nndist
Nearest neighbour distances
Computes the distance from each point to its nearest neighbour in a point pattern. Alternatively computes the distance to the second nearest neighbour, or third nearest, etc.
Usage
nndist(X, ...) "nndist"(X, ..., k=1, by=NULL, method="C") "nndist"(X, Y=NULL, ..., k=1, by=NULL, method="C")
Arguments
 X,Y

Arguments specifying the locations of
a set of points.
For
nndist.ppp
, the argumentX
should be a point pattern (object of class"ppp"
). Fornndist.default
, typicallyX
andY
would be numeric vectors of equal length. AlternativelyY
may be omitted andX
may be a list with two componentsx
andy
, or a matrix with two columns.  ...

Ignored by
nndist.ppp
andnndist.default
.  k

Integer, or integer vector. The algorithm will compute the distance to the
k
th nearest neighbour.  by

Optional. A factor, which separates
X
into groups. The algorithm will compute the distance to the nearest point in each group.  method
 String specifying which method of calculation to use.
Values are
"C"
and"interpreted"
.
Details
This function computes the Euclidean distance from each point
in a point pattern to its nearest neighbour (the nearest other
point of the pattern). If k
is specified, it computes the
distance to the k
th nearest neighbour.
The function nndist
is generic, with
a method for point patterns (objects of class "ppp"
),
and a default method for coordinate vectors.
There is also a method for line segment patterns, nndist.psp
.
The method for point patterns expects a single
point pattern argument X
and returns the vector of its
nearest neighbour distances.
The default method expects that X
and Y
will determine
the coordinates of a set of points. Typically X
and
Y
would be numeric vectors of equal length. Alternatively
Y
may be omitted and X
may be a list with two components
named x
and y
, or a matrix or data frame with two columns.
The argument k
may be a single integer, or an integer vector.
If it is a vector, then the $k$th nearest neighbour distances are
computed for each value of $k$ specified in the vector.
If the argument by
is given, it should be a factor
,
of length equal to the number of points in X
.
This factor effectively partitions X
into subsets,
each subset associated with one of the levels of X
.
The algorithm will then compute, for each point of X
,
the distance to the nearest neighbour in each subset.
The argument method
is not normally used. It is
retained only for checking the validity of the software.
If method = "interpreted"
then the distances are
computed using interpreted R code only. If method="C"
(the default) then C code is used.
The C code is faster by two to three orders of magnitude
and uses much less memory.
If there is only one point (if x
has length 1),
then a nearest neighbour distance of Inf
is returned.
If there are no points (if x
has length zero)
a numeric vector of length zero is returned.
To identify which point is the nearest neighbour of a given point,
use nnwhich
.
To use the nearest neighbour distances for statistical inference,
it is often advisable to use the edgecorrected empirical distribution,
computed by Gest
.
To find the nearest neighbour distances from one point pattern
to another point pattern, use nncross
.
Value

Numeric vector or matrix containing the
nearest neighbour distances for each point.If
k = 1
(the default), the return value is a
numeric vector v
such that v[i]
is the
nearest neighbour distance for the i
th data point.If k
is a single integer, then the return value is a
numeric vector v
such that v[i]
is the
k
th nearest neighbour distance for the
i
th data point.If k
is a vector, then the return value is a
matrix m
such that m[i,j]
is the
k[j]
th nearest neighbour distance for the
i
th data point.If the argument by
is given, then the result is a data frame
containing the distances described above, from each point of X
,
to the nearest point in each subset of X
defined by the factor by
.
Nearest neighbours of each type
If X
is a multitype point pattern
and by=marks(X)
, then the algorithm will compute,
for each point of X
, the distance to the nearest neighbour
of each type. See the Examples. To find the minimum distance from any point of type i
to the nearest point of type j
, for all combinations of i
and
j
, use the R function aggregate
as
suggested in the Examples.
Warnings
An infinite or NA
value is returned if the
distance is not defined (e.g. if there is only one point
in the point pattern).
See Also
nndist.psp
,
pairdist
,
Gest
,
nnwhich
,
nncross
.
Examples
data(cells)
# nearest neighbours
d < nndist(cells)
# second nearest neighbours
d2 < nndist(cells, k=2)
# first, second and third nearest
d1to3 < nndist(cells, k=1:3)
x < runif(100)
y < runif(100)
d < nndist(x, y)
# Stienen diagram
plot(cells %mark% (nndist(cells)/2), markscale=1)
# distance to nearest neighbour of each type
nnda < nndist(ants, by=marks(ants))
head(nnda)
# For nest number 1, the nearest Cataglyphis nest is 87.32125 units away
# Use of 'aggregate':
# minimum distance between each pair of types
aggregate(nnda, by=list(from=marks(ants)), min)
# Always a symmetric matrix
# mean nearest neighbour distances
aggregate(nnda, by=list(from=marks(ants)), mean)
# The mean distance from a Messor nest to
# the nearest other Messor nest is 59.02549 units