/* interpolation/interp_poly.c

 * 

 * Copyright (C) 2001 DAN, HO-JIN

 * Copyright (C) 2013 Patrick Alken

 * 

 * 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.

 */

/* Modified for standalone use in polynomial directory, B.Gough 2001 */

#include <config.h>

#include <gsl/gsl_errno.h>

#include <gsl/gsl_poly.h>

int

gsl_poly_dd_init (double dd[], const double xa[], const double ya[],

                  size_t size)

{

  size_t i, j;

  /* Newton's divided differences */

  dd[0] = ya[0];

  for (j = size - 1; j >= 1; j--)

    {

      dd[j] = (ya[j] - ya[j - 1]) / (xa[j] - xa[j - 1]);

    }

  for (i = 2; i < size; i++)

    {

      for (j = size - 1; j >= i; j--)

        {

          dd[j] = (dd[j] - dd[j - 1]) / (xa[j] - xa[j - i]);

        }

    }

  return GSL_SUCCESS;

}

int

gsl_poly_dd_taylor (double c[], double xp, 

                    const double dd[], const double xa[], size_t size,

                    double w[])

{

  size_t i, j;

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

    {

      c[i] = 0.0;

      w[i] = 0.0;

    }

  w[size - 1] = 1.0;

  c[0] = dd[0];

  for (i = size - 1; i-- > 0;)

    {

      w[i] = -w[i + 1] * (xa[size - 2 - i] - xp);

      for (j = i + 1; j < size - 1; j++)

        {

          w[j] = w[j] - w[j + 1] * (xa[size - 2 - i] - xp);

        }

      for (j = i; j < size; j++)

        {

          c[j - i] += w[j] * dd[size - i - 1];

        }

    }

  return GSL_SUCCESS;

}

/*

gsl_poly_dd_hermite_init()

  Compute divided difference representation of data

for Hermite polynomial interpolation

Inputs: dd   - (output) array of size 2*size containing

               divided differences, dd[k] = f[z_0,z_1,...,z_k]

        za   - (output) array of size 2*size containing

               z values

        xa   - x data

        ya   - y data

        dya  - dy/dx data

        size - size of xa,ya,dya arrays

Return: success

*/

int

gsl_poly_dd_hermite_init (double dd[], double za[], const double xa[], const double ya[],

                          const double dya[], const size_t size)

{

  const size_t N = 2 * size;

  size_t i, j;

  /* Hermite divided differences */

  dd[0] = ya[0];

  /* compute: dd[j] = f[z_{j-1},z_j] for j \in [1,N-1] */

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

    {

      za[2*j] = xa[j];

      za[2*j + 1] = xa[j];

      if (j != 0)

        {

          dd[2*j] = (ya[j] - ya[j - 1]) / (xa[j] - xa[j - 1]);

          dd[2*j - 1] = dya[j - 1];

        }

    }

  dd[N - 1] = dya[size - 1];

  for (i = 2; i < N; i++)

    {

      for (j = N - 1; j >= i; j--)

        {

          dd[j] = (dd[j] - dd[j - 1]) / (za[j] - za[j - i]);

        }

    }

  return GSL_SUCCESS;

} /* gsl_poly_dd_hermite_init() */