Operations for Riemannian Manifolds
Returns the angle representation of SO(3) matrices c.f. [https://en.wi...
Obtain an orthonormal basis on the tangent space
Transform the coordinates for the tangent space into a tangent vector
Create an object to symbolize the manifold.
Dimensions in this package
Geodesic distance
Matrix exponential
Calculate the Fréchet mean
Calculate the Fréchet median
Obtain the geodesic curve
Helper function for simulations
Tell whether a manifold is a finite-dimensional one
List all available manifold names
Matrix logarithm
Matrix logarithm of a symmetric positive definite
Make a symmetric matrix by specifying a near-symmetric matrix M, or th...
manifold: Operations for Riemannian manifolds
Returns the Riemannian metric
Norm on the tangent space induced by the Riemannian metric
Normalize a vector
Returns the origin of the manifold
Project data points in the ambient space onto the manifold
Project data points in the ambient space onto the tangent space
Riemannian exponential map
Riemannian logarithm map
Generate random variables on the manifold
Generate uniform random variables on the unit sphere
Transform tangent vectors to their coordinates on the tangent space
Implements operations for Riemannian manifolds, e.g., geodesic distance, Riemannian metric, exponential and logarithm maps, etc. Also incorporates random object generator on the manifolds. See Dai, Lin, and Müller (2021) <doi:10.1111/biom.13385>.