sim.rf: Simulates a Stationary Gaussian random field

Description

Simulates a stationary Gaussian random field on a regular grid.

Usage

sim.rf(obj)

Arguments

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.

Examples

Run this code

#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 ...")