# olhDesign: Nguyen's Orthogonal Latin Hypercube Designs In DiceDesign: Designs of Computer Experiments

## 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

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

## 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

## Value

A list with components:

 `n ` the number of lines/experiments `dimension ` the number of columns/input variables `design ` the design of experiments

## Author(s)

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.

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

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11``` ```## 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) ```

### Example output

```\$n
[1] 9

\$dimension
[1] 4

\$design
[,1] [,2] [,3] [,4]
[1,]    5    6    7    8
[2,]    6    3    0    7
[3,]    7    8    3    2
[4,]    8    1    6    3
[5,]    4    4    4    4
[6,]    3    2    1    0
[7,]    2    5    8    1
[8,]    1    0    5    6
[9,]    0    7    2    5

\$n
[1] 9

\$dimension
[1] 4

\$design
[,1] [,2] [,3] [,4]
[1,]    1    2    3    4
[2,]    2   -1   -4    3
[3,]    3    4   -1   -2
[4,]    4   -3    2   -1
[5,]    0    0    0    0
[6,]   -1   -2   -3   -4
[7,]   -2    1    4   -3
[8,]   -3   -4    1    2
[9,]   -4    3   -2    1

\$n
[1] 9

\$dimension
[1] 4

\$design
[,1]  [,2]  [,3]  [,4]
[1,] 0.625 0.750 0.875 1.000
[2,] 0.750 0.375 0.000 0.875
[3,] 0.875 1.000 0.375 0.250
[4,] 1.000 0.125 0.750 0.375
[5,] 0.500 0.500 0.500 0.500
[6,] 0.375 0.250 0.125 0.000
[7,] 0.250 0.625 1.000 0.125
[8,] 0.125 0.000 0.625 0.750
[9,] 0.000 0.875 0.250 0.625

\$n
[1] 9

\$dimension
[1] 4

\$design
[,1]  [,2]  [,3]  [,4]
[1,]  0.25  0.50  0.75  1.00
[2,]  0.50 -0.25 -1.00  0.75
[3,]  0.75  1.00 -0.25 -0.50
[4,]  1.00 -0.75  0.50 -0.25
[5,]  0.00  0.00  0.00  0.00
[6,] -0.25 -0.50 -0.75 -1.00
[7,] -0.50  0.25  1.00 -0.75
[8,] -0.75 -1.00  0.25  0.50
[9,] -1.00  0.75 -0.50  0.25

T1    T2    T3    T4
1   2.5   5.0   7.5  10.0
2   5.0  -2.5 -10.0   7.5
3   7.5  10.0  -2.5  -5.0
4  10.0  -7.5   5.0  -2.5
5   0.0   0.0   0.0   0.0
6  -2.5  -5.0  -7.5 -10.0
7  -5.0   2.5  10.0  -7.5
8  -7.5 -10.0   2.5   5.0
9 -10.0   7.5  -5.0   2.5
[[1]]
[,1]
[1,]  0.5
[2,]  1.0
[3,]  0.0
[4,] -0.5
[5,] -1.0

[[2]]
[,1] [,2]
[1,]  0.5  1.0
[2,]  1.0 -0.5
[3,]  0.0  0.0
[4,] -0.5 -1.0
[5,] -1.0  0.5

[[3]]
[,1]  [,2]  [,3]
[1,]  0.25  0.50  0.75
[2,]  0.50 -0.25 -1.00
[3,]  0.75  1.00 -0.25
[4,]  1.00 -0.75  0.50
[5,]  0.00  0.00  0.00
[6,] -0.25 -0.50 -0.75
[7,] -0.50  0.25  1.00
[8,] -0.75 -1.00  0.25
[9,] -1.00  0.75 -0.50

[[4]]
[,1]  [,2]  [,3]  [,4]
[1,]  0.25  0.50  0.75  1.00
[2,]  0.50 -0.25 -1.00  0.75
[3,]  0.75  1.00 -0.25 -0.50
[4,]  1.00 -0.75  0.50 -0.25
[5,]  0.00  0.00  0.00  0.00
[6,] -0.25 -0.50 -0.75 -1.00
[7,] -0.50  0.25  1.00 -0.75
[8,] -0.75 -1.00  0.25  0.50
[9,] -1.00  0.75 -0.50  0.25

[[5]]
[,1]   [,2]   [,3]   [,4]   [,5]
[1,]  0.125  0.250  0.375  0.500  0.625
[2,]  0.250 -0.125 -0.500  0.375  0.750
[3,]  0.375  0.500 -0.125 -0.250 -0.875
[4,]  0.500 -0.375  0.250 -0.125 -1.000
[5,]  0.625  0.750  0.875  1.000 -0.125
[6,]  0.750 -0.625 -1.000  0.875 -0.250
[7,]  0.875  1.000 -0.625 -0.750  0.375
[8,]  1.000 -0.875  0.750 -0.625  0.500
[9,]  0.000  0.000  0.000  0.000  0.000
[10,] -0.125 -0.250 -0.375 -0.500 -0.625
[11,] -0.250  0.125  0.500 -0.375 -0.750
[12,] -0.375 -0.500  0.125  0.250  0.875
[13,] -0.500  0.375 -0.250  0.125  1.000
[14,] -0.625 -0.750 -0.875 -1.000  0.125
[15,] -0.750  0.625  1.000 -0.875  0.250
[16,] -0.875 -1.000  0.625  0.750 -0.375
[17,] -1.000  0.875 -0.750  0.625 -0.500
```

DiceDesign documentation built on Feb. 13, 2021, 1:06 a.m.