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diff --git a/docs/source/auto_examples/plot_partial_wass_and_gromov.rst b/docs/source/auto_examples/plot_partial_wass_and_gromov.rst deleted file mode 100644 index 2d51210..0000000 --- a/docs/source/auto_examples/plot_partial_wass_and_gromov.rst +++ /dev/null @@ -1,312 +0,0 @@ -.. only:: html - - .. note:: - :class: sphx-glr-download-link-note - - Click :ref:`here <sphx_glr_download_auto_examples_plot_partial_wass_and_gromov.py>` to download the full example code - .. rst-class:: sphx-glr-example-title - - .. _sphx_glr_auto_examples_plot_partial_wass_and_gromov.py: - - -================================================== -Partial Wasserstein and Gromov-Wasserstein example -================================================== - -This example is designed to show how to use the Partial (Gromov-)Wassertsein -distance computation in POT. - - -.. code-block:: default - - - # Author: Laetitia Chapel <laetitia.chapel@irisa.fr> - # License: MIT License - - # necessary for 3d plot even if not used - from mpl_toolkits.mplot3d import Axes3D # noqa - import scipy as sp - import numpy as np - import matplotlib.pylab as pl - import ot - - - - - - - - - -Sample two 2D Gaussian distributions and plot them --------------------------------------------------- - -For demonstration purpose, we sample two Gaussian distributions in 2-d -spaces and add some random noise. - - -.. code-block:: default - - - - n_samples = 20 # nb samples (gaussian) - n_noise = 20 # nb of samples (noise) - - mu = np.array([0, 0]) - cov = np.array([[1, 0], [0, 2]]) - - xs = ot.datasets.make_2D_samples_gauss(n_samples, mu, cov) - xs = np.append(xs, (np.random.rand(n_noise, 2) + 1) * 4).reshape((-1, 2)) - xt = ot.datasets.make_2D_samples_gauss(n_samples, mu, cov) - xt = np.append(xt, (np.random.rand(n_noise, 2) + 1) * -3).reshape((-1, 2)) - - M = sp.spatial.distance.cdist(xs, xt) - - fig = pl.figure() - ax1 = fig.add_subplot(131) - ax1.plot(xs[:, 0], xs[:, 1], '+b', label='Source samples') - ax2 = fig.add_subplot(132) - ax2.scatter(xt[:, 0], xt[:, 1], color='r') - ax3 = fig.add_subplot(133) - ax3.imshow(M) - pl.show() - - - - -.. image:: /auto_examples/images/sphx_glr_plot_partial_wass_and_gromov_001.png - :class: sphx-glr-single-img - - -.. rst-class:: sphx-glr-script-out - - Out: - - .. code-block:: none - - /home/rflamary/PYTHON/POT/examples/plot_partial_wass_and_gromov.py:51: UserWarning: Matplotlib is currently using agg, which is a non-GUI backend, so cannot show the figure. - pl.show() - - - - -Compute partial Wasserstein plans and distance ----------------------------------------------- - - -.. code-block:: default - - - p = ot.unif(n_samples + n_noise) - q = ot.unif(n_samples + n_noise) - - w0, log0 = ot.partial.partial_wasserstein(p, q, M, m=0.5, log=True) - w, log = ot.partial.entropic_partial_wasserstein(p, q, M, reg=0.1, m=0.5, - log=True) - - print('Partial Wasserstein distance (m = 0.5): ' + str(log0['partial_w_dist'])) - print('Entropic partial Wasserstein distance (m = 0.5): ' + - str(log['partial_w_dist'])) - - pl.figure(1, (10, 5)) - pl.subplot(1, 2, 1) - pl.imshow(w0, cmap='jet') - pl.title('Partial Wasserstein') - pl.subplot(1, 2, 2) - pl.imshow(w, cmap='jet') - pl.title('Entropic partial Wasserstein') - pl.show() - - - - - -.. image:: /auto_examples/images/sphx_glr_plot_partial_wass_and_gromov_002.png - :class: sphx-glr-single-img - - -.. rst-class:: sphx-glr-script-out - - Out: - - .. code-block:: none - - Partial Wasserstein distance (m = 0.5): 0.507323938973194 - Entropic partial Wasserstein distance (m = 0.5): 0.5205305886057896 - /home/rflamary/PYTHON/POT/examples/plot_partial_wass_and_gromov.py:76: UserWarning: Matplotlib is currently using agg, which is a non-GUI backend, so cannot show the figure. - pl.show() - - - - -Sample one 2D and 3D Gaussian distributions and plot them ---------------------------------------------------------- - -The Gromov-Wasserstein distance allows to compute distances with samples that -do not belong to the same metric space. For demonstration purpose, we sample -two Gaussian distributions in 2- and 3-dimensional spaces. - - -.. code-block:: default - - - n_samples = 20 # nb samples - n_noise = 10 # nb of samples (noise) - - p = ot.unif(n_samples + n_noise) - q = ot.unif(n_samples + n_noise) - - mu_s = np.array([0, 0]) - cov_s = np.array([[1, 0], [0, 1]]) - - mu_t = np.array([0, 0, 0]) - cov_t = np.array([[1, 0, 0], [0, 1, 0], [0, 0, 1]]) - - - xs = ot.datasets.make_2D_samples_gauss(n_samples, mu_s, cov_s) - xs = np.concatenate((xs, ((np.random.rand(n_noise, 2) + 1) * 4)), axis=0) - P = sp.linalg.sqrtm(cov_t) - xt = np.random.randn(n_samples, 