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# This file is a part of Julia. License is MIT: https://julialang.org/license
module TestSpecial
using Test, LinearAlgebra, SparseArrays, Random
using LinearAlgebra: rmul!
n= 10 #Size of matrix to test
Random.seed!(1)
@testset "Interconversion between special matrix types" begin
a = [1.0:n;]
A = Diagonal(a)
@testset for newtype in [Diagonal, Bidiagonal, SymTridiagonal, Tridiagonal, Matrix]
@test Matrix(convert(newtype, A)) == Matrix(A)
@test Matrix(convert(newtype, Diagonal(GenericArray(a)))) == Matrix(A)
end
@testset for isupper in (true, false)
A = Bidiagonal(a, [1.0:n-1;], ifelse(isupper, :U, :L))
for newtype in [Bidiagonal, Tridiagonal, Matrix]
@test Matrix(convert(newtype, A)) == Matrix(A)
@test Matrix(newtype(A)) == Matrix(A)
end
@test_throws ArgumentError convert(SymTridiagonal, A)
tritype = isupper ? UpperTriangular : LowerTriangular
@test Matrix(tritype(A)) == Matrix(A)
A = Bidiagonal(a, zeros(n-1), ifelse(isupper, :U, :L)) #morally Diagonal
for newtype in [Diagonal, Bidiagonal, SymTridiagonal, Tridiagonal, Matrix]
@test Matrix(convert(newtype, A)) == Matrix(A)
@test Matrix(newtype(A)) == Matrix(A)
end
@test Matrix(tritype(A)) == Matrix(A)
end
A = SymTridiagonal(a, [1.0:n-1;])
for newtype in [Tridiagonal, Matrix]
@test Matrix(convert(newtype, A)) == Matrix(A)
end
for newtype in [Diagonal, Bidiagonal]
@test_throws ArgumentError convert(newtype,A)
end
A = SymTridiagonal(a, zeros(n-1))
@test Matrix(convert(Bidiagonal,A)) == Matrix(A)
A = Tridiagonal(zeros(n-1), [1.0:n;], zeros(n-1)) #morally Diagonal
for newtype in [Diagonal, Bidiagonal, SymTridiagonal, Matrix]
@test Matrix(convert(newtype, A)) == Matrix(A)
end
A = Tridiagonal(fill(1., n-1), [1.0:n;], fill(1., n-1)) #not morally Diagonal
for newtype in [SymTridiagonal, Matrix]
@test Matrix(convert(newtype, A)) == Matrix(A)
end
for newtype in [Diagonal, Bidiagonal]
@test_throws ArgumentError convert(newtype,A)
end
A = Tridiagonal(zeros(n-1), [1.0:n;], fill(1., n-1)) #not morally Diagonal
@test Matrix(convert(Bidiagonal, A)) == Matrix(A)
A = UpperTriangular(Tridiagonal(zeros(n-1), [1.0:n;], fill(1., n-1)))
@test Matrix(convert(Bidiagonal, A)) == Matrix(A)
A = Tridiagonal(fill(1., n-1), [1.0:n;], zeros(n-1)) #not morally Diagonal
@test Matrix(convert(Bidiagonal, A)) == Matrix(A)
A = LowerTriangular(Tridiagonal(fill(1., n-1), [1.0:n;], zeros(n-1)))
@test Matrix(convert(Bidiagonal, A)) == Matrix(A)
@test_throws ArgumentError convert(SymTridiagonal,A)
A = LowerTriangular(Matrix(Diagonal(a))) #morally Diagonal
for newtype in [Diagonal, Bidiagonal, SymTridiagonal, LowerTriangular, Matrix]
@test Matrix(convert(newtype, A)) == Matrix(A)
end
A = UpperTriangular(Matrix(Diagonal(a))) #morally Diagonal
for newtype in [Diagonal, Bidiagonal, SymTridiagonal, UpperTriangular, Matrix]
@test Matrix(convert(newtype, A)) == Matrix(A)
end
A = UpperTriangular(triu(rand(n,n)))
for newtype in [Diagonal, Bidiagonal, Tridiagonal, SymTridiagonal]
@test_throws ArgumentError convert(newtype,A)
end
end
@testset "Binary ops among special types" begin
a=[1.0:n;]
A=Diagonal(a)
Spectypes = [Diagonal, Bidiagonal, Tridiagonal, Matrix]
for (idx, type1) in enumerate(Spectypes)
for type2 in Spectypes
B = convert(type1,A)
C = convert(type2,A)
@test Matrix(B + C) ≈ Matrix(A + A)
@test Matrix(B - C) ≈ Matrix(A - A)
end
end
B = SymTridiagonal(a, fill(1., n-1))
for Spectype in [Diagonal, Bidiagonal, Tridiagonal, Matrix]
@test Matrix(B + convert(Spectype,A)) ≈ Matrix(B + A)
