9.9 Examples
The example program below creates a random permutation (by shuffling the
elements of the identity) and finds its inverse.
| | #include <stdio.h>
#include <gsl/gsl_rng.h>
#include <gsl/gsl_randist.h>
#include <gsl/gsl_permutation.h>
int
main (void)
{
const size_t N = 10;
const gsl_rng_type * T;
gsl_rng * r;
gsl_permutation * p = gsl_permutation_alloc (N);
gsl_permutation * q = gsl_permutation_alloc (N);
gsl_rng_env_setup();
T = gsl_rng_default;
r = gsl_rng_alloc (T);
printf ("initial permutation:");
gsl_permutation_init (p);
gsl_permutation_fprintf (stdout, p, " %u");
printf ("\n");
printf (" random permutation:");
gsl_ran_shuffle (r, p->data, N, sizeof(size_t));
gsl_permutation_fprintf (stdout, p, " %u");
printf ("\n");
printf ("inverse permutation:");
gsl_permutation_inverse (q, p);
gsl_permutation_fprintf (stdout, q, " %u");
printf ("\n");
gsl_permutation_free (p);
gsl_permutation_free (q);
gsl_rng_free (r);
return 0;
}
|
Here is the output from the program,
| | $ ./a.out
initial permutation: 0 1 2 3 4 5 6 7 8 9
random permutation: 1 3 5 2 7 6 0 4 9 8
inverse permutation: 6 0 3 1 7 2 5 4 9 8
|
The random permutation p[i] and its inverse q[i] are
related through the identity p[q[i]] = i, which can be verified
from the output.
The next example program steps forwards through all possible third order
permutations, starting from the identity,
| | #include <stdio.h>
#include <gsl/gsl_permutation.h>
int
main (void)
{
gsl_permutation * p = gsl_permutation_alloc (3);
gsl_permutation_init (p);
do
{
gsl_permutation_fprintf (stdout, p, " %u");
printf ("\n");
}
while (gsl_permutation_next(p) == GSL_SUCCESS);
gsl_permutation_free (p);
return 0;
}
|
Here is the output from the program,
| | $ ./a.out
0 1 2
0 2 1
1 0 2
1 2 0
2 0 1
2 1 0
|
The permutations are generated in lexicographic order. To reverse the
sequence, begin with the final permutation (which is the reverse of the
identity) and replace gsl_permutation_next with
gsl_permutation_prev.
