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* Support for Zygote and ReverseDiff gradients

* Add Zygote test dependency

* bump ambiguity limit because of Zygote

* fix tests and Zygote backend

* bump Julia to 1.5

* fixing some issues on Julia 1.7-rc1

* more fixing for Julia 1.7

* formatting

* reduce tangent vector length in a test

since the approximation only works very locally (and they changed the default random number generator)

* Update Project.toml

Co-authored-by: Ronny Bergmann <git@ronnybergmann.net>

* bump atol on Rotations

* reduce tangent vector size even further.

* adapt one more tolerance

Co-authored-by: Ronny Bergmann <git@ronnybergmann.net>
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Manifolds.jl
Documentation Source Citation
Code Style: Blue arXiv
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codecov.io

Package Manifolds.jl aims to provide both a unified interface to define and use manifolds as well as a library of manifolds to use for your projects. This package is under development, and subject to changes as needed.

Getting started

To install the package just type

] add Manifolds

Then you can directly start, for example to stop half way from the north pole on the Sphere to a point on the the equator, you can generate the shortest_geodesic. It internally employs exp and log.

using Manifolds
M = Sphere(2)
γ = shortest_geodesic(M, [0., 0., 1.], [0., 1., 0.])
γ(0.5)

Citation

If you use Manifolds.jl in your work, please cite the following

@online{2106.08777,
  Author = {Seth D. Axen and Mateusz Baran and Ronny Bergmann and Krzysztof Rzecki},
  Title = {Manifolds.jl: An Extensible {J}ulia Framework for Data Analysis on Manifolds},
  Year = {2021},
  Eprint = {2106.08777},
  Eprinttype = {arXiv},
}

To refer to a certain version we recommend to also cite for example

@softawre{manifoldsjl-zenodo-mostrecent,
  Author = {Seth D. Axen and Mateusz Baran and Ronny Bergmann},
  Title = {Manifolds.jl},
  Doi = {10.5281/ZENODO.4292129},
  Url = {https://zenodo.org/record/4292129},
  Publisher = {Zenodo},
  Year = {2021},
  Copyright = {MIT License}
}

for the most recent version or a corresponding version specific DOI, see the list of all versions. Note that both citations are in BibLaTeX format.

About

Manifolds.jl aims to provide both a unified interface to define and use manifolds as well as a library of manifolds to use for your projects.

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