update notebooks

1 files changed, 256 insertions, 251 deletions

diff --git a/docs/source/auto_examples/plot_gromov_barycenter.rst b/docs/source/auto_examples/plot_gromov_barycenter.rst
index ca2d4e9..531ee22 100644
--- a/docs/source/auto_examples/plot_gromov_barycenter.rst
+++ b/docs/source/auto_examples/plot_gromov_barycenter.rst
@@ -14,285 +14,285 @@ computation in POT.
 
 .. code-block:: python
 
-

-    # Author: Erwan Vautier <erwan.vautier@gmail.com>

-    #         Nicolas Courty <ncourty@irisa.fr>

-    #

-    # License: MIT License

-

-

-    import numpy as np

-    import scipy as sp

-

-    import scipy.ndimage as spi

-    import matplotlib.pylab as pl

-    from sklearn import manifold

-    from sklearn.decomposition import PCA

-

-    import ot

-

 
+    # Author: Erwan Vautier <erwan.vautier@gmail.com>
+    #         Nicolas Courty <ncourty@irisa.fr>
+    #
+    # License: MIT License
 
 
+    import numpy as np
+    import scipy as sp
 
+    import scipy.ndimage as spi
+    import matplotlib.pylab as pl
+    from sklearn import manifold
+    from sklearn.decomposition import PCA
 
+    import ot
 
-Smacof MDS

- ----------

-

- This function allows to find an embedding of points given a dissimilarity matrix

- that will be given by the output of the algorithm

+
+
+
+
+
+
+Smacof MDS
+----------
+
+This function allows to find an embedding of points given a dissimilarity matrix
+that will be given by the output of the algorithm
 
 
 
 .. code-block:: python
 
-

-

-    def smacof_mds(C, dim, max_iter=3000, eps=1e-9):

-        """

-        Returns an interpolated point cloud following the dissimilarity matrix C

-        using SMACOF multidimensional scaling (MDS) in specific dimensionned

-        target space

-

-        Parameters

-        ----------

-        C : ndarray, shape (ns, ns)

-            dissimilarity matrix

-        dim : int

-              dimension of the targeted space

-        max_iter :  int

-            Maximum number of iterations of the SMACOF algorithm for a single run

-        eps : float

-            relative tolerance w.r.t stress to declare converge

-

-        Returns

-        -------

-        npos : ndarray, shape (R, dim)

-               Embedded coordinates of the interpolated point cloud (defined with

-               one isometry)

-        """

-

-        rng = np.random.RandomState(seed=3)

-

-        mds = manifold.MDS(

-            dim,

-            max_iter=max_iter,

-            eps=1e-9,

-            dissimilarity='precomputed',

-            n_init=1)

-        pos = mds.fit(C).embedding_

-

-        nmds = manifold.MDS(

-            2,

-            max_iter=max_iter,

-            eps=1e-9,

-            dissimilarity="precomputed",

-            random_state=rng,

-            n_init=1)

-        npos = nmds.fit_transform(C, init=pos)

-

-        return npos

-

-

-
-
-
-
-
-
-Data preparation

- ----------------

-

- The four distributions are constructed from 4 simple images

+
+
+    def smacof_mds(C, dim, max_iter=3000, eps=1e-9):
+        """
+        Returns an interpolated point cloud following the dissimilarity matrix C
+        using SMACOF multidimensional scaling (MDS) in specific dimensionned
+        target space
+
+        Parameters
+        ----------
+        C : ndarray, shape (ns, ns)
+            dissimilarity matrix
+        dim : int
+              dimension of the targeted space
+        max_iter :  int
+            Maximum number of iterations of the SMACOF algorithm for a single run
+        eps : float
+            relative tolerance w.r.t stress to declare converge
+
+        Returns
+        -------
+        npos : ndarray, shape (R, dim)
+               Embedded coordinates of the interpolated point cloud (defined with
+               one isometry)
+        """
+
+        rng = np.random.RandomState(seed=3)
+
+        mds = manifold.MDS(
+            dim,
+            max_iter=max_iter,
+            eps=1e-9,
+            dissimilarity='precomputed',
+            n_init=1)
+        pos = mds.fit(C).embedding_
+
+        nmds = manifold.MDS(
+            2,
+            max_iter=max_iter,
+            eps=1e-9,
+            dissimilarity="precomputed",
+            random_state=rng,
+            n_init=1)
+        npos = nmds.fit_transform(C, init=pos)
+
+        return npos
+
+
+
+
+
+
+
+
+Data preparation
+----------------
+
+The four distributions are constructed from 4 simple images
 
