DET && return r, z, "stopped on a singular Jacobian, |det ∂(B_R,B_Z)/∂(R,Z)| < $AXIS_SINGULAR_DET"
+ # Δx = -J⁻¹ F
+ δr = (bfield.brz * bfield.bz - bfield.bzz * bfield.br) / det
+ δz = (bfield.bzr * bfield.br - bfield.brr * bfield.bz) / det
+ step = hypot(δr, δz)
+ step > cap && ((δr, δz) = (δr * cap / step, δz * cap / step))
+ r += δr
+ z += δz
+ abs(δr) <= AXIS_STEP_RTOL * abs(r) && abs(δz) <= AXIS_STEP_RTOL * abs(r) && return r, z, nothing
+ end
+ return r, z, "stopped without convergence in $AXIS_NEWTON_ITERATIONS iterations"
+end
+
+"""
+ _axis_bisection_seed(rp, bfield, sq_in_deriv, r, z, halfwidth; passes) -> (r, z, failure)
+
+Seed for the Newton restart: alternate 1-D bisections on `B_Z` along `R` and on `B_R` along `Z`, each bracketed by doubling
+`halfwidth` up to the grid edges. The sweep is a nonlinear Gauss–Seidel iteration that contracts by ψ_RZ²/(ψ_RR ψ_ZZ) per
+pass, so stopping once a pass moves the point by less than `AXIS_SEED_CELL_TOL` cells leaves it within about a cell of the
+axis for contractions up to 0.9. `failure` names a missing sign change or a sweep that did not settle in `passes` passes.
+"""
+function _axis_bisection_seed(rp::DirectRunInput, bfield::DirectBField, sq_in_deriv, r::Float64, z::Float64, halfwidth::Float64;
+ passes::Int=AXIS_SEED_PASSES)
+ _bz(rr, zz) = (direct_get_bfield!(bfield, rr, zz, rp.psi_in, rp.sq_in, sq_in_deriv, rp.psio; derivs=1); bfield.bz)
+ _br(rr, zz) = (direct_get_bfield!(bfield, rr, zz, rp.psi_in, rp.sq_in, sq_in_deriv, rp.psio; derivs=1); bfield.br)
+ hr = (rp.rmax - rp.rmin) / (length(rp.psi_in_xs) - 1)
+ hz = (rp.zmax - rp.zmin) / (length(rp.psi_in_ys) - 1)
+ # Nearest sign change of f around x, bisected to a hundredth of a cell h; `nothing` if the whole grid line has none.
+ function _bracketed_root(f, x, xmin, xmax, h)
+ hw = halfwidth
+ while true
+ lo, hi = max(x - hw, xmin), min(x + hw, xmax)
+ sign(f(lo)) * sign(f(hi)) <= 0 && return find_zero(f, (lo, hi), Roots.Bisection(); xatol=0.01 * h)
+ (lo == xmin && hi == xmax) && return nothing
+ hw *= 2
+ end
+ end
+ for _ in 1:passes
+ r_new = _bracketed_root(rr -> _bz(rr, z), r, rp.rmin, rp.rmax, hr)
+ r_new === nothing && return r, z, "B_z has no sign change along Z = $z"
+ z_new = _bracketed_root(zz -> _br(r_new, zz), z, rp.zmin, rp.zmax, hz)
+ z_new === nothing && return r, z, "B_r has no sign change along R = $r_new"
+ moved = max(abs(r_new - r) / hr, abs(z_new - z) / hz)
+ r, z = r_new, z_new
+ moved < AXIS_SEED_CELL_TOL && return r, z, nothing
+ end
+ return r, z, "the bisection sweep did not settle in $passes passes"
+end
+
+"""
+ _axis_failure(rp, bfield, sq_in_deriv, r, z; bound_residual) -> failure
+
+Why `(r, z)` is not an acceptable magnetic axis, or `nothing`. It must lie on the ψ grid (a root off it is an artifact of
+spline extrapolation), be an O-point (`det ∂(B_R,B_Z)/∂(R,Z) = det(Hess ψ)/R² > 0`; an X-point has `det < 0`) that is a
+maximum of ψ (`ψ_RR < 0` and `ψ > 0`), and carry ψ within `AXIS_PSI_RATIO` of ψ₀, which rejects a secondary maximum
+elsewhere in the grid. With `bound_residual`, `|B_p| ≤ AXIS_RESIDUAL_RTOL × B_scale` must hold as well.
+"""
+function _axis_failure(rp::DirectRunInput, bfield::DirectBField, sq_in_deriv, r::Float64, z::Float64; bound_residual::Bool)
+ (rp.rmin <= r <= rp.rmax && rp.zmin <= z <= rp.zmax) ||
+ return "converged at (R, Z) = ($r, $z), outside the ψ grid R ∈ [$(rp.rmin), $(rp.rmax)], Z ∈ [$(rp.zmin), $(rp.zmax)]"
+ direct_get_bfield!(bfield, r, z, rp.psi_in, rp.sq_in, sq_in_deriv, rp.psio; derivs=2)
+ det = _axis_jacobian_det(bfield)
+ residual = hypot(bfield.br, bfield.bz)
+ det > 0 || return "converged at (R, Z) = ($r, $z), which is not an O-point (det ∂(B_R,B_Z)/∂(R,Z) = $det ≤ 0, |B_p| = $residual T)"
+ (bfield.psirr < 0 && bfield.psi > 0) ||
+ return "converged at (R, Z) = ($r, $z), an O-point that is not the maximum of ψ (ψ = $(bfield.psi), ψ_RR = $(bfield.psirr))"
+ lo, hi = AXIS_PSI_RATIO
+ lo < bfield.psi / rp.psio < hi ||
+ return "converged at (R, Z) = ($r, $z), a maximum of ψ that is not the main axis (ψ/ψ₀ = $(bfield.psi / rp.psio), outside ($lo, $hi))"
+ if bound_residual
+ bound = AXIS_RESIDUAL_RTOL * _axis_field_scale(rp, r)
+ residual <= bound || return "converged at (R, Z) = ($r, $z) with |B_p| = $residual T, above $AXIS_RESIDUAL_RTOL × B_scale = $bound T"
+ end
+ return nothing
+end
+
+# Field diagnostics at an accepted axis, for the restart warning.
+function _axis_diagnostics(rp::DirectRunInput, bfield::DirectBField, sq_in_deriv, r::Float64, z::Float64)
+ direct_get_bfield!(bfield, r, z, rp.psi_in, rp.sq_in, sq_in_deriv, rp.psio; derivs=2)
+ residual = hypot(bfield.br, bfield.bz)
+ return "at (R, Z) = ($r, $z) with |B_p| = $residual T ($(residual / _axis_field_scale(rp, r)) × B_scale) and " *
+ "det ∂(B_R,B_Z)/∂(R,Z) = $(_axis_jacobian_det(bfield)) T²/m²"
+end
+
+"""
+ _find_magnetic_axis(rp, bfield, sq_in_deriv, r0, z0, march_step) -> (r, z)
+
+The magnetic axis, by the first attempt whose Newton result passes `_axis_failure`: plain Newton from the midplane guess
+`(r0, z0)`, accepted on the step test alone, then Newton restarted from
+a bisection seed with steps capped at one march step and the residual bound added. A restart warns with the field at the
+axis; two failures error.
+"""
+function _find_magnetic_axis(rp::DirectRunInput, bfield::DirectBField, sq_in_deriv, r0::Float64, z0::Float64, march_step::Float64)
+ restart_cap = march_step # Newton step cap on the restart path
+ seed_halfwidth = march_step # initial bracket half-width of the bisection seed
+ attempts = (
+ (label="Newton from the midplane guess", seed=() -> (r0, z0, nothing), cap=Inf, bound_residual=false),
+ (label="Newton restarted from a first-derivative bisection seed",
+ seed=() -> _axis_bisection_seed(rp, bfield, sq_in_deriv, r0, z0, seed_halfwidth), cap=restart_cap, bound_residual=true)
+ )
+ failures = String[]
+ for a in attempts
+ rs, zs, why = a.seed()
+ if why !== nothing
+ push!(failures, "$(a.label): the seed failed, $why")
+ continue
+ end
+ r, z, why = _axis_newton(rp, bfield, sq_in_deriv, rs, zs, a.cap)
+ why === nothing && (why = _axis_failure(rp, bfield, sq_in_deriv, r, z; bound_residual=a.bound_residual))
+ if why === nothing
+ isempty(failures) || @warn "$(join(failures, "; ")); magnetic axis found by $(a.label) " *
+ "$(_axis_diagnostics(rp, bfield, sq_in_deriv, r, z)). Check ψ near the axis in the equilibrium file."
+ return r, z
+ end
+ push!(failures, "$(a.label) $why")
+ end
+ error("Failed to find magnetic axis: $(join(failures, "; ")).")
+end
+
+"""
+ _separatrix_crossing(rp, bfield, sq_in_deriv, ro, zo, r_edge, label) -> r
+
+Midplane separatrix crossing on the `r_edge` side of the axis: unbracketed Newton `δR = −ψ/ψ_R` toward ψ = 0 of the
+renormalized spline, as in the Fortran, so that it extrapolates past the grid edge for limited equilibria whose box hugs
+the LCFS. Each failed attempt moves the initial guess, a blend of `r_edge` and the axis, inward.
+"""
+function _separatrix_crossing(rp::DirectRunInput, bfield::DirectBField, sq_in_deriv, ro::Float64, zo::Float64, r_edge::Float64, label::String)
+ for restart in 0:5
+ r = ((3 - 0.5 * restart) * r_edge + ro) / (4 - 0.5 * restart)
+ for _ in 1:SEPARATRIX_STEPS
+ direct_get_bfield!(bfield, r, zo, rp.psi_in, rp.sq_in, sq_in_deriv, rp.psio; derivs=1)
+ dr = -bfield.psi / bfield.psir
+ r += dr
+ if abs(dr) <= AXIS_STEP_RTOL * abs(r)
+ @info "$label separatrix found at R = $(@sprintf("%.3f", r))"
+ return r
+ end
+ end
+ end
+ error("Took too many steps to find $label separatrix.")
+end
+
+"""
+ direct_position!(raw_profile)
+
+Finds the magnetic axis (O-point, see `_find_magnetic_axis`) and the inboard and outboard separatrix crossings on its
+midplane, and replaces the `ψ(R, Z)` spline in `raw_profile` by one renormalized so that ψ at the axis equals ψ₀.
+A g-file whose header signs disagree with its ψ grid errors here.
+
+## Returns
+
+ - `ro`, `zo`: magnetic axis coordinates, in m
+ - `rs1`, `rs2`: R of the inboard and outboard separatrix crossings, in m
+"""
+function direct_position!(raw_profile::DirectRunInput)
+ bfield = DirectBField()
+ sq_in_deriv = deriv1(raw_profile.sq_in)
+
+ r0, z0, march_step = _midplane_axis_guess(raw_profile, bfield, sq_in_deriv)
+ ro, zo = _find_magnetic_axis(raw_profile, bfield, sq_in_deriv, r0, z0, march_step)
+ @info "Magnetic axis found at R = $(@sprintf("%.3f", ro)), Z = $(@sprintf("%.3f", zo))"
+
+ # Renormalize psi based on the value at the magnetic axis
+ direct_get_bfield!(bfield, ro, zo, raw_profile.psi_in, raw_profile.sq_in, sq_in_deriv, raw_profile.psio; derivs=0)
+ x_coords = raw_profile.psi_in_xs
+ y_coords = raw_profile.psi_in_ys
+ # partials[1, :, :] holds the nodal ψ values
+ new_psi_fs = raw_profile.psi_in.nodal_derivs.partials[1, :, :] .* raw_profile.psio / bfield.psi
+ raw_profile.psi_in = cubic_interp((x_coords, y_coords), new_psi_fs; extrap=ExtendExtrap())
+
+ rs1 = _separatrix_crossing(raw_profile, bfield, sq_in_deriv, ro, zo, raw_profile.rmin, "inboard")
+ rs2 = _separatrix_crossing(raw_profile, bfield, sq_in_deriv, ro, zo, raw_profile.rmax, "outboard")
+
+ return ro, zo, rs1, rs2
+end
+
+"""
+ sfl_sample_time(sol, ts, sfl, sfl_index, x) -> (t, lo)
+
+Solver time `t` at which the normalised straight-fieldline angle reaches `x` ∈ [0, 1], and the index
+`lo` of the saved step that starts its bracket. `sfl` is the SFL integral ∫jac·dl/Bp at the saved
+times `ts`; it is monotone, so it brackets the root to one step, and Brent finishes on component
+`sfl_index` of the dense solution.
+"""
+function sfl_sample_time(sol, ts::Vector{Float64}, sfl::AbstractVector{Float64}, sfl_index::Int, x::Float64)
+ n = length(ts)
+ x <= 0 && return ts[1], 1
+ x >= 1 && return ts[n], n - 1
+ target = x * sfl[n]
+ hi = clamp(searchsortedfirst(sfl, target), 2, n)
+ lo = hi - 1
+ flo, fhi = sfl[lo] - target, sfl[hi] - target
+ flo == 0 && return ts[lo], lo
+ fhi == 0 && return ts[hi], lo
+ flo < 0 < fhi || error("sfl_sample_time: SFL integral is not monotone across a solver step (x = $x)")
+ return find_zero(t -> sol(t)[sfl_index] - target, (ts[lo], ts[hi]), Roots.Brent()), lo
+end
+
+"""
+ sample_trace_at_sfl_angles(sol, y_out, sfl_index, theta_nodes, state_row) -> Matrix{Float64}
+
+Sample a traced flux surface at the straight-fieldline angles `theta_nodes` (0 to 1). Row `i` is
+`state_row(sol(t), t, lo)` at the time `t` where the normalised SFL angle reaches `theta_nodes[i]`
+(see `sfl_sample_time`), in the 5-column `y_out` layout. The last row is the saved closed endpoint,
+so the surface totals `y_out[end, :]` are exact. Every surface sharing the same abscissae keeps the
+resample error from varying between neighbouring surfaces. Every field-line tracer must return its
+surface through this function.
+"""
+function sample_trace_at_sfl_angles(sol, y_out::Matrix{Float64}, sfl_index::Int, theta_nodes, state_row::F) where {F}
+ ts = sol.t::Vector{Float64}
+ sfl = view(y_out, :, 5)
+ samples = Matrix{Float64}(undef, length(theta_nodes), 5)
+ for i in 1:(length(theta_nodes)-1)
+ t, lo = sfl_sample_time(sol, ts, sfl, sfl_index, Float64(theta_nodes[i]))
+ samples[i, :] .= state_row(sol(t), t, lo)
+ end
+ samples[end, :] .= @view y_out[end, :]
+ return samples
+end
+
+"""
+ direct_fieldline_int(psifac, raw_profile, ro, zo, rs2, theta_nodes) -> (y_out, bfield)
+
+Traces the flux surface `psifac` (ψ_norm) in the geometric angle η from the outboard midplane, refining onto the
+surface after every step.
+
+## Arguments
+
+ - `ro`, `zo`: magnetic axis coordinates, in m
+ - `rs2`: R of the outboard separatrix crossing, in m
+ - `theta_nodes`: straight-fieldline angles (0 to 1) at which to sample the surface
+
+## Returns
+
+ - `y_out`: rows at `theta_nodes` (see `sample_trace_at_sfl_angles`), columns η, ∫dl/Bp, rfac (distance from the axis),
+ ∫dl/(R²Bp), ∫jac·dl/Bp
+ - `bfield`: the `DirectBField` at the start point
+"""
+function direct_fieldline_int(psifac::Float64, raw_profile::DirectRunInput, ro::Float64, zo::Float64, rs2::Float64,
+ theta_nodes)::Tuple{Matrix{Float64},DirectBField}
+
+ # Find the starting point on the flux surface (outboard midplane)
+ psi0_guess = raw_profile.psio * (1.0 - psifac)
+ r = ro + sqrt(psifac) * (rs2 - ro)
+ z = zo
+ bfield = DirectBField()
+ sq_in_deriv = deriv1(raw_profile.sq_in)
+
+ # Refine starting R: find r where ψ(r, zo) = ψ₀. The df closure reads bfield.psir
+ # which is populated by the preceding f call — Newton guarantees f is evaluated first.
+ r = find_zero(
+ (r -> (direct_get_bfield!(bfield, r, z, raw_profile.psi_in, raw_profile.sq_in, sq_in_deriv, raw_profile.psio; derivs=1); bfield.psi - psi0_guess),
+ _ -> bfield.psir),
+ r, Roots.Newton()
+ )
+
+ direct_get_bfield!(bfield, r, z, raw_profile.psi_in, raw_profile.sq_in, sq_in_deriv, raw_profile.psio; derivs=2)
+ psi0 = bfield.psi
+
+ # Initial state [∫dl/Bp, rfac, ∫dl/(R²Bp), ∫jac·dl/Bp]
+ u0 = zeros(Float64, 4)
+ u0[2] = sqrt((r - ro)^2 + (z - zo)^2)
+
+ # The ODE right-hand side overwrites its own field buffer, so keep `bfield` at the start point (F, P at ψ₀).
+ bfield_ode = DirectBField()
+ equil_config = raw_profile.config
+ params = FieldLineDerivParams(ro, zo, raw_profile.psi_in, raw_profile.sq_in, sq_in_deriv, raw_profile.psio,
+ equil_config.power_bp, equil_config.power_b, equil_config.power_r, equil_config.power_rc, bfield_ode)
+
+ # Use a callback to refine the solution at each step to stay on the flux surface
+ function refine_affect!(integrator)
+ integrator.u[2] = direct_refine(integrator.u[2], integrator.t, psi0, params)
+ end
+
+ # Save each step before refinement, as the Fortran does
+ callback = DiscreteCallback((u, t, i) -> true, refine_affect!; save_positions=(true, false))
+
+ prob = ODEProblem{true}(direct_fieldline_der!, u0, (0.0, 2π), params)
+ # Dense output so the surface can be sampled at prescribed SFL angles between solver steps.
+ rtol = equil_config.flux_surface_rtol
+ sol = solve(prob, Vern9(); callback=callback, reltol=rtol, abstol=equil_abstol(rtol), dt=2π / 200, adaptive=true, dense=true)
+
+ # A failed solve returns a truncated solution instead of throwing; check both the retcode and
+ # that the field line reached η = 2π, since a callback can end it early and still report Success.
+ if sol.retcode != ReturnCode.Success
+ error(
+ "direct_fieldline_int: field-line integration failed at psifac = " *
+ "$(@sprintf("%.6f", psifac)) (retcode $(sol.retcode)); the flux surface did not " *
+ "close. This usually means psihigh is too close to the separatrix for the " *
+ "equilibrium grid to resolve."
+ )
+ end
+ if !isapprox(sol.t[end], 2π; atol=1e-8)
+ error(
+ "direct_fieldline_int: field-line integration at psifac = " *
+ "$(@sprintf("%.6f", psifac)) stopped at eta = $(@sprintf("%.6f", sol.t[end])) " *
+ "instead of 2*pi; the flux surface did not close."
+ )
+ end
+
+ sol_matrix = reduce(hcat, sol.u::Vector{Vector{Float64}})'
+ y_out = hcat(sol.t::Vector{Float64}, sol_matrix)
+ # State is [∫dl/Bp, rfac, ∫dl/(R²Bp), ∫jac·dl/Bp] and the integration variable is η itself.
+ return sample_trace_at_sfl_angles(sol, y_out, 4, theta_nodes, (u, eta, _) -> (eta, u[1], u[2], u[3], u[4])), bfield
+end
+
+"""
+ direct_fieldline_der!(dy, y, params, eta)
+
+Right-hand side of the geometric-angle field-line ODE, with state `y = [∫dl/Bp, rfac, ∫dl/(R²Bp), ∫jac·dl/Bp]` and
+independent variable the geometric angle `eta`. Port of Fortran `direct_fl_der`, guarded against a vanishing denominator.
+"""
+function direct_fieldline_der!(dy, y, params::FieldLineDerivParams, eta)
+
+ cos_eta, sin_eta = cos(eta), sin(eta)
+ r = params.ro + y[2] * cos_eta
+ z = params.zo + y[2] * sin_eta
+ direct_get_bfield!(params.bfield, r, z, params.psi_in, params.sq_in, params.sq_in_deriv, params.psio; derivs=1)
+
+ bp = sqrt(params.bfield.br^2 + params.bfield.bz^2)
+ bt = params.bfield.f / r
+ b = sqrt(bp^2 + bt^2)
+ rfac = y[2]
+ jac = (bp^params.power_bp) * (b^params.power_b) / (r^params.power_r * rfac^params.power_rc)
+
+ # Denominator for d(l_pol)/d(eta) = rfac |B_pol|/denominator
+ denominator = params.bfield.bz * cos_eta - params.bfield.br * sin_eta
+ if abs(denominator) < 1e-14
+ fill!(dy, 1e20) # Return large derivatives for solver to handle stiffness
+ @warn "Denominator in direct_fieldline_der! near zero at eta=$eta."
+ return
+ end
+
+ # d/dη [∫(dl/Bp)] = 1/|B_P| dl/d(eta) = rfac/denominator
+ dy[1] = y[2] / denominator
+ # d(rfac)/d(eta) = rfac/denom *( Br cos(eta) + Bz sin(eta) )
+ dy[2] = dy[1] * (params.bfield.br * cos_eta + params.bfield.bz * sin_eta)
+ # d/dη [∫(dl/(R²Bp))]
+ dy[3] = dy[1] / (r^2)
+ # d/dη [∫(jac*dl/Bp)]
+ dy[4] = dy[1] * jac
+end
+
+"""
+ direct_refine(rfac, eta, psi0, params) -> Float64
+
+Newton-refines the distance `rfac` from the axis at geometric angle `eta` so the point lies on the surface ψ = `psi0`.
+"""
+function direct_refine(rfac::Float64, eta::Float64, psi0::Float64, params::FieldLineDerivParams)::Float64
+ cos_eta, sin_eta = cos(eta), sin(eta)
+
+ function f(rfac_inner)
+ r = params.ro + rfac_inner * cos_eta
+ z = params.zo + rfac_inner * sin_eta
+ direct_get_bfield!(params.bfield, r, z, params.psi_in, params.sq_in,
+ params.sq_in_deriv, params.psio; derivs=0)
+ return params.bfield.psi - psi0
+ end
+
+ function fp(rfac_inner)
+ r = params.ro + rfac_inner * cos_eta
+ z = params.zo + rfac_inner * sin_eta
+ direct_get_bfield!(params.bfield, r, z, params.psi_in, params.sq_in,
+ params.sq_in_deriv, params.psio; derivs=1)
+ return params.bfield.psir * cos_eta + params.bfield.psiz * sin_eta
+ end
+
+ return find_zero((f, fp), rfac, Roots.Newton();
+ atol=1e-12 * abs(psi0), rtol=1e-12, maxevals=50)
+end
+
+"""
+ equilibrium_solver(raw_profile, fieldline_int=direct_fieldline_int; override_psi_nodes=nothing) -> PlasmaEquilibrium
+
+Direct equilibrium driver: locates the axis, traces each flux surface with `fieldline_int`, and builds the profile,
+`rzphi` coordinate and `eqfun` splines in straight-fieldline coordinates.
+
+## Arguments
+
+ - `fieldline_int`: flux-surface tracer, called as `fieldline_int(psifac, raw_profile, ro, zo, rs2, theta_nodes) -> (y_out, bfield)`
+ with `y_out` sampled at `theta_nodes` through `sample_trace_at_sfl_angles`
+ - `override_psi_nodes`: explicit ψ grid used instead of the configured one
+"""
+@with_pool pool function equilibrium_solver(raw_profile::DirectRunInput, fieldline_int=direct_fieldline_int;
+ override_psi_nodes::Union{Nothing,Vector{Float64}}=nothing)
+
+ equil_params = raw_profile.config
+ psio = raw_profile.psio
+ mtheta = equil_params.mtheta
+ psilow = equil_params.psilow
+ psihigh = raw_profile.psihigh_resolved
+
+ # Locate the magnetic axis and separatrix for the field-line integrations
+ ro, zo, _, rs2 = direct_position!(raw_profile)
+
+ psi_nodes = override_psi_nodes === nothing ?
+ _build_psi_grid(equil_params, psilow, psihigh) :
+ _validate_psi_nodes(override_psi_nodes, psilow, psihigh)
+ mpsi = length(psi_nodes) - 1
+ theta_nodes = range(0.0, 1.0; length=mtheta + 1)
+
+ ff_x_nodes = collect(theta_nodes)
+ sq_nodes = zeros!(pool, Float64, mpsi + 1, 4)
+ rzphi_nodes = zeros!(pool, Float64, mpsi + 1, mtheta + 1, 4)
+ ff_val = zeros!(pool, Float64, 4)
+ ff_deriv_val = zeros!(pool, Float64, 4)
+
+ for ipsi in (mpsi+1):-1:1 # outermost to innermost
+ # Every tracer returns the surface sampled at theta_nodes, so all surfaces share SFL abscissae.
+ y_out, bfield = fieldline_int(psi_nodes[ipsi], raw_profile, ro, zo, rs2, theta_nodes)
+ checkpoint!(pool, Float64)
+
+ ff_fs_nodes = acquire!(pool, Float64, mtheta + 1, 4)
+ @. ff_fs_nodes[:, 1] = @view(y_out[:, 3])^2
+ @. ff_fs_nodes[:, 2] = @view(y_out[:, 1]) / (2π) - ff_x_nodes
+ @. ff_fs_nodes[:, 3] = bfield.f * (@view(y_out[:, 4]) - ff_x_nodes * y_out[end, 4])
+ @. ff_fs_nodes[:, 4] = @view(y_out[:, 2]) / y_out[end, 2] - ff_x_nodes
+
+ ff_fs_nodes[end, :] .= ff_fs_nodes[1, :] # enforce periodic endpoint
+
+ ff_interp = cubic_interp(ff_x_nodes, Series(ff_fs_nodes); bc=PeriodicBC())
+ ff_deriv = deriv1(ff_interp)
+
+ # Evaluate the θ-fit and its derivative at the nodes (the Jacobian needs the derivative)
+ for itheta in 1:(mtheta+1)
+ theta = theta_nodes[itheta]
+ ff_interp(ff_val, theta)
+ ff_deriv(ff_deriv_val, theta)
+
+ rzphi_nodes[ipsi, itheta, 1] = ff_val[1]
+ rzphi_nodes[ipsi, itheta, 2] = ff_val[2]
+ rzphi_nodes[ipsi, itheta, 3] = ff_val[3]
+ rzphi_nodes[ipsi, itheta, 4] = (1.0 + ff_deriv_val[4]) * y_out[end, 2] * 2π * psio
+ end
+
+ sq_nodes[ipsi, 1] = bfield.f * 2π
+ sq_nodes[ipsi, 2] = bfield.p
+ sq_nodes[ipsi, 3] = y_out[end, 2] * 2π * psio
+ sq_nodes[ipsi, 4] = y_out[end, 4] * bfield.f / (2π)
+ rewind!(pool, Float64)
+ end
+
+ # Temporary splines for q0 extrapolation and optional newq0 revision
+ profiles = ProfileSplines(
+ psi_nodes,
+ sq_nodes[:, 1], # F * 2π
+ sq_nodes[:, 2], # P * μ₀
+ sq_nodes[:, 3], # dV/dψ
+ sq_nodes[:, 4] # q
+ )
+ # q(0) by linear extrapolation from innermost surface
+ q0 = profiles.q_spline.y[1] - profiles.q_deriv(psi_nodes[1]; hint=Ref(1)) * psi_nodes[1]
+ if q0 <= 0.0
+ @warn "q0 extrapolation to axis gives q0 = $(@sprintf("%.3f", q0)) ≤ 0 — likely a spline artifact from psilow being too large; check psilow or use newq0 to override."
+ end
+ newq0 = equil_params.newq0
+ if newq0 != 0.0
+ @info "Revising q-profile for newq0 = $(@sprintf("%.3f", newq0))"
+ f0 = profiles.F_spline.y[1] - profiles.F_deriv(psi_nodes[1]; hint=Ref(1)) * psi_nodes[1]
+ f0fac = f0^2 * ((newq0 / q0)^2 - 1.0)
+ for i in 1:(mpsi+1)
+ ffac = sqrt(1.0 + f0fac / profiles.F_spline.y[i]^2)
+ sq_nodes[i, 1] *= ffac
+ sq_nodes[i, 4] *= ffac
+ rzphi_nodes[i, :, 3] .*= ffac
+ end
+ profiles = ProfileSplines(
+ psi_nodes,
+ sq_nodes[:, 1], # F * 2π
+ sq_nodes[:, 2], # P * μ₀
+ sq_nodes[:, 3], # dV/dψ
+ sq_nodes[:, 4] # q
+ )
+ end
+
+ rzphi_xs = psi_nodes
+ # rzphi_ys is a materialized Vector (not the Range) so PlasmaEquilibrium can index it directly
+ rzphi_ys = collect(theta_nodes)
+
+ grid2d = (rzphi_xs, theta_nodes)
+ opts2d = (bc=(CubicFit(), PeriodicBC()), extrap=(ExtendExtrap(), WrapExtrap()))
+
+ # Snap periodic endpoint: ff_interp evaluation at theta_nodes[end] may drift by machine eps from theta_nodes[1]
+ @views rzphi_nodes[:, end, :] .= rzphi_nodes[:, 1, :]
+
+ rzphi_rsquared = cubic_interp(grid2d, rzphi_nodes[:, :, 1]; opts2d...)
+ rzphi_offset = cubic_interp(grid2d, rzphi_nodes[:, :, 2]; opts2d...)
+ rzphi_nu = cubic_interp(grid2d, rzphi_nodes[:, :, 3]; opts2d...)
+ rzphi_jac = cubic_interp(grid2d, rzphi_nodes[:, :, 4]; opts2d...)
+
+ eqfun_B, eqfun_metric1, eqfun_metric2 = _eqfun_from_geometry(
+ profiles, rzphi_rsquared, rzphi_offset, rzphi_nu, rzphi_jac, ro, psio, grid2d, opts2d)
+
+ geometry = compute_geometry_profiles(rzphi_xs, rzphi_ys,
+ rzphi_rsquared, rzphi_offset, rzphi_jac, ro)
+
+ params = EquilibriumParameters()
+ params.bt_sign = raw_profile.bt_sign
+ params.ip_sign = raw_profile.ip_sign
+ params.psihigh_resolved = psihigh
+
+ return PlasmaEquilibrium(raw_profile.config, params, profiles, geometry,
+ rzphi_xs, rzphi_ys,
+ rzphi_rsquared, rzphi_offset, rzphi_nu, rzphi_jac,
+ eqfun_B, eqfun_metric1, eqfun_metric2,
+ ro, zo, psio)
+end
+
+# Reuse the processed geometry when restoring a frozen equilibrium snapshot.
+function _eqfun_from_geometry(profiles, rzphi_rsquared, rzphi_offset, rzphi_nu, rzphi_jac, ro, psio, grid2d, opts2d)
+ mpsi = length(grid2d[1]) - 1
+ theta_nodes = grid2d[2]
+ mtheta = length(theta_nodes) - 1
+ eqfun_fs_nodes = zeros(Float64, mpsi + 1, mtheta + 1, 3)
+ v = @MMatrix zeros(Float64, 2, 3)
+ for ipsi in 1:(mpsi+1)
+ q = profiles.q_spline.y[ipsi]
+ f_val = profiles.F_spline.y[ipsi]
+ for itheta in 1:(mtheta+1)
+ theta_norm = theta_nodes[itheta]
+ # partials indexing: [1,:,:] = f, [2,:,:] = ∂f/∂x, [3,:,:] = ∂f/∂y, [4,:,:] = ∂²f/∂x∂y
+ f = (
+ rzphi_rsquared.nodal_derivs.partials[1, ipsi, itheta],
+ rzphi_offset.nodal_derivs.partials[1, ipsi, itheta],
+ rzphi_nu.nodal_derivs.partials[1, ipsi, itheta],
+ rzphi_jac.nodal_derivs.partials[1, ipsi, itheta]
+ )
+ fx = (
+ rzphi_rsquared.nodal_derivs.partials[2, ipsi, itheta],
+ rzphi_offset.nodal_derivs.partials[2, ipsi, itheta],
+ rzphi_nu.nodal_derivs.partials[2, ipsi, itheta],
+ rzphi_jac.nodal_derivs.partials[2, ipsi, itheta]
+ )
+ fy = (
+ rzphi_rsquared.nodal_derivs.partials[3, ipsi, itheta],
+ rzphi_offset.nodal_derivs.partials[3, ipsi, itheta],
+ rzphi_nu.nodal_derivs.partials[3, ipsi, itheta],
+ rzphi_jac.nodal_derivs.partials[3, ipsi, itheta]
+ )
+ rfac = sqrt(max(0.0, f[1])) # guard against spline overshoot near separatrix
+ eta = 2π * (theta_norm + f[2])
+ r = ro + rfac * cos(eta)
+ jacfac = f[4]
+
+ v[1, 1] = (rfac > 0) ? fx[1] / (2.0 * rfac) : 0.0 # 1/(2rfac) * d(rfac)/d(psi_norm)
+ v[1, 2] = fx[2] * 2π * rfac # 2π*rfac * d(eta)/d(psi_norm)
+ v[1, 3] = fx[3] * r # r * d(phi_s)/d(psi_norm)
+ v[2, 1] = (rfac > 0) ? fy[1] / (2.0 * rfac) : 0.0 # 1/(2rfac) d(rfac)/d(theta_new)
+ v[2, 2] = (1.0 + fy[2]) * 2π * rfac # 2π*rfac * d(eta)/d(theta_new)
+ v[2, 3] = fy[3] * r # r * d(phi_s)/d(theta_new)
+ v33 = 2π * r
+ w11 = (jacfac != 0) ? (1.0 + fy[2]) * (2π)^2 * rfac * r / jacfac : 0.0
+ w12 = (jacfac * rfac != 0) ? -fy[1] * π * r / (rfac * jacfac) : 0.0
+ delpsi_norm = sqrt(w11^2 + w12^2)
+ modB = sqrt(((2π * psio * delpsi_norm)^2 + f_val^2) / (2π * r)^2)
+
+ eqfun_fs_nodes[ipsi, itheta, 1] = modB
+ denom = jacfac * modB^2
+ if abs(denom) > 1e-20
+ numerator_2 = dot(v[1, :], v[2, :]) + q * v33 * v[1, 3] # gyrokinetic C1
+ eqfun_fs_nodes[ipsi, itheta, 2] = numerator_2 / denom
+ numerator_3 = v[2, 3] * v33 + q * v33^2 # gyrokinetic C2
+ eqfun_fs_nodes[ipsi, itheta, 3] = numerator_3 / denom
+ else
+ eqfun_fs_nodes[ipsi, itheta, 2] = 0.0
+ eqfun_fs_nodes[ipsi, itheta, 3] = 0.0
+ end
+ end
+ end
+
+ @views eqfun_fs_nodes[:, end, :] .= eqfun_fs_nodes[:, 1, :]
+
+ eqfun_B = cubic_interp(grid2d, eqfun_fs_nodes[:, :, 1]; opts2d...)
+ eqfun_metric1 = cubic_interp(grid2d, eqfun_fs_nodes[:, :, 2]; opts2d...)
+ eqfun_metric2 = cubic_interp(grid2d, eqfun_fs_nodes[:, :, 3]; opts2d...)
+
+ return eqfun_B, eqfun_metric1, eqfun_metric2
+end
diff --git a/src/Equilibrium/Axisymmetric/DirectArcLength.jl b/src/Equilibrium/Axisymmetric/DirectArcLength.jl
new file mode 100644
index 0000000000..2d60e54854
--- /dev/null
+++ b/src/Equilibrium/Axisymmetric/DirectArcLength.jl
@@ -0,0 +1,156 @@
+"""
+Arc-length parameterized field-line integration for the direct (EFIT) equilibrium path.
+
+Provides `arclength_fieldline_int`, a drop-in replacement for `direct_fieldline_int` selected by
+`eq_type = "efit_arclength"` in `gpec.toml`. Integrating along the tangent to ψ = const avoids the
+denominator singularity of the geometric-angle ODE near x-points.
+"""
+
+"""
+ arclength_fieldline_der!(dy, y, params, s)
+
+RHS for the arc-length-parameterized level-set ODE.
+
+State `y = [R, Z, ∫dl/Bp, ∫dl/(R²Bp), ∫jac·dl/Bp]`.
+The independent variable `s` is arc length, in m.
+
+The tangent direction `(dR/ds, dZ/ds) = (∂ψ/∂Z, −∂ψ/∂R) / |∇ψ|` follows the
+ψ = const level set counterclockwise, staying on the flux surface without correction.
+
+Near x-points where Bp → 0, the position integration (dy[1:2]) remains well-behaved
+because `grad_norm` never appears in the denominator alone. dy[3:5] use abstol=1e20
+so the solver never restricts step size for them.
+"""
+@with_pool pool function arclength_fieldline_der!(dy, y, params::FieldLineDerivParams, _s)
+ R, Z = y[1], y[2]
+ direct_get_bfield!(params.bfield, R, Z, params.psi_in, params.sq_in, params.sq_in_deriv, params.psio; derivs=1)
+
+ psir = params.bfield.psir # ∂ψ/∂R
+ psiz = params.bfield.psiz # ∂ψ/∂Z
+ grad_norm = sqrt(psir^2 + psiz^2)
+
+ if grad_norm < 1e-14
+ fill!(dy, 0.0)
+ @warn "Near-zero |∇ψ| at (R=$R, Z=$Z) in arc-length ODE — likely near O-point."
+ return
+ end
+
+ # Level-set tangent (CCW orientation)
+ dy[1] = psiz / grad_norm # dR/ds
+ dy[2] = -psir / grad_norm # dZ/ds
+
+ # Bp = |∇ψ| / R (poloidal field [T])
+ Bp = grad_norm / R
+
+ Bp_eff = max(Bp, eps(Float64)) # absolute guard against exact Bp=0 only
+ dy[3] = 1.0 / Bp_eff # d/ds [∫dl/Bp]
+ dy[4] = 1.0 / (R^2 * Bp_eff) # d/ds [∫dl/(R²Bp)]
+
+ # d/ds [∫jac·dl/Bp]: integrand = Bp^(power_bp−1) · B^power_b / (R^power_r · rfac^power_rc)
+ Bt = params.bfield.f / R
+ B_val = sqrt(Bp^2 + Bt^2)
+ rfac = sqrt((R - params.ro)^2 + (Z - params.zo)^2)
+ rfac_eff = max(rfac, eps(Float64))
+ dy[5] = Bp_eff^(params.power_bp - 1) * B_val^params.power_b / (R^params.power_r * rfac_eff^params.power_rc)
+end
+
+"""
+ arclength_fieldline_int(psifac, raw_profile, ro, zo, rs2, theta_nodes) -> (y_out, bfield)
+
+Arc-length-parameterized flux surface integration. Drop-in replacement for
+`direct_fieldline_int` with identical return format, sampled at the straight-fieldline angles
+`theta_nodes` (see `sample_trace_at_sfl_angles`):
+
+ - `y_out[:, 1]`: geometric angle η ∈ 0 to 2π (CCW from outboard midplane)
+ - `y_out[:, 2]`: accumulated ∫dl/Bp
+ - `y_out[:, 3]`: rfac = √((R−ro)² + (Z−zo)²)
+ - `y_out[:, 4]`: accumulated ∫dl/(R²Bp)
+ - `y_out[:, 5]`: accumulated ∫jac·dl/Bp
+
+The ODE is terminated by a `ContinuousCallback` that detects the return to the
+outboard midplane (Z = zo, R > ro) after a minimum arc-length guard.
+"""
+@with_pool pool function arclength_fieldline_int(
+ psifac::Float64, raw_profile::DirectRunInput, ro::Float64, zo::Float64, rs2::Float64, theta_nodes
+)::Tuple{Matrix{Float64},DirectBField}
+
+ psi0_guess = raw_profile.psio * (1.0 - psifac)
+ r = ro + sqrt(psifac) * (rs2 - ro)
+ z = zo
+ bfield = DirectBField()
+ sq_in_deriv = deriv1(raw_profile.sq_in)
+
+ # Refine starting point — same Newton solve as direct_fieldline_int
+ r = find_zero(
+ (r_in -> (direct_get_bfield!(bfield, r_in, z, raw_profile.psi_in, raw_profile.sq_in, sq_in_deriv, raw_profile.psio; derivs=1); bfield.psi - psi0_guess),
+ _ -> bfield.psir),
+ r, Roots.Newton()
+ )
+
+ direct_get_bfield!(bfield, r, z, raw_profile.psi_in, raw_profile.sq_in, sq_in_deriv, raw_profile.psio; derivs=2)
+
+ # Initial state: [R, Z, ∫dl/Bp, ∫dl/(R²Bp), ∫jac·dl/Bp]
+ u0 = Float64[r, z, 0.0, 0.0, 0.0]
+
+ equil_config = raw_profile.config
+ bfield_ode = DirectBField()
+ params = FieldLineDerivParams(ro, zo, raw_profile.psi_in, raw_profile.sq_in, sq_in_deriv, raw_profile.psio,
+ equil_config.power_bp, equil_config.power_b, equil_config.power_r, equil_config.power_rc, bfield_ode)
+
+ t_min = π * (r - ro) # minimum arc before termination (half-circumference lower bound)
+ condition(u, _t, integrator) = u[2] - zo
+ function affect_upward!(integrator)
+ if integrator.t > t_min
+ terminate!(integrator)
+ end
+ end
+ callback = ContinuousCallback(condition, affect_upward!, nothing; save_positions=(true, false))
+
+ prob = ODEProblem{true}(arclength_fieldline_der!, u0, (0.0, 1.0e4), params)
+ # Tight tolerances on position (y[1:2]); integrals (y[3:5]) effectively unconstrained near x-points
+ reltol_vec = [equil_config.flux_surface_rtol, equil_config.flux_surface_rtol, 1e20, 1e20, 1e20]
+ abstol_vec = [equil_abstol(equil_config.flux_surface_rtol), equil_abstol(equil_config.flux_surface_rtol), 1e20, 1e20, 1e20]
+ sol = solve(prob, BS5(); callback=callback, reltol=reltol_vec, abstol=abstol_vec,
+ dt=2π / 200, adaptive=true, dense=true)
+ # The only complete ending is the callback's terminate! on return to the midplane; Success means it never fired.
+ sol.retcode == ReturnCode.Terminated || error(
+ "arclength_fieldline_int: field line at psifac = $(@sprintf("%.6f", psifac)) did not return to the midplane " *
+ "(retcode $(sol.retcode) at arc length $(sol.t[end])); the flux surface did not close. " *
+ "This usually means psihigh is too close to the separatrix for the equilibrium grid to resolve."
+ )
+
+ n = length(sol.u)
+ y_out = Matrix{Float64}(undef, n, 5)
+
+ # Compute geometric angles and unwrap to monotone [0, 2π]
+ η_atan = [atan(sol.u[i][2] - zo, sol.u[i][1] - ro) for i in 1:n]
+ η_raw = copy(η_atan)
+ for i in 2:n
+ Δ = η_raw[i] - η_raw[i-1]
+ if Δ > π
+ η_raw[i:end] .-= 2π
+ elseif Δ < -π
+ η_raw[i:end] .+= 2π
+ end
+ end
+ η_unwrapped = η_raw .- η_raw[1] # shift so first point is 0
+ η_unwrapped[end] = 2π # enforce exact 2π at the closed endpoint
+
+ for i in 1:n
+ R_i, Z_i = sol.u[i][1], sol.u[i][2]
+ y_out[i, 1] = η_unwrapped[i]
+ y_out[i, 2] = sol.u[i][3]
+ y_out[i, 3] = sqrt((R_i - ro)^2 + (Z_i - zo)^2)
+ y_out[i, 4] = sol.u[i][4]
+ y_out[i, 5] = sol.u[i][5]
+ end
+
+ # The integration variable is arc length, so η at a sample is unwrapped against its bracketing step.
+ function state_row(u, _s, lo)
+ η = y_out[lo, 1] + rem2pi(atan(u[2] - zo, u[1] - ro) - η_atan[lo], RoundNearest)
+ return (η, u[3], sqrt((u[1] - ro)^2 + (u[2] - zo)^2), u[4], u[5])
+ end
+
+ # bfield at the starting point carries F and P for the surface-averaged quantities
+ return sample_trace_at_sfl_angles(sol, y_out, 5, theta_nodes, state_row), bfield
+end
diff --git a/src/Equilibrium/Axisymmetric/DirectByInversion.jl b/src/Equilibrium/Axisymmetric/DirectByInversion.jl
new file mode 100644
index 0000000000..a9d06444d3
--- /dev/null
+++ b/src/Equilibrium/Axisymmetric/DirectByInversion.jl
@@ -0,0 +1,704 @@
+"""
+Contour-tracing flux surface reconstruction for the direct (EFIT) equilibrium path.
+
+Traces level sets of ψ(R,Z) using marching squares (`Contour.jl`), resamples each
+closed curve to a uniform geometric-angle grid, constructs an `InverseRunInput`,
+and delegates to the existing `equilibrium_solver(::InverseRunInput)`.
+
+Select via `eq_type = "efit_by_inversion"` in `gpec.toml`.
+"""
+
+import Contour as Ctr
+
+# Round-trip (ψ,θ)→(R,Z)→ψ residual above which the traced edge geometry is not trusted.
+const ROUNDTRIP_TOL = 2e-3
+# Fraction of the radial grid treated as "the edge" for the round-trip check.
+const ROUNDTRIP_EDGE_FRAC = 0.9
+# Max midpoint/on-knot residual ratio before the splines are judged to ring between knots;
+# healthy grids read ~1 and rung ones 10^2-10^3, so the exact value is uncritical.
+const ROUNDTRIP_RATIO_TOL = 10.0
+# Midpoint residual below which the ratio is ignored, as both residuals are then rounding noise.
+const ROUNDTRIP_RINGING_FLOOR = ROUNDTRIP_TOL / 20
+
+# :too_large, :ringing (midpoints far above knots though both are small), or :ok.
+function _roundtrip_verdict(knot_err, mid_err)
+ (knot_err > ROUNDTRIP_TOL || mid_err > ROUNDTRIP_TOL) && return :too_large
+ (mid_err > ROUNDTRIP_RINGING_FLOOR && mid_err > ROUNDTRIP_RATIO_TOL * knot_err) && return :ringing
+ return :ok
+end
+
+"""
+ _is_closed_curve(curve)
+
+Returns true if the Contour.jl curve is closed (first ≈ last vertex).
+"""
+function _is_closed_curve(curve)
+ verts = Ctr.vertices(curve)
+ length(verts) < 3 && return false
+ dx = abs(verts[1][1] - verts[end][1])
+ dz = abs(verts[1][2] - verts[end][2])
+ return dx < 1e-8 && dz < 1e-8
+end
+
+"""
+ _winding_number_verts(verts, r_test, z_test)
+
+Winding number point-in-polygon test (Sunday algorithm) on a `Ctr.vertices` vector.
+Returns the signed winding count; nonzero means the test point is inside the polygon.
+More robust than ray-casting for near-collinear edges (e.g., surfaces near an x-point).
+"""
+function _winding_number_verts(verts, r_test::Float64, z_test::Float64)::Int
+ n = length(verts)
+ wn = 0
+ j = n
+ @inbounds for i in 1:n
+ ri, zi = verts[i]
+ rj, zj = verts[j]
+ if zj <= z_test
+ if zi > z_test
+ cross = (rj - r_test) * (zi - z_test) - (ri - r_test) * (zj - z_test)
+ cross > 0 && (wn += 1)
+ end
+ else
+ if zi <= z_test
+ cross = (rj - r_test) * (zi - z_test) - (ri - r_test) * (zj - z_test)
+ cross < 0 && (wn -= 1)
+ end
+ end
+ j = i
+ end
+ return wn
+end
+
+"""
+ select_plasma_contour(curve_list, ro, zo)
+
+From the list of Contour.jl curves at a given ψ level, return the closed curve
+whose interior contains the magnetic axis (ro, zo).
+
+Returns `nothing` if no qualifying closed curve is found.
+"""
+function select_plasma_contour(curve_list, ro::Float64, zo::Float64)
+ for curve in curve_list
+ _is_closed_curve(curve) || continue
+ verts = Ctr.vertices(curve)
+ _winding_number_verts(verts, ro, zo) != 0 && return curve
+ end
+ return nothing
+end
+
+"""
+ clamp_psihigh_to_separatrix(raw_profile) -> (clamped_psihigh, was_adjusted)
+
+Binary-searches for the highest psihigh ≤ `raw_profile.psihigh_resolved` at which the
+ψ level set is still a closed curve in the EFIT grid. Returns the safe value and a
+Bool indicating whether any clamping occurred.
+"""
+function clamp_psihigh_to_separatrix(raw_profile::DirectRunInput)
+ psihigh = raw_profile.psihigh_resolved
+ ψ_coarse = raw_profile.psi_in.nodal_derivs.partials[1, :, :]
+
+ has_closed_contour(ψ_high) = any(
+ _is_closed_curve,
+ Ctr.lines(Ctr.contour(raw_profile.psi_in_xs, raw_profile.psi_in_ys,
+ ψ_coarse, raw_profile.psio * (1.0 - ψ_high)))
+ )
+
+ has_closed_contour(psihigh) && return (psihigh, false)
+
+ lo = min(0.99, psihigh - 0.1)
+ hi = psihigh
+ for _ in 1:52
+ hi - lo < 1e-10 && break
+ mid = (lo + hi) / 2.0
+ has_closed_contour(mid) ? (lo = mid) : (hi = mid)
+ end
+ return (lo, true)
+end
+
+"""
+ resolve_psihigh!(raw_profile) -> raw_profile
+
+Clamp `raw_profile.psihigh_resolved` to the outermost closed flux surface, warning if the
+requested `psihigh` had none. Mutates and returns the input; `config.psihigh` keeps the request.
+"""
+function resolve_psihigh!(raw_profile::DirectRunInput)
+ psihigh_safe, adjusted = clamp_psihigh_to_separatrix(raw_profile)
+ if adjusted
+ @warn "psihigh=$(raw_profile.psihigh_resolved) has no closed flux surface in EFIT grid; " *
+ "clamped to $(round(psihigh_safe; sigdigits=7))"
+ raw_profile.psihigh_resolved = psihigh_safe
+ end
+ return raw_profile
+end
+
+"""
+ resample_contour_to_theta_grid!(R_out, Z_out, curve, ro, zo, theta_grid)
+
+Resample a Contour.jl curve onto the geometric-angle grid `theta_grid` (in turns), writing into `R_out` and `Z_out`.
+Fits a periodic cubic spline to log ρ(η) about the axis (ro, zo), so the resampled radius stays positive and the
+curve cannot self-intersect, which keeps it robust near x-points where R(η), Z(η) splines overshoot.
+"""
+function resample_contour_to_theta_grid!(
+ R_out::AbstractVector{Float64}, Z_out::AbstractVector{Float64},
+ curve, ro::Float64, zo::Float64, theta_grid::AbstractVector{Float64}
+)
+ verts = Ctr.vertices(curve)
+ nv = length(verts)
+
+ # Drop duplicate closing vertex (Contour.jl closed curves repeat first==last)
+ if nv > 1
+ r1, z1 = verts[1]
+ rn, zn = verts[nv]
+ if abs(r1 - rn) < 1e-8 && abs(z1 - zn) < 1e-8
+ nv -= 1
+ end
+ end
+
+ # Compute geometric angle η and log-radius logρ in one pass
+ η_buf = Vector{Float64}(undef, nv)
+ logρ_buf = Vector{Float64}(undef, nv)
+ @inbounds for i in 1:nv
+ r, z = verts[i]
+ η_buf[i] = mod(atan(z - zo, r - ro), 2π)
+ logρ_buf[i] = log(sqrt((r - ro)^2 + (z - zo)^2))
+ end
+
+ idx = sortperm(η_buf)
+
+ # Build extended (nv+1) sorted arrays with periodic wrap appended
+ n_ext = nv + 1
+ η_ext = Vector{Float64}(undef, n_ext)
+ logρ_ext = Vector{Float64}(undef, n_ext)
+ @inbounds for i in 1:nv
+ k = idx[i]
+ η_ext[i] = η_buf[k]
+ logρ_ext[i] = logρ_buf[k]
+ end
+ η_ext[n_ext] = η_ext[1] + 2π
+ logρ_ext[n_ext] = logρ_ext[1]
+
+ logρ_spl = cubic_interp(η_ext, logρ_ext; bc=PeriodicBC())
+
+ # theta_grid is in turns [0, 1]; sample at 2π*θ radians and convert polar → Cartesian.
+ # Monotonically increasing η → shared hint gives O(1) lookups per step.
+ hint = Ref(1)
+ @inbounds for k in eachindex(theta_grid, R_out, Z_out)
+ η = 2π * theta_grid[k]
+ ρ = exp(logρ_spl(η; hint=hint))
+ R_out[k] = ro + ρ * cos(η)
+ Z_out[k] = zo + ρ * sin(η)
+ end
+end
+
+"""
+ classify_topology(raw_profile, psio; xpt_threshold=0.05) → Symbol
+
+Classify the plasma topology as `:limited`, `:sn_lower`, `:sn_upper`, or `:double_null`
+by evaluating ψ on the (R, Z) grid and finding the minimum in each Z half-domain.
+
+An x-point is detected when the minimum ψ in a half-domain falls below `xpt_threshold * psio`.
+"""
+function classify_topology(raw_profile::DirectRunInput, psio::Float64;
+ xpt_threshold::Float64=0.05)
+ R_grid = raw_profile.psi_in_xs
+ Z_grid = raw_profile.psi_in_ys
+ nZ = length(Z_grid)
+ mid_Z = nZ ÷ 2
+ hint = (Ref(1), Ref(1))
+
+ min_ψ_lower = Inf
+ for jZ in 1:mid_Z
+ hint[1][] = 1 # reset R hint at start of each row; Z hint advances naturally
+ z = Z_grid[jZ]
+ for R in R_grid
+ ψ = raw_profile.psi_in((R, z); hint=hint)
+ min_ψ_lower = min(min_ψ_lower, ψ)
+ end
+ end
+
+ min_ψ_upper = Inf
+ for jZ in (mid_Z+1):nZ
+ hint[1][] = 1
+ z = Z_grid[jZ]
+ for R in R_grid
+ ψ = raw_profile.psi_in((R, z); hint=hint)
+ min_ψ_upper = min(min_ψ_upper, ψ)
+ end
+ end
+
+ has_lower = min_ψ_lower / psio < xpt_threshold
+ has_upper = min_ψ_upper / psio < xpt_threshold
+ if has_lower && has_upper
+ return :double_null
+ elseif has_lower
+ return :sn_lower
+ elseif has_upper
+ return :sn_upper
+ else
+ return :limited
+ end
+end
+
+"""
+ make_multi_stretched_grid(lo, hi, centers, n, β) → Vector{Float64}
+
+Build a 1D grid of length `n` on `[lo, hi]` with sinh-stretching toward each point in
+`centers`. The domain is split at each interior concentration point; each resulting
+sub-interval uses:
+
+ - symmetric (double-ended) sinh when both endpoints are concentration points
+ - one-sided sinh fine at the concentration-point end otherwise
+
+Domain boundaries (`lo`, `hi`) are concentration points only if they appear in `centers`, as x-points do on the
+clipped plasma bounding box. Returns a uniform grid if `β ≤ 0`.
+"""
+function make_multi_stretched_grid(lo::Float64, hi::Float64,
+ centers::Vector{Float64}, n::Int, β::Float64)
+ β ≤ 0.0 && return collect(range(lo, hi; length=n))
+ lo_is_conc = any(c -> abs(c - lo) < 1e-12, centers)
+ hi_is_conc = any(c -> abs(c - hi) < 1e-12, centers)
+ interior = sort!(unique!(filter(c -> lo < c < hi, copy(centers))))
+ nodes = [lo; interior; hi]
+ n_segs = length(nodes) - 1
+ n_segs == 0 && return collect(range(lo, hi; length=n))
+
+ total_len = hi - lo
+ # Distribute n points across segments proportionally; last segment takes the remainder
+ # so concatenation (dropping n_segs-1 shared endpoints) gives exactly n total points.
+ n_segi = Vector{Int}(undef, n_segs)
+ allocated = 0
+ for k in 1:(n_segs-1)
+ n_segi[k] = max(2, round(Int, n * (nodes[k+1] - nodes[k]) / total_len))
+ allocated += n_segi[k]
+ end
+ n_segi[n_segs] = max(2, n + (n_segs - 1) - allocated)
+
+ result = Float64[]
+ for k in 1:n_segs
+ a, b = nodes[k], nodes[k+1]
+ left_fine = k > 1 || lo_is_conc
+ right_fine = k < n_segs || hi_is_conc
+ sub = if left_fine && right_fine
+ _sinh_both_ends(a, b, n_segi[k], β)
+ elseif left_fine
+ _sinh_left(a, b, n_segi[k], β)
+ elseif right_fine
+ _sinh_right(a, b, n_segi[k], β)
+ else
+ collect(range(a, b; length=n_segi[k]))
+ end
+ isempty(result) ? append!(result, sub) : append!(result, sub[2:end])
+ end
+ return result
+end
+
+# sinh grid fine at left end a: x(v) = a + Δ·sinh(β·v)/sinh(β)
+function _sinh_left(a::Float64, b::Float64, n::Int, β::Float64)
+ Δ = b - a
+ s = sinh(β)
+ [a + Δ * sinh(β * (k - 1) / (n - 1)) / s for k in 1:n]
+end
+
+# sinh grid fine at right end b: x(v) = b − Δ·sinh(β·(1−v))/sinh(β)
+function _sinh_right(a::Float64, b::Float64, n::Int, β::Float64)
+ Δ = b - a
+ s = sinh(β)
+ [b - Δ * sinh(β * (1.0 - (k - 1) / (n - 1))) / s for k in 1:n]
+end
+
+# symmetric sinh fine at both ends a and b
+function _sinh_both_ends(a::Float64, b::Float64, n::Int, β::Float64)
+ Δ = b - a
+ s = sinh(β)
+ grid = Vector{Float64}(undef, n)
+ @inbounds for k in 1:n
+ v = (k - 1) / (n - 1)
+ grid[k] = v ≤ 0.5 ? (a + 0.5Δ * sinh(β * 2v) / s) :
+ (b - 0.5Δ * sinh(β * 2(1.0 - v)) / s)
+ end
+ return grid
+end
+
+"""
+ make_stretched_r_grid(r_lo, r_hi, ro, nr, β_r) → Vector{Float64}
+
+Grid of `nr` points on `[r_lo, r_hi]` concentrated near `ro` (magnetic axis).
+Thin wrapper around `make_multi_stretched_grid`.
+"""
+function make_stretched_r_grid(r_lo::Float64, r_hi::Float64, ro::Float64, nr::Int, β_r::Float64)
+ return make_multi_stretched_grid(r_lo, r_hi, [ro], nr, β_r)
+end
+
+"""
+ make_stretched_z_grid(z_lo, z_hi, zo, nz, topology, β_z) → Vector{Float64}
+
+Grid of `nz` points on `[z_lo, z_hi]` concentrated near `zo` (magnetic axis) **and**
+near each x-point boundary (at `z_lo` for `:sn_lower`/`:double_null`, at `z_hi` for
+`:sn_upper`/`:double_null`). Thin wrapper around `make_multi_stretched_grid`.
+"""
+function make_stretched_z_grid(z_lo::Float64, z_hi::Float64, zo::Float64, nz::Int,
+ topology::Symbol, β_z::Float64)
+ centers = Float64[zo]
+ topology ∈ (:sn_lower, :double_null) && push!(centers, z_lo)
+ topology ∈ (:sn_upper, :double_null) && push!(centers, z_hi)
+ return make_multi_stretched_grid(z_lo, z_hi, centers, nz, β_z)
+end
+
+"""
+ adaptive_grid_params(raw_profile, ro, zo, r_lo, r_hi, z_lo, z_hi,
+ psilow, Δψ, bbox_curve) → (nr, nz, β_r, β_z)
+
+Physics-based Cartesian grid sizing for contour-tracing equilibrium reconstruction.
+
+Computes required cell widths from the bilinear interpolation error bound
+δψ ≈ (dR²·|ψ_RR| + dZ²·|ψ_ZZ|)/8 ≤ Δψ → dR_req = √(8Δψ/|ψ_RR|)
+sampled at each LCFS vertex (reusing `bbox_curve`), plus an axis constraint ensuring
+the innermost surface (psilow) has ≥ 5 cells per semi-axis on the global grid.
+
+β = acosh(h_max/h_min) from the ratio of coarsest to finest required cell widths.
+n = 1 + ⌈span·sinch(β)/h_min⌉ where sinch(β) = β/sinh(β).
+"""
+function adaptive_grid_params(
+ raw_profile::DirectRunInput,
+ ro::Float64, zo::Float64,
+ r_lo::Float64, r_hi::Float64,
+ z_lo::Float64, z_hi::Float64,
+ psilow::Float64, Δψ::Float64,
+ bbox_curve
+)
+ psio = raw_profile.psio
+ dR_reqs = Float64[]
+ dZ_reqs = Float64[]
+
+ # Required cell widths at each LCFS vertex from bilinear interpolation error formula
+ if bbox_curve !== nothing
+ for (R, Z) in Ctr.vertices(bbox_curve)
+ ψ_RR = abs(raw_profile.psi_in((R, Z); deriv=DerivOp(2, 0)))
+ ψ_ZZ = abs(raw_profile.psi_in((R, Z); deriv=DerivOp(0, 2)))
+ ψ_RR > 0 && push!(dR_reqs, sqrt(8 * Δψ / ψ_RR))
+ ψ_ZZ > 0 && push!(dZ_reqs, sqrt(8 * Δψ / ψ_ZZ))
+ end
+ end
+
+ # Axis constraint: cell ≤ 0.2 × a_low, the smaller semi-axis of the innermost surface, in both directions.
+ ψ_RR_ax = abs(raw_profile.psi_in((ro, zo); deriv=DerivOp(2, 0)))
+ ψ_ZZ_ax = abs(raw_profile.psi_in((ro, zo); deriv=DerivOp(0, 2)))
+ a_low_ax = min(sqrt(2 * psilow * psio / ψ_RR_ax), sqrt(2 * psilow * psio / ψ_ZZ_ax))
+ push!(dR_reqs, 0.2 * a_low_ax)
+ push!(dZ_reqs, 0.2 * a_low_ax)
+
+ function _params_1d(reqs, span)
+ h_min = max(minimum(reqs), span / 4000)
+ h_max = min(max(maximum(reqs), h_min), span / 4)
+ β = h_max > h_min * (1.0 + 1e-10) ? acosh(h_max / h_min) : 0.0
+ # Cap at 3.0: allows aggressive concentration at x-points and axis while keeping
+ # h_max/h_min = cosh(3)≈10 reasonable for intermediate flux surfaces.
+ β = clamp(β, 0.0, 3.0)
+ sinchβ = β < 1e-6 ? 1.0 : β / sinh(β)
+ n = max(4, 1 + ceil(Int, span * sinchβ / h_min))
+ return n, β
+ end
+
+ nr_fine, β_r = _params_1d(dR_reqs, r_hi - r_lo)
+ nz_fine, β_z = _params_1d(dZ_reqs, z_hi - z_lo)
+ return nr_fine, nz_fine, β_r, β_z
+end
+
+"""
+ equilibrium_solver_by_inversion(raw_profile; resolution_factor=4.0, override_psi_nodes=nothing) -> PlasmaEquilibrium
+
+Driver for contour-tracing equilibrium reconstruction.
+
+Grid parameters (n and β in each direction) are computed adaptively from the bilinear
+interpolation error bound along the LCFS and an axis constraint. `resolution_factor`
+scales both n values uniformly (higher → more points, same β).
+
+Select via `eq_type = "efit_by_inversion"` in `gpec.toml`.
+"""
+function equilibrium_solver_by_inversion(
+ raw_profile::DirectRunInput;
+ resolution_factor::Float64=4.0,
+ override_psi_nodes::Union{Nothing,Vector{Float64}}=nothing
+)
+ equil_params = raw_profile.config
+ psio = raw_profile.psio
+ mtheta = equil_params.mtheta
+ psilow = equil_params.psilow
+ psihigh = raw_profile.psihigh_resolved
+
+ # Locate the magnetic axis and separatrix for the contour tracing
+ ro, zo, _, rs2 = direct_position!(raw_profile)
+
+ psi_nodes = override_psi_nodes === nothing ?
+ _build_psi_grid(equil_params, psilow, psihigh) :
+ _validate_psi_nodes(override_psi_nodes, psilow, psihigh)
+ mpsi = length(psi_nodes) - 1
+
+ # Detect plasma topology for sinh-stretching direction
+ topology = classify_topology(raw_profile, psio)
+ @info "efit_by_inversion: topology = $topology"
+
+ # Clip the fine grid to the plasma bounding box, from one coarse contour of the nodal ψ near psihigh, plus a margin.
+ ψ_coarse = raw_profile.psi_in.nodal_derivs.partials[1, :, :]
+ ψ_bbox_target = psio * max(1.0 - psihigh, 1e-3) # outermost needed surface, ≥ 0.001·psio
+ cl_bbox = Ctr.contour(raw_profile.psi_in_xs, raw_profile.psi_in_ys, ψ_coarse, ψ_bbox_target)
+ bbox_curve = select_plasma_contour(Ctr.lines(cl_bbox), ro, zo)
+ if bbox_curve !== nothing
+ bv = Ctr.vertices(bbox_curve)
+ r_bbox_lo, r_bbox_hi = extrema(v[1] for v in bv)
+ z_bbox_lo, z_bbox_hi = extrema(v[2] for v in bv)
+ r_margin = (r_bbox_hi - r_bbox_lo) * 0.05
+ z_margin = (z_bbox_hi - z_bbox_lo) * 0.12
+ r_lo = max(raw_profile.rmin, r_bbox_lo - r_margin)
+ r_hi = min(raw_profile.rmax, r_bbox_hi + r_margin)
+ z_lo = max(raw_profile.zmin, z_bbox_lo - z_margin)
+ z_hi = min(raw_profile.zmax, z_bbox_hi + z_margin)
+ else
+ r_lo, r_hi = raw_profile.rmin, raw_profile.rmax
+ z_lo, z_hi = raw_profile.zmin, raw_profile.zmax
+ end
+
+ # ψ curvature at axis: needed for near_axis_threshold and zoomed core grid sizing.
+ # a_low = min semi-axis of the innermost flux surface (at psilow) from ψ ≈ ½|ψ_RR|dR².
+ ψ_RR_abs = abs(raw_profile.psi_in((ro, zo); deriv=DerivOp(2, 0)))
+ ψ_ZZ_abs = abs(raw_profile.psi_in((ro, zo); deriv=DerivOp(0, 2)))
+ a_low = min(sqrt(2 * psilow * psio / ψ_RR_abs), sqrt(2 * psilow * psio / ψ_ZZ_abs))
+
+ # Compute physics-based (n, β) from LCFS curvature sampling and axis constraint.
+ # resolution_factor scales n; β is determined by h_max/h_min curvature ratio alone.
+ Δψ = psio * (psihigh - psilow) / mpsi
+ nr_adp, nz_adp, β_r, β_z = adaptive_grid_params(
+ raw_profile, ro, zo, r_lo, r_hi, z_lo, z_hi, psilow, Δψ, bbox_curve)
+ nr_fine = max(4, round(Int, nr_adp * resolution_factor))
+ nz_fine = max(4, round(Int, nz_adp * resolution_factor))
+ r_fine = make_stretched_r_grid(r_lo, r_hi, ro, nr_fine, β_r)
+ z_grid = make_stretched_z_grid(z_lo, z_hi, zo, nz_fine, topology, β_z)
+
+ iro = clamp(searchsortedfirst(r_fine, ro), 2, length(r_fine))
+ izo = clamp(searchsortedfirst(z_grid, zo), 2, length(z_grid))
+ dR_axis = r_fine[iro] - r_fine[iro-1]
+ dZ_axis = z_grid[izo] - z_grid[izo-1]
+
+ # Near-axis threshold: surfaces spanning fewer than n_min_cells global-grid cells per
+ # semi-axis are re-traced by the zoomed core grid.
+ d_max = max(dR_axis, dZ_axis)
+ n_min_cells = 10
+ near_axis_threshold = (n_min_cells * d_max)^2 * max(ψ_RR_abs, ψ_ZZ_abs) / (2 * psio)
+
+ @info "efit_by_inversion: a_low=$(@sprintf("%.1f", a_low*1000)) mm; grid=$(nr_fine)×$(nz_fine) β_r=$(@sprintf("%.2f", β_r)) β_z=$(@sprintf("%.2f", β_z)) (dR=$(@sprintf("%.2f", dR_axis*1000)) mm dZ=$(@sprintf("%.2f", dZ_axis*1000)) mm); zoom threshold ψ<$(@sprintf("%.4f", near_axis_threshold))"
+
+ # Evaluate ψ on the fine grid column by column in parallel; one hint pair per thread, reset at each column.
+ ψ_fine = Matrix{Float64}(undef, nr_fine, nz_fine)
+ thread_hints = [(Ref(1), Ref(1)) for _ in 1:Threads.maxthreadid()]
+ Threads.@threads for j in 1:nz_fine
+ z = z_grid[j]
+ h = thread_hints[Threads.threadid()]
+ h[1][] = 1
+ h[2][] = 1
+ @inbounds for i in 1:nr_fine
+ ψ_fine[i, j] = raw_profile.psi_in((r_fine[i], z); hint=h)
+ end
+ end
+
+ # Theta grid in fractional turns [0, 1] as required by InverseEquilibrium.
+ theta_grid = collect(range(0.0, 1.0; length=mtheta + 1))
+
+ # Build R(ψ, θ) and Z(ψ, θ) tables
+ R_table = Matrix{Float64}(undef, mpsi + 1, mtheta + 1)
+ Z_table = Matrix{Float64}(undef, mpsi + 1, mtheta + 1)
+
+ # Trace surfaces in parallel (Ctr.contour has no global state).
+ # surface_status: 0 = traced on the global grid, 1 = deferred to the zoomed pass, -1 = failed.
+ surface_status = Vector{Int8}(undef, mpsi + 1)
+
+ Threads.@threads for ipsi in 1:(mpsi+1)
+ psifac = psi_nodes[ipsi]
+
+ # Surface too small for the global grid to resolve with n_min=10: defer to zoomed pass.
+ if psifac <= near_axis_threshold
+ surface_status[ipsi] = 1
+ continue
+ end
+
+ ψ_target = psio * (1.0 - psifac)
+ cl = Ctr.contour(r_fine, z_grid, ψ_fine, ψ_target)
+ curve = select_plasma_contour(Ctr.lines(cl), ro, zo)
+
+ if curve === nothing
+ surface_status[ipsi] = -1
+ continue
+ end
+
+ resample_contour_to_theta_grid!(
+ @view(R_table[ipsi, :]), @view(Z_table[ipsi, :]),
+ curve, ro, zo, theta_grid
+ )
+ surface_status[ipsi] = 0
+ end
+
+ # Report failures after the threaded pass
+ for ipsi in 1:(mpsi+1)
+ if surface_status[ipsi] == -1
+ psifac = psi_nodes[ipsi]
+ error(
+ "efit_by_inversion: No closed flux surface found at psifac = $(@sprintf("%.4f", psifac)) " *
+ "— psihigh likely exceeds the separatrix or is outside the EFIT domain."
+ )
+ end
+ end
+ n_contour_success = count(==(0), surface_status)
+ n_near_axis_fill = count(==(1), surface_status)
+
+ # Zoomed core pass: re-trace near-axis surfaces on a dedicated axis-centered grid.
+ # Extended to zoom_extend_factor × threshold so global and zoomed grids overlap smoothly.
+ if n_near_axis_fill > 0
+ zoom_extend_factor = 9
+ psi_zoom_max = zoom_extend_factor * near_axis_threshold
+ n_zoom_surfaces = count(<=(psi_zoom_max), psi_nodes)
+
+ # Zoomed bbox: semi-axes sized for psi_zoom_max (not just the threshold), +20%.
+ a_zoom_r = sqrt(2 * psi_zoom_max * psio / ψ_RR_abs) * 1.2
+ a_zoom_z = sqrt(2 * psi_zoom_max * psio / ψ_ZZ_abs) * 1.2
+ r_zoom_lo = max(r_lo, ro - a_zoom_r)
+ r_zoom_hi = min(r_hi, ro + a_zoom_r)
+ z_zoom_lo = max(z_lo, zo - a_zoom_z)
+ z_zoom_hi = min(z_hi, zo + a_zoom_z)
+
+ # Grid sizing: n_min_cells at (ro, zo) required for the SMALLEST surface (psilow).
+ # sinh-center cell ≈ (4β/sinh(β)) · a_zoom / (n/2) → n ≥ 8β·a_zoom·n_min / (sinh(β)·a_low)
+ sinh_β_r = β_r_use > 1e-6 ? sinh(β_r_use) : 1.0
+ sinh_β_z = β_z_use > 1e-6 ? sinh(β_z_use) : 1.0
+ nr_zoom = max(200, ceil(Int, 8 * β_r_use * a_zoom_r * n_min_cells / (sinh_β_r * a_low)))
+ nz_zoom = max(200, ceil(Int, 8 * β_z_use * a_zoom_z * n_min_cells / (sinh_β_z * a_low)))
+ r_zoom_grid = make_stretched_r_grid(r_zoom_lo, r_zoom_hi, ro, nr_zoom, β_r_use)
+ z_zoom_grid = make_stretched_r_grid(z_zoom_lo, z_zoom_hi, zo, nz_zoom, β_z_use)
+
+ iro_z = clamp(searchsortedfirst(r_zoom_grid, ro), 2, length(r_zoom_grid))
+ izo_z = clamp(searchsortedfirst(z_zoom_grid, zo), 2, length(z_zoom_grid))
+ dR_zoom = r_zoom_grid[iro_z] - r_zoom_grid[iro_z-1]
+ dZ_zoom = z_zoom_grid[izo_z] - z_zoom_grid[izo_z-1]
+ @info "efit_by_inversion: zoomed core grid $(nr_zoom)×$(nz_zoom) covering [ro±$(@sprintf("%.0f", a_zoom_r*1000)) mm, zo±$(@sprintf("%.0f", a_zoom_z*1000)) mm]; dR=$(@sprintf("%.2f", dR_zoom*1000)) mm, dZ=$(@sprintf("%.2f", dZ_zoom*1000)) mm (target ≤ $(@sprintf("%.2f", a_low/n_min_cells*1000)) mm); tracing $n_zoom_surfaces surfaces (threshold=$n_near_axis_fill + $zoom_extend_factor× overlap)"
+
+ ψ_zoom = Matrix{Float64}(undef, nr_zoom, nz_zoom)
+ Threads.@threads for j in 1:nz_zoom
+ z = z_zoom_grid[j]
+ h = thread_hints[Threads.threadid()]
+ h[1][] = 1
+ h[2][] = 1
+ @inbounds for i in 1:nr_zoom
+ ψ_zoom[i, j] = raw_profile.psi_in((r_zoom_grid[i], z); hint=h)
+ end
+ end
+
+ Threads.@threads for ipsi in 1:n_zoom_surfaces
+ psifac = psi_nodes[ipsi]
+ ψ_target = psio * (1.0 - psifac)
+ cl_z = Ctr.contour(r_zoom_grid, z_zoom_grid, ψ_zoom, ψ_target)
+ curve_z = select_plasma_contour(Ctr.lines(cl_z), ro, zo)
+ if curve_z === nothing
+ surface_status[ipsi] = -1
+ continue
+ end
+ resample_contour_to_theta_grid!(
+ @view(R_table[ipsi, :]), @view(Z_table[ipsi, :]),
+ curve_z, ro, zo, theta_grid
+ )
+ surface_status[ipsi] = 0
+ end
+
+ for ipsi in 1:n_zoom_surfaces
+ if surface_status[ipsi] == -1
+ psifac = psi_nodes[ipsi]
+ error(
+ "efit_by_inversion: Zoomed core grid failed to find flux surface at ψ = $(@sprintf("%.4f", psifac)). " *
+ "Try increasing psilow or reducing the zoom bbox margin."
+ )
+ end
+ end
+ @info "efit_by_inversion: $(mpsi + 1 - n_zoom_surfaces) surfaces traced by global grid, $n_zoom_surfaces by zoomed core grid ($n_near_axis_fill below threshold + $(n_zoom_surfaces - n_near_axis_fill) overlap)"
+ else
+ @info "efit_by_inversion: $n_contour_success surfaces traced by global grid"
+ end
+
+ # ρ must increase with ipsi at each angle (nested surfaces); warn once with the first and worst violation.
+ n_violations = 0
+ first_ipsi = 0
+ first_k = 0
+ worst_Δρ = 0.0
+ worst_ipsi = 0
+ worst_k = 0
+ # Skip column mtheta+1, the periodic copy of column 1.
+ @inbounds for k in 1:mtheta
+ ρ_prev = sqrt((R_table[1, k] - ro)^2 + (Z_table[1, k] - zo)^2)
+ for ipsi in 2:(mpsi+1)
+ ρ = sqrt((R_table[ipsi, k] - ro)^2 + (Z_table[ipsi, k] - zo)^2)
+ if ρ < ρ_prev
+ n_violations += 1
+ if n_violations == 1
+ first_ipsi = ipsi
+ first_k = k
+ end
+ Δρ = ρ_prev - ρ
+ if Δρ > worst_Δρ
+ worst_Δρ = Δρ
+ worst_ipsi = ipsi
+ worst_k = k
+ end
+ end
+ ρ_prev = ρ
+ end
+ end
+ if n_violations > 0
+ @warn "efit_by_inversion: ρ non-monotone at $n_violations (ipsi,θ) locations — adjacent surfaces may intersect. " *
+ "First: ipsi=$first_ipsi θ=$(@sprintf("%.3f", theta_grid[first_k])). " *
+ "Worst: ipsi=$worst_ipsi θ=$(@sprintf("%.3f", theta_grid[worst_k])) Δρ=$(@sprintf("%.3g", worst_Δρ)) m."
+ end
+
+ # Build InverseRunInput — same type consumed by equilibrium_solver(::InverseRunInput)
+ rz_in_xs = psi_nodes
+ rz_in_ys = theta_grid
+ itp_opts2d = (bc=(CubicFit(), PeriodicBC()), extrap=(ExtendExtrap(), WrapExtrap()))
+
+ @views R_table[:, end] .= R_table[:, 1]
+ @views Z_table[:, end] .= Z_table[:, 1]
+
+ rz_in_R = cubic_interp((rz_in_xs, rz_in_ys), R_table; itp_opts2d...)
+ rz_in_Z = cubic_interp((rz_in_xs, rz_in_ys), Z_table; itp_opts2d...)
+
+ # Intermediate inverse input; the captured DirectIngest rides on the original eq_input,
+ # which PlasmaEquilibrium forwards onto the equilibrium, so this one carries ingest=nothing.
+ inv_input = InverseRunInput(raw_profile.config, raw_profile.sq_in,
+ rz_in_xs, rz_in_ys, rz_in_R, rz_in_Z, ro, zo, psio, nothing, raw_profile.psihigh_resolved)
+
+ pe = equilibrium_solver(inv_input; override_psi_nodes)
+
+ # Round-trip residual (ψ,θ) → (R,Z) → ψ on the outer grid, at knots and at knot midpoints:
+ # the splines are exact at their own knots, so only the midpoints can see inter-knot ringing.
+ rt_residual(ψ_samples) = maximum(
+ begin
+ r2 = pe.rzphi_rsquared((ψ_check, θ_check))
+ off = pe.rzphi_offset((ψ_check, θ_check))
+ rfac = sqrt(max(r2, 0.0))
+ η = 2π * (θ_check + off)
+ abs((1.0 - raw_profile.psi_in((pe.ro + rfac * cos(η), pe.zo + rfac * sin(η))) / psio) - ψ_check)
+ end
+ for ψ_check in ψ_samples, θ_check in (0.0, 0.25, 0.5, 0.75))
+
+ xs = pe.rzphi_xs
+ knots = @view xs[max(1, ceil(Int, length(xs) * ROUNDTRIP_EDGE_FRAC)):end]
+ max_rt_err = rt_residual(knots)
+ mids = [(knots[i] + knots[i+1]) / 2 for i in 1:(length(knots)-1)]
+ rt_mid = isempty(mids) ? NaN : rt_residual(mids)
+
+ verdict = _roundtrip_verdict(max_rt_err, rt_mid)
+ msg = "efit_by_inversion: round-trip error at edge = $(@sprintf("%.2e", max_rt_err)) on knots, $(@sprintf("%.2e", rt_mid)) at knot midpoints"
+ if verdict === :ok
+ @info msg
+ else
+ problem = verdict === :ringing ? "ringing between knots" : "inaccurate"
+ @warn "$msg; the rzphi splines are $problem near psihigh. Consider reducing psihigh or increasing resolution_factor."
+ end
+
+ return pe
+end
diff --git a/src/Equilibrium/Axisymmetric/GradShafranovResidual.jl b/src/Equilibrium/Axisymmetric/GradShafranovResidual.jl
new file mode 100644
index 0000000000..13153d71a3
--- /dev/null
+++ b/src/Equilibrium/Axisymmetric/GradShafranovResidual.jl
@@ -0,0 +1,169 @@
+"""
+ equilibrium_gse!(equil::PlasmaEquilibrium)
+
+Computes the Grad-Shafranov residual on the grid and, with `diagnose_src`, writes it to HDF5 files.
+Port of Fortran `equil_out_gse`.
+
+Returns `(; xs, ys, flux_x, flux_y, source, total, error, errori)` on the `rzphi` (ψ, θ) nodes: the two
+flux-divergence terms, the source, the residual `total = flux_x - flux_y + source`, `error = |total|` over
+the largest term on the grid, and `errori`, the magnitude of the θ-integrated residual on each surface.
+"""
+function equilibrium_gse!(equil::PlasmaEquilibrium)
+
+ profiles = equil.profiles
+ mpsi = length(equil.rzphi_xs) - 1
+ mtheta = length(equil.rzphi_ys) - 1
+ ro, zo = equil.ro, equil.zo
+ psio = equil.psio
+ verbose = equil.params.verbose
+ diagnose_src = equil.params.diagnose_src
+ diagnose_maxima = equil.params.diagnose_maxima
+
+ if verbose
+ @info "Diagnosing Grad-Shafranov solution"
+ end
+
+ # Compute R, Z coordinates using nodal_derivs access
+ r = zeros(Float64, mpsi + 1, mtheta + 1)
+ z = zeros(Float64, mpsi + 1, mtheta + 1)
+
+ for ipsi in 1:(mpsi+1)
+ rfac = @. sqrt(equil.rzphi_rsquared.nodal_derivs.partials[1, ipsi, :])
+ angle = @. 2π * (equil.rzphi_ys + equil.rzphi_offset.nodal_derivs.partials[1, ipsi, :])
+ r[ipsi, :] .= ro .+ rfac .* cos.(angle)
+ z[ipsi, :] .= zo .+ rfac .* sin.(angle)
+ end
+
+ # Compute flux quantities using direct array access at grid points
+ flux_fs = zeros(Float64, mpsi + 1, mtheta + 1, 2)
+ flux_fsx = zeros(Float64, mpsi + 1, mtheta + 1, 2) # x-derivatives
+ flux_fsy = zeros(Float64, mpsi + 1, mtheta + 1, 2) # y-derivatives
+ for ipsi in 1:(mpsi+1)
+ for itheta in 1:(mtheta+1)
+ f1 = equil.rzphi_rsquared.nodal_derivs.partials[1, ipsi, itheta]
+ f2 = equil.rzphi_offset.nodal_derivs.partials[1, ipsi, itheta]
+ f4 = equil.rzphi_jac.nodal_derivs.partials[1, ipsi, itheta]
+ fy1 = equil.rzphi_rsquared.nodal_derivs.partials[3, ipsi, itheta]
+ fy2 = equil.rzphi_offset.nodal_derivs.partials[3, ipsi, itheta]
+ fx1 = equil.rzphi_rsquared.nodal_derivs.partials[2, ipsi, itheta]
+ fx2 = equil.rzphi_offset.nodal_derivs.partials[2, ipsi, itheta]
+
+ flux_fs[ipsi, itheta, 1] = fy1^2 / (4π^2 * f1) + (1 + fy2)^2 * 4 * f1
+ flux_fs[ipsi, itheta, 2] = fx1 * fy1 / (4π^2 * f1) + fx2 * (1 + fy2) * 4 * f1
+
+ flux_fs[ipsi, itheta, 1] *= 2π * psio / f4
+ flux_fs[ipsi, itheta, 2] *= 2π * psio / f4
+ end
+ end
+ # Create flux interpolants for Grad-Shafranov diagnostics
+ @views flux_fs[:, end, :] .= flux_fs[:, 1, :]
+ flux_opts = (bc=(CubicFit(), PeriodicBC()), extrap=(ExtendExtrap(), WrapExtrap()))
+ flux1 = cubic_interp((equil.rzphi_xs, equil.rzphi_ys), flux_fs[:, :, 1]; flux_opts...)
+ flux2 = cubic_interp((equil.rzphi_xs, equil.rzphi_ys), flux_fs[:, :, 2]; flux_opts...)
+
+ # Compute flux derivatives at all grid points for diagnostics
+ hint2d = (Ref(1), Ref(1)) # Shared 2D hint for hot loop optimization
+ for ipsi in 0:mpsi
+ for itheta in 0:mtheta
+ query_point = (equil.rzphi_xs[ipsi+1], equil.rzphi_ys[itheta+1])
+ flux_fsx[ipsi+1, itheta+1, 1] = flux1(query_point; deriv=DerivOp(1, 0), hint=hint2d)
+ flux_fsx[ipsi+1, itheta+1, 2] = flux2(query_point; deriv=DerivOp(1, 0), hint=hint2d)
+ flux_fsy[ipsi+1, itheta+1, 1] = flux1(query_point; deriv=DerivOp(0, 1), hint=hint2d)
+ flux_fsy[ipsi+1, itheta+1, 2] = flux2(query_point; deriv=DerivOp(0, 1), hint=hint2d)
+ end
+ end
+
+ # Compute source term using direct array access
+ source = zeros(Float64, mpsi + 1, mtheta + 1)
+ hint = Ref(1) # Linear search hint for sequential psi access
+ for ipsi in 1:(mpsi+1)
+ psi = profiles.xs[ipsi]
+ s1 = profiles.F_spline.y[ipsi]
+ s1p = profiles.F_deriv(psi; hint=hint)
+ s2p = profiles.P_deriv(psi; hint=hint)
+ for itheta in 1:(mtheta+1)
+ f4 = equil.rzphi_jac.nodal_derivs.partials[1, ipsi, itheta]
+ denom = (2π * r[ipsi, itheta])^2
+ source[ipsi, itheta] = f4 / (2π * psio * π^2) * (s1 * s1p / denom + s2p)
+ end
+ end
+
+ total = flux_fsx[:, :, 1] .- flux_fsy[:, :, 2] .+ source
+ error = abs.(total) ./ maximum([maximum(abs.(flux_fsx[:, :, 1])), maximum(abs.(flux_fsy[:, :, 2])), maximum(abs.(source))])
+ errlog = ifelse.(error .> 0, log10.(error), 0.0)
+
+ if diagnose_maxima
+ fxmax = maximum(abs.(flux_fsx[:, :, 1]))
+ fymax = maximum(abs.(flux_fsy[:, :, 2]))
+ smax = maximum(abs.(source))
+ emax = maximum(abs.(error))
+ lmax = maximum(errlog)
+ jmax = ind2sub(size(errlog), argmax(errlog))
+ @info "GS residuals: fxmax = $(@sprintf("%.3e", fxmax)), fymax = $(@sprintf("%.3e", fymax)), smax = $(@sprintf("%.3e", smax)), emax = $(@sprintf("%.3e", emax)), lmax = $(@sprintf("%.3f", lmax)), maxloc = $(jmax .- 1)"
+ end
+
+ # Integrated error criterion
+ term = zeros(Float64, mpsi + 1, 2)
+ for ipsi in 1:(mpsi+1)
+ fs_matrix = zeros(Float64, mtheta + 1, 2)
+ fs_matrix[:, 1] = flux_fsx[ipsi, :, 1]
+ fs_matrix[:, 2] = source[ipsi, :]
+ # Snap the repeated endpoint exactly equal to the start
+ fs_matrix[end, :] .= fs_matrix[1, :]
+
+ # Compute total integral using FastInterpolations native integration
+ itp = cubic_interp(equil.rzphi_ys, Series(fs_matrix); bc=PeriodicBC())
+ term[ipsi, :] .= FastInterpolations.integrate(itp)
+ end
+
+ totali = sum(term; dims=2)
+ errori = abs.(totali)
+ errlogi = @. ifelse(errori > 0, log10(errori), 0.0)
+
+ if diagnose_src
+ if verbose
+ @info "Writing diagnostics to HDF5 files"
+ end
+
+ # Write contour data
+ h5open(joinpath(dirname(equil.config.eq_filename), "gsec.h5"), "w") do file
+ file["mpsi"] = mpsi
+ file["mtheta"] = mtheta
+ file["r"] = Float32.(r)
+ file["z"] = Float32.(z)
+ file["flux_fsx"] = Float32.(flux_fsx[:, :, 1])
+ file["flux_fsy"] = Float32.(flux_fsy[:, :, 2])
+ file["source"] = Float32.(source)
+ file["total"] = Float32.(total)
+ file["error"] = Float32.(error)
+ file["errlog"] = Float32.(errlog)
+ end
+
+ # Write xy plot data
+ h5open(joinpath(dirname(equil.config.eq_filename), "gse.h5"), "w") do file
+ gse_data = Array{Float32,3}(undef, mpsi + 1, mtheta + 1, 7)
+ for ipsi in 0:mpsi
+ for itheta in 0:mtheta
+ gse_data[ipsi+1, itheta+1, 1] = Float32(flux.ys[itheta+1])
+ gse_data[ipsi+1, itheta+1, 2] = Float32(flux.xs[ipsi+1])
+ gse_data[ipsi+1, itheta+1, 3] = Float32(flux_fs[ipsi+1, itheta+1, 1])
+ gse_data[ipsi+1, itheta+1, 4] = Float32(flux_fs[ipsi+1, itheta+1, 2])
+ gse_data[ipsi+1, itheta+1, 5] = Float32(source[ipsi+1, itheta+1])
+ gse_data[ipsi+1, itheta+1, 6] = Float32(total[ipsi+1, itheta+1])
+ gse_data[ipsi+1, itheta+1, 7] = Float32(error[ipsi+1, itheta+1])
+ end
+ end
+ file["gse_data"] = gse_data
+ end
+
+ # Write integrated error criterion
+ h5open(joinpath(dirname(equil.config.eq_filename), "gsei.h5"), "w") do file
+ file["xs"] = Float32.(flux.xs)
+ file["term"] = Float32.(term)
+ file["totali"] = Float32.(totali)
+ file["errori"] = Float32.(errori)
+ file["errlogi"] = Float32.(errlogi)
+ end
+ end
+ return (; xs=equil.rzphi_xs, ys=equil.rzphi_ys, flux_x=flux_fsx[:, :, 1], flux_y=flux_fsy[:, :, 2], source, total, error, errori=vec(errori))
+end
diff --git a/src/Equilibrium/Axisymmetric/Inverse.jl b/src/Equilibrium/Axisymmetric/Inverse.jl
new file mode 100644
index 0000000000..440bee1b04
--- /dev/null
+++ b/src/Equilibrium/Axisymmetric/Inverse.jl
@@ -0,0 +1,391 @@
+"""
+Converts an inverse equilibrium (`InverseRunInput`, R and Z on a (ψ, θ) grid) to straight-fieldline coordinates.
+Based on Fortran inverse.f.
+"""
+
+"""
+ inverse_extrap(xx::Matrix{Float64}, ff::Matrix{Float64}, x::Float64) -> Vector{Float64}
+
+Component-wise Lagrange extrapolation of a vector-valued function to `x`.
+
+## Arguments
+
+ - `xx`: `m × n` abscissae, row `i` holding the x-values of point `i` for each of the n components
+ - `ff`: `m × n` function values at `xx`
+"""
+function inverse_extrap(xx::Matrix{Float64}, ff::Matrix{Float64}, x::Float64)::Vector{Float64}
+ m, n = size(ff) # m = number of data points, n = number of components
+ f = zeros(Float64, n) # Output vector
+
+ for i in 1:m
+ term = copy(ff[i, :]) # Start with f_i (vector)
+ for j in 1:m
+ if j == i
+ continue
+ end
+ term .= term .* ((x .- xx[j, :]) ./ (xx[i, :] .- xx[j, :]))
+ end
+ f .+= term # Accumulate to output
+ end
+
+ return f
+end
+
+
+
+"""
+ resolve_psihigh!(input::InverseRunInput) -> InverseRunInput
+
+Clamp `input.psihigh_resolved` to the outermost input surface (below ψ_N = 1 for an i-file that
+carries the LCFS bounds), warning when it moves. `config.psihigh` keeps the request.
+"""
+function resolve_psihigh!(input::InverseRunInput)
+ psi_edge = input.rz_in_xs[end]
+ if input.psihigh_resolved > psi_edge
+ @warn "psihigh = $(input.psihigh_resolved) exceeds the outermost input surface ψ_N = $psi_edge; clamped to it"
+ input.psihigh_resolved = psi_edge
+ end
+ return input
+end
+
+function equilibrium_solver(input::InverseRunInput; override_psi_nodes::Union{Nothing,Vector{Float64}}=nothing)
+ @info "Starting Inverse Equilibrium Processing"
+ # Extract input parameters
+
+ config = input.config
+ rz_in_xs = input.rz_in_xs
+ rz_in_ys = input.rz_in_ys
+ rz_in_R = input.rz_in_R
+ rz_in_Z = input.rz_in_Z
+ sq_in = input.sq_in
+ ro = input.ro
+ zo = input.zo
+ psio = input.psio
+
+ grid_type = config.grid_type
+ mpsi = config.mpsi
+ mtheta = config.mtheta
+ psilow = config.psilow
+ psihigh = input.psihigh_resolved
+ newq0 = config.newq0
+
+ # Access grid dimensions from the interpolants
+ mx = length(rz_in_xs) - 1
+ my = length(rz_in_ys) - 1
+
+ # Extract R and Z nodal values from interpolants
+ R_data = rz_in_R.nodal_derivs.partials[1, :, :]
+ Z_data = rz_in_Z.nodal_derivs.partials[1, :, :]
+
+ x = R_data .- ro
+ y = Z_data .- zo
+ r2 = x .^ 2 .+ y .^ 2
+
+ twopi = 2 * π
+
+ deta = zeros(Float64, mx + 1, my + 1)
+ for ipsi in 0:mx, itheta in 0:my
+ if r2[ipsi+1, itheta+1] == 0.0
+ deta[ipsi+1, itheta+1] = 0.0
+ else
+ deta[ipsi+1, itheta+1] = atan(y[ipsi+1, itheta+1], x[ipsi+1, itheta+1]) / twopi
+ end
+ end
+
+ # Transform input coordinates from Cartesian to polar
+ for ipsi in 0:mx
+ for itheta in 1:my
+ Δ = deta[ipsi+1, itheta+1] - deta[ipsi+1, itheta]
+ if Δ > 0.5
+ deta[ipsi+1, itheta+1] -= 1
+ elseif Δ < -0.5
+ deta[ipsi+1, itheta+1] += 1
+ end
+ end
+ for itheta in 0:my
+ if r2[ipsi+1, itheta+1] > 0
+ deta[ipsi+1, itheta+1] -= rz_in_ys[itheta+1]
+ end
+ end
+ end
+
+ # As in Fortran inverse.f: when the grid includes the axis, extrapolate deta there from the innermost surfaces.
+ me = 3
+ if rz_in_xs[1] == 0.0
+ deta[1, :] .= inverse_extrap(r2[2:(me+1), :], deta[2:(me+1), :], 0.0)
+ end
+
+ # Restore exact θ periodicity, broken by subtracting rz_in_ys
+ @views r2[:, end] .= r2[:, 1]
+ @views deta[:, end] .= deta[:, 1]
+
+ itp_opts2d = (bc=(CubicFit(), PeriodicBC()), extrap=(ExtendExtrap(), WrapExtrap()))
+
+ # Create 2D interpolants for r² and dη
+ rz_rsq = cubic_interp((rz_in_xs, rz_in_ys), r2; itp_opts2d...)
+ rz_deta = cubic_interp((rz_in_xs, rz_in_ys), deta; itp_opts2d...)
+ # Radial grid
+ if override_psi_nodes !== nothing
+ sq_xs = _validate_psi_nodes(override_psi_nodes, psilow, psihigh)
+ mpsi = length(sq_xs) - 1
+ elseif grid_type == "auto"
+ if mpsi == 0 && config.psi_accuracy > 0
+ # Two-pass auto grid: pass-1 layout sized to resolve the gradient structure so pass 2
+ # is well-provisioned; the driver refines and re-forms (GridRefinement.jl, PASS1_INTERVALS).
+ mpsi = PASS1_INTERVALS
+ @info "Auto psi grid: forming pass-1 equilibrium on $(mpsi)-interval log_asymptotic grid pending curvature-based refinement"
+ elseif mpsi == 0
+ mpsi = 128
+ end
+ log_core = log(0.03 / psilow)
+ log_mid = log(0.98 / 0.03)
+ log_edge = log((1.0 - 0.98) / (1.0 - psihigh))
+ log_total = log_core + log_mid + log_edge
+ N_edge = clamp(round(Int, mpsi * log_edge / log_total), 2, mpsi ÷ 2)
+ N_core = round(Int, mpsi * log_core / log_total)
+ N_mid = mpsi - N_edge - N_core
+ sq_xs = make_optimal_psi_grid(psilow, psihigh, N_core, N_mid, N_edge)
+ elseif grid_type == "core_edge_packed"
+ if mpsi == 0
+ mpsi = 128
+ end
+ sq_xs = psilow .+ (psihigh - psilow) .* (sin.(range(0.0, 1.0; length=mpsi + 1) .* (π / 2))) .^ 2
+ elseif grid_type == "pow1"
+ if mpsi == 0
+ mpsi = 128
+ end
+ sq_xs = [psilow + (psihigh - psilow) * (3(i / mpsi) - (i / mpsi)^3) / 2 for i in 0:mpsi]
+ elseif grid_type == "rho"
+ if mpsi == 0
+ mpsi = 128
+ end
+ # Uniform in √ψ from psilow to psihigh (Fortran's rho ignores psilow)
+ sq_xs = [(sqrt(psilow) + (sqrt(psihigh) - sqrt(psilow)) * i / mpsi)^2 for i in 0:mpsi]
+ elseif grid_type in ("original", "orig")
+ # The input's own ψ nodes, ended by psilow and psihigh as the other grids are; mpsi is ignored
+ sq_xs = [psilow; filter(x -> psilow < x < psihigh, rz_in_xs); psihigh]
+ mpsi = length(sq_xs) - 1
+ elseif grid_type == "uniform"
+ if mpsi == 0
+ mpsi = 128
+ end
+ sq_xs = collect(range(psilow, psihigh; length=mpsi + 1))
+ else
+ error("Unsupported grid_type: $grid_type")
+ end
+ # Floor node spacing on the fixed grids (core_edge_packed/pow1 pack the edge below the integration-noise
+ # scale at high mpsi); the auto grid floors its refined grid in refined_psi_grid, an override
+ # grid arrives already floored, and the original grid keeps the input's nodes.
+ if override_psi_nodes === nothing && !(grid_type in ("auto", "original", "orig"))
+ sq_xs = enforce_min_spacing(sq_xs, MIN_KNOT_SPACING)
+ mpsi = length(sq_xs) - 1
+ end
+ sq_fs = zeros(Float64, mpsi + 1, 4)
+ sq = cubic_interp(sq_xs, Series(sq_fs); extrap=ExtendExtrap())
+
+ # Coordinate grids
+ if mtheta == 0
+ mtheta = my
+ end
+
+ theta_range = range(0.0, 1.0; length=mtheta + 1)
+
+ # rzphi components: r², deta, dphi, jac
+ rzphi_fs = zeros(Float64, mpsi + 1, mtheta + 1, 4)
+ rzphi_xs = copy(sq_xs)
+ # Vector copy stored in PlasmaEquilibrium; interpolants use the faster Range theta_range (equal to machine precision).
+ rzphi_ys = collect(theta_range)
+
+ # eqfun components: |B|, metric1, metric2
+ eqfun_fs = zeros(Float64, mpsi + 1, mtheta + 1, 3)
+ eqfun_xs = copy(sq_xs)
+
+ # Preallocate arrays for periodic spline fitting in the loop
+ spl_xs = zeros(Float64, mtheta + 1)
+ spl_fs = zeros(Float64, mtheta + 1, 5)
+ spl_post_buf = Vector{Float64}(undef, 5) # scratch for post-SFL spline evaluation
+
+ # q: i-files use the field-line integral, as Fortran `inverse_run`; a tabulated q splined in ψ is
+ # inaccurate where edge surfaces are coarse (q ~ log(1-ψ)). Other inputs keep their input q (the
+ # field-line q is inaccurate in cylindrical LAR geometry).
+ q_from_geometry = config.eq_type == "ifile"
+ f_sq_in_buf = Vector{Float64}(undef, size(sq_in.y, 2))
+ sq_in_hint = Ref(1)
+ hint2d = (Ref(1), Ref(1))
+ for ipsi in 0:mpsi
+ psifac = rzphi_xs[ipsi+1]
+ sq_in(f_sq_in_buf, psifac; hint=sq_in_hint)
+ spl_xs .= rzphi_ys
+ for itheta in 0:mtheta
+ theta = rzphi_ys[itheta+1]
+ # Evaluate r² and dη interpolants separately
+ query_point = (psifac, theta)
+ f_rsq = rz_rsq(query_point; hint=hint2d)
+ f_deta = rz_deta(query_point; hint=hint2d)
+ fx_rsq = rz_rsq(query_point; deriv=DerivOp(1, 0), hint=hint2d)
+ fx_deta = rz_deta(query_point; deriv=DerivOp(1, 0), hint=hint2d)
+ fy_rsq = rz_rsq(query_point; deriv=DerivOp(0, 1), hint=hint2d)
+ fy_deta = rz_deta(query_point; deriv=DerivOp(0, 1), hint=hint2d)
+
+ if f_rsq < 0
+ error("Invalid extrapolation near axis, rerun with larger value of psilow")
+ end
+
+ rfac = sqrt(f_rsq)
+ r = ro + rfac * cos(twopi * (theta + f_deta))
+ jacfac = fx_rsq * (1 + fy_deta) - fy_rsq * fx_deta
+ w11 = (1 + fy_deta) * twopi^2 * rfac / jacfac
+ w12 = -fy_rsq * pi / (rfac * jacfac)
+ bp = psio * sqrt(w11 * w11 + w12 * w12) / r
+ bt = f_sq_in_buf[1] / r
+ b = sqrt(bp * bp + bt * bt)
+
+ spl_fs[itheta+1, 1] = f_rsq
+ spl_fs[itheta+1, 2] = f_deta
+ spl_fs[itheta+1, 3] = r * jacfac
+ spl_fs[itheta+1, 4] = spl_fs[itheta+1, 3] / (r * r)
+ spl_fs[itheta+1, 5] = spl_fs[itheta+1, 3] * bp^config.power_bp * b^config.power_b / (r^config.power_r * max(rfac, eps(Float64))^config.power_rc)
+
+ end
+ # Fit periodic splines in θ and integrate; snap the periodic endpoint first
+ @views spl_fs[end, :] .= spl_fs[1, :]
+
+ spl = cubic_interp(spl_xs, Series(spl_fs); bc=PeriodicBC())
+ spl_fsi = FastInterpolations.cumulative_integrate(spl)
+
+ spl_xs .= spl_fsi[:, 5] ./ spl_fsi[mtheta+1, 5]
+ if any(diff(spl_xs) .<= 0)
+ @warn "InverseEquilibrium: SFL theta grid non-monotone at ipsi=$ipsi (psifac=$(round(psifac, sigdigits=4))). The SFL weight function (Jacobian × poloidal element) has a near-zero or negative segment; this surface's geometry may be corrupted."
+ end
+ @views spl_fs[:, 2] .+= rzphi_ys .- spl_xs
+ @views spl_fs[:, 4] .= (spl_fs[:, 3] ./ spl_fsi[mtheta+1, 3]) ./ (spl_fs[:, 5] ./ spl_fsi[mtheta+1, 5]) .* (spl_fsi[mtheta+1, 3] * twopi * pi)
+ @views spl_fs[:, 3] .= (f_sq_in_buf[1] * pi / psio) .* (spl_fsi[:, 4] .- spl_fsi[mtheta+1, 4] .* spl_xs)
+
+ # Re-spline on the SFL angles spl_xs and evaluate at the uniform rzphi_ys (spl.y holds pre-transform values).
+ spl_post = cubic_interp(spl_xs, Series(spl_fs); bc=PeriodicBC())
+ hint_post = Ref(1)
+ for itheta in 0:mtheta
+ spl_post(spl_post_buf, rzphi_ys[itheta+1]; hint=hint_post)
+ @views rzphi_fs[ipsi+1, itheta+1, :] .= spl_post_buf[1:4]
+ end
+
+ sq_fs[ipsi+1, 1] = f_sq_in_buf[1] * twopi
+ sq_fs[ipsi+1, 2] = f_sq_in_buf[2]
+ sq_fs[ipsi+1, 3] = spl_fsi[mtheta+1, 3] * twopi * pi # dV/d(psi)
+ sq_fs[ipsi+1, 4] = q_from_geometry ? spl_fsi[mtheta+1, 4] * sq_fs[ipsi+1, 1] / (2 * twopi * psio) : f_sq_in_buf[3]
+ end
+
+ sq = cubic_interp(sq_xs, Series(sq_fs); extrap=ExtendExtrap())
+
+ # Access sq nodal values directly (evaluating at own knots returns stored data)
+ f_sq = sq.y
+ sq_deriv = deriv1(sq)
+ f1_sq_lo = sq_deriv(sq_xs[1])
+ f1_sq_hi = sq_deriv(sq_xs[end])
+ q0 = f_sq[1, 4] - f1_sq_lo[4] * sq_xs[1]
+
+ if newq0 != 0
+ f0 = f_sq[1, 1] - f1_sq_lo[1] * sq_xs[1]
+ f0fac = f0^2 * ((newq0 / q0)^2 - 1)
+ q0 = newq0
+ for ipsi in 0:mpsi
+ ffac = sqrt(1 + f0fac / f_sq[ipsi+1, 1]^2)
+ sq_fs[ipsi+1, 1] *= ffac
+ sq_fs[ipsi+1, 4] *= ffac
+ rzphi_fs[ipsi+1, :, 3] *= ffac
+ end
+ sq = cubic_interp(sq_xs, Series(sq_fs); extrap=ExtendExtrap())
+ f_sq = sq.y
+ sq_deriv = deriv1(sq)
+ f1_sq_hi = sq_deriv(sq_xs[end])
+ end
+ qa = f_sq[mpsi+1, 4] + f1_sq_hi[4] * (1 - sq_xs[mpsi+1])
+ # Create 2D interpolants for geometric quantities (rzphi)
+ rzphi_grid2d = (rzphi_xs, theta_range)
+
+ @views rzphi_fs[:, end, :] .= rzphi_fs[:, 1, :]
+
+ rzphi_rsquared = cubic_interp(rzphi_grid2d, rzphi_fs[:, :, 1]; itp_opts2d...)
+ rzphi_offset = cubic_interp(rzphi_grid2d, rzphi_fs[:, :, 2]; itp_opts2d...)
+ rzphi_nu = cubic_interp(rzphi_grid2d, rzphi_fs[:, :, 3]; itp_opts2d...)
+ rzphi_jac = cubic_interp(rzphi_grid2d, rzphi_fs[:, :, 4]; itp_opts2d...)
+
+ v = zeros(Float64, 3, 3)
+ for ipsi in 0:mpsi
+ f_sq_vec = @view sq.y[ipsi+1, :]
+ for itheta in 0:mtheta
+ # Evaluate rzphi interpolants at grid points using nodal_derivs
+ f_rzphi = (
+ rzphi_rsquared.nodal_derivs.partials[1, ipsi+1, itheta+1],
+ rzphi_offset.nodal_derivs.partials[1, ipsi+1, itheta+1],
+ rzphi_nu.nodal_derivs.partials[1, ipsi+1, itheta+1],
+ rzphi_jac.nodal_derivs.partials[1, ipsi+1, itheta+1]
+ )
+ fx_rzphi = (
+ rzphi_rsquared.nodal_derivs.partials[2, ipsi+1, itheta+1],
+ rzphi_offset.nodal_derivs.partials[2, ipsi+1, itheta+1],
+ rzphi_nu.nodal_derivs.partials[2, ipsi+1, itheta+1],
+ rzphi_jac.nodal_derivs.partials[2, ipsi+1, itheta+1]
+ )
+ fy_rzphi = (
+ rzphi_rsquared.nodal_derivs.partials[3, ipsi+1, itheta+1],
+ rzphi_offset.nodal_derivs.partials[3, ipsi+1, itheta+1],
+ rzphi_nu.nodal_derivs.partials[3, ipsi+1, itheta+1],
+ rzphi_jac.nodal_derivs.partials[3, ipsi+1, itheta+1]
+ )
+ rfac = sqrt(f_rzphi[1])
+ eta = twopi * (itheta / mtheta + f_rzphi[2])
+ r = ro + rfac * cos(eta)
+ jacfac = f_rzphi[4]
+
+ fill!(v, 0.0)
+ v[1, 1] = fx_rzphi[1] / (2 * rfac)
+ v[1, 2] = fx_rzphi[2] * twopi * rfac
+ v[1, 3] = fx_rzphi[3] * r
+ v[2, 1] = fy_rzphi[1] / (2 * rfac)
+ v[2, 2] = (1 + fy_rzphi[2]) * twopi * rfac
+ v[2, 3] = fy_rzphi[3] * r
+ v[3, 3] = twopi * r
+
+ w11 = (1 + fy_rzphi[2]) * twopi^2 * rfac * r / jacfac
+ w12 = -fy_rzphi[1] * pi * r / (rfac * jacfac)
+
+ delpsi = sqrt(w11^2 + w12^2)
+ eqfun_fs[ipsi+1, itheta+1, 1] = sqrt(((twopi * psio * delpsi)^2 + f_sq_vec[1]^2) / (twopi * r)^2)
+ eqfun_fs[ipsi+1, itheta+1, 2] = (sum(v[1, :] .* v[2, :]) + f_sq_vec[4] * v[3, 3] * v[1, 3]) / (jacfac * eqfun_fs[ipsi+1, itheta+1, 1]^2)
+ eqfun_fs[ipsi+1, itheta+1, 3] = (v[2, 3] * v[3, 3] + f_sq_vec[4] * v[3, 3]^2) / (jacfac * eqfun_fs[ipsi+1, itheta+1, 1]^2)
+ end
+ end
+ # Create 2D interpolants for physics quantities (eqfun)
+ eqfun_grid2d = (eqfun_xs, theta_range)
+ @views eqfun_fs[:, end, :] .= eqfun_fs[:, 1, :]
+ eqfun_B = cubic_interp(eqfun_grid2d, eqfun_fs[:, :, 1]; itp_opts2d...)
+ eqfun_metric1 = cubic_interp(eqfun_grid2d, eqfun_fs[:, :, 2]; itp_opts2d...)
+ eqfun_metric2 = cubic_interp(eqfun_grid2d, eqfun_fs[:, :, 3]; itp_opts2d...)
+
+ # Create ProfileSplines from sq interpolant
+ # sq_fs columns: [F*2π, P, dV/dψ, q]
+ profiles = ProfileSplines(
+ sq_xs,
+ sq_fs[:, 1], # F values (already includes 2π factor)
+ sq_fs[:, 2], # P values
+ sq_fs[:, 3], # dV/dψ values
+ sq_fs[:, 4] # q values
+ )
+
+ geometry = compute_geometry_profiles(rzphi_xs, rzphi_ys,
+ rzphi_rsquared, rzphi_offset, rzphi_jac, ro)
+
+ return PlasmaEquilibrium(
+ input.config,
+ EquilibriumParameters(; psihigh_resolved=psihigh),
+ profiles,
+ geometry,
+ rzphi_xs, rzphi_ys,
+ rzphi_rsquared, rzphi_offset, rzphi_nu, rzphi_jac,
+ eqfun_B, eqfun_metric1, eqfun_metric2,
+ ro,
+ zo,
+ psio
+ )
+end
diff --git a/src/Equilibrium/Axisymmetric/Separatrix.jl b/src/Equilibrium/Axisymmetric/Separatrix.jl
new file mode 100644
index 0000000000..2e3819829e
--- /dev/null
+++ b/src/Equilibrium/Axisymmetric/Separatrix.jl
@@ -0,0 +1,260 @@
+# Separatrix.jl
+#
+# Safety factor between the outermost grid surface and the separatrix of a diverted equilibrium,
+# taken from the X-point(s) of the equilibrium's own poloidal flux rather than fitted, and the
+# separatrix's midplane and extremal points (`equilibrium_separatrix_find!`).
+#
+# Near a separatrix a field line stalls poloidally at each X-point it passes, so
+#
+# q(ψ) = c + Σ_i A_i ln[1 / (ψ_Xi − ψ)], A_i = F / (2π R_Xi sqrt(−det H_i)),
+#
+# with ψ_Xi the flux at saddle i of ψ(R, Z), H_i its Hessian there, and F = R B_φ. The constant is
+# fixed by the traced q on the outermost grid surface, so nothing is fitted. One term describes a
+# single null, two coincident terms a connected double null, and a second term at larger flux a
+# disconnected one.
+#
+# The saddles are selected from the last closed flux surface itself: each minimum of the poloidal
+# field along the outermost traced surface is followed to the critical point it leads to. On a
+# single-null shape this usually also reaches the far secondary X-point; its term is small. A
+# limited plasma with an X-point nearby is not told apart from a diverted one. Divertors with a
+# second null beside the primary one (snowflake) or on the leg (x-point target) are not modelled;
+# the shear check below is the backstop.
+
+# Accepted disagreement between the law's dq/dψ and the traced profile's over the outer knots. A
+# law missing one of two equal X-points is low by a factor of two, so the bound sits well inside it.
+const SEPARATRIX_SHEAR_RATIO = 1.5
+# Outer knots the shear check is taken over.
+const SEPARATRIX_CHECK_KNOTS = 4
+# Closest approach to the separatrix flux a surface is placed at, in normalized flux.
+const SEPARATRIX_PSI_GAP = 1e-9
+
+# Gradient and Hessian of the 2D flux at (r, z).
+function _flux_derivatives(psi_in, r::Float64, z::Float64)
+ pr = Float64(psi_in((r, z); deriv=DerivOp(1, 0)))
+ pz = Float64(psi_in((r, z); deriv=DerivOp(0, 1)))
+ prr = Float64(psi_in((r, z); deriv=DerivOp(2, 0)))
+ prz = Float64(psi_in((r, z); deriv=DerivOp(1, 1)))
+ pzz = Float64(psi_in((r, z); deriv=DerivOp(0, 2)))
+ return (; pr, pz, prr, prz, pzz, det=prr * pzz - prz^2)
+end
+
+# Follow |∇ψ|² downhill from a seed with damped Newton steps on ∇ψ = 0. Returns the critical point,
+# or `nothing` when the descent leaves the flux grid or stalls short of one.
+function _descend_to_critical_point(psi_in, ingest::DirectIngest, r::Float64, z::Float64, grad_tol::Float64)
+ for _ in 1:100
+ d = _flux_derivatives(psi_in, r, z)
+ g = d.pr^2 + d.pz^2
+ sqrt(g) <= grad_tol && return (; r, z, det=d.det)
+ d.det == 0.0 && return nothing
+ dr = -(d.pzz * d.pr - d.prz * d.pz) / d.det
+ dz = -(d.prr * d.pz - d.prz * d.pr) / d.det
+ t = 1.0
+ stepped = false
+ while t >= 1e-6
+ rn, zn = r + t * dr, z + t * dz
+ if ingest.rmin <= rn <= ingest.rmax && ingest.zmin <= zn <= ingest.zmax
+ dn = _flux_derivatives(psi_in, rn, zn)
+ if dn.pr^2 + dn.pz^2 < g
+ r, z, stepped = rn, zn, true
+ break
+ end
+ end
+ t /= 2
+ end
+ stepped || return nothing
+ end
+ return nothing
+end
+
+"""
+ separatrix_q_law(equil; psi_max=equil.profiles.xs[end], shear_ratio=SEPARATRIX_SHEAR_RATIO)
+ -> nothing | (; psi_x, A, r_x, z_x, psi_anchor, q_anchor, shear_ratio)
+
+Safety factor beyond the equilibrium's ψ grid from the X-point(s) on its last closed flux surface:
+
+ q(ψ) = q_anchor + Σ_i A_i ln[(psi_x_i − psi_anchor) / (psi_x_i − ψ)]
+
+`psi_x` are the normalized fluxes of the selected saddles (ascending, so `psi_x[1]` is where q
+diverges), `A` their logarithmic coefficients `F / (2π R_X sqrt(−det H))`, `r_x`/`z_x` their
+positions, and the anchor is the traced q at `psi_max`. `psi_x[1]` need not equal 1: a
+reconstruction may place its boundary slightly inside the X-point flux.
+
+Returns `nothing` when the law does not apply or cannot be trusted:
+
+ - the equilibrium is not a direct (2D flux) one — an inverse equilibrium carries its own q;
+ - no minimum of the poloidal field on the outermost surface leads to a saddle outside the grid
+ (a plasma with no X-point nearby; a limited plasma that has one still gets a law);
+ - q is not rising at the anchor;
+ - the law's dq/dψ and the traced profile's differ by more than `shear_ratio` over the outer
+ knots (returned as `shear_ratio`, law over traced).
+"""
+function separatrix_q_law(equil::PlasmaEquilibrium;
+ psi_max::Real=Float64(equil.profiles.xs[end]),
+ shear_ratio::Real=SEPARATRIX_SHEAR_RATIO)
+ ingest = equil.ingest
+ ingest isa DirectIngest || return nothing
+ psi_in = cubic_interp((ingest.psi_xs, ingest.psi_ys), ingest.psi_rz; extrap=ExtendExtrap())
+ xs = equil.profiles.xs
+ psi_anchor = min(Float64(psi_max), Float64(xs[end]))
+ q_anchor = Float64(equil.profiles.q_spline(psi_anchor))
+ q_slope = Float64(equil.profiles.q_deriv(psi_anchor))
+ (isfinite(q_anchor) && q_anchor * q_slope > 0) || return nothing
+
+ # Poloidal field along the outermost traced surface.
+ psi_surface = Float64(equil.rzphi_xs[end])
+ thetas = equil.rzphi_ys[1:(end-1)]
+ hint2d = (Ref(1), Ref(1))
+ rs, zs, bp = similar(thetas), similar(thetas), similar(thetas)
+ for (i, theta) in enumerate(thetas)
+ r_minor = sqrt(equil.rzphi_rsquared((psi_surface, theta); hint=hint2d))
+ theta_cyl = 2π * (theta + equil.rzphi_offset((psi_surface, theta); hint=hint2d))
+ rs[i] = equil.ro + r_minor * cos(theta_cyl)
+ zs[i] = equil.zo + r_minor * sin(theta_cyl)
+ d = _flux_derivatives(psi_in, rs[i], zs[i])
+ bp[i] = hypot(d.pr, d.pz) / rs[i]
+ end
+
+ # Each minimum of the poloidal field is where the surface passes a null; follow it there.
+ n = length(bp)
+ grad_tol = 1e-10 * maximum(bp .* rs)
+ merge_dist = 1e-6 * (ingest.rmax - ingest.rmin)
+ f_edge = abs(Float64(ingest.sq_fs[end, 1]))
+ saddles = NamedTuple{(:psi, :A, :r, :z),NTuple{4,Float64}}[]
+ for i in 1:n
+ (bp[i] < bp[mod1(i - 1, n)] && bp[i] <= bp[mod1(i + 1, n)]) || continue
+ cp = _descend_to_critical_point(psi_in, ingest, rs[i], zs[i], grad_tol)
+ (cp === nothing || cp.det >= 0) && continue
+ psi_x = 1.0 - Float64(psi_in((cp.r, cp.z))) / ingest.psio
+ psi_x > psi_anchor || continue
+ any(s -> hypot(s.r - cp.r, s.z - cp.z) < merge_dist, saddles) && continue
+ push!(saddles, (psi=psi_x, A=f_edge / (2π * cp.r * sqrt(-cp.det)), r=cp.r, z=cp.z))
+ end
+ isempty(saddles) && return nothing
+ sort!(saddles; by=s -> s.psi)
+
+ law = (psi_x=[s.psi for s in saddles], A=[s.A for s in saddles], r_x=[s.r for s in saddles],
+ z_x=[s.z for s in saddles], psi_anchor=psi_anchor, q_anchor=q_anchor)
+
+ # The law must reproduce the traced profile's own shear where the two overlap.
+ knots = filter(i -> xs[i] <= psi_anchor, eachindex(xs))
+ isempty(knots) && return nothing
+ band = knots[max(1, end - SEPARATRIX_CHECK_KNOTS + 1):end]
+ hint = Ref(1)
+ ratio = median([separatrix_q_dqdpsi(law, xs[i]) / Float64(equil.profiles.q_deriv(xs[i]; hint=hint)) for i in band])
+ (isfinite(ratio) && inv(shear_ratio) <= ratio <= shear_ratio) || return nothing
+ return merge(law, (; shear_ratio=ratio))
+end
+
+"""
+dq/dψ on the separatrix law.
+"""
+separatrix_q_dqdpsi(law, psi::Real) = sign(law.q_anchor) * sum(A / (px - psi) for (A, px) in zip(law.A, law.psi_x))
+
+"""
+q on the separatrix law.
+"""
+separatrix_q(law, psi::Real) =
+ law.q_anchor + sign(law.q_anchor) * sum(A * log((px - law.psi_anchor) / (px - psi)) for (A, px) in zip(law.A, law.psi_x))
+
+"""
+ψ at which the separatrix law reaches `q_target`. Returns `nothing` when the target is not beyond
+the anchor, or lies closer to the separatrix flux than `psi_gap`.
+"""
+function separatrix_q_psi(law, q_target::Real; psi_gap::Real=SEPARATRIX_PSI_GAP)
+ s = sign(law.q_anchor)
+ s * (q_target - law.q_anchor) > 0 || return nothing
+ psi_sep = law.psi_x[1]
+ psi_gap < psi_sep - law.psi_anchor || return nothing
+ # Solve in the logarithmic distance to the separatrix, where q is close to linear.
+ residual(u) = s * (separatrix_q(law, psi_sep - exp(u)) - q_target)
+ u_near, u_far = log(psi_gap), log(psi_sep - law.psi_anchor)
+ residual(u_near) > 0 || return nothing
+ return psi_sep - exp(find_zero(residual, (u_near, u_far), Roots.Brent()))
+end
+
+"""
+ equilibrium_separatrix_find!(pe::PlasmaEquilibrium)
+
+Find the separatrix midplane radii `rsep` and the top/bottom extremal points (`rext`, `zext`, with
+`zsep = zext`), store them in `pe.params`, and return them. Port of Fortran `equil_out_sep_find`.
+"""
+function equilibrium_separatrix_find!(pe::PlasmaEquilibrium)
+ mpsi = length(pe.rzphi_xs) - 1
+ edge_idx = mpsi + 1 # Edge flux surface index
+ psi_edge = pe.rzphi_xs[edge_idx]
+ rsep = zeros(2)
+
+ # Outboard and inboard midplane R via bracketed Brent on θ + η(θ) - η₀ = 0.
+ # iside=1 → outboard (η₀=0.0, θ near 0), iside=2 → inboard (η₀=0.5, θ near 0.5).
+ for iside in 1:2
+ eta0 = (iside == 1) ? 0.0 : 0.5
+ hint2d = (Ref(1), Ref(1))
+ theta_lo, theta_hi = (iside == 1) ? (-0.25, 0.25) : (0.25, 0.75)
+ side_label = (iside == 1) ? "outboard" : "inboard"
+ theta = try
+ find_zero(
+ theta -> theta + pe.rzphi_offset((psi_edge, theta); hint=hint2d) - eta0,
+ (theta_lo, theta_hi), Roots.Brent();
+ atol=1e-12, rtol=1e-12)
+ catch e
+ error("Separatrix $side_label midplane root not found in bracket " *
+ "[$(theta_lo), $(theta_hi)]: $(e.msg)")
+ end
+ r2 = pe.rzphi_rsquared((psi_edge, theta))
+ offset = pe.rzphi_offset((psi_edge, theta))
+ rsep[iside] = pe.ro + sqrt(r2) * cos(2π * (theta + offset))
+ end
+
+ # Top and bottom separatrix Z extrema via bracketed Brent on ∂z/∂θ = 0.
+ # iside=1 → top (θ ∈ [0.0, 0.5]), iside=2 → bottom (θ ∈ [0.5, 1.0]), as in Fortran.
+ zsep = zeros(2)
+ rext = zeros(2)
+ zext = zeros(2)
+
+ for iside in 1:2
+ hint2d = (Ref(1), Ref(1))
+
+ # Cache variables populated by z_deriv, read after convergence
+ rfac = Ref(0.0)
+ cos_phase = Ref(0.0)
+ z_val = Ref(0.0)
+
+ # ∂z/∂θ where z(θ) = zo + √r²(θ) · sin(2π(θ + η(θ)))
+ function z_deriv(theta_inner)
+ r2 = pe.rzphi_rsquared((psi_edge, theta_inner); hint=hint2d)
+ r2y = pe.rzphi_rsquared((psi_edge, theta_inner); deriv=DerivOp(0, 1), hint=hint2d)
+ η = pe.rzphi_offset((psi_edge, theta_inner); hint=hint2d)
+ η1 = pe.rzphi_offset((psi_edge, theta_inner); deriv=DerivOp(0, 1), hint=hint2d)
+ rfac_local = sqrt(max(0.0, r2))
+ rfac1 = (rfac_local > 0) ? r2y / (2 * rfac_local) : 0.0
+ phase1 = 2π * (1 + η1)
+ sin_phase = sin(2π * (theta_inner + η))
+ cos_phase_local = cos(2π * (theta_inner + η))
+
+ rfac[] = rfac_local
+ cos_phase[] = cos_phase_local
+ z_val[] = pe.zo + rfac_local * sin_phase
+
+ return rfac_local * phase1 * cos_phase_local + rfac1 * sin_phase
+ end
+
+ theta_lo, theta_hi = (iside == 1) ? (0.0, 0.5) : (0.5, 1.0)
+ side_label = (iside == 1) ? "top" : "bottom"
+ theta = try
+ find_zero(z_deriv, (theta_lo, theta_hi), Roots.Brent();
+ atol=1e-12, rtol=1e-12)
+ catch e
+ error("Separatrix $side_label Z-extremum root not found in bracket " *
+ "[$(theta_lo), $(theta_hi)]: $(e.msg)")
+ end
+
+ rext[iside] = pe.ro + rfac[] * cos_phase[]
+ zsep[iside] = zext[iside] = z_val[]
+ end
+
+ pe.params.rsep = rsep
+ pe.params.zsep = zsep
+ pe.params.rext = rext
+ pe.params.zext = zext
+ return (rsep, zsep, rext, zext)
+end
diff --git a/src/Equilibrium/Axisymmetric/SolveTolerances.jl b/src/Equilibrium/Axisymmetric/SolveTolerances.jl
new file mode 100644
index 0000000000..238f29465f
--- /dev/null
+++ b/src/Equilibrium/Axisymmetric/SolveTolerances.jl
@@ -0,0 +1,28 @@
+# SolveTolerances.jl
+#
+# Absolute tolerance and completion check shared by the equilibrium ODE solves
+# (direct field-line, large-aspect-ratio and TJ-analytic integrations).
+
+"""
+Ceiling on the absolute tolerance of the equilibrium ODE solves, so a loose `flux_surface_rtol` never loosens abstol.
+"""
+const EQUIL_ABSTOL_MAX = 1e-8
+
+"""
+ equil_abstol(rtol, cap=EQUIL_ABSTOL_MAX)
+
+Absolute tolerance of an equilibrium ODE solve: follows `flux_surface_rtol` but is never looser than `cap`.
+"""
+equil_abstol(rtol::Real, cap::Real=EQUIL_ABSTOL_MAX) = min(rtol, cap)
+
+"""
+ check_equil_solve(sol, what)
+
+Return the equilibrium ODE solution `sol`, or raise an error naming the solve `what` if the integrator
+stopped early (step limit, step-size underflow, instability) instead of finishing or terminating on its callback.
+"""
+function check_equil_solve(sol, what::AbstractString)
+ sol.retcode == ReturnCode.Success || sol.retcode == ReturnCode.Terminated ||
+ error("Equilibrium ODE solve ($what) stopped early at t = $(sol.t[end]) with retcode $(sol.retcode).")
+ return sol
+end
diff --git a/src/Equilibrium/Config.jl b/src/Equilibrium/Config.jl
new file mode 100644
index 0000000000..9738fae5b1
--- /dev/null
+++ b/src/Equilibrium/Config.jl
@@ -0,0 +1,317 @@
+"""
+ IonSpecies(; z, m, fraction=NaN, density="")
+
+One main-ion species of the plasma. `z`/`m` are the charge (e) and mass (proton masses). The
+density is given by exactly one of `fraction` or `density`, which select a fraction of the total
+`n_i` profile or an explicit per-species profile (`n_*` dataset) in the kinetic file.
+"""
+struct IonSpecies
+ z::Int
+ m::Int
+ fraction::Float64
+ density::String
+end
+
+IonSpecies(; z::Integer, m::Integer, fraction=NaN, density="") =
+ IonSpecies(Int(z), Int(m), Float64(fraction), String(density))
+IonSpecies(d::AbstractDict) = IonSpecies(; (Symbol(k) => v for (k, v) in d)...)
+Base.convert(::Type{Vector{IonSpecies}}, v::AbstractVector) =
+ IonSpecies[x isa IonSpecies ? x : IonSpecies(x) for x in v]
+
+"""
+ EquilibriumConfig(...)
+
+An immutable struct containing configuration parameters for equilibrium reconstruction
+specified in the input.
+
+## Fields
+
+ - `eq_type::String` - Type of equilibrium file ("efit", "chease", "ifile", "imas", ...); an analytic config implies its own
+ - `eq_filename::String` - Path to equilibrium input file
+ - `jac_type::String` - Jacobian coordinate type ("hamada", "pest", "equal_arc", "boozer", "park", "custom")
+ - `power_bp::Int` - Poloidal field power exponent for Jacobian (internal, derived from `jac_type`; not a deck key)
+ - `power_b::Int` - Total field power exponent for Jacobian (internal, derived from `jac_type`; not a deck key)
+ - `power_r::Int` - Major radius power exponent for Jacobian (internal, derived from `jac_type`; not a deck key)
+ - `power_rc::Int` - Minor radius (rfac = √((R-R₀)²+(Z-Z₀)²)) power exponent for Jacobian (internal, derived from `jac_type`; not a deck key)
+ - `jac_custom_power_bp::Int` - Poloidal-field exponent for a custom Jacobian `J = Bp^bp · B^b / (R^r · rfac^rc)`; read only when `jac_type = "custom"`, ignored for named types
+ - `jac_custom_power_b::Int` - Total-field exponent for a custom Jacobian; read only when `jac_type = "custom"`, ignored for named types
+ - `jac_custom_power_r::Int` - Major-radius exponent for a custom Jacobian; read only when `jac_type = "custom"`, ignored for named types
+ - `jac_custom_power_rc::Int` - Minor-radius (rfac) exponent for a custom Jacobian; read only when `jac_type = "custom"`, ignored for named types
+ - `r0_norm::Float64` - Major radius normalization for CHEASE/EQDSK [m]
+ - `b0_norm::Float64` - On-axis toroidal field normalization for CHEASE/EQDSK [T]
+ - `grid_type::String` - Grid type for flux surface discretization ("auto" — two-pass measured-curvature
+ refinement when mpsi=0, three-region log layout when mpsi>0; "core_edge_packed" (sin² spacing, dense at axis and edge), "pow1", "uniform";
+ inverse equilibria also "rho" (uniform in √ψ from psilow to psihigh) and "original" (the input
+ file's own ψ nodes between psilow and psihigh; ignores mpsi))
+ - `psilow::Float64` - Lower limit of normalized flux coordinate
+ - `psihigh::Float64` - Requested upper limit of normalized flux coordinate; the value the
+ equilibrium is actually formed on is `EquilibriumParameters.psihigh_resolved`.
+ - `mpsi::Int` - Number of radial grid intervals; 0 with grid_type="auto" selects the two-pass auto
+ grid. Standalone `PlasmaEquilibrium` callers get the coarse pass-1 grid unless they refine via
+ `refined_psi_grid` + `override_psi_nodes`.
+ - `psi_accuracy::Float64` - Target relative accuracy τ of splined profile derivatives for the
+ two-pass auto grid (knot count scales as τ^(-1/3))
+ - `mtheta::Int` - Number of poloidal grid points
+ - `newq0::Float64` - Target on-axis safety factor q(0); the q and F profiles are rescaled to
+ meet it (0 = use input value); q is positive, so negative values are rejected
+ - `flux_surface_rtol::Float64` - Relative tolerance of the ODE solves that trace each flux surface; their absolute tolerance
+ is `equil_abstol(flux_surface_rtol)`, i.e. `flux_surface_rtol` capped at `EQUIL_ABSTOL_MAX`
+ - `imas_cocos::Int` - Expected COCOS convention of an IMAS `dd.equilibrium` input (11 = IMAS standard, 2 = GPEC internal)
+ - `kinetic_file::String` - Kinetic-profile file read once into `PlasmaEquilibrium.kinetic` (see [`read_kinetic_file`](@ref));
+ empty for none. Every kinetic consumer (NTV, tearing, the layer-overlap scan, grid refinement) derives its view from it.
+ - `kinetic_group::String` - HDF5 group of `kinetic_file` holding the profiles
+ - `kinetic_format::String` - Column layout of an ASCII `kinetic_file`: `"legacy"` (6 columns) or `"rates-v1"` (9 columns,
+ appending supplied `lnLambda nu_i nu_e`); see [`read_kinetic_file`](@ref)
+ - `ion_species`, `impurity_charge`, `impurity_mass`, `zeff_default`, `chi_e_default`, `chi_i_default`,
+ `chi_phi_default`, `tau_E`, `resistivity_model`, `lnLambda_form` - The plasma composition, profile defaults
+ and resistivity closure applied to the profiles of `kinetic_file` (see [`KineticProfileData`](@ref)); `nothing`
+ keeps the `KineticProfileData` default. Setting any of them needs `kinetic_file`.
+"""
+@kwdef struct EquilibriumConfig
+ eq_type::String = "efit"
+ eq_filename::String = "mypath"
+ r0_norm::Float64 = 1.0
+ b0_norm::Float64 = 1.0
+
+ jac_type::String = "hamada"
+ power_bp::Int = 0
+ power_b::Int = 0
+ power_r::Int = 0
+ power_rc::Int = 0
+
+ jac_custom_power_bp::Int = 0
+ jac_custom_power_b::Int = 0
+ jac_custom_power_r::Int = 0
+ jac_custom_power_rc::Int = 0
+
+ grid_type::String = "auto"
+ psilow::Float64 = 1e-2
+ psihigh::Float64 = 0.9995
+ mpsi::Int = 0
+ psi_accuracy::Float64 = 0.001
+ mtheta::Int = 512
+
+ newq0::Float64 = 0.0
+ flux_surface_rtol::Float64 = 1e-10
+
+ imas_cocos::Int = 11
+
+ kinetic_file::String = ""
+ kinetic_group::String = "/"
+ kinetic_format::String = "legacy"
+ ion_species::Union{Nothing,Vector{IonSpecies}} = nothing
+ impurity_charge::Union{Nothing,Int} = nothing
+ impurity_mass::Union{Nothing,Int} = nothing
+ zeff_default::Union{Nothing,Float64} = nothing
+ chi_e_default::Union{Nothing,Float64} = nothing
+ chi_i_default::Union{Nothing,Float64} = nothing
+ chi_phi_default::Union{Nothing,Float64} = nothing
+ tau_E::Union{Nothing,Float64} = nothing
+ resistivity_model::Union{Nothing,Symbol} = nothing
+ lnLambda_form::Union{Nothing,Symbol} = nothing
+
+ """
+ Inner constructor that derives the Jacobian exponents from `jac_type` and validates the inputs.
+ """
+ # The `_` slots are the `power_*` fields, always derived from `jac_type` here.
+ function EquilibriumConfig(eq_type, eq_filename, r0_norm, b0_norm, jac_type, _, _, _, _,
+ jac_custom_power_bp, jac_custom_power_b, jac_custom_power_r, jac_custom_power_rc,
+ grid_type, psilow, psihigh, mpsi, psi_accuracy, mtheta, newq0, flux_surface_rtol,
+ imas_cocos, kinetic_file, kinetic_group, kinetic_format, composition...)
+ if jac_type == "hamada"
+ @info "Forcing hamada coordinate jacobian exponents: power_*"
+ power_b = 0
+ power_bp = 0
+ power_r = 0
+ power_rc = 0
+ elseif jac_type == "pest"
+ @info "Forcing pest coordinate jacobian exponents: power_*"
+ power_b = 0
+ power_bp = 0
+ power_r = 2
+ power_rc = 0
+ elseif jac_type == "equal_arc"
+ @info "Forcing equal_arc coordinate jacobian exponents: power_*"
+ power_b = 0
+ power_bp = 1
+ power_r = 0
+ power_rc = 0
+ elseif jac_type == "boozer"
+ @info "Forcing boozer coordinate jacobian exponents: power_*"
+ power_b = 2
+ power_bp = 0
+ power_r = 0
+ power_rc = 0
+ elseif jac_type == "park"
+ @info "Forcing park coordinate jacobian exponents: power_*"
+ power_b = 1
+ power_bp = 0
+ power_r = 0
+ power_rc = 0
+ elseif jac_type == "custom"
+ # Custom Jacobian: the user-facing knobs define the exponents.
+ power_bp = jac_custom_power_bp
+ power_b = jac_custom_power_b
+ power_r = jac_custom_power_r
+ power_rc = jac_custom_power_rc
+ # Normalize to a named type when the powers match, so fast paths are taken.
+ if power_b == 0 && power_bp == 0 && power_r == 0 && power_rc == 0
+ jac_type = "hamada"
+ @info "Recognized hamada jacobian from power exponents"
+ elseif power_b == 0 && power_bp == 0 && power_r == 2 && power_rc == 0
+ jac_type = "pest"
+ @info "Recognized pest jacobian from power exponents"
+ elseif power_b == 0 && power_bp == 1 && power_r == 0 && power_rc == 0
+ jac_type = "equal_arc"
+ @info "Recognized equal_arc jacobian from power exponents"
+ elseif power_b == 2 && power_bp == 0 && power_r == 0 && power_rc == 0
+ jac_type = "boozer"
+ @info "Recognized boozer jacobian from power exponents"
+ elseif power_b == 1 && power_bp == 0 && power_r == 0 && power_rc == 0
+ jac_type = "park"
+ @info "Recognized park jacobian from power exponents"
+ else
+ @info "Using manual jacobian exponents: power b, bp, r, rc = $(power_b), $(power_bp), $(power_r), $(power_rc)"
+ end
+ else
+ error("Cannot recognize jac_type = $(jac_type)")
+ end
+ (isfinite(flux_surface_rtol) && flux_surface_rtol > 0) || error("flux_surface_rtol = $flux_surface_rtol must be a positive, finite relative tolerance")
+ newq0 >= 0 || error("newq0 = $newq0 is not supported: q must be positive. Use newq0 = 0 (keep the input q) or newq0 > 0.")
+ if psihigh > 1.0
+ @warn "psihigh = $psihigh exceeds 1.0 (separatrix); clamping to 1.0"
+ end
+ psihigh = min(psihigh, 1.0)
+ kinetic_format in KINETIC_FORMATS || error("kinetic_format = \"$kinetic_format\" must be one of $KINETIC_FORMATS")
+ isempty(kinetic_file) && any(!isnothing, composition) &&
+ error("the kinetic composition keys of [Equilibrium] describe the profiles of kinetic_file; set kinetic_file")
+ return new(eq_type, eq_filename, r0_norm, b0_norm, jac_type, power_bp, power_b, power_r, power_rc,
+ jac_custom_power_bp, jac_custom_power_b, jac_custom_power_r, jac_custom_power_rc,
+ grid_type, psilow, psihigh, mpsi, psi_accuracy, mtheta, newq0, flux_surface_rtol,
+ imas_cocos, kinetic_file, kinetic_group, kinetic_format, composition...)
+ end
+end
+
+# ASCII kinetic-table layouts, named as Fortran PENTRC `kinetic_format`, and their column counts.
+const KINETIC_FORMATS = ("legacy", "rates-v1")
+const KINETIC_FORMAT_COLUMNS = Dict("legacy" => 6, "rates-v1" => 9)
+
+# The kinetic composition keys of a config, the ones it sets, as `KineticProfileData` keywords.
+const KINETIC_COMPOSITION_KEYS = (:ion_species, :impurity_charge, :impurity_mass, :zeff_default, :chi_e_default, :chi_i_default,
+ :chi_phi_default, :tau_E, :resistivity_model, :lnLambda_form)
+kinetic_composition(config::EquilibriumConfig) =
+ (; (k => getfield(config, k) for k in KINETIC_COMPOSITION_KEYS if getfield(config, k) !== nothing)...)
+
+"""
+ EquilibriumParameters
+
+A mutable struct containing computed equilibrium parameters and diagnostic flags.
+
+## Fields
+
+ - `ro::Union{Nothing,Float64}` - R-coordinate of the magnetic axis [m]
+ - `zo::Union{Nothing,Float64}` - Z-coordinate of the magnetic axis [m]
+ - `psio::Union{Nothing,Float64}` - Total flux difference |ψ_axis - ψ_boundary| [Wb/rad]
+ - `psihigh_resolved::Union{Nothing,Float64}` - Outer flux limit the equilibrium was formed on
+ (the outermost ψ node); the plasma edge downstream of `PlasmaEquilibrium`.
+ - `rsep::Union{Nothing,Vector{Float64}}` - R-coordinates of the plasma boundary [m]
+ - `zsep::Union{Nothing,Vector{Float64}}` - Z-coordinates of the plasma boundary [m]
+ - `rext::Union{Nothing,Vector{Float64}}` - R-coordinates of the plasma edge [m]
+ - `zext::Union{Nothing,Vector{Float64}}` - Z-coordinates of the plasma edge [m]
+ - `psi0::Union{Nothing,Float64}` - Normalized poloidal flux at reference location
+ - `b0::Union{Nothing,Float64}` - Total magnetic field strength at the axis [T]
+ - `q0::Union{Nothing,Float64}` - Safety factor at the axis
+ - `qmin::Union{Nothing,Float64}` - Minimum safety factor in the plasma
+ - `qmax::Union{Nothing,Float64}` - Maximum safety factor in the plasma
+ - `qa::Union{Nothing,Float64}` - Safety factor at the plasma edge
+ - `q95::Union{Nothing,Float64}` - Safety factor at 95% flux surface
+ - `qextrema_psi::Union{Nothing,Vector{Float64}}` - Normalized flux values at q extrema
+ - `qextrema_q::Union{Nothing,Vector{Float64}}` - Safety factor values at extrema
+ - `mextrema::Union{Nothing,Int}` - Number of extrema in q-profile
+ - `psi_norm::Union{Nothing,Float64}` - Normalized poloidal flux
+ - `psi_axis::Union{Nothing,Float64}` - Poloidal flux at the axis
+ - `psi_boundary::Union{Nothing,Float64}` - Poloidal flux at the boundary
+ - `psi_boundary_norm::Union{Nothing,Float64}` - Normalized boundary flux
+ - `psi_boundary_offset::Union{Nothing,Float64}` - Boundary flux offset
+ - `psi_axis_offset::Union{Nothing,Float64}` - Axis flux offset
+ - `psi_boundary_sign::Union{Nothing,Int}` - Sign of boundary flux
+ - `psi_axis_sign::Union{Nothing,Int}` - Sign of axis flux
+ - `psi_boundary_zero::Union{Nothing,Bool}` - Whether boundary flux is zero
+ - `rmean::Union{Nothing,Float64}` - Mean major radius [m]
+ - `amean::Union{Nothing,Float64}` - Mean minor radius [m]
+ - `aratio::Union{Nothing,Float64}` - Aspect ratio (R0/a)
+ - `kappa::Union{Nothing,Float64}` - Plasma elongation
+ - `delta1::Union{Nothing,Float64}` - Upper triangularity
+ - `delta2::Union{Nothing,Float64}` - Lower triangularity
+ - `bt0::Union{Nothing,Float64}` - Toroidal field at axis [T]
+ - `crnt::Union{Nothing,Float64}` - Plasma current [A], always positive
+ - `bt_sign::Int` - Sign of the toroidal field (+1 or -1; `bt0` is always positive)
+ - `ip_sign::Int` - Sign of the plasma current as the source file states it (+1 or -1)
+ - `bwall::Union{Nothing,Float64}` - Toroidal field at wall [T]
+ - `verbose::Bool` - Enable verbose output
+ - `diagnose_src::Bool` - Enable source data diagnostics
+ - `diagnose_maxima::Bool` - Enable extrema diagnostics
+ - `volume::Union{Nothing,Float64}` - Plasma volume [m³]
+ - `betat::Union{Nothing,Float64}` - Toroidal beta
+ - `betan::Union{Nothing,Float64}` - Normalized beta
+ - `betaj::Union{Nothing,Float64}` - Total beta
+ - `betap1::Union{Nothing,Float64}` - Poloidal beta (definition 1)
+ - `betap2::Union{Nothing,Float64}` - Poloidal beta (definition 2)
+ - `betap3::Union{Nothing,Float64}` - Poloidal beta (definition 3)
+ - `li1::Union{Nothing,Float64}` - Internal inductance (definition 1)
+ - `li2::Union{Nothing,Float64}` - Internal inductance (definition 2)
+ - `li3::Union{Nothing,Float64}` - Internal inductance (definition 3)
+"""
+@kwdef mutable struct EquilibriumParameters
+ ro::Union{Nothing,Float64} = nothing
+ zo::Union{Nothing,Float64} = nothing
+ psio::Union{Nothing,Float64} = nothing
+ psihigh_resolved::Union{Nothing,Float64} = nothing
+ rsep::Union{Nothing,Vector{Float64}} = nothing
+ zsep::Union{Nothing,Vector{Float64}} = nothing
+ rext::Union{Nothing,Vector{Float64}} = nothing
+ zext::Union{Nothing,Vector{Float64}} = nothing
+ psi0::Union{Nothing,Float64} = nothing
+ b0::Union{Nothing,Float64} = nothing
+ q0::Union{Nothing,Float64} = nothing
+ qmin::Union{Nothing,Float64} = nothing
+ qmax::Union{Nothing,Float64} = nothing
+ qa::Union{Nothing,Float64} = nothing
+ q95::Union{Nothing,Float64} = nothing
+ qextrema_psi::Union{Nothing,Vector{Float64}} = nothing
+ qextrema_q::Union{Nothing,Vector{Float64}} = nothing
+ mextrema::Union{Nothing,Int} = nothing
+ psi_norm::Union{Nothing,Float64} = nothing
+ psi_axis::Union{Nothing,Float64} = nothing
+ psi_boundary::Union{Nothing,Float64} = nothing
+ psi_boundary_norm::Union{Nothing,Float64} = nothing
+ psi_boundary_offset::Union{Nothing,Float64} = nothing
+ psi_axis_offset::Union{Nothing,Float64} = nothing
+ psi_boundary_sign::Union{Nothing,Int} = nothing
+ psi_axis_sign::Union{Nothing,Int} = nothing
+ psi_boundary_zero::Union{Nothing,Bool} = nothing
+ rmean::Union{Nothing,Float64} = nothing
+ amean::Union{Nothing,Float64} = nothing
+ aratio::Union{Nothing,Float64} = nothing
+ kappa::Union{Nothing,Float64} = nothing
+ delta1::Union{Nothing,Float64} = nothing
+ delta2::Union{Nothing,Float64} = nothing
+ bt0::Union{Nothing,Float64} = nothing
+ crnt::Union{Nothing,Float64} = nothing
+ bt_sign::Int = 1
+ ip_sign::Int = 1
+ bwall::Union{Nothing,Float64} = nothing
+ verbose::Bool = false
+ diagnose_src::Bool = false
+ diagnose_maxima::Bool = false
+ volume::Union{Nothing,Float64} = nothing
+ betat::Union{Nothing,Float64} = nothing
+ betan::Union{Nothing,Float64} = nothing
+ betaj::Union{Nothing,Float64} = nothing
+ betap1::Union{Nothing,Float64} = nothing
+ betap2::Union{Nothing,Float64} = nothing
+ betap3::Union{Nothing,Float64} = nothing
+ li1::Union{Nothing,Float64} = nothing
+ li2::Union{Nothing,Float64} = nothing
+ li3::Union{Nothing,Float64} = nothing
+end
diff --git a/src/Equilibrium/Construction.jl b/src/Equilibrium/Construction.jl
new file mode 100644
index 0000000000..bec6e81746
--- /dev/null
+++ b/src/Equilibrium/Construction.jl
@@ -0,0 +1,163 @@
+# Construction.jl
+#
+# How a PlasmaEquilibrium is formed: the solver input for each source type, the constructors,
+# and re-forming on a new grid.
+
+"""
+ run_input(eq_config::EquilibriumConfig, source) -> DirectRunInput or InverseRunInput
+
+Build the solver input for `eq_config` from `source`: `nothing` reads `eq_config.eq_filename`, an
+[`AnalyticEquilibriumConfig`](@ref) runs its analytic solver, an `IMASdd.dd` is read by
+[`read_imas`](@ref), and a run input rebuilt from a stored ingest is rebound onto `eq_config`.
+"""
+function run_input(eq_config::EquilibriumConfig, ::Nothing)
+ eq_type = eq_config.eq_type
+ eq_type in EFIT_KINDS && return resolve_psihigh!(read_efit(eq_config))
+ eq_type in ("chease2", "chease_ascii") && return read_chease_ascii(eq_config)
+ eq_type in ("chease", "chease_binary") && return read_chease_binary(eq_config)
+ eq_type == "ifile" && return resolve_psihigh!(read_ifile(eq_config))
+ if haskey(ANALYTIC_EQ, eq_type)
+ spec = ANALYTIC_EQ[eq_type]
+ error("analytic eq_type=\"$eq_type\" needs its $(spec.config_type) as the source (a deck states it as a [$(spec.section)] section)")
+ end
+ eq_type == "imas" && error("eq_type=\"imas\" needs an IMASdd.dd as the source")
+ return error("Equilibrium type $(eq_type) is not implemented")
+end
+
+function run_input(eq_config::EquilibriumConfig, cfg::AnalyticEquilibriumConfig)
+ spec = get(ANALYTIC_EQ, eq_config.eq_type, nothing)
+ spec !== nothing && cfg isa spec.config_type ||
+ error("eq_type=\"$(eq_config.eq_type)\" is not an analytic kind solved from a $(typeof(cfg))")
+ return spec.run_fn(eq_config, cfg)
+end
+
+function run_input(eq_config::EquilibriumConfig, dd::IMASdd.dd)
+ eq_config.eq_type == "imas" || error("an IMASdd.dd source needs eq_type=\"imas\", not \"$(eq_config.eq_type)\"")
+ return read_imas(eq_config, dd)
+end
+
+# A run input rebuilt from an ingest is rebound onto the current config, resetting psihigh so a
+# pass-1 clamped value does not shadow a psihigh overridden in the rerun TOML.
+function run_input(eq_config::EquilibriumConfig, input::DirectRunInput)
+ input.config = eq_config
+ input.psihigh_resolved = eq_config.psihigh
+ return eq_config.eq_type in EFIT_KINDS ? resolve_psihigh!(input) : input
+end
+
+function run_input(eq_config::EquilibriumConfig, input::InverseRunInput)
+ input.config = eq_config
+ input.psihigh_resolved = eq_config.psihigh
+ return resolve_psihigh!(input)
+end
+
+"""
+ PlasmaEquilibrium(eq_config::EquilibriumConfig, source=nothing; override_psi_nodes=nothing, kinetic=nothing) -> PlasmaEquilibrium
+
+Form the equilibrium `eq_config` describes from `source` (see [`run_input`](@ref)), run the
+solver, and return it with global parameters, q-profile, and GSE diagnostics. Every other
+constructor ends here.
+
+`override_psi_nodes` bypasses the config-driven radial grid (`grid_type`/`mpsi`) and forms
+the equilibrium on the given strictly increasing ψ_N node vector, whose endpoints must match
+`psilow`/`psihigh` (used by [`reform`](@ref)). The kinetic profiles named by `kinetic_file` are read
+and attached, unless `kinetic` passes already-read ones.
+"""
+function PlasmaEquilibrium(eq_config::EquilibriumConfig, source=nothing; override_psi_nodes::Union{Nothing,Vector{Float64}}=nothing,
+ kinetic::Union{Nothing,KineticProfileData}=nothing)
+ eq_input = run_input(eq_config, source)
+
+ plasma_equilibrium = if eq_config.eq_type == "efit_by_inversion"
+ equilibrium_solver_by_inversion(eq_input; override_psi_nodes)
+ elseif eq_config.eq_type == "efit_arclength"
+ equilibrium_solver(eq_input, arclength_fieldline_int; override_psi_nodes)
+ else
+ equilibrium_solver(eq_input; override_psi_nodes)
+ end
+
+ # Forward the captured ingest so the gpec.h5 writer can snapshot it (nothing for analytic).
+ plasma_equilibrium.ingest = eq_input.ingest
+ # Analytic configs are still mutable; copy so later edits by the caller cannot change a re-form.
+ source isa AnalyticEquilibriumConfig && (plasma_equilibrium.analytic = source)
+ plasma_equilibrium.kinetic = kinetic === nothing ? configured_kinetic_profiles(eq_config) : kinetic
+
+ equilibrium_global_parameters!(plasma_equilibrium)
+ equilibrium_qfind!(plasma_equilibrium)
+ equilibrium_gse!(plasma_equilibrium)
+
+ return plasma_equilibrium
+end
+
+"""
+ reform(equil::PlasmaEquilibrium, psi_nodes::Vector{Float64}) -> PlasmaEquilibrium
+
+Re-form `equil` on the ψ_N nodes `psi_nodes` from the source it remembers: the stored
+`analytic` config, else its raw `ingest`, so no file is re-read; with neither it re-reads
+`config.eq_filename`. Its kinetic profiles carry over. The node endpoints must match `psilow`/`psihigh`.
+"""
+function reform(equil::PlasmaEquilibrium, psi_nodes::Vector{Float64})
+ source = if equil.analytic !== nothing
+ equil.analytic
+ elseif equil.ingest isa DirectIngest
+ build_direct_from_ingest(equil.config, equil.ingest)
+ elseif equil.ingest isa InverseIngest
+ build_inverse_from_ingest(equil.config, equil.ingest)
+ else
+ nothing
+ end
+ return PlasmaEquilibrium(equil.config, source; override_psi_nodes=psi_nodes, kinetic=equil.kinetic)
+end
+
+"""
+ PlasmaEquilibrium(path::AbstractString; eq_type="efit", kwargs...) -> PlasmaEquilibrium
+
+Read the equilibrium file at `path` and return the processed equilibrium. Convenience entry
+point of the scripting API: `kwargs` are [`EquilibriumConfig`](@ref) fields, so
+`PlasmaEquilibrium("g000001.00001"; jac_type="hamada", mpsi=128)` is the whole setup.
+
+Only file-based equilibria go through this constructor. Analytic and IMAS equilibria have
+their own `PlasmaEquilibrium(::AnalyticEquilibriumConfig)` and `PlasmaEquilibrium(::IMASdd.dd)` forms.
+
+```julia
+eq = PlasmaEquilibrium("input.geqdsk"; jac_type="hamada")
+```
+"""
+function PlasmaEquilibrium(path::AbstractString; eq_type::String="efit", kwargs...)
+ haskey(ANALYTIC_EQ, eq_type) &&
+ error("$eq_type is an analytic equilibrium: build it with PlasmaEquilibrium($(ANALYTIC_EQ[eq_type].config_type)(...)) instead")
+ return PlasmaEquilibrium(EquilibriumConfig(; eq_type, eq_filename=abspath(path), kwargs...))
+end
+
+"""
+ analytic_eq_type(cfg::AnalyticEquilibriumConfig) -> String
+
+The internal `eq_type` token of the `ANALYTIC_EQ` row whose config type `cfg` is.
+"""
+analytic_eq_type(cfg::AnalyticEquilibriumConfig) = only(k for (k, spec) in ANALYTIC_EQ if spec.config_type === typeof(cfg))
+
+"""
+ PlasmaEquilibrium(cfg::AnalyticEquilibriumConfig; kwargs...) -> PlasmaEquilibrium
+
+Solve the analytic equilibrium described by `cfg` and return the processed equilibrium. The
+`eq_type` is implied by the config type. `kwargs` are [`EquilibriumConfig`](@ref) fields.
+
+```julia
+eq = PlasmaEquilibrium(Equilibrium.SolovevConfig(; elongation=1.5); mpsi=0, psi_accuracy=1e-3)
+```
+"""
+function PlasmaEquilibrium(cfg::AnalyticEquilibriumConfig; kwargs...)
+ return PlasmaEquilibrium(EquilibriumConfig(; eq_type=analytic_eq_type(cfg), kwargs...), cfg)
+end
+
+"""
+ PlasmaEquilibrium(dd::IMASdd.dd; kwargs...) -> PlasmaEquilibrium
+
+Read the active equilibrium time slice of the IMAS data dictionary `dd` and return the processed
+equilibrium. `kwargs` are [`EquilibriumConfig`](@ref) fields; `imas_cocos` sets the ψ convention.
+
+```julia
+eq = PlasmaEquilibrium(dd; imas_cocos=11, jac_type="hamada")
+```
+"""
+function PlasmaEquilibrium(dd::IMASdd.dd; kwargs...)
+ return PlasmaEquilibrium(EquilibriumConfig(; eq_type="imas", kwargs...), dd)
+end
diff --git a/src/Equilibrium/Derived/CoordinateInvariant.jl b/src/Equilibrium/Derived/CoordinateInvariant.jl
new file mode 100644
index 0000000000..656ea7238f
--- /dev/null
+++ b/src/Equilibrium/Derived/CoordinateInvariant.jl
@@ -0,0 +1,126 @@
+"""
+Coordinate-invariant (root-area-weighted field) flux-surface operators.
+
+These building blocks implement the √area weighting of Pharr (2026),
+"Coordinate-invariant flux-surface Fourier analysis in tokamaks". They are the
+single source of truth for translating a flux-surface field component between the
+three field representations (all in tesla), shared by the ForceFreeStates and
+PerturbedEquilibrium modules:
+
+ - `b` bare / normal field (Fourier weight W = 1)
+ - `b̃` root-area-weighted field (W = √(J|∇ψ|)) — the coordinate-invariant field
+ - `b̄` area-weighted field (W = J|∇ψ|)
+
+With `Σ ≡ sqrtamat` (the mpert×mpert √weight convolution) and the scalar surface area
+`A ≡ jarea = ∫ J|∇ψ| dθ`, the mode-space vectors are related by
+
+ b̃ = Σ·b, b̄ = (Σ/√A)·b̃, Φ = A·b̄ = Σ·√A·b̃ (poloidal flux, weber)
+
+The √-weight (`b̃`) basis is the one in which an operator's singular values / spectra are
+independent of the straight-field-line (working) coordinate; `b` and `b̄` are not
+coordinate-invariant and are provided only as field/flux recovery views. Poloidal flux is
+recovered, whenever needed, as the scalar product `Φ = A·b̄` — it is never stored.
+"""
+
+"""
+ compute_jac_delpsi(equil, psi, mtheta) -> Vector{Float64}
+
+Compute J·|∇ψ| at `mtheta` equally-spaced θ points on the flux surface at `psi`.
+This is the area weight function that maps a bare field component `b(θ)` to its
+area-weighted form `J|∇ψ|·b(θ)` in θ-space, the flux per unit-norm cell.
+"""
+function compute_jac_delpsi(equil::PlasmaEquilibrium, psi::Float64, mtheta::Int)
+ jac_delpsi = Vector{Float64}(undef, mtheta)
+
+ hint2d = (Ref(1), Ref(1))
+ for itheta in 0:(mtheta-1)
+ theta = itheta / mtheta # normalized to [0, 1)
+ m = flux_surface_metric(equil, psi, theta; hint=hint2d)
+ jac_delpsi[itheta+1] = abs(m.jac * m.delpsi)
+ end
+
+ return jac_delpsi
+end
+
+"""
+ compute_sqrt_jac_delpsi(equil, psi, mtheta) -> Vector{Float64}
+
+Compute √(J·|∇ψ|) at `mtheta` equally-spaced θ points on the flux surface at `psi`.
+This is the √weight function that maps a field component `b(θ)` to its
+root-area-weighted form `√(J|∇ψ|)·b(θ)` in θ-space.
+"""
+compute_sqrt_jac_delpsi(equil::PlasmaEquilibrium, psi::Float64, mtheta::Int) = sqrt.(compute_jac_delpsi(equil, psi, mtheta))
+
+"""
+ compute_sqrtamat(equil, psi, ft) -> Matrix{ComplexF64}
+
+Build the √A convolution matrix `sqrtamat`. Produces a Hermitian Toeplitz matrix
+with entries sqrtamat[m',k] = ŵ_{m_k − m'} where ŵ_n = (1/N)Σ w_j exp(+inθ_j) and
+w(θ) = √(J·|∇ψ|).
+
+For Fourier coefficients `b_fft` of a field b it satisfies `‖sqrtamat·b_fft‖² = ∫ |b|² · J|∇ψ| dθ`
+(θ normalized to one period), which is Jacobian-invariant on a given flux surface.
+`sqrtamat/√jarea` is the matrix Fortran GPEC writes as `J_surf_2`.
+"""
+function compute_sqrtamat(
+ equil::PlasmaEquilibrium,
+ psi::Float64,
+ ft::Utilities.FourierTransforms.FourierTransform
+)
+ mpert = ft.mpert
+ mtheta = ft.mtheta
+
+ sqrt_jdp = compute_sqrt_jac_delpsi(equil, psi, mtheta)
+ sqrtamat = zeros(ComplexF64, mpert, mpert)
+
+ e_k = zeros(ComplexF64, mpert)
+ for k in 1:mpert
+ e_k .= 0.0
+ e_k[k] = 1.0 + 0.0im
+
+ # Unit mode to θ-space, f(θ_j) = exp(+i m_k θ_j)
+ theta_vec = Utilities.FourierTransforms.inverse(ft, e_k)
+
+ theta_vec .*= sqrt_jdp
+
+ # Back to mode space (exp(+imθ) convention)
+ sqrtamat[:, k] .= ft(theta_vec)
+ end
+
+ return sqrtamat
+end
+
+"""
+ rootarea_to_area_weight(equil, psi, ft) -> Matrix{ComplexF64}
+
+Build the root-area-weighted → area-weighted field operator `Σ/√A = sqrtamat ./ √jarea` at the
+flux surface `psi`, where `jarea = ∫ J|∇ψ| dθ` is the scalar flux-surface area. It maps the
+coordinate-invariant root-area-weighted field `b̃` to the area-weighted field `b̄`: `b̄ = (Σ/√A)·b̃`
+(both in tesla); `b̄` is not coordinate-invariant and serves only to recover field or flux
+(`Φ = A·b̄`). Pharr 2026.
+"""
+function rootarea_to_area_weight(
+ equil::PlasmaEquilibrium,
+ psi::Float64,
+ ft::Utilities.FourierTransforms.FourierTransform
+)
+ sqrtamat = compute_sqrtamat(equil, psi, ft)
+ jarea = flux_surface_area(equil, psi, ft.mtheta)
+ return sqrtamat ./ sqrt(jarea)
+end
+
+"""
+ area_to_rootarea_weight(equil, psi, ft) -> Matrix{ComplexF64}
+
+Inverse of [`rootarea_to_area_weight`](@ref): the area-weighted → root-area-weighted field operator
+`√A·Σ⁻¹ = √jarea · inv(sqrtamat)`, mapping `b̄ → b̃` (`b̃ = √A·Σ⁻¹·b̄`). Pharr 2026.
+"""
+function area_to_rootarea_weight(
+ equil::PlasmaEquilibrium,
+ psi::Float64,
+ ft::Utilities.FourierTransforms.FourierTransform
+)
+ sqrtamat = compute_sqrtamat(equil, psi, ft)
+ jarea = flux_surface_area(equil, psi, ft.mtheta)
+ return sqrt(jarea) .* inv(sqrtamat)
+end
diff --git a/src/Equilibrium/Derived/FluxSurfaceMetrics.jl b/src/Equilibrium/Derived/FluxSurfaceMetrics.jl
new file mode 100644
index 0000000000..5d033c4bc9
--- /dev/null
+++ b/src/Equilibrium/Derived/FluxSurfaceMetrics.jl
@@ -0,0 +1,58 @@
+"""
+ rzphi_primitives(equil, psi, theta; hint=(Ref(1), Ref(1))) -> (; r2, deta, jac, r2_y, deta_y)
+
+Evaluate the smooth `rzphi` primitives at `(psi, theta)`: `r²`, the `η`-offset, the Jacobian and the
+θ-derivatives of `r²` and the offset; `metric_from_primitives` turns them into the metric.
+ψ-derivatives are not provided because the bicubic is only C¹ in ψ; differentiate a ψ-resample instead.
+"""
+function rzphi_primitives(equil::PlasmaEquilibrium, psi::Float64, theta::Float64; hint=(Ref(1), Ref(1)))
+ pt = (psi, theta)
+ r2 = equil.rzphi_rsquared(pt; hint=hint)
+ deta = equil.rzphi_offset(pt; hint=hint)
+ jac = equil.rzphi_jac(pt; hint=hint)
+ r2_y = equil.rzphi_rsquared(pt; deriv=DerivOp(0, 1), hint=hint)
+ deta_y = equil.rzphi_offset(pt; deriv=DerivOp(0, 1), hint=hint)
+ return (; r2, deta, jac, r2_y, deta_y)
+end
+
+"""
+ metric_from_primitives(ro, theta, p) -> (; rfac, r, jac, delpsi)
+
+The gpout.f flux-surface metric at one point from the `rzphi` primitives `p` (the fields of
+`rzphi_primitives`): minor radius `rfac = √r²`, major radius `r`, Jacobian `jac` and
+`delpsi = |∇ψ|`. The primitives may come from evaluating the bicubic or from its nodal values.
+"""
+function metric_from_primitives(ro::Float64, theta::Float64, p)
+ rfac = sqrt(abs(p.r2))
+ r = ro + rfac * cos(2π * (theta + p.deta))
+ w11 = (1.0 + p.deta_y) * (2π)^2 * rfac * r / p.jac
+ w12 = rfac > 0 ? -p.r2_y * π * r / (rfac * p.jac) : 0.0
+ return (; rfac, r, jac=p.jac, delpsi=sqrt(w11^2 + w12^2))
+end
+
+"""
+ flux_surface_metric(equil, psi, theta; hint=(Ref(1), Ref(1))) -> (; r, jac, delpsi)
+
+Evaluate the flux-surface geometry at `(psi, theta)`: major radius `r`, Jacobian `jac`, and the
+flux-gradient magnitude `delpsi = |∇ψ|`, by `metric_from_primitives` on the bicubic at that point.
+"""
+function flux_surface_metric(equil::PlasmaEquilibrium, psi::Float64, theta::Float64; hint=(Ref(1), Ref(1)))
+ (; r, jac, delpsi) = metric_from_primitives(equil.ro, theta, rzphi_primitives(equil, psi, theta; hint=hint))
+ return (; r, jac, delpsi)
+end
+
+"""
+ flux_surface_area(equil, psi, mtheta) -> Float64
+
+Compute ⟨J·|∇ψ|⟩_θ on the flux surface at `psi`: the periodic trapezoidal rule on `mtheta` equally
+spaced θ points (θ = 1 duplicates θ = 0).
+"""
+function flux_surface_area(equil::PlasmaEquilibrium, psi::Float64, mtheta::Int)
+ hint = (Ref(1), Ref(1))
+ area = 0.0
+ for itheta in 0:(mtheta-1)
+ m = flux_surface_metric(equil, psi, itheta / mtheta; hint=hint)
+ area += m.jac * m.delpsi
+ end
+ return area / mtheta
+end
diff --git a/src/Equilibrium/Derived/GeometryProfiles.jl b/src/Equilibrium/Derived/GeometryProfiles.jl
new file mode 100644
index 0000000000..171a4ad1c3
--- /dev/null
+++ b/src/Equilibrium/Derived/GeometryProfiles.jl
@@ -0,0 +1,65 @@
+"""
+ GeometryProfiles
+
+Flux-surface-averaged geometric quantities (area, ⟨r⟩, ⟨R⟩) computed once at
+equilibrium construction time. Port of Fortran `set_geom` (pentrc/dcon_interface.f).
+"""
+
+"""
+ compute_geometry_profiles(rzphi_xs, rzphi_ys,
+ rzphi_rsquared, rzphi_offset, rzphi_jac, ro)
+ → GeometryProfileSplines
+
+Build named cubic splines for flux-surface-averaged area, ⟨r⟩, and ⟨R⟩ from the
+equilibrium's 2D rzphi interpolants, by trapezoidal sums over the θ nodes at the bicubic's nodal values.
+"""
+function compute_geometry_profiles(
+ rzphi_xs::Vector{Float64},
+ rzphi_ys::Vector{Float64},
+ rzphi_rsquared::FastInterpolations.CubicInterpolantND,
+ rzphi_offset::FastInterpolations.CubicInterpolantND,
+ rzphi_jac::FastInterpolations.CubicInterpolantND,
+ ro::Float64
+)
+ npsi = length(rzphi_xs)
+ mthsurf = length(rzphi_ys) - 1 # skip the periodic duplicate at θ = 1
+
+ area_vals = zeros(Float64, npsi)
+ avg_r_vals = zeros(Float64, npsi)
+ avg_R_vals = zeros(Float64, npsi)
+
+ for ipsi in 1:npsi
+ area_psi = 0.0
+ r_int = 0.0
+ R_int = 0.0
+ for itheta in 1:mthsurf
+ p = (r2=rzphi_rsquared.nodal_derivs.partials[1, ipsi, itheta], deta=rzphi_offset.nodal_derivs.partials[1, ipsi, itheta],
+ jac=rzphi_jac.nodal_derivs.partials[1, ipsi, itheta], r2_y=rzphi_rsquared.nodal_derivs.partials[3, ipsi, itheta],
+ deta_y=rzphi_offset.nodal_derivs.partials[3, ipsi, itheta])
+ (; rfac, r, jac, delpsi) = metric_from_primitives(ro, rzphi_ys[itheta], p)
+ weight = jac * delpsi / mthsurf
+
+ area_psi += weight # wegt=0, ave=0
+ r_int += weight * rfac # wegt=3, ave=1
+ R_int += weight * r # wegt=1, ave=1
+ end
+ area_vals[ipsi] = area_psi
+ avg_r_vals[ipsi] = (area_psi > 0) ? r_int / area_psi : 0.0
+ avg_R_vals[ipsi] = (area_psi > 0) ? R_int / area_psi : ro
+ end
+
+ return GeometryProfileSplines(rzphi_xs, area_vals, avg_r_vals, avg_R_vals)
+end
+
+"""
+ compute_geometry_profiles(pe::PlasmaEquilibrium) → GeometryProfileSplines
+
+Convenience method that takes the rzphi grids and interpolants from a `PlasmaEquilibrium`.
+"""
+function compute_geometry_profiles(pe::PlasmaEquilibrium)
+ return compute_geometry_profiles(
+ pe.rzphi_xs, pe.rzphi_ys,
+ pe.rzphi_rsquared, pe.rzphi_offset, pe.rzphi_jac,
+ pe.ro
+ )
+end
diff --git a/src/Equilibrium/Derived/GlobalParameters.jl b/src/Equilibrium/Derived/GlobalParameters.jl
new file mode 100644
index 0000000000..65685dd1ab
--- /dev/null
+++ b/src/Equilibrium/Derived/GlobalParameters.jl
@@ -0,0 +1,207 @@
+"""
+ equilibrium_global_parameters!(pe::PlasmaEquilibrium)
+
+Compute the global equilibrium parameters (rmean, amean, kappa, bt0, crnt, betas, li, ...) and store
+them in `pe.params`. Port of Fortran `equil_out_global`.
+"""
+function equilibrium_global_parameters!(pe::PlasmaEquilibrium)
+ profiles = pe.profiles
+ mpsi = length(pe.rzphi_xs) - 1
+ mtheta = length(pe.rzphi_ys) - 1
+
+ rsep, zsep, rext, _ = equilibrium_separatrix_find!(pe)
+
+ rmean = (rsep[1] + rsep[2]) / 2
+ amean = (rsep[1] - rsep[2]) / 2
+ aratio = rmean / amean
+ kappa = (zsep[1] - zsep[2]) / (rsep[1] - rsep[2])
+ delta1 = (rmean - rext[1]) / amean
+ delta2 = (rmean - rext[2]) / amean
+ dpsi = 1.0 - pe.rzphi_xs[mpsi+1]
+ psi_edge = profiles.xs[end]
+ bt0 = (profiles.F_spline.y[end] + profiles.F_deriv(psi_edge; hint=Ref(profiles.npts_minus_1)) * dpsi) / (2π * rmean)
+
+ pe.params.rmean = rmean
+ pe.params.amean = amean
+ pe.params.aratio = aratio
+ pe.params.kappa = kappa
+ pe.params.delta1 = delta1
+ pe.params.delta2 = delta2
+ pe.params.bt0 = bt0
+
+ psio = pe.psio
+ gs1 = zeros(Float64, mtheta + 1)
+ gs2 = zeros(Float64, mtheta + 1)
+
+ # Edge-surface integrals for the plasma current, from the nodal values and θ-derivatives
+ for itheta in 0:mtheta
+ r2 = pe.rzphi_rsquared.nodal_derivs.partials[1, end, itheta+1]
+ offset = pe.rzphi_offset.nodal_derivs.partials[1, end, itheta+1]
+ jac = pe.rzphi_jac.nodal_derivs.partials[1, end, itheta+1]
+ r2_y = pe.rzphi_rsquared.nodal_derivs.partials[3, end, itheta+1]
+ offset_y = pe.rzphi_offset.nodal_derivs.partials[3, end, itheta+1]
+
+ chi1 = 2π * psio / jac
+ jacfac = π / jac
+ rfac = sqrt(r2)
+ eta = 2π * (pe.rzphi_ys[itheta+1] + offset)
+ r = pe.ro + rfac * cos(eta)
+ v21 = jacfac * r2_y / (2π * rfac)
+ v22 = jacfac * (1 + offset_y) * (2 * rfac)
+ v33 = jacfac * 2π * (r / π)
+ dvsq = (v21^2 + v22^2) * (v33 * jac^2)^2
+ gs1[itheta+1] = sqrt(dvsq) / (2π * r)
+ gs2[itheta+1] = chi1 * dvsq / (2π * r)^2
+ end
+
+ int1 = sum(gs1) / (mtheta + 1)
+ int2 = sum(gs2) / (mtheta + 1)
+ crnt = int2 / (1e6 * mu0)
+ bp0 = int2 / int1
+ bwall = 1e6 * mu0 * crnt / (2π * amean)
+
+ pe.params.crnt = crnt
+ pe.params.bwall = bwall
+
+ # Integrals over ψ_N from 0 to 1; ExtendExtrap carries them past the first/last grid points.
+ xs = profiles.xs
+ fsi(y) = FastInterpolations.integrate(cubic_interp(xs, y; extrap=ExtendExtrap()), 0.0, 1.0)
+ P_vals = profiles.P_spline.y
+ dVdpsi_vals = profiles.dVdpsi_spline.y
+
+ fsi_pdv = fsi(P_vals .* dVdpsi_vals) # ∫ p dV/dψ
+ fsi_dv = fsi(dVdpsi_vals) # ∫ dV/dψ
+ fsi_p2dv = fsi(P_vals .^ 2 .* dVdpsi_vals) # ∫ p² dV/dψ
+ volume = fsi_dv
+
+ # Poloidal-field surface integral hs_bp2(ψ) = ψ₀² ∮dθ |∇ψ|² / (R² J), the integrand for li1/li2/li3.
+ hs_bp2 = zeros(Float64, mpsi + 1)
+ for ipsi in 0:mpsi
+ acc = 0.0
+ for itheta in 0:mtheta
+ r2 = pe.rzphi_rsquared.nodal_derivs.partials[1, ipsi+1, itheta+1]
+ offset = pe.rzphi_offset.nodal_derivs.partials[1, ipsi+1, itheta+1]
+ jac = pe.rzphi_jac.nodal_derivs.partials[1, ipsi+1, itheta+1]
+ r2_y = pe.rzphi_rsquared.nodal_derivs.partials[3, ipsi+1, itheta+1]
+ offset_y = pe.rzphi_offset.nodal_derivs.partials[3, ipsi+1, itheta+1]
+
+ jacfac = π / jac
+ rfac = sqrt(r2)
+ eta = 2π * (pe.rzphi_ys[itheta+1] + offset)
+ r = pe.ro + rfac * cos(eta)
+ v21 = jacfac * r2_y / (2π * rfac)
+ v22 = jacfac * (1 + offset_y) * (2 * rfac)
+ v33 = jacfac * 2π * (r / π)
+ dvsq = (v21^2 + v22^2) * (v33 * jac^2)^2
+ acc += dvsq / (r^2) / jac
+ end
+ # Plain mean over the θ nodes, as for int1/int2 above.
+ hs_bp2[ipsi+1] = (acc / (mtheta + 1)) * psio^2
+ end
+ fsi_bp2 = fsi(hs_bp2)
+
+ p0 = P_vals[1] - profiles.P_deriv(profiles.xs[1]; hint=Ref(1)) * profiles.xs[1] # linear extrapolation
+ betat = 2 * (fsi_pdv / fsi_dv) / bt0^2
+ betaj = 2 * sqrt(fsi_p2dv / fsi_dv) / bwall^2
+ betan = 100 * amean * bt0 * betat / crnt
+ betap1 = 2 * (fsi_pdv / fsi_dv) / bp0^2
+ betap2 = 4 * fsi_pdv / ((1e6 * mu0 * crnt)^2 * pe.ro)
+ betap3 = 4 * fsi_pdv / ((1e6 * mu0 * crnt)^2 * rmean)
+ li1 = fsi_bp2 / fsi_dv / bp0^2
+ li2 = 2 * fsi_bp2 / ((1e6 * mu0 * crnt)^2 * pe.ro)
+ li3 = 2 * fsi_bp2 / ((1e6 * mu0 * crnt)^2 * rmean)
+
+ pe.params.psi0 = psio
+ pe.params.psi_axis = pe.psio
+ pe.params.psi_boundary = 1.0
+ pe.params.psi_boundary_norm = 1.0
+ pe.params.psi_norm = 0.0
+ pe.params.psi_axis_offset = 0.0
+ pe.params.psi_boundary_offset = 0.0
+ pe.params.psi_axis_sign = 1
+ pe.params.psi_boundary_sign = -1
+ pe.params.psi_boundary_zero = false
+
+ pe.params.q0 = profiles.q_spline.y[1]
+ pe.params.b0 = bt0
+
+ pe.params.volume = volume
+ pe.params.betat = betat
+ pe.params.betan = betan
+ pe.params.betaj = betaj
+ pe.params.betap1 = betap1
+ pe.params.betap2 = betap2
+ pe.params.betap3 = betap3
+ pe.params.li1 = li1
+ pe.params.li2 = li2
+ pe.params.li3 = li3
+end
+
+"""
+ equilibrium_qfind!(equil::PlasmaEquilibrium)
+
+Find the extrema of q(ψ) and store them with q0, qmin, qmax, qa and q95 in `equil.params`.
+Port of Fortran `equil_out_qfind`.
+"""
+function equilibrium_qfind!(equil::PlasmaEquilibrium)
+
+ profiles = equil.profiles
+ xs = profiles.xs
+ mpsi = length(xs) - 1
+ psiexl = Float64[]
+ qexl = Float64[]
+
+ q_spline = profiles.q_spline
+ q_d1 = deriv1(q_spline)
+ q_d2 = deriv2(q_spline)
+ q_d3 = deriv3(q_spline)
+
+ # Left endpoint
+ push!(psiexl, xs[1])
+ push!(qexl, q_spline.y[1])
+
+ # Search for extrema in q(ψ)
+ for ipsi in 1:mpsi
+ x0 = xs[ipsi]
+ x1 = xs[ipsi+1]
+ xmax = x1 - x0
+
+ a = q_spline(x0)
+ b = q_d1(x0)
+ c = q_d2(x0)
+ d = q_d3(x0)
+
+ disc = c^2 - 2b * d
+ if disc ≥ 0
+ s = -(c + copysign(sqrt(disc), c)) / 2
+ for x in (disc > 0 ? (2s / d, b / s) : (2s / d,))
+ if 0 ≤ x < xmax
+ ψ = x0 + x
+ push!(psiexl, ψ)
+ push!(qexl, q_spline(ψ))
+ end
+ end
+ end
+ end
+
+ # Right endpoint
+ push!(psiexl, xs[end])
+ push!(qexl, q_spline.y[end])
+
+ equil.params.qextrema_psi = psiexl
+ equil.params.qextrema_q = qexl
+ equil.params.mextrema = length(psiexl)
+ q0 = q_spline.y[1] - profiles.q_deriv(xs[1]; hint=Ref(1)) * xs[1]
+ qmax_edge = q_spline.y[end]
+ qmin = min(minimum(qexl), q0)
+ qmax = max(maximum(qexl), qmax_edge)
+ qa = q_spline.y[end] + profiles.q_deriv(xs[end]; hint=Ref(profiles.npts_minus_1)) * (1.0 - xs[end])
+
+ q95 = q_spline(0.95)
+
+ equil.params.q0 = q0
+ equil.params.qmin = qmin
+ equil.params.qmax = qmax
+ equil.params.qa = qa
+ equil.params.q95 = q95
+end
diff --git a/src/Equilibrium/DirectEquilibrium.jl b/src/Equilibrium/DirectEquilibrium.jl
deleted file mode 100644
index 587c24b186..0000000000
--- a/src/Equilibrium/DirectEquilibrium.jl
+++ /dev/null
@@ -1,629 +0,0 @@
-#=
-This file contains the logic for the "direct" equilibrium reconstruction method.
-It takes parsed data and splines from the IO module and calculates the final flux-coordinate
-representation of the plasma equilibrium.
-=#
-
-
-# --- Internal Helper Structs ---
-"""
- DirectBField
-
-Internal mutable struct to hold B-field components and their derivatives at a point.
-It is used as a temporary workspace to avoid allocations in tight loops.
-"""
-mutable struct DirectBField
- psi::Float64
- psir::Float64 # d(psi)/dr
- psiz::Float64 # d(psi)/dz
- psirz::Float64 # d2(psi)/drdz
- psirr::Float64 # d2(psi)/drdr
- psizz::Float64 # d2(psi)/dzdz
- f::Float64 # F = R*Bt
- f1::Float64 # dF/d(psi_norm)
- p::Float64 # mu0*Pressure
- p1::Float64 # dP/d(psi_norm)
- br::Float64 # Br
- bz::Float64 # Bz
- brr::Float64 # d(Br)/dr
- brz::Float64 # d(Br)/dz
- bzr::Float64 # d(Bz)/dr
- bzz::Float64 # d(Bz)/dz
-
- DirectBField() = new(zeros(Float64, 16)...)
-end
-
-"""
- FieldLineDerivParams
-
-A struct to hold constant parameters for the ODE integration, making them
-easily accessible within the derivative function `direct_fl_der!`.
-"""
-struct FieldLineDerivParams
- ro::Float64
- zo::Float64
- psi_in::Spl.BicubicSpline
- sq_in::Spl.CubicSpline
- psio::Float64
- power_bp::Int
- power_b::Int
- power_r::Int
-end
-
-
-"""
- direct_get_bfield!(bf_out, r, z, psi_in, sq_in, psio; derivs=0)
-
-Calculates the magnetic field and its derivatives at a given (R,Z) point.
-The results are stored in-place in the `bf_out` object.
-
-## Arguments:
-- `bf_out`: A mutable `DirectBField` struct to store the results.
-- `r`: The R-coordinate [m].
-- `z`: The Z-coordinate [m].
-- `psi_in`: The 2D bicubic spline for poloidal flux `ψ(R,Z)`.
-- `sq_in`: The 1D cubic spline for profiles `F(ψ_norm)` and `P(ψ_norm)`.
-- `psio`: The total flux difference `|ψ_axis - ψ_boundary|`.
-
-## Keyword Arguments:
-- `derivs`: An integer specifying the derivative level to compute.
- - `0`: Calculates `ψ`, `F`, and `P`.
- - `1`: Also calculates 1st derivatives of `ψ` and `B` field components.
- - `2`: Also calculates 2nd derivatives of `ψ` and 1st derivatives of `B`.
-
-## Returns:
-- `nothing`. The `bf_out` object is modified in-place.
-"""
-function direct_get_bfield!(
- bf_out::DirectBField,
- r::Float64,
- z::Float64,
- psi_in::Spl.BicubicSpline,
- sq_in::Spl.CubicSpline,
- psio::Float64;
- derivs::Int=0
-)
- # 1. Evaluate 2D spline for psi(r,z) and its derivatives
- if derivs == 0
- f_psi = Spl.bicube_eval(psi_in, r, z, 0)
- bf_out.psi = f_psi[1]
- elseif derivs == 1
- f_psi, fx_psi, fy_psi = Spl.bicube_eval(psi_in, r, z, 1)
- bf_out.psi = f_psi[1]
- bf_out.psir = fx_psi[1]
- bf_out.psiz = fy_psi[1]
- else # derivs >= 2
- f_psi, fx_psi, fy_psi, fxx_psi, fxy_psi, fyy_psi = Spl.bicube_eval(psi_in, r, z, 2)
- bf_out.psi = f_psi[1]
- bf_out.psir = fx_psi[1]
- bf_out.psiz = fy_psi[1]
- bf_out.psirr = fxx_psi[1]
- bf_out.psirz = fxy_psi[1]
- bf_out.psizz = fyy_psi[1]
- end
-
- # 2. Evaluate 1D splines for F(psi_norm) and P(psi_norm)
- # psi_norm = 0 at axis, 1 at boundary.
- psi_norm = (psio > 1e-12) ? (1.0 - bf_out.psi / psio) : 0.0
- psi_norm = clamp(psi_norm, 0.0, 1.0)
-
- f_sq, f1_sq = Spl.spline_eval(sq_in, psi_norm, 1)
- bf_out.f = f_sq[1] # F = R*Bt
- bf_out.f1 = f1_sq[1] # dF/d(psi_norm)
- bf_out.p = f_sq[2] # mu0*Pressure
- bf_out.p1 = f1_sq[2] # dP/d(psi_norm)
-
- (derivs < 1) && return
-
- # 3. Evaluate magnetic field components (derivs >= 1)
- bf_out.br = bf_out.psiz / r # Br = (1/R) * ∂ψ/∂Z
- bf_out.bz = -bf_out.psir / r # Bz = -(1/R) * ∂ψ/∂R
-
- (derivs < 2) && return
-
- # 4. Evaluate derivatives of B-field components (derivs >= 2)
- bf_out.brr = (bf_out.psirz - bf_out.br) / r #d(Br)/dr
- bf_out.brz = bf_out.psizz / r #d(Br)/dz
- bf_out.bzr = -(bf_out.psirr + bf_out.bz) / r #d(Bz)/dr
- bf_out.bzz = -bf_out.psirz / r # d(Bz)/dz
-
- return
-end
-
-
-"""
- direct_position(psi_in, sq_in, psio, ro_guess, zo_guess, rmin, rmax)
-
-Finds the key geometric locations of the equilibrium: the magnetic axis (O-point)
-and the inboard/outboard separatrix crossings on the midplane.
-
-## Arguments:
-- `psi_in`: The 2D `ψ(R,Z)` spline.
-- `sq_in`: The 1D profile spline.
-- `psio`: Initial flux difference.
-- `ro_guess`, `zo_guess`: Initial guess for the magnetic axis location [m].
-- `rmin`, `rmax`: Radial bounds of the computational domain [m].
-
-## Returns:
-- `ro`: R-coordinate of the magnetic axis [m].
-- `zo`: Z-coordinate of the magnetic axis [m].
-- `rs1`: R-coordinate of the inboard separatrix crossing [m].
-- `rs2`: R-coordinate of the outboard separatrix crossing [m].
-- `psi_in_new` : returns psi_in renormalized by * psio/psi(ro,zo)
-"""
-function direct_position(
- psi_in::Spl.BicubicSpline,
- sq_in::Spl.CubicSpline,
- psio::Float64,
- ro_guess::Float64,
- zo_guess::Float64,
- rmin::Float64,
- rmax::Float64
-)
- bf_temp = DirectBField()
- r, z = ro_guess, zo_guess
- max_newton_iter = 200
-
- # 1. Find the magnetic axis (O-point) using Newton-Raphson
- println("Finding magnetic axis...")
- # (Initial coarse search for r if guess is 0.0)
- # find o point coarse guess by finding point psi extrema by Bz.
- if r ≈ 0.0
- r_mid, z_mid = (rmax + rmin) / 2.0, zo_guess
- dr_scan = (rmax - rmin) / 20.0
- r = r_mid
- for _ in 1:20
- direct_get_bfield!(bf_temp, r, z_mid, psi_in, sq_in, psio, derivs=1)
- if bf_temp.bz >= 0.0; break; end
- r += dr_scan
- end
- z = z_mid
- end
-
- for iter in 1:20
- direct_get_bfield!(bf_temp, r, z, psi_in, sq_in, psio, derivs=2)
- det = bf_temp.brr * bf_temp.bzz - bf_temp.brz * bf_temp.bzr
- if abs(det) < 1e-20; error("Jacobian matrix is singular near ($r, $z)."); end
- # Δx = -J^-1 F
- dr = (bf_temp.brz * bf_temp.bz - bf_temp.bzz * bf_temp.br) / det
- dz = (bf_temp.bzr * bf_temp.br - bf_temp.brr * bf_temp.bz) / det
- r += dr; z += dz
- @printf " Iter %2d: R = %.6f, Z = %.6f, |ΔR|=%.2e, |ΔZ|=%.2e\n" iter r z abs(dr) abs(dz)
- if abs(dr) <= 1e-12 * abs(r) && abs(dz) <= 1e-12 * abs(r)
- println("Magnetic axis found at R=$(r), Z=$(z).")
- break
- end
- (iter == 20) && @warn "O-point search did not converge."
- end
- ro, zo = r, z
-
- # 2. Psi Renormalization
- # renormalize psi_in by psi_in * psio/psi(ro,zo)
- # Redefined to avoid direct modification of the psi_rz structure.
- # However, if it is determined that redefining psi_rz will not cause major problems,
- # modification may be permitted.
- direct_get_bfield!(bf_temp, ro, zo, psi_in, sq_in, psio, derivs=0)
- psi_at_axis = bf_temp.psi
- fac = psio/psi_at_axis
- new_psi_fs = psi_in.fs * fac
- x_coords = Vector(psi_in.xs)
- y_coords = Vector(psi_in.ys)
- psi_in_new = Spl.BicubicSpline(x_coords, y_coords, new_psi_fs, bctypex=4, bctypey=4)
-
- if abs(psi_at_axis - psio) / psio > 1e-3
- @warn "Psi at located axis (O-point) differs from expected psio. " *
- "Psi(axis)=$(psi_at_axis), psio=$(psio). Proceeding without re-fitting."
- end
-
- # 3. Find inboard (rs1) and outboard (rs2) separatrix positions
- # Helper function for robust Newton-Raphson search with restarts
- function find_separatrix_crossing(start_r, end_r, label)
- println("Finding $label separatrix crossing...")
- local r_sol::Float64
- found = false
- for ird in 0:5 # 6 restart attempts
- r_sep = (start_r * (3.0 - 0.5 * ird) + end_r) / (4.0 - 0.5 * ird)
- @printf " Restart attempt %d/6 with initial R = %.6f\n" (ird + 1) r_sep
- for _ in 1:max_newton_iter
-
- direct_get_bfield!(bf_temp, r_sep, zo, psi_in_new, sq_in, psio, derivs=1)
- if abs(bf_temp.psir) < 1e-14; @warn "d(psi)/dr is near zero."; break; end
- dr = -bf_temp.psi / bf_temp.psir
- r_sep += dr
- if abs(dr) <= 1e-12 * abs(r_sep); r_sol = r_sep; found = true; break; end
- end
- if found; break; end
- end
- !found && error("Could not find $label separatrix after all attempts.")
- println("$label separatrix found at R=$(r_sol).")
- return r_sol
- end
-
- rs1 = find_separatrix_crossing(ro, rmin, "inboard")
- rs2 = find_separatrix_crossing(ro, rmax, "outboard")
-
- # 4. Return the new spline
- return ro, zo, rs1, rs2, psi_in_new
-end
-
-
-"""
- direct_fl_int(ipsi, psifac, raw_profile, ro, zo, rs2)
-
-Performs the field-line integration for a single flux surface.
-
-## Arguments:
-- `ipsi`: The index of the current flux surface.
-- `psifac`: The normalized psi value for the surface (ψ_norm).
-- `raw_profile`: The `DirectRunInput` object containing splines and parameters.
-- `ro`, `zo`: Coordinates of the magnetic axis [m].
-- `rs2`: R-coordinate of the outboard separatrix [m].
-
-## Returns:
-- `y_out`: A matrix containing the integrated quantities vs. the geometric angle `η`.
-- `bf_start`: A `DirectBField` object with values at the integration start point.
-"""
-function direct_fl_int(
- ipsi::Int,
- psifac::Float64,
- raw_profile::DirectRunInput,
- ro::Float64,
- zo::Float64,
- rs2::Float64
-)
- # 1. Find the starting point on the flux surface (outboard midplane)
- psi0_target = raw_profile.psio * (1.0 - psifac)
- r_start = ro + sqrt(psifac) * (rs2 - ro)
- z_start = zo
-
- bf_start = DirectBField()
- for _ in 1:10 # Refine starting R using Newton's method
- direct_get_bfield!(bf_start, r_start, z_start, raw_profile.psi_in, raw_profile.sq_in, raw_profile.psio, derivs=1)
- dr = (psi0_target - bf_start.psi) / bf_start.psir
- r_start += dr
- if abs(dr) <= 1e-12 * r_start; break; end
- end
- direct_get_bfield!(bf_start, r_start, z_start, raw_profile.psi_in, raw_profile.sq_in, raw_profile.psio, derivs=2)
- psi0_actual = bf_start.psi
-
- # 2. Set up and solve the ODE for field line following
- u0 = zeros(Float64, 4)
- #[1]:∫(dl/Bp)
- #[2]: rfac (radial distance from magnetic axis)
- #[3]: ∫(dl/(R²Bp))
- #[4]: ∫(jac*dl/Bp)
- u0[2] = sqrt((r_start - ro)^2 + (z_start - zo)^2) # Initial rfac
- tspan = (0.0, 2.0 * pi)
-
- equil_input = raw_profile.config.control
-
- params = FieldLineDerivParams(ro, zo, raw_profile.psi_in, raw_profile.sq_in, raw_profile.psio,
- equil_input.power_bp, equil_input.power_b, equil_input.power_r)
-
- # Use a callback to refine the solution at each step to stay on the flux surface
- saved_values = Vector{Vector{Float64}}()
- function refine_and_save_affect!(integrator)
- rfac_refined = direct_refine(integrator.u[2], integrator.t, psi0_actual, params)
- integrator.u[2] = rfac_refined
- push!(saved_values, [integrator.t; integrator.u])
- end
- callback = DiscreteCallback((u,t,i) -> true, refine_and_save_affect!, save_positions=(false,false))
-
- # Add the initial state
- push!(saved_values, [0.0; u0])
-
- prob = ODEProblem(direct_fl_der!, u0, tspan, params)
- sol = solve(prob, Tsit5(), callback=callback, reltol=1e-6, abstol=1e-8, dt=2*pi/200, adaptive=true)
-
- if sol.retcode != :Success && sol.retcode != :Terminated
- error("ODE integration failed for ipsi=$ipsi with code: $(sol.retcode)")
- end
-
- # 3. Finalize output
- y_out = hcat(saved_values...)' # Convert vector of vectors to a matrix
- return y_out, bf_start
-end
-
-
-"""
- direct_fl_der!(dy, y, params, eta)
-
-The derivative function for the field-line integration ODE. This is passed to
-the `DifferentialEquations.jl` solver.
-
-## Arguments:
-- `dy`: The derivative vector (output, modified in-place).
-- `y`: The state vector `[∫(dl/Bp), rfac, ∫(dl/(R²Bp)), ∫(jac*dl/Bp)]`.
-- `params`: A `FieldLineDerivParams` struct with all necessary parameters.
-- `eta`: The independent variable (geometric angle `η`).
-"""
-function direct_fl_der!(dy, y, params::FieldLineDerivParams, eta)
- cos_eta, sin_eta = cos(eta), sin(eta)
- r = params.ro + y[2] * cos_eta
- z = params.zo + y[2] * sin_eta
-
- bf_temp = DirectBField()
- direct_get_bfield!(bf_temp, r, z, params.psi_in, params.sq_in, params.psio, derivs=1)
-
- bp_sq = bf_temp.br^2 + bf_temp.bz^2
- bp = bp_sq > 1e-28 ? sqrt(bp_sq) : 1e-14
- bt = bf_temp.f / r
- b_sq = bp_sq + bt^2
- b = sqrt(b_sq)
- jacfac = (bp^params.power_bp) * (b^params.power_b) / (r^params.power_r)
-
- # Denominator for d(l_pol)/d(eta) = rfac |B_pol|/denominator
- denominator = bf_temp.bz * cos_eta - bf_temp.br * sin_eta
- if abs(denominator) < 1e-14
- fill!(dy, 1e20) # Return large derivatives for solver to handle stiffness
- @warn "Denominator in direct_fl_der! near zero at eta=$eta."
- return
- end
-
- # dy/d(eta)
- dy[1] = y[2] / denominator # d/dη [∫(dl/Bp)] = 1/|B_P| dl/d(eta) = rfac/denominator
- dy[2] = dy[1] * (bf_temp.br * cos_eta + bf_temp.bz * sin_eta)
- # d(rfac)/d(eta) = rfac/denom *( Br cos(eta) + Bz sin(eta) )
- dy[3] = dy[1] / (r^2) # d/dη [∫(dl/(R²Bp))]
- dy[4] = dy[1] * jacfac # d/dη [∫(jac*dl/Bp)]
- return
-end
-
-
-"""
- direct_refine(rfac, eta, psi0, params)
-
-Refines the radial distance `rfac` at a given angle `eta` to ensure the
-point lies exactly on the target flux surface `psi0`.
-
-## Arguments:
-- `rfac`: The current guess for the radial distance from the magnetic axis.
-- `eta`: The geometric poloidal angle.
-- `psi0`: The target `ψ` value for the flux surface.
-- `params`: A `FieldLineDerivParams` struct.
-
-## Returns:
-- The refined `rfac` value.
-"""
-function direct_refine(rfac::Float64, eta::Float64, psi0::Float64, params::FieldLineDerivParams; max_iter::Int=10)::Float64
- cos_eta, sin_eta = cos(eta), sin(eta)
- bf_temp = DirectBField()
-
- for _ in 1:max_iter
- r_current = params.ro + rfac * cos_eta
- z_current = params.zo + rfac * sin_eta
- direct_get_bfield!(bf_temp, r_current, z_current, params.psi_in, params.sq_in, params.psio, derivs=1)
- dpsi = bf_temp.psi - psi0
-
- # Newton's method derivative: d(psi)/d(rfac)
- dpsi_drfac = bf_temp.psir * cos_eta + bf_temp.psiz * sin_eta
- if abs(dpsi_drfac) < 1e-14
- @warn "Refinement failed at eta=$eta: d(psi)/d(rfac) is zero."
- return rfac # Return current best guess
- end
-
- drfac = -dpsi / dpsi_drfac
- rfac += drfac
-
- if abs(dpsi) <= 1e-12 || abs(drfac) <= 1e-12 * abs(rfac)
- return rfac # Converged
- end
- end
-
- @warn "direct_refine did not converge after $max_iter iterations at eta=$eta."
- return rfac
-end
-
-
-"""
- equilibrium_solver(raw_profile)
-
-The main driver for the direct equilibrium reconstruction. It orchestrates the entire
-process from finding the magnetic axis to integrating along field lines and
-constructing the final coordinate and physics quantity splines.
-
-## Arguments:
-- `raw_profile`: A `DirectRunInput` object containing the initial splines (`psi_in`, `sq_in`)
- and run parameters (`equil_input`).
-
-## Returns:
-- A `PlasmaEquilibrium` object containing the final, processed equilibrium data,
- including the profile spline (`sq`), the coordinate mapping spline (`rzphi`), and
- the physics quantity spline (`eqfun`).
-"""
-function equilibrium_solver(raw_profile::DirectRunInput)
- println("--- Starting Direct Equilibrium Processing ---")
-
- # 1. Unpack initial data
- equil_params = raw_profile.config.control
- sq_in = raw_profile.sq_in
- psi_in = raw_profile.psi_in
- psio = raw_profile.psio
- mtheta = equil_params.mtheta
-
- # 2. Setup the new output radial grid (`ψ_norm`)
- mpsi = equil_params.mpsi
- psilow = equil_params.psilow
- psihigh = equil_params.psihigh
-
- sq_x_nodes = zeros(Float64, mpsi + 1)
- if equil_params.grid_type == "ldp"
- for i in 0:mpsi
- x_param = Float64(i) / mpsi
- sq_x_nodes[i+1] = psilow + (psihigh - psilow) * sin(x_param * pi / 2.0)^2
- end
- else
- error("Unsupported grid_type: $(equil_params.grid_type)")
- end
- # need to add more grid type
-
- #2pi*F, mu0P, dvdpsi, q
- sq_fs_nodes = zeros(Float64, mpsi + 1, 4)
-
- ro_guess = (raw_profile.rmin + raw_profile.rmax) / 2.0
- zo_guess = (raw_profile.zmin + raw_profile.zmax) / 2.0
-
-
-
- # 3. Find key geometric positions and perform normalization
- ro, zo, rs1, rs2, psi_in_norm = direct_position(psi_in, sq_in, psio,
- ro_guess, zo_guess, # initial guess
- raw_profile.rmin, raw_profile.rmax)
-
-
-
- normalized_profile = DirectRunInput(
- raw_profile.config,
- raw_profile.sq_in,
- psi_in_norm,
- raw_profile.rmin,
- raw_profile.rmax,
- raw_profile.zmin,
- raw_profile.zmax,
- raw_profile.psio
- )
-
- # 4. Main integration loop over flux surfaces
- local rzphi::Spl.BicubicSpline
- local eqfun::Spl.BicubicSpline
- local rzphi_fs_nodes
-
- println("Starting loop over flux surfaces...")
- # Loop from edge inwards (index mpsi+1 down to 1)
- for ipsi in (mpsi+1):-1:1
- psi_norm_surf = sq_x_nodes[ipsi]
- @printf "--> Processing surface ipsi = %d / %d (ψ_norm = %.4f)\n" (ipsi-1) mpsi psi_norm_surf
-
- # a. Integrate along the field line for this surface
- y_out, bf_start = direct_fl_int(ipsi, psi_norm_surf, normalized_profile, ro, zo, rs2)
- #y_out
- #[1]: eta
- #[2]:∫(dl/Bp)
- #[3]: rfac (radial distance from magnetic axis)
- #[4]: ∫(dl/(R²Bp))
- #[5]: ∫(jac*dl/Bp)
-
- # b. Process integration results into a temporary periodic spline `ff(θ_new)`
- theta_new_nodes = y_out[:, 5] ./ y_out[end, 5] #SFL angle θ_new
- ff_fs_nodes = hcat(
- y_out[:, 3].^2, # 1: rfac²
- y_out[:, 1] / (2*pi) .- theta_new_nodes, # 2: η/(2π) - θ_new
- bf_start.f * (y_out[:, 4] .- theta_new_nodes .* y_out[end, 4]), # 3: Toroidal stream function term (term for calculate q)
- y_out[:, 2] ./ y_out[end, 2] .- theta_new_nodes # 4: Jacobian-related term
- )
- ff = Spl.CubicSpline(theta_new_nodes, ff_fs_nodes, bctype="periodic")
-
- # c. On first iteration, allocate the main output data array
- if ipsi == (mpsi+1)
- rzphi_fs_nodes = zeros(Float64, mpsi + 1, mtheta + 1, 4)
- end
-
- # d. Interpolate `ff` onto the uniform `theta` grid for `rzphi`
- rzphi_y_nodes = range(0.0, 1.0, length=mtheta + 1)
- for itheta in 1:(mtheta + 1)
- theta_val = rzphi_y_nodes[itheta]
- f, f1 = Spl.spline_eval(ff, theta_val, 1)
-
- rzphi_fs_nodes[ipsi, itheta, 1:3] = f[1:3]
- jac_term = (1.0 + f1[4]) * y_out[end, 2] * (2*pi) * psio
- rzphi_fs_nodes[ipsi, itheta, 4] = jac_term
- end
-
- # e. Store surface-averaged quantities for the `sq` spline
- sq_fs_nodes[ipsi, 1] = bf_start.f * (2pi) # 2pi*F
- sq_fs_nodes[ipsi, 2] = bf_start.p
- sq_fs_nodes[ipsi, 3] = y_out[end, 5] * (2pi) *psio # dV/d(psi)
- sq_fs_nodes[ipsi, 4] = y_out[end, 4] * bf_start.f / (2pi) # q-profile
- end
- println("...Loop over flux surfaces finished.")
-
- # 5. Finalize splines and perform q-profile revision if needed
- sq = Spl.CubicSpline(sq_x_nodes, sq_fs_nodes, bctype=4)
-
- if equil_params.newq0 != 0.0
- println("Revising q-profile for newq0 = $(equil_params.newq0)...")
- f = Spl.spline_eval(sq, 0.0, 0)
- # q0_old = q(psi=0) = f[4] at x=0
- # f0_old = f[1] at x=0
- q0_old = f[4]
- f0_old = f[1]
-
- f0_fac_sq = f0_old^2 * ((equil_params.newq0 / q0_old)^2 - 1.0)
-
- for i in 1:(mpsi+1)
- f_current_sq = sq_fs_nodes[i, 1]^2
- ffac = sqrt(max(0.0, 1.0 + f0_fac_sq / f_current_sq)) * sign(equil_params.newq0/q0_old)
- sq_fs_nodes[i, 1] *= ffac # F
- sq_fs_nodes[i, 4] *= ffac # q
- rzphi_fs_nodes[i, :, 3] .*= ffac # Toroidal stream function
- end
- # Re-create the spline with the revised data
- sq = Spl.CubicSpline(sq_x_nodes, sq_fs_nodes, bctype=4)
- println("...q-profile revision complete.")
- end
-
- # Create the final geometric spline `rzphi`. Periodic in theta (y-dimension)
- rzphi_y_nodes = range(0.0, 1.0, length=mtheta + 1)
- rzphi = Spl.BicubicSpline(sq_x_nodes, collect(rzphi_y_nodes), rzphi_fs_nodes, bctypex=4, bctypey=2)
- println("Final geometric spline 'rzphi' is fitted.")
-
- # 6. Calculate final physics quantities (B-field, metric components, etc.)
- println("Calculating final physics quantities (B, g_ij)...")
- eqfun_fs_nodes = zeros(Float64, mpsi + 1, mtheta + 1, 3)
- v = zeros(Float64, 2, 3)
-
- for ipsi in 1:(mpsi+1), itheta in 1:(mtheta+1)
- psi_norm = sq_x_nodes[ipsi]
- theta_new = rzphi_y_nodes[itheta]
-
- f = Spl.spline_eval(sq, psi_norm, 0)
- q = f[4]
- f_val = f[1]
-
- f, fx, fy = Spl.bicube_eval(rzphi, psi_norm, theta_new, 1)
- rfac_sq = max(0.0, f[1])
- rfac = sqrt(rfac_sq)
- eta = 2.0 * pi * (theta_new + f[2])
- r_coord = ro + rfac * cos(eta)
- jacfac = f[4]
-
-
- v[1,1] = (rfac > 0) ? fx[1] / (2.0 * rfac) : 0.0 # 1/(2rfac) * d(rfac)/d(psi_norm)
- v[1,2] = fx[2] * 2.0 * pi * rfac # 2pi*rfac * d(eta)/d(psi_norm)
- v[1,3] = fx[3] * r_coord # r_coord * d(phi_s)/d(psi_norm)
- v[2,1] = (rfac > 0) ? fy[1] / (2.0 * rfac) : 0.0 # 1/(2rfac) d(rfac)/d(theta_new)
- v[2,2] = (1.0 + fy[2]) * 2.0 * pi * rfac # 2pi*rfac * d(eta)/d(theta_new)
- v[2,3] = fy[3] * r_coord # r_coord * d(phi_s)/d(theta_new)
- v33 = 2.0 * pi * r_coord # 2pi * r_coord
-
-
- w11 = (1.0 + fy[2]) * (2.0*pi)^2 * rfac * r_coord / jacfac
- w12 = (jacfac*rfac != 0) ? -fy[1] * pi * r_coord / (rfac * jacfac) : 0.0
- delpsi_norm = sqrt(w11^2 + w12^2)
-
- b_sq = ((psio *2pi *delpsi_norm)^2 + (f_val/(2pi*r_coord))^2)
- eqfun_fs_nodes[ipsi, itheta, 1] = b_sq # B_total
-
- denom = jacfac * b_sq
- if abs(denom) > 1e-20
- # 2. Gyrokinetic coefficient C1
- numerator_2 = dot(v[1,:], v[2,:]) + q * v33 * v[1,3]
- eqfun_fs_nodes[ipsi, itheta, 2] = numerator_2 / denom
-
- # 3. Gyrokinetic coefficient C2
- numerator_3 = v[2,3] * v33 + q * v33^2
- eqfun_fs_nodes[ipsi, itheta, 3] = numerator_3 / denom
- else
- eqfun_fs_nodes[ipsi, itheta, 2] = 0.0
- eqfun_fs_nodes[ipsi, itheta, 3] = 0.0
- end
- end
- println("...done.")
-
- eqfun = Spl.BicubicSpline(sq_x_nodes, collect(rzphi_y_nodes), eqfun_fs_nodes, bctypex=4, bctypey=2)
-
- println("--- Direct Equilibrium Processing Finished ---")
-
- return PlasmaEquilibrium(raw_profile.config,EquilibriumParameters(), sq, rzphi, eqfun, ro, zo, psio)
-end
-
diff --git a/src/Equilibrium/Equilibrium.jl b/src/Equilibrium/Equilibrium.jl
index d136d30e4f..769b2cfe52 100644
--- a/src/Equilibrium/Equilibrium.jl
+++ b/src/Equilibrium/Equilibrium.jl
@@ -1,530 +1,76 @@
+"""
+ Equilibrium
+
+Reads or solves an MHD equilibrium and maps it to straight-field-line flux coordinates as a
+[`PlasmaEquilibrium`](@ref).
+
+## Where code goes
+
+ - `Config.jl`: the run configuration (`EquilibriumConfig`) and global parameters (`EquilibriumParameters`).
+ - `PlasmaEquilibrium.jl`: the result type and its spline containers.
+ - `Construction.jl`: `run_input` for each source type, the `PlasmaEquilibrium` constructors, and `reform`.
+ - `Sources/`: one file per input format, each building a `DirectRunInput` or `InverseRunInput`
+ (`Ingest.jl` holds those and the ingest types). A new analytic model is one file in
+ `Sources/Analytic/` holding its config and solver, plus one `ANALYTIC_EQ` row.
+ - `Grid/`: radial ψ grids, first-pass and refined.
+ - `Axisymmetric/`: code that assumes axisymmetry (the 2D solvers, the Grad-Shafranov residual,
+ separatrix finding). A non-axisymmetric equilibrium gets a sibling folder.
+ - `Derived/`: quantities computed from a formed `PlasmaEquilibrium`.
+"""
module Equilibrium
# --- Module-level Dependencies ---
-import ..Spl
using Printf, OrdinaryDiffEq, DiffEqCallbacks, LinearAlgebra, HDF5
+using Statistics: median
+using Roots
using TOML
-
-
-# --- Internal Module Structure ---
-include("EquilibriumTypes.jl")
-include("ReadEquilibrium.jl")
-include("DirectEquilibrium.jl")
-include("InverseEquilibrium.jl")
-include("AnalyticEquilibrium.jl")
-
-# --- Expose types and functions to the user ---
-
-export setup_equilibrium, EquilibriumConfig, EquilibriumControl, EquilibriumOutput, PlasmaEquilibrium, EquilibriumParameters
+using FastInterpolations
+using AdaptiveArrayPools
+import StaticArrays: @MMatrix, SVector
+import ..Utilities
+import IMASdd
# --- Constants ---
-const mu0 = 4.0 * pi * 1e-7
-
-
-"""
- setup_equilibrium(equil_input::EquilInput)
-
-The main public API for the `Equilibrium` module. It orchestrates the entire
-process of reading an equilibrium file, running the appropriate solver, and
-returning the final processed `PlasmaEquilibrium` object.
-
-## Arguments:
-- `equil_input`: An `EquilInput` object containing all necessary setup parameters.
-## Returns:
-- A `PlasmaEquilibrium` object containing the final result.
-"""
-function setup_equilibrium(path::String = "equil.toml")
- return setup_equilibrium( EquilibriumConfig(path))
-end
-function setup_equilibrium(eq_config::EquilibriumConfig, additional_input=nothing)
-
- @printf "Equilibrium file: %s\n" eq_config.control.eq_filename
-
- eq_type = eq_config.control.eq_type
- # Parse file and prepare initial data structures and splines
- if eq_type == "efit"
- eq_input = read_efit(eq_config)
- elseif eq_type == "chease2"
- eq_input = read_chease2(eq_config)
- elseif eq_type == "chease"
- eq_input = read_chease(eq_config)
- elseif eq_type == "lar"
-
- if additional_input === nothing
- additional_input = LargeAspectRatioConfig(eq_config.control.eq_filename)
- end
-
- eq_input = lar_run(eq_config, additional_input)
- elseif eq_type == "sol"
-
- if additional_input === nothing
- additional_input = SolevevConfig(eq_config.control.eq_filename)
- end
-
- eq_input = sol_run(eq_config, additional_input)
- elseif eq_type == "inverse_testing"
- # Example 1D spline setup
- xs = collect(0.0:0.1:1.0)
- fs = sin.(2π .* xs) # vector of Float64
- spline_ex = Spl.CubicSpline(xs, fs)
- #println(spline_ex)
- # Example 2D bicubic spline setup
- xs = 0.0:0.1:1.0
- ys = 0.0:0.2:1.0
- fs = [sin(2π*x)*cos(2π*y) for x in xs, y in ys, _ in 1:1]
- bicube_ex = Spl.BicubicSpline(collect(xs), collect(ys), fs)
- #println(bicube_ex)
- eq_input = InverseRunInput(
- eq_config,
- spline_ex, #sq_in
- bicube_ex, #rz_in
- 0.0, #ro
- 0.0, #zo
- 1.0 #psio
- )
- else
- error("Equilibrium type $(equil_in.eq_type) is not implemented")
- end
-
- # Run the appropriate solver (direct or inverse) to get a PlasmaEquilibrium struct
- plasma_equilibrium = equilibrium_solver(eq_input)
-
- # add global parameters to the PlasmaEquilibrium struct
- equilibrium_global_parameters!(plasma_equilibrium)
-
- # Find q information
- equilibrium_qfind!(plasma_equilibrium)
-
- # Diagnoses grad-shafranov solution.
- equilibrium_gse!(plasma_equilibrium)
-
- println("--- Equilibrium Setup Complete ---")
- return plasma_equilibrium
-end
-
-
-"""
- equilibrium_separatrix_find!(pe::PlasmaEquilibrium)
-Finds the separatrix locations in the plasma equilibrium (rsep, zsep, rext, zext).
