| /* roots/brent.c |
| * |
| * Copyright (C) 1996, 1997, 1998, 1999, 2000 Reid Priedhorsky, 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 root 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_roots.h> |
| |
| #include "roots.h" |
| |
| |
| typedef struct |
| { |
| double a, b, c, d, e; |
| double fa, fb, fc; |
| } |
| brent_state_t; |
| |
| static int brent_init (void * vstate, gsl_function * f, double * root, double x_lower, double x_upper); |
| static int brent_iterate (void * vstate, gsl_function * f, double * root, double * x_lower, double * x_upper); |
| |
| |
| static int |
| brent_init (void * vstate, gsl_function * f, double * root, double x_lower, double x_upper) |
| { |
| brent_state_t * state = (brent_state_t *) vstate; |
| |
| double f_lower, f_upper ; |
| |
| *root = 0.5 * (x_lower + x_upper) ; |
| |
| SAFE_FUNC_CALL (f, x_lower, &f_lower); |
| SAFE_FUNC_CALL (f, x_upper, &f_upper); |
| |
| state->a = x_lower; |
| state->fa = f_lower; |
| |
| state->b = x_upper; |
| state->fb = f_upper; |
| |
| state->c = x_upper; |
| state->fc = f_upper; |
| |
| state->d = x_upper - x_lower ; |
| state->e = x_upper - x_lower ; |
| |
| if ((f_lower < 0.0 && f_upper < 0.0) || (f_lower > 0.0 && f_upper > 0.0)) |
| { |
| GSL_ERROR ("endpoints do not straddle y=0", GSL_EINVAL); |
| } |
| |
| return GSL_SUCCESS; |
| |
| } |
| |
| static int |
| brent_iterate (void * vstate, gsl_function * f, double * root, double * x_lower, double * x_upper) |
| { |
| brent_state_t * state = (brent_state_t *) vstate; |
| |
| double tol, m; |
| |
| int ac_equal = 0; |
| |
| double a = state->a, b = state->b, c = state->c; |
| double fa = state->fa, fb = state->fb, fc = state->fc; |
| double d = state->d, e = state->e; |
| |
| if ((fb < 0 && fc < 0) || (fb > 0 && fc > 0)) |
| { |
| ac_equal = 1; |
| c = a; |
| fc = fa; |
| d = b - a; |
| e = b - a; |
| } |
| |
| if (fabs (fc) < fabs (fb)) |
| { |
| ac_equal = 1; |
| a = b; |
| b = c; |
| c = a; |
| fa = fb; |
| fb = fc; |
| fc = fa; |
| } |
| |
| tol = 0.5 * GSL_DBL_EPSILON * fabs (b); |
| m = 0.5 * (c - b); |
| |
| if (fb == 0) |
| { |
| *root = b; |
| *x_lower = b; |
| *x_upper = b; |
| |
| return GSL_SUCCESS; |
| } |
| |
| if (fabs (m) <= tol) |
| { |
| *root = b; |
| |
| if (b < c) |
| { |
| *x_lower = b; |
| *x_upper = c; |
| } |
| else |
| { |
| *x_lower = c; |
| *x_upper = b; |
| } |
| |
| return GSL_SUCCESS; |
| } |
| |
| if (fabs (e) < tol || fabs (fa) <= fabs (fb)) |
| { |
| d = m; /* use bisection */ |
| e = m; |
| } |
| else |
| { |
| double p, q, r; /* use inverse cubic interpolation */ |
| double s = fb / fa; |
| |
| if (ac_equal) |
| { |
| p = 2 * m * s; |
| q = 1 - s; |
| } |
| else |
| { |
| q = fa / fc; |
| r = fb / fc; |
| p = s * (2 * m * q * (q - r) - (b - a) * (r - 1)); |
| q = (q - 1) * (r - 1) * (s - 1); |
| } |
| |
| if (p > 0) |
| { |
| q = -q; |
| } |
| else |
| { |
| p = -p; |
| } |
| |
| if (2 * p < GSL_MIN (3 * m * q - fabs (tol * q), fabs (e * q))) |
| { |
| e = d; |
| d = p / q; |
| } |
| else |
| { |
| /* interpolation failed, fall back to bisection */ |
| |
| d = m; |
| e = m; |
| } |
| } |
| |
| a = b; |
| fa = fb; |
| |
| if (fabs (d) > tol) |
| { |
| b += d; |
| } |
| else |
| { |
| b += (m > 0 ? +tol : -tol); |
| } |
| |
| SAFE_FUNC_CALL (f, b, &fb); |
| |
| state->a = a ; |
| state->b = b ; |
| state->c = c ; |
| state->d = d ; |
| state->e = e ; |
| state->fa = fa ; |
| state->fb = fb ; |
| state->fc = fc ; |
| |
| /* Update the best estimate of the root and bounds on each |
| iteration */ |
| |
| *root = b; |
| |
| if ((fb < 0 && fc < 0) || (fb > 0 && fc > 0)) |
| { |
| c = a; |
| } |
| |
| if (b < c) |
| { |
| *x_lower = b; |
| *x_upper = c; |
| } |
| else |
| { |
| *x_lower = c; |
| *x_upper = b; |
| } |
| |
| return GSL_SUCCESS ; |
| } |
| |
| |
| static const gsl_root_fsolver_type brent_type = |
| {"brent", /* name */ |
| sizeof (brent_state_t), |
| &brent_init, |
| &brent_iterate}; |
| |
| const gsl_root_fsolver_type * gsl_root_fsolver_brent = &brent_type; |