Augment a Latin Hypercube Design

Share:

Description

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

Usage

1
augmentLHS(lhs, m=1)

Arguments

lhs

The Latin Hypercube Design to which points are to be added

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

1
2
3
  a <- randomLHS(4,3)
  a
  augmentLHS(a, 2)