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blas.jl
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blas.jl
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# This file is a part of Julia. License is MIT: http:https://julialang.org/license
import Base.LinAlg, Base.LinAlg.BlasReal, Base.LinAlg.BlasComplex
srand(100)
## BLAS tests - testing the interface code to BLAS routines
@testset for elty in [Float32, Float64, Complex64, Complex128]
@testset "syr2k!" begin
U = randn(5,2)
V = randn(5,2)
if elty == Complex64 || elty == Complex128
U = complex.(U, U)
V = complex.(V, V)
end
U = convert(Array{elty, 2}, U)
V = convert(Array{elty, 2}, V)
@test tril(LinAlg.BLAS.syr2k('L','N',U,V)) ≈ tril(U*V.' + V*U.')
@test triu(LinAlg.BLAS.syr2k('U','N',U,V)) ≈ triu(U*V.' + V*U.')
@test tril(LinAlg.BLAS.syr2k('L','T',U,V)) ≈ tril(U.'*V + V.'*U)
@test triu(LinAlg.BLAS.syr2k('U','T',U,V)) ≈ triu(U.'*V + V.'*U)
end
if elty in (Complex64, Complex128)
@testset "her2k!" begin
U = randn(5,2)
V = randn(5,2)
U = complex.(U, U)
V = complex.(V, V)
U = convert(Array{elty, 2}, U)
V = convert(Array{elty, 2}, V)
@test tril(LinAlg.BLAS.her2k('L','N',U,V)) ≈ tril(U*V' + V*U')
@test triu(LinAlg.BLAS.her2k('U','N',U,V)) ≈ triu(U*V' + V*U')
@test tril(LinAlg.BLAS.her2k('L','C',U,V)) ≈ tril(U'*V + V'*U)
@test triu(LinAlg.BLAS.her2k('U','C',U,V)) ≈ triu(U'*V + V'*U)
end
end
o4 = ones(elty, 4)
z4 = zeros(elty, 4)
I4 = eye(elty, 4)
I43 = eye(elty, 4, 3)
L4 = tril(ones(elty, (4,4)))
U4 = triu(ones(elty, (4,4)))
Z4 = zeros(elty, (4,4))
elm1 = convert(elty, -1)
el2 = convert(elty, 2)
v14 = convert(Vector{elty}, [1:4;])
v41 = convert(Vector{elty}, [4:-1:1;])
let n = 10
@testset "dot products" begin
if elty <: Real
x1 = convert(Vector{elty}, randn(n))
x2 = convert(Vector{elty}, randn(n))
@test BLAS.dot(x1,x2) ≈ sum(x1.*x2)
@test_throws DimensionMismatch BLAS.dot(x1,rand(elty, n + 1))
else
z1 = convert(Vector{elty}, complex.(randn(n),randn(n)))
z2 = convert(Vector{elty}, complex.(randn(n),randn(n)))
@test BLAS.dotc(z1,z2) ≈ sum(conj(z1).*z2)
@test BLAS.dotu(z1,z2) ≈ sum(z1.*z2)
@test_throws DimensionMismatch BLAS.dotc(z1,rand(elty, n + 1))
@test_throws DimensionMismatch BLAS.dotu(z1,rand(elty, n + 1))
end
end
@testset "iamax" begin
if elty <: Real
x = convert(Vector{elty}, randn(n))
@test BLAS.iamax(x) == indmax(abs.(x))
else
z = convert(Vector{elty}, complex.(randn(n),randn(n)))
@test BLAS.iamax(z) == indmax(map(x -> abs(real(x)) + abs(imag(x)), z))
end
end
@testset "axpy" begin
if elty <: Real
x1 = convert(Vector{elty}, randn(n))
x2 = convert(Vector{elty}, randn(n))
α = rand(elty)
@test BLAS.axpy!(α,copy(x1),copy(x2)) ≈ x2 + α*x1
@test_throws DimensionMismatch BLAS.axpy!(α, copy(x1), rand(elty, n + 1))
