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+
+
+.. _sphx_glr_auto_examples_plot_OT_L1_vs_L2.py:
+
+
+==========================================
+2D Optimal transport for different metrics
+==========================================
+
+Stole the figure idea from Fig. 1 and 2 in 
+https://arxiv.org/pdf/1706.07650.pdf
+
+
+@author: rflamary
+
+
+
+
+.. rst-class:: sphx-glr-horizontal
+
+
+    *
+
+      .. image:: /auto_examples/images/sphx_glr_plot_OT_L1_vs_L2_001.png
+            :scale: 47
+
+    *
+
+      .. image:: /auto_examples/images/sphx_glr_plot_OT_L1_vs_L2_002.png
+            :scale: 47
+
+    *
+
+      .. image:: /auto_examples/images/sphx_glr_plot_OT_L1_vs_L2_003.png
+            :scale: 47
+
+    *
+
+      .. image:: /auto_examples/images/sphx_glr_plot_OT_L1_vs_L2_004.png
+            :scale: 47
+
+    *
+
+      .. image:: /auto_examples/images/sphx_glr_plot_OT_L1_vs_L2_005.png
+            :scale: 47
+
+    *
+
+      .. image:: /auto_examples/images/sphx_glr_plot_OT_L1_vs_L2_006.png
+            :scale: 47
+
+
+
+
+
+.. code-block:: python
+
+
+    import numpy as np
+    import matplotlib.pylab as pl
+    import ot
+
+    #%% parameters and data generation
+
+    for data in range(2):
+
+        if data:
+            n=20 # nb samples
+            xs=np.zeros((n,2))
+            xs[:,0]=np.arange(n)+1
+            xs[:,1]=(np.arange(n)+1)*-0.001 # to make it strictly convex...
+        
+            xt=np.zeros((n,2))
+            xt[:,1]=np.arange(n)+1
+        else:
+        
+            n=50 # nb samples
+            xtot=np.zeros((n+1,2))
+            xtot[:,0]=np.cos((np.arange(n+1)+1.0)*0.9/(n+2)*2*np.pi)
+            xtot[:,1]=np.sin((np.arange(n+1)+1.0)*0.9/(n+2)*2*np.pi)
+        
+            xs=xtot[:n,:]
+            xt=xtot[1:,:]
+        
+        
+    
+        a,b = ot.unif(n),ot.unif(n) # uniform distribution on samples
+    
+        # loss matrix
+        M1=ot.dist(xs,xt,metric='euclidean')
+        M1/=M1.max()
+    
+        # loss matrix
+        M2=ot.dist(xs,xt,metric='sqeuclidean')
+        M2/=M2.max()
+    
+        # loss matrix
+        Mp=np.sqrt(ot.dist(xs,xt,metric='euclidean'))
+        Mp/=Mp.max()
+    
+        #%% plot samples
+    
+        pl.figure(1+3*data)
+        pl.clf()
+        pl.plot(xs[:,0],xs[:,1],'+b',label='Source samples')
+        pl.plot(xt[:,0],xt[:,1],'xr',label='Target samples')
+        pl.axis('equal')
+        pl.title('Source and traget distributions')
+    
+        pl.figure(2+3*data,(15,5))
+        pl.subplot(1,3,1)
+        pl.imshow(M1,interpolation='nearest')
+        pl.title('Eucidean cost')
+        pl.subplot(1,3,2)
+        pl.imshow(M2,interpolation='nearest')
+        pl.title('Squared Euclidean cost')
+    
+        pl.subplot(1,3,3)
+        pl.imshow(Mp,interpolation='nearest')
+        pl.title('Sqrt Euclidean cost')
+        #%% EMD
+    
+        G1=ot.emd(a,b,M1)
+        G2=ot.emd(a,b,M2)
+        Gp=ot.emd(a,b,Mp)
+    
+        pl.figure(3+3*data,(15,5))
+    
+        pl.subplot(1,3,1)
+        ot.plot.plot2D_samples_mat(xs,xt,G1,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.axis('equal')
+        #pl.legend(loc=0)
+        pl.title('OT Euclidean')
+    
+        pl.subplot(1,3,2)
+    
+        ot.plot.plot2D_samples_mat(xs,xt,G2,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.axis('equal')
+        #pl.legend(loc=0)
+        pl.title('OT squared Euclidean')
+    
+        pl.subplot(1,3,3)
+    
+        ot.plot.plot2D_samples_mat(xs,xt,Gp,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.axis('equal')
+        #pl.legend(loc=0)
+        pl.title('OT sqrt Euclidean')
+
+**Total running time of the script:** ( 0 minutes  1.417 seconds)
+
+
+
+.. container:: sphx-glr-footer
+
+
+  .. container:: sphx-glr-download
+
+     :download:`Download Python source code: plot_OT_L1_vs_L2.py <plot_OT_L1_vs_L2.py>`
+
+
+
+  .. container:: sphx-glr-download
+
+     :download:`Download Jupyter notebook: plot_OT_L1_vs_L2.ipynb <plot_OT_L1_vs_L2.ipynb>`
+
+.. rst-class:: sphx-glr-signature
+
+    `Generated by Sphinx-Gallery <http://sphinx-gallery.readthedocs.io>`_