[MRG] Solve bug of contribution link in docs + automated insert of readme in doc (#301)

* first try

* bug solve

* attempt to use m2r2

* More elegant dependency

* readme.rst now generated automatically from readme.md

* weird attempt

* Revert "weird attempt"

This reverts commit b45f0e6495148877ad3e93ad608b3b0cfe9bbb16.

* fixing readme links

* Revert "fixing readme links"

This reverts commit 0c6ca7612ea297674a3afc50f8e6538c58c27701.

* full link for readme

* correct CONTRIBUTING guidelines mistakes

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-POT: Python Optimal Transport
-=============================
-
-|PyPI version| |Anaconda Cloud| |Build Status| |Codecov Status|
-|Downloads| |Anaconda downloads| |License|
-
-This open source Python library provide several solvers for optimization
-problems related to Optimal Transport for signal, image processing and
-machine learning.
-
-Website and documentation: https://PythonOT.github.io/
-
-Source Code (MIT): https://github.com/PythonOT/POT
-
-POT provides the following generic OT solvers (links to examples):
-
--  `OT Network Simplex
-   solver <auto_examples/plot_OT_1D.html>`__
-   for the linear program/ Earth Movers Distance [1] .
--  `Conditional
-   gradient <auto_examples/plot_optim_OTreg.html>`__
-   [6] and `Generalized conditional
-   gradient <auto_examples/plot_optim_OTreg.html>`__
-   for regularized OT [7].
--  Entropic regularization OT solver with `Sinkhorn Knopp
-   Algorithm <auto_examples/plot_OT_1D.html>`__
-   [2] , stabilized version [9] [10] [34], greedy Sinkhorn [22] and
-   `Screening Sinkhorn
-   [26] <auto_examples/plot_screenkhorn_1D.html>`__.
--  Bregman projections for `Wasserstein
-   barycenter <auto_examples/barycenters/plot_barycenter_lp_vs_entropic.html>`__
-   [3], `convolutional
-   barycenter <auto_examples/barycenters/plot_convolutional_barycenter.html>`__
-   [21] and unmixing [4].
--  Sinkhorn divergence [23] and entropic regularization OT from
-   empirical data.
--  Debiased Sinkhorn barycenters `Sinkhorn divergence
-   barycenter <auto_examples/barycenters/plot_debiased_barycenter.html>`__
-   [37]
--  `Smooth optimal transport
-   solvers <auto_examples/plot_OT_1D_smooth.html>`__
-   (dual and semi-dual) for KL and squared L2 regularizations [17].
--  Non regularized `Wasserstein barycenters
-   [16] <auto_examples/barycenters/plot_barycenter_lp_vs_entropic.html>`__)
-   with LP solver (only small scale).
--  `Gromov-Wasserstein
-   distances <auto_examples/gromov/plot_gromov.html>`__
-   and `GW
-   barycenters <auto_examples/gromov/plot_gromov_barycenter.html>`__
-   (exact [13] and regularized [12]), differentiable using gradients
-   from
--  `Fused-Gromov-Wasserstein distances
-   solver <auto_examples/gromov/plot_fgw.html#sphx-glr-auto-examples-plot-fgw-py>`__
-   and `FGW
-   barycenters <auto_examples/gromov/plot_barycenter_fgw.html>`__
-   [24]
--  `Stochastic
-   solver <auto_examples/plot_stochastic.html>`__
-   for Large-scale Optimal Transport (semi-dual problem [18] and dual
-   problem [19])
--  `Stochastic solver of Gromov
-   Wasserstein <auto_examples/gromov/plot_gromov.html>`__
-   for large-scale problem with any loss functions [33]
--  Non regularized `free support Wasserstein
-   barycenters <auto_examples/barycenters/plot_free_support_barycenter.html>`__
-   [20].
--  `Unbalanced
-   OT <auto_examples/unbalanced-partial/plot_UOT_1D.html>`__
-   with KL relaxation and
-   `barycenter <auto_examples/unbalanced-partial/plot_UOT_barycenter_1D.html>`__
-   [10, 25].
--  `Partial Wasserstein and
-   Gromov-Wasserstein <auto_examples/unbalanced-partial/plot_partial_wass_and_gromov.html>`__
-   (exact [29] and entropic [3] formulations).
--  `Sliced
-   Wasserstein <auto_examples/sliced-wasserstein/plot_variance.html>`__
-   [31, 32] and Max-sliced Wasserstein [35] that can be used for
-   gradient flows [36].
--  `Several
-   backends <https://pythonot.github.io/quickstart.html#solving-ot-with-multiple-backends>`__
-   for easy use of POT with
-   `Pytorch <https://pytorch.org/>`__/`jax <https://github.com/google/jax>`__/`Numpy <https://numpy.org/>`__
-   arrays.
-
-POT provides the following Machine Learning related solvers:
-
--  `Optimal transport for domain
-   adaptation <auto_examples/domain-adaptation/plot_otda_classes.html>`__
-   with `group lasso
-   regularization <auto_examples/domain-adaptation/plot_otda_classes.html>`__,
-   `Laplacian
-   regularization <auto_examples/domain-adaptation/plot_otda_laplacian.html>`__
-   [5] [30] and `semi supervised
-   setting <auto_examples/domain-adaptation/plot_otda_semi_supervised.html>`__.
--  `Linear OT
