| /* roots/secant.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. |
| */ |
| |
| /* secant.c -- secant root finding algorithm |
| |
| The secant algorithm is a variant of the Newton algorithm with the |
| derivative term replaced by a numerical estimate from the last two |
| function evaluations. |
| |
| x[i+1] = x[i] - f(x[i]) / f'_est |
| |
| where f'_est = (f(x[i]) - f(x[i-1])) / (x[i] - x[i-1]) |
| |
| The exact derivative is used for the initial value of f'_est. |
| |
| */ |
| |
| #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; |
| double df; |
| } |
| secant_state_t; |
| |
| static int secant_init (void * vstate, gsl_function_fdf * fdf, double * root); |
| static int secant_iterate (void * vstate, gsl_function_fdf * fdf, double * root); |
| |
| static int |
| secant_init (void * vstate, gsl_function_fdf * fdf, double * root) |
| { |
| secant_state_t * state = (secant_state_t *) vstate; |
| |
| const double x = *root; |
| |
| GSL_FN_FDF_EVAL_F_DF (fdf, x, &(state->f), &(state->df)); |
| |
| return GSL_SUCCESS; |
| |
| } |
| |
| static int |
| secant_iterate (void * vstate, gsl_function_fdf * fdf, double * root) |
| { |
| secant_state_t * state = (secant_state_t *) vstate; |
| |
| const double x = *root ; |
| const double f = state->f; |
| const double df = state->df; |
| |
| double x_new, f_new, df_new; |
| |
| if (state->df == 0.0) |
| { |
| GSL_ERROR("derivative is zero", GSL_EZERODIV); |
| } |
| |
| x_new = x - (f / df); |
| |
| f_new = GSL_FN_FDF_EVAL_F(fdf, x_new) ; |
| df_new = (f_new - f) / (x_new - x) ; |
| |
| *root = x_new ; |
| |
| state->f = f_new ; |
| state->df = df_new ; |
| |
| if (!finite (f_new)) |
| { |
| GSL_ERROR ("function value is not finite", GSL_EBADFUNC); |
| } |
| |
| if (!finite (df_new)) |
| { |
| GSL_ERROR ("derivative value is not finite", GSL_EBADFUNC); |
| } |
| |
| return GSL_SUCCESS; |
| } |
| |
| |
| static const gsl_root_fdfsolver_type secant_type = |
| {"secant", /* name */ |
| sizeof (secant_state_t), |
| &secant_init, |
| &secant_iterate}; |
| |
| const gsl_root_fdfsolver_type * gsl_root_fdfsolver_secant = &secant_type; |