From dd3546baf9c59733b2109a971293eba48d2eaed3 Mon Sep 17 00:00:00 2001
From: Rémi Flamary <remi.flamary@gmail.com>
Date: Fri, 15 Sep 2017 13:57:01 +0200
Subject: add all files for doc

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 docs/source/auto_examples/plot_gromov.rst | 180 ++++++++++++++++++++++++++++++
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+
+
+.. _sphx_glr_auto_examples_plot_gromov.py:
+
+
+==========================
+Gromov-Wasserstein example
+==========================
+
+This example is designed to show how to use the Gromov-Wassertsein distance
+computation in POT.
+
+
+
+.. code-block:: python
+
+
+    # Author: Erwan Vautier <erwan.vautier@gmail.com>
+    #         Nicolas Courty <ncourty@irisa.fr>
+    #
+    # License: MIT License
+
+    import scipy as sp
+    import numpy as np
+    import matplotlib.pylab as pl
+    from mpl_toolkits.mplot3d import Axes3D  # noqa
+    import ot
+
+
+
+
+
+
+
+
+Sample two Gaussian distributions (2D and 3D)
+ ---------------------------------------------
+
+ 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:: python
+
+
+
+    n_samples = 30  # nb samples
+
+    mu_s = np.array([0, 0])
+    cov_s = np.array([[1, 0], [0, 1]])
+
+    mu_t = np.array([4, 4, 4])
+    cov_t = np.array([[1, 0, 0], [0, 1, 0], [0, 0, 1]])
+
+
+    xs = ot.datasets.get_2D_samples_gauss(n_samples, mu_s, cov_s)
+    P = sp.linalg.sqrtm(cov_t)
+    xt = np.random.randn(n_samples, 3).dot(P) + mu_t
+
+
+
+
+
+
+
+
+Plotting the distributions
+--------------------------
+
+
+
+.. code-block:: python
+
+
+
+    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_gromov_001.png
+    :align: center
+
+
+
+
+Compute distance kernels, normalize them and then display
+---------------------------------------------------------
+
+
+
+.. code-block:: python
+
+
+
+    C1 = sp.spatial.distance.cdist(xs, xs)
+    C2 = sp.spatial.distance.cdist(xt, xt)
+
+    C1 /= C1.max()
+    C2 /= C2.max()
+
+    pl.figure()
+    pl.subplot(121)
+    pl.imshow(C1)
+    pl.subplot(122)
+    pl.imshow(C2)
+    pl.show()
+
+
+
+
+.. image:: /auto_examples/images/sphx_glr_plot_gromov_002.png
+    :align: center
+
+
+
+
+Compute Gromov-Wasserstein plans and distance
+---------------------------------------------
+
+
+
+.. code-block:: python
+
+
+
+    p = ot.unif(n_samples)
+    q = ot.unif(n_samples)
+
+    gw = ot.gromov_wasserstein(C1, C2, p, q, 'square_loss', epsilon=5e-4)
+    gw_dist = ot.gromov_wasserstein2(C1, C2, p, q, 'square_loss', epsilon=5e-4)
+
+    print('Gromov-Wasserstein distances between the distribution: ' + str(gw_dist))
+
+    pl.figure()
+    pl.imshow(gw, cmap='jet')
+    pl.colorbar()
+    pl.show()
+
+
+
+.. image:: /auto_examples/images/sphx_glr_plot_gromov_003.png
+    :align: center
+
+
+.. rst-class:: sphx-glr-script-out
+
+ Out::
+
+    Gromov-Wasserstein distances between the distribution: 0.225058076974
+
+
+**Total running time of the script:** ( 0 minutes  4.070 seconds)
+
+
+
+.. container:: sphx-glr-footer
+
+
+  .. container:: sphx-glr-download
+
+     :download:`Download Python source code: plot_gromov.py <plot_gromov.py>`
+
+
+
+  .. container:: sphx-glr-download
+
+     :download:`Download Jupyter notebook: plot_gromov.ipynb <plot_gromov.ipynb>`
+
+.. rst-class:: sphx-glr-signature
+
+    `Generated by Sphinx-Gallery <http://sphinx-gallery.readthedocs.io>`_
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