/* ode-initval/gear2.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 2 */

/* Author:  G. Jungman

 */

#include <config.h>

#include <stdlib.h>

#include <string.h>

#include <gsl/gsl_math.h>

#include <gsl/gsl_errno.h>

#include "odeiv_util.h"

#include <gsl/gsl_odeiv.h>

/* gear2 state object */

typedef struct

{

  int primed;                   /* flag indicating that yim1 is ready */

  double t_primed;              /* system was primed for this value of t */

  double last_h;                /* last step size */

  gsl_odeiv_step *primer;       /* stepper to use for priming */

  double *yim1;                 /* y_{i-1}    */

  double *k;                    /* work space */

  double *y0;                   /* work space */

  double *y0_orig;

  double *y_onestep;

  int stutter;

}

gear2_state_t;

static void *

gear2_alloc (size_t dim)

{

  gear2_state_t *state = (gear2_state_t *) malloc (sizeof (gear2_state_t));

  if (state == 0)

    {

      GSL_ERROR_NULL ("failed to allocate space for gear2_state", GSL_ENOMEM);

    }

  state->yim1 = (double *) malloc (dim * sizeof (double));

  if (state->yim1 == 0)

    {

      free (state);

      GSL_ERROR_NULL ("failed to allocate space for yim1", GSL_ENOMEM);

    }

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

  if (state->k == 0)

    {

      free (state->yim1);

      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->yim1);

      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->yim1);

      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->yim1);

      free (state);

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

    }

  state->primed = 0;

  state->primer = gsl_odeiv_step_alloc (gsl_odeiv_step_rk4imp, dim);

  if (state->primer == 0)

    {

      free (state->y_onestep);

      free (state->y0_orig);

      free (state->y0);

      free (state->k);

      free (state->yim1);

      free (state);

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

    }

  state->last_h = 0.0;

  return state;

}

static int

gear2_step (double *y, gear2_state_t * state,

            const double h, const double t,

            const size_t dim, const gsl_odeiv_system * sys)

{

  /* Makes a Gear2 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 *yim1 = state->yim1;

  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 < dim; i++)

        {

          y[i] = ((4.0 * y0[i] - yim1[i]) + 2.0 * h * k[i]) / 3.0;

        }

    }

  return GSL_SUCCESS;

}

static int

gear2_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)

{

  gear2_state_t *state = (gear2_state_t *) vstate;

  state->stutter = 0;

  if (state->primed == 0 || t == state->t_primed || h != state->last_h)

    {

      /* Execute a single-step method to prime the process.  Note that

       * we do this if the step size changes, so frequent step size

       * changes will cause the method to stutter. 

       * 

       * Note that we reuse this method if the time has not changed,

       * which can occur when the adaptive driver is attempting to find

       * an appropriate step-size on its first iteration */

      int status;

      DBL_MEMCPY (state->yim1, y, dim);

      status =

        gsl_odeiv_step_apply (state->primer, t, h, y, yerr, dydt_in, dydt_out,

                              sys);

      /* Make note of step size and indicate readiness for a Gear step. */

      state->primed = 1;

      state->t_primed = t;

      state->last_h = h;

      state->stutter = 1;

      return status;

    }

  else

    {

      /* We have a previous y value in the buffer, and the step

       * sizes match, so we go ahead with the Gear step.

       */

      double *const k = state->k;

      double *const y0 = state->y0;

      double *const y0_orig = state->y0_orig;

      double *const yim1 = state->yim1;

      double *y_onestep = state->y_onestep;

      int s;

      size_t i;

      /* initialization */

      DBL_MEMCPY (y0, y, dim);

      /* Save initial values for possible failures */

      DBL_MEMCPY (y0_orig, y, dim);

      /* iterative solution */

      if (dydt_out != NULL)

        {

          DBL_MEMCPY (k, dydt_out, dim);

        }

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

      DBL_MEMCPY (y_onestep, y, dim);

      s = gear2_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) */

      s = gear2_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);

      s = gear2_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)

        {

          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;

            }

        }

      /* Estimate error and update the state buffer. */

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

        {

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

          yim1[i] = y0[i];

        }

      /* Make note of step size. */

      state->last_h = h;

      return 0;

    }

}

static int

gear2_reset (void *vstate, size_t dim)

{

  gear2_state_t *state = (gear2_state_t *) vstate;

  DBL_ZERO_MEMSET (state->yim1, dim);

  DBL_ZERO_MEMSET (state->k, dim);

  DBL_ZERO_MEMSET (state->y0, dim);

  state->primed = 0;

  state->last_h = 0.0;

  return GSL_SUCCESS;

}

static unsigned int

gear2_order (void *vstate)

{

  gear2_state_t *state = (gear2_state_t *) vstate;

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

  return 3;

}

static void

gear2_free (void *vstate)

{

  gear2_state_t *state = (gear2_state_t *) vstate;

  free (state->yim1);

  free (state->k);

  free (state->y0);

  free (state->y0_orig);

  free (state->y_onestep);

  gsl_odeiv_step_free (state->primer);

  free (state);

}

static const gsl_odeiv_step_type gear2_type = { "gear2",        /* name */

  1,                            /* can use dydt_in */

  0,                            /* gives exact dydt_out */

  &gear2_alloc,

  &gear2_apply,

  &gear2_reset,

  &gear2_order,

  &gear2_free

};

const gsl_odeiv_step_type *gsl_odeiv_step_gear2 = &gear2_type;