Struct SignedMeasure 

pub struct SignedMeasure {
    pub positive_density: Box<dyn Fn(&[f64]) -> f64>,
    pub negative_density: Box<dyn Fn(&[f64]) -> f64>,
    pub domain: MeasurableSet,
    pub n_samples: usize,
}

A signed measure represented as a difference of two non-negative measures.

By the Jordan decomposition theorem, every signed measure ν can be written as ν = ν⁺ − ν⁻ where ν⁺, ν⁻ ≥ 0 are mutually singular.

Here we work numerically with density functions.

Fields

positive_density: Box<dyn Fn(&[f64]) -> f64>

The positive part density f⁺(x) ≥ 0.

negative_density: Box<dyn Fn(&[f64]) -> f64>

The negative part density f⁻(x) ≥ 0.

domain: MeasurableSet

Domain of integration.

n_samples: usize

Number of Monte Carlo samples.

Implementations

impl SignedMeasure

pub fn new( positive_density: impl Fn(&[f64]) -> f64 + 'static, negative_density: impl Fn(&[f64]) -> f64 + 'static, domain: MeasurableSet, n_samples: usize, ) -> Self

Create a signed measure from positive and negative densities.

pub fn from_density( density: impl Fn(&[f64]) -> f64 + 'static, domain: MeasurableSet, n_samples: usize, ) -> Self

Create a signed measure from a single (possibly negative) density f.

pub fn evaluate(&self, set: &MeasurableSet) -> f64

Evaluate the signed measure on a set: ν(A) = ∫_A (f⁺ − f⁻) dx.

pub fn total_variation(&self, set: &MeasurableSet) -> f64

Total variation: |ν|(A) = ∫_A (f⁺ + f⁻) dx.

pub fn hahn_positive_set_samples(&self, n: usize) -> Vec<Vec<f64>>

Hahn decomposition: identify the positive set P where f⁺ > f⁻.

Returns a sample of points in P within the domain.

pub fn jordan_decomposition(&self) -> (f64, f64)

Jordan decomposition: return estimates of ν⁺(domain) and ν⁻(domain).