InterleavedMaximinD: Interleaved lattice-based maximin distance designs

In LatticeDesign: Lattice-Based Space-Filling Designs

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));

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.

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.

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);

LatticeDesign documentation built on Nov. 13, 2022, 9:06 a.m.