423 lines
15 KiB
Julia
423 lines
15 KiB
Julia
# This file is a part of Julia. License is MIT: https://julialang.org/license
|
|
|
|
using Base.Test
|
|
|
|
## Test Julia fallbacks to BLAS routines
|
|
|
|
# matrices with zero dimensions
|
|
@test ones(0,5)*ones(5,3) == zeros(0,3)
|
|
@test ones(3,5)*ones(5,0) == zeros(3,0)
|
|
@test ones(3,0)*ones(0,4) == zeros(3,4)
|
|
@test ones(0,5)*ones(5,0) == zeros(0,0)
|
|
@test ones(0,0)*ones(0,4) == zeros(0,4)
|
|
@test ones(3,0)*ones(0,0) == zeros(3,0)
|
|
@test ones(0,0)*ones(0,0) == zeros(0,0)
|
|
@test Array{Float64}(5, 0) |> t -> t't == zeros(0,0)
|
|
@test Array{Float64}(5, 0) |> t -> t*t' == zeros(5,5)
|
|
@test Array{Complex128}(5, 0) |> t -> t't == zeros(0,0)
|
|
@test Array{Complex128}(5, 0) |> t -> t*t' == zeros(5,5)
|
|
|
|
# 2x2
|
|
let
|
|
AA = [1 2; 3 4]
|
|
BB = [5 6; 7 8]
|
|
AAi = AA+(0.5*im).*BB
|
|
BBi = BB+(2.5*im).*AA[[2,1],[2,1]]
|
|
for Atype = ["Array", "SubArray"], Btype = ["Array", "SubArray"]
|
|
A = Atype == "Array" ? AA : view(AA, 1:2, 1:2)
|
|
B = Btype == "Array" ? BB : view(BB, 1:2, 1:2)
|
|
@test A*B == [19 22; 43 50]
|
|
@test At_mul_B(A, B) == [26 30; 38 44]
|
|
@test A_mul_Bt(A, B) == [17 23; 39 53]
|
|
@test At_mul_Bt(A, B) == [23 31; 34 46]
|
|
|
|
Ai = Atype == "Array" ? AAi : view(AAi, 1:2, 1:2)
|
|
Bi = Btype == "Array" ? BBi : view(BBi, 1:2, 1:2)
|
|
@test Ai*Bi == [-21+53.5im -4.25+51.5im; -12+95.5im 13.75+85.5im]
|
|
@test Ac_mul_B(Ai, Bi) == [68.5-12im 57.5-28im; 88-3im 76.5-25im]
|
|
@test A_mul_Bc(Ai, Bi) == [64.5+5.5im 43+31.5im; 104-18.5im 80.5+31.5im]
|
|
@test Ac_mul_Bc(Ai, Bi) == [-28.25-66im 9.75-58im; -26-89im 21-73im]
|
|
@test_throws DimensionMismatch [1 2; 0 0; 0 0] * [1 2]
|
|
end
|
|
CC = ones(3, 3)
|
|
@test_throws DimensionMismatch A_mul_B!(CC, AA, BB)
|
|
end
|
|
# 3x3
|
|
let
|
|
AA = [1 2 3; 4 5 6; 7 8 9].-5
|
|
BB = [1 0 5; 6 -10 3; 2 -4 -1]
|
|
AAi = AA+(0.5*im).*BB
|
|
BBi = BB+(2.5*im).*AA[[2,1,3],[2,3,1]]
|
|
for Atype = ["Array", "SubArray"], Btype = ["Array", "SubArray"]
|
|
A = Atype == "Array" ? AA : view(AA, 1:3, 1:3)
|
|
B = Btype == "Array" ? BB : view(BB, 1:3, 1:3)
|
|
@test A*B == [-26 38 -27; 1 -4 -6; 28 -46 15]
|
|
@test Ac_mul_B(A, B) == [-6 2 -25; 3 -12 -18; 12 -26 -11]
|
|
@test A_mul_Bc(A, B) == [-14 0 6; 4 -3 -3; 22 -6 -12]
|
|
@test Ac_mul_Bc(A, B) == [6 -8 -6; 12 -9 -9; 18 -10 -12]
|
|
|
|
Ai = Atype == "Array" ? AAi : view(AAi, 1:3, 1:3)
