[FBumann]

Prompt: We need to not resolve for such a feature!! What can we achieve without it ?

Prompt: No, no solve for now

Note

The following content was generated by AI.

parameter_dual now prices a value on a where: threshold by what its rise switches on or off, from the same solve and with no re-solve. A jump is ±inf. What one solve cannot decide keeps the rate as built, and a warning names it.

result.parameter_dual('p_max')     # dispatch.yaml, solar at p_max = 0 under `where: p_max > 0`
# wind   -120.0
# solar   -75.0   # was 0.0: its first unit replaces gas in three snapshots, 25 cheaper each
# gas       0.0

What each threshold reports, how, verification, what is left out

What a rise past a threshold reports

A rise…	Example (tests/test_parameter_dual_thresholds.py)	Reported
switches on a column whose bound is the value	solar, upper: p_max	its reduced cost: -75
the same, maximized	-sum(p * cost)	+75
switches on a column capped by a zero-slack row that came with it	p <= avail * p_max, solar avail = 0.4	reduced cost × 0.4: -30
the same cap, written with a coefficient	2 * p <= 2 * avail * p_max	-30
switches on a zero-slack row that forces a column up	p >= p_min under where: p_min > 0, gas	gas's reduced cost: 40
switches on a row a running column already meets	the same row, wind	0
switches on a column with a fixed bound it would use	solar, upper: 100	-inf
switches on a row the solve violates	p >= 10 under where: p_min > 0, gas	+inf
switches off a row with a dual	p <= 30 under where: tight <= 0, wind	-inf
switches off a column the solve uses	where: retire <= 0, gas	+inf
switches on a floor that rises faster than the column's cap	p >= ramp * p_max, solar ramp = 2	+inf
switches on a zero-slack row across several columns	a pooled row	as built, warned
crosses a mask that reads it through a sum, shift, lookup or count	where: … and sum(p_min, over=generator) <= 0	as built, warned
crosses a when:	cases: when: p_min > 0	as built, warned
switches rows of a quadratic constraint	p * p <= 1e6 under where: p_min > 0 (gurobi, QCPDual)	as built, warned

Signs mirror under maximize. A bool parameter has no rise, so nothing crosses. Each finite case matches a forward re-solve at rel 1e-5. Each infinite case is checked by a forward re-solve that moves the objective the same way by more than 1e3 times the step, or loses its solution.

How

• Find the crossings. _risen raises every value of the parameter by 1e-9 × max(1, |v|). The masks that read it at their own coordinate are evaluated again, and the coordinates that change are the crossings. Each crossing is charged to the parameter row its coordinate projects onto.
• Price the new columns. A switched-on column gets a label past the solve's last, primal 0. It is priced by compiling with that variable varied over the grown frame, the same pass that gives a bound's reduced cost in feat(api): a result gives the rate at which its objective moves with each value of a parameter, also where a where: condition switches at that value #2073.
• Evaluate the new rows. They are compiled as a build with the parameter varied too. Its labels are now negative (varied_label), so variables and parameter rows share one compile without colliding, and a variable × parameter product is a quadratic term. One pass gives each row's slack at the solve, its columns, and its rate in each parameter row.
• Decide each column. It moves the way its reduced cost prices as a gain, as far as the tightest zero-distance cap allows: its own bounds, at rate 1 where they are the charged row, and the zero-slack single-column rows. Its rate is the reduced cost times that move. If no cap stops it that way, or a cap would push it past another, the rate is a jump.
• No solve, no full build. Only the declarations whose mask reads the parameter, or that read a variable that flipped, are evaluated again.

The parameter dual moves from _engine/readback.py to _engine/parameter_dual.py, and the architecture table follows. Result.parameter_dual raises the notes as SpecsolveWarning. The how-to What a change is worth, from #2073, now prices solar at -75, and says what an infinite rate and a warning mean.

The reader was marginal when this PR opened. #2073 renamed it parameter_dual (the reason is in #2073), and 3dc9195 carries the rename here, to the module and the test files too.

