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+
+
+.. _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
+
+    `Generated by Sphinx-Gallery <http://sphinx-gallery.readthedocs.io>`_