Struct GaussianManifold 

pub struct GaussianManifold;

The manifold of univariate Gaussian distributions parameterized by (μ, σ) with σ > 0.

Implementations

impl GaussianManifold

pub fn new() -> Self

Create a new GaussianManifold.

pub fn fisher_metric(&self, _mu: f64, sigma: f64) -> [[f64; 2]; 2]

Fisher information metric for Gaussian: diag(1/σ², 2/σ²) at (μ, σ).

pub fn geodesic_distance( &self, mu1: f64, sigma1: f64, mu2: f64, sigma2: f64, ) -> f64

Geodesic distance between two Gaussians (μ1,σ1) and (μ2,σ2).

Uses the closed-form expression on the Poincaré upper half-plane.

pub fn exponential_map( &self, mu: f64, sigma: f64, v_mu: f64, v_sigma: f64, t: f64, ) -> (f64, f64)

Exponential map at (μ, σ) in direction (v_μ, v_σ) for step t.

Returns the point (μ', σ') reached by following the geodesic.

pub fn logarithmic_map( &self, mu: f64, sigma: f64, mu2: f64, sigma2: f64, ) -> (f64, f64)

Logarithmic map at (μ, σ) pointing toward (μ2, σ2).

Returns the tangent vector (v_μ, v_σ) such that exp_{(μ,σ)}(v) = (μ2, σ2).

Trait Implementations

impl Clone for GaussianManifold

fn clone(&self) -> GaussianManifold

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Debug for GaussianManifold

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

Formats the value using the given formatter.

impl Default for GaussianManifold

fn default() -> Self

Returns the “default value” for a type.