nolhdrDesign: De Rainville's Nearly Orthogonal Latin Hypercube Designs
In DiceDesign: Designs of Computer Experiments
Description
Usage
Arguments
Value
Author(s)
See Also
Examples
Description
This function generates a NOLH design of dimension 2 to 29 and normalizes it to the selected range. From 2 to 7 input variables, the design is extracted from Cioppa's NOLHdesigns list and from 8 to 29 input variables it is extracted from De Rainville's NOLHDRdesigns list.
Usage
1
nolhdrDesign(dimension, range = c(0, 1))
Arguments
dimension
number of input variables
range
the scale (min and max) of the inputs. Range (0, 0) and (1, 1) are special cases and call integer ranges (-m, m) and (0, 2m). 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)
T.M. Cioppa and F.-M. De Rainville for the designs. P. Kiener for the R code.
See Also
De Rainville's list NOLHDRdesigns. Other NOLH or OLH designs: nolhDesign, olhDesign.
Examples
1
2
3
4
5
6
7
8
9
10
11
## Classical normalizations
nolhdrDesign(8, range = c(1, 1))
nolhdrDesign(8, range = c(0, 1))
nolhdrDesign(8, range = c(0, 0))
nolhdrDesign(8, range = c(-1, 1))
## Change the dimnames, adjust to range (-10, 10) and round to 2 digits
xDRDN(nolhdrDesign(8), letter = "T", dgts = 2, range = c(-10, 10))
## A list of designs
lapply(5:9, function(n) nolhdrDesign(n, range = c(-1, 1))$design)
Example output
$n
[1] 33
$dimension
[1] 8
$design
[,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8]
[1,] -14 -8 -10 -1 4 15 6 13
[2,] 4 -5 -15 -3 -7 -13 15 12
[3,] -2 -13 -3 -9 13 9 -7 10
[4,] 1 -16 -11 7 -14 -3 -10 6
[5,] -13 2 -7 2 1 8 -11 -16
[6,] 16 1 -6 -10 3 -4 -12 -1
[7,] -8 14 -9 -15 -8 11 -2 -5
[8,] 5 4 -12 13 11 -12 1 -9
[9,] -9 -10 8 5 16 -2 14 -7
[10,] 12 -15 5 -12 -10 7 4 -15
[11,] -7 -3 13 -14 9 -16 -13 3
[12,] 6 -11 16 11 -6 10 -5 2
[13,] -3 7 2 16 -2 1 -16 11
[14,] 11 6 1 -8 12 5 -3 14
[15,] -10 9 14 -4 -15 -6 8 8
[16,] 15 12 4 6 5 14 9 4
[17,] 0 0 0 0 0 0 0 0
[18,] 14 8 10 1 -4 -15 -6 -13
[19,] -4 5 15 3 7 13 -15 -12
[20,] 2 13 3 9 -13 -9 7 -10
[21,] -1 16 11 -7 14 3 10 -6
[22,] 13 -2 7 -2 -1 -8 11 16
[23,] -16 -1 6 10 -3 4 12 1
[24,] 8 -14 9 15 8 -11 2 5
[25,] -5 -4 12 -13 -11 12 -1 9
[26,] 9 10 -8 -5 -16 2 -14 7
[27,] -12 15 -5 12 10 -7 -4 15
[28,] 7 3 -13 14 -9 16 13 -3
[29,] -6 11 -16 -11 6 -10 5 -2
[30,] 3 -7 -2 -16 2 -1 16 -11
[31,] -11 -6 -1 8 -12 -5 3 -14
[32,] 10 -9 -14 4 15 6 -8 -8
[33,] -15 -12 -4 -6 -5 -14 -9 -4
$n
[1] 33
$dimension
[1] 8
$design
[,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8]
[1,] 0.06250 0.25000 0.18750 0.46875 0.62500 0.96875 0.68750 0.90625
[2,] 0.62500 0.34375 0.03125 0.40625 0.28125 0.09375 0.96875 0.87500
[3,] 0.43750 0.09375 0.40625 0.21875 0.90625 0.78125 0.28125 0.81250
[4,] 0.53125 0.00000 0.15625 0.71875 0.06250 0.40625 0.18750 0.68750
[5,] 0.09375 0.56250 0.28125 0.56250 0.53125 0.75000 0.15625 0.00000
[6,] 1.00000 0.53125 0.31250 0.18750 0.59375 0.37500 0.12500 0.46875
[7,] 0.25000 0.93750 0.21875 0.03125 0.25000 0.84375 0.43750 0.34375
[8,] 0.65625 0.62500 0.12500 0.90625 0.84375 0.12500 0.53125 0.21875
[9,] 0.21875 0.18750 0.75000 0.65625 1.00000 0.43750 0.93750 0.28125
[10,] 0.87500 0.03125 0.65625 0.12500 0.18750 0.71875 0.62500 0.03125
[11,] 0.28125 0.40625 0.90625 0.06250 0.78125 0.00000 0.09375 0.59375
[12,] 0.68750 0.15625 1.00000 0.84375 0.31250 0.81250 0.34375 0.56250
[13,] 0.40625 0.71875 0.56250 1.00000 0.43750 0.53125 0.00000 0.84375
[14,] 0.84375 0.68750 0.53125 0.25000 0.87500 0.65625 0.40625 0.93750
[15,] 0.18750 0.78125 0.93750 0.37500 0.03125 0.31250 0.75000 0.75000
