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
|
// Copyright ©2020 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"
"math"
"testing"
"golang.org/x/exp/rand"
"gonum.org/v1/gonum/blas"
"gonum.org/v1/gonum/floats"
"gonum.org/v1/gonum/lapack"
)
type Dlantber interface {
Dlantb(norm lapack.MatrixNorm, uplo blas.Uplo, diag blas.Diag, n, k int, a []float64, lda int, work []float64) float64
}
func DlantbTest(t *testing.T, impl Dlantber) {
rnd := rand.New(rand.NewSource(1))
for _, norm := range []lapack.MatrixNorm{lapack.MaxAbs, lapack.MaxRowSum, lapack.MaxColumnSum, lapack.Frobenius} {
for _, uplo := range []blas.Uplo{blas.Lower, blas.Upper} {
for _, diag := range []blas.Diag{blas.NonUnit, blas.Unit} {
name := normToString(norm) + uploToString(uplo) + diagToString(diag)
t.Run(name, func(t *testing.T) {
for _, n := range []int{0, 1, 2, 3, 4, 5, 10} {
for _, k := range []int{0, 1, 2, 3, n, n + 2} {
for _, lda := range []int{k + 1, k + 3} {
for iter := 0; iter < 10; iter++ {
dlantbTest(t, impl, rnd, norm, uplo, diag, n, k, lda)
}
}
}
}
})
}
}
}
}
func dlantbTest(t *testing.T, impl Dlantber, rnd *rand.Rand, norm lapack.MatrixNorm, uplo blas.Uplo, diag blas.Diag, n, k, lda int) {
const tol = 1e-14
name := fmt.Sprintf("n=%v,k=%v,lda=%v", n, k, lda)
// Deal with zero-sized matrices early.
if n == 0 {
got := impl.Dlantb(norm, uplo, diag, n, k, nil, lda, nil)
if got != 0 {
t.Errorf("%v: unexpected result for zero-sized matrix", name)
}
return
}
a := make([]float64, max(0, (n-1)*lda+k+1))
if rnd.Float64() < 0.5 {
// Sometimes fill A with elements between -0.5 and 0.5 so that for
// blas.Unit matrices the largest element is the 1 on the main diagonal.
for i := range a {
// Between -0.5 and 0.5.
a[i] = rnd.Float64() - 0.5
}
} else {
for i := range a {
// Between -2 and 2.
a[i] = 4*rnd.Float64() - 2
}
}
// Sometimes put a NaN into A.
if rnd.Float64() < 0.5 {
a[rnd.Intn(len(a))] = math.NaN()
}
// Make a copy of A for later comparison.
aCopy := make([]float64, len(a))
copy(aCopy, a)
var work []float64
if norm == lapack.MaxColumnSum {
work = make([]float64, n)
}
// Fill work with random garbage.
for i := range work {
work[i] = rnd.NormFloat64()
}
got := impl.Dlantb(norm, uplo, diag, n, k, a, lda, work)
if !floats.Same(a, aCopy) {
t.Fatalf("%v: unexpected modification of a", name)
}
// Generate a dense representation of A and compute the wanted result.
ldaGen := n
aGen := make([]float64, n*ldaGen)
if uplo == blas.Upper {
for i := 0; i < n; i++ {
for j := 0; j < min(n-i, k+1); j++ {
aGen[i*ldaGen+i+j] = a[i*lda+j]
}
}
} else {
for i := 0; i < n; i++ {
for j := max(0, k-i); j < k+1; j++ {
aGen[i*ldaGen+i-(k-j)] = a[i*lda+j]
}
}
}
if diag == blas.Unit {
for i := 0; i < n; i++ {
aGen[i*ldaGen+i] = 1
}
}
want := dlange(norm, n, n, aGen, ldaGen)
if math.IsNaN(want) {
if !math.IsNaN(got) {
t.Errorf("%v: unexpected result with NaN element; got %v, want %v", name, got, want)
}
return
}
if norm == lapack.MaxAbs {
if got != want {
t.Errorf("%v: unexpected result; got %v, want %v", name, got, want)
}
return
}
diff := math.Abs(got - want)
if diff > tol {
t.Errorf("%v: unexpected result; got %v, want %v, diff=%v", name, got, want, diff)
}
}
|
