# pppdist

##### Optimal Match Between Two Point Patterns

Given two point patterns, find the optimal match between them.

##### Usage

`pppdist(X, Y, q = 1, precision = 7, show.rprimal = FALSE, belowone = TRUE, timelag = 0)`

##### Arguments

- X,Y
- Two point patterns (objects of class
`"ppp"`

). - q
- Exponent of the Wasserstein distance
(or
`Inf`

for the Prohorov distance). - precision
- Index controlling accuracy of algorithm.
Interpoint distances will be rounded to the nearest multiple of
`10^(-precision)`

. - show.rprimal
- Logical. Whether to display a plot showing the iterative solution of the restricted primal problem.
- belowone
- Logical. Experimental use only. Indicates whether to rescale the distances by a fudge factor.
- timelag
- Time lag, in seconds, between successive displays of the iterative solution of the restricted primal problem.

##### Details

Finds the matching between the point patterns `X`

and `Y`

which minimises the sum of the distances between matched points
(if `q=1`

), the maximum distance between matched points
(if `q=Inf`

), and in general the `1/q`

th power of the sum of
the `q`

th powers of the distances between matched points.
If $q < 1$ this is known as the Wasserstein distance,
and if $q=Inf$ it is the Prohorov distance.

For finite exponents `q`

, there is a fast C algorithm,
which will handle patterns of 100 points without difficulty,
but should not be used with thousands of points.
If `show.rprimal=TRUE`

, slower interpreted code is used
to demonstrate the algorithm.
For `q=Inf`

, even slower interpreted R code is used,
and this works only for very small point patterns.

##### Value

- An object of class
`pppmatching`

that represents the matching. There are methods for`plot`

,`print`

and`summary`

for this class.

##### Examples

```
X <- runifpoint(42)
Y <- runifpoint(42)
pppdist(X, Y)
pppdist(X[1:10], Y[1:10], q=Inf)
```

*Documentation reproduced from package spatstat, version 1.11-2, License: GPL version 2 or newer*