Rebase of #28526 on master (#34989)

* fix \ SparseVector

* split (\) for sparsevector;
test for Factor and Symmetric Sparse Matrix

Co-authored-by: Chi Po Choi <choi.chi.po@gmail.com>
(cherry picked from commit d2f9677)

stdlib/SuiteSparse/src/cholmod.jl

@@ -1713,7 +1713,8 @@ end
 
 (\)(L::Factor, B::Sparse) = spsolve(CHOLMOD_A, L, B)
 # When right hand side is sparse, we have to ensure that the rhs is not marked as symmetric.
-(\)(L::Factor, B::SparseVecOrMat) = sparse(spsolve(CHOLMOD_A, L, Sparse(B, 0)))
+(\)(L::Factor, B::SparseMatrixCSC) = sparse(spsolve(CHOLMOD_A, L, Sparse(B, 0)))
+(\)(L::Factor, B::SparseVector) = sparse(spsolve(CHOLMOD_A, L, Sparse(B)))
 
 \(adjL::Adjoint{<:Any,<:Factor}, B::Dense) = (L = adjL.parent; solve(CHOLMOD_A, L, B))
 \(adjL::Adjoint{<:Any,<:Factor}, B::Sparse) = (L = adjL.parent; spsolve(CHOLMOD_A, L, B))

stdlib/SuiteSparse/test/cholmod.jl

@@ -706,6 +706,16 @@ end
     @test A\view(Matrix(1.0I, 5, 5), :, :) ≈ Matrix(Diagonal(x))
 end
 
+@testset "Test \\ for Factor and SparseVecOrMat" begin
+    sparseI = sparse(1.0I, 100, 100)
+    sparseb = sprandn(100, 0.5)
+    sparseB = sprandn(100, 100, 0.5)
+    chI = cholesky(sparseI)
+    @test chI \ sparseb ≈ sparseb
+    @test chI \ sparseB ≈ sparseB
+    @test chI \ sparseI ≈ sparseI
+end
+
 @testset "Real factorization and complex rhs" begin
     A = sprandn(5, 5, 0.4) |> t -> t't + I
     B = complex.(randn(5, 2), randn(5, 2))