This function evaluates the Sobol G function on a set of input samples
generated via crude Monte Carlos. It returns both the sampled
inputs and the corresponding function outputs.
Usage
sobol_fun(N, a = c(0, 1, 4.5, 9, 99, 99, 99, 99))
Value
A list with two elements:
x: a numeric matrix of size N x 8 containing the input samples.
y: a numeric vector of length N with the corresponding function outputs.
Arguments
N
Integer. Number of input samples to generate.
a
(default: c(0, 1, 4.5, 9, 99, 99, 99, 99)) Numeric vector of non-negative parameters of length 8.
These parameters control the sensitivity of each input dimension.
Details
The Sobol G function is defined as:
$$
Y = \prod_{j=1}^{8} \frac{|\ 4 X_j - 2\ | + a_j}{1 + a_j}
$$
where \(X_j \sim \mathcal{U}(0, 1)\) independently.