Struct ProductManifold 

pub struct ProductManifold { /* private fields */ }

Product manifold: M = E^e × H^h × S^s

Implementations

impl ProductManifold

pub fn new( euclidean_dim: usize, hyperbolic_dim: usize, spherical_dim: usize, ) -> Self

Create a new product manifold

Arguments

• euclidean_dim - Dimension of Euclidean component
• hyperbolic_dim - Dimension of hyperbolic component (Poincaré ball)
• spherical_dim - Dimension of spherical component

pub fn from_config(config: ProductManifoldConfig) -> Self

Create from configuration

pub fn config(&self) -> &ProductManifoldConfig

Get configuration

pub fn dim(&self) -> usize

Total dimension

pub fn euclidean_component<'a>(&self, point: &'a [f64]) -> &'a [f64]

Extract Euclidean component from point

pub fn hyperbolic_component<'a>(&self, point: &'a [f64]) -> &'a [f64]

Extract hyperbolic component from point

pub fn spherical_component<'a>(&self, point: &'a [f64]) -> &'a [f64]

Extract spherical component from point

pub fn project(&self, point: &[f64]) -> Result<Vec<f64>>

Project point onto the product manifold

• Euclidean: no projection needed
• Hyperbolic: project into Poincaré ball
• Spherical: normalize to unit sphere

pub fn distance(&self, x: &[f64], y: &[f64]) -> Result<f64>

Compute distance in product manifold

d(x, y)² = w_e d_E(x_e, y_e)² + w_h d_H(x_h, y_h)² + w_s d_S(x_s, y_s)²

pub fn exp_map(&self, x: &[f64], v: &[f64]) -> Result<Vec<f64>>

Exponential map at point x with tangent vector v

pub fn log_map(&self, x: &[f64], y: &[f64]) -> Result<Vec<f64>>

Logarithmic map at point x toward point y

pub fn frechet_mean( &self, points: &[Vec<f64>], weights: Option<&[f64]>, ) -> Result<Vec<f64>>

Compute Fréchet mean on product manifold

impl ProductManifold

Batch operations on product manifolds

pub fn pairwise_distances(&self, points: &[Vec<f64>]) -> Result<Vec<Vec<f64>>>

Compute pairwise distances between all points Uses parallel computation when ‘parallel’ feature is enabled

pub fn knn( &self, query: &[f64], points: &[Vec<f64>], k: usize, ) -> Result<Vec<(usize, f64)>>

Find k-nearest neighbors Uses parallel computation when ‘parallel’ feature is enabled

pub fn geodesic(&self, x: &[f64], y: &[f64], t: f64) -> Result<Vec<f64>>

Geodesic interpolation between two points

Returns point at fraction t along geodesic from x to y

pub fn geodesic_path( &self, x: &[f64], y: &[f64], num_points: usize, ) -> Result<Vec<Vec<f64>>>

Sample points along geodesic

pub fn parallel_transport( &self, x: &[f64], y: &[f64], v: &[f64], ) -> Result<Vec<f64>>

Parallel transport vector v from x to y

pub fn variance(&self, points: &[Vec<f64>], mean: Option<&[f64]>) -> Result<f64>

Compute variance of points on manifold

pub fn project_gradient( &self, point: &[f64], gradient: &[f64], ) -> Result<Vec<f64>>

Project gradient to tangent space at point

For product manifolds, this projects each component appropriately

Trait Implementations

impl Clone for ProductManifold

fn clone(&self) -> ProductManifold

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Debug for ProductManifold

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

Formats the value using the given formatter.