1 /* min/bracketing.c
2 *
3 * Copyright (C) 1996, 1997, 1998, 1999, 2000 Fabrice Rossi
4 *
5 * This program is free software; you can redistribute it and/or modify
6 * it under the terms of the GNU General Public License as published by
7 * the Free Software Foundation; either version 3 of the License, or (at
8 * your option) any later version.
9 *
10 * This program is distributed in the hope that it will be useful, but
11 * WITHOUT ANY WARRANTY; without even the implied warranty of
12 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
13 * General Public License for more details.
14 *
15 * You should have received a copy of the GNU General Public License
16 * along with this program; if not, write to the Free Software
17 * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
18 */
19
20 /* bracketing.c -- find an initial bracketing interval for a function to minimize */
21
22 #include "gsl__config.h"
23 #include "gsl_math.h"
24 #include "gsl_errno.h"
25 #include "gsl_min.h"
26 #include "gsl_machine.h"
27
28 #include "gsl_min__min.h"
29
30 int
gsl_min_find_bracket(gsl_function * f,double * x_minimum,double * f_minimum,double * x_lower,double * f_lower,double * x_upper,double * f_upper,size_t eval_max)31 gsl_min_find_bracket(gsl_function *f,double *x_minimum,double * f_minimum,
32 double * x_lower, double * f_lower,
33 double * x_upper, double * f_upper,
34 size_t eval_max)
35 {
36 /* The three following variables must be declared volatile to avoid storage
37 in extended precision registers available on some architecture. The code
38 relies on the ability to compare double values. As the values will be
39 store in regular memory, the extended precision will then be lost and
40 values that are different in extended precision might have equal
41 representation in double precision. This behavior might break the
42 algorithm.
43 */
44 volatile double f_left = *f_lower;
45 volatile double f_right = *f_upper;
46 volatile double f_center;
47 double x_left = *x_lower;
48 double x_right= *x_upper;
49 double x_center;
50 const double golden = 0.3819660; /* golden = (3 - sqrt(5))/2 */
51 size_t nb_eval = 0;
52
53
54 if (f_right >= f_left)
55 {
56 x_center = (x_right - x_left) * golden + x_left;
57 nb_eval++;
58 SAFE_FUNC_CALL (f, x_center, &f_center);
59 }
60 else
61 {
62 x_center = x_right ;
63 f_center = f_right ;
64 x_right = (x_center - x_left) / golden + x_left;
65 nb_eval++;
66 SAFE_FUNC_CALL (f, x_right, &f_right);
67 }
68
69 do
70 {
71 if (f_center < f_left )
72 {
73 if (f_center < f_right)
74 {
75 *x_lower = x_left;
76 *x_upper = x_right;
77 *x_minimum = x_center;
78 *f_lower = f_left;
79 *f_upper = f_right;
80 *f_minimum = f_center;
81 /* gsl_ieee_printf_double (&f_left);
82 printf(" ");
83 gsl_ieee_printf_double (&f_center);
84 printf("\n");*/
85 return GSL_SUCCESS;
86 }
87 else if (f_center > f_right)
88 {
89 x_left = x_center;
90 f_left = f_center;
91 x_center = x_right;
92 f_center = f_right;
93 x_right = (x_center - x_left) / golden + x_left;
94 nb_eval++;
95 SAFE_FUNC_CALL (f, x_right, &f_right);
96 }
97 else /* f_center == f_right */
98 {
99 x_right = x_center;
100 f_right = f_center;
101 x_center = (x_right - x_left) * golden + x_left;
102 nb_eval++;
103 SAFE_FUNC_CALL (f, x_center, &f_center);
104 }
105 }
106 else /* f_center >= f_left */
107 {
108 x_right = x_center;
109 f_right = f_center;
110 x_center = (x_right - x_left) * golden + x_left;
111 nb_eval++;
112 SAFE_FUNC_CALL (f, x_center, &f_center);
113 }
114 }
115 while (nb_eval < eval_max
116 && (x_right - x_left) > GSL_SQRT_DBL_EPSILON * ( (x_right + x_left) * 0.5 ) + GSL_SQRT_DBL_EPSILON);
117 *x_lower = x_left;
118 *x_upper = x_right;
119 *x_minimum = x_center;
120 *f_lower = f_left;
121 *f_upper = f_right;
122 *f_minimum = f_center;
123 return GSL_FAILURE;
124 }
125
126