sim.rf: Simulates a random field

Description

Simulates a random Gaussian 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 (See the FIELDS manual for more details.) The simple fix is increase the size of the domain so that the correlation sale becomes smaller relative to the extent of th domain.

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 the grid point values for x and y N and M is the size of the larger grid that is used for simulation ( usually M= 2*m and N=2*n) to minimize periodic effects. 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 ...")