Quasi Randum Numbers via Halton Sequences
These functions provide quasi random numbers or space filling or low discrepancy sequences in the p-dimensional unit cube.
sHalton(n.max, n.min = 1, base = 2, leap = 1) QUnif (n, min = 0, max = 1, n.min = 1, p, leap = 1)
n.max |
maximal (sequence) number. |
n.min |
minimal sequence number. |
n |
number of p-dimensional points generated in
|
base |
integer >= 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 |
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 |
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.
For leap Kocis and Whiten recommend values of
L=31,61,149,409, and particularly the L=409 for dimensions
up to 400.
Martin Maechler
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.
32*sHalton(20, base=2) QUnif(n=10,p=2,leap=409)
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