NOLHdesigns: List of Cioppa's Nearly Orthogonal Latin Hypercubes designs
In DiceDesign: Designs of Computer Experiments
Description
Usage
Format
Author(s)
Source
References
See Also
Examples
Description
A list of the NOLH designs for 2 to 29 input variables proposed by Cioppa in 2007. These designs combine a latin structure, orthogonality between the main terms and the interactions (+ squares) and reduced correlations between the interactions (+ squares).
This list combines the Excel spreadsheets published by Sanchez (see Source). It is used internally by the function nolhDesign which provides various normalizations.
Usage
1
Format
A list of 5 matrices representing designs of experiments for 8 to 29 input variables:
nolh2_7: 2 to 7 input variables, 17 experiments.
nolh8_11: 8 to 11 input variables, 33 experiments.
nolh12_16: 12 to 16 input variables, 65 experiments.
nolh17_22: 17 to 22 input variables, 129 experiments.
nolh23_29: 23 to 29 input variables, 257 experiments.
Author(s)
T.M. Cioppa for the designs. P. Kiener for the R code.
Source
Sanchez, S. M. (2011). NOLHdesigns in Excel file. Available online at https://nps.edu/web/seed/software-downloads/
References
Cioppa T.M., Lucas T.W. (2007). Efficient nearly orthogonal and space-filling Latin hypercubes. Technometrics 49, 45-55.
Kleijnen, J.P.C., Sanchez S.M., T.W. Lucas and Cioppa T. M.. A user's guide to the brave new world of designing simulation experiments. INFORMS Journal on Computing 17(3): 263-289.
Ye, K. Q. (1998). Orthogonal Latin hypercubes and their application in computer experiments. J. Amer. Statist. Asso. 93, 1430-
1439.
See Also
The main function nolhDesign. De Rainville's NOLH design list: NOLHDRdesigns.
Examples
1
2
3
4
5
6
7
8
## data(NOLHdesigns)
## all matrices
names(NOLHdesigns)
lapply(NOLHDRdesigns, tail, 2)
## The first matrix/design
NOLHdesigns[["nolh2_7"]]
Example output
[1] "nolh2_7" "nolh8_11" "nolh12_16" "nolh17_22" "nolh23_29"
$nolhdr08
X1 X2 X3 X4 X5 X6 X7 X8
32 10 -9 -14 4 15 6 -8 -8
33 -15 -12 -4 -6 -5 -14 -9 -4
$nolhdr09
X1 X2 X3 X4 X5 X6 X7 X8 X9
32 -15 10 -3 -9 -14 15 6 -8 -8
33 -10 -15 -11 -12 -4 -5 -14 -9 -4
$nolhdr10
X1 X2 X3 X4 X5 X6 X7 X8 X9 X10
32 -15 10 -3 -9 -14 4 15 6 -8 -8
33 -10 -15 -11 -12 -4 -6 -5 -14 -9 -4
$nolhdr11
X1 X2 X3 X4 X5 X6 X7 X8 X9 X10 X11
32 -15 10 -3 -9 -14 4 15 6 -8 2 -8
33 -10 -15 -11 -12 -4 -6 -5 -14 -9 -1 -4
$nolhdr12
X1 X2 X3 X4 X5 X6 X7 X8 X9 X10 X11 X12
