update example with rst titles

1 files changed, 242 insertions, 109 deletions

diff --git a/docs/source/auto_examples/plot_OT_L1_vs_L2.rst b/docs/source/auto_examples/plot_OT_L1_vs_L2.rst
index ba52bfe..83a7491 100644
--- a/docs/source/auto_examples/plot_OT_L1_vs_L2.rst
+++ b/docs/source/auto_examples/plot_OT_L1_vs_L2.rst
@@ -7,6 +7,8 @@
 2D Optimal transport for different metrics
 ==========================================
 
+2D OT on empirical distributio  with different gound metric.
+
 Stole the figure idea from Fig. 1 and 2 in
 https://arxiv.org/pdf/1706.07650.pdf
 
@@ -14,6 +16,80 @@ https://arxiv.org/pdf/1706.07650.pdf
 
 
 
+.. code-block:: python
+
+
+    # Author: Remi Flamary <remi.flamary@unice.fr>
+    #
+    # License: MIT License
+
+    import numpy as np
+    import matplotlib.pylab as pl
+    import ot
+
+
+
+
+
+
+
+Dataset 1 : uniform sampling
+#############################################################################
+
+
+
+.. code-block:: python
+
+
+    n = 20  # nb samples
+    xs = np.zeros((n, 2))
+    xs[:, 0] = np.arange(n) + 1
+    xs[:, 1] = (np.arange(n) + 1) * -0.001  # to make it strictly convex...
+
+    xt = np.zeros((n, 2))
+    xt[:, 1] = np.arange(n) + 1
+
+    a, b = ot.unif(n), ot.unif(n)  # uniform distribution on samples
+
+    # loss matrix
+    M1 = ot.dist(xs, xt, metric='euclidean')
+    M1 /= M1.max()
+
+    # loss matrix
+    M2 = ot.dist(xs, xt, metric='sqeuclidean')
+    M2 /= M2.max()
+
+    # loss matrix
+    Mp = np.sqrt(ot.dist(xs, xt, metric='euclidean'))
+    Mp /= Mp.max()
+
+    # Data
+    pl.figure(1, figsize=(7, 3))
+    pl.clf()
+    pl.plot(xs[:, 0], xs[:, 1], '+b', label='Source samples')
+    pl.plot(xt[:, 0], xt[:, 1], 'xr', label='Target samples')
+    pl.axis('equal')
+    pl.title('Source and traget distributions')
+
+
+    # Cost matrices
+    pl.figure(2, figsize=(7, 3))
+
+    pl.subplot(1, 3, 1)
+    pl.imshow(M1, interpolation='nearest')
+    pl.title('Euclidean cost')
+
+    pl.subplot(1, 3, 2)
+    pl.imshow(M2, interpolation='nearest')
+    pl.title('Squared Euclidean cost')
+
+    pl.subplot(1, 3, 3)
+    pl.imshow(Mp, interpolation='nearest')
+    pl.title('Sqrt Euclidean cost')
+    pl.tight_layout()
+
+
+
 
 .. rst-class:: sphx-glr-horizontal
 
@@ -28,138 +104,195 @@ https://arxiv.org/pdf/1706.07650.pdf
       .. image:: /auto_examples/images/sphx_glr_plot_OT_L1_vs_L2_002.png
             :scale: 47
 
-    *
 
-      .. image:: /auto_examples/images/sphx_glr_plot_OT_L1_vs_L2_003.png
-            :scale: 47
 
