gen.USD: Doehlert's Uniform Shell Designs (USDs)
In VdgRsm: Plots of Scaled Prediction Variances for Response Surface Designs
Description
Usage
Arguments
Value
References
Examples
Description
Generate uniform shell designs for k = 2 to 6
Usage
1
gen.USD(k, alpha = 1)
Arguments
k
The number of factors or independent variables, k = 2 to 6.
alpha
A scaling factor. See examples.
Value
gen.USD is called to generate the data frame of the design matrix of the USD.
References
Doehlert, D. H (1970), Uniform Shell Designs, Journal of the Royal Statistical Society, 19(3):231-239
Examples
1
2
3
4
Example output
X1 X2
1 0.0 0.00000
2 1.0 0.00000
3 -1.0 0.00000
4 0.5 0.86602
5 -0.5 -0.86602
6 0.5 -0.86602
7 -0.5 0.86602
X1 X2 X3
1 0.0000000 0.0000000 0.000000
2 1.7320508 0.0000000 0.000000
3 -1.7320508 0.0000000 0.000000
4 0.8660254 1.4999906 0.000000
5 -0.8660254 -1.4999906 0.000000
6 0.8660254 -1.4999906 0.000000
7 -0.8660254 1.4999906 0.000000
8 0.8660254 0.5000084 1.414219
9 -0.8660254 -0.5000084 -1.414219
10 0.8660254 -0.5000084 -1.414219
11 0.0000000 0.9999995 -1.414219
12 -0.8660254 0.5000084 1.414219
13 0.0000000 -0.9999995 1.414219
X1 X2 X3 X4 X5 X6
1 0.0 0.00000 0.00000 0.00000 0.0000 0.00000
2 1.0 0.00000 0.00000 0.00000 0.0000 0.00000
3 -1.0 0.00000 0.00000 0.00000 0.0000 0.00000
4 0.5 0.86602 0.00000 0.00000 0.0000 0.00000
5 -0.5 -0.86602 0.00000 0.00000 0.0000 0.00000
6 0.5 -0.86602 0.00000 0.00000 0.0000 0.00000
7 -0.5 0.86602 0.00000 0.00000 0.0000 0.00000
8 0.5 0.28868 0.81650 0.00000 0.0000 0.00000
9 -0.5 -0.28868 -0.81650 0.00000 0.0000 0.00000
10 0.5 -0.28868 -0.81650 0.00000 0.0000 0.00000
11 0.0 0.57735 -0.81650 0.00000 0.0000 0.00000
12 -0.5 0.28868 0.81650 0.00000 0.0000 0.00000
13 0.0 -0.57735 0.81650 0.00000 0.0000 0.00000
14 0.5 0.28868 0.20413 0.79057 0.0000 0.00000
15 -0.5 -0.28868 -0.20413 -0.79057 0.0000 0.00000
16 0.5 -0.28868 -0.20413 -0.79057 0.0000 0.00000
17 0.0 0.57735 -0.20413 -0.79057 0.0000 0.00000
18 0.0 0.00000 0.61238 -0.79057 0.0000 0.00000
19 -0.5 0.28868 0.20413 0.79057 0.0000 0.00000
20 0.0 -0.57735 0.20413 0.79057 0.0000 0.00000
21 0.0 0.00000 -0.61238 0.79057 0.0000 0.00000
22 0.5 0.28868 0.20413 0.15812 0.7746 0.00000
23 -0.5 -0.28868 -0.20413 -0.15812 -0.7746 0.00000
24 0.5 -0.28868 -0.20413 -0.15812 -0.7746 0.00000
25 0.0 0.57735 -0.20413 -0.15812 -0.7746 0.00000
26 0.0 0.00000 0.61238 -0.15812 -0.7746 0.00000
27 0.0 0.00000 0.00000 0.63246 -0.7746 0.00000
28 -0.5 0.28868 0.20413 0.15812 0.7746 0.00000
29 0.0 -0.57735 0.20413 0.15812 0.7746 0.00000
30 0.0 0.00000 -0.61238 0.15812 0.7746 0.00000
31 0.0 0.00000 0.00000 -0.63246 0.7746 0.00000
32 0.5 0.28868 0.20413 0.15812 0.1291 0.76376
33 -0.5 -0.28868 -0.20413 -0.15812 -0.1291 -0.76376
34 0.5 -0.28868 -0.20413 -0.15812 -0.1291 -0.76376
35 0.0 0.57735 -0.20413 -0.15812 -0.1291 -0.76376
36 0.0 0.00000 0.61238 -0.15812 -0.1291 -0.76376
37 0.0 0.00000 0.00000 0.63246 -0.1291 -0.76376
38 0.0 0.00000 0.00000 0.00000 0.6455 -0.76376