[16,] 0.96875 0.87500 0.62500 0.68750 0.65625 0.93750 0.78125 0.62500
[17,] 0.50000 0.50000 0.50000 0.50000 0.50000 0.50000 0.50000 0.50000
[18,] 0.93750 0.75000 0.81250 0.53125 0.37500 0.03125 0.31250 0.09375
[19,] 0.37500 0.65625 0.96875 0.59375 0.71875 0.90625 0.03125 0.12500
[20,] 0.56250 0.90625 0.59375 0.78125 0.09375 0.21875 0.71875 0.18750
[21,] 0.46875 1.00000 0.84375 0.28125 0.93750 0.59375 0.81250 0.31250
[22,] 0.90625 0.43750 0.71875 0.43750 0.46875 0.25000 0.84375 1.00000
[23,] 0.00000 0.46875 0.68750 0.81250 0.40625 0.62500 0.87500 0.53125
[24,] 0.75000 0.06250 0.78125 0.96875 0.75000 0.15625 0.56250 0.65625
[25,] 0.34375 0.37500 0.87500 0.09375 0.15625 0.87500 0.46875 0.78125
[26,] 0.78125 0.81250 0.25000 0.34375 0.00000 0.56250 0.06250 0.71875
[27,] 0.12500 0.96875 0.34375 0.87500 0.81250 0.28125 0.37500 0.96875
[28,] 0.71875 0.59375 0.09375 0.93750 0.21875 1.00000 0.90625 0.40625
[29,] 0.31250 0.84375 0.00000 0.15625 0.68750 0.18750 0.65625 0.43750
[30,] 0.59375 0.28125 0.43750 0.00000 0.56250 0.46875 1.00000 0.15625
[31,] 0.15625 0.31250 0.46875 0.75000 0.12500 0.34375 0.59375 0.06250
[32,] 0.81250 0.21875 0.06250 0.62500 0.96875 0.68750 0.25000 0.25000
[33,] 0.03125 0.12500 0.37500 0.31250 0.34375 0.06250 0.21875 0.37500
$n
[1] 33
$dimension
[1] 8
$design
[,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8]
[1,] 2 8 6 15 20 31 22 29
[2,] 20 11 1 13 9 3 31 28
[3,] 14 3 13 7 29 25 9 26
[4,] 17 0 5 23 2 13 6 22
[5,] 3 18 9 18 17 24 5 0
[6,] 32 17 10 6 19 12 4 15
[7,] 8 30 7 1 8 27 14 11
[8,] 21 20 4 29 27 4 17 7
[9,] 7 6 24 21 32 14 30 9
[10,] 28 1 21 4 6 23 20 1
[11,] 9 13 29 2 25 0 3 19
[12,] 22 5 32 27 10 26 11 18
[13,] 13 23 18 32 14 17 0 27
[14,] 27 22 17 8 28 21 13 30
[15,] 6 25 30 12 1 10 24 24
[16,] 31 28 20 22 21 30 25 20
[17,] 16 16 16 16 16 16 16 16
[18,] 30 24 26 17 12 1 10 3
[19,] 12 21 31 19 23 29 1 4
[20,] 18 29 19 25 3 7 23 6
[21,] 15 32 27 9 30 19 26 10
[22,] 29 14 23 14 15 8 27 32
[23,] 0 15 22 26 13 20 28 17
[24,] 24 2 25 31 24 5 18 21
[25,] 11 12 28 3 5 28 15 25
[26,] 25 26 8 11 0 18 2 23
[27,] 4 31 11 28 26 9 12 31
[28,] 23 19 3 30 7 32 29 13
[29,] 10 27 0 5 22 6 21 14
[30,] 19 9 14 0 18 15 32 5
[31,] 5 10 15 24 4 11 19 2
[32,] 26 7 2 20 31 22 8 8
[33,] 1 4 12 10 11 2 7 12
$n
[1] 33
$dimension
[1] 8
$design
[,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8]
[1,] -0.8750 -0.5000 -0.6250 -0.0625 0.2500 0.9375 0.3750 0.8125
[2,] 0.2500 -0.3125 -0.9375 -0.1875 -0.4375 -0.8125 0.9375 0.7500
[3,] -0.1250 -0.8125 -0.1875 -0.5625 0.8125 0.5625 -0.4375 0.6250
[4,] 0.0625 -1.0000 -0.6875 0.4375 -0.8750 -0.1875 -0.6250 0.3750
[5,] -0.8125 0.1250 -0.4375 0.1250 0.0625 0.5000 -0.6875 -1.0000
[6,] 1.0000 0.0625 -0.3750 -0.6250 0.1875 -0.2500 -0.7500 -0.0625
[7,] -0.5000 0.8750 -0.5625 -0.9375 -0.5000 0.6875 -0.1250 -0.3125
[8,] 0.3125 0.2500 -0.7500 0.8125 0.6875 -0.7500 0.0625 -0.5625
[9,] -0.5625 -0.6250 0.5000 0.3125 1.0000 -0.1250 0.8750 -0.4375
[10,] 0.7500 -0.9375 0.3125 -0.7500 -0.6250 0.4375 0.2500 -0.9375
[11,] -0.4375 -0.1875 0.8125 -0.8750 0.5625 -1.0000 -0.8125 0.1875
[12,] 0.3750 -0.6875 1.0000 0.6875 -0.3750 0.6250 -0.3125 0.1250
[13,] -0.1875 0.4375 0.1250 1.0000 -0.1250 0.0625 -1.0000 0.6875
[14,] 0.6875 0.3750 0.0625 -0.5000 0.7500 0.3125 -0.1875 0.8750
[15,] -0.6250 0.5625 0.8750 -0.2500 -0.9375 -0.3750 0.5000 0.5000
[16,] 0.9375 0.7500 0.2500 0.3750 0.3125 0.8750 0.5625 0.2500
[17,] 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
[18,] 0.8750 0.5000 0.6250 0.0625 -0.2500 -0.9375 -0.3750 -0.8125
