https://github.com/cran/fields
Tip revision: 6769ffc81115fbf0bf7d9c566cf7ac81be0049dc authored by Doug Nychka on 25 July 2005, 00:00:00 UTC
version 3.04
version 3.04
Tip revision: 6769ffc
Exponential.Rd
\name{Exponential}
\alias{Exponential}
\alias{Matern}
\title{Covariance functions}
\description{
Functional form of covariance function assuming the argument is a
distance between locations.
}
\usage{
Exponential(d, range = 1, alpha = 1/range, phi = 1)
Matern (d , scale = 1, range = 1,alpha=1/range,
smoothness = 0.5, nu= smoothness, phi=scale)
}
%- maybe also 'usage' for other objects documented here.
\arguments{
\item{d}{ Vector of distances }
\item{range}{ Range parameter default is one. Note
that the scale can also be specified through the "theta"
scaling argument used in fields covariance functions) }
\item{alpha}{1/range }
\item{scale}{Same as phi }
\item{phi}{ Marginal variance.}
\item{smoothness}{ Smoothness parameter in Matern. Controls the number
of derivatives in the process. Default is 1/2 corresponding to an exponential
covariance.}
\item{nu}{ Same as smoothness}
}
\details{
Exponential:
phi* exp( -d/range)
Matern:
\eqn{phi*con*(d^nu) * besselK(d , nu )}
Matern covariance function transcribed from Stein's book page 31
nu==smoothness, alpha == 1/range
GeoR parameters map to kappa==smoothness and phi == range
check for negative distances
\code{con} is a constant that normalizes the expression to be 1.0 when phi=1.0
and d=0.
}
\value{
A vector of covariances.
}
\references{ Stein's book}
\author{Doug Nychka}
\seealso{stationary.cov, stationary.image.cov}
}
\keyword{spatial}% at least one, from doc/KEYWORDS