The last criterion, ESE, is implemented by the authors of SMT (more details about such method could be found in 2). This is sampling utility implementing Latin hypercube sampling from multivariate normal, uniform & empirical distribution. The four first criteria are the same than in pyDOE (for more details, see 1). Optimize the design using the Enhanced Stochastic Evolutionary algorithm (ESE). The benefit of this approach is that it ensures that at least one value from each region is included in the sample. Minimize the maximum correlation coefficient. The idea behind one-dimensional latin hypercube sampling is simple: Divide a given CDF into n different regions and randomly choose one value from each region to obtain a sample of size n. Maximize the minimum distance between points and center the point within its interval. Maximize the minimum distance between points and place the point in a randomized location within its interval. Five criteria for the construction of LHS are implemented in SMT:Ĭenter the points within the sampling intervals. XLHSDESIGNCON(N,P,LB,UB,ISEXP) generates a. The LHS method uses the pyDOE package (Design of Experiments for Python) 1. Generate an NxP latin hypercube sample with bounds and linear constraints and optional exponential distribution. Sections where n is the number of sampling points, and we put only one point in each section. LHS is built as follows: we cut each dimension space, which represents a variable, into n Instead, the figures of merit were expressed in terms of the input space (e.g., the minimum distance between points). It is among the most popular sampling techniques in computer experiments thanks to its simplicity and projection properties with high-dimensional problems. and outputs (although covariance among inputs was often a topic such as when Latin hypercube sampling is used for multivariate integration).
In your case you already have your distribution z in the code above and you also have mu, sigma and 'n' (the size of your distribution), just replace them and you should be able to create your Latin Hypercube.The LHS design is a statistical method for generating a quasi-random sampling distribution. These levels are randomly combined to generate a random Latin Hypercube as the initial DOE design matrix with n n points (each level of a factor studies only once). cube sampling (LHS), a type of stratified Monte Carlo sampling 2,3 that is an. In the Optimal Latin Hypercube technique the design space for each factor is divided uniformly (the same number of divisions, n n, for all factors). % Similar to tiedrank, but no adjustment for ties here The toolbox is built in Matlab, a numerical mathematical software. X(:,i) = norminv(x(:,i),mu(i), sqrt(sigma(i,i))) en 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). % maintaining the ranks (and therefore rank correlations) from the % Transform each column back to the desired marginal distribution, % Get gridded or smoothed-out values on the unit interval
% correlation structure - in this case multivariate normal % Generate a random sample with a specified distribution and % Copyright 1993-2010 The MathWorks, Inc.
% sample before the marginals are adjusted to obtain X. % =LHSNORM(.) also returns Z, the original multivariate normal % 0.5/N we use a value having a uniform distribution on the % If 'ONOFF' is 'on' (the default), each column has points uniformly % normal cumulative distribution for that column''s marginal distribution. In other words, each column is a permutation If 'ONOFF' is 'off', each column has points equally spaced % X=LHSNORM(MU,SIGMA,N,'ONOFF') controls the amount of smoothing in the % is close to its theoretical normal distribution. % of each column is adjusted so that its sample marginal distribution % the multivariate normal distribution, but the marginal distribution % N from the multivariate normal distribution with mean vector MU For each column of X, the n values are randomly distributed with one from each interval (0,1/n), (1/n,2/n). % X=LHSNORM(MU,SIGMA,N) generates a latin hypercube sample X of size Description example X lhsdesign (n,p) returns a Latin hypercube sample matrix of size n -by- p. This is sampling utility implementing Latin hypercube sampling from multivariate normal, uniform & empirical distribution. %LHSNORM Generate a latin hypercube sample with a normal distribution The following Matlab project contains the source code and Matlab examples used for latin hypercube sampling. In matlab : edit lhsnorm : function = lhsnorm(mu,sigma,n,dosmooth) An edit of the lhsnorm function can probably answer your question.