// ???
// int gsl_permutation_canonical_to_linear (gsl_permutation * p, const gsl_permutation * q)
// This function converts a permutation q in canonical form back into linear form storing it in the output argument p. (viceversa, it seems to me)
#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 = 3;
    const gsl_rng_type * T;
    gsl_rng * r;

    gsl_permutation * p = gsl_permutation_alloc (N);
    gsl_permutation * q1 = gsl_permutation_alloc (N);
    gsl_permutation * q2 = 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("gsl_permutation_linear_to_canonical(q1,p)\n");
    gsl_permutation_linear_to_canonical(q1,p);
    printf("q1: ");
    gsl_permutation_fprintf (stdout, q1, " %u");
    printf("\np: ");
    gsl_permutation_fprintf (stdout, p, " %u");
    printf("\n");
    printf("gsl_permutation_canonical_to_linear(q2,q1)\n");
    gsl_permutation_canonical_to_linear(q2,q1); 
    printf("q1: "); // both q1 and q2 change, none makes sense
    gsl_permutation_fprintf (stdout, q1, " %u");
    printf("\nq2: ");
    gsl_permutation_fprintf (stdout, q2, " %u");
    printf("\n");
      
  return 0;
}
/*
 initial permutation: 0 1 2
  random permutation: 1 0 2
  gsl_permutation_linear_to_canonical(q1,p)
q1:  2 0 1
p:  1 0 2
gsl_permutation_canonical_to_linear(q2,q1)
q1:  0 1 2
q2:  0 0 0
 */