[19,] -0.2500 0.3125 0.9375 0.1875 0.4375 0.8125 -0.9375 -0.7500
[20,] 0.1250 0.8125 0.1875 0.5625 -0.8125 -0.5625 0.4375 -0.6250
[21,] -0.0625 1.0000 0.6875 -0.4375 0.8750 0.1875 0.6250 -0.3750
[22,] 0.8125 -0.1250 0.4375 -0.1250 -0.0625 -0.5000 0.6875 1.0000
[23,] -1.0000 -0.0625 0.3750 0.6250 -0.1875 0.2500 0.7500 0.0625
[24,] 0.5000 -0.8750 0.5625 0.9375 0.5000 -0.6875 0.1250 0.3125
[25,] -0.3125 -0.2500 0.7500 -0.8125 -0.6875 0.7500 -0.0625 0.5625
[26,] 0.5625 0.6250 -0.5000 -0.3125 -1.0000 0.1250 -0.8750 0.4375
[27,] -0.7500 0.9375 -0.3125 0.7500 0.6250 -0.4375 -0.2500 0.9375
[28,] 0.4375 0.1875 -0.8125 0.8750 -0.5625 1.0000 0.8125 -0.1875
[29,] -0.3750 0.6875 -1.0000 -0.6875 0.3750 -0.6250 0.3125 -0.1250
[30,] 0.1875 -0.4375 -0.1250 -1.0000 0.1250 -0.0625 1.0000 -0.6875
[31,] -0.6875 -0.3750 -0.0625 0.5000 -0.7500 -0.3125 0.1875 -0.8750
[32,] 0.6250 -0.5625 -0.8750 0.2500 0.9375 0.3750 -0.5000 -0.5000
[33,] -0.9375 -0.7500 -0.2500 -0.3750 -0.3125 -0.8750 -0.5625 -0.2500
T1 T2 T3 T4 T5 T6 T7 T8
1 -8.75 -5.00 -6.25 -0.62 2.50 9.38 3.75 8.12
2 2.50 -3.12 -9.38 -1.88 -4.38 -8.12 9.38 7.50
3 -1.25 -8.12 -1.88 -5.62 8.12 5.62 -4.38 6.25
4 0.62 -10.00 -6.88 4.38 -8.75 -1.88 -6.25 3.75
5 -8.12 1.25 -4.38 1.25 0.62 5.00 -6.88 -10.00
6 10.00 0.62 -3.75 -6.25 1.88 -2.50 -7.50 -0.62
7 -5.00 8.75 -5.62 -9.38 -5.00 6.88 -1.25 -3.12
8 3.12 2.50 -7.50 8.12 6.88 -7.50 0.62 -5.62
9 -5.62 -6.25 5.00 3.12 10.00 -1.25 8.75 -4.38
10 7.50 -9.38 3.12 -7.50 -6.25 4.38 2.50 -9.38
11 -4.38 -1.88 8.12 -8.75 5.62 -10.00 -8.12 1.88
12 3.75 -6.88 10.00 6.88 -3.75 6.25 -3.12 1.25
13 -1.88 4.38 1.25 10.00 -1.25 0.62 -10.00 6.88
14 6.88 3.75 0.62 -5.00 7.50 3.12 -1.88 8.75
15 -6.25 5.62 8.75 -2.50 -9.38 -3.75 5.00 5.00
16 9.38 7.50 2.50 3.75 3.12 8.75 5.62 2.50
17 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
18 8.75 5.00 6.25 0.62 -2.50 -9.38 -3.75 -8.12
19 -2.50 3.12 9.38 1.88 4.38 8.12 -9.38 -7.50
20 1.25 8.12 1.88 5.62 -8.12 -5.62 4.38 -6.25
21 -0.62 10.00 6.88 -4.38 8.75 1.88 6.25 -3.75
22 8.12 -1.25 4.38 -1.25 -0.62 -5.00 6.88 10.00
23 -10.00 -0.62 3.75 6.25 -1.88 2.50 7.50 0.62
24 5.00 -8.75 5.62 9.38 5.00 -6.88 1.25 3.12
25 -3.12 -2.50 7.50 -8.12 -6.88 7.50 -0.62 5.62
26 5.62 6.25 -5.00 -3.12 -10.00 1.25 -8.75 4.38
27 -7.50 9.38 -3.12 7.50 6.25 -4.38 -2.50 9.38
28 4.38 1.88 -8.12 8.75 -5.62 10.00 8.12 -1.88
29 -3.75 6.88 -10.00 -6.88 3.75 -6.25 3.12 -1.25
30 1.88 -4.38 -1.25 -10.00 1.25 -0.62 10.00 -6.88
31 -6.88 -3.75 -0.62 5.00 -7.50 -3.12 1.88 -8.75
32 6.25 -5.62 -8.75 2.50 9.38 3.75 -5.00 -5.00
33 -9.38 -7.50 -2.50 -3.75 -3.12 -8.75 -5.62 -2.50
[[1]]
[,1] [,2] [,3] [,4] [,5]
[1,] -0.375 1.000 0.625 -0.250 -0.500
[2,] -0.875 -0.500 0.750 0.125 -1.000
[3,] -0.750 -0.125 -0.875 -0.500 0.250
[4,] -0.625 0.250 -0.375 1.000 0.125
[5,] 0.500 0.875 -0.125 -0.750 -0.375
[6,] 1.000 -0.375 -0.250 0.625 -0.875
[7,] 0.250 -0.625 1.000 -0.375 0.750
[8,] 0.125 0.750 0.500 0.875 0.625
[9,] 0.000 0.000 0.000 0.000 0.000
[10,] 0.375 -1.000 -0.625 0.250 0.500
[11,] 0.875 0.500 -0.750 -0.125 1.000
[12,] 0.750 0.125 0.875 0.500 -0.250
[13,] 0.625 -0.250 0.375 -1.000 -0.125
[14,] -0.500 -0.875 0.125 0.750 0.375
[15,] -1.000 0.375 0.250 -0.625 0.875
[16,] -0.250 0.625 -1.000 0.375 -0.750
[17,] -0.125 -0.750 -0.500 -0.875 -0.625
[[2]]
[,1] [,2] [,3] [,4] [,5] [,6]
[1,] -0.375 1.000 0.625 -0.250 -0.500 0.875
[2,] -0.875 -0.500 0.750 0.125 -1.000 -0.375
[3,] -0.750 -0.125 -0.875 -0.500 0.250 0.625
[4,] -0.625 0.250 -0.375 1.000 0.125 -0.750
[5,] 0.500 0.875 -0.125 -0.750 -0.375 -1.000
