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\name{CovarianceUpper}
\alias{ExponentialUpper}
\title{
Evaluate covariance over upper triangle of distance matrix
}
\description{
Evaluates the covariance over the upper triangle of a distance matrix 
  rather than over the entire matrix to reduce computation time.  Note 
  that the \code{chol} function only requires the upper triangle of 
  the covariance matrix to perform the Cholesky decomposition.
}
\usage{
ExponentialUpper(distMat, range = 1, alpha = 1/range, theta = NULL)
}
\arguments{
  \item{distMat}{
The distance matrix to evaluate the covariance over.
}
  \item{range}{
Range parameter default is one. Note that the scale can also
  be specified through the "aRange" scaling argument used in
  fields covariance functions)
}

\item{alpha}{
1/range}
  
\item{theta}{
Also the range parameter.}

}
\value{
The covariance matrix, where only the upper triangle is calculated.
}
\author{
John Paige
}
\seealso{
\code{\link[fields]{Exponential}}
}
\examples{
set.seed(123)

#a  distance matrix 
coords = matrix(runif(10), ncol=2)
distMat = rdist(coords)

#compute covariance matrix, but only over the upper triangle
upperCov = ExponentialUpper(distMat, range=.1)

print(distMat)
print(upperCov)
}
\keyword{ covariance }