RNAmf (version 1.0.1)

NestedX: Constructing the nested design sets for RNA model.

Description

The function constructs the nested design sets with two fidelity levels \(\mathcal{X}_2 \subseteq \mathcal{X}_{1}\) for RNAmf_two_level or three fidelity levels \(\mathcal{X}_3 \subseteq \mathcal{X}_2 \subseteq \mathcal{X}_{1}\) for RNAmf_three_level.

Usage

NestedX(n, d)

Value

A list containing the design at each level, i.e., \(\mathcal{X}_{1}, \mathcal{X}_{2}\) or \(\mathcal{X}_{1}, \mathcal{X}_{2}, \mathcal{X}_{3}\).

Arguments

n

vector of the number of design points at each fidelity level \(l\). Thus, the vector must have a positive value \(n_1, n_2\) or \(n_1, n_2, n_3\) where \(n_1 > n_2 > n_3\).

d

constant of the dimension of the design.

Details

The procedure replace the points of lower level design \(\mathcal{X}_{l-1}\) to the closest points of higher level design \(\mathcal{X}_{l}\). The length of the \(\mathcal{X}_{l-1}\) could be larger than the user specified. For details, see "NestedDesign".

References

L. Le Gratiet and J. Garnier (2014). Recursive co-kriging model for design of computer experiments with multiple levels of fidelity. International Journal for Uncertainty Quantification, 4(5), 365-386; tools:::Rd_expr_doi("doi:10.1615/Int.J.UncertaintyQuantification.2014006914")

Examples

### number of design points ###
n1 <- 30
n2 <- 15

### dimension of the design ###
d <- 2

### fix seed to reproduce the result ###
set.seed(1)

### generate the nested design ###
NX <- NestedX(c(n1, n2), d)

### visualize nested design ###
plot(NX[[1]], col="red", pch=1, xlab="x1", ylab="x2")
points(NX[[2]], col="blue", pch=4)