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Commit d121bf8

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[MRG] Update doc and exemples (#754)
* update readme * big reoganization of exmaples * documenttaion withe xmaple in multiple sections * add all chnages * add all chnages * add bure bary to gaussian section * other example * fix readme links * update readme * change coot imahe
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‎CONTRIBUTORS.md‎

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## Contributors
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<a href="https://github.com/PythonOT/POT/graphs/contributors">
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<img src="https://contrib.rocks/image?repo=PythonOT/POT" />
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</a>
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The contributors to this library are:
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* [Rémi Flamary](http://remi.flamary.com/) (EMD wrapper, Pytorch backend, DA
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* [Julie Delon](https://judelo.github.io/) (GMM OT)
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* [Samuel Boïté](https://samuelbx.github.io/) (GMM OT)
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## Acknowledgments
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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):

‎README.md‎

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Website and documentation: [https://PythonOT.github.io/](https://PythonOT.github.io/)
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Source Code (MIT): [https://github.com/PythonOT/POT](https://github.com/PythonOT/POT)
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Source Code (MIT):
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[https://github.com/PythonOT/POT](https://github.com/PythonOT/POT)
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POT provides the following generic OT solvers (links to examples):
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POT has the following main features:
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* A large set of differentiable solvers for optimal transport problems, including:
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* Exact linear OT, entropic and quadratic regularized OT,
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* Gromov-Wasserstein (GW) distances, Fused GW distances and variants of
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quadratic OT,
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* Unbalanced and partial OT for different divergences,
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* OT barycenters (Wasserstein and GW) for fixed and free support,
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* Fast OT solvers in 1D, on the circle and between Gaussian Mixture Models (GMMs),
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* Many ML related solvers, such as domain adaptation, optimal transport mapping
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estimation, subspace learning, Graph Neural Networks (GNNs) layers.
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* Several backends for easy use with Pytorch, Jax, Tensorflow, Numpy and Cupy arrays.
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### Implemented Features
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POT provides the following generic OT solvers:
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* [OT Network Simplex solver](https://pythonot.github.io/auto_examples/plot_OT_1D.html) for the linear program/ Earth Movers Distance [1] .
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* [Conditional gradient](https://pythonot.github.io/auto_examples/plot_optim_OTreg.html) [6] and [Generalized conditional gradient](https://pythonot.github.io/auto_examples/plot_optim_OTreg.html) for regularized OT [7].
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* Entropic regularization OT solver with [Sinkhorn Knopp
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Algorithm](https://pythonot.github.io/auto_examples/plot_OT_1D.html) [2] ,
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stabilized version [9] [10] [34], lazy CPU/GPU solver from geomloss [60] [61], greedy Sinkhorn [22] and [Screening
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Sinkhorn [26]
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](https://pythonot.github.io/auto_examples/plot_screenkhorn_1D.html).
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stabilized version [9] [10] [34], lazy CPU/GPU solver from geomloss [60] [61], greedy Sinkhorn [22] and Screening
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Sinkhorn [26].
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* Bregman projections for [Wasserstein barycenter](https://pythonot.github.io/auto_examples/barycenters/plot_barycenter_lp_vs_entropic.html) [3], [convolutional barycenter](https://pythonot.github.io/auto_examples/barycenters/plot_convolutional_barycenter.html) [21] and unmixing [4].
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* Sinkhorn divergence [23] and entropic regularization OT from empirical data.
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* Debiased Sinkhorn barycenters [Sinkhorn divergence barycenter](https://pythonot.github.io/auto_examples/barycenters/plot_debiased_barycenter.html) [37]
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* [Smooth optimal transport solvers](https://pythonot.github.io/auto_examples/plot_OT_1D_smooth.html) (dual and semi-dual) for KL and squared L2 regularizations [17].
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* Smooth optimal transport solvers (dual and semi-dual) for KL and squared L2 regularizations [17].
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* Weak OT solver between empirical distributions [39]
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* Non regularized [Wasserstein barycenters [16] ](https://pythonot.github.io/auto_examples/barycenters/plot_barycenter_lp_vs_entropic.html) with LP solver (only small scale).
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* [Gromov-Wasserstein distances](https://pythonot.github.io/auto_examples/gromov/plot_gromov.html) and [GW barycenters](https://pythonot.github.io/auto_examples/gromov/plot_gromov_barycenter.html) (exact [13] and regularized [12,51]), differentiable using gradients from Graph Dictionary Learning [38]
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* [One dimensional Unbalanced OT](https://pythonot.github.io/auto_examples/unbalanced-partial/plot_UOT_1D.html) with KL relaxation and [barycenter](https://pythonot.github.io/auto_examples/unbalanced-partial/plot_UOT_barycenter_1D.html) [10, 25]. Also [exact unbalanced OT](https://pythonot.github.io/auto_examples/unbalanced-partial/plot_unbalanced_ot.html) with KL and quadratic regularization and the [regularization path of UOT](https://pythonot.github.io/auto_examples/unbalanced-partial/plot_regpath.html) [41]
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* [Partial Wasserstein and Gromov-Wasserstein](https://pythonot.github.io/auto_examples/unbalanced-partial/plot_partial_wass_and_gromov.html) and [Partial Fused Gromov-Wasserstein](https://pythonot.github.io/auto_examples/gromov/plot_partial_fgw.html) (exact [29] and entropic [3] formulations).
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* [Sliced Wasserstein](https://pythonot.github.io/auto_examples/sliced-wasserstein/plot_variance.html) [31, 32] and Max-sliced Wasserstein [35] that can be used for gradient flows [36].
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* [Wasserstein distance on the circle](https://pythonot.github.io/auto_examples/plot_compute_wasserstein_circle.html) [44, 45]
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* [Spherical Sliced Wasserstein](https://pythonot.github.io/auto_examples/sliced-wasserstein/plot_variance_ssw.html) [46]
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* [Wasserstein distance on the
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circle](https://pythonot.github.io/auto_examples/sliced-wasserstein/plot_compute_wasserstein_circle.html)
