/* roots/bisection.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.

 */

/* bisection.c -- bisection 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 f_lower, f_upper;

  }

bisection_state_t;

static int bisection_init (void * vstate, gsl_function * f, double * root, double x_lower, double x_upper);

static int bisection_iterate (void * vstate, gsl_function * f, double * root, double * x_lower, double * x_upper);

static int

bisection_init (void * vstate, gsl_function * f, double * root, double x_lower, double x_upper)

{

  bisection_state_t * state = (bisection_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

bisection_iterate (void * vstate, gsl_function * f, double * root, double * x_lower, double * x_upper)

{

  bisection_state_t * state = (bisection_state_t *) vstate;

  double x_bisect, f_bisect;

  const double x_left = *x_lower ;

  const double x_right = *x_upper ;

  const double f_lower = state->f_lower; 

  const double f_upper = state->f_upper;

  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;

    }

  x_bisect = (x_left + x_right) / 2.0;

  SAFE_FUNC_CALL (f, x_bisect, &f_bisect);

  if (f_bisect == 0.0)

    {

      *root = x_bisect;

      *x_lower = x_bisect;

      *x_upper = x_bisect;

      return GSL_SUCCESS;

    }

  /* Discard the half of the interval which doesn't contain the root. */

  if ((f_lower > 0.0 && f_bisect < 0.0) || (f_lower < 0.0 && f_bisect > 0.0))

    {

      *root = 0.5 * (x_left + x_bisect) ;

      *x_upper = x_bisect;

      state->f_upper = f_bisect;

    }

  else

    {

      *root = 0.5 * (x_bisect + x_right) ;

      *x_lower = x_bisect;

      state->f_lower = f_bisect;

    }

  return GSL_SUCCESS;

}

static const gsl_root_fsolver_type bisection_type =

{"bisection",                           /* name */

 sizeof (bisection_state_t),

 &bisection_init,

 &bisection_iterate};

const gsl_root_fsolver_type  * gsl_root_fsolver_bisection = &bisection_type;