`nearestdist.Rd`

This function computes and returns specific elements of distance matrix computed by using the specified distance measure.

```
nearest.dist( x, y=NULL, method = "euclidean",
delta = 1, upper = if (is.null(y)) FALSE else NULL,
p = 2, miles = TRUE, R = NULL, fortran = FALSE)
```

- x
Matrix of first set of locations where each row gives the coordinates of a particular point. See also ‘Details’.

- y
Matrix of second set of locations where each row gives the coordinates of a particular point. If this is missing

`x`

is used. See also ‘Details’.- method
the distance measure to be used. This must be one of

`"euclidean"`

,`"maximum"`

,`"minkowski"`

or`"greatcircle"`

. Any unambiguous substring can be given.- delta
only distances smaller than

`delta`

are recorded, see Details.- upper
Should the entire matrix (

`NULL`

) or only the upper-triagonal (`TRUE`

) or lower-triagonal (`FALSE`

) values be calculated.- p
The power of the Minkowski distance.

- miles
For great circle distance: If true distances are in statute miles if false distances in kilometers.

- R
For great circle distance: Radius to use for sphere to find spherical distances. If

`NULL`

the radius is either in miles or kilometers depending on the values of the miles argument. If`R=1`

then distances are of course in radians.- fortran
Should the C++ (

`FALSE`

) or the Fortran code (`TRUE`

) be used. If 64-bit matrices are needed, the argument is set to (`TRUE`

).

A `spam`

object containing the distances spanned between
zero and `delta`

. The sparse matrix may contain many zeros
(e.g., collocated data). However, to calculate covariances, these zeros
are essential.

For great circle distance, the matrices `x`

and `y`

contain the degrees longitudes in the first and the degrees latitudes
in the second column. `delta`

is in
degrees. Hence to restrict to distances smaller than `delta.km`

,
one has to specify `delta=delta.km*360/(6378.388*2*pi)`

.

The distances are calculated based on spherical law of cosines.
Care is needed for `zero' distances due to the final acosin:
`acos(1-1e-16)`

, especially with an actual radius.

Default value of Earth's radius is 3963.34miles (6378.388km).

There are many other packages providing distance functions. Especially
for great circle distances there are considerable differences between
the implementations. For high precision results, `sp::spDists`

is
a good candidate and distances of large amount of locations can be
processed in parallel with the `parallelDist`

package.

The formerly depreciated arguments `eps`

and `diag`

are now
eliminated.

`x`

and `y`

can be any object with an existing
`as.matrix`

method.

The Fortran code is based on a idea of Doug Nychka.

```
# Note that upper=T and using t(X)+X is quicker than upper=NULL;
# upper=T marginally slower than upper=F.
# To compare nearest.dist with dist, use as.dist(...)
nx <- 4
x <- expand.grid(as.double(1:nx),as.double(1:nx))
sum( ( as.dist(nearest.dist( x, delta=nx*2))-
dist(x) )^2)
#> [1] 0
# Create nearest neighbor structures:
par(mfcol=c(1,2))
x <- expand.grid(1:nx,1:(2*nx))
display( nearest.dist( x, delta=1))
#> Warning: default value for 'cex' in 'display' might not be the optimal choice
x <- expand.grid(1:(2*nx),1:nx)
display( nearest.dist( x, delta=1))
#> Warning: default value for 'cex' in 'display' might not be the optimal choice
```