#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)

{

  (void)(dim); /* avoid unused parameter warnings */

  (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;

}