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\name{RMuser}
\alias{RMuser}
\alias{RM_USER}
\title{User-Defined Function}
\description{
\command{RMuser} allows for a user-defined covariance function, variogram
model, or arbitrary function.
\bold{RMuser is very slow -- users should avoid this model whenever possible.}
}
\usage{
RMuser(type, domain, isotropy, vdim, beta,
coordnames = c("x", "y", "z", "T"), fctn, fst, snd, envir,
var, scale, Aniso, proj)
}
\arguments{
\item{type}{ See \code{\link[=RMmodelgenerator-class]{RMmodelgenerator}} for
the range of values of the arguments.
Default: \code{"shape function"}.
}
\item{domain}{ See \code{\link[=RMmodelgenerator-class]{RMmodelgenerator}} for
the range of values of the arguments.
Default: \code{XONLY}.
}
\item{isotropy}{See
\code{\link[=RMmodelgenerator-class]{RMmodelgenerator}} for
the range of values of the arguments.
Default:
\itemize{
\item \code{'isotropic'} if \code{type}
equals \code{'tail correlation function'}, \code{'positive definite'}
or \code{'negative definite'};
\item
\code{'cartesian system'} if
\code{type} indicates a process or simulation method or a shape
function.
}
}
\item{vdim}{multivariability.
Default: \code{vdim} is identified from \code{beta} if given;
otherwise the default value is \code{1}.
}
\item{beta}{a fixed matrix that is multiplied to the return value of the
given function; the dimension must match.
Defining a vector valued function and \code{beta} as a vector,
an arbitrary linear model can be defined. Estimation of \code{beta}
is, however, not established yet.
}
\item{coordnames}{
Just the names of the variables. More variable names might
be given here than used in the function.
See Details for the interpretation of variables.
}
\item{fctn, fst, snd}{a user-defined function and its first,
second and third derivative, given as
\code{quote(myfunction(x))} or as
\code{quote(myfunction(x, y))}, see Details and Examples below.
}
\item{envir}{the environment where the given function shall be evaluated}
\item{var,scale,Aniso,proj}{optional arguments; same meaning for any
\command{\link{RMmodel}}. If not passed, the above
covariance function remains unmodified.}
}
\details{
Primarily, a function is expected that depends on
a vector whose components, \eqn{x, y, z, T}, are given separately as
scalar quantities.
Alternatively, the function might depend only on the first argument
given by \code{coordnames}.
A kernel should depend on the first two arguments
given by \code{coordnames}.
}
\value{
\command{\link{RMuser}} returns an object of class
\code{\link[=RMmodel-class]{RMmodel}}.
}
\note{
\itemize{
\item
The use of \command{RMuser} is completely on the risk of the
user. There is no
way to check whether the expressions of the user are
correct in any sense.
\item
Note that \code{x}, \code{y}, \code{z} and \code{T} are reserved
argument names that define solely the coordinates.
Hence, none of these names might be used for
other arguments within these functions.
\item
In user-defined functions, the models of
\pkg{RandomFields} are not recognized, so they cannot be included
in the function definitions.
\item
\command{\link{RMuser}} may not be used in connection with obsolete
commands of RandomFields.
}
}
\me
\seealso{
\command{\link{RMcovariate}},
\command{\link{RMfixcov}},
\command{\link{RFfit}},
\code{\link[=RMmodelgenerator-class]{RMmodelgenerator}},
\command{\link{RMmodel}},
\command{\link{RFsimulate}},
\link{RC_ISO_NAMES}, \link{RC_DOMAIN_NAMES}.
}
\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
## Alternatively to 'model <- RMexp()' one may define the following
## (which is, however, much slower and cannot use all features of
## RandomFields)
\dontshow{if (RFoptions()$general$storing) {
cat("This examples requires 'RFoptions(storing=FALSE)', what is set now.\n");
RFoptions(storing=FALSE)
}}
## user-defined exponential covariance model
model <- RMuser(type="positive definite", domain="single variable",
iso="isotropic", fctn=exp(-x))
x <- y <- seq(1, 10, len=100)
plot(model)
z <- RFsimulate(model, x=x, y=y)
plot(z)
## the kernel, which is the scalar product (see RMprod)
model <- RMnugget(var=1e-5) +
RMuser(type="positive definite", domain="kernel",
iso="symmetric", fctn=sum(x * y))
x <- y <- seq(1, 10, len=35)
z <- RFsimulate(model, x=x, y=y, n=6, svdtol=1e-9)
plot(z)
\dontshow{FinalizeExample()}}
|
