halton function

Halton sequence

Calculate elements of the Halton sequence and of some other pseudo-random sequences.

halton(
  n = 1L,
  base = as.integer(c(2)),
  start = 1L,
  random = "NO",
  type = "halton",
  scrambler = "NO",
  is_validation = TRUE,
  n_cores = 1L
)

Arguments

• n: positive integer representing the number of sequence elements.

• base: vector of positive integers greater then one representing the bases for each of the sequences.

• start: non-negative integer representing the index of the first element of the sequence to be included in the output sequence.

• random: string representing the method of randomization to be applied to the sequence. If random = "NO" (default) then there is no randomization. If random = "Tuffin" then standard uniform random variable will be added to each element of the sequence and the difference between this sum and it's 'floor' will be returned as a new element of the sequence.

• type: string representing type of the sequence. Default is "halton" that is Halton sequence. The alternative is "richtmyer" corresponding to Richtmyer sequence.

• scrambler: string representing scrambling method for the Halton sequence. Possible options are "NO" (default), "root"

  and "negroot" which described in S. Kolenikov (2012).

• is_validation: logical value indicating whether input arguments should be validated. Set it to FALSE to get performance boost (default value is TRUE).

• n_cores: positive integer representing the number of CPU cores used for parallel computing. Currently it is not recommended to set n_cores > 1 if vectorized arguments include less then 100000 elements.

Returns

The function returns a matrix which i-th column is a sequence with base base[i] and elements with indexes from start to start + n.

Details

Function seqPrimes could be used to provide the prime numbers for the base input argument.

Examples

halton(n = 100, base = c(2, 3, 5), start = 10)

References

J. Halton (1964) doi:10.2307/2347972

S. Kolenikov (2012) doi:10.1177/1536867X1201200103