Solve with AdjointFactorization of Cholmod and Adjoint rhs (#595)

Fixes #594.

src/solvers/cholmod.jl

@@ -15,7 +15,7 @@ import Base: (*), convert, copy, eltype, getindex, getproperty, show, size,
 using Base: require_one_based_indexing
 
 using LinearAlgebra
-using LinearAlgebra: RealHermSymComplexHerm, AdjOrTrans
+using LinearAlgebra: RealHermSymComplexHerm, AdjOrTrans, AdjOrTransAbsMat
 import LinearAlgebra: (\), AdjointFactorization,
                  cholesky, cholesky!, det, diag, ishermitian, isposdef,
                  issuccess, issymmetric, ldiv!, ldlt, ldlt!, logdet,
@@ -1928,6 +1928,7 @@ function \(adjL::AdjointFactorization{<:VTypes,<:Factor}, B::StridedMatrix)
     L = adjL.parent
     return Matrix(solve(CHOLMOD_A, L, Dense(B)))
 end
+(\)(adjL::AdjointFactorization{<:VTypes,<:Factor}, B::AdjOrTransAbsMat) = adjL \ copy(B)
 
 const RealHermSymComplexHermSSL{Ti, Tr} = Union{
     Symmetric{Tr, SparseMatrixCSC{Tr, Ti}},

test/cholmod.jl

@@ -1019,6 +1019,21 @@ end
     # @test_throws ErrorException cholesky(view(A, :, :), NoPivot())
 end
 
+@testset "solve with adjoint factorization and adjoint rhs" begin
+    n = 10
+    A = sprand(Tv, n, n, 1/n)
+    A = A + A' + 10I
+
+    B = rand(n, 2)
+    Bt = Matrix(B')
+    Bts = sparse(B')
+
+    F = cholesky(A)'
+    @test F \ B ≈ F \ Bt'
+    @test F \ B ≈ F \ Bts'
+    @test issparse(F \ Bts')
+end
+
 end # for Tv ∈ (Float32, Float64)
 
 end # Base.USE_GPL_LIBS