for a multitype point pattern, computes the dot-type version of the local K function.
localKdot(X, from, ..., rmax = NULL,
correction = "Ripley", verbose = TRUE, rvalue=NULL)
localLdot(X, from, ..., rmax = NULL, correction = "Ripley")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
together with columns containing the values of the
neighbourhood density function for each point in the pattern.
Column i corresponds to the ith point
of type from.
The last two columns contain the r and theo values.
A multitype point pattern (object of class "ppp"
with marks which are a factor).
Further arguments passed from localLdot to
localKdot.
Optional. Maximum desired value of the argument \(r\).
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.
String specifying the edge correction to be applied.
Options are "none", "translate", "translation",
"Ripley",
"isotropic" or "best".
Only one correction may be specified.
Logical flag indicating whether to print progress reports during the calculation.
Optional. A single value of the distance argument \(r\) at which the function L or K should be computed.
Ege Rubak rubak@math.aau.dk and Adrian Baddeley Adrian.Baddeley@curtin.edu.au.
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
\(L(r) = \sqrt{K(r)/(2\pi)}\).
Kdot,
Ldot,
localK,
localL.
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)
Run the code above in your browser using DataLab