# localKdot

##### Local Multitype K Function (Dot-Type)

for a multitype point pattern, computes the dot-type version of the local K function.

- Keywords
- spatial, nonparametric

##### Usage

```
localKdot(X, from, …, rmax = NULL,
correction = "Ripley", verbose = TRUE, rvalue=NULL)
localLdot(X, from, …, rmax = NULL, correction = "Ripley")
```

##### Arguments

- X
A multitype point pattern (object of class

`"ppp"`

with marks which are a factor).- …
Further arguments passed from

`localLdot`

to`localKdot`

.- rmax
Optional. Maximum desired value of the argument \(r\).

- from
Type of points from which distances should be measured. A single value; one of the possible levels of

`marks(X)`

, or an integer indicating which level.- correction
String specifying the edge correction to be applied. Options are

`"none"`

,`"translate"`

,`"translation"`

,`"Ripley"`

,`"isotropic"`

or`"best"`

. Only one correction may be specified.- verbose
Logical flag indicating whether to print progress reports during the calculation.

- rvalue
Optional. A

*single*value of the distance argument \(r\) at which the function L or K should be computed.

##### Details

Given a multitype spatial point pattern `X`

,
the local dot-type \(K\) function `localKdot`

is the local version of the multitype \(K\) function
`Kdot`

.
Recall that `Kdot(X, from)`

is a sum of contributions
from all pairs of points in `X`

where
the first point belongs to `from`

.
The *local* dot-type \(K\)
function is defined for each point `X[i]`

that belongs to
type `from`

, and it consists of all the contributions to
the dot-type \(K\) function that originate from point `X[i]`

:
$$
K_{i,from,to}(r) = \sqrt{\frac a {(n-1) \pi} \sum_j e_{ij}}
$$
where the sum is over all points \(j \neq i\)
that lie within a distance \(r\) of the \(i\)th point,
\(a\) is the area of the observation window, \(n\) is the number
of points in `X`

, and \(e_{ij}\) is an edge correction
term (as described in `Kest`

).
The value of \(K_{i,from}(r)\)
can also be interpreted as one
of the summands that contributes to the global estimate of the
`Kdot`

function.

By default, the function \(K_{i,from}(r)\)
is computed for a range of \(r\) values
for each point \(i\) belonging to type `from`

.
The results are stored as a function value
table (object of class `"fv"`

) with a column of the table
containing the function estimates for each point of the pattern
`X`

belonging to type `from`

.

Alternatively, if the argument `rvalue`

is given, and it is a
single number, then the function will only be computed for this value
of \(r\), and the results will be returned as a numeric vector,
with one entry of the vector for each point of the pattern `X`

belonging to type `from`

.

The local dot-type \(L\) function `localLdot`

is computed by applying the transformation
\(L(r) = \sqrt{K(r)/(2\pi)}\).

##### Value

If `rvalue`

is given, the result is a numeric vector
of length equal to the number of points in the point pattern
that belong to type `from`

.

If `rvalue`

is absent, the result is
an object of class `"fv"`

, see `fv.object`

,
which can be plotted directly using `plot.fv`

.
Essentially a data frame containing columns

the vector of values of the argument \(r\) at which the function \(K\) has been estimated

the theoretical value \(K(r) = \pi r^2\) or \(L(r)=r\) for a stationary Poisson process

##### See Also

##### Examples

```
# NOT RUN {
X <- amacrine
# compute all the local Ldot functions
L <- localLdot(X)
# plot all the local Ldot functions against r
plot(L, main="local Ldot functions for amacrine", legend=FALSE)
# plot only the local L function for point number 7
plot(L, iso007 ~ r)
# compute the values of L(r) for r = 0.1 metres
L12 <- localLdot(X, rvalue=0.1)
# }
```

*Documentation reproduced from package spatstat, version 1.63-0, License: GPL (>= 2)*