/* From: "COMPUTATIONAL PHYSICS, 2nd Ed" 
   by RH Landau, MJ Paez, and CC Bordeianu 
   Copyright Wiley-VCH, 2007.
   Electronic Materials copyright: R Landau, Oregon State Univ, 2007;
   MJ Paez, Univ Antioquia, 2007; & CC Bordeianu, Univ Bucharest, 2007
   Support by National Science Foundation                              
*/                                
//  bessel.c: Spherical Bessel functions via up and down recursion

#include <stdio.h>
#include <math.h>

#define xmax 40.0                                         // max of x
#define xmin 0.25                                      // min of x >0
#define step 0.1                                           // delta x
#define order 10                          // order of Bessel function
#define start 50                       // used for downward algorithm

main()  {
	
   double x;
   double down(double x, int n, int m);         // downward algorithm
   double up(double x, int n);                    // upward algorithm
   
   FILE *out;
   out = fopen("bessel.dat","w");
   
   for (x=xmin; x<=xmax; x+=step) fprintf(out, "%f\t%f\t%f\n",
		                         x, down(x,order,start), up(x,order));
   printf("data stored in bessel.dat.\n");
   fclose(out);
}
                  
double down (double x, int n, int m) { 
	                                              // downward recursion
   double scale, j[start+2];     
   int k;
   j[m+1] = j[m] = 1.;                      // start with "something"
   for (k=m; k>0 ; k--)
      j[k-1] = ((2.*(double)k + 1.)/x)*j[k] - j[k+1];        // recur
      scale = ((sin(x))/x)/j[0];                  // scale the result
   return(j[n]*scale);
}

double up (double x, int n) {            
	                                 // function using upward recursion
   double one, two, thr;
   int k;
   one = (sin(x))/x;                       // start with lowest order
   two = (sin(x) - x*cos(x))/(x*x);
	                                      // loop for order of function
   for (k = 1 ; k<n ; k+=1)   {         
      thr = ((2.*k + 1.)/x)*two - one;         // recurrence relation
      one = two;
      two = thr;
   }
   return(thr);
}