|
|
Bi = Btype == "Array" ? BBi : view(BBi, 1:3, 1:3)
|
|
@test Ai*Bi == [-44.75+13im 11.75-25im -38.25+30im; -47.75-16.5im -51.5+51.5im -56+6im; 16.75-4.5im -53.5+52im -15.5im]
|
|
@test Ac_mul_B(Ai, Bi) == [-21+2im -1.75+49im -51.25+19.5im; 25.5+56.5im -7-35.5im 22+35.5im; -3+12im -32.25+43im -34.75-2.5im]
|
|
@test A_mul_Bc(Ai, Bi) == [-20.25+15.5im -28.75-54.5im 22.25+68.5im; -12.25+13im -15.5+75im -23+27im; 18.25+im 1.5+94.5im -27-54.5im]
|
|
@test Ac_mul_Bc(Ai, Bi) == [1+2im 20.75+9im -44.75+42im; 19.5+17.5im -54-36.5im 51-14.5im; 13+7.5im 11.25+31.5im -43.25-14.5im]
|
|
@test_throws DimensionMismatch [1 2 3; 0 0 0; 0 0 0] * [1 2 3]
|
|
end
|
|
CC = ones(4, 4)
|
|
@test_throws DimensionMismatch A_mul_B!(CC, AA, BB)
|
|
end
|
|
# Generic integer matrix multiplication
|
|
# Generic AbstractArrays
|
|
module MyArray15367
|
|
using Base.Test
|
|
struct MyArray{T,N} <: AbstractArray{T,N}
|
|
data::Array{T,N}
|
|
end
|
|
|
|
Base.size(A::MyArray) = size(A.data)
|
|
Base.getindex(A::MyArray, indexes...) = A.data[indexes...]
|
|
|
|
A = MyArray(rand(4,5))
|
|
b = rand(5)
|
|
@test A*b ≈ A.data*b
|
|
end
|
|
|
|
let
|
|
AA = [1 2 3; 4 5 6] .- 3
|
|
BB = [2 -2; 3 -5; -4 7]
|
|
for Atype = ["Array", "SubArray"], Btype = ["Array", "SubArray"]
|
|
A = Atype == "Array" ? AA : view(AA, 1:2, 1:3)
|
|
B = Btype == "Array" ? BB : view(BB, 1:3, 1:2)
|
|
@test A*B == [-7 9; -4 9]
|
|
@test At_mul_Bt(A, B) == [-6 -11 15; -6 -13 18; -6 -15 21]
|
|
end
|
|
AA = ones(Int, 2, 100)
|
|
BB = ones(Int, 100, 3)
|
|
for Atype = ["Array", "SubArray"], Btype = ["Array", "SubArray"]
|
|
A = Atype == "Array" ? AA : view(AA, 1:2, 1:100)
|
|
B = Btype == "Array" ? BB : view(BB, 1:100, 1:3)
|
|
@test A*B == [100 100 100; 100 100 100]
|
|
end
|
|
AA = rand(1:20, 5, 5) .- 10
|
|
BB = rand(1:20, 5, 5) .- 10
|
|
CC = Array{Int}(size(AA, 1), size(BB, 2))
|
|
for Atype = ["Array", "SubArray"], Btype = ["Array", "SubArray"], Ctype = ["Array", "SubArray"]
|
|
A = Atype == "Array" ? AA : view(AA, 1:5, 1:5)
|
|
B = Btype == "Array" ? BB : view(BB, 1:5, 1:5)
|
|
C = Btype == "Array" ? CC : view(CC, 1:5, 1:5)
|
|
@test At_mul_B(A, B) == A'*B
|
|
@test A_mul_Bt(A, B) == A*B'
|
|
# Preallocated
|
|
@test A_mul_B!(C, A, B) == A*B
|
|
@test At_mul_B!(C, A, B) == A'*B
|
|
@test A_mul_Bt!(C, A, B) == A*B'
|
|
@test At_mul_Bt!(C, A, B) == A'*B'
|
|
@test Base.LinAlg.Ac_mul_Bt!(C, A, B) == A'*B.'
