R: Augment a Latin Hypercube Design

augmentLHS {lhs} | R Documentation

## Augment a Latin Hypercube Design

### Description

Augments an existing Latin Hypercube Sample, adding points to the design, while maintaining the latin properties of the design.

### Usage

    augmentLHS(lhs, m = 1)

### Arguments

`lhs` | The Latin Hypercube Design to which points are to be added. Contains an existing latin hypercube design with a number of rows equal to the points in the design (simulations) and a number of columns equal to the number of variables (parameters). The values of each cell must be between 0 and 1 and uniformly distributed
`m` | The number of additional points to add to matrix `lhs`

### Details

Augments an existing Latin Hypercube Sample, adding points to the design, while maintaining the latin properties of the design. Augmentation is perfomed in a random manner.

The algorithm used by this function has the following steps. First, create a new matrix to hold the candidate points after the design has been re-partitioned into (n+m)^2 cells, where n is number of points in the original `lhs` matrix. Then randomly sweep through each column (1...`k`) in the repartitioned design to find the missing cells. For each column (variable), randomly search for an empty row, generate a random value that fits in that row, record the value in the new matrix. The new matrix can contain more filled cells than `m` unles m = 2n, in which case the new matrix will contain exactly `m` filled cells. Finally, keep only the first m rows of the new matrix. It is guaranteed to have `m` full rows in the new matrix. The deleted rows are partially full. The additional candidate points are selected randomly due to the random search for empty cells.

### Value

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

### Author(s)

Rob Carnell

### References

Stein, M. (1987) Large Sample Properties of Simulations Using Latin Hypercube Sampling. Technometrics. 29, 143–151.

### See Also

[randomLHS()], [geneticLHS()], [improvedLHS()], [maximinLHS()], and [optimumLHS()] to generate Latin Hypercube Samples. [optAugmentLHS()] and [optSeededLHS()] to modify and augment existing designs.

### Examples

    set.seed(1234)
    a <- randomLHS(4,3)
    b <- augmentLHS(a, 2)

[Package lhs version 1.1.3 Index]