sfsmisc: QUnif – R documentation

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QUnif

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, silent = FALSE)

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 >= 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 `leap`th entry should be taken.
`silent`	logical asking to suppress the message about enlarging the prime table for large `p`.

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) Computational Investigations of Low-Discrepancy Sequences. ACM Transactions of Mathematical Software 23, 2, 266–294.

Examples

32*sHalton(20, base=2)

stopifnot(sHalton(20, base=3, leap=2) ==
          sHalton(20, base=3)[1+2*(0:9)])
## ------- a 2D Visualization -------

Uplot <- function(xy, axes=FALSE, xlab="", ylab="", ...) {
  plot(xy, xaxs="i", yaxs="i", xlim=0:1, ylim=0:1, xpd = FALSE,
       axes=axes, xlab=xlab, ylab=ylab, ...)
  box(lty=2, col="gray40")
}

do4 <- function(n, ...) {
  op <- mult.fig(4, main=paste("n =", n,": Quasi vs. (Pseudo) Random"),
                 marP=c(-2,-2,-1,0))$old.par
  on.exit(par(op))
  for(i in 1:2) {
     Uplot(QUnif(n, p=2), main="QUnif", ...)
     Uplot(cbind(runif(n), runif(n)), main="runif", ...)
  }
}
do4(100)
do4(500)
do4(1000, cex = 0.8, col="slateblue")
do4(10000, pch= ".", col="slateblue")
do4(40000, pch= ".", col="slateblue")

sfsmisc

Utilities from 'Seminar fuer Statistik' ETH Zurich

v1.1-11

GPL (>= 2)

Authors

Martin Maechler [aut, cre] (<https://orcid.org/0000-0002-8685-9910>), Werner Stahel [ctb] (Functions: compresid2way(), f.robftest(), last(), p.scales(), p.dnorm()), Andreas Ruckstuhl [ctb] (Functions: p.arrows(), p.profileTraces(), p.res.2x()), Christian Keller [ctb] (Functions: histBxp(), p.tachoPlot()), Kjetil Halvorsen [ctb] (Functions: KSd(), ecdf.ksCI()), Alain Hauser [ctb] (Functions: cairoSwd(), is.whole(), toLatex.numeric()*), Christoph Buser [ctb] (to function Duplicated()), Lorenz Gygax [ctb] (to function p.res.2fact()), Bill Venables [ctb] (Functions: empty.dimnames(), primes()), Tony Plate [ctb] (to inv.seq()), Isabelle Fl<fc>ckiger [ctb], Marcel Wolbers [ctb], Markus Keller [ctb], Sandrine Dudoit [ctb], Jane Fridlyand [ctb], Greg Snow [ctb] (to loessDemo()), Henrik Aa. Nielsen [ctb] (to loessDemo()), Vincent Carey [ctb], Ben Bolker [ctb], Philippe Grosjean [ctb], Fr<e9>d<e9>ric Ibanez [ctb], Caterina Savi [ctb], Charles Geyer [ctb], Jens Oehlschl<e4>gel [ctb]

Initial release

2021-04-03