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/**********************************************************************
Spherical_Bessel.c:
Spherical_Bessel.c is a subroutine to calculate the spherical
Bessel functions and its derivative from 0 to lmax
Log of Spherical_Bessel.c:
08/Nov/2005 Released by T.Ozaki
***********************************************************************/
#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include "openmx_common.h"
#define xmin 0.0
#define asize_lmax 20
void Spherical_Bessel( double x, int lmax, double *sb, double *dsb )
{
int m,n,nmax;
double tsb[asize_lmax+10];
double invx,vsb0,vsb1,vsb2,vsbi;
double j0,j1,j0p,j1p,sf,tmp,si,co,ix,ix2;
if (x<0.0){
printf("minus x is invalid for Spherical_Bessel\n");
exit(0);
}
/* find an appropriate nmax */
nmax = lmax + 3*x + 20;
if (nmax<100) nmax = 100;
if (asize_lmax<(lmax+1)){
printf("asize_lmax should be larger than %d in Spherical_Bessel.c\n",lmax+1);
exit(0);
}
/* if x is larger than xmin */
if ( xmin < x ){
invx = 1.0/x;
/* initial values */
vsb0 = 0.0;
vsb1 = 1.0e-14;
/* downward recurrence from nmax-2 to lmax+2 */
for ( n=nmax-1; (lmax+2)<n; n-- ){
vsb2 = (2.0*n + 1.0)*invx*vsb1 - vsb0;
if (1.0e+250<vsb2){
tmp = 1.0/vsb2;
vsb2 *= tmp;
vsb1 *= tmp;
}
vsbi = vsb0;
vsb0 = vsb1;
vsb1 = vsb2;
}
/* downward recurrence from lmax+1 to 0 */
n = lmax + 3;
tsb[n-1] = vsb1;
tsb[n ] = vsb0;
tsb[n+1] = vsbi;
tmp = tsb[n-1];
tsb[n-1] /= tmp;
tsb[n ] /= tmp;
for ( n=lmax+2; 0<n; n-- ){
tsb[n-1] = (2.0*n + 1.0)*invx*tsb[n] - tsb[n+1];
if (1.0e+250<tsb[n-1]){
tmp = tsb[n-1];
for (m=n-1; m<=lmax+1; m++){
tsb[m] /= tmp;
}
}
}
/* normalization */
si = sin(x);
co = cos(x);
ix = 1.0/x;
ix2 = ix*ix;
j0 = si*ix;
j1 = si*ix*ix - co*ix;
if (fabs(tsb[1])<fabs(tsb[0])) sf = j0/tsb[0];
else sf = j1/tsb[1];
/* tsb to sb */
for ( n=0; n<=lmax+1; n++ ){
sb[n] = tsb[n]*sf;
}
/* derivative of sb */
dsb[0] = co*ix - si*ix*ix;
for ( n=1; n<=lmax; n++ ){
dsb[n] = ( (double)n*sb[n-1] - (double)(n+1.0)*sb[n+1] )/(2.0*(double)n + 1.0);
}
}
/* if x is smaller than xmin */
else {
/* sb */
for ( n=0; n<=lmax; n++ ){
sb[n] = 0.0;
}
sb[0] = 1.0;
/* derivative of sb */
dsb[0] = 0.0;
for ( n=1; n<=lmax; n++ ){
dsb[n] = ( (double)n*sb[n-1] - (double)(n+1.0)*sb[n+1] )/(2.0*(double)n + 1.0);
}
}
}
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