Issue with iterative refinement

[amontoison]

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

using Random
Random.seed!(666)

function example1(T::DataType, n::Int, ir::Int)
	A_cpu = sprand(T, n, n, 0.05) + I
	x_cpu = zeros(T, n)
	b_cpu = rand(T, n)

	A_gpu = CuSparseMatrixCSR(A_cpu)
	x_gpu = CuVector(x_cpu)
	b_gpu = CuVector(b_cpu)

	solver = CudssSolver(A_gpu, "G", 'F')
	cudss_set(solver, "ir_n_steps", ir)

	cudss("analysis", solver, x_gpu, b_gpu)
	cudss("factorization", solver, x_gpu, b_gpu)
	cudss("solve", solver, x_gpu, b_gpu)

	r_gpu = b_gpu - A_gpu * x_gpu
	norm(r_gpu)
end

function example2(T::DataType, n::Int, ir::Int)
	p = 5
	A_cpu = sprand(T, n, n, 0.05) + I
	A_cpu = A_cpu + A_cpu'
	X_cpu = zeros(T, n, p)
	B_cpu = rand(T, n, p)

	A_gpu = CuSparseMatrixCSR(A_cpu |> tril)
	X_gpu = CuMatrix(X_cpu)
	B_gpu = CuMatrix(B_cpu)

	structure = T <: Real ? "S" : "H"
	solver = CudssSolver(A_gpu, structure, 'L')
	cudss_set(solver, "ir_n_steps", ir)
	
	# Required with CUDSS 0.1.0
	(T <: Complex) && cudss_set(solver, "pivot_type", 'N')

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

	R_gpu = B_gpu - CuSparseMatrixCSR(A_cpu) * X_gpu
	norm(R_gpu)
end

function example3(T::DataType, n::Int, ir::Int)
	p = 5
	A_cpu = sprand(T, n, n, 0.01)
	A_cpu = A_cpu * A_cpu' + I
	X_cpu = zeros(T, n, p)
	B_cpu = rand(T, n, p)

	A_gpu = CuSparseMatrixCSR(A_cpu |> triu)
	X_gpu = CuMatrix(X_cpu)
	B_gpu = CuMatrix(B_cpu)

	structure = T <: Real ? "SPD" : "HPD"
	solver = CudssSolver(A_gpu, structure, 'U')
	cudss_set(solver, "ir_n_steps", ir)

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

	R_gpu = B_gpu - CuSparseMatrixCSR(A_cpu) * X_gpu
	norm(R_gpu)
end

# Size of the random linear systems
n = 100

for ir in (0,1,2)
	println("Number of iterations of iterative refinement: $ir")

	for T in (Float32, Float64, ComplexF32, ComplexF64)
		println("Precision: $T")

		r1 = example1(T, n, ir)
		println("Residual norm for example1: $r1")

		r2 = example2(T, n, ir)
		println("Residual norm for example2: $r2")

		r3 = example3(T, n, ir)
		println("Residual norm for example3: $r3")
	end

	println()
end

Number of iterations of iterative refinement: 0
Precision: Float32
Residual norm for example1: 3.692087e-5
Residual norm for example2: 0.0002999944
Residual norm for example3: 8.5040307e-7
Precision: Float64
Residual norm for example1: 3.999599835861191e-13
Residual norm for example2: 1.8113843282606318e-13
Residual norm for example3: 1.438189339051409e-15
Precision: ComplexF32
Residual norm for example1: 7.7133656e-5
Residual norm for example2: 0.0015232839
Residual norm for example3: 1.3667711e-6
Precision: ComplexF64
Residual norm for example1: 5.983645231861647e-14
Residual norm for example2: 3.5220521611201605e-12
Residual norm for example3: 2.6205255057235815e-15

Number of iterations of iterative refinement: 1
Precision: Float32
Residual norm for example1: 689.0252
Residual norm for example2: 35.675114
Residual norm for example3: 19.295319
Precision: Float64
Residual norm for example1: 17.012903059690192
Residual norm for example2: 128.73250852726014
Residual norm for example3: 19.50544156059542
Precision: ComplexF32
Residual norm for example1: 91.10225
Residual norm for example2: 169.85542
Residual norm for example3: 37.091965
Precision: ComplexF64
Residual norm for example1: 66.7120050629793
Residual norm for example2: 178.9033657822368
Residual norm for example3: 33.54613616599457

Number of iterations of iterative refinement: 2
Precision: Float32
Residual norm for example1: 398.21548
Residual norm for example2: 144.65608
Residual norm for example3: 53.373383
Precision: Float64
Residual norm for example1: 351.5959719021192
Residual norm for example2: 785.4054754458682
Residual norm for example3: 52.362171222079056
Precision: ComplexF32
Residual norm for example1: 69.65438
Residual norm for example2: 869.5622
Residual norm for example3: 134.29175
Precision: ComplexF64
Residual norm for example1: 4401.508407855525
Residual norm for example2: 2843.681478289806
Residual norm for example3: 117.71330055583913

[amontoison]

The issue is fixed with the release 0.2.1:

Number of iterations of iterative refinement: 0
Precision: Float32
Residual norm for example1: 1.847538e-5
Residual norm for example2: 0.00021071904
Residual norm for example3: 8.379088e-7
Precision: Float64
Residual norm for example1: 3.340602287924343e-13
Residual norm for example2: 1.6954324066196217e-13
Residual norm for example3: 1.4466012900106264e-15
Precision: ComplexF32
Residual norm for example1: 5.618822e-5
Residual norm for example2: 0.001547979
Residual norm for example3: 1.3792666e-6
Precision: ComplexF64
Residual norm for example1: 8.186746897843183e-14
Residual norm for example2: 3.8232027439101534e-12
Residual norm for example3: 2.616020123074188e-15

Number of iterations of iterative refinement: 1
Precision: Float32
Residual norm for example1: 2.7082282e-5
Residual norm for example2: 3.2331143e-6
Residual norm for example3: 4.3392834e-7
Precision: Float64
Residual norm for example1: 1.3756521229420242e-15
Residual norm for example2: 1.9698506979498538e-14
Residual norm for example3: 7.778218420081461e-16
Precision: ComplexF32
Residual norm for example1: 4.42893e-6
Residual norm for example2: 1.5342164e-5
Residual norm for example3: 8.035846e-7
Precision: ComplexF64
Residual norm for example1: 6.0055395163591184e-15
Residual norm for example2: 3.628518735237144e-14
Residual norm for example3: 1.6393136883834072e-15

Number of iterations of iterative refinement: 2
Precision: Float32
Residual norm for example1: 2.8285526e-6
Residual norm for example2: 2.5343484e-6
Residual norm for example3: 4.0934142e-7
Precision: Float64
Residual norm for example1: 4.907009938517242e-15
Residual norm for example2: 1.1293433006802389e-14
Residual norm for example3: 7.538526237535183e-16
Precision: ComplexF32
Residual norm for example1: 1.4131082e-6
Residual norm for example2: 8.459211e-6
Residual norm for example3: 7.952513e-7
Precision: ComplexF64
Residual norm for example1: 1.2464818569137624e-14
Residual norm for example2: 3.1703465299248516e-14
Residual norm for example3: 1.3548190347378863e-15