Verified

• On fb3d219: pixi run check 5910 passed, 579 skipped, 4 xfailed. docs-build (strict): no issues. docs-test: 116 passed.
• On 864d079, after merging feat(api): a result gives the rate at which its objective moves with each value of a parameter, also where a where: condition switches at that value #2073's how-to: pixi run check 5911 passed. docs-build (strict), docs-test (116 passed), and test_doc_examples, test_docs_site and test_changelog (162 passed) are clean.
• On 3dc9195, after merging the rename: pixi run check 5927 passed, 579 skipped, 4 xfailed. docs-build (strict): no issues. docs-test: 116 passed. The rendered how-to prints solar at -75.

Not run: test-via-pyarrow, test-floors, test-bench.

Mutation table

Taken before the rename, so the paths read marginal.py, now parameter_dual.py. Each guard was deleted in turn, and the full suite was run each time. The rows marked tool come from tools/mutate.py. The rows marked hand replace a branch or a constant the tool cannot express, with the same precautions (git checkout -- restore, __pycache__ dropped on both sides). The tree came back clean after every run.

The first run left six survivors, and one range the tool could not apply. Each got a probe in 3c7d44f, and the second run, on 3c7d44f, caught them all.

Guard	How	First run (54fe6ff)	On 3c7d44f
a parameter that is not a number crosses nothing	tool	green	caught
a used column switched off is a jump	tool	caught	—
a when: on a threshold is named	tool	green	caught
a quadratic row is held as built	tool	green	caught
a row with a dual switched off is a jump	hand	not applied by the tool	caught
a violated row switched on is a jump	tool	caught	—
a zero-slack row over several columns is held as built	tool	caught	—
a mask that reads through a sum is not charged	hand	green	caught
no rise: nothing crosses (_RISE = 0)	hand	caught	—
a column that gains by rising is priced	hand	caught	—
a column that gains by falling is priced	hand	caught	—
a cap that crosses its push is a jump	hand	green	caught
a cap is divided by its coefficient	hand	green	caught

Left out

• Coupled zero-slack rows. A switched-on row at zero slack across several columns needs a small LP over the crossed columns. It stays as built and warned, by decision: no solve for now.
• The size of a jump. It is not given; the warning names the rows.
• when: flips, and masks read through a shift, sum, lookup or count. These stay as built and warned, because a flip cannot be charged to one parameter row cheaply there.
• Quadratic constraints whose rows a rise switches. These stay as built and warned.
• Cost not measured. The threshold pass runs only when a mask reads the parameter. Its cost on the published ladder is not measured.

Coverage that moved

test_a_value_a_mask_reads_is_held_where_the_mask_put_it, from #2073's tests/test_parameter_dual.py, asserted the held-as-built 0. tests/test_parameter_dual_thresholds.py replaces it.

🤖 Generated with Claude Code

https://claude.ai/code/session_018B3nA1Q4XLWBq2jJFFLFWR

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• CHANGELOG.md
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• docs/howto/prices.md
• src/specsolve/_api.py
• src/specsolve/_archive.py
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• src/specsolve/_engine/engine.py
• src/specsolve/_engine/parameter_dual.py
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[read-the-docs-community]

Documentation build overview

📚 specsolve | 🛠️ Build #35545621 | 📁 Comparing 0c043e9 against latest (5a78e3f)

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• about/linopy/index.html
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• examples/facility_location/index.html
• examples/genx_piecewise_fuel/index.html
• examples/multi_period/index.html
• examples/osemosys_utopia/index.html
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• and 103 more...

[codspeed]

Merging this PR will not alter performance

✅ 104 untouched benchmarks
⏩ 307 skipped benchmarks¹

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_{Comparing claude/specsolve-marginal-thresholds-w3yt75 (0c043e9) with claude/specsolve-feature-differentiation-w3yt75 (a248849)}

Footnotes

1. 307 benchmarks were skipped, so the baseline results were used instead. If they were deleted from the codebase, click here and archive them to remove them from the performance reports. ↩