.. only:: html

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

        Click :ref:`here <sphx_glr_download_auto_examples_plot_screenkhorn_1D.py>`     to download the full example code
    .. rst-class:: sphx-glr-example-title

    .. _sphx_glr_auto_examples_plot_screenkhorn_1D.py:


===============================
1D Screened optimal transport
===============================

This example illustrates the computation of Screenkhorn:
Screening Sinkhorn Algorithm for Optimal transport.


.. code-block:: default


    # Author: Mokhtar Z. Alaya <mokhtarzahdi.alaya@gmail.com>
    #
    # License: MIT License

    import numpy as np
    import matplotlib.pylab as pl
    import ot.plot
    from ot.datasets import make_1D_gauss as gauss
    from ot.bregman import screenkhorn








Generate data
-------------


.. code-block:: default


    n = 100  # nb bins

    # bin positions
    x = np.arange(n, dtype=np.float64)

    # Gaussian distributions
    a = gauss(n, m=20, s=5)  # m= mean, s= std
    b = gauss(n, m=60, s=10)

    # loss matrix
    M = ot.dist(x.reshape((n, 1)), x.reshape((n, 1)))
    M /= M.max()








Plot distributions and loss matrix
----------------------------------


.. code-block:: default


    pl.figure(1, figsize=(6.4, 3))
    pl.plot(x, a, 'b', label='Source distribution')
    pl.plot(x, b, 'r', label='Target distribution')
    pl.legend()

    # plot distributions and loss matrix

    pl.figure(2, figsize=(5, 5))
    ot.plot.plot1D_mat(a, b, M, 'Cost matrix M')




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


    *

      .. image:: /auto_examples/images/sphx_glr_plot_screenkhorn_1D_001.png
            :class: sphx-glr-multi-img

    *

      .. image:: /auto_examples/images/sphx_glr_plot_screenkhorn_1D_002.png
            :class: sphx-glr-multi-img





Solve Screenkhorn
-----------------------


.. code-block:: default


    # Screenkhorn
    lambd = 2e-03  # entropy parameter
    ns_budget = 30  # budget number of points to be keeped in the source distribution
    nt_budget = 30  # budget number of points to be keeped in the target distribution

    G_screen = screenkhorn(a, b, M, lambd, ns_budget, nt_budget, uniform=False, restricted=True, verbose=True)
    pl.figure(4, figsize=(5, 5))
    ot.plot.plot1D_mat(a, b, G_screen, 'OT matrix Screenkhorn')
    pl.show()



.. image:: /auto_examples/images/sphx_glr_plot_screenkhorn_1D_003.png
    :class: sphx-glr-single-img


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

 Out:

 .. code-block:: none

    /home/rflamary/PYTHON/POT/ot/bregman.py:2056: UserWarning: Bottleneck module is not installed. Install it from https://pypi.org/project/Bottleneck/ for better performance.
      "Bottleneck module is not installed. Install it from https://pypi.org/project/Bottleneck/ for better performance.")
    epsilon = 0.020986042861303855

    kappa = 3.7476531411890917

    Cardinality of selected points: |Isel| = 30      |Jsel| = 30 

    /home/rflamary/PYTHON/POT/examples/plot_screenkhorn_1D.py:68: UserWarning: Matplotlib is currently using agg, which is a non-GUI backend, so cannot show the figure.
      pl.show()





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

   **Total running time of the script:** ( 0 minutes  0.228 seconds)


.. _sphx_glr_download_auto_examples_plot_screenkhorn_1D.py:


.. only :: html

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



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

     :download:`Download Python source code: plot_screenkhorn_1D.py <plot_screenkhorn_1D.py>`



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

     :download:`Download Jupyter notebook: plot_screenkhorn_1D.ipynb <plot_screenkhorn_1D.ipynb>`


.. only:: html

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

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