/* ode-initval/rk4.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.

 */

/* Runge-Kutta 4th order, Classical */

/* Author:  G. Jungman

 */

/* Reference: Abramowitz & Stegun, section 25.5. equation 25.5.10 

   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.

*/

#include <config.h>

#include <stdlib.h>

#include <string.h>

#include <gsl/gsl_errno.h>

#include <gsl/gsl_odeiv.h>

#include "odeiv_util.h"

typedef struct

{

  double *k;

  double *k1;

  double *y0;

  double *ytmp;

  double *y_onestep;

}

rk4_state_t;

static void *

rk4_alloc (size_t dim)

{

  rk4_state_t *state = (rk4_state_t *) malloc (sizeof (rk4_state_t));

  if (state == 0)

    {

      GSL_ERROR_NULL ("failed to allocate space for rk4_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->k1 = (double *) malloc (dim * sizeof (double));

  if (state->k1 == 0)

    {

      free (state->k);

      free (state);

      GSL_ERROR_NULL ("failed to allocate space for k1", GSL_ENOMEM);

    }

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

  if (state->y0 == 0)

    {

      free (state->k);

      free (state->k1);

      free (state);

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

    }

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

  if (state->ytmp == 0)

    {

      free (state->y0);

      free (state->k);

      free (state->k1);

      free (state);

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

    }

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

  if (state->y_onestep == 0)

    {

      free (state->ytmp);

      free (state->y0);

      free (state->k);

      free (state->k1);

      free (state);

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

    }

  return state;

}

static int

rk4_step (double *y, const rk4_state_t *state,

	  const double h, const double t, const size_t dim,

	  const gsl_odeiv_system *sys)

{

  /* Makes a Runge-Kutta 4th order advance with step size h. */

  /* initial values of variables y. */

  const double *y0 = state->y0;

  /* work space */

  double *ytmp = state->ytmp;

  /* Runge-Kutta coefficients. Contains values of coefficient k1

     in the beginning 

  */

  double *k = state->k;

  size_t i;

  /* k1 step */

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

    {

      y[i] += h / 6.0 * k[i];

      ytmp[i] = y0[i] + 0.5 * h * k[i];

    }

  /* k2 step */

  {

    int s = GSL_ODEIV_FN_EVAL (sys, t + 0.5 * h, ytmp, k);

    if (s != GSL_SUCCESS)

      {

	return s;

      }

  }

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

    {

      y[i] += h / 3.0 * k[i];

      ytmp[i] = y0[i] + 0.5 * h * k[i];

    }

  /* k3 step */

  {

    int s = GSL_ODEIV_FN_EVAL (sys, t + 0.5 * h, ytmp, k);

    if (s != GSL_SUCCESS)

      {

	return s;

      }

  }

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

    {

      y[i] += h / 3.0 * k[i];

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

    }

  /* k4 step */

  {

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

    if (s != GSL_SUCCESS)

      {

	return s;

      }

  }

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

    {

      y[i] += h / 6.0 * k[i];

    }

  return GSL_SUCCESS;

}

static int

rk4_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)

{

  rk4_state_t *state = (rk4_state_t *) vstate;

  size_t i;

  double *const k = state->k;

  double *const k1 = state->k1;

  double *const y0 = state->y0;

  double *const y_onestep = state->y_onestep;

  DBL_MEMCPY (y0, y, dim);

  if (dydt_in != NULL)

    {

      DBL_MEMCPY (k, dydt_in, dim);

    }

  else

    {

      int s = GSL_ODEIV_FN_EVAL (sys, t, y0, k);

      if (s != GSL_SUCCESS)

	{

	  return s;

	}

    }

  /* Error estimation is done by step doubling procedure */

  /* Save first point derivatives*/

  DBL_MEMCPY (k1, k, dim);

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

  DBL_MEMCPY (y_onestep, y, dim);

  {

    int s = rk4_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) */ 

  DBL_MEMCPY (k, k1, dim);

  {

    int s = rk4_step (y, state, h/2.0, t, dim, sys);

    if (s != GSL_SUCCESS)

      {

	/* Restore original values */

	DBL_MEMCPY (y, y0, dim);

	return s;

    }

  }

  /* Update before second step */

  {

    int s = GSL_ODEIV_FN_EVAL (sys, t + h/2.0, y, k);

    if (s != GSL_SUCCESS)

      {

	/* Restore original values */

	DBL_MEMCPY (y, y0, dim);

	return s;

      }

  }

  /* Save original y0 to k1 for possible failures */

  DBL_MEMCPY (k1, y0, dim);

  /* Update y0 for second step */

  DBL_MEMCPY (y0, y, dim);

  {

    int s = rk4_step (y, state, h/2.0, t + h/2.0, dim, sys);

    if (s != GSL_SUCCESS)

      {

	/* Restore original values */

	DBL_MEMCPY (y, k1, dim);

	return s;

      }

  }

  /* Derivatives at output */

  if (dydt_out != NULL) {

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

    if (s != GSL_SUCCESS)

      {

	/* Restore original values */

	DBL_MEMCPY (y, k1, dim);

	return s;

      }

  }

  /* Error estimation

     yerr = C * 0.5 * | y(onestep) - y(twosteps) | / (2^order - 1)

     constant C is approximately 8.0 to ensure 90% of samples lie within

     the error (assuming a gaussian distribution with prior p(sigma)=1/sigma.)

  */

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

    {

      yerr[i] = 4.0 * (y[i] - y_onestep[i]) / 15.0;

    }

  return GSL_SUCCESS;

}

static int

rk4_reset (void *vstate, size_t dim)

{

  rk4_state_t *state = (rk4_state_t *) vstate;

  DBL_ZERO_MEMSET (state->k, dim);

  DBL_ZERO_MEMSET (state->k1, dim);

  DBL_ZERO_MEMSET (state->y0, dim);

  DBL_ZERO_MEMSET (state->ytmp, dim);

  DBL_ZERO_MEMSET (state->y_onestep, dim);

  return GSL_SUCCESS;

}

static unsigned int

rk4_order (void *vstate)

{

  rk4_state_t *state = (rk4_state_t *) vstate;

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

  return 4;

}

static void

rk4_free (void *vstate)

{

  rk4_state_t *state = (rk4_state_t *) vstate;

  free (state->k);

  free (state->k1);

  free (state->y0);

  free (state->ytmp);

  free (state->y_onestep);

  free (state);

}

static const gsl_odeiv_step_type rk4_type = { "rk4",    /* name */

  1,                            /* can use dydt_in */

  1,                            /* gives exact dydt_out */

  &rk4_alloc,

  &rk4_apply,

  &rk4_reset,

  &rk4_order,

  &rk4_free

};

const gsl_odeiv_step_type *gsl_odeiv_step_rk4 = &rk4_type;