|
|
|
|
#test DimensionMismatch for generic_matmatmul
|
|
@test_throws DimensionMismatch Base.LinAlg.Ac_mul_Bt!(C,A,ones(Int,4,4))
|
|
@test_throws DimensionMismatch Base.LinAlg.Ac_mul_Bt!(C,ones(Int,4,4),B)
|
|
end
|
|
vv = [1,2]
|
|
CC = Array{Int}(2, 2)
|
|
for vtype = ["Array", "SubArray"], Ctype = ["Array", "SubArray"]
|
|
v = vtype == "Array" ? vv : view(vv, 1:2)
|
|
C = Ctype == "Array" ? CC : view(CC, 1:2, 1:2)
|
|
@test @inferred(A_mul_Bc!(C, v, v)) == [1 2; 2 4]
|
|
end
|
|
end
|
|
|
|
#and for generic_matvecmul
|
|
let
|
|
AA = rand(5,5)
|
|
BB = rand(5)
|
|
for Atype = ["Array", "SubArray"], Btype = ["Array", "SubArray"]
|
|
A = Atype == "Array" ? AA : view(AA, 1:5, 1:5)
|
|
B = Btype == "Array" ? BB : view(BB, 1:5)
|
|
@test_throws DimensionMismatch Base.LinAlg.generic_matvecmul!(zeros(6),'N',A,B)
|
|
@test_throws DimensionMismatch Base.LinAlg.generic_matvecmul!(B,'N',A,zeros(6))
|
|
end
|
|
vv = [1,2,3]
|
|
CC = Array{Int}(3, 3)
|
|
for vtype = ["Array", "SubArray"], Ctype = ["Array", "SubArray"]
|
|
v = vtype == "Array" ? vv : view(vv, 1:3)
|
|
C = Ctype == "Array" ? CC : view(CC, 1:3, 1:3)
|
|
@test A_mul_Bt!(C, v, v) == v*v'
|
|
end
|
|
vvf = map(Float64,vv)
|
|
CC = Array{Float64}(3, 3)
|
|
for vtype = ["Array", "SubArray"], Ctype = ["Array", "SubArray"]
|
|
vf = vtype == "Array" ? vvf : view(vvf, 1:3)
|
|
C = Ctype == "Array" ? CC : view(CC, 1:3, 1:3)
|
|
@test A_mul_Bt!(C, vf, vf) == vf*vf'
|
|
end
|
|
end
|
|
|
|
# fallbacks & such for BlasFloats
|
|
let
|
|
AA = rand(Float64,6,6)
|
|
BB = rand(Float64,6,6)
|
|
CC = zeros(Float64,6,6)
|
|
for Atype = ["Array", "SubArray"], Btype = ["Array", "SubArray"], Ctype = ["Array", "SubArray"]
|
|
A = Atype == "Array" ? AA : view(AA, 1:6, 1:6)
|
|
B = Btype == "Array" ? BB : view(BB, 1:6, 1:6)
|
|
C = Ctype == "Array" ? CC : view(CC, 1:6, 1:6)
|
|
@test Base.LinAlg.At_mul_Bt!(C,A,B) == A.'*B.'
|
|
@test Base.LinAlg.A_mul_Bc!(C,A,B) == A*B.'
