Metadata-Version: 2.1
Name: POT
Version: 0.5.1
Summary: Python Optimal Transport Library
Home-page: https://github.com/rflamary/POT
Author: Remi Flamary, Nicolas Courty
Author-email: remi.flamary@gmail.com, ncourty@gmail.com
License: MIT
Download-URL: https://github.com/rflamary/POT/archive/0.5.1.tar.gz
Description: # POT: Python Optimal Transport
        
        [![PyPI version](https://badge.fury.io/py/POT.svg)](https://badge.fury.io/py/POT)
        [![Anaconda Cloud](https://anaconda.org/conda-forge/pot/badges/version.svg)](https://anaconda.org/conda-forge/pot)
        [![Build Status](https://travis-ci.org/rflamary/POT.svg?branch=master)](https://travis-ci.org/rflamary/POT)
        [![Documentation Status](https://readthedocs.org/projects/pot/badge/?version=latest)](http://pot.readthedocs.io/en/latest/?badge=latest)
        [![Downloads](https://pepy.tech/badge/pot)](https://pepy.tech/project/pot)
        [![Anaconda downloads](https://anaconda.org/conda-forge/pot/badges/downloads.svg)](https://anaconda.org/conda-forge/pot)
        [![License](https://anaconda.org/conda-forge/pot/badges/license.svg)](https://github.com/rflamary/POT/blob/master/LICENSE)
        
        
        
        This open source Python library provide several solvers for optimization problems related to Optimal Transport for signal, image processing and machine learning.
        
        It provides the following solvers:
        
        * OT Network Flow solver for the linear program/ Earth Movers Distance [1].
        * Entropic regularization OT solver with Sinkhorn Knopp Algorithm [2] and stabilized version [9][10] and greedy SInkhorn [22] with optional GPU implementation (requires cupy).
        * Smooth optimal transport solvers (dual and semi-dual) for KL and squared L2 regularizations [17].
        * Non regularized Wasserstein barycenters [16] with LP solver (only small scale).
        * Bregman projections for Wasserstein barycenter [3], convolutional barycenter [21] and unmixing [4].
        * Optimal transport for domain adaptation with group lasso regularization [5]
        * Conditional gradient [6] and Generalized conditional gradient for regularized OT [7].
        * Linear OT [14] and Joint OT matrix and mapping estimation [8].
        * Wasserstein Discriminant Analysis [11] (requires autograd + pymanopt).
        * Gromov-Wasserstein distances and barycenters ([13] and regularized [12])
        * Stochastic Optimization for Large-scale Optimal Transport (semi-dual problem [18] and dual problem [19])
        * Non regularized free support Wasserstein barycenters [20].
        
        Some demonstrations (both in Python and Jupyter Notebook format) are available in the examples folder.
        
        #### Using and citing the toolbox
        
        If you use this toolbox in your research and find it useful, please cite POT using the following bibtex reference:
        ```
        @misc{flamary2017pot,
        title={POT Python Optimal Transport library},
        author={Flamary, R{'e}mi and Courty, Nicolas},
        url={https://github.com/rflamary/POT},
        year={2017}
        }
        ```
        
        ## Installation
        
        The library has been tested on Linux, MacOSX and Windows. It requires a C++ compiler for using the EMD solver and relies on the following Python modules:
        
        - Numpy (>=1.11)
        - Scipy (>=1.0)
        - Cython (>=0.23)
        - Matplotlib (>=1.5)
        
        #### Pip installation
        
        You can install the toolbox through PyPI with:
        ```
        pip install POT
        ```
        or get the very latest version by downloading it and then running:
        ```
        python setup.py install --user # for user install (no root)
        ```
        
        #### Anaconda installation with conda-forge
        
        If you use the Anaconda python distribution, POT is available in [conda-forge](https://conda-forge.org). To install it and the required dependencies:
        ```
        conda install -c conda-forge pot
        ```
        
        #### Post installation check
        After a correct installation, you should be able to import the module without errors:
        ```python
        import ot
        ```
        Note that for easier access the module is name ot instead of pot.
        
