https://github.com/cran/RandomFields
Tip revision: 0e562f038613e9388e8c33a6cf59f7f57ae62bf5 authored by Martin Schlather on 03 August 2014, 00:00:00 UTC
version 3.0.32
version 3.0.32
Tip revision: 0e562f0
RMvector.Rd
\name{RMvector}
\alias{RMvector}
\title{Vector Covariance Model}
\description{
\command{\link{RMvector}} is a multivariate covariance model which depends on
a univariate covariance model that is stationary in the first \eqn{Dspace}
coordinates \eqn{h}{h} and where the covariance function phi(h,t)
is twice differentiable in the first component \eqn{h}{h}.
The corresponding matrix-valued covariance function C of the model
only depends on the difference \eqn{h}{h} between two points in the
first component.
It is given by
\deqn{
C(h,t)=( -0.5 * (a + 1) \Delta + a \nabla \nabla^T ) C_0(h, t)
}
where the operator is applied to the first component \eqn{h}{h} only.
}
\usage{
RMvector(phi, a, Dspace, var, scale, Aniso, proj)
}
\arguments{
\item{phi}{an \command{\link{RMmodel}}; has two components \eqn{h}{h} (2 or 3
dimensional and stationary) and \eqn{t}{t} (arbitrary dimension)}
\item{a}{a numerical value; should be in the interval \eqn{[-1,1]}.}
\item{Dspace}{an integer; either 2 or 3; the first \eqn{Dspace}
coordinates give the first component \eqn{h}{h}}
\item{var,scale,Aniso,proj}{optional arguments; same meaning for any
\command{\link{RMmodel}}. If not passed, the above
covariance function remains unmodified.}
}
\details{
\eqn{C_0} is either a spatiotemporal model (then \eqn{t} is the
time component) or it is an isotropic model. Then, the first \eqn{Dspace}
coordinates are considered as \eqn{h} coordinates and the remaining
ones as \eqn{t} coordinates. By default, \eqn{Dspace} equals the
dimension of the field (and there is no \eqn{t} component).
If \eqn{a=-1} then the field is curl free; if \eqn{a=1} then the field is
divergence free.
}
\value{
\command{\link{RMvector}} returns an object of class \code{\link[=RMmodel-class]{RMmodel}}
}
\references{
\itemize{
\item Scheuerer, M. and Schlather, M. (2012)
Covariance Models for Divergence-Free and Curl-Free Random Vector Fields.
\emph{Stochastic Models} \bold{28:3}.
}
}
\author{Martin Schlather, \email{schlather@math.uni-mannheim.de}
}
\seealso{
\command{\link{RMcurlfree}},
\command{\link{RMdivfree}},
\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
% source("RandomFields/tests/source.R")
model <- RMvector(RMgauss(), scale=0.3)
x <- seq(0, 10, if (interactive()) 0.4 else 3)
plot(RFsimulate(model, x=x, y=x, z=0), select.variables=list(1:2))
\dontshow{FinalizeExample()}
}