# pppmatching.object

##### Class of Point Matchings

A class `"pppmatching"`

to represent a matching of two planar
point patterns.
Optionally includes information about the construction of the matching
and its associated distance between the point patterns.

##### Details

This class represents a (possibly weighted and incomplete) matching
between two planar point patterns (objects of class `"ppp"`

).

A matching can be thought of as a bipartite weighted graph where the vertices are given by the two point patterns and edges of positive weights are drawn each time a point of the first point pattern is "matched" with a point of the second point pattern.

If `m`

is an object of type `pppmatching`

, it contains the
following elements
`pp1, pp2`

the two point patterns to be matched (vertices)
`matrix`

a matrix specifying which points are matched
and with what weights (edges)
`type`

(optional) a character string for the type of
the matching (one of `"spa"`

, `"ace"`

or `"mat"`

)
`cutoff`

(optional) cutoff value for interpoint distances
`q`

(optional) the order for taking averages of
interpoint distances
`distance`

(optional) the distance associated with the matching
}

The element `matrix`

is a "generalized adjacency matrix".
The numbers of rows
and columns match the cardinalities of the first and second point
patterns, respectively. The `[i,j]`

-th entry is positive if
the `i`

-th point of `X`

and the `j`

-th point of
`Y`

are matched (zero otherwise) and its value then gives
the corresponding weight of the match. For an unweighted matching
all the weights are set to $1$.

The optional elements are for saving details about matchings in the context of
optimal point matching techniques. `type`

can be one of `"spa"`

(for
"subpattern assignment"), `"ace"`

(for "assignment only if
cardinalities differ") or `"mat"`

(for "mass transfer"). `cutoff`

is a positive numerical value that specifies the maximal interpoint distance and
`q`

is a value in $[1,\infty]$ that gives the order of the average
applied to the interpoint distances. See the help files for `pppdist`

and `matchingdist`

for detailed information about these elements.
Objects of class `"pppmatching"`

may be created by the function
`pppmatching`

, and are most commonly obtained as output of the
function `pppdist`

. There are methods `plot`

, `print`

and
`summary`

for this class.

##### See Also

##### Examples

```
# a random complete unweighted matching
X <- runifpoint(10)
Y <- runifpoint(10)
am <- r2dtable(1, rep(1,10), rep(1,10))[[1]]
# generates a random permutation matrix
m <- pppmatching(X, Y, am)
summary(m)
m$matrix
plot(m)
# an optimal complete unweighted matching
m2 <- pppdist(X,Y)
summary(m2)
m2$matrix
plot(m2)
```

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