1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
|
# This file is a part of Julia. License is MIT: https://julialang.org/license
module TestStructuredBroadcast
using Test, LinearAlgebra
@testset "broadcast[!] over combinations of scalars, structured matrices, and dense vectors/matrices" begin
N = 10
s = rand()
fV = rand(N)
fA = rand(N, N)
Z = copy(fA)
D = Diagonal(rand(N))
B = Bidiagonal(rand(N), rand(N - 1), :U)
T = Tridiagonal(rand(N - 1), rand(N), rand(N - 1))
U = UpperTriangular(rand(N,N))
L = LowerTriangular(rand(N,N))
M = Matrix(rand(N,N))
structuredarrays = (D, B, T, U, L, M)
fstructuredarrays = map(Array, structuredarrays)
for (X, fX) in zip(structuredarrays, fstructuredarrays)
@test (Q = broadcast(sin, X); typeof(Q) == typeof(X) && Q == broadcast(sin, fX))
@test broadcast!(sin, Z, X) == broadcast(sin, fX)
@test (Q = broadcast(cos, X); Q isa Matrix && Q == broadcast(cos, fX))
@test broadcast!(cos, Z, X) == broadcast(cos, fX)
@test (Q = broadcast(*, s, X); typeof(Q) == typeof(X) && Q == broadcast(*, s, fX))
@test broadcast!(*, Z, s, X) == broadcast(*, s, fX)
@test (Q = broadcast(+, fV, fA, X); Q isa Matrix && Q == broadcast(+, fV, fA, fX))
@test broadcast!(+, Z, fV, fA, X) == broadcast(+, fV, fA, fX)
@test (Q = broadcast(*, s, fV, fA, X); Q isa Matrix && Q == broadcast(*, s, fV, fA, fX))
@test broadcast!(*, Z, s, fV, fA, X) == broadcast(*, s, fV, fA, fX)
@test X .* 2.0 == X .* (2.0,) == fX .* 2.0
@test X .* 2.0 isa typeof(X)
@test X .* (2.0,) isa typeof(X)
@test isequal(X .* Inf, fX .* Inf)
two = 2
@test X .^ 2 == X .^ (2,) == fX .^ 2 == X .^ two
@test X .^ 2 isa typeof(X)
@test X .^ (2,) isa typeof(X)
@test X .^ two isa typeof(X)
@test X .^ 0 == fX .^ 0
@test X .^ -1 == fX .^ -1
for (Y, fY) in zip(structuredarrays, fstructuredarrays)
@test broadcast(+, X, Y) == broadcast(+, fX, fY)
@test broadcast!(+, Z, X, Y) == broadcast(+, fX, fY)
@test broadcast(*, X, Y) == broadcast(*, fX, fY)
@test broadcast!(*, Z, X, Y) == broadcast(*, fX, fY)
end
end
diagonals = (D, B, T)
fdiagonals = map(Array, diagonals)
for (X, fX) in zip(diagonals, fdiagonals)
for (Y, fY) in zip(diagonals, fdiagonals)
@test broadcast(+, X, Y)::Union{Diagonal,Bidiagonal,Tridiagonal} == broadcast(+, fX, fY)
@test broadcast!(+, Z, X, Y) == broadcast(+, fX, fY)
@test broadcast(*, X, Y)::Union{Diagonal,Bidiagonal,Tridiagonal} == broadcast(*, fX, fY)
@test broadcast!(*, Z, X, Y) == broadcast(*, fX, fY)
end
end
end
@testset "broadcast! where the destination is a structured matrix" begin
N = 5
A = rand(N, N)
sA = A + copy(A')
D = Diagonal(rand(N))
Bu = Bidiagonal(rand(N), rand(N - 1), :U)
Bl = Bidiagonal(rand(N), rand(N - 1), :L)
T = Tridiagonal(rand(N - 1), rand(N), rand(N - 1))
◣ = LowerTriangular(rand(N,N))
