https://github.com/cran/RandomFields
Tip revision: f5e4e9ee01c1569e39dffdd0295f7a2131c83516 authored by Martin Schlather on 13 January 2015, 00:00:00 UTC
version 3.0.55
version 3.0.55
Tip revision: f5e4e9e
RPsequential.Rd
\name{Square roots}
\alias{Direct}
\alias{RPdirect}
\alias{Sequential}
\alias{RPsequential}
\title{Methods relying on square roots of the covariance matrix}
\description{
Methods relying on square roots of the covariance matrix
}
\usage{
RPdirect(phi, root_method, svdtolerance, max_variab)
RPsequential(phi, max_variables, back_steps, initial)
}
\arguments{
\item{phi}{object of class \code{\link[=RMmodel-class]{RMmodel}};
specifies the covariance model to be simulated.}
% \item{loggauss}{optional argument; same meaning as for
% \command{\link{RPgauss}}.}
\item{root_method}{Decomposition of the covariance matrix.
If \code{root_method=1} or \code{3}, Cholesky
decomposition will not be attempted, but singular value
decomposition
performed instead.
In case of a multivariate random field, \code{root_method = 2}
or \code{3} orders the covariance such that first all components are
considered for the first variable, then all components for the
second one, and so on. If \code{root_method = 0} or \code{1}
it starts with the first component of all locations, then the
second components follow, etc.
Default: \code{0} .}
\item{svdtolerance}{ If SVD decomposition is used for calculating the square root of
the covariance matrix then the absolute componentwise difference between
the covariance matrix and square of the square root must be less
than \code{svdtolerance}. No check is performed if
\code{svdtolerance} is negative.
Default: \code{1e-12} .
}
\item{max_variab}{If the number of variables to generate is
greater than \code{maxvariables}, then any matrix decomposition
method is rejected. It is important that this option is set
conveniently to avoid great losses of time during the automatic
search of a simulation method (\code{method="any method"}).
Default: \code{8192}
}
\item{max_variables}{The maximum size of the conditional covariance matrix
(default to 5000)}
\item{back_steps}{
Number of previous instances on which
the algorithm should condition.
If less than one then the number of previous instances
equals \code{max} / (number of spatial points).
Default: \code{10} .
}
\item{initial}{
First, N=(number of spatial points) * \code{back_steps}
number of points are simulated. Then, sequentially,
all spatial points for the next time instance
are simulated at once, based on the previous \code{back_steps}
instances. The distribution of the first N points
is the correct distribution, but
differs, in general, from the distribution of the sequentially
simulated variables. We prefer here to have the same distribution
all over (although only approximatively the correct one),
hence do some initial sequential steps first.
If \code{initial} is non-negative, then \code{initial}
first steps are performed.
If \code{initial} is negative, then
\code{back_steps} - \code{initial}
initial steps are performed. The latter ensures that
none of the very first N variables are returned.
Default: \code{-10} .
}
}
\details{
\command{RPdirect}
is based on the well-known method for simulating
any multivariate Gaussian distribution, using the square root of the
covariance matrix. The method is pretty slow and limited to
about 8000 points, i.e. a 20x20x20 grid in three dimensions.
This implementation can use the Cholesky decomposition and
the singular value decomposition.
It allows for arbitrary points and arbitrary grids.
\command{RPsequential}
is programmed for spatio-temporal models
where the field is modelled sequentially in the time direction
conditioned on the previous \eqn{k} instances.
For \eqn{k=5} the method has its limits for about 1000 spatial
points. It is an approximative method. The larger \eqn{k} the
better.
It also works for certain grids where the last dimension should
contain the highest number of grid points.
}
\value{
\command{\link{RPsequential}} returns an object of class \code{\link[=RMmodel-class]{RMmodel}}
}
\references{
\itemize{
\item
Schlather, M. (1999) \emph{An introduction to positive definite
functions and to unconditional simulation of random fields.}
Technical report ST 99-10, Dept. of Maths and Statistics,
Lancaster University.
}}
\author{Martin Schlather, \email{schlather@math.uni-mannheim.de}
}
\seealso{
\link{RP},
\command{\link{RPcoins}},
\command{\link{RPhyperplane}},
\command{\link{RPspectral}},
\command{\link{RPtbm}}.
}
\keyword{methods}
\examples{
RFoptions(seed=0) ## *ANY* simulation will have the random seed 0; set
## RFoptions(seed=NA) to make them all random again
model <- RMgauss(var=10, s=10) + RMnugget(var=0.01)
plot(model, xlim=c(-25, 25))
z <- RFsimulate(model=RPdirect(model), 0:10, 0:10, n=4)
plot(z)
\dontshow{FinalizeExample()}
}