Sample Creation with Latin Hypercube Sampling and Spatial Correlation Using Cholesky Decomposition Algorithm

This document presents a source code implementation that generates random fields over a square spatial domain. The random field generation employs Latin Hypercube Sampling (LHS) for sample creation, while the spatial correlation structure is modeled using the Cholesky decomposition algorithm. Notably, Latin Hypercube Sampling represents an efficient sampling technique that ensures uniform distribution of sample points across the parameter space, thereby enhancing sampling accuracy and coverage. The Cholesky decomposition algorithm, a matrix factorization method, is implemented to compute and enforce the spatial correlation structure within the random field. Through the integration of these two techniques, the code produces highly accurate random fields that can accommodate various practical application requirements. The implementation typically involves generating correlated random variables by applying the Cholesky factor to uncorrelated samples obtained from LHS, effectively transforming them into spatially correlated field realizations with specified covariance structures.