-"""
-function equilibrium_separatrix_find!(pe::PlasmaEquilibrium)
- rzphi = pe.rzphi
- mpsi = size(rzphi.fs, 1) - 1
- mtheta = size(rzphi.fs, 2) - 1
- twopi = 2π
-
- # Allocate vector to store eta offset from rzphi
- vector = zeros(Float64, mtheta + 1)
- for it in 0:mtheta
- f = Spl.bicube_eval(rzphi, rzphi.xs[mpsi+1], rzphi.ys[it+1], 0)
- vector[it+1] = rzphi.ys[it+1] + f[2]
- end
-
- psifac = rzphi.xs[mpsi+1]
- eta0 = 0.0
- idx = findmin(abs.(vector .- eta0))[2]
- theta = rzphi.ys[idx]
- rsep = zeros(2)
-
- for iside in 1:2
- it = 0
- while true
- it += 1
- f, _, fy = Spl.bicube_eval(rzphi, psifac, theta, 1)
- eta = theta + f[2] - eta0
- eta_theta = 1 + fy[2]
- dtheta = -eta / eta_theta
- theta += dtheta
- if abs(eta) <= 1e-10 || it > 100
- break
- end
- end
- f = Spl.bicube_eval(rzphi, psifac, theta, 0)
- rsep[iside] = pe.ro + sqrt(f[1]) * cos(twopi * (theta + f[2]))
- eta0 = 0.5
- idx = findmin(abs.(vector .- eta0))[2]
- theta = rzphi.ys[idx]
- end
-
- # Top and bottom separatrix locations using Newton iteration
- zsep = zeros(2)
- rext = zeros(2)
- zext = zeros(2)
-
- for iside in 1:2
- eta0 = (iside == 1) ? 0.0 : 0.5
- idx = findmin(abs.(vector .- eta0))[2]
- theta = rzphi.ys[idx]
- rfac = 0.0
- cosfac = 0.0
- z = 0.0
- while true
- f, fx, fy, fxx, fxy, fyy = Spl.bicube_eval(rzphi, psifac, theta, 2)
- r2, r2y, r2yy = f[1], fy[1], fyy[1]
- eta, eta1, eta2 = f[2], fy[2], fyy[2]
-
- rfac = sqrt(r2)
- rfac1 = r2y / (2 * rfac)
- rfac2 = (r2yy - r2y * rfac1 / rfac) / (2 * rfac)
- phase = twopi * (theta + eta)
- phase1 = twopi * (1 + eta1)
- phase2 = twopi * eta2
- cosfac = cos(phase)
- sinfac = sin(phase)
- z = pe.zo + rfac * sinfac
- z1 = rfac * phase1 * cosfac + rfac1 * sinfac
- z2 = (2 * rfac1 * phase1 + rfac * phase2) * cosfac + (rfac2 - rfac * phase1^2) * sinfac
- dtheta = -z1 / z2
- theta += dtheta
- if abs(dtheta) < 1e-12 * abs(theta)
- break
- end
- end
- rext[iside] = pe.ro + rfac * cosfac
- zsep[iside] = z
- zext[iside] = z
- end
-
- pe.params.rsep = rsep
- pe.params.zsep = zsep
- pe.params.rext = rext
- pe.params.zext = zext
- return (rsep, zsep, rext, zext)
-end
-
-
-function equilibrium_global_parameters!(pe::PlasmaEquilibrium)
- rzphi = pe.rzphi
- sq = pe.sq
- mpsi = size(rzphi.fs, 1) - 1
- mtheta = size(rzphi.fs, 2) - 1
- twopi = 2π
- mu0 = 4π * 1e-7
-
- # Use separatrix geometry
- rsep, zsep, rext, _ = equilibrium_separatrix_find!(pe)
-
- rmean = (rsep[2] + rsep[1]) / 2
- amean = (rsep[2] - rsep[1]) / 2
- aratio = rmean / amean
- kappa = (zsep[1] - zsep[2]) / (rsep[2] - rsep[1])
- delta1 = (rmean - rext[1]) / amean
- delta2 = (rmean - rext[2]) / amean
- dpsi = 1.0 - rzphi.xs[mpsi+1]
- bt0 = (sq.fs[mpsi+1, 1] + sq.fs1[mpsi+1, 1] * dpsi) / (twopi * rmean)
-
- pe.params.rmean = rmean
- pe.params.amean = amean
- pe.params.aratio = aratio
- pe.params.kappa = kappa
- pe.params.delta1 = delta1
- pe.params.delta2 = delta2
- pe.params.bt0 = bt0
-
- psio = pe.psio
- gs1 = zeros(Float64, mtheta+1)
- gs2 = zeros(Float64, mtheta+1)
-
- for itheta in 0:mtheta
- f, _, fy = Spl.bicube_eval(rzphi, rzphi.xs[mpsi+1], rzphi.ys[itheta+1], 1)
- jac = f[4]
- chi1 = twopi * psio / jac
- jacfac = π / jac
- rfac = sqrt(f[1])
- eta = twopi * (rzphi.ys[itheta+1] + f[2])
- r = pe.ro + rfac * cos(eta)
- v21 = jacfac * fy[1] / (twopi * rfac)
- v22 = jacfac * (1 + fy[2]) * (2 * rfac)
- v33 = jacfac * twopi * (r / π)
- dvsq = (v21^2 + v22^2) * (v33 * jac^2)^2
- gs1[itheta+1] = sqrt(dvsq) / (twopi * r)
- gs2[itheta+1] = chi1 * dvsq / (twopi * r)^2
- end
-
- int1 = sum(gs1) / (mtheta+1)
- int2 = sum(gs2) / (mtheta+1)
- crnt = int2 / (1e6 * mu0)
- bp0 = int2 / int1
- bwall = 1e6 * mu0 * crnt / (twopi * amean)
-
- pe.params.crnt = crnt
- pe.params.bwall = bwall
-
- # Flux surface integrals
- hs1 = sq.fs[:,2] .* sq.fs[:,3] # p * dV/dpsi
- hs2 = sq.fs[:,3] # dV/dpsi
- hs3 = sq.fs[:,2].^2 .* sq.fs[:,3] # p^2 * dV/dpsi
-
- dpsi_vec = diff(sq.xs)
- fsi1 = sum((hs1[1:end-1] .+ hs1[2:end]) .* dpsi_vec) / 2
- fsi2 = sum((hs2[1:end-1] .+ hs2[2:end]) .* dpsi_vec) / 2
- fsi3 = sum((hs3[1:end-1] .+ hs3[2:end]) .* dpsi_vec) / 2
-
- volume = sum((sq.fs[1:end-1,3] .+ sq.fs[2:end,3]) .* dpsi_vec) / 2
-
- p0 = sq.fs[1,2] - sq.fs1[1,2] * sq.xs[1] # linear extrapolation
- betat = 2 * (fsi1 / fsi2) / bt0^2
- betaj = 2 * sqrt(fsi3 / fsi2) / bwall^2
- betan = 100 * amean * bt0 * betat / crnt
- betap1 = 2 * (fsi1 / fsi2) / bp0^2
- betap2 = 4 * fsi1 / ((1e6 * mu0 * crnt)^2 * pe.ro)
- betap3 = 4 * fsi1 / ((1e6 * mu0 * crnt)^2 * rmean)
- li1 = fsi3 / fsi2 / bp0^2
- li2 = 2 * fsi3 / ((1e6 * mu0 * crnt)^2 * pe.ro)
- li3 = 2 * fsi3 / ((1e6 * mu0 * crnt)^2 * rmean)
-
- pe.params.psi0 = psio
- pe.params.psi_axis = pe.psio
- pe.params.psi_boundary = 1.0
- pe.params.psi_boundary_norm = 1.0
- pe.params.psi_axis_norm = 0.0
- pe.params.psi_norm = 0.0
- pe.params.psi_axis_offset = 0.0
- pe.params.psi_boundary_offset = 0.0
- pe.params.psi_axis_sign = 1
- pe.params.psi_boundary_sign = -1
- pe.params.psi_boundary_zero = false
+const mu0 = 4π * 1e-7
- pe.params.q0 = sq.fs[1,4]
- pe.params.b0 = bt0
+# efit-family equilibrium kinds that share the separatrix-clamp / inversion handling.
+const EFIT_KINDS = ("efit", "efit_arclength", "efit_by_inversion")
- pe.params.volume = volume
- pe.params.betat = betat
- pe.params.betan = betan
- pe.params.betaj = betaj
- pe.params.betap1 = betap1
- pe.params.betap2 = betap2
- pe.params.betap3 = betap3
- pe.params.li1 = li1
- pe.params.li2 = li2
- pe.params.li3 = li3
-end
-
-
-
-
-
-
-function equilibrium_qfind!(equil::PlasmaEquilibrium)
- println("Finding q profile...")
-
- sq = equil.sq
- mpsi = length(sq.xs) - 1
- psiexl = Float64[]
- qexl = Float64[]
-
- # Left endpoint
- push!(psiexl, sq.xs[1])
- push!(qexl, sq.fs[1, 4])
-
- # Search for extrema in q(ψ)
- for ipsi in 1:mpsi
- x0 = sq.xs[ipsi]
- x1 = sq.xs[ipsi + 1]
- xmax = x1 - x0
-
- f, f1, f2, f3 = Spl.spline_eval(sq, x0, 3)
- a, b, c, d = f[4], f1[4], f2[4], f3[4]
-
- if d != 0.0
- xcrit = -c / d
- dx2 = xcrit^2 - 2b / d
- if dx2 ≥ 0
- dx = sqrt(dx2)
- for delta in (dx, -dx)
- x = xcrit - delta
- if 0 ≤ x < xmax
- ψ = x0 + x
- fψ, = Spl.spline_eval(sq, ψ, 0)
- push!(psiexl, ψ)
- push!(qexl, fψ[4])
- end
- end
- end
- end
- end
-
- # Right endpoint
- push!(psiexl, sq.xs[end])
- push!(qexl, sq.fs[end, 4])
-
- equil.params.qextrema_psi = psiexl
- equil.params.qextrema_q = qexl
- equil.params.mextrema = length(psiexl)
- # Compute derived q-values
- q0 = sq.fs[1, 4] - sq.fs1[1, 4] * sq.xs[1]
- qmax_edge = sq.fs[end, 4]
- qmin = min(minimum(qexl), q0)
- qmax = max(maximum(qexl), qmax_edge)
- qa = sq.fs[end, 4] + sq.fs1[end, 4] * (1.0 - sq.xs[end])
-
- f95 = Spl.spline_eval(sq, 0.95, 0)
- q95 = f95[4]
-
-
- # Print and store
- println("q0: $q0, qmin: $qmin, qmax: $qmax, qa: $qa, q95: $q95, qmax_edge: $qmax_edge, psiexl: $(equil.params.qextrema_psi), qexl: $(equil.params.qextrema_q), mextrema: $(equil.params.mextrema)")
-
- equil.params.q0 = q0
- equil.params.qmin = qmin
- equil.params.qmax = qmax
- equil.params.qa = qa
- equil.params.q95 = q95
-
- return equil
-end
-
-
-
-
-
-function equilibrium_gse!(equil::PlasmaEquilibrium)
- println("Diagnosing Grad-Shafranov solution...")
-
- rzphi = equil.rzphi
- sq = equil.sq
- mpsi, mtheta = rzphi.mx, rzphi.my
- ro, zo = equil.ro, equil.zo
- psio = equil.psio
- verbose = equil.params.verbose
- diagnose_src = true #equil.params.diagnose_src
- diagnose_maxima = equil.params.diagnose_maxima
-
- rfac = zeros(Float64, mtheta+1)
- angle = zeros(Float64, mtheta+1)
- r = zeros(Float64, mpsi+1, mtheta+1)
- z = zeros(Float64, mpsi+1, mtheta+1)
-
- for ipsi in 0:mpsi
- for itheta in 0:mtheta
- rz_eval = Spl.bicube_eval(rzphi, rzphi.xs[ipsi+1], rzphi.ys[itheta+1], 0)
- rfac[itheta+1] = sqrt(rz_eval[1])
- angle[itheta+1] = 2π * (rzphi.ys[itheta+1] + rz_eval[2])
- end
- r[ipsi+1, :] .= ro .+ rfac .* cos.(angle)
- z[ipsi+1, :] .= zo .+ rfac .* sin.(angle)
- end
-
- flux_fs = zeros(Float64, mpsi+1, mtheta+1, 2)
- for ipsi in 0:mpsi
- for itheta in 0:mtheta
- f, fx, fy = Spl.bicube_eval(rzphi, rzphi.xs[ipsi+1], rzphi.ys[itheta+1], 1)
- f1, f2, f4 = f[1], f[2], f[4]
-
- fy1 = rzphi._fsy[ipsi+1, itheta+1, 1]
- fy2 = rzphi._fsy[ipsi+1, itheta+1, 2]
- fx1 = rzphi._fsx[ipsi+1, itheta+1, 1]
- fx2 = rzphi._fsx[ipsi+1, itheta+1, 2]
-
- flux_fs[ipsi+1, itheta+1, 1] = fy1^2 / (4π^2 * f1) + (1 + fy2)^2 * 4 * f1
- flux_fs[ipsi+1, itheta+1, 2] = fx1 * fy1 / (4π^2 * f1) + fx2 * (1 + fy2) * 4 * f1
-
- for iqty in 1:2
- flux_fs[ipsi+1, itheta+1, iqty] *= 2π * psio / f4
- end
- end
- end
-
-
-
- flux = Spl.BicubicSpline(collect(rzphi.xs), collect(rzphi.ys), flux_fs; bctypex=2, bctypey=2)
-
- source = zeros(Float64, mpsi+1, mtheta+1)
- for ipsi in 0:mpsi
- for itheta in 0:mtheta
- rz_eval = Spl.bicube_eval(rzphi, rzphi.xs[ipsi+1], rzphi.ys[itheta+1], 0)
- f4 = rz_eval[4]
- s1 = sq.fs[ipsi+1, 1]
- s1p = sq.fs1[ipsi+1, 1]
- s2p = sq.fs1[ipsi+1, 2]
-
- denom = (2π * r[ipsi+1, itheta+1])^2
- source[ipsi+1, itheta+1] = f4 / (2π * psio * π^2) * (s1 * s1p / denom + s2p)
- end
- end
-
- total = flux.fsx[:, :, 1] .- flux.fsy[:, :, 2] .+ source
- error = abs.(total) ./ maximum([maximum(abs.(flux.fsx[:, :, 1])), maximum(abs.(flux.fsy[:, :, 2])), maximum(abs.(source))])
- errlog = ifelse.(error .> 0, log10.(error), 0.0)
-
- if diagnose_maxima
- fxmax = maximum(abs.(flux.fsx[:, :, 1]))
- fymax = maximum(abs.(flux.fsy[:, :, 2]))
- smax = maximum(abs.(source))
- emax = maximum(abs.(error))
- lmax = maximum(errlog)
- jmax = ind2sub(size(errlog), argmax(errlog))
- println(" fxmax = $fxmax, fymax = $fymax, smax = $smax")
- println(" emax = $emax, lmax = $lmax, maxloc = ", jmax .- 1)
- end
-
- # Integrated error criterion
- term = zeros(Float64, mpsi+1, 2)
- for ipsi in 0:mpsi
- fs_matrix = zeros(Float64, mtheta+1, 2)
- fs_matrix[:, 1] = flux.fsx[ipsi+1, :, 1]
- fs_matrix[:, 2] = source[ipsi+1, :]
-
- spline = Spl.CubicSpline(Vector(flux.ys), fs_matrix; bctype=2)
- Spl.spline_integrate!(spline)
-
- term[ipsi+1, :] .= spline.fsi[end, :]
- # spline will be automatically deallocated by finalizer
- end
-
- totali = sum(term, dims=2)
- errori = abs.(totali)
- errlogi = @. ifelse(errori > 0, log10(errori), 0.0)
-
- if diagnose_src
- println("Writing diagnostics to HDF5 files...")
-
- # Write contour data
- h5open(joinpath(dirname(equil.config.control.eq_filename), "gsec.h5"), "w") do file
- file["mpsi"] = mpsi
- file["mtheta"] = mtheta
- file["r"] = Float32.(r)
- file["z"] = Float32.(z)
- file["flux_fsx"] = Float32.(flux.fsx[:, :, 1])
- file["flux_fsy"] = Float32.(flux.fsy[:, :, 2])
- file["source"] = Float32.(source)
- file["total"] = Float32.(total)
- file["error"] = Float32.(error)
- file["errlog"] = Float32.(errlog)
- end
-
- # Write xy plot data
- h5open(joinpath(dirname(equil.config.control.eq_filename), "gse.h5"), "w") do file
- gse_data = Array{Float32, 3}(undef, mpsi+1, mtheta+1, 7)
- for ipsi in 0:mpsi
- for itheta in 0:mtheta
- gse_data[ipsi+1, itheta+1, 1] = Float32(flux.ys[itheta+1])
- gse_data[ipsi+1, itheta+1, 2] = Float32(flux.xs[ipsi+1])
- gse_data[ipsi+1, itheta+1, 3] = Float32(flux.fs[ipsi+1, itheta+1, 1])
- gse_data[ipsi+1, itheta+1, 4] = Float32(flux.fs[ipsi+1, itheta+1, 2])
- gse_data[ipsi+1, itheta+1, 5] = Float32(source[ipsi+1, itheta+1])
- gse_data[ipsi+1, itheta+1, 6] = Float32(total[ipsi+1, itheta+1])
- gse_data[ipsi+1, itheta+1, 7] = Float32(error[ipsi+1, itheta+1])
- end
- end
- file["gse_data"] = gse_data
- end
-
- # Write integrated error criterion
- h5open(joinpath(dirname(equil.config.control.eq_filename), "gsei.h5"), "w") do file
- file["xs"] = Float32.(flux.xs)
- file["term"] = Float32.(term)
- file["totali"] = Float32.(totali)
- file["errori"] = Float32.(errori)
- file["errlogi"] = Float32.(errlogi)
- end
- end
-
-
- return equil
+# --- Internal Module Structure ---
+include("Config.jl")
+include("Sources/Ingest.jl")
+include("Sources/Analytic/Analytic.jl")
+include("PlasmaEquilibrium.jl")
+include("Axisymmetric/SolveTolerances.jl")
+include("Grid/GridRefinement.jl")
+include("Grid/PsiGrid.jl")
+include("Axisymmetric/Separatrix.jl")
+include("Derived/FluxSurfaceMetrics.jl")
+include("Derived/CoordinateInvariant.jl")
+include("Sources/GFile.jl")
+include("Sources/Chease.jl")
+include("Sources/IFile.jl")
+include("Sources/IMAS.jl")
+include("Axisymmetric/Direct.jl")
+include("Axisymmetric/DirectArcLength.jl")
+include("Axisymmetric/DirectByInversion.jl")
+include("Axisymmetric/Inverse.jl")
+include("Derived/GeometryProfiles.jl")
+include("KineticProfiles.jl")
+include("Construction.jl")
+include("Derived/GlobalParameters.jl")
+include("Axisymmetric/GradShafranovResidual.jl")
-end
+# --- Expose types and functions to the user ---
+export reform, EquilibriumConfig, PlasmaEquilibrium, EquilibriumParameters, AnalyticEquilibriumConfig,
+ ProfileSplines, GeometryProfileSplines, compute_geometry_profiles,
+ KineticProfileSplines, kinetic_profile_splines, shift_exb_rotation,
+ KineticProfileData, IonSpecies, read_kinetic_file, write_kinetic_h5, attach_kinetic_profiles!
+export flux_surface_metric, flux_surface_area
+export wants_two_pass, refined_psi_grid, merge_mandatory_nodes, bracket_mandatory_nodes, enforce_min_spacing, implied_knot_count
+export compute_jac_delpsi, compute_sqrt_jac_delpsi, compute_sqrtamat, rootarea_to_area_weight, area_to_rootarea_weight
+include("Output.jl")
-end # module Equilibrium
\ No newline at end of file
+end # module Equilibrium
diff --git a/src/Equilibrium/EquilibriumTypes.jl b/src/Equilibrium/EquilibriumTypes.jl
deleted file mode 100644
index 4816a5cada..0000000000
--- a/src/Equilibrium/EquilibriumTypes.jl
+++ /dev/null
@@ -1,394 +0,0 @@
-#=
-This file is the one stop shop for all the fundemental structures used in
- creating equilibrium descriptions for the DCON ODE to use.
-=#
-
-using Base: @kwdef
-
-# --- Helper function ---
-
-
-function symbolize_keys(dict::Dict{String,Any})
- return Dict(Symbol(k) => v for (k, v) in dict)
-end
-
-
-# --- Main Structures for the Equilibrium Code ---
-
-
-@kwdef mutable struct EquilibriumControl
- eq_type::String = "efit"
- eq_filename::String = "mypath"
-
- jac_type::String = "hamada"
- power_bp::Int = 0
- power_b::Int = 0
- power_r::Int = 0
-
- grid_type::String = "ldp"
- psilow::Float64 = 1e-2
- psihigh::Float64 = 0.994
- mpsi::Int = 128
- mtheta::Int = 256
-
- newq0::Int = 0
- etol::Float64 = 1e-7
- use_classic_splines::Bool = false
-
- input_only::Bool = false
- use_galgrid::Bool = true
-
- """
- Modified internal constructor that enforces self consistency within the inputs
- """
- function EquilibriumControl(eq_type, eq_filename, jac_type, power_bp, power_b, power_r,
- grid_type, psilow, psihigh, mpsi, mtheta, newq0, etol, use_classic_splines,
- input_only, use_galgrid)
- if jac_type == "hamada"
- @info "Forcing hamada coordinate jacobian exponents: power_*"
- power_b = 0
- power_bp = 0
- power_r = 0
- elseif jac_type == "pest"
- @info "Forcing pest coordinate jacobian exponents: power_*"
- power_b = 0
- power_bp = 0
- power_r = 2
- elseif jac_type == "equal_arc"
- @info "Forcing equal_arc coordinate jacobian exponents: power_*"
- power_b = 0
- power_bp = 1
- power_r = 0
- elseif jac_type == "boozer"
- @info "Forcing boozer coordinate jacobian exponents: power_*"
- power_b = 2
- power_bp = 0
- power_r = 0
- elseif jac_type == "park"
- @info "Forcing park coordinate jacobian exponents: power_*"
- power_b = 1
- power_bp = 0
- power_r = 0
- elseif jac_type == "other"
- @info "Using manual jacobian exponents: power b, bp, r = $(power_b), $(power_bp), $(power_r)"
- elseif jac_type != "other"
- error("Cannot recognize jac_type = $(jac_type)")
- end
- return new(eq_type, eq_filename, jac_type, power_bp, power_b, power_r,
- grid_type, psilow, psihigh, mpsi, mtheta, newq0, etol, use_classic_splines,
- input_only, use_galgrid)
- end
-end
-
-@kwdef mutable struct EquilibriumOutput
- gse_flag::Bool = false
- out_eq_1d::Bool = false
- bin_eq_1d::Bool = false
- out_eq_2d::Bool = false
- bin_eq_2d::Bool = true
- out_2d::Bool = false
- bin_2d::Bool = false
- dump_flag::Bool = false
-end
-
-
-"""
- EquilibriumConfig(...)
-
-A container struct that bundles all necessary configuration settings originally specified in the equil
- fortran namelsits.
-"""
-@kwdef mutable struct EquilibriumConfig
- control::EquilibriumControl = EquilibriumControl()
- output::EquilibriumOutput = EquilibriumOutput()
-end
-#
-
-"""
-Constructor that allows users to form a EquilibriumConfig struct from dictionaries
- for convinience when most of the defaults are fine.
-"""
-function EquilibriumConfig(control::Dict, output::Dict)
- construct = EquilibriumControl(; control...)
- outstruct = EquilibriumOutput(; output...)
- return EquilibriumConfig(control=construct, output=outstruct)
-end
-
-"""
-Outer constructor for EquilibriumConfig that enables a toml file
- interface for specifying the configuration settings
-"""
-# if this also have default, then conflicts with @kwdef mutable struct EquilibriumConfig.
-function EquilibriumConfig(path::String)
- raw = TOML.parsefile(path)
-
- # Extract EQUIL_CONTROL with default fallback
- control_data = get(raw, "EQUIL_CONTROL", Dict())
- output_data = get(raw, "EQUIL_OUTPUT", Dict())
-
- # Check for required fields in control_data
- required_keys = ("eq_filename", "eq_type")
- missingkeys = filter(k -> !haskey(control_data, k), required_keys)
-
- if !isempty(missingkeys)
- error("Missing required key(s) in [EQUIL_CONTROL]: $(join(missing, ", "))")
- end
-
- # Construct validated structs
- control = EquilibriumControl(; symbolize_keys(control_data)...)
- if !isabspath(control.eq_filename)
- control.eq_filename = normpath(joinpath(dirname(path), control.eq_filename))
- end
- output = EquilibriumOutput(; symbolize_keys(output_data)...)
-
- return EquilibriumConfig(control=control, output=output)
-end
-
-
-
-"""
- LargeAspectRatioConfig(...)
-
-A mutable struct holding parameters for the Large Aspect Ratio (LAR) plasma equilibrium model.
-
-## Fields:
-
-- `lar_r0`: The major radius of the plasma [m].
-- `lar_a`: The minor radius of the plasma [m].
-- `beta0`: The beta value on axis (normalized pressure).
-- `q0`: The safety factor on axis.
-- `p_pres`: The exponent for the pressure profile, defined as `p00 * (1 - (r / a)^2)^p_pres`.
-- `p_sig`: The exponent that determines the shape of the current-related function profile.
-- `sigma_type`: The type of sigma profile, can be "default" or "wesson". If "wesson", the sigma profile is defined as `sigma0 * (1 - (r / a)^2)^p_sig`.
-- `mtau`: The number of grid points in the poloidal direction.
-- `ma`: The number of grid points in the radial direction.
-- `zeroth`: If set to true, it neglects the Shafranov shift
-"""
-@kwdef mutable struct LargeAspectRatioConfig
- lar_r0::Float64 = 10.0 # Major radius of the plasma
- lar_a::Float64 = 1.0 # Minor radius of the plasma
-
- beta0::Float64 = 1e-3 # beta on axis
- q0::Float64 = 1.5 # q (safety factor) on axis
-
- p_pres::Float64 = 2.0 # p00 * (1-(r/a)**2)**p_pres
- p_sig::Float64 = 1.0 # The exponent that determines the shape of the current-related function profile
-
- sigma_type::String = "default" # can be 'default' or 'wesson'. If 'wesson', switch sigma profile to sigma0*(1-(r/a)**2)**p_sig
-
- mtau::Int = 128 # the number of grid points in the poloidal direction
- ma::Int = 128 # the number of grid points in the radial direction
-
- zeroth::Bool = false # If set to true, it neglects the Shafranov shift, creating an ideal concentric circular cross-section.
-end
-
-"""
-Outer constructor for LargeAspectRatioConfig that enables a toml file
- interface for specifying the configuration settings
-"""
-function LargeAspectRatioConfig(path::String)
- raw = TOML.parsefile(path)
- input_data = get(raw, "LAR_INPUT", Dict())
- return LargeAspectRatioConfig(; symbolize_keys(input_data)...)
-end
-
-
-
-"""
- SolevevConfig(...)
-
-A mutable struct holding parameters for the Solev'ev (SOL) plasma equilibrium model.
-
-## Fields:
-
-- `mr`: number of radial grid zones
-- `mz`: number of axial grid zones
-- `ma`: number of flux grid zones
-- `e`: elongation
-- `a`: minor radius
-- `r0`: major radius
-- `q0`: safety factor at the o-point
-- `p0fac`: scale on-axis pressure (P-> P+P0*p0fac. beta changes. Phi,q constant)
-- `b0fac`: scale toroidal field at constant beta (s*Phi,s*f,s^2*P. bt changes. Shape,beta constant)
-- `f0fac`: scale toroidal field at constant pressure (s*f. beta,q changes. Phi,p,bp constant)
-"""
-@kwdef mutable struct SolevevConfig
- mr::Int = 128 # number of radial grid zones
- mz::Int = 128 # number of axial grid zones
- ma::Int = 128 # number of flux grid zones
- e::Float64 = 1.6 # elongation
- a::Float64 = 0.33 # minor radius
- r0::Float64 = 1.0 # major radius
- q0::Float64 = 1.9 # safety factor at the o-point
- p0fac::Float64 = 1 # scale on-axis pressure (P-> P+P0*p0fac. beta changes. Phi,q constant)
- b0fac::Float64 = 1 # scale toroidal field at constant beta (s*Phi,s*f,s^2*P. bt changes. Shape,beta constant)
- f0fac::Float64 = 1 # scale toroidal field at constant pressure (s*f. beta,q changes. Phi,p,bp constant)
-end
-
-"""
-Outer constructor for LarConfig that enables a toml file
- interface for specifying the configuration settings
-"""
-function SolevevConfig(path::String) # if we use @kwdef, it generates SolevevConfig() so it conflicts with this line.
- raw = TOML.parsefile(path)
- input_data = get(raw, "SOL_INPUT", Dict())
- return SolevevConfig(; symbolize_keys(input_data)...)
-end
-
-
-"""
- DirectRunInput(...)
-
-A container struct that bundles all necessary inputs for the `direct_run` function.
-It is created by the `_read_efit` function after parsing the raw equilibrium file
-and preparing the initial splines.
-
-## Fields:
-- `equil_input`: The original `EquilInput` object.
-- `sq_in`
- # x value: psin
- # Quantity 1: F = R*Bt [m T]
- # Quantity 2: mu0 * Pressure (non-negative) [nt^2 / m^2 * mu0 = T^2]
- # Quantity 3: q-profile
- # Quantity 4: sqrt(psi_norm)
-- `psi_in`:
- # x, y value: R, Z [m]
- # z value : poloidal flux adjusted to be zero at the boundary [Weber/radian]
- # 1. ψ(R,Z) = ψ_boundary - ψ(R,Z)
- # 2. if ψ = ψ * sign(ψ(centerR,centerZ))
-- `rmin`: Minimum R-coordinate of the computational grid [m].
-- `rmax`: Maximum R-coordinate of the computational grid [m].
-- `zmin`: Minimum Z-coordinate of the computational grid [m].
-- `zmax`: Maximum Z-coordinate of the computational grid [m].
-- `psio`: The total flux difference `abs(ψ_axis - ψ_boundary)` [Weber / radian].
-"""
-mutable struct DirectRunInput
- config::EquilibriumConfig
- sq_in::Any # 1D profile spline (CubicSpline)
- psi_in::Any # 2D flux spline (BicubicSpline)
- rmin::Float64 # Minimum R-coordinate of the computational grid [m].
- rmax::Float64 # Maximum R-coordinate of the computational grid [m].
- zmin::Float64 # Minimum Z-coordinate of the computational grid [m].
- zmax::Float64 # Maximum Z-coordinate of the computational grid [m].
- psio::Float64 # The total flux difference |ψ_axis - ψ_boundary| [Weber / radian].
-end
-
-"""
- InverseRunInput(...)
-
-A container struct for inputs to the `inverse_run` function.
-
-## Fields:
-- `equil_input`: The original `EquilInput` object.
-"""
-mutable struct InverseRunInput
- config::EquilibriumConfig
- sq_in::Any # 1D spline input profile (e.g. F*Bt, Pressure, q)
- rz_in::Any # 2D bicubic spline input for (R,Z) geometry
- ro::Float64 # R axis location
- zo::Float64 # Z axis location
- psio::Float64 # Total flux difference |psi_axis - psi_boundary|
-end
-
-
-
-@kwdef mutable struct EquilibriumParameters
- ro::Union{Nothing,Float64} = nothing # R-coordinate of the magnetic axis [m]
- zo::Union{Nothing,Float64} = nothing # Z-coordinate of the magnetic axis [m]
- psio::Union{Nothing,Float64} = nothing # Total flux difference |Ψ_axis - Ψ_boundary| [Weber / radian]
- rsep::Union{Nothing,Vector{Float64}} = nothing # R-coordinates of the plasma boundary [m]
- zsep::Union{Nothing,Vector{Float64}} = nothing # Z-coordinates of the plasma boundary [m]
- rext::Union{Nothing,Vector{Float64}} = nothing # R-coordinates of the plasma edge [m]
- zext::Union{Nothing,Vector{Float64}} = nothing # Z-coordinates of the plasma edge [m]
- psi0::Union{Nothing,Float64} = nothing # Normalized poloidal flux
- b0::Union{Nothing,Float64} = nothing # Total magnetic field strength at the axis [T]
- q0::Union{Nothing,Float64} = nothing # Safety factor at the axis
- qmin::Union{Nothing,Float64} = nothing # Minimum safety factor in the plasma
- qmax::Union{Nothing,Float64} = nothing # Maximum safety factor in the plasma
- qa::Union{Nothing,Float64} = nothing # Safety factor at the plasma edge
- q95::Union{Nothing,Float64} = nothing # Safety factor at 95% flux surface
- qextrema_psi::Union{Nothing,Vector{Float64}} = nothing # Normalized poloidal flux values where q has extrema
- qextrema_q::Union{Nothing,Vector{Float64}} = nothing # Safety factor values at the extrema points
- mextrema::Union{Nothing,Int} = nothing # Number of extrema points in the q-profile
- psi_norm::Union{Nothing,Float64} = nothing # Normalized poloidal flux at the axis
- b_norm::Union{Nothing,Float64} = nothing # Normalized total magnetic field strength at the axis
- psi_axis::Union{Nothing,Float64} = nothing # Normalized poloidal flux at the axis
- psi_boundary::Union{Nothing,Float64} = nothing # Poloidal flux at the boundary
- psi_boundary_norm::Union{Nothing,Float64} = nothing # Normalized poloidal flux at the boundary
- psi_axis_norm::Union{Nothing,Float64} = nothing # Normalized poloidal flux at the axis
- psi_boundary_offset::Union{Nothing,Float64} = nothing # Offset for the boundary poloidal flux
- psi_axis_offset::Union{Nothing,Float64} = nothing # Offset for the axis poloidal flux
- psi_boundary_sign::Union{Nothing,Int} = nothing # Sign of the boundary poloidal flux
- psi_axis_sign::Union{Nothing,Int} = nothing # Sign of the axis poloidal flux
- psi_boundary_zero::Union{Nothing,Bool} = nothing # Whether the boundary poloidal flux is zero
- rmean::Union{Nothing,Float64} = nothing # Mean R-coordinate of the plasma [m]
- amean::Union{Nothing,Float64} = nothing # Mean minor radius of the plasma [m]
- aratio::Union{Nothing,Float64} = nothing # Aspect ratio of the plasma (R0/a)
- kappa::Union{Nothing,Float64} = nothing # Elongation of the plasma cross-section
- delta1::Union{Nothing,Float64} = nothing # Triangularity of the plasma cross-section (upper triangularity)
- delta2::Union{Nothing,Float64} = nothing # Triangularity of the plasma cross-section (lower triangularity)
- bt0::Union{Nothing,Float64} = nothing # Toroidal magnetic field at the axis [T]
- crnt::Union{Nothing,Float64} = nothing # Plasma current at the axis [A]
- bwall::Union{Nothing,Float64} = nothing # Toroidal magnetic field at the wall [T]
- verbose::Bool = false # Whether to print verbose output
- diagnose_src::Bool = false # Whether to diagnose source data
- diagnose_maxima::Bool = false # Whether to diagnose maxima in the equilibrium
- volume::Union{Nothing,Float64} = nothing # Plasma volume [m³]
- betat::Union{Nothing,Float64} = nothing # Toroidal beta (normalized pressure) at the axis
- betan::Union{Nothing,Float64} = nothing # Normalized beta at the axis
- betaj::Union{Nothing,Float64} = nothing # Total beta at the axis
- betap1::Union{Nothing,Float64} = nothing # Pressure beta at the axis
- betap2::Union{Nothing,Float64} = nothing # Toroidal beta at the axis
- betap3::Union{Nothing,Float64} = nothing # Poloidal beta at the axis
- li1::Union{Nothing,Float64} = nothing # Internal inductance at the axis
- li2::Union{Nothing,Float64} = nothing # External inductance at the axis
- li3::Union{Nothing,Float64} = nothing # Total inductance at the axis
-end
-
-
-
-
-
-"""
- PlasmaEquilibrium(...)
-
-The final, self-contained result of the equilibrium reconstruction. This object
-provides a complete representation of the processed plasma equilibrium in flux coordinates.
-
-## Fields:
-- `equil_input`: The original `EquilInput` object used for the reconstruction.
-- `sq`: The final 1D profile spline (`CubicSpline{Float64}`).
- # x value: normalized psi
- # Quantity 1: Toroidal Field Function * 2π, `F * 2π` (where `F = R * B_toroidal`)
- # Quantity 2: Pressure * μ₀, `P * μ₀`.
- # Quantity 3: dVdpsi
- # Quantity 4: q
-- `rzphi`: The final 2D flux-coordinate mapping spline (`BicubicSpline`).
- # x value: normlized psi
- # y value: SFL poloidal angle [0,1]
- # Quantity 1: r_coord² = (R - ro)² + (Z - zo)²
- # Quantity 2: Offset between the geometric poloidal angle (η) and the new angle (θ_new)
- `η / (2π) - θ_new
- # Quantity 3: ν in ϕ=2πζ+ν(ψ,θ)
- # Quantity 4: Jacobian.
-- `eqfun`: A 2D spline storing local physics and geometric quantities that vary across the flux surfaces.
- # These are pre-calculated for efficient use in subsequent stability and transport codes.
- # x value: Normalized poloidal flux, ψ_norm ∈ [0, 1].
- # y value: SFL poloidal angle, θ_new ∈ [0, 1].
- # Quantity 1: Total magnetic field strength, B [T]
- # Quantity 2: (e₁⋅e₂ + q⋅e₃⋅e₁) / (J⋅B²).
- # Quantity 3: (e₂⋅e₃ + q⋅e₃⋅e₃) / (J⋅B²).
-- `ro`: R-coordinate of the magnetic axis [m].
-- `zo`: Z-coordinate of the magnetic axis [m].
-- `psio`: Total flux difference `|Ψ_axis - Ψ_boundary|` [Weber / radian].
-"""
-mutable struct PlasmaEquilibrium
- config::EquilibriumConfig
- params::EquilibriumParameters # Parameters for the equilibrium
- sq::Spl.CubicSpline # Final 1D profile spline
- rzphi::Spl.BicubicSpline # Final 2D coordinate mapping spline
- eqfun::Spl.BicubicSpline
- ro::Float64
- zo::Float64
- psio::Float64
-end
diff --git a/src/Equilibrium/Grid/GridRefinement.jl b/src/Equilibrium/Grid/GridRefinement.jl
new file mode 100644
index 0000000000..772635b8c4
--- /dev/null
+++ b/src/Equilibrium/Grid/GridRefinement.jl
@@ -0,0 +1,480 @@
+"""
+Radial grid refinement utilities for the two-pass auto ψ grid.
+
+Pass 1 forms the equilibrium on a coarse grid; `refined_psi_grid` then derives a knot
+density from the measured nodal data (1D profiles, 2D geometry channels, and optional
+kinetic profiles) and equidistributes it, pinning mandatory knots (e.g. rational surfaces)
+via `merge_mandatory_nodes`. Pass 2 re-forms the equilibrium on the refined grid through
+the `override_psi_nodes` keyword of `PlasmaEquilibrium`.
+
+Knot spacing follows the cubic spline *derivative* error model err(f′) ≈ h³|f''''|/24 ≤ τ·f_scale
+(the stability physics consumes spline derivatives), so knot counts scale as psi_accuracy^(-1/3).
+The curvature |f''''| comes from three sources:
+
+ 1. *Measured* (mid-radius and edge): 5-point divided differences of the pass-1 nodal values.
+ 2. *Separatrix model* (edge floor, ψ ≥ 0.9): q ≈ −A·ln(1−ψ) gives geometric packing in log(1−ψ),
+ independent of A; applied only when `edge_q_law` finds a diverging edge.
+ 3. *Axis model* (core, ψ ≤ 0.03): a power law in ψ gives geometric packing in log(ψ). It replaces
+ the measurement there, since the smallest surfaces' nodal data is dominated by integration noise.
+
+Measured curvature is taken against ρ = √ψ_N, in which the equilibrium is regular at the axis, and
+mapped back to a ψ density through dψ/dρ = 2√ψ_N.
+"""
+
+# Cubic spline derivative interpolation error constant: err(f′) ≈ h³|f''''|/24
+const CUBIC_DERIV_ERR_CONST = 24.0
+# |f''''|/f_scale below this is treated as integrator noise, not curvature; on tightly packed sample
+# grids the floor grows as NODE_NOISE_REL/h⁴, since divided differences amplify nodal noise as h⁻⁴.
+const D4_NOISE_FLOOR = 1e3
+const NODE_NOISE_REL = 1e-8
+# Floor on a channel's value-scale, so an all-zero profile/geometry channel cannot divide by zero
+const F_SCALE_FLOOR = 1e-12
+# Per-quantity target spacing clamp (ψ_N units)
+const H_TARGET_MIN = 1e-4
+const H_TARGET_MAX = 0.2
+# Model-region splits (ψ_N): below CORE the axis model replaces measured curvature; above EDGE the
+# separatrix model floors it.
+const CORE_MODEL_PSI_MAX = 0.03
+const EDGE_MODEL_PSI_MIN = 0.9
+# θ-lines subsample stride for the 2D geometry channels
+const THETA_STRIDE = 8
+# Edge q-law gate.
+# Minimum knots in the edge band before a fit is attempted.
+const EDGE_FIT_MIN_KNOTS = 4
+# Weak backstop against a fit that describes nothing; no absolute r2 separates diverted from limited
+# edges, so that discrimination is the r2_log > r2_linear comparison.
+const EDGE_FIT_MIN_R2 = 0.5
+# Accepted factor between the fitted `A` and the measured local log shear -(1-psi)*q'(psi).
+const EDGE_FIT_SHEAR_RATIO = 2.0
+
+# Least-squares slope and coefficient of determination for y = a + b*x.
+function _linfit_r2(x::Vector{Float64}, y::Vector{Float64})
+ x_bar = sum(x) / length(x)
+ y_bar = sum(y) / length(y)
+ sxx = sum((x .- x_bar) .^ 2)
+ sxx > 0 || return (NaN, NaN, NaN, NaN)
+ b = sum((x .- x_bar) .* (y .- y_bar)) / sxx
+ ss_res = sum((y .- (y_bar .+ b .* (x .- x_bar))) .^ 2)
+ ss_tot = sum((y .- y_bar) .^ 2)
+ r2 = ss_tot > 0 ? 1 - ss_res / ss_tot : NaN
+ return (b, r2, x_bar, y_bar)
+end
+
+"""
+ edge_q_law(equil; psi_max, psi_min=EDGE_MODEL_PSI_MIN, min_knots=EDGE_FIT_MIN_KNOTS,
+ min_r2=EDGE_FIT_MIN_R2, shear_ratio=EDGE_FIT_SHEAR_RATIO)
+ -> nothing | (; A, q_bar, u_bar, n_knots, r2_log, r2_linear)
+
+Least-squares fit of the separatrix edge law `q = q̄ + A·(ln(1−ψ) − ū)` over the equilibrium's
+outer knots. It only gates the grid-refinement edge density floor; placing surfaces beyond the grid
+is [`separatrix_q_law`](@ref), and geometric X-point detection is [`classify_topology`](@ref).
+
+Returns `nothing` when the diverging model does not describe the edge:
+
+ - fewer than `min_knots` knots in the band;
+ - `A ≥ 0`, i.e. q not rising toward ψ = 1;
+ - `r2_log < min_r2`;
+ - `r2_log ≤ r2_linear` (a linear-in-ψ fit does at least as well, as for a limited plasma);
+ - the fitted `A` and the measured `-(1−ψ)·q′` differ by more than `shear_ratio`.
+"""
+function edge_q_law(equil::PlasmaEquilibrium;
+ psi_max::Real=Float64(equil.profiles.xs[end]),
+ psi_min::Real=EDGE_MODEL_PSI_MIN,
+ min_knots::Int=EDGE_FIT_MIN_KNOTS,
+ min_r2::Real=EDGE_FIT_MIN_R2,
+ shear_ratio::Real=EDGE_FIT_SHEAR_RATIO)
+ xs = collect(Float64, equil.profiles.xs)
+ band = findall(x -> x >= psi_min && x < psi_max, xs)
+ if length(band) < min_knots
+ n_tail = max(min_knots, length(xs) ÷ 10)
+ band = filter(i -> xs[i] < psi_max, collect(max(1, length(xs) - n_tail + 1):length(xs)))
+ end
+ length(band) >= min_knots || return nothing
+
+ q = [Float64(equil.profiles.q_spline(xs[i])) for i in band]
+ u = [log(1.0 - xs[i]) for i in band]
+ all(isfinite, u) && all(isfinite, q) || return nothing
+
+ A, r2_log, u_bar, q_bar = _linfit_r2(u, q)
+ _, r2_linear, _, _ = _linfit_r2([xs[i] for i in band], q)
+ (isfinite(A) && A < 0) || return nothing # q must rise toward the edge
+ (isfinite(r2_log) && r2_log >= min_r2) || return nothing
+ (isfinite(r2_linear) && r2_log > r2_linear) || return nothing
+
+ # The fitted slope is the local logarithmic shear; it must match the profile's -(1-psi)*q'.
+ hint = Ref(1)
+ A_meas = median([-(1.0 - xs[i]) * Float64(equil.profiles.q_deriv(xs[i]; hint=hint)) for i in band])
+ isfinite(A_meas) && A_meas < 0 || return nothing
+ ratio = A / A_meas
+ (ratio >= inv(shear_ratio) && ratio <= shear_ratio) || return nothing
+
+ return (A=A, q_bar=q_bar, u_bar=u_bar, n_knots=length(band), r2_log=r2_log, r2_linear=r2_linear)
+end
+
+
+# Rational-surface bracket half-width in units of the Δ′ matching stencil dpsi = singfac_min/|n·q′|.
+# A knot inside the stencil makes the cubic 3rd derivative jump mid-stencil and Δ′ non-convergent;
+# > 1 leaves margin for the pass-1 → pass-2 shift of ψ_s.
+const BRACKET_COEF = 4.0
+# Global minimum knot spacing for every grid; below it cubic high derivatives are integration noise.
+const MIN_KNOT_SPACING = 1.0e-4
+# Fixed (τ-independent) knot spacing within RATIONAL_RES_RADIUS of each rational surface, so Δ′ gets the
+# local resolution it needs at any accuracy target.
+const RATIONAL_RES_SPACING = 5.0e-4
+const RATIONAL_RES_RADIUS = 5.0e-3
+# Cap on the refined pass-2 interval count (density integral is clamped to this).
+const REFINED_N_CAP = 1024
+# Pass-1 interval count for the two-pass auto grid. The curvature estimate grows with this grid, so a
+# larger pass 1 also enlarges pass 2.
+const PASS1_INTERVALS = 1024
+
+"""
+ wants_two_pass(config::EquilibriumConfig) -> Bool
+
+True when the config requests the automatic two-pass grid: `grid_type = "auto"` with `mpsi = 0`
+and a positive `psi_accuracy`.
+"""
+wants_two_pass(config::EquilibriumConfig) =
+ config.grid_type == "auto" && config.mpsi == 0 && config.psi_accuracy > 0
+
+"""
+ _validate_psi_nodes(psi_nodes, psilow, psihigh) -> Vector{Float64}
+
+Check that an externally supplied ψ node vector is strictly increasing and spans exactly
+`psilow` to `psihigh`; errors otherwise.
+"""
+function _validate_psi_nodes(psi_nodes::Vector{Float64}, psilow::Real, psihigh::Real)
+ length(psi_nodes) >= 2 || error("override_psi_nodes must contain at least 2 nodes")
+ all(diff(psi_nodes) .> 0) || error("override_psi_nodes must be strictly increasing")
+ isapprox(psi_nodes[1], psilow; atol=1e-12) ||
+ error("override_psi_nodes[1]=$(psi_nodes[1]) must equal psilow=$psilow")
+ isapprox(psi_nodes[end], psihigh; atol=1e-12) ||
+ error("override_psi_nodes[end]=$(psi_nodes[end]) must equal psihigh=$psihigh")
+ return psi_nodes
+end
+
+"""
+ _fourth_derivative_nodes(xs, ys) -> Vector{Float64}
+
+Estimate |f''''| at each node of a (possibly nonuniform) grid by 5-point Newton divided
+differences: f'''' ≈ 4!·f[x_{i-2},…,x_{i+2}]. The two nodes at each boundary reuse the
+nearest interior stencil. Returns zeros when fewer than 5 nodes are available.
+"""
+function _fourth_derivative_nodes(xs::AbstractVector{<:Real}, ys::AbstractVector{<:Real})
+ n = length(xs)
+ d4 = zeros(Float64, n)
+ n < 5 && return d4
+ @inbounds for i in 1:n
+ j = clamp(i - 2, 1, n - 4) # stencil start: centered where possible, one-sided at ends
+ # Newton divided-difference table over xs[j:j+4]
+ c = Float64[ys[j+k] for k in 0:4]
+ for order in 1:4
+ for k in 4:-1:order
+ c[k+1] = (c[k+1] - c[k]) / (xs[j+k] - xs[j+k-order])
+ end
+ end
+ d4[i] = abs(24.0 * c[5])
+ end
+ return d4
+end
+
+"""
+ _density_from_curvature!(rho, d4, f_scale, tau; xs=nothing)
+
+Accumulate (in place, by max) the knot density implied by the h³ derivative error model
+for one quantity: ρ = 1/h_target with h_target = (24·τ·f_scale/|f''''|)^(1/3), clamped to
+[`H_TARGET_MIN`, `H_TARGET_MAX`]. Normalized curvature below the noise floor is ignored;
+when `xs` is given the floor grows as `NODE_NOISE_REL`/h_local⁴ on tightly packed sample
+grids, where divided differences amplify nodal noise.
+"""
+function _density_from_curvature!(rho::Vector{Float64}, d4::Vector{Float64}, f_scale::Float64, tau::Float64;
+ xs::Union{Nothing,Vector{Float64}}=nothing)
+ n = length(rho)
+ @inbounds for i in 1:n
+ noise_floor = D4_NOISE_FLOOR
+ if xs !== nothing
+ h_loc = (xs[min(i + 2, n)] - xs[max(i - 2, 1)]) / 4
+ noise_floor = max(noise_floor, NODE_NOISE_REL / h_loc^4)
+ end
+ d4n = d4[i] / f_scale
+ d4n < noise_floor && continue
+ h = clamp((CUBIC_DERIV_ERR_CONST * tau / d4n)^(1 / 3), H_TARGET_MIN, H_TARGET_MAX)
+ rho[i] = max(rho[i], 1.0 / h)
+ end
+ return rho
+end
+
+"""
+ _knot_density(equil::PlasmaEquilibrium; tau, kin=nothing) -> Vector{Float64}
+
+Knot density ρ(ψ) (knots per unit ψ_N) at the pass-1 nodes `equil.profiles.xs`: the max of the
+measured curvature density of the 1D profiles (F, P, dV/dψ, q), the four rzphi geometry channels
+(every `THETA_STRIDE`-th θ-line), and the kinetic profiles when `kin` is given, smoothed by a running
+max over ±1 node, then the core and edge model regions and a global minimum density.
+"""
+function _knot_density(equil::PlasmaEquilibrium; tau::Float64, kin::Union{Nothing,KineticProfileSplines}=nothing)
+ xs = equil.profiles.xs
+ n = length(xs)
+ # Curvature is measured against ρ = √ψ (regular at the axis) and converted to a ψ density at the end.
+ rs = sqrt.(xs)
+ rho_r = zeros(Float64, n)
+
+ # 1D profiles
+ for spl in (equil.profiles.F_spline, equil.profiles.P_spline, equil.profiles.dVdpsi_spline, equil.profiles.q_spline)
+ vals = spl.y
+ f_scale = max(maximum(abs, vals), F_SCALE_FLOOR)
+ _density_from_curvature!(rho_r, _fourth_derivative_nodes(rs, vals), f_scale, tau; xs=rs)
+ end
+
+ # 2D geometry channels: per-θ-line curvature along ρ, max over θ, plane-wide scale
+ for interp in (equil.rzphi_rsquared, equil.rzphi_offset, equil.rzphi_nu, equil.rzphi_jac)
+ vals2d = @view interp.nodal_derivs.partials[1, :, :]
+ f_scale = max(maximum(abs, vals2d), F_SCALE_FLOOR)
+ for itheta in 1:THETA_STRIDE:size(vals2d, 2)
+ _density_from_curvature!(rho_r, _fourth_derivative_nodes(rs, @view(vals2d[:, itheta])), f_scale, tau; xs=rs)
+ end
+ end
+
+ # Kinetic profiles on their own grid, rebroadcast onto xs
+ if kin !== nothing
+ rs_kin = sqrt.(kin.xs)
+ rho_kin = zeros(Float64, length(kin.xs))
+ for spl in (kin.ni_spline, kin.ne_spline, kin.Ti_spline, kin.Te_spline, kin.omegaE_spline)
+ vals = spl.y
+ f_scale = max(maximum(abs, vals), F_SCALE_FLOOR)
+ _density_from_curvature!(rho_kin, _fourth_derivative_nodes(rs_kin, vals), f_scale, tau; xs=rs_kin)
+ end
+ kin_itp = cubic_interp(rs_kin, rho_kin; extrap=ExtendExtrap())
+ @inbounds for i in 1:n
+ (rs_kin[1] <= rs[i] <= rs_kin[end]) || continue
+ rho_r[i] = max(rho_r[i], kin_itp(rs[i]))
+ end
+ end
+
+ # Convert the ρ-space density to ψ space: ρ_ψ(ψ) = ρ_ρ(ρ)·dρ/dψ = ρ_ρ/(2√ψ)
+ rho = [rho_r[i] / (2.0 * rs[i]) for i in 1:n]
+
+ # Running max over ±1 node
+ rho_s = copy(rho)
+ @inbounds for i in 1:n
+ i > 1 && (rho_s[i] = max(rho_s[i], rho[i-1]))
+ i < n && (rho_s[i] = max(rho_s[i], rho[i+1]))
+ end
+
+ # Model regions: geometric core (replaces measurement) and geometric edge floor.
+ dlog = (4.0 * tau)^(1 / 3)
+ # The edge floor assumes a diverging edge q, so it applies only when the edge law fits.
+ edge_diverges = edge_q_law(equil) !== nothing
+ @inbounds for i in 1:n
+ if xs[i] <= CORE_MODEL_PSI_MAX
+ rho_s[i] = 1.0 / (dlog * xs[i])
+ elseif edge_diverges && xs[i] >= EDGE_MODEL_PSI_MIN
+ rho_s[i] = max(rho_s[i], 1.0 / (dlog * (1.0 - xs[i])))
+ end
+ rho_s[i] = max(rho_s[i], 1.0 / H_TARGET_MAX)
+ end
+
+ return rho_s
+end
+
+"""
+ _equidistribute(xs, rho, N) -> Vector{Float64}
+
+Place N+1 nodes from `xs[1]` to `xs[end]` by equidistributing the density integral M(ψ) = ∫ρ dψ
+(trapezoid, piecewise-linear inversion). Requires ρ > 0 everywhere.
+"""
+function _equidistribute(xs::Vector{Float64}, rho::Vector{Float64}, N::Int)
+ all(>(0), rho) || error("_equidistribute requires strictly positive density")
+ n = length(xs)
+ M = zeros(Float64, n)
+ @inbounds for i in 2:n
+ M[i] = M[i-1] + 0.5 * (rho[i] + rho[i-1]) * (xs[i] - xs[i-1])
+ end
+ nodes = Vector{Float64}(undef, N + 1)
+ nodes[1] = xs[1]
+ nodes[end] = xs[end]
+ k = 2
+ @inbounds for j in 1:(N-1)
+ target = M[end] * j / N
+ while M[k] < target
+ k += 1
+ end
+ frac = (target - M[k-1]) / (M[k] - M[k-1])
+ nodes[j+1] = xs[k-1] + frac * (xs[k] - xs[k-1])
+ end
+ return nodes
+end
+
+"""
+ merge_mandatory_nodes(grid, mandatory; delta_frac=0.25, collapse_atol=1e-7) -> Vector{Float64}
+
+Insert mandatory knots into a base grid without moving them: non-mandatory nodes within
+δ_min = `delta_frac` × (containing base-grid interval) of a mandatory node are dropped. Endpoints
+always win, so mandatory nodes outside the open span or within δ_min of an endpoint are discarded.
+Mandatory nodes within `collapse_atol` of an earlier one are treated as duplicates and collapsed.
+"""
+function merge_mandatory_nodes(grid::Vector{Float64}, mandatory::Vector{Float64}; delta_frac::Float64=0.25, collapse_atol::Float64=1e-7)
+ isempty(mandatory) && return copy(grid)
+ lo, hi = grid[1], grid[end]
+ mand = sort(unique(mandatory))
+
+ # Local base spacing of the interval containing x (from the original base grid)
+ base_h = function (x)
+ k = clamp(searchsortedlast(grid, x), 1, length(grid) - 1)
+ return grid[k+1] - grid[k]
+ end
+
+ kept = Tuple{Float64,Bool}[(g, false) for g in grid] # (value, is_mandatory)
+ last_mand = -Inf
+ for m in mand
+ (lo < m < hi) || continue
+ δ = delta_frac * base_h(m)
+ (m - lo < δ || hi - m < δ) && continue
+ if m - last_mand < collapse_atol
+ @debug "merge_mandatory_nodes: collapsing mandatory node ψ=$m onto ψ=$last_mand (spacing < collapse_atol)"
+ continue
+ end
+ # Snap: drop non-mandatory, non-endpoint nodes within δ of the mandatory node
+ filter!(t -> t[2] || t[1] == lo || t[1] == hi || abs(t[1] - m) >= δ, kept)
+ push!(kept, (m, true))
+ last_mand = m
+ end
+ sort!(kept; by=first)
+
+ merged = [t[1] for t in kept]
+ all(diff(merged) .> 0) || error("merge_mandatory_nodes produced a non-increasing grid")
+ return merged
+end
+
+"""
+ enforce_min_spacing(grid, hmin) -> Vector{Float64}
+
+Drop interior nodes so no two kept nodes are closer than `hmin`, preserving both endpoints. Guards
+against noise-level packing, e.g. the edge of a `core_edge_packed`/`pow1` grid at high mpsi.
+"""
+function enforce_min_spacing(grid::Vector{Float64}, hmin::Float64)
+ n = length(grid)
+ (n < 3 || hmin <= 0) && return copy(grid)
+ kept = Float64[grid[1]]
+ for i in 2:(n-1)
+ grid[i] - kept[end] >= hmin && push!(kept, grid[i])
+ end
+ # Keep the far endpoint; if the last retained interior node crowds it, drop that node instead.
+ length(kept) > 1 && grid[n] - kept[end] < hmin && pop!(kept)
+ push!(kept, grid[n])
+ return kept
+end
+
+"""
+ bracket_mandatory_nodes(grid, centers, min_half_widths, min_spacing; collapse_atol=1e-7) -> Vector{Float64}
+
+Center each rational `centers[i]` inside a single clean spline interval by replacing the knots
+straddling it with a symmetric pair at `centers[i] ± w`, so the cubic 3rd derivative the Δ′
+extraction samples does not jump mid-stencil. `w` is the larger of `min_half_widths[i]` (the
+Δ′-stencil floor) and half the local grid spacing, capped at half the distance to neighboring centers
+(and, for the stencil part, to the nearer domain edge). Knots within `w` of the center or within
+`min_spacing` of a new bracket knot are dropped; endpoints always win. Warns when a cap cuts a bracket
+below its stencil floor, since Δ′ there is less accurate.
+"""
+function bracket_mandatory_nodes(grid::Vector{Float64}, centers::Vector{Float64}, min_half_widths::Vector{Float64}, min_spacing::Float64; collapse_atol::Float64=1e-7)
+ isempty(centers) && return copy(grid)
+ length(centers) == length(min_half_widths) || error("bracket_mandatory_nodes: centers and min_half_widths length mismatch")
+ lo, hi = grid[1], grid[end]
+ # In-domain centers in increasing order; centers closer than collapse_atol share one bracket.
+ cs, hws = Float64[], Float64[]
+ for idx in sortperm(centers)
+ c = centers[idx]
+ (lo < c < hi) || continue
+ (isempty(cs) || c - cs[end] >= collapse_atol) || continue
+ push!(cs, c)
+ push!(hws, min_half_widths[idx])
+ end
+ kept = Tuple{Float64,Bool}[(g, false) for g in grid] # (value, is_bracket_knot)
+ capped = Tuple{Float64,Float64,Float64}[] # (center, capped half-width, stencil floor)
+ for (i, c) in enumerate(cs)
+ k = clamp(searchsortedlast(grid, c), 1, length(grid) - 1)
+ cap_nb = 0.5 * min(i > 1 ? c - cs[i-1] : Inf, i < length(cs) ? cs[i+1] - c : Inf)
+ cap_edge = 0.5 * min(c - lo, hi - c)
+ # Stencil floor capped by neighbors and edges; blend to half the local spacing capped by neighbors only.
+ w = max(min(hws[i], cap_nb, cap_edge), min(0.5 * (grid[k+1] - grid[k]), cap_nb))
+ w < hws[i] && push!(capped, (c, w, hws[i]))
+ left, right = c - w, c + w
+ # Drop non-bracket, non-endpoint knots inside the zone or crowding a new bracket knot.
+ filter!(kept) do t
+ t[2] || t[1] == lo || t[1] == hi ||
+ !(left < t[1] < right || abs(t[1] - left) < min_spacing || abs(t[1] - right) < min_spacing)
+ end
+ left > lo && push!(kept, (left, true))
+ right < hi && push!(kept, (right, true))
+ end
+ isempty(capped) || @warn "$(length(capped)) rational surface(s) have grid bracket half-widths capped below their Δ′ stencil " *
+ "(neighboring surface or domain edge too close, or a near-tangent surface with q′ ≈ 0); Δ′ there is less accurate. " *
+ "(ψ, half-width, stencil): $(join(capped, ", "))"
+ sort!(kept; by=first)
+ merged = Float64[]
+ for (v, _) in kept
+ (isempty(merged) || v - merged[end] > collapse_atol) && push!(merged, v)
+ end
+ all(diff(merged) .> 0) || error("bracket_mandatory_nodes produced a non-increasing grid")
+ return merged
+end
+
+"""
+ refined_psi_grid(equil::PlasmaEquilibrium; tau, kin=nothing, mandatory=Float64[], pinned=Float64[],
+ singfac_min=1e-4, n_min=1, bracket_coef=BRACKET_COEF,
+ min_spacing=MIN_KNOT_SPACING, N_cap=REFINED_N_CAP) -> Vector{Float64}
+
+Build the refined pass-2 ψ grid from a formed pass-1 equilibrium: knot density, equidistribution,
+`enforce_min_spacing`, then `bracket_mandatory_nodes` around rational surfaces.
+
+## Arguments
+
+ - `tau` - target interpolation accuracy (`psi_accuracy`)
+ - `kin` - optional kinetic profiles whose gradients attract knots
+ - `mandatory` - rational-surface ψ values to bracket (never knotted on)
+ - `pinned` - ψ values inserted as plain knots without a cleared zone
+ - `singfac_min`, `n_min` - set each surface's half-stencil `dpsi = singfac_min/(n_min·|q′|)`; the
+ bracket half-width is `bracket_coef·dpsi`, floored at `min_spacing`
+"""
+function refined_psi_grid(equil::PlasmaEquilibrium;
+ tau::Float64,
+ kin::Union{Nothing,KineticProfileSplines}=nothing,
+ mandatory::Vector{Float64}=Float64[],
+ pinned::Vector{Float64}=Float64[],
+ singfac_min::Float64=1e-4,
+ n_min::Int=1,
+ bracket_coef::Float64=BRACKET_COEF,
+ min_spacing::Float64=MIN_KNOT_SPACING,
+ N_cap::Int=REFINED_N_CAP)
+ xs = equil.profiles.xs
+ rho = _knot_density(equil; tau, kin)
+ # Fixed fine patch around each rational surface (see RATIONAL_RES_SPACING).
+ if !isempty(mandatory)
+ h_rat = max(RATIONAL_RES_SPACING, min_spacing)
+ @inbounds for m in mandatory, i in eachindex(xs)
+ abs(xs[i] - m) <= RATIONAL_RES_RADIUS && (rho[i] = max(rho[i], 1.0 / h_rat))
+ end
+ end
+ M_total = sum(0.5 * (rho[i] + rho[i-1]) * (xs[i] - xs[i-1]) for i in 2:length(xs))
+ N = clamp(ceil(Int, M_total), 32, N_cap)
+ N == N_cap && M_total > N_cap &&
+ @warn "refined_psi_grid: knot count capped at $N_cap (density integral wants $(ceil(Int, M_total))); psi_accuracy=$tau may not be attainable"
+ grid = enforce_min_spacing(_equidistribute(xs, rho, N), min_spacing)
+ # Pinned knots go in before bracketing so a rational's bracket wins where the two overlap.
+ grid = isempty(pinned) ? grid : merge_mandatory_nodes(grid, pinned)
+ isempty(mandatory) && return grid
+ min_half_widths = [max(bracket_coef * singfac_min / (n_min * abs(equil.profiles.q_deriv(m))), min_spacing) for m in mandatory]
+ return bracket_mandatory_nodes(grid, mandatory, min_half_widths, min_spacing)
+end
+
+"""
+ implied_knot_count(equil::PlasmaEquilibrium; tau, kin=nothing) -> Int
+
+Knot count the density model implies for a formed equilibrium; a post-refinement diagnostic that
+flags a pass-1 grid that under- or over-sampled a feature.
+"""
+function implied_knot_count(equil::PlasmaEquilibrium; tau::Float64, kin::Union{Nothing,KineticProfileSplines}=nothing)
+ xs = equil.profiles.xs
+ rho = _knot_density(equil; tau, kin)
+ return ceil(Int, sum(0.5 * (rho[i] + rho[i-1]) * (xs[i] - xs[i-1]) for i in 2:length(xs)))
+end
diff --git a/src/Equilibrium/Grid/PsiGrid.jl b/src/Equilibrium/Grid/PsiGrid.jl
new file mode 100644
index 0000000000..106aa23803
--- /dev/null
+++ b/src/Equilibrium/Grid/PsiGrid.jl
@@ -0,0 +1,63 @@
+"""
+ make_optimal_psi_grid(psilow, psihigh, N_core, N_mid, N_edge; psi_split_core, psi_split_edge)
+
+Build a three-region ψ grid with (N_core + N_mid + N_edge)+1 knots, using the counts
+directly as provided — core and edge are geometric in log(ψ) and log(1−ψ) respectively;
+middle is uniform in ψ.
+"""
+function make_optimal_psi_grid(psilow, psihigh, N_core, N_mid, N_edge;
+ psi_split_core=0.03, psi_split_edge=0.98)
+ # Core: [psilow, psi_split_core], geometric in log(ψ)
+ core_pts = [psilow * (psi_split_core / psilow)^(i / N_core) for i in 0:N_core]
+ # Middle: [psi_split_core, psi_split_edge], uniform (skip first to avoid duplicate)
+ mid_pts = [psi_split_core + (psi_split_edge - psi_split_core) * i / N_mid for i in 1:N_mid]
+ # Edge: [psi_split_edge, psihigh], geometric in log(1−ψ) (skip first to avoid duplicate)
+ edge_pts = [1.0 - (1.0 - psi_split_edge) * ((1.0 - psihigh) / (1.0 - psi_split_edge))^(i / N_edge) for i in 1:N_edge]
+
+ return vcat(core_pts, mid_pts, edge_pts)
+end
+
+"""
+ _build_psi_grid(equil_params, psilow, psihigh)
+
+Resolve `mpsi` and build `psi_nodes` for any supported `grid_type`. For `"auto"` with `mpsi=0`
+this is the coarse pass-1 layout of the two-pass refinement (see `refined_psi_grid`).
+"""
+function _build_psi_grid(equil_params, psilow, psihigh)
+ mpsi = equil_params.mpsi
+ if equil_params.grid_type == "auto" && mpsi == 0 && equil_params.psi_accuracy > 0
+ # Pass-1 layout of the two-pass auto grid.
+ mpsi = PASS1_INTERVALS
+ @info "Auto psi grid: forming pass-1 equilibrium on $(mpsi)-interval log_asymptotic grid pending curvature-based refinement"
+ elseif mpsi == 0
+ mpsi = 128
+ end
+
+ psi_nodes = if equil_params.grid_type == "auto"
+ psihigh > 0.98 ||
+ @warn "grid_type = \"$(equil_params.grid_type)\" needs psihigh > 0.98 (its grid has a fixed edge region on [0.98, psihigh]); " *
+ "psihigh = $psihigh gives a non-monotonic ψ grid and the equilibrium will fail. Use grid_type = \"core_edge_packed\" instead."
+ # Distribute mpsi across the three regions by log-weights
+ log_core = log(0.03 / psilow)
+ log_mid = log(0.98 / 0.03)
+ log_edge = log((1.0 - 0.98) / (1.0 - psihigh))
+ log_total = log_core + log_mid + log_edge
+ N_edge = clamp(round(Int, mpsi * log_edge / log_total), 2, mpsi ÷ 2)
+ N_core = round(Int, mpsi * log_core / log_total)
+ N_mid = mpsi - N_edge - N_core
+ make_optimal_psi_grid(psilow, psihigh, N_core, N_mid, N_edge)
+ elseif equil_params.grid_type == "core_edge_packed"
+ [psilow + (psihigh - psilow) * sin((ipsi / mpsi) * (π / 2))^2 for ipsi in 0:mpsi]
+ elseif equil_params.grid_type == "pow1"
+ # Fortran powspace(psilow, psihigh, 1, mpsi+1, "upper"): edge-packed grid.
+ [psilow + (psihigh - psilow) * (3(ipsi / mpsi) - (ipsi / mpsi)^3) / 2 for ipsi in 0:mpsi]
+ elseif equil_params.grid_type == "uniform"
+ # Evenly spaced surfaces, e.g. for profile diagnostics at constant resolution
+ collect(range(psilow, psihigh; length=mpsi + 1))
+ else
+ error("Unsupported grid_type: $(equil_params.grid_type)")
+ end
+ # Floor node spacing on the fixed grids, whose edge packing at high mpsi drops below integration noise;
+ # the auto grid is floored in refined_psi_grid.
+ return equil_params.grid_type == "auto" ? psi_nodes : enforce_min_spacing(psi_nodes, MIN_KNOT_SPACING)
+end
diff --git a/src/Equilibrium/InverseEquilibrium.jl b/src/Equilibrium/InverseEquilibrium.jl
deleted file mode 100644
index 5d02f29d8e..0000000000
--- a/src/Equilibrium/InverseEquilibrium.jl
+++ /dev/null
@@ -1,221 +0,0 @@
-"""
-Converts inverse equilibrium to straight-fieldline coordinates. Based on inverse.f
-Of the entries we need to return: PlasmaEquilibrium(equil_params, sq_out, rzphi_out, eqfun_out, ro, zo, psio),
-we only need to generate: sq_out, rzphi_out, eqfun_out. This is because we pass in InverseRunInput(equil_in,
-sq_in, rz_in, ro, zo, psio).
-
-"""
-
-"""
- inverse_extrap(xx::Matrix{Float64}, ff::Matrix{Float64}, x::Float64) -> Vector{Float64}
-
-Performs component-wise Lagrange extrapolation for a vector-valued function.
-
-## Arguments:
-- `xx`: A (m × n) matrix where each row contains the x-values for each component.
-- `ff`: A (m × n) matrix where each row contains function values at the corresponding `xx`.
-- `x`: A scalar Float64 value at which to extrapolate.
-
-## Returns:
-- A vector of length n representing the extrapolated function values at `x`.
-"""
-function inverse_extrap(xx::Matrix{Float64}, ff::Matrix{Float64}, x::Float64)::Vector{Float64}
- m, n = size(ff) # m = number of data points, n = number of components
- f = zeros(Float64, n) # Output vector
-
- for i in 1:m
- term = copy(ff[i, :]) # Start with f_i (vector)
- for j in 1:m
- if j == i
- continue
- end
- term .= term .* ((x .- xx[j, :]) ./ (xx[i, :] .- xx[j, :]))
- end
- f .+= term # Accumulate to output
- end
-
- return f
-end
-
-
-
-function equilibrium_solver(input::InverseRunInput)
- println("--- Starting Inverse Equilibrium Processing ---")
- # Extract input parameters
-
- config = input.config
- rz_in = input.rz_in
- sq_in = input.sq_in
- ro = input.ro
- zo = input.zo
- psio = input.psio
-
- grid_type = config.control.grid_type
- mpsi = config.control.mpsi
- mtheta = config.control.mtheta
- psilow = config.control.psilow
- psihigh = config.control.psihigh
- newq0 = config.control.newq0
-
- me = 3
- interp = false
- diagnose_rz_in = false
- diagnose_rzphi = false
-
- # c-----------------------------------------------------------------------
- # c allocate and define local arrays.
- # c-----------------------------------------------------------------------
- # sq_in._fs[:, 3] .= sqrt.(sq_in._xs)
- rz_in._xs = sq_in._xs
- rz_in._ys = collect(0:rz_in.my) ./ rz_in.my
-
- mx = rz_in.mx
- my = rz_in.my
-
- x = rz_in.fs[:, :, 1] .- ro
- y = rz_in.fs[:, :, 2] .- zo
- r2 = x.^2 .+ y.^2
-
- twopi = 2 * pi
-
- deta = zeros(Float64, mx+1, my+1)
- for ipsi in 0:mx, itheta in 0:my
- if r2[ipsi+1, itheta+1] == 0.0
- deta[ipsi+1, itheta+1] = 0.0
- else
- deta[ipsi+1, itheta+1] = atan(y[ipsi+1, itheta+1], x[ipsi+1, itheta+1]) / twopi
- end
- end
-
- # c-----------------------------------------------------------------------
- # c transform input coordinates from cartesian to polar.
- # c-----------------------------------------------------------------------
- for ipsi in 0:mx
- for itheta in 1:my
- Δ = deta[ipsi+1, itheta+1] - deta[ipsi+1, itheta]
- if Δ > 0.5
- deta[ipsi+1, itheta+1] -= 1
- elseif Δ < -0.5
- deta[ipsi+1, itheta+1] += 1
- end
- end
- for itheta in 0:my
- if r2[ipsi+1, itheta+1] > 0
- deta[ipsi+1, itheta+1] -= rz_in.ys[itheta+1]
- end
- end
- end
-
- deta[1, :] = inverse_extrap(r2[2:me+1, :], deta[2:me+1, :], 0.0)
-
- rz_in_fs = zeros(Float64, mx+1, my+1, 3)
- rz_in_fs[:, :, 1] = r2
- rz_in_fs[:, :, 2] = deta
-
- rz_spline = Spl.BicubicSpline(rz_, rz_in.xs, rz_in.ys; bctypex="extrap", bctypey="periodic")
-
- # c-----------------------------------------------------------------------
- # c prepare new spline type for surface quantities.
- # c-----------------------------------------------------------------------
-
- if grid_type in ["original", "orig"]
- mpsi = size(sq_in._fs, 1) - 1
- end
-
- # c-----------------------------------------------------------------------
- # c set up radial grid (only "ldp" implemented)
- # c-----------------------------------------------------------------------
- if grid_type == "ldp"
- xs = psilow .+ (psihigh - psilow) .* (sin.(range(0.0, 1.0; length=mpsi+1) .* (π/2))).^2
- fs = zeros(Float64, mpsi+1, 4)
- sq = Spl.spline_setup(xs, fs; bctype="extrap")
- else
- error("Only 'ldp' grid_type is implemented for now.")
- end
-
- local rzphi::Spl.BicubicSplineType
- local eqfun::Spl.BicubicSplineType
-
- # c-----------------------------------------------------------------------
- # c prepare new bicube type for coordinates.
- # c-----------------------------------------------------------------------
- if mtheta == 0
- mtheta = rz_in.my
- end
-
- # (/" r2 "," deta "," dphi "," jac "/)
- rzphi_fs = zeros(Float64, mpsi+1, mtheta+1, 4)
- rzphi_xs = copy(sq_xs)
- rzphi_ys = collect(0:mtheta) ./ mtheta
-
- # (/" b0 "," "," " /)
- eqfun_fs = zeros(Float64, mpsi+1, mtheta+1, 3)
- eqfun_xs = copy(sq_xs)
- eqfun_ys = collect(0:mtheta) ./ mtheta
-
- rzphi = Spl.bicube_setup(copy(sq.xs), collect(0:mtheta) ./ mtheta, rzphi_fs)
- eqfun = Spl.bicube_setup(copy(sq.xs), collect(0:mtheta) ./ mtheta, eqfun_fs)
-
-
- # spl_xs = zeros(Float64,mtheta+1)
- # spl_fs = zeros(Float64,mtheta+1, 5)
- # spl = Spl.spline_setup(spl_xs, spl_fs; bctype="extrap")
-
- for ipsi in 0:mpsi
- psifac = rzphi_xs[ipsi+1]
- f_sq_in = Spl.spline_eval(sq_in, psifac, 0)
- spl_xs .= rzphi_ys
- for itheta in 0:mtheta
- theta = rzphi_ys[itheta+1]
- f_rz_in, fx_rz_in, fy_rz_in = Spl.bicube_eval(new_rz_in, psifac, theta, 1)
- f_sq_in = Spl.spline_eval(sq_in, psifac, 0)
-
- if f_rz_in[1] < 0
- error("Invalid extrapolation near axis, rerun with larger value of psilow")
- end
-
- rfac = sqrt(f_rz_in[1])
- r = ro + rfac * cos(twopi * (theta + f_rz_in[2]))
- jacfac = fx_rz_in[1] * (1 + fy_rz_in[2]) - fy_rz_in[1] * fx_rz_in[2]
- w11 = (1 + fy_rz_in[2]) * twopi^ 2 * rfac / jacfac
- w12 = -fy_rz_in[1] * pi / (rfac * jacfac)
- bp = psio * sqrt(w11*w11 + w12*w12) / r
- bt = f_sq_in[1] / r
- b = sqrt(bp*bp + bt*bt)
-
- # spl.fs[itheta+1, 1] = f_rz_[1]
- # spl.fs[itheta+1, 2] = f_rz_[2]
- # spl.fs[itheta+1, 3] = r*jacfac
- # spl.fs[itheta+1, 4] = spl.fs[itheta+1, 3]/(r*r)
- # spl.fs[itheta+1, 5] = spl.fs[itheta+1, 3]*bp^(config.power_bp)*b^(config.power_b)/r^(config.power_r)
- end
-
- # spl.xs = spl.integral!()
- # spl.xs = spl.fsi[:, 5] ./ spl.fs[end, 5]
- # spl.fs[:, 2] .= spl.fs[:, 2] .+ rzphi.ys .- spl.xs
- # spl.fs[:, 4] .= (spl.fs[:, 3] ./ spl.fsi[end, 3]) ./ (spl.fs[:, 5] ./ spl.fsi[end, 5]) .* spl.fsi[end, 3] * twopi * pi
- # spl.fs[:, 3] .= f_sq[1] * pi / psio .* (spl.fsi[:, 4] .- spl.fsi[end, 4] .* spl.xs)
- # # spl.xs = Spl.spline_setup(spl.xs, spl.fs; bctype="periodic").integral!()
-
- for itheta in 0:mtheta
- theta = rzphi_ys[itheta+1]
- fs = Spl.spline_eval(spl, theta, 0)
- rzphi_fs[ipsi+1, itheta+1, :] = fs[1:4]
- end
-
- sq_fs[ipsi+1, 1] = f_sq_in[1] * twopi
- sq_fs[ipsi+1, 2] = f_sq_in[2]
- sq_fs[ipsi+1, 3] = spl.fsi[mtheta+1, 3] * twopi * pi # dV/d(psi)
- sq_fs[ipsi+1, 4] = spl.fsi[mtheta+1, 4] * sq_fs[ipsi+1, 1] / (2 * twopi * psio) # q-profile
- end
-
- # # sq = Spl.spline_setup(sq.xs, sq.fs; bctype="extrap")
- # f = Spl.spline_eval(sq, sq.xs[1], 0)
- # _, f1 = Spl.spline_eval(sq, sq.xs[1], 1)
- # q0 = f[4] - f1[4] * sq.xs[1]
-
- # if newq0 == -1
- # newq0 = -q0
- # end
-
-end
\ No newline at end of file
diff --git a/src/Equilibrium/KineticProfiles.jl b/src/Equilibrium/KineticProfiles.jl
new file mode 100644
index 0000000000..8cb343f7dd
--- /dev/null
+++ b/src/Equilibrium/KineticProfiles.jl
@@ -0,0 +1,596 @@
+"""
+ KineticProfiles
+
+Reading and processing kinetic profile data (density, temperature, rotation,
+and optionally transport diffusivities) from the GPEC HDF5 kinetic format or
+from legacy 6-column ASCII tables (`.gpeckf`/`.kin`). The processed output is a
+`KineticProfileSplines` of independent named splines that downstream physics
+modules (KineticForces NTV, etc.) read directly.
+"""
+
+using DelimitedFiles
+using HDF5
+
+# Physical constants and collisionality normalizations shared by `kinetic_profile_splines` and
+# `resolve_ntv_species` (Krook collision frequency, Logan & Park 2013 Eq. 6).
+const _EV_J = 1.602e-19 # eV → J
+const _E_CHARGE = 1.602e-19 # elementary charge [C] (PENTRC-parity value, not CODATA)
+const _NKIN = 100 # kinetic-profile resample: uniform ψ_n grid of _NKIN+1 points
+const _KEV_J = 1.602e-16 # 1 keV in J (temperature normalization in the collision frequency)
+const _NU_PREFAC = 3.5e17 # Krook collision-frequency prefactor
+const _MP = 1.672_614e-27 # proton mass [kg]
+const _ME = 9.109_1e-31 # electron mass [kg]
+const _T_FLOOR_KEV = 1.0e-6 # collision-model temperature floor (1 meV), as Fortran PENTRC
+
+# Temperature in keV for the collision model, floored so a cold edge node keeps a finite, positive ν.
+_collision_tkev(T) = max(T / _KEV_J, _T_FLOOR_KEV)
+
+# NRL-formulary Coulomb logarithm (natural log) at the floored temperature, floored at 1; n_e in m⁻³, T_e in J.
+_coulomb_log(ne, Te) = max(17.3 - 0.5 * log(ne / 1.0e20) + 1.5 * log(_collision_tkev(Te)), 1.0)
+
+# Warn once per kinetic source, as Fortran PENTRC, when a cold node engages the temperature or Coulomb-logarithm floor
+# of a model rate (supplied rates in `data` use neither).
+function _warn_collision_floors(source, data, ne, Te, Ti)
+ data.nu_i !== nothing && data.nu_e !== nothing && return nothing
+ any(T -> T / _KEV_J < _T_FLOOR_KEV, Te) | any(T -> T / _KEV_J < _T_FLOOR_KEV, Ti) &&
+ @warn "$source: flooring T at 1 meV in the collision frequencies" maxlog = 1 _id = Symbol("T_floor ", source)
+ data.lnLambda === nothing && any(i -> 17.3 - 0.5 * log(ne[i] / 1.0e20) + 1.5 * log(_collision_tkev(Te[i])) < 1, eachindex(ne)) &&
+ @warn "$source: flooring the Coulomb logarithm at 1 in the collision frequencies" maxlog = 1 _id = Symbol("lnLambda_floor ", source)
+ return nothing
+end
+
+# Names kinetic profiles in error messages by their provenance, when they carry one.
+_describe(data) = isempty(data.provenance) ? "kinetic profiles" : "kinetic profiles ($(data.provenance))"
+
+# Supplied rate on the kinetic grid: pchip in log space, as Fortran rates-v1, so it stays positive between points.
+_supplied_rate(psi_in, v, psi_reg) = v === nothing ? nothing : exp.(_pchip_resample(psi_in, log.(v), psi_reg))
+
+# Hard stop on an unphysical negative density or temperature (bad input or an extrapolation past the table).
+function _assert_nonneg_profile(source, label, arr, psi_reg)
+ i = findfirst(<(0), arr)
+ i === nothing ||
+ error("$source: negative $label = $(arr[i]) at ψ_n = $(psi_reg[i]) — unphysical")
+end
+
+# Hard stop on a non-positive electron or main-ion density, which the collision model divides by.
+function _assert_positive_density(source, label, arr, psi_reg)
+ i = findfirst(<=(0), arr)
+ i === nothing ||
+ error("$source: $label = $(arr[i]) at ψ_n = $(psi_reg[i]) — densities must be positive")
+end
+
+"""
+ ResolvedNTVSpecies{P}
+
+One fully-resolved species in the NTV sum — a main ion, the neutrality-closing impurity, or the
+electrons. Fields: charge `z`, mass `m` (proton masses), `electron` flag, `label`, and `profiles`
+(a `KineticProfileSplines` view carrying this species' density as `ni_spline` and its
+full-composition collision frequency as `nui_spline`). Produced by `resolve_ntv_species`; both NTV
+paths — the KineticForces ψ-quadrature and the self-consistent kinetic-matrix build — iterate this
+and sum τ = Σ_s τ_s.
+"""
+struct ResolvedNTVSpecies{P}
+ z::Int
+ m::Int
+ electron::Bool
+ label::String
+ profiles::P
+end
+
+const _KINETIC_H5_EXTS = (".h5", ".hdf5", ".he5")
+
+# The optional profile datasets of the HDF5 kinetic schema and their units, one row per `KineticProfileData`
+# field of the same name; the reader and writer both iterate it, so a new profile is a row here plus its field.
+const _KINETIC_H5_PROFILES = ("n_i" => "m^-3", "n_e" => "m^-3", "T_i" => "eV", "T_e" => "eV", "omega_E" => "rad/s",
+ "omega_tor" => "rad/s", "chi_e" => "m^2/s", "chi_i" => "m^2/s", "chi_phi" => "m^2/s", "zeff" => "dimensionless",
+ "lnLambda" => "dimensionless", "nu_i" => "1/s", "nu_e" => "1/s")
+
+"""
+ read_kinetic_file(path; group="/", format="legacy") -> KineticProfileData
+
+Read a kinetic-profile file, dispatching on extension: HDF5 (`.h5`/`.hdf5`) via
+the GPEC kinetic schema, otherwise an ASCII table (`.gpeckf`/`.kin`/`.dat`) whose layout `format` names:
+`"legacy"`, 6 columns `psi_n n_i n_e T_i[eV] T_e[eV] omega_E`, or `"rates-v1"`, 9 columns that append
+`lnLambda nu_i[1/s] nu_e[1/s]` (the Fortran PENTRC rates-v1 table). Returns the raw columns; downstream
+consumers validate the fields they require.
+"""
+function read_kinetic_file(path::AbstractString; group::AbstractString="/", format::AbstractString="legacy")
+ isfile(path) || error("Kinetic profile file not found: $path")
+ format in KINETIC_FORMATS || throw(ArgumentError("kinetic format \"$format\" must be one of $KINETIC_FORMATS"))
+ ext = lowercase(splitext(path)[2])
+ return ext in _KINETIC_H5_EXTS ? _read_kinetic_h5(path; group=group) : _read_kinetic_ascii(path, format)
+end
+
+"""
+Read an ASCII kinetic table in the layout `format` names into a `KineticProfileData`.
+"""
+function _read_kinetic_ascii(path::AbstractString, format::AbstractString)
+ cols = _read_kinetic_table(path)
+ ncol = KINETIC_FORMAT_COLUMNS[format]
+ length(cols) == ncol ||
+ error("kinetic file $path has $(length(cols)) columns, but kinetic_format = \"$format\" needs $ncol " *
+ "(\"legacy\": 6; \"rates-v1\": 9, appending lnLambda nu_i nu_e)")
+ rates = format == "rates-v1" ? (; lnLambda=cols[7], nu_i=cols[8], nu_e=cols[9]) : (;)
+ return KineticProfileData(; psi=cols[1], n_i=cols[2], n_e=cols[3], T_i=cols[4], T_e=cols[5], omega_E=cols[6], rates...,
+ provenance="ASCII $(length(cols))-column: $(basename(path))")
+end
+
+"""
+Read the GPEC HDF5 kinetic schema. Only `psi` is required; other standard datasets are
+optional and surfaced as-is. Non-standard `n_*` datasets become named per-species densities.
+"""
+function _read_kinetic_h5(path::AbstractString; group::AbstractString="/")
+ h5open(f -> _read_kinetic_group(group == "/" ? f : f[group], "kinetic HDF5 '$path' group '$group'"), path, "r")
+end
+
+# The kinetic profiles in the open HDF5 file or group `g`; `label` names it in errors.
+function _read_kinetic_group(g, label::AbstractString)
+ haskey(g, "psi") || error("$label: missing required dataset 'psi'")
+ rd(name) = haskey(g, name) ? Float64.(vec(read(g[name]))) : nothing
+ prov = ""
+ ats = attributes(g)
+ haskey(ats, "provenance") && (prov = string(read(ats["provenance"])))
+ # Non-standard datasets named `n_*` (e.g. "n_D", "n_T") are named per-species density
+ # profiles for explicit multi-ion input; other names are reserved for future schema fields.
+ extras = Dict{String,Vector{Float64}}()
+ for k in keys(g)
+ (k == "psi" || any(p -> first(p) == k, _KINETIC_H5_PROFILES) || !startswith(k, "n_")) && continue
+ v = read(g[k])
+ v isa AbstractArray && (extras[k] = Float64.(vec(v)))
+ end
+ return KineticProfileData(; psi=Float64.(vec(read(g["psi"]))),
+ (Symbol(name) => rd(name) for (name, _) in _KINETIC_H5_PROFILES)...,
+ species_densities=(isempty(extras) ? nothing : extras), provenance=prov)
+end
+
+"""
+ attach_kinetic_profiles!(equil, path; group="/", format="legacy", kwargs...) -> equil
+ attach_kinetic_profiles!(equil, data::KineticProfileData) -> equil
+
+Attach kinetic profiles to `equil` as `equil.kinetic`. Every kinetic consumer (the NTV torque, the
+calculated kinetic matrices, tearing, the layer-overlap scan and the two-pass grid refinement) derives its
+own view from them, so the file is read once. Equilibria built from a config with `kinetic_file` set
+attach it on construction; use this for analytic or IMAS equilibria built without it, or in-memory data.
+Keywords are the composition, default and closure fields of [`KineticProfileData`](@ref), e.g.
+`ion_species`, `impurity_charge`, `chi_e_default`, `resistivity_model`.
+"""
+function attach_kinetic_profiles!(equil::PlasmaEquilibrium, data::KineticProfileData)
+ equil.kinetic = data
+ return equil
+end
+
+attach_kinetic_profiles!(equil::PlasmaEquilibrium, path::AbstractString; group::AbstractString="/", format::AbstractString="legacy",
+ kwargs...) =
+ attach_kinetic_profiles!(equil, KineticProfileData(read_kinetic_file(path; group=group, format=format); kwargs...))
+
+# The kinetic profiles a config names with its composition applied, read once at construction; `nothing` when it names none.
+configured_kinetic_profiles(config::EquilibriumConfig) =
+ isempty(config.kinetic_file) ? nothing :
+ KineticProfileData(read_kinetic_file(config.kinetic_file; group=config.kinetic_group, format=config.kinetic_format); kinetic_composition(config)...)
+
+"""
+ write_kinetic_h5(path, data; group="/", schema_version="1.0", provenance=data.provenance)
+
+Write a `KineticProfileData` to the GPEC HDF5 kinetic schema. Each present field
+is written as a dataset with a `units` attribute; absent (`nothing`) fields are
+skipped. Named per-species densities (`species_densities`, `n_*` datasets) round-trip
+with `read_kinetic_file`. The group carries `schema_version` and `provenance` attributes.
+"""
+function write_kinetic_h5(path::AbstractString, data::KineticProfileData;
+ group::AbstractString="/", schema_version::AbstractString="1.0",
+ provenance::AbstractString=data.provenance)
+ h5open(f -> write_kinetic_group!(group == "/" ? f : create_group(f, group), data; schema_version, provenance), path, "w")
+ return path
+end
+
+"""
+ write_kinetic_group!(g, data; schema_version="1.0", provenance=data.provenance) -> g
+
+Write the profiles of `data` into the open HDF5 file or group `g` in the GPEC kinetic schema, as
+[`write_kinetic_h5`](@ref) does for a new file; the composition and closure fields are not written.
+"""
+function write_kinetic_group!(g, data::KineticProfileData; schema_version::AbstractString="1.0", provenance::AbstractString=data.provenance)
+ function put(name, v, units)
+ v === nothing && return
+ g[name] = collect(Float64, v)
+ attributes(g[name])["units"] = units
+ end
+ put("psi", data.psi, "normalized poloidal flux")
+ for (name, units) in _KINETIC_H5_PROFILES
+ put(name, getfield(data, Symbol(name)), units)
+ end
+ # Named per-species densities (multi-ion input); dataset names must be `n_*` to round-trip.
+ if data.species_densities !== nothing
+ for (name, v) in data.species_densities
+ startswith(name, "n_") ||
+ error("species density dataset `$name` must be named `n_*` to be readable as a per-species profile")
+ g[name] = collect(Float64, v)
+ attributes(g[name])["units"] = "m^-3"
+ end
+ end
+ attributes(g)["schema_version"] = schema_version
+ attributes(g)["provenance"] = provenance
+ return g
+end
+
+"""
+ multi_ion_composition(zs, ns, ne; zimp, mimp) -> (zeff, zpitch, n_main, n_imp)
+
+Full-composition effective charge and pitch-angle enhancement at one ψ point for a plasma with an
+arbitrary number of main-ion species:
+
+ - `zs`, `ns`: main-ion charges and number densities (one entry per species)
+ - `ne`: electron density
+ - `zimp`, `mimp`: single trailing impurity charge / mass; its density closes quasineutrality
+
+Composition (per point):
+
+ n_main = Σ_s n_s total main-ion number density
+ n_imp = (n_e − Σ_s z_s n_s) / z_imp impurity density from quasineutrality
+ Zeff = (Σ_s z_s² n_s + z_imp² n_imp) / n_e
+ zpitch = 1 + (1+m_imp)/(2 m_imp)·z_imp·(Zeff−1)/(z_imp−Zeff) momentum-restoring closure
+
+Reduces exactly to the single-ion form `Zeff = z_imp − (n_i/n_e)·z_i·(z_imp−z_i)` for one main-ion species.
+"""
+function multi_ion_composition(zs::AbstractVector, ns::AbstractVector, ne::Real;
+ zimp::Real, mimp::Real)
+ n_main = sum(ns)
+ # Vacuum point (ne ≤ 0): neutral composition, no impurity — avoids the zpitch pole at Zeff = zimp.
+ ne > 0 || return (1.0, 1.0, n_main, 0.0)
+ charge_density = sum(z * n for (z, n) in zip(zs, ns)) # Σ z_s n_s
+ n_imp = (ne - charge_density) / zimp
+ zeff = (sum(z^2 * n for (z, n) in zip(zs, ns)) + zimp^2 * n_imp) / ne
+ zpitch = 1.0 + (1.0 + mimp) / (2.0 * mimp) * zimp * (zeff - 1.0) / (zimp - zeff)
+ return (zeff, zpitch, n_main, n_imp)
+end
+
+"""
+ resolve_ntv_species(data::KineticProfileData, ion_species; electron, zimp, mimp, ...) -> Vector{ResolvedNTVSpecies}
+
+Resolve the full NTV species set for a multi-ion run: the main ions, the neutrality-closing
+impurity (`zimp`, `mimp`, density from quasineutrality), and the electrons if `electron`. Both NTV
+paths (the KineticForces quadrature and the self-consistent kinetic-matrix build) loop over and sum
+this set. Errors on any negative density.
+
+Each descriptor's `profiles` carries that species' density as `ni_spline` and its full-composition
+Krook collision frequency (Logan & Park 2013 Eq. 6) as `nui_spline`, or, when `nu_i` is supplied, that rate
+scaled by (z_s/z₁)²·√(m₁/m_s); the other profiles are shared.
+A main ion's density is `fraction · n_i` (`n_i` is the total main-ion density) or the named `n_*`
+dataset given by `density` (e.g. `"n_D"`). In a mixed fraction/density list the impurity content is
+set by the file's n_i/n_e deficit. The `zpitch` closure is exact for z=1 main ions and approximate
+otherwise. Reduces to [`kinetic_profile_splines`](@ref) for one z=1 main ion with `fraction=1`.
+"""
+function resolve_ntv_species(data::KineticProfileData, ion_species::AbstractVector;
+ electron::Bool=false, zimp::Integer=6, mimp::Integer=12,
+ density_factor::Float64=1.0, temperature_factor::Float64=1.0,
+ ExB_rotation_factor::Float64=1.0, toroidal_rotation_factor::Float64=1.0)
+
+ (density_factor == 1.0 && temperature_factor == 1.0 && ExB_rotation_factor == 1.0 &&
+ toroidal_rotation_factor == 1.0) ||
+ error("profile scaling factors are not yet supported together with a multi-ion ion_species list")
+
+ source = _describe(data)
+ _need(f, n) = f === nothing ? error("$source missing required '$n'") : f
+ psi_in = data.psi
+ ne_in = _need(data.n_e, "n_e")
+ Ti_in = _need(data.T_i, "T_i")
+ Te_in = _need(data.T_e, "T_e")
+ omE_in = _need(data.omega_E, "omega_E")
+ ni_in = data.n_i === nothing ? copy(ne_in) : data.n_i # TOTAL main-ion density
+
+ nkin = _NKIN
+ psi_reg = collect(0:nkin) ./ nkin
+ ne = _pchip_resample(psi_in, ne_in, psi_reg)
+ ni_total = _pchip_resample(psi_in, ni_in, psi_reg)
+ Ti = _pchip_resample(psi_in, Ti_in, psi_reg) .* _EV_J
+ Te = _pchip_resample(psi_in, Te_in, psi_reg) .* _EV_J
+ omegaE = _pchip_resample(psi_in, omE_in, psi_reg)
+ _assert_positive_density(source, "n_e", ne, psi_reg)
+ _assert_positive_density(source, "n_i (total)", ni_total, psi_reg)
+ _assert_nonneg_profile(source, "T_i", Ti, psi_reg)
+ _assert_nonneg_profile(source, "T_e", Te, psi_reg)
+ _warn_collision_floors(source, data, ne, Te, Ti)
+
+ # Fractions are shares of the total n_i: never above 1, and exactly 1 when every species is fraction-specified.
+ fracs = [s.fraction for s in ion_species if !isnan(s.fraction)]
+ if !isempty(fracs)
+ fsum = sum(fracs)
+ fsum <= 1.0 + 1e-6 ||
+ error("ion_species fractions sum to $fsum > 1 — fractions are shares of the total main-ion density n_i")
+ length(fracs) == length(ion_species) && abs(fsum - 1.0) > 1e-6 &&
+ error(
+ "ion_species fractions sum to $fsum ≠ 1 — with all species fraction-specified the shares must account for the full n_i " *
+ "(the impurity content is set by the file's n_i/n_e deficit, not by a fraction shortfall)"
+ )
+ end
+
+ # The momentum-restoring zpitch closure assumes the declared main ions are lighter/lower-z than
+ # the trailing impurity; z_s ≥ z_imp can drive Zeff to the zpitch pole at Zeff = z_imp.
+ all(s.z < zimp for s in ion_species) ||
+ error("every ion_species charge must satisfy z < zimp = $zimp (declare heavier species as the impurity)")
+
+ # Resolve each species' resonant density: `fraction` ⇒ share of the total n_i; `density` ⇒
+ # an explicit named profile from the (HDF5) kinetic file (resampled to the working grid).
+ zs = [Int(s.z) for s in ion_species]
+ ns = Vector{Vector{Float64}}(undef, length(ion_species))
+ for (si, s) in enumerate(ion_species)
+ has_frac = !isnan(s.fraction)
+ has_dens = !isempty(s.density)
+ (has_frac ⊻ has_dens) || error("ion_species[$si]: specify exactly one of `fraction` or `density`")
+ if has_dens
+ (data.species_densities !== nothing && haskey(data.species_densities, s.density)) ||
+ error(
+ "ion_species[$si]: density profile `$(s.density)` not found in the kinetic profiles " *
+ "(available: $(data.species_densities === nothing ? "none — ASCII files carry only n_i" : join(keys(data.species_densities), ", ")))"
+ )
+ ns[si] = _pchip_resample(psi_in, data.species_densities[s.density], psi_reg)
+ else
+ ns[si] = s.fraction .* ni_total
+ end
+ _assert_nonneg_profile(source, "ion_species[$si] density", ns[si], psi_reg)
+ end
+
+ # Shared composition + collisionality (natural-log Coulomb log), per grid point.
+ npts = length(psi_reg)
+ zeff = zeros(npts)
+ zpitch = zeros(npts)
+ loglam = zeros(npts)
+ n_main = zeros(npts)
+ n_imp = zeros(npts)
+ nue = zeros(npts)
+ lnL_sup, nui_sup, nue_sup = (_supplied_rate(psi_in, getfield(data, f), psi_reg) for f in (:lnLambda, :nu_i, :nu_e))
+ for i in 1:npts
+ z, zp, nm, nimp = multi_ion_composition(zs, [ns[si][i] for si in eachindex(ion_species)], ne[i]; zimp=zimp, mimp=mimp)
+ zeff[i] = z
+ zpitch[i] = zp
+ n_main[i] = nm
+ n_imp[i] = nimp
+ loglam[i] = lnL_sup === nothing ? _coulomb_log(ne[i], Te[i]) : lnL_sup[i]
+ nue[i] = (zp / _NU_PREFAC) * ne[i] * loglam[i] / (sqrt(_ME / _MP) * _collision_tkev(Te[i])^1.5)
+ end
+ nue_sup === nothing || (nue .= nue_sup)
+ # A negative impurity density means the main ions over-neutralize (Σ z_s n_s > n_e) — unphysical.
+ _assert_nonneg_profile(source, "impurity density (n_e < Σ z_s n_s)", n_imp, psi_reg)
+ # Approaching the zpitch pole at Zeff = zimp signals a dilute main-ion mix taken up by impurity.
+ maximum(zeff) > 0.9 * zimp &&
+ @warn "max(Zeff) = $(maximum(zeff)) is within 10% of zimp = $zimp — zpitch closure near its pole; check ion_species densities/fractions"
+
+ # Per-species Krook ν (Logan & Park 2013 Eq. 6) with a test-particle z_s²; `zpitch` is a main-ion closure,
+ # applied approximately to the impurity/electron test species.
+ # A supplied ν_i is the first main ion's rate; the others keep the model's (z_s/z₁)²·√(m₁/m_s) ratio to it.
+ z1, m1 = ion_species[1].z, ion_species[1].m
+ _nu(zsp, msp) =
+ nui_sup === nothing ?
+ [(zpitch[i] / _NU_PREFAC) * zsp^2 * n_main[i] * loglam[i] / (sqrt(Float64(msp)) * _collision_tkev(Ti[i])^1.5) for i in 1:npts] :
+ nui_sup .* ((zsp / z1)^2 * sqrt(m1 / msp))
+ _view(dens, nu) = KineticProfileSplines(psi_reg, dens, ne, Ti, Te, omegaE, loglam, nu, nue, zeff)
+
+ # Full NTV species set: main ions, the neutrality-closing impurity, and (optionally) electrons.
+ # Labels become HDF5 group names under KineticForces/PerSpecies/; a repeated (z, m) gets a numeric suffix.
+ species = ResolvedNTVSpecies[]
+ seen_labels = Dict{String,Int}()
+ function _unique_label(base)
+ n = get(seen_labels, base, 0) + 1
+ seen_labels[base] = n
+ return n == 1 ? base : "$(base)_$(n)"
+ end
+ for (si, s) in enumerate(ion_species)
+ label = _unique_label("ion_z$(s.z)_m$(s.m)")
+ push!(species, ResolvedNTVSpecies(Int(s.z), Int(s.m), false, label, _view(ns[si], _nu(s.z, s.m))))
+ end
+ if any(>(0), n_imp)
+ push!(species, ResolvedNTVSpecies(Int(zimp), Int(mimp), false, "impurity_z$(zimp)_m$(mimp)", _view(n_imp, _nu(zimp, mimp))))
+ end
+ if electron
+ # The electron view's `ni_spline` is unused (the electron path reads `ne_spline`); carry ne.
+ push!(species, ResolvedNTVSpecies(-1, 1, true, "electron", _view(ne, nue)))
+ end
+ return identity.(species) # narrow to a concrete-eltype Vector{ResolvedNTVSpecies{...}}
+end
+
+"""
+ has_ntv_fields(data::KineticProfileData) -> Bool
+
+Whether `data` carries the profiles the NTV view needs (`n_e`, `T_i`, `T_e` and `omega_E`), so that
+`kinetic_profile_splines` and `resolve_ntv_species` can be built from it.
+"""
+has_ntv_fields(data::KineticProfileData) = all(!isnothing, (data.n_e, data.T_i, data.T_e, data.omega_E))
+
+"""
+ ntv_profiles_usable(data::KineticProfileData) -> Bool
+
+Whether `data` has the NTV fields with positive densities and non-negative temperatures at its table points,
+the inputs `kinetic_profile_splines` accepts.
+"""
+ntv_profiles_usable(data::KineticProfileData) =
+ has_ntv_fields(data) && all(>(0), data.n_e) && (data.n_i === nothing || all(>(0), data.n_i)) &&
+ all(>=(0), data.T_i) && all(>=(0), data.T_e)
+
+"""
+ kinetic_profile_splines(data::KineticProfileData;
+ zi::Int=1, zimp::Int=6, mi::Int=2, mimp::Int=12,
+ density_factor::Float64=1.0, temperature_factor::Float64=1.0,
+ ExB_rotation_factor::Float64=1.0, toroidal_rotation_factor::Float64=1.0,
+ chi1::Union{Nothing,Float64}=nothing)
+ → KineticProfileSplines
+
+The NTV view of raw kinetic profiles (e.g. `equil.kinetic`): interpolate onto a regular
+101-point ψ grid, optionally apply profile scaling knobs, derive collisional / Z_eff
+diagnostics, and return a `KineticProfileSplines` of named splines (pchip for lnΛ and ν, cubic otherwise).
+
+Needs `n_e`, `T_i`, `T_e` and `omega_E`; `n_i` defaults to `n_e`. Supplied `lnLambda`, `nu_i` and `nu_e`
+replace the model's values and are not rescaled by the scaling factors. See [`read_kinetic_file`](@ref)
+for the file formats.
+
+# Arguments
+
+ - `data`: Raw kinetic profiles (`KineticProfileData`)
+ - `zi`, `zimp`: Main ion and impurity charge numbers
+ - `mi`, `mimp`: Main ion and impurity mass numbers (in proton masses)
+ - `density_factor`: Density scaling factor (applied to ni, ne)
+ - `temperature_factor`: Temperature scaling factor (applied to Ti, Te)
+ - `ExB_rotation_factor`: ExB rotation scaling factor (applied to omegaE after rotation reform)
+ - `toroidal_rotation_factor`: Toroidal rotation scaling factor (scales total wphi = omegaE + wdian + wdiat)
+ - `chi1`: Poloidal flux normalization `2π·ψ₀` — required when `density_factor`, `temperature_factor`, or `toroidal_rotation_factor` differ from 1.0
+
+# Scaling
+
+When `density_factor`, `temperature_factor` or `toroidal_rotation_factor` differ from 1, the total
+rotation `wphi = omegaE + wdian + wdiat` is held from the unscaled profiles, the diamagnetic frequencies
+scale with `temperature_factor` (`density_factor` cancels), and `omegaE` is reformed as
+`toroidal_rotation_factor * wphi - wdian - wdiat`. `ExB_rotation_factor` then multiplies `omegaE`.
+
+Collisionality is recomputed from the scaled profiles (unlike Fortran PENTRC); use `nufac`
+(in `KineticForcesControl`) to scale collisionality independently.
+"""
+function kinetic_profile_splines(data::KineticProfileData;
+ zi::Int=1, zimp::Int=6, mi::Int=2, mimp::Int=12,
+ density_factor::Float64=1.0, temperature_factor::Float64=1.0,
+ ExB_rotation_factor::Float64=1.0, toroidal_rotation_factor::Float64=1.0,
+ chi1::Union{Nothing,Float64}=nothing)
+
+ density_factor > 0 && temperature_factor > 0 ||
+ throw(ArgumentError("density_factor = $density_factor and temperature_factor = $temperature_factor must be positive"))
+ # n_i defaults to n_e (quasineutrality); omega_tor and the diffusivities are unused here.
+ _need(field, name) = field === nothing ? error("$(_describe(data)) missing required '$name'") : field
+ psi_input = data.psi
+ ne_input = _need(data.n_e, "n_e")
+ Ti_input_eV = _need(data.T_i, "T_i")
+ Te_input_eV = _need(data.T_e, "T_e")
+ omegaE_input = _need(data.omega_E, "omega_E")
+ ni_input = data.n_i === nothing ? copy(ne_input) : data.n_i
+
+ nkin = _NKIN
+ psi_reg = collect(0:nkin) ./ nkin
+
+ # Monotone resample as in Fortran PENTRC; linear interpolation misplaces ω_E zero crossings and so the resonance.
+ ni = _pchip_resample(psi_input, ni_input, psi_reg)
+ ne = _pchip_resample(psi_input, ne_input, psi_reg)
+ Ti = _pchip_resample(psi_input, Ti_input_eV, psi_reg) .* _EV_J
+ Te = _pchip_resample(psi_input, Te_input_eV, psi_reg) .* _EV_J
+ omegaE = _pchip_resample(psi_input, omegaE_input, psi_reg)
+ _assert_positive_density(_describe(data), "n_e", ne, psi_reg)
+ _assert_positive_density(_describe(data), "n_i", ni, psi_reg)
+ _assert_nonneg_profile(_describe(data), "T_i", Ti, psi_reg)
+ _assert_nonneg_profile(_describe(data), "T_e", Te, psi_reg)
+
+ needs_rotation_reform = density_factor != 1.0 || temperature_factor != 1.0 || toroidal_rotation_factor != 1.0
+ any_scaling = needs_rotation_reform || ExB_rotation_factor != 1.0
+
+ if any_scaling
+ @info "KineticProfiles: scaling applied — density_factor=$density_factor, temperature_factor=$temperature_factor, ExB_rotation_factor=$ExB_rotation_factor, toroidal_rotation_factor=$toroidal_rotation_factor"
+ end
+
+ if needs_rotation_reform
+ (chi1 === nothing || chi1 == 0.0) && error("chi1 (= 2π·ψ₀) required when density_factor, temperature_factor, or toroidal_rotation_factor != 1.0")
+
+ # First-pass splines for cubic derivatives (unscaled profiles)
+ ni_spl = cubic_interp(collect(Float64, psi_reg), collect(Float64, ni); extrap=ExtendExtrap())
+ Ti_spl = cubic_interp(collect(Float64, psi_reg), collect(Float64, Ti); extrap=ExtendExtrap())
+ dni_dpsi = deriv1(ni_spl)
+ dTi_dpsi = deriv1(Ti_spl)
+
+ # Compute original wdian, wdiat, wphi and reform omegaE at each grid point
+ chrg_ion = zi * _E_CHARGE
+ for i in eachindex(omegaE)
+ ψ = psi_reg[i]
+ wdian_i = ni[i] > 0 ? -2π * Ti[i] * dni_dpsi(ψ) / (chrg_ion * chi1 * ni[i]) : 0.0
+ wdiat_i = -2π * dTi_dpsi(ψ) / (chrg_ion * chi1)
+ wphi_i = omegaE[i] + wdian_i + wdiat_i
+
+ # Scaled diamagnetic: density_factor cancels in T*(dn/dψ)/n; temperature_factor enters linearly
+ wdian_new = temperature_factor * wdian_i
+ wdiat_new = temperature_factor * wdiat_i
+
+ omegaE[i] = toroidal_rotation_factor * wphi_i - wdian_new - wdiat_new
+ end
+
+ ni .*= density_factor
+ ne .*= density_factor
+ Ti .*= temperature_factor
+ Te .*= temperature_factor
+ end
+
+ if ExB_rotation_factor != 1.0
+ omegaE .*= ExB_rotation_factor
+ end
+ # After scaling, so a small temperature_factor that engages the floor is reported.
+ _warn_collision_floors(_describe(data), data, ne, Te, Ti)
+
+ loglam = zeros(Float64, nkin + 1)
+ nui = zeros(Float64, nkin + 1)
+ nue = zeros(Float64, nkin + 1)
+ zeff = zeros(Float64, nkin + 1)
+ lnL_sup, nui_sup, nue_sup = (_supplied_rate(psi_input, getfield(data, f), psi_reg) for f in (:lnLambda, :nu_i, :nu_e))
+
+ for i in 1:(nkin+1)
+ n_i = ni[i]
+ n_e = ne[i]
+ T_i = Ti[i]
+ T_e = Te[i]
+
+ z = zimp - (n_i / n_e) * zi * (zimp - zi)
+ zpitch = 1.0 + (1.0 + mimp) / (2.0 * mimp) * zimp * (z - 1.0) / (zimp - z)
+
+ ll = lnL_sup === nothing ? _coulomb_log(n_e, T_e) : lnL_sup[i]
+ loglam[i] = ll
+
+ # Krook ν (Logan & Park 2013 Eq. 6) with a test-particle z²; the single-species limit of resolve_ntv_species.
+ nui[i] = (zpitch / _NU_PREFAC) * zi^2 * n_i * ll / (sqrt(1.0 * mi) * _collision_tkev(T_i)^1.5)
+ nue[i] = (zpitch / _NU_PREFAC) * n_e * ll / (sqrt(_ME / _MP) * _collision_tkev(T_e)^1.5)
+ zeff[i] = z
+ end
+ # Supplied rates replace the model's, as Fortran PENTRC `rates-v1`; the profile scaling factors do not rescale them.
+ nui_sup === nothing || (nui .= nui_sup)
+ nue_sup === nothing || (nue .= nue_sup)
+
+ return KineticProfileSplines(psi_reg, ni, ne, Ti, Te, omegaE, loglam, nui, nue, zeff)
+end
+
+"""
+Parse a 6- or 9-column kinetic profile table, dropping `#` comments and non-numeric header rows.
+Returns the columns.
+"""
+function _read_kinetic_table(kinetic_file::AbstractString)
+ table = DelimitedFiles.readdlm(kinetic_file; comments=true)
+
+ # readdlm pads a short row with empty strings, so a data row (numeric first entry) that is not all numeric is ragged.
+ ragged = findfirst(row -> row[1] isa Number && !all(x -> isa(x, Number), row), collect(eachrow(table)))
+ ragged === nothing ||
+ error("kinetic file $kinetic_file: data row $ragged has fewer columns than the others; every data row needs 6 columns, or 9 with lnLambda nu_i nu_e")
+
+ # Keep numeric rows and stack them row-wise (reshape(:, 6) is column-major and would scramble columns).
+ numeric_rows = [collect(row) for row in eachrow(table) if all(x -> isa(x, Number), row)]
+ if isempty(numeric_rows)
+ error("No numeric data rows found in kinetic file: $kinetic_file")
+ end
+ ncol = length(numeric_rows[1])
+ ncol in (6, 9) ||
+ error("kinetic file $kinetic_file: every data row needs 6 columns, or 9 with lnLambda nu_i nu_e")
+ table = reduce(vcat, (reshape(Float64.(r), 1, ncol) for r in numeric_rows))
+ return [collect(table[:, j]) for j in 1:ncol]
+end
+
+"""
+Monotone (pchip) fit of `y(x)` on the irregular input grid, evaluated at `x_new` with
+extrapolation, as Fortran PENTRC `spline_fit_pchip`: no overshoot between table points.
+"""
+function _pchip_resample(x::AbstractVector, y::AbstractVector, x_new::AbstractVector)
+ spl = pchip_interp(collect(Float64, x), collect(Float64, y); extrap=ExtendExtrap())
+ return [spl(xv) for xv in x_new]
+end
+
+"""
+ shift_exb_rotation(kp::KineticProfileSplines, Δω::Real) -> KineticProfileSplines
+
+The same kinetic profiles with the E×B rotation rigidly shifted, `ω_E(ψ) + Δω` (rad/s), and
+every other profile unchanged. A rotation change moves the E×B frequency and leaves the
+diamagnetic frequencies, which the torque kernel derives from the density and temperature
+gradients, where they are; this is the scan variable of a torque-versus-rotation table.
+"""
+function shift_exb_rotation(kp::KineticProfileSplines, Δω::Real)
+ xs = kp.xs
+ sample(s) = Float64[s(ψ) for ψ in xs]
+ return KineticProfileSplines(xs, sample(kp.ni_spline), sample(kp.ne_spline), sample(kp.Ti_spline), sample(kp.Te_spline),
+ sample(kp.omegaE_spline) .+ Float64(Δω), sample(kp.loglam_spline), sample(kp.nui_spline), sample(kp.nue_spline), sample(kp.zeff_spline))
+end
diff --git a/src/Equilibrium/Output.jl b/src/Equilibrium/Output.jl
new file mode 100644
index 0000000000..25f071e8f5
--- /dev/null
+++ b/src/Equilibrium/Output.jl
@@ -0,0 +1,41 @@
+import ..Utilities: save_to_hdf5
+import ..Utilities: EQUIL_H5_NAMES, EQUIL_H5_SKIP, MAIN_H5_ANNOTATIONS
+import ..Utilities.HDF5Annotations: replace_group!
+using HDF5
+
+"""
+ save_to_hdf5(target, equil::PlasmaEquilibrium)
+
+Save the processed equilibrium profiles, geometry, and derived scalar quantities, and record its deck sections in `Input/`.
+"""
+function save_to_hdf5(out_h5::Union{HDF5.File,HDF5.Group}, equil::PlasmaEquilibrium)
+ replace_group!(out_h5, "Equilibrium")
+ for f in fieldnames(EquilibriumParameters)
+ f in EQUIL_H5_SKIP && continue
+ val = getfield(equil.params, f)
+ val === nothing && continue
+ out_h5["Equilibrium/$(get(EQUIL_H5_NAMES, f, String(f)))"] = val
+ end
+ out_h5["Equilibrium/psi_total"] = equil.psio
+ out_h5["Equilibrium/R_axis"] = equil.ro
+ out_h5["Equilibrium/Z_axis"] = equil.zo
+
+ # Write equilibrium profile and geometry arrays (from the named splines)
+ profiles = equil.profiles
+ out_h5["Equilibrium/Profiles/psi"] = profiles.xs
+ out_h5["Equilibrium/Profiles/2piF"] = profiles.F_spline.y
+ out_h5["Equilibrium/Profiles/mu0p"] = profiles.P_spline.y
+ out_h5["Equilibrium/Profiles/dVdpsi"] = profiles.dVdpsi_spline.y
+ out_h5["Equilibrium/Profiles/q"] = profiles.q_spline.y
+ out_h5["Equilibrium/Geometry/psi"] = equil.rzphi_xs
+ out_h5["Equilibrium/Geometry/theta"] = equil.rzphi_ys
+ # Extract grid point values from interpolants for HDF5 output
+ out_h5["Equilibrium/Geometry/rcoords"] = equil.rzphi_rsquared.nodal_derivs.partials[1, :, :]
+ out_h5["Equilibrium/Geometry/offset"] = equil.rzphi_offset.nodal_derivs.partials[1, :, :]
+ out_h5["Equilibrium/Geometry/nu"] = equil.rzphi_nu.nodal_derivs.partials[1, :, :]
+ out_h5["Equilibrium/Geometry/jac"] = equil.rzphi_jac.nodal_derivs.partials[1, :, :]
+
+ Utilities.HDF5Annotations.annotate!(out_h5, MAIN_H5_ANNOTATIONS)
+ Utilities.record_inputs!(out_h5, equil)
+ return nothing
+end
diff --git a/src/Equilibrium/PlasmaEquilibrium.jl b/src/Equilibrium/PlasmaEquilibrium.jl
new file mode 100644
index 0000000000..52d62d72b2
--- /dev/null
+++ b/src/Equilibrium/PlasmaEquilibrium.jl
@@ -0,0 +1,403 @@
+"""
+ ProfileSplines
+
+Named 1D cubic spline interpolants for equilibrium profiles.
+
+# Fields
+
+ - `xs::Vector{Float64}`: Shared x-axis (normalized psi)
+ - `F_spline`: 2π*F (toroidal flux function, where F = R * B_toroidal)
+ - `P_spline`: μ₀*P (plasma pressure × μ₀)
+ - `dVdpsi_spline`: dV/dψ (volume derivative)
+ - `q_spline`: q (safety factor)
+
+# Derivative Interpolants (for continuous derivative evaluation)
+
+ - `F_deriv`, `P_deriv`, `dVdpsi_deriv`, `q_deriv`: First derivative interpolants
+
+# Notes
+
+ - Node values at grid points: Access via `spline.y[i]`
+ - Derivative at any point: Call `deriv(x)` (derivative views are callable)
+ - Grid: Access via `xs` field or `spline.cache.x`
+"""
+struct ProfileSplines{S,D}
+ xs::Vector{Float64}
+ npts::Int # length(xs), avoids redundant length() calls
+ npts_minus_1::Int # npts - 1, for hint at last interval
+ # Value interpolants
+ F_spline::S
+ P_spline::S
+ dVdpsi_spline::S
+ q_spline::S
+ # Derivative views (callable, share data with value interpolants)
+ F_deriv::D
+ P_deriv::D
+ dVdpsi_deriv::D
+ q_deriv::D
+end
+
+"""
+ ProfileSplines(xs, F_vals, P_vals, dVdpsi_vals, q_vals; extrap=ExtendExtrap())
+
+Create ProfileSplines from arrays of profile values.
+Uses CubicFit boundary conditions with extension extrapolation.
+"""
+function ProfileSplines(xs::Vector{Float64},
+ F_vals::Vector{Float64},
+ P_vals::Vector{Float64},
+ dVdpsi_vals::Vector{Float64},
+ q_vals::Vector{Float64};
+ extrap::AbstractExtrap=ExtendExtrap())
+ npts = length(xs)
+ npts_minus_1 = npts - 1
+ @assert length(F_vals) == npts
+ @assert length(P_vals) == npts
+ @assert length(dVdpsi_vals) == npts
+ @assert length(q_vals) == npts
+
+ # Create value interpolants with CubicFit BC (default) for sequential psi access
+ F_spline = cubic_interp(xs, F_vals; extrap=extrap)
+ P_spline = cubic_interp(xs, P_vals; extrap=extrap)
+ dVdpsi_spline = cubic_interp(xs, dVdpsi_vals; extrap=extrap)
+ q_spline = cubic_interp(xs, q_vals; extrap=extrap)
+
+ # Create derivative views (these share data with value interpolants, no extra storage)
+ F_deriv = deriv1(F_spline)
+ P_deriv = deriv1(P_spline)
+ dVdpsi_deriv = deriv1(dVdpsi_spline)
+ q_deriv = deriv1(q_spline)
+
+ ProfileSplines{typeof(F_spline),typeof(F_deriv)}(
+ xs, npts, npts_minus_1,
+ F_spline, P_spline, dVdpsi_spline, q_spline,
+ F_deriv, P_deriv, dVdpsi_deriv, q_deriv
+ )
+end
+
+"""
+ GeometryProfileSplines
+
+Named 1D cubic spline interpolants for flux-surface-averaged geometric quantities.
+Built once during equilibrium construction so they are available to every downstream
+module without per-caller recomputation.
+
+# Fields
+
+ - `xs::Vector{Float64}`: Shared ψ axis (matches `rzphi_xs`)
+ - `area_spline`: Flux-surface area ∫ dA(ψ) [m²]
+ - `avg_r_spline`: Surface-average minor radius ⟨r⟩(ψ) [m]
+ - `avg_R_spline`: Surface-average major radius ⟨R⟩(ψ) [m]
+"""
+struct GeometryProfileSplines{S}
+ xs::Vector{Float64}
+ npts::Int
+ npts_minus_1::Int
+ area_spline::S
+ avg_r_spline::S
+ avg_R_spline::S
+end
+
+"""
+ GeometryProfileSplines(xs, area_vals, avg_r_vals, avg_R_vals; extrap=ExtendExtrap())
+
+Construct `GeometryProfileSplines` from arrays of surface-averaged values defined
+on the shared ψ grid `xs`. Uses CubicFit boundary conditions to match `ProfileSplines`.
+"""
+function GeometryProfileSplines(xs::Vector{Float64},
+ area_vals::Vector{Float64},
+ avg_r_vals::Vector{Float64},
+ avg_R_vals::Vector{Float64};
+ extrap::AbstractExtrap=ExtendExtrap())
+ npts = length(xs)
+ @assert length(area_vals) == npts
+ @assert length(avg_r_vals) == npts
+ @assert length(avg_R_vals) == npts
+
+ area_spline = cubic_interp(xs, area_vals; extrap=extrap)
+ avg_r_spline = cubic_interp(xs, avg_r_vals; extrap=extrap)
+ avg_R_spline = cubic_interp(xs, avg_R_vals; extrap=extrap)
+
+ GeometryProfileSplines{typeof(area_spline)}(
+ xs, npts, npts - 1,
+ area_spline, avg_r_spline, avg_R_spline
+ )
+end
+
+"""
+ KineticProfileData
+
+The kinetic description of the plasma: the raw profile columns read from a kinetic file (HDF5 or
+ASCII), before resampling and spline construction, plus the plasma's species composition, the
+values that stand in for profiles the file omits, and the resistivity closure. `psi` (normalized
+poloidal flux) is always present; every profile field is `nothing` when the source omits it, so
+each consumer validates only the fields it needs. Units: densities m⁻³, temperatures eV,
+frequencies rad/s, diffusivities m²/s. Every consumer (KineticForces, the tearing layers, the
+layer-overlap scan) reads the composition and closure from here, so they all see one plasma.
+
+| field | meaning |
+|:------------------- |:----------------------------------------------------------------------------------------------------------------- |
+| `n_i` | main-ion density |
+| `n_e` | electron density |
+| `T_i`/`T_e` | ion / electron temperature |
+| `omega_E` | ExB rotation |
+| `omega_tor` | toroidal rotation (optional) |
+| `chi_e` | electron perpendicular heat diffusivity χ⊥,e |
+| `chi_i` | ion perpendicular heat diffusivity χ⊥,i |
+| `chi_phi` | toroidal momentum diffusivity χ_φ |
+| `zeff` | effective charge Z_eff(ψ) supplied directly (optional); the resistive-layer analysis prefers it to its closure |
+| `lnLambda` | Coulomb logarithm supplied directly (optional); replaces the internal one in the NTV collision model |
+| `nu_i`/`nu_e` | main-ion / electron collision rates in 1/s supplied directly (optional); replace the internal collision model |
+| `species_densities` | named per-species densities (e.g. `"n_D"`, `"n_T"`) for explicit multi-ion input; `nothing` for ASCII / no extras |
+| `provenance` | short string recording the source file/format |
+| `ion_species` | main-ion species, a `Vector{IonSpecies}`; default one deuterium ion carrying all of `n_i` |
+| `impurity_charge` | charge of the single impurity species that closes quasi-neutrality (default 6, carbon) |
+| `impurity_mass` | impurity mass in proton masses (default 12) |
+| `zeff_default` | Z_eff used where neither a `zeff` profile nor `n_i`/`n_e` gives one (default 1) |
+| `chi_e_default` | χ⊥,e used where the file has no usable `chi_e` (default 1) |
+| `chi_i_default` | χ⊥,i used where the file has no usable `chi_i`; `nothing` (default) makes a model that needs it fail |
+| `chi_phi_default` | χ_φ used where the file has no usable `chi_phi` (default 1) |
+| `tau_E` | whole-plasma energy confinement time in s; `nothing` (default) when unknown |
+| `resistivity_model` | parallel-resistivity closure: `:sauter` (default), `:redl`, `:spitzer`, `:spitzer_harm` |
+| `lnLambda_form` | Coulomb-logarithm form of the closure: `:nrl` (default), `:sauter`, `:wesson` |
+
+A profile dataset that is absent or all-zero counts as not provided, so its `*_default` applies.
+Build a copy with different settings with `KineticProfileData(data; ion_species=..., ...)`.
+"""
+struct KineticProfileData
+ psi::Vector{Float64}
+ n_i::Union{Nothing,Vector{Float64}}
+ n_e::Union{Nothing,Vector{Float64}}
+ T_i::Union{Nothing,Vector{Float64}}
+ T_e::Union{Nothing,Vector{Float64}}
+ omega_E::Union{Nothing,Vector{Float64}}
+ omega_tor::Union{Nothing,Vector{Float64}}
+ chi_e::Union{Nothing,Vector{Float64}}
+ chi_i::Union{Nothing,Vector{Float64}}
+ chi_phi::Union{Nothing,Vector{Float64}}
+ zeff::Union{Nothing,Vector{Float64}}
+ lnLambda::Union{Nothing,Vector{Float64}}
+ nu_i::Union{Nothing,Vector{Float64}}
+ nu_e::Union{Nothing,Vector{Float64}}
+ species_densities::Union{Nothing,Dict{String,Vector{Float64}}}
+ provenance::String
+ ion_species::Vector{IonSpecies}
+ impurity_charge::Int
+ impurity_mass::Int
+ zeff_default::Float64
+ chi_e_default::Union{Nothing,Float64}
+ chi_i_default::Union{Nothing,Float64}
+ chi_phi_default::Union{Nothing,Float64}
+ tau_E::Union{Nothing,Float64}
+ resistivity_model::Symbol
+ lnLambda_form::Symbol
+end
+
+const _RESISTIVITY_MODELS = (:sauter, :redl, :spitzer, :spitzer_harm)
+const _LNLAMBDA_FORMS = (:nrl, :sauter, :wesson)
+
+function KineticProfileData(; psi, n_i=nothing, n_e=nothing, T_i=nothing, T_e=nothing,
+ omega_E=nothing, omega_tor=nothing, chi_e=nothing, chi_i=nothing, chi_phi=nothing, zeff=nothing,
+ lnLambda=nothing, nu_i=nothing, nu_e=nothing, species_densities=nothing, provenance="",
+ ion_species=[IonSpecies(; z=1, m=2, fraction=1.0)], impurity_charge=6, impurity_mass=12,
+ zeff_default=1.0, chi_e_default=1.0, chi_i_default=nothing, chi_phi_default=1.0, tau_E=nothing,
+ resistivity_model=:sauter, lnLambda_form=:nrl)
+ _v(x) = x === nothing ? nothing : Float64.(collect(x))
+ _s(x) = x === nothing ? nothing : Float64(x)
+ species = convert(Vector{IonSpecies}, ion_species)
+ isempty(species) && throw(ArgumentError("KineticProfileData: ion_species needs at least one main ion"))
+ impurity_charge > 1 || throw(ArgumentError("KineticProfileData: impurity_charge = $impurity_charge must exceed the main-ion charge 1"))
+ for (name, v) in (("chi_e_default", chi_e_default), ("chi_i_default", chi_i_default), ("chi_phi_default", chi_phi_default),
+ ("tau_E", tau_E))
+ v === nothing || (isfinite(v) && v > 0) || throw(ArgumentError("KineticProfileData: $name must be positive and finite; got $v"))
+ end
+ model, form = Symbol(resistivity_model), Symbol(lnLambda_form)
+ model in _RESISTIVITY_MODELS || throw(ArgumentError("KineticProfileData: resistivity_model = $model not in $_RESISTIVITY_MODELS"))
+ form in _LNLAMBDA_FORMS || throw(ArgumentError("KineticProfileData: lnLambda_form = $form not in $_LNLAMBDA_FORMS"))
+ # An all-zero rate dataset counts as not supplied, like the other optional profiles.
+ _rate(x) = x === nothing || all(iszero, x) ? nothing : x
+ lnLambda, nu_i, nu_e = _rate(lnLambda), _rate(nu_i), _rate(nu_e)
+ for (name, v) in (("lnLambda", lnLambda), ("nu_i", nu_i), ("nu_e", nu_e))
+ v === nothing || all(x -> isfinite(x) && x > 0, v) ||
+ throw(ArgumentError("KineticProfileData: supplied $name must be positive and finite everywhere"))
+ end
+ return KineticProfileData(Float64.(collect(psi)), _v(n_i), _v(n_e), _v(T_i), _v(T_e),
+ _v(omega_E), _v(omega_tor), _v(chi_e), _v(chi_i), _v(chi_phi), _v(zeff), _v(lnLambda), _v(nu_i), _v(nu_e),
+ species_densities, String(provenance),
+ species, Int(impurity_charge), Int(impurity_mass), Float64(zeff_default), _s(chi_e_default), _s(chi_i_default),
+ _s(chi_phi_default), _s(tau_E), model, form)
+end
+
+# A copy of `data` with some fields replaced, e.g. the composition a deck or script sets on loaded profiles.
+KineticProfileData(data::KineticProfileData; kwargs...) =
+ KineticProfileData(; (f => getfield(data, f) for f in fieldnames(KineticProfileData))..., kwargs...)
+
+"""
+ KineticProfileSplines
+
+Named 1D spline interpolants for kinetic profiles (densities, temperatures, ExB rotation,
+collisional diagnostics) on the regular kinetic ψ grid, with derivative views of the densities and
+temperatures for the diamagnetic frequencies of the NTV kernel. The Coulomb logarithm and collision
+frequencies are monotone (pchip) interpolants, so a steep cold edge cannot ring below zero.
+
+# Fields
+
+ - `xs::Vector{Float64}`: Shared ψ axis (the regular kinetic grid)
+ - `ni_spline`, `ne_spline`: Ion / electron number densities [m⁻³]
+ - `Ti_spline`, `Te_spline`: Ion / electron temperatures [J]
+ - `omegaE_spline`: ExB rotation ω_E [rad/s]
+ - `loglam_spline`: Coulomb logarithm
+ - `nui_spline`, `nue_spline`: Krook collision frequencies [s⁻¹]
+ - `zeff_spline`: Effective charge Z_eff
+ - `ni_deriv`, `ne_deriv`, `Ti_deriv`, `Te_deriv`: Derivative views for ψ-derivative access
+"""
+struct KineticProfileSplines{S,D,C}
+ xs::Vector{Float64}
+ npts::Int
+ npts_minus_1::Int
+ ni_spline::S
+ ne_spline::S
+ Ti_spline::S
+ Te_spline::S
+ omegaE_spline::S
+ loglam_spline::C
+ nui_spline::C
+ nue_spline::C
+ zeff_spline::S
+ ni_deriv::D
+ ne_deriv::D
+ Ti_deriv::D
+ Te_deriv::D
+end
+
+"""
+ KineticProfileSplines(xs, ni, ne, Ti, Te, omegaE, loglam, nui, nue, zeff;
+ extrap=ExtendExtrap())
+
+Build the kinetic profile splines from arrays of values defined on the shared
+ψ grid `xs`. Uses CubicFit boundary conditions to match `ProfileSplines`, and pchip for the
+Coulomb logarithm and collision frequencies as Fortran PENTRC.
+Temperatures must already be in Joules.
+"""
+function KineticProfileSplines(xs::Vector{Float64},
+ ni::Vector{Float64}, ne::Vector{Float64},
+ Ti::Vector{Float64}, Te::Vector{Float64},
+ omegaE::Vector{Float64}, loglam::Vector{Float64},
+ nui::Vector{Float64}, nue::Vector{Float64}, zeff::Vector{Float64};
+ extrap::AbstractExtrap=ExtendExtrap())
+ npts = length(xs)
+ @assert all(length(v) == npts for v in (ni, ne, Ti, Te, omegaE, loglam, nui, nue, zeff))
+
+ ni_spline = cubic_interp(xs, ni; extrap=extrap)
+ ne_spline = cubic_interp(xs, ne; extrap=extrap)
+ Ti_spline = cubic_interp(xs, Ti; extrap=extrap)
+ Te_spline = cubic_interp(xs, Te; extrap=extrap)
+ omegaE_spline = cubic_interp(xs, omegaE; extrap=extrap)
+ loglam_spline = pchip_interp(xs, loglam; extrap=extrap)
+ nui_spline = pchip_interp(xs, nui; extrap=extrap)
+ nue_spline = pchip_interp(xs, nue; extrap=extrap)
+ zeff_spline = cubic_interp(xs, zeff; extrap=extrap)
+
+ ni_deriv = deriv1(ni_spline)
+ ne_deriv = deriv1(ne_spline)
+ Ti_deriv = deriv1(Ti_spline)
+ Te_deriv = deriv1(Te_spline)
+
+ KineticProfileSplines{typeof(ni_spline),typeof(ni_deriv),typeof(nui_spline)}(
+ xs, npts, npts - 1,
+ ni_spline, ne_spline, Ti_spline, Te_spline,
+ omegaE_spline, loglam_spline, nui_spline, nue_spline, zeff_spline,
+ ni_deriv, ne_deriv, Ti_deriv, Te_deriv
+ )
+end
+
+"""
+ PlasmaEquilibrium(...)
+
+The final, self-contained result of the equilibrium reconstruction, in flux coordinates.
+
+# Fields
+
+ - `config::EquilibriumConfig`:
+ The equilibrium configuration object used for the reconstruction.
+
+ - `params::EquilibriumParameters`:
+ Computed equilibrium parameters and diagnostics.
+ - `profiles::ProfileSplines`:
+ Named 1D profile splines (F, P, dV/dψ, q) on normalized psi grid.
+ Access values at grid points via `profiles.F_spline.y[i]`, etc.
+ Access derivatives via `profiles.F_deriv.y[i]` or `profiles.F_deriv(psi)`.
+ - `geometry::GeometryProfileSplines`:
+ Named 1D splines for flux-surface-averaged geometry (area, ⟨r⟩, ⟨R⟩),
+ populated automatically by `compute_geometry_profiles` during construction.
+ - **Grid coordinates (shared by all rzphi/eqfun interpolants):**
+
+ + `rzphi_xs::Vector{Float64}`: ψ coordinates (length mpsi+1)
+ + `rzphi_ys::Vector{Float64}`: θ coordinates (length mtheta+1)
+ - **Geometric quantities (rzphi, 4 interpolants):**
+ 2D cubic interpolants for flux-coordinate mapping with periodic BC in theta.
+
+ + **x value:** normalized ψ
+ + **y value:** SFL poloidal angle ∈ [0, 1]
+ + `rzphi_rsquared::CubicInterpolantND`: r_coord² = (R - ro)² + (Z - zo)²
+ + `rzphi_offset::CubicInterpolantND`: η/(2π) - θₙₑw (angle offset)
+ + `rzphi_nu::CubicInterpolantND`: ν in ϕ = 2πζ + ν(ψ, θ)
+ + `rzphi_jac::CubicInterpolantND`: Jacobian
+ - **Physics quantities (eqfun, 3 interpolants):**
+ 2D cubic interpolants storing local physics and geometric quantities.
+
+ + **x value:** normalized ψ
+ + **y value:** SFL poloidal angle θₙₑw
+ + `eqfun_B::CubicInterpolantND`: Total magnetic field strength [T]
+ + `eqfun_metric1::CubicInterpolantND`: (e₁⋅e₂ + q⋅e₃⋅e₁)/(J⋅B²)
+ + `eqfun_metric2::CubicInterpolantND`: (e₂⋅e₃ + q⋅e₃⋅e₃)/(J⋅B²)
+ - `ro::Float64`: R-coordinate of the magnetic axis [m]
+ - `zo::Float64`: Z-coordinate of the magnetic axis [m]
+ - `psio::Float64`: Total flux difference |Ψ_axis - Ψ_boundary| [Weber/radian]
+ - `ingest::EquilibriumIngest`: raw arrays forwarded from the equilibrium input for the
+ `gpec.h5` rerun snapshot — a [`DirectIngest`](@ref)/[`InverseIngest`](@ref) for file-based
+ equilibria, or `nothing` for analytic ones (regenerated from their deck section on replay)
+ - `analytic::Union{Nothing,AnalyticEquilibriumConfig}`: the parameters an analytic kind
+ (`sol`, `lar`, `tj_analytic`) was solved from, so [`reform`](@ref) can re-solve it on a new
+ grid; `nothing` for file-based and IMAS equilibria.
+ - `kinetic::Union{Nothing,KineticProfileData}`: the raw kinetic profiles of `config.kinetic_file` (or of
+ [`attach_kinetic_profiles!`](@ref)), on the file's own ψ grid; `nothing` when none are attached
+"""
+mutable struct PlasmaEquilibrium{P<:ProfileSplines,G<:GeometryProfileSplines,I2D<:FastInterpolations.CubicInterpolantND}
+ config::EquilibriumConfig
+ params::EquilibriumParameters
+ profiles::P
+ geometry::G
+
+ # Grid coordinates (shared by all 2D interpolants)
+ rzphi_xs::Vector{Float64}
+ rzphi_ys::Vector{Float64}
+
+ # Geometric quantities (4 interpolants)
+ rzphi_rsquared::I2D
+ rzphi_offset::I2D
+ rzphi_nu::I2D
+ rzphi_jac::I2D
+
+ # Physics quantities (3 interpolants)
+ eqfun_B::I2D
+ eqfun_metric1::I2D
+ eqfun_metric2::I2D
+
+ ro::Float64
+ zo::Float64
+ psio::Float64
+
+ ingest::EquilibriumIngest
+ analytic::Union{Nothing,AnalyticEquilibriumConfig}
+ kinetic::Union{Nothing,KineticProfileData}
+end
+
+# Solvers build the equilibrium before PlasmaEquilibrium records its source and attaches the kinetic
+# profiles, so allow construction without them; ingest, analytic and kinetic default to nothing.
+PlasmaEquilibrium(config, params, profiles, geometry, rzphi_xs, rzphi_ys,
+ rzphi_rsquared, rzphi_offset, rzphi_nu, rzphi_jac,
+ eqfun_B, eqfun_metric1, eqfun_metric2, ro, zo, psio) =
+ PlasmaEquilibrium(config, params, profiles, geometry, rzphi_xs, rzphi_ys,
+ rzphi_rsquared, rzphi_offset, rzphi_nu, rzphi_jac,
+ eqfun_B, eqfun_metric1, eqfun_metric2, ro, zo, psio, nothing, nothing, nothing)
diff --git a/src/Equilibrium/ReadEquilibrium.jl b/src/Equilibrium/ReadEquilibrium.jl
deleted file mode 100644
index 9f645b0e75..0000000000
--- a/src/Equilibrium/ReadEquilibrium.jl
+++ /dev/null
@@ -1,409 +0,0 @@
-#=
-This file contains functions for reading equilibrium files from diferent codes
- that use different formating and collecting the inputs required to form
- a complete PlasmaEquilibrium using either direct or inverse construction
-=#
-
-
-"""
-_read_1d_gfile_format(lines_block, num_values)
-
-Internal helper function to parse Fortran-style fixed-width numerical blocks
-from a vector of strings.
-
-## Arguments:
-- `lines_block`: A `Vector{String}` containing the lines to parse.
-- `num_values`: The total number of `Float64` values to read from the block.
-## Returns:
-- A `Vector{Float64}` containing the parsed values.
-"""
-function _read_1d_gfile_format(lines_block::Vector{String}, num_values::Int)
- data_str = join(lines_block)
- field_width = 16
- parsed_values = Float64[]
- num_read = 0
-
- # Ensure the string length is a multiple of the field width for safe processing
- safe_len = (length(data_str) ÷ field_width) * field_width
- for i in 1:field_width:safe_len
- num_read >= num_values && break
- val_str = strip(data_str[i : i + field_width - 1])
- if !isempty(val_str)
- try
- push!(parsed_values, parse(Float64, val_str))
- num_read += 1
- catch e
- @warn "Parsing error for substring: '$val_str'. Error: $e. Skipping."
- end
- end
- end
-
- if num_read < num_values
- @warn "Expected $num_values values, but only read $num_read."
- end
- return parsed_values
-end
-
-"""
- _read_efit(equil_in)
-
-Parses an EFIT g-file, creates initial 1D and 2D splines, and bundles
-them into a `DirectRunInput` object.
-
-## Arguments:
-- `equil_in`: The `EquilInput` object containing the filename and parameters.
-## Returns:
-- A `DirectRunInput` object ready for the direct solver.
-"""
-function read_efit(config::EquilibriumConfig)
- println("--> Processing EFIT g-file: $(config.control.eq_filename)")
- lines = readlines(config.control.eq_filename)
-
- # --- Parse Header ---
- header1_parts = split(lines[1])
- nw = parse(Int, header1_parts[end-1])
- nh = parse(Int, header1_parts[end])
- println("--> Parsed from header: nw=$nw, nh=$nh")
-
- header_vals = _read_1d_gfile_format(lines[2:5], 20)
- rdim, zdim, rcentr, rleft, zmid = header_vals[1:5]
- rmaxis, zmaxis, simag, sibry = header_vals[6:9]
-
- # --- Parse Data Blocks ---
- current_line_idx = 6
- function parse_block(num_pts)
- num_lines = ceil(Int, num_pts / 5)
- block = lines[current_line_idx : current_line_idx + num_lines - 1]
- data = _read_1d_gfile_format(block, num_pts)
- current_line_idx += num_lines
- return data
- end
-
- fpol_data = parse_block(nw)
- pres_data = parse_block(nw)
- ffprime_data = parse_block(nw)
- pprime_data = parse_block(nw)
- psi_flat_vec = parse_block(nw * nh)
- qprof_data = parse_block(nw)
-
- psi_rz = reshape(psi_flat_vec, nw, nh)
- println("--> All main data blocks parsed successfully.")
-
- # --- Create 1D Profile Spline (sq_in) ---
- println("--> Creating 1D profile splines...")
- psi_norm_grid = range(0.0, 1.0, length=nw)
- sq_fs_nodes = hcat(
- abs.(fpol_data),
- max.(pres_data .* mu0, 0.0),
- qprof_data,
- sqrt.(psi_norm_grid)
- )
- # According to Spline_document.txt, bctype=4 is Not-a-Knot
- sq_in = Spl.CubicSpline(collect(psi_norm_grid), sq_fs_nodes, bctype=4)
- println("--> 1D Spline fitting complete.")
-
- # --- Process and Normalize 2D Psi Data ---
- psio_signed = sibry - simag
- psi_proc = (sibry .- psi_rz)
- psio = abs(psio_signed)
- # Ensure psi at the magnetic axis is positive relative to the boundary
- if psio_signed < 0.0
- psi_proc .*= -1.0
- end
-
- # --- Create 2D Psi Spline (psi_in) ---
- println("--> Creating 2D psi spline...")
- r_grid = range(rleft, rleft + rdim, length=nw)
- z_grid = range(zmid - zdim / 2, zmid + zdim / 2, length=nh)
- rmin, rmax = extrema(r_grid)
- zmin, zmax = extrema(z_grid)
-
- psi_proc_3d = reshape(psi_proc, (nw, nh, 1))
- psi_in = Spl.BicubicSpline(collect(r_grid), collect(z_grid), psi_proc_3d, bctypex=4, bctypey=4)
- println("--> 2D Spline fitting complete.")
-
- # --- Bundle everything for the solver ---
- return DirectRunInput(config, sq_in, psi_in, rmin, rmax, zmin, zmax, psio)
-end
-
-"""
- _read_chease2(equil_in)
-
-Parses a chease2 file, creates initial 1D and 2D splines, finds magnetic axis, and bundles
-them into a `InverseRunInput` object.
-
-## Arguments:
-- `equil_in`: The `EquilInput` object containing the filename and parameters.
-## Returns:
-- A `InverseRunInput` object ready for the inverse solver.
-"""
-function read_chease2(config::EquilibriumConfig)
- println("--> Reading CHEASE file: $(config.control.eq_filename)")
- lines = readlines(config.control.eq_filename)
-
- # --- Parse Header (FORMAT 10: 3I5) ---
- header_parts = split(lines[1])
- ntnova = parse(Int, header_parts[1])
- npsi1 = parse(Int, header_parts[2])
- nsym = parse(Int, header_parts[3])
-
- # --- Parse axx (FORMAT 20: 1E22.15) ---
- axx = parse(Float64, split(lines[2])[1])
-
- # --- Pre-allocate Arrays ---
- zcpr = zeros(npsi1 - 1)
- zcppr = zeros(npsi1)
- zq = zeros(npsi1)
- zdq = zeros(npsi1)
- ztmf = zeros(npsi1)
- ztp = zeros(npsi1)
- zfb = zeros(npsi1)
- zfbp = zeros(npsi1)
- zpsi = zeros(npsi1)
- zpsim = zeros(npsi1 - 1)
-
- zrcp = zeros(ntnova + 3, npsi1)
- zzcp = zeros(ntnova + 3, npsi1)
- zjacm = zeros(ntnova + 3, npsi1)
- zjac = zeros(ntnova + 3, npsi1)
-
- # --- Helper to parse 5E22.15 data per line ---
- function parse_floats(lines_range)
- data = Float64[]
- for line in lines[lines_range]
- for i in 0:4
- s = strip(line[22*i+1:min(end, 22*(i+1))])
- if !isempty(s)
- push!(data, parse(Float64, s))
- end
- end
- end
- return data
- end
-
- # --- Compute line offsets ---
- line_idx = 3 # Start after header (line 1) and axx (line 2)
-
- function load_vector!(vec)
- count = length(vec)
- lines_needed = cld(count, 5)
- vec .= parse_floats(line_idx : line_idx + lines_needed - 1)
- line_idx += lines_needed
- end
-
- function load_matrix!(mat)
- count = size(mat, 1) * size(mat, 2)
- lines_needed = cld(count, 5)
- data = parse_floats(line_idx : line_idx + lines_needed - 1)
- line_idx += lines_needed
- # Fill column-major (Fortran-style)
- for j in 1:size(mat, 2)
- for i in 1:size(mat, 1)
- mat[i, j] = data[(j-1)*size(mat,1) + i]
- end
- end
- end
-
- # --- Read Vectors ---
- load_vector!(zcpr)
- load_vector!(zcppr)
- load_vector!(zq)
- load_vector!(zdq)
- load_vector!(ztmf)
- load_vector!(ztp)
- load_vector!(zfb)
- load_vector!(zfbp)
- load_vector!(zpsi)
- load_vector!(zpsim)
-
- # --- Read Matrices ---
- load_matrix!(zrcp)
- load_matrix!(zzcp)
- load_matrix!(zjacm)
- load_matrix!(zjac)
-
- println("--> Parsed from header: ntnova = $ntnova, npsi1 = $npsi1, nsym = $nsym")
-
- # Number of spline intervals
- ma = npsi1 - 1
- # Total ψ range for normalization
- psio = zpsi[end] - zpsi[1]
- # Normalize ψ to [0, 1]
- xs = (zpsi .- zpsi[1]) ./ psio
- # Construct fs matrix: (npsi1 rows, 4 columns)
- fs = zeros(npsi1, 4)
- fs[:, 1] .= zq .* zfb
- fs[:, 2] .= zcppr
- fs[:, 3] .= zq
- # Fit spline with extrapolation boundary condition (bctype = 3)
- sq_in = Spl.CubicSpline(xs, fs; bctype=3)
- # --- Integrate pressure ---
- Spl.spline_integrate!(sq_in) # Integrate in-place, sq_in.fsi filled
- # Make a writable copy of the fs array
- fs_copy = copy(sq_in.fs)
- # Normalize pressure integral column (2nd column)
- fs_copy[:, 2] .= (sq_in.fsi[:, 2] .- sq_in.fsi[ma, 2]) .* psio
- # Refit spline using the modified fs_copy
- sq_in = Spl.CubicSpline(sq_in._xs, fs_copy; bctype=3)
-
- # --- Copy 2D geometry arrays ---
- mtau = ntnova+1
- ro = zrcp[1, 1]
- zo = zzcp[1, 1]
- ys = range(0, 2π, length=mtau) |> collect
- # Allocate and fill fs array (radial × poloidal × 2 quantities)
- fs = zeros(length(xs), length(ys), 2)
- fs[:, :, 1] .= transpose(zrcp[1:ntnova+1, :])
- fs[:, :, 2] .= transpose(zzcp[1:ntnova+1, :])
-
-
- # Setup bicubic spline with periodic boundary conditions (bctype=2)
- rz_in = Spl.BicubicSpline(xs, ys, fs; bctypex=2, bctypey=2)
- println("--> Finished reading CHEASE equilibrium.")
- println(" Magnetic axis at (ro=$ro, zo=$zo), psio=$psio")
- return InverseRunInput(config,sq_in,rz_in,ro,zo,psio)
-end
-
-"""
- _read_chease(equil_config)
-
-Parses a binary CHEASE file, creates initial 1D and 2D splines, and bundles
-them into a `InverseRunInput` object.
-
-## Arguments:
-- `equil_config`: The `EquilConfig` object containing the filename and parameters.
-## Returns:
-- A `InverseRunInput` object ready for the inverse solver.
-"""
-
-function read_chease(config::EquilibriumConfig)
- println("--> Reading CHEASE file: $(config.control.eq_filename)")
- diagnostics = false # Set to true to enable detailed print output
- open(config.control.eq_filename, "r") do io
- # Read first 3 integers
- seekstart(io)
- read(io, UInt32) # skip record length at start
- ntnova = read(io, Int32)
- npsi1 = read(io, Int32)
- nsym = read(io, Int32)
- read(io, UInt32) # skip record length at end
-
- if diagnostics
- println("Header:")
- println(" ntnova = $ntnova Type=$(typeof(ntnova)) Bytes=$(sizeof(ntnova))")
- println(" npsi1 = $npsi1 Type=$(typeof(npsi1)) Bytes=$(sizeof(npsi1))")
- println(" nsym = $nsym Type=$(typeof(nsym)) Bytes=$(sizeof(nsym))")
- end
-
- # Read next 5 Float64 values (axx)
- read(io, UInt32) # skip record length at start
- axx = [read(io, Float64) for _ in 1:5]
- if diagnostics
- println("\naxx array (expected 5 Float64 values):")
- for (i, val) in enumerate(axx)
- println(" axx[$i] = $val Type=$(typeof(val)) Bytes=$(sizeof(val))")
- end
- end
- read(io, UInt32) # skip record length at end
-
- # --- Helper function ---
- function print_summary(name, arr)
- n = length(arr)
- first5 = arr[1:min(5, n)]
- last5 = arr[max(1, n-4):end]
- println("$name first 5: ", first5)
- println("$name last 5: ", last5)
- end
-
- # --- Pre-allocate Arrays ---
- zcpr = zeros(npsi1 - 1)
- zcppr = zeros(npsi1)
- zq = zeros(npsi1)
- zdq = zeros(npsi1)
- ztmf = zeros(npsi1)
- ztp = zeros(npsi1)
- zfb = zeros(npsi1)
- zfbp = zeros(npsi1)
- zpsi = zeros(npsi1)
- zpsim = zeros(npsi1 - 1)
-
- # --- Read 1D arrays from file ---
- for (name, arr) in zip(
- ("zcpr","zcppr","zq","zdq","ztmf","ztp","zfb","zfbp","zpsi","zpsim"),
- (zcpr, zcppr, zq, zdq, ztmf, ztp, zfb, zfbp, zpsi, zpsim)
- )
- read(io, UInt32) # skip record length at start
- read!(io, arr)
- read(io, UInt32) # skip record length at end
- if diagnostics print_summary(name, arr); end
- end
-
- # --- Prepare spline & geometry ---
- ma = npsi1 - 1
- psio = zpsi[npsi1] - zpsi[1]
- xs = (zpsi .- zpsi[1]) ./ psio
-
- fs = zeros(npsi1, 4)
- fs[:, 1] .= ztmf
- fs[:, 2] .= zcppr
- fs[:, 3] .= zq
-
- sq_in = Spl.spline_setup(xs, fs; bctype=3)
- Spl.spline_integrate!(sq_in)
- fs_copy = copy(sq_in.fs)
- fs_copy[:, 2] .= (sq_in.fsi[:, 2] .- sq_in.fsi[ma, 2]) .* psio
- sq_in = Spl.spline_setup(sq_in._xs, fs_copy; bctype=3)
-
- # --- Setup parameters ---
- mtau = ntnova
-
- # Allocate fs array (radial × poloidal × 2)
- fs = zeros(npsi1, mtau, 2)
-
- # Allocate buffer (Fortran: ALLOCATE(buffer(ntnova+3, npsi1)))
- buffer = zeros(Float64, ntnova+3, npsi1)
-
- # --- First read (R data) ---
- read(io, UInt32) # skip record length at start
- read!(io, buffer) # READ(in_unit) buffer
- read(io, UInt32) # skip record length at end
- ro = buffer[1, 1] # ro = buffer(1,1)
- if diagnostics println("ro = $ro"); end
-
- # Fill with r-coordinates
- fs[:, :, 1] .= transpose(buffer[1:ntnova, :])
-
- # --- Second read (Z data) ---
- read(io, UInt32) # skip record length at start
- read!(io, buffer) # READ(in_unit) buffer
- read(io, UInt32) # skip record length at end
- zo = buffer[1, 1] # zo = buffer(1,1)
- if diagnostics println("zo = $zo"); end
-
- # Fill with z-coordinates
- fs[:, :, 2] .= transpose(buffer[1:ntnova, :])
-
- # Construct ys grid (0..2π, length = mtau)
- ys = range(0, 2π, length=mtau) |> collect
-
- # Setup bicubic spline with periodic boundary conditions
- rz_in = Spl.bicube_setup(xs, ys, fs; bctypex=2, bctypey=2)
-
- if diagnostics
- # --- Print first 5 and last 5 entries of each slice ---
- for k in 1:2
- flat = vec(fs[:, :, k]) # flatten to 1D
- n = length(flat)
- println("Slice $k:")
- println(" First 5 entries: ", flat[1:5])
- println(" Last 5 entries: ", flat[n-4:n])
- end
- end
-
-
- println("--> Finished reading CHEASE equilibrium.")
- println(" Magnetic axis at (ro=$ro, zo=$zo), psio=$psio")
-
- return InverseRunInput(config, sq_in, rz_in, ro, zo, psio)
- end
-end
\ No newline at end of file
diff --git a/src/Equilibrium/Sources/Analytic/Analytic.jl b/src/Equilibrium/Sources/Analytic/Analytic.jl
new file mode 100644
index 0000000000..a4aa5c1413
--- /dev/null
+++ b/src/Equilibrium/Sources/Analytic/Analytic.jl
@@ -0,0 +1,39 @@
+"""
+ AnalyticEquilibriumConfig
+
+Supertype of the parameter structs of the analytic equilibrium kinds. Each subtype is the
+`config_type` of one `ANALYTIC_EQ` row, which pairs it with an `eq_type`, its deck section,
+and its solver.
+"""
+abstract type AnalyticEquilibriumConfig end
+
+include("Solovev.jl")
+include("LargeAspectRatio.jl")
+include("TJAnalytic.jl")
+
+"""
+ AnalyticEqSpec
+
+Single-source-of-truth entry describing one analytic-equilibrium kind: the `gpec.toml`
+section that carries its parameters, the `*Config` type built from that section, and the
+run function that turns the config into solver input.
+
+## Fields
+
+ - `section::String` — `gpec.toml` section, the config type's name without `Config` (e.g. `"Solovev"`)
+ - `config_type::DataType` — `*Config` type, built from the section's keys as keywords
+ - `run_fn::Function` — `(EquilibriumConfig, config) -> eq_input` solver entry point
+"""
+struct AnalyticEqSpec
+ section::String
+ config_type::DataType
+ run_fn::Function
+end
+
+# Registry of analytic equilibrium kinds, keyed by the internal eq_type each config implies. `run_input` and the
+# deck parser both dispatch off this table, so adding a new analytic kind is one new row.
+const ANALYTIC_EQ = Dict(
+ "sol" => AnalyticEqSpec("Solovev", SolovevConfig, sol_run),
+ "lar" => AnalyticEqSpec("LargeAspectRatio", LargeAspectRatioConfig, lar_run),
+ "tj_analytic" => AnalyticEqSpec("TJAnalytic", TJAnalyticConfig, tj_analytic_run)
+)
diff --git a/src/Equilibrium/Sources/Analytic/LargeAspectRatio.jl b/src/Equilibrium/Sources/Analytic/LargeAspectRatio.jl
new file mode 100644
index 0000000000..e6f4882c50
--- /dev/null
+++ b/src/Equilibrium/Sources/Analytic/LargeAspectRatio.jl
@@ -0,0 +1,260 @@
+"""
+ LargeAspectRatioConfig(...)
+
+A struct holding parameters for the Large Aspect Ratio (LAR) plasma equilibrium model.
+
+## Fields:
+
+ - `r0`: The major radius of the plasma [m].
+ - `a`: The minor radius of the plasma [m].
+ - `beta0`: The beta value on axis (normalized pressure).
+ - `q0`: The safety factor on axis.
+ - `qa`: Edge safety factor; not used by any current `sigma_type`.
+ - `B0`: On-axis toroidal field in T (scales F and P).
+ - `p_pres`: The exponent for the pressure profile, defined as `p00 * (1 - (r / a)^2)^p_pres`.
+ - `p_sig`: The exponent that determines the shape of the current-related function profile.
+ - `sigma_type`: The sigma profile, "default", "wesson" (`sigma0 * (1 - (r / a)^2)^p_sig`) or "hollow"
+ (`sigma0 * (1 + hollow * (r / a)^2) * (1 - (r / a)^2)^p_sig`, reversed shear when `hollow` is large enough).
+ - `hollow`: The off-axis current enhancement of the "hollow" sigma profile (unused by the other profiles).
+ - `mtheta`: The number of grid points in the poloidal direction.
+ - `ma`: The number of grid points in the radial direction.
+ - `zeroth`: If set to true, it neglects the Shafranov shift
+"""
+@kwdef struct LargeAspectRatioConfig <: AnalyticEquilibriumConfig
+ r0::Float64 = 10.0
+ a::Float64 = 1.0
+ beta0::Float64 = 1e-3
+ q0::Float64 = 1.5
+ qa::Float64 = 3.6 # Edge safety factor (legacy field; not consumed by current sigma_type options)
+ B0::Float64 = 1.0 # On-axis toroidal field [T] (scales F and P)
+ p_pres::Float64 = 2.0
+ p_sig::Float64 = 1.0
+ sigma_type::String = "default"
+ hollow::Float64 = 0.0
+ mtheta::Int = 128
+ ma::Int = 128
+ zeroth::Bool = false
+end
+
+"""
+ lar_init_conditions(rmin, lar_input) -> (r, y)
+
+Initializes the starting radius and state vector for solving the LAR ODE system.
+
+## Arguments:
+
+ - `rmin`: Normalized starting radius (as a fraction of `lar_a`).
+ - `lar_input`: A `LargeAspectRatioConfig` object containing equilibrium parameters.
+
+## Returns:
+
+ - `r`: Physical radius corresponding to `rmin * lar_a`.
+ - `y`: Initial state vector of length 5.
+"""
+function lar_init_conditions(rmin::Float64, lar_input::LargeAspectRatioConfig)
+ lar_a = lar_input.a
+ lar_r0 = lar_input.r0
+ q0 = lar_input.q0
+
+ # Keep rmin away from the r = 0 singularity of the LAR equations.
+ if rmin < 1e-6
+ @warn "Setting rmin to at least 1e-6 to avoid singularities in LAR equations."
+ rmin_safe = 1e-6
+ else
+ rmin_safe = rmin
+ end
+
+ r = rmin_safe * lar_a
+ y = zeros(5)
+
+ y[1] = r^2 / (lar_r0 * q0)
+ y[2] = 1.0
+ y[3] = y[1] * lar_r0 / 2
+
+ dy = zeros(5)
+ lar_der(dy, r, y, lar_input)
+
+ y[5] = dy[5] * r / 4
+
+ q = r^2 * y[2] / (lar_r0 * y[1])
+ y[4] = (q / r)^2 * y[5] / 2
+
+ return r, y
+end
+
+# Current profile σ(x), x = r/a, with σ(0) = sigma0 for every `sigma_type`.
+function _lar_sigma(x::Float64, sigma0::Float64, lar_input::LargeAspectRatioConfig)
+ p_sig = lar_input.p_sig
+ lar_input.sigma_type == "wesson" && return sigma0 * (1 - x^2)^p_sig
+ lar_input.sigma_type == "hollow" && return sigma0 * (1 + lar_input.hollow * x^2) * (1 - x^2)^p_sig
+ return sigma0 / (1 + x^(2 * p_sig))^(1 + 1 / p_sig)
+end
+
+"""
+ lar_der(dy, r, y, lar_input)
+
+Evaluates the spatial derivatives of the LAR (Large Aspect Ratio) equilibrium ODE system
+at a given radius `r`, using the current state vector `y` and equilibrium parameters.
+
+## Arguments:
+- `dy`: A preallocated vector where the computed derivatives will be stored (in-place).
+- `r`: The radial position at which the derivative is evaluated.
+- `y`: The current state vector.
+- `lar_input`: A `LargeAspectRatioConfig` object containing equilibrium shaping parameters.
+
+## Returns:
+- 0; the derivatives are written to `dy` in place.
+"""
+
+function lar_der(dy::Vector{Float64}, r::Float64, y::Vector{Float64}, lar_input::LargeAspectRatioConfig)
+ lar_a = lar_input.a
+ lar_r0 = lar_input.r0
+
+ q0 = lar_input.q0
+
+ beta0 = lar_input.beta0
+ p00 = beta0 / 2.0
+ p_pres = lar_input.p_pres
+
+ x = r / lar_a
+ xfac = 1 - x^2
+ pp = -2 * p_pres * p00 * x * xfac^(p_pres - 1) # p'
+ sigma0 = 2.0 / (q0 * lar_r0)
+
+ sigma = _lar_sigma(x, sigma0, lar_input)
+
+ # LAR equations have singularities at r=0; ensure we never evaluate there
+ @assert r > 0.0 "LAR equations require r > 0 (called with r=$r)"
+
+ bsq = (y[1] / r)^2 + y[2]^2 # B²
+ q = r^2 * y[2] / (lar_r0 * y[1])
+
+ dy[1] = -pp / bsq * y[1] + sigma * y[2] * r
+ dy[2] = -pp / bsq * y[2] - sigma * y[1] / r
+ dy[3] = y[1] * lar_r0 / r
+ dy[4] = (q / r)^2 * y[5] / r
+ dy[5] = y[2] * (r / q)^2 * (r / lar_r0) * (1 - 2 * (lar_r0 * q / y[2])^2 * pp)
+
+ return 0
+end
+
+"""
+ lar_run(equil_input, lar_config) -> InverseRunInput
+
+Solve the LAR radial ODE system for the profiles of `lar_config` and return the profiles and
+Shafranov-shifted circular flux surfaces as inverse-solver input.
+"""
+
+function lar_run(equil_input::EquilibriumConfig, lar_config::LargeAspectRatioConfig)
+ # The profile ODEs need a pressure exponent above 1.
+ fields = (f => getfield(lar_config, f) for f in fieldnames(LargeAspectRatioConfig))
+ lar_input = LargeAspectRatioConfig(; fields..., p_pres=max(lar_config.p_pres, 1.001))
+ rmin = 1e-4
+ lar_a = lar_input.a
+ lar_r0 = lar_input.r0
+ q0 = lar_input.q0
+ beta0 = lar_input.beta0
+
+ p00 = beta0 / 2.0
+
+ sigma0 = 2.0 / (q0 * lar_r0)
+
+ ma = lar_input.ma
+ mtau = lar_input.mtheta
+
+ function dydr(du, u, p, r)
+ lar_input = p
+ return lar_der(du, r, u, lar_input)
+ end
+
+ r0, y0 = lar_init_conditions(rmin, lar_input)
+ tspan = (r0, lar_a)
+ p = lar_input
+
+ prob = ODEProblem(dydr, y0, tspan, p)
+
+ sol = solve(prob, Rosenbrock23(; autodiff=false); reltol=equil_input.flux_surface_rtol, abstol=equil_abstol(equil_input.flux_surface_rtol), dense=false)
+ check_equil_solve(sol, "large-aspect-ratio radial profiles")
+
+ r_arr = sol.t
+ y_mat = reduce(hcat, sol.u)'
+ steps = length(r_arr)
+
+ temp = zeros(steps, 9)
+ for i in 1:steps
+ r = r_arr[i]
+ @views y = y_mat[i, :]
+ x = r / lar_a
+ xfac = 1 - x^2
+ pval = p00 * xfac^lar_input.p_pres
+ sigma = _lar_sigma(x, sigma0, lar_input)
+ q = r^2 * y[2] / (lar_r0 * y[1])
+ temp[i, 1] = r
+ temp[i, 2] = y[1]
+ temp[i, 3] = y[2]
+ temp[i, 4] = y[3]
+ temp[i, 5] = y[4]
+ temp[i, 6] = y[5]
+ temp[i, 7] = pval
+ temp[i, 8] = sigma
+ temp[i, 9] = q
+ end
+
+ xs_r = temp[:, 1]
+ fs_r = temp[:, 2:9]
+ spl = cubic_interp(xs_r, Series(fs_r); extrap=ExtendExtrap())
+ spl_deriv = deriv1(spl)
+
+ dr = lar_a / (ma + 1)
+ r = 0.0
+ psio = temp[end, 4] # ψ_edge
+
+ sq_xs = zeros(ma + 1)
+ sq_fs = zeros(ma + 1, 3)
+ r_nodes = zeros(ma + 1)
+ rzphi_y_nodes = range(0.0, 1.0; length=mtau + 1)
+ rzphi_fs_nodes = zeros(ma + 1, mtau + 1, 2)
+
+ hint = Ref(1)
+ for ia in 1:(ma+1)
+ r += dr
+ r_nodes[ia] = r
+ f = spl(r; hint=hint)
+ f1 = spl_deriv(r; hint=hint)
+ dψdr = f1[3]
+
+ # Fill spline data for sq_in
+ sq_xs[ia] = f[3] / psio # ψ / psio
+ sq_fs[ia, 1] = lar_r0 * f[2] # F = R0 * Bphi
+ sq_fs[ia, 2] = f[6] # P
+ sq_fs[ia, 3] = f[8] # q
+
+ # Compute Shafranov shift and fill rzphi grid
+ r2 = -(f[4] * r / f[8]) / dψdr
+ if lar_input.zeroth
+ r2 = 0.0
+ end
+ for itau in 1:(mtau+1)
+ θ = 2π * (itau - 1) / mtau
+ cosθ, sinθ = cos(θ), sin(θ)
+ rfac = r + r2 * cosθ
+ rzphi_fs_nodes[ia, itau, 1] = lar_r0 + rfac * cosθ
+ rzphi_fs_nodes[ia, itau, 2] = rfac * sinθ
+ end
+ end
+
+ sq_in = cubic_interp(sq_xs, Series(sq_fs); extrap=ExtendExtrap())
+ # rz_in_xs is ψ_N (see InverseRunInput), not physical r; the two only coincide when lar_a ≈ 1.
+ rz_in_xs = sq_xs
+ rz_in_ys = collect(rzphi_y_nodes)
+
+ @views rzphi_fs_nodes[:, end, :] .= rzphi_fs_nodes[:, 1, :]
+
+ itp_2d_opts = (bc=(CubicFit(), PeriodicBC()), extrap=(ExtendExtrap(), WrapExtrap()))
+ rz_in_R = cubic_interp((rz_in_xs, rz_in_ys), rzphi_fs_nodes[:, :, 1]; itp_2d_opts...)
+ rz_in_Z = cubic_interp((rz_in_xs, rz_in_ys), rzphi_fs_nodes[:, :, 2]; itp_2d_opts...)
+
+ # LAR equilibrium has midplane symmetry, so magnetic axis is at Z = 0.
+ # Analytic: ingest=nothing — replay regenerates from the [LargeAspectRatio] deck section.
+ return InverseRunInput(equil_input, sq_in, rz_in_xs, rz_in_ys, rz_in_R, rz_in_Z, lar_r0, 0.0, psio, nothing)
+end
diff --git a/src/Equilibrium/Sources/Analytic/Solovev.jl b/src/Equilibrium/Sources/Analytic/Solovev.jl
new file mode 100644
index 0000000000..ed8dbff05f
--- /dev/null
+++ b/src/Equilibrium/Sources/Analytic/Solovev.jl
@@ -0,0 +1,95 @@
+"""
+ SolovevConfig(...)
+
+A struct holding parameters for the Solov'ev (SOL) plasma equilibrium model.
+
+## Fields:
+
+ - `mr`: number of radial grid zones
+ - `mz`: number of axial grid zones
+ - `ma`: number of flux grid zones
+ - `elongation`: elongation
+ - `a`: minor radius
+ - `r0`: major radius
+ - `q0`: safety factor at the o-point
+ - `p0fac`: scale on-axis pressure (P-> P+P0*p0fac. beta changes. Phi,q constant)
+ - `b0fac`: scale toroidal field at constant beta (s*Phi,s*f,s^2*P. bt changes. Shape,beta constant)
+ - `f0fac`: scale toroidal field at constant pressure (s*f. beta,q changes. Phi,p,bp constant)
+"""
+@kwdef struct SolovevConfig <: AnalyticEquilibriumConfig
+ mr::Int = 128 # number of radial grid zones
+ mz::Int = 128 # number of axial grid zones
+ ma::Int = 128 # number of flux grid zones
+ elongation::Float64 = 1.6 # elongation
+ a::Float64 = 0.33 # minor radius
+ r0::Float64 = 1.0 # major radius
+ q0::Float64 = 1.9 # safety factor at the o-point
+ p0fac::Float64 = 1 # scale on-axis pressure (P-> P+P0*p0fac. beta changes. Phi,q constant)
+ b0fac::Float64 = 1 # scale toroidal field at constant beta (s*Phi,s*f,s^2*P. bt changes. Shape,beta constant)
+ f0fac::Float64 = 1 # scale toroidal field at constant pressure (s*f. beta,q changes. Phi,p,bp constant)
+end
+
+"""
+ sol_run(equil_inputs, sol_inputs) -> DirectRunInput
+
+Build the Solov'ev analytic ψ(R, Z) and 1D profiles from `sol_inputs` as direct-solver input.
+Port of Fortran `sol.f`.
+"""
+function sol_run(equil_inputs::EquilibriumConfig, sol_inputs::SolovevConfig)
+
+ mr = sol_inputs.mr
+ mz = sol_inputs.mz
+ ma = sol_inputs.ma
+ e = sol_inputs.elongation
+ a = sol_inputs.a
+ r0 = sol_inputs.r0
+ q0 = sol_inputs.q0
+ p0fac = sol_inputs.p0fac
+ b0fac = sol_inputs.b0fac
+ f0fac = sol_inputs.f0fac
+
+ # Validate inputs
+ if p0fac < 1.0
+ @warn "Forcing p0fac ≥ 1 (no negative pressure)"
+ p0fac = 1.0
+ end
+
+ # Compute scalar data
+ f0 = r0 * b0fac
+ psio = e * f0 * a * a / (2 * q0 * r0)
+ psifac = psio / (a * r0)^2
+ efac = 1 / (e * e)
+ pfac = 2 * psio^2 * (e * e + 1) / (a * r0 * e)^2
+ rmin = r0 - 1.5 * a
+ rmax = r0 + 1.5 * a
+ zmax = 1.5 * e * a
+ zmin = -zmax
+
+ # zeros, not undef: only columns 1-3 are filled, so column 4 must stay a deterministic 0.
+ sqfs = zeros(ma + 1, 4)
+ psis = [(ia / (ma + 1))^2 for ia in 1:(ma+1)]
+ sqfs[:, 1] .= f0 .* f0fac
+ sqfs[:, 2] .= pfac .* (1 .* p0fac .- psis)
+ sqfs[:, 3] .= 0.0
+ sq_in = cubic_interp(psis, Series(sqfs); extrap=ExtendExtrap())
+
+ # Compute 2D data and spline
+ r = [rmin + i * (rmax - rmin) / mr for i in 0:mr]
+ z = [zmin + j * (zmax - zmin) / mz for j in 0:mz]
+ psifs = Array{Float64}(undef, mr + 1, mz + 1)
+ for iz in 1:(mz+1)
+ for ir in 1:(mr+1)
+ psifs[ir, iz] = psio - psifac * (efac * (r[ir] * z[iz])^2 + (r[ir]^2 - r0^2)^2 / 4)
+ end
+ end
+ psi_in_xs = r
+ psi_in_ys = z
+ psi_in = cubic_interp((psi_in_xs, psi_in_ys), psifs; extrap=ExtendExtrap())
+
+ # Print out equilibrium info
+ @info "Generating Solovev equilibrium: mr=$mr, mz=$mz, ma=$ma, e=$(@sprintf("%.3f", e)), a=$(@sprintf("%.3f", a)), r0=$(@sprintf("%.3f", r0)), q0=$(@sprintf("%.3f", q0))"
+
+ # 1 is bt_sign=+1: Solovev has positive Bt by construction (f0 = r0 * b0fac > 0).
+ # Analytic equilibria carry positive field and current; ingest=nothing — replay regenerates from the [Solovev] deck section.
+ return DirectRunInput(equil_inputs, sq_in, psi_in, psi_in_xs, psi_in_ys, rmin, rmax, zmin, zmax, psio, 1, 1, nothing)
+end
diff --git a/src/Equilibrium/Sources/Analytic/TJAnalytic.jl b/src/Equilibrium/Sources/Analytic/TJAnalytic.jl
new file mode 100644
index 0000000000..6d67691a05
--- /dev/null
+++ b/src/Equilibrium/Sources/Analytic/TJAnalytic.jl
@@ -0,0 +1,501 @@
+"""
+ TJAnalyticConfig(...)
+
+Parameters for the TJ-analytic cylindrical large-aspect-ratio equilibrium, a GPEC adaptation of
+the analytic profile family of R. Fitzpatrick's TJ code (https://github.com/rfitzp/TJ), not a
+re-implementation of TJ. The q profile is
+
+ f1(r) = [1 - (1-r²)^ν] / (ν·q0)
+ q(r) = r² / f1(r)
+
+with the current peaking ν solved so q matches `qa` at the edge (ν = qa/q0 at lowest order). The
+pressure is p₂(r) = p0·(1-r²)^μ with μ = `pressure_peaking`. Lengths are normalized to R₀, fields
+to B₀. `solver` picks the pipeline: `:inverse` feeds the flux-surface geometry to the inverse
+solver, `:direct` builds ψ(R, Z) for the direct solver.
+"""
+@kwdef struct TJAnalyticConfig <: AnalyticEquilibriumConfig
+ r0::Float64 = 10.0 # Major radius R₀ [m]
+ a::Float64 = 1.0 # Minor radius a [m] (ε = a/R₀)
+ q0::Float64 = 1.5 # On-axis safety factor
+ qa::Float64 = 3.6 # Edge safety factor
+ p0::Float64 = 0.001 # Normalized on-axis pressure
+ pressure_peaking::Float64 = 2.0 # Pressure peaking exponent μ: p₂ = p0·(1-r²)^μ
+ B0::Float64 = 12.0 # On-axis toroidal field [T]
+ ma::Int = 128 # Radial grid points
+ mtheta::Int = 128 # Poloidal grid points
+ zeroth::Bool = false # If true, suppress Shafranov shift
+ solver::Symbol = :inverse # Equilibrium pipeline: :inverse or :direct
+end
+
+"""
+ tj_analytic_f1(x, nu, qc)
+
+TJ-analytic poloidal flux function f1(x) where x = r/a, following the
+analytic-profile parameterization of R. Fitzpatrick's TJ code
+(https://github.com/rfitzp/TJ). Uses a Taylor expansion near the axis
+for numerical stability.
+"""
+function tj_analytic_f1(x::Float64, nu::Float64, qc::Float64)
+ if x < 0.1
+ x2 = x * x
+ return x2 * (1 - (nu - 1) * x2 / 2 + (nu - 1) * (nu - 2) * x2 * x2 / 6 -
+ (nu - 1) * (nu - 2) * (nu - 3) * x2 * x2 * x2 / 24) / qc
+ else
+ return (1 - (1 - x * x)^nu) / (nu * qc)
+ end
+end
+
+"""
+ tj_analytic_f1p(x, nu, qc)
+
+Derivative of the TJ-analytic f1 with respect to x (= r/a). See
+R. Fitzpatrick's TJ code (https://github.com/rfitzp/TJ) for the original
+parameterization.
+"""
+function tj_analytic_f1p(x::Float64, nu::Float64, qc::Float64)
+ if x < 0.1
+ x2 = x * x
+ return 2 * x * (1 - (nu - 1) * x2 + (nu - 1) * (nu - 2) * x2 * x2 / 2 -
+ (nu - 1) * (nu - 2) * (nu - 3) * x2 * x2 * x2 / 6) / qc
+ else
+ return 2 * x * (1 - x * x)^(nu - 1) / qc
+ end
+end
+
+"""
+Internal parameter bundle for the TJ-analytic shape ODE (ψ, g₂, H₁, H₁', f₃) —
+GPEC adaptation of the analytic shape ODE used in R. Fitzpatrick's TJ code
+(https://github.com/rfitzp/TJ), shared by the inverse and direct pipelines.
+
+Fields:
+
+ - physical: a, R0, qc, mu, pc, B0
+ - derived: epsa2 = (a/R0)²
+ - near-axis BC constants: rmin, x0 = rmin, r0 = rmin·a, f1c = 1/qc,
+ p2ppc = d²p₂/dx²|_0 = −2·μ·pc
+"""
+struct TJAnalyticShapeParams
+ a::Float64
+ R0::Float64
+ qc::Float64
+ mu::Float64
+ pc::Float64
+ B0::Float64
+ epsa2::Float64
+ rmin::Float64
+ x0::Float64
+ r0::Float64
+ f1c::Float64
+ p2ppc::Float64
+end
+
+function TJAnalyticShapeParams(tj::TJAnalyticConfig; rmin::Float64=1e-4)
+ a, R0 = tj.a, tj.r0
+ mu = max(tj.pressure_peaking, 1.001)
+ return TJAnalyticShapeParams(
+ a, R0, tj.q0, mu, tj.p0, tj.B0,
+ (a / R0)^2,
+ rmin, rmin, rmin * a,
+ 1.0 / tj.q0,
+ -2.0 * mu * tj.p0
+ )
+end
+
+"""
+RHS for the TJ-analytic shape ODE (R. Fitzpatrick's TJ code parameterization,
+https://github.com/rfitzp/TJ). State: y[1]=ψ, y[2]=g₂, y[3]=H₁, y[4]=H₁',
+y[5]=f₃. The original derivation is written in x = r/a; we advance in
+physical r = a·x so d/dr = (1/a)·d/dx.
+
+The params argument carries TJAnalyticShapeParams fields plus the current `nu`.
+"""
+function tj_analytic_shape_rhs!(dy, y, params, r)
+ (; a, B0, qc, mu, pc, epsa2, nu) = params
+ x = r / a
+ xfac = max(1 - x^2, 0.0)
+ f1 = tj_analytic_f1(x, nu, qc)
+ f1px = tj_analytic_f1p(x, nu, qc)
+ p2px = -2 * mu * pc * x * xfac^(mu - 1)
+
+ # The TJ-analytic model writes its physical ψ as εa²·B₀·R₀²·Psi_norm where
+ # dPsi_norm/dr_norm = (f1 + εa²·f3)/r_norm (cf. Fitzpatrick's TJ code).
+ # Converting to physical r = a·r_norm gives dψ/dr = a²·B₀·(f1+εa²·f3)/r.
+ f3_cur = y[5]
+ dy[1] = B0 * (f1 + epsa2 * f3_cur) * a^2 / r
+
+ # g₂'(x) = −p2'(x) − f1·f1'(x)/x²
+ dy[2] = (-p2px - f1 * f1px / (x * x)) / a
+
+ # H₁''(x) = −(2f1'/f1 − 1/x)·H₁' − 1 + 2x³·p2'/f1²
+ facf = 2 * f1px / f1 - 1 / x
+ facp = 2 * x^3 * p2px / (f1 * f1)
+ H1, H1p = y[3], y[4]
+ dy[3] = H1p / a
+ dy[4] = (-facf * H1p - 1 + facp) / a
+
+ # f₃'(x) for Hₙ = Vₙ = 0 (n ≥ 2 harmonics rescaled to zero, as in the
+ # TJ-analytic benchmark configuration of Fitzpatrick's TJ code).
+ g2, f3 = y[2], y[5]
+ f3p_x =
+ -f3 * f1px / f1 -
+ f1 * (3 * x^2 / 2 - 2 * x * H1p + H1p^2) / x +
+ f1px * (g2 - 3 * x^2 / 4 + H1 + 3 * H1p^2 / 2) +
+ x^2 * p2px * (g2 + x^2 / 2 - 3 * x * H1p - 2 * H1) / f1
+ dy[5] = f3p_x / a
+ return nothing
+end
+
+"""
+Initial conditions at x = x0, matching the TJ-analytic model's near-axis
+expansion (cf. R. Fitzpatrick's TJ code, https://github.com/rfitzp/TJ).
+"""
+function tj_analytic_shape_initial(p::TJAnalyticShapeParams, nu::Float64)
+ f1_0 = tj_analytic_f1(p.x0, nu, p.qc)
+ y0 = zeros(5)
+ y0[1] = p.B0 * f1_0 * p.a^2 / 2 # ψ(r0)
+ y0[2] = -(p.f1c^2 + p.p2ppc / 2) * p.x0^2 # g₂
+ y0[3] = (2 * p.p2ppc / p.f1c^2 - 1) * p.x0^2 / 8 # H₁
+ y0[4] = (2 * p.p2ppc / p.f1c^2 - 1) * p.x0 / 4 # H₁'
+ y0[5] = 0.0 # f₃
+ return y0
+end
+
+"""
+Integrate the TJ-analytic shape ODE for the given ν. Pass `saveat` to collect
+output on a prescribed dense grid (used by `tj_analytic_run_direct` so the
+downstream Hₙ / ψ splines sit on uniform nodes); leave it `nothing` for
+the default adaptive save pattern used by `tj_analytic_run_inverse`. `reltol` and `abstol` go to the
+Vern9 solve; `abstol` defaults to `equil_abstol(reltol)`.
+"""
+function tj_analytic_shape_solve(p::TJAnalyticShapeParams, nu::Float64;
+ reltol::Float64=1e-7, abstol::Float64=equil_abstol(reltol),
+ saveat=nothing)
+ rhs_params = (; p.a, p.B0, p.qc, p.mu, p.pc, p.epsa2, nu=nu)
+ prob = ODEProblem(tj_analytic_shape_rhs!, tj_analytic_shape_initial(p, nu), (p.r0, p.a), rhs_params)
+ sol = if saveat === nothing
+ solve(prob, Vern9(); reltol, abstol, dense=false)
+ else
+ solve(prob, Vern9(); reltol, abstol, saveat=saveat)
+ end
+ return check_equil_solve(sol, "TJ-analytic shaping functions at ν = $nu")
+end
+
+"""
+TJ-analytic ν root-find (Fitzpatrick's `Setnu` / `GetNu` in
+https://github.com/rfitzp/TJ): solve for ν so that q₂(x=1) matches
+`qa_target`.
+
+`q₂ = x²·(1+εa²·g₂)·exp(−εa²·f3/f1)/f1`; at x=1 and low β this picks up an
+O(εa²) correction relative to the lowest-order guess ν = qa/qc, which
+matters for the TJ-analytic benchmark at large ε. Falls back to the
+lowest-order ν if the root-find has no bracket or does not converge; an
+error from a trial shaping solve propagates.
+"""
+function tj_analytic_find_nu(p::TJAnalyticShapeParams, qa_target::Float64; reltol::Float64=1e-7, abstol::Float64=equil_abstol(reltol))
+ function q2_edge(nu::Float64)
+ sol = tj_analytic_shape_solve(p, nu; reltol, abstol)
+ g2end = sol.u[end][2]
+ f3end = sol.u[end][5]
+ f1end = tj_analytic_f1(1.0, nu, p.qc)
+ return (1 + p.epsa2 * g2end) * exp(-p.epsa2 * f3end / f1end) / f1end
+ end
+ nu_guess = qa_target / p.qc
+ return try
+ find_zero(nu -> q2_edge(nu) - qa_target, (0.5 * nu_guess, 2 * nu_guess);
+ atol=1e-8, rtol=1e-10)
+ catch err
+ # Only a failed root-find falls back; a shaping solve that stopped early must propagate.
+ fallback = err isa Roots.ConvergenceFailed || (err isa ArgumentError && occursin("not a bracketing interval", err.msg))
+ fallback || rethrow()
+ @warn "ν root-find failed for TJ-analytic equilibrium; falling back to lowest-order ν = qa/qc" exception = (err, catch_backtrace())
+ nu_guess
+ end
+end
+
+"""
+ tj_analytic_run(equil_input, tj_input)
+
+Solve the TJ-analytic equilibrium with the pipeline `tj_input.solver` names, `:inverse`
+([`tj_analytic_run_inverse`](@ref)) or `:direct` ([`tj_analytic_run_direct`](@ref)).
+"""
+function tj_analytic_run(equil_input::EquilibriumConfig, tj::TJAnalyticConfig)
+ tj.solver === :inverse && return tj_analytic_run_inverse(equil_input, tj)
+ tj.solver === :direct && return tj_analytic_run_direct(equil_input, tj)
+ return error("TJAnalytic solver = \"$(tj.solver)\" is not one of \"inverse\", \"direct\"")
+end
+
+"""
+ tj_analytic_run_inverse(equil_input, tj_input)
+
+Build the TJ-analytic equilibrium of `tj` as inverse-solver input. With zero
+edge shaping (Hna = Vna = 0, the TJ benchmark configuration) the flux surfaces are shifted circles
+
+ R(r,θ) = R₀ + Δ(r) + α(r)·r·cos θ
+ Z(r,θ) = α(r)·r·sin θ
+
+with Δ = R₀·εa²·H₁(x), α = 1 − εa²·(x²/8 − H₁/2), εa = a/R₀ and x = r/a, from the shaping ODE.
+The output profiles are F = R₀·B₀·(1 + εa²·g₂) and q₂ = x²·(1 + εa²·g₂)·exp(−εa²·f₃/f1)/f1.
+The n ≥ 2 shaping harmonics Hₙ, Vₙ are not included.
+"""
+function tj_analytic_run_inverse(equil_input::EquilibriumConfig, tj::TJAnalyticConfig)
+ a, R0 = tj.a, tj.r0
+ qc, mu = tj.q0, max(tj.pressure_peaking, 1.001)
+ pc, B0 = tj.p0, tj.B0
+ ma, mtau = tj.ma, tj.mtheta
+ p = TJAnalyticShapeParams(tj)
+ epsa2 = p.epsa2
+ p00_phys = B0^2 * epsa2 * pc # μ₀P = B₀²·εa²·p₂ at axis
+
+ nu = tj_analytic_find_nu(p, tj.qa; reltol=equil_input.flux_surface_rtol)
+ sol = tj_analytic_shape_solve(p, nu; reltol=equil_input.flux_surface_rtol)
+
+ r_arr = sol.t
+ y_mat = reduce(hcat, sol.u)'
+ steps = length(r_arr)
+
+ # Profile table columns: r, F, P, q, ψ, g₂, H₁ (F and q as in TJ's EFIT writer).
+ temp = zeros(steps, 7)
+ for i in 1:steps
+ r = r_arr[i]
+ x = r / a
+ xfac = max(1 - x^2, 0.0)
+ f1 = tj_analytic_f1(x, nu, qc)
+
+ ψ = y_mat[i, 1]
+ g2 = y_mat[i, 2]
+ H1 = y_mat[i, 3]
+ f3 = y_mat[i, 5]
+
+ F = R0 * B0 * (1 + epsa2 * g2)
+ P = p00_phys * xfac^mu
+ q = x > 1e-10 ? x^2 * (1 + epsa2 * g2) * exp(-epsa2 * f3 / f1) / f1 : qc
+
+ temp[i, 1] = r
+ temp[i, 2] = F
+ temp[i, 3] = P
+ temp[i, 4] = q
+ temp[i, 5] = ψ
+ temp[i, 6] = g2
+ temp[i, 7] = H1
+ end
+
+ xs_r = temp[:, 1]
+ fs_r = temp[:, 2:7]
+ spl = cubic_interp(xs_r, Series(fs_r); extrap=ExtendExtrap())
+
+ dr = a / (ma + 1)
+ r = 0.0
+ psio = temp[end, 5]
+
+ sq_xs = zeros(ma + 1)
+ sq_fs = zeros(ma + 1, 3)
+ r_nodes = zeros(ma + 1)
+ rzphi_y_nodes = range(0.0, 1.0; length=mtau + 1)
+ rzphi_fs_nodes = zeros(ma + 1, mtau + 1, 2)
+
+ hint = Ref(1)
+ for ia in 1:(ma+1)
+ r += dr
+ r_nodes[ia] = r
+ f = spl(r; hint=hint)
+ # f[1]=F, f[2]=P, f[3]=q, f[4]=ψ, f[5]=g₂, f[6]=H₁
+
+ sq_xs[ia] = f[4] / psio
+ sq_fs[ia, 1] = f[1] # F
+ sq_fs[ia, 2] = f[2] # P
+ sq_fs[ia, 3] = f[3] # q
+
+ if tj.zeroth
+ Δ = 0.0
+ α = 1.0
+ else
+ x = r / a
+ H1_r = f[6]
+ Δ = R0 * epsa2 * H1_r
+ α = 1 - epsa2 * (x^2 / 8 - H1_r / 2)
+ end
+
+ for itau in 1:(mtau+1)
+ θ = 2π * (itau - 1) / mtau
+ rzphi_fs_nodes[ia, itau, 1] = R0 + Δ + α * r * cos(θ)
+ rzphi_fs_nodes[ia, itau, 2] = α * r * sin(θ)
+ end
+ end
+
+ sq_in = cubic_interp(sq_xs, Series(sq_fs); extrap=ExtendExtrap())
+ # rz_in_xs is ψ_N (see InverseRunInput), not physical r; the two only coincide when a ≈ 1.
+ rz_in_xs = sq_xs
+ rz_in_ys = collect(rzphi_y_nodes)
+
+ itp_2d_opts = (bc=(CubicFit(), PeriodicBC()), extrap=(ExtendExtrap(), WrapExtrap()))
+ rz_in_R = cubic_interp((rz_in_xs, rz_in_ys), rzphi_fs_nodes[:, :, 1]; itp_2d_opts...)
+ rz_in_Z = cubic_interp((rz_in_xs, rz_in_ys), rzphi_fs_nodes[:, :, 2]; itp_2d_opts...)
+
+ # Analytic: ingest=nothing — replay regenerates from the [TJAnalytic] deck section.
+ return InverseRunInput(equil_input, sq_in, rz_in_xs, rz_in_ys, rz_in_R, rz_in_Z, R0, 0.0, psio, nothing)
+end
+
+"""
+ tj_analytic_run_direct(equil_input, tj_input; nrbox=257, nzbox=257, rc=1.2)
+
+Build ψ(R, Z) on an `nrbox × nzbox` grid from the TJ-analytic model and return it as direct-solver
+input, so q and δW are recomputed from the 2D geometry instead of taken from the prescribed q₂ (the
+inverse pipeline under-drives the external kink at large ε). Each grid point is mapped to (r, w) by
+the fixed-point iteration of TJ's EFIT writer; ψ comes from the radial ψ-ODE for r < 1, TJ's vacuum
+solution `GetPSIvac` for 1 ≤ r < `rc`, and that value at `rc` scaled by r²/rc² beyond (r, `rc` in
+units of a). Edge shaping is `Hna = Vna = 0`, so only the H₁ Shafranov shift contributes.
+"""
+function tj_analytic_run_direct(equil_input::EquilibriumConfig, tj::TJAnalyticConfig;
+ nrbox::Int=257, nzbox::Int=257, rc::Float64=1.2)
+ a, R0 = tj.a, tj.r0
+ qc, mu = tj.q0, max(tj.pressure_peaking, 1.001)
+ pc, B0 = tj.p0, tj.B0
+ p = TJAnalyticShapeParams(tj)
+ epsa, epsa2 = p.a / p.R0, p.epsa2
+ p00_phys = B0^2 * epsa2 * pc
+
+ # ν root-find (cf. Fitzpatrick TJ's Setnu): q₂(1) = qa_target.
+ nu = tj_analytic_find_nu(p, tj.qa; reltol=equil_input.flux_surface_rtol)
+
+ # Dense uniform saveat: on the adaptive steps the (R, Z) → (r, w) iteration hits spline artifacts.
+ # That inversion also needs a tighter abstol ceiling (1e-10) than the other equilibrium solves.
+ dense_r = collect(range(p.r0, p.a; length=1024))
+ sol = tj_analytic_shape_solve(p, nu; reltol=equil_input.flux_surface_rtol, abstol=equil_abstol(equil_input.flux_surface_rtol, 1e-10), saveat=dense_r)
+ r_arr = sol.t
+ y_mat = reduce(hcat, sol.u)'
+
+ # Radial splines in the TJ-analytic dimensionless x = r/a on a clean grid for H₁ etc.
+ x_nodes = r_arr ./ a
+ ψ_of_r = cubic_interp(r_arr, y_mat[:, 1]; extrap=ExtendExtrap())
+ H1_of_x = cubic_interp(x_nodes, y_mat[:, 3]; extrap=ExtendExtrap())
+ H1p_of_x = cubic_interp(x_nodes, y_mat[:, 4]; extrap=ExtendExtrap())
+ g2_of_x = cubic_interp(x_nodes, y_mat[:, 2]; extrap=ExtendExtrap())
+ f3_of_x = cubic_interp(x_nodes, y_mat[:, 5]; extrap=ExtendExtrap())
+
+ # Edge values needed by GetPSIvac
+ f1a = tj_analytic_f1(1.0, nu, qc)
+ f3a = f3_of_x(1.0)
+ H1a = H1_of_x(1.0)
+ H1ap = H1p_of_x(1.0)
+ psio = ψ_of_r(a) # ψ at r = a (boundary)
+
+ # Psi scaling factor matching the TJ-analytic EFIT writer: Psi_phys = εa²·B0·R0²·Psi_norm
+ psi_scale = epsa2 * B0 * R0^2
+
+ # TJ-analytic GetHHvac for n = 1 (cf. Fitzpatrick's TJ). The n ≥ 2 vacuum
+ # Hₙ vanishes because H_n(1) = H_n'(1) = 0 after the Hna/Vna rescaling.
+ function H1_vac(r::Float64)
+ return H1a - 0.5 * r^2 * log(r) + 0.25 * (2 * H1ap + 1) * (r^2 - 1)
+ end
+
+ # TJ's shifts of (R, Z) from the nominal circle with Hₙ = Vₙ = 0 for n ≥ 2, L(r) = r³/8 − r·H₁(r)/2:
+ # f_R = εa²·H₁(r) + εa³·L(r)·cos(w)
+ # f_Z = −εa³·L(r)·sin(w)
+ # As in TJ, frozen at r = rc and scaled by r²/rc² beyond, so the iteration does not diverge in the far vacuum.
+ function f_R_shift(r::Float64, w::Float64)
+ if r >= rc
+ return f_R_shift(rc - 1e-8, w) * r^2 / rc^2
+ end
+ H1 = (r < 1.0) ? H1_of_x(r) : H1_vac(r)
+ L = r^3 / 8 - r * H1 / 2
+ return epsa2 * H1 + epsa2 * epsa * L * cos(w)
+ end
+ function f_Z_shift(r::Float64, w::Float64)
+ if r >= rc
+ return f_Z_shift(rc - 1e-8, w) * r^2 / rc^2
+ end
+ H1 = (r < 1.0) ? H1_of_x(r) : H1_vac(r)
+ L = r^3 / 8 - r * H1 / 2
+ return -epsa2 * epsa * L * sin(w)
+ end
+
+ # (R_norm, Z_norm) → (r, w) by the 10-step fixed-point iteration of TJ's EFIT writer; R_norm, Z_norm are normalized to R₀.
+ function find_rw(R_norm::Float64, Z_norm::Float64)
+ r = sqrt((R_norm - 1.0)^2 + Z_norm^2) / epsa
+ w = atan(Z_norm, 1.0 - R_norm)
+ for _ in 1:10
+ RR = R_norm - f_R_shift(r, w)
+ ZZ = Z_norm - f_Z_shift(r, w)
+ r = sqrt((RR - 1.0)^2 + ZZ^2) / epsa
+ w = atan(ZZ, 1.0 - RR)
+ end
+ return r, w
+ end
+
+ # TJ's GetPSIvac with Hₙ = Vₙ = 0 for n ≥ 2, in normalized units (callers multiply by psi_scale).
+ function psi_vac(r::Float64)
+ logr = log(r)
+ sum1 = 1.0 - H1ap + H1ap^2
+ sum2 = -H1ap * r^2 * logr + 0.5 * r^2 * logr^2 +
+ 0.5 * (1.0 + H1ap^2) * (r^2 - 1.0)
+ return f1a * logr + epsa2 * f3a * logr -
+ 0.5 * epsa2 * f1a * (-sum1 * logr + sum2)
+ end
+
+ # ψ(r) inside the plasma from the ψ-ODE (≈ 0 on axis, psio at r = a), clamped to the data range [p.r0, p.a].
+ function psi_plasma_physical(r::Float64)
+ r_phys = clamp(r * p.a, p.r0, p.a)
+ return ψ_of_r(r_phys)
+ end
+
+ # Direct-solver convention: ψ positive at the axis, zero at the LCFS, negative outside.
+ # The grid spans R₀ ± rc·a by ±rc·a, a margin for the separatrix finder.
+ r_span = rc * a
+ psi_in_xs = collect(range(R0 - r_span, R0 + r_span; length=nrbox))
+ psi_in_ys = collect(range(-r_span, r_span; length=nzbox))
+ psi_rz = zeros(Float64, nrbox, nzbox)
+
+ for i in 1:nrbox, j in 1:nzbox
+ R_norm = psi_in_xs[i] / R0
+ Z_norm = psi_in_ys[j] / R0
+ r_lbl, _ = find_rw(R_norm, Z_norm)
+
+ if r_lbl < 1.0
+ ψ_p = psi_plasma_physical(r_lbl)
+ psi_rz[i, j] = psio - ψ_p # plasma: +psio at axis, 0 at LCFS
+ elseif r_lbl < rc
+ psi_rz[i, j] = -psi_scale * psi_vac(r_lbl) # vacuum: 0 at LCFS, neg. outside
+ else
+ psi_rz[i, j] = -psi_scale * psi_vac(rc) * r_lbl^2 / rc^2
+ end
+ end
+
+ # 2D spline consumed by direct-GS
+ psi_in = cubic_interp((psi_in_xs, psi_in_ys), psi_rz; extrap=ExtendExtrap())
+
+ # 1D profile spline in read_efit's 4-column layout, with q₂ consistent with the ψ(R, Z) above.
+ psi_norm_grid = range(0.0, 1.0; length=nrbox)
+ F_nodes = zeros(nrbox)
+ P_nodes = zeros(nrbox)
+ q_nodes = zeros(nrbox)
+ for i in 1:nrbox
+ ψN = psi_norm_grid[i]
+ # Solve ψ_plasma(r) = ψN·psio for r (ψ_plasma is monotonic in r).
+ target = ψN * psio
+ rlocal = if ψN ≤ 0.0
+ p.r0
+ elseif ψN ≥ 1.0
+ p.a
+ else
+ find_zero(r -> ψ_of_r(r) - target, (p.r0, p.a); atol=1e-10, rtol=1e-12)
+ end
+ x = rlocal / p.a
+ f1 = tj_analytic_f1(x, nu, qc)
+ g2_val = g2_of_x(x)
+ f3_val = f3_of_x(x)
+ xfac = max(1 - x^2, 0.0)
+ F_nodes[i] = R0 * B0 * (1 + epsa2 * g2_val)
+ P_nodes[i] = p00_phys * xfac^mu
+ q_nodes[i] = (x > 1e-10) ? x^2 * (1 + epsa2 * g2_val) *
+ exp(-epsa2 * f3_val / f1) / f1 : qc
+ end
+ sq_fs_nodes = hcat(F_nodes, P_nodes, q_nodes, sqrt.(collect(psi_norm_grid)))
+ sq_in = cubic_interp(collect(psi_norm_grid), Series(sq_fs_nodes); extrap=ExtendExtrap())
+
+ rmin_grid, rmax_grid = extrema(psi_in_xs)
+ zmin_grid, zmax_grid = extrema(psi_in_ys)
+
+ # Analytic: ingest=nothing — replay regenerates from the [TJAnalytic] deck section.
+ return DirectRunInput(equil_input, sq_in, psi_in, psi_in_xs, psi_in_ys,
+ rmin_grid, rmax_grid, zmin_grid, zmax_grid, psio, 1, 1, nothing)
+end
diff --git a/src/Equilibrium/Sources/Chease.jl b/src/Equilibrium/Sources/Chease.jl
new file mode 100644
index 0000000000..085532955f
--- /dev/null
+++ b/src/Equilibrium/Sources/Chease.jl
@@ -0,0 +1,245 @@
+# CHEASE supplies q directly and GPEC requires q > 0, so a non-positive q stops here, as Fortran's chease reader does.
+_chease_q(zq, config) =
+ minimum(zq) > 0 ? zq : error("CHEASE input $(config.eq_filename) has q = $(minimum(zq)) ≤ 0; GPEC requires q > 0")
+
+"""
+ read_chease_binary(config) -> InverseRunInput
+
+Parses a binary CHEASE file, creates initial 1D and 2D splines with proper
+normalization (R0, B0 scaling), and bundles them into a `InverseRunInput` object.
+"""
+function read_chease_binary(config::EquilibriumConfig)
+ @info "Reading CHEASE file (Binary): $(config.eq_filename)"
+
+ R0EXP = config.r0_norm
+ B0EXP = config.b0_norm
+
+ open(config.eq_filename, "r") do io
+ seekstart(io)
+ read(io, UInt32)
+ ntnova = read(io, Int32)
+ npsi1 = read(io, Int32)
+ nsym = read(io, Int32)
+ read(io, UInt32)
+
+ axx = _read_fortran_reals(io, 5)
+
+ # 1D array allocation
+ zcpr, zcppr, zq, zdq, ztmf, ztp, zfb, zfbp, zpsi, zpsim =
+ [zeros(i == 1 || i == 10 ? npsi1 - 1 : npsi1) for i in 1:10]
+
+ for arr in (zcpr, zcppr, zq, zdq, ztmf, ztp, zfb, zfbp, zpsi, zpsim)
+ arr .= _read_fortran_reals(io, length(arr))
+ end
+
+ # --- Normalization (1D) ---
+ ztmf .*= (R0EXP * B0EXP)
+ zcppr .*= (B0EXP / R0EXP^2)
+ psio_norm = zpsi[npsi1] - zpsi[1]
+ psio = psio_norm * R0EXP^2 * B0EXP
+
+ ma = npsi1 - 1
+ xs = (zpsi .- zpsi[1]) ./ psio_norm
+
+ fs = zeros(npsi1, 4)
+ fs[:, 1] .= ztmf
+ fs[:, 2] .= zcppr
+ fs[:, 3] .= _chease_q(zq, config)
+
+ # Pressure from the cumulative integral of the P′ column.
+ itp_pressure = cubic_interp(xs, fs[:, 2])
+ fsi_pressure = FastInterpolations.cumulative_integrate(itp_pressure)
+ fs_copy = copy(fs)
+ fs_copy[:, 2] .= (fsi_pressure .- fsi_pressure[ma]) .* psio
+ sq_in = cubic_interp(xs, Series(fs_copy); extrap=ExtendExtrap())
+
+ # --- 2D Geometry ---
+ mtau = ntnova + 1 # Same with ASCII
+ poloidal_start = 3 # skip the two ghost points CHEASE stores for derivatives
+ poloidal_stop = ntnova + 3
+
+ fs_2d = zeros(npsi1, mtau, 2)
+ buffer = zeros(Float64, ntnova + 3, npsi1) # CHEASE binary record size
+
+ # Reading R data
+ buffer .= reshape(_read_fortran_reals(io, length(buffer)), size(buffer))
+ buffer .*= R0EXP
+
+ ro = buffer[poloidal_start, 1]
+ fs_2d[:, :, 1] .= transpose(buffer[poloidal_start:poloidal_stop, :])
+
+ # Reading Z data
+ buffer .= reshape(_read_fortran_reals(io, length(buffer)), size(buffer))
+ buffer .*= R0EXP
+
+ zo = buffer[poloidal_start, 1]
+ fs_2d[:, :, 2] .= transpose(buffer[poloidal_start:poloidal_stop, :])
+
+ # Create separate interpolants for R and Z coordinates
+ rz_in_xs = xs
+ rz_in_ys = range(0, 1; length=mtau) |> collect
+ rz_in_R = cubic_interp((rz_in_xs, rz_in_ys), fs_2d[:, :, 1]; bc=(CubicFit(), PeriodicBC()), extrap=(ExtendExtrap(), WrapExtrap()))
+ rz_in_Z = cubic_interp((rz_in_xs, rz_in_ys), fs_2d[:, :, 2]; bc=(CubicFit(), PeriodicBC()), extrap=(ExtendExtrap(), WrapExtrap()))
+
+ # Capture the raw arrays that reconstruct sq_in, rz_in_R, rz_in_Z.
+ ingest = InverseIngest(collect(xs), fs_copy, collect(rz_in_xs), collect(rz_in_ys), fs_2d[:, :, 1], fs_2d[:, :, 2], ro, zo, psio)
+
+ @info "Finished reading CHEASE equilibrium (Binary)"
+ return InverseRunInput(config, sq_in, rz_in_xs, rz_in_ys, rz_in_R, rz_in_Z, ro, zo, psio, ingest)
+ end
+end
+
+
+"""
+ read_chease_ascii(config) -> InverseRunInput
+
+Parse an ASCII CHEASE file, build the 1D and 2D splines with R0/B0 normalization, find the
+magnetic axis, and bundle them into an `InverseRunInput` for the inverse solver.
+"""
+function read_chease_ascii(config::EquilibriumConfig)
+ @info "Reading CHEASE file (ASCII): $(config.eq_filename)"
+ lines = readlines(config.eq_filename)
+ R0EXP = config.r0_norm
+ B0EXP = config.b0_norm
+
+ # --- Parse Header (FORMAT 10: 3I5) ---
+ header_parts = split(lines[1])
+ ntnova = parse(Int, header_parts[1])
+ npsi1 = parse(Int, header_parts[2])
+ nsym = parse(Int, header_parts[3])
+
+ # --- Parse axx (FORMAT 20: 1E22.15) ---
+ axx = parse(Float64, split(lines[2])[1]) # RBOXLEN, computational box length
+ # --- Pre-allocate Arrays ---
+ zcpr = zeros(npsi1 - 1) # normalized P(ψ)
+ zcppr = zeros(npsi1) # normalized dP/dψ
+ zq = zeros(npsi1) # q(ψ)
+ zdq = zeros(npsi1) # dq/dψ
+ ztmf = zeros(npsi1) # normalized F(ψ)
+ ztp = zeros(npsi1) # normalized dF/dψ
+ zfb = zeros(npsi1) # normalized F(ψ)/q(ψ)
+ zfbp = zeros(npsi1) # d/dψ [F(ψ)/q(ψ) ]
+ zpsi = zeros(npsi1) # ψ Poloidal flux
+ zpsim = zeros(npsi1 - 1) # ψ mid
+
+ zrcp = zeros(ntnova + 3, npsi1) # normalized R
+ zzcp = zeros(ntnova + 3, npsi1) # normalized Z
+ zjacm = zeros(ntnova + 3, npsi1) # 𝒥 (Jacobian)
+ zjac = zeros(ntnova + 3, npsi1) # 𝒥 (Jacobian)
+
+ # --- Helper to parse 5E22.15 data per line ---
+ function parse_floats(lines_range)
+ data = Float64[]
+ for line in lines[lines_range]
+ for i in 0:4
+ s = strip(line[(22*i+1):min(end, 22 * (i + 1))])
+ if !isempty(s)
+ push!(data, parse(Float64, s))
+ end
+ end
+ end
+ return data
+ end
+
+ # --- Compute line offsets ---
+ line_idx = 3 # Start after header (line 1) and axx (line 2)
+
+ function load_vector!(vec)
+ count = length(vec)
+ lines_needed = cld(count, 5)
+ vec .= parse_floats(line_idx:(line_idx+lines_needed-1))
+ return line_idx += lines_needed
+ end
+
+ function load_matrix!(mat)
+ count = size(mat, 1) * size(mat, 2)
+ lines_needed = cld(count, 5)
+ data = parse_floats(line_idx:(line_idx+lines_needed-1))
+ line_idx += lines_needed
+ # Fill column-major (Fortran-style)
+ for j in 1:size(mat, 2)
+ for i in 1:size(mat, 1)
+ mat[i, j] = data[(j-1)*size(mat, 1)+i]
+ end
+ end
+ end
+
+ # --- Read Vectors ---
+ load_vector!(zcpr)
+ load_vector!(zcppr)
+ load_vector!(zq)
+ load_vector!(zdq)
+ load_vector!(ztmf)
+ load_vector!(ztp)
+ load_vector!(zfb)
+ load_vector!(zfbp)
+ load_vector!(zpsi)
+ load_vector!(zpsim)
+
+ # --- Read Matrices ---
+ load_matrix!(zrcp)
+ load_matrix!(zzcp)
+ load_matrix!(zjacm)
+ load_matrix!(zjac)
+ @info "Parsed from header: ntnova = $ntnova, npsi1 = $npsi1, nsym = $nsym"
+
+ # --- Apply Normalization ---
+ # Scale geometry
+ zrcp .*= R0EXP
+ zzcp .*= R0EXP
+
+ # Scale flux
+ # Psi_phys = Psi_norm * R0^2 * B0
+ psio_norm = zpsi[end] - zpsi[1]
+ psio = psio_norm * R0EXP^2 * B0EXP
+
+ # Scale Toroidal Field Function F
+ ztmf .*= (R0EXP * B0EXP)
+
+ # Scale Pressure Gradient P'
+ zcppr .*= (B0EXP / R0EXP^2)
+
+ # Number of spline intervals
+ ma = npsi1 - 1
+
+ # Normalize ψ to [0, 1]
+ xs = (zpsi .- zpsi[1]) ./ psio_norm # Use normalized range for x axis [0,1]
+
+ fs = zeros(npsi1, 4)
+ # ztmf equals zq .* zfb (both are F).
+ fs[:, 1] .= ztmf
+ fs[:, 2] .= zcppr # normalized Pressure
+ fs[:, 3] .= _chease_q(zq, config) # q profile
+ # Pressure from the cumulative integral of the P′ column.
+ itp_pressure = cubic_interp(xs, fs[:, 2])
+ fsi_pressure = FastInterpolations.cumulative_integrate(itp_pressure)
+ fs_copy = copy(fs)
+ fs_copy[:, 2] .= (fsi_pressure .- fsi_pressure[ma]) .* psio
+ sq_in = cubic_interp(xs, Series(fs_copy); extrap=ExtendExtrap())
+
+ # --- Copy 2D geometry arrays ---
+ mtau = ntnova + 1
+ poloidal_start = 3
+ poloidal_stop = ntnova + 3
+ ro = zrcp[poloidal_start, 1] # Already scaled
+ zo = zzcp[poloidal_start, 1] # Already scaled
+ rz_in_ys = range(0, 1; length=mtau) |> collect
+ # CHEASE includes 2 ghost points at the start (wrap-around); drop them.
+ R_data = transpose(zrcp[poloidal_start:poloidal_stop, :])
+ Z_data = transpose(zzcp[poloidal_start:poloidal_stop, :])
+
+ # Create separate interpolants for R and Z coordinates
+ rz_in_xs = xs
+
+ @views R_data[:, end] .= R_data[:, 1]
+ @views Z_data[:, end] .= Z_data[:, 1]
+
+ opts2d = (bc=(CubicFit(), PeriodicBC()), extrap=(ExtendExtrap(), WrapExtrap()))
+ rz_in_R = cubic_interp((rz_in_xs, rz_in_ys), R_data; opts2d...)
+ rz_in_Z = cubic_interp((rz_in_xs, rz_in_ys), Z_data; opts2d...)
+ # Capture the raw arrays that reconstruct sq_in, rz_in_R, rz_in_Z.
+ ingest = InverseIngest(collect(xs), fs_copy, collect(rz_in_xs), collect(rz_in_ys), Matrix(R_data), Matrix(Z_data), ro, zo, psio)
+
+ @info "Finished reading CHEASE equilibrium. Magnetic axis at (ro=$(@sprintf("%.3f", ro)), zo=$(@sprintf("%.3f", zo))), psio=$(@sprintf("%.3e", psio))"
+ return InverseRunInput(config, sq_in, rz_in_xs, rz_in_ys, rz_in_R, rz_in_Z, ro, zo, psio, ingest)
+end
diff --git a/src/Equilibrium/Sources/GFile.jl b/src/Equilibrium/Sources/GFile.jl
new file mode 100644
index 0000000000..ecab71be9b
--- /dev/null
+++ b/src/Equilibrium/Sources/GFile.jl
@@ -0,0 +1,124 @@
+"""
+ _read_1d_gfile_format(lines_block, num_values) -> Vector{Float64}
+
+Parse `num_values` reals from Fortran fixed-width (16-character) fields in `lines_block`, warning on
+unparsable fields or a short read.
+"""
+function _read_1d_gfile_format(lines_block::Vector{String}, num_values::Int)
+ data_str = join(lines_block)
+ field_width = 16
+ parsed_values = Float64[]
+ num_read = 0
+
+ # Only whole fields
+ safe_len = (length(data_str) ÷ field_width) * field_width
+ for i in 1:field_width:safe_len
+ num_read >= num_values && break
+ val_str = strip(@view(data_str[i:(i+field_width-1)]))
+ if !isempty(val_str)
+ try
+ push!(parsed_values, parse(Float64, val_str))
+ num_read += 1
+ catch e
+ @warn "Parsing error for substring: '$val_str'. Error: $e. Skipping."
+ end
+ end
+ end
+
+ if num_read < num_values
+ @warn "Expected $num_values values, but only read $num_read."
+ end
+ return parsed_values
+end
+
+"""
+ gfile_fpol_single_precision(filename) -> Bool
+
+Whether the g-file's FPOL column was written in single precision: every value lies within 1e-8
+(relative) of its Float32 rounding. Double-precision values printed to the format's ten digits
+sit about 1.5e-8 from it on average, so a whole column below 1e-8 is single precision.
+"""
+function gfile_fpol_single_precision(filename::AbstractString)
+ lines = readlines(filename)
+ nw = parse(Int, split(lines[1])[end-1])
+ fpol = _read_1d_gfile_format(lines[6:(5+cld(nw, 5))], nw)
+ return all(f -> abs(Float64(Float32(f)) - f) <= 1e-8 * abs(f), fpol)
+end
+
+"""
+ read_efit(config::EquilibriumConfig) -> DirectRunInput
+
+Parse the EFIT g-file `config.eq_filename` into the 1D profile spline and 2D ψ(R, Z) interpolant
+for the direct solver.
+"""
+function read_efit(config::EquilibriumConfig)
+ @info "Processing EFIT g-file: $(config.eq_filename)"
+ lines = readlines(config.eq_filename)
+
+ # --- Parse Header ---
+ header1_parts = split(lines[1])
+ nw = parse(Int, header1_parts[end-1])
+ nh = parse(Int, header1_parts[end])
+ @info "Parsed from header: nw=$nw, nh=$nh"
+
+ header_vals = _read_1d_gfile_format(lines[2:5], 20)
+ rdim, zdim, rcentr, rleft, zmid = header_vals[1:5]
+ rmaxis, zmaxis, simag, sibry = header_vals[6:9]
+ ip_sign = Int(sign(header_vals[11])) # the g-file's plasma current; its sign sets the helicity
+ ip_sign == 0 && (ip_sign = 1)
+
+ # --- Parse Data Blocks ---
+ current_line_idx = 6
+ function parse_block(num_pts)
+ num_lines = ceil(Int, num_pts / 5)
+ block = lines[current_line_idx:(current_line_idx+num_lines-1)]
+ data = _read_1d_gfile_format(block, num_pts)
+ current_line_idx += num_lines
+ return data
+ end
+
+ fpol_data = parse_block(nw)
+ fpol_sign = Int(sign(fpol_data[end])) # sign of toroidal field (before abs is applied below)
+ pres_data = parse_block(nw)
+ ffprime_data = parse_block(nw)
+ pprime_data = parse_block(nw)
+ psi_flat_vec = parse_block(nw * nh)
+ qprof_data = parse_block(nw)
+
+ psi_rz = reshape(psi_flat_vec, nw, nh)
+
+ # --- Create 1D Profile Spline (sq_in) ---
+ psi_norm_grid = range(0.0, 1.0; length=nw)
+ sq_fs_nodes = hcat(
+ abs.(fpol_data),
+ max.(pres_data .* mu0, 0.0),
+ qprof_data,
+ sqrt.(psi_norm_grid)
+ )
+ sq_xs = collect(psi_norm_grid)
+ sq_in = cubic_interp(sq_xs, Series(sq_fs_nodes); extrap=ExtendExtrap())
+
+ # --- Process and Normalize 2D Psi Data ---
+ psio_signed = sibry - simag
+ psi_proc = (sibry .- psi_rz)
+ psio = abs(psio_signed)
+ # Ensure psi at the magnetic axis is positive relative to the boundary
+ if psio_signed < 0.0
+ psi_proc .*= -1.0
+ end
+
+ # --- Create 2D Psi interpolant (psi_in) ---
+ r_grid = range(rleft, rleft + rdim; length=nw)
+ z_grid = range(zmid - zdim / 2, zmid + zdim / 2; length=nh)
+ rmin, rmax = extrema(r_grid)
+ zmin, zmax = extrema(z_grid)
+
+ psi_in_xs = collect(r_grid)
+ psi_in_ys = collect(z_grid)
+ psi_in = cubic_interp((psi_in_xs, psi_in_ys), psi_proc; extrap=ExtendExtrap())
+
+ # Raw arrays that rebuild sq_in and psi_in, so a rerun from gpec.h5 skips the g-file parse
+ ingest = DirectIngest(sq_xs, sq_fs_nodes, psi_in_xs, psi_in_ys, psi_proc, rmin, rmax, zmin, zmax, psio, fpol_sign, ip_sign)
+
+ return DirectRunInput(config, sq_in, psi_in, psi_in_xs, psi_in_ys, rmin, rmax, zmin, zmax, psio, fpol_sign, ip_sign, ingest)
+end
diff --git a/src/Equilibrium/Sources/IFile.jl b/src/Equilibrium/Sources/IFile.jl
new file mode 100644
index 0000000000..4e036cfef8
--- /dev/null
+++ b/src/Equilibrium/Sources/IFile.jl
@@ -0,0 +1,76 @@
+"""
+ _read_fortran_reals(io, n) -> Vector{Float64}
+
+Read one little-endian Fortran sequential unformatted record of `n` reals, stored as real*4 or real*8
+(told apart by the record length).
+"""
+function _read_fortran_reals(io::IO, n::Int)
+ nbytes = ltoh(read(io, Int32))
+ T = nbytes == 8n ? Float64 : nbytes == 4n ? Float32 : error("Fortran record holds $nbytes bytes, expected $n reals")
+ data = ltoh.(read!(io, Vector{T}(undef, n)))
+ ltoh(read(io, Int32)) == nbytes || error("Fortran record end marker does not match its start")
+ return Float64.(data)
+end
+
+"""
+ read_ifile(config) -> InverseRunInput
+
+Read an inverse i-file, such as TokaMaker `save_ifile` writes: little-endian Fortran unformatted records,
+reals as real*8 or real*4, axis first, θ fastest.
+
+ - `mx, my` (int32); `psi(mx)` [Wb/rad], `f(mx)` = R·Bt [T·m], `p(mx)` [Pa], `q(mx)`
+ - `r(my, mx)`, `z(my, mx)` [m], with the periodic θ point duplicated
+ - optional `FF′(mx)`, `p′(mx)` per Wb/rad, skipped
+ - optional `[ψ_axis, ψ_LCFS]`: ψ_N is then normalized to this LCFS, so the last file surface (written just
+ inside it) sits below ψ_N = 1
+
+Port of Fortran `read_eq_ldp_i`.
