add example norm

Author: rflamary

examples/plot_OT_L1_vs_L2.py

@@ -0,0 +1,110 @@
+# -*- coding: utf-8 -*-
+"""
+====================================================
+2D Optimal transport between empirical distributions
+====================================================
+
+Stoile the figure idea from:
+https://arxiv.org/pdf/1706.07650.pdf
+
+
+@author: rflamary
+"""
+
+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')
+
+#%% sinkhorn