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+
+
+.. _sphx_glr_auto_examples_plot_OTDA_2D.py:
+
+
+==============================
+OT for empirical distributions
+==============================
+
+
+
+
+
+.. rst-class:: sphx-glr-horizontal
+
+
+    *
+
+      .. image:: /auto_examples/images/sphx_glr_plot_OTDA_2D_001.png
+            :scale: 47
+
+    *
+
+      .. image:: /auto_examples/images/sphx_glr_plot_OTDA_2D_002.png
+            :scale: 47
+
+    *
+
+      .. image:: /auto_examples/images/sphx_glr_plot_OTDA_2D_003.png
+            :scale: 47
+
+    *
+
+      .. image:: /auto_examples/images/sphx_glr_plot_OTDA_2D_004.png
+            :scale: 47
+
+
+
+
+
+.. code-block:: python
+
+
+    import numpy as np
+    import matplotlib.pylab as pl
+    import ot
+
+
+
+    #%% parameters
+
+    n=150 # nb bins
+
+    xs,ys=ot.datasets.get_data_classif('3gauss',n)
+    xt,yt=ot.datasets.get_data_classif('3gauss2',n)
+
+    a,b = ot.unif(n),ot.unif(n)
+    # loss matrix
+    M=ot.dist(xs,xt)
+    #M/=M.max()
+
+    #%% plot samples
+
+    pl.figure(1)
+
+    pl.subplot(2,2,1)
+    pl.scatter(xs[:,0],xs[:,1],c=ys,marker='+',label='Source samples')
+    pl.legend(loc=0)
+    pl.title('Source  distributions')
+
+    pl.subplot(2,2,2)
+    pl.scatter(xt[:,0],xt[:,1],c=yt,marker='o',label='Target samples')
+    pl.legend(loc=0)
+    pl.title('target  distributions')
+
+    pl.figure(2)
+    pl.imshow(M,interpolation='nearest')
+    pl.title('Cost matrix M')
+
+
+    #%% OT estimation
+
+    # EMD
+    G0=ot.emd(a,b,M)
+
+    # sinkhorn
+    lambd=1e-1
+    Gs=ot.sinkhorn(a,b,M,lambd)
+
+
+    # Group lasso regularization
+    reg=1e-1
+    eta=1e0
+    Gg=ot.da.sinkhorn_lpl1_mm(a,ys.astype(np.int),b,M,reg,eta)
+
+
+    #%% visu matrices
+
+    pl.figure(3)
+
+    pl.subplot(2,3,1)
+    pl.imshow(G0,interpolation='nearest')
+    pl.title('OT matrix ')
+
+    pl.subplot(2,3,2)
+    pl.imshow(Gs,interpolation='nearest')
+    pl.title('OT matrix Sinkhorn')
+
+    pl.subplot(2,3,3)
+    pl.imshow(Gg,interpolation='nearest')
+    pl.title('OT matrix Group lasso')
+
+    pl.subplot(2,3,4)
+    ot.plot.plot2D_samples_mat(xs,xt,G0,c=[.5,.5,1])
+    pl.scatter(xs[:,0],xs[:,1],c=ys,marker='+',label='Source samples')
+    pl.scatter(xt[:,0],xt[:,1],c=yt,marker='o',label='Target samples')
+
+
+    pl.subplot(2,3,5)
+    ot.plot.plot2D_samples_mat(xs,xt,Gs,c=[.5,.5,1])
+    pl.scatter(xs[:,0],xs[:,1],c=ys,marker='+',label='Source samples')
+    pl.scatter(xt[:,0],xt[:,1],c=yt,marker='o',label='Target samples')
+
+    pl.subplot(2,3,6)
+    ot.plot.plot2D_samples_mat(xs,xt,Gg,c=[.5,.5,1])
+    pl.scatter(xs[:,0],xs[:,1],c=ys,marker='+',label='Source samples')
+    pl.scatter(xt[:,0],xt[:,1],c=yt,marker='o',label='Target samples')
+
+    #%% sample interpolation
+
+    xst0=n*G0.dot(xt)
+    xsts=n*Gs.dot(xt)
+    xstg=n*Gg.dot(xt)
+
+    pl.figure(4)
+    pl.subplot(2,3,1)
+
+
+    pl.scatter(xt[:,0],xt[:,1],c=yt,marker='o',label='Target samples',alpha=0.5)
+    pl.scatter(xst0[:,0],xst0[:,1],c=ys,marker='+',label='Transp samples',s=30)
+    pl.title('Interp samples')
+    pl.legend(loc=0)
+
+    pl.subplot(2,3,2)
+
+
+    pl.scatter(xt[:,0],xt[:,1],c=yt,marker='o',label='Target samples',alpha=0.5)
+    pl.scatter(xsts[:,0],xsts[:,1],c=ys,marker='+',label='Transp samples',s=30)
+    pl.title('Interp samples Sinkhorn')
+
+    pl.subplot(2,3,3)
+
+    pl.scatter(xt[:,0],xt[:,1],c=yt,marker='o',label='Target samples',alpha=0.5)
+    pl.scatter(xstg[:,0],xstg[:,1],c=ys,marker='+',label='Transp samples',s=30)
+    pl.title('Interp samples Grouplasso')
+**Total running time of the script:** ( 0 minutes  17.372 seconds)
+
+
+
+.. container:: sphx-glr-footer
+
+
+  .. container:: sphx-glr-download
+
+     :download:`Download Python source code: plot_OTDA_2D.py <plot_OTDA_2D.py>`
+
+
+
+  .. container:: sphx-glr-download
+
+     :download:`Download Jupyter notebook: plot_OTDA_2D.ipynb <plot_OTDA_2D.ipynb>`
+
+.. rst-class:: sphx-glr-signature
+
+    `Generated by Sphinx-Gallery <http://sphinx-gallery.readthedocs.io>`_