update notebooks

10 files changed, 208 insertions, 107 deletions

diff --git a/docs/source/auto_examples/auto_examples_jupyter.zip b/docs/source/auto_examples/auto_examples_jupyter.zip
index 42f42de..4703026 100644
--- a/docs/source/auto_examples/auto_examples_jupyter.zip
+++ b/docs/source/auto_examples/auto_examples_jupyter.zip
diff --git a/docs/source/auto_examples/auto_examples_python.zip b/docs/source/auto_examples/auto_examples_python.zip
index 0fb2cda..7c7ff86 100644
--- a/docs/source/auto_examples/auto_examples_python.zip
+++ b/docs/source/auto_examples/auto_examples_python.zip
diff --git a/docs/source/auto_examples/images/sphx_glr_plot_gromov_001.png b/docs/source/auto_examples/images/sphx_glr_plot_gromov_001.png
index 09864f2..8672249 100644
--- a/docs/source/auto_examples/images/sphx_glr_plot_gromov_001.png
+++ b/docs/source/auto_examples/images/sphx_glr_plot_gromov_001.png
diff --git a/docs/source/auto_examples/images/sphx_glr_plot_gromov_002.png b/docs/source/auto_examples/images/sphx_glr_plot_gromov_002.png
index b2e3fa4..c4eb8e0 100644
--- a/docs/source/auto_examples/images/sphx_glr_plot_gromov_002.png
+++ b/docs/source/auto_examples/images/sphx_glr_plot_gromov_002.png
diff --git a/docs/source/auto_examples/images/sphx_glr_plot_gromov_003.png b/docs/source/auto_examples/images/sphx_glr_plot_gromov_003.png
index 73a322d..c17d386 100644
--- a/docs/source/auto_examples/images/sphx_glr_plot_gromov_003.png
+++ b/docs/source/auto_examples/images/sphx_glr_plot_gromov_003.png
diff --git a/docs/source/auto_examples/images/thumb/sphx_glr_plot_gromov_thumb.png b/docs/source/auto_examples/images/thumb/sphx_glr_plot_gromov_thumb.png
index c54f6b3..210c010 100644
--- a/docs/source/auto_examples/images/thumb/sphx_glr_plot_gromov_thumb.png
+++ b/docs/source/auto_examples/images/thumb/sphx_glr_plot_gromov_thumb.png
diff --git a/docs/source/auto_examples/index.rst b/docs/source/auto_examples/index.rst
index 227c40c..9d7c0f0 100644
--- a/docs/source/auto_examples/index.rst
+++ b/docs/source/auto_examples/index.rst
@@ -49,13 +49,13 @@ This is a gallery of all the POT example files.
 
 .. raw:: html
 
-    <div class="sphx-glr-thumbcontainer" tooltip="Illustration of 2D optimal transport between discributions that are weighted sum of diracs. The...">
+    <div class="sphx-glr-thumbcontainer" tooltip="This example is designed to show how to use the Gromov-Wassertsein distance computation in POT....">
 
 .. only:: html
 
-    .. figure:: /auto_examples/images/thumb/sphx_glr_plot_OT_2D_samples_thumb.png
+    .. figure:: /auto_examples/images/thumb/sphx_glr_plot_gromov_thumb.png
 
-        :ref:`sphx_glr_auto_examples_plot_OT_2D_samples.py`
+        :ref:`sphx_glr_auto_examples_plot_gromov.py`
 
 .. raw:: html
 
@@ -65,17 +65,17 @@ This is a gallery of all the POT example files.
 .. toctree::
    :hidden:
 
-   /auto_examples/plot_OT_2D_samples
+   /auto_examples/plot_gromov
 
 .. raw:: html
 
-    <div class="sphx-glr-thumbcontainer" tooltip="Shows how to compute multiple EMD and Sinkhorn with two differnt ground metrics and plot their ...">
+    <div class="sphx-glr-thumbcontainer" tooltip="Illustration of 2D optimal transport between discributions that are weighted sum of diracs. The...">
 
 .. only:: html
 
-    .. figure:: /auto_examples/images/thumb/sphx_glr_plot_compute_emd_thumb.png
+    .. figure:: /auto_examples/images/thumb/sphx_glr_plot_OT_2D_samples_thumb.png
 
