A 3D orthogonal array of strength 2

Description

A 3-dimensional linear orthogonal array (OA) of strength 2 with 49 points. The design points are equally spaced into 2 dimensional coordinate planes. However by construction, such OAs satisfy a linear relation, here: x1 + 3*x2 + x3 = 0 (mod 7). As a consequence, the design points are contained in parallel planes orthogonal to (1,3,1). Actually, they are also contained in parallel planes orthogonal to other directions, as (2,-1,2) or (3,2,3), since the congruence relation leads to 2*x1 - x2 + 2*x3 = 0 (mod 7) or 3*x1 + 2*x2 + 3*x3 = 0 (mod 7). For instance, they are contained in 4 parallel planes orthogonal to (2,-1,2).

Usage

data(OA131)

Format

A data frame with 49 observations on the following 3 variables.

x1

first coordinate

x2

second coordinate

x3

third coordinate

Source

Roustant O., Franco J., Carraro L., Jourdan A. (2010), A radial scanning statistic for selecting space-filling designs in computer experiments, MODA-9 proceedings, www.emse.fr/~roustant

Examples

data(OA131)

# centering and reducing to [0,1]^3
OA <- (OA131 + 0.5)/7

pairs(OA, xlim=c(0,1), ylim=c(0,1))
## Not run: library(lattice)
cloud(x3~x1+x2, data=OA, xlim=c(0,1), ylim=c(0,1), zlim=c(0,1), 
    screen = list(z = 50, x = -70, y = 0))
## End(Not run)

Results

R version 3.3.1 (2016-06-21) -- "Bug in Your Hair"
Copyright (C) 2016 The R Foundation for Statistical Computing
Platform: x86_64-pc-linux-gnu (64-bit)

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> library(DiceDesign)
> png(filename="/home/ddbj/snapshot/RGM3/R_CC/result/DiceDesign/OA131.Rd_%03d_medium.png", width=480, height=480)
> ### Name: OA131
> ### Title: A 3D orthogonal array of strength 2
> ### Aliases: OA131
> ### Keywords: datasets
> 
> ### ** Examples
> 
> data(OA131)
> 
> # centering and reducing to [0,1]^3
> OA <- (OA131 + 0.5)/7
> 
> pairs(OA, xlim=c(0,1), ylim=c(0,1))
> ## Not run: 
> ##D library(lattice)
> ##D cloud(x3~x1+x2, data=OA, xlim=c(0,1), ylim=c(0,1), zlim=c(0,1), 
> ##D     screen = list(z = 50, x = -70, y = 0))
> ## End(Not run)
> 
> 
> 
> 
> 
> dev.off()
null device 
          1 
>