PosDefManifold.jl

PosDefManifold is a Julia package for manipulating data in the manifold P of real or complex positive definite matrices. The package supports 10 metrics acting on P, four of which define Riemannian manifolds: the Fisher-Rao (affine-invariant), log-Euclidean, log-Cholesky and Wassertein metric.

This package computes distances, geodesics and weighted Fréchet means for the supported metrics, graph Laplacians, Lapacian eigen maps and a special solution of the Procrustes problem in P. Key functions are multi-threaded.

The documentation is rich and gives all mathematical details pertaining to the implemented functions (click the 'docs|stable' button).

For similar code resources in other programming languages see here.

To cite the package use: Congedo M, Jain S (2019) A Julia Package for manipulating Brain-Computer Interface Data in the Manifold of Positive Definite Matrices, Int IEEE Systems, Man and Cybernetics Conf.