◥ = UpperTriangular(rand(N,N))
M = Matrix(rand(N,N))
@test broadcast!(sin, copy(D), D) == Diagonal(sin.(D))
@test broadcast!(sin, copy(Bu), Bu) == Bidiagonal(sin.(Bu), :U)
@test broadcast!(sin, copy(Bl), Bl) == Bidiagonal(sin.(Bl), :L)
@test broadcast!(sin, copy(T), T) == Tridiagonal(sin.(T))
@test broadcast!(sin, copy(◣), ◣) == LowerTriangular(sin.(◣))
@test broadcast!(sin, copy(◥), ◥) == UpperTriangular(sin.(◥))
@test broadcast!(sin, copy(M), M) == Matrix(sin.(M))
@test broadcast!(*, copy(D), D, A) == Diagonal(broadcast(*, D, A))
@test broadcast!(*, copy(Bu), Bu, A) == Bidiagonal(broadcast(*, Bu, A), :U)
@test broadcast!(*, copy(Bl), Bl, A) == Bidiagonal(broadcast(*, Bl, A), :L)
@test broadcast!(*, copy(T), T, A) == Tridiagonal(broadcast(*, T, A))
@test broadcast!(*, copy(◣), ◣, A) == LowerTriangular(broadcast(*, ◣, A))
@test broadcast!(*, copy(◥), ◥, A) == UpperTriangular(broadcast(*, ◥, A))
@test broadcast!(*, copy(M), M, A) == Matrix(broadcast(*, M, A))
@test_throws ArgumentError broadcast!(cos, copy(D), D) == Diagonal(sin.(D))
@test_throws ArgumentError broadcast!(cos, copy(Bu), Bu) == Bidiagonal(sin.(Bu), :U)
@test_throws ArgumentError broadcast!(cos, copy(Bl), Bl) == Bidiagonal(sin.(Bl), :L)
@test_throws ArgumentError broadcast!(cos, copy(T), T) == Tridiagonal(sin.(T))
@test_throws ArgumentError broadcast!(cos, copy(◣), ◣) == LowerTriangular(sin.(◣))
@test_throws ArgumentError broadcast!(cos, copy(◥), ◥) == UpperTriangular(sin.(◥))
@test_throws ArgumentError broadcast!(+, copy(D), D, A) == Diagonal(broadcast(*, D, A))
@test_throws ArgumentError broadcast!(+, copy(Bu), Bu, A) == Bidiagonal(broadcast(*, Bu, A), :U)
@test_throws ArgumentError broadcast!(+, copy(Bl), Bl, A) == Bidiagonal(broadcast(*, Bl, A), :L)
@test_throws ArgumentError broadcast!(+, copy(T), T, A) == Tridiagonal(broadcast(*, T, A))
@test_throws ArgumentError broadcast!(+, copy(◣), ◣, A) == LowerTriangular(broadcast(*, ◣, A))
@test_throws ArgumentError broadcast!(+, copy(◥), ◥, A) == UpperTriangular(broadcast(*, ◥, A))
end
@testset "map[!] over combinations of structured matrices" begin
N = 10
fA = rand(N, N)
Z = copy(fA)
D = Diagonal(rand(N))
B = Bidiagonal(rand(N), rand(N - 1), :U)
T = Tridiagonal(rand(N - 1), rand(N), rand(N - 1))
U = UpperTriangular(rand(N,N))
L = LowerTriangular(rand(N,N))
M = Matrix(rand(N,N))
structuredarrays = (M, D, B, T, U, L)
fstructuredarrays = map(Array, structuredarrays)
for (X, fX) in zip(structuredarrays, fstructuredarrays)
@test (Q = map(sin, X); typeof(Q) == typeof(X) && Q == map(sin, fX))
@test map!(sin, Z, X) == map(sin, fX)
@test (Q = map(cos, X); Q isa Matrix && Q == map(cos, fX))
@test map!(cos, Z, X) == map(cos, fX)
@test (Q = map(+, fA, X); Q isa Matrix && Q == map(+, fA, fX))
