Struct SpdManifold 

pub struct SpdManifold { /* private fields */ }

Implementations

impl SpdManifold

pub const fn new(n: usize) -> Self

Trait Implementations

impl Clone for SpdManifold

fn clone(&self) -> SpdManifold

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Debug for SpdManifold

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

Formats the value using the given formatter.

impl Eq for SpdManifold

impl PartialEq for SpdManifold

fn eq(&self, other: &SpdManifold) -> bool

Tests for self and other values to be equal, and is used by ==.

fn ne(&self, other: &Rhs) -> bool

Tests for !=. The default implementation is almost always sufficient, and should not be overridden without very good reason.

impl RiemannianManifold for SpdManifold

fn tangent_basis( &self, point: ArrayView1<'_, f64>, ) -> GeometryResult<Array2<f64>>

Basis of the symmetric tangent space, orthonormal under the affine-invariant metric ⟨U,V⟩_P = tr(P⁻¹U P⁻¹V) (i.e. Qᵀ W Q = I with W = metric_tensor(point) = P⁻¹ ⊗ P⁻¹). The hand-rolled Frobenius-orthonormal basis used previously is orthonormal only under the embedded tr(UV) inner product, which is not the SPD metric off the identity point, so it produced a basis that did not satisfy Qᵀ W Q = I. We Gram–Schmidt the projected symmetric standard basis under W instead.

fn dim(&self) -> usize

fn ambient_dim(&self) -> usize

fn exp_map( &self, point: ArrayView1<'_, f64>, tangent_vec: ArrayView1<'_, f64>, ) -> GeometryResult<Array1<f64>>

fn log_map( &self, p_from: ArrayView1<'_, f64>, p_to: ArrayView1<'_, f64>, ) -> GeometryResult<Array1<f64>>

fn parallel_transport( &self, point_along: ArrayView2<'_, f64>, vec: ArrayView1<'_, f64>, ) -> GeometryResult<Array1<f64>>

fn metric_tensor( &self, point: ArrayView1<'_, f64>, ) -> GeometryResult<Array2<f64>>

fn christoffel_symbols( &self, point: ArrayView1<'_, f64>, ) -> GeometryResult<Vec<Array2<f64>>>

fn sectional_curvature( &self, point: ArrayView1<'_, f64>, tangent_pair: (ArrayView1<'_, f64>, ArrayView1<'_, f64>), ) -> GeometryResult<f64>

fn project_tangent( &self, point: ArrayView1<'_, f64>, vec: ArrayView1<'_, f64>, ) -> GeometryResult<Array1<f64>>

fn exp_map_vjp( &self, point: ArrayView1<'_, f64>, tangent_vec: ArrayView1<'_, f64>, grad_output: ArrayView1<'_, f64>, ) -> GeometryResult<(Array1<f64>, Array1<f64>)>

Vector–Jacobian product of the ambient map exp_p(v).

fn retract( &self, point: ArrayView1<'_, f64>, tangent_vec: ArrayView1<'_, f64>, ) -> GeometryResult<Array1<f64>>

impl StructuralPartialEq for SpdManifold