[6,] 1.000 -0.375 -0.250 0.625 -0.875 0.500
[7,] 0.250 -0.625 1.000 -0.375 0.750 -0.125
[8,] 0.125 0.750 0.500 0.875 0.625 0.250
[9,] 0.000 0.000 0.000 0.000 0.000 0.000
[10,] 0.375 -1.000 -0.625 0.250 0.500 -0.875
[11,] 0.875 0.500 -0.750 -0.125 1.000 0.375
[12,] 0.750 0.125 0.875 0.500 -0.250 -0.625
[13,] 0.625 -0.250 0.375 -1.000 -0.125 0.750
[14,] -0.500 -0.875 0.125 0.750 0.375 1.000
[15,] -1.000 0.375 0.250 -0.625 0.875 -0.500
[16,] -0.250 0.625 -1.000 0.375 -0.750 0.125
[17,] -0.125 -0.750 -0.500 -0.875 -0.625 -0.250
[[3]]
[,1] [,2] [,3] [,4] [,5] [,6] [,7]
[1,] -0.375 1.000 0.625 -0.250 -0.500 0.875 0.125
[2,] -0.875 -0.500 0.750 0.125 -1.000 -0.375 0.250
[3,] -0.750 -0.125 -0.875 -0.500 0.250 0.625 1.000
[4,] -0.625 0.250 -0.375 1.000 0.125 -0.750 0.500
[5,] 0.500 0.875 -0.125 -0.750 -0.375 -1.000 0.625
[6,] 1.000 -0.375 -0.250 0.625 -0.875 0.500 0.750
[7,] 0.250 -0.625 1.000 -0.375 0.750 -0.125 0.875
[8,] 0.125 0.750 0.500 0.875 0.625 0.250 0.375
[9,] 0.000 0.000 0.000 0.000 0.000 0.000 0.000
[10,] 0.375 -1.000 -0.625 0.250 0.500 -0.875 -0.125
[11,] 0.875 0.500 -0.750 -0.125 1.000 0.375 -0.250
[12,] 0.750 0.125 0.875 0.500 -0.250 -0.625 -1.000
[13,] 0.625 -0.250 0.375 -1.000 -0.125 0.750 -0.500
[14,] -0.500 -0.875 0.125 0.750 0.375 1.000 -0.625
[15,] -1.000 0.375 0.250 -0.625 0.875 -0.500 -0.750
[16,] -0.250 0.625 -1.000 0.375 -0.750 0.125 -0.875
[17,] -0.125 -0.750 -0.500 -0.875 -0.625 -0.250 -0.375
[[4]]
[,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8]
[1,] -0.8750 -0.5000 -0.6250 -0.0625 0.2500 0.9375 0.3750 0.8125
[2,] 0.2500 -0.3125 -0.9375 -0.1875 -0.4375 -0.8125 0.9375 0.7500
[3,] -0.1250 -0.8125 -0.1875 -0.5625 0.8125 0.5625 -0.4375 0.6250
[4,] 0.0625 -1.0000 -0.6875 0.4375 -0.8750 -0.1875 -0.6250 0.3750
[5,] -0.8125 0.1250 -0.4375 0.1250 0.0625 0.5000 -0.6875 -1.0000
[6,] 1.0000 0.0625 -0.3750 -0.6250 0.1875 -0.2500 -0.7500 -0.0625
[7,] -0.5000 0.8750 -0.5625 -0.9375 -0.5000 0.6875 -0.1250 -0.3125
[8,] 0.3125 0.2500 -0.7500 0.8125 0.6875 -0.7500 0.0625 -0.5625
[9,] -0.5625 -0.6250 0.5000 0.3125 1.0000 -0.1250 0.8750 -0.4375
[10,] 0.7500 -0.9375 0.3125 -0.7500 -0.6250 0.4375 0.2500 -0.9375
[11,] -0.4375 -0.1875 0.8125 -0.8750 0.5625 -1.0000 -0.8125 0.1875
[12,] 0.3750 -0.6875 1.0000 0.6875 -0.3750 0.6250 -0.3125 0.1250
[13,] -0.1875 0.4375 0.1250 1.0000 -0.1250 0.0625 -1.0000 0.6875
[14,] 0.6875 0.3750 0.0625 -0.5000 0.7500 0.3125 -0.1875 0.8750
[15,] -0.6250 0.5625 0.8750 -0.2500 -0.9375 -0.3750 0.5000 0.5000
[16,] 0.9375 0.7500 0.2500 0.3750 0.3125 0.8750 0.5625 0.2500
[17,] 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
[18,] 0.8750 0.5000 0.6250 0.0625 -0.2500 -0.9375 -0.3750 -0.8125
[19,] -0.2500 0.3125 0.9375 0.1875 0.4375 0.8125 -0.9375 -0.7500
[20,] 0.1250 0.8125 0.1875 0.5625 -0.8125 -0.5625 0.4375 -0.6250
[21,] -0.0625 1.0000 0.6875 -0.4375 0.8750 0.1875 0.6250 -0.3750
[22,] 0.8125 -0.1250 0.4375 -0.1250 -0.0625 -0.5000 0.6875 1.0000
[23,] -1.0000 -0.0625 0.3750 0.6250 -0.1875 0.2500 0.7500 0.0625
[24,] 0.5000 -0.8750 0.5625 0.9375 0.5000 -0.6875 0.1250 0.3125
[25,] -0.3125 -0.2500 0.7500 -0.8125 -0.6875 0.7500 -0.0625 0.5625
[26,] 0.5625 0.6250 -0.5000 -0.3125 -1.0000 0.1250 -0.8750 0.4375
[27,] -0.7500 0.9375 -0.3125 0.7500 0.6250 -0.4375 -0.2500 0.9375
[28,] 0.4375 0.1875 -0.8125 0.8750 -0.5625 1.0000 0.8125 -0.1875
[29,] -0.3750 0.6875 -1.0000 -0.6875 0.3750 -0.6250 0.3125 -0.1250
[30,] 0.1875 -0.4375 -0.1250 -1.0000 0.1250 -0.0625 1.0000 -0.6875
[31,] -0.6875 -0.3750 -0.0625 0.5000 -0.7500 -0.3125 0.1875 -0.8750
