# 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 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

- 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

```
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 1.36-0, License: GPL (>= 2)*