Fix default algorithm for sparse CUDA matrices to LUFactorization

Previously:
- CuSparseMatrixCSC defaulted to GenericLU (not GPU compatible)
- CuSparseMatrixCSR fell back to Krylov when CUDSS unavailable (not GPU compatible)
- Symmetric sparse matrices defaulted to Cholesky (not GPU compatible)

Changes:
- Both CuSparseMatrixCSC and CuSparseMatrixCSR now default to LUFactorization
- Removed Krylov fallback - if CUDSS is not loaded, clear error message is shown
- Added cudss_loaded() support for CuSparseMatrixCSC
- Added error_no_cudss_lu() for CuSparseMatrixCSC

Fixes #827

🤖 Generated with [Claude Code](https://claude.com/claude-code)

Co-Authored-By: Claude <noreply@anthropic.com>

Author: ChrisRackauckas

ext/LinearSolveCUDAExt.jl

@@ -20,15 +20,12 @@ end
 
 function LinearSolve.defaultalg(A::CUDA.CUSPARSE.CuSparseMatrixCSR{Tv, Ti}, b,
         assump::OperatorAssumptions{Bool}) where {Tv, Ti}
-    if LinearSolve.cudss_loaded(A)
-        LinearSolve.DefaultLinearSolver(LinearSolve.DefaultAlgorithmChoice.LUFactorization)
-    else
-        if !LinearSolve.ALREADY_WARNED_CUDSS[]
-            @warn("CUDSS.jl is required for LU Factorizations on CuSparseMatrixCSR. Please load this library. Falling back to Krylov")
-            LinearSolve.ALREADY_WARNED_CUDSS[] = true
-        end
-        LinearSolve.DefaultLinearSolver(LinearSolve.DefaultAlgorithmChoice.KrylovJL_GMRES)
-    end
+    LinearSolve.DefaultLinearSolver(LinearSolve.DefaultAlgorithmChoice.LUFactorization)
+end
+
+function LinearSolve.defaultalg(A::CUDA.CUSPARSE.CuSparseMatrixCSC{Tv, Ti}, b,
+        assump::OperatorAssumptions{Bool}) where {Tv, Ti}
+    LinearSolve.DefaultLinearSolver(LinearSolve.DefaultAlgorithmChoice.LUFactorization)
 end
 
 function LinearSolve.error_no_cudss_lu(A::CUDA.CUSPARSE.CuSparseMatrixCSR)
@@ -38,6 +35,13 @@ function LinearSolve.error_no_cudss_lu(A::CUDA.CUSPARSE.CuSparseMatrixCSR)
     nothing
 end
 
+function LinearSolve.error_no_cudss_lu(A::CUDA.CUSPARSE.CuSparseMatrixCSC)
+    if !LinearSolve.cudss_loaded(A)
+        error("CUDSS.jl is required for LU Factorizations on CuSparseMatrixCSC. Please load this library.")
+    end
+    nothing
+end
+
 function SciMLBase.solve!(cache::LinearSolve.LinearCache, alg::CudaOffloadLUFactorization;
         kwargs...)
     if cache.isfresh

ext/LinearSolveCUDSSExt.jl

@@ -4,5 +4,6 @@ using LinearSolve: LinearSolve, cudss_loaded
 using CUDSS
 
 LinearSolve.cudss_loaded(A::CUDSS.CUDA.CUSPARSE.CuSparseMatrixCSR) = true
+LinearSolve.cudss_loaded(A::CUDSS.CUDA.CUSPARSE.CuSparseMatrixCSC) = true
 
 end