-        :ref:`sphx_glr_auto_examples_plot_compute_emd.py`
+        :ref:`sphx_glr_auto_examples_plot_OT_2D_samples.py`
 
 .. raw:: html
 
@@ -85,17 +85,17 @@ This is a gallery of all the POT example files.
 .. toctree::
    :hidden:
 
-   /auto_examples/plot_compute_emd
+   /auto_examples/plot_OT_2D_samples
 
 .. raw:: html
 
-    <div class="sphx-glr-thumbcontainer" tooltip="This example illustrate the use of WDA as proposed in [11].">
+    <div class="sphx-glr-thumbcontainer" tooltip="Shows how to compute multiple EMD and Sinkhorn with two differnt ground metrics and plot their ...">
 
 .. only:: html
 
-    .. figure:: /auto_examples/images/thumb/sphx_glr_plot_WDA_thumb.png
+    .. figure:: /auto_examples/images/thumb/sphx_glr_plot_compute_emd_thumb.png
 
-        :ref:`sphx_glr_auto_examples_plot_WDA.py`
+        :ref:`sphx_glr_auto_examples_plot_compute_emd.py`
 
 .. raw:: html
 
@@ -105,17 +105,17 @@ This is a gallery of all the POT example files.
 .. toctree::
    :hidden:
 
-   /auto_examples/plot_WDA
+   /auto_examples/plot_compute_emd
 
 .. raw:: html
 
-    <div class="sphx-glr-thumbcontainer" tooltip="This example is designed to show how to use the Gromov-Wassertsein distance computation in POT....">
+    <div class="sphx-glr-thumbcontainer" tooltip="This example illustrate the use of WDA as proposed in [11].">
 
 .. only:: html
 
-    .. figure:: /auto_examples/images/thumb/sphx_glr_plot_gromov_thumb.png
+    .. figure:: /auto_examples/images/thumb/sphx_glr_plot_WDA_thumb.png
 
-        :ref:`sphx_glr_auto_examples_plot_gromov.py`
+        :ref:`sphx_glr_auto_examples_plot_WDA.py`
 
 .. raw:: html
 
@@ -125,7 +125,7 @@ This is a gallery of all the POT example files.
 .. toctree::
    :hidden:
 
