/* 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
*/
/* SplineAppl.c  Cubic Spline fit to data, based on Press et al
input array x[n], y[n] =  tabulation function y(x),x0 < x1,  
output yout for given xout yp1 and ypn: 1st derivs at endpoints,
evaluated internally, y2[n]: array of 2nd derivatives
(setting yp1 or  ypn >0.99e30 produces natural spline) */ 

#include<stdio.h>
#include<math.h>
#define n 9
#define np 15
#define Nfit 3000 // enter the desired number of points to fit

main()   {	
	
  FILE *output1, *output2;
  output1 = fopen("Spline.dat","w");      // save data in Spline.dat
  output2 = fopen("Input.dat","w");
  // input data, enter your own data here!
  double x[] = {0., 0.12, 0.25, 0.37, 0.5, 0.62, 0.75, 0.87, 0.99}; 
  double y[] = {108.6, 16.,845.,883.5,52.8, 19.9, 10.8, 88.25, 84.7};
  double xout, yout; 
  double y2[9];
  int i, klo,khi,k ;
  double h,b,a,p,qn,sig,un,yp1,ypn, u[n];
	                                                          // input
  for (i = 0;i<n;i++) fprintf (output2,"%f\t%f\n",x[i],y[i]);     
	                                      // 1st deriv at initial point
  yp1 =  (y[1]-y[0])/(x[1]-x[0])      
    - (y[2]-y[1])/(x[2]-x[1]) + (y[2]-y[0])/(x[2]-x[0]);
		                                        // 1st deriv at end point
  ypn = (y[n-1]-y[n-2])/(x[n-1]-x[n-2]) - (y[n-2]-y[n-3])/
	                 (x[n-2]-x[n-3]) +(y[n-1]-y[n-3])/(x[n-1]-x[n-3]);
									                             // natural spline test
  if (yp1 > 0.99e30) y2[0]= u[0]= 0.0;         
    else {
      y2[0] =  (-0.5);
      u[0] = (3.0/(x[1]-x[0]))*((y[1]-y[0])/(x[1]-x[0])-yp1);
    }
                                              // decomposition loop; 
		for (i = 1; i<= n-2; i++) {               
      sig = (x[i]-x[i-1])/(x[i+1]-x[i-1]);
      p = sig*y2[i-1]+2.0;
      y2[i] = (sig-1.0)/p;
      u[i] = (y[i+1]-y[i])/(x[i+1]-x[i])-(y[i]-y[i-1])/(x[i]-x[i-1]);
      u[i] = (6.0*u[i]/(x[i+1]-x[i-1])-sig*u[i-1])/p;
    }
		                                              // test for natural
    if (ypn > 0.99e30) qn = un = 0.0;            
    else   {                      // else evaluate second derivative
      qn = 0.5;
      un = ((3.0)/(x[n-1]-x[n-2]))
			                      *(ypn-(y[n-1]-y[n-2])/(x[n-1]-x[n-2]));
    }
    y2[n-1] = (un-qn*u[n-2])/(qn*y2[n-2]+1.0);
    for (k= n-2;k>= 0;k--) { y2[k] = y2[k]*y2[k+1]+u[k]; }  
                 // splint (initialization) ends, Begin *spline* fit
    for ( i = 1; i<=  Nfit; i++ ) {         // loop over xout values
      xout = x[0] + (x[n-1]-x[0])*(i-1)/(Nfit);
      klo = 0;             // Bisection algor to find place in table
      khi = n-1;                      // klo, khi bracket xout value
      while (khi-klo > 1) {
        k = (khi+klo) >> 1;
        if (x[k] > xout) khi = k;
        else klo= k;     
			}
      h = x[khi]-x[klo];
      if (x[k] > xout) khi= k;
      else klo= k;
      h = x[khi]-x[klo];
      a = (x[khi]-xout)/h;
      b = (xout-x[klo])/h;
      yout = (a*y[klo]+b*y[khi]+((a*a*a-a)*y2[klo]
                   +(b*b*b-b)*y2[khi])*(h*h)/6.0);
      fprintf (output1,"%f\t%f\n",xout,yout);    // gnuplot 3D format
    }
    fclose(output1);
    fclose(output2);
    printf("data stored in Spline.dat"); 
}