+"""
+function read_ifile(config::EquilibriumConfig)
+ @info "Reading inverse i-file: $(config.eq_filename)"
+
+ psi, f, p, q, r, z, bounds = open(config.eq_filename, "r") do io
+ ltoh(read(io, Int32)) == 8 || error("i-file header record is not two int32")
+ mx, my = Int.(ltoh.(read!(io, Vector{Int32}(undef, 2))))
+ read(io, Int32)
+ profiles = [_read_fortran_reals(io, mx) for _ in 1:4]
+ r, z = (reshape(_read_fortran_reals(io, my * mx), my, mx) for _ in 1:2)
+ # Optional records, told apart by length: FF′ and p′ (mx each, unused), then the ψ bounds (2)
+ bounds = nothing
+ while !eof(io)
+ nbytes = ltoh(read(io, Int32))
+ if nbytes in (4mx, 8mx)
+ skip(io, nbytes + 4)
+ else
+ skip(io, -4)
+ bounds = _read_fortran_reals(io, 2)
+ end
+ end
+ return (profiles..., r, z, bounds)
+ end
+ mx, my = length(psi), size(r, 1)
+ @info "Parsed from header: mx = $mx surfaces, my = $my poloidal points"
+
+ psi_axis, psi_lcfs = bounds === nothing ? (psi[1], psi[end]) : bounds
+ psio_signed = psi_lcfs - psi_axis
+ psio = abs(psio_signed)
+ xs = (psi .- psi_axis) ./ psio_signed
+ bounds === nothing ||
+ @info "i-file ψ bounds: ψ_axis = $psi_axis, ψ_LCFS = $psi_lcfs; file surfaces span ψ_N ∈ [$(xs[1]), $(xs[end])]"
+
+ sq_fs = hcat(abs.(f), p .* mu0, q, sqrt.(xs))
+ sq_in = cubic_interp(xs, Series(sq_fs); extrap=ExtendExtrap())
+
+ R_data = Matrix(transpose(r))
+ Z_data = Matrix(transpose(z))
+ ro, zo = R_data[1, 1], Z_data[1, 1]
+ rz_in_ys = collect(range(0, 1; length=my))
+
+ opts2d = (bc=(CubicFit(), PeriodicBC()), extrap=(ExtendExtrap(), WrapExtrap()))
+ rz_in_R = cubic_interp((xs, rz_in_ys), R_data; opts2d...)
+ rz_in_Z = cubic_interp((xs, rz_in_ys), Z_data; opts2d...)
+ ingest = InverseIngest(xs, sq_fs, xs, rz_in_ys, R_data, Z_data, ro, zo, psio)
+
+ @info "Finished reading i-file. Magnetic axis at (ro=$(@sprintf("%.3f", ro)), zo=$(@sprintf("%.3f", zo))), psio=$(@sprintf("%.3e", psio))"
+ return InverseRunInput(config, sq_in, xs, rz_in_ys, rz_in_R, rz_in_Z, ro, zo, psio, ingest)
+end
diff --git a/src/Equilibrium/Sources/IMAS.jl b/src/Equilibrium/Sources/IMAS.jl
new file mode 100644
index 0000000000..c1c587c519
--- /dev/null
+++ b/src/Equilibrium/Sources/IMAS.jl
@@ -0,0 +1,112 @@
+"""
+ read_imas(config::EquilibriumConfig, dd) -> DirectRunInput
+
+Load an equilibrium from an IMAS data dictionary and return a `DirectRunInput`.
+
+The `dd.equilibrium.time_slice[]` is used (active time slice). Poloidal flux is
+converted from the IMAS COCOS convention (set by `config.imas_cocos`) to the
+internal COCOS 2 convention:
+
+ - `imas_cocos = 11` (default, IMAS standard): divide ψ by 2π
+ - `imas_cocos = 2` (GPEC internal): no conversion
+
+## Arguments
+
+ - `config`: `EquilibriumConfig` with `eq_type = "imas"` and `imas_cocos` set.
+
+ - `dd`: populated `IMASdd.dd` with `dd.equilibrium.time_slice[]` containing:
+
+ + `global_quantities.psi_axis`, `global_quantities.psi_boundary`
+ + `profiles_1d.psi`, `profiles_1d.f`, `profiles_1d.pressure`, `profiles_1d.q`
+ + the `profiles_2d` entry with `grid_type.index == 1` (rectangular), supplying `grid.dim1` (R), `grid.dim2` (Z) and `psi`
+"""
+function read_imas(config::EquilibriumConfig, dd)
+ @info "Processing IMAS equilibrium at global_time = $(dd.global_time) s"
+
+ eqt = dd.equilibrium.time_slice[]
+
+ # COCOS 11 (IMAS standard) stores ψ_IMAS = 2π × ψ_internal
+ if config.imas_cocos == 11
+ cocos_factor = 1.0 / (2π)
+ @info "Converting IMAS data from COCOS 11 to internal (COCOS 2)"
+ elseif config.imas_cocos == 2
+ cocos_factor = 1.0
+ @info "IMAS data in COCOS 2 (no conversion needed)"
+ else
+ error("read_imas: unsupported imas_cocos = $(config.imas_cocos). Use 2 or 11.")
+ end
+
+ psi_axis = eqt.global_quantities.psi_axis * cocos_factor
+ psi_boundary = eqt.global_quantities.psi_boundary * cocos_factor
+
+ psio = abs(psi_boundary - psi_axis)
+
+ if psio < 1e-10
+ error("read_imas: |psi_axis - psi_boundary| = $psio is too small. " *
+ "Check that dd.equilibrium is properly populated.")
+ end
+
+ psi_1d = eqt.profiles_1d.psi .* cocos_factor
+ f_1d = eqt.profiles_1d.f # F(ψ) = R·Bt [T·m], COCOS-independent
+ p_1d = eqt.profiles_1d.pressure # plasma pressure P(ψ) [Pa], COCOS-independent
+ q_1d = eqt.profiles_1d.q # safety factor, COCOS-independent
+
+ # Toroidal-field sign from the boundary F, before abs() below
+ bt_sign = isempty(f_1d) ? 1 : Int(sign(f_1d[end]))
+ bt_sign == 0 && (bt_sign = 1)
+ # Plasma-current sign (missing or zero → +1); getproperty with a default because reading an absent ip throws
+ ip_imas = getproperty(eqt.global_quantities, :ip, 0.0)
+ ip_sign = ip_imas == 0 ? 1 : Int(sign(ip_imas))
+
+ nw = length(psi_1d)
+ psi_norm_grid = (psi_1d .- psi_axis) ./ (psi_boundary - psi_axis)
+ @assert all(diff(psi_norm_grid) .> 0) "read_imas: profiles_1d.psi must increase strictly from psi_axis to psi_boundary"
+ @assert 0 <= psi_norm_grid[1] && psi_norm_grid[end] <= 1 "read_imas: profiles_1d.psi must lie between psi_axis and psi_boundary"
+
+ # GPEC uses |F| = R·|Bt|; the sign is kept in bt_sign
+ sq_fs_nodes = hcat(
+ abs.(f_1d),
+ max.(p_1d .* mu0, 0.0),
+ q_1d,
+ sqrt.(psi_norm_grid)
+ )
+ sq_xs = collect(psi_norm_grid)
+ sq_in = cubic_interp(sq_xs, Series(sq_fs_nodes); extrap=ExtendExtrap())
+
+ # 2D ψ(R,Z) map
+ if isempty(eqt.profiles_2d)
+ error("read_imas: no profiles_2d found in equilibrium time slice. " *
+ "Ensure the 2D ψ(R,Z) map is stored in dd.equilibrium.")
+ end
+ prof2d = findfirst(:rectangular, eqt.profiles_2d)
+ prof2d === nothing && error("read_imas: no rectangular profiles_2d found.")
+ r_grid = prof2d.grid.dim1
+ z_grid = prof2d.grid.dim2
+
+ psi_rz = prof2d.psi .* cocos_factor
+
+ # Shift so psi_in = 0 at boundary, psi_in = psio at axis
+ psi_proc = psi_boundary .- psi_rz
+ if psi_boundary - psi_axis < 0.0
+ psi_proc .*= -1.0
+ end
+
+ rmin, rmax = extrema(r_grid)
+ zmin, zmax = extrema(z_grid)
+
+ psi_in_xs = collect(r_grid)
+ psi_in_ys = collect(z_grid)
+ psi_in = cubic_interp((psi_in_xs, psi_in_ys), psi_proc; extrap=ExtendExtrap())
+
+ @info "IMAS equilibrium loaded:" *
+ "\n psio = $(round(psio; sigdigits=5)) Wb" *
+ "\n 1D profile points: nw = $nw" *
+ "\n 2D grid: nR = $(length(r_grid)), nZ = $(length(z_grid))" *
+ "\n R ∈ [$(round(rmin; sigdigits=4)), $(round(rmax; sigdigits=4))] m" *
+ "\n Z ∈ [$(round(zmin; sigdigits=4)), $(round(zmax; sigdigits=4))] m"
+
+ # Raw arrays so an IMAS run can be replayed from gpec.h5 without the dd
+ ingest = DirectIngest(sq_xs, sq_fs_nodes, psi_in_xs, psi_in_ys, Matrix(psi_proc), rmin, rmax, zmin, zmax, psio, bt_sign, ip_sign)
+
+ return DirectRunInput(config, sq_in, psi_in, psi_in_xs, psi_in_ys, rmin, rmax, zmin, zmax, psio, bt_sign, ip_sign, ingest)
+end
diff --git a/src/Equilibrium/Sources/Ingest.jl b/src/Equilibrium/Sources/Ingest.jl
new file mode 100644
index 0000000000..dfb8897760
--- /dev/null
+++ b/src/Equilibrium/Sources/Ingest.jl
@@ -0,0 +1,186 @@
+"""
+ DirectIngest
+
+Raw arrays and scalars captured by a direct-equilibrium reader (`read_efit`, `read_imas`), enough to
+rebuild a `DirectRunInput`'s splines via `build_direct_from_ingest`. Written to `gpec.h5` so a run can be
+replayed without the original source.
+
+## Fields
+
+ - `sq_xs::Vector{Float64}` — normalized-ψ knots for the 1D profile spline
+ - `sq_fs::Matrix{Float64}` — 1D profile node values (F, μ₀P, q, √ψ_norm)
+ - `psi_xs::Vector{Float64}` — R grid for the 2D flux map [m]
+ - `psi_ys::Vector{Float64}` — Z grid for the 2D flux map [m]
+ - `psi_rz::Matrix{Float64}` — processed poloidal flux on the (R, Z) grid [Wb/rad]
+ - `rmin/rmax/zmin/zmax::Float64` — computational-grid bounds [m]
+ - `psio::Float64` — total flux difference |ψ_axis - ψ_boundary| [Wb/rad]
+ - `bt_sign::Int` — sign of the toroidal field (+1 or -1)
+ - `ip_sign::Int` — sign of the plasma current (+1 or -1) as the source file states it
+"""
+struct DirectIngest
+ sq_xs::Vector{Float64}
+ sq_fs::Matrix{Float64}
+ psi_xs::Vector{Float64}
+ psi_ys::Vector{Float64}
+ psi_rz::Matrix{Float64}
+ rmin::Float64
+ rmax::Float64
+ zmin::Float64
+ zmax::Float64
+ psio::Float64
+ bt_sign::Int
+ ip_sign::Int
+end
+
+"""
+ InverseIngest
+
+Raw arrays and scalars captured by an inverse-equilibrium reader (`read_chease_ascii`, `read_chease_binary`,
+`read_ifile`), enough to rebuild an `InverseRunInput`'s splines via `build_inverse_from_ingest`. The inverse
+counterpart of [`DirectIngest`](@ref).
+
+## Fields
+
+ - `sq_xs::Vector{Float64}` — normalized-ψ knots for the 1D profile spline
+ - `sq_fs::Matrix{Float64}` — 1D profile node values
+ - `rz_xs::Vector{Float64}` — ψ grid for the R, Z maps
+ - `rz_ys::Vector{Float64}` — θ grid for the R, Z maps
+ - `R_nodes::Matrix{Float64}` — R node values on the (ψ, θ) grid [m]
+ - `Z_nodes::Matrix{Float64}` — Z node values on the (ψ, θ) grid [m]
+ - `ro::Float64` — R of magnetic axis [m]
+ - `zo::Float64` — Z of magnetic axis [m]
+ - `psio::Float64` — total flux difference |ψ_axis - ψ_boundary| [Wb/rad]
+"""
+struct InverseIngest
+ sq_xs::Vector{Float64}
+ sq_fs::Matrix{Float64}
+ rz_xs::Vector{Float64}
+ rz_ys::Vector{Float64}
+ R_nodes::Matrix{Float64}
+ Z_nodes::Matrix{Float64}
+ ro::Float64
+ zo::Float64
+ psio::Float64
+end
+
+# Equilibria captured for replay carry one of these; analytic equilibria carry `nothing`
+# and are regenerated from their TOML section instead.
+const EquilibriumIngest = Union{Nothing,DirectIngest,InverseIngest}
+
+"""
+ DirectRunInput(...)
+
+Inputs to `direct_run`, built by a direct-equilibrium reader from the raw data.
+
+## Fields
+
+ - `config::EquilibriumConfig` — the equilibrium configuration
+ - `sq_in` — 1D spline in normalized ψ of `|F| = R·|B_t|` (m·T), `μ₀P` clipped at zero (T²), `q`, `√ψ_norm`
+ - `psi_in` — 2D interpolant of the poloidal flux on (R, Z), `ψ_boundary - ψ` signed positive at the axis (Wb/rad)
+ - `psi_in_xs::Vector{Float64}` — R coordinate grid for psi_in [m]
+ - `psi_in_ys::Vector{Float64}` — Z coordinate grid for psi_in [m]
+ - `rmin::Float64` — Minimum R-coordinate of the computational grid [m]
+ - `rmax::Float64` — Maximum R-coordinate of the computational grid [m]
+ - `zmin::Float64` — Minimum Z-coordinate of the computational grid [m]
+ - `zmax::Float64` — Maximum Z-coordinate of the computational grid [m]
+ - `psio::Float64` — Total flux difference `|ψ_axis - ψ_boundary|` [Wb/rad]
+ - `bt_sign::Int` — Sign of the toroidal field (+1 or -1), from the sign of F
+ - `ip_sign::Int` — Sign of the plasma current (+1 or -1) as the source states it (g-file `current`, IMAS
+ `global_quantities.ip`); the internal flux is always positive at the axis, so this sign, not the computed
+ current, sets the SFL→machine handedness `helicity = bt_sign × ip_sign`
+ - `ingest::EquilibriumIngest` — captured raw arrays for the `gpec.h5` rerun snapshot
+ (a [`DirectIngest`](@ref) for file-based reads, or `nothing` for analytic equilibria)
+ - `psihigh_resolved::Float64` — outer flux limit the solvers build their ψ grid on: `config.psihigh`, clamped
+ to the outermost closed flux surface by [`resolve_psihigh!`](@ref) for efit-family equilibria (not IMAS)
+"""
+mutable struct DirectRunInput{S<:FastInterpolations.CubicSeriesInterpolant,I2D<:FastInterpolations.CubicInterpolantND}
+ config::EquilibriumConfig
+ sq_in::S
+ psi_in::I2D
+ psi_in_xs::Vector{Float64}
+ psi_in_ys::Vector{Float64}
+ rmin::Float64
+ rmax::Float64
+ zmin::Float64
+ zmax::Float64
+ psio::Float64
+ bt_sign::Int
+ ip_sign::Int
+ ingest::EquilibriumIngest
+ psihigh_resolved::Float64
+end
+
+# Readers construct without a resolved psihigh; it starts at the request until `resolve_psihigh!` clamps it
+DirectRunInput(config::EquilibriumConfig, sq_in, psi_in, psi_in_xs, psi_in_ys,
+ rmin, rmax, zmin, zmax, psio, bt_sign, ip_sign, ingest) =
+ DirectRunInput(config, sq_in, psi_in, psi_in_xs, psi_in_ys,
+ rmin, rmax, zmin, zmax, psio, bt_sign, ip_sign, ingest, config.psihigh)
+
+"""
+ InverseRunInput(...)
+
+Inputs to `inverse_run`, built by an inverse-equilibrium reader.
+
+## Fields
+
+ - `config::EquilibriumConfig` - The equilibrium configuration object
+ - `sq_in::CubicSeriesInterpolant` - 1D profile spline for F, P, q
+ - `rz_in_xs::Vector{Float64}` - ψ coordinate grid for rz_in
+ - `rz_in_ys::Vector{Float64}` - θ coordinate grid for rz_in
+ - `rz_in_R::CubicInterpolantND` - R coordinate interpolant [m]
+ - `rz_in_Z::CubicInterpolantND` - Z coordinate interpolant [m]
+ - `ro::Float64` - R-coordinate of magnetic axis [m]
+ - `zo::Float64` - Z-coordinate of magnetic axis [m]
+ - `psio::Float64` - Total flux difference |ψ_axis - ψ_boundary| [Wb/rad]
+ - `ingest::EquilibriumIngest` - captured raw arrays for the `gpec.h5` rerun snapshot
+ (an [`InverseIngest`](@ref) for file-based reads, or `nothing` for analytic equilibria)
+ - `psihigh_resolved::Float64` - outer flux limit the solvers build their ψ grid on: `config.psihigh`, clamped
+ to the outermost input surface for i-files and reruns (`resolve_psihigh!`); `efit_by_inversion` forwards
+ the value clamped on its `DirectRunInput`
+"""
+mutable struct InverseRunInput{S<:FastInterpolations.CubicSeriesInterpolant,I2D<:FastInterpolations.CubicInterpolantND}
+ config::EquilibriumConfig
+ sq_in::S
+ rz_in_xs::Vector{Float64}
+ rz_in_ys::Vector{Float64}
+ rz_in_R::I2D
+ rz_in_Z::I2D
+ ro::Float64
+ zo::Float64
+ psio::Float64
+ ingest::EquilibriumIngest
+ psihigh_resolved::Float64
+end
+
+InverseRunInput(config::EquilibriumConfig, sq_in, rz_in_xs, rz_in_ys, rz_in_R, rz_in_Z,
+ ro, zo, psio, ingest) =
+ InverseRunInput(config, sq_in, rz_in_xs, rz_in_ys, rz_in_R, rz_in_Z,
+ ro, zo, psio, ingest, config.psihigh)
+
+"""
+ build_direct_from_ingest(config::EquilibriumConfig, ingest::DirectIngest) -> DirectRunInput
+
+Rebuild a `DirectRunInput`'s splines from a [`DirectIngest`](@ref) (from `read_efit`/`read_imas`, or restored
+from `Input/RawInputs/Equilibrium/` in `gpec.h5`), so a rerun skips the g-file/IMAS parse.
+"""
+function build_direct_from_ingest(config::EquilibriumConfig, ingest::DirectIngest)
+ sq_in = cubic_interp(ingest.sq_xs, Series(ingest.sq_fs); extrap=ExtendExtrap())
+ psi_in = cubic_interp((ingest.psi_xs, ingest.psi_ys), ingest.psi_rz; extrap=ExtendExtrap())
+ return DirectRunInput(config, sq_in, psi_in, ingest.psi_xs, ingest.psi_ys,
+ ingest.rmin, ingest.rmax, ingest.zmin, ingest.zmax, ingest.psio, ingest.bt_sign, ingest.ip_sign, ingest)
+end
+
+"""
+ build_inverse_from_ingest(config::EquilibriumConfig, ingest::InverseIngest) -> InverseRunInput
+
+Rebuild an `InverseRunInput`'s splines from an [`InverseIngest`](@ref), so a rerun skips the CHEASE or
+i-file parse.
+"""
+function build_inverse_from_ingest(config::EquilibriumConfig, ingest::InverseIngest)
+ sq_in = cubic_interp(ingest.sq_xs, Series(ingest.sq_fs); extrap=ExtendExtrap())
+ opts2d = (bc=(CubicFit(), PeriodicBC()), extrap=(ExtendExtrap(), WrapExtrap()))
+ rz_in_R = cubic_interp((ingest.rz_xs, ingest.rz_ys), ingest.R_nodes; opts2d...)
+ rz_in_Z = cubic_interp((ingest.rz_xs, ingest.rz_ys), ingest.Z_nodes; opts2d...)
+ return InverseRunInput(config, sq_in, ingest.rz_xs, ingest.rz_ys, rz_in_R, rz_in_Z,
+ ingest.ro, ingest.zo, ingest.psio, ingest)
+end
diff --git a/src/ErrorFields/Assessment.jl b/src/ErrorFields/Assessment.jl
new file mode 100644
index 0000000000..bb2d910f18
--- /dev/null
+++ b/src/ErrorFields/Assessment.jl
@@ -0,0 +1,120 @@
+"""
+ ErrorFieldsResult
+
+The error-field assessment of a plasma response, from [`error_fields`](@ref). Products that were not requested are
+`nothing`.
+
+## Fields
+
+ - `sensitivities::CoilSensitivities` - The coil sets' rigid-body sensitivities on the control surface.
+ - `dominant::DominantCoupling` - The singular modes of the resonant coupling the overlaps project on.
+ - `tolerances::Union{Nothing,ToleranceSet}` - The manufacturing tolerances, validated against the coil sets.
+ - `monte_carlo::Union{Nothing,MonteCarloResult}` - The tolerance Monte Carlo; needs `tolerances`.
+ - `risk::Union{Nothing,RiskResult}` - The locking risk; needs the Monte Carlo and a `scenario`.
+ - `scan::Union{Nothing,ToleranceScan}` - The locking risk against a tolerance scale; needs `RiskControl.scan_scales`.
+ - `couplings::Union{Nothing,Vector{EFCCoupling}}` - The correction arrays' couplings and NTV torques; needs `NTVControl.efc_coils`.
+ - `response::PerturbedEquilibrium.PlasmaResponse` - The plasma response the assessment was made on.
+ - `settings::NamedTuple` - The settings it was made with: `ctrl`, `monte_carlo`, `risk`, `ntv`, `kinetic`,
+ `scenario` and `regularization_width`, as given to `error_fields`.
+"""
+struct ErrorFieldsResult
+ sensitivities::CoilSensitivities
+ dominant::DominantCoupling
+ tolerances::Union{Nothing,ToleranceSet}
+ monte_carlo::Union{Nothing,MonteCarloResult}
+ risk::Union{Nothing,RiskResult}
+ scan::Union{Nothing,ToleranceScan}
+ couplings::Union{Nothing,Vector{EFCCoupling}}
+ response::PerturbedEquilibrium.PlasmaResponse
+ settings::NamedTuple
+end
+
+"""
+ error_fields(resp, coil_sets, coil_config; ctrl=ErrorFieldsControl(), tolerances=nothing,
+ monte_carlo=MonteCarloControl(), scenario=nothing, risk=RiskControl(), ntv=NTVControl(),
+ kinetic=KineticForcesControl(), regularization_width=0.0, verbose=false) -> ErrorFieldsResult
+
+Assess the error field of `coil_sets` on the plasma response `resp`: the coil sensitivities always; the tolerance
+Monte Carlo when `tolerances` (a [`ToleranceSet`](@ref)) is given; the locking risk when a `scenario` (a
+[`ScenarioParameters`](@ref)) is given too; and the couplings of the correction arrays named in `ntv.efc_coils`, whose
+NTV torque uses the `kinetic` settings and the perturbed-equilibrium `regularization_width`. `coil_config` sets the
+boundary grid the coil spectra are evaluated on. The coil sets in `ctrl.exclude_coils` and `ntv.efc_coils` are left
+out of the error field. Call `save_to_hdf5(target, ef)` to save the result.
+
+```julia
+resp = plasma_response(ffs)
+ef = error_fields(resp, coil_sets, ForcingTerms.CoilConfig(ft_ctrl); tolerances=read_tolerance_toml("tolerances.toml"))
+```
+"""
+function error_fields(
+ resp::PerturbedEquilibrium.PlasmaResponse,
+ coil_sets::Vector{CoilSet},
+ coil_config::CoilConfig;
+ ctrl::ErrorFieldsControl=ErrorFieldsControl(),
+ tolerances::Union{Nothing,ToleranceSet}=nothing,
+ monte_carlo::MonteCarloControl=MonteCarloControl(),
+ scenario::Union{Nothing,ScenarioParameters}=nothing,
+ risk::RiskControl=RiskControl(),
+ ntv::NTVControl=NTVControl(),
+ kinetic::KineticForces.KineticForcesControl=KineticForces.KineticForcesControl(),
+ regularization_width::Real=0.0,
+ verbose::Bool=false
+)
+ ffs = resp.ffs
+ equil = ffs.equil
+ rc = ResonantCoupling(resp)
+ sens = compute_coil_sensitivities(coil_sets, rc, equil, coil_config, ctrl; psi=ffs.psilim, b_t0=equil.params.bt0, verbose)
+ excluded = unique(String[ctrl.exclude_coils; ntv.efc_coils])
+
+ if tolerances !== nothing
+ tolerances = validate_tolerances(tolerances, sens.coil_names)
+ check_excluded_tolerances(tolerances, excluded)
+ @info "Tolerances: $(length(tolerances.coils)) coil sets, $(length(tolerances.groups)) coherent groups"
+ end
+
+ # The run's Monte Carlo is the full-window, dominant-mode summary; other windows are re-run post hoc.
+ dom = dominant_coupling(rc)
+ table = without_coils(sensitivity_table(sens, dom), excluded)
+ isempty(excluded) || @info "Error field: $(join(table.coil_names, ", ")); excluded $(join(excluded, ", "))"
+ mc = nothing
+ if tolerances !== nothing
+ mc_start = time()
+ mc = run_monte_carlo(table, tolerances, coil_sets, monte_carlo)
+ @info "Monte Carlo: $(monte_carlo.nbatch) × $(monte_carlo.nsample) samples in $(@sprintf("%.2f", time() - mc_start)) s; " *
+ "⟨|δ|⟩ = $(@sprintf("%.3e", mc.abs_delta_sampled_mean)) intrinsic, $(@sprintf("%.3e", mc.abs_delta_efc_sampled_mean)) corrected " *
+ "(nominal $(@sprintf("%.3e", mc.abs_delta_total_as_designed)))"
+ end
+
+ lock = nothing
+ scan = nothing
+ if mc !== nothing && scenario !== nothing
+ n_scaling = single_toroidal_mode(ffs.nlow, ffs.nhigh; where="the in-run locking risk of this run")
+ sc = threshold_scaling(; n=n_scaling, year=risk.year, dataset=risk.dataset, fit=risk.fit)
+ risk_start = time()
+ lock = locking_risk(mc, sc, scenario; ctrl=risk)
+ @info "Locking risk ($(scaling_label(sc))): threshold $(@sprintf("%.3e", lock.threshold_fit)); " *
+ "P_lock = $(@sprintf("%.2f", lock.locking_probability_percent)) % intrinsic, $(@sprintf("%.2f", lock.locking_probability_efc_percent)) % corrected, " *
+ "$(@sprintf("%.2f", lock.locking_probability_as_designed_percent)) % as designed ($(@sprintf("%.2f", time() - risk_start)) s)"
+ if !isempty(risk.scan_scales)
+ scan_start = time()
+ scan = tolerance_scan(table, tolerances, coil_sets, monte_carlo, sc, scenario; scales=risk.scan_scales, risk_ctrl=risk)
+ @info "Tolerance scan over $(length(scan.tolerance_scale)) scales in $(@sprintf("%.2f", time() - scan_start)) s"
+ end
+ end
+
+ # Correction-coil couplings: overlap per kAt and the NTV torque of the full and residual fields.
+ couplings = nothing
+ if !isempty(ntv.efc_coils)
+ efc_sets = [cs for cs in coil_sets if cs.name in ntv.efc_coils]
+ missing = setdiff(ntv.efc_coils, [cs.name for cs in efc_sets])
+ isempty(missing) || error("NTVControl efc_coils not among the coil sets: $(join(missing, ", "))")
+ ntv_start = time()
+ couplings = efc_couplings(resp, efc_sets, rc, dom, coil_config, kinetic; method=ntv.method, verbose, regularization_width,
+ rotation_scan=ntv.rotation_scan, scan_points=ntv.rotation_scan_points, scan_max_points=ntv.rotation_scan_max_points,
+ scan_tolerance=ntv.rotation_scan_tolerance, span_factor=ntv.rotation_span_factor, offset_factor=ntv.rotation_offset_factor)
+ @info "NTV couplings of $(length(couplings)) correction arrays in $(@sprintf("%.1f", time() - ntv_start)) s"
+ end
+
+ settings = (; ctrl, monte_carlo, risk, ntv, kinetic, scenario, regularization_width=Float64(regularization_width))
+ return ErrorFieldsResult(sens, dom, tolerances, mc, lock, scan, couplings, resp, settings)
+end
diff --git a/src/ErrorFields/Correction.jl b/src/ErrorFields/Correction.jl
new file mode 100644
index 0000000000..613b72da33
--- /dev/null
+++ b/src/ErrorFields/Correction.jl
@@ -0,0 +1,145 @@
+# The linear correction requirement of a set of correction arrays. Included after NTVLimits.jl (reads an EFCCoupling).
+
+"""
+ CorrectionRequirement
+
+Field names follow the ErrorFields result grammar `[_instance][_efc][_statistic][_unit]` (see the manual's
+"Result names"); every field name is also its HDF5 dataset name.
+
+The linear correction requirement of one error-field source against a set of correction arrays, on
+the rational surfaces of one run. Each needed current is given as a complex factor on the array's
+current as given (`−1` on an array identical to the source cancels it exactly) and in kilo-ampere-turns.
+
+## Fields
+
+ - `source_name`, `array_names`: the coil sets, `[narray]` for the arrays
+ - `rational_psi`, `rational_q`, `rational_m`, `rational_n`: the surfaces, `[nsurface]`
+ - `current_factor_dominant`: the factor on each array *alone* that cancels the source's
+ dominant-mode overlap, `−δ_source / δ_array`; `NaN` for an array with no overlap `[narray]`.
+ Not a joint solution: for two or more arrays the dominant-mode condition leaves an
+ `(narray − 1)`-dimensional family of solutions
+ - `current_factor_dominant_minimum_norm`: the member of that family with the smallest total current
+ `Σ|I_k|²` `[narray]`, `I_k = −δ_source · conj(δ_k/a_k) / Σ|δ/a|²` with `a_k` the array's ampere-turns
+ (`a_k = 1` when any array's ampere-turns are unknown)
+ - `current_factor_least_squares`: the factors on every array together that minimize the resonant
+ field on every surface, `argmin ‖C·(b̃_source + Σ_k f_k b̃_k)‖` `[narray]`; unique when
+ `least_squares_rank == narray`, otherwise the minimizer with the smallest total current in the
+ same sense
+ - `least_squares_rank`: rank of the `nsurface × narray` system the least squares solves
+ - `current_dominant_kat`, `current_dominant_minimum_norm_kat`, `current_least_squares_kat`: the
+ three factors times each array's `ampere_turns_kat`, complex kilo-ampere-turns (magnitude and
+ toroidal phase) `[narray]`; `NaN` for an array whose ampere-turns are unknown
+ - `resonant_field_source_t`: the source's resonant field on each surface, `C·b̃_source`, tesla `[nsurface]`
+ - `resonant_field_dominant_t`: the same after each array's dominant-mode correction alone, tesla `[nsurface × narray]`
+ - `resonant_field_least_squares_t`: the same after the joint least-squares correction, tesla `[nsurface]`
+ - `cosine_similarity`: `|⟨b̃_array, b̃_source⟩| / (‖b̃_array‖ ‖b̃_source‖)`, how much of the source's
+ spectrum each array can see at all; `NaN` for a round-off field `[narray]`
+"""
+struct CorrectionRequirement
+ source_name::String
+ array_names::Vector{String}
+ rational_psi::Vector{Float64}
+ rational_q::Vector{Float64}
+ rational_m::Vector{Int}
+ rational_n::Vector{Int}
+ current_factor_dominant::Vector{ComplexF64}
+ current_factor_dominant_minimum_norm::Vector{ComplexF64}
+ current_factor_least_squares::Vector{ComplexF64}
+ least_squares_rank::Int
+ current_dominant_kat::Vector{ComplexF64}
+ current_dominant_minimum_norm_kat::Vector{ComplexF64}
+ current_least_squares_kat::Vector{ComplexF64}
+ resonant_field_source_t::Vector{ComplexF64}
+ resonant_field_dominant_t::Matrix{ComplexF64}
+ resonant_field_least_squares_t::Vector{ComplexF64}
+ cosine_similarity::Vector{Float64}
+end
+
+"""
+ correction_requirement(ctx, source::CoilOverlap, arrays) -> CorrectionRequirement
+ correction_requirement(h5path, source_name, array_names; mode=1, coil_sets=nothing, kwargs...) -> CorrectionRequirement
+
+The currents a set of arrays needs to correct one error field, and what is left: each array's solo
+dominant-mode factor, the minimum-current dominant-mode solution, and the joint least-squares factors
+that minimize the resonant field `C·(b̃_source + Σ_k f_k b̃_k)` over every rational surface, with the
+resonant field left after each. Every input is a [`CoilOverlap`](@ref), so any geometry can be a source
+or an array. The `h5path` form takes names among the run's coil sets (or `coil_sets` when given) and
+evaluates them on the run's control surface. See [`uncorrectable_probability`](@ref) for the
+NTV-limited counterpart.
+"""
+function correction_requirement(ctx::ResonantDriveContext, source::CoilOverlap, arrays::AbstractVector{CoilOverlap})
+ isempty(arrays) && throw(ArgumentError("correction_requirement: give at least one correction array"))
+ N = length(source.spectrum)
+ for o in arrays
+ o.mode == source.mode || throw(ArgumentError("correction_requirement: \"$(o.coil_name)\" is projected onto mode $(o.mode), the source onto mode $(source.mode)"))
+ length(o.spectrum) == N || throw(DimensionMismatch("correction_requirement: \"$(o.coil_name)\" carries $(length(o.spectrum)) modes, the source $N"))
+ end
+ size(ctx.rc.C, 2) == N || throw(DimensionMismatch("correction_requirement: the coupling has $(size(ctx.rc.C, 2)) columns, the spectra $N entries"))
+ C = ctx.rc.C
+ r_source = C * source.spectrum
+ R = hcat((C * o.spectrum for o in arrays)...)
+ f_dom = [abs(o.delta) > 0 ? -source.delta / o.delta : NaN + NaN * im for o in arrays]
+ r_dom = hcat((isnan(f_dom[k]) ? fill(NaN + NaN * im, length(r_source)) : r_source .+ R[:, k] .* f_dom[k] for k in eachindex(arrays))...)
+ kat = [o.ampere_turns_kat for o in arrays]
+ # Minimum-norm solutions are taken in kilo-ampere-turns when every array's ampere-turns are known,
+ # so arrays given at different pattern currents are weighed by physical current, not bookkeeping.
+ a = all(k -> isfinite(k) && k > 0, kat) ? kat : ones(length(kat))
+ δ = [o.delta for o in arrays] ./ a
+ f_mn = sum(abs2, δ) > 0 ? (-source.delta .* conj.(δ) ./ sum(abs2, δ)) ./ a : fill(NaN + NaN * im, length(δ))
+ f_ls = -(pinv(R ./ a') * r_source) ./ a
+ r_ls = r_source .+ R * f_ls
+ n_src = norm(source.spectrum)
+ cosines = [(n = norm(o.spectrum); n > 0 && n_src > 0 ? abs(dot(o.spectrum, source.spectrum)) / (n * n_src) : NaN) for o in arrays]
+ return CorrectionRequirement(source.coil_name, [o.coil_name for o in arrays], copy(ctx.rc.rational_psi), copy(ctx.rc.rational_q),
+ copy(ctx.rc.rational_m), copy(ctx.rc.rational_n), f_dom, f_mn, f_ls, rank(R), f_dom .* kat, f_mn .* kat, f_ls .* kat, r_source, r_dom, r_ls, cosines)
+end
+function correction_requirement(h5path::AbstractString, source_name::AbstractString, array_names::AbstractVector{<:AbstractString}; mode::Int=1,
+ coil_sets=nothing, psi_low::Real=0.0, psi_high::Real=PerturbedEquilibrium.CORE_PSI_HIGH, kwargs...)
+ ctx = ResonantDriveContext(h5path; psi_low, psi_high, kwargs...)
+ sets = coil_sets === nothing ? ForcingTerms.load_coil_sets(ctx.cfg, 1; equil=ctx.equil) : collect(coil_sets)
+ by_name = Dict(cs.name => cs for cs in sets)
+ pick(nm) = haskey(by_name, nm) ? by_name[nm] : throw(ArgumentError("no coil set named \"$nm\" (have $(join(sort(collect(keys(by_name))), ", ")))"))
+ overlaps = coil_overlaps(ctx, vcat([pick(source_name)], [pick(nm) for nm in array_names]); mode)
+ return correction_requirement(ctx, overlaps[1], overlaps[2:end])
+end
+
+"""
+ needed_current_distribution(mc::MonteCarloResult, array::CoilOverlap) -> NamedTuple
+
+The Monte Carlo's intrinsic `|δ|` histogram re-expressed as the current on `array` that cancels
+each sampled overlap's dominant mode: as the factor `|δ| / |δ_array|` on the array's current as
+given, fields `current_factor_bin_edges` and `current_factor_pdf` (density per unit factor,
+integrating to one), and in kilo-ampere-turns through the array's `ampere_turns_kat`, fields
+`current_bin_edges_kat` and `current_pdf_per_kat` (`NaN` when the ampere-turns are unknown).
+"""
+function needed_current_distribution(mc::MonteCarloResult, array::CoilOverlap)
+ a = abs(array.delta)
+ a > 0 || throw(ArgumentError("needed_current_distribution: array \"$(array.coil_name)\" has no dominant-mode overlap to correct with"))
+ kat = array.ampere_turns_kat
+ return (; current_factor_bin_edges=mc.abs_delta_bin_edges ./ a, current_factor_pdf=mc.abs_delta_pdf .* a,
+ current_bin_edges_kat=mc.abs_delta_bin_edges .* (kat / a), current_pdf_per_kat=mc.abs_delta_pdf .* (a / kat))
+end
+
+"""
+ uncorrectable_probability(mc::MonteCarloResult, c::EFCCoupling; delta_threshold, torque_budget, safety_factor=1.0, model=:auto, rotation_exponent=1.0) -> NamedTuple
+
+How often the sampled machine's overlap exceeds what the array can correct: the fraction of the
+Monte Carlo's intrinsic `|δ|` beyond `max_correctable_overlap`'s `with_ntv` limit for the array,
+as a percentage. The explicit-correction counterpart of the corrected locking probability's
+`efc_factor` model. Fields `abs_delta_max_correctable`, `probability_percent`, and the `model` resolved.
+"""
+function uncorrectable_probability(mc::MonteCarloResult, c::EFCCoupling; delta_threshold::Real, torque_budget::Real, safety_factor::Real=1.0,
+ model::Symbol=:auto, rotation_exponent::Real=1.0)
+ limits = max_correctable_overlap(c; delta_threshold, torque_budget, safety_factor, model, rotation_exponent)
+ limit = limits.with_ntv
+ edges = mc.abs_delta_bin_edges
+ widths = diff(edges)
+ beyond = 0.0
+ for i in eachindex(widths)
+ lo, hi = edges[i], edges[i+1]
+ hi <= limit && continue
+ beyond += mc.abs_delta_pdf[i] * (lo >= limit ? widths[i] : hi - limit)
+ end
+ # Samples past the last edge sit in the last bin; if the limit is beyond the grid nothing exceeds it.
+ return (; abs_delta_max_correctable=limit, probability_percent=isfinite(limit) ? clamp(100 * beyond, 0.0, 100.0) : 0.0, model=_resolve_model(c, model))
+end
diff --git a/src/ErrorFields/ErrorFields.jl b/src/ErrorFields/ErrorFields.jl
new file mode 100644
index 0000000000..58256bc7e3
--- /dev/null
+++ b/src/ErrorFields/ErrorFields.jl
@@ -0,0 +1,95 @@
+module ErrorFields
+
+"""
+ErrorFields - Error-field sensitivity of a perturbed equilibrium to coil misalignment
+
+Given one perturbed-equilibrium solve and its coil sets, the module linearizes the resonant
+drive of each named coil set with respect to its rigid-body degrees of freedom, so that any
+tolerance question downstream (Monte Carlo over manufacturing tolerances, locking risk,
+allowable-tolerance scans) reduces to cheap linear algebra on a small table instead of a new
+plasma solve or a new Biot-Savart integration.
+
+## Module Structure
+
+- `ErrorFieldsStructs.jl`: `ErrorFieldsControl` (the `[ErrorFields]` TOML section),
+ `CoilSensitivities` (the cached linearization: as-designed spectra and their derivatives),
+ `SensitivityTable` (that linearization projected onto one dominant coupling mode)
+- `Overlap.jl`: `ResonantDriveContext` (everything a finished run offers for judging coil geometry,
+ gathered once), `coil_overlaps`, `combine_overlaps`, `applied_spectrum` — the entry point for
+ evaluating a coil design against a stored solve without re-running the plasma
+- `Sensitivity.jl`: `compute_coil_sensitivities` (central-difference sweep of every rigid
+ shift and tilt of every coil set on one shared boundary grid), `sensitivity_table`
+- `Output.jl`: HDF5 writer under `ErrorFields/CoilSensitivities/` and the matching reader
+- `ToleranceTOML.jl`: the tolerance input file — `read_tolerance_toml`, `ToleranceSet`,
+ `validate_tolerances`, and the tilt unit conversion `tilt_tolerance_deg`
+- `Sampling.jl`: random misalignment draws within a tolerance — the `RadialDistribution`
+ shapes, `sample_disk`, `sample_uncertainty`, and the additive and cylinder tolerance models
+- `MonteCarlo.jl`: `run_monte_carlo`, the batched, seeded recombination of a `SensitivityTable`
+ with a `ToleranceSet` into intrinsic and corrected `|δ|` histograms
+- `Linearity.jl`: `linearity_check`, the linear model against finite displacements out to the
+ tolerance edge, one Biot–Savart pass per row
+- `Risk.jl`: the ITPA penetration-threshold scalings, keyed by publication year (the 2020 n = 1
+ and n = 2 fits, the 2026 n = 1 OLS and WLS fits), `locking_risk` (the overlap distribution
+ convolved with the threshold distribution), `tolerance_scan` and `allowable_tolerance`
+- `Phasing.jl`: `phasing_map`, the closed-form overlap of several coil arrays against their
+ relative current-pattern phases
+- `NTVLimits.jl`: how much error field a correction coil can cancel before its own NTV torque
+ costs the rotation that holds the threshold up (`EFCCoupling`, `correction_current`)
+- `Correction.jl`: `correction_requirement`, the currents a set of arrays needs to cancel an error
+ field on every rational surface and what remains, and `uncorrectable_probability`, how often the
+ Monte Carlo's overlap exceeds what an NTV-limited array can correct
+
+The stored primitive is the derivative of each coil set's root-area-weighted control-surface
+spectrum b̃, not a scalar: the overlap with any dominant mode is linear in b̃, so the ψ_N window,
+the mode index, and the field normalization stay post-hoc analysis choices.
+"""
+
+using LinearAlgebra
+using HDF5
+using Printf
+using TOML
+using Random
+import Random: AbstractRNG
+using FastInterpolations: cubic_interp, linear_interp
+using Roots: find_zero, Brent
+
+import ..Equilibrium
+import ..ForcingTerms
+import ..ForcingTerms: CoilSet, CoilSetConfig, CoilConfig, ForcingMode, CoilForcingGrid, coil_forcing_modes, apply_transforms
+import ..PerturbedEquilibrium
+import ..KineticForces
+import ..PerturbedEquilibrium: ResonantCoupling, DominantCoupling, dominant_coupling, rootarea_field, coupling_overlap
+import ..Utilities
+
+include("ErrorFieldsStructs.jl")
+include("Overlap.jl")
+include("Sensitivity.jl")
+include("ToleranceTOML.jl")
+include("Sampling.jl")
+include("MonteCarlo.jl")
+include("Linearity.jl")
+include("Risk.jl")
+include("Phasing.jl")
+include("NTVLimits.jl")
+include("Correction.jl")
+include("Assessment.jl")
+include("Output.jl")
+
+export ErrorFieldsControl, CoilSensitivities, SensitivityTable
+export compute_coil_sensitivities, sensitivity_table, without_coils, excluded_coil_names, cancelling_offset, LinearityCheck, linearity_check
+export ResonantDriveContext, CoilOverlap, coil_overlaps, combine_overlaps, resonant_fraction_percent
+export applied_spectrum, forcing_grids, regrid, MIN_NZETA_PER_PERIOD
+export ToleranceSet, CoilTolerance, CoherentGroupTolerance, OtherFieldBudget
+export read_tolerance_toml, parse_tolerance_toml, validate_tolerances, check_excluded_tolerances, tilt_tolerance_deg
+export RadialDistribution, Flat, UniformArea, Hollow, Ring, PowerLaw, randpow, radial_distribution
+export disk_radius, sample_disk, sample_uncertainty, sample_additive, sample_cylinder
+export MonteCarloControl, MonteCarloResult, run_monte_carlo, worst_case_terms, apply_current_factors, update
+export ThresholdScaling, ITPA_THRESHOLD_SCALINGS, threshold_scaling, scaling_label, ScenarioParameters, fitted_threshold, threshold_samples
+export RiskControl, RiskResult, locking_risk, ToleranceScan, tolerance_scan, allowable_tolerance, risk_convergence, single_toroidal_mode
+export PhasingMap, phasing_map, extreme_phasing
+export error_fields, ErrorFieldsResult, efc_couplings
+export NTVControl, EFCCoupling, residual_spectrum, correction_current, correction_current_upper, max_correctable_overlap, efc_current_curve, read_efc_couplings
+export CorrectionRequirement, correction_requirement, needed_current_distribution, uncorrectable_probability
+export has_rotation_scan, rotation_scan_span, torque_at, torque_zero_crossings, rotation_shift, threshold_factor
+
+end # module ErrorFields
diff --git a/src/ErrorFields/ErrorFieldsStructs.jl b/src/ErrorFields/ErrorFieldsStructs.jl
new file mode 100644
index 0000000000..9b882c3795
--- /dev/null
+++ b/src/ErrorFields/ErrorFieldsStructs.jl
@@ -0,0 +1,118 @@
+"""
+ ErrorFieldsControl
+
+Control parameters for the `[ErrorFields]` TOML section. The sweep needs a coil-forced
+perturbed-equilibrium solve (`forcing_data_format = "coil"` with the singular-coupling step on);
+everything here concerns only how the coil linearization is taken and where it is written.
+Analysis choices (which resonant surfaces count, which singular mode, which normalization) are
+never inputs: the full spectra are stored and projected post hoc with [`sensitivity_table`](@ref).
+
+## Fields
+
+ - `fd_step_shift_m`: central-difference step for the rigid shifts, in metres
+ - `fd_step_tilt_deg`: central-difference step for the rigid tilts, in degrees
+ - `rotation_center`: pivot of the tilt taps — `"conductor"` rotates every conductor of a set
+ about its own arc-length centre, `"set"` rotates the whole set rigidly about its common
+ arc-length centre (a winding pack moving as one body)
+ - `exclude_coils`: coil sets of the run that are not error-field sources (e.g. a correction array).
+ Their sensitivities are tabulated, but they are left out of the error field, Monte Carlo,
+ worst-case bound and scans, and no tolerance may name them. `[ErrorFields.NTV] efc_coils` are always excluded
+"""
+Base.@kwdef struct ErrorFieldsControl
+ fd_step_shift_m::Float64 = 1e-3
+ fd_step_tilt_deg::Float64 = 0.1
+ rotation_center::String = "conductor"
+ exclude_coils::Vector{String} = String[]
+end
+
+"""
+ CoilSensitivities
+
+Field names follow the ErrorFields result grammar `[_instance][_efc][_statistic][_unit]` (see the manual's
+"Result names"); every field name is also its HDF5 dataset name.
+
+Linearization of each coil set's control-surface spectrum with respect to its six rigid-body
+degrees of freedom, on the (m, n) column ordering of the [`ResonantCoupling`](@ref) it was built
+against. Spectra are root-area-weighted fields b̃ in tesla, the vector the coupling matrix and
+its singular vectors act on, so projecting any of them onto a mode is one inner product.
+
+Shifts are Cartesian translations of the whole set; tilts are rotations about the machine
+x, y, z axes through the pivot selected by `ErrorFieldsControl.rotation_center`. A coil set's
+spectrum is proportional to its currents, so the table is specific to the current pattern it
+was evaluated with; `peak_current` and `winding_multiplier` let a user renormalize per ampere-turn.
+
+## Fields
+
+ - `coil_names`: name of each coil set `[ncoil_set]`
+ - `m_modes`, `n_modes`: poloidal and toroidal mode number of each spectrum entry `[numpert_total]`
+ - `b_t0`: toroidal field magnitude on axis, tesla — the normalization that makes the overlap a
+ dimensionless δ
+ - `field_as_designed`: b̃ of each set as built, tesla `[numpert_total × ncoil_set]`
+ - `shift_sensitivity_per_m`: ∂b̃/∂(Δx, Δy, Δz), tesla per metre `[numpert_total × 3 × ncoil_set]`
+ - `tilt_sensitivity_per_deg`: ∂b̃/∂(θx, θy, θz), tesla per degree `[numpert_total × 3 × ncoil_set]`
+ - `shift_linearity_residual`, `tilt_linearity_residual`: ‖b̃(+h) + b̃(−h) − 2b̃(0)‖ of each tap
+ relative to the set's largest first difference ‖b̃(+h) − b̃(−h)‖ over all six taps, a
+ window-independent measure of how much second-order response the linearization drops at
+ the step taken `[3 × ncoil_set]`
+ - `peak_current`: largest conductor current magnitude of each set, amperes `[ncoil_set]`
+ - `winding_multiplier`: turns per conductor element of each set `[ncoil_set]`
+ - `major_radius_m`: arc-length-weighted major radius of each set, metres `[ncoil_set]` — the lever
+ arm that turns a tilt angle into the rim displacement engineering tolerances are written in
+"""
+struct CoilSensitivities
+ coil_names::Vector{String}
+ m_modes::Vector{Int}
+ n_modes::Vector{Int}
+ b_t0::Float64
+ field_as_designed::Matrix{ComplexF64}
+ shift_sensitivity_per_m::Array{ComplexF64,3}
+ tilt_sensitivity_per_deg::Array{ComplexF64,3}
+ shift_linearity_residual::Matrix{Float64}
+ tilt_linearity_residual::Matrix{Float64}
+ peak_current::Vector{Float64}
+ winding_multiplier::Vector{Float64}
+ major_radius_m::Vector{Float64}
+end
+
+"""
+ SensitivityTable
+
+Field names follow the ErrorFields result grammar `[_instance][_efc][_statistic][_unit]` (see the manual's
+"Result names"); every field name is also its HDF5 dataset name.
+
+A [`CoilSensitivities`](@ref) projected onto one singular mode of a [`DominantCoupling`](@ref)
+and normalized by the axis toroidal field: the dimensionless overlap δ of each coil set and its
+derivatives, which is all a tolerance Monte Carlo consumes. Built by [`sensitivity_table`](@ref).
+
+With `S = (S_x, S_y)` the in-plane shift sensitivities, a rigid shift `(Δx, Δy)` moves the overlap
+by `S_x·Δx + S_y·Δy`; the same holds for the tilts. Singular vectors carry an arbitrary phase, so
+only magnitudes and relative phases within one table are meaningful.
+
+## Fields
+
+ - `coil_names`: name of each coil set `[ncoil_set]`
+ - `mode`: index of the singular mode projected onto (1 is the dominant mode)
+ - `delta_as_designed`: overlap of each set as built `[ncoil_set]`
+ - `shift_sensitivity_per_m`: ∂δ/∂(Δx, Δy, Δz), per metre `[3 × ncoil_set]`
+ - `tilt_sensitivity_per_deg`: ∂δ/∂(θx, θy, θz), per degree `[3 × ncoil_set]`
+ - `abs_delta_shift_per_mm`: direction-averaged in-plane magnitude `√((|S_x|² + |S_y|²)/2)` of the
+ shift sensitivity, per millimetre `[ncoil_set]` — the single-number sensitivity to placement
+ - `abs_delta_tilt_per_deg`: the same average over the tilt sensitivities, per degree `[ncoil_set]`
+ - `abs_delta_rim_per_mm`: that tilt sensitivity expressed as rim displacement at `major_radius_m`,
+ per millimetre `[ncoil_set]` — the unit mechanical tolerances usually arrive in
+ - `cancelling_shift_m`: the in-plane shift `(Δx, Δy)` that cancels `delta_as_designed`, metres
+ `[2 × ncoil_set]`, see [`cancelling_offset`](@ref)
+ - `cancelling_tilt_deg`: the in-plane tilt `(θx, θy)` that cancels `delta_as_designed`, degrees `[2 × ncoil_set]`
+"""
+struct SensitivityTable
+ coil_names::Vector{String}
+ mode::Int
+ delta_as_designed::Vector{ComplexF64}
+ shift_sensitivity_per_m::Matrix{ComplexF64}
+ tilt_sensitivity_per_deg::Matrix{ComplexF64}
+ abs_delta_shift_per_mm::Vector{Float64}
+ abs_delta_tilt_per_deg::Vector{Float64}
+ abs_delta_rim_per_mm::Vector{Float64}
+ cancelling_shift_m::Matrix{Float64}
+ cancelling_tilt_deg::Matrix{Float64}
+end
diff --git a/src/ErrorFields/Linearity.jl b/src/ErrorFields/Linearity.jl
new file mode 100644
index 0000000000..55eafa05ae
--- /dev/null
+++ b/src/ErrorFields/Linearity.jl
@@ -0,0 +1,119 @@
+# The linear sensitivity model checked at finite displacements. Included after MonteCarlo.jl (uses group_tilt_deg).
+
+"""
+ LinearityCheck
+
+Field names follow the ErrorFields result grammar `[_instance][_efc][_statistic][_unit]` (see the manual's
+"Result names"); every field name is also its HDF5 dataset name.
+
+The linear sensitivity model against finite rigid displacements, one row per coil set (or
+coherent group), degree of freedom, scale and sign. Vectors are all `[nrow]`.
+
+## Fields
+
+ - `name`: coil set or coherent group
+ - `kind`: `:shift` or `:tilt`
+ - `axis`: 1 for x, 2 for y (a group's rows use axis 1)
+ - `scale`: the displacement as a multiple of the tolerance
+ - `displacement`: the signed displacement applied, metres for a shift and degrees for a tilt
+ - `delta_as_designed`: δ of the undisplaced geometry
+ - `delta_linear`: the model's prediction `δ_as_designed + S·Δ` (or `T·θ`, with a group's lateral
+ rotation term as the Monte Carlo applies it)
+ - `delta_actual`: δ of the displaced geometry from a fresh Biot–Savart pass
+ - `relative_error`: `|δ_actual − δ_linear| / |δ_linear − δ_as_designed|`, the error of the
+ predicted change; `NaN` where the linear change vanishes
+"""
+struct LinearityCheck
+ name::Vector{String}
+ kind::Vector{Symbol}
+ axis::Vector{Int}
+ scale::Vector{Float64}
+ displacement::Vector{Float64}
+ delta_as_designed::Vector{ComplexF64}
+ delta_linear::Vector{ComplexF64}
+ delta_actual::Vector{ComplexF64}
+ relative_error::Vector{Float64}
+end
+
+"""
+ linearity_check(ctx, coil_sets, tolerances; scales=(1.0, 2.0), mode=1, ctrl=ErrorFieldsControl()) -> LinearityCheck
+ linearity_check(h5path; scales=(1.0, 2.0), mode=1, psi_low=0.0, psi_high=CORE_PSI_HIGH, ctrl=ErrorFieldsControl(), kwargs...) -> LinearityCheck
+
+Compare the linear overlap model of [`sensitivity_table`](@ref) with the overlap recomputed for finite
+displacements: each toleranced coil set is shifted and tilted in-plane by `±scale × tolerance` (a
+cylinder coil's tilt range is `atan(shift_tol / half_height)`), and each coherent group is shifted and
+rigidly rotated about its pivot. Include the largest scale a tolerance scan will use. Costs one
+Biot–Savart pass per row. The file form rebuilds its inputs from `gpec.h5`.
+"""
+function linearity_check(ctx::ResonantDriveContext, coil_sets::AbstractVector{CoilSet}, ts::ToleranceSet;
+ scales=(1.0, 2.0), mode::Int=1, ctrl::ErrorFieldsControl=ErrorFieldsControl())
+ sets = collect(coil_sets)
+ validate_tolerances(ts, [cs.name for cs in sets])
+ all(>(0), scales) || throw(ArgumentError("scales must be positive multiples of the tolerance"))
+ table = sensitivity_table(compute_coil_sensitivities(ctx, sets, ctrl), ctx.dom; mode)
+ set_of = Dict(cs.name => cs for cs in sets)
+ index = Dict(nm => i for (i, nm) in enumerate(table.coil_names))
+ overlap(cs) = coupling_overlap(ctx.dom, applied_spectrum(cs, ctx.rc, ctx.grids))[mode] / ctx.b_t0
+ S, T = table.shift_sensitivity_per_m, table.tilt_sensitivity_per_deg
+ name = String[]
+ kind = Symbol[]
+ axis = Int[]
+ scale = Float64[]
+ disp = Float64[]
+ δ0s = ComplexF64[]
+ lins = ComplexF64[]
+ acts = ComplexF64[]
+ function record!(nm, k, a, s, Δ, δ0, lin, act)
+ push!(name, nm)
+ push!(kind, k)
+ push!(axis, a)
+ push!(scale, s)
+ push!(disp, Δ)
+ push!(δ0s, δ0)
+ push!(lins, lin)
+ push!(acts, act)
+ end
+ for t in ts.coils
+ cs = set_of[t.name]
+ i = index[t.name]
+ pivot = ctrl.rotation_center == "set" ? _set_center(cs) : nothing
+ tilt_tol = t.tolerance_model == "cylinder" ? rad2deg(atan(t.shift_tol_m / t.cylinder_half_height_m)) : tilt_tolerance_deg(t, cs)
+ δ0 = table.delta_as_designed[i]
+ for (k, tol, M) in ((:shift, t.shift_tol_m, S), (:tilt, tilt_tol, T)), a in 1:2, s in scales, sgn in (-1, 1)
+ Δ = sgn * s * tol
+ Δ == 0 && continue
+ record!(t.name, k, a, s, Δ, δ0, δ0 + M[a, i] * Δ, overlap(_rigidly_perturbed(cs, k, a, Δ, pivot)))
+ end
+ end
+ for g in ts.groups
+ members = [set_of[m] for m in g.members]
+ idx = [index[m] for m in g.members]
+ δ0 = sum(table.delta_as_designed[idx])
+ tilt_tol = g.tolerance_model == "cylinder" ? rad2deg(atan(g.shift_tol_m / g.cylinder_half_height_m)) : group_tilt_deg(g, set_of)
+ pivot = (0.0, 0.0, g.rotation_center_z_m)
+ for (k, tol) in ((:shift, g.shift_tol_m), (:tilt, tilt_tol)), s in scales, sgn in (-1, 1)
+ Δ = sgn * s * tol
+ Δ == 0 && continue
+ if k === :shift
+ lin = δ0 + sum(S[1, i] * Δ for i in idx)
+ act = sum(overlap(_rigidly_perturbed(cs, :shift, 1, Δ, nothing)) for cs in members)
+ else
+ # A rigid rotation about the pivot on the machine axis tilts each member and shifts it
+ # laterally by −h·θ, the term the Monte Carlo carries as R; the geometry pass does both at once.
+ θ = deg2rad(Δ)
+ lin = δ0 + sum(T[1, i] * Δ - (_set_center(set_of[g.members[j]])[3] - g.rotation_center_z_m) * S[2, i] * θ for (j, i) in enumerate(idx))
+ act = sum(overlap(_rigidly_perturbed(cs, :tilt, 1, Δ, pivot)) for cs in members)
+ end
+ record!(g.name, k, 1, s, Δ, δ0, lin, act)
+ end
+ end
+ change = abs.(lins .- δ0s)
+ rel = [c > 0 ? abs(a - l) / c : NaN for (a, l, c) in zip(acts, lins, change)]
+ return LinearityCheck(name, kind, axis, scale, disp, δ0s, lins, acts, rel)
+end
+function linearity_check(h5path::AbstractString; scales=(1.0, 2.0), mode::Int=1, psi_low::Real=0.0, psi_high::Real=PerturbedEquilibrium.CORE_PSI_HIGH,
+ ctrl::ErrorFieldsControl=ErrorFieldsControl(), kwargs...)
+ _, ts, coil_sets = _monte_carlo_inputs(h5path; psi_low, psi_high, mode)
+ ctx = ResonantDriveContext(h5path; psi_low, psi_high, kwargs...)
+ return linearity_check(ctx, coil_sets, ts; scales, mode, ctrl)
+end
diff --git a/src/ErrorFields/MonteCarlo.jl b/src/ErrorFields/MonteCarlo.jl
new file mode 100644
index 0000000000..3c7b517ba2
--- /dev/null
+++ b/src/ErrorFields/MonteCarlo.jl
@@ -0,0 +1,478 @@
+"""
+ MonteCarlo
+
+The tolerance Monte Carlo: recombine a [`SensitivityTable`](@ref) with a [`ToleranceSet`](@ref)
+by drawing every coil set's misalignment within its tolerance many times and histogramming the
+resulting dominant-mode overlap `|δ|`. Because the overlap is linear in the misalignments, one
+sample is a handful of complex multiply-adds per coil set; no field is recomputed. Two
+histograms are accumulated per run, the intrinsic `|δ|` and the corrected one in which every
+correctable contribution is divided by the error-field-correction factor.
+
+The run writes the full-window summary; [`run_monte_carlo`](@ref) re-evaluates any other ψ_N window
+or singular mode in memory or from `gpec.h5`.
+"""
+
+"""
+ MonteCarloControl
+
+Settings of the tolerance Monte Carlo, the `[ErrorFields.MonteCarlo]` TOML table.
+
+## Fields
+
+ - `nsample`: samples per batch
+ - `nbatch`: independent batches; their spread is the statistical error bar of every derived quantity
+ - `seed`: base seed; batch `b` uses `Xoshiro(hash((seed, b)))`, so results are bit-identical for
+ any thread count
+ - `nbins`: histogram bins, linear on `[0, delta_max]`
+ - `delta_max`: upper edge of the histogram; `0` means `1.5 ×` the worst-case alignment
+ `Σ(|δ_as_designed| + tolerance × |sensitivity|)`, which the tolerance draws cannot exceed (only
+ the Gaussian uncertainties and the unattributed budget can, and those land in the last bin)
+ - `tolerance_scale`: multiplies every shift and tilt tolerance, for allowable-tolerance scans;
+ uncertainties and the unattributed budget are not scaled
+ - `coil_subset`: coil set names whose tolerances are sampled; every other coil set contributes
+ only its as-designed overlap, and a coherent group is sampled only if all its members are listed.
+ Empty means all
+ - `scale_subset`: coil set and group names that `tolerance_scale` applies to; every other name
+ keeps its own tolerance (scale 1). Empty means `tolerance_scale` applies to all. This is how one
+ class of coils is scanned while another holds its tolerance
+ - `scale_map`: an explicit multiplier per coil set or group name, applied on top of
+ `tolerance_scale`; names absent from the map are unscaled by it. A name in `scale_subset` or
+ `scale_map` that is neither a coil set of the run nor a group of the tolerance file is an error
+
+The effective multiplier of a name is `(name in scale_subset or scale_subset empty ? tolerance_scale : 1) × get(scale_map, name, 1)`.
+None of these change which random numbers are drawn.
+"""
+Base.@kwdef struct MonteCarloControl
+ nsample::Int = 1_000_000
+ nbatch::Int = 10
+ seed::Int = 1
+ nbins::Int = 300
+ delta_max::Float64 = 0.0
+ tolerance_scale::Float64 = 1.0
+ coil_subset::Vector{String} = String[]
+ scale_subset::Vector{String} = String[]
+ scale_map::Dict{String,Float64} = Dict{String,Float64}()
+end
+
+# The tolerance multiplier of one coil set or group under a control.
+function _scale_of(ctrl::MonteCarloControl, name::AbstractString)
+ base = isempty(ctrl.scale_subset) || name in ctrl.scale_subset ? ctrl.tolerance_scale : 1.0
+ return base * get(ctrl.scale_map, name, 1.0)
+end
+
+function _check_scale_names(ctrl::MonteCarloControl, coil_names, group_names)
+ known = Set{String}(vcat(String.(coil_names), String.(group_names)))
+ for (what, names) in (("scale_subset", ctrl.scale_subset), ("scale_map", collect(keys(ctrl.scale_map))))
+ bad = [n for n in names if !(n in known)]
+ isempty(bad) || throw(ArgumentError("$what names neither a coil set of the run nor a coherent group: $(join(bad, ", ")) (known: $(join(sort(collect(known)), ", ")))"))
+ end
+ all(>=(0), values(ctrl.scale_map)) || throw(ArgumentError("scale_map multipliers must be ≥ 0"))
+ return nothing
+end
+
+"""
+ apply_current_factors(table::SensitivityTable, ts::ToleranceSet) -> SensitivityTable
+
+The table with every coil set's as-designed overlap and sensitivities multiplied by its
+`current_factor` from the tolerance file. The spectrum is linear in current, so the nominal
+overlap, the worst-case bound and every sampled overlap scale together; the cancelling offsets
+do not change, since they are ratios. Returns the table itself when every factor is 1.
+"""
+function apply_current_factors(table::SensitivityTable, ts::ToleranceSet)
+ factor = Dict(t.name => t.current_factor for t in ts.coils)
+ f = [get(factor, nm, 1.0) for nm in table.coil_names]
+ all(==(1.0), f) && return table
+ scale_cols(m) = m .* permutedims(f)
+ return SensitivityTable(copy(table.coil_names), table.mode, table.delta_as_designed .* f,
+ scale_cols(table.shift_sensitivity_per_m), scale_cols(table.tilt_sensitivity_per_deg),
+ table.abs_delta_shift_per_mm .* abs.(f), table.abs_delta_tilt_per_deg .* abs.(f), table.abs_delta_rim_per_mm .* abs.(f),
+ copy(table.cancelling_shift_m), copy(table.cancelling_tilt_deg))
+end
+
+"""
+ MonteCarloResult
+
+Field names follow the ErrorFields result grammar `[_instance][_efc][_statistic][_unit]` (see the manual's
+"Result names"); every field name is also its HDF5 dataset name.
+
+Histograms of the dominant-mode overlap magnitude over the sampled misalignments.
+
+## Fields
+
+ - `abs_delta_bin_edges`: `|δ|` bin edges `[nbins + 1]`; samples above the last edge are counted in the last bin
+ - `abs_delta_pdf`, `abs_delta_efc_pdf`: probability density of the intrinsic and of the corrected `|δ|`, averaged
+ over batches `[nbins]`
+ - `abs_delta_pdf_batches`, `abs_delta_efc_pdf_batches`: the same per batch `[nbins × nbatch]`
+ - `abs_delta_total_as_designed`: `|Σ δ_as_designed|`, the as-designed overlap with every coil at its design position
+ - `abs_delta_worst_case`: the worst-case alignment bound used to size the histogram
+ - `abs_delta_sampled_mean`, `abs_delta_efc_sampled_mean`: sample means of the two magnitudes
+ - `clamped_fraction`: fraction of samples whose intrinsic `|δ|` landed beyond `abs_delta_bin_edges[end]`
+ (the corrected histogram clamps too but is not separately tallied)
+ - `nsample`, `nbatch`, `seed`: as run
+"""
+struct MonteCarloResult
+ abs_delta_bin_edges::Vector{Float64}
+ abs_delta_pdf::Vector{Float64}
+ abs_delta_efc_pdf::Vector{Float64}
+ abs_delta_pdf_batches::Matrix{Float64}
+ abs_delta_efc_pdf_batches::Matrix{Float64}
+ abs_delta_total_as_designed::Float64
+ abs_delta_worst_case::Float64
+ abs_delta_sampled_mean::Float64
+ abs_delta_efc_sampled_mean::Float64
+ clamped_fraction::Float64
+ nsample::Int
+ nbatch::Int
+ seed::Int
+end
+
+const _ADDITIVE = 1
+const _CYLINDER = 2
+
+const _HISTOGRAM_MARGIN = 1.5 # default delta_max = _HISTOGRAM_MARGIN × the worst-case alignment
+const _WORST_CASE_SIGMA = 3 # standard deviations at which Gaussian uncertainties enter the worst-case bound
+
+_model_code(tolerance_model::AbstractString) = tolerance_model == "cylinder" ? _CYLINDER : _ADDITIVE
+_radial_p(radial_shape::AbstractString) = randpow(radial_distribution(radial_shape))
+
+# Everything the sample loop needs, resolved to plain arrays once per run: no names, no
+# dictionaries, no dispatch inside the loop.
+struct _CoilTerms
+ delta0::Vector{ComplexF64}
+ Sx::Vector{ComplexF64}
+ Sy::Vector{ComplexF64}
+ Tx::Vector{ComplexF64}
+ Ty::Vector{ComplexF64}
+ shift_tol::Vector{Float64} # m, scaled
+ tilt_tol::Vector{Float64} # deg, scaled
+ shift_sigma::Vector{Float64} # m
+ tilt_sigma::Vector{Float64} # deg
+ p_radial::Vector{Float64}
+ model::Vector{Int}
+ z_top::Vector{Float64}
+ correctable::Vector{Bool}
+end
+
+struct _GroupTerms
+ Sx::Vector{ComplexF64} # Σ_members S_x
+ Sy::Vector{ComplexF64}
+ Tx::Vector{ComplexF64}
+ Ty::Vector{ComplexF64}
+ Rx::Vector{ComplexF64} # Σ_members (z_m − z_pivot)·S_x, the lateral shift of a rigid rotation
+ Ry::Vector{ComplexF64}
+ shift_tol::Vector{Float64}
+ tilt_tol::Vector{Float64}
+ p_radial::Vector{Float64}
+ model::Vector{Int}
+ z_top::Vector{Float64}
+ phase_index::Vector{Int}
+ nphase::Int
+ correctable::Vector{Bool}
+end
+
+"""
+ run_monte_carlo(table, tolerances, coil_sets, ctrl=MonteCarloControl()) -> MonteCarloResult
+ run_monte_carlo(h5path; psi_low=0.0, psi_high=CORE_PSI_HIGH, mode=1, kwargs...) -> MonteCarloResult
+
+Sample every coil set's misalignment within its tolerance and histogram the dominant-mode
+overlap. Per sample and coil set `c` with sensitivities `S = (S_x, S_y)` per metre and
+`T = (T_x, T_y)` per degree,
+
+```
+δ = Σ_c [δ_as_designed,c + S_c·(Δ_c + u_c) + T_c·(θ_c + v_c)] + Σ_g [S_g·(Δ_g + Δ_rot) + T_g·θ_g] + δ_other
+```
+
+where `(Δ_c, θ_c)` is the coil's own draw (additive: independent shift and tilt disks; cylinder:
+[`sample_cylinder`](@ref)), `u_c`, `v_c` its Gaussian placement uncertainties, `(Δ_g, θ_g)` one
+draw shared by every member of coherent group `g` (groups with equal `phase_group` share the
+direction), `Δ_rot = −(z_m − z_pivot)·(θy_g + iθx_g)` the lateral shift a rigid rotation of the
+group about its pivot (in the sense `apply_transforms` uses) gives a member at height `z_m`, and
+`δ_other` the unattributed budget with a random direction. `S·Δ` means `S_x·real(Δ) + S_y·imag(Δ)`.
+The corrected histogram divides every correctable term (coils and groups not listed as
+uncorrectable, and the unattributed budget) by `efc_factor`.
+
+`coil_sets` supply the major radii for tilt tolerances given in metres and the heights of
+group members; coil sets without a tolerance block contribute their nominal overlap only. The file
+form rebuilds the inputs from `gpec.h5`; `kwargs` are [`MonteCarloControl`](@ref) fields.
+"""
+function run_monte_carlo(table::SensitivityTable, ts::ToleranceSet, coil_sets::Vector{CoilSet}, ctrl::MonteCarloControl=MonteCarloControl())
+ ctrl.nsample > 0 && ctrl.nbatch > 0 && ctrl.nbins > 0 || throw(ArgumentError("nsample, nbatch and nbins must be positive"))
+ ctrl.tolerance_scale >= 0 || throw(ArgumentError("tolerance_scale must be ≥ 0"))
+ validate_tolerances(ts, table.coil_names)
+ table = apply_current_factors(table, ts)
+ coils, groups = _resolve_terms(table, ts, coil_sets, ctrl)
+ other = ts.other_field
+ p_other = _radial_p(other.radial_shape)
+ efc = ts.efc_factor
+
+ abs_delta_total_as_designed = abs(sum(table.delta_as_designed))
+ abs_delta_worst_case = _worst_case(table, coils, groups, other)
+ delta_max = ctrl.delta_max > 0 ? ctrl.delta_max : _HISTOGRAM_MARGIN * abs_delta_worst_case
+ delta_max > 0 || throw(ArgumentError("the histogram range is zero: no nominal overlap, tolerance, or budget to sample"))
+ edges = collect(range(0.0, delta_max; length=ctrl.nbins + 1))
+ width = edges[2] - edges[1]
+
+ counts = zeros(Int, ctrl.nbins, ctrl.nbatch)
+ counts_efc = zeros(Int, ctrl.nbins, ctrl.nbatch)
+ sums = zeros(ctrl.nbatch)
+ sums_efc = zeros(ctrl.nbatch)
+ clamped = zeros(Int, ctrl.nbatch)
+
+ Threads.@threads for b in 1:ctrl.nbatch
+ rng = Xoshiro(hash((ctrl.seed, b)))
+ cnt = view(counts, :, b)
+ cnt_efc = view(counts_efc, :, b)
+ s = 0.0
+ s_efc = 0.0
+ nclamp = 0
+ phases = zeros(4, groups.nphase)
+ for _ in 1:ctrl.nsample
+ δ_corr, δ_uncorr = _sample_delta!(rng, phases, coils, groups, other, p_other)
+ a = abs(δ_corr + δ_uncorr)
+ a_efc = abs(δ_corr / efc + δ_uncorr)
+ s += a
+ s_efc += a_efc
+ i = min(floor(Int, a / width) + 1, ctrl.nbins)
+ a >= delta_max && (nclamp += 1)
+ cnt[i] += 1
+ cnt_efc[min(floor(Int, a_efc / width) + 1, ctrl.nbins)] += 1
+ end
+ sums[b] = s
+ sums_efc[b] = s_efc
+ clamped[b] = nclamp
+ end
+
+ norm = ctrl.nsample * width
+ abs_delta_pdf_batches = counts ./ norm
+ abs_delta_efc_pdf_batches = counts_efc ./ norm
+ total = ctrl.nsample * ctrl.nbatch
+ return MonteCarloResult(edges, vec(sum(abs_delta_pdf_batches; dims=2)) ./ ctrl.nbatch, vec(sum(abs_delta_efc_pdf_batches; dims=2)) ./ ctrl.nbatch,
+ abs_delta_pdf_batches, abs_delta_efc_pdf_batches, abs_delta_total_as_designed, abs_delta_worst_case, sum(sums) / total, sum(sums_efc) / total,
+ sum(clamped) / total, ctrl.nsample, ctrl.nbatch, ctrl.seed)
+end
+
+function run_monte_carlo(h5path::AbstractString; psi_low::Real=0.0, psi_high::Real=PerturbedEquilibrium.CORE_PSI_HIGH, mode::Int=1, kwargs...)
+ table, ts, coil_sets = _monte_carlo_inputs(h5path; psi_low, psi_high, mode)
+ return run_monte_carlo(table, ts, coil_sets, MonteCarloControl(; kwargs...))
+end
+
+# The three inputs of a post-hoc Monte Carlo rebuilt from a run file: the windowed sensitivity
+# table, the echoed tolerances, and the coil geometry snapshot.
+function _monte_carlo_inputs(h5path::AbstractString; psi_low::Real, psi_high::Real, mode::Int)
+ ts = read_tolerance_snapshot(h5path)
+ ts === nothing && throw(ArgumentError("$h5path carries no tolerance snapshot (the run named no tolerance_file)"))
+ table = without_coils(sensitivity_table(h5path; psi_low, psi_high, mode), excluded_coil_names(h5path))
+ coil_sets = h5open(h5path, "r") do f
+ haskey(f, "Input/RawInputs/Coils") || throw(ArgumentError("$h5path has no Input/RawInputs/Coils snapshot"))
+ sets = CoilSet[]
+ ForcingTerms.load_coils_from_h5_group!(sets, f["Input/RawInputs/Coils"])
+ sets
+ end
+ return table, ts, coil_sets
+end
+
+# One sample: returns (correctable, uncorrectable) complex overlaps. `phases` is scratch for
+# the per-phase-group directions (shift, tilt, cylinder top, cylinder bottom).
+@inline function _sample_delta!(rng::AbstractRNG, phases::Matrix{Float64}, coils::_CoilTerms, groups::_GroupTerms, other::OtherFieldBudget, p_other::Float64)
+ δc = zero(ComplexF64)
+ δu = zero(ComplexF64)
+ @inbounds for c in eachindex(coils.delta0)
+ if coils.model[c] == _CYLINDER
+ shift, tilt = sample_cylinder(rng, coils.shift_tol[c], coils.z_top[c], coils.p_radial[c])
+ else
+ shift, tilt = sample_additive(rng, coils.shift_tol[c], coils.p_radial[c], coils.tilt_tol[c], coils.p_radial[c])
+ end
+ shift += sample_uncertainty(rng, coils.shift_sigma[c])
+ tilt += sample_uncertainty(rng, coils.tilt_sigma[c])
+ d = coils.delta0[c] + coils.Sx[c] * real(shift) + coils.Sy[c] * imag(shift) + coils.Tx[c] * real(tilt) + coils.Ty[c] * imag(tilt)
+ coils.correctable[c] ? (δc += d) : (δu += d)
+ end
+ @inbounds for k in 1:groups.nphase, q in 1:4
+ phases[q, k] = 2π * rand(rng)
+ end
+ @inbounds for g in eachindex(groups.Sx)
+ k = groups.phase_index[g]
+ if groups.model[g] == _CYLINDER
+ shift, tilt = sample_cylinder(rng, groups.shift_tol[g], groups.z_top[g], groups.p_radial[g]; phase_top=phases[3, k], phase_bot=phases[4, k])
+ else
+ shift, tilt = sample_additive(rng, groups.shift_tol[g], groups.p_radial[g], groups.tilt_tol[g], groups.p_radial[g];
+ phase_shift=phases[1, k], phase_tilt=phases[2, k])
+ end
+ # A rigid rotation by (θx, θy) about the pivot moves a member at height h by −h·(θy + iθx).
+ θ = deg2rad(tilt)
+ d = groups.Sx[g] * real(shift) + groups.Sy[g] * imag(shift) + groups.Tx[g] * real(tilt) + groups.Ty[g] * imag(tilt) -
+ groups.Rx[g] * imag(θ) - groups.Ry[g] * real(θ)
+ groups.correctable[g] ? (δc += d) : (δu += d)
+ end
+ if other.magnitude > 0 || other.sigma > 0
+ amp = other.magnitude * rand(rng)^p_other + other.sigma * randn(rng)
+ δc += amp * cis(2π * rand(rng))
+ end
+ return δc, δu
+end
+
+"""
+ group_tilt_deg(g::CoherentGroupTolerance, set_of) -> Float64
+
+The rigid rotation angle, in degrees, that a coherent group's tilt tolerance stands for.
+
+A tilt in metres is a rim displacement and names one angle only if the members share a major radius
+(or `tilt_lever_arm_m` is set); errors when their radii differ by more than 1%. Declare such a group in degrees.
+"""
+function group_tilt_deg(g::CoherentGroupTolerance, set_of)
+ g.tilt_units == "deg" && return Float64(g.tilt_tol)
+ isnan(g.tilt_lever_arm_m) || return tilt_tolerance_deg(g.tilt_tol, g.tilt_units, g.tilt_lever_arm_m; name="coherent group $(g.name)")
+ radii = [ForcingTerms.nominal_major_radius(set_of[m]) for m in g.members]
+ lo, hi = extrema(radii)
+ hi - lo <= 0.01 * hi || throw(
+ ArgumentError(
+ "coherent group \"$(g.name)\" gives its tilt in metres, but its members span nominal radii " *
+ "$(round(lo; digits=3))-$(round(hi; digits=3)) m, so a rim displacement does not name one " *
+ "rotation angle. Declare this group's tilt in degrees (tilt_units = \"deg\").")
+ )
+ return tilt_tolerance_deg(g.tilt_tol, g.tilt_units, set_of[g.members[argmin(radii)]])
+end
+
+function _resolve_terms(table::SensitivityTable, ts::ToleranceSet, coil_sets::Vector{CoilSet}, ctrl::MonteCarloControl)
+ names = table.coil_names
+ index = Dict(n => i for (i, n) in enumerate(names))
+ set_of = Dict(cs.name => cs for cs in coil_sets)
+ for n in names
+ haskey(set_of, n) || throw(ArgumentError("no coil set geometry named \"$n\" among the given coil sets"))
+ end
+ active(n) = isempty(ctrl.coil_subset) || n in ctrl.coil_subset
+ uncorrectable = Set(ts.uncorrectable_coils)
+ _check_scale_names(ctrl, names, [g.name for g in ts.groups])
+ scale_of(n) = _scale_of(ctrl, n)
+
+ n = length(names)
+ shift_tol = zeros(n)
+ tilt_tol = zeros(n)
+ shift_sigma = zeros(n)
+ tilt_sigma = zeros(n)
+ p_radial = ones(n)
+ model = fill(_ADDITIVE, n)
+ z_top = zeros(n)
+ for t in ts.coils
+ i = index[t.name]
+ active(t.name) || continue
+ cs = set_of[t.name]
+ shift_tol[i] = scale_of(t.name) * t.shift_tol_m
+ tilt_tol[i] = scale_of(t.name) * tilt_tolerance_deg(t, cs)
+ shift_sigma[i] = t.shift_sigma_m
+ tilt_sigma[i] = tilt_tolerance_deg(t.tilt_sigma, t.tilt_units, cs)
+ p_radial[i] = _radial_p(t.radial_shape)
+ model[i] = _model_code(t.tolerance_model)
+ z_top[i] = t.cylinder_half_height_m
+ end
+ coils = _CoilTerms(collect(table.delta_as_designed), table.shift_sensitivity_per_m[1, :], table.shift_sensitivity_per_m[2, :], table.tilt_sensitivity_per_deg[1, :],
+ table.tilt_sensitivity_per_deg[2, :],
+ shift_tol, tilt_tol, shift_sigma, tilt_sigma, p_radial, model, z_top, [!(nm in uncorrectable) for nm in names])
+
+ kept = [g for g in ts.groups if all(active, g.members)]
+ ng = length(kept)
+ gSx = zeros(ComplexF64, ng)
+ gSy = zeros(ComplexF64, ng)
+ gTx = zeros(ComplexF64, ng)
+ gTy = zeros(ComplexF64, ng)
+ gRx = zeros(ComplexF64, ng)
+ gRy = zeros(ComplexF64, ng)
+ g_shift = zeros(ng)
+ g_tilt = zeros(ng)
+ g_p = ones(ng)
+ g_model = fill(_ADDITIVE, ng)
+ g_ztop = zeros(ng)
+ g_corr = trues(ng)
+ labels = unique(g.phase_group for g in kept)
+ phase_index = [findfirst(==(g.phase_group), labels) for g in kept]
+ for (gi, g) in enumerate(kept)
+ for m in g.members
+ i = index[m]
+ h = _set_center(set_of[m])[3] - g.rotation_center_z_m
+ gSx[gi] += table.shift_sensitivity_per_m[1, i]
+ gSy[gi] += table.shift_sensitivity_per_m[2, i]
+ gTx[gi] += table.tilt_sensitivity_per_deg[1, i]
+ gTy[gi] += table.tilt_sensitivity_per_deg[2, i]
+ gRx[gi] += h * table.shift_sensitivity_per_m[1, i]
+ gRy[gi] += h * table.shift_sensitivity_per_m[2, i]
+ m in uncorrectable && (g_corr[gi] = false)
+ end
+ g_shift[gi] = scale_of(g.name) * g.shift_tol_m
+ g_tilt[gi] = scale_of(g.name) * group_tilt_deg(g, set_of)
+ g_p[gi] = _radial_p(g.radial_shape)
+ g_model[gi] = _model_code(g.tolerance_model)
+ g_ztop[gi] = g.cylinder_half_height_m
+ end
+ groups = _GroupTerms(gSx, gSy, gTx, gTy, gRx, gRy, g_shift, g_tilt, g_p, g_model, g_ztop, phase_index, length(labels), g_corr)
+ return coils, groups
+end
+
+# Worst-case alignment bound used to size the histogram: every term at its tolerance edge and in
+# phase. Gaussian uncertainties enter at _WORST_CASE_SIGMA standard deviations, not a hard limit.
+function _worst_case(table::SensitivityTable, coils::_CoilTerms, groups::_GroupTerms, other::OtherFieldBudget)
+ w = sum(abs, table.delta_as_designed)
+ for c in eachindex(coils.delta0)
+ s_in = max(abs(coils.Sx[c]), abs(coils.Sy[c]))
+ t_in = max(abs(coils.Tx[c]), abs(coils.Ty[c]))
+ tilt_reach = coils.model[c] == _CYLINDER ? rad2deg(atan(coils.shift_tol[c] / coils.z_top[c])) : coils.tilt_tol[c]
+ w += s_in * (coils.shift_tol[c] + _WORST_CASE_SIGMA * coils.shift_sigma[c]) + t_in * (tilt_reach + _WORST_CASE_SIGMA * coils.tilt_sigma[c])
+ end
+ for g in eachindex(groups.Sx)
+ s_in = max(abs(groups.Sx[g]), abs(groups.Sy[g]))
+ # Rx, Ry carry the rotation term's per-radian sensitivity; deg2rad(1) folds it into T's per-degree units.
+ t_in = max(abs(groups.Tx[g]), abs(groups.Ty[g])) + deg2rad(1) * max(abs(groups.Rx[g]), abs(groups.Ry[g]))
+ tilt_reach = groups.model[g] == _CYLINDER ? rad2deg(atan(groups.shift_tol[g] / groups.z_top[g])) : groups.tilt_tol[g]
+ w += s_in * groups.shift_tol[g] + t_in * tilt_reach
+ end
+ return w + other.magnitude + _WORST_CASE_SIGMA * other.sigma
+end
+
+"""
+ worst_case_terms(table, tolerances, coil_sets; tolerance_scale=1.0) -> NamedTuple
+ worst_case_terms(h5path; psi_low=0.0, psi_high=CORE_PSI_HIGH, mode=1, tolerance_scale=1.0) -> NamedTuple
+
+The worst-case alignment bound `abs_delta_worst_case` of [`run_monte_carlo`](@ref) split into the terms
+that make it up, so the tolerance budget can be read coil by coil. Per coil set: `abs_delta_as_designed` is
+`|δ_as_designed|`, `abs_delta_shift_tolerance` is `max(|S_x|, |S_y|)·(shift_tol + 3σ_shift)` and `abs_delta_tilt_tolerance` is
+`max(|T_x|, |T_y|)·(tilt_reach + 3σ_tilt)`, where `tilt_reach` is the tilt tolerance in degrees
+or, under the cylinder model, the angle the axis line can reach, `atan(shift_tol / half_height)`.
+Per coherent group (`group_names`): `abs_delta_group_shift_tolerance` and `abs_delta_group_tilt_tolerance`, the latter including the
+lateral displacement a rigid rotation gives each member. `abs_delta_unattributed` is the unattributed budget at
+`magnitude + 3σ`. `abs_delta_worst_case` is the sum of every term. Every coil set is counted (no `coil_subset`);
+`tolerance_scale`, `scale_subset`, `scale_map` and `current_factor` apply as in the Monte Carlo.
+"""
+function worst_case_terms(table::SensitivityTable, ts::ToleranceSet, coil_sets::Vector{CoilSet}; tolerance_scale::Real=1.0,
+ scale_subset::AbstractVector{<:AbstractString}=String[], scale_map::AbstractDict=Dict{String,Float64}())
+ validate_tolerances(ts, table.coil_names)
+ table = apply_current_factors(table, ts)
+ coils, groups = _resolve_terms(table, ts, coil_sets, MonteCarloControl(; tolerance_scale, scale_subset=String.(scale_subset), scale_map=Dict{String,Float64}(scale_map)))
+ other = ts.other_field
+ nominal = abs.(table.delta_as_designed)
+ shift = similar(nominal)
+ tilt = similar(nominal)
+ for c in eachindex(coils.delta0)
+ s_in = max(abs(coils.Sx[c]), abs(coils.Sy[c]))
+ t_in = max(abs(coils.Tx[c]), abs(coils.Ty[c]))
+ tilt_reach = coils.model[c] == _CYLINDER ? rad2deg(atan(coils.shift_tol[c] / coils.z_top[c])) : coils.tilt_tol[c]
+ shift[c] = s_in * (coils.shift_tol[c] + _WORST_CASE_SIGMA * coils.shift_sigma[c])
+ tilt[c] = t_in * (tilt_reach + _WORST_CASE_SIGMA * coils.tilt_sigma[c])
+ end
+ ng = length(groups.Sx)
+ group_shift = zeros(ng)
+ group_tilt = zeros(ng)
+ for g in 1:ng
+ s_in = max(abs(groups.Sx[g]), abs(groups.Sy[g]))
+ t_in = max(abs(groups.Tx[g]), abs(groups.Ty[g])) + deg2rad(1) * max(abs(groups.Rx[g]), abs(groups.Ry[g]))
+ tilt_reach = groups.model[g] == _CYLINDER ? rad2deg(atan(groups.shift_tol[g] / groups.z_top[g])) : groups.tilt_tol[g]
+ group_shift[g] = s_in * groups.shift_tol[g]
+ group_tilt[g] = t_in * tilt_reach
+ end
+ group_names = [g.name for g in ts.groups]
+ return (; coil_names=copy(table.coil_names), abs_delta_as_designed=nominal, abs_delta_shift_tolerance=shift, abs_delta_tilt_tolerance=tilt, group_names,
+ abs_delta_group_shift_tolerance=group_shift, abs_delta_group_tilt_tolerance=group_tilt, abs_delta_unattributed=other.magnitude + _WORST_CASE_SIGMA * other.sigma,
+ abs_delta_worst_case=_worst_case(table, coils, groups, other))
+end
+function worst_case_terms(h5path::AbstractString; psi_low::Real=0.0, psi_high::Real=PerturbedEquilibrium.CORE_PSI_HIGH, mode::Int=1, kwargs...)
+ table, ts, coil_sets = _monte_carlo_inputs(h5path; psi_low, psi_high, mode)
+ return worst_case_terms(table, ts, coil_sets; kwargs...)
+end
diff --git a/src/ErrorFields/NTVLimits.jl b/src/ErrorFields/NTVLimits.jl
new file mode 100644
index 0000000000..4504a8b457
--- /dev/null
+++ b/src/ErrorFields/NTVLimits.jl
@@ -0,0 +1,610 @@
+"""
+ NTVLimits
+
+How much error field a correction coil can cancel before the neoclassical toroidal viscosity
+(NTV) torque of its own field costs the rotation that keeps the penetration threshold up. A
+correction coil array cancels the dominant-mode overlap at `C_c` per kilo-ampere-turn, but the
+non-resonant remainder of its field drives an NTV torque that does not go away when the
+resonant part is cancelled.
+
+Per kilo-ampere-turn, the torque `T_full` of the coil's whole field and `T_residual` of its field with
+the dominant mode projected out are tabulated against a rigid shift `Δω` of the E×B rotation (diamagnetic
+frequencies held fixed) on an adaptive grid spanning both senses of rotation past the neoclassical offset.
+
+The correction current then follows from a zero-dimensional torque balance: with the torque
+budget `T_0` the torque that would bring the reference rotation `ω_ref` to rest, the rotation
+shift under a current `I` solves `Δω·T_0/ω_ref = T(Δω)·I²`, and the threshold falls as
+`δ_thresh·(ω/ω_0)^α = δ_thresh·(1 + Δω/ω_ref)^α`. The current that corrects an intrinsic overlap
+`δ_EF` down to `s·δ_thresh` solves `δ_EF − C_c·I = s·δ_thresh·(1 + Δω(I)/ω_ref)^α`. When the
+balance loses its root the rotation has bifurcated away and the overlap is not correctable. A
+constant braking torque with `α = 1` reduces this to the closed-form quadratic
+`δ_EF − C_c·I = s·δ_thresh·(1 − T·I²/T_0)` of the original analysis, kept as the `:linear` model.
+
+The condition is on the magnitude of the residual, `|δ_EF − C_c·I| = s·δ_thresh·f(I)`, so the correctable
+currents are a window: [`correction_current`](@ref) returns its lower edge and
+[`correction_current_upper`](@ref) its upper edge, past which the over-correction is itself above threshold.
+
+The `:linear` model holds only while `T·I² < T_0` (current capped at `I_max = √(T_0/T)`) and ignores the
+neoclassical offset; the tabulated torque balance is the default whenever the run carries a rotation
+scan. The linear model is that of Logan et al., Nucl. Fusion (2026), doi:10.1088/1741-4326/ae6086,
+Eqs. (5)–(7), and of Leuthold et al., J. Plasma Phys. 92, E49 (2026), doi:10.1017/S0022377826101421,
+Eq. (A2).
+"""
+
+"""
+ NTVControl
+
+Settings of the correction-coil NTV evaluation, the `[ErrorFields.NTV]` TOML table.
+
+## Fields
+
+ - `efc_coils`: coil set names of the correction arrays to evaluate (empty: stage off)
+ - `method`: KineticForces torque method to use (`"fgar"` by default; it must be enabled in `[KineticForces]`)
+ - `rotation_scan`: tabulate the torques against a rigid E×B rotation shift (`true`); `false` evaluates only the nominal rotation (`:linear` model only)
+ - `rotation_scan_points`: points of the initial symmetric shift grid (made odd so that the unshifted point is one of them)
+ - `rotation_scan_max_points`: cap on the number of kinetic evaluations per spectrum after adaptive refinement
+ - `rotation_scan_tolerance`: refinement stops when every interval's midpoint prediction error is below this fraction of the torque range
+ - `rotation_span_factor`: the scan covers `±span_factor × max(|ω_E|, offset_factor·|ω_*T|)` evaluated at the innermost kinetic surface
+ - `rotation_offset_factor`: neoclassical offset in units of the ion temperature-gradient diamagnetic frequency `ω_*T` (about 2, Park, Boozer and Menard 2009), sizes the scan
+"""
+Base.@kwdef struct NTVControl
+ efc_coils::Vector{String} = String[]
+ method::String = "fgar"
+ rotation_scan::Bool = true
+ rotation_scan_points::Int = 9
+ rotation_scan_max_points::Int = 21
+ rotation_scan_tolerance::Float64 = 0.05
+ rotation_span_factor::Float64 = 1.0
+ rotation_offset_factor::Float64 = 2.0
+end
+
+"""
+Sign relating the kinetic torque to the rotation it acts on: `−1` means a positive `T_φ` lowers
+the E×B rotation shift `Δω` (the kernel reports braking as positive). A property of the kinetic
+kernel's sign convention, fixed empirically on the DIII-D error-field example; no run checks it.
+"""
+const TORQUE_ROTATION_SIGN = -1.0
+
+"""
+ EFCCoupling
+
+Field names follow the ErrorFields result grammar `[_instance][_efc][_statistic][_unit]` (see the manual's
+"Result names"); every field name is also its HDF5 dataset name.
+
+The couplings of one correction coil array, per kilo-ampere-turn of its current pattern.
+
+## Fields
+
+ - `coil_name`: the array
+ - `delta_per_kat`: dominant-mode overlap `|δ|` per kAt (`C_c`)
+ - `resonant_fraction_percent`: resonant fraction of the array's field, `100·|Vᴴb̃|/‖b̃‖`
+ - `torque_full_per_kat2`: NTV torque of the whole field per kAt², N·m, with its sign, at the nominal rotation
+ - `torque_residual_per_kat2`: NTV torque of the field with the dominant mode projected out, per kAt², N·m, with its sign, at the nominal rotation
+ - `rotation_shift`: the scanned rigid E×B rotation shifts `Δω`, rad/s, sorted and containing 0 (a single 0 when no scan was made)
+ - `torque_full_scan`, `torque_residual_scan`: the two torques at each shift, N·m per kAt²
+ - `omega_reference`: the reference rotation `ω_ref`, rad/s, the ion toroidal rotation weighted by density and volume; `NaN` without a scan
+ - `omega_offset_estimate`: the rough neoclassical offset used to size the scan, rad/s; `NaN` without a scan
+ - `psi`: kinetic ψ_N grid of the torque profiles (empty without a scan)
+ - `torque_full_profile`, `torque_residual_profile`: cumulative torque `T(ψ)` at each shift, `length(psi) × length(rotation_shift)`, N·m per kAt²
+
+The constructor that omits the rotation-scan fields builds a coupling with no scan, the nominal torques only.
+"""
+struct EFCCoupling
+ coil_name::String
+ delta_per_kat::Float64
+ resonant_fraction_percent::Float64
+ torque_full_per_kat2::Float64
+ torque_residual_per_kat2::Float64
+ rotation_shift::Vector{Float64}
+ torque_full_scan::Vector{Float64}
+ torque_residual_scan::Vector{Float64}
+ omega_reference::Float64
+ omega_offset_estimate::Float64
+ psi::Vector{Float64}
+ torque_full_profile::Matrix{Float64}
+ torque_residual_profile::Matrix{Float64}
+end
+
+EFCCoupling(coil_name, delta_per_kat, resonant_fraction_percent, torque_full_per_kat2, torque_residual_per_kat2) =
+ EFCCoupling(coil_name, delta_per_kat, resonant_fraction_percent, torque_full_per_kat2, torque_residual_per_kat2,
+ [0.0], [Float64(torque_full_per_kat2)], [Float64(torque_residual_per_kat2)], NaN, NaN, Float64[], zeros(0, 1), zeros(0, 1))
+
+# Field-wise equality (the default falls back to identity for the array fields); NaN equals NaN.
+Base.:(==)(a::EFCCoupling, b::EFCCoupling) = all(isequal(getfield(a, f), getfield(b, f)) for f in fieldnames(EFCCoupling))
+
+"""
+ has_rotation_scan(c::EFCCoupling) -> Bool
+
+Whether the coupling carries a torque-versus-rotation table (more than the nominal point and a finite reference rotation).
+"""
+has_rotation_scan(c::EFCCoupling) = length(c.rotation_shift) > 1 && isfinite(c.omega_reference)
+
+"""
+ rotation_scan_span(omega_e, omega_star_T; span_factor=1.0, offset_factor=2.0) -> (; span, offset_estimate)
+
+Half-width of the symmetric rotation-shift scan, `span_factor × max(|ω_E|, offset_factor·|ω_*T|)`,
+from the E×B and ion temperature-gradient diamagnetic frequencies at the innermost kinetic
+surface, and the signed rough offset `offset_factor·ω_*T` it was sized against.
+"""
+function rotation_scan_span(omega_e::Real, omega_star_T::Real; span_factor::Real=1.0, offset_factor::Real=2.0)
+ offset_estimate = offset_factor * omega_star_T
+ span = span_factor * max(abs(omega_e), abs(offset_estimate))
+ span > 0 || throw(ArgumentError("rotation_scan_span: both ω_E and ω_*T vanish at the innermost surface; nothing to scan"))
+ return (; span, offset_estimate)
+end
+
+"""
+ residual_spectrum(dom::DominantCoupling, b̃; mode=1) -> Vector{ComplexF64}
+
+The applied root-area-weighted spectrum with singular mode `mode` projected out,
+`b̃ − V_k (V_kᴴ b̃)`: what a perfect single-mode correction leaves behind.
+"""
+function residual_spectrum(dom::DominantCoupling, b̃::AbstractVector{<:Number}; mode::Int=1)
+ v = dom.right_singular_vectors[:, mode]
+ return Vector{ComplexF64}(b̃) .- v .* dot(v, b̃)
+end
+
+_scan_values(c::EFCCoupling, field::Symbol) =
+ field === :residual ? c.torque_residual_scan :
+ field === :full ? c.torque_full_scan :
+ throw(ArgumentError("field must be :residual or :full, got $field"))
+
+# Zero of a continuous g inside [a, b]; NaN when the interval does not bracket one.
+function _bracketed_zero(g, a::Float64, b::Float64)
+ ga, gb = g(a), g(b)
+ ga == 0 && return a
+ gb == 0 && return b
+ ga * gb < 0 || return NaN
+ return find_zero(g, (a, b), Brent())
+end
+
+# Spline of a tabulated torque against the rotation shift; a scan too short for a cubic falls back to linear.
+function _scan_spline(c::EFCCoupling, field::Symbol)
+ x, y = c.rotation_shift, _scan_values(c, field)
+ return length(x) >= 4 ? cubic_interp(x, y) : linear_interp(x, y)
+end
+
+"""
+ torque_at(c::EFCCoupling, Δω; field=:residual) -> Float64
+
+The tabulated torque, N·m per kAt², at rotation shift `Δω` from a cubic spline through the scan
+points; `NaN` outside the scanned span. Without a scan the nominal torque, for any shift.
+"""
+function torque_at(c::EFCCoupling, Δω::Real; field::Symbol=:residual)
+ T = _scan_values(c, field)
+ x = c.rotation_shift
+ length(x) == 1 && return T[1]
+ (Δω < x[1] || Δω > x[end]) && return NaN
+ return _scan_spline(c, field)(Float64(Δω))
+end
+
+"""
+ torque_zero_crossings(c::EFCCoupling; field=:residual) -> Vector{Float64}
+
+Rotation shifts at which the tabulated torque changes sign: each sign change between scan
+points is bracketed and the zero of the cubic spline found inside it. These are the
+neoclassical offsets of this field, as found rather than estimated.
+"""
+function torque_zero_crossings(c::EFCCoupling; field::Symbol=:residual)
+ T = _scan_values(c, field)
+ x = c.rotation_shift
+ length(x) == 1 && return Float64[]
+ s = _scan_spline(c, field)
+ out = Float64[]
+ for i in 1:(length(x)-1)
+ if T[i] * T[i+1] < 0
+ push!(out, _bracketed_zero(s, x[i], x[i+1]))
+ elseif T[i] == 0 && (i == 1 || T[i-1] != 0)
+ push!(out, x[i])
+ end
+ end
+ return out
+end
+
+"""
+ rotation_shift(c::EFCCoupling, current; torque_budget, omega_reference=c.omega_reference, field=:residual) -> Float64
+
+Steady rotation shift `Δω` (rad/s) of the zero-dimensional torque balance
+`Δω·T_0/ω_ref = T(Δω)·I²` under `current` kAt of the array, on the branch continuous from the
+unshifted state: the first root met walking from `Δω = 0` in the direction the torque pushes.
+`NaN` when no root lies inside the scanned span, which is the rotation bifurcating away (or a
+span that was too small; the scan settings say which). `torque_budget` is `T_0`, N·m; the
+reference rotation may be overridden, e.g. by the rotation at the dominant rational surface.
+"""
+function rotation_shift(c::EFCCoupling, current::Real; torque_budget::Real, omega_reference::Real=c.omega_reference, field::Symbol=:residual)
+ has_rotation_scan(c) || throw(ArgumentError("rotation_shift needs a coupling with a rotation scan (see NTVControl.rotation_scan)"))
+ torque_budget > 0 || throw(ArgumentError("torque_budget must be positive"))
+ isfinite(omega_reference) && omega_reference != 0 || throw(ArgumentError("omega_reference must be finite and nonzero"))
+ current == 0 && return 0.0
+ friction = torque_budget / omega_reference
+ g(Δ) = Δ * friction - TORQUE_ROTATION_SIGN * torque_at(c, Δ; field) * current^2
+ x = c.rotation_shift
+ i0 = findfirst(==(0.0), x)
+ i0 === nothing && throw(ArgumentError("the rotation scan must contain the unshifted point"))
+ T0 = _scan_values(c, field)[i0]
+ T0 == 0 && return 0.0
+ # Walk outward in the direction the torque pushes the rotation (sign of Δ ≈ ω_ref·T·I²/T_0).
+ step = sign(TORQUE_ROTATION_SIGN * T0 * omega_reference) > 0 ? 1 : -1
+ i = i0
+ while 1 <= i + step <= length(x)
+ a, b = x[i], x[i+step]
+ # The first crossing in the push direction is the stable balance whatever the torque's slope there:
+ # a torque that grows as the rotation brakes just brings the bifurcation (no root, NaN) closer.
+ g(a) * g(b) <= 0 && return _bracketed_zero(g, min(a, b), max(a, b))
+ i += step
+ end
+ return NaN
+end
+
+"""
+ threshold_factor(c::EFCCoupling, current; torque_budget, rotation_exponent=1.0, omega_reference=c.omega_reference,
+ model=:torque_balance, field=:residual) -> Float64
+
+Factor by which the penetration threshold is reduced under `current` kAt: `(1 + Δω/ω_ref)^α`
+with the balance's rotation shift for `model = :torque_balance` (`NaN` past the bifurcation
+or once the rotation is brought to rest), or `1 − |T|·I²/T_0` for `model = :linear`; `field`
+selects the residual (default) or the whole field's torque.
+"""
+function threshold_factor(c::EFCCoupling, current::Real; torque_budget::Real, rotation_exponent::Real=1.0,
+ omega_reference::Real=c.omega_reference, model::Symbol=:torque_balance, field::Symbol=:residual)
+ if model === :linear
+ T = field === :residual ? c.torque_residual_per_kat2 : c.torque_full_per_kat2
+ return 1 - abs(T) * current^2 / torque_budget
+ elseif model === :torque_balance
+ Δ = rotation_shift(c, current; torque_budget, omega_reference, field)
+ isnan(Δ) && return NaN
+ ratio = 1 + Δ / omega_reference
+ ratio > 0 || return NaN # the rotation is brought to rest: nothing left to protect the threshold
+ return ratio^rotation_exponent
+ end
+ throw(ArgumentError("model must be :torque_balance or :linear, got $model"))
+end
+
+_resolve_model(c::EFCCoupling, model::Symbol) = model === :auto ? (has_rotation_scan(c) ? :torque_balance : :linear) : model
+
+"""
+ correction_current(δ_ef, c::EFCCoupling; delta_threshold, torque_budget, safety_factor=1.0, ntv=true,
+ model=:auto, rotation_exponent=1.0, omega_reference=c.omega_reference) -> Float64
+
+Correction current, kAt, that brings an intrinsic overlap `δ_ef` down to
+`safety_factor × delta_threshold`. Without NTV (`ntv = false`) that is the linear
+`(δ_ef − s·δ_thresh) / C_c`, zero when no correction is needed. With NTV the residual torque
+lowers the threshold by [`threshold_factor`](@ref): for the `:torque_balance` model (the default
+when the coupling carries a rotation scan) the current is the root of
+`δ_ef − C_c·I − s·δ_thresh·(1 + Δω(I)/ω_ref)^α`; for `:linear` it is the smaller root of the
+closed-form quadratic, provided the residual torque has not exhausted the budget there. `NaN`
+when no such root exists, i.e. the overlap is beyond [`max_correctable_overlap`](@ref). The
+returned current is the lower edge of the correctable window; [`correction_current_upper`](@ref)
+gives the upper edge, past which the over-correction is itself above threshold.
+"""
+function correction_current(δ_ef::Real, c::EFCCoupling; delta_threshold::Real, torque_budget::Real, safety_factor::Real=1.0, ntv::Bool=true,
+ model::Symbol=:auto, rotation_exponent::Real=1.0, omega_reference::Real=c.omega_reference)
+ target = safety_factor * delta_threshold
+ excess = δ_ef - target
+ excess <= 0 && return 0.0
+ ntv || return excess / c.delta_per_kat
+ model = _resolve_model(c, model)
+ if model === :linear
+ a = target * abs(c.torque_residual_per_kat2) / torque_budget
+ a == 0 && return excess / c.delta_per_kat
+ disc = c.delta_per_kat^2 - 4a * excess
+ disc < 0 && return NaN
+ I = 2excess / (c.delta_per_kat + sqrt(disc))
+ # The budget must not be exhausted at the root: a negative threshold is no correction (OMFIT masked these).
+ return abs(c.torque_residual_per_kat2) * I^2 < torque_budget ? I : NaN
+ end
+ h(I) = δ_ef - c.delta_per_kat * I - target * threshold_factor(c, I; torque_budget, rotation_exponent, omega_reference, model)
+ I_lin = excess / c.delta_per_kat
+ h_lin = h(I_lin)
+ isnan(h_lin) && return NaN # the linear current alone already collapses the rotation
+ h_lin <= 0 && return _bracketed_zero(h, 0.0, I_lin) # an accelerating torque: less current than the linear one
+ # A braking torque: the root lies above the linear current, before the balance fails. Find the minimum of h
+ # there (the root is a tangency at the correctable limit) and bisect down to the smaller root.
+ I_hi = _largest_finite(I -> threshold_factor(c, I; torque_budget, rotation_exponent, omega_reference, model), I_lin, 1e3 * I_lin)
+ isinf(I_hi) && (I_hi = 1e3 * I_lin)
+ I_star = _argmin_unimodal(h, I_lin, I_hi)
+ h(I_star) > 0 && return NaN
+ return _bracketed_zero(h, I_lin, I_star)
+end
+
+# Golden-section minimum of a unimodal g on [a, b]; NaN values count as +Inf.
+function _argmin_unimodal(g, a::Float64, b::Float64; maxiter::Int=200)
+ φ = (sqrt(5.0) - 1) / 2
+ val(x) = (v = g(x); isnan(v) ? Inf : v)
+ c, d = b - φ * (b - a), a + φ * (b - a)
+ gc, gd = val(c), val(d)
+ for _ in 1:maxiter
+ if gc < gd
+ b, d, gd = d, c, gc
+ c = b - φ * (b - a)
+ gc = val(c)
+ else
+ a, c, gc = c, d, gd
+ d = a + φ * (b - a)
+ gd = val(d)
+ end
+ (b - a) <= 1e-12 * max(abs(a), abs(b), 1e-300) && break
+ end
+ x = 0.5 * (a + b)
+ return val(x) <= min(gc, gd) ? x : (gc < gd ? c : d)
+end
+
+"""
+ max_correctable_overlap(c::EFCCoupling; delta_threshold, torque_budget, safety_factor=1.0, model=:auto,
+ rotation_exponent=1.0, omega_reference=c.omega_reference) -> (; with_ntv, residual_only, torque_only)
+
+The largest intrinsic overlap the array can correct. `with_ntv`: the overlap beyond which
+[`correction_current`](@ref) has no root (for the `:linear` model in closed form: the
+quadratic's tangency `s·δ_thresh + C_c² T_0 / (4 s δ_thresh T_residual)`, or
+`C_c √(T_0 / T_residual)` when the residual torque exhausts the budget before that; for
+`:torque_balance` by bisection).
+`residual_only`: the overlap cancelled by the current at which the residual torque alone brings
+the rotation to rest (`C_c √(T_0 / T_residual)` for `:linear`), the zero-rotation limit of
+Logan et al. (2026) Eq. (7); it coincides with `with_ntv` whenever the quadratic's vertex lies
+outside the rotating range.
+`torque_only`: the overlap cancelled by the current at which the whole field's torque alone
+exhausts the budget (`C_c √(T_0 / T_full)`) or, with the balance, brings the reference rotation
+to rest or breaks the balance.
+`Inf` when there is no limit inside the model's reach.
+"""
+function max_correctable_overlap(c::EFCCoupling; delta_threshold::Real, torque_budget::Real, safety_factor::Real=1.0, model::Symbol=:auto,
+ rotation_exponent::Real=1.0, omega_reference::Real=c.omega_reference)
+ target = safety_factor * delta_threshold
+ model = _resolve_model(c, model)
+ if model === :linear
+ t_res, t_full = abs(c.torque_residual_per_kat2), abs(c.torque_full_per_kat2)
+ if t_res > 0
+ # The quadratic's tangency, unless the residual torque exhausts the budget first (root at √(T_0/T_res)).
+ tangency = target + c.delta_per_kat^2 * torque_budget / (4 * target * t_res)
+ exhausted = c.delta_per_kat * sqrt(torque_budget / t_res)
+ with_ntv = exhausted <= 2 * target ? tangency : exhausted
+ residual_only = exhausted
+ else
+ with_ntv = Inf
+ residual_only = Inf
+ end
+ torque_only = t_full > 0 ? c.delta_per_kat * sqrt(torque_budget / t_full) : Inf
+ return (; with_ntv, residual_only, torque_only)
+ end
+ kw = (; delta_threshold, torque_budget, safety_factor, model, rotation_exponent, omega_reference)
+ with_ntv = _largest_finite(δ -> correction_current(δ, c; kw...), target, 1e4 * target)
+ # The whole field's torque alone brings the rotation to rest (factor 0) or breaks the balance.
+ stops(I) = (f = threshold_factor(c, I; torque_budget, rotation_exponent, omega_reference, model, field=:full); isfinite(f) && f > 0 ? f : NaN)
+ torque_only = c.delta_per_kat * _largest_finite(stops, 0.0, 1e4 * (target / c.delta_per_kat))
+ # The residual torque alone brings the rotation to rest or breaks the balance: the zero-rotation limit.
+ stops_res(I) = (f = threshold_factor(c, I; torque_budget, rotation_exponent, omega_reference, model, field=:residual); isfinite(f) && f > 0 ? f : NaN)
+ residual_only = c.delta_per_kat * _largest_finite(stops_res, 0.0, 1e4 * (target / c.delta_per_kat))
+ return (; with_ntv, residual_only, torque_only)
+end
+
+# Largest x in [lo, hi] for which f(x) is finite, assuming finiteness holds on [lo, x*) only; Inf if finite up to hi.
+function _largest_finite(f, lo::Real, hi::Real)
+ isfinite(f(hi)) && return Inf
+ a, b = Float64(lo), Float64(hi)
+ for _ in 1:200
+ m = 0.5 * (a + b)
+ if isfinite(f(m))
+ a = m
+ else
+ b = m
+ end
+ (b - a) <= 1e-8 * max(b, 1e-300) && break
+ end
+ return a
+end
+
+"""
+ correction_current_upper(δ_ef, c::EFCCoupling; delta_threshold, torque_budget, safety_factor=1.0, ntv=true,
+ model=:auto, rotation_exponent=1.0, omega_reference=c.omega_reference) -> Float64
+
+Upper edge of the correctable current window, kAt: the current past which the over-correction
+`C_c·I − δ_ef` is itself above `safety_factor × delta_threshold`, so the field locks again from
+the other side. Without NTV it is `(δ_ef + s·δ_thresh) / C_c`. For the `:linear` model it is the
+larger root of the same quadratic, capped at `I_max`; for `:torque_balance` it is the root of
+`C_c·I − δ_ef − s·δ_thresh·(1 + Δω(I)/ω_ref)^α` above the null, or the current at which the
+balance fails if that comes first. `NaN` whenever [`correction_current`](@ref) is `NaN`.
+"""
+function correction_current_upper(δ_ef::Real, c::EFCCoupling; delta_threshold::Real, torque_budget::Real, safety_factor::Real=1.0, ntv::Bool=true,
+ model::Symbol=:auto, rotation_exponent::Real=1.0, omega_reference::Real=c.omega_reference)
+ target = safety_factor * delta_threshold
+ isnan(correction_current(δ_ef, c; delta_threshold, torque_budget, safety_factor, ntv, model, rotation_exponent, omega_reference)) && return NaN
+ ntv || return (δ_ef + target) / c.delta_per_kat
+ model = _resolve_model(c, model)
+ if model === :linear
+ t_res = abs(c.torque_residual_per_kat2)
+ t_res == 0 && return (δ_ef + target) / c.delta_per_kat
+ # Over-correction side: C·I − δ_ef = target·(1 − t_res·I²/T_0), i.e. a·I² + C·I − (δ_ef + target) = 0
+ # with the same a as the under-correction quadratic; its positive root is the upper edge.
+ a = target * t_res / torque_budget
+ upper = 2(δ_ef + target) / (c.delta_per_kat + sqrt(c.delta_per_kat^2 + 4a * (δ_ef + target)))
+ return min(upper, sqrt(torque_budget / t_res))
+ end
+ g(I) = c.delta_per_kat * I - δ_ef - target * threshold_factor(c, I; torque_budget, rotation_exponent, omega_reference, model)
+ I_null = max(δ_ef / c.delta_per_kat, 0.0)
+ isnan(g(I_null)) && return NaN
+ span = 1e3 * max(I_null, target / c.delta_per_kat)
+ I_hi = _largest_finite(I -> threshold_factor(c, I; torque_budget, rotation_exponent, omega_reference, model), I_null, span)
+ isinf(I_hi) && (I_hi = span)
+ root = _bracketed_zero(g, I_null, I_hi)
+ return isnan(root) ? I_hi : root # no crossing before the balance fails: the failure is the edge
+end
+
+"""
+ efc_current_curve(c::EFCCoupling; delta_threshold, torque_budget, safety_factor=1.0, delta_max=15, npoints=500,
+ model=:auto, rotation_exponent=1.0, omega_reference=c.omega_reference,
+ torque_rtol=0.0, budget_rtol=0.0) -> NamedTuple
+
+The correction current against the intrinsic overlap from 0 to `delta_max × delta_threshold`:
+`current_linear` (no NTV), `current_ntv` and `current_ntv_upper` (the two edges of the correctable
+window under the model), the `threshold_factor` along the lower edge, the resolved `model`, and the
+limits of [`max_correctable_overlap`](@ref) spliced in (`with_ntv`, `residual_only`,
+`torque_only`). Nonzero `torque_rtol` and `budget_rtol` (fractional uncertainties of the torque
+coefficients and of `T_0`) add `current_ntv_pessimistic`/`current_ntv_optimistic` and
+`limits_pessimistic`/`limits_optimistic`: scaling the torques by `1 ± torque_rtol` is the same as
+scaling the budget by its inverse, since both models depend on `T/T_0` only.
+"""
+function efc_current_curve(c::EFCCoupling; delta_threshold::Real, torque_budget::Real, safety_factor::Real=1.0, delta_max::Real=15, npoints::Int=500,
+ model::Symbol=:auto, rotation_exponent::Real=1.0, omega_reference::Real=c.omega_reference, torque_rtol::Real=0.0, budget_rtol::Real=0.0)
+ (0 <= torque_rtol < 1 && 0 <= budget_rtol < 1) ||
+ throw(ArgumentError("torque_rtol and budget_rtol are fractional uncertainties in [0, 1); got $torque_rtol and $budget_rtol"))
+ model = _resolve_model(c, model)
+ kw(budget) = (; delta_threshold, torque_budget=budget, safety_factor, model, rotation_exponent, omega_reference)
+ δ = collect(range(0.0, delta_max * delta_threshold; length=npoints))
+ lin = [correction_current(d, c; delta_threshold, torque_budget, safety_factor, ntv=false) for d in δ]
+ ntv_at(budget) = [correction_current(d, c; kw(budget)...) for d in δ]
+ ntv = ntv_at(torque_budget)
+ upper = [correction_current_upper(d, c; kw(torque_budget)...) for d in δ]
+ factor = [isnan(I) ? NaN : threshold_factor(c, I; torque_budget, rotation_exponent, omega_reference, model) for I in ntv]
+ pessimistic = torque_budget * (1 - budget_rtol) / (1 + torque_rtol)
+ optimistic = torque_budget * (1 + budget_rtol) / (1 - torque_rtol)
+ return (; delta_ef=δ, current_linear=lin, current_ntv=ntv, current_ntv_upper=upper, threshold_factor=factor, model,
+ current_ntv_pessimistic=ntv_at(pessimistic), current_ntv_optimistic=ntv_at(optimistic),
+ limits_pessimistic=max_correctable_overlap(c; kw(pessimistic)...),
+ limits_optimistic=max_correctable_overlap(c; kw(optimistic)...),
+ max_correctable_overlap(c; kw(torque_budget)...)...)
+end
+
+"""
+ efc_couplings(resp, coil_sets, rc, dom, cfg, kf_ctrl; mode=1, method="fgar", rotation_scan=true, scan_points=9,
+ scan_max_points=21, scan_tolerance=0.05, span_factor=1.0, offset_factor=2.0,
+ regularization_width=0.0, verbose=false) -> Vector{EFCCoupling}
+
+The couplings of each correction coil array in `coil_sets` per kilo-ampere-turn: its
+dominant-mode overlap and resonant fraction from its spectrum on the control surface, and its
+NTV torque (kinetic method `method`, with sign) for the whole field and for the field with mode `mode`
+of `dom` projected out, tabulated against the rotation shift when `rotation_scan`. `cfg` is the run's
+`[ForcingTerms]` coil configuration and `rc` must be the coupling of `resp`; the torque uses the kinetic
+profiles attached to `resp.ffs.equil`. The spectrum is normalized by `|nw| × max|I|`, keeping the
+array's winding sense and current pattern as the phase reference.
+"""
+function efc_couplings(
+ resp::PerturbedEquilibrium.PlasmaResponse,
+ coil_sets::Vector{CoilSet},
+ rc::ResonantCoupling,
+ dom::DominantCoupling,
+ cfg::CoilConfig,
+ kf_ctrl::KineticForces.KineticForcesControl;
+ mode::Int=1,
+ method::AbstractString="fgar",
+ rotation_scan::Bool=true,
+ scan_points::Int=9,
+ scan_max_points::Int=21,
+ scan_tolerance::Real=0.05,
+ span_factor::Real=1.0,
+ offset_factor::Real=2.0,
+ regularization_width::Real=0.0,
+ verbose::Bool=false
+)
+ ffs = resp.ffs
+ ffs.equil.kinetic === nothing && error("efc_couplings needs kinetic profiles: set kinetic_file in [Equilibrium]")
+ getfield(kf_ctrl, Symbol(method * "_flag")) || error("efc_couplings: KineticForces method \"$method\" is not enabled in the control")
+ equil = ffs.equil
+ grids = [(n, CoilForcingGrid(equil, cfg, n; psi=ffs.psilim)) for n in sort(unique(rc.n_modes))]
+ m_low, m_high = extrema(rc.m_modes)
+ v = dom.right_singular_vectors[:, mode]
+
+ # Reference rotation and scan span from the kinetic profiles, with the torque kernel's own
+ # diamagnetic frequencies (Logan & Park 2013 Eq. 7): ω_φ = ω_E + ω_*n + ω_*T.
+ kp = KineticForces.ntv_profiles(kf_ctrl, equil)
+ chi1 = 2π * equil.psio
+ chrg = KineticForces.main_ion(equil)[1] * Utilities.E_CHG
+ ψk = kp.xs
+ ω_E = [kp.omegaE_spline(ψ) for ψ in ψk]
+ ω_star_T = [-2π * kp.Ti_deriv(ψ) / (chrg * chi1) for ψ in ψk]
+ ω_star_n = [
+ (n = kp.ni_spline(ψ); n > 0 ? -2π * kp.Ti_spline(ψ) * kp.ni_deriv(ψ) / (chrg * chi1 * n) : 0.0) for ψ in ψk
+ ]
+ ω_φ = ω_E .+ ω_star_n .+ ω_star_T
+ # Momentum weight n_i·dV/dψ with ⟨R²⟩ taken as R₀², inside the plasma only.
+ w = [ψ <= ffs.psilim ? max(kp.ni_spline(ψ), 0.0) * equil.profiles.dVdpsi_spline(clamp(ψ, equil.profiles.xs[1], equil.profiles.xs[end])) : 0.0 for ψ in ψk]
+ ω_ref = sum(w .* ω_φ) / sum(w)
+ span, ω_offset = rotation_scan_span(ω_E[1], ω_star_T[1]; span_factor, offset_factor)
+ npts = isodd(scan_points) ? scan_points : scan_points + 1
+ grid0 = rotation_scan ? collect(range(-span, span; length=max(npts, 3))) : [0.0]
+ verbose && @info "NTV couplings: ω_ref = $(@sprintf("%.3e", ω_ref)) rad/s, rough offset $(@sprintf("%.3e", ω_offset)) rad/s, " *
+ "scan ±$(@sprintf("%.3e", span)) rad/s on $(length(grid0)) initial points (max $(scan_max_points))"
+
+ function response_of(modes::Vector{ForcingMode})
+ pe_state = PerturbedEquilibrium.compute_perturbed_equilibrium(resp, ForcingTerms.RMPField(modes); regularization_width, verbose)
+ kf_intr = KineticForces.KineticForcesInternal(equil; verbose=verbose)
+ KineticForces.set_perturbation_data!(kf_intr, pe_state, ffs, equil, ffs.metric)
+ return kf_intr
+ end
+ # One quiet logger for the whole scan, so a `maxlog` warning prints once per scan rather than once per point.
+ logger = verbose ? Base.CoreLogging.current_logger() : Base.CoreLogging.SimpleLogger(stderr, Base.CoreLogging.Warn)
+ # Torque and cumulative torque profile (resampled onto the kinetic ψ grid) of one perturbation at one rotation.
+ function torque_of(kf_intr, profiles)
+ kf_state = KineticForces.KineticForcesState()
+ Base.CoreLogging.with_logger(logger) do
+ KineticForces.compute_torque_all_methods!(kf_state, kf_intr, kf_ctrl, equil, profiles)
+ end
+ r = kf_state.method_results[String(method)]
+ T = real(r.total_torque)
+ prof = zeros(Float64, length(ψk))
+ if length(r.psi_grid) >= 2
+ # Cubic spline of the cumulative torque on the quadrature's own ψ points (deduplicated), zero
+ # inside the first point and the total beyond the last.
+ keep = [i == 1 || r.psi_grid[i] > r.psi_grid[i-1] for i in eachindex(r.psi_grid)]
+ pg, tc = r.psi_grid[keep], real.(r.t_cumulative[keep])
+ spl = length(pg) >= 4 ? cubic_interp(pg, tc) : nothing
+ for (k, ψ) in enumerate(ψk)
+ prof[k] = ψ <= pg[1] ? 0.0 : ψ >= pg[end] ? tc[end] : spl === nothing ? tc[searchsortedlast(pg, ψ)] : spl(ψ)
+ end
+ end
+ return T, prof
+ end
+
+ out = EFCCoupling[]
+ for cs in coil_sets
+ kat = abs(cs.nw) * maximum(abs, cs.currents) / 1e3
+ kat > 0 || error("efc_couplings: coil set \"$(cs.name)\" carries no current")
+ # Unit-current spectrum: per kilo-ampere-turn of the array's current pattern.
+ modes = ForcingMode[]
+ for (n, grid) in grids
+ append!(modes, coil_forcing_modes(cs, grid, n, m_low, m_high))
+ end
+ modes = [ForcingMode(; n=m.n, m=m.m, amplitude=m.amplitude / kat) for m in modes]
+ b̃ = rootarea_field(rc, modes)
+ δ = dot(v, b̃) / equil.params.bt0
+ overlap = 100 * abs(dot(v, b̃)) / norm(b̃)
+ # The residual field as forcing modes: back through the conform operator to Φ_x.
+ Φ_res = rc.flux_conform * residual_spectrum(dom, b̃; mode)
+ residual_modes = [ForcingMode(; n=rc.n_modes[k], m=rc.m_modes[k], amplitude=Φ_res[k]) for k in eachindex(Φ_res)]
+ t_start = time()
+ kf_full = response_of(modes)
+ kf_res = response_of(residual_modes)
+ profiles_full = Dict{Float64,Vector{Float64}}()
+ profiles_res = Dict{Float64,Vector{Float64}}()
+ function torques(Δ)
+ profiles = Δ == 0 ? kp : Equilibrium.shift_exb_rotation(kp, Δ)
+ T_f, p_f = torque_of(kf_full, profiles)
+ T_r, p_r = torque_of(kf_res, profiles)
+ profiles_full[Δ] = p_f
+ profiles_res[Δ] = p_r
+ verbose && @info " $(cs.name) Δω = $(@sprintf("%+.3e", Δ)) rad/s: torque $(@sprintf("%.3e", T_f)) N·m per kAt² (residual $(@sprintf("%.3e", T_r)))"
+ return [T_f, T_r]
+ end
+ if rotation_scan
+ Δs, Ts = Utilities.adaptive_sample(torques, grid0; max_points=scan_max_points, rtol=scan_tolerance)
+ else
+ Δs = [0.0]
+ Ts = permutedims(torques(0.0))
+ end
+ i0 = findfirst(==(0.0), Δs)
+ T_full, T_res = Ts[i0, 1], Ts[i0, 2]
+ c = EFCCoupling(cs.name, abs(δ), overlap, T_full, T_res, Δs, Ts[:, 1], Ts[:, 2],
+ rotation_scan ? ω_ref : NaN, rotation_scan ? ω_offset : NaN, rotation_scan ? collect(ψk) : Float64[],
+ rotation_scan ? reduce(hcat, profiles_full[Δ] for Δ in Δs) : zeros(0, 1),
+ rotation_scan ? reduce(hcat, profiles_res[Δ] for Δ in Δs) : zeros(0, 1))
+ if rotation_scan
+ crossings = torque_zero_crossings(c)
+ isempty(crossings) && @warn "NTV couplings: the residual torque of $(cs.name) does not change sign within ±$(@sprintf("%.3e", span)) rad/s; " *
+ "raise rotation_span_factor to reach the neoclassical offset"
+ end
+ verbose && @info " $(cs.name): |δ| = $(@sprintf("%.3e", abs(δ))) per kAt, resonant fraction $(@sprintf("%.1f", overlap)) %, " *
+ "torque $(@sprintf("%.3e", T_full)) N·m per kAt² (residual $(@sprintf("%.3e", T_res))) at the nominal rotation, " *
+ "$(length(Δs)) scan points in $(@sprintf("%.1f", time() - t_start)) s"
+ push!(out, c)
+ end
+ return out
+end
diff --git a/src/ErrorFields/Output.jl b/src/ErrorFields/Output.jl
new file mode 100644
index 0000000000..2333f5dbcd
--- /dev/null
+++ b/src/ErrorFields/Output.jl
@@ -0,0 +1,392 @@
+import ..Utilities: save_to_hdf5
+import ..Utilities.HDF5Annotations: ensure_group, replace_group!, write_fields!
+
+"""
+ Output
+
+HDF5 output for the ErrorFields coil linearization, under `ErrorFields/CoilSensitivities/`,
+and the reader that rebuilds a `CoilSensitivities` from it.
+"""
+
+const _H5_GROUP = "ErrorFields/CoilSensitivities"
+
+# Metadata table for ErrorFields/CoilSensitivities/ (paths relative to the group). Spectra are
+# root-area-weighted control-surface fields b̃ on the Info/mn_index ordering; the DominantMode/
+# summary is the full-window mode-1 projection, the windowed table being a post-hoc analysis.
+const EF_H5_ANNOTATIONS = [
+ "coil_name" => (; long_name="name of each coil set"),
+ "field_as_designed" => (; long_name="root-area-weighted control-surface field b̃ of each coil set as built", units="T", dims=("mode", "coil_set")),
+ "shift_sensitivity_per_m" => (; long_name="∂b̃/∂(Δx, Δy, Δz) of each coil set under a rigid Cartesian shift", units="T/m", dims=("mode", "axis", "coil_set")),
+ "tilt_sensitivity_per_deg" =>
+ (; long_name="∂b̃/∂(θx, θy, θz) of each coil set under a rigid rotation about the machine axes", units="T/deg", dims=("mode", "axis", "coil_set")),
+ "shift_linearity_residual" =>
+ (; long_name="finite-difference curvature ‖b̃(+h)+b̃(−h)−2b̃(0)‖ of each shift tap relative to the set's largest first difference", dims=("axis", "coil_set")),
+ "tilt_linearity_residual" =>
+ (; long_name="finite-difference curvature ‖b̃(+h)+b̃(−h)−2b̃(0)‖ of each tilt tap relative to the set's largest first difference", dims=("axis", "coil_set")),
+ "peak_current" => (; long_name="largest conductor current magnitude of each coil set at which the spectra were evaluated", units="A"),
+ "winding_multiplier" => (; long_name="turns per conductor element of each coil set"),
+ "major_radius_m" => (; long_name="arc-length-weighted major radius of each coil set, the lever arm converting a tilt angle to rim displacement", units="m"),
+ "DominantMode/delta_as_designed" => (; long_name="overlap δ = Vᴴ₁·b̃ / B_T0 of each coil set with the full-window dominant mode"),
+ "DominantMode/shift_sensitivity_per_m" => (; long_name="∂δ/∂(Δx, Δy, Δz) on the full-window dominant mode", units="1/m", dims=("axis", "coil_set")),
+ "DominantMode/tilt_sensitivity_per_deg" => (; long_name="∂δ/∂(θx, θy, θz) on the full-window dominant mode", units="1/deg", dims=("axis", "coil_set")),
+ "DominantMode/abs_delta_shift_per_mm" => (; long_name="direction-averaged in-plane shift sensitivity √((|∂δ/∂Δx|²+|∂δ/∂Δy|²)/2)", units="1/mm"),
+ "DominantMode/abs_delta_tilt_per_deg" => (; long_name="direction-averaged in-plane tilt sensitivity √((|∂δ/∂θx|²+|∂δ/∂θy|²)/2)", units="1/deg"),
+ "DominantMode/abs_delta_rim_per_mm" => (; long_name="the same tilt sensitivity as rim displacement at major_radius_m", units="1/mm"),
+ "DominantMode/cancelling_shift_m" => (; long_name="in-plane shift (Δx, Δy) that cancels delta_as_designed to linear order", units="m", dims=("axis", "coil_set")),
+ "DominantMode/cancelling_tilt_deg" => (; long_name="in-plane tilt (θx, θy) that cancels delta_as_designed to linear order", units="deg", dims=("axis", "coil_set"))
+]
+
+"""
+ save_to_hdf5(h5file::Union{HDF5.File,HDF5.Group}, sens::CoilSensitivities; dom::DominantCoupling)
+
+Write the coil linearization to `ErrorFields/CoilSensitivities/` — the spectra and their
+derivatives, plus a `DominantMode/` summary projected onto mode 1 of `dom` (the run's
+full-window decomposition). An existing group is replaced. The mode labels are the file's
+`Info/mn_index` and the field normalization its `Equilibrium/B_T_axis`, neither duplicated here.
+"""
+function save_to_hdf5(h5file::Union{HDF5.File,HDF5.Group}, sens::CoilSensitivities; dom::DominantCoupling)
+ g = replace_group!(h5file, _H5_GROUP)
+ g["coil_name"] = sens.coil_names
+ g["field_as_designed"] = sens.field_as_designed
+ g["shift_sensitivity_per_m"] = sens.shift_sensitivity_per_m
+ g["tilt_sensitivity_per_deg"] = sens.tilt_sensitivity_per_deg
+ g["shift_linearity_residual"] = sens.shift_linearity_residual
+ g["tilt_linearity_residual"] = sens.tilt_linearity_residual
+ g["peak_current"] = sens.peak_current
+ g["winding_multiplier"] = sens.winding_multiplier
+ g["major_radius_m"] = sens.major_radius_m
+
+ table = sensitivity_table(sens, dom; mode=1)
+ d = create_group(g, "DominantMode")
+ d["delta_as_designed"] = table.delta_as_designed
+ d["shift_sensitivity_per_m"] = table.shift_sensitivity_per_m
+ d["tilt_sensitivity_per_deg"] = table.tilt_sensitivity_per_deg
+ d["abs_delta_shift_per_mm"] = table.abs_delta_shift_per_mm
+ d["abs_delta_tilt_per_deg"] = table.abs_delta_tilt_per_deg
+ d["abs_delta_rim_per_mm"] = table.abs_delta_rim_per_mm
+ d["cancelling_shift_m"] = table.cancelling_shift_m
+ d["cancelling_tilt_deg"] = table.cancelling_tilt_deg
+
+ Utilities.HDF5Annotations.annotate!(g, EF_H5_ANNOTATIONS)
+ return g
+end
+
+"""
+ CoilSensitivities(h5path::AbstractString)
+
+Read the coil linearization back from a `gpec.h5` written with an `[ErrorFields]` section, with
+the mode labels from `Info/mn_index` and the normalization field from `Equilibrium/B_T_axis`.
+"""
+function CoilSensitivities(h5path::AbstractString)
+ h5open(h5path, "r") do f
+ haskey(f, _H5_GROUP) || throw(ArgumentError("$h5path has no $_H5_GROUP group (run with an [ErrorFields] section)"))
+ haskey(f, "Info/mn_index") || throw(ArgumentError("$h5path has no Info/mn_index mode labels"))
+ haskey(f, "Equilibrium/B_T_axis") || throw(ArgumentError("$h5path has no Equilibrium/B_T_axis"))
+ g = f[_H5_GROUP]
+ mn = read(f["Info/mn_index"])
+ return CoilSensitivities(
+ read(g["coil_name"]), mn[:, 1], mn[:, 2], Float64(read(f["Equilibrium/B_T_axis"])),
+ read(g["field_as_designed"]), read(g["shift_sensitivity_per_m"]), read(g["tilt_sensitivity_per_deg"]),
+ read(g["shift_linearity_residual"]), read(g["tilt_linearity_residual"]),
+ read(g["peak_current"]), read(g["winding_multiplier"]), read(g["major_radius_m"])
+ )
+ end
+end
+
+const _TOLERANCE_SNAPSHOT = "Input/RawInputs/ErrorFields/tolerance_toml_raw"
+
+"""
+ save_to_hdf5(target, ef::ErrorFieldsResult)
+
+Write every product of the error-field assessment: the coil sensitivities with their dominant-mode projections, the
+tolerance set echoed into `Input/RawInputs/`, and the Monte Carlo, locking risk and correction-coil couplings when
+they were computed.
+"""
+function save_to_hdf5(h5file::Union{HDF5.File,HDF5.Group}, ef::ErrorFieldsResult)
+ save_to_hdf5(h5file, ef.sensitivities; dom=ef.dominant)
+ ef.tolerances === nothing || write_tolerance_snapshot!(h5file, ef.tolerances)
+ ef.monte_carlo === nothing || save_to_hdf5(h5file, ef.monte_carlo)
+ ef.risk === nothing || save_to_hdf5(h5file, ef.risk; scan=ef.scan)
+ ef.couplings === nothing || save_to_hdf5(h5file, ef.couplings)
+ Utilities.record_inputs!(h5file, ef)
+ return nothing
+end
+
+"""
+ write_tolerance_snapshot!(h5file, ts::ToleranceSet)
+
+Echo the tolerance file's text into `Input/RawInputs/ErrorFields/tolerance_toml_raw`, the raw
+input snapshot a replay reads back with [`read_tolerance_snapshot`](@ref). Replaces an existing echo.
+"""
+function write_tolerance_snapshot!(h5file::Union{HDF5.File,HDF5.Group}, ts::ToleranceSet)
+ haskey(h5file, _TOLERANCE_SNAPSHOT) && delete_object(h5file, _TOLERANCE_SNAPSHOT)
+ h5file[_TOLERANCE_SNAPSHOT] = ts.raw
+ return h5file
+end
+
+"""
+ read_tolerance_snapshot(h5path) -> ToleranceSet
+
+The tolerance set a run used, parsed from the raw echo in its `gpec.h5`; `nothing` when the run
+named no tolerance file.
+"""
+function read_tolerance_snapshot(h5path::AbstractString)
+ h5open(h5path, "r") do f
+ haskey(f, _TOLERANCE_SNAPSHOT) || return nothing
+ return parse_tolerance_toml(read(f[_TOLERANCE_SNAPSHOT]))
+ end
+end
+
+const _MC_GROUP = "ErrorFields/MonteCarlo"
+
+# Metadata table for ErrorFields/MonteCarlo/ (paths relative to the group). abs_delta_bin_edges has one
+# more entry than the densities, so it is documented rather than attached as a dimension scale.
+const MC_H5_ANNOTATIONS = [
+ "abs_delta_bin_edges" => (; long_name="|δ| bin edges of the overlap histograms (nbins + 1); samples beyond the last edge are counted in the last bin"),
+ "abs_delta_pdf" => (; long_name="probability density of the intrinsic dominant-mode overlap |δ| over the sampled misalignments, batch average", dims=("delta_bin",)),
+ "abs_delta_efc_pdf" => (; long_name="probability density of the corrected overlap |δ| (correctable terms divided by efc_factor), batch average", dims=("delta_bin",)),
+ "abs_delta_pdf_batches" => (; long_name="probability density of the intrinsic overlap |δ| per batch", dims=("delta_bin", "batch")),
+ "abs_delta_efc_pdf_batches" => (; long_name="probability density of the corrected overlap |δ| per batch", dims=("delta_bin", "batch")),
+ "abs_delta_total_as_designed" =>
+ (; long_name="|Σ δ_as_designed|, the as-designed overlap with every error-field coil set at its design position (correction arrays and excluded sets left out)"),
+ "abs_delta_worst_case" => (; long_name="worst-case alignment bound Σ(|δ_as_designed| + tolerance × |sensitivity|) used to size the histogram"),
+ "abs_delta_sampled_mean" => (; long_name="sample mean of the intrinsic overlap |δ|"),
+ "abs_delta_efc_sampled_mean" => (; long_name="sample mean of the corrected overlap |δ|"),
+ "clamped_fraction" => (; long_name="fraction of samples beyond the last bin edge")
+]
+
+"""
+ save_to_hdf5(h5file::Union{HDF5.File,HDF5.Group}, mc::MonteCarloResult)
+
+Write the tolerance Monte Carlo histograms to `ErrorFields/MonteCarlo/`. The sampling settings
+(`nsample`, `nbatch`, `seed`) live in the run's `[ErrorFields.MonteCarlo]` table under
+`Input/gpec_toml_raw`; the tolerances in `Input/RawInputs/ErrorFields/tolerance_toml_raw`.
+An existing group is replaced.
+"""
+function save_to_hdf5(h5file::Union{HDF5.File,HDF5.Group}, mc::MonteCarloResult)
+ g = replace_group!(h5file, _MC_GROUP)
+ g["abs_delta_bin_edges"] = mc.abs_delta_bin_edges
+ g["abs_delta_pdf"] = mc.abs_delta_pdf
+ g["abs_delta_efc_pdf"] = mc.abs_delta_efc_pdf
+ g["abs_delta_pdf_batches"] = mc.abs_delta_pdf_batches
+ g["abs_delta_efc_pdf_batches"] = mc.abs_delta_efc_pdf_batches
+ g["abs_delta_total_as_designed"] = mc.abs_delta_total_as_designed
+ g["abs_delta_worst_case"] = mc.abs_delta_worst_case
+ g["abs_delta_sampled_mean"] = mc.abs_delta_sampled_mean
+ g["abs_delta_efc_sampled_mean"] = mc.abs_delta_efc_sampled_mean
+ g["clamped_fraction"] = mc.clamped_fraction
+ Utilities.HDF5Annotations.annotate!(g, MC_H5_ANNOTATIONS)
+ return g
+end
+
+"""
+ MonteCarloResult(h5path::AbstractString)
+
+Read the tolerance Monte Carlo of a run back from its `gpec.h5`, with the sampling settings
+from the `[ErrorFields.MonteCarlo]` table of the stored deck.
+"""
+function MonteCarloResult(h5path::AbstractString)
+ h5open(h5path, "r") do f
+ haskey(f, _MC_GROUP) || throw(ArgumentError("$h5path has no $_MC_GROUP group (run with a tolerance_file)"))
+ g = f[_MC_GROUP]
+ inputs = TOML.parse(read(f["Input/gpec_toml_raw"]))
+ # Read only the needed settings by name, so files with extra keys stay readable.
+ mc_tbl = get(get(inputs, "ErrorFields", Dict{String,Any}()), "MonteCarlo", Dict{String,Any}())
+ defaults = MonteCarloControl()
+ nsample = get(mc_tbl, "nsample", defaults.nsample)
+ seed = get(mc_tbl, "seed", defaults.seed)
+ abs_delta_pdf_batches = read(g["abs_delta_pdf_batches"])
+ return MonteCarloResult(read(g["abs_delta_bin_edges"]), read(g["abs_delta_pdf"]), read(g["abs_delta_efc_pdf"]), abs_delta_pdf_batches, read(g["abs_delta_efc_pdf_batches"]),
+ read(g["abs_delta_total_as_designed"]), read(g["abs_delta_worst_case"]), read(g["abs_delta_sampled_mean"]), read(g["abs_delta_efc_sampled_mean"]),
+ read(g["clamped_fraction"]), nsample, size(abs_delta_pdf_batches, 2), seed)
+ end
+end
+
+const _RISK_GROUP = "ErrorFields/Risk"
+
+# Metadata table for ErrorFields/Risk/ (paths relative to the group). Percentages are stored as
+# such; the threshold density and P(lock|δ) share the Monte Carlo's |δ| grid.
+const RISK_H5_ANNOTATIONS = [
+ "threshold_pdf" => (; long_name="probability density of the sampled ITPA penetration threshold on the Monte Carlo |δ| bins", dims=("delta_bin",)),
+ "locking_probability_given_delta" =>
+ (; long_name="probability that an overlap equal to each Monte Carlo bin edge locks (threshold cumulative distribution)", dims=("delta_edge",)),
+ "threshold_fit" => (; long_name="ITPA penetration threshold at the fitted exponents"),
+ "locking_probability_percent" => (; long_name="locking probability of the intrinsic overlap distribution, 100 ∫ pdf(δ) P(lock|δ) dδ, batch average", units="%"),
+ "locking_probability_efc_percent" => (; long_name="locking probability of the corrected overlap distribution, batch average", units="%"),
+ "locking_probability_batches_percent" => (; long_name="locking probability of the intrinsic distribution per Monte Carlo batch", units="%"),
+ "locking_probability_efc_batches_percent" => (; long_name="locking probability of the corrected distribution per Monte Carlo batch", units="%"),
+ "locking_probability_as_designed_percent" => (; long_name="locking probability of the as-designed machine, 100 P(lock | |Σ δ_as_designed|)", units="%"),
+ "locking_probability_fit_threshold_percent" => (; long_name="locking probability if the threshold were exactly its fitted value, 100 P(|δ| > threshold_fit)", units="%"),
+ "ToleranceScan/tolerance_scale" => (; long_name="multiplier applied to every shift and tilt tolerance"),
+ "ToleranceScan/locking_probability_percent" =>
+ (; long_name="locking probability of the intrinsic distribution at each tolerance scale", units="%", dims=("tolerance_scale",)),
+ "ToleranceScan/locking_probability_efc_percent" =>
+ (; long_name="locking probability of the corrected distribution at each tolerance scale", units="%", dims=("tolerance_scale",)),
+ "ToleranceScan/locking_probability_spread_percent" =>
+ (; long_name="range of the intrinsic locking probability over the Monte Carlo batches at each scale", units="%", dims=("tolerance_scale",)),
+ "ToleranceScan/locking_probability_efc_spread_percent" =>
+ (; long_name="range of the corrected locking probability over the Monte Carlo batches at each scale", units="%", dims=("tolerance_scale",))
+]
+
+"""
+ save_to_hdf5(h5file::Union{HDF5.File,HDF5.Group}, risk::RiskResult; scan=nothing)
+
+Write the locking risk to `ErrorFields/Risk/`, with the tolerance scan under
+`ErrorFields/Risk/ToleranceScan/` when given. The threshold fit, scenario and sampling settings
+live in the run's `[ErrorFields.Risk]` and `[ErrorFields.scenario]` tables under
+`Input/gpec_toml_raw`. An existing group is replaced.
+"""
+function save_to_hdf5(h5file::Union{HDF5.File,HDF5.Group}, risk::RiskResult; scan::Union{Nothing,ToleranceScan}=nothing)
+ g = replace_group!(h5file, _RISK_GROUP)
+ g["threshold_pdf"] = risk.threshold_pdf
+ g["locking_probability_given_delta"] = risk.locking_probability_given_delta
+ g["threshold_fit"] = risk.threshold_fit
+ g["locking_probability_percent"] = risk.locking_probability_percent
+ g["locking_probability_efc_percent"] = risk.locking_probability_efc_percent
+ g["locking_probability_batches_percent"] = risk.locking_probability_batches_percent
+ g["locking_probability_efc_batches_percent"] = risk.locking_probability_efc_batches_percent
+ g["locking_probability_as_designed_percent"] = risk.locking_probability_as_designed_percent
+ g["locking_probability_fit_threshold_percent"] = risk.locking_probability_fit_threshold_percent
+ if scan !== nothing
+ sg = create_group(g, "ToleranceScan")
+ sg["tolerance_scale"] = scan.tolerance_scale
+ sg["locking_probability_percent"] = scan.locking_probability_percent
+ sg["locking_probability_efc_percent"] = scan.locking_probability_efc_percent
+ sg["locking_probability_spread_percent"] = scan.locking_probability_spread_percent
+ sg["locking_probability_efc_spread_percent"] = scan.locking_probability_efc_spread_percent
+ end
+ Utilities.HDF5Annotations.annotate!(g, RISK_H5_ANNOTATIONS)
+ return g
+end
+
+"""
+ ToleranceScan(h5path::AbstractString)
+
+Read a run's tolerance scan back from `ErrorFields/Risk/ToleranceScan/`.
+"""
+function ToleranceScan(h5path::AbstractString)
+ h5open(h5path, "r") do f
+ path = _RISK_GROUP * "/ToleranceScan"
+ haskey(f, path) || throw(ArgumentError("$h5path has no $path group (set scan_scales in [ErrorFields.Risk])"))
+ g = f[path]
+ return ToleranceScan(read(g["tolerance_scale"]), read(g["locking_probability_percent"]), read(g["locking_probability_efc_percent"]),
+ read(g["locking_probability_spread_percent"]),
+ read(g["locking_probability_efc_spread_percent"]), read(f[_RISK_GROUP*"/locking_probability_as_designed_percent"]))
+ end
+end
+
+const _NTV_GROUP = "ErrorFields/NTV"
+
+# Metadata table for ErrorFields/NTV/ (paths relative to the group): per correction-coil array,
+# per kilo-ampere-turn of its current pattern.
+const NTV_H5_ANNOTATIONS = [
+ "coil_name" => (; long_name="name of each correction coil array"),
+ "delta_per_kat" => (; long_name="dominant-mode overlap |δ| of each array per kilo-ampere-turn", units="1/kAt"),
+ "resonant_fraction_percent" => (; long_name="resonant fraction of each array's field, 100·|Vᴴb̃|/‖b̃‖", units="%"),
+ "torque_full_per_kat2" => (; long_name="NTV torque of each array's whole field per kilo-ampere-turn squared", units="N*m/kAt^2"),
+ "torque_residual_per_kat2" => (; long_name="NTV torque of each array's field with the dominant mode projected out, per kilo-ampere-turn squared", units="N*m/kAt^2"),
+ "omega_reference" => (; long_name="reference rotation ω_ref of each array's torque balance: ion toroidal rotation weighted by density and volume", units="rad/s"),
+ "omega_offset_estimate" =>
+ (; long_name="rough neoclassical offset rotation the scan span was sized against, offset_factor·ω_*T at the innermost kinetic surface", units="rad/s")
+]
+
+# ErrorFields/NTV/RotationScan/: the torques against a rigid E×B rotation shift, one column per
+# array; the adaptive grids differ in length, so shorter scans are padded with NaN.
+const NTV_SCAN_H5_ANNOTATIONS = [
+ "coil_name" => (; long_name="name of each scanned correction coil array"),
+ "rotation_shift" =>
+ (; long_name="rigid shift Δω of the E×B rotation profile at each scan point of each array (NaN-padded)", units="rad/s", dims=("scan_point", "coil_set")),
+ "torque_full" =>
+ (; long_name="NTV torque of the whole field at each rotation shift, per kilo-ampere-turn squared (NaN-padded)", units="N*m/kAt^2", dims=("scan_point", "coil_set")),
+ "torque_residual" => (;
+ long_name="NTV torque of the field with the dominant mode projected out at each rotation shift, per kilo-ampere-turn squared (NaN-padded)",
+ units="N*m/kAt^2",
+ dims=("scan_point", "coil_set")
+ ),
+ "psi" => (; long_name="kinetic normalized poloidal flux grid of the torque profiles", scale="psi"),
+ "torque_full_profile" => (;
+ long_name="cumulative NTV torque of the whole field from the axis to ψ_N, at each rotation shift of each array, per kilo-ampere-turn squared (NaN-padded)",
+ units="N*m/kAt^2",
+ dims=("psi", "scan_point", "coil_set")
+ ),
+ "torque_residual_profile" => (;
+ long_name="cumulative NTV torque of the residual field from the axis to ψ_N, at each rotation shift of each array, per kilo-ampere-turn squared (NaN-padded)",
+ units="N*m/kAt^2",
+ dims=("psi", "scan_point", "coil_set")
+ )
+]
+
+"""
+ save_to_hdf5(h5file::Union{HDF5.File,HDF5.Group}, couplings::Vector{EFCCoupling})
+
+Write the correction-coil couplings to `ErrorFields/NTV/`, and the torque-versus-rotation tables
+of the arrays that have one to `ErrorFields/NTV/RotationScan/` (one column per array, shorter
+scans NaN-padded). The torque budget, threshold, rotation exponent and safety factor that turn
+them into a correction-current curve are analysis choices left to [`efc_current_curve`](@ref).
+An existing group is replaced.
+"""
+function save_to_hdf5(h5file::Union{HDF5.File,HDF5.Group}, couplings::Vector{EFCCoupling})
+ g = replace_group!(h5file, _NTV_GROUP)
+ g["coil_name"] = [c.coil_name for c in couplings]
+ g["delta_per_kat"] = [c.delta_per_kat for c in couplings]
+ g["resonant_fraction_percent"] = [c.resonant_fraction_percent for c in couplings]
+ g["torque_full_per_kat2"] = [c.torque_full_per_kat2 for c in couplings]
+ g["torque_residual_per_kat2"] = [c.torque_residual_per_kat2 for c in couplings]
+ g["omega_reference"] = [c.omega_reference for c in couplings]
+ g["omega_offset_estimate"] = [c.omega_offset_estimate for c in couplings]
+ Utilities.HDF5Annotations.annotate!(g, NTV_H5_ANNOTATIONS)
+ scanned = filter(has_rotation_scan, couplings)
+ if !isempty(scanned)
+ nmax = maximum(length(c.rotation_shift) for c in scanned)
+ ψ = scanned[1].psi
+ all(c.psi == ψ for c in scanned) || error("save_to_hdf5: the rotation scans of the arrays are on different ψ grids")
+ pad(v) = vcat(Float64.(v), fill(NaN, nmax - length(v)))
+ padm(m) = hcat(Float64.(m), fill(NaN, size(m, 1), nmax - size(m, 2)))
+ sg = create_group(g, "RotationScan")
+ sg["coil_name"] = [c.coil_name for c in scanned]
+ sg["rotation_shift"] = reduce(hcat, pad(c.rotation_shift) for c in scanned)
+ sg["torque_full"] = reduce(hcat, pad(c.torque_full_scan) for c in scanned)
+ sg["torque_residual"] = reduce(hcat, pad(c.torque_residual_scan) for c in scanned)
+ sg["psi"] = ψ
+ sg["torque_full_profile"] = cat((padm(c.torque_full_profile) for c in scanned)...; dims=3)
+ sg["torque_residual_profile"] = cat((padm(c.torque_residual_profile) for c in scanned)...; dims=3)
+ Utilities.HDF5Annotations.annotate!(sg, NTV_SCAN_H5_ANNOTATIONS)
+ end
+ return g
+end
+
+"""
+ read_efc_couplings(h5path::AbstractString) -> Vector{EFCCoupling}
+
+Read a run's correction-coil couplings back from `ErrorFields/NTV/`, with their
+torque-versus-rotation tables when the run made them.
+"""
+function read_efc_couplings(h5path::AbstractString)
+ h5open(h5path, "r") do f
+ haskey(f, _NTV_GROUP) || throw(ArgumentError("$h5path has no $_NTV_GROUP group (set efc_coils in [ErrorFields.NTV])"))
+ g = f[_NTV_GROUP]
+ names = read(g["coil_name"])
+ δ, ov = read(g["delta_per_kat"]), read(g["resonant_fraction_percent"])
+ Tf, Tr = read(g["torque_full_per_kat2"]), read(g["torque_residual_per_kat2"])
+ ω_ref = haskey(g, "omega_reference") ? read(g["omega_reference"]) : fill(NaN, length(names))
+ ω_off = haskey(g, "omega_offset_estimate") ? read(g["omega_offset_estimate"]) : fill(NaN, length(names))
+ scan = haskey(g, "RotationScan") ? g["RotationScan"] : nothing
+ scan_names = scan === nothing ? String[] : read(scan["coil_name"])
+ out = EFCCoupling[]
+ for i in eachindex(names)
+ j = findfirst(==(names[i]), scan_names)
+ if j === nothing
+ push!(out, EFCCoupling(names[i], δ[i], ov[i], Tf[i], Tr[i]))
+ else
+ shifts = read(scan["rotation_shift"])[:, j]
+ n = count(!isnan, shifts)
+ push!(
+ out,
+ EFCCoupling(names[i], δ[i], ov[i], Tf[i], Tr[i], shifts[1:n], read(scan["torque_full"])[1:n, j], read(scan["torque_residual"])[1:n, j],
+ ω_ref[i], ω_off[i], read(scan["psi"]), read(scan["torque_full_profile"])[:, 1:n, j], read(scan["torque_residual_profile"])[:, 1:n, j])
+ )
+ end
+ end
+ return out
+ end
+end
diff --git a/src/ErrorFields/Overlap.jl b/src/ErrorFields/Overlap.jl
new file mode 100644
index 0000000000..1d89eaf5b5
--- /dev/null
+++ b/src/ErrorFields/Overlap.jl
@@ -0,0 +1,220 @@
+"""
+Minimum toroidal boundary points per field period below which a post-hoc evaluation warns.
+Helical windings alias on a coarse toroidal grid; 16 points per period is about 1 % off, 32 is converged.
+"""
+const MIN_NZETA_PER_PERIOD = ForcingTerms.NZETA_POINTS_PER_PERIOD
+
+"""
+ forcing_grids(rc::ResonantCoupling, equil, cfg::CoilConfig; psi) -> Vector{Tuple{Int,CoilForcingGrid}}
+
+One boundary sampling per toroidal mode of `rc`, on the surface `psi`. The grids depend only on the
+equilibrium and grid dimensions, so they are built once and shared by every coil set.
+"""
+function forcing_grids(rc::ResonantCoupling, equil::Equilibrium.PlasmaEquilibrium, cfg::CoilConfig; psi::Float64)
+ return [(n, CoilForcingGrid(equil, cfg, n; psi)) for n in sort(unique(rc.n_modes))]
+end
+
+"""
+ applied_spectrum(cs::CoilSet, rc::ResonantCoupling, grids) -> Vector{ComplexF64}
+
+The root-area-weighted control-surface field b̃ that one coil set drives, on `rc`'s (m, n) column
+ordering: Biot-Savart on each grid of `grids`, Fourier decomposition, then the conform through
+[`rootarea_field`](@ref).
+"""
+function applied_spectrum(cs::CoilSet, rc::ResonantCoupling, grids::AbstractVector{<:Tuple{Int,CoilForcingGrid}})
+ m_low, m_high = extrema(rc.m_modes)
+ modes = ForcingMode[]
+ for (n, grid) in grids
+ append!(modes, coil_forcing_modes(cs, grid, n, m_low, m_high))
+ end
+ return rootarea_field(rc, modes)
+end
+
+"""
+ ResonantDriveContext
+
+Everything from a finished run needed to evaluate the resonant field any coil geometry drives,
+built once and independent of the coils. Build it with the `gpec.h5` constructor and hand it to [`coil_overlaps`](@ref) or
+[`compute_coil_sensitivities`](@ref).
+
+## Fields
+
+ - `equil`: the run's equilibrium, rebuilt on its own ψ grid
+ - `psilim`: the control surface the solve integrated to
+ - `cfg`: coil configuration, with any grid or directory override already applied
+ - `rc`: the resonant coupling matrix and its mode ordering
+ - `dom`: the singular decomposition over the requested ψ window
+ - `b_t0`: axis toroidal field magnitude, tesla
+ - `grids`: one boundary sampling per toroidal mode, shared by every coil set evaluated
+"""
+struct ResonantDriveContext
+ equil::Equilibrium.PlasmaEquilibrium
+ psilim::Float64
+ cfg::CoilConfig
+ rc::ResonantCoupling
+ dom::DominantCoupling
+ b_t0::Float64
+ grids::Vector{Tuple{Int,CoilForcingGrid}}
+end
+
+"""
+ regrid(cfg::CoilConfig; mtheta_coil=nothing, nzeta_coil=nothing, dat_dir=nothing) -> CoilConfig
+
+`cfg` with the boundary resolution or geometry directory replaced. Each keyword left as `nothing`
+keeps the value `cfg` already carries.
+"""
+function regrid(cfg::CoilConfig; mtheta_coil=nothing, nzeta_coil=nothing, dat_dir=nothing)
+ return CoilConfig(;
+ machine=cfg.machine,
+ dat_dir=dat_dir === nothing ? cfg.dat_dir : String(dat_dir),
+ mtheta_coil=mtheta_coil === nothing ? cfg.mtheta_coil : Int(mtheta_coil),
+ nzeta_coil=nzeta_coil === nothing ? cfg.nzeta_coil : Int(nzeta_coil),
+ coil_sets=cfg.coil_sets
+ )
+end
+
+"""
+ ResonantDriveContext(equil, rc, cfg; psilim, b_t0, psi_low=CORE_PSI_LOW, psi_high=CORE_PSI_HIGH,
+ mtheta_coil=nothing, nzeta_coil=nothing)
+ ResonantDriveContext(h5path; psi_low=CORE_PSI_LOW, psi_high=CORE_PSI_HIGH, mtheta_coil=nothing,
+ nzeta_coil=nothing, dat_dir=nothing)
+
+Assemble the context. The ψ window selects which rational surfaces the dominant mode is built from.
+`mtheta_coil` and `nzeta_coil` override the boundary resolution from the stored deck; a toroidal grid
+coarser than [`MIN_NZETA_PER_PERIOD`](@ref) warns. The `h5path` method lives in `Rerun.jl`.
+"""
+function ResonantDriveContext(
+ equil::Equilibrium.PlasmaEquilibrium,
+ rc::ResonantCoupling,
+ cfg::CoilConfig;
+ psilim::Real,
+ b_t0::Real,
+ psi_low::Real=PerturbedEquilibrium.CORE_PSI_LOW,
+ psi_high::Real=PerturbedEquilibrium.CORE_PSI_HIGH,
+ mtheta_coil=nothing,
+ nzeta_coil=nothing
+)
+ b_t0 > 0 || throw(ArgumentError("ResonantDriveContext: b_t0 must be a positive field magnitude (got $b_t0)"))
+ cfg = regrid(cfg; mtheta_coil, nzeta_coil)
+ _warn_coarse_toroidal_grid(cfg, rc)
+ dom = dominant_coupling(rc; psi_low, psi_high)
+ grids = forcing_grids(rc, equil, cfg; psi=Float64(psilim))
+ return ResonantDriveContext(equil, Float64(psilim), cfg, rc, dom, Float64(b_t0), grids)
+end
+
+function _warn_coarse_toroidal_grid(cfg::CoilConfig, rc::ResonantCoupling)
+ for n in sort(unique(rc.n_modes))
+ nzeta = cfg.nzeta_coil > 0 ? cfg.nzeta_coil : ForcingTerms.NZETA_POINTS_PER_PERIOD * max(1, abs(n))
+ per_period = nzeta / max(1, abs(n))
+ per_period < MIN_NZETA_PER_PERIOD && @warn "Toroidal boundary grid is $(round(per_period; digits=1)) points per period for n = $n, " *
+ "below the $MIN_NZETA_PER_PERIOD where helical coils are converged. Pass nzeta_coil to override the stored deck's value."
+ end
+end
+
+"""
+ CoilOverlap
+
+Field names follow the ErrorFields result grammar `[_instance][_efc][_statistic][_unit]` (see the manual's
+"Result names"); every field name is also its HDF5 dataset name.
+
+How strongly one coil set drives the resonant field, in every normalization it is quoted in.
+
+## Fields
+
+ - `coil_name`: name of the coil set
+ - `mode`: index of the singular mode projected onto (1 is the dominant mode)
+ - `delta`: `Vᴴb̃ / B_T0`, the dimensionless overlap
+ - `resonant_field_t`: `Vᴴb̃`, tesla, the same projection unnormalized
+ - `resonant_fraction_percent`: `100·|Vᴴb̃| / ‖b̃‖`, how much of this set's own spectrum is resonant;
+ `NaN` when the set's field at the run's toroidal mode is round-off (see [`resonant_fraction_percent`](@ref))
+ - `spectrum_norm_t`: `‖b̃‖` in tesla
+ - `b_t0`: the axis toroidal field the normalization used, tesla
+ - `ampere_turns_kat`: the set's current in kilo-ampere-turns, `|winding multiplier| × max |conductor current| / 1000`;
+ `NaN` for a combination of sets
+ - `spectrum`: b̃ itself, on the [`ResonantCoupling`](@ref) column ordering
+"""
+struct CoilOverlap
+ coil_name::String
+ mode::Int
+ delta::ComplexF64
+ resonant_field_t::ComplexF64
+ resonant_fraction_percent::Float64
+ spectrum_norm_t::Float64
+ b_t0::Float64
+ ampere_turns_kat::Float64
+ spectrum::Vector{ComplexF64}
+end
+
+"""
+ coil_overlaps(ctx::ResonantDriveContext, coil_sets; mode=1) -> Vector{CoilOverlap}
+ coil_overlaps(h5path, coil_sets; mode=1, kwargs...) -> Vector{CoilOverlap}
+
+Resonant overlap of each coil set against a finished run, evaluated on the run's own control
+surface. `coil_sets` is any geometry, not necessarily the run's; no solve is repeated.
+The `h5path` method takes [`ResonantDriveContext`](@ref)'s keywords and lives in `Rerun.jl`. For
+sensitivities to rigid motion as well, use [`compute_coil_sensitivities`](@ref).
+"""
+function coil_overlaps(ctx::ResonantDriveContext, coil_sets::AbstractVector{CoilSet}; mode::Int=1)
+ 1 <= mode <= length(ctx.dom.singular_values) ||
+ throw(ArgumentError("mode $mode is outside the $(length(ctx.dom.singular_values)) singular modes of the decomposition"))
+ spectra = [applied_spectrum(cs, ctx.rc, ctx.grids) for cs in coil_sets]
+ norms = norm.(spectra)
+ nrm_ref = isempty(norms) ? 0.0 : maximum(norms)
+ return map(zip(coil_sets, spectra, norms)) do (cs, b, nrm)
+ raw = coupling_overlap(ctx.dom, b)[mode]
+ CoilOverlap(cs.name, mode, raw / ctx.b_t0, raw, resonant_fraction_percent(raw, nrm, nrm_ref), nrm, ctx.b_t0, abs(cs.nw) * maximum(abs, cs.currents) / 1e3, b)
+ end
+end
+
+const _RESONANT_FRACTION_FLOOR = 1e-8 # of the largest spectrum norm among the coil sets judged together
+const _RESONANT_FRACTION_FLOOR_T = 1e-12 # absolute, tesla
+
+"""
+ resonant_fraction_percent(raw, nrm, nrm_ref) -> Float64
+
+`100·|raw| / nrm`, the share of a coil set's applied field `b̃` (norm `nrm`) that lies along the
+dominant mode (`raw = Vᴴb̃`), or `NaN` when `nrm` is below `1e-8 × nrm_ref` (the largest norm among
+the coil sets judged together) or below `1e-12` T, where the field is round-off (e.g. an
+axisymmetric hoop at n = 1) and the ratio is meaningless.
+"""
+function resonant_fraction_percent(raw, nrm::Real, nrm_ref::Real)
+ nrm > max(_RESONANT_FRACTION_FLOOR * nrm_ref, _RESONANT_FRACTION_FLOOR_T) || return NaN
+ return 100 * abs(raw) / nrm
+end
+
+coil_overlaps(ctx::ResonantDriveContext, cs::CoilSet; kwargs...) = coil_overlaps(ctx, [cs]; kwargs...)
+
+"""
+ combine_overlaps(overlaps, "A" => 20.0, "B" => -15.0; name="combined") -> CoilOverlap
+
+Coherent sum of several coil sets' spectra at relative weights, re-derived into the same
+[`CoilOverlap`](@ref). An unmatched coil name is an error.
+
+**Weights multiply each spectrum as it was evaluated**, not absolute currents: evaluate every
+conductor at 1 kA and weight by the design current in kA to make the weights read as currents.
+"""
+function combine_overlaps(overlaps::AbstractVector{CoilOverlap}, weights::Pair{<:AbstractString,<:Real}...; name::AbstractString="combined")
+ isempty(weights) && throw(ArgumentError("combine_overlaps: give at least one coil => weight pair"))
+ isempty(overlaps) && throw(ArgumentError("combine_overlaps: no overlaps to combine"))
+ by_name = Dict(o.coil_name => o for o in overlaps)
+ mode = first(overlaps).mode
+ b_t0 = first(overlaps).b_t0
+ b = zeros(ComplexF64, length(first(overlaps).spectrum))
+ raw = zero(ComplexF64)
+
+ for (nm, w) in weights
+ haskey(by_name, nm) ||
+ throw(ArgumentError("combine_overlaps: no coil named \"$nm\"; have $(join(sort(collect(keys(by_name))), ", "))"))
+ o = by_name[nm]
+ o.mode == mode ||
+ throw(ArgumentError("combine_overlaps: \"$nm\" is projected onto mode $(o.mode) but the first entry is mode $mode"))
+ length(o.spectrum) == length(b) ||
+ throw(DimensionMismatch("combine_overlaps: \"$nm\" carries $(length(o.spectrum)) modes but the first entry carries $(length(b))"))
+ b .+= w .* o.spectrum
+ raw += w * o.resonant_field_t # projection is linear, so this is exactly Vᴴ of the summed spectrum
+ end
+
+ nrm = norm(b)
+ nrm_ref = maximum(o.spectrum_norm_t for o in overlaps)
+ return CoilOverlap(String(name), mode, raw / b_t0, raw, resonant_fraction_percent(raw, nrm, max(nrm, nrm_ref)), nrm, b_t0, NaN, b)
+end
diff --git a/src/ErrorFields/Phasing.jl b/src/ErrorFields/Phasing.jl
new file mode 100644
index 0000000000..973b4ca006
--- /dev/null
+++ b/src/ErrorFields/Phasing.jl
@@ -0,0 +1,113 @@
+"""
+ Phasing
+
+Coil-array phasing: how the dominant-mode overlap of several independently powered coil
+arrays (an error-field correction coil set's upper, middle and lower rows, say) depends on the
+relative toroidal phases of their current patterns. The overlap is linear in each array's
+field, so the map is the closed form `|Σ_k δ_k e^{iφ_k}|` on a grid of relative phases, per
+kilo-ampere-turn of each array, together with the fraction of the applied field that is resonant.
+"""
+
+"""
+ PhasingMap
+
+Field names follow the ErrorFields result grammar `[_instance][_efc][_statistic][_unit]` (see the manual's
+"Result names"); every field name is also its HDF5 dataset name.
+
+Dominant-mode overlap of `N` coil arrays against the `N − 1` relative phases of their current
+patterns, from [`phasing_map`](@ref). Array 1 sets the reference; array `k > 1` is rotated by
+the cumulative phase `Δφ_2 + … + Δφ_k`, so axis `k − 1` of the maps is the phase of array `k`
+relative to array `k − 1` (the two-row EFCC convention `Δφ_ML`, `Δφ_UM`).
+
+## Fields
+
+ - `coil_names`: the arrays in order `[N]`
+ - `phase_deg`: grid of each relative phase, degrees `[N − 1]` vectors
+ - `delta_per_kat`: `|δ|` per kilo-ampere-turn of every array at each grid point `[n_1 × … × n_{N−1}]`
+ - `resonant_fraction_percent`: `100·|Vᴴb̃| / ‖b̃‖`, the fraction of the applied root-area-weighted field
+ that lies along the dominant mode, at each grid point
+ - `delta_per_kat_each`: `|δ_k|` per kilo-ampere-turn of each array alone `[N]`
+"""
+struct PhasingMap
+ coil_names::Vector{String}
+ phase_deg::Vector{Vector{Float64}}
+ delta_per_kat::Array{Float64}
+ resonant_fraction_percent::Array{Float64}
+ delta_per_kat_each::Vector{Float64}
+end
+
+"""
+ phasing_map(sens::CoilSensitivities, dom::DominantCoupling, coil_names; mode=1, nphase=180) -> PhasingMap
+ phasing_map(h5path, coil_names; psi_low=0.0, psi_high=CORE_PSI_HIGH, mode=1, nphase=180) -> PhasingMap
+
+Scan the relative phases of the current patterns of the named coil arrays and evaluate, at
+each grid point, the dominant-mode overlap per kilo-ampere-turn and the resonant fraction of
+the applied field. Rotating a current pattern by `Δφ` multiplies the spectrum by `e^{iΔφ}` (the
+phase of the pattern itself, `n` times the toroidal angle it is rotated through). `nphase`
+points per phase axis, spanning `[0, 360)` degrees.
+
+Each array's spectrum is normalized by the magnitude of its ampere-turns,
+`|winding_multiplier| × peak_current`, so the zero of each phase axis is the array's current pattern
+exactly as the run specified it, winding sign included.
+"""
+function phasing_map(sens::CoilSensitivities, dom::DominantCoupling, coil_names::AbstractVector{<:AbstractString}; mode::Int=1, nphase::Int=180)
+ length(coil_names) >= 2 || throw(ArgumentError("phasing_map needs at least two coil arrays"))
+ nphase >= 2 || throw(ArgumentError("nphase must be ≥ 2"))
+ 1 <= mode <= length(dom.singular_values) || throw(ArgumentError("mode $mode is outside the decomposition"))
+ PerturbedEquilibrium.check_mode_basis(dom, sens.m_modes, sens.n_modes, "phasing_map")
+ idx = [findfirst(==(String(nm)), sens.coil_names) for nm in coil_names]
+ any(isnothing, idx) && throw(ArgumentError("coil arrays not in the sensitivities: $(join(coil_names[isnothing.(idx)], ", "))"))
+ v = dom.right_singular_vectors[:, mode]
+ N = length(idx)
+ kat = [abs(sens.winding_multiplier[i]) * sens.peak_current[i] / 1e3 for i in idx]
+ all(>(0), kat) || throw(ArgumentError("every array needs a non-zero current to normalize per kilo-ampere-turn"))
+ spectra = [sens.field_as_designed[:, i] ./ kat[j] for (j, i) in enumerate(idx)] # b̃ per kAt
+ deltas = [dot(v, b) / sens.b_t0 for b in spectra] # δ per kAt
+ grid = collect(range(0.0, 360.0; length=nphase + 1))[1:end-1]
+ dims = ntuple(_ -> nphase, N - 1)
+ delta_map = zeros(dims)
+ overlap_map = zeros(dims)
+ b_sum = similar(spectra[1])
+ for I in CartesianIndices(dims)
+ fill!(b_sum, 0)
+ δ = deltas[1]
+ b_sum .+= spectra[1]
+ cumulative = 0.0
+ for k in 2:N
+ cumulative += deg2rad(grid[I[k-1]])
+ rot = cis(cumulative)
+ δ += deltas[k] * rot
+ b_sum .+= spectra[k] .* rot
+ end
+ delta_map[I] = abs(δ)
+ overlap_map[I] = 100 * abs(δ) * sens.b_t0 / norm(b_sum)
+ end
+ return PhasingMap(String.(collect(coil_names)), [copy(grid) for _ in 1:N-1], delta_map, overlap_map, abs.(deltas))
+end
+
+function phasing_map(
+ h5path::AbstractString,
+ coil_names::AbstractVector{<:AbstractString};
+ psi_low::Real=0.0,
+ psi_high::Real=PerturbedEquilibrium.CORE_PSI_HIGH,
+ mode::Int=1,
+ nphase::Int=180
+)
+ dom = dominant_coupling(ResonantCoupling(h5path); psi_low, psi_high)
+ return phasing_map(CoilSensitivities(h5path), dom, coil_names; mode, nphase)
+end
+
+"""
+ extreme_phasing(map::PhasingMap; quantity=:delta_per_kat, which=:max) -> (value, phases_deg)
+
+The largest (or smallest) value of a map and the relative phases, in degrees, where it occurs.
+"""
+function extreme_phasing(map::PhasingMap; quantity::Symbol=:delta_per_kat, which::Symbol=:max)
+ arr =
+ quantity === :delta_per_kat ? map.delta_per_kat :
+ quantity === :resonant_fraction_percent ? map.resonant_fraction_percent :
+ throw(ArgumentError("quantity must be :delta_per_kat or :resonant_fraction_percent"))
+ which in (:max, :min) || throw(ArgumentError("which must be :max or :min"))
+ I = which === :max ? argmax(arr) : argmin(arr)
+ return arr[I], [map.phase_deg[k][I[k]] for k in 1:length(map.phase_deg)]
+end
diff --git a/src/ErrorFields/Risk.jl b/src/ErrorFields/Risk.jl
new file mode 100644
index 0000000000..6f869f22e9
--- /dev/null
+++ b/src/ErrorFields/Risk.jl
@@ -0,0 +1,483 @@
+"""
+ Risk
+
+From an overlap distribution to a locking risk. The empirical ITPA penetration-threshold
+scalings give the overlap δ at which an error field locks as a power law in density, field,
+major radius, β_N/l_i and (for the 2026 fits) plasma current, with fitted exponents and their
+uncertainties; sampling the exponents turns the threshold into a distribution and its cumulative
+distribution into the probability that an overlap δ locks. Convolving that with the Monte Carlo
+distribution of `|δ|` gives the locking probability of the assembled machine, and repeating the
+Monte Carlo over a range of tolerance scales gives the allowable tolerance for a target risk.
+
+Each fit is identified by its toroidal mode number, publication year, plasma dataset and fitting
+method, `"n= "`:
+
+ - 2020, n = 1: Logan et al., "Robustness of the tokamak error field correction tolerance
+ scaling", Plasma Phys. Control. Fusion 62 (2020) 084001 — datasets `"O,L"` and `"O,L,H"`,
+ fits `"OLS"`, `"DSOLS"`, `"WLS"`.
+ - 2020, n = 2: Logan et al., "Empirical scaling of the n = 2 error field penetration threshold
+ in tokamaks", Nucl. Fusion 60 (2020) 086010 — datasets `"O,L"`, `"O,L,-C"`, `"O,L,N"`, fit `"WLS"`.
+ - 2026, n = 1: Bursch et al., "Improved n=1 empirical error field penetration threshold scaling
+ with Ohmic and L-mode conventional tokamak plasma discharges", Plasma Phys. Control. Fusion
+ (2026), doi:10.1088/1361-6587/aea7d6 — dataset `"O,L"`, fits `"OLS"` (Eq. 7) and `"WLS"` (Eq. 8).
+"""
+
+"""
+ ThresholdScaling
+
+One fit of the ITPA error-field penetration threshold,
+`δ_thresh = 10^α_c · n_e^α_n · B_T^α_B · R_0^α_R · (β_N/l_i)^α_β · I_p^α_I`, with `n_e` in 10¹⁹ m⁻³,
+`B_T` in tesla, `R_0` in metres and `I_p` in MA. Each exponent carries the fit's standard error. Only
+the 2026 fits have a current term; the 2020 fits carry `α_I = (0, 0)`.
+
+## Fields
+
+ - `n`: toroidal mode number of the scaling
+ - `year`: publication year of the fit, `2020` or `2026`; the two years fit different databases
+ - `dataset`: plasma dataset the fit was made on (`"O,L"` ohmic and L-mode, `"O,L,H"` with H-modes, ...)
+ - `fit`: fitting method (`"OLS"`, `"DSOLS"` downsampled, `"WLS"` weighted)
+ - `alpha_c`, `alpha_n`, `alpha_b`, `alpha_r`, `alpha_beta`, `alpha_ip`: `(value, standard error)` of each exponent
+"""
+struct ThresholdScaling
+ n::Int
+ year::Int
+ dataset::String
+ fit::String
+ alpha_c::Tuple{Float64,Float64}
+ alpha_n::Tuple{Float64,Float64}
+ alpha_b::Tuple{Float64,Float64}
+ alpha_r::Tuple{Float64,Float64}
+ alpha_beta::Tuple{Float64,Float64}
+ alpha_ip::Tuple{Float64,Float64}
+end
+
+# The fits without a plasma-current term (the 2020 fits).
+ThresholdScaling(n, year, dataset, fit, alpha_c, alpha_n, alpha_b, alpha_r, alpha_beta) =
+ ThresholdScaling(n, year, dataset, fit, alpha_c, alpha_n, alpha_b, alpha_r, alpha_beta, (0.0, 0.0))
+
+"""
+ scaling_label(sc::ThresholdScaling) -> String
+
+The fit's key in `ITPA_THRESHOLD_SCALINGS`, `"n= "`.
+"""
+scaling_label(sc::ThresholdScaling) = "n=$(sc.n) $(sc.year) $(sc.dataset) $(sc.fit)"
+
+# The published ITPA fits, keyed "n= ". Exponent order: α_c, α_n, α_B, α_R, α_β[, α_I].
+const ITPA_THRESHOLD_SCALINGS = Dict{String,ThresholdScaling}(
+ # 2020 n = 1: Logan et al., PPCF 62 (2020) 084001.
+ "n=1 2020 O,L OLS" => ThresholdScaling(1, 2020, "O,L", "OLS", (-3.75, 0.05), (0.63, 0.09), (-0.98, 0.12), (0.15, 0.08), (-0.13, 0.10)),
+ "n=1 2020 O,L DSOLS" => ThresholdScaling(1, 2020, "O,L", "DSOLS", (-3.39, 0.06), (0.58, 0.08), (-1.08, 0.10), (0.19, 0.07), (0.26, 0.10)),
+ "n=1 2020 O,L WLS" => ThresholdScaling(1, 2020, "O,L", "WLS", (-3.46, 0.05), (0.64, 0.06), (-1.14, 0.08), (0.20, 0.07), (0.15, 0.07)),
+ "n=1 2020 O,L,H OLS" => ThresholdScaling(1, 2020, "O,L,H", "OLS", (-3.64, 0.04), (0.60, 0.08), (-0.95, 0.08), (0.12, 0.08), (-0.30, 0.05)),
+ "n=1 2020 O,L,H DSOLS" => ThresholdScaling(1, 2020, "O,L,H", "DSOLS", (-3.58, 0.04), (0.45, 0.06), (-0.94, 0.08), (0.09, 0.07), (-0.15, 0.05)),
+ "n=1 2020 O,L,H WLS" => ThresholdScaling(1, 2020, "O,L,H", "WLS", (-3.62, 0.04), (0.53, 0.06), (-0.95, 0.07), (0.14, 0.08), (-0.19, 0.05)),
+ # 2026 n = 1: Bursch et al., PPCF 2026 (doi:10.1088/1361-6587/aea7d6) Eq. 7 (OLS, R² = 0.63) and Eq. 8 (KDE-weighted WLS, R² = 0.66): ohmic and L-mode
+ # discharges of conventional tokamaks (C-Mod, DIII-D, EAST, JET, J-TEXT, KSTAR), no NSTX or COMPASS, with |B_T| and |I_p|.
+ "n=1 2026 O,L OLS" => ThresholdScaling(1, 2026, "O,L", "OLS", (-4.31, 0.09), (0.77, 0.08), (0.19, 0.09), (1.88, 0.16), (0.25, 0.08), (-0.97, 0.08)),
+ "n=1 2026 O,L WLS" => ThresholdScaling(1, 2026, "O,L", "WLS", (-4.26, 0.09), (0.56, 0.08), (0.30, 0.10), (1.57, 0.15), (0.13, 0.06), (-1.01, 0.07)),
+ # 2020 n = 2: Logan et al., NF 60 (2020) 086010.
+ "n=2 2020 O,L WLS" => ThresholdScaling(2, 2020, "O,L", "WLS", (-3.36, 0.06), (1.07, 0.09), (-1.52, 0.2), (1.46, 0.09), (0.36, 0.11)),
+ "n=2 2020 O,L,-C WLS" => ThresholdScaling(2, 2020, "O,L,-C", "WLS", (-2.98, 0.05), (0.93, 0.08), (-1.28, 0.15), (0.0, 0.0), (0.41, 0.08)),
+ "n=2 2020 O,L,N WLS" => ThresholdScaling(2, 2020, "O,L,N", "WLS", (-3.16, 0.05), (0.64, 0.06), (-1.14, 0.08), (0.20, 0.07), (0.15, 0.07))
+)
+
+"""
+ threshold_scaling(; n=1, year=2020, dataset="O,L", fit="WLS") -> ThresholdScaling
+
+Look up a published ITPA fit by toroidal mode number, publication year, dataset and fitting
+method; the available keys are those of `ITPA_THRESHOLD_SCALINGS`.
+"""
+function threshold_scaling(; n::Int=1, year::Int=2020, dataset::AbstractString="O,L", fit::AbstractString="WLS")
+ key = "n=$n $year $dataset $fit"
+ haskey(ITPA_THRESHOLD_SCALINGS, key) ||
+ throw(ArgumentError("no ITPA threshold scaling \"$key\"; available: $(join(sort(collect(keys(ITPA_THRESHOLD_SCALINGS))), ", "))"))
+ return ITPA_THRESHOLD_SCALINGS[key]
+end
+
+"""
+ ScenarioParameters
+
+Operating point the threshold scaling is evaluated at. Density is not an ideal-MHD equilibrium
+output and must be given; the others default from the equilibrium when built with
+`ScenarioParameters(equil; n_e)`. The plasma current only enters the fits that carry a current
+term, so the keyword constructor leaves it `NaN` unless given and those fits refuse to evaluate
+without it.
+
+## Fields
+
+ - `n_e`: electron density, 10¹⁹ m⁻³
+ - `b_t0`: toroidal field magnitude on axis, tesla
+ - `r_0`: major radius of the magnetic axis, metres
+ - `beta_n`: normalized beta
+ - `l_i`: normalized internal inductance (`l_i(1)`)
+ - `i_p`: plasma current magnitude, MA (`NaN`: not given)
+"""
+struct ScenarioParameters
+ n_e::Float64
+ b_t0::Float64
+ r_0::Float64
+ beta_n::Float64
+ l_i::Float64
+ i_p::Float64
+ # Keyword-only: the five positive scalars are easy to transpose positionally without any guard noticing.
+ function ScenarioParameters(; n_e, b_t0, r_0, beta_n, l_i, i_p=NaN)
+ all(>(0), (n_e, b_t0, r_0, beta_n, l_i)) || throw(ArgumentError("scenario parameters must be positive (got n_e=$n_e, B_T0=$b_t0, R_0=$r_0, β_N=$beta_n, l_i=$l_i)"))
+ (isnan(i_p) || i_p > 0) || throw(ArgumentError("the plasma current must be a positive magnitude in MA (got I_p=$i_p)"))
+ return new(n_e, b_t0, r_0, beta_n, l_i, i_p)
+ end
+end
+
+"""
+ ScenarioParameters(equil::PlasmaEquilibrium; n_e, b_t0=equil.params.bt0, r_0=equil.ro, beta_n=equil.params.betan, l_i=equil.params.li1, i_p=equil.params.crnt)
+ ScenarioParameters(h5path; n_e, kwargs...)
+
+Build the operating point from an equilibrium (or a run's `Equilibrium/` scalars), with the
+density supplied and any other parameter overridable. The current is the equilibrium's computed
+`crnt` (`Equilibrium/I_p`), a positive magnitude in MA.
+"""
+function ScenarioParameters(equil::Equilibrium.PlasmaEquilibrium; n_e::Real, b_t0::Real=equil.params.bt0, r_0::Real=equil.ro,
+ beta_n::Real=equil.params.betan, l_i::Real=equil.params.li1, i_p::Union{Nothing,Real}=equil.params.crnt)
+ return ScenarioParameters(; n_e, b_t0, r_0, beta_n, l_i, i_p=something(i_p, NaN))
+end
+
+function ScenarioParameters(h5path::AbstractString; n_e::Real, kwargs...)
+ vals = h5open(h5path, "r") do f
+ (b_t0=read(f["Equilibrium/B_T_axis"]), r_0=read(f["Equilibrium/R_axis"]), beta_n=read(f["Equilibrium/beta_N"]), l_i=read(f["Equilibrium/l_i_1"]),
+ i_p=haskey(f, "Equilibrium/I_p") ? read(f["Equilibrium/I_p"]) : NaN)
+ end
+ merged = merge(vals, values(kwargs))
+ return ScenarioParameters(; n_e, b_t0=merged.b_t0, r_0=merged.r_0, beta_n=merged.beta_n, l_i=merged.l_i, i_p=merged.i_p)
+end
+
+_has_current_term(sc::ThresholdScaling) = sc.alpha_ip != (0.0, 0.0)
+
+function _check_current(sc::ThresholdScaling, scen::ScenarioParameters)
+ (_has_current_term(sc) && isnan(scen.i_p)) && throw(ArgumentError(
+ "the $(scaling_label(sc)) threshold scaling has a plasma-current term; give i_p (MA) in the scenario"))
+ return nothing
+end
+
+# A fit without a current term never touches I_p, so a scenario without one evaluates it.
+_threshold(sc::ThresholdScaling, scen::ScenarioParameters, αc, αn, αb, αr, αβ, αI) =
+ 10.0^αc * scen.n_e^αn * scen.b_t0^αb * scen.r_0^αr * (scen.beta_n / scen.l_i)^αβ * (αI == 0 ? 1.0 : scen.i_p^αI)
+
+"""
+ fitted_threshold(sc::ThresholdScaling, scen::ScenarioParameters) -> Float64
+
+The penetration threshold at the fitted exponents.
+"""
+function fitted_threshold(sc::ThresholdScaling, scen::ScenarioParameters)
+ _check_current(sc, scen)
+ return _threshold(sc, scen, sc.alpha_c[1], sc.alpha_n[1], sc.alpha_b[1], sc.alpha_r[1], sc.alpha_beta[1], sc.alpha_ip[1])
+end
+
+"""
+ threshold_samples(rng, sc, scen; nsample=1_000_000, dist="normal") -> Vector{Float64}
+
+Thresholds with the exponents drawn around their fitted values: `"normal"` (Gaussian with
+the standard error), `"flat"` (uniform within one standard error), or `"normal_truncated"`
+(Gaussian, redrawn beyond 1.5 standard errors). The current exponent is drawn only for fits that
+have one, so the other fits' sample streams do not depend on it.
+"""
+function threshold_samples(rng::AbstractRNG, sc::ThresholdScaling, scen::ScenarioParameters; nsample::Int=1_000_000, dist::AbstractString="normal")
+ draw = if dist == "normal"
+ () -> randn(rng)
+ elseif dist == "flat"
+ () -> 2 * rand(rng) - 1
+ elseif dist == "normal_truncated"
+ () -> begin
+ x = randn(rng)
+ while abs(x) > 1.5
+ x = randn(rng)
+ end
+ x
+ end
+ else
+ throw(ArgumentError("dist must be \"normal\", \"flat\", or \"normal_truncated\" (got \"$dist\")"))
+ end
+ _check_current(sc, scen)
+ with_ip = _has_current_term(sc)
+ out = Vector{Float64}(undef, nsample)
+ for i in 1:nsample
+ αc, αn, αb = sc.alpha_c[1] + sc.alpha_c[2] * draw(), sc.alpha_n[1] + sc.alpha_n[2] * draw(), sc.alpha_b[1] + sc.alpha_b[2] * draw()
+ αr, αβ = sc.alpha_r[1] + sc.alpha_r[2] * draw(), sc.alpha_beta[1] + sc.alpha_beta[2] * draw()
+ αI = with_ip ? sc.alpha_ip[1] + sc.alpha_ip[2] * draw() : 0.0
+ out[i] = _threshold(sc, scen, αc, αn, αb, αr, αβ, αI)
+ end
+ return out
+end
+
+"""
+ RiskControl
+
+Settings of the locking-risk evaluation, the `[ErrorFields.Risk]` TOML table.
+
+## Fields
+
+ - `year`, `dataset`, `fit`: which ITPA threshold fit to use (the toroidal mode number is the
+ run's). n = 1, `year = 2020`: `"O,L"` or `"O,L,H"` with `"OLS"`, `"DSOLS"` or `"WLS"`;
+ n = 1, `year = 2026`: `"O,L"` with `"OLS"` or `"WLS"` (with a plasma-current term);
+ n = 2, `year = 2020`: `"O,L"`, `"O,L,-C"` or `"O,L,N"` with `"WLS"`
+ - `distribution`: how the fit exponents are sampled — `"normal"`, `"flat"`, or `"normal_truncated"`
+ - `nsample_threshold`: threshold samples
+ - `seed`: seed of the threshold sampling
+ - `scan_scales`: tolerance multipliers of the allowable-tolerance scan (empty: no scan); each
+ is a fresh Monte Carlo with every shift and tilt tolerance multiplied by the scale
+"""
+Base.@kwdef struct RiskControl
+ year::Int = 2020
+ dataset::String = "O,L"
+ fit::String = "WLS"
+ distribution::String = "normal"
+ nsample_threshold::Int = 1_000_000
+ seed::Int = 1
+ scan_scales::Vector{Float64} = Float64[]
+end
+
+"""
+ RiskResult
+
+Field names follow the ErrorFields result grammar `[_instance][_efc][_statistic][_unit]` (see the manual's
+"Result names"); every field name is also its HDF5 dataset name.
+
+The locking risk of a Monte Carlo overlap distribution under one threshold scaling. All
+probabilities are percentages.
+
+## Fields
+
+ - `abs_delta_bin_edges`: the Monte Carlo's `|δ|` grid `[nbins + 1]`
+ - `threshold_pdf`: probability density of the sampled penetration threshold on that grid `[nbins]`
+ - `locking_probability_given_delta`: probability that an overlap equal to each bin edge locks, the
+ threshold's cumulative distribution `[nbins + 1]`
+ - `threshold_fit`: the threshold at the fitted exponents
+ - `locking_probability_percent`, `locking_probability_efc_percent`: locking probability of the intrinsic and of the corrected distribution,
+ `100 ∫ pdf(δ) P(lock|δ) dδ`, batch averages
+ - `locking_probability_batches_percent`, `locking_probability_efc_batches_percent`: the same per Monte Carlo batch `[nbatch]`; their ranges
+ are the statistical error bars
+ - `locking_probability_as_designed_percent`: locking probability of the as-designed machine, `100 P(lock | |Σ δ_as_designed|)`
+ - `locking_probability_fit_threshold_percent`: locking probability if the threshold were exactly its fitted value, `100 P(|δ| > threshold_fit)`
+ - `scaling`: the threshold fit used
+"""
+struct RiskResult
+ abs_delta_bin_edges::Vector{Float64}
+ threshold_pdf::Vector{Float64}
+ locking_probability_given_delta::Vector{Float64}
+ threshold_fit::Float64
+ locking_probability_percent::Float64
+ locking_probability_efc_percent::Float64
+ locking_probability_batches_percent::Vector{Float64}
+ locking_probability_efc_batches_percent::Vector{Float64}
+ locking_probability_as_designed_percent::Float64
+ locking_probability_fit_threshold_percent::Float64
+ scaling::ThresholdScaling
+end
+
+"""
+ locking_risk(mc::MonteCarloResult, sc::ThresholdScaling, scen::ScenarioParameters; ctrl=RiskControl()) -> RiskResult
+ locking_risk(mc, thresholds::AbstractVector, sc, scen) -> RiskResult
+
+Convolve an overlap distribution with the threshold distribution: `P(lock|δ)` is the fraction of
+sampled thresholds below `δ`, and the locking probability is `100 ∫ pdf(δ) P(lock|δ) dδ` over
+the Monte Carlo's bins, evaluated per batch. Thresholds are sampled with `ctrl` or passed in.
+"""
+function locking_risk(mc::MonteCarloResult, sc::ThresholdScaling, scen::ScenarioParameters; ctrl::RiskControl=RiskControl())
+ thresholds = threshold_samples(Xoshiro(ctrl.seed), sc, scen; nsample=ctrl.nsample_threshold, dist=ctrl.distribution)
+ return locking_risk(mc, thresholds, sc, scen)
+end
+
+function locking_risk(mc::MonteCarloResult, thresholds::AbstractVector{<:Real}, sc::ThresholdScaling, scen::ScenarioParameters)
+ edges = mc.abs_delta_bin_edges
+ sorted = sort(Float64.(thresholds))
+ n = length(sorted)
+ cdf_at(x) = searchsortedlast(sorted, x) / n
+ p_given = [e == 0 ? 0.0 : cdf_at(e) for e in edges]
+ threshold_pdf = diff(p_given) ./ diff(edges)
+ # Bin-average of P(lock|δ) times the bin's probability mass; the last bin also holds the
+ # clamped tail, whose overlaps are at least the last edge.
+ weights = (p_given[1:end-1] .+ p_given[2:end]) ./ 2
+ widths = diff(edges)
+ # Densities integrate to one only to round-off, so the percentage is clamped to [0, 100].
+ probability_of(pdf) = clamp(100 * sum(pdf .* widths .* weights), 0.0, 100.0)
+ plock_b = [probability_of(view(mc.abs_delta_pdf_batches, :, b)) for b in 1:size(mc.abs_delta_pdf_batches, 2)]
+ plock_efc_b = [probability_of(view(mc.abs_delta_efc_pdf_batches, :, b)) for b in 1:size(mc.abs_delta_efc_pdf_batches, 2)]
+ nominal = fitted_threshold(sc, scen)
+ locking_probability_fit_threshold_percent = clamp(100 * (1 - sum(mc.abs_delta_pdf[edges[2:end].<=nominal] .* widths[edges[2:end].<=nominal])), 0.0, 100.0)
+ return RiskResult(copy(edges), threshold_pdf, p_given, nominal, sum(plock_b) / length(plock_b), sum(plock_efc_b) / length(plock_efc_b),
+ plock_b, plock_efc_b, 100 * cdf_at(mc.abs_delta_total_as_designed), locking_probability_fit_threshold_percent, sc)
+end
+
+"""
+ locking_risk(h5path; n_e, psi_low=0.0, psi_high=CORE_PSI_HIGH, mode=1, risk_ctrl=RiskControl(), kwargs...) -> RiskResult
+
+Post-hoc locking risk from a run: the Monte Carlo is re-run from the file for the given window
+and mode with [`MonteCarloControl`](@ref) `kwargs`, the threshold fit is chosen by `risk_ctrl`
+for the run's toroidal mode number, and the scenario is the run's equilibrium at density `n_e`.
+"""
+function locking_risk(
+ h5path::AbstractString;
+ n_e::Real,
+ psi_low::Real=0.0,
+ psi_high::Real=PerturbedEquilibrium.CORE_PSI_HIGH,
+ mode::Int=1,
+ risk_ctrl::RiskControl=RiskControl(),
+ kwargs...
+)
+ mc = run_monte_carlo(h5path; psi_low, psi_high, mode, kwargs...)
+ n = scaling_toroidal_mode(h5path)
+ sc = threshold_scaling(; n, year=risk_ctrl.year, dataset=risk_ctrl.dataset, fit=risk_ctrl.fit)
+ return locking_risk(mc, sc, ScenarioParameters(h5path; n_e); ctrl=risk_ctrl)
+end
+
+"""
+ scaling_toroidal_mode(h5path) -> Int
+
+The toroidal mode number whose ITPA threshold scaling applies to a run; errors on a multi-n run
+(see [`single_toroidal_mode`](@ref)).
+"""
+function scaling_toroidal_mode(h5path::AbstractString)
+ return h5open(h5path, "r") do f
+ single_toroidal_mode(Int(read(f["Info/nlow"])), Int(read(f["Info/nhigh"])); where=h5path)
+ end
+end
+
+"""
+ single_toroidal_mode(nlow, nhigh; where="the run") -> nlow
+
+The one toroidal mode number a locking-threshold scaling is fitted for, or an `ArgumentError`
+when the run spans several.
+"""
+function single_toroidal_mode(nlow::Integer, nhigh::Integer; where::AbstractString="the run")
+ nlow == nhigh || throw(
+ ArgumentError(
+ "$where carries n = $nlow:$nhigh, but a locking-threshold scaling is fitted for one " *
+ "toroidal mode number. Re-run the assessment for a single n, or project onto one n's " *
+ "coupling before asking for a risk.")
+ )
+ return Int(nlow)
+end
+
+"""
+ ToleranceScan
+
+Field names follow the ErrorFields result grammar `[_instance][_efc][_statistic][_unit]` (see the manual's
+"Result names"); every field name is also its HDF5 dataset name.
+
+Locking risk against a multiplier of every shift and tilt tolerance, from repeated Monte
+Carlos on the same sensitivities. Percentages throughout.
+
+## Fields
+
+ - `tolerance_scale`: tolerance multipliers `[nscale]`
+ - `locking_probability_percent`, `locking_probability_efc_percent`: locking probability at each scale, batch averages
+ - `locking_probability_spread_percent`, `locking_probability_efc_spread_percent`: range of the batch values at each scale
+ - `locking_probability_as_designed_percent`: risk of the as-designed machine (independent of the scale)
+"""
+struct ToleranceScan
+ tolerance_scale::Vector{Float64}
+ locking_probability_percent::Vector{Float64}
+ locking_probability_efc_percent::Vector{Float64}
+ locking_probability_spread_percent::Vector{Float64}
+ locking_probability_efc_spread_percent::Vector{Float64}
+ locking_probability_as_designed_percent::Float64
+end
+
+"""
+ tolerance_scan(table, ts, coil_sets, mc_ctrl, sc, scen; scales, risk_ctrl=RiskControl()) -> ToleranceScan
+ tolerance_scan(h5path; scales, psi_low=0.0, psi_high=CORE_PSI_HIGH, mode=1, n_e, risk_ctrl=RiskControl(), kwargs...) -> ToleranceScan
+
+Run the Monte Carlo once per tolerance multiplier in `scales` and evaluate the locking risk of
+each with one threshold sampling. The file form takes the run's tolerances, coil geometry and
+equilibrium scalars from `gpec.h5`; `kwargs` are [`MonteCarloControl`](@ref) fields, and the
+threshold fit is chosen with `risk_ctrl`.
+"""
+function tolerance_scan(table::SensitivityTable, ts::ToleranceSet, coil_sets::Vector{CoilSet}, mc_ctrl::MonteCarloControl,
+ sc::ThresholdScaling, scen::ScenarioParameters; scales::AbstractVector{<:Real}, risk_ctrl::RiskControl=RiskControl())
+ isempty(scales) && throw(ArgumentError("tolerance_scan needs at least one scale"))
+ all(>=(0), scales) || throw(ArgumentError("tolerance scales must be ≥ 0"))
+ thresholds = threshold_samples(Xoshiro(risk_ctrl.seed), sc, scen; nsample=risk_ctrl.nsample_threshold, dist=risk_ctrl.distribution)
+ fields = (f => getfield(mc_ctrl, f) for f in fieldnames(MonteCarloControl) if f != :tolerance_scale)
+ locking_probability_percent = Float64[]
+ locking_probability_efc_percent = Float64[]
+ spread = Float64[]
+ spread_efc = Float64[]
+ nominal = 0.0
+ for s in scales
+ mc = run_monte_carlo(table, ts, coil_sets, MonteCarloControl(; fields..., tolerance_scale=Float64(s)))
+ risk = locking_risk(mc, thresholds, sc, scen)
+ push!(locking_probability_percent, risk.locking_probability_percent)
+ push!(locking_probability_efc_percent, risk.locking_probability_efc_percent)
+ push!(spread, maximum(risk.locking_probability_batches_percent) - minimum(risk.locking_probability_batches_percent))
+ push!(spread_efc, maximum(risk.locking_probability_efc_batches_percent) - minimum(risk.locking_probability_efc_batches_percent))
+ nominal = risk.locking_probability_as_designed_percent
+ end
+ return ToleranceScan(Float64.(collect(scales)), locking_probability_percent, locking_probability_efc_percent, spread, spread_efc, nominal)
+end
+
+function tolerance_scan(h5path::AbstractString; scales::AbstractVector{<:Real}, psi_low::Real=0.0, psi_high::Real=PerturbedEquilibrium.CORE_PSI_HIGH, mode::Int=1,
+ n_e::Real, risk_ctrl::RiskControl=RiskControl(), kwargs...)
+ ts = read_tolerance_snapshot(h5path)
+ ts === nothing && throw(ArgumentError("$h5path carries no tolerance snapshot (the run named no tolerance_file)"))
+ table = without_coils(sensitivity_table(h5path; psi_low, psi_high, mode), excluded_coil_names(h5path))
+ coil_sets, _ = h5open(h5path, "r") do f
+ haskey(f, "Input/RawInputs/Coils") || throw(ArgumentError("$h5path has no Input/RawInputs/Coils snapshot"))
+ sets = CoilSet[]
+ ForcingTerms.load_coils_from_h5_group!(sets, f["Input/RawInputs/Coils"])
+ sets, nothing
+ end
+ n = scaling_toroidal_mode(h5path)
+ sc = threshold_scaling(; n, year=risk_ctrl.year, dataset=risk_ctrl.dataset, fit=risk_ctrl.fit)
+ scen = ScenarioParameters(h5path; n_e)
+ return tolerance_scan(table, ts, coil_sets, MonteCarloControl(; kwargs...), sc, scen; scales, risk_ctrl)
+end
+
+"""
+ allowable_tolerance(scan::ToleranceScan, target_percent; corrected=false) -> Float64
+
+The tolerance multiplier at which the locking risk reaches `target_percent`, by linear
+interpolation in the logarithms of both the scale and the risk between the two scan points
+that bracket the target (the scan need not be monotonic; the first bracketing pair from the
+smallest scale is used). A pair that starts at scale 0 is interpolated linearly in the scale.
+Returns `NaN` when no pair brackets the target. `corrected` reads the
+error-field-corrected curve.
+"""
+function allowable_tolerance(scan::ToleranceScan, target_percent::Real; corrected::Bool=false)
+ target_percent > 0 || throw(ArgumentError("target_percent must be positive"))
+ p = corrected ? scan.locking_probability_efc_percent : scan.locking_probability_percent
+ lt = log10(target_percent)
+ for i in 1:length(scan.tolerance_scale)-1
+ p1, p2 = p[i], p[i+1]
+ (p1 > 0 && p2 > 0) || continue
+ l1, l2 = log10(p1), log10(p2)
+ (min(l1, l2) <= lt <= max(l1, l2)) || continue
+ s1, s2 = scan.tolerance_scale[i], scan.tolerance_scale[i+1]
+ lt == l1 && return s1
+ lt == l2 && return s2
+ f = (lt - l1) / (l2 - l1)
+ return s1 > 0 ? 10^(log10(s1) + f * (log10(s2) - log10(s1))) : s1 + f * (s2 - s1)
+ end
+ return NaN
+end
+
+"""
+ risk_convergence(table, tolerances, coil_sets, sc, scen; nsamples, nbins_list, ctrl=MonteCarloControl(), risk_ctrl=RiskControl()) -> NamedTuple
+
+The locking probability and its batch spread against the Monte Carlo's sample count and bin count,
+to check a quoted risk is free of sampling and binning bias. Each sweep holds the other control at
+`ctrl`'s value and reuses one threshold sample. Fields: `nsample`, `locking_probability_percent_by_nsample`,
+`locking_probability_spread_percent_by_nsample`, `nbins`, `locking_probability_percent_by_nbins`,
+`locking_probability_spread_percent_by_nbins`.
+"""
+function risk_convergence(table::SensitivityTable, ts::ToleranceSet, coil_sets::Vector{CoilSet}, sc::ThresholdScaling, scen::ScenarioParameters;
+ nsamples::AbstractVector{<:Integer}, nbins_list::AbstractVector{<:Integer}, ctrl::MonteCarloControl=MonteCarloControl(), risk_ctrl::RiskControl=RiskControl())
+ thresholds = threshold_samples(Xoshiro(risk_ctrl.seed), sc, scen; nsample=risk_ctrl.nsample_threshold, dist=risk_ctrl.distribution)
+ fields = (f => getfield(ctrl, f) for f in fieldnames(MonteCarloControl) if f != :nsample && f != :nbins)
+ function at(nsample, nbins)
+ risk = locking_risk(run_monte_carlo(table, ts, coil_sets, MonteCarloControl(; fields..., nsample, nbins)), thresholds, sc, scen)
+ b = risk.locking_probability_batches_percent
+ return risk.locking_probability_percent, maximum(b) - minimum(b)
+ end
+ by_n = [at(n, ctrl.nbins) for n in nsamples]
+ by_b = [at(ctrl.nsample, b) for b in nbins_list]
+ return (; nsample=collect(Int, nsamples), locking_probability_percent_by_nsample=first.(by_n), locking_probability_spread_percent_by_nsample=last.(by_n),
+ nbins=collect(Int, nbins_list), locking_probability_percent_by_nbins=first.(by_b), locking_probability_spread_percent_by_nbins=last.(by_b))
+end
diff --git a/src/ErrorFields/Sampling.jl b/src/ErrorFields/Sampling.jl
new file mode 100644
index 0000000000..6dbcdc49bc
--- /dev/null
+++ b/src/ErrorFields/Sampling.jl
@@ -0,0 +1,180 @@
+"""
+ Sampling
+
+Random draws of coil misalignment within a tolerance, the primitives a tolerance Monte Carlo
+recombines with the coil sensitivities. A tolerance is one number, the radius of the disk the
+coil centre (or axis endpoint) may lie in; the direction is random and the radial density is a
+[`RadialDistribution`](@ref). Samplers take a caller-supplied `rng` and scalar arguments.
+
+Displacements are complex numbers `Δx + iΔy` in metres and tilts `θx + iθy` in degrees, the
+rotation angles about the machine x and y axes that `apply_transforms` and the stored
+sensitivities use, so an overlap moves by `S_x·real(Δ) + S_y·imag(Δ) + T_x·real(θ) + T_y·imag(θ)`.
+For an axisymmetric coil `S_y = −i·S_x`, which makes that `S_x·conj(Δ)`.
+"""
+
+"""
+ RadialDistribution
+
+Radial density of a point drawn in a disk of radius `R`: `r = R·u^p` with `u` uniform on
+`[0, 1]` and `p = randpow(d)`. Subtypes: [`Flat`](@ref) (`p = 1`, uniform in radius),
+[`UniformArea`](@ref) (`p = 1/2`, uniform over the disk area), [`Hollow`](@ref) (`p = 1/3`,
+peaked toward the edge), [`Ring`](@ref) (`p = 0`, always on the edge), and [`PowerLaw`](@ref)
+for any exponent. The radial cumulative distribution is `(r/R)^(1/p)`.
+"""
+abstract type RadialDistribution end
+
+"""
+ Flat <: RadialDistribution
+
+Uniform in radius (`p = 1`): the density of `|Δ|` is constant on `[0, R]`, the OMFIT tool's
+`flat` shape. Note this is not uniform over the disk area — see [`UniformArea`](@ref).
+"""
+struct Flat <: RadialDistribution end
+
+"""
+ UniformArea <: RadialDistribution
+
+Uniform over the disk area (`p = 1/2`): every patch of the tolerance disk is equally likely.
+"""
+struct UniformArea <: RadialDistribution end
+
+"""
+ Hollow <: RadialDistribution
+
+Peaked toward the edge (`p = 1/3`, radial CDF `(r/R)³`): the OMFIT tool's default, standing in
+for a manufacturing process that uses most of its tolerance.
+"""
+struct Hollow <: RadialDistribution end
+
+"""
+ Ring <: RadialDistribution
+
+Always on the edge (`p = 0`, `r = R`): the worst-case magnitude with a random direction.
+"""
+struct Ring <: RadialDistribution end
+
+"""
+ PowerLaw(p) <: RadialDistribution
+
+`r = R·u^p` for a user-chosen exponent `p ≥ 0`.
+"""
+struct PowerLaw <: RadialDistribution
+ p::Float64
+ function PowerLaw(p::Real)
+ p >= 0 || throw(ArgumentError("PowerLaw exponent must be ≥ 0 (got $p)"))
+ return new(Float64(p))
+ end
+end
+
+"""
+ randpow(d::RadialDistribution) -> Float64
+
+The exponent `p` in `r = R·u^p` of a radial distribution.
+"""
+randpow(::Flat) = 1.0
+randpow(::UniformArea) = 0.5
+randpow(::Hollow) = 1 / 3
+randpow(::Ring) = 0.0
+randpow(d::PowerLaw) = d.p
+
+"""
+ radial_distribution(name::AbstractString) -> RadialDistribution
+
+The distribution named by a tolerance file's `radial_shape`: `"flat"`, `"uniform_area"`,
+`"hollow"`, or `"ring"` (the `RADIAL_SHAPES` the parser accepts).
+"""
+function radial_distribution(name::AbstractString)
+ s = lowercase(name)
+ s == "flat" && return Flat()
+ s == "uniform_area" && return UniformArea()
+ s == "hollow" && return Hollow()
+ s == "ring" && return Ring()
+ throw(ArgumentError("unknown radial shape \"$name\" (expected one of $(join(RADIAL_SHAPES, ", ")))"))
+end
+
+"""
+ disk_radius(rng, R, p) -> Float64
+
+A radius drawn in `[0, R]` with density exponent `p` (see [`RadialDistribution`](@ref)):
+`R·rand()^p`, with `sqrt`/`cbrt`/identity fast paths for the common exponents.
+"""
+@inline function disk_radius(rng::AbstractRNG, R::Real, p::Real)
+ u = rand(rng)
+ pf = Float64(p)
+ r = pf == 1.0 ? u : pf == 0.5 ? sqrt(u) : pf == (1 / 3) ? cbrt(u) : pf == 0.0 ? 1.0 : u^pf
+ return Float64(R) * r
+end
+
+"""
+ sample_disk(rng, R, p; phase=2π·rand(rng)) -> ComplexF64
+ sample_disk(rng, R, d::RadialDistribution; phase) -> ComplexF64
+
+A point in the disk of radius `R`, as `Δx + iΔy`: radius from [`disk_radius`](@ref) and a
+uniform direction unless `phase` is given (coherent groups sharing a direction pass one phase
+and draw their own radii).
+"""
+sample_disk(rng::AbstractRNG, R::Real, p::Real; phase::Real=2π * rand(rng)) = disk_radius(rng, R, p) * cis(Float64(phase))
+sample_disk(rng::AbstractRNG, R::Real, d::RadialDistribution; kwargs...) = sample_disk(rng, R, randpow(d); kwargs...)
+
+"""
+ sample_uncertainty(rng, σ; phase=2π·rand(rng)) -> ComplexF64
+
+The Gaussian uncertainty on where a coil actually sits, added to the tolerance draw: a signed
+normal amplitude of standard deviation `σ` times a uniform direction, `σ·randn()·e^{iφ}` — the
+OMFIT tool's construction, whose magnitude is a half-normal rather than the Rayleigh a
+two-dimensional Gaussian would give. Zero `σ` returns zero without consuming random numbers.
+"""
+function sample_uncertainty(rng::AbstractRNG, σ::Real; phase::Union{Nothing,Real}=nothing)
+ σ == 0 && return zero(ComplexF64)
+ φ = phase === nothing ? 2π * rand(rng) : Float64(phase)
+ return Float64(σ) * randn(rng) * cis(φ)
+end
+
+"""
+ sample_additive(rng, R_shift, p_shift, R_tilt, p_tilt; phase_shift, phase_tilt) -> (shift, tilt)
+
+The additive tolerance model: an in-plane shift drawn in the disk of radius `R_shift` metres
+and, independently, a tilt drawn in the disk of radius `R_tilt` degrees, each with its own
+radial exponent and an optional shared direction. Returns `(Δx + iΔy, θx + iθy)`.
+"""
+function sample_additive(rng::AbstractRNG, R_shift::Real, p_shift::Real, R_tilt::Real, p_tilt::Real;
+ phase_shift::Real=2π * rand(rng), phase_tilt::Real=2π * rand(rng))
+ shift = sample_disk(rng, R_shift, p_shift; phase=phase_shift)
+ tilt = sample_disk(rng, R_tilt, p_tilt; phase=phase_tilt)
+ return shift, tilt
+end
+
+"""
+ sample_cylinder(rng, R, z_top, p; phase_top, phase_bot) -> (shift, tilt)
+
+The cylinder tolerance model: the coil's axis line must lie inside a cylinder of radius `R`
+metres and half-height `z_top` metres centred on the coil. Its two endpoints are drawn
+independently in the top and bottom disks (radial exponent `p`, optional fixed directions);
+the coil then sits at the axis's midplane crossing and is tilted by the axis's lean:
+
+```
+shift = (p_top + p_bot) / 2 # metres, Δx + iΔy
+α = atan(|p_top − p_bot|, 2 z_top) # lean angle
+tilt = −α · (sin φ_d + i cos φ_d) in degrees, φ_d = arg(p_top − p_bot)
+```
+
+Shift and tilt are therefore correlated, and the tilt magnitude never exceeds `atan(R / z_top)`.
+The tilt is expressed as the rotation angles `(θx, θy)` about the machine axes that lean the
+axis top toward the direction `φ_d`, in the sense `apply_transforms` uses: a positive `θx`
+leans the top toward −y and a positive `θy` toward −x.
+
+Unlike the OMFIT tool's version, this works in physical units with independent endpoint directions,
+so it agrees with that tool only in kind.
+"""
+function sample_cylinder(rng::AbstractRNG, R::Real, z_top::Real, p::Real;
+ phase_top::Real=2π * rand(rng), phase_bot::Real=2π * rand(rng))
+ z_top > 0 || throw(ArgumentError("the cylinder half-height must be positive (got $z_top)"))
+ p_top = sample_disk(rng, R, p; phase=phase_top)
+ p_bot = sample_disk(rng, R, p; phase=phase_bot)
+ shift = (p_top + p_bot) / 2
+ d = p_top - p_bot
+ α = rad2deg(atan(abs(d), 2 * Float64(z_top)))
+ φ = angle(d)
+ tilt = -α * complex(sin(φ), cos(φ))
+ return shift, tilt
+end
diff --git a/src/ErrorFields/Sensitivity.jl b/src/ErrorFields/Sensitivity.jl
new file mode 100644
index 0000000000..f8261085a6
--- /dev/null
+++ b/src/ErrorFields/Sensitivity.jl
@@ -0,0 +1,229 @@
+"""
+ compute_coil_sensitivities(coil_sets, rc, equil, cfg, ctrl=ErrorFieldsControl(); psi, b_t0, verbose=false) -> CoilSensitivities
+
+Linearize the control-surface spectrum of every coil set in `coil_sets` with respect to its six
+rigid-body degrees of freedom, by central differences of the Biot-Savart spectrum on the surface
+`psi` (the solve's integration limit, `ffs.psilim`) sampled once per toroidal mode of `rc`.
+The nominal spectrum is evaluated too. Tilt taps rotate about the pivot named by
+`ctrl.rotation_center`, in degrees; `b_t0` is the axis toroidal field (tesla) for the δ
+normalization. Errors on a set carrying no current.
+
+Spectra are on `rc`'s (m, n) ordering, conformed with [`rootarea_field`](@ref), so
+[`coupling_overlap`](@ref) applies directly.
