.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/others/plot_factored_coupling.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        :ref:`Go to the end <sphx_glr_download_auto_examples_others_plot_factored_coupling.py>`
        to download the full example code

.. rst-class:: sphx-glr-example-title

.. _sphx_glr_auto_examples_others_plot_factored_coupling.py:


==========================================
Optimal transport with factored couplings
==========================================

Illustration of the factored coupling OT between 2D empirical distributions

.. GENERATED FROM PYTHON SOURCE LINES 10-22

.. code-block:: Python


    # Author: Remi Flamary <remi.flamary@polytechnique.edu>
    #
    # License: MIT License

    # sphinx_gallery_thumbnail_number = 2

    import numpy as np
    import matplotlib.pylab as pl
    import ot
    import ot.plot








.. GENERATED FROM PYTHON SOURCE LINES 23-25

Generate data an plot it
------------------------

.. GENERATED FROM PYTHON SOURCE LINES 25-40

.. code-block:: Python


    # parameters and data generation

    np.random.seed(42)

    n = 100  # nb samples

    xs = np.random.rand(n, 2) - .5

    xs = xs + np.sign(xs)

    xt = np.random.rand(n, 2) - .5

    a, b = ot.unif(n), ot.unif(n)  # uniform distribution on samples








.. GENERATED FROM PYTHON SOURCE LINES 41-49

.. code-block:: Python


    pl.figure(1)
    pl.plot(xs[:, 0], xs[:, 1], '+b', label='Source samples')
    pl.plot(xt[:, 0], xt[:, 1], 'xr', label='Target samples')
    pl.legend(loc=0)
    pl.title('Source and target distributions')





.. image-sg:: /auto_examples/others/images/sphx_glr_plot_factored_coupling_001.png
   :alt: Source and target distributions
   :srcset: /auto_examples/others/images/sphx_glr_plot_factored_coupling_001.png
   :class: sphx-glr-single-img


.. rst-class:: sphx-glr-script-out

 .. code-block:: none


    Text(0.5, 1.0, 'Source and target distributions')



.. GENERATED FROM PYTHON SOURCE LINES 50-52

Compute Factored OT and exact OT solutions
------------------------------------------

.. GENERATED FROM PYTHON SOURCE LINES 54-57

.. code-block:: Python

    M = ot.dist(xs, xt)
    G0 = ot.emd(a, b, M)








.. GENERATED FROM PYTHON SOURCE LINES 58-62

.. code-block:: Python


    Ga, Gb, xb = ot.factored_optimal_transport(xs, xt, a, b, r=4)









.. GENERATED FROM PYTHON SOURCE LINES 63-65

Plot factored OT and exact OT solutions
---------------------------------------

.. GENERATED FROM PYTHON SOURCE LINES 65-87

.. code-block:: Python


    pl.figure(2, (14, 4))

    pl.subplot(1, 3, 1)
    ot.plot.plot2D_samples_mat(xs, xt, G0, c=[.2, .2, .2], alpha=0.1)
    pl.plot(xs[:, 0], xs[:, 1], '+b', label='Source samples')
    pl.plot(xt[:, 0], xt[:, 1], 'xr', label='Target samples')
    pl.title('Exact OT with samples')

    pl.subplot(1, 3, 2)
    ot.plot.plot2D_samples_mat(xs, xb, Ga, c=[.6, .6, .9], alpha=0.5)
    ot.plot.plot2D_samples_mat(xb, xt, Gb, c=[.9, .6, .6], alpha=0.5)
    pl.plot(xs[:, 0], xs[:, 1], '+b', label='Source samples')
    pl.plot(xt[:, 0], xt[:, 1], 'xr', label='Target samples')
    pl.plot(xb[:, 0], xb[:, 1], 'og', label='Template samples')
    pl.title('Factored OT with template samples')

    pl.subplot(1, 3, 3)
    ot.plot.plot2D_samples_mat(xs, xt, Ga.dot(Gb), c=[.2, .2, .2], alpha=0.1)
    pl.plot(xs[:, 0], xs[:, 1], '+b', label='Source samples')
    pl.plot(xt[:, 0], xt[:, 1], 'xr', label='Target samples')
    pl.title('Factored OT low rank OT plan')



.. image-sg:: /auto_examples/others/images/sphx_glr_plot_factored_coupling_002.png
   :alt: Exact OT with samples, Factored OT with template samples, Factored OT low rank OT plan
   :srcset: /auto_examples/others/images/sphx_glr_plot_factored_coupling_002.png
   :class: sphx-glr-single-img


.. rst-class:: sphx-glr-script-out

 .. code-block:: none


    Text(0.5, 1.0, 'Factored OT low rank OT plan')




.. rst-class:: sphx-glr-timing

   **Total running time of the script:** (0 minutes 2.132 seconds)


.. _sphx_glr_download_auto_examples_others_plot_factored_coupling.py:

.. only:: html

  .. container:: sphx-glr-footer sphx-glr-footer-example

    .. container:: sphx-glr-download sphx-glr-download-jupyter

      :download:`Download Jupyter notebook: plot_factored_coupling.ipynb <plot_factored_coupling.ipynb>`

    .. container:: sphx-glr-download sphx-glr-download-python

      :download:`Download Python source code: plot_factored_coupling.py <plot_factored_coupling.py>`


.. only:: html

 .. rst-class:: sphx-glr-signature

    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_