/* 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 "gsl__config.h"
#include <stdlib.h>
#include <string.h>
#include "gsl_math.h"
#include "gsl_errno.h"
#include "gsl_ode-initval__odeiv_util.h"
#include "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;

      DBL_MEMCPY (y0, 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;
