R: Quasirandom Patterns

quasirandom {spatstat} | R Documentation

## Quasirandom Patterns

### Description

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 `ppx` indicating whether point patterns of dimension 2 or 3 should be returned as objects of class `"ppp"` or `"pp3"` respectively (`simplify=TRUE`, the default) or as objects of class `"ppx"` (`simplify=FALSE`).

### 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 `Halton` and `Hammersley`, an object of class `"ppp"`, `"pp3"` or `"ppx"`; or if `raw=TRUE`, a numeric matrix.

### Author(s)

Adrian Baddeley Adrian.Baddeley@curtin.edu.au

, Rolf Turner r.turner@auckland.ac.nz

and Ege Rubak rubak@math.aau.dk.

### 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

`rQuasi`

### Examples

       vdCorput(10, 2)

       plot(Halton(256, c(2,3)))

       plot(Hammersley(256, 3))

[Package spatstat version 1.63-3 Index]