MATLAB Function Description and Examples.

In matlab : edit lhsnorm: function = lhsnorm(mu,sigma,n,dosmooth)%LHSNORM Generate a latin hypercube sample with a normal distribution% X=LHSNORM(MU,SIGMA,N) generates a latin hypercube sample X of size% N from the multivariate normal distribution with mean vector MU% and covariance matrix SIGMA. Correlation among variables can be sprecified. This is sampling utility implementing Latin hypercube sampling from multivariate normal, uniform & empirical distribution.

Latin hypercube sampling in matlab The following Matlab project contains the source code and Matlab examples used for latin hypercube sampling. For each column of X, the n values are randomly distributed with one from each interval (0,1/n), (1/n,2/n), (1 - 1/n,1), and randomly permuted. X = lhsdesign (n,p) returns a Latin hypercube sample matrix of size n -by- p. For each column of X, the n values are randomly distributed with one from each interval (0,1/n), (1/n,2/n), (1-1/n,1), and they are randomly permuted. X = lhsdesign (n,p) returns an n -by- p matrix, X, containing a Latin hypercube sample of n values on each of p variables. X = lhsnorm(mu,sigma,n) returns an n-by-p matrix, X, containing a Latin hypercube sample of size n from a p-dimensional multivariate normal distribution with mean vector, mu, and covariance matrix, sigma. For each column of X, the n values are randomly distributed with one from each interval (0,1/n), (1/n,2/n), , (1 - 1/n,1), and randomly permuted. The actual sampled values are used to form vectors of variables commonly used as input to computer models for sensitivity and uncertainty analyses studies.X = lhsdesign(n,p) returns a Latin hypercube sample matrix of size n-by-p. 2 - Method of solution: The Latin hypercube technique employs a constrained sampling scheme, whereas random sampling corresponds to a simple Monte Carlo technique. In addition, the samples from the uniform and log-uniform distributions may be modified by changing the frequency of the sampling within subintervals, and a subroutine which can be modified by the user to generate samples from other distributions (including empirical data) is provided. The following distributions are built into the program: normal, lognormal, uniform, log-uniform, triangular, and beta. The generation of these samples is based on user-specified parameters which dictate the characteristics of the generated samples, such as type of sample (LHS or random), sample size, number of samples desired, correlation structure of input variables, and type of distribution specified on each variable. 1 - Description of program or function: LHS was written for the generation of multivariate samples either completely at random or by a constrained randomization termed Latin hypercube sampling (LHS).

Matlab latin hypercube sampling