DiceDesign (version 1.10)

olhDesign: Nguyen's Orthogonal Latin Hypercube Designs

Description

Generate the Orthogonal Latin Hypercube (OLH) designs proposed by Nguyen in 2008. These OLHs have a latin structure, an orthogonality between the main terms and the interactions (+ squares) and low correlations between the interactions (+ squares). Very larges matrices can be obtained as the number of input variables and hence the number of lines is unconstrained. When the number of input variables is a power of 2, OLHs have \(d\) columns and \(n = 2d + 1\) lines (experiments). A vertical truncature is applied when the number of input variables is not a power of 2. Various normalizations can be applied.

Usage

olhDesign(dimension, range = c(0, 1))

Value

A list with components:

n

the number of lines/experiments

dimension

the number of columns/input variables

design

the design of experiments

Arguments

dimension

number of input variables

range

the scale (min and max) of the inputs. Ranges (0, 0) and (1, 1) are special cases and call integer ranges \((-d, d)\) and \((0, 2d)\). See the examples

Author

N.K. Nguyen for the algorithm. P. Kiener for the recursive R code.

References

Nguyen N.K. (2008) A new class of orthogonal Latinhypercubes, Statistics and Applications, Volume 6, issues 1 and 2, pp.119-123.

See Also

Cioppa's and De Rainville's NOLH designs: nolhDesign, nolhdrDesign.

Examples

## Classical normalizations
olhDesign(4, range = c(0, 0))
olhDesign(4, range = c(1, 1))
olhDesign(4, range = c(0, 1))
olhDesign(4, range = c(-1, 1))

## Change the dimnames, adjust to range (-10, 10) and round to 2 digits
xDRDN(olhDesign(4), letter = "T", dgts = 2, range = c(-10, 10))

## A list of designs
lapply(1:5, function(n) olhDesign(n, range = c(-1, 1))$design)