| /* 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; |