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https://github.com/JuliaManifolds/Manifolds.jl
Manifolds.jl provides a library of manifolds aiming for an easy-to-use and fast implementation.
https://github.com/JuliaManifolds/Manifolds.jl
julia manifolds
Last synced: 27 days ago
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Manifolds.jl provides a library of manifolds aiming for an easy-to-use and fast implementation.
- Host: GitHub
- URL: https://github.com/JuliaManifolds/Manifolds.jl
- Owner: JuliaManifolds
- License: mit
- Created: 2019-06-05T18:27:27.000Z (about 5 years ago)
- Default Branch: master
- Last Pushed: 2024-05-07T11:53:12.000Z (about 2 months ago)
- Last Synced: 2024-05-08T07:32:18.915Z (about 2 months ago)
- Topics: julia, manifolds
- Language: Julia
- Homepage: https://juliamanifolds.github.io/Manifolds.jl
- Size: 53 MB
- Stars: 354
- Watchers: 13
- Forks: 51
- Open Issues: 50
-
Metadata Files:
- Readme: README.md
- Contributing: CONTRIBUTING.md
- License: LICENSE
- Citation: CITATION.bib
Lists
- awesome-stars - JuliaManifolds/Manifolds.jl - Manifolds.jl provides a library of manifolds aiming for an easy-to-use and fast implementation. (Julia)
README
| **Documentation** | **Source** | **Citation** |
|:-----------------:|:----------------------:|:------------:|
| [](https://juliamanifolds.github.io/Manifolds.jl/stable/) | [](https://github.com/invenia/BlueStyle) | [](https://arxiv.org/abs/2106.08777) |
| [](https://juliamanifolds.github.io/Manifolds.jl/latest/) | [](https://github.com/JuliaManifolds/Manifolds.jl/actions?query=workflow%3ACI+branch%3Amaster) | [](https://zenodo.org/badge/latestdoi/190447542) |
| | [](https://codecov.io/gh/JuliaManifolds/Manifolds.jl/) |
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 mostly stable, see https://github.com/JuliaManifolds/Manifolds.jl/issues/438 for planned upcoming changes.
## Getting started
To install the package just type
```julia
using Pkg; Pkg.add("Manifolds")
```
Then you can directly start, for example to stop half way from the north pole on the [`Sphere`](https://juliamanifolds.github.io/Manifolds.jl/stable/manifolds/sphere.html) to a point on the equator, you can generate the [`shortest_geodesic`](https://juliamanifolds.github.io/ManifoldsBase.jl/stable/functions.html#ManifoldsBase.shortest_geodesic-Tuple{AbstractManifold,%20Any,%20Any}).
It internally employs [`exp`](https://juliamanifolds.github.io/ManifoldsBase.jl/stable/functions.html#Base.exp-Tuple{AbstractManifold,%20Any,%20Any}) and [`log`](https://juliamanifolds.github.io/ManifoldsBase.jl/stable/functions.html#Base.log-Tuple{AbstractManifold,%20Any,%20Any}).
```julia
using Manifolds
M = Sphere(2)
γ = shortest_geodesic(M, [0., 0., 1.], [0., 1., 0.])
γ(0.5)
```
## Ecosystem highlights
* A wide selection of Riemannian manifolds like spheres, hyperbolic spaces, Stiefel and Grassmann manifolds.
* Support for optimization on manifolds using [Manopt.jl](https://github.com/JuliaManifolds/Manopt.jl/).
* Support for many operations used in optimization and manifold-valued statistics with a focus on performance and ease of use.
* Connection manifolds.
* Lie groups.
* Atlases, charts and custom metrics (work in progress).
* A lightweight interface package: [ManifoldsBase.jl](https://github.com/JuliaManifolds/ManifoldsBase.jl).
* Differential equations on manifolds: [ManifoldDiffEq.jl](https://github.com/JuliaManifolds/ManifoldDiffEq.jl).
* Finite differences and automatic differentiation on manifolds using [ManifoldDiff.jl](https://github.com/JuliaManifolds/ManifoldDiff.jl) (work in progress).
* Integration and measures on manifolds: [ManifoldMeasures.jl](https://github.com/JuliaManifolds/ManifoldMeasures.jl) (work in progress).
* Functional manifolds: [FunManifolds.jl](https://github.com/JuliaManifolds/FunManifolds.jl) (work in progress).
## Support
If you have any questions regarding the Manifolds.jl ecosystem feel free to reach us using [Github discussion forums](https://github.com/JuliaManifolds/Manifolds.jl/discussions), [Julia Slack](https://julialang.org/slack/), [Julia Zulip](https://julialang.zulipchat.com/) or [Julia discourse](https://discourse.julialang.org/) forums. We are interested in new applications and methods on manifolds -- sharing your work is welcome!
## Citation
If you use `Manifolds.jl` in your work, please cite the following open access article
```biblatex
@article{AxenBaranBergmannRzecki:2023,
AUTHOR = {Axen, Seth D. and Baran, Mateusz and Bergmann, Ronny and Rzecki, Krzysztof},
ARTICLENO = {33},
DOI = {10.1145/3618296},
JOURNAL = {ACM Transactions on Mathematical Software},
MONTH = {dec},
NUMBER = {4},
TITLE = {Manifolds.Jl: An Extensible Julia Framework for Data Analysis on Manifolds},
VOLUME = {49},
YEAR = {2023}
}
```
To refer to a certain version we recommend to also cite for example
```biblatex
@software{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](https://zenodo.org/search?page=1&size=20&q=conceptrecid:%224292129%22&sort=-version&all_versions=True).
Note that both citations are in [BibLaTeX](https://ctan.org/pkg/biblatex) format.