NestedX {RNAmf}

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)

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".

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}.

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; 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)