+"""
+function compute_coil_sensitivities(
+ coil_sets::Vector{CoilSet},
+ rc::ResonantCoupling,
+ equil::Equilibrium.PlasmaEquilibrium,
+ cfg::CoilConfig,
+ ctrl::ErrorFieldsControl=ErrorFieldsControl();
+ psi::Float64,
+ b_t0::Float64,
+ verbose::Bool=false
+)
+ isempty(coil_sets) && throw(ArgumentError("compute_coil_sensitivities: no coil sets given"))
+ ctrl.rotation_center in ("conductor", "set") ||
+ throw(ArgumentError("rotation_center must be \"conductor\" or \"set\" (got \"$(ctrl.rotation_center)\")"))
+ (ctrl.fd_step_shift_m > 0 && ctrl.fd_step_tilt_deg > 0) ||
+ throw(ArgumentError("finite-difference steps must be positive (got $(ctrl.fd_step_shift_m) m, $(ctrl.fd_step_tilt_deg) deg)"))
+ b_t0 > 0 || throw(ArgumentError("b_t0 must be a positive field magnitude (got $b_t0)"))
+ for cs in coil_sets
+ all(iszero, cs.currents) &&
+ throw(ArgumentError("coil set \"$(cs.name)\" carries no current; its spectrum and sensitivities would vanish identically"))
+ end
+
+ N = length(rc.m_modes)
+ nset = length(coil_sets)
+ grids = forcing_grids(rc, equil, cfg; psi)
+ spectrum(cs::CoilSet) = applied_spectrum(cs, rc, grids)
+
+ nominal = zeros(ComplexF64, N, nset)
+ shift = zeros(ComplexF64, N, 3, nset)
+ tilt = zeros(ComplexF64, N, 3, nset)
+ shift_resid = zeros(3, nset)
+ tilt_resid = zeros(3, nset)
+ h_shift = ctrl.fd_step_shift_m
+ h_tilt = ctrl.fd_step_tilt_deg
+
+ for (j, cs) in enumerate(coil_sets)
+ t_start = time()
+ b0 = spectrum(cs)
+ nominal[:, j] = b0
+ pivot = ctrl.rotation_center == "set" ? _set_center(cs) : nothing
+
+ first_norm = zeros(3, 2)
+ second_norm = zeros(3, 2)
+ for axis in 1:3, (kind, h, out) in ((:shift, h_shift, shift), (:tilt, h_tilt, tilt))
+ plus = spectrum(_rigidly_perturbed(cs, kind, axis, h, pivot))
+ minus = spectrum(_rigidly_perturbed(cs, kind, axis, -h, pivot))
+ out[:, axis, j] = (plus .- minus) ./ (2h)
+ col = kind === :shift ? 1 : 2
+ first_norm[axis, col] = norm(plus .- minus)
+ second_norm[axis, col] = norm(plus .+ minus .- 2 .* b0)
+ end
+
+ # Curvature relative to the set's largest linear response, so a tap vanishing by symmetry is not judged against itself.
+ scale = maximum(first_norm)
+ resid = scale > 0 ? second_norm ./ scale : zeros(3, 2)
+ shift_resid[:, j] = resid[:, 1]
+ tilt_resid[:, j] = resid[:, 2]
+
+ worst = maximum(resid)
+ worst > 1e-2 &&
+ @warn "Coil set \"$(cs.name)\": finite-difference curvature $(@sprintf("%.2e", worst)) of the first difference; reduce fd_step_shift_m / fd_step_tilt_deg"
+ verbose &&
+ @info " $(cs.name): |b̃| = $(@sprintf("%.3e", norm(b0))) T, " *
+ "max |∂b̃/∂x| = $(@sprintf("%.3e", maximum(norm, eachslice(shift[:, :, j]; dims=2)))) T/m, " *
+ "max |∂b̃/∂θ| = $(@sprintf("%.3e", maximum(norm, eachslice(tilt[:, :, j]; dims=2)))) T/deg, curvature $(@sprintf("%.1e", worst)) ($(@sprintf("%.2f", time() - t_start)) s)"
+ end
+
+ return CoilSensitivities(
+ [cs.name for cs in coil_sets], copy(rc.m_modes), copy(rc.n_modes), b_t0,
+ nominal, shift, tilt, shift_resid, tilt_resid,
+ [maximum(abs, cs.currents) for cs in coil_sets], [cs.nw for cs in coil_sets],
+ [ForcingTerms.nominal_major_radius(cs) for cs in coil_sets]
+ )
+end
+
+"""
+ compute_coil_sensitivities(ctx::ResonantDriveContext, coil_sets, ctrl=ErrorFieldsControl(); verbose=false) -> CoilSensitivities
+
+Sweep `coil_sets` against an already-assembled [`ResonantDriveContext`](@ref), reusing its boundary grids.
+Equivalent to the five-argument method and the way to apply a grid or ψ-window override.
+"""
+function compute_coil_sensitivities(ctx::ResonantDriveContext, coil_sets::Vector{CoilSet}, ctrl::ErrorFieldsControl=ErrorFieldsControl(); verbose::Bool=false)
+ return compute_coil_sensitivities(coil_sets, ctx.rc, ctx.equil, ctx.cfg, ctrl; psi=ctx.psilim, b_t0=ctx.b_t0, verbose)
+end
+
+"""
+ _rigidly_perturbed(cs, kind, axis, h, pivot) -> CoilSet
+
+The coil set moved rigidly by `h` along one degree of freedom: `kind = :shift` translates every
+conductor by `h` metres along `axis` (x, y, z); `kind = :tilt` rotates every conductor by `h`
+degrees about `axis` through `pivot`, or about its own arc-length centre when `pivot === nothing`.
+Both go through `apply_transforms` with the toroidal modulation that makes the motion rigid
+(`n_tilt = 0` for the shift, `n_tilt = 1` for the tilt).
+"""
+function _rigidly_perturbed(cs::CoilSet, kind::Symbol, axis::Int, h::Real, pivot)
+ per_conductor = fill(Float64(h), cs.ncoil)
+ component(a) = a == axis ? per_conductor : Float64[]
+ if kind === :shift
+ cfg = CoilSetConfig(; shiftx=component(1), shifty=component(2), shiftz=component(3))
+ return apply_transforms(cs, cfg; n_tilt=0)
+ end
+ nom(i) = pivot === nothing ? Float64[] : fill(pivot[i], cs.ncoil)
+ cfg = CoilSetConfig(; tiltx=component(1), tilty=component(2), tiltz=component(3),
+ rotation_center_x=nom(1), rotation_center_y=nom(2), rotation_center_z=nom(3), tilt_in_meters=false)
+ return apply_transforms(cs, cfg; n_tilt=1)
+end
+
+"""
+ _set_center(cs::CoilSet) -> (x0, y0, z0)
+
+Arc-length-weighted centre of the whole coil set, over every conductor and strand: the pivot of
+a rigid tilt of a multi-filament winding pack.
+"""
+function _set_center(cs::CoilSet)
+ total = 0.0
+ cx = cy = cz = 0.0
+ for j in 1:cs.ncoil, k in 1:cs.s, l in 1:(cs.nsec-1)
+ dl = hypot(cs.x[j, k, l+1] - cs.x[j, k, l], cs.y[j, k, l+1] - cs.y[j, k, l], cs.z[j, k, l+1] - cs.z[j, k, l])
+ cx += dl * (cs.x[j, k, l] + cs.x[j, k, l+1]) / 2
+ cy += dl * (cs.y[j, k, l] + cs.y[j, k, l+1]) / 2
+ cz += dl * (cs.z[j, k, l] + cs.z[j, k, l+1]) / 2
+ total += dl
+ end
+ total > 0 || return (0.0, 0.0, 0.0)
+ return (cx / total, cy / total, cz / total)
+end
+
+"""
+ sensitivity_table(sens::CoilSensitivities, dom::DominantCoupling; mode=1) -> SensitivityTable
+ sensitivity_table(h5path; psi_low=CORE_PSI_LOW, psi_high=CORE_PSI_HIGH, mode=1) -> SensitivityTable
+
+Project a coil linearization onto singular mode `mode` of `dom` and normalize by the axis
+toroidal field: `δ = dot(V[:, mode], b̃) / B_T0` for the nominal spectrum and each derivative,
+the dimensionless overlap and its sensitivities per coil set. The window and mode are analysis
+choices, so re-evaluate freely on the same `sens`; the file form rebuilds the coupling from
+`gpec.h5`, windows it to `psi_low ≤ ψ_N ≤ psi_high`, and reads the stored linearization.
+"""
+function sensitivity_table(sens::CoilSensitivities, dom::DominantCoupling; mode::Int=1)
+ 1 <= mode <= length(dom.singular_values) ||
+ throw(ArgumentError("mode $mode is outside the $(length(dom.singular_values)) singular modes of the decomposition"))
+ size(dom.right_singular_vectors, 1) == length(sens.m_modes) ||
+ throw(DimensionMismatch("the decomposition acts on $(size(dom.right_singular_vectors, 1)) modes but the sensitivities carry $(length(sens.m_modes))"))
+ PerturbedEquilibrium.check_mode_basis(dom, sens.m_modes, sens.n_modes, "sensitivity_table")
+ v = dom.right_singular_vectors[:, mode]
+ project(b̃) = dot(v, b̃) / sens.b_t0
+ nset = length(sens.coil_names)
+
+ delta_as_designed = [project(view(sens.field_as_designed, :, j)) for j in 1:nset]
+ shift = [project(view(sens.shift_sensitivity_per_m, :, a, j)) for a in 1:3, j in 1:nset]
+ tilt = [project(view(sens.tilt_sensitivity_per_deg, :, a, j)) for a in 1:3, j in 1:nset]
+ inplane_rms(S) = [sqrt((abs2(S[1, j]) + abs2(S[2, j])) / 2) for j in 1:nset]
+ cancelling(S) = [cancelling_offset(delta_as_designed[j], S[1, j], S[2, j])[i] for i in 1:2, j in 1:nset]
+
+ per_deg = inplane_rms(tilt)
+ # A tilt of one degree sweeps the rim through r·π/180 metres, the form mechanical tolerances take.
+ mm_per_deg = [sens.major_radius_m[j] * pi / 180 * 1000 for j in 1:nset]
+ per_mm_rim = [mm_per_deg[j] > 0 ? per_deg[j] / mm_per_deg[j] : 0.0 for j in 1:nset]
+
+ return SensitivityTable(copy(sens.coil_names), mode, delta_as_designed, shift, tilt,
+ 1e-3 .* inplane_rms(shift), per_deg, per_mm_rim, cancelling(shift), cancelling(tilt))
+end
+
+function sensitivity_table(h5path::AbstractString; psi_low::Real=PerturbedEquilibrium.CORE_PSI_LOW, psi_high::Real=PerturbedEquilibrium.CORE_PSI_HIGH, mode::Int=1)
+ rc = ResonantCoupling(h5path)
+ dom = dominant_coupling(rc; psi_low, psi_high)
+ return sensitivity_table(CoilSensitivities(h5path), dom; mode)
+end
+
+"""
+ without_coils(table::SensitivityTable, names) -> SensitivityTable
+
+The table with the named coil sets (e.g. correction arrays) dropped, leaving the error-field
+sources the Monte Carlo, worst case and scans use. Every name must be in the table.
+"""
+function without_coils(table::SensitivityTable, names)
+ names = String[String(n) for n in names]
+ unknown = setdiff(names, table.coil_names)
+ isempty(unknown) || throw(ArgumentError("coil sets to exclude not among the run's coil sets ($(join(table.coil_names, ", "))): $(join(unknown, ", "))"))
+ keep = [i for (i, n) in enumerate(table.coil_names) if !(n in names)]
+ return SensitivityTable(table.coil_names[keep], table.mode, table.delta_as_designed[keep], table.shift_sensitivity_per_m[:, keep], table.tilt_sensitivity_per_deg[:, keep],
+ table.abs_delta_shift_per_mm[keep], table.abs_delta_tilt_per_deg[keep], table.abs_delta_rim_per_mm[keep], table.cancelling_shift_m[:, keep],
+ table.cancelling_tilt_deg[:, keep])
+end
+
+"""
+ excluded_coil_names(ef_raw::AbstractDict) -> Vector{String}
+ excluded_coil_names(h5path::AbstractString) -> Vector{String}
+
+The coil sets a run leaves out of its error field: `[ErrorFields] exclude_coils` together with
+the correction arrays in `[ErrorFields.NTV] efc_coils`, read from the parsed `[ErrorFields]`
+section of a deck or from the deck recorded in a run file (none when the file carries no deck).
+"""
+function excluded_coil_names(ef_raw::AbstractDict)
+ listed = vcat(get(ef_raw, "exclude_coils", String[]), get(get(ef_raw, "NTV", Dict{String,Any}()), "efc_coils", String[]))
+ return unique(String[String(n) for n in listed])
+end
+function excluded_coil_names(h5path::AbstractString)
+ return h5open(h5path, "r") do f
+ haskey(f, "Input/gpec_toml_raw") || return String[]
+ excluded_coil_names(get(TOML.parse(read(f["Input/gpec_toml_raw"])), "ErrorFields", Dict{String,Any}()))
+ end
+end
+
+"""
+ cancelling_offset(δ_as_designed, S_x, S_y) -> (Δx, Δy)
+
+The real in-plane displacement that cancels a coil set's nominal overlap to linear order,
+`S_x·Δx + S_y·Δy = −δ_as_designed`, as the least-squares solution of the 2×2 real system on the
+real and imaginary parts. For an axisymmetric hoop (`S_y = −i·S_x`) the solution is
+`conj(−δ_as_designed / S_x)`; dropping the conjugate mirrors the offset about the x axis. A degenerate
+pair returns the minimum-norm solution.
+"""
+function cancelling_offset(δ_as_designed::Number, S_x::Number, S_y::Number)
+ A = [real(S_x) real(S_y); imag(S_x) imag(S_y)]
+ Δ = pinv(A) * [-real(δ_as_designed), -imag(δ_as_designed)]
+ return (Δ[1], Δ[2])
+end
diff --git a/src/ErrorFields/ToleranceTOML.jl b/src/ErrorFields/ToleranceTOML.jl
new file mode 100644
index 0000000000..e9673b2e5b
--- /dev/null
+++ b/src/ErrorFields/ToleranceTOML.jl
@@ -0,0 +1,373 @@
+"""
+ ToleranceTOML
+
+The manufacturing-tolerance input of an error-field assessment: a TOML file, separate from
+`gpec.toml` and named by a deck's `[ErrorFields] tolerance_file`, holding one `[[ErrorFields.coil]]`
+block per coil set that may move on its own, `[[ErrorFields.coherent_group]]` blocks for coil
+sets that move together, and the `[ErrorFields.correctability]` and `[ErrorFields.other_field]`
+tables. Tolerances are human-authored engineering data, so the format is diffable, commentable
+text; the raw file is echoed into `Input/RawInputs/ErrorFields/tolerance_toml_raw` for replay.
+
+```toml
+[ErrorFields.defaults] # fallbacks for keys a coil block leaves out (all optional)
+tilt_units = "deg"
+radial_shape = "hollow"
+
+[[ErrorFields.coil]]
+name = "PF1U" # a coil set name of the run
+shift_tol_mm = 0.5 # radius of the in-plane displacement disk the coil may sit in
+tilt_tol = 0.019 # tilt tolerance, in tilt_units
+tolerance_model = "cylinder" # axis line inside a cylinder: shift and tilt drawn together
+cylinder_half_height_m = 1.5
+
+[[ErrorFields.coherent_group]]
+name = "upper_pf_brace"
+members = ["PF1U", "PF2U"] # move together with one shared draw per sample
+shift_tol_mm = 2.0
+tilt_tol = 0.0
+phase_group = "braces" # groups naming the same phase_group share the random direction
+
+[ErrorFields.correctability]
+uncorrectable_coils = ["EFCC_U"] # excluded from the error-field-correction division
+efc_factor = 2.0
+
+[ErrorFields.other_field]
+magnitude = 8.2e-6 # overlap budget of sources not attributed to any coil
+```
+"""
+
+const RADIAL_SHAPES = ("flat", "uniform_area", "hollow", "ring")
+const TOLERANCE_MODELS = ("additive", "cylinder")
+const TILT_UNITS = ("deg", "m")
+
+"""
+ CoilTolerance
+
+Manufacturing tolerance of one coil set that moves independently. Lengths are in metres and
+the tilt tolerance in `tilt_units`; convert it to the degrees the sensitivities are stored in
+with [`tilt_tolerance_deg`](@ref).
+
+## Fields
+
+ - `name`: coil set name; must match a coil set of the run
+ - `shift_tol_m`: radius of the in-plane displacement disk the coil centre may lie in, metres
+ - `shift_sigma_m`: Gaussian uncertainty added to the sampled shift, metres
+ - `tilt_tol`: tilt tolerance, in `tilt_units`
+ - `tilt_sigma`: Gaussian uncertainty added to the sampled tilt, in `tilt_units`
+ - `tilt_units`: `"deg"`, or `"m"` for a rim displacement converted through the coil's
+ nominal major radius
+ - `radial_shape`: radial sampling density on the disk: `"flat"` (uniform in radius),
+ `"uniform_area"`, `"hollow"` (peaked toward the edge), or `"ring"` (always at the edge)
+ - `tolerance_model`: `"additive"` (independent shift and tilt draws) or `"cylinder"` (the
+ coil axis line confined to a cylinder of radius `shift_tol_m`, shift and tilt drawn together)
+ - `cylinder_half_height_m`: half-height of that cylinder, metres; sets the tilt reachable at
+ the given radius
+ - `current_factor`: multiplier on the coil set's current as built relative to the run, applied
+ to its as-designed overlap and its sensitivities alike (the spectrum is linear in current);
+ `1` is the run's current, `0` switches the coil off, a negative value reverses it
+"""
+struct CoilTolerance
+ name::String
+ shift_tol_m::Float64
+ shift_sigma_m::Float64
+ tilt_tol::Float64
+ tilt_sigma::Float64
+ tilt_units::String
+ radial_shape::String
+ tolerance_model::String
+ cylinder_half_height_m::Float64
+ current_factor::Float64
+end
+
+"""
+ CoherentGroupTolerance
+
+Tolerance of a set of coils that move together: every member receives the same displacement
+(and the same rotation about a common pivot) from one random draw per sample. Groups that name
+the same `phase_group` share the random direction of that draw while keeping independent
+amplitudes.
+
+## Fields
+
+ - `name`: label of the group
+ - `members`: coil set names moving together
+ - `shift_tol_m`, `tilt_tol`, `tilt_units`, `radial_shape`, `tolerance_model`,
+ `cylinder_half_height_m`: as in [`CoilTolerance`](@ref), applied to the shared draw
+ - `phase_group`: groups with equal labels share the random direction; defaults to `name`
+ - `rotation_center_z_m`: height of the pivot of the group's rigid rotation on the machine axis,
+ metres; a member at height `z` tilted by θ also shifts laterally by `(z − z_pivot)·θ`
+ - `tilt_lever_arm_m`: the lever arm, metres, that converts a tilt tolerance given in metres
+ into the group's rotation angle (`asin(tilt_tol / lever_arm)`); `NaN` uses the members' common
+ major radius
+"""
+struct CoherentGroupTolerance
+ name::String
+ members::Vector{String}
+ shift_tol_m::Float64
+ tilt_tol::Float64
+ tilt_units::String
+ radial_shape::String
+ tolerance_model::String
+ cylinder_half_height_m::Float64
+ phase_group::String
+ rotation_center_z_m::Float64
+ tilt_lever_arm_m::Float64
+end
+
+"""
+ OtherFieldBudget
+
+Overlap budget for error-field sources not attributed to any coil, sampled once per Monte
+Carlo sample as an incoherent contribution with a random direction.
+
+## Fields
+
+ - `magnitude`: dimensionless overlap magnitude of the budget
+ - `sigma`: Gaussian uncertainty on that magnitude
+ - `radial_shape`: radial sampling density of the magnitude, as in [`CoilTolerance`](@ref)
+"""
+struct OtherFieldBudget
+ magnitude::Float64
+ sigma::Float64
+ radial_shape::String
+end
+
+"""
+ ToleranceSet
+
+Everything a tolerance TOML file specifies, parsed and validated by [`read_tolerance_toml`](@ref).
+
+## Fields
+
+ - `coils`: independently moving coil sets `[ncoil]`
+ - `groups`: coherently moving groups `[ngroup]`
+ - `uncorrectable_coils`: coil set names whose error field the correction system cannot reduce
+ - `efc_factor`: divisor applied to the correctable contributions when error-field correction is on
+ - `other_field`: the unattributed budget
+ - `raw`: the file's text, echoed into the output for replay
+"""
+struct ToleranceSet
+ coils::Vector{CoilTolerance}
+ groups::Vector{CoherentGroupTolerance}
+ uncorrectable_coils::Vector{String}
+ efc_factor::Float64
+ other_field::OtherFieldBudget
+ raw::String
+end
+
+# Built-in fallbacks for the per-coil keys, overridable by [ErrorFields.defaults]. The radial
+# shape and the other-field shape follow the OMFIT tool's defaults.
+const _COIL_KEY_DEFAULTS = Dict{String,Any}(
+ "shift_sigma_mm" => 0.0, "tilt_sigma" => 0.0, "tilt_units" => "deg", "radial_shape" => "hollow",
+ "tolerance_model" => "additive", "cylinder_half_height_m" => 0.0, "current_factor" => 1.0
+)
+const _GROUP_ONLY_KEYS = ("members", "phase_group", "rotation_center_z_m", "tilt_lever_arm_m")
+
+"""
+ read_tolerance_toml(path) -> ToleranceSet
+ parse_tolerance_toml(text) -> ToleranceSet
+
+Read and validate a tolerance TOML file (see the module docstring for the schema). Every key is
+checked against the schema so a misspelled key errors instead of silently taking a default;
+tolerances must be non-negative, names unique, enumerated fields one of their allowed values,
+`efc_factor ≥ 1`, a cylinder model needs a positive half-height, a `current_factor` must be
+finite and a `tilt_lever_arm_m` positive. Names are checked against the run's coil sets
+separately by [`validate_tolerances`](@ref).
+"""
+read_tolerance_toml(path::AbstractString) = parse_tolerance_toml(read(path, String))
+
+function parse_tolerance_toml(text::AbstractString)
+ root = TOML.parse(String(text))
+ haskey(root, "ErrorFields") || throw(ArgumentError("tolerance TOML has no [ErrorFields] tables (blocks are [[ErrorFields.coil]], ...)"))
+ ef = root["ErrorFields"]
+ _check_keys(ef, ("defaults", "coil", "coherent_group", "correctability", "other_field"), "ErrorFields")
+
+ defaults = merge(_COIL_KEY_DEFAULTS, get(ef, "defaults", Dict{String,Any}()))
+ _check_keys(defaults, collect(keys(_COIL_KEY_DEFAULTS)), "ErrorFields.defaults")
+
+ coils = [_parse_coil(d, defaults) for d in get(ef, "coil", Dict{String,Any}[])]
+ groups = [_parse_group(d, defaults) for d in get(ef, "coherent_group", Dict{String,Any}[])]
+ _unique_names([c.name for c in coils], "[[ErrorFields.coil]]")
+ _unique_names([g.name for g in groups], "[[ErrorFields.coherent_group]]")
+
+ corr = get(ef, "correctability", Dict{String,Any}())
+ _check_keys(corr, ("uncorrectable_coils", "efc_factor"), "ErrorFields.correctability")
+ uncorrectable = String.(get(corr, "uncorrectable_coils", String[]))
+ efc_factor = Float64(get(corr, "efc_factor", 2.0))
+ efc_factor >= 1 || throw(ArgumentError("efc_factor must be ≥ 1 (got $efc_factor)"))
+
+ other = get(ef, "other_field", Dict{String,Any}())
+ _check_keys(other, ("magnitude", "sigma", "radial_shape"), "ErrorFields.other_field")
+ other_field = OtherFieldBudget(_nonneg(get(other, "magnitude", 0.0), "other_field.magnitude"),
+ _nonneg(get(other, "sigma", 0.0), "other_field.sigma"),
+ _enum(get(other, "radial_shape", "ring"), RADIAL_SHAPES, "other_field.radial_shape"))
+
+ return ToleranceSet(coils, groups, uncorrectable, efc_factor, other_field, String(text))
+end
+
+function _parse_coil(d::Dict{String,Any}, defaults::Dict{String,Any})
+ _check_keys(d, vcat("name", "shift_tol_mm", "tilt_tol", collect(keys(_COIL_KEY_DEFAULTS))), "[[ErrorFields.coil]]")
+ haskey(d, "name") || throw(ArgumentError("a [[ErrorFields.coil]] block has no name"))
+ name = String(d["name"])
+ get_key(k) = get(d, k, defaults[k])
+ model = _enum(get_key("tolerance_model"), TOLERANCE_MODELS, "$name.tolerance_model")
+ half_height = _nonneg(get_key("cylinder_half_height_m"), "$name.cylinder_half_height_m")
+ model == "cylinder" && half_height <= 0 && throw(ArgumentError("coil $name: the cylinder model needs cylinder_half_height_m > 0"))
+ factor = Float64(get_key("current_factor"))
+ isfinite(factor) || throw(ArgumentError("coil $name: current_factor must be finite (got $factor)"))
+ return CoilTolerance(name,
+ 1e-3 * _nonneg(get(d, "shift_tol_mm", 0.0), "$name.shift_tol_mm"),
+ 1e-3 * _nonneg(get_key("shift_sigma_mm"), "$name.shift_sigma_mm"),
+ _nonneg(get(d, "tilt_tol", 0.0), "$name.tilt_tol"),
+ _nonneg(get_key("tilt_sigma"), "$name.tilt_sigma"),
+ _enum(get_key("tilt_units"), TILT_UNITS, "$name.tilt_units"),
+ _enum(get_key("radial_shape"), RADIAL_SHAPES, "$name.radial_shape"),
+ model, half_height, factor)
+end
+
+function _parse_group(d::Dict{String,Any}, defaults::Dict{String,Any})
+ _check_keys(d, vcat("name", "shift_tol_mm", "tilt_tol", "tilt_units", "radial_shape", "tolerance_model",
+ "cylinder_half_height_m", collect(_GROUP_ONLY_KEYS)), "[[ErrorFields.coherent_group]]")
+ haskey(d, "name") || throw(ArgumentError("a [[ErrorFields.coherent_group]] block has no name"))
+ name = String(d["name"])
+ members = String.(get(d, "members", String[]))
+ isempty(members) && throw(ArgumentError("coherent group $name lists no members"))
+ _unique_names(members, "coherent group $name members")
+ get_key(k) = get(d, k, defaults[k])
+ model = _enum(get_key("tolerance_model"), TOLERANCE_MODELS, "$name.tolerance_model")
+ half_height = _nonneg(get_key("cylinder_half_height_m"), "$name.cylinder_half_height_m")
+ model == "cylinder" && half_height <= 0 && throw(ArgumentError("coherent group $name: the cylinder model needs cylinder_half_height_m > 0"))
+ lever = Float64(get(d, "tilt_lever_arm_m", NaN))
+ isnan(lever) || lever > 0 || throw(ArgumentError("coherent group $name: tilt_lever_arm_m must be > 0 (got $lever)"))
+ return CoherentGroupTolerance(name, members,
+ 1e-3 * _nonneg(get(d, "shift_tol_mm", 0.0), "$name.shift_tol_mm"),
+ _nonneg(get(d, "tilt_tol", 0.0), "$name.tilt_tol"),
+ _enum(get_key("tilt_units"), TILT_UNITS, "$name.tilt_units"),
+ _enum(get_key("radial_shape"), RADIAL_SHAPES, "$name.radial_shape"),
+ model, half_height,
+ String(get(d, "phase_group", name)),
+ Float64(get(d, "rotation_center_z_m", 0.0)), lever)
+end
+
+"""
+ update(x; field=value, ...) -> x′
+
+A copy of a `ToleranceSet`, `CoilTolerance`, `CoherentGroupTolerance` or `OtherFieldBudget` with
+the named fields replaced, for programmatic scans over quantities the TOML fixes: a coil's
+`current_factor` or `shift_sigma_m`, the unattributed `magnitude`, a group's `tilt_lever_arm_m`.
+Unknown fields and an `efc_factor` below 1 are errors. The copy of a set carries an empty `raw`
+text, since the echoed file no longer describes it.
+
+```julia
+ts2 = update(ts; coils=[c.name == "F6A" ? update(c; current_factor=0.5) : c for c in ts.coils])
+ts3 = update(ts; other_field=update(ts.other_field; magnitude=2e-5))
+```
+"""
+function update(x::T; kwargs...) where {T<:Union{CoilTolerance,CoherentGroupTolerance,OtherFieldBudget}}
+ return T(_replaced_fields(x; kwargs...)...)
+end
+function update(ts::ToleranceSet; kwargs...)
+ vals = _replaced_fields(ts; kwargs...)
+ out = ToleranceSet(vals[1:5]..., haskey(kwargs, :raw) ? vals[6] : "")
+ out.efc_factor >= 1 || throw(ArgumentError("efc_factor must be ≥ 1 (got $(out.efc_factor))"))
+ return out
+end
+function _replaced_fields(x::T; kwargs...) where {T}
+ names = fieldnames(T)
+ vals = Any[getfield(x, f) for f in names]
+ for (k, v) in kwargs
+ i = findfirst(==(k), names)
+ i === nothing && throw(ArgumentError("$(nameof(T)) has no field $k (fields: $(join(names, ", ")))"))
+ vals[i] = v
+ end
+ return vals
+end
+
+function _check_keys(d::Dict{String,Any}, allowed, where::String)
+ for k in keys(d)
+ k in allowed || throw(ArgumentError("unknown key \"$k\" in $where (allowed: $(join(allowed, ", ")))"))
+ end
+end
+
+function _unique_names(names, where::String)
+ length(unique(names)) == length(names) || throw(ArgumentError("duplicate names in $where: $(join(unique(filter(n -> count(==(n), names) > 1, names)), ", "))"))
+end
+
+function _nonneg(v, what::String)
+ x = Float64(v)
+ x >= 0 || throw(ArgumentError("$what must be ≥ 0 (got $x)"))
+ return x
+end
+
+function _enum(v, allowed, what::String)
+ s = lowercase(String(v))
+ s in allowed || throw(ArgumentError("$what must be one of $(join(allowed, ", ")) (got \"$v\")"))
+ return s
+end
+
+"""
+ validate_tolerances(ts::ToleranceSet, coil_names) -> ts
+
+Check every coil, group member, and uncorrectable-coil name of `ts` against the coil set names
+of a run (for instance `CoilSensitivities.coil_names`), throwing an `ArgumentError` that lists
+the unknown names. Coil sets of the run that carry no tolerance are allowed: they contribute
+only their nominal overlap.
+"""
+function validate_tolerances(ts::ToleranceSet, coil_names::AbstractVector{<:AbstractString})
+ known = Set(String.(coil_names))
+ unknown = String[]
+ for c in ts.coils
+ c.name in known || push!(unknown, "coil $(c.name)")
+ end
+ for g in ts.groups, m in g.members
+ m in known || push!(unknown, "member $m of group $(g.name)")
+ end
+ for u in ts.uncorrectable_coils
+ u in known || push!(unknown, "uncorrectable coil $u")
+ end
+ isempty(unknown) || throw(ArgumentError("tolerance names not among the run's coil sets ($(join(sort(collect(known)), ", "))): $(join(unknown, "; "))"))
+ return ts
+end
+
+"""
+ check_excluded_tolerances(ts::ToleranceSet, excluded) -> ts
+
+Throw if a tolerance, a coherent-group member or an uncorrectable-coil entry names a coil set the
+run excludes from its error field: a correction array is not an error-field source, so a
+tolerance on it has nothing to act on.
+"""
+function check_excluded_tolerances(ts::ToleranceSet, excluded)
+ excluded = Set(String[String(n) for n in excluded])
+ named = String[]
+ for c in ts.coils
+ c.name in excluded && push!(named, "coil $(c.name)")
+ end
+ for g in ts.groups, m in g.members
+ m in excluded && push!(named, "member $m of group $(g.name)")
+ end
+ for u in ts.uncorrectable_coils
+ u in excluded && push!(named, "uncorrectable coil $u")
+ end
+ isempty(named) || throw(ArgumentError("tolerances name coil sets excluded from the error field (a correction array carries no tolerance): $(join(named, "; "))"))
+ return ts
+end
+
+"""
+ tilt_tolerance_deg(tilt, tilt_units, cs::CoilSet) -> Float64
+ tilt_tolerance_deg(tilt, tilt_units, r_nom::Real; name="the coil set") -> Float64
+ tilt_tolerance_deg(t::CoilTolerance, cs::CoilSet) -> Float64
+
+A tilt tolerance in the degrees the stored sensitivities use. `"deg"` passes through; `"m"` is
+a rim displacement converted through the coil set's arc-length-weighted major radius exactly as
+`apply_transforms` converts `tilt_in_meters`: `asin(t / R_nom)`. The radius form takes that
+radius directly, as a run stores it in `ErrorFields/CoilSensitivities/major_radius_m`, for
+readers that have the file but not the geometry.
+"""
+function tilt_tolerance_deg(tilt::Real, tilt_units::AbstractString, r_nom::Real; name::AbstractString="the coil set")
+ tilt_units == "deg" && return Float64(tilt)
+ tilt <= r_nom || throw(ArgumentError("tilt $tilt m exceeds the nominal radius $r_nom m of $name"))
+ return rad2deg(asin(tilt / r_nom))
+end
+tilt_tolerance_deg(tilt::Real, tilt_units::AbstractString, cs::CoilSet) =
+ tilt_tolerance_deg(tilt, tilt_units, ForcingTerms.nominal_major_radius(cs); name="coil set $(cs.name)")
+tilt_tolerance_deg(t::CoilTolerance, cs::CoilSet) = tilt_tolerance_deg(t.tilt_tol, t.tilt_units, cs)
diff --git a/src/ForceFreeStates/CoreTypes.jl b/src/ForceFreeStates/CoreTypes.jl
new file mode 100644
index 0000000000..1cb794f65c
--- /dev/null
+++ b/src/ForceFreeStates/CoreTypes.jl
@@ -0,0 +1,160 @@
+# Module-wide types: ModeSpace, ForceFreeStatesInternal, ForceFreeStatesControl.
+
+"""
+ ModeSpace
+
+Supertype for objects that carry the resolved (m, n) mode space — `mlow`, `mhigh`, `mpert`,
+`nlow`, `nhigh`, `npert`, `numpert_total`. Both the solve-time scratch
+[`ForceFreeStatesInternal`](@ref) and the published [`ForceFreeStatesResult`](@ref) are
+`ModeSpace`s, so kernels that need nothing but the mode indexing (`el_derivatives!`,
+`materialize_derivative_stores!`, `build_kinetic_metric_matrices`) accept either.
+"""
+abstract type ModeSpace end
+
+"""
+ ForceFreeStatesInternal
+
+Solve-time scratch state for a force-balance solve: the resolved mode space, singular surfaces and integration limits.
+
+## Fields
+
+ - `mlow::Int` - Lowest poloidal mode number
+ - `mhigh::Int` - Highest poloidal mode number
+ - `mpert::Int` - Number of poloidal modes (mhigh - mlow + 1)
+ - `nlow::Int` - Lowest toroidal mode number, resolved from `ctrl.nn_low`/`nn_high`
+ - `nhigh::Int` - Highest toroidal mode number, resolved from `ctrl.nn_low`/`nn_high`
+ - `npert::Int` - Number of toroidal modes (nhigh - nlow + 1)
+ - `numpert_total::Int` - Total number of modes (mpert × npert)
+ - `msing::Int` - Number of ideal singular surfaces
+ - `kmsing::Int` - Number of kinetic singular surfaces (det(F̄) near-zeros)
+ - `sing::Vector{SingType}` - Vector of ideal singular surface data
+ - `kinsing::Vector{SingType}` - Vector of kinetic singular surface data
+ - `kinsing_scan_psi::Vector{Float64}` - ψ grid used by `find_kinetic_singular_surfaces!` for the cond(F̄) scan (empty unless the finder has run)
+ - `kinsing_scan_cond::Vector{Float64}` - cond(F̄) values on that grid; the finder locates peaks that exceed `kinsing_scan_threshold`
+ - `kinsing_scan_threshold::Float64` - Threshold on cond(F̄) used to accept a peak as a kinetic singular surface
+ - `psilim::Float64` - Flux limit for integration
+ - `qlim::Float64` - Safety factor at psilim
+ - `q1lim::Float64` - Safety factor derivative at psilim
+ - `wall_settings::Union{Nothing,Vacuum.WallSettings}` - Wall shape settings for vacuum calculations
+ - `verbose::Bool` - Log solve progress; set from the `verbose` keyword of `solve`
+"""
+@kwdef mutable struct ForceFreeStatesInternal <: ModeSpace
+ mlow::Int = 0
+ mhigh::Int = 0
+ mpert::Int = 0
+ nlow::Int = 0
+ nhigh::Int = 0
+ npert::Int = 0
+ numpert_total::Int = 0
+ msing::Int = 0
+ kmsing::Int = 0
+ sing::Vector{SingType} = SingType[]
+ kinsing::Vector{SingType} = SingType[]
+ kinsing_scan_psi::Vector{Float64} = Float64[]
+ kinsing_scan_cond::Vector{Float64} = Float64[]
+ kinsing_scan_threshold::Float64 = 0.0
+ psilim::Float64 = 0.0
+ psilow::Float64 = 0.0 # lower integration bound; the outermost crossing of q = qlow (sing_min!), else the first grid node
+ qlim::Float64 = 0.0
+ q1lim::Float64 = 0.0
+ wall_settings::Union{Nothing,Vacuum.WallSettings} = nothing
+ verbose::Bool = false
+ """
+ Inter-surface Δ' matrix, `msing × msing`, PEST3 convention: the odd-parity projection of
+ `delta_prime_raw`, set by `compute_delta_prime_matrix!` (Riccati path only).
+ """
+ delta_prime_matrix::Matrix{ComplexF64} = Matrix{ComplexF64}(undef, 0, 0)
+
+ """
+ Edge coil-response matrix, `2msing × numpert_total`: column k is the resonant small-solution
+ response at each surface side to a unit source on edge mode k (Eq. 37 rpec edge condition,
+ `_solve_bvp_edge_coil`). Empty unless the S-axis vacuum-edge BVP was assembled.
+ """
+ delta_coil::Matrix{ComplexF64} = Matrix{ComplexF64}(undef, 0, 0)
+
+ """
+ Raw `2msing × 2msing` outer-region matching matrix D' (Pletzer–Dewar 1991, before parity
+ rotation), side-major ordering `[L_s1, R_s1, …, L_sm, R_sm]`. `pest3_decompose` recovers the
+ A', B', Γ', Δ' blocks. No ½ prefactor (matches Fortran rdcon; the paper applies ½).
+ Empty unless the Riccati integrator was used.
+ """
+ delta_prime_raw::Matrix{ComplexF64} = Matrix{ComplexF64}(undef, 0, 0)
+end
+
+"""
+ ForceFreeStatesControl
+
+Physical and workflow controls for a force-balance solve, together with its selected algorithm.
+
+## Fields
+
+ - `algorithm::AbstractIntegrator` - Selected integrator and its numerical settings.
+ - `vac_flag::Bool` - Enable vacuum region calculation
+ - `mtheta_vacuum::Int` - Number of vacuum poloidal grid points (corresponds to `mtheta` in VacuumInput)
+ - `nzeta_vacuum::Int` - Number of vacuum toroidal grid points (corresponds to `nzeta` in VacuumInput3D)
+ - `frobenius_psi_max::Float64` - Largest starting ψ_N at which the opt-in diagonal Frobenius start is used; default `0` always uses the fixed start U₁ = 0, U₂ = I. The
+ Frobenius start is currently unreliable (warns when used); leave at 0 unless testing it.
+ - `nn_low::Int` - Lower bound for toroidal modes
+ - `nn_high::Int` - Upper bound for toroidal modes
+ - `delta_mlow::Int` - Expands lower bound of Fourier harmonics by delta_mlow
+ - `delta_mhigh::Int` - Expands upper bound of Fourier harmonics by delta_mhigh
+ - `singfac_min::Float64` - Fractional distance from rational q at which the ideal jump condition is enforced. Default 1e-4 suits the Riccati Δ′ (smaller values add a
+ spurious imaginary part); Forward runs feeding PerturbedEquilibrium need about 1e-6 for the outer-surface singular coupling to converge.
+ - `truncate_at_rational_offset::Bool` - Truncate the domain at `(last_rational_q + rational_offset_fraction) / n` instead of at `qhigh` / `psihigh`, avoiding a spurious
+ δW kink when the integration ends just below a rational. Right for diverted equilibria (default `true`); set `false` for limited/analytic equilibria with finite edge
+ q (Solovev, LAR), where it cuts too much edge. Multi-n runs warn and fall back to `qhigh` / `psihigh`.
+ - `psilim_from_layer_overlap::Union{Bool,InnerLayer.SLAYERModel}` - Cap `qlim` where adjacent rational surfaces' resistive layers overlap (Fitzpatrick, Nucl. Fusion
+ 2025 Sect. 5.9); `rational_offset_fraction` / `qhigh` still pick the final surface inside the cap. `true` uses the default `SLAYERModel()` closures, a
+ `SLAYERModel(; ...)` its own (a deck's `[SLAYER]` section). Requires the equilibrium's kinetic data; the result carries the scan as `layer_overlap`. Default `false`.
+ - `rational_offset_fraction::Float64` - Distance beyond the last rational surface, in units of 1/n, in [0, 1). Used only when `truncate_at_rational_offset` is true. Default 0.2.
+ - `frobenius_order::Int` - Order of the Frobenius expansion at rational surfaces. Default 6.
+ - `qhigh::Float64` - Integration terminated at q limit determined by minimum of qhigh and qa from equil
+ - `kinetic` - Kinetic source of the force operator: `nothing` (ideal), a `KineticForces.KineticForcesControl` (the drift-kinetic matrices of the KineticForces model
+ evaluated on the equilibrium's kinetic profiles; needs `Forward()`), `TestKineticMatrices` (synthetic test matrices), or the `KineticMatrices` of an earlier
+ evaluation, reused. A deck selects the KineticForces model with `kinetic = "KineticForces"`, using its `[KineticForces]` section.
+ - `kinetic_factor::Float64` - Uniform scale on the kinetic matrices of a kinetic run. Default 1.
+ - `qlow::Float64` - Integration starts at the outermost crossing of q = qlow, excluding the q < qlow region inside it (a core, or a reversed-shear ring); no effect when
+ q ≥ qlow everywhere
+ - `dW_edge_scan_start::Float64` - If below psilim, records a dW(ψ) diagnostic scan over [dW_edge_scan_start, psilim] on `odet.edge_scan`. Does not change the domain
+ unless `truncate_at_dW_peak` is set.
+ - `truncate_at_dW_peak::Bool` - When `true` and `dW_edge_scan_start < psilim`, adopt the edge-dW scan's peak as the plasma edge, equivalent to setting `psihigh` to the
+ peak by hand. Δ' then depends on where the peak falls in the edge band. Default `false`.
+ - `write_el_matrices::Bool` - Write the ideal (and on a kinetic run, kinetic) Euler-Lagrange matrices on the ψ grid to `ForceFreeStates/EulerLagrangeMatrices`; scales
+ as numpert_total²·npsi and dominates the file size. Default `false`.
+"""
+@kwdef struct ForceFreeStatesControl{A<:AbstractIntegrator}
+ algorithm::A = Riccati()
+ vac_flag::Bool = false
+ mtheta_vacuum::Int = 480
+ nzeta_vacuum::Int = 1
+ nn_low::Int = 0
+ nn_high::Int = 0
+ delta_mlow::Int = 0
+ delta_mhigh::Int = 0
+ singfac_min::Float64 = 1e-4 # Required nonzero for the Riccati path.
+ truncate_at_rational_offset::Bool = true
+ psilim_from_layer_overlap::Union{Bool,InnerLayer.SLAYERModel} = false
+ rational_offset_fraction::Float64 = 0.2
+ frobenius_order::Int = 6
+ qhigh::Float64 = 1e3
+ kinetic::Any = nothing
+ kinetic_factor::Float64 = 1.0
+ qlow::Float64 = 0.0
+ dW_edge_scan_start::Float64 = 0.99
+ truncate_at_dW_peak::Bool = false
+ write_el_matrices::Bool = false
+
+ frobenius_psi_max::Float64 = 0.0
+end
+
+ForceFreeStatesControl(algorithm::A, fields...) where {A<:AbstractIntegrator} = ForceFreeStatesControl{A}(algorithm, fields...)
+
+# Galerkin solves from the fixed start on the full domain, so the start and edge-truncation controls must keep their defaults.
+function validate_algorithm(ctrl::ForceFreeStatesControl)
+ if ctrl.algorithm isa Galerkin
+ for (name, default) in ((:frobenius_psi_max, 0.0), (:truncate_at_dW_peak, false), (:dW_edge_scan_start, 0.99))
+ getfield(ctrl, name) == default || throw(ArgumentError("Galerkin does not support non-default `$name`."))
+ end
+ end
+ return ctrl
+end
diff --git a/src/ForceFreeStates/EulerLagrange.jl b/src/ForceFreeStates/EulerLagrange.jl
new file mode 100644
index 0000000000..d407000592
--- /dev/null
+++ b/src/ForceFreeStates/EulerLagrange.jl
@@ -0,0 +1,1193 @@
+"""
+EdgeScanState
+
+Holds the state and results for the edge dW stability scan over ψ ∈ [dW_edge_scan_start, psilim].
+Initialized and populated by `findmax_dW_edge!`; results written to HDF5 under `EdgeScan/`.
+The energies are generalized (W, N) pencil values: power-normalized and invariant to the
+working (Jacobian) coordinate (see `power_norm_matrix!`).
+
+## Fields
+
+ - `wvmat` - Precomputed wv matrix spline (raw, no singfac); singfac applied analytically in `free_compute_total`.
+ - `wv_hint::Base.RefValue{Int}` - Search hint for wvmat spline (different grid from equilibrium profiles).
+ - `psi, q` - ψ and q values at each edge scan step.
+ - `total_eigenvalue, plasma_energy, vacuum_energy, vacuum_eigenvalue` - Power-normalized energy components at each step (NaN for steps where the wp solve was singular).
+ These drive the truncation choice and are written to `EdgeScan/`.
+"""
+@kwdef mutable struct EdgeScanState
+ numpert_total::Int
+ N_edge::Int
+
+ # Vacuum matrix spline and evaluation infrastructure
+ wvmat::CubicSeriesInterpolant{Float64,ComplexF64} = _empty_series_interp_complex(numpert_total^2)
+ wv_hint::Base.RefValue{Int} = Ref(1)
+
+ # Scan results; NaN where the wp solve was singular
+ psi::Vector{Float64} = Vector{Float64}(undef, N_edge)
+ q::Vector{Float64} = Vector{Float64}(undef, N_edge)
+ total_eigenvalue::Vector{ComplexF64} = fill(complex(NaN), N_edge)
+ plasma_energy::Vector{ComplexF64} = fill(complex(NaN), N_edge)
+ vacuum_energy::Vector{ComplexF64} = fill(complex(NaN), N_edge)
+ vacuum_eigenvalue::Vector{Float64} = fill(NaN, N_edge)
+end
+
+EdgeScanState(numpert_total::Int, N_edge::Int) = EdgeScanState(; numpert_total, N_edge)
+
+"""
+OdeState
+
+Mutable state of a Forward Euler-Lagrange integration: the stored solution, Gaussian-reduction
+records needed to undo it, and singular-surface asymptotic coefficients.
+
+## Fields
+
+ - `numpert_total::Int` - Total number of (m, n) modes.
+ - `numunorms_init::Int` - Allocated number of Gaussian-reduction records.
+ - `msing::Int` - Number of singular surfaces (sizes `ca_l`/`ca_r`).
+ - `numsteps_init::Int` - Initial allocation of stored steps.
+ - `step::Int` - Index of the next stored step (1-based).
+ - `total_steps::Int` - Total ODE steps taken, saved or not.
+ - `psi_store::Vector{Float64}` - ψ at each stored step.
+ - `q_store::Vector{Float64}` - q at each stored step.
+ - `u_store::Array{ComplexF64,4}` - Solution `(u₁, u₂)` at each stored step, shape `(numpert_total, numpert_total, 2, nstep)`.
+ - `du_store::Array{ComplexF64,3}` - du₁/dψ at each stored step, shape `(numpert_total, numpert_total, step)`; empty until `materialize_derivative_stores!` fills it (the
+ galerkin-matched path supplies it at construction).
+ - `xi_s_store::Array{ComplexF64,3}` - Clebsch displacement Ξ_s (Glasser 2016 Eq. 18) at each stored step; empty until materialized, like `du_store`.
+ - `u_store_el_basis::Bool` - True when `u_store` holds the Euler-Lagrange state; false on the sparse parallel path (Riccati-basis chunk endpoints), where derivative
+ stores cannot be materialized.
+ - `du_store_populated::Bool` - True once `du_store`/`xi_s_store` hold valid data in the final basis.
+ - `crit_store::Vector{Float64}` - Critical eigenvalue (smallest eigenvalue of W⁻¹) at each stored step.
+ - `ca_r::Array{ComplexF64,4}` - Asymptotic coefficients right of each singular surface, shape `(numpert_total, numpert_total, 2, msing)`.
+ - `ca_l::Array{ComplexF64,4}` - Asymptotic coefficients left of each singular surface, same shape.
+ - `ca_populated::Bool` - True once an ideal crossing has filled `ca_l`/`ca_r`; false on kinetic and galerkin-matched runs, where the writer emits zero-extent datasets.
+ - `edge_scan::EdgeScanState` - Edge dW scan results; a disabled sentinel (`N_edge = 0`) unless `findmax_dW_edge!` ran.
+ - `psifac::Float64` - Current ψ of the integrator.
+ - `q::Float64` - q at `psifac`.
+ - `u::Array{ComplexF64,3}` - Current solution, shape `(numpert_total, numpert_total, 2)`.
+ - `ising_start::Int` - Index of the last singular surface inside the starting ψ.
+ - `needs_crossing::Bool` - Whether a rational surface must be crossed after the current region.
+ - `nzero::Int` - Number of detected zero crossings of the critical eigenvalue.
+ - `new::Bool` - Whether the next norm call records fresh reference norms `unorm0`.
+ - `unorm::Vector{Float64}` - Current solution-column norms.
+ - `unorm0::Vector{Float64}` - Reference norms since the last reduction.
+ - `ifix::Int` - Number of Gaussian reductions performed.
+ - `index::Array{Int,2}` - Pivot column order for each reduction, shape `(numpert_total, numunorms_init)`.
+ - `sing_flag::Vector{Bool}` - Whether each reduction was at a singular surface.
+ - `zeroed_idx::Vector{Vector{Int}}` - For each ideal crossing, the positions in `index` of the zeroed resonant solutions.
+ - `fixfac::Array{ComplexF64,3}` - Gaussian-reduction factors, shape `(numpert_total, numpert_total, numunorms_init)`.
+ - `fixstep::Vector{Int64}` - Last stored step before each reduction.
+ - `spline_hint::Base.RefValue{Int}` - Shared interval hint for profile splines evaluated at the same ψ.
+ - `mats_hint::Base.RefValue{Int}` - Interval hint for the matrix splines; per `OdeState`, so per-thread copies do not race.
+"""
+@kwdef mutable struct OdeState
+ # Initialization parameters
+ numpert_total::Int
+ numunorms_init::Int
+ msing::Int
+ numsteps_init::Int
+
+ # Saved data throughout integration
+ step::Int = 1
+ total_steps::Int = 0
+ psi_store::Vector{Float64} = Vector{Float64}(undef, numsteps_init)
+ q_store::Vector{Float64} = Vector{Float64}(undef, numsteps_init)
+ u_store::Array{ComplexF64,4} = Array{ComplexF64}(undef, numpert_total, numpert_total, 2, numsteps_init)
+ du_store::Array{ComplexF64,3} = Array{ComplexF64}(undef, numpert_total, numpert_total, 0)
+ xi_s_store::Array{ComplexF64,3} = Array{ComplexF64}(undef, numpert_total, numpert_total, 0)
+ u_store_el_basis::Bool = true
+ du_store_populated::Bool = false
+ crit_store::Vector{Float64} = Vector{Float64}(undef, numsteps_init)
+ ca_r::Array{ComplexF64,4} = zeros(ComplexF64, numpert_total, numpert_total, 2, msing)
+ ca_l::Array{ComplexF64,4} = zeros(ComplexF64, numpert_total, numpert_total, 2, msing)
+ ca_populated::Bool = false
+
+ edge_scan::EdgeScanState = EdgeScanState(numpert_total, 0)
+
+ # Data for integrator
+ psifac::Float64 = 0.0
+ q::Float64 = 0.0
+ u::Array{ComplexF64,3} = zeros(ComplexF64, numpert_total, numpert_total, 2)
+ ising_start::Int = 0
+ needs_crossing::Bool = false
+ nzero::Int = 0
+
+ # Used for Gaussian reduction
+ new::Bool = true
+ unorm::Vector{Float64} = zeros(Float64, numpert_total)
+ unorm0::Vector{Float64} = zeros(Float64, numpert_total)
+ ifix::Int = 0
+ index::Array{Int,2} = zeros(Int, numpert_total, numunorms_init)
+ sing_flag::Vector{Bool} = falses(numunorms_init)
+ zeroed_idx::Vector{Vector{Int}} = [Int[] for _ in 1:numunorms_init]
+ fixfac::Array{ComplexF64,3} = zeros(ComplexF64, numpert_total, numpert_total, numunorms_init)
+ fixstep::Vector{Int64} = zeros(Int64, numunorms_init)
+
+ # Spline interval hints
+ spline_hint::Base.RefValue{Int} = Ref(1)
+ mats_hint::Base.RefValue{Int} = Ref(1)
+end
+
+OdeState(numpert_total::Int, numsteps_init::Int, numunorms_init::Int, msing::Int) =
+ OdeState(; numpert_total, numsteps_init, numunorms_init, msing)
+
+"""
+ compute_delta_prime_from_ca!(odet, intr, equil)
+
+**Stub, not physically valid.** Per-surface Δ' estimate `(ca_r[i,i,2,s] - ca_l[i,i,2,s]) / (4π²·psio)`
+from the asymptotic coefficients. It ignores inter-surface coupling and the vacuum, so it does not
+agree with the physical `ForceFreeStatesInternal.delta_prime_matrix`. Used only by tests.
+"""
+function compute_delta_prime_from_ca!(odet::OdeState, intr::ForceFreeStatesInternal, equil::Equilibrium.PlasmaEquilibrium)
+ denom = (2π)^2 * equil.psio # = twopi * chi1 in SingularCoupling.jl
+ for s in 1:intr.msing
+ sing = intr.sing[s]
+ n_modes = length(sing.m)
+ resize!(intr.sing[s].delta_prime, n_modes)
+ for i in 1:n_modes
+ ipert_res = 1 + sing.m[i] - intr.mlow + (sing.n[i] - intr.nlow) * intr.mpert
+ if 1 <= ipert_res <= intr.numpert_total
+ Δca = odet.ca_r[ipert_res, ipert_res, 2, s] - odet.ca_l[ipert_res, ipert_res, 2, s]
+ intr.sing[s].delta_prime[i] = Δca / denom
+ else
+ intr.sing[s].delta_prime[i] = 0.0 + 0.0im
+ end
+ end
+ end
+end
+
+# Empirical (a, b) of STRIDE's log-divergent ODE cost model at the axis, rational surfaces and edge.
+# Changing them changes the chunk split, and hence every Riccati output.
+const ODE_COST_AXIS = (a=39695.0, b=212830.0)
+const ODE_COST_RAT = (a=17147.0, b=470710.0)
+const ODE_COST_EDGE = (a=1646.0, b=4683.0)
+
+"""
+ ode_itime_cost(psi1, psi2, intr) -> Float64
+
+Relative ODE integration cost of [ψ₁, ψ₂] from STRIDE's empirical log-divergent model (Glasser 2018),
+with coefficients `ODE_COST_AXIS`, `ODE_COST_RAT`, `ODE_COST_EDGE`. Additive over sub-intervals,
+so `balance_integration_chunks` can bisect for equal cost.
+"""
+function ode_itime_cost(psi1::Float64, psi2::Float64, intr::ForceFreeStatesInternal)
+ _logdiv(a, b, x1, x2) = (a / b) * abs(log(1.0 + b * abs(x2)) - log(1.0 + b * abs(x1)))
+
+ cost = _logdiv(ODE_COST_AXIS.a, ODE_COST_AXIS.b, psi1, psi2)
+ for sing in intr.sing
+ cost += _logdiv(ODE_COST_RAT.a, ODE_COST_RAT.b, psi1 - sing.psifac, psi2 - sing.psifac)
+ end
+ cost += _logdiv(ODE_COST_EDGE.a, ODE_COST_EDGE.b, psi1 - intr.psilim, psi2 - intr.psilim)
+ return cost
+end
+
+"""
+ balance_integration_chunks(chunks, ctrl, intr) -> Vector{IntegrationChunk}
+
+Split the highest-`ode_itime_cost` chunk at its equal-cost midpoint until the count reaches
+`ctrl.algorithm.nchunks` (`0` = auto). The target never depends on the thread count, so Riccati
+output is thread-count independent. Only the last sub-chunk of a split keeps its crossing.
+"""
+function balance_integration_chunks(chunks::Vector{IntegrationChunk}, ctrl::ForceFreeStatesControl, intr::ForceFreeStatesInternal)
+ min_chunks = 2 * intr.msing + 3
+ # Enough sub-chunks per segment that no single long-span propagator is too ill-conditioned for the BVP
+ min_bvp_intervals = 8 * (intr.msing + 1) + intr.msing
+ if ctrl.algorithm.nchunks > 0
+ if ctrl.algorithm.nchunks < min_chunks
+ @warn "nchunks = $(ctrl.algorithm.nchunks) is below the $min_chunks chunks required by $(intr.msing) singular surfaces; clamping up."
+ end
+ target_n = max(ctrl.algorithm.nchunks, min_chunks)
+ else
+ target_n = max(min_chunks, min_bvp_intervals)
+ end
+
+ result = collect(chunks)
+
+ while length(result) < target_n
+ # Find the highest-cost splittable chunk
+ best_idx = 0
+ best_cost = -Inf
+ for (i, chunk) in enumerate(result)
+ width = chunk.psi_end - chunk.psi_start
+ if width > 1e-8
+ c = ode_itime_cost(chunk.psi_start, chunk.psi_end, intr)
+ if c > best_cost
+ best_cost = c
+ best_idx = i
+ end
+ end
+ end
+
+ best_idx == 0 && break # No more splittable chunks
+
+ chunk = result[best_idx]
+ total_cost = best_cost
+ target_cost = total_cost / 2.0
+
+ # Bisect for ψ_mid with cost(psi_start, ψ_mid) ≈ target_cost
+ lo, hi = chunk.psi_start, chunk.psi_end
+ for _ in 1:50
+ mid = (lo + hi) / 2.0
+ if ode_itime_cost(chunk.psi_start, mid, intr) < target_cost
+ lo = mid
+ else
+ hi = mid
+ end
+ end
+ psi_mid = (lo + hi) / 2.0
+
+ left = IntegrationChunk(; psi_start=chunk.psi_start, psi_end=psi_mid,
+ needs_crossing=false, ising=0, direction=1)
+ right = IntegrationChunk(; psi_start=psi_mid, psi_end=chunk.psi_end,
+ needs_crossing=chunk.needs_crossing, ising=chunk.ising,
+ direction=chunk.direction)
+ splice!(result, best_idx, [left, right])
+ end
+
+ return result
+end
+
+"""
+ eulerlagrange_integration(ctrl, equil, mats, intr) -> (odet, propagators, chunks, S_left)
+
+Integrate the Euler-Lagrange equations from the axis to `intr.psilim`, crossing each singular
+surface on the way. Dispatches on `ctrl.algorithm` to
+[`riccati_eulerlagrange_integration`](@ref) (the chunked propagator BVP) or
+[`forward_eulerlagrange_integration`](@ref).
+
+Only the Riccati branch populates `propagators` / `chunks` / `S_left`, which
+`compute_delta_prime_matrix!` consumes for the Δ' BVP; the forward branch returns `nothing`
+for all three.
+"""
+function eulerlagrange_integration(ctrl::ForceFreeStatesControl, equil::Equilibrium.PlasmaEquilibrium, mats::MatrixSplines, intr::ForceFreeStatesInternal)
+
+ if ctrl.algorithm isa Riccati
+ ctrl.kinetic !== nothing && error("Riccati() does not support kinetic runs; use Forward().")
+ return riccati_eulerlagrange_integration(ctrl, equil, mats, intr)
+ elseif ctrl.algorithm isa Forward
+ return forward_eulerlagrange_integration(ctrl, equil, mats, intr)
+ elseif ctrl.algorithm isa Galerkin
+ error("Galerkin() solves the Euler-Lagrange system variationally, not by ODE integration; " *
+ "it is dispatched to galerkin_solve.")
+ end
+ error("Unknown integrator: $(typeof(ctrl.algorithm)). Expected Forward, Riccati or Galerkin.")
+end
+
+"""
+ forward_eulerlagrange_integration(ctrl, equil, mats, intr; verbose=intr.verbose) -> (odet, nothing, nothing, nothing)
+
+Forward branch of [`eulerlagrange_integration`](@ref): integrates chunk by chunk from the axis,
+applying Gaussian reduction whenever a solution norm ratio exceeds `ctrl.algorithm.renorm_threshold` and undoing it
+via `transform_u!` at the end, so `odet.u_store` comes back dense in the axis basis. Call
+directly to force this branch regardless of `ctrl.algorithm`; `verbose` overrides
+`intr.verbose` for progress logging.
+"""
+function forward_eulerlagrange_integration(ctrl::ForceFreeStatesControl, equil::Equilibrium.PlasmaEquilibrium, mats::MatrixSplines, intr::ForceFreeStatesInternal;
+ verbose::Bool=intr.verbose)
+
+ odet = OdeState(intr.numpert_total, ctrl.algorithm.numsteps_init, ctrl.algorithm.numunorms_init, intr.msing)
+ initialize_el_at_axis!(odet, ctrl, mats, equil.profiles, intr)
+
+ chunks = chunk_el_integration_bounds(odet, ctrl, intr)
+
+ if verbose
+ @info " ψ = $((@sprintf "%.3f" odet.psifac)), q = $((@sprintf "%.3f" equil.profiles.q_spline(odet.psifac)))"
+ end
+
+ for chunk in chunks
+ integrate_el_region!(odet, ctrl, equil, mats, intr, chunk)
+ if verbose
+ @info " ψ = $((@sprintf "%.3f" odet.psifac)), q = $((@sprintf "%.3f" odet.q)), steps = $(odet.total_steps)"
+ end
+
+ # Cross a singular surface after integration if this chunk requires it
+ if chunk.needs_crossing
+ if ctrl.kinetic !== nothing
+ cross_kinetic_singular_surf!(odet, ctrl, equil, mats, intr, chunk.ising)
+ else
+ cross_ideal_singular_surf!(odet, ctrl, equil, mats, intr, chunk.ising)
+ end
+ end
+ end
+
+ # `odet.step` points one past the last stored step; trim unused storage
+ odet.step -= 1
+ trim_storage!(odet)
+
+ scan_edge_dW!(odet, ctrl, equil, mats, intr; verbose)
+
+ if verbose
+ @info "Evaluating fixed-boundary stability criterion"
+ end
+ odet.nzero = evaluate_stability_criterion!(odet, equil.profiles)
+
+ # Undo Gaussian reduction to get true solution vectors
+ transform_u!(odet, intr)
+
+ return (odet, nothing, nothing, nothing)
+end
+
+"""
+ compute_axis_init(mats, profiles, intr, psi_low) -> (U1_init, U2_init)
+
+Opt-in diagonal approximation to the axis Frobenius problem [Glasser Phys. Plasmas 2016 112506 Eq. 51],
+evaluated at finite `psi_low` rather than in the limit ψ → 0. Used only when `frobenius_psi_max` is
+positive and the integration starts at or below it.
+
+For each mode, forms the 2×2 diagonal block of ψ_low · M from the diagonal entries of F̄⁻¹, K̄, and Ḡ,
+discards mode coupling, and returns that block's eigenvector normalized so that U₂ = I (or U₁ = 1, U₂ = 0
+when the momentum component underflows). The component ratio does not scale as a positive power of
+`psi_low`. A negative Ḡ diagonal, including the m = 0 block, gives an imaginary conjugate pair, so the
+returned U₁ is non-real and which branch is stored follows the eigen-solver's column order.
+"""
+function compute_axis_init(mats::MatrixSplines, profiles::Equilibrium.ProfileSplines,
+ intr::ForceFreeStatesInternal, psi_low::Float64)
+ N = intr.numpert_total
+ hint = Ref(1)
+
+ F_lower = zeros(ComplexF64, N, N)
+ kmat = zeros(ComplexF64, N, N)
+ gmat = zeros(ComplexF64, N, N)
+ mats.ideal.F_spline_lower(vec(F_lower), psi_low; hint=hint)
+ mats.ideal.K_spline(vec(kmat), psi_low; hint=hint)
+ mats.ideal.G_spline(vec(gmat), psi_low; hint=hint)
+
+ # singfac[j] = 1 / (m_j − n_j · q) for each mode j
+ q0 = profiles.q_spline(psi_low; hint=hint)
+ singfac = vec(1.0 ./ ((intr.mlow:intr.mhigh) .- q0 .* (intr.nlow:intr.nhigh)'))
+
+ # F̄⁻¹ = (F_lower · F_lower')⁻¹ via the Cholesky factor
+ Finv = Matrix{ComplexF64}(I, N, N)
+ ldiv!(LowerTriangular(F_lower), Finv)
+ ldiv!(UpperTriangular(F_lower'), Finv)
+
+ U1_init = zeros(ComplexF64, N, N)
+ U2_init = Matrix{ComplexF64}(I, N, N)
+
+ for j in 1:N
+ sf = singfac[j]
+ fi = Finv[j, j]
+ k = kmat[j, j]
+ kd = conj(k) # K̄†[j,j]
+ g = gmat[j, j]
+
+ # 2×2 ODE matrix block for mode j [Glasser 2016 Eq. 22-24, diagonal approximation]
+ m11 = -sf * fi * k
+ m12 = sf^2 * fi
+ m21 = g - kd * fi * k
+ m22 = sf * kd * fi
+
+ # Frobenius matrix A₀_j = ψ_low · M_j [Glasser 2016 Eq. 51]
+ #! format: off
+ F_eig = eigen([psi_low*m11 psi_low*m12;
+ psi_low*m21 psi_low*m22])
+ #! format: on
+ eig_vals = F_eig.values
+ eig_vecs = F_eig.vectors
+
+ # Regular eigenvector: larger Re(a); if degenerate (m = 0), the one dominated by U₁
+ r1 = real(eig_vals[1])
+ r2 = real(eig_vals[2])
+ i_reg = if abs(r1 - r2) > Base.sqrt(Base.eps(Float64))
+ r1 > r2 ? 1 : 2
+ else
+ abs(eig_vecs[1, 1]) >= abs(eig_vecs[2, 1]) ? 1 : 2
+ end
+
+ v1, v2 = eig_vecs[1, i_reg], eig_vecs[2, i_reg]
+
+ # Normalize to U₂ = 1, or U₁ = 1, U₂ = 0 if v₂ ≈ 0
+ if abs(v2) > Base.sqrt(Base.eps(Float64)) * abs(v1)
+ U1_init[j, j] = v1 / v2
+ else
+ U1_init[j, j] = one(ComplexF64)
+ U2_init[j, j] = zero(ComplexF64)
+ end
+ end
+
+ return U1_init, U2_init
+end
+
+"""
+ initialize_el_at_axis!(odet::OdeState, ctrl::ForceFreeStatesControl, mats::MatrixSplines, profiles::Equilibrium.ProfileSplines, intr::ForceFreeStatesInternal)
+
+Initialize the OdeState at the axis start: `psifac`, `ising_start` and `u`.
+The default `ctrl.frobenius_psi_max = 0` uses the fixed start, U₁ = 0, U₂ = I, with no warning. The
+Frobenius start is used only when `frobenius_psi_max` is positive and the starting surface lies at or
+below it.
+"""
+function initialize_el_at_axis!(odet::OdeState, ctrl::ForceFreeStatesControl, mats::MatrixSplines,
+ profiles::Equilibrium.ProfileSplines, intr::ForceFreeStatesInternal)
+
+ # Start at the qlow bound set by sing_min!, or the first grid node
+ odet.psifac = max(intr.psilow, profiles.xs[1])
+
+ # Last singular (kinsing on kinetic runs) surface inside the start
+ if ctrl.kinetic !== nothing
+ odet.ising_start = searchsortedfirst(getfield.(intr.kinsing, :psifac), odet.psifac) - 1
+ else
+ odet.ising_start = searchsortedfirst(getfield.(intr.sing, :psifac), odet.psifac) - 1
+ end
+
+ fixed_start = odet.psifac > ctrl.frobenius_psi_max
+ if fixed_start
+ # U₁ = 0, U₂ = I: ξ^ψ = 0 at the starting surface [Glasser 2016 §VI]
+ for ipert in 1:intr.numpert_total
+ odet.u[ipert, ipert, 2] = 1
+ end
+ else
+ @warn "Frobenius axis start at ψ_N = $(round(odet.psifac; sigdigits=4)). " *
+ "This start is currently unreliable - use only if explicitly requested." *
+ "Set frobenius_psi_max = 0 for the fixed start (U₁ = 0, U₂ = I)."
+ U1_init, U2_init = compute_axis_init(mats, profiles, intr, odet.psifac)
+ odet.u[:, :, 1] .= U1_init
+ odet.u[:, :, 2] .= U2_init
+ end
+end
+
+"""
+ chunk_el_integration_bounds(odet::OdeState, ctrl::ForceFreeStatesControl, intr::ForceFreeStatesInternal)
+
+Split the domain from `odet.psifac` to the edge into `IntegrationChunk`s, each ending
+`singfac_min` short of the next singular surface to cross (kinetic runs: kinetic singular surfaces).
+"""
+function chunk_el_integration_bounds(odet::OdeState, ctrl::ForceFreeStatesControl, intr::ForceFreeStatesInternal; bidirectional::Bool=false)
+ chunks = IntegrationChunk[]
+
+ psi_current = odet.psifac
+ ising_current = odet.ising_start
+
+ # Next singular surface that is resonant in [mlow, mhigh] or beyond psilim
+ function find_next_resonant_surface!(ising::Int, intr::ForceFreeStatesInternal)
+ ising += 1
+ while ising <= intr.msing
+ if intr.psilim < intr.sing[ising].psifac ||
+ any(m -> intr.mlow <= m <= intr.mhigh, intr.sing[ising].m)
+ break
+ end
+ ising += 1
+ end
+ return ising
+ end
+
+ # Next kinetic singular surface that is resonant in [mlow, mhigh] or beyond psilim
+ function find_next_kinsing!(ising::Int, intr::ForceFreeStatesInternal)
+ ising += 1
+ while ising <= intr.kmsing
+ if intr.psilim < intr.kinsing[ising].psifac
+ break
+ end
+ nq = intr.kinsing[ising].q * minimum(intr.kinsing[ising].n)
+ if intr.mlow <= nq && nq <= intr.mhigh
+ break
+ end
+ ising += 1
+ end
+ return ising
+ end
+
+ if ctrl.kinetic !== nothing && intr.kmsing > 0 && ctrl.singfac_min > 0
+ # Kinetic: chunk around each kinetic singular surface, where F̄⁻¹ blows up
+ ising_current = find_next_kinsing!(ising_current, intr)
+ while ising_current <= intr.kmsing && intr.psilim >= intr.kinsing[ising_current].psifac && ctrl.singfac_min != 0
+ # Stop singfac_min/|n q'| short of the surface
+ psi_end = intr.kinsing[ising_current].psifac -
+ ctrl.singfac_min / abs(minimum(intr.kinsing[ising_current].n) * intr.kinsing[ising_current].q1)
+
+ if psi_current >= psi_end
+ # The crossing standoff reaches back past the current chunk start: skip this surface, loudly.
+ ks = intr.kinsing[ising_current]
+ @warn "Skipping kinetic singular surface m/n=$(join(string.(ks.m, "/", ks.n), ", ")) at ψ=$(ks.psifac) (q'=$(ks.q1)): " *
+ "its crossing standoff singfac_min/|n q'| = $(ks.psifac - psi_end) reaches back past the current chunk start ψ=$psi_current."
+ ising_current = find_next_kinsing!(ising_current, intr)
+ continue
+ end
+
+ push!(chunks, IntegrationChunk(;
+ psi_start=psi_current,
+ psi_end=psi_end,
+ needs_crossing=true,
+ ising=ising_current
+ ))
+
+ # After crossing, jump to the other side of the singular surface
+ dpsi = intr.kinsing[ising_current].psifac - psi_end
+ psi_current = psi_end + 2 * dpsi
+
+ ising_current = find_next_kinsing!(ising_current, intr)
+ end
+
+ # Final chunk to the edge
+ push!(chunks, IntegrationChunk(;
+ psi_start=psi_current,
+ psi_end=(intr.psilim * (1 - eps)),
+ needs_crossing=false,
+ ising=0
+ ))
+ elseif ctrl.kinetic !== nothing
+ # Kinetic with no kinsing surfaces (or singfac_min = 0): a single chunk
+ push!(chunks, IntegrationChunk(;
+ psi_start=psi_current,
+ psi_end=(intr.psilim * (1 - eps)),
+ needs_crossing=false,
+ ising=0
+ ))
+ else
+ ising_current = find_next_resonant_surface!(ising_current, intr)
+ while ising_current <= intr.msing && intr.psilim >= intr.sing[ising_current].psifac && ctrl.singfac_min != 0
+ psi_end = intr.sing[ising_current].psifac - ctrl.singfac_min /
+ abs(minimum(intr.sing[ising_current].n) * intr.sing[ising_current].q1)
+
+ # The crossing standoff singfac_min/|n q'| must not reach back past the current chunk start.
+ if psi_end <= psi_current
+ sg = intr.sing[ising_current]
+ error(
+ "Singular surface q=$(sg.q) at ψ=$(sg.psifac) (q'=$(sg.q1)): its crossing standoff " *
+ "singfac_min/|n q'| = $(sg.psifac - psi_end) reaches back past the current chunk start ψ=$psi_current. " *
+ "Move the domain start (psilow, or a qlow that lands on this surface) off it, or lower singfac_min if a neighboring crossing is too close."
+ )
+ end
+ @assert isempty(chunks) || psi_current >= chunks[end].psi_end "Overlapping chunks detected"
+
+ push!(chunks, IntegrationChunk(;
+ psi_start=psi_current,
+ psi_end=psi_end,
+ needs_crossing=true,
+ ising=ising_current,
+ direction=bidirectional ? -1 : 1
+ ))
+
+ # After crossing, jump to the other side of the singular surface
+ dpsi = intr.sing[ising_current].psifac - psi_end
+ psi_current = psi_end + 2 * dpsi
+
+ ising_current = find_next_resonant_surface!(ising_current, intr)
+ end
+
+ @assert psi_current < intr.psilim * (1 - eps) "Final chunk has invalid bounds"
+ @assert isempty(chunks) || psi_current >= chunks[end].psi_end "Final chunk overlaps with previous chunk"
+
+ push!(chunks, IntegrationChunk(;
+ psi_start=psi_current,
+ psi_end=(intr.psilim * (1 - eps)),
+ needs_crossing=false,
+ ising=0
+ ))
+ end
+
+ return chunks
+end
+
+"""
+ cross_ideal_singular_surf!(odet::OdeState, ctrl::ForceFreeStatesControl, equil::Equilibrium.PlasmaEquilibrium, mats::MatrixSplines, intr::ForceFreeStatesInternal)
+
+Cross ideal singular surface `ising`: reduce on the resonant rows, record the left asymptotic
+coefficients, replace the resonant solutions by the small asymptotic solutions on the far side,
+and record the right coefficients. Port of Fortran `ode_ideal_cross`.
+"""
+function cross_ideal_singular_surf!(
+ odet::OdeState,
+ ctrl::ForceFreeStatesControl,
+ equil::Equilibrium.PlasmaEquilibrium,
+ mats::MatrixSplines,
+ intr::ForceFreeStatesInternal,
+ ising::Int
+)
+
+ singp = intr.sing[ising]
+ ipert_res = 1 .+ singp.m .- intr.mlow .+ (singp.n .- intr.nlow) .* intr.mpert
+ nres = length(ipert_res)
+
+ # Reduce on the resonant rows so the solutions removed below are the resonant ones
+ compute_solution_norms!(odet.u, odet, ctrl, intr, true; resonant_rows=ipert_res)
+
+ sing_asymp_right = compute_sing_asymptotics(singp, ctrl, equil, mats, intr; sig=1.0)
+ sing_asymp_left = compute_sing_asymptotics(singp, ctrl, equil, mats, intr; sig=-1.0)
+ dpsi = singp.psifac - odet.psifac # ψ_res - ψ (positive)
+
+ ua = sing_get_ua(sing_asymp_left, dpsi)
+ odet.ca_l[:, :, :, ising] .= sing_get_ca(odet.u, ua, intr)
+
+ # The reduction put the column pivoted on ipert_res[i] at index position i; zeroed_idx records it for transform_u!
+ odet.zeroed_idx[odet.ifix] = collect(1:nres)
+ for i in 1:nres
+ odet.u[:, odet.index[i, odet.ifix], :] .= 0
+ end
+
+ # Trapezoidal step across the surface
+ params = (ctrl, equil, mats, intr, odet, IntegrationChunk(0.0, 0.0, false, ising, 1))
+ du1 = zeros(ComplexF64, intr.numpert_total, intr.numpert_total, 2)
+ du2 = zeros(ComplexF64, intr.numpert_total, intr.numpert_total, 2)
+ sing_der!(du1, odet.u, params, odet.psifac)
+ odet.psifac += 2 * dpsi
+ sing_der!(du2, odet.u, params, odet.psifac)
+ odet.u .+= (du1 .+ du2) .* dpsi
+
+ # Swap in the small resonant asymptotic solution on the right side
+ ua = sing_get_ua(sing_asymp_right, dpsi)
+ for i in 1:nres
+ odet.u[ipert_res[i], :, :] .= 0
+ odet.u[:, odet.index[i, odet.ifix], :] .= ua[:, ipert_res[i]+intr.numpert_total, :]
+ end
+ odet.ca_r[:, :, :, ising] .= sing_get_ca(odet.u, ua, intr)
+ odet.ca_populated = true
+
+ # No Δ' here: it needs the Riccati gauge (U₂ = I); see compute_delta_prime_matrix!
+ odet.q = equil.profiles.q_spline(odet.psifac; hint=odet.spline_hint)
+ store_ode_data!(odet, odet.psifac, odet.u)
+end
+
+"""
+ cross_kinetic_singular_surf!(odet, ctrl, equil, mats, intr, ising)
+
+Cross kinetic singular surface `ising` with a trapezoidal step between the two sides, with no
+asymptotics. Port of Fortran `ode_kin_cross` with `con_flag=true`.
+"""
+function cross_kinetic_singular_surf!(
+ odet::OdeState,
+ ctrl::ForceFreeStatesControl,
+ equil::Equilibrium.PlasmaEquilibrium,
+ mats::MatrixSplines,
+ intr::ForceFreeStatesInternal,
+ ising::Int
+)
+ compute_solution_norms!(odet.u, odet, ctrl, intr, true)
+
+ # Trapezoidal step across the surface
+ ksurf = intr.kinsing[ising]
+ dpsi = ksurf.psifac - odet.psifac
+
+ params = (ctrl, equil, mats, intr, odet, IntegrationChunk(0.0, 0.0, false, ising, 1))
+ du1 = zeros(ComplexF64, intr.numpert_total, intr.numpert_total, 2)
+ du2 = zeros(ComplexF64, intr.numpert_total, intr.numpert_total, 2)
+
+ sing_der!(du1, odet.u, params, odet.psifac)
+ odet.psifac = ksurf.psifac + dpsi
+ sing_der!(du2, odet.u, params, odet.psifac)
+ odet.u .+= (du1 .+ du2) .* dpsi
+
+ odet.q = equil.profiles.q_spline(odet.psifac; hint=odet.spline_hint)
+ store_ode_data!(odet, odet.psifac, odet.u)
+end
+
+"""
+ column_abstol!(abstol, u, rtol) -> abstol
+
+Per-column absolute tolerance `max|u[:, j, k]|·rtol` for each column `j` of U₁ (`k = 1`) and U₂ (`k = 2`),
+so each solution column's error is controlled relative to its own magnitude. An all-zero block (e.g. U₁ = 0
+at a fixed start) takes the scale of its column's other block; the blocks differ in units, so this is a first-step safeguard.
+"""
+function column_abstol!(abstol::AbstractArray{Float64,3}, u::AbstractArray{<:Number,3}, rtol::Real)
+ for j in axes(u, 2)
+ a1 = maximum(abs, @view u[:, j, 1])
+ a2 = maximum(abs, @view u[:, j, 2])
+ afill = max(a1, a2, floatmin(Float64)) # keeps an all-zero column's abstol nonzero
+ abstol[:, j, 1] .= (a1 > 0 ? a1 : afill) * rtol
+ abstol[:, j, 2] .= (a2 > 0 ? a2 : afill) * rtol
+ end
+ return abstol
+end
+
+column_abstol(u::AbstractArray{<:Number,3}, rtol::Real) = column_abstol!(similar(u, Float64), u, rtol)
+
+function refresh_column_abstol!(integrator)
+ column_abstol!(integrator.opts.abstol, integrator.u, integrator.opts.reltol)
+ u_modified!(integrator, false)
+end
+
+# Refresh-only callback for solves with no reduction, renormalization or storage of their own.
+const COLUMN_ABSTOL_CALLBACK = DiscreteCallback((u, t, integrator) -> true, refresh_column_abstol!; save_positions=(false, false))
+
+"""
+ solve_el(prob, rtol; callback=COLUMN_ABSTOL_CALLBACK)
+
+Vern9 solve of an Euler-Lagrange problem returning the end state, with the per-column abstol of `column_abstol!`.
+A custom `callback` must refresh that abstol itself, after any reduction or renormalization of the state.
+Errors when the solver stops short of the interval's end (e.g. the step size underflows), naming the ψ reached.
+"""
+function solve_el(prob, rtol; callback=COLUMN_ABSTOL_CALLBACK)
+ sol = solve(prob, Vern9(); reltol=rtol, abstol=column_abstol(prob.u0, rtol), callback, save_everystep=false, save_end=true)
+ SciMLBase.successful_retcode(sol) ||
+ error(
+ "Euler-Lagrange integration aborted at ψ = $(@sprintf("%.6f", sol.t[end])) before ψ = $(@sprintf("%.6f", prob.tspan[2])) " *
+ "(retcode $(sol.retcode)). Loosen eulerlagrange_tolerance or refine the ψ grid; for kinetic runs, lower kinetic_factor."
+ )
+ return sol
+end
+
+"""
+ integrate_el_region!(odet, ctrl, equil, mats, intr, chunk)
+
+Integrate the Euler-Lagrange equations over `chunk`, applying Gaussian reduction and storing steps
+in `odet` from a per-step callback. Steps are stored densely near both chunk ends (in q), in the
+edge-scan band, and every `save_interval` steps otherwise.
+"""
+function integrate_el_region!(
+ odet::OdeState,
+ ctrl::ForceFreeStatesControl,
+ equil::Equilibrium.PlasmaEquilibrium,
+ mats::MatrixSplines,
+ intr::ForceFreeStatesInternal,
+ chunk::IntegrationChunk
+)
+
+ # Fraction of the chunk's q-range stored densely at each end
+ near_q_frac = 0.05
+
+ q_start = equil.profiles.q_spline(chunk.psi_start)
+ q_end = equil.profiles.q_spline(chunk.psi_end)
+ q_range = abs(q_end - q_start)
+
+ steps_in_segment = Ref(0)
+
+ function segment_callback!(integrator)
+ ctrl, _, _, intr, odet, chunk = integrator.p
+
+ odet.total_steps += 1
+ steps_in_segment[] += 1
+
+ compute_solution_norms!(integrator.u, odet, ctrl, intr, false)
+ column_abstol!(integrator.opts.abstol, integrator.u, integrator.opts.reltol)
+
+ # The first step is always saved, even when q_range ≈ 0
+ near_start = abs(odet.q - q_start) < near_q_frac * q_range || steps_in_segment[] == 1
+ near_end = abs(odet.q - q_end) < near_q_frac * q_range
+ # Always save in the edge scan region so findmax_dW_edge! has dense q coverage.
+ in_edge_scan = ctrl.dW_edge_scan_start < intr.psilim && integrator.t >= ctrl.dW_edge_scan_start
+
+ if near_start || near_end || (odet.total_steps % ctrl.algorithm.save_interval == 0) || in_edge_scan
+ # q at the accepted point, not the last internal Runge-Kutta stage
+ odet.q = equil.profiles.q_spline(integrator.t; hint=odet.spline_hint)
+ store_ode_data!(odet, integrator.t, integrator.u)
+ end
+ end
+
+ cb = DiscreteCallback((u, t, integrator) -> true, segment_callback!)
+ prob = ODEProblem(sing_der!, odet.u, (chunk.psi_start, chunk.psi_end), (ctrl, equil, mats, intr, odet, chunk))
+ rtol = ctrl.algorithm.eulerlagrange_tolerance
+ sol = solve_el(prob, rtol; callback=cb)
+
+ # Always store the final (pre-crossing or edge) state
+ if odet.step == 1 || odet.psi_store[odet.step-1] != sol.t[end]
+ odet.q = equil.profiles.q_spline(sol.t[end]; hint=odet.spline_hint)
+ store_ode_data!(odet, sol.t[end], sol.u[end])
+ end
+
+ odet.u .= sol.u[end]
+ odet.psifac = sol.t[end]
+end
+
+"""
+ compute_solution_norms!(u::Array{ComplexF64,3}, odet::OdeState, ctrl::ForceFreeStatesControl, intr::ForceFreeStatesInternal, sing_flag::Bool; resonant_rows=Int[])
+
+Compute the column norms of u₁ and apply `apply_gaussian_reduction!` to `u` in place when their
+growth since the last reduction exceeds `ctrl.algorithm.renorm_threshold`, and always when `sing_flag` is set.
+The first call after a reduction records reference norms; if `sing_flag` forces a reduction there, it keeps
+the previous reduction's pivot order. Errors if any norm is zero. Port of Fortran `ode_unorm`.
+
+### Arguments
+
+ - `u` - Solution array, updated in place (the integrator state, to avoid copies)
+ - `sing_flag` - Whether this call is at a singular surface
+ - `resonant_rows` - Resonant rows at an ideal crossing, pivoted on first
+"""
+function compute_solution_norms!(u::Array{ComplexF64,3}, odet::OdeState, ctrl::ForceFreeStatesControl, intr::ForceFreeStatesInternal, sing_flag::Bool;
+ resonant_rows=Int[])
+
+ odet.unorm .= norm.(eachcol(u[:, :, 1]))
+ if minimum(odet.unorm) == 0
+ jmax = argmin(odet.unorm)
+ error("One of the first solution vector norms unorm(1,$jmax) = 0")
+ end
+
+ # A singular surface always reduces; otherwise reduce when the growth since the last reduction is too uneven
+ fix_required = sing_flag
+ if odet.new
+ odet.new = false
+ odet.unorm0 .= odet.unorm
+ # A forced reduction right after another keeps that reduction's pivot order (none to keep before the first)
+ if sing_flag && odet.ifix > 0
+ @views odet.unorm[odet.index[:, odet.ifix]] .= (intr.numpert_total-1):-1:0
+ end
+ else
+ odet.unorm ./= odet.unorm0
+ fix_required |= maximum(odet.unorm) / minimum(odet.unorm) > ctrl.algorithm.renorm_threshold
+ end
+
+ if fix_required
+ if odet.ifix < ctrl.algorithm.numunorms_init
+ odet.ifix += 1
+ else
+ @warn "unorm storage reached, no longer saving fixfac data. Stability outputs and unorming will be correct, but cannot reconstruct `u`. \n
+ Increase `numunorms_init` if needed. Automatic resizing will be added in a future version."
+ end
+ apply_gaussian_reduction!(u, odet, intr, sing_flag; resonant_rows)
+ odet.new = true
+ end
+end
+
+"""
+ apply_gaussian_reduction!(u::Array{ComplexF64,3}, odet::OdeState, intr::ForceFreeStatesInternal, sing_flag::Bool; resonant_rows=Int[])
+
+Triangularize the solution columns of `u` in place by Gaussian reduction, recording the factors in
+`odet.fixfac`/`odet.index` for `transform_u!`. Port of Fortran `ode_fixup`.
+
+At an ideal crossing, the first pivots are the `resonant_rows`, each on the remaining column largest
+there. Growth order cannot pick the resonant solution if a `renorm_threshold` reduction fired just before the
+crossing, since every column has then grown alike.
+"""
+function apply_gaussian_reduction!(u::Array{ComplexF64,3}, odet::OdeState, intr::ForceFreeStatesInternal, sing_flag::Bool; resonant_rows=Int[])
+
+ ifix = odet.ifix
+ odet.sing_flag[ifix] = sing_flag
+ # The previous region ends at the step before this fixup
+ odet.fixstep[ifix] = odet.step - 1
+
+ for isol in 1:intr.numpert_total
+ odet.fixfac[isol, isol, ifix] = 1
+ end
+
+ # Triangularize primary solutions, resonant rows first, then columns from largest to smallest growth
+ growth_order = sortperm(odet.unorm; rev=true)
+ row_free = trues(intr.numpert_total)
+ col_free = trues(intr.numpert_total)
+ for isol in 1:intr.numpert_total
+ if isol <= length(resonant_rows)
+ kpert = resonant_rows[isol]
+ ksol = argmax(j -> col_free[j] ? abs(u[kpert, j, 1]) : -Inf, 1:intr.numpert_total)
+ else
+ ksol = growth_order[findfirst(j -> col_free[j], growth_order)]
+ @views kpert = argmax(abs.(u[:, ksol, 1]) .* row_free)
+ end
+ odet.index[isol, ifix] = ksol
+ col_free[ksol] = false
+ row_free[kpert] = false
+ # Eliminate other solution vectors below the pivot
+ for jsol in 1:intr.numpert_total
+ if col_free[jsol]
+ odet.fixfac[ksol, jsol, ifix] = -u[kpert, jsol, 1] / u[kpert, ksol, 1]
+ @. @views u[:, jsol, :] .= u[:, jsol, :] .+ u[:, ksol, :] .* odet.fixfac[ksol, jsol, ifix]
+ u[kpert, jsol, 1] = 0
+ end
+ end
+ end
+end
+
+"""
+ findmax_dW_edge!(odet::OdeState, ctrl::ForceFreeStatesControl, equil::Equilibrium.PlasmaEquilibrium, mats::MatrixSplines, intr::ForceFreeStatesInternal)
+
+Fill `odet.edge_scan` with the total dW at every stored step in [`ctrl.dW_edge_scan_start`, `intr.psilim`]
+and return the stored-step index of the peak total eigenvalue (NaN steps ignored).
+"""
+function findmax_dW_edge!(odet::OdeState, ctrl::ForceFreeStatesControl, equil::Equilibrium.PlasmaEquilibrium, mats::MatrixSplines, intr::ForceFreeStatesInternal)
+
+ # Stored steps from dW_edge_scan_start on are contiguous
+ edge_start = findfirst(i -> odet.psi_store[i] >= ctrl.dW_edge_scan_start, 1:odet.step)
+ N_edge = odet.step - edge_start + 1
+
+ odet.edge_scan = EdgeScanState(intr.numpert_total, N_edge)
+ es = odet.edge_scan
+
+ es.psi .= odet.psi_store[edge_start:odet.step]
+ es.q .= odet.q_store[edge_start:odet.step]
+
+ es.wvmat = free_compute_wv_spline(ctrl, equil, intr)
+
+ # Steps with a singular wp solve stay NaN
+ for j in 1:N_edge
+ istep = edge_start + j - 1
+ odet.psifac = odet.psi_store[istep]
+ odet.u .= odet.u_store[:, :, :, istep]
+ try
+ result = free_compute_total(equil, mats, intr, odet)
+ es.total_eigenvalue[j] = result.total_eigenvalue
+ es.plasma_energy[j] = result.plasma_energy
+ es.vacuum_energy[j] = result.vacuum_energy
+ es.vacuum_eigenvalue[j] = result.vacuum_eigenvalue
+ catch e
+ e isa LinearAlgebra.SingularException || rethrow()
+ end
+ end
+
+ peak_j = argmax(j -> isnan(real(es.total_eigenvalue[j])) ? typemin(Float64) : real(es.total_eigenvalue[j]), 1:N_edge)
+ return edge_start + peak_j - 1
+end
+
+"""
+ scan_edge_dW!(odet, ctrl, equil, mats, intr; verbose=intr.verbose) -> Bool
+
+Record the edge-dW scan over [dW_edge_scan_start, psilim] on `odet.edge_scan`. With `truncate_at_dW_peak`, the
+scan's peak becomes the plasma edge via `truncate_integration!`; otherwise the integration is left
+untouched. Returns whether it truncated.
+"""
+function scan_edge_dW!(odet::OdeState, ctrl::ForceFreeStatesControl, equil::Equilibrium.PlasmaEquilibrium,
+ mats::MatrixSplines, intr::ForceFreeStatesInternal; verbose::Bool=intr.verbose)
+ ctrl.dW_edge_scan_start < intr.psilim || return false
+ saved_psifac, saved_u = odet.psifac, copy(odet.u)
+ peak_step = findmax_dW_edge!(odet, ctrl, equil, mats, intr)
+ psi_peak, q_peak = odet.psi_store[peak_step], odet.q_store[peak_step]
+ if ctrl.truncate_at_dW_peak
+ truncate_integration!(odet, intr, equil, peak_step)
+ else
+ odet.psifac = saved_psifac
+ odet.u .= saved_u
+ end
+ verbose && @info "Edge-dW peak at ψ = $(@sprintf("%.4f", psi_peak)), q = $(@sprintf("%.3f", q_peak)); " *
+ (ctrl.truncate_at_dW_peak ? "adopted as the plasma edge" : "integration domain unchanged")
+ return ctrl.truncate_at_dW_peak
+end
+
+"""
+ transform_u!(odet::OdeState, intr::ForceFreeStatesInternal)
+
+Undo the Gaussian reductions applied during integration, transforming the stored solutions in
+`odet` in place into the true solution vectors.
+"""
+function transform_u!(odet::OdeState, intr::ForceFreeStatesInternal)
+
+ gauss = Array{ComplexF64,3}(undef, intr.numpert_total, intr.numpert_total, odet.ifix)
+ # Transformation matrices for each region between fixups (ifix + 1 regions)
+ transforms = Array{ComplexF64,3}(undef, intr.numpert_total, intr.numpert_total, odet.ifix + 1)
+ gauss_buffer = Matrix{ComplexF64}(undef, intr.numpert_total, intr.numpert_total)
+ identity = Matrix{ComplexF64}(I, intr.numpert_total, intr.numpert_total)
+ temp = Matrix{ComplexF64}(undef, intr.numpert_total, intr.numpert_total)
+ mask = trues(intr.numpert_total)
+
+ # Construct gaussian reduction matrices for each fixup
+ for ifix in 1:odet.ifix
+ gauss[:, :, ifix] .= identity
+ mask .= true
+ for isol in 1:intr.numpert_total
+ ksol = odet.index[isol, ifix]
+ mask[ksol] = false
+ temp .= identity
+ for jsol in 1:intr.numpert_total
+ if mask[jsol]
+ temp[ksol, jsol] = odet.fixfac[ksol, jsol, ifix]
+ end
+ end
+ mul!(gauss_buffer, view(gauss, :, :, ifix), temp)
+ gauss[:, :, ifix] .= gauss_buffer
+ end
+ # Drop the resonant solutions zeroed at an ideal crossing
+ if odet.sing_flag[ifix]
+ for zeroed_idx in odet.zeroed_idx[ifix]
+ gauss[:, odet.index[zeroed_idx, ifix], ifix] .= 0.0
+ end
+ end
+ end
+
+ # Region i lies between fixups i-1 and i; its transform is the product of all later reductions
+ transforms[:, :, end] .= identity
+ for ifix in odet.ifix:-1:1
+ mul!(view(transforms, :, :, ifix), view(gauss, :, :, ifix), view(transforms, :, :, (ifix + 1)))
+ end
+
+ jfix = 1
+ for ifix in 1:(odet.ifix+1)
+ kfix = ifix != odet.ifix + 1 ? odet.fixstep[ifix] : odet.step
+ @views for istep in jfix:kfix
+ mul!(gauss_buffer, odet.u_store[:, :, 1, istep], transforms[:, :, ifix])
+ odet.u_store[:, :, 1, istep] .= gauss_buffer
+ mul!(gauss_buffer, odet.u_store[:, :, 2, istep], transforms[:, :, ifix])
+ odet.u_store[:, :, 2, istep] .= gauss_buffer
+ # Only analytically supplied (galerkin) derivative stores exist yet; materialized ones come after
+ if !isempty(odet.du_store)
+ mul!(gauss_buffer, odet.du_store[:, :, istep], transforms[:, :, ifix])
+ odet.du_store[:, :, istep] .= gauss_buffer
+ mul!(gauss_buffer, odet.xi_s_store[:, :, istep], transforms[:, :, ifix])
+ odet.xi_s_store[:, :, istep] .= gauss_buffer
+ end
+ end
+ jfix = kfix + 1
+ end
+end
+
+"""
+ sing_der!(
+ du::Array{ComplexF64,3},
+ u::Array{ComplexF64,3},
+ params::Tuple{ForceFreeStatesControl, Equilibrium.PlasmaEquilibrium, MatrixSplines, ForceFreeStatesInternal, OdeState, IntegrationChunk},
+ psieval::Float64
+ )
+
+In-place Euler-Lagrange derivative du/dψ at `psieval` [Glasser Phys. Plasmas 2016 112506 Eq. 24],
+ideal or kinetic, in the `(du, u, p, t)` form the ODE solver calls; `du` and `u` have shape
+`(numpert_total, numpert_total, 2)`. Ξ_s is not computed here; see [`compute_node_xi_s!`](@ref).
+"""
+function sing_der!(du::Array{ComplexF64,3}, u::Array{ComplexF64,3},
+ params::Tuple{ForceFreeStatesControl,Equilibrium.PlasmaEquilibrium,
+ MatrixSplines,ForceFreeStatesInternal,OdeState,IntegrationChunk},
+ psieval::Float64)
+ ctrl, equil, mats, intr, odet, _ = params
+ return sing_der!(du, u, ctrl, equil, mats, intr, odet, psieval)
+end
+
+"""
+ sing_der!(du, u, ctrl, equil, mats, intr, odet, psieval)
+
+Unpacked-argument form of the Euler-Lagrange derivative, using `odet`'s spline hints and
+recording q at `psieval` in `odet.q`. Not safe to call concurrently on a shared `odet`;
+multi-threaded callers should use [`el_derivatives!`](@ref) with their own hints.
+"""
+function sing_der!(du::Array{ComplexF64,3}, u::Array{ComplexF64,3},
+ ctrl::ForceFreeStatesControl, equil::Equilibrium.PlasmaEquilibrium, mats::MatrixSplines,
+ intr::ForceFreeStatesInternal, odet::OdeState, psieval::Float64)
+ odet.q = el_derivatives!(du, u, ctrl.kinetic !== nothing, equil, mats, intr, psieval, odet.spline_hint, odet.mats_hint)
+ return nothing
+end
+
+"""
+ el_derivatives!(du, u, kinetic, equil, mats, intr, psieval, spline_hint, mats_hint) -> q
+
+Euler-Lagrange (or, when `kinetic` is true, FKG) derivative kernel: writes du₁/dψ and du₂/dψ at
+`psieval` into `du` and returns q there. Holds no state of its own — the two hints are the
+caller's interval-search accelerators, so concurrent callers just pass their own.
+"""
+@with_pool pool function el_derivatives!(du::Array{ComplexF64,3}, u::Array{ComplexF64,3},
+ kinetic::Bool, equil::Equilibrium.PlasmaEquilibrium, mats::MatrixSplines,
+ intr::ModeSpace, psieval::Float64, spline_hint::Base.RefValue{Int}, mats_hint::Base.RefValue{Int})
+
+ Npert = intr.numpert_total
+
+ singfac_vec = acquire!(pool, Float64, Npert)
+ singfac_mat = reshape(singfac_vec, intr.mpert, intr.npert)
+
+ fmat_lower = acquire!(pool, ComplexF64, Npert, Npert)
+ kmat = similar!(pool, fmat_lower)
+ gmat = similar!(pool, fmat_lower)
+ tmp_mat = similar!(pool, fmat_lower)
+
+ fill!(tmp_mat, zero(ComplexF64))
+ u1 = @view(u[:, :, 1])
+ u2 = @view(u[:, :, 2])
+ du1 = @view(du[:, :, 1])
+ du2 = @view(du[:, :, 2])
+
+ # singfac = 1 / (m - nq)
+ q = equil.profiles.q_spline(psieval; hint=spline_hint)
+ singfac_mat .= 1.0 ./ ((intr.mlow:intr.mhigh) .- q .* (intr.nlow:intr.nhigh)')
+
+ kin = mats.kinetic
+ if kinetic
+ kin === nothing && error("el_derivatives! called with kinetic=true but mats carries no kinetic matrices")
+ # Kinetic path: FKG matrices, evaluated with the caller's hint (never a shared one)
+ f0mat = similar!(pool, fmat_lower)
+ pmat_kin = similar!(pool, fmat_lower)
+ paat_kin = similar!(pool, fmat_lower)
+ kkmat_kin = similar!(pool, fmat_lower)
+ kkaat_kin = similar!(pool, fmat_lower)
+ r1mat_kin = similar!(pool, fmat_lower)
+ r2mat_kin = similar!(pool, fmat_lower)
+ r3mat_kin = similar!(pool, fmat_lower)
+ gaat_kin = similar!(pool, fmat_lower)
+
+ kin.F0_spline(vec(f0mat), psieval; hint=mats_hint)
+ kin.P_spline(vec(pmat_kin), psieval; hint=mats_hint)
+ kin.P_spline_adj(vec(paat_kin), psieval; hint=mats_hint)
+ kin.Kk_spline(vec(kkmat_kin), psieval; hint=mats_hint)
+ kin.Kk_spline_adj(vec(kkaat_kin), psieval; hint=mats_hint)
+ kin.R1_spline(vec(r1mat_kin), psieval; hint=mats_hint)
+ kin.R2_spline(vec(r2mat_kin), psieval; hint=mats_hint)
+ kin.R3_spline(vec(r3mat_kin), psieval; hint=mats_hint)
+ kin.G_spline_adj(vec(gaat_kin), psieval; hint=mats_hint)
+
+ # Build singfac-dependent F̄, K̄, K̄†, Ḡ† matrices (Logan 2015 Appendix C, Eqs C.5-C.11):
+ # F̄(i,j) = q1*f0*q2 - q1*P - P†'*q2 + R1
+ # K̄(i,j) = q1*KK + R2
+ # K̄†(i,j) = KK†*q2 + R3
+ # where q1 = (m₁ - n*q), q2 = (m₂ - n*q) — direct singfac, NOT 1/(m-nq) as in ideal path
+ singfac_direct = acquire!(pool, Float64, Npert)
+ singfac_direct_mat = reshape(singfac_direct, intr.mpert, intr.npert)
+ singfac_direct_mat .= (intr.mlow:intr.mhigh) .- q .* (intr.nlow:intr.nhigh)'
+
+ # fmat_lower, kmat, kaat_kin hold F̄, K̄, K̄†
+ kaat_kin = similar!(pool, fmat_lower)
+ for j in 1:Npert
+ q2 = singfac_direct[j]
+ for i in 1:Npert
+ q1 = singfac_direct[i]
+ fmat_lower[i, j] = q1 * f0mat[i, j] * q2 - q1 * pmat_kin[i, j] -
+ conj(paat_kin[j, i]) * q2 + r1mat_kin[i, j]
+ kmat[i, j] = q1 * kkmat_kin[i, j] + r2mat_kin[i, j]
+ kaat_kin[i, j] = kkaat_kin[i, j] * q2 + r3mat_kin[i, j]
+ end
+ end
+ gmat .= gaat_kin
+
+ # Kinetic ODE (Logan 2015 Eq 7.46): singfac absorbed into F̄/K̄/K̄†, no explicit Q⁻¹
+ # du₁ = F̄⁻¹(u₂ - K̄·u₁)
+ du1 .= u2
+ mul!(tmp_mat, kmat, u1)
+ du1 .-= tmp_mat
+ # Kinetic F̄ is non-Hermitian: LU rather than Cholesky
+ _, ipiv2, _ = LAPACK.getrf!(fmat_lower)
+ LAPACK.getrs!('N', fmat_lower, ipiv2, du1)
+
+ # du₂ = Ḡ†·u₁ + K̄†·du₁ (Logan 2015 Eq C.10-C.11)
+ mul!(tmp_mat, gmat, u1)
+ du2 .= tmp_mat
+ mul!(tmp_mat, kaat_kin, du1)
+ du2 .+= tmp_mat
+
+ else
+ # Ideal path [Glasser 2016 Eqs. 22-24]
+ mats.ideal.F_spline_lower(vec(fmat_lower), psieval; hint=mats_hint)
+ mats.ideal.K_spline(vec(kmat), psieval; hint=mats_hint)
+ mats.ideal.G_spline(vec(gmat), psieval; hint=mats_hint)
+
+ # du[1] = - F̄⁻¹ * K̄ * u[1] + F̄⁻¹ * Q⁻¹ * u[2]
+ du1 .= u2 .* singfac_vec
+ mul!(tmp_mat, kmat, u1)
+ du1 .-= tmp_mat
+ ldiv!(LowerTriangular(fmat_lower), du1)
+ ldiv!(UpperTriangular(fmat_lower'), du1)
+ # du[2] = G * u[1] + K̄^† * du[1] = G * u[1] - K̄^† * F̄⁻¹ * K̄ * u[1] + K̄^† * F̄⁻¹ * Q⁻¹ * u[2]
+ mul!(tmp_mat, gmat, u1)
+ du2 .= tmp_mat
+ mul!(tmp_mat, adjoint(kmat), du1)
+ du2 .+= tmp_mat
+ # du[1] = - Q⁻¹ * F̄⁻¹ * K̄ * u[1] + Q⁻¹ * F̄⁻¹ * Q⁻¹ * u[2]
+ du1 .*= singfac_vec
+ end
+ return q
+end
+
+"""
+ compute_node_xi_s!(xi_s, du1, u1, mats, psieval; kinetic=false, hint=Ref(1))
+
+Evaluate Ξ_s = -A⁻¹(B·Ξ′_ψ + C·Ξ_ψ) [Glasser Phys. Plasmas 2016 112506 Eq. 18] at `psieval` into
+`xi_s`. `du1` and `u1` are the Ξ′_ψ and Ξ_ψ blocks at that ψ (an `el_derivatives!` result and its input).
+With `kinetic=true` the non-Hermitian kinetic A is used.
+"""
+@with_pool pool function compute_node_xi_s!(xi_s::AbstractMatrix{ComplexF64}, du1::AbstractMatrix{ComplexF64},
+ u1::AbstractMatrix{ComplexF64}, mats::MatrixSplines, psieval::Float64; kinetic::Bool=false, hint::Base.RefValue{Int}=Ref(1))
+
+ Npert = size(u1, 1)
+ amat = acquire!(pool, ComplexF64, Npert, Npert)
+ bmat = similar!(pool, amat)
+ cmat = similar!(pool, amat)
+ tmp_mat = similar!(pool, amat)
+
+ # The kinetic A is non-Hermitian, hence LU below instead of Cholesky
+ active_mats = kinetic ? mats.kinetic : mats.ideal
+ active_mats === nothing && error("compute_node_xi_s! called with kinetic=true but mats carries no kinetic matrices")
+ active_mats.A_spline(vec(amat), psieval; hint=hint)
+ active_mats.B_spline(vec(bmat), psieval; hint=hint)
+ active_mats.C_spline(vec(cmat), psieval; hint=hint)
+
+ # bmat = A⁻¹ bmat, cmat = A⁻¹ cmat in place
+ if kinetic
+ _, ipiv, _ = LAPACK.getrf!(amat)
+ LAPACK.getrs!('N', amat, ipiv, bmat)
+ LAPACK.getrs!('N', amat, ipiv, cmat)
+ else
+ LAPACK.potrf!('U', amat)
+ LAPACK.potrs!('U', amat, bmat)
+ LAPACK.potrs!('U', amat, cmat)
+ end
+
+ mul!(tmp_mat, bmat, du1)
+ xi_s .= .-tmp_mat
+ mul!(tmp_mat, cmat, u1)
+ xi_s .-= tmp_mat
+ return xi_s
+end
diff --git a/src/ForceFreeStates/FixedBoundaryStability.jl b/src/ForceFreeStates/FixedBoundaryStability.jl
new file mode 100644
index 0000000000..29896ac3db
--- /dev/null
+++ b/src/ForceFreeStates/FixedBoundaryStability.jl
@@ -0,0 +1,108 @@
+"""
+ evaluate_stability_criterion!(odet, profiles) -> nzero
+
+Fill `odet.crit_store` over all saved steps and return the number of zero crossings of the
+critical eigenvalue (each signals a fixed-boundary instability). Warns with a count if W⁻¹ was
+non-Hermitian beyond tolerance at any step.
+"""
+function evaluate_stability_criterion!(odet::OdeState, profiles::Equilibrium.ProfileSplines)
+
+ resize!(odet.crit_store, odet.step)
+ nzero = 0
+ nonherm_count = 0
+
+ for istep in 1:odet.step
+ zero_cross, nonherm = check_for_zero_crossings!(odet, profiles, istep)
+ if zero_cross
+ nzero += 1
+ end
+ if nonherm
+ nonherm_count += 1
+ end
+ end
+
+ if nonherm_count > 0
+ @warn "W inverse matrix was non-Hermitian beyond tolerance at $nonherm_count integration step(s)"
+ end
+
+ return nzero
+end
+
+"""
+ check_for_zero_crossings!(odet, profiles, istep) -> zero_cross, nonherm
+
+Compute `crit` (smallest-magnitude eigenvalue of W⁻¹, scaled by (dV/dψ)²) at step `istep` into
+`odet.crit_store`, and report whether it changed sign since the previous step. A sign change counts
+only if the interpolated midpoint confirms it is a genuine crossing rather than noise.
+
+### Returns
+
+ - `zero_cross::Bool`: True if a physical zero crossing was detected
+ - `nonherm::Bool`: True if W⁻¹ was non-Hermitian beyond tolerance
+"""
+@with_pool pool function check_for_zero_crossings!(odet::OdeState, profiles::Equilibrium.ProfileSplines, istep::Int)
+
+ u = acquire!(pool, eltype(odet.u_store), size(odet.u_store)[1:3])
+ psi = odet.psi_store[istep]
+ u .= odet.u_store[:, :, :, istep]
+ dVdpsi = profiles.dVdpsi_spline(psi; hint=odet.spline_hint)
+ crit_val, nonherm = compute_smallest_eigenvalue(u)
+ odet.crit_store[istep] = crit_val * dVdpsi^2
+
+ zero_cross = false
+ if istep > 1 && odet.crit_store[istep] * odet.crit_store[istep-1] < 0
+ crit = odet.crit_store[istep]
+ crit_prev = odet.crit_store[istep-1]
+ # Reject noise: crit at the interpolated crossing must lie between and well below both neighbors
+ fac = crit / (crit - crit_prev)
+ psi_mid = psi - fac * (psi - odet.psi_store[istep-1])
+ u_mid = u .- fac .* (u .- @view(odet.u_store[:, :, :, istep-1]))
+ dVdpsi = profiles.dVdpsi_spline(psi_mid; hint=odet.spline_hint)
+ crit_mid_val, _ = compute_smallest_eigenvalue(u_mid)
+ crit_mid = crit_mid_val * dVdpsi^2
+ if (crit_mid - crit) * (crit_mid - crit_prev) < 0 && abs(crit_mid) < 0.5 * min(abs(crit), abs(crit_prev))
+ zero_cross = true
+ @info "Zero crossing detected at ψ = $(@sprintf("%.3f", psi_mid))"
+ end
+ end
+ return zero_cross, nonherm
+end
+
+"""
+ compute_smallest_eigenvalue(u) -> crit, nonherm
+
+Form W⁻¹ = U₁U₂⁻¹ from the solution `u`, symmetrize it, and return its signed eigenvalue of
+smallest magnitude. Also flags whether W⁻¹ was non-Hermitian beyond tolerance before symmetrizing.
+
+### Returns
+
+ - `crit::Float64`: the computed scaled critical eigenvalue
+ - `nonherm::Bool`: true if W⁻¹ was non-Hermitian beyond tolerance (> 1e-3)
+"""
+@with_pool pool function compute_smallest_eigenvalue(u::AbstractArray{ComplexF64,3})
+
+ # In-place wp_inverse = u[:, :, 1] / u[:, :, 2]
+ wp_inverse = acquire!(pool, ComplexF64, size(u, 1), size(u, 2))
+ U2_tmp = similar!(pool, wp_inverse)
+ wp_inverse .= @view u[:, :, 1]
+ U2_tmp .= @view u[:, :, 2]
+ rdiv!(wp_inverse, lu!(U2_tmp))
+
+ # Measure non-Hermiticity; taking the Hermitian part differs from Hermitian(), which reads one triangle only
+ adjoint_wp_inverse = similar!(pool, wp_inverse)
+ tmp_mat1 = similar!(pool, wp_inverse)
+ tmp_mat2 = similar!(pool, wp_inverse)
+ adjoint!(adjoint_wp_inverse, wp_inverse)
+ @. tmp_mat1 = 0.5 * (wp_inverse + adjoint_wp_inverse)
+ @. tmp_mat2 = 0.5 * (wp_inverse - adjoint_wp_inverse)
+
+ nonherm_error = norm(tmp_mat2) / norm(tmp_mat1)
+ nonherm = nonherm_error > 1e-3
+
+ hermitianpart!(wp_inverse)
+
+ # Return the eigenvalue of smallest magnitude, keeping its sign so the caller can detect crossings
+ evals = eigvals!(Hermitian(wp_inverse))
+ crit = evals[findmin(abs, evals)[2]]
+ return crit, nonherm
+end
diff --git a/src/ForceFreeStates/FixedKineticMatrices.jl b/src/ForceFreeStates/FixedKineticMatrices.jl
new file mode 100644
index 0000000000..388c8ebab7
--- /dev/null
+++ b/src/ForceFreeStates/FixedKineticMatrices.jl
@@ -0,0 +1,94 @@
+"""
+ TestKineticMatrices(; scale)
+
+Synthetic X-shaped kinetic matrices for exercising the kinetic code path in tests, with no
+physical meaning: `scale` times the ideal matrices' Frobenius norms (Ak, Dk, Hk Hermitian; Bk, Ck,
+Ek not). Pass it as `ForceBalanceProblem(eq; kinetic=TestKineticMatrices(; scale))`; a deck cannot
+select it.
+
+## Fields
+
+ - `scale::Float64` - Size of the test matrices relative to the ideal matrix norms.
+"""
+@kwdef struct TestKineticMatrices
+ scale::Float64
+end
+
+"""
+ _build_x_matrix(mpert, mlow, sigma; hermitian=true)
+
+Build an mpert×mpert X-shaped matrix: σ on the diagonal, and on the m ↔ -m anti-diagonal
+i·sign(m)·σ (`hermitian=true`, for Ak, Dk, Hk; Logan 2015 Eqs 7.30, 7.33, 7.35) or
+sign(m)·σ (`hermitian=false`, for Bk, Ck, Ek; Eqs 7.31, 7.32, 7.34).
+"""
+function _build_x_matrix(mpert::Int, mlow::Int, sigma::Float64; hermitian::Bool=true)
+ W = zeros(ComplexF64, mpert, mpert)
+ for i in 1:mpert
+ m_i = mlow + i - 1
+ W[i, i] = sigma
+
+ # Anti-diagonal partner: m_j = -m_i
+ j = -m_i - mlow + 1
+ if 1 <= j <= mpert && i != j
+ if hermitian
+ W[i, j] = im * sign(m_i) * sigma
+ else
+ W[i, j] = sign(m_i) * sigma
+ end
+ end
+ end
+ return W
+end
+
+"""
+ fixed_kinetic_matrices(mpert, np, mpsi, sigma, mlow, mats, xs)
+
+Build X-shaped test kinetic energy matrices for all 6 components, each scaled by `sigma` times the
+Frobenius norm of the corresponding ideal matrix at each ψ, so σ is a dimensionless strength:
+
+| Component | Matrix | Coupling | Hermitian | Relative to |
+|:--------- |:------ |:-------- |:--------- |:----------- |
+| 1 | Ak | Wz†·Wz | Yes | ‖A(ψ)‖_F |
+| 2 | Bk | Wz†·Wx | No | ‖B(ψ)‖_F |
+| 3 | Ck | Wz†·Wy | No | ‖C(ψ)‖_F |
+| 4 | Dk | Wx†·Wx | Yes | ‖D(ψ)‖_F |
+| 5 | Ek | Wx†·Wy | No | ‖E(ψ)‖_F |
+| 6 | Hk | Wy†·Wy | Yes | ‖H(ψ)‖_F |
+
+Torque matrices are zero. Returns `(kw_flat, kt_flat)`, each of shape `(mpsi, np^2, 6)`.
+"""
+function fixed_kinetic_matrices(
+ mpert::Int, np::Int, mpsi::Int, sigma::Float64, mlow::Int,
+ mats::MatrixSplines, xs::Vector{Float64}
+)
+ kw_flat = zeros(ComplexF64, mpsi, np^2, 6)
+ kt_flat = zeros(ComplexF64, mpsi, np^2, 6)
+
+ ideal_splines = [mats.ideal.A_spline, mats.ideal.B_spline, mats.ideal.C_spline, mats.ideal.D_spline_prim, mats.ideal.E_spline_prim, mats.ideal.H_spline]
+ # Ak, Dk, Hk (X†X) are Hermitian; Bk, Ck, Ek (X†Y) are not. Logan 2015 p.169 lists "Ak, Ck, Hk", a typo.
+ is_hermitian = [true, false, false, true, false, true]
+
+ X_herm = _build_x_matrix(mpert, mlow, 1.0; hermitian=true)
+ X_nonherm = _build_x_matrix(mpert, mlow, 1.0; hermitian=false)
+
+ hint = Ref(1)
+ for ipsi in 1:mpsi
+ psi = xs[ipsi]
+ for ic in 1:6
+ ideal_mat = reshape(ideal_splines[ic](psi; hint=hint), np, np)
+ norm_ideal = norm(ideal_mat) # Frobenius norm
+
+ X = is_hermitian[ic] ? X_herm : X_nonherm
+ # Tile the mpert×mpert pattern over each n block, scaled by σ‖ideal(ψ)‖_F
+ W = zeros(ComplexF64, np, np)
+ for jn in 0:(np÷mpert-1)
+ offset = jn * mpert
+ W[(offset+1):(offset+mpert), (offset+1):(offset+mpert)] .= X
+ end
+ W .*= sigma * norm_ideal
+ kw_flat[ipsi, :, ic] .= vec(W)
+ end
+ end
+
+ return kw_flat, kt_flat
+end
diff --git a/src/ForceFreeStates/ForceBalance.jl b/src/ForceFreeStates/ForceBalance.jl
new file mode 100644
index 0000000000..f4db1a240b
--- /dev/null
+++ b/src/ForceFreeStates/ForceBalance.jl
@@ -0,0 +1,288 @@
+# ForceBalance.jl: the force-balance problem and its solve.
+
+# The solve's layer-overlap cap and kinetic model come from Tearing and KineticForces, which load after
+# ForceFreeStates, so they reach it through these functions: Tearing adds the `layer_overlap_scan` method for a
+# `SLAYERModel`, and KineticForces the kinetic-model methods.
+"""
+ layer_overlap_scan(equil, model, ns)
+
+The binding resistive-layer overlap scan over the toroidal mode numbers `ns`, with `model`'s layer closures; its
+`psihigh` caps the domain. Methods live in `Tearing`.
+"""
+function layer_overlap_scan end
+
+"""
+ kinetic_grid_inputs(source, ctrl, equil, intr; rationals) -> (kinetic_profiles, pinned)
+
+The kinetic profiles the two-pass ψ grid refines on and the kinetic-resonance surfaces it pins, for the kinetic
+`source` of the solve (any source, or `nothing`). The method lives in `KineticForces`.
+"""
+function kinetic_grid_inputs end
+
+"""
+ kinetic_model_source(model, equil, intr) -> (calculated_source, axis_validity_psi_c)
+
+The callback that evaluates a kinetic model's matrices for [`evaluate_kinetic_matrices`](@ref), and the model's
+axis-validity boundary. The method for `KineticForcesControl` lives in `KineticForces`.
+"""
+function kinetic_model_source end
+
+"""
+ ForceBalanceProblem(equil; nn, wall=nothing, kwargs...)
+
+The perturbed force-balance problem posed on an equilibrium, whose solutions are the force-free
+(or, with a `kinetic` source, kinetic) perturbed states. With kinetic terms the force operator
+is not self-adjoint, so this is not always an energy extremization. The integrator passed to
+[`solve`](@ref) sets the numerics; inner-layer matching is a separate `MatchProblem` on the finished solve.
+
+`nn` is the toroidal mode number or range and `wall` the vacuum wall shape. Remaining keywords describe physics and workflow controls;
+numerical settings belong on the integrator passed to `solve`. `nn_low`/`nn_high` are rejected — they
+come from `nn`.
+
+## Fields
+
+ - `equil::Equilibrium.PlasmaEquilibrium` - The equilibrium the problem is posed on.
+ - `wall::Union{Nothing,Vacuum.WallSettings}` - Vacuum wall shape for the free-boundary energies.
+ - `ctrl_kwargs::Dict{Symbol,Any}` - `ForceFreeStatesControl` keywords, `nn` already folded in.
+"""
+struct ForceBalanceProblem
+ equil::Equilibrium.PlasmaEquilibrium
+ wall::Union{Nothing,Vacuum.WallSettings}
+ ctrl_kwargs::Dict{Symbol,Any}
+end
+
+function ForceBalanceProblem(
+ equil::Equilibrium.PlasmaEquilibrium;
+ nn::Union{Int,AbstractUnitRange{Int}},
+ wall::Union{Nothing,Vacuum.WallSettings}=nothing,
+ kwargs...
+)
+ ctrl_kwargs = Dict{Symbol,Any}(kwargs)
+ allowed = setdiff(fieldnames(ForceFreeStatesControl), (:algorithm,))
+ for name in keys(ctrl_kwargs)
+ name in allowed || throw(ArgumentError("`$name` is not a ForceBalanceProblem keyword; numerical settings belong on the integrator."))
+ end
+ (haskey(ctrl_kwargs, :nn_low) || haskey(ctrl_kwargs, :nn_high)) &&
+ error("the toroidal mode range comes from the `nn` keyword; drop nn_low/nn_high")
+ ctrl_kwargs[:nn_low] = first(nn)
+ ctrl_kwargs[:nn_high] = last(nn)
+ return ForceBalanceProblem(equil, wall, ctrl_kwargs)
+end
+
+"""
+ solve(prob::ForceBalanceProblem, alg; verbose=false) -> ForceFreeStatesResult
+ solve(equil, alg; nn, verbose=false, kwargs...) -> ForceFreeStatesResult
+
+Solve the perturbed-plasma [`ForceBalanceProblem`](@ref) with the formalism `alg` —
+[`Forward`](@ref), [`Riccati`](@ref) or [`Galerkin`](@ref) — and return the published
+[`ForceFreeStatesResult`](@ref). This is the scripting entry point; it runs the same stages
+a `gpec.toml` run of `main` does and produces the same result object. The second form is
+sugar building the problem from an equilibrium and the problem keywords in one call.
+
+Knobs owned by `alg` are rejected as `ForceFreeStatesControl` keywords. Kinetic runs
+(a `kinetic` source) take `Forward()`. `kinetic=KineticForcesControl(; ...)` evaluates the
+KineticForces model with those settings on the equilibrium's kinetic profiles (`kinetic_file`, or
+`attach_kinetic_profiles!`); `kinetic=TestKineticMatrices(; scale)` uses synthetic test matrices; `kinetic=km` reuses
+the [`KineticMatrices`](@ref) from [`kinetic_matrices`](@ref).
+
+```julia
+eq = PlasmaEquilibrium("input.geqdsk"; jac_type="hamada")
+prob = ForceBalanceProblem(eq; nn=1, delta_mlow=8, delta_mhigh=8, vac_flag=true)
+ffs = solve(prob, Riccati())
+ffs = solve(eq, Riccati(); nn=1, vac_flag=true) # equivalent one-line form
+```
+"""
+function CommonSolve.solve(prob::ForceBalanceProblem, alg::AbstractIntegrator; verbose::Bool=false)
+ total_start = time()
+ ctrl, intr, equil, metric, mats, layer_overlap = _prepare_solve(prob, alg; verbose)
+ result = run_force_free_states(ctrl, equil, mats, intr, metric; cut_solution=alg isa Galerkin && alg.cut_solution)
+ result = _with(result; problem=prob, algorithm=alg, layer_overlap=layer_overlap)
+
+ @info "Force-Free States completed in $(@sprintf("%.3f", time() - total_start)) s"
+
+ return result
+end
+
+"""
+ kinetic_matrices(prob::ForceBalanceProblem, alg=Forward(); verbose=false) -> KineticMatrices
+
+Evaluate the kinetic matrices of `prob`'s kinetic source once, running the part of [`solve`](@ref) before the
+Euler-Lagrange integration. Pass them back as the problem's `kinetic` to solve without evaluating them again: the solve
+is identical to one with the source itself, and may change `kinetic_factor`.
+
+```julia
+km = kinetic_matrices(ForceBalanceProblem(eq; nn=1, kinetic=KineticForcesControl()))
+scan = [solve(ForceBalanceProblem(eq; nn=1, kinetic=km, kinetic_factor=f), Forward()) for f in (0.5, 1.0, 2.0)]
+```
+"""
+function kinetic_matrices(prob::ForceBalanceProblem, alg::Forward=Forward(); verbose::Bool=false)
+ get(prob.ctrl_kwargs, :kinetic, nothing) === nothing &&
+ error("kinetic_matrices: the problem has no kinetic source; pass kinetic=KineticForcesControl(...) or TestKineticMatrices(; scale)")
+ return last(_prepare_solve(prob, alg; verbose))
+end
+
+# Everything solve does before the integration: the control, the mode space, the (re-formed) equilibrium, the metric,
+# the matrices, the layer-overlap scan and the kinetic matrices.
+function _prepare_solve(prob::ForceBalanceProblem, alg::AbstractIntegrator; verbose::Bool=false)
+ equil = prob.equil
+ ctrl_kwargs = copy(prob.ctrl_kwargs)
+ ctrl = ForceFreeStatesControl(; algorithm=alg, ctrl_kwargs...)
+ validate_algorithm(ctrl)
+
+ ctrl.kinetic === nothing && ctrl.kinetic_factor != 1 &&
+ error("kinetic_factor scales the kinetic matrices, but no kinetic source is set: pass kinetic=... " *
+ "([ForceFreeStates] kinetic = \"KineticForces\")")
+ # A kinetic model (not supplied or synthetic matrices) is evaluated on the equilibrium's kinetic profiles.
+ ctrl.kinetic === nothing || ctrl.kinetic isa Union{KineticMatrices,TestKineticMatrices} || equil.kinetic !== nothing ||
+ error("the KineticForces kinetic source needs kinetic profiles on the equilibrium: set kinetic_file or call attach_kinetic_profiles!")
+ ctrl.kinetic isa Union{Nothing,KineticMatrices,TestKineticMatrices} || Equilibrium.has_ntv_fields(equil.kinetic) ||
+ error("the KineticForces kinetic source needs n_e, T_i, T_e and omega_E in the kinetic profiles; the kinetic file lacks at least one")
+ ctrl.kinetic !== nothing && !(alg isa Forward) &&
+ error("$(nameof(typeof(alg)))() does not support kinetic runs; use Forward().")
+
+ # GPEC differentiates the spline of F, so single-precision FPOL rounding becomes noise in Δ′.
+ eq_config = equil.config
+ if eq_config.eq_type in Equilibrium.EFIT_KINDS && alg isa Union{Riccati,Galerkin} &&
+ isfile(eq_config.eq_filename) && Equilibrium.gfile_fpol_single_precision(eq_config.eq_filename)
+ @warn "The g-file's FPOL is single precision. Its rounding puts noise of order ±2–3 on Δ′ at 257 radial " *
+ "nodes; regenerate the file in double precision for converged Δ′." file = eq_config.eq_filename
+ end
+
+ intr = ForceFreeStatesInternal(; verbose)
+ intr.wall_settings = prob.wall
+
+ resolve_mode_space!(intr, ctrl)
+
+ equil = maybe_reform_equilibrium(equil, intr, ctrl)
+
+ metric, mats, layer_overlap, km = prepare_force_free_states!(intr, ctrl, equil)
+ return ctrl, intr, equil, metric, mats, layer_overlap, km
+end
+
+"""
+ solve(equil::PlasmaEquilibrium, alg; nn, verbose=false, kwargs...) -> ForceFreeStatesResult
+
+Convenience form of [`solve`](@ref): builds the [`ForceBalanceProblem`](@ref) from the
+equilibrium and the problem keywords, then solves it with `alg`.
+"""
+CommonSolve.solve(equil::Equilibrium.PlasmaEquilibrium, alg::AbstractIntegrator; verbose::Bool=false, kwargs...) =
+ CommonSolve.solve(ForceBalanceProblem(equil; kwargs...), alg; verbose)
+
+"""
+ maybe_reform_equilibrium(equil, intr, ctrl) -> equil
+
+Two-pass auto grid: measure the pass-1 equilibrium's curvature (profiles, geometry, and the kinetic
+model's view of its attached kinetic profiles), pin knots on rational surfaces, and re-form on the refined
+grid with `Equilibrium.reform` from the source the equilibrium remembers. Returns `equil` untouched
+when its configuration wants a single pass.
+"""
+function maybe_reform_equilibrium(
+ equil::Equilibrium.PlasmaEquilibrium,
+ intr::ForceFreeStatesInternal,
+ ctrl::ForceFreeStatesControl
+)
+ eq_config = equil.config
+ Equilibrium.wants_two_pass(eq_config) || return equil
+
+ mandatory = rational_psi_nodes(equil; nlow=intr.nlow, nhigh=intr.nhigh)
+ # Kinetic-resonance nodes are located here rather than at the call site so the validity
+ # boundary that filters them is cleared against this pass's rationals (intr.sing is empty yet).
+ kinetic_profiles, pinned = kinetic_grid_inputs(kinetic_source(ctrl.kinetic), ctrl, equil, intr; rationals=mandatory)
+ # Smallest |n| in the run sets the widest matching half-stencil dpsi = singfac_min/(n_min·|q′|),
+ # so the rational-surface brackets clear a zone large enough for every mode.
+ n_min = minimum(abs(n) for n in intr.nlow:intr.nhigh if n != 0)
+ isempty(pinned) ||
+ @info "Pinning $(length(pinned)) kinetic-resonance surfaces into the ψ grid: $(round.(sort(pinned); digits=3))"
+ psi_nodes = Equilibrium.refined_psi_grid(equil;
+ tau=eq_config.psi_accuracy, kin=kinetic_profiles, mandatory=mandatory, pinned=pinned,
+ singfac_min=ctrl.singfac_min, n_min=n_min)
+ equil = Equilibrium.reform(equil, psi_nodes)
+ implied = Equilibrium.implied_knot_count(equil; tau=eq_config.psi_accuracy, kin=kinetic_profiles)
+ if implied > 1.5 * (length(psi_nodes) - 1)
+ @warn "Two-pass psi grid: refined equilibrium implies $implied knots vs $(length(psi_nodes) - 1) used — " *
+ "pass 1 may have under-sampled a feature; consider tightening psi_accuracy"
+ end
+ @info "Two-pass psi grid: $(length(psi_nodes)) knots, $(length(mandatory)) rational surfaces pinned (n=$(_mode_range_label(intr)))"
+
+ return equil
+end
+
+"""
+ prepare_force_free_states!(intr, ctrl, equil) -> (metric, mats, overlap, km)
+
+Set up the force-free-states solve on `intr`: integration limits, the surviving singular
+surfaces and their GGJ coefficients, the poloidal mode range, and the metric plus
+Euler-Lagrange (and, when requested, kinetic) matrices. `km` is the run's [`KineticMatrices`](@ref), or `nothing`.
+"""
+function prepare_force_free_states!(
+ intr::ForceFreeStatesInternal,
+ ctrl::ForceFreeStatesControl,
+ equil::Equilibrium.PlasmaEquilibrium
+)
+ # Resistive-layer overlap: where adjacent rational surfaces' layers run into each other bounds the domain, when asked.
+ cap = ctrl.psilim_from_layer_overlap
+ overlap = cap === false ? nothing : layer_overlap_scan(equil, cap === true ? InnerLayer.SLAYERModel() : cap, intr.nlow:intr.nhigh)
+
+ # psilim and qlim, the integration limits
+ sing_lim!(intr, ctrl, equil; psilim_cap=overlap === nothing ? nothing : overlap.psihigh)
+
+ sing_find!(intr, equil)
+
+ # Lower bound from qlow for every integrator, then keep only surfaces inside [psilow, psilim],
+ # so the Δ' BVP sees only crossable ones.
+ sing_min!(intr, ctrl, equil)
+ remove_singular_surfs!(intr; psimin=intr.psilow)
+
+ # GGJ geometric coefficients (E, F, G, H, K, M) of each surviving singular surface; `ggj_parameters` adds τ_A / τ_R.
+ if intr.msing > 0
+ resist_eval_all!(intr, equil)
+ end
+
+ # Poloidal mode range; delta_mhigh is doubled to match Fortran.
+ delta_mhigh = 2 * ctrl.delta_mhigh
+ if ctrl.delta_mlow < 0 || ctrl.delta_mhigh < 0
+ error("Negative delta_mlow or delta_mhigh not allowed")
+ end
+ intr.mlow = trunc(Int, min(intr.nlow * equil.params.qmin, 0)) - 4 - ctrl.delta_mlow
+ intr.mhigh = trunc(Int, intr.nhigh * equil.params.qmax) + delta_mhigh
+ intr.mpert = intr.mhigh - intr.mlow + 1
+ intr.numpert_total = intr.mpert * intr.npert
+
+ if intr.verbose
+ @info "Run parameters:\n" *
+ " q0 = $(@sprintf("%.3f", equil.params.q0)), qmin = $(@sprintf("%.3f", equil.params.qmin)), qmax = $(@sprintf("%.3f", equil.params.qmax)), q95 = $(@sprintf("%.3f", equil.params.q95))\n" *
+ " qlim = $(@sprintf("%.3f", intr.qlim)), psilim = $(@sprintf("%.3f", intr.psilim))\n" *
+ " betat = $(@sprintf("%.3f", equil.params.betat)), betan = $(@sprintf("%.3f", equil.params.betan)), betap1 = $(@sprintf("%.3f", equil.params.betap1))\n" *
+ " mlow = $(@sprintf("%4i", intr.mlow)), mhigh = $(@sprintf("%4i", intr.mhigh)), mpert = $(@sprintf("%4i", intr.mpert))\n" *
+ " nlow = $(@sprintf("%4i", intr.nlow)), nhigh = $(@sprintf("%4i", intr.nhigh)), npert = $(@sprintf("%4i", intr.npert))"
+ end
+
+ metric = make_metric(equil, intr.mpert)
+
+ if intr.verbose
+ @info "Computing F, G, and K matrices"
+ end
+
+ mats = build_matrix_splines(equil, intr, metric)
+
+ km = nothing
+ if ctrl.kinetic isa KineticMatrices
+ check_kinetic_matrices(ctrl.kinetic, intr, metric)
+ km = ctrl.kinetic
+ elseif ctrl.kinetic isa TestKineticMatrices
+ intr.verbose && @info "Computing kinetic matrices (synthetic test matrices, scale $(ctrl.kinetic.scale))"
+ km = evaluate_kinetic_matrices(ctrl, equil, mats, intr, metric)
+ elseif ctrl.kinetic !== nothing
+ intr.verbose && @info "Computing kinetic matrices (KineticForces model)"
+ calculated_cb, axis_psi_c = kinetic_model_source(ctrl.kinetic, equil, intr)
+ km = evaluate_kinetic_matrices(ctrl, equil, mats, intr, metric; calculated_source=calculated_cb, axis_validity_psi_c=axis_psi_c)
+ end
+ km === nothing || (mats = build_kinetic_matrix_splines(mats, equil, intr, metric, km, ctrl.kinetic_factor))
+
+ # Kinetically displaced singular surfaces (zeros of det(F̄)) for ODE crossings; singfac_min == 0 keeps a single chunk.
+ if ctrl.kinetic !== nothing && ctrl.singfac_min > 0
+ find_kinetic_singular_surfaces!(mats, equil, intr)
+ end
+
+ return metric, mats, overlap, km
+end
diff --git a/src/ForceFreeStates/ForceFreeStates.jl b/src/ForceFreeStates/ForceFreeStates.jl
new file mode 100644
index 0000000000..f1374dae3d
--- /dev/null
+++ b/src/ForceFreeStates/ForceFreeStates.jl
@@ -0,0 +1,80 @@
+module ForceFreeStates
+
+using LinearAlgebra
+using LinearAlgebra.LAPACK
+using TOML
+using FFTW
+using OrdinaryDiffEq
+using HDF5
+using JLD2
+using FastInterpolations
+using AdaptiveArrayPools
+using Roots
+using FastGaussQuadrature: gausslobatto
+using QuadGK: quadgk, quadgk!
+import CommonSolve
+
+import ..Equilibrium
+import ..Utilities
+import ..Utilities: save_to_hdf5
+using ..Utilities.HermiteFEM: hermite_basis, pack_grid
+import ..Vacuum
+import ..InnerLayer
+using Printf
+using DoubleFloats
+import StaticArrays: @MMatrix
+
+# Types with cross-subsystem consumers, loaded before the code that dispatches on them
+include("Surfaces/Types.jl")
+include("Integrators.jl")
+include("CoreTypes.jl")
+include("Riccati/Types.jl")
+include("Fourfit.jl")
+include("Matching/DeltaPrime.jl")
+
+include("EulerLagrange.jl")
+
+# Singular-surface machinery: finding/filtering, Frobenius asymptotics, GGJ coefficients
+include("Surfaces/Finding.jl")
+include("Surfaces/Asymptotics.jl")
+include("Surfaces/ResistEval.jl")
+
+# Outer<->inner resistive matching
+include("Matching/ResonantMatch.jl")
+
+include("FixedKineticMatrices.jl")
+include("Kinetic.jl")
+include("FixedBoundaryStability.jl")
+include("Utils.jl")
+include("Free.jl")
+
+# Chunked fundamental-matrix (Riccati/STRIDE) driver
+include("Riccati/Propagators.jl")
+include("Riccati/Crossings.jl")
+include("Riccati/DeltaPrimeBVP.jl")
+include("Riccati/Driver.jl")
+
+# RDCON outer-region singular Galerkin Δ′ solver (gal_solve port)
+include("Galerkin/GalerkinStructs.jl")
+include("Galerkin/GalerkinGrid.jl")
+include("Galerkin/GalerkinAssembly.jl")
+include("Galerkin/GalerkinSolution.jl")
+include("Galerkin/GalerkinSolve.jl")
+
+
+# The published solve product; last, so it can name every type the stages above define.
+include("Result.jl")
+
+# Post-solve inner-layer matching: consumes and produces ForceFreeStatesResult, so it loads
+# after the result machinery.
+include("Matching/MatchProblem.jl")
+include("InputSnapshot.jl")
+include("Output.jl")
+include("Run.jl")
+include("ForceBalance.jl")
+
+# Small tolerance and root-finder iteration cap used throughout ForceFreeStates
+global eps = 1e-10
+global itmax = 50
+
+end
diff --git a/src/ForceFreeStates/Fourfit.jl b/src/ForceFreeStates/Fourfit.jl
new file mode 100644
index 0000000000..8b49b311da
--- /dev/null
+++ b/src/ForceFreeStates/Fourfit.jl
@@ -0,0 +1,613 @@
+"""
+ IdealMatrices
+
+Ideal-MHD stability matrix ψ-splines assembled by [`build_matrix_splines`](@ref). Each field flattens a
+`numpert_total × numpert_total` matrix to `numpert_total^2` complex series (`J_spline` to `2·mpert−1`),
+following the appendix of Glasser Phys. Plasmas 2016 112506.
+
+Suffixes: `_prim` is a primitive (pre-Schur-complement) form, kept because the kinetic reduction
+needs the unreduced matrix; `_lower` is a Cholesky factor rather than the matrix itself; `_gal` is
+the Galerkin solver's variant of the same matrix.
+
+## Fields
+
+ - `A_spline`, `B_spline`, `C_spline` - the ideal A, B, C. In a kinetic run these are NOT what the
+ ODE integrates; see [`FKGMatrices`](@ref).
+ - `D_spline_prim`, `E_spline_prim` - pre-Schur-reduction geometric forms
+ (D = χ₁·(g23 + q·g33·m/n); E = (-χ₁/n)·(q'·χ₁·g33 - 2π·i·χ₁·g31·singfac + jθ·I)). Downstream
+ kinetic FKG Schur complements consume these primitive forms.
+ - `H_spline` - primitive Ḡ before the Schur complement (Ḡ = H − C†A⁻¹C), also consumed by the
+ kinetic reduction.
+ - `F_spline_lower` - reduced F̄ as its lower-triangular Cholesky factor L, F̄ = L·Lᴴ. The ideal
+ Euler-Lagrange kernel only ever solves against F̄, so the factor is stored instead of F̄ itself.
+ - `F_spline_prim` - primitive F before the Schur complement (for kinetic).
+ - `F_spline_gal` - independently interpolated reduced Hermitian F̄, retained for coefficient diagnostics.
+ - `K_spline`, `G_spline` - reduced K̄ and Ḡ of the Euler-Lagrange system
+ d/dψ(F̄·ξ′ + K̄·ξ) = K̄†·ξ′ + Ḡ·ξ (Eqs A5-A7).
+ - `J_spline` - Jacobian Fourier band (2·mpert−1 conjugate-symmetric coefficients per surface), used
+ to assemble the power-normalization matrix N in Free.jl.
+"""
+@kwdef struct IdealMatrices{S<:CubicSeriesInterpolant}
+ A_spline::S
+ B_spline::S
+ C_spline::S
+ D_spline_prim::S
+ E_spline_prim::S
+ H_spline::S
+ F_spline_lower::S
+ F_spline_prim::S
+ F_spline_gal::S
+ K_spline::S
+ G_spline::S
+ J_spline::S
+end
+
+"""
+ FKGMatrices
+
+Kinetic-MHD matrix ψ-splines assembled by [`build_kinetic_matrix_splines`](@ref). Present on a
+[`MatrixSplines`](@ref) only for kinetic runs; its presence means the solution obeys the FKG ODE
+rather than the ideal Euler-Lagrange relation.
+
+The FKG system is non-Hermitian, so the adjoint side of each reduced block is a distinct matrix
+rather than a transpose of the forward one. The `_adj` suffix marks those adjoint-side counterparts
+(Fortran's `aat` arrays); they must be evaluated, never derived from their unsuffixed partner.
+
+## Fields
+
+ - `A_spline`, `B_spline`, `C_spline` - the kinetic-modified A, B, C consumed by `sing_der!`. Unlike their
+ ideal counterparts, A here is non-Hermitian and requires an LU rather than a Cholesky.
+ - `F0_spline` - reduced F̄ of the kinetic system, F₀ = F_prim − D†A_kin⁻¹D.
+ - `P_spline`, `P_spline_adj` - P = (iD)†A_kin⁻¹B_k and its adjoint-side counterpart.
+ - `Kk_spline`, `Kk_spline_adj` - kinetic K̄ = E − (iD)†A_kin⁻¹C_kin and its adjoint-side counterpart.
+ - `R1_spline`, `R2_spline`, `R3_spline` - blocks built from the D- and E-perturbation kinetic
+ components of the kinetic energy and torque matrices, which have no ideal counterpart. R3 is the
+ adjoint-side partner of R2.
+ - `G_spline_adj` - adjoint-side Ḡ, Ḡ_adj = H_kin − C_adj†A_kin⁻¹C_kin.
+
+All nine reduced blocks are pre-computed per ψ by the FKG Schur complement
+(Logan 2015 Appendix C, Eqs C.1-C.11) so `sing_der!` can assemble the ODE right-hand side with
+explicit (m−nq) factors instead of 1/(m−nq).
+"""
+@kwdef struct FKGMatrices{S<:CubicSeriesInterpolant}
+ A_spline::S
+ B_spline::S
+ C_spline::S
+ F0_spline::S
+ P_spline::S
+ P_spline_adj::S
+ Kk_spline::S
+ Kk_spline_adj::S
+ R1_spline::S
+ R2_spline::S
+ R3_spline::S
+ G_spline_adj::S
+end
+
+"""
+ MatrixSplines
+
+Fourier-fitted stability matrices for one run. `kinetic === nothing` marks an ideal run; otherwise
+the kinetic matrices are authoritative for the ODE and the ideal ones remain available for output
+and for the Galerkin/vacuum paths that are defined only in the ideal basis.
+
+## Fields
+
+ - `ideal::IdealMatrices` - always present.
+ - `kinetic::Union{Nothing,FKGMatrices}` - present iff the solve is kinetic (`ctrl.kinetic !== nothing`).
+ - `_hint::Base.RefValue{Int}` - shared bracket-search hint for sequential (single-threaded)
+ evaluation. Not thread-safe: parallel paths must pass their own hint.
+"""
+@kwdef struct MatrixSplines{S<:CubicSeriesInterpolant}
+ ideal::IdealMatrices{S}
+ kinetic::Union{Nothing,FKGMatrices{S}} = nothing
+ _hint::Base.RefValue{Int} = Ref(1)
+end
+
+# Helper to create an empty complex series interpolant for default initialization
+function _empty_series_interp_complex(n_series::Int)
+ xs = collect(range(0.0, 1.0; length=5))
+ Y = zeros(ComplexF64, 5, n_series)
+ return cubic_interp(xs, Series(Y))
+end
+
+"""
+ MetricData
+
+Metric tensor components on the (ψ, θ) grid and their Fourier representation.
+
+## Fields
+
+ - `mpsi::Int`: Number of radial grid points minus one.
+ - `mtheta::Int`: Number of poloidal grid points minus one.
+ - `xs::Vector{Float64}`: Radial coordinates (normalized poloidal flux `ψ_norm`).
+ - `ys::Vector{Float64}`: Poloidal angle coordinates `θ` in radians (0 to 2π).
+ - `fs::Array{Float64, 3}`: The raw metric data on the grid, size `(mpsi, mtheta, 8)`.
+ The 8 quantities are: `g¹¹`, `g²²`, `g³³`, `g²³`, `g³¹`, `g¹²`, `J`, `∂J/∂ψ`.
+ - `fourier_coeffs::Utilities.FourierCoefficients`: The FFT coefficients (no spline interpolation needed).
+"""
+@kwdef mutable struct MetricData
+ mpsi::Int
+ mtheta::Int
+ xs::Vector{Float64} = zeros(mpsi)
+ ys::Vector{Float64} = zeros(mtheta)
+ fs::Array{Float64,3} = zeros(mpsi, mtheta, 8)
+ fourier_coeffs::Utilities.FourierCoefficients = Utilities.empty_FourierCoefficients()
+end
+
+MetricData(mpsi::Int, mtheta::Int) = MetricData(; mpsi, mtheta)
+
+"""
+ make_metric(equil::Equilibrium.PlasmaEquilibrium, mpert::Int) -> MetricData
+
+Construct the metric tensor data on the (ψ, θ) grid of `equil`, Fourier-decomposed up to
+harmonic `mpert - 1`. The coefficients stored in `metric.fs` are:
+
+ 1. g_ψψ / J
+ 2. g_θθ / J
+ 3. g_ζζ / J
+ 4. g_θζ / J
+ 5. g_ζψ / J
+ 6. g_ψθ / J
+ 7. J (Jacobian)
+ 8. ∂J/∂ψ
+"""
+function make_metric(equil::Equilibrium.PlasmaEquilibrium, mpert::Int)
+
+ # --- Extract data from the PlasmaEquilibrium object ---
+ mpsi = length(equil.rzphi_xs)
+ mtheta = length(equil.rzphi_ys)
+
+ # Set coordinate grids based on the input equilibrium
+ # The equil.rzphi_ys is normalized (0 to 1), so scale to radians.
+ metric = MetricData(mpsi, mtheta)
+ metric.xs .= equil.rzphi_xs
+ metric.ys .= equil.rzphi_ys .* 2π
+
+ # Temporary array for the covariant basis vectors over J
+ v = @MMatrix zeros(Float64, 3, 3)
+
+ # --- Main computation loop over the (ψ, θ) grid ---
+ # Access grid point values and derivatives directly from interpolant storage
+ for ipsi in 1:mpsi
+ for jtheta in 1:mtheta
+ theta_norm = equil.rzphi_ys[jtheta] # θ is from 0 to 1
+
+ # Grid point values: nodal_derivs.partials[1,:,:] = f, [2,:,:] = ∂f/∂ψ, [3,:,:] = ∂f/∂θ
+ r_coord_sq = equil.rzphi_rsquared.nodal_derivs.partials[1, ipsi, jtheta]
+ eta_offset = equil.rzphi_offset.nodal_derivs.partials[1, ipsi, jtheta]
+ jac = equil.rzphi_jac.nodal_derivs.partials[1, ipsi, jtheta]
+ jac1 = equil.rzphi_jac.nodal_derivs.partials[2, ipsi, jtheta] # ∂J/∂ψ
+
+ rfac = sqrt(r_coord_sq)
+ eta = 2π * (theta_norm + eta_offset)
+ r_major = equil.ro + rfac * cos(eta) # This is the R coordinate
+
+ # --- Covariant basis vectors e_ψ, e_θ, e_ζ divided by J ---
+ fx1 = equil.rzphi_rsquared.nodal_derivs.partials[2, ipsi, jtheta]
+ fx2 = equil.rzphi_offset.nodal_derivs.partials[2, ipsi, jtheta]
+ fx3 = equil.rzphi_nu.nodal_derivs.partials[2, ipsi, jtheta]
+ fy1 = equil.rzphi_rsquared.nodal_derivs.partials[3, ipsi, jtheta]
+ fy2 = equil.rzphi_offset.nodal_derivs.partials[3, ipsi, jtheta]
+ fy3 = equil.rzphi_nu.nodal_derivs.partials[3, ipsi, jtheta]
+
+ v[1, 1] = fx1 / (2.0 * rfac * jac)
+ v[1, 2] = fx2 * 2π * rfac / jac
+ v[1, 3] = fx3 * r_major / jac
+ v[2, 1] = fy1 / (2.0 * rfac * jac)
+ v[2, 2] = (1.0 + fy2) * 2π * rfac / jac
+ v[2, 3] = fy3 * r_major / jac
+ v[3, 3] = 2π * r_major / jac
+
+ # Store results
+ v1 = @view v[1, :]
+ v2 = @view v[2, :]
+ metric.fs[ipsi, jtheta, 1] = dot(v1, v1) * jac
+ metric.fs[ipsi, jtheta, 2] = dot(v2, v2) * jac
+ metric.fs[ipsi, jtheta, 3] = v[3, 3] * v[3, 3] * jac
+ metric.fs[ipsi, jtheta, 4] = v[2, 3] * v[3, 3] * jac
+ metric.fs[ipsi, jtheta, 5] = v[3, 3] * v[1, 3] * jac
+ metric.fs[ipsi, jtheta, 6] = dot(v1, v2) * jac
+ metric.fs[ipsi, jtheta, 7] = jac
+ metric.fs[ipsi, jtheta, 8] = jac1
+ end
+ end
+
+ # FFT after dropping the duplicated θ=2π endpoint (matches Fortran fspline_fit_2)
+ metric.fourier_coeffs = Utilities.FourierCoefficients(metric.xs, metric.ys, metric.fs, mpert - 1)
+ return metric
+end
+
+"""
+ build_kinetic_metric_matrices(equil, intr, metric) → NamedTuple
+
+Compute the 5 kinetic geometric matrices (s, t, x, y, z) needed by
+`KineticForces.BounceAveraging` for kinetic W vector outer products, for every toroidal mode n in
+`intr.nlow:intr.nhigh`. Only Y (through m - nq) and Z (through n) depend on n; S, T and X are
+repeated in each block so all five share one layout.
+
+# Returns
+
+NamedTuple `(smats, tmats, xmats, ymats, zmats)` of `CubicSeriesInterpolant`s, each mapping
+ψ → a complex vector of `npert` stacked mpert×mpert blocks (column-major, length mpert²·npert);
+block k holds n = nlow + k - 1. Use `kinetic_metric_block` to extract one block.
+
+Reference: [Logan et al., Phys. Plasmas 20, 122507 (2013)]
+"""
+function build_kinetic_metric_matrices(equil::Equilibrium.PlasmaEquilibrium,
+ intr::ModeSpace,
+ metric::MetricData)
+ (; mpert, nlow, nhigh, mlow, mhigh) = intr
+ mpsi = metric.mpsi
+ mtheta = metric.mtheta
+ chi1 = 2π * equil.psio
+
+ # Allocate fmodb grid: 8 quantities on (ψ,θ)
+ fmodb_fs = zeros(Float64, mpsi, mtheta, 8)
+
+ # Temporary for the covariant basis vectors (Fortran style, WITHOUT /jac)
+ v = @MMatrix zeros(Float64, 3, 3)
+ hint = Ref(1)
+
+ for ipsi in 1:mpsi
+ psi = metric.xs[ipsi]
+ p1 = equil.profiles.P_deriv(psi; hint=hint)
+ q = equil.profiles.q_spline.y[ipsi]
+
+ for jtheta in 1:mtheta
+ # Grid point values via nodal_derivs (same grid as make_metric)
+ r_coord_sq = equil.rzphi_rsquared.nodal_derivs.partials[1, ipsi, jtheta]
+ eta_offset = equil.rzphi_offset.nodal_derivs.partials[1, ipsi, jtheta]
+ jac = equil.rzphi_jac.nodal_derivs.partials[1, ipsi, jtheta]
+ jac1 = equil.rzphi_jac.nodal_derivs.partials[2, ipsi, jtheta]
+
+ rfac = sqrt(r_coord_sq)
+ theta_norm = equil.rzphi_ys[jtheta]
+ eta = 2π * (theta_norm + eta_offset)
+ rs = equil.ro + rfac * cos(eta) # R coordinate
+
+ # ∂/∂ψ and ∂/∂θ of (r², offset, nu)
+ fx1 = equil.rzphi_rsquared.nodal_derivs.partials[2, ipsi, jtheta]
+ fx2 = equil.rzphi_offset.nodal_derivs.partials[2, ipsi, jtheta]
+ fx3 = equil.rzphi_nu.nodal_derivs.partials[2, ipsi, jtheta]
+ fy1 = equil.rzphi_rsquared.nodal_derivs.partials[3, ipsi, jtheta]
+ fy2 = equil.rzphi_offset.nodal_derivs.partials[3, ipsi, jtheta]
+ fy3 = equil.rzphi_nu.nodal_derivs.partials[3, ipsi, jtheta]
+
+ # Covariant basis vectors WITHOUT /jac (unlike make_metric)
+ v[1, 1] = fx1 / (2.0 * rfac)
+ v[1, 2] = fx2 * 2π * rfac
+ v[1, 3] = fx3 * rs
+ v[2, 1] = fy1 / (2.0 * rfac)
+ v[2, 2] = (1.0 + fy2) * 2π * rfac
+ v[2, 3] = fy3 * rs
+ v[3, 3] = 2π * rs
+
+ # Raw covariant metric g_ij
+ g12 = v[1, 1] * v[2, 1] + v[1, 2] * v[2, 2] + v[1, 3] * v[2, 3]
+ g13 = v[3, 3] * v[1, 3]
+ g22 = v[2, 1]^2 + v[2, 2]^2 + v[2, 3]^2
+ g23 = v[2, 3] * v[3, 3]
+ g33 = v[3, 3]^2
+
+ # B field and derivatives
+ B = equil.eqfun_B.nodal_derivs.partials[1, ipsi, jtheta]
+ dBdpsi = equil.eqfun_B.nodal_derivs.partials[2, ipsi, jtheta]
+ dBdtheta = equil.eqfun_B.nodal_derivs.partials[3, ipsi, jtheta]
+ b2h = B^2 / 2
+ b2hp = B * dBdpsi
+ b2ht = B * dBdtheta
+
+ # θ-derivatives of eqfun metric quantities (Fortran eqfun%fy(2), eqfun%fy(3))
+ eqfun_fy2 = equil.eqfun_metric1.nodal_derivs.partials[3, ipsi, jtheta]
+ eqfun_fy3 = equil.eqfun_metric2.nodal_derivs.partials[3, ipsi, jtheta]
+
+ # 8 fmodb quantities
+ fmodb_fs[ipsi, jtheta, 1] = jac * (p1 + b2hp) -
+ chi1^2 * b2ht * (g12 + q * g13) / (jac * b2h * 2) # sband
+ fmodb_fs[ipsi, jtheta, 2] =
+ chi1^2 * b2ht * (g23 + q * g33) / (jac * b2h * 2) # tband
+ fmodb_fs[ipsi, jtheta, 3] = jac * b2h * 2 # xband
+ fmodb_fs[ipsi, jtheta, 4] = jac1 * b2h * 2 -
+ chi1^2 * b2h * 2 * eqfun_fy2 # yband1
+ fmodb_fs[ipsi, jtheta, 5] =
+ -2π * chi1^2 / jac * (g12 + q * g13) # yband2
+ fmodb_fs[ipsi, jtheta, 6] =
+ chi1^2 * b2h * 2 * eqfun_fy3 # zband1
+ fmodb_fs[ipsi, jtheta, 7] =
+ 2π * chi1^2 / jac * (g23 + q * g33) # zband2
+ fmodb_fs[ipsi, jtheta, 8] =
+ 2π * chi1^2 / jac * (g22 + q * g23) # zband3
+ end
+ end
+
+ # Fourier decompose (same approach as metric)
+ fmodb_fc = Utilities.FourierCoefficients(metric.xs, metric.ys, fmodb_fs, mpert - 1)
+
+ # Allocate flat storage for mpert×mpert matrices at each ψ
+ npert = nhigh - nlow + 1
+ smats_flat = zeros(ComplexF64, mpsi, mpert^2 * npert)
+ tmats_flat = zeros(ComplexF64, mpsi, mpert^2 * npert)
+ xmats_flat = zeros(ComplexF64, mpsi, mpert^2 * npert)
+ ymats_flat = zeros(ComplexF64, mpsi, mpert^2 * npert)
+ zmats_flat = zeros(ComplexF64, mpsi, mpert^2 * npert)
+
+ # Fourier band storage
+ sband = Vector{ComplexF64}(undef, 2 * mpert - 1)
+ tband = Vector{ComplexF64}(undef, 2 * mpert - 1)
+ xband = Vector{ComplexF64}(undef, 2 * mpert - 1)
+ yband1 = Vector{ComplexF64}(undef, 2 * mpert - 1)
+ yband2 = Vector{ComplexF64}(undef, 2 * mpert - 1)
+ zband1 = Vector{ComplexF64}(undef, 2 * mpert - 1)
+ zband2 = Vector{ComplexF64}(undef, 2 * mpert - 1)
+ zband3 = Vector{ComplexF64}(undef, 2 * mpert - 1)
+
+ for ipsi in 1:mpsi
+ q = equil.profiles.q_spline.y[ipsi]
+
+ # Fourier bands, conjugate-symmetric for ± modes
+ for m in 0:(mpert-1)
+ sband[mpert-m] = Utilities.get_complex_coeff(fmodb_fc, ipsi, m, 1)
+ tband[mpert-m] = Utilities.get_complex_coeff(fmodb_fc, ipsi, m, 2)
+ xband[mpert-m] = Utilities.get_complex_coeff(fmodb_fc, ipsi, m, 3)
+ yband1[mpert-m] = Utilities.get_complex_coeff(fmodb_fc, ipsi, m, 4)
+ yband2[mpert-m] = Utilities.get_complex_coeff(fmodb_fc, ipsi, m, 5)
+ zband1[mpert-m] = Utilities.get_complex_coeff(fmodb_fc, ipsi, m, 6)
+ zband2[mpert-m] = Utilities.get_complex_coeff(fmodb_fc, ipsi, m, 7)
+ zband3[mpert-m] = Utilities.get_complex_coeff(fmodb_fc, ipsi, m, 8)
+ end
+ for k in 1:(mpert-1)
+ sband[k+mpert] = conj(sband[mpert-k])
+ tband[k+mpert] = conj(tband[mpert-k])
+ xband[k+mpert] = conj(xband[mpert-k])
+ yband1[k+mpert] = conj(yband1[mpert-k])
+ yband2[k+mpert] = conj(yband2[mpert-k])
+ zband1[k+mpert] = conj(zband1[mpert-k])
+ zband2[k+mpert] = conj(zband2[mpert-k])
+ zband3[k+mpert] = conj(zband3[mpert-k])
+ end
+
+ # Assemble the mpert×mpert block of each n
+ for n in nlow:nhigh
+ block_offset = (n - nlow) * mpert^2
+ for m1 in mlow:mhigh
+ ipert = m1 - mlow + 1
+ nq = n * q
+ for dm in (1-ipert):(mpert-ipert)
+ m2 = m1 + dm
+ singfac2 = m2 - nq
+ jpert = ipert + dm
+ dmidx = dm + mpert
+ iflat = block_offset + ipert + (jpert - 1) * mpert
+
+ smats_flat[ipsi, iflat] = sband[dmidx]
+ tmats_flat[ipsi, iflat] = tband[dmidx]
+ xmats_flat[ipsi, iflat] = xband[dmidx]
+ ymats_flat[ipsi, iflat] = yband1[dmidx] + im * singfac2 * yband2[dmidx]
+ zmats_flat[ipsi, iflat] = zband1[dmidx] + im * (m2 * zband2[dmidx] + n * zband3[dmidx])
+ end
+ end
+ end
+ end
+
+ # Create CubicSeriesInterpolants over ψ
+ itp_opts = (; extrap=ExtendExtrap())
+ smats = cubic_interp(metric.xs, Series(smats_flat); itp_opts...)
+ tmats = cubic_interp(metric.xs, Series(tmats_flat); itp_opts...)
+ xmats = cubic_interp(metric.xs, Series(xmats_flat); itp_opts...)
+ ymats = cubic_interp(metric.xs, Series(ymats_flat); itp_opts...)
+ zmats = cubic_interp(metric.xs, Series(zmats_flat); itp_opts...)
+
+ return (; smats, tmats, xmats, ymats, zmats)
+end
+
+"""
+ kinetic_metric_block(itp, psi, mpert, k) → Matrix{ComplexF64}
+
+The mpert×mpert block `k` (toroidal mode n = nlow + k - 1) at ψ of a geometric-matrix
+interpolant from `build_kinetic_metric_matrices`.
+"""
+function kinetic_metric_block(itp, psi::Real, mpert::Int, k::Int)
+ v = itp(psi)
+ return reshape(v[((k-1)*mpert^2+1):(k*mpert^2)], mpert, mpert)
+end
+
+
+"""
+ core_capped_knots(xs, rationals) -> Vector{Int}
+
+Indices of `xs` the EL coefficient splines keep. Below the innermost rational (or ψ = 0.1, whichever
+is smaller) knots are thinned to log-uniform spacing Δψ ≥ 0.05·ψ, which resolves the near-axis
+Frobenius power laws at constant relative accuracy and stops dense core packing from amplifying node
+error into spline third-derivative jumps that throttle the Euler-Lagrange step size. Knots inside a
+rational's resolution window (`Equilibrium.RATIONAL_RES_RADIUS`) are always kept.
+"""
+function core_capped_knots(xs::Vector{Float64}, rationals::Vector{Float64})::Vector{Int}
+ length(xs) < 3 && return collect(eachindex(xs))
+ cap_edge = 0.1
+ isempty(rationals) || (cap_edge = min(cap_edge, minimum(rationals) - Equilibrium.RATIONAL_RES_RADIUS))
+ in_rational_window(x) = any(abs(x - r) <= Equilibrium.RATIONAL_RES_RADIUS for r in rationals)
+ keep = Int[1]
+ for i in 2:(length(xs)-1)
+ x = xs[i]
+ (x >= cap_edge || in_rational_window(x) || (x - xs[keep[end]]) >= 0.05 * x) && push!(keep, i)
+ end
+ push!(keep, length(xs))
+ return keep
+end
+
+"""
+ build_matrix_splines(equil::Equilibrium.PlasmaEquilibrium, intr::ForceFreeStatesInternal, metric::MetricData) -> MatrixSplines
+
+Assemble the ideal-MHD stability matrices on every ψ surface of `metric` and fit them as ψ-splines
+(Glasser Phys. Plasmas 2016 112506 Appendix A). F̄ is stored as its lower Cholesky factor
+(F̄ = L·Lᴴ), since `sing_der!` only solves against it; see [`IdealMatrices`](@ref) for the fields.
+"""
+function build_matrix_splines(equil::Equilibrium.PlasmaEquilibrium, intr::ForceFreeStatesInternal, metric::MetricData)
+
+ # --- Extract inputs ---
+ profiles = equil.profiles
+ mpsi = metric.mpsi
+
+ # Flat storage for the spline fits; zeros (not undef) keeps the n≠n' blocks zero for multi-n
+ amats_flat = zeros(ComplexF64, mpsi, intr.numpert_total^2)
+ bmats_flat = zeros(ComplexF64, mpsi, intr.numpert_total^2)
+ cmats_flat = zeros(ComplexF64, mpsi, intr.numpert_total^2)
+ dmats_flat = zeros(ComplexF64, mpsi, intr.numpert_total^2)
+ emats_flat = zeros(ComplexF64, mpsi, intr.numpert_total^2)
+ hmats_flat = zeros(ComplexF64, mpsi, intr.numpert_total^2)
+ fmats_lower_flat = zeros(ComplexF64, mpsi, intr.numpert_total^2)
+ fmats_prim_flat = zeros(ComplexF64, mpsi, intr.numpert_total^2) # primitive F before Schur complement (for kinetic)
+ fmats_gal_flat = zeros(ComplexF64, mpsi, intr.numpert_total^2) # reduced Hermitian F̄ (before Cholesky) for the Galerkin solver
+ gmats_flat = zeros(ComplexF64, mpsi, intr.numpert_total^2)
+ kmats_flat = zeros(ComplexF64, mpsi, intr.numpert_total^2)
+ g11 = Vector{ComplexF64}(undef, 2 * intr.mpert - 1)
+ g22 = Vector{ComplexF64}(undef, 2 * intr.mpert - 1)
+ g33 = Vector{ComplexF64}(undef, 2 * intr.mpert - 1)
+ g23 = Vector{ComplexF64}(undef, 2 * intr.mpert - 1)
+ g31 = Vector{ComplexF64}(undef, 2 * intr.mpert - 1)
+ g12 = Vector{ComplexF64}(undef, 2 * intr.mpert - 1)
+ jmat = Vector{ComplexF64}(undef, 2 * intr.mpert - 1)
+ jmat1 = Vector{ComplexF64}(undef, 2 * intr.mpert - 1)
+ jmats_flat = zeros(ComplexF64, mpsi, 2 * intr.mpert - 1)
+ a_inv_dmat_temp = Matrix{ComplexF64}(undef, intr.numpert_total, intr.numpert_total)
+ a_inv_cmat_temp = Matrix{ComplexF64}(undef, intr.numpert_total, intr.numpert_total)
+
+ imat = zeros(ComplexF64, 2 * intr.mpert - 1)
+ imat[intr.mpert] = 1 + 0im
+
+ hint = Ref(1) # Linear search hint for sequential psi access
+ for ipsi in 1:mpsi
+ # --- Create views for this surface ---
+ amats_flatview = @view amats_flat[ipsi, :]
+ bmats_flatview = @view bmats_flat[ipsi, :]
+ cmats_flatview = @view cmats_flat[ipsi, :]
+ dmats_flatview = @view dmats_flat[ipsi, :]
+ emats_flatview = @view emats_flat[ipsi, :]
+ hmats_flatview = @view hmats_flat[ipsi, :]
+ fmats_lower_flatview = @view fmats_lower_flat[ipsi, :]
+ gmats_flatview = @view gmats_flat[ipsi, :]
+ kmats_flatview = @view kmats_flat[ipsi, :]
+ # --- Profiles ---
+ psi = profiles.xs[ipsi]
+ p1 = profiles.P_deriv(psi; hint=hint)
+ q = profiles.q_spline.y[ipsi]
+ q1 = profiles.q_deriv(psi; hint=hint)
+ jtheta = -profiles.F_deriv(psi; hint=hint)
+ chi1 = 2π * equil.psio
+
+ # Fill modes 0, 1, ..., mpert-1 with conjugate symmetry for ± modes
+ fc = metric.fourier_coeffs
+ for m in 0:(intr.mpert-1)
+ g11[intr.mpert-m] = Utilities.get_complex_coeff(fc, ipsi, m, 1)
+ g22[intr.mpert-m] = Utilities.get_complex_coeff(fc, ipsi, m, 2)
+ g33[intr.mpert-m] = Utilities.get_complex_coeff(fc, ipsi, m, 3)
+ g23[intr.mpert-m] = Utilities.get_complex_coeff(fc, ipsi, m, 4)
+ g31[intr.mpert-m] = Utilities.get_complex_coeff(fc, ipsi, m, 5)
+ g12[intr.mpert-m] = Utilities.get_complex_coeff(fc, ipsi, m, 6)
+ jmat[intr.mpert-m] = Utilities.get_complex_coeff(fc, ipsi, m, 7)
+ jmat1[intr.mpert-m] = Utilities.get_complex_coeff(fc, ipsi, m, 8)
+ end
+ for k in 1:(intr.mpert-1)
+ g11[k+intr.mpert] = conj(g11[intr.mpert-k])
+ g22[k+intr.mpert] = conj(g22[intr.mpert-k])
+ g33[k+intr.mpert] = conj(g33[intr.mpert-k])
+ g23[k+intr.mpert] = conj(g23[intr.mpert-k])
+ g31[k+intr.mpert] = conj(g31[intr.mpert-k])
+ g12[k+intr.mpert] = conj(g12[intr.mpert-k])
+ jmat[k+intr.mpert] = conj(jmat[intr.mpert-k])
+ jmat1[k+intr.mpert] = conj(jmat1[intr.mpert-k])
+ end
+ # Save the Jacobian Fourier band at every surface for the power-normalization spline
+ @views jmats_flat[ipsi, :] .= jmat
+
+ for n in intr.nlow:intr.nhigh
+ ipert_n = n - intr.nlow + 1
+ nq = n * q
+ # Construct primitive matrices via m1/dm loops
+ for m1 in intr.mlow:intr.mhigh
+ ipert_m = m1 - intr.mlow + 1
+ singfac1 = m1 - nq
+ for dm in (1-ipert_m):(intr.mpert-ipert_m)
+ m2 = m1 + dm
+ singfac2 = m2 - nq
+ jpert_m = ipert_m + dm
+ dmidx = dm + intr.mpert
+ # Flattened (m, n) × (m', n') index; n' = n in 2D
+ ipert = ipert_m + (ipert_n - 1) * intr.mpert
+ jpert = jpert_m + (ipert_n - 1) * intr.mpert
+ ipert_flat = ipert + (jpert - 1) * intr.numpert_total
+
+ # dmat/emat are the subterms of the composite matrices in Eqs. A7-A8, not the D, E of Eq. A6
+ amats_flatview[ipert_flat] = (2π)^2 * (n^2 * g22[dmidx] + n * (m1 + m2) * g23[dmidx] + m1 * m2 * g33[dmidx])
+ bmats_flatview[ipert_flat] = -2π * im * chi1 * (n * g22[dmidx] + (m1 + nq) * g23[dmidx] + m1 * q * g33[dmidx])
+ cmats_flatview[ipert_flat] =
+ 2π * im * ((2π * im * chi1 * singfac2 * (n * g12[dmidx] + m1 * g31[dmidx])) -
+ (q1 * chi1 * (n * g23[dmidx] + m1 * g33[dmidx]))) -
+ 2π * im * (jtheta * singfac1 * imat[dmidx] + n * p1 / chi1 * jmat[dmidx])
+ dmats_flatview[ipert_flat] = 2π * chi1 * (g23[dmidx] + g33[dmidx] * m1 / n)
+ emats_flatview[ipert_flat] = -chi1 / n * (q1 * chi1 * g33[dmidx] - 2π * im * chi1 * g31[dmidx] * singfac2 + jtheta * imat[dmidx])
+ hmats_flatview[ipert_flat] =
+ (q1 * chi1)^2 * g33[dmidx] +
+ (2π * chi1)^2 * singfac1 * singfac2 * g11[dmidx] -
+ 2π * im * chi1 * dm * q1 * chi1 * g31[dmidx] +
+ jtheta * q1 * chi1 * imat[dmidx] +
+ p1 * jmat1[dmidx]
+ fmats_lower_flatview[ipert_flat] = (chi1 / n)^2 * g33[dmidx]
+ kmats_flatview[ipert_flat] = 2π * im * chi1 * (g23[dmidx] + g33[dmidx] * m1 / n)
+ end
+ end
+ end
+
+ # Factorize and build composite matrices [Glasser Phys. Plasmas 2016 112506 Appendix A]
+ # Nonsingular forms F̄ and K̄ with F = QF̄Qᴴ, K = QK̄ [Glasser Phys. Plasmas 2016 112506 eq. 29]
+ # We multiply by Q (singfac = m - n*q) later when performing computations
+ amat = reshape(amats_flatview, intr.numpert_total, intr.numpert_total)
+ cmat = reshape(cmats_flatview, intr.numpert_total, intr.numpert_total)
+ dmat = reshape(dmats_flatview, intr.numpert_total, intr.numpert_total)
+ emat = reshape(emats_flatview, intr.numpert_total, intr.numpert_total)
+ hmat = reshape(hmats_flatview, intr.numpert_total, intr.numpert_total)
+ fmat = reshape(fmats_lower_flatview, intr.numpert_total, intr.numpert_total)
+ kmat = reshape(kmats_flatview, intr.numpert_total, intr.numpert_total)
+ gmat = reshape(gmats_flatview, intr.numpert_total, intr.numpert_total)
+
+ # Save primitive F for kinetic matrix construction (before Schur complement)
+ @views fmats_prim_flat[ipsi, :] .= fmats_lower_flatview
+
+ # Schur complement reduction [Glasser Phys. Plasmas 2016 112506 eq. A5-A7]
+ amat_fact = cholesky(Hermitian(amat, :L))
+ ldiv!(a_inv_dmat_temp, amat_fact, dmat) # A⁻¹D
+ ldiv!(a_inv_cmat_temp, amat_fact, cmat) # A⁻¹C
+ fmat .-= adjoint(dmat) * a_inv_dmat_temp # F̃ = F - D†A⁻¹D
+ kmat .= emat .- (adjoint(kmat) * a_inv_cmat_temp) # K̃ = E - K†A⁻¹C
+ gmat .= hmat .- (adjoint(cmat) * a_inv_cmat_temp) # G̃ = H - C†A⁻¹C
+
+ # Keep the full reduced F̄ before it is overwritten by its Cholesky factor below
+ @views fmats_gal_flat[ipsi, :] .= vec(fmat)
+
+ # Store F̄ as its lower Cholesky factor; consumers only ever solve against F̄
+ fmat .= cholesky(Hermitian(fmat)).L
+ end
+
+ # Complex series interpolants over the core-capped knot grid
+ itp_opts = (; extrap=ExtendExtrap())
+ keep = core_capped_knots(metric.xs, [s.psifac for s in intr.sing])
+ mxs = metric.xs[keep]
+ length(mxs) < length(metric.xs) &&
+ @info "EL coefficient-spline grid: $(length(metric.xs)) -> $(length(mxs)) knots after core density cap"
+ ideal = IdealMatrices(;
+ A_spline=cubic_interp(mxs, Series(amats_flat[keep, :]); itp_opts...),
+ B_spline=cubic_interp(mxs, Series(bmats_flat[keep, :]); itp_opts...),
+ C_spline=cubic_interp(mxs, Series(cmats_flat[keep, :]); itp_opts...),
+ D_spline_prim=cubic_interp(mxs, Series(dmats_flat[keep, :]); itp_opts...),
+ E_spline_prim=cubic_interp(mxs, Series(emats_flat[keep, :]); itp_opts...),
+ H_spline=cubic_interp(mxs, Series(hmats_flat[keep, :]); itp_opts...),
+ F_spline_lower=cubic_interp(mxs, Series(fmats_lower_flat[keep, :]); itp_opts...),
+ F_spline_prim=cubic_interp(mxs, Series(fmats_prim_flat[keep, :]); itp_opts...),
+ F_spline_gal=cubic_interp(mxs, Series(fmats_gal_flat[keep, :]); itp_opts...),
+ G_spline=cubic_interp(mxs, Series(gmats_flat[keep, :]); itp_opts...),
+ K_spline=cubic_interp(mxs, Series(kmats_flat[keep, :]); itp_opts...),
+ # Jacobian Fourier band ψ-spline, used for the power normalization in Free.jl
+ J_spline=cubic_interp(mxs, Series(jmats_flat[keep, :]); itp_opts...))
+ return MatrixSplines(; ideal)
+end
diff --git a/src/ForceFreeStates/Free.jl b/src/ForceFreeStates/Free.jl
new file mode 100644
index 0000000000..0d971fa07f
--- /dev/null
+++ b/src/ForceFreeStates/Free.jl
@@ -0,0 +1,317 @@
+"""
+ FreeBoundaryResult
+
+Result of the free-boundary calculation, returned by `free_run`. All matrices are in the ξ Fourier
+basis and are `numpert_total × numpert_total`; the energies are generalized (W, N) pencil values,
+power-normalized and invariant to the working (Jacobian) coordinate.
+
+## Fields
+
+ - `wt::Matrix{ComplexF64}` - Eigenvector matrix of W·v = λ·N·v. Columns are eigenmodes sorted most-unstable first, normalized to unit power norm v†·N·v = 1.
+ - `wt0::Matrix{ComplexF64}` - Total-energy matrix W = wp + wv before diagonalisation
+ - `wp::Matrix{ComplexF64}` - Plasma energy matrix
+ - `wv::Matrix{ComplexF64}` - Vacuum energy matrix, singfac-scaled at `qlim`
+ - `ep::Vector{ComplexF64}` - Plasma energy per eigenmode (power quotient v†·wp·v with v†·N·v = 1)
+ - `ev::Vector{ComplexF64}` - Vacuum energy per eigenmode (power quotient v†·wv·v with v†·N·v = 1)
+ - `et::Vector{ComplexF64}` - Total energy eigenvalues of the pencil (W, N); et = ep + ev per mode
+ - `n_tor_idx::Vector{Int}` - 0-based toroidal mode number index of each sorted eigenvalue
+ - `vacuum_eigenvalue::Float64` - Least stable (minimum) eigenvalue of the pencil (wv, N), clamped to zero
+ - `plasma_pts`, `wall_pts::Matrix{Float64}` - Cartesian (x, y, z) surface coordinates, `numpoints × 3`, retained for HDF5 output
+"""
+struct FreeBoundaryResult
+ wt::Matrix{ComplexF64}
+ wt0::Matrix{ComplexF64}
+ wp::Matrix{ComplexF64}
+ wv::Matrix{ComplexF64}
+ ep::Vector{ComplexF64}
+ ev::Vector{ComplexF64}
+ et::Vector{ComplexF64}
+ n_tor_idx::Vector{Int}
+ vacuum_eigenvalue::Float64
+ plasma_pts::Matrix{Float64}
+ wall_pts::Matrix{Float64}
+end
+
+"""
+ power_norm_matrix!(Nmat, jmat, mpert, npert, dV_dpsi) -> Nmat
+
+Assemble the power-normalization (surface-norm) matrix N from the conjugate-symmetric Jacobian
+Fourier band `jmat` (length 2·mpert−1, evaluated from the `mats.ideal.J_spline` spline), such that
+
+ ξ†·N·ξ = ∮ J |ξ(θ)|² dθ / (dV/dψ) = ⟨|ξ|²⟩
+
+is the flux-surface average of the squared boundary displacement. N is Hermitian Toeplitz within each
+n-block, block-diagonal over n, and positive definite. It is the metric of the pencil W·v = λ·N·v in
+`free_run` and `free_compute_total`, whose eigenvalues are therefore invariant to the working (Jacobian)
+coordinate.
+"""
+function power_norm_matrix!(Nmat::AbstractMatrix{ComplexF64}, jmat::AbstractVector{ComplexF64}, mpert::Int, npert::Int, dV_dpsi::Float64)
+ fill!(Nmat, 0.0 + 0.0im)
+ for ipert_n in 1:npert
+ off = (ipert_n - 1) * mpert
+ # N[m, m'] = J_{m−m'}; jmat stores J_d at index mpert − d, so J_0 sits at mpert
+ for ipert_m in 1:mpert, jpert_m in 1:mpert
+ Nmat[off+jpert_m, off+ipert_m] = jmat[ipert_m-jpert_m+mpert] / dV_dpsi
+ end
+ end
+ return Nmat
+end
+
+"""
+ normalize_eigenfunctions!(odet::OdeState, wt::AbstractMatrix{ComplexF64}, psio::Float64) -> OdeState
+
+Rescale the stored EL solution vectors in `odet.u_store` (and `du_store`/`xi_s_store` when a
+path has already filled them) so the edge displacement matches the free-boundary eigenvectors
+`wt` (scaled by `2π·psio·1e-3`). Modifies `odet` in place. Call after `free_run` when
+downstream code consumes the stored ξ profiles.
+"""
+@with_pool pool function normalize_eigenfunctions!(odet::OdeState, wt::AbstractMatrix{ComplexF64}, psio::Float64)
+ N = size(wt, 1)
+ tmp_mat = zeros!(pool, ComplexF64, N, N)
+ coeffs = odet.u[:, :, 1, end] \ (wt .* (2π * psio * 1e-3))
+ @views for istep in 1:odet.step
+ mul!(tmp_mat, odet.u_store[:, :, 1, istep], coeffs)
+ odet.u_store[:, :, 1, istep] .= tmp_mat
+ mul!(tmp_mat, odet.u_store[:, :, 2, istep], coeffs)
+ odet.u_store[:, :, 2, istep] .= tmp_mat
+ # Only the galerkin path carries derivative stores this early; materialized ones
+ # are built from the normalized u_store afterwards.
+ if !isempty(odet.du_store)
+ mul!(tmp_mat, odet.du_store[:, :, istep], coeffs)
+ odet.du_store[:, :, istep] .= tmp_mat
+ mul!(tmp_mat, odet.xi_s_store[:, :, istep], coeffs)
+ odet.xi_s_store[:, :, istep] .= tmp_mat
+ end
+ end
+ return odet
+end
+
+"""
+ compute_scaled_wv(ctrl::ForceFreeStatesControl, equil::Equilibrium.PlasmaEquilibrium, intr::ForceFreeStatesInternal) -> (wv, vac)
+
+Vacuum response matrix at the control surface `intr.psilim`, scaled by the singular factors
+`(m - n·q)(m' - n'·q)` [Chance Phys. Plasmas 1997 2161 eq. 126]. Handles 2D single-n, 2D
+multi-n block-diagonal and 3D vacuum problems through `Vacuum.compute_vacuum_response`.
+
+Needs no ODE state, so both the free-boundary calculation and the standalone Galerkin solve
+share it. Returns the scaled `wv` alongside the full vacuum response `vac`, whose surface
+point clouds the free-boundary result carries to HDF5. `wv` aliases `vac.wv`, which is
+scaled in place.
+"""
+function compute_scaled_wv(ctrl::ForceFreeStatesControl, equil::Equilibrium.PlasmaEquilibrium, intr::ForceFreeStatesInternal)
+ (; mlow, mhigh, nlow, nhigh, psilim, qlim, wall_settings) = intr
+ vac_inputs = Vacuum.VacuumInput(equil, psilim, ctrl.mtheta_vacuum, ctrl.nzeta_vacuum, mlow:mhigh, nlow:nhigh)
+ vac = Vacuum.compute_vacuum_response(vac_inputs, wall_settings)
+ wv = vac.wv
+ singfac = vec((mlow:mhigh) .- qlim .* (nlow:nhigh)')
+ wv .*= singfac .* singfac'
+ return wv, vac
+end
+
+"""
+ free_run(odet::OdeState, ctrl::ForceFreeStatesControl, equil::Equilibrium.PlasmaEquilibrium, mats::MatrixSplines, intr::ForceFreeStatesInternal) -> FreeBoundaryResult
+
+Free-boundary energies at `intr.psilim`: the plasma response from the ODE edge state plus the
+singfac-scaled vacuum matrix, diagonalized as the pencil (W, N). Returns the eigenmodes and their
+plasma/vacuum/total energies as a [`FreeBoundaryResult`](@ref).
+"""
+@with_pool pool function free_run(odet::OdeState, ctrl::ForceFreeStatesControl, equil::Equilibrium.PlasmaEquilibrium, mats::MatrixSplines, intr::ForceFreeStatesInternal)
+
+ # Initializations and allocations
+ (; mpert, numpert_total, psilim, npert) = intr
+ wpt = zeros!(pool, ComplexF64, numpert_total, numpert_total)
+ wvt = zeros!(pool, ComplexF64, numpert_total, numpert_total)
+ tmp_mat = zeros!(pool, ComplexF64, numpert_total, numpert_total)
+
+ # Evaluate dV/dpsi at the plasma edge
+ dV_dpsi = equil.profiles.dVdpsi_spline(psilim)
+
+ # Compute plasma response matrix W = U₂ * U₁⁻¹
+ wp = zeros(ComplexF64, numpert_total, numpert_total)
+ @views wp .= (odet.u[:, :, 2] / odet.u[:, :, 1]) ./ equil.psio^2
+
+ wv, vac = compute_scaled_wv(ctrl, equil, intr)
+
+ # Power-normalization matrix N at the plasma edge: ξ†·N·ξ = ⟨|ξ|²⟩ (see power_norm_matrix!).
+ # The Jacobian band is evaluated at psilim (same surface as W), not at the last grid surface.
+ Nmat = zeros!(pool, ComplexF64, numpert_total, numpert_total)
+ jmat_edge = zeros!(pool, ComplexF64, 2 * mpert - 1)
+ mats.ideal.J_spline(jmat_edge, psilim; hint=mats._hint)
+ power_norm_matrix!(Nmat, jmat_edge, mpert, npert, dV_dpsi)
+
+ # Least stable eigenvalue of the vacuum matrix alone, power-normalized via the pencil
+ # (wv, N) so it shares the units of the mode energies (should be PSD; clamp noise to zero)
+ vacuum_eigenvalue = max(0.0, minimum(real.(eigvals(Hermitian(wv), Hermitian(Nmat)))))
+
+ # Generalized eigenproblem W·v = λ·N·v: eigenvalues are power-normalized, Jacobian-invariant mode energies
+ wt = wp .+ wv
+ wt0 = copy(wt)
+ Ev = eigen(wt, Nmat)
+ et = Ev.values
+ eindex = sortperm(real.(et); rev=true)
+
+ # Rearrange wt columns for ascending real eigenvalues (most unstable first)
+ etemp = copy(et)
+ n_tor_idx = zeros(Int, numpert_total)
+ for ipert in 1:numpert_total
+ orig = eindex[numpert_total+1-ipert]
+ wt[:, ipert] .= Ev.vectors[:, orig]
+ et[ipert] = etemp[orig]
+ # n index of each eigenvector from its dominant entry (relies on n-block-diagonal W)
+ imax = argmax(abs.(Ev.vectors[:, orig]))
+ n_tor_idx[ipert] = (imax - 1) ÷ mpert
+ end
+
+ # Normalize eigenvectors to unit power norm v†·N·v = 1. The generalized eigenvalues are
+ # already the power-normalized energies, so et is not rescaled here.
+ for isol in 1:numpert_total
+ v = @view wt[:, isol]
+ v ./= sqrt(real(dot(v, Nmat, v)))
+ end
+
+ # Normalize phase
+ imax = 0
+ for isol in 1:numpert_total
+ imax = argmax(abs.(wt[:, isol]))
+ phase = abs(wt[imax, isol]) / wt[imax, isol]
+ wt[:, isol] .*= phase
+ end
+
+ # Project W_p and W_v into the eigenmode basis. Diagonal entries give
+ # the plasma/vacuum energy split for each mode: et[i] = ep[i] + ev[i]
+ mul!(tmp_mat, wp, wt)
+ mul!(wpt, wt', tmp_mat)
+ mul!(tmp_mat, wv, wt)
+ mul!(wvt, wt', tmp_mat)
+ ep = diag(wpt)
+ ev = diag(wvt)
+
+ # Write energies to screen
+ if intr.verbose
+ @info "Least Stable Eigenmode Energies:\n" *
+ " Plasma = $((@sprintf "%+.3e %+.3ei" real(ep[1]) imag(ep[1])))\n" *
+ " Vacuum = $((@sprintf "%+.3e %+.3ei" real(ev[1]) imag(ev[1])))\n" *
+ " Total = $((@sprintf "%+.3e %+.3ei" real(et[1]) imag(et[1])))"
+ end
+
+ return FreeBoundaryResult(wt, wt0, wp, wv, ep, ev, et, n_tor_idx, vacuum_eigenvalue, vac.plasma_pts, vac.wall_pts)
+end
+
+"""
+ free_compute_wv_spline(ctrl::ForceFreeStatesControl, equil::Equilibrium.PlasmaEquilibrium, intr::ForceFreeStatesInternal)
+
+Cubic ψ-spline of the raw (not singfac-scaled) vacuum response matrices from
+`ctrl.dW_edge_scan_start` to `intr.psilim`, sampled evenly in q with at least 4 points per q-window,
+for fast evaluation in `free_compute_total` during the edge dW scan.
+"""
+@with_pool pool function free_compute_wv_spline(ctrl::ForceFreeStatesControl, equil::Equilibrium.PlasmaEquilibrium, intr::ForceFreeStatesInternal)
+
+ profiles = equil.profiles
+
+ # Number of psi grid points for the spline: 4 per q-window minimum
+ qedge = profiles.q_spline(ctrl.dW_edge_scan_start)
+ npsi = max(4, ceil(Int, (intr.qlim - qedge) * intr.nhigh * 4))
+ psi_array = zeros!(pool, Float64, npsi + 1)
+ wv_array = zeros!(pool, ComplexF64, npsi + 1, intr.numpert_total, intr.numpert_total)
+
+ for i in 1:(npsi+1)
+ # Space points evenly in q over [qedge, qlim] (i=1 → qedge, i=npsi+1 → qlim)
+ qi = qedge + (intr.qlim - qedge) * ((i - 1) / npsi)
+
+ psii = ctrl.dW_edge_scan_start + (intr.psilim - ctrl.dW_edge_scan_start) * ((i - 1) / npsi)
+ psi_array[i] = find_zero(
+ (psi -> profiles.q_spline(psi) - qi,
+ psi -> profiles.q_deriv(psi)),
+ psii, Roots.Newton()
+ )
+
+ # Compute raw vacuum matrix at the actual scan psi (singfac NOT applied; free_compute_total applies it analytically)
+ vac_inputs = Vacuum.VacuumInput(equil, psi_array[i], ctrl.mtheta_vacuum, ctrl.nzeta_vacuum, intr.mlow:intr.mhigh, intr.nlow:intr.nhigh)
+ vac = Vacuum.compute_vacuum_response(vac_inputs, intr.wall_settings)
+ @views wv_array[i, :, :] .= vac.wv
+ end
+
+ # Flatten 3D array to (npsi+1 × numpert_total^2) for series interpolant
+ wv_flat = reshape(wv_array, npsi + 1, intr.numpert_total^2)
+
+ # Complex series interpolant; the default CubicFit handles the endpoints
+ wvmat = cubic_interp(psi_array, Series(wv_flat); extrap=ExtendExtrap())
+
+ return wvmat
+end
+
+"""
+ free_compute_total(equil::Equilibrium.PlasmaEquilibrium, mats::MatrixSplines, intr::ForceFreeStatesInternal, odet::OdeState) -> NamedTuple
+
+Energies of the least stable mode at `odet.psifac`: a trimmed `free_run` called by `findmax_dW_edge!` at
+each step of the edge dW scan. The raw vacuum matrix comes from `odet.edge_scan.wvmat`
+(see `free_compute_wv_spline`) and is singfac-scaled here.
+
+## Returns
+
+NamedTuple `(total_eigenvalue, plasma_energy, vacuum_energy, vacuum_eigenvalue)`.
+"""
+@with_pool pool function free_compute_total(equil::Equilibrium.PlasmaEquilibrium, mats::MatrixSplines, intr::ForceFreeStatesInternal, odet::OdeState)
+
+ Npert = intr.numpert_total
+ wp = zeros!(pool, ComplexF64, Npert, Npert)
+ eigenvalues = zeros!(pool, ComplexF64, Npert)
+ wt = zeros!(pool, ComplexF64, Npert, Npert)
+ wv = zeros!(pool, ComplexF64, Npert, Npert)
+ Nmat = zeros!(pool, ComplexF64, Npert, Npert)
+ jmat_local = zeros!(pool, ComplexF64, 2 * intr.mpert - 1)
+ eindex = zeros!(pool, Int, Npert)
+ evals_real = zeros!(pool, Float64, Npert)
+ tmp_v = zeros!(pool, ComplexF64, Npert)
+
+ dV_dpsi = equil.profiles.dVdpsi_spline(odet.psifac)
+
+ # Compute plasma response matrix
+ @views wp .= (odet.u[:, :, 2] / odet.u[:, :, 1]) ./ equil.psio^2
+
+ # Retrieve raw vacuum matrix from spline and apply singfac analytically at the local q.
+ # Singfac is not pre-applied in the spline (see free_compute_wv_spline) to avoid interpolating
+ # a zero-crossing function near rational surfaces, which would distort the peaks.
+ es = odet.edge_scan
+ es.wvmat(vec(wv), odet.psifac; hint=es.wv_hint)
+ q_at_psifac = equil.profiles.q_spline(odet.psifac)
+ # Scale by (m - n*q)(m' - n'*q) [Chance Phys. Plasmas 1997 2161 eq. 126]
+ singfac = vec((intr.mlow:intr.mhigh) .- q_at_psifac .* (intr.nlow:intr.nhigh)')
+ wv .*= singfac .* singfac'
+
+ # Local power-normalization matrix N(ψ) from the Jacobian Fourier band spline, so the
+ # power quotient uses the same surface as W (see power_norm_matrix!)
+ mats.ideal.J_spline(jmat_local, odet.psifac; hint=mats._hint)
+ power_norm_matrix!(Nmat, jmat_local, intr.mpert, intr.npert, dV_dpsi)
+
+ # Total energy matrix and generalized eigen-decomposition of the pencil (W, N) — the
+ # eigenvalues are power-normalized, Jacobian-invariant mode energies
+ wt .= wp .+ wv
+ Ev = eigen(wt, Nmat)
+
+ # Sort eigenvalues by descending real part
+ @inbounds for i in 1:Npert
+ evals_real[i] = real(Ev.values[i])
+ end
+ sortperm!(eindex, evals_real; rev=true)
+ for ipert in 1:Npert
+ wt[:, ipert] .= Ev.vectors[:, eindex[Npert+1-ipert]]
+ eigenvalues[ipert] = Ev.values[eindex[Npert+1-ipert]]
+ end
+
+ # Plasma and vacuum energy components for the leading eigenvector via power quotients:
+ # plasma_energy + vacuum_energy = total_eigenvalue (wt = wp + wv; λ = v'*wt*v / v'*N*v).
+ v = @view wt[:, 1]
+ vnorm = real(dot(v, Nmat, v))
+ mul!(tmp_v, wp, v)
+ plasma_energy = ComplexF64(dot(v, tmp_v)) / vnorm
+ mul!(tmp_v, wv, v)
+ vacuum_energy = ComplexF64(dot(v, tmp_v)) / vnorm
+
+ # Smallest eigenvalue of the vacuum matrix alone via the pencil (wv, N), so all four outputs
+ # share the power-normalized units. The singfac-scaled wv should be PSD by construction
+ # (congruence of PSD wv_raw); clamp numerical noise to zero.
+ vacuum_eigenvalue = max(0.0, minimum(real.(eigvals(Hermitian(wv), Hermitian(Nmat)))))
+
+ return (total_eigenvalue=eigenvalues[1], plasma_energy=plasma_energy, vacuum_energy=vacuum_energy, vacuum_eigenvalue=vacuum_eigenvalue)
+end
diff --git a/src/ForceFreeStates/Galerkin/GalerkinAssembly.jl b/src/ForceFreeStates/Galerkin/GalerkinAssembly.jl
new file mode 100644
index 0000000000..55d0931940
--- /dev/null
+++ b/src/ForceFreeStates/Galerkin/GalerkinAssembly.jl
@@ -0,0 +1,457 @@
+# GalerkinAssembly.jl
+#
+# Element-level assembly for the outer-region Galerkin solver. Ports:
+# gal_hermite (gal.f) Hermite cubic basis: Utilities.HermiteFEM.hermite_basis
+# gal_get_fkg (gal.f) F, K, G at a point from F̄/K̄/Ḡ + singfac
+# gal_gauss_quad (gal.f) nonresonant stiffness via Gauss-Lobatto quadrature
+# gal_extension (gal.f) extension-cell matrix/rhs (big-solution driving + surface terms)
+# gal_resonant (gal.f) resonant-cell integral (QuadGK in place of Fortran LSODE)
+# gal_assemble_mat (gal.f) scatter cell blocks into the full-band global matrix
+# gal_assemble_rhs (gal.f) scatter cell rhs into the global RHS
+# gal_set_boundary (gal.f) axis identity + edge (vacuum or fixed) BCs
+#
+# Hermite DOF index ip (Fortran 0:3) ↔ Julia array index ip+1 throughout.
+
+# Two-sided asymptotic evaluation (z = ψ - ψ_s). Right (z≥0) uses the sig=+1 series at z; left (z<0)
+# uses the sig=-1 series at the positive distance |z| (real √, no renorm), matching Fortran sing.f.
+# The derivative on the left picks up d|z|/dψ = -1. Only the big (col 1) and small (col 2) resonant
+# columns are evaluated (sing_get_ua_res/sing_get_dua_res); the in-place `!` forms write into a
+# caller-owned (numpert_total, 2, 2) buffer for the hot quadrature/reconstruction loops.
+@inline sing_get_ua_gal(g::GalSingAsymp, z::Float64) =
+ z >= 0 ? sing_get_ua_res(g.right, z) : sing_get_ua_res(g.left, -z)
+@inline sing_get_dua_gal(g::GalSingAsymp, z::Float64) =
+ z >= 0 ? sing_get_dua_res(g.right, z) : (-1) .* sing_get_dua_res(g.left, -z)
+
+# Leading-order ("cut") resonant basis, used to build the cut outer solution that the inner-layer
+# solution is added to. Same two-sided convention as `sing_get_ua_gal`.
+@inline sing_get_ua_gal_cut(g::GalSingAsymp, z::Float64) =
+ z >= 0 ? sing_get_ua_res_cut(g.right, z) : sing_get_ua_res_cut(g.left, -z)
+
+@inline sing_get_ua_gal!(out, g::GalSingAsymp, z::Float64) =
+ z >= 0 ? sing_get_ua_res!(out, g.right, z) : sing_get_ua_res!(out, g.left, -z)
+@inline function sing_get_dua_gal!(out, g::GalSingAsymp, z::Float64)
+ if z >= 0
+ sing_get_dua_res!(out, g.right, z)
+ else
+ sing_get_dua_res!(out, g.left, -z)
+ @inbounds for i in eachindex(out)
+ out[i] = -out[i]
+ end
+ end
+ return out
+end
+
+"""
+ gal_get_fkg(mats, intr, x, q; Fbuf=nothing, Kbuf=nothing, Gbuf=nothing) -> (F, K, G)
+
+Evaluate the ideal-MHD Euler–Lagrange coefficients of the outer-region weak form (Glasser 2016, PoP 23,
+112506), `F = Q F̄ Qᴴ`, `K = Q K̄`, `G = Ḡ`, at flux `x` with safety factor `q`, where `Q = diag(m - n q)`.
+F̄ is rebuilt from its Cholesky factor `mats.ideal.F_spline_lower`, matching the Euler–Lagrange kernel.
+Optional `*buf` matrices are filled and returned instead of allocating. Port of `gal_get_fkg` (gal.f).
+"""
+function gal_get_fkg(mats::MatrixSplines, intr::ForceFreeStatesInternal, x::Float64, q::Float64;
+ Fbuf::Union{Nothing,Matrix{ComplexF64}}=nothing, Kbuf::Union{Nothing,Matrix{ComplexF64}}=nothing,
+ Gbuf::Union{Nothing,Matrix{ComplexF64}}=nothing)
+ N = intr.numpert_total
+ sf = vec((intr.mlow:intr.mhigh) .- q .* (intr.nlow:intr.nhigh)')
+
+ F = Fbuf === nothing ? Matrix{ComplexF64}(undef, N, N) : Fbuf
+ K = Kbuf === nothing ? Matrix{ComplexF64}(undef, N, N) : Kbuf
+ G = Gbuf === nothing ? Matrix{ComplexF64}(undef, N, N) : Gbuf
+ # Reuse G as factor scratch before evaluating Ḡ.
+ mats.ideal.F_spline_lower(vec(G), x; hint=mats._hint)
+ mul!(F, LowerTriangular(G), adjoint(LowerTriangular(G)))
+ mats.ideal.K_spline(vec(K), x; hint=mats._hint)
+ mats.ideal.G_spline(vec(G), x; hint=mats._hint)
+
+ # scale F̄→F=Q F̄ Qᴴ and K̄→K=Q K̄ in place (Q = diag(sf))
+ @inbounds for j in 1:N, i in 1:N
+ F[i, j] = F[i, j] * sf[i] * sf[j]
+ K[i, j] = K[i, j] * sf[i]
+ end
+ return F, K, G
+end
+
+"""
+ gal_gauss_quad!(cell, mats, profiles, intr, nodes, weights, swap_edge)
+
+Accumulate the nonresonant Hermite stiffness block `cell.mat` by Gauss-Lobatto quadrature. Port of
+`gal_gauss_quad` (gal.f). When `swap_edge` (the final cell of the last interval), the
+right-node value/slope DOFs (Fortran pb(2)↔pb(3)) are swapped so the edge-value DOF lands at index 3,
+matching the free-boundary BC (gal.f).
+"""
+function gal_gauss_quad!(cell::GalCell, mats::MatrixSplines, profiles, intr::ForceFreeStatesInternal,
+ nodes::Vector{Float64}, weights::Vector{Float64}, swap_edge::Bool)
+
+ N = intr.numpert_total
+ np = GAL_NP
+ fill!(cell.mat, 0)
+ x1, x2 = cell.x
+ x0c = (x2 + x1) / 2
+ dxc = (x2 - x1) / 2
+ qhint = Ref(1)
+ Fbuf = Matrix{ComplexF64}(undef, N, N)
+ Kbuf = Matrix{ComplexF64}(undef, N, N)
+ Gbuf = Matrix{ComplexF64}(undef, N, N)
+
+ @inbounds for iq in eachindex(nodes)
+ x = x0c + dxc * nodes[iq]
+ w = dxc * weights[iq]
+ q = profiles.q_spline(x; hint=qhint)
+ F, K, G = gal_get_fkg(mats, intr, x, q; Fbuf=Fbuf, Kbuf=Kbuf, Gbuf=Gbuf)
+ pbt, qbt = hermite_basis(x, x1, x2)
+ # swap the right-node value/slope DOFs (Fortran pb(2)↔pb(3)) for the free-boundary edge
+ pb = swap_edge ? (pbt[1], pbt[2], pbt[4], pbt[3]) : pbt
+ qb = swap_edge ? (qbt[1], qbt[2], qbt[4], qbt[3]) : qbt
+ for ip in 0:np, ipert in 1:N, jp in 0:np, jpert in 1:N
+ cell.mat[ipert, jpert, ip+1, jp+1] +=
+ w * (
+ F[ipert, jpert] * qb[ip+1] * qb[jp+1] +
+ K[ipert, jpert] * qb[ip+1] * pb[jp+1] +
+ conj(K[jpert, ipert]) * pb[ip+1] * qb[jp+1] +
+ G[ipert, jpert] * pb[ip+1] * pb[jp+1])
+ end
+ end
+ return cell
+end
+
+# Resolve (jsing, ψ_s, sign) for an extension/resonant cell from its side.
+@inline function _cell_jsing(cell::GalCell, ising::Int)
+ return cell.extra == GAL_SIDE_LEFT ? ising + 1 : ising
+end
+
+"""
+ gal_extension!(cell, ising, mats, profiles, intr, asymps, sings, nn, nodes, weights)
+
+Build `cell.emat`, `cell.ediag`, `cell.rhs`, `cell.erhs` for an extension cell (`ext`/`ext1`/`ext2`).
+Port of `gal_extension` (gal.f). The big solution (column 1 of the gal asymptotic) drives the RHS;
+for `ext` cells the small solution (column 2) also forms the resonant coupling `emat`/`ediag`.
+"""
+function gal_extension!(cell::GalCell, ising::Int, mats::MatrixSplines, profiles,
+ intr::ForceFreeStatesInternal, asymps::Vector{GalSingAsymp}, sings::Vector{SingType},
+ nn::Int, nodes::Vector{Float64}, weights::Vector{Float64})
+
+ N = intr.numpert_total
+ np = GAL_NP
+ x1, x2 = cell.x
+ qhint = Ref(1)
+ # Reused F/K/G buffers for gal_get_fkg (each call's result is consumed before the next).
+ Fbuf = Matrix{ComplexF64}(undef, N, N)
+ Kbuf = Matrix{ComplexF64}(undef, N, N)
+ Gbuf = Matrix{ComplexF64}(undef, N, N)
+
+ jsing = _cell_jsing(cell, ising)
+ asymp = asymps[jsing]
+ psi_s = sings[jsing].psifac
+ # sing_get_*_gal returns only the two resonant columns: 1 = big solution, 2 = small solution.
+ ua_at(x) = sing_get_ua_gal(asymp, x - psi_s)
+ dua_at(x) = sing_get_dua_gal(asymp, x - psi_s)
+
+ # Boundary node and weights (gal.f)
+ if cell.extra == GAL_SIDE_LEFT
+ jp = 2 # Fortran jp (0-based) -> Julia jp+1
+ xb = x2
+ ws = -1.0
+ else
+ jp = 0
+ xb = x1
+ ws = 1.0
+ end
+ if cell.etype == GCT_EXT || cell.etype == GCT_EXT1
+ w1 = 1.0
+ w2 = 1.0
+ else # GCT_EXT2
+ w1 = (cell.extra == GAL_SIDE_LEFT) ? 0.0 : 1.0
+ w2 = (cell.extra == GAL_SIDE_LEFT) ? 1.0 : 0.0
+ end
+
+ fill!(cell.emat, 0)
+ cell.ediag = zero(ComplexF64)
+
+ # --- emat and ediag (ext cells only) (gal.f) ---
+ if cell.etype == GCT_EXT
+ uab = ua_at(xb)
+ duab = dua_at(xb)
+ u = uab[:, 2, 1] # small solution
+ du = duab[:, 2, 1]
+ for ipert in 1:N
+ @views cell.emat .+= cell.mat[:, ipert, :, jp+1] .* u[ipert] .+
+ cell.mat[:, ipert, :, jp+2] .* du[ipert]
+ end
+ for ipert in 1:N
+ cell.ediag += conj(u[ipert]) * cell.emat[ipert, jp+1] +
+ conj(du[ipert]) * cell.emat[ipert, jp+2]
+ end
+ # surface term at xb
+ qb = profiles.q_spline(xb; hint=qhint)
+ Fb, Kb, _ = gal_get_fkg(mats, intr, xb, qb; Fbuf=Fbuf, Kbuf=Kbuf, Gbuf=Gbuf)
+ pbt, _ = hermite_basis(xb, x1, x2)
+ Fdu_Ku = Fb * du .+ Kb * u
+ for ip in 0:np
+ @views cell.emat[:, ip+1] .+= Fdu_Ku .* (pbt[ip+1] * ws)
+ end
+ cell.ediag += sum(conj.(u) .* Fdu_Ku) * ws
+ end
+
+ # --- rhs (gal.f) ---
+ ua1 = ua_at(x1)[:, 1, 1] # big solution at left node
+ du1 = dua_at(x1)[:, 1, 1]
+ ua2 = ua_at(x2)[:, 1, 1] # big solution at right node
+ du2 = dua_at(x2)[:, 1, 1]
+ fill!(cell.rhs, 0)
+
+ if cell.etype == GCT_EXT || cell.etype == GCT_EXT1
+ cell.erhs = zero(ComplexF64)
+ x0c = (x2 + x1) / 2
+ dxc = (x2 - x1) / 2
+ for iq in eachindex(nodes)
+ x = x0c + dxc * nodes[iq]
+ w = dxc * weights[iq]
+ q = profiles.q_spline(x; hint=qhint)
+ F, K, G = gal_get_fkg(mats, intr, x, q; Fbuf=Fbuf, Kbuf=Kbuf, Gbuf=Gbuf)
+ pbt, qbt = hermite_basis(x, x1, x2)
+ uax = ua_at(x)
+ ub = uax[:, 1, 1]
+ dub = dua_at(x)[:, 1, 1]
+ term1 = F * dub .+ K * ub
+ term2 = adjoint(K) * dub .+ G * ub
+ for ip in 0:np
+ @views cell.rhs[:, ip+1] .-= (term1 .* qbt[ip+1] .+ term2 .* pbt[ip+1]) .* w
+ end
+ end
+ if cell.etype == GCT_EXT
+ for ipert in 1:N
+ cell.erhs += conj(ua_at(xb)[ipert, 2, 1]) * cell.rhs[ipert, jp+1] +
+ conj(dua_at(xb)[ipert, 2, 1]) * cell.rhs[ipert, jp+2]
+ end
+ end
+ elseif cell.etype == GCT_EXT2
+ for ipert in 1:N
+ @views cell.rhs .-= w1 .* (cell.mat[:, ipert, :, 0+1] .* ua1[ipert] .+
+ cell.mat[:, ipert, :, 1+1] .* du1[ipert])
+ @views cell.rhs .-= w2 .* (cell.mat[:, ipert, :, 2+1] .* ua2[ipert] .+
+ cell.mat[:, ipert, :, 3+1] .* du2[ipert])
+ end
+ end
+
+ # --- surface terms (always; gal.f) ---
+ q_l = profiles.q_spline(x1; hint=qhint)
+ Fl, Kl, _ = gal_get_fkg(mats, intr, x1, q_l; Fbuf=Fbuf, Kbuf=Kbuf, Gbuf=Gbuf)
+ pbt, _ = hermite_basis(x1, x1, x2)
+ surf_l = Fl * du1 .+ Kl * ua1
+ for ip in 0:np
+ @views cell.rhs[:, ip+1] .-= surf_l .* (pbt[ip+1] * w1)
+ end
+ if cell.etype == GCT_EXT && cell.extra == GAL_SIDE_RIGHT
+ cell.erhs -= sum(conj.(ua_at(x1)[:, 2, 1]) .* surf_l)
+ end
+
+ q_r = profiles.q_spline(x2; hint=qhint)
+ Fr, Kr, _ = gal_get_fkg(mats, intr, x2, q_r; Fbuf=Fbuf, Kbuf=Kbuf, Gbuf=Gbuf)
+ pbt, _ = hermite_basis(x2, x1, x2)
+ surf_r = Fr * du2 .+ Kr * ua2
+ for ip in 0:np
+ @views cell.rhs[:, ip+1] .+= surf_r .* (pbt[ip+1] * w2)
+ end
+ if cell.etype == GCT_EXT && cell.extra == GAL_SIDE_LEFT
+ cell.erhs += sum(conj.(ua_at(x2)[:, 2, 1]) .* surf_r)
+ end
+ return cell
+end
+
+"""
+ gal_resonant!(cell, ising, mats, profiles, intr, asymps, sings, nn, gal_tol, gal_gnstep, verbose)
+
+Compute the resonant-cell contributions `cell.erhs`, `cell.ediag`, `cell.rhs`, `cell.emat` by adaptive
+quadrature (QuadGK) of the residual-operator integrand. Port of `gal_lsode_int`/`gal_lsode_der`
+(gal.f): the Fortran LSODE accumulation is replaced by `quadgk` over `[x_bdy, x_lsode]`.
+"""
+function gal_resonant!(cell::GalCell, ising::Int, mats::MatrixSplines, profiles,
+ intr::ForceFreeStatesInternal, asymps::Vector{GalSingAsymp}, sings::Vector{SingType},
+ nn::Int, gal_tol::Float64, gal_gnstep::Int, verbose::Bool)
+
+ N = intr.numpert_total
+ np = GAL_NP
+ x1, x2 = cell.x
+ qhint = Ref(1)
+
+ jsing = _cell_jsing(cell, ising)
+ asymp = asymps[jsing]
+ psi_s = sings[jsing].psifac
+
+ # Integration limits (gal.f): right → [x2, x_lsode]; left → [x1, x_lsode]
+ x0 = (cell.extra == GAL_SIDE_LEFT) ? x1 : x2
+ x1l = cell.x_lsode
+ sgn_u = (cell.extra == GAL_SIDE_RIGHT) ? -1.0 : 1.0
+
+ # Preallocated buffers (col 1 = big, col 2 = small) so the integrand allocates nothing
+ ua_buf = Array{ComplexF64,3}(undef, N, 2, 2)
+ dua_buf = Array{ComplexF64,3}(undef, N, 2, 2)
+ kmat = Matrix{ComplexF64}(undef, N, N)
+ gmat = Matrix{ComplexF64}(undef, N, N)
+ d1 = Vector{ComplexF64}(undef, N)
+ mvtmp = Vector{ComplexF64}(undef, N)
+ sfvec = Vector{Float64}(undef, N)
+ mv = Matrix{ComplexF64}(undef, N, 2)
+ w = Vector{ComplexF64}(undef, N)
+ pbuf = Vector{ComplexF64}(undef, N)
+
+ L = 2 + 2 * N * (np + 1)
+ function integrand!(out, x)
+ z = x - psi_s
+ sing_get_ua_gal!(ua_buf, asymp, z)
+ sing_get_dua_gal!(dua_buf, asymp, z)
+ q = profiles.q_spline(x; hint=qhint)
+ sing_matvec!(mv, kmat, gmat, d1, mvtmp, sfvec, mats, intr, x, q, ua_buf, dua_buf) # N×2 (col1=big, col2=small)
+ pbt, _ = hermite_basis(x, x1, x2)
+ # Pairwise sum over the materialized product (reuses buffers) — matches sum(w .* mv) bit-for-bit.
+ w .= conj.(@view ua_buf[:, 2, 1]) # conj small solution, qty1
+ pbuf .= w .* @view mv[:, 1]
+ out[1] = sum(pbuf) # res1
+ pbuf .= w .* @view mv[:, 2]
+ out[2] = sum(pbuf) # res2
+ idx = 3
+ @inbounds for ip in 0:np, ipert in 1:N
+ out[idx] = pbt[ip+1] * mv[ipert, 1] # hbig (ipert fastest, then ip)
+ idx += 1
+ end
+ @inbounds for ip in 0:np, ipert in 1:N
+ out[idx] = pbt[ip+1] * mv[ipert, 2] # hsmall
+ idx += 1
+ end
+ return out
+ end
+
+ # QuadGK replaces Fortran LSODE over the same integrand (not bit-exact); gal_gnstep caps evals so a
+ # near-singular integrand cannot hang.
+ result = Vector{ComplexF64}(undef, L)
+ raw, qerr = quadgk!(integrand!, result, x0, x1l; rtol=gal_tol, atol=1e-30, maxevals=gal_gnstep)
+ if verbose
+ @info " resonant jsing=$jsing side=$(cell.extra) qerr=$(qerr) res1=$(raw[1]) res2=$(raw[2])"
+ end
+ hbig = reshape(@view(raw[3:(2+N*(np+1))]), N, np + 1)
+ hsmall = reshape(@view(raw[(3+N*(np+1)):end]), N, np + 1)
+
+ # Apply the right-side negation and the gal_make_arrays signs (gal.f gal_make_arrays)
+ cell.erhs = -sgn_u * raw[1]
+ cell.ediag = sgn_u * raw[2]
+ cell.rhs .= (-sgn_u) .* hbig
+ cell.emat .= sgn_u .* hsmall
+ return cell
+end
+
+"""
+ gal_assemble_mat!(ws, mpert)
+
+Scatter every cell's `mat`/`emat`/`ediag` into the full-band global matrix `ws.mat`
+(`offset = kl+ku+1`). Port of `gal_assemble_mat` (gal.f).
+"""
+function gal_assemble_mat!(ws::GalWorkspace, mpert::Int)
+ np = ws.np
+ msing = length(ws.intvl) - 1
+ offset = ws.kl + ws.ku + 1
+
+ for ising in 0:msing
+ for cell in ws.intvl[ising+1].cells
+ res = cell.etype == GCT_RES || cell.etype == GCT_EXT
+ for ip in 0:np, ipert in 1:mpert
+ i = cell.map[ipert, ip+1]
+ # nonresonant stiffness
+ for jp in 0:np, jpert in 1:mpert
+ j = cell.map[jpert, jp+1]
+ ws.mat[offset+i-j, j] += cell.mat[ipert, jpert, ip+1, jp+1]
+ end
+ # resonant coupling (res/ext only)
+ if res
+ j = cell.emap
+ e = cell.emat[ipert, ip+1]
+ ws.mat[offset+i-j, j] += e
+ ws.mat[offset+j-i, i] += conj(e)
+ end
+ end
+ if res
+ ws.mat[offset, cell.emap] += cell.ediag
+ end
+ end
+ end
+ return ws
+end
+
+"""
+ gal_assemble_rhs!(ws, mpert)
+
+Scatter every cell's `rhs`/`erhs` into the global RHS `ws.rhs`. Port of `gal_assemble_rhs`
+(gal.f). A new RHS column (`isol`) begins at each big-solution driver: an `ext2`-left cell or a
+`res`-right cell.
+"""
+function gal_assemble_rhs!(ws::GalWorkspace, mpert::Int)
+ np = ws.np
+ msing = length(ws.intvl) - 1
+ isol = 0
+ for ising in 0:msing
+ for cell in ws.intvl[ising+1].cells
+ cell.etype == GCT_NONE && continue
+ if cell.etype == GCT_EXT2 && cell.extra == GAL_SIDE_LEFT
+ isol += 1
+ elseif cell.etype == GCT_RES && cell.extra == GAL_SIDE_RIGHT
+ isol += 1
+ end
+ for ip in 0:np, ipert in 1:mpert
+ imap = cell.map[ipert, ip+1]
+ ws.rhs[imap, isol] += cell.rhs[ipert, ip+1]
+ end
+ if cell.etype == GCT_EXT || cell.etype == GCT_RES
+ ws.rhs[cell.emap, isol] += cell.erhs
+ end
+ end
+ end
+ return ws
+end
+
+"""
+ gal_set_boundary!(ws, mpert, wv_edge)
+
+Apply the axis (`u(0)=0` identity) and edge boundary conditions to the boundary cells' `mat`, plus the
+rpec coil-source RHS injection, before global assembly. Port of `gal_set_boundary` (gal.f). The edge
+branch is one of:
+
+ - rpec (`ncoil = ws.nsol - 2*msing > 0`): identity edge and a unit source at the edge value DOF of coil
+ column `2*msing+ipert` for each poloidal mode `ipert`. `gal_assemble_rhs!` only fills columns
+ `1:2*msing`, so the injection is not clobbered.
+ - free boundary (`wv_edge !== nothing`): add the vacuum block `wvac·psio²` at the edge value DOF.
+ - fixed boundary (else): identity edge.
+"""
+function gal_set_boundary!(ws::GalWorkspace, mpert::Int, wv_edge::Union{Nothing,Matrix{ComplexF64}})
+ msing = length(ws.intvl) - 1
+ ncoil = ws.nsol - 2 * msing
+
+ # axis u(0): first cell of interval 0, Hermite value DOF ip=0 (Julia index 1)
+ cell = ws.intvl[1].cells[1]
+ cell.mat[:, :, 1, :] .= 0
+ for idx in 1:mpert
+ cell.mat[idx, idx, 1, 1] = 1
+ end
+
+ # edge u(1): last cell of last interval, edge-value DOF ip=3 (Julia index 4, see gauss_quad swap)
+ cell = ws.intvl[msing+1].cells[ws.nx]
+ if ncoil > 0
+ # rpec: identity edge + unit coil sources (gal.f)
+ cell.mat[:, :, 4, :] .= 0
+ for idx in 1:mpert
+ cell.mat[idx, idx, 4, 4] = 1
+ end
+ for ipert in 1:mpert
+ ws.rhs[cell.map[ipert, 4], 2*msing+ipert] = 1
+ end
+ elseif wv_edge !== nothing
+ # free boundary: vacuum block wvac·psio² (gal.f)
+ @views cell.mat[:, :, 4, 4] .+= wv_edge
+ else
+ # fixed boundary: identity edge (gal.f)
+ cell.mat[:, :, 4, :] .= 0
+ for idx in 1:mpert
+ cell.mat[idx, idx, 4, 4] = 1
+ end
+ end
+ return ws
+end
diff --git a/src/ForceFreeStates/Galerkin/GalerkinGrid.jl b/src/ForceFreeStates/Galerkin/GalerkinGrid.jl
new file mode 100644
index 0000000000..513a692bd0
--- /dev/null
+++ b/src/ForceFreeStates/Galerkin/GalerkinGrid.jl
@@ -0,0 +1,207 @@
+# GalerkinGrid.jl
+#
+# Grid construction and local→global DOF mapping for the outer-region Galerkin solver.
