/* ode-initval2/rksubs.c

 * 

 * Copyright (C) 2008, 2009, 2010 Tuomo Keskitalo

 * 

 * 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.

 */

static int

rksubs (double y[], const double h, const double y0[], const double fY[],

        const double b[], const size_t stage, const size_t dim)

{

  /* The final substitution step in Runge-Kutta equation:

     Calculates new values y by substituting the value of step size

     (h), current initial values of y (y0), function f values at

     Runge-Kutta points (fY), Runge-Kutta b-coefficients (b) and

     method stage (stage) into the equation

     y = y0 + h * sum j=1..stage (b_j * fY_j)

     dim is the number of ODEs.

   */

  size_t i, j;

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

    {

      y[i] = 0.0;

      for (j = 0; j < stage; j++)

        y[i] += b[j] * fY[j * dim + i];

    }

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

    {

      y[i] *= h;

      y[i] += y0[i];

    }

  return GSL_SUCCESS;

}