/*** Integrates the pendlum using Runge-Kutta method ***/
/*** rk4 from numerical recipes                      ***/

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

#define select select_nr            /* otherwise: twice defined */
#include "nr.h"
#include "nrutil.h"

/** sets f[]=derivates at point x of variables y[] **/
/** y[1]=phi, y[2]=omega                           **/
void derivs(float x, float *y, float *f)
{
  f[1] = y[2];
  f[2] = -sin(y[1]);
}

int main(int argc, char **argv)
{
  float y[3];        /* phase space variables: unused,phi,omega */
  float f[3];                                    /* derivatives */
  float h;                                          /* stepsize */
  int n, n_max;                           /* step, maximum step */
  float t;                                              /* time */

  sscanf(argv[1], "%f", &h);       /* first argument = stepsize */
  sscanf(argv[2], "%d", &n_max); /*2nd argument = numb. of steps */
  y[1]=0; y[2]=1.0; t = 0;

  derivs(t, y, f);
  for(n=1; n<=n_max; n++)              /* iterate over all times */
  {
    printf("%f %f %f\n", t, y[1], y[2]);        /* print results */
    rk4(y, f, 2, t, h, y, derivs);           /* call Runge-Kutta */
    t += h;
  }
  return(0);
}