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/*
* Copyright (c) 2002, 2017 Jens Keiner, Stefan Kunis, Daniel Potts
*
* 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 2 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.
*/
#include "infft.h"
/**
* Compute damping factor for modified Fejer kernel:
* /f$\frac{2}{N}\left(1-\frac{\left|2k+1\right|}{N}\right)/f$
*/
R Y(modified_fejer)(const INT N, const INT kk)
{
return (K(2.0) / ((R) (N * N))
* (K(1.0) - FABS(K(2.0) * ((R) kk) + K(1.0) ) / ((R) N)));
}
/** Compute damping factor for modified Jackson kernel. */
R Y(modified_jackson2)(const INT N, const INT kk)
{
INT kj;
const R n = (((R) N) / K(2.0) + K(1.0) ) / K(2.0);
R result, k;
for (result = K(0.0), kj = kk; kj <= kk + 1; kj++)
{
k = (R)(ABS(kj));
if (k / n < K(1.0) )
result += K(1.0)
- (K(3.0) * k + K(6.0) * n * POW(k, K(2.0) )
- K(3.0) * POW(k, K(3.0) ))
/ (K(2.0) * n * (K(2.0) * POW(n, K(2.0) ) + K(1.0) ));
else
result += (K(2.0) * n - k) * (POW(2 * n - k, K(2.0) ) - K(1.0) )
/ (K(2.0) * n * (K(2.0) * POW(n, K(2.0) ) + K(1.0) ));
}
return result;
}
/** Compute damping factor for modified generalised Jackson kernel. */
R Y(modified_jackson4)(const INT N, const INT kk)
{
INT kj;
const R n = (((R) N) / K(2.0) + K(3.0) ) / K(4.0);
const R normalisation = (K(2416.0) * POW(n, K(7.0) )
+ K(1120.0) * POW(n, K(5.0) ) + K(784.0) * POW(n, K(3.0) ) + K(720.0) * n);
R result, k;
for (result = K(0.0), kj = kk; kj <= kk + 1; kj++)
{
k = (R)(ABS(kj));
if (k / n < K(1.0) )
result += K(1.0)
- (K(1260.0) * k
+ (K(1680.0) * POW(n, K(5.0) ) + K(2240.0) * POW(n, K(3.0) )
+ K(2940.0) * n) * POW(k, K(2.0) )
- K(1715.0) * POW(k, K(3.0) )
- (K(560.0) * POW(n, K(3.0) ) + K(1400.0) * n) * POW(k, K(4.0) )
+ K(490.0) * POW(k, K(5.0) ) + K(140.0) * n * POW(k, K(6.0) )
- K(35.0) * POW(k, K(7.0) )) / normalisation;
if ((K(1.0) <= k / n) && (k / n < K(2.0) ))
result += ((K(2472.0) * POW(n, K(7.0) ) + K(336.0) * POW(n, K(5.0) )
+ K(3528.0) * POW(n, K(3.0) ) - K(1296.0) * n)
- (K(392.0) * POW(n, K(6.0) ) - K(3920.0) * POW(n, K(4.0) )
+ K(8232.0) * POW(n, K(2.0) ) - K(756.0) )*k
- (K(504.0)*POW(n, K(5.0)) + K(10080.0)*POW(n, K(3.0))
- K(5292.0)*n)*POW(k, K(2.0)) - (K(1960.0)*POW(n, K(4.0))
- K(7840.0)*POW(n, K(2.0)) + K(1029.0))*POW(k, K(3.0))
+ (K(2520.0)*POW(n, K(3.0)) - K(2520.0)*n) * POW(k, K(4.0))
- (K(1176.0)*POW(n, K(2.0)) - K(294.0)) * POW(k, K(5.0))
+ K(252.0)*n*POW(k, K(6.0)) - K(21.0)*POW(k, K(7.0)))/normalisation;
if ((K(2.0) <= k / n) && (k / n < K(3.0) ))
result += (-(K(1112.0) * POW(n, K(7.0) ) - K(12880.0) * POW(n, K(5.0) )
+ K(7448.0) * POW(n, K(3.0) ) - K(720.0) * n)
+ (K(12152.0) * POW(n, K(6.0) ) - K(27440.0) * POW(n, K(4.0) )
+ K(8232.0) * POW(n, K(2.0) ) - K(252.0) )*k
- (K(19320.0)*POW(n, K(5.0)) - K(21280.0)*POW(n, K(3.0))
+ K(2940.0)*n)*POW(k, K(2.0)) + (K(13720.0)*POW(n, K(4.0))
- K(7840.0)*POW(n, K(2.0)) + K(343.0))*POW(k, K(3.0))
- (K(5320.0)*POW(n, K(3.0)) - K(1400.0)*n)*POW(k, K(4.0))
+ (K(1176.0)*POW(n, K(2.0)) - K(98.0))*POW(k, K(5.0))
- K(140.0)*n*POW(k, K(6.0)) + K(7.0) * POW(k, K(7.0)))/normalisation;
if ((K(3.0) <= k / n) && (k / n < K(4.0) ))
result += ((4 * n - k)
* (POW(4 * n - k, K(2.0) ) - K(1.0) )*(POW(4*n-k, K(2.0))
- K(4.0))*(POW(4*n-k, K(2.0)) - K(9.0)))/normalisation;
}
return result;
}
/** Compute damping factor for modified Sobolev kernel. */
R Y(modified_sobolev)(const R mu, const INT kk)
{
R result;
INT kj, k;
for (result = K(0.0), kj = kk; kj <= kk + 1; kj++)
{
k = ABS(kj);
if (k == 0)
result += K(1.0);
else
result += POW((R) k, -K(2.0) * mu);
}
return result;
}
/** Comput damping factor for modified multiquadric kernel. */
R Y(modified_multiquadric)(const R mu, const R c, const INT kk)
{
R result;
INT kj, k;
for (result = K(0.0), kj = kk; kj <= kk + 1; kj++)
{
k = ABS(kj);
result += POW((R)(k * k) + c * c, -mu);
}
return result;
}
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