[32,] 0.6250 -0.5625 -0.8750 0.2500 0.9375 0.3750 -0.5000 -0.5000
[33,] -0.9375 -0.7500 -0.2500 -0.3750 -0.3125 -0.8750 -0.5625 -0.2500
[[5]]
[,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9]
[1,] 0.2500 -0.8750 -0.1250 -0.5000 -0.6250 0.2500 0.9375 0.3750 0.8125
[2,] 0.8750 0.2500 -0.0625 -0.3125 -0.9375 -0.4375 -0.8125 0.9375 0.7500
[3,] 0.0625 -0.1250 0.8750 -0.8125 -0.1875 0.8125 0.5625 -0.4375 0.6250
[4,] 0.1250 0.0625 0.2500 -1.0000 -0.6875 -0.8750 -0.1875 -0.6250 0.3750
[5,] 1.0000 -0.8125 -0.5000 0.1250 -0.4375 0.0625 0.5000 -0.6875 -1.0000
[6,] 0.8125 1.0000 -0.3125 0.0625 -0.3750 0.1875 -0.2500 -0.7500 -0.0625
[7,] 0.3125 -0.5000 0.8125 0.8750 -0.5625 -0.5000 0.6875 -0.1250 -0.3125
[8,] 0.5000 0.3125 1.0000 0.2500 -0.7500 0.6875 -0.7500 0.0625 -0.5625
[9,] 0.7500 -0.5625 -0.4375 -0.6250 0.5000 1.0000 -0.1250 0.8750 -0.4375
[10,] 0.5625 0.7500 -0.3750 -0.9375 0.3125 -0.6250 0.4375 0.2500 -0.9375
[11,] 0.3750 -0.4375 0.5625 -0.1875 0.8125 0.5625 -1.0000 -0.8125 0.1875
[12,] 0.4375 0.3750 0.7500 -0.6875 1.0000 -0.3750 0.6250 -0.3125 0.1250
[13,] 0.6875 -0.1875 -0.6250 0.4375 0.1250 -0.1250 0.0625 -1.0000 0.6875
[14,] 0.1875 0.6875 -0.9375 0.3750 0.0625 0.7500 0.3125 -0.1875 0.8750
[15,] 0.9375 -0.6250 0.1875 0.5625 0.8750 -0.9375 -0.3750 0.5000 0.5000
[16,] 0.6250 0.9375 0.6875 0.7500 0.2500 0.3125 0.8750 0.5625 0.2500
[17,] 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
[18,] -0.2500 0.8750 0.1250 0.5000 0.6250 -0.2500 -0.9375 -0.3750 -0.8125
[19,] -0.8750 -0.2500 0.0625 0.3125 0.9375 0.4375 0.8125 -0.9375 -0.7500
[20,] -0.0625 0.1250 -0.8750 0.8125 0.1875 -0.8125 -0.5625 0.4375 -0.6250
[21,] -0.1250 -0.0625 -0.2500 1.0000 0.6875 0.8750 0.1875 0.6250 -0.3750
[22,] -1.0000 0.8125 0.5000 -0.1250 0.4375 -0.0625 -0.5000 0.6875 1.0000
[23,] -0.8125 -1.0000 0.3125 -0.0625 0.3750 -0.1875 0.2500 0.7500 0.0625
[24,] -0.3125 0.5000 -0.8125 -0.8750 0.5625 0.5000 -0.6875 0.1250 0.3125
[25,] -0.5000 -0.3125 -1.0000 -0.2500 0.7500 -0.6875 0.7500 -0.0625 0.5625
[26,] -0.7500 0.5625 0.4375 0.6250 -0.5000 -1.0000 0.1250 -0.8750 0.4375
[27,] -0.5625 -0.7500 0.3750 0.9375 -0.3125 0.6250 -0.4375 -0.2500 0.9375
[28,] -0.3750 0.4375 -0.5625 0.1875 -0.8125 -0.5625 1.0000 0.8125 -0.1875
[29,] -0.4375 -0.3750 -0.7500 0.6875 -1.0000 0.3750 -0.6250 0.3125 -0.1250
[30,] -0.6875 0.1875 0.6250 -0.4375 -0.1250 0.1250 -0.0625 1.0000 -0.6875
[31,] -0.1875 -0.6875 0.9375 -0.3750 -0.0625 -0.7500 -0.3125 0.1875 -0.8750
[32,] -0.9375 0.6250 -0.1875 -0.5625 -0.8750 0.9375 0.3750 -0.5000 -0.5000
[33,] -0.6250 -0.9375 -0.6875 -0.7500 -0.2500 -0.3125 -0.8750 -0.5625 -0.2500
DiceDesign documentation built on Feb. 13, 2021, 1:06 a.m.
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Description Usage Arguments Value Author(s) See Also Examples
Description
This function generates a NOLH design of dimension 2 to 29 and normalizes it to the selected range. From 2 to 7 input variables, the design is extracted from Cioppa's NOLHdesigns list and from 8 to 29 input variables it is extracted from De Rainville's NOLHDRdesigns list.
Usage
1 | nolhdrDesign(dimension, range = c(0, 1))
|
Arguments
dimension |
number of input variables |
range |
the scale (min and max) of the inputs. Range (0, 0) and (1, 1) are special cases and call integer ranges (-m, m) and (0, 2m). 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)
T.M. Cioppa and F.-M. De Rainville for the designs. P. Kiener for the R code.
See Also
De Rainville's list NOLHDRdesigns. Other NOLH or OLH designs: nolhDesign, olhDesign.
