# NestedDesign: Definition of nested experimental design sets for... In MuFiCokriging: Multi-Fidelity Cokriging models

## Description

Build an object of class S3 (`"NestDesign"`) defining nested experimental design sets used to build multi-fidelity Cokriging models.

## Usage

 `1` ``` NestedDesign(x, nlevel , indices = NULL, n = NULL) ```

## Arguments

 `x` a matrix representing the experimental design set of the code level 1. `nlevel ` an integer representing the number of code levels. `indices` a list of vectors. The ith element of the list contains the indices of the points in the experimental design set of the level i-1 constituting the experimental design set of the level i. If `indices = NULL` they are randomly sampled according to the number of observations defining in `n`. `n` a vector containing the number of observations at level k=2,...,nlevel. It is not taking into account if `indices` is different from `NULL`.

## Details

The procedure does not change the experimental design set of the highest code level. During the procedure, the points of D_{k-1} the closest to those of D_k with k=2,...,nlevel are removed and they are replaced by the points of D_k . Thus, the length of the final D_{k-1} could be larger than the one of the initial D_{k-1}. (see `"MuFicokm"`)

## Value

an object of class (`"NestDesign"`) representing a nested experimental design set.

Loic Le Gratiet

## References

LE GRATIET, L. & GARNIER, J. (2012), Recursive co-kriging model for Design of Computer Experiments with multiple levels of fidelity, arXiv:1210.0686.

`MuFicokm`, `ExtractNestDesign`, `NestedDesignBuild`
 ```1 2 3 4 5 6 7``` ```#-- Nested Experimental design sets dimension <- 3 nD1 <- 100 nD2 <- 50 nD3 <- 20 set.seed(1);D1 <- matrix(runif(n=nD1*dimension, 0,1),ncol=dimension) NestDesign <- NestedDesign(D1, nlevel=3 , n = c(nD2,nD3)) ```