64 -26 -16 -13 31 2 27 -1 -17 -16 -29 -6 -10
65 -4 -27 -5 -6 -1 -32 -17 -16 -7 -9 -32 -17
$nolhdr13
X1 X2 X3 X4 X5 X6 X7 X8 X9 X10 X11 X12 X13
64 -26 4 -1 -29 31 2 27 -1 -26 -17 -16 -6 -10
65 -4 -26 -3 -24 -6 -1 -32 -17 11 -16 -7 -32 -17
$nolhdr14
X1 X2 X3 X4 X5 X6 X7 X8 X9 X10 X11 X12 X13 X14
64 -26 4 -16 -13 31 2 27 -1 -26 -17 -16 -29 -6 -10
65 -4 -26 -27 -5 -6 -1 -32 -17 11 -16 -7 -9 -32 -17
$nolhdr15
X1 X2 X3 X4 X5 X6 X7 X8 X9 X10 X11 X12 X13 X14 X15
64 -26 4 -16 -1 -29 31 2 27 -1 -26 -17 -16 -29 -6 -10
65 -4 -26 -27 -3 -24 -6 -1 -32 -17 11 -16 -7 -9 -32 -17
$nolhdr16
X1 X2 X3 X4 X5 X6 X7 X8 X9 X10 X11 X12 X13 X14 X15 X16
64 -26 4 -16 -1 -29 -13 31 2 27 -1 -26 -17 -16 -29 -6 -10
65 -4 -26 -27 -3 -24 -5 -6 -1 -32 -17 11 -16 -7 -9 -32 -17
$nolhdr17
X1 X2 X3 X4 X5 X6 X7 X8 X9 X10 X11 X12 X13 X14 X15 X16 X17
128 -11 60 -17 -33 -5 -27 -8 59 7 -17 -36 -54 -25 -37 -49 -21 -28
129 -60 -11 -62 -47 -6 -46 -7 -16 2 -33 1 -4 -51 -5 -36 -61 1
$nolhdr18
X1 X2 X3 X4 X5 X6 X7 X8 X9 X10 X11 X12 X13 X14 X15 X16 X17 X18
128 -11 60 -17 -33 -5 -27 -8 59 7 -17 -14 -36 -54 -25 -37 -49 -21 -28
129 -60 -11 -62 -47 -6 -46 -7 -16 2 -33 -56 1 -4 -51 -5 -36 -61 1
$nolhdr19
X1 X2 X3 X4 X5 X6 X7 X8 X9 X10 X11 X12 X13 X14 X15 X16 X17 X18 X19
128 -11 60 -17 -33 -5 -27 -8 62 59 35 13 -17 -14 -54 -64 -25 -37 -49 -21
129 -60 -11 -62 -47 -6 -46 -7 -15 -16 -49 4 -33 -56 -4 -12 -51 -5 -36 -61
$nolhdr20
X1 X2 X3 X4 X5 X6 X7 X8 X9 X10 X11 X12 X13 X14 X15 X16 X17 X18 X19
128 -11 60 -17 -33 -5 -27 -8 59 7 35 -17 -14 -36 -54 -64 -25 -37 -49 -21
129 -60 -11 -62 -47 -6 -46 -7 -16 2 -49 -33 -56 1 -4 -12 -51 -5 -36 -61
X20
128 -28
129 1
$nolhdr21
X1 X2 X3 X4 X5 X6 X7 X8 X9 X10 X11 X12 X13 X14 X15 X16 X17 X18 X19
128 -11 60 -17 -33 -5 -27 -8 62 59 7 35 13 -17 -14 -54 -64 -25 -37 -49
129 -60 -11 -62 -47 -6 -46 -7 -15 -16 2 -49 4 -33 -56 -4 -12 -51 -5 -36
X20 X21
128 -21 -28
129 -61 1
$nolhdr22
X1 X2 X3 X4 X5 X6 X7 X8 X9 X10 X11 X12 X13 X14 X15 X16 X17 X18 X19
128 -11 60 -17 -33 -5 -27 -8 62 59 7 35 13 -17 -14 -36 -54 -64 -25 -37
129 -60 -11 -62 -47 -6 -46 -7 -15 -16 2 -49 4 -33 -56 1 -4 -12 -51 -5
X20 X21 X22
128 -49 -21 -28
129 -36 -61 1
$nolhdr23
X1 X2 X3 X4 X5 X6 X7 X8 X9 X10 X11 X12 X13 X14 X15 X16 X17
256 -6 102 -120 -113 -21 -65 -52 -108 120 17 36 19 40 10 -75 -97 -104
257 -102 -6 -95 -29 -24 -41 -58 -9 -119 -114 -12 -69 -61 -111 -4 -52 -9
X18 X19 X20 X21 X22 X23
256 -45 -99 -115 -61 -3 -52
257 -110 -21 -128 -108 -11 -97
