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/* 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;
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