@test_throws DimensionMismatch BLAS.axpy!(α, copy(x1), 1:div(n,2), copy(x2), 1:n)
@test_throws ArgumentError BLAS.axpy!(α, copy(x1), 0:div(n,2), copy(x2), 1:(div(n, 2) + 1))
@test_throws ArgumentError BLAS.axpy!(α, copy(x1), 1:div(n,2), copy(x2), 0:(div(n, 2) - 1))
@test BLAS.axpy!(α,copy(x1),1:n,copy(x2),1:n) ≈ x2 + α*x1
else
z1 = convert(Vector{elty}, complex.(randn(n), randn(n)))
z2 = convert(Vector{elty}, complex.(randn(n), randn(n)))
α = rand(elty)
@test BLAS.axpy!(α, copy(z1), copy(z2)) ≈ z2 + α * z1
@test_throws DimensionMismatch BLAS.axpy!(α, copy(z1), rand(elty, n + 1))
@test_throws DimensionMismatch BLAS.axpy!(α, copy(z1), 1:div(n, 2), copy(z2), 1:(div(n, 2) + 1))
@test_throws ArgumentError BLAS.axpy!(α, copy(z1), 0:div(n,2), copy(z2), 1:(div(n, 2) + 1))
@test_throws ArgumentError BLAS.axpy!(α, copy(z1), 1:div(n,2), copy(z2), 0:(div(n, 2) - 1))
@test BLAS.axpy!(α,copy(z1),1:n,copy(z2),1:n) ≈ z2 + α*z1
end
end
@testset "nrm2, iamax, and asum for StridedVectors" begin
a = rand(elty,n)
b = view(a,2:2:n,1)
@test BLAS.nrm2(b) ≈ norm(b)
if elty <: Real
@test BLAS.asum(b) ≈ sum(abs.(b))
@test BLAS.iamax(b) ≈ indmax(abs.(b))
else
@test BLAS.asum(b) ≈ sum(abs.(real(b))) + sum(abs.(imag(b)))
@test BLAS.iamax(b) == indmax(map(x -> abs(real(x)) + abs(imag(x)), b))
end
end
# scal
α = rand(elty)
a = rand(elty,n)
@test BLAS.scal(n,α,a,1) ≈ α * a
@testset "trsv" begin
A = triu(rand(elty,n,n))
x = rand(elty,n)
@test A\x ≈ BLAS.trsv('U','N','N',A,x)
@test_throws DimensionMismatch BLAS.trsv('U','N','N',A,ones(elty,n+1))
end
@testset "ger, her, syr" begin
A = rand(elty,n,n)
α = rand(elty)
x = rand(elty,n)
y = rand(elty,n)
@test BLAS.ger!(α,x,y,copy(A)) ≈ A + α*x*y'
@test_throws DimensionMismatch BLAS.ger!(α,ones(elty,n+1),y,copy(A))
A = rand(elty,n,n)
A = A + A.'
@test issymmetric(A)
@test triu(BLAS.syr!('U',α,x,copy(A))) ≈ triu(A + α*x*x.')
@test_throws DimensionMismatch BLAS.syr!('U',α,ones(elty,n+1),copy(A))
if elty <: Complex
A = rand(elty,n,n)
A = A + A'
α = real(α)
@test triu(BLAS.her!('U',α,x,copy(A))) ≈ triu(A + α*x*x')
@test_throws DimensionMismatch BLAS.her!('U',α,ones(elty,n+1),copy(A))
end
end
@testset "copy" begin
x1 = convert(Vector{elty}, randn(n))
x2 = convert(Vector{elty}, randn(n))
BLAS.copy!(x2, 1:n, x1, 1:n)
@test x2 == x1
@test_throws DimensionMismatch BLAS.copy!(x2, 1:n, x1, 1:(n - 1))
@test_throws ArgumentError BLAS.copy!(x1, 0:div(n, 2), x2, 1:(div(n, 2) + 1))
@test_throws ArgumentError BLAS.copy!(x1, 1:(div(n, 2) + 1), x2, 0:div(n, 2))
end
# trmv
A = triu(rand(elty,n,n))
x = rand(elty,n)
@test BLAS.trmv('U','N','N',A,x) ≈ A*x
@testset "symmetric/Hermitian multiplication" begin
x = rand(elty,n)
A = rand(elty,n,n)
Aherm = A + A'
Asymm = A + A.'