+# Ports gal_make_grid (gal.f) and gal_make_map (gal.f); gal_pack is Utilities.HermiteFEM.pack_grid.
+#
+# Node arrays use Fortran 0-based `x(0:nx)` mapped to Julia `xn[i+1]` (so Fortran `x(i)` is `xn[i+1]`).
+# Cells are 1-based in both. Intervals `0:msing` (Fortran) are `ws.intvl[ising+1]` in Julia.
+# The optional `gal_xmin_flag`/`sing1_xmin` adaptive-width branch is intentionally not ported.
+
+"""
+ gal_resonant_surfaces(intr, equil) -> (sings, psilow, psihigh)
+
+Resonant surfaces inside the integration domain, in increasing ψ (Fortran `sing(1:msing)`), with the
+domain bounds. `psilow` is raised above the axis by `sing_min!` when q < qlow somewhere on the grid (excludes
+that region); it falls back to the equilibrium axis bound if `sing_min!` was not run (`intr.psilow` still 0).
+"""
+function gal_resonant_surfaces(intr::ForceFreeStatesInternal, equil)
+ psilow = intr.psilow > 0 ? intr.psilow : equil.profiles.xs[1]
+ psihigh = intr.psilim
+ sings = [s for s in intr.sing if psilow < s.psifac < psihigh && intr.mlow <= s.m[1] <= intr.mhigh]
+ return sings, psilow, psihigh
+end
+
+"""
+ gal_make_grid!(intvl::GalInterval, ising::Int, msing::Int, sings::Vector{SingType},
+ nn::Int, psilow::Float64, psihigh::Float64, ctrl::ForceFreeStatesControl)
+
+Set the cell types (`res`/`ext`/`ext1`/`ext2`/`none`), sides, resonant integration limits, and packed
+node positions for interval `ising` (0-based, `0:msing`). Port of Fortran `gal_make_grid`
+(gal.f), `dx1dx2_flag=true` path. `intvl.x`/`intvl.dx` have length `nx+1`, `intvl.cells` length
+`nx` (preallocated by the caller). `sings` is the filtered list of resonant surfaces (1-based,
+`sings[ising]` = Fortran `sing(ising)`).
+
+Note (faithful to Fortran): the lower-surface width scale uses `|nn·q1|` (gal.f) but the
+upper-surface scale uses `|q1|` without `nn` (gal.f). Identical for `nn = 1`.
+"""
+function gal_make_grid!(intvl::GalInterval, ising::Int, msing::Int, sings::Vector{SingType},
+ nn::Int, psilow::Float64, psihigh::Float64, ctrl::ForceFreeStatesControl)
+
+ nx = ctrl.algorithm.nx
+ dx0 = ctrl.algorithm.dx0
+ dx1 = ctrl.algorithm.dx1
+ dx2 = ctrl.algorithm.dx2
+ pfac = ctrl.algorithm.pfac
+ cutoff = ctrl.algorithm.cutoff
+ xn = intvl.x
+ cells = intvl.cells
+
+ # Reset cell flags
+ for c in cells
+ c.etype = GCT_NONE
+ c.extra = GAL_SIDE_NONE
+ end
+
+ # --- lower bound (gal.f) ---
+ local ixmin::Int
+ if ising == 0
+ ixmin = 0
+ xn[0+1] = psilow
+ else
+ x0 = sings[ising].psifac
+ nq1 = abs(nn * sings[ising].q1)
+ xn[0+1] = x0
+ cells[1].x_lsode = x0 + dx0 / nq1
+ if ctrl.algorithm.dx1dx2_flag
+ xn[1+1] = x0 + dx1 / nq1
+ xn[2+1] = x0 + (dx1 + dx2) / nq1
+ ixmin = 2
+ else
+ ixmin = 0
+ end
+ cells[1].extra = GAL_SIDE_RIGHT
+ cells[2].extra = GAL_SIDE_RIGHT
+ cells[1].etype = GCT_RES
+ cells[2].etype = GCT_EXT
+ for ix in 3:(cutoff+1)
+ cells[ix].etype = GCT_EXT1
+ cells[ix].extra = GAL_SIDE_RIGHT
+ end
+ ix_ext2 = max(cutoff + 2, 3) # Fortran loop-exit value of ix (gal.f)
+ (ix_ext2 > nx || cells[ix_ext2].etype != GCT_NONE) &&
+ error("gal_make_grid: too many elements include the big solution (right side)")
+ cells[ix_ext2].etype = GCT_EXT2
+ cells[ix_ext2].extra = GAL_SIDE_RIGHT
+ end
+
+ # --- upper bound (gal.f) ---
+ local ixmax::Int
+ if ising == msing
+ ixmax = nx
+ xn[nx+1] = psihigh
+ else
+ x1 = sings[ising+1].psifac
+ nq1 = abs(nn * sings[ising+1].q1)
+ xn[nx+1] = x1
+ cells[nx].x_lsode = x1 - dx0 / nq1
+ if ctrl.algorithm.dx1dx2_flag
+ xn[(nx-1)+1] = x1 - dx1 / nq1
+ xn[(nx-2)+1] = x1 - (dx1 + dx2) / nq1
+ ixmax = nx - 2
+ else
+ ixmax = nx
+ end
+ cells[nx-1].extra = GAL_SIDE_LEFT
+ cells[nx].extra = GAL_SIDE_LEFT
+ cells[nx-1].etype = GCT_EXT
+ cells[nx].etype = GCT_RES
+ for ix in (nx-2):-1:(nx-cutoff)
+ cells[ix].etype = GCT_EXT1
+ cells[ix].extra = GAL_SIDE_LEFT
+ end
+ ix_ext2 = min(nx - cutoff - 1, nx - 2) # Fortran loop-exit value of ix (gal.f)
+ (ix_ext2 < 1 || cells[ix_ext2].etype != GCT_NONE) &&
+ error("gal_make_grid: too many elements include the big solution (left side)")
+ cells[ix_ext2].etype = GCT_EXT2
+ cells[ix_ext2].extra = GAL_SIDE_LEFT
+ end
+
+ # --- interior packed grid (gal.f) ---
+ x0 = xn[ixmin+1]
+ x1 = xn[ixmax+1]
+ xm = (xn[ixmax+1] + xn[ixmin+1]) / 2
+ dxh = (xn[ixmax+1] - xn[ixmin+1]) / 2
+ mx = (ixmax - ixmin) ÷ 2
+ # Default: symmetric "both" pack (faithful to gal.f). With gal_edge_onesided, the two end
+ # intervals pack only toward their single rational end, leaving the regular boundary (psilow at
+ # interval 0, psihigh at interval msing) at coarse spacing — removes the gratuitous fine edge cell.
+ side = "both"
+ if ctrl.algorithm.edge_onesided && msing > 0
+ if ising == 0
+ side = "right" # rational sits at the upper (ixmax) end
+ elseif ising == msing
+ side = "left" # rational sits at the lower (ixmin) end
+ end
+ end
+ packed = pack_grid(mx, pfac, side) # length 2*mx+1 = (ixmax-ixmin)+1
+ for k in 0:(ixmax-ixmin)
+ xn[ixmin+1+k] = xm + dxh * packed[k+1]
+ end
+ xn[ixmin+1] = x0
+ xn[ixmax+1] = x1
+
+ intvl.dx[0+1] = 0.0
+ for i in 1:nx
+ intvl.dx[i+1] = xn[i+1] - xn[i]
+ end
+ for ix in 1:nx
+ cells[ix].x = (xn[ix], xn[ix+1]) # Fortran (x(ix-1), x(ix))
+ end
+ return intvl
+end
+
+"""
+ gal_make_map!(ws::GalWorkspace, mpert::Int)
+
+Build the local→global DOF numbering with the `2*mpert` C¹ overlap between adjacent Hermite cells and
+the interleaved extra (small resonant) DOFs (`emap`). Port of Fortran `gal_make_map` (gal.f).
+Sets `ws.ndim`. The `skip`/`emap` bookkeeping reserves a global slot for each resonant coefficient and
+shares it between the `res` cell and its neighbouring `ext` cell.
+"""
+function gal_make_map!(ws::GalWorkspace, mpert::Int)
+ np = ws.np
+ msing = length(ws.intvl) - 1
+ imap = 1
+ skip = false
+ emap = 0
+ for ising in 0:msing
+ intvl = ws.intvl[ising+1]
+ for ix in 1:ws.nx
+ cell = intvl.cells[ix]
+ # Nonresonant Hermite DOFs (with 2*mpert overlap onto the previous cell)
+ if imap > 1
+ imap -= 2 * mpert
+ end
+ for ip in 0:np
+ for ipert in 1:mpert
+ cell.map[ipert, ip+1] = imap
+ imap += 1
+ end
+ if ip == 1 && skip
+ imap += 1
+ skip = false
+ end
+ end
+ # Extra (small resonant) DOF, shared between res and adjacent ext cell
+ if cell.extra == GAL_SIDE_LEFT
+ if cell.etype == GCT_EXT
+ emap = imap
+ cell.emap = emap
+ skip = true
+ elseif cell.etype == GCT_RES
+ cell.emap = emap
+ end
+ elseif cell.extra == GAL_SIDE_RIGHT
+ if cell.etype == GCT_RES
+ emap = imap
+ cell.emap = emap
+ skip = true
+ elseif cell.etype == GCT_EXT
+ cell.emap = emap
+ end
+ end
+ end
+ end
+ ws.ndim = imap - 1
+ return ws
+end
diff --git a/src/ForceFreeStates/Galerkin/GalerkinSolution.jl b/src/ForceFreeStates/Galerkin/GalerkinSolution.jl
new file mode 100644
index 0000000000..bed9c57780
--- /dev/null
+++ b/src/ForceFreeStates/Galerkin/GalerkinSolution.jl
@@ -0,0 +1,224 @@
+# GalerkinSolution.jl
+#
+# Reconstruct the outer-region radial displacement ξ(ψ) AND its analytic derivative ξ′(ψ) from the
+# solved Galerkin coefficients. Ports:
+# gal_get_solution (gal.f) ξ (and optional ξ′) at one ψ for one solution column
+# gal_output_solution (gal.f) evaluate (ξ, ξ′) on a gal-native packed grid, all columns
+#
+# ξ′ is evaluated analytically from the Hermite derivative basis (gal_hermite qb) and the asymptotic-series
+# derivative (sing_get_dua_gal), never by spline-differentiating ξ at the packed edge.
+#
+# The `cut=true` path swaps the resonant Frobenius series for its leading-order term
+# (`sing_get_ua_gal_cut`); the resulting cut solution supplies the regular background that the
+# resistive inner-layer solution is added to when forming the composite solution at a rational
+# surface (see MatchProblem).
+
+# Sampling points per cell, matching Fortran interp_np_res / interp_np (gal.f): coarse in regular cells,
+# dense in resonant/extension cells to resolve the near-singular asymptotic series.
+const GAL_INTERP_NP = 3
+const GAL_INTERP_NP_RES = 60
+
+# Advance the monotone (iintvl, icell) cursor to the cell containing x. Port of gal.f.
+@inline function gal_locate_cell(ws::GalWorkspace, x::Float64, iintvl::Int, icell::Int)
+ msing = length(ws.intvl) - 1
+ for _ in 1:((msing+1)*ws.nx+1) # bounded scan: at most one full wrap over all cells
+ cell = ws.intvl[iintvl+1].cells[icell]
+ if cell.x[1] <= x <= cell.x[2]
+ return iintvl, icell, cell
+ end
+ icell += 1
+ if icell > ws.nx
+ icell = 1
+ iintvl += 1
+ end
+ if iintvl > msing
+ iintvl = 0
+ end
+ end
+ error("gal_locate_cell: x=$x not found in any cell")
+end
+
+"""
+ gal_get_solution(ws, asymps, sings, intr, x, iintvl, icell, isol; want_d=true, cut_delta=nothing)
+ -> (sol, dsol, iintvl, icell)
+
+Reconstruct the displacement `sol` (length `mpert`) — and, when `want_d`, its analytic radial
+derivative `dsol = d(sol)/dψ` — at flux `x` for solution column `isol`, from the solved Galerkin
+coefficients `ws.sol`. Port of `gal_get_solution` (gal.f). `iintvl`/`icell`
+are a monotone cell cursor advanced and returned for the next call. `dsol` is `nothing` if `!want_d`.
+
+Passing `cut_delta` (the `(nsol, 2·msing)` small-solution coefficient matrix, i.e. `GalerkinResult.delta`)
+selects the *cut* solution: the leading-order resonant content is subtracted from the reconstruction,
+leaving the smooth background that the resistive inner-layer solution is added to when forming the
+composite solution at a rational surface. `want_d` is forced off in that case.
+"""
+function gal_get_solution(ws::GalWorkspace, asymps::Vector{GalSingAsymp}, sings::Vector{SingType},
+ intr::ForceFreeStatesInternal, x::Float64, iintvl::Int, icell::Int, isol::Int; want_d::Bool=true,
+ cut_delta::Union{Nothing,AbstractMatrix{ComplexF64}}=nothing)
+
+ cut_delta === nothing || (want_d = false)
+
+ msing = length(ws.intvl) - 1
+ mpert = intr.numpert_total
+ np = GAL_NP
+ iintvl, icell, cell = gal_locate_cell(ws, x, iintvl, icell)
+
+ sol = zeros(ComplexF64, mpert)
+ dsol = want_d ? zeros(ComplexF64, mpert) : nothing
+
+ # --- non-resonant (Hermite) part: same coefficients, value basis pb → ξ, derivative basis qb → ξ′ ---
+ pbt, qbt = hermite_basis(x, cell.x[1], cell.x[2])
+ swap = iintvl == msing && icell == ws.nx # last edge cell: swap node-2/3 DOFs (gal.f)
+ pb = swap ? (pbt[1], pbt[2], pbt[4], pbt[3]) : pbt
+ qb = swap ? (qbt[1], qbt[2], qbt[4], qbt[3]) : qbt
+ for ip in 0:np
+ u = @view ws.sol[cell.map[:, ip+1], isol]
+ @views sol .+= u .* pb[ip+1]
+ want_d && (@views dsol .+= u .* qb[ip+1])
+ end
+
+ cell.etype == GCT_NONE && return sol, dsol, iintvl, icell
+
+ # --- small & large resonant/extension solutions (gal.f) ---
+ jsing = _cell_jsing(cell, iintvl) # left → iintvl+1, right → iintvl (gal_get_solution)
+ asymp = asymps[jsing]
+ psi_s = sings[jsing].psifac
+ # sing_get_*_gal returns only the two resonant columns: 1 = big solution, 2 = small solution.
+
+ # Edge Hermite weights (fresh, unswapped) for ext/ext2 cells (gal.f)
+ pbe, qbe = hermite_basis(x, cell.x[1], cell.x[2])
+ if cell.extra == GAL_SIDE_LEFT
+ epb1, epb2 = pbe[3], pbe[4]
+ eqb1, eqb2 = qbe[3], qbe[4]
+ xext = cell.x[2]
+ else
+ epb1, epb2 = pbe[1], pbe[2]
+ eqb1, eqb2 = qbe[1], qbe[2]
+ xext = cell.x[1]
+ end
+
+ need_in = cell.etype == GCT_RES || cell.etype == GCT_EXT || cell.etype == GCT_EXT1
+ need_ext = cell.etype == GCT_EXT || cell.etype == GCT_EXT2
+ ua = need_in ? sing_get_ua_gal(asymp, x - psi_s) : nothing
+ dua = (need_in && want_d) ? sing_get_dua_gal(asymp, x - psi_s) : nothing
+ uaext = need_ext ? sing_get_ua_gal(asymp, xext - psi_s) : nothing
+ duaext = need_ext ? sing_get_dua_gal(asymp, xext - psi_s) : nothing
+
+ # small solution Δ-coefficient restore (ext/res only), coeff = ws.sol[emap,isol] (gal.f)
+ if cell.etype == GCT_RES || cell.etype == GCT_EXT
+ delta = ws.sol[cell.emap, isol]
+ if cell.etype == GCT_RES
+ @views sol .+= delta .* ua[:, 2, 1]
+ want_d && (@views dsol .+= delta .* dua[:, 2, 1])
+ else # GCT_EXT: series held at the fixed edge xext, x-dependence only via Hermite weights
+ @views sol .+= delta .* (epb1 .* uaext[:, 2, 1] .+ epb2 .* duaext[:, 2, 1])
+ want_d && (@views dsol .+= delta .* (eqb1 .* uaext[:, 2, 1] .+ eqb2 .* duaext[:, 2, 1]))
+ end
+ end
+
+ # large solution (coeff 1) only for the column driving this surface/side (gal.f)
+ driving = (isol == 2jsing - 1 && cell.extra == GAL_SIDE_LEFT) ||
+ (isol == 2jsing && cell.extra == GAL_SIDE_RIGHT)
+ if driving
+ if cell.etype == GCT_RES || cell.etype == GCT_EXT || cell.etype == GCT_EXT1
+ @views sol .+= ua[:, 1, 1]
+ want_d && (@views dsol .+= dua[:, 1, 1])
+ elseif cell.etype == GCT_EXT2
+ @views sol .+= epb1 .* uaext[:, 1, 1] .+ epb2 .* duaext[:, 1, 1]
+ want_d && (@views dsol .+= eqb1 .* uaext[:, 1, 1] .+ eqb2 .* duaext[:, 1, 1])
+ end
+ end
+
+ # Cut solution (gal.f cut_flag block): remove the leading-order resonant content, evaluated at x
+ # for every resonant cell type. The small coefficient comes from the Δ′ matrix rather than
+ # `cell.emap` because ext1/ext2 cells carry no emap.
+ if cut_delta !== nothing
+ jsol = cell.extra == GAL_SIDE_LEFT ? 2jsing - 1 : 2jsing
+ ua_cut = sing_get_ua_gal_cut(asymp, x - psi_s)
+ @views sol .-= cut_delta[isol, jsol] .* ua_cut[:, 2, 1]
+ driving && (@views sol .-= ua_cut[:, 1, 1])
+ end
+
+ return sol, dsol, iintvl, icell
+end
+
+"""
+ gal_output_solution(ws, asymps, sings, intr, profiles, psihigh; delta=nothing) -> GalerkinSolution
+
+Build the gal-native packed radial grid (inner→edge; `GAL_INTERP_NP_RES` points per resonant/extension
+cell, `GAL_INTERP_NP` elsewhere, plus the edge point ψ=psihigh) and evaluate ξ AND the analytic ξ′ over
+it for every solution column. Port of `gal_output_solution` (gal.f), returning ξ rather than b^ψ.
+
+When `delta` (the `(nsol, 2·msing)` small-solution coefficient matrix) is supplied, the cut solution
+`xi_cut` is evaluated on the same grid, as the background of MatchProblem's composite inner solution.
+"""
+function gal_output_solution(ws::GalWorkspace, asymps::Vector{GalSingAsymp}, sings::Vector{SingType},
+ intr::ForceFreeStatesInternal, profiles, psihigh::Float64;
+ delta::Union{Nothing,AbstractMatrix{ComplexF64}}=nothing)
+
+ mpert = intr.numpert_total
+ msing = length(ws.intvl) - 1
+
+ # --- grid (gal.f): per-cell left-inclusive sampling, then the edge point ---
+ psi = Float64[]
+ issing = Bool[]
+ for iintvl in 0:msing
+ for icell in 1:ws.nx
+ cell = ws.intvl[iintvl+1].cells[icell]
+ npts = (cell.etype == GCT_RES || cell.etype == GCT_EXT) ? GAL_INTERP_NP_RES : GAL_INTERP_NP
+ x1, x2 = cell.x
+ for k in 0:(npts-1)
+ push!(psi, x1 + (x2 - x1) * (k / npts))
+ # res-right cell's first point sits exactly on the surface (gal.f)
+ push!(issing, k == 0 && cell.extra == GAL_SIDE_RIGHT && cell.etype == GCT_RES)
+ end
+ end
+ end
+ push!(psi, psihigh)
+ push!(issing, false)
+
+ qhint = Ref(1)
+ q = [profiles.q_spline(p; hint=qhint) for p in psi]
+
+ # --- evaluate (gal.f) ---
+ ngrid = length(psi)
+ xi = zeros(ComplexF64, mpert, ngrid, ws.nsol)
+ xi_deriv = zeros(ComplexF64, mpert, ngrid, ws.nsol)
+ xi_cut = delta === nothing ? zeros(ComplexF64, 0, 0, 0) : zeros(ComplexF64, mpert, ngrid, ws.nsol)
+ for isol in 1:ws.nsol
+ iintvl = 0
+ icell = 1
+ for ip in 1:ngrid
+ issing[ip] && continue
+ sol, dsol, iintvl, icell = gal_get_solution(ws, asymps, sings, intr, psi[ip], iintvl, icell, isol)
+ @views xi[:, ip, isol] .= sol
+ @views xi_deriv[:, ip, isol] .= dsol
+ end
+ delta === nothing && continue
+ iintvl = 0
+ icell = 1
+ for ip in 1:ngrid
+ issing[ip] && continue
+ solc, _, iintvl, icell = gal_get_solution(ws, asymps, sings, intr, psi[ip], iintvl, icell, isol;
+ cut_delta=delta)
+ @views xi_cut[:, ip, isol] .= solc
+ end
+ end
+
+ # ψ span of the resonant + extension cells flanking each surface: outside it the cut subtracts
+ # nothing, so the composite inner-region solution is only defined within these bounds
+ # (Fortran `outs%xext`).
+ cut_range = zeros(Float64, 0, 0)
+ if delta !== nothing
+ cut_range = hcat(fill(Inf, msing), fill(-Inf, msing))
+ for iintvl in 0:msing, icell in 1:ws.nx
+ cell = ws.intvl[iintvl+1].cells[icell]
+ cell.etype == GCT_NONE && continue
+ js = _cell_jsing(cell, iintvl)
+ cut_range[js, 1] = min(cut_range[js, 1], cell.x[1])
+ cut_range[js, 2] = max(cut_range[js, 2], cell.x[2])
+ end
+ end
+
+ return GalerkinSolution(psi, q, issing, xi, xi_deriv, xi_cut, cut_range)
+end
diff --git a/src/ForceFreeStates/Galerkin/GalerkinSolve.jl b/src/ForceFreeStates/Galerkin/GalerkinSolve.jl
new file mode 100644
index 0000000000..5d4f6d2df5
--- /dev/null
+++ b/src/ForceFreeStates/Galerkin/GalerkinSolve.jl
@@ -0,0 +1,410 @@
+# GalerkinSolve.jl
+#
+# Top-level driver for the RDCON outer-region singular Galerkin Δ′ solve, plus the per-cell assembly
+# orchestration, the banded solve, Δ′ extraction, PEST-3 blocks, and HDF5 output.
+# Ports gal_make_arrays (gal.f), gal_solve (gal.f), and gal_write_pest3_data
+# (gal.f). Inner-layer matching is applied afterwards by MatchProblem.
+
+"""
+ gal_make_arrays!(ws, ctrl, equil, mats, intr, asymps, sings, nn, wv_edge)
+
+Assemble the global banded matrix and RHS. For each cell: Gauss-Lobatto Hermite stiffness
+(`gal_gauss_quad!`), then the resonant (`gal_resonant!`) or extension (`gal_extension!`) contributions;
+then the boundary conditions and the scatter into `ws.mat`/`ws.rhs`. Port of `gal_make_arrays`.
+"""
+function gal_make_arrays!(ws::GalWorkspace, ctrl::ForceFreeStatesControl, equil, mats::MatrixSplines,
+ intr::ForceFreeStatesInternal, asymps::Vector{GalSingAsymp}, sings::Vector{SingType},
+ nn::Int, wv_edge::Union{Nothing,Matrix{ComplexF64}})
+
+ mpert = intr.numpert_total
+ msing = length(ws.intvl) - 1
+ profiles = equil.profiles
+ nodes, weights = gausslobatto(ws.nq + 1)
+
+ for ising in 0:msing
+ for (ix, cell) in enumerate(ws.intvl[ising+1].cells)
+ swap_edge = (ising == msing && ix == ws.nx)
+ gal_gauss_quad!(cell, mats, profiles, intr, nodes, weights, swap_edge)
+ if cell.etype == GCT_RES
+ gal_resonant!(cell, ising, mats, profiles, intr, asymps, sings, nn, ctrl.algorithm.tol, ctrl.algorithm.gnstep, intr.verbose)
+ elseif cell.etype == GCT_EXT || cell.etype == GCT_EXT1 || cell.etype == GCT_EXT2
+ gal_extension!(cell, ising, mats, profiles, intr, asymps, sings, nn, nodes, weights)
+ end
+ end
+ end
+
+ gal_set_boundary!(ws, mpert, wv_edge)
+ gal_assemble_mat!(ws, mpert)
+ gal_assemble_rhs!(ws, mpert)
+ return ws
+end
+
+"""
+Empty `GalerkinResult` for a domain with no resonant surfaces.
+"""
+function empty_galerkin_result()
+ return GalerkinResult(0, Float64[], Float64[], Int[], Int[], Float64[], ComplexF64[], nothing, "none")
+end
+
+"""
+ galerkin_solve(ctrl::ForceFreeStatesControl, equil, mats::MatrixSplines,
+ intr::ForceFreeStatesInternal; wv=nothing, cut_solution=false) -> (GalerkinResult, Union{Nothing,DeltaPrimeData})
+
+Compute the outer-region Δ′ matching matrix by the singular Galerkin method. Port of `gal_solve`
+(gal.f). Single toroidal mode only (`intr.npert == 1`). Returns the solver internals as a
+`GalerkinResult` alongside the Δ′ payload as the shared [`DeltaPrimeData`](@ref); if there are no
+resonant surfaces in the domain it returns an empty result and `nothing`.
+
+`wv` is the vacuum energy matrix from `free_run`, which supplies the free-boundary edge term
+`wv_edge = wv · psio²`; pass `nothing` for a fixed-boundary edge. `cut_solution` also keeps the
+cut solution, for a later `MatchProblem`'s composite inner profiles.
+"""
+function galerkin_solve(ctrl::ForceFreeStatesControl, equil, mats::MatrixSplines,
+ intr::ForceFreeStatesInternal; wv=nothing, cut_solution::Bool=false)
+
+ intr.npert == 1 || error("galerkin_solve: only single-n (npert == 1) is supported")
+ validate_algorithm(ctrl)
+ nn = intr.nlow
+ mpert = intr.numpert_total
+ np = GAL_NP
+
+ sings, psilow, psihigh = gal_resonant_surfaces(intr, equil)
+ msing = length(sings)
+ if msing == 0
+ intr.verbose && @info "galerkin_solve: no resonant surfaces in domain; skipping Δ′ solve"
+ return empty_galerkin_result(), nothing
+ end
+
+ intr.verbose && @info "Starting outer-region Galerkin Δ′ solve (msing=$msing, automatic factorization)"
+
+ # Per-surface two-sided asymptotic series (sig = ±1). Each side uses its own resonant block.
+ asymps = GalSingAsymp[]
+ for s in sings
+ sing_order = ctrl.frobenius_order
+ ar = compute_sing_asymptotics(s, ctrl, equil, mats, intr; sig=1.0, sing_order=sing_order)
+ if ctrl.algorithm.frobenius_order_ceiling
+ # The order is raised for high-Mercier-index surfaces
+ order = ctrl.frobenius_order + ceil(Int, 2 * real(ar.alpha[1]))
+ if order > ctrl.frobenius_order
+ sing_order = order
+ ar = compute_sing_asymptotics(s, ctrl, equil, mats, intr; sig=1.0, sing_order=sing_order)
+ end
+ end
+ al = compute_sing_asymptotics(s, ctrl, equil, mats, intr; sig=-1.0, sing_order=sing_order)
+ push!(asymps, GalSingAsymp(ar, al))
+ end
+
+ # --- allocate workspace ---
+ nx = ctrl.algorithm.nx
+ kl = mpert * (np + 1)
+ ku = kl
+ ldab = 2kl + ku + 1
+ # rpec_flag (RDCON, gal.f): append mpert coil-response columns. Each is a unit source at
+ # the edge value DOF in one poloidal mode; the recorded plasma response is the coil block of Δ_gw.
+ ncoil = ctrl.algorithm.rpec_flag ? mpert : 0
+ nsol = 2 * msing + ncoil
+ intvl = [GalInterval(zeros(Float64, nx + 1), zeros(Float64, nx + 1), [GalCell(mpert) for _ in 1:nx])
+ for _ in 0:msing]
+ ws = GalWorkspace("auto", nx, ctrl.algorithm.nq, np, 0, kl, ku, ldab, nsol,
+ intvl, Matrix{ComplexF64}(undef, 0, 0), Matrix{ComplexF64}(undef, 0, 0), Matrix{ComplexF64}(undef, 0, 0))
+
+ for ising in 0:msing
+ gal_make_grid!(ws.intvl[ising+1], ising, msing, sings, nn, psilow, psihigh, ctrl)
+ end
+ gal_make_map!(ws, mpert)
+
+ ws.mat = zeros(ComplexF64, ldab, ws.ndim)
+ ws.rhs = zeros(ComplexF64, ws.ndim, nsol)
+ ws.sol = zeros(ComplexF64, ws.ndim, nsol)
+
+ # Free-boundary edge term wvac·psio² (wv is already singfac-scaled at qlim in free_run).
+ # rpec passes wv_edge=nothing; gal_set_boundary! then applies the identity edge AND injects the coil
+ # unit sources (its three-way branch). The vacuum block is only built for the non-rpec free case.
+ wv_edge = nothing
+ if ctrl.vac_flag && wv !== nothing && ncoil == 0
+ wv_edge = Matrix{ComplexF64}(wv .* equil.psio^2)
+ end
+
+ gal_make_arrays!(ws, ctrl, equil, mats, intr, asymps, sings, nn, wv_edge)
+
+ if intr.verbose
+ offdbg = ws.kl + ws.ku + 1
+ @info "Galerkin assembly: ndim=$(ws.ndim) nsol=$nsol kl=$(ws.kl) ldab=$(ws.ldab) |rhs|=$(norm(ws.rhs))"
+ for ising in 0:msing
+ for cell in ws.intvl[ising+1].cells
+ if cell.etype == GCT_RES || cell.etype == GCT_EXT
+ @info " cell ising=$ising etype=$(cell.etype) side=$(cell.extra) emap=$(cell.emap) ediag=$(cell.ediag) erhs=$(cell.erhs) |rhs|=$(norm(cell.rhs)) |emat|=$(norm(cell.emat)) matdiag[emap]=$(ws.mat[offdbg, cell.emap])"
+ end
+ end
+ end
+ end
+
+ # --- banded solve (gal.f) ---
+ ws.sol .= ws.rhs
+ ws.solver = gal_banded_solve!(ws.mat, ws.sol, ws.kl, ws.ku, "auto")
+ intr.verbose && @info "Galerkin banded solve: $(ws.solver)"
+
+ # --- extract Δ′ from the small resonant coefficients (gal.f) ---
+ delta = zeros(ComplexF64, nsol, 2 * msing)
+ jsol = 0
+ for ising in 0:msing
+ for cell in ws.intvl[ising+1].cells
+ if cell.etype == GCT_RES
+ jsol += 1
+ @views delta[:, jsol] .= ws.sol[cell.emap, :]
+ end
+ end
+ end
+
+ Ap, Bp, Gammap, Deltap = gal_pest3_blocks(delta, msing)
+
+ # Mercier index D_I = -Re(α²). α is the half-separation of the resonant exponents.
+ di = [real(-asymps[i].right.alpha[1]^2) for i in 1:msing]
+ alpha = [asymps[i].right.alpha[1] for i in 1:msing]
+
+ # Pack the Δ′ payload in the shared layout: the raw D′ is the leading 2msing×2msing side-major
+ # block, and the coil-response rows 2*msing+1 : 2*msing+mpert (rpec_flag) transpose into the
+ # (surface-side × edge mode) orientation the Riccati BVP also produces.
+ dp_raw = delta[1:(2*msing), 1:(2*msing)]
+ dp_coil = ncoil > 0 ? permutedims(delta[(2*msing+1):(2*msing+ncoil), :]) : Matrix{ComplexF64}(undef, 0, 0)
+ dp = DeltaPrimeData(Deltap, dp_raw, dp_coil, Ap, Bp, Gammap)
+
+ # Reconstruct ξ(ψ) AND analytic ξ′(ψ) on the gal-native grid (gal_output_solution); the cut
+ # solution only when a later match needs the composite inner profiles.
+ intr.verbose && @info "Reconstructing outer-region ξ and analytic ξ′ on the gal grid"
+ solution = gal_output_solution(ws, asymps, sings, intr, equil.profiles, psihigh;
+ delta=(cut_solution ? delta : nothing))
+
+ sing_psi = [s.psifac for s in sings]
+ sing_q = [s.q for s in sings]
+ sing_m = [s.m[1] for s in sings]
+ sing_n = [s.n[1] for s in sings]
+ return GalerkinResult(msing, sing_psi, sing_q, sing_m, sing_n, di, alpha, solution, ws.solver), dp
+end
+
+"""
+ gal_scaled_lu_solve!(mat, sol, kl, ku) -> sol
+
+Banded LU solve in place: `mat` (LAPACK `gbtrf!` band storage, `ldab = 2kl + ku + 1`) is overwritten by
+its factor and `sol` (the right-hand sides on entry) by the solution. The system is first symmetrically
+Jacobi-scaled, `D·A·D` with `d_j = |A_jj|^(-1/2)` (1 for a zero diagonal): the assembled diagonal spans
+~25 decades, and unscaled banded LU loses the small resonant coefficients that carry Δ′.
+"""
+function gal_scaled_lu_solve!(mat::Matrix{ComplexF64}, sol::AbstractVecOrMat{ComplexF64}, kl::Int, ku::Int)
+ n = size(mat, 2)
+ off = kl + ku + 1 # band row holding the diagonal
+ d = [iszero(mat[off, j]) ? 1.0 : 1 / sqrt(abs(mat[off, j])) for j in 1:n]
+ for j in 1:n, i in max(1, j - ku):min(n, j + kl)
+ mat[off+i-j, j] *= d[i] * d[j]
+ end
+ sol .*= d
+ _, ipiv = LAPACK.gbtrf!(kl, ku, n, mat)
+ LAPACK.gbtrs!('N', kl, ku, n, mat, ipiv, sol)
+ sol .*= d
+ return sol
+end
+
+"""
+ gal_pest3_blocks(delta, msing) -> (Ap, Bp, Gammap, Deltap)
+
+PEST-3 matching blocks (each `msing×msing`) as ± combinations of the left/right Δ′ entries. Port of
+`gal_write_pest3_data`. Row index `2i-1`/`2i` = left/right of surface `i`.
+"""
+function gal_pest3_blocks(delta::Matrix{ComplexF64}, msing::Int)
+ Ap = zeros(ComplexF64, msing, msing)
+ Bp = zeros(ComplexF64, msing, msing)
+ Gammap = zeros(ComplexF64, msing, msing)
+ Deltap = zeros(ComplexF64, msing, msing)
+ for i in 1:msing, j in 1:msing
+ d11 = delta[2i-1, 2j-1]
+ d12 = delta[2i-1, 2j]
+ d21 = delta[2i, 2j-1]
+ d22 = delta[2i, 2j]
+ Ap[i, j] = d22 + d21 + d12 + d11
+ Bp[i, j] = d22 - d21 + d12 - d11
+ Gammap[i, j] = d22 + d21 - d12 - d11
+ Deltap[i, j] = d22 - d21 - d12 + d11
+ end
+ return Ap, Bp, Gammap, Deltap
+end
+
+"""
+ write_galerkin!(out_h5, result::GalerkinResult; basis_output=false)
+
+Write the Galerkin surface list (a subset of `SingularSurfaces/` when the domain or the m-band excludes
+rationals) under `ForceFreeStates/Solutions/GalerkinIntegration/`. The Δ′/PEST-3 matrices and closed ξ
+profiles are written by the driver writer, not here. With `basis_output`, the raw per-interval
+outer-region basis functions (solver internals) are written under `Basis/`.
+"""
+function write_galerkin!(out_h5, result::GalerkinResult; basis_output::Bool=false)
+ gal = "ForceFreeStates/Solutions/GalerkinIntegration"
+ out_h5["$gal/rational_count"] = result.msing
+ out_h5["$gal/solver"] = result.solver
+ if result.msing == 0
+ annotate_galerkin!(out_h5)
+ return nothing
+ end
+ out_h5["$gal/rational_psi"] = result.sing_psi
+ out_h5["$gal/rational_q"] = result.sing_q
+ out_h5["$gal/rational_m"] = result.sing_m
+ out_h5["$gal/rational_n"] = result.sing_n
+ out_h5["$gal/D_I"] = result.di
+ out_h5["$gal/alpha"] = result.alpha
+ if basis_output && result.solution !== nothing
+ sol = result.solution
+ out_h5["$gal/Basis/psi"] = sol.psi
+ out_h5["$gal/Basis/is_rational"] = collect(sol.issing)
+ out_h5["$gal/Basis/xi_psi"] = permutedims(sol.xi, (1, 3, 2))
+ out_h5["$gal/Basis/dxi_psidpsi"] = permutedims(sol.xi_deriv, (1, 3, 2))
+ isempty(sol.xi_cut) || (out_h5["$gal/Basis/xi_psi_cut"] = permutedims(sol.xi_cut, (1, 3, 2)))
+ isempty(sol.cut_range) || (out_h5["$gal/Basis/cut_range"] = sol.cut_range)
+ end
+ annotate_galerkin!(out_h5)
+ return nothing
+end
+
+# Metadata tables for the Galerkin outputs (see docs/development/hdf5-conventions.md).
+const GALERKIN_H5_ANNOTATIONS = [
+ "ForceFreeStates/Solutions/GalerkinIntegration/rational_count" => (; long_name="number of rational (singular) surfaces in the Galerkin solve"),
+ "ForceFreeStates/Solutions/GalerkinIntegration/solver" =>
+ (; long_name="banded solver used for the Galerkin system: cholesky, LU, or none when no rational surfaces were present"),
+ "ForceFreeStates/Solutions/GalerkinIntegration/psi" => (; long_name="normalized poloidal flux ψ_N grid of the closed Galerkin solution", scale="psi_gal"),
+ "ForceFreeStates/Solutions/GalerkinIntegration/q" =>
+ (; long_name="safety factor q on the Galerkin solution grid", dims=("psi",), attach=(1 => "ForceFreeStates/Solutions/GalerkinIntegration/psi",)),
+ "ForceFreeStates/Solutions/GalerkinIntegration/xi_psi" =>
+ (;
+ long_name="closed axis-to-edge ξ^ψ profiles (ideal or inner-layer closure; identity-at-edge basis)",
+ dims=("mode", "solution", "psi"),
+ attach=(3 => "ForceFreeStates/Solutions/GalerkinIntegration/psi",)
+ ),
+ "ForceFreeStates/Solutions/GalerkinIntegration/dxi_psidpsi" =>
+ (; long_name="analytic ψ_N derivative of the closed ξ^ψ profiles", dims=("mode", "solution", "psi"), attach=(3 => "ForceFreeStates/Solutions/GalerkinIntegration/psi",)),
+ "ForceFreeStates/Solutions/GalerkinIntegration/xi_s" =>
+ (;
+ long_name="surface displacement ξ_s from the outer ideal-MHD relation",
+ dims=("mode", "solution", "psi"),
+ attach=(3 => "ForceFreeStates/Solutions/GalerkinIntegration/psi",)
+ ),
+ "ForceFreeStates/Solutions/GalerkinIntegration/Basis/psi" => (; long_name="normalized poloidal flux ψ_N grid of the raw Galerkin basis", scale="psi_gal_basis"),
+ "ForceFreeStates/Solutions/GalerkinIntegration/Basis/is_rational" =>
+ (; long_name="flag: grid node lies on a rational surface", dims=("psi",), attach=(1 => "ForceFreeStates/Solutions/GalerkinIntegration/Basis/psi",)),
+ "ForceFreeStates/Solutions/GalerkinIntegration/Basis/xi_psi" =>
+ (; long_name="raw Galerkin outer-region basis functions ξ^ψ (per-interval, unconstrained at the rationals; debug output)", dims=("mode", "solution", "psi")),
+ "ForceFreeStates/Solutions/GalerkinIntegration/Basis/dxi_psidpsi" =>
+ (; long_name="ψ_N derivative of the raw Galerkin basis functions (debug output)", dims=("mode", "solution", "psi")),
+ "ForceFreeStates/Solutions/GalerkinIntegration/Basis/xi_psi_cut" =>
+ (; long_name="raw Galerkin basis functions with the leading-order resonant response excised (debug output)", dims=("mode", "solution", "psi")),
+ "ForceFreeStates/Solutions/GalerkinIntegration/Basis/cut_range" =>
+ (; long_name="ψ_N bounds of the excised resonant + extension cells per surface", dims=("surface", "bound")),
+ "ForceFreeStates/Solutions/GalerkinIntegration/rational_psi" =>
+ (; long_name="normalized poloidal flux ψ_N of each rational surface in the Galerkin solve", scale="psi_gal_rational"),
+ "ForceFreeStates/Solutions/GalerkinIntegration/rational_q" =>
+ (; long_name="safety factor q = m/n at each rational surface in the Galerkin solve", dims=("surface",),
+ attach=(1 => "ForceFreeStates/Solutions/GalerkinIntegration/rational_psi",)),
+ "ForceFreeStates/Solutions/GalerkinIntegration/rational_m" =>
+ (; long_name="resonant poloidal mode number m at each rational surface in the Galerkin solve", dims=("surface",),
+ attach=(1 => "ForceFreeStates/Solutions/GalerkinIntegration/rational_psi",)),
+ "ForceFreeStates/Solutions/GalerkinIntegration/rational_n" =>
+ (; long_name="resonant toroidal mode number n at each rational surface in the Galerkin solve", dims=("surface",),
+ attach=(1 => "ForceFreeStates/Solutions/GalerkinIntegration/rational_psi",)),
+ "ForceFreeStates/Solutions/GalerkinIntegration/D_I" =>
+ (; long_name="Mercier D_I at each rational surface in the Galerkin solve", dims=("surface",),
+ attach=(1 => "ForceFreeStates/Solutions/GalerkinIntegration/rational_psi",)),
+ "ForceFreeStates/Solutions/GalerkinIntegration/alpha" =>
+ (; long_name="Frobenius small-solution exponent α at each rational surface in the Galerkin solve", dims=("surface",),
+ attach=(1 => "ForceFreeStates/Solutions/GalerkinIntegration/rational_psi",))
+]
+
+# Attach long_name/units/dims + dimension scales (declared in-table) to everything
+# write_galerkin! wrote.
+function annotate_galerkin!(out_h5)
+ Utilities.HDF5Annotations.annotate!(out_h5, GALERKIN_H5_ANNOTATIONS)
+ return nothing
+end
+
+"""
+ gal_banded_solve!(mat, sol, kl, ku, solver) -> String
+
+Solve the full-band system `mat` (LAPACK `gbtrf` storage) in place of `sol` and return the
+solver used. `"auto"` tries `gal_cholesky_solve!` and reports a fallback to
+`gal_scaled_lu_solve!` for unequal bandwidths, asymmetric off-diagonal entries, or a
+non-positive-definite real-diagonal system. `"cholesky"` errors instead of falling back.
+"""
+function gal_banded_solve!(mat::Matrix{ComplexF64}, sol::AbstractVecOrMat{ComplexF64}, kl::Int, ku::Int, solver::String)
+ if solver != "LU"
+ if kl != ku
+ solver == "cholesky" && throw(ArgumentError("solver=\"cholesky\" requires equal lower and upper bandwidths (kl=$kl, ku=$ku)"))
+ @info "Galerkin Cholesky requires equal lower and upper bandwidths; solving by LU" kl ku
+ else
+ gal_cholesky_solve!(mat, sol, kl, ku) && return "cholesky"
+ solver == "cholesky" &&
+ error("solver=\"cholesky\": off-diagonal entries are not Hermitian or the real-diagonal system is not positive definite; use \"auto\" or \"LU\"")
+ @info "Galerkin off-diagonal entries are not Hermitian or the real-diagonal system is not positive definite; solving by LU"
+ end
+ end
+ gal_scaled_lu_solve!(mat, sol, kl, ku)
+ return "LU"
+end
+
+"""
+ gal_cholesky_solve!(mat, sol, kl, ku) -> Bool
+
+Banded Cholesky solve of the full-band system `mat`, leaving `mat` untouched. Rows that are
+identity rows (Dirichlet DOFs: axis, fixed or coil edge) have their columns moved to the
+right-hand side. The free block's off-diagonal entries must agree with their conjugate
+partners within `1e-10 * sqrt(abs(A_ii)) * sqrt(abs(A_jj))`. Cholesky uses the lower band
+and deliberately projects the diagonal onto its real part. Returns `false`, with `sol`
+unchanged, for unequal bandwidths, nonfinite entries, off-diagonal asymmetry, or a
+non-positive-definite projected matrix.
+"""
+function gal_cholesky_solve!(mat::Matrix{ComplexF64}, sol::AbstractVecOrMat{ComplexF64}, kl::Int, ku::Int)
+ kl == ku || return false
+ n = size(mat, 2)
+ off = 2kl + 1
+ a(i, j) = mat[off+i-j, j]
+ band(i) = max(1, i - kl):min(n, i + kl)
+ fixed = [all(j == i ? a(i, j) == 1 : iszero(a(i, j)) for j in band(i)) for i in 1:n]
+ for j in 1:n
+ isfinite(a(j, j)) || return false
+ for i in (j+1):min(n, j + kl)
+ isfinite(a(i, j)) && isfinite(a(j, i)) || return false
+ fixed[i] || fixed[j] ||
+ abs(a(i, j) - conj(a(j, i))) <= 1e-10 * sqrt(abs(a(i, i))) * sqrt(abs(a(j, j))) || return false
+ end
+ end
+ ab = zeros(ComplexF64, kl + 1, n)
+ for j in 1:n, i in j:min(n, j + kl)
+ ab[1+i-j, j] = fixed[i] || fixed[j] ? (i == j ? one(ComplexF64) : zero(ComplexF64)) : a(i, j)
+ end
+ gal_zpbtrf!(ab, kl) || return false
+ for c in 1:n
+ fixed[c] || continue
+ for r in band(c)
+ r == c || fixed[r] || (@views sol[r, :] .-= a(r, c) .* sol[c, :])
+ end
+ end
+ gal_zpbtrs!(ab, kl, sol)
+ return true
+end
+
+# Lower-band Hermitian Cholesky (LAPACK zpbtrf/zpbtrs, 'L'). LinearAlgebra.LAPACK has no
+# pbtrf!/pbtrs! wrapper, so call LAPACK directly. Returns false if not positive definite.
+function gal_zpbtrf!(AB::Matrix{ComplexF64}, kd::Int)
+ info = Ref{LinearAlgebra.BlasInt}()
+ ccall((LinearAlgebra.BLAS.@blasfunc(zpbtrf_), LinearAlgebra.libblastrampoline), Cvoid,
+ (Ref{UInt8}, Ref{LinearAlgebra.BlasInt}, Ref{LinearAlgebra.BlasInt}, Ptr{ComplexF64}, Ref{LinearAlgebra.BlasInt},
+ Ref{LinearAlgebra.BlasInt}, Clong),
+ 'L', size(AB, 2), kd, AB, max(1, stride(AB, 2)), info, 1)
+ LAPACK.chklapackerror(min(info[], 0))
+ return info[] == 0
+end
+
+function gal_zpbtrs!(AB::Matrix{ComplexF64}, kd::Int, B::AbstractVecOrMat{ComplexF64})
+ info = Ref{LinearAlgebra.BlasInt}()
+ ccall((LinearAlgebra.BLAS.@blasfunc(zpbtrs_), LinearAlgebra.libblastrampoline), Cvoid,
+ (Ref{UInt8}, Ref{LinearAlgebra.BlasInt}, Ref{LinearAlgebra.BlasInt}, Ref{LinearAlgebra.BlasInt}, Ptr{ComplexF64},
+ Ref{LinearAlgebra.BlasInt}, Ptr{ComplexF64}, Ref{LinearAlgebra.BlasInt}, Ref{LinearAlgebra.BlasInt}, Clong),
+ 'L', size(AB, 2), kd, size(B, 2), AB, max(1, stride(AB, 2)), B, max(1, stride(B, 2)), info, 1)
+ LAPACK.chklapackerror(info[])
+ return B
+end
diff --git a/src/ForceFreeStates/Galerkin/GalerkinStructs.jl b/src/ForceFreeStates/Galerkin/GalerkinStructs.jl
new file mode 100644
index 0000000000..e0cb88afc9
--- /dev/null
+++ b/src/ForceFreeStates/Galerkin/GalerkinStructs.jl
@@ -0,0 +1,164 @@
+# Data structures for the RDCON outer-region singular Galerkin solver (Fortran `gal.f` types `cell_type`,
+# `interval_type`, `gal_type`). Fortran `0:np`/`0:msing` dimensions are 1-based here with a `+1` shift
+# (Hermite DOF `ip` ↔ index `ip+1`; interval `ising` ↔ `intvl[ising+1]`).
+#
+# Reference: A. H. Glasser, Z. R. Wang & J.-K. Park, Phys. Plasmas 23, 112506 (2016).
+
+# Hermite-cubic order: 4 DOFs per node-pair (value + slope at each end), indexed 0:np in Fortran.
+const GAL_NP = 3
+
+"""
+Cell type flanking a singular surface (Fortran `cell%etype`, gal.f).
+"""
+@enum GalCellType GCT_NONE GCT_RES GCT_EXT GCT_EXT1 GCT_EXT2
+
+"""
+Which side of the adjacent singular surface a cell lies on (Fortran `cell%extra`).
+"""
+@enum GalSide GAL_SIDE_NONE GAL_SIDE_LEFT GAL_SIDE_RIGHT
+
+"""
+ GalCell
+
+One grid cell of the Galerkin discretization. Port of Fortran `cell_type` (gal.f).
+
+## Fields
+
+ - `etype::GalCellType` — none / resonant / extension(1,2)
+ - `extra::GalSide` — none / left / right (side of the neighbouring singular surface)
+ - `emap::Int` — global index of the extra (small resonant) DOF; 0 if none
+ - `map::Matrix{Int}` — `(mpert, np+1)` local→global DOF map (Fortran `cell%map(mpert, 0:np)`)
+ - `x::NTuple{2,Float64}` — `[x_left, x_right]` of the cell
+ - `x_lsode::Float64` — resonant-integration truncation point (res cells only)
+ - `erhs::ComplexF64`, `ediag::ComplexF64` — resonant RHS and diagonal contributions
+ - `rhs::Matrix{ComplexF64}` — `(mpert, np+1)` cell RHS (driving term from the big solution)
+ - `emat::Matrix{ComplexF64}` — `(mpert, np+1)` coupling of the extra DOF to the Hermite DOFs
+ - `mat::Array{ComplexF64,4}` — `(mpert, mpert, np+1, np+1)` cell stiffness block
+"""
+mutable struct GalCell
+ etype::GalCellType
+ extra::GalSide
+ emap::Int
+ map::Matrix{Int}
+ x::NTuple{2,Float64}
+ x_lsode::Float64
+ erhs::ComplexF64
+ ediag::ComplexF64
+ rhs::Matrix{ComplexF64}
+ emat::Matrix{ComplexF64}
+ mat::Array{ComplexF64,4}
+end
+
+"""
+Construct an empty `GalCell` for `mpert` poloidal modes and Hermite order `np`.
+"""
+function GalCell(mpert::Int, np::Int=GAL_NP)
+ return GalCell(GCT_NONE, GAL_SIDE_NONE, 0,
+ zeros(Int, mpert, np + 1), (0.0, 0.0), 0.0,
+ zero(ComplexF64), zero(ComplexF64),
+ zeros(ComplexF64, mpert, np + 1),
+ zeros(ComplexF64, mpert, np + 1),
+ zeros(ComplexF64, mpert, mpert, np + 1, np + 1))
+end
+
+"""
+ GalInterval
+
+One interval between consecutive singular surfaces (or between a surface and a domain edge).
+Port of Fortran `interval_type` (gal.f). `x`/`dx` are length `nx+1` (Fortran `0:nx`).
+"""
+struct GalInterval
+ x::Vector{Float64}
+ dx::Vector{Float64}
+ cells::Vector{GalCell}
+end
+
+"""
+ GalWorkspace
+
+Global workspace for the Galerkin solve. Port of Fortran `gal_type` (gal.f).
+
+`intvl` has length `msing+1` (Fortran `intvl(0:msing)`, accessed as `intvl[ising+1]`).
+`kl = ku = mpert*(np+1)`. `mat` is stored full band, `ldab = 2*kl + ku + 1` (LAPACK `gbtrf!`
+layout); `solver` records the factorization `gal_banded_solve!` used (`"cholesky"` or `"LU"`).
+"""
+mutable struct GalWorkspace
+ solver::String
+ nx::Int
+ nq::Int
+ np::Int
+ ndim::Int
+ kl::Int
+ ku::Int
+ ldab::Int
+ nsol::Int
+ intvl::Vector{GalInterval}
+ mat::Matrix{ComplexF64}
+ rhs::Matrix{ComplexF64}
+ sol::Matrix{ComplexF64}
+end
+
+"""
+ GalSingAsymp
+
+Two-sided singular asymptotics for the Galerkin solver: separate right (sig=+1) and left (sig=−1)
+power series, mirroring Fortran sing.f `vmatr`/`vmatl`. Each is evaluated at a positive distance
+`|ψ−ψ_s|` (real √, real pfac, no z<0 renormalization), so the directly-extracted Δ′ matches gal.f.
+"""
+struct GalSingAsymp
+ right::SingAsymptotics
+ left::SingAsymptotics
+end
+
+"""
+ GalerkinSolution
+
+Reconstructed outer-region radial solution on the gal-native grid (ξ and analytic ξ′ consumed by
+PerturbedEquilibrium). Populated by `gal_output_solution` (GalerkinSolution.jl).
+
+ - `psi::Vector{Float64}`, `q::Vector{Float64}` — radial grid (inner→edge) and its safety factor.
+ - `issing::Vector{Bool}` — grid points sitting on a singular surface (skipped; left zero).
+ - `xi::Array{ComplexF64,3}`, `xi_deriv::Array{ComplexF64,3}` — `(mpert, ngrid, nsol)` ξ and dξ/dψ.
+ - `xi_cut::Array{ComplexF64,3}` — `(mpert, ngrid, nsol)` ξ with the leading-order resonant content removed,
+ the background the inner-layer solution is added to for the composite solution. `(0,0,0)` unless `cut_solution`.
+ - `cut_range::Matrix{Float64}` — `(msing, 2)` ψ bounds of the resonant + extension cells around each surface;
+ the composite inner solution is only meaningful inside them. `(0,0)` unless `cut_solution`.
+"""
+struct GalerkinSolution
+ psi::Vector{Float64}
+ q::Vector{Float64}
+ issing::Vector{Bool}
+ xi::Array{ComplexF64,3}
+ xi_deriv::Array{ComplexF64,3}
+ xi_cut::Array{ComplexF64,3}
+ cut_range::Matrix{Float64}
+end
+
+"""
+ GalerkinResult
+
+Solver internals and FEM diagnostics of the outer-region Galerkin solve. The Δ′ payload is not here;
+`galerkin_solve` returns it separately as a [`DeltaPrimeData`](@ref) (`ForceFreeStatesResult.delta_prime`).
+
+## Fields
+
+ - `msing::Int` — number of resonant surfaces solved; may be fewer than `result.surfaces`, since only
+ surfaces inside the domain and the resolved m-band are kept (`gal_resonant_surfaces`).
+ - `sing_psi, sing_q::Vector{Float64}`, `sing_m, sing_n::Vector{Int}` — per-surface identifiers,
+ core→edge, in the order the Δ′ matrices are indexed.
+ - `di::Vector{Float64}`, `alpha::Vector{ComplexF64}` — Mercier index and exponent per surface.
+ - `solution::Union{Nothing,GalerkinSolution}` — reconstructed radial ξ(ψ) and analytic ξ′(ψ) on the
+ gal-native grid; `nothing` if no resonant surfaces.
+ - `solver::String` — factorization actually used: `"cholesky"`, `"LU"`, or `"none"` when no resonant surfaces were present.
+"""
+struct GalerkinResult
+ msing::Int
+ sing_psi::Vector{Float64}
+ sing_q::Vector{Float64}
+ sing_m::Vector{Int}
+ sing_n::Vector{Int}
+ di::Vector{Float64}
+ alpha::Vector{ComplexF64}
+ solution::Union{Nothing,GalerkinSolution}
+ solver::String
+end
diff --git a/src/ForceFreeStates/InputSnapshot.jl b/src/ForceFreeStates/InputSnapshot.jl
new file mode 100644
index 0000000000..1aa1c0c864
--- /dev/null
+++ b/src/ForceFreeStates/InputSnapshot.jl
@@ -0,0 +1,28 @@
+"""
+ save_equilibrium_ingest!(out_h5, equil)
+
+Record the equilibrium's raw input arrays under `Input/RawInputs/Equilibrium/`, so a file-based rerun never needs the
+original g-file, CHEASE file or IMAS source. Analytic equilibria are regenerated from their deck section instead.
+"""
+function save_equilibrium_ingest!(out_h5, equil)
+ equil.ingest === nothing && return nothing
+ eq_group = "Input/RawInputs/Equilibrium" # read back by Rerun.read_equilibrium_ingest
+ out_h5["$eq_group/ingest_kind"] = equil.ingest isa Equilibrium.DirectIngest ? "direct" : "inverse"
+ for f in fieldnames(typeof(equil.ingest))
+ out_h5["$eq_group/$f"] = getfield(equil.ingest, f)
+ end
+ return nothing
+end
+
+"""
+ save_input_files!(out_h5, equil, wall_settings)
+
+Record the external files a run read, so a rerun and `equilibrium_from_h5` replay them without the originals:
+the equilibrium's kinetic profiles under `Input/RawInputs/Kinetic/` (the kinetic HDF5 schema; the composition is
+restated by the deck) and a file wall's text as `Input/RawInputs/Wall/wall_file_raw`.
+"""
+function save_input_files!(out_h5, equil, wall_settings)
+ equil.kinetic === nothing || Equilibrium.write_kinetic_group!(create_group(out_h5, "Input/RawInputs/Kinetic"), equil.kinetic)
+ wall_settings isa Vacuum.FileWall && (out_h5["Input/RawInputs/Wall/wall_file_raw"] = read(wall_settings.file, String))
+ return nothing
+end
diff --git a/src/ForceFreeStates/Integrators.jl b/src/ForceFreeStates/Integrators.jl
new file mode 100644
index 0000000000..8210f4f8cc
--- /dev/null
+++ b/src/ForceFreeStates/Integrators.jl
@@ -0,0 +1,101 @@
+"""
+ AbstractIntegrator
+
+Numerical algorithms for the force-balance problem. Physical inputs remain on the
+problem; each integrator carries its own accuracy, storage, and discretization settings.
+"""
+abstract type AbstractIntegrator end
+
+"""
+ Forward(; kwargs...)
+
+Serial forward integration with Gaussian reduction and dense solution profiles.
+
+## Fields
+
+ - `eulerlagrange_tolerance::Float64` - Relative tolerance for ODE integration.
+ - `renorm_threshold::Float64` - Column-norm growth threshold for Gaussian reduction or Riccati renormalization.
+ - `numsteps_init::Int` - Initial capacity for stored ODE solution steps.
+ - `numunorms_init::Int` - Initial capacity for solution-normalization records.
+ - `save_interval::Int` - Save every Nth ODE step; always retain steps near rational surfaces.
+"""
+@kwdef struct Forward <: AbstractIntegrator
+ eulerlagrange_tolerance::Float64 = 1e-8
+ renorm_threshold::Float64 = 1e3
+ numsteps_init::Int = 4000
+ numunorms_init::Int = 100
+ save_interval::Int = 1
+end
+
+"""
+ Riccati(; kwargs...)
+
+Chunked Riccati integration and the singular-surface boundary-value solve.
+
+## Fields
+
+ - `eulerlagrange_tolerance::Float64` - Relative tolerance for ODE integration.
+ - `renorm_threshold::Float64` - Column-norm growth threshold for Gaussian reduction or Riccati renormalization.
+ - `numsteps_init::Int` - Initial capacity for stored ODE solution steps.
+ - `numunorms_init::Int` - Initial capacity for solution-normalization records.
+ - `save_interval::Int` - Save every Nth ODE step; always retain steps near rational surfaces.
+ - `nchunks::Int` - Target chunk count; zero derives the count from the singular surfaces.
+ - `extended_precision_bvp::Bool` - Use Complex{Double64} for the Delta-prime BVP and PEST3 combination to reduce cancellation error.
+"""
+@kwdef struct Riccati <: AbstractIntegrator
+ eulerlagrange_tolerance::Float64 = 1e-8
+ renorm_threshold::Float64 = 1e3
+ numsteps_init::Int = 4000
+ numunorms_init::Int = 100
+ save_interval::Int = 1
+ nchunks::Int = 0
+ extended_precision_bvp::Bool = true
+end
+
+"""
+ Galerkin(; nx=256, ...)
+
+RDCON outer-region singular Galerkin solver: solves the same Euler-Lagrange system
+variationally on a finite-element grid packed around the rational surfaces, producing Δ′
+without a radial ODE sweep. Maps onto `integrator = "Galerkin"`; every field is the
+corresponding discretization setting. Factorization is selected automatically.
+
+## Fields
+
+ - `nx::Int` - Elements per interval between singular surfaces.
+ - `nq::Int` - Gauss-Lobatto quadrature order per element.
+ - `pfac::Float64` - Grid packing ratio near singular surfaces.
+ - `dx0::Float64` - Resonant-element integration truncation distance, in units of 1/|n q′|.
+ - `dx1::Float64` - Resonant-element size, in units of 1/|n q′|.
+ - `dx2::Float64` - Extension-element size, in units of 1/|n q′|.
+ - `cutoff::Int` - Number of elements carrying the large solution as driving term.
+ - `tol::Float64` - Resonant-quadrature tolerance.
+ - `gnstep::Int` - Maximum resonant-quadrature evaluations.
+ - `dx1dx2_flag::Bool` - Enable the special dx1/dx2 treatment of resonant and extension elements.
+ - `frobenius_order_ceiling::Bool` - Auto-raise the order per surface for a high Mercier index.
+ - `rpec_flag::Bool` - Append the mpert coil-response columns to the Δ′ solve. Required for a later `MatchProblem` solve on the result.
+ - `edge_onesided::Bool` - Pack the two end intervals one-sided toward their single rational end instead of the Fortran symmetric pack.
+ - `basis_output::Bool` - Save the raw Galerkin basis for development diagnostics.
+ - `cut_solution::Bool` - Also keep the cut solution, for a later `MatchProblem`'s composite inner profiles.
+"""
+@kwdef struct Galerkin <: AbstractIntegrator
+ nx::Int = 256
+ nq::Int = 6
+ pfac::Float64 = 0.001
+ dx0::Float64 = 5e-4
+ dx1::Float64 = 1e-3
+ dx2::Float64 = 1e-3
+ cutoff::Int = 10
+ tol::Float64 = 1e-10
+ gnstep::Int = 20000
+ dx1dx2_flag::Bool = true
+ frobenius_order_ceiling::Bool = true
+ rpec_flag::Bool = false
+ edge_onesided::Bool = false
+ cut_solution::Bool = false
+ basis_output::Bool = false
+end
+
+_integrator_symbol(::Forward) = :forward
+_integrator_symbol(::Riccati) = :riccati
+_integrator_symbol(::Galerkin) = :galerkin
diff --git a/src/ForceFreeStates/Kinetic.jl b/src/ForceFreeStates/Kinetic.jl
new file mode 100644
index 0000000000..51351e5561
--- /dev/null
+++ b/src/ForceFreeStates/Kinetic.jl
@@ -0,0 +1,377 @@
+
+# Knots across the envelope's [ψ_c, 2ψ_c] quintic-smoothstep transition, enough for a cubic spline
+# to follow it without overshoot even on coarse decks.
+const BAND_KNOTS = 9
+
+"""
+ refine_grid_at_fbar_peaks(xs, kw, kt, evaluate, kin, equil, intr, psi_c;
+ ngrid=1000, relaxed_frac=0.01, target=3, max_add=24) → (xs, kw, kt)
+
+Insert kinetic evaluation knots across near-singular structure of F̄ that the grid does not
+resolve. Scans cond(F̄) (the same operator `find_kinetic_singular_surfaces!` searches — Park &
+Logan Eq. 70, so shifted and split resonances are included), takes peaks between
+`relaxed_frac`·threshold and the singular threshold, measures each peak's FWHM, and adds knots
+only where fewer than `target` knots lie inside it. New points respect `MIN_KNOT_SPACING`, stay
+above the near-axis validity band, and are capped at `max_add`; each costs one kernel evaluation
+and the existing values are reused. A well-resolved grid inserts nothing.
+"""
+function refine_grid_at_fbar_peaks(xs::Vector{Float64}, kw::Array{ComplexF64,3}, kt::Array{ComplexF64,3},
+ evaluate::Function, kin::FKGMatrices, equil::Equilibrium.PlasmaEquilibrium,
+ intr::ForceFreeStatesInternal, psi_c::Float64;
+ ngrid::Int=1000, relaxed_frac::Float64=KINETIC_RELAXED_FRAC, target::Int=3, max_add::Int=24,
+ cond_threshold::Float64=KINETIC_SINGULAR_COND)
+
+ lo, hi = xs[1], xs[end]
+ scan = collect(range(lo, hi; length=ngrid))
+ hint = Ref(1)
+ cond_vals = [
+ try
+ evaluate_fbar_condition(x, kin, equil, intr; hint=hint)
+ catch
+ Inf
+ end for x in scan
+ ]
+
+ add = Float64[]
+ for i in 2:(ngrid-1)
+ c = cond_vals[i]
+ (c > cond_vals[i-1] && c > cond_vals[i+1] && relaxed_frac * cond_threshold < c <= cond_threshold) || continue
+ l = i
+ while l > 1 && cond_vals[l] > c / 2
+ l -= 1
+ end
+ r = i
+ while r < ngrid && cond_vals[r] > c / 2
+ r += 1
+ end
+ inside = count(x -> scan[l] <= x <= scan[r], xs)
+ inside >= target && continue
+ w = (scan[r] - scan[l]) / 3
+ for x in (scan[i], scan[i] - w, scan[i] + w)
+ (lo < x < hi && x > 2 * psi_c) || continue
+ any(y -> abs(y - x) < Equilibrium.MIN_KNOT_SPACING, xs) && continue
+ any(y -> abs(y - x) < Equilibrium.MIN_KNOT_SPACING, add) && continue
+ push!(add, x)
+ end
+ end
+ isempty(add) && return xs, kw, kt
+ length(add) > max_add && (add = sort(add)[1:max_add])
+
+ sort!(add)
+ @info "Kinetic grid: $(length(add)) knot(s) added across unresolved near-singular F̄ structure at " *
+ "ψ=$(round.(add; digits=4)) (cond peaks below the singular threshold)"
+ kw_new, kt_new = evaluate(add)
+ allxs = vcat(xs, add)
+ perm = sortperm(allxs)
+ kw_all = cat(kw, kw_new; dims=1)[perm, :, :]
+ kt_all = cat(kt, kt_new; dims=1)[perm, :, :]
+ return allxs[perm], kw_all, kt_all
+end
+
+"""
+ KineticMatrices
+
+The kinetic energy and torque matrices of one perturbed-plasma problem, from [`kinetic_matrices`](@ref) or computed
+inside `solve`. Pass them back as `ForceBalanceProblem(eq; kinetic=km)` to solve again without evaluating the kinetic
+model, for example in a `kinetic_factor` scan; `solve` rejects matrices made for another ψ grid or mode range. The
+matrices are stored unscaled and `solve` applies its own `kinetic_factor`, but the knots the build added where F̄ is
+near-singular were placed at the `kinetic_factor` recorded here.
+
+## Fields
+
+ - `source` - The kinetic source evaluated: a `KineticForces.KineticForcesControl` or a [`TestKineticMatrices`](@ref).
+ - `kinetic_factor::Float64` - The `kinetic_factor` the ψ grid was refined at.
+ - `psi::Vector{Float64}` - The ψ grid of the matrices: the problem's grid plus the knots the build added.
+ - `problem_psi::Vector{Float64}` - The problem's own ψ grid, which a solve reusing the matrices must have.
+ - `nlow`, `nhigh`, `mlow`, `mhigh` - The toroidal and poloidal mode ranges.
+ - `axis_psi_c::Float64` - The near-axis validity boundary of the kinetic model; 0 for test matrices.
+ - `kw::Array{ComplexF64,3}`, `kt::Array{ComplexF64,3}` - The energy (W) and torque (T) matrices, indexed (ψ, mode
+ pair, component) with the six components A, B, C, D, E, H.
+"""
+struct KineticMatrices
+ source::Any
+ kinetic_factor::Float64
+ psi::Vector{Float64}
+ problem_psi::Vector{Float64}
+ nlow::Int
+ nhigh::Int
+ mlow::Int
+ mhigh::Int
+ axis_psi_c::Float64
+ kw::Array{ComplexF64,3}
+ kt::Array{ComplexF64,3}
+end
+
+# The kinetic source behind a problem's `kinetic`, looking through reused matrices.
+kinetic_source(kinetic) = kinetic isa KineticMatrices ? kinetic.source : kinetic
+
+"""
+ evaluate_kinetic_matrices(ctrl, equil, mats, intr, metric; calculated_source=nothing, axis_validity_psi_c=0.0)
+ -> KineticMatrices
+
+Evaluate the kinetic energy (W) and torque (T) matrices of `ctrl.kinetic` on the problem's ψ grid:
+
+ - [`TestKineticMatrices`](@ref): X-shaped test matrices of its `scale` relative to
+ ideal matrix Frobenius norms (Ak, Dk, Hk Hermitian; Bk, Ck, Ek non-Hermitian)
+ - a `KineticForcesControl`: compute via the `calculated_source` callback, which receives
+ `(ctrl, equil, intr, metric, mats)` and returns `(kw_flat, kt_flat)` of shape `(mpsi, np^2, 6)`.
+ `solve` injects `KineticForces.compute_calculated_kinetic_matrices`, because ForceFreeStates is loaded
+ before KineticForces. Knots are added across the near-axis validity band and where F̄ at
+ `ctrl.kinetic_factor` has near-singular structure the grid does not resolve.
+"""
+function evaluate_kinetic_matrices(
+ ctrl::ForceFreeStatesControl,
+ equil::Equilibrium.PlasmaEquilibrium,
+ mats::MatrixSplines,
+ intr::ForceFreeStatesInternal,
+ metric::MetricData;
+ calculated_source::Union{Nothing,Function}=nothing,
+ axis_validity_psi_c::Float64=0.0
+)
+ xs = metric.xs
+ mpsi = length(xs)
+ factor = ctrl.kinetic_factor
+ matrices(psi, kw, kt) = KineticMatrices(ctrl.kinetic, factor, psi, collect(metric.xs), intr.nlow, intr.nhigh, intr.mlow, intr.mhigh,
+ axis_validity_psi_c, kw, kt)
+
+ # Coarse equilibrium grids cannot represent env·(increment) across the validity band, and the
+ # spline overshoot can land on a rational; pin the band ends (C² there) and resolve the middle.
+ band_knots(lo, hi) = axis_validity_psi_c > 0 ?
+ [x for x in range(axis_validity_psi_c, 2 * axis_validity_psi_c; length=BAND_KNOTS) if lo < x < hi] : Float64[]
+
+ if ctrl.kinetic isa TestKineticMatrices
+ kw_flat, kt_flat = fixed_kinetic_matrices(intr.mpert, intr.numpert_total, mpsi, ctrl.kinetic.scale, intr.mlow, mats, xs)
+ return matrices(collect(xs), kw_flat, kt_flat)
+ end
+ isnothing(calculated_source) && error(
+ "The KineticForces kinetic source requires the KineticForces callback: solve the problem, or pass " *
+ "`calculated_source=KineticForces.compute_calculated_kinetic_matrices` explicitly."
+ )
+ band = band_knots(xs[1], xs[end])
+ if isempty(band)
+ kw_flat, kt_flat = calculated_source(ctrl, equil, intr, metric, mats)
+ else
+ xs = sort!(unique!(vcat(collect(xs), band)))
+ kw_flat, kt_flat = calculated_source(ctrl, equil, intr, metric, mats; psis=xs)
+ end
+ km = matrices(collect(xs), kw_flat, kt_flat)
+
+ # The FKG splines now exist, so F̄ can be scanned: add knots only where near-singular structure
+ # (shifted/split kinetic resonances) falls in an interval that does not resolve it.
+ fkg = build_kinetic_matrix_splines(mats, equil, intr, metric, km, factor).kinetic
+ fkg === nothing && return km
+ xs2, kw_flat, kt_flat = refine_grid_at_fbar_peaks(km.psi, kw_flat, kt_flat,
+ psis -> calculated_source(ctrl, equil, intr, metric, mats; psis=psis), fkg, equil, intr, axis_validity_psi_c)
+ return matrices(xs2, kw_flat, kt_flat)
+end
+
+"""
+ build_kinetic_matrix_splines(mats, equil, intr, metric, km::KineticMatrices, kinetic_factor) -> MatrixSplines
+
+Scale the kinetic matrices `km` by `kinetic_factor` and pre-compute the FKG derived matrices used by `sing_der!`,
+returning a new `MatrixSplines` carrying them alongside the ideal matrices of `mats`.
+"""
+build_kinetic_matrix_splines(mats::MatrixSplines, equil::Equilibrium.PlasmaEquilibrium, intr::ForceFreeStatesInternal, metric::MetricData,
+ km::KineticMatrices, kinetic_factor::Real) =
+ _compute_fkg_matrices(mats, equil, intr, metric, km.kw .* kinetic_factor, km.kt .* kinetic_factor; xs=km.psi)
+
+"""
+ check_kinetic_matrices(km::KineticMatrices, intr, metric)
+
+Throw unless `km` was evaluated on this problem's ψ grid and mode range.
+"""
+function check_kinetic_matrices(km::KineticMatrices, intr::ForceFreeStatesInternal, metric::MetricData)
+ made = (km.nlow, km.nhigh, km.mlow, km.mhigh)
+ here = (intr.nlow, intr.nhigh, intr.mlow, intr.mhigh)
+ made == here || error("the kinetic matrices were made for (nlow, nhigh, mlow, mhigh) = $made, but this problem has $here")
+ km.problem_psi == metric.xs ||
+ error("the kinetic matrices were made on another ψ grid ($(length(km.problem_psi)) points, this problem has $(length(metric.xs)))")
+ return nothing
+end
+
+"""
+ _compute_fkg_matrices(mats, equil, intr, metric, kw_flat, kt_flat) -> MatrixSplines
+
+Pre-compute the derived F, K, G kinetic matrices at each ψ grid point and return a new `MatrixSplines`
+whose `kinetic` field holds them alongside the kinetic-modified A/B/C; `mats.ideal` is carried over.
+These are the Schur-complement reductions of the ideal (A,B,C,D,E,H) and kinetic (W,T) primitives
+for the non-Hermitian kinetic ODE system (Logan 2015 Appendix C, Eqs C.1-C.11).
+Port of Fortran `fourfit_kinetic_matrix` method=0 (fourfit.F).
+"""
+function _compute_fkg_matrices(
+ mats::MatrixSplines,
+ equil::Equilibrium.PlasmaEquilibrium,
+ intr::ForceFreeStatesInternal,
+ metric::MetricData,
+ kw_flat::Array{ComplexF64,3},
+ kt_flat::Array{ComplexF64,3};
+ xs::Vector{Float64}=metric.xs
+)
+ mpsi = length(xs)
+ np = intr.numpert_total
+ mpert = intr.mpert
+ npert = intr.npert
+ ideal = mats.ideal
+
+ # Allocate output arrays — kinetic-modified A/B/C stored for sing_der! FKG path
+ ak_flat = zeros(ComplexF64, mpsi, np^2)
+ bk_flat = zeros(ComplexF64, mpsi, np^2)
+ ck_flat = zeros(ComplexF64, mpsi, np^2)
+ f0_flat = zeros(ComplexF64, mpsi, np^2)
+ p_flat = zeros(ComplexF64, mpsi, np^2)
+ pa_flat = zeros(ComplexF64, mpsi, np^2)
+ kk_flat = zeros(ComplexF64, mpsi, np^2)
+ kka_flat = zeros(ComplexF64, mpsi, np^2)
+ r1_flat = zeros(ComplexF64, mpsi, np^2)
+ r2_flat = zeros(ComplexF64, mpsi, np^2)
+ r3_flat = zeros(ComplexF64, mpsi, np^2)
+ ga_flat = zeros(ComplexF64, mpsi, np^2)
+
+ # Each ψ writes its own row of the *_flat arrays; the only shared mutable is the
+ # bracket-search hint, one per thread. `:static` pins tasks so threadid() indexing is sound.
+ thread_hints = [Ref(1) for _ in 1:Threads.maxthreadid()]
+
+ Threads.@threads :static for ipsi in 1:mpsi
+ hint = thread_hints[Threads.threadid()]
+ psi = xs[ipsi]
+
+ # Evaluate ideal and kinetic matrices from splines (full np×np, block-diagonal in n)
+ amat_full = reshape(ideal.A_spline(psi; hint=hint), np, np)
+ bmat_full = reshape(ideal.B_spline(psi; hint=hint), np, np)
+ cmat_full = reshape(ideal.C_spline(psi; hint=hint), np, np)
+ dmat_full = reshape(ideal.D_spline_prim(psi; hint=hint), np, np)
+ emat_full = reshape(ideal.E_spline_prim(psi; hint=hint), np, np)
+ hmat_full = reshape(ideal.H_spline(psi; hint=hint), np, np)
+ fmat_prim_full = reshape(ideal.F_spline_prim(psi; hint=hint), np, np)
+
+ kwmat_full = zeros(ComplexF64, np, np, 6)
+ ktmat_full = zeros(ComplexF64, np, np, 6)
+ for ic in 1:6
+ kwmat_full[:, :, ic] .= reshape(@view(kw_flat[ipsi, :, ic]), np, np)
+ ktmat_full[:, :, ic] .= reshape(@view(kt_flat[ipsi, :, ic]), np, np)
+ end
+
+ # Process each n-block independently (matrices are block-diagonal in n)
+ for in_idx in 1:npert
+ n = intr.nlow + in_idx - 1
+ rng = ((in_idx-1)*mpert+1):(in_idx*mpert)
+
+ # Extract n-block slices
+ amat = amat_full[rng, rng]
+ bmat = bmat_full[rng, rng]
+ cmat = cmat_full[rng, rng]
+ dmat = dmat_full[rng, rng]
+ emat = emat_full[rng, rng]
+ hmat = hmat_full[rng, rng]
+ fmat_prim = fmat_prim_full[rng, rng]
+ kwmat = zeros(ComplexF64, mpert, mpert, 6)
+ ktmat = zeros(ComplexF64, mpert, mpert, 6)
+ for ic in 1:6
+ kwmat[:, :, ic] .= kwmat_full[rng, rng, ic]
+ ktmat[:, :, ic] .= ktmat_full[rng, rng, ic]
+ end
+
+ # Add kinetic contributions to ideal matrices
+ amat_kin = amat .+ kwmat[:, :, 1] .+ ktmat[:, :, 1]
+ bmat_kin = bmat .+ kwmat[:, :, 2] .+ ktmat[:, :, 2]
+ cmat_kin = cmat .+ kwmat[:, :, 3] .+ ktmat[:, :, 3]
+ hmat_kin = hmat .+ kwmat[:, :, 6] .+ ktmat[:, :, 6]
+ caat = cmat_kin .- 2 .* ktmat[:, :, 3] # C† analog for non-Hermitian system
+
+ # b1mat = i*D (Fortran convention)
+ b1mat = im .* dmat
+
+ # LU factorization of kinetic A matrix (non-Hermitian)
+ amat_lu = lu(amat_kin)
+
+ # f0mat = F_prim - D†A_kin⁻¹D
+ temp1 = amat_lu \ dmat
+ f0mat = fmat_prim .- dmat' * temp1
+
+ # pmat
+ psio_over_n = equil.psio / n # chi1/(2πn) = psio/n — toroidal flux per mode number
+ bkmat = kwmat[:, :, 2] .+ ktmat[:, :, 2] .+ im * psio_over_n .* (kwmat[:, :, 1] .+ ktmat[:, :, 1])
+ bkaat = kwmat[:, :, 2] .- ktmat[:, :, 2] .+ im * psio_over_n .* (kwmat[:, :, 1] .+ ktmat[:, :, 1])
+ temp2 = amat_lu \ bkmat
+ pmat_val = b1mat' * temp2
+
+ # paat
+ temp2 = amat_lu \ b1mat
+ # aamat = amat_kin^H · A_kin⁻¹ (as Fortran sing.f); not the identity for non-Hermitian amat_kin.
+ aamat_temp = amat_lu' \ amat_kin # = A_kin^{-H} · amat_kin
+ aamat = aamat_temp' # = amat_kin^H · A_kin⁻¹
+ umat_diff = I - aamat
+ paat_val = (bkaat' * temp2 .- im * psio_over_n .* umat_diff * b1mat)'
+
+ # r1mat
+ temp1_r1 = kwmat[:, :, 1] .+ ktmat[:, :, 1]
+ temp2 = amat_lu \ bkmat
+ r1mat_val =
+ kwmat[:, :, 4] .+ ktmat[:, :, 4] .-
+ psio_over_n^2 .* temp1_r1' .+
+ im * psio_over_n .* bkaat' .-
+ im * psio_over_n .* aamat * bkmat .-
+ bkaat' * temp2
+
+ # kkmat
+ temp1 = amat_lu \ cmat_kin
+ kkmat_val = emat .- b1mat' * temp1
+
+ # kkaat
+ temp1 = amat_lu \ b1mat
+ kkaat_val = emat' .- caat' * temp1
+
+ # r2mat
+ temp1_r2 = kwmat[:, :, 5] .+ ktmat[:, :, 5] .- im * psio_over_n .* (kwmat[:, :, 3] .+ ktmat[:, :, 3])
+ temp2 = amat_lu \ cmat_kin
+ r2mat_val = temp1_r2 .+ im * psio_over_n .* umat_diff * cmat_kin .- bkaat' * temp2
+
+ # r3mat
+ temp1_r3 = kwmat[:, :, 5] .- ktmat[:, :, 5] .- im * psio_over_n .* (kwmat[:, :, 3] .- ktmat[:, :, 3])
+ temp2 = amat_lu \ bkmat
+ r3mat_val = temp1_r3' .- caat' * temp2
+
+ # gaat
+ temp2 = amat_lu \ cmat_kin
+ gaat_val = hmat_kin .- caat' * temp2
+
+ # Store n-block results into full flat arrays
+ for (j_local, j_global) in enumerate(rng)
+ col_offset = (j_global - 1) * np
+ for (i_local, i_global) in enumerate(rng)
+ idx = i_global + col_offset
+ ak_flat[ipsi, idx] = amat_kin[i_local, j_local]
+ bk_flat[ipsi, idx] = bmat_kin[i_local, j_local]
+ ck_flat[ipsi, idx] = cmat_kin[i_local, j_local]
+ f0_flat[ipsi, idx] = f0mat[i_local, j_local]
+ p_flat[ipsi, idx] = pmat_val[i_local, j_local]
+ pa_flat[ipsi, idx] = paat_val[i_local, j_local]
+ kk_flat[ipsi, idx] = kkmat_val[i_local, j_local]
+ kka_flat[ipsi, idx] = kkaat_val[i_local, j_local]
+ r1_flat[ipsi, idx] = r1mat_val[i_local, j_local]
+ r2_flat[ipsi, idx] = r2mat_val[i_local, j_local]
+ r3_flat[ipsi, idx] = r3mat_val[i_local, j_local]
+ ga_flat[ipsi, idx] = gaat_val[i_local, j_local]
+ end
+ end
+ end
+ end
+
+ itp_opts = (; extrap=ExtendExtrap())
+ kinetic = FKGMatrices(;
+ # kinetic-modified A/B/C consumed by sing_der!; A is non-Hermitian here
+ A_spline=cubic_interp(xs, Series(ak_flat); itp_opts...),
+ B_spline=cubic_interp(xs, Series(bk_flat); itp_opts...),
+ C_spline=cubic_interp(xs, Series(ck_flat); itp_opts...),
+ F0_spline=cubic_interp(xs, Series(f0_flat); itp_opts...),
+ P_spline=cubic_interp(xs, Series(p_flat); itp_opts...),
+ P_spline_adj=cubic_interp(xs, Series(pa_flat); itp_opts...),
+ Kk_spline=cubic_interp(xs, Series(kk_flat); itp_opts...),
+ Kk_spline_adj=cubic_interp(xs, Series(kka_flat); itp_opts...),
+ R1_spline=cubic_interp(xs, Series(r1_flat); itp_opts...),
+ R2_spline=cubic_interp(xs, Series(r2_flat); itp_opts...),
+ R3_spline=cubic_interp(xs, Series(r3_flat); itp_opts...),
+ G_spline_adj=cubic_interp(xs, Series(ga_flat); itp_opts...))
+
+ return MatrixSplines(mats.ideal, kinetic, mats._hint)
+end
diff --git a/src/ForceFreeStates/Matching/DeltaPrime.jl b/src/ForceFreeStates/Matching/DeltaPrime.jl
new file mode 100644
index 0000000000..7358dceee5
--- /dev/null
+++ b/src/ForceFreeStates/Matching/DeltaPrime.jl
@@ -0,0 +1,35 @@
+"""
+ DeltaPrimeData
+
+The solve's Δ′/outer-region matching payload, in the PEST-3 convention shared by the Riccati
+boundary-value problem and the Galerkin solve, so consumers never branch on which integrator ran.
+
+Matrices are indexed by the surfaces the formalism solved across, core→edge: `result.surfaces` for
+Riccati, its in-domain in-band subset for Galerkin (`gal_resonant_surfaces`). Side-major orderings
+run `[L_s1, R_s1, L_s2, R_s2, …]`.
+
+## Fields
+
+ - `matrix::Matrix{ComplexF64}` - Inter-surface Δ′ of shape (msing × msing) in PEST3
+ convention, the tearing↔tearing parity projection of `raw`. Same as `Delta` of the
+ PEST-3 block set. Both formalisms.
+ - `raw::Matrix{ComplexF64}` - Raw outer-region matching matrix D′ of shape
+ (2msing × 2msing), side-major on both axes. Both formalisms.
+ - `coil::Matrix{ComplexF64}` - Edge coil-response matrix of shape
+ (2msing × numpert_total); column k is the resonant small-solution response at each
+ surface side to a unit source on edge poloidal mode k. Riccati fills it from the
+ vacuum-edge BVP, Galerkin from its `rpec_flag` columns. Empty when neither ran.
+ - `A::Union{Nothing,Matrix{ComplexF64}}` - PEST-3 interchange↔interchange block
+ (msing × msing). Galerkin only; `nothing` for Riccati, which persists only `raw` and
+ recovers the blocks on demand via `pest3_decompose`.
+ - `B::Union{Nothing,Matrix{ComplexF64}}` - PEST-3 interchange↔tearing block; see `A`.
+ - `Gamma::Union{Nothing,Matrix{ComplexF64}}` - PEST-3 tearing↔interchange block; see `A`.
+"""
+struct DeltaPrimeData
+ matrix::Matrix{ComplexF64}
+ raw::Matrix{ComplexF64}
+ coil::Matrix{ComplexF64}
+ A::Union{Nothing,Matrix{ComplexF64}}
+ B::Union{Nothing,Matrix{ComplexF64}}
+ Gamma::Union{Nothing,Matrix{ComplexF64}}
+end
diff --git a/src/ForceFreeStates/Matching/MatchProblem.jl b/src/ForceFreeStates/Matching/MatchProblem.jl
new file mode 100644
index 0000000000..f80f52eb46
--- /dev/null
+++ b/src/ForceFreeStates/Matching/MatchProblem.jl
@@ -0,0 +1,288 @@
+# MatchProblem.jl
+#
+# Driven inner-layer matching on a finished solve (rmatch match_rpec + match_output_solution, match.f).
+
+"""
+ MatchProblem(ffs; eta=nothing, rho=nothing, rotation=nothing, gamma=5/3, ideal=false)
+
+Driven inner-layer matching on a finished force-free-states solve `ffs`: each rational surface
+is matched at the forced eigenvalue γ = 2πi·n·f, with f the plasma rotation frequency there.
+`solve(prob, GGJModel())` returns a copy of `ffs` with the matched solution and the penetrated
+field `bpen`. `ffs` needs the Δ′ coil block, from `Galerkin(; rpec_flag=true)` or `Riccati()`
+with `vac_flag=true`.
+
+# Keywords
+
+ - `eta`, `rho`, `rotation`: resistivity in Ω·m, mass density in kg/m³ and rotation frequency
+ in Hz, a scalar for every surface or one value per `ffs.surfaces` entry (core to edge).
+ Each one not given comes from the equilibrium's kinetic data, as the tearing problem's do:
+ η from [`InnerLayer.layer_eta`](@ref), ρ from [`InnerLayer.layer_rho`](@ref), and the
+ rotation f = Ω_E/2π from the E×B rotation of [`InnerLayer.layer_omega_E`](@ref). Unused
+ with `ideal=true`.
+ - `gamma`: ratio of specific heats.
+ - `ideal`: skip the inner layer and return the perfectly shielding solution.
+
+## Fields
+
+ - `ffs` - The outer solve being matched; held by reference, not copied.
+ - `eta`, `rho`, `rotation` - Per-surface η in Ω·m, ρ in kg/m³ and rotation frequency in Hz, following `ffs.surfaces`.
+ - `gamma` - Ratio of specific heats.
+ - `ideal` - Whether the inner layer is skipped.
+
+Ref: Fortran rmatch `match_rpec` (match.f).
+"""
+struct MatchProblem{R<:ForceFreeStatesResult}
+ ffs::R
+ eta::Vector{Float64}
+ rho::Vector{Float64}
+ rotation::Vector{Float64}
+ gamma::Float64
+ ideal::Bool
+end
+
+function MatchProblem(
+ ffs::ForceFreeStatesResult;
+ eta::Union{Nothing,Real,AbstractVector{<:Real}}=nothing,
+ rho::Union{Nothing,Real,AbstractVector{<:Real}}=nothing,
+ rotation::Union{Nothing,Real,AbstractVector{<:Real}}=nothing,
+ gamma::Real=5 / 3,
+ ideal::Bool=false
+)
+ ffs.npert == 1 || error("MatchProblem: matching is single-n; the result spans n = $(ffs.nlow):$(ffs.nhigh)")
+ ffs.closure === :matched && error("MatchProblem: the result is already matched; pose the match on the outer solve")
+ dp = ffs.delta_prime
+ dp === nothing &&
+ error("MatchProblem: the $(ffs.integrator) result has no Δ′; solve with Galerkin(; rpec_flag=true), or Riccati() with vac_flag=true")
+ isempty(dp.coil) &&
+ error("MatchProblem: the Δ′ coil block is empty; solve with Galerkin(; rpec_flag=true), or Riccati() with vac_flag=true")
+
+ msing = length(ffs.surfaces)
+ if ffs.galerkin !== nothing
+ dropped = [s.psifac for s in ffs.surfaces if !(s.psifac in ffs.galerkin.sing_psi)]
+ isempty(dropped) || error("MatchProblem: the Galerkin solve dropped the surfaces at ψ = $dropped (on the domain edge or " *
+ "outside mlow:mhigh); matching needs every surface")
+ end
+ size(dp.raw, 1) == 2msing ||
+ error("MatchProblem: Δ′ raw block is $(size(dp.raw, 1))×$(size(dp.raw, 2)) but the result carries $msing surfaces")
+
+ ideal && return MatchProblem(ffs, zeros(msing), zeros(msing), zeros(msing), Float64(gamma), true)
+ InnerLayer._require_layer_inputs("MatchProblem", ffs.equil; eta, rho, rotation)
+ eta === nothing && (eta = InnerLayer.layer_eta(ffs.equil, ffs.surfaces))
+ rho === nothing && (rho = InnerLayer.layer_rho(ffs.equil, ffs.surfaces))
+ if rotation === nothing
+ omega_E = InnerLayer.layer_omega_E(ffs.equil, ffs.surfaces)
+ any(isnan, omega_E) && error("MatchProblem: the kinetic data carry no omega_E; give rotation")
+ rotation = omega_E ./ 2π
+ end
+ per_surface(name, v) =
+ v isa Real ? fill(Float64(v), msing) :
+ length(v) == msing ? collect(Float64, v) :
+ error("MatchProblem: $name has length $(length(v)), expected $msing (one per surface, core to edge)")
+ return MatchProblem(ffs, per_surface("eta", eta), per_surface("rho", rho), per_surface("rotation", rotation), Float64(gamma), false)
+end
+
+"""
+ closure_capable(model) -> Bool
+
+Whether `model` can solve a [`MatchProblem`](@ref): `GGJModel` with the `:ray` or `:galerkin`
+backend can (they reconstruct the layer profiles); `SLAYERModel` (slab, tearing parity only)
+cannot.
+"""
+closure_capable(::InnerLayer.GGJModel{S}) where {S} = S in (:ray, :galerkin)
+closure_capable(::InnerLayer.SLAYERModel) = false
+
+"""
+ solve(prob::MatchProblem, model) -> ForceFreeStatesResult
+
+Match `prob.ffs` to the inner layer of `model`. The result has `closure = :matched` (`:ideal`
+with `ideal=true`), `bpen`, the [`MatchResult`](@ref) in `result.match` and, for a Galerkin
+solve, the matched ξ. A `:matched` result drops the ideal δW (`wp`, `free_boundary`), so
+PerturbedEquilibrium skips its response rather than mixing ideal and matched physics.
+"""
+function CommonSolve.solve(prob::MatchProblem, model::InnerLayer.InnerLayerModel)
+ closure_capable(model) ||
+ error("$(nameof(typeof(model))) cannot solve a MatchProblem (use GGJModel(); SLAYERModel is for TearingProblem)")
+ match = _compute_match(prob, model)
+ return _matched_result(prob.ffs, match, prob.ideal)
+end
+
+# Inner-layer Δ per surface, the matching system, then the matched outer and inner profiles.
+function _compute_match(prob::MatchProblem, model::InnerLayer.GGJModel)
+ ffs = prob.ffs
+ dp = ffs.delta_prime
+ sings = ffs.surfaces
+ msing = length(sings)
+ mcoil = size(dp.coil, 2)
+ nn = ffs.nlow
+ equil = ffs.equil
+ chi1 = 2π * equil.psio
+
+ gal_sol = ffs.galerkin === nothing ? nothing : ffs.galerkin.solution
+
+ if prob.ideal
+ # Ideal limit (rmatch coil%ideal_flag): no inner layer, cout = 0.
+ cout = zeros(ComplexF64, 2msing, mcoil)
+ cin = zeros(ComplexF64, 2msing, mcoil)
+ deltar = zeros(ComplexF64, msing, 2)
+ bpen = zeros(ComplexF64, msing, mcoil)
+ inner_psi = Vector{Float64}[]
+ inner_xi = Matrix{ComplexF64}[]
+ inner_b = Matrix{ComplexF64}[]
+ inner_params = InnerLayer.GGJParameters[]
+ rpec_eig = zeros(ComplexF64, msing)
+ residual = 0.0
+ else
+ # Inner-layer Δ and profiles per surface (match.f deltac_run, intotsol).
+ deltar = zeros(ComplexF64, msing, 2)
+ rpec_eig = zeros(ComplexF64, msing)
+ # Layer-center field weight per parity (match.f intotsol_b).
+ pen = zeros(ComplexF64, msing, 2)
+ inner_psi = Vector{Vector{Float64}}(undef, msing) # ψ_s ± X·dψdx, ascending
+ inner_odd = Vector{Vector{ComplexF64}}(undef, msing) # Ξ₋, odd about ψ_s
+ inner_even = Vector{Vector{ComplexF64}}(undef, msing) # Ξ₊, even
+ inner_bodd = Vector{Vector{ComplexF64}}(undef, msing) # b^ψ from Ψ₋, even
+ inner_beven = Vector{Vector{ComplexF64}}(undef, msing) # b^ψ from Ψ₊, odd
+ inner_params = Vector{InnerLayer.GGJParameters}(undef, msing)
+ profiles = true
+ for i in 1:msing
+ params = ggj_parameters(sings[i], equil; eta=prob.eta[i], rho=prob.rho[i],
+ gamma=prob.gamma, ising=i)
+ inner_params[i] = params
+ γ = 2π * im * nn * prob.rotation[i] # forced eigenvalue, f in Hz
+ rpec_eig[i] = γ
+ inner = InnerLayer.solve_inner_profile(model, params, γ) # parity columns (Δ₊, Δ₋)
+ deltar[i, 1] = inner.Δ[1]
+ deltar[i, 2] = inner.Δ[2]
+ profΨ, profΞ, xg = inner.Ψ, inner.Ξ, inner.x
+ resc = inner.rescale # inner big-branch amplitude → outer δψ normalization
+ # b_m = 2πi·χ₁·(m−nq)·ξ_m with m−nq = −n·q′·dψdx·X and Ψ = XΞ at leading order (GWP2016 Eqs. 16, 27; Ψ normalization Eq. A17) ⇒ b_m = scale·resc·Ψ.
+ scale = -2π * chi1 * im * nn * sings[i].q1 * inner.dψdx
+ pen[i, 1] = scale * profΨ[1, 1] * resc # X = 0, even parity (Ψ(0) = 0)
+ pen[i, 2] = scale * profΨ[1, 2] * resc # odd parity
+ # A backend returning only layer-center values (real-ψ profiles not requested) skips the inner profiles.
+ if length(xg) == 1
+ profiles = false
+ continue
+ end
+ xvar = xg .* inner.dψdx # X → ψ distance
+ inner_psi[i] = vcat(reverse(sings[i].psifac .- xvar), sings[i].psifac .+ xvar)
+ inner_odd[i] = resc .* vcat(reverse(.-profΞ[:, 2]), profΞ[:, 2])
+ inner_even[i] = resc .* vcat(reverse(profΞ[:, 1]), profΞ[:, 1])
+ inner_bodd[i] = (scale * resc) .* vcat(reverse(profΨ[:, 2]), profΨ[:, 2])
+ inner_beven[i] = (scale * resc) .* vcat(reverse(.-profΨ[:, 1]), profΨ[:, 1])
+ end
+
+ cout, cin, residual = _match_system(dp.raw, dp.coil, deltar)
+
+ # Penetrated field at each layer center (match.f intotsol_b); cin rows per surface are (d₊, d₋).
+ bpen = zeros(ComplexF64, msing, mcoil)
+ for i in 1:msing, j in 1:mcoil
+ bpen[i, j] = pen[i, 1] * cin[2i-1, j] + pen[i, 2] * cin[2i, j]
+ end
+
+ # Matched inner ξ_ψ and b^ψ per coil: odd parity × cin[2i], even × cin[2i-1] (match.f intotsol).
+ if profiles
+ inner_xi = [inner_odd[i] * transpose(cin[2i, :]) .+ inner_even[i] * transpose(cin[2i-1, :]) for i in 1:msing]
+ inner_b = [inner_bodd[i] * transpose(cin[2i, :]) .+ inner_beven[i] * transpose(cin[2i-1, :]) for i in 1:msing]
+ else
+ inner_psi = Vector{Float64}[]
+ inner_xi = Matrix{ComplexF64}[]
+ inner_b = Matrix{ComplexF64}[]
+ end
+ end
+
+ reconnected_flux = Matrix{ComplexF64}(dp.coil .+ transpose(dp.raw) * cout)
+
+ # Matched outer ξ per coil: coil column + Σ cout·plasma columns (needs the Galerkin basis).
+ if gal_sol === nothing
+ xi = Array{ComplexF64,3}(undef, 0, 0, 0)
+ xi_deriv = Array{ComplexF64,3}(undef, 0, 0, 0)
+ empty!(inner_psi)
+ empty!(inner_xi)
+ empty!(inner_b)
+ else
+ sols = gal_sol.xi # (mpert, ngrid, nsol)
+ sols_deriv = gal_sol.xi_deriv
+ mpert = size(sols, 1)
+ ngrid = size(sols, 2)
+ xi = zeros(ComplexF64, mpert, ngrid, mcoil)
+ xi_deriv = zeros(ComplexF64, mpert, ngrid, mcoil)
+ for j in 1:mcoil
+ csol = 2msing + j
+ @views xi[:, :, j] .= sols[:, :, csol]
+ @views xi_deriv[:, :, j] .= sols_deriv[:, :, csol]
+ for isol in 1:2msing
+ @views xi[:, :, j] .+= cout[isol, j] .* sols[:, :, isol]
+ @views xi_deriv[:, :, j] .+= cout[isol, j] .* sols_deriv[:, :, isol]
+ end
+ end
+
+ # Composite inner solution: add back the outer background the cut removed (match.f intotsol).
+ if !isempty(inner_psi)
+ sols_cut = gal_sol.xi_cut
+ if isempty(sols_cut)
+ @warn "MatchProblem: the solve retained no cut solution (set cut_solution=true on Galerkin), " *
+ "so the composite inner-region profiles are skipped; bpen and the matched outer ξ are unaffected" maxlog = 1
+ empty!(inner_psi)
+ empty!(inner_xi)
+ empty!(inner_b)
+ else
+ cut_range = gal_sol.cut_range
+ keep = .!gal_sol.issing
+ psi_keep = gal_sol.psi[keep]
+ for i in 1:msing
+ m_res = round(Int, nn * sings[i].q)
+ ires = m_res - ffs.mlow + 1
+ # Keep only points inside the cut window.
+ lo, hi = cut_range[i, 1], cut_range[i, 2]
+ inside = findall(p -> lo <= p <= hi, inner_psi[i])
+ if isempty(inside)
+ @warn "MatchProblem: inner layer at ψ=$(round(sings[i].psifac, digits=5)) lies outside the " *
+ "resonant/extension cells (ψ ∈ [$lo, $hi]); raise gal_dx1/gal_dx2 to overlap the layer" surface = i
+ continue
+ end
+ length(inside) < length(inner_psi[i]) && @info "MatchProblem: surface $i inner region clipped to the " *
+ "cut window ($(length(inside)) of $(length(inner_psi[i])) points)"
+ inner_psi[i] = inner_psi[i][inside]
+ inner_xi[i] = inner_xi[i][inside, :]
+ inner_b[i] = inner_b[i][inside, :]
+
+ # Cut outer background of the resonant harmonic, per coil.
+ cutmn = Matrix{ComplexF64}(undef, length(psi_keep), mcoil)
+ for j in 1:mcoil
+ @views cutmn[:, j] .= sols_cut[ires, keep, 2msing+j]
+ for isol in 1:2msing
+ @views cutmn[:, j] .+= cout[isol, j] .* sols_cut[ires, keep, isol]
+ end
+ end
+ itp = cubic_interp(psi_keep, Series(cutmn); extrap=ExtendExtrap())
+ buf = Vector{ComplexF64}(undef, mcoil)
+ hint = Ref(1)
+ for (ip, psi_p) in enumerate(inner_psi[i])
+ itp(buf, psi_p; hint=hint)
+ singfac = m_res - nn * equil.profiles.q_spline(psi_p)
+ @views inner_xi[i][ip, :] .+= buf
+ @views inner_b[i][ip, :] .+= (2π * im * chi1 * singfac) .* buf
+ end
+ end
+ end
+ end
+ end
+
+ return MatchResult(cout, cin, deltar, rpec_eig, residual, bpen, reconnected_flux,
+ xi, xi_deriv, inner_psi, inner_xi, inner_b, inner_params, model, prob)
+end
+
+# Copy of ffs with the match applied; the ideal reference keeps closure :ideal, its zero bpen and δW.
+function _matched_result(ffs::ForceFreeStatesResult, match::MatchResult, ideal::Bool)
+ gal = ffs.galerkin
+ solution = (gal !== nothing && gal.solution !== nothing && !isempty(match.xi)) ?
+ _matched_gal_profiles(gal, match, ffs.mats, ffs) : ffs.solution
+ ideal && return _with(ffs; match=match, solution=solution)
+ # The ideal δW does not describe the matched plasma; PE gates on its absence.
+ return _with(ffs; closure=:matched, bpen=match.bpen, match=match, solution=solution,
+ wp=nothing, free_boundary=nothing)
+end
+
+# A copy of the immutable `x` with the named fields replaced.
+_with(x; fields...) = typeof(x).name.wrapper((get(fields, f, getfield(x, f)) for f in fieldnames(typeof(x)))...)
diff --git a/src/ForceFreeStates/Matching/ResonantMatch.jl b/src/ForceFreeStates/Matching/ResonantMatch.jl
new file mode 100644
index 0000000000..3c542f3327
--- /dev/null
+++ b/src/ForceFreeStates/Matching/ResonantMatch.jl
@@ -0,0 +1,139 @@
+# ResonantMatch.jl
+#
+# Matching result and the 4·msing outer↔inner system (rmatch match_rpec; Wang et al., Phys. Plasmas 27, 122503 (2020), Eq. 11).
+
+"""
+ MatchResult
+
+Matching coefficients and matched profiles, found in `result.match`. The profile
+fields are empty when the solve kept no Galerkin basis; the inner fields are empty with `ideal`.
+
+## Fields
+
+ - `cout`, `cin`: `(2msing, ncoil)` outer and inner coefficients.
+ - `deltar`: `(msing, 2)` inner-layer Δ per surface, columns (Δ₊, Δ₋) = (interchange, tearing).
+ - `rpec_eig`: forced eigenvalue γ = 2πi·n·f per surface.
+ - `residual`: relative residual of the linear solve.
+ - `bpen`: `(msing, ncoil)` penetrated resonant field at each layer center.
+ - `reconnected_flux`: `(2msing, ncoil)` `Δ_coil + Δ_outᵀ·cout`.
+ - `xi`, `xi_deriv`: `(mpert, ngrid, ncoil)` matched outer ξ and ξ′, one column per coil.
+ - `inner_psi`, `inner_xi`, `inner_b`: per surface, the inner ψ grid and the composite ξ_ψ and b^ψ on it; empty unless the
+ inner model returns real-ψ profiles (`GGJModel(; solver=:galerkin)` or `GGJModel(; real_profiles=true)`).
+ - `inner_params`: per-surface `GGJParameters` used.
+ - `model`: the inner-layer model solved, with its backend options.
+ - `problem`: the [`MatchProblem`](@ref) solved, with its per-surface η, ρ and rotation.
+"""
+struct MatchResult{P}
+ cout::Matrix{ComplexF64}
+ cin::Matrix{ComplexF64}
+ deltar::Matrix{ComplexF64}
+ rpec_eig::Vector{ComplexF64}
+ residual::Float64
+ bpen::Matrix{ComplexF64}
+ reconnected_flux::Matrix{ComplexF64}
+ xi::Array{ComplexF64,3}
+ xi_deriv::Array{ComplexF64,3}
+ inner_psi::Vector{Vector{Float64}}
+ inner_xi::Vector{Matrix{ComplexF64}}
+ inner_b::Vector{Matrix{ComplexF64}}
+ inner_params::Vector{InnerLayer.GGJParameters}
+ model::InnerLayer.InnerLayerModel
+ problem::P
+end
+
+# Solve the 4·msing system mat·[cout; cin] = rmat (rmatch match_rpec).
+function _match_system(dp_raw::AbstractMatrix, dp_coil::AbstractMatrix, deltar::AbstractMatrix)
+ msing = size(dp_raw, 1) ÷ 2
+ ncoil = size(dp_coil, 2)
+ mat = zeros(ComplexF64, 4msing, 4msing)
+ rmat = zeros(ComplexF64, 4msing, ncoil)
+ @views mat[(2msing+1):4msing, 1:2msing] .= transpose(dp_raw) # Δ_out
+ @views rmat[(2msing+1):4msing, :] .= .-dp_coil # −Δ_coil
+ for ising in 1:msing
+ idx1 = 2ising - 1
+ idx2 = 2ising
+ idx3 = idx1 + 2msing
+ idx4 = idx2 + 2msing
+ delta1 = deltar[ising, 1] # Δ₊; unknowns idx3, idx4 (cin rows 2i−1, 2i) are d₊, d₋ (GWP2016 Eqs. 36–37)
+ delta2 = deltar[ising, 2] # Δ₋
+ mat[idx1, idx1] = 1
+ mat[idx2, idx2] = 1
+ mat[idx1, idx3] = -1
+ mat[idx1, idx4] = 1
+ mat[idx2, idx3] = -1
+ mat[idx2, idx4] = -1
+ # inner-layer Δ block (match.f signs)
+ mat[idx3, idx3] = -delta1
+ mat[idx3, idx4] = delta2
+ mat[idx4, idx3] = -delta1
+ mat[idx4, idx4] = -delta2
+ end
+
+ cof = mat \ rmat
+ residual = norm(mat * cof - rmat) / max(norm(rmat), 1e-300)
+ return cof[1:2msing, :], cof[(2msing+1):4msing, :], residual
+end
+
+# Write `m` under SingularSurfaces/Match/, annotated per the metadata contract.
+function save_to_hdf5(out_h5::Union{HDF5.File,HDF5.Group}, m::MatchResult)
+ g = "SingularSurfaces/Match"
+ out_h5["$g/cout"] = m.cout
+ out_h5["$g/cin"] = m.cin
+ out_h5["$g/Delta_r"] = m.deltar
+ out_h5["$g/bpen"] = m.bpen
+ out_h5["$g/reconnected_flux"] = m.reconnected_flux
+ out_h5["$g/rpec_eig"] = m.rpec_eig
+ # Per-surface inner-layer ξ_ψ(ψ) (match.f intotsol); ragged grids → one dataset pair per surface.
+ for i in eachindex(m.inner_psi)
+ out_h5["$g/Inner/psi_$i"] = m.inner_psi[i]
+ out_h5["$g/Inner/xi_$i"] = m.inner_xi[i]
+ out_h5["$g/Inner/b_$i"] = m.inner_b[i]
+ end
+ out_h5["$g/residual"] = m.residual
+ if !isempty(m.inner_params)
+ for f in (:E, :F, :G, :H, :K, :M)
+ out_h5["$g/InnerParams/$(f)"] = [getfield(pp, f) for pp in m.inner_params]
+ end
+ # Literature names, matching the Tearing PerSurface mapping for the same fields.
+ out_h5["$g/InnerParams/tau_A"] = [pp.taua for pp in m.inner_params]
+ out_h5["$g/InnerParams/tau_R"] = [pp.taur for pp in m.inner_params]
+ out_h5["$g/InnerParams/dVdpsi"] = [pp.v1 for pp in m.inner_params]
+ end
+ a = attrs(out_h5[g])
+ a["inner_model"] = InnerLayer.model_name(m.model)
+ m.model isa InnerLayer.GGJModel && (a["inner_model_options"] = string(m.model.options))
+ inner = ["$g/Inner/$(v)_$i" => meta for i in eachindex(m.inner_psi) for (v, meta) in _MATCH_INNER_H5_ANNOTATIONS]
+ Utilities.HDF5Annotations.annotate!(out_h5, vcat(MATCH_H5_ANNOTATIONS, inner))
+ return nothing
+end
+
+# Matching quantities are per unit coil-response column (the Δ′ coil block's normalization).
+const _MATCH_SURF = (; dims=("surface",))
+const MATCH_H5_ANNOTATIONS = [
+ "SingularSurfaces/Match/cout" =>
+ (; long_name="outer-region matching coefficients per surface parity, per unit coil-response column", dims=("surface_parity", "coil")),
+ "SingularSurfaces/Match/cin" =>
+ (; long_name="inner-region matching coefficients per surface parity, per unit coil-response column", dims=("surface_parity", "coil")),
+ "SingularSurfaces/Match/Delta_r" =>
+ (; long_name="inner-layer Δ per surface and parity, (Δ₊ interchange, Δ₋ tearing)", dims=("surface", "parity")),
+ "SingularSurfaces/Match/bpen" =>
+ (; long_name="penetrated resonant field b^ψ at each layer center, per unit coil-response column", dims=("surface", "coil")),
+ "SingularSurfaces/Match/reconnected_flux" =>
+ (; long_name="reconnected flux Δ_coil + Δ_outᵀ·cout per surface parity, per unit coil-response column", dims=("surface_parity", "coil")),
+ "SingularSurfaces/Match/rpec_eig" => (; long_name="forced eigenvalue γ = 2πi·n·f at each surface", units="rad/s", _MATCH_SURF...),
+ "SingularSurfaces/Match/residual" => (; long_name="relative residual of the matching linear solve"),
+ "SingularSurfaces/Match/InnerParams/E" => (; long_name="Glasser-Greene-Johnson coefficient E per surface", _MATCH_SURF...),
+ "SingularSurfaces/Match/InnerParams/F" => (; long_name="Glasser-Greene-Johnson coefficient F per surface", _MATCH_SURF...),
+ "SingularSurfaces/Match/InnerParams/G" => (; long_name="Glasser-Greene-Johnson coefficient G per surface", _MATCH_SURF...),
+ "SingularSurfaces/Match/InnerParams/H" => (; long_name="Glasser-Greene-Johnson coefficient H per surface", _MATCH_SURF...),
+ "SingularSurfaces/Match/InnerParams/K" => (; long_name="Glasser-Greene-Johnson coefficient K per surface", _MATCH_SURF...),
+ "SingularSurfaces/Match/InnerParams/M" => (; long_name="Glasser-Greene-Johnson coefficient M per surface", _MATCH_SURF...),
+ "SingularSurfaces/Match/InnerParams/tau_A" => (; long_name="Alfvén time τ_A per surface", units="s", _MATCH_SURF...),
+ "SingularSurfaces/Match/InnerParams/tau_R" => (; long_name="resistive diffusion time τ_R per surface", units="s", _MATCH_SURF...),
+ "SingularSurfaces/Match/InnerParams/dVdpsi" => (; long_name="dV/dψ_N at each surface", units="m^3", _MATCH_SURF...)
+]
+const _MATCH_INNER_H5_ANNOTATIONS = [
+ "psi" => (; long_name="normalized poloidal flux ψ_N grid across the inner layer of this surface", dims=("inner_psi",)),
+ "xi" => (; long_name="composite inner-layer ξ^ψ per unit coil-response column", dims=("inner_psi", "coil")),
+ "b" => (; long_name="composite inner-layer b^ψ per unit coil-response column", dims=("inner_psi", "coil"))
+]
diff --git a/src/ForceFreeStates/Output.jl b/src/ForceFreeStates/Output.jl
new file mode 100644
index 0000000000..ba8480148c
--- /dev/null
+++ b/src/ForceFreeStates/Output.jl
@@ -0,0 +1,288 @@
+import ..Utilities: save_to_hdf5
+import ..LocalStability
+import ..ForcingTerms
+import ..Utilities: apply_main_h5_metadata!
+
+"""
+ save_to_hdf5(target, result::ForceFreeStatesResult; git_version="unknown", local_stability=nothing)
+
+Save the FFS solutions, operators, singular-surface diagnostics, and vacuum products, and record the deck that
+reproduces the solve (equilibrium, force balance and any match) in `Input/`. The associated equilibrium and optional
+local-stability result use their own save methods. Unavailable numerical products use empty datasets.
+"""
+function save_to_hdf5(
+ out_h5::Union{HDF5.File,HDF5.Group},
+ result::ForceFreeStatesResult;
+ git_version::String="unknown",
+ local_stability::Union{LocalStability.LocalStabilityResult,Nothing}=nothing
+)
+
+ ctrl = result.control
+ equil = result.equil
+ mats = result.mats
+ free_energies = result.free_boundary
+ gal_data = result.galerkin
+ diag = result.diagnostics
+ msing = length(result.surfaces)
+ # Closed ξ profiles are written into the producing formalism's Solutions group with the
+ # same dataset names and (mode, solution, psi) axis order: ForwardIntegration for the
+ # axis-basis sweep, GalerkinIntegration for the matched gal solution (its own grid).
+ xi_solution = (result.solution !== nothing && result.solution.basis === :el_axis) ? result.solution : nothing
+ gal_solution = (result.solution !== nothing && result.solution.basis === :gal_native) ? result.solution : nothing
+
+
+ # File-level metadata contract (schema_version, Conventions, title, date).
+ Utilities.HDF5Annotations.write_root_attrs!(out_h5; title="GPEC output: $(basename(dirname(abspath(HDF5.filename(out_h5)))))")
+
+ # Store git version for reproducibility
+ out_h5["Info/git_version"] = git_version
+
+ # Outer-region Galerkin solver outputs (RDCON), if it ran
+ if gal_data !== nothing
+ write_galerkin!(out_h5, gal_data; basis_output=result.control.algorithm.basis_output)
+ end
+
+ if gal_solution !== nothing
+ gal = "ForceFreeStates/Solutions/GalerkinIntegration"
+ out_h5["$gal/psi"] = gal_solution.psi_store
+ out_h5["$gal/q"] = gal_solution.q_store
+ out_h5["$gal/xi_psi"] = gal_solution.u_store[:, :, 1, :]
+ out_h5["$gal/dxi_psidpsi"] = gal_solution.du_store
+ out_h5["$gal/xi_s"] = gal_solution.xi_s_store
+ end
+
+ save_equilibrium_ingest!(out_h5, equil)
+ save_input_files!(out_h5, equil, result.wall_settings)
+ Utilities.record_inputs!(out_h5, result)
+
+ # Write derived run parameters
+ out_h5["Info/mpert"] = result.mpert
+ out_h5["Info/mlow"] = result.mlow
+ out_h5["Info/mhigh"] = result.mhigh
+ out_h5["Info/npert"] = result.npert
+ out_h5["Info/nlow"] = result.nlow
+ out_h5["Info/nhigh"] = result.nhigh
+ m = [(i - 1) % result.mpert + result.mlow for i in 1:(result.numpert_total)]
+ n = [(i - 1) ÷ result.mpert + result.nlow for i in 1:(result.numpert_total)]
+ out_h5["Info/mn_index"] = hcat(m, n) # (N, 2) matrix
+ out_h5["Info/psilim"] = result.psilim
+ out_h5["Info/qlim"] = result.qlim
+ out_h5["Info/dqdpsi_lim"] = result.q1lim
+
+ save_to_hdf5(out_h5, equil)
+
+ ls = local_stability
+ if ls !== nothing
+ save_to_hdf5(out_h5, ls)
+ else
+ for name in (:psi, :D_I, :D_R, :ballooning_Delta_prime, :ballooning_psi, :alpha, :alpha_critical)
+ out_h5["LocalStability/$name"] = Float64[]
+ end
+ end
+ out_h5["SingularSurfaces/D_I"] = (ls !== nothing && !isempty(result.surfaces)) ?
+ [LocalStability.mercier_D_I(ls, sing.psifac) for sing in result.surfaces] : Float64[]
+
+ # Resistive-layer overlap scan, present when psilim_from_layer_overlap capped the domain.
+ if result.layer_overlap !== nothing
+ lo = result.layer_overlap
+ out_h5["ForceFreeStates/LayerOverlap/m"] = lo.m
+ out_h5["ForceFreeStates/LayerOverlap/n"] = lo.n
+ out_h5["ForceFreeStates/LayerOverlap/psi"] = lo.psi
+ out_h5["ForceFreeStates/LayerOverlap/r_s"] = lo.rs
+ out_h5["ForceFreeStates/LayerOverlap/delta_s_abs"] = lo.delta_s_m
+ out_h5["ForceFreeStates/LayerOverlap/width_delta_s"] = lo.width_delta_s
+ out_h5["ForceFreeStates/LayerOverlap/width_visco"] = lo.width_visco
+ out_h5["ForceFreeStates/LayerOverlap/width_dr"] = lo.width_dr
+ out_h5["ForceFreeStates/LayerOverlap/extrapolated"] = Int.(lo.extrapolated)
+ out_h5["ForceFreeStates/LayerOverlap/psilim_overlap"] =
+ lo.psihigh === nothing ? NaN : lo.psihigh
+ out_h5["ForceFreeStates/LayerOverlap/first_overlap_index"] =
+ lo.first_overlap === nothing ? -1 : lo.first_overlap
+ # "applied" records that the bound was active going into sing_lim!, not that it set
+ # the final psilim -- rational_offset_fraction/qhigh may truncate deeper inside it.
+ out_h5["ForceFreeStates/LayerOverlap/applied"] =
+ Int(lo.psihigh !== nothing &&
+ lo.psihigh < equil.params.psihigh_resolved)
+ end
+
+ # Write integration data: the ψ trace and integrator diagnostics from the raw ODE state,
+ # the ξ profiles from the solution. Either may be absent (Galerkin has no ODE state;
+ # Riccati has no ξ solution), in which case the datasets are written empty.
+ fwd = "ForceFreeStates/Solutions/ForwardIntegration"
+ out_h5["$fwd/nstep"] = diag !== nothing ? diag.step : 0 # Number of saved solution snapshots
+ out_h5["$fwd/nstep_total"] = diag !== nothing ? diag.total_steps : 0 # Total ODE solver steps taken
+ out_h5["$fwd/psi"] = diag !== nothing ? diag.psi_store : Float64[]
+ out_h5["$fwd/q"] = diag !== nothing ? diag.q_store : Float64[]
+ out_h5["$fwd/xi_psi"] = xi_solution !== nothing ? xi_solution.u_store[:, :, 1, :] : ComplexF64[]
+ out_h5["$fwd/u2"] = xi_solution !== nothing ? xi_solution.u_store[:, :, 2, :] : ComplexF64[] # conjugate momenta of ξ_ψ
+ out_h5["$fwd/dxi_psidpsi"] = xi_solution !== nothing ? xi_solution.du_store : ComplexF64[]
+ out_h5["$fwd/xi_s"] = xi_solution !== nothing ? xi_solution.xi_s_store : ComplexF64[]
+ out_h5["$fwd/crit"] = diag !== nothing ? diag.crit_store : Float64[]
+
+ # Write edge stability scan data (only present when dW_edge_scan_start < psilim).
+ # Generalized (W, N) pencil energies — power-normalized, Jacobian-invariant; these are
+ # the values findmax_dW_edge! uses to choose the truncation point.
+ if diag !== nothing && !isempty(diag.edge_scan.psi)
+ es = diag.edge_scan
+ out_h5["ForceFreeStates/EdgeScan/psi"] = es.psi
+ out_h5["ForceFreeStates/EdgeScan/q"] = es.q
+ out_h5["ForceFreeStates/EdgeScan/total_energy"] = es.total_eigenvalue
+ out_h5["ForceFreeStates/EdgeScan/plasma_energy"] = es.plasma_energy
+ out_h5["ForceFreeStates/EdgeScan/vacuum_energy"] = es.vacuum_energy
+ out_h5["ForceFreeStates/EdgeScan/vacuum_eigenvalue"] = es.vacuum_eigenvalue
+ end
+
+ # Write singular surface data
+ out_h5["SingularSurfaces/rational_count"] = msing
+ out_h5["SingularSurfaces/rational_psi"] = [sing.psifac for sing in result.surfaces]
+ out_h5["SingularSurfaces/rational_q"] = [sing.q for sing in result.surfaces]
+ out_h5["SingularSurfaces/dqdpsi"] = [sing.q1 for sing in result.surfaces]
+ # Kinetic and galerkin-matched runs never populate ca_l/ca_r (only ideal surface
+ # crossings do); emit zero-extent sentinels instead of unpopulated arrays.
+ out_h5["SingularSurfaces/ca_left"] = (diag !== nothing && diag.ca_populated) ? diag.ca_l : zeros(ComplexF64, 0, 0, 0, 0)
+ out_h5["SingularSurfaces/ca_right"] = (diag !== nothing && diag.ca_populated) ? diag.ca_r : zeros(ComplexF64, 0, 0, 0, 0)
+
+ if msing > 0
+ # Mode numbers at each surface (jagged — pad with 0 to max_modes width)
+ max_modes = maximum(s -> length(s.m), result.surfaces)
+ m_matrix = zeros(Int, msing, max_modes)
+ n_matrix = zeros(Int, msing, max_modes)
+ for (s, sing) in enumerate(result.surfaces)
+ for i in 1:length(sing.m)
+ m_matrix[s, i] = sing.m[i]
+ n_matrix[s, i] = sing.n[i]
+ end
+ end
+ out_h5["SingularSurfaces/rational_m"] = m_matrix
+ out_h5["SingularSurfaces/rational_n"] = n_matrix
+
+ # GGJ coefficients and geometric surface averages, enough for ggj_parameters to rebuild τ_A / τ_R from any kinetic profiles.
+ if all(s -> s.restype !== nothing, result.surfaces)
+ out_h5["SingularSurfaces/E"] = [s.restype.E for s in result.surfaces]
+ out_h5["SingularSurfaces/F"] = [s.restype.F for s in result.surfaces]
+ out_h5["SingularSurfaces/G"] = [s.restype.G for s in result.surfaces]
+ out_h5["SingularSurfaces/H"] = [s.restype.H for s in result.surfaces]
+ out_h5["SingularSurfaces/K"] = [s.restype.K for s in result.surfaces]
+ out_h5["SingularSurfaces/M"] = [s.restype.M for s in result.surfaces]
+ out_h5["SingularSurfaces/avg_bsq_over_dpsisq"] = [s.restype.avg_bsq_over_dpsisq for s in result.surfaces]
+ out_h5["SingularSurfaces/avg_bsq"] = [s.restype.avg_bsq for s in result.surfaces]
+ out_h5["SingularSurfaces/mu0p"] = [s.restype.p_local for s in result.surfaces]
+ out_h5["SingularSurfaces/dmu0pdpsi"] = [s.restype.p1_local for s in result.surfaces]
+ out_h5["SingularSurfaces/dVdpsi"] = [s.restype.v1_local for s in result.surfaces]
+ end
+ end
+
+ # Per-surface ca-based Δ' (`sing.delta_prime`) is a stub; only the BVP matrix is emitted (see SingType.delta_prime docstring).
+
+ # Write the Δ' payload on one set of canonical paths, whichever formalism produced it
+ # (Riccati BVP or Galerkin): both compute the same quantities in the same PEST-3
+ # convention. Surface indexing follows the producing formalism's surface list, which for
+ # Galerkin is the in-domain in-band subset of `SingularSurfaces/`.
+ dp = result.delta_prime
+ if msing > 0 && dp !== nothing
+ # Inter-surface Δ' matrix, shape [msing × msing] — PEST3-convention deltap.
+ out_h5["SingularSurfaces/Delta_prime_matrix"] = dp.matrix
+
+ # Edge coil-response matrix, stored (numpert_total × 2msing) = (edge mode, surface-side)
+ # so H5Web heatmaps read x = edge mode, y = surface-side. The carried matrix stays
+ # (2msing × numpert_total); transpose only at write.
+ isempty(dp.coil) || (out_h5["SingularSurfaces/Delta_coil"] = permutedims(dp.coil))
+
+ # Raw 2msing×2msing outer-region D' matrix, side-major [L_s1, R_s1, L_s2, R_s2, …]; pest3_decompose recovers (A', B', Γ', Δ').
+ isempty(dp.raw) || (out_h5["SingularSurfaces/Delta_prime_raw"] = dp.raw)
+
+ # Remaining PEST-3 parity blocks, when the formalism persisted them (Galerkin);
+ # Riccati recovers them from Delta_prime_raw via pest3_decompose.
+ dp.A === nothing || (out_h5["SingularSurfaces/pest3_A"] = dp.A)
+ dp.B === nothing || (out_h5["SingularSurfaces/pest3_B"] = dp.B)
+ dp.Gamma === nothing || (out_h5["SingularSurfaces/pest3_Gamma"] = dp.Gamma)
+ end
+ result.match === nothing || save_to_hdf5(out_h5, result.match)
+
+ # Write kinetic singular surface data (det(F̄) near-zeros) and the cond(F̄) scan
+ # used to find them. Populated only when kinetic crossings were searched for.
+ out_h5["SingularSurfaces/Kinetic/rational_count"] = result.kinetic.kmsing
+ out_h5["SingularSurfaces/Kinetic/rational_psi"] = [s.psifac for s in result.kinetic.kinsing]
+ out_h5["SingularSurfaces/Kinetic/rational_q"] = [s.q for s in result.kinetic.kinsing]
+ out_h5["SingularSurfaces/Kinetic/dqdpsi"] = [s.q1 for s in result.kinetic.kinsing]
+ out_h5["SingularSurfaces/Kinetic/scan_psi"] = result.kinetic.scan_psi
+ out_h5["SingularSurfaces/Kinetic/scan_cond"] = result.kinetic.scan_cond
+ out_h5["SingularSurfaces/Kinetic/scan_threshold"] = result.kinetic.scan_threshold
+
+ # Free-boundary stability: eigenmode energies are generalized eigenvalues of the (W, N) pencil (power-normalized,
+ # Jacobian-invariant); eigenmode columns are sorted most-unstable first, unit power norm, largest entry real-positive.
+ fbs = "ForceFreeStates/FreeBoundaryStability"
+ out_h5["$fbs/W_freeboundary"] = free_energies !== nothing ? free_energies.wt0 : ComplexF64[]
+ out_h5["$fbs/W_plasma"] = free_energies !== nothing ? free_energies.wp : ComplexF64[]
+ out_h5["$fbs/W_vacuum"] = free_energies !== nothing ? free_energies.wv : ComplexF64[]
+ out_h5["$fbs/W_freeboundary_eigenmodes"] = free_energies !== nothing ? free_energies.wt : ComplexF64[]
+ out_h5["$fbs/eigenmode_energies"] = free_energies !== nothing ? free_energies.et : ComplexF64[]
+ out_h5["$fbs/eigenmode_plasma_energies"] = free_energies !== nothing ? free_energies.ep : ComplexF64[]
+ out_h5["$fbs/eigenmode_vacuum_energies"] = free_energies !== nothing ? free_energies.ev : ComplexF64[]
+ out_h5["$fbs/vacuum_eigenvalue"] = free_energies !== nothing ? free_energies.vacuum_eigenvalue : NaN
+
+ # Cartesian surface point clouds for visualization.
+ out_h5["SurfaceGeometries/Plasma/x"] = free_energies !== nothing ? free_energies.plasma_pts[:, 1] : Float64[]
+ out_h5["SurfaceGeometries/Plasma/y"] = free_energies !== nothing ? free_energies.plasma_pts[:, 2] : Float64[]
+ out_h5["SurfaceGeometries/Plasma/z"] = free_energies !== nothing ? free_energies.plasma_pts[:, 3] : Float64[]
+ out_h5["SurfaceGeometries/Wall/x"] = free_energies !== nothing ? free_energies.wall_pts[:, 1] : Float64[]
+ out_h5["SurfaceGeometries/Wall/y"] = free_energies !== nothing ? free_energies.wall_pts[:, 2] : Float64[]
+ out_h5["SurfaceGeometries/Wall/z"] = free_energies !== nothing ? free_energies.wall_pts[:, 3] : Float64[]
+
+ if ctrl.write_el_matrices
+ # Write fundamental matrices on the ψ grid
+ xs = equil.rzphi_xs
+ npsi = length(xs)
+ np = result.numpert_total
+
+ # Helper: evaluate a matrix spline on the psi grid → (npsi, np, np) array
+ function _eval_mat_spline(spline)
+ arr = zeros(ComplexF64, npsi, np, np)
+ hint = Ref(1)
+ for i in 1:npsi
+ arr[i, :, :] .= reshape(spline(xs[i]; hint=hint), np, np)
+ end
+ return arr
+ end
+
+ elm = "ForceFreeStates/EulerLagrangeMatrices"
+ out_h5["$elm/psi"] = xs
+ # Ideal primitive matrices (A, B, C, D, E, H)
+ out_h5["$elm/Ideal/A"] = _eval_mat_spline(mats.ideal.A_spline)
+ out_h5["$elm/Ideal/B"] = _eval_mat_spline(mats.ideal.B_spline)
+ out_h5["$elm/Ideal/C"] = _eval_mat_spline(mats.ideal.C_spline)
+ out_h5["$elm/Ideal/D"] = _eval_mat_spline(mats.ideal.D_spline_prim)
+ out_h5["$elm/Ideal/E"] = _eval_mat_spline(mats.ideal.E_spline_prim)
+ out_h5["$elm/Ideal/H"] = _eval_mat_spline(mats.ideal.H_spline)
+
+ # Ideal derived matrices (F, K, G)
+ out_h5["$elm/Ideal/F"] = _eval_mat_spline(mats.ideal.F_spline_lower)
+ out_h5["$elm/Ideal/K"] = _eval_mat_spline(mats.ideal.K_spline)
+ out_h5["$elm/Ideal/G"] = _eval_mat_spline(mats.ideal.G_spline)
+
+ # Kinetic-modified matrices
+ kin = mats.kinetic
+ if kin !== nothing
+ out_h5["$elm/Kinetic/A"] = _eval_mat_spline(kin.A_spline)
+ out_h5["$elm/Kinetic/B"] = _eval_mat_spline(kin.B_spline)
+ out_h5["$elm/Kinetic/C"] = _eval_mat_spline(kin.C_spline)
+ out_h5["$elm/Kinetic/f0"] = _eval_mat_spline(kin.F0_spline)
+ out_h5["$elm/Kinetic/K"] = _eval_mat_spline(kin.Kk_spline)
+ out_h5["$elm/Kinetic/G"] = _eval_mat_spline(kin.G_spline_adj)
+ end
+ end
+
+ # Self-describing metadata pass (long_name/units/dims + dimension scales).
+ apply_main_h5_metadata!(out_h5)
+ write_kinetic_validity!(out_h5, ctrl.kinetic, result)
+ return nothing
+end
+
+"""
+ write_kinetic_validity!(target, kinetic, result)
+
+Write the validity diagnostics of the force operator's kinetic source `kinetic`. A no-op unless the module that
+owns the source adds a method (KineticForces does, for `KineticForcesControl`).
+"""
+write_kinetic_validity!(target, kinetic, result) = nothing
+write_kinetic_validity!(target, km::KineticMatrices, result) = write_kinetic_validity!(target, km.source, result)
diff --git a/src/ForceFreeStates/Result.jl b/src/ForceFreeStates/Result.jl
new file mode 100644
index 0000000000..207d2f6a34
--- /dev/null
+++ b/src/ForceFreeStates/Result.jl
@@ -0,0 +1,244 @@
+"""
+ SolutionProfiles
+
+The solve's ξ solution on its radial grid, in the exact shape PerturbedEquilibrium consumes.
+Field names mirror the `OdeState` store subset so the consumers read the same names whichever
+formalism produced the solution.
+
+## Fields
+
+ - `basis::Symbol` - Which formalism's basis the profiles are in: `:el_axis` (forward
+ integrator, axis Euler-Lagrange basis) or `:gal_native` (inner-layer-matched Galerkin
+ solution, identity-at-edge basis).
+ - `step::Int` - Number of stored radial nodes.
+ - `psi_store::Vector{Float64}` - ψ at each node.
+ - `q_store::Vector{Float64}` - Safety factor at each node.
+ - `u_store::Array{ComplexF64,4}` - `(N, N, 2, step)` solution state: Ξ_ψ in the first
+ component and its conjugate momentum in the second.
+ - `du_store::Array{ComplexF64,3}` - `(N, N, step)` dΞ_ψ/dψ.
+ - `xi_s_store::Array{ComplexF64,3}` - `(N, N, step)` Clebsch displacement Ξ_s.
+"""
+struct SolutionProfiles
+ basis::Symbol
+ step::Int
+ psi_store::Vector{Float64}
+ q_store::Vector{Float64}
+ u_store::Array{ComplexF64,4}
+ du_store::Array{ComplexF64,3}
+ xi_s_store::Array{ComplexF64,3}
+end
+
+"""
+ ForceFreeStatesResult
+
+The published product of a force-free-states solve: everything downstream stages
+(PerturbedEquilibrium, KineticForces, SLAYER, the HDF5 writer) are allowed to read.
+`ForceFreeStatesInternal` remains solve-time scratch and does not cross a module boundary
+once this has been built.
+
+Optional fields are `Union{Nothing,T}` and follow a presence-equals-capability rule: a
+consumer that needs one gates on [`require`](@ref) (or [`require_solution`](@ref) for the
+ξ profiles) and warns-and-skips rather than erroring, so a result from an integrator that
+cannot supply a given product still flows through the pipeline. PerturbedEquilibrium refuses
+Galerkin and `:matched` results instead, since they publish no `wp` or `free_boundary` yet.
+
+A jump condition at the rational surfaces is always applied before a final result is built,
+so bpen and closure are always present.
+
+## Fields
+
+ - `integrator::Symbol` - `:forward`, `:riccati`, or `:galerkin`.
+ - `control::ForceFreeStatesControl` - Provenance snapshot of the controls the solve ran with.
+ - `equil::Equilibrium.PlasmaEquilibrium` - The equilibrium actually integrated against (the re-formed one on the two-pass path).
+ - `mlow`, `mhigh`, `mpert`, `nlow`, `nhigh`, `npert`, `numpert_total` - Resolved (m, n) mode space; see `ModeSpace`.
+ - `psilow`, `psilim`, `qlim`, `q1lim` - Integration bounds, and q with its ψ-derivative at `psilim`.
+ - `problem`, `algorithm` - Problem and integrator retained by the public solve for reproducible output.
+ - `wall_settings::Union{Nothing,Vacuum.WallSettings}` - Wall shape used by the vacuum calculation.
+ - `metric::MetricData`, `mats::MatrixSplines` - Metric data and Euler-Lagrange matrix interpolants.
+ - `surfaces::Vector{SingType}` - Ideal singular surfaces in the integration domain, with asymptotic bases and GGJ coefficients.
+ - `kinetic::NamedTuple` - Kinetic singular-surface scan (`kmsing`, `kinsing`, `scan_psi`, `scan_cond`, `scan_threshold`); empty unless the finder ran.
+ - `closure::Symbol` - How the basis is closed at the rationals: `:ideal` (the ideal jump
+ condition was imposed) or `:matched` (an inner-layer solution was matched in). A
+ `:matched` result carries no ideal δW: `wp` and `free_boundary` are `nothing`.
+ - `bpen::Matrix{ComplexF64}` - `(msing × numpert_total)` penetrated resonant field from the
+ inner layer, per surface (rows follow `surfaces`) and driving mode; all zeros under `:ideal` closure.
+ - `match::Union{Nothing,MatchResult}` - The [`MatchResult`](@ref) of a `MatchProblem` solve; `nothing` otherwise.
+ - `solution::Union{Nothing,SolutionProfiles}` - THE solve's ξ solution; `nothing` when the
+ formalism produced none (Riccati, and Galerkin without a match).
+ - `diagnostics::Union{Nothing,OdeState}` - The integrator's raw ODE state (ψ trace, `crit`,
+ edge scan, asymptotic coefficients). Written to HDF5; not a consumable solution.
+ - `wp::Union{Nothing,Matrix{ComplexF64}}` - Fixed-boundary plasma energy matrix `W_p = (U₂·U₁⁻¹)/ψ₀²` at
+ `psilim`. Present for any Euler-Lagrange sweep regardless of `vac_flag`; equals `free_boundary.wp` when that ran.
+ - `free_boundary::Union{Nothing,FreeBoundaryResult}` - Free-boundary energies and eigenmodes; `nothing` when the vacuum step was skipped or the formalism computes none.
+ - `delta_prime::Union{Nothing,DeltaPrimeData}` - Δ′/outer-region matching payload from
+ whichever formalism ran (Riccati BVP or Galerkin); `nothing` when neither produced one.
+ - `galerkin::Union{Nothing,GalerkinResult}` - RDCON Galerkin solver internals and FEM
+ diagnostics. Its Δ′ payload lives in `delta_prime`, not here.
+ - `layer_overlap` - The binding resistive-layer overlap scan (`Tearing.LayerOverlapScan`) when
+ `psilim_from_layer_overlap` capped the domain; `nothing` otherwise.
+"""
+struct ForceFreeStatesResult{E<:Equilibrium.PlasmaEquilibrium,F<:MatrixSplines,P,A,C<:ForceFreeStatesControl,L} <: ModeSpace
+ problem::P
+ algorithm::A
+ integrator::Symbol
+ control::C
+ equil::E
+
+ # Mode space and integration domain, copied out of the solve-time scratch.
+ mlow::Int
+ mhigh::Int
+ mpert::Int
+ nlow::Int
+ nhigh::Int
+ npert::Int
+ numpert_total::Int
+ psilow::Float64
+ psilim::Float64
+ qlim::Float64
+ q1lim::Float64
+ wall_settings::Union{Nothing,Vacuum.WallSettings}
+
+ # Assembly products, always present.
+ metric::MetricData
+ mats::F
+ surfaces::Vector{SingType}
+ kinetic::@NamedTuple{kmsing::Int, kinsing::Vector{SingType}, scan_psi::Vector{Float64}, scan_cond::Vector{Float64}, scan_threshold::Float64}
+
+ # Closure of the basis at the rationals, always present.
+ closure::Symbol
+ bpen::Matrix{ComplexF64}
+ match::Union{Nothing,MatchResult}
+
+ # Per-formalism products; presence is the capability signal.
+ solution::Union{Nothing,SolutionProfiles}
+ diagnostics::Union{Nothing,OdeState}
+ wp::Union{Nothing,Matrix{ComplexF64}}
+ free_boundary::Union{Nothing,FreeBoundaryResult}
+ delta_prime::Union{Nothing,DeltaPrimeData}
+ galerkin::Union{Nothing,GalerkinResult}
+ layer_overlap::L
+end
+
+"""
+ require(result::ForceFreeStatesResult, field::Symbol, calc::AbstractString) -> Bool
+
+Warn-and-skip gate: `true` iff the optional field `field` was populated by the integrator
+that produced `result`. Warns naming the calculation being skipped otherwise.
+"""
+function require(result::ForceFreeStatesResult, field::Symbol, calc::AbstractString)
+ getfield(result, field) === nothing || return true
+ @warn "Skipping $calc: `$field` was not produced by the $(result.integrator) integrator"
+ return false
+end
+
+"""
+ require_solution(result::ForceFreeStatesResult, calc::AbstractString) -> Bool
+
+Warn-and-skip gate for ξ-profile consumers: [`require`](@ref) specialized to `solution`,
+with a message naming what a solution takes to produce.
+"""
+function require_solution(result::ForceFreeStatesResult, calc::AbstractString)
+ result.solution === nothing || return true
+ @warn "Skipping $calc: no ξ solution — dense profiles require a Forward (or matched Galerkin) run; " *
+ "this result came from the $(result.integrator) integrator"
+ return false
+end
+
+# Pack the matched Galerkin solution into `SolutionProfiles`: on-surface `issing` points are dropped, Ξ′ is the
+# analytic Galerkin derivative, and Ξ_s = −A⁻¹(B·Ξ′ + C·Ξ) as in `sing_der!`. Grid runs inner→edge.
+function _matched_gal_profiles(gal_result::GalerkinResult, m::MatchResult, mats::MatrixSplines, intr::ModeSpace)
+ sol = gal_result.solution
+ npert = intr.numpert_total
+
+ keep = .!sol.issing
+ psi_f = sol.psi[keep]
+ q_f = sol.q[keep]
+ xi_f = m.xi[:, keep, :] # (npert, ngrid_f, mcoil)
+ dxi_f = m.xi_deriv[:, keep, :]
+ ngrid_f = length(psi_f)
+
+ # u_store[:, :, 2] stays zero: the conjugate momentum has no consumer on this path and no
+ # Galerkin counterpart (matches Fortran's unused u2 in the gal branch).
+ u_store = zeros(ComplexF64, npert, npert, 2, ngrid_f)
+ du_store = zeros(ComplexF64, npert, npert, ngrid_f)
+ xi_s_store = zeros(ComplexF64, npert, npert, ngrid_f)
+
+ hint = Ref(1)
+ for ip in 1:ngrid_f
+ ξ = @view xi_f[:, ip, :]
+ ξ′ = @view dxi_f[:, ip, :]
+ @views u_store[:, :, 1, ip] .= ξ
+ @views du_store[:, :, ip] .= ξ′
+ @views compute_node_xi_s!(xi_s_store[:, :, ip], ξ′, ξ, mats, psi_f[ip]; hint=hint)
+ end
+
+ return SolutionProfiles(:gal_native, ngrid_f, psi_f, q_f, u_store, du_store, xi_s_store)
+end
+
+"""
+ build_result(integrator, ctrl, equil, intr, metric, mats, odet, free_energies, gal_data, gal_dp)
+ -> ForceFreeStatesResult
+
+Assemble the published result once the solve is finished, with the ideal closure (a `MatchProblem`
+solve transforms it afterwards). Materializes the forward path's derivative stores and forms `W_p`
+when the free-boundary stage did not run; everything else is copied or aliased.
+
+`odet` is the ODE state (`nothing` for Galerkin); `gal_data`/`gal_dp` are the Galerkin internals and
+its Δ′ payload (`nothing` otherwise).
+"""
+function build_result(
+ integrator::Symbol,
+ ctrl::ForceFreeStatesControl,
+ equil::Equilibrium.PlasmaEquilibrium,
+ intr::ForceFreeStatesInternal,
+ metric::MetricData,
+ mats::MatrixSplines,
+ odet::Union{Nothing,OdeState},
+ free_energies::Union{Nothing,FreeBoundaryResult},
+ gal_data::Union{Nothing,GalerkinResult},
+ gal_dp::Union{Nothing,DeltaPrimeData}
+)
+ # The forward sweep is the only formalism whose stores need materializing; doing it here
+ # keeps `SolutionProfiles.du_store`/`xi_s_store` populated by construction.
+ solution = if integrator === :forward && odet !== nothing
+ materialize_derivative_stores!(odet, equil, mats, intr)
+ SolutionProfiles(:el_axis, odet.step, odet.psi_store, odet.q_store,
+ odet.u_store, odet.du_store, odet.xi_s_store)
+ else
+ nothing
+ end
+
+ # One Δ′ payload whichever formalism produced it; Riccati leaves the PEST-3 blocks unfilled
+ # because it persists only the raw D′ and recovers them on demand via `pest3_decompose`.
+ delta_prime = if gal_dp !== nothing
+ gal_dp
+ elseif !isempty(intr.delta_prime_matrix)
+ DeltaPrimeData(intr.delta_prime_matrix, intr.delta_prime_raw, intr.delta_coil, nothing, nothing, nothing)
+ else
+ nothing
+ end
+ kinetic = (kmsing=intr.kmsing, kinsing=intr.kinsing, scan_psi=intr.kinsing_scan_psi,
+ scan_cond=intr.kinsing_scan_cond, scan_threshold=intr.kinsing_scan_threshold)
+
+ closure = :ideal
+ bpen = zeros(ComplexF64, intr.msing, intr.numpert_total)
+
+ # Fixed-boundary plasma energy matrix at the edge; free of any vacuum dependence, so a
+ # vac_flag=false run still publishes its energy product. Aliases free_run's when it ran.
+ wp = if free_energies !== nothing
+ free_energies.wp
+ elseif odet !== nothing
+ (odet.u[:, :, 2] / odet.u[:, :, 1]) ./ equil.psio^2
+ else
+ nothing
+ end
+
+ return ForceFreeStatesResult(
+ nothing, nothing, integrator, ctrl, equil,
+ intr.mlow, intr.mhigh, intr.mpert, intr.nlow, intr.nhigh, intr.npert, intr.numpert_total,
+ intr.psilow, intr.psilim, intr.qlim, intr.q1lim, intr.wall_settings,
+ metric, mats, intr.sing, kinetic,
+ closure, bpen, nothing,
+ solution, odet, wp, free_energies, delta_prime, gal_data, nothing
+ )
+end
diff --git a/src/ForceFreeStates/Riccati/Crossings.jl b/src/ForceFreeStates/Riccati/Crossings.jl
new file mode 100644
index 0000000000..d0b157d4aa
--- /dev/null
+++ b/src/ForceFreeStates/Riccati/Crossings.jl
@@ -0,0 +1,131 @@
+# Singular-surface crossing algorithms for the Riccati/fundamental-matrix integration.
+
+"""
+ riccati_cross_ideal_singular_surf!(odet, ctrl, equil, mats, intr, ising)
+
+Cross a singular surface on the Riccati path: the Riccati counterpart of `cross_ideal_singular_surf!`,
+without Gaussian reduction (S is bounded) and zeroing the resonant columns `ipert_res` directly.
+
+Expects `odet.u` in the bounded (U₁, U₂) form from `riccati_integrate_chunk!` with `needs_crossing=true`.
+`ca_l`/`ca_r` are captured before `renormalize_riccati!` restores the (S, I) form, so the introduced
+small solution has `ca_r[ipert_res, ipert_res, 2] = 1`.
+"""
+function riccati_cross_ideal_singular_surf!(
+ odet::OdeState, ctrl::ForceFreeStatesControl, equil::Equilibrium.PlasmaEquilibrium,
+ mats::MatrixSplines, intr::ForceFreeStatesInternal, ising::Int
+)
+ # Skip Gaussian reduction — S is bounded so no large-norm columns exist.
+ singp = intr.sing[ising]
+ dpsi = singp.psifac - odet.psifac # ψ_res - ψ_current (positive)
+ ipert_res = 1 .+ singp.m .- intr.mlow .+ (singp.n .- intr.nlow) .* intr.mpert
+
+ sing_asymp_left, sing_asymp_right = _two_sided_singular_asymptotics(singp, ctrl, equil, mats, intr)
+ _log_riccati_crossing_diagnostics(odet, intr, ising, singp, dpsi, sing_asymp_left, sing_asymp_right)
+
+ _capture_left_crossing_data!(odet, singp, sing_asymp_left, dpsi, intr, ising)
+ _predict_across_singular_surface!(odet, ctrl, equil, mats, intr, ising, ipert_res, dpsi, sing_asymp_right)
+ _capture_right_crossing_data!(odet, singp, sing_asymp_right, dpsi, intr, ising, ipert_res, ctrl)
+
+ _stash_per_surface_delta_prime_stub!(odet, intr, ising, ipert_res, sing_asymp_right, equil, ctrl)
+ _store_crossing_step!(odet)
+
+ # Restore canonical (S_new, I) form before continuing integration.
+ renormalize_riccati!(odet, intr)
+end
+
+"""
+ _two_sided_singular_asymptotics(singp, ctrl, equil, mats, intr) -> (left, right)
+
+Left (`sig=-1`) and right (`sig=+1`) singular asymptotics, each from its own resonant block.
+"""
+function _two_sided_singular_asymptotics(singp::SingType, ctrl::ForceFreeStatesControl,
+ equil::Equilibrium.PlasmaEquilibrium, mats::MatrixSplines,
+ intr::ForceFreeStatesInternal)
+ sing_asymp_right = compute_sing_asymptotics(singp, ctrl, equil, mats, intr; sig=1.0)
+ sing_asymp_left = compute_sing_asymptotics(singp, ctrl, equil, mats, intr; sig=-1.0)
+ return sing_asymp_left, sing_asymp_right
+end
+
+# @debug-only per-crossing diagnostics. Enable via JULIA_DEBUG=GeneralizedPerturbedEquilibrium.
+function _log_riccati_crossing_diagnostics(odet, intr, ising, singp, dpsi, sing_asymp_left, sing_asymp_right)
+ @debug begin
+ ipert_res_diag = 1 .+ singp.m .- intr.mlow .+ (singp.n .- intr.nlow) .* intr.mpert
+ msg = " ising=$ising: psi_sing=$(@sprintf("%.10f", singp.psifac)), psi_eval=$(@sprintf("%.10f", odet.psifac)), dpsi=$(@sprintf("%.10e", dpsi))\n"
+ msg *= " alpha_L = $(sing_asymp_left.alpha), alpha_R = $(sing_asymp_right.alpha)\n"
+ for ip in ipert_res_diag
+ msg *= " vmatL[0] big: vmat[$ip,$ip,1,1]=$(@sprintf("%.8e", real(sing_asymp_left.vmat[ip,ip,1,1]))), vmat[$ip,$ip,2,1]=$(@sprintf("%.8e", real(sing_asymp_left.vmat[ip,ip,2,1])))\n"
+ msg *= " vmatR[0] big: vmat[$ip,$ip,1,1]=$(@sprintf("%.8e", real(sing_asymp_right.vmat[ip,ip,1,1]))), vmat[$ip,$ip,2,1]=$(@sprintf("%.8e", real(sing_asymp_right.vmat[ip,ip,2,1])))\n"
+ end
+ msg
+ end
+end
+
+# Capture left-side asymptotic data into odet.ca_l and singp.ua_left/psi_ua_left.
+function _capture_left_crossing_data!(odet::OdeState, singp::SingType, sing_asymp_left,
+ dpsi::Float64, intr::ForceFreeStatesInternal, ising::Int)
+ ua = sing_get_ua(sing_asymp_left, dpsi)
+ singp.ua_left = copy(ua)
+ singp.psi_ua_left = odet.psifac
+ odet.ca_l[:, :, :, ising] .= sing_get_ca(odet.u, ua, intr)
+end
+
+# Trapezoidal predictor across the singular surface with the resonant columns zeroed (they stay zero).
+function _predict_across_singular_surface!(odet::OdeState, ctrl::ForceFreeStatesControl,
+ equil::Equilibrium.PlasmaEquilibrium, mats::MatrixSplines,
+ intr::ForceFreeStatesInternal, ising::Int,
+ ipert_res, dpsi::Float64, sing_asymp_right)
+ if ctrl.kinetic === nothing
+ for i in eachindex(sing_asymp_right.r1)
+ odet.u[:, ipert_res[i], :] .= 0
+ end
+ end
+ params = (ctrl, equil, mats, intr, odet, IntegrationChunk(0.0, 0.0, false, ising, 1))
+ du1 = zeros(ComplexF64, intr.numpert_total, intr.numpert_total, 2)
+ du2 = zeros(ComplexF64, intr.numpert_total, intr.numpert_total, 2)
+ sing_der!(du1, odet.u, params, odet.psifac)
+ odet.psifac += 2 * dpsi # jump to other side of singular surface
+ sing_der!(du2, odet.u, params, odet.psifac)
+ odet.u .+= (du1 .+ du2) .* dpsi
+end
+
+# Inject the right-side small asymptotic into the resonant columns, then capture odet.ca_r and singp.ua_right.
+function _capture_right_crossing_data!(odet::OdeState, singp::SingType, sing_asymp_right,
+ dpsi::Float64, intr::ForceFreeStatesInternal, ising::Int,
+ ipert_res, ctrl::ForceFreeStatesControl)
+ ua = sing_get_ua(sing_asymp_right, dpsi)
+ singp.ua_right = copy(ua)
+ singp.psi_ua_right = odet.psifac
+ if ctrl.kinetic === nothing
+ for i in eachindex(sing_asymp_right.r1)
+ odet.u[ipert_res[i], :, :] .= 0
+ odet.u[:, ipert_res[i], :] .= ua[:, ipert_res[i]+intr.numpert_total, :]
+ end
+ end
+ odet.ca_r[:, :, :, ising] .= sing_get_ca(odet.u, ua, intr)
+ odet.ca_populated = true
+end
+
+# STUB: per-surface ca-based Δ' (not physically valid; see SingType.delta_prime docstring).
+# The canonical Δ' is intr.delta_prime_matrix from compute_delta_prime_matrix!.
+function _stash_per_surface_delta_prime_stub!(odet::OdeState, intr::ForceFreeStatesInternal,
+ ising::Int, ipert_res, sing_asymp_right,
+ equil::Equilibrium.PlasmaEquilibrium,
+ ctrl::ForceFreeStatesControl)
+ ctrl.kinetic === nothing || return
+ denom = (2π)^2 * equil.psio
+ n_res = length(sing_asymp_right.r1)
+ N = intr.numpert_total
+ resize!(intr.sing[ising].delta_prime, n_res)
+ intr.sing[ising].delta_prime_col = zeros(ComplexF64, N, n_res)
+ for i in eachindex(sing_asymp_right.r1)
+ Δca_col = (odet.ca_r[:, ipert_res[i], 2, ising] - odet.ca_l[:, ipert_res[i], 2, ising]) / denom
+ intr.sing[ising].delta_prime_col[:, i] .= Δca_col
+ intr.sing[ising].delta_prime[i] = Δca_col[ipert_res[i]]
+ end
+end
+
+# Store (U₁_new, U₂_new) into u_store before renormalization so that
+# evaluate_stability_criterion! can recover S_new = U₁_new / U₂_new via compute_smallest_eigenvalue.
+function _store_crossing_step!(odet::OdeState)
+ store_ode_data!(odet, odet.psifac, odet.u)
+end
diff --git a/src/ForceFreeStates/Riccati/DeltaPrimeBVP.jl b/src/ForceFreeStates/Riccati/DeltaPrimeBVP.jl
new file mode 100644
index 0000000000..fcac7b1151
--- /dev/null
+++ b/src/ForceFreeStates/Riccati/DeltaPrimeBVP.jl
@@ -0,0 +1,676 @@
+# STRIDE global boundary-value problem: Delta-prime matrix assembly, solve, PEST-3 decomposition.
+
+"""
+ compute_delta_prime_matrix!(intr, propagators, chunks; wv, psio, debug, S_at_surface_left, ctrl, equil, mats)
+
+Compute the inter-surface tearing stability matrix (msing × msing) using the
+STRIDE global BVP formulation [Glasser 2018 Phys. Plasmas 25, 032501, Sec. III.B].
+
+The BVP encodes the full plasma response with unknowns at each surface boundary:
+
+```
+ x_axis (N): free IC parameters at the axis (U₁ = 0 regular solutions)
+ x_left[j] (2N): state at left inner-layer boundary of surface j
+ x_right[j] (2N): state at right inner-layer boundary of surface j
+ x_edge (N): free IC parameters at the edge
+ Total unknowns: nMat = (2 + 4·msing)·N
+```
+
+## Boundary conditions
+
+With `wv` (the singfac-scaled vacuum response) the edge BC is `U₁ = c, U₂ = -wv·ψ₀²·c`, i.e.
+`wp + wv = 0`; with `wv = nothing` it is a conducting wall (`U₁ = 0`). When `S_at_surface_left`
+is given (one per crossed surface), the axis is matched through a QR-conditioned axis propagator and
+ua-initialized shooting propagators; otherwise through a Gaussian-reduced axis FM (STRIDE `ode_fixup`),
+which requires forward crossing chunks.
+
+## Output: PEST3-convention Δ' (deltap)
+
+The raw BVP solution is a 2·msing × 2·msing matrix `dp` with left/right
+sub-indices at each surface, stored in `intr.delta_prime_raw`. The PEST3-convention Δ' is
+[Chance, PPPL-2527]:
+
+```
+ deltap(i,j) = dp(2i,2j) - dp(2i,2j-1) - dp(2i-1,2j) + dp(2i-1,2j-1)
+```
+
+stored in `intr.delta_prime_matrix` (msing × msing).
+
+## Limitations
+
+Assumes one resonant mode per surface: if any surface carries several (a multi-`n` run where one
+q satisfies two `(m, n)`, e.g. q = 2 with (2, 1) and (4, 2)), it warns and skips the BVP.
+
+`intr.delta_prime_matrix` is the only physically valid Δ'; the per-surface ca-based
+`intr.sing[*].delta_prime` is a diagnostic placeholder and need not agree with it.
+"""
+function compute_delta_prime_matrix!(
+ intr::ForceFreeStatesInternal,
+ propagators::Vector{ChunkPropagator},
+ chunks::Vector{IntegrationChunk};
+ wv::Union{Nothing,Matrix{ComplexF64}}=nothing,
+ psio::Float64=0.0,
+ debug::Bool=false,
+ S_at_surface_left::Union{Nothing,Vector{Matrix{ComplexF64}}}=nothing,
+ ctrl::Union{Nothing,ForceFreeStatesControl}=nothing,
+ equil::Union{Nothing,Equilibrium.PlasmaEquilibrium}=nothing,
+ mats::Union{Nothing,MatrixSplines}=nothing
+)
+ intr.msing == 0 && return
+ _has_unsupported_multi_resonance(intr) && return
+
+ sing, i_crossings, msing = _select_active_surfaces(intr, chunks)
+ msing == 0 && return
+ N = intr.numpert_total
+
+ use_S_axis = S_at_surface_left !== nothing && length(S_at_surface_left) == msing
+
+ # The FM-axis fallback uses crossing-chunk propagators as forward maps; backward chunks would give a wrong Δ'.
+ if !use_S_axis
+ for ic in i_crossings
+ chunks[ic].direction == 1 ||
+ error(
+ "compute_delta_prime_matrix!: FM-axis fallback (use_S_axis=false) requires forward crossing chunks; " *
+ "chunk $ic has direction=$(chunks[ic].direction). Either provide S_at_surface_left or use bidirectional=false."
+ )
+ end
+ end
+
+ Phi_L_mats, Phi_R_mats, Phi_R_halves = _assemble_segment_propagators(
+ propagators, chunks, i_crossings, msing, N, use_S_axis)
+
+ ipert_all = [1 + sing[j].m[1] - intr.mlow + (sing[j].n[1] - intr.nlow) * intr.mpert for j in 1:msing]
+ has_ua = all(j -> !isempty(sing[j].ua_left), 1:msing)
+ T_left_mats, T_right_mats, T_left_inv, T_right_inv =
+ _build_asymptotic_basis_matrices(sing, has_ua, N, msing)
+
+ debug && _log_bvp_setup(chunks, sing, S_at_surface_left, use_S_axis, has_ua,
+ Phi_L_mats, Phi_R_mats, Phi_R_halves, ipert_all, wv, psio, N, msing)
+
+ if use_S_axis
+ uShootR, uShootL, uAxis = _build_S_axis_shooting_propagators(
+ propagators, chunks, i_crossings, sing, msing, N,
+ T_left_mats, T_right_mats, has_ua, ctrl, equil, mats, intr, debug)
+ debug && _log_S_axis_shooting_propagators(uShootR, uShootL, uAxis,
+ S_at_surface_left, T_left_mats,
+ ipert_all, has_ua, msing, N)
+ M, nMat, col_edge = _assemble_bvp_S_axis(
+ uShootR, uShootL, uAxis, ipert_all, msing, N, wv, psio)
+ else
+ M, nMat, col_edge = _assemble_bvp_FM_axis(
+ Phi_L_mats, Phi_R_mats, ipert_all, msing, N,
+ T_left_inv, T_right_inv, has_ua, wv, psio)
+ end
+
+ if debug
+ @info "Δ' BVP: nMat=$nMat, rank(M)=$(rank(M)), cond(M)=$(@sprintf("%.2e", cond(M)))"
+ end
+
+ # rpec coil-response block: needs the S-axis row layout that `_solve_bvp_edge_coil` assumes
+ # for its edge rows, and a vacuum edge in the assembled matrix (col_edge in junc_rows).
+ if use_S_axis && wv !== nothing
+ intr.delta_coil = _solve_bvp_edge_coil(M, col_edge, msing, N, ipert_all)
+ end
+
+ deltap, dp_raw_persisted = _solve_bvp_and_combine_pest3(
+ M, msing, N, nMat, use_S_axis, ipert_all, col_edge, ctrl, debug)
+
+ # The raw side-major D' (Fortran gal_write_delta layout) feeds `pest3_decompose`.
+ intr.delta_prime_matrix = deltap
+ intr.delta_prime_raw = dp_raw_persisted
+end
+
+# Column index helpers for the BVP matrix. j is the 1-based singular-surface index,
+# N is numpert_total. Layout: c_axis(N), c_left[1](2N), c_right[1](2N), ..., c_edge(N).
+_col_left(j::Int, N::Int) = (N+4N*(j-1)+1):(N+4N*(j-1)+2N)
+_col_right(j::Int, N::Int) = (N+4N*(j-1)+2N+1):(N+4N*j)
+
+# True (with a warning) if any surface carries more than one resonant (m, n), which the BVP does not handle.
+function _has_unsupported_multi_resonance(intr::ForceFreeStatesInternal)
+ msing = intr.msing
+ n_res_per_surface = [length(intr.sing[j].m) for j in 1:msing]
+ any(>(1), n_res_per_surface) || return false
+ offenders = [(j, intr.sing[j].m, intr.sing[j].n) for j in 1:msing if n_res_per_surface[j] > 1]
+ @warn "compute_delta_prime_matrix!: skipping inter-surface Δ' BVP because some surfaces carry more than one resonant mode " *
+ "(multi-n collision; generalization tracked as follow-up). " *
+ "Per-surface Δ' is unaffected. Multi-resonance surfaces: $offenders"
+ return true
+end
+
+# Map BVP surface index (1:msing_active) → intr.sing index using chunk.ising. Surfaces
+# may be excluded at either end (below qlow or beyond psilim); each crossing chunk
+# records its original surface index. Returns (sing alias, i_crossings, msing_active).
+function _select_active_surfaces(intr::ForceFreeStatesInternal, chunks::Vector{IntegrationChunk})
+ msing = intr.msing
+ i_crossings = findall(c -> c.needs_crossing, chunks)
+ sing_indices = [chunks[ic].ising for ic in i_crossings]
+ msing_active = length(i_crossings)
+ if msing_active < msing
+ excluded = setdiff(1:msing, sing_indices)
+ excluded_ms = [intr.sing[j].m for j in excluded]
+ @debug "compute_delta_prime_matrix!: $msing singular surfaces, $msing_active crossed (excluded: m=$excluded_ms)"
+ end
+ sing = [intr.sing[si] for si in sing_indices]
+ return sing, i_crossings, msing_active
+end
+
+# Assemble per-surface crossing FMs (Phi_L), inter-surface and edge FMs (Phi_R; Phi_R[1] only for the
+# FM-axis fallback), and midpoint-split halves (Phi_R_halves) used only by the debug diagnostics.
+function _assemble_segment_propagators(propagators::Vector{ChunkPropagator},
+ chunks::Vector{IntegrationChunk},
+ i_crossings::Vector{Int}, msing::Int, N::Int,
+ use_S_axis::Bool)
+ Phi_L_mats = [assemble_fm_matrix(propagators, i_crossings[j]:i_crossings[j]) for j in 1:msing]
+ Phi_R_mats = Vector{Matrix{ComplexF64}}(undef, msing + 1)
+ if !use_S_axis
+ Phi_R_mats[1] = assemble_fm_matrix(propagators, 1:(i_crossings[1]-1); condition=true)
+ end
+ for j in 2:msing
+ Phi_R_mats[j] = assemble_fm_matrix(propagators, (i_crossings[j-1]+1):(i_crossings[j]-1))
+ end
+ Phi_R_mats[msing+1] = assemble_fm_matrix(propagators, (i_crossings[msing]+1):length(chunks))
+
+ Phi_R_halves = Vector{Tuple{Matrix{ComplexF64},Matrix{ComplexF64}}}(undef, msing - 1)
+ for j in 1:(msing-1)
+ chunk_start = i_crossings[j] + 1
+ chunk_end = i_crossings[j+1] - 1
+ n_chunks = chunk_end - chunk_start + 1
+ if n_chunks >= 2
+ i_mid = chunk_start + div(n_chunks, 2) - 1
+ Phi_left_half = assemble_fm_matrix(propagators, chunk_start:i_mid)
+ Phi_right_half = assemble_fm_matrix(propagators, (i_mid+1):chunk_end)
+ Phi_R_halves[j] = (Phi_left_half, Phi_right_half)
+ else
+ Phi_R_halves[j] = (Matrix{ComplexF64}(I, 2N, 2N), Phi_R_mats[j+1])
+ end
+ end
+ return Phi_L_mats, Phi_R_mats, Phi_R_halves
+end
+
+# Asymptotic-basis transformation T = [ua[:,:,1]; ua[:,:,2]] maps (big, small) coefficients to the raw
+# state; ua columns 1:N are big (z^{-α}) and N+1:2N small (z^{+α}) solutions.
+function _build_asymptotic_basis_matrices(sing::Vector{SingType}, has_ua::Bool, N::Int, msing::Int)
+ T_left_mats = Vector{Matrix{ComplexF64}}(undef, msing)
+ T_right_mats = Vector{Matrix{ComplexF64}}(undef, msing)
+ T_left_inv = Vector{Matrix{ComplexF64}}(undef, msing)
+ T_right_inv = Vector{Matrix{ComplexF64}}(undef, msing)
+ if has_ua
+ for j in 1:msing
+ sp = sing[j]
+ T_left_mats[j] = [sp.ua_left[:, :, 1]; sp.ua_left[:, :, 2]]
+ T_right_mats[j] = [sp.ua_right[:, :, 1]; sp.ua_right[:, :, 2]]
+ T_left_inv[j] = inv(T_left_mats[j])
+ T_right_inv[j] = inv(T_right_mats[j])
+ end
+ end
+ return T_left_mats, T_right_mats, T_left_inv, T_right_inv
+end
+
+# Build the S-axis shooting propagators uShootR (surface j right → midpoint), uShootL (surface j
+# left → midpoint, backward), and the QR-conditioned axis propagator uAxis that uShootL[1] meets.
+function _build_S_axis_shooting_propagators(
+ propagators::Vector{ChunkPropagator}, chunks::Vector{IntegrationChunk},
+ i_crossings::Vector{Int}, sing::Vector{SingType}, msing::Int, N::Int,
+ T_left_mats::Vector{Matrix{ComplexF64}}, T_right_mats::Vector{Matrix{ComplexF64}},
+ has_ua::Bool, ctrl, equil, mats, intr::ForceFreeStatesInternal, debug::Bool)
+
+ can_reintegrate = has_ua && ctrl !== nothing && equil !== nothing && mats !== nothing
+ uShootR = Vector{Matrix{ComplexF64}}(undef, msing)
+ uShootL = Vector{Matrix{ComplexF64}}(undef, msing) # uShootL[1] handled separately below
+
+ for j in 1:msing
+ shoot_range_R = _midpoint_shoot_range(chunks, i_crossings, j, msing; side=:right)
+ if debug && !isempty(shoot_range_R)
+ psi_surf_R = chunks[first(shoot_range_R)].psi_start
+ psi_mid_R = chunks[last(shoot_range_R)].psi_end
+ psi_ua_R = sing[j].psi_ua_right
+ @info " uShootR[$j]: shoot_range=$(shoot_range_R), psi_chunk=$(@sprintf("%.6f", psi_surf_R)), psi_ua=$(@sprintf("%.6f", psi_ua_R)), psi_mid=$(@sprintf("%.6f", psi_mid_R)), Δψ_fix=$(@sprintf("%.6e", psi_ua_R - psi_surf_R))"
+ end
+ if can_reintegrate && !isempty(shoot_range_R)
+ uShootR[j] = integrate_fm_with_ua_ic(chunks, shoot_range_R, sing[j].ua_right,
+ ctrl, equil, mats, intr; backward=false, psi_ua=sing[j].psi_ua_right)
+ else
+ T_init = has_ua ? T_right_mats[j] : nothing
+ uShootR[j] = assemble_fm_matrix(propagators, shoot_range_R; T_init=T_init)
+ end
+
+ # uShootL[j>=2]: backward from surface j left to midpoint. uShootL[1] handled below.
+ j == 1 && continue
+ shoot_range_L = _midpoint_shoot_range(chunks, i_crossings, j, msing; side=:left)
+ if debug
+ psi_mid = chunks[first(shoot_range_L)].psi_start
+ psi_surf = chunks[last(shoot_range_L)].psi_end
+ psi_ua_L = sing[j].psi_ua_left
+ @info " uShootL[$j]: shoot_range=$(shoot_range_L), psi_mid=$(@sprintf("%.6f", psi_mid)), psi_chunk=$(@sprintf("%.6f", psi_surf)), psi_ua=$(@sprintf("%.6f", psi_ua_L)), Δψ_fix=$(@sprintf("%.6e", psi_ua_L - psi_surf))"
+ end
+ if can_reintegrate && !isempty(shoot_range_L)
+ uShootL[j] = integrate_fm_with_ua_ic(chunks, shoot_range_L, sing[j].ua_left,
+ ctrl, equil, mats, intr; backward=true, psi_ua=sing[j].psi_ua_left)
+ else
+ T_init = has_ua ? T_left_mats[j] : nothing
+ uShootL[j] = assemble_fm_matrix(propagators, shoot_range_L; T_init=T_init)
+ end
+ end
+
+ uAxis, i_axis_mid = _build_conditioned_axis_propagator(propagators, i_crossings, N)
+ uShootL[1] = _build_uShootL_first(propagators, chunks, i_crossings, sing,
+ T_left_mats, has_ua, can_reintegrate, i_axis_mid,
+ ctrl, equil, mats, intr, N)
+ if debug
+ shoot_range_L1 = (i_axis_mid+1):(i_crossings[1]-1)
+ @info " Axis propagator: $(i_axis_mid) chunks, cond=$(@sprintf("%.2e", cond(uAxis)))"
+ @info " uShootL[1]: range=$(shoot_range_L1), cond=$(@sprintf("%.2e", cond(uShootL[1])))"
+ end
+ return uShootR, uShootL, uAxis
+end
+
+# Chunk range from surface j to the ψ midpoint toward the next surface (`:right`; the edge for
+# j == msing) or from the midpoint after surface j-1 to surface j (`:left`). The ψ midpoint, not the
+# chunk-index midpoint, matches Fortran since chunks pack tighter near singularities.
+function _midpoint_shoot_range(chunks::Vector{IntegrationChunk}, i_crossings::Vector{Int},
+ j::Int, msing::Int; side::Symbol)
+ if side === :right
+ j == msing && return (i_crossings[msing]+1):length(chunks)
+ chunk_start = i_crossings[j] + 1
+ chunk_end = i_crossings[j+1] - 1
+ else # :left, j >= 2
+ chunk_start = i_crossings[j-1] + 1
+ chunk_end = i_crossings[j] - 1
+ end
+ psi_mid_target = (chunks[chunk_start].psi_start + chunks[chunk_end].psi_end) / 2
+ i_mid_inter = chunk_start
+ for ic in chunk_start:(chunk_end-1)
+ if chunks[ic].psi_end >= psi_mid_target
+ i_mid_inter = ic
+ break
+ end
+ i_mid_inter = ic
+ end
+ return side === :right ? (chunk_start:i_mid_inter) : ((i_mid_inter+1):chunk_end)
+end
+
+# Propagate [0; I] from the axis with a QR fixup after each chunk (Fortran ode_fixup), stopping one
+# chunk before the first surface so uShootL[1] spans a single well-conditioned chunk.
+function _build_conditioned_axis_propagator(propagators::Vector{ChunkPropagator},
+ i_crossings::Vector{Int}, N::Int)
+ n_pre_cross = i_crossings[1] - 1
+ i_axis_mid = max(1, n_pre_cross - 1)
+ uAxis = zeros(ComplexF64, 2N, N)
+ for i in 1:N
+ uAxis[N+i, i] = 1
+ end
+ for ic in 1:i_axis_mid
+ prop = propagators[ic]
+ upper_old = uAxis[1:N, :]
+ lower_old = uAxis[(N+1):2N, :]
+ uAxis[1:N, :] .= prop.block_upper_ic[:, :, 1] * upper_old .+ prop.block_lower_ic[:, :, 1] * lower_old
+ uAxis[(N+1):2N, :] .= prop.block_upper_ic[:, :, 2] * upper_old .+ prop.block_lower_ic[:, :, 2] * lower_old
+ Q, _ = qr(uAxis)
+ uAxis .= Matrix(Q)[:, 1:N]
+ end
+ for j in 1:N
+ uAxis[:, j] ./= norm(@view uAxis[:, j])
+ end
+ return uAxis, i_axis_mid
+end
+
+# uShootL[1]: backward propagator from surface 1's left boundary to the axis midpoint; T_left_mats[1]
+# (or the identity without ua) when that range is empty.
+function _build_uShootL_first(propagators::Vector{ChunkPropagator},
+ chunks::Vector{IntegrationChunk}, i_crossings::Vector{Int},
+ sing::Vector{SingType}, T_left_mats::Vector{Matrix{ComplexF64}},
+ has_ua::Bool, can_reintegrate::Bool, i_axis_mid::Int,
+ ctrl, equil, mats, intr::ForceFreeStatesInternal, N::Int)
+ shoot_range_L1 = (i_axis_mid+1):(i_crossings[1]-1)
+ if can_reintegrate && !isempty(shoot_range_L1)
+ return integrate_fm_with_ua_ic(chunks, shoot_range_L1, sing[1].ua_left,
+ ctrl, equil, mats, intr;
+ backward=true, psi_ua=sing[1].psi_ua_left)
+ elseif !isempty(shoot_range_L1)
+ return assemble_fm_matrix(propagators, shoot_range_L1;
+ T_init=has_ua ? T_left_mats[1] : nothing)
+ else
+ return has_ua ? T_left_mats[1] : Matrix{ComplexF64}(I, 2N, 2N)
+ end
+end
+
+# Assemble the BVP matrix M with the axis matched to the conditioned axis propagator, avoiding the
+# ill-conditioned full axis FM. Fortran-matched layout, nMat = (2 + 4·msing)·N. Returns (M, nMat, col_edge).
+function _assemble_bvp_S_axis(uShootR::Vector{Matrix{ComplexF64}},
+ uShootL::Vector{Matrix{ComplexF64}},
+ uAxis::Matrix{ComplexF64}, ipert_all::Vector{Int},
+ msing::Int, N::Int,
+ wv::Union{Nothing,Matrix{ComplexF64}}, psio::Float64)
+ # STRIDE global BVP block structure [Glasser-Kolemen 2018 PoP 25, 032501 Eq. 37].
+ nMat = (2 + 4 * msing) * N
+ col_axis = 1:N
+ col_edge = (nMat-N+1):nMat
+ M = zeros(ComplexF64, nMat, nMat)
+
+ # Axis matching: uShootL[1] · c_left[1] = uAxis · c_axis (2N equations)
+ M[1:2N, _col_left(1, N)] .= uShootL[1]
+ M[1:2N, col_axis] .= -uAxis
+ row_offset = 2N
+
+ for j in 1:msing
+ ipert_j = ipert_all[j]
+ # Crossing: non-resonant modes continuity (asymptotic basis = identity)
+ for i in 1:2N
+ if i != ipert_j && i != ipert_j + N
+ row_offset += 1
+ M[row_offset, _col_left(j, N)[i]] = 1
+ M[row_offset, _col_right(j, N)[i]] = -1
+ end
+ end
+
+ junc_rows = (row_offset+1):(row_offset+2N)
+ if j < msing
+ # Midpoint matching between consecutive surfaces
+ M[junc_rows, _col_right(j, N)] .= -uShootR[j]
+ M[junc_rows, _col_left(j + 1, N)] .= uShootL[j+1]
+ else
+ # Edge junction
+ M[junc_rows, _col_right(msing, N)] .= uShootR[msing]
+ if wv !== nothing
+ M[junc_rows[1:N], col_edge] .= -I(N)
+ M[junc_rows[(N+1):end], col_edge] .= wv .* psio^2
+ else
+ M[junc_rows[(N+1):end], col_edge] .= -I(N)
+ end
+ end
+ row_offset = last(junc_rows)
+ end
+
+ # Driving rows: set big-solution coefficient = 1 at each surface (asymptotic basis)
+ for j in 1:msing
+ ipert_j = ipert_all[j]
+ row_offset += 1
+ M[row_offset, _col_left(j, N)[ipert_j]] = 1
+ row_offset += 1
+ M[row_offset, _col_right(j, N)[ipert_j]] = 1
+ end
+ @assert row_offset == nMat "Row count mismatch: expected $nMat, got $row_offset"
+ return M, nMat, col_edge
+end
+
+# Coil-response block for the Eq. (37) edge [Glasser-Kolemen 2018 PoP 25, 032501]: impose the rpec edge BC
+# (RDCON `gal_set_boundary`, unit source per poloidal mode) and read the small-solution coefficient at each
+# surface side, solving all N modes with one factorization. Returns delta_coil (2·msing × N).
+function _solve_bvp_edge_coil(M::Matrix{ComplexF64}, col_edge, msing::Int, N::Int, ipert_all::Vector{Int})
+ nMat = size(M, 1)
+ bot = (nMat-2msing-N+1):(nMat-2msing) # Eq. (38) bottom rows, carrying the W_V block
+ Mc = copy(M)
+ Mc[bot, :] .= 0
+ Mc[bot, col_edge] .= I(N) # Dirichlet edge: the edge coefficients equal the source
+ B = zeros(ComplexF64, nMat, N)
+ B[bot, :] .= I(N) # unit drive, one column per edge poloidal mode
+ X = lu(Mc) \ B
+ delta_coil = zeros(ComplexF64, 2msing, N)
+ for j in 1:msing
+ row_left = _col_left(j, N)[ipert_all[j]+N]
+ row_right = _col_right(j, N)[ipert_all[j]+N]
+ @views delta_coil[2j-1, :] .= X[row_left, :]
+ @views delta_coil[2j, :] .= X[row_right, :]
+ end
+ return delta_coil
+end
+
+# Fallback BVP assembly with FM-based axis BC (used when no Riccati S matrices are available).
+# Uses the conditioned axis propagator Phi_R[1][:,N+1:2N] in place of S-axis matching.
+function _assemble_bvp_FM_axis(Phi_L_mats::Vector{Matrix{ComplexF64}},
+ Phi_R_mats::Vector{Matrix{ComplexF64}}, ipert_all::Vector{Int},
+ msing::Int, N::Int,
+ T_left_inv::Vector{Matrix{ComplexF64}},
+ T_right_inv::Vector{Matrix{ComplexF64}}, has_ua::Bool,
+ wv::Union{Nothing,Matrix{ComplexF64}}, psio::Float64)
+ nMat = (2 + 4 * msing) * N
+ col_axis = 1:N
+ col_edge = (N+4N*msing+1):nMat
+ M = zeros(ComplexF64, nMat, nMat)
+
+ M[1:2N, (N+1):(N+2N)] .= Phi_L_mats[1]
+ M[1:2N, col_axis] .= -view(Phi_R_mats[1], :, (N+1):2N)
+
+ row_drive_base = 2N + (4N - 2) * msing
+ for j in 1:msing
+ ipert_j = ipert_all[j]
+ cl = _col_left(j, N)
+ cr = _col_right(j, N)
+ row_cont = 2N + (4N - 2) * (j - 1)
+ for i in 1:2N
+ if i != ipert_j && i != ipert_j + N
+ row_cont += 1
+ M[row_cont, cl[i]] = 1
+ M[row_cont, cr[i]] = -1
+ end
+ end
+ junc_rows = (row_cont+1):(2N+(4N-2)*j)
+ if j < msing
+ M[junc_rows, cr] .= Phi_R_mats[j+1]
+ M[junc_rows, _col_left(j + 1, N)] .= -Phi_L_mats[j+1]
+ else
+ M[junc_rows, cr] .= Phi_R_mats[msing+1]
+ if wv !== nothing
+ M[junc_rows[1:N], col_edge] .= -I(N)
+ M[junc_rows[(N+1):end], col_edge] .= wv .* psio^2
+ else
+ M[junc_rows[(N+1):end], col_edge] .= -I(N)
+ end
+ end
+ if has_ua
+ M[row_drive_base+2j-1, cl] .= T_left_inv[j][ipert_j, :]
+ M[row_drive_base+2j, cr] .= T_right_inv[j][ipert_j, :]
+ else
+ M[row_drive_base+2j-1, cl[ipert_j]] = 1
+ M[row_drive_base+2j, cr[ipert_j]] = 1
+ end
+ end
+ return M, nMat, col_edge
+end
+
+# Solve the BVP and apply the PEST3 four-term combination.
+function _solve_bvp_and_combine_pest3(M::Matrix{ComplexF64}, msing::Int, N::Int, nMat::Int,
+ use_S_axis::Bool, ipert_all::Vector{Int}, col_edge,
+ ctrl, debug::Bool)
+ s2 = 2 * msing
+ Tc = (ctrl === nothing || ctrl.algorithm.extended_precision_bvp) ? Complex{Double64} : ComplexF64
+ M_solve = Tc.(M)
+ M_lu = lu(M_solve; check=false)
+ use_lu = issuccess(M_lu)
+ M_pinv = use_lu ? nothing : pinv(M_solve)
+ if !use_lu
+ @warn "Δ' BVP: LU factorization singular (rank $(rank(M))/$nMat), using pseudo-inverse fallback"
+ end
+
+ dp_raw = zeros(Tc, s2, s2)
+ b = zeros(Tc, nMat)
+ for jsing in 1:msing, side in 1:2
+ dRow = 2jsing - (2 - side)
+ fill!(b, 0)
+ drive_row = use_S_axis ? (nMat - s2 + dRow) : (2N + (4N - 2) * msing + dRow)
+ b[drive_row] = 1
+ x = use_lu ? (M_lu \ b) : (M_pinv * b)
+
+ debug && _log_bvp_solve(x, b, M_solve, jsing, side, dRow, msing, N,
+ ipert_all, col_edge, use_S_axis)
+
+ for ksing in 1:msing
+ ipert_k = ipert_all[ksing]
+ dp_raw[dRow, 2ksing-1] = x[_col_left(ksing, N)[ipert_k+N]]
+ dp_raw[dRow, 2ksing] = x[_col_right(ksing, N)[ipert_k+N]]
+ end
+ end
+
+ # PEST3 four-term combination [Chance PPPL-2527; Glasser-Kolemen 2018 PoP 25, 032501 Eq. 31].
+ # Δ'[i,j] = (NW − NE − SW + SE) on each 2×2 block of dp_raw.
+ deltap = zeros(Tc, msing, msing)
+ for i in 1:msing, j in 1:msing
+ deltap[i, j] = dp_raw[2i, 2j] - dp_raw[2i, 2j-1] - dp_raw[2i-1, 2j] + dp_raw[2i-1, 2j-1]
+ end
+
+ debug && _log_bvp_pest3(dp_raw, deltap, s2, msing)
+ return ComplexF64.(deltap), ComplexF64.(dp_raw)
+end
+
+# Logging helpers for `compute_delta_prime_matrix!`. Called only when debug=true.
+function _log_bvp_setup(chunks, sing, S_at_surface_left, use_S_axis, has_ua,
+ Phi_L_mats, Phi_R_mats, Phi_R_halves, ipert_all, wv, psio, N, msing)
+ @info "Δ' BVP: $(length(chunks)) chunks, $msing surfaces, N=$N"
+ @info "Δ' BVP: Axis BC: $(use_S_axis ? "S-based (Riccati)" : "FM-based (conditioned)")"
+ @info "Δ' BVP: Asymptotic basis: $(has_ua ? "available" : "NOT available (raw basis driving)")"
+ if use_S_axis
+ for j in 1:msing
+ @info " S_left[$j]: max=$(@sprintf("%.2e", maximum(abs, S_at_surface_left[j]))), cond=$(@sprintf("%.2e", cond(S_at_surface_left[j])))"
+ end
+ end
+ if has_ua
+ for j in 1:msing
+ sp = sing[j]
+ T_l = [sp.ua_left[:, :, 1]; sp.ua_left[:, :, 2]]
+ T_r = [sp.ua_right[:, :, 1]; sp.ua_right[:, :, 2]]
+ @info " Surface $j: cond(T_left)=$(@sprintf("%.2e", cond(T_l))), cond(T_right)=$(@sprintf("%.2e", cond(T_r)))"
+ ipert_j = ipert_all[j]
+ @info " Surface $j ua_left (ipert=$ipert_j, psi_ua_left=$(@sprintf("%.8f", sp.psi_ua_left))):"
+ for i in 1:min(5, N)
+ @info " ua($i,$ipert_j,1)=$(@sprintf("%16.8e %16.8e", real(sp.ua_left[i,ipert_j,1]), imag(sp.ua_left[i,ipert_j,1]))) ua($i,$ipert_j,2)=$(@sprintf("%16.8e %16.8e", real(sp.ua_left[i,ipert_j,2]), imag(sp.ua_left[i,ipert_j,2])))"
+ end
+ @info " small: ua(1,$(ipert_j+N),1)=$(@sprintf("%16.8e %16.8e", real(sp.ua_left[1,ipert_j+N,1]), imag(sp.ua_left[1,ipert_j+N,1])))"
+ end
+ end
+ for j in 1:(msing-1)
+ Phi_L_h, Phi_R_h = Phi_R_halves[j]
+ @info " Inter-surface $j→$(j+1): half_L cond=$(@sprintf("%.2e",cond(Phi_L_h))), half_R cond=$(@sprintf("%.2e",cond(Phi_R_h))), full cond=$(@sprintf("%.2e",cond(Phi_R_mats[j+1])))"
+ end
+ @info " Phi_R[$(msing+1)] (edge): cond=$(@sprintf("%.2e",cond(Phi_R_mats[msing+1])))"
+ for j in 1:msing
+ @info " Surface $j (m=$(sing[j].m[1])): ipert=$(ipert_all[j]), cond(Phi_L)=$(@sprintf("%.2e", cond(Phi_L_mats[j])))"
+ end
+ @info "Δ' BVP: Vacuum BC $(wv === nothing ? "off (conducting wall)" : "on (psio=$psio)")"
+ for j in 1:msing
+ if !isempty(sing[j].delta_prime)
+ @info " Surface $j ca-based Δ' = $(@sprintf("%.6f%+.6fi", real(sing[j].delta_prime[1]), imag(sing[j].delta_prime[1])))"
+ end
+ end
+end
+
+function _log_S_axis_shooting_propagators(uShootR, uShootL, uAxis, S_at_surface_left,
+ T_left_mats, ipert_all, has_ua, msing, N)
+ @info " Shooting propagators (S-based axis BC, no axis unknowns):"
+ for j in 1:msing
+ shoot_R_str = @sprintf("%.2e", cond(uShootR[j]))
+ shoot_L_str = j >= 2 ? @sprintf("%.2e", cond(uShootL[j])) : "N/A (S axis BC)"
+ @info " uShootL[$j]: cond=$shoot_L_str, uShootR[$j]: cond=$shoot_R_str"
+ end
+ S1 = S_at_surface_left[1]
+ if has_ua
+ T1 = T_left_mats[1]
+ axis_BC = T1[1:N, :] - S1 * T1[(N+1):2N, :]
+ @info " S-axis BC matrix: cond=$(@sprintf("%.2e", cond(axis_BC)))"
+ end
+ for j in 1:msing
+ ipert_j = ipert_all[j]
+ col_norms_R = [norm(view(uShootR[j], :, k)) for k in 1:2N]
+ @info " uShootR[$j] column norms: min=$(@sprintf("%.2e", minimum(col_norms_R))), max=$(@sprintf("%.2e", maximum(col_norms_R)))"
+ @info " uShootR[$j] col ipert=$ipert_j norm=$(@sprintf("%.2e", col_norms_R[ipert_j])), col ipert+N=$(ipert_j+N) norm=$(@sprintf("%.2e", col_norms_R[ipert_j+N]))"
+ if j >= 2
+ col_norms_L = [norm(view(uShootL[j], :, k)) for k in 1:2N]
+ @info " uShootL[$j] column norms: min=$(@sprintf("%.2e", minimum(col_norms_L))), max=$(@sprintf("%.2e", maximum(col_norms_L)))"
+ @info " uShootL[$j] col ipert=$ipert_j norm=$(@sprintf("%.2e", col_norms_L[ipert_j])), col ipert+N=$(ipert_j+N) norm=$(@sprintf("%.2e", col_norms_L[ipert_j+N]))"
+ end
+ end
+ for j in 1:(msing-1)
+ mid_block = hcat(uShootR[j], -uShootL[j+1])
+ @info " Midpoint $j→$(j+1): cond([uShootR[$j] | -uShootL[$(j+1)]]) = $(@sprintf("%.2e", cond(mid_block)))"
+ col_norms_Ljp1 = [norm(view(uShootL[j+1], :, k)) for k in 1:2N]
+ @info " uShootL[$(j+1)] all col norms: $([(@sprintf("%.2e", c)) for c in col_norms_Ljp1])"
+ end
+end
+
+function _log_bvp_solve(x, b, M_solve, jsing, side, dRow, msing, N,
+ ipert_all, col_edge, use_S_axis)
+ residual = norm(ComplexF64.(M_solve * x - b))
+ side_str = side == 1 ? "left" : "right"
+ @info " BVP solve: jsing=$jsing side=$side_str (dRow=$dRow): ||Mx-b||=$(@sprintf("%.2e", residual)), ||x||=$(@sprintf("%.2e", Float64(norm(x))))"
+ for ks in 1:msing
+ ipert_ks = ipert_all[ks]
+ cl = _col_left(ks, N)
+ cr = _col_right(ks, N)
+ xl_big = ComplexF64(x[cl[ipert_ks]])
+ xl_small = ComplexF64(x[cl[ipert_ks+N]])
+ xr_big = ComplexF64(x[cr[ipert_ks]])
+ xr_small = ComplexF64(x[cr[ipert_ks+N]])
+ @info " surf $ks: x_left[big]=$(@sprintf("%+.4e%+.4ei", real(xl_big), imag(xl_big))), x_left[small]=$(@sprintf("%+.4e%+.4ei", real(xl_small), imag(xl_small)))"
+ @info " surf $ks: x_right[big]=$(@sprintf("%+.4e%+.4ei", real(xr_big), imag(xr_big))), x_right[small]=$(@sprintf("%+.4e%+.4ei", real(xr_small), imag(xr_small)))"
+ @info " surf $ks: ||x_left||=$(@sprintf("%.2e", Float64(norm(x[cl])))), ||x_right||=$(@sprintf("%.2e", Float64(norm(x[cr]))))"
+ end
+ if use_S_axis
+ @info " ||x_edge||=$(@sprintf("%.2e", Float64(norm(x[col_edge]))))"
+ end
+end
+
+function _log_bvp_pest3(dp_raw, deltap, s2, msing)
+ @info "Δ' BVP: Full dp_raw matrix ($(s2)×$(s2)):"
+ for i in 1:s2
+ row_str = join([@sprintf("%+.6e", Float64(real(dp_raw[i, j]))) for j in 1:s2], " ")
+ @info " dp_raw[$i,:] = $row_str"
+ end
+ @info "Δ' BVP: Raw dp diagonal = $([@sprintf("%.4f%+.4fi", Float64(real(dp_raw[i,i])), Float64(imag(dp_raw[i,i]))) for i in 1:s2])"
+ @info "Δ' BVP: deltap diagonal = $([@sprintf("%.4f%+.4fi", real(deltap[i,i]), imag(deltap[i,i])) for i in 1:msing])"
+end
+
+"""
+ pest3_decompose(dp_raw::AbstractMatrix) -> NamedTuple{(:A, :B, :Γ, :Δ)}
+
+Rotate the raw 2m×2m outer-region matching matrix `dp_raw` (side-major
+ordering `[L_s1, R_s1, L_s2, R_s2, …]`) into the Pletzer–Dewar 1991 parity
+blocks. Given rows and columns paired by surface (odd index = left, even
+index = right), the Fortran RDCON parity combination is
+
+```
+A'(i,j) = RR + RL + LR + LL (even-i, even-j) — interchange↔interchange
+B'(i,j) = RR − RL + LR − LL (even-i, odd-j) — interchange↔tearing
+Γ'(i,j) = RR + RL − LR − LL (odd-i, even-j) — tearing↔interchange
+Δ'(i,j) = RR − RL − LR + LL (odd-i, odd-j) — tearing↔tearing
+```
+
+where `RR = dp_raw[2i, 2j]`, `RL = dp_raw[2i, 2j−1]`,
+`LR = dp_raw[2i−1, 2j]`, `LL = dp_raw[2i−1, 2j−1]`. Each block is m×m.
+
+No Pletzer–Dewar ½ prefactor, matching Fortran RDCON; it cancels in `det(D' − D(γ)) = 0`.
+
+The Δ' block returned here equals `intr.delta_prime_matrix` (the m×m PEST3
+tearing projection computed inside `compute_delta_prime_matrix!`).
+
+# Arguments
+
+ - `dp_raw` — 2m×2m complex matrix (typically `intr.delta_prime_raw`).
+
+# Returns
+
+Named tuple `(A, B, Γ, Δ)` of m×m matrices, the blocks of `D' = [[A' B'] [Γ' Δ']]` in the
+`det(D' − D(γ)) = 0` problem (interchange upper-left, tearing lower-right).
+"""
+function pest3_decompose(dp_raw::AbstractMatrix)
+ s2 = size(dp_raw, 1)
+ size(dp_raw, 2) == s2 ||
+ throw(ArgumentError("pest3_decompose: dp_raw must be square, got $(size(dp_raw))"))
+ iseven(s2) ||
+ throw(ArgumentError("pest3_decompose: dp_raw side must be 2m for integer m, got $s2"))
+ m = s2 ÷ 2
+ Tc = eltype(dp_raw)
+ Ap = zeros(Tc, m, m)
+ Bp = zeros(Tc, m, m)
+ Gp = zeros(Tc, m, m)
+ Dp = zeros(Tc, m, m)
+ for i in 1:m, j in 1:m
+ LL = dp_raw[2i-1, 2j-1]
+ LR = dp_raw[2i-1, 2j]
+ RL = dp_raw[2i, 2j-1]
+ RR = dp_raw[2i, 2j]
+ Ap[i, j] = RR + RL + LR + LL
+ Bp[i, j] = RR - RL + LR - LL
+ Gp[i, j] = RR + RL - LR - LL
+ Dp[i, j] = RR - RL - LR + LL
+ end
+ return (A=Ap, B=Bp, Γ=Gp, Δ=Dp)
+end
diff --git a/src/ForceFreeStates/Riccati/Driver.jl b/src/ForceFreeStates/Riccati/Driver.jl
new file mode 100644
index 0000000000..ef85b7bfa4
--- /dev/null
+++ b/src/ForceFreeStates/Riccati/Driver.jl
@@ -0,0 +1,228 @@
+"""
+ Riccati/ - Dual Riccati reformulation of the Euler-Lagrange ODE
+
+Tracks the dual Riccati matrix S = U₁·U₂⁻¹ = P⁻¹ (P = U₂·U₁⁻¹ the plasma response matrix), which stays
+bounded near singular surfaces where U₁ and U₂ grow exponentially. Reference: Glasser (2018) Phys. Plasmas
+25, 032507 — Eq. 19 (dual form), dS/dψ = w†·F̄⁻¹·w − S·Ḡ·S with w = Q − K̄·S.
+
+The explicit Riccati ODE is not integrated directly: its quadratic term defeats relative error control when
+|S| is large. Instead the linear EL ODE (`sing_der!`) is integrated in (U₁, U₂), and the exact change of
+variables `renormalize_riccati_inplace!` resets the state to (S, I) whenever max(|U₁|) or max(|U₂|) exceeds
+`renorm_threshold`, the Riccati analogue of Gaussian reduction.
+
+## Storage convention
+
+ - During a chunk: u[:,:,1] = U₁ (starts as S), u[:,:,2] = U₂ (starts as I).
+ - After renormalization: u[:,:,1] = S, u[:,:,2] = I, so downstream U₁/U₂ ratios (wp in Free.jl, the
+ fixed-boundary criterion) read S directly.
+ - Axis: S(ψ₀) = 0 (U₁ = 0, U₂ = I), unless a positive `ctrl.frobenius_psi_max` at or above the start
+ opts into the diagonal Frobenius init (U₂ = I, per-mode U₁).
+
+Unlike the forward path, `riccati_integrator_callback!` renormalizes instead of Gaussian reduction,
+`riccati_cross_ideal_singular_surf!` crosses without Gaussian reduction, and `transform_u!` is a no-op.
+"""
+
+"""
+ riccati_eulerlagrange_integration(ctrl, equil, mats, intr) -> (odet, propagators, chunks, S_left)
+
+The Riccati/STRIDE integrator: solves the same system as [`forward_eulerlagrange_integration`](@ref)
+by integrating chunk fundamental matrices (propagators) concurrently with `Threads.@threads`,
+assembling them serially with Riccati crossings (no Gaussian reduction), and re-integrating the
+outer plasma with `riccati_integrate_chunk!` for dense, bounded checkpoints. Crossing chunks are
+integrated backward and inverted by LU, which keeps them well-conditioned at large N (STRIDE,
+Glasser 2018 Phys. Plasmas 25, 032501). The trailing three return values feed the Δ' BVP in
+`compute_delta_prime_matrix!`; this is the only branch that produces them.
+
+Select with `Riccati()`, or `integrator = "Riccati"` in a deck's `[ForceFreeStates]`. Requires
+`singfac_min != 0`. Results do not depend on the thread count; `ctrl.algorithm.nchunks` is the only
+tunable. `odet.u_store` holds chunk-endpoint Riccati states, not the EL basis
+(`odet.u_store_el_basis == false`), so PerturbedEquilibrium and the HDF5 ξ datasets require `Forward()`.
+"""
+function riccati_eulerlagrange_integration(
+ ctrl::ForceFreeStatesControl, equil::Equilibrium.PlasmaEquilibrium,
+ mats::MatrixSplines, intr::ForceFreeStatesInternal
+)
+ odet = _initialize_parallel_odet(ctrl, equil, mats, intr)
+ chunks, propagators, odet_proxies = _setup_parallel_chunks_and_proxies(odet, ctrl, intr)
+ intr.verbose && _log_parallel_start(odet, equil, chunks)
+
+ _run_parallel_bvp_phase!(propagators, chunks, ctrl, equil, mats, intr, odet_proxies)
+
+ # Harvest thread-local solver-step counts; the outer re-integration counts via its own callback.
+ odet.total_steps += sum(p.total_steps for p in odet_proxies)
+
+ S_at_surface_left, last_crossing_step =
+ _assemble_propagators_serially!(odet, propagators, chunks, ctrl, equil, mats, intr)
+
+ _reintegrate_outer_plasma!(odet, last_crossing_step, ctrl, equil, mats, intr)
+
+ chunks, propagators = _handle_edge_dW_scan!(odet, chunks, propagators, ctrl, equil, mats, intr)
+ resize!(S_at_surface_left, intr.msing) # one per surviving surface, as the Δ' BVP requires
+
+ # compute_delta_prime_matrix! runs later, after free_run supplies the vacuum edge response wv.
+ if intr.verbose
+ @info "Evaluating fixed-boundary stability criterion"
+ end
+ odet.nzero = evaluate_stability_criterion!(odet, equil.profiles)
+ transform_u!(odet, intr) # no-op when ifix=0 (no Gaussian reduction)
+
+ return odet, propagators, chunks, S_at_surface_left
+end
+
+# Build odet and initialize at the magnetic axis. Same path as serial eulerlagrange_integration.
+function _initialize_parallel_odet(ctrl::ForceFreeStatesControl,
+ equil::Equilibrium.PlasmaEquilibrium,
+ mats::MatrixSplines,
+ intr::ForceFreeStatesInternal)
+ odet = OdeState(intr.numpert_total, ctrl.algorithm.numsteps_init, ctrl.algorithm.numunorms_init, intr.msing)
+ initialize_el_at_axis!(odet, ctrl, mats, equil.profiles, intr)
+ # No Gaussian reduction on the Riccati path.
+ odet.new = false
+ fill!(odet.unorm0, 1.0)
+ return odet
+end
+
+# Build the bidirectional chunk list, per-chunk propagators, and per-thread proxy OdeStates
+# (sized by maxthreadid(), since threadid() can exceed nthreads() with an interactive pool).
+function _setup_parallel_chunks_and_proxies(odet::OdeState, ctrl::ForceFreeStatesControl,
+ intr::ForceFreeStatesInternal)
+ # Crossing chunks get direction=-1: growing EL solutions decay backward, so Φ_bwd is well-conditioned.
+ base_chunks = chunk_el_integration_bounds(odet, ctrl, intr; bidirectional=true)
+ chunks = balance_integration_chunks(base_chunks, ctrl, intr)
+ N = intr.numpert_total
+ propagators = [ChunkPropagator(N) for _ in chunks]
+ odet_proxies = [OdeState(N, 1, 1, 0) for _ in 1:Threads.maxthreadid()]
+ return chunks, propagators, odet_proxies
+end
+
+function _log_parallel_start(odet::OdeState, equil::Equilibrium.PlasmaEquilibrium, chunks::Vector{IntegrationChunk})
+ @info " ψ = $((@sprintf "%.3f" odet.psifac)), q = $((@sprintf "%.3f" equil.profiles.q_spline(odet.psifac)))"
+ @info " Riccati FM: $(length(chunks)) chunks over $(Threads.nthreads()) thread$(Threads.nthreads() == 1 ? "" : "s")"
+end
+
+# Integrate each chunk's propagator from identity IC in parallel; chunks are independent, so the
+# result does not depend on the thread layout. :static makes threadid() a stable proxy index.
+function _run_parallel_bvp_phase!(propagators::Vector{ChunkPropagator},
+ chunks::Vector{IntegrationChunk},
+ ctrl::ForceFreeStatesControl,
+ equil::Equilibrium.PlasmaEquilibrium, mats::MatrixSplines,
+ intr::ForceFreeStatesInternal,
+ odet_proxies::Vector{OdeState})
+ nblas = BLAS.get_num_threads()
+ BLAS.set_num_threads(1)
+ try
+ Threads.@threads :static for i in eachindex(chunks)
+ integrate_propagator_chunk!(propagators[i], chunks[i], ctrl, equil, mats, intr,
+ odet_proxies[Threads.threadid()])
+ end
+ finally
+ BLAS.set_num_threads(nblas)
+ end
+end
+
+# Apply chunk propagators serially, renormalizing to (S, I) after each (STRIDE's ode_fixup role:
+# keeps conditioning at O(cond_per_chunk) instead of its K-th power). Backward chunks are applied
+# via apply_propagator_inverse!. S_at_surface_left is the Riccati S at each surface's left boundary,
+# the Δ' BVP axis BC. Returns (S_at_surface_left, last_crossing_step).
+function _assemble_propagators_serially!(odet::OdeState, propagators::Vector{ChunkPropagator},
+ chunks::Vector{IntegrationChunk},
+ ctrl::ForceFreeStatesControl,
+ equil::Equilibrium.PlasmaEquilibrium,
+ mats::MatrixSplines, intr::ForceFreeStatesInternal)
+ N = intr.numpert_total
+ S_at_surface_left = Matrix{ComplexF64}[]
+ last_crossing_step = 1
+ for (i, chunk) in enumerate(chunks)
+ if chunk.direction == -1
+ apply_propagator_inverse!(odet, propagators[i])
+ else
+ apply_propagator!(odet, propagators[i])
+ end
+ renormalize_riccati_inplace!(odet.u, N)
+ odet.psifac = chunk.psi_end
+ odet.q = equil.profiles.q_spline(odet.psifac)
+
+ if intr.verbose
+ @info " ψ = $((@sprintf "%.3f" odet.psifac)), q= $((@sprintf "%.3f" odet.q)), max(S) = $((@sprintf "%.2e" maximum(abs, odet.u[:,:,1]))), steps = $(odet.step-1)"
+ end
+
+ if chunk.needs_crossing
+ ctrl.kinetic !== nothing && error("Riccati() does not support kinetic runs; use Forward().")
+ # State is (S, I) from the renorm above — well-conditioned at the surface's left boundary.
+ push!(S_at_surface_left, copy(odet.u[:, :, 1]))
+ riccati_cross_ideal_singular_surf!(odet, ctrl, equil, mats, intr, chunk.ising)
+ last_crossing_step = odet.step - 1
+ else
+ # Store the chunk-endpoint state; these are Riccati states, not the EL basis.
+ odet.u_store_el_basis = false
+ if odet.step >= size(odet.u_store, 4)
+ resize_storage!(odet)
+ end
+ odet.psi_store[odet.step] = odet.psifac
+ odet.q_store[odet.step] = odet.q
+ @views odet.u_store[:, :, :, odet.step] .= odet.u
+ odet.step += 1
+ end
+ end
+ return S_at_surface_left, last_crossing_step
+end
+
+# Re-integrate last rational surface → psilim with Riccati: FM propagation loses precision there at
+# high N, and findmax_dW_edge! needs dense checkpoints. Starts from the pre-renorm crossing state.
+function _reintegrate_outer_plasma!(odet::OdeState, last_crossing_step::Int,
+ ctrl::ForceFreeStatesControl,
+ equil::Equilibrium.PlasmaEquilibrium, mats::MatrixSplines,
+ intr::ForceFreeStatesInternal)
+ N = intr.numpert_total
+ odet.u .= odet.u_store[:, :, :, last_crossing_step]
+ odet.psifac = odet.psi_store[last_crossing_step]
+ odet.q = odet.q_store[last_crossing_step]
+ odet.step = last_crossing_step + 1
+ renormalize_riccati_inplace!(odet.u, N)
+ outer_chunk = IntegrationChunk(; psi_start=odet.psifac, psi_end=intr.psilim * (1 - eps),
+ needs_crossing=false, ising=0)
+ riccati_integrate_chunk!(odet, ctrl, equil, mats, intr, outer_chunk)
+ # Post: odet.u is in (S, I) form; odet.step points to next empty slot.
+end
+
+# Edge-dW scan; on truncation, also cut the Δ' chunks and propagators back to the new edge.
+function _handle_edge_dW_scan!(odet::OdeState, chunks::Vector{IntegrationChunk},
+ propagators::Vector{ChunkPropagator},
+ ctrl::ForceFreeStatesControl,
+ equil::Equilibrium.PlasmaEquilibrium, mats::MatrixSplines,
+ intr::ForceFreeStatesInternal)
+ N = intr.numpert_total
+ odet.step -= 1
+ trim_storage!(odet)
+ scan_edge_dW!(odet, ctrl, equil, mats, intr) || return chunks, propagators
+
+ renormalize_riccati_inplace!(odet.u, N) # stored snapshot may be pre-renorm
+ rebuild = truncate_chunks!(chunks, intr.psilim, intr.msing)
+ resize!(propagators, length(chunks))
+ if rebuild !== nothing
+ integrate_propagator_chunk!(propagators[rebuild], chunks[rebuild], ctrl, equil, mats, intr, OdeState(N, 1, 1, 0))
+ end
+ return chunks, propagators
+end
+
+"""
+ truncate_chunks!(chunks, psi_edge, msing) -> Union{Int,Nothing}
+
+Cut `chunks` back to an edge at `psi_edge`: drop those past it, end the straddling one at it, and
+clear any crossing onto a surface no longer in the plasma. Returns the index of a chunk that was
+shortened and so must be re-integrated.
+"""
+function truncate_chunks!(chunks::Vector{IntegrationChunk}, psi_edge::Real, msing::Int)
+ last = findlast(c -> c.psi_start < psi_edge, chunks)
+ last === nothing && error("truncate_chunks!: edge ψ=$psi_edge lies before all chunk starts")
+ resize!(chunks, last)
+ c = chunks[last]
+ shortened = c.psi_end > psi_edge
+ # ising <= msing means the surface survived: edge truncation drops surfaces from the outside only.
+ crosses = c.needs_crossing && c.ising <= msing
+ if shortened || crosses != c.needs_crossing
+ chunks[last] = IntegrationChunk(; psi_start=c.psi_start, psi_end=min(c.psi_end, psi_edge),
+ needs_crossing=crosses, ising=crosses ? c.ising : 0, direction=c.direction)
+ end
+ return shortened ? last : nothing
+end
diff --git a/src/ForceFreeStates/Riccati/Propagators.jl b/src/ForceFreeStates/Riccati/Propagators.jl
new file mode 100644
index 0000000000..81bd3d831c
--- /dev/null
+++ b/src/ForceFreeStates/Riccati/Propagators.jl
@@ -0,0 +1,430 @@
+# Chunk-propagator integration: EL-ODE fundamental matrices, Riccati renormalization, assembly.
+
+# `riccati_integrator_callback!` saves every step within this fraction of the span (or absolute ψ
+# floor, for short chunks) of a segment's right end; elsewhere every `save_interval`-th step.
+const SAVE_NEAR_END_FRAC = 0.05
+const SAVE_NEAR_END_PSI = 1e-4
+
+"""
+ assemble_fm_matrix(propagators, idx_range; condition=false, T_init=nothing) -> Matrix{ComplexF64}
+
+Assemble the 2N×2N fundamental matrix Φ_end * ... * Φ_start * T_init over chunks `idx_range`,
+mapping the IC at the start of `idx_range[1]` to the state at the end of `idx_range[end]`
+(`T_init` defaults to the identity).
+
+Each `ChunkPropagator` stores the 2N columns of Φ split into two N×N×2 blocks:
+
+```
+ block_upper_ic[:,:,1:2] ↔ Φ[:,1:N] (result from IC=(I,0))
+ block_lower_ic[:,:,1:2] ↔ Φ[:,N+1:2N] (result from IC=(0,I))
+```
+
+`condition=true` applies `condition_propagator!` after each product (STRIDE's `ode_fixup`), so only
+the N U₂ columns survive. Use it only for the axis→first-surface segment, where the axis BC (U₁ = 0)
+needs only U₂ ICs; never for inter-surface segments, where both halves carry information.
+"""
+function assemble_fm_matrix(propagators::Vector{ChunkPropagator}, idx_range;
+ condition::Bool=false,
+ T_init::Union{Nothing,Matrix{ComplexF64}}=nothing)
+ # Take N from T_init when given, so an empty idx_range (or propagator list) still works.
+ N = if T_init !== nothing
+ size(T_init, 1) ÷ 2
+ elseif !isempty(idx_range)
+ size(propagators[first(idx_range)].block_upper_ic, 1)
+ else
+ @assert !isempty(propagators) "assemble_fm_matrix: cannot infer N from empty propagators with no T_init"
+ size(propagators[1].block_upper_ic, 1)
+ end
+ Phi = T_init !== nothing ? copy(T_init) : Matrix{ComplexF64}(I, 2N, 2N)
+ isempty(idx_range) && return Phi
+ for i in idx_range
+ p = propagators[i]
+ #! format: off
+ Phi_i = [p.block_upper_ic[:,:,1] p.block_lower_ic[:,:,1];
+ p.block_upper_ic[:,:,2] p.block_lower_ic[:,:,2]]
+ #! format: on
+ Phi = Phi_i * Phi
+ if condition
+ condition_propagator!(Phi, N)
+ end
+ end
+ return Phi
+end
+
+"""
+ condition_propagator!(Phi, N)
+
+Apply Gaussian reduction to the U₂-columns (columns N+1:2N) of a 2N×2N propagator
+matrix in-place, following STRIDE's `ode_fixup` convention. Triangularizes the U₁
+(upper N rows) subblock by pivoted elimination, improving the condition number so
+the propagator can be used in a BVP without losing numerical rank.
+
+After conditioning, only the U₂ columns carry meaningful information; the U₁ columns
+(1:N) are zeroed. The BVP axis block uses `Phi[:, N+1:2N]` (the conditioned half).
+"""
+function condition_propagator!(Phi::Matrix{ComplexF64}, N::Int)
+ # Work on the right half: columns N+1:2N (U₂ initial conditions)
+ cols = view(Phi, :, N+1:2N)
+
+ # Sort columns by norm of the U₁ (upper N) block — largest first
+ norms = [norm(view(cols, 1:N, k)) for k in 1:N]
+ order = sortperm(norms; rev=true)
+
+ mask_col = trues(N) # which columns remain to process
+ mask_row = trues(N) # which pivot rows remain available
+
+ for isol in 1:N
+ kcol = order[isol]
+ mask_col[kcol] = false
+
+ # Find best pivot row (largest |element| among unmasked rows)
+ best_row = 0
+ best_val = 0.0
+ for r in 1:N
+ if mask_row[r] && abs(cols[r, kcol]) > best_val
+ best_val = abs(cols[r, kcol])
+ best_row = r
+ end
+ end
+ if best_row == 0 || best_val == 0
+ continue
+ end
+ mask_row[best_row] = false
+
+ # Eliminate this pivot from all other unmasked columns
+ pivot = cols[best_row, kcol]
+ for jcol in 1:N
+ if mask_col[jcol]
+ factor = -cols[best_row, jcol] / pivot
+ @views cols[:, jcol] .+= factor .* cols[:, kcol]
+ cols[best_row, jcol] = 0 # exact zero
+ end
+ end
+ end
+
+ # Zero the U₁ columns (left half) — they are no longer meaningful
+ Phi[:, 1:N] .= 0
+ return Phi
+end
+
+"""
+ riccati_der!(du, u, params, psieval)
+
+Evaluate the explicit dual Riccati ODE right-hand side:
+dS/dψ = w†·F̄⁻¹·w - S·Ḡ·S, w = Q - K̄·S
+
+where Q = diag(1/(m - n·q)) is the diagonal singular factor matrix.
+The identity slice u[:,:,2] = I does not evolve (du[:,:,2] = 0).
+
+Reference implementation, not called in production: the quadratic S·Ḡ·S term makes the explicit
+Riccati ODE unstable for explicit solvers, so the driver integrates `sing_der!` with
+`renormalize_riccati_inplace!` instead. Exercised only by unit tests.
+
+See: Glasser (2018) Phys. Plasmas 25, 032507 — Eq. 19 (dual Riccati form)
+"""
+@with_pool pool function riccati_der!(
+ du::Array{ComplexF64,3},
+ u::Array{ComplexF64,3},
+ params::Tuple{ForceFreeStatesControl,Equilibrium.PlasmaEquilibrium,
+ MatrixSplines,ForceFreeStatesInternal,OdeState,IntegrationChunk},
+ psieval::Float64
+)
+
+ _, equil, mats, intr, odet, _ = params
+
+ Npert = intr.numpert_total
+ S = @view u[:, :, 1]
+ dS = @view du[:, :, 1]
+ @view(du[:, :, 2]) .= 0 # identity does not evolve
+
+ # Compute singfac = 1/(m - n·q) as column vector Q = diag(singfac_vec)
+ # [Glasser 2016 eq. 24]
+ singfac_vec = acquire!(pool, Float64, Npert)
+ singfac_mat = reshape(singfac_vec, intr.mpert, intr.npert)
+ odet.q = equil.profiles.q_spline(psieval; hint=odet.spline_hint)
+ singfac_mat .= 1.0 ./ ((intr.mlow:intr.mhigh) .- odet.q .* (intr.nlow:intr.nhigh)')
+
+ fmat_lower = acquire!(pool, ComplexF64, Npert, Npert)
+ kmat = similar!(pool, fmat_lower)
+ gmat = similar!(pool, fmat_lower)
+ w = similar!(pool, fmat_lower) # w = Q - K̄·S
+ v = similar!(pool, fmat_lower) # v = F̄⁻¹·w (then reused for S·Ḡ·S)
+ tmp = similar!(pool, fmat_lower) # scratch
+
+ # Evaluate F̄ (Cholesky factor), K̄, Ḡ splines at current ψ
+ mats.ideal.F_spline_lower(vec(fmat_lower), psieval; hint=mats._hint)
+ mats.ideal.K_spline(vec(kmat), psieval; hint=mats._hint)
+ mats.ideal.G_spline(vec(gmat), psieval; hint=mats._hint)
+
+ # w = Q - K̄·S; Q is diagonal, so singfac_vec is added on the diagonal only.
+ mul!(w, kmat, S) # w = K̄·S
+ @. w = -w # w = -K̄·S
+ for i in 1:Npert
+ @inbounds w[i, i] += singfac_vec[i] # add diagonal Q: w = Q - K̄·S
+ end
+
+ # v = F̄⁻¹·w (in-place Cholesky solve with stored lower-triangular factor)
+ v .= w
+ ldiv!(LowerTriangular(fmat_lower), v)
+ ldiv!(UpperTriangular(fmat_lower'), v)
+
+ # dS = w†·v - S·Ḡ·S [Glasser 2018 eq. 19, dual Riccati]
+ mul!(dS, adjoint(w), v) # dS = w†·v
+
+ # Subtract S·Ḡ·S (reuse v and tmp to avoid extra allocation)
+ mul!(tmp, gmat, S) # tmp = Ḡ·S
+ mul!(v, S, tmp) # v = S·Ḡ·S
+ dS .-= v
+end
+
+"""
+ riccati_integrator_callback!(integrator)
+
+Per-step callback for `riccati_integrate_chunk!`: counts the step, applies
+`renormalize_riccati_inplace!` when max(|U₁|) or max(|U₂|) exceeds `ctrl.algorithm.renorm_threshold`
+(the Riccati analogue of Gaussian reduction), refreshes the per-column abstol, and stores selected steps.
