/* ode-initval/gear1.c

 * 

 * Copyright (C) 1996, 1997, 1998, 1999, 2000 Gerard Jungman

 * 

 * 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.

 */

/* Gear 1. This is the implicit Euler a.k.a backward Euler method. */

/* Author:  G. Jungman

 */

/* Error estimation by step doubling, see eg. Ascher, U.M., Petzold,

   L.R., Computer methods for ordinary differential and

   differential-algebraic equations, SIAM, Philadelphia, 1998.

   The method is also described in eg. this reference.

*/

#include <config.h>

#include <stdlib.h>

#include <string.h>

#include <gsl/gsl_math.h>

#include <gsl/gsl_errno.h>

#include <gsl/gsl_odeiv.h>

#include "odeiv_util.h"

typedef struct

{

  double *k;

  double *y0;

  double *y0_orig;

  double *y_onestep;

}

gear1_state_t;

static void *

gear1_alloc (size_t dim)

{

  gear1_state_t *state = (gear1_state_t *) malloc (sizeof (gear1_state_t));

  if (state == 0)

    {

      GSL_ERROR_NULL ("failed to allocate space for gear1_state", GSL_ENOMEM);

    }

  state->k = (double *) malloc (dim * sizeof (double));

  if (state->k == 0)

    {

      free (state);

      GSL_ERROR_NULL ("failed to allocate space for k", GSL_ENOMEM);

    }

  state->y0 = (double *) malloc (dim * sizeof (double));

  if (state->y0 == 0)

    {

      free (state->k);

      free (state);

      GSL_ERROR_NULL ("failed to allocate space for y0", GSL_ENOMEM);

    }

  state->y0_orig = (double *) malloc (dim * sizeof (double));

  if (state->y0_orig == 0)

    {

      free (state->y0);

      free (state->k);

      free (state);

      GSL_ERROR_NULL ("failed to allocate space for y0_orig", GSL_ENOMEM);

    }

  state->y_onestep = (double *) malloc (dim * sizeof (double));

  if (state->y_onestep == 0)

    {

      free (state->y0_orig);

      free (state->y0);

      free (state->k);

      free (state);

      GSL_ERROR_NULL ("failed to allocate space for y_onestep", GSL_ENOMEM);

    }

  return state;

}

static int

gear1_step (double *y, gear1_state_t *state, 

	    const double h, const double t, 

	    const size_t dim, const gsl_odeiv_system *sys)

{

  /* Makes an implicit Euler advance with step size h.

     y0 is the initial values of variables y. 

     The implicit matrix equations to solve are:

     k = y0 + h * f(t + h, k)

     y = y0 + h * f(t + h, k)

  */

  const int iter_steps = 3;

  int nu;

  size_t i;

  double *y0 = state->y0;

  double *k = state->k;

  /* Iterative solution of k = y0 + h * f(t + h, k)

     Note: This method does not check for convergence of the

     iterative solution! 

  */

  for (nu = 0; nu < iter_steps; nu++) 

    {

      int s = GSL_ODEIV_FN_EVAL(sys, t + h, y, k);

      if (s != GSL_SUCCESS)

	{

	  return s;

	}     

      for (i=0; i

	{

	  y[i] = y0[i] + h * k[i];

	}

    }

  return GSL_SUCCESS;

}

static int

gear1_apply(void * vstate,

            size_t dim,

            double t,

            double h,

            double y[],

            double yerr[],

            const double dydt_in[],

            double dydt_out[],

            const gsl_odeiv_system * sys)

{

  gear1_state_t *state = (gear1_state_t *) vstate;

  size_t i;

  double *y0 = state->y0;

  double *y0_orig = state->y0_orig;

  double *y_onestep = state->y_onestep;

  /* initialization */

  DBL_MEMCPY(y0, y, dim);

  /* Save initial values for possible failures */

  DBL_MEMCPY (y0_orig, y, dim);

  /* First traverse h with one step (save to y_onestep) */

  DBL_MEMCPY (y_onestep, y, dim);

  {

    int s = gear1_step (y_onestep, state, h, t, dim, sys);

    if (s != GSL_SUCCESS) 

      {

        return s;

      }

  }    

 /* Then with two steps with half step length (save to y) */ 

  {

    int s = gear1_step (y, state, h / 2.0, t, dim, sys);

    if (s != GSL_SUCCESS) 

      {

        /* Restore original y vector */

        DBL_MEMCPY (y, y0_orig, dim);

        return s;

      }

  }

  DBL_MEMCPY (y0, y, dim);

  {

    int s = gear1_step (y, state, h / 2.0, t + h / 2.0, dim, sys);

    if (s != GSL_SUCCESS) 

      {

        /* Restore original y vector */

        DBL_MEMCPY (y, y0_orig, dim);

        return s;

      }

  }

  /* Cleanup update */

  if (dydt_out != NULL) 

    {

      int s = GSL_ODEIV_FN_EVAL (sys, t + h, y, dydt_out);

      if (s != GSL_SUCCESS)

        {

          /* Restore original y vector */

          DBL_MEMCPY (y, y0_orig, dim);

          return s;

        } 

    }

  /* Error estimation */

  for (i = 0; i < dim; i++) 

    {

      yerr[i] = 4.0 * (y[i] - y_onestep[i]);

    }

  return GSL_SUCCESS;

}

static int

gear1_reset (void *vstate, size_t dim)

{

  gear1_state_t *state = (gear1_state_t *) vstate;

  DBL_ZERO_MEMSET (state->y_onestep, dim);

  DBL_ZERO_MEMSET (state->y0_orig, dim);

  DBL_ZERO_MEMSET (state->y0, dim);

  DBL_ZERO_MEMSET (state->k, dim);

  return GSL_SUCCESS;

}

static unsigned int

gear1_order (void *vstate)

{

  gear1_state_t *state = (gear1_state_t *) vstate;

  state = 0; /* prevent warnings about unused parameters */

  return 1;

}

static void

gear1_free (void *vstate)

{

  gear1_state_t *state = (gear1_state_t *) vstate;

  free (state->y_onestep);

  free (state->y0_orig);

  free (state->y0);

  free (state->k);

  free (state);

}

static const gsl_odeiv_step_type gear1_type = { "gear1",        /* name */

  0,                            /* can use dydt_in? */

  1,                            /* gives exact dydt_out? */

  &gear1_alloc,

  &gear1_apply,

  &gear1_reset,

  &gear1_order,

  &gear1_free

};

const gsl_odeiv_step_type *gsl_odeiv_step_gear1 = &gear1_type;