        
        ### Dependencies
        
        Some sub-modules require additional dependences which are discussed below
        
        * **ot.dr** (Wasserstein dimensionality reduction) depends on autograd and pymanopt that can be installed with:
        ```
        pip install pymanopt autograd
        ```
        * **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).
        
        
        obviously you need CUDA installed and a compatible GPU.
        
        ## Examples
        
        ### Short examples
        
        * Import the toolbox
        ```python
        import ot
        ```
        * Compute Wasserstein distances
        ```python
        # a,b are 1D histograms (sum to 1 and positive)
        # M is the ground cost matrix
        Wd=ot.emd2(a,b,M) # exact linear program
        Wd_reg=ot.sinkhorn2(a,b,M,reg) # entropic regularized OT
        # if b is a matrix compute all distances to a and return a vector
        ```
        * Compute OT matrix
        ```python
        # a,b are 1D histograms (sum to 1 and positive)
        # M is the ground cost matrix
        T=ot.emd(a,b,M) # exact linear program
        T_reg=ot.sinkhorn(a,b,M,reg) # entropic regularized OT
        ```
        * Compute Wasserstein barycenter
        ```python
        # A is a n*d matrix containing d  1D histograms
        # M is the ground cost matrix
        ba=ot.barycenter(A,M,reg) # reg is regularization parameter
        ```
        
        
        
        
        ### Examples and Notebooks
        
        The examples folder contain several examples and use case for the library. The full documentation is available on [Readthedocs](http://pot.readthedocs.io/).
        
        
        Here is a list of the Python notebooks available [here](https://github.com/rflamary/POT/blob/master/notebooks/) if you want a quick look:
        
        * [1D optimal transport](https://github.com/rflamary/POT/blob/master/notebooks/plot_OT_1D.ipynb)
        * [OT Ground Loss](https://github.com/rflamary/POT/blob/master/notebooks/plot_OT_L1_vs_L2.ipynb)
        * [Multiple EMD computation](https://github.com/rflamary/POT/blob/master/notebooks/plot_compute_emd.ipynb)
        * [2D optimal transport on empirical distributions](https://github.com/rflamary/POT/blob/master/notebooks/plot_OT_2D_samples.ipynb)
        * [1D Wasserstein barycenter](https://github.com/rflamary/POT/blob/master/notebooks/plot_barycenter_1D.ipynb)
        * [OT with user provided regularization](https://github.com/rflamary/POT/blob/master/notebooks/plot_optim_OTreg.ipynb)
        * [Domain adaptation with optimal transport](https://github.com/rflamary/POT/blob/master/notebooks/plot_otda_d2.ipynb)
        * [Color transfer in images](https://github.com/rflamary/POT/blob/master/notebooks/plot_otda_color_images.ipynb)
        * [OT mapping estimation for domain adaptation](https://github.com/rflamary/POT/blob/master/notebooks/plot_otda_mapping.ipynb)
        * [OT mapping estimation for color transfer in images](https://github.com/rflamary/POT/blob/master/notebooks/plot_otda_mapping_colors_images.ipynb)
        * [Wasserstein Discriminant Analysis](https://github.com/rflamary/POT/blob/master/notebooks/plot_WDA.ipynb)
        * [Gromov Wasserstein](https://github.com/rflamary/POT/blob/master/notebooks/plot_gromov.ipynb)
        * [Gromov Wasserstein Barycenter](https://github.com/rflamary/POT/blob/master/notebooks/plot_gromov_barycenter.ipynb)
        
        
        
        You can also see the notebooks with [Jupyter nbviewer](https://nbviewer.jupyter.org/github/rflamary/POT/tree/master/notebooks/).
        
        ## Acknowledgements
        
        The contributors to this library are:
        
        * [Rémi Flamary](http://remi.flamary.com/)
        * [Nicolas Courty](http://people.irisa.fr/Nicolas.Courty/)
        * [Alexandre Gramfort](http://alexandre.gramfort.net/)
        * [Laetitia Chapel](http://people.irisa.fr/Laetitia.Chapel/)
        * [Michael Perrot](http://perso.univ-st-etienne.fr/pem82055/) (Mapping estimation)
        * [Léo Gautheron](https://github.com/aje) (GPU implementation)
        * [Nathalie Gayraud](https://www.linkedin.com/in/nathalie-t-h-gayraud/?ppe=1)
        * [Stanislas Chambon](https://slasnista.github.io/)
        * [Antoine Rolet](https://arolet.github.io/)
        * Erwan Vautier (Gromov-Wasserstein)
        * [Kilian Fatras](https://kilianfatras.github.io/)
        * [Alain Rakotomamonjy](https://sites.google.com/site/alainrakotomamonjy/home)
        
