https://github.com/cran/RandomFields
Tip revision: fd4911aa390fd49ddab92bd139bbbf35422e32e5 authored by Martin Schlather on 06 February 2020, 05:20:37 UTC
version 3.3.8
version 3.3.8
Tip revision: fd4911a
RMintrinsic.Rd
\name{RMintrinsic}
\alias{RMintrinsic}
\title{Intrinsic Embedding Covariance Model}
\description{
\command{\link{RMintrinsic}} is a univariate stationary isotropic covariance
model which depends on a univariate stationary isotropic covariance model.
The corresponding covariance function C of the model
only depends on the distance \eqn{r \ge 0}{r \ge 0} between
two points and is given by
\deqn{C(r)=a_0 + a_2 r^2 + \phi(r), 0\le r \le diameter}
\deqn{C(r)=b_0 (rawR D - r)^3/(r), diameter \le r \le rawR * diameter}
\deqn{C(r) = 0, rawR * diameter \le r}
}
\usage{
RMintrinsic(phi, diameter, rawR, var, scale, Aniso, proj)
}
\arguments{
\item{phi}{an \command{\link{RMmodel}}; has to be stationary and isotropic}
\item{diameter}{a numerical value; positive; should be the diameter of
the domain on which simulation is done}
\item{rawR}{a numerical value; greater or equal to 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 parameters \eqn{a_0}, \eqn{a_2} and \eqn{b_0}
are chosen internally such that \eqn{C} becomes a smooth function.
See formulas (3.8)-(3.10) in Gneiting et alii (2006).
This model corresponds to the method Intrinsic Embedding.
See also \code{\link{RPintrinsic}}.
NOTE: The algorithm that checks the given parameters knows
only about some few necessary conditions.
Hence it is not ensured that
the Stein-model is a valid covariance function for any
choice of \eqn{\phi} and the parameters.
For certain models \eqn{\phi}{phi}, i.e. \code{stable},
\code{whittle}, \code{gencauchy}, and the variogram
model \code{fractalB} some sufficient conditions are known.
}
\value{
\command{\link{RMintrinsic}} 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
}
}
\me
\seealso{
\command{\link{RPintrinsic}},
\command{\link{RMmodel}},
\command{\link{RFsimulate}},
\command{\link{RFfit}}.
}
\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
x.max <- 10
model <- RMintrinsic(RMfbm(alpha=1), diameter=x.max)
x <- seq(0, x.max, 0.02)
plot(model)
plot(RFsimulate(model, x=x))
\dontshow{FinalizeExample()}}