|
|
@test Base.LinAlg.Ac_mul_B!(C,A,B) == A.'*B
|
|
end
|
|
end
|
|
|
|
# matrix algebra with subarrays of floats (stride != 1)
|
|
let
|
|
A = reshape(map(Float64,1:20),5,4)
|
|
Aref = A[1:2:end,1:2:end]
|
|
Asub = view(A, 1:2:5, 1:2:4)
|
|
b = [1.2,-2.5]
|
|
@test (Aref*b) == (Asub*b)
|
|
@test At_mul_B(Asub, Asub) == At_mul_B(Aref, Aref)
|
|
@test A_mul_Bt(Asub, Asub) == A_mul_Bt(Aref, Aref)
|
|
Ai = A .+ im
|
|
Aref = Ai[1:2:end,1:2:end]
|
|
Asub = view(Ai, 1:2:5, 1:2:4)
|
|
@test Ac_mul_B(Asub, Asub) == Ac_mul_B(Aref, Aref)
|
|
@test A_mul_Bc(Asub, Asub) == A_mul_Bc(Aref, Aref)
|
|
end
|
|
|
|
# issue #15286
|
|
let A = reshape(map(Float64, 1:20), 5, 4), C = zeros(8, 8), sC = view(C, 1:2:8, 1:2:8), B = reshape(map(Float64,-9:10),5,4)
|
|
@test At_mul_B!(sC, A, A) == A'*A
|
|
@test At_mul_B!(sC, A, B) == A'*B
|
|
|
|
Aim = A .- im
|
|
C = zeros(Complex128,8,8)
|
|
sC = view(C, 1:2:8, 1:2:8)
|
|
B = reshape(map(Float64,-9:10),5,4) .+ im
|
|
@test Ac_mul_B!(sC, Aim, Aim) == Aim'*Aim
|
|
@test Ac_mul_B!(sC, Aim, B) == Aim'*B
|
|
end
|
|
|
|
# syrk & herk
|
|
let
|
|
AA = reshape(1:1503, 501, 3).-750.0
|
|
res = Float64[135228751 9979252 -115270247; 9979252 10481254 10983256; -115270247 10983256 137236759]
|
|
for Atype = ["Array", "SubArray"]
|
|
A = Atype == "Array" ? AA : view(AA, 1:501, 1:3)
|
|
@test At_mul_B(A, A) == res
|
|
@test A_mul_Bt(A',A') == res
|
|
end
|
|
cutoff = 501
|
|
A = reshape(1:6*cutoff,2*cutoff,3).-(6*cutoff)/2
|
|
Asub = view(A, 1:2:2*cutoff, 1:3)
|
|
Aref = A[1:2:2*cutoff, 1:3]
|
|
@test At_mul_B(Asub, Asub) == At_mul_B(Aref, Aref)
|
|
Ai = A .- im
|
|
Asub = view(Ai, 1:2:2*cutoff, 1:3)
|
|
Aref = Ai[1:2:2*cutoff, 1:3]
|
|
@test Ac_mul_B(Asub, Asub) == Ac_mul_B(Aref, Aref)
|
|
|
|
@test_throws DimensionMismatch Base.LinAlg.syrk_wrapper!(zeros(5,5),'N',ones(6,5))
|
|
@test_throws DimensionMismatch Base.LinAlg.herk_wrapper!(zeros(5,5),'N',ones(6,5))
|
|
end
|
|
|
|
# matmul for types w/o sizeof (issue #1282)
|
|
let
|
|
AA = fill(complex(1,1), 10, 10)
|
|
for Atype = ["Array", "SubArray"]
|
|
A = Atype == "Array" ? AA : view(AA, 1:10, 1:10)
|
|
A2 = A^2
|
|
@test A2[1,1] == 20im
|
|
end
|
|
end
|
|
|
|
let
|
|
AA = zeros(5, 5)
|
|
BB = ones(5)
|
|
CC = rand(5, 6)
|
|
for Atype = ["Array", "SubArray"], Btype = ["Array", "SubArray"]
|
|
for Ctype = ["Array", "SubArray"]
|
|
A = Atype == "Array" ? AA : view(AA, 1:5, 1:5)
|
|
B = Btype == "Array" ? BB : view(BB, 1:5)
|
|
C = Ctype == "Array" ? CC : view(CC, 1:5, 1:6)
|
|
|
|
