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README.md

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[![Anaconda Cloud](https://anaconda.org/conda-forge/pot/badges/version.svg)](https://anaconda.org/conda-forge/pot)
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[![Build Status](https://travis-ci.org/rflamary/POT.svg?branch=master)](https://travis-ci.org/rflamary/POT)
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[![Documentation Status](https://readthedocs.org/projects/pot/badge/?version=latest)](http://pot.readthedocs.io/en/latest/?badge=latest)
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[![Downloads](https://pepy.tech/badge/pot)](https://pepy.tech/project/pot)
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[![Anaconda downloads](https://anaconda.org/conda-forge/pot/badges/downloads.svg)](https://anaconda.org/conda-forge/pot)
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[![License](https://anaconda.org/conda-forge/pot/badges/license.svg)](https://github.com/rflamary/POT/blob/master/LICENSE)
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It provides the following solvers:
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* OT Network Flow solver for the linear program/ Earth Movers Distance [1].
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* Entropic regularization OT solver with Sinkhorn Knopp Algorithm [2] and stabilized version [9][10] with optional GPU implementation (requires cudamat).
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* Entropic regularization OT solver with Sinkhorn Knopp Algorithm [2], stabilized version [9][10] and greedy Sinkhorn [22] with optional GPU implementation (requires cupy).
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* Sinkhorn divergence [23] and entropic regularization OT from empirical data.
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* Smooth optimal transport solvers (dual and semi-dual) for KL and squared L2 regularizations [17].
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* Non regularized Wasserstein barycenters [16] with LP solver (only small scale).
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* Bregman projections for Wasserstein barycenter [3] and unmixing [4].
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* Bregman projections for Wasserstein barycenter [3], convolutional barycenter [21] and unmixing [4].
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* Optimal transport for domain adaptation with group lasso regularization [5]
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* Conditional gradient [6] and Generalized conditional gradient for regularized OT [7].
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* Linear OT [14] and Joint OT matrix and mapping estimation [8].
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* Wasserstein Discriminant Analysis [11] (requires autograd + pymanopt).
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* Gromov-Wasserstein distances and barycenters ([13] and regularized [12])
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* Stochastic Optimization for Large-scale Optimal Transport (semi-dual problem [18] and dual problem [19])
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* Non regularized free support Wasserstein barycenters [20].
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Some demonstrations (both in Python and Jupyter Notebook format) are available in the examples folder.
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Some sub-modules require additional dependences which are discussed below
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* **ot.dr** (Wasserstein dimensionality rediuction) depends on autograd and pymanopt that can be installed with:
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* **ot.dr** (Wasserstein dimensionality reduction) depends on autograd and pymanopt that can be installed with:
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```
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pip install pymanopt autograd
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```
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* **ot.gpu** (GPU accelerated OT) depends on cudamat that have to be installed with:
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```
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git clone https://github.com/cudamat/cudamat.git
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cd cudamat
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python setup.py install --user # for user install (no root)
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```
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* **ot.gpu** (GPU accelerated OT) depends on cupy that have to be installed following instructions on [this page](https://docs-cupy.chainer.org/en/stable/install.html).
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obviously you need CUDA installed and a compatible GPU.
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* [Stanislas Chambon](https://slasnista.github.io/)
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* [Antoine Rolet](https://arolet.github.io/)
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* Erwan Vautier (Gromov-Wasserstein)
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* [Kilian Fatras](https://kilianfatras.github.io/)
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* [Alain Rakotomamonjy](https://sites.google.com/site/alainrakotomamonjy/home)
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This toolbox benefit a lot from open source research and we would like to thank the following persons for providing some code (in various languages):
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ot/bregman.py

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# Nicolas Courty <ncourty@irisa.fr>
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# Kilian Fatras <kilian.fatras@irisa.fr>
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# Titouan Vayer <titouan.vayer@irisa.fr>
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#
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# License: MIT License
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import numpy as np

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