fix cholesky linear solve with sparse rhs (#709)

Closes #630

Author: araujoms

src/solvers/cholmod.jl

@@ -990,7 +990,7 @@ function Sparse(A::SparseMatrixCSC{<:Union{ComplexF16, ComplexF32}}, stype::Inte
 end
 
 # convert SparseVectors into CHOLMOD Sparse types through a mx1 CSC matrix
-Sparse(A::SparseVector) = Sparse(SparseMatrixCSC(A))
+Sparse(A::SparseVector) = Sparse(SparseMatrixCSC(A), 0)
 function Sparse{Tv, Ti}(A::SparseMatrixCSC) where {Tv<:VTypes, Ti<:ITypes}
     o = Sparse{Tv, Ti}(A, 0)
     # check if array is symmetric and change stype if it is
@@ -1135,6 +1135,7 @@ function SparseVector{Tv, Ti}(A::Sparse{Tv, Ti}) where {Tv, Ti<:ITypes}
     end
     args = _extract_args(s, Tv)
     s.sorted == 0 && _sort_buffers!(args...);
+    _trim_nz_builder!(args...)
     return SparseVector(args[1], args[4], args[5])
 end
 

test/cholmod.jl

@@ -807,6 +807,14 @@ end
     @test chI \ sparseI ≈ sparseI
 end
 
+@testset "Issue 630" begin
+    sparseI = sparse(1.0I, 1, 1)
+    @test cholesky(sparseI) \ sparse([1.0]) == [1]
+    sparseI = sparse(1.0I, 2, 2)
+    res = cholesky(sparseI) \ spzeros(2)
+    @test isempty(nonzeros(res))
+end
+
 @testset "Real factorization and complex rhs" begin
     A = sprandn(5, 5, 0.4) |> t -> t't + I
     B = complex.(randn(5, 5), randn(5, 5))