# pppdist

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##### Optimal Match Between Two Point Patterns

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

Keywords
spatial, math
##### 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/qth power of the sum of the qth 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.

• pppdist
##### 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 1.11-8, License: GPL version 2 or newer

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