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TWignerd.cxx
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TWignerd.cxx
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// Author: Marcelo Zimbres Silva <mailto:mzimbres@gmail.com>
/* Copyright (C) 2009, 2010, 2011 Marcelo Zimbres Silva
*
* 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.
*/
#include <iostream>
#include <complex>
#include <cmath>
// SWAT
#include "TWignerd.h"
using namespace std;
///////////////////////////////////////////////////////////////////////
// //
// Calculation of the fourier coefficients of wigner d functions //
// using recurrence. //
// //
// Calculation of spherical harmonics and Wigner d functions by FFT. //
// Article: Acta Crystallographica Section A, Foundations of //
// Crystallography. //
// Authors: Stefano Trapani and Jorge Navasa. //
// //
// Refer to macro wig_graph.C in tutorials directory for an example //
// how to use this class to sample wigner d functions. //
// //
///////////////////////////////////////////////////////////////////////
//_______________________________________________________________
void TWignerd::Recurse()
{
// Advances one step in the recursion, from l to l+1
++fL;
std::vector<double> fTemp(fSize);
fTemp[fIndex(fL,0)] = -sqrt(1 - 0.5/fL)*fMatrix[fIndex(fL-1,0)];
for (int n = 1; n <= fL; ++n){
double a = sqrt((fL*(fL - 0.5))/((fL+n)*(fL+n-1)));
fTemp[fIndex(fL,n)] = a*fMatrix[fIndex(fL-1,n-1)];
}
for(int m=fL-1;m>=0;--m){
for(int n=0;n<=m;++n){
double a = static_cast<double>(n << 1)/sqrt((fL-m)*(fL+m+1));
double b = -sqrt((fL-m-1)*(fL+m+2.)/((fL-m)*(fL+m+1)));
fTemp[fIndex(m,n)] = a*fTemp[fIndex(m+1,n)] + b*fTemp[fIndex(m+2,n)];
}
}
fMatrix = fTemp;
}
//__________________________________________________________________________
void TWignerd::Advance(int l)
{
// Advances using a loop in Recurse(), so that fL = l.
for (int i = 0; i < l; ++i)
Recurse();
}