.. _sphx_glr_auto_examples_plot_OT_2D_samples.py:


====================================================
2D Optimal transport between empirical distributions
====================================================

@author: rflamary




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


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      .. image:: /auto_examples/images/sphx_glr_plot_OT_2D_samples_001.png
            :scale: 47

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      .. image:: /auto_examples/images/sphx_glr_plot_OT_2D_samples_002.png
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      .. image:: /auto_examples/images/sphx_glr_plot_OT_2D_samples_003.png
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      .. image:: /auto_examples/images/sphx_glr_plot_OT_2D_samples_004.png
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      .. image:: /auto_examples/images/sphx_glr_plot_OT_2D_samples_005.png
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      .. image:: /auto_examples/images/sphx_glr_plot_OT_2D_samples_006.png
            :scale: 47


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

 Out::

    ('Warning: numerical errors at iteration', 0)




|


.. code-block:: python


    import numpy as np
    import matplotlib.pylab as pl
    import ot

    #%% parameters and data generation

    n=50 # nb samples

    mu_s=np.array([0,0])
    cov_s=np.array([[1,0],[0,1]])

    mu_t=np.array([4,4])
    cov_t=np.array([[1,-.8],[-.8,1]])

    xs=ot.datasets.get_2D_samples_gauss(n,mu_s,cov_s)
    xt=ot.datasets.get_2D_samples_gauss(n,mu_t,cov_t)

    a,b = ot.unif(n),ot.unif(n) # uniform distribution on samples

    # loss matrix
    M=ot.dist(xs,xt)
    M/=M.max()

    #%% plot samples

    pl.figure(1)
    pl.plot(xs[:,0],xs[:,1],'+b',label='Source samples')
    pl.plot(xt[:,0],xt[:,1],'xr',label='Target samples')
    pl.legend(loc=0)
    pl.title('Source and traget distributions')

    pl.figure(2)
    pl.imshow(M,interpolation='nearest')
    pl.title('Cost matrix M')


    #%% EMD

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

    pl.figure(3)
    pl.imshow(G0,interpolation='nearest')
    pl.title('OT matrix G0')

    pl.figure(4)
    ot.plot.plot2D_samples_mat(xs,xt,G0,c=[.5,.5,1])
    pl.plot(xs[:,0],xs[:,1],'+b',label='Source samples')
    pl.plot(xt[:,0],xt[:,1],'xr',label='Target samples')
    pl.legend(loc=0)
    pl.title('OT matrix with samples')


    #%% sinkhorn

    # reg term
    lambd=5e-4

    Gs=ot.sinkhorn(a,b,M,lambd)

    pl.figure(5)
    pl.imshow(Gs,interpolation='nearest')
    pl.title('OT matrix sinkhorn')

    pl.figure(6)
    ot.plot.plot2D_samples_mat(xs,xt,Gs,color=[.5,.5,1])
    pl.plot(xs[:,0],xs[:,1],'+b',label='Source samples')
    pl.plot(xt[:,0],xt[:,1],'xr',label='Target samples')
    pl.legend(loc=0)
    pl.title('OT matrix Sinkhorn with samples')

**Total running time of the script:** ( 0 minutes  0.623 seconds)



.. container:: sphx-glr-footer


  .. container:: sphx-glr-download

     :download:`Download Python source code: plot_OT_2D_samples.py <plot_OT_2D_samples.py>`



  .. container:: sphx-glr-download

     :download:`Download Jupyter notebook: plot_OT_2D_samples.ipynb <plot_OT_2D_samples.ipynb>`

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

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