# multiplicity.ppp

From spatstat v1.13-1
by Adrian Baddeley

##### Count Multiplicity of Duplicate Points

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

##### Usage

`multiplicity.ppp(x)`

##### Arguments

- x
- A spatial point pattern
(object of class
`"ppp"`

).

##### 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`

, this function counts how many
points are identical to it, and returns the vector of counts.

##### 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), c(2,2,1), window=square(3))
m <- multiplicity.ppp(X)
# unique points in X, marked by multiplicity
first <- !duplicated(X)
Y <- X[first] %mark% m[first]
```

*Documentation reproduced from package spatstat, version 1.13-1, License: GPL (>= 2)*

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