# gen.USD: Doehlert's Uniform Shell Designs (USDs) In VdgRsm: Plots of Scaled Prediction Variances for Response Surface Designs

## 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``` ``` gen.USD(2) gen.USD(3, alpha = sqrt(3)) gen.USD(6) gen.USD(6, alpha = sqrt(6)) ```

### 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 30, 2017, 8:05 a.m.