# Documentation

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# lhsdesign

Latin hypercube sample

## Syntax

`X = lhsdesign(n,p)X = lhsdesign(...,'smooth','off')X = lhsdesign(...,'criterion',criterion)X = lhsdesign(...,'iterations',k)`

## Description

`X = lhsdesign(n,p)` returns an n-by-p matrix, `X`, containing a latin hypercube sample of `n` values on each of `p` variables. 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(...,'smooth','off')` produces points at the midpoints of the above intervals: `0.5/n`, `1.5/n`, ..., `1-0.5/n`. The default is `'on'`.

`X = lhsdesign(...,'criterion',criterion)` iteratively generates latin hypercube samples to find the best one according to `criterion`, which can be `'none'`, `'maximin'`, or `'correlation'`.

CriterionDescription

`'none'`

No iteration.

`'maximin'`

Maximize minimum distance between points. This is the default.

`'correlation'`

Reduce correlation.

`X = lhsdesign(...,'iterations',k)` iterates up to `k` times in an attempt to improve the design according to the specified criterion. The default is ```k = 5```.