# wspDesign: WSP algorithm In DiceDesign: Designs of Computer Experiments

## Description

The WSP (Wooton, Sergent, Phan-Tan-Luu) algorithm is an iterative algorithm based on suppression of some experiments from an initial design in each step. WSP leads to a space filling design

## Usage

 `1` ```wspDesign(design, dmin, init = "center") ```

## Arguments

 `design` a matrix (or a data.frame) corresponding to the design of experiments `dmin` a minimum bound for mindist value of the final design `init` defines the initialization point (input coordinates) of the algorithm: "center" (default value) takes the central point of the domain "random" takes a random point inside the domain

## Details

WSP enables to create a design D which is such that mindist(D)>dmin. However, it cannot assess the number of experiments. Similarly to straussDesign function, WSP is a powerful algorithm to construct space filling designs in high dimension

## Value

A list containing:

 `InitialDesign` the starting design `dmin` minimum bound for mindist value of the final design `design` the matrix of the final design `ResidualDesign` the matrix of the residual design (points of InitialDesign not in design)

## Author(s)

G. Damblin & B. Iooss

## References

J. Santiago, M. Claeys-Bruno, M.Sergent (2012). Construction of space filling designs using WSP algorithm for high dimensional spaces, Chenometrics and Intelligent Laboratory Systems, 113:26-31.

## Examples

 ```1 2 3 4 5 6``` ```dimension <- 2 n <- 100 X <- matrix(runif(n*dimension), n, dimension) m <- wspDesign(X, 0.1) plot(m\$design) xDRDN(m, letter = "T", dgts = 2, range = c(-10, 10)) ```

### Example output

```      T1     T2
1  -0.19  -0.15
2  -1.80   1.19
3  -4.52   0.82
4  -4.58   3.10
5  -2.97   4.57
6  -0.70   4.00
7   1.65   4.68
8   3.75   4.10
9   6.00   6.15
10  9.34   7.21
11  8.88   9.41
12  4.78   9.98
13  2.53   8.13
14  0.35   7.76
15 -0.37  10.00
16 -2.02   7.77
17 -4.58   8.33
18 -7.80   8.46
19 -8.72   3.15
20 -6.56  -0.81
21 -8.61  -2.56
22 -8.34  -4.58
23 -6.34  -3.71
24 -4.44  -2.56
25 -4.05  -5.37
26 -5.48  -7.84
27 -9.28  -8.35
28 -1.74  -9.77
29 -1.10  -7.17
30  1.46  -7.54
31  3.90  -6.56
32  5.94  -6.25
33  8.02  -5.00
34  8.13  -2.35
35  8.10   0.34
36  5.54  -0.61
37  3.55  -1.49
38  0.18  -2.92
39  4.54 -10.00
40  8.85  -9.66
41  9.24   4.00
```

DiceDesign documentation built on Feb. 13, 2021, 1:06 a.m.