        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):
        
        * [Gabriel Peyré](http://gpeyre.github.io/) (Wasserstein Barycenters in Matlab)
        * [Nicolas Bonneel](http://liris.cnrs.fr/~nbonneel/) ( C++ code for EMD)
        * [Marco Cuturi](http://marcocuturi.net/) (Sinkhorn Knopp in Matlab/Cuda)
        
        
        ## Contributions and code of conduct
        
        Every contribution is welcome and should respect the [contribution guidelines](CONTRIBUTING.md). Each member of the project is expected to follow the [code of conduct](CODE_OF_CONDUCT.md).
        
        ## Support
        
        You can ask questions and join the development discussion:
        
        * On the [POT Slack channel](https://pot-toolbox.slack.com)
        * On the POT [mailing list](https://mail.python.org/mm3/mailman3/lists/pot.python.org/)
        
        
        You can also post bug reports and feature requests in Github issues. Make sure to read our [guidelines](CONTRIBUTING.md) first.
        
        ## References
        
        [1] Bonneel, N., Van De Panne, M., Paris, S., & Heidrich, W. (2011, December). [Displacement interpolation using Lagrangian mass transport](https://people.csail.mit.edu/sparis/publi/2011/sigasia/Bonneel_11_Displacement_Interpolation.pdf). In ACM Transactions on Graphics (TOG) (Vol. 30, No. 6, p. 158). ACM.
        
        [2] Cuturi, M. (2013). [Sinkhorn distances: Lightspeed computation of optimal transport](https://arxiv.org/pdf/1306.0895.pdf). In Advances in Neural Information Processing Systems (pp. 2292-2300).
        
        [3] Benamou, J. D., Carlier, G., Cuturi, M., Nenna, L., & Peyré, G. (2015). [Iterative Bregman projections for regularized transportation problems](https://arxiv.org/pdf/1412.5154.pdf). SIAM Journal on Scientific Computing, 37(2), A1111-A1138.
        
        [4] S. Nakhostin, N. Courty, R. Flamary, D. Tuia, T. Corpetti, [Supervised planetary unmixing with optimal transport](https://hal.archives-ouvertes.fr/hal-01377236/document), Whorkshop on Hyperspectral Image and Signal Processing : Evolution in Remote Sensing (WHISPERS), 2016.
        
        [5] N. Courty; R. Flamary; D. Tuia; A. Rakotomamonjy, [Optimal Transport for Domain Adaptation](https://arxiv.org/pdf/1507.00504.pdf), in IEEE Transactions on Pattern Analysis and Machine Intelligence , vol.PP, no.99, pp.1-1
        
        [6] Ferradans, S., Papadakis, N., Peyré, G., & Aujol, J. F. (2014). [Regularized discrete optimal transport](https://arxiv.org/pdf/1307.5551.pdf). SIAM Journal on Imaging Sciences, 7(3), 1853-1882.
        
        [7] Rakotomamonjy, A., Flamary, R., & Courty, N. (2015). [Generalized conditional gradient: analysis of convergence and applications](https://arxiv.org/pdf/1510.06567.pdf). arXiv preprint arXiv:1510.06567.
        
        [8] M. Perrot, N. Courty, R. Flamary, A. Habrard (2016), [Mapping estimation for discrete optimal transport](http://remi.flamary.com/biblio/perrot2016mapping.pdf), Neural Information Processing Systems (NIPS).
        
        [9] Schmitzer, B. (2016). [Stabilized Sparse Scaling Algorithms for Entropy Regularized Transport Problems](https://arxiv.org/pdf/1610.06519.pdf). arXiv preprint arXiv:1610.06519.
        
        [10] Chizat, L., Peyré, G., Schmitzer, B., & Vialard, F. X. (2016). [Scaling algorithms for unbalanced transport problems](https://arxiv.org/pdf/1607.05816.pdf). arXiv preprint arXiv:1607.05816.
        
