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manifold (version 0.1.2)

Operations for Riemannian Manifolds

Description

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) .

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Version

Install

install.packages('manifold')

Monthly Downloads

203

Version

0.1.2

License

GPL (>= 2)

Maintainer

Xiongtao Dai

Last Published

December 1st, 2025

Functions in manifold (0.1.2)

projectTangent.Euclidean

Project data points in the ambient space onto the tangent space

Generate uniform random variables on the unit sphere

rieLog.Euclidean

Riemannian logarithm map

Generate random variables on the manifold

Transform tangent vectors to their coordinates on the tangent space

rieExp.Euclidean

Riemannian exponential map

origin.Euclidean

Returns the origin of the manifold

project.Euclidean

Project data points in the ambient space onto the manifold

Norm on the tangent space induced by the Riemannian metric

Matrix logarithm

basisTan.Euclidean

Obtain an orthonormal basis on the tangent space

Normalize a vector

Matrix exponential

Returns the angle representation of SO(3) matrices c.f. https://en.wikipedia.org/wiki/Axis-angle_representation

Matrix logarithm of a symmetric positive definite

Make a symmetric matrix by specifying a near-symmetric matrix M, or the lower triangular elements lowerTri with diagonal.

Helper function for simulations

Transform the coordinates for the tangent space into a tangent vector

Create an object to symbolize the manifold.

Dimensions in this package

metric.Euclidean

Returns the Riemannian metric

Obtain the geodesic curve

Tell whether a manifold is a finite-dimensional one

distance.Euclidean

Geodesic distance

manifold: Operations for Riemannian manifolds

Calculate the Fréchet mean

Calculate the Fréchet median

List all available manifold names