@testset "symv and hemv" begin
@test BLAS.symv('U',Asymm,x) ≈ Asymm*x
@test_throws DimensionMismatch BLAS.symv!('U',one(elty),Asymm,x,one(elty),ones(elty,n+1))
@test_throws DimensionMismatch BLAS.symv('U',ones(elty,n,n+1),x)
if elty <: BlasComplex
@test BLAS.hemv('U',Aherm,x) ≈ Aherm*x
@test_throws DimensionMismatch BLAS.hemv('U',ones(elty,n,n+1),x)
@test_throws DimensionMismatch BLAS.hemv!('U',one(elty),Aherm,x,one(elty),ones(elty,n+1))
end
end
@testset "symm error throwing" begin
@test_throws DimensionMismatch BLAS.symm('L','U',ones(elty,n,n-1),rand(elty,n,n))
@test_throws DimensionMismatch BLAS.symm('R','U',ones(elty,n-1,n),rand(elty,n,n))
@test_throws DimensionMismatch BLAS.symm!('L','U',one(elty),Asymm,ones(elty,n,n),one(elty),rand(elty,n-1,n))
@test_throws DimensionMismatch BLAS.symm!('L','U',one(elty),Asymm,ones(elty,n,n),one(elty),rand(elty,n,n-1))
if elty <: BlasComplex
@test_throws DimensionMismatch BLAS.hemm('L','U',ones(elty,n,n-1),rand(elty,n,n))
@test_throws DimensionMismatch BLAS.hemm('R','U',ones(elty,n-1,n),rand(elty,n,n))
@test_throws DimensionMismatch BLAS.hemm!('L','U',one(elty),Aherm,ones(elty,n,n),one(elty),rand(elty,n-1,n))
@test_throws DimensionMismatch BLAS.hemm!('L','U',one(elty),Aherm,ones(elty,n,n),one(elty),rand(elty,n,n-1))
end
end
end
@testset "trmm error throwing" begin
@test_throws DimensionMismatch BLAS.trmm('L','U','N','N',one(elty),triu(rand(elty,n,n)),ones(elty,n+1,n))
@test_throws DimensionMismatch BLAS.trmm('R','U','N','N',one(elty),triu(rand(elty,n,n)),ones(elty,n,n+1))
end
#trsm
A = triu(rand(elty,n,n))
B = rand(elty,(n,n))
@test BLAS.trsm('L','U','N','N',one(elty),A,B) ≈ A\B
#will work for SymTridiagonal,Tridiagonal,Bidiagonal!
@testset "banded matrix mv" begin
@testset "gbmv" begin
TD = Tridiagonal(rand(elty,n-1),rand(elty,n),rand(elty,n-1))
x = rand(elty,n)
#put TD into the BLAS format!
fTD = zeros(elty,3,n)
fTD[1,2:n] = TD.du
fTD[2,:] = TD.d
fTD[3,1:n-1] = TD.dl
@test BLAS.gbmv('N',n,1,1,fTD,x) ≈ TD*x
end
#will work for SymTridiagonal only!
@testset "sbmv" begin
if elty <: BlasReal
ST = SymTridiagonal(rand(elty,n),rand(elty,n-1))
x = rand(elty,n)
#put TD into the BLAS format!
