#include <stdlib.h>
#include <gsl/gsl_math.h> 
#include <gsl/gsl_monte.h> 
#include <gsl/gsl_monte_plain.h> 
#include <gsl/gsl_monte_miser.h> 
#include <gsl/gsl_monte_vegas.h>
/* Computation of the integral, I = int (dx dy dz)/(2pi)^3 1/(1-cos(x)cos(y)cos(z)) over (-pi,-pi,-pi) to (+pi, +pi, +pi). 
The exact answer is Gamma(1/4)^4/(4 pi^3). This example is taken from C.Itzykson, J.M.Drouffe, "Statistical Field Theory - Volume 1", Section 1.1, p21, which cites the original paper M.L.Glasser, I.J.Zucker, Proc.Natl.Acad.Sci.USA 74 1800 (1977) */
/* For simplicity we compute the integral over the region (0,0,0) -> (pi,pi,pi) and multiply by 8 */
double exact = 1.3932039296856768591842462603255;
double
g (double *k, size_t dim, void *params) 
{
  double A = 1.0 / (M_PI * M_PI * M_PI);
  return A / (1.0 - cos (k[0]) * cos (k[1]) * cos (k[2])); 
}
void display_results (char *title, double result, double error) 
{
  printf ("%s ==================\n", title);
  printf ("result = % .6f\n", result);
  printf ("sigma = % .6f\n", error);
  printf ("exact = % .6f\n", exact);
  printf ("error = % .6f = %.2g sigma\n", result - exact,fabs (result - exact) / error);
}
int main (void)
{
  double res, err;
  double xl[3] = { 0, 0, 0 };
  double xu[3] = { M_PI, M_PI, M_PI };
  const gsl_rng_type *T; gsl_rng *r;
  gsl_monte_function G = { &g, 3, 0 }; 
  size_t calls = 500000; gsl_rng_env_setup ();
  T = gsl_rng_default;
  r = gsl_rng_alloc (T);
  {
    gsl_monte_plain_state *s = gsl_monte_plain_alloc (3);
    gsl_monte_plain_integrate (&G, xl, xu, 3, calls, r, s, &res, &err);
    gsl_monte_plain_free (s);
    display_results ("plain",res,err);
  }
  {
    gsl_monte_miser_state *s = gsl_monte_miser_alloc (3);
    gsl_monte_miser_integrate (&G, xl, xu, 3, calls, r, s, &res, &err);
    gsl_monte_miser_free (s);
    display_results ("miser",res,err);
  }
  {
    gsl_monte_vegas_state *s = gsl_monte_vegas_alloc (3);
    gsl_monte_vegas_integrate (&G, xl, xu, 3, 10000, r, s, &res, &err);
    display_results ("vegas warm-up", res, err);
    printf ("converging...\n");
    do
      {
	gsl_monte_vegas_integrate (&G, xl, xu, 3, calls/5, r, s, &res, &err);
	printf ("result = % .6f sigma = % .6f ""chisq/dof = %.1f\n", res, err, gsl_monte_vegas_chisq (s));
      }
    while (fabs (gsl_monte_vegas_chisq (s) - 1.0) > 0.5);
    display_results ("vegas final", res, err);
    gsl_monte_vegas_free (s);
  }
  gsl_rng_free (r);
  return 0; 
}
