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Strongly heterogeneous media arise in several applications that include radiation shields, nuclear fuel, BWR moderators, clouds, planetary and stellar atmospheres, turbulent gases and plasmas. The theory and simulation of random variables and vectors is also reviewed for = , Second, we provide simple algorithms that can be used to generate independent samples of general stochastic models. First, we provide some theoretical background on stochastic processes and random fields that can be used to model phenomena that are random in space and/or time. While numerous algorithms and tools currently exist to generate samples of simple random variables and vectors, no cohesive simulation tool yet exists for generating samples of stochastic processes and/or random fields. The use of Monte Carlo simulation requires methods and algorithms to generate samples of the appropriate stochastic model these samples then become inputs and/or boundary conditions to established deterministic simulation codes. Mathematical models for these random phenomena are referred to as stochastic processes and/or random fields, and Monte Carlo simulation is the only general-purpose tool for solving problems of this type. Examples are diverse and include turbulent flow over an aircraft wing, Earth climatology, material microstructure, and the financial markets.
#Matlab latin hypercube sampling lognormal code#
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.Many problems in applied science and engineering involve physical phenomena that behave randomly in time and/or space. % Similar to tiedrank, but no adjustment for ties here % 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
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% the multivariate normal distribution, but the marginal distribution % N from the multivariate normal distribution with mean vector MU % X=LHSNORM(MU,SIGMA,N) generates a latin hypercube sample X of size %LHSNORM Generate a latin hypercube sample with a normal distribution In matlab : edit lhsnorm : function = lhsnorm(mu,sigma,n,dosmooth) An edit of the lhsnorm function can probably answer your question.