@test_throws DimensionMismatch scale!(A, B, C)
|
|
end
|
|
end
|
|
end
|
|
|
|
# issue #6450
|
|
@test dot(Any[1.0,2.0], Any[3.5,4.5]) === 12.5
|
|
|
|
for elty in (Float32,Float64,Complex64,Complex128)
|
|
x = convert(Vector{elty},[1.0,2.0,3.0])
|
|
y = convert(Vector{elty},[3.5,4.5,5.5])
|
|
@test_throws DimensionMismatch dot(x, 1:2, y, 1:3)
|
|
@test_throws BoundsError dot(x, 1:4, y, 1:4)
|
|
@test_throws BoundsError dot(x, 1:3, y, 2:4)
|
|
@test dot(x,1:2,y,1:2) == convert(elty,12.5)
|
|
@test x.'*y == convert(elty,29.0)
|
|
end
|
|
|
|
vecdot_(x,y) = invoke(vecdot, Tuple{Any,Any}, x,y) # generic vecdot
|
|
let AA = [1+2im 3+4im; 5+6im 7+8im], BB = [2+7im 4+1im; 3+8im 6+5im]
|
|
for Atype = ["Array", "SubArray"], Btype = ["Array", "SubArray"]
|
|
A = Atype == "Array" ? AA : view(AA, 1:2, 1:2)
|
|
B = Btype == "Array" ? BB : view(BB, 1:2, 1:2)
|
|
@test vecdot(A,B) == dot(vec(A),vec(B)) == vecdot_(A,B) == vecdot(float.(A),float.(B))
|
|
@test vecdot(Int[], Int[]) == 0 == vecdot_(Int[], Int[])
|
|
@test_throws MethodError vecdot(Any[], Any[])
|
|
@test_throws MethodError vecdot_(Any[], Any[])
|
|
for n1 = 0:2, n2 = 0:2, d in (vecdot, vecdot_)
|
|
if n1 != n2
|
|
@test_throws DimensionMismatch d(1:n1, 1:n2)
|
|
else
|
|
@test d(1:n1, 1:n2) ≈ vecnorm(1:n1)^2
|
|
end
|
|
end
|
|
end
|
|
end
|
|
|
|
# Issue 11978
|
|
let
|
|
A = Array{Matrix{Float64}}(2, 2)
|
|
A[1,1] = eye(3)
|
|
A[1,2] = eye(3,2)
|
|
A[2,1] = eye(2,3)
|
|
A[2,2] = eye(2)
|
|
b = Array{Vector{Float64}}(2)
|
|
b[1] = ones(3)
|
|
b[2] = ones(2)
|
|
@test A*b == Vector{Float64}[[2,2,1], [2,2]]
|
|
end
|
|
|
|
@test_throws ArgumentError Base.LinAlg.copytri!(ones(10,10),'Z')
|
|
|
|
for elty in [Float32,Float64,Complex128,Complex64]
|
|
@test_throws DimensionMismatch Base.LinAlg.gemv!(ones(elty,10),'N',rand(elty,10,10),ones(elty,11))
|
|
@test_throws DimensionMismatch Base.LinAlg.gemv!(ones(elty,11),'N',rand(elty,10,10),ones(elty,10))
|
|
@test Base.LinAlg.gemv!(ones(elty,0),'N',rand(elty,0,0),rand(elty,0)) == ones(elty,0)
|
|
@test Base.LinAlg.gemv!(ones(elty,10), 'N',ones(elty,10,0),ones(elty,0)) == zeros(elty,10)
|
|
|
|
@test Base.LinAlg.gemm_wrapper('N','N',eye(elty,10,10),eye(elty,10,10)) == eye(elty,10,10)
|
|
@test_throws DimensionMismatch Base.LinAlg.gemm_wrapper!(eye(elty,10,10),'N','N',eye(elty,10,11),eye(elty,10,10))
|
|
@test_throws DimensionMismatch Base.LinAlg.gemm_wrapper!(eye(elty,10,10),'N','N',eye(elty,0,0),eye(elty,0,0))
|
|
|
|
A = rand(elty,3,3)
|
|
@test Base.LinAlg.matmul3x3('T','N',A,eye(elty,3)) == A.'
