forked from gonum/gonum
-
Notifications
You must be signed in to change notification settings - Fork 0
/
dpocon.go
158 lines (147 loc) · 4.1 KB
/
dpocon.go
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
// Copyright ©2015 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 (
"log"
"testing"
"golang.org/x/exp/rand"
"gonum.org/v1/gonum/blas"
"gonum.org/v1/gonum/blas/blas64"
"gonum.org/v1/gonum/floats"
"gonum.org/v1/gonum/lapack"
)
type Dpoconer interface {
Dpotrfer
Dgeconer
Dlansy(norm lapack.MatrixNorm, uplo blas.Uplo, n int, a []float64, lda int, work []float64) float64
Dpocon(uplo blas.Uplo, n int, a []float64, lda int, anorm float64, work []float64, iwork []int) float64
}
func DpoconTest(t *testing.T, impl Dpoconer) {
for _, test := range []struct {
a []float64
n int
cond float64
uplo blas.Uplo
}{
{
a: []float64{
89, 59, 77,
0, 107, 59,
0, 0, 89,
},
uplo: blas.Upper,
n: 3,
cond: 0.050052137643379,
},
{
a: []float64{
89, 0, 0,
59, 107, 0,
77, 59, 89,
},
uplo: blas.Lower,
n: 3,
cond: 0.050052137643379,
},
// Dgecon does not match Dpocon for this case. https://github.com/xianyi/OpenBLAS/issues/664.
{
a: []float64{
2.9995576045549965, -2.0898894566158663, 3.965560740124006,
0, 1.9634729526261008, -2.8681002706874104,
0, 0, 5.502416670471008,
},
uplo: blas.Upper,
n: 3,
cond: 0.024054837369015203,
},
} {
n := test.n
a := make([]float64, len(test.a))
copy(a, test.a)
lda := n
uplo := test.uplo
work := make([]float64, 3*n)
anorm := impl.Dlansy(lapack.MaxColumnSum, uplo, n, a, lda, work)
// Compute cholesky decomposition
ok := impl.Dpotrf(uplo, n, a, lda)
if !ok {
t.Errorf("Bad test, matrix not positive definite")
continue
}
iwork := make([]int, n)
cond := impl.Dpocon(uplo, n, a, lda, anorm, work, iwork)
// Error if not the same order, otherwise log the difference.
if !floats.EqualWithinAbsOrRel(cond, test.cond, 1e0, 1e0) {
t.Errorf("Cond mismatch. Want %v, got %v.", test.cond, cond)
} else if !floats.EqualWithinAbsOrRel(cond, test.cond, 1e-14, 1e-14) {
log.Printf("Dpocon cond mismatch. Want %v, got %v.", test.cond, cond)
}
}
rnd := rand.New(rand.NewSource(1))
bi := blas64.Implementation()
// Randomized tests compared against Dgecon.
for _, uplo := range []blas.Uplo{blas.Lower, blas.Upper} {
for _, test := range []struct {
n, lda int
}{
{3, 0},
{3, 5},
} {
for trial := 0; trial < 100; trial++ {
n := test.n
lda := test.lda
if lda == 0 {
lda = n
}
a := make([]float64, n*lda)
for i := range a {
a[i] = rnd.NormFloat64()
}
// Multiply a by itself to make it symmetric positive definite.
aCopy := make([]float64, len(a))
copy(aCopy, a)
bi.Dgemm(blas.Trans, blas.NoTrans, n, n, n, 1, aCopy, lda, aCopy, lda, 0, a, lda)
aDat := make([]float64, len(aCopy))
copy(aDat, a)
aDense := make([]float64, len(a))
if uplo == blas.Upper {
for i := 0; i < n; i++ {
for j := i; j < n; j++ {
v := a[i*lda+j]
aDense[i*lda+j] = v
aDense[j*lda+i] = v
}
}
} else {
for i := 0; i < n; i++ {
for j := 0; j <= i; j++ {
v := a[i*lda+j]
aDense[i*lda+j] = v
aDense[j*lda+i] = v
}
}
}
work := make([]float64, 4*n)
iwork := make([]int, n)
anorm := impl.Dlansy(lapack.MaxColumnSum, uplo, n, a, lda, work)
ok := impl.Dpotrf(uplo, n, a, lda)
if !ok {
t.Errorf("Bad test, matrix not positive definite")
continue
}
got := impl.Dpocon(uplo, n, a, lda, anorm, work, iwork)
denseNorm := impl.Dlange(lapack.MaxColumnSum, n, n, aDense, lda, work)
ipiv := make([]int, n)
impl.Dgetrf(n, n, aDense, lda, ipiv)
want := impl.Dgecon(lapack.MaxColumnSum, n, aDense, lda, denseNorm, work, iwork)
// Error if not the same order, otherwise log the difference.
if !floats.EqualWithinAbsOrRel(want, got, 1e0, 1e0) {
t.Errorf("Dpocon and Dgecon mismatch. Dpocon %v, Dgecon %v.", got, want)
} else if !floats.EqualWithinAbsOrRel(want, got, 1e-14, 1e-14) {
log.Printf("Dpocon and Dgecon mismatch. Dpocon %v, Dgecon %v.", got, want)
}
}
}
}
}