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Manifolds.jl

swMATH ID: 39726
Software Authors: Seth D. Axen, Mateusz Baran, Ronny Bergmann, Krzysztof Rzecki
Description: Manifolds.jl: An Extensible Julia Framework for Data Analysis on Manifolds. For data given on a nonlinear space, like angles, symmetric positive matrices, the sphere, or the hyperbolic space, there is often enough structure to form a Riemannian manifold. We present the Julia package Manifolds.jl, providing a fast and easy to use library of Riemannian manifolds and Lie groups. We introduce a common interface, available in ManifoldsBase.jl, with which new manifolds, applications, and algorithms can be implemented. We demonstrate the utility of Manifolds.jl using BĂ©zier splines, an optimization task on manifolds, and a principal component analysis on nonlinear data. In a benchmark, Manifolds.jl outperforms existing packages in Matlab or Python by several orders of magnitude and is about twice as fast as a comparable package implemented in C++.
Homepage: https://juliamanifolds.github.io/Manifolds.jl/latest/
Source Code:  https://github.com/JuliaManifolds/Manifolds.jl
Keywords: Mathematical Software; arXiv_cs.MS; Manifolds.jl; Riemannian manifold; Lie group; nonlinear spaces; exponential map; logarithmic map; Julia; scientific computing; optimization on manifolds
Related Software: ROPTLIB; Pymanopt; Manopt; Julia; Manopt.jl; MVIRT; Geoopt; McTorch; geomstats
Cited in: 0 Publications

Standard Articles

1 Publication describing the Software Year
Manifolds.jl: An Extensible Julia Framework for Data Analysis on Manifolds
Seth D. Axen, Mateusz Baran, Ronny Bergmann, Krzysztof Rzecki
2021