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/*
* Recursive computation of (arbitrary degree) normalization constants
* for spherical harmonics, according to Gumerov and Duraiswami,
* "The Fast Multipole Methods for the Helmholtz Equation in Three Dimensions",
* Elsevier, 2005.
*
* Implementation by Franz Zotter, Institute of Electronic Music and Acoustics
* (IEM), University of Music and Dramatic Arts (KUG), Graz, Austria
* http://iem.at/Members/zotter, 2007.
*
* This code is published under the Gnu General Public License, see
* "LICENSE.txt"
*/
#include "mtx_spherical_harmonics/sharmonics_normalization.h"
SHNorml *sharmonics_normalization_new (const size_t nmax) {
SHNorml *wn;
unsigned int n,n0,m;
const double oneoversqrt2 = 1.0/sqrt(2);
// memory allocation
if ((wn=(SHNorml*)calloc(1,sizeof(SHNorml)))!=0) {
wn->nmax=nmax;
if ((wn->n=(double*)calloc((nmax+1)*(nmax+2)/2,sizeof(double)))==0) {
free(wn);
wn=0;
}
else {
/*
deprecated:
// computing N_n^m for m=0, wrongly normalized
wn->n[0]=sqrt(1/(2*M_PI));
*/
// computing N_n^m for m=0,
wn->n[0]=oneoversqrt2;
for (n=1,n0=1; n<=nmax; n++) {
wn->n[n0]=wn->n[0] * sqrt(2*n+1);
n0+=n+1;
}
// computing N_n^m for 0<m<=n
for (n=1,n0=1; n<=nmax; n++) {
for (m=1; m<=n; m++) {
wn->n[n0+m]= - wn->n[n0+m-1] / sqrt((n+m)*(n-m+1));
}
n0+=n+1;
}
/*
deprecated:
// correcting normalization of N_n^0
for (n=0,n0=0; n<=nmax; n++) {
wn->n[n0]*=oneoversqrt2;
n0+=n+1;
}
*/
}
}
return wn;
}
void sharmonics_normalization_free(SHNorml *wn) {
if (wn!=0) {
free(wn->n);
free(wn);
}
}
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