123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119120121122123124125126127128129130131132133134135136137138139140141142143144145146147148149150151152153154155156157158159160161162163164165166167168169170171172173174175176177178179180181182183184185186187188189190191192193194195196197198199200201202203204205206207208209210211212213214215216217218219220221222223224 |
- /* min/brent.c
- *
- * Copyright (C) 1996, 1997, 1998, 1999, 2000, 2007 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 minimum 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_min.h"
- #include "gsl_min__min.h"
- typedef struct
- {
- double d, e, v, w;
- double f_v, f_w;
- }
- brent_state_t;
- static int brent_init (void *vstate, gsl_function * f, double x_minimum, double f_minimum, double x_lower, double f_lower, double x_upper, double f_upper);
- static int brent_iterate (void *vstate, gsl_function * f, double *x_minimum, double * f_minimum, double * x_lower, double * f_lower, double * x_upper, double * f_upper);
- static int
- brent_init (void *vstate, gsl_function * f, double x_minimum, double f_minimum, double x_lower, double f_lower, double x_upper, double f_upper)
- {
- brent_state_t *state = (brent_state_t *) vstate;
- const double golden = 0.3819660; /* golden = (3 - sqrt(5))/2 */
- double v = x_lower + golden * (x_upper - x_lower);
- double w = v;
- double f_vw;
- x_minimum = 0 ; /* avoid warnings about unused varibles */
- f_minimum = 0 ;
- f_lower = 0 ;
- f_upper = 0 ;
- state->v = v;
- state->w = w;
- state->d = 0;
- state->e = 0;
- SAFE_FUNC_CALL (f, v, &f_vw);
- state->f_v = f_vw;
- state->f_w = f_vw;
- return GSL_SUCCESS;
- }
- static int
- brent_iterate (void *vstate, gsl_function * f, double *x_minimum, double * f_minimum, double * x_lower, double * f_lower, double * x_upper, double * f_upper)
- {
- brent_state_t *state = (brent_state_t *) vstate;
- const double x_left = *x_lower;
- const double x_right = *x_upper;
- const double z = *x_minimum;
- double d = state->e;
- double e = state->d;
- double u, f_u;
- const double v = state->v;
- const double w = state->w;
- const double f_v = state->f_v;
- const double f_w = state->f_w;
- const double f_z = *f_minimum;
- const double golden = 0.3819660; /* golden = (3 - sqrt(5))/2 */
- const double w_lower = (z - x_left);
- const double w_upper = (x_right - z);
- const double tolerance = GSL_SQRT_DBL_EPSILON * fabs (z);
- double p = 0, q = 0, r = 0;
- const double midpoint = 0.5 * (x_left + x_right);
- if (fabs (e) > tolerance)
- {
- /* fit parabola */
- r = (z - w) * (f_z - f_v);
- q = (z - v) * (f_z - f_w);
- p = (z - v) * q - (z - w) * r;
- q = 2 * (q - r);
- if (q > 0)
- {
- p = -p;
- }
- else
- {
- q = -q;
- }
- r = e;
- e = d;
- }
- if (fabs (p) < fabs (0.5 * q * r) && p < q * w_lower && p < q * w_upper)
- {
- double t2 = 2 * tolerance ;
- d = p / q;
- u = z + d;
- if ((u - x_left) < t2 || (x_right - u) < t2)
- {
- d = (z < midpoint) ? tolerance : -tolerance ;
- }
- }
- else
- {
- e = (z < midpoint) ? x_right - z : -(z - x_left) ;
- d = golden * e;
- }
- if (fabs (d) >= tolerance)
- {
- u = z + d;
- }
- else
- {
- u = z + ((d > 0) ? tolerance : -tolerance) ;
- }
- state->e = e;
- state->d = d;
- SAFE_FUNC_CALL(f, u, &f_u);
- if (f_u <= f_z)
- {
- if (u < z)
- {
- *x_upper = z;
- *f_upper = f_z;
- }
- else
- {
- *x_lower = z;
- *f_lower = f_z;
- }
- state->v = w;
- state->f_v = f_w;
- state->w = z;
- state->f_w = f_z;
- *x_minimum = u;
- *f_minimum = f_u;
- return GSL_SUCCESS;
- }
- else
- {
- if (u < z)
- {
- *x_lower = u;
- *f_lower = f_u;
- return GSL_SUCCESS;
- }
- else
- {
- *x_upper = u;
- *f_upper = f_u;
- return GSL_SUCCESS;
- }
- if (f_u <= f_w || w == z)
- {
- state->v = w;
- state->f_v = f_w;
- state->w = u;
- state->f_w = f_u;
- return GSL_SUCCESS;
- }
- else if (f_u <= f_v || v == z || v == w)
- {
- state->v = u;
- state->f_v = f_u;
- return GSL_SUCCESS;
- }
- }
- return GSL_FAILURE;
- }
- static const gsl_min_fminimizer_type brent_type =
- {"brent", /* name */
- sizeof (brent_state_t),
- &brent_init,
- &brent_iterate};
- const gsl_min_fminimizer_type *gsl_min_fminimizer_brent = &brent_type;
|