$nolhdr24
X1 X2 X3 X4 X5 X6 X7 X8 X9 X10 X11 X12 X13 X14 X15 X16 X17
256 -6 102 -120 -21 -65 -52 -108 120 17 36 19 40 10 -97 -104 -45 -31
257 -102 -6 -95 -24 -41 -58 -9 -119 -114 -12 -69 -61 -111 -52 -9 -110 22
X18 X19 X20 X21 X22 X23 X24
256 -37 -99 -115 -61 -3 -52 -33
257 -51 -21 -128 -108 -11 -97 21
$nolhdr25
X1 X2 X3 X4 X5 X6 X7 X8 X9 X10 X11 X12 X13 X14 X15 X16 X17
256 -6 102 -120 -113 -21 -65 -52 -108 120 17 36 19 40 10 -75 -97 -104
257 -102 -6 -95 -29 -24 -41 -58 -9 -119 -114 -12 -69 -61 -111 -4 -52 -9
X18 X19 X20 X21 X22 X23 X24 X25
256 -12 -45 -31 -99 -115 -81 -61 -52
257 -2 -110 22 -21 -128 10 -108 -97
$nolhdr26
X1 X2 X3 X4 X5 X6 X7 X8 X9 X10 X11 X12 X13 X14 X15 X16 X17
256 -6 102 -120 -113 -21 -65 -52 -108 120 17 36 19 40 10 -75 -97 -104
257 -102 -6 -95 -29 -24 -41 -58 -9 -119 -114 -12 -69 -61 -111 -4 -52 -9
X18 X19 X20 X21 X22 X23 X24 X25 X26
256 -12 -45 -31 -37 -99 -115 -81 -61 -52
257 -2 -110 22 -51 -21 -128 10 -108 -97
$nolhdr27
X1 X2 X3 X4 X5 X6 X7 X8 X9 X10 X11 X12 X13 X14 X15 X16 X17
256 -6 102 -120 -113 -21 -65 -52 -108 120 17 36 19 40 10 -75 -97 -104
257 -102 -6 -95 -29 -24 -41 -58 -9 -119 -114 -12 -69 -61 -111 -4 -52 -9
X18 X19 X20 X21 X22 X23 X24 X25 X26 X27
256 -12 -45 -31 -37 -99 -115 -81 -61 -3 -52
257 -2 -110 22 -51 -21 -128 10 -108 -11 -97
$nolhdr28
X1 X2 X3 X4 X5 X6 X7 X8 X9 X10 X11 X12 X13 X14 X15 X16 X17
256 -6 102 -120 -113 -21 -65 -52 -108 120 17 36 19 40 10 -75 -97 -104
257 -102 -6 -95 -29 -24 -41 -58 -9 -119 -114 -12 -69 -61 -111 -4 -52 -9
X18 X19 X20 X21 X22 X23 X24 X25 X26 X27 X28
256 -12 -45 -37 -99 -115 -81 -61 -3 -98 -52 -33
257 -2 -110 -51 -21 -128 10 -108 -11 1 -97 21
$nolhdr29
X1 X2 X3 X4 X5 X6 X7 X8 X9 X10 X11 X12 X13 X14 X15 X16 X17
256 -6 102 -120 -113 -21 -65 -52 -108 120 17 36 19 40 10 -75 -97 -104
257 -102 -6 -95 -29 -24 -41 -58 -9 -119 -114 -12 -69 -61 -111 -4 -52 -9
X18 X19 X20 X21 X22 X23 X24 X25 X26 X27 X28 X29
256 -12 -45 -31 -37 -99 -115 -81 -61 -3 -98 -52 -33
257 -2 -110 22 -51 -21 -128 10 -108 -11 1 -97 21
X1 X2 X3 X4 X5 X6 X7
1 -3 8 5 -2 -4 7 1
2 -7 -4 6 1 -8 -3 2
3 -6 -1 -7 -4 2 5 8
4 -5 2 -3 8 1 -6 4
5 4 7 -1 -6 -3 -8 5
6 8 -3 -2 5 -7 4 6
7 2 -5 8 -3 6 -1 7
8 1 6 4 7 5 2 3
9 0 0 0 0 0 0 0
10 3 -8 -5 2 4 -7 -1
11 7 4 -6 -1 8 3 -2
12 6 1 7 4 -2 -5 -8
13 5 -2 3 -8 -1 6 -4
14 -4 -7 1 6 3 8 -5
15 -8 3 2 -5 7 -4 -6
16 -2 5 -8 3 -6 1 -7
17 -1 -6 -4 -7 -5 -2 -3
DiceDesign documentation built on Feb. 13, 2021, 1:06 a.m.