-   /auto_examples/plot_gromov
+   /auto_examples/plot_WDA
 
 .. raw:: html
 
diff --git a/docs/source/auto_examples/plot_gromov.ipynb b/docs/source/auto_examples/plot_gromov.ipynb
index 6d6b522..57d6a4a 100644
--- a/docs/source/auto_examples/plot_gromov.ipynb
+++ b/docs/source/auto_examples/plot_gromov.ipynb
@@ -1,54 +1,126 @@
 {
+  "nbformat_minor": 0,
+  "nbformat": 4,
+  "metadata": {
+    "language_info": {
+      "file_extension": ".py",
+      "codemirror_mode": {
+        "version": 3,
+        "name": "ipython"
+      },
+      "nbconvert_exporter": "python",
+      "mimetype": "text/x-python",
+      "version": "3.5.2",
+      "name": "python",
+      "pygments_lexer": "ipython3"
+    },
+    "kernelspec": {
+      "display_name": "Python 3",
+      "name": "python3",
+      "language": "python"
+    }
+  },
   "cells": [
     {
+      "outputs": [],
+      "source": [
+        "%matplotlib inline"
+      ],
       "execution_count": null,
       "metadata": {
         "collapsed": false
       },
+      "cell_type": "code"
+    },
+    {
+      "source": [
+        "\n# Gromov-Wasserstein example\n\n\nThis example is designed to show how to use the Gromov-Wassertsein distance\ncomputation in POT.\n\n"
+      ],
+      "metadata": {},
+      "cell_type": "markdown"
+    },
+    {
       "outputs": [],
       "source": [
-        "%matplotlib inline"
+        "# Author: Erwan Vautier <erwan.vautier@gmail.com>\n#         Nicolas Courty <ncourty@irisa.fr>\n#\n# License: MIT License\n\nimport scipy as sp\nimport numpy as np\nimport matplotlib.pylab as pl\nfrom mpl_toolkits.mplot3d import Axes3D  # noqa\nimport ot"
       ],
+      "execution_count": null,
+      "metadata": {
+        "collapsed": false
+      },
       "cell_type": "code"
     },
     {
-      "metadata": {},
       "source": [
-        "\n# Gromov-Wasserstein example\n\n\nThis example is designed to show how to use the Gromov-Wassertsein distance\ncomputation in POT.\n\n"
+        "Sample two Gaussian distributions (2D and 3D)\n---------------------------------------------\n\nThe Gromov-Wasserstein distance allows to compute distances with samples that\ndo not belong to the same metric space. For demonstration purpose, we sample\ntwo Gaussian distributions in 2- and 3-dimensional spaces.\n\n"
       ],
+      "metadata": {},
       "cell_type": "markdown"
     },
     {
+      "outputs": [],
+      "source": [
+        "n_samples = 30  # nb samples\n\nmu_s = np.array([0, 0])\ncov_s = np.array([[1, 0], [0, 1]])\n\nmu_t = np.array([4, 4, 4])\ncov_t = np.array([[1, 0, 0], [0, 1, 0], [0, 0, 1]])\n\n\nxs = ot.datasets.get_2D_samples_gauss(n_samples, mu_s, cov_s)\nP = sp.linalg.sqrtm(cov_t)\nxt = np.random.randn(n_samples, 3).dot(P) + mu_t"
+      ],
       "execution_count": null,
       "metadata": {
         "collapsed": false
       },
+      "cell_type": "code"
+    },
+    {
+      "source": [
+        "Plotting the distributions\n--------------------------\n\n"
+      ],
+      "metadata": {},
+      "cell_type": "markdown"
+    },
+    {
       "outputs": [],
       "source": [
-        "# Author: Erwan Vautier <erwan.vautier@gmail.com>\n#         Nicolas Courty <ncourty@irisa.fr>\n#\n# License: MIT License\n\nimport scipy as sp\nimport numpy as np\nimport matplotlib.pylab as pl\nfrom mpl_toolkits.mplot3d import Axes3D  # noqa\nimport ot\n\n\n#\n# Sample two Gaussian distributions (2D and 3D)\n# ---------------------------------------------\n#\n# The Gromov-Wasserstein distance allows to compute distances with samples that\n# do not belong to the same metric space. For demonstration purpose, we sample\n# two Gaussian distributions in 2- and 3-dimensional spaces.