Symbolic Factorization Reuse in the standard LUFactorization

[ChrisRackauckas]

This should be sufficient for CUDSS.jl to be optimally used as well

[codecov]

Codecov Report

Attention: Patch coverage is 51.85185% with 39 lines in your changes are missing coverage. Please review.

Project coverage is 62.61%. Comparing base (d050e01) to head (084d0d6).

Files	Patch %	Lines
ext/LinearSolveCUDAExt.jl	0.00%	27 Missing ⚠️
src/LinearSolve.jl	78.43%	11 Missing ⚠️
ext/LinearSolveCUDSSExt.jl	0.00%	1 Missing ⚠️

Additional details and impacted files

@@             Coverage Diff             @@
##             main     #493       +/-   ##
===========================================
+ Coverage   25.10%   62.61%   +37.50%     
===========================================
  Files          28       29        +1     
  Lines        2167     2212       +45     
===========================================
+ Hits          544     1385      +841     
+ Misses       1623      827      -796     

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[ChrisRackauckas]

This is hard to test, but it is now working with CUDSS and I can check the symbolic factorizations are reused! MWE:

using CUDA, CUDA.CUSPARSE
using CUDSS
using SparseArrays, LinearAlgebra
using LinearSolve

T = Float64
n = 100
A_cpu = sprand(T, n, n, 0.05) + I
x_cpu = zeros(T, n)
b_cpu = rand(T, n)

A_gpu = CuSparseMatrixCSR(A_cpu)
x_gpu = CuVector(x_cpu)
b_gpu = CuVector(b_cpu)
prob = LinearProblem(A_gpu, b_gpu)
sol = solve(prob, LUFactorization())

cache = init(prob, LUFactorization())
solve!(cache)
cache.b = CuVector(rand(T, n))
solve!(cache)
cache.A = CuSparseMatrixCSR(A_cpu + 3I)
solve!(cache)
cache.b = CuVector(rand(T, n))
solve!(cache)

This is with JuliaArrays/ArrayInterface.jl#433 and exanauts/CUDSS.jl#33