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ott.tools

.. module:: ott.tools

.. currentmodule:: ott.tools

The :mod:`~ott.tools` package contains high level functions that build on outputs produced by lower-level components in the toolbox, such as :mod:`~ott.solvers`.

In particular, we provide user-friendly APIs to unregularized OT quantities, such as the :term:`Wasserstein distance` for two point clouds of the same size. We also provide functions to pad efficiently point clouds when doing large scale OT between them in parallel, implementations of the Sinkhorn divergence :cite:`genevay:18,sejourne:19`, sliced Wasserstein distances :cite:`rabin:12`, differentiable approximations to ranks and quantile functions :cite:`cuturi:19`, and various tools to study Gaussians with the 2-:term:`Wasserstein distance` :cite:`gelbrich:90,delon:20`.

Unregularized Optimal Transport

.. autosummary::
    :toctree: _autosummary

    unreg.hungarian
    unreg.HungarianOutput
    unreg.wassdis_p

Segmented Sinkhorn

.. autosummary::
    :toctree: _autosummary

    segment_sinkhorn.segment_sinkhorn

Sinkhorn Divergence

.. autosummary::
    :toctree: _autosummary

    sinkhorn_divergence.sinkdiv
    sinkhorn_divergence.sinkhorn_divergence
    sinkhorn_divergence.SinkhornDivergenceOutput
    sinkhorn_divergence.segment_sinkhorn_divergence

Sliced Wasserstein Distance

.. autosummary::
    :toctree: _autosummary

    sliced.random_proj_sphere
    sliced.sliced_wasserstein

ProgOT

.. autosummary::
    :toctree: _autosummary

    progot.ProgOT
    progot.ProgOTOutput
    progot.get_alpha_schedule
    progot.get_epsilon_schedule

Soft Sorting Algorithms

.. autosummary::
    :toctree: _autosummary

    soft_sort.multivariate_cdf_quantile_maps
    soft_sort.quantile
    soft_sort.quantile_normalization
    soft_sort.quantize
    soft_sort.ranks
    soft_sort.sort
    soft_sort.sort_with
    soft_sort.topk_mask

Clustering

.. autosummary::
    :toctree: _autosummary

    k_means.k_means
    k_means.KMeansOutput

Plotting

.. autosummary::
    :toctree: _autosummary

    plot.Plot

ott.tools.gaussian_mixture package

.. currentmodule:: ott.tools.gaussian_mixture

.. automodule:: ott.tools.gaussian_mixture

This package implements various tools to manipulate Gaussian mixtures with a slightly modified Wasserstein geometry: here a Gaussian mixture is no longer strictly regarded as a density \mathbb{R}^d, but instead as a point cloud in the space of Gaussians in \mathbb{R}^d. This viewpoint provides a new approach to compare, and fit Gaussian mixtures, as described for instance in :cite:`delon:20` and references therein.

Gaussian Mixtures

.. autosummary::
    :toctree: _autosummary

    gaussian.Gaussian
    gaussian_mixture.GaussianMixture
    gaussian_mixture_pair.GaussianMixturePair
    fit_gmm.initialize
    fit_gmm.fit_model_em
    fit_gmm_pair.get_fit_model_em_fn