-    *
 
-      .. image:: /auto_examples/images/sphx_glr_plot_OT_L1_vs_L2_004.png
-            :scale: 47
+Dataset 1 : Plot OT Matrices
+#############################################################################
+
+
+
+.. code-block:: python
+
+
+
+
+    #%% EMD
+    G1 = ot.emd(a, b, M1)
+    G2 = ot.emd(a, b, M2)
+    Gp = ot.emd(a, b, Mp)
+
+    # OT matrices
+    pl.figure(3, figsize=(7, 3))
+
+    pl.subplot(1, 3, 1)
+    ot.plot.plot2D_samples_mat(xs, xt, G1, c=[.5, .5, 1])
+    pl.plot(xs[:, 0], xs[:, 1], '+b', label='Source samples')
+    pl.plot(xt[:, 0], xt[:, 1], 'xr', label='Target samples')
+    pl.axis('equal')
+    # pl.legend(loc=0)
+    pl.title('OT Euclidean')
+
+    pl.subplot(1, 3, 2)
+    ot.plot.plot2D_samples_mat(xs, xt, G2, c=[.5, .5, 1])
+    pl.plot(xs[:, 0], xs[:, 1], '+b', label='Source samples')
+    pl.plot(xt[:, 0], xt[:, 1], 'xr', label='Target samples')
+    pl.axis('equal')
+    # pl.legend(loc=0)
+    pl.title('OT squared Euclidean')
+
+    pl.subplot(1, 3, 3)
+    ot.plot.plot2D_samples_mat(xs, xt, Gp, c=[.5, .5, 1])
+    pl.plot(xs[:, 0], xs[:, 1], '+b', label='Source samples')
+    pl.plot(xt[:, 0], xt[:, 1], 'xr', label='Target samples')
+    pl.axis('equal')
+    # pl.legend(loc=0)
+    pl.title('OT sqrt Euclidean')
+    pl.tight_layout()
+
+    pl.show()
+
+
+
+
+
+.. image:: /auto_examples/images/sphx_glr_plot_OT_L1_vs_L2_005.png
+    :align: center
+
+
+
+
+Dataset 2 : Partial circle
+#############################################################################
+
+
+
+.. code-block:: python
+
+
+    n = 50  # nb samples
+    xtot = np.zeros((n + 1, 2))
+    xtot[:, 0] = np.cos(
+        (np.arange(n + 1) + 1.0) * 0.9 / (n + 2) * 2 * np.pi)
+    xtot[:, 1] = np.sin(
+        (np.arange(n + 1) + 1.0) * 0.9 / (n + 2) * 2 * np.pi)
+
+    xs = xtot[:n, :]
+    xt = xtot[1:, :]
+
+    a, b = ot.unif(n), ot.unif(n)  # uniform distribution on samples
+
+    # loss matrix
+    M1 = ot.dist(xs, xt, metric='euclidean')
+    M1 /= M1.max()
+
+    # loss matrix
+    M2 = ot.dist(xs, xt, metric='sqeuclidean')
+    M2 /= M2.max()
+
+    # loss matrix
+    Mp = np.sqrt(ot.dist(xs, xt, metric='euclidean'))
+    Mp /= Mp.max()
+
+
+    # Data
+    pl.figure(4, figsize=(7, 3))
+    pl.clf()
+    pl.plot(xs[:, 0], xs[:, 1], '+b', label='Source samples')
+    pl.plot(xt[:, 0], xt[:, 1], 'xr', label='Target samples')
+    pl.axis('equal')
+    pl.title('Source and traget distributions')
+
+
+    # Cost matrices
+    pl.figure(5, figsize=(7, 3))
+
+    pl.subplot(1, 3, 1)
+    pl.imshow(M1, interpolation='nearest')
+    pl.title('Euclidean cost')
+
+    pl.subplot(1, 3, 2)
+    pl.imshow(M2, interpolation='nearest')
+    pl.title('Squared Euclidean cost')
+
+    pl.subplot(1, 3, 3)
+    pl.imshow(Mp, interpolation='nearest')
+    pl.title('Sqrt Euclidean cost')
+    pl.tight_layout()
+
+
+
+
+.. rst-class:: sphx-glr-horizontal
+
 
     *
 
-      .. image:: /auto_examples/images/sphx_glr_plot_OT_L1_vs_L2_005.png
+      .. image:: /auto_examples/images/sphx_glr_plot_OT_L1_vs_L2_007.png
             :scale: 47
 
     *
 
-      .. image:: /auto_examples/images/sphx_glr_plot_OT_L1_vs_L2_006.png
+      .. image:: /auto_examples/images/sphx_glr_plot_OT_L1_vs_L2_008.png
             :scale: 47
 
 
 
 
+Dataset 2 : Plot  OT Matrices
+#############################################################################
+
+
 
 .. code-block:: python
 
 
-    # Author: Remi Flamary <remi.flamary@unice.fr>
-    #
-    # License: MIT License
 