39 -0.5 0.28868 0.20413 0.15812 0.1291 0.76376
40 0.0 -0.57735 0.20413 0.15812 0.1291 0.76376
41 0.0 0.00000 -0.61238 0.15812 0.1291 0.76376
42 0.0 0.00000 0.00000 -0.63246 0.1291 0.76376
43 0.0 0.00000 0.00000 0.00000 -0.6455 0.76376
X1 X2 X3 X4 X5 X6
1 0.000000 0.0000000 0.0000000 0.0000000 0.0000000 0.000000
2 2.449490 0.0000000 0.0000000 0.0000000 0.0000000 0.000000
3 -2.449490 0.0000000 0.0000000 0.0000000 0.0000000 0.000000
4 1.224745 2.1213071 0.0000000 0.0000000 0.0000000 0.000000
5 -1.224745 -2.1213071 0.0000000 0.0000000 0.0000000 0.000000
6 1.224745 -2.1213071 0.0000000 0.0000000 0.0000000 0.000000
7 -1.224745 2.1213071 0.0000000 0.0000000 0.0000000 0.000000
8 1.224745 0.7071187 2.0000084 0.0000000 0.0000000 0.000000
9 -1.224745 -0.7071187 -2.0000084 0.0000000 0.0000000 0.000000
10 1.224745 -0.7071187 -2.0000084 0.0000000 0.0000000 0.000000
11 0.000000 1.4142129 -2.0000084 0.0000000 0.0000000 0.000000
12 -1.224745 0.7071187 2.0000084 0.0000000 0.0000000 0.000000
13 0.000000 -1.4142129 2.0000084 0.0000000 0.0000000 0.000000
14 1.224745 0.7071187 0.5000143 1.9364931 0.0000000 0.000000
15 -1.224745 -0.7071187 -0.5000143 -1.9364931 0.0000000 0.000000
16 1.224745 -0.7071187 -0.5000143 -1.9364931 0.0000000 0.000000
17 0.000000 1.4142129 -0.5000143 -1.9364931 0.0000000 0.000000
18 0.000000 0.0000000 1.5000185 -1.9364931 0.0000000 0.000000
19 -1.224745 0.7071187 0.5000143 1.9364931 0.0000000 0.000000
20 0.000000 -1.4142129 0.5000143 1.9364931 0.0000000 0.000000
21 0.000000 0.0000000 -1.5000185 1.9364931 0.0000000 0.000000
22 1.224745 0.7071187 0.5000143 0.3873133 1.8973748 0.000000
23 -1.224745 -0.7071187 -0.5000143 -0.3873133 -1.8973748 0.000000
24 1.224745 -0.7071187 -0.5000143 -0.3873133 -1.8973748 0.000000
25 0.000000 1.4142129 -0.5000143 -0.3873133 -1.8973748 0.000000
26 0.000000 0.0000000 1.5000185 -0.3873133 -1.8973748 0.000000
27 0.000000 0.0000000 0.0000000 1.5492043 -1.8973748 0.000000
28 -1.224745 0.7071187 0.5000143 0.3873133 1.8973748 0.000000
29 0.000000 -1.4142129 0.5000143 0.3873133 1.8973748 0.000000
30 0.000000 0.0000000 -1.5000185 0.3873133 1.8973748 0.000000
31 0.000000 0.0000000 0.0000000 -1.5492043 1.8973748 0.000000
32 1.224745 0.7071187 0.5000143 0.3873133 0.3162291 1.870822
33 -1.224745 -0.7071187 -0.5000143 -0.3873133 -0.3162291 -1.870822
34 1.224745 -0.7071187 -0.5000143 -0.3873133 -0.3162291 -1.870822
35 0.000000 1.4142129 -0.5000143 -0.3873133 -0.3162291 -1.870822
36 0.000000 0.0000000 1.5000185 -0.3873133 -0.3162291 -1.870822
37 0.000000 0.0000000 0.0000000 1.5492043 -0.3162291 -1.870822
38 0.000000 0.0000000 0.0000000 0.0000000 1.5811456 -1.870822
39 -1.224745 0.7071187 0.5000143 0.3873133 0.3162291 1.870822
40 0.000000 -1.4142129 0.5000143 0.3873133 0.3162291 1.870822
41 0.000000 0.0000000 -1.5000185 0.3873133 0.3162291 1.870822
42 0.000000 0.0000000 0.0000000 -1.5492043 0.3162291 1.870822
43 0.000000 0.0000000 0.0000000 0.0000000 -1.5811456 1.870822
VdgRsm documentation built on May 2, 2019, 3:48 p.m.
