Module benchmark 

Test functions whose Sobol’ indices are known in closed form, to check an analysis against.

Guide: Sensitivity analysis’s Checked against section shows both methods on them.

• Ishigami: y = sin x₁ + a sin² x₂ + b x₃⁴ sin x₁ on [−π, π]³. It is nonlinear and not additive: x₃ does nothing alone (S₃ = 0) but a quarter of the variance with x₁.
• SobolG: y = Πᵢ (|4xᵢ − 2| + aᵢ)/(1 + aᵢ) on [0, 1]^k. Each aᵢ ≥ 0 sets how much factor i matters, from most at aᵢ = 0 to almost nothing at aᵢ = 99.

Each evaluates a point given as a slice, the form super::morris and super::sobol pass, and gives NaN for a point of the wrong length, which an analysis then refuses.

Structs

Ishigami

Ishigami and Homma’s function, y = sin x₁ + a sin² x₂ + b x₃⁴ sin x₁, each xᵢ uniform on [−π, π].

SobolG

Sobol’s g function, y = Πᵢ gᵢ(xᵢ) with gᵢ = (|4xᵢ − 2| + aᵢ)/(1 + aᵢ), each xᵢ uniform on [0, 1].