-   mapping <auto_examples/domain-adaptation/plot_otda_linear_mapping.html>`__
-   [14] and `Joint OT mapping
-   estimation <auto_examples/domain-adaptation/plot_otda_mapping.html>`__
-   [8].
--  `Wasserstein Discriminant
-   Analysis <auto_examples/others/plot_WDA.html>`__
-   [11] (requires autograd + pymanopt).
--  `JCPOT algorithm for multi-source domain adaptation with target
-   shift <auto_examples/domain-adaptation/plot_otda_jcpot.html>`__
-   [27].
-
-Some other examples are available in the
-`documentation <auto_examples/index.html>`__.
-
-Using and citing the toolbox
-^^^^^^^^^^^^^^^^^^^^^^^^^^^^
-
-If you use this toolbox in your research and find it useful, please cite
-POT using the following reference from our `JMLR
-paper <https://jmlr.org/papers/v22/20-451.html>`__:
-
-::
-
-    Rémi Flamary, Nicolas Courty, Alexandre Gramfort, Mokhtar Z. Alaya, Aurélie Boisbunon, Stanislas Chambon, Laetitia Chapel, Adrien Corenflos, Kilian Fatras, Nemo Fournier, Léo Gautheron, Nathalie T.H. Gayraud, Hicham Janati, Alain Rakotomamonjy, Ievgen Redko, Antoine Rolet, Antony Schutz, Vivien Seguy, Danica J. Sutherland, Romain Tavenard, Alexander Tong, Titouan Vayer,
-    POT Python Optimal Transport library,
-    Journal of Machine Learning Research, 22(78):1−8, 2021.
-    Website: https://pythonot.github.io/
-
-In Bibtex format:
-
-.. code:: bibtex
-
-    @article{flamary2021pot,
-      author  = {R{\'e}mi Flamary and Nicolas Courty and Alexandre Gramfort and Mokhtar Z. Alaya and Aur{\'e}lie Boisbunon and Stanislas Chambon and Laetitia Chapel and Adrien Corenflos and Kilian Fatras and Nemo Fournier and L{\'e}o Gautheron and Nathalie T.H. Gayraud and Hicham Janati and Alain Rakotomamonjy and Ievgen Redko and Antoine Rolet and Antony Schutz and Vivien Seguy and Danica J. Sutherland and Romain Tavenard and Alexander Tong and Titouan Vayer},
-      title   = {POT: Python Optimal Transport},
-      journal = {Journal of Machine Learning Research},
-      year    = {2021},
-      volume  = {22},
-      number  = {78},
-      pages   = {1-8},
-      url     = {http://jmlr.org/papers/v22/20-451.html}
-    }
-
-Installation
-------------
-
-The library has been tested on Linux, MacOSX and Windows. It requires a
-C++ compiler for building/installing the EMD solver and relies on the
-following Python modules:
-
--  Numpy (>=1.16)
--  Scipy (>=1.0)
--  Cython (>=0.23) (build only, not necessary when installing from pip
-   or conda)
-
-Pip installation
-^^^^^^^^^^^^^^^^
-
-You can install the toolbox through PyPI with:
-
-.. code:: console
-
-    pip install POT
-
-or get the very latest version by running:
-
-.. code:: console
-
-    pip install -U https://github.com/PythonOT/POT/archive/master.zip # with --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:
-
-.. code:: console
-
-    conda install -c conda-forge pot
-
-Post installation check
-^^^^^^^^^^^^^^^^^^^^^^^
-
-After a correct installation, you should be able to import the module
-without errors:
-
-.. code:: python
-
-    import ot
-
-Note that for easier access the module is named ``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:
-
-.. code:: shell
-
-    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 will need CUDA installed and a compatible GPU. Note
-   that this module is deprecated since version 0.8 and will be deleted
-   in the future. GPU is now handled automatically through the backends
-   and several solver already can run on GPU using the Pytorch backend.
-
-Examples
---------
-
-Short examples
-~~~~~~~~~~~~~~
-
--  Import the toolbox
-
-.. code:: python
-
-    import ot
-
--  Compute Wasserstein distances
-
-.. code:: 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
-
-.. code:: 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
-
-.. code:: 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 with examples and output is available on
-https://PythonOT.github.io/.
-
-Acknowledgements
-----------------
-
-This toolbox has been created and is maintained by
-
--  `Rémi Flamary <http://remi.flamary.com/>`__
--  `Nicolas Courty <http://people.irisa.fr/Nicolas.Courty/>`__
-
-The contributors to this library are
-
--  `Alexandre Gramfort <http://alexandre.gramfort.net/>`__ (CI,
-   documentation)
--  `Laetitia Chapel <http://people.irisa.fr/Laetitia.Chapel/>`__
-   (Partial OT)
--  `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>`__
-   (DA classes)
--  `Stanislas Chambon <https://slasnista.github.io/>`__ (DA classes)
--  `Antoine Rolet <https://arolet.github.io/>`__ (EMD solver debug)
--  Erwan Vautier (Gromov-Wasserstein)
--  `Kilian Fatras <https://kilianfatras.github.io/>`__ (Stochastic
-   solvers)
--  `Alain
