Optimal Augmented Latin Hypercube Sample

Augments an existing Latin Hypercube Sample, adding points to the design, while maintaining the latin properties of the design. This function attempts to add the points to the design in an optimal way.

Usage

optAugmentLHS(lhs, m = 1, mult = 2)

Arguments

lhs

The Latin Hypercube Design to which points are to be added

m

The number of additional points to add to matrix lhs

mult

m*mult random candidate points will be created.

Value

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

Details

Augments an existing Latin Hypercube Sample, adding points to the design, while maintaining the latin properties of the design. This function attempts to add the points to the design in a way that maximizes S optimality.

S-optimality seeks to maximize the mean distance from each design point to all the other points in the design, so the points are as spread out as possible.

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. [optSeededLHS()] and [augmentLHS()] to modify and augment existing designs.

Examples

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