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Diffstat (limited to 'gsl-1.9/min/brent.c')
| -rw-r--r-- | gsl-1.9/min/brent.c | 223 |
1 files changed, 223 insertions, 0 deletions
diff --git a/gsl-1.9/min/brent.c b/gsl-1.9/min/brent.c new file mode 100644 index 0000000..499e015 --- /dev/null +++ b/gsl-1.9/min/brent.c @@ -0,0 +1,223 @@ +/* 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; |