Make lu/qr of ComponentMatrix preserve the wrapper on factors

[ChrisRackauckas-Claude]

Note

Please ignore this PR until it has been reviewed by @ChrisRackauckas.

Fixes the Downstream CI failure seen in https://github.com/SciML/ComponentArrays.jl/actions/runs/29140401332/job/86512903689 (Issue 36 test in test/Downstream/diffeq_tests.jl).

Root cause

LinearSolve >= v3.87 (and v5) types its LUFactorization cache slot from ArrayInterface.lu_instance(A) but stores lu(A, check = false) when not aliasing A. For a ComponentMatrix:

• ArrayInterface.lu_instance(::ComponentMatrix) (defined here) returns an LU wrapping a ComponentMatrix,
• lu!(A) also keeps the wrapper (ComponentMatrix is strided, so it hits LAPACK directly),
• but lu(A) copies through similar(A, T, dims), which drops the axes and demotes to a plain Matrix.

Storing the LU{..., Matrix, ...} into the LU{..., ComponentMatrix, ...}-typed slot throws TypeError: in setfield!, which is exactly the downstream error:

TypeError: in setfield!, expected LinearAlgebra.LU{Float64, ComponentArrays.ComponentMatrix{...}, Vector{Int64}}, got a value of type LinearAlgebra.LU{Float64, Matrix{Float64}, Vector{Int64}}

This reproduces without OrdinaryDiffEq via a plain solve(LinearProblem(A, b)) on a 2000x2000 ComponentMatrix.

Fix

Make lu(::ComponentMatrix) factorize getdata(A) (keeping the LAPACK fast path) and rewrap the factors, so lu, lu!, and lu_instance all return the same type. The same treatment is applied to qr/ArrayInterface.qr_instance, because LinearSolve's default solver falls back to QRFactorization on singular matrices (safetyfallback) and do_factorization uses the in-place qr!(A, pivot) there, which hits the identical mismatch (slot typed QRCompactWY{..., Matrix, ...} from qr_instance, value QRCompactWY{..., ComponentMatrix, ...}) — i.e. any ODE solve whose W matrix goes singular would crash instead of falling back.

Note GenericLUFactorization (chosen by the default solver for sizes <= 10) stores generic_lufact!(A), which wraps A itself, so its slot genuinely must be LU{..., ComponentMatrix, ...} — that is why the fix preserves the wrapper everywhere rather than demoting lu_instance to Matrix (which would just move the mismatch to the small-size path that currently passes).

Verification (all run locally)

• MWE solve(LinearProblem(A, b)) on a 2000x2000 ComponentMatrix: fails with the CI TypeError before, passes after (LinearSolve v5.0.0, Julia 1.12.6).
• Default solver sweep over sizes 4-2000 with alias_A in (false, true): all pass.
• Explicit LUFactorization, GenericLUFactorization, QRFactorization, KrylovJL_GMRES: all pass.
• Singular-matrix default solve (LU -> QR fallback): no longer throws, returns Success with the least-squares fallback.
• Type consistency typeof(f(A)) === typeof(f!(copy(A))) === typeof(instance(A)) for lu and qr (NoPivot and ColumnNorm): verified on Julia 1.12.6 and 1.10.11.
• GROUP=Core Pkg.test() (Julia 1.12): pass, including new regression tests in test/math_tests.jl.
• GROUP=Downstream Pkg.test() (Julia 1.12): 6 passed, 1 broken (the broken one is the pre-existing @test_broken Sundials Issue 53), versus 4 passed, 1 errored, 1 broken on CI before this change.

Runic has been run on all changed files. Version bumped to 0.15.42.

🤖 Generated with Claude Code

https://claude.ai/code/session_01PZG7J62sLGGMUmvNsKHVMA