### 20.40 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

     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 some output from the program, four 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;
    }

Here is the output of the program,

    prob(x < 2.000000) = 0.977250
    prob(x > 2.000000) = 0.022750
    Pinv(0.977250) = 2.000000
    Qinv(0.022750) = 2.000000