 
 
 .. code-block:: python
 
-

-

-    def im2mat(I):

-        """Converts and image to matrix (one pixel per line)"""

-        return I.reshape((I.shape[0] * I.shape[1], I.shape[2]))

-

-

-    square = spi.imread('../data/square.png').astype(np.float64)[:, :, 2] / 256

-    cross = spi.imread('../data/cross.png').astype(np.float64)[:, :, 2] / 256

-    triangle = spi.imread('../data/triangle.png').astype(np.float64)[:, :, 2] / 256

-    star = spi.imread('../data/star.png').astype(np.float64)[:, :, 2] / 256

-

-    shapes = [square, cross, triangle, star]

-

-    S = 4

-    xs = [[] for i in range(S)]

-

-

-    for nb in range(4):

-        for i in range(8):

-            for j in range(8):

-                if shapes[nb][i, j] < 0.95:

-                    xs[nb].append([j, 8 - i])

-

-    xs = np.array([np.array(xs[0]), np.array(xs[1]),

-                   np.array(xs[2]), np.array(xs[3])])

-

 
 
+    def im2mat(I):
+        """Converts and image to matrix (one pixel per line)"""
+        return I.reshape((I.shape[0] * I.shape[1], I.shape[2]))
+
+
+    square = spi.imread('../data/square.png').astype(np.float64)[:, :, 2] / 256
+    cross = spi.imread('../data/cross.png').astype(np.float64)[:, :, 2] / 256
+    triangle = spi.imread('../data/triangle.png').astype(np.float64)[:, :, 2] / 256
+    star = spi.imread('../data/star.png').astype(np.float64)[:, :, 2] / 256
+
+    shapes = [square, cross, triangle, star]
+
+    S = 4
+    xs = [[] for i in range(S)]
+
 
+    for nb in range(4):
+        for i in range(8):
+            for j in range(8):
+                if shapes[nb][i, j] < 0.95:
+                    xs[nb].append([j, 8 - i])
 
+    xs = np.array([np.array(xs[0]), np.array(xs[1]),
+                   np.array(xs[2]), np.array(xs[3])])
 
 
-Barycenter computation

-----------------------

+
+
+
+
+
+Barycenter computation
+----------------------
 
 
 
 .. code-block:: python
 
-

-

-    ns = [len(xs[s]) for s in range(S)]

-    n_samples = 30

-

-    """Compute all distances matrices for the four shapes"""

-    Cs = [sp.spatial.distance.cdist(xs[s], xs[s]) for s in range(S)]

-    Cs = [cs / cs.max() for cs in Cs]

-

-    ps = [ot.unif(ns[s]) for s in range(S)]

-    p = ot.unif(n_samples)

-

-

-    lambdast = [[float(i) / 3, float(3 - i) / 3] for i in [1, 2]]

-

-    Ct01 = [0 for i in range(2)]

-    for i in range(2):

-        Ct01[i] = ot.gromov.gromov_barycenters(n_samples, [Cs[0], Cs[1]],

-                                               [ps[0], ps[1]

-                                                ], p, lambdast[i], 'square_loss', 5e-4,

-                                               max_iter=100, tol=1e-3)

-

-    Ct02 = [0 for i in range(2)]

-    for i in range(2):

-        Ct02[i] = ot.gromov.gromov_barycenters(n_samples, [Cs[0], Cs[2]],

-                                               [ps[0], ps[2]

-                                                ], p, lambdast[i], 'square_loss', 5e-4,

