Lattice {mined}

Good lattice points

Description

Generate good rank-1 lattice points with prime number of points by using the fast component-by-component construction algorithm of Nuyens and Cools (2006). Refer Nuyens (2007) for more details.

Usage

Lattice(n, p)

Arguments

n

The number of points, which should be a prime.

p

The number of dimensions.

Value

An n-by-p matrix containing the good lattice points.

Author(s)

Dianpeng Wang <[e-mail]> and V. Roshan Joseph <[e-mail]>

References

Nuyens, D. and Cools, R. (2006). "Fast algorithms for component-by-component construction of rank-1 lattice rules in shift-invariant reproducing kernel Hilbert spaces.", Mathematics of Computation, 75, 903-920.

Nuyens, D. (2007). "Fast Construction of Good Lattice Rules.", Ph.D Thesis, Katholieke Universiteit Leuven, Leuven, Belgium.

Examples

library(mined)
res <- Lattice(101, 2)
plot(res[, 1], res[, 2], col='red',xlab='First dimension', ylab='Second dimension', pch=15)