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Diffstat (limited to 'examples/plot_OT_L1_vs_L2.py')
| -rw-r--r-- | examples/plot_OT_L1_vs_L2.py | 149 |
1 files changed, 78 insertions, 71 deletions
diff --git a/examples/plot_OT_L1_vs_L2.py b/examples/plot_OT_L1_vs_L2.py index 9bb92fe..dfc9462 100644 --- a/examples/plot_OT_L1_vs_L2.py +++ b/examples/plot_OT_L1_vs_L2.py @@ -4,13 +4,16 @@ 2D Optimal transport for different metrics ========================================== -Stole the figure idea from Fig. 1 and 2 in +Stole the figure idea from Fig. 1 and 2 in https://arxiv.org/pdf/1706.07650.pdf -@author: rflamary """ +# Author: Remi Flamary <remi.flamary@unice.fr> +# +# License: MIT License + import numpy as np import matplotlib.pylab as pl import ot @@ -20,89 +23,93 @@ import ot 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 + 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 - + + 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() - + M1 = ot.dist(xs, xt, metric='euclidean') + M1 /= M1.max() + # loss matrix - M2=ot.dist(xs,xt,metric='sqeuclidean') - M2/=M2.max() - + M2 = ot.dist(xs, xt, metric='sqeuclidean') + M2 /= M2.max() + # loss matrix - Mp=np.sqrt(ot.dist(xs,xt,metric='euclidean')) - Mp/=Mp.max() - + Mp = np.sqrt(ot.dist(xs, xt, metric='euclidean')) + Mp /= Mp.max() + #%% plot samples - - pl.figure(1+3*data) + + pl.figure(1 + 3 * data, figsize=(7, 3)) pl.clf() - pl.plot(xs[:,0],xs[:,1],'+b',label='Source samples') - pl.plot(xt[:,0],xt[:,1],'xr',label='Target samples') + 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.figure(2 + 3 * data, figsize=(7, 3)) + + pl.subplot(1, 3, 1) + pl.imshow(M1, interpolation='nearest') + pl.title('Euclidean 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.subplot(1, 3, 3) + pl.imshow(Mp, interpolation='nearest') pl.title('Sqrt Euclidean cost') + pl.tight_layout() + #%% 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') + G1 = ot.emd(a, b, M1) + G2 = ot.emd(a, b, M2) + Gp = ot.emd(a, b, Mp) + + pl.figure(3 + 3 * data, figsize=(7, 3)) + + 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.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.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.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.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.legend(loc=0) pl.title('OT sqrt Euclidean') + pl.tight_layout() + +pl.show() |