1 /* roots/bisection.c
2 *
3 * Copyright (C) 1996, 1997, 1998, 1999, 2000, 2007 Reid Priedhorsky, Brian Gough
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
21 /* bisection.c -- bisection root finding algorithm */
22
23 #include <config.h>
24
25 #include <stddef.h>
26 #include <stdlib.h>
27 #include <stdio.h>
28 #include <math.h>
29 #include <float.h>
30
31 #include <gsl/gsl_math.h>
32 #include <gsl/gsl_errno.h>
33 #include <gsl/gsl_roots.h>
34
35 #include "roots.h"
36
37 typedef struct
38 {
39 double f_lower, f_upper;
40 }
41 bisection_state_t;
42
43 static int bisection_init (void * vstate, gsl_function * f, double * root, double x_lower, double x_upper);
44 static int bisection_iterate (void * vstate, gsl_function * f, double * root, double * x_lower, double * x_upper);
45
46 static int
bisection_init(void * vstate,gsl_function * f,double * root,double x_lower,double x_upper)47 bisection_init (void * vstate, gsl_function * f, double * root, double x_lower, double x_upper)
48 {
49 bisection_state_t * state = (bisection_state_t *) vstate;
50
51 double f_lower, f_upper ;
52
53 *root = 0.5 * (x_lower + x_upper) ;
54
55 SAFE_FUNC_CALL (f, x_lower, &f_lower);
56 SAFE_FUNC_CALL (f, x_upper, &f_upper);
57
58 state->f_lower = f_lower;
59 state->f_upper = f_upper;
60
61 if ((f_lower < 0.0 && f_upper < 0.0) || (f_lower > 0.0 && f_upper > 0.0))
62 {
63 GSL_ERROR ("endpoints do not straddle y=0", GSL_EINVAL);
64 }
65
66 return GSL_SUCCESS;
67
68 }
69
70 static int
bisection_iterate(void * vstate,gsl_function * f,double * root,double * x_lower,double * x_upper)71 bisection_iterate (void * vstate, gsl_function * f, double * root, double * x_lower, double * x_upper)
72 {
73 bisection_state_t * state = (bisection_state_t *) vstate;
74
75 double x_bisect, f_bisect;
76
77 const double x_left = *x_lower ;
78 const double x_right = *x_upper ;
79
80 const double f_lower = state->f_lower;
81 const double f_upper = state->f_upper;
82
83 if (f_lower == 0.0)
84 {
85 *root = x_left ;
86 *x_upper = x_left;
87 return GSL_SUCCESS;
88 }
89
90 if (f_upper == 0.0)
91 {
92 *root = x_right ;
93 *x_lower = x_right;
94 return GSL_SUCCESS;
95 }
96
97 x_bisect = (x_left + x_right) / 2.0;
98
99 SAFE_FUNC_CALL (f, x_bisect, &f_bisect);
100
101 if (f_bisect == 0.0)
102 {
103 *root = x_bisect;
104 *x_lower = x_bisect;
105 *x_upper = x_bisect;
106 return GSL_SUCCESS;
107 }
108
109 /* Discard the half of the interval which doesn't contain the root. */
110
111 if ((f_lower > 0.0 && f_bisect < 0.0) || (f_lower < 0.0 && f_bisect > 0.0))
112 {
113 *root = 0.5 * (x_left + x_bisect) ;
114 *x_upper = x_bisect;
115 state->f_upper = f_bisect;
116 }
117 else
118 {
119 *root = 0.5 * (x_bisect + x_right) ;
120 *x_lower = x_bisect;
121 state->f_lower = f_bisect;
122 }
123
124 return GSL_SUCCESS;
125 }
126
127
128 static const gsl_root_fsolver_type bisection_type =
129 {"bisection", /* name */
130 sizeof (bisection_state_t),
131 &bisection_init,
132 &bisection_iterate};
133
134 const gsl_root_fsolver_type * gsl_root_fsolver_bisection = &bisection_type;
135