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Geomstats is an open-source Python package for computations and statistics on manifolds. The package is organized into two main modules: geometry and learning.

The module geometry implements concepts in differential geometry, and the module learning implements statistics and learning algorithms for data on manifolds.

  • To get an overview of geomstats, see our introductory video.
  • To get started with geomstats, see the examples and notebooks directories.
  • The documentation of geomstats can be found on the documentation website.
  • If you find geomstats useful, please kindly cite our paper.
  • To follow the scientific literature on geometric statistics, follow our twitter-bot @geomstats-papers !

Install geomstats via pip3

From a terminal (OS X & Linux), you can install geomstats and its requirements with pip3 as follows:

pip3 install geomstats

This method installs the latest version of geomstats that is uploaded on PyPi. Note that geomstats is only available with Python3.

Install geomstats via Git

From a terminal (OS X & Linux), you can install geomstats and its requirements via git as follows:

git clone
pip3 install -r requirements.txt

This method installs the latest GitHub version of geomstats. Developers should install this version, together with the development requirements and the optional requirements to enable tensorflow and pytorch backends:

pip3 install -r dev-requirements.txt -r opt-requirements.txt

Choose the backend

Geomstats can run seemlessly with numpy, tensorflow or pytorch. Note that pytorch and tensorflow requirements are optional, as geomstats can be used with numpy only. By default, the numpy backend is used. The visualizations are only available with this backend.

To get the tensorflow and pytorch versions compatible with geomstats, install the optional requirements:

pip3 install -r opt-requirements.txt

You can choose your backend by setting the environment variable GEOMSTATS_BACKEND to numpy, tensorflow or pytorch, and importing the backend module. From the command line:

export GEOMSTATS_BACKEND=pytorch

and in the Python3 code:

import geomstats.backend as gs

Getting started

To use geomstats for learning algorithms on Riemannian manifolds, you need to follow three steps:

  • instantiate the manifold of interest,
  • instantiate the learning algorithm of interest,
  • run the algorithm.

The data should be represented by a gs.array. This structure represents numpy arrays, or tensorflow/pytorch tensors, depending on the choice of backend.

The following code snippet shows the use of tangent Principal Component Analysis on simulated data on the space of 3D rotations.

from geomstats.geometry.special_orthogonal import SpecialOrthogonal
from geomstats.learning.pca import TangentPCA

so3 = SpecialOrthogonal(n=3, point_type='vector')
metric = so3.bi_invariant_metric

data = so3.random_uniform(n_samples=10)

tpca = TangentPCA(metric=metric, n_components=2)
tpca =
tangent_projected_data = tpca.transform(data)

All geometric computations are performed behind the scenes. The user only needs a high-level understanding of Riemannian geometry. Each algorithm can be used with any of the manifolds and metric implemented in the package.

To see additional examples, go to the examples or notebooks directories.


See our contributing guidelines!


This work is supported by:

  • the Inria-Stanford associated team GeomStats,
  • the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation program (grant agreement G-Statistics No. 786854),
  • the French society for applied and industrial mathematics (SMAI),
  • the National Science Foundation (grant NSF DMS RTG 1501767).


Computations and statistics on manifolds with geometric structures.

Geomstats Info

⭐ Stars670
🔗 Source
🕒 Last Update10 months ago
🕒 Created5 years ago
🐞 Open Issues124
➗ Star-Issue Ratio5
😎 Authorgeomstats