Finds the nearest neighbour of each point in a point pattern.

```
nnwhich(X, …)
# S3 method for ppp
nnwhich(X, …, k=1, by=NULL, method="C")
# S3 method for default
nnwhich(X, Y=NULL, …, k=1, by=NULL, method="C")
```

X,Y

Arguments specifying the locations of
a set of points.
For `nnwhich.ppp`

, the argument `X`

should be a point
pattern (object of class `"ppp"`

).
For `nnwhich.default`

, 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 `x`

and `y`

,
or a matrix with two columns.

…

Ignored by `nnwhich.ppp`

and `nnwhich.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 find the nearest neighbour in each group.

method

String specifying which method of calculation to use.
Values are `"C"`

and `"interpreted"`

.

Numeric vector or matrix giving, for each point,
the index of its nearest neighbour (or `k`

th nearest neighbour).

If `k = 1`

(the default), the return value is a
numeric vector `v`

giving the indices of the nearest neighbours
(the nearest neighbout of the `i`

th point is
the `j`

th point where `j = v[i]`

).

If `k`

is a single integer, then the return value is a
numeric vector giving the indices of the
`k`

th nearest neighbours.

If `k`

is a vector, then the return value is a
matrix `m`

such that `m[i,j]`

is the
index of the `k[j]`

th nearest neighbour for the
`i`

th data point.

If the argument `by`

is given, then the result is a data frame
containing the indices described above, from each point of `X`

,
to the nearest point in each subset of `X`

defined by the factor `by`

.

If `X`

is a multitype point pattern
and `by=marks(X)`

, then the algorithm will find,
for each point of `X`

, the nearest neighbour
of each type. See the Examples.

A value of `NA`

is returned if there is only one point
in the point pattern.

For each point in the given point pattern, this function finds
its nearest neighbour (the nearest other point of the pattern).
By default it returns a vector giving, for each point,
the index of the point's
nearest neighbour. If `k`

is specified, the algorithm finds
each point's `k`

th nearest neighbour.

The function `nnwhich`

is generic, with
method for point patterns (objects of class `"ppp"`

)
and a default method which are described here, as well as a method for
three-dimensional point patterns (objects of class `"pp3"`

,
described in `nnwhich.pp3`

.

The method `nnwhich.ppp`

expects a single
point pattern argument `X`

.
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 find, for each point of `X`

,
the nearest neighbour *in each subset*.

If there are no points (if `x`

has length zero)
a numeric vector of length zero is returned.
If there is only one point (if `x`

has length 1),
then the nearest neighbour is undefined, and a value of `NA`

is returned. In general if the number of points is less than or equal
to `k`

, then a vector of `NA`

's is returned.

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.

To evaluate the *distance* between a point and its nearest
neighbour, use `nndist`

.

To find the nearest neighbours from one point pattern
to another point pattern, use `nncross`

.

# NOT RUN { data(cells) plot(cells) m <- nnwhich(cells) m2 <- nnwhich(cells, k=2) # plot nearest neighbour links b <- cells[m] arrows(cells$x, cells$y, b$x, b$y, angle=15, length=0.15, col="red") # find points which are the neighbour of their neighbour self <- (m[m] == seq(m)) # plot them A <- cells[self] B <- cells[m[self]] plot(cells) segments(A$x, A$y, B$x, B$y) # nearest neighbours of each type head(nnwhich(ants, by=marks(ants))) # }