@test Matrix(convert(Spectype,A) + B) ≈ Matrix(B + A)
@test Matrix(B - convert(Spectype,A)) ≈ Matrix(B - A)
@test Matrix(convert(Spectype,A) - B) ≈ Matrix(A - B)
end
C = rand(n,n)
for TriType in [LinearAlgebra.UnitLowerTriangular, LinearAlgebra.UnitUpperTriangular, UpperTriangular, LowerTriangular]
D = TriType(C)
for Spectype in [Diagonal, Bidiagonal, Tridiagonal, Matrix]
@test Matrix(D + convert(Spectype,A)) ≈ Matrix(D + A)
@test Matrix(convert(Spectype,A) + D) ≈ Matrix(A + D)
@test Matrix(D - convert(Spectype,A)) ≈ Matrix(D - A)
@test Matrix(convert(Spectype,A) - D) ≈ Matrix(A - D)
end
end
end
@testset "Triangular Types and QR" begin
for typ in [UpperTriangular,LowerTriangular,LinearAlgebra.UnitUpperTriangular,LinearAlgebra.UnitLowerTriangular]
a = rand(n,n)
atri = typ(a)
b = rand(n,n)
qrb = qr(b,Val(true))
@test *(atri, adjoint(qrb.Q)) ≈ Matrix(atri) * qrb.Q'
@test rmul!(copy(atri), adjoint(qrb.Q)) ≈ Matrix(atri) * qrb.Q'
qrb = qr(b,Val(false))
@test *(atri, adjoint(qrb.Q)) ≈ Matrix(atri) * qrb.Q'
@test rmul!(copy(atri), adjoint(qrb.Q)) ≈ Matrix(atri) * qrb.Q'
end
end
# should all yield sparse arrays
@testset "concatenations of combinations of special and other matrix types" begin
N = 4
# Test concatenating pairwise combinations of special matrices
diagmat = Diagonal(1:N)
bidiagmat = Bidiagonal(1:N, 1:(N-1), :U)
tridiagmat = Tridiagonal(1:(N-1), 1:N, 1:(N-1))
symtridiagmat = SymTridiagonal(1:N, 1:(N-1))
specialmats = (diagmat, bidiagmat, tridiagmat, symtridiagmat)
for specialmata in specialmats, specialmatb in specialmats
@test issparse(hcat(specialmata, specialmatb))
@test issparse(vcat(specialmata, specialmatb))
@test issparse(hvcat((1,1), specialmata, specialmatb))
@test issparse(cat(specialmata, specialmatb; dims=(1,2)))
end
# Test concatenating pairwise combinations of special matrices with sparse matrices,
# dense matrices, or dense vectors
densevec = fill(1., N)
densemat = diagm(0 => densevec)
spmat = spdiagm(0 => densevec)
for specialmat in specialmats
# --> Tests applicable only to pairs of matrices
for othermat in (spmat, densemat)
@test issparse(vcat(specialmat, othermat))
@test issparse(vcat(othermat, specialmat))
end
# --> Tests applicable also to pairs including vectors
for specialmat in specialmats, othermatorvec in (spmat, densemat, densevec)
@test issparse(hcat(specialmat, othermatorvec))
@test issparse(hcat(othermatorvec, specialmat))
@test issparse(hvcat((2,), specialmat, othermatorvec))
@test issparse(hvcat((2,), othermatorvec, specialmat))
@test issparse(cat(specialmat, othermatorvec; dims=(1,2)))
@test issparse(cat(othermatorvec, specialmat; dims=(1,2)))
end
end
end
# Test that concatenations of annotated sparse/special matrix types with other matrix
# types yield sparse arrays, and that the code which effects that does not make concatenations
# strictly involving un/annotated dense matrices yield sparse arrays
#
# TODO: As with the associated code, these tests should be moved to a more appropriate
# location, particularly some future equivalent of base/linalg/special.jl dedicated to
# intereactions between a broader set of matrix types
@testset "concatenations of annotated types" begin
N = 4
# The tested annotation types
testfull = Bool(parse(Int,(get(ENV, "JULIA_TESTFULL", "0"))))
utriannotations = (UpperTriangular, LinearAlgebra.UnitUpperTriangular)
ltriannotations = (LowerTriangular, LinearAlgebra.UnitLowerTriangular)
triannotations = (utriannotations..., ltriannotations...)
