| /* min/brent.c |
| * |
| * Copyright (C) 1996, 1997, 1998, 1999, 2000 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. |
| */ |
| |
| /* brent.c -- brent minimum finding algorithm */ |
| |
| #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_min.h> |
| |
| #include "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; |