Struct SphericalSpace 

pub struct SphericalSpace { /* private fields */ }

Spherical space operations

Implementations

impl SphericalSpace

pub fn new(ambient_dim: usize) -> Self

Create a new spherical space S^{n-1} embedded in R^n

Arguments

• ambient_dim - Dimension of ambient Euclidean space

pub fn with_config(self, config: SphericalConfig) -> Self

Set configuration

pub fn ambient_dim(&self) -> usize

Get ambient dimension

pub fn intrinsic_dim(&self) -> usize

Get intrinsic dimension (ambient_dim - 1)

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

Project a point onto the sphere

pub fn is_on_sphere(&self, point: &[f64]) -> bool

Check if point is on the sphere

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

Geodesic distance on the sphere: d(x, y) = arccos(⟨x, y⟩)

This is the great-circle distance.

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

Squared geodesic distance (useful for optimization)

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

Exponential map: exp_x(v) - move from x in direction v

exp_x(v) = cos(||v||) x + sin(||v||) (v / ||v||)

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

Logarithmic map: log_x(y) - tangent vector at x pointing toward y

log_x(y) = (θ / sin(θ)) (y - cos(θ) x) where θ = d(x, y) = arccos(⟨x, y⟩)

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

Parallel transport vector v from x to y

Transports tangent vector at x along geodesic to y

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

Fréchet mean on the sphere (spherical centroid)

Minimizes: Σᵢ wᵢ d(m, xᵢ)²

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

Geodesic interpolation: point at fraction t along geodesic from x to y

γ(t) = sin((1-t)θ)/sin(θ) x + sin(tθ)/sin(θ) y

pub fn sample_uniform(&self, rng: &mut impl Rng) -> Vec<f64>

Sample uniformly from the sphere

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

Von Mises-Fisher mean direction MLE

Computes the mean direction (mode of vMF distribution)

Trait Implementations

impl Clone for SphericalSpace

fn clone(&self) -> SphericalSpace

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Debug for SphericalSpace

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

Formats the value using the given formatter.