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Description Usage Format Author(s) Source References See Also Examples
Description
A list of the NOLH designs for 2 to 29 input variables proposed by Cioppa in 2007. These designs combine a latin structure, orthogonality between the main terms and the interactions (+ squares) and reduced correlations between the interactions (+ squares).
This list combines the Excel spreadsheets published by Sanchez (see Source). It is used internally by the function nolhDesign which provides various normalizations.
Usage
1 |
Format
A list of 5 matrices representing designs of experiments for 8 to 29 input variables:
nolh2_7:2 to 7 input variables, 17 experiments.
nolh8_11:8 to 11 input variables, 33 experiments.
nolh12_16:12 to 16 input variables, 65 experiments.
nolh17_22:17 to 22 input variables, 129 experiments.
nolh23_29:23 to 29 input variables, 257 experiments.
Author(s)
T.M. Cioppa for the designs. P. Kiener for the R code.
Source
Sanchez, S. M. (2011). NOLHdesigns in Excel file. Available online at https://nps.edu/web/seed/software-downloads/
References
Cioppa T.M., Lucas T.W. (2007). Efficient nearly orthogonal and space-filling Latin hypercubes. Technometrics 49, 45-55.
Kleijnen, J.P.C., Sanchez S.M., T.W. Lucas and Cioppa T. M.. A user's guide to the brave new world of designing simulation experiments. INFORMS Journal on Computing 17(3): 263-289.
Ye, K. Q. (1998). Orthogonal Latin hypercubes and their application in computer experiments. J. Amer. Statist. Asso. 93, 1430- 1439.
See Also
The main function nolhDesign. De Rainville's NOLH design list: NOLHDRdesigns.
Examples
1 2 3 4 5 6 7 8 | ## data(NOLHdesigns)
## all matrices
names(NOLHdesigns)
lapply(NOLHDRdesigns, tail, 2)
## The first matrix/design
NOLHdesigns[["nolh2_7"]]
|
Example output
[1] "nolh2_7" "nolh8_11" "nolh12_16" "nolh17_22" "nolh23_29"
$nolhdr08
X1 X2 X3 X4 X5 X6 X7 X8
32 10 -9 -14 4 15 6 -8 -8
33 -15 -12 -4 -6 -5 -14 -9 -4
$nolhdr09
X1 X2 X3 X4 X5 X6 X7 X8 X9
32 -15 10 -3 -9 -14 15 6 -8 -8
33 -10 -15 -11 -12 -4 -5 -14 -9 -4
$nolhdr10
X1 X2 X3 X4 X5 X6 X7 X8 X9 X10
32 -15 10 -3 -9 -14 4 15 6 -8 -8
33 -10 -15 -11 -12 -4 -6 -5 -14 -9 -4
$nolhdr11
X1 X2 X3 X4 X5 X6 X7 X8 X9 X10 X11
32 -15 10 -3 -9 -14 4 15 6 -8 2 -8
33 -10 -15 -11 -12 -4 -6 -5 -14 -9 -1 -4
$nolhdr12
X1 X2 X3 X4 X5 X6 X7 X8 X9 X10 X11 X12
64 -26 -16 -13 31 2 27 -1 -17 -16 -29 -6 -10
