Define LU factorization for JLArray

[ChrisRackauckas-Claude]

Ignore this PR until reviewed by @ChrisRackauckas.

Summary

JLArrays now defines LinearAlgebra.lu for JLArray matrices by explicitly copying to the host representation before calling host LU. Matching ldiv! methods copy right-hand sides through host memory so the returned factorization can be used by solver code without triggering JLArray to Ptr conversion.

This addresses the regression described in SciML/OrdinaryDiffEq.jl#4179. JLArrays 0.3.2 intentionally rejects implicit CPU pointer conversion, while the generic LinearAlgebra LU path still reaches LAPACK with a JLArray.

Verification

Before the fix, on the unmodified branch:

julia --project=test --startup-file=no -e 'using JLArrays, LinearAlgebra; A = jl([2.0 1.0; 1.0 3.0]); lu(A; check = false)'

failed with:

ERROR: Illegal conversion of a JLArray to a Ptr
[3] getrf!(A::JLArray{Float64, 2}, ipiv::JLArray{Int64, 1}; check::Bool)
    @ LinearAlgebra.LAPACK .../LinearAlgebra/src/lapack.jl:587

With this patch:

julia --project=test --startup-file=no test/jlarrays_lu.jl

passed:

Test Summary: | Pass  Total  Time
JLArray LU    |    3      3  1.3s

The OrdinaryDiffEq reproduction also passed for both TRBDF2 and Rodas5P:

(SciMLBase.ReturnCode.Success, SciMLBase.ReturnCode.Success, [0.04713496106370036, 0.04713496106370036, 0.04713496106370036])

The full GPUArrays suite passed:

Test Summary: |  Pass  Total      Time
  Overall     | 21022  21022  16m23.0s
   SUCCESS
    Testing GPUArrays tests passed

Also ran typos on the changed files and git diff --check. GPU-specific backends and downstream packages were not tested.

[ChrisRackauckas]

It was effectively doing this before the pointer conversion was removed

[kshyatt]

Brother what is this PR description

[ChrisRackauckas]

ehh have your llm summarize it.

[ChrisRackauckas]

Anything left here?