ls_mlkit.util.manifold.riemannian_manifold module

Riemannian Manifold

class ls_mlkit.util.manifold.riemannian_manifold.RiemannianManifold

Bases: ABC

Riemannian Manifold

abstractmethod exp(p, v)

Exponential map $$exp_p(v)$$ map a point in tangent space to a point on the manifold $$ T_p M to M $$

abstractmethod grad(f, p)

Gradient $$nabla_p f$$ is the gradient of $$f$$ at point $$p$$

abstractmethod log(p, q)

Logarithm map $$log_p(q)$$ map a point on the manifold to a point in tangent space $$ M to T_p M $$

abstractmethod metric(p, v, w)

Inner product $$<v, w>_p$$ is the inner product of $$v$$ and $$w$$ at point $$p$$

abstractmethod random_tangent(p, random_type='gaussian', std=1.0)

Sample noise in the tangent space at point p $$T_p M$$