Manifolds.jl
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Manifolds.jl provides a library of manifolds aiming for an easy-to-use and fast implementation.
Semi-Riemannian manifolds require different methods, see https://arxiv.org/abs/1812.07643 . * [ ] Finding ONBs, * [ ] indefinite orthogonal group, * [ ] pseudo-spheres, * [ ] pseudo-hyperbolic spaces, * [...
http://arxiv.org/abs/2103.12046 gives an efficient shooting algorithm (Alg 2) for computing the logarithmic map on the `Stiefel(n, k)` manifold for `n ≥ 2k` for a family of metrics that includes both...
This issue narrows the discussion in https://github.com/JuliaNLSolvers/Manifolds.jl/issues/3 to implementing distributions on Manifolds. It also continues some discussion from https://discourse.julialang.org/t/rfc-taking-directional-orientational-statistics-seriously/31951 and on the Slack channel. There are a few generic distributions...
I've accidentally found this paper about optimization on flag manifolds: https://www.stat.uchicago.edu/~lekheng/work/flag.pdf . I don't have time to read it right now but it may be interesting. cc @kellertuer
What do you think about getting an overview homepage at juliamanifolds.github.com ? We could (for a start) refer to the separate documentations (currently 2 but soon there will be more)...
The current solution only really works for metrics on the Euclidean space. I think we need ManifoldDiffEq for the generic case.
geomstats
I've just found this nice package for geometric statistics: https://github.com/geomstats/geomstats . It would be nice to look at how they do things, in particular there are a few things we...
Perhaps there already is a function to extract the rotation matrix from `SpecialOrthogonal(n)` or `Rotations(n)`? If not, would `affine_matrix` be the right API, since rotations can be implemented as a...
@jlumpe pointed out on slack that we don't have mutating variants of metric-related functions and it sounds like a very good idea. Functions: * [ ] `christoffel_symbols_first` * [ ]...
Hi, I just checked back, it seems there has been lots of activity on this project, great! Is it ready for prime time? In particular, can we replace Optim's implementation...