# applynbd

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##### Apply Function to Every Neighbourhood in a Point Pattern

Visit each point in a point pattern, find the neighbouring points, and apply a given function to them.

Keywords
spatial, programming, iteration
##### Usage
applynbd(X, FUN, N=NULL, R=NULL, criterion=NULL, exclude=FALSE, …)
##### Arguments
X

Point pattern. An object of class "ppp", or data which can be converted into this format by as.ppp.

FUN

Function to be applied to each neighbourhood. The arguments of FUN are described under Details.

N

Integer. If this argument is present, the neighbourhood of a point of X is defined to consist of the N points of X which are closest to it.

R

Nonnegative numeric value. If this argument is present, the neighbourhood of a point of X is defined to consist of all points of X which lie within a distance R of it.

criterion

Function. If this argument is present, the neighbourhood of a point of X is determined by evaluating this function. See under Details.

exclude

Logical. If TRUE then the point currently being visited is excluded from its own neighbourhood.

extra arguments passed to the function FUN. They must be given in the form name=value.

##### Details

This is an analogue of apply for point patterns. It visits each point in the point pattern X, determines which points of X are neighbours'' of the current point, applies the function FUN to this neighbourhood, and collects the values returned by FUN.

The definition of neighbours'' depends on the arguments N, R and criterion. Also the argument exclude determines whether the current point is excluded from its own neighbourhood.

• If N is given, then the neighbours of the current point are the N points of X which are closest to the current point (including the current point itself unless exclude=TRUE).

• If R is given, then the neighbourhood of the current point consists of all points of X which lie closer than a distance R from the current point.

• If criterion is given, then it must be a function with two arguments dist and drank which will be vectors of equal length. The interpretation is that dist[i] will be the distance of a point from the current point, and drank[i] will be the rank of that distance (the three points closest to the current point will have rank 1, 2 and 3). This function must return a logical vector of the same length as dist and drank whose i-th entry is TRUE if the corresponding point should be included in the neighbourhood. See the examples below.

• If more than one of the arguments N, R and criterion is given, the neighbourhood is defined as the intersection of the neighbourhoods specified by these arguments. For example if N=3 and R=5 then the neighbourhood is formed by finding the 3 nearest neighbours of current point, and retaining only those neighbours which lie closer than 5 units from the current point.

When applynbd is executed, each point of X is visited, and the following happens for each point:

• the neighbourhood of the current point is determined according to the chosen rule, and stored as a point pattern Y;

• the function FUN is called as:

FUN(Y=Y, current=current, dists=dists, dranks=dranks, …)

where current is the location of the current point (in a format explained below), dists is a vector of distances from the current point to each of the points in Y, dranks is a vector of the ranks of these distances with respect to the full point pattern X, and … are the arguments passed from the call to applynbd;

• The result of the call to FUN is stored.

The results of each call to FUN are collected and returned according to the usual rules for apply and its relatives. See the Value section of this help file.

The format of the argument current is as follows. If X is an unmarked point pattern, then current is a vector of length 2 containing the coordinates of the current point. If X is marked, then current is a point pattern containing exactly one point, so that current$x is its $x$-coordinate and current$marks is its mark value. In either case, the coordinates of the current point can be referred to as current$x and current$y.

Note that FUN will be called exactly as described above, with each argument named explicitly. Care is required when writing the function FUN to ensure that the arguments will match up. See the Examples.

See markstat for a common use of this function.

To simply tabulate the marks in every R-neighbourhood, use marktable.

##### Value

Similar to the result of apply. If each call to FUN returns a single numeric value, the result is a vector of dimension npoints(X), the number of points in X. If each call to FUN returns a vector of the same length m, then the result is a matrix of dimensions c(m,n); note the transposition of the indices, as usual for the family of apply functions. If the calls to FUN return vectors of different lengths, the result is a list of length npoints(X).

ppp.object, apply, markstat, marktable

• applynbd
##### Examples
# NOT RUN {
redwood
# count the number of points within radius 0.2 of each point of X
nneighbours <- applynbd(redwood, R=0.2, function(Y, ...){npoints(Y)-1})
# equivalent to:
nneighbours <- applynbd(redwood, R=0.2, function(Y, ...){npoints(Y)}, exclude=TRUE)

# compute the distance to the second nearest neighbour of each point
secondnndist <- applynbd(redwood, N = 2,
function(dists, ...){max(dists)},
exclude=TRUE)

# marked point pattern
trees <- longleaf

# }
# NOT RUN {
# compute the median of the marks of all neighbours of a point
dbh.med <- applynbd(trees, R=90, exclude=TRUE,
function(Y, ...) { median(marks(Y))})

# ANIMATION explaining the definition of the K function
# (arguments fullpicture' and 'rad' are passed to FUN)

if(interactive()) {
showoffK <- function(Y, current, dists, dranks, fullpicture,rad) {
plot(fullpicture, main="")
points(Y, cex=2)
ux <- current[["x"]]
uy <- current[["y"]]
points(ux, uy, pch="+",cex=3)
theta <- seq(0,2*pi,length=100)
if(interactive()) Sys.sleep(if(runif(1) < 0.1) 1.5 else 0.3)
return(npoints(Y))
}
applynbd(redwood, R=0.2, showoffK, fullpicture=redwood, rad=0.2, exclude=TRUE)

# animation explaining the definition of the G function

showoffG <- function(Y, current, dists, dranks, fullpicture) {
plot(fullpicture, main="")
points(Y, cex=2)
u <- current
points(u,u,pch="+",cex=3)
v <- c(Y$x,Y$y)
segments(u,u,v,v,lwd=2)
w <- (u + v)/2
nnd <- dists
text(w,w,round(nnd,3),cex=2)
if(interactive()) Sys.sleep(if(runif(1) < 0.1) 1.5 else 0.3)
return(nnd)
}

applynbd(cells, N=1, showoffG, exclude=TRUE, fullpicture=cells)
}
# }
`
Documentation reproduced from package spatstat, version 1.61-0, License: GPL (>= 2)

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