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Note that we can't provide technical support on individual packages. You should contact the package authors for that.
Description Usage Arguments Value References Examples
Description
Generate uniform shell designs for k = 2 to 6
Usage
1 | gen.USD(k, alpha = 1)
|
Arguments
k |
The number of factors or independent variables, k = 2 to 6. |
alpha |
A scaling factor. See examples. |
Value
gen.USD is called to generate the data frame of the design matrix of the USD.
References
Doehlert, D. H (1970), Uniform Shell Designs, Journal of the Royal Statistical Society, 19(3):231-239
Examples
1 2 3 4 |
Example output
X1 X2
1 0.0 0.00000
2 1.0 0.00000
3 -1.0 0.00000
4 0.5 0.86602
5 -0.5 -0.86602
6 0.5 -0.86602
7 -0.5 0.86602
X1 X2 X3
1 0.0000000 0.0000000 0.000000
2 1.7320508 0.0000000 0.000000
3 -1.7320508 0.0000000 0.000000
4 0.8660254 1.4999906 0.000000
5 -0.8660254 -1.4999906 0.000000
6 0.8660254 -1.4999906 0.000000
7 -0.8660254 1.4999906 0.000000
8 0.8660254 0.5000084 1.414219
9 -0.8660254 -0.5000084 -1.414219
10 0.8660254 -0.5000084 -1.414219
11 0.0000000 0.9999995 -1.414219
12 -0.8660254 0.5000084 1.414219
13 0.0000000 -0.9999995 1.414219
X1 X2 X3 X4 X5 X6
1 0.0 0.00000 0.00000 0.00000 0.0000 0.00000
2 1.0 0.00000 0.00000 0.00000 0.0000 0.00000
3 -1.0 0.00000 0.00000 0.00000 0.0000 0.00000
4 0.5 0.86602 0.00000 0.00000 0.0000 0.00000
5 -0.5 -0.86602 0.00000 0.00000 0.0000 0.00000
6 0.5 -0.86602 0.00000 0.00000 0.0000 0.00000
7 -0.5 0.86602 0.00000 0.00000 0.0000 0.00000
8 0.5 0.28868 0.81650 0.00000 0.0000 0.00000
9 -0.5 -0.28868 -0.81650 0.00000 0.0000 0.00000
10 0.5 -0.28868 -0.81650 0.00000 0.0000 0.00000
11 0.0 0.57735 -0.81650 0.00000 0.0000 0.00000
12 -0.5 0.28868 0.81650 0.00000 0.0000 0.00000
13 0.0 -0.57735 0.81650 0.00000 0.0000 0.00000
14 0.5 0.28868 0.20413 0.79057 0.0000 0.00000
15 -0.5 -0.28868 -0.20413 -0.79057 0.0000 0.00000
16 0.5 -0.28868 -0.20413 -0.79057 0.0000 0.00000
17 0.0 0.57735 -0.20413 -0.79057 0.0000 0.00000
18 0.0 0.00000 0.61238 -0.79057 0.0000 0.00000
19 -0.5 0.28868 0.20413 0.79057 0.0000 0.00000
20 0.0 -0.57735 0.20413 0.79057 0.0000 0.00000
21 0.0 0.00000 -0.61238 0.79057 0.0000 0.00000
22 0.5 0.28868 0.20413 0.15812 0.7746 0.00000
23 -0.5 -0.28868 -0.20413 -0.15812 -0.7746 0.00000
24 0.5 -0.28868 -0.20413 -0.15812 -0.7746 0.00000
25 0.0 0.57735 -0.20413 -0.15812 -0.7746 0.00000
26 0.0 0.00000 0.61238 -0.15812 -0.7746 0.00000
27 0.0 0.00000 0.00000 0.63246 -0.7746 0.00000
28 -0.5 0.28868 0.20413 0.15812 0.7746 0.00000
29 0.0 -0.57735 0.20413 0.15812 0.7746 0.00000
30 0.0 0.00000 -0.61238 0.15812 0.7746 0.00000
31 0.0 0.00000 0.00000 -0.63246 0.7746 0.00000
32 0.5 0.28868 0.20413 0.15812 0.1291 0.76376
33 -0.5 -0.28868 -0.20413 -0.15812 -0.1291 -0.76376
34 0.5 -0.28868 -0.20413 -0.15812 -0.1291 -0.76376
35 0.0 0.57735 -0.20413 -0.15812 -0.1291 -0.76376
36 0.0 0.00000 0.61238 -0.15812 -0.1291 -0.76376
37 0.0 0.00000 0.00000 0.63246 -0.1291 -0.76376
38 0.0 0.00000 0.00000 0.00000 0.6455 -0.76376
