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
|
/* multifit/convergence.c
*
* Copyright (C) 1996, 1997, 1998, 1999, 2000, 2007 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 3 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_multifit_nlin.h>
#include <gsl/gsl_blas.h>
static double scaled_infnorm(const gsl_vector *x, const gsl_vector *g);
/*
gsl_multifit_fdfsolver_test()
Convergence tests for nonlinear minimization
(1) |dx_i| <= xtol * (1 + |x_i|) for all i
(2) || g .* x ||_inf <= gtol ||f||^2
(3) ||f(x+dx) - f(x)|| <= ftol * max(||f(x)||, 1)
Inputs: s - fdfsolver
xtol - tolerance for step size
gtol - tolerance for gradient vector
ftol - tolerance for residual vector
info - (output)
1 - stopped by small x step
2 - stopped by small gradient
3 - stopped by small residual vector change
*/
int
gsl_multifit_fdfsolver_test (const gsl_multifit_fdfsolver * s,
const double xtol, const double gtol,
const double ftol, int *info)
{
int status;
double gnorm, fnorm, phi;
*info = 0;
status = gsl_multifit_test_delta(s->dx, s->x, xtol*xtol, xtol);
if (status == GSL_SUCCESS)
{
*info = 1;
return GSL_SUCCESS;
}
/* compute gradient g = J^T f */
(s->type->gradient) (s->state, s->g);
/* compute gnorm = max_i( g_i * max(x_i, 1) ) */
gnorm = scaled_infnorm(s->x, s->g);
/* compute fnorm = ||f|| */
fnorm = gsl_blas_dnrm2(s->f);
phi = 0.5 * fnorm * fnorm;
if (gnorm <= gtol * GSL_MAX(phi, 1.0))
{
*info = 2;
return GSL_SUCCESS;
}
#if 0
if (dfnorm <= ftol * GSL_MAX(fnorm, 1.0))
{
*info = 3;
return GSL_SUCCESS;
}
#endif
return GSL_CONTINUE;
} /* gsl_multifit_fdfsolver_test() */
int
gsl_multifit_test_delta (const gsl_vector * dx, const gsl_vector * x,
double epsabs, double epsrel)
{
size_t i;
int ok = 1;
const size_t n = x->size ;
if (epsrel < 0.0)
{
GSL_ERROR ("relative tolerance is negative", GSL_EBADTOL);
}
for (i = 0 ; i < n ; i++)
{
double xi = gsl_vector_get(x,i);
double dxi = gsl_vector_get(dx,i);
double tolerance = epsabs + epsrel * fabs(xi) ;
if (fabs(dxi) < tolerance)
{
ok = 1;
}
else
{
ok = 0;
break;
}
}
if (ok)
return GSL_SUCCESS ;
return GSL_CONTINUE;
}
int
gsl_multifit_test_gradient (const gsl_vector * g, double epsabs)
{
size_t i;
double residual = 0;
const size_t n = g->size;
if (epsabs < 0.0)
{
GSL_ERROR ("absolute tolerance is negative", GSL_EBADTOL);
}
for (i = 0 ; i < n ; i++)
{
double gi = gsl_vector_get(g, i);
residual += fabs(gi);
}
if (residual < epsabs)
{
return GSL_SUCCESS;
}
return GSL_CONTINUE ;
}
static double
scaled_infnorm(const gsl_vector *x, const gsl_vector *g)
{
const size_t n = x->size;
size_t i;
double norm = 0.0;
for (i = 0; i < n; ++i)
{
double xi = GSL_MAX(gsl_vector_get(x, i), 1.0);
double gi = gsl_vector_get(g, i);
double tmp = fabs(xi * gi);
if (tmp > norm)
norm = tmp;
}
return norm;
}
|
