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
RPspectral.Rd
\name{Spectral}
\alias{Spectral}
\alias{RPspectral}
\title{Spectral turning bands method}
\description{The spectral turning bands method is
a simulation method for stationary
Gaussian random fields (Mantoglou and Wilson, 1982).
It makes use of
Bochners's theorem and the corresponding spectral measure
\eqn{\Xi}{\Xi}
for a given covariance function \eqn{C(h)}. For \eqn{x \in
{\bf R}^d}{x in R^d},
the field \deqn{Y(x)= \sqrt{2} cos(<V,x> + 2 \pi U)}{Y(x)=\sqrt{2}
cos(<V,x> + 2 pi U)}
with \eqn{V ~ \Xi } and \eqn{U ~ Ufo((0,1))} is a random field with
covariance function \eqn{C(h)}.
A scaled superposition of many independent realizations of \eqn{Y}{Y}
gives a Gaussian field according to the central limit theorem. For details
see Lantuejoul (2002). The standard method
allows for the simulation of 2-dimensional random
fields defined on arbitrary points or arbitrary grids.
}
\usage{
RPspectral(phi, boxcox, sp_lines, sp_grid, prop_factor, sigma)
}
\arguments{
\item{phi}{object of class \code{\link[=RMmodel-class]{RMmodel}};
specifies the covariance model to be simulated.}
% \item{loggauss}{see \command{\link{RPgauss}}.}
\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{sp_lines}{
Number of lines used (in total for all additive components of the
covariance function).
Default: \code{2500}.
}
\item{sp_grid}{Logical.
The angle of the lines is random if
\code{grid=FALSE},
and \eqn{k\pi/}\code{sp_lines}
for \eqn{k}{k} in \code{1:sp_lines},
otherwise. This argument is only considered
if the spectral measure, not the density is used.
Default: \code{TRUE}.
}
\item{prop_factor}{ % to do: use RRrectangular
positive real value.
Sometimes, the spectral density must be sampled by MCMC.
Let \eqn{p} be the average rejection rate. Then
the chain is sampled every \eqn{n}th point where
\eqn{n = |log(p)| *}\code{prop_factor}.
Default: \code{50}.
}
\item{sigma}{real. Considered if the Metropolis
algorithm is used. It gives the standard deviation of the
multivariate normal distribution of the proposing
distribution.
If \code{sigma}
is not positive then \code{RandomFields} tries to find a good
choice for
\code{sigma} itself.
Default: \code{0}.
}
}
\value{
\code{RPspectral} returns an object of class
\code{\link[=RMmodel-class]{RMmodel}}.
}
\references{
\itemize{
\item Lantuejoul, C. (2002)
\emph{Geostatistical Simulation: Models and Algorithms.}
Springer.
\item Mantoglou, A. and J. L. Wilson (1982),
\emph{The Turning Bands Method for simulation of random fields using
line generation by a spectral method.}
Water Resour. Res., 18(5), 1379-1394.
}}
\me
\seealso{\link{Gaussian},
\link{RP},
\command{\link{RPtbm}}.
}
\keyword{methods}
\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 <- RPspectral(RMmatern(nu=1))
y <- x <- seq(0,10, len=400)
z <- RFsimulate(model, x, y, n=2)
plot(z)
\dontshow{FinalizeExample()}}