diff options
author | RĂ©mi Flamary <remi.flamary@gmail.com> | 2017-09-15 14:54:21 +0200 |
---|---|---|
committer | GitHub <noreply@github.com> | 2017-09-15 14:54:21 +0200 |
commit | 81b2796226f3abde29fc024752728444da77509a (patch) | |
tree | c52cec3c38552f9f8c15361758aa9a80c30c3ef3 /docs/source/auto_examples/plot_OT_L1_vs_L2.rst | |
parent | e70d5420204db78691af2d0fbe04cc3d4416a8f4 (diff) | |
parent | 7fea2cd3e8ad29bf3fa442d7642bae124ee2bab0 (diff) |
Merge pull request #27 from rflamary/autonb
auto notebooks + release update (fixes #16)
Diffstat (limited to 'docs/source/auto_examples/plot_OT_L1_vs_L2.rst')
-rw-r--r-- | docs/source/auto_examples/plot_OT_L1_vs_L2.rst | 350 |
1 files changed, 244 insertions, 106 deletions
diff --git a/docs/source/auto_examples/plot_OT_L1_vs_L2.rst b/docs/source/auto_examples/plot_OT_L1_vs_L2.rst index 4e94bef..a569b50 100644 --- a/docs/source/auto_examples/plot_OT_L1_vs_L2.rst +++ b/docs/source/auto_examples/plot_OT_L1_vs_L2.rst @@ -7,11 +7,86 @@ 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 + + + +.. code-block:: python + + + # Author: Remi Flamary <remi.flamary@unice.fr> + # + # License: MIT License + + import numpy as np + import matplotlib.pylab as pl + import ot + + + + + + + +Dataset 1 : uniform sampling +---------------------------- + + + +.. code-block:: python + + + 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() @@ -29,130 +104,193 @@ https://arxiv.org/pdf/1706.07650.pdf .. image:: /auto_examples/images/sphx_glr_plot_OT_L1_vs_L2_002.png :scale: 47 - * - .. image:: /auto_examples/images/sphx_glr_plot_OT_L1_vs_L2_003.png - :scale: 47 - * - .. image:: /auto_examples/images/sphx_glr_plot_OT_L1_vs_L2_004.png - :scale: 47 +Dataset 1 : Plot OT Matrices +---------------------------- + + + +.. code-block:: python + + + + #%% 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() + + + + + +.. image:: /auto_examples/images/sphx_glr_plot_OT_L1_vs_L2_005.png + :align: center + + + + +Dataset 2 : Partial circle +-------------------------- + + + +.. code-block:: python + + + 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() + + + + +.. rst-class:: sphx-glr-horizontal + * - .. image:: /auto_examples/images/sphx_glr_plot_OT_L1_vs_L2_005.png + .. image:: /auto_examples/images/sphx_glr_plot_OT_L1_vs_L2_007.png :scale: 47 * - .. image:: /auto_examples/images/sphx_glr_plot_OT_L1_vs_L2_006.png + .. image:: /auto_examples/images/sphx_glr_plot_OT_L1_vs_L2_008.png :scale: 47 +Dataset 2 : Plot OT Matrices +----------------------------- + + .. code-block:: python - 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') - -**Total running time of the script:** ( 0 minutes 1.417 seconds) + #%% 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() + + + +.. image:: /auto_examples/images/sphx_glr_plot_OT_L1_vs_L2_011.png + :align: center + + + + +**Total running time of the script:** ( 0 minutes 1.976 seconds) |