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diff --git a/docs/source/auto_examples/plot_OT_L1_vs_L2.rst b/docs/source/auto_examples/plot_OT_L1_vs_L2.rst new file mode 100644 index 0000000..5db4b55 --- /dev/null +++ b/docs/source/auto_examples/plot_OT_L1_vs_L2.rst @@ -0,0 +1,318 @@ + + +.. _sphx_glr_auto_examples_plot_OT_L1_vs_L2.py: + + +========================================== +2D Optimal transport for different metrics +========================================== + +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 + + + + + +.. code-block:: python + + + # Author: Remi Flamary <remi.flamary@unice.fr> + # + # License: MIT License + + import numpy as np + import matplotlib.pylab as pl + import ot + import ot.plot + + + + + + + +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 target 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() + + + + +.. rst-class:: sphx-glr-horizontal + + + * + + .. image:: /auto_examples/images/sphx_glr_plot_OT_L1_vs_L2_001.png + :scale: 47 + + * + + .. image:: /auto_examples/images/sphx_glr_plot_OT_L1_vs_L2_002.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_007.png + :scale: 47 + + * + + .. image:: /auto_examples/images/sphx_glr_plot_OT_L1_vs_L2_008.png + :scale: 47 + + + + +Dataset 2 : 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(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 0.958 seconds) + + + +.. only :: html + + .. container:: sphx-glr-footer + + + .. container:: sphx-glr-download + + :download:`Download Python source code: plot_OT_L1_vs_L2.py <plot_OT_L1_vs_L2.py>` + + + + .. container:: sphx-glr-download + + :download:`Download Jupyter notebook: plot_OT_L1_vs_L2.ipynb <plot_OT_L1_vs_L2.ipynb>` + + +.. only:: html + + .. rst-class:: sphx-glr-signature + + `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.readthedocs.io>`_ |