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Diffstat (limited to 'docs/source/auto_examples/plot_OT_L1_vs_L2.py')
-rw-r--r-- | docs/source/auto_examples/plot_OT_L1_vs_L2.py | 285 |
1 files changed, 192 insertions, 93 deletions
diff --git a/docs/source/auto_examples/plot_OT_L1_vs_L2.py b/docs/source/auto_examples/plot_OT_L1_vs_L2.py index 9bb92fe..090e809 100644 --- a/docs/source/auto_examples/plot_OT_L1_vs_L2.py +++ b/docs/source/auto_examples/plot_OT_L1_vs_L2.py @@ -4,105 +4,204 @@ 2D Optimal transport for different metrics ========================================== -Stole the figure idea from Fig. 1 and 2 in +2D OT on empirical distributio with different gound metric. + +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 -#%% 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') +############################################################################## +# Dataset 1 : uniform sampling +# ---------------------------- + +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 + +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() + +# Data +pl.figure(1, 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.axis('equal') +pl.title('Source and traget distributions') + + +# Cost matrices +pl.figure(2, 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.title('Sqrt Euclidean cost') +pl.tight_layout() + +############################################################################## +# Dataset 1 : Plot OT Matrices +# ---------------------------- + + +#%% EMD +G1 = ot.emd(a, b, M1) +G2 = ot.emd(a, b, M2) +Gp = ot.emd(a, b, Mp) + +# OT matrices +pl.figure(3, 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.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') +pl.tight_layout() + +pl.show() + + +############################################################################## +# Dataset 2 : Partial circle +# -------------------------- + +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() + + +# Data +pl.figure(4, 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.axis('equal') +pl.title('Source and traget distributions') + + +# Cost matrices +pl.figure(5, 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.title('Sqrt Euclidean cost') +pl.tight_layout() + +############################################################################## +# Dataset 2 : Plot OT Matrices +# ----------------------------- + + +#%% EMD +G1 = ot.emd(a, b, M1) +G2 = ot.emd(a, b, M2) +Gp = ot.emd(a, b, Mp) + +# OT matrices +pl.figure(6, 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.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') +pl.tight_layout() + +pl.show() |