65 -4 -27 -5 -6 -1 -32 -17 -16 -7 -9 -32 -17
$nolhdr13
X1 X2 X3 X4 X5 X6 X7 X8 X9 X10 X11 X12 X13
64 -26 4 -1 -29 31 2 27 -1 -26 -17 -16 -6 -10
65 -4 -26 -3 -24 -6 -1 -32 -17 11 -16 -7 -32 -17
$nolhdr14
X1 X2 X3 X4 X5 X6 X7 X8 X9 X10 X11 X12 X13 X14
64 -26 4 -16 -13 31 2 27 -1 -26 -17 -16 -29 -6 -10
65 -4 -26 -27 -5 -6 -1 -32 -17 11 -16 -7 -9 -32 -17
$nolhdr15
X1 X2 X3 X4 X5 X6 X7 X8 X9 X10 X11 X12 X13 X14 X15
64 -26 4 -16 -1 -29 31 2 27 -1 -26 -17 -16 -29 -6 -10
65 -4 -26 -27 -3 -24 -6 -1 -32 -17 11 -16 -7 -9 -32 -17
$nolhdr16
X1 X2 X3 X4 X5 X6 X7 X8 X9 X10 X11 X12 X13 X14 X15 X16
64 -26 4 -16 -1 -29 -13 31 2 27 -1 -26 -17 -16 -29 -6 -10
65 -4 -26 -27 -3 -24 -5 -6 -1 -32 -17 11 -16 -7 -9 -32 -17
$nolhdr17
X1 X2 X3 X4 X5 X6 X7 X8 X9 X10 X11 X12 X13 X14 X15 X16 X17
128 -11 60 -17 -33 -5 -27 -8 59 7 -17 -36 -54 -25 -37 -49 -21 -28
129 -60 -11 -62 -47 -6 -46 -7 -16 2 -33 1 -4 -51 -5 -36 -61 1
$nolhdr18
X1 X2 X3 X4 X5 X6 X7 X8 X9 X10 X11 X12 X13 X14 X15 X16 X17 X18
128 -11 60 -17 -33 -5 -27 -8 59 7 -17 -14 -36 -54 -25 -37 -49 -21 -28
129 -60 -11 -62 -47 -6 -46 -7 -16 2 -33 -56 1 -4 -51 -5 -36 -61 1
$nolhdr19
X1 X2 X3 X4 X5 X6 X7 X8 X9 X10 X11 X12 X13 X14 X15 X16 X17 X18 X19
128 -11 60 -17 -33 -5 -27 -8 62 59 35 13 -17 -14 -54 -64 -25 -37 -49 -21
129 -60 -11 -62 -47 -6 -46 -7 -15 -16 -49 4 -33 -56 -4 -12 -51 -5 -36 -61
$nolhdr20
X1 X2 X3 X4 X5 X6 X7 X8 X9 X10 X11 X12 X13 X14 X15 X16 X17 X18 X19
128 -11 60 -17 -33 -5 -27 -8 59 7 35 -17 -14 -36 -54 -64 -25 -37 -49 -21
129 -60 -11 -62 -47 -6 -46 -7 -16 2 -49 -33 -56 1 -4 -12 -51 -5 -36 -61
X20
128 -28
129 1
$nolhdr21
X1 X2 X3 X4 X5 X6 X7 X8 X9 X10 X11 X12 X13 X14 X15 X16 X17 X18 X19
128 -11 60 -17 -33 -5 -27 -8 62 59 7 35 13 -17 -14 -54 -64 -25 -37 -49
129 -60 -11 -62 -47 -6 -46 -7 -15 -16 2 -49 4 -33 -56 -4 -12 -51 -5 -36
X20 X21
128 -21 -28
129 -61 1
$nolhdr22
X1 X2 X3 X4 X5 X6 X7 X8 X9 X10 X11 X12 X13 X14 X15 X16 X17 X18 X19
128 -11 60 -17 -33 -5 -27 -8 62 59 7 35 13 -17 -14 -36 -54 -64 -25 -37
129 -60 -11 -62 -47 -6 -46 -7 -15 -16 2 -49 4 -33 -56 1 -4 -12 -51 -5
X20 X21 X22
128 -49 -21 -28
129 -36 -61 1
$nolhdr23
X1 X2 X3 X4 X5 X6 X7 X8 X9 X10 X11 X12 X13 X14 X15 X16 X17
256 -6 102 -120 -113 -21 -65 -52 -108 120 17 36 19 40 10 -75 -97 -104
257 -102 -6 -95 -29 -24 -41 -58 -9 -119 -114 -12 -69 -61 -111 -4 -52 -9
X18 X19 X20 X21 X22 X23
256 -45 -99 -115 -61 -3 -52
257 -110 -21 -128 -108 -11 -97
$nolhdr24
