NestedX: Constructing nested design sets for the RNA model.

In RNAmf: Recursive Non-Additive Emulator for Multi-Fidelity Data

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)

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".

Value

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

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; \Sexpr[results=rd]{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)

RNAmf documentation built on June 8, 2025, 10:43 a.m.