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
|
// Copyright ©2016 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 testlapack
import (
"fmt"
"testing"
"golang.org/x/exp/rand"
"gonum.org/v1/gonum/blas"
"gonum.org/v1/gonum/blas/blas64"
"gonum.org/v1/gonum/lapack"
)
type Dsytrder interface {
Dsytrd(uplo blas.Uplo, n int, a []float64, lda int, d, e, tau, work []float64, lwork int)
Dorgqr(m, n, k int, a []float64, lda int, tau, work []float64, lwork int)
Dorgql(m, n, k int, a []float64, lda int, tau, work []float64, lwork int)
}
func DsytrdTest(t *testing.T, impl Dsytrder) {
const tol = 1e-14
rnd := rand.New(rand.NewSource(1))
for tc, test := range []struct {
n, lda int
}{
{1, 0},
{2, 0},
{3, 0},
{4, 0},
{10, 0},
{50, 0},
{100, 0},
{150, 0},
{300, 0},
{1, 3},
{2, 3},
{3, 7},
{4, 9},
{10, 20},
{50, 70},
{100, 120},
{150, 170},
{300, 320},
} {
for _, uplo := range []blas.Uplo{blas.Upper, blas.Lower} {
for _, wl := range []worklen{minimumWork, mediumWork, optimumWork} {
n := test.n
lda := test.lda
if lda == 0 {
lda = n
}
a := randomGeneral(n, n, lda, rnd)
for i := 1; i < n; i++ {
for j := 0; j < i; j++ {
a.Data[i*a.Stride+j] = a.Data[j*a.Stride+i]
}
}
aCopy := cloneGeneral(a)
d := nanSlice(n)
e := nanSlice(n - 1)
tau := nanSlice(n - 1)
var lwork int
switch wl {
case minimumWork:
lwork = 1
case mediumWork:
work := make([]float64, 1)
impl.Dsytrd(uplo, n, a.Data, a.Stride, d, e, tau, work, -1)
lwork = (int(work[0]) + 1) / 2
lwork = max(1, lwork)
case optimumWork:
work := make([]float64, 1)
impl.Dsytrd(uplo, n, a.Data, a.Stride, d, e, tau, work, -1)
lwork = int(work[0])
}
work := make([]float64, lwork)
impl.Dsytrd(uplo, n, a.Data, a.Stride, d, e, tau, work, lwork)
prefix := fmt.Sprintf("Case #%v: uplo=%c,n=%v,lda=%v,work=%v",
tc, uplo, n, lda, wl)
if !generalOutsideAllNaN(a) {
t.Errorf("%v: out-of-range write to A", prefix)
}
// Extract Q by doing what Dorgtr does.
q := cloneGeneral(a)
if uplo == blas.Upper {
for j := 0; j < n-1; j++ {
for i := 0; i < j; i++ {
q.Data[i*q.Stride+j] = q.Data[i*q.Stride+j+1]
}
q.Data[(n-1)*q.Stride+j] = 0
}
for i := 0; i < n-1; i++ {
q.Data[i*q.Stride+n-1] = 0
}
q.Data[(n-1)*q.Stride+n-1] = 1
if n > 1 {
work = make([]float64, n-1)
impl.Dorgql(n-1, n-1, n-1, q.Data, q.Stride, tau, work, len(work))
}
} else {
for j := n - 1; j > 0; j-- {
q.Data[j] = 0
for i := j + 1; i < n; i++ {
q.Data[i*q.Stride+j] = q.Data[i*q.Stride+j-1]
}
}
q.Data[0] = 1
for i := 1; i < n; i++ {
q.Data[i*q.Stride] = 0
}
if n > 1 {
work = make([]float64, n-1)
impl.Dorgqr(n-1, n-1, n-1, q.Data[q.Stride+1:], q.Stride, tau, work, len(work))
}
}
if resid := residualOrthogonal(q, false); resid > tol*float64(n) {
t.Errorf("%v: Q is not orthogonal; resid=%v, want<=%v", prefix, resid, tol*float64(n))
}
// Construct symmetric tridiagonal T from d and e.
tMat := zeros(n, n, n)
for i := 0; i < n; i++ {
tMat.Data[i*tMat.Stride+i] = d[i]
}
if uplo == blas.Upper {
for j := 1; j < n; j++ {
tMat.Data[(j-1)*tMat.Stride+j] = e[j-1]
tMat.Data[j*tMat.Stride+j-1] = e[j-1]
}
} else {
for j := 0; j < n-1; j++ {
tMat.Data[(j+1)*tMat.Stride+j] = e[j]
tMat.Data[j*tMat.Stride+j+1] = e[j]
}
}
// Compute Qᵀ*A*Q - T.
qa := zeros(n, n, n)
blas64.Gemm(blas.Trans, blas.NoTrans, 1, q, aCopy, 0, qa)
blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, qa, q, -1, tMat)
// Check that |Qᵀ*A*Q - T| is small.
resid := dlange(lapack.MaxColumnSum, n, n, tMat.Data, tMat.Stride)
if resid > tol*float64(n) {
t.Errorf("%v: |Qᵀ*A*Q - T|=%v, want<=%v", prefix, resid, tol*float64(n))
}
}
}
}
}
|