\n\n\nn_samples = 30  # nb samples\n\nmu_s = np.array([0, 0])\ncov_s = np.array([[1, 0], [0, 1]])\n\nmu_t = np.array([4, 4, 4])\ncov_t = np.array([[1, 0, 0], [0, 1, 0], [0, 0, 1]])\n\n\nxs = ot.datasets.get_2D_samples_gauss(n_samples, mu_s, cov_s)\nP = sp.linalg.sqrtm(cov_t)\nxt = np.random.randn(n_samples, 3).dot(P) + mu_t\n\n\n#\n# Plotting the distributions\n# --------------------------\n\n\nfig = pl.figure()\nax1 = fig.add_subplot(121)\nax1.plot(xs[:, 0], xs[:, 1], '+b', label='Source samples')\nax2 = fig.add_subplot(122, projection='3d')\nax2.scatter(xt[:, 0], xt[:, 1], xt[:, 2], color='r')\npl.show()\n\n\n#\n# Compute distance kernels, normalize them and then display\n# ---------------------------------------------------------\n\n\nC1 = sp.spatial.distance.cdist(xs, xs)\nC2 = sp.spatial.distance.cdist(xt, xt)\n\nC1 /= C1.max()\nC2 /= C2.max()\n\npl.figure()\npl.subplot(121)\npl.imshow(C1)\npl.subplot(122)\npl.imshow(C2)\npl.show()\n\n#\n# Compute Gromov-Wasserstein plans and distance\n# ---------------------------------------------\n\np = ot.unif(n_samples)\nq = ot.unif(n_samples)\n\ngw0, log0 = ot.gromov.gromov_wasserstein(\n    C1, C2, p, q, 'square_loss', verbose=True, log=True)\n\ngw, log = ot.gromov.entropic_gromov_wasserstein(\n    C1, C2, p, q, 'square_loss', epsilon=5e-4, log=True, verbose=True)\n\n\nprint('Gromov-Wasserstein distances: ' + str(log0['gw_dist']))\nprint('Entropic Gromov-Wasserstein distances: ' + str(log['gw_dist']))\n\n\npl.figure(1, (10, 5))\n\npl.subplot(1, 2, 1)\npl.imshow(gw0, cmap='jet')\npl.title('Gromov Wasserstein')\n\npl.subplot(1, 2, 2)\npl.imshow(gw, cmap='jet')\npl.title('Entropic Gromov Wasserstein')\n\npl.show()"
+        "fig = pl.figure()\nax1 = fig.add_subplot(121)\nax1.plot(xs[:, 0], xs[:, 1], '+b', label='Source samples')\nax2 = fig.add_subplot(122, projection='3d')\nax2.scatter(xt[:, 0], xt[:, 1], xt[:, 2], color='r')\npl.show()"
       ],
+      "execution_count": null,
+      "metadata": {
+        "collapsed": false
+      },
       "cell_type": "code"
-    }
-  ],
-  "metadata": {
-    "language_info": {
-      "name": "python",
-      "codemirror_mode": {
-        "name": "ipython",
-        "version": 3
+    },
+    {
+      "source": [
+        "Compute distance kernels, normalize them and then display\n---------------------------------------------------------\n\n"
+      ],
+      "metadata": {},
+      "cell_type": "markdown"
+    },
+    {
+      "outputs": [],
+      "source": [
+        "C1 = sp.spatial.distance.cdist(xs, xs)\nC2 = sp.spatial.distance.cdist(xt, xt)\n\nC1 /= C1.max()\nC2 /= C2.max()\n\npl.figure()\npl.subplot(121)\npl.imshow(C1)\npl.subplot(122)\npl.imshow(C2)\npl.show()"
+      ],
+      "execution_count": null,
+      "metadata": {
+        "collapsed": false
       },
-      "nbconvert_exporter": "python",
-      "version": "3.5.2",
-      "pygments_lexer": "ipython3",
-      "file_extension": ".py",
-      "mimetype": "text/x-python"
+      "cell_type": "code"
     },
-    "kernelspec": {
-      "display_name": "Python 3",
-      "name": "python3",
-      "language": "python"
+    {
+      "source": [
+        "Compute Gromov-Wasserstein plans and distance\n---------------------------------------------\n\n"
+      ],
+      "metadata": {},
+      "cell_type": "markdown"
+    },
+    {
+      "outputs": [],
+      "source": [
+        "p = ot.unif(n_samples)\nq = ot.unif(n_samples)\n\ngw0, log0 = ot.gromov.gromov_wasserstein(\n    C1, C2, p, q, 'square_loss', verbose=True, log=True)\n\ngw, log = ot.gromov.entropic_gromov_wasserstein(\n    C1, C2, p, q, 'square_loss', epsilon=5e-4, log=True, verbose=True)\n\n\nprint('Gromov-Wasserstein distances: ' + str(log0['gw_dist']))\nprint('Entropic Gromov-Wasserstein distances: ' + str(log['gw_dist']))\n\n\npl.figure(1, (10, 5))\n\npl.subplot(1, 2, 1)\npl.imshow(gw0, cmap='jet')\npl.title('Gromov Wasserstein')\n\npl.subplot(1, 2, 2)\npl.imshow(gw, cmap='jet')\npl.title('Entropic Gromov Wasserstein')\n\npl.show()"
+      ],
+      "execution_count": null,
+      "metadata": {
+        "collapsed": false
+      },
+      "cell_type": "code"
     }
-  },
-  "nbformat_minor": 0,
-  "nbformat": 4
+  ]
 }
\ No newline at end of file
diff --git a/docs/source/auto_examples/plot_gromov.py b/docs/source/auto_examples/plot_gromov.py
index 9188da9..5cd40f6 100644
--- a/docs/source/auto_examples/plot_gromov.py
+++ b/docs/source/auto_examples/plot_gromov.py
@@ -19,7 +19,7 @@ import matplotlib.pylab as pl
 from mpl_toolkits.mplot3d import Axes3D  # noqa

