halton: Compute points in the Halton sequence.
In semmons1/TEST-SDraw: Spatially Balanced Samples of Spatial Objects

Description Usage Arguments Details Value Author(s) References See Also Examples

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

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

`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.

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.

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

Trent McDonald

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.

halton.indices