-   Rakotomamonjy <https://sites.google.com/site/alainrakotomamonjy/home>`__
--  `Vayer Titouan <https://tvayer.github.io/>`__ (Gromov-Wasserstein -,
-   Fused-Gromov-Wasserstein)
--  `Hicham Janati <https://hichamjanati.github.io/>`__ (Unbalanced OT,
-   Debiased barycenters)
--  `Romain Tavenard <https://rtavenar.github.io/>`__ (1d Wasserstein)
--  `Mokhtar Z. Alaya <http://mzalaya.github.io/>`__ (Screenkhorn)
--  `Ievgen Redko <https://ievred.github.io/>`__ (Laplacian DA, JCPOT)
--  `Adrien Corenflos <https://adriencorenflos.github.io/>`__ (Sliced
-   Wasserstein Distance)
--  `Tanguy Kerdoncuff <https://hv0nnus.github.io/>`__ (Sampled Gromov
-   Wasserstein)
--  `Minhui Huang <https://mhhuang95.github.io>`__ (Projection Robust
-   Wasserstein Distance)
-
-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)
--  `Mathieu Blondel <https://mblondel.org/>`__ (original implementation
-   smooth OT)
--  `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 <.github/CONTRIBUTING.md>`__. Each member of the project is
-expected to follow the `code of conduct <.github/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 `gitter channel <https://gitter.im/PythonOT/community>`__
--  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 <.github/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
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-
-[6] Ferradans, S., Papadakis, N., Peyré, G., & Aujol, J. F. (2014).
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-transport <https://arxiv.org/pdf/1307.5551.pdf>`__. SIAM Journal on
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-
-[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
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-
-[10] Chizat, L., Peyré, G., Schmitzer, B., & Vialard, F. X. (2016).
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-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
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-
-[12] Gabriel Peyré, Marco Cuturi, and Justin Solomon (2016),
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-[13] Mémoli, Facundo (2011). `Gromov–Wasserstein distances and the
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-[15] Peyré, G., & Cuturi, M. (2018). `Computational Optimal
-Transport <https://arxiv.org/pdf/1803.00567.pdf>`__ .
-
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-[17] Blondel, M., Seguy, V., & Rolet, A. (2018). `Smooth and Sparse
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-[18] Genevay, A., Cuturi, M., Peyré, G. & Bach, F. (2016) `Stochastic
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-
-[19] Seguy, V., Bhushan Damodaran, B., Flamary, R., Courty, N., Rolet,
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-
-[20] Cuturi, M. and Doucet, A. (2014) `Fast Computation of Wasserstein
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-[21] Solomon, J., De Goes, F., Peyré, G., Cuturi, M., Butscher, A.,
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-[23] Aude, G., Peyré, G., Cuturi, M., `Learning Generative Models with
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-[24] Vayer, T., Chapel, L., Flamary, R., Tavenard, R. and Courty, N.
-(2019). `Optimal Transport for structured data with application on
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-
-[27] Redko I., Courty N., Flamary R., Tuia D. (2019). `Optimal Transport
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-[28] Caffarelli, L. A., McCann, R. J. (2010). `Free boundaries in
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-
-[29] Chapel, L., Alaya, M., Gasso, G. (2020). `Partial Optimal Transport
-with Applications on Positive-Unlabeled
-Learning <https://arxiv.org/abs/2002.08276>`__, Advances in Neural
-Information Processing Systems (NeurIPS), 2020.
-
-[30] Flamary R., Courty N., Tuia D., Rakotomamonjy A. (2014). `Optimal
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-[31] Bonneel, Nicolas, et al. `Sliced and radon wasserstein barycenters
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-(ICML).
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-[34] Feydy, J., Séjourné, T., Vialard, F. X., Amari, S. I., Trouvé, A.,
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-MMD using Sinkhorn
-divergences <http://proceedings.mlr.press/v89/feydy19a/feydy19a.pdf>`__.
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-[35] Deshpande, I., Hu, Y. T., Sun, R., Pyrros, A., Siddiqui, N.,
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-[36] Liutkus, A., Simsekli, U., Majewski, S., Durmus, A., & Stöter, F.
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-
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