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/* 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() */
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