.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/plot_OT_1D_smooth.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_plot_OT_1D_smooth.py>`
        to download the full example code

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

.. _sphx_glr_auto_examples_plot_OT_1D_smooth.py:


================================
Smooth and sparse OT example
================================

This example illustrates the computation of
Smooth and Sparse (KL an L2 reg.) OT and
sparsity-constrained OT, together with their visualizations.

.. GENERATED FROM PYTHON SOURCE LINES 12-25

.. code-block:: Python


    # Author: Remi Flamary <remi.flamary@unice.fr>
    #
    # License: MIT License

    # sphinx_gallery_thumbnail_number = 5

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








.. GENERATED FROM PYTHON SOURCE LINES 26-28

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

.. GENERATED FROM PYTHON SOURCE LINES 31-46

.. code-block:: Python


    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 47-49

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

.. GENERATED FROM PYTHON SOURCE LINES 51-57

.. code-block:: Python


    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()




.. image-sg:: /auto_examples/images/sphx_glr_plot_OT_1D_smooth_001.png
   :alt: plot OT 1D smooth
   :srcset: /auto_examples/images/sphx_glr_plot_OT_1D_smooth_001.png
   :class: sphx-glr-single-img


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

 .. code-block:: none


    <matplotlib.legend.Legend object at 0x7f072146b070>



.. GENERATED FROM PYTHON SOURCE LINES 58-63

.. code-block:: Python


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





.. image-sg:: /auto_examples/images/sphx_glr_plot_OT_1D_smooth_002.png
   :alt: Cost matrix M
   :srcset: /auto_examples/images/sphx_glr_plot_OT_1D_smooth_002.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 64-66

Solve Smooth OT
---------------

.. GENERATED FROM PYTHON SOURCE LINES 69-79

.. code-block:: Python


    lambd = 2e-3
    Gsm = ot.smooth.smooth_ot_dual(a, b, M, lambd, reg_type='kl')

    pl.figure(3, figsize=(5, 5))
    ot.plot.plot1D_mat(a, b, Gsm, 'OT matrix Smooth OT KL reg.')

    pl.show()





.. image-sg:: /auto_examples/images/sphx_glr_plot_OT_1D_smooth_003.png
   :alt: OT matrix Smooth OT KL reg.
   :srcset: /auto_examples/images/sphx_glr_plot_OT_1D_smooth_003.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 80-89

.. code-block:: Python


    lambd = 1e-1
    Gsm = ot.smooth.smooth_ot_dual(a, b, M, lambd, reg_type='l2')

    pl.figure(4, figsize=(5, 5))
    ot.plot.plot1D_mat(a, b, Gsm, 'OT matrix Smooth OT l2 reg.')

    pl.show()




.. image-sg:: /auto_examples/images/sphx_glr_plot_OT_1D_smooth_004.png
   :alt: OT matrix Smooth OT l2 reg.
   :srcset: /auto_examples/images/sphx_glr_plot_OT_1D_smooth_004.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 90-100

.. code-block:: Python


    lambd = 1e-1

    max_nz = 2  # two non-zero entries are permitted per column of the OT plan
    Gsc = ot.smooth.smooth_ot_dual(
        a, b, M, lambd, reg_type='sparsity_constrained', max_nz=max_nz)
    pl.figure(5, figsize=(5, 5))
    ot.plot.plot1D_mat(a, b, Gsc, 'Sparsity constrained OT matrix; k=2.')

    pl.show()



.. image-sg:: /auto_examples/images/sphx_glr_plot_OT_1D_smooth_005.png
   :alt: Sparsity constrained OT matrix; k=2.
   :srcset: /auto_examples/images/sphx_glr_plot_OT_1D_smooth_005.png
   :class: sphx-glr-single-img






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

   **Total running time of the script:** (0 minutes 1.003 seconds)


.. _sphx_glr_download_auto_examples_plot_OT_1D_smooth.py:

.. only:: html

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

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

      :download:`Download Jupyter notebook: plot_OT_1D_smooth.ipynb <plot_OT_1D_smooth.ipynb>`

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

      :download:`Download Python source code: plot_OT_1D_smooth.py <plot_OT_1D_smooth.py>`


.. only:: html

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

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