Struct WassersteinBall 

pub struct WassersteinBall {
    pub center_samples: Vec<Vec<f64>>,
    pub radius: f64,
}

Describes a Wasserstein-1 ball around a set of centre samples.

The ball B_ε(P_N) = {Q : W_1(Q, P_N) ≤ ε} contains all probability measures within Wasserstein distance ε of the empirical distribution P_N.

Fields

center_samples: Vec<Vec<f64>>

Centre samples {x_1, …, x_N} defining the empirical distribution P_N.

radius: f64

Ball radius ε ≥ 0.

Implementations

impl WassersteinBall

pub fn new(center_samples: Vec<Vec<f64>>, radius: f64) -> OptimizeResult<Self>

Create a new Wasserstein ball.

Returns an error when radius < 0 or center_samples is empty.

pub fn distance_to_point(&self, q: &[f64]) -> f64

Wasserstein-1 distance from the empirical centre to a single point q.

For a discrete empirical distribution P_N the W_1 distance to the Dirac mass δ_q is min_i ‖x_i − q‖_2 (the nearest-centre distance).

pub fn contains_point(&self, q: &[f64]) -> bool

Check whether q is within the Wasserstein ball of the empirical centre.

Returns true iff distance_to_point(q) ≤ self.radius.

Trait Implementations

impl Clone for WassersteinBall

fn clone(&self) -> WassersteinBall

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Debug for WassersteinBall

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

Formats the value using the given formatter.