|
|
end
|
|
|
|
# 13593, #13488
|
|
let
|
|
aa = rand(3,3)
|
|
bb = rand(3,3)
|
|
for atype = ["Array", "SubArray"], btype = ["Array", "SubArray"]
|
|
a = atype == "Array" ? aa : view(aa, 1:3, 1:3)
|
|
b = btype == "Array" ? bb : view(bb, 1:3, 1:3)
|
|
@test_throws ArgumentError A_mul_B!(a, a, b)
|
|
@test_throws ArgumentError A_mul_B!(a, b, a)
|
|
@test_throws ArgumentError A_mul_B!(a, a, a)
|
|
end
|
|
end
|
|
|
|
# Number types that lack conversion to the destination type (#14293)
|
|
struct RootInt
|
|
i::Int
|
|
end
|
|
import Base: *, transpose
|
|
(*)(x::RootInt, y::RootInt) = x.i*y.i
|
|
transpose(x::RootInt) = x
|
|
@test Base.promote_op(*, RootInt, RootInt) === Int
|
|
|
|
a = [RootInt(3)]
|
|
C = [0]
|
|
A_mul_Bt!(C, a, a)
|
|
@test C[1] == 9
|
|
a = [RootInt(2),RootInt(10)]
|
|
@test a*a' == [4 20; 20 100]
|
|
A = [RootInt(3) RootInt(5)]
|
|
@test A*a == [56]
|
|
|
|
function test_mul(C, A, B)
|
|
A_mul_B!(C, A, B)
|
|
@test Array(A) * Array(B) ≈ C
|
|
@test A*B ≈ C
|
|
end
|
|
|
|
let
|
|
eltypes = [Float32, Float64, Int64]
|
|
for k in [3, 4, 10]
|
|
T = rand(eltypes)
|
|
bi1 = Bidiagonal(rand(T, k), rand(T, k-1), rand(Bool))
|
|
bi2 = Bidiagonal(rand(T, k), rand(T, k-1), rand(Bool))
|
|
tri1 = Tridiagonal(rand(T,k-1), rand(T, k), rand(T, k-1))
|
|
tri2 = Tridiagonal(rand(T,k-1), rand(T, k), rand(T, k-1))
|
|
stri1 = SymTridiagonal(rand(T, k), rand(T, k-1))
|
|
stri2 = SymTridiagonal(rand(T, k), rand(T, k-1))
|
|
C = rand(T, k, k)
|
|
specialmatrices = (bi1, bi2, tri1, tri2, stri1, stri2)
|
|
for A in specialmatrices
|
|
B = specialmatrices[rand(1:length(specialmatrices))]
|
|
test_mul(C, A, B)
|
|
end
|
|
for S in specialmatrices
|
|
l = rand(1:6)
|
|
B = randn(k, l)
|
|
C = randn(k, l)
|
|
test_mul(C, S, B)
|
|
A = randn(l, k)
|
|
C = randn(l, k)
|
|
test_mul(C, A, S)
|
|
end
|
|
end
|
|
for T in eltypes
|
|
A = Bidiagonal(rand(T, 2), rand(T, 1), rand(Bool))
|
|
B = Bidiagonal(rand(T, 2), rand(T, 1), rand(Bool))
|
|
C = randn(2,2)
|
|
test_mul(C, A, B)
|
|
B = randn(2, 9)
|
|
C = randn(2, 9)
|
|
test_mul(C, A, B)
|
|
end
|
|
let
|
|
tri44 = Tridiagonal(randn(3), randn(4), randn(3))
|
|
tri33 = Tridiagonal(randn(2), randn(3), randn(2))
|
|
full43 = randn(4, 3)
|
|
full24 = randn(2, 4)
|
|
full33 = randn(3, 3)
|
|
full44 = randn(4, 4)
|
|
@test_throws DimensionMismatch A_mul_B!(full43, tri44, tri33)
|
|
@test_throws DimensionMismatch A_mul_B!(full44, tri44, tri33)
|
|
@test_throws DimensionMismatch A_mul_B!(full44, tri44, full43)
|
|
@test_throws DimensionMismatch A_mul_B!(full43, tri33, full43)
|
|
@test_throws DimensionMismatch A_mul_B!(full43, full43, tri44)
|
|
end
|
|
end
|
|
|
|
# #18218
|
|
module TestPR18218
|
|
using Base.Test
|
|
import Base.*, Base.+, Base.zero
|
|
struct TypeA
|
|
x::Int
|
|
end
|
|
Base.convert(::Type{TypeA}, x::Int) = TypeA(x)
|
|
struct TypeB
|
|
x::Int
|
|
end
|
|
struct TypeC
|
|
x::Int
|
|
end
|
|
Base.convert(::Type{TypeC}, x::Int) = TypeC(x)
|
|
zero(c::TypeC) = TypeC(0)
|
|
zero(::Type{TypeC}) = TypeC(0)
|
|
(*)(x::Int, a::TypeA) = TypeB(x*a.x)
|
|
(*)(a::TypeA, x::Int) = TypeB(a.x*x)
|
|
(+)(a::Union{TypeB,TypeC}, b::Union{TypeB,TypeC}) = TypeC(a.x+b.x)
|
|
A = TypeA[1 2; 3 4]
|
|
b = [1, 2]
|
|
d = A * b
|
|
@test typeof(d) == Vector{TypeC}
|
|
@test d == TypeC[5, 11]
|
|
end
|