-                                               max_iter=100, tol=1e-3)

-

-    Ct13 = [0 for i in range(2)]

-    for i in range(2):

-        Ct13[i] = ot.gromov.gromov_barycenters(n_samples, [Cs[1], Cs[3]],

-                                               [ps[1], ps[3]

-                                                ], p, lambdast[i], 'square_loss', 5e-4,

-                                               max_iter=100, tol=1e-3)

-

-    Ct23 = [0 for i in range(2)]

-    for i in range(2):

-        Ct23[i] = ot.gromov.gromov_barycenters(n_samples, [Cs[2], Cs[3]],

-                                               [ps[2], ps[3]

-                                                ], p, lambdast[i], 'square_loss', 5e-4,

-                                               max_iter=100, tol=1e-3)

-

-

-
-
-
-
-
-
-Visualization

- -------------

-

- The PCA helps in getting consistency between the rotations

+
+
+    ns = [len(xs[s]) for s in range(S)]
+    n_samples = 30
+
+    """Compute all distances matrices for the four shapes"""
+    Cs = [sp.spatial.distance.cdist(xs[s], xs[s]) for s in range(S)]
+    Cs = [cs / cs.max() for cs in Cs]
+
+    ps = [ot.unif(ns[s]) for s in range(S)]
+    p = ot.unif(n_samples)
+
+
+    lambdast = [[float(i) / 3, float(3 - i) / 3] for i in [1, 2]]
+
+    Ct01 = [0 for i in range(2)]
+    for i in range(2):
+        Ct01[i] = ot.gromov.gromov_barycenters(n_samples, [Cs[0], Cs[1]],
+                                               [ps[0], ps[1]
+                                                ], p, lambdast[i], 'square_loss',  # 5e-4,
+                                               max_iter=100, tol=1e-3)
+
+    Ct02 = [0 for i in range(2)]
+    for i in range(2):
+        Ct02[i] = ot.gromov.gromov_barycenters(n_samples, [Cs[0], Cs[2]],
+                                               [ps[0], ps[2]
+                                                ], p, lambdast[i], 'square_loss',  # 5e-4,
+                                               max_iter=100, tol=1e-3)
+
+    Ct13 = [0 for i in range(2)]
+    for i in range(2):
+        Ct13[i] = ot.gromov.gromov_barycenters(n_samples, [Cs[1], Cs[3]],
+                                               [ps[1], ps[3]
+                                                ], p, lambdast[i], 'square_loss',  # 5e-4,
+                                               max_iter=100, tol=1e-3)
+
+    Ct23 = [0 for i in range(2)]
+    for i in range(2):
+        Ct23[i] = ot.gromov.gromov_barycenters(n_samples, [Cs[2], Cs[3]],
+                                               [ps[2], ps[3]
+                                                ], p, lambdast[i], 'square_loss',  # 5e-4,
+                                               max_iter=100, tol=1e-3)
+
+
+
+
+
+
+
+
+Visualization
+-------------
+
+The PCA helps in getting consistency between the rotations
 
 
 
 .. code-block:: python
 
-

-

-    clf = PCA(n_components=2)

-    npos = [0, 0, 0, 0]

-    npos = [smacof_mds(Cs[s], 2) for s in range(S)]

-

-    npost01 = [0, 0]

-    npost01 = [smacof_mds(Ct01[s], 2) for s in range(2)]

-    npost01 = [clf.fit_transform(npost01[s]) for s in range(2)]

-

-    npost02 = [0, 0]

-    npost02 = [smacof_mds(Ct02[s], 2) for s in range(2)]

-    npost02 = [clf.fit_transform(npost02[s]) for s in range(2)]

-

-    npost13 = [0, 0]

-    npost13 = [smacof_mds(Ct13[s], 2) for s in range(2)]

-    npost13 = [clf.fit_transform(npost13[s]) for s in range(2)]

-

-    npost23 = [0, 0]

-    npost23 = [smacof_mds(Ct23[s], 2) for s in range(2)]

-    npost23 = [clf.fit_transform(npost23[s]) for s in range(2)]

