RNAmf (version 1.1.1)

NestedX: Constructing nested design sets for the RNA model.

Description

The function constructs nested design sets with multiple fidelity levels \(\mathcal{X}_l \subseteq \cdots \subseteq \mathcal{X}_{1}\) for use in RNAmf.

Usage

NestedX(n, d)

Value

A list containing the nested design sets at each level, i.e., \(\mathcal{X}_{1}, \ldots, \mathcal{X}_{l}\).

Arguments

n

A vector specifying the number of design points at each fidelity level \(l\). Thus, the vector must have a positive value \(n_1, \ldots, n_l\) where \(n_1 > \cdots > n_l\).

d

A positive integer specifying the dimension of the design.

Details

The procedure replace the points of lower level design \(\mathcal{X}_{l-1}\) with the closest points from higher level design \(\mathcal{X}_{l}\). The length of \(\mathcal{X}_{l-1}\) may be larger than the user specified size. 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)