% fields, Tools for spatial data
% Copyright 2004-2011, Institute for Mathematics Applied Geosciences
% University Corporation for Atmospheric Research
% Licensed under the GPL -- www.gpl.org/licenses/gpl.html

\name{rdist}
\alias{rdist}
\alias{fields.rdist.near}

\title{
  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{
\item{x1}{
Matrix of first set of locations where each row gives the coordinates of a
particular
point.
}
\item{x2}{
Matrix of second set of locations where each row gives the coordinates of
a particular point. If this is missing x1 is used. 
}
\item{delta}{ Threshhold distance. All pairs of points that separated by more than 
delta in distance are ignored. }

\item{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. }

\item{mean.neighbor}{ Sets the temp space for max.points}
 
}
\section{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 ).

\code{rdist}
The distance matrix D is returned. 

\code{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:
\describe{
\item{ind}{ Row  and column indices of elements }
\item{ra}{ (Distances ( D.ij)}
\item{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. 

}

\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. 

}

\seealso{  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

}
\keyword{spatial}
% docclass is function
% Converted by Sd2Rd version 1.21.