-

-

-    fig = pl.figure(figsize=(10, 10))

-

-    ax1 = pl.subplot2grid((4, 4), (0, 0))

-    pl.xlim((-1, 1))

-    pl.ylim((-1, 1))

-    ax1.scatter(npos[0][:, 0], npos[0][:, 1], color='r')

-

-    ax2 = pl.subplot2grid((4, 4), (0, 1))

-    pl.xlim((-1, 1))

-    pl.ylim((-1, 1))

-    ax2.scatter(npost01[1][:, 0], npost01[1][:, 1], color='b')

-

-    ax3 = pl.subplot2grid((4, 4), (0, 2))

-    pl.xlim((-1, 1))

-    pl.ylim((-1, 1))

-    ax3.scatter(npost01[0][:, 0], npost01[0][:, 1], color='b')

-

-    ax4 = pl.subplot2grid((4, 4), (0, 3))

-    pl.xlim((-1, 1))

-    pl.ylim((-1, 1))

-    ax4.scatter(npos[1][:, 0], npos[1][:, 1], color='r')

-

-    ax5 = pl.subplot2grid((4, 4), (1, 0))

-    pl.xlim((-1, 1))

-    pl.ylim((-1, 1))

-    ax5.scatter(npost02[1][:, 0], npost02[1][:, 1], color='b')

-

-    ax6 = pl.subplot2grid((4, 4), (1, 3))

-    pl.xlim((-1, 1))

-    pl.ylim((-1, 1))

-    ax6.scatter(npost13[1][:, 0], npost13[1][:, 1], color='b')

-

-    ax7 = pl.subplot2grid((4, 4), (2, 0))

-    pl.xlim((-1, 1))

-    pl.ylim((-1, 1))

-    ax7.scatter(npost02[0][:, 0], npost02[0][:, 1], color='b')

-

-    ax8 = pl.subplot2grid((4, 4), (2, 3))

-    pl.xlim((-1, 1))

-    pl.ylim((-1, 1))

-    ax8.scatter(npost13[0][:, 0], npost13[0][:, 1], color='b')

-

-    ax9 = pl.subplot2grid((4, 4), (3, 0))

-    pl.xlim((-1, 1))

-    pl.ylim((-1, 1))

-    ax9.scatter(npos[2][:, 0], npos[2][:, 1], color='r')

-

-    ax10 = pl.subplot2grid((4, 4), (3, 1))

-    pl.xlim((-1, 1))

-    pl.ylim((-1, 1))

-    ax10.scatter(npost23[1][:, 0], npost23[1][:, 1], color='b')

-

-    ax11 = pl.subplot2grid((4, 4), (3, 2))

-    pl.xlim((-1, 1))

-    pl.ylim((-1, 1))

-    ax11.scatter(npost23[0][:, 0], npost23[0][:, 1], color='b')

-

-    ax12 = pl.subplot2grid((4, 4), (3, 3))

-    pl.xlim((-1, 1))

-    pl.ylim((-1, 1))

-    ax12.scatter(npos[3][:, 0], npos[3][:, 1], color='r')

