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/* roots/secant.c
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*
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* Copyright (C) 1996, 1997, 1998, 1999, 2000, 2007 Reid Priedhorsky, Brian Gough
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*
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* This program is free software; you can redistribute it and/or modify
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* it under the terms of the GNU General Public License as published by
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* the Free Software Foundation; either version 3 of the License, or (at
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* your option) any later version.
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*
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* This program is distributed in the hope that it will be useful, but
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* WITHOUT ANY WARRANTY; without even the implied warranty of
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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* General Public License for more details.
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*
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* You should have received a copy of the GNU General Public License
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* along with this program; if not, write to the Free Software
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* Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
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*/
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/* secant.c -- secant root finding algorithm
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The secant algorithm is a variant of the Newton algorithm with the
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derivative term replaced by a numerical estimate from the last two
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function evaluations.
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x[i+1] = x[i] - f(x[i]) / f'_est
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where f'_est = (f(x[i]) - f(x[i-1])) / (x[i] - x[i-1])
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The exact derivative is used for the initial value of f'_est.
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*/
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#include <config.h>
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#include <stddef.h>
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#include <stdlib.h>
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#include <stdio.h>
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#include <math.h>
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#include <float.h>
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#include <gsl/gsl_math.h>
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#include <gsl/gsl_errno.h>
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#include <gsl/gsl_roots.h>
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#include "roots.h"
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typedef struct
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{
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double f;
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double df;
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}
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secant_state_t;
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static int secant_init (void * vstate, gsl_function_fdf * fdf, double * root);
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static int secant_iterate (void * vstate, gsl_function_fdf * fdf, double * root);
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static int
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secant_init (void * vstate, gsl_function_fdf * fdf, double * root)
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{
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secant_state_t * state = (secant_state_t *) vstate;
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const double x = *root;
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GSL_FN_FDF_EVAL_F_DF (fdf, x, &(state->f), &(state->df));
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return GSL_SUCCESS;
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}
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static int
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secant_iterate (void * vstate, gsl_function_fdf * fdf, double * root)
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{
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secant_state_t * state = (secant_state_t *) vstate;
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const double x = *root ;
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const double f = state->f;
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const double df = state->df;
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double x_new, f_new, df_new;
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if(f == 0.0)
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{
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return GSL_SUCCESS;
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}
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if(df == 0.0)
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{
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GSL_ERROR("derivative is zero", GSL_EZERODIV);
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}
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x_new = x - (f / df);
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f_new = GSL_FN_FDF_EVAL_F(fdf, x_new) ;
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df_new = df * ((f - f_new) / f);
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*root = x_new ;
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state->f = f_new ;
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state->df = df_new ;
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if (!gsl_finite (f_new))
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{
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GSL_ERROR ("function value is not finite", GSL_EBADFUNC);
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}
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if (!gsl_finite (df_new))
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{
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GSL_ERROR ("derivative value is not finite", GSL_EBADFUNC);
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}
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return GSL_SUCCESS;
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}
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static const gsl_root_fdfsolver_type secant_type =
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{"secant", /* name */
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sizeof (secant_state_t),
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&secant_init,
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&secant_iterate};
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const gsl_root_fdfsolver_type * gsl_root_fdfsolver_secant = &secant_type;
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