39 -0.5 0.28868 0.20413 0.15812 0.1291 0.76376
40 0.0 -0.57735 0.20413 0.15812 0.1291 0.76376
41 0.0 0.00000 -0.61238 0.15812 0.1291 0.76376
42 0.0 0.00000 0.00000 -0.63246 0.1291 0.76376
43 0.0 0.00000 0.00000 0.00000 -0.6455 0.76376
X1 X2 X3 X4 X5 X6
1 0.000000 0.0000000 0.0000000 0.0000000 0.0000000 0.000000
2 2.449490 0.0000000 0.0000000 0.0000000 0.0000000 0.000000
3 -2.449490 0.0000000 0.0000000 0.0000000 0.0000000 0.000000
4 1.224745 2.1213071 0.0000000 0.0000000 0.0000000 0.000000
5 -1.224745 -2.1213071 0.0000000 0.0000000 0.0000000 0.000000
6 1.224745 -2.1213071 0.0000000 0.0000000 0.0000000 0.000000
7 -1.224745 2.1213071 0.0000000 0.0000000 0.0000000 0.000000
8 1.224745 0.7071187 2.0000084 0.0000000 0.0000000 0.000000
9 -1.224745 -0.7071187 -2.0000084 0.0000000 0.0000000 0.000000
10 1.224745 -0.7071187 -2.0000084 0.0000000 0.0000000 0.000000
11 0.000000 1.4142129 -2.0000084 0.0000000 0.0000000 0.000000
12 -1.224745 0.7071187 2.0000084 0.0000000 0.0000000 0.000000
13 0.000000 -1.4142129 2.0000084 0.0000000 0.0000000 0.000000
14 1.224745 0.7071187 0.5000143 1.9364931 0.0000000 0.000000
15 -1.224745 -0.7071187 -0.5000143 -1.9364931 0.0000000 0.000000
16 1.224745 -0.7071187 -0.5000143 -1.9364931 0.0000000 0.000000
17 0.000000 1.4142129 -0.5000143 -1.9364931 0.0000000 0.000000
18 0.000000 0.0000000 1.5000185 -1.9364931 0.0000000 0.000000
19 -1.224745 0.7071187 0.5000143 1.9364931 0.0000000 0.000000
20 0.000000 -1.4142129 0.5000143 1.9364931 0.0000000 0.000000
21 0.000000 0.0000000 -1.5000185 1.9364931 0.0000000 0.000000
22 1.224745 0.7071187 0.5000143 0.3873133 1.8973748 0.000000
23 -1.224745 -0.7071187 -0.5000143 -0.3873133 -1.8973748 0.000000
24 1.224745 -0.7071187 -0.5000143 -0.3873133 -1.8973748 0.000000
25 0.000000 1.4142129 -0.5000143 -0.3873133 -1.8973748 0.000000
26 0.000000 0.0000000 1.5000185 -0.3873133 -1.8973748 0.000000
27 0.000000 0.0000000 0.0000000 1.5492043 -1.8973748 0.000000
28 -1.224745 0.7071187 0.5000143 0.3873133 1.8973748 0.000000
29 0.000000 -1.4142129 0.5000143 0.3873133 1.8973748 0.000000
30 0.000000 0.0000000 -1.5000185 0.3873133 1.8973748 0.000000
31 0.000000 0.0000000 0.0000000 -1.5492043 1.8973748 0.000000
32 1.224745 0.7071187 0.5000143 0.3873133 0.3162291 1.870822
33 -1.224745 -0.7071187 -0.5000143 -0.3873133 -0.3162291 -1.870822
34 1.224745 -0.7071187 -0.5000143 -0.3873133 -0.3162291 -1.870822
35 0.000000 1.4142129 -0.5000143 -0.3873133 -0.3162291 -1.870822
36 0.000000 0.0000000 1.5000185 -0.3873133 -0.3162291 -1.870822
37 0.000000 0.0000000 0.0000000 1.5492043 -0.3162291 -1.870822
38 0.000000 0.0000000 0.0000000 0.0000000 1.5811456 -1.870822
39 -1.224745 0.7071187 0.5000143 0.3873133 0.3162291 1.870822
40 0.000000 -1.4142129 0.5000143 0.3873133 0.3162291 1.870822
41 0.000000 0.0000000 -1.5000185 0.3873133 0.3162291 1.870822
42 0.000000 0.0000000 0.0000000 -1.5492043 0.3162291 1.870822
43 0.000000 0.0000000 0.0000000 0.0000000 -1.5811456 1.870822
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