LatticeDesign (version 3.0-1)

InterleavedMaximinD: Interleaved lattice-based maximin distance designs

Description

Generates an interleaved lattice-based maximin distance design.

Usage

InterleavedMaximinD(p,n,weight=rep(1,p));
InterleavedMaximinDAlg1(p,n,weight=rep(1,p));
InterleavedMaximinDAlg2(p,n,weight=rep(1,p));
InterleavedMaximinDAlg3(p,n,weight=rep(1,p));

Value

The value returned from the function is a list containing the following components:

Design

The generated design.

SeparationDistance

The separation distance of the generated design.

m

The actual number of points of the generated design.

DesignTransformed

The generated design that is transformed to the rectangular design space given the weights.

weight

The weight used in the distance measure, higher for more important variable.

s_vector

The numbers of distinct levels of the generated design.

L01

The base design.

Arguments

p

Number of dimensions, must be an integer greater than one.

n

Targeted number of points, must be an integer greater than one.

weight

Optional, the weights used in the distance measure, higher for more important variable.

Details

This function generates an interleaved lattice-based maximin distance design in p dimensions and at least n points, following the algorithms provided in the paper "Interleaved lattice-based maximin distance designs". Function InterleavedMaximinD uses the recommended algorithm provided in the paper. Functions InterleavedMaximinDAlg1, InterleavedMaximinDAlg2, and InterleavedMaximinDAlg3 use Algorithm 1, 2, and 3, respectively. For InterleavedMaximinDAlg1, p must be no greater than 5. For InterleavedMaximinDAlg3, p must be greater than 8.

References

He, Xu (2019). "Interleaved lattice-based maximin distance designs", Biometrika, 106(2): 453-464.

Examples

InterleavedMaximinD(p=3,n=10,weight=rep(1,3));
InterleavedMaximinDAlg1(p=3,n=10);
InterleavedMaximinDAlg2(p=6,n=10);
InterleavedMaximinDAlg3(p=9,n=257);