## Circulant Embedding method for generating stationary Gaussian field

version 2.0.0.0 (2.24 KB) by
Fast simulation of Gaussian random fields via the Fast Fourier Transform

Updated 22 Jan 2016

simulating stationary Gaussian field over an 'm' times 'n' grid
INPUT:
- 'm' and 'n' for evaluating the field over the m*n grid;
note that size of covariance matrix is m^2*n^2;
- scalar function rho(h), where 'h' is a two dimensional vector
input and cov(X_t,Y_s)=rho(t-s) is the cov. function of a
2-dimensional stationary Gaussian field; see reference below;
OUTPUT:
- two statistically independent fields 'field1' and 'field2'
over the m*n grid;
- vectors 'tx' and 'ty' so that the field is plotted via
imagesc(tx,ty,field1)
Example:
rho=@(h)((1-h(1)^2/50^2-h(1)*h(2)/(15*50)-h(2)^2/15^2)...
*exp(-(h(1)^2/50^2+h(2)^2/15^2))); % define covariance function
stationary_Gaussian_process(512,384,rho); % plot when no output wanted
Reference:
Kroese, D. P., & Botev, Z. I. (2015). Spatial Process Simulation.
In Stochastic Geometry, Spatial Statistics and Random Fields(pp. 369-404)
Springer International Publishing, DOI: 10.1007/978-3-319-10064-7_12

### Cite As

Zdravko Botev (2022). Circulant Embedding method for generating stationary Gaussian field (https://www.mathworks.com/matlabcentral/fileexchange/38880-circulant-embedding-method-for-generating-stationary-gaussian-field), MATLAB Central File Exchange. Retrieved .

##### MATLAB Release Compatibility
Created with R2015b
Compatible with any release
##### Platform Compatibility
Windows macOS Linux

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