quasirandom
Quasirandom Patterns
Generates quasirandom sequences of numbers and quasirandom spatial patterns of points in any dimension.
Usage
vdCorput(n, base)Halton(n, bases = c(2, 3), raw = FALSE, simplify = TRUE)
Hammersley(n, bases = 2, raw = FALSE, simplify = TRUE)
Arguments
- n
- Number of points to generate.
- base
- A prime number giving the base of the sequence.
- bases
- Vector of prime numbers giving the bases of the sequences for each coordinate axis.
- raw
- Logical value indicating whether to return the coordinates
as a matrix (
raw=TRUE) or as a spatial point pattern (raw=FALSE, the default). - simplify
- Argument passed to
ppxindicating whether point patterns of dimension 2 or 3 should be returned as objects of class"ppp"or"pp3"respectively (simplify=TRUE,
Details
The function vdCorput generates the quasirandom sequence
of Van der Corput (1935) of length n with the given
base. These are numbers between 0 and 1 which are in
some sense uniformly distributed over the interval.
The function Halton generates the Halton quasirandom sequence
of points in d-dimensional space, where
d = length(bases). The values of the $i$-th coordinate
of the points are generated using the van der Corput sequence with
base equal to bases[i].
The function Hammersley generates the Hammersley set
of points in d+1-dimensional space, where
d = length(bases). The first d coordinates
of the points are generated using the van der Corput sequence with
base equal to bases[i]. The d+1-th coordinate
is the sequence 1/n, 2/n, ..., 1.
If raw=FALSE (the default) then the Halton and Hammersley
sets are interpreted as spatial point patterns of the
appropriate dimension. They are returned as objects of
class "ppx" (multidimensional point patterns)
unless simplify=TRUE and d=2 or d=3
when they are returned as objects of class "ppp"
or "pp3".
If raw=TRUE, the coordinates are returned as a matrix
with n rows and D columns where D is the spatial
dimension.
Value
- For
vdCorput, a numeric vector.For
HaltonandHammersley, an object of class"ppp","pp3"or"ppx"; or ifraw=TRUE, a numeric matrix.
References
Van der Corput, J. G. (1935) Verteilungsfunktionen. Proc. Ned. Akad. v. Wetensch. 38: 813--821.
Kuipers, L. and Niederreiter, H. (2005) Uniform distribution of sequences, Dover Publications.
See Also
Examples
vdCorput(10, 2)
plot(Halton(256, c(2,3)))
plot(Hammersley(256, 3))