@test map!(+, Z, fA, X) == map(+, fA, fX)
for (Y, fY) in zip(structuredarrays, fstructuredarrays)
@test map(+, X, Y) == map(+, fX, fY)
@test map!(+, Z, X, Y) == map(+, fX, fY)
@test map(*, X, Y) == map(*, fX, fY)
@test map!(*, Z, X, Y) == map(*, fX, fY)
@test map(+, X, fA, Y) == map(+, fX, fA, fY)
@test map!(+, Z, X, fA, Y) == map(+, fX, fA, fY)
end
end
diagonals = (D, B, T)
fdiagonals = map(Array, diagonals)
for (X, fX) in zip(diagonals, fdiagonals)
for (Y, fY) in zip(diagonals, fdiagonals)
@test map(+, X, Y)::Union{Diagonal,Bidiagonal,Tridiagonal} == broadcast(+, fX, fY)
@test map!(+, Z, X, Y) == broadcast(+, fX, fY)
@test map(*, X, Y)::Union{Diagonal,Bidiagonal,Tridiagonal} == broadcast(*, fX, fY)
@test map!(*, Z, X, Y) == broadcast(*, fX, fY)
end
end
end
@testset "Issue #33397" begin
N = 5
U = UpperTriangular(rand(N, N))
L = LowerTriangular(rand(N, N))
UnitU = UnitUpperTriangular(rand(N, N))
UnitL = UnitLowerTriangular(rand(N, N))
D = Diagonal(rand(N))
@test U .+ L .+ D == U + L + D
@test L .+ U .+ D == L + U + D
@test UnitU .+ UnitL .+ D == UnitU + UnitL + D
@test UnitL .+ UnitU .+ D == UnitL + UnitU + D
@test U .+ UnitL .+ D == U + UnitL + D
@test L .+ UnitU .+ D == L + UnitU + D
@test L .+ U .+ L .+ U == L + U + L + U
@test U .+ L .+ U .+ L == U + L + U + L
@test L .+ UnitL .+ UnitU .+ U .+ D == L + UnitL + UnitU + U + D
@test L .+ U .+ D .+ D .+ D .+ D == L + U + D + D + D + D
end
@testset "Broadcast Returned Types" begin
# Issue 35245
N = 3
dV = rand(N)
evu = rand(N-1)
evl = rand(N-1)
Bu = Bidiagonal(dV, evu, :U)
Bl = Bidiagonal(dV, evl, :L)
T = Tridiagonal(evl, dV * 2, evu)
@test typeof(Bu .+ Bl) <: Tridiagonal
@test typeof(Bl .+ Bu) <: Tridiagonal
@test typeof(Bu .+ Bu) <: Bidiagonal
@test typeof(Bl .+ Bl) <: Bidiagonal
@test Bu .+ Bl == T
@test Bl .+ Bu == T
@test Bu .+ Bu == Bidiagonal(dV * 2, evu * 2, :U)
@test Bl .+ Bl == Bidiagonal(dV * 2, evl * 2, :L)
@test typeof(Bu .* Bl) <: Tridiagonal
@test typeof(Bl .* Bu) <: Tridiagonal
@test typeof(Bu .* Bu) <: Bidiagonal
@test typeof(Bl .* Bl) <: Bidiagonal
@test Bu .* Bl == Tridiagonal(zeros(N-1), dV .* dV, zeros(N-1))
@test Bl .* Bu == Tridiagonal(zeros(N-1), dV .* dV, zeros(N-1))
@test Bu .* Bu == Bidiagonal(dV .* dV, evu .* evu, :U)
@test Bl .* Bl == Bidiagonal(dV .* dV, evl .* evl, :L)
Bu2 = Bu .* 2
@test typeof(Bu2) <: Bidiagonal && Bu2.uplo == 'U'
Bu2 = 2 .* Bu
@test typeof(Bu2) <: Bidiagonal && Bu2.uplo == 'U'
Bl2 = Bl .* 2
@test typeof(Bl2) <: Bidiagonal && Bl2.uplo == 'L'
Bu2 = 2 .* Bl
@test typeof(Bl2) <: Bidiagonal && Bl2.uplo == 'L'
# Example of Nested Brodacasts
tmp = (1 .* 2) .* (Bidiagonal(1:3, 1:2, 'U') .* (3 .* 4)) .* (5 .* Bidiagonal(1:3, 1:2, 'L'))
@test typeof(tmp) <: Tridiagonal
end
end
|