-    import numpy as np
-    import matplotlib.pylab as pl
-    import ot
 
-    #%% parameters and data generation
-
-    for data in range(2):
-
-        if data:
-            n = 20  # nb samples
-            xs = np.zeros((n, 2))
-            xs[:, 0] = np.arange(n) + 1
-            xs[:, 1] = (np.arange(n) + 1) * -0.001  # to make it strictly convex...
-
-            xt = np.zeros((n, 2))
-            xt[:, 1] = np.arange(n) + 1
-        else:
-
-            n = 50  # nb samples
-            xtot = np.zeros((n + 1, 2))
-            xtot[:, 0] = np.cos(
-                (np.arange(n + 1) + 1.0) * 0.9 / (n + 2) * 2 * np.pi)
-            xtot[:, 1] = np.sin(
-                (np.arange(n + 1) + 1.0) * 0.9 / (n + 2) * 2 * np.pi)
-
-            xs = xtot[:n, :]
-            xt = xtot[1:, :]
-
-        a, b = ot.unif(n), ot.unif(n)  # uniform distribution on samples
-
-        # loss matrix
-        M1 = ot.dist(xs, xt, metric='euclidean')
-        M1 /= M1.max()
-
-        # loss matrix
-        M2 = ot.dist(xs, xt, metric='sqeuclidean')
-        M2 /= M2.max()
-
-        # loss matrix
-        Mp = np.sqrt(ot.dist(xs, xt, metric='euclidean'))
-        Mp /= Mp.max()
-
-        #%% plot samples
-
-        pl.figure(1 + 3 * data, figsize=(7, 3))
-        pl.clf()
-        pl.plot(xs[:, 0], xs[:, 1], '+b', label='Source samples')
-        pl.plot(xt[:, 0], xt[:, 1], 'xr', label='Target samples')
-        pl.axis('equal')
-        pl.title('Source and traget distributions')
-
-        pl.figure(2 + 3 * data, figsize=(7, 3))
-
-        pl.subplot(1, 3, 1)
-        pl.imshow(M1, interpolation='nearest')
-        pl.title('Euclidean cost')
-
-        pl.subplot(1, 3, 2)
-        pl.imshow(M2, interpolation='nearest')
-        pl.title('Squared Euclidean cost')
-
-        pl.subplot(1, 3, 3)
-        pl.imshow(Mp, interpolation='nearest')
-        pl.title('Sqrt Euclidean cost')
-        pl.tight_layout()
-
-        #%% EMD
-        G1 = ot.emd(a, b, M1)
-        G2 = ot.emd(a, b, M2)
-        Gp = ot.emd(a, b, Mp)
-
-        pl.figure(3 + 3 * data, figsize=(7, 3))
-
-        pl.subplot(1, 3, 1)
-        ot.plot.plot2D_samples_mat(xs, xt, G1, c=[.5, .5, 1])
-        pl.plot(xs[:, 0], xs[:, 1], '+b', label='Source samples')
-        pl.plot(xt[:, 0], xt[:, 1], 'xr', label='Target samples')
-        pl.axis('equal')
-        # pl.legend(loc=0)
-        pl.title('OT Euclidean')
-
-        pl.subplot(1, 3, 2)
-        ot.plot.plot2D_samples_mat(xs, xt, G2, c=[.5, .5, 1])
-        pl.plot(xs[:, 0], xs[:, 1], '+b', label='Source samples')
-        pl.plot(xt[:, 0], xt[:, 1], 'xr', label='Target samples')
-        pl.axis('equal')
-        # pl.legend(loc=0)
-        pl.title('OT squared Euclidean')
-
-        pl.subplot(1, 3, 3)
-        ot.plot.plot2D_samples_mat(xs, xt, Gp, c=[.5, .5, 1])
-        pl.plot(xs[:, 0], xs[:, 1], '+b', label='Source samples')
-        pl.plot(xt[:, 0], xt[:, 1], 'xr', label='Target samples')
-        pl.axis('equal')
-        # pl.legend(loc=0)
-        pl.title('OT sqrt Euclidean')
-        pl.tight_layout()
+    #%% EMD
+    G1 = ot.emd(a, b, M1)
+    G2 = ot.emd(a, b, M2)
+    Gp = ot.emd(a, b, Mp)
+
+    # OT matrices
+    pl.figure(6, figsize=(7, 3))
+
+    pl.subplot(1, 3, 1)
+    ot.plot.plot2D_samples_mat(xs, xt, G1, c=[.5, .5, 1])
+    pl.plot(xs[:, 0], xs[:, 1], '+b', label='Source samples')
+    pl.plot(xt[:, 0], xt[:, 1], 'xr', label='Target samples')
+    pl.axis('equal')
+    # pl.legend(loc=0)
+    pl.title('OT Euclidean')
+
+    pl.subplot(1, 3, 2)
+    ot.plot.plot2D_samples_mat(xs, xt, G2, c=[.5, .5, 1])
+    pl.plot(xs[:, 0], xs[:, 1], '+b', label='Source samples')
+    pl.plot(xt[:, 0], xt[:, 1], 'xr', label='Target samples')
+    pl.axis('equal')
+    # pl.legend(loc=0)
+    pl.title('OT squared Euclidean')
+
+    pl.subplot(1, 3, 3)
+    ot.plot.plot2D_samples_mat(xs, xt, Gp, c=[.5, .5, 1])
+    pl.plot(xs[:, 0], xs[:, 1], '+b', label='Source samples')
+    pl.plot(xt[:, 0], xt[:, 1], 'xr', label='Target samples')
+    pl.axis('equal')
+    # pl.legend(loc=0)
+    pl.title('OT sqrt Euclidean')
+    pl.tight_layout()
 
     pl.show()
 
-**Total running time of the script:** ( 0 minutes  1.906 seconds)
+
+
+.. image:: /auto_examples/images/sphx_glr_plot_OT_L1_vs_L2_011.png
+    :align: center
+
+
+
+
+**Total running time of the script:** ( 0 minutes  1.217 seconds)
 
 
 
@@ -178,4 +311,4 @@ https://arxiv.org/pdf/1706.07650.pdf
 
 .. rst-class:: sphx-glr-signature
 
-    `Generated by Sphinx-Gallery <http://sphinx-gallery.readthedocs.io>`_
+    `Generated by Sphinx-Gallery <https://sphinx-gallery.readthedocs.io>`_