`schur_full`/`schur_vals` select `DiagonalAlgorithm` for `Diagonal` but it is not implemented

[lkdvos]

schur_full/schur_vals select DiagonalAlgorithm for Diagonal inputs, but no such implementation exists, so both throw a MethodError.

Reproduction

On MatrixAlgebraKit v0.6.9, Julia 1.12.6:

julia> using LinearAlgebra, MatrixAlgebraKit

julia> D = Diagonal([2.0, 3.0, 5.0]);

julia> MatrixAlgebraKit.select_algorithm(MatrixAlgebraKit.schur_full!, D, nothing)
DiagonalAlgorithm{@NamedTuple{}}(NamedTuple())

julia> schur_full(D)
ERROR: MethodError: no method matching schur_full!(::Diagonal{Float64, Vector{Float64}}, ::Tuple{Diagonal{Float64, Vector{Float64}}, Matrix{Float64}, Vector{ComplexF64}}, ::DiagonalAlgorithm{@NamedTuple{}})

julia> schur_vals(D)
ERROR: MethodError: no method matching schur_vals!(...)

julia> eig_full(D)   # control: works

Cause

Schur reuses eig's algorithm selection, which routes Diagonal to DiagonalAlgorithm:

• src/interface/schur.jl:44-48 — default_algorithm(::typeof(schur_full!), ::Type{A}; kwargs...) = default_eig_algorithm(A; kwargs...), for both schur_full! and schur_vals!
• src/interface/eig.jl:167-169 — default_eig_algorithm(::Type{T}) where {T <: Diagonal} = DiagonalAlgorithm(; kwargs...)

But src/implementations/schur.jl only implements QRIteration (lines 92 and 97). There is no DiagonalAlgorithm method, nor check_input/initialize_output for it — the existing ones at lines 7-38 are ::AbstractAlgorithm, so selection succeeds and dispatch then fails.

eig, eigh, svd, qr and lq all have DiagonalAlgorithm implementations; schur appears to be the one that was missed.

Suggested fix

Add the diagonal case to src/implementations/schur.jl. A diagonal matrix is already in Schur form, so T = A, Z = I, vals = complex.(diagview(A)) — mirroring eigh_full!(A::Diagonal, DV, ::DiagonalAlgorithm) at src/implementations/eigh.jl:179. Unlike eigh, no sorting is implied by the Schur interface.

Alternatively, give schur its own default_schur_algorithm instead of reusing default_eig_algorithm, so Diagonal no longer selects an unimplemented algorithm. That turns the MethodError into a clearer one but still leaves schur_full(::Diagonal) unsupported.

Happy to open a PR for whichever direction you prefer.

Note: src/interface/schur.jl:23 already carries # TODO: is this useful? Is there any difference with simply eig_vals? above schur_vals. If the answer is to drop schur_vals, that covers half of this.

Downstream impact

This reaches TensorKit.DiagonalTensorMap, which forwards to select_algorithm like every other factorization:

julia> using TensorKit

julia> d = DiagonalTensorMap(randn(4), Vect[Z2Irrep](0 => 2, 1 => 2));

julia> schur_full(d)   # MethodError; eig_full(d) and svd_compact(d) are fine

Found via JET.report_package(TensorKit).