# nnwhich

##### Nearest neighbour

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

##### Usage

```
nnwhich(X, ...)
## S3 method for class 'ppp':
nnwhich(X, \dots, k=1, by=NULL, method="C")
## S3 method for class 'default':
nnwhich(X, Y=NULL, \dots, k=1, by=NULL, method="C")
```

##### Arguments

- 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 - ...
- 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"`

.

##### Details

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`

.

##### Value

- 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`

.

##### Nearest neighbours of each type

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.

##### Warnings

A value of `NA`

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

##### See Also

##### Examples

```
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)))
```

*Documentation reproduced from package spatstat, version 1.42-2, License: GPL (>= 2)*