symannotations = (Symmetric, Hermitian)
annotations = testfull ? (triannotations..., symannotations...) : (LowerTriangular, Symmetric)
# Concatenations involving these types, un/annotated, should yield sparse arrays
spvec = spzeros(N)
spmat = sparse(1.0I, N, N)
diagmat = Diagonal(1:N)
bidiagmat = Bidiagonal(1:N, 1:(N-1), :U)
tridiagmat = Tridiagonal(1:(N-1), 1:N, 1:(N-1))
symtridiagmat = SymTridiagonal(1:N, 1:(N-1))
sparseconcatmats = testfull ? (spmat, diagmat, bidiagmat, tridiagmat, symtridiagmat) : (spmat, diagmat)
# Concatenations involving strictly these types, un/annotated, should yield dense arrays
densevec = fill(1., N)
densemat = fill(1., N, N)
# Annotated collections
annodmats = [annot(densemat) for annot in annotations]
annospcmats = [annot(spcmat) for annot in annotations, spcmat in sparseconcatmats]
# Test that concatenations of pairwise combinations of annotated sparse/special
# yield sparse matrices
for annospcmata in annospcmats, annospcmatb in annospcmats
@test issparse(vcat(annospcmata, annospcmatb))
@test issparse(hcat(annospcmata, annospcmatb))
@test issparse(hvcat((2,), annospcmata, annospcmatb))
@test issparse(cat(annospcmata, annospcmatb; dims=(1,2)))
end
# Test that concatenations of pairwise combinations of annotated sparse/special
# matrices and other matrix/vector types yield sparse matrices
for annospcmat in annospcmats
# --> Tests applicable to pairs including only matrices
for othermat in (densemat, annodmats..., sparseconcatmats...)
@test issparse(vcat(annospcmat, othermat))
@test issparse(vcat(othermat, annospcmat))
end
# --> Tests applicable to pairs including other vectors or matrices
for other in (spvec, densevec, densemat, annodmats..., sparseconcatmats...)
@test issparse(hcat(annospcmat, other))
@test issparse(hcat(other, annospcmat))
@test issparse(hvcat((2,), annospcmat, other))
@test issparse(hvcat((2,), other, annospcmat))
@test issparse(cat(annospcmat, other; dims=(1,2)))
@test issparse(cat(other, annospcmat; dims=(1,2)))
end
end
# The preceding tests should cover multi-way combinations of those types, but for good
# measure test a few multi-way combinations involving those types
@test issparse(vcat(spmat, densemat, annospcmats[1], annodmats[2]))
@test issparse(vcat(densemat, spmat, annodmats[1], annospcmats[2]))
@test issparse(hcat(spvec, annodmats[1], annospcmats[3], densevec, diagmat))
@test issparse(hcat(annodmats[2], annospcmats[4], spvec, densevec, diagmat))
@test issparse(hvcat((5,), diagmat, densevec, spvec, annodmats[1], annospcmats[1]))
@test issparse(hvcat((5,), spvec, annodmats[2], diagmat, densevec, annospcmats[2]))
@test issparse(cat(annodmats[1], diagmat, annospcmats[3], densevec, spvec; dims=(1,2)))
@test issparse(cat(spvec, diagmat, densevec, annospcmats[4], annodmats[2]; dims=(1,2)))
# Test that concatenations strictly involving un/annotated dense matrices/vectors
# yield dense arrays
for densemata in (densemat, annodmats...)
# --> Tests applicable to pairs including only matrices
for densematb in (densemat, annodmats...)
@test !issparse(vcat(densemata, densematb))
@test !issparse(vcat(densematb, densemata))
end
# --> Tests applicable to pairs including vectors or matrices
for otherdense in (densevec, densemat, annodmats...)
@test !issparse(hcat(densemata, otherdense))
@test !issparse(hcat(otherdense, densemata))
@test !issparse(hvcat((2,), densemata, otherdense))
@test !issparse(hvcat((2,), otherdense, densemata))
@test !issparse(cat(densemata, otherdense; dims=(1,2)))
@test !issparse(cat(otherdense, densemata; dims=(1,2)))
end
end
end
@testset "vcat of Vectors with SparseVectors should yield SparseVector (#22225)" begin
@test isa((@inferred vcat(Float64[], spzeros(1))), SparseVector)
end
end # module TestSpecial
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