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[44, 45] and [Spherical Sliced Wasserstein](https://pythonot.github.io/auto_examples/sliced-wasserstein/plot_variance_ssw.html) [46]
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* [Graph Dictionary Learning solvers](https://pythonot.github.io/auto_examples/gromov/plot_gromov_wasserstein_dictionary_learning.html) [38].
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* [Semi-relaxed (Fused) Gromov-Wasserstein divergences](https://pythonot.github.io/auto_examples/gromov/plot_semirelaxed_fgw.html) with corresponding [barycenter solvers](https://pythonot.github.io/auto_examples/gromov/plot_semirelaxed_gromov_wasserstein_barycenter.hmtl) (exact and regularized [48]).
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* [Quantized (Fused) Gromov-Wasserstein distances](https://pythonot.github.io/auto_examples/gromov/plot_quantized_gromov_wasserstein.html) [68].
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* [Efficient Discrete Multi Marginal Optimal Transport Regularization](https://pythonot.github.io/auto_examples/others/plot_demd_gradient_minimize.html) [50].
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* [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/)/[Cupy](https://cupy.dev/)/[Tensorflow](https://www.tensorflow.org/) arrays.
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* [Smooth Strongly Convex Nearest Brenier Potentials](https://pythonot.github.io/auto_examples/others/plot_SSNB.html#sphx-glr-auto-examples-others-plot-ssnb-py) [58], with an extension to bounding potentials using [59].
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* [Gaussian Mixture Model OT](https://pythonot.github.io/auto_examples/others/plot_GMMOT_plan.html#sphx-glr-auto-examples-others-plot-gmmot-plan-py) [69].
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* [Gaussian Mixture Model OT](https://pythonot.github.io/auto_examples/gaussian_gmm/plot_GMMOT_plan.html#sphx-glr-auto-examples-others-plot-gmmot-plan-py) [69].
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* [Co-Optimal Transport](https://pythonot.github.io/auto_examples/others/plot_COOT.html) [49] and
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[unbalanced Co-Optimal Transport](https://pythonot.github.io/auto_examples/others/plot_learning_weights_with_COOT.html) [71].
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* Fused unbalanced Gromov-Wasserstein [70].
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```python
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# a,b are 1D histograms (sum to 1 and positive)
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# M is the ground cost matrix
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# With the unified API :
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Wd = ot.solve(M, a, b).value # exact linear program
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Wd_reg = ot.solve(M, a, b, reg=reg).value # entropic regularized OT
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# With the old API :
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Wd = ot.emd2(a, b, M) # exact linear program
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Wd_reg = ot.sinkhorn2(a, b, M, reg) # entropic regularized OT
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# if b is a matrix compute all distances to a and return a vector
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```python
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# With the unified API :
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T = ot.solve(M, a, b).plan # exact linear program
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T_reg = ot.solve(M, a, b, reg=reg).plan # entropic regularized OT
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# With the old API :
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T = ot.emd(a, b, M) # exact linear program
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T_reg = ot.sinkhorn(a, b, M, reg) # entropic regularized OT
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```
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* Compute OT on empirical distributions
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```python
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# X and Y are two 2D arrays of shape (n_samples, n_features)
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# with squared euclidean metric
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T = ot.solve_sample(X, Y).plan # exact linear program
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T_reg = ot.solve_sample(X, Y, reg=reg).plan # entropic regularized OT
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Wass_2 = ot.solve_sample(X, Y).value # Squared Wasserstein_2
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Wass_1 = ot.solve_sample(X, Y, metric='euclidean').value # Wasserstein 1
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```
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* Compute Wasserstein barycenter
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```python
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* [Rémi Flamary](https://remi.flamary.com/)
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* [Cédric Vincent-Cuaz](https://cedricvincentcuaz.github.io/)
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The numerous contributors to this library are listed [here](CONTRIBUTORS.md).
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The POT contributors to this library are listed [here](CONTRIBUTORS.md).
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<a href="https://github.com/PythonOT/POT/graphs/contributors">
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<img src="https://contrib.rocks/image?repo=PythonOT/POT" />
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</a>
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POT has benefited from the financing or manpower from the following partners:
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‎RELEASES.md‎

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- Fix reg_div function compatibility with numpy in `ot.unbalanced.lbfgsb_unbalanced` via new function `ot.utils.fun_to_numpy` (PR #731)
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- Added to each example in the examples gallery the information about the release version in which it was introduced (PR #743)
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- Removed release information from quickstart guide (PR #744)
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- Update REAMDE with new API and reorganize examples (PR #754)
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#### Closed issues
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- Fixed `ot.mapping` solvers which depended on deprecated `cvxpy` `ECOS` solver (PR #692, Issue #668)

‎docs/source/conf.py‎

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copyright = "2016-{}, POT Contributors".format(datetime.datetime.now().year)
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"copyfile_regex": r"index.rst",
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}

‎examples/README.txt‎

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‎examples/backends/README.txt‎

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‎examples/backends/index.rst‎

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Differentiable OT with PyTorch
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------------------------------
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‎examples/barycenters/plot_free_support_sinkhorn_barycenter.py‎

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# sphinx_gallery_thumbnail_number = 2
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import numpy as np
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import ot
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Domain adaptation examples
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Domain adaptation with OT
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--------------------------

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