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/*
* Recursive computation of (arbitrary degree) spherical Bessel/Neumann/Hankel functions,
* 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 <math.h>
#include "sph_radial.h"
#define EPS 1e-10
static void radialRecurrence (double x, double *y, int n);
// the two recurrences for higher n:
// by now no numeric stabilization for the bessel function is performed
static void radialRecurrence (double x, double *y, int n) {
int k;
for (k=1;k<n;k++) {
y[k+1] = -y[k-1] + y[k]/x * (2*k+1);
}
}
static void radialDiffRecurrence (double x, double *y1, double *yd, int n) {
int k;
for (k=0;k<n;k++) {
yd[k] = y1[k]/x * n - y1[k+1];
}
}
void sphBessel (double x, double *y, int n) { //TODO: small values!
if (y==0)
return;
if (n>=0)
y[0] = (x<EPS)?1.0:sin(x)/x;
if (n>=1)
y[1] = -cos(x)/x + y[0]/x;
radialRecurrence (x,y,n);
}
void sphNeumann (double x, double *y, int n) {
if (y==0)
return;
if (n>=0)
y[0] = -cos(x)/x;
if (n>=1)
y[1] = ((x<EPS)?1.0:sin(x)/x) - y[0]/x;
radialRecurrence (x,y,n);
}
void sphBesselDiff (double x, double *y, int n) {
double *y1;
if (n<0)
return;
if ((y1 = (double*)calloc(n+2,sizeof(double)))==0)
return;
sphBessel (x,y1,n+1);
radialDiffRecurrence (x,y1,y,n);
free(y1);
}
void sphNeumannDiff (double x, double *y, int n) {
double *y1;
if (n<0)
return;
if ((y1 = (double*)calloc(n+2,sizeof(double)))==0)
return;
sphNeumann (x,y,n+1);
radialDiffRecurrence (x,y1,y,n);
free(y1);
}
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