Complete allocation-free dense LU refactorization: generic-kernel pivot reuse + regression tests

[ChrisRackauckas-Claude]

Note: This PR should be ignored until reviewed by @ChrisRackauckas.

Motivation

SciML/NonlinearSolve.jl#1038 makes every dense Newton iteration hit the alias_A = true dense-LU refactorization path (cache.A = J; solve!(cache)), so any per-refactorization allocation there is paid on every Newton step. #1078 (merged) already eliminated the fresh ipiv/LU-wrapper allocation for the LAPACK fast path (strided BLAS matrices + RowMaximum, Julia >= 1.11) via the preallocated-ipiv LAPACK.getrf!. This PR completes the picture:

1. Generic-kernel path pivot reuse. With alias_A = true, NoPivot/RowNonZero pivoting and non-BLAS element types still went through lu!(A, pivot; check = false), which allocates a fresh pivot vector and LU wrapper on every refactorization. They now call the vendored generic_lufact! directly with the cached ipiv (the same kernel/check = false/info semantics lu! dispatches to for these inputs, and the same pattern GenericLUFactorization already uses). Unlike the getrf! method this works on every supported Julia version, so this path is allocation-free on 1.10 (LTS) too. Size changes fall back to lu! (which produces a right-sized pivot that is then cached), exactly like the existing BLAS branch.
2. Regression tests for the whole warm-refactorization contract, which GESVFactorization + dense LU pivot-buffer reuse (v4.2.0) #1078 shipped without: test/Core/lu_refactorization.jl (53 assertions on 1.12), registered in the Core group.

The non-aliased copy path, sparse paths, and all other algorithms are untouched.

Measured: 51×51 Matrix{Float64}, warm refactorize+solve cycle (copyto!(Awork, A); cache.A = Awork; solve!(cache) under @allocated, post-warmup), Julia 1.12.6

path (alias_A = true)	pre-#1078 (v4.2.1)	main (#1078)	this PR
LUFactorization() (RowMaximum)	480 B	0 B	0 B
LUFactorization(pivot = NoPivot())	480 B	480 B	0 B
default algorithm (init(prob, nothing))	480 B	0 B	0 B

On Julia 1.10.11 the NoPivot path also measures 0 B with this PR (the BLAS paths keep the pre-existing allocating lu! there by design — getrf! has no preallocated-ipiv method before 1.11).

Tests

New test/Core/lu_refactorization.jl, run standalone on Julia 1.10.11, 1.12.6, and 1.13.0-rc1 (all pass), covering:

• zero-allocation warm refactorization cycles for LUFactorization() (RowMaximum), LUFactorization(pivot = NoPivot()), and the default algorithm, with per-version ceilings asserted (== 0 wherever reuse is active) plus a direct cacheval.ipiv === ipiv_before identity check;
• correctness vs A \ b across repeated refactorize+solve cycles;
• singular refactorization returns ReturnCode.Failure without throwing (check = false semantics preserved) and the cache recovers on the next nonsingular matrix, for both RowMaximum and NoPivot;
• DefaultLinearSolver's safetyfallback QR rescue still works when a warm alias_A = true cycle hands it a singular matrix (LU fails → column-pivoted QR least-squares, ReturnCode.Success);
• generic (BigFloat) eltype correctness through the reuse branch;
• pivot reallocation on size change via resize!(cache, n) and return to 0-alloc cycles at the new size.

Full local runs:

• GROUP=Core Pkg.test() on Julia 1.12.6: passed ("Testing LinearSolve tests passed"), including the new testset (53/53).
• GROUP=QA Pkg.test(): fails on unmodified main with a pre-existing ExplicitImports no_implicit_imports error (unqualified issuccess from GESVFactorization + dense LU pivot-buffer reuse (v4.2.0) #1078); reproduced on clean main and fixed separately in Qualify issuccess as LinearAlgebra.issuccess to fix QA ExplicitImports failure #1081. All other QA checks pass with this branch.

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