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- /* roots/bisection.c
- *
- * Copyright (C) 1996, 1997, 1998, 1999, 2000, 2007 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 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.
- */
- /* bisection.c -- bisection root finding algorithm */
- #include "gsl__config.h"
- #include <stddef.h>
- #include <stdlib.h>
- #include <stdio.h>
- #include <math.h>
- #include <float.h>
- #include "gsl_math.h"
- #include "gsl_errno.h"
- #include "gsl_roots.h"
- #include "gsl_roots__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;
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