Examples
1 2 3 4 5 6 7 8 9 10 11 | ## Classical normalizations
nolhdrDesign(8, range = c(1, 1))
nolhdrDesign(8, range = c(0, 1))
nolhdrDesign(8, range = c(0, 0))
nolhdrDesign(8, range = c(-1, 1))
## Change the dimnames, adjust to range (-10, 10) and round to 2 digits
xDRDN(nolhdrDesign(8), letter = "T", dgts = 2, range = c(-10, 10))
## A list of designs
lapply(5:9, function(n) nolhdrDesign(n, range = c(-1, 1))$design)
|
Example output
$n
[1] 33
$dimension
[1] 8
$design
[,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8]
[1,] -14 -8 -10 -1 4 15 6 13
[2,] 4 -5 -15 -3 -7 -13 15 12
[3,] -2 -13 -3 -9 13 9 -7 10
[4,] 1 -16 -11 7 -14 -3 -10 6
[5,] -13 2 -7 2 1 8 -11 -16
[6,] 16 1 -6 -10 3 -4 -12 -1
[7,] -8 14 -9 -15 -8 11 -2 -5
[8,] 5 4 -12 13 11 -12 1 -9
[9,] -9 -10 8 5 16 -2 14 -7
[10,] 12 -15 5 -12 -10 7 4 -15
[11,] -7 -3 13 -14 9 -16 -13 3
[12,] 6 -11 16 11 -6 10 -5 2
[13,] -3 7 2 16 -2 1 -16 11
[14,] 11 6 1 -8 12 5 -3 14
[15,] -10 9 14 -4 -15 -6 8 8
[16,] 15 12 4 6 5 14 9 4
[17,] 0 0 0 0 0 0 0 0
[18,] 14 8 10 1 -4 -15 -6 -13
[19,] -4 5 15 3 7 13 -15 -12
[20,] 2 13 3 9 -13 -9 7 -10
[21,] -1 16 11 -7 14 3 10 -6
[22,] 13 -2 7 -2 -1 -8 11 16
[23,] -16 -1 6 10 -3 4 12 1
[24,] 8 -14 9 15 8 -11 2 5
[25,] -5 -4 12 -13 -11 12 -1 9
[26,] 9 10 -8 -5 -16 2 -14 7
[27,] -12 15 -5 12 10 -7 -4 15
[28,] 7 3 -13 14 -9 16 13 -3
[29,] -6 11 -16 -11 6 -10 5 -2
[30,] 3 -7 -2 -16 2 -1 16 -11
[31,] -11 -6 -1 8 -12 -5 3 -14
[32,] 10 -9 -14 4 15 6 -8 -8
[33,] -15 -12 -4 -6 -5 -14 -9 -4
$n
[1] 33
$dimension
[1] 8
$design
[,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8]
[1,] 0.06250 0.25000 0.18750 0.46875 0.62500 0.96875 0.68750 0.90625
[2,] 0.62500 0.34375 0.03125 0.40625 0.28125 0.09375 0.96875 0.87500
[3,] 0.43750 0.09375 0.40625 0.21875 0.90625 0.78125 0.28125 0.81250
[4,] 0.53125 0.00000 0.15625 0.71875 0.06250 0.40625 0.18750 0.68750
[5,] 0.09375 0.56250 0.28125 0.56250 0.53125 0.75000 0.15625 0.00000
[6,] 1.00000 0.53125 0.31250 0.18750 0.59375 0.37500 0.12500 0.46875
[7,] 0.25000 0.93750 0.21875 0.03125 0.25000 0.84375 0.43750 0.34375
[8,] 0.65625 0.62500 0.12500 0.90625 0.84375 0.12500 0.53125 0.21875
[9,] 0.21875 0.18750 0.75000 0.65625 1.00000 0.43750 0.93750 0.28125
[10,] 0.87500 0.03125 0.65625 0.12500 0.18750 0.71875 0.62500 0.03125
[11,] 0.28125 0.40625 0.90625 0.06250 0.78125 0.00000 0.09375 0.59375
[12,] 0.68750 0.15625 1.00000 0.84375 0.31250 0.81250 0.34375 0.56250
[13,] 0.40625 0.71875 0.56250 1.00000 0.43750 0.53125 0.00000 0.84375
[14,] 0.84375 0.68750 0.53125 0.25000 0.87500 0.65625 0.40625 0.93750
[15,] 0.18750 0.78125 0.93750 0.37500 0.03125 0.31250 0.75000 0.75000
[16,] 0.96875 0.87500 0.62500 0.68750 0.65625 0.93750 0.78125 0.62500
[17,] 0.50000 0.50000 0.50000 0.50000 0.50000 0.50000 0.50000 0.50000
[18,] 0.93750 0.75000 0.81250 0.53125 0.37500 0.03125 0.31250 0.09375
[19,] 0.37500 0.65625 0.96875 0.59375 0.71875 0.90625 0.03125 0.12500
[20,] 0.56250 0.90625 0.59375 0.78125 0.09375 0.21875 0.71875 0.18750
[21,] 0.46875 1.00000 0.84375 0.28125 0.93750 0.59375 0.81250 0.31250
[22,] 0.90625 0.43750 0.71875 0.43750 0.46875 0.25000 0.84375 1.00000
[23,] 0.00000 0.46875 0.68750 0.81250 0.40625 0.62500 0.87500 0.53125
[24,] 0.75000 0.06250 0.78125 0.96875 0.75000 0.15625 0.56250 0.65625
[25,] 0.34375 0.37500 0.87500 0.09375 0.15625 0.87500 0.46875 0.78125
[26,] 0.78125 0.81250 0.25000 0.34375 0.00000 0.56250 0.06250 0.71875
[27,] 0.12500 0.96875 0.34375 0.87500 0.81250 0.28125 0.37500 0.96875
