.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/plot_screenkhorn_1D.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. 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 [26].

[26] Alaya M. Z., Bérar M., Gasso G., Rakotomamonjy A. (2019).
Screening Sinkhorn Algorithm for Regularized Optimal Transport,
Advances in Neural Information Processing Systems 33 (NeurIPS).

.. GENERATED FROM PYTHON SOURCE LINES 13-24

.. 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








.. GENERATED FROM PYTHON SOURCE LINES 25-27

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

.. GENERATED FROM PYTHON SOURCE LINES 29-43

.. 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()








.. GENERATED FROM PYTHON SOURCE LINES 44-46

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

.. GENERATED FROM PYTHON SOURCE LINES 48-59

.. 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-sg:: /auto_examples/images/sphx_glr_plot_screenkhorn_1D_001.png
         :alt: plot screenkhorn 1D
         :srcset: /auto_examples/images/sphx_glr_plot_screenkhorn_1D_001.png
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /auto_examples/images/sphx_glr_plot_screenkhorn_1D_002.png
         :alt: Cost matrix M
         :srcset: /auto_examples/images/sphx_glr_plot_screenkhorn_1D_002.png
         :class: sphx-glr-multi-img





.. GENERATED FROM PYTHON SOURCE LINES 60-62

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

.. GENERATED FROM PYTHON SOURCE LINES 62-72

.. 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-sg:: /auto_examples/images/sphx_glr_plot_screenkhorn_1D_003.png
   :alt: OT matrix Screenkhorn
   :srcset: /auto_examples/images/sphx_glr_plot_screenkhorn_1D_003.png
   :class: sphx-glr-single-img


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

 .. code-block:: none

    /home/circleci/project/ot/bregman.py:3318: UserWarning: Bottleneck module is not installed. Install it from https://pypi.org/project/Bottleneck/ for better performance.
      warnings.warn(
    epsilon = 0.020986042861303855

    kappa = 3.7476531411890917

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






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

   **Total running time of the script:** ( 0 minutes  0.251 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>`_