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- /* roots/brent.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.
- */
- /* brent.c -- brent root finding algorithm */
- #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 a, b, c, d, e;
- double fa, fb, fc;
- }
- brent_state_t;
- static int brent_init (void * vstate, gsl_function * f, double * root, double x_lower, double x_upper);
- static int brent_iterate (void * vstate, gsl_function * f, double * root, double * x_lower, double * x_upper);
- static int
- brent_init (void * vstate, gsl_function * f, double * root, double x_lower, double x_upper)
- {
- brent_state_t * state = (brent_state_t *) vstate;
- double f_lower, f_upper ;
- *root = 0.5 * (x_lower + x_upper) ;
- SAFE_FUNC_CALL (f, x_lower, &f_lower);
- SAFE_FUNC_CALL (f, x_upper, &f_upper);
-
- state->a = x_lower;
- state->fa = f_lower;
- state->b = x_upper;
- state->fb = f_upper;
- state->c = x_upper;
- state->fc = f_upper;
- state->d = x_upper - x_lower ;
- state->e = x_upper - x_lower ;
- if ((f_lower < 0.0 && f_upper < 0.0) || (f_lower > 0.0 && f_upper > 0.0))
- {
- GSL_ERROR ("endpoints do not straddle y=0", GSL_EINVAL);
- }
- return GSL_SUCCESS;
- }
- static int
- brent_iterate (void * vstate, gsl_function * f, double * root, double * x_lower, double * x_upper)
- {
- brent_state_t * state = (brent_state_t *) vstate;
- double tol, m;
- int ac_equal = 0;
- double a = state->a, b = state->b, c = state->c;
- double fa = state->fa, fb = state->fb, fc = state->fc;
- double d = state->d, e = state->e;
-
- if ((fb < 0 && fc < 0) || (fb > 0 && fc > 0))
- {
- ac_equal = 1;
- c = a;
- fc = fa;
- d = b - a;
- e = b - a;
- }
-
- if (fabs (fc) < fabs (fb))
- {
- ac_equal = 1;
- a = b;
- b = c;
- c = a;
- fa = fb;
- fb = fc;
- fc = fa;
- }
-
- tol = 0.5 * GSL_DBL_EPSILON * fabs (b);
- m = 0.5 * (c - b);
-
- if (fb == 0)
- {
- *root = b;
- *x_lower = b;
- *x_upper = b;
-
- return GSL_SUCCESS;
- }
-
- if (fabs (m) <= tol)
- {
- *root = b;
- if (b < c)
- {
- *x_lower = b;
- *x_upper = c;
- }
- else
- {
- *x_lower = c;
- *x_upper = b;
- }
- return GSL_SUCCESS;
- }
-
- if (fabs (e) < tol || fabs (fa) <= fabs (fb))
- {
- d = m; /* use bisection */
- e = m;
- }
- else
- {
- double p, q, r; /* use inverse cubic interpolation */
- double s = fb / fa;
-
- if (ac_equal)
- {
- p = 2 * m * s;
- q = 1 - s;
- }
- else
- {
- q = fa / fc;
- r = fb / fc;
- p = s * (2 * m * q * (q - r) - (b - a) * (r - 1));
- q = (q - 1) * (r - 1) * (s - 1);
- }
-
- if (p > 0)
- {
- q = -q;
- }
- else
- {
- p = -p;
- }
-
- if (2 * p < GSL_MIN (3 * m * q - fabs (tol * q), fabs (e * q)))
- {
- e = d;
- d = p / q;
- }
- else
- {
- /* interpolation failed, fall back to bisection */
-
- d = m;
- e = m;
- }
- }
-
- a = b;
- fa = fb;
-
- if (fabs (d) > tol)
- {
- b += d;
- }
- else
- {
- b += (m > 0 ? +tol : -tol);
- }
-
- SAFE_FUNC_CALL (f, b, &fb);
- state->a = a ;
- state->b = b ;
- state->c = c ;
- state->d = d ;
- state->e = e ;
- state->fa = fa ;
- state->fb = fb ;
- state->fc = fc ;
-
- /* Update the best estimate of the root and bounds on each
- iteration */
-
- *root = b;
-
- if ((fb < 0 && fc < 0) || (fb > 0 && fc > 0))
- {
- c = a;
- }
- if (b < c)
- {
- *x_lower = b;
- *x_upper = c;
- }
- else
- {
- *x_lower = c;
- *x_upper = b;
- }
- return GSL_SUCCESS ;
- }
-
- static const gsl_root_fsolver_type brent_type =
- {"brent", /* name */
- sizeof (brent_state_t),
- &brent_init,
- &brent_iterate};
- const gsl_root_fsolver_type * gsl_root_fsolver_brent = &brent_type;
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