.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/others/plot_COOT.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_COOT.py>`
        to download the full example code

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

.. _sphx_glr_auto_examples_others_plot_COOT.py:


===================================================
Row and column alignments with CO-Optimal Transport
===================================================

This example is designed to show how to use the CO-Optimal Transport [47]_ in POT.
CO-Optimal Transport allows to calculate the distance between two **arbitrary-size**
matrices, and to align their rows and columns. In this example, we consider two
random matrices :math:`X_1` and :math:`X_2` defined by
:math:`(X_1)_{i,j} = \cos(\frac{i}{n_1} \pi) + \cos(\frac{j}{d_1} \pi) + \sigma \mathcal N(0,1)`
and :math:`(X_2)_{i,j} = \cos(\frac{i}{n_2} \pi) + \cos(\frac{j}{d_2} \pi) + \sigma \mathcal N(0,1)`.

.. [49] Redko, I., Vayer, T., Flamary, R., and Courty, N. (2020).
   `CO-Optimal Transport <https://proceedings.neurips.cc/paper/2020/file/cc384c68ad503482fb24e6d1e3b512ae-Paper.pdf>`_.
   Advances in Neural Information Processing Systems, 33.

.. GENERATED FROM PYTHON SOURCE LINES 18-29

.. code-block:: Python


    # Author: Remi Flamary <remi.flamary@unice.fr>
    #         Quang Huy Tran <quang-huy.tran@univ-ubs.fr>
    # License: MIT License

    from matplotlib.patches import ConnectionPatch
    import matplotlib.pylab as pl
    import numpy as np
    from ot.coot import co_optimal_transport as coot
    from ot.coot import co_optimal_transport2 as coot2








.. GENERATED FROM PYTHON SOURCE LINES 30-31

Generating two random matrices

.. GENERATED FROM PYTHON SOURCE LINES 31-49

.. code-block:: Python


    n1 = 20
    n2 = 10
    d1 = 16
    d2 = 8
    sigma = 0.2

    X1 = (
        np.cos(np.arange(n1) * np.pi / n1)[:, None] +
        np.cos(np.arange(d1) * np.pi / d1)[None, :] +
        sigma * np.random.randn(n1, d1)
    )
    X2 = (
        np.cos(np.arange(n2) * np.pi / n2)[:, None] +
        np.cos(np.arange(d2) * np.pi / d2)[None, :] +
        sigma * np.random.randn(n2, d2)
    )








.. GENERATED FROM PYTHON SOURCE LINES 50-51

Visualizing the matrices

.. GENERATED FROM PYTHON SOURCE LINES 51-63

.. code-block:: Python


    pl.figure(1, (8, 5))
    pl.subplot(1, 2, 1)
    pl.imshow(X1)
    pl.title('$X_1$')

    pl.subplot(1, 2, 2)
    pl.imshow(X2)
    pl.title("$X_2$")

    pl.tight_layout()




.. image-sg:: /auto_examples/others/images/sphx_glr_plot_COOT_001.png
   :alt: $X_1$, $X_2$
   :srcset: /auto_examples/others/images/sphx_glr_plot_COOT_001.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 64-65

Visualizing the alignments of rows and columns, and calculating the CO-Optimal Transport distance

.. GENERATED FROM PYTHON SOURCE LINES 65-98

.. code-block:: Python


    pi_sample, pi_feature, log = coot(X1, X2, log=True, verbose=True)
    coot_distance = coot2(X1, X2)
    print('CO-Optimal Transport distance = {:.5f}'.format(coot_distance))

    fig = pl.figure(4, (9, 7))
    pl.clf()

    ax1 = pl.subplot(2, 2, 3)
    pl.imshow(X1)
    pl.xlabel('$X_1$')

    ax2 = pl.subplot(2, 2, 2)
    ax2.yaxis.tick_right()
    pl.imshow(np.transpose(X2))
    pl.title("Transpose($X_2$)")
    ax2.xaxis.tick_top()

    for i in range(n1):
        j = np.argmax(pi_sample[i, :])
        xyA = (d1 - .5, i)
        xyB = (j, d2 - .5)
        con = ConnectionPatch(xyA=xyA, xyB=xyB, coordsA=ax1.transData,
                              coordsB=ax2.transData, color="black")
        fig.add_artist(con)

    for i in range(d1):
        j = np.argmax(pi_feature[i, :])
        xyA = (i, -.5)
        xyB = (-.5, j)
        con = ConnectionPatch(
            xyA=xyA, xyB=xyB, coordsA=ax1.transData, coordsB=ax2.transData, color="blue")
        fig.add_artist(con)



.. image-sg:: /auto_examples/others/images/sphx_glr_plot_COOT_002.png
   :alt: Transpose($X_2$)
   :srcset: /auto_examples/others/images/sphx_glr_plot_COOT_002.png
   :class: sphx-glr-single-img


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

 .. code-block:: none

    CO-Optimal Transport cost at iteration 1: 0.10903416567681642
    CO-Optimal Transport cost at iteration 2: 0.0987568083692249
    CO-Optimal Transport cost at iteration 3: 0.09685398028260428
    CO-Optimal Transport distance = 0.09685





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

   **Total running time of the script:** (0 minutes 0.401 seconds)


.. _sphx_glr_download_auto_examples_others_plot_COOT.py:

.. only:: html

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

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

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

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

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


.. only:: html

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

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