add em2 computation example

Author: rflamary

examples/plot_compute_emd.py

@@ -0,0 +1,57 @@
+# -*- coding: utf-8 -*-
+"""
+====================
+1D optimal transport
+====================
+
+@author: rflamary
+"""
+
+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=10 # 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
+M=ot.dist(x.reshape((n,1)),x.reshape((n,1)),'euclidean')
+M2=ot.dist(x.reshape((n,1)),x.reshape((n,1)),'sqeuclidean')
+
+#%% 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')
+
+#%% plot distributions and loss matrix
+
+emd=ot.emd2(a,B,M)
+emd2=ot.emd2(a,B,M2)
+pl.figure(2)
+pl.plot(emd,label='Euclidean loss')
+pl.plot(emd,label='Squared Euclidean loss')
+pl.legend()
+