+"""
+function riccati_integrator_callback!(integrator)
+
+ ctrl, _, _, intr, odet, chunk = integrator.p
+
+ odet.total_steps += 1 # count every accepted solver step (saved or not), as segment_callback! does
+
+ # Renormalize to (S, I) when either block exceeds renorm_threshold.
+ if maximum(abs, @view(integrator.u[:, :, 1])) > ctrl.algorithm.renorm_threshold ||
+ maximum(abs, @view(integrator.u[:, :, 2])) > ctrl.algorithm.renorm_threshold
+ renormalize_riccati_inplace!(integrator.u, intr.numpert_total)
+ end
+
+ # Refresh after any renorm so the tolerance matches the current state.
+ column_abstol!(integrator.opts.abstol, integrator.u, ctrl.algorithm.eulerlagrange_tolerance)
+
+ # Save the first two steps, every step near the right end, and every save_interval-th step otherwise.
+ psi_range = abs(integrator.sol.prob.tspan[2] - integrator.sol.prob.tspan[1])
+ psi_remaining = abs(integrator.sol.prob.tspan[2] - integrator.t)
+ near_end = psi_remaining < SAVE_NEAR_END_FRAC * psi_range || psi_remaining < SAVE_NEAR_END_PSI
+ steps_in_segment = length(integrator.sol.t)
+ near_start = steps_in_segment <= 2
+ should_save = near_start || near_end || (odet.step % ctrl.algorithm.save_interval == 0)
+
+ if should_save
+ store_ode_data!(odet, integrator.t, integrator.u)
+ end
+end
+
+"""
+ riccati_integrate_chunk!(odet, ctrl, equil, mats, intr, chunk)
+
+Integrate the Riccati state from `chunk.psi_start` to `chunk.psi_end` with `sing_der!` and
+`riccati_integrator_callback!`, starting from u = (S, I). The end state is renormalized to (S, I)
+unless `chunk.needs_crossing`, in which case the bounded (U₁, U₂) is left for the crossing.
+"""
+function riccati_integrate_chunk!(
+ odet::OdeState, ctrl::ForceFreeStatesControl, equil::Equilibrium.PlasmaEquilibrium,
+ mats::MatrixSplines, intr::ForceFreeStatesInternal, chunk::IntegrationChunk
+)
+ cb = DiscreteCallback((u, t, integrator) -> true, riccati_integrator_callback!)
+ rtol = ctrl.algorithm.eulerlagrange_tolerance
+ prob = ODEProblem(sing_der!, odet.u, (chunk.psi_start, chunk.psi_end),
+ (ctrl, equil, mats, intr, odet, chunk))
+ sol = solve_el(prob, rtol; callback=cb)
+ odet.u .= sol.u[end]
+ odet.psifac = sol.t[end]
+ # Before a crossing, skip the renorm so ca_l and ca_r share the pre-renorm normalization (needed for Δ').
+ if !chunk.needs_crossing
+ renormalize_riccati_inplace!(odet.u, intr.numpert_total)
+ end
+end
+
+"""
+ renormalize_riccati_inplace!(u, N)
+
+In-place Riccati renormalization on an arbitrary N×N×2 array:
+u[:,:,1] = U₁ · U₂⁻¹ (new S)
+u[:,:,2] = I
+
+The Riccati analogue of Gaussian reduction: keeps the inputs to `sing_der!` bounded.
+"""
+function renormalize_riccati_inplace!(u::Array{ComplexF64,3}, N::Int)
+ U2_copy = copy(@view u[:, :, 2])
+ rdiv!(@view(u[:, :, 1]), lu!(U2_copy))
+ fill!(@view(u[:, :, 2]), 0)
+ for i in 1:N
+ u[i, i, 2] = 1
+ end
+end
+
+"""
+ renormalize_riccati!(odet, intr)
+
+[`renormalize_riccati_inplace!`](@ref) on `odet.u`. After a singular surface crossing, which leaves
+u[:,:,2] = U₂_new ≠ I, it restores the canonical storage u[:,:,1] = S_new = U₁_new·U₂_new⁻¹, u[:,:,2] = I
+before the integration continues. The crossing's u_store entry keeps U₁_new and U₂_new, so
+`compute_smallest_eigenvalue` is unaffected.
+"""
+renormalize_riccati!(odet::OdeState, intr::ForceFreeStatesInternal) = renormalize_riccati_inplace!(odet.u, intr.numpert_total)
+
+"""
+ integrate_propagator_chunk!(prop, chunk, ctrl, equil, mats, intr, odet_proxy)
+
+Fill `prop` with the chunk's fundamental matrix by integrating the EL ODE from IC (I, 0) into
+`prop.block_upper_ic` and from (0, I) into `prop.block_lower_ic`, without renormalization or storage.
+`odet_proxy` holds the `sing_der!` side effects; concurrent calls need distinct proxies.
+"""
+function integrate_propagator_chunk!(
+ prop::ChunkPropagator,
+ chunk::IntegrationChunk,
+ ctrl::ForceFreeStatesControl,
+ equil::Equilibrium.PlasmaEquilibrium,
+ mats::MatrixSplines,
+ intr::ForceFreeStatesInternal,
+ odet_proxy::OdeState
+)
+ N = intr.numpert_total
+ # Backward chunks integrate psi_end → psi_start, where forward-growing solutions decay.
+ tspan = chunk.direction == 1 ?
+ (chunk.psi_start, chunk.psi_end) :
+ (chunk.psi_end, chunk.psi_start)
+ rtol = ctrl.algorithm.eulerlagrange_tolerance
+ params = (ctrl, equil, mats, intr, odet_proxy, chunk)
+
+ # Upper block IC: U₁ = I, U₂ = 0
+ u_upper = zeros(ComplexF64, N, N, 2)
+ for i in 1:N
+ u_upper[i, i, 1] = 1
+ end
+ odet_proxy.spline_hint[] = 1
+ odet_proxy.mats_hint[] = 1
+ prob = ODEProblem(sing_der!, u_upper, tspan, params)
+ sol = solve_el(prob, rtol)
+ prop.block_upper_ic .= sol.u[end]
+ odet_proxy.total_steps += sol.stats.naccept # thread-local; summed into odet after the BVP barrier
+
+ # Lower block IC: U₁ = 0, U₂ = I
+ u_lower = zeros(ComplexF64, N, N, 2)
+ for i in 1:N
+ u_lower[i, i, 2] = 1
+ end
+ odet_proxy.spline_hint[] = 1
+ odet_proxy.mats_hint[] = 1
+ prob = ODEProblem(sing_der!, u_lower, tspan, params)
+ sol = solve_el(prob, rtol)
+ prop.block_lower_ic .= sol.u[end]
+ odet_proxy.total_steps += sol.stats.naccept
+end
+
+"""
+ integrate_fm_with_ua_ic(chunks, chunk_range, ua, ctrl, equil, mats, intr;
+ backward=false, psi_ua=NaN) -> Matrix{ComplexF64}
+
+Re-integrate a span of chunks from the asymptotic solutions `ua` as initial conditions (Fortran
+STRIDE `uFM_sing_init`). Column j of the 2N×2N result is the solution at the far end with IC
+column j of T = [ua[:,:,1]; ua[:,:,2]]. With `backward=true` the IC sits at the span's right end
+and the integration runs toward its start. `psi_ua`, when given, replaces the chunk boundary as the
+IC location. Integrating from `ua` keeps the small solutions that multiplying an identity-IC
+propagator by T loses to roundoff.
+"""
+function integrate_fm_with_ua_ic(
+ chunks::Vector{IntegrationChunk},
+ chunk_range::UnitRange{Int},
+ ua::Array{ComplexF64,3},
+ ctrl::ForceFreeStatesControl,
+ equil::Equilibrium.PlasmaEquilibrium,
+ mats::MatrixSplines,
+ intr::ForceFreeStatesInternal;
+ backward::Bool=false,
+ psi_ua::Float64=NaN
+)
+ N = intr.numpert_total
+ psi_start = chunks[first(chunk_range)].psi_start
+ psi_end = chunks[last(chunk_range)].psi_end
+ # ua lives at the inner-layer boundary psi_ua, which may differ slightly from the chunk boundary.
+ if backward && !isnan(psi_ua)
+ psi_end = psi_ua
+ elseif !backward && !isnan(psi_ua)
+ psi_start = psi_ua
+ end
+ tspan = backward ? (psi_end, psi_start) : (psi_start, psi_end)
+ rtol = ctrl.algorithm.eulerlagrange_tolerance
+
+ result = zeros(ComplexF64, 2N, 2N)
+ odet_proxy = OdeState(N, 1, 1, 0)
+ dummy_chunk = IntegrationChunk(psi_start, psi_end, false, 0, backward ? -1 : 1)
+ params = (ctrl, equil, mats, intr, odet_proxy, dummy_chunk)
+
+ # Batch 1: columns 1:N of T (big solutions)
+ u0 = zeros(ComplexF64, N, N, 2)
+ u0[:, :, 1] .= ua[:, 1:N, 1]
+ u0[:, :, 2] .= ua[:, 1:N, 2]
+ odet_proxy.spline_hint[] = 1
+ odet_proxy.mats_hint[] = 1
+ prob = ODEProblem(sing_der!, u0, tspan, params)
+ sol = solve_el(prob, rtol)
+ result[1:N, 1:N] .= sol.u[end][:, :, 1]
+ result[N+1:2N, 1:N] .= sol.u[end][:, :, 2]
+
+ # Batch 2: columns N+1:2N of T (small solutions)
+ u0[:, :, 1] .= ua[:, N+1:2N, 1]
+ u0[:, :, 2] .= ua[:, N+1:2N, 2]
+ odet_proxy.spline_hint[] = 1
+ odet_proxy.mats_hint[] = 1
+ prob = ODEProblem(sing_der!, u0, tspan, params)
+ sol = solve_el(prob, rtol)
+ result[1:N, N+1:2N] .= sol.u[end][:, :, 1]
+ result[N+1:2N, N+1:2N] .= sol.u[end][:, :, 2]
+
+ return result
+end
+
+"""
+ apply_propagator!(odet, prop)
+
+Apply the chunk propagator `prop` to any state `odet.u` (including the Riccati (S, I) form) in-place.
+Implements the subpropagator composition Φ(ψ₂, ψ₀) = Φ(ψ₂, ψ₁) · Φ(ψ₁, ψ₀) of
+Glasser-Kolemen (2018) Phys. Plasmas 25, 032501 Eq. 29.
+"""
+function apply_propagator!(odet::OdeState, prop::ChunkPropagator)
+ U1_upper = @view prop.block_upper_ic[:, :, 1]
+ U2_upper = @view prop.block_upper_ic[:, :, 2]
+ U1_lower = @view prop.block_lower_ic[:, :, 1]
+ U2_lower = @view prop.block_lower_ic[:, :, 2]
+
+ u1_prev = copy(@view odet.u[:, :, 1])
+ u2_prev = copy(@view odet.u[:, :, 2])
+ tmp = similar(u1_prev)
+
+ # U₁_new = U1_upper · u1_prev + U1_lower · u2_prev
+ mul!(view(odet.u, :, :, 1), U1_upper, u1_prev)
+ mul!(tmp, U1_lower, u2_prev)
+ odet.u[:, :, 1] .+= tmp
+
+ # U₂_new = U2_upper · u1_prev + U2_lower · u2_prev
+ mul!(view(odet.u, :, :, 2), U2_upper, u1_prev)
+ mul!(tmp, U2_lower, u2_prev)
+ odet.u[:, :, 2] .+= tmp
+end
+
+"""
+ apply_propagator_inverse!(odet, prop)
+
+Apply the *inverse* of the chunk propagator `prop` to the current state `odet.u` in-place.
+
+Used for backward chunks: the well-conditioned Φ_bwd maps `psi_end` → `psi_start`, so solving
+Φ_bwd · x = u_old by LU advances the state `psi_start` → `psi_end` far more accurately than Φ_fwd.
+
+Implements the inverse subpropagator identity Φ(ψ₂, ψ₁) = Φ(ψ₁, ψ₂)⁻¹ of
+Glasser-Kolemen (2018) Phys. Plasmas 25, 032501 Eq. 33.
+"""
+function apply_propagator_inverse!(odet::OdeState, prop::ChunkPropagator)
+ N = size(odet.u, 1)
+ # Assemble 2N×2N backward FM Φ_bwd
+ #! format: off
+ Φ = [prop.block_upper_ic[:,:,1] prop.block_lower_ic[:,:,1];
+ prop.block_upper_ic[:,:,2] prop.block_lower_ic[:,:,2]]
+ #! format: on
+ # x = Φ_bwd⁻¹ · [U₁_old; U₂_old] advances psi_start → psi_end.
+ u_old = [odet.u[:, :, 1]; odet.u[:, :, 2]] # 2N × N
+ u_new = Φ \ u_old # LU solve, 2N × N
+ odet.u[:, :, 1] .= u_new[1:N, :]
+ odet.u[:, :, 2] .= u_new[N+1:2N, :]
+end
diff --git a/src/ForceFreeStates/Riccati/Types.jl b/src/ForceFreeStates/Riccati/Types.jl
new file mode 100644
index 0000000000..04fd25355a
--- /dev/null
+++ b/src/ForceFreeStates/Riccati/Types.jl
@@ -0,0 +1,46 @@
+# Integration-chunk and chunk-propagator types for the fundamental-matrix (Riccati/STRIDE) driver.
+
+"""
+ IntegrationChunk
+
+A struct representing a region of integration in the Euler-Lagrange solver.
+
+## Fields
+
+ - `psi_start::Float64` - Starting ψ coordinate for this integration region
+ - `psi_end::Float64` - Ending ψ coordinate for this integration region
+ - `needs_crossing::Bool` - Whether a rational surface crossing is needed after this chunk
+ - `ising::Int` - Index of the singular surface associated with this chunk (0 if none)
+ - `direction::Int` - +1 forward, -1 backward. A backward chunk still has `psi_start < psi_end` but
+ its propagator maps the state at `psi_end` to `psi_start`; used for well-conditioned crossing chunks.
+"""
+@kwdef struct IntegrationChunk
+ psi_start::Float64
+ psi_end::Float64
+ needs_crossing::Bool
+ ising::Int = 0
+ direction::Int = 1 # +1 forward, -1 backward
+end
+
+"""
+ ChunkPropagator
+
+Fundamental matrix for one integration chunk, stored as two N×N×2 solution blocks.
+Represents the propagator Φ(ψ₂,ψ₁) computed by integrating the EL ODE from two
+identity-block initial conditions:
+
+ - `block_upper_ic`: result of integrating with IC = (I_N, 0_N) (U₁ = I, U₂ = 0)
+ - `block_lower_ic`: result of integrating with IC = (0_N, I_N) (U₁ = 0, U₂ = I)
+
+Applying the propagator to the current state `u_prev`:
+
+u₁_new = block_upper_ic[:,:,1] · u₁_prev + block_lower_ic[:,:,1] · u₂_prev
+u₂_new = block_upper_ic[:,:,2] · u₁_prev + block_lower_ic[:,:,2] · u₂_prev
+
+Each chunk starts from an identity IC rather than the accumulated state, so chunks integrate in parallel.
+"""
+struct ChunkPropagator
+ block_upper_ic::Array{ComplexF64,3} # shape (N, N, 2) — result from IC = (I, 0)
+ block_lower_ic::Array{ComplexF64,3} # shape (N, N, 2) — result from IC = (0, I)
+end
+ChunkPropagator(N::Int) = ChunkPropagator(zeros(ComplexF64, N, N, 2), zeros(ComplexF64, N, N, 2))
diff --git a/src/ForceFreeStates/Run.jl b/src/ForceFreeStates/Run.jl
new file mode 100644
index 0000000000..7e440b1f59
--- /dev/null
+++ b/src/ForceFreeStates/Run.jl
@@ -0,0 +1,116 @@
+# Run.jl: the force-free-states solve on a prepared equilibrium, from the toroidal mode range to the published result.
+
+"""
+ _mode_range_label(intr) -> String
+
+Compact label for the resolved toroidal mode range, `"1"` for a single `n` and `"1:3"` for a range.
+"""
+_mode_range_label(intr::ForceFreeStatesInternal) = intr.npert == 1 ? "$(intr.nlow)" : "$(intr.nlow):$(intr.nhigh)"
+
+"""
+ resolve_mode_space!(intr, ctrl) -> intr
+
+Resolve the requested toroidal mode range onto `intr`, filling an unspecified bound from the
+other one and rejecting ranges that contain no supported `n >= 1` mode.
+"""
+function resolve_mode_space!(intr::ForceFreeStatesInternal, ctrl::ForceFreeStatesControl)
+ # Determine toroidal mode numbers (n >= 1 required; 0 means "not specified")
+ intr.nlow, intr.nhigh = ctrl.nn_low, ctrl.nn_high
+ if intr.nlow == 0 && intr.nhigh == 0
+ error("the toroidal mode number nn must be set")
+ elseif intr.nlow == 0
+ intr.nlow = intr.nhigh
+ elseif intr.nhigh == 0
+ intr.nhigh = intr.nlow
+ end
+ if intr.nlow > intr.nhigh
+ error("the toroidal mode range $(intr.nlow):$(intr.nhigh) is empty")
+ end
+ if intr.nhigh < 1
+ error("All requested toroidal modes (n=$(intr.nlow):$(intr.nhigh)) are below 1; " *
+ "n < 1 modes are not supported")
+ end
+ if intr.nlow < 1
+ @warn "Clamping the lowest toroidal mode from $(intr.nlow) to 1; n < 1 modes are not supported"
+ intr.nlow = 1
+ end
+ intr.npert = intr.nhigh - intr.nlow + 1
+ return intr
+end
+
+"""
+ run_force_free_states(ctrl, equil, mats, intr, metric; cut_solution=false) -> ForceFreeStatesResult
+
+Run the formalism selected by `ctrl.algorithm` — the standalone Galerkin solve, or the
+Euler-Lagrange sweep with its free-boundary energies and Δ′ BVP — and publish its products as a
+`ForceFreeStatesResult`. `cut_solution` is the scripting-only `Galerkin(; cut_solution)` option.
+"""
+function run_force_free_states(
+ ctrl::ForceFreeStatesControl,
+ equil::Equilibrium.PlasmaEquilibrium,
+ mats,
+ intr::ForceFreeStatesInternal,
+ metric;
+ cut_solution::Bool=false
+)
+ nstring = _mode_range_label(intr)
+
+ # The three formalisms are exclusive. Galerkin solves the same Euler-Lagrange system
+ # variationally rather than by radial ODE integration, so it replaces both the integration
+ # and the free-boundary energies, and supplies its own vacuum response at psilim.
+ odet = nothing
+ free_energies = nothing
+ gal_data = nothing
+ gal_dp = nothing
+ if ctrl.algorithm isa Galerkin
+ ctrl.kinetic === nothing ||
+ error("Galerkin() does not support kinetic runs; use Forward().")
+ gal_start = time()
+ wv = ctrl.vac_flag ? first(compute_scaled_wv(ctrl, equil, intr)) : nothing
+ gal_data, gal_dp = galerkin_solve(ctrl, equil, mats, intr; wv=wv, cut_solution=cut_solution)
+ gal_dt = time() - gal_start
+ @info "Galerkin solve completed in $(@sprintf("%.3f", gal_dt)) s"
+ else
+ if intr.verbose
+ @info "Integrating Euler-Lagrange equation"
+ end
+ odet, fm_propagators, fm_chunks, fm_S_left = eulerlagrange_integration(ctrl, equil, mats, intr)
+ if odet.nzero > 0 && intr.verbose
+ @warn "Fixed-boundary mode unstable for n = $nstring"
+ end
+
+ if ctrl.vac_flag
+ if intr.verbose
+ wall_desc = intr.wall_settings === nothing ? "no wall" : nameof(typeof(intr.wall_settings))
+ @info "Computing free boundary energies ($wall_desc)"
+ end
+ free_energies = free_run(odet, ctrl, equil, mats, intr)
+ normalize_eigenfunctions!(odet, free_energies.wt, equil.psio)
+ if real(free_energies.et[1]) < 0
+ if intr.verbose
+ @warn "Free-boundary mode unstable for n = $nstring"
+ end
+ else
+ if intr.verbose
+ @info "All free-boundary modes stable for n = $nstring"
+ end
+ end
+
+ # Inter-surface Δ' (STRIDE BVP): needs Riccati() propagators and wv from free_run.
+ if ctrl.kinetic === nothing && intr.msing > 0 && fm_propagators !== nothing
+ if intr.verbose
+ @info "Computing Δ' matrix (STRIDE BVP with vacuum coupling)"
+ end
+ compute_delta_prime_matrix!(intr, fm_propagators, fm_chunks;
+ wv=free_energies.wv, psio=equil.psio, debug=intr.verbose,
+ S_at_surface_left=fm_S_left,
+ ctrl=ctrl, equil=equil, mats=mats)
+ end
+ end
+ end
+
+ # Publish the solve: from here on the downstream stages read the result, never `intr`.
+ result = build_result(_integrator_symbol(ctrl.algorithm), ctrl, equil, intr, metric, mats, odet, free_energies, gal_data, gal_dp)
+
+ return result
+end
diff --git a/src/ForceFreeStates/Surfaces/Asymptotics.jl b/src/ForceFreeStates/Surfaces/Asymptotics.jl
new file mode 100644
index 0000000000..0d3f3af248
--- /dev/null
+++ b/src/ForceFreeStates/Surfaces/Asymptotics.jl
@@ -0,0 +1,752 @@
+# Frobenius asymptotics and resonant-basis evaluation at singular surfaces.
+
+"""
+ resonant_block_exponents(m0, sig) -> (α, p_big, p_small)
+
+Eigenvalues λ = tr/2 ∓ √(tr²/4 − det) of one resonant 2×2 M₀ block.
+α = √(tr²/4 − det) is the Mercier half-separation. Powers are sig·λ, big solution
+(more negative real part) first. A traceless block returns α = √(−det) and (−α, +α).
+When tr²/4 − det is negative (Mercier-unstable), α is taken with Im α > 0, so both sides
+of the surface get the same α and the same big root whatever the round-off sign.
+"""
+function resonant_block_exponents(m0::AbstractMatrix, sig::Real)
+ tr = m0[1, 1] + m0[2, 2]
+ det = m0[1, 1] * m0[2, 2] - m0[2, 1] * m0[1, 2]
+ α = sqrt(ComplexF64(tr * tr / 4 - det))
+ abs(real(α)) <= 64 * Base.eps(Float64) * abs(α) && (α = ComplexF64(0, abs(imag(α))))
+ p_minus = sig * (tr / 2 - α)
+ p_plus = sig * (tr / 2 + α)
+ # Equal real parts: sig ≥ 0 keeps big = sig·(tr/2 − α).
+ if real(p_minus) < real(p_plus) || (real(p_minus) == real(p_plus) && sig >= 0)
+ return α, p_minus, p_plus
+ else
+ return α, p_plus, p_minus
+ end
+end
+
+# Scale the big and small resonant columns by dpsi^power.
+function _apply_column_powers!(big_cols, small_cols, p_big, p_small, dpsi)
+ big_cols .*= dpsi^p_big
+ small_cols .*= dpsi^p_small
+end
+
+"""
+ compute_sing_asymptotics(singp, ctrl, equil, mats, intr; sig=1.0, sing_order=ctrl.frobenius_order) -> SingAsymptotics
+
+Frobenius power series (`vmat`) of the asymptotic solutions on one side of a singular surface, Glasser
+Phys. Plasmas 2016 112506 Eqs. 41-48.
+
+### Arguments
+
+ - `singp::SingType`: Singular surface parameters
+ - `sig`: Side of the surface, `-1.0` left or `+1.0` right
+ - `sing_order`: Expansion order, defaulting to `ctrl.frobenius_order`. The Galerkin path overrides it
+ per surface (`frobenius_order`, raised for high-Mercier-index surfaces).
+
+Warns once per surface when a resonant block has `abs(tr(M₀))/2` above both `1e-3 * abs(α)` and the
+round-off floor `64 * Base.eps(Float64) * opnorm(M₀, Inf)`.
+"""
+function compute_sing_asymptotics(
+ singp::SingType,
+ ctrl::ForceFreeStatesControl,
+ equil::Equilibrium.PlasmaEquilibrium,
+ mats::MatrixSplines,
+ intr::ForceFreeStatesInternal;
+ sig::Float64=1.0,
+ sing_order::Int=ctrl.frobenius_order
+)
+
+ vmat = zeros(ComplexF64, intr.numpert_total, 2 * intr.numpert_total, 2, 2 * sing_order + 1)
+ mmat = zeros(ComplexF64, intr.numpert_total, 2 * intr.numpert_total, 2, 2 * sing_order + 3)
+ power = zeros(ComplexF64, 2 * intr.numpert_total)
+
+ # Resonant (r) and nonresonant (n) indices of the shearing transformation (Glasser 2016 Eq. 41);
+ # 1 indexes the numpert_total dimension, 2 the 2·numpert_total dimension
+ ipert_res = 1 .+ singp.m .- intr.mlow .+ (singp.n .- intr.nlow) .* intr.mpert
+ r1 = ipert_res
+ r2 = vec([ipert_res[i] + j * intr.numpert_total for j in 0:1, i in eachindex(ipert_res)])
+ n1 = [i for i in 1:intr.numpert_total if !(i in ipert_res)]
+ n2 = vec([i + j * intr.numpert_total for j in 0:1, i in n1])
+
+ # Compute mmat Taylor coefficients with direction parameter sig.
+ # Fortran computes separate mmatl (sig=-1) and mmatr (sig=+1) — the sig flips
+ # odd derivatives of all input quantities (q, F, G, K splines).
+ compute_sing_mmat!(mmat, singp, ctrl, equil.profiles, mats, intr; sig=sig, sing_order=sing_order)
+
+ # Extract direction-specific m0mat from zeroth-order mmat
+ m0mat = if length(r1) == 1
+ Matrix(transpose(mmat[r1[1], r2, :, 1]))
+ else
+ Matrix(vcat([transpose(mmat[r1[i], r2, :, 1]) for i in eachindex(r1)]...))
+ end
+
+ # Zeroth-order non-resonant solutions. Nonresonant powers stay 0.
+ for ipert in 1:intr.numpert_total
+ vmat[ipert, ipert, 1, 1] = 1
+ vmat[ipert, ipert+intr.numpert_total, 2, 1] = 1
+ end
+
+ # This side's block: power is sig·λ (big first); the ξ' row is the eigenvector for λ.
+ alpha = Vector{ComplexF64}(undef, length(r1))
+ for i in eachindex(r1)
+ m0mat_block = m0mat[(2*(i-1)+1):(2*i), (2*(i-1)+1):(2*i)]
+ alpha_i, p_big, p_small = resonant_block_exponents(m0mat_block, sig)
+ alpha[i] = alpha_i
+ # Warn once on the right side, ignoring traces at the block's round-off scale.
+ block_tr = m0mat_block[1, 1] + m0mat_block[2, 2]
+ trace_floor = 64 * Base.eps(Float64) * opnorm(m0mat_block, Inf)
+ sig > 0 && abs(block_tr) / 2 > max(1e-3 * abs(alpha_i), trace_floor) &&
+ @warn @sprintf("Resonant M₀ block at ψ=%.6f, m=%d (sig=%+.0f): |tr|/2 = %.3e is not small against |α| = %.3e",
+ singp.psifac, singp.m[i], sig, abs(block_tr) / 2, abs(alpha_i)) _id = (:resonant_trace, objectid(intr), singp.psifac, singp.m[i]) maxlog = 1
+ r1_i = r1[i]
+ power[r1_i] = p_big
+ power[r1_i+intr.numpert_total] = p_small
+ r2_i = r1_i + intr.numpert_total
+ vmat[r1_i, r1_i, 1, 1] = 1
+ vmat[r1_i, r2_i, 1, 1] = 1
+ vmat[r1_i, r1_i, 2, 1] = -(m0mat_block[1, 1] - sig * p_big) / m0mat_block[1, 2]
+ vmat[r1_i, r2_i, 2, 1] = -(m0mat_block[1, 1] - sig * p_small) / m0mat_block[1, 2]
+ end
+
+ # Higher order solutions — sig propagates through the recursion (Fortran STRIDE sing_solve).
+ for k in 1:(2*sing_order)
+ solve_higher_order_vmat!(vmat, mmat, m0mat, alpha, r1, r2, n1, n2, power, intr, k; sig=sig)
+ end
+
+ # Per-crossing m0mat / vmat diagnostics matching Fortran sing_vmat output.
+ # @debug-only: enable via JULIA_DEBUG=GeneralizedPerturbedEquilibrium.
+ @debug begin
+ side_str = sig > 0 ? "right" : "left"
+ ipert0 = r1[1]
+ N = intr.numpert_total
+ msg = " === sing_asymptotics debug: m=$(singp.m[1]) sig=$sig ($side_str)\n"
+ msg *= @sprintf(" m0mat(1,1)= %+.12e %+.12ei\n", real(m0mat[1, 1]), imag(m0mat[1, 1]))
+ msg *= @sprintf(" m0mat(1,2)= %+.12e %+.12ei\n", real(m0mat[1, 2]), imag(m0mat[1, 2]))
+ msg *= @sprintf(" m0mat(2,1)= %+.12e %+.12ei\n", real(m0mat[2, 1]), imag(m0mat[2, 1]))
+ msg *= @sprintf(" m0mat(2,2)= %+.12e %+.12ei\n", real(m0mat[2, 2]), imag(m0mat[2, 2]))
+ block_det = m0mat[1, 1] * m0mat[2, 2] - m0mat[2, 1] * m0mat[1, 2]
+ block_tr = m0mat[1, 1] + m0mat[2, 2]
+ msg *= @sprintf(" det= %+.12e, tr= %+.12e %+.12ei\n", real(block_det), real(block_tr), imag(block_tr))
+ msg *= @sprintf(" alpha= %+.12e %+.12ei\n", real(alpha[1]), imag(alpha[1]))
+ msg *= @sprintf(" psifac= %+.12e, r1=%d, ipert0=%d\n", singp.psifac, r1[1], ipert0)
+ msg *= @sprintf(" vmat(ip,ip,2,0)= %+.8e %+.8ei\n", real(vmat[ipert0, ipert0, 2, 1]), imag(vmat[ipert0, ipert0, 2, 1]))
+ msg *= @sprintf(" vmat(ip,ip+N,2,0)= %+.8e %+.8ei\n", real(vmat[ipert0, ipert0+N, 2, 1]), imag(vmat[ipert0, ipert0+N, 2, 1]))
+ for k in 0:(2*sing_order)
+ msg *= @sprintf(" k=%2d vmat(ip,ip,1)=%+.8e %+.8ei vmat(ip,ip,2)=%+.8e %+.8ei\n",
+ k, real(vmat[ipert0, ipert0, 1, k+1]), imag(vmat[ipert0, ipert0, 1, k+1]),
+ real(vmat[ipert0, ipert0, 2, k+1]), imag(vmat[ipert0, ipert0, 2, k+1]))
+ msg *= @sprintf(" k=%2d vmat(ip,ip+N,1)=%+.8e %+.8ei vmat(ip,ip+N,2)=%+.8e %+.8ei\n",
+ k, real(vmat[ipert0, ipert0+N, 1, k+1]), imag(vmat[ipert0, ipert0+N, 1, k+1]),
+ real(vmat[ipert0, ipert0+N, 2, k+1]), imag(vmat[ipert0, ipert0+N, 2, k+1]))
+ end
+ msg
+ end
+
+ return SingAsymptotics(sing_order, alpha, r1, r2, power, vmat)
+end
+
+"""
+ compute_sing_mmat!(mmat, singp, ctrl, profiles, mats, intr; sig=1.0, sing_order=ctrl.frobenius_order)
+
+Fill `mmat` with the Taylor coefficients M_k of the matrix M at a singular surface (Glasser 2016 Eqs. 43-44),
+with `sig` flipping odd ψ-derivatives for the left side. Port of Fortran `sing_mmat`, with dense matrices;
+Hermitian matrices store only their lower triangle (suffix `_lower`) and are used through `Hermitian(·, :L)`.
+"""
+@with_pool pool function compute_sing_mmat!(
+ mmat::Array{ComplexF64,4},
+ singp::SingType,
+ ctrl::ForceFreeStatesControl,
+ profiles::Equilibrium.ProfileSplines,
+ mats::MatrixSplines,
+ intr::ForceFreeStatesInternal;
+ sig::Float64=1.0,
+ sing_order::Int=ctrl.frobenius_order
+)
+
+ q_spline = profiles.q_spline
+ q_d1 = profiles.q_deriv
+ q_d2 = deriv2(q_spline)
+ q_d3 = deriv3(q_spline)
+
+ Npert = intr.numpert_total
+
+ singfac = zeros!(pool, Float64, Npert, 4)
+ f_lower_interp = zeros!(pool, ComplexF64, Npert, Npert, 4)
+ g_interp = zeros!(pool, ComplexF64, Npert, Npert, 4)
+ k_interp = zeros!(pool, ComplexF64, Npert, Npert, 4)
+ f_lower = zeros!(pool, ComplexF64, Npert, Npert, sing_order + 1)
+ f0_lower = zeros!(pool, ComplexF64, Npert, Npert)
+ ff_lower = zeros!(pool, ComplexF64, Npert, Npert, sing_order + 1)
+ g_lower = zeros!(pool, ComplexF64, Npert, Npert, sing_order + 1)
+ k = zeros!(pool, ComplexF64, Npert, Npert, sing_order + 1)
+ v = zeros!(pool, ComplexF64, Npert, 2 * Npert, 2)
+ x = zeros!(pool, ComplexF64, Npert, 2 * Npert, 2, sing_order + 1)
+ tmp_vec = acquire!(pool, ComplexF64, Npert)
+
+ # Evaluate q spline and its derivatives, applying sig to odd derivatives.
+ # Fortran STRIDE sing_mmat: q(1)=sig*q', q(2)=q'', q(3)=sig*q'''
+ q = (q_spline(singp.psifac),
+ sig * q_d1(singp.psifac),
+ q_d2(singp.psifac),
+ sig * q_d3(singp.psifac))
+
+ # Evaluate F_spline_lower and derivatives, applying sig to odd derivatives.
+ # Fortran sing_mmat multiplies fmats_f1 and fmats_f3 by sig in the Taylor products.
+ mats.ideal.F_spline_lower(vec(@view(f_lower_interp[:, :, 1])), singp.psifac; hint=mats._hint)
+ mats.ideal.F_spline_lower(vec(@view(f_lower_interp[:, :, 2])), singp.psifac; deriv=DerivOp(1))
+ mats.ideal.F_spline_lower(vec(@view(f_lower_interp[:, :, 3])), singp.psifac; deriv=DerivOp(2))
+ mats.ideal.F_spline_lower(vec(@view(f_lower_interp[:, :, 4])), singp.psifac; deriv=DerivOp(3))
+ @views f_lower_interp[:, :, 2] .*= sig # 1st derivative
+ @views f_lower_interp[:, :, 4] .*= sig # 3rd derivative
+
+ # Evaluate G_spline and derivatives, applying sig to odd derivatives
+ mats.ideal.G_spline(vec(@view(g_interp[:, :, 1])), singp.psifac; hint=mats._hint)
+ mats.ideal.G_spline(vec(@view(g_interp[:, :, 2])), singp.psifac; deriv=DerivOp(1))
+ mats.ideal.G_spline(vec(@view(g_interp[:, :, 3])), singp.psifac; deriv=DerivOp(2))
+ mats.ideal.G_spline(vec(@view(g_interp[:, :, 4])), singp.psifac; deriv=DerivOp(3))
+ @views g_interp[:, :, 2] .*= sig
+ @views g_interp[:, :, 4] .*= sig
+
+ # Evaluate K_spline and derivatives, applying sig to odd derivatives
+ mats.ideal.K_spline(vec(@view(k_interp[:, :, 1])), singp.psifac; hint=mats._hint)
+ mats.ideal.K_spline(vec(@view(k_interp[:, :, 2])), singp.psifac; deriv=DerivOp(1))
+ mats.ideal.K_spline(vec(@view(k_interp[:, :, 3])), singp.psifac; deriv=DerivOp(2))
+ mats.ideal.K_spline(vec(@view(k_interp[:, :, 4])), singp.psifac; deriv=DerivOp(3))
+ @views k_interp[:, :, 2] .*= sig
+ @views k_interp[:, :, 4] .*= sig
+
+ # Evaluate Taylor series coefficients for diagonal matrix Qᵢ = mᵢ - nᵢq(ψ) = [mᵢ - nᵢq, -nᵢq', -nᵢq'', -nᵢq''']
+ singfac[:, 1] .= vec((intr.mlow:intr.mhigh) .- q[1] .* (intr.nlow:intr.nhigh)')
+ for i in 2:4
+ singfac[:, i] .= repeat(-(intr.nlow:intr.nhigh) .* q[i]; inner=intr.mpert)
+ end
+ # For resonant modes mᵢ - nᵢq(ψ) = [-nᵢq', -nᵢq'', -nᵢq'''] - shift up terms by 1 index
+ # Add scaling to account for hardcoding coefficients in computations below
+ for (mres, nres) in zip(singp.m, singp.n)
+ ipert_res = 1 + mres - intr.mlow + (nres - intr.nlow) * intr.mpert
+ singfac[ipert_res, 1:4] .= (-nres * q[2], -nres * q[3] / 2, -nres * q[4] / 3, 0)
+ end
+
+ # F = QL̄L̄ᴴQᴴ: first the Taylor coefficients of QL̄ without the 1/n! scaling, leaving binomial coefficients
+ # f_lower = QL̄ = [QL̄, QL̄' + Q' L̄, 1/2 (QL̄'' + 2Q' L̄' + QQ'' L̄), 1/6 (QL̄''' + 3Q' L̄'' + 3Q'' L̄' + Q'''L̄), ...] (but without 1/2, 1/6, etc)
+ for ipert_n in 1:intr.npert
+ for jpert_m in 1:intr.mpert
+ for ipert_m in jpert_m:intr.mpert
+ ipert = ipert_m + (ipert_n - 1) * intr.mpert
+ jpert = jpert_m + (ipert_n - 1) * intr.mpert
+ f_lower[ipert, jpert, 1] = singfac[ipert, 1] * f_lower_interp[ipert, jpert, 1]
+ if sing_order ≥ 1
+ f_lower[ipert, jpert, 2] = singfac[ipert, 1] * f_lower_interp[ipert, jpert, 2] +
+ singfac[ipert, 2] * f_lower_interp[ipert, jpert, 1]
+ end
+ if sing_order ≥ 2
+ f_lower[ipert, jpert, 3] =
+ singfac[ipert, 1] * f_lower_interp[ipert, jpert, 3] +
+ 2 * singfac[ipert, 2] * f_lower_interp[ipert, jpert, 2] +
+ singfac[ipert, 3] * f_lower_interp[ipert, jpert, 1]
+ end
+ if sing_order ≥ 3
+ f_lower[ipert, jpert, 4] =
+ singfac[ipert, 1] * f_lower_interp[ipert, jpert, 4] +
+ 3 * singfac[ipert, 2] * f_lower_interp[ipert, jpert, 3] +
+ 3 * singfac[ipert, 3] * f_lower_interp[ipert, jpert, 2] +
+ singfac[ipert, 4] * f_lower_interp[ipert, jpert, 1]
+ end
+ if sing_order ≥ 4
+ f_lower[ipert, jpert, 5] =
+ 4 * singfac[ipert, 2] * f_lower_interp[ipert, jpert, 4] +
+ 6 * singfac[ipert, 3] * f_lower_interp[ipert, jpert, 3] +
+ 4 * singfac[ipert, 4] * f_lower_interp[ipert, jpert, 2]
+ end
+ if sing_order ≥ 5
+ f_lower[ipert, jpert, 6] = 10 * singfac[ipert, 3] * f_lower_interp[ipert, jpert, 4] +
+ 10 * singfac[ipert, 4] * f_lower_interp[ipert, jpert, 3]
+ end
+ if sing_order ≥ 6
+ f_lower[ipert, jpert, 7] = 20 * singfac[ipert, 4] * f_lower_interp[ipert, jpert, 4]
+ end
+ end
+ end
+ end
+ @views f0_lower .= f_lower[:, :, 1]
+
+ # Taylor coefficients of F = QL̄L̄ᴴQᴴ (lower half) from QL̄; fac1 = (n choose j) and fac0 = n! give 1/((n-j)! j!)
+ fac0 = 1
+ for n in 0:sing_order
+ fac1 = 1
+ for j in 0:n
+ for ipert_n in 1:intr.npert
+ for jpert_m in 1:intr.mpert
+ for ipert_m in jpert_m:intr.mpert
+ for kpert_m in 1:jpert_m
+ ipert = ipert_m + (ipert_n - 1) * intr.mpert
+ jpert = jpert_m + (ipert_n - 1) * intr.mpert
+ kpert = kpert_m + (ipert_n - 1) * intr.mpert
+ ff_lower[ipert, jpert, n+1] += fac1 * f_lower[ipert, kpert, j+1] * conj(f_lower[jpert, kpert, n-j+1])
+ end
+ end
+ end
+ end
+ fac1 *= (n - j) / (j + 1)
+ end
+ @views ff_lower[:, :, n+1] ./= fac0
+ fac0 *= (n + 1)
+ end
+
+ # Compute non-Hermitian matrix K = QK̄ Taylor series coefficients
+ # K = [QK̄, QK̄' + Q'K̄, QK̄''/2 + Q'K̄' + Q̄''K̄/2, ...]
+ for ipert_n in 1:intr.npert
+ for jpert_m in 1:intr.mpert
+ for ipert_m in 1:intr.mpert
+ ipert = ipert_m + (ipert_n - 1) * intr.mpert
+ jpert = jpert_m + (ipert_n - 1) * intr.mpert
+ k[ipert, jpert, 1] = singfac[ipert, 1] * k_interp[ipert, jpert, 1]
+ if sing_order ≥ 1
+ k[ipert, jpert, 2] = singfac[ipert, 1] * k_interp[ipert, jpert, 2] +
+ singfac[ipert, 2] * k_interp[ipert, jpert, 1]
+ end
+ if sing_order ≥ 2
+ k[ipert, jpert, 3] =
+ singfac[ipert, 1] * k_interp[ipert, jpert, 3] / 2 +
+ singfac[ipert, 2] * k_interp[ipert, jpert, 2] +
+ singfac[ipert, 3] * k_interp[ipert, jpert, 1] / 2
+ end
+ if sing_order ≥ 3
+ k[ipert, jpert, 4] =
+ singfac[ipert, 1] * k_interp[ipert, jpert, 4] / 6 +
+ singfac[ipert, 2] * k_interp[ipert, jpert, 3] / 2 +
+ singfac[ipert, 3] * k_interp[ipert, jpert, 2] / 2 +
+ singfac[ipert, 4] * k_interp[ipert, jpert, 1] / 6
+ end
+ if sing_order ≥ 4
+ k[ipert, jpert, 5] =
+ singfac[ipert, 2] * k_interp[ipert, jpert, 4] / 6 +
+ singfac[ipert, 3] * k_interp[ipert, jpert, 3] / 4 +
+ singfac[ipert, 4] * k_interp[ipert, jpert, 2] / 6
+ end
+ if sing_order ≥ 5
+ k[ipert, jpert, 6] = singfac[ipert, 3] * k_interp[ipert, jpert, 4] / 12 +
+ singfac[ipert, 4] * k_interp[ipert, jpert, 3] / 12
+ end
+ if sing_order ≥ 6
+ k[ipert, jpert, 7] = singfac[ipert, 4] * k_interp[ipert, jpert, 4] / 36
+ end
+ end
+ end
+ end
+
+ # Compute Hermitian matrix G (lower half only) Taylor series coefficients
+ # G = [G, G', G''/2, G'''/6]
+ for ipert_n in 1:intr.npert
+ for jpert_m in 1:intr.mpert
+ for ipert_m in jpert_m:intr.mpert
+ ipert = ipert_m + (ipert_n - 1) * intr.mpert
+ jpert = jpert_m + (ipert_n - 1) * intr.mpert
+ g_lower[ipert, jpert, 1] = g_interp[ipert, jpert, 1]
+ if sing_order ≥ 1
+ g_lower[ipert, jpert, 2] = g_interp[ipert, jpert, 2]
+ end
+ if sing_order ≥ 2
+ g_lower[ipert, jpert, 3] = g_interp[ipert, jpert, 3] / 2
+ end
+ if sing_order ≥ 3
+ g_lower[ipert, jpert, 4] = g_interp[ipert, jpert, 4] / 6
+ end
+ end
+ end
+ end
+
+ # Taylor expansion of x = Lv (Glasser 2016 Eq. 23), with v the identity
+ for ipert in 1:intr.numpert_total
+ v[ipert, ipert, 1] = 1
+ v[ipert, ipert+intr.numpert_total, 2] = 1
+ end
+
+ # Solve the Taylor expansion according to F * x¹ = v² - K v¹ at each order
+ # 0ᵗʰ order: x¹₀ = F⁻¹(v² - K v¹)
+ for isol in 1:(2*intr.numpert_total)
+ @views mul!(tmp_vec, k[:, :, 1], v[:, isol, 1])
+ @views x[:, isol, 1, 1] .= v[:, isol, 2] .- tmp_vec
+ end
+ @views x[:, :, 1, 1] = UpperTriangular(f0_lower') \ (LowerTriangular(f0_lower) \ x[:, :, 1, 1])
+
+ # Higher-order: ∑Fⱼx¹ₙ₋ⱼ = -Kₙv¹ → x¹ₙ = F₀⁻¹(-∑Fⱼxₙ₋ⱼ - Kₙv¹)
+ for i in 1:sing_order
+ for isol in 1:(2*intr.numpert_total)
+ for j in 1:i
+ @views mul!(tmp_vec, Hermitian(ff_lower[:, :, j+1], :L), x[:, isol, 1, i-j+1])
+ @views x[:, isol, 1, i+1] .-= tmp_vec
+ end
+ @views mul!(tmp_vec, k[:, :, i+1], v[:, isol, 1])
+ @views x[:, isol, 1, i+1] .-= tmp_vec
+ end
+ @views x[:, :, 1, i+1] = UpperTriangular(f0_lower') \ (LowerTriangular(f0_lower) \ x[:, :, 1, i+1])
+ end
+
+ # Solve x²ₙ = (G - K^†F⁻¹K)v¹ + K^†F⁻¹v² = Gₙv¹ + ∑Kⱼ^† x¹ₙ₋ⱼ at each order
+ for i in 0:sing_order
+ for isol in 1:(2*intr.numpert_total)
+ for j in 0:i
+ @views mul!(tmp_vec, adjoint(k[:, :, j+1]), x[:, isol, 1, i-j+1])
+ @views x[:, isol, 2, i+1] .+= tmp_vec
+ end
+ @views mul!(tmp_vec, Hermitian(g_lower[:, :, i+1], :L), v[:, isol, 1])
+ @views x[:, isol, 2, i+1] .+= tmp_vec
+ end
+ end
+
+ # Power series of M = zS⁻¹(LS - S') in √z (Glasser 2023 PoP Eq. 28)
+ ipert_res = 1 .+ singp.m .- intr.mlow .+ (singp.n .- intr.nlow) .* intr.mpert
+ r1 = ipert_res
+ r2 = vec([ipert_res[i] + j * intr.numpert_total for j in 0:1, i in eachindex(ipert_res)])
+ n1 = [i for i in 1:intr.numpert_total if !(i in ipert_res)]
+ n2 = vec([i + j * intr.numpert_total for j in 0:1, i in n1])
+
+ j = 0
+ # S⁻¹LS part (Glasser 2023 Eq. 39): order k of L feeds z^k (RLR), z^(k+1/2) (RLA, ALR), z^(k+1) (ALA)
+ for i in 0:sing_order
+ mmat[r1, r2, :, j+1] .= x[r1, r2, :, i+1]
+ mmat[r1, n2, :, j+2] .= x[r1, n2, :, i+1]
+ mmat[n1, r2, :, j+2] .= x[n1, r2, :, i+1]
+ mmat[n1, n2, :, j+3] .= x[n1, n2, :, i+1]
+ # Half-power index steps by 2 per order
+ j += 2
+ end
+ # Shearing term -zS⁻¹S' = 0.5 [R, 0; 0, -R] at zeroth order (Glasser 2023 Eqs. 25, 28)
+ for i in eachindex(r1)
+ mmat[r1[i], r2[2*i-1], 1, 1] += 0.5 * sig
+ mmat[r1[i], r2[2*i], 2, 1] -= 0.5 * sig
+ end
+end
+
+"""
+ solve_higher_order_vmat!(vmat, mmat, m0mat, alpha, r1, r2, n1, n2, power, intr, k; sig=1.0)
+
+Solve for order `k` of the power series `vmat` (Glasser 2016 Eq. 47). Port of Fortran `sing_solve`.
+
+### Arguments
+
+ - `vmat::Array{ComplexF64,4}`: V matrix power series (modified in-place)
+ - `mmat::Array{ComplexF64,4}`: M matrix power series
+ - `m0mat::Matrix{ComplexF64}`: Zeroth order M matrix
+ - `alpha::Vector{ComplexF64}`: Mercier exponent of each resonant block
+ - `r1, r2, n1, n2::Vector{Int}`: Resonant and nonresonant indices
+ - `power::Vector{ComplexF64}`: Frobenius power of each solution column (0 for nonresonant)
+ - `k::Int`: The current order in the power series expansion
+"""
+@with_pool pool function solve_higher_order_vmat!(
+ vmat::Array{ComplexF64,4},
+ mmat::Array{ComplexF64,4},
+ m0mat::Matrix{ComplexF64},
+ alpha::Vector{ComplexF64},
+ r1::Vector{Int},
+ r2::Vector{Int},
+ n1::Vector{Int},
+ n2::Vector{Int},
+ power::Vector{ComplexF64},
+ intr::ForceFreeStatesInternal,
+ k::Int;
+ sig::Float64=1.0
+)
+
+ tmp_arr = zeros!(pool, ComplexF64, size(vmat)[1:3])
+ # Compute ∑Mₗvₖ₋ₗ
+ for l in 1:k
+ @views sing_matmul!(tmp_arr, mmat[:, :, :, l+1], vmat[:, :, :, k-l+1])
+ vmat[:, :, :, k+1] .+= tmp_arr
+ end
+
+ a = zeros!(pool, ComplexF64, 2, 2)
+ for isol in 1:(2*intr.numpert_total)
+ for i in eachindex(r1)
+ # Fortran sing_solve: a(i,i) = m0mat(i,i) - sig*(k/2 + power(isol))
+ @views m0mat_block = m0mat[(2*(i-1)+1):(2*i), (2*(i-1)+1):(2*i)]
+ a .= m0mat_block
+ a[1, 1] -= sig * (k / 2.0 + power[isol])
+ a[2, 2] -= sig * (k / 2.0 + power[isol])
+ det = a[1, 1] * a[2, 2] - a[1, 2] * a[2, 1]
+ # Solve the resonant indices
+ x1 = -vmat[r1[i], isol, 1, k+1]
+ x2 = -vmat[r1[i], isol, 2, k+1]
+ vmat[r1[i], isol, 1, k+1] = (a[2, 2] * x1 - a[1, 2] * x2) / det
+ vmat[r1[i], isol, 2, k+1] = (a[1, 1] * x2 - a[2, 1] * x1) / det
+ end
+ # Fortran sing_solve: vmat(n1,isol,:,k) *= sig/(power(isol)+k/2)
+ vmat[n1, isol, :, k+1] .*= sig / (power[isol] + k / 2.0)
+ end
+end
+
+"""
+ sing_matmul!(out, a, b) -> out
+
+Matrix product of two asymptotic-series coefficient arrays into `out`, as the Fortran `sing_matmul`:
+`b` is `(m, n, 2)`, `a` is `(·, 2m, 2)`, and `out` is `(size(a, 1), n, 2)`.
+"""
+@with_pool pool function sing_matmul!(out::AbstractArray{ComplexF64,3}, a::AbstractArray{ComplexF64,3}, b::AbstractArray{ComplexF64,3})
+ m = size(b, 1)
+ n = size(b, 2)
+
+ if size(a, 2) != 2 * m
+ error("Sing_matmul: size(a,2) = $(size(a,2)) != 2*size(b,1) = $(2*m)")
+ end
+
+ fill!(out, zero(ComplexF64))
+ tmp = acquire!(pool, ComplexF64, size(a, 1))
+ for i in 1:n
+ for j in 1:2
+ @views mul!(tmp, a[:, 1:m, j], b[:, i, 1])
+ @views out[:, i, j] .+= tmp
+ @views mul!(tmp, a[:, (m+1):(2*m), j], b[:, i, 2])
+ @views out[:, i, j] .+= tmp
+ end
+ end
+
+ return out
+end
+
+"""
+ sing_get_ua(sing_asymp::SingAsymptotics, dpsi::Float64) -> ua
+
+Evaluate the asymptotic solutions at distance `dpsi` from the surface, on the side `sing_asymp` was built
+for. Port of Fortran STRIDE `sing_get_ua`.
+
+### Arguments
+
+ - `sing_asymp::SingAsymptotics`: Pre-computed asymptotic data (must be left or right specific)
+ - `dpsi::Float64`: Positive distance from singular surface = |ψ - ψ_res|
+"""
+function sing_get_ua(sing_asymp::SingAsymptotics, dpsi::Float64)
+
+ r1 = sing_asymp.r1
+ r2 = sing_asymp.r2
+
+ # dpsi ≥ 0 always; the side is carried by the sig of the SingAsymptotics.
+ sqrtfac = sqrt(dpsi)
+
+ # Compute power series via Horner's method (eq. 45 in Glasser 2016)
+ ua = copy(sing_asymp.vmat[:, :, :, 2*sing_asymp.sing_order+1])
+ for iorder in (2*sing_asymp.sing_order-1):-1:0
+ ua .= ua .* sqrtfac .+ sing_asymp.vmat[:, :, :, iorder+1]
+ end
+
+ # Restore powers (unshear v→u). Resonant columns use their Frobenius powers.
+ for i in eachindex(r1)
+ _apply_column_powers!(@view(ua[:, r2[2*i-1], :]), @view(ua[:, r2[2*i], :]),
+ sing_asymp.power[r2[2*i-1]], sing_asymp.power[r2[2*i]], dpsi)
+ ua[r1[i], :, 1] ./= sqrtfac # resonant row ξ: /√dpsi
+ ua[r1[i], :, 2] .*= sqrtfac # resonant row ξ': *√dpsi
+ end
+
+ return ua
+end
+
+# Column-restricted evaluation for the outer-region Galerkin solver: only the big (r2[1]) and small (r2[2])
+# resonant columns, into a caller-provided (N, 2, 2) buffer. Requires a single resonance (length(r1) == 1);
+# numerically identical to slicing `sing_get_ua` to [r2[1], r2[2]].
+
+"""
+ sing_get_ua_res!(out, sing_asymp, dpsi) -> out
+
+Evaluate only the big (col 1) and small (col 2) resonant columns of `sing_get_ua` into the
+caller-provided `out` of shape `(numpert_total, 2, 2)`. Allocation-free. See the section comment.
+"""
+function sing_get_ua_res!(out::AbstractArray{ComplexF64,3}, sing_asymp::SingAsymptotics, dpsi::Float64)
+ vmat = sing_asymp.vmat
+ order = sing_asymp.sing_order
+ N = size(vmat, 1)
+ sqrtfac = sqrt(dpsi)
+ ρ = sing_asymp.r1[1]
+ cbig = sing_asymp.r2[1]
+ csml = sing_asymp.r2[2]
+ nterm = 2 * order
+
+ @inbounds for k in 1:2, ii in 1:N
+ ab = vmat[ii, cbig, k, nterm+1]
+ as = vmat[ii, csml, k, nterm+1]
+ for t in (nterm-1):-1:0
+ ab = ab * sqrtfac + vmat[ii, cbig, k, t+1]
+ as = as * sqrtfac + vmat[ii, csml, k, t+1]
+ end
+ out[ii, 1, k] = ab
+ out[ii, 2, k] = as
+ end
+
+ # Unshear v→u by the column Frobenius powers; resonant row /√dpsi (qty1), *√dpsi (qty2).
+ _apply_column_powers!(@view(out[:, 1, :]), @view(out[:, 2, :]),
+ sing_asymp.power[cbig], sing_asymp.power[csml], dpsi)
+ @inbounds out[ρ, 1, 1] /= sqrtfac
+ @inbounds out[ρ, 2, 1] /= sqrtfac
+ @inbounds out[ρ, 1, 2] *= sqrtfac
+ @inbounds out[ρ, 2, 2] *= sqrtfac
+ return out
+end
+
+"""
+ sing_get_dua_res!(out, sing_asymp, dpsi) -> out
+
+Derivative of the asymptotic series with respect to the positive distance `dpsi = |ψ − ψ_res|`, for
+the big (col 1) and small (col 2) resonant columns only, into the caller-provided `out` of shape
+`(numpert_total, 2, 2)`; Fortran `sing_get_dua` restricted to those columns. Direction is carried by the
+left or right `SingAsymptotics`, so `dpsi` is positive and the caller applies the d/dψ sign on the
+left. Allocation-free; scalar per-term exponents replace a full `power` array. See the section comment.
+"""
+function sing_get_dua_res!(out::AbstractArray{ComplexF64,3}, sing_asymp::SingAsymptotics, dpsi::Float64)
+ vmat = sing_asymp.vmat
+ order = sing_asymp.sing_order
+ N = size(vmat, 1)
+ sqrtfac = sqrt(dpsi)
+ ρ = sing_asymp.r1[1]
+ cbig = sing_asymp.r2[1]
+ csml = sing_asymp.r2[2]
+ p_big = sing_asymp.power[cbig]
+ p_small = sing_asymp.power[csml]
+ nterm = 2 * order
+
+ # Exponent base in half-powers of dpsi: 2·order + resonant-row offset (∓1 by qty) + 2·power.
+ @inbounds for k in 1:2, ii in 1:N
+ roff = ii == ρ ? (k == 1 ? ComplexF64(-1) : ComplexF64(1)) : ComplexF64(0)
+ pb = nterm + roff + 2 * p_big
+ ps = nterm + roff + 2 * p_small
+ ab = vmat[ii, cbig, k, nterm+1] * pb
+ as = vmat[ii, csml, k, nterm+1] * ps
+ for t in (nterm-1):-1:0
+ pb -= 1
+ ps -= 1
+ ab = ab * sqrtfac + vmat[ii, cbig, k, t+1] * pb
+ as = as * sqrtfac + vmat[ii, csml, k, t+1] * ps
+ end
+ out[ii, 1, k] = ab
+ out[ii, 2, k] = as
+ end
+
+ _apply_column_powers!(@view(out[:, 1, :]), @view(out[:, 2, :]), p_big, p_small, dpsi)
+ twodpsi = 2 * dpsi
+ @inbounds out[ρ, 1, 1] /= sqrtfac
+ @inbounds out[ρ, 2, 1] /= sqrtfac
+ @inbounds out[ρ, 1, 2] *= sqrtfac
+ @inbounds out[ρ, 2, 2] *= sqrtfac
+ # Divide (not multiply by the reciprocal), as Fortran sing_get_dua does; the resonant QuadGK and the
+ # ill-conditioned near-singular solve amplify a 1e-16 input change into ~1e-3 in Δ′.
+ @inbounds for idx in eachindex(out)
+ out[idx] /= twodpsi
+ end
+ return out
+end
+
+"""
+Allocating wrapper for [`sing_get_ua_res!`](@ref); returns the big/small columns as `(N, 2, 2)`.
+"""
+sing_get_ua_res(sing_asymp::SingAsymptotics, dpsi::Float64) =
+ sing_get_ua_res!(Array{ComplexF64,3}(undef, size(sing_asymp.vmat, 1), 2, 2), sing_asymp, dpsi)
+
+"""
+ sing_get_ua_res_cut!(out, sing_asymp, dpsi) -> out
+
+Leading-order ("cut") form of [`sing_get_ua_res!`](@ref): keeps only the `t = 0` term of the
+Frobenius series instead of summing all `2·sing_order` terms, then applies the same unshear.
+
+Used for the *cut* outer solution, the background the resistive inner-layer solution is added to in the
+composite solution; full minus cut is the higher-order content the layer solution replaces.
+"""
+function sing_get_ua_res_cut!(out::AbstractArray{ComplexF64,3}, sing_asymp::SingAsymptotics, dpsi::Float64)
+ vmat = sing_asymp.vmat
+ N = size(vmat, 1)
+ sqrtfac = sqrt(dpsi)
+ ρ = sing_asymp.r1[1]
+ cbig = sing_asymp.r2[1]
+ csml = sing_asymp.r2[2]
+
+ @inbounds for k in 1:2, ii in 1:N
+ out[ii, 1, k] = vmat[ii, cbig, k, 1]
+ out[ii, 2, k] = vmat[ii, csml, k, 1]
+ end
+
+ _apply_column_powers!(@view(out[:, 1, :]), @view(out[:, 2, :]),
+ sing_asymp.power[cbig], sing_asymp.power[csml], dpsi)
+ @inbounds out[ρ, 1, 1] /= sqrtfac
+ @inbounds out[ρ, 2, 1] /= sqrtfac
+ @inbounds out[ρ, 1, 2] *= sqrtfac
+ @inbounds out[ρ, 2, 2] *= sqrtfac
+ return out
+end
+
+"""
+Allocating wrapper for [`sing_get_ua_res_cut!`](@ref); returns the big/small columns as `(N, 2, 2)`.
+"""
+sing_get_ua_res_cut(sing_asymp::SingAsymptotics, dpsi::Float64) =
+ sing_get_ua_res_cut!(Array{ComplexF64,3}(undef, size(sing_asymp.vmat, 1), 2, 2), sing_asymp, dpsi)
+
+"""
+Allocating wrapper for [`sing_get_dua_res!`](@ref); returns the big/small columns as `(N, 2, 2)`.
+"""
+sing_get_dua_res(sing_asymp::SingAsymptotics, dpsi::Float64) =
+ sing_get_dua_res!(Array{ComplexF64,3}(undef, size(sing_asymp.vmat, 1), 2, 2), sing_asymp, dpsi)
+
+"""
+ sing_matvec!(matvec, kmat, gmat, d1, tmp, sfvec, mats, intr, psi, q, ua, dua) -> matvec
+
+Apply the Euler-Lagrange residual operator `L u = -(F u' + K u)' + (K† u' + G u)` to the asymptotic
+solutions `ua` and their ψ-derivatives `dua`, as Fortran `sing_matvec` (sing.f), for the resonant-quadrature
+integrand. It uses the reduced K̄ and Ḡ splines with the direct singular factor `sfvec = m − n q` on
+`u' = dua[:,:,1]`; `ua[:,:,2]` is the canonical momentum `F u' + K u`, so `-dua[:,:,2] = -(F u' + K u)'`.
+All scratch is caller-owned: `kmat`/`gmat` are `N×N`, `d1`/`tmp`/`sfvec` are length-`N`, `matvec` is
+`N×size(ua,2)`. The accumulation order (separate `gmat*ua` into `tmp`, then add) is kept on purpose: a
+fused 5-arg `mul!` would round differently, and the ill-conditioned near-singular resonant solve amplifies
+a 1e-16 change into ~1e-3 in Δ′.
+"""
+function sing_matvec!(matvec::AbstractMatrix{ComplexF64}, kmat::Matrix{ComplexF64}, gmat::Matrix{ComplexF64},
+ d1::Vector{ComplexF64}, tmp::Vector{ComplexF64}, sfvec::Vector{Float64}, mats::MatrixSplines,
+ intr::ForceFreeStatesInternal, psi::Float64, q::Float64, ua::AbstractArray{ComplexF64,3}, dua::AbstractArray{ComplexF64,3})
+
+ N = intr.numpert_total
+ msol = size(ua, 2)
+
+ # Direct singular factor (m - n q), NOT 1/(m - n q); flat order matches vec((m) .- q.*(n)').
+ idx = 0
+ @inbounds for nn in intr.nlow:intr.nhigh, mm in intr.mlow:intr.mhigh
+ idx += 1
+ sfvec[idx] = mm - q * nn
+ end
+
+ mats.ideal.K_spline(vec(kmat), psi; hint=mats._hint)
+ mats.ideal.G_spline(vec(gmat), psi; hint=mats._hint)
+ kdag = adjoint(kmat)
+
+ for isol in 1:msol
+ @views d1 .= dua[:, isol, 1] .* sfvec # u' · singfac
+ @views mul!(matvec[:, isol], kdag, d1) # K̄† (u' · singfac)
+ @views mul!(tmp, gmat, ua[:, isol, 1]) # Ḡ u
+ @views matvec[:, isol] .+= tmp # + Ḡ u
+ @views matvec[:, isol] .-= dua[:, isol, 2] # - (F u' + K u)'
+ end
+ return matvec
+end
+
+"""
+ sing_get_ca(u::Array{ComplexF64,3}, ua::Array{ComplexF64,3}, intr::ForceFreeStatesInternal)
+
+Asymptotic expansion coefficients `ca` of `u` in the basis `ua` (Glasser 2016 Eq. 50). Port of Fortran `sing_get_ca`.
+
+### Arguments
+
+ - `u::Array{ComplexF64,3}`: Current solution matrix, shape (numpert_total, numpert_total, 2)
+ - `ua::Array{ComplexF64,3}`: Asymptotic solution matrix, shape (numpert_total, 2·numpert_total, 2)
+"""
+function sing_get_ca(u::Array{ComplexF64,3}, ua::Array{ComplexF64,3}, intr::ForceFreeStatesInternal)
+
+ temp1 = zeros(ComplexF64, 2 * intr.numpert_total, 2 * intr.numpert_total)
+ temp1[1:intr.numpert_total, :] .= ua[:, :, 1]
+ temp1[(intr.numpert_total+1):(2*intr.numpert_total), :] .= ua[:, :, 2]
+
+ temp2 = zeros(ComplexF64, 2 * intr.numpert_total, intr.numpert_total)
+ temp2[1:intr.numpert_total, :] .= u[:, :, 1]
+ temp2[(intr.numpert_total+1):(2*intr.numpert_total), :] .= u[:, :, 2]
+
+ temp2 .= lu!(temp1) \ temp2
+
+ ca = zeros(ComplexF64, intr.numpert_total, intr.numpert_total, 2)
+ @views ca[:, :, 1] .= temp2[1:intr.numpert_total, :]
+ @views ca[:, :, 2] .= temp2[(intr.numpert_total+1):(2*intr.numpert_total), :]
+
+ return ca
+end
diff --git a/src/ForceFreeStates/Surfaces/Finding.jl b/src/ForceFreeStates/Surfaces/Finding.jl
new file mode 100644
index 0000000000..8bf9f6d3e8
--- /dev/null
+++ b/src/ForceFreeStates/Surfaces/Finding.jl
@@ -0,0 +1,425 @@
+# Rational-surface finding: ideal (q = m/n) and kinetic (cond(F) peak) singular surfaces.
+
+"""
+ _find_rational_surfaces(equil::Equilibrium.PlasmaEquilibrium, nlow::Int, nhigh::Int)
+
+Locate all rational q-surfaces q = m/n for n in `nlow:nhigh` by Brent bisection between
+consecutive extrema of the q-profile (reverse shear gives one root per monotone segment).
+Returns a vector of `(m, n, psifac)` named tuples in discovery order (n outer, ψ-interval
+inner). Requires `equilibrium_qfind!` to have populated `equil.params.qextrema_*`.
+"""
+function _find_rational_surfaces(equil::Equilibrium.PlasmaEquilibrium, nlow::Int, nhigh::Int)
+ profiles = equil.profiles
+ surfaces = @NamedTuple{m::Int, n::Int, psifac::Float64}[]
+
+ for n in nlow:nhigh
+ hint = Ref(1)
+ # Loop over extrema of q, find all rational values in between
+ for iex in 2:equil.params.mextrema
+ dq = equil.params.qextrema_q[iex] - equil.params.qextrema_q[iex-1]
+ dq == 0 && continue
+ m = trunc(Int, n * equil.params.qextrema_q[iex-1])
+ if dq > 0
+ m += 1
+ end
+ dm = Int(sign(dq * n))
+
+ while (m - n * equil.params.qextrema_q[iex-1]) * (m - n * equil.params.qextrema_q[iex]) <= 0
+ psi0 = equil.params.qextrema_psi[iex-1]
+ psi1 = equil.params.qextrema_psi[iex]
+
+ psifac = find_zero(psi -> m - n * profiles.q_spline(psi; hint=hint), (psi0, psi1), Roots.Brent())
+ push!(surfaces, (m=m, n=n, psifac=psifac))
+ m += dm
+ end
+ end
+ end
+ return surfaces
+end
+
+"""
+ rational_psi_nodes(equil::Equilibrium.PlasmaEquilibrium; nlow::Int, nhigh::Int=nlow)
+
+Unique ψ_N locations of all rational surfaces q = m/n for n in `nlow:nhigh`, sorted
+increasing. Used as mandatory knots for the two-pass equilibrium grid refinement. Roots
+are deduplicated by (q, ψ), so several (m, n) of equal ratio collapse to one node while the
+two crossings of one rational on a reverse-shear profile stay distinct.
+"""
+function rational_psi_nodes(equil::Equilibrium.PlasmaEquilibrium; nlow::Int, nhigh::Int=nlow)
+ surfaces = _find_rational_surfaces(equil, nlow, nhigh)
+ kept = @NamedTuple{q::Float64, psifac::Float64}[]
+ for s in surfaces
+ q = s.m / s.n
+ any(k -> _same_surface(k.q, k.psifac, q, s.psifac), kept) && continue
+ push!(kept, (q=q, psifac=s.psifac))
+ end
+ return sort!([k.psifac for k in kept])
+end
+
+# Two rational-surface roots are one physical surface when both q and ψ agree.
+const SURFACE_TOLERANCE = 1e-8
+_same_surface(q_a, psi_a, q_b, psi_b) = isapprox(q_a, q_b; atol=SURFACE_TOLERANCE) && isapprox(psi_a, psi_b; atol=SURFACE_TOLERANCE)
+
+"""
+ sing_find!(intr::ForceFreeStatesInternal, equil::Equilibrium.PlasmaEquilibrium)
+
+Locate singular rational q-surfaces (q = m/n) by bisection between extrema of the q-profile,
+and store their properties in `intr.sing`, sorted by increasing ψ. Roots of equal ratio m/n at
+the same ψ (e.g. (2,1) and (4,2)) merge into one surface carrying all its (m, n); the two
+crossings of one rational on a reverse-shear profile stay separate surfaces with opposite-sign q′.
+"""
+function sing_find!(intr::ForceFreeStatesInternal, equil::Equilibrium.PlasmaEquilibrium)
+ profiles = equil.profiles
+ hint = Ref(1)
+
+ for s in _find_rational_surfaces(equil, intr.nlow, intr.nhigh)
+ m, n, psifac = s.m, s.n, s.psifac
+ idx = findfirst(sg -> _same_surface(sg.q, sg.psifac, m / n, psifac), intr.sing)
+ if idx !== nothing
+ push!(intr.sing[idx].m, m)
+ push!(intr.sing[idx].n, n)
+ else
+ push!(intr.sing, SingType(;
+ m=[m],
+ n=[n],
+ psifac=psifac,
+ rho=sqrt(psifac),
+ q=m / n,
+ q1=profiles.q_deriv(psifac; hint=hint)
+ ))
+ intr.msing += 1
+ end
+ end
+ intr.sing = sort(intr.sing; by=s -> s.psifac)
+end
+
+"""
+ sing_lim!(intr::ForceFreeStatesInternal, ctrl::ForceFreeStatesControl, equil::Equilibrium.PlasmaEquilibrium;
+ psilim_cap=nothing)
+
+Set the outer integration limits `intr.psilim`, `intr.qlim` and `intr.q1lim`.
+
+The target `qlim` starts at `min(equil.params.qmax, ctrl.qhigh)`. When `psilim_cap` is given
+and lies inside the domain, `qlim` is further capped at `q(psilim_cap)`: the resistive-layer
+overlap point of Fitzpatrick, Nucl. Fusion 2025 Sect. 5.9, past which no surface retains a
+well-separated inner region. The cap only ever narrows the domain; one beyond `psihigh` is inert.
+
+If `truncate_at_rational_offset` is true, `qlim` is then moved to `(last rational + rational_offset_fraction) / n` and
+stepped back by `1/n` until it no longer exceeds the bound above, so `rational_offset_fraction` never extends the
+domain past `qmax`, `qhigh` or the cap. A bound that falls exactly on, or less than `rational_offset_fraction / n`
+above, a rational excludes that rational. If `qlim < qmax`, a Newton iteration finds the matching
+`psilim` (outer crossing on a reversed-shear profile); otherwise the equilibrium edge values are used.
+"""
+function sing_lim!(intr::ForceFreeStatesInternal, ctrl::ForceFreeStatesControl, equil::Equilibrium.PlasmaEquilibrium;
+ psilim_cap::Union{Nothing,Real}=nothing)
+
+ profiles = equil.profiles
+
+ # Initial guesses based on equilibrium
+ intr.qlim = min(equil.params.qmax, ctrl.qhigh) # equilibrium solve only goes up to qmax, so we're capped there
+ intr.q1lim = profiles.q_deriv(profiles.xs[end]; hint=Ref(profiles.npts_minus_1))
+ intr.psilim = equil.params.psihigh_resolved
+
+ # Resistive-layer overlap caps qlim (not psilim), so rational_offset_fraction below still picks a surface inside it.
+ if psilim_cap !== nothing && psilim_cap < intr.psilim
+ q_cap = profiles.q_spline(Float64(psilim_cap))
+ if q_cap < intr.qlim
+ @info "Resistive-layer overlap caps the domain: qlim $(@sprintf("%.3f", intr.qlim)) -> " *
+ "$(@sprintf("%.3f", q_cap)) (psi $(@sprintf("%.6f", intr.psilim)) -> $(@sprintf("%.6f", Float64(psilim_cap))))"
+ intr.qlim = q_cap
+ end
+ end
+
+ # Rational-offset cutoff needs the resolved single-n range on `intr`; multi-n falls back to qhigh / psihigh.
+ if ctrl.truncate_at_rational_offset && intr.nlow <= 0
+ error(
+ "sing_lim!: truncate_at_rational_offset = true requires a resolved toroidal range, but got intr.nlow=$(intr.nlow). " *
+ "Assign intr.nlow / intr.nhigh (resolve_mode_space!) before calling sing_lim!, " *
+ "or set truncate_at_rational_offset = false to truncate via qhigh / psihigh instead."
+ )
+ elseif ctrl.truncate_at_rational_offset && intr.nlow != intr.nhigh
+ @warn "truncate_at_rational_offset = true is ignored for multi-n runs (n = $(intr.nlow):$(intr.nhigh)); falling back to qhigh / psihigh truncation."
+ elseif ctrl.truncate_at_rational_offset
+ @info "Setting psilim via rational_offset_fraction: initial qlim = $(@sprintf("%.3f", intr.qlim)), rational_offset_fraction = $(@sprintf("%.3f", ctrl.rational_offset_fraction))"
+ # Normalize rational_offset_fraction ∈ [0,1)
+ rational_offset_fraction = mod(ctrl.rational_offset_fraction, 1.0)
+ # qlim already holds min(qmax, qhigh, overlap cap); rational_offset_fraction must never step past any of them.
+ qlim_bound = intr.qlim
+ intr.qlim = (trunc(Int, intr.nlow * intr.qlim) + rational_offset_fraction) / intr.nlow
+
+ # Step back one rational at a time until inside the bound, keeping the rational_offset_fraction offset
+ while intr.qlim > qlim_bound
+ intr.qlim -= 1.0 / intr.nlow
+ end
+ end
+
+ # A target below q_min has no psilim: say why instead of failing in the root find, as Fortran's "Can't find psilim"
+ intr.qlim >= equil.params.qmin ||
+ error(
+ "sing_lim!: the integration limit qlim = $(@sprintf("%.3f", intr.qlim)) lies below q_min = $(@sprintf("%.3f", equil.params.qmin)), " *
+ "so no flux surface reaches it. With truncate_at_rational_offset no rational surface of n = $(intr.nlow) is left to truncate at; " *
+ "widen the domain (qhigh, the layer-overlap cap) or set truncate_at_rational_offset = false."
+ )
+
+ # qlim below qmax: Newton-solve q(psilim) = qlim
+ if intr.qlim < equil.params.qmax
+ # Seed from the edge inward at the outermost node with q ≤ qlim, so a reversed-shear profile, which crosses
+ # qlim on both legs of its minimum, gets the outer crossing.
+ qy = profiles.q_spline.y
+ jpsi = something(findlast(<=(intr.qlim), qy), argmin(abs.(qy .- intr.qlim)))
+ jpsi = min(jpsi, length(profiles.xs) - 1)
+
+ hint = Ref(jpsi)
+ intr.psilim = find_zero(
+ (psi -> profiles.q_spline(psi; hint=hint) - intr.qlim,
+ psi -> profiles.q_deriv(psi; hint=hint)),
+ profiles.xs[jpsi], Roots.Newton()
+ )
+ intr.q1lim = profiles.q_deriv(intr.psilim)
+ end
+end
+
+"""
+ remove_singular_surfs!(intr; psimin=-Inf, psimax=intr.psilim) -> keep
+
+Drop rational surfaces outside `psimin ≤ psifac ≤ psimax` from `intr.sing`, logging any dropped,
+and return the indices of those kept.
+"""
+function remove_singular_surfs!(intr::ForceFreeStatesInternal; psimin::Real=-Inf, psimax::Real=intr.psilim)
+ keep = [j for j in 1:intr.msing if psimin <= intr.sing[j].psifac <= psimax]
+ if length(keep) < intr.msing
+ excluded = [(intr.sing[j].m, intr.sing[j].q) for j in setdiff(1:intr.msing, keep)]
+ @info "Filtered $(length(excluded)) singular surface(s) outside integration domain: $(excluded)"
+ intr.sing = intr.sing[keep]
+ intr.msing = length(keep)
+ end
+ return keep
+end
+
+"""
+ qlow_start_psi(qlow, equil) -> ψ
+
+Lower integration bound set by `qlow`: the outermost crossing of q = qlow, so the whole q < qlow
+region inside it is excluded, whether a monotonic core (q ≤ 1 sawtooth surfaces) or a reversed-shear
+ring around q_min. Read from the same spline q extrema `sing_find!` brackets its roots with, so a dip
+between grid nodes counts; the root is bracketed on the monotone stretch past the outermost extremum
+below qlow. Returns the first grid node when q ≥ qlow everywhere.
+"""
+function qlow_start_psi(qlow::Real, equil::Equilibrium.PlasmaEquilibrium)
+ psiex, qex = equil.params.qextrema_psi, equil.params.qextrema_q
+ k = findlast(<(qlow), qex)
+ k === nothing && return equil.profiles.xs[1]
+ k < length(qex) || error("qlow=$qlow: q < qlow up to the edge of the ψ grid (q there is $(qex[end])), so no integration domain remains.")
+ return find_zero(psi -> equil.profiles.q_spline(psi) - qlow, (psiex[k], psiex[k+1]), Roots.Brent())
+end
+
+"""
+ sing_min!(intr::ForceFreeStatesInternal, ctrl::ForceFreeStatesControl, equil::Equilibrium.PlasmaEquilibrium)
+
+Set the lower integration bound `intr.psilow` to `qlow_start_psi`, the one bound every
+integrator starts from. Excluding the q < qlow region matters most for the outer-region Galerkin
+solve, whose Hermite FEM would otherwise integrate through unhandled q ≤ 1 ideal singularities and
+contaminate Δ′ at the innermost kept surface.
+"""
+function sing_min!(intr::ForceFreeStatesInternal, ctrl::ForceFreeStatesControl, equil::Equilibrium.PlasmaEquilibrium)
+ profiles = equil.profiles
+ intr.psilow = qlow_start_psi(ctrl.qlow, equil)
+ intr.psilow > profiles.xs[1] &&
+ @info "sing_min: qlow=$(@sprintf("%.3f", ctrl.qlow)); raising psilow from $(@sprintf("%.5f", profiles.xs[1])) " *
+ "to $(@sprintf("%.5f", intr.psilow)) (excludes the q < qlow region)"
+ return intr.psilow
+end
+
+"""
+ fbar_block_conditions(psi, kin, equil, intr; hint=Ref(1)) -> Vector{Float64}
+
+Condition number of each toroidal-mode block of the kinetic F̄ matrix at ψ, one entry per n in
+`intr.nlow:intr.nhigh`.
+
+F̄(i,j) = q₁·f0(i,j)·q₂ - q₁·P(i,j) - conj(P†(j,i))·q₂ + R1(i,j)
+
+where q₁ = m₁ - n·q(ψ), q₂ = m₂ - n·q(ψ) are the direct singularity factors. The axisymmetric F̄ is
+block-diagonal in n, so each block is conditioned on its own; the condition number of the whole
+matrix would mix the scales of different n.
+"""
+function fbar_block_conditions(psi::Float64, kin::FKGMatrices, equil::Equilibrium.PlasmaEquilibrium, intr::ForceFreeStatesInternal; hint=Ref(1))
+ np = intr.numpert_total
+ mpert = intr.mpert
+
+ q = equil.profiles.q_spline(psi; hint=hint)
+
+ f0_vec = zeros(ComplexF64, np * np)
+ p_vec = zeros(ComplexF64, np * np)
+ pa_vec = zeros(ComplexF64, np * np)
+ r1_vec = zeros(ComplexF64, np * np)
+ kin.F0_spline(f0_vec, psi; hint=hint)
+ kin.P_spline(p_vec, psi; hint=hint)
+ kin.P_spline_adj(pa_vec, psi; hint=hint)
+ kin.R1_spline(r1_vec, psi; hint=hint)
+ f0mat = reshape(f0_vec, np, np)
+ pmat = reshape(p_vec, np, np)
+ paat = reshape(pa_vec, np, np)
+ r1mat = reshape(r1_vec, np, np)
+
+ # Assemble each n-block of F̄
+ conds = zeros(Float64, intr.npert)
+ fbar = zeros(ComplexF64, mpert, mpert)
+ for in_idx in 1:intr.npert
+ n = intr.nlow + in_idx - 1
+ off = (in_idx - 1) * mpert
+ for j in 1:mpert
+ q2 = (intr.mlow + j - 1) - n * q
+ for i in 1:mpert
+ q1 = (intr.mlow + i - 1) - n * q
+ fbar[i, j] = q1 * f0mat[off+i, off+j] * q2 - q1 * pmat[off+i, off+j] - conj(paat[off+j, off+i]) * q2 + r1mat[off+i, off+j]
+ end
+ end
+ conds[in_idx] = cond(fbar)
+ end
+ return conds
+end
+
+"""
+ evaluate_fbar_condition(psi, kin, equil, intr; hint=Ref(1))
+
+Largest per-n-block condition number of the kinetic F̄ matrix at ψ (see `fbar_block_conditions`),
+a scale-invariant measure of how close any toroidal mode is to a kinetic singularity.
+"""
+evaluate_fbar_condition(psi::Float64, kin::FKGMatrices, equil::Equilibrium.PlasmaEquilibrium, intr::ForceFreeStatesInternal; hint=Ref(1)) =
+ maximum(fbar_block_conditions(psi, kin, equil, intr; hint=hint))
+
+# Kinetic F̄ counts as singular above this condition number; structure within
+# KINETIC_RELAXED_FRAC of it is reported as near-singular (the shifted/split resonances).
+const KINETIC_SINGULAR_COND = 1.0e8
+const KINETIC_RELAXED_FRAC = 0.01
+
+"""
+ find_kinetic_singular_surfaces!(mats, equil, intr; ngrid=2000, cond_threshold=1e8)
+
+Find kinetically displaced singular surfaces, where cond(F̄) of the kinetic F̄ matrix peaks, and populate
+`intr.kinsing`, `intr.kmsing` and the `intr.kinsing_scan_*` diagnostics. Condition-number peaks are used
+instead of det(F̄) zeros for scale invariance.
+
+Each toroidal-mode block of F̄ is scanned on a dense ψ grid on its own; its local maxima are refined
+by golden-section minimization of -cond and filtered by threshold and the resonance condition. Each
+surface records the (m, n) of the blocks that produced it, and peaks of different n within one scan
+spacing of each other are merged into a single surface.
+"""
+function find_kinetic_singular_surfaces!(
+ mats::MatrixSplines,
+ equil::Equilibrium.PlasmaEquilibrium,
+ intr::ForceFreeStatesInternal;
+ ngrid::Int=2000,
+ cond_threshold::Float64=KINETIC_SINGULAR_COND
+)
+ kin = mats.kinetic
+ kin === nothing && error("find_kinetic_singular_surfaces! requires a kinetic fit; call build_kinetic_matrix_splines first")
+ psilow = equil.profiles.xs[1]
+ psihigh = intr.psilim
+ npert = intr.npert
+
+ # Evaluate cond(F̄) of every n-block on a dense grid
+ psi_grid = collect(range(psilow, psihigh; length=ngrid))
+ block_conds = zeros(ngrid, npert)
+ hint = Ref(1)
+ for i in 1:ngrid
+ try
+ block_conds[i, :] .= fbar_block_conditions(psi_grid[i], kin, equil, intr; hint=hint)
+ catch
+ block_conds[i, :] .= Inf # singular matrix — definitely a kinsing surface
+ end
+ end
+ cond_vals = vec(maximum(block_conds; dims=2))
+
+ # Keep the scan for output, to show why peaks were or were not accepted
+ intr.kinsing_scan_psi = psi_grid
+ intr.kinsing_scan_cond = cond_vals
+ intr.kinsing_scan_threshold = cond_threshold
+
+ # Local maxima of each block's cond(F̄): points where cond increases then decreases
+ is_peak(c, i) = c[i] > c[i-1] && c[i] > c[i+1]
+ block_peaks = [[i for i in 2:(ngrid-1) if is_peak(view(block_conds, :, k), i)] for k in 1:npert]
+
+ # Peaks below threshold mark near-singular structure (the shifted/split resonances of Park &
+ # Logan Eq. 70); report the strongest few so sharp kinetic structure is visible rather than silent.
+ subthreshold = [(i, k) for k in 1:npert for i in block_peaks[k] if KINETIC_RELAXED_FRAC * cond_threshold < block_conds[i, k] <= cond_threshold]
+ if !isempty(subthreshold)
+ top = sort(subthreshold; by=ik -> block_conds[ik...], rev=true)[1:min(3, length(subthreshold))]
+ @info "Kinetic F̄ near-singular structure below the singular threshold at " *
+ join(["ψ=$(round(psi_grid[i]; digits=4)) (n=$(intr.nlow + k - 1), cond=$(round(block_conds[i, k]; sigdigits=3)))" for (i, k) in top], ", ") *
+ " — full scan in SingularSurfaces/Kinetic/scan_cond; check the ψ grid resolves these if results look grid-sensitive"
+ end
+
+ # Refine each block's peaks on that block's condition number
+ found = Tuple{Float64,Int}[] # (ψ, n)
+ for k in 1:npert
+ n = intr.nlow + k - 1
+ for idx in block_peaks[k]
+ block_conds[idx, k] > cond_threshold || continue
+ psi_lo = psi_grid[max(idx - 1, 1)]
+ psi_hi = psi_grid[min(idx + 1, ngrid)]
+ psi_refined = _golden_section_max(psi_lo, psi_hi, psi -> fbar_block_conditions(psi, kin, equil, intr)[k])
+ nq = n * equil.profiles.q_spline(psi_refined)
+ intr.mlow <= nq <= intr.mhigh || continue
+ push!(found, (psi_refined, n))
+ end
+ end
+ sort!(found)
+
+ # Merge peaks of different n that coincide to within one scan spacing (e.g. integer q at n = 1 and 2)
+ dpsi = psi_grid[2] - psi_grid[1]
+ groups = Vector{Vector{Tuple{Float64,Int}}}()
+ for f in found
+ if !isempty(groups) && f[1] - groups[end][1][1] <= dpsi && all(g -> g[2] != f[2], groups[end])
+ push!(groups[end], f)
+ else
+ push!(groups, [f])
+ end
+ end
+
+ kinsing_surfaces = SingType[]
+ for g in groups
+ psi_s = g[1][1]
+ hint_ref = Ref(1)
+ q_val = equil.profiles.q_spline(psi_s; hint=hint_ref)
+ q1_val = equil.profiles.q_deriv(psi_s; hint=hint_ref)
+ ns = [f[2] for f in g]
+ push!(kinsing_surfaces, SingType(; psifac=psi_s, rho=sqrt(psi_s), m=[round(Int, n * q_val) for n in ns], n=ns, q=q_val, q1=q1_val))
+ end
+
+ intr.kinsing = kinsing_surfaces
+ intr.kmsing = length(kinsing_surfaces)
+
+ if intr.kmsing > 0
+ @info "Found $(intr.kmsing) kinetic singular surface(s):"
+ for (i, ks) in enumerate(intr.kinsing)
+ @info @sprintf(" kinsing[%d]: ψ = %.6f, q = %.4f, n = %s", i, ks.psifac, ks.q, join(ks.n, ","))
+ end
+ else
+ @info "No kinetic singular surfaces found (cond threshold = $(cond_threshold))"
+ end
+
+ return nothing
+end
+
+"""
+Golden-section search to find the ψ that maximizes f(ψ) on [a, b].
+"""
+function _golden_section_max(a::Float64, b::Float64, f::Function; tol::Float64=1e-10)
+ gr = (sqrt(5) + 1) / 2
+ c = b - (b - a) / gr
+ d = a + (b - a) / gr
+ for _ in 1:100
+ if abs(b - a) < tol
+ break
+ end
+ if f(c) > f(d)
+ b = d
+ else
+ a = c
+ end
+ c = b - (b - a) / gr
+ d = a + (b - a) / gr
+ end
+ return (a + b) / 2
+end
diff --git a/src/ForceFreeStates/Surfaces/ResistEval.jl b/src/ForceFreeStates/Surfaces/ResistEval.jl
new file mode 100644
index 0000000000..9e3ae70790
--- /dev/null
+++ b/src/ForceFreeStates/Surfaces/ResistEval.jl
@@ -0,0 +1,198 @@
+# Per-singular-surface Glasser-Greene-Johnson geometric coefficients (E, F, G, H, K, M) and the flux-surface
+# averages needed for τ_A / τ_R, the toroidal critical-Δ factor and neoclassical resistivity.
+#
+# θ-integrands, each weighted by `jac / v1` before integration (1-6 follow Fortran `resist_eval`):
+# 1: B² / |∇ψ|² 2: 1 / |∇ψ|² 3: 1 / B² 4: 1 / (B² · |∇ψ|²) 5: B² 6: |∇ψ|² / B²
+# 7: B (for the Lin-Liu & Miller 1995 trapped fraction) 8: |∇ψ|² (toroidal critical-Δ, ⟨|∇V|²⟩ = v1²⟨|∇ψ_N|²⟩)
+
+"""
+ ResistGeometry
+
+Per-singular-surface Glasser-Greene-Johnson geometric coefficients and
+supporting flux-surface averages. All averages ⟨·⟩ are normalized flux-surface
+averages (⟨1⟩ = 1), and `‖∇ψ_N‖` is the gradient of the normalized poloidal flux.
+
+| field | meaning |
+|:--------------------- |:-------------------------------------------------------- |
+| `E`, `F` | Glasser interchange parameters (enter `D_I = E+F+H-¼`) |
+| `G` | Coupling coefficient (curvature × pressure gradient) |
+| `H` | Pfirsch-Schlüter coefficient |
+| `K` | Glasser parameter |
+| `M` | Mass factor |
+| `avg_bsq_over_dpsisq` | ⟨B²/‖∇ψ_N‖²⟩ — needed for τ_R |
+| `avg_bsq` | ⟨B²⟩ — needed for τ_R |
+| `avg_dpsisq` | ⟨‖∇ψ_N‖²⟩ — needed for the toroidal critical-Δ |
+| `f_trap` | Lin-Liu & Miller 1995 trapped-particle fraction |
+| `R_major` | major radius (R_max + R_min)/2 over the surface, in m |
+| `eps_local` | (R_max − R_min)/2 / R_major — local inverse aspect ratio |
+| `p_local` | Plasma pressure at this surface [Pa] |
+| `p1_local` | dp/dψ at this surface |
+| `v1_local` | dV/dψ at this surface |
+
+`H` equals the `H` from `mercier_scan!` (`LocalStability/h`). `f_trap`, `R_major` and `eps_local` feed
+`NeoclassicalResistivity.eta_neoclassical` (Sauter, Angioni & Lin-Liu 1999, Phys. Plasmas 6, 2834;
+Lin-Liu & Miller 1995, Phys. Plasmas 2, 1666).
+"""
+struct ResistGeometry
+ E::Float64
+ F::Float64
+ G::Float64
+ H::Float64
+ K::Float64
+ M::Float64
+ avg_bsq_over_dpsisq::Float64
+ avg_bsq::Float64
+ avg_dpsisq::Float64
+ f_trap::Float64
+ R_major::Float64
+ eps_local::Float64
+ p_local::Float64
+ p1_local::Float64
+ v1_local::Float64
+end
+
+"""
+ resist_geometry(equil, psifac, q1; gamma=5/3) -> ResistGeometry
+
+Glasser, Greene & Johnson 1975 (Phys. Fluids 18, 875) resistive-layer coefficients at `psifac`,
+geometric part only (no η or ρ); `ggj_parameters` adds τ_A and τ_R. Port of Fortran RDCON `resist_eval`.
+
+# Arguments
+
+ - `equil::PlasmaEquilibrium` — the fully-solved equilibrium
+ - `psifac` — normalized flux coordinate of the singular surface
+ - `q1` — dq/dψ at this surface (from `SingType.q1`)
+
+# Keyword arguments
+
+ - `gamma` — adiabatic index (default 5/3)
+
+!!! note "Contract"
+
+ `psifac` must be an interior surface (`0 < ψ < 1`) with nonzero `q1`, `p1 = dp/dψ` and `p`; the axis,
+ a flat-pressure or a zero-shear surface gives `Inf`/`NaN`.
+"""
+function resist_geometry(equil::Equilibrium.PlasmaEquilibrium,
+ psifac::Real, q1::Real; gamma::Real=5 / 3)
+ profiles = equil.profiles
+ twopi = 2π
+ chi1 = twopi * equil.psio
+ psi_f = Float64(psifac)
+
+ twopif = profiles.F_spline(psi_f)
+ p = profiles.P_spline(psi_f)
+ p1 = profiles.P_deriv(psi_f)
+ v1 = profiles.dVdpsi_spline(psi_f)
+ v2 = profiles.dVdpsi_deriv(psi_f)
+ q = profiles.q_spline(psi_f)
+
+ # θ-integrands (see file header) plus running extrema of B and R for f_trap and ε.
+ ntheta = length(equil.rzphi_ys)
+ ff = zeros(Float64, ntheta, 8)
+ B_max = -Inf
+ B_min = Inf
+ R_max = -Inf
+ R_min = Inf
+ for itheta in 1:ntheta
+ theta = equil.rzphi_ys[itheta]
+ f1 = equil.rzphi_rsquared((psi_f, theta))
+ f2 = equil.rzphi_offset((psi_f, theta))
+ jac = equil.rzphi_jac((psi_f, theta))
+ fy1 = FastInterpolations.deriv_view(equil.rzphi_rsquared, (0, 1))((psi_f, theta))
+ fy2 = FastInterpolations.deriv_view(equil.rzphi_offset, (0, 1))((psi_f, theta))
+ fy3 = FastInterpolations.deriv_view(equil.rzphi_nu, (0, 1))((psi_f, theta))
+
+ rfac = sqrt(f1)
+ eta = twopi * (theta + f2)
+ r = equil.ro + rfac * cos(eta)
+
+ v21 = fy1 / (2 * rfac * jac)
+ v22 = (1 + fy2) * twopi * rfac / jac
+ v23 = fy3 * r / jac
+ v33 = twopi * r / jac
+ bsq = chi1^2 * (v21^2 + v22^2 + (v23 + q * v33)^2)
+ dpsisq = (twopi * r)^2 * (v21^2 + v22^2)
+
+ B_here = sqrt(bsq)
+ B_max = max(B_max, B_here)
+ B_min = min(B_min, B_here)
+ R_max = max(R_max, r)
+ R_min = min(R_min, r)
+
+ ff[itheta, 1] = bsq / dpsisq
+ ff[itheta, 2] = 1.0 / dpsisq
+ ff[itheta, 3] = 1.0 / bsq
+ ff[itheta, 4] = 1.0 / (bsq * dpsisq)
+ ff[itheta, 5] = bsq
+ ff[itheta, 6] = dpsisq / bsq
+ ff[itheta, 7] = B_here
+ ff[itheta, 8] = dpsisq
+ @views ff[itheta, :] .*= jac / v1
+ end
+ # Snap the repeated endpoint exactly equal to the start
+ @views ff[end, :] .= ff[1, :]
+
+ # Periodic cubic-spline θ-integral of each column, as in Mercier.jl
+ itp = cubic_interp(equil.rzphi_ys, Series(ff); bc=PeriodicBC())
+ avg = FastInterpolations.integrate(itp)
+ avg_B = avg[7]
+ R_major = 0.5 * (R_max + R_min)
+ eps_local = R_major > 0 ? 0.5 * (R_max - R_min) / R_major : 0.0
+ f_trap = Utilities.NeoclassicalResistivity.trapped_fraction(avg_B, avg[5], B_min, B_max)
+
+ # GGJ coefficients (Fortran RDCON resist_eval)
+ E_coef = p1 * v1 / (q1 * chi1^2)^2 * avg[1] *
+ (twopif * q1 * chi1 / avg[5] - v2)
+ F_coef = (p1 * v1 / (q1 * chi1^2))^2 *
+ (avg[1] * avg[3] + (twopif / chi1)^2 *
+ (avg[1] * avg[4] - avg[2]^2))
+ H_coef = twopif * p1 * v1 / (q1 * chi1^3) * (avg[2] - avg[1] / avg[5])
+ M_coef = avg[1] *
+ (avg[6] + (twopif / chi1)^2 * (avg[3] - 1.0 / avg[5]))
+ G_coef = avg[5] / (M_coef * gamma * p)
+ K_coef = (q1 * chi1^2 / (p1 * v1))^2 *
+ avg[5] / (M_coef * avg[1])
+
+ return ResistGeometry(
+ E_coef, F_coef, G_coef, H_coef, K_coef, M_coef,
+ avg[1], avg[5], avg[8],
+ f_trap, R_major, eps_local,
+ p, p1, v1
+ )
+end
+
+"""
+ ggj_parameters(sing, equil; eta, rho, gamma=5/3, ising=0) -> InnerLayer.GGJParameters
+
+GGJ layer parameters at `sing` from its `restype` geometry and the local η (Ω·m) and ρ (kg/m³).
+"""
+function ggj_parameters(sing::SingType, equil::Equilibrium.PlasmaEquilibrium;
+ eta::Real, rho::Real, gamma::Real=5 / 3, ising::Int=0)
+ rg = sing.restype
+ rg === nothing && throw(ArgumentError("ggj_parameters: the surface at ψ=$(sing.psifac) has restype = nothing; run resist_eval_all! first"))
+ equil.params.volume === nothing && throw(ArgumentError("ggj_parameters: equil.params.volume is nothing"))
+ MU_0 = Utilities.PhysicalConstants.MU_0
+ chi1 = 2π * equil.psio
+ taua = sqrt(rho * rg.M * MU_0) / abs(2π * Int(sing.n[1]) * sing.q1 * chi1 / rg.v1_local)
+ taur = (rg.avg_bsq_over_dpsisq / rg.avg_bsq) * MU_0 / eta
+ G = rg.avg_bsq / (rg.M * gamma * rg.p_local)
+ return InnerLayer.GGJParameters(; E=rg.E, F=rg.F, G=G, H=rg.H, K=rg.K, M=rg.M,
+ taua=taua, taur=taur, v1=rg.v1_local / equil.params.volume, ising=ising)
+end
+
+"""
+ resist_eval_all!(intr::ForceFreeStatesInternal, equil; gamma=5/3)
+
+Populate `sing.restype` for every `SingType` in `intr.sing` using
+`resist_geometry`. No-op for surfaces whose `restype` has already been
+filled.
+"""
+function resist_eval_all!(intr::ForceFreeStatesInternal,
+ equil::Equilibrium.PlasmaEquilibrium;
+ gamma::Real=5 / 3)
+ for sing in intr.sing
+ sing.restype === nothing || continue
+ sing.restype = resist_geometry(equil, sing.psifac, sing.q1; gamma=gamma)
+ end
+ return intr
+end
diff --git a/src/ForceFreeStates/Surfaces/Types.jl b/src/ForceFreeStates/Surfaces/Types.jl
new file mode 100644
index 0000000000..0099590ab1
--- /dev/null
+++ b/src/ForceFreeStates/Surfaces/Types.jl
@@ -0,0 +1,58 @@
+# Singular-surface data types shared across subsystems.
+
+"""
+ SingType
+
+A mutable struct holding data related to the singular surfaces in the equilibrium.
+
+## Fields
+
+ - `psifac::Float64` - Normalized flux coordinate at the singular surface
+ - `rho::Float64` - Radial coordinate (√ψ)
+ - `m::Vector{Int}` - Poloidal mode number(s)
+ - `n::Vector{Int}` - Toroidal mode number(s)
+ - `q::Float64` - Safety factor (= m/n)
+ - `q1::Float64` - Derivative of safety factor with respect to ψ
+ - `delta_prime::Vector{ComplexF64}` - **Debug stub, not physically valid.** Per-surface ca-based Δ' estimate;
+ use `ForceFreeStatesInternal.delta_prime_matrix` (STRIDE global BVP, Glasser 2018 PoP 25, 032501) for tearing stability.
+ - `delta_prime_col::Matrix{ComplexF64}` - **Debug stub, not physically valid.** Per-surface ca-based Δ' columns, `(numpert_total, n_res_modes)`,
+ `delta_prime_col[j, i] = (ca_r[j,ipert_res_i,2] - ca_l[j,ipert_res_i,2]) / (4π²·psio)`; diagonal matches `delta_prime`. Riccati/parallel paths only.
+"""
+@kwdef mutable struct SingType
+ psifac::Float64 = 0.0
+ rho::Float64 = 0.0
+ m::Vector{Int} = Int[]
+ n::Vector{Int} = Int[]
+ q::Float64 = 0.0
+ q1::Float64 = 0.0
+ delta_prime::Vector{ComplexF64} = ComplexF64[]
+ delta_prime_col::Matrix{ComplexF64} = Matrix{ComplexF64}(undef, 0, 0)
+ ua_left::Array{ComplexF64,3} = Array{ComplexF64}(undef, 0, 0, 0) # asymptotic basis at left inner-layer boundary
+ ua_right::Array{ComplexF64,3} = Array{ComplexF64}(undef, 0, 0, 0) # asymptotic basis at right inner-layer boundary
+ psi_ua_left::Float64 = 0.0 # ψ where ua_left was evaluated (left inner-layer boundary)
+ psi_ua_right::Float64 = 0.0 # ψ where ua_right was evaluated (right inner-layer boundary)
+ restype::Any = nothing # ResistGeometry from ResistEval.jl (populated by resist_eval_all!); typed `Any` to avoid a cross-file type reference
+end
+
+"""
+ SingAsymptotics
+
+Frobenius asymptotic expansion at one side of a singular surface, built by `compute_sing_asymptotics`.
+
+## Fields
+
+ - `sing_order::Int` - Frobenius expansion order
+ - `alpha::Vector{ComplexF64}` - Mercier exponent α = √(tr²/4 − det) of each resonant block.
+ - `r1::Vector{Int}` - Resonant indices along first index
+ - `r2::Vector{Int}` - Resonant indices along second index
+ - `power::Vector{ComplexF64}` - Frobenius power of each column in |ψ − ψ_s| (0 off resonance). Resonant powers are sig·λ of that side's M₀ block, big solution (more negative real part) first.
+ - `vmat::Array{ComplexF64,4}` - Power series of V matrix for asymptotic analysis
+"""
+struct SingAsymptotics
+ sing_order::Int
+ alpha::Vector{ComplexF64}
+ r1::Vector{Int}
+ r2::Vector{Int}
+ power::Vector{ComplexF64}
+ vmat::Array{ComplexF64,4}
+end
diff --git a/src/ForceFreeStates/Utils.jl b/src/ForceFreeStates/Utils.jl
new file mode 100644
index 0000000000..b7948380af
--- /dev/null
+++ b/src/ForceFreeStates/Utils.jl
@@ -0,0 +1,117 @@
+"""
+ resize_storage!(odet::OdeState)
+
+Double the length of `u_store`, `psi_store` and `q_store`, keeping the stored steps. The derivative
+stores are not grown here; `materialize_derivative_stores!` fills them at exact size after integration.
+"""
+function resize_storage!(odet::OdeState)
+ oldlen = size(odet.u_store, 4)
+ newlen = 2 * oldlen
+
+ u_new = Array{ComplexF64,4}(undef, odet.numpert_total, odet.numpert_total, 2, newlen)
+ psi_new = Vector{Float64}(undef, newlen)
+ q_new = Vector{Float64}(undef, newlen)
+
+ u_new[:, :, :, 1:odet.step] = odet.u_store[:, :, :, 1:odet.step]
+ psi_new[1:odet.step] = odet.psi_store[1:odet.step]
+ q_new[1:odet.step] = odet.q_store[1:odet.step]
+
+ odet.u_store = u_new
+ odet.psi_store = psi_new
+ odet.q_store = q_new
+end
+
+"""
+ trim_storage!(odet::OdeState)
+
+Trim `u_store`, `psi_store` and `q_store` to the current step count. The derivative stores are left
+alone: they are either empty (filled later by `materialize_derivative_stores!`) or already exact-size.
+"""
+function trim_storage!(odet::OdeState)
+ resize!(odet.psi_store, odet.step)
+ resize!(odet.q_store, odet.step)
+ odet.u_store = odet.u_store[:, :, :, 1:odet.step]
+end
+
+"""
+ truncate_integration!(odet, intr, equil, step)
+
+Make stored step `step` the plasma edge, resetting every piece of state derived from the old one:
+the stores, the fixups recorded beyond it, the edge limits, and the rational surfaces outside it.
+"""
+function truncate_integration!(odet::OdeState, intr::ForceFreeStatesInternal, equil::Equilibrium.PlasmaEquilibrium, step::Int)
+ odet.step = step
+ trim_storage!(odet)
+ # fixstep is nondecreasing; a fixup at fixstep == step was applied after the last stored step.
+ odet.ifix = count(<(step), view(odet.fixstep, 1:odet.ifix))
+ @views odet.u .= odet.u_store[:, :, :, end]
+ odet.psifac, odet.q = odet.psi_store[end], odet.q_store[end]
+ intr.psilim, intr.qlim = odet.psifac, odet.q
+ intr.q1lim = equil.profiles.q_deriv(intr.psilim)
+ keep = remove_singular_surfs!(intr)
+ odet.ca_l, odet.ca_r = odet.ca_l[:, :, :, keep], odet.ca_r[:, :, :, keep]
+ return odet
+end
+
+"""
+ store_ode_data!(odet::OdeState, psi::Float64, u)
+
+Save the current integration state at `psi`: `u` plus `odet.q`, which callers set for the
+accepted point. Derivatives are not stored — `materialize_derivative_stores!` recomputes
+them from `(psi_store, u_store)` after integration, where they are actually consumed.
+"""
+function store_ode_data!(odet::OdeState, psi::Float64, u)
+ if odet.step >= size(odet.u_store, 4)
+ resize_storage!(odet)
+ end
+ odet.psi_store[odet.step] = psi
+ odet.q_store[odet.step] = odet.q
+ @views odet.u_store[:, :, :, odet.step] .= u
+ odet.step += 1
+end
+
+"""
+ materialize_derivative_stores!(odet, equil, mats, intr) -> Bool
+
+Fill `odet.du_store` (dΞ_ψ/dψ) and `odet.xi_s_store` from the stored solution, returning
+whether they hold valid data afterwards. Idempotent: a no-op when `du_store_populated` is
+already true, so the galerkin-matched path keeps its analytic derivatives.
+
+Derivatives are recomputed rather than accumulated during integration because they are
+needed only at saved nodes, not at every Runge-Kutta stage. Recomputing after the Gaussian
+fixup transforms and the free-boundary normalization is exact rather than merely close: the
+Euler-Lagrange system is linear in `u`, and both operations right-multiply the solution by a
+mixing matrix `T`, so `du(ψ, u·T) = du(ψ, u)·T`.
+
+Returns `false` without allocating when there is nothing to work from — no `mats`, no stored
+steps, or a solution held in a basis the Euler-Lagrange kernel does not apply to (the sparse
+parallel path, which stores chunk-endpoint Riccati matrices).
+"""
+function materialize_derivative_stores!(
+ odet::OdeState,
+ equil::Equilibrium.PlasmaEquilibrium,
+ mats::Union{MatrixSplines,Nothing},
+ intr::ModeSpace
+)
+ odet.du_store_populated && return true
+ (isnothing(mats) || odet.step == 0 || isempty(odet.u_store) || !odet.u_store_el_basis) && return false
+
+ kinetic = mats.kinetic !== nothing
+ nstep = min(odet.step, size(odet.u_store, 4))
+ npert = odet.numpert_total
+ odet.du_store = Array{ComplexF64}(undef, npert, npert, nstep)
+ odet.xi_s_store = Array{ComplexF64}(undef, npert, npert, nstep)
+
+ du = zeros(ComplexF64, npert, npert, 2)
+ u = zeros(ComplexF64, npert, npert, 2)
+ @views for istep in 1:nstep
+ u .= odet.u_store[:, :, :, istep]
+ odet.q = el_derivatives!(du, u, kinetic, equil, mats, intr, odet.psi_store[istep], odet.spline_hint, odet.mats_hint)
+ odet.du_store[:, :, istep] .= du[:, :, 1]
+ compute_node_xi_s!(odet.xi_s_store[:, :, istep], du[:, :, 1], u[:, :, 1], mats, odet.psi_store[istep];
+ kinetic=kinetic, hint=odet.mats_hint)
+ end
+
+ odet.du_store_populated = true
+ return true
+end
diff --git a/src/ForcingTerms/BiotSavart.jl b/src/ForcingTerms/BiotSavart.jl
new file mode 100644
index 0000000000..697ee3b5fa
--- /dev/null
+++ b/src/ForcingTerms/BiotSavart.jl
@@ -0,0 +1,254 @@
+"""
+ BiotSavart
+
+Biot-Savart field calculation for 3D coil geometries.
+
+Each conductor is a polyline of straight filament segments, and each segment contributes
+its exact field (Hanson & Hirshman 2002, Phys. Plasmas 9, 4410, Eq. 8; SI units):
+
+ B⃗ = (μ₀/4π) × I × nw × 2(Rᵢ + R_f) / (Rᵢ R_f ((Rᵢ + R_f)² - L²)) × (dl⃗ × R⃗ᵢ)
+
+where μ₀/4π = 1e-7 [T⋅m/A], I is the current [A], nw is the winding multiplier,
+dl⃗ is the segment vector of length L, and R⃗ᵢ, R⃗_f are the displacements from the
+segment start and end to the observation point, with lengths Rᵢ and R_f.
+"""
+
+const MU0_OVER_4PI = 1e-7 # T⋅m/A
+
+# Minimum squared distance [m²] from a segment (r ~ 1 μm) below which its contribution is
+# skipped; avoids the singularity when an observation point lies on a conductor.
+const BIOT_SAVART_MIN_DIST_SQ = 1e-12
+
+"""
+ _segment_field(rx, ry, rz, dlx, dly, dlz, len) -> (bx, by, bz)
+
+Exact field of a straight unit-current filament segment of vector `dl⃗` and length `len`,
+without the μ₀/4π prefactor, at displacement `r⃗` from the segment start
+(Hanson & Hirshman 2002, Eq. 8). With ε = Rᵢ + R_f - L, the effective squared distance
+ρ² = 2RᵢR_f ε / (Rᵢ + R_f) reduces to the perpendicular distance squared near the
+segment, so the contribution is zero for ρ² below `BIOT_SAVART_MIN_DIST_SQ`.
+"""
+@inline function _segment_field(rx::Float64, ry::Float64, rz::Float64,
+ dlx::Float64, dly::Float64, dlz::Float64, len::Float64)
+ ri = sqrt(rx * rx + ry * ry + rz * rz)
+ fx = rx - dlx
+ fy = ry - dly
+ fz = rz - dlz
+ rf = sqrt(fx * fx + fy * fy + fz * fz)
+ sum_r = ri + rf
+ rho2_num = 2 * ri * rf * (sum_r - len)
+ # Guard: zero contribution if observer is on conductor (avoids Inf/NaN)
+ on_wire = rho2_num <= BIOT_SAVART_MIN_DIST_SQ * sum_r
+ factor = ifelse(on_wire, 0.0, 4 * sum_r / (ifelse(on_wire, 1.0, rho2_num) * (sum_r + len)))
+ return (dly * rz - dlz * ry) * factor, (dlz * rx - dlx * rz) * factor, (dlx * ry - dly * rx) * factor
+end
+
+"""
+ PrecomputedSegments
+
+Pre-computed segment vectors, lengths and start points for one conductor strand, stored
+in contiguous arrays for cache-friendly access in the inner Biot-Savart loop.
+"""
+struct PrecomputedSegments
+ dlx::Vector{Float64}
+ dly::Vector{Float64}
+ dlz::Vector{Float64}
+ len::Vector{Float64}
+ x0::Vector{Float64}
+ y0::Vector{Float64}
+ z0::Vector{Float64}
+ prefactor::Float64 # MU0_OVER_4PI * current * nw
+ nseg::Int
+end
+
+"""
+ precompute_segments(cs, j, k, current_nw) → PrecomputedSegments
+
+Build contiguous segment-vector, length and start-point arrays for strand `(j,k)` of coil set `cs`.
+"""
+function precompute_segments(cs::CoilSet, j::Int, k::Int, current_nw::Float64)
+ nsec = cs.nsec
+ nseg = nsec - 1
+ dlx = Vector{Float64}(undef, nseg)
+ dly = Vector{Float64}(undef, nseg)
+ dlz = Vector{Float64}(undef, nseg)
+ len = Vector{Float64}(undef, nseg)
+ x0 = Vector{Float64}(undef, nseg)
+ y0 = Vector{Float64}(undef, nseg)
+ z0 = Vector{Float64}(undef, nseg)
+
+ @inbounds for l in 1:nseg
+ x1 = cs.x[j, k, l]
+ x2 = cs.x[j, k, l+1]
+ y1 = cs.y[j, k, l]
+ y2 = cs.y[j, k, l+1]
+ z1 = cs.z[j, k, l]
+ z2 = cs.z[j, k, l+1]
+ dlx[l] = x2 - x1
+ dly[l] = y2 - y1
+ dlz[l] = z2 - z1
+ len[l] = sqrt(dlx[l]^2 + dly[l]^2 + dlz[l]^2)
+ x0[l] = x1
+ y0[l] = y1
+ z0[l] = z1
+ end
+
+ return PrecomputedSegments(dlx, dly, dlz, len, x0, y0, z0,
+ MU0_OVER_4PI * current_nw, nseg)
+end
+
+"""
+ accumulate_strand_field!(Bx, By, Bz, i, obs_x, obs_y, obs_z, xs, ys, zs, current_nw)
+
+Accumulate the Biot-Savart contribution from one conductor strand onto observation point `i`.
+
+Each straight segment from point `l` to `l+1` contributes its exact filament field,
+see `_segment_field`.
+
+## Arguments
+
+ - `Bx`, `By`, `Bz`: pre-allocated output arrays (Cartesian field, Tesla); updated in-place
+ - `i`: observation point index
+ - `obs_x/y/z`: observer Cartesian coordinates [m]
+ - `xs`, `ys`, `zs`: strand point coordinates [nsec], Cartesian [m]
+ - `current_nw`: effective current = I × nw [A⋅turns]
+"""
+function accumulate_strand_field!(
+ Bx::AbstractVector{Float64},
+ By::AbstractVector{Float64},
+ Bz::AbstractVector{Float64},
+ i::Int,
+ obs_x::Float64, obs_y::Float64, obs_z::Float64,
+ xs::AbstractVector{Float64},
+ ys::AbstractVector{Float64},
+ zs::AbstractVector{Float64},
+ current_nw::Float64
+)
+ nsec = length(xs)
+ prefactor = MU0_OVER_4PI * current_nw
+
+ @inbounds for l in 1:(nsec-1)
+ # Segment vector dl⃗
+ dlx = xs[l+1] - xs[l]
+ dly = ys[l+1] - ys[l]
+ dlz = zs[l+1] - zs[l]
+
+ # Displacement r⃗ from segment start to observer
+ rx = obs_x - xs[l]
+ ry = obs_y - ys[l]
+ rz = obs_z - zs[l]
+
+ bx, by, bz = _segment_field(rx, ry, rz, dlx, dly, dlz, sqrt(dlx * dlx + dly * dly + dlz * dlz))
+ Bx[i] += bx * prefactor
+ By[i] += by * prefactor
+ Bz[i] += bz * prefactor
+ end
+end
+
+"""
+ _accumulate_precomputed(ox, oy, oz, seg) -> (dbx, dby, dbz)
+
+Sum the exact segment fields of one `PrecomputedSegments` strand at `(ox, oy, oz)`, scaled by its prefactor.
+"""
+@inline function _accumulate_precomputed(
+ ox::Float64, oy::Float64, oz::Float64,
+ seg::PrecomputedSegments
+)
+ bx_acc = 0.0
+ by_acc = 0.0
+ bz_acc = 0.0
+ pf = seg.prefactor
+
+ @inbounds @simd for l in 1:seg.nseg
+ bx, by, bz = _segment_field(ox - seg.x0[l], oy - seg.y0[l], oz - seg.z0[l],
+ seg.dlx[l], seg.dly[l], seg.dlz[l], seg.len[l])
+ bx_acc += bx
+ by_acc += by
+ bz_acc += bz
+ end
+
+ return bx_acc * pf, by_acc * pf, bz_acc * pf
+end
+
+"""
+ compute_biot_savart_boundary!(B_R, B_phi, B_Z, obs_R, obs_phi, obs_Z, coil_sets)
+
+Compute the total Biot-Savart field from all coil sets at every observation point.
+
+Observation points are specified in cylindrical coordinates `(R, φ, Z)` and the
+returned field components are also cylindrical.
+
+Threaded over observation points; strands with zero current are skipped.
+
+## Arguments
+
+ - `B_R`, `B_phi`, `B_Z`: output field arrays [Tesla], length `nobs`; overwritten
+ - `obs_R`, `obs_phi`, `obs_Z`: observation point cylindrical coordinates [m, rad, m]
+ - `coil_sets`: conductor geometry and current data
+"""
+function compute_biot_savart_boundary!(
+ B_R::AbstractVector{Float64},
+ B_phi::AbstractVector{Float64},
+ B_Z::AbstractVector{Float64},
+ obs_R::AbstractVector{Float64},
+ obs_phi::AbstractVector{Float64},
+ obs_Z::AbstractVector{Float64},
+ coil_sets::Vector{CoilSet}
+)
+ nobs = length(obs_R)
+ @assert length(obs_phi) == nobs && length(obs_Z) == nobs
+ @assert length(B_R) == nobs && length(B_phi) == nobs && length(B_Z) == nobs
+
+ # Segment geometry for all strands carrying current
+ all_segments = PrecomputedSegments[]
+ for cs in coil_sets
+ for j in 1:cs.ncoil
+ I_nw = cs.currents[j] * cs.nw
+ iszero(I_nw) && continue
+ for k in 1:cs.s
+ push!(all_segments, precompute_segments(cs, j, k, I_nw))
+ end
+ end
+ end
+
+ # sincos for the cylindrical ↔ Cartesian conversion
+ cos_phi = Vector{Float64}(undef, nobs)
+ sin_phi = Vector{Float64}(undef, nobs)
+ obs_x = Vector{Float64}(undef, nobs)
+ obs_y = Vector{Float64}(undef, nobs)
+
+ @inbounds for i in 1:nobs
+ sp, cp = sincos(obs_phi[i])
+ sin_phi[i] = sp
+ cos_phi[i] = cp
+ obs_x[i] = obs_R[i] * cp
+ obs_y[i] = obs_R[i] * sp
+ end
+
+ Threads.@threads for i in 1:nobs
+ @inbounds begin
+ ox = obs_x[i]
+ oy = obs_y[i]
+ oz = obs_Z[i]
+ bx_total = 0.0
+ by_total = 0.0
+ bz_total = 0.0
+
+ for seg in all_segments
+ dbx, dby, dbz = _accumulate_precomputed(ox, oy, oz, seg)
+ bx_total += dbx
+ by_total += dby
+ bz_total += dbz
+ end
+
+ # Cartesian → cylindrical
+ cp = cos_phi[i]
+ sp = sin_phi[i]
+ B_R[i] = bx_total * cp + by_total * sp
+ B_phi[i] = -bx_total * sp + by_total * cp
+ B_Z[i] = bz_total
+ end
+ end
+end
+
+export accumulate_strand_field!, compute_biot_savart_boundary!
diff --git a/src/ForcingTerms/CoilFourier.jl b/src/ForcingTerms/CoilFourier.jl
new file mode 100644
index 0000000000..524737b712
--- /dev/null
+++ b/src/ForcingTerms/CoilFourier.jl
@@ -0,0 +1,442 @@
+"""
+ CoilFourier
+
+Converts coil Biot-Savart fields on the plasma boundary into Fourier mode amplitudes
+suitable for the perturbed equilibrium pipeline.
+
+## Pipeline
+- `sample_boundary_grid` — evaluate (R, Z) and unit-norm metric on the plasma boundary
+- `CoilForcingGrid` — the boundary grid with its observation points laid out, shared by every coil evaluation
+- `compute_biot_savart_boundary!` (BiotSavart.jl) — compute B at all grid points
+- `project_normal_flux!` — compute flux Φ_x = 2π×R×(B_R ∂Z/∂θ − B_Z ∂R/∂θ)
+- `fourier_decompose_bn` — 2D Fourier decompose to get bmn amplitudes
+- `coil_forcing_modes` — Biot-Savart → projection → decomposition for any coil set(s) on a `CoilForcingGrid`
+- `compute_coil_forcing_modes!` — top-level entry point combining all steps for a whole assembly
+"""
+
+using FastInterpolations: cubic_interp, PeriodicBC, DerivOp
+
+# Default toroidal points per period when nzeta_coil is not specified
+const NZETA_POINTS_PER_PERIOD = 32
+
+"""
+ BoundaryGrid
+
+Pre-computed plasma boundary grid for evaluating coil fields.
+
+## Fields
+
+ - `mtheta`, `nzeta`: grid dimensions
+ - `R`, `Z`: cylindrical coordinates `[mtheta]` (same for all ζ, axisymmetric)
+ - `phi_grid`: base toroidal angle grid `[nzeta]` in radians = `-helicity × 2π × j/nzeta`
+ - `phi_offset`: per-θ toroidal angle correction `[mtheta]` from SFL coordinates:
+ `ν(ψ, θ)` scaled by `-helicity`, so the physical toroidal angle at `(i, j)` is
+ `phi_grid[j] + phi_offset[i]`, as Fortran's `phi = -helicity*(2π*ζ + dphi(ψ,θ))`
+ - `dR_dtheta`, `dZ_dtheta`: poloidal derivatives w.r.t. unit-norm angle θ_norm ∈ [0,1]
+ `dR_dtheta[i] = dR/dθ_norm = 2π × dR/dθ_phys`
+"""
+struct BoundaryGrid
+ mtheta::Int
+ nzeta::Int
+ R::Vector{Float64}
+ Z::Vector{Float64}
+ phi_grid::Vector{Float64}
+ phi_offset::Vector{Float64}
+ dR_dtheta::Vector{Float64}
+ dZ_dtheta::Vector{Float64}
+end
+
+"""
+ sample_boundary_grid(equil, mtheta, nzeta; psi=equil.rzphi_xs[end]) -> BoundaryGrid
+
+Evaluate the plasma geometry on a uniform `mtheta × nzeta` grid on the flux surface `psi`, from the
+`equil.rzphi_rsquared`, `rzphi_offset` and `rzphi_nu` splines. dR/dθ_norm and dZ/dθ_norm (θ_norm ∈ [0,1])
+come from periodic cubic splines of R and Z.
+
+The default `psi` is the outermost computed surface `psihigh`, the last knot of the geometry splines;
+ψ_N = 1 would extrapolate them and can drive `rzphi_rsquared` negative. The physical control surface is
+`psilim` (Fortran evaluates the coil field there, `field_bs_psi`), which lies inside `psihigh` when edge
+truncation fires: pass `psi = psilim` whenever a ForceFreeStates solve is at hand, as the production paths do.
+
+Toroidal grid direction (Fortran GPEC convention): `phi_j = -helicity × 2π × j/nzeta`, with
+`helicity = sign(Bt) × sign(Ip)` from `equil.params.bt_sign` and `equil.params.ip_sign`.
+"""
+function sample_boundary_grid(equil::Equilibrium.PlasmaEquilibrium, mtheta::Int, nzeta::Int;
+ psi::Float64=equil.rzphi_xs[end])
+ # Build uniform theta grid (same convention as equil.rzphi_ys, but potentially finer)
+ theta_grid = range(0; length=mtheta, step=1.0 / mtheta)
+
+ R_arr = zeros(mtheta)
+ Z_arr = zeros(mtheta)
+ hint2d = (Ref(1), Ref(1))
+
+ for (i, θ_sfl) in enumerate(theta_grid)
+ r_minor = sqrt(equil.rzphi_rsquared((psi, θ_sfl); hint=hint2d))
+ θ_cyl = 2π * (θ_sfl + equil.rzphi_offset((psi, θ_sfl); hint=hint2d))
+ R_arr[i] = equil.ro + r_minor * cos(θ_cyl)
+ Z_arr[i] = equil.zo + r_minor * sin(θ_cyl)
+ end
+
+ # Compute dR/dθ_norm and dZ/dθ_norm via periodic cubic splines on the boundary contour.
+ # Use unit-norm θ_norm ∈ [0,1] as the spline x-axis (matches equilibrium convention).
+ spline_R = cubic_interp(theta_grid, R_arr; bc=PeriodicBC(; endpoint=:exclusive, period=1.0))
+ spline_Z = cubic_interp(theta_grid, Z_arr; bc=PeriodicBC(; endpoint=:exclusive, period=1.0))
+
+ dR_dθ = zeros(mtheta)
+ dZ_dθ = zeros(mtheta)
+ hint_R = Ref(1)
+ hint_Z = Ref(1)
+ for i in 1:mtheta
+ dR_dθ[i] = spline_R(theta_grid[i]; deriv=DerivOp(1), hint=hint_R) # dR/dθ_norm
+ dZ_dθ[i] = spline_Z(theta_grid[i]; deriv=DerivOp(1), hint=hint_Z) # dZ/dθ_norm
+ end
+
+ # Toroidal grid direction: phi_j = -helicity × 2π × j/nzeta (Fortran convention)
+ helicity = equil.params.bt_sign * equil.params.ip_sign
+ phi_grid = collect(range(0; length=nzeta, step=(-helicity * 2π / nzeta)))
+
+ # SFL toroidal offset: φ_phys = -helicity*(2π*ζ_SFL + ν(ψ,θ_SFL)), as Fortran's phi = -helicity*(twopi*czeta + crzphi_f(3))
+ phi_offset = zeros(mtheta)
+ hint_nu = (Ref(1), Ref(1))
+ for (i, θ_sfl) in enumerate(theta_grid)
+ phi_offset[i] = -helicity * equil.rzphi_nu((psi, θ_sfl); hint=hint_nu)
+ end
+
+ return BoundaryGrid(mtheta, nzeta, R_arr, Z_arr, phi_grid, phi_offset, dR_dθ, dZ_dθ)
+end
+
+"""
+ project_normal_flux!(bn, B_R, B_Z, grid)
+
+Project the cylindrical magnetic field (B_R, B_Z) onto the plasma boundary normal
+direction ∇ψ and store in `bn[mtheta, nzeta]`.
+
+Computes the unit-norm flux element Phi_x per (θ_norm, ζ_norm) cell [T·m²]:
+bn(θ_norm, ζ_norm) = 2π × R(θ_norm) × (B_R × ∂Z/∂θ_norm - B_Z × ∂R/∂θ_norm)
+
+The `2π` factor comes from the toroidal Jacobian ∂r/∂ζ_norm = 2π·R·ê_φ in the
+cross-product ∂r/∂θ_norm × ∂r/∂ζ_norm. The derivatives dR/dθ_norm and dZ/dθ_norm
+are stored in `grid.dR_dtheta` and `grid.dZ_dtheta` (unit-norm convention from
+`sample_boundary_grid`).
+
+The output matches Fortran GPEC's `Phi_x` convention directly (no extra factor needed).
+
+## Arguments
+
+ - `bn`: output array `[mtheta, nzeta]`; overwritten in-place
+ - `B_R`, `B_Z`: cylindrical field components, length `mtheta × nzeta` (flat, θ-major)
+ - `grid`: pre-computed boundary geometry from `sample_boundary_grid`
+"""
+function project_normal_flux!(
+ bn::Matrix{Float64},
+ B_R::AbstractVector{Float64},
+ B_Z::AbstractVector{Float64},
+ grid::BoundaryGrid
+)
+ mtheta = grid.mtheta
+ nzeta = grid.nzeta
+ @assert size(bn) == (mtheta, nzeta)
+ @assert length(B_R) == mtheta * nzeta
+ @assert length(B_Z) == mtheta * nzeta
+
+ @inbounds for j in 1:nzeta
+ for i in 1:mtheta
+ idx = i + (j - 1) * mtheta
+ bn[i, j] = 2π * grid.R[i] * (B_R[idx] * grid.dZ_dtheta[i] - B_Z[idx] * grid.dR_dtheta[i])
+ end
+ end
+end
+
+"""
+ fourier_decompose_bn(bn, grid, n, m_low, m_high) -> Vector{ForcingMode}
+
+2D Fourier decompose `bn[mtheta, nzeta]` to extract mode amplitudes for toroidal
+mode number `n` and poloidal range `m_low:m_high`.
+
+Coefficients are computed as:
+bmn = (2 / (mtheta × nzeta)) × Σ_{i,j} bn[i,j] × exp(-i(m×θᵢ - n×ζⱼ))
+
+The factor 2 matches the GPEC/DCON convention for real signals where positive
+and negative m modes are related by conjugation.
+
+When called after `project_normal_flux!`, the returned amplitudes are in unit-norm
+convention equal to Fortran `Phi_x` (T·m² per unit-norm cell).
+"""
+function fourier_decompose_bn(
+ bn::Matrix{Float64},
+ grid::BoundaryGrid,
+ n::Int,
+ m_low::Int,
+ m_high::Int
+)
+ mtheta = grid.mtheta
+ nzeta = grid.nzeta
+
+ # Build Fourier basis: exp(-i*(m*θ - n*ζ))
+ # Using 3D call with npert=1, nlow=n gives shape (mpert, mtheta*nzeta)
+ basis = compute_fourier_coefficients(mtheta, m_low:m_high, nzeta, [n])
+
+ bn_flat = vec(bn) # column-major: bn_flat[i + (j-1)*mtheta] = bn[i,j]
+ scale = 2.0 / (mtheta * nzeta)
+
+ bmn = scale .* (basis * bn_flat)
+
+ modes = ForcingMode[]
+ for (idx, m) in enumerate(m_low:m_high)
+ push!(modes, ForcingMode(; n=n, m=m, amplitude=bmn[idx]))
+ end
+ return modes
+end
+
+"""
+ reconstruct_bn(amplitudes, m_modes, n_modes; ntheta=256, nzeta=180, theta_range=(-pi, pi)) -> (; theta, zeta, bn)
+ reconstruct_bn(modes::AbstractVector{ForcingMode}; kwargs...) -> (; theta, zeta, bn)
+
+Evaluate the real normal-flux pattern `bn(θ, ζ)` of a spectrum on an arbitrary angular grid,
+inverting the basis of [`fourier_decompose_bn`](@ref):
+
+ bn(θ, ζ) = Re Σ_k amplitudes[k] × exp(+i(m_k×θ - n_k×ζ))
+
+The real part rather than a sum over ±m is what the decomposition's factor of 2 already accounts
+for: each retained `(m, n)` stands for itself and its conjugate partner `(-m, -n)`.
+
+`theta_range` defaults to `(-π, π)` so the outboard midplane falls in the middle of a map rather
+than being cut in half at its edges. The grid is independent of the one the spectrum was measured
+on, so a coarse decomposition can still be drawn smoothly.
+"""
+function reconstruct_bn(
+ amplitudes::AbstractVector{<:Number},
+ m_modes::AbstractVector{<:Integer},
+ n_modes::AbstractVector{<:Integer};
+ ntheta::Int=256,
+ nzeta::Int=180,
+ theta_range::Tuple{Real,Real}=(-pi, pi)
+)
+ length(amplitudes) == length(m_modes) == length(n_modes) ||
+ throw(DimensionMismatch("reconstruct_bn: amplitudes, m_modes and n_modes must have equal length"))
+ (ntheta > 0 && nzeta > 0) || throw(ArgumentError("reconstruct_bn: ntheta and nzeta must be positive"))
+
+ theta = collect(range(theta_range[1], theta_range[2]; length=ntheta))
+ zeta = collect(range(0, 2pi; length=nzeta))
+ bn = zeros(ntheta, nzeta)
+ for k in eachindex(amplitudes), (j, z) in enumerate(zeta)
+ @. bn[:, j] += real(amplitudes[k] * cis(m_modes[k] * theta - n_modes[k] * z))
+ end
+ return (; theta, zeta, bn)
+end
+
+function reconstruct_bn(modes::AbstractVector{ForcingMode}; kwargs...)
+ return reconstruct_bn([m.amplitude for m in modes], [m.m for m in modes], [m.n for m in modes]; kwargs...)
+end
+
+"""
+ CoilForcingGrid
+
+The plasma-boundary sampling that every coil-field evaluation for one equilibrium and
+toroidal mode number shares: the `BoundaryGrid` at the control surface and its observation
+points laid out in cylindrical `(R, φ, Z)`. Build it once and evaluate any number of coil
+sets against it with [`coil_forcing_modes`](@ref).
+
+## Fields
+
+ - `grid::BoundaryGrid` - boundary geometry and unit-norm metric
+ - `obs_R`, `obs_phi`, `obs_Z` - observation points `[mtheta × nzeta]`, θ-major, with the
+ SFL toroidal offset applied
+"""
+struct CoilForcingGrid
+ grid::BoundaryGrid
+ obs_R::Vector{Float64}
+ obs_phi::Vector{Float64}
+ obs_Z::Vector{Float64}
+end
+
+"""
+ CoilForcingGrid(equil, cfg, n; psi=equil.rzphi_xs[end])
+
+Sample the control surface `psi` at `cfg.mtheta_coil × nzeta` points, with `nzeta` taken
+from `cfg.nzeta_coil` or `NZETA_POINTS_PER_PERIOD` per toroidal period of `n`. Pass
+`psi = psilim` whenever a solve is at hand (see `sample_boundary_grid`).
+"""
+function CoilForcingGrid(equil::Equilibrium.PlasmaEquilibrium, cfg::CoilConfig, n::Int; psi::Float64=equil.rzphi_xs[end])
+ nzeta = cfg.nzeta_coil > 0 ? cfg.nzeta_coil : NZETA_POINTS_PER_PERIOD * max(1, abs(n))
+ grid = sample_boundary_grid(equil, cfg.mtheta_coil, nzeta; psi)
+
+ # Lay out observation points: (theta_i, zeta_j) → cylindrical (R, phi, Z)
+ nobs = grid.mtheta * grid.nzeta
+ obs_R = zeros(nobs)
+ obs_phi = zeros(nobs)
+ obs_Z = zeros(nobs)
+ for j in 1:grid.nzeta
+ for i in 1:grid.mtheta
+ idx = i + (j - 1) * grid.mtheta
+ obs_R[idx] = grid.R[i]
+ obs_phi[idx] = grid.phi_grid[j] + grid.phi_offset[i]
+ obs_Z[idx] = grid.Z[i]
+ end
+ end
+ return CoilForcingGrid(grid, obs_R, obs_phi, obs_Z)
+end
+
+"""
+ coil_forcing_modes(coil_sets, forcing_grid::CoilForcingGrid, n, m_low, m_high; verbose=false) -> Vector{ForcingMode}
+
+Fourier mode amplitudes, in the unit-norm `Φ_x` convention, of the normal flux that
+`coil_sets` — a `Vector{CoilSet}` or a single `CoilSet` — drive on the boundary sampled by
+`forcing_grid`: threaded Biot-Savart at every observation point, projection onto the boundary
+normal, then the 2D decomposition for toroidal mode `n` and `m_low:m_high`. The field is
+linear in the coils, so evaluating sets one at a time on the same grid gives each set's own
+spectrum, and the sum of those is the spectrum of the assembly.
+"""
+function coil_forcing_modes(
+ coil_sets::Vector{CoilSet},
+ forcing_grid::CoilForcingGrid,
+ n::Int,
+ m_low::Int,
+ m_high::Int;
+ verbose::Bool=false
+)
+ nobs = length(forcing_grid.obs_R)
+ B_R = zeros(nobs)
+ B_phi = zeros(nobs)
+ B_Z = zeros(nobs)
+ compute_biot_savart_boundary!(B_R, B_phi, B_Z, forcing_grid.obs_R, forcing_grid.obs_phi, forcing_grid.obs_Z, coil_sets)
+
+ verbose && @info " Max |B_R| = $(maximum(abs, B_R)) T, Max |B_Z| = $(maximum(abs, B_Z)) T"
+
+ bn = zeros(forcing_grid.grid.mtheta, forcing_grid.grid.nzeta)
+ project_normal_flux!(bn, B_R, B_Z, forcing_grid.grid)
+
+ verbose && @info " Max |bn| = $(maximum(abs, bn)) T·m²"
+
+ return fourier_decompose_bn(bn, forcing_grid.grid, n, m_low, m_high)
+end
+
+coil_forcing_modes(coil_set::CoilSet, forcing_grid::CoilForcingGrid, args...; kwargs...) = coil_forcing_modes([coil_set], forcing_grid, args...; kwargs...)
+
+"""
+ compute_coil_forcing_modes!(forcing_modes, coil_sets, equil, cfg, n, m_low, m_high; psi, verbose)
+
+Top-level entry point: compute Fourier mode amplitudes of the normal magnetic flux from all
+coil sets on the plasma boundary — a [`CoilForcingGrid`](@ref) at `psi` followed by
+[`coil_forcing_modes`](@ref) over the whole assembly in one Biot-Savart pass.
+
+Output amplitudes are in unit-norm convention (= Fortran `Phi_x`) and drive a plasma response
+directly. `forcing_modes` is overwritten with the result.
+"""
+function compute_coil_forcing_modes!(
+ forcing_modes::Vector{ForcingMode},
+ coil_sets::Vector{CoilSet},
+ equil::Equilibrium.PlasmaEquilibrium,
+ cfg::CoilConfig,
+ n::Int,
+ m_low::Int,
+ m_high::Int;
+ psi::Float64=equil.rzphi_xs[end], # outermost computed surface (psihigh), not ψ_N=1 — see sample_boundary_grid
+ verbose::Bool=false
+)
+ forcing_grid = CoilForcingGrid(equil, cfg, n; psi)
+ verbose && @info "Computing coil forcing modes: mtheta=$(forcing_grid.grid.mtheta), nzeta=$(forcing_grid.grid.nzeta), n=$n, m=$m_low:$m_high, psi=$psi"
+
+ modes = coil_forcing_modes(coil_sets, forcing_grid, n, m_low, m_high; verbose)
+
+ empty!(forcing_modes)
+ append!(forcing_modes, modes)
+
+ verbose && @info " Computed $(length(modes)) forcing modes for n=$n"
+end
+
+"""
+ convert_forcing_normalization(modes, from_tag, equil, n, m_out; psi, mtheta) -> Vector{ForcingMode}
+
+Convert `ForcingMode` amplitudes from `from_tag` normalization to the internal
+unit-norm convention (= Fortran `Phi_x`) that `perturbed_equilibrium` applies the plasma response to.
+
+If `from_tag == "sfl_flux_Wb"`, the user has provided amplitudes in the 2π-angle
+SFL-flux convention. These are scaled by (2π)² to reach unit-norm, keeping their harmonics.
+
+If `from_tag == "normal_field_T"`, the amplitudes represent Fourier modes of B·n̂
+in Tesla (2π-angle convention). Conversion to unit-norm Phi_x:
+
+ - Inverse-Fourier reconstruct B·n̂(θ) from every harmonic in the file
+ - Multiply pointwise by the area weight J|∇ψ| (`Equilibrium.compute_jac_delpsi`)
+ - Fourier transform onto every harmonic in `m_out`
+
+This conversion is a mode-mixing operation because J|∇ψ| varies poloidally, so the flux has
+sidebands beyond the file's own harmonics; `m_out` should be the run's full range. Each output
+harmonic is an exact projection of the full product, so a file wider than `m_out` loses nothing.
+The θ grid is widened past `mtheta` when the harmonics would otherwise alias.
+
+The file's spectrum is itself a truncation of the true field, and the missing harmonics would
+mix into `m_out` too. Following the last-coefficient rule of thumb for spectral series (Boyd,
+*Chebyshev and Fourier Spectral Methods*), the first missing harmonic is taken to be comparable to
+the last one kept, so the flux each edge harmonic drives estimates what the truncation loses.
+A warning is issued when that exceeds `truncation_tol` of the total flux. Files with fewer than
+three harmonics have no edge to judge and are not checked.
+
+## Arguments
+
+ - `modes`: `Vector{ForcingMode}` of one toroidal mode `n` (not modified)
+ - `from_tag`: source normalization — `"normal_field_T"`, `"sfl_flux_Wb"`, or `"unit_flux"` for modes already in the
+ unit-norm Φ_x convention the response consumes (a run's materialized forcing, recorded for replay)
+ - `equil`: `PlasmaEquilibrium` providing boundary geometry
+ - `n`: toroidal mode number
+ - `m_out`: poloidal harmonics of the converted flux
+ - `psi`: flux surface for boundary geometry (default `equil.rzphi_xs[end]`)
+ - `mtheta`: minimum θ grid resolution for the conversion (default 256)
+ - `truncation_tol`: relative flux change from one edge harmonic that triggers the warning
+"""
+function convert_forcing_normalization(
+ modes::Vector{ForcingMode},
+ from_tag::String,
+ equil::Equilibrium.PlasmaEquilibrium,
+ n::Int,
+ m_out::UnitRange{Int};
+ psi::Float64=equil.rzphi_xs[end], # outermost computed surface (psihigh), not ψ_N=1 — see sample_boundary_grid
+ mtheta::Int=256,
+ truncation_tol::Float64=0.1
+)
+ from_tag == "unit_flux" && return [ForcingMode(; n=mode.n, m=mode.m, amplitude=mode.amplitude) for mode in modes]
+ if from_tag == "sfl_flux_Wb"
+ # User provided 2π-angle SFL flux; scale by (2π)² to reach unit-norm (= Phi_x)
+ return [ForcingMode(; n=mode.n, m=mode.m, amplitude=(2π)^2 * mode.amplitude) for mode in modes]
+ end
+
+ if from_tag != "normal_field_T"
+ error("Unknown forcing normalization: \"$from_tag\". Supported: \"normal_field_T\", \"sfl_flux_Wb\", \"unit_flux\".")
+ end
+
+ m_in = minimum(mode.m for mode in modes):maximum(mode.m for mode in modes)
+ amp = zeros(ComplexF64, length(m_in))
+ for mode in modes
+ amp[mode.m-first(m_in)+1] = mode.amplitude
+ end
+ @info "Converting forcing file B·n̂ (normal_field_T) to flux: n=$n, file m=$m_in → run m=$m_out"
+
+ # Keep the product's harmonics, up to |m_in| + |m_out|, well inside the grid's Nyquist limit.
+ mtheta = max(mtheta, 4 * maximum(abs, (first(m_in), last(m_in), first(m_out), last(m_out))))
+ ft_in = FourierTransforms.FourierTransform(mtheta, length(m_in), first(m_in))
+ ft_out = FourierTransforms.FourierTransform(mtheta, length(m_out), first(m_out))
+ weight = Equilibrium.compute_jac_delpsi(equil, psi, mtheta)
+ to_flux(a) = ft_out(weight .* FourierTransforms.inverse(ft_in, a))
+ flux = to_flux(amp)
+
+ if length(modes) >= 3 && norm(flux) > 0
+ for idx in (1, length(amp))
+ edge = zeros(ComplexF64, length(amp))
+ edge[idx] = amp[idx]
+ change = norm(to_flux(edge)) / norm(flux)
+ change > truncation_tol &&
+ @warn "Forcing file n=$n may be truncated: its edge harmonic m=$(m_in[idx]) carries " *
+ "$(round(100change; digits=1))% of the converted flux on m=$m_out, so the harmonics " *
+ "beyond it are likely not negligible. Extend the file's m range."
+ end
+ end
+
+ return [ForcingMode(; n=n, m=m, amplitude=flux[i]) for (i, m) in enumerate(m_out)]
+end
+
+export BoundaryGrid, sample_boundary_grid
+export project_normal_flux!, fourier_decompose_bn
+export CoilForcingGrid, coil_forcing_modes
+export compute_coil_forcing_modes!
+export convert_forcing_normalization
diff --git a/src/ForcingTerms/CoilGeometry.jl b/src/ForcingTerms/CoilGeometry.jl
new file mode 100644
index 0000000000..e13277bdee
--- /dev/null
+++ b/src/ForcingTerms/CoilGeometry.jl
@@ -0,0 +1,1069 @@
+"""
+ CoilGeometry
+
+Structs and I/O for 3D coil geometries used in Biot-Savart field calculations.
+
+Coil geometry files use the Fortran GPEC ASCII format:
+ - Header: `ncoil s nsec nw`
+ - Data: `ncoil × s × nsec` rows, each with `X Y Z` in meters (Cartesian, lab frame)
+"""
+
+# Sentinel value used when nom coordinates are not user-specified (matches Fortran coil.F)
+const _NOM_UNSET_SENTINEL = 1e10
+# Threshold below which a nom value is treated as user-specified (vs. the unset sentinel)
+const _NOM_THRESHOLD = 1e3
+
+"""
+ CoilSet
+
+Geometry and current data for a single coil set (one .dat file).
+
+## Fields
+
+ - `name`: coil set identifier (e.g. "il", "iu")
+ - `ncoil`: number of independent conductors
+ - `s`: sub-systems (strand groups) per conductor
+ - `nw`: winding multiplier (turns per conductor element)
+ - `nsec`: number of Cartesian points per strand
+ - `x`, `y`, `z`: conductor coordinates `[ncoil, s, nsec]` in meters (Cartesian)
+ - `currents`: current per conductor `[ncoil]` in Amperes
+"""
+struct CoilSet
+ name::String
+ ncoil::Int
+ s::Int
+ nw::Float64
+ nsec::Int
+ x::Array{Float64,3}
+ y::Array{Float64,3}
+ z::Array{Float64,3}
+ currents::Vector{Float64}
+end
+
+"""
+ CoilSetConfig
+
+Per-coil-set configuration from a `[[ForcingTerms.coil_set]]` TOML block.
+
+A coil set comes from one of several sources, selected by `source`:
+
+ - `""` or `"file"`: read a geometry file — `.dat` (legacy ASCII) or `.h5` (modern), chosen
+ by extension. The file path comes from `dat_file`/`h5_file` or the `machine`+`name` convention.
+ - `"pf_hoop"`: an analytic horizontal circular loop (`radius`, `height`).
+ - `"window_pane"`: an analytic rectangular picture-frame array, placed EITHER by explicit
+ corners (`rz_corners`) OR by physical standoff from the plasma surface (`standoff`,
+ `poloidal_angle`, `poloidal_length`, `poloidal_tilt`); shared toroidal layout via
+ `n_coils`, `gap_fraction`, `phi0`.
+ - `"helical"`: an analytic helical array on a circular cross-section torus
+ (`R0`, `a`, `m_hel`, `n_hel`, `theta_lo`, `theta_hi`, `n_coils`, `gap_fraction`, `phi0`, `offset`).
+
+Shifts/tilts apply to every source (the analytic geometry is built first, then transformed).
+
+## Fields
+
+ - `name`: coil set name; resolves to `{dat_dir}/{machine}_{name}.dat`, or selects a set by name
+ from a multi-set `.h5` file
+ - `source`: coil source discriminator (see above); empty/`"file"` reads a geometry file
+ - `dat_file`: explicit path to .dat file (overrides `machine`+`name` convention)
+ - `h5_file`: explicit path to .h5 file (multi-set; `name` selects which set, else the sole set)
+ - `currents`: current [A] per conductor `[ncoil]`; shorter arrays pad with zeros
+ - `shiftx`, `shifty`, `shiftz`: per-conductor translation [m] `[ncoil]`
+ - `tiltx`, `tilty`, `tiltz`: per-conductor tilt in degrees (or meters if `tilt_in_meters`)
+ - `rotation_center_x`, `rotation_center_y`, `rotation_center_z`: explicit rotation center [m]; defaults to arc-length-weighted center of mass
+ - `n_tilt`: toroidal mode number for tilt/shift modulation; -1 means inherit run's n
+ - `tilt_in_meters`: interpret tilt as displacement [m] instead of angle [degrees]
+
+Analytic-source parameters (used only for the matching `source`):
+
+ - `radius`, `height`: PF hoop circle radius and Z height [m]
+ - `rz_corners`: window-pane cross-section as two opposite `[R, Z]` corners in m (corner mode)
+ - `gap_fraction`: toroidal gap between adjacent coils as a fraction of their spacing
+ - `phi0`: toroidal angle offset of the first generated coil [rad]
+ - `R0`, `a`: helical torus major radius and minor (circle) radius [m]
+ - `m_hel`, `n_hel`: helical poloidal/toroidal mode numbers setting the pitch
+ - `theta_lo`, `theta_hi`: helical poloidal extent in degrees; a full turn when `theta_hi-theta_lo == 360`
+ - `n_coils`: number of coils in a generated window-pane or helical array
+ - `offset`: helical coil radial offset from the torus surface [m]
+ - `points_per_coil`: optional override of the generated point count per coil
+
+Window-pane standoff placement (alternative to `rz_corners`; needs an equilibrium):
+
+ - `standoff`: outward-normal distance from the control surface to the frame center [m]
+ - `poloidal_angle`: cylindrical poloidal angle of the frame center, in degrees
+ - `poloidal_length`: poloidal leg span (corner-to-corner) along the surface tangent [m]
+ - `poloidal_tilt`: extra tilt of the legs in degrees; 0 means tangential to the surface
+"""
+Base.@kwdef struct CoilSetConfig
+ name::String = ""
+ source::String = ""
+ dat_file::String = ""
+ h5_file::String = ""
+ currents::Vector{Float64} = Float64[]
+ shiftx::Vector{Float64} = Float64[]
+ shifty::Vector{Float64} = Float64[]
+ shiftz::Vector{Float64} = Float64[]
+ tiltx::Vector{Float64} = Float64[]
+ tilty::Vector{Float64} = Float64[]
+ tiltz::Vector{Float64} = Float64[]
+ rotation_center_x::Vector{Float64} = Float64[]
+ rotation_center_y::Vector{Float64} = Float64[]
+ rotation_center_z::Vector{Float64} = Float64[]
+ n_tilt::Int = -1
+ tilt_in_meters::Bool = false
+
+ # Analytic-source parameters
+ radius::Float64 = 0.0
+ height::Float64 = 0.0
+ rz_corners::Vector{Vector{Float64}} = Vector{Float64}[]
+ gap_fraction::Float64 = 0.0
+ phi0::Float64 = 0.0
+ R0::Float64 = 0.0
+ a::Float64 = 0.0
+ m_hel::Int = 0
+ n_hel::Int = 0
+ theta_lo::Float64 = 0.0
+ theta_hi::Float64 = 360.0
+ n_coils::Int = 0
+ offset::Float64 = 0.0
+ points_per_coil::Int = 0
+
+ # Window-pane standoff placement (alternative to rz_corners)
+ standoff::Float64 = NaN
+ poloidal_angle::Float64 = NaN
+ poloidal_length::Float64 = 0.0
+ poloidal_tilt::Float64 = 0.0
+end
+
+"""
+ CoilConfig
+
+Top-level coil configuration from the `[ForcingTerms]` TOML section when
+`forcing_data_format = "coil"`.
+
+## Fields
+
+ - `machine`: machine name prefix for .dat files (e.g. "d3d")
+ - `dat_dir`: directory containing .dat files; defaults to bundled `coil_geometries/`
+ - `mtheta_coil`: poloidal grid resolution for boundary field evaluation (default: 480)
+ - `nzeta_coil`: toroidal grid resolution; 0 = auto (32 × n)
+ - `coil_sets`: parsed `[[ForcingTerms.coil_set]]` blocks
+"""
+Base.@kwdef struct CoilConfig
+ machine::String = ""
+ dat_dir::String = ""
+ mtheta_coil::Int = 480
+ nzeta_coil::Int = 0
+ coil_sets::Vector{CoilSetConfig} = CoilSetConfig[]
+end
+
+"""
+ CoilConfig(ft_ctrl::ForcingTermsControl)
+
+Construct a `CoilConfig` from a `ForcingTermsControl` populated from TOML.
+"""
+function CoilConfig(ft_ctrl::ForcingTermsControl)
+ dat_dir = isempty(ft_ctrl.dat_dir) ?
+ joinpath(@__DIR__, "coil_geometries") :
+ ft_ctrl.dat_dir
+
+ coil_sets = CoilSetConfig[_parse_coil_set_config(d) for d in ft_ctrl.coil_sets_raw]
+
+ return CoilConfig(;
+ machine=ft_ctrl.machine,
+ dat_dir=dat_dir,
+ mtheta_coil=ft_ctrl.mtheta_coil,
+ nzeta_coil=ft_ctrl.nzeta_coil,
+ coil_sets=coil_sets
+ )
+end
+
+function _parse_coil_set_config(d::Dict{String,Any})
+ known = Set(String.(fieldnames(CoilSetConfig)))
+ unknown = sort([k for k in keys(d) if !(k in known)])
+ isempty(unknown) || throw(ArgumentError("unknown keys $(unknown) in [[ForcingTerms.coil_set]]. Known: $(sort(collect(known)))."))
+ fvec(key) = Float64.(get(d, key, Float64[]))
+ # rz_corners arrives as a Vector of [R, Z] pairs (TOML array of arrays)
+ corners = [Float64.(c) for c in get(d, "rz_corners", Vector{Float64}[])]
+ return CoilSetConfig(;
+ name=get(d, "name", ""),
+ source=get(d, "source", ""),
+ dat_file=get(d, "dat_file", ""),
+ h5_file=get(d, "h5_file", ""),
+ currents=fvec("currents"),
+ shiftx=fvec("shiftx"),
+ shifty=fvec("shifty"),
+ shiftz=fvec("shiftz"),
+ tiltx=fvec("tiltx"),
+ tilty=fvec("tilty"),
+ tiltz=fvec("tiltz"),
+ rotation_center_x=fvec("rotation_center_x"),
+ rotation_center_y=fvec("rotation_center_y"),
+ rotation_center_z=fvec("rotation_center_z"),
+ n_tilt=get(d, "n_tilt", -1),
+ tilt_in_meters=get(d, "tilt_in_meters", false),
+ radius=Float64(get(d, "radius", 0.0)),
+ height=Float64(get(d, "height", 0.0)),
+ rz_corners=corners,
+ gap_fraction=Float64(get(d, "gap_fraction", 0.0)),
+ phi0=Float64(get(d, "phi0", 0.0)),
+ R0=Float64(get(d, "R0", 0.0)),
+ a=Float64(get(d, "a", 0.0)),
+ m_hel=get(d, "m_hel", 0),
+ n_hel=get(d, "n_hel", 0),
+ theta_lo=Float64(get(d, "theta_lo", 0.0)),
+ theta_hi=Float64(get(d, "theta_hi", 360.0)),
+ n_coils=get(d, "n_coils", 0),
+ offset=Float64(get(d, "offset", 0.0)),
+ points_per_coil=get(d, "points_per_coil", 0),
+ standoff=Float64(get(d, "standoff", NaN)),
+ poloidal_angle=Float64(get(d, "poloidal_angle", NaN)),
+ poloidal_length=Float64(get(d, "poloidal_length", 0.0)),
+ poloidal_tilt=Float64(get(d, "poloidal_tilt", 0.0))
+ )
+end
+
+"""
+ read_coil_dat(filepath::String) -> CoilSet
+
+Parse an ASCII coil geometry file.
+
+Format:
+
+```
+ncoil s nsec nw
+X₁ Y₁ Z₁
+X₂ Y₂ Z₂
+...
+```
+
+Data rows are ordered: for each conductor 1:ncoil, for each sub-system 1:s, read nsec points.
+Coordinates are Cartesian in meters (lab frame).
+"""
+function read_coil_dat(filepath::String)
+ isfile(filepath) || error("Coil geometry file not found: $filepath")
+
+ lines = readlines(filepath)
+ # Skip comment/blank lines to find header
+ header_idx = findfirst(l -> !isempty(strip(l)) && !startswith(strip(l), "#"), lines)
+ isnothing(header_idx) && error("Empty coil file: $filepath")
+
+ header = split(strip(lines[header_idx]))
+ length(header) >= 4 || error("Invalid header in $filepath: expected 'ncoil s nsec nw'")
+
+ ncoil = parse(Int, header[1])
+ s = parse(Int, header[2])
+ nsec = parse(Int, header[3])
+ nw = parse(Float64, header[4])
+
+ x = zeros(ncoil, s, nsec)
+ y = zeros(ncoil, s, nsec)
+ z = zeros(ncoil, s, nsec)
+
+ row = header_idx + 1
+ for j in 1:ncoil
+ for k in 1:s
+ for l in 1:nsec
+ # Skip blank/comment lines between data rows
+ while row <= length(lines) &&
+ (isempty(strip(lines[row])) || startswith(strip(lines[row]), "#"))
+ row += 1
+ end
+ row > length(lines) && error(
+ "Unexpected end of file in $filepath at conductor $j, sub $k, point $l"
+ )
+ vals = split(strip(lines[row]))
+ length(vals) >= 3 || error(
+ "Expected 3 columns at line $row in $filepath, got $(length(vals))"
+ )
+ x[j, k, l] = parse(Float64, vals[1])
+ y[j, k, l] = parse(Float64, vals[2])
+ z[j, k, l] = parse(Float64, vals[3])
+ row += 1
+ end
+ end
+ end
+
+ name = splitext(basename(filepath))[1]
+ return CoilSet(name, ncoil, s, nw, nsec, x, y, z, zeros(ncoil))
+end
+
+"""
+ make_pf_hoop(; radius, height, nsec=361, name="pf_hoop") -> CoilSet
+
+Build a single horizontal circular loop (PF hoop) of `radius` [m] centered on the
+machine axis at vertical position `height` [m], discretized into `nsec` points.
+
+The loop is closed (point `nsec` coincides with point 1). A bare hoop is axisymmetric
+and produces only an n=0 field; tilting or shifting it (via [`apply_transforms`](@ref))
+breaks axisymmetry to produce n≠0 forcing. Currents are zeroed; `load_coil_sets` fills them.
+"""
+function make_pf_hoop(; radius::Real, height::Real, nsec::Int=361, name::String="pf_hoop")
+ radius > 0 || error("make_pf_hoop: radius must be > 0 (got $radius)")
+ nsec >= 361 || error("make_pf_hoop: nsec must be >= 361 (got $nsec); a full poloidal hoop needs at least ~1° resolution to be smooth")
+ phis = range(0; length=nsec, stop=2π) # closed: phis[end] == phis[1] + 2π
+ x = reshape([radius * cos(p) for p in phis], 1, 1, nsec)
+ y = reshape([radius * sin(p) for p in phis], 1, 1, nsec)
+ z = reshape(fill(Float64(height), nsec), 1, 1, nsec)
+ return CoilSet(name, 1, 1, 1.0, nsec, x, y, z, zeros(1))
+end
+
+"""
+ conductors(cs::CoilSet) -> Vector{CoilSet}
+
+Split a coil set into one single-conductor set per conductor, each carrying that conductor's own
+current and named `"_"`. A set that already holds one conductor is returned unchanged
+in a one-element vector.
+
+Legacy geometry files often pack several physically separate coils into one file, so comparing
+against a design that names them separately needs them one at a time. Evaluating a split set costs
+only its own conductor, where zeroing the other currents would compute and discard their fields.
+"""
+function conductors(cs::CoilSet)
+ cs.ncoil == 1 && return [cs]
+ return [CoilSet("$(cs.name)_$j", 1, cs.s, cs.nw, cs.nsec,
+ cs.x[j:j, :, :], cs.y[j:j, :, :], cs.z[j:j, :, :], [cs.currents[j]]) for j in 1:cs.ncoil]
+end
+
+"""
+ surface_point_and_normal(equil, theta_cyl; psi=equil.rzphi_xs[end]) -> (R, Z, nR, nZ)
+
+Locate the control-surface point at cylindrical poloidal angle `theta_cyl` (radians) and return
+it with the outward unit normal `(nR, nZ)` in the R-Z plane.
+
+The flux-surface splines are parametrized by the SFL angle `theta_sfl`, related to the cylindrical
+angle by `theta_cyl = 2π*(theta_sfl + rzphi_offset(psi, theta_sfl))`. Since the offset is a small
+smooth perturbation, `theta_sfl` is recovered by fixed-point iteration. The tangent is
+taken by central-differencing `R(theta_sfl), Z(theta_sfl)`, and the normal `(dZ/dθ, -dR/dθ)` is
+normalized and oriented outward (positive dot with `(R-ro, Z-zo)`), matching the normal-flux
+convention of `project_normal_flux!`.
+"""
+function surface_point_and_normal(equil, theta_cyl::Real; psi::Real=equil.rzphi_xs[end])
+ hint = (Ref(1), Ref(1))
+ target = mod(theta_cyl / (2π), 1.0) # normalized cylindrical angle in [0,1)
+
+ # Solve theta_cyl/2π = theta_sfl + offset(theta_sfl) for theta_sfl (offset slope ≪ 1).
+ theta_sfl = target
+ for _ in 1:50
+ off = equil.rzphi_offset((psi, mod(theta_sfl, 1.0)); hint=hint)
+ residual = mod(theta_sfl + off - target, 1.0)
+ residual -= round(residual) # wrap to (-0.5, 0.5]
+ abs(residual) < 1e-13 && break
+ theta_sfl -= residual
+ end
+ theta_sfl = mod(theta_sfl, 1.0)
+
+ point(tn) = begin
+ tw = mod(tn, 1.0)
+ r_minor = sqrt(equil.rzphi_rsquared((psi, tw); hint=hint))
+ tc = 2π * (tw + equil.rzphi_offset((psi, tw); hint=hint))
+ (equil.ro + r_minor * cos(tc), equil.zo + r_minor * sin(tc))
+ end
+
+ R, Z = point(theta_sfl)
+ h = 1.0e-5
+ Rp, Zp = point(theta_sfl + h)
+ Rm, Zm = point(theta_sfl - h)
+ dR = (Rp - Rm) / (2h)
+ dZ = (Zp - Zm) / (2h)
+
+ nR, nZ = dZ, -dR
+ nrm = hypot(nR, nZ)
+ nR /= nrm
+ nZ /= nrm
+ if nR * (R - equil.ro) + nZ * (Z - equil.zo) < 0 # force outward orientation
+ nR, nZ = -nR, -nZ
+ end
+ return (R, Z, nR, nZ)
+end
+
+"""
+ make_window_pane_standoff(equil; standoff, poloidal_angle, poloidal_length,
+ poloidal_tilt=0.0, ncoil, gap_fraction=0.0, phi0=0.0,
+ name="window_pane") -> CoilSet
+
+Build a window-pane array placed by physical standoff instead of explicit corners. The frame
+center sits `standoff` [m] along the outward surface normal at cylindrical `poloidal_angle`
+(degrees); its poloidal legs span `poloidal_length` [m] along the surface tangent, rotated by
+`poloidal_tilt` (degrees, 0 = tangential). The control surface is the boundary
+`equil.rzphi_xs[end]`. Toroidal layout (`ncoil`, `gap_fraction`, `phi0`) and the leg/arc
+construction are delegated to [`make_window_pane`](@ref).
+
+The poloidal legs wind in the same sense as `make_window_pane`'s `c1 -> c2` ordering (lower-Z to
+higher-Z at the outboard midplane), so positive current produces positive `b_n_x` near the coil,
+matching the corner-built window pane.
+"""
+function make_window_pane_standoff(equil; standoff::Real, poloidal_angle::Real,
+ poloidal_length::Real, poloidal_tilt::Real=0.0, ncoil::Int,
+ gap_fraction::Real=0.0, phi0::Real=0.0, name::String="window_pane")
+ poloidal_length > 0 || error("make_window_pane_standoff: poloidal_length must be > 0 (got $poloidal_length)")
+
+ R, Z, nR, nZ = surface_point_and_normal(equil, deg2rad(poloidal_angle))
+
+ # Frame center: standoff along the outward normal.
+ Rc = R + standoff * nR
+ Zc = Z + standoff * nZ
+
+ # Tangent = outward normal rotated +90° (c1->c2 winding, see docstring), then by poloidal_tilt.
+ tR, tZ = -nZ, nR
+ c, s = cos(deg2rad(poloidal_tilt)), sin(deg2rad(poloidal_tilt))
+ uR = c * tR - s * tZ
+ uZ = s * tR + c * tZ
+
+ half = poloidal_length / 2
+
+ # Reject coils that cross the boundary: on a convex boundary the nearest corner's normal
+ # clearance is standoff - half*|sin(tilt)|.
+ clearance = standoff - half * abs(sin(deg2rad(poloidal_tilt)))
+ clearance > 0 || error(
+ "make_window_pane_standoff: coil intersects the plasma boundary " *
+ "(standoff=$standoff, poloidal_length=$poloidal_length, poloidal_tilt=$poloidal_tilt); " *
+ "an external coil must lie outside the control surface — increase standoff or reduce " *
+ "poloidal_length/poloidal_tilt"
+ )
+
+ c1 = [Rc - half * uR, Zc - half * uZ]
+ c2 = [Rc + half * uR, Zc + half * uZ]
+
+ return make_window_pane(; ncoil=ncoil, rz_corners=[c1, c2],
+ gap_fraction=gap_fraction, phi0=phi0, name=name)
+end
+
+"""
+ make_window_pane(; ncoil, rz_corners, gap_fraction=0.0, phi0=0.0,
+ np_pol=20, np_tor=40, name="window_pane") -> CoilSet
+
+Build an array of `ncoil` rectangular "picture-frame" (window-pane) saddle coils, evenly
+spaced toroidally. The two `[R, Z]` points in `rz_corners` are the endpoints of the poloidal
+legs; the legs run along the straight segment between them at the two toroidal edges of the
+coil, joined by toroidal arcs at each corner. For a vertical frame give the two corners the
+same `R` (legs run in Z); for a horizontal frame give them the same `Z`. Adjacent coils are
+separated by a toroidal gap of `gap_fraction` times their angular spacing; the first coil is
+centered at toroidal angle `phi0` [rad].
+
+Each coil is a closed loop with `np_pol` points per poloidal leg and `np_tor` per toroidal arc.
+Currents are zeroed; `load_coil_sets` fills them.
+"""
+function make_window_pane(; ncoil::Int, rz_corners::AbstractVector,
+ gap_fraction::Real=0.0, phi0::Real=0.0,
+ np_pol::Int=20, np_tor::Int=40, name::String="window_pane")
+ ncoil >= 1 || error("make_window_pane: ncoil must be >= 1 (got $ncoil)")
+ length(rz_corners) == 2 || error("make_window_pane: rz_corners must hold exactly two [R, Z] corners")
+ 0.0 <= gap_fraction < 1.0 || error("make_window_pane: gap_fraction must be in [0, 1) (got $gap_fraction)")
+ np_pol >= 2 && np_tor >= 2 || error("make_window_pane: np_pol and np_tor must be >= 2")
+ c1, c2 = rz_corners[1], rz_corners[2]
+ length(c1) == 2 && length(c2) == 2 || error("make_window_pane: each rz_corner must be [R, Z]")
+ R1, Z1 = Float64(c1[1]), Float64(c1[2])
+ R2, Z2 = Float64(c2[1]), Float64(c2[2])
+
+ # Closed loop: leg(np_pol) + arc(np_tor-1) + leg(np_pol-1) + arc(np_tor-1), last == first.
+ nsec = 2 * np_pol + 2 * np_tor - 3
+ x = zeros(ncoil, 1, nsec)
+ y = zeros(ncoil, 1, nsec)
+ z = zeros(ncoil, 1, nsec)
+
+ dphi_coil = 2π / ncoil
+ half_span = (dphi_coil / 2) * (1 - gap_fraction)
+ lin(lo, hi, n) = range(lo; stop=hi, length=n)
+
+ Rs = Float64[]
+ phis = Float64[]
+ Zs = Float64[]
+ for j in 0:(ncoil-1)
+ empty!(Rs)
+ empty!(phis)
+ empty!(Zs)
+ phi_c = phi0 + j * dphi_coil
+ phi_a = phi_c - half_span
+ phi_b = phi_c + half_span
+
+ # Poloidal leg corner1 -> corner2 at phi_a (segment in the R-Z plane)
+ for s in lin(0.0, 1.0, np_pol)
+ push!(Rs, R1 + s * (R2 - R1))
+ push!(phis, phi_a)
+ push!(Zs, Z1 + s * (Z2 - Z1))
+ end
+ # Toroidal arc at corner2: phi_a -> phi_b (drop shared junction)
+ for p in lin(phi_a, phi_b, np_tor)[2:end]
+ push!(Rs, R2)
+ push!(phis, p)
+ push!(Zs, Z2)
+ end
+ # Poloidal leg corner2 -> corner1 at phi_b
+ for s in lin(0.0, 1.0, np_pol)[2:end]
+ push!(Rs, R2 + s * (R1 - R2))
+ push!(phis, phi_b)
+ push!(Zs, Z2 + s * (Z1 - Z2))
+ end
+ # Toroidal arc at corner1: phi_b -> phi_a, last point closes onto the first
+ for p in lin(phi_b, phi_a, np_tor)[2:end]
+ push!(Rs, R1)
+ push!(phis, p)
+ push!(Zs, Z1)
+ end
+
+ for l in 1:nsec
+ x[j+1, 1, l] = Rs[l] * cos(phis[l])
+ y[j+1, 1, l] = Rs[l] * sin(phis[l])
+ z[j+1, 1, l] = Zs[l]
+ end
+ end
+ return CoilSet(name, ncoil, 1, 1.0, nsec, x, y, z, zeros(ncoil))
+end
+
+"""
+ make_helical(; R0, a, m, n, theta_lo=0.0, theta_hi=360.0, n_coils,
+ gap_fraction=0.0, phi0=0.0, offset=0.0, npts=720,
+ name="helical") -> CoilSet
+
+Build an array of `n_coils` analytic helical coils wound on a circular cross-section torus
+of major radius `R0` and minor radius `a` [m], offset radially outward by `offset` [m].
+The helical pitch is set by the poloidal/toroidal mode numbers `m`/`n` via `ζ = (m/n)·θ + φ`.
+
+The poloidal extent `theta_lo`/`theta_hi` is in degrees. For a full poloidal turn
+(`theta_hi - theta_lo == 360`) each coil is a single helical strand. For a partial poloidal
+range the coil is closed into a loop with two helical legs joined by toroidal arcs (matching
+OMFIT `form_helical_array.py`). `npts` sets the strand resolution.
+Currents are zeroed; `load_coil_sets` fills them.
+"""
+function make_helical(; R0::Real, a::Real, m::Int, n::Int,
+ theta_lo::Real=0.0, theta_hi::Real=360.0, n_coils::Int,
+ gap_fraction::Real=0.0, phi0::Real=0.0, offset::Real=0.0,
+ npts::Int=720, name::String="helical")
+ R0 > 0 || error("make_helical: R0 must be > 0 (got $R0)")
+ a > 0 || error("make_helical: a must be > 0 (got $a)")
+ n != 0 || error("make_helical: n must be nonzero (sets the helical pitch m/n)")
+ n_coils >= 1 || error("make_helical: n_coils must be >= 1 (got $n_coils)")
+ 0.0 <= gap_fraction < 1.0 || error("make_helical: gap_fraction must be in [0, 1) (got $gap_fraction)")
+
+ # User-facing poloidal extent is in degrees; the internal winding math works in radians.
+ theta_lo = deg2rad(theta_lo)
+ theta_hi = deg2rad(theta_hi)
+
+ pitch = m / n
+ rr = a + offset
+ surf_R(θ) = R0 + rr * cos(θ)
+ surf_Z(θ) = rr * sin(θ)
+
+ dphi_coil = 2π / n_coils
+ coil_width = dphi_coil * (1 - gap_fraction)
+ full_turn = isapprox(theta_hi - theta_lo, 2π; atol=1e-9)
+ lin(lo, hi, np) = range(lo; stop=hi, length=np)
+
+ Rs = Float64[]
+ phis = Float64[]
+ Zs = Float64[]
+ strands = Vector{NTuple{3,Vector{Float64}}}(undef, n_coils)
+ for j in 0:(n_coils-1)
+ empty!(Rs)
+ empty!(phis)
+ empty!(Zs)
+ phi_c = phi0 + j * dphi_coil
+ if full_turn
+ for θ in lin(theta_lo, theta_hi, npts)
+ ζ = phi_c + pitch * θ
+ push!(Rs, surf_R(θ))
+ push!(phis, ζ)
+ push!(Zs, surf_Z(θ))
+ end
+ else
+ np_leg = npts ÷ 2
+ np_arc = max(2, npts ÷ 8)
+ half_w = coil_width / 2
+ # Up leg: theta_lo -> theta_hi at toroidal edge -half_w
+ for θ in lin(theta_lo, theta_hi, np_leg)
+ ζ = phi_c - half_w + pitch * θ
+ push!(Rs, surf_R(θ))
+ push!(phis, ζ)
+ push!(Zs, surf_Z(θ))
+ end
+ # Top arc at theta_hi, sweep toroidally by +coil_width
+ ζ_top = phi_c - half_w + pitch * theta_hi
+ for ζ in lin(ζ_top, ζ_top + coil_width, np_arc)[2:end]
+ push!(Rs, surf_R(theta_hi))
+ push!(phis, ζ)
+ push!(Zs, surf_Z(theta_hi))
+ end
+ # Down leg: theta_hi -> theta_lo at toroidal edge +half_w
+ for θ in lin(theta_hi, theta_lo, np_leg)[2:end]
+ ζ = phi_c + half_w + pitch * θ
+ push!(Rs, surf_R(θ))
+ push!(phis, ζ)
+ push!(Zs, surf_Z(θ))
+ end
+ # Bottom arc at theta_lo, sweep back by -coil_width, closing the loop
+ ζ_bot = phi_c + half_w + pitch * theta_lo
+ for ζ in lin(ζ_bot, ζ_bot - coil_width, np_arc)[2:end]
+ push!(Rs, surf_R(theta_lo))
+ push!(phis, ζ)
+ push!(Zs, surf_Z(theta_lo))
+ end
+ end
+ strands[j+1] = (copy(Rs), copy(phis), copy(Zs))
+ end
+
+ nsec = length(strands[1][1])
+ x = zeros(n_coils, 1, nsec)
+ y = zeros(n_coils, 1, nsec)
+ z = zeros(n_coils, 1, nsec)
+ for j in 1:n_coils
+ Rj, Pj, Zj = strands[j]
+ length(Rj) == nsec || error("make_helical: inconsistent strand length across coils")
+ for l in 1:nsec
+ x[j, 1, l] = Rj[l] * cos(Pj[l])
+ y[j, 1, l] = Rj[l] * sin(Pj[l])
+ z[j, 1, l] = Zj[l]
+ end
+ end
+ return CoilSet(name, n_coils, 1, 1.0, nsec, x, y, z, zeros(n_coils))
+end
+
+# HDF5 coil geometry I/O: one subgroup per set under a parent group; other content is ignored.
+# //x Float64[ncoil, s, nsec] (shape gives ncoil, s, nsec)
+# //y Float64[ncoil, s, nsec]
+# //z Float64[ncoil, s, nsec]
+# //currents Float64[ncoil]
+# / attr nw Float64
+
+"""
+ save_coils_to_h5(coil_sets::Vector{CoilSet}, group)
+
+Write each coil set as a subgroup (named by `CoilSet.name`) under an already-open
+HDF5 `group`. Inverse of [`load_coils_from_h5_group!`](@ref). Used by the gpec.h5
+snapshot writer so a coil run can be replayed from the output file alone.
+"""
+function save_coils_to_h5(coil_sets::Vector{CoilSet}, group)
+ for cs in coil_sets
+ g = create_group(group, cs.name)
+ g["x"] = cs.x
+ g["y"] = cs.y
+ g["z"] = cs.z
+ g["currents"] = cs.currents
+ HDF5.attrs(g)["nw"] = cs.nw
+ end
+ return nothing
+end
+
+"""
+ load_coils_from_h5_group!(coil_sets::Vector{CoilSet}, group) -> Vector{CoilSet}
+
+Populate `coil_sets` from an already-open HDF5 `group`, reading every subgroup that
+holds `x`/`y`/`z` datasets as a [`CoilSet`](@ref). Any other datasets or subgroups
+under `group` are silently ignored, so the group may live inside a larger file
+(e.g. `gpec.h5`). Mirror of [`save_coils_to_h5`](@ref).
+"""
+function load_coils_from_h5_group!(coil_sets::Vector{CoilSet}, group)
+ empty!(coil_sets)
+ for key in keys(group)
+ sub = group[key]
+ sub isa HDF5.Group || continue
+ (haskey(sub, "x") && haskey(sub, "y") && haskey(sub, "z")) || continue
+ x = Float64.(read(sub, "x"))
+ y = Float64.(read(sub, "y"))
+ z = Float64.(read(sub, "z"))
+ size(x) == size(y) == size(z) || error("x/y/z shape mismatch in coil set '$key'")
+ ndims(x) == 3 || error("coil set '$key' x/y/z must be 3D [ncoil, s, nsec]")
+ ncoil, s, nsec = size(x)
+ nw = haskey(HDF5.attrs(sub), "nw") ? Float64(HDF5.attrs(sub)["nw"]) : 1.0
+ currents = haskey(sub, "currents") ? Float64.(read(sub, "currents")) : zeros(ncoil)
+ push!(coil_sets, CoilSet(String(key), ncoil, s, nw, nsec, x, y, z, currents))
+ end
+ return coil_sets
+end
+
+"""
+ read_coil_h5(filepath; group="coils", set=nothing) -> Vector{CoilSet}
+
+Read coil sets from an HDF5 file. Coil data is expected under the `group` path;
+all coil-set subgroups there are returned (or, if `set` names one, just that set).
+Unrelated content elsewhere in the file is ignored. See [`save_coils_to_h5`](@ref)
+for the layout.
+"""
+function read_coil_h5(filepath::String; group::String="coils", set::Union{Nothing,String}=nothing)
+ isfile(filepath) || error("Coil geometry file not found: $filepath")
+ return h5open(filepath, "r") do file
+ haskey(file, group) || error("HDF5 file $filepath has no '$group' group")
+ coil_sets = CoilSet[]
+ load_coils_from_h5_group!(coil_sets, file[group])
+ isempty(coil_sets) && error("No coil sets found under '$group' in $filepath")
+ if set !== nothing
+ idx = findfirst(cs -> cs.name == set, coil_sets)
+ isnothing(idx) && error("Coil set '$set' not found under '$group' in $filepath")
+ return CoilSet[coil_sets[idx]]
+ end
+ return coil_sets
+ end
+end
+
+"""
+ write_coil_h5(filepath, coil_sets; group="coils")
+
+Write `coil_sets` to a new HDF5 file under the `group` path, one subgroup per set.
+Convenience file-level wrapper around [`save_coils_to_h5`](@ref) for export and the
+`.dat`→`.h5` converter.
+"""
+function write_coil_h5(filepath::String, coil_sets::Vector{CoilSet}; group::String="coils")
+ h5open(filepath, "w") do file
+ save_coils_to_h5(coil_sets, create_group(file, group))
+ end
+ return filepath
+end
+
+"""
+ write_coil_dat(filepath, cs::CoilSet)
+
+Write a single coil set to an ASCII `.dat` file in the legacy Fortran GPEC format
+(`ncoil s nsec nw` header, then `ncoil×s×nsec` rows of `X Y Z`).
+"""
+function write_coil_dat(filepath::String, cs::CoilSet)
+ open(filepath, "w") do io
+ println(io, "$(cs.ncoil) $(cs.s) $(cs.nsec) $(cs.nw)")
+ for j in 1:cs.ncoil, k in 1:cs.s, l in 1:cs.nsec
+ println(io, " $(cs.x[j,k,l]) $(cs.y[j,k,l]) $(cs.z[j,k,l])")
+ end
+ end
+ return filepath
+end
+
+"""
+ convert_coil_dat_to_h5(dat_path, h5_path; group="coils") -> String
+
+Convert a legacy ASCII `.dat` coil file to the modern HDF5 format (single set).
+"""
+function convert_coil_dat_to_h5(dat_path::String, h5_path::String; group::String="coils")
+ cs = read_coil_dat(dat_path)
+ return write_coil_h5(h5_path, CoilSet[cs]; group=group)
+end
+
+"""
+ convert_coil_h5_to_dat(h5_path, dat_path; group="coils", set=nothing) -> String
+
+Convert one coil set from an HDF5 file to a legacy ASCII `.dat` file. If the file holds
+multiple sets, `set` selects which one by name (required when more than one is present).
+"""
+function convert_coil_h5_to_dat(h5_path::String, dat_path::String;
+ group::String="coils", set::Union{Nothing,String}=nothing)
+ coil_sets = read_coil_h5(h5_path; group=group, set=set)
+ length(coil_sets) == 1 ||
+ error("convert_coil_h5_to_dat: $h5_path holds $(length(coil_sets)) sets; pass `set` to pick one")
+ return write_coil_dat(dat_path, coil_sets[1])
+end
+
+"""
+ nominal_major_radius(x, y, z) -> Float64
+ nominal_major_radius(cs::CoilSet) -> Float64
+
+Arc-length-weighted major radius √(x²+y²) of a strand, or of every strand of a coil set: the
+radius through which a rim displacement in metres converts to a tilt angle, `asin(t / R_nom)`,
+as `apply_transforms` does for `tilt_in_meters`. A strand with no length returns 1.
+"""
+function nominal_major_radius(x::AbstractVector, y::AbstractVector, z::AbstractVector)
+ weighted_r, total_len = _weighted_major_radius(x, y, z)
+ return total_len > 0 ? weighted_r / total_len : 1.0
+end
+
+function nominal_major_radius(cs::CoilSet)
+ weighted_r = 0.0
+ total_len = 0.0
+ for j in 1:cs.ncoil, k in 1:cs.s
+ w, l = _weighted_major_radius(view(cs.x, j, k, :), view(cs.y, j, k, :), view(cs.z, j, k, :))
+ weighted_r += w
+ total_len += l
+ end
+ return total_len > 0 ? weighted_r / total_len : 1.0
+end
+
+# Arc-length-weighted major radius sum and total arc length of one strand.
+function _weighted_major_radius(x::AbstractVector, y::AbstractVector, z::AbstractVector)
+ total_len = 0.0
+ weighted_r = 0.0
+ for l in 1:(length(x)-1)
+ xm = (x[l] + x[l+1]) / 2
+ ym = (y[l] + y[l+1]) / 2
+ dl = sqrt((x[l+1] - x[l])^2 + (y[l+1] - y[l])^2 + (z[l+1] - z[l])^2)
+ weighted_r += sqrt(xm^2 + ym^2) * dl
+ total_len += dl
+ end
+ return weighted_r, total_len
+end
+
+"""
+ _arc_length_center(x, y, z) -> (x0, y0, z0)
+
+Compute the arc-length-weighted centroid of a strand (1D array of points).
+Matches Fortran center-of-mass convention using midpoints weighted by segment length.
+"""
+function _arc_length_center(x::AbstractVector, y::AbstractVector, z::AbstractVector)
+ nsec = length(x)
+ nsec > 1 || return (x[1], y[1], z[1])
+
+ total_length = 0.0
+ x0 = 0.0
+ y0 = 0.0
+ z0 = 0.0
+ for l in 1:(nsec-1)
+ xm = (x[l] + x[l+1]) / 2
+ ym = (y[l] + y[l+1]) / 2
+ zm = (z[l] + z[l+1]) / 2
+ dl = sqrt((x[l+1] - x[l])^2 + (y[l+1] - y[l])^2 + (z[l+1] - z[l])^2)
+ x0 += xm * dl
+ y0 += ym * dl
+ z0 += zm * dl
+ total_length += dl
+ end
+ total_length > 0 || return (x[1], y[1], z[1])
+ return (x0 / total_length, y0 / total_length, z0 / total_length)
+end
+
+"""
+ apply_transforms(cs::CoilSet, cfg::CoilSetConfig; n_tilt::Int=1) -> CoilSet
+
+Apply per-conductor shifts and tilts to a coil set, returning a modified copy.
+
+Port of the Fortran `coil_read` shift/tilt logic (coil.F):
+
+ - Tilts are rotations around the arc-length-weighted center of mass (unless `rotation_center_x/_y/_z` specified)
+ - `n_tilt` controls the toroidal periodicity of tilt/shift modulation
+ - n_tilt = 0: rigid shift only (no tilts applied)
+ - n_tilt ≥ 1: n-fold modulated perturbations
+"""
+function apply_transforms(cs::CoilSet, cfg::CoilSetConfig; n_tilt::Int=1)
+ ncoil = cs.ncoil
+ s = cs.s
+ nsec = cs.nsec
+
+ # Pad config vectors to ncoil length with zeros
+ _pad(v, n) = length(v) >= n ? Float64.(v[1:n]) : vcat(Float64.(v), zeros(n - length(v)))
+
+ shiftx = _pad(cfg.shiftx, ncoil)
+ shifty = _pad(cfg.shifty, ncoil)
+ shiftz = _pad(cfg.shiftz, ncoil)
+ tiltx_cfg = _pad(cfg.tiltx, ncoil)
+ tilty_cfg = _pad(cfg.tilty, ncoil)
+ tiltz_cfg = _pad(cfg.tiltz, ncoil)
+
+ xnom_cfg = _pad(isempty(cfg.rotation_center_x) ? fill(_NOM_UNSET_SENTINEL, ncoil) : cfg.rotation_center_x, ncoil)
+ ynom_cfg = _pad(isempty(cfg.rotation_center_y) ? fill(_NOM_UNSET_SENTINEL, ncoil) : cfg.rotation_center_y, ncoil)
+ znom_cfg = _pad(isempty(cfg.rotation_center_z) ? fill(_NOM_UNSET_SENTINEL, ncoil) : cfg.rotation_center_z, ncoil)
+
+ # n_tilt = 0 applies no tilts (Fortran: no n=0 component)
+ apply_tilt = n_tilt != 0
+
+ new_x = copy(cs.x)
+ new_y = copy(cs.y)
+ new_z = copy(cs.z)
+
+ for j in 1:ncoil
+ sx = shiftx[j]
+ sy = shifty[j]
+ sz = shiftz[j]
+ tx_deg = tiltx_cfg[j]
+ ty_deg = tilty_cfg[j]
+ tz_deg = tiltz_cfg[j]
+
+ has_shift = abs(sx) + abs(sy) + abs(sz) > 0
+ has_tilt = apply_tilt && (abs(tx_deg) + abs(ty_deg) + abs(tz_deg) > 0)
+ (has_shift || has_tilt) || continue
+
+ for k in 1:s
+ # Compute rotation center for this strand
+ x0, y0, z0 = begin
+ cx, cy, cz = _arc_length_center(
+ view(cs.x, j, k, :), view(cs.y, j, k, :), view(cs.z, j, k, :)
+ )
+ # Use user-specified center if provided (|nom| < _NOM_THRESHOLD, matching Fortran)
+ x0 = abs(xnom_cfg[j]) < _NOM_THRESHOLD ? xnom_cfg[j] : cx
+ y0 = abs(ynom_cfg[j]) < _NOM_THRESHOLD ? ynom_cfg[j] : cy
+ z0 = abs(znom_cfg[j]) < _NOM_THRESHOLD ? znom_cfg[j] : cz
+ (x0, y0, z0)
+ end
+
+ # Nominal radius for the tilt_in_meters conversion
+ r_nom = cfg.tilt_in_meters ? nominal_major_radius(view(cs.x, j, k, :), view(cs.y, j, k, :), view(cs.z, j, k, :)) : 1.0
+
+ # Convert tilt to radians
+ dtor = π / 180.0
+ tiltx, tilty, tiltz = if cfg.tilt_in_meters
+ asin(tx_deg / r_nom), asin(ty_deg / r_nom), asin(tz_deg / r_nom)
+ else
+ tx_deg * dtor, ty_deg * dtor, tz_deg * dtor
+ end
+
+ for l in 1:nsec
+ # Work in center frame. Tilts are superposed as independent small-angle
+ # perturbations (linear addition), matching Fortran coil.F convention.
+ xc = cs.x[j, k, l] - x0
+ yc = cs.y[j, k, l] - y0
+ zc = cs.z[j, k, l] - z0
+
+ # Perturbations start at center offset (so final = original + perturbations)
+ dx = x0
+ dy = y0
+ dz = z0
+ phi = atan(yc, xc)
+
+ # Z-tilt: rotate in xy-plane (toroidal clocking)
+ if tiltz != 0
+ r = sqrt(xc^2 + yc^2)
+ ang = atan(yc, xc) + tiltz * cos((n_tilt - 1) * phi)
+ dx += r * cos(ang) - xc
+ dy += r * sin(ang) - yc
+ end
+
+ # Y-tilt: rotate in xz-plane
+ if tilty != 0
+ r = sqrt(xc^2 + zc^2)
+ ang = atan(zc, xc) + tilty * cos((n_tilt - 1) * phi)
+ dx += r * cos(ang) - xc
+ dz += r * sin(ang) - zc
+ end
+
+ # X-tilt: rotate in yz-plane (n=1 is constant, n>1 is sin-modulated)
+ if tiltx != 0
+ r = sqrt(zc^2 + yc^2)
+ ang = if n_tilt == 1
+ atan(zc, yc) + tiltx
+ else
+ atan(zc, yc) + tiltx * sin((n_tilt - 1) * phi)
+ end
+ dy += r * cos(ang) - yc
+ dz += r * sin(ang) - zc
+ end
+
+ # Shift: n=0 is rigid; n>0 is radial petal pattern
+ if n_tilt == 0
+ dx += sx
+ dy += sy
+ else
+ dr = sx * cos(n_tilt * phi) + sy * sin(n_tilt * phi)
+ dx += dr * cos(phi)
+ dy += dr * sin(phi)
+ end
+ dz += sz
+
+ new_x[j, k, l] = xc + dx
+ new_y[j, k, l] = yc + dy
+ new_z[j, k, l] = zc + dz
+ end
+ end
+ end
+
+ return CoilSet(cs.name, ncoil, s, cs.nw, nsec, new_x, new_y, new_z, cs.currents)
+end
+
+"""
+ _resolve_coil_path(cfg::CoilConfig, set_cfg::CoilSetConfig) -> String
+
+Resolve the path to a coil geometry file. Prefers `set_cfg.h5_file`, then
+`set_cfg.dat_file`, otherwise constructs `{dat_dir}/{machine}_{name}.dat`.
+"""
+function _resolve_coil_path(cfg::CoilConfig, set_cfg::CoilSetConfig)
+ isempty(set_cfg.h5_file) || return set_cfg.h5_file
+ isempty(set_cfg.dat_file) || return set_cfg.dat_file
+ isempty(set_cfg.name) &&
+ error("CoilSetConfig must specify a `source`, or a `name`/`dat_file`/`h5_file`")
+ prefix = isempty(cfg.machine) ? "" : "$(cfg.machine)_"
+ return joinpath(cfg.dat_dir, "$(prefix)$(set_cfg.name).dat")
+end
+
+"""
+ _build_raw_coil_set(cfg::CoilConfig, sc::CoilSetConfig; equil=nothing) -> CoilSet
+
+Produce the un-transformed coil set for a config block, dispatching on `sc.source`:
+analytic generators (`pf_hoop`/`window_pane`/`helical`) or a geometry file
+(`.h5` → [`read_coil_h5`](@ref), else `.dat` → [`read_coil_dat`](@ref)). Currents and
+shifts/tilts are applied by the caller, so all sources share the same downstream path.
+"""
+function _build_raw_coil_set(cfg::CoilConfig, sc::CoilSetConfig; equil=nothing)
+ if sc.source == "pf_hoop"
+ kw = sc.points_per_coil > 0 ? (; nsec=sc.points_per_coil) : (;)
+ return make_pf_hoop(; radius=sc.radius, height=sc.height,
+ name=isempty(sc.name) ? "pf_hoop" : sc.name, kw...)
+ elseif sc.source == "window_pane"
+ has_corners = !isempty(sc.rz_corners)
+ has_standoff = !isnan(sc.standoff) && !isnan(sc.poloidal_angle)
+ if has_corners && has_standoff
+ error("window_pane: provide EITHER rz_corners (corner mode) OR " *
+ "standoff+poloidal_angle (standoff mode), not both")
+ elseif has_standoff
+ equil === nothing &&
+ error("window_pane standoff mode (standoff/poloidal_angle) requires an equilibrium; " *
+ "pass `equil` to load_coil_sets, or use rz_corners for corner mode")
+ return make_window_pane_standoff(equil; standoff=sc.standoff,
+ poloidal_angle=sc.poloidal_angle, poloidal_length=sc.poloidal_length,
+ poloidal_tilt=sc.poloidal_tilt, ncoil=sc.n_coils,
+ gap_fraction=sc.gap_fraction, phi0=sc.phi0,
+ name=isempty(sc.name) ? "window_pane" : sc.name)
+ elseif has_corners
+ return make_window_pane(; ncoil=sc.n_coils, rz_corners=sc.rz_corners,
+ gap_fraction=sc.gap_fraction, phi0=sc.phi0,
+ name=isempty(sc.name) ? "window_pane" : sc.name)
+ else
+ error("window_pane: supply rz_corners (corner mode) or " *
+ "standoff+poloidal_angle (standoff mode)")
+ end
+ elseif sc.source == "helical"
+ kw = sc.points_per_coil > 0 ? (; npts=sc.points_per_coil) : (;)
+ return make_helical(; R0=sc.R0, a=sc.a, m=sc.m_hel, n=sc.n_hel,
+ theta_lo=sc.theta_lo, theta_hi=sc.theta_hi, n_coils=sc.n_coils,
+ gap_fraction=sc.gap_fraction, phi0=sc.phi0, offset=sc.offset,
+ name=isempty(sc.name) ? "helical" : sc.name, kw...)
+ elseif sc.source == "" || sc.source == "file"
+ path = _resolve_coil_path(cfg, sc)
+ ext = lowercase(splitext(path)[2])
+ if ext in (".h5", ".hdf5")
+ sets = read_coil_h5(path; set=isempty(sc.name) ? nothing : sc.name)
+ length(sets) == 1 ||
+ error("h5 coil file $path holds $(length(sets)) sets; set `name` to pick one")
+ return sets[1]
+ end
+ return read_coil_dat(path)
+ else
+ error("Unknown coil set source: '$(sc.source)' " *
+ "(expected \"\", \"file\", \"pf_hoop\", \"window_pane\", or \"helical\")")
+ end
+end
+
+"""
+ load_coil_sets(cfg::CoilConfig, n_tilt::Int; equil=nothing) -> Vector{CoilSet}
+
+Build all coil sets from config (file or analytic source), apply currents and
+shifts/tilts, and return ready-to-use coil data. `n_tilt` is the toroidal mode number
+for modulated perturbations (typically the run's n). `equil` is required only when a
+`window_pane` set uses standoff placement (it locates the surface point and normal).
+"""
+function load_coil_sets(cfg::CoilConfig, n_tilt::Int; equil=nothing)
+ isempty(cfg.coil_sets) && error("No coil sets specified in [ForcingTerms] configuration")
+
+ coil_sets = CoilSet[]
+ for set_cfg in cfg.coil_sets
+ cs_raw = _build_raw_coil_set(cfg, set_cfg; equil=equil)
+
+ # Set currents (pad or truncate to ncoil)
+ ncoil = cs_raw.ncoil
+ currents = if isempty(set_cfg.currents)
+ zeros(ncoil)
+ else
+ len = length(set_cfg.currents)
+ len >= ncoil ? Float64.(set_cfg.currents[1:ncoil]) :
+ vcat(Float64.(set_cfg.currents), zeros(ncoil - len))
+ end
+ cs_with_currents = CoilSet(
+ cs_raw.name, ncoil, cs_raw.s, cs_raw.nw, cs_raw.nsec,
+ cs_raw.x, cs_raw.y, cs_raw.z, currents
+ )
+
+ # Resolve n_tilt: -1 means inherit from run
+ effective_n = set_cfg.n_tilt == -1 ? n_tilt : set_cfg.n_tilt
+
+ cs = apply_transforms(cs_with_currents, set_cfg; n_tilt=effective_n)
+ push!(coil_sets, cs)
+ end
+ return coil_sets
+end
+
+export CoilSet, CoilSetConfig, CoilConfig
+export read_coil_dat, apply_transforms, load_coil_sets, nominal_major_radius
+export make_pf_hoop, make_window_pane, make_helical
+export make_window_pane_standoff, surface_point_and_normal
+export read_coil_h5, write_coil_h5, write_coil_dat, save_coils_to_h5, load_coils_from_h5_group!
+export convert_coil_dat_to_h5, convert_coil_h5_to_dat
diff --git a/src/ForcingTerms/ForcingTerms.jl b/src/ForcingTerms/ForcingTerms.jl
new file mode 100644
index 0000000000..98738ad6ae
--- /dev/null
+++ b/src/ForcingTerms/ForcingTerms.jl
@@ -0,0 +1,401 @@
+module ForcingTerms
+# Module for external field specification and forcing term calculations
+
+using DelimitedFiles
+using HDF5
+using LinearAlgebra
+
+import ..Equilibrium
+import ..Utilities.FourierTransforms
+import ..Utilities.FourierTransforms: compute_fourier_coefficients
+
+"""
+ ForcingTermsControl
+
+User-facing control parameters from TOML [ForcingTerms] section. A deck run resolves its relative
+file paths against the deck directory; a script's resolve against the working directory.
+
+## Fields
+
+Forcing Data:
+
+ - `forcing_data_file::String` - Path to forcing data file (n, m, complex amplitude)
+ - `forcing_data_format::String` - Format: "ascii", "hdf5", or "coil"
+
+Coil settings (used when `forcing_data_format = "coil"`):
+
+ - `machine::String` - Machine name prefix for .dat files (e.g. "d3d")
+ - `dat_dir::String` - Directory containing .dat files; defaults to bundled `coil_geometries/`
+ - `mtheta_coil::Int` - Poloidal grid resolution for boundary field evaluation (default: 480)
+ - `nzeta_coil::Int` - Toroidal grid resolution; 0 = auto (32 × n)
+ - `coil_sets_raw::Vector{Dict{String,Any}}` - Parsed `[[ForcingTerms.coil_set]]` TOML blocks
+"""
+@kwdef struct ForcingTermsControl
+ # Forcing data file settings (ascii/hdf5 formats)
+ forcing_data_file::String = "forcing.dat"
+ forcing_data_format::String = "ascii"
+
+ # Coil calculation settings (coil format)
+ machine::String = ""
+ dat_dir::String = ""
+ mtheta_coil::Int = 480
+ nzeta_coil::Int = 0
+ coil_sets_raw::Vector{Dict{String,Any}} = Dict{String,Any}[]
+end
+
+"""
+ ForcingMode
+
+Data structure for a single forcing mode.
+
+## Fields
+
+ - `n::Int` - Toroidal mode number
+
+ - `m::Int` - Poloidal mode number
+ - `amplitude::ComplexF64` - Complex amplitude in unit-norm convention (= Fortran Phi_x,
+ T·m² per unit-norm cell) after loading. File inputs are tagged by their input convention:
+
+ + `"normal_field_T"`: B·n̂ in Tesla (2π-angle); converted to unit-norm on load
+ + `"sfl_flux_Wb"`: SFL flux in 2π-angle convention; multiplied by (2π)² on load
+ + `"unit_flux"`: already unit-norm (a run's materialized forcing, recorded for replay); loaded as is
+"""
+Base.@kwdef mutable struct ForcingMode
+ n::Int = 0
+ m::Int = 0
+ amplitude::ComplexF64 = 0.0 + 0.0im
+end
+
+"""
+ load_forcing_data!(forcing_modes, filepath, forcing_data_format, verbose=false) -> String
+
+Load forcing data from ASCII or HDF5 file. Returns the normalization tag read
+from the file (or `"normal_field_T"` by default if no tag is present).
+
+**Normalization tags** (set in the file, not in the TOML):
+
+ - `"normal_field_T"` (default): Fourier modes of B·n̂ [Tesla], 2π-angle convention;
+ converted to unit-norm (Phi_x) on load.
+ - `"sfl_flux_Wb"`: SFL flux R×(B_R·∂Z/∂θ - B_Z·∂R/∂θ) [T·m²], 2π-angle convention.
+ Multiplied by (2π)² on load to reach unit-norm (Phi_x).
+ - `"unit_flux"`: already unit-norm (Phi_x), as a run records its materialized forcing for replay; loaded as is.
+
+**ASCII format** — optional `# normalization: ` header line, then data rows:
+
+```
+# normalization: normal_field_T
+1 2 0.5 0.1
+1 3 0.3 -0.2
+```
+
+Columns: n, m, amplitude_real, amplitude_imag
+
+**HDF5 format** — optional root attribute `normalization` (string), plus datasets:
+
+ - `"n"`: Integer array of toroidal mode numbers
+ - `"m"`: Integer array of poloidal mode numbers
+ - `"amplitude_real"`: Real parts of amplitudes
+ - `"amplitude_imag"`: Imaginary parts of amplitudes
+"""
+function load_forcing_data!(
+ forcing_modes::Vector{ForcingMode},
+ filepath::String,
+ forcing_data_format::String,
+ verbose::Bool=false
+)::String
+
+ if verbose
+ @info "Loading forcing data from $filepath"
+ end
+
+ norm_tag = if forcing_data_format == "ascii"
+ load_forcing_ascii!(forcing_modes, filepath, verbose)
+ elseif forcing_data_format == "hdf5"
+ load_forcing_hdf5!(forcing_modes, filepath, verbose)
+ else
+ error("Unknown forcing data format: $(forcing_data_format). Use 'ascii' or 'hdf5'.")
+ end
+
+ if verbose
+ @info "Loaded $(length(forcing_modes)) forcing modes (normalization: $norm_tag)"
+ end
+ return norm_tag
+end
+
+"""
+ load_forcing_ascii!(forcing_modes, filepath, verbose) -> String
+
+Load forcing data from ASCII file. Returns normalization tag (`"normal_field_T"` by default).
+
+Optional first `# normalization: ` header line sets the normalization.
+Remaining `#`-prefixed lines and blank lines are ignored. Data columns: n, m, amplitude_real, amplitude_imag.
+"""
+function load_forcing_ascii!(
+ forcing_modes::Vector{ForcingMode},
+ filepath::String,
+ verbose::Bool
+)::String
+ if !isfile(filepath)
+ error("Forcing data file not found: $filepath")
+ end
+
+ norm_tag = "normal_field_T" # default
+
+ # Scan header lines for normalization tag before passing to readdlm
+ open(filepath, "r") do io
+ for line in eachline(io)
+ stripped = strip(line)
+ isempty(stripped) && continue
+ startswith(stripped, '#') || break # stop at first non-comment line
+ m = match(r"#\s*normalization\s*:\s*(\S+)", stripped)
+ if !isnothing(m)
+ norm_tag = m.captures[1]
+ end
+ end
+ end
+
+ data = readdlm(filepath; comments=true, comment_char=('#'))
+ nrows = size(data, 1)
+ ncols = size(data, 2)
+
+ if ncols < 4
+ error("ASCII forcing file must have 4 columns (n, m, amplitude_real, amplitude_imag)")
+ end
+
+ empty!(forcing_modes)
+
+ for i in 1:nrows
+ n = Int(data[i, 1])
+ m = Int(data[i, 2])
+ real_part = Float64(data[i, 3])
+ imag_part = Float64(data[i, 4])
+
+ push!(forcing_modes, ForcingMode(;
+ n=n,
+ m=m,
+ amplitude=complex(real_part, imag_part)
+ ))
+ end
+ return norm_tag
+end
+
+"""
+ load_forcing_hdf5!(forcing_modes, filepath, verbose) -> String
+
+Load forcing data from HDF5 file. Returns normalization tag (`"normal_field_T"` by default).
+
+Optional root attribute `normalization` (string) sets the normalization.
+Required datasets: `n`, `m`, `amplitude_real`, `amplitude_imag`.
+"""
+function load_forcing_hdf5!(
+ forcing_modes::Vector{ForcingMode},
+ filepath::String,
+ verbose::Bool
+)::String
+ if !isfile(filepath)
+ error("Forcing data file not found: $filepath")
+ end
+ return h5open(file -> load_forcing_from_h5_group!(forcing_modes, file), filepath, "r")
+end
+
+# Coil-forcing helpers; these depend on ForcingTermsControl and ForcingMode defined above.
+include("CoilGeometry.jl")
+include("BiotSavart.jl")
+include("CoilFourier.jl")
+
+"""
+ save_forcing_to_h5(forcing_modes::Vector{ForcingMode}, group; normalization="normal_field_T")
+
+Write forcing modes to an open HDF5 group (or file root) in the layout `load_forcing_hdf5!`
+consumes: datasets `n`, `m`, `amplitude_real`, `amplitude_imag` and the `normalization`
+attribute. Used by the gpec.h5 snapshot writer so the replay path can re-read forcing data
+from the output file with no reference to the original ASCII/HDF5 ingest file.
+"""
+function save_forcing_to_h5(forcing_modes::Vector{ForcingMode}, group; normalization::String="normal_field_T")
+ group["n"] = Int[mode.n for mode in forcing_modes]
+ group["m"] = Int[mode.m for mode in forcing_modes]
+ group["amplitude_real"] = Float64[real(mode.amplitude) for mode in forcing_modes]
+ group["amplitude_imag"] = Float64[imag(mode.amplitude) for mode in forcing_modes]
+ HDF5.attrs(group)["normalization"] = normalization
+ return nothing
+end
+
+"""
+ load_forcing_from_h5_group!(forcing_modes::Vector{ForcingMode}, group) -> String
+
+Populate `forcing_modes` from an already-open HDF5 group (or file root) with datasets `n`,
+`m`, `amplitude_real`, `amplitude_imag`, and return its `normalization` attribute
+(`"normal_field_T"` when absent). Mirror of `save_forcing_to_h5`, shared by the forcing-file
+reader and the rerun path that reads `gpec.h5/Input/RawInputs/ForcingTerms/`.
+"""
+function load_forcing_from_h5_group!(forcing_modes::Vector{ForcingMode}, group)::String
+ tag = haskey(HDF5.attrs(group), "normalization") ? HDF5.attrs(group)["normalization"] : "normal_field_T"
+ n_array = read(group, "n")
+ m_array = read(group, "m")
+ amp_real = read(group, "amplitude_real")
+ amp_imag = read(group, "amplitude_imag")
+
+ if length(n_array) != length(m_array) || length(n_array) != length(amp_real)
+ error("Inconsistent array lengths in HDF5 forcing group")
+ end
+
+ empty!(forcing_modes)
+ for i in eachindex(n_array)
+ push!(forcing_modes, ForcingMode(;
+ n=Int(n_array[i]),
+ m=Int(m_array[i]),
+ amplitude=complex(amp_real[i], amp_imag[i])
+ ))
+ end
+ return tag
+end
+
+"""
+ RMPField
+
+Abstract supertype of every external-forcing description the scripting API accepts: a
+resonant-magnetic-perturbation field, described by where it comes from and how strongly it
+drives (a forcing-mode file, a coil set with currents, or a precomputed spectrum).
+
+Nothing is read or computed at construction; the modes are materialized against an equilibrium
+when the perturbed-equilibrium stage runs, so one `RMPField` can drive several solves.
+
+## Construction
+
+ RMPField(path; format=..., scale=1.0, kwargs...)
+ RMPField(coil_sets::Vector{Dict{String,Any}}; scale=1.0, kwargs...)
+ RMPField(ctrl::ForcingTermsControl; scale=1.0)
+ RMPField(modes::Vector{ForcingMode}; scale=1.0)
+
+The first form points at a forcing-mode file, `format` defaulting to `"hdf5"` for an `.h5`
+or `.hdf5` extension and `"ascii"` otherwise. The second form takes TOML-shaped coil blocks
+(the `[[ForcingTerms.coil_set]]` layout) and selects the coil format. Remaining `kwargs` are
+[`ForcingTermsControl`](@ref) fields. These three return a single-source leaf
+([`RMPSource`](@ref)). The last form takes a control-surface spectrum computed elsewhere, already in
+the unit-norm `Φ_x` convention, and returns a spectrum-literal leaf ([`RMPSpectrum`](@ref)).
+
+## Algebra
+
+`+`, `-` and multiplication by a real or complex scalar (a complex factor phase-rotates the
+perturbation) build lazy linear combinations. The response is linear in the forcing, so each term
+is materialized on the control surface and the mode amplitudes are summed.
+
+```julia
+nominal = RMPField("nominal_efc.dat")
+weld_field = RMPField("weld_fields.h5"; scale=0.5)
+total = 2.0 * nominal + weld_field # lazy: records terms and weights, computes nothing
+pe = perturbed_equilibrium(plasma_response(ffs), total) # materializes each term, sums, drives PE
+```
+
+Physical amplitude lives in the forcing description (per-conductor currents for coils,
+`ForcingMode.amplitude` for files). `scale` is NOT a physical amplitude: it is the source's weight
+in a linear combination, applied uniformly to the materialized spectrum of every toroidal mode.
+A source that is not a scalar multiple of another needs its own description: a coil set with a
+failed conductor is `nominal - failed_coil`, not `0.9 * nominal`.
+"""
+abstract type RMPField end
+
+"""
+ RMPSource
+
+A single-source [`RMPField`](@ref) leaf: one forcing description plus a complex weight.
+Built by the `RMPField` constructors; scalar multiplication rescales the weight.
+
+## Fields
+
+ - `ctrl::ForcingTermsControl` - The forcing source: format, file path or machine, and the raw coil-set blocks.
+ - `scale::ComplexF64` - The source's weight in a linear combination, applied to the materialized control-surface spectrum (complex = phase rotation). Not a physical amplitude.
+"""
+struct RMPSource <: RMPField
+ ctrl::ForcingTermsControl
+ scale::ComplexF64
+end
+
+"""
+ RMPSpectrum
+
+A spectrum-literal [`RMPField`](@ref) leaf: control-surface forcing modes computed elsewhere, in the
+unit-norm `Φ_x` convention the response consumes, plus a complex weight. Built by
+`RMPField(modes::Vector{ForcingMode})`; scalar multiplication rescales the weight.
+
+## Fields
+
+ - `modes::Vector{ForcingMode}` - The control-surface spectrum, copied at construction.
+ - `scale::ComplexF64` - The leaf's weight in a linear combination, as for [`RMPSource`](@ref).
+"""
+struct RMPSpectrum <: RMPField
+ modes::Vector{ForcingMode}
+ scale::ComplexF64
+end
+
+"""
+ RMPFieldSum
+
+A lazy linear combination of [`RMPSource`](@ref) and [`RMPSpectrum`](@ref) leaves, built by `+`/`-` on
+[`RMPField`](@ref)s. Holds the flattened term list; scalar multiplication distributes onto
+the leaves. Materialization evaluates each term against the equilibrium and sums the mode
+amplitudes — valid because the perturbed-equilibrium response is linear in the forcing.
+
+## Fields
+
+ - `terms::Vector{Union{RMPSource,RMPSpectrum}}` - The flattened weighted leaves.
+"""
+struct RMPFieldSum <: RMPField
+ terms::Vector{Union{RMPSource,RMPSpectrum}}
+end
+
+"""
+ _infer_format(path) -> String
+
+Forcing-data format implied by a file extension: `"hdf5"` for `.h5`/`.hdf5`, else `"ascii"`.
+"""
+_infer_format(path::AbstractString) = lowercase(splitext(path)[2]) in (".h5", ".hdf5") ? "hdf5" : "ascii"
+
+RMPField(ctrl::ForcingTermsControl; scale::Number=1.0) = RMPSource(ctrl, ComplexF64(scale))
+
+function RMPField(path::AbstractString; format::String=_infer_format(path), scale::Number=1.0, kwargs...)
+ ctrl = ForcingTermsControl(; forcing_data_file=abspath(path), forcing_data_format=format, kwargs...)
+ return RMPSource(ctrl, ComplexF64(scale))
+end
+
+function RMPField(coil_sets::Vector{Dict{String,Any}}; scale::Number=1.0, kwargs...)
+ ctrl = ForcingTermsControl(; forcing_data_format="coil", coil_sets_raw=coil_sets, kwargs...)
+ return RMPSource(ctrl, ComplexF64(scale))
+end
+
+RMPField(modes::Vector{ForcingMode}; scale::Number=1.0) =
+ RMPSpectrum([ForcingMode(; n=mode.n, m=mode.m, amplitude=mode.amplitude) for mode in modes], ComplexF64(scale))
+
+"""
+Flattened weighted-leaf list of any [`RMPField`](@ref).
+"""
+_rmp_terms(f::Union{RMPSource,RMPSpectrum}) = Union{RMPSource,RMPSpectrum}[f]
+_rmp_terms(f::RMPFieldSum) = f.terms
+
+Base.:+(a::RMPField, b::RMPField) = RMPFieldSum(vcat(_rmp_terms(a), _rmp_terms(b)))
+Base.:-(a::RMPField) = -1 * a
+Base.:-(a::RMPField, b::RMPField) = a + (-1 * b)
+Base.:*(c::Number, f::RMPSource) = RMPSource(f.ctrl, ComplexF64(c) * f.scale)
+Base.:*(c::Number, f::RMPSpectrum) = RMPSpectrum(f.modes, ComplexF64(c) * f.scale)
+Base.:*(c::Number, f::RMPFieldSum) = RMPFieldSum([c * t for t in f.terms])
+Base.:*(f::RMPField, c::Number) = c * f
+
+"""
+ snapshot_forcing_modes(ft_ctrl; verbose=false) -> Union{Nothing,Tuple{Vector{ForcingMode},String}}
+
+The raw file-based forcing modes of `ft_ctrl` and their normalization tag, so they land in
+`Input/RawInputs/ForcingTerms/` alongside the TOML blob; `nothing` for coil forcing, which is
+recomputed from the `[[coil_set]]` TOML blob on replay. They feed only the writer:
+the PE stage reads and normalizes the forcing file itself.
+"""
+function snapshot_forcing_modes(ft_ctrl::ForcingTermsControl; verbose::Bool=false)
+ ft_ctrl.forcing_data_format in ("ascii", "hdf5") || return nothing
+ modes = ForcingMode[]
+ normalization = load_forcing_data!(modes, ft_ctrl.forcing_data_file, ft_ctrl.forcing_data_format, verbose)
+ return modes, normalization
+end
+
+
+export ForcingTermsControl, ForcingMode, RMPField, load_forcing_data!, save_forcing_to_h5, load_forcing_from_h5_group!
+
+end # module ForcingTerms
diff --git a/src/ForcingTerms/coil_geometries/README.md b/src/ForcingTerms/coil_geometries/README.md
new file mode 100644
index 0000000000..cb56f30ef9
--- /dev/null
+++ b/src/ForcingTerms/coil_geometries/README.md
@@ -0,0 +1,50 @@
+# Coil Geometry Files
+
+3D coil winding geometry files for various fusion devices, ported from the
+Fortran GPEC coil library.
+
+## File Format
+
+Each `.dat` file uses the Fortran GPEC ASCII format:
+- **Header line**: `ncoil s nsec nw`
+ - `ncoil`: number of coils in the toroidal array
+ - `s`: number of strands per coil
+ - `nsec`: number of cross-section points per strand
+ - `nw`: number of winding turns
+- **Data lines**: `ncoil × s × nsec` rows, each with `X Y Z` in meters (Cartesian lab frame)
+
+All `ncoil` conductors are stored explicitly (the Biot-Savart computation iterates over
+every one); a toroidal array is written out as its full set of conductors, not a single
+representative coil.
+
+## HDF5 format
+
+Coil geometry can also be stored in HDF5, which is the modern format and the one used for
+the self-contained `gpec.h5` rerun snapshot. One file holds one **subgroup per coil set**
+under a parent group (default `coils`), and any unrelated content in the file is ignored:
+
+```text
+//x Float64 ncoil×s×nsec Cartesian metres
+//y Float64 ncoil×s×nsec
+//z Float64 ncoil×s×nsec
+//currents Float64 ncoil optional
+/ attr nw Float64 winding multiplier, default 1.0
+```
+
+The bundled device library is kept as `.dat` files (human-readable and diff-able in git);
+use `convert_coil_dat_to_h5` / `convert_coil_h5_to_dat` to move between formats.
