\name{ShowModels}
\alias{ShowModels}
\title{Interactive Choice of Models and Parameters}
\description{
\code{ShowModels} is an interactive plot for
the selection of
models and their one- or two-dimensional simulations;
it also allows for the fitting of variogram models by eye.
}
\usage{
ShowModels(x, y=NULL,
covx=ifelse(is.null(empirical), diff(range(x))/5,
max(empirical$c)),
fixed.rs=TRUE, method=NULL, empirical=NULL,
model=NULL, param=NULL, all.param=NULL,
legends = TRUE,
register=0, Mean=NULL, erase=TRUE,
x.fraction=0.60, cex.names=1, covx.default = 100,
link.fct=NULL, Zlim=NULL,
Col.rect="red", Col.bg="blue", Col.sep="grey",
Col.line="red", Col.txt="black", Col.flash="red",
Col.vario="blue", Col.main="black",
Col.model=c("red", "black"), vario.lty=c(1,2),
cex.leg = 0.7 * cex.names, cex.eval = 0.8 * cex.names,
update=TRUE, screen.new=TRUE, use.outer.RFparameters=FALSE,
debug=FALSE, ...)
}
\arguments{
\item{x}{if \code{NULL} simulations are not performed; otherwise it gives the
\eqn{x}{x} coordinates of a grid as a sequence of increasing numbers
}
\item{y}{if \code{NULL} at most one-dimensional simulations
are performed (depending on the value of \code{x}); otherwise
\code{y} gives
the \eqn{y}{y} coordinates of a two-dimensional grid (as a sequence
of increasing numbers).}
\item{covx}{if a single value is given, it is the largest distance
for which the covariance functions or the
variograms are plotted; otherwise the models are plotted for the given
values, and the origin.}
\item{fixed.rs}{if \code{TRUE} then the same random seed is used for
all simulations until the user clicks on the formula, the title
or the subtitles.}
\item{method}{simulation method, see \link{RFMethods}; if \code{NULL}
then a suitable simulation method is chosen automatically.}
\item{empirical}{empirical variogram; a list as returned by
\code{\link{EmpiricalVariogram}}. Also empirical variograms with
a pair number of anisotropy directions may be passed. Then the first
and the middle one are taken.
}
\item{model}{covariance model, see \code{\link{CovarianceFct}}, or
type \code{\link{PrintModelList}()} to get all options. If given,
this model is shown at the beginning.
Additive or multiplicative models are not allowed.
However, model can also be given by a simple list definition,
see \code{\link{CovarianceFct}}. Then \code{param} must not be
given.
In this case also anisotropic models can be defined.
}
\item{param}{parameter vector:
\code{param=c(mean, variance, nugget, scale,...)};
the parameters must be given
in this order; see \code{\link{CovarianceFct}} for more details.
Only considered if \code{model} is given.
If given, \code{model} is initialised by \code{param}.}
\item{all.param}{%% ## var, nugg, scale
\code{all.param=c(mean, variance, nugget, scale)};
the parameters must be given in this order;
If \code{all.param} is given then the parameters of all covariance
functions are set to the given values. The values are overwritten
for a specific model if \code{model} and \code{param} are given.
Note that it is not possible to set the values of additional (form)
parameters
of a parametrised class by means of \code{all.param}.
In case of an anisotropic model the anisotropy matrix is by default
diagonal with both entries equal to \eqn{1/\code{all.param[4]}}.
}
\item{legends}{if \code{TRUE} then a legend is added to the
two-dimensional plot.}
\item{register}{register where intermediate results of the simulations
are stored, see also \code{\link{GaussRF}}.}
\item{Mean}{mean of the random field}
\item{erase}{parameter of \code{\link{split.screen}}, which is called
at the very beginning}
\item{x.fraction}{the current screen is split into 2 x 2 screens.
The parameter \code{x.fraction} gives the size of the left screens in
the x directions as part of 1. See also the Details.}
\item{cex.names}{font size for model names}
\item{covx.default}{if \code{length(cov.x)==1} then \eqn{[0,
\code{cov.x}]} is covered by \code{covx.default} points of equal
distance}
\item{link.fct}{\code{NULL} or \code{function(values)} or "MaxStable".
Transformation of the Gaussian random field.
\cr\cr
If \code{link.fct="MaxStable"} then
max-stable random fields are simulated for the given covariance
function and the extremal coefficient function is given (up the
constant -1) instead of the variogram or the covariance function
}
\item{Zlim}{Vector of two elements or list of two vectors of two
elements. Graphical limits for the Gaussian random process (and the
transformed field).}
\item{Col.rect}{colour for interactive plot; see
\code{\link{eval.parameters}}.}
\item{Col.bg}{colour for interactive plot; see \code{\link{eval.parameters}}.}
\item{Col.sep}{colour for interactive plot; see \code{\link{eval.parameters}}.}
\item{Col.line}{colour for interactive plot; see
\code{\link{eval.parameters}}.}
\item{Col.txt}{colour for interactive plot; see \code{\link{eval.parameters}}.}
\item{Col.flash}{colour for the previously chosen model}
\item{Col.vario}{colour for the empirical variogram plot}
\item{Col.main}{colour for the title of the random field}
\item{Col.model}{vector of two colours for plotting the variogram of
the Gaussian random field and the transformed field}
\item{vario.lty}{vector of two line types for primary and secondary
axis of the variogram}
\item{cex.leg}{font size used in the legends}
\item{cex.eval}{font size used in the menue entries}
\item{update}{logical. If \code{TRUE} the plots are updated after
each interactive change of the values. Otherwise, the bottom
'simulate' is added in the menu.}
\item{screen.new}{logical. If \code{FALSE} the screen is erased
before a simulation and completely rebuild; otherwise the screen is
updated. If \code{FALSE} flickering appears during the update of the
current screen, otherwise it may happen during the reorganisation of
any window (and may take quite a lot of time).
