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
|
// 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 gonum
import (
"math"
"gonum.org/v1/gonum/blas"
"gonum.org/v1/gonum/lapack"
)
// Dlansb returns the given norm of an n×n symmetric band matrix with kd
// super-diagonals.
//
// When norm is lapack.MaxColumnSum or lapack.MaxRowSum, the length of work must
// be at least n.
func (impl Implementation) Dlansb(norm lapack.MatrixNorm, uplo blas.Uplo, n, kd int, ab []float64, ldab int, work []float64) float64 {
switch {
case norm != lapack.MaxAbs && norm != lapack.MaxRowSum && norm != lapack.MaxColumnSum && norm != lapack.Frobenius:
panic(badNorm)
case uplo != blas.Upper && uplo != blas.Lower:
panic(badUplo)
case n < 0:
panic(nLT0)
case kd < 0:
panic(kdLT0)
case ldab < kd+1:
panic(badLdA)
}
// Quick return if possible.
if n == 0 {
return 0
}
switch {
case len(ab) < (n-1)*ldab+kd+1:
panic(shortAB)
case len(work) < n && (norm == lapack.MaxColumnSum || norm == lapack.MaxRowSum):
panic(shortWork)
}
var value float64
switch norm {
case lapack.MaxAbs:
if uplo == blas.Upper {
for i := 0; i < n; i++ {
for j := 0; j < min(n-i, kd+1); j++ {
aij := math.Abs(ab[i*ldab+j])
if aij > value || math.IsNaN(aij) {
value = aij
}
}
}
} else {
for i := 0; i < n; i++ {
for j := max(0, kd-i); j < kd+1; j++ {
aij := math.Abs(ab[i*ldab+j])
if aij > value || math.IsNaN(aij) {
value = aij
}
}
}
}
case lapack.MaxColumnSum, lapack.MaxRowSum:
work = work[:n]
var sum float64
if uplo == blas.Upper {
for i := range work {
work[i] = 0
}
for i := 0; i < n; i++ {
sum := work[i] + math.Abs(ab[i*ldab])
for j := i + 1; j < min(i+kd+1, n); j++ {
aij := math.Abs(ab[i*ldab+j-i])
sum += aij
work[j] += aij
}
if sum > value || math.IsNaN(sum) {
value = sum
}
}
} else {
for i := 0; i < n; i++ {
sum = 0
for j := max(0, i-kd); j < i; j++ {
aij := math.Abs(ab[i*ldab+kd+j-i])
sum += aij
work[j] += aij
}
work[i] = sum + math.Abs(ab[i*ldab+kd])
}
for _, sum := range work {
if sum > value || math.IsNaN(sum) {
value = sum
}
}
}
case lapack.Frobenius:
scale := 0.0
sum := 1.0
if uplo == blas.Upper {
if kd > 0 {
// Sum off-diagonals.
for i := 0; i < n-1; i++ {
ilen := min(n-i-1, kd)
scale, sum = impl.Dlassq(ilen, ab[i*ldab+1:], 1, scale, sum)
}
sum *= 2
}
// Sum diagonal.
scale, sum = impl.Dlassq(n, ab, ldab, scale, sum)
} else {
if kd > 0 {
// Sum off-diagonals.
for i := 1; i < n; i++ {
ilen := min(i, kd)
scale, sum = impl.Dlassq(ilen, ab[i*ldab+kd-ilen:], 1, scale, sum)
}
sum *= 2
}
// Sum diagonal.
scale, sum = impl.Dlassq(n, ab[kd:], ldab, scale, sum)
}
value = scale * math.Sqrt(sum)
}
return value
}
|
