rmpoint: Generate N Random Multitype Points

Description

Generate a random multitype point pattern with a fixed number of points, or a fixed number of points of each type.

Usage

rmpoint(n, f=1, fmax=NULL, win=unit.square(),
         types, ptypes,
         ..., giveup=1000, verbose=FALSE)

Arguments

Number of marked points to generate. Either a single number specifying the total number of points, or a vector specifying the number of points of each type.

The probability density of the multitype points, usually un-normalised. Either a constant, a vector, a function f(x,y,m, ...), a pixel image, a list of functions f(x,y,...) or a list of pixel images.

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 or list of pixel images.

types

All the possible types for the multitype pattern.

ptypes

Optional vector of probabilities for each type.

...

Arguments passed to f if it is a function.

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.

Value

The simulated point pattern (an object of class "ppp").

Details

This function generates random multitype point patterns consisting of a fixed number of points. Three different models are available: [object Object],[object Object],[object Object] Note that the density f is normalised in different ways in Model I and Models II and III. In Model I the normalised joint density is $g(x,y,m)=f(x,y,m)/Z$ where $$Z = \sum_m \int\int \lambda(x,y,m) {\rm d}x \, {\rm d}y$$ while in Models II and III the normalised conditional density is $g(x,y\mid m) = f(x,y,m)/Z_m$ where $$Z_m = \int\int \lambda(x,y,m) {\rm d}x \, {\rm d}y.$$ In Model I, the marginal distribution of types is $p_m = Z_m/Z$. The unnormalised density f may be specified in any of the following ways. [object Object],[object Object],[object Object],[object Object],[object Object],[object Object] The implementation uses the rejection method. For Model I, rmpoispp is called repeatedly until n points have been generated. It gives up after giveup calls if there are still fewer than n points. For Model II, the types are first generated according to ptypes, then the locations of the points of each type are generated using rpoint. For Model III, the locations of the points of each type are generated using rpoint.

Examples

Run this code

abc <- c("a","b","c")

##### Model I

rmpoint(25, types=abc)
rmpoint(25, 1, types=abc)
# 25 points, equal probability for each type, uniformly distributed locations

rmpoint(25, function(x,y,m) {rep(1, length(x))}, types=abc)
# same as above
rmpoint(25, list(function(x,y){rep(1, length(x))},
                 function(x,y){rep(1, length(x))},
                 function(x,y){rep(1, length(x))}),
             types=abc)
# same as above

rmpoint(25, function(x,y,m) { x }, types=abc)
# 25 points, equal probability for each type,
# locations nonuniform with density proportional to x

rmpoint(25, function(x,y,m) { ifelse(m == "a", 1, x) }, types=abc)
rmpoint(25, list(function(x,y) { rep(1, length(x)) },
                function(x,y) { x },
                function(x,y) { x }),
                types=abc)
# 25 points, UNEQUAL probabilities for each type,
# type "a" points uniformly distributed,
# type "b" and "c" points nonuniformly distributed.

##### Model II

rmpoint(25, 1, types=abc, ptypes=rep(1,3)/3)
rmpoint(25, 1, types=abc, ptypes=rep(1,3))
# 25 points, equal probability for each type,
# uniformly distributed locations

rmpoint(25, function(x,y,m) {rep(1, length(x))}, types=abc, ptypes=rep(1,3))
# same as above
rmpoint(25, list(function(x,y){rep(1, length(x))},
                 function(x,y){rep(1, length(x))},
                 function(x,y){rep(1, length(x))}),
             types=abc, ptypes=rep(1,3))
# same as above

rmpoint(25, function(x,y,m) { x }, types=abc, ptypes=rep(1,3))
# 25 points, equal probability for each type,
# locations nonuniform with density proportional to x

rmpoint(25, function(x,y,m) { ifelse(m == "a", 1, x) }, types=abc, ptypes=rep(1,3))
# 25 points, EQUAL probabilities for each type,
# type "a" points uniformly distributed,
# type "b" and "c" points nonuniformly distributed.

###### Model III

rmpoint(c(12, 8, 4), 1, types=abc)
# 12 points of type "a",
# 8 points of type "b",
# 4 points of type "c",
# each uniformly distributed

rmpoint(c(12, 8, 4), function(x,y,m) { ifelse(m=="a", 1, x)}, types=abc)
rmpoint(c(12, 8, 4), list(function(x,y) { rep(1, length(x)) },
                               function(x,y) { x },
                               function(x,y) { x }),
             types=abc)

# 12 points of type "a", uniformly distributed
# 8 points of type "b", nonuniform
# 4 points of type "c", nonuniform


#########

## Randomising an existing point pattern:
data(demopat)
X <- demopat

# same numbers of points of each type, uniform random locations (Model III)
rmpoint(table(X$marks), 1, types=levels(X$marks), win=X$window)

# same total number of points, distribution of types estimated from X,
# uniform random locations (Model II)
rmpoint(X$n, 1, types=levels(X$marks), win=X$window,
       ptypes=table(X$marks))