X1 X2 X3 X4 X5 X6 X7 X8 X9 X10 X11 X12 X13 X14 X15 X16 X17
256 -6 102 -120 -21 -65 -52 -108 120 17 36 19 40 10 -97 -104 -45 -31
257 -102 -6 -95 -24 -41 -58 -9 -119 -114 -12 -69 -61 -111 -52 -9 -110 22
X18 X19 X20 X21 X22 X23 X24
256 -37 -99 -115 -61 -3 -52 -33
257 -51 -21 -128 -108 -11 -97 21
$nolhdr25
X1 X2 X3 X4 X5 X6 X7 X8 X9 X10 X11 X12 X13 X14 X15 X16 X17
256 -6 102 -120 -113 -21 -65 -52 -108 120 17 36 19 40 10 -75 -97 -104
257 -102 -6 -95 -29 -24 -41 -58 -9 -119 -114 -12 -69 -61 -111 -4 -52 -9
X18 X19 X20 X21 X22 X23 X24 X25
256 -12 -45 -31 -99 -115 -81 -61 -52
257 -2 -110 22 -21 -128 10 -108 -97
$nolhdr26
X1 X2 X3 X4 X5 X6 X7 X8 X9 X10 X11 X12 X13 X14 X15 X16 X17
256 -6 102 -120 -113 -21 -65 -52 -108 120 17 36 19 40 10 -75 -97 -104
257 -102 -6 -95 -29 -24 -41 -58 -9 -119 -114 -12 -69 -61 -111 -4 -52 -9
X18 X19 X20 X21 X22 X23 X24 X25 X26
256 -12 -45 -31 -37 -99 -115 -81 -61 -52
257 -2 -110 22 -51 -21 -128 10 -108 -97
$nolhdr27
X1 X2 X3 X4 X5 X6 X7 X8 X9 X10 X11 X12 X13 X14 X15 X16 X17
256 -6 102 -120 -113 -21 -65 -52 -108 120 17 36 19 40 10 -75 -97 -104
257 -102 -6 -95 -29 -24 -41 -58 -9 -119 -114 -12 -69 -61 -111 -4 -52 -9
X18 X19 X20 X21 X22 X23 X24 X25 X26 X27
256 -12 -45 -31 -37 -99 -115 -81 -61 -3 -52
257 -2 -110 22 -51 -21 -128 10 -108 -11 -97
$nolhdr28
X1 X2 X3 X4 X5 X6 X7 X8 X9 X10 X11 X12 X13 X14 X15 X16 X17
256 -6 102 -120 -113 -21 -65 -52 -108 120 17 36 19 40 10 -75 -97 -104
257 -102 -6 -95 -29 -24 -41 -58 -9 -119 -114 -12 -69 -61 -111 -4 -52 -9
X18 X19 X20 X21 X22 X23 X24 X25 X26 X27 X28
256 -12 -45 -37 -99 -115 -81 -61 -3 -98 -52 -33
257 -2 -110 -51 -21 -128 10 -108 -11 1 -97 21
$nolhdr29
X1 X2 X3 X4 X5 X6 X7 X8 X9 X10 X11 X12 X13 X14 X15 X16 X17
256 -6 102 -120 -113 -21 -65 -52 -108 120 17 36 19 40 10 -75 -97 -104
257 -102 -6 -95 -29 -24 -41 -58 -9 -119 -114 -12 -69 -61 -111 -4 -52 -9
X18 X19 X20 X21 X22 X23 X24 X25 X26 X27 X28 X29
256 -12 -45 -31 -37 -99 -115 -81 -61 -3 -98 -52 -33
257 -2 -110 22 -51 -21 -128 10 -108 -11 1 -97 21
X1 X2 X3 X4 X5 X6 X7
1 -3 8 5 -2 -4 7 1
2 -7 -4 6 1 -8 -3 2
3 -6 -1 -7 -4 2 5 8
4 -5 2 -3 8 1 -6 4
5 4 7 -1 -6 -3 -8 5
6 8 -3 -2 5 -7 4 6
7 2 -5 8 -3 6 -1 7
8 1 6 4 7 5 2 3
9 0 0 0 0 0 0 0
10 3 -8 -5 2 4 -7 -1
11 7 4 -6 -1 8 3 -2
12 6 1 7 4 -2 -5 -8
13 5 -2 3 -8 -1 6 -4
14 -4 -7 1 6 3 8 -5
15 -8 3 2 -5 7 -4 -6
16 -2 5 -8 3 -6 1 -7
17 -1 -6 -4 -7 -5 -2 -3
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