https://github.com/cran/RandomFields
Tip revision: e5a7a2f272b7834f96c925ced7acfa0c6456a87f authored by Martin Schlather on 17 April 2017, 22:09:51 UTC
version 3.1.50
version 3.1.50
Tip revision: e5a7a2f
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, boxcox)
RPsequential(phi, boxcox, back_steps, initial)
}
\arguments{
\item{phi}{object of class \code{\link[=RMmodel-class]{RMmodel}};
specifies the covariance model to be simulated.}
\item{boxcox}{the one or two parameters of the box cox transformation.
If not given, the globally defined parameters are used.
see \command{\link{RFboxcox}} for Details.
}
\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{Gaussian},
\link{RP},
}
\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()}
}