example+rst titles

10 files changed, 447 insertions, 133 deletions

diff --git a/docs/source/auto_examples/auto_examples_jupyter.zip b/docs/source/auto_examples/auto_examples_jupyter.zip
index 3bb8ecf..92aa027 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 273c751..d9e26c4 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_optim_OTreg_003.png b/docs/source/auto_examples/images/sphx_glr_plot_optim_OTreg_003.png
index c9ed489..a75e649 100644
--- a/docs/source/auto_examples/images/sphx_glr_plot_optim_OTreg_003.png
+++ b/docs/source/auto_examples/images/sphx_glr_plot_optim_OTreg_003.png
diff --git a/docs/source/auto_examples/images/sphx_glr_plot_optim_OTreg_004.png b/docs/source/auto_examples/images/sphx_glr_plot_optim_OTreg_004.png
index 0af4542..7afdb53 100644
--- a/docs/source/auto_examples/images/sphx_glr_plot_optim_OTreg_004.png
+++ b/docs/source/auto_examples/images/sphx_glr_plot_optim_OTreg_004.png
diff --git a/docs/source/auto_examples/plot_OT_1D.ipynb b/docs/source/auto_examples/plot_OT_1D.ipynb
index 7d3fdd1..97c593e 100644
--- a/docs/source/auto_examples/plot_OT_1D.ipynb
+++ b/docs/source/auto_examples/plot_OT_1D.ipynb
@@ -24,7 +24,79 @@
       "execution_count": null, 
       "cell_type": "code", 
       "source": [
-        "# Author: Remi Flamary <remi.flamary@unice.fr>\n#\n# License: MIT License\n\nimport numpy as np\nimport matplotlib.pylab as pl\nimport ot\nfrom ot.datasets import get_1D_gauss as gauss\n\n#%% parameters\n\nn = 100  # nb bins\n\n# bin positions\nx = np.arange(n, dtype=np.float64)\n\n# Gaussian distributions\na = gauss(n, m=20, s=5)  # m= mean, s= std\nb = gauss(n, m=60, s=10)\n\n# loss matrix\nM = ot.dist(x.reshape((n, 1)), x.reshape((n, 1)))\nM /= M.max()\n\n#%% plot the distributions\n\npl.figure(1, figsize=(6.4, 3))\npl.plot(x, a, 'b', label='Source distribution')\npl.plot(x, b, 'r', label='Target distribution')\npl.legend()\n\n#%% plot distributions and loss matrix\n\npl.figure(2, figsize=(5, 5))\not.plot.plot1D_mat(a, b, M, 'Cost matrix M')\n\n#%% EMD\n\nG0 = ot.emd(a, b, M)\n\npl.figure(3, figsize=(5, 5))\not.plot.plot1D_mat(a, b, G0, 'OT matrix G0')\n\n#%% Sinkhorn\n\nlambd = 1e-3\nGs = ot.sinkhorn(a, b, M, lambd, verbose=True)\n\npl.figure(4, figsize=(5, 5))\not.plot.plot1D_mat(a, b, Gs, 'OT matrix Sinkhorn')\n\npl.show()"
+        "# Author: Remi Flamary <remi.flamary@unice.fr>\n#\n# License: MIT License\n\nimport numpy as np\nimport matplotlib.pylab as pl\nimport ot\nfrom ot.datasets import get_1D_gauss as gauss"
+      ], 
+      "outputs": [], 
+      "metadata": {
+        "collapsed": false
+      }
+    }, 
+    {
+      "source": [
+        "Generate data\n#############################################################################\n\n"
+      ], 
+      "cell_type": "markdown", 
+      "metadata": {}
+    }, 
+    {
+      "execution_count": null, 
+      "cell_type": "code", 
+      "source": [
+        "#%% parameters\n\nn = 100  # nb bins\n\n# bin positions\nx = np.arange(n, dtype=np.float64)\n\n# Gaussian distributions\na = gauss(n, m=20, s=5)  # m= mean, s= std\nb = gauss(n, m=60, s=10)\n\n# loss matrix\nM = ot.dist(x.reshape((n, 1)), x.reshape((n, 1)))\nM /= M.max()"
+      ], 
+      "outputs": [], 
+      "metadata": {
+        "collapsed": false
+      }
+    }, 
+    {
+      "source": [
+        "Plot distributions and loss matrix\n#############################################################################\n\n"
+      ], 
+      "cell_type": "markdown", 
+      "metadata": {}
+    }, 
+    {
+      "execution_count": null, 
+      "cell_type": "code", 
+      "source": [
+        "#%% plot the distributions\n\npl.figure(1, figsize=(6.4, 3))\npl.plot(x, a, 'b', label='Source distribution')\npl.plot(x, b, 'r', label='Target distribution')\npl.legend()\n\n#%% plot distributions and loss matrix\n\npl.figure(2, figsize=(5, 5))\not.plot.plot1D_mat(a, b, M, 'Cost matrix M')"
+      ], 
+      "outputs": [], 
+      "metadata": {
+        "collapsed": false
+      }
+    }, 
+    {
+      "source": [
+        "Solve EMD \n#############################################################################\n\n"
+      ], 
+      "cell_type": "markdown", 
+      "metadata": {}
+    }, 
+    {
+      "execution_count": null, 
+      "cell_type": "code", 
+      "source": [
+        "#%% EMD\n\nG0 = ot.emd(a, b, M)\n\npl.figure(3, figsize=(5, 5))\not.plot.plot1D_mat(a, b, G0, 'OT matrix G0')"
+      ], 
+      "outputs": [], 
+      "metadata": {
+        "collapsed": false
+      }
+    }, 
+    {
+      "source": [
+        "Solve Sinkhorn\n#############################################################################\n\n"
+      ], 
+      "cell_type": "markdown", 
+      "metadata": {}
+    }, 
+    {
+      "execution_count": null, 
+      "cell_type": "code", 
+      "source": [
+        "#%% Sinkhorn\n\nlambd = 1e-3\nGs = ot.sinkhorn(a, b, M, lambd, verbose=True)\n\npl.figure(4, figsize=(5, 5))\not.plot.plot1D_mat(a, b, Gs, 'OT matrix Sinkhorn')\n\npl.show()"
       ], 
       "outputs": [], 
       "metadata": {
diff --git a/docs/source/auto_examples/plot_OT_1D.py b/docs/source/auto_examples/plot_OT_1D.py
index 0f3a26a..be6f5b3 100644
--- a/docs/source/auto_examples/plot_OT_1D.py
+++ b/docs/source/auto_examples/plot_OT_1D.py
@@ -15,6 +15,10 @@ import matplotlib.pylab as pl
 import ot
 from ot.datasets import get_1D_gauss as gauss
 
