# multiplicity.ppp

##### Count Multiplicity of Duplicate Points

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

##### Usage

`multiplicity(x)` # S3 method for ppp
multiplicity(x)

# S3 method for ppx
multiplicity(x)

# S3 method for data.frame
multiplicity(x)

# S3 method for default
multiplicity(x)

##### Arguments

- x
A spatial point pattern (object of class

`"ppp"`

or`"ppx"`

) or a vector, matrix or data frame.

##### 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 `i`

th row.

##### Value

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

.

##### See Also

##### Examples

```
# NOT RUN {
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]
# }
```

*Documentation reproduced from package spatstat, version 1.61-0, License: GPL (>= 2)*