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
|
// Copyright ©2019 The Gonum Authors. All rights reserved.
// Use of this source code is governed by a BSD-style
// license that can be found in the LICENSE file.
package testblas
import (
"fmt"
"testing"
"golang.org/x/exp/rand"
"gonum.org/v1/gonum/blas"
)
type Ztrsmer interface {
Ztrsm(side blas.Side, uplo blas.Uplo, transA blas.Transpose, diag blas.Diag, m, n int, alpha complex128, a []complex128, lda int, b []complex128, ldb int)
}
func ZtrsmTest(t *testing.T, impl Ztrsmer) {
for _, side := range []blas.Side{blas.Left, blas.Right} {
for _, uplo := range []blas.Uplo{blas.Lower, blas.Upper} {
for _, trans := range []blas.Transpose{blas.NoTrans, blas.Trans, blas.ConjTrans} {
for _, diag := range []blas.Diag{blas.Unit, blas.NonUnit} {
name := sideString(side) + "-" + uploString(uplo) + "-" + transString(trans) + "-" + diagString(diag)
t.Run(name, func(t *testing.T) {
for _, m := range []int{0, 1, 2, 3, 4, 5} {
for _, n := range []int{0, 1, 2, 3, 4, 5} {
ztrsmTest(t, impl, side, uplo, trans, diag, m, n)
}
}
})
}
}
}
}
}
func ztrsmTest(t *testing.T, impl Ztrsmer, side blas.Side, uplo blas.Uplo, trans blas.Transpose, diag blas.Diag, m, n int) {
const tol = 1e-13
rnd := rand.New(rand.NewSource(1))
nA := m
if side == blas.Right {
nA = n
}
for _, lda := range []int{max(1, nA), nA + 2} {
for _, ldb := range []int{max(1, n), n + 3} {
for _, alpha := range []complex128{0, 1, complex(0.7, -0.9)} {
// Allocate the matrix A and fill it with random numbers.
a := make([]complex128, nA*lda)
for i := range a {
a[i] = rndComplex128(rnd)
}
// Set some elements of A to 0 and 1 to cover special cases in Ztrsm.
if nA > 2 {
if uplo == blas.Upper {
a[nA-2] = 1
a[nA-1] = 0
} else {
a[(nA-2)*lda] = 1
a[(nA-1)*lda] = 0
}
}
// Create a copy of A for checking that Ztrsm
// does not modify its triangle opposite to uplo.
aCopy := make([]complex128, len(a))
copy(aCopy, a)
// Create a dense representation of A for
// computing the right-hand side matrix using zmm.
aTri := make([]complex128, len(a))
copy(aTri, a)
if uplo == blas.Upper {
for i := 0; i < nA; i++ {
// Zero out the lower triangle.
for j := 0; j < i; j++ {
aTri[i*lda+j] = 0
}
if diag == blas.Unit {
aTri[i*lda+i] = 1
}
}
} else {
for i := 0; i < nA; i++ {
if diag == blas.Unit {
aTri[i*lda+i] = 1
}
// Zero out the upper triangle.
for j := i + 1; j < nA; j++ {
aTri[i*lda+j] = 0
}
}
}
// Allocate the right-hand side matrix B and fill it with random numbers.
b := make([]complex128, m*ldb)
for i := range b {
b[i] = rndComplex128(rnd)
}
// Set some elements of B to 0 to cover special cases in Ztrsm.
if m > 1 && n > 1 {
b[0] = 0
b[(m-1)*ldb+n-1] = 0
}
bCopy := make([]complex128, len(b))
copy(bCopy, b)
// Compute the solution matrix X using Ztrsm.
// X is overwritten on B.
impl.Ztrsm(side, uplo, trans, diag, m, n, alpha, a, lda, b, ldb)
x := b
prefix := fmt.Sprintf("m=%v,n=%v,lda=%v,ldb=%v,alpha=%v", m, n, lda, ldb, alpha)
if !zsame(a, aCopy) {
t.Errorf("%v: unexpected modification of A", prefix)
continue
}
// Compute the left-hand side matrix of op(A)*X=alpha*B or X*op(A)=alpha*B
// using an internal Zgemm implementation.
var lhs []complex128
if side == blas.Left {
lhs = zmm(trans, blas.NoTrans, m, n, m, 1, aTri, lda, x, ldb, 0, b, ldb)
} else {
lhs = zmm(blas.NoTrans, trans, m, n, n, 1, x, ldb, aTri, lda, 0, b, ldb)
}
// Compute the right-hand side matrix alpha*B.
rhs := bCopy
for i := 0; i < m; i++ {
for j := 0; j < n; j++ {
rhs[i*ldb+j] *= alpha
}
}
if !zEqualApprox(lhs, rhs, tol) {
t.Errorf("%v: unexpected result", prefix)
}
}
}
}
}
|
