rmpoint
Generate N Random Multitype Points
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
- n
- 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.
- f
- 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 functionsf(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
fis 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
fif 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.
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.
Value
- The simulated point pattern (an object of class
"ppp").
See Also
Examples
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))