LDL' factorizations are failing with complex Hermitian matrices

[amontoison]

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

using Random
Random.seed!(1)

n = 100
p = 5
T = ComplexF64
R = real(T)
A_cpu = sprand(T, n, n, 0.01) + I
A_cpu = A_cpu + A_cpu'
X_cpu = zeros(T, n, p)
B_cpu = rand(T, n, p)

A_gpu = CuSparseMatrixCSR(A_cpu)
X_gpu = CuMatrix(X_cpu)
B_gpu = CuMatrix(B_cpu)

matrix = CudssMatrix(A_gpu, "H", 'F', index='O')
config = CudssConfig()
data = CudssData()
solver = CudssSolver(matrix, config, data)

cudss("analysis", solver, X_gpu, B_gpu)
cudss("factorization", solver, X_gpu, B_gpu)

nnz_decomposition = cudss_get(solver, "lu_nnz")
inertia = cudss_get(solver, "inertia")

cudss("solve", solver, X_gpu, B_gpu)

R_gpu = B_gpu - CuSparseMatrixCSR(A_cpu) * X_gpu
@test norm(R_gpu) ≤ √eps(R)

Y_cpu = zeros(T, n, n)
Y_gpu = CuMatrix(Y_cpu)
C_cpu = Matrix{T}(I, n, n)
C_gpu = CuMatrix(C_cpu)

cudss("solve", solver, Y_gpu, C_gpu)

RR_gpu = C_gpu - CuSparseMatrixCSR(A_cpu) * Y_gpu
@test norm(RR_gpu) ≤ √eps(R)

using MatrixMarket

MatrixMarket.mmwrite("cudss_A.mtx", A_gpu |> SparseMatrixCSC)
MatrixMarket.mmwrite("cudss_B.mtx", B_gpu |> Matrix |> sparse)
MatrixMarket.mmwrite("cudss_X.mtx", X_gpu |> Matrix |> sparse)
MatrixMarket.mmwrite("cudss_Y.mtx", Y_gpu |> Matrix |> sparse)

[amontoison]

It works if we remove the pivoting with

cudss_set(solver, "pivot_type", 'N')

This issue will be fixed in the next release.

[amontoison]

Fixed by #17