RMdivfree.Rd
\name{RMdivfree}
\alias{RMdivfree}
\title{Divfree Covariance Model}
\description{
\command{\link{RMdivfree}}
is a multivariate covariance model which depends on
a univariate stationary covariance model where the covariance function phi(h)
is twice differentiable.
The corresponding matrix-valued covariance function C of the model
only depends on the difference \eqn{h}{h} between two points and it is
given by
\deqn{
C(h)=( - \Delta E + \nabla \nabla^T ) C_0(h)
}
}
\usage{
RMdivfree(phi, var, scale, Aniso, proj)
}
\arguments{
\item{phi}{a univariate stationary covariance model (in 2 or 3 dimensions).}
\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 model returns the potential field in the first component, the
corresponding divfree field and the field of curl strength in the last component.
See also the models \command{\link{RMcurlfree}} and \command{\link{RMvector}}.
}
\value{
\command{\link{RMdivfree}} 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{RMvector}},
\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 <- RMdivfree(RMgauss(), scale=4)
plot(model, dim=2)
x.seq <- y.seq <- seq(-10, 10, 0.2)
simulated <- RFsimulate(model=model, x=x.seq, y=y.seq)
plot(simulated)
plot(simulated, select.variables=1)
plot(simulated, select.variables=2:3)
plot(simulated, select.variables=list(2:3))
plot(simulated, select.variables=list(1, 2:3, 4))
plot(simulated, select.variables=list(1, c(1, 2:3), 4))
\dontshow{FinalizeExample()}
}