Struct Ishigami 

pub struct Ishigami {
    pub a: f64,
    pub b: f64,
}

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

Its mean is a/2 and its variance and the parts of it are (I. M. Sobol’ and Y. L. Levitan, “On the use of variance reducing multipliers in Monte Carlo computations of a global sensitivity index”, Computer Physics Communications 117, 52–61, 1999, https://doi.org/10.1016/S0010-4655(98)00156-8, p. 57, §5; A. Saltelli and others, Global Sensitivity Analysis: The Primer, Wiley, 2008, pp. 179–182)

• V = 1/2 + a²/8 + bπ⁴/5 + b²π⁸/18,
• V₁ = (1 + bπ⁴/5)²/2, V₂ = a²/8, V₃ = 0,
• V₁₃ = (1/18 − 1/50) b²π⁸ = 8b²π⁸/225, every other part zero,

so Sᵢ = Vᵢ/V, S_T₁ = (V₁ + V₁₃)/V, S_T₂ = V₂/V and S_T₃ = V₁₃/V. The usual parameters, Ishigami::STANDARD, are a = 7, b = 0.1. T. Ishigami and T. Homma, “An importance quantification technique in uncertainty analysis for computer models”, Proceedings of ISUMA ’90, 398–403, 1990, https://doi.org/10.1109/ISUMA.1990.151285, introduced it.

Fields

a: f64

The weight of sin² x₂.

b: f64

The weight of x₃⁴ sin x₁.

Implementations

impl Ishigami

pub const STANDARD: Self

a = 7, b = 0.1.

pub fn factors() -> Result<Vec<Factor>, AnalysisError>

Its three factors, x1 to x3, each on [−π, π].

Errors

None in practice; Factor::new’s, as the type requires.

pub fn evaluate(&self, x: &[f64]) -> f64

y at x = [x₁, x₂, x₃]; NaN for a slice of another length.

pub fn mean(&self) -> f64

Its mean, a/2.

pub fn variance(&self) -> f64

Its variance, V.

pub fn first_order(&self) -> [f64; 3]

The first-order indices, S₁, S₂, S₃.

pub fn total(&self) -> [f64; 3]

The total indices, S_T₁, S_T₂, S_T₃.

Trait Implementations

impl Clone for Ishigami

fn clone(&self) -> Ishigami

Returns a duplicate of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl Copy for Ishigami

impl Debug for Ishigami

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.

impl<'de> Deserialize<'de> for Ishigami

fn deserialize<__D>(__deserializer: __D) -> Result<Self, __D::Error>

where __D: Deserializer<'de>,

Deserialize this value from the given Serde deserializer.

impl PartialEq for Ishigami

fn eq(&self, other: &Ishigami) -> bool

Tests for self and other values to be equal, and is used by ==.

fn ne(&self, other: &Rhs) -> bool

Tests for !=. The default implementation is almost always sufficient, and should not be overridden without very good reason.

impl Serialize for Ishigami

fn serialize<__S>(&self, __serializer: __S) -> Result<__S::Ok, __S::Error>

where __S: Serializer,

Serialize this value into the given Serde serializer.

impl StructuralPartialEq for Ishigami