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/* 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;
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