| rmpoispp {spatstat} | R Documentation |
Generate a random point pattern, a realisation of the (homogeneous or inhomogeneous) multitype Poisson process.
rmpoispp(lambda, lmax=NULL, win, types, ...)
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.
|
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.
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.
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
seq(lambda).
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.
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 seq(lambda).
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.
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 seq(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)/lmax.
The simulated multitype point pattern (an object of class "ppp"
with a component marks which is a factor).
Adrian Baddeley adrian@maths.uwa.edu.au http://www.maths.uwa.edu.au/~adrian/ and Rolf Turner rolf@math.unb.ca http://www.math.unb.ca/~rolf
# 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
data(letterR)
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)