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# This file is a part of Julia. License is MIT: https://julialang.org/license
using SuiteSparse: increment!
using LinearAlgebra: Adjoint, Transpose, SingularException
@testset "UMFPACK wrappers" begin
se33 = sparse(1.0I, 3, 3)
do33 = fill(1., 3)
@test isequal(se33 \ do33, do33)
# based on deps/Suitesparse-4.0.2/UMFPACK/Demo/umfpack_di_demo.c
A0 = sparse(increment!([0,4,1,1,2,2,0,1,2,3,4,4]),
increment!([0,4,0,2,1,2,1,4,3,2,1,2]),
[2.,1.,3.,4.,-1.,-3.,3.,6.,2.,1.,4.,2.], 5, 5)
@testset "Core functionality for $Tv elements" for Tv in (Float64, ComplexF64)
# We might be able to support two index sizes one day
for Ti in Base.uniontypes(SuiteSparse.UMFPACK.UMFITypes)
A = convert(SparseMatrixCSC{Tv,Ti}, A0)
lua = lu(A)
@test nnz(lua) == 18
@test_throws ErrorException lua.Z
L,U,p,q,Rs = lua.:(:)
@test (Diagonal(Rs) * A)[p,q] ≈ L * U
det(lua) ≈ det(Array(A))
b = [8., 45., -3., 3., 19.]
x = lua\b
@test x ≈ float([1:5;])
@test A*x ≈ b
z = complex.(b)
x = LinearAlgebra.ldiv!(lua, z)
@test x ≈ float([1:5;])
@test z === x
y = similar(z)
LinearAlgebra.ldiv!(y, lua, complex.(b))
@test y ≈ x
@test A*x ≈ b
b = [8., 20., 13., 6., 17.]
x = lua'\b
@test x ≈ float([1:5;])
@test A'*x ≈ b
z = complex.(b)
x = LinearAlgebra.ldiv!(adjoint(lua), z)
@test x ≈ float([1:5;])
@test x === z
y = similar(x)
LinearAlgebra.ldiv!(y, adjoint(lua), complex.(b))
@test y ≈ x
@test A'*x ≈ b
x = transpose(lua) \ b
@test x ≈ float([1:5;])
@test transpose(A) * x ≈ b
x = LinearAlgebra.ldiv!(transpose(lua), complex.(b))
@test x ≈ float([1:5;])
y = similar(x)
LinearAlgebra.ldiv!(y, transpose(lua), complex.(b))
@test y ≈ x
@test transpose(A) * x ≈ b
# Element promotion and type inference
@inferred lua\fill(1, size(A, 2))
end
end
@testset "More tests for complex cases" begin
Ac0 = complex.(A0,A0)
for Ti in Base.uniontypes(SuiteSparse.UMFPACK.UMFITypes)
Ac = convert(SparseMatrixCSC{ComplexF64,Ti}, Ac0)
x = fill(1.0 + im, size(Ac,1))
lua = lu(Ac)
L,U,p,q,Rs = lua.:(:)
@test (Diagonal(Rs) * Ac)[p,q] ≈ L * U
b = Ac*x
@test Ac\b ≈ x
b = Ac'*x
@test Ac'\b ≈ x
b = transpose(Ac)*x
@test transpose(Ac)\b ≈ x
end
end
@testset "Rectangular cases. elty=$elty, m=$m, n=$n" for
elty in (Float64, ComplexF64),
(m, n) in ((10,5), (5, 10))
Random.seed!(30072018)
A = sparse([1:min(m,n); rand(1:m, 10)], [1:min(m,n); rand(1:n, 10)], elty == Float64 ? randn(min(m, n) + 10) : complex.(randn(min(m, n) + 10), randn(min(m, n) + 10)))
F = lu(A)
L, U, p, q, Rs = F.:(:)
@test (Diagonal(Rs) * A)[p,q] ≈ L * U
end
@testset "Issue #4523 - complex sparse \\" begin
A, b = sparse((1.0 + im)I, 2, 2), fill(1., 2)
@test A * (lu(A)\b) ≈ b
@test det(sparse([1,3,3,1], [1,1,3,3], [1,1,1,1])) == 0
end
@testset "UMFPACK_ERROR_n_nonpositive" begin
@test_throws ArgumentError lu(sparse(Int[], Int[], Float64[], 5, 0))
end
@testset "Issue #15099" for (Tin, Tout) in (
(ComplexF16, ComplexF64),
(ComplexF32, ComplexF64),
(ComplexF64, ComplexF64),
(Float16, Float64),
(Float32, Float64),
(Float64, Float64),
(Int, Float64),
)
F = lu(sparse(fill(Tin(1), 1, 1)))
L = sparse(fill(Tout(1), 1, 1))
@test F.p == F.q == [1]
@test F.Rs == [1.0]
@test F.L == F.U == L
@test F.:(:) == (L, L, [1], [1], [1.0])
end
@testset "BigFloat not supported" for T in (BigFloat, Complex{BigFloat})
@test_throws ArgumentError lu(sparse(fill(T(1), 1, 1)))
end
@testset "size(::UmfpackLU)" begin
m = n = 1
F = lu(sparse(fill(1., m, n)))
@test size(F) == (m, n)
@test size(F, 1) == m
@test size(F, 2) == n
@test size(F, 3) == 1
@test_throws ArgumentError size(F,-1)
end
@testset "Test aliasing" begin
a = rand(5)
@test_throws ArgumentError SuiteSparse.UMFPACK.solve!(a, lu(sparse(1.0I, 5, 5)), a, SuiteSparse.UMFPACK.UMFPACK_A)
aa = complex(a)
@test_throws ArgumentError SuiteSparse.UMFPACK.solve!(aa, lu(sparse((1.0im)I, 5, 5)), aa, SuiteSparse.UMFPACK.UMFPACK_A)
end
@testset "Issues #18246,18244 - lu sparse pivot" begin
A = sparse(1.0I, 4, 4)
A[1:2,1:2] = [-.01 -200; 200 .001]
F = lu(A)
@test F.p == [3 ; 4 ; 2 ; 1]
end
@testset "Test that A[c|t]_ldiv_B!{T<:Complex}(X::StridedMatrix{T}, lu::UmfpackLU{Float64}, B::StridedMatrix{T}) works as expected." begin
N = 10
p = 0.5
A = N*I + sprand(N, N, p)
X = zeros(Complex{Float64}, N, N)
B = complex.(rand(N, N), rand(N, N))
luA, lufA = lu(A), lu(Array(A))
@test LinearAlgebra.ldiv!(copy(X), luA, B) ≈ LinearAlgebra.ldiv!(copy(X), lufA, B)
@test LinearAlgebra.ldiv!(copy(X), adjoint(luA), B) ≈ LinearAlgebra.ldiv!(copy(X), adjoint(lufA), B)
@test LinearAlgebra.ldiv!(copy(X), transpose(luA), B) ≈ LinearAlgebra.ldiv!(copy(X), transpose(lufA), B)
end
@testset "singular matrix" begin
for A in sparse.((Float64[1 2; 0 0], ComplexF64[1 2; 0 0]))
@test_throws SingularException lu(A)
@test !issuccess(lu(A; check = false))
end
end
end
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