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

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

.. _sphx_glr_auto_examples_others_plot_WeakOT_VS_OT.py:


====================================================
Weak Optimal Transport VS exact Optimal Transport
====================================================

Illustration of 2D optimal transport between distributions that are weighted
sum of Diracs. The OT matrix is plotted with the samples.

.. GENERATED FROM PYTHON SOURCE LINES 11-23

.. code-block:: Python


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

    # sphinx_gallery_thumbnail_number = 4

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








.. GENERATED FROM PYTHON SOURCE LINES 24-26

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

.. GENERATED FROM PYTHON SOURCE LINES 28-46

.. code-block:: Python


    n = 50  # nb samples

    mu_s = np.array([0, 0])
    cov_s = np.array([[1, 0], [0, 1]])

    mu_t = np.array([4, 4])
    cov_t = np.array([[1, -.8], [-.8, 1]])

    xs = ot.datasets.make_2D_samples_gauss(n, mu_s, cov_s)
    xt = ot.datasets.make_2D_samples_gauss(n, mu_t, cov_t)

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

    # loss matrix
    M = ot.dist(xs, xt)
    M /= M.max()








.. GENERATED FROM PYTHON SOURCE LINES 47-59

.. 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')

    pl.figure(2)
    pl.imshow(M, interpolation='nearest')
    pl.title('Cost matrix M')





.. rst-class:: sphx-glr-horizontal


    *

      .. image-sg:: /auto_examples/others/images/sphx_glr_plot_WeakOT_VS_OT_001.png
         :alt: Source and target distributions
         :srcset: /auto_examples/others/images/sphx_glr_plot_WeakOT_VS_OT_001.png
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /auto_examples/others/images/sphx_glr_plot_WeakOT_VS_OT_002.png
         :alt: Cost matrix M
         :srcset: /auto_examples/others/images/sphx_glr_plot_WeakOT_VS_OT_002.png
         :class: sphx-glr-multi-img


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

 .. code-block:: none


    Text(0.5, 1.0, 'Cost matrix M')



.. GENERATED FROM PYTHON SOURCE LINES 60-62

Compute Weak OT and exact OT solutions
--------------------------------------

.. GENERATED FROM PYTHON SOURCE LINES 64-67

.. code-block:: Python


    G0 = ot.emd(a, b, M)








.. GENERATED FROM PYTHON SOURCE LINES 68-72

.. code-block:: Python


    Gweak = ot.weak_optimal_transport(xs, xt, a, b)









.. GENERATED FROM PYTHON SOURCE LINES 73-75

Plot weak OT and exact OT solutions
--------------------------------------

.. GENERATED FROM PYTHON SOURCE LINES 75-99

.. code-block:: Python


    pl.figure(3, (8, 5))

    pl.subplot(1, 2, 1)
    pl.imshow(G0, interpolation='nearest')
    pl.title('OT matrix')

    pl.subplot(1, 2, 2)
    pl.imshow(Gweak, interpolation='nearest')
    pl.title('Weak OT matrix')

    pl.figure(4, (8, 5))

    pl.subplot(1, 2, 1)
    ot.plot.plot2D_samples_mat(xs, xt, G0, c=[.5, .5, 1])
    pl.plot(xs[:, 0], xs[:, 1], '+b', label='Source samples')
    pl.plot(xt[:, 0], xt[:, 1], 'xr', label='Target samples')
    pl.title('OT matrix with samples')

    pl.subplot(1, 2, 2)
    ot.plot.plot2D_samples_mat(xs, xt, Gweak, c=[.5, .5, 1])
    pl.plot(xs[:, 0], xs[:, 1], '+b', label='Source samples')
    pl.plot(xt[:, 0], xt[:, 1], 'xr', label='Target samples')
    pl.title('Weak OT matrix with samples')



.. rst-class:: sphx-glr-horizontal


    *

      .. image-sg:: /auto_examples/others/images/sphx_glr_plot_WeakOT_VS_OT_003.png
         :alt: OT matrix, Weak OT matrix
         :srcset: /auto_examples/others/images/sphx_glr_plot_WeakOT_VS_OT_003.png
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /auto_examples/others/images/sphx_glr_plot_WeakOT_VS_OT_004.png
         :alt: OT matrix with samples, Weak OT matrix with samples
         :srcset: /auto_examples/others/images/sphx_glr_plot_WeakOT_VS_OT_004.png
         :class: sphx-glr-multi-img


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

 .. code-block:: none


    Text(0.5, 1.0, 'Weak OT matrix with samples')




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

   **Total running time of the script:** (0 minutes 2.368 seconds)


.. _sphx_glr_download_auto_examples_others_plot_WeakOT_VS_OT.py:

.. only:: html

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

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

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

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

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


.. only:: html

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

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