Sobol G function evaluation

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))

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.

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.

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.

See also

ishi_homma_fun, gaussian_fun

Examples

result <- sobol_fun(1000)
head(result$x)
#>             X1        X2         X3        X4        X5          X6         X7
#> [1,] 0.8336769 0.3482587 0.68735827 0.3343985 0.1063165 0.648367345 0.17086912
#> [2,] 0.6894955 0.4466470 0.29258650 0.7959399 0.2118618 0.007476662 0.73724916
#> [3,] 0.5746480 0.8284600 0.59923234 0.7537201 0.9551472 0.225094068 0.30623252
#> [4,] 0.1020558 0.7184446 0.90163744 0.4497658 0.1815488 0.496164552 0.04597023
#> [5,] 0.4036010 0.4013458 0.47526941 0.6295620 0.2172066 0.313823511 0.22045919
#> [6,] 0.9683687 0.9211852 0.02474348 0.7432475 0.2371152 0.690876706 0.90556190
#>             X8
#> [1,] 0.7974711
#> [2,] 0.4254239
#> [3,] 0.6467902
#> [4,] 0.3462589
#> [5,] 0.6898496
#> [6,] 0.9185341
head(result$y)
#> [1] 0.9956661 0.4554667 0.3088842 1.5190787 0.2134684 2.9514805