SDraw (version 2.1.13)

halton: Compute points in the Halton sequence.

Description

Computes points in a multi-dimensional Halton sequence, beginning at specified indices and using specified co-prime bases.

Usage

halton(n, dim = 1, start = 0, bases = NULL)

Arguments

n

A scalar giving the number of values in the Halton points to produce.

dim

A scalar giving the number of dimensions, equal to the number of van der Corput sequences. Technically, dim==1 produces a van der Corput sequence, dim>=2 produces Halton sequences.

start

A scalar or a length dim vector giving the starting index (location) for each van der Corput sequence. Origin of each sequence is 0. all(start>=0) must be true.

bases

A length dim vector giving the base to use for each dimension. For a Halton sequence, bases must all be co-prime. No check for common prime factors is performed. If bases is NULL, the first dim primes starting at 2 are used as bases of the Halton sequence. For example, the 4-dimensional Halton sequence would use bases 2, 3, 5, and 7. The 6-dimensional Halton sequence would use 2, 3, 5, 7, 11, and 13. Etc.

Value

A matrix of size n X dim. Each column corresponds to a dimension. Each row is a dim-dimensional Halton point.

Details

The Halton sequence is a sequence of dim-dimensional numbers where each dimension is a (1-dimensional) co-prime van der Corput sequence. Here, all van der Corput sequences use bases that are prime numbers. See references below.

References

van der Corput sequences are described here: http://en.wikipedia.org/wiki/Van_der_Corput_sequence

Halton sequences are described here: http://en.wikipedia.org/wiki/Halton_sequence

Robertson, B.L., J. A. Brown, T. L. McDonald, and P. Jaksons (2013) BAS: "Balanced Acceptance Sampling of Natural Resources", Biometrics, v69, p. 776-784.

See Also

halton.indices

Examples

# NOT RUN {
halton(10,2)
halton(10,2, floor(runif(2,max=100000))) # A random-start 2-D Halton sequence of length 10

# }