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%#
%# fields is a package for analysis of spatial data written for
%# the R software environment.
%# Copyright (C) 2024 Colorado School of Mines
%# 1500 Illinois St., Golden, CO 80401
%# Contact: Douglas Nychka, douglasnychka@gmail.edu,
%#
%# This program is free software; you can redistribute it and/or modify
%# it under the terms of the GNU General Public License as published by
%# the Free Software Foundation; either version 2 of the License, or
%# (at your option) any later version.
%# This program is distributed in the hope that it will be useful,
%# but WITHOUT ANY WARRANTY; without even the implied warranty of
%# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
%# GNU General Public License for more details.
%#
%# You should have received a copy of the GNU General Public License
%# along with the R software environment if not, write to the Free Software
%# Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
%# or see http://www.r-project.org/Licenses/GPL-2
%##END HEADER
%##END HEADER
\name{rdist}
\alias{rdist}
\alias{fields.rdist.near}
\alias{rdist.vec}
\title{
Euclidean distance matrix or vector
}
\description{
Given two sets of locations \code{rdist} and \code{fields.rdist.near} computes the full
Euclidean distance matrix among all pairings or a sparse version for points within a
fixed threshhold distance. \code{rdist.vec} computes a vector of pairwise distances
between corresponding elements of the input locations and is used in empirical
variogram calculations.
}
\usage{
rdist(x1, x2 = NULL, compact = FALSE)
fields.rdist.near(x1,x2, delta, max.points= NULL, mean.neighbor = 50)
rdist.vec(x1, x2)
}
\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 not passed or given as NULL x1 is used.
}
\item{compact}{
Whether or not to return a distance matrix in compact form inheriting class ``dist'' (as returned by the \code{dist} function in base R). Only values for one triangle of the symmetric distance matrix are returned. This saves time evaluating the returned matrix and the covariance. Note that this option is ignored when \code{x2} is not NULL.
}
\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.
}
\author{Doug Nychka, John Paige}
\seealso{ \link{stationary.cov}, \link{Exp.cov}, \link{rdist.earth}, \link{dist}, ind2spam, ind2full }
\examples{
out<- rdist( ChicagoO3$x)
# out is a 20X20 matrix.
out2<- rdist( ChicagoO3$x[1:5,], ChicagoO3$x[11:20,])
#out2 is a 5X10 matrix
set.seed(123)
x1<- matrix( runif( 20*2), 20,2)
x2<- matrix( runif( 15*2), 15,2)
out3<- fields.rdist.near( x1,x2, delta=.5)
# out3 is a sparse structure in list format
# or to "save" work space decrease size of temp array
out3<- fields.rdist.near( x1,x2, delta=.5,max.points=20*15)
# explicitly reforming as a full matrix
temp<- matrix( NA, nrow=out3$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
#compute pairwise distance vector
x1 = 1:10
x2 = seq(from=10, to=1)
rdist.vec(x1, x2)
#calculate output matrix in compact form:
distOut = rdist(1:10, compact=TRUE)
distOut
as.vector(distOut)
}
\keyword{spatial}
% docclass is function
% Converted by Sd2Rd version 1.21.
|
