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.