brent.c

Go to the documentation of this file.

/* min/brent.c
 *
 * Copyright (C) 1996, 1997, 1998, 1999, 2000 Brian Gough
 *
 * Taken from 'GSL - The GNU Scientific Library':
 *             "One dimensional Minimization"
 *             http://sources.redhat.com/gsl/
 * modified by Stefano Menegon 2004
 *
 * 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
 */
 
#include <stdlib.h>
#include <stdio.h>
#include <math.h>
#include <float.h>
 
#define GSL_SQRT_DBL_EPSILON 1.e-4
#define GSL_DBL_EPSILON      1.e-8
 
/*
   #define SAFE_FUNC_CALL(f, x, yp) \
   do { \
   *yp = GSL_FN_EVAL(f,x); \
   if (!finite(*yp)) \
   fprintf(stderr,"function not continuous\n");\
   } while (0)
 */
 
typedef struct {
    double d, e, v, w;
    double f_v, f_w;
} brent_state_t;
 
static int brent(void *vstate, double (*f)(double), 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 - z) < 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); */
    f_u = (*f)(u);
 
    if (f_u > f_z) {
        if (u < z) {
            *x_lower = u;
            *f_lower = f_u;
            return 0;
        }
        else {
            *x_upper = u;
            *f_upper = f_u;
            return 0;
        }
    }
    else 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 0;
    }
    else if (f_u <= f_w || w == z) {
        state->v = w;
        state->f_v = f_w;
        state->w = u;
        state->f_w = f_u;
        return 0;
    }
    else if (f_u <= f_v || v == z || v == w) {
        state->v = u;
        state->f_v = f_u;
        return 0;
    }
    else {
        return -1;
    }
}
 
/* Code modified by Stefano Menegon 1st of February 2004 */
 
double brent_iterate(double (*f)(double), double x_lower, double x_upper,
                     int maxiter)
{
    int i;
    double x_minimum = (x_upper + x_lower) / 2.;
    double f_minimum;
    double f_lower;
    double f_upper;
 
    /* stato iterazione */
    brent_state_t itstate;
    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;
 
    f_lower = (*f)(x_lower);
    f_upper = (*f)(x_upper);
    f_minimum = (*f)(x_minimum);
 
    itstate.v = v;
    itstate.w = w;
 
    itstate.d = 0.;
    itstate.e = 0.;
 
    /*  SAFE_FUNC_CALL (f, v, &f_vw); */
 
    f_vw = (*f)(v);
 
    itstate.f_v = f_vw;
    itstate.f_w = f_vw;
 
    for (i = 0; i < maxiter; i++) {
        brent(&itstate, f, &x_minimum, &f_minimum, &x_lower, &f_lower, &x_upper,
              &f_upper);
        if (fabs(f_upper - f_lower) < GSL_DBL_EPSILON * fabs(f_minimum)) {
            return x_minimum;
        }
    }
 
    return x_minimum;
}