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+
+
+.. _sphx_glr_auto_examples_plot_OT_2D_samples.py:
+
+
+====================================================
+2D Optimal transport between empirical distributions
+====================================================
+
+@author: rflamary
+
+
+
+
+.. rst-class:: sphx-glr-horizontal
+
+
+    *
+
+      .. image:: /auto_examples/images/sphx_glr_plot_OT_2D_samples_001.png
+            :scale: 47
+
+    *
+
+      .. image:: /auto_examples/images/sphx_glr_plot_OT_2D_samples_002.png
+            :scale: 47
+
+    *
+
+      .. image:: /auto_examples/images/sphx_glr_plot_OT_2D_samples_003.png
+            :scale: 47
+
+    *
+
+      .. image:: /auto_examples/images/sphx_glr_plot_OT_2D_samples_004.png
+            :scale: 47
+
+    *
+
+      .. image:: /auto_examples/images/sphx_glr_plot_OT_2D_samples_005.png
+            :scale: 47
+
+    *
+
+      .. image:: /auto_examples/images/sphx_glr_plot_OT_2D_samples_006.png
+            :scale: 47
+
+
+
+
+
+.. code-block:: python
+
+
+    import numpy as np
+    import matplotlib.pylab as pl
+    import ot
+
+    #%% parameters and data generation
+
+    n=20 # 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-3
+
+    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  1.051 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
+
+    `Generated by Sphinx-Gallery <http://sphinx-gallery.readthedocs.io>`_