+##############################################################################
+# Generate data
+##############################################################################
+
 #%% parameters
 
 n = 100  # nb bins
@@ -30,6 +34,11 @@ b = gauss(n, m=60, s=10)
 M = ot.dist(x.reshape((n, 1)), x.reshape((n, 1)))
 M /= M.max()
 
+
+##############################################################################
+# Plot distributions and loss matrix
+##############################################################################
+
 #%% plot the distributions
 
 pl.figure(1, figsize=(6.4, 3))
@@ -42,6 +51,10 @@ pl.legend()
 pl.figure(2, figsize=(5, 5))
 ot.plot.plot1D_mat(a, b, M, 'Cost matrix M')
 
+##############################################################################
+# Solve EMD 
+##############################################################################
+
 #%% EMD
 
 G0 = ot.emd(a, b, M)
@@ -49,6 +62,10 @@ G0 = ot.emd(a, b, M)
 pl.figure(3, figsize=(5, 5))
 ot.plot.plot1D_mat(a, b, G0, 'OT matrix G0')
 
+##############################################################################
+# Solve Sinkhorn
+##############################################################################
+
 #%% Sinkhorn
 
 lambd = 1e-3
diff --git a/docs/source/auto_examples/plot_OT_1D.rst b/docs/source/auto_examples/plot_OT_1D.rst
index a36e13c..252d387 100644
--- a/docs/source/auto_examples/plot_OT_1D.rst
+++ b/docs/source/auto_examples/plot_OT_1D.rst
@@ -10,68 +10,32 @@
 
 
 
-
-.. rst-class:: sphx-glr-horizontal
+.. code-block:: python
 
 
-    *
+    # Author: Remi Flamary <remi.flamary@unice.fr>
+    #
+    # License: MIT License
 
-      .. image:: /auto_examples/images/sphx_glr_plot_OT_1D_001.png
-            :scale: 47
+    import numpy as np
+    import matplotlib.pylab as pl
+    import ot
+    from ot.datasets import get_1D_gauss as gauss
 
-    *
 
-      .. image:: /auto_examples/images/sphx_glr_plot_OT_1D_002.png
-            :scale: 47
 
-    *
 
-      .. image:: /auto_examples/images/sphx_glr_plot_OT_1D_003.png
-            :scale: 47
 
-    *
 
-      .. image:: /auto_examples/images/sphx_glr_plot_OT_1D_004.png
-            :scale: 47
 
+Generate data
+#############################################################################
 
-.. rst-class:: sphx-glr-script-out
-
- Out::
-
-    It.  |Err         
-    -------------------
-        0|8.187970e-02|
-       10|3.460174e-02|
-       20|6.633335e-03|
-       30|9.797798e-04|
-       40|1.389606e-04|
-       50|1.959016e-05|
-       60|2.759079e-06|
-       70|3.885166e-07|
-       80|5.470605e-08|
-       90|7.702918e-09|
-      100|1.084609e-09|
-      110|1.527180e-10|
-
-
-
-
-|
 
 
 .. code-block:: python
 
 
-    # Author: Remi Flamary <remi.flamary@unice.fr>
-    #
-    # License: MIT License
-
-    import numpy as np
-    import matplotlib.pylab as pl
-    import ot
-    from ot.datasets import get_1D_gauss as gauss
-
     #%% parameters
 
     n = 100  # nb bins
@@ -87,6 +51,21 @@
     M = ot.dist(x.reshape((n, 1)), x.reshape((n, 1)))
     M /= M.max()
 