fST = zeros(elty,2,n)
fST[1,2:n] = ST.ev
fST[2,:] = ST.dv
@test BLAS.sbmv('U',1,fST,x) ≈ ST*x
else
dv = real(rand(elty,n))
ev = rand(elty,n-1)
bH = zeros(elty,2,n)
bH[1,2:n] = ev
bH[2,:] = dv
fullH = diagm(dv) + diagm(conj(ev),-1) + diagm(ev,1)
@test BLAS.hbmv('U',1,bH,x) ≈ fullH*x
end
end
end
end
@testset "gemv" begin
@test all(BLAS.gemv('N', I4, o4) .== o4)
@test all(BLAS.gemv('T', I4, o4) .== o4)
@test all(BLAS.gemv('N', el2, I4, o4) .== el2 * o4)
@test all(BLAS.gemv('T', el2, I4, o4) .== el2 * o4)
@test_throws DimensionMismatch BLAS.gemv('N',I43,o4)
o4cp = copy(o4)
@test_throws DimensionMismatch BLAS.gemv!('T',one(elty),I43,o4,one(elty),o4cp)
@test_throws DimensionMismatch BLAS.gemv!('C',one(elty),I43,o4,one(elty),o4cp)
@test all(BLAS.gemv!('N', one(elty), I4, o4, elm1, o4cp) .== z4)
@test all(o4cp .== z4)
o4cp[:] = o4
@test all(BLAS.gemv!('T', one(elty), I4, o4, elm1, o4cp) .== z4)
@test all(o4cp .== z4)
@test all(BLAS.gemv('N', U4, o4) .== v41)
@test all(BLAS.gemv('N', U4, o4) .== v41)
end
@testset "gemm" begin
@test all(BLAS.gemm('N', 'N', I4, I4) .== I4)
@test all(BLAS.gemm('N', 'T', I4, I4) .== I4)
@test all(BLAS.gemm('T', 'N', I4, I4) .== I4)
@test all(BLAS.gemm('T', 'T', I4, I4) .== I4)
@test all(BLAS.gemm('N', 'N', el2, I4, I4) .== el2 * I4)
@test all(BLAS.gemm('N', 'T', el2, I4, I4) .== el2 * I4)
@test all(BLAS.gemm('T', 'N', el2, I4, I4) .== el2 * I4)
@test all(LinAlg.BLAS.gemm('T', 'T', el2, I4, I4) .== el2 * I4)
I4cp = copy(I4)
@test all(BLAS.gemm!('N', 'N', one(elty), I4, I4, elm1, I4cp) .== Z4)
@test all(I4cp .== Z4)
I4cp[:] = I4
@test all(BLAS.gemm!('N', 'T', one(elty), I4, I4, elm1, I4cp) .== Z4)
@test all(I4cp .== Z4)
I4cp[:] = I4
@test all(BLAS.gemm!('T', 'N', one(elty), I4, I4, elm1, I4cp) .== Z4)
@test all(I4cp .== Z4)
I4cp[:] = I4
@test all(BLAS.gemm!('T', 'T', one(elty), I4, I4, elm1, I4cp) .== Z4)
@test all(I4cp .== Z4)
@test all(BLAS.gemm('N', 'N', I4, U4) .== U4)
@test all(BLAS.gemm('N', 'T', I4, U4) .== L4)
@test_throws DimensionMismatch BLAS.gemm!('N','N', one(elty), I4, I4, elm1, eye(elty,5))
@test_throws DimensionMismatch BLAS.gemm!('N','N', one(elty), I43, I4, elm1, I4)
@test_throws DimensionMismatch BLAS.gemm!('T','N', one(elty), I43, I4, elm1, I43)
@test_throws DimensionMismatch BLAS.gemm!('N','T', one(elty), I43, I43, elm1, I43)
@test_throws DimensionMismatch BLAS.gemm!('T','T', one(elty), I43, I43, elm1, I43')
end
@testset "gemm compared to (sy)(he)rk" begin
if eltype(elm1) <: Complex
@test all(triu(BLAS.herk('U', 'N', U4)) .== triu(BLAS.gemm('N', 'T', U4, U4)))
@test all(tril(BLAS.herk('L', 'N', U4)) .== tril(BLAS.gemm('N', 'T', U4, U4)))
