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\name{RMfixcov}
\alias{RMfixcov}
\title{Fixed Covariance Matrix}
\description{
\command{\link{RMfixcov}} is a user-defined covariance according to
the given covariance matrix.
It extends to the space through a Voronoi tessellation.
}
\usage{
RMfixcov(M, x, y=NULL, z=NULL, T=NULL, grid, var, proj, raw, norm)
}
\arguments{
\item{M}{a numerical matrix defining the user-defined covariance for a
random field; the matrix should be positive definite, symmetric and
its dimension should be equal to the length of observation or
simulation vector.}
\item{x,y,z,T,grid}{optional.
The usual arguments as in \command{\link{RFsimulate}} to define the
locations where the covariates are given.
}
\item{var,proj}{optional arguments; same meaning for any
\command{\link{RMmodel}}. If not passed, the above
covariance function remains unmodified.}
\item{raw}{\argRaw}
\item{norm}{\argNorm}
% \item{vdim}{an integer value; defining the response dimension.}
}
\note{
Starting with version 3.0.64, the former argument \code{element}
is replaced by the \code{general} option \code{set} in
\command{\link{RFoptions}}.
}
\details{
The covariances passed are implemented for the given locations.
Within any Voronoi cell (around a given location) the correlation is
assumed to be one.
In particular, it is used in \command{\link{RFfit}} to define neighbour or network structure in the data.
}
\value{
\command{\link{RMfixcov}} returns an object of class \code{\link[=RMmodel-class]{RMmodel}}.
}
\references{
\itemize{
\item Ober, U., Ayroles, J.F., Stone, E.A., Richards, S., Zhu, D., Gibbs, R.A., Stricker, C., Gianola, D., Schlather, M., Mackay, T.F.C., Simianer, H. (2012): \emph{Using Whole Genome Sequence Data to Predict Quantitative Trait Phenotypes in Drosophila melanogaster}. PLoS Genet 8(5): e1002685.
}
}
\me
\seealso{
\command{\link{RMcovariate}},
\command{\link{RMmodel}},
\command{\link{RFsimulate}},
\command{\link{RFfit}},
\command{\link{RMuser}}.
}
\keyword{spatial}
\keyword{models}
\examples{\dontshow{StartExample(reduce=FALSE)}
RFoptions(seed=0) ## *ANY* simulation will have the random seed 0; set
## RFoptions(seed=NA) to make them all random again
## Example 1 showing that the covariance structure is correctly implemented
n <- 10
C <- matrix(runif(n^2), nc=n)
(C <- C \%*\% t(C))
RFcovmatrix(RMfixcov(C), 1:n)
## Example 2 showing that the covariance structure is interpolated
RFcovmatrix(RMfixcov(C, 1:n), c(2, 2.1, 2.5, 3))
## Example 3 showing the use in a separable space-time model
model <- RMfixcov(C, 1:n, proj="space") * RMexp(s=40, proj="time")
(z <- RFsimulate(model, x = seq(0,12, 0.5), T=1:100))
plot(z)
\dontshow{FinalizeExample()}}
|
