https://github.com/cran/RandomFields
Tip revision: 919f138ae97c73da2321579cf0a01351bf9ebff3 authored by Martin Schlather on 11 October 2016, 18:32:27 UTC
version 3.1.24.1
version 3.1.24.1
Tip revision: 919f138
RMcutoff.Rd
\name{RMcutoff}
\alias{RMcutoff}
\title{Gneiting's modification towards finite range}
\description{
\command{\link{RMcutoff}} is a functional on univariate stationary
isotropic covariance functions \eqn{\phi}{phi}.
The corresponding function \eqn{C} (which is not necessarily a
covariance function,
see details) only depends on the distance \eqn{r}{r} between two
points in \eqn{d}-dimensional space and is given by
\deqn{C(r)=\phi(r), 0\le r \le d}
\deqn{C(r) = b_0 ((dR)^a - r^a)^{2 a}, d \le r \le dR}
\deqn{C(r) = 0, dR \le r}
The parameters \eqn{R} and \eqn{b_0}
are chosen internally such that \eqn{C} is a smooth function.
}
\usage{
RMcutoff(phi, diameter, a, var, scale, Aniso, proj)
}
\arguments{
\item{phi}{a univariate stationary isotropic covariance model.
See, for instance,
\code{RFgetModelNames(type="positive definite",
domain="single variable", isotropy="isotropic", vdim=1)}.
}
\item{diameter}{a numerical value; should be greater than 0; the
diameter of the domain on which the simulation is done}
\item{a}{a numerical value; should be greater than 0; has been shown to be
optimal for \eqn{a = 1/2} or \eqn{a =1}.}
\item{var,scale,Aniso,proj}{optional arguments; same meaning for any
\command{\link{RMmodel}}. If not passed, the above
covariance function remains unmodified.}
}
\details{The algorithm that checks the given parameters knows
only about some few necessary conditions.
Hence it is not ensured that
the cutoff-model is a valid covariance function for any
choice of \eqn{\phi} and the parameters.
For certain models \eqn{\phi}{phi}, e.g. \command{\link{RMstable}},
\command{\link{RMwhittle}} and \command{\link{RMgencauchy}}, some
sufficient conditions
are known (cf. Gneiting et al. (2006)).
}
\value{
\command{\link{RMcutoff}} returns an object of class \code{\link[=RMmodel-class]{RMmodel}}
}
\references{
\itemize{
\item Gneiting, T., Sevecikova, H, Percival, D.B., Schlather M.,
Jiang Y. (2006) Fast and Exact Simulation of Large {G}aussian
Lattice Systems in {$R^2$}: Exploring the Limits.
\emph{J. Comput. Graph. Stat.} \bold{15}, 483--501.
\item Stein, M.L. (2002) Fast and exact simulation of fractional
Brownian surfaces. \emph{J. Comput. Graph. Statist.} \bold{11}, 587--599
}
}
\author{Martin Schlather, \email{schlather@math.uni-mannheim.de}
}
\seealso{
\command{\link{RMmodel}},
\command{\link{RFsimulate}},
\command{\link{RFfit}}.
}
\keyword{spatial}
\keyword{models}
\examples{
RFoptions(seed=0) ## *ANY* simulation will have the random seed 0; set
## RFoptions(seed=NA) to make them all random again
\dontshow{StartExample()}
model <- RMexp()
plot(model, model.cutoff=RMcutoff(model, diameter=1), xlim=c(0, 4))
model <- RMstable(alpha = 0.8)
plot(model, model.cutoff=RMcutoff(model, diameter=2), xlim=c(0, 5))
x <- y <- seq(0, 4, 0.05)
plot(RFsimulate(RMcutoff(model), x=x, y = y))
\dontshow{FinalizeExample()}
}