.. _sphx_glr_auto_examples_plot_compute_emd.py:


=================
Plot multiple EMD
=================

Shows how to compute multiple EMD and Sinkhorn with two differnt
ground metrics and plot their values for diffeent distributions.





.. code-block:: python


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

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








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



.. code-block:: python


    #%% parameters

    n = 100  # nb bins
    n_target = 50  # nb target distributions


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

    lst_m = np.linspace(20, 90, n_target)

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

    B = np.zeros((n, n_target))

    for i, m in enumerate(lst_m):
        B[:, i] = gauss(n, m=m, s=5)

    # loss matrix and normalization
    M = ot.dist(x.reshape((n, 1)), x.reshape((n, 1)), 'euclidean')
    M /= M.max()
    M2 = ot.dist(x.reshape((n, 1)), x.reshape((n, 1)), 'sqeuclidean')
    M2 /= M2.max()







Plot data
---------



.. code-block:: python


    #%% plot the distributions

    pl.figure(1)
    pl.subplot(2, 1, 1)
    pl.plot(x, a, 'b', label='Source distribution')
    pl.title('Source distribution')
    pl.subplot(2, 1, 2)
    pl.plot(x, B, label='Target distributions')
    pl.title('Target distributions')
    pl.tight_layout()





.. image:: /auto_examples/images/sphx_glr_plot_compute_emd_001.png
    :align: center




Compute EMD for the different losses
------------------------------------



.. code-block:: python


    #%% Compute and plot distributions and loss matrix

    d_emd = ot.emd2(a, B, M)  # direct computation of EMD
    d_emd2 = ot.emd2(a, B, M2)  # direct computation of EMD with loss M2


    pl.figure(2)
    pl.plot(d_emd, label='Euclidean EMD')
    pl.plot(d_emd2, label='Squared Euclidean EMD')
    pl.title('EMD distances')
    pl.legend()




.. image:: /auto_examples/images/sphx_glr_plot_compute_emd_003.png
    :align: center




Compute Sinkhorn for the different losses
-----------------------------------------



.. code-block:: python


    #%%
    reg = 1e-2
    d_sinkhorn = ot.sinkhorn2(a, B, M, reg)
    d_sinkhorn2 = ot.sinkhorn2(a, B, M2, reg)

    pl.figure(2)
    pl.clf()
    pl.plot(d_emd, label='Euclidean EMD')
    pl.plot(d_emd2, label='Squared Euclidean EMD')
    pl.plot(d_sinkhorn, '+', label='Euclidean Sinkhorn')
    pl.plot(d_sinkhorn2, '+', label='Squared Euclidean Sinkhorn')
    pl.title('EMD distances')
    pl.legend()

    pl.show()



.. image:: /auto_examples/images/sphx_glr_plot_compute_emd_004.png
    :align: center




**Total running time of the script:** ( 0 minutes  0.446 seconds)



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 .. container:: sphx-glr-footer


  .. container:: sphx-glr-download

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



  .. container:: sphx-glr-download

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


.. only:: html

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

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