+
+## Naming Convention
+
+Files are named `{device}_{coil_name}.dat`:
+- `d3d_c` / `d3d_il` / `d3d_iu` — DIII-D C-coil, I-coil lower/upper
+- `nstx_*` / `nstx_u*` — NSTX and NSTX-U coils
+- `iter_*` — ITER ELM/VS/blanket coils
+- `kstar_*` — KSTAR IVCC/FEC coils
+- `jet_*` — JET EFCC/saddle coils
+- `mast_*` / `mastu_*` — MAST and MAST-U coils
+- `aug_*` — ASDEX Upgrade B-coils
+- `east_*` — EAST RMP coils
+- `compass_*` — COMPASS saddle coils
+- `rfxmod_*` — RFX-mod coils
+- `jtext_*` — J-TEXT coils
diff --git a/src/ForcingTerms/coil_geometries/aug_bl.dat b/src/ForcingTerms/coil_geometries/aug_bl.dat
new file mode 100644
index 0000000000..36029c3200
--- /dev/null
+++ b/src/ForcingTerms/coil_geometries/aug_bl.dat
@@ -0,0 +1,809 @@
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diff --git a/src/ForcingTerms/coil_geometries/aug_bu.dat b/src/ForcingTerms/coil_geometries/aug_bu.dat
new file mode 100644
index 0000000000..f7cdcd3b2f
--- /dev/null
+++ b/src/ForcingTerms/coil_geometries/aug_bu.dat
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diff --git a/src/ForcingTerms/coil_geometries/compass_bottom.dat b/src/ForcingTerms/coil_geometries/compass_bottom.dat
new file mode 100644
index 0000000000..82c3dd44fc
--- /dev/null
+++ b/src/ForcingTerms/coil_geometries/compass_bottom.dat
@@ -0,0 +1,1065 @@
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diff --git a/src/ForcingTerms/coil_geometries/compass_hfs_down.dat b/src/ForcingTerms/coil_geometries/compass_hfs_down.dat
new file mode 100644
index 0000000000..4036946176
--- /dev/null
+++ b/src/ForcingTerms/coil_geometries/compass_hfs_down.dat
@@ -0,0 +1,737 @@
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diff --git a/src/ForcingTerms/coil_geometries/compass_hfs_up.dat b/src/ForcingTerms/coil_geometries/compass_hfs_up.dat
new file mode 100644
index 0000000000..3662426b2e
--- /dev/null
+++ b/src/ForcingTerms/coil_geometries/compass_hfs_up.dat
@@ -0,0 +1,737 @@
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diff --git a/src/ForcingTerms/coil_geometries/compass_lfs_down.dat b/src/ForcingTerms/coil_geometries/compass_lfs_down.dat
new file mode 100644
index 0000000000..d4f1be6bbc
--- /dev/null
+++ b/src/ForcingTerms/coil_geometries/compass_lfs_down.dat
@@ -0,0 +1,841 @@
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diff --git a/src/ForcingTerms/coil_geometries/compass_lfs_mid.dat b/src/ForcingTerms/coil_geometries/compass_lfs_mid.dat
new file mode 100644
index 0000000000..c8e2132f63
--- /dev/null
+++ b/src/ForcingTerms/coil_geometries/compass_lfs_mid.dat
@@ -0,0 +1,1097 @@
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diff --git a/src/ForcingTerms/coil_geometries/compass_lfs_mid_down.dat b/src/ForcingTerms/coil_geometries/compass_lfs_mid_down.dat
new file mode 100644
index 0000000000..5a0b9c5d11
--- /dev/null
+++ b/src/ForcingTerms/coil_geometries/compass_lfs_mid_down.dat
@@ -0,0 +1,849 @@
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diff --git a/src/ForcingTerms/coil_geometries/compass_lfs_mid_up.dat b/src/ForcingTerms/coil_geometries/compass_lfs_mid_up.dat
new file mode 100644
index 0000000000..073e91b1e7
--- /dev/null
+++ b/src/ForcingTerms/coil_geometries/compass_lfs_mid_up.dat
@@ -0,0 +1,841 @@
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diff --git a/src/ForcingTerms/coil_geometries/compass_lfs_up.dat b/src/ForcingTerms/coil_geometries/compass_lfs_up.dat
new file mode 100644
index 0000000000..d23a8b23fd
--- /dev/null
+++ b/src/ForcingTerms/coil_geometries/compass_lfs_up.dat
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diff --git a/src/ForcingTerms/coil_geometries/compass_top.dat b/src/ForcingTerms/coil_geometries/compass_top.dat
new file mode 100644
index 0000000000..7d553181fb
--- /dev/null
+++ b/src/ForcingTerms/coil_geometries/compass_top.dat
@@ -0,0 +1,1065 @@
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diff --git a/src/ForcingTerms/coil_geometries/d3d_c.dat b/src/ForcingTerms/coil_geometries/d3d_c.dat
new file mode 100644
index 0000000000..1faf0077fc
--- /dev/null
+++ b/src/ForcingTerms/coil_geometries/d3d_c.dat
@@ -0,0 +1,1459 @@
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diff --git a/src/ForcingTerms/coil_geometries/d3d_il.dat b/src/ForcingTerms/coil_geometries/d3d_il.dat
new file mode 100644
index 0000000000..d29dd12faf
--- /dev/null
+++ b/src/ForcingTerms/coil_geometries/d3d_il.dat
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diff --git a/src/ForcingTerms/coil_geometries/d3d_il_old.dat b/src/ForcingTerms/coil_geometries/d3d_il_old.dat
new file mode 100644
index 0000000000..3a8d1e50dc
--- /dev/null
+++ b/src/ForcingTerms/coil_geometries/d3d_il_old.dat
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diff --git a/src/ForcingTerms/coil_geometries/d3d_im_design.dat b/src/ForcingTerms/coil_geometries/d3d_im_design.dat
new file mode 100644
index 0000000000..dec75e77bf
--- /dev/null
+++ b/src/ForcingTerms/coil_geometries/d3d_im_design.dat
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diff --git a/src/ForcingTerms/coil_geometries/d3d_im_design_slim.dat b/src/ForcingTerms/coil_geometries/d3d_im_design_slim.dat
new file mode 100644
index 0000000000..292b89cbc1
--- /dev/null
+++ b/src/ForcingTerms/coil_geometries/d3d_im_design_slim.dat
@@ -0,0 +1,1453 @@
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diff --git a/src/ForcingTerms/coil_geometries/d3d_iu.dat b/src/ForcingTerms/coil_geometries/d3d_iu.dat
new file mode 100644
index 0000000000..72a12ba0e8
--- /dev/null
+++ b/src/ForcingTerms/coil_geometries/d3d_iu.dat
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diff --git a/src/ForcingTerms/coil_geometries/d3d_iu_old.dat b/src/ForcingTerms/coil_geometries/d3d_iu_old.dat
new file mode 100644
index 0000000000..daf61e09a4
--- /dev/null
+++ b/src/ForcingTerms/coil_geometries/d3d_iu_old.dat
@@ -0,0 +1,769 @@
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diff --git a/src/ForcingTerms/coil_geometries/d3d_n1.dat b/src/ForcingTerms/coil_geometries/d3d_n1.dat
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--- /dev/null
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diff --git a/src/ForcingTerms/coil_geometries/d3d_tbm_racetrack.dat b/src/ForcingTerms/coil_geometries/d3d_tbm_racetrack.dat
new file mode 100644
index 0000000000..6ef34943bb
--- /dev/null
+++ b/src/ForcingTerms/coil_geometries/d3d_tbm_racetrack.dat
@@ -0,0 +1,83 @@
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diff --git a/src/ForcingTerms/coil_geometries/d3d_tbm_racetrack_2014.dat b/src/ForcingTerms/coil_geometries/d3d_tbm_racetrack_2014.dat
new file mode 100644
index 0000000000..cc0c48e474
--- /dev/null
+++ b/src/ForcingTerms/coil_geometries/d3d_tbm_racetrack_2014.dat
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diff --git a/src/ForcingTerms/coil_geometries/d3d_tbm_solenoid.dat b/src/ForcingTerms/coil_geometries/d3d_tbm_solenoid.dat
new file mode 100644
index 0000000000..c44af85606
--- /dev/null
+++ b/src/ForcingTerms/coil_geometries/d3d_tbm_solenoid.dat
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diff --git a/src/ForcingTerms/coil_geometries/d3d_tbm_solenoid_2014.dat b/src/ForcingTerms/coil_geometries/d3d_tbm_solenoid_2014.dat
new file mode 100644
index 0000000000..f795b96880
--- /dev/null
+++ b/src/ForcingTerms/coil_geometries/d3d_tbm_solenoid_2014.dat
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diff --git a/src/ForcingTerms/coil_geometries/east_down.dat b/src/ForcingTerms/coil_geometries/east_down.dat
new file mode 100644
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--- /dev/null
+++ b/src/ForcingTerms/coil_geometries/east_down.dat
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diff --git a/src/ForcingTerms/coil_geometries/east_up.dat b/src/ForcingTerms/coil_geometries/east_up.dat
new file mode 100644
index 0000000000..a7a52ae95d
--- /dev/null
+++ b/src/ForcingTerms/coil_geometries/east_up.dat
@@ -0,0 +1,377 @@
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diff --git a/src/ForcingTerms/coil_geometries/iter_amp_cs_pf.dat b/src/ForcingTerms/coil_geometries/iter_amp_cs_pf.dat
new file mode 100644
index 0000000000..fd87a02789
--- /dev/null
+++ b/src/ForcingTerms/coil_geometries/iter_amp_cs_pf.dat
@@ -0,0 +1,2413 @@
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diff --git a/src/ForcingTerms/coil_geometries/iter_amp_tf.dat b/src/ForcingTerms/coil_geometries/iter_amp_tf.dat
new file mode 100644
index 0000000000..eee16098cf
--- /dev/null
+++ b/src/ForcingTerms/coil_geometries/iter_amp_tf.dat
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diff --git a/src/ForcingTerms/coil_geometries/iter_avvl.dat b/src/ForcingTerms/coil_geometries/iter_avvl.dat
new file mode 100644
index 0000000000..24b00a359c
--- /dev/null
+++ b/src/ForcingTerms/coil_geometries/iter_avvl.dat
@@ -0,0 +1,2674 @@
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diff --git a/src/ForcingTerms/coil_geometries/iter_avvm.dat b/src/ForcingTerms/coil_geometries/iter_avvm.dat
new file mode 100644
index 0000000000..fcdf397c42
--- /dev/null
+++ b/src/ForcingTerms/coil_geometries/iter_avvm.dat
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diff --git a/src/ForcingTerms/coil_geometries/iter_avvu.dat b/src/ForcingTerms/coil_geometries/iter_avvu.dat
new file mode 100644
index 0000000000..2db31c8fdc
--- /dev/null
+++ b/src/ForcingTerms/coil_geometries/iter_avvu.dat
@@ -0,0 +1,2791 @@
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diff --git a/src/ForcingTerms/coil_geometries/iter_bl2l.dat b/src/ForcingTerms/coil_geometries/iter_bl2l.dat
new file mode 100644
index 0000000000..92498218a9
--- /dev/null
+++ b/src/ForcingTerms/coil_geometries/iter_bl2l.dat
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diff --git a/src/ForcingTerms/coil_geometries/iter_bl2m.dat b/src/ForcingTerms/coil_geometries/iter_bl2m.dat
new file mode 100644
index 0000000000..6a64de1b2e
--- /dev/null
+++ b/src/ForcingTerms/coil_geometries/iter_bl2m.dat
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diff --git a/src/ForcingTerms/coil_geometries/iter_bl2u.dat b/src/ForcingTerms/coil_geometries/iter_bl2u.dat
new file mode 100644
index 0000000000..590c92b937
--- /dev/null
+++ b/src/ForcingTerms/coil_geometries/iter_bl2u.dat
@@ -0,0 +1,2116 @@
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diff --git a/src/ForcingTerms/coil_geometries/iter_efcl.dat b/src/ForcingTerms/coil_geometries/iter_efcl.dat
new file mode 100644
index 0000000000..edccad54d4
--- /dev/null
+++ b/src/ForcingTerms/coil_geometries/iter_efcl.dat
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diff --git a/src/ForcingTerms/coil_geometries/iter_efcm.dat b/src/ForcingTerms/coil_geometries/iter_efcm.dat
new file mode 100644
index 0000000000..de9c853138
--- /dev/null
+++ b/src/ForcingTerms/coil_geometries/iter_efcm.dat
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diff --git a/src/ForcingTerms/coil_geometries/iter_efcu.dat b/src/ForcingTerms/coil_geometries/iter_efcu.dat
new file mode 100644
index 0000000000..c1b33216bb
--- /dev/null
+++ b/src/ForcingTerms/coil_geometries/iter_efcu.dat
@@ -0,0 +1,2383 @@
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diff --git a/src/ForcingTerms/coil_geometries/jet_ex_mid.dat b/src/ForcingTerms/coil_geometries/jet_ex_mid.dat
new file mode 100644
index 0000000000..639e8ca414
--- /dev/null
+++ b/src/ForcingTerms/coil_geometries/jet_ex_mid.dat
@@ -0,0 +1,169 @@
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diff --git a/src/ForcingTerms/coil_geometries/jet_rmpm.dat b/src/ForcingTerms/coil_geometries/jet_rmpm.dat
new file mode 100644
index 0000000000..02f81b4c3a
--- /dev/null
+++ b/src/ForcingTerms/coil_geometries/jet_rmpm.dat
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diff --git a/src/ForcingTerms/coil_geometries/jet_rmpu.dat b/src/ForcingTerms/coil_geometries/jet_rmpu.dat
new file mode 100644
index 0000000000..1610d3c96d
--- /dev/null
+++ b/src/ForcingTerms/coil_geometries/jet_rmpu.dat
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diff --git a/src/ForcingTerms/coil_geometries/jet_sad1.dat b/src/ForcingTerms/coil_geometries/jet_sad1.dat
new file mode 100644
index 0000000000..f3c1a9f180
--- /dev/null
+++ b/src/ForcingTerms/coil_geometries/jet_sad1.dat
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diff --git a/src/ForcingTerms/coil_geometries/jet_sad2.dat b/src/ForcingTerms/coil_geometries/jet_sad2.dat
new file mode 100644
index 0000000000..2395d78acb
--- /dev/null
+++ b/src/ForcingTerms/coil_geometries/jet_sad2.dat
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diff --git a/src/ForcingTerms/coil_geometries/jet_sad3.dat b/src/ForcingTerms/coil_geometries/jet_sad3.dat
new file mode 100644
index 0000000000..34a9d84ec5
--- /dev/null
+++ b/src/ForcingTerms/coil_geometries/jet_sad3.dat
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new file mode 100644
index 0000000000..476b554510
--- /dev/null
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new file mode 100644
index 0000000000..9defc821f6
--- /dev/null
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new file mode 100644
index 0000000000..b70ef435f6
--- /dev/null
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diff --git a/src/ForcingTerms/coil_geometries/kstar_fecl.dat b/src/ForcingTerms/coil_geometries/kstar_fecl.dat
new file mode 100644
index 0000000000..8ab7972348
--- /dev/null
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diff --git a/src/ForcingTerms/coil_geometries/kstar_fecm.dat b/src/ForcingTerms/coil_geometries/kstar_fecm.dat
new file mode 100644
index 0000000000..6ea477ae3f
--- /dev/null
+++ b/src/ForcingTerms/coil_geometries/kstar_fecm.dat
@@ -0,0 +1,1981 @@
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diff --git a/src/ForcingTerms/coil_geometries/kstar_fecu.dat b/src/ForcingTerms/coil_geometries/kstar_fecu.dat
new file mode 100644
index 0000000000..14be666654
--- /dev/null
+++ b/src/ForcingTerms/coil_geometries/kstar_fecu.dat
@@ -0,0 +1,1601 @@
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diff --git a/src/ForcingTerms/coil_geometries/kstar_ivccb.dat b/src/ForcingTerms/coil_geometries/kstar_ivccb.dat
new file mode 100644
index 0000000000..f1ea735a1e
--- /dev/null
+++ b/src/ForcingTerms/coil_geometries/kstar_ivccb.dat
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diff --git a/src/ForcingTerms/coil_geometries/kstar_ivccm.dat b/src/ForcingTerms/coil_geometries/kstar_ivccm.dat
new file mode 100644
index 0000000000..ef54f1aec0
--- /dev/null
+++ b/src/ForcingTerms/coil_geometries/kstar_ivccm.dat
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diff --git a/src/ForcingTerms/coil_geometries/kstar_ivcct.dat b/src/ForcingTerms/coil_geometries/kstar_ivcct.dat
new file mode 100644
index 0000000000..9a78f404d4
--- /dev/null
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diff --git a/src/ForcingTerms/coil_geometries/mast_ml.dat b/src/ForcingTerms/coil_geometries/mast_ml.dat
new file mode 100644
index 0000000000..f1bc76eca3
--- /dev/null
+++ b/src/ForcingTerms/coil_geometries/mast_ml.dat
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diff --git a/src/ForcingTerms/coil_geometries/mast_mu.dat b/src/ForcingTerms/coil_geometries/mast_mu.dat
new file mode 100644
index 0000000000..da34958461
--- /dev/null
+++ b/src/ForcingTerms/coil_geometries/mast_mu.dat
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diff --git a/src/ForcingTerms/coil_geometries/mastu_efcc.dat b/src/ForcingTerms/coil_geometries/mastu_efcc.dat
new file mode 100644
index 0000000000..5259e11ccb
--- /dev/null
+++ b/src/ForcingTerms/coil_geometries/mastu_efcc.dat
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diff --git a/src/ForcingTerms/coil_geometries/mastu_rmpl.dat b/src/ForcingTerms/coil_geometries/mastu_rmpl.dat
new file mode 100644
index 0000000000..1bb9ca7855
--- /dev/null
+++ b/src/ForcingTerms/coil_geometries/mastu_rmpl.dat
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diff --git a/src/ForcingTerms/coil_geometries/mastu_rmpu.dat b/src/ForcingTerms/coil_geometries/mastu_rmpu.dat
new file mode 100644
index 0000000000..ba2a4e14f8
--- /dev/null
+++ b/src/ForcingTerms/coil_geometries/mastu_rmpu.dat
@@ -0,0 +1,169 @@
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diff --git a/src/ForcingTerms/coil_geometries/nstx_hhfw.dat b/src/ForcingTerms/coil_geometries/nstx_hhfw.dat
new file mode 100644
index 0000000000..ca313b9108
--- /dev/null
+++ b/src/ForcingTerms/coil_geometries/nstx_hhfw.dat
@@ -0,0 +1,985 @@
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diff --git a/src/ForcingTerms/coil_geometries/nstx_pf5ef.dat b/src/ForcingTerms/coil_geometries/nstx_pf5ef.dat
new file mode 100644
index 0000000000..f5acb82803
--- /dev/null
+++ b/src/ForcingTerms/coil_geometries/nstx_pf5ef.dat
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diff --git a/src/ForcingTerms/coil_geometries/nstx_ppl.dat b/src/ForcingTerms/coil_geometries/nstx_ppl.dat
new file mode 100644
index 0000000000..e34d44657e
--- /dev/null
+++ b/src/ForcingTerms/coil_geometries/nstx_ppl.dat
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diff --git a/src/ForcingTerms/coil_geometries/nstx_ppu.dat b/src/ForcingTerms/coil_geometries/nstx_ppu.dat
new file mode 100644
index 0000000000..93d4d0ec02
--- /dev/null
+++ b/src/ForcingTerms/coil_geometries/nstx_ppu.dat
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diff --git a/src/ForcingTerms/coil_geometries/nstx_psl.dat b/src/ForcingTerms/coil_geometries/nstx_psl.dat
new file mode 100644
index 0000000000..6503ba6e91
--- /dev/null
+++ b/src/ForcingTerms/coil_geometries/nstx_psl.dat
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diff --git a/src/ForcingTerms/coil_geometries/nstx_psu.dat b/src/ForcingTerms/coil_geometries/nstx_psu.dat
new file mode 100644
index 0000000000..a73261debf
--- /dev/null
+++ b/src/ForcingTerms/coil_geometries/nstx_psu.dat
@@ -0,0 +1,685 @@
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diff --git a/src/ForcingTerms/coil_geometries/nstx_rwmef.dat b/src/ForcingTerms/coil_geometries/nstx_rwmef.dat
new file mode 100644
index 0000000000..311f6c8b7e
--- /dev/null
+++ b/src/ForcingTerms/coil_geometries/nstx_rwmef.dat
@@ -0,0 +1,1807 @@
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diff --git a/src/ForcingTerms/coil_geometries/nstx_tfef.dat b/src/ForcingTerms/coil_geometries/nstx_tfef.dat
new file mode 100644
index 0000000000..9ba347f27e
--- /dev/null
+++ b/src/ForcingTerms/coil_geometries/nstx_tfef.dat
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diff --git a/src/ForcingTerms/coil_geometries/nstx_tfef_amp.dat b/src/ForcingTerms/coil_geometries/nstx_tfef_amp.dat
new file mode 100644
index 0000000000..04c1aceb3c
--- /dev/null
+++ b/src/ForcingTerms/coil_geometries/nstx_tfef_amp.dat
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diff --git a/src/ForcingTerms/coil_geometries/nstx_u1mms_pf1al.dat b/src/ForcingTerms/coil_geometries/nstx_u1mms_pf1al.dat
new file mode 100644
index 0000000000..9499956a5d
--- /dev/null
+++ b/src/ForcingTerms/coil_geometries/nstx_u1mms_pf1al.dat
@@ -0,0 +1,102 @@
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diff --git a/src/ForcingTerms/coil_geometries/nstx_u1mms_pf1au.dat b/src/ForcingTerms/coil_geometries/nstx_u1mms_pf1au.dat
new file mode 100644
index 0000000000..eece53b70c
--- /dev/null
+++ b/src/ForcingTerms/coil_geometries/nstx_u1mms_pf1au.dat
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new file mode 100644
index 0000000000..80306e3f84
--- /dev/null
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new file mode 100644
index 0000000000..ba73c72e53
--- /dev/null
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new file mode 100644
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new file mode 100644
index 0000000000..a7e95ec8d6
--- /dev/null
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new file mode 100644
index 0000000000..c9e60849bd
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new file mode 100644
index 0000000000..8749b090fd
--- /dev/null
+++ b/src/ForcingTerms/coil_geometries/nstx_u1mms_pf2u.dat
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new file mode 100644
index 0000000000..9fc5af8196
--- /dev/null
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new file mode 100644
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--- /dev/null
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new file mode 100644
index 0000000000..937e4ba73e
--- /dev/null
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new file mode 100644
index 0000000000..ed4ef2b2c0
--- /dev/null
+++ b/src/ForcingTerms/coil_geometries/nstx_u1mms_pf4u.dat
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new file mode 100644
index 0000000000..9734b68152
--- /dev/null
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diff --git a/src/ForcingTerms/coil_geometries/nstx_u1mms_pf5u.dat b/src/ForcingTerms/coil_geometries/nstx_u1mms_pf5u.dat
new file mode 100644
index 0000000000..f4d061c974
--- /dev/null
+++ b/src/ForcingTerms/coil_geometries/nstx_u1mms_pf5u.dat
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diff --git a/src/ForcingTerms/coil_geometries/nstx_u1mms_plasma.dat b/src/ForcingTerms/coil_geometries/nstx_u1mms_plasma.dat
new file mode 100644
index 0000000000..b73d71061d
--- /dev/null
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diff --git a/src/ForcingTerms/coil_geometries/nstx_u1mms_tf.dat b/src/ForcingTerms/coil_geometries/nstx_u1mms_tf.dat
new file mode 100644
index 0000000000..8255a01132
--- /dev/null
+++ b/src/ForcingTerms/coil_geometries/nstx_u1mms_tf.dat
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diff --git a/src/ForcingTerms/coil_geometries/nstx_u1mms_tf_inner.dat b/src/ForcingTerms/coil_geometries/nstx_u1mms_tf_inner.dat
new file mode 100644
index 0000000000..967f286a63
--- /dev/null
+++ b/src/ForcingTerms/coil_geometries/nstx_u1mms_tf_inner.dat
@@ -0,0 +1,301 @@
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diff --git a/src/ForcingTerms/coil_geometries/nstx_u1mms_tf_outer.dat b/src/ForcingTerms/coil_geometries/nstx_u1mms_tf_outer.dat
new file mode 100644
index 0000000000..2b492d83fa
--- /dev/null
+++ b/src/ForcingTerms/coil_geometries/nstx_u1mms_tf_outer.dat
@@ -0,0 +1,673 @@
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diff --git a/src/ForcingTerms/coil_geometries/nstx_u1mmt_pf1al.dat b/src/ForcingTerms/coil_geometries/nstx_u1mmt_pf1al.dat
new file mode 100644
index 0000000000..549ee09d4f
--- /dev/null
+++ b/src/ForcingTerms/coil_geometries/nstx_u1mmt_pf1al.dat
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diff --git a/src/ForcingTerms/coil_geometries/nstx_u1mmt_pf1au.dat b/src/ForcingTerms/coil_geometries/nstx_u1mmt_pf1au.dat
new file mode 100644
index 0000000000..87e49704bd
--- /dev/null
+++ b/src/ForcingTerms/coil_geometries/nstx_u1mmt_pf1au.dat
@@ -0,0 +1,102 @@
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new file mode 100644
index 0000000000..7e04ecc795
--- /dev/null
+++ b/src/ForcingTerms/coil_geometries/nstx_u1mmt_pf1bl.dat
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new file mode 100644
index 0000000000..a65f3f80ab
--- /dev/null
+++ b/src/ForcingTerms/coil_geometries/nstx_u1mmt_pf1bu.dat
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diff --git a/src/ForcingTerms/coil_geometries/nstx_u1mmt_pf1cl.dat b/src/ForcingTerms/coil_geometries/nstx_u1mmt_pf1cl.dat
new file mode 100644
index 0000000000..586f90dffb
--- /dev/null
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new file mode 100644
index 0000000000..9930754ac7
--- /dev/null
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diff --git a/src/ForcingTerms/coil_geometries/nstx_u1mmt_pf2l.dat b/src/ForcingTerms/coil_geometries/nstx_u1mmt_pf2l.dat
new file mode 100644
index 0000000000..7bd2c5a49f
--- /dev/null
+++ b/src/ForcingTerms/coil_geometries/nstx_u1mmt_pf2l.dat
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diff --git a/src/ForcingTerms/coil_geometries/nstx_u1mmt_pf2u.dat b/src/ForcingTerms/coil_geometries/nstx_u1mmt_pf2u.dat
new file mode 100644
index 0000000000..fa9535fbbe
--- /dev/null
+++ b/src/ForcingTerms/coil_geometries/nstx_u1mmt_pf2u.dat
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diff --git a/src/ForcingTerms/coil_geometries/nstx_u1mmt_pf3l.dat b/src/ForcingTerms/coil_geometries/nstx_u1mmt_pf3l.dat
new file mode 100644
index 0000000000..4921a34c9e
--- /dev/null
+++ b/src/ForcingTerms/coil_geometries/nstx_u1mmt_pf3l.dat
@@ -0,0 +1,102 @@
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diff --git a/src/ForcingTerms/coil_geometries/nstx_u1mmt_pf3u.dat b/src/ForcingTerms/coil_geometries/nstx_u1mmt_pf3u.dat
new file mode 100644
index 0000000000..f1fe6273f4
--- /dev/null
+++ b/src/ForcingTerms/coil_geometries/nstx_u1mmt_pf3u.dat
@@ -0,0 +1,102 @@
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diff --git a/src/ForcingTerms/coil_geometries/nstx_u1mmt_pf4l.dat b/src/ForcingTerms/coil_geometries/nstx_u1mmt_pf4l.dat
new file mode 100644
index 0000000000..84f052b192
--- /dev/null
+++ b/src/ForcingTerms/coil_geometries/nstx_u1mmt_pf4l.dat
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diff --git a/src/ForcingTerms/coil_geometries/nstx_u1mmt_pf4u.dat b/src/ForcingTerms/coil_geometries/nstx_u1mmt_pf4u.dat
new file mode 100644
index 0000000000..bca185ee0a
--- /dev/null
+++ b/src/ForcingTerms/coil_geometries/nstx_u1mmt_pf4u.dat
@@ -0,0 +1,102 @@
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diff --git a/src/ForcingTerms/coil_geometries/nstx_u1mmt_pf5l.dat b/src/ForcingTerms/coil_geometries/nstx_u1mmt_pf5l.dat
new file mode 100644
index 0000000000..1be76aabb4
--- /dev/null
+++ b/src/ForcingTerms/coil_geometries/nstx_u1mmt_pf5l.dat
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diff --git a/src/ForcingTerms/coil_geometries/nstx_u1mmt_pf5u.dat b/src/ForcingTerms/coil_geometries/nstx_u1mmt_pf5u.dat
new file mode 100644
index 0000000000..232b8dd910
--- /dev/null
+++ b/src/ForcingTerms/coil_geometries/nstx_u1mmt_pf5u.dat
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diff --git a/src/ForcingTerms/coil_geometries/nstx_u1mmt_tf.dat b/src/ForcingTerms/coil_geometries/nstx_u1mmt_tf.dat
new file mode 100644
index 0000000000..81b9d00220
--- /dev/null
+++ b/src/ForcingTerms/coil_geometries/nstx_u1mmt_tf.dat
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diff --git a/src/ForcingTerms/coil_geometries/nstx_u1mmt_tf_inner.dat b/src/ForcingTerms/coil_geometries/nstx_u1mmt_tf_inner.dat
new file mode 100644
index 0000000000..d69932640d
--- /dev/null
+++ b/src/ForcingTerms/coil_geometries/nstx_u1mmt_tf_inner.dat
@@ -0,0 +1,301 @@
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diff --git a/src/ForcingTerms/coil_geometries/nstx_u1mmt_tf_outer.dat b/src/ForcingTerms/coil_geometries/nstx_u1mmt_tf_outer.dat
new file mode 100644
index 0000000000..e3321164ad
--- /dev/null
+++ b/src/ForcingTerms/coil_geometries/nstx_u1mmt_tf_outer.dat
@@ -0,0 +1,673 @@
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diff --git a/src/ForcingTerms/coil_geometries/nstx_upf4efs_v3.dat b/src/ForcingTerms/coil_geometries/nstx_upf4efs_v3.dat
new file mode 100644
index 0000000000..02db2afbe7
--- /dev/null
+++ b/src/ForcingTerms/coil_geometries/nstx_upf4efs_v3.dat
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diff --git a/src/ForcingTerms/coil_geometries/nstx_upf4eft_v3.dat b/src/ForcingTerms/coil_geometries/nstx_upf4eft_v3.dat
new file mode 100644
index 0000000000..0f6e9b74d3
--- /dev/null
+++ b/src/ForcingTerms/coil_geometries/nstx_upf4eft_v3.dat
@@ -0,0 +1,203 @@
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diff --git a/src/ForcingTerms/coil_geometries/nstx_upf5ef.dat b/src/ForcingTerms/coil_geometries/nstx_upf5ef.dat
new file mode 100644
index 0000000000..51c12088be
--- /dev/null
+++ b/src/ForcingTerms/coil_geometries/nstx_upf5ef.dat
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diff --git a/src/ForcingTerms/coil_geometries/nstx_upf5ef_v2.dat b/src/ForcingTerms/coil_geometries/nstx_upf5ef_v2.dat
new file mode 100644
index 0000000000..44f70ea7c5
--- /dev/null
+++ b/src/ForcingTerms/coil_geometries/nstx_upf5ef_v2.dat
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diff --git a/src/ForcingTerms/coil_geometries/nstx_upf5efs_v3.dat b/src/ForcingTerms/coil_geometries/nstx_upf5efs_v3.dat
new file mode 100644
index 0000000000..e7f824c774
--- /dev/null
+++ b/src/ForcingTerms/coil_geometries/nstx_upf5efs_v3.dat
@@ -0,0 +1,203 @@
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diff --git a/src/ForcingTerms/coil_geometries/nstx_upf5eft_v3.dat b/src/ForcingTerms/coil_geometries/nstx_upf5eft_v3.dat
new file mode 100644
index 0000000000..2cd427e96a
--- /dev/null
+++ b/src/ForcingTerms/coil_geometries/nstx_upf5eft_v3.dat
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diff --git a/src/ForcingTerms/coil_geometries/nstx_utfef.dat b/src/ForcingTerms/coil_geometries/nstx_utfef.dat
new file mode 100644
index 0000000000..5a5ad179f1
--- /dev/null
+++ b/src/ForcingTerms/coil_geometries/nstx_utfef.dat
@@ -0,0 +1,37 @@
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diff --git a/src/ForcingTerms/coil_geometries/nstx_utfef_amp.dat b/src/ForcingTerms/coil_geometries/nstx_utfef_amp.dat
new file mode 100644
index 0000000000..b5f09d8861
--- /dev/null
+++ b/src/ForcingTerms/coil_geometries/nstx_utfef_amp.dat
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diff --git a/src/ForcingTerms/coil_geometries/nstx_utfef_shift.dat b/src/ForcingTerms/coil_geometries/nstx_utfef_shift.dat
new file mode 100644
index 0000000000..6b8c91fe50
--- /dev/null
+++ b/src/ForcingTerms/coil_geometries/nstx_utfef_shift.dat
@@ -0,0 +1,37 @@
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diff --git a/src/ForcingTerms/coil_geometries/nstx_utfef_tilt.dat b/src/ForcingTerms/coil_geometries/nstx_utfef_tilt.dat
new file mode 100644
index 0000000000..7686e5063b
--- /dev/null
+++ b/src/ForcingTerms/coil_geometries/nstx_utfef_tilt.dat
@@ -0,0 +1,37 @@
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diff --git a/src/ForcingTerms/coil_geometries/nstx_vpl.dat b/src/ForcingTerms/coil_geometries/nstx_vpl.dat
new file mode 100644
index 0000000000..da131ae1d1
--- /dev/null
+++ b/src/ForcingTerms/coil_geometries/nstx_vpl.dat
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diff --git a/src/ForcingTerms/coil_geometries/nstx_vpu.dat b/src/ForcingTerms/coil_geometries/nstx_vpu.dat
new file mode 100644
index 0000000000..f1940de45f
--- /dev/null
+++ b/src/ForcingTerms/coil_geometries/nstx_vpu.dat
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diff --git a/src/ForcingTerms/coil_geometries/nstx_vsl.dat b/src/ForcingTerms/coil_geometries/nstx_vsl.dat
new file mode 100644
index 0000000000..def9e20f37
--- /dev/null
+++ b/src/ForcingTerms/coil_geometries/nstx_vsl.dat
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diff --git a/src/ForcingTerms/coil_geometries/nstx_vsu.dat b/src/ForcingTerms/coil_geometries/nstx_vsu.dat
new file mode 100644
index 0000000000..a5f900896b
--- /dev/null
+++ b/src/ForcingTerms/coil_geometries/nstx_vsu.dat
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diff --git a/src/ForcingTerms/coil_geometries/rfxmod_down.dat b/src/ForcingTerms/coil_geometries/rfxmod_down.dat
new file mode 100644
index 0000000000..aa46bdf5e0
--- /dev/null
+++ b/src/ForcingTerms/coil_geometries/rfxmod_down.dat
@@ -0,0 +1,3889 @@
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diff --git a/src/ForcingTerms/coil_geometries/rfxmod_ext.dat b/src/ForcingTerms/coil_geometries/rfxmod_ext.dat
new file mode 100644
index 0000000000..7f14326074
--- /dev/null
+++ b/src/ForcingTerms/coil_geometries/rfxmod_ext.dat
@@ -0,0 +1,3889 @@
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diff --git a/src/ForcingTerms/coil_geometries/rfxmod_int.dat b/src/ForcingTerms/coil_geometries/rfxmod_int.dat
new file mode 100644
index 0000000000..b3aa5e3d43
--- /dev/null
+++ b/src/ForcingTerms/coil_geometries/rfxmod_int.dat
@@ -0,0 +1,3889 @@
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diff --git a/src/ForcingTerms/coil_geometries/rfxmod_up.dat b/src/ForcingTerms/coil_geometries/rfxmod_up.dat
new file mode 100644
index 0000000000..4c6c0c5e89
--- /dev/null
+++ b/src/ForcingTerms/coil_geometries/rfxmod_up.dat
@@ -0,0 +1,3889 @@
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+ 2.2107e+00 -4.5350e-01 5.2175e-01
+ 2.1710e+00 -4.4561e-01 5.3978e-01
+ 2.1301e+00 -4.3747e-01 5.5468e-01
+ 2.0882e+00 -4.2913e-01 5.6637e-01
+ 2.0455e+00 -4.2064e-01 5.7476e-01
+ 2.0023e+00 -4.1205e-01 5.7981e-01
+ 1.9589e+00 -4.0341e-01 5.8150e-01
+ 1.9155e+00 -3.9477e-01 5.7981e-01
+ 1.8723e+00 -3.8619e-01 5.7476e-01
+ 1.8296e+00 -3.7770e-01 5.6637e-01
+ 1.7877e+00 -3.6936e-01 5.5468e-01
+ 1.7468e+00 -3.6122e-01 5.3978e-01
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+ 1.6688e+00 -3.4572e-01 5.0068e-01
+ 1.6323e+00 -3.3844e-01 4.7671e-01
+ 1.5976e+00 -3.3155e-01 4.4997e-01
+ 1.5651e+00 -3.2508e-01 4.2062e-01
+ 1.5632e+00 -3.3399e-01 4.2062e-01
+ 1.5613e+00 -3.4290e-01 4.2062e-01
+ 1.5593e+00 -3.5179e-01 4.2062e-01
+ 1.5573e+00 -3.6067e-01 4.2062e-01
+ 1.5552e+00 -3.6955e-01 4.2062e-01
+ 1.5530e+00 -3.7840e-01 4.2062e-01
+ 1.5509e+00 -3.8725e-01 4.2062e-01
+ 1.5486e+00 -3.9609e-01 4.2062e-01
+ 1.5463e+00 -4.0491e-01 4.2062e-01
+ 1.5440e+00 -4.1372e-01 4.2062e-01
+ 1.5416e+00 -4.2251e-01 4.2062e-01
+ 1.5392e+00 -4.3129e-01 4.2062e-01
+ 1.5367e+00 -4.4006e-01 4.2062e-01
+ 1.5342e+00 -4.4881e-01 4.2062e-01
+ 1.5316e+00 -4.5755e-01 4.2062e-01
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+ 1.5235e+00 -4.8367e-01 4.2062e-01
+ 1.5208e+00 -4.9235e-01 4.2062e-01
+ 1.5179e+00 -5.0101e-01 4.2062e-01
+ 1.5494e+00 -5.1168e-01 4.4997e-01
+ 1.5828e+00 -5.2304e-01 4.7671e-01
+ 1.6181e+00 -5.3502e-01 5.0068e-01
+ 1.6550e+00 -5.4755e-01 5.2175e-01
+ 1.6933e+00 -5.6056e-01 5.3978e-01
+ 1.7329e+00 -5.7397e-01 5.5468e-01
+ 1.7733e+00 -5.8771e-01 5.6637e-01
+ 1.8145e+00 -6.0170e-01 5.7476e-01
+ 1.8562e+00 -6.1585e-01 5.7981e-01
+ 1.8982e+00 -6.3008e-01 5.8150e-01
+ 1.9401e+00 -6.4431e-01 5.7981e-01
+ 1.9818e+00 -6.5846e-01 5.7476e-01
+ 2.0230e+00 -6.7245e-01 5.6637e-01
+ 2.0634e+00 -6.8619e-01 5.5468e-01
+ 2.1030e+00 -6.9960e-01 5.3978e-01
+ 2.1413e+00 -7.1261e-01 5.2175e-01
+ 2.1782e+00 -7.2514e-01 5.0068e-01
+ 2.2135e+00 -7.3712e-01 4.7671e-01
+ 2.2469e+00 -7.4848e-01 4.4997e-01
+ 2.2784e+00 -7.5915e-01 4.2062e-01
+ 2.3580e+00 -4.5527e-01 4.2062e-01
+ 2.3607e+00 -4.4115e-01 4.2062e-01
+ 2.3633e+00 -4.2702e-01 4.2062e-01
+ 2.3658e+00 -4.1287e-01 4.2062e-01
+ 2.3682e+00 -3.9871e-01 4.2062e-01
+ 2.3705e+00 -3.8454e-01 4.2062e-01
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+ 2.3771e+00 -3.4193e-01 4.2062e-01
+ 2.3791e+00 -3.2770e-01 4.2062e-01
+ 2.3810e+00 -3.1346e-01 4.2062e-01
+ 2.3828e+00 -2.9921e-01 4.2062e-01
+ 2.3846e+00 -2.8495e-01 4.2062e-01
+ 2.3862e+00 -2.7068e-01 4.2062e-01
+ 2.3878e+00 -2.5640e-01 4.2062e-01
+ 2.3893e+00 -2.4211e-01 4.2062e-01
+ 2.3907e+00 -2.2781e-01 4.2062e-01
+ 2.3920e+00 -2.1350e-01 4.2062e-01
+ 2.3933e+00 -1.9919e-01 4.2062e-01
+ 2.3944e+00 -1.8486e-01 4.2062e-01
+ 2.3955e+00 -1.7054e-01 4.2062e-01
+ 2.3623e+00 -1.6836e-01 4.4997e-01
+ 2.3271e+00 -1.6605e-01 4.7671e-01
+ 2.2899e+00 -1.6362e-01 5.0068e-01
+ 2.2510e+00 -1.6107e-01 5.2175e-01
+ 2.2106e+00 -1.5842e-01 5.3978e-01
+ 2.1690e+00 -1.5569e-01 5.5468e-01
+ 2.1263e+00 -1.5289e-01 5.6637e-01
+ 2.0829e+00 -1.5005e-01 5.7476e-01
+ 2.0390e+00 -1.4717e-01 5.7981e-01
+ 1.9948e+00 -1.4427e-01 5.8150e-01
+ 1.9506e+00 -1.4138e-01 5.7981e-01
+ 1.9067e+00 -1.3850e-01 5.7476e-01
+ 1.8633e+00 -1.3565e-01 5.6637e-01
+ 1.8206e+00 -1.3286e-01 5.5468e-01
+ 1.7790e+00 -1.3013e-01 5.3978e-01
+ 1.7386e+00 -1.2748e-01 5.2175e-01
+ 1.6997e+00 -1.2493e-01 5.0068e-01
+ 1.6625e+00 -1.2249e-01 4.7671e-01
+ 1.6272e+00 -1.2018e-01 4.4997e-01
+ 1.5941e+00 -1.1801e-01 4.2062e-01
+ 1.5934e+00 -1.2710e-01 4.2062e-01
+ 1.5927e+00 -1.3618e-01 4.2062e-01
+ 1.5919e+00 -1.4525e-01 4.2062e-01
+ 1.5910e+00 -1.5433e-01 4.2062e-01
+ 1.5901e+00 -1.6339e-01 4.2062e-01
+ 1.5891e+00 -1.7246e-01 4.2062e-01
+ 1.5881e+00 -1.8151e-01 4.2062e-01
+ 1.5871e+00 -1.9056e-01 4.2062e-01
+ 1.5860e+00 -1.9960e-01 4.2062e-01
+ 1.5848e+00 -2.0864e-01 4.2062e-01
+ 1.5836e+00 -2.1767e-01 4.2062e-01
+ 1.5823e+00 -2.2670e-01 4.2062e-01
+ 1.5810e+00 -2.3571e-01 4.2062e-01
+ 1.5796e+00 -2.4472e-01 4.2062e-01
+ 1.5782e+00 -2.5372e-01 4.2062e-01
+ 1.5767e+00 -2.6271e-01 4.2062e-01
+ 1.5752e+00 -2.7170e-01 4.2062e-01
+ 1.5736e+00 -2.8067e-01 4.2062e-01
+ 1.5720e+00 -2.8964e-01 4.2062e-01
+ 1.5703e+00 -2.9859e-01 4.2062e-01
+ 1.6029e+00 -3.0507e-01 4.4997e-01
+ 1.6375e+00 -3.1196e-01 4.7671e-01
+ 1.6741e+00 -3.1923e-01 5.0068e-01
+ 1.7123e+00 -3.2684e-01 5.2175e-01
+ 1.7520e+00 -3.3474e-01 5.3978e-01
+ 1.7930e+00 -3.4288e-01 5.5468e-01
+ 1.8349e+00 -3.5122e-01 5.6637e-01
+ 1.8776e+00 -3.5970e-01 5.7476e-01
+ 1.9207e+00 -3.6829e-01 5.7981e-01
+ 1.9642e+00 -3.7693e-01 5.8150e-01
+ 2.0076e+00 -3.8557e-01 5.7981e-01
+ 2.0508e+00 -3.9416e-01 5.7476e-01
+ 2.0934e+00 -4.0265e-01 5.6637e-01
+ 2.1354e+00 -4.1098e-01 5.5468e-01
+ 2.1763e+00 -4.1913e-01 5.3978e-01
+ 2.2160e+00 -4.2702e-01 5.2175e-01
+ 2.2542e+00 -4.3463e-01 5.0068e-01
+ 2.2908e+00 -4.4190e-01 4.7671e-01
+ 2.3254e+00 -4.4879e-01 4.4997e-01
+ 2.3580e+00 -4.5527e-01 4.2062e-01
diff --git a/src/GeneralizedPerturbedEquilibrium.jl b/src/GeneralizedPerturbedEquilibrium.jl
new file mode 100755
index 0000000000..76c5515b57
--- /dev/null
+++ b/src/GeneralizedPerturbedEquilibrium.jl
@@ -0,0 +1,313 @@
+# GeneralizedPerturbedEquilibrium.jl
+module GeneralizedPerturbedEquilibrium
+
+# External dependencies used by main and the rerun helpers
+using TOML
+using Printf
+using HDF5
+using FastInterpolations
+import IMASdd
+
+import CommonSolve: solve
+
+const _BANNER = "="^60
+const _SECTION = "-"^40
+
+include("Utilities/Utilities.jl")
+import .Utilities as Utilities
+export Utilities
+import .Utilities: save_to_hdf5
+export save_to_hdf5
+
+include("Equilibrium/Equilibrium.jl")
+import .Equilibrium as Equilibrium
+export Equilibrium
+
+# Local high-n stability (Mercier, resistive interchange, ballooning Δ'); depends only on Equilibrium.
+include("LocalStability/LocalStability.jl")
+import .LocalStability as LocalStability
+export LocalStability
+
+include("Vacuum/Vacuum.jl")
+import .Vacuum as Vacuum
+export Vacuum
+
+# InnerLayer holds the pure inner-region solvers and must load before
+# ForceFreeStates, which calls them for the matched-Δ′ Galerkin solve.
+include("InnerLayer/InnerLayer.jl")
+import .InnerLayer as InnerLayer
+export InnerLayer
+
+include("ForcingTerms/ForcingTerms.jl")
+import .ForcingTerms as ForcingTerms
+export ForcingTerms
+
+include("ForceFreeStates/ForceFreeStates.jl")
+import .ForceFreeStates as ForceFreeStates
+export ForceFreeStates
+
+include("Tearing/Tearing.jl")
+import .Tearing as Tearing
+export Tearing
+import .Tearing.CriticalResonantField as CriticalResonantField
+
+include("PerturbedEquilibrium/PerturbedEquilibrium.jl")
+import .PerturbedEquilibrium as PerturbedEquilibrium
+export PerturbedEquilibrium
+
+include("KineticForces/KineticForces.jl")
+import .KineticForces as KineticForces
+export KineticForces
+
+include("ErrorFields/ErrorFields.jl")
+import .ErrorFields as ErrorFields
+export ErrorFields
+
+include("Analysis/Analysis.jl")
+import .Analysis as Analysis
+export Analysis
+
+include("Rerun.jl")
+
+# Scripting-API surface: the integrator selectors, the published result, the equilibrium
+# constructor and the forcing description, re-exported so a user needs one `using`.
+using .ForceFreeStates: AbstractIntegrator, Forward, Riccati, Galerkin, TestKineticMatrices, KineticMatrices, ForceFreeStatesResult
+using .ForceFreeStates: MatchProblem
+using .InnerLayer: GGJModel, SLAYERModel
+using .Tearing: TearingProblem, TearingConfig, TearingResult, CriticalResonantFieldControl
+using .LocalStability: LocalStabilityProblem, Ballooning, LocalStabilityResult
+using .Equilibrium: PlasmaEquilibrium, KineticProfileData, IonSpecies, attach_kinetic_profiles!
+using .ForcingTerms: RMPField
+using .PerturbedEquilibrium: plasma_response, perturbed_equilibrium, PlasmaResponse
+using .KineticForces: kinetic_torque, KineticForcesControl, KineticForcesResult
+using .ErrorFields: error_fields, ErrorFieldsResult
+
+using .ForceFreeStates: ForceBalanceProblem, kinetic_matrices, _prepare_solve, maybe_reform_equilibrium, ForceFreeStatesControl, kinetic_source
+include("Deck.jl")
+
+function main(args::Vector{String}=String[]; dd::Union{IMASdd.dd,Nothing}=nothing)
+ # Every input source builds a ready `(inputs, eq_config, additional_input)` and hands it to
+ # `main_from_inputs`: a gpec.toml working directory, an IMAS `dd`, or a gpec.h5 snapshot.
+ if !isempty(args) && endswith(lowercase(args[1]), ".h5")
+ inputs, eq_config, additional_input, path, git_version, preloaded_coils = build_inputs_from_h5(args)
+ return main_from_inputs(inputs, eq_config, additional_input, path, git_version; preloaded_coil_sets=preloaded_coils)
+ end
+
+ path = length(args) >= 1 ? args[1] : "./"
+
+ # Capture git version for reproducibility
+ git_version = _gpec_git_version()
+
+ @info "\n$_BANNER\n GPEC - Generalized Perturbed Equilibrium Code [$git_version]\n$_BANNER"
+
+ inputs, eq_config, additional_input = build_inputs_from_toml(path; dd=dd)
+ return main_from_inputs(inputs, eq_config, additional_input, path, git_version)
+end
+
+"""
+ build_inputs_from_toml(path; dd=nothing) -> (inputs, eq_config, additional_input)
+
+Build the pipeline inputs from a working directory containing `gpec.toml`. Returns the
+parsed `inputs` dict, the `EquilibriumConfig`, and the `additional_input` consumed by
+`PlasmaEquilibrium` — the analytic `*Config` a `[Solovev]`, `[LargeAspectRatio]` or
+`[TJAnalytic]` section states, the `dd` data dictionary for IMAS, or `nothing` for file-based
+equilibria (efit, chease) that `PlasmaEquilibrium` reads from disk.
+"""
+function build_inputs_from_toml(path::String; dd::Union{IMASdd.dd,Nothing}=nothing)
+ inputs = TOML.parsefile(joinpath(path, "gpec.toml"))
+
+ _stop_on_deprecated_deck_keys(inputs)
+ eq_config = equilibrium_config(inputs, path)
+
+ # An equilibrium is IMAS-fed (via the dd kwarg), analytic (stated by its section), or read from a file (nothing).
+ additional_input = eq_config.eq_type == "imas" ? dd : analytic_config(inputs)
+
+ return inputs, eq_config, additional_input
+end
+
+"""
+ main_from_inputs(inputs, eq_config, additional_input, path, git_version;
+ preloaded_coil_sets=nothing)
+
+Run the pipeline every input source (`build_inputs_from_*`) funnels into. `additional_input` is forwarded
+to `PlasmaEquilibrium`: a prebuilt `DirectRunInput`/`InverseRunInput` (rerun), an analytic `*Config` or
+IMAS `dd`, or `nothing` for file-based equilibria.
+
+Each section present runs its stage through the public API, exactly as a script would, and saves
+the result into the one `[Run] output_file`; a deck without `[ForceFreeStates]` stops after the
+equilibrium and writes nothing. The raw forcing file contents are captured in
+`Input/RawInputs/ForcingTerms/`, and `preloaded_coil_sets` lets the rerun path inject the coil
+geometry stored in `Input/RawInputs/Coils/`.
+
+Returns `(; equil, local_stability, ffs, match, resp, pe, kinetic, error_fields, tearing)`, each
+`nothing` when its section is absent. `equil` is the equilibrium the stages used (the solve's, on
+the two-pass grid), `ffs` the result the later stages read (the matched one when the deck has
+`[Match]`), and `match` its `MatchResult`.
+"""
+function main_from_inputs(
+ inputs::Dict{String,Any},
+ eq_config::Equilibrium.EquilibriumConfig,
+ additional_input,
+ path::String,
+ git_version::String;
+ preloaded_coil_sets::Union{Nothing,Vector{ForcingTerms.CoilSet}}=nothing
+)
+ total_start = time()
+ # Per-stage wall-clock seconds, written to Info/Runtimes at the end of the run.
+ runtimes = Vector{Pair{String,Float64}}()
+ deck = parse_deck(inputs, path)
+ (; output_file, verbose) = deck.run
+ local_stability = ffs = match = resp = pe = kinetic = error_fields = tearing = nothing
+
+ equil = _timed_stage(runtimes, "equilibrium", "Equilibrium") do
+ Equilibrium.PlasmaEquilibrium(eq_config, additional_input)
+ end
+ # The KineticForces stage needs the NTV view; stop before any solve rather than after the perturbed equilibrium.
+ deck.kinetic_forces !== nothing && equil.kinetic !== nothing && !Equilibrium.has_ntv_fields(equil.kinetic) &&
+ error("[KineticForces] needs n_e, T_i, T_e and omega_E in the kinetic profiles; the kinetic file lacks at least one")
+
+ if deck.force_balance !== nothing
+ ffs = _timed_stage(runtimes, "force_free_states", "Force-Free States") do
+ solve(ForceBalanceProblem(equil; deck.force_balance.keywords...), deck.force_balance.algorithm; verbose)
+ end
+ # Every later stage, local stability included, sees the equilibrium the solve formed (re-formed on the two-pass grid).
+ equil = ffs.equil
+ if deck.local_stability !== nothing
+ local_stability = _timed_stage(runtimes, "local_stability", "Local Stability") do
+ solve(LocalStabilityProblem(equil; deck.local_stability.problem...), deck.local_stability.algorithm; verbose)
+ end
+ end
+ if deck.match !== nothing
+ ffs = _timed_stage(runtimes, "match", "Match") do
+ solve(MatchProblem(ffs; deck.match.problem...), deck.match.model)
+ end
+ match = ffs.match
+ end
+ h5open(output_file, "w") do target
+ save_to_hdf5(target, ffs; git_version, local_stability)
+ end
+ @info "Results written to $output_file"
+ end
+
+ if deck.perturbed_equilibrium !== nothing
+ pe = _timed_stage(runtimes, "perturbed_equilibrium", "Perturbed Equilibrium") do
+ perturbed_equilibrium(plasma_response(ffs; verbose, deck.perturbed_equilibrium.response...), RMPField(deck.forcing);
+ coil_sets=preloaded_coil_sets, verbose, deck.perturbed_equilibrium.drive...)
+ end
+ resp = pe.response
+ save_to_hdf5(output_file, pe)
+ end
+
+ # Without [PerturbedEquilibrium], [KineticForces] only sets the kinetic source of the force-free-states solve.
+ if deck.kinetic_forces !== nothing && pe !== nothing
+ kinetic = _timed_stage(runtimes, "kinetic_forces", "KineticForces") do
+ kinetic_torque(pe, deck.kinetic_forces; verbose)
+ end
+ save_to_hdf5(output_file, kinetic)
+ end
+
+ if deck.error_fields !== nothing
+ ef = deck.error_fields
+ error_fields = _timed_stage(runtimes, "error_fields", "ErrorFields") do
+ scenario = ef.scenario === nothing ? nothing : ErrorFields.ScenarioParameters(equil; ef.scenario...)
+ ErrorFields.error_fields(resp, pe.coil_sets, ForcingTerms.CoilConfig(deck.forcing); ef.ctrl, ef.tolerances, ef.monte_carlo,
+ scenario, ef.risk, ef.ntv, kinetic=something(deck.kinetic_forces, KineticForcesControl()), pe.regularization_width, verbose)
+ end
+ save_to_hdf5(output_file, error_fields)
+ end
+
+ if deck.tearing !== nothing
+ tearing = _timed_stage(runtimes, "tearing", "Tearing") do
+ solve(TearingProblem(ffs; deck.tearing.problem...), deck.tearing.model; config=deck.tearing.config)
+ end
+ save_to_hdf5(output_file, tearing)
+ end
+
+ total_dt = time() - total_start
+ push!(runtimes, "total" => total_dt)
+ ffs === nothing || _write_runtimes!(output_file, runtimes)
+ @info "\n$_BANNER\n GPEC completed successfully in $(@sprintf("%.3f", total_dt)) s\n$_BANNER"
+
+ return (; equil, local_stability, ffs, match, resp, pe, kinetic, error_fields, tearing)
+end
+
+"""
+ _timed_stage(f, runtimes, key, label) -> f()
+
+Run the pipeline stage `f` under a `label` section banner, log its wall-clock time and record
+it in `runtimes` as `key => seconds` for the `Info/Runtimes` record.
+"""
+function _timed_stage(f, runtimes::Vector{Pair{String,Float64}}, key::String, label::String)
+ @info "\n $label\n$_SECTION"
+ start = time()
+ out = f()
+ dt = time() - start
+ push!(runtimes, key => dt)
+ @info "$label completed in $(@sprintf("%.3f", dt)) s"
+ return out
+end
+
+"""
+ _write_runtimes!(h5_path::String, runtimes)
+
+Write the `stage => seconds` pairs of `runtimes` into `Info/Runtimes/` of an existing gpec.h5. The
+timings are informational, never a regression quantity. Call it only when this run produced the file:
+the `isfile` guard alone would also stamp a stale gpec.h5.
+"""
+function _write_runtimes!(h5_path::String, runtimes)
+ isfile(h5_path) || return nothing
+ h5open(h5_path, "r+") do out_h5
+ haskey(out_h5, "Info/Runtimes") && HDF5.delete_object(out_h5, "Info/Runtimes")
+ for (stage, dt) in runtimes
+ out_h5["Info/Runtimes/$stage"] = dt
+ end
+ Utilities.HDF5Annotations.annotate!(out_h5, Utilities.RUNTIME_H5_ANNOTATIONS)
+ end
+ return nothing
+end
+
+"""
+ write_imas(dd, result)
+
+Write one `dd.mhd_linear` `toroidal_mode` entry per toroidal mode number, with the least-stable
+(minimum real part) free-boundary `energy_perturbed` of that n. `result` is the named tuple `main` returns.
+"""
+function write_imas(dd, result)
+ ffs = result.ffs
+ if ffs.free_boundary === nothing
+ @warn "Skipping IMAS mhd_linear write: the $(ffs.integrator) run produced no free-boundary energies. " *
+ "Set vac_flag=true in [ForceFreeStates]."
+ return
+ end
+ free_energies = ffs.free_boundary
+
+ # Top-level metadata
+ dd.mhd_linear.code.name = "GPEC"
+ dd.mhd_linear.ideal_flag = 1
+
+ # Time slice at the current global_time; wipe=false reuses an existing one or appends.
+ ts = resize!(dd.mhd_linear.time_slice; wipe=false)
+
+ # n_tor_idx[i] (0-based) is the n-block of eigenvalue i.
+ resize!(ts.toroidal_mode, ffs.npert)
+ for j in 0:(ffs.npert-1)
+ n_indices = findall(==(j), free_energies.n_tor_idx) # indices of eigenvalues in the j-th n-block
+ mode = ts.toroidal_mode[j+1]
+ mode.n_tor = ffs.nlow + j
+ mode.energy_perturbed = minimum(real.(free_energies.et[n_indices])) # least-stable energy for this n-toroidal mode
+ end
+
+ return dd
+end
+
+export main, write_imas
+export solve, plasma_response, perturbed_equilibrium, kinetic_torque, error_fields
+export KineticProfileData, IonSpecies, attach_kinetic_profiles!
+export PlasmaEquilibrium, ForceBalanceProblem, Forward, Riccati, Galerkin, TestKineticMatrices, KineticMatrices, kinetic_matrices, ForceFreeStatesResult, RMPField, PlasmaResponse
+export MatchProblem, TearingProblem, TearingConfig, TearingResult, GGJModel, SLAYERModel
+export LocalStabilityProblem, Ballooning, LocalStabilityResult
+export KineticForcesControl, KineticForcesResult, ErrorFieldsResult
+
+include("Precompile.jl")
+
+end # module GeneralizedPerturbedEquilibrium
diff --git a/src/InnerLayer/GGJ/GGJ.jl b/src/InnerLayer/GGJ/GGJ.jl
new file mode 100644
index 0000000000..59082f6469
--- /dev/null
+++ b/src/InnerLayer/GGJ/GGJ.jl
@@ -0,0 +1,98 @@
+# GGJ.jl
+#
+# Glasser–Greene–Johnson resistive inner-layer model, with three solvers selected by the
+# `solver` type parameter of `GGJModel`:
+#
+# - `:shooting` – backward shoot from X_max → 0; valid only for |Q| ≪ 1 (tests and comparisons)
+# - `:galerkin` – Hermite-cubic finite elements with resonant/extension matching cells
+# (GWP2016 Sec. III); accuracy depends on the surface and arg Q
+# - `:ray` – the same Hermite assembly on the rotated contour (Ray.jl), with the far-field
+# condition marched in from where the series converges; robust to |Q| ~ 500
+#
+# They return the matching data Δ± of GWP2016 Eqs. (34)–(35). Parity is that of the displacement Ξ:
+# Δ₊ (even) is the interchange channel, Δ₋ (odd) the tearing channel. Positional pairs are always
+# ordered (Δ₊, Δ₋), as d₊, d₋ in GWP2016 Eq. (38) and Pletzer, Bondeson & Dewar (1994) Eqs. 83, 85.
+#
+# Main source papers, cited by equation number throughout:
+#
+# GWP2016 — A. H. Glasser, Z. R. Wang & J.-K. Park, "Computation of resistive
+# instabilities by matched asymptotic expansions", Phys. Plasmas 23,
+# 112506 (2016). Inner-region equations (Eq. 11), singular-Galerkin method
+# (Sec. III), matching data (Eqs. 34–35), scale factors (Appendix, Eqs. A8–A16).
+#
+# GW2020 — A. H. Glasser & Z. R. Wang, "Asymptotic solutions and convergence
+# studies of the resistive inner region equations", Phys. Plasmas 27,
+# 012506 (2020). Wasow construction of the large-x asymptotic basis
+# (Eqs. 1–55); implemented in InnerAsymptotics.jl.
+
+module GGJ
+
+using LinearAlgebra
+using StaticArrays
+using Random
+using Printf
+using DoubleFloats: Double64
+using ...Utilities.HermiteFEM: hermite_basis, pack_grid
+
+import ..InnerLayerModel, ..InnerLayerResponse, ..InnerLayerParameters
+import ..solve_inner, ..solve_inner_profile
+
+"""
+ GGJModel{S,O} <: InnerLayerModel
+ GGJModel(; solver=:ray, options...)
+
+Glasser–Greene–Johnson resistive inner-layer model. `S` selects the solver
+backend: `:ray` (default; rotated contour with an inward-marched far-field condition,
+robust at large |Q|), `:galerkin` (real-axis Hermite FEM with resonant/extension matching
+cells; accuracy depends on the surface and arg Q, even at small |Q|), or `:shooting` (|Q| ≪ 1 only). Backend keywords given at
+construction, e.g. `GGJModel(; solver=:galerkin, nx=1280)`, apply to every solve; a keyword the backend does not
+take is an error here, not at the first solve.
+
+## Fields
+
+ - `options::NamedTuple` - Backend keywords forwarded to every solve; call-site keywords win.
+"""
+struct GGJModel{S,O<:NamedTuple} <: InnerLayerModel
+ options::O
+end
+
+function GGJModel(; solver::Symbol=:ray, options...)
+ allowed = _ggj_options(solver)
+ unknown = setdiff(keys(options), allowed)
+ isempty(unknown) || throw(ArgumentError("GGJModel(solver=:$solver) does not take $(join(unknown, ", ")); its options are $(join(allowed, ", "))"))
+ return GGJModel{solver,typeof(values(options))}(values(options))
+end
+GGJModel{S}() where {S} = GGJModel{S,@NamedTuple{}}((;))
+
+# The backends implement the option-free model; a model carrying options forwards them.
+const _BareGGJ{S} = GGJModel{S,@NamedTuple{}}
+function solve_inner(m::GGJModel{S}, params, γ::Number; kwargs...) where {S}
+ m isa _BareGGJ && throw(MethodError(solve_inner, (m, params, γ)))
+ return solve_inner(GGJModel{S}(), params, γ; m.options..., kwargs...)
+end
+function solve_inner_profile(m::GGJModel{S}, params, γ::Number; kwargs...) where {S}
+ m isa _BareGGJ && throw(MethodError(solve_inner_profile, (m, params, γ)))
+ return solve_inner_profile(GGJModel{S}(), params, γ; m.options..., kwargs...)
+end
+
+include("GGJParameters.jl")
+include("InnerAsymptotics.jl")
+include("Reference.jl")
+include("Shooting.jl")
+include("Galerkin.jl")
+include("Ray.jl")
+
+# Each backend's option names: the keywords of the functions its solves forward them to.
+_kwarg_names(f) = unique!(Symbol[k for m in methods(f) for k in Base.kwarg_decl(m) if !endswith(string(k), "...")])
+function _ggj_options(solver::Symbol)
+ solver === :ray && return union(_kwarg_names(solve_ray), (:real_profiles, :npc, :certify_rtol))
+ solver === :galerkin && return _kwarg_names(_galerkin_solve)
+ solver === :shooting && return Base.kwarg_decl(which(solve_inner, (_BareGGJ{:shooting}, GGJParameters, ComplexF64)))
+ throw(ArgumentError("GGJModel: unknown solver :$solver (expected :ray, :galerkin or :shooting)"))
+end
+
+export GGJModel, GGJParameters
+export mercier_di, mercier_dr, inner_Q, rescale_delta
+export solve_ray, pick_smax, delta_convergence, solution_profile, asymptotic_profile
+
+end # module GGJ
diff --git a/src/InnerLayer/GGJ/GGJParameters.jl b/src/InnerLayer/GGJ/GGJParameters.jl
new file mode 100644
index 0000000000..3d5f59e8b4
--- /dev/null
+++ b/src/InnerLayer/GGJ/GGJParameters.jl
@@ -0,0 +1,116 @@
+# GGJParameters.jl
+#
+# Physical parameters for the Glasser–Greene–Johnson inner-layer model and
+# the derived scale factors that map between physical and inner-layer
+# (Wasow-normalized) variables.
+
+"""
+ GGJParameters
+
+Dimensionless parameters of the Glasser–Greene–Johnson inner-layer model
+at a single rational surface, plus the local Alfvén/resistive timescales
+needed to scale the matching data back to physical Δ. The equilibrium
+coefficients `E, F, G, H, K, M` are the flux-surface averages defined in
+GWP2016 Eq. (A8); E, F, G, H, K enter the inner-region equations (Eq. 11).
+
+## Fields
+
+| field | meaning |
+|:------- |:-------------------------------------------------------------- |
+| `E` | Glasser interchange parameter (enters Mercier `D_I = E+F+H−¼`) |
+| `F` | Glasser interchange parameter |
+| `G` | Coupling coefficient (curvature × pressure gradient) |
+| `H` | Pfirsch–Schlüter coefficient |
+| `K` | Glasser parameter |
+| `M` | Inertia factor (A8; enters K and Q₀, X₀); held, not used here |
+| `taua` | Local Alfvén time at the rational surface |
+| `taur` | Local resistive time at the rational surface |
+| `v1` | Coordinate scale: inner X = v₁·δψ/X₀; enters `rescale_delta` |
+| `ising` | Index of the singular surface (traceability only) |
+
+The growth rate `γ` is not stored here; it is a separate argument to `solve_inner`.
+"""
+Base.@kwdef struct GGJParameters <: InnerLayerParameters
+ E::Float64
+ F::Float64
+ G::Float64
+ H::Float64
+ K::Float64
+ M::Float64 = 0.0
+ taua::Float64
+ taur::Float64
+ v1::Float64 = 1.0
+ ising::Int = 0
+end
+
+"""
+ mercier_di(p::GGJParameters) -> Float64
+
+Mercier interchange index `D_I = E + F + H − 1/4` (GWP2016 Eq. A9); `D_I > 0` means local ideal interchange instability.
+"""
+mercier_di(p::GGJParameters) = p.E + p.F + p.H - 0.25
+
+"""
+ mercier_dr(p::GGJParameters) -> Float64
+
+Resistive interchange index `D_R = E + F + H²` (GWP2016 Eq. A10); `D_R > 0` means local resistive interchange instability.
+"""
+mercier_dr(p::GGJParameters) = p.E + p.F + p.H * p.H
+
+"""
+ p1(p::GGJParameters) -> Float64
+
+`p₁ = √(−D_I)`, setting the large-x Frobenius exponents `r± = 3/2 ± p₁`
+(GW2020 Eq. 49). Throws unless `D_I < 0` (Mercier-stable required).
+"""
+function p1(p::GGJParameters)
+ di = mercier_di(p)
+ di < 0 || throw(ArgumentError("GGJParameters: D_I = $di must be negative (Mercier-stable required for inner-layer model)"))
+ return sqrt(-di)
+end
+
+"""
+ sfac(p::GGJParameters) -> Float64
+
+Lundquist number `S = τ_R / τ_A`.
+"""
+sfac(p::GGJParameters) = p.taur / p.taua
+
+"""
+ x0(p::GGJParameters) -> Float64
+
+Inner-layer length scale `X₀ = S^(−1/3)` (GWP2016 Eq. A16); physical `x = X₀ X` (Eq. A11).
+"""
+x0(p::GGJParameters) = sfac(p)^(-1.0 / 3.0)
+
+"""
+ q0(p::GGJParameters) -> Float64
+
+Growth-rate scale `Q₀ = X₀ / τ_A` (GWP2016 Eq. A16); physical rate `= Q₀ Q` (Eq. A11).
+"""
+q0(p::GGJParameters) = x0(p) / p.taua
+
+"""
+ inner_Q(p::GGJParameters, γ::Number) -> ComplexF64
+
+Scaled inner-layer growth rate `Q = γ / Q₀` (GWP2016 Eq. A11).
+"""
+inner_Q(p::GGJParameters, γ::Number) = ComplexF64(γ) / q0(p)
+
+"""
+ rescale_delta(Δ, p::GGJParameters) -> SVector{2,ComplexF64}
+
+Rescale the matching data to physical Δ by `S^(2√(−D_I)/3) · v₁^(2√(−D_I))`, element-wise
+on the pair (Δ₊, Δ₋). The factor X₀^(−2√(−D_I)) = S^(2√(−D_I)/3) is Wang et al., Phys. Plasmas
+27, 122503 (2020), text after Eq. 11.
+"""
+function rescale_delta(Δ::AbstractVector, p::GGJParameters)
+ s = sfac(p)
+ pp = p1(p)
+ fac = s^(2.0 * pp / 3.0) * p.v1^(2.0 * pp)
+ return SVector{2,ComplexF64}(Δ[1] * fac, Δ[2] * fac)
+end
+
+# Profile conversions for solve_inner_profile: δψ per unit inner coordinate (X = v₁·δψ/X₀) and the
+# large-solution amplitude rescale (v₁/X₀)^(1/2+p₁) to the outer δψ normalization.
+_profile_conversions(p::GGJParameters) = (; dψdx=x0(p) / p.v1, rescale=(p.v1 / x0(p))^(0.5 + p1(p)))
diff --git a/src/InnerLayer/GGJ/Galerkin.jl b/src/InnerLayer/GGJ/Galerkin.jl
new file mode 100644
index 0000000000..1fa75c2401
--- /dev/null
+++ b/src/InnerLayer/GGJ/Galerkin.jl
@@ -0,0 +1,819 @@
+# Galerkin.jl
+#
+# Hermite-cubic finite-element (Galerkin) solver for the GGJ inner layer, porting the GWP2016
+# Sec. III singular-Galerkin method: the half-domain weak form (Eq. 32) on a packed grid
+# (Eq. 33), parity conditions at x = 0, and resonant/extension cells at x_max supplying the
+# matching data (Eqs. 34–35). Fortran deltac configuration: "resonant" + noexp + inps,
+# Hermite basis, mpert = 3 (Ψ, Ξ, Υ). `_assemble_and_solve_point!` reuses the assembly on the
+# rotated ray with a point far-field condition (Ray.jl).
+
+using LinearAlgebra
+using FastGaussQuadrature: gausslobatto
+using QuadGK: quadgk
+
+"""
+ ggj_rows([CT,] params, Q, x) -> (Ũ, Ṽ)
+
+GWP2016 Eq. 11 solved for the second derivatives, `u'' = Ũ·u + Ṽ·u'` for u = (Ψ, Ξ, Υ), at real or complex
+`x` (used as given). `CT` is the element type (default `ComplexF64`). The Galerkin weak form scales the rows by
+diag(1, Q², Q) ([`_physical_uv`](@ref)); the ray march takes them as the lower half of its companion matrix
+([`ode_matrix`](@ref)).
+"""
+ggj_rows(params::GGJParameters, Q::Number, x::Number) = ggj_rows(ComplexF64, params, Q, x)
+
+function ggj_rows(::Type{CT}, params::GGJParameters, Q::Number, x::Number) where {CT<:Complex}
+ e = CT(params.E)
+ f = CT(params.F)
+ g = CT(params.G)
+ h = CT(params.H)
+ k = CT(params.K)
+ q = CT(Q)
+ q2 = q * q
+ x2 = x * x
+ # Ψ'' = Q Ψ − Q x Ξ + H Υ'; Ξ'' = −(x/Q) Ψ + (x²/Q) Ξ − ((E+F)/Q²) Υ − (H/Q²) Ψ';
+ # Υ'' = −(x/Q) Ψ − Q(G−KE) Ξ + (x²/Q + Q(G+KF)) Υ + HKQ Ψ'
+ #! format: off
+ Ũ = SMatrix{3,3,CT}(
+ q, -x / q, -x / q,
+ -q * x, x2 / q, -(g - k * e) * q,
+ 0, -(e + f) / q2, x2 / q + (g + k * f) * q)
+ Ṽ = SMatrix{3,3,CT}(
+ 0, -h / q2, h * k * q,
+ 0, 0, 0,
+ h, 0, 0)
+ #! format: on
+ return Ũ, Ṽ
+end
+
+"""
+ _physical_uv(params, Q, x) -> (I, U, V)
+
+3×3 coefficients of `I·u'' − V·u' − U·u = 0` for u = (Ψ, Ξ, Υ) at real or complex `x`, with
+(I, V, U) = (A, −B, −C) of GWP2016 Eqs. 12–15: the rows of [`ggj_rows`](@ref) scaled by diag(1, Q², Q).
+"""
+function _physical_uv(params::GGJParameters, Q::ComplexF64, x::Number)
+ Ũ, Ṽ = ggj_rows(params, Q, x)
+ q, q2 = Q, Q * Q
+ Imat = @SMatrix ComplexF64[1 0 0; 0 q2 0; 0 0 q]
+ #! format: off
+ U = @SMatrix ComplexF64[
+ Ũ[1, 1] Ũ[1, 2] 0
+ Ũ[2, 1] * q2 Ũ[2, 2] * q2 Ũ[2, 3] * q2
+ Ũ[3, 1] * q Ũ[3, 2] * q Ũ[3, 3] * q
+ ]
+ V = @SMatrix ComplexF64[
+ 0 0 Ṽ[1, 3]
+ Ṽ[2, 1] * q2 0 0
+ Ṽ[3, 1] * q 0 0
+ ]
+ #! format: on
+ return Imat, U, V
+end
+
+# x_max and the two thin matching cells inside it, from where the series residual (GW2020 Eq. 54)
+# crosses three tolerances. Returns (xmax, dx1, dx2, cache).
+function _xmax_3level(params::GGJParameters, Q::ComplexF64;
+ kmax::Int=8, xfac::Float64=1.0,
+ eps_vec::NTuple{3,Float64}=(1e-2, 5e-7, 1e-7))
+ cache = build_asymptotics(params, Q; kmax=kmax)
+
+ # Bracket each crossing on a coarse log sweep, then bisect.
+ dxfac = 10.0^0.01
+ xmax_vals = zeros(Float64, 3)
+ brackets = Vector{Tuple{Float64,Float64}}(undef, 3)
+ set = [true, true, true]
+ x_prev = 0.1
+ delta_prev = maximum(asymptotic_residual(cache, x_prev))
+ x = x_prev * dxfac
+ for _ in 1:1000
+ dmax = maximum(asymptotic_residual(cache, x))
+ for i in 1:3
+ if delta_prev >= eps_vec[i] && dmax < eps_vec[i] && set[i]
+ brackets[i] = (x_prev, x)
+ set[i] = false
+ end
+ end
+ if !any(set)
+ break
+ end
+ x_prev = x
+ delta_prev = dmax
+ x *= dxfac
+ end
+ any(set) && error("_xmax_3level: failed to bracket all xmax levels")
+
+ # Bisect each bracket to find smooth xmax
+ for i in 1:3
+ lo, hi = brackets[i]
+ for _ in 1:60 # 60 bisections ≈ machine precision
+ mid = (lo + hi) / 2
+ if maximum(asymptotic_residual(cache, mid)) < eps_vec[i]
+ hi = mid
+ else
+ lo = mid
+ end
+ end
+ xmax_vals[i] = (lo + hi) / 2
+ end
+
+ xmax_vals[2] *= xfac
+ xmax_vals[3] *= xfac
+ xmax = xmax_vals[3]
+ dx1 = xmax_vals[3] - xmax_vals[2]
+ dx2 = dx1 / 2
+ return (; xmax, dx1, dx2, cache)
+end
+
+# Cell types toward x_max (GWP2016 Sec. III text after Eq. 33; the outer-region analogue is Fig. 1):
+# normal Hermite cells (CT_NONE), extension cells blending the asymptotic solutions into the Hermite
+# basis (CT_EXT2, CT_EXT1, CT_EXT), and the resonant cell (CT_RES) whose large-solution coefficient is
+# the matching data. x = 0 carries the parity conditions.
+@enum CellType CT_NONE CT_EXT2 CT_EXT1 CT_EXT CT_RES
+
+"""
+ GalerkinCell
+
+One finite element of the Galerkin grid.
+
+## Fields
+
+ - `etype` - Cell type (`CT_NONE`, `CT_EXT2`, `CT_EXT1`, `CT_EXT`, `CT_RES`).
+ - `x_left`, `x_right` - Cell end points.
+ - `x_lsode` - Upper limit of the resonant-cell integral and the x_max surface term (`CT_RES` only).
+ - `np` - Highest local Hermite slot per component: 3 for Hermite cells, 1 for `CT_EXT` (left node only), −1 for `CT_RES`.
+ - `map` - `(mpert, np+1)` local-to-global DOF map; `CT_EXT` appends a column of asymptotic DOFs, `CT_RES` holds only those.
+ - `emap` - Asymptotic DOF indices shared by `CT_EXT` and `CT_RES`; only `emap[1]` is active (noexp).
+"""
+struct GalerkinCell
+ etype::CellType
+ x_left::Float64
+ x_right::Float64
+ x_lsode::Float64
+ np::Int
+ map::Matrix{Int}
+ emap::Vector{Int}
+end
+
+"""
+ GalerkinWorkspace
+
+Grid, banded system and scratch buffers of one Galerkin solve.
+
+## Fields
+
+ - `cells` - Grid cells from x = 0 outward.
+ - `ndim` - Number of global unknowns.
+ - `nx` - Number of cells.
+ - `kl` - Banded half-bandwidth (`ku = kl`).
+ - `mat` - `(2kl+ku+1, ndim, 2)` LAPACK banded matrices, one per parity (1 = even/Δ₊, 2 = odd/Δ₋).
+ - `rhs`, `sol` - `(ndim, 2)` right-hand sides and solutions per parity.
+ - `cell_mat_buf`, `cell_mat_ext_buf` - `(3, 3, 4, 4)` per-cell scratch for the Hermite and extension terms.
+ - `cell_rhs_ext_buf` - `(3, 4)` per-cell extension RHS scratch.
+ - `ab_buf`, `rhs_buf` - Scratch copies for the banded LU solve.
+"""
+struct GalerkinWorkspace
+ cells::Vector{GalerkinCell}
+ ndim::Int
+ nx::Int
+ kl::Int
+ mat::Array{ComplexF64,3}
+ rhs::Matrix{ComplexF64}
+ sol::Matrix{ComplexF64}
+ cell_mat_buf::Array{ComplexF64,4}
+ cell_mat_ext_buf::Array{ComplexF64,4}
+ cell_rhs_ext_buf::Matrix{ComplexF64}
+ ab_buf::Matrix{ComplexF64}
+ rhs_buf::Vector{ComplexF64}
+end
+
+function _build_grid_and_workspace(nx::Int, xmax::Float64, dx1::Float64, dx2::Float64,
+ pfac::Float64, cutoff::Int)
+ side = pfac < 1 ? "left" : "right"
+
+ # Cell types
+ etypes = fill(CT_NONE, nx)
+ etypes[nx] = CT_RES
+ etypes[nx-1] = CT_EXT
+ for ix in (nx-2):-1:(nx-cutoff)
+ etypes[ix] = CT_EXT1
+ end
+ etypes[nx-cutoff-1] = CT_EXT2
+
+ # Grid nodes: x[0..nx] in 1-based → x[1..nx+1]
+ x_nodes = zeros(Float64, nx + 1)
+ x_nodes[1] = 0.0
+ x_nodes[nx+1] = xmax
+ x_nodes[nx] = xmax - dx1
+ x_nodes[nx-1] = xmax - (dx1 + dx2)
+ ixmax = nx - 2 # packed region is 0..ixmax
+
+ x0 = x_nodes[1]
+ x1_packed = x_nodes[ixmax+1]
+ xm = (x1_packed + x0) / 2
+ dxp = (x1_packed - x0) / 2
+ mx = ixmax ÷ 2
+ packed = xm .+ dxp .* pack_grid(mx, pfac, side)
+ for i in 1:(ixmax+1)
+ x_nodes[i] = packed[i]
+ end
+ x_nodes[1] = 0.0
+ x_nodes[ixmax+1] = x1_packed
+
+ return _galerkin_workspace(x_nodes, etypes)
+end
+
+# Cells, local-to-global Hermite DOF maps, bandwidth and buffers for given nodes and cell types.
+# The stock layout ends in an EXT/RES pair; an all-CT_NONE layout is the plain Hermite grid
+# used with an external far-field condition (`_assemble_and_solve_point!`).
+function _galerkin_workspace(x_nodes::Vector{Float64}, etypes::Vector{CellType})
+ mpert = 3
+ np = 3
+ nx = length(etypes)
+ has_res = etypes[end] == CT_RES
+
+ # Build cells and local-to-global mapping
+ cells = Vector{GalerkinCell}(undef, nx)
+ imap = 1
+ for ix in 1:nx
+ et = etypes[ix]
+ xl = x_nodes[ix]
+ xr = x_nodes[ix+1]
+
+ cell_np = if et == CT_NONE || et == CT_EXT1 || et == CT_EXT2
+ np
+ elseif et == CT_EXT
+ 1 # left-node Hermite pair only, plus one asymptotic DOF
+ else # CT_RES
+ -1 # no Hermite DOFs
+ end
+
+ x_lsode = (et == CT_RES) ? xr : 0.0
+
+ # Build local-to-global Hermite DOF map.
+ if et == CT_RES
+ # Will be set after the loop
+ map_local = zeros(Int, mpert, 1) # map(:, 0:0)
+ emap_local = zeros(Int, 1)
+ cells[ix] = GalerkinCell(et, xl, xr, x_lsode, cell_np, map_local, emap_local)
+ continue
+ end
+
+ # Standard Hermite mapping with overlap
+ if imap > 1
+ imap -= 2 * mpert
+ end
+ map_local = zeros(Int, mpert, cell_np + 1) # map(:, 0:cell_np)
+ for ip in 0:cell_np
+ for ipert in 1:mpert
+ map_local[ipert, ip+1] = imap
+ imap += 1
+ end
+ end
+
+ emap_local = Int[]
+ if et == CT_EXT
+ # Asymptotic DOFs (imap, imap+1, imap+2); with noexp only emap[1] ≤ ndim, the rest are skipped.
+ emap_local = [imap, imap + 1, imap + 2]
+ map_extra = [imap; imap + 1; imap + 2] # 3-element column
+ map_local = hcat(map_local, map_extra)
+ end
+
+ cells[ix] = GalerkinCell(et, xl, xr, x_lsode, cell_np, map_local, emap_local)
+ end
+
+ # Set resonant cell mapping: shares emap with ext cell
+ if has_res
+ ext_cell = cells[nx-1]
+ emap_vals = ext_cell.emap
+ res_map = reshape(copy(emap_vals), mpert, 1)
+ cells[nx] = GalerkinCell(CT_RES, x_nodes[nx], x_nodes[nx+1], x_nodes[nx+1],
+ -1, res_map, copy(emap_vals))
+ end
+
+ ndim = has_res ? imap : imap - 1 # noexp → ndim = imap (only emap[1] ≤ ndim); plain grid: Hermite DOFs only
+
+ # Bandwidth
+ kl = mpert * (np + 1) # one cell's mpert·(np+1) DOFs
+ ku = kl
+ ldab = 2kl + ku + 1
+
+ mat = zeros(ComplexF64, ldab, ndim, 2)
+ rhs = zeros(ComplexF64, ndim, 2)
+ sol = zeros(ComplexF64, ndim, 2)
+ # Scratch buffers sized for np + 1 = 4; smaller cells use a zeroed sub-slice.
+ cell_mat_buf = zeros(ComplexF64, mpert, mpert, np + 1, np + 1)
+ cell_mat_ext_buf = zeros(ComplexF64, mpert, mpert, np + 1, np + 1)
+ cell_rhs_ext_buf = zeros(ComplexF64, mpert, np + 1)
+ ab_buf = zeros(ComplexF64, ldab, ndim)
+ rhs_buf = zeros(ComplexF64, ndim)
+
+ return GalerkinWorkspace(cells, ndim, nx, kl, mat, rhs, sol,
+ cell_mat_buf, cell_mat_ext_buf, cell_rhs_ext_buf,
+ ab_buf, rhs_buf)
+end
+
+# One cell's GWP2016 Eq. 32 bilinear form after integrating the A-term by parts,
+# I·(αᵢ' αⱼ') + V·(αᵢ αⱼ') + U·(αᵢ αⱼ), by Gauss–Lobatto quadrature.
+function _gauss_quad!(cell_mat::Array{ComplexF64,4}, cell::GalerkinCell,
+ quad_nodes::Vector{Float64}, quad_weights::Vector{Float64},
+ params::GGJParameters, Q::ComplexF64; θ::Float64=0.0)
+ np_cell = cell.np
+ nq = length(quad_nodes)
+ x0 = (cell.x_right + cell.x_left) / 2
+ dx = (cell.x_right - cell.x_left) / 2
+ fill!(cell_mat, 0)
+
+ @inbounds for iq in 1:nq
+ x = x0 + dx * quad_nodes[iq]
+ w = dx * quad_weights[iq]
+ if iszero(θ)
+ Imat, Umat, Vmat = _physical_uv(params, Q, x)
+ else
+ # Rotated contour x = e^{iθ}s: d/dx = e^{-iθ} d/ds; times e^{2iθ}, I is unchanged, V gains e^{iθ}, U gains e^{2iθ}.
+ Imat, U0, V0 = _physical_uv(params, Q, cis(θ) * x)
+ Umat, Vmat = cis(2θ) * U0, cis(θ) * V0
+ end
+ pb, qb = hermite_basis(x, cell.x_left, cell.x_right)
+
+ for ip in 0:np_cell, jp in 0:np_cell
+ for jpert in 1:3, ipert in 1:3
+ cell_mat[ipert, jpert, ip+1, jp+1] +=
+ w * (
+ Imat[ipert, jpert] * qb[ip+1] * qb[jp+1] +
+ Vmat[ipert, jpert] * pb[ip+1] * qb[jp+1] +
+ Umat[ipert, jpert] * pb[ip+1] * pb[jp+1]
+ )
+ end
+ end
+ end
+end
+
+# Extension cells (GWP2016 Sec. III): the large resonant solution (column 1) is blended into the
+# Hermite cubics with C¹ continuity as an extra DOF; the small one (column 2) drives the RHS.
+function _extension!(cell_mat::Array{ComplexF64,4}, cell_rhs::Matrix{ComplexF64},
+ cell::GalerkinCell,
+ quad_nodes::Vector{Float64}, quad_weights::Vector{Float64},
+ params::GGJParameters, Q::ComplexF64,
+ cache::InnerAsymptoticsCache)
+ np_cell = cell.np
+ x0c = (cell.x_right + cell.x_left) / 2
+ dxc = (cell.x_right - cell.x_left) / 2
+ nq = length(quad_nodes)
+
+ if cell.etype == CT_EXT
+ # Asymptotic basis at right boundary of ext cell
+ ua_bdy, dua_bdy = physical_ua_dua(cache, cell.x_right)
+ ep = np_cell + 1 # index of the extra DOF (1-based → ep+1 in array)
+
+ @inbounds for iq in 1:nq
+ x = x0c + dxc * quad_nodes[iq]
+ w = dxc * quad_weights[iq]
+ uax, duax = physical_ua_dua(cache, x)
+ Imat, Umat, Vmat = _physical_uv(params, Q, x)
+ pb, qb = hermite_basis(x, cell.x_left, cell.x_right)
+
+ # Extra DOF φ = ua₁(x_r)·H₁₀ + ua₁'(x_r)·H₁₁, the large solution Hermite-blended at the right
+ # node; assembles (hᵢ, Lφ), (φ, Lhᵢ) and (φ, Lφ).
+ jp = 1 # column 1 = large solution (noexp)
+ ua1 = ua_bdy[:, jp] * pb[3] + dua_bdy[:, jp] * pb[4]
+ dua1 = ua_bdy[:, jp] * qb[3] + dua_bdy[:, jp] * qb[4]
+
+ for ip in 0:np_cell
+ term1 = qb[ip+1] * (Imat * dua1) + pb[ip+1] * (Vmat * dua1) + pb[ip+1] * (Umat * ua1)
+ cell_mat[:, 1, ip+1, ep+1] .+= w .* term1
+
+ ua2 = ua_bdy[:, jp] * pb[3] + dua_bdy[:, jp] * pb[4]
+ dua2 = ua_bdy[:, jp] * qb[3] + dua_bdy[:, jp] * qb[4]
+ term2 = qb[ip+1] * transpose(transpose(dua2) * Imat) + qb[ip+1] * transpose(transpose(ua2) * Vmat) + pb[ip+1] * transpose(transpose(ua2) * Umat)
+ cell_mat[1, :, ep+1, ip+1] .+= w .* term2
+ end
+
+ # (φ, Lφ) self-interaction
+ ua2_s = ua_bdy[:, 1] * pb[3] + dua_bdy[:, 1] * pb[4]
+ dua2_s = ua_bdy[:, 1] * qb[3] + dua_bdy[:, 1] * qb[4]
+ term = transpose(dua2_s) * Imat * dua1 + transpose(ua2_s) * Vmat * dua1 + transpose(ua2_s) * Umat * ua1
+ cell_mat[1, 1, ep+1, ep+1] += w * term
+
+ # RHS: driven by the small solution (column 2)
+ ua_drv = uax[:, 2]
+ dua_drv = duax[:, 2]
+ for ip in 0:np_cell
+ term_r = qb[ip+1] * (Imat * dua_drv) + pb[ip+1] * (Vmat * dua_drv) + pb[ip+1] * (Umat * ua_drv)
+ cell_rhs[:, ip+1] .-= w .* term_r
+ end
+ # RHS for asymptotic test function
+ term_re = transpose(dua2_s) * Imat * dua_drv + transpose(ua2_s) * Vmat * dua_drv + transpose(ua2_s) * Umat * ua_drv
+ cell_rhs[1, ep+1] -= w * term_re
+ end
+
+ elseif cell.etype == CT_EXT1 || cell.etype == CT_EXT2
+ # Only RHS contribution (driving term)
+ @inbounds for iq in 1:nq
+ x = x0c + dxc * quad_nodes[iq]
+ w = dxc * quad_weights[iq]
+ Imat, Umat, Vmat = _physical_uv(params, Q, x)
+ pb, qb = hermite_basis(x, cell.x_left, cell.x_right)
+
+ if cell.etype == CT_EXT1
+ uax, duax = physical_ua_dua(cache, x)
+ ua_drv = uax[:, 2]
+ dua_drv = duax[:, 2]
+ else # CT_EXT2
+ ua_bdy, dua_bdy = physical_ua_dua(cache, cell.x_right)
+ ua_drv = ua_bdy[:, 2] * pb[3] + dua_bdy[:, 2] * pb[4]
+ dua_drv = ua_bdy[:, 2] * qb[3] + dua_bdy[:, 2] * qb[4]
+ end
+
+ for ip in 0:np_cell
+ term_r = qb[ip+1] * (Imat * dua_drv) + pb[ip+1] * (Vmat * dua_drv) + pb[ip+1] * (Umat * ua_drv)
+ cell_rhs[:, ip+1] .-= w .* term_r
+ end
+ end
+ end
+end
+
+# Resonant-cell scalar products ∫ ua₁ᵀ L ua_j dx (j = 1 stiffness, j = 2 RHS) with the asymptotic
+# solutions as test and trial functions; non-analytic, so adaptive QuadGK (GWP2016 Sec. III).
+function _resonant_integral(cell::GalerkinCell, params::GGJParameters,
+ Q::ComplexF64, cache::InnerAsymptoticsCache;
+ tol::Float64=1e-5)
+ x_left = cell.x_left
+ x_right = cell.x_lsode
+
+ function integrand_11(x)
+ ua, dua = physical_ua_dua(cache, x)
+ Imat, Umat, Vmat = _physical_uv(params, Q, x)
+ ua1 = ua[:, 1]
+ dua1 = dua[:, 1]
+ return transpose(dua1) * Imat * dua1 + transpose(ua1) * Vmat * dua1 + transpose(ua1) * Umat * ua1
+ end
+
+ function integrand_12(x)
+ ua, dua = physical_ua_dua(cache, x)
+ Imat, Umat, Vmat = _physical_uv(params, Q, x)
+ dua1 = dua[:, 1]
+ ua1 = ua[:, 1]
+ ua2 = ua[:, 2]
+ dua2 = dua[:, 2]
+ return transpose(dua1) * Imat * dua2 + transpose(ua1) * Vmat * dua2 + transpose(ua1) * Umat * ua2
+ end
+
+ val_11, _ = quadgk(integrand_11, x_left, x_right; rtol=tol)
+ val_12, _ = quadgk(integrand_12, x_left, x_right; rtol=tol)
+
+ return ComplexF64(val_11), ComplexF64(val_12)
+end
+
+# Global assembly and solve.
+
+function _assemble_and_solve!(ws::GalerkinWorkspace,
+ params::GGJParameters, Q::ComplexF64,
+ cache::InnerAsymptoticsCache;
+ nq::Int=4, tol_res::Float64=1e-5)
+ mpert = 3
+ np = 3
+ quad_nodes, quad_weights = gausslobatto(nq + 1)
+ offset = ws.kl + ws.kl + 1 # kl + ku + 1 since ku = kl
+
+ fill!(ws.mat, 0)
+ fill!(ws.rhs, 0)
+
+ cell_mat = ws.cell_mat_buf
+ cell_mat_ext = ws.cell_mat_ext_buf
+ cell_rhs_ext = ws.cell_rhs_ext_buf
+ for ix in 1:ws.nx
+ cell = ws.cells[ix]
+
+ # Hermite contribution (all cells but CT_RES)
+ if cell.np >= 0
+ np_eff = cell.np
+ fill!(cell_mat, 0)
+ _gauss_quad!(cell_mat, cell, quad_nodes, quad_weights, params, Q)
+ _scatter_cell!(ws, cell, cell_mat, np_eff)
+ end
+
+ # Extension terms
+ if cell.etype in (CT_EXT, CT_EXT1, CT_EXT2)
+ # CT_EXT carries one extra (asymptotic) slot after its Hermite pair.
+ np_eff = cell.etype == CT_EXT ? cell.np + 1 : cell.np
+ fill!(cell_mat_ext, 0)
+ fill!(cell_rhs_ext, 0)
+ _extension!(cell_mat_ext, cell_rhs_ext, cell, quad_nodes, quad_weights, params, Q, cache)
+
+ npp = np_eff
+ for ip in 0:npp, ipert in 1:mpert
+ i = ip < size(cell.map, 2) ? cell.map[ipert, ip+1] : cell.emap[1]
+ # For the extra DOF, only ipert=1 is meaningful (noexp)
+ if cell.etype == CT_EXT && ip == cell.np + 1 && ipert > 1
+ continue
+ end
+ if i > ws.ndim
+ continue
+ end
+ for jp in 0:npp, jpert in 1:mpert
+ j = jp < size(cell.map, 2) ? cell.map[jpert, jp+1] : cell.emap[1]
+ if cell.etype == CT_EXT && jp == cell.np + 1 && jpert > 1
+ continue
+ end
+ if j > ws.ndim
+ continue
+ end
+ ws.mat[offset+i-j, j, 1] += cell_mat_ext[ipert, jpert, ip+1, jp+1]
+ end
+ # RHS (both parities get the same base RHS)
+ ws.rhs[i, 1] += cell_rhs_ext[ipert, ip+1]
+ end
+ end
+
+ # Resonant integral
+ if cell.etype == CT_RES
+ val_11, val_12 = _resonant_integral(cell, params, Q, cache; tol=tol_res)
+ emap1 = cell.emap[1]
+ if emap1 <= ws.ndim
+ ws.mat[offset, emap1, 1] += val_11 # diagonal: i=j=emap1
+ ws.rhs[emap1, 1] -= val_12
+ end
+ end
+ end
+
+ # IBP surface term [αᵢ A uⱼ'] at x_max, dropped in GWP2016 Eq. 32 and kept here because the resonant cell carries Δ.
+ res_cell = ws.cells[ws.nx]
+ x_lsode = res_cell.x_lsode
+ ua_xmax, dua_xmax = physical_ua_dua(cache, x_lsode)
+ Imat_xmax, _, _ = _physical_uv(params, Q, x_lsode)
+ emap1 = res_cell.emap[1]
+ if emap1 <= ws.ndim
+ # Surface term: -ua_1^T I dua_1 at x_lsode (stiffness)
+ surf_11 = transpose(ua_xmax[:, 1]) * Imat_xmax * dua_xmax[:, 1]
+ ws.mat[offset, emap1, 1] -= surf_11
+ # Surface term: +ua_1^T I dua_2 at x_lsode (RHS)
+ surf_12 = transpose(ua_xmax[:, 1]) * Imat_xmax * dua_xmax[:, 2]
+ ws.rhs[emap1, 1] += surf_12
+ end
+
+ _parity_bcs_and_solve!(ws, params, Q, ws.ndim)
+end
+
+# Add one cell's Hermite block to the base (isol = 1) banded matrix; both parities share it.
+function _scatter_cell!(ws::GalerkinWorkspace, cell::GalerkinCell, cell_mat::Array{ComplexF64,4}, np_eff::Int)
+ mpert = 3
+ offset = ws.kl + ws.kl + 1
+ for ip in 0:np_eff, ipert in 1:mpert
+ i = cell.map[ipert, ip+1]
+ if i > ws.ndim
+ continue
+ end
+ for jp in 0:np_eff, jpert in 1:mpert
+ j = cell.map[jpert, jp+1]
+ if j > ws.ndim
+ continue
+ end
+ ws.mat[offset+i-j, j, 1] += cell_mat[ipert, jpert, ip+1, jp+1]
+ end
+ end
+end
+
+# Copy the base system to both parities, impose the x = 0 parity conditions, and solve the
+# leading n×n banded system of each parity by LAPACK banded LU.
+function _parity_bcs_and_solve!(ws::GalerkinWorkspace, params::GGJParameters, Q::ComplexF64, n::Int)
+ mpert = 3
+ offset = ws.kl + ws.kl + 1
+
+ ws.mat[:, :, 2] .= ws.mat[:, :, 1]
+ ws.rhs[:, 2] .= ws.rhs[:, 1]
+
+ cell1 = ws.cells[1]
+ Imat0, _, _ = _physical_uv(params, Q, cell1.x_left)
+
+ # IBP surface term at x = 0
+ for ipert in 1:mpert, jpert in 1:mpert
+ i = cell1.map[ipert, 1] # ip=0
+ j = cell1.map[jpert, 2] # ip=1
+ if i <= ws.ndim && j <= ws.ndim
+ ws.mat[offset+i-j, j, 1] += Imat0[ipert, jpert]
+ ws.mat[offset+i-j, j, 2] += Imat0[ipert, jpert]
+ end
+ end
+
+ # Parity conditions at X = 0 (GWP2016 Sec. III), parity of the displacement Ξ (Eq. 34):
+ # isol = 1 even (Δ₊, interchange), isol = 2 odd (Δ₋, tearing). The ip = 0 rows are replaced.
+ for isol in 1:2
+ # Zero out ip=0 rows in the global matrix
+ for ipert in 1:mpert
+ i = cell1.map[ipert, 1] # ip=0 DOFs
+ if i > ws.ndim
+ continue
+ end
+ for jj in max(1, i - ws.kl):min(ws.ndim, i + ws.kl)
+ ws.mat[offset+i-jj, jj, isol] = 0
+ end
+ end
+ # Even: Ψ(0) = Ξ'(0) = Υ'(0) = 0; odd: Ψ'(0) = Ξ(0) = Υ(0) = 0 (ip = 1 slots are derivatives).
+ if isol == 1
+ i = cell1.map[1, 1]
+ j = cell1.map[1, 1]
+ ws.mat[offset+i-j, j, isol] = 1
+ for ipert in 2:3
+ i = cell1.map[ipert, 1]
+ j = cell1.map[ipert, 2]
+ ws.mat[offset+i-j, j, isol] = 1
+ end
+ else
+ i = cell1.map[1, 1]
+ j = cell1.map[1, 2]
+ ws.mat[offset+i-j, j, isol] = 1
+ for ipert in 2:3
+ i = cell1.map[ipert, 1]
+ j = cell1.map[ipert, 1]
+ ws.mat[offset+i-j, j, isol] = 1
+ end
+ end
+ for ipert in 1:mpert
+ i = cell1.map[ipert, 1]
+ if i <= ws.ndim
+ ws.rhs[i, isol] = 0
+ end
+ end
+ end
+
+ # Solve for each parity using LAPACK banded LU (gbtrf! + gbtrs!)
+ kl = ws.kl
+ ku = kl
+ ab = @view ws.ab_buf[:, 1:n]
+ rb = @view ws.rhs_buf[1:n]
+ for isol in 1:2
+ copyto!(ab, @view(ws.mat[:, 1:n, isol]))
+ copyto!(rb, @view(ws.rhs[1:n, isol]))
+ _, ipiv = LinearAlgebra.LAPACK.gbtrf!(kl, ku, n, ab)
+ LinearAlgebra.LAPACK.gbtrs!('N', kl, ku, n, ab, ipiv, rb)
+ ws.sol[1:n, isol] .= rb
+ end
+end
+
+"""
+ _assemble_and_solve_point!(ws, params, Q, θ, Us, Ub, E; nq=6) -> (Δraw, cexp)
+
+Hermite Galerkin solve on the all-`CT_NONE` grid of `ws` along the ray x = e^{iθ}s, with the
+far-field condition imposed strongly at the last node: its state is v = Us + Δ·Ub + c₁E₁ + c₂E₂,
+with Us, Ub, E given as (Ψ, Ξ, Υ, Ψ', Ξ', Υ') in x-derivatives; the last node's six DOFs are
+replaced by (Δ, c₁, c₂). Returns the raw Δ and decaying-pair coefficients per parity
+(isol = 1 even/Δ₊, 2 odd/Δ₋); `ws.sol` holds the full nodal solution afterwards.
+"""
+function _assemble_and_solve_point!(ws::GalerkinWorkspace, params::GGJParameters, Q::ComplexF64,
+ θ::Float64, Us::Vector{ComplexF64}, Ub::Vector{ComplexF64}, E::Matrix{ComplexF64}; nq::Int=6)
+ quad_nodes, quad_weights = gausslobatto(nq + 1)
+ offset = ws.kl + ws.kl + 1
+ N = ws.nx
+ fill!(ws.mat, 0)
+ fill!(ws.rhs, 0)
+ cell_mat = ws.cell_mat_buf
+ for ix in 1:(N-1)
+ _gauss_quad!(cell_mat, ws.cells[ix], quad_nodes, quad_weights, params, Q; θ=θ)
+ _scatter_cell!(ws, ws.cells[ix], cell_mat, ws.cells[ix].np)
+ end
+
+ # Last cell as a dense 12×12 block, local DOF index 3·ip + ipert (ip = 0..3 Hermite slots); the
+ # far-field state is imposed at its right node.
+ cell = ws.cells[N]
+ _gauss_quad!(cell_mat, cell, quad_nodes, quad_weights, params, Q; θ=θ)
+ Kc = zeros(ComplexF64, 12, 12)
+ for ip in 0:3, jp in 0:3, ipert in 1:3, jpert in 1:3
+ Kc[3ip+ipert, 3jp+jpert] = cell_mat[ipert, jpert, ip+1, jp+1]
+ end
+ # IBP boundary term at the far end, mirroring the x = 0 term of `_parity_bcs_and_solve!` (I is x-independent).
+ Imat, _, _ = _physical_uv(params, Q, 0.0)
+ for ipert in 1:3, jpert in 1:3
+ Kc[6+ipert, 9+jpert] -= Imat[ipert, jpert]
+ end
+
+ # Far-field trace in DOF units (values, s-derivatives = e^{iθ}·x-derivatives); Ub normalized.
+ dof(v) = ComplexF64[v[1], v[2], v[3], cis(θ)*v[4], cis(θ)*v[5], cis(θ)*v[6]]
+ βb = norm(Ub)
+ Bd = hcat(dof(Ub) ./ βb, dof(E[:, 1]), dof(E[:, 2]))
+ usd = dof(Us)
+ # Tl maps the 9 reduced unknowns (left node's 6 DOFs, Δ̃, c₁, c₂) to the cell's 12 Hermite DOFs; test space = Tlᵀ.
+ Tl = zeros(ComplexF64, 12, 9)
+ for k in 1:6
+ Tl[k, k] = 1
+ end
+ Tl[7:12, 7:9] .= Bd
+ K9 = transpose(Tl) * Kc * Tl
+ r9 = -(transpose(Tl) * (Kc[:, 7:12] * usd))
+ # (Δ̃, c₁, c₂) occupy the last node's value slots; its derivative slots drop out of the reduced system.
+ yslots = cell.map[:, 3]
+ glob = vcat(cell.map[:, 1], cell.map[:, 2], yslots)
+ for a in 1:9
+ i = glob[a]
+ ws.rhs[i, 1] += r9[a]
+ for b in 1:9
+ j = glob[b]
+ ws.mat[offset+i-j, j, 1] += K9[a, b]
+ end
+ end
+
+ _parity_bcs_and_solve!(ws, params, Q, yslots[end])
+
+ Δraw = MVector{2,ComplexF64}(0, 0)
+ cexp = zeros(MMatrix{2,2,ComplexF64})
+ for isol in 1:2
+ y = ws.sol[yslots, isol]
+ Δraw[isol] = y[1] / βb
+ cexp[1, isol] = y[2]
+ cexp[2, isol] = y[3]
+ ws.sol[vcat(cell.map[:, 3], cell.map[:, 4]), isol] .= usd .+ Bd * y # reconstruct the last node for profiles
+ end
+ return SVector(Δraw), SMatrix(cexp)
+end
+
+# Profiles (Ψ, Ξ, Υ) from the Hermite DOFs, columns 1 = even/Δ₊, 2 = odd/Δ₋; CT_EXT/CT_RES cells are
+# skipped because their solution lives in the asymptotic emap DOF.
+function _solution_profile(ws::GalerkinWorkspace; npc::Int=10)
+ mpert = 3
+ # Every Hermite cell contributes npc points.
+ npts = 0
+ for cell in ws.cells
+ (cell.etype == CT_RES || cell.etype == CT_EXT) && continue
+ cell.np >= 0 || continue
+ npts += npc
+ end
+ xs = Vector{Float64}(undef, npts)
+ Ψ = Matrix{ComplexF64}(undef, npts, 2)
+ Ξ = Matrix{ComplexF64}(undef, npts, 2)
+ Υ = Matrix{ComplexF64}(undef, npts, 2)
+ vals = zeros(ComplexF64, mpert, 2)
+ k = 0
+ for cell in ws.cells
+ (cell.etype == CT_RES || cell.etype == CT_EXT) && continue
+ cell.np >= 0 || continue
+ for t in range(0, 1; length=npc + 1)[1:(end-1)]
+ x = cell.x_left + t * (cell.x_right - cell.x_left)
+ pb, _ = hermite_basis(x, cell.x_left, cell.x_right)
+ fill!(vals, 0)
+ for isol in 1:2, ipert in 1:mpert, ip in 0:cell.np
+ g = cell.map[ipert, ip+1]
+ g <= ws.ndim && (vals[ipert, isol] += ws.sol[g, isol] * pb[ip+1])
+ end
+ k += 1
+ xs[k] = x
+ Ψ[k, 1] = vals[1, 1]
+ Ψ[k, 2] = vals[1, 2]
+ Ξ[k, 1] = vals[2, 1]
+ Ξ[k, 2] = vals[2, 2]
+ Υ[k, 1] = vals[3, 1]
+ Υ[k, 2] = vals[3, 2]
+ end
+ end
+ p = sortperm(xs)
+ return (; x=xs[p], Ψ=Ψ[p, :], Ξ=Ξ[p, :], Υ=Υ[p, :])
+end
+
+# Stock Galerkin solve shared by `solve_inner` and `solve_inner_profile`. The matching data are the
+# resonant cell's emap DOF, the coefficient of the large resonant solution (GWP2016 Eqs. 34–35), per
+# parity isol = 1 (even, Δ₊), 2 (odd, Δ₋); returns them rescaled, with the solved workspace.
+function _galerkin_solve(params::GGJParameters, γ::Number;
+ kmax::Int=8, nx::Int=512, nq::Int=4, pfac::Float64=1.0,
+ cutoff::Int=5, xfac::Float64=1.0, tol_res::Float64=1e-5)
+ Q = inner_Q(params, γ)
+ xmax_info = _xmax_3level(params, Q; kmax=kmax, xfac=xfac)
+ ws = _build_grid_and_workspace(nx, xmax_info.xmax, xmax_info.dx1, xmax_info.dx2, pfac, cutoff)
+ _assemble_and_solve!(ws, params, Q, xmax_info.cache; nq=nq, tol_res=tol_res)
+ emap1 = ws.cells[ws.nx].emap[1]
+ return rescale_delta(SVector{2,ComplexF64}(ws.sol[emap1, 1], ws.sol[emap1, 2]), params), ws
+end
+
+"""
+ solve_inner_profile(::GGJModel{:galerkin}, params::GGJParameters, γ::Number; kwargs...)
+ -> (; Δ, x, Ψ, Ξ, dψdx, rescale)
+
+Hermite-FEM implementation of the [`solve_inner_profile`](@ref) interface:
+real-axis solve, so `Δ` and the profiles come from the same solution. Same
+numerics/kwargs as `solve_inner(GGJModel(; solver=:galerkin), ...)`.
+"""
+function solve_inner_profile(::_BareGGJ{:galerkin}, params::GGJParameters, γ::Number; kwargs...)
+ Δ, ws = _galerkin_solve(params, γ; kwargs...)
+ prof = _solution_profile(ws)
+ return (; Δ=Δ, x=prof.x, Ψ=prof.Ψ, Ξ=prof.Ξ, _profile_conversions(params)...)
+end
+
+"""
+ solve_inner(::GGJModel{:galerkin}, params::GGJParameters, γ::Number;
+ kmax::Int=8, nx::Int=512, nq::Int=4, pfac::Float64=1.0,
+ cutoff::Int=5, xfac::Float64=1.0, tol_res::Float64=1e-5)
+ -> InnerLayerResponse
+
+Solve the GGJ inner-layer matching problem using the Hermite-cubic finite
+element (Galerkin) method (GWP2016 Sec. III), in the "resonant + noexp + inps"
+configuration.
+
+Returns the parity-projected matching data (GWP2016 Eqs. 34–35), rescaled by
+[`rescale_delta`](@ref), as an `InnerLayerResponse`: `interchange` is the even-parity Δ₊
+(isol = 1), `tearing` the odd-parity Δ₋ (isol = 2).
+
+Knobs: `kmax` series order; `nx` cell count; `nq` Gauss–Lobatto order; `pfac` grid packing;
+`cutoff` extension-cell span (cells nx−cutoff−1 … nx−1); `xfac` scale on the two inner matching radii; `tol_res`
+resonant-cell quadrature tolerance.
+"""
+function solve_inner(::_BareGGJ{:galerkin}, params::GGJParameters, γ::Number; kwargs...)
+ Δ, _ = _galerkin_solve(params, γ; kwargs...)
+ return InnerLayerResponse(; interchange=Δ[1], tearing=Δ[2])
+end
diff --git a/src/InnerLayer/GGJ/InnerAsymptotics.jl b/src/InnerLayer/GGJ/InnerAsymptotics.jl
new file mode 100644
index 0000000000..8f30f4310d
--- /dev/null
+++ b/src/InnerLayer/GGJ/InnerAsymptotics.jl
@@ -0,0 +1,585 @@
+# InnerAsymptotics.jl
+#
+# Wasow asymptotic basis ("inps" basis) for the GGJ inner-layer system.
+#
+# Reference: A. H. Glasser & Z. R. Wang, Phys. Plasmas 27, 012506 (2020)
+# ("GW2020"), Secs. II.A–II.G (Eqs. 1–53) and III (Eqs. 54–55). Notation map (all equation
+# numbers are GW2020):
+#
+# A0/A1/A2 -> Eqs. 3–5 (A = A₀+x⁻²A₁+x⁻⁴A₂ (Eq. 3); A₀, A₂ Eq. 4; A₁ Eq. 5)
+# T, Tinv -> Eqs. 6–8 (Jordan basis of A₀; u = Tv, v' = xJv, λ = Q^{-1/2})
+# J0/J1/J2 -> Eqs. 9–10 (Jₖ = T^{-1} Aₖ T)
+# P_k, B_k -> Eqs. 11–24 (splitting transformation V = PW; Lyapunov solve Eq. 22)
+# Q_k, C_k -> Eqs. 25–39 (2×2 inner-block diagonalization W = QX)
+# D_k -> Eqs. 40–43 (shearing transformation X = SY)
+# Y0, R -> Eqs. 48–49 (lowest-order solution; Mercier Frobenius exponents r±)
+# Y_k, Z_k -> Eqs. 50–52 (Y-series Y = Y₀Z in shifted-exponent form)
+# U(x) -> Eq. 53 (final asymptotic solution U = TPQSY at large x)
+# residual -> Eq. 54 (convergence measure Δ±, used to pick the matching radius)
+
+using LinearAlgebra
+using StaticArrays
+
+"""
+ InnerAsymptoticsCache
+
+Frozen `inps` Wasow asymptotic-basis construction for one `(GGJParameters, Q)`
+pair, stored as `SMatrix`/`SVector` for allocation-free evaluation. Index
+convention: `P[k+1]` holds the k-th-order matrix `P_k`, etc.
+
+## Fields
+
+ - `params, Q, kmax` — input parameters and series truncation order.
+ - `R = (r₊, r₋)` — Mercier-shifted Frobenius exponents at infinity (Eq. 49).
+ - `T` — 6×6 eigenvector basis of A₀ (Eq. 7).
+ - `J` — `(J₀, J₁, J₂)`, the J-rotated coefficient matrices (Eqs. 9–10).
+ - `P` — splitting matrices, k = 0..kmax+2 (Eqs. 16, 22).
+ - `Qmat` — 2×2 inner-block transformation matrices, k = 0..kmax+2 (Eqs. 32–39).
+ - `Y` — 2×2 series matrices Y_k = Y₀Z_k, k = 0..kmax (Eqs. 50–52).
+"""
+struct InnerAsymptoticsCache
+ params::GGJParameters
+ Q::ComplexF64
+ kmax::Int
+ R::SVector{2,Float64}
+ T::SMatrix{6,6,ComplexF64,36}
+ J::NTuple{3,SMatrix{6,6,ComplexF64,36}}
+ P::Vector{SMatrix{6,6,ComplexF64,36}}
+ Qmat::Vector{SMatrix{2,2,ComplexF64,4}}
+ Y::Vector{SMatrix{2,2,ComplexF64,4}}
+end
+
+# T, T⁻¹, λ = Q^{-1/2} and J_i = T⁻¹A_iT from the coefficient matrices A₀–A₂ (GW2020 Eqs. 3–10).
+
+function _build_tjmat(p::GGJParameters, Q::ComplexF64)
+ e = ComplexF64(p.E)
+ f = ComplexF64(p.F)
+ h = ComplexF64(p.H)
+ g = ComplexF64(p.G)
+ k = ComplexF64(p.K)
+ q = Q
+ q2 = q * q
+ λ = 1 / sqrt(q)
+
+ # T (Eq. 7) and T⁻¹ (Eq. 8), listed row by row.
+ #! format: off
+ T = @SMatrix ComplexF64[
+ 1 0 h*q q2/λ h*q -q2/λ
+ 0 0 0 -1/λ 0 1/λ
+ 0 0 -1/λ 0 1/λ 0
+ 0 1 -h/λ -q2 h/λ -q2
+ 0 0 0 1 0 1
+ 0 0 1 0 1 0
+ ]
+
+ Tinv = @SMatrix ComplexF64[
+ 1 q2 0 0 0 -h*q
+ 0 0 -h 1 q2 0
+ 0 0 -λ/2 0 0 1/2
+ 0 -λ/2 0 0 1/2 0
+ 0 0 λ/2 0 0 1/2
+ 0 λ/2 0 0 1/2 0
+ ]
+ #! format: on
+
+ # A₀ and A₂: GW2020 Eq. (4); A₁: Eq. (5).
+ A0 = zeros(ComplexF64, 6, 6)
+ A1 = zeros(ComplexF64, 6, 6)
+ A2 = zeros(ComplexF64, 6, 6)
+
+ # A0
+ A0[4, 2] = -q
+ A0[5, 2] = 1 / q
+ A0[6, 3] = 1 / q
+ A0[1, 4] = 1
+ A0[2, 5] = 1
+ A0[3, 6] = 1
+ A0[4, 6] = h
+
+ # A1
+ A1[4, 1] = q
+ A1[5, 1] = -1 / q
+ A1[6, 1] = -1 / q
+ A1[6, 2] = -(g - k * e) * q
+ A1[5, 3] = -(e + f) / q2
+ A1[6, 3] = (g + k * f) * q
+ A1[4, 4] = 1
+ A1[5, 4] = -h / q2
+ A1[6, 4] = h * k * q
+ A1[5, 5] = -1
+ A1[6, 6] = -1
+
+ # A2
+ A2[4, 1] = -2
+ A2[5, 1] = h / q2
+ A2[6, 1] = -h * k * q
+
+ A0s = SMatrix{6,6,ComplexF64}(A0)
+ A1s = SMatrix{6,6,ComplexF64}(A1)
+ A2s = SMatrix{6,6,ComplexF64}(A2)
+
+ J0 = Tinv * A0s * T
+ J1 = Tinv * A1s * T
+ J2 = Tinv * A2s * T
+
+ return T, (J0, J1, J2), λ
+end
+
+# Closed-form solve of the GW2020 Eq. (22) Lyapunov equations for the off-diagonal blocks of P_k,
+# using the structure of J₀'s lower-right block; B_k is the block-diagonal part of K_k (Eq. 21).
+function _lyap_solve(K::SMatrix{6,6,ComplexF64}, λ::ComplexF64)
+ Bm = zeros(ComplexF64, 6, 6)
+ Pm = zeros(ComplexF64, 6, 6)
+
+ # B is block-diagonal in the (r1, r2) split.
+ Bm[1, 1] = K[1, 1]
+ Bm[1, 2] = K[1, 2]
+ Bm[2, 1] = K[2, 1]
+ Bm[2, 2] = K[2, 2]
+ for i in 3:6, j in 3:6
+ Bm[i, j] = K[i, j]
+ end
+
+ # P[r1, r2] = P[1:2, 3:6] (top-right off-diagonal block)
+ @inbounds begin
+ Pm[2, 3] = -K[2, 3] / λ
+ Pm[2, 4] = -K[2, 4] / λ
+ Pm[2, 5] = K[2, 5] / λ
+ Pm[2, 6] = K[2, 6] / λ
+ Pm[1, 3] = -(K[1, 3] + Pm[2, 3]) / λ
+ Pm[1, 4] = -(K[1, 4] + Pm[2, 4]) / λ
+ Pm[1, 5] = (K[1, 5] + Pm[2, 5]) / λ
+ Pm[1, 6] = (K[1, 6] + Pm[2, 6]) / λ
+ end
+
+ # P[r2, r1] = P[3:6, 1:2] (bottom-left off-diagonal block)
+ @inbounds begin
+ Pm[3, 1] = K[3, 1] / λ
+ Pm[4, 1] = K[4, 1] / λ
+ Pm[5, 1] = -K[5, 1] / λ
+ Pm[6, 1] = -K[6, 1] / λ
+ Pm[3, 2] = (K[3, 2] - Pm[3, 1]) / λ
+ Pm[4, 2] = (K[4, 2] - Pm[4, 1]) / λ
+ Pm[5, 2] = -(K[5, 2] - Pm[5, 1]) / λ
+ Pm[6, 2] = -(K[6, 2] - Pm[6, 1]) / λ
+ end
+
+ return SMatrix{6,6,ComplexF64}(Bm), SMatrix{6,6,ComplexF64}(Pm)
+end
+
+# Splitting recurrence (GW2020 Eqs. 14–19): P_k, B_k for k = 0..kmax+2, each order by `_lyap_solve` of K_k.
+function _split_recurrence(J::NTuple{3,SMatrix{6,6,ComplexF64}}, λ::ComplexF64, kmax::Int)
+ N = kmax + 3 # store k = 0..kmax+2
+ P = Vector{SMatrix{6,6,ComplexF64,36}}(undef, N)
+ B = Vector{SMatrix{6,6,ComplexF64,36}}(undef, N)
+
+ Z6 = zero(SMatrix{6,6,ComplexF64})
+ P[1] = SMatrix{6,6,ComplexF64}(I) # P_0 = I
+ B[1] = J[1] # B_0 = J_0
+
+ for k in 1:(kmax+2)
+ kk = k + 1 # 1-based slot for B/P at index k
+ # K_k starts as J_k (only k = 1, 2 contribute), else 0
+ Kacc = (k <= 2) ? J[k+1] : Z6
+ # +2*(k-1)*P_{k-1} (k > 1 only)
+ if k > 1
+ Kacc = Kacc + ComplexF64(2 * (k - 1)) * P[k]
+ end
+ # convolution: l = 1..k-1
+ for l in 1:(k-1)
+ kml = k - l
+ if kml <= 2
+ Kacc = Kacc + J[kml+1] * P[l+1]
+ end
+ Kacc = Kacc - P[l+1] * B[kml+1]
+ end
+ Bk, Pk = _lyap_solve(Kacc, λ)
+ B[kk] = Bk
+ P[kk] = Pk
+ end
+ return P, B
+end
+
+# Reduced 2×2 construction (GW2020 Eqs. 25–52): Q_k, C_k via K2_k, shearing D_k, lowest-order Y₀
+# with exponents r±, and the series Y_k = Y₀Z_k.
+function _coefs(B::Vector{SMatrix{6,6,ComplexF64,36}},
+ R::SVector{2,Float64}, kmax::Int)
+
+ N = kmax + 3
+ Z2 = zero(SMatrix{2,2,ComplexF64})
+ I2 = SMatrix{2,2,ComplexF64}(I)
+
+ K2 = Vector{SMatrix{2,2,ComplexF64,4}}(undef, N)
+ Qm = Vector{SMatrix{2,2,ComplexF64,4}}(undef, N)
+ Cm = Vector{SMatrix{2,2,ComplexF64,4}}(undef, N)
+
+ K2[1] = Z2
+ Qm[1] = I2
+ # B_0[r1, r1] = first-2x2 block of B_0
+ B0_11 = SMatrix{2,2,ComplexF64}(@view B[1][1:2, 1:2])
+ Cm[1] = B0_11
+
+ for k in 1:(kmax+2)
+ Bk_11 = SMatrix{2,2,ComplexF64}(@view B[k+1][1:2, 1:2])
+ K2acc = Bk_11 + ComplexF64(2 * (k - 1)) * Qm[k]
+ for l in 1:(k-1)
+ Bkml_11 = SMatrix{2,2,ComplexF64}(@view B[k-l+1][1:2, 1:2])
+ K2acc = K2acc + Bkml_11 * Qm[l+1] - Qm[l+1] * Cm[k-l+1]
+ end
+ K2[k+1] = K2acc
+
+ Qm[k+1] = @SMatrix ComplexF64[
+ 0 0
+ -K2acc[1, 1] -K2acc[1, 2]
+ ]
+ Cm[k+1] = @SMatrix ComplexF64[
+ 0 0
+ K2acc[2, 1] K2acc[1, 1]+K2acc[2, 2]
+ ]
+ end
+
+ # Build D_k for k = 0..kmax — GW2020 Eq. (43); c_2^21 = −(E+F+H+2) is Eq. (39).
+ D = Vector{SMatrix{2,2,ComplexF64,4}}(undef, kmax + 1)
+ D[1] = @SMatrix ComplexF64[
+ 0 1
+ Cm[3][2, 1] 3
+ ]
+ for k in 1:kmax
+ D[k+1] = @SMatrix ComplexF64[
+ 0 0
+ Cm[k+3][2, 1] Cm[k+2][2, 2]
+ ]
+ end
+
+ # Lowest-order Y solution and inverse — GW2020 Eq. (48), with exponents r± from Eq. (49).
+ r1 = ComplexF64(R[1])
+ r2 = ComplexF64(R[2])
+ Y0 = @SMatrix ComplexF64[
+ 1 1
+ r1 r2
+ ]
+ Y0inv = (1 / (r1 - r2)) * @SMatrix ComplexF64[
+ -r2 1
+ r1 -1
+ ]
+
+ # Z_k and Y_k = Y₀Z_k from the GW2020 Eqs. (50)–(52) recurrence, with E_l = Y₀⁻¹D_lY₀ (Eq. 51).
+ Y = Vector{SMatrix{2,2,ComplexF64,4}}(undef, kmax + 1)
+ Z = Vector{SMatrix{2,2,ComplexF64,4}}(undef, kmax + 1)
+ Z[1] = I2
+ Y[1] = Y0
+ for k in 1:kmax
+ Zacc = Z2
+ for l in 1:k
+ El = Y0inv * D[l+1] * Y0
+ Zacc = Zacc + El * Z[k-l+1]
+ end
+ Zk = MMatrix{2,2,ComplexF64}(Zacc)
+ for i in 1:2, j in 1:2
+ Zk[i, j] = Zk[i, j] / (R[j] - R[i] - 2 * k)
+ end
+ Z[k+1] = SMatrix{2,2,ComplexF64}(Zk)
+ Y[k+1] = Y0 * Z[k+1]
+ end
+
+ return Qm, Y
+end
+
+"""
+ build_asymptotics(params::GGJParameters, Q::ComplexF64; kmax::Int=8) -> InnerAsymptoticsCache
+
+Construct the `inps` Wasow asymptotic basis (GW2020 Eqs. 7–53), truncating
+each power series at order `kmax`. Evaluate with [`evaluate_asymptotics`](@ref);
+pick a matching radius with [`pick_smax`](@ref).
+"""
+function build_asymptotics(params::GGJParameters, Q::ComplexF64; kmax::Int=8)
+ p1v = p1(params)
+ # Mercier Frobenius exponents r± = 3/2 ± √(−D_I) — GW2020 Eq. (49).
+ R = SVector{2,Float64}(p1v + 1.5, -p1v + 1.5)
+
+ T, J, λ = _build_tjmat(params, Q)
+ P, B = _split_recurrence(J, λ, kmax)
+ Qm, Y = _coefs(B, R, kmax)
+ return InnerAsymptoticsCache(params, Q, kmax, R, T, J, P, Qm, Y)
+end
+
+build_asymptotics(params::GGJParameters, Q::Number; kmax::Int=8) =
+ build_asymptotics(params, ComplexF64(Q); kmax=kmax)
+
+# Horner sum y[i] = (Σ_{k=0..n} c[i,k+1] zᵏ)·z^rvec[i] and its z-derivative, z = 1/x² (GW2020 Eq. 14 form);
+# rvec = −R/2 gives the x^R Mercier prefactor. c is n_components × (n+1); complex z uses the principal branch.
+function _horner(x::Number, c::AbstractMatrix{ComplexF64};
+ rvec::Union{Nothing,AbstractVector{<:Real}}=nothing,
+ derivative::Bool=false)
+ nrows, ncols = size(c)
+ n = ncols - 1 # highest power
+
+ y = ComplexF64.(c[:, ncols])
+ @inbounds for k in (n-1):-1:0
+ for i in 1:nrows
+ y[i] = y[i] * x + c[i, k+1]
+ end
+ end
+
+ if rvec !== nothing
+ xrvec = [x^rvec[i] for i in 1:nrows]
+ @inbounds for i in 1:nrows
+ y[i] *= xrvec[i]
+ end
+ end
+
+ if !derivative
+ return y, nothing
+ end
+
+ dy = similar(y)
+ if rvec !== nothing
+ @inbounds for i in 1:nrows
+ dy[i] = c[i, ncols] * (rvec[i] + n)
+ end
+ @inbounds for k in (n-1):-1:0
+ for i in 1:nrows
+ dy[i] = dy[i] * x + c[i, k+1] * (rvec[i] + k)
+ end
+ end
+ @inbounds for i in 1:nrows
+ xrv_i = x^rvec[i]
+ dy[i] = dy[i] * xrv_i / x
+ end
+ else
+ @inbounds for i in 1:nrows
+ dy[i] = c[i, ncols] * n
+ end
+ @inbounds for k in (n-1):-1:0
+ for i in 1:nrows
+ dy[i] = dy[i] * x + c[i, k+1] * k
+ end
+ end
+ @inbounds for i in 1:nrows
+ dy[i] = dy[i] / x
+ end
+ end
+ return y, dy
+end
+
+# Pack Y, and Qmat with P[3:6, 1:2], column-major into `_horner`'s n_components × (kmax+1) layout.
+function _pack_y_coefs(cache::InnerAsymptoticsCache)
+ kmax = cache.kmax
+ cc = Matrix{ComplexF64}(undef, 4, kmax + 1)
+ @inbounds for k in 0:kmax
+ Yk = cache.Y[k+1]
+ # Column-major reshape of (2,2) → 4 entries:
+ # (Y[1,1], Y[2,1], Y[1,2], Y[2,2])
+ cc[1, k+1] = Yk[1, 1]
+ cc[2, k+1] = Yk[2, 1]
+ cc[3, k+1] = Yk[1, 2]
+ cc[4, k+1] = Yk[2, 2]
+ end
+ return cc
+end
+
+function _pack_qp_coefs(cache::InnerAsymptoticsCache)
+ kmax = cache.kmax
+ dd = Matrix{ComplexF64}(undef, 12, kmax + 1)
+ @inbounds for k in 0:kmax
+ Qk = cache.Qmat[k+1]
+ Pk = cache.P[k+1]
+ # dd[1:4] from Q (column-major reshape of 2×2)
+ dd[1, k+1] = Qk[1, 1]
+ dd[2, k+1] = Qk[2, 1]
+ dd[3, k+1] = Qk[1, 2]
+ dd[4, k+1] = Qk[2, 2]
+ # dd[5:12] from P[r2, r1] = P[3:6, 1:2] (4×2 → column-major 8 entries)
+ dd[5, k+1] = Pk[3, 1]
+ dd[6, k+1] = Pk[4, 1]
+ dd[7, k+1] = Pk[5, 1]
+ dd[8, k+1] = Pk[6, 1]
+ dd[9, k+1] = Pk[3, 2]
+ dd[10, k+1] = Pk[4, 2]
+ dd[11, k+1] = Pk[5, 2]
+ dd[12, k+1] = Pk[6, 2]
+ end
+ return dd
+end
+
+# Evaluator: U = TPQSY of GW2020 Eq. (53).
+
+"""
+ evaluate_asymptotics(cache::InnerAsymptoticsCache, x::Number; derivative=true, apply_T=true) -> (U, dU)
+
+Evaluate the inps asymptotic basis at `x`, real (`x > 0`) or complex on a
+rotated contour (principal branch of `x^r`; the series is in 1/x², so valid for |arg x| < π/2).
+Returns the 6×2 complex matrix `U` whose two columns are the power-like (Mercier) solutions of
+the GGJ system (column 1 large, column 2 small), and (if `derivative=true`) the
+6×2 matrix `dU` of their derivatives `dU/dx`.
+
+If `apply_T=false`, the result is left in the J-rotated basis (used by `asymptotic_residual`).
+The default `apply_T=true` returns it in the GW2020 Eq. (2) state basis, which
+[`physical_ua_dua`](@ref) converts to (Ψ, Ξ, Υ).
+"""
+function evaluate_asymptotics(cache::InnerAsymptoticsCache, x::Number;
+ derivative::Bool=true, apply_T::Bool=true)
+ xfac = 1.0 / (x * x)
+ R = cache.R
+ rvec = SVector(-R[1] / 2, -R[1] / 2, -R[2] / 2, -R[2] / 2)
+
+ cc = _pack_y_coefs(cache)
+ dd = _pack_qp_coefs(cache)
+
+ yy, dyy = _horner(xfac, cc; rvec=rvec, derivative=derivative)
+ zz, dzz = _horner(xfac, dd; derivative=derivative)
+
+ # Reshape yy → y (2×2), zz → q (2×2) and p21 (4×2)
+ y = SMatrix{2,2,ComplexF64}(yy[1], yy[2], yy[3], yy[4])
+ q = SMatrix{2,2,ComplexF64}(zz[1], zz[2], zz[3], zz[4])
+ p21 = SMatrix{4,2,ComplexF64}(zz[5], zz[6], zz[7], zz[8],
+ zz[9], zz[10], zz[11], zz[12])
+
+ # Splitting matrix pp (6×2): top 2×2 = I, bottom 4×2 = p21.
+ pp_m = zeros(ComplexF64, 6, 2)
+ pp_m[1, 1] = 1
+ pp_m[2, 2] = 1
+ @inbounds for i in 1:4, j in 1:2
+ pp_m[i+2, j] = p21[i, j]
+ end
+ pp = SMatrix{6,2,ComplexF64}(pp_m)
+
+ # Shearing matrix S = diag(1, 1/x²) — GW2020 Eq. (41); here 1/x² = xfac.
+ smat = @SMatrix ComplexF64[1 0; 0 xfac]
+
+ # U = T·P·Q·S·Y, the asymptotic solution of GW2020 Eq. (53) (T applied below).
+ qsy = q * smat * y
+ U = pp * qsy
+
+ if derivative
+ # Horner derivatives are with respect to xfac = 1/x²; d(xfac)/dx = −2·xfac/x.
+ chain = -2 * xfac / x
+ dy_v = chain .* dyy
+ dz_v = chain .* dzz
+
+ dy = SMatrix{2,2,ComplexF64}(dy_v[1], dy_v[2], dy_v[3], dy_v[4])
+ dq = SMatrix{2,2,ComplexF64}(dz_v[1], dz_v[2], dz_v[3], dz_v[4])
+ dp21 = SMatrix{4,2,ComplexF64}(dz_v[5], dz_v[6], dz_v[7], dz_v[8],
+ dz_v[9], dz_v[10], dz_v[11], dz_v[12])
+
+ dpp_m = zeros(ComplexF64, 6, 2)
+ @inbounds for i in 1:4, j in 1:2
+ dpp_m[i+2, j] = dp21[i, j]
+ end
+ dpp = SMatrix{6,2,ComplexF64}(dpp_m)
+
+ dsmat = @SMatrix ComplexF64[0 0; 0 (-2*xfac/x)]
+ dqsy = q * smat * dy + q * dsmat * y + dq * smat * y
+ dU = pp * dqsy + dpp * qsy
+
+ if apply_T
+ U = cache.T * U
+ dU = cache.T * dU
+ end
+ return U, dU
+ else
+ if apply_T
+ U = cache.T * U
+ end
+ return U, nothing
+ end
+end
+
+"""
+ physical_ua_dua(cache, x::Number) -> (ua, dua)
+
+Convert the inps 6×2 basis at real or complex `x` to physical `(Ψ, Ξ, Υ)`
+values and x-derivatives, each 3×2 (column 1 = large power solution, 2 = small).
+The inps columns are in the GW2020 Eq. (2) state `u = (xΨ, Ξ, Υ, (xΨ)'/x, Ξ'/x, Υ'/x)`,
+hence the /x and ·x factors; same map as the deltac `inpso_get_ua/dua` convention.
+"""
+function physical_ua_dua(cache::InnerAsymptoticsCache, x::Number)
+ U, dU = evaluate_asymptotics(cache, x; derivative=true, apply_T=true)
+ ua = zeros(ComplexF64, 3, 2)
+ dua = zeros(ComplexF64, 3, 2)
+ @inbounds for j in 1:2
+ ua[1, j] = U[1, j] / x
+ ua[2, j] = U[2, j]
+ ua[3, j] = U[3, j]
+ dua[1, j] = U[4, j] - U[1, j] / (x * x)
+ dua[2, j] = U[5, j] * x
+ dua[3, j] = U[6, j] * x
+ end
+ return ua, dua
+end
+
+"""
+ asymptotic_residual(cache::InnerAsymptoticsCache, x::Number) -> SVector{2,Float64}
+
+Convergence measure of the asymptotic basis at real or complex `x` for each of the two algebraic
+columns, the analogue of GW2020 Eq. 54 in the J-rotated basis. Returns
+`‖dU − x·matrix·U‖∞ / max(‖dU‖∞, ‖x·matrix·U‖∞)` per column, where
+`matrix = J₀ + xfac·J₁ + xfac²·J₂` is the J-rotated coefficient matrix (the
+residual of `v' = xJv`, GW2020 Eq. 6).
+"""
+function asymptotic_residual(cache::InnerAsymptoticsCache, x::Number)
+ U, dU = evaluate_asymptotics(cache, x; derivative=true, apply_T=false)
+
+ xfac = 1.0 / (x * x)
+ M = cache.J[1]
+ if cache.kmax > 0
+ M = M + xfac * cache.J[2]
+ end
+ if cache.kmax > 1
+ M = M + xfac * xfac * cache.J[3]
+ end
+
+ matvec1 = dU
+ matvec2 = -x * (M * U)
+ matvec0 = matvec1 + matvec2
+
+ delta = MVector{2,Float64}(0.0, 0.0)
+ @inbounds for j in 1:2
+ n0 = 0.0
+ n1 = 0.0
+ n2 = 0.0
+ for i in 1:6
+ n0 = max(n0, abs(matvec0[i, j]))
+ n1 = max(n1, abs(matvec1[i, j]))
+ n2 = max(n2, abs(matvec2[i, j]))
+ end
+ denom = max(n1, n2)
+ delta[j] = denom == 0 ? 0.0 : n0 / denom
+ end
+ return SVector{2,Float64}(delta)
+end
+
+"""
+ pick_smax(params, Q; θ=angle(Q)/4, eps=1e-9, kmax=12, cache=nothing,
+ slogmin=-1.0, slogmax=6.5, dslog=0.01) -> (S, cache, achieved)
+
+Sweep `s` log-uniformly upward and return the smallest `s` at which the series residual
+(GW2020 Eq. 54) along `x = e^{iθ}s` drops below `eps`. If never reached, returns the
+residual-minimizing `s` with `achieved = false`.
+"""
+function pick_smax(params::GGJParameters, Q::ComplexF64;
+ θ::Float64=angle(Q) / 4, eps::Float64=1e-9, kmax::Int=12,
+ cache::Union{Nothing,InnerAsymptoticsCache}=nothing,
+ slogmin::Float64=-1.0, slogmax::Float64=6.5, dslog::Float64=0.01)
+ c = cache === nothing ? build_asymptotics(params, Q; kmax=kmax) : cache
+ ph = cis(θ)
+ best_s = 10.0^slogmin
+ best_r = Inf
+ slog = slogmin
+ while slog <= slogmax
+ s = 10.0^slog
+ r = maximum(asymptotic_residual(c, ph * s))
+ if r < eps
+ return s, c, true
+ end
+ if r < best_r
+ best_r = r
+ best_s = s
+ end
+ slog += dslog
+ end
+ return best_s, c, false
+end
+
+pick_smax(params::GGJParameters, Q::Number; kwargs...) =
+ pick_smax(params, ComplexF64(Q); kwargs...)
diff --git a/src/InnerLayer/GGJ/Ray.jl b/src/InnerLayer/GGJ/Ray.jl
new file mode 100644
index 0000000000..32136da918
--- /dev/null
+++ b/src/InnerLayer/GGJ/Ray.jl
@@ -0,0 +1,511 @@
+# Ray.jl
+#
+# Rotated-contour backend (`GGJModel{:ray}`): the GGJ equations continued onto x = e^{iθ}s,
+# θ = arg(Q)/4. Far-field series data at the radius S are marched inward to s_m modulo the
+# decaying exponential pair, then the Galerkin.jl Hermite assembly solves [0, s_m] with
+# v(s_m) = Us + Δ·Ub + c₁E₁ + c₂E₂. Method and rationale: docs/src/inner_layer.md.
+
+"""
+ ode_matrix([CT,] p::GGJParameters, Q, x) -> SMatrix{6,6,CT}
+
+Coefficient matrix `M(x)` of GWP2016 Eq. 11 as `dv/dx = M v`, `v = (Ψ, Ξ, Υ, Ψ', Ξ', Υ')`, for
+real or complex `x`. `M` is polynomial in `x`, so x = 0 is an ordinary point and the system
+continues analytically to complex `x`. `CT` selects the element type (default `ComplexF64`;
+`Complex{Double64}` for the extended-precision march).
+"""
+ode_matrix(p::GGJParameters, Q::ComplexF64, x::Number) =
+ ode_matrix(ComplexF64, p, Q, x)
+
+function ode_matrix(::Type{CT}, p::GGJParameters, Q::Number, x::Number) where {CT<:Complex}
+ Ũ, Ṽ = ggj_rows(CT, p, Q, CT(x))
+ m = zeros(MMatrix{6,6,CT})
+ # rows 1–3: (Ψ, Ξ, Υ)' = (Ψ', Ξ', Υ'); rows 4–6: GWP2016 Eq. 11
+ m[1, 4] = 1
+ m[2, 5] = 1
+ m[3, 6] = 1
+ m[4:6, 1:3] = Ũ
+ m[4:6, 4:6] = Ṽ
+ return SMatrix{6,6,CT}(m)
+end
+
+"""
+ ray_breaks(params, Q, θ, S; cfl=0.2, min_cells=1024) -> Vector{Float64}
+
+Cell boundaries `0 = s₀ < s₁ < … = S` for the Hermite BVP: each cell resolves the full
+local WKB rate μ + ρs (fast Ohm and Υ-family pair μ = |√Q| + √(|Q|·|G+KF|), parabolic pair
+ρ = Re(e^{2iθ}/√Q)) whether or not the mode is present, since unresolved dormant modes
+alias into spurious discrete ones. `min_cells` floors the resolution where the local rates
+are small (|Q| ≪ 1).
+"""
+function ray_breaks(params::GGJParameters, Q::ComplexF64, θ::Float64, S::Float64;
+ cfl::Float64=0.2, min_cells::Int=1024)
+ sq = sqrt(Q)
+ ρ = real(cis(2θ) / sq)
+ ρ > 0 || throw(ArgumentError("contour angle θ=$θ gives non-decaying parabolic pair (ρ=$ρ ≤ 0); use θ ≈ arg(Q)/4"))
+ μ = abs(sq) + sqrt(abs(Q) * abs(params.G + params.K * params.F))
+ hmax = S / min_cells
+ breaks = [0.0]
+ while breaks[end] < S
+ h = min(cfl / (μ + ρ * breaks[end]), hmax)
+ snew = breaks[end] + h
+ push!(breaks, snew >= S - 0.25 * h ? S : snew)
+ end
+ return breaks
+end
+
+# Far-field boundary data. The admissible solutions at large s are the power pair (u_small, u_big)
+# from the inps series and the forward-decaying exponential pair E. The series is trusted only at
+# S, which can lie far beyond s_m, so the power pair is marched S → s_m by 2-stage Radau IIA,
+# R(z) = 2(3+z)/(z² − 4z + 6). Unresolved steps (z > 8, clear of |R| > 1 on 0 < z < 6) damp the
+# exponential directions, which is harmless because Δ is defined modulo E.
+
+# Small and large power-like solutions at x as 6-component states (Ψ, Ξ, Υ, Ψ', Ξ', Υ').
+function _power_states(cache::InnerAsymptoticsCache, x::Number)
+ ua, dua = physical_ua_dua(cache, x)
+ return vcat(ua[:, 2], dua[:, 2]), vcat(ua[:, 1], dua[:, 1])
+end
+
+# Condition number of the column-normalized boundary basis [Us, Ub, E].
+_basis_cond(Us, Ub, E) = cond(hcat(Us ./ norm(Us), Ub ./ norm(Ub), E))
+
+"""
+ decaying_pair(params, Q, θ, S; growth=30.0, seed=20260707, dp_res=20.0) -> E (6×2)
+
+Orthonormal basis of the forward-decaying pair at s = S on the ray: random
+seeds integrated backward over [S, S+ΔS] with fully-resolved RK4, ΔS sized so
+the pair separates from everything else by ≈ `growth` e-folds.
+"""
+function decaying_pair(params::GGJParameters, Q::ComplexF64, θ::Float64, S::Float64;
+ growth::Float64=30.0, seed::Int=20260707, dp_res::Float64=20.0)
+ sq = sqrt(Q)
+ ρ = real(cis(2θ) / sq)
+ ρ > 0 || throw(ArgumentError("θ=$θ gives ρ=$ρ ≤ 0; decaying pair undefined"))
+ ph = cis(θ)
+ # Window ΔS: the slowest backward grower separates from the power pair by `growth` e-folds.
+ g2 = Inf
+ gmax_loc = 0.0
+ for λ in eigvals(Matrix(ph * ode_matrix(params, Q, ph * S)))
+ g = -real(λ)
+ g > 20.0 / S && (g2 = min(g2, g))
+ gmax_loc = max(gmax_loc, abs(real(λ)))
+ end
+ gsep = isfinite(g2) ? max(g2 - 20.0 / S, 0.05 * g2) : ρ * S
+ ΔS = min(growth / gsep, 3.0 * S)
+
+ # Resolve the true local spectrum; ρs + |√Q| under-counts the Υ-family rate √|Q(G+KF)|.
+ for λ in eigvals(Matrix(ph * ode_matrix(params, Q, ph * (S + ΔS))))
+ gmax_loc = max(gmax_loc, abs(real(λ)))
+ end
+ rate = max(ρ * (S + ΔS) + abs(sq), gmax_loc)
+ nsteps = clamp(ceil(Int, dp_res * rate * ΔS), 200, 2_000_000)
+ h = -ΔS / nsteps
+
+ rng = MersenneTwister(seed)
+ v = randn(rng, ComplexF64, 6, 2)
+ v = Matrix(qr(v).Q)
+
+ f(s, y) = (ph * ode_matrix(params, Q, ph * s)) * y
+
+ s = S + ΔS
+ for istep in 1:nsteps
+ k1 = f(s, v)
+ k2 = f(s + h / 2, v + (h / 2) * k1)
+ k3 = f(s + h / 2, v + (h / 2) * k2)
+ k4 = f(s + h, v + h * k3)
+ v = v + (h / 6) * (k1 + 2k2 + 2k3 + k4)
+ s += h
+ if istep % 50 == 0
+ v = Matrix(qr(v).Q)
+ end
+ end
+ return Matrix(qr(v).Q)
+end
+
+"""
+ march_boundary(params, Q, θ, S, s_m, Us, Ub; rtol=1e-9, ztrk=0.3, purge_budget=2.5,
+ growth=30.0, seed=20260707, dp_res=20.0)
+ -> (Us_m, Ub_m, F)
+
+Transport the power-pair boundary data from the series radius `S` inward to
+`s_m` along the ray, modulo the decaying exponential pair (the quotient in
+which Δ is defined): 2-stage Radau IIA with purges against a carried decaying frame.
+`rtol` sets the step factor c = (rtol/100)^{1/3}; `ztrk` caps resolved-band steps at ztrk/g_max;
+`purge_budget` is the e-folds between purges; `growth`, `seed`, `dp_res` go to [`decaying_pair`](@ref).
+"""
+function march_boundary(params::GGJParameters, Q::ComplexF64, θ::Float64,
+ S::Float64, s_m::Float64, Us::Vector{ComplexF64}, Ub::Vector{ComplexF64};
+ rtol::Float64=1e-9, growth::Float64=30.0, seed::Int=20260707,
+ ztrk::Float64=0.3, purge_budget::Float64=2.5, dp_res::Float64=20.0)
+ ph = cis(θ)
+ 𝔐(s) = ph * ode_matrix(params, Q, ph * s)
+
+ W = hcat(copy(Us), copy(Ub))
+ function purge!(W, s)
+ Floc = decaying_pair(params, Q, θ, s; growth=growth, seed=seed, dp_res=dp_res)
+ W .-= Floc * (Floc' * W)
+ return Floc
+ end
+
+ # One Radau IIA step in the precision of W (`Mfun` returns the matrix in that precision):
+ # A = [5/12 -1/12; 3/4 1/4], c = (1/3, 1), b = A[2,:].
+ function radau_step(Mfun, s, W, h)
+ CT = eltype(W)
+ hc = real(CT)(h)
+ Id = Matrix{CT}(I, 6, 6)
+ M1 = Mfun(s + h / 3)
+ M2 = Mfun(s + h)
+ Ablk = [Id-(5hc/12)*M1 (hc/12)*M1; -(3hc / 4)*M2 Id-(hc/4)*M2]
+ K = Ablk \ [M1 * W; M2 * W]
+ return W + hc * ((CT(3) / 4) * @view(K[1:6, :]) + (CT(1) / 4) * @view(K[7:12, :]))
+ end
+
+ # Damped-zone steps have cond ~ z ≫ 1; their structured LU backward error mixes u_small into u_big
+ # by ~eps·ρS²/2·‖u_big‖/‖u_small‖, so that zone runs in Double64.
+ CTd = Complex{Double64}
+ phd = CTd(cos(Double64(θ)), sin(Double64(θ)))
+ 𝔐d(s) = phd * Matrix(ode_matrix(CTd, params, Q, phd * Double64(s)))
+
+ # Step law, from the local growth rates g of 𝔐(s):
+ # damped zone (every grower has g·c·s > 8): h = −c·s with c = (rtol/100)^{1/3}, so the step
+ # count grows only like ln(S/s_m);
+ # resolved band: h = −min(c·s, ztrk/g_max), with the decaying frame F carried by the same
+ # steps and purged from W every `purge_budget` e-folds.
+ # On the real axis with imaginary Q the band entry lands on the turning point x² = −Q²(G+KF),
+ # where F cannot be identified; the default θ keeps it off the contour.
+ c = clamp(cbrt(rtol / 100.0), 2e-5, 2e-3)
+
+ # Damped zone, in Double64 from the first purge at S to the resolved-band entry.
+ Wd = CTd.(W)
+ let Floc = decaying_pair(params, Q, θ, S; growth=growth, seed=seed, dp_res=dp_res)
+ Fd = CTd.(Floc)
+ Wd .-= Fd * (Fd' * Wd)
+ end
+ s = S
+ nstep = 0
+ while s > s_m + 1e-12 * S
+ λs = eigvals(Matrix(𝔐(s)))
+ gmin = Inf
+ for λ in λs
+ g = -real(λ)
+ g > 10.0 / s && (gmin = min(gmin, g))
+ end
+ (isfinite(gmin) && gmin * c * s < 8.0) && break # resolved-band entry
+ h = -min(c * s, s - s_m)
+ Wd = radau_step(𝔐d, s, Wd, h)
+ s += h
+ nstep += 1
+ nstep > 5_000_000 && error("march_boundary: step limit exceeded (s=$s)")
+ end
+ W = ComplexF64.(Wd)
+
+ # Resolved band, in Float64 with the carried frame.
+ Φ = 0.0
+ F = Matrix{ComplexF64}(undef, 6, 2)
+ have_F = false
+ while s > s_m + 1e-12 * S
+ # Backward-growing rates (Re λ < 0); rates ≲ 10/s belong to the algebraic power pair.
+ λs = eigvals(Matrix(𝔐(s)))
+ gmin, gmax = Inf, 0.0
+ for λ in λs
+ g = -real(λ)
+ if g > 10.0 / s
+ gmin = min(gmin, g)
+ gmax = max(gmax, g)
+ end
+ end
+ resolved = isfinite(gmin) && gmin * c * s < 8.0
+ h = resolved ? -min(c * s, ztrk / gmax, s - s_m) : -min(c * s, s - s_m)
+ if resolved && !have_F
+ F = decaying_pair(params, Q, θ, s; growth=growth, seed=seed, dp_res=dp_res)
+ W .-= F * (F' * W)
+ have_F = true
+ Φ = 0.0
+ end
+ W = radau_step(𝔐, s, W, h)
+ if have_F
+ F = radau_step(𝔐, s, F, h)
+ F = Matrix(qr(F).Q)
+ Φ += gmax * abs(h)
+ if Φ > purge_budget
+ W .-= F * (F' * W)
+ Φ = 0.0
+ end
+ end
+ s += h
+ nstep += 1
+ nstep > 5_000_000 && error("march_boundary: step limit exceeded (s=$s)")
+ end
+ # E must span the solutions that decay at infinity, which differ from the locally decaying pair at
+ # s_m once the mode families morph (s ~ |Q|); the carried F is that subspace. Local extraction is
+ # the fallback when the march never entered the resolved band.
+ if have_F
+ W .-= F * (F' * W)
+ else
+ F = purge!(W, s_m)
+ end
+ return W[:, 1], W[:, 2], F
+end
+
+"""
+ boundary_basis(params, Q, cache, θ, S; growth=30.0, seed=20260707, dp_res=20.0)
+ -> (Us, Ub, E, cond_est)
+
+Boundary data at s = S taken directly from the inps series, used when the BVP edge is S itself
+(s_m ≳ S): `Us`, `Ub` are the small/large power-like solutions as 6-component states in the inps
+normalization, `E` the numerically generated decaying pair, `cond_est` the condition number of the
+column-normalized basis.
+"""
+function boundary_basis(params::GGJParameters, Q::ComplexF64,
+ cache::InnerAsymptoticsCache, θ::Float64, S::Float64;
+ growth::Float64=30.0, seed::Int=20260707, dp_res::Float64=20.0)
+ Us, Ub = _power_states(cache, cis(θ) * S)
+ E = decaying_pair(params, Q, θ, S; growth=growth, seed=seed, dp_res=dp_res)
+ return Us, Ub, E, _basis_cond(Us, Ub, E)
+end
+
+# Driver: series radius S, BVP edge s_m, march S → s_m, Hermite BVP on [0, s_m].
+
+"""
+ RaySolveResult
+
+Output of [`solve_ray`](@ref).
+
+## Fields
+
+ - `Δ`: rescaled matching data (Δ₊, Δ₋) = (interchange, tearing), the even (isol = 1) and
+ odd (isol = 2) parities of the displacement Ξ.
+ - `Δraw`: the same pair in raw inps normalization, before `rescale_delta`.
+ - `cexp`: decaying-pair coefficients (c₁, c₂) at s_m, one column per parity.
+ - `Q`, `θ`: scaled eigenvalue and contour angle.
+ - `S`: series radius where the far-field data were taken.
+ - `series_ok`: whether `pick_smax` reached its residual tolerance.
+ - `bc_cond`: condition number of the column-normalized boundary basis [Us, Ub, E].
+ - `breaks`: Hermite cell boundaries on [0, s_m].
+ - `cfl`, `min_cells`: mesh resolution parameters used by [`ray_breaks`](@ref).
+ - `ws`: the full Galerkin workspace of the BVP (system buffers included); the nodal solution is `ws.sol`, both parities.
+"""
+struct RaySolveResult
+ Δ::SVector{2,ComplexF64}
+ Δraw::SVector{2,ComplexF64}
+ cexp::SMatrix{2,2,ComplexF64,4}
+ Q::ComplexF64
+ θ::Float64
+ S::Float64
+ series_ok::Bool
+ bc_cond::Float64
+ breaks::Vector{Float64}
+ cfl::Float64
+ min_cells::Int
+ ws::GalerkinWorkspace
+end
+
+"""
+ solve_ray(params::GGJParameters, Q; θ=angle(Q)/4, kmax=12, S=nothing, smax_tol=1e-9,
+ cfl=0.2, min_cells=1024, warn_cells=6000, nq=6, verbose=false, …) -> RaySolveResult
+
+Solve the GGJ inner-layer problem on the rotated ray x = e^{iθ}s. `Δ` is the rescaled pair
+(Δ₊, Δ₋) = (interchange, tearing), directly comparable to the `:galerkin` backend; θ = 0 is a
+real-axis solve.
+
+`S` defaults to the smallest radius where the series residual is below `smax_tol` at order `kmax`
+([`pick_smax`](@ref); warns and uses the best point otherwise). The BVP edge s_m is where every
+exponential family has decayed 45 e-folds from the origin, scaled by `sm_fac`. `cfl`, `min_cells` set
+the Hermite grid ([`ray_breaks`](@ref)) and `nq` its quadrature. The grid is not residual-refined and
+no error estimate is returned (at small |Q| Δ is good to about 1e-8–2e-7 relative); use
+[`delta_convergence`](@ref) for an error bar. More than `warn_cells` cells warns once (cost guard).
+`march_rtol` is [`march_boundary`](@ref)'s `rtol`; `growth`, `seed`, `ztrk`, `purge_budget`, `dp_res`
+go to `march_boundary`/[`decaying_pair`](@ref); `handoff` (diagnostic) supplies (Us, Ub) at S.
+"""
+function solve_ray(params::GGJParameters, Q::ComplexF64;
+ θ::Float64=angle(Q) / 4, kmax::Int=12,
+ S::Union{Nothing,Float64}=nothing, smax_tol::Float64=1e-9,
+ growth::Float64=30.0, march_rtol::Float64=1e-9, sm_fac::Float64=1.0,
+ cfl::Float64=0.2, min_cells::Int=1024, warn_cells::Int=6000, nq::Int=6, seed::Int=20260707,
+ ztrk::Float64=0.3, purge_budget::Float64=2.5, dp_res::Float64=20.0,
+ handoff::Union{Nothing,NTuple{2,Vector{ComplexF64}}}=nothing,
+ verbose::Bool=false)
+
+ cache = build_asymptotics(params, Q; kmax=kmax)
+ series_ok = true
+ if S === nothing
+ Sv, cache, series_ok = pick_smax(params, Q; θ=θ, eps=smax_tol, kmax=kmax, cache=cache)
+ series_ok || @warn "pick_smax: series residual target $smax_tol not reached; using best point S=$Sv"
+ else
+ Sv = S
+ end
+
+ # s_m: where every exponential family has decayed 45 e-folds from the origin, from the local spectrum.
+ # When s_m ≳ S (small |Q|) the series data are applied at S directly.
+ s_m = let acc = 0.0, sprev = 0.0, out = Sv
+ for sk in exp10.(range(-2, log10(Sv); length=400))
+ gdec = Inf
+ for λ in eigvals(Matrix(cis(θ) * ode_matrix(params, Q, cis(θ) * sk)))
+ g = -real(λ) # backward-growth = forward-decay rate
+ g > 10.0 / sk && (gdec = min(gdec, g))
+ end
+ isfinite(gdec) && (acc += gdec * (sk - sprev))
+ sprev = sk
+ if acc >= 45.0
+ out = sk
+ break
+ end
+ end
+ sm_fac * max(out, 2.0)
+ end
+
+ local Us, Ub, E, bc_cond, Sbvp
+ if s_m < 0.98 * Sv
+ UsS, UbS = handoff === nothing ? _power_states(cache, cis(θ) * Sv) : handoff
+ Us, Ub, E = march_boundary(params, Q, θ, Sv, s_m, UsS, UbS;
+ rtol=march_rtol, growth=growth, seed=seed,
+ ztrk=ztrk, purge_budget=purge_budget, dp_res=dp_res)
+ Sbvp = s_m
+ bc_cond = _basis_cond(Us, Ub, E)
+ verbose && @printf(" march: S=%.4g → s_m=%.4g, bc_cond=%.1e\n", Sv, s_m, bc_cond)
+ else
+ Us, Ub, E, bc_cond = boundary_basis(params, Q, cache, θ, Sv;
+ growth=growth, seed=seed, dp_res=dp_res)
+ Sbvp = Sv
+ end
+ bc_cond < 1e12 || @warn "boundary basis poorly conditioned (cond ≈ $bc_cond)"
+
+ breaks = ray_breaks(params, Q, θ, Sbvp; cfl=cfl, min_cells=min_cells)
+ length(breaks) - 1 > warn_cells &&
+ @warn "GGJ ray: $(length(breaks) - 1) Hermite cells exceed warn_cells = $warn_cells, so the solve is slow; the grid follows cfl = $cfl, min_cells = $min_cells and the local rates at this Q" Q maxlog =
+ 1 _id = (:ggj_ray_cells, warn_cells)
+ ws = _galerkin_workspace(breaks, fill(CT_NONE, length(breaks) - 1))
+ Δraw, cexp = _assemble_and_solve_point!(ws, params, Q, θ, Us, Ub, E; nq=nq)
+ verbose && @printf(" BVP: %d Hermite cells on [0, %.4g], Δraw[1] = %.6e %+.6eim\n",
+ length(breaks) - 1, Sbvp, real(Δraw[1]), imag(Δraw[1]))
+
+ Δ = rescale_delta(Δraw, params)
+
+ return RaySolveResult(Δ, Δraw, cexp, Q, θ, Sv, series_ok, bc_cond, breaks, cfl, min_cells, ws)
+end
+
+solve_ray(params::GGJParameters, Q::Number; kwargs...) =
+ solve_ray(params, ComplexF64(Q); kwargs...)
+
+"""
+ solve_inner(::GGJModel{:ray}, params::GGJParameters, γ::Number; kwargs...)
+ -> InnerLayerResponse
+
+Rotated-ray backend: converts γ via `inner_Q`, forwards keywords to
+[`solve_ray`](@ref), and returns the parity-projected matching data (Δ₊, Δ₋) as the
+`interchange` and `tearing` fields of [`InnerLayerResponse`](@ref).
+Preferred for |Q| ≳ 1 and near the imaginary axis; use `solve_ray` directly
+when the full [`RaySolveResult`](@ref) is wanted. `real_profiles`, `npc` and `certify_rtol` are
+profile-only model options (see `solve_inner_profile`) and are ignored here.
+"""
+function solve_inner(::_BareGGJ{:ray}, params::GGJParameters, γ::Number;
+ real_profiles=nothing, npc=nothing, certify_rtol=nothing, kwargs...)
+ res = solve_ray(params, inner_Q(params, γ); kwargs...)
+ return InnerLayerResponse(; interchange=res.Δ[1], tearing=res.Δ[2])
+end
+
+"""
+ solve_inner_profile(::GGJModel{:ray}, params::GGJParameters, γ::Number;
+ real_profiles=false, npc=8, certify_rtol=1e-3, kwargs...)
+ -> (; Δ, x, Ψ, Ξ, dψdx, rescale, certΔ)
+
+Rotated-ray implementation of the [`solve_inner_profile`](@ref) interface. `Δ` and the
+layer-center fields come from the solve at θ = arg(Q)/4; x = 0 lies on every contour, so
+Ψ(0), Ξ(0) are the real-axis values, and by default only they are returned (`x = [0.0]`,
+`certΔ = NaN`). With `real_profiles = true` the fields across the layer (x > 0) come from an
+extra θ = 0 solve (`npc` points per cell), a diagnostic; the x = 0 row stays the rotated
+solve's, and `certΔ` is the largest relative difference of the two solves' Δ₊, Δ₋, warned
+above `certify_rtol`. Other keywords forward to [`solve_ray`](@ref), except θ.
+"""
+function solve_inner_profile(::_BareGGJ{:ray}, params::GGJParameters, γ::Number;
+ real_profiles::Bool=false, npc::Int=8, certify_rtol::Float64=1e-3, kwargs...)
+ Q = inner_Q(params, γ)
+ rr = solve_ray(params, Q; kwargs...) # Δ and layer-center fields (optimal θ)
+ c = solution_profile(rr; npc=1) # first point is s = 0
+ if !real_profiles
+ return (; Δ=rr.Δ, x=[0.0], Ψ=c.Ψ[1:1, :], Ξ=c.Ξ[1:1, :], _profile_conversions(params)..., certΔ=NaN)
+ end
+ r0 = solve_ray(params, Q; θ=0.0, kwargs...) # real-axis profile solve
+ certΔ = maximum(abs.(r0.Δ .- rr.Δ) ./ max.(abs.(rr.Δ), 1e-300))
+ certΔ > certify_rtol && @warn "GGJ ray: θ=0 profile solve disagrees with certified Δ" ising = params.ising Q certΔ
+ prof = solution_profile(r0; npc=npc)
+ prof.Ψ[1, :] .= c.Ψ[1, :] # x = 0 from the rotated solve, as without profiles
+ prof.Ξ[1, :] .= c.Ξ[1, :]
+ return (; Δ=rr.Δ, x=prof.s, Ψ=prof.Ψ, Ξ=prof.Ξ, _profile_conversions(params)..., certΔ=certΔ)
+end
+
+"""
+ solution_profile(res::RaySolveResult; npc=8) -> (; s, x, Ψ, Ξ, Υ)
+
+Reconstruct (Ψ, Ξ, Υ) on the solution contour from the Hermite nodal solution, `npc`
+points per cell; each field is `npts × 2` with columns (even, odd) as in `Δ`, and `x = e^{iθ}s`.
+For rotated solves the fields live on the ray, not the real axis.
+"""
+function solution_profile(res::RaySolveResult; npc::Int=8)
+ prof = _solution_profile(res.ws; npc=npc)
+ return (; s=prof.x, x=cis(res.θ) .* prof.x, Ψ=prof.Ψ, Ξ=prof.Ξ, Υ=prof.Υ)
+end
+
+"""
+ asymptotic_profile(params, res::RaySolveResult, srange) -> (; s, x, Ψ, Ξ, Υ)
+
+Evaluate the analytic representation `u_small + Δ·u_big` on the ray for
+`s ≥ res.S`; concatenated with [`solution_profile`](@ref) it should join
+the numeric solution seamlessly across the march zone.
+"""
+function asymptotic_profile(params::GGJParameters, res::RaySolveResult,
+ srange::AbstractVector{<:Real})
+ cache = build_asymptotics(params, res.Q; kmax=12)
+ n = length(srange)
+ Ψ = Matrix{ComplexF64}(undef, n, 2)
+ Ξ = Matrix{ComplexF64}(undef, n, 2)
+ Υ = Matrix{ComplexF64}(undef, n, 2)
+ for (k, s) in enumerate(srange)
+ ua, _ = physical_ua_dua(cache, cis(res.θ) * s)
+ for isol in 1:2
+ Δ = res.Δraw[isol]
+ Ψ[k, isol] = ua[1, 2] + Δ * ua[1, 1]
+ Ξ[k, isol] = ua[2, 2] + Δ * ua[2, 1]
+ Υ[k, isol] = ua[3, 2] + Δ * ua[3, 1]
+ end
+ end
+ return (; s=collect(float.(srange)), x=cis(res.θ) .* srange, Ψ=Ψ, Ξ=Ξ, Υ=Υ)
+end
+
+"""
+ delta_convergence(params, Q; verbose=true, kwargs...) -> (; Δ, spread, base, table)
+
+Error bar for the matching data: re-solve with each numerical knob perturbed in turn (contour
+angle, mesh, series order and radius, march tolerance, BVP edge s_m, decaying-pair separation) and
+report the relative change of (Δ₊, Δ₋); `spread` is the worst case per parity. θ moves outward
+only, away from the pseudo-resonance x² = −Q²(G+KF).
+"""
+function delta_convergence(params::GGJParameters, Q::ComplexF64; verbose::Bool=true, kwargs...)
+ base = solve_ray(params, Q; kwargs...)
+ variations = [
+ ("θ → 1.2θ", (; θ=(base.θ == 0 ? 0.1 : 1.2 * base.θ))),
+ ("mesh ×2", (; cfl=(base.cfl / 2), min_cells=2 * base.min_cells)),
+ ("kmax+4, S↑", (; kmax=16, smax_tol=1e-10)),
+ ("march_rtol/100", (; march_rtol=1e-11)),
+ ("sm_fac 1→1.4", (; sm_fac=1.4)),
+ ("growth 30→45", (; growth=45.0))
+ ]
+ table = NamedTuple[]
+ spread = MVector{2,Float64}(0.0, 0.0)
+ verbose && @printf("Δ convergence check, Q = %s:\n", string(Q))
+ verbose && @printf(" baseline: Δ₊ = %+.8e %+.8eim, Δ₋ = %+.8e %+.8eim\n",
+ real(base.Δ[1]), imag(base.Δ[1]), real(base.Δ[2]), imag(base.Δ[2]))
+ for (name, kw) in variations
+ r = solve_ray(params, Q; kwargs..., kw...)
+ d1 = abs(r.Δ[1] - base.Δ[1]) / abs(base.Δ[1])
+ d2 = abs(r.Δ[2] - base.Δ[2]) / abs(base.Δ[2])
+ spread[1] = max(spread[1], d1)
+ spread[2] = max(spread[2], d2)
+ push!(table, (; name, d1, d2))
+ verbose && @printf(" %-16s δΔ₊ = %.2e δΔ₋ = %.2e\n", name, d1, d2)
+ end
+ verbose && @printf(" %-16s δΔ₊ = %.2e δΔ₋ = %.2e\n", "WORST CASE", spread[1], spread[2])
+ return (; Δ=base.Δ, spread=SVector(spread), base=base, table=table)
+end
+
+delta_convergence(params::GGJParameters, Q::Number; kwargs...) =
+ delta_convergence(params, ComplexF64(Q); kwargs...)
diff --git a/src/InnerLayer/GGJ/Reference.jl b/src/InnerLayer/GGJ/Reference.jl
new file mode 100644
index 0000000000..13168d3d98
--- /dev/null
+++ b/src/InnerLayer/GGJ/Reference.jl
@@ -0,0 +1,36 @@
+# Reference.jl
+#
+# Hard-coded benchmark parameter sets for cross-validation of the GGJ
+# inner-layer solvers. Values are taken from published papers.
+
+"""
+ glasser_wang_2020_eq55(; taua=1.0, taur=1e6, v1=1.0) -> GGJParameters
+
+D-shaped aspect-ratio-2, q = 2 surface from Glasser & Wang, Phys. Plasmas
+**27**, 012506 (2020), Eq. 55 (coefficients transcribed verbatim), the benchmark of their
+inps Wasow-basis convergence study (Figs. 1–3). At its operating point `Q = 1.234e-1`
+(Fig. 1) the GGJ backends are cross-checked against the Fortran `rmatch deltac`; the
+paper's `Δ_±` (Eq. 54) is a series-convergence norm, not matching data.
+
+`taua`, `taur`, `v1` default to a unit normalization; override them for physical cases.
+"""
+function glasser_wang_2020_eq55(; taua::Float64=1.0, taur::Float64=1e6, v1::Float64=1.0)
+ return GGJParameters(;
+ E=-3.369e-2, F=2.409e-3, G=8.950e1, H=1.292e-2, K=2.332e2,
+ taua=taua, taur=taur, v1=v1
+ )
+end
+
+"""
+ q4_surface_benchmark() -> GGJParameters
+
+Physical q = 4 rational-surface benchmark point (S = τ_R/τ_A ≈ 4.58×10⁶,
+D_I ≈ −0.31166, p₁ = √(−D_I) ≈ 0.5583). Primary validation point for the
+rotated-ray backend on the imaginary-Q axis (pinned at Q = 500i in the test suite).
+"""
+function q4_surface_benchmark()
+ return GGJParameters(;
+ E=-0.13733, F=0.022202, G=7.60633, H=0.053468, K=14.66987,
+ M=30.26883, taua=2.11226e-7, taur=0.968219, v1=1.55009
+ )
+end
diff --git a/src/InnerLayer/GGJ/Shooting.jl b/src/InnerLayer/GGJ/Shooting.jl
new file mode 100644
index 0000000000..13f0f8b5e4
--- /dev/null
+++ b/src/InnerLayer/GGJ/Shooting.jl
@@ -0,0 +1,365 @@
+# Shooting.jl
+#
+# Backward shooting solver for the GGJ inner layer, valid only for |Q| ≪ 1 (the large-t initial
+# condition underflows at large |Q|); used for tests and backend comparisons. It follows the Fourier-
+# transform method of Glasser, Jardin & Tesauro, Phys. Fluids 27, 1225 (1984), Sec. V: the 4×4 system
+# in the transform variable t is diagonalized at the origin (exponents `al0 = (p1, 1/2, −p1, −1/2)`,
+# p1 = √(−D_I), GJT Eqs. 49, 56), integrated from `tmax` on the decaying large-t solutions back to
+# `tmin`, projected onto the origin Frobenius basis, and Δ± read off from the coefficient ratios
+# (GJT Eqs. 90–91).
+
+using LinearAlgebra
+using SpecialFunctions: gamma
+using OrdinaryDiffEq
+
+"""
+ GGJShootingSystem
+
+Precomputed origin- and infinity-side arrays for the backward shoot.
+Construct via [`_build_shooting_system`](@ref).
+
+## Fields
+
+ - `params`, `Q` - Layer parameters and scaled growth rate.
+ - `p1`, `pplus` - p₁ = √(−D_I) and p₁ − 1/2.
+ - `al0` - Origin Frobenius exponents (p₁, 1/2, −p₁, −1/2), the diagonal of the origin exponent matrix.
+ - `al1` - First-order coupling in the origin-diagonalized basis.
+ - `d0`, `d0inv` - Origin diagonalizing matrix and its inverse.
+ - `ups` - `(4, 4, nps)` origin power-series coefficients in t², `ups[:, :, 1] = I`.
+ - `nps` - Origin series length.
+ - `d1` - Diagonalizing matrix at large t.
+ - `pexp` - Logarithmic exponents of the large-t asymptotic basis.
+ - `bl1` - Coefficients ±√Q of t²/2 in the large-t exponentials.
+ - `tmax`, `tmin` - Shoot start (large t) and end (small t).
+"""
+struct GGJShootingSystem
+ params::GGJParameters
+ Q::ComplexF64
+ p1::Float64
+ pplus::Float64
+ al0::SVector{4,Float64}
+ al1::SMatrix{4,4,ComplexF64,16}
+ d0::SMatrix{4,4,ComplexF64,16}
+ d0inv::SMatrix{4,4,ComplexF64,16}
+ ups::Array{ComplexF64,3}
+ nps::Int
+ d1::SMatrix{4,4,ComplexF64,16}
+ pexp::SVector{4,ComplexF64}
+ bl1::SVector{4,ComplexF64}
+ tmax::Float64
+ tmin::Float64
+end
+
+# -----------------------------------------------------------------------
+# Origin arrays for the origin-diagonalized Frobenius basis.
+# -----------------------------------------------------------------------
+
+function _build_origin_arrays(p::GGJParameters, Q::ComplexF64; nps::Int=8, rtol::Float64=1e-6)
+ p1v = p1(p)
+ pplus = -0.5 + p1v
+
+ e = ComplexF64(p.E)
+ f = ComplexF64(p.F)
+ h = ComplexF64(p.H)
+ g = ComplexF64(p.G)
+ k = ComplexF64(p.K)
+ q = Q
+
+ q3 = q^3
+ kk1 = 1 + k * q3
+ a1 = (g - k * e) * q * q / kk1
+ a2 = sqrt(0.5 / (p1v * q))
+ aplus = h - 0.5 + p1v
+ aminus = h - 0.5 - p1v
+
+ # d0 — diagonalizing matrix at the origin.
+ d0_m = zeros(ComplexF64, 4, 4)
+ d0_m[1, 1] = q * a2
+ d0_m[1, 2] = 1
+ d0_m[1, 3] = -q * a2
+ d0_m[1, 4] = 0
+ d0_m[2, 2] = 1
+ d0_m[3, 1] = aplus * a2
+ d0_m[3, 3] = -aminus * a2
+ d0_m[4, 1] = -aplus * a2
+ d0_m[4, 2] = -a1
+ d0_m[4, 3] = aminus * a2
+ d0_m[4, 4] = 1
+
+ # d0inv — explicit antisymmetry pattern of the origin diagonalizer inverse.
+ d0inv_m = zeros(ComplexF64, 4, 4)
+ d0inv_m[1, 1] = d0_m[3, 3]
+ d0inv_m[2, 2] = d0_m[4, 4]
+ d0inv_m[1, 2] = d0_m[4, 3]
+ d0inv_m[2, 1] = d0_m[3, 4]
+ d0inv_m[3, 3] = d0_m[1, 1]
+ d0inv_m[4, 4] = d0_m[2, 2]
+ d0inv_m[3, 4] = d0_m[2, 1]
+ d0inv_m[4, 3] = d0_m[1, 2]
+ d0inv_m[1, 3] = -d0_m[1, 3]
+ d0inv_m[2, 4] = -d0_m[2, 4]
+ d0inv_m[1, 4] = -d0_m[2, 3]
+ d0inv_m[2, 3] = -d0_m[1, 4]
+ d0inv_m[3, 1] = -d0_m[3, 1]
+ d0inv_m[4, 2] = -d0_m[4, 2]
+ d0inv_m[3, 2] = -d0_m[4, 1]
+ d0inv_m[4, 1] = -d0_m[3, 2]
+
+ # al0 — origin exponents.
+ al0 = SVector{4,Float64}(p1v, 0.5, -p1v, -0.5)
+
+ # al1 in the original basis, then transform via d0inv * al1 * d0.
+ al1_m = zeros(ComplexF64, 4, 4)
+ al1_m[1, 3] = 1
+ al1_m[2, 4] = -kk1
+ al1_m[3, 1] = q
+ al1_m[4, 2] = -q / kk1
+
+ d0_s = SMatrix{4,4,ComplexF64}(d0_m)
+ d0inv_s = SMatrix{4,4,ComplexF64}(d0inv_m)
+ al1_s = d0inv_s * SMatrix{4,4,ComplexF64}(al1_m) * d0_s
+
+ # ups[i, j, k] — origin power-series coefficients.
+ # ups(:,:,1) = I; higher orders from the al1 recurrence.
+ ups = zeros(ComplexF64, 4, 4, nps)
+ @inbounds for i in 1:4
+ ups[i, i, 1] = 1
+ end
+ @inbounds for kk in 2:nps
+ for j in 1:4, i in 1:4
+ acc = ComplexF64(0)
+ for l in 1:4
+ acc += al1_s[i, l] * ups[l, j, kk-1]
+ end
+ ups[i, j, kk] = acc / (al0[j] - al0[i] + 2 * (kk - 1))
+ end
+ end
+
+ # tmin from the truncation-error bound on the origin series.
+ unmax = 0.0
+ @inbounds for j in 1:4, i in 1:4
+ unmax = max(unmax, abs(ups[i, j, nps]))
+ end
+ fmin = 1.0
+ tmin = fmin * 0.5 * (rtol / unmax)^(0.5 / nps)
+
+ return (; al0, al1=al1_s, d0=d0_s, d0inv=d0inv_s, ups, nps, p1v, pplus, tmin)
+end
+
+# Large-t asymptotic basis, leading order only.
+
+function _build_infinity_arrays(p::GGJParameters, Q::ComplexF64,
+ d0inv::SMatrix{4,4,ComplexF64};
+ rtol::Float64=1e-6, fmax::Float64=1.0)
+ e = ComplexF64(p.E)
+ f = ComplexF64(p.F)
+ h = ComplexF64(p.H)
+ g = ComplexF64(p.G)
+ k = ComplexF64(p.K)
+ q = Q
+ dr = mercier_dr(p)
+
+ q3 = q^3
+ kk1 = 1 + k * q3
+ a1 = (g - k * e) * q * q / kk1
+ lamda = sqrt(q)
+ lamdaq = lamda * q
+ bb = -0.25 * lamdaq * (1 + g + k * (dr - e))
+ cc = 0.25 * kk1 * (a1 * q * (1 - dr / q3) + dr - h * h)
+ ddsq = bb * bb - cc
+ dd = sqrt(ddsq)
+
+ # m matrix (2×2) — large-t asymptotic coupling.
+ m11 = -lamdaq + dr / lamdaq
+ m12 = h - dr / lamdaq
+ m21 = kk1 * (h + dr / lamdaq)
+ m22 = -kk1 * (a1 / lamda + dr / lamdaq)
+
+ pexp = SVector{4,ComplexF64}(bb - dd, bb + dd, -bb + dd, -bb - dd)
+
+ # bmmat (2×2) and the first 2 columns of d1.
+ d1_m = zeros(ComplexF64, 4, 4)
+ bmmat = zeros(ComplexF64, 2, 2)
+ @inbounds for j in 1:2
+ bmmat[1, j] = m12
+ bmmat[2, j] = 2 * pexp[j] - m11
+ for i in 1:4
+ d1_m[i, j] = d0inv[i, 1] * bmmat[1, j] + d0inv[i, 2] * bmmat[2, j] +
+ lamda * (-d0inv[i, 3] * bmmat[1, j] +
+ d0inv[i, 4] * bmmat[2, j] / kk1)
+ end
+ end
+
+ # bpmat (2×2) and columns 3,4 of d1.
+ sigma = bmmat[1, 2] / bmmat[2, 2]
+ tau = bmmat[2, 1] / bmmat[1, 1]
+ stfac = 0.5 / (1 - sigma * tau)
+ bpmat = zeros(ComplexF64, 2, 2)
+ bpmat[1, 1] = stfac / bmmat[1, 1]
+ bpmat[2, 2] = stfac / bmmat[2, 2]
+ bpmat[1, 2] = -tau * bpmat[2, 2]
+ bpmat[2, 1] = -sigma * bpmat[1, 1]
+ @inbounds for j in 1:2
+ for i in 1:4
+ d1_m[i, j+2] = (d0inv[i, 1] * bpmat[1, j] -
+ d0inv[i, 2] * bpmat[2, j] * kk1) / lamda +
+ d0inv[i, 3] * bpmat[1, j] +
+ d0inv[i, 4] * bpmat[2, j]
+ end
+ end
+
+ d1 = SMatrix{4,4,ComplexF64}(d1_m)
+ bl1 = SVector{4,ComplexF64}(-lamda, -lamda, lamda, lamda)
+
+ # tmax: the smaller of the asymptotic-validity bound and 6/|Q|.
+ p1v = sqrt(-mercier_di(p))
+ tmax_inner = sqrt((max(0.5, p1v)^2 - log(rtol)) / abs(lamda))
+ tmax_outer = 6.0 / abs(q)
+ tmax = fmax * min(tmax_inner, tmax_outer)
+
+ return (; d1, pexp, bl1, tmax)
+end
+
+"""
+ _build_shooting_system(p::GGJParameters, Q::ComplexF64; nps=8, rtol=1e-6, fmax=1.0)
+
+Construct a [`GGJShootingSystem`](@ref) for the given parameters `p` and
+complex frequency `Q`, precomputing the origin and infinity asymptotic arrays
+used by the backward shoot.
+"""
+function _build_shooting_system(p::GGJParameters, Q::ComplexF64;
+ nps::Int=8, rtol::Float64=1e-6, fmax::Float64=1.0)
+ o = _build_origin_arrays(p, Q; nps=nps, rtol=rtol)
+ inf = _build_infinity_arrays(p, Q, o.d0inv; rtol=rtol, fmax=fmax)
+ return GGJShootingSystem(
+ p, Q, o.p1v, o.pplus,
+ o.al0, o.al1, o.d0, o.d0inv, o.ups, o.nps,
+ inf.d1, inf.pexp, inf.bl1, inf.tmax, o.tmin
+ )
+end
+
+# -----------------------------------------------------------------------
+# Origin Frobenius basis evaluator.
+# Returns the 4×4 matrix `u(t)` whose columns are the 4 fundamental
+# origin solutions evaluated at `t`. Solving `u * c0 = y` then projects a
+# 4-component integrated state onto the origin basis.
+# -----------------------------------------------------------------------
+
+function _origin_basis(sys::GGJShootingSystem, t::Real)
+ nps = sys.nps
+ t2 = t * t
+ u = zeros(ComplexF64, 4, 4)
+ @inbounds for j in 1:4, i in 1:4
+ # Horner in t² over k = nps..1
+ acc = sys.ups[i, j, nps]
+ for kk in (nps-1):-1:1
+ acc = acc * t2 + sys.ups[i, j, kk]
+ end
+ u[i, j] = acc
+ end
+ @inbounds for j in 1:4
+ tj = t^sys.al0[j]
+ for i in 1:4
+ u[i, j] *= tj
+ end
+ end
+ return SMatrix{4,4,ComplexF64}(u)
+end
+
+# Initial condition at tmax: the two decaying modes of the large-t basis, d1[:, 1:2]·exp(bl1·t²/2 + pexp·ln t).
+
+function _initial_condition(sys::GGJShootingSystem)
+ t = sys.tmax
+ fac1 = exp(0.5 * sys.bl1[1] * t * t + sys.pexp[1] * log(t))
+ fac2 = exp(0.5 * sys.bl1[2] * t * t + sys.pexp[2] * log(t))
+ y = zeros(ComplexF64, 4, 2)
+ @inbounds for i in 1:4
+ y[i, 1] = sys.d1[i, 1] * fac1
+ y[i, 2] = sys.d1[i, 2] * fac2
+ end
+ return y
+end
+
+# -----------------------------------------------------------------------
+# ODE right-hand side.
+# dy/dt = al1 * y * t + diag(al0) * y / t
+# -----------------------------------------------------------------------
+
+function _ggj_der!(dy::AbstractMatrix{ComplexF64}, y::AbstractMatrix{ComplexF64},
+ sys::GGJShootingSystem, t::Real)
+ mul!(dy, sys.al1, y)
+ @inbounds for j in axes(y, 2), i in axes(y, 1)
+ dy[i, j] = dy[i, j] * t + sys.al0[i] * y[i, j] / t
+ end
+ return nothing
+end
+
+# -----------------------------------------------------------------------
+# Parity-projected matching ratio.
+# c0 is a 4×2 complex matrix whose rows are the four origin-mode
+# coefficients of the two integrated solutions (modes 1: x^{p1},
+# 2: x^{1/2}, 3: x^{−p1}, 4: x^{−1/2}).
+# -----------------------------------------------------------------------
+
+function _delta_from_c0(c0::AbstractMatrix{ComplexF64}, sys::GGJShootingSystem)
+ pplus = sys.pplus
+ dfac = -sys.d0[1, 3] / sys.d0[1, 1]
+ phase = pplus * pi / 2
+ gamfac = -pi / (sin(2 * phase) * gamma(1 + pplus)^2)
+
+ delta1 = dfac * gamfac / tan(phase) *
+ (c0[4, 1] * c0[3, 2] - c0[4, 2] * c0[3, 1]) /
+ (c0[4, 1] * c0[1, 2] - c0[4, 2] * c0[1, 1])
+
+ delta2 = dfac * gamfac * tan(phase) *
+ (c0[2, 1] * c0[3, 2] - c0[2, 2] * c0[3, 1]) /
+ (c0[2, 1] * c0[1, 2] - c0[2, 2] * c0[1, 1])
+
+ return SVector{2,ComplexF64}(delta1, delta2)
+end
+
+# -----------------------------------------------------------------------
+# Top-level shooting solver.
+# -----------------------------------------------------------------------
+
+"""
+ solve_inner(::GGJModel{:shooting}, params::GGJParameters, γ::Number;
+ reltol::Float64=1e-6, abstol::Float64=1e-6,
+ rtol_origin::Float64=1e-6, nps::Int=8,
+ fmax::Float64=1.0, solver=Tsit5()) -> InnerLayerResponse
+
+Solve the GGJ inner-layer matching problem by stable backward shooting in
+the origin-diagonalized 4×4 basis.
+
+Returns an `InnerLayerResponse` rescaled by [`rescale_delta`](@ref), with `interchange` = Δ₊
+(Ξ even) and `tearing` = Δ₋ (Ξ odd), the same convention as the other GGJ backends.
+
+Tolerances `reltol`/`abstol` are the integrator tolerances; `rtol_origin`
+controls the truncation error of the origin Frobenius series and the
+choice of `tmin`.
+"""
+function solve_inner(::_BareGGJ{:shooting}, params::GGJParameters, γ::Number;
+ reltol::Float64=1e-6, abstol::Float64=1e-6,
+ rtol_origin::Float64=1e-6, nps::Int=8,
+ fmax::Float64=1.0, solver=Tsit5())
+ Q = inner_Q(params, γ)
+ sys = _build_shooting_system(params, Q; nps=nps, rtol=rtol_origin, fmax=fmax)
+
+ y0 = _initial_condition(sys)
+
+ prob = ODEProblem{true}(_ggj_der!, y0, (sys.tmax, sys.tmin), sys)
+ sol = solve(prob, solver; reltol=reltol, abstol=abstol, save_everystep=false)
+
+ y_end = sol.u[end]
+
+ # Project onto origin Frobenius basis: solve u(tmin) * c0 = y_end.
+ u = _origin_basis(sys, sys.tmin)
+ c0 = Matrix(u) \ Matrix(y_end)
+
+ Δ_raw = _delta_from_c0(c0, sys)
+ Δ_rescaled = rescale_delta(Δ_raw, params)
+ return InnerLayerResponse(; interchange=Δ_rescaled[1], tearing=Δ_rescaled[2])
+end
+
+solve_inner(::_BareGGJ{:shooting}, params::GGJParameters, γ::Real; kwargs...) =
+ solve_inner(GGJModel{:shooting}(), params, ComplexF64(γ); kwargs...)
diff --git a/src/InnerLayer/InnerLayer.jl b/src/InnerLayer/InnerLayer.jl
new file mode 100644
index 0000000000..a7205b6cde
--- /dev/null
+++ b/src/InnerLayer/InnerLayer.jl
@@ -0,0 +1,46 @@
+# InnerLayer.jl
+#
+# Resistive inner-layer models for matched-asymptotic resistive/extended MHD stability.
+# Provides an abstract `InnerLayerModel` interface and its implementations: the GGJ
+# (Glasser–Greene–Johnson) and SLAYER submodules.
+
+module InnerLayer
+
+using LinearAlgebra
+using StaticArrays
+using FastInterpolations: cubic_interp
+
+using ..Utilities
+
+include("InnerLayerInterface.jl")
+include("GGJ/GGJ.jl")
+include("SLAYER/SLAYER.jl")
+
+import .GGJ: GGJModel, GGJParameters, mercier_di, mercier_dr, inner_Q, rescale_delta
+import .GGJ: solve_ray, pick_smax, delta_convergence, solution_profile, asymptotic_profile
+
+import .SLAYER: SLAYERModel, SLAYERParameters, slayer_parameters, r_based_shear
+import .SLAYER: riccati_del_s, slayer_layer_thickness, LayerWidths
+import .SLAYER: surface_minor_radius, surface_da_dpsi, radial_label, build_slayer_inputs, toroidal_dgeo, toroidal_kpar
+
+include("LayerPlasma.jl")
+
+"""
+ model_name(model) -> String
+
+The `inner_model` token the tearing output records for `model`, e.g. `"ggj_ray"` or `"slayer_fitzpatrick"`.
+"""
+model_name(::GGJModel{S}) where {S} = "ggj_$S"
+model_name(::SLAYERModel{S}) where {S} = "slayer_$S"
+
+export InnerLayerModel, InnerLayerParameters, InnerLayerResponse, solve_inner, solve_inner_profile, layer_response
+export layer_eta, layer_rho, layer_omega_E
+export GGJ, GGJModel, GGJParameters
+export mercier_di, mercier_dr, inner_Q, rescale_delta
+export solve_ray, pick_smax, delta_convergence, solution_profile, asymptotic_profile
+
+export SLAYER, SLAYERModel, SLAYERParameters, slayer_parameters, r_based_shear
+export riccati_del_s, slayer_layer_thickness, LayerWidths
+export surface_minor_radius, surface_da_dpsi, radial_label, build_slayer_inputs, toroidal_dgeo, toroidal_kpar
+
+end # module InnerLayer
diff --git a/src/InnerLayer/InnerLayerInterface.jl b/src/InnerLayer/InnerLayerInterface.jl
new file mode 100644
index 0000000000..2639eb9f70
--- /dev/null
+++ b/src/InnerLayer/InnerLayerInterface.jl
@@ -0,0 +1,104 @@
+# InnerLayerInterface.jl
+#
+# Abstract interface for resistive inner-layer models. Concrete models (GGJ, SLAYER) live in
+# submodules and specialize `solve_inner`.
+
+"""
+ InnerLayerModel
+
+Abstract supertype for resistive inner-layer models. Each concrete model is a
+small, parameter-free type tag (often parameterized by a solver-choice symbol)
+that selects a `solve_inner` method.
+
+Implementations live in submodules of `InnerLayer`, e.g. `InnerLayer.GGJ`.
+"""
+abstract type InnerLayerModel end
+
+"""
+ InnerLayerParameters
+
+Abstract supertype for the per-surface physical-parameter structs consumed by
+the inner-layer models (`SLAYERParameters`, `GGJParameters`). Lets the
+dispersion runner and HDF5 output dispatch generically over a vector of
+single-model parameters.
+"""
+abstract type InnerLayerParameters end
+
+"""
+ InnerLayerResponse
+
+Parity-projected inner-layer matching data at one rational surface. The two
+components correspond to the homogeneous parity solutions of the half-domain
+inner-layer problem (parity boundary conditions imposed at X = 0). They are
+the `Δ_{j,±}(γ)` of Glasser, Wang & Park, Phys. Plasmas **23**, 112506
+(2016), Eqs. (34)–(35).
+
+# Fields
+
+ - `tearing` — odd-parity matching coefficient Δ₋: Ξ odd, Ψ even, the reconnecting channel
+ whose Δ is the constant-ψ tearing Δ′ (Pletzer, Bondeson & Dewar, J. Comput. Phys. 115, 530
+ (1994), Eqs. 77, 86–87, 89). Every resistive inner-layer model populates it.
+ - `interchange` — even-parity matching coefficient Δ₊: Ξ even, Ψ odd, the non-reconnecting
+ interchange channel carrying the Glasser, Greene & Johnson (1975) stabilization.
+ Pressureless models (SLAYER) set it to zero.
+
+Parity is that of the displacement Ξ, matched to the outer ξ (GWP2016 Eq. 34; Pletzer,
+Bondeson & Dewar Eqs. 32–33), with + even and − odd. The fields are named by the physics
+channel because the parity of the flux Ψ is the opposite. Positional
+pairs elsewhere in `InnerLayer` (e.g. the `Δ` of [`solve_inner_profile`](@ref)) are
+ordered (Δ₊, Δ₋) = (interchange, tearing).
+"""
+struct InnerLayerResponse
+ tearing::ComplexF64
+ interchange::ComplexF64
+end
+
+InnerLayerResponse(; tearing::Number=0, interchange::Number=0) =
+ InnerLayerResponse(ComplexF64(tearing), ComplexF64(interchange))
+
+"""
+ solve_inner(model::InnerLayerModel, params, s::Number; kwargs...) -> InnerLayerResponse
+
+Compute the parity-projected matching data (the `tearing` and `interchange` fields of
+`InnerLayerResponse`) for the given inner-layer `model`, physical parameters `params`, and complex
+growth rate `s = γ − iω` in 1/s, in the surface's E×B frame. Every model takes this same `s`.
+Concrete models specialize this function.
+
+See `InnerLayerResponse` for the physics-oriented field definitions.
+Pressureless models (SLAYER) populate only `tearing` and leave
+`interchange` at zero; finite-pressure models (GGJ) populate both.
+"""
+function solve_inner end
+
+"""
+ layer_response(model::InnerLayerModel, params, z::Number; kwargs...) -> InnerLayerResponse
+
+[`solve_inner`](@ref) in the variable `model`'s dispersion scans run in, so the layer is evaluated at exactly the value
+scanned: the growth rate `s` itself for GGJ, and Q = (ω + iγ)·τ_k = i·s·τ_k for SLAYER.
+"""
+layer_response(model::InnerLayerModel, params, z::Number; kwargs...) = solve_inner(model, params, z; kwargs...)
+
+"""
+ solve_inner_profile(model::InnerLayerModel, params, γ::Number; kwargs...)
+ -> (; Δ, x, Ψ, Ξ, dψdx, rescale, ...)
+
+Compute the inner-layer matching data **and** the reconstructed layer field
+profiles for the given `model` — everything an outer↔inner matching driver
+needs from the layer, so drivers never touch model internals. Returns a named
+tuple with at least:
+
+ - `Δ` — the same matching data as [`solve_inner`](@ref), as the pair
+ (Δ₊, Δ₋) = (interchange, tearing)
+ - `x` — real ascending grid in the model's stretched inner coordinate,
+ `x ≥ 0` with the rational surface at `x = 0`
+ - `Ψ`, `Ξ` — `length(x) × 2` profiles, columns in the order of `Δ`, in the
+ model's inner normalization: `Ψ` the normal-field
+ (reconnected-flux) variable, `Ξ` the displacement
+ - `dψdx` — conversion to poloidal-flux distance, `δψ = dψdx · x`
+ - `rescale` — amplitude factor converting the inner-normalized profiles to
+ the outer δψ-normalized convention (companion of the Δ rescale)
+
+Concrete models may return additional diagnostic fields (e.g. a solve-quality
+certificate). Solver-knob keywords are model-specific.
+"""
+function solve_inner_profile end
diff --git a/src/InnerLayer/LayerPlasma.jl b/src/InnerLayer/LayerPlasma.jl
new file mode 100644
index 0000000000..f8dd77105d
--- /dev/null
+++ b/src/InnerLayer/LayerPlasma.jl
@@ -0,0 +1,57 @@
+# LayerPlasma.jl: the plasma at the rational surfaces, from the equilibrium's kinetic data. The tearing and matching
+# problems both default their layer inputs from these, so every layer model sees one plasma.
+
+function _layer_kinetic_data(equil, what::AbstractString)
+ equil.kinetic === nothing &&
+ throw(ArgumentError("the layer $what comes from the equilibrium's kinetic data: give it explicitly, or set kinetic_file or call attach_kinetic_profiles!"))
+ return equil.kinetic
+end
+
+# Throw, naming exactly the layer inputs `who` was not given, when there is no kinetic data to derive them from.
+function _require_layer_inputs(who::AbstractString, equil; given...)
+ absent = [String(name) for (name, value) in pairs(given) if value === nothing]
+ (isempty(absent) || equil.kinetic !== nothing) && return nothing
+ throw(ArgumentError("$who: give $(join(absent, ", ", " and ")), or load kinetic profiles to derive them " *
+ "(kinetic_file in [Equilibrium], or attach_kinetic_profiles!)"))
+end
+
+"""
+ layer_eta(equil, surfaces) -> Vector{Float64}
+
+Resistivity η in Ω·m at each rational surface of `surfaces` (core to edge), from the equilibrium's kinetic data by
+its resistivity closure, the one the SLAYER layer uses.
+"""
+function layer_eta(equil, surfaces)
+ data = _layer_kinetic_data(equil, "resistivity η")
+ loaded = SLAYER._slayer_profiles(data, nothing)
+ return SLAYER.layer_resistivity(equil, surfaces, loaded.profiles; zeff=SLAYER._layer_zeff(loaded, data),
+ resistivity_model=SLAYER._build_resistivity_model(data.resistivity_model), lnLambda_form=data.lnLambda_form)
+end
+
+"""
+ layer_rho(equil, surfaces) -> Vector{Float64}
+
+Ion mass density ρ = μ·m_p·n_e in kg/m³ at each rational surface of `surfaces`, from the equilibrium's kinetic data:
+μ is the mean ion mass per electron of the main ions and the impurity at the layer Z_eff, the density the SLAYER
+layer uses.
+"""
+function layer_rho(equil, surfaces)
+ data = _layer_kinetic_data(equil, "mass density ρ")
+ loaded = SLAYER._slayer_profiles(data, nothing)
+ mu = SLAYER._layer_mass_per_electron(data, SLAYER._layer_zeff(loaded, data))
+ _at(x, ψ) = x isa Real ? x : x(ψ)
+ return Float64[_at(mu, s.psifac) * Utilities.M_P * loaded.profiles.n_e(s.psifac) for s in surfaces]
+end
+
+"""
+ layer_omega_E(equil, surfaces) -> Vector{Float64}
+
+E×B rotation Ω_E per unit n in rad/s at each rational surface of `surfaces`, from the kinetic data's `omega_E`;
+NaN when the equilibrium carries no kinetic data or the data no `omega_E`.
+"""
+function layer_omega_E(equil, surfaces)
+ data = equil.kinetic
+ (data === nothing || data.omega_E === nothing) && return fill(NaN, length(surfaces))
+ spline = SLAYER._slayer_profiles(data, nothing).profiles.omega_E
+ return Float64[spline(s.psifac) for s in surfaces]
+end
diff --git a/src/InnerLayer/SLAYER/KineticView.jl b/src/InnerLayer/SLAYER/KineticView.jl
new file mode 100644
index 0000000000..b404b6b7da
--- /dev/null
+++ b/src/InnerLayer/SLAYER/KineticView.jl
@@ -0,0 +1,95 @@
+# KineticView.jl: the inner layers' view of the equilibrium's kinetic data (`equil.kinetic`), shared by the
+# tearing and matching problems.
+
+using ...Equilibrium: KineticProfileData
+
+# Layer view of raw kinetic profiles (`equil.kinetic`) on their own ψ grid: the `KineticProfiles`, the χ⊥,e/χ⊥,i/χ_φ(ψ)
+# callables the `SLAYERModel` uses (`nothing` when absent, so the caller uses `chi_*_default`), Z_eff(ψ) (the data's
+# `zeff`, else from n_i/n_e, else `nothing` for `zeff_default`) with its source, and whether the data carry `omega_E`.
+function _slayer_profiles(data::KineticProfileData, control)
+ source = isempty(data.provenance) ? "kinetic profiles" : "kinetic profiles ($(data.provenance))"
+ for (name, v) in (("n_e", data.n_e), ("T_e", data.T_e), ("T_i", data.T_i))
+ v === nothing &&
+ error("Inner layer: $source missing required dataset '$name' for the SLAYER inner layer.")
+ end
+ # `omega_E` carries the E×B rotation Ω_E (per unit n) when the data have it, else zero (no shift);
+ # ω_*e/ω_*i are derived per surface from the density and temperature splines by `build_slayer_inputs`.
+ omega_E = data.omega_E === nothing ? zeros(length(data.psi)) : data.omega_E
+ profiles = KineticProfiles(; psi=data.psi, n_e=data.n_e, T_e=data.T_e,
+ T_i=data.T_i, omega_E=omega_E)
+
+ # χ⊥(ψ)/χ_φ(ψ) splines; an absent or all-zero array means "not provided" and defers to the data's `chi_*_default`.
+ psi_xs = collect(Float64, data.psi)
+ function _chi_spline(name, v)
+ (v === nothing || all(iszero, v)) && return nothing
+ minimum(v) > 0 || error("Inner layer: $source has $name with minimum $(minimum(v)) ≤ 0; diffusivities must be positive")
+ return cubic_interp(psi_xs, collect(Float64, v))
+ end
+ # `control === nothing` reads no diffusivity, for callers that need only the densities, temperatures and Z_eff.
+ model = control === nothing ? nothing : control.P_perp_model
+ # With chi_perp_Dc set, the critical Δ takes it in place of χ⊥,e, so only P_perp can need the file's chi_e.
+ uses_e = model in (:chi_perp_e, :D_perp) || (control !== nothing && control.D_c_type !== :none && control.chi_perp_Dc === nothing)
+ chi_perp_e = uses_e ? _chi_spline("chi_e", data.chi_e) : nothing
+ chi_perp_i = model in (:chi_perp_i, :D_perp) ? _chi_spline("chi_i", data.chi_i) : nothing
+ chi_tor = model !== nothing && model !== :tau_E ? _chi_spline("chi_phi", data.chi_phi) : nothing
+ # Z_eff(ψ): the file's profile wins; else quasi-neutrality with one impurity of charge `impurity_charge` and a
+ # charge-1 main ion, Z_eff = impurity_charge − (n_i/n_e)(impurity_charge − 1).
+ _usable(v) = v !== nothing && !all(iszero, v)
+ zeff = if _usable(data.zeff)
+ minimum(data.zeff) >= 1.0 - 1e-8 ||
+ error("Inner layer: $source has zeff = $(minimum(data.zeff)) < 1 — unphysical")
+ cubic_interp(psi_xs, collect(Float64, data.zeff))
+ elseif !_usable(data.n_i)
+ nothing
+ else
+ zimp = Float64(data.impurity_charge)
+ z = [ne > 0 ? zimp - (ni / ne) * (zimp - 1.0) : zimp for (ni, ne) in zip(data.n_i, data.n_e)]
+ minimum(z) >= 1.0 - 1e-8 ||
+ error("Inner layer: $source has n_i > n_e, giving Z_eff = $(minimum(z)) < 1 — unphysical")
+ cubic_interp(psi_xs, z)
+ end
+ zeff_source = _usable(data.zeff) ? :file : zeff === nothing ? :scalar : :closure
+ return (profiles=profiles, chi_perp_e=chi_perp_e, chi_perp_i=chi_perp_i, chi_tor=chi_tor, zeff=zeff, zeff_source=zeff_source,
+ has_omega_E=(data.omega_E !== nothing))
+end
+
+# Map the TOML resistivity_model symbol to a NeoResistivityModel instance.
+function _build_resistivity_model(name::Symbol)
+ name === :sauter && return SauterNeoModel()
+ name === :redl && return RedlNeoModel()
+ name === :spitzer && return SpitzerModel()
+ name === :spitzer_harm && return SpitzerHarmModel()
+ throw(ArgumentError("_build_resistivity_model: unknown model $name"))
+end
+
+# The layers' main-ion mass in proton masses: the fraction-weighted mean over the main-ion species.
+function _layer_ion_mass(data::KineticProfileData)
+ total = sum(s.fraction for s in data.ion_species)
+ total > 0 || throw(ArgumentError("the layer ion mass needs main-ion species with positive fractions"))
+ return sum(s.fraction * s.m for s in data.ion_species) / total
+end
+
+# Mean ion mass per electron μ in proton masses, so ρ = μ·m_p·n_e: charge-1 main ions of mass μ_i and one impurity
+# of charge Z and mass μ_Z, split by quasi-neutrality and Z_eff, μ = μ_i(Z − Z_eff)/(Z − 1) + μ_Z(Z_eff − 1)/(Z(Z − 1)).
+# `zeff` is a number or a ψ-callable; the result is the same kind.
+function _layer_mass_per_electron(data::KineticProfileData, zeff)
+ mu_i, Z, mu_Z = _layer_ion_mass(data), Float64(data.impurity_charge), Float64(data.impurity_mass)
+ function mu(z)
+ 1 - 1e-8 <= z <= Z + 1e-8 ||
+ throw(ArgumentError("Z_eff = $z lies outside [1, $Z]: no split between the main ions and the charge-$Z impurity gives it"))
+ return mu_i * (Z - z) / (Z - 1) + mu_Z * (z - 1) / (Z * (Z - 1))
+ end
+ return zeff isa Real ? mu(Float64(zeff)) : (ψ -> mu(Float64(zeff(ψ))))
+end
+
+# Z_eff(ψ) for the layers, reporting where it came from: the file's profile, the n_i/n_e closure, or the default.
+function _layer_zeff(loaded, data::KineticProfileData)
+ if loaded.zeff_source === :scalar
+ @warn "Inner layer: kinetic file has no usable zeff or n_i profile (dataset absent or all-zero); " *
+ "using zeff_default = $(data.zeff_default) at every surface."
+ return data.zeff_default
+ end
+ zeff_origin = loaded.zeff_source === :file ? "zeff profile" : "n_i/n_e with impurity_charge = $(data.impurity_charge)"
+ @info "Inner layer: Z_eff(ψ) from the kinetic file's $zeff_origin"
+ return loaded.zeff
+end
diff --git a/src/InnerLayer/SLAYER/LayerInputs.jl b/src/InnerLayer/SLAYER/LayerInputs.jl
new file mode 100644
index 0000000000..3a77f7fd87
--- /dev/null
+++ b/src/InnerLayer/SLAYER/LayerInputs.jl
@@ -0,0 +1,469 @@
+# LayerInputs.jl
+#
+# Build per-surface `SLAYERParameters` from an in-memory `PlasmaEquilibrium`, the `SingType` rational-surface
+# data from `ForceFreeStates`, and a `KineticProfiles` object.
+
+using ..Utilities: KineticProfiles
+using ...Utilities.NeoclassicalResistivity: NeoResistivityModel, SpitzerModel,
+ coulomb_log_e, nu_star_e
+using FastInterpolations: DerivOp, integrate, cubic_interp, cumulative_integrate, ExtendExtrap
+
+"""
+ surface_minor_radius(equil, psi; theta=0.0) -> Float64
+
+Minor radius at normalized flux `psi` and poloidal angle `theta`,
+computed from `equil.rzphi_rsquared` as `√((R − R₀)² + (Z − Z₀)²)`.
+`theta` is normalized to [0, 1): `0.0` (outboard midplane) is the default and
+`0.5` is the inboard midplane.
+"""
+function surface_minor_radius(equil, psi::Real; theta::Real=0.0)
+ r_sq = equil.rzphi_rsquared((Float64(psi), Float64(theta)))
+ return sqrt(r_sq)
+end
+
+"""
+ surface_da_dpsi(equil, psi; theta=0.0) -> Float64
+
+Analytic ψ-derivative of the minor radius at `psi` and poloidal angle
+`theta`, taken from the `rzphi_rsquared` interpolant's own ψ-derivative as
+`da/dψ = (∂r²/∂ψ) / (2a)`. Valid wherever the interpolant is, including
+under extrapolation past the ψ grid. Diverges at the magnetic axis, where
+`a ~ √ψ`; callers evaluating near `ψ = 0` must check `isfinite`.
+"""
+function surface_da_dpsi(equil, psi::Real; theta::Real=0.0)
+ return _da_dpsi_at_theta(equil, Float64(psi), Float64(theta))
+end
+
+# d(√r²)/dψ at one (ψ, θ) from the interpolant's own ψ-derivative. Shared by all radial-label
+# conventions so none carries its own stencil.
+@inline function _da_dpsi_at_theta(equil, psi::Float64, theta::Float64)
+ r_sq = equil.rzphi_rsquared((psi, theta))
+ a = sqrt(max(r_sq, 0.0))
+ a > 0 || return Inf # magnetic axis: a ~ √ψ, so da/dψ genuinely diverges
+ return equil.rzphi_rsquared((psi, theta); deriv=DerivOp(1, 0)) / (2a)
+end
+
+"""
+ radial_label(equil; rs_method=:flux, theta=0.0, q_beyond=nothing) -> (r_at, dr_dpsi_at)
+
+Build the pair of closures `r_at(ψ)` and `dr_dpsi_at(ψ)` defining one radial
+label for the layer stack. Both closures must come from the same label,
+because the r-based shear `(r/q)dq/dr`, `τ_R = μ₀r²/η`, `τ_E = r²/χ`, the
+`d_β/r` normalization, the Δ' reference-length factor `k_ref = r_s/(da/dψ)`,
+and any metre-to-ψ width conversion all have to live in one coordinate; a
+mismatched `r` and `dr/dψ` silently corrupts every one of them. All
+derivatives are analytic — no label carries a finite-difference stencil.
+
+# Labels
+
+ - `:midplane` -- outboard-midplane chord from the magnetic axis at `theta`
+ natural for comparison with midplane diagnostics.
+ - `:halfwidth` -- midplane half-chord, the mean of the outboard and inboard
+ chords at `θ = 0` and `θ = 0.5`; shift-free. Coincides with the flux label
+ on circular equilibria but is its own convention on shaped ones.
+ - `:fsa` -- θ-mean surface radius, a 128-point midpoint mean of the local
+ minor radius; the closest geometric approximation to `:flux` at interior
+ surfaces of shaped equilibria.
+ - `:volume` -- cylinder-equivalent label `√(V(ψ)/(2π²R₀))`, the
+ Rutherford-literature convention.
+ - `:flux` -- toroidal-flux label. Fitzpatrick, Nucl. Fusion (2025),
+ Eq. 30: `dψ_p/dr = B₀ r g/q` integrates to `ψ_t = B₀r²/2`, so
+ `r = √(2ψ_t/B₀)` with `ψ_t = psio·∫₀^ψ (q/g) dψ′` and `g = F/(B₀R₀)`,
+ `F = R·B_tor`. Note `profiles.F_spline` stores `2πF`, so the
+ implementation divides it by 2π to form `g`.
+ Defined from flux alone, it carries no circular-cross-section assumption,
+ and its derivative `dr/dψ ∝ q` grows toward a separatrix where the
+ geometric labels' `da/dψ` collapses. Beyond the ψ grid the q spline is a
+ cubic extrapolation that does not follow that growth, so `q_beyond`, a
+ callable of ψ, supplies q there when the caller knows it.
+
+On shaped equilibria the labels agree at low-q surfaces and diverge strongly
+near the edge, where the slab-layer matching is label-ambiguous regardless of
+choice. The label is selected programmatically; it is not exposed via TOML.
+"""
+function radial_label(equil; rs_method::Symbol=:flux, theta::Real=0.0, q_beyond=nothing)
+ theta_f = Float64(theta)
+
+ _flux_r, _flux_dr = if rs_method === :flux
+ b0f = Float64(equil.params.b0)
+ R0f = Float64(equil.ro)
+ psiof = Float64(equil.psio)
+ xs_f = collect(Float64, equil.profiles.xs)
+ # Carry g = F/(B0 R0) rather than assuming g = 1: r² = 2∫(q/g)dψ_p/B0.
+ _g_at(x) = Float64(equil.profiles.F_spline(x)) / (2π * b0f * R0f)
+ qg = [Float64(equil.profiles.q_spline(x)) / _g_at(x) for x in xs_f]
+ Phi = collect(Float64, cumulative_integrate(cubic_interp(xs_f, qg)))
+ r_knots = sqrt.(max.(2 .* psiof .* Phi ./ b0f, 0.0))
+ rspl = cubic_interp(xs_f, r_knots; extrap=ExtendExtrap())
+ _q_at(ψ) = (q_beyond !== nothing && ψ > xs_f[end]) ? Float64(q_beyond(ψ)) : Float64(equil.profiles.q_spline(ψ))
+ (ψ -> Float64(rspl(Float64(ψ))),
+ ψ -> psiof * _q_at(Float64(ψ)) /
+ (b0f * _g_at(Float64(ψ)) * max(Float64(rspl(Float64(ψ))), eps())))
+ else
+ (nothing, nothing)
+ end
+
+ _a_at(ψ, θ) = sqrt(max(equil.rzphi_rsquared((Float64(ψ), Float64(θ))), 0.0))
+
+ _rs_at(ψ) =
+ if rs_method === :fsa
+ N = 128
+ s = 0.0
+ @inbounds for k in 1:N
+ s += _a_at(ψ, (k - 0.5) / N)
+ end
+ s / N
+ elseif rs_method === :halfwidth
+ 0.5 * (_a_at(ψ, 0.0) + _a_at(ψ, 0.5))
+ elseif rs_method === :volume
+ # Lower bound just off the axis, where dV/dψ is extrapolated; the omitted sliver
+ # of core volume is negligible for an edge-surface label.
+ V = integrate(equil.profiles.dVdpsi_spline, 1e-4, Float64(ψ))
+ sqrt(max(V, 0.0) / (2π^2 * equil.ro))
+ elseif rs_method === :flux
+ _flux_r(ψ)
+ else
+ surface_minor_radius(equil, ψ; theta=theta_f)
+ end
+
+ _da_dpsi_at(ψ) =
+ if rs_method === :fsa
+ N = 128
+ s = 0.0
+ @inbounds for k in 1:N
+ s += _da_dpsi_at_theta(equil, Float64(ψ), (k - 0.5) / N)
+ end
+ s / N
+ elseif rs_method === :halfwidth
+ 0.5 * (_da_dpsi_at_theta(equil, Float64(ψ), 0.0) + _da_dpsi_at_theta(equil, Float64(ψ), 0.5))
+ elseif rs_method === :volume
+ Float64(equil.profiles.dVdpsi_spline(ψ)) / (4π^2 * equil.ro * max(_rs_at(ψ), eps()))
+ elseif rs_method === :flux
+ _flux_dr(ψ)
+ else
+ _da_dpsi_at_theta(equil, Float64(ψ), theta_f)
+ end
+
+ return (_rs_at, _da_dpsi_at)
+end
+
+"""
+ toroidal_dgeo(; chi1, v1, q, q1, n, avg_bsq, avg_dpsisq, k_ref) -> Float64
+
+Geometric factor of the toroidal critical-Δ, Connor, Ham, Hastie & Liu 2015
+(PPCF 57 065001) Eq. 59, `V_s·(α²Λ²/(⟨B²⟩⟨|∇V|²⟩))^{1/4}`, converted from the
+paper's `Y = (V−V_s)/V_s` reference to the `x̂ = (r−r_s)/r_s` reference shared
+by the slab layer, the `:fitzpatrick` critical-Δ, and the reference-length-converted
+outer Δ'. In GPEC quantities, with `V` the flux-surface volume, `ψ_N` the
+normalized poloidal flux, and `'` = d/dV:
+
+ - `α = 2πn/χ'` with `χ' = chi1/v1` (`χ` the full poloidal flux,
+ `chi1 = 2π·psio`, `v1 = dV/dψ_N`)
+ - `Λ = ψ_t'²·(ι/2π)'` with `ψ_t' = q·chi1/v1` (toroidal flux) and
+ `(ι/2π)' = −q1/(q²·v1)` (`q1 = dq/dψ_N`)
+ - `⟨|∇V|²⟩ = v1²·⟨|∇ψ_N|²⟩`, both averages being normalized flux-surface
+ averages (⟨1⟩ = 1)
+ - the reference conversion `r_s·(dV/dr)/V_s = k_ref·v1/V_s` with
+ `k_ref = r_s·dψ_N/dr`, so `V_s` cancels and is never integrated.
+
+At large aspect ratio this reduces to `√(n·s·r_s/R₀)` with `s = (r_s/q)·dq/dr`,
+so `dc_type=:toroidal` coincides with `:fitzpatrick` there; the paper's own Eq. 61
+is recovered after dividing by `r_s`.
+
+The reference conversion is deliberately linear (Frobenius exponent ½, the
+paper's H = 0 ordering): the critical-Δ is a layer-side quantity like the slab
+Δ̂(Q) and W_d, whereas the outer Δ' carries the Mercier exponent `α_M = √(−D_I)`
+and is converted with `K^(2α_M)`.
+"""
+function toroidal_dgeo(; chi1::Real, v1::Real, q::Real, q1::Real, n::Integer,
+ avg_bsq::Real, avg_dpsisq::Real, k_ref::Real)
+ alpha, lambda = _connor_alpha_lambda("toroidal_dgeo", chi1, v1, q, q1, n)
+ grad_v_sq = v1^2 * avg_dpsisq
+ return k_ref * v1 * (alpha^2 * lambda^2 / (avg_bsq * grad_v_sq))^0.25
+end
+
+"""
+ toroidal_kpar(; chi1, v1, q, q1, n, avg_bsq, k_ref) -> Float64
+
+Parallel-wavenumber gradient `K∥` [1/m] of the toroidal critical-Δ closure: an island of normalized
+width `W` (in the `x̂ = (r−r_s)/r_s` reference) sees `k∥ = K∥·W`. From Connor, Ham, Hastie & Liu 2015
+(PPCF 57 065001) Eq. 20, whose transport balance reads `χ⊥⟨|∇V|²⟩ ∂²_x = χ∥ (α²Λ²/⟨B²⟩) x²` in
+`x = V − V_s`, the parallel wavenumber is `k∥ = |αΛ|·x/√⟨B²⟩`; with `x = W·r_s·(dV/dr) = W·k_ref·v1`,
+
+```
+K∥ = |α·Λ|·k_ref·v1 / √⟨B²⟩,
+```
+
+with `α`, `Λ` as in [`toroidal_dgeo`](@ref). At large aspect ratio it reduces to Fitzpatrick's
+(1995, Phys. Plasmas 2 825, Eq. 132) cylindrical `n·s/R₀`. It is not a function of `D_geo` alone:
+`K∥ = (D_geo²/r_s)·r_s√⟨|∇ψ_N|²⟩/k_ref`, and the last factor is 1 only in a cylinder.
+"""
+function toroidal_kpar(; chi1::Real, v1::Real, q::Real, q1::Real, n::Integer, avg_bsq::Real, k_ref::Real)
+ alpha, lambda = _connor_alpha_lambda("toroidal_kpar", chi1, v1, q, q1, n)
+ return abs(alpha * lambda) * k_ref * v1 / sqrt(avg_bsq)
+end
+
+# Connor et al. 2015 α = 2πn/χ' and Λ = ψ_t'²·(ι/2π)' (' = d/dV) from ψ_N-grid quantities.
+function _connor_alpha_lambda(caller, chi1, v1, q, q1, n)
+ v1 > 0 || throw(ArgumentError("$caller: dV/dψ_N must be positive, got $v1"))
+ chi1 != 0 || throw(ArgumentError("$caller: chi1 must be non-zero"))
+ alpha = 2π * n * v1 / chi1
+ psit1 = q * chi1 / v1
+ lambda = psit1^2 * (-q1 / (q^2 * v1))
+ return alpha, lambda
+end
+
+"""
+ build_slayer_inputs(equil, sings, profiles; …) -> Vector{SLAYERParameters}
+
+Build a `SLAYERParameters` for each rational surface in `sings` from the in-memory `equil::PlasmaEquilibrium`
+(geometry, q, dq/dψ, R₀) and `profiles::KineticProfiles` (n_e, T_e, T_i, and ω\\_\\*e, ω\\_\\*i from their gradients).
+Keywords documented as scalar-or-callable are evaluated per surface at ψ.
