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diff --git a/docs/source/auto_examples/plot_OT_2D_samples.rst b/docs/source/auto_examples/plot_OT_2D_samples.rst new file mode 100644 index 0000000..1f1d713 --- /dev/null +++ b/docs/source/auto_examples/plot_OT_2D_samples.rst @@ -0,0 +1,273 @@ + + +.. _sphx_glr_auto_examples_plot_OT_2D_samples.py: + + +==================================================== +2D Optimal transport between empirical distributions +==================================================== + +Illustration of 2D optimal transport between discributions that are weighted +sum of diracs. The OT matrix is plotted with the samples. + + + + +.. code-block:: python + + + # Author: Remi Flamary <remi.flamary@unice.fr> + # Kilian Fatras <kilian.fatras@irisa.fr> + # + # License: MIT License + + import numpy as np + import matplotlib.pylab as pl + import ot + import ot.plot + + + + + + + +Generate data +------------- + + + +.. code-block:: python + + + #%% parameters and data generation + + n = 50 # 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.make_2D_samples_gauss(n, mu_s, cov_s) + xt = ot.datasets.make_2D_samples_gauss(n, mu_t, cov_t) + + a, b = np.ones((n,)) / n, np.ones((n,)) / n # uniform distribution on samples + + # loss matrix + M = ot.dist(xs, xt) + M /= M.max() + + + + + + + +Plot data +--------- + + + +.. code-block:: python + + + #%% 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 target distributions') + + pl.figure(2) + pl.imshow(M, interpolation='nearest') + pl.title('Cost matrix M') + + + + +.. rst-class:: sphx-glr-horizontal + + + * + + .. image:: /auto_examples/images/sphx_glr_plot_OT_2D_samples_001.png + :scale: 47 + + * + + .. image:: /auto_examples/images/sphx_glr_plot_OT_2D_samples_002.png + :scale: 47 + + + + +Compute EMD +----------- + + + +.. code-block:: python + + + #%% 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') + + + + + +.. rst-class:: sphx-glr-horizontal + + + * + + .. image:: /auto_examples/images/sphx_glr_plot_OT_2D_samples_005.png + :scale: 47 + + * + + .. image:: /auto_examples/images/sphx_glr_plot_OT_2D_samples_006.png + :scale: 47 + + + + +Compute Sinkhorn +---------------- + + + +.. code-block:: python + + + #%% sinkhorn + + # reg term + lambd = 1e-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') + + pl.show() + + + + + +.. rst-class:: sphx-glr-horizontal + + + * + + .. image:: /auto_examples/images/sphx_glr_plot_OT_2D_samples_009.png + :scale: 47 + + * + + .. image:: /auto_examples/images/sphx_glr_plot_OT_2D_samples_010.png + :scale: 47 + + + + +Emprirical Sinkhorn +---------------- + + + +.. code-block:: python + + + #%% sinkhorn + + # reg term + lambd = 1e-3 + + Ges = ot.bregman.empirical_sinkhorn(xs, xt, lambd) + + pl.figure(7) + pl.imshow(Ges, interpolation='nearest') + pl.title('OT matrix empirical sinkhorn') + + pl.figure(8) + ot.plot.plot2D_samples_mat(xs, xt, Ges, 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 from samples') + + pl.show() + + + +.. rst-class:: sphx-glr-horizontal + + + * + + .. image:: /auto_examples/images/sphx_glr_plot_OT_2D_samples_013.png + :scale: 47 + + * + + .. image:: /auto_examples/images/sphx_glr_plot_OT_2D_samples_014.png + :scale: 47 + + +.. rst-class:: sphx-glr-script-out + + Out:: + + Warning: numerical errors at iteration 0 + + +**Total running time of the script:** ( 0 minutes 2.616 seconds) + + + +.. only :: html + + .. container:: sphx-glr-footer + + + .. container:: sphx-glr-download + + :download:`Download Python source code: plot_OT_2D_samples.py <plot_OT_2D_samples.py>` + + + + .. container:: sphx-glr-download + + :download:`Download Jupyter notebook: plot_OT_2D_samples.ipynb <plot_OT_2D_samples.ipynb>` + + +.. only:: html + + .. rst-class:: sphx-glr-signature + + `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.readthedocs.io>`_ |