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");
       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);
         }
       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;
     }

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