[28,] 0.71875 0.59375 0.09375 0.93750 0.21875 1.00000 0.90625 0.40625
[29,] 0.31250 0.84375 0.00000 0.15625 0.68750 0.18750 0.65625 0.43750
[30,] 0.59375 0.28125 0.43750 0.00000 0.56250 0.46875 1.00000 0.15625
[31,] 0.15625 0.31250 0.46875 0.75000 0.12500 0.34375 0.59375 0.06250
[32,] 0.81250 0.21875 0.06250 0.62500 0.96875 0.68750 0.25000 0.25000
[33,] 0.03125 0.12500 0.37500 0.31250 0.34375 0.06250 0.21875 0.37500
$n
[1] 33
$dimension
[1] 8
$design
[,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8]
[1,] 2 8 6 15 20 31 22 29
[2,] 20 11 1 13 9 3 31 28
[3,] 14 3 13 7 29 25 9 26
[4,] 17 0 5 23 2 13 6 22
[5,] 3 18 9 18 17 24 5 0
[6,] 32 17 10 6 19 12 4 15
[7,] 8 30 7 1 8 27 14 11
[8,] 21 20 4 29 27 4 17 7
[9,] 7 6 24 21 32 14 30 9
[10,] 28 1 21 4 6 23 20 1
[11,] 9 13 29 2 25 0 3 19
[12,] 22 5 32 27 10 26 11 18
[13,] 13 23 18 32 14 17 0 27
[14,] 27 22 17 8 28 21 13 30
[15,] 6 25 30 12 1 10 24 24
[16,] 31 28 20 22 21 30 25 20
[17,] 16 16 16 16 16 16 16 16
[18,] 30 24 26 17 12 1 10 3
[19,] 12 21 31 19 23 29 1 4
[20,] 18 29 19 25 3 7 23 6
[21,] 15 32 27 9 30 19 26 10
[22,] 29 14 23 14 15 8 27 32
[23,] 0 15 22 26 13 20 28 17
[24,] 24 2 25 31 24 5 18 21
[25,] 11 12 28 3 5 28 15 25
[26,] 25 26 8 11 0 18 2 23
[27,] 4 31 11 28 26 9 12 31
[28,] 23 19 3 30 7 32 29 13
[29,] 10 27 0 5 22 6 21 14
[30,] 19 9 14 0 18 15 32 5
[31,] 5 10 15 24 4 11 19 2
[32,] 26 7 2 20 31 22 8 8
[33,] 1 4 12 10 11 2 7 12
$n
[1] 33
$dimension
[1] 8
$design
[,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8]
[1,] -0.8750 -0.5000 -0.6250 -0.0625 0.2500 0.9375 0.3750 0.8125
[2,] 0.2500 -0.3125 -0.9375 -0.1875 -0.4375 -0.8125 0.9375 0.7500
[3,] -0.1250 -0.8125 -0.1875 -0.5625 0.8125 0.5625 -0.4375 0.6250
[4,] 0.0625 -1.0000 -0.6875 0.4375 -0.8750 -0.1875 -0.6250 0.3750
[5,] -0.8125 0.1250 -0.4375 0.1250 0.0625 0.5000 -0.6875 -1.0000
[6,] 1.0000 0.0625 -0.3750 -0.6250 0.1875 -0.2500 -0.7500 -0.0625
[7,] -0.5000 0.8750 -0.5625 -0.9375 -0.5000 0.6875 -0.1250 -0.3125
[8,] 0.3125 0.2500 -0.7500 0.8125 0.6875 -0.7500 0.0625 -0.5625
[9,] -0.5625 -0.6250 0.5000 0.3125 1.0000 -0.1250 0.8750 -0.4375
[10,] 0.7500 -0.9375 0.3125 -0.7500 -0.6250 0.4375 0.2500 -0.9375
[11,] -0.4375 -0.1875 0.8125 -0.8750 0.5625 -1.0000 -0.8125 0.1875
[12,] 0.3750 -0.6875 1.0000 0.6875 -0.3750 0.6250 -0.3125 0.1250
[13,] -0.1875 0.4375 0.1250 1.0000 -0.1250 0.0625 -1.0000 0.6875
[14,] 0.6875 0.3750 0.0625 -0.5000 0.7500 0.3125 -0.1875 0.8750
[15,] -0.6250 0.5625 0.8750 -0.2500 -0.9375 -0.3750 0.5000 0.5000
[16,] 0.9375 0.7500 0.2500 0.3750 0.3125 0.8750 0.5625 0.2500
[17,] 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
[18,] 0.8750 0.5000 0.6250 0.0625 -0.2500 -0.9375 -0.3750 -0.8125
[19,] -0.2500 0.3125 0.9375 0.1875 0.4375 0.8125 -0.9375 -0.7500
[20,] 0.1250 0.8125 0.1875 0.5625 -0.8125 -0.5625 0.4375 -0.6250
[21,] -0.0625 1.0000 0.6875 -0.4375 0.8750 0.1875 0.6250 -0.3750
[22,] 0.8125 -0.1250 0.4375 -0.1250 -0.0625 -0.5000 0.6875 1.0000
[23,] -1.0000 -0.0625 0.3750 0.6250 -0.1875 0.2500 0.7500 0.0625
[24,] 0.5000 -0.8750 0.5625 0.9375 0.5000 -0.6875 0.1250 0.3125
[25,] -0.3125 -0.2500 0.7500 -0.8125 -0.6875 0.7500 -0.0625 0.5625
[26,] 0.5625 0.6250 -0.5000 -0.3125 -1.0000 0.1250 -0.8750 0.4375
[27,] -0.7500 0.9375 -0.3125 0.7500 0.6250 -0.4375 -0.2500 0.9375
[28,] 0.4375 0.1875 -0.8125 0.8750 -0.5625 1.0000 0.8125 -0.1875
[29,] -0.3750 0.6875 -1.0000 -0.6875 0.3750 -0.6250 0.3125 -0.1250
[30,] 0.1875 -0.4375 -0.1250 -1.0000 0.1250 -0.0625 1.0000 -0.6875
[31,] -0.6875 -0.3750 -0.0625 0.5000 -0.7500 -0.3125 0.1875 -0.8750
