.. _sphx_glr_auto_examples_plot_UOT_1D.py:


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

This example illustrates the computation of Unbalanced Optimal transport
using a Kullback-Leibler relaxation.



.. code-block:: python


    # Author: Hicham Janati <hicham.janati@inria.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:: python



    #%% parameters

    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)

    # make distributions unbalanced
    b *= 5.

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








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



.. code-block:: python


    #%% plot the distributions

    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_UOT_1D_001.png
            :scale: 47

    *

      .. image:: /auto_examples/images/sphx_glr_plot_UOT_1D_002.png
            :scale: 47




Solve Unbalanced Sinkhorn
--------------



.. code-block:: python



    # Sinkhorn

    epsilon = 0.1  # entropy parameter
    alpha = 1.  # Unbalanced KL relaxation parameter
    Gs = ot.unbalanced.sinkhorn_unbalanced(a, b, M, epsilon, alpha, verbose=True)

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

    pl.show()



.. image:: /auto_examples/images/sphx_glr_plot_UOT_1D_006.png
    :align: center


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

 Out::

    It.  |Err         
    -------------------
        0|1.838786e+00|
       10|1.242379e-01|
       20|2.581314e-03|
       30|5.674552e-05|
       40|1.252959e-06|
       50|2.768136e-08|
       60|6.116090e-10|


**Total running time of the script:** ( 0 minutes  0.259 seconds)



.. only :: html

 .. container:: sphx-glr-footer


  .. container:: sphx-glr-download

     :download:`Download Python source code: plot_UOT_1D.py <plot_UOT_1D.py>`



  .. container:: sphx-glr-download

     :download:`Download Jupyter notebook: plot_UOT_1D.ipynb <plot_UOT_1D.ipynb>`


.. only:: html

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

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