Generate AR1 spatial data

Generates spatial data using an AR1 process with normal error distribution.

This script generates artificial spatial data using a first order spatial autoregressive process (AR1)
The process is
X(i,j) = PHI*(X(i,j-1)+X(i,j+1)+X(i-1,j)+X(i+1,j) + error

To generate a 10x10, periodic spatial pattern, with normal error distribution, and a variance of SIGMA, the command is

spatialPatternAR1([10,10],PHI,SIGMA)

or equivalently,
spatialPatternAR1([10,10],PHI,SIGMA,1)

the same pattern, but with a rigid boundary is generated with

spatialPatternAR1([10,10],PHI,SIGMA,0)

Different error distributions can be used. Using the current script this can be done by extracting the generator matrix, M

M = spatialPatternAR1([10,10],PHI,SIGMA,1,1)

M is a 100x100 matrix.
Then given a random vector, error (size = 100x1) with indepedent elements sampled from the required error distribution, the spatial pattern is given by

x = reshape(M * error,[10,10])