 import ot

 

-

+#############################################################################

 #

 # Sample two Gaussian distributions (2D and 3D)

 # ---------------------------------------------

@@ -42,7 +42,7 @@ 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

 # --------------------------

@@ -55,7 +55,7 @@ ax2 = fig.add_subplot(122, projection='3d')
 ax2.scatter(xt[:, 0], xt[:, 1], xt[:, 2], color='r')

 pl.show()

 

-

+#############################################################################

 #

 # Compute distance kernels, normalize them and then display

 # ---------------------------------------------------------

@@ -74,6 +74,7 @@ pl.subplot(122)
 pl.imshow(C2)

 pl.show()

 

+#############################################################################

 #

 # Compute Gromov-Wasserstein plans and distance

 # ---------------------------------------------

diff --git a/docs/source/auto_examples/plot_gromov.rst b/docs/source/auto_examples/plot_gromov.rst
index ad29f7a..131861f 100644
--- a/docs/source/auto_examples/plot_gromov.rst
+++ b/docs/source/auto_examples/plot_gromov.rst
@@ -12,77 +12,38 @@ computation in POT.
 
 
 
+.. code-block:: python
 
-.. rst-class:: sphx-glr-horizontal
-
-
-    *
 
-      .. image:: /auto_examples/images/sphx_glr_plot_gromov_001.png
-            :scale: 47
+    # 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
 
-      .. image:: /auto_examples/images/sphx_glr_plot_gromov_002.png
-            :scale: 47
 
 
-.. rst-class:: sphx-glr-script-out
 
- Out::
 
-    It.  |Loss        |Delta loss
-    --------------------------------
-        0|4.042674e-02|0.000000e+00
-        1|2.432476e-02|-6.619583e-01
-        2|2.170023e-02|-1.209448e-01
-        3|1.941223e-02|-1.178640e-01
-        4|1.823606e-02|-6.449667e-02
-        5|1.446641e-02|-2.605800e-01
-        6|1.184011e-02|-2.218140e-01
-        7|1.173274e-02|-9.150805e-03
-        8|1.173127e-02|-1.253458e-04
-        9|1.173126e-02|-1.256842e-06
-       10|1.173126e-02|-1.256876e-08
-       11|1.173126e-02|-1.256885e-10
-    It.  |Err         
-    -------------------
-        0|7.034302e-02|
-       10|1.044218e-03|
-       20|5.426783e-08|
-       30|3.532029e-12|
-    Gromov-Wasserstein distances: 0.0117312557987
-    Entropic Gromov-Wasserstein distances: 0.0101639418389
 
 
+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
 
 
-    # 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.
-
 
     n_samples = 30  # nb samples
 
@@ -98,9 +59,18 @@ computation in POT.
     xt = np.random.randn(n_samples, 3).dot(P) + mu_t
 
 
-    #
-    # Plotting the distributions
-    # --------------------------
+
+
+
+
+
+Plotting the distributions
+--------------------------
+
+
+
+.. code-block:: python
+
 
 
     fig = pl.figure()
@@ -111,9 +81,21 @@ computation in POT.
     pl.show()
 
 
-    #
-    # Compute distance kernels, normalize them and then display
-    # ---------------------------------------------------------
+
+
+.. 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)
@@ -129,9 +111,22 @@ computation in POT.
     pl.imshow(C2)
     pl.show()
 
-    #
-    # Compute Gromov-Wasserstein plans and distance
-    # ---------------------------------------------
+
+
+
+.. 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)
@@ -159,7 +154,40 @@ computation in POT.
 
     pl.show()
 
-**Total running time of the script:** ( 0 minutes  1.465 seconds)
+
+
+.. image:: /auto_examples/images/sphx_glr_plot_gromov_003.png
+    :align: center
+
+
+.. rst-class:: sphx-glr-script-out
+
+ Out::
+
+    It.  |Loss        |Delta loss
+    --------------------------------
+        0|4.517558e-02|0.000000e+00
+        1|2.563483e-02|-7.622736e-01
+        2|2.443903e-02|-4.892972e-02
+        3|2.231600e-02|-9.513496e-02
+        4|1.676188e-02|-3.313541e-01
+        5|1.464792e-02|-1.443180e-01
+        6|1.454315e-02|-7.204526e-03
+        7|1.454142e-02|-1.185811e-04
+        8|1.454141e-02|-1.190466e-06
+        9|1.454141e-02|-1.190512e-08
+       10|1.454141e-02|-1.190520e-10
+    It.  |Err         
+    -------------------
+        0|6.743761e-02|
+       10|5.477003e-04|
+       20|2.461503e-08|
+       30|1.205155e-11|
+    Gromov-Wasserstein distances: 0.014541405718693563
+    Entropic Gromov-Wasserstein distances: 0.015800739725237274
+
+
+**Total running time of the script:** ( 0 minutes  1.448 seconds)