.. _sphx_glr_auto_examples_demo_OT_1D_test.py:


Demo for 1D optimal transport

@author: rflamary



.. 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

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

    # Gaussian distributions
    a=gauss(n,m=n*.2,s=5) # m= mean, s= std
    b=gauss(n,m=n*.6,s=10)

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

    #%% plot the distributions

    pl.figure(1)
    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)
    ot.plot.plot1D_mat(a,b,M,'Cost matrix M')

    #%% EMD

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

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

    #%% Sinkhorn

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

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

    #%% Sinkhorn

    lambd=1e-4
    Gss,log=ot.bregman.sinkhorn_stabilized(a,b,M,lambd,verbose=True,log=True)
    Gss2,log2=ot.bregman.sinkhorn_stabilized(a,b,M,lambd,verbose=True,log=True,warmstart=log['warmstart'])

    pl.figure(5)
    ot.plot.plot1D_mat(a,b,Gss,'OT matrix Sinkhorn stabilized')

    #%% Sinkhorn

    lambd=1e-11
    Gss=ot.bregman.sinkhorn_epsilon_scaling(a,b,M,lambd,verbose=True)

    pl.figure(5)
    ot.plot.plot1D_mat(a,b,Gss,'OT matrix Sinkhorn stabilized')

**Total running time of the script:** ( 0 minutes  0.000 seconds)



.. container:: sphx-glr-footer


  .. container:: sphx-glr-download

     :download:`Download Python source code: demo_OT_1D_test.py <demo_OT_1D_test.py>`



  .. container:: sphx-glr-download

     :download:`Download Jupyter notebook: demo_OT_1D_test.ipynb <demo_OT_1D_test.ipynb>`

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

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