The example program below creates a random permutation by shuffling 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_invert (q, p); gsl_permutation_fprintf (stdout, q, " %u"); printf("\n"); return 0; }
Here is the output from the program,
bash$ ./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 3-rd 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); return 0; }
Here is the output from the program,
bash$ ./a.out 0 1 2 0 2 1 1 0 2 1 2 0 2 0 1 2 1 0
All 6 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
.