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/* roots/newton.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.
*/
/* newton.c -- newton root finding algorithm
This is the classical Newton-Raphson iteration.
x[i+1] = x[i] - f(x[i])/f'(x[i])
*/
#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, df;
}
newton_state_t;
static int newton_init (void * vstate, gsl_function_fdf * fdf, double * root);
static int newton_iterate (void * vstate, gsl_function_fdf * fdf, double * root);
static int
newton_init (void * vstate, gsl_function_fdf * fdf, double * root)
{
newton_state_t * state = (newton_state_t *) vstate;
const double x = *root ;
state->f = GSL_FN_FDF_EVAL_F (fdf, x);
state->df = GSL_FN_FDF_EVAL_DF (fdf, x) ;
return GSL_SUCCESS;
}
static int
newton_iterate (void * vstate, gsl_function_fdf * fdf, double * root)
{
newton_state_t * state = (newton_state_t *) vstate;
double root_new, f_new, df_new;
if (state->df == 0.0)
{
GSL_ERROR("derivative is zero", GSL_EZERODIV);
}
root_new = *root - (state->f / state->df);
*root = root_new ;
GSL_FN_FDF_EVAL_F_DF(fdf, root_new, &f_new, &df_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 newton_type =
{"newton", /* name */
sizeof (newton_state_t),
&newton_init,
&newton_iterate};
const gsl_root_fdfsolver_type * gsl_root_fdfsolver_newton = &newton_type;
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