Kriging.Rd
\name{Kriging}
\alias{Kriging}
\title{Kriging methods}
\description{
The function allows for different methods of kriging.
}
\usage{
Kriging(krige.method, x, y=NULL, z=NULL, T=NULL, grid,
gridtriple=FALSE, model, param, given, data, trend, pch=".",
return.variance=FALSE, internal=FALSE)
}
%- maybe also `usage' for other objects documented here.
\arguments{
\item{krige.method}{kriging method; currently only 'S' (simple
kriging) and 'O' (ordinary kriging) implemented.}
\item{x}{\eqn{(n \times d)}{(n x d)} matrix or vector of \code{x}
coordinates; coordinates of \eqn{n} points to be kriged}
\item{y}{vector of \code{y} coordinates.}
\item{z}{vector of \code{z} coordinates.}
\item{T}{vector in grid triple form for the time coordinates.}
\item{grid}{logical; determines whether the vectors \code{x},
\code{y}, and \code{z} should be
interpreted as a grid definition, see Details.}
\item{gridtriple}{logical. Only relevant if \code{grid==TRUE}.
If \code{gridtriple==TRUE}
then \code{x}, \code{y}, and \code{z} are of the
form \code{c(start,end,step)}; if
\code{gridtriple==FALSE} then \code{x}, \code{y}, and \code{z}
must be vectors of ascending values.
}
\item{model}{string; covariance model, see \code{\link{CovarianceFct}}, or
type \code{\link{PrintModelList}()} to get all options.}
\item{param}{parameter vector:
\code{param=c(mean, variance, nugget, scale,...)};
the parameters must be given
in this order. Further parameters are to be added in case of a
parametrised class of covariance functions, see
\link{CovarianceFct}.
The value of \code{mean} must be finite
in the case of simple kriging, and is ignored otherwise.}
\item{given}{matrix or vector of points where data are available.}
\item{data}{the data values given at \code{given}; it might be a
vector or a matrix. If a matrix is given multivariate data are
assumed which are kriged \emph{separately}.}
\item{trend}{not programmed yet (will be used in case of universal kriging)}
\item{pch}{Kriging procedures are quite time consuming in general.
The character \code{pch} is printed after roughly
each 80th part of calculation.}
\item{return.variance}{logical. If \code{FALSE} the kriged field is
returned. If \code{TRUE} a list of two elements, \code{estim} and
\code{var}, i.e. the kriged field and the kriging variances,
is returned.}
\item{internal}{
\code{FALSE}. \code{internal} should not be set to \code{TRUE}
by the user.
(In case \code{internal=TRUE},
various consistency checks for the input variables
are not performed. Further, \code{grid} must be \code{FALSE},
and \code{model} must be given in the output format of
\code{\link{PrepareModel}}.)
}
}
\details{
\itemize{
\item \code{grid==FALSE} : the vectors \code{x}, \code{y},
and \code{z} are interpreted as vectors of coordinates
\item \code{(grid==TRUE) && (gridtriple==FALSE)} : the vectors
\code{x}, \code{y}, and \code{z}
are increasing sequences with identical lags for each sequence.
A corresponding
grid is created (as given by \code{expand.grid}).
\item \code{(grid==TRUE) && (gridtriple==TRUE)} : the vectors
\code{x}, \code{y}, and \code{z}
are triples of the form (start,end,step) defining a grid
(as given by \code{expand.grid(seq(x$start,x$end,x$step),
seq(y$start,y$end,y$step),
seq(z$start,z$end,z$step))})
}
}
\value{
If \code{variance.return=FALSE} \code{Kriging} returns a vector or matrix
of kriged values corresponding to the
specification of \code{x}, \code{y}, \code{z}, and
\code{grid}, and \code{data}.\cr
\code{data}: a vector or matrix with \emph{one} column\cr
* \code{grid==FALSE}. A vector of simulated values is
returned (independent of the dimension of the random field)\cr
* \code{grid==TRUE}. An array of the dimension of the
random field is returned (according to the specification
of \code{x}, \code{y}, and \code{z}).\cr
\code{data}: a matrix with \emph{at least two} columns\cr
* \code{grid==FALSE}. A matrix with the \code{ncol(data)} columns
is returned.\cr
* \code{grid==TRUE}. An array of dimension
\eqn{d+1}{d+1}, where \eqn{d}{d} is the dimension of
the random field, is returned (according to the specification
of \code{x}, \code{y}, and \code{z}). The last
dimension contains the repetitions.
If \code{variance.return=TRUE} a list of two elements, \code{estim} and
\code{var}, i.e. the kriged field and the kriging variances,
is returned. The format of \code{estim} is the same as described
above.
The format of \code{var} is accordingly.
}
\references{
Chiles, J.-P. and Delfiner, P. (1999)
\emph{Geostatistics. Modeling Spatial Uncertainty.}
New York: Wiley.
Cressie, N.A.C. (1993)
\emph{Statistics for Spatial Data.}
New York: Wiley.
Goovaerts, P. (1997) \emph{Geostatistics for Natural Resources
Evaluation.} New York: Oxford University Press.
Wackernagel, H. (1998) \emph{Multivariate Geostatistics.} Berlin:
Springer, 2nd edition.
}
\author{Martin Schlather, \email{schlath@hsu-hh.de}
\url{http://www.unibw-hamburg.de/WWEB/math/schlath/schlather.html}}
%\note{}
\seealso{
\code{\link{CondSimu}},
\code{\link{CovarianceFct}},
\code{\link{EmpiricalVariogram}},
\code{\link{RandomFields}},
}
\examples{
## creating random variables first
## here, a grid is chosen, but does not matter
step <- 0.25
x <- seq(0,7,step)
param <- c(0,1,0,1)
model <- "exponential"
RFparameters(PracticalRange=FALSE)
p <- 1:7
points <- as.matrix(expand.grid(p,p))
data <- GaussRF(points, grid=FALSE, model=model, param=param)
## visualise generated spatial data
zlim <- c(-2.6,2.6)
colour <- rainbow(100)
image(p, p, xlim=range(x), ylim=range(x),
matrix(data,ncol=length(p)),
col=colour,zlim=zlim)
## now: kriging
krige.method <- "O" ## ordinary kriging
z <- Kriging(krige.method=krige.method,
x=x, y=x, grid=TRUE,
model=model, param=param,
given=points, data=data)
image(x,x,z,col=colour,zlim=zlim)
}
\keyword{spatial}%-- one or more ...
