lhs (version 0.16)

improvedLHS: Improved Latin Hypercube Sample

Description

Draws a Latin Hypercube Sample from a set of uniform distributions for use in creating a Latin Hypercube Design. This function attempts to optimize the sample with respect to an optimum euclidean distance between design points.

Usage

improvedLHS(n, k, dup=1)

Arguments

n

The number of partitions (simulations or design points)

k

The number of replications (variables)

dup

A factor that determines the number of candidate points used in the search. A multiple of the number of remaining points than can be added.

Value

An n by k Latin Hypercube Sample matrix with values uniformly distributed on [0,1]

Details

Latin hypercube sampling (LHS) was developed to generate a distribution of collections of parameter values from a multidimensional distribution. A square grid containing possible sample points is a Latin square iff there is only one sample in each row and each column. A Latin hypercube is the generalisation of this concept to an arbitrary number of dimensions. When sampling a function of k variables, the range of each variable is divided into n equally probable intervals. n sample points are then drawn such that a Latin Hypercube is created. Latin Hypercube sampling generates more efficient estimates of desired parameters than simple Monte Carlo sampling.

This program generates a Latin Hypercube Sample by creating random permutations of the first n integers in each of k columns and then transforming those integers into n sections of a standard uniform distribution. Random values are then sampled from within each of the n sections. Once the sample is generated, the uniform sample from a column can be transformed to any distribution by using the quantile functions, e.g. qnorm(). Different columns can have different distributions.

This function attempts to optimize the sample with respect to an optimum euclidean distance between design points. $$Optimum distance = frac{n}{n^{\frac{1.0}{k}}}$$

References

Beachkofski, B., Grandhi, R. (2002) Improved Distributed Hypercube Sampling American Institute of Aeronautics and Astronautics Paper 1274.

This function is based on the MATLAB program written by John Burkardt and modified 16 Feb 2005 http://www.csit.fsu.edu/~burkardt/m_src/ihs/ihs.m

See Also

randomLHS, geneticLHS, maximinLHS, and optimumLHS to generate Latin Hypercube Samples. optAugmentLHS, optSeededLHS, and augmentLHS to modify and augment existing designs.

Examples

# NOT RUN {
  improvedLHS(4, 3, 2)
# }