# augmentLHS

##### Augment a Latin Hypercube Design

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

- Keywords
- 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]

##### 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

```
# NOT RUN {
set.seed(1234)
a <- randomLHS(4,3)
b <- augmentLHS(a, 2)
# }
```

*Documentation reproduced from package lhs, version 1.0.1, License: GPL-3*