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19.39 Examples

The following program demonstrates the use of a random number generator to produce variates from a distribution. It prints 10 samples from the Poisson distribution with a mean of 3.

#include <stdio.h>
#include <gsl/gsl_rng.h>
#include <gsl/gsl_randist.h>

int
main (void)
{
  const gsl_rng_type * T;
  gsl_rng * r;

  int i, n = 10;
  double mu = 3.0;

  /* create a generator chosen by the 
     environment variable GSL_RNG_TYPE */

  gsl_rng_env_setup();

  T = gsl_rng_default;
  r = gsl_rng_alloc (T);

  /* print n random variates chosen from 
     the poisson distribution with mean 
     parameter mu */

  for (i = 0; i < n; i++) 
    {
      unsigned int k = gsl_ran_poisson (r, mu);
      printf (" %u", k);
    }

  printf ("\n");
  gsl_rng_free (r);
  return 0;
}

If the library and header files are installed under ‘/usr/local’ (the default location) then the program can be compiled with these options,

$ gcc -Wall demo.c -lgsl -lgslcblas -lm

Here is the output of the program,

$ ./a.out 
 2 5 5 2 1 0 3 4 1 1

The variates depend on the seed used by the generator. The seed for the default generator type gsl_rng_default can be changed with the GSL_RNG_SEED environment variable to produce a different stream of variates,

$ GSL_RNG_SEED=123 ./a.out 
GSL_RNG_SEED=123
 4 5 6 3 3 1 4 2 5 5

The following program generates a random walk in two dimensions.

#include <stdio.h>
#include <gsl/gsl_rng.h>
#include <gsl/gsl_randist.h>

int
main (void)
{
  int i;
  double x = 0, y = 0, dx, dy;

  const gsl_rng_type * T;
  gsl_rng * r;

  gsl_rng_env_setup();
  T = gsl_rng_default;
  r = gsl_rng_alloc (T);

  printf ("%g %g\n", x, y);

  for (i = 0; i < 10; i++)
    {
      gsl_ran_dir_2d (r, &dx, &dy);
      x += dx; y += dy; 
      printf ("%g %g\n", x, y);
    }

  gsl_rng_free (r);
  return 0;
}

Here is the output from the program, three 10-step random walks from the origin,

The following program computes the upper and lower cumulative distribution functions for the standard normal distribution at x=2.

#include <stdio.h>
#include <gsl/gsl_cdf.h>

int
main (void)
{
  double P, Q;
  double x = 2.0;

  P = gsl_cdf_ugaussian_P (x);
  printf ("prob(x < %f) = %f\n", x, P);

  Q = gsl_cdf_ugaussian_Q (x);
  printf ("prob(x > %f) = %f\n", x, Q);

  x = gsl_cdf_ugaussian_Pinv (P);
  printf ("Pinv(%f) = %f\n", P, x);

  x = gsl_cdf_ugaussian_Qinv (Q);
  printf ("Qinv(%f) = %f\n", Q, x);

  return 0;
}