add rst file for documentation

Author: rflamary

docs/source/auto_examples/plot_partial_wass_and_gromov.rst

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+.. 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 <[email protected]>
+    # 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,
+by transporting 50% of the mass
+----------------------------------------------
+
+
+.. 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): 0.29721185147886475
+    Entropic partial Wasserstein distance (m = 0.5): 0.31204119793315976
+    /home/rflamary/PYTHON/POT/examples/plot_partial_wass_and_gromov.py:77: 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:113: 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,
+by transporting 100% and 2/3 of the mass
+-----------------------------------------------------
+
+
+.. code-block:: default
+
+
+    C1 = sp.spatial.distance.cdist(xs, xs)
+    C2 = sp.spatial.distance.cdist(xt, xt)
+
+    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('Partial Wasserstein distance (m = 1): ' + str(log0['partial_gw_dist']))
+    print('Entropic partial 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('Partial Wasserstein')
+    pl.subplot(1, 2, 2)
+    pl.imshow(res, cmap='jet')
+    pl.title('Entropic partial Wasserstein')
+    pl.show()
+
+    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
+    Partial Wasserstein distance (m = 1): 56.18870587756925
+    Entropic partial Wasserstein distance (m = 1): 57.63642536818668
+    /home/rflamary/PYTHON/POT/examples/plot_partial_wass_and_gromov.py:144: 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): 0.18550643334550976
+    Entropic partial Wasserstein distance (m = 2/3): 1.0781947761552997
+    /home/rflamary/PYTHON/POT/examples/plot_partial_wass_and_gromov.py:159: 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:162: 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:165: 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  1.656 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>`_