3).dot(P) + mu_t - xt = np.concatenate((xt, ((np.random.rand(n_noise, 3) + 1) * 10)), axis=0) - - fig = pl.figure() - ax1 = fig.add_subplot(121) - ax1.plot(xs[:, 0], xs[:, 1], '+b', label='Source samples') - ax2 = fig.add_subplot(122, projection='3d') - ax2.scatter(xt[:, 0], xt[:, 1], xt[:, 2], color='r') - pl.show() - - - - - -.. image:: /auto_examples/images/sphx_glr_plot_partial_wass_and_gromov_003.png - :class: sphx-glr-single-img - - -.. rst-class:: sphx-glr-script-out - - Out: - - .. code-block:: none - - /home/rflamary/PYTHON/POT/examples/plot_partial_wass_and_gromov.py:112: UserWarning: Matplotlib is currently using agg, which is a non-GUI backend, so cannot show the figure. - pl.show() - - - - -Compute partial Gromov-Wasserstein plans and distance ------------------------------------------------------ - - -.. code-block:: default - - - C1 = sp.spatial.distance.cdist(xs, xs) - C2 = sp.spatial.distance.cdist(xt, xt) - - # transport 100% of the mass - print('-----m = 1') - m = 1 - res0, log0 = ot.partial.partial_gromov_wasserstein(C1, C2, p, q, m=m, log=True) - res, log = ot.partial.entropic_partial_gromov_wasserstein(C1, C2, p, q, 10, - m=m, log=True) - - print('Wasserstein distance (m = 1): ' + str(log0['partial_gw_dist'])) - print('Entropic Wasserstein distance (m = 1): ' + str(log['partial_gw_dist'])) - - pl.figure(1, (10, 5)) - pl.title("mass to be transported m = 1") - pl.subplot(1, 2, 1) - pl.imshow(res0, cmap='jet') - pl.title('Wasserstein') - pl.subplot(1, 2, 2) - pl.imshow(res, cmap='jet') - pl.title('Entropic Wasserstein') - pl.show() - - # transport 2/3 of the mass - print('-----m = 2/3') - m = 2 / 3 - res0, log0 = ot.partial.partial_gromov_wasserstein(C1, C2, p, q, m=m, log=True) - res, log = ot.partial.entropic_partial_gromov_wasserstein(C1, C2, p, q, 10, - m=m, log=True) - - print('Partial Wasserstein distance (m = 2/3): ' + - str(log0['partial_gw_dist'])) - print('Entropic partial Wasserstein distance (m = 2/3): ' + - str(log['partial_gw_dist'])) - - pl.figure(1, (10, 5)) - pl.title("mass to be transported m = 2/3") - pl.subplot(1, 2, 1) - pl.imshow(res0, cmap='jet') - pl.title('Partial Wasserstein') - pl.subplot(1, 2, 2) - pl.imshow(res, cmap='jet') - pl.title('Entropic partial Wasserstein') - pl.show() - - - -.. image:: /auto_examples/images/sphx_glr_plot_partial_wass_and_gromov_004.png - :class: sphx-glr-single-img - - -.. rst-class:: sphx-glr-script-out - - Out: - - .. code-block:: none - - -----m = 1 - Wasserstein distance (m = 1): 63.65368600872179 - Entropic Wasserstein distance (m = 1): 65.23659085946916 - /home/rflamary/PYTHON/POT/examples/plot_partial_wass_and_gromov.py:141: UserWarning: Matplotlib is currently using agg, which is a non-GUI backend, so cannot show the figure. - pl.show() - -----m = 2/3 - Partial Wasserstein distance (m = 2/3): 0.23235485397666825 - Entropic partial Wasserstein distance (m = 2/3): 1.4645434781619244 - /home/rflamary/PYTHON/POT/examples/plot_partial_wass_and_gromov.py:157: MatplotlibDeprecationWarning: Adding an axes using the same arguments as a previous axes currently reuses the earlier instance. In a future version, a new instance will always be created and returned. Meanwhile, this warning can be suppressed, and the future behavior ensured, by passing a unique label to each axes instance. - pl.subplot(1, 2, 1) - /home/rflamary/PYTHON/POT/examples/plot_partial_wass_and_gromov.py:160: MatplotlibDeprecationWarning: Adding an axes using the same arguments as a previous axes currently reuses the earlier instance. In a future version, a new instance will always be created and returned. Meanwhile, this warning can be suppressed, and the future behavior ensured, by passing a unique label to each axes instance. - pl.subplot(1, 2, 2) - /home/rflamary/PYTHON/POT/examples/plot_partial_wass_and_gromov.py:163: UserWarning: Matplotlib is currently using agg, which is a non-GUI backend, so cannot show the figure. - pl.show() - - - - - -.. rst-class:: sphx-glr-timing - - **Total running time of the script:** ( 0 minutes 1.543 seconds) - - -.. _sphx_glr_download_auto_examples_plot_partial_wass_and_gromov.py: - - -.. only :: html - - .. container:: sphx-glr-footer - :class: sphx-glr-footer-example - - - - .. container:: sphx-glr-download sphx-glr-download-python - - :download:`Download Python source code: plot_partial_wass_and_gromov.py <plot_partial_wass_and_gromov.py>` - - - - .. container:: sphx-glr-download sphx-glr-download-jupyter - - :download:`Download Jupyter notebook: plot_partial_wass_and_gromov.ipynb <plot_partial_wass_and_gromov.ipynb>` - - -.. only:: html - - .. rst-class:: sphx-glr-signature - - `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_ |