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Diffstat (limited to 'gsl-1.9/roots/secant.c')
-rw-r--r-- | gsl-1.9/roots/secant.c | 117 |
1 files changed, 117 insertions, 0 deletions
diff --git a/gsl-1.9/roots/secant.c b/gsl-1.9/roots/secant.c new file mode 100644 index 0000000..c44eea5 --- /dev/null +++ b/gsl-1.9/roots/secant.c @@ -0,0 +1,117 @@ +/* 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; |