+
+
+
+
+
+
+
+Plot distributions and loss matrix
+#############################################################################
+
+
+
+.. code-block:: python
+
+
     #%% plot the distributions
 
     pl.figure(1, figsize=(6.4, 3))
@@ -99,6 +78,33 @@
     pl.figure(2, figsize=(5, 5))
     ot.plot.plot1D_mat(a, b, M, 'Cost matrix M')
 
+
+
+
+.. rst-class:: sphx-glr-horizontal
+
+
+    *
+
+      .. image:: /auto_examples/images/sphx_glr_plot_OT_1D_001.png
+            :scale: 47
+
+    *
+
+      .. image:: /auto_examples/images/sphx_glr_plot_OT_1D_002.png
+            :scale: 47
+
+
+
+
+Solve EMD 
+#############################################################################
+
+
+
+.. code-block:: python
+
+
     #%% EMD
 
     G0 = ot.emd(a, b, M)
@@ -106,6 +112,23 @@
     pl.figure(3, figsize=(5, 5))
     ot.plot.plot1D_mat(a, b, G0, 'OT matrix G0')
 
+
+
+
+.. image:: /auto_examples/images/sphx_glr_plot_OT_1D_005.png
+    :align: center
+
+
+
+
+Solve Sinkhorn
+#############################################################################
+
+
+
+.. code-block:: python
+
+
     #%% Sinkhorn
 
     lambd = 1e-3
@@ -116,7 +139,33 @@
 
     pl.show()
 
-**Total running time of the script:** ( 0 minutes  1.050 seconds)
+
+
+.. image:: /auto_examples/images/sphx_glr_plot_OT_1D_007.png
+    :align: center
+
+
+.. rst-class:: sphx-glr-script-out
+
+ Out::
+
+    It.  |Err         
+    -------------------
+        0|8.187970e-02|
+       10|3.460174e-02|
+       20|6.633335e-03|
+       30|9.797798e-04|
+       40|1.389606e-04|
+       50|1.959016e-05|
+       60|2.759079e-06|
+       70|3.885166e-07|
+       80|5.470605e-08|
+       90|7.702918e-09|
+      100|1.084609e-09|
+      110|1.527180e-10|
+
+
+**Total running time of the script:** ( 0 minutes  1.065 seconds)
 
 
 
diff --git a/docs/source/auto_examples/plot_optim_OTreg.ipynb b/docs/source/auto_examples/plot_optim_OTreg.ipynb
index 0cb6ef2..9d26e4d 100644
--- a/docs/source/auto_examples/plot_optim_OTreg.ipynb
+++ b/docs/source/auto_examples/plot_optim_OTreg.ipynb
@@ -24,7 +24,97 @@
       "execution_count": null, 
       "cell_type": "code", 
       "source": [
-        "import numpy as np\nimport matplotlib.pylab as pl\nimport ot\n\n\n#%% parameters\n\nn = 100  # nb bins\n\n# bin positions\nx = np.arange(n, dtype=np.float64)\n\n# Gaussian distributions\na = ot.datasets.get_1D_gauss(n, m=20, s=5)  # m= mean, s= std\nb = ot.datasets.get_1D_gauss(n, m=60, s=10)\n\n# loss matrix\nM = ot.dist(x.reshape((n, 1)), x.reshape((n, 1)))\nM /= M.max()\n\n#%% EMD\n\nG0 = ot.emd(a, b, M)\n\npl.figure(3, figsize=(5, 5))\not.plot.plot1D_mat(a, b, G0, 'OT matrix G0')\n\n#%% Example with Frobenius norm regularization\n\n\ndef f(G):\n    return 0.5 * np.sum(G**2)\n\n\ndef df(G):\n    return G\n\n\nreg = 1e-1\n\nGl2 = ot.optim.cg(a, b, M, reg, f, df, verbose=True)\n\npl.figure(3)\not.plot.plot1D_mat(a, b, Gl2, 'OT matrix Frob. reg')\n\n#%% Example with entropic regularization\n\n\ndef f(G):\n    return np.sum(G * np.log(G))\n\n\ndef df(G):\n    return np.log(G) + 1.\n\n\nreg = 1e-3\n\nGe = ot.optim.cg(a, b, M, reg, f, df, verbose=True)\n\npl.figure(4, figsize=(5, 5))\not.plot.plot1D_mat(a, b, Ge, 'OT matrix Entrop. reg')\n\n#%% Example with Frobenius norm + entropic regularization with gcg\n\n\ndef f(G):\n    return 0.5 * np.sum(G**2)\n\n\ndef df(G):\n    return G\n\n\nreg1 = 1e-3\nreg2 = 1e-1\n\nGel2 = ot.optim.gcg(a, b, M, reg1, reg2, f, df, verbose=True)\n\npl.figure(5, figsize=(5, 5))\not.plot.