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/* roots/falsepos.c
*
* Copyright (C) 1996, 1997, 1998, 1999, 2000, 2007 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 3 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.
*/
/* falsepos.c -- falsepos root finding algorithm
The false position algorithm uses bracketing by linear interpolation.
If a linear interpolation step would decrease the size of the
bracket by less than a bisection step would then the algorithm
takes a bisection step instead.
The last linear interpolation estimate of the root is used. If a
bisection step causes it to fall outside the brackets then it is
replaced by the bisection estimate (x_upper + x_lower)/2.
*/
#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 f_lower, f_upper;
}
falsepos_state_t;
static int falsepos_init (void * vstate, gsl_function * f, double * root, double x_lower, double x_upper);
static int falsepos_iterate (void * vstate, gsl_function * f, double * root, double * x_lower, double * x_upper);
static int
falsepos_init (void * vstate, gsl_function * f, double * root, double x_lower, double x_upper)
{
falsepos_state_t * state = (falsepos_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->f_lower = f_lower;
state->f_upper = f_upper;
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
falsepos_iterate (void * vstate, gsl_function * f, double * root, double * x_lower, double * x_upper)
{
falsepos_state_t * state = (falsepos_state_t *) vstate;
double x_linear, f_linear;
double x_bisect, f_bisect;
double x_left = *x_lower ;
double x_right = *x_upper ;
double f_lower = state->f_lower;
double f_upper = state->f_upper;
double w ;
if (f_lower == 0.0)
{
*root = x_left ;
*x_upper = x_left;
return GSL_SUCCESS;
}
if (f_upper == 0.0)
{
*root = x_right ;
*x_lower = x_right;
return GSL_SUCCESS;
}
/* Draw a line between f(*lower_bound) and f(*upper_bound) and
note where it crosses the X axis; that's where we will
split the interval. */
x_linear = x_right - (f_upper * (x_left - x_right) / (f_lower - f_upper));
SAFE_FUNC_CALL (f, x_linear, &f_linear);
if (f_linear == 0.0)
{
*root = x_linear;
*x_lower = x_linear;
*x_upper = x_linear;
return GSL_SUCCESS;
}
/* Discard the half of the interval which doesn't contain the root. */
if ((f_lower > 0.0 && f_linear < 0.0) || (f_lower < 0.0 && f_linear > 0.0))
{
*root = x_linear ;
*x_upper = x_linear;
state->f_upper = f_linear;
w = x_linear - x_left ;
}
else
{
*root = x_linear ;
*x_lower = x_linear;
state->f_lower = f_linear;
w = x_right - x_linear;
}
if (w < 0.5 * (x_right - x_left))
{
return GSL_SUCCESS ;
}
x_bisect = 0.5 * (x_left + x_right);
SAFE_FUNC_CALL (f, x_bisect, &f_bisect);
if ((f_lower > 0.0 && f_bisect < 0.0) || (f_lower < 0.0 && f_bisect > 0.0))
{
*x_upper = x_bisect;
state->f_upper = f_bisect;
if (*root > x_bisect)
*root = 0.5 * (x_left + x_bisect) ;
}
else
{
*x_lower = x_bisect;
state->f_lower = f_bisect;
if (*root < x_bisect)
*root = 0.5 * (x_bisect + x_right) ;
}
return GSL_SUCCESS;
}
static const gsl_root_fsolver_type falsepos_type =
{"falsepos", /* name */
sizeof (falsepos_state_t),
&falsepos_init,
&falsepos_iterate};
const gsl_root_fsolver_type * gsl_root_fsolver_falsepos = &falsepos_type;
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