#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;

}