/* 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;