multiplicity.ppp: Count Multiplicity of Duplicate Points

Description

Counts the number of duplicates for each point in a spatial point pattern.

Usage

multiplicity(x)
 ## S3 method for class 'ppp':
multiplicity(x)
 ## S3 method for class 'ppx':
multiplicity(x)
 ## S3 method for class 'data.frame':
multiplicity(x)
 ## S3 method for class 'default':
multiplicity(x)

Arguments

A spatial point pattern (object of class "ppp" or "ppx") or a vector, matrix or data frame.

Value

A vector of integers (multiplicities) of length equal to the number of points in x.

Details

Two points in a point pattern are deemed to be identical if their $x,y$ coordinates are the same, and their marks are also the same (if they carry marks). The Examples section illustrates how it is possible for a point pattern to contain a pair of identical points.

For each point in x, the function multiplicity counts how many points are identical to it, and returns the vector of counts.

The argument x can also be a vector, a matrix or a data frame. When x is a vector, m <- multiplicity(x) is a vector of the same length as x, and m[i] is the number of elements of x that are identical to x[i]. When x is a matrix or data frame, m <- multiplicity(x) is a vector of length equal to the number of rows of x, and m[i] is the number of rows of x that are identical to the ith row.

Examples

Run this code

X <- ppp(c(1,1,0.5,1), c(2,2,1,2), window=square(3), check=FALSE)
   m <- multiplicity(X)

   # unique points in X, marked by their multiplicity
   first <- !duplicated(X)
   Y <- X[first] %mark% m[first]

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