rdist {fields} | R Documentation

## Euclidean distance matrix

### Description

Given two sets of locations computes the full Euclidean distance matrix among all pairings or a sparse version for points within a fixed threshhold distance.

### Usage

    rdist(x1, x2)

    fields.rdist.near(x1,x2, delta, max.points= NULL, mean.neighbor = 50)

### Arguments

`x1` | Matrix of first set of locations where each row gives the coordinates of a particular point.
`x2` | Matrix of second set of locations where each row gives the coordinates of a particular point. If this is missing x1 is used.
`delta` | Threshhold distance. All pairs of points that separated by more than delta in distance are ignored.
`max.points` | Size of the expected number of pairs less than or equal to delta. The default is set to the nrow(x1)*mean.neighbor.
`mean.neighbor` | Sets the temp space for max.points

### Details

More about fields.rdist.near:

The sparse version is designed to work with the sparse covariance functions in fields and anticipates that the full matrix, D is too large to store. The argument max.points is set as a default to nrow( x1)*100 and allocates the space to hold the sparse elements. In case that there are more points that are within delta the function stops with an error but lists the offending rows. Just rerun the function with a larger choice for max.points

It possible that for certain x1 points there are no x2 points within a distance delta. This situation will cause an error if the list is converted to spam format.

### Returned values

Let D be the mXn distance matrix, with m= nrow(x1) and n=nrow( x2). The elements are the Euclidean distances between the all locations x1[i,] and x2[j,]. That is,

D.ij = sqrt( sum.k (( x1[i,k] - x2[j,k]) **2 ).

`rdist` The distance matrix D is returned.

`fields.rdist.near` The elements of D that are less than or equal to delta are returned in the form of a list.

List components:

ind
  Row and column indices of elements
ra
  (Distances ( D.ij)
da
  Dimensions of full distance matrix.

This is a simple sparse format that can be manipulated by several fields functions. E.g. ind2spam will convert this list to the format used by the spam sparse matrix package. ind2full will convert this to an ordinary matrix with zeroes.

### See Also

Exp.cov, rdist.earth, ind2spam, ind2full

### Examples

    out<- rdist( ozone$x)
    # out is a 20X20 matrix.

    out2<- rdist( ozone$x[1:5,], ozone$x[11:20,])
    #out2 is a 5X10 matrix

    set.seed(123)
    x1<- matrix( runif( 20*2), 20,2)
    x2<-  matrix( runif( 15*2), 15,2)

    out3<- fields.rdist.near( x1,x2, delta=.5)
    # out3 is a sparse structure in list format

    # or to "save"  work space decrease size of temp array

     out3<- fields.rdist.near( x1,x2, delta=.5,max.points=20*15)

    # explicitly reforming as a full matrix
    temp<- matrix( NA, nrow=out3$da[1], ncol= out3$da[2])
    temp[ out3$ind] <- out3$ra

    #       or justuse

      temp<- spind2full( out3)
      image( temp)

    # this is  identical to
     temp2<- rdist( x1,x2)
     temp2[ temp2<= .5] <- NA

[Package fields version 5.02 Index]