DPMPD: Densest packing-based maximum projection designs

In LatticeDesign: Lattice-Based Space-Filling Designs

Densest packing-based maximum projection designs

Description

Generates a densest packing-based maximum projection design.

Usage

DPMPD(p,n,rotation="magic",w=100)

Arguments

p	Number of dimensions, must be an integer greater than one and no higher than eight.
n	Number of points, must be an integer greater than one.
rotation	Optional, whether to use magic rotation matrices (for p=2,3,4,6,8, recommended) or random rotation matrices.
w	Number of rotation matrices to try.

Details

This function generates a densest packing-based maximum projection design in two to eight dimensions. For p=2,4,8 with rotation="magic", the designs are generated following the Biometrika paper "Lattice-based designs possessing quasi-optimal separation distance on all projections". For p=3,6 with rotation="magic", the designs are generated following the arXiv paper "Lattice-based designs with quasi-uniform projections". For other p or rotation!="magic", the designs are generated from random rotations.

Value

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

Design	The generated design.
ProjectiveSeparationDistance	The projective separation distance of the generated design, from one-dimensional projections to the unprojected design.

References

He, Xu (2020). "Lattice-based designs possessing quasi-optimal separation distance on all projections", Biometrika, accepted, DOI:10.1093/biomet/asaa057.

He, Xu (2018). "Lattice-based designs with quasi-uniform projections", arXiv:1709.02062v2.

Examples

DPMPD(p=4,n=200,w=100)

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