.. _sphx_glr_auto_examples_plot_compute_emd.py:


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

@author: rflamary




.. rst-class:: sphx-glr-horizontal


    *

      .. image:: /auto_examples/images/sphx_glr_plot_compute_emd_001.png
            :scale: 47

    *

      .. image:: /auto_examples/images/sphx_glr_plot_compute_emd_002.png
            :scale: 47





.. code-block:: python


    import numpy as np
    import matplotlib.pylab as pl
    import ot
    from ot.datasets import get_1D_gauss as gauss


    #%% 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 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')

    #%% 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 M3


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

    #%%
    reg=1e-2
    d_sinkhorn=ot.sinkhorn(a,B,M,reg)
    d_sinkhorn2=ot.sinkhorn(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()
**Total running time of the script:** ( 0 minutes  0.521 seconds)



.. 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>`

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

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