Add SciML test setup and correctness tests

[ChrisRackauckas-Claude]

Please ignore until reviewed by @ChrisRackauckas.

Summary

• Restructures test/ around a GROUP env split (Core/QA, plus per-factorization subgroups QR/LU/Cholesky/Cross)
• Adds the standard SciML QA tests: Aqua + ExplicitImports, gated behind GROUP=QA
• Adds SafeTestsets isolation for each test file
• Adds a GitHub Actions CI matrix (Julia 1.11 + 1, Linux/Mac/Windows, Core + QA groups, codecov)
• Substantially expands correctness coverage for cs_qr, cs_lu, cs_cholesky
• Test count: 245 → 626 passing

New correctness tests

For each factorization and each (Tv, Ti) ∈ {Float64, ComplexF64} × {Int32, Int64}:

• Known-answer hand-computed matrices (e.g. [2 1; 0 3] \ [4; 6] = [1; 2])
• Identity / diagonal / tridiagonal test matrices
• n = 1 trivial case
• Input matrix immutability: A.colptr/rowval/nzval snapshot equals post-factorization and post-solve state
• RHS immutability: b is unchanged after F \ b and ldiv!(x, F, b)
• Multiple solves on one factorization: 5 different RHS, all match dense backslash
• ldiv! returns the destination (identity test)
• Explicit finalize(F) is safe and idempotent (no double-free)
• Cross-factorization consistency: on a square non-singular matrix cs_qr ≈ cs_lu ≈ dense\; on an SPD matrix cs_qr ≈ cs_lu ≈ cs_cholesky ≈ dense\ to rtol=1e-9

Factorization-specific:

• QR: overdetermined least-squares now compared coefficient-wise to dense Adense \ b (the existing test only compared residual norms)
• LU: requires-pivoting matrix (zero on diagonal), singular matrix rejected, upper-triangular hand-check
• Cholesky: zero-diagonal rejection, Hermitian (not just real-symmetric) test with non-trivial complex off-diagonals, small known-answer matrix

QA-driven source/compat fixes

• src/CXSparse.jl: using LinearAlgebra → using LinearAlgebra: LinearAlgebra, ldiv! (ExplicitImports flagged the implicit import; the qualified LinearAlgebra.ldiv! calls in the body still work).
• Project.toml:
  • Added compat for Random and Test (Aqua flagged them as extras-without-compat)
  • Bumped julia compat 1.10 → 1.11. The package's actual minimum is 1.11: CXSparse_jll@4 requires SuiteSparse_jll ≥ 7.7, but Julia 1.10 stdlib pins SuiteSparse_jll 7.2.1. Resolver fails on 1.10 (confirmed locally), so the previous claim was incorrect.

Test plan

• Pkg.test() passes locally on Julia 1.11 (626 tests, no failures)
• GROUP=Core runs only factorization tests
• GROUP=QA runs only Aqua + ExplicitImports
• GROUP=QR / LU / Cholesky / Cross subset selectors work
• CI passes on the matrix (Linux/Mac/Windows × Julia 1.11/1)

🤖 Generated with Claude Code

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