[32,] 0.6250 -0.5625 -0.8750 0.2500 0.9375 0.3750 -0.5000 -0.5000
[33,] -0.9375 -0.7500 -0.2500 -0.3750 -0.3125 -0.8750 -0.5625 -0.2500
T1 T2 T3 T4 T5 T6 T7 T8
1 -8.75 -5.00 -6.25 -0.62 2.50 9.38 3.75 8.12
2 2.50 -3.12 -9.38 -1.88 -4.38 -8.12 9.38 7.50
3 -1.25 -8.12 -1.88 -5.62 8.12 5.62 -4.38 6.25
4 0.62 -10.00 -6.88 4.38 -8.75 -1.88 -6.25 3.75
5 -8.12 1.25 -4.38 1.25 0.62 5.00 -6.88 -10.00
6 10.00 0.62 -3.75 -6.25 1.88 -2.50 -7.50 -0.62
7 -5.00 8.75 -5.62 -9.38 -5.00 6.88 -1.25 -3.12
8 3.12 2.50 -7.50 8.12 6.88 -7.50 0.62 -5.62
9 -5.62 -6.25 5.00 3.12 10.00 -1.25 8.75 -4.38
10 7.50 -9.38 3.12 -7.50 -6.25 4.38 2.50 -9.38
11 -4.38 -1.88 8.12 -8.75 5.62 -10.00 -8.12 1.88
12 3.75 -6.88 10.00 6.88 -3.75 6.25 -3.12 1.25
13 -1.88 4.38 1.25 10.00 -1.25 0.62 -10.00 6.88
14 6.88 3.75 0.62 -5.00 7.50 3.12 -1.88 8.75
15 -6.25 5.62 8.75 -2.50 -9.38 -3.75 5.00 5.00
16 9.38 7.50 2.50 3.75 3.12 8.75 5.62 2.50
17 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
18 8.75 5.00 6.25 0.62 -2.50 -9.38 -3.75 -8.12
19 -2.50 3.12 9.38 1.88 4.38 8.12 -9.38 -7.50
20 1.25 8.12 1.88 5.62 -8.12 -5.62 4.38 -6.25
21 -0.62 10.00 6.88 -4.38 8.75 1.88 6.25 -3.75
22 8.12 -1.25 4.38 -1.25 -0.62 -5.00 6.88 10.00
23 -10.00 -0.62 3.75 6.25 -1.88 2.50 7.50 0.62
24 5.00 -8.75 5.62 9.38 5.00 -6.88 1.25 3.12
25 -3.12 -2.50 7.50 -8.12 -6.88 7.50 -0.62 5.62
26 5.62 6.25 -5.00 -3.12 -10.00 1.25 -8.75 4.38
27 -7.50 9.38 -3.12 7.50 6.25 -4.38 -2.50 9.38
28 4.38 1.88 -8.12 8.75 -5.62 10.00 8.12 -1.88
29 -3.75 6.88 -10.00 -6.88 3.75 -6.25 3.12 -1.25
30 1.88 -4.38 -1.25 -10.00 1.25 -0.62 10.00 -6.88
31 -6.88 -3.75 -0.62 5.00 -7.50 -3.12 1.88 -8.75
32 6.25 -5.62 -8.75 2.50 9.38 3.75 -5.00 -5.00
33 -9.38 -7.50 -2.50 -3.75 -3.12 -8.75 -5.62 -2.50
[[1]]
[,1] [,2] [,3] [,4] [,5]
[1,] -0.375 1.000 0.625 -0.250 -0.500
[2,] -0.875 -0.500 0.750 0.125 -1.000
[3,] -0.750 -0.125 -0.875 -0.500 0.250
[4,] -0.625 0.250 -0.375 1.000 0.125
[5,] 0.500 0.875 -0.125 -0.750 -0.375
[6,] 1.000 -0.375 -0.250 0.625 -0.875
[7,] 0.250 -0.625 1.000 -0.375 0.750
[8,] 0.125 0.750 0.500 0.875 0.625
[9,] 0.000 0.000 0.000 0.000 0.000
[10,] 0.375 -1.000 -0.625 0.250 0.500
[11,] 0.875 0.500 -0.750 -0.125 1.000
[12,] 0.750 0.125 0.875 0.500 -0.250
[13,] 0.625 -0.250 0.375 -1.000 -0.125
[14,] -0.500 -0.875 0.125 0.750 0.375
[15,] -1.000 0.375 0.250 -0.625 0.875
[16,] -0.250 0.625 -1.000 0.375 -0.750
[17,] -0.125 -0.750 -0.500 -0.875 -0.625
[[2]]
[,1] [,2] [,3] [,4] [,5] [,6]
[1,] -0.375 1.000 0.625 -0.250 -0.500 0.875
[2,] -0.875 -0.500 0.750 0.125 -1.000 -0.375
[3,] -0.750 -0.125 -0.875 -0.500 0.250 0.625
[4,] -0.625 0.250 -0.375 1.000 0.125 -0.750
[5,] 0.500 0.875 -0.125 -0.750 -0.375 -1.000
[6,] 1.000 -0.375 -0.250 0.625 -0.875 0.500
[7,] 0.250 -0.625 1.000 -0.375 0.750 -0.125
[8,] 0.125 0.750 0.500 0.875 0.625 0.250
[9,] 0.000 0.000 0.000 0.000 0.000 0.000
[10,] 0.375 -1.000 -0.625 0.250 0.500 -0.875
[11,] 0.875 0.500 -0.750 -0.125 1.000 0.375
[12,] 0.750 0.125 0.875 0.500 -0.250 -0.625
[13,] 0.625 -0.250 0.375 -1.000 -0.125 0.750
[14,] -0.500 -0.875 0.125 0.750 0.375 1.000
[15,] -1.000 0.375 0.250 -0.625 0.875 -0.500
[16,] -0.250 0.625 -1.000 0.375 -0.750 0.125
[17,] -0.125 -0.750 -0.500 -0.875 -0.625 -0.250
[[3]]
[,1] [,2] [,3] [,4] [,5] [,6] [,7]
[1,] -0.375 1.000 0.625 -0.250 -0.500 0.875 0.125
[2,] -0.875 -0.500 0.750 0.125 -1.000 -0.375 0.250
[3,] -0.750 -0.125 -0.875 -0.500 0.250 0.625 1.000
[4,] -0.625 0.250 -0.375 1.000 0.125 -0.750 0.500
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