Shuffling and Sampling

The following functions allow the shuffling and sampling of a set of objects. The algorithms rely on a random number generator as source of randomness and a poor quality generator can lead to correlations in the output. In particular it is important to avoid generators with a short period. For more information see Knuth, v2, 3rd ed, Section 3.4.2, "Random Sampling and Shuffling".

Random: void gsl_ran_shuffle (const gsl_rng * r, void * base, size_t n, size_t size)

This function randomly shuffles the order of n objects, each of size size, stored in the array base[0..n-1]. The output of the random number generator r is used to produce the permutation. The algorithm generates all possible @math{n!} permutations with equal probability, assuming a perfect source of random numbers.

The following code shows how to shuffle the numbers from 0 to 51,

int a[52];

for (i = 0; i < 52; i++)
  {
    a[i] = i;
  }

gsl_ran_shuffle (r, a, 52, sizeof (int));

Random: int gsl_ran_choose (const gsl_rng * r, void * dest, size_t k, void * src, size_t n, size_t size)

This function fills the array dest[k] with k objects taken randomly from the n elements of the array src[0..n-1]. The objects are each of size size. The output of the random number generator r is used to make the selection. The algorithm ensures all possible samples are equally likely, assuming a perfect source of randomness.

The objects are sampled without replacement, thus each object can only appear once in dest[k]. It is required that k be less than or equal to n. The objects in dest will be in the same relative order as those in src. You will need to call gsl_ran_shuffle(r, dest, n, size) if you want to randomize the order.

The following code shows how to select a random sample of three unique numbers from the set 0 to 99,

double a[3], b[100];

for (i = 0; i < 100; i++)
  {
    b[i] = (double) i;
  }

gsl_ran_choose (r, a, 3, b, 100, sizeof (double));

Random: void gsl_ran_sample (const gsl_rng * r, void * dest, size_t k, void * src, size_t n, size_t size)

This function is like gsl_ran_choose but samples k items from the original array of n items src with replacement, so the same object can appear more than once in the output sequence dest. There is no requirement that k be less than n in this case.