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/* Random kit 1.6 */
/*
* Copyright (c) 2004-2006, Jean-Sebastien Roy (js@jeannot.org)
*
* Original algorithm from Numerical Recipes, 2nd edition, by Press et al.
* The inverse normal cdf formulas are from Peter J. Acklam.
* The initialization directions are reproduced from Ferdinando Ametrano's
* implementation in QuantLib.
*
* Permission is hereby granted, free of charge, to any person obtaining a
* copy of this software and associated documentation files (the
* "Software"), to deal in the Software without restriction, including
* without limitation the rights to use, copy, modify, merge, publish,
* distribute, sublicense, and/or sell copies of the Software, and to
* permit persons to whom the Software is furnished to do so, subject to
* the following conditions:
*
* The above copyright notice and this permission notice shall be included
* in all copies or substantial portions of the Software.
*
* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
* OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
* MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.
* IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY
* CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT,
* TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE
* SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
*/
static char const rcsid[] =
"@(#) $Jeannot: sobol_example.c,v 1.7 2006/02/19 13:48:34 js Exp $";
#include <stdlib.h>
#include <stdio.h>
#include <math.h>
#include "randomkit.h"
#ifndef M_PI
#define M_PI 3.14159265358979323846
#endif
/* Gamma(n/2) for n a (small) positive integer */
static double gamma_half(int n);
double gamma_half(int n)
{
double x = 1.0;
if (n & 1)
x = sqrt(M_PI)*0.5;
for (n-=2; n>1; n-=2)
x *= n*0.5;
return x;
}
int main(int argc, char **argv)
{
rk_sobol_state s;
rk_sobol_error rc;
size_t dimension = 3, d, runs = 5, draws = 100000, run, draw;
unsigned long drawn_in = 0; /* number of draws in ball */
double *x, estimated_volume, correct_volume;
x = malloc(sizeof(*x)*dimension);
if (!x)
{
fprintf(stderr, "not enough memory\n");
exit(EXIT_FAILURE);
}
/* Initialize the sobol QRNG */
if ((rc = rk_sobol_init(dimension, &s, NULL, rk_sobol_Ldirections, NULL)))
{
fprintf(stderr, "sobol_init error: %s\n", rk_sobol_strerror[rc]);
exit(EXIT_FAILURE);
}
printf("RQMC estimation of the volume of a %d-dimensional ball.\n",
dimension);
printf("%d runs with %d draws per run.\n", runs, draws);
for (run = 0; run < runs; run++)
{
if (run > 0)
/* Re-initilize the sobol QRNG */
rk_sobol_reinit(&s);
/* Randomly shift the sobol QRNG for Randomized Quasi Monte-Carlo */
rk_sobol_randomshift(&s, NULL);
for (draw = 0; draw < draws; draw++)
{
double length = 0;
rk_sobol_double(&s, x);
for (d = 0; d < dimension; d++)
length += x[d]*x[d];
if (length <= 1.0)
drawn_in ++;
}
}
/* Free allocated memory */
rk_sobol_free(&s);
free(x);
estimated_volume = pow(2.0, dimension)*drawn_in/(((double)runs)*draws);
correct_volume = pow(M_PI,dimension*0.5)/gamma_half(2+dimension);
printf("Estimated volume: %g\n", estimated_volume);
printf("Correct volume: %g\n", correct_volume);
printf("Error: %g\n", estimated_volume-correct_volume);
return 0;
}
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