        [11] Flamary, R., Cuturi, M., Courty, N., & Rakotomamonjy, A. (2016). [Wasserstein Discriminant Analysis](https://arxiv.org/pdf/1608.08063.pdf). arXiv preprint arXiv:1608.08063.
        
        [12] Gabriel Peyré, Marco Cuturi, and Justin Solomon (2016), [Gromov-Wasserstein averaging of kernel and distance matrices](http://proceedings.mlr.press/v48/peyre16.html)  International Conference on Machine Learning (ICML).
        
        [13] Mémoli, Facundo (2011). [Gromov–Wasserstein distances and the metric approach to object matching](https://media.adelaide.edu.au/acvt/Publications/2011/2011-Gromov%E2%80%93Wasserstein%20Distances%20and%20the%20Metric%20Approach%20to%20Object%20Matching.pdf). Foundations of computational mathematics 11.4 : 417-487.
        
        [14] Knott, M. and Smith, C. S. (1984).[On the optimal mapping of distributions](https://link.springer.com/article/10.1007/BF00934745), Journal of Optimization Theory and Applications Vol 43.
        
        [15] Peyré, G., & Cuturi, M. (2018). [Computational Optimal Transport](https://arxiv.org/pdf/1803.00567.pdf) .
        
        [16] Agueh, M., & Carlier, G. (2011). [Barycenters in the Wasserstein space](https://hal.archives-ouvertes.fr/hal-00637399/document). SIAM Journal on Mathematical Analysis, 43(2), 904-924.
        
        [17] Blondel, M., Seguy, V., & Rolet, A. (2018). [Smooth and Sparse Optimal Transport](https://arxiv.org/abs/1710.06276). Proceedings of the Twenty-First International Conference on Artificial Intelligence and Statistics (AISTATS).
        
        [18] Genevay, A., Cuturi, M., Peyré, G. & Bach, F. (2016) [Stochastic Optimization for Large-scale Optimal Transport](https://arxiv.org/abs/1605.08527). Advances in Neural Information Processing Systems (2016).
        
        [19] Seguy, V., Bhushan Damodaran, B., Flamary, R., Courty, N., Rolet, A.& Blondel, M. [Large-scale Optimal Transport and Mapping Estimation](https://arxiv.org/pdf/1711.02283.pdf). International Conference on Learning Representation (2018)
        
        [20] Cuturi, M. and Doucet, A. (2014) [Fast Computation of Wasserstein Barycenters](http://proceedings.mlr.press/v32/cuturi14.html). International Conference in Machine Learning
        
        [21] Solomon, J., De Goes, F., Peyré, G., Cuturi, M., Butscher, A., Nguyen, A. & Guibas, L. (2015). [Convolutional wasserstein distances: Efficient optimal transportation on geometric domains](https://dl.acm.org/citation.cfm?id=2766963). ACM Transactions on Graphics (TOG), 34(4), 66.
        
        [22] J. Altschuler, J.Weed, P. Rigollet, (2017) [Near-linear time approximation algorithms for optimal transport via Sinkhorn iteration](https://papers.nips.cc/paper/6792-near-linear-time-approximation-algorithms-for-optimal-transport-via-sinkhorn-iteration.pdf), Advances in Neural Information Processing Systems (NIPS) 31
        
Platform: linux
Platform: macosx
Platform: windows
Classifier: Development Status :: 4 - Beta
Classifier: Intended Audience :: Developers
Classifier: Environment :: Console
Classifier: Operating System :: OS Independent
Classifier: Operating System :: MacOS
Classifier: Operating System :: POSIX
Classifier: Programming Language :: Python
Classifier: Topic :: Utilities
Classifier: Programming Language :: Python :: 2
Classifier: Programming Language :: Python :: 2.7
Classifier: Programming Language :: Python :: 3
Classifier: Programming Language :: Python :: 3.4
Classifier: Programming Language :: Python :: 3.5
Classifier: Programming Language :: Python :: 3.6
Requires: numpy
Requires: scipy
Requires: cython
Requires: matplotlib
Description-Content-Type: text/markdown
