closepairs

0th

Percentile

Close Pairs of Points

Low-level functions to find all close pairs of points.

Keywords
spatial, math
Usage
closepaircounts(X, r)

crosspaircounts(X, Y, r)

closepairs(X, rmax, …)

# S3 method for ppp closepairs(X, rmax, twice=TRUE, what=c("all","indices","ijd"), distinct=TRUE, neat=TRUE, periodic=FALSE, …)

crosspairs(X, Y, rmax, …)

# S3 method for ppp crosspairs(X, Y, rmax, what=c("all", "indices", "ijd"), …)

Arguments
X,Y

Point patterns (objects of class "ppp").

r,rmax

Maximum distance between pairs of points to be counted as close pairs.

twice

Logical value indicating whether all ordered pairs of close points should be returned. If twice=TRUE (the default), each pair will appear twice in the output, as (i,j) and again as (j,i). If twice=FALSE, then each pair will appear only once, as the pair (i,j) with i < j.

what

String specifying the data to be returned for each close pair of points. If what="all" (the default) then the returned information includes the indices i,j of each pair, their x,y coordinates, and the distance between them. If what="indices" then only the indices i,j are returned. If what="ijd" then the indices i,j and the distance d are returned.

distinct

Logical value indicating whether to return only the pairs of points with different indices i and j (distinct=TRUE, the default) or to also include the pairs where i=j (distinct=FALSE).

neat

Logical value indicating whether to ensure that i < j in each output pair, when twice=FALSE.

periodic

Logical value indicating whether to use the periodic edge correction. The window of X should be a rectangle. Opposite pairs of edges of the window will be treated as identical.

Extra arguments, ignored by methods.

Details

These are the efficient low-level functions used by spatstat to find all close pairs of points in a point pattern or all close pairs between two point patterns.

closepaircounts(X,r) counts the number of neighbours for each point in the pattern X. That is, for each point X[i], it counts the number of other points X[j] with j != i such that d(X[i],X[j]) <= r where d denotes Euclidean distance. The result is an integer vector v such that v[i] is the number of neighbours of X[i].

crosspaircounts(X,Y,r) counts, for each point in the pattern X, the number of neighbours in the pattern Y. That is, for each point X[i], it counts the number of points Y[j] such that d(X[i],X[j]) <= r. The result is an integer vector v such that v[i] is the number of neighbours of X[i] in the pattern Y.

closepairs(X,rmax) identifies all pairs of distinct neighbours in the pattern X and returns them. The result is a list with the following components:

i

Integer vector of indices of the first point in each pair.

j

Integer vector of indices of the second point in each pair.

xi,yi

Coordinates of the first point in each pair.

xj,yj

Coordinates of the second point in each pair.

dx

Equal to xj-xi

dy

Equal to yj-yi

d

Euclidean distance between each pair of points.

If what="indices" then only the components i and j are returned. This is slightly faster and more efficient with use of memory.

crosspairs(X,rmax) identifies all pairs of neighbours (X[i], Y[j]) between the patterns X and Y, and returns them. The result is a list with the same format as for closepairs.

Value

For closepaircounts and crosspaircounts, an integer vector of length equal to the number of points in X.

For closepairs and crosspairs, a list with components i and j, and possibly other components as described under Details.

Warning about accuracy

The results of these functions may not agree exactly with the correct answer (as calculated by a human) and may not be consistent between different computers and different installations of R. The discrepancies arise in marginal cases where the interpoint distance is equal to, or very close to, the threshold rmax.

Floating-point numbers in a computer are not mathematical Real Numbers: they are approximations using finite-precision binary arithmetic. The approximation is accurate to a tolerance of about .Machine$double.eps.

If the true interpoint distance \(d\) and the threshold rmax are equal, or if their difference is no more than .Machine$double.eps, the result may be incorrect.

See Also

closepairs.pp3 for the corresponding functions for 3D point patterns.

Kest, Kcross, nndist, nncross, applynbd, markstat for functions which use these capabilities.

Aliases
  • closepairs
  • crosspairs
  • closepairs.ppp
  • crosspairs.ppp
  • closepaircounts
  • crosspaircounts
Examples
# NOT RUN {
   a <- closepaircounts(cells, 0.1)
   sum(a)

   Y <- split(amacrine)
   b <- crosspaircounts(Y$on, Y$off, 0.1)

   d <- closepairs(cells, 0.1)
   e <- crosspairs(Y$on, Y$off, 0.1)
# }
Documentation reproduced from package spatstat, version 1.57-1, License: GPL (>= 2)

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