.. only:: html

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

        Click :ref:`here <sphx_glr_download_auto_examples_plot_OT_1D.py>`     to download the full example code
    .. rst-class:: sphx-glr-example-title

    .. _sphx_glr_auto_examples_plot_OT_1D.py:


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

This example illustrates the computation of EMD and Sinkhorn transport plans
and their visualization.



.. code-block:: default


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

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








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()




.. image:: /auto_examples/images/sphx_glr_plot_OT_1D_001.png
    :class: sphx-glr-single-img


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

 Out:

 .. code-block:: none


    <matplotlib.legend.Legend object at 0x7f4c75f9fcc0>




.. code-block:: default


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




.. image:: /auto_examples/images/sphx_glr_plot_OT_1D_002.png
    :class: sphx-glr-single-img





Solve EMD
---------


.. code-block:: default


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

    pl.figure(3, figsize=(5, 5))
    ot.plot.plot1D_mat(a, b, G0, 'OT matrix G0')




.. image:: /auto_examples/images/sphx_glr_plot_OT_1D_003.png
    :class: sphx-glr-single-img





Solve Sinkhorn
--------------


.. code-block:: default


    lambd = 1e-3
    Gs = ot.sinkhorn(a, b, M, lambd, verbose=True)

    pl.figure(4, figsize=(5, 5))
    ot.plot.plot1D_mat(a, b, Gs, 'OT matrix Sinkhorn')

    pl.show()



.. image:: /auto_examples/images/sphx_glr_plot_OT_1D_004.png
    :class: sphx-glr-single-img


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

 Out:

 .. code-block:: none

    It.  |Err         
    -------------------
        0|2.861463e-01|
       10|1.860154e-01|
       20|8.144529e-02|
       30|3.130143e-02|
       40|1.178815e-02|
       50|4.426078e-03|
       60|1.661047e-03|
       70|6.233110e-04|
       80|2.338932e-04|
       90|8.776627e-05|
      100|3.293340e-05|
      110|1.235791e-05|
      120|4.637176e-06|
      130|1.740051e-06|
      140|6.529356e-07|
      150|2.450071e-07|
      160|9.193632e-08|
      170|3.449812e-08|
      180|1.294505e-08|
      190|4.857493e-09|
    It.  |Err         
    -------------------
      200|1.822723e-09|
      210|6.839572e-10|
    /home/rflamary/PYTHON/POT/examples/plot_OT_1D.py:84: 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  0.665 seconds)


.. _sphx_glr_download_auto_examples_plot_OT_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_OT_1D.py <plot_OT_1D.py>`



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

     :download:`Download Jupyter notebook: plot_OT_1D.ipynb <plot_OT_1D.ipynb>`


.. only:: html

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

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