RMderiv.Rd
\name{RMderiv}
\alias{RMderiv}
\alias{derivative}
\alias{gradient}
\title{Gradient of a field}
\description{
\command{\link{RMderiv}}
is a multivariate covariance model which
models a field and its gradient.
For an isotropic covariance model \eqn{varphi}, the covariance \eqn{C} given by
\command{RMderiv} equals
\deqn{C_{11}(x,y) = \varphi(\| x - y\|)}
\deqn{C_{j1}(x,y) = -C_{1j}(x,y) = \partial \varphi(\|x - y\|) /
\partial x}
\deqn{C_{i,j}(x,y) = \partial^2 \varphi(\|x - y\|) /
\partial x \partial y}
for \eqn{i,j = 2,\ldots, d} where \eqn{d} is the dimension of the field.
}
\usage{
RMderiv(phi, which, var, scale, Aniso, proj)
}
\arguments{
\item{phi}{a univariate stationary covariance model (in 2 or 3 dimensions).}
\item{which}{vector of integers. If not given all components are
returned; otherwise the selected components are returned.
}
\item{var,scale,Aniso,proj}{optional arguments; same meaning for any
\command{\link{RMmodel}}. If not passed, the above
covariance function remains unmodified.}
}
\value{
\command{\link{RMderiv}} returns an object of class \code{\link[=RMmodel-class]{RMmodel}}.
}
\references{
\itemize{
\item Matheron
}
}
\me
\seealso{
\command{\link{RMcurlfree}},
\command{\link{RMdivfree}},
\command{\link{RMvector}}
}
\keyword{spatial}
\keyword{models}
\examples{\dontshow{StartExample()}
RFoptions(seed=0) ## *ANY* simulation will have the random seed 0; set
## RFoptions(seed=NA) to make them all random again
model <- RMderiv(RMgauss(), scale=4)
plot(model, dim=2)
x.seq <- y.seq <- seq(-10, 10, 0.4)
simulated <- RFsimulate(model=model, x=x.seq, y=y.seq)
plot(simulated)
\dontshow{FinalizeExample()}}