OSFD (version 3.0)

OSFD: Output Space-Filling Design

Description

This function is for producing designs that fill the output space.

Usage

OSFD(
  D = NULL,
  f,
  p,
  q,
  n_ini = NA,
  n,
  scale = TRUE,
  method = "EI",
  CAND = NULL,
  rand_out = FALSE,
  rand_in = FALSE
)

Value

D

the final design points in the input space

Y

the output points

Arguments

D

a matrix of the initial design. If not specified, a random Latin hypercube design of size n_ini and dimension p will be generated as initial design.

f

black-box function.

p

input dimension.

q

output dimension.

n_ini

the size of initial design. This initial size must be specified if D is not provided.

n

the size of the final design.

scale

whether to scale the output points to 0 to 1 for each dimension.

method

two choices: 'EI' or 'Greedy'; the default is 'EI'.

CAND

the candidate points in the input space. If Null, it will be automatically generated.

rand_out

whether to use random uniform points or quasi random points by twinning algorithm for generating points in spheres for output space approximation. The default value is FALSE.

rand_in

whether to use random uniform points or quasi random points by twinning algorithm for generating points in spheres for input space candidate sets. The default value is FALSE.

Details

OSFD produces a design that fills the output space using the sequential algorithm by Wang et al. (2024).

References

Wang, Shangkun, Adam P. Generale, Surya R. Kalidindi, and V. Roshan Joseph. (2024), "Sequential designs for filling output spaces", Technometrics, 66, 65–76.

Examples

# test function: inverse-radius function (Wang et.al 2024)
inverse_r = function(x){
epsilon = 0.1
y1 = 1 / (x[1]^2 + x[2]^2 + epsilon^2) ^ (1/2)
if (x[2]==0){
 y2 = 0
}else if (x[1]==0) {
  y2 = pi / 2}else{
    y2 = atan(x[2] / x[1])
  }
return (c(y1=y1, y2=y2))
}

set.seed(2022)
p = 2
q = 2
f = inverse_r
n_ini = 10
n = 50
osfd = OSFD(f=f, p=p, q=q, n_ini=n_ini, n=n)
D = osfd$D
Y = osfd$Y