QUnif {GLDEX}

Quasi Randum Numbers via Halton Sequences

Description

These functions provide quasi random numbers or space filling or low discrepancy sequences in the p-dimensional unit cube.

Usage

sHalton(n.max, n.min = 1, base = 2, leap = 1)
 QUnif (n, min = 0, max = 1, n.min = 1, p, leap = 1)

Arguments

n.max

maximal (sequence) number.

n.min

minimal sequence number.

n

number of p-dimensional points generated in QUnif. By default, n.min = 1, leap = 1 and the maximal sequence number is n.max = n.min + (n-1)*leap.

base

integer \ge 2: The base with respect to which the Halton sequence is built.

min, max

lower and upper limits of the univariate intervals. Must be of length 1 or p.

p

dimensionality of space (the unit cube) in which points are generated.

leap

integer indicating (if > 1) if the series should be leaped, i.e., only every leapth entry should be taken.

Value

sHalton(n,m) returns a numeric vector of length n-m+1 of values in [0,1].

QUnif(n, min, max, n.min, p=p) generates n-n.min+1 p-dimensional points in [min,max]^p returning a numeric matrix with p columns.

Note

For leap Kocis and Whiten recommend values of L=31,61,149,409, and particularly the L=409 for dimensions up to 400.

Author(s)

Martin Maechler

References

James Gentle (1998) Random Number Generation and Monte Carlo Simulation; sec.\ 6.3. Springer.

Kocis, L. and Whiten, W.J. (1997) Computationsl Investigations of Low-Discrepancy Sequences. ACM Transactions of Mathematical Software 23, 2, 266–294.

Examples

32*sHalton(20, base=2)
QUnif(n=10,p=2,leap=409)