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
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
|
/* multifit/covar.c
*
* Copyright (C) 1996, 1997, 1998, 1999, 2000, 2004 Brian Gough
*
* This program is free software; you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation; either version 2 of the License, or (at
* your option) any later version.
*
* This program is distributed in the hope that it will be useful, but
* WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
* General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with this program; if not, write to the Free Software
* Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
*/
#include <config.h>
#include <gsl/gsl_math.h>
#include <gsl/gsl_errno.h>
#include <gsl/gsl_permutation.h>
#include <gsl/gsl_linalg.h>
#include <gsl/gsl_multifit_nlin.h>
/* Compute the covariance matrix
cov = inv (J^T J)
by QRP^T decomposition of J
*/
int
gsl_multifit_covar (const gsl_matrix * J, double epsrel, gsl_matrix * covar)
{
double tolr;
size_t i, j, k;
size_t kmax = 0;
gsl_matrix * r;
gsl_vector * tau;
gsl_vector * norm;
gsl_permutation * perm;
size_t m = J->size1, n = J->size2 ;
if (m < n)
{
GSL_ERROR ("Jacobian be rectangular M x N with M >= N", GSL_EBADLEN);
}
if (covar->size1 != covar->size2 || covar->size1 != n)
{
GSL_ERROR ("covariance matrix must be square and match second dimension of jacobian", GSL_EBADLEN);
}
r = gsl_matrix_alloc (m, n);
tau = gsl_vector_alloc (n);
perm = gsl_permutation_alloc (n) ;
norm = gsl_vector_alloc (n) ;
{
int signum = 0;
gsl_matrix_memcpy (r, J);
gsl_linalg_QRPT_decomp (r, tau, perm, &signum, norm);
}
/* Form the inverse of R in the full upper triangle of R */
tolr = epsrel * fabs(gsl_matrix_get(r, 0, 0));
for (k = 0 ; k < n ; k++)
{
double rkk = gsl_matrix_get(r, k, k);
if (fabs(rkk) <= tolr)
{
break;
}
gsl_matrix_set(r, k, k, 1.0/rkk);
for (j = 0; j < k ; j++)
{
double t = gsl_matrix_get(r, j, k) / rkk;
gsl_matrix_set (r, j, k, 0.0);
for (i = 0; i <= j; i++)
{
double rik = gsl_matrix_get (r, i, k);
double rij = gsl_matrix_get (r, i, j);
gsl_matrix_set (r, i, k, rik - t * rij);
}
}
kmax = k;
}
/* Form the full upper triangle of the inverse of R^T R in the full
upper triangle of R */
for (k = 0; k <= kmax ; k++)
{
for (j = 0; j < k; j++)
{
double rjk = gsl_matrix_get (r, j, k);
for (i = 0; i <= j ; i++)
{
double rij = gsl_matrix_get (r, i, j);
double rik = gsl_matrix_get (r, i, k);
gsl_matrix_set (r, i, j, rij + rjk * rik);
}
}
{
double t = gsl_matrix_get (r, k, k);
for (i = 0; i <= k; i++)
{
double rik = gsl_matrix_get (r, i, k);
gsl_matrix_set (r, i, k, t * rik);
};
}
}
/* Form the full lower triangle of the covariance matrix in the
strict lower triangle of R and in w */
for (j = 0 ; j < n ; j++)
{
size_t pj = gsl_permutation_get (perm, j);
for (i = 0; i <= j; i++)
{
size_t pi = gsl_permutation_get (perm, i);
double rij;
if (j > kmax)
{
gsl_matrix_set (r, i, j, 0.0);
rij = 0.0 ;
}
else
{
rij = gsl_matrix_get (r, i, j);
}
if (pi > pj)
{
gsl_matrix_set (r, pi, pj, rij);
}
else if (pi < pj)
{
gsl_matrix_set (r, pj, pi, rij);
}
}
{
double rjj = gsl_matrix_get (r, j, j);
gsl_matrix_set (covar, pj, pj, rjj);
}
}
/* symmetrize the covariance matrix */
for (j = 0 ; j < n ; j++)
{
for (i = 0; i < j ; i++)
{
double rji = gsl_matrix_get (r, j, i);
gsl_matrix_set (covar, j, i, rji);
gsl_matrix_set (covar, i, j, rji);
}
}
gsl_matrix_free (r);
gsl_permutation_free (perm);
gsl_vector_free (tau);
gsl_vector_free (norm);
return GSL_SUCCESS;
}
|
