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
|
// 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 gonum
import (
"math"
"gonum.org/v1/gonum/blas"
"gonum.org/v1/gonum/blas/blas64"
"gonum.org/v1/gonum/lapack"
)
// Dgecon estimates and returns the reciprocal of the condition number of the
// n×n matrix A, in either the 1-norm or the ∞-norm, using the LU factorization
// computed by Dgetrf.
//
// An estimate is obtained for norm(A⁻¹), and the reciprocal of the condition
// number rcond is computed as
//
// rcond 1 / ( norm(A) * norm(A⁻¹) ).
//
// If n is zero, rcond is always 1.
//
// anorm is the 1-norm or the ∞-norm of the original matrix A. anorm must be
// non-negative, otherwise Dgecon will panic. If anorm is 0 or infinity, Dgecon
// returns 0. If anorm is NaN, Dgecon returns NaN.
//
// work must have length at least 4*n and iwork must have length at least n,
// otherwise Dgecon will panic.
func (impl Implementation) Dgecon(norm lapack.MatrixNorm, n int, a []float64, lda int, anorm float64, work []float64, iwork []int) float64 {
switch {
case norm != lapack.MaxColumnSum && norm != lapack.MaxRowSum:
panic(badNorm)
case n < 0:
panic(nLT0)
case lda < max(1, n):
panic(badLdA)
case anorm < 0:
panic(negANorm)
}
// Quick return if possible.
if n == 0 {
return 1
}
switch {
case len(a) < (n-1)*lda+n:
panic(shortA)
case len(work) < 4*n:
panic(shortWork)
case len(iwork) < n:
panic(shortIWork)
}
// Quick return if possible.
switch {
case anorm == 0:
return 0
case math.IsNaN(anorm):
// Propagate NaN.
return anorm
case math.IsInf(anorm, 1):
return 0
}
bi := blas64.Implementation()
var rcond, ainvnm float64
var kase int
var normin bool
isave := new([3]int)
onenrm := norm == lapack.MaxColumnSum
smlnum := dlamchS
kase1 := 2
if onenrm {
kase1 = 1
}
for {
ainvnm, kase = impl.Dlacn2(n, work[n:], work, iwork, ainvnm, kase, isave)
if kase == 0 {
if ainvnm != 0 {
rcond = (1 / ainvnm) / anorm
}
return rcond
}
var sl, su float64
if kase == kase1 {
sl = impl.Dlatrs(blas.Lower, blas.NoTrans, blas.Unit, normin, n, a, lda, work, work[2*n:])
su = impl.Dlatrs(blas.Upper, blas.NoTrans, blas.NonUnit, normin, n, a, lda, work, work[3*n:])
} else {
su = impl.Dlatrs(blas.Upper, blas.Trans, blas.NonUnit, normin, n, a, lda, work, work[3*n:])
sl = impl.Dlatrs(blas.Lower, blas.Trans, blas.Unit, normin, n, a, lda, work, work[2*n:])
}
scale := sl * su
normin = true
if scale != 1 {
ix := bi.Idamax(n, work, 1)
if scale == 0 || scale < math.Abs(work[ix])*smlnum {
return rcond
}
impl.Drscl(n, scale, work, 1)
}
}
}
|
