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- /* roots/newton.c
- *
- * Copyright (C) 1996, 1997, 1998, 1999, 2000, 2007 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 3 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 "gsl__config.h"
- #include <stddef.h>
- #include <stdlib.h>
- #include <stdio.h>
- #include <math.h>
- #include <float.h>
- #include "gsl_math.h"
- #include "gsl_errno.h"
- #include "gsl_roots.h"
- #include "gsl_roots__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 (!gsl_finite(f_new))
- {
- GSL_ERROR ("function value is not finite", GSL_EBADFUNC);
- }
- if (!gsl_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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