Reuse direct BLAS LU workspaces during refactorization (#1099)

* Reuse Apple Accelerate LU workspaces

Co-Authored-By: Chris Rackauckas <accounts@chrisrackauckas.com>

* Avoid boxed Apple Accelerate log bindings

Co-Authored-By: Chris Rackauckas <accounts@chrisrackauckas.com>

* Reuse direct OpenBLAS and BLIS LU workspaces

Keep factor, pivot, and status storage stable across direct BLAS refactorizations, and expose transient factorization views to reverse-mode rules.

Co-Authored-By: Chris Rackauckas <accounts@chrisrackauckas.com>

* Use stdlib pivots in Apple factorization views

Convert Accelerate's Int32 pivots only when constructing the transient generic LU view used by reverse-mode rules.

Co-Authored-By: Chris Rackauckas <accounts@chrisrackauckas.com>

* Dispatch adjoint factorization reuse by solver

Co-Authored-By: Chris Rackauckas <accounts@chrisrackauckas.com>

* Audit reverse factorization reuse

Co-Authored-By: Chris Rackauckas <accounts@chrisrackauckas.com>

* Add allocation QA for direct LU refactorization

Co-Authored-By: Chris Rackauckas <accounts@chrisrackauckas.com>

* Resolve Julia 1.13 BLAS symbols eagerly

Co-Authored-By: Chris Rackauckas <accounts@chrisrackauckas.com>

---------

Co-authored-by: ChrisRackauckas-Claude <accounts@chrisrackauckas.com>

Author: ChrisRackauckas-Claude

Project.toml

@@ -213,6 +213,7 @@ InteractiveUtils = "b77e0a4c-d291-57a0-90e8-8db25a27a240"
 IterativeSolvers = "42fd0dbc-a981-5370-80f2-aaf504508153"
 JacobiDavidson = "11c68b98-9c9b-11e8-267b-bbb95576cead"
 KrylovKit = "0b1a1467-8014-51b9-945f-bf0ae24f4b77"
+LAPACK_jll = "51474c39-65e3-53ba-86ba-03b1b862ec14"
 MultiFloats = "bdf0d083-296b-4888-a5b6-7498122e68a5"
 Pkg = "44cfe95a-1eb2-52ea-b672-e2afdf69b78f"
 PureUMFPACK = "b7e1f0a2-3c4d-4e5f-9a0b-1c2d3e4f5a6b"
@@ -228,6 +229,7 @@ StableRNGs = "860ef19b-820b-49d6-a774-d7a799459cd3"
 StaticArrays = "90137ffa-7385-5640-81b9-e52037218182"
 Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
 Zygote = "e88e6eb3-aa80-5325-afca-941959d7151f"
+blis_jll = "6136c539-28a5-5bf0-87cc-b183200dce32"
 
 [targets]
-test = ["AlgebraicMultigrid", "Arpack", "ArnoldiMethod", "BandedMatrices", "BlockDiagonals", "CliqueTrees", "ComponentArrays", "FastAlmostBandedMatrices", "FastLapackInterface", "FiniteDiff", "FixedSizeArrays", "ForwardDiff", "InteractiveUtils", "IterativeSolvers", "JacobiDavidson", "KrylovKit", "MultiFloats", "Pkg", "PureUMFPACK", "Random", "RecursiveFactorization", "STRUMPACK_jll", "SafeTestsets", "SciMLTesting", "SparseArrays", "Sparspak", "SpecializingFactorizations", "StableRNGs", "StaticArrays", "Test", "Zygote"]
+test = ["AlgebraicMultigrid", "Arpack", "ArnoldiMethod", "BandedMatrices", "BlockDiagonals", "CliqueTrees", "ComponentArrays", "FastAlmostBandedMatrices", "FastLapackInterface", "FiniteDiff", "FixedSizeArrays", "ForwardDiff", "InteractiveUtils", "IterativeSolvers", "JacobiDavidson", "KrylovKit", "LAPACK_jll", "MultiFloats", "Pkg", "PureUMFPACK", "Random", "RecursiveFactorization", "STRUMPACK_jll", "SafeTestsets", "SciMLTesting", "SparseArrays", "Sparspak", "SpecializingFactorizations", "StableRNGs", "StaticArrays", "Test", "Zygote", "blis_jll"]