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/* roots/brent.c
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*
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* Copyright (C) 1996, 1997, 1998, 1999, 2000, 2007 Reid Priedhorsky, Brian Gough
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*
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* This program is free software; you can redistribute it and/or modify
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* it under the terms of the GNU General Public License as published by
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* the Free Software Foundation; either version 3 of the License, or (at
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* your option) any later version.
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*
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* This program is distributed in the hope that it will be useful, but
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* WITHOUT ANY WARRANTY; without even the implied warranty of
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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* General Public License for more details.
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*
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* You should have received a copy of the GNU General Public License
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* along with this program; if not, write to the Free Software
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* Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
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*/
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/* brent.c -- brent root finding algorithm */
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#include <config.h>
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#include <stddef.h>
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#include <stdlib.h>
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#include <stdio.h>
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#include <math.h>
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#include <float.h>
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#include <gsl/gsl_math.h>
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#include <gsl/gsl_errno.h>
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#include <gsl/gsl_roots.h>
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#include "roots.h"
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typedef struct
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{
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double a, b, c, d, e;
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double fa, fb, fc;
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}
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brent_state_t;
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static int brent_init (void * vstate, gsl_function * f, double * root, double x_lower, double x_upper);
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static int brent_iterate (void * vstate, gsl_function * f, double * root, double * x_lower, double * x_upper);
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static int
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brent_init (void * vstate, gsl_function * f, double * root, double x_lower, double x_upper)
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{
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brent_state_t * state = (brent_state_t *) vstate;
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double f_lower, f_upper ;
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*root = 0.5 * (x_lower + x_upper) ;
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SAFE_FUNC_CALL (f, x_lower, &f_lower);
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SAFE_FUNC_CALL (f, x_upper, &f_upper);
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state->a = x_lower;
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state->fa = f_lower;
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state->b = x_upper;
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state->fb = f_upper;
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state->c = x_upper;
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state->fc = f_upper;
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state->d = x_upper - x_lower ;
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state->e = x_upper - x_lower ;
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if ((f_lower < 0.0 && f_upper < 0.0) || (f_lower > 0.0 && f_upper > 0.0))
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{
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GSL_ERROR ("endpoints do not straddle y=0", GSL_EINVAL);
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}
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return GSL_SUCCESS;
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}
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static int
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brent_iterate (void * vstate, gsl_function * f, double * root, double * x_lower, double * x_upper)
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{
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brent_state_t * state = (brent_state_t *) vstate;
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double tol, m;
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int ac_equal = 0;
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double a = state->a, b = state->b, c = state->c;
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double fa = state->fa, fb = state->fb, fc = state->fc;
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double d = state->d, e = state->e;
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if ((fb < 0 && fc < 0) || (fb > 0 && fc > 0))
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{
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ac_equal = 1;
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c = a;
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fc = fa;
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d = b - a;
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e = b - a;
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}
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if (fabs (fc) < fabs (fb))
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{
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ac_equal = 1;
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a = b;
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b = c;
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c = a;
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fa = fb;
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fb = fc;
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fc = fa;
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}
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tol = 0.5 * GSL_DBL_EPSILON * fabs (b);
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m = 0.5 * (c - b);
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if (fb == 0)
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{
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*root = b;
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*x_lower = b;
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*x_upper = b;
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return GSL_SUCCESS;
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}
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if (fabs (m) <= tol)
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{
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*root = b;
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if (b < c)
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{
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*x_lower = b;
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*x_upper = c;
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}
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else
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{
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*x_lower = c;
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*x_upper = b;
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}
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return GSL_SUCCESS;
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}
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if (fabs (e) < tol || fabs (fa) <= fabs (fb))
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{
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d = m; /* use bisection */
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e = m;
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}
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else
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{
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double p, q, r; /* use inverse cubic interpolation */
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double s = fb / fa;
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if (ac_equal)
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{
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p = 2 * m * s;
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q = 1 - s;
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}
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else
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{
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q = fa / fc;
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r = fb / fc;
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p = s * (2 * m * q * (q - r) - (b - a) * (r - 1));
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q = (q - 1) * (r - 1) * (s - 1);
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}
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if (p > 0)
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{
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q = -q;
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}
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else
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{
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p = -p;
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}
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if (2 * p < GSL_MIN (3 * m * q - fabs (tol * q), fabs (e * q)))
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{
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e = d;
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d = p / q;
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}
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else
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{
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/* interpolation failed, fall back to bisection */
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d = m;
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e = m;
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}
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}
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a = b;
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fa = fb;
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if (fabs (d) > tol)
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{
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b += d;
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}
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else
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{
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b += (m > 0 ? +tol : -tol);
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}
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SAFE_FUNC_CALL (f, b, &fb;;
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state->a = a ;
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state->b = b ;
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state->c = c ;
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state->d = d ;
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state->e = e ;
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state->fa = fa ;
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state->fb = fb ;
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state->fc = fc ;
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/* Update the best estimate of the root and bounds on each
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iteration */
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*root = b;
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if ((fb < 0 && fc < 0) || (fb > 0 && fc > 0))
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{
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c = a;
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}
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if (b < c)
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{
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*x_lower = b;
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*x_upper = c;
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}
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else
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{
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*x_lower = c;
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*x_upper = b;
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}
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return GSL_SUCCESS ;
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}
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static const gsl_root_fsolver_type brent_type =
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{"brent", /* name */
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sizeof (brent_state_t),
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&brent_init,
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&brent_iterate};
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const gsl_root_fsolver_type * gsl_root_fsolver_brent = &brent_type;
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