rpoint
Generate N Random Points
Generate a random point pattern containing \(n\) independent, identically distributed random points with any specified distribution.
Usage
rpoint(n, f, fmax=NULL, win=unit.square(),
…, giveup=1000, verbose=FALSE,
nsim=1, drop=TRUE)
Arguments
- n
Number of points to generate.
- f
The probability density of the points, possibly un-normalised. Either a constant, a function
f(x,y,...)
, or a pixel image object.- fmax
An upper bound on the values of
f
. If missing, this number will be estimated.- win
Window in which to simulate the pattern. Ignored if
f
is a pixel image.- …
Arguments passed to the function
f
.- giveup
Number of attempts in the rejection method after which the algorithm should stop trying to generate new points.
- verbose
Flag indicating whether to report details of performance of the simulation algorithm.
- nsim
Number of simulated realisations to be generated.
- drop
Logical. If
nsim=1
anddrop=TRUE
(the default), the result will be a point pattern, rather than a list containing a point pattern.
Details
This function generates n
independent, identically distributed
random points with common probability density proportional to
f
.
The argument f
may be
- a numerical constant:
uniformly distributed random points will be generated.
- a function:
random points will be generated in the window
win
with probability density proportional tof(x,y,...)
wherex
andy
are the cartesian coordinates. The functionf
must accept two vectors of coordinatesx,y
and return the corresponding vector of function values. Additional arguments...
of any kind may be passed to the function.- a pixel image:
if
f
is a pixel image object of class"im"
(seeim.object
) then random points will be generated in the window of this pixel image, with probability density proportional to the pixel values off
.
The algorithm is as follows:
If
f
is a constant, we invokerunifpoint
.If
f
is a function, then we use the rejection method. Proposal points are generated from the uniform distribution. A proposal point \((x,y)\) is accepted with probabilityf(x,y,...)/fmax
and otherwise rejected. The algorithm continues untiln
points have been accepted. It gives up aftergiveup * n
proposals if there are still fewer thann
points.If
f
is a pixel image, then a random sequence of pixels is selected (usingsample
) with probabilities proportional to the pixel values off
. Then for each pixel in the sequence we generate a uniformly distributed random point in that pixel.
The algorithm for pixel images is more efficient than that for functions.
Value
A point pattern (an object of class "ppp"
)
if nsim=1
, or a list of point patterns if nsim > 1
.
See Also
Examples
# NOT RUN {
# 100 uniform random points in the unit square
X <- rpoint(100)
# 100 random points with probability density proportional to x^2 + y^2
X <- rpoint(100, function(x,y) { x^2 + y^2}, 1)
# `fmax' may be omitted
X <- rpoint(100, function(x,y) { x^2 + y^2})
# irregular window
data(letterR)
X <- rpoint(100, function(x,y) { x^2 + y^2}, win=letterR)
# make a pixel image
Z <- setcov(letterR)
# 100 points with density proportional to pixel values
X <- rpoint(100, Z)
# }