Struct AlphaGeometry 

pub struct AlphaGeometry {
    pub alpha: f64,
}

α-geometry: a one-parameter family of affine connections on statistical manifolds, introduced by Amari.

For α = 0 this reduces to the Levi-Civita connection; α = ±1 give the mixture and exponential connections.

Fields

alpha: f64

The α parameter controlling the connection.

Implementations

impl AlphaGeometry

pub fn new(alpha: f64) -> Self

Create a new AlphaGeometry with the given alpha.

pub fn alpha_connection(&self, params: &[f64]) -> Vec<Vec<Vec<f64>>>

Compute the α-connection coefficients Γ^(α)_{ijk} at params.

Returns a [dim][dim][dim] array. Uses the formula Γ^(α) = Γ^(0) − (α/2) T_{ijk} where T is the skewness tensor (approximated via finite differences here).

pub fn dual_connection(&self, params: &[f64]) -> Vec<Vec<Vec<f64>>>

Compute the dual (−α) connection.

pub fn curvature_tensor(&self, params: &[f64]) -> Vec<Vec<Vec<Vec<f64>>>>

Compute the curvature tensor R^l_{kij} of the α-connection.

R^l_{kij} = ∂_i Γ^l_{jk} − ∂_j Γ^l_{ik} + Γ^l_{im} Γ^m_{jk} − Γ^l_{jm} Γ^m_{ik}

Trait Implementations

impl Clone for AlphaGeometry

fn clone(&self) -> AlphaGeometry

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Debug for AlphaGeometry

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

Formats the value using the given formatter.