+
+# Arguments
+
+ - `equil` -- `PlasmaEquilibrium`
+ - `sings` -- `Vector{SingType}`, one per resonant surface
+ - `profiles` -- `KineticProfiles` valid across all `sings` ψ values
+
+# Keyword arguments
+
+ - `bt` -- toroidal field in T, scalar or callable; `nothing` (default) uses B_T = F(ψ)/(2π·R₀). `equil.config.b0_norm` is a
+ normalization, not this field
+ - `R0` -- major radius in m (default `equil.ro`)
+ - `rs_method` -- radial label of the whole layer stack: `:flux` (default), `:midplane`, `:halfwidth`, `:fsa` or `:volume`;
+ see [`radial_label`](@ref). Programmatic only, not exposed via TOML
+ - `q_beyond` -- callable q(ψ) the `:flux` label uses beyond the ψ grid (default `nothing`)
+ - `mu_i` -- main-ion mass in proton masses (default `2.0`, D)
+ - `mu_rho` -- mean ion mass per electron in proton masses for the mass density, scalar or callable (default `mu_i`)
+ - `zeff` -- effective charge, scalar or callable (default `1.0`)
+ - `z_i` -- main-ion charge entering ω_*i (default `1.0`)
+ - `chi_perp_e` -- electron perpendicular heat diffusivity in m²/s, scalar or callable (default `1.0`)
+ - `chi_perp_i` -- ion perpendicular heat diffusivity in m²/s, scalar or callable; needed by `P_perp_model = :chi_perp_i` and `:D_perp`
+ - `chi_perp_Dc` -- electron χ⊥ in m²/s used only by the critical Δ, scalar or callable; `nothing` (default) uses `chi_perp_e`
+ - `tau_E` -- whole-plasma energy confinement time τ̄_E in s, needed by `P_perp_model = :tau_E`, which takes `a` from the `:flux` label
+ - `P_perp_model` -- how `P_perp` is built (default `:D_perp`); see [`slayer_parameters`](@ref)
+ - `chi_tor` -- toroidal momentum diffusivity χ_φ in m²/s, scalar or callable, setting P_tor = τ_R/τ_φ with τ_φ = r_s²/χ_φ
+ (Fitzpatrick, Phys. Plasmas 30, 092512 (2023)) (default `1.0`)
+ - `dr_val` -- resistive interchange index D_R = E + F + H² (Glasser-Greene-Johnson 1975) of the critical Δ, **not** the Mercier
+ D_I; `nothing` (default) derives it from `sing.restype`, a scalar or callable overrides it
+ - `dgeo_val` -- Connor et al. 2015 (PPCF 57 065001) Eq. 59 factor in the `r_s` reference ([`toroidal_dgeo`](@ref)), used only by
+ `dc_type = :toroidal`; `nothing` (default) derives it from `sing.restype` (required then). A prescribed value must already be in
+ the `r_s` reference, i.e. Eq. 59 times `k_ref·v1/V_s` (≈ 2 at large aspect ratio)
+ - `dc_type` -- critical-Δ formula: `:none` (default), `:lar`, `:fitzpatrick` or `:toroidal`; `:toroidal` takes K∥ from
+ [`toroidal_kpar`](@ref), or the cylindrical `n·|s|/R₀` with a warning when the surface has no `ResistGeometry`
+ - `theta` -- poloidal angle of the minor-radius chord, used only by `rs_method = :midplane` (default `0.0`, outboard midplane)
+ - `resistivity_model` -- `SauterNeoModel()` (default), `RedlNeoModel()`, `SpitzerModel()` or `SpitzerHarmModel()`; the
+ neoclassical `f_trap` and ν*_e come from `sing.restype` when populated, else the ε-only forms
+ - `lnLambda_form` -- Coulomb-log form (default `:nrl`; `:wesson` with `SpitzerHarmModel()` reproduces the legacy SLAYER)
+"""
+function build_slayer_inputs(equil, sings, profiles::KineticProfiles;
+ bt=nothing,
+ R0=nothing,
+ rs_method::Symbol=:flux,
+ q_beyond=nothing,
+ mu_i::Real=2.0,
+ mu_rho=mu_i,
+ zeff=1.0,
+ z_i::Real=1.0,
+ chi_perp_e=1.0,
+ chi_perp_i=nothing,
+ chi_perp_Dc=nothing,
+ tau_E::Union{Real,Nothing}=nothing,
+ P_perp_model::Symbol=:D_perp,
+ chi_tor=1.0,
+ dr_val=nothing,
+ dgeo_val=nothing,
+ dc_type::Symbol=:none,
+ theta::Real=0.0,
+ resistivity_model::NeoResistivityModel=SauterNeoModel(),
+ lnLambda_form::Symbol=:nrl)
+ R0_use = R0 === nothing ? equil.ro : Float64(R0)
+ _eval(x, ψ) = x === nothing ? nothing : x isa Real ? Float64(x) : Float64(x(ψ))
+
+ # Physical B_T = F(ψ) / (2π·R₀) per surface when `bt` is not supplied.
+ _bt_at(ψ) =
+ if bt === nothing
+ Float64(equil.profiles.F_spline(ψ)) / (2π * R0_use)
+ elseif bt isa Real
+ Float64(bt)
+ else
+ Float64(bt(ψ))
+ end
+
+ _rs_at, _da_dpsi_at = radial_label(equil; rs_method=rs_method, theta=theta, q_beyond=q_beyond)
+ # Boundary minor radius on the flux label, needed only to turn a whole-plasma τ̄_E into a uniform χ_E.
+ a_minor = P_perp_model === :tau_E ? first(radial_label(equil; rs_method=:flux, theta=theta, q_beyond=q_beyond))(1.0) : nothing
+
+ # Per-surface ω_*e, ω_*i from spline derivatives: ω_* = n·(dp/dψ)/(e·n_e) in flux coordinates, with n_i = n_e.
+ chi1 = 2π * equil.psio
+ _kinetic_at(ψ) = (n_e=Float64(profiles.n_e(ψ)), dn_e=Float64(profiles.n_e(ψ; deriv=DerivOp(1))),
+ T_e=Float64(profiles.T_e(ψ)), dT_e=Float64(profiles.T_e(ψ; deriv=DerivOp(1))),
+ T_i=Float64(profiles.T_i(ψ)), dT_i=Float64(profiles.T_i(ψ; deriv=DerivOp(1))))
+ _omega_star_at(ψ, n_tor) = begin
+ (; n_e, dn_e, T_e, dT_e, T_i, dT_i) = _kinetic_at(ψ)
+ ω_star_e = n_tor * (2π / chi1) * (T_e * dn_e / n_e + dT_e)
+ ω_star_i = -n_tor * (2π / (Float64(z_i) * chi1)) * (T_i * dn_e / n_e + dT_i)
+ return (ω_star_e, ω_star_i)
+ end
+
+ out = Vector{SLAYERParameters}(undef, length(sings))
+ for (k, sing) in enumerate(sings)
+ psi = sing.psifac
+ q = sing.q
+ q1 = sing.q1
+
+ rs = _rs_at(psi)
+ da_dpsi = _da_dpsi_at(psi)
+ sval_r = r_based_shear(rs, q, q1, da_dpsi)
+
+ # Resonant (m, n): the first entry of `sing.m`/`sing.n`, which may hold several.
+ m_res = sing.m[1]
+ n_res = sing.n[1]
+
+ prof = profiles(psi)
+ kin = _kinetic_at(psi)
+ # ω_*e, ω_*i from the density and temperature spline derivatives, at this surface's n.
+ ω_e_use, ω_i_use = _omega_star_at(psi, n_res)
+
+ # Trapped-fraction inputs from ResistGeometry when populated; else slayer_parameters uses the ε-only forms.
+ rg = sing.restype
+ (; f_trap, nu_e_star, R_major_eff) = _resistivity_geometry(rg, prof.n_e, prof.T_e, q, _eval(zeff, psi);
+ resistivity_model=resistivity_model, lnLambda_form=lnLambda_form)
+
+ # Resistive interchange index D_R = E + F + H² (Glasser-Greene-Johnson 1975), the (−D_R) of Connor et al. 2015 Eq. 59;
+ # not the Mercier index D_I = E + F + H − 1/4.
+ dr_val_k = if dr_val === nothing
+ rg === nothing &&
+ throw(
+ ArgumentError(
+ "build_slayer_inputs: dr_val=nothing " *
+ "requires `sing.restype` populated by " *
+ "ForceFreeStates.resist_eval_all!. " *
+ "Surface k=$k has restype=nothing."
+ )
+ )
+ rg.E + rg.F + rg.H^2
+ else
+ _eval(dr_val, psi)
+ end
+
+ # Reference-length conversion inputs for the outer Δ': K = r_s·(dψ_N/dr)|_s and
+ # α = √(−D_I) (Glasser-Greene-Johnson 1975 Eq. 48), with α clamped to 0 on Mercier-unstable
+ # surfaces (the factor turns complex there) and K = 1 whenever da/dψ is not a usable
+ # positive number (zero/non-finite/negative would corrupt the Δ' diagonal).
+ k_ref_k = if isfinite(da_dpsi) && da_dpsi > 0.0
+ rs / da_dpsi
+ else
+ @warn("build_slayer_inputs: da/dψ = $da_dpsi at ψ = $psi is not usable; leaving " *
+ "Δ' and the toroidal critical-Δ unconverted (k_ref = 1) at this surface.", maxlog = 3)
+ 1.0
+ end
+
+ # dgeo_val and kpar_val: Connor et al. 2015 Eq. 59 geometric factor in the r_s reference and
+ # the Eq. 20 parallel-wavenumber gradient (see `toroidal_dgeo`, `toroidal_kpar`), derived
+ # whenever the surface carries a ResistGeometry; only dc_type=:toroidal consumes them.
+ kpar_val_k = if rg === nothing
+ dc_type === :toroidal && @warn(
+ "build_slayer_inputs: no ResistGeometry, so the toroidal critical-Δ χ∥ closure uses " *
+ "the cylindrical parallel wavenumber n·|s|/R₀.", maxlog = 1)
+ nothing
+ else
+ toroidal_kpar(; chi1=chi1, v1=rg.v1_local, q=q, q1=q1, n=n_res, avg_bsq=rg.avg_bsq, k_ref=k_ref_k)
+ end
+ dgeo_val_k = if dgeo_val === nothing
+ if rg !== nothing
+ toroidal_dgeo(; chi1=chi1, v1=rg.v1_local, q=q, q1=q1, n=n_res,
+ avg_bsq=rg.avg_bsq, avg_dpsisq=rg.avg_dpsisq, k_ref=k_ref_k)
+ elseif dc_type === :toroidal
+ throw(
+ ArgumentError(
+ "build_slayer_inputs: dc_type=:toroidal with " *
+ "dgeo_val=nothing requires `sing.restype` populated " *
+ "by ForceFreeStates.resist_eval_all!. " *
+ "Surface k=$k has restype=nothing."
+ )
+ )
+ else
+ 0.0
+ end
+ else
+ _eval(dgeo_val, psi)
+ end
+
+ alpha_k = if rg === nothing
+ @warn(
+ "build_slayer_inputs: sing.restype not populated; using the " *
+ "slab Mercier exponent α = 1/2 for the Δ' reference-length " *
+ "conversion at all such surfaces.", maxlog = 1)
+ 0.5
+ else
+ sqrt(max(-(rg.E + rg.F + rg.H - 0.25), 0.0))
+ end
+
+ out[k] = slayer_parameters(;
+ n_e=prof.n_e, t_e=prof.T_e, t_i=prof.T_i,
+ omega_e=ω_e_use, omega_i=ω_i_use,
+ qval=q, sval_r=sval_r, bt=_bt_at(psi),
+ rs=rs, R0=R0_use, mu_i=mu_i, mu_rho=_eval(mu_rho, psi), zeff=_eval(zeff, psi),
+ chi_perp_e=_eval(chi_perp_e, psi),
+ chi_tor=_eval(chi_tor, psi),
+ chi_perp_i=_eval(chi_perp_i, psi),
+ chi_perp_Dc=_eval(chi_perp_Dc, psi),
+ dlnn=kin.dn_e / kin.n_e, dlnTe=kin.dT_e / kin.T_e, dlnTi=kin.dT_i / kin.T_i,
+ tau_E=tau_E, a_minor=a_minor,
+ P_perp_model=P_perp_model,
+ m=m_res, n=n_res,
+ dr_val=dr_val_k,
+ dgeo_val=dgeo_val_k,
+ kpar_val=kpar_val_k,
+ dc_type=dc_type, ising=k,
+ resistivity_model=resistivity_model,
+ f_trap=f_trap,
+ nu_e_star=nu_e_star,
+ R_major_eff=R_major_eff,
+ lnLambda_form=lnLambda_form,
+ k_ref=k_ref_k,
+ alpha_mercier=alpha_k
+ )
+ end
+ return out
+end
+
+# Trapped fraction, electron collisionality and effective major radius of the neoclassical resistivity
+# closure at one surface, from its `ResistGeometry` when populated; `nothing` lets `surface_resistivity`
+# fall back to the ε = r_s/R form.
+function _resistivity_geometry(rg, n_e, T_e, q, zeff; resistivity_model::NeoResistivityModel, lnLambda_form::Symbol)
+ rg === nothing && return (f_trap=nothing, nu_e_star=nothing, R_major_eff=nothing)
+ nu_e_star = if resistivity_model isa Union{SpitzerModel,SpitzerHarmModel}
+ nothing
+ else
+ lnL = coulomb_log_e(n_e, T_e; form=lnLambda_form)
+ nu_star_e(n_e, T_e, rg.R_major, rg.eps_local, q, zeff; lnLamb=lnL)
+ end
+ return (f_trap=rg.f_trap, nu_e_star=nu_e_star, R_major_eff=rg.R_major)
+end
+
+"""
+ layer_resistivity(equil, sings, profiles::KineticProfiles; zeff=1.0, R0=nothing, rs_method=:midplane,
+ theta=0.0, q_beyond=nothing, resistivity_model=SauterNeoModel(), lnLambda_form=:nrl) -> Vector{Float64}
+
+Parallel resistivity η in Ω·m at each surface of `sings`, with the same closure and per-surface inputs
+`build_slayer_inputs` gives the SLAYER layer, so every resistive inner layer of a run sees one η.
+`zeff` is a scalar or a callable of ψ.
+"""
+function layer_resistivity(equil, sings, profiles::KineticProfiles;
+ zeff=1.0, R0=nothing, rs_method::Symbol=:midplane, theta::Real=0.0, q_beyond=nothing,
+ resistivity_model::NeoResistivityModel=SauterNeoModel(), lnLambda_form::Symbol=:nrl)
+ R0_use = R0 === nothing ? equil.ro : Float64(R0)
+ rs_at, _ = radial_label(equil; rs_method=rs_method, theta=theta, q_beyond=q_beyond)
+ return map(sings) do sing
+ psi = sing.psifac
+ prof = profiles(psi)
+ z = zeff isa Real ? Float64(zeff) : Float64(zeff(psi))
+ geometry = _resistivity_geometry(sing.restype, prof.n_e, prof.T_e, sing.q, z;
+ resistivity_model=resistivity_model, lnLambda_form=lnLambda_form)
+ surface_resistivity(; n_e=prof.n_e, t_e=prof.T_e, zeff=z, qval=sing.q, rs=rs_at(psi), R0=R0_use,
+ resistivity_model=resistivity_model, lnLambda_form=lnLambda_form, geometry...)
+ end
+end
diff --git a/src/InnerLayer/SLAYER/LayerParameters.jl b/src/InnerLayer/SLAYER/LayerParameters.jl
new file mode 100644
index 0000000000..639d4fd8f2
--- /dev/null
+++ b/src/InnerLayer/SLAYER/LayerParameters.jl
@@ -0,0 +1,415 @@
+# LayerParameters.jl
+#
+# `SLAYERParameters`: the dimensionless Fitzpatrick layer parameters of one rational surface, plus the dimensional
+# factors that convert normalized frequencies and Δ back to physical units.
+
+"""
+ SLAYERParameters
+
+Dimensionless layer-physics parameters at one rational surface for the
+Fitzpatrick two-fluid drift-MHD SLAYER inner-layer model (Fitzpatrick
+2023; Park 2022), plus dimensional auxiliaries required for
+de-normalization.
+
+| field | meaning |
+|:--------------- |:------------------------------------------------------------------------------------------------------------------------------------------------------- |
+| `ising` | Singular-surface index (traceability only) |
+| `m`, `n` | Poloidal / toroidal mode numbers at this surface |
+| `tau` | T_i / T_e |
+| `lu` | Lundquist number S = τ_R / τ_H |
+| `c_beta` | Compressibility √(β_local / (1 + β_local)) |
+| `D_norm` | (d_β/r_s) · S^(1/3) · √ι_e (Fitzpatrick normalized scale) |
+| `P_perp` | Perpendicular Prandtl number τ_R / τ_⊥ (set by `P_perp_model`) |
+| `P_tor` | Momentum Prandtl number τ_R / τ_φ, τ_φ = r_s²/χ_φ |
+| `Q_e` | Normalized electron diamagnetic: −tauk · ω_*e |
+| `Q_i` | Normalized ion diamagnetic: −tauk · ω_*i |
+| `iota_e` | Q_e / (Q_e − Q_i) |
+| `tauk` | Q-conversion factor S^(1/3) · τ_H [s] — multiplies ω to get Q |
+| `tau_r` | Resistive diffusion time [s] |
+| `delta_n` | Δ-normalization factor S^(1/3) / r_s [m⁻¹] |
+| `rs` | Minor radius at this surface [m] |
+| `R0` | Major radius [m] |
+| `bt` | Toroidal field [T] |
+| `sval_r` | r-based magnetic shear r_s · (dq/dr) / q (Fitzpatrick convention) |
+| `dr_val` | Resistive interchange D_R = E + F + H² (critical-Δ input; auto-derived from GGJ coefficients unless overridden) |
+| `dgeo_val` | Connor et al. 2015 Eq. 59 toroidal critical-Δ geometric factor in the r_s reference (see `toroidal_dgeo`) |
+| `kpar_val` | Parallel-wavenumber gradient K∥ [1/m] of the `:toroidal` χ∥ closure, k∥ = K∥·W_d (see `toroidal_kpar`); the cylindrical n·abs(s)/R₀ when not derived |
+| `eta` | Parallel resistivity entering τ_R = μ₀r_s²/η [Ω·m] |
+| `d_beta` | Beta-weighted ion length scale c_β · d_i [m] |
+| `dc_tmp` | Critical-Δ offset from chi_parallel matching (for `:toroidal`, W_d and the free-streaming χ∥ use `dgeo_val` and `kpar_val`) |
+| `dc_type` | Selector for `dc_tmp` formula |
+| `k_ref` | Reference-length ratio K = r_s · (dψ_N/dr) at this surface (1 = no Δ' conversion) |
+| `alpha_mercier` | Mercier Frobenius exponent α = √(−D_I) (Glasser-Greene-Johnson 1975 Eq. 48) governing the Δ' reference-length conversion (1/2 = slab/cylindrical value) |
+
+`k_ref` and `alpha_mercier` convert the ψ_N-referenced outer Δ' to the `x̂ = (r−r_s)/r_s` reference of the layer
+(`delta_prime_to_rs_reference` in the Tearing runner); the default `k_ref = 1` makes that the identity.
+
+The complex normalized growth rate `Q = ω + iγ` is **not** stored here;
+it is passed as a separate argument to `solve_inner`.
+"""
+Base.@kwdef struct SLAYERParameters <: InnerLayerParameters
+ # Surface identity
+ ising::Int = 0
+ m::Int = 0
+ n::Int = 0
+
+ # Normalized layer parameters consumed by riccati_f
+ tau::Float64
+ lu::Float64
+ c_beta::Float64
+ D_norm::Float64
+ P_perp::Float64
+ P_tor::Float64
+ Q_e::Float64
+ Q_i::Float64
+ iota_e::Float64
+
+ # Conversion factors (Q ↔ ω in rad/s)
+ tauk::Float64
+ tau_r::Float64
+ delta_n::Float64
+
+ # Geometric / fluid auxiliaries
+ rs::Float64
+ R0::Float64
+ bt::Float64
+ sval_r::Float64
+ dr_val::Float64 = 0.0
+ dgeo_val::Float64 = 0.0
+ kpar_val::Float64 = n * abs(sval_r) / R0
+ eta::Float64
+ d_beta::Float64
+
+ # Critical-Δ offset
+ dc_tmp::Float64 = 0.0
+ dc_type::Symbol = :none
+
+ # Reference-length conversion inputs for the outer Δ' (ψ_N → r_s-based x̂)
+ k_ref::Float64 = 1.0
+ alpha_mercier::Float64 = 0.5
+end
+
+# Allowed dc_type values for the critical-Δ offset (`:none` gives `dc_tmp = 0`).
+const ALLOWED_DC_TYPES = (:none, :lar, :fitzpatrick, :toroidal)
+
+"""
+ surface_resistivity(; n_e, t_e, zeff, qval, rs, R0, resistivity_model=SauterNeoModel(), lnLambda_form=:nrl,
+ f_trap=nothing, nu_e_star=nothing, R_major_eff=nothing, lnLamb=nothing) -> Float64
+
+Parallel resistivity η in Ω·m at a rational surface, the closure every resistive inner layer shares
+(n_e in m⁻³, t_e in eV). The model selects it:
+
+ - `SpitzerHarmModel()` -- Fitzpatrick Spitzer-Härm σ_∥; with `lnLambda_form = :wesson` this is
+ bit-identical to the legacy SLAYER η
+ - `SpitzerModel()` -- Sauter 18a fit (the legacy 1.65e-9 form under `:wesson`)
+ - `SauterNeoModel()` / `RedlNeoModel()` -- the F_33 trapped-particle correction using `f_trap` and
+ ν*_e, each from the caller (`ResistGeometry`) or else the ε = r_s/R form with R = `R_major_eff`
+ (default `R0`)
+"""
+function surface_resistivity(; n_e::Real, t_e::Real, zeff::Real, qval::Real, rs::Real, R0::Real,
+ resistivity_model::NeoResistivityModel=SauterNeoModel(), lnLambda_form::Symbol=:nrl,
+ f_trap::Union{Real,Nothing}=nothing, nu_e_star::Union{Real,Nothing}=nothing,
+ R_major_eff::Union{Real,Nothing}=nothing, lnLamb::Union{Real,Nothing}=nothing)
+ lnLamb = lnLamb === nothing ? coulomb_log_e(n_e, t_e; form=lnLambda_form) : lnLamb
+ resistivity_model isa SpitzerModel && lnLambda_form === :wesson && return 1.65e-9 * lnLamb / (t_e / 1e3)^1.5
+ resistivity_model isa Union{SpitzerModel,SpitzerHarmModel} &&
+ return eta_neoclassical(resistivity_model, n_e, t_e, zeff, 0.0, 0.0; lnLamb=lnLamb)
+ R_eff = R_major_eff === nothing ? R0 : Float64(R_major_eff)
+ eps_here = clamp(rs / R_eff, 1e-6, 1.0 - 1e-6)
+ ft_here = f_trap === nothing ? trapped_fraction_eps(eps_here) : Float64(f_trap)
+ nue_here = nu_e_star === nothing ? nu_star_e(n_e, t_e, R_eff, eps_here, qval, zeff; lnLamb=lnLamb) : Float64(nu_e_star)
+ return eta_neoclassical(resistivity_model, n_e, t_e, zeff, ft_here, nue_here; lnLamb=lnLamb)
+end
+
+# Allowed P_perp_model values selecting how P_perp is built.
+const ALLOWED_P_PERP_MODELS = (:chi_perp_e, :chi_perp_i, :P_phi, :D_perp, :c_beta, :tau_E)
+
+"""
+ r_based_shear(rs, q, dq_dpsi, da_dpsi) -> Float64
+
+Convert a ψ-based shear to the r-based (Fitzpatrick) convention used throughout SLAYER:
+
+```
+s_r = r_s · (dq/dr) / q = r_s · (dq/dψ) / (q · da/dψ)
+```
+
+`dq_dpsi` and `da_dpsi` (minor radius) must be taken with respect to the **same** ψ, normalized or physical;
+the conversion factor cancels in the ratio.
+"""
+function r_based_shear(rs::Real, q::Real, dq_dpsi::Real, da_dpsi::Real)
+ da_dpsi != 0 || throw(ArgumentError("r_based_shear: da/dψ must be non-zero"))
+ q != 0 || throw(ArgumentError("r_based_shear: q must be non-zero"))
+ return rs * dq_dpsi / (q * da_dpsi)
+end
+
+# Internal: solve the Wd self-consistency loop for the chi_parallel-based critical Δ. W_d and the
+# smfp/lmfp chi_parallel blend follow Fitzpatrick, Phys. Plasmas 32, 062509 (2025); the toroidal and
+# large-aspect-ratio offsets are Connor, Ham, Hastie & Liu, PPCF 57, 065001 (2015) Eqs. (59) and (61),
+# after Lütjens, Luciani & Garbet, Phys. Plasmas 8, 4267 (2001). Returns dc_tmp as a Float64.
+function _solve_dc_tmp(; dc_type::Symbol, dr_val::Real, dgeo_val::Real,
+ chi_perp_e::Real, t_e::Real, zeff::Real, tau_ee::Real,
+ rs::Real, R0::Real, sval_r::Real, n_tor::Integer,
+ kpar_val::Union{Real,Nothing}=nothing,
+ max_iter::Integer=100, tol::Real=1e-10)
+ dc_type in ALLOWED_DC_TYPES ||
+ throw(ArgumentError("SLAYERParameters: unknown dc_type=$dc_type. " *
+ "Allowed: $(ALLOWED_DC_TYPES)"))
+ (dc_type === :none || dr_val == 0.0 || (dc_type === :toroidal && dgeo_val == 0.0)) && return 0.0
+
+ vte = sqrt(2.0 * t_e * E_CHG / M_E)
+ chi_par_smfp = (1.581 * tau_ee * vte^2) / (1.0 + 0.2535 * zeff)
+
+ # W_d balance χ∥k∥² = χ⊥k⊥² (Fitzpatrick 1995 Sec. VII): W_d = √8·(χ⊥/χ∥)^¼/g_w, free-streaming k∥ = K∥·W_d.
+ # Cylindrical g_w = √(n|s|r_s/R₀), K∥ = n|s|/R₀; :toroidal uses Connor et al. 2015 Eqs. 20/59 (toroidal_dgeo/kpar).
+ kpar_cyl = n_tor * abs(sval_r) / R0
+ g_w, kpar = if dc_type === :toroidal
+ (dgeo_val, kpar_val === nothing ? kpar_cyl : kpar_val)
+ else
+ (sqrt((rs / R0) * abs(sval_r) * n_tor), kpar_cyl)
+ end
+ isfinite(g_w) && g_w > 0 && isfinite(kpar) && kpar > 0 ||
+ throw(ArgumentError("SLAYERParameters: the $dc_type critical Δ needs a positive, finite geometric factor and K∥; " *
+ "got g_w = $g_w, K∥ = $kpar"))
+
+ Wd = 0.1
+ converged = false
+ for _ in 1:max_iter
+ chi_par_lmfp = (2.0 * vte) / (sqrt(π) * kpar * Wd)
+ chi_par = (chi_par_smfp * chi_par_lmfp) /
+ (chi_par_smfp + chi_par_lmfp)
+ Wd_new = sqrt(8.0) * (chi_perp_e / chi_par)^0.25 / g_w
+ if abs(Wd_new - Wd) / max(abs(Wd), 1e-30) < tol
+ Wd = Wd_new
+ converged = true
+ break
+ end
+ Wd = Wd_new
+ end
+ converged || error("SLAYERParameters: Wd iteration failed to converge")
+
+ chi_par_lmfp = (2.0 * vte) / (sqrt(π) * kpar * Wd)
+ chi_par = (chi_par_smfp * chi_par_lmfp) / (chi_par_smfp + chi_par_lmfp)
+
+ if dc_type === :lar
+ return 0.5 * (-dr_val) * π^1.5 *
+ (chi_par / chi_perp_e)^0.25 *
+ sqrt((n_tor * abs(sval_r)) / (R0 * rs))
+ elseif dc_type === :fitzpatrick
+ return -(sqrt(2.0) * π^1.5 * dr_val) / Wd
+ elseif dc_type === :toroidal
+ return 0.5 * (-dr_val) * π^1.5 *
+ (chi_par / chi_perp_e)^0.25 * dgeo_val
+ end
+ return 0.0
+end
+
+"""
+ slayer_parameters(; n_e, t_e, t_i, omega_e, omega_i, qval, sval_r, bt, rs, R0, mu_i, zeff, chi_perp_e, chi_tor, m, n,
+ mu_rho=mu_i, chi_perp_i=nothing, tau_E=nothing, a_minor=nothing, dlnn=nothing, dlnTe=nothing, dlnTi=nothing,
+ P_perp_model=:D_perp, chi_perp_Dc=nothing, dr_val=0.0, dgeo_val=0.0, kpar_val=nothing,
+ dc_type=:none, ising=0, resistivity_model=SauterNeoModel(), f_trap=nothing, nu_e_star=nothing,
+ R_major_eff=nothing, lnLambda_form=:nrl, k_ref=1.0, alpha_mercier=0.5) -> SLAYERParameters
+
+Build the `SLAYERParameters` of one rational surface from dimensional equilibrium and kinetic-profile inputs, in the
+Fitzpatrick two-fluid layer parametrization. The diamagnetic frequencies normalize as `Q_e = -tauk·ω_*e`, `Q_i = -tauk·ω_*i`,
+so the usual ω_*e < 0 < ω_*i gives `Q_e > 0 > Q_i`; they must have opposite signs (`iota_e > 0`). An input the selected
+model does not use may be left `nothing`; one it uses must be given, positive and finite.
+
+# Arguments
+
+ - `n_e` -- electron density in m⁻³
+
+ - `t_e`, `t_i` -- electron and ion temperatures in eV
+ - `omega_e`, `omega_i` -- electron and ion diamagnetic frequencies in rad/s
+ - `qval` -- safety factor at the surface
+ - `sval_r` -- **r-based** magnetic shear r·(dq/dr)/q (Fitzpatrick); convert a ψ-based shear with `r_based_shear`
+ - `bt` -- toroidal field in T
+ - `rs`, `R0` -- minor radius at the surface and major radius, in m
+ - `mu_i` -- main-ion mass in proton masses (2.0 for D), for the ion sound radius and skin depth
+ - `mu_rho` -- mean ion mass per electron in proton masses, for the mass density ρ = mu_rho·m_p·n_e (default `mu_i`)
+ - `zeff` -- effective charge
+ - `chi_perp_e`, `chi_tor` -- electron perpendicular heat and toroidal momentum diffusivities in m²/s
+ - `m`, `n` -- poloidal and toroidal mode numbers
+ - `chi_perp_i` -- ion perpendicular heat diffusivity in m²/s; needed by `P_perp_model = :chi_perp_i` and `:D_perp`
+ - `tau_E` -- whole-plasma energy confinement time τ̄_E in s; needed by `:tau_E`
+ - `a_minor` -- plasma minor radius `a` in m; needed by `:tau_E`
+ - `dlnn`, `dlnTe`, `dlnTi` -- radial log-gradients of n, T_e, T_i in any common radial variable (only ratios enter); needed by `:D_perp`
+ - `P_perp_model` -- how `P_perp` is built (default `:D_perp`, as in the `[SLAYER]` deck):
+
+ + `:D_perp` -- τ_R/τ_⊥ with τ_⊥ = r_s²/D_⊥, Fitzpatrick, Phys. Plasmas 29, 032507 (2022), Eq. 16 (with Eqs. 4-6 and
+ η_⊥ = η_∥); its τ = (T_e/T_i)(1+η_e)/(1+η_i) is the inverse of the `tau` field; flat temperatures give the `:c_beta` value
+ + `:chi_perp_e`, `:chi_perp_i` -- τ_R·χ⊥/r_s² with the electron or ion χ⊥
+ + `:P_phi` -- P_perp = P_tor (Fitzpatrick, Phys. Plasmas 30, 092512 (2023), Eq. 143)
+ + `:c_beta` -- P_perp = c_β² (J.-K. Park, Phys. Plasmas 29, 072506 (2022), Eq. 9 with K = 0), the χ⊥ → 0 limit of `:D_perp`
+ + `:tau_E` -- P_perp = P_tor = τ_R/τ_E(r_s) from a uniform χ_E = κ_e a²/τ̄_E with κ_e = 3/16 for T_e ∝ 1 − r̂² (Fitzpatrick 2023,
+ Eqs. 37-38, 81-83 and 131; other profile shapes change κ_e by a factor 2-3); `chi_tor` is ignored
+ - `chi_perp_Dc` -- electron χ⊥ in m²/s used only by the critical Δ; `nothing` uses `chi_perp_e`, which otherwise sets `dc_tmp` in every mode
+ - `dr_val` -- resistive interchange index `D_R` of the critical Δ
+ - `dgeo_val` -- Connor et al. 2015 Eq. 59 toroidal geometric factor in the `r_s` reference (`toroidal_dgeo`)
+ - `kpar_val` -- parallel-wavenumber gradient K∥ in 1/m of the `:toroidal` χ∥ closure (`toroidal_kpar`); `nothing` uses `n·|s|/R₀`
+ - `dc_type` -- critical-Δ formula: `:none`, `:lar`, `:fitzpatrick` or `:toroidal`
+ - `ising` -- singular-surface index, for traceability
+ - `resistivity_model` -- η closure setting τ_R = μ₀r_s²/η and hence S: `SauterNeoModel()` (default, Sauter 1999 F_33),
+ `RedlNeoModel()`, `SpitzerModel()` or `SpitzerHarmModel()` (with `lnLambda_form = :wesson` reproduces the legacy SLAYER τ_R)
+ - `f_trap`, `nu_e_star` -- trapped fraction and ν*_e for the neoclassical models; `nothing` uses the Lin-Liu-Miller ε-only form
+ and Sauter 1999 Eq. 18b with ε = `rs / R_major_eff`
+ - `R_major_eff` -- ⟨R⟩ at the surface for the ν*_e formula (default `R0`)
+ - `lnLambda_form` -- Coulomb-log form: `:nrl` (default), `:sauter` or `:wesson`
+ - `k_ref` -- K = r_s·(dψ_N/dr), converting the ψ_N-referenced outer Δ' to the r_s reference (default 1, no conversion)
+ - `alpha_mercier` -- Mercier exponent α = √(−D_I) of the same conversion (default 0.5, the slab value)
+"""
+function slayer_parameters(;
+ n_e::Real, t_e::Real, t_i::Real,
+ omega_e::Real, omega_i::Real,
+ qval::Real, sval_r::Real, bt::Real,
+ rs::Real, R0::Real, mu_i::Real, zeff::Real,
+ chi_perp_e::Real, chi_tor::Real,
+ m::Integer, n::Integer,
+ mu_rho::Real=mu_i,
+ chi_perp_i::Union{Real,Nothing}=nothing, tau_E::Union{Real,Nothing}=nothing, a_minor::Union{Real,Nothing}=nothing,
+ dlnn::Union{Real,Nothing}=nothing, dlnTe::Union{Real,Nothing}=nothing, dlnTi::Union{Real,Nothing}=nothing,
+ P_perp_model::Symbol=:D_perp, chi_perp_Dc::Union{Real,Nothing}=nothing,
+ dr_val::Real=0.0, dgeo_val::Real=0.0,
+ kpar_val::Union{Real,Nothing}=nothing,
+ dc_type::Symbol=:none, ising::Integer=0,
+ resistivity_model::NeoResistivityModel=SauterNeoModel(),
+ f_trap::Union{Real,Nothing}=nothing,
+ nu_e_star::Union{Real,Nothing}=nothing,
+ R_major_eff::Union{Real,Nothing}=nothing,
+ lnLambda_form::Symbol=:nrl,
+ k_ref::Real=1.0,
+ alpha_mercier::Real=0.5)
+
+ # Coulomb logarithm shared by the resistivity closure and τ_ee.
+ lnLamb = coulomb_log_e(n_e, t_e; form=lnLambda_form)
+
+ eta = surface_resistivity(; n_e=n_e, t_e=t_e, zeff=zeff, qval=qval, rs=rs, R0=R0,
+ resistivity_model=resistivity_model, lnLambda_form=lnLambda_form, f_trap=f_trap, nu_e_star=nu_e_star,
+ R_major_eff=R_major_eff, lnLamb=lnLamb)
+
+ # Basic plasma quantities
+ tau = t_i / t_e
+ rho = mu_rho * M_P * n_e
+
+ # Electron-electron collision time, used by the χ_∥-matching critical Δ whatever the resistivity model.
+ tau_ee = tau_ee_spitzer_harm(n_e, t_e; lnLamb=lnLamb)
+
+ # Length scales and fundamental timescales.
+ rho_s = 1.02e-4 * sqrt(mu_i * t_e) / bt # ion Larmor [m]
+ d_i = sqrt((mu_i * M_P) / (n_e * E_CHG^2 * MU_0)) # ion skin depth [m]
+
+ # Alfvén time from the r-based shear; |s| since the layer depends only on |dq/dr| and s < 0 would make lu < 0.
+ tau_h = R0 * sqrt(MU_0 * rho) / (n * abs(sval_r) * bt)
+ # Resistive diffusion time τ_R = μ₀ r_s² / η (Fitzpatrick 2023).
+ tau_r = MU_0 * rs^2 / eta
+
+ # Lundquist number and Q-conversion factor
+ lu = tau_r / tau_h
+ tauk = lu^(1.0 / 3.0) * tau_h # = Qconv
+
+ # Normalized diamagnetic frequencies Q = -tauk·ω (sign convention in the docstring).
+ Q_e = -tauk * omega_e
+ Q_i = -tauk * omega_i
+ Q_e_minus_Q_i = Q_e - Q_i
+ # iota_e is singular for degenerate ω_*e == ω_*i, and the Riccati coefficients divide by it.
+ Q_e_minus_Q_i != 0 ||
+ throw(
+ ArgumentError(
+ "slayer_parameters: Q_e == Q_i (degenerate " *
+ "electron/ion diamagnetic frequencies) makes " *
+ "iota_e = Q_e/(Q_e - Q_i) singular. Check the " *
+ "diamagnetic-frequency inputs ω_*e, ω_*i."
+ )
+ )
+ iota_e = Q_e / Q_e_minus_Q_i
+ iota_e > 0 ||
+ throw(
+ ArgumentError(
+ "slayer_parameters: iota_e = Q_e/(Q_e - Q_i) = $iota_e is " *
+ "not positive, so the ion-sound-radius normalization " *
+ "D_norm = (d_beta/r_s)·S^(1/3)·sqrt(iota_e) is undefined. " *
+ "Check the diamagnetic-frequency inputs ω_*e, ω_*i — they " *
+ "are expected to carry opposite signs."
+ )
+ )
+
+ # Plasma beta and compressibility
+ lbeta = (5.0 / 3.0) * MU_0 * n_e * E_CHG * (t_e + t_i) / bt^2
+ c_beta = sqrt(lbeta / (1.0 + lbeta))
+
+ # Effective Prandtl-like transport ratios. A diffusivity the model uses must be given, finite and positive.
+ _need(name, v) = (v !== nothing && isfinite(v) && v > 0) ||
+ throw(ArgumentError("slayer_parameters: P_perp_model=:$P_perp_model needs a positive, finite $name; got $v"))
+ _need("chi_perp_e", chi_perp_e)
+ P_perp_model === :tau_E || _need("chi_tor", chi_tor)
+ P_perp_model in (:chi_perp_i, :D_perp) && _need("chi_perp_i", chi_perp_i)
+ chi_perp_Dc === nothing || (isfinite(chi_perp_Dc) && chi_perp_Dc > 0) ||
+ throw(ArgumentError("slayer_parameters: chi_perp_Dc must be positive and finite when given; got $chi_perp_Dc"))
+ tau_tor = rs^2 / chi_tor
+ P_tor = tau_r / tau_tor
+ if P_perp_model === :tau_E
+ _need("tau_E", tau_E)
+ _need("a_minor", a_minor)
+ # Fitzpatrick 2023, Eqs. 37-38, 81-83 and 131.
+ chi_E = (3 / 16) * a_minor^2 / tau_E
+ P_tor = tau_r / (rs^2 / chi_E)
+ end
+ P_perp = if P_perp_model === :chi_perp_e
+ tau_r / (rs^2 / chi_perp_e)
+ elseif P_perp_model === :chi_perp_i
+ tau_r / (rs^2 / chi_perp_i)
+ elseif P_perp_model === :P_phi || P_perp_model === :tau_E
+ P_tor
+ elseif P_perp_model === :D_perp
+ # Fitzpatrick, Phys. Plasmas 29, 032507 (2022), Eqs. 4-6 and 16 with η_⊥ = η_∥, written over the pressure gradient p′/n.
+ all(x -> x !== nothing && isfinite(x), (dlnn, dlnTe, dlnTi)) ||
+ throw(ArgumentError("slayer_parameters: P_perp_model=:D_perp needs finite dlnn, dlnTe and dlnTi; got $dlnn, $dlnTe, $dlnTi"))
+ dp = t_e * (dlnn + dlnTe) + t_i * (dlnn + dlnTi)
+ dp != 0 || throw(
+ ArgumentError(
+ "slayer_parameters: P_perp_model=:D_perp is undefined where the pressure gradient vanishes " *
+ "(t_e(dlnn+dlnTe) + t_i(dlnn+dlnTi) = 0); choose another P_perp_model for this surface"
+ )
+ )
+ D_perp = c_beta^2 * eta / MU_0 +
+ (2 / 3) * (1 - c_beta^2) * (t_e * dlnTe * chi_perp_e + t_i * dlnTi * chi_perp_i) / dp
+ tau_r / (rs^2 / D_perp)
+ elseif P_perp_model === :c_beta
+ c_beta^2
+ else
+ throw(ArgumentError("slayer_parameters: unknown P_perp_model=$P_perp_model. " *
+ "Allowed: $(ALLOWED_P_PERP_MODELS)"))
+ end
+ isfinite(P_perp) && P_perp > 0 ||
+ throw(
+ ArgumentError(
+ "slayer_parameters: P_perp_model=:$P_perp_model gave P_perp=$P_perp; check its inputs " *
+ "(chi_perp_e=$chi_perp_e, chi_perp_i=$chi_perp_i, dlnn=$dlnn, dlnTe=$dlnTe, dlnTi=$dlnTi)"
+ )
+ )
+
+ # Normalized beta-related width and Δ-normalization
+ d_beta = c_beta * d_i
+ D_norm = (d_beta / rs) * lu^(1.0 / 3.0) * sqrt(iota_e)
+ delta_n = lu^(1.0 / 3.0) / rs
+
+ # Critical-Δ offset from chi_parallel matching; its χ⊥,e is chi_perp_Dc when given
+ dc_tmp = _solve_dc_tmp(; dc_type=dc_type, dr_val=dr_val, dgeo_val=dgeo_val,
+ chi_perp_e=chi_perp_Dc === nothing ? chi_perp_e : chi_perp_Dc, t_e=t_e, zeff=zeff,
+ tau_ee=tau_ee, rs=rs, R0=R0, sval_r=sval_r,
+ n_tor=n, kpar_val=kpar_val)
+
+ return SLAYERParameters(;
+ ising=ising, m=m, n=n,
+ tau=tau, lu=lu, c_beta=c_beta, D_norm=D_norm,
+ P_perp=P_perp, P_tor=P_tor,
+ Q_e=Q_e, Q_i=Q_i, iota_e=iota_e,
+ tauk=tauk, tau_r=tau_r, delta_n=delta_n,
+ rs=rs, R0=R0, bt=bt, sval_r=sval_r,
+ dr_val=dr_val, dgeo_val=dgeo_val,
+ kpar_val=kpar_val === nothing ? n * abs(sval_r) / R0 : kpar_val,
+ eta=eta, d_beta=d_beta,
+ dc_tmp=dc_tmp, dc_type=dc_type,
+ k_ref=k_ref, alpha_mercier=alpha_mercier
+ )
+end
diff --git a/src/InnerLayer/SLAYER/LayerThickness.jl b/src/InnerLayer/SLAYER/LayerThickness.jl
new file mode 100644
index 0000000000..a7fca7096f
--- /dev/null
+++ b/src/InnerLayer/SLAYER/LayerThickness.jl
@@ -0,0 +1,197 @@
+# LayerThickness.jl
+#
+# Resistive inner-layer *width* (del_s) diagnostic for the SLAYER two-fluid drift-MHD slab layer (Fitzpatrick,
+# Tearing Mode Dynamics in Tokamak Plasmas, IOP 2023; Park 2022, Phys. Plasmas 29, 072506; Burgess et al. 2026).
+# Distinct from the matching Δ of Riccati.jl: a reduced Riccati ODE at the electron diamagnetic frequency gives the
+# ratio delta_s/d_beta, which depends only on Q_e, P_perp, P_tor, tau and D_norm.
+
+using OrdinaryDiffEq
+
+# ---------------------------------------------------------------------
+# Pre-computed q-independent constants for the del_s Riccati ODE.
+# Normalisation block:
+# Q_hat = (Q_e (1+tau)/tau) / D_norm^4
+# P_perp_hat = P_perp / D_norm^6
+# P_tor_hat = P_tor / D_norm^6
+# `one_plus = 1 + 1/tau`, `inv_c = 1/(1+1/tau)` recur in E, F and the
+# boundary/extraction prefactor, so they are cached here too.
+# ---------------------------------------------------------------------
+struct _DelSConsts
+ Q_hat::Float64 # normalised electron diamagnetic frequency
+ Pperp_hat::Float64 # normalised perpendicular Prandtl number
+ Ptor_hat::Float64 # normalised toroidal Prandtl number
+ one_plus::Float64 # 1 + 1/tau
+ inv_c::Float64 # 1 / (1 + 1/tau)
+end
+
+@inline function _build_dels_consts(p::SLAYERParameters)
+ one_plus = 1.0 + 1.0 / p.tau # (1+tau)/tau
+ D2 = p.D_norm * p.D_norm
+ D4 = D2 * D2
+ D6 = D4 * D2
+ return _DelSConsts(
+ (p.Q_e * one_plus) / D4,
+ p.P_perp / D6,
+ p.P_tor / D6,
+ one_plus,
+ 1.0 / one_plus
+ )
+end
+
+# Scalar ODE right-hand side dW/dq of the del_s Riccati; E and F are complex through the `im·Q_hat` terms.
+@inline function _dels_rhs(W::Number, c::_DelSConsts, q::Real)
+ q2 = q * q
+ q4 = q2 * q2
+ E = -(c.Q_hat^2) * c.inv_c -
+ im * c.Q_hat * (c.Pperp_hat + c.Ptor_hat) * q2 +
+ c.Pperp_hat * c.Ptor_hat * q4
+ F = c.Pperp_hat - im * c.Q_hat + c.one_plus * c.Ptor_hat * q2
+ return W / q - (W * W) / q + (q * E) / F
+end
+
+# Analytic Jacobian dF/dW: the q·E/F term is W-independent, leaving
+# d/dW(W/q - W²/q) = 1/q - 2W/q.
+@inline _dels_jac(W::Number, c::_DelSConsts, q::Real) = 1.0 / q - 2.0 * W / q
+
+"""
+ riccati_del_s(p::SLAYERParameters;
+ q_start=5*p.D_norm, q_min=1e-5,
+ reltol=1e-10, abstol=1e-10, maxiters=50_000,
+ solver=Rodas5P(autodiff=false)) -> ComplexF64
+
+Solve the SLAYER `del_s` inner-layer Riccati ODE and return the
+**dimensionless** layer-thickness ratio `δ_s / d_β` at one rational
+surface.
+
+Integrates `dW/dq = W/q − W²/q + q·E/F` inward from `q_start = 5·D_norm`
+to `q_min`, with asymptotic boundary value `W = −α·q_start² − 0.5`,
+`α = √(P̂_⊥ / (1 + 1/τ))`. The result is
+`−(π / √(1 + 1/τ)) · W′(q_min)`, evaluated from a single RHS call at the
+inner endpoint.
+
+Returns `NaN + NaN·im` if the stiff integration does not converge (the
+caller treats this as a missing diagnostic rather than a hard error).
+
+Multiply the result by `p.d_beta` to obtain the resistive layer
+thickness in meters (see [`slayer_layer_thickness`](@ref)).
+"""
+function riccati_del_s(p::SLAYERParameters;
+ q_start::Real=5.0 * p.D_norm,
+ q_min::Real=1e-5,
+ reltol::Real=1e-10,
+ abstol::Real=1e-10,
+ maxiters::Integer=50_000,
+ solver=Rodas5P(; autodiff=false))
+ if !(q_start > q_min)
+ @debug "riccati_del_s: degenerate integration span" q_start q_min p.D_norm
+ return ComplexF64(NaN, NaN)
+ end
+
+ c = _build_dels_consts(p)
+
+ # Asymptotic boundary condition at large q (α and W₀ are real).
+ α = sqrt(c.Pperp_hat * c.inv_c)
+ W0 = ComplexF64(-α * q_start^2 - 0.5)
+
+ f = ODEFunction{false}(_dels_rhs; jac=_dels_jac)
+ prob = ODEProblem(f, W0, (q_start, q_min), c)
+ sol = solve(prob, solver;
+ reltol=reltol, abstol=abstol, maxiters=maxiters,
+ save_everystep=false, dense=false)
+
+ if sol.retcode != ReturnCode.Success
+ @debug "SLAYER riccati_del_s did not return Success" sol.retcode
+ return ComplexF64(NaN, NaN)
+ end
+
+ W_end = sol.u[end]
+ dW_end = _dels_rhs(W_end, c, q_min)
+ return -(π / sqrt(c.one_plus)) * dW_end
+end
+
+"""
+ LayerWidths
+
+Resistive inner-layer length scales at one rational surface, in meters.
+The primary quantity is `delta_s_m`, the resistive layer thickness from
+the SLAYER `del_s` Riccati solve; `d_beta` is the β-weighted ion scale it
+is built from, retained as a drift-scale reference.
+
+# Fields
+
+ - `ising`, `m`, `n` -- surface index and mode numbers (traceability)
+ - `dels_db` -- dimensionless `δ_s / d_β` from [`riccati_del_s`](@ref)
+ - `delta_s` -- complex layer thickness `δ_s = dels_db · d_β` [m]
+ - `delta_s_m` -- `|δ_s|`, the resistive layer thickness in meters (primary)
+ - `d_beta` -- β-weighted ion scale `c_β·d_i` in meters (drift reference)
+ - `delta_norm` -- layer normalization length `r_s · S^(-1/3)` in meters (`Δ̂' = Δ'·delta_norm`), the reciprocal of
+ `SLAYERParameters.delta_n`, shared by all four regimes of Burgess et al. (2026) Eqs. (10)-(13); **not** the
+ Furth-Killeen-Rosenbluth `S^(-2/5)` tearing width
+ - `delta_dr` -- diffusive-resistive layer thickness in meters, Fitzpatrick (2025) Eq. (100), equal to
+ `rs · lu^(-1/2) P_perp^(1/4) / d_beta_hat^(1/2)` with `d_beta_hat = d_beta/rs` (SLAYER's `lu` already carries the paper's
+ `(n|s|)^(1/2)`). Strong shear forces edge layers into this (`nu = 1/4`) regime, so it is the width the edge overlap
+ criterion compares against surface spacing
+ - `delta_visco` -- viscous-resistive scale `delta_norm · P_perp^(1/6)` in meters,
+ from the `P^(1/6)` broadening of the VR-regime growth rate, Burgess et al.
+ (2026) Eq. (11). The paper gives the growth rate rather than an explicit width;
+ this is the corresponding length
+
+`delta_s_m` should sit within a few orders of magnitude of `d_beta` for a
+well-posed surface (`dels_db` is O(1)); a large gap flags a normalisation
+or input problem.
+"""
+struct LayerWidths
+ ising::Int
+ m::Int
+ n::Int
+ dels_db::ComplexF64
+ delta_s::ComplexF64
+ delta_s_m::Float64
+ d_beta::Float64
+ delta_norm::Float64
+ delta_visco::Float64
+ delta_dr::Float64
+end
+
+"""
+ slayer_algebraic_widths(p::SLAYERParameters) -> (; delta_norm, delta_visco, delta_dr)
+
+The three comparison scales that follow from `p` alone, with no Riccati solve. `delta_dr` is
+the channel the resistive-layer overlap criterion uses, so a scan needs only this.
+"""
+function slayer_algebraic_widths(p::SLAYERParameters)
+ # Layer normalization length: exactly 1/delta_n (delta_n = S^(1/3)/r_s), computed
+ # from rs and lu so it reads as a length. Burgess et al. (2026), the Δ̂' = Δ'/S^(1/3)
+ # normalization preceding Eq. (10).
+ delta_norm = p.rs * p.lu^(-1.0 / 3.0)
+ # Viscous-resistive broadening, P^(1/6) coefficient of Burgess et al. (2026) Eq. (11).
+ delta_visco = delta_norm * p.P_perp^(1.0 / 6.0)
+ # Diffusive-resistive width, Fitzpatrick (2025) Eq. (100). The paper's tau_A (Eq. 74) has no shear, while SLAYER's
+ # tau_h divides by n|s|, so lu = (n|s|)·tau_R/tau_A already supplies Eq. (100)'s (n|s|)^(-1/2).
+ d_beta_hat = p.d_beta / p.rs
+ delta_dr = d_beta_hat > 0 ? p.rs * p.lu^(-0.5) * p.P_perp^(0.25) / sqrt(d_beta_hat) : NaN
+ return (; delta_norm, delta_visco, delta_dr)
+end
+
+"""
+ slayer_layer_thickness(p::SLAYERParameters; kwargs...) -> LayerWidths
+
+Compute the resistive inner-layer thickness in meters at one rational
+surface.
+
+Runs [`riccati_del_s`](@ref) for the dimensionless `δ_s / d_β` and scales
+by `p.d_beta` to obtain `δ_s` in meters. Keyword arguments are forwarded
+to `riccati_del_s`.
+
+The algebraic comparison scales `delta_norm`, `delta_visco` and `delta_dr` come from `p`
+directly and do not depend on the Riccati solve; [`slayer_algebraic_widths`](@ref) returns
+just those, for callers that do not need `delta_s`.
+"""
+function slayer_layer_thickness(p::SLAYERParameters; kwargs...)
+ dels_db = riccati_del_s(p; kwargs...)
+ delta_s = dels_db * p.d_beta
+ w = slayer_algebraic_widths(p)
+ return LayerWidths(p.ising, p.m, p.n,
+ dels_db, delta_s, abs(delta_s),
+ p.d_beta, w.delta_norm, w.delta_visco, w.delta_dr)
+end
diff --git a/src/InnerLayer/SLAYER/Riccati.jl b/src/InnerLayer/SLAYER/Riccati.jl
new file mode 100644
index 0000000000..05cceb9733
--- /dev/null
+++ b/src/InnerLayer/SLAYER/Riccati.jl
@@ -0,0 +1,183 @@
+# Riccati.jl
+#
+# Inner-layer Δ from the Fitzpatrick two-fluid drift-MHD layer Riccati ODE (Fitzpatrick, Tearing Mode Dynamics in
+# Tokamak Plasmas, IOP 2023; Park 2022, Phys. Plasmas 29, 072506; Burgess et al. 2026) for the pressureless tearing
+# channel (no parallel flow, pe = 0), keeping the full C(p) form in every regime.
+#
+# The layer is evaluated at Fitzpatrick's normalized eigenvalue ĝ = (γ − iω)·τ_k: `solve_inner` takes the
+# growth rate s = γ − iω (ĝ = s·τ_k) and `layer_response` the dispersion scans' Q = (ω + iγ)·τ_k (ĝ = −i·Q).
+# Only the `tearing` channel of the returned `InnerLayerResponse` is populated; the interchange channel is zero.
+
+using OrdinaryDiffEq
+
+# ---------------------------------------------------------------------
+# Coefficients of the two-fluid layer A, B, C terms (Fitzpatrick 2023).
+# ---------------------------------------------------------------------
+
+# x-independent constants of the Riccati ODE, built once per solve from (p, ĝ) and passed as the integrator `params`.
+struct _RiccatiConsts
+ g_minus_iQe::ComplexF64 # constant part of denom = g − iQe + x²
+ A::ComplexF64 # g·(g − iQi) — fB constant term
+ B::ComplexF64 # (g − iQi)·(P_perp + P_tor) — fB · x² coefficient
+ C::Float64 # P_perp · P_tor — fB · x⁴ coefficient
+ E::ComplexF64 # (g − iQi) · D² + P_perp — fC · x² coefficient
+ G::Float64 # P_tor · D² / iota_e — fC · x⁴ coefficient
+end
+
+@inline function _build_riccati_consts(p::SLAYERParameters, g::ComplexF64)
+ g_minus_iQe = g - im * p.Q_e
+ g_minus_iQi = g - im * p.Q_i
+ D2 = p.D_norm * p.D_norm
+ return _RiccatiConsts(
+ g_minus_iQe,
+ g * g_minus_iQi, # A
+ g_minus_iQi * (p.P_perp + p.P_tor), # B
+ p.P_perp * p.P_tor, # C
+ p.P_perp + g_minus_iQi * D2, # E
+ p.P_tor * D2 / p.iota_e # G
+ )
+end
+
+# Riccati RHS coefficients fA, fA', fB, fC at x.
+@inline function _riccati_f_coeffs(c::_RiccatiConsts, x::Real)
+ p2 = x * x
+ p4 = p2 * p2
+ denom = c.g_minus_iQe + p2
+
+ fA = p2 / denom
+ # (denom − 2p²)/denom, not the equal 1 − 2·fA: the identity drifts ~3e-3 relative near marginal stability.
+ fA_prime = (denom - 2 * p2) / denom
+
+ fB = c.A + c.B * p2 + c.C * p4
+ fC = c.g_minus_iQe + c.E * p2 + c.G * p4
+
+ return fA, fA_prime, fB, fC
+end
+
+# Scalar ODE right-hand side dW/dp; a scalar `ComplexF64` state keeps the integrator allocation-free.
+@inline function _riccati_f_rhs(W::Number, consts::_RiccatiConsts, x::Real)
+ fA, fA_prime, fB, fC = _riccati_f_coeffs(consts, x)
+ return -(fA_prime / x) * W - W * W / x + (fB / (fA * fC)) * (x * x * x)
+end
+
+# Analytic 1×1 Jacobian of the Riccati RHS (only the W-dependent terms survive).
+@inline function _riccati_f_jac(W::Number, consts::_RiccatiConsts, x::Real)
+ p2 = x * x
+ denom = consts.g_minus_iQe + p2
+ fA_prime = (denom - 2 * p2) / denom
+ return -(fA_prime / x) - 2 * W / x
+end
+
+# ---------------------------------------------------------------------
+# Boundary-condition selection (large-p asymptotics, Fitzpatrick 2023): regime set by D_norm² vs iota_e·P_perp/P_tor^(2/3).
+# ---------------------------------------------------------------------
+
+# Returns (p_start, W_at_p_start, branch) where `branch ∈ (:large_D, :small_D)`.
+function _riccati_f_initial(p::SLAYERParameters, g::ComplexF64;
+ p_floor::Real=6.0)
+ D2 = p.D_norm * p.D_norm
+ Pperp_over_Ptor23 = p.P_perp / p.P_tor^(2 / 3)
+
+ if D2 > p.iota_e * Pperp_over_Ptor23
+ # Large-D_norm branch. In ((P_tor·D²)/(iota_e·P_tor·P_perp))^(1/4)
+ # the P_tor factor cancels — written out for traceability.
+ p_start = max(((p.P_tor * D2) / (p.iota_e * p.P_tor * p.P_perp))^0.25,
+ p_floor)
+
+ ak = -(g - im * p.Q_e)
+ bk = (p.iota_e * p.P_perp * p.P_tor) / (p.P_tor * D2)
+ ck = bk * (1 + (g - im * p.Q_i) * ((p.P_tor + p.P_perp) /
+ (p.P_tor * p.P_perp))
+ -
+ (p.P_perp + (g - im * p.Q_i) * D2) *
+ (p.iota_e / (p.P_tor * D2)))
+ sqrt_bk = sqrt(bk)
+ xk = (ck - sqrt_bk * (1 - sqrt_bk * ak)) / (2 * sqrt_bk)
+
+ W_bound = xk - sqrt_bk * p_start
+ return p_start, W_bound, :large_D
+ else
+ # Small-D_norm branch.
+ p_start = max(1.0 / p.P_tor^(1 / 6), p_floor)
+
+ ak = -(g - im * p.Q_e)
+ bk = ComplexF64(p.P_tor) # promoted to ComplexF64 for sqrt below
+ ck = im * (p.Q_e - p.Q_i) * (p.P_tor / p.P_perp) + (g - im * p.Q_i)
+ sqrt_bk = sqrt(bk)
+ xk = (ak * bk - ck) / (2 * sqrt_bk)
+
+ W_bound = -1.0 + xk * p_start - sqrt_bk * p_start^3
+ return p_start, W_bound, :small_D
+ end
+end
+
+# ---------------------------------------------------------------------
+# solve_inner dispatch for SLAYERModel{:fitzpatrick}.
+# ---------------------------------------------------------------------
+
+"""
+ solve_inner(::SLAYERModel{:fitzpatrick}, p::SLAYERParameters, s::Number;
+ pmin=1e-6, p_floor=6.0, reltol=1e-10, abstol=1e-10, maxiters=50_000,
+ solver=Rodas5P(autodiff=false)) -> InnerLayerResponse
+
+Solve the Fitzpatrick SLAYER inner-layer Riccati ODE at the complex growth rate `s = γ − iω` in 1/s, in the
+surface's E×B frame. The layer is evaluated at Fitzpatrick's normalized eigenvalue ĝ = s·τ_k (Fitzpatrick 2023:
+γ = Re(ĝ)/τ_k, ω = −Im(ĝ)/τ_k), and the diamagnetic drifts enter as ĝ − i·Q_e and ĝ − i·Q_i, so the layer co-rotates
+with the electron fluid at ω = ω_*e. Returns an `InnerLayerResponse` with `tearing = Δ` and `interchange = 0`: SLAYER's
+pressureless layer produces only the tearing channel.
+
+Integrates `dW/dp = -(fA'/p)·W − W²/p + (fB/(fA·fC))·p³` (Fitzpatrick 2023; Park 2022) from a large `p_start`
+inward to `pmin` and returns `Δ = π / W'(pmin)`.
+
+**Solver swaps:** tiny differences between ODE solvers change the outer AMR's cell flagging and hence the
+classified root/pole inventory, so validate a new `solver` against `n_valid_roots` and `n_poles`, not just γ.
+
+# Keyword arguments
+
+ - `pmin` -- inner-layer cutoff (default 1e-6)
+ - `p_floor` -- floor on `p_start` (default 6.0)
+ - `reltol`,`abstol`,`maxiters` -- stiff-solver tolerance/iteration limits
+ - `solver` -- any OrdinaryDiffEq algorithm; pass `Tsit5()` for the
+ non-stiff path (rarely needed here)
+"""
+solve_inner(::SLAYERModel{:fitzpatrick}, p::SLAYERParameters, s::Number; kwargs...) = _slayer_delta(p, ComplexF64(s) * p.tauk; kwargs...)
+
+# The dispersion scans run in the plane Q = (ω + iγ)·τ_k (Park et al. 2022), a −90° rotation of ĝ: ĝ = −i·Q.
+layer_response(::SLAYERModel{:fitzpatrick}, p::SLAYERParameters, Q::Number; kwargs...) =
+ _slayer_delta(p, ComplexF64(imag(Q), -real(Q)); kwargs...)
+
+# Δ of the layer at the normalized eigenvalue ĝ.
+function _slayer_delta(p::SLAYERParameters, g::ComplexF64;
+ pmin::Real=1e-6,
+ p_floor::Real=6.0,
+ reltol::Real=1e-10,
+ abstol::Real=1e-10,
+ maxiters::Integer=50_000,
+ solver=Rodas5P(; autodiff=false))
+
+ p_start, W_bound, _ = _riccati_f_initial(p, g; p_floor=p_floor)
+
+ rhs_params = _build_riccati_consts(p, g)
+
+ # Scalar state with the out-of-place form (`ODEFunction{false}`) avoids per-step allocations.
+ u0 = ComplexF64(W_bound)
+ f = ODEFunction{false}(_riccati_f_rhs; jac=_riccati_f_jac)
+ prob = ODEProblem(f, u0, (p_start, pmin), rhs_params)
+ sol = solve(prob, solver;
+ reltol=reltol, abstol=abstol, maxiters=maxiters,
+ save_everystep=false, dense=false)
+
+ if sol.retcode != ReturnCode.Success
+ # NaN sentinel so the scan/AMR isfinite checks flag this cell; @debug since failures cluster near poles.
+ @debug "SLAYER Riccati integration did not return Success" sol.retcode
+ return InnerLayerResponse(ComplexF64(NaN, NaN), zero(ComplexF64))
+ end
+
+ # Δ = π / W'(pmin) from one RHS evaluation at the inner endpoint.
+ W_end = sol.u[end]
+ dW_end = _riccati_f_rhs(W_end, rhs_params, pmin)
+ Δ::ComplexF64 = π / dW_end
+
+ # The pressureless layer has no interchange (Δ₊) channel.
+ return InnerLayerResponse(Δ, zero(ComplexF64))
+end
diff --git a/src/InnerLayer/SLAYER/SLAYER.jl b/src/InnerLayer/SLAYER/SLAYER.jl
new file mode 100644
index 0000000000..a244eb7796
--- /dev/null
+++ b/src/InnerLayer/SLAYER/SLAYER.jl
@@ -0,0 +1,99 @@
+# SLAYER.jl
+#
+# SLAYER (Slab Layer) two-fluid drift-MHD inner-layer model (Fitzpatrick,
+# Tearing Mode Dynamics in Tokamak Plasmas, IOP 2023; Park 2022,
+# Phys. Plasmas 29, 072506; Burgess et al. 2026). The dispersion path uses
+# the Fitzpatrick layer formulation — P_perp / P_tor transport, c_beta
+# compressibility, D_norm normalized ion-skin scale, two-fluid drift
+# coupling via Q_e, Q_i, iota_e (see `Riccati.jl`).
+#
+# A separate `del_s` layer-thickness diagnostic (`slayer_layer_thickness` in
+# `LayerThickness.jl`) returns the resistive layer width in meters at each
+# rational surface.
+#
+# Type-parameter `S` of `SLAYERModel{S}` selects the Riccati formulation
+# used for the dispersion relation; only `:fitzpatrick` is implemented.
+
+module SLAYER
+
+using LinearAlgebra
+using StaticArrays
+
+import ..InnerLayerModel, ..InnerLayerResponse, ..solve_inner, ..layer_response, ..InnerLayerParameters
+using ...Utilities.PhysicalConstants
+using ...Utilities.NeoclassicalResistivity
+using ...Utilities.NeoclassicalResistivity: NeoResistivityModel, SpitzerModel,
+ SpitzerHarmModel, SauterNeoModel, RedlNeoModel,
+ coulomb_log_e, eta_spitzer, tau_ee_spitzer_harm, eta_spitzer_harm,
+ trapped_fraction_eps, nu_star_e, eta_neoclassical
+
+"""
+ SLAYERModel(; variant=:fitzpatrick, P_perp_model=:D_perp, D_c_type=:none, D_R=nothing, D_geo=nothing, chi_perp_Dc=nothing,
+ theta_sample=0.0)
+
+SLAYER inner-layer model: the Riccati formulation and the layer closures that turn the plasma
+(the equilibrium's kinetic data) into layer parameters. The type parameter `S` of
+`SLAYERModel{S}` is the formulation:
+
+ - `:fitzpatrick` -- P_perp/P_tor Fitzpatrick formulation (default;
+ Fitzpatrick 2023 two-fluid drift-MHD layer)
+
+The `del_s` formulation is exposed separately as the layer-thickness diagnostic [`slayer_layer_thickness`](@ref), not as
+a dispersion `solve_inner` path.
+
+## Fields
+
+ - `P_perp_model` - How the perpendicular Prandtl number is built: `:D_perp` (default; needs χ⊥,i),
+ `:chi_perp_e`, `:chi_perp_i`, `:P_phi`, `:c_beta` or `:tau_E`; see [`slayer_parameters`](@ref).
+ - `D_c_type` - Critical-Δ offset: `:none` (default), `:lar`, `:fitzpatrick` or `:toroidal`
+ (χ_‖-matching formulas of Connor, Ham, Hastie & Liu 2015).
+ - `D_R`, `D_geo` - Critical-Δ inputs; `nothing` (default) derives them per surface from the equilibrium:
+ `D_R = E + F + H²`, and `D_geo` the Connor et al. 2015 Eq. 59 toroidal geometric factor in the `r_s`
+ reference (consumed only by `:toroidal`, which also takes its parallel wavenumber from the equilibrium,
+ `toroidal_kpar`). An explicit `D_R = 0.0` disables the offset for every `D_c_type`; `D_geo = 0.0` only for `:toroidal`.
+ - `chi_perp_Dc` - Electron perpendicular heat diffusivity [m²/s] used only by the critical Δ; `nothing` (default)
+ uses the χ⊥,e that P_perp sees. Set it when P_perp is built from a diffusivity the critical Δ should not use. It
+ replaces χ⊥,e in the critical Δ at every surface, over any `chi_e` profile, reaches the critical resonant field through
+ the critical Δ, and has no effect with `D_c_type = :none`.
+ - `theta_sample` - Poloidal angle (normalized to [0, 1)) of the minor-radius chord of the `:midplane`
+ radial label, used only by API callers that pass `rs_method = :midplane`; the default toroidal-flux
+ label does not depend on angle, so a nonzero value warns (default 0, the outboard midplane).
+"""
+struct SLAYERModel{S} <: InnerLayerModel
+ P_perp_model::Symbol
+ D_c_type::Symbol
+ D_R::Union{Nothing,Float64}
+ D_geo::Union{Nothing,Float64}
+ chi_perp_Dc::Union{Nothing,Float64}
+ theta_sample::Float64
+end
+
+const _D_C_TYPES = (:none, :lar, :fitzpatrick, :toroidal)
+
+function SLAYERModel(; variant::Symbol=:fitzpatrick, P_perp_model=:D_perp, D_c_type=:none, D_R=nothing, D_geo=nothing,
+ chi_perp_Dc=nothing, theta_sample::Real=0.0)
+ P_perp_model, D_c_type = Symbol(P_perp_model), Symbol(D_c_type)
+ P_perp_model in ALLOWED_P_PERP_MODELS || throw(ArgumentError("SLAYERModel: P_perp_model = $P_perp_model not in $ALLOWED_P_PERP_MODELS"))
+ D_c_type in _D_C_TYPES || throw(ArgumentError("SLAYERModel: D_c_type = $D_c_type not in $_D_C_TYPES"))
+ chi_perp_Dc === nothing || (isfinite(chi_perp_Dc) && chi_perp_Dc > 0) ||
+ throw(ArgumentError("SLAYERModel: chi_perp_Dc must be positive and finite [m²/s]; got $chi_perp_Dc"))
+ iszero(theta_sample) || @warn "SLAYERModel: theta_sample = $theta_sample has no effect: the layer quantities " *
+ "use the toroidal-flux radial label, which does not depend on poloidal angle." maxlog = 1
+ return SLAYERModel{variant}(P_perp_model, D_c_type, D_R === nothing ? nothing : Float64(D_R),
+ D_geo === nothing ? nothing : Float64(D_geo), chi_perp_Dc === nothing ? nothing : Float64(chi_perp_Dc), Float64(theta_sample))
+end
+
+include("LayerParameters.jl")
+include("Riccati.jl")
+include("LayerThickness.jl")
+include("LayerInputs.jl")
+include("KineticView.jl")
+
+export SLAYERModel, SLAYERParameters, slayer_parameters
+export r_based_shear
+export riccati_del_s, slayer_layer_thickness, slayer_algebraic_widths, LayerWidths
+export surface_minor_radius, surface_da_dpsi, radial_label, build_slayer_inputs, surface_resistivity, layer_resistivity,
+ toroidal_dgeo, toroidal_kpar
+export NeoResistivityModel, SpitzerModel, SpitzerHarmModel, SauterNeoModel, RedlNeoModel
+
+end # module SLAYER
diff --git a/src/JPEC.jl b/src/JPEC.jl
deleted file mode 100644
index ed5cb889ba..0000000000
--- a/src/JPEC.jl
+++ /dev/null
@@ -1,23 +0,0 @@
-# JPEC.jl
-module JPEC
-
-include("Splines/Splines.jl")
-import .SplinesMod as Spl
-export SplinesMod, Spl
-
-include("Equilibrium/Equilibrium.jl")
-import .Equilibrium as Equilibrium
-export Equilibrium
-
-include("Vacuum/Vacuum.jl")
-import .VacuumMod as VacuumMod
-export VacuumMod
-
-include("DCON/DCON.jl")
-import .DCON as DCON
-export DCON
-
-include(joinpath(@__DIR__, "..", "deps", "build_helpers.jl"))
-export build_fortran, build_spline_fortran, build_vacuum_fortran
-
-end # module JPEC
\ No newline at end of file
diff --git a/src/KineticForces/BounceAveraging.jl b/src/KineticForces/BounceAveraging.jl
new file mode 100644
index 0000000000..c8e6975295
--- /dev/null
+++ b/src/KineticForces/BounceAveraging.jl
@@ -0,0 +1,1194 @@
+"""
+ BounceAveraging
+
+Bounce-averaging infrastructure for GAR NTV calculations.
+Computes bounce-averaged frequencies (ωb, ωd) and perturbation action (|δJ|²)
+as functions of pitch angle λ. For kinetic matrix methods, also computes
+bounce-averaged W_μ, W_E vectors and their outer products.
+
+Reference: Logan et al., Phys. Plasmas 20, 122507 (2013). Follows the GAR bounce loop of Fortran torque.F90.
+"""
+
+# Guard against a non-terminating spline cell walk; θ grids are O(10²) cells.
+const MAX_SPLINE_CELLS = 100_000
+# Stationary points closer than this in θ are the same root seen from both sides
+# of a cell boundary.
+const EXTREMUM_MERGE_TOL = 1e-12
+# Cells a hinted cell search may step before falling back to bisection.
+const HINT_STEP_BUDGET = 8
+# Slack on the root-count tests below. Generous by design: a wrongly admitted repeated
+# root is a near-touch at a stationary point, which the monotone-window filter rejects.
+const ROOT_COUNT_TOL = 64 * eps(Float64)
+
+# ============================================================================
+# BounceData struct
+# ============================================================================
+
+"""
+ BounceData
+
+Bounce-averaged quantities as functions of pitch angle λ, produced by `bounce_harmonic` and
+consumed by the pitch integration.
+
+## Fields
+
+ - `nlmda`, `lambda`: number of pitch-angle points and the λ grid
+ - `sigma`: 0 trapped, 1 passing, per λ
+ - `wb`, `wd`: bounce frequency ωb(λ) and precession drift ωd(λ), in rad/s
+ - `dJdJ`: ωb|δJ|²/ro² per λ (real; scalar torque path)
+ - `wmats_vs_lambda`: packed W outer products, `(nlmda, nqty_matrix(mpert))`, in the 3-Hermitian-triangle +
+ 3-full-block layout of `nqty_matrix` (Logan 2015 Eqs 7.30–7.35); `nothing` on the scalar path
+"""
+struct BounceData
+ nlmda::Int
+ lambda::Vector{Float64}
+ sigma::Vector{Int}
+ wb::Vector{Float64}
+ wd::Vector{Float64}
+ dJdJ::Vector{Float64}
+ wmats_vs_lambda::Union{Nothing,Matrix{ComplexF64}}
+end
+
+"""
+ BounceGeometry
+
+The bounce-harmonic-independent part of the bounce averaging at one (ψ, n): per λ, the orbit's θ
+sub-grid samples that every ℓ reuses. Produced by `compute_bounce_geometry`, consumed by
+`bounce_harmonic`, which adds the ℓ-dependent phase and reduces to a `BounceData`.
+
+## Fields
+
+ - `nlmda`, `lambda`, `sigma`: the λ grid, as in `BounceData`
+ - `wb`, `wd`: bounce and precession frequencies, in rad/s
+ - `wbbar::Vector{Float64}`: normalized bounce frequency per λ (`wb = wbbar·bhat`)
+ - `total_wb::Vector{Float64}`: full bounce-action integral per λ, the phase normalization
+ - `fsi_wb::Matrix{Float64}`: `ntheta × nlmda` cumulative bounce action along the orbit
+ - `jvtheta::Matrix{ComplexF64}`: `ntheta × nlmda` action integrand samples
+ - `wmu_mt`, `wen_mt`: `mpert × ntheta × nlmda` W_μ, W_E samples (matrix path, else `nothing`)
+ - `valid::Vector{Bool}`: false where the bounce integral degenerated; every output of that λ is zero
+"""
+struct BounceGeometry
+ nlmda::Int
+ lambda::Vector{Float64}
+ sigma::Vector{Int}
+ wb::Vector{Float64}
+ wd::Vector{Float64}
+ wbbar::Vector{Float64}
+ total_wb::Vector{Float64}
+ fsi_wb::Matrix{Float64}
+ jvtheta::Matrix{ComplexF64}
+ wmu_mt::Union{Nothing,Array{ComplexF64,3}}
+ wen_mt::Union{Nothing,Array{ComplexF64,3}}
+ valid::Vector{Bool}
+end
+
+
+# ============================================================================
+# Packed layout for kinetic matrix per-λ storage
+# ============================================================================
+# Of the six Logan-2015 matrices (Eqs 7.30–7.35), A = W_Z†W_Z, D = W_X†W_X,
+# and H = W_Y†W_Y are Hermitian; B = W_Z†W_X, C = W_Z†W_Y, E = W_X†W_Y are not.
+# We store only the upper triangle (i ≤ j) for the three Hermitian blocks and
+# the full mpert² for the three non-Hermitian blocks. Block packing order:
+# A-tri, D-tri, H-tri, B-full, C-full, E-full.
+
+"""
+Number of packed complex entries per λ for the 6 kinetic matrices.
+"""
+@inline nqty_matrix(mpert::Int) = 3 * (mpert * (mpert + 1)) ÷ 2 + 3 * mpert^2
+
+"""
+Upper-triangle index (1 ≤ i ≤ j ≤ mpert) within a triangular block.
+"""
+@inline _tri_idx(i::Int, j::Int) = (j * (j - 1)) ÷ 2 + i
+
+"""
+Full-block index (column-major) within a non-Hermitian block.
+"""
+@inline _full_idx(i::Int, j::Int, mpert::Int) = (j - 1) * mpert + i
+
+
+# ============================================================================
+# Grid generation
+# ============================================================================
+
+"""
+ powspace(xmin, xmax, pow, num, endpoints) → (points, weights)
+
+Generate a grid with power-law concentration near endpoints.
+Port of Fortran `powspace_sub` from equil/grid.f90.
+
+# Arguments
+
+ - `xmin, xmax`: Grid bounds
+ - `pow::Int`: Power of grid concentration (higher = more refined near edges)
+ - `num::Int`: Number of grid points
+ - `endpoints::String`: Where to concentrate: "lower", "upper", or "both"
+
+# Returns
+
+ - `points::Vector{Float64}`: Grid point locations
+ - `weights::Vector{Float64}`: Derivatives dx/dnorm (integration weights)
+"""
+function powspace(xmin::Float64, xmax::Float64, pow::Int, num::Int, endpoints::String)
+ if xmax <= xmin
+ error("powspace: xmax ($xmax) must be greater than xmin ($xmin)")
+ end
+
+ # Linear base grid in [-1,1], [0,1], or [-1,0]
+ x = if endpoints == "lower"
+ collect(range(-1.0, 0.0; length=num))
+ elseif endpoints == "upper"
+ collect(range(0.0, 1.0; length=num))
+ elseif endpoints == "both"
+ collect(range(-1.0, 1.0; length=num))
+ else
+ error("powspace: invalid endpoints '$endpoints' — use lower, upper, or both")
+ end
+
+ # Concentration weight: |(x-1)(x+1)|^pow
+ weights = abs.((x .- 1.0) .* (x .+ 1.0)) .^ pow
+
+ # Antiderivative of |(1-x²)|^pow — analytic for pow ≤ 9
+ points = _powspace_antideriv(x, pow)
+
+ # Stretch to desired range [xmin, xmax]
+ deltay = points[end] - points[1]
+ deltax = xmax - xmin
+ scale = deltax / deltay
+ points .= points .* scale
+ weights .= weights .* scale
+ points .= points .- points[1] .+ xmin
+
+ # Weight includes the base grid span
+ weights .= weights .* (x[end] - x[1])
+
+ return points, weights
+end
+
+"""
+ _powspace_antideriv(x, pow)
+
+Analytic antiderivative of |(1-x²)|^pow for pow 1-9.
+Matches Fortran powspace_sub cases exactly.
+"""
+function _powspace_antideriv(x::Vector{Float64}, pow::Int)
+ if pow == 1
+ return @. -x + x^3 / 3
+ elseif pow == 2
+ return @. x - (2x^3) / 3 + x^5 / 5
+ elseif pow == 3
+ return @. -x + x^3 - (3x^5) / 5 + x^7 / 7
+ elseif pow == 4
+ return @. x - (4x^3) / 3 + (6x^5) / 5 - (4x^7) / 7 + x^9 / 9
+ elseif pow == 5
+ return @. -x + (5x^3) / 3 - 2x^5 + (10x^7) / 7 - (5x^9) / 9 + x^11 / 11
+ elseif pow == 6
+ return @. x - 2x^3 + 3x^5 - (20x^7) / 7 + (5x^9) / 3 - (6x^11) / 11 + x^13 / 13
+ elseif pow == 7
+ return @. -x + (7x^3) / 3 - (21x^5) / 5 + 5x^7 - (35x^9) / 9 + (21x^11) / 11 - (7x^13) / 13 + x^15 / 15
+ elseif pow == 8
+ return @. x - (8x^3) / 3 + (28x^5) / 5 - 8x^7 + (70x^9) / 9 - (56x^11) / 11 + (28x^13) / 13 - (8x^15) / 15 + x^17 / 17
+ elseif pow == 9
+ return @. -x + 3x^3 - (36x^5) / 5 + 12x^7 - 14x^9 + (126x^11) / 11 - (84x^13) / 13 + (12x^15) / 5 - (9x^17) / 17 + x^19 / 19
+ else
+ error("powspace: pow=$pow not in analytic database (1-9)")
+ end
+end
+
+
+# ============================================================================
+# Core bounce averaging
+# ============================================================================
+
+"""
+ compute_bounce_data(psi, n, l, q, bo, bmax, bmin, theta_bmax,
+ tspl, B_vpar, mfac, chi1, ro, dbob_m_f, divx_m_f,
+ divxfac, wdfac, mass, chrg, T_s, method;
+ nlmda=128, ntheta=128,
+ smat=nothing, tmat=nothing, xmat=nothing,
+ ymat=nothing, zmat=nothing) → BounceData
+
+Compute bounce-averaged quantities as functions of pitch angle λ for bounce harmonic `l`:
+`compute_bounce_geometry` followed by `bounce_harmonic`. A caller looping over harmonics should build the
+geometry once and call `bounce_harmonic` per ℓ.
+
+# Arguments
+
+ - `psi`: Normalized poloidal flux
+ - `n`: Toroidal mode number
+ - `l`: Bounce harmonic number
+ - `q`: Safety factor at this ψ
+ - `bo`: On-axis toroidal field [T]
+ - `bmax, bmin`: Max/min of B(θ) at this ψ
+ - `theta_bmax`: θ location of Bmax (nodal knot; the passing-transit start)
+ - `tspl`: Periodic poloidal interpolant: tspl(θ) → [B, dB/dψ, dB/dθ, J, dJ/dψ]
+ - `B_vpar`: Periodic cubic of B(θ) used for v_par and the bounce-point roots
+ - `mfac`: Poloidal mode numbers `mlow:mhigh`
+ - `chi1`: 2π·ψ₀ flux normalization
+ - `ro`: Major radius [m]
+ - `dbob_m_f`: δB/B Fourier modes at this ψ (ComplexF64 vector, length mpert)
+ - `divx_m_f`: ∇·ξ⊥ Fourier modes at this ψ (ComplexF64 vector, length mpert)
+ - `divxfac, wdfac`: Scaling factors
+ - `mass`: Particle mass [kg]
+ - `chrg`: Particle charge [C]
+ - `T_s`: Species temperature at this ψ [J]
+ - `method`: Method string (first char: f/t/p determines λ range)
+
+# Keyword Arguments
+
+ - `nlmda`: Number of pitch angle grid points (default 128)
+ - `ntheta`: Number of poloidal grid points per bounce (default 128)
+ - `smat, tmat, xmat, ymat, zmat`: Geometric matrices (mpert×mpert) for kinetic matrix path
+ - `surface_field`: Prebuilt `_surface_b_field(B_vpar)`, shared across the harmonics of a surface
+"""
+function compute_bounce_data(
+ psi::Float64, n::Int, l::Int, q::Float64,
+ bo::Float64, bmax::Float64, bmin::Float64,
+ theta_bmax::Float64,
+ tspl, B_vpar, mfac::Vector{Int}, chi1::Float64, ro::Float64,
+ dbob_m_f::Vector{ComplexF64}, divx_m_f::Vector{ComplexF64},
+ divxfac::Float64, wdfac::Float64,
+ mass::Float64, chrg::Float64,
+ T_s::Float64, method::String;
+ nlmda::Int=128, ntheta::Int=128,
+ smat::Union{Nothing,Matrix{ComplexF64}}=nothing,
+ tmat::Union{Nothing,Matrix{ComplexF64}}=nothing,
+ xmat::Union{Nothing,Matrix{ComplexF64}}=nothing,
+ ymat::Union{Nothing,Matrix{ComplexF64}}=nothing,
+ zmat::Union{Nothing,Matrix{ComplexF64}}=nothing,
+ surface_field=nothing
+)
+ geometry = compute_bounce_geometry(
+ psi, n, q, bo, bmax, bmin, theta_bmax,
+ tspl, B_vpar, mfac, chi1, ro, dbob_m_f, divx_m_f, divxfac, wdfac,
+ mass, chrg, T_s, method;
+ nlmda, ntheta, do_matrices=!isnothing(smat), surface_field)
+ return bounce_harmonic(geometry, l, n, q, ro, length(mfac); smat, tmat, xmat, ymat, zmat)
+end
+
+"""
+ compute_bounce_geometry(psi, n, q, bo, bmax, bmin, theta_bmax, tspl, B_vpar, mfac, chi1, ro,
+ dbob_m_f, divx_m_f, divxfac, wdfac, mass, chrg, T_s, method;
+ nlmda=128, ntheta=128, do_matrices=false, surface_field=nothing) → BounceGeometry
+
+The bounce-harmonic-independent half of `compute_bounce_data`: for every λ of the grid, locate the
+orbit, sample the bounce integrands on its θ sub-grid and integrate them. The harmonic enters only
+through the phase `exp(−2πi·lnq·∫J B/v_∥)`, applied by `bounce_harmonic`. Arguments as for
+`compute_bounce_data`; `do_matrices` stores the W_μ, W_E samples the kinetic matrix path needs.
+"""
+function compute_bounce_geometry(
+ psi::Float64, n::Int, q::Float64,
+ bo::Float64, bmax::Float64, bmin::Float64,
+ theta_bmax::Float64,
+ tspl, B_vpar, mfac::Vector{Int}, chi1::Float64, ro::Float64,
+ dbob_m_f::Vector{ComplexF64}, divx_m_f::Vector{ComplexF64},
+ divxfac::Float64, wdfac::Float64,
+ mass::Float64, chrg::Float64,
+ T_s::Float64, method::String;
+ nlmda::Int=128, ntheta::Int=128,
+ do_matrices::Bool=false,
+ surface_field=nothing
+)
+ mpert = length(mfac)
+
+ # Per-surface scratch, reused across all λ.
+ scr = BounceScratch(ntheta, mpert)
+
+ # B(θ) decomposed into its cells and stationary points: once per surface, reused by every λ.
+ bf = surface_field === nothing ? _surface_b_field(B_vpar) : surface_field
+ bpts_buf = Float64[]
+ # One resumable cell hint per monotone interval; λ ascends, so each interval's
+ # crossing advances steadily and the next λ starts where the last one finished.
+ hints = ones(Int, length(bf.theta) + 1)
+
+ # Trapped-passing boundary and λ range
+ lmdatpb = bo / bmax
+ lmdamax = bo / bmin
+
+ # λ grid from the method variant
+ method_char = method[1]
+ lambda = _build_lambda_grid(method_char, lmdatpb, lmdamax, nlmda)
+
+ wb_arr = zeros(Float64, nlmda)
+ wd_arr = zeros(Float64, nlmda)
+ wbbar_arr = zeros(Float64, nlmda)
+ total_wb_arr = zeros(Float64, nlmda)
+ sigma_arr = zeros(Int, nlmda)
+ valid = falses(nlmda)
+ fsi_wb = zeros(Float64, ntheta, nlmda)
+ jvtheta = zeros(ComplexF64, ntheta, nlmda)
+ wmu_mt = do_matrices ? zeros(ComplexF64, mpert, ntheta, nlmda) : nothing
+ wen_mt = do_matrices ? zeros(ComplexF64, mpert, ntheta, nlmda) : nothing
+
+ # Thermal speed and drift normalization
+ bhat = sqrt(2 * T_s / mass) / ro
+ dhat = (T_s / chrg) / (bo * ro^2)
+
+ for ilmda in 1:nlmda
+ lmda = lambda[ilmda]
+
+ # Trapped/passing
+ sigma = lmda > (bo / bmax) ? 0 : 1
+ sigma_arr[ilmda] = sigma
+
+ # Find bounce points and build θ sub-grid
+ _, _, tdt_pts, tdt_wts = _find_bounce_points_and_grid(
+ lmda, bo, sigma, B_vpar, theta_bmax, psi, ntheta, bf, bpts_buf, hints)
+
+ # Bounce integrands sampled along the orbit
+ total_wb, total_wd = _bounce_samples!(
+ view(fsi_wb, :, ilmda), view(jvtheta, :, ilmda),
+ do_matrices ? view(wmu_mt, :, :, ilmda) : nothing,
+ do_matrices ? view(wen_mt, :, :, ilmda) : nothing,
+ tdt_pts, tdt_wts, lmda, n, q, bo,
+ tspl, B_vpar, chi1, mfac, dbob_m_f, divx_m_f, divxfac,
+ do_matrices, mpert, scr)
+
+ # Degenerate orbit: every output of this λ stays zero.
+ total_wb ≈ 0.0 && continue
+ valid[ilmda] = true
+ total_wb_arr[ilmda] = total_wb
+
+ # Units: wbbar already carries one ro and dhat removes only two, so the drift prefactor takes ro,
+ # not ro²; with ro² ω_D = wdbar·dhat would come out in m/s instead of 1/s.
+ wbbar = ro * twopi / ((2 - sigma) * total_wb)
+ wdbar = ro * bo * wdfac * wbbar * 2 * (2 - sigma) * total_wd
+ wbbar_arr[ilmda] = wbbar
+
+ # Physical frequencies
+ wb_arr[ilmda] = wbbar * bhat
+ wd_arr[ilmda] = wdbar * dhat
+ end
+
+ return BounceGeometry(nlmda, lambda, sigma_arr, wb_arr, wd_arr, wbbar_arr, total_wb_arr,
+ fsi_wb, jvtheta, wmu_mt, wen_mt, valid)
+end
+
+"""
+ bounce_harmonic(geometry::BounceGeometry, l, n, q, ro, mpert;
+ smat=nothing, tmat=nothing, xmat=nothing, ymat=nothing, zmat=nothing) → BounceData
+
+Apply bounce harmonic `l` to a `BounceGeometry`: per λ the phase factor with
+`lnq = l + σ·n·q`, the action bounce integral |δJ|², and (matrix path, when the geometric
+matrices are given and the geometry carries the W samples) the packed W outer products.
+"""
+function bounce_harmonic(geometry::BounceGeometry, l::Int, n::Int, q::Float64, ro::Float64, mpert::Int;
+ smat::Union{Nothing,Matrix{ComplexF64}}=nothing,
+ tmat::Union{Nothing,Matrix{ComplexF64}}=nothing,
+ xmat::Union{Nothing,Matrix{ComplexF64}}=nothing,
+ ymat::Union{Nothing,Matrix{ComplexF64}}=nothing,
+ zmat::Union{Nothing,Matrix{ComplexF64}}=nothing)
+ nlmda = geometry.nlmda
+ ntheta = size(geometry.fsi_wb, 1)
+ do_matrices = !isnothing(smat) && !isnothing(geometry.wmu_mt)
+ scr = BounceScratch(ntheta, mpert)
+
+ dJdJ_arr = zeros(Float64, nlmda)
+ wmats_arr = do_matrices ? zeros(ComplexF64, nlmda, nqty_matrix(mpert)) : nothing
+
+ for ilmda in 1:nlmda
+ geometry.valid[ilmda] || continue
+ sigma = geometry.sigma[ilmda]
+ lnq = l + sigma * n * q # effective resonance number
+
+ dJdJ_val, wmats_lmda = _bounce_harmonic_tail(
+ view(geometry.fsi_wb, :, ilmda), view(geometry.jvtheta, :, ilmda),
+ do_matrices ? view(geometry.wmu_mt, :, :, ilmda) : nothing,
+ do_matrices ? view(geometry.wen_mt, :, :, ilmda) : nothing,
+ geometry.total_wb[ilmda], geometry.wbbar[ilmda], lnq, sigma, ro,
+ do_matrices, mpert, smat, tmat, xmat, ymat, zmat, scr)
+ dJdJ_arr[ilmda] = dJdJ_val
+
+ if do_matrices && !isnothing(wmats_lmda)
+ @inbounds for iq in eachindex(wmats_lmda)
+ wmats_arr[ilmda, iq] = wmats_lmda[iq]
+ end
+ end
+ end
+
+ return BounceData(nlmda, geometry.lambda, geometry.sigma,
+ geometry.wb, geometry.wd, dJdJ_arr, wmats_arr)
+end
+
+
+"""
+ BounceScratch(ntheta, mpert)
+
+Per-surface scratch for the bounce-averaging inner loops, allocated once per surface in
+`compute_bounce_geometry` and `bounce_harmonic` and reused across every λ. Sizes are fixed for a flux surface
+(`ntheta` sub-grid points, `mpert` Fourier modes). Buffers the loops populate only
+partially are `fill!`-reset per λ.
+
+## Fields
+
+ - `g_wb::Vector{Float64}`: length `ntheta` — bounce-action integrand samples
+ - `g_wd::Vector{Float64}`: length `ntheta` — drift integrand samples
+ - `cum_wb_arr::Vector{Float64}`: length `ntheta` — cumulative bounce-action integral
+ - `jvtheta::Vector{ComplexF64}`: length `ntheta` — action integrand
+ - `bj_samples::Vector{ComplexF64}`: length `ntheta` — action bounce-integral samples
+ - `wsamp::Vector{ComplexF64}`: length `ntheta` — per-mode W bounce-integral samples
+ - `wmu_mt::Matrix{ComplexF64}`: `mpert × ntheta` — W_μ per θ
+ - `wen_mt::Matrix{ComplexF64}`: `mpert × ntheta` — W_E per θ
+ - `expm::Vector{ComplexF64}`: length `mpert` — Fourier basis at a θ
+ - `pl::Vector{ComplexF64}`: length `ntheta` — bounce phase factor
+ - `wmu_ba::Vector{ComplexF64}`: length `mpert` — bounce-averaged W_μ
+ - `wen_ba::Vector{ComplexF64}`: length `mpert` — bounce-averaged W_E
+ - `wmats_lmda::Vector{ComplexF64}`: length `nqty_matrix(mpert)` — packed W outer products
+ - `tspl_f::Vector{Float64}`: length 5 — in-place tspl(θ) evaluation
+ - `int_w::Vector{Float64}`, `cumint_W::Matrix{Float64}`: precomputed exact-cubic
+ quadrature weights on the fixed unit θ-grid (`∫ = int_w·y`, `cumulative = cumint_W·y`);
+ shared read-only across surfaces, see `_quadrature_weights`
+"""
+struct BounceScratch
+ g_wb::Vector{Float64}
+ g_wd::Vector{Float64}
+ cum_wb_arr::Vector{Float64}
+ jvtheta::Vector{ComplexF64}
+ bj_samples::Vector{ComplexF64}
+ wsamp::Vector{ComplexF64}
+ wmu_mt::Matrix{ComplexF64}
+ wen_mt::Matrix{ComplexF64}
+ expm::Vector{ComplexF64}
+ pl::Vector{ComplexF64}
+ wmu_ba::Vector{ComplexF64}
+ wen_ba::Vector{ComplexF64}
+ wmats_lmda::Vector{ComplexF64}
+ tspl_f::Vector{Float64}
+ int_w::Vector{Float64}
+ cumint_W::Matrix{Float64}
+end
+
+function BounceScratch(ntheta::Int, mpert::Int)
+ int_w, cumint_W = _quadrature_weights(ntheta)
+ return BounceScratch(
+ Vector{Float64}(undef, ntheta),
+ Vector{Float64}(undef, ntheta),
+ Vector{Float64}(undef, ntheta),
+ Vector{ComplexF64}(undef, ntheta),
+ Vector{ComplexF64}(undef, ntheta),
+ Vector{ComplexF64}(undef, ntheta),
+ Matrix{ComplexF64}(undef, mpert, ntheta),
+ Matrix{ComplexF64}(undef, mpert, ntheta),
+ Vector{ComplexF64}(undef, mpert),
+ Vector{ComplexF64}(undef, ntheta),
+ Vector{ComplexF64}(undef, mpert),
+ Vector{ComplexF64}(undef, mpert),
+ Vector{ComplexF64}(undef, nqty_matrix(mpert)),
+ Vector{Float64}(undef, 5),
+ int_w,
+ cumint_W
+ )
+end
+
+# Exact-cubic θ-quadrature weights on the fixed unit grid, cached by ntheta.
+const _QUAD_WEIGHTS = Dict{Int,Tuple{Vector{Float64},Matrix{Float64}}}()
+const _QUAD_WEIGHTS_LOCK = ReentrantLock()
+
+"""
+ reset_caches!()
+
+Empty KineticForces' run-filled module-level caches (the θ-quadrature weights by ntheta). Called
+after the precompile workload so no run state is serialized into the package image.
+"""
+function reset_caches!()
+ @lock _QUAD_WEIGHTS_LOCK empty!(_QUAD_WEIGHTS)
+ return nothing
+end
+
+"""
+ _quadrature_weights(ntheta) → (int_w, cumint_W)
+
+Exact integral of the `CubicFit`-endpoint spline on the fixed grid `range(0,1,ntheta)`
+is a constant linear functional of the node samples, so `∫ = int_w·y` and the cumulative
+integral is `cumint_W·y`. The weights are obtained once per `ntheta` by evaluating the
+public `integrate` / `cumulative_integrate!` on the unit basis vectors — bit-faithful to
+fitting and integrating each sample vector directly, but reducing the per-λ hot loop to a
+`dot`/`mul!`. Cached (build guarded by a lock); the returned arrays are read-only.
+"""
+function _quadrature_weights(ntheta::Int)
+ lock(_QUAD_WEIGHTS_LOCK) do
+ get!(_QUAD_WEIGHTS, ntheta) do
+ xs = collect(range(0.0, 1.0; length=ntheta))
+ int_w = zeros(Float64, ntheta)
+ cumint_W = zeros(Float64, ntheta, ntheta)
+ ej = zeros(Float64, ntheta)
+ cbuf = zeros(Float64, ntheta)
+ for j in 1:ntheta
+ ej[j] = 1.0
+ itp = cubic_interp(xs, ej; bc=CubicFit())
+ int_w[j] = FastInterpolations.integrate(itp)
+ FastInterpolations.cumulative_integrate!(cbuf, itp)
+ @views cumint_W[:, j] .= cbuf
+ ej[j] = 0.0
+ end
+ (int_w, cumint_W)
+ end
+ end
+end
+
+
+# ============================================================================
+# Internal helpers
+# ============================================================================
+
+"""
+Build λ grid based on method character (f/t/p), with endpoints excluded.
+"""
+function _build_lambda_grid(method_char::Char, lmdatpb::Float64, lmdamax::Float64, nlmda::Int)
+ lmdamin = 0.0
+
+ if method_char == 't'
+ # Trapped only: λ ∈ (lmdatpb, lmdamax), exclude endpoints
+ pts_inc, _ = powspace(lmdatpb, lmdamax, 1, 2 + nlmda, "both")
+ return pts_inc[2:end-1]
+
+ elseif method_char == 'p'
+ # Passing only: λ ∈ (lmdamin, lmdatpb), exclude endpoints
+ pts_inc, _ = powspace(lmdamin, lmdatpb, 1, 2 + nlmda, "both")
+ return pts_inc[2:end-1]
+
+ else # 'f' = full
+ if lmdatpb ≈ lmdamax
+ @warn "bmax ≈ bmin at this flux surface" maxlog = 1
+ end
+ # Passing half with refinement near upper boundary
+ nhalf_p = nlmda ÷ 2
+ nhalf_t = nlmda - nhalf_p
+ pts_p, _ = powspace(lmdamin, lmdatpb, 2, 2 + nhalf_p, "upper")
+ pts_t, _ = powspace(lmdatpb, lmdamax, 2, 2 + nhalf_t, "lower")
+ # Exclude boundary points
+ return vcat(pts_p[2:end-1], pts_t[2:end-1])
+ end
+end
+
+
+"""
+Parallel-velocity factor `v_par = 1 − (λ/bo)·B(θ)` from the periodic cubic of B
+(`B_vpar`, built where the surface interpolants are constructed), keeping v_par
+consistent with the bounce-point roots as in Fortran's `vspl`.
+"""
+@inline _vpar_from_spline(B_vpar, lmda::Float64, bo::Float64, θ::Float64) =
+ 1.0 - (lmda / bo) * B_vpar(mod(θ, 1.0))
+
+
+"""
+ SurfaceBField
+
+The periodic cubic B(θ) of one flux surface, decomposed once and reused for every λ.
+Holds the per-cell polynomial coefficients, B at every knot, and the stationary points
+of B. Consecutive stationary points bound intervals on which B is monotone, so each
+holds at most one bounce point; within such an interval the cached knot values locate
+the cell by bisection and the cell's cubic is then solved in closed form.
+
+## Fields
+
+ - `knot::Vector{Float64}`: cell boundaries, ascending, `knot[1] = 0`, `knot[end] = 1`
+ - `bknot::Vector{Float64}`: B at each knot
+ - `poly::Vector{NTuple{4,Float64}}`: per-cell `(d, c, b, a)` of `S(u) = d + cu + bu² + au³`,
+ in the cell-local coordinate `u = θ − knot[i]`
+ - `theta::Vector{Float64}`: stationary points of B, ascending, in [0,1)
+ - `bval::Vector{Float64}`: B at each stationary point
+"""
+struct SurfaceBField
+ knot::Vector{Float64}
+ bknot::Vector{Float64}
+ poly::Vector{NTuple{4,Float64}}
+ theta::Vector{Float64}
+ bval::Vector{Float64}
+end
+
+"""
+Decompose the cubic `B_vpar` by walking its cells once, recording each cell's
+polynomial and endpoint value and solving the quadratic dS/dθ = 0 on each to get the
+exact stationary points. Uses only the public `coeffs`/`CellPoly` interface, so it
+holds for whatever θ grid the surface interpolant was built on.
+"""
+function _surface_b_field(B_vpar)
+ knot = Float64[0.0]
+ bknot = Float64[]
+ poly = NTuple{4,Float64}[]
+ theta = Float64[]
+
+ x = 0.0
+ while true
+ cell = coeffs(B_vpar, x)
+ h = cell.xR - cell.xL
+ d, c, b, a = cell.p
+ push!(poly, (d, c, b, a))
+ push!(bknot, d) # S(0) = B at the cell's left knot
+ push!(knot, cell.xR)
+
+ # S'(u) = c + 2b·u + 3a·u² on [0, h); a double stationary point returns twice and dedupes below.
+ n, u1, u2, _ = _quadratic_real_roots(3a, 2b, c)
+ for (k, u) in ((1, u1), (2, u2))
+ k <= n || break
+ (0.0 <= u < h) && push!(theta, cell.xL + u)
+ end
+
+ cell.xR >= 1.0 && break
+ x = cell.xR
+ length(poly) > MAX_SPLINE_CELLS && error("ERROR: _surface_b_field - cell walk did not reach θ=1")
+ end
+ push!(bknot, evalpoly(knot[end] - knot[end-1], poly[end])) # B at θ = 1
+
+ sort!(theta)
+ # A stationary point on a cell boundary is reported by both neighbouring cells.
+ if length(theta) > 1
+ keep = 1
+ for i in 2:length(theta)
+ if theta[i] - theta[keep] > EXTREMUM_MERGE_TOL
+ keep += 1
+ theta[keep] = theta[i]
+ end
+ end
+ resize!(theta, keep)
+ end
+
+ bval = [_b_at(knot, poly, t) for t in theta]
+ return SurfaceBField(knot, bknot, poly, theta, bval)
+end
+
+"""
+Cell index holding θ ∈ [0,1], from the ascending knot vector.
+"""
+@inline _cell_index(knot::Vector{Float64}, θ::Float64) =
+ clamp(searchsortedlast(knot, θ), 1, length(knot) - 1)
+
+"""
+Evaluate B at θ from the cached cell polynomials.
+"""
+@inline function _b_at(knot::Vector{Float64}, poly::Vector{NTuple{4,Float64}}, θ::Float64)
+ i = _cell_index(knot, θ)
+ return evalpoly(θ - knot[i], poly[i])
+end
+
+"""
+Real roots of `a·u³ + b·u² + c·u + d = 0` as `(count, r1, r2, r3)`, unused slots `NaN`.
+The count comes from a conditioned ratio test rather than the sign of the discriminant,
+which cancels to rounding noise when two roots nearly coincide; three real roots use the
+trigonometric form. A degenerate leading coefficient falls through to `_quadratic_real_roots`.
+"""
+function _real_cubic_roots(a::Float64, b::Float64, c::Float64, d::Float64)
+ abs(a) <= eps(Float64) * max(abs(b), abs(c), abs(d), 1.0) && return _quadratic_real_roots(b, c, d)
+
+ B, C, D = b / a, c / a, d / a
+ shift = B / 3
+ p = C - B * B / 3
+ q = 2 * B^3 / 27 - B * C / 3 + D
+
+ if p < 0
+ # Three real roots iff |q/2| ≤ r³, r = √(−p/3): the ratio test stays conditioned where
+ # the discriminant cancels. A ratio a rounding step past 1 is a repeated root; clamp.
+ r = sqrt(-p / 3)
+ arg = -q / (2 * r^3)
+ if abs(arg) <= 1 + ROOT_COUNT_TOL
+ φ = acos(clamp(arg, -1.0, 1.0)) / 3
+ return (3, 2r * cos(φ) - shift, 2r * cos(φ - 2π / 3) - shift, 2r * cos(φ - 4π / 3) - shift)
+ end
+ end
+
+ # One real root (p ≥ 0: monotone; p < 0: |arg| > 1). The max guards sqrt against rounding.
+ s = sqrt(max(0.0, (q / 2)^2 + (p / 3)^3))
+ t = cbrt(-q / 2 + s) + cbrt(-q / 2 - s)
+ return (1, t - shift, NaN, NaN)
+end
+
+"""
+Real roots of `a·u² + b·u + c = 0` in the `(count, r1, r2, r3)` shape of `_real_cubic_roots`,
+`r3` always `NaN`. A discriminant within rounding of zero is a double root rather than none;
+a degenerate leading coefficient falls through to the linear case.
+"""
+function _quadratic_real_roots(a::Float64, b::Float64, c::Float64)
+ if abs(a) <= eps(Float64) * max(abs(b), abs(c), 1.0)
+ b == 0 && return (0, NaN, NaN, NaN)
+ return (1, -c / b, NaN, NaN)
+ end
+ disc = b * b - 4 * a * c
+ if abs(disc) <= ROOT_COUNT_TOL * max(b * b, abs(4 * a * c))
+ r = -b / (2a)
+ return (2, r, r, NaN)
+ end
+ disc < 0 && return (0, NaN, NaN, NaN)
+ sq = sqrt(disc)
+ # Cancellation-free form (Numerical Recipes §5.6).
+ q = b == 0 ? -0.5 * sq : -0.5 * (b + copysign(sq, b))
+ r1 = q / a
+ r2 = q == 0 ? r1 : c / q
+ return (2, r1, r2, NaN)
+end
+
+"""
+Solve `B(θ) = btarget` inside cell `ic`, restricted to `θ ∈ [θlo, θhi]`. The cubic is
+solved in closed form and polished with one Newton step, which recovers the digits the
+closed form loses when two of its roots are nearly coincident. Returns `NaN` if no root
+lies in the restricted range.
+"""
+function _cell_level_root(bf::SurfaceBField, ic::Int, btarget::Float64, θlo::Float64, θhi::Float64)
+ d, c, b, a = bf.poly[ic]
+ x0 = bf.knot[ic]
+ ulo, uhi = θlo - x0, θhi - x0
+ # Admit roots a rounding step outside the cell: θlo/θhi are stationary points and
+ # cell edges, and the root can sit exactly on one.
+ pad = 8 * eps(Float64) * max(abs(ulo), abs(uhi), bf.knot[ic+1] - x0)
+
+ n, r1, r2, r3 = _real_cubic_roots(a, b, c, d - btarget)
+ best, bestres = NaN, Inf
+ for k in 1:n
+ u = k == 1 ? r1 : (k == 2 ? r2 : r3)
+ (isfinite(u) && ulo - pad <= u <= uhi + pad) || continue
+ u = clamp(u, ulo, uhi)
+ # One Newton step on S(u) − btarget, skipped at a stationary point.
+ deriv = c + u * (2b + u * 3a)
+ if deriv != 0
+ un = u - (evalpoly(u, (d - btarget, c, b, a))) / deriv
+ (ulo - pad <= un <= uhi + pad) && (u = clamp(un, ulo, uhi))
+ end
+ res = abs(evalpoly(u, (d - btarget, c, b, a)))
+ if res < bestres
+ best, bestres = u, res
+ end
+ end
+ return isnan(best) ? NaN : x0 + best
+end
+
+"""
+Where `btarget` sits relative to cell `ic` of a monotone span: `-1` before it, `0`
+inside, `+1` past it. `s` carries the span's direction so one comparison serves both.
+The span's first and last cells are entered part-way, at the stationary points bounding
+it, so their outer edge value comes from `ba`/`bb` rather than from a knot.
+"""
+@inline function _cell_position(
+ bf::SurfaceBField, ic::Int, ia::Int, ib::Int,
+ ba::Float64, bb::Float64, btarget::Float64, s::Float64
+)
+ left = ic == ia ? ba : bf.bknot[ic]
+ right = ic == ib ? bb : bf.bknot[ic+1]
+ s * btarget < s * left && return -1
+ s * btarget > s * right && return 1
+ return 0
+end
+
+"""
+Cell holding the `B = btarget` crossing on a monotone span running from cell `ia` to
+cell `ib`. λ ascends, so resuming from the previous λ's cell (`hint`) usually costs a step
+or two; bisection is the fallback when the hint is more than `HINT_STEP_BUDGET` cells off.
+"""
+function _locate_cell(
+ bf::SurfaceBField, ia::Int, ib::Int, ba::Float64, bb::Float64,
+ btarget::Float64, hint::Int
+)
+ s = bb >= ba ? 1.0 : -1.0
+ ic = clamp(hint, ia, ib)
+ pos = _cell_position(bf, ic, ia, ib, ba, bb, btarget, s)
+ steps = 0
+ while pos != 0 && steps < HINT_STEP_BUDGET
+ ic += pos
+ (ia <= ic <= ib) || return _bisect_cell(bf, ia, ib, btarget, s)
+ pos = _cell_position(bf, ic, ia, ib, ba, bb, btarget, s)
+ steps += 1
+ end
+ return pos == 0 ? ic : _bisect_cell(bf, ia, ib, btarget, s)
+end
+
+"""
+Bisection on the span's monotone knot values, for when the hint does not pay off.
+"""
+function _bisect_cell(bf::SurfaceBField, ia::Int, ib::Int, btarget::Float64, s::Float64)
+ ia >= ib && return ia
+ s * bf.bknot[ia+1] > s * btarget && return ia
+ s * bf.bknot[ib] <= s * btarget && return ib
+ lo, hi = ia + 1, ib
+ while hi - lo > 1
+ mid = (lo + hi) >>> 1
+ s * bf.bknot[mid] <= s * btarget ? (lo = mid) : (hi = mid)
+ end
+ return lo
+end
+
+"""
+Solve the single `B = btarget` crossing on `[θa, θb]`, a span on which B is monotone and
+which does not cross the θ = 0/1 seam. Returns `(θ, cell)`; the cell feeds back as the
+next λ's hint. `θ` is `NaN` when no root lies in the span.
+"""
+function _monotone_segment_root(
+ bf::SurfaceBField, θa::Float64, θb::Float64,
+ btarget::Float64, hint::Int
+)
+ ia = _cell_index(bf.knot, θa)
+ ib = max(_cell_index(bf.knot, θb), ia)
+ ba = _b_at(bf.knot, bf.poly, θa)
+ bb = _b_at(bf.knot, bf.poly, θb)
+
+ ic = ia == ib ? ia : _locate_cell(bf, ia, ib, ba, bb, btarget, hint)
+ root = _cell_level_root(bf, ic, btarget, max(θa, bf.knot[ic]), min(θb, bf.knot[ic+1]))
+ # A target landing within rounding of a knot can select the neighbouring cell.
+ isnan(root) && ic > ia && (root = _cell_level_root(bf, ic - 1, btarget, max(θa, bf.knot[ic-1]), min(θb, bf.knot[ic])))
+ isnan(root) && ic < ib && (root = _cell_level_root(bf, ic + 1, btarget, max(θa, bf.knot[ic+1]), min(θb, bf.knot[ic+2])))
+ return root, ic
+end
+
+"""
+Bounce points of `v_par(θ) = 1 − (λ/bo)·B(θ)` for a trapped particle. `B = bo/λ` at a
+bounce point, so a monotone interval between stationary points of B contains one iff
+`bo/λ` lies strictly between its endpoint B values; the crossing is then solved from the
+cell's cubic, with `hints` carrying each interval's cell over from the previous λ.
+
+Returns roots sorted ascending, as Fortran `spline_roots`, so the deepest-well search pairs neighbouring
+roots; fewer than two roots signals a degenerate λ and sends the caller to
+the fallback. `hints` is sized `length(bf.theta) + 1`, the extra slot being the far half
+of the interval that wraps through the seam.
+"""
+function _bounce_points_at_lambda!(
+ bpts::Vector{Float64}, hints::Vector{Int},
+ bf::SurfaceBField, lmda::Float64, bo::Float64
+)
+ empty!(bpts)
+ k = length(bf.theta)
+ k < 2 && return bpts
+
+ btarget = bo / lmda
+ for i in 1:k
+ j = i == k ? 1 : i + 1
+ (bf.bval[i] - btarget) * (bf.bval[j] - btarget) < 0 || continue
+ θa, θb = bf.theta[i], bf.theta[j]
+
+ root = NaN
+ if i < k
+ root, hints[i] = _monotone_segment_root(bf, θa, θb, btarget, hints[i])
+ else
+ # The last interval wraps through θ = 0/1. Split it at the seam, where B is
+ # continuous for the periodic fit, and solve whichever half spans btarget.
+ if (bf.bval[i] - btarget) * (bf.bknot[end] - btarget) <= 0
+ root, hints[k] = _monotone_segment_root(bf, θa, 1.0, btarget, hints[k])
+ else
+ root, hints[k+1] = _monotone_segment_root(bf, 0.0, θb, btarget, hints[k+1])
+ end
+ end
+
+ isnan(root) && return empty!(bpts)
+ push!(bpts, mod(root, 1.0))
+ end
+
+ sort!(bpts)
+ return bpts
+end
+
+
+"""
+Find bounce points for trapped/passing particles and build θ sub-grid.
+Returns (t1, t2, theta_points, theta_weights).
+"""
+function _find_bounce_points_and_grid(
+ lmda::Float64, bo::Float64, sigma::Int,
+ B_vpar, theta_bmax::Float64, psi::Float64,
+ ntheta::Int, bf::SurfaceBField, bpts_buf::Vector{Float64}, hints::Vector{Int}
+)
+ if sigma == 0 # trapped
+ # Bounce points: roots of v_par(θ) in (0,1), sorted ascending so neighbours bound one well or barrier.
+ bpts = _bounce_points_at_lambda!(bpts_buf, hints, bf, lmda, bo)
+
+ if length(bpts) < 2
+ # Degenerate λ (v_par tangent to zero at an extremum, or < 2 stationary points of B): rare,
+ # so fall back to an adaptive whole-interval root scan.
+ vpar_fn = θ -> _vpar_from_spline(B_vpar, lmda, bo, θ)
+ bpts = sort!(Roots.find_zeros(vpar_fn, 0.0, 1.0))
+ end
+
+ nbpts = length(bpts)
+ if nbpts < 1
+ @warn "No bounce points found at psi=$psi, λ=$lmda — using full transit" maxlog = 3
+ t1 = theta_bmax
+ t2 = theta_bmax + 1.0
+ elseif nbpts < 2
+ # Marginally trapped
+ t1 = bpts[1]
+ t2 = bpts[1] + 1.0
+ else
+ t1, t2 = _find_deepest_well(bpts, B_vpar, lmda, bo)
+ end
+
+ # Power-law grid refined near bounce points
+ tdt_pts, tdt_wts = powspace(t1, t2, 4, ntheta, "both")
+
+ else # passing — full transit
+ t1 = theta_bmax
+ t2 = theta_bmax + 1.0
+ tdt_pts, tdt_wts = powspace(t1, t2, 2, ntheta, "both")
+ end
+
+ return t1, t2, tdt_pts, tdt_wts
+end
+
+
+"""
+Find the deepest potential well (largest midpoint v_par) among bounce-point pairs,
+handling pairs that wrap through θ = 0/1.
+"""
+function _find_deepest_well(bpts::Vector{Float64}, B_vpar, lmda::Float64, bo::Float64)
+ nbpts = length(bpts)
+ best_vpar = 0.0
+ best_t1 = 0.0
+ best_t2 = 1.0
+
+ for i in 1:nbpts
+ j = (i % nbpts) + 1 # next bounce point, wrapping
+ if bpts[i] > bpts[j]
+ # Wrapping case: midpoint crosses θ=0/1 boundary
+ θmid = mod(0.5 * (bpts[i] + bpts[j] + 1.0), 1.0)
+ else
+ θmid = 0.5 * (bpts[i] + bpts[j])
+ end
+ vpar_mid = _vpar_from_spline(B_vpar, lmda, bo, θmid)
+ if vpar_mid > best_vpar
+ best_t1 = bpts[i]
+ best_t2 = bpts[j]
+ if best_t2 < best_t1
+ best_t2 += 1.0
+ end
+ best_vpar = vpar_mid
+ end
+ end
+
+ if best_vpar ≈ 0.0
+ @warn "Could not find potential well with positive v_par" maxlog = 1
+ end
+
+ return best_t1, best_t2
+end
+
+
+"""
+ _bounce_samples!(fsi_wb, jvtheta, wmu_mt, wen_mt, tdt_pts, tdt_wts, lmda, n, q, bo, tspl, B_vpar,
+ chi1, mfac, dbob_m_f, divx_m_f, divxfac, do_matrices, mpert, scr) → (total_wb, total_wd)
+
+Sample the bounce integrands of one orbit on its θ sub-grid and integrate them: writes the cumulative
+bounce action into `fsi_wb`, the action integrand into `jvtheta` and, on the matrix path, the W_μ/W_E
+samples into `wmu_mt`/`wen_mt`; returns the total bounce-action and drift integrals. Nothing here depends
+on the bounce harmonic.
+"""
+function _bounce_samples!(
+ fsi_wb::AbstractVector{Float64}, jvtheta::AbstractVector{ComplexF64}, wmu_mt, wen_mt,
+ tdt_pts::Vector{Float64}, tdt_wts::Vector{Float64},
+ lmda::Float64, n::Int, q::Float64, bo::Float64,
+ tspl, B_vpar, chi1::Float64,
+ mfac::Vector{Int}, dbob_m_f::Vector{ComplexF64}, divx_m_f::Vector{ComplexF64},
+ divxfac::Float64, do_matrices::Bool, mpert::Int, scr::BounceScratch
+)
+ ntheta = length(tdt_pts)
+ theta0 = tdt_pts[1]
+
+ # θ-sample integrands (zero-reset per λ: the loop populates 2:ntheta-1 with
+ # continue/break paths that rely on unwritten entries staying 0)
+ g_wb = scr.g_wb # J·B/√v_par · dθ/dx
+ g_wd = scr.g_wd # drift integrand · dθ/dx
+ fill!(g_wb, 0.0)
+ fill!(g_wd, 0.0)
+
+ # Action integrand
+ fill!(jvtheta, ComplexF64(0.0))
+
+ # W vectors for matrix path
+ if do_matrices
+ fill!(wmu_mt, ComplexF64(0.0))
+ fill!(wen_mt, ComplexF64(0.0))
+ end
+
+ # Scratch for hot-loop tspl evaluation + Fourier-basis buffer (fully written per use).
+ tspl_f = scr.tspl_f
+ expm = scr.expm
+
+ for i in 2:ntheta-1 # Edge weights are 0 from powspace
+ θ = tdt_pts[i]
+ dt = tdt_wts[i]
+ θmod = mod(θ, 1.0)
+
+ tspl(tspl_f, θmod)
+ B_val = tspl_f[1]
+ dBdpsi = tspl_f[2]
+ jac = tspl_f[4]
+ djdpsi = tspl_f[5]
+
+ # v_par from the periodic cubic (consistent with the bounce points);
+ # the periodic tspl B_val remains the numerator field in the integrands.
+ vpar = 1.0 - (lmda / bo) * B_vpar(θmod)
+
+ if vpar <= 0
+ # Negative v_par near a bounce point: same fill rules as the Fortran bounce loop.
+ if i < ntheta ÷ 2
+ # Before midpoint: restart — zero everything up to this sample.
+ fill!(view(g_wb, 1:i), 0.0)
+ fill!(view(g_wd, 1:i), 0.0)
+ fill!(view(jvtheta, 1:i), ComplexF64(0.0))
+ continue
+ else
+ # After midpoint: hold the previous sample to the end of the grid.
+ fill!(view(g_wb, i:ntheta), g_wb[i-1])
+ fill!(view(g_wd, i:ntheta), g_wd[i-1])
+ fill!(view(jvtheta, i:ntheta), jvtheta[i-1])
+ break
+ end
+ end
+
+ sqrt_vpar = sqrt(vpar)
+
+ # Bounce integrands
+ g_wb[i] = dt * jac * B_val / sqrt_vpar
+ g_wd[i] = dt * jac * dBdpsi * (1.0 - 1.5 * lmda * B_val / bo) / sqrt_vpar +
+ dt * djdpsi * B_val * sqrt_vpar
+
+ # Fourier modes at this θ
+ @inbounds for mi in 1:mpert
+ expm[mi] = cis(twopi * mfac[mi] * θ)
+ end
+ dbob = ComplexF64(0.0)
+ divx = ComplexF64(0.0)
+ @inbounds for mi in 1:mpert
+ dbob += dbob_m_f[mi] * expm[mi]
+ divx += divx_m_f[mi] * expm[mi]
+ end
+ divx *= divxfac
+
+ # Action integrand
+ phase = cis(-twopi * n * q * (θ - theta0))
+ jvtheta[i] = dt * jac * B_val *
+ (divx * sqrt_vpar + dbob * (1.0 - 1.5 * lmda * B_val / bo) / sqrt_vpar) *
+ phase
+
+ # W vectors for matrix path
+ if do_matrices
+ wmu_pre = dt * (lmda / bo)
+ wen_pre = dt
+ @inbounds for mi in 1:mpert
+ wmu_mt[mi, i] = wmu_pre * expm[mi] / sqrt_vpar * phase / (2 * chi1)
+ wen_mt[mi, i] = wen_pre * expm[mi] / (B_val * sqrt_vpar) * phase / (2 * chi1)
+ end
+ end
+
+ # Smooth backfill for points zeroed before a restart. Exact equality with
+ # 0.0 is safe: the restart branch set these entries with fill!(…, 0.0).
+ if i >= 3 && g_wb[i-1] == 0.0
+ fill!(view(g_wb, 3:i-1), g_wb[i])
+ fill!(view(g_wd, 3:i-1), g_wd[i])
+ fill!(view(jvtheta, 2:i-1), jvtheta[i])
+ end
+ end
+
+ # Total bounce integrals by exact-cubic quadrature on the unit x-grid (see `_quadrature_weights`);
+ # with the 1/√v_par endpoint singularities the scheme matters at leading order, so not a trapezoid sum.
+ cum_wb = scr.cum_wb_arr # per-surface scratch; fully overwritten
+ mul!(cum_wb, scr.cumint_W, g_wb)
+ copyto!(fsi_wb, cum_wb)
+ total_wb = cum_wb[ntheta]
+ total_wd = dot(scr.int_w, g_wd)
+ return total_wb, total_wd
+end
+
+"""
+ _bounce_harmonic_tail(fsi_wb, jvtheta, wmu_mt, wen_mt, total_wb, wbbar, lnq, sigma, ro,
+ do_matrices, mpert, smat, tmat, xmat, ymat, zmat, scr) → (dJdJ, wmats_lmda)
+
+The bounce-harmonic-dependent end of the bounce integral for one λ: the phase factor
+`exp(−2πi·lnq·fsi_wb/((2−σ)·total_wb))`, the action bounce integral |δJ|² and, on the matrix path,
+the bounce-averaged W vectors and their packed outer products.
+"""
+function _bounce_harmonic_tail(
+ fsi_wb::AbstractVector{Float64}, jvtheta::AbstractVector{ComplexF64}, wmu_mt, wen_mt,
+ total_wb::Float64, wbbar::Float64, lnq::Float64, sigma::Int, ro::Float64,
+ do_matrices::Bool, mpert::Int, smat, tmat, xmat, ymat, zmat, scr::BounceScratch
+)
+ ntheta = length(fsi_wb)
+
+ # Phase factor pl_i = exp(-2πi·lnq·fsi_wb(θ_i)/((2-σ)·total_wb)), using the
+ # cumulative spline integral of the bounce action.
+ pl_denom = (2 - sigma) * total_wb
+ one_minus_sigma = 1 - sigma
+ pl = scr.pl # per-surface scratch; fully overwritten
+ @inbounds for i in 1:ntheta
+ pl[i] = cis(-twopi * lnq * fsi_wb[i] / pl_denom)
+ end
+
+ # Action bounce integral (exact-cubic quadrature, as for the totals above).
+ bj_samples = scr.bj_samples
+ @inbounds for i in 1:ntheta
+ bj_samples[i] = conj(jvtheta[i]) * (pl[i] + one_minus_sigma / pl[i])
+ end
+ bj_integral = dot(scr.int_w, bj_samples)
+
+ # |δJ|² — division by 2 corrects the quadratic form
+ dJdJ_val = wbbar * abs(bj_integral)^2 / 2.0 / ro^2
+
+ # Matrix path: bounce-average W vectors and form outer products
+ wmats_lmda = nothing
+ if do_matrices
+ # Per mode, exact-cubic quadrature of conj(W_m(θ))·(pl + (1-σ)/pl),
+ # matching the action bounce integral above.
+ wmu_ba = scr.wmu_ba
+ wen_ba = scr.wen_ba
+ wsamp = scr.wsamp
+ @inbounds for mi in 1:mpert
+ for i in 1:ntheta
+ wsamp[i] = conj(wmu_mt[mi, i]) * (pl[i] + one_minus_sigma / pl[i])
+ end
+ wmu_ba[mi] = conj(dot(scr.int_w, wsamp))
+ for i in 1:ntheta
+ wsamp[i] = conj(wen_mt[mi, i]) * (pl[i] + one_minus_sigma / pl[i])
+ end
+ wen_ba[mi] = conj(dot(scr.int_w, wsamp))
+ end
+
+ # Reshape as 1×mpert for matrix multiply
+ wmmt = reshape(wmu_ba, 1, mpert)
+ wemt = reshape(wen_ba, 1, mpert)
+
+ # Build W_X, W_Y, W_Z via geometric matrices
+ wxmt = wmmt * xmat
+ wymt = wmmt * (3 * smat + ymat) - 2.0 * wemt * smat
+ wzmt = wmmt * (3 * tmat + zmat) - 2.0 * wemt * tmat
+
+ # Flatten the 1×mpert row vectors to mpert-vectors for outer-product loops.
+ wx = vec(wxmt)
+ wy = vec(wymt)
+ wz = vec(wzmt)
+
+ # Scale by wbbar/ro²
+ scale = wbbar / ro^2
+ Mu = (mpert * (mpert + 1)) ÷ 2
+ wmats_lmda = scr.wmats_lmda
+ # Fill with NaN to catch uninitialized entries
+ fill!(wmats_lmda, ComplexF64(NaN, NaN))
+
+ # A (Hermitian): upper triangle of W_Z†W_Z, rank-1 → conj(wz[i])·wz[j].
+ off = 0
+ @inbounds for j in 1:mpert, i in 1:j
+ wmats_lmda[off+_tri_idx(i, j)] = conj(wz[i]) * wz[j] * scale
+ end
+ off += Mu
+ # D (Hermitian): upper triangle of W_X†W_X.
+ @inbounds for j in 1:mpert, i in 1:j
+ wmats_lmda[off+_tri_idx(i, j)] = conj(wx[i]) * wx[j] * scale
+ end
+ off += Mu
+ # H (Hermitian): upper triangle of W_Y†W_Y.
+ @inbounds for j in 1:mpert, i in 1:j
+ wmats_lmda[off+_tri_idx(i, j)] = conj(wy[i]) * wy[j] * scale
+ end
+ off += Mu
+ # B (full): W_Z†W_X.
+ @inbounds for j in 1:mpert, i in 1:mpert
+ wmats_lmda[off+_full_idx(i, j, mpert)] = conj(wz[i]) * wx[j] * scale
+ end
+ off += mpert^2
+ # C (full): W_Z†W_Y.
+ @inbounds for j in 1:mpert, i in 1:mpert
+ wmats_lmda[off+_full_idx(i, j, mpert)] = conj(wz[i]) * wy[j] * scale
+ end
+ off += mpert^2
+ # E (full): W_X†W_Y.
+ @inbounds for j in 1:mpert, i in 1:mpert
+ wmats_lmda[off+_full_idx(i, j, mpert)] = conj(wx[i]) * wy[j] * scale
+ end
+ end
+
+ return dJdJ_val, wmats_lmda
+end
diff --git a/src/KineticForces/CalculatedKineticMatrices.jl b/src/KineticForces/CalculatedKineticMatrices.jl
new file mode 100644
index 0000000000..7ffea77ce2
--- /dev/null
+++ b/src/KineticForces/CalculatedKineticMatrices.jl
@@ -0,0 +1,199 @@
+"""
+ CalculatedKineticMatrices
+
+Bridge from KineticForces' bounce-averaged matrix kernels into the kinetic-MHD
+stability path in ForceFreeStates. Used by `evaluate_kinetic_matrices` when
+the force-balance problem's `kinetic` source is a `KineticForcesControl` (via the
+`calculated_source` callback injected by the force-balance solve).
+"""
+
+"""
+ compute_calculated_kinetic_matrices(ffs_ctrl, equil, ffs_intr, metric, mats;
+ kf_ctrl=KineticForcesControl(), kinetic_profiles,
+ species=nothing, psis=Float64[], axis_psi_c=0.0)
+ → (kw_flat, kt_flat)
+
+Drive the KineticForces matrix kernel over the ψ grid (`metric.xs` unless `psis` is given) and
+return `(kw_flat, kt_flat)` arrays of shape `(mpsi, np^2, 6)` matching the
+contract that `ForceFreeStates._compute_fkg_matrices` consumes.
+
+The arrays carry the six bounce-averaged kinetic energy / torque matrices
+(Logan 2015 Eqs 7.30–7.35) for every ψ on the equilibrium grid, packed as
+block-diagonal matrices over toroidal mode number n ∈ [nlow, nhigh] and
+flattened to `(np = mpert·npert)²`. The species contributions are summed.
+
+# Arguments
+
+ - `ffs_ctrl`: ForceFreeStatesControl (unused; kept for the callback signature)
+ - `equil`: PlasmaEquilibrium with 2D interpolants and named profile/geometry splines
+ - `ffs_intr`: ForceFreeStatesInternal (mode indexing)
+ - `metric`: MetricData (default ψ grid `metric.xs`, Fourier fit for the geometric matrices)
+ - `mats`: MatrixSplines (unused)
+
+# Keyword arguments
+
+ - `kf_ctrl`: KineticForcesControl with the kinetic model settings ForceFreeStatesControl does not expose
+ - `kinetic_profiles::Equilibrium.KineticProfileSplines`: Required. Named kinetic-profile splines
+ built by `Equilibrium.kinetic_profile_splines`.
+ - `species`: resolved species set to sum; `nothing` uses the equilibrium's main ion alone
+ - `psis`: ψ grid for the kernel; empty (default) evaluates on `metric.xs`
+ - `axis_psi_c`: near-axis validity boundary; used when `kf_ctrl.axis_validity_suppression` is set
+
+# Returns
+
+ - `kw_flat::Array{ComplexF64,3}`: Energy matrices, shape `(mpsi, np^2, 6)`
+ - `kt_flat::Array{ComplexF64,3}`: Torque matrices, shape `(mpsi, np^2, 6)`
+"""
+function compute_calculated_kinetic_matrices(
+ _ffs_ctrl,
+ equil,
+ ffs_intr,
+ metric,
+ mats;
+ kf_ctrl::KineticForcesControl=KineticForcesControl(),
+ kinetic_profiles::Equilibrium.KineticProfileSplines,
+ species::Union{Nothing,AbstractVector{<:Equilibrium.ResolvedNTVSpecies}}=nothing,
+ psis::Vector{Float64}=Float64[],
+ axis_psi_c::Float64=0.0
+)
+ # The kernel is a pure function of psi (it evaluates equilibrium splines), so it can be
+ # driven over any knot list; default is the full equilibrium grid.
+ xs = isempty(psis) ? metric.xs : psis
+ mpsi = length(xs)
+ mpert = ffs_intr.mpert
+ npert = ffs_intr.npert
+ np = ffs_intr.numpert_total
+
+ kw_flat = zeros(ComplexF64, mpsi, np^2, 6)
+ kt_flat = zeros(ComplexF64, mpsi, np^2, 6)
+
+ # Build the KineticForces internal state from equilibrium + ForceFreeStates mode indexing.
+ kf_intr = KineticForcesInternal(equil; verbose=ffs_intr.verbose)
+ kf_intr.mlow = ffs_intr.mlow
+ kf_intr.mhigh = ffs_intr.mhigh
+ kf_intr.mpert = mpert
+ kf_intr.nlow = ffs_intr.nlow
+ kf_intr.nhigh = ffs_intr.nhigh
+ kf_intr.npert = npert
+ kf_intr.numpert_total = np
+ kf_intr.mfac = collect(ffs_intr.mlow:ffs_intr.mhigh)
+
+ # Geometric matrices for the kinetic W kernel come from ForceFreeStates' Fourier fit.
+ geom_mats = ForceFreeStates.build_kinetic_metric_matrices(equil, ffs_intr, metric)
+ kf_intr.smats = geom_mats.smats
+ kf_intr.tmats = geom_mats.tmats
+ kf_intr.xmats = geom_mats.xmats
+ kf_intr.ymats = geom_mats.ymats
+ kf_intr.zmats = geom_mats.zmats
+
+ # Loop over flux surfaces and n-blocks, accumulating bounce harmonics into
+ # per-n blocks placed on the diagonal of the full np×np block-diagonal matrix.
+ # The ψ-loop is embarrassingly parallel: each iteration writes its own ipsi row of
+ # kw_flat/kt_flat, and the kernel only reads kf_intr, so it is shared across threads.
+ nl = kf_ctrl.bounce_harmonic_max
+ rtol_pitch = matrix_pitch_rtol(kf_ctrl)
+ nthreads = Threads.maxthreadid()
+ thread_full_w = [zeros(ComplexF64, mpert, mpert, 6) for _ in 1:nthreads]
+ thread_full_t = [zeros(ComplexF64, mpert, mpert, 6) for _ in 1:nthreads]
+ thread_block_w = [zeros(ComplexF64, mpert, mpert, 6) for _ in 1:nthreads]
+ thread_block_t = [zeros(ComplexF64, mpert, mpert, 6) for _ in 1:nthreads]
+
+ # Species summed into the matrices (additive over species): the resolved set, else the main ion alone.
+ splist = species === nothing ?
+ [Equilibrium.ResolvedNTVSpecies(main_ion(equil)..., kf_ctrl.electron, "single", kinetic_profiles)] : species
+
+
+ # Near-axis validity envelope: suppresses the drift-kinetic increments where the zero-orbit-width
+ # ordering fails (kernel evaluation skipped where it is 0). The same real scalar must scale kw and
+ # kt at the same ψ — that is what keeps the blocks Hermitian and the energy/torque relation intact.
+ env = ones(Float64, mpsi)
+ if kf_ctrl.axis_validity_suppression
+ psi_c = axis_psi_c
+ if psi_c > 0
+ env .= kinetic_axis_validity_envelope.(xs, psi_c)
+ @info "Kinetic axis-validity suppression: psi_c=$(round(psi_c; sigdigits=3)), envelope reaches 1 at " *
+ "psi=$(round(2 * psi_c; sigdigits=3)) (kernel evaluation skipped below psi_c)" maxlog = 1
+ end
+ end
+
+ for sp in splist
+ # Hoisted per-species scalars: the closure then captures concrete values, not a
+ # union-typed `sp` (the ternary above mixes the resolved vector with the fallback).
+ z_s, m_s, el_s, prof_s = sp.z, sp.m, sp.electron, sp.profiles
+ # :static pins one task per thread so the threadid() buffer indexing below is sound
+ # (dynamic scheduling may migrate tasks at yield points, silently sharing buffers).
+ Threads.@threads :static for ipsi in 1:mpsi
+ tid = Threads.threadid()
+ full_w = thread_full_w[tid]
+ full_t = thread_full_t[tid]
+ block_w = thread_block_w[tid]
+ block_t = thread_block_t[tid]
+ psi = xs[ipsi]
+ env[ipsi] == 0.0 && continue # inside the near-axis validity band: kernel skipped
+ # (n, ℓ)-independent surface setup, built once per ψ.
+ state = _setup_surface_state(psi, z_s, m_s, el_s, equil, kf_intr, prof_s)
+ for in_idx in 1:npert
+ n = ffs_intr.nlow + in_idx - 1
+ fill!(full_w, 0)
+ fill!(full_t, 0)
+ # The bounce geometry depends on (ψ, n) only; the harmonics share it.
+ geometry = _matrix_bounce_geometry(state, psi, n, kf_ctrl.magnetic_drift_factor, kf_intr)
+ for ell in -nl:nl
+ fill!(block_w, 0)
+ fill!(block_t, 0)
+ compute_kinetic_matrices_at_psi!(
+ block_w, block_t, psi, n, ell,
+ z_s, m_s, kf_ctrl.magnetic_drift_factor,
+ el_s, equil, kf_intr, prof_s;
+ nutype=kf_ctrl.nutype, f0type=kf_ctrl.f0type, nufac=kf_ctrl.collisionality_factor,
+ atol_xlmda=kf_ctrl.atol_pitch, rtol_xlmda=rtol_pitch,
+ atol_x=kf_ctrl.atol_x, rtol_x=kf_ctrl.rtol_x,
+ nested_tolerance_margin=kf_ctrl.nested_tolerance_margin,
+ state, geometry
+ )
+ full_w .+= block_w
+ full_t .+= block_t
+ end
+
+ # Place the n-block on the diagonal of the full np×np matrix and accumulate.
+ row_offset = (in_idx - 1) * mpert
+ for k in 1:6, j in 1:mpert, i in 1:mpert
+ idx = (row_offset + j - 1) * np + (row_offset + i)
+ kw_flat[ipsi, idx, k] += env[ipsi] * full_w[i, j, k]
+ kt_flat[ipsi, idx, k] += env[ipsi] * full_t[i, j, k]
+ end
+ end
+ end
+ end
+
+ return kw_flat, kt_flat
+end
+
+# The force-balance solve's two-pass grid inputs: the kinetic profiles as the KineticForces model views them (its
+# control when the source is one, else the default control) and the kinetic-resonance surfaces to pin. The model
+# needs the NTV view, so an unusable profile errors; otherwise profiles read for another consumer (e.g. SLAYER without
+# omega_E, or with a zero edge density) are left out and the grid follows the equilibrium alone.
+function ForceFreeStates.kinetic_grid_inputs(source, ctrl, equil, intr; rationals)
+ kf_ctrl = source isa KineticForcesControl ? source : KineticForcesControl()
+ data = equil.kinetic
+ ntv = source isa KineticForcesControl || (data !== nothing && Equilibrium.ntv_profiles_usable(data))
+ data !== nothing && !ntv &&
+ @info "Two-pass psi grid: the kinetic profiles lack an NTV field (n_e, T_i, T_e, omega_E) or have a non-positive density " *
+ "or negative temperature, so the grid follows the equilibrium alone"
+ kinetic_profiles = ntv ? ntv_profiles(kf_ctrl, equil) : nothing
+ species = ntv ? ntv_species(kf_ctrl, equil) : nothing
+ pinned = resonance_grid_nodes(ctrl, kf_ctrl, kinetic_profiles, species, equil, intr; rationals)
+ return kinetic_profiles, pinned
+end
+
+# The force-balance solve's kinetic matrices from the KineticForces model: the evaluation callback and the axis-validity
+# boundary, one for the whole run (the widest-orbit species, moved clear of any rational surface whose window the
+# transition band would otherwise cut through).
+function ForceFreeStates.kinetic_model_source(kf_ctrl::KineticForcesControl, equil, intr)
+ kinetic_profiles = ntv_profiles(kf_ctrl, equil)
+ species = ntv_species(kf_ctrl, equil)
+ axis_psi_c = axis_validity_boundary(kf_ctrl, species, kinetic_profiles, equil, Float64[sng.psifac for sng in intr.sing])
+ calculated_source = (c, e, i, m, f; psis::Vector{Float64}=Float64[]) ->
+ compute_calculated_kinetic_matrices(c, e, i, m, f; kf_ctrl, kinetic_profiles, species, psis, axis_psi_c)
+ return calculated_source, axis_psi_c
+end
diff --git a/src/KineticForces/Compute.jl b/src/KineticForces/Compute.jl
new file mode 100644
index 0000000000..dd087dc941
--- /dev/null
+++ b/src/KineticForces/Compute.jl
@@ -0,0 +1,487 @@
+"""
+ Compute
+
+High-level computation functions for KineticForces.
+Orchestrates torque/energy calculations across multiple methods
+using adaptive Gauss-Kronrod quadrature at all levels (ψ, λ, energy).
+"""
+
+# ============================================================================
+# Adaptive Gauss-Kronrod ψ integration via QuadGK.BatchIntegrand
+# ============================================================================
+
+# Minimum ψ separation for quadrature panel boundaries: interior points closer than this to
+# each other or to a domain bound are merged/dropped, so coincident rational and kinetic-
+# resonance surfaces do not create degenerate (near-zero-width) Gauss-Kronrod panels.
+const PANEL_MERGE_ATOL = 1e-8
+
+"""
+ psi_panel_points(interior, x0, xout) → Vector{Float64}
+
+Build the ψ-quadrature node list `[x0, interior points strictly inside (x0, xout), xout]`.
+`interior` is the unsorted union of resonant-surface locations; points closer than `PANEL_MERGE_ATOL`
+to each other or to a bound are dropped to avoid degenerate panels. Paneling at these surfaces puts
+the narrow resonant torque-density peaks on Gauss-Kronrod interval endpoints.
+"""
+function psi_panel_points(interior::Vector{Float64}, x0::Float64, xout::Float64)
+ pts = sort(filter(p -> x0 + PANEL_MERGE_ATOL < p < xout - PANEL_MERGE_ATOL, interior))
+ deduped = [p for (i, p) in enumerate(pts) if i == 1 || p - pts[i-1] > PANEL_MERGE_ATOL]
+ return [x0; deduped; xout]
+end
+
+"""
+ check_psi_quadrature_convergence(total, quad_err, ctrl, method)
+
+Warn when the ψ torque quadrature terminated without satisfying the requested tolerances
+(hit `maxevals_psi`), or when a nonzero user-set `atol_psi` dominated termination — the
+silent-garbage scenario for weak applied fields, since NTV scales as δB². Error when the
+torque or its error estimate is not finite, which the tolerance comparisons cannot catch.
+"""
+function check_psi_quadrature_convergence(total::ComplexF64, quad_err::Float64,
+ ctrl::KineticForcesControl, method::String)
+ isfinite(total) && isfinite(quad_err) || error("ψ torque quadrature ($method) returned a non-finite torque $total (error estimate $quad_err).")
+ if quad_err > max(ctrl.atol_psi, ctrl.rtol_psi * abs(total))
+ @warn "ψ torque quadrature ($method) did not converge within maxevals_psi=$(ctrl.maxevals_psi): " *
+ "error estimate $quad_err vs |T|=$(abs(total)) N·m. Raise maxevals_psi or loosen rtol_psi."
+ elseif ctrl.atol_psi > ctrl.rtol_psi * abs(total)
+ @warn "atol_psi=$(ctrl.atol_psi) N·m dominated ψ quadrature termination ($method): " *
+ "|T|=$(abs(total)) N·m is small relative to atol_psi, so the relative error is uncontrolled. " *
+ "NTV scales as δB², so weak applied fields shrink the torque quadratically — recommend atol_psi=0 (rtol-only)."
+ end
+ return nothing
+end
+
+"""
+ integrate_psi_quadgk(n, nl, zi, mi, wdfac, divxfac, electron, method,
+ equil, intr, ctrl, kinetic_profiles; psi_min, psi_max, axis_psi_c) → NamedTuple
+
+Integrate torque over ψ using adaptive Gauss-Kronrod quadrature with
+`QuadGK.BatchIntegrand`. Every integrand evaluation is logged as a diagnostic T(ψ) profile.
+
+# Returns
+
+NamedTuple with:
+
+ - `total::ComplexF64`: Total integrated torque
+ - `torque_profile`: NamedTuple `(psi, dtdpsi, t_cumulative, dtdpsi_ell, ell)` from the evaluation points
+ - `matrix_integrated`: Trapezoidal-integrated mpert×mpert×6 matrix (if matrix method)
+ - `psi_nsteps::Int`: Number of integrand evaluations
+ - `psi_quad_error::Float64`: Quadrature error estimate for the total torque
+ - `panel_psis::Vector{Float64}`: Quadrature panel boundaries actually used (bounds + interior resonant surfaces)
+ - `resonance_psis::Vector{Float64}`: Located kinetic-resonance ψ surfaces (Ω_ℓ(x=1)=0), for diagnostics/plotting
+
+The integral is paneled at the rational surfaces (`intr.sing_psis`) and kinetic resonances, and capped
+at `ctrl.maxevals_psi` evaluations; a warning is emitted if the quadrature fails to reach
+`ctrl.rtol_psi`/`ctrl.atol_psi` or if a nonzero `atol_psi` dominates termination.
+"""
+function integrate_psi_quadgk(
+ n::Int, nl::Int, zi::Int, mi::Int,
+ wdfac::Float64, divxfac::Float64, electron::Bool,
+ method::String, equil, intr::KineticForcesInternal, ctrl::KineticForcesControl,
+ kinetic_profiles::Equilibrium.KineticProfileSplines;
+ psi_min::Float64=0.0, psi_max::Float64=1.0, axis_psi_c::Float64=0.0
+)
+ is_matrix_method = occursin("mm", method)
+ mpert = intr.mpert
+
+ # Start at psilow (degenerate bounce/drift frequencies at the axis); stop at intr.psilim, where the
+ # perturbation data ends.
+ x0 = max(psi_min, equil.config.psilow)
+ xout = min(psi_max, intr.psilim, 1.0 - 1e-6)
+
+ if x0 >= xout
+ return (total=ComplexF64(0.0), torque_profile=nothing, matrix_integrated=nothing, psi_nsteps=0, psi_quad_error=0.0,
+ panel_psis=Float64[], resonance_psis=Float64[])
+ end
+
+ # Near-axis validity suppression on the torque density. `axis_psi_c` is the run's single
+ # boundary (widest-orbit species, cleared of rationals), so the quadrature domain matches the
+ # EL kinetic matrices and the Validity output; below it the integrand is identically zero.
+ psi_c = ctrl.axis_validity_suppression ? axis_psi_c : 0.0
+ x0 = max(x0, psi_c)
+ if x0 >= xout
+ return (total=ComplexF64(0.0), torque_profile=nothing, matrix_integrated=nothing, psi_nsteps=0, psi_quad_error=0.0,
+ panel_psis=Float64[], resonance_psis=Float64[])
+ end
+ psi_c > 0 && @info "Kinetic axis-validity suppression in ψ torque quadrature: domain starts at psi_c=$(round(psi_c; sigdigits=3))"
+
+ # Each batch is threaded in two passes, `chunk` nodes at a time: per-node surface setup, then every
+ # (node, ℓ) pitch quadrature. Harmonics are reduced in fixed ℓ order, so the sum is independent of
+ # thread count. `:static` keeps the threadid()-indexed slots sound; never nest it.
+ nharm = 1 + 2 * nl
+ rtol_pitch = torque_pitch_rtol(ctrl)
+ nth = Threads.maxthreadid()
+ chunk = is_matrix_method ? nth : 2 * nth
+ thread_tpsi = [Ref{ComplexF64}(0.0im) for _ in 1:nth]
+ thread_wtw = is_matrix_method ? [zeros(ComplexF64, mpert, mpert, 6) for _ in 1:nth] : nothing
+
+ logged_psi = Float64[]
+ logged_dtdpsi = ComplexF64[]
+ logged_dtdpsi_ell = Vector{Vector{ComplexF64}}()
+ logged_elems = is_matrix_method ? Vector{Array{ComplexF64,3}}() : nothing
+
+ function psi_batch!(y::AbstractVector{ComplexF64}, x::AbstractVector)
+ for c0 in 1:chunk:length(x)
+ idx = c0:min(c0 + chunk - 1, length(x))
+ nc = length(idx)
+
+ surfaces = Vector{Any}(undef, nc)
+ Threads.@threads :static for j in 1:nc
+ surfaces[j] = _torque_surface(Float64(x[idx[j]]), zi, mi, electron, method, equil, intr, kinetic_profiles;
+ need_matrices=is_matrix_method, n, wdfac, divxfac)
+ end
+
+ harm_vals = Matrix{ComplexF64}(undef, nharm, nc)
+ harm_elems = is_matrix_method ? [zeros(ComplexF64, mpert, mpert, 6) for _ in 1:nharm, _ in 1:nc] : nothing
+ Threads.@threads :static for item in 1:(nc*nharm)
+ j, ell_idx = divrem(item - 1, nharm) .+ 1
+ tid = Threads.threadid()
+ l = ell_idx - 1 - nl
+ w = is_matrix_method ? thread_wtw[tid] : nothing
+ is_matrix_method && fill!(w, 0)
+ tpsi!(thread_tpsi[tid], Float64(x[idx[j]]), n, l, zi, mi, wdfac, divxfac,
+ electron, method, equil, intr, kinetic_profiles;
+ op_wmats=w, surface=surfaces[j],
+ atol_xlmda=ctrl.atol_pitch, rtol_xlmda=rtol_pitch,
+ atol_x=ctrl.atol_x, rtol_x=ctrl.rtol_x,
+ nested_tolerance_margin=ctrl.nested_tolerance_margin)
+ harm_vals[ell_idx, j] = thread_tpsi[tid][]
+ is_matrix_method && (harm_elems[ell_idx, j] .= w)
+ end
+
+ for j in 1:nc
+ k = idx[j]
+ psi = Float64(x[k])
+ # Reduce in fixed ℓ order (bit-identical to the serial sum).
+ total = ComplexF64(0.0)
+ for ell_idx in 1:nharm
+ total += harm_vals[ell_idx, j]
+ end
+ envelope = kinetic_axis_validity_envelope(psi, psi_c)
+ total *= envelope
+ y[k] = total
+
+ push!(logged_psi, psi)
+ push!(logged_dtdpsi, total)
+ # Same envelope as `total` so Σ_ℓ still reproduces it.
+ push!(logged_dtdpsi_ell, harm_vals[:, j] .* envelope)
+ if is_matrix_method
+ elems_accum = zeros(ComplexF64, mpert, mpert, 6)
+ for ell_idx in 1:nharm
+ elems_accum .+= harm_elems[ell_idx, j]
+ end
+ elems_accum .*= envelope
+ push!(logged_elems, elems_accum)
+ end
+ end
+ end
+ end
+
+ # Panels at the rational surfaces the run resolved plus the kinetic-resonance
+ # surfaces (thermal-energy Ω_ℓ = 0 for ℓ ∈ -nl:nl) — both are torque-density peaks.
+ resonance_psis = kinetic_resonance_psi_nodes(kinetic_profiles, equil; n, nl, zi, mi, electron, wdfac)
+ pts = psi_panel_points(vcat(intr.sing_psis, resonance_psis, [2 * psi_c]), x0, xout)
+
+ bi = QuadGK.BatchIntegrand(psi_batch!, ComplexF64[], Float64[])
+ total, quad_err = quadgk(bi, pts...; atol=ctrl.atol_psi, rtol=ctrl.rtol_psi, maxevals=ctrl.maxevals_psi)
+
+ check_psi_quadrature_convergence(total, quad_err, ctrl, method)
+
+ # Sort logs by ψ for the diagnostic torque profile.
+ perm = sortperm(logged_psi)
+ sorted_psi = logged_psi[perm]
+ sorted_dtdpsi = logged_dtdpsi[perm]
+ # Per-ℓ profile, permuted by the SAME `perm`: QuadGK visits nodes in refinement order, not in
+ # ψ order, so a per-ℓ log left unsorted would misalign with `sorted_psi` without any error.
+ # `reduce(hcat, ...)` builds (nharm, npsi); transpose so ψ is the first axis, as `dtdpsi` is.
+ sorted_dtdpsi_ell = isempty(logged_dtdpsi_ell) ? zeros(ComplexF64, 0, 0) :
+ permutedims(reduce(hcat, logged_dtdpsi_ell[perm]))
+
+ # Cumulative trapezoidal integration for T(ψ) profile
+ npts = length(sorted_psi)
+ t_cumulative = Vector{ComplexF64}(undef, npts)
+ if npts >= 1
+ t_cumulative[1] = ComplexF64(0.0)
+ for i in 2:npts
+ dpsi = sorted_psi[i] - sorted_psi[i-1]
+ t_cumulative[i] = t_cumulative[i-1] + 0.5 * (sorted_dtdpsi[i-1] + sorted_dtdpsi[i]) * dpsi
+ end
+ end
+
+ torque_profile = npts > 1 ?
+ (psi=sorted_psi, dtdpsi=sorted_dtdpsi, t_cumulative=t_cumulative,
+ dtdpsi_ell=sorted_dtdpsi_ell, ell=collect(-nl:nl)) : nothing
+
+ # Trapezoidal integration of kinetic matrices over ψ (matrix methods only)
+ matrix_integrated = nothing
+ if is_matrix_method && !isnothing(logged_elems) && length(logged_elems) > 1
+ sorted_elems = logged_elems[perm]
+ matrix_integrated = zeros(ComplexF64, mpert, mpert, 6)
+ for i in 2:npts
+ dpsi = sorted_psi[i] - sorted_psi[i-1]
+ matrix_integrated .+= 0.5 .* (sorted_elems[i-1] .+ sorted_elems[i]) .* dpsi
+ end
+ end
+
+ in_span(p) = x0 + PANEL_MERGE_ATOL < p < xout - PANEL_MERGE_ATOL
+ n_rational = count(in_span, intr.sing_psis)
+ n_resonance = count(in_span, resonance_psis)
+ @info "ψ torque quadrature ($method): T=$total N·m, error estimate $quad_err, $npts integrand evaluations over " *
+ "$(length(pts) - 1) panels ($n_rational rational + $n_resonance kinetic resonance surfaces)"
+
+ return (total=total, torque_profile=torque_profile, matrix_integrated=matrix_integrated, psi_nsteps=npts, psi_quad_error=quad_err,
+ panel_psis=pts, resonance_psis=sort(resonance_psis))
+end
+
+
+# ============================================================================
+# High-level orchestration
+# ============================================================================
+
+"""
+ _accumulate_interp!(acc, grid, xs, ys)
+
+Add the linear interpolant of `(xs, ys)` onto `grid` into `acc`, contributing zero outside
+`[xs[1], xs[end]]`. `xs` must be sorted ascending. A duplicate node or the right endpoint takes
+`ys[j]` directly rather than dividing by a zero interval. Shared by the total and per-ℓ profiles in
+[`combine_species_states`](@ref) so both use identical interpolation.
+"""
+function _accumulate_interp!(acc, grid, xs::AbstractVector{Float64}, ys::AbstractVector{ComplexF64})
+ for (k, ψ) in enumerate(grid)
+ (ψ < xs[1] || ψ > xs[end]) && continue
+ j = searchsortedlast(xs, ψ)
+ if j == length(xs) || xs[j+1] == xs[j] # endpoint or duplicate node: no interpolation
+ acc[k] += ys[j]
+ else
+ t = (ψ - xs[j]) / (xs[j+1] - xs[j])
+ acc[k] += (1 - t) * ys[j] + t * ys[j+1]
+ end
+ end
+ return acc
+end
+
+"""
+ combine_species_states(states) -> KineticForcesState
+
+Sum per-species [`KineticForcesState`](@ref) results into a single total (τ = Σ_s τ_s). Per
+method the scalar `total_torque`/`total_energy` are summed exactly; dT/dψ is summed by linear
+interpolation onto the union of the species ψ grids and `t_cumulative` re-integrated by trapezoid, so
+its endpoint need not equal the summed `total_torque`. Per-species diagnostics (`torque_profile`,
+`records`, `panel_psis`, `resonance_psis`) are not aggregated and are left at their defaults.
+"""
+function combine_species_states(states::AbstractVector{KineticForcesState})
+ combined = KineticForcesState()
+ isempty(states) && return combined
+ method_names = sort(unique(Iterators.flatten(keys(s.method_results) for s in states)))
+ for mname in method_names
+ results = [s.method_results[mname] for s in states if haskey(s.method_results, mname)]
+ isempty(results) && continue
+ grid = sort(unique(reduce(vcat, (r.psi_grid for r in results); init=Float64[])))
+ # Sum each species' dT/dψ onto the union grid; zero outside a species' ψ range.
+ dtdpsi = zeros(ComplexF64, length(grid))
+ for r in results
+ length(r.psi_grid) >= 2 || continue
+ o = sortperm(r.psi_grid)
+ _accumulate_interp!(dtdpsi, grid, r.psi_grid[o], r.dtdpsi[o])
+ end
+
+ # Per-ℓ profile, interpolated onto the same union grid column by column. Only combined
+ # when every species carries it on an identical ℓ range; otherwise left empty.
+ ell = first(results).ell
+ has_ell = !isempty(ell) && all(r -> r.ell == ell && size(r.dtdpsi_ell, 2) == length(ell) &&
+ size(r.dtdpsi_ell, 1) == length(r.psi_grid), results)
+ dtdpsi_ell = zeros(ComplexF64, has_ell ? length(grid) : 0, has_ell ? length(ell) : 0)
+ if has_ell
+ for r in results
+ length(r.psi_grid) >= 2 || continue
+ o = sortperm(r.psi_grid)
+ xs = r.psi_grid[o]
+ for j in eachindex(ell)
+ _accumulate_interp!(view(dtdpsi_ell, :, j), grid, xs, r.dtdpsi_ell[o, j])
+ end
+ end
+ # Take the total from the per-ℓ row sum so Σ_ℓ ≡ dtdpsi holds exactly rather than to
+ # interpolation roundoff. Linear interpolation commutes with the sum, so this is the
+ # same quantity the loop above produced.
+ dtdpsi = vec(sum(dtdpsi_ell; dims=2))
+ end
+
+ tcum = zeros(ComplexF64, length(grid))
+ for j in 2:length(grid)
+ tcum[j] = tcum[j-1] + 0.5 * (dtdpsi[j] + dtdpsi[j-1]) * (grid[j] - grid[j-1])
+ end
+ combined.method_results[mname] = MethodResult(;
+ method=mname, nn=first(results).nn,
+ total_torque=sum(r.total_torque for r in results),
+ total_energy=sum(r.total_energy for r in results),
+ psi_grid=grid, dtdpsi=dtdpsi, t_cumulative=tcum,
+ dtdpsi_ell=dtdpsi_ell, ell=(has_ell ? ell : Int[]),
+ psi_nsteps=sum(r.psi_nsteps for r in results))
+ end
+ return combined
+end
+
+"""
+ compute_torque_all_methods!(state::KineticForcesState, intr::KineticForcesInternal,
+ ctrl::KineticForcesControl, equil, kinetic_profiles;
+ axis_psi_c=0.0, z, m, electron)
+
+Calculate torque/energy for all enabled methods by ψ quadrature (`integrate_psi_quadgk`), summing over
+toroidal mode numbers and assembling block-diagonal kinetic matrices for the matrix methods.
+
+# Arguments
+
+ - `state::KineticForcesState`: Accumulates results for all methods
+ - `intr::KineticForcesInternal`: Internal state with equilibrium data
+ - `ctrl::KineticForcesControl`: Control parameters specifying which methods to run
+ - `equil`: PlasmaEquilibrium with 2D interpolants
+ - `kinetic_profiles::Equilibrium.KineticProfileSplines`: Named kinetic-profile splines
+ - `axis_psi_c`: the run's near-axis validity boundary, suppressing the torque density below it
+ (`KineticForces.axis_validity_boundary`); 0 disables the suppression
+ - `z`, `m`, `electron`: the species whose torque this is; default the equilibrium's main ion, with
+ `ctrl.electron`. The species sum calls this once per resolved species.
+"""
+function compute_torque_all_methods!(state::KineticForcesState, intr::KineticForcesInternal,
+ ctrl::KineticForcesControl, equil,
+ kinetic_profiles::Equilibrium.KineticProfileSplines;
+ axis_psi_c::Float64=0.0, z::Int=main_ion(equil)[1], m::Int=main_ion(equil)[2], electron::Bool=ctrl.electron)
+
+ for entry in METHOD_REGISTRY
+ getfield(ctrl, entry.flag) || continue
+
+ method = entry.name
+ intr.method = method
+ is_matrix_method = occursin("mm", method)
+
+ if intr.verbose
+ println("---------------------------------------------")
+ println("$method - $(entry.doc)")
+ end
+
+ # Allocate full block-diagonal matrix if needed
+ op_wmats_full = nothing
+ if is_matrix_method && intr.numpert_total > 0
+ op_wmats_full = zeros(ComplexF64, intr.numpert_total, intr.numpert_total, 6)
+ end
+
+ total_torque = ComplexF64(0.0)
+ npert = max(intr.npert, 1)
+
+ # Capture per-ψ profile and step count from the single-n case (or the
+ # first n when npert > 1) for output diagnostics.
+ psi_grid_out = Float64[]
+ dtdpsi_out = ComplexF64[]
+ t_cum_out = ComplexF64[]
+ dtdpsi_ell_out = zeros(ComplexF64, 0, 0)
+ ell_out = Int[]
+ psi_nsteps_total = 0
+ panel_psis_out = Float64[]
+ resonance_psis_out = Float64[]
+
+ for n_idx in 1:npert
+ n = intr.nlow + n_idx - 1
+
+ # Adaptive QuadGK integration over ψ
+ result = integrate_psi_quadgk(
+ n, ctrl.bounce_harmonic_max, z, m,
+ ctrl.magnetic_drift_factor, ctrl.divxi_factor, electron,
+ method, equil, intr, ctrl, kinetic_profiles;
+ psi_min=ctrl.psilims[1], psi_max=ctrl.psilims[2], axis_psi_c=axis_psi_c)
+
+ total_torque += result.total
+ psi_nsteps_total += result.psi_nsteps
+
+ if n_idx == 1
+ panel_psis_out = result.panel_psis
+ resonance_psis_out = result.resonance_psis
+ if !isnothing(result.torque_profile)
+ psi_grid_out = result.torque_profile.psi
+ dtdpsi_out = result.torque_profile.dtdpsi
+ t_cum_out = result.torque_profile.t_cumulative
+ # Profiles come from the first n only, while `total_torque` sums over all n.
+ # So sum(dtdpsi_ell; dims=2) == dtdpsi always, but neither integrates to
+ # `total_torque` when npert > 1.
+ dtdpsi_ell_out = result.torque_profile.dtdpsi_ell
+ ell_out = result.torque_profile.ell
+ end
+ end
+
+ # Insert n-block into full matrix
+ if is_matrix_method && !isnothing(result.matrix_integrated) && !isnothing(op_wmats_full)
+ i_start = (n_idx - 1) * intr.mpert + 1
+ i_end = n_idx * intr.mpert
+ op_wmats_full[i_start:i_end, i_start:i_end, :] .= result.matrix_integrated
+ end
+ end
+
+ # Eq. (19) Logan et al. PoP 20, 122507 (2013): Im(T) = 2n·δW_k. δW_k is real.
+ total_energy = imag(total_torque) / (2 * intr.nlow)
+
+ result_entry = MethodResult(;
+ method=method,
+ nn=intr.nlow,
+ total_torque=total_torque,
+ total_energy=total_energy,
+ psi_grid=psi_grid_out,
+ dtdpsi=dtdpsi_out,
+ t_cumulative=t_cum_out,
+ dtdpsi_ell=dtdpsi_ell_out,
+ ell=ell_out,
+ psi_nsteps=psi_nsteps_total,
+ panel_psis=panel_psis_out,
+ resonance_psis=resonance_psis_out
+ )
+ state.method_results[method] = result_entry
+
+ if is_matrix_method && !isnothing(op_wmats_full)
+ state.kinetic_matrices[method] = op_wmats_full
+ end
+
+ if intr.verbose
+ @printf("%-24s%11.3e\n", "Total torque = ", real(total_torque))
+ @printf("%-24s%11.3e\n", "Total Kinetic Energy = ", imag(total_torque) / (2 * intr.nlow))
+ if imag(total_torque) != 0.0
+ @printf("%-24s%11.3e\n", "alpha/s = ", real(total_torque) / (-1 * imag(total_torque)))
+ end
+ println("$method - Finished")
+ println("---------------------------------------------")
+ end
+ end
+end
+
+"""
+ kinetic_torque(pe, ctrl::KineticForcesControl; verbose=false) -> KineticForcesResult
+
+The kinetic (NTV) torque of the perturbed equilibrium `pe`, evaluated with the model settings `ctrl` on the
+kinetic profiles attached to its equilibrium. A multi-species plasma adds each species' contribution.
+Call `save_to_hdf5(target, kf)` to save the result.
+
+```julia
+pe = perturbed_equilibrium(plasma_response(ffs), RMPField("forcing.dat"))
+kf = kinetic_torque(pe, KineticForcesControl())
+```
+"""
+function kinetic_torque(pe::PerturbedEquilibrium.PerturbedEquilibriumState, ctrl::KineticForcesControl; verbose::Bool=false)
+ ffs = pe.response.ffs
+ equil = ffs.equil
+ equil.kinetic === nothing && error("kinetic_torque needs kinetic profiles on the equilibrium: set kinetic_file or call attach_kinetic_profiles!")
+ kinetic_profiles = ntv_profiles(ctrl, equil)
+ species = ntv_species(ctrl, equil)
+ # One boundary for the whole run, shared with the EL kinetic matrices and the Validity output.
+ axis_psi_c = axis_validity_boundary(ctrl, species, kinetic_profiles, equil, Float64[sng.psifac for sng in ffs.surfaces])
+
+ kf_intr = KineticForcesInternal(equil; verbose)
+ set_perturbation_data!(kf_intr, pe, ffs, equil, ffs.metric)
+ if species === nothing
+ total = KineticForcesState()
+ compute_torque_all_methods!(total, kf_intr, ctrl, equil, kinetic_profiles; axis_psi_c)
+ return KineticForcesResult(total, Pair{String,KineticForcesState}[], axis_psi_c, pe, ctrl)
+ end
+ per_species = Pair{String,KineticForcesState}[]
+ for sp in species
+ state = KineticForcesState()
+ compute_torque_all_methods!(state, kf_intr, ctrl, equil, sp.profiles; axis_psi_c, z=sp.z, m=sp.m, electron=sp.electron)
+ push!(per_species, String(sp.label) => state)
+ end
+ return KineticForcesResult(combine_species_states(last.(per_species)), per_species, axis_psi_c, pe, ctrl)
+end
diff --git a/src/KineticForces/EnergyIntegration.jl b/src/KineticForces/EnergyIntegration.jl
new file mode 100644
index 0000000000..54bf50fdcc
--- /dev/null
+++ b/src/KineticForces/EnergyIntegration.jl
@@ -0,0 +1,396 @@
+"""
+ EnergyIntegration
+
+Energy-space integration for the kinetic resonance operator; the integrand is
+[Logan, Park, et al., Phys. Plasmas, 2013] Eq. (8). The integral over x = E/T runs over
+`[0, X_ENERGY_MAX]`: resonance poles are removed analytically (Sokhotski-Plemelj) and the smooth
+remainder is integrated with QuadGK in u = √x. The collisionless case is the exact ν→0 limit.
+"""
+
+"""
+ EnergyParams
+
+Parameters for the energy integrand evaluation.
+"""
+struct EnergyParams
+ wn::Float64 # density gradient diamagnetic drift frequency
+ wt::Float64 # temperature gradient diamagnetic drift frequency
+ we::Float64 # electric precession frequency
+ wd::Float64 # magnetic precession frequency
+ wb::Float64 # bounce frequency / sqrt(x)
+ nuk::Float64 # effective Krook collision frequency
+ leff::Float64 # effective bounce harmonic
+ n::Int # toroidal mode number
+ nutype::String # collision operator type
+ f0type::String # distribution function type
+ nufac::Float64 # collisionality scaling factor
+ qt::Bool # heat flux calculation flag
+ nutype_id::Int # `nutype` as an integer code (see `_NUTYPE_IDS`), for the hot loop
+ f0type_id::Int # `f0type` as an integer code (see `_F0TYPE_IDS`)
+end
+
+const _NUTYPE_IDS = Dict("zero" => 1, "small" => 2, "krook" => 3, "harmonic" => 4)
+const _F0TYPE_IDS = Dict("maxwellian" => 1, "park" => 2, "cgl" => 3)
+
+function EnergyParams(wn, wt, we, wd, wb, nuk, leff, n, nutype::String, f0type::String, nufac, qt)
+ haskey(_NUTYPE_IDS, nutype) || error("nutype must be zero, small, krook, or harmonic")
+ haskey(_F0TYPE_IDS, f0type) || error("f0type must be maxwellian, park, or cgl")
+ return EnergyParams(wn, wt, we, wd, wb, nuk, leff, n, nutype, f0type, nufac, qt, _NUTYPE_IDS[nutype], _F0TYPE_IDS[f0type])
+end
+
+"""
+ _energy_collision_frequency(x::Float64, p::EnergyParams) → Float64
+
+Collision frequency ν(x) at normalized energy x = E/T.
+
+ - `"zero"`: collisionless (ν = 0)
+ - `"small"`: 1e-5 * |we|, a positive Krook width for either rotation direction
+ - `"krook"`: unmodified Krook operator
+ - `"harmonic"`: (1 + (l/2)²) * krook * x^(-3/2)
+"""
+@inline function _energy_collision_frequency(x::Float64, p::EnergyParams)::Float64
+ id = p.nutype_id
+ nux = if id == 1
+ 0.0
+ elseif id == 2
+ 1e-5 * abs(p.we)
+ elseif id == 3
+ p.nuk
+ else
+ x <= 0.0 ? floatmax(Float64) : p.nuk * (1 + 0.25 * p.leff^2) / (x * sqrt(x))
+ end
+ return p.nufac * nux
+end
+
+"""
+ _energy_numerator(x::Float64, p::EnergyParams) → ComplexF64
+
+Numerator N(x) of the energy integrand, **without** the resonance denominator
+and **without** the Maxwellian weight exp(-x). The physical x-space integrand is
+N(x)·exp(-x)/denom(x); the residue at a pole uses N(x_res)·exp(-x_res).
+
+For CGL there is no resonance denominator: N_cgl = x^2.5 / (i·n).
+"""
+@inline function _energy_numerator(x::Float64, p::EnergyParams)::ComplexF64
+ x25 = x * x * sqrt(x) # x^2.5
+ id = p.f0type_id
+ fx = if id == 1
+ ComplexF64((p.we + p.wn + p.wt * (x - 1.5)) * x25)
+ elseif id == 2
+ ComplexF64((p.we + p.wn + p.wt * 2) * x25)
+ else
+ complex(0.0, -x25 / p.n) # x^2.5 / (i*n)
+ end
+ if p.qt
+ fx *= (x - 2.5)
+ end
+ return fx
+end
+
+"""
+ _energy_numerator_deriv(x::Float64, p::EnergyParams) → ComplexF64
+
+x-derivative dN/dx of `_energy_numerator`, used for the analytic regular-part
+limit at a real-axis (ν=0) resonance pole. CGL is excluded — the real-pole path
+never carries a CGL numerator (CGL has no pole).
+"""
+@inline function _energy_numerator_deriv(x::Float64, p::EnergyParams)::ComplexF64
+ sx = sqrt(x)
+ x15 = x * sx # x^1.5
+ x25 = x * x15 # x^2.5
+ if p.f0type_id == 1
+ a = p.we + p.wn + p.wt * (x - 1.5)
+ nn = ComplexF64(a * x25)
+ dn = ComplexF64(p.wt * x25 + a * 2.5 * x15) # d/dx[(…)·x^2.5]
+ elseif p.f0type_id == 2
+ a = p.we + p.wn + p.wt * 2
+ nn = ComplexF64(a * x25)
+ dn = ComplexF64(a * 2.5 * x15)
+ else
+ error("_energy_numerator_deriv supports maxwellian and park")
+ end
+ return p.qt ? dn * (x - 2.5) + nn : dn # d/dx[N·(x-2.5)] = N′·(x-2.5) + N
+end
+
+"""
+ _energy_integrand_real(x::Float64, p::EnergyParams) → ComplexF64
+
+Physical energy integrand in x-space, N(x)·exp(-x)/denom(x), evaluated on the
+real axis. Used both by the production integral (`integrate_energy` via
+`_integrate_energy_resonant`) and for diagnostics (`evaluate_energy_integrand`).
+"""
+@inline function _energy_integrand_real(x::Float64, p::EnergyParams)::ComplexF64
+ sqx = sqrt(x)
+ nux = _energy_collision_frequency(x, p)
+ # Resonance denominator: i*(l_eff*wb*sqrt(x) + n*(we + wd*x)) - nu
+ denom = complex(-nux, p.leff * p.wb * sqx + p.n * (p.we + p.wd * x))
+ emx = exp(-x)
+ if p.f0type_id == 3
+ # CGL has no resonance denominator.
+ fx = complex(0.0, -x * x * sqx * emx / p.n)
+ return p.qt ? (x - 2.5) * fx : fx
+ end
+ return _energy_numerator(x, p) * emx / denom
+end
+
+"""
+ energy_integrand_scalar(x::Float64, p::EnergyParams) → ComplexF64
+
+Evaluate the physical energy integrand N(x)·exp(-x)/denom(x) at normalized
+energy x = E/T. Implements [Logan, Park, et al., Phys. Plasmas, 2013] Eq. (8).
+"""
+energy_integrand_scalar(x::Float64, p::EnergyParams)::ComplexF64 = _energy_integrand_real(x, p)
+
+"""
+ find_resonance_energies(leff, wb, n, we, wd) → Vector{Float64}
+
+Real positive energies x_res where the resonance condition vanishes:
+
+ Ω(x) = leff·wb·√x + n·(we + wd·x) = 0
+
+With s = √x this is the quadratic n·wd·s² + leff·wb·s + n·we = 0. Returns the
+x = s² values for the positive real roots (the locations of the resonance
+poles of the energy integrand).
+"""
+function find_resonance_energies(leff::Float64, wb::Float64, n::Int, we::Float64, wd::Float64)::Vector{Float64}
+ a = n * wd
+ b = leff * wb
+ c = n * we
+ roots = Float64[]
+ if abs(a) < SINGULAR_EPS
+ # Linear case: b·s + c = 0
+ abs(b) < SINGULAR_EPS && return roots
+ s = -c / b
+ s > 0.0 && push!(roots, s^2)
+ else
+ disc = b^2 - 4 * a * c
+ disc < 0.0 && return roots
+ sd = sqrt(disc)
+ for s in ((-b + sd) / (2 * a), (-b - sd) / (2 * a))
+ s > 0.0 && push!(roots, s^2)
+ end
+ end
+ return roots
+end
+
+# Upper limit of the real-x energy integral. Integrand and poles decay as x^p·exp(-x)
+# (p ≤ 3.5); at x=100 the tail is ~1e-37, far below any quadrature tolerance.
+const X_ENERGY_MAX = 100.0
+# A pole whose collisional width ν/Ω′ is below this fraction of its position gets width-scaled
+# breakpoints (±2, ±10 widths) so the quadrature's first pass already resolves it; poles beyond
+# NARROW_POLE_XMAX sit under the Maxwellian tail (x^3.5·e^-x < 1e-6) and are not worth the panels.
+const NARROW_POLE_FRACTION = 0.05
+const NARROW_POLE_XMAX = 25.0
+# Most breakpoints one energy integral can carry: two ends, two poles, four width points per pole.
+const MAX_ENERGY_BREAKS = 12
+
+"""
+ _quadgk_breaks(f, pts, atol, rtol, segbuf) → (I, E)
+
+`quadgk(f, pts...)` for a runtime-length sorted breakpoint vector of 2 to `MAX_ENERGY_BREAKS`
+points, dispatched on the length so each call is a constant-arity splat (a Vector splat is
+type-unstable in the hot loop).
+"""
+function _quadgk_breaks(f, pts::Vector{Float64}, atol::Float64, rtol::Float64, segbuf)
+ n = length(pts)
+ @inbounds if n == 2
+ quadgk(f, pts[1], pts[2]; atol, rtol, segbuf)
+ elseif n == 3
+ quadgk(f, pts[1], pts[2], pts[3]; atol, rtol, segbuf)
+ elseif n == 4
+ quadgk(f, pts[1], pts[2], pts[3], pts[4]; atol, rtol, segbuf)
+ elseif n == 5
+ quadgk(f, pts[1], pts[2], pts[3], pts[4], pts[5]; atol, rtol, segbuf)
+ elseif n == 6
+ quadgk(f, pts[1], pts[2], pts[3], pts[4], pts[5], pts[6]; atol, rtol, segbuf)
+ elseif n == 7
+ quadgk(f, pts[1], pts[2], pts[3], pts[4], pts[5], pts[6], pts[7]; atol, rtol, segbuf)
+ elseif n == 8
+ quadgk(f, pts[1], pts[2], pts[3], pts[4], pts[5], pts[6], pts[7], pts[8]; atol, rtol, segbuf)
+ elseif n == 9
+ quadgk(f, pts[1], pts[2], pts[3], pts[4], pts[5], pts[6], pts[7], pts[8], pts[9]; atol, rtol, segbuf)
+ elseif n == 10
+ quadgk(f, pts[1], pts[2], pts[3], pts[4], pts[5], pts[6], pts[7], pts[8], pts[9], pts[10]; atol, rtol, segbuf)
+ elseif n == 11
+ quadgk(f, pts[1], pts[2], pts[3], pts[4], pts[5], pts[6], pts[7], pts[8], pts[9], pts[10], pts[11]; atol, rtol, segbuf)
+ else
+ quadgk(f, pts[1], pts[2], pts[3], pts[4], pts[5], pts[6], pts[7], pts[8], pts[9], pts[10], pts[11], pts[12]; atol, rtol, segbuf)
+ end
+end
+
+"""
+ _real_pole_regular_part(xr, p, leff, wb, n, wd) → ComplexF64
+
+Laurent regular part (finite limit at `x → x_res`) of the pole-subtracted
+real-axis (ν=0) integrand `N(x)·exp(-x)/(i·Ω(x)) − R/(x − x_res)`, with
+`Ω(x) = leff·wb·√x + n·(we+wd·x)` and `R = N(x_res)·exp(-x_res)/(i·Ω′)`.
+
+Writing `h(x) = N(x)·exp(-x)`, the limit is
+`[h′(x_res) − h(x_res)·Ω″/(2Ω′)] / (i·Ω′)`, with `h′ = (N′ − N)·exp(-x)`,
+`Ω′ = leff·wb/(2√x) + n·wd`, `Ω″ = −leff·wb/(4·x^{3/2})`.
+"""
+@inline function _real_pole_regular_part(xr::Float64, p::EnergyParams, leff::Float64,
+ wb::Float64, n::Int, wd::Float64)::ComplexF64
+ sx = sqrt(xr)
+ op = leff * wb / (2.0 * sx) + n * wd # Ω′(x_res)
+ opp = -leff * wb / (4.0 * xr * sx) # Ω″(x_res)
+ nn = _energy_numerator(xr, p) # N(x_res)
+ dn = _energy_numerator_deriv(xr, p) # N′(x_res)
+ return exp(-xr) * ((dn - nn) - nn * opp / (2.0 * op)) / (im * op)
+end
+
+# Real x-space integrand minus the pole parts; a named function keeps allocation out of the QuadGK loop.
+@inline function _resonant_integrand(x::Float64, p::EnergyParams,
+ residues::Vector{ComplexF64}, x_poles::Vector{ComplexF64}, npole::Int,
+ leff::Float64, wb::Float64, n::Int, wd::Float64)::ComplexF64
+ val = _energy_integrand_real(x, p)
+ @inbounds for k in 1:npole
+ val -= residues[k] / (x - x_poles[k])
+ end
+ # At a ν=0 pole Ω rounds to 0 and the physical term is 0/0; substitute the nearest
+ # pole's analytic regular-part limit, keeping the other (finite) pole subtractions.
+ if !isfinite(val)
+ k = 1
+ @inbounds for j in 2:npole
+ abs(x - real(x_poles[j])) < abs(x - real(x_poles[k])) && (k = j)
+ end
+ val = _real_pole_regular_part(real(x_poles[k]), p, leff, wb, n, wd)
+ @inbounds for j in 1:npole
+ j == k && continue
+ val -= residues[j] / (x - x_poles[j])
+ end
+ end
+ return val
+end
+
+"""
+ _integrate_energy_resonant(p, leff, wb, n, we, wd, atol, rtol, segbuf=nothing) → ComplexF64
+
+Energy integral over real `x ∈ [0, X_ENERGY_MAX]`, as in Fortran PENTRC (energy.f90). Each resonance pole
+`x_pole = x_res − i·ν/Ω′` is removed by principal value + residue (Sokhotski-Plemelj) and the smooth remainder is
+integrated in `u = √x`. The collisionless case is the exact ν→0⁺ limit: the signed zero of `−pole_offset` carries its
+causal branch and the analytic regular-part limit its on-axis `0/0`. Poles narrower than `NARROW_POLE_FRACTION` of
+their position get extra breakpoints at ±2 and ±10 widths.
+"""
+function _integrate_energy_resonant(p::EnergyParams, leff::Float64, wb::Float64,
+ n::Int, we::Float64, wd::Float64,
+ atol::Float64, rtol::Float64, segbuf=nothing)::ComplexF64
+ x_res_list = find_resonance_energies(leff, wb, n, we, wd) # ≤ 2 roots of a quadratic in √x
+ x_poles = ComplexF64[]
+ residues = ComplexF64[]
+ sizehint!(x_poles, length(x_res_list))
+ sizehint!(residues, length(x_res_list))
+ pole_contribution = ComplexF64(0.0)
+
+ for xr in x_res_list
+ # Poles beyond X_ENERGY_MAX (exp(-xr) negligible) lie outside the domain — drop them.
+ (xr <= 0.0 || xr >= X_ENERGY_MAX) && continue
+ # Ω′(x_res) = d/dx[leff·wb·√x + n·(we + wd·x)]
+ omega_prime = leff * wb / (2.0 * sqrt(xr)) + n * wd
+ abs(omega_prime) < SINGULAR_EPS && continue
+ # Collisions shift the pole off-axis: x_pole = x_res - i·ν/Ω′. Skip if ν overflows
+ # (harmonic ν at tiny x_res): pole infinitely broadened, integrand stays smooth.
+ pole_offset = _energy_collision_frequency(xr, p) / omega_prime
+ isfinite(pole_offset) || continue
+ x_pole = complex(xr, -pole_offset) # signed-zero imag part for ν=0 carries the causal branch
+ # Residue of N(x)·exp(-x)/(i·Ω(x)) at x_res, where Ω ≈ Ω′·(x - x_res) near the pole.
+ R = _energy_numerator(xr, p) * exp(-xr) / (im * omega_prime)
+ # Add-back ∫₀^xmax R/(x - x_pole) dx = R·[log(xmax - x_pole) - log(-x_pole)].
+ pole_contribution += R * (log(X_ENERGY_MAX - x_pole) - log(-x_pole))
+ push!(x_poles, x_pole)
+ push!(residues, R)
+ end
+
+ npole = length(residues)
+
+ # Physical integrand N(x)·exp(-x)/(i·Ω) minus the subtracted pole parts, in u = √x.
+ integrand_u = u -> 2u * _resonant_integrand(u * u, p, residues, x_poles, npole, leff, wb, n, wd)
+ u_max = sqrt(X_ENERGY_MAX)
+
+ if npole == 0
+ val, err = quadgk(integrand_u, 0.0, u_max; atol=atol, rtol=rtol, segbuf=segbuf)
+ check_inner_quadrature(val, err, atol, rtol, "energy")
+ return val
+ end
+
+ # Breakpoints: each pole's real part, plus ±2 and ±10 widths around a narrow pole, in u.
+ pts = Vector{Float64}(undef, 0)
+ sizehint!(pts, MAX_ENERGY_BREAKS)
+ push!(pts, 0.0)
+ push!(pts, u_max)
+ for xp in x_poles
+ xr = real(xp)
+ push!(pts, sqrt(xr))
+ w = abs(imag(xp))
+ if 0 < w < NARROW_POLE_FRACTION * xr && xr < NARROW_POLE_XMAX
+ for d in (-10w, -2w, 2w, 10w)
+ xb = xr + d
+ 0.0 < xb < X_ENERGY_MAX && push!(pts, sqrt(xb))
+ end
+ end
+ end
+ sort!(pts)
+ unique!(pts)
+ smooth_val, err = _quadgk_breaks(integrand_u, pts, atol, rtol, segbuf)
+ check_inner_quadrature(smooth_val, err, atol, rtol, "energy")
+ return smooth_val + pole_contribution
+end
+
+"""
+ integrate_energy(wn, wt, we, wd, wb, nuk, ell, leff, n, psi, lambda, method;
+ nutype="harmonic", f0type="maxwellian", nufac=1.0,
+ qt=false, atol=1e-7, rtol=1e-5) → ComplexF64
+
+Integrate the kinetic resonance operator ∫₀^∞ N(x)·exp(-x)/denom(x) dx over normalized energy x = E/T,
+with resonance poles handled by `_integrate_energy_resonant`; CGL has no pole and is integrated directly.
+
+Collision operator types (`nutype`): `"zero"`, `"small"`, `"krook"`, `"harmonic"`.
+Distribution function types (`f0type`): `"maxwellian"`, `"park"`, `"cgl"`.
+"""
+function integrate_energy(wn::Float64, wt::Float64, we::Float64, wd::Float64,
+ wb::Float64, nuk::Float64, ell::Int, leff::Float64,
+ n::Int, psi::Float64, lambda::Float64, method::String;
+ nutype::String="harmonic", f0type::String="maxwellian",
+ nufac::Float64=1.0, qt::Bool=false,
+ atol::Float64=1e-7, rtol::Float64=1e-5, segbuf=nothing)::ComplexF64
+
+ p = EnergyParams(wn, wt, we, wd, wb, nuk, leff, n,
+ nutype, f0type, nufac, qt)
+
+ # CGL has no resonance denominator and no pole — integrate the physical
+ # x-space integrand directly over the half line (QuadGK maps [0,∞) itself).
+ if f0type == "cgl"
+ val, err = quadgk(x -> _energy_integrand_real(x, p), 0.0, Inf; atol=atol, rtol=rtol, segbuf=segbuf)
+ check_inner_quadrature(val, err, atol, rtol, "CGL energy")
+ return val
+ end
+
+ # One resonant path for any collisionality: pole x_pole = x_res - i·ν/Ω′ (real for ν≡0).
+ return _integrate_energy_resonant(p, leff, wb, n, we, wd, atol, rtol, segbuf)
+end
+
+"""
+ evaluate_energy_integrand(x_grid; wn, wt, we, wd, wb, nuk, leff, n,
+ nutype="harmonic", f0type="maxwellian",
+ nufac=1.0, qt=false) → Vector{ComplexF64}
+
+Diagnostic: evaluate the energy integrand N(x)·exp(-x)/denom(x) (not the integral) at each x = E/T in `x_grid`.
+
+# Example
+
+```julia
+x = 10 .^ range(-2; stop=2, length=500)
+f = KineticForces.evaluate_energy_integrand(x; wn=1e3, wt=2e3, we=5e4,
+ wd=1e2, wb=3e4, nuk=1e3, leff=1.0, n=1)
+plot(x, real.(f); xscale=:log10, xlabel="x = E/T", ylabel="Re(integrand)")
+```
+"""
+function evaluate_energy_integrand(x_grid::AbstractVector{Float64};
+ wn::Float64, wt::Float64, we::Float64,
+ wd::Float64, wb::Float64, nuk::Float64,
+ leff::Float64, n::Int,
+ nutype::String="harmonic", f0type::String="maxwellian",
+ nufac::Float64=1.0, qt::Bool=false)
+ p = EnergyParams(wn, wt, we, wd, wb, nuk, leff, n, nutype, f0type, nufac, qt)
+ return [energy_integrand_scalar(x, p) for x in x_grid]
+end
diff --git a/src/KineticForces/KineticForces.jl b/src/KineticForces/KineticForces.jl
new file mode 100644
index 0000000000..26b2c4c4e4
--- /dev/null
+++ b/src/KineticForces/KineticForces.jl
@@ -0,0 +1,60 @@
+module KineticForces
+
+"""
+KineticForces - neoclassical toroidal viscosity (NTV) torque and kinetic energy of a perturbed equilibrium.
+
+Computes the torque by bounce-averaged pitch-angle and energy integration, and supplies the calculated kinetic
+matrices to ForceFreeStates when the problem's kinetic source is a `KineticForcesControl`.
+"""
+
+using LinearAlgebra
+using LinearAlgebra.LAPACK
+using FFTW
+using QuadGK
+using HDF5
+using Printf
+using Statistics
+
+using FastInterpolations
+using Roots
+import ..ForceFreeStates
+import ..Equilibrium
+using ..Equilibrium: IonSpecies
+import ..Utilities
+import ..PerturbedEquilibrium
+
+# Supporting data structures and utilities
+include("KineticForcesStructs.jl")
+include("Utils.jl")
+include("Output.jl")
+
+# Core library functions
+include("BounceAveraging.jl")
+include("Torque.jl")
+include("EnergyIntegration.jl")
+include("PitchIntegration.jl")
+
+# High-level computation functions
+include("Compute.jl")
+include("CalculatedKineticMatrices.jl")
+
+# Global constants
+const mp = 1.672_614e-27 # proton mass (kg)
+const me = 9.109_1e-31 # electron mass (kg)
+const e = 1.602_191_7e-19 # elementary charge (C)
+const eV = e # joules per electron-volt
+
+const twopi = 2π
+const μ₀ = 4e-7 * π
+const rad2deg = 180 / π
+const deg2rad = π / 180
+
+# Treat-as-zero threshold for singular denominators and degenerate coefficients.
+const SINGULAR_EPS = 1e-30
+
+export kinetic_torque, KineticForcesResult
+
+# Diagnostic exports for interactive energy-integrand inspection
+export evaluate_energy_integrand, energy_integrand_scalar, EnergyParams
+
+end # module KineticForces
diff --git a/src/KineticForces/KineticForcesStructs.jl b/src/KineticForces/KineticForcesStructs.jl
new file mode 100644
index 0000000000..33cadb66be
--- /dev/null
+++ b/src/KineticForces/KineticForcesStructs.jl
@@ -0,0 +1,453 @@
+"""
+ METHOD_REGISTRY
+
+Single source of truth for the NTV calculation methods. Each entry is a NamedTuple
+`(name, flag, kind, doc)`:
+
+ - `name` — short method identifier used as the HDF5 group key and in `intr.method`
+ - `flag` — the `KineticForcesControl` field symbol that enables the method
+ - `kind` — dispatch routing tag consumed by `method_kind` / `Torque.jl`
+ (`:gar` for the GAR/matrix family, `:fcgl` for the fluid CGL method)
+ - `doc` — one-line description printed in verbose output
+
+To add a method: append an entry here and add the matching `*_flag` field
+to `KineticForcesControl`.
+"""
+const METHOD_REGISTRY = (
+ (name="fgar", flag=:fgar_flag, kind=:gar, doc="Full general-aspect-ratio calculation"),
+ (name="tgar", flag=:tgar_flag, kind=:gar, doc="Trapped particle general-aspect-ratio calculation"),
+ (name="pgar", flag=:pgar_flag, kind=:gar, doc="Passing particle general-aspect-ratio calculation"),
+ (name="fcgl", flag=:fcgl_flag, kind=:fcgl, doc="Fluid Chew–Goldberger–Low calculation"),
+ (name="fwmm", flag=:fwmm_flag, kind=:gar, doc="Full energy calculation using MXM Euler–Lagrange matrix"),
+ (name="twmm", flag=:twmm_flag, kind=:gar, doc="Trapped energy calculation using MXM Euler–Lagrange matrix"),
+ (name="pwmm", flag=:pwmm_flag, kind=:gar, doc="Passing energy calculation using MXM Euler–Lagrange matrix"),
+ (name="ftmm", flag=:ftmm_flag, kind=:gar, doc="Full torque calculation using MXM Euler–Lagrange matrix"),
+ (name="ttmm", flag=:ttmm_flag, kind=:gar, doc="Trapped torque calculation using MXM Euler–Lagrange matrix"),
+ (name="ptmm", flag=:ptmm_flag, kind=:gar, doc="Passing torque calculation using MXM Euler–Lagrange matrix"),
+ (name="fkmm", flag=:fkmm_flag, kind=:gar, doc="Full MXM Euler–Lagrange energy matrix norm calculation"),
+ (name="tkmm", flag=:tkmm_flag, kind=:gar, doc="Trapped MXM Euler–Lagrange energy matrix norm calculation"),
+ (name="pkmm", flag=:pkmm_flag, kind=:gar, doc="Passing MXM Euler–Lagrange energy matrix norm calculation"),
+ (name="frmm", flag=:frmm_flag, kind=:gar, doc="Full MXM Euler–Lagrange torque matrix norm calculation"),
+ (name="trmm", flag=:trmm_flag, kind=:gar, doc="Trapped MXM Euler–Lagrange torque matrix norm calculation"),
+ (name="prmm", flag=:prmm_flag, kind=:gar, doc="Passing MXM Euler–Lagrange torque matrix norm calculation"))
+
+"""
+ method_kind(name) -> Symbol
+
+Return the dispatch routing tag (`:gar` or `:fcgl`) for the NTV
+method `name`, looked up from [`METHOD_REGISTRY`]. Errors on an unknown method.
+"""
+function method_kind(name::AbstractString)
+ for entry in METHOD_REGISTRY
+ entry.name == name && return entry.kind
+ end
+ error("ERROR: torque - unknown method: $name")
+end
+
+
+
+
+"""
+ KineticForcesControl
+
+User-facing control parameters from the TOML `[KineticForces]` section.
+Configures which NTV methods to run, whether electrons join the species sum, and tolerances. The species
+composition comes from the equilibrium's kinetic data (`equil.kinetic`).
+
+Constructed via keyword arguments or from a TOML dict:
+
+```julia
+ctrl = KineticForcesControl(; (Symbol(k) => v for (k, v) in inputs["KineticForces"])...)
+```
+
+Immutable: vary a field by building a new control.
+
+## Fields
+
+ - `axis_validity_suppression::Bool` - Suppress the calculated kinetic terms below ψ_c, where the zero-orbit-width
+ ordering fails (a thermal orbit width of the widest-orbit species reaches ⟨r⟩; moved clear of rational surfaces),
+ rising to full strength at 2ψ_c through a C² envelope. No tuning parameters. Default `true`.
+ - Quadrature tolerances form a ladder, outermost in: `rtol_psi` (default 1e-2) ⊃ `rtol_pitch` (default
+ `psi_tolerance_margin × rtol_psi` = 1e-3) ⊃ `rtol_x` (default `nested_tolerance_margin × rtol_pitch` = 1e-5).
+ Each inner level is resolved one margin tighter than the outer and no further. Set `rtol_pitch`/`rtol_x`
+ explicitly to override (see `torque_pitch_rtol`, `matrix_pitch_rtol`).
+"""
+@kwdef struct KineticForcesControl
+ # Method flags (which methods to calculate)
+ fgar_flag::Bool = true # Full general-aspect-ratio
+ tgar_flag::Bool = false # Trapped particle GAR
+ pgar_flag::Bool = false # Passing particle GAR
+ fcgl_flag::Bool = false # Fluid Chew-Goldberger-Low
+ fwmm_flag::Bool = false # Full energy via MXM E-L matrix
+ twmm_flag::Bool = false # Trapped energy via MXM E-L matrix
+ pwmm_flag::Bool = false # Passing energy via MXM E-L matrix
+ ftmm_flag::Bool = false # Full torque via MXM E-L matrix
+ ttmm_flag::Bool = false # Trapped torque via MXM E-L matrix
+ ptmm_flag::Bool = false # Passing torque via MXM E-L matrix
+ fkmm_flag::Bool = false # Full MXM E-L energy matrix norm
+ tkmm_flag::Bool = false # Trapped MXM E-L energy matrix norm
+ pkmm_flag::Bool = false # Passing MXM E-L energy matrix norm
+ frmm_flag::Bool = false # Full MXM E-L torque matrix norm
+ trmm_flag::Bool = false # Trapped MXM E-L torque matrix norm
+ prmm_flag::Bool = false # Passing MXM E-L torque matrix norm
+
+ # Species summed in the NTV; the composition itself is the equilibrium's (`equil.kinetic`)
+ electron::Bool = false # Add electron NTV in addition to the ion species
+
+ # Mode numbers
+ bounce_harmonic_max::Int = 1 # Bounce harmonics summed over ℓ = -max:max
+
+ # Tolerances, outermost to innermost: ψ quadrature ⊃ λ (pitch) ⊃ x (energy). Each level derives from the one
+ # enclosing it by a margin unless set explicitly (NaN ⇒ derived), so no integrator chases its integrand's noise.
+ atol_pitch::Float64 = 1e-8 # Absolute tolerance for the pitch integration (median-normalized kernel)
+ rtol_pitch::Float64 = NaN # Relative tolerance for the pitch integration (NaN ⇒ psi_tolerance_margin × rtol_psi)
+ psi_tolerance_margin::Float64 = 1e-1 # Factor relating the derived pitch tolerance to rtol_psi
+ atol_x::Float64 = NaN # Absolute tolerance for the energy integration (NaN ⇒ derived)
+ rtol_x::Float64 = NaN # Relative tolerance for the energy integration (NaN ⇒ derived)
+ # Energy tolerances default to this fraction of the pitch ones (the pitch integrand is itself an energy integral).
+ nested_tolerance_margin::Float64 = 1e-2 # Factor relating derived energy tolerances to the pitch ones
+ # Primary convergence knob (~2 sig figs matches NTV model validity); the pitch and energy levels derive from it.
+ rtol_psi::Float64 = 1e-2 # Relative tolerance for outer ψ quadrature
+ # Amplitude-sensitive (NTV ∝ δB²); default 0 (rtol-only). Nonzero is an expert opt-out for near-zero-torque cases and warns when it dominates.
+ atol_psi::Float64 = 0.0 # Absolute tolerance for outer ψ quadrature [N·m]
+ # Runaway guard for rtol-only control (e.g. sign-cancelling torque density); warns when hit.
+ maxevals_psi::Int = 2000 # Max integrand evaluations for outer ψ quadrature
+
+ # Scaling factors
+ density_factor::Float64 = 1.0 # Density scaling (ni, ne)
+ temperature_factor::Float64 = 1.0 # Temperature scaling (Ti, Te)
+ ExB_rotation_factor::Float64 = 1.0 # ExB rotation scaling (omegaE)
+ magnetic_drift_factor::Float64 = 1.0 # Magnetic drift scaling
+ toroidal_rotation_factor::Float64 = 1.0 # Total toroidal rotation scaling (wphi)
+
+ collisionality_factor::Float64 = 1.0 # Collisionality scaling
+ divxi_factor::Float64 = 1.0 # div(xi_perp) scaling
+ axis_validity_suppression::Bool = true # see the `## Fields` docstring
+
+ # Energy integration parameters
+ nutype::String = "harmonic" # Collision operator: "zero", "small", "krook", "harmonic"
+ f0type::String = "maxwellian" # Distribution function: "maxwellian", "park", "cgl"
+
+ # Diagnostic parameters
+ psilims::Vector{Float64} = [0.0, 1.0] # Integration limits in psi
+end
+
+"""
+ torque_pitch_rtol(ctrl::KineticForcesControl) -> Float64
+
+Relative tolerance of the pitch (λ) quadrature inside the ψ torque quadrature: `ctrl.rtol_pitch` when set,
+otherwise `ctrl.psi_tolerance_margin × ctrl.rtol_psi`, so the λ integrand is resolved one margin tighter than
+the ψ integral asks for and the ψ error estimate is not polluted by λ quadrature noise.
+"""
+torque_pitch_rtol(ctrl::KineticForcesControl) = isnan(ctrl.rtol_pitch) ? ctrl.psi_tolerance_margin * ctrl.rtol_psi : ctrl.rtol_pitch
+
+# Pitch tolerance of the kinetic matrix build when `rtol_pitch` is left derived. There is no ψ quadrature to
+# derive from; this value moves the free-boundary eigen-energies by ≤ 1e-4 relative to a 100× tighter build.
+const MATRIX_RTOL_PITCH = 1e-3
+
+"""
+ matrix_pitch_rtol(ctrl::KineticForcesControl) -> Float64
+
+Relative tolerance of the pitch (λ) quadrature in the calculated kinetic matrix build: `ctrl.rtol_pitch` when
+set, otherwise `MATRIX_RTOL_PITCH` (1e-3). The matrices are splined over ψ and fed to the Euler–Lagrange
+solve, so there is no outer quadrature tolerance to derive from.
+"""
+matrix_pitch_rtol(ctrl::KineticForcesControl) = isnan(ctrl.rtol_pitch) ? MATRIX_RTOL_PITCH : ctrl.rtol_pitch
+
+
+# Internal state
+
+# Concrete type of the `ForceFreeStates.build_kinetic_metric_matrices` interpolants, so the smats..zmats
+# fields below are concretely typed and their per-ψ reads in `Torque.jl` dispatch statically.
+const GeomInterp = typeof(cubic_interp(collect(0.0:0.25:1.0), Series(zeros(ComplexF64, 5, 1)); extrap=ExtendExtrap()))
+
+"""
+ KineticForcesInternal
+
+Internal working state for KineticForces calculations: equilibrium-derived scalars, mode indexing, and
+perturbation and geometric-matrix interpolants. Equilibrium and kinetic profiles are read from the
+`PlasmaEquilibrium` and `KineticProfileSplines`, not copied here.
+
+## Fields
+
+ - `ro`, `bo`, `chi1`: Equilibrium geometry parameters
+ - `mthsurf`, `mfac`: Poloidal grid info
+ - `dbob_m`, `divx_m`: Perturbation mode interpolants
+ - `sing_psis`: Sorted rational-surface ψ locations, used as panel boundaries of the outer ψ torque
+ quadrature so resonant peaks fall on interval endpoints
+"""
+@kwdef mutable struct KineticForcesInternal
+ # Equilibrium-derived quantities
+ ro::Float64 = 0.0 # Major radius [m]
+ bo::Float64 = 0.0 # Toroidal field on axis [T]
+ chi1::Float64 = 0.0 # 2π * ψ_o (flux normalization)
+ mthsurf::Int = 0 # Number of poloidal grid points
+ mfac::Vector{Int} = Int[] # Poloidal mode numbers [mlow:mhigh]
+ # Multi-n mode indexing (matching ForceFreeStatesInternal)
+ nlow::Int = 0 # Lowest toroidal mode number
+ nhigh::Int = 0 # Highest toroidal mode number
+ npert::Int = 0 # Number of toroidal modes
+ mlow::Int = 0 # Lowest poloidal mode number
+ mhigh::Int = 0 # Highest poloidal mode number
+ mpert::Int = 0 # Number of poloidal modes
+ numpert_total::Int = 0 # Total modes: mpert × npert
+
+ # Perturbation mode interpolants (populated from PerturbedEquilibriumState)
+ dbob_m::Any = nothing # δB/B perturbation modes (CubicSeriesInterpolant)
+ divx_m::Any = nothing # ∇·ξ⊥ perturbation modes (CubicSeriesInterpolant)
+
+ # Upper ψ bound (FFS psilim); the perturbation interpolants are invalid beyond it,
+ # so the outer ψ quadrature clips here.
+ psilim::Float64 = 1.0
+
+ # Rational-surface ψ locations for ψ-quadrature paneling (see docstring).
+ sing_psis::Vector{Float64} = Float64[]
+
+ # θ knot grid (length mthsurf+1) read by the per-surface setup; never written after construction.
+ tpsi_xs::Vector{Float64} = Float64[]
+
+ # Geometric matrices s/t/x/y/z for the kinetic W vectors (not the DCON a/b/c/d/e/h matrices)
+ smats::Union{Nothing,GeomInterp} = nothing # CubicSeriesInterpolant over ψ, one mpert² block per n
+ tmats::Union{Nothing,GeomInterp} = nothing
+ xmats::Union{Nothing,GeomInterp} = nothing
+ ymats::Union{Nothing,GeomInterp} = nothing
+ zmats::Union{Nothing,GeomInterp} = nothing
+
+ # Clebsch displacement vectors for mode-coupled dW contraction
+ xs_m::Any = nothing # Vector of 3 CubicSeriesInterpolants: [ξ^ψ, ∂ξ^ψ/∂ψ, ξ^α]
+
+ # Method tracking — available methods/docs come from `METHOD_REGISTRY`.
+ method::String = ""
+
+ verbose::Bool = false
+end
+
+"""
+ KineticForcesInternal(equil; verbose=false)
+
+Construct KineticForcesInternal from a PlasmaEquilibrium, extracting
+the equilibrium geometry parameters needed for NTV calculations.
+"""
+function KineticForcesInternal(equil; verbose::Bool=false)
+ mthsurf = length(equil.rzphi_ys) - 1
+ nth = mthsurf + 1
+ # Axis toroidal field F(0)/ro that normalizes λ = μ·bo/E; F_spline stores 2πF.
+ bo_axis = abs(equil.profiles.F_spline(0.0)) / (2π * equil.ro)
+ KineticForcesInternal(;
+ ro=equil.ro,
+ bo=bo_axis,
+ chi1=2π * equil.psio,
+ mthsurf,
+ tpsi_xs=collect(range(0.0, 1.0; length=nth)),
+ verbose
+ )
+end
+
+"""
+ set_perturbation_data!(kf_intr, pe_state, ffs, equil, metric)
+
+Populate the perturbation interpolants of `kf_intr` from the PE Clebsch displacements: `xs_m`
+([ξ^ψ, ∂ξ^ψ/∂ψ, ξ^α] over ψ), and the δB/B (`dbob_m`) and ∇·ξ⊥ (`divx_m`) Fourier modes, obtained by applying
+the S,T,X,Y,Z geometric matrices and removing the J·B² weight (see `_jbb_deweight!`). Port of Fortran
+`set_peq` (pentrc/inputs.f90). Errors unless the run has a single toroidal mode.
+"""
+function set_perturbation_data!(kf_intr::KineticForcesInternal, pe_state::PerturbedEquilibrium.PerturbedEquilibriumState,
+ ffs::ForceFreeStates.ForceFreeStatesResult,
+ equil::Equilibrium.PlasmaEquilibrium,
+ metric::ForceFreeStates.MetricData)
+ ffs.npert == 1 || error("KineticForces supports a single toroidal mode; this run has n = $(ffs.nlow):$(ffs.nhigh).")
+
+ # Copy mode numbers from FFS
+ kf_intr.mlow = ffs.mlow
+ kf_intr.mhigh = ffs.mhigh
+ kf_intr.mpert = ffs.mpert
+ kf_intr.nlow = ffs.nlow
+ kf_intr.nhigh = ffs.nhigh
+ kf_intr.npert = ffs.npert
+ kf_intr.numpert_total = ffs.numpert_total
+ kf_intr.mfac = collect(ffs.mlow:ffs.mhigh)
+ kf_intr.psilim = ffs.psilim
+
+ # Rational-surface ψ locations (ideal + kinetic EL) become panel boundaries for the
+ # outer ψ torque quadrature; dedupe against coincident points happens in psi_panel_points.
+ kf_intr.sing_psis = sort!(vcat([s.psifac for s in ffs.surfaces], [s.psifac for s in ffs.kinetic.kinsing]))
+
+ # Bail if no xi_modes available (PE didn't run or failed)
+ if pe_state.xi_modes === nothing || isempty(pe_state.psi_grid)
+ @warn "set_perturbation_data!: no xi_modes available, skipping perturbation build"
+ return
+ end
+
+ xi_modes = pe_state.xi_modes
+ psi_grid = pe_state.psi_grid
+ npsi = length(psi_grid)
+ mpert = ffs.mpert
+
+ # Build xs_m: 3 CubicSeriesInterpolants from Clebsch displacement matrices
+ # xs_m[1] = ξ^ψ (unregularized), xs_m[2] = ∂ξ^ψ/∂ψ (regularized), xs_m[3] = ξ^α
+ itp_opts = (; extrap=ExtendExtrap())
+ # clebsch_alpha is already the physical ξ^α = xms/χ₁ (as Fortran gpout_xclebsch writes it); use directly.
+ clebsch_alpha_mat = xi_modes.clebsch_alpha
+ xs_m_1 = cubic_interp(psi_grid, Series(xi_modes.clebsch_psi); itp_opts...)
+ xs_m_2 = cubic_interp(psi_grid, Series(xi_modes.clebsch_psi1); itp_opts...)
+ xs_m_3 = cubic_interp(psi_grid, Series(clebsch_alpha_mat); itp_opts...)
+ kf_intr.xs_m = [xs_m_1, xs_m_2, xs_m_3]
+
+ # Build geometric matrices (S,T,X,Y,Z) for JBB deweighting
+ geom_mats = ForceFreeStates.build_kinetic_metric_matrices(equil, ffs, metric)
+
+ # Build FourierTransform for the JBB deweighting DFT round-trip
+ mthsurf = kf_intr.mthsurf
+ ft = Utilities.FourierTransforms.FourierTransform(mthsurf, mpert, ffs.mlow)
+
+ # JBB deweighting: convert Clebsch modes → physical δB/B and ∇·ξ⊥ modes
+ dbob_m_data = zeros(ComplexF64, npsi, mpert)
+ divx_m_data = zeros(ComplexF64, npsi, mpert)
+
+ # Pre-allocate buffers
+ smat_flat = Vector{ComplexF64}(undef, mpert^2)
+ tmat_flat = Vector{ComplexF64}(undef, mpert^2)
+ xmat_flat = Vector{ComplexF64}(undef, mpert^2)
+ ymat_flat = Vector{ComplexF64}(undef, mpert^2)
+ zmat_flat = Vector{ComplexF64}(undef, mpert^2)
+ jbb_kapx = Vector{ComplexF64}(undef, mpert)
+ jbb_divx = Vector{ComplexF64}(undef, mpert)
+ jbb_dbob = Vector{ComplexF64}(undef, mpert)
+ theta_buf = Vector{ComplexF64}(undef, mthsurf)
+
+ hint_s = Ref(1)
+ hint_t = Ref(1)
+ hint_x = Ref(1)
+ hint_y = Ref(1)
+ hint_z = Ref(1)
+
+ for ipsi in 1:npsi
+ psi = psi_grid[ipsi]
+
+ # Get Clebsch displacement vectors at this ψ
+ xsp = view(xi_modes.clebsch_psi, ipsi, :) # ξ^ψ [mpert]
+ xmp1 = view(xi_modes.clebsch_psi1, ipsi, :) # ∂ξ^ψ/∂ψ [mpert]
+ xms = view(clebsch_alpha_mat, ipsi, :) # ξ^α [mpert]
+
+ # Evaluate geometric matrices at ψ → mpert² flat vectors, reshape to mpert×mpert
+ geom_mats.smats(smat_flat, psi; hint=hint_s)
+ geom_mats.tmats(tmat_flat, psi; hint=hint_t)
+ geom_mats.xmats(xmat_flat, psi; hint=hint_x)
+ geom_mats.ymats(ymat_flat, psi; hint=hint_y)
+ geom_mats.zmats(zmat_flat, psi; hint=hint_z)
+
+ smat = reshape(smat_flat, mpert, mpert)
+ tmat = reshape(tmat_flat, mpert, mpert)
+ xmat = reshape(xmat_flat, mpert, mpert)
+ ymat = reshape(ymat_flat, mpert, mpert)
+ zmat = reshape(zmat_flat, mpert, mpert)
+
+ # jbb_kapx = smat·xsp + tmat·xms; jbb_divx = xmat·xmp1 + ymat·xsp + zmat·xms
+ mul!(jbb_kapx, smat, xsp)
+ mul!(jbb_kapx, tmat, xms, 1.0 + 0.0im, 1.0 + 0.0im) # += tmat * xms
+ mul!(jbb_divx, xmat, xmp1)
+ mul!(jbb_divx, ymat, xsp, 1.0 + 0.0im, 1.0 + 0.0im) # += ymat * xsp
+ mul!(jbb_divx, zmat, xms, 1.0 + 0.0im, 1.0 + 0.0im) # += zmat * xms
+ @. jbb_dbob = -(jbb_divx + jbb_kapx)
+
+ # Inverse DFT to θ-space, divide by J·B², forward DFT back
+ _jbb_deweight!(view(dbob_m_data, ipsi, :), jbb_dbob, ft, psi, equil, mthsurf, theta_buf)
+ _jbb_deweight!(view(divx_m_data, ipsi, :), jbb_divx, ft, psi, equil, mthsurf, theta_buf)
+ end
+
+ # Build CubicSeriesInterpolants over ψ for dbob_m and divx_m
+ kf_intr.dbob_m = cubic_interp(psi_grid, Series(dbob_m_data); itp_opts...)
+ kf_intr.divx_m = cubic_interp(psi_grid, Series(divx_m_data); itp_opts...)
+
+ if kf_intr.verbose
+ @info "set_perturbation_data!: built dbob_m/divx_m/xs_m interpolants " *
+ "(npsi=$npsi, mpert=$mpert)"
+ end
+end
+
+"""
+ _jbb_deweight!(out, jbb_modes, ft, psi, equil, mthsurf, theta_buf)
+
+Remove the J·B² weight from m-space modes: inverse DFT, divide by J(ψ,θ)·B(ψ,θ)², forward DFT into `out`.
+"""
+function _jbb_deweight!(out::AbstractVector{ComplexF64}, jbb_modes::Vector{ComplexF64},
+ ft::Utilities.FourierTransforms.FourierTransform,
+ psi::Float64, equil::Equilibrium.PlasmaEquilibrium,
+ mthsurf::Int, theta_buf::Vector{ComplexF64})
+ # Inverse DFT: m-space → θ-space
+ theta_buf .= Utilities.FourierTransforms.inverse(ft, jbb_modes)
+
+ # Divide by J·B² at each θ point
+ for j in 1:mthsurf
+ theta_norm = (j - 1) / mthsurf # θ ∈ [0, 1)
+ pt = (psi, theta_norm)
+ jac = equil.rzphi_jac(pt)
+ B = equil.eqfun_B(pt)
+ theta_buf[j] /= jac * B^2
+ end
+
+ # Forward DFT: θ-space → m-space
+ out .= ft(theta_buf)
+ return nothing
+end
+
+
+# Result structs
+
+"""
+ MethodResult
+
+Results for one NTV computation method across all flux surfaces.
+"""
+@kwdef mutable struct MethodResult
+ method::String = ""
+ nn::Int = 0
+ torque_profile::Any = nothing # Interpolant of dT/dψ(ψ) from ψ integration
+ total_torque::ComplexF64 = 0.0 + 0.0im # complex T: Re = torque T_φ [N·m], Im = 2n·δW_k (Logan 2013 Eq. 19)
+ total_energy::Float64 = 0.0 # real kinetic energy δW_k = Im(T)/(2n) [J]
+ # Per-step ψ profile from outer quadrature
+ psi_grid::Vector{Float64} = Float64[]
+ dtdpsi::Vector{ComplexF64} = ComplexF64[]
+ t_cumulative::Vector{ComplexF64} = ComplexF64[]
+ # dT/dψ resolved by bounce harmonic ℓ, shape (length(psi_grid), length(ell)) with ell = -nl:nl.
+ # Summing over ℓ reproduces `dtdpsi`. Empty when no ψ profile was produced.
+ dtdpsi_ell::Matrix{ComplexF64} = zeros(ComplexF64, 0, 0)
+ ell::Vector{Int} = Int[]
+ psi_nsteps::Int = 0
+ # ψ-quadrature panel boundaries and the located kinetic-resonance surfaces (first n)
+ panel_psis::Vector{Float64} = Float64[]
+ resonance_psis::Vector{Float64} = Float64[]
+end
+
+"""
+ KineticForcesState
+
+Accumulated results from all KineticForces computations.
+Written to gpec.h5 under the "KineticForces" group.
+"""
+@kwdef mutable struct KineticForcesState
+ method_results::Dict{String,MethodResult} = Dict{String,MethodResult}()
+ # Block-diagonal kinetic matrices: key=method, value=(numpert_total, numpert_total, 6)
+ kinetic_matrices::Dict{String,Array{ComplexF64,3}} = Dict{String,Array{ComplexF64,3}}()
+end
+
+"""
+ KineticForcesResult
+
+The kinetic torque of a perturbed equilibrium, from [`kinetic_torque`](@ref).
+
+## Fields
+
+ - `total::KineticForcesState` - The torque by method, summed over species.
+ - `species::Vector{Pair{String,KineticForcesState}}` - Each species' contribution by label; empty for a single-ion run.
+ - `axis_psi_c::Float64` - The near-axis validity boundary the ψ quadrature used.
+ - `pe::PerturbedEquilibrium.PerturbedEquilibriumState` - The perturbed equilibrium the torque was evaluated on.
+ - `control::KineticForcesControl` - The kinetic model settings.
+"""
+struct KineticForcesResult
+ total::KineticForcesState
+ species::Vector{Pair{String,KineticForcesState}}
+ axis_psi_c::Float64
+ pe::PerturbedEquilibrium.PerturbedEquilibriumState
+ control::KineticForcesControl
+end
diff --git a/src/KineticForces/Output.jl b/src/KineticForces/Output.jl
new file mode 100644
index 0000000000..4810d1d8a9
--- /dev/null
+++ b/src/KineticForces/Output.jl
@@ -0,0 +1,220 @@
+import ..Utilities: save_to_hdf5
+import ..Utilities.HDF5Annotations: ensure_group, replace_group!, write_fields!
+
+"""
+ Output
+
+HDF5 output for KineticForces results.
+All results accumulate in KineticForcesState during computation,
+then write to gpec.h5 in a single pass.
+"""
+
+"""
+ save_to_hdf5(h5file::Union{HDF5.File,HDF5.Group}, state::KineticForcesState; dVdpsi_spline=nothing,
+ species_label=nothing)
+
+Write KineticForces results to the "KineticForces" group in gpec.h5.
+
+# Arguments
+
+ - `h5file::Union{HDF5.File,HDF5.Group}`: Open HDF5 file handle
+ - `state::KineticForcesState`: Accumulated computation results
+ - `dVdpsi_spline`: Optional dV/dψ_N profile interpolant; when given, dV/dψ_N is
+ written at the quadrature points so the torque density dT/dV = (dT/dψ)/(dV/dψ)
+ is directly available
+ - `species_label`: `nothing` writes the run total to `KineticForces//`; a label
+ (e.g. `"ion_z1_m2"`, `"electron"`) writes one species' contribution to
+ `KineticForces/PerSpecies/