Local Multitype K Function (Cross-Type)
for a multitype point pattern, computes the cross-type version of the local K function.
localKcross(X, from, to, ..., rmax = NULL,
correction = "Ripley", verbose = TRUE, rvalue=NULL)
localLcross(X, from, to, ..., rmax = NULL, correction = "Ripley")X |
A multitype point pattern (object of class |
... |
Further arguments passed from |
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 |
to |
Type of points to which distances should be measured.
A single value;
one of the possible levels of |
correction |
String specifying the edge correction to be applied.
Options are |
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. |
Given a multitype spatial point pattern X,
the local cross-type K function localKcross
is the local version of the multitype K function
Kcross.
Recall that Kcross(X, from, to) is a sum of contributions
from all pairs of points in X where
the first point belongs to from
and the second point belongs to type to.
The local cross-type K
function is defined for each point X[i] that belongs to
type from, and it consists of all the contributions to
the cross-type K function that originate from point X[i]:
K[i,from,to](r) = sqrt( (a/((n-1)* pi)) * sum[j] e[i,j])
where the sum is over all points j != i
belonging to type to, that lie
within a distance r of the ith point,
a is the area of the observation window, n is the number
of points in X, and e[i,j] is an edge correction
term (as described in Kest).
The value of K[i,from,to](r)
can also be interpreted as one
of the summands that contributes to the global estimate of the
Kcross function.
By default, the function K[i,from,to](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 cross-type L function localLcross
is computed by applying the transformation
L(r) = sqrt(K(r)/(2*pi)).
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.
r |
the vector of values of the argument r at which the function K has been estimated |
theo |
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.
Ege Rubak rubak@math.aau.dk and Adrian Baddeley Adrian.Baddeley@curtin.edu.au.
Inhomogeneous counterparts of localK and localL
are computed by localKcross.inhom and
localLinhom.
X <- amacrine # compute all the local Lcross functions L <- localLcross(X) # plot all the local Lcross functions against r plot(L, main="local Lcross 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 <- localLcross(X, rvalue=0.1)
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