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authorRémi Flamary <remi.flamary@gmail.com>2016-12-02 15:38:59 +0100
committerRémi Flamary <remi.flamary@gmail.com>2016-12-02 15:38:59 +0100
commite458b7a58d9790e7c5ff40dea235402d9c4c8662 (patch)
treeac9da575654c78aa04a177723603935051b5d42d /docs/source/auto_examples/plot_OT_2D_samples.py
parent7609f9e6a4103e13beb294873f4dac562b1d45e1 (diff)
add doc for gallery
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+# -*- coding: utf-8 -*-
+"""
+====================================================
+2D Optimal transport between empirical distributions
+====================================================
+
+@author: rflamary
+"""
+
+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')