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
|
/* roots/bisection.c
*
* Copyright (C) 1996, 1997, 1998, 1999, 2000 Reid Priedhorsky, 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.
*/
/* bisection.c -- bisection root finding algorithm */
#include <config.h>
#include <stddef.h>
#include <stdlib.h>
#include <stdio.h>
#include <math.h>
#include <float.h>
#include <gsl/gsl_math.h>
#include <gsl/gsl_errno.h>
#include <gsl/gsl_roots.h>
#include "roots.h"
typedef struct
{
double f_lower, f_upper;
}
bisection_state_t;
static int bisection_init (void * vstate, gsl_function * f, double * root, double x_lower, double x_upper);
static int bisection_iterate (void * vstate, gsl_function * f, double * root, double * x_lower, double * x_upper);
static int
bisection_init (void * vstate, gsl_function * f, double * root, double x_lower, double x_upper)
{
bisection_state_t * state = (bisection_state_t *) vstate;
double f_lower, f_upper ;
*root = 0.5 * (x_lower + x_upper) ;
SAFE_FUNC_CALL (f, x_lower, &f_lower);
SAFE_FUNC_CALL (f, x_upper, &f_upper);
state->f_lower = f_lower;
state->f_upper = f_upper;
if ((f_lower < 0.0 && f_upper < 0.0) || (f_lower > 0.0 && f_upper > 0.0))
{
GSL_ERROR ("endpoints do not straddle y=0", GSL_EINVAL);
}
return GSL_SUCCESS;
}
static int
bisection_iterate (void * vstate, gsl_function * f, double * root, double * x_lower, double * x_upper)
{
bisection_state_t * state = (bisection_state_t *) vstate;
double x_bisect, f_bisect;
const double x_left = *x_lower ;
const double x_right = *x_upper ;
const double f_lower = state->f_lower;
const double f_upper = state->f_upper;
if (f_lower == 0.0)
{
*root = x_left ;
*x_upper = x_left;
return GSL_SUCCESS;
}
if (f_upper == 0.0)
{
*root = x_right ;
*x_lower = x_right;
return GSL_SUCCESS;
}
x_bisect = (x_left + x_right) / 2.0;
SAFE_FUNC_CALL (f, x_bisect, &f_bisect);
if (f_bisect == 0.0)
{
*root = x_bisect;
*x_lower = x_bisect;
*x_upper = x_bisect;
return GSL_SUCCESS;
}
/* Discard the half of the interval which doesn't contain the root. */
if ((f_lower > 0.0 && f_bisect < 0.0) || (f_lower < 0.0 && f_bisect > 0.0))
{
*root = 0.5 * (x_left + x_bisect) ;
*x_upper = x_bisect;
state->f_upper = f_bisect;
}
else
{
*root = 0.5 * (x_bisect + x_right) ;
*x_lower = x_bisect;
state->f_lower = f_bisect;
}
return GSL_SUCCESS;
}
static const gsl_root_fsolver_type bisection_type =
{"bisection", /* name */
sizeof (bisection_state_t),
&bisection_init,
&bisection_iterate};
const gsl_root_fsolver_type * gsl_root_fsolver_bisection = &bisection_type;
|