@test all(triu(BLAS.herk('U', 'N', L4)) .== triu(BLAS.gemm('N', 'T', L4, L4)))
@test all(tril(BLAS.herk('L', 'N', L4)) .== tril(BLAS.gemm('N', 'T', L4, L4)))
@test all(triu(BLAS.herk('U', 'C', U4)) .== triu(BLAS.gemm('T', 'N', U4, U4)))
@test all(tril(BLAS.herk('L', 'C', U4)) .== tril(BLAS.gemm('T', 'N', U4, U4)))
@test all(triu(BLAS.herk('U', 'C', L4)) .== triu(BLAS.gemm('T', 'N', L4, L4)))
@test all(tril(BLAS.herk('L', 'C', L4)) .== tril(BLAS.gemm('T', 'N', L4, L4)))
ans = similar(L4)
@test all(tril(BLAS.herk('L','C', L4)) .== tril(BLAS.herk!('L', 'C', real(one(elty)), L4, real(zero(elty)), ans)))
@test all(Base.LinAlg.copytri!(ans, 'L') .== LinAlg.BLAS.gemm('T', 'N', L4, L4))
@test_throws DimensionMismatch BLAS.herk!('L','N',real(one(elty)),eye(elty,5),real(one(elty)),eye(elty,6))
else
@test all(triu(BLAS.syrk('U', 'N', U4)) .== triu(BLAS.gemm('N', 'T', U4, U4)))
@test all(tril(BLAS.syrk('L', 'N', U4)) .== tril(BLAS.gemm('N', 'T', U4, U4)))
@test all(triu(BLAS.syrk('U', 'N', L4)) .== triu(BLAS.gemm('N', 'T', L4, L4)))
@test all(tril(BLAS.syrk('L', 'N', L4)) .== tril(BLAS.gemm('N', 'T', L4, L4)))
@test all(triu(BLAS.syrk('U', 'T', U4)) .== triu(BLAS.gemm('T', 'N', U4, U4)))
@test all(tril(BLAS.syrk('L', 'T', U4)) .== tril(BLAS.gemm('T', 'N', U4, U4)))
@test all(triu(BLAS.syrk('U', 'T', L4)) .== triu(BLAS.gemm('T', 'N', L4, L4)))
@test all(tril(BLAS.syrk('L', 'T', L4)) .== tril(BLAS.gemm('T', 'N', L4, L4)))
ans = similar(L4)
@test all(tril(BLAS.syrk('L','T', L4)) .== tril(BLAS.syrk!('L', 'T', one(elty), L4, zero(elty), ans)))
@test all(Base.LinAlg.copytri!(ans, 'L') .== BLAS.gemm('T', 'N', L4, L4))
@test_throws DimensionMismatch BLAS.syrk!('L','N',one(elty),eye(elty,5),one(elty),eye(elty,6))
end
end
end
@testset "syr for eltype $elty" for elty in (Float32, Float64, Complex{Float32}, Complex{Float64})
A = rand(elty, 5, 5)
@test triu(A[1,:] * A[1,:].') ≈ BLAS.syr!('U', one(elty), A[1,:], zeros(elty, 5, 5))
@test tril(A[1,:] * A[1,:].') ≈ BLAS.syr!('L', one(elty), A[1,:], zeros(elty, 5, 5))
@test triu(A[1,:] * A[1,:].') ≈ BLAS.syr!('U', one(elty), view(A, 1, :), zeros(elty, 5, 5))
@test tril(A[1,:] * A[1,:].') ≈ BLAS.syr!('L', one(elty), view(A, 1, :), zeros(elty, 5, 5))
end
@testset "her for eltype $elty" for elty in (Complex{Float32}, Complex{Float64})
A = rand(elty, 5, 5)
@test triu(A[1,:] * A[1,:]') ≈ BLAS.her!('U', one(real(elty)), A[1,:], zeros(elty, 5, 5))
@test tril(A[1,:] * A[1,:]') ≈ BLAS.her!('L', one(real(elty)), A[1,:], zeros(elty, 5, 5))
@test triu(A[1,:] * A[1,:]') ≈ BLAS.her!('U', one(real(elty)), view(A, 1, :), zeros(elty, 5, 5))
@test tril(A[1,:] * A[1,:]') ≈ BLAS.her!('L', one(real(elty)), view(A, 1, :), zeros(elty, 5, 5))
end