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
|
/* multimin/steepest_descent.c
*
* Copyright (C) 1996, 1997, 1998, 1999, 2000 Fabrice Rossi
*
* 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.
*/
/* steepest_descent.c -- the steepest descent algorithm */
/* Modified by Brian Gough to use single iteration structure */
#include <config.h>
#include <gsl/gsl_multimin.h>
#include <gsl/gsl_blas_types.h>
#include <gsl/gsl_blas.h>
typedef struct
{
double step;
double max_step;
double tol;
gsl_vector *x1;
gsl_vector *g1;
}
steepest_descent_state_t;
static int
steepest_descent_alloc (void *vstate, size_t n)
{
steepest_descent_state_t *state = (steepest_descent_state_t *) vstate;
state->x1 = gsl_vector_alloc (n);
if (state->x1 == NULL)
{
GSL_ERROR ("failed to allocate space for x1", GSL_ENOMEM);
}
state->g1 = gsl_vector_alloc (n);
if (state->g1 == NULL)
{
gsl_vector_free (state->x1);
GSL_ERROR ("failed to allocate space for g1", GSL_ENOMEM);
}
return GSL_SUCCESS;
}
static int
steepest_descent_set (void *vstate, gsl_multimin_function_fdf * fdf,
const gsl_vector * x, double *f,
gsl_vector * gradient, double step_size, double tol)
{
steepest_descent_state_t *state = (steepest_descent_state_t *) vstate;
GSL_MULTIMIN_FN_EVAL_F_DF (fdf, x, f, gradient);
state->step = step_size;
state->max_step = step_size;
state->tol = tol;
return GSL_SUCCESS;
}
static void
steepest_descent_free (void *vstate)
{
steepest_descent_state_t *state = (steepest_descent_state_t *) vstate;
gsl_vector_free (state->x1);
gsl_vector_free (state->g1);
}
static int
steepest_descent_restart (void *vstate)
{
steepest_descent_state_t *state = (steepest_descent_state_t *) vstate;
state->step = state->max_step;
return GSL_SUCCESS;
}
static int
steepest_descent_iterate (void *vstate, gsl_multimin_function_fdf * fdf,
gsl_vector * x, double *f,
gsl_vector * gradient, gsl_vector * dx)
{
steepest_descent_state_t *state = (steepest_descent_state_t *) vstate;
gsl_vector *x1 = state->x1;
gsl_vector *g1 = state->g1;
double f0 = *f;
double f1;
double step = state->step, tol = state->tol;
int failed = 0;
/* compute new trial point at x1= x - step * dir, where dir is the
normalized gradient */
double gnorm = gsl_blas_dnrm2 (gradient);
if (gnorm == 0.0)
{
gsl_vector_set_zero (dx);
return GSL_ENOPROG;
}
trial:
gsl_vector_set_zero (dx);
gsl_blas_daxpy (-step / gnorm, gradient, dx);
gsl_vector_memcpy (x1, x);
gsl_blas_daxpy (1.0, dx, x1);
/* evaluate function and gradient at new point x1 */
GSL_MULTIMIN_FN_EVAL_F_DF (fdf, x1, &f1, g1);
if (f1 > f0)
{
/* downhill step failed, reduce step-size and try again */
failed = 1;
step *= tol;
goto trial;
}
if (failed)
step *= tol;
else
step *= 2.0;
state->step = step;
gsl_vector_memcpy (x, x1);
gsl_vector_memcpy (gradient, g1);
*f = f1;
return GSL_SUCCESS;
}
static const gsl_multimin_fdfminimizer_type steepest_descent_type =
{ "steepest_descent", /* name */
sizeof (steepest_descent_state_t),
&steepest_descent_alloc,
&steepest_descent_set,
&steepest_descent_iterate,
&steepest_descent_restart,
&steepest_descent_free
};
const gsl_multimin_fdfminimizer_type
* gsl_multimin_fdfminimizer_steepest_descent = &steepest_descent_type;
|