+
+
+    clf = PCA(n_components=2)
+    npos = [0, 0, 0, 0]
+    npos = [smacof_mds(Cs[s], 2) for s in range(S)]
+
+    npost01 = [0, 0]
+    npost01 = [smacof_mds(Ct01[s], 2) for s in range(2)]
+    npost01 = [clf.fit_transform(npost01[s]) for s in range(2)]
+
+    npost02 = [0, 0]
+    npost02 = [smacof_mds(Ct02[s], 2) for s in range(2)]
+    npost02 = [clf.fit_transform(npost02[s]) for s in range(2)]
+
+    npost13 = [0, 0]
+    npost13 = [smacof_mds(Ct13[s], 2) for s in range(2)]
+    npost13 = [clf.fit_transform(npost13[s]) for s in range(2)]
+
+    npost23 = [0, 0]
+    npost23 = [smacof_mds(Ct23[s], 2) for s in range(2)]
+    npost23 = [clf.fit_transform(npost23[s]) for s in range(2)]
+
+
+    fig = pl.figure(figsize=(10, 10))
+
+    ax1 = pl.subplot2grid((4, 4), (0, 0))
+    pl.xlim((-1, 1))
+    pl.ylim((-1, 1))
+    ax1.scatter(npos[0][:, 0], npos[0][:, 1], color='r')
+
+    ax2 = pl.subplot2grid((4, 4), (0, 1))
+    pl.xlim((-1, 1))
+    pl.ylim((-1, 1))
+    ax2.scatter(npost01[1][:, 0], npost01[1][:, 1], color='b')
+
+    ax3 = pl.subplot2grid((4, 4), (0, 2))
+    pl.xlim((-1, 1))
+    pl.ylim((-1, 1))
+    ax3.scatter(npost01[0][:, 0], npost01[0][:, 1], color='b')
+
+    ax4 = pl.subplot2grid((4, 4), (0, 3))
+    pl.xlim((-1, 1))
+    pl.ylim((-1, 1))
+    ax4.scatter(npos[1][:, 0], npos[1][:, 1], color='r')
+
+    ax5 = pl.subplot2grid((4, 4), (1, 0))
+    pl.xlim((-1, 1))
+    pl.ylim((-1, 1))
+    ax5.scatter(npost02[1][:, 0], npost02[1][:, 1], color='b')
+
+    ax6 = pl.subplot2grid((4, 4), (1, 3))
+    pl.xlim((-1, 1))
+    pl.ylim((-1, 1))
+    ax6.scatter(npost13[1][:, 0], npost13[1][:, 1], color='b')
+
+    ax7 = pl.subplot2grid((4, 4), (2, 0))
+    pl.xlim((-1, 1))
+    pl.ylim((-1, 1))
+    ax7.scatter(npost02[0][:, 0], npost02[0][:, 1], color='b')
+
+    ax8 = pl.subplot2grid((4, 4), (2, 3))
+    pl.xlim((-1, 1))
+    pl.ylim((-1, 1))
+    ax8.scatter(npost13[0][:, 0], npost13[0][:, 1], color='b')
+
+    ax9 = pl.subplot2grid((4, 4), (3, 0))
+    pl.xlim((-1, 1))
+    pl.ylim((-1, 1))
+    ax9.scatter(npos[2][:, 0], npos[2][:, 1], color='r')
+
+    ax10 = pl.subplot2grid((4, 4), (3, 1))
+    pl.xlim((-1, 1))
+    pl.ylim((-1, 1))
+    ax10.scatter(npost23[1][:, 0], npost23[1][:, 1], color='b')
+
+    ax11 = pl.subplot2grid((4, 4), (3, 2))
+    pl.xlim((-1, 1))
+    pl.ylim((-1, 1))
+    ax11.scatter(npost23[0][:, 0], npost23[0][:, 1], color='b')
+
+    ax12 = pl.subplot2grid((4, 4), (3, 3))
+    pl.xlim((-1, 1))
+    pl.ylim((-1, 1))
+    ax12.scatter(npos[3][:, 0], npos[3][:, 1], color='r')
 
 
 
@@ -302,11 +302,13 @@ Visualization
 
 
 
-**Total running time of the script:** ( 8 minutes  43.875 seconds)
+**Total running time of the script:** ( 0 minutes  5.906 seconds)
+
 
 
+.. only :: html
 
-.. container:: sphx-glr-footer
+ .. container:: sphx-glr-footer
 
 
   .. container:: sphx-glr-download
@@ -319,6 +321,9 @@ Visualization
 
      :download:`Download Jupyter notebook: plot_gromov_barycenter.ipynb <plot_gromov_barycenter.ipynb>`
 
-.. rst-class:: sphx-glr-signature
 
-    `Generated by Sphinx-Gallery <http://sphinx-gallery.readthedocs.io>`_
+.. only:: html
+
+ .. rst-class:: sphx-glr-signature
+
+    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.readthedocs.io>`_