}
\item{use.outer.RFparameters}{logical.
If \code{FALSE} the following parameters usually set by
\command{\link{RFparameters}} are internally set
\itemize{
\item \code{PracticalRange=FALSE}
\item \code{PrintLevel=1} if \code{debug=FALSE} and \code{5} otherwise.
\item \code{maxstable.maxGauss=2}
\item \code{CE.force=TRUE}
\item \code{CE.trials=1}
\item \code{CE.mmin=-4}
\item \code{CE.userfft=TRUE}
}
}
\item{debug}{logical. If \code{TRUE} then internally the
\code{RFparameter()$PrintLevel} is set to 5.
}
\item{...}{additional graphics options for the plot of the one- or
two-dimensional simulations, see \code{\link{plot}} and
\code{\link{image}}.}
}
\details{
The interactive plot consists of 3 parts:
\itemize{
\item top left: graph of the covariance function or the
variogram. In case \code{empirical} is given the empirical
variogram is also plotted. If \code{link.fct} is given, then also
the covariance function or the variogram is plotted. If the
correlation model is for a non-stationary random field,
the variogram for the transformed random field is not estimated in
a primitive way -- this is indicated with a star in the legend
\item bottom left: one- or two-dimensional simulation
\item right:
\itemize {
\item
list of implemented models; a specific
model is chosen by the left mouse button, or:
\item menu for the parameters of the chosen model.
The list includes the variance, a nugget effect, the mean and the
scale or the anisotropy parameters. Further, some global parameters
can be changed. They are the \code{PracticalRange} (see
\code{\link{RFparameters}} for details) and the angle of the
main variogram direction (or NA, then it follows the angle of the
anisotropy). Finally, the user can choose between the plot of the
covariance and the corresponding variogram.
}
}
The interactive plot is left by clicking any mouse button different
from the left when the top right part is active.
}
\value{
list of the last model and its parameters.
}
\author{Martin Schlather, \email{schlath@hsu-hh.de}
\url{http://www.unibw-hamburg.de/WWEB/math/schlath/schlather.html}}
\seealso{\code{\link{CovarianceFct}}, \code{\link{eval.parameters}},
\code{\link{GaussRF}},
\code{\link{RFMethods}}, \code{\link{RandomFields}}.}
\examples{
%library(RandomFields, lib="~/TMP"); source("~/article/R/NEW.RF/RandomFields/R/ShowModels.R");source("~/article/R/NEW.RF/RandomFields/R/rf.R");source("~/article/R/NEW.RF/RandomFields/R/auxiliary.R")
# first example: one-dimensional simulations
options(locatorBell=FALSE)
x <- seq(1,10,0.1);
ShowModels(x=x)
# second example: two-dimensional simulations and
# empirical variogram
dx <- runif(300,0,8)
dy <- runif(300,0,8)
dz <- GaussRF(x=dx, y=dy, grid=FALSE, model="gaus",
param=c(1,2,1,2))
ev <- EmpiricalVariogram(x=dx, y=dy, data=dz, grid=FALSE,
bin=(-1:20)/4)
x <- seq(1,5,0.1);
ShowModels(x=x, y=x, empirical=ev)
# third example: two-dimensional anistropic simulations and
# link function
% library(RandomFields, lib="~/TMP"); source("~/article/R/NEW.RF/RandomFields/R/ShowModels.R");RFparameters(Print=5,CE.trials=1);ShowModels(x=x, y=x, link=function(x) x^2,model=list(list(model="exp", var=1,aniso=c(1,0,0,5))));
x <- seq(1,10,0.1)
ShowModels(x=x, y=x, link=function(x) exp(x),
model=list(list(model="spheric", var=1, aniso=c(1,0,0,5))))
x <- seq(1,10,0.1)
ShowModels(x=x, link=function(x) exp(x),
model=list(list(model="spheric",var=1, scale=1)))
% library(RandomFields, lib="~/TMP"); source("~/article/R/NEW.RF/RandomFields/R/ShowModels.R");x <- seq(1,10,0.05);ShowModels(x=x, link="MaxStable", fixed.rs=TRUE,model=list(list(model="gauss",var=1, scale=1)), type="l")
x <- seq(1,10,0.1)
ShowModels(x=x, link="MaxStable", fixed.rs=TRUE,
model=list(list(model="gauss",var=1, scale=1)), type="l")
}
\keyword{spatial}
