olhDesign: Nguyen's Orthogonal Latin Hypercube Designs
In DiceDesign: Designs of Computer Experiments
Description
Usage
Arguments
Value
Author(s)
References
See Also
Examples
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
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.
See Also
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.
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Description Usage Arguments Value Author(s) References See Also Examples
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 |
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.
See Also
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
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