rmpoispp {spatstat.random}

Generate Multitype Poisson Point Pattern

Description

Generate a random point pattern, a realisation of the (homogeneous or inhomogeneous) multitype Poisson process.

Usage

 rmpoispp(lambda, lmax=NULL, win, types, ...,
          nsim=1, drop=TRUE, warnwin=!missing(win))

Arguments

lambda

Intensity of the multitype Poisson process. Either a single positive number, a vector, a function(x,y,m, ...), a pixel image, a list of functions function(x,y, ...), or a list of pixel images.

lmax

An upper bound for the value of lambda. May be omitted

win

Window in which to simulate the pattern. An object of class "owin" or something acceptable to as.owin. Ignored if lambda is a pixel image or list of images.

types

All the possible types for the multitype pattern.

...

Arguments passed to lambda if it is a function.

nsim

Number of simulated realisations to be generated.

drop

Logical. If nsim=1 and drop=TRUE (the default), the result will be a point pattern, rather than a list containing a point pattern.

warnwin

Logical value specifying whether to issue a warning when win is ignored.

Details

This function generates a realisation of the marked Poisson point process with intensity lambda.

Note that the intensity function \lambda(x,y,m) is the average number of points of type m per unit area near the location (x,y). Thus a marked point process with a constant intensity of 10 and three possible types will have an average of 30 points per unit area, with 10 points of each type on average.

The intensity function may be specified in any of the following ways.

single number:

If lambda is a single number, then this algorithm generates a realisation of the uniform marked Poisson process inside the window win with intensity lambda for each type. The total intensity of points of all types is lambda * length(types). The argument types must be given and determines the possible types in the multitype pattern.

vector:

If lambda is a numeric vector, then this algorithm generates a realisation of the stationary marked Poisson process inside the window win with intensity lambda[i] for points of type types[i]. The total intensity of points of all types is sum(lambda). The argument types defaults to names(lambda), or if that is null, 1:length(lambda).

function:

If lambda is a function, the process has intensity lambda(x,y,m,...) at spatial location (x,y) for points of type m. The function lambda must work correctly with vectors x, y and m, returning a vector of function values. (Note that m will be a factor with levels equal to types.) The value lmax, if present, must be an upper bound on the values of lambda(x,y,m,...) for all locations (x, y) inside the window win and all types m. The argument types must be given.

list of functions:

If lambda is a list of functions, the process has intensity lambda[[i]](x,y,...) at spatial location (x,y) for points of type types[i]. The function lambda[[i]] must work correctly with vectors x and y, returning a vector of function values. The value lmax, if given, must be an upper bound on the values of lambda(x,y,...) for all locations (x, y) inside the window win. The argument types defaults to names(lambda), or if that is null, 1:length(lambda).

pixel image:

If lambda is a pixel image object of class "im" (see im.object), the intensity at a location (x,y) for points of any type is equal to the pixel value of lambda for the pixel nearest to (x,y). The argument win is ignored; the window of the pixel image is used instead. The argument types must be given.

list of pixel images:

If lambda is a list of pixel images, then the image lambda[[i]] determines the intensity of points of type types[i]. The argument win is ignored; the window of the pixel image is used instead. The argument types defaults to names(lambda), or if that is null, 1:length(lambda).

If lmax is missing, an approximate upper bound will be calculated.

To generate an inhomogeneous Poisson process the algorithm uses “thinning”: it first generates a uniform Poisson process of intensity lmax for points of each type m, then randomly deletes or retains each point independently, with retention probability p(x,y,m) = \lambda(x,y,m)/\mbox{lmax}.

Value

A point pattern (an object of class "ppp") if nsim=1, or a list of point patterns if nsim > 1. Each point pattern is multitype (it carries a vector of marks which is a factor).

Author(s)

Adrian Baddeley [e-mail]

and Rolf Turner [e-mail]

See Also

rpoispp for unmarked Poisson point process; rmpoint for a fixed number of random marked points; im.object, owin.object, ppp.object.

Examples

 # uniform bivariate Poisson process with total intensity 100 in unit square
 pp <- rmpoispp(50, types=c("a","b"))
 
 # stationary bivariate Poisson process with intensity A = 30, B = 70
 pp <- rmpoispp(c(30,70), types=c("A","B"))
 pp <- rmpoispp(c(30,70))

 # works in any window
 pp <- rmpoispp(c(30,70), win=letterR, types=c("A","B"))

 # inhomogeneous lambda(x,y,m)
 # note argument 'm' is a factor 
 lam <- function(x,y,m) { 50 * (x^2 + y^3) * ifelse(m=="A", 2, 1)}
 pp <- rmpoispp(lam, win=letterR, types=c("A","B"))
 # extra arguments
 lam <- function(x,y,m,scal) { scal * (x^2 + y^3) * ifelse(m=="A", 2, 1)}
 pp <- rmpoispp(lam, win=letterR, types=c("A","B"), scal=50)

 # list of functions lambda[[i]](x,y)
 lams <- list(function(x,y){50 * x^2}, function(x,y){20 * abs(y)})
 pp <- rmpoispp(lams, win=letterR, types=c("A","B"))
 pp <- rmpoispp(lams, win=letterR)
 # functions with extra arguments
 lams <- list(function(x,y,scal){5 * scal * x^2},
              function(x,y, scal){2 * scal * abs(y)})
 pp <- rmpoispp(lams, win=letterR, types=c("A","B"), scal=10)
 pp <- rmpoispp(lams, win=letterR, scal=10)

 # florid example
 lams <- list(function(x,y){
   			   100*exp((6*x + 5*y - 18*x^2 + 12*x*y - 9*y^2)/6)
                         }
                         # log quadratic trend
              ,
              function(x,y){
                         	   100*exp(-0.6*x+0.5*y)
                         }
                        # log linear trend
              )
  X <- rmpoispp(lams, win=unit.square(), types=c("on", "off"))   

 # pixel image
 Z <- as.im(function(x,y){30 * (x^2 + y^3)}, letterR)
 pp <- rmpoispp(Z, types=c("A","B"))

 # list of pixel images
 ZZ <- list(
          as.im(function(x,y){20 * (x^2 + y^3)}, letterR),
          as.im(function(x,y){40 * (x^3 + y^2)}, letterR))
 pp <- rmpoispp(ZZ, types=c("A","B"))
 pp <- rmpoispp(ZZ)

 # randomising an existing point pattern
 rmpoispp(intensity(amacrine), win=Window(amacrine))