/* ode-initval/rk2.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 2(3), Euler-Cauchy */

/* Author:  G. Jungman

 */

/* Reference: Abramowitz & Stegun, section 25.5. Runge-Kutta 2nd (25.5.7)

   and 3rd (25.5.8) order methods */

#include <config.h>

#include <stdlib.h>

#include <string.h>

#include <gsl/gsl_errno.h>

#include <gsl/gsl_odeiv2.h>

#include "odeiv_util.h"

#include "step_utils.c"

typedef struct

{

  double *k1;

  double *k2;

  double *k3;

  double *ytmp;

}

rk2_state_t;

static void *

rk2_alloc (size_t dim)

{

  rk2_state_t *state = (rk2_state_t *) malloc (sizeof (rk2_state_t));

  if (state == 0)

    {

      GSL_ERROR_NULL ("failed to allocate space for rk2_state", GSL_ENOMEM);

    }

  state->k1 = (double *) malloc (dim * sizeof (double));

  if (state->k1 == 0)

    {

      free (state);

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

    }

  state->k2 = (double *) malloc (dim * sizeof (double));

  if (state->k2 == 0)

    {

      free (state->k1);

      free (state);

      GSL_ERROR_NULL ("failed to allocate space for k2", GSL_ENOMEM);

    }

  state->k3 = (double *) malloc (dim * sizeof (double));

  if (state->k3 == 0)

    {

      free (state->k2);

      free (state->k1);

      free (state);

      GSL_ERROR_NULL ("failed to allocate space for k3", GSL_ENOMEM);

    }

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

  if (state->ytmp == 0)

    {

      free (state->k3);

      free (state->k2);

      free (state->k1);

      free (state);

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

    }

  return state;

}

static int

rk2_apply (void *vstate,

           size_t dim,

           double t,

           double h,

           double y[],

           double yerr[],

           const double dydt_in[],

           double dydt_out[], const gsl_odeiv2_system * sys)

{

  rk2_state_t *state = (rk2_state_t *) vstate;

  size_t i;

  double *const k1 = state->k1;

  double *const k2 = state->k2;

  double *const k3 = state->k3;

  double *const ytmp = state->ytmp;

  /* k1 step */

  /* k1 = f(t,y) */

  if (dydt_in != NULL)

    {

      DBL_MEMCPY (k1, dydt_in, dim);

    }

  else

    {

      int s = GSL_ODEIV_FN_EVAL (sys, t, y, k1);

      if (s != GSL_SUCCESS)

        {

          return s;

        }

    }

  /* k2 step */

  /* k2 = f(t + 0.5*h, y + 0.5*k1) */

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

    {

      ytmp[i] = y[i] + 0.5 * h * k1[i];

    }

  {

    int s = GSL_ODEIV_FN_EVAL (sys, t + 0.5 * h, ytmp, k2);

    if (s != GSL_SUCCESS)

      {

        return s;

      }

  }

  /* k3 step */

  /* for 3rd order estimates, is used for error estimation

     k3 = f(t + h, y - k1 + 2*k2) */

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

    {

      ytmp[i] = y[i] + h * (-k1[i] + 2.0 * k2[i]);

    }

  {

    int s = GSL_ODEIV_FN_EVAL (sys, t + h, ytmp, k3);

    if (s != GSL_SUCCESS)

      {

        return s;

      }

  }

  /* final sum */

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

    {

      /* Save original values if derivative evaluation below fails */

      ytmp[i] = y[i];

      {

        const double ksum3 = (k1[i] + 4.0 * k2[i] + k3[i]) / 6.0;

        y[i] += h * ksum3;

      }

    }

  /* 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, ytmp, dim);

          return s;

        }

    }

  /* Error estimation */

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

    {

      const double ksum3 = (k1[i] + 4.0 * k2[i] + k3[i]) / 6.0;

      yerr[i] = h * (k2[i] - ksum3);

    }

  return GSL_SUCCESS;

}

static int

rk2_reset (void *vstate, size_t dim)

{

  rk2_state_t *state = (rk2_state_t *) vstate;

  DBL_ZERO_MEMSET (state->k1, dim);

  DBL_ZERO_MEMSET (state->k2, dim);

  DBL_ZERO_MEMSET (state->k3, dim);

  DBL_ZERO_MEMSET (state->ytmp, dim);

  return GSL_SUCCESS;

}

static unsigned int

rk2_order (void *vstate)

{

  rk2_state_t *state = (rk2_state_t *) vstate;

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

  return 2;

}

static void

rk2_free (void *vstate)

{

  rk2_state_t *state = (rk2_state_t *) vstate;

  free (state->k1);

  free (state->k2);

  free (state->k3);

  free (state->ytmp);

  free (state);

}

static const gsl_odeiv2_step_type rk2_type = { "rk2",   /* name */

  1,                            /* can use dydt_in */

  1,                            /* gives exact dydt_out */

  &rk2_alloc,

  &rk2_apply,

  &stepper_set_driver_null,

  &rk2_reset,

  &rk2_order,

  &rk2_free

};

const gsl_odeiv2_step_type *gsl_odeiv2_step_rk2 = &rk2_type;