% fields, Tools for spatial data
% Copyright 2004-2013, Institute for Mathematics Applied Geosciences
% University Corporation for Atmospheric Research
% Licensed under the GPL -- www.gpl.org/licenses/gpl.html

\name{sim.rf}
\alias{sim.rf}
\title{
  Simulates a Stationary Gaussian random field  
}
\description{
Simulates a stationary Gaussian random field on a regular grid. 
}
\usage{
sim.rf(obj)
}
\arguments{
\item{obj}{
A covariance object that includes information about the covariance function 
and the grid for evaluation. Usually this is created by a setup call to 
Exp.image.cov. (See details below.) 
}
\item{\dots}{
Additional arguments passed to a particular method.}

}
\value{
A matrix with the random field values 
}
\details{
This function takes an object that includes some preliminary calculations 
and so is more efficient for simulating more than one field from the same 
covariance. However, the algorithm using a 2-d FFT may not always work if 
the correlation scale is large.
The simple fix is to increase the size of the domain so that the correlation 
scale becomes smaller relative to the extent of the domain. Increasing the size can be computationally expensive however and so this method has some limitations.  

For a stationary model the covariance object has the components: 

names( obj) 
 "m"    "n"    "grid" "N"    "M"    "wght",   

where m and n are the number of grid points in x and y, grid  is a list with 
components  x and y giving the grid points in each coordinate. 
N and M is the size of the larger grid 
that is used for simulation. Usually M = 2*m and N =2*n and results in an 
exact simulation of the stationary Gaussian field.  wght is a matrix from the FFT of the covariance 
function.  The easiest way to create this object is to use for example 
Exp.image.cov with setup=T ( see below). 

The classic reference for this algorithm is 
Wood, A.T.A. and Chan, G. (1994).
    Simulation of Stationary Gaussian Processes in [0,1]^d . Journal of
Computational and Graphical Statistics, 3, 409-432. 

}
\seealso{
Exp.image.cov, matern.image.cov  
}
\examples{
#Simulate a Gaussian random field with an exponential covariance function,  
#range parameter = 2.0 and the domain is  [0,5]X [0,5] evaluating the 
#field at a 100X100 grid.  
grid<- list( x= seq( 0,5,,100), y= seq(0,5,,100)) 
obj<-Exp.image.cov( grid=grid, theta=.5, setup=TRUE)
look<- sim.rf( obj)
# Now simulate another ... 
look2<- sim.rf( obj)
# take a look 
set.panel(2,1)
 image.plot( grid$x, grid$y, look) 
 title("simulated gaussian field")
 image.plot( grid$x, grid$y, look2) 
 title("another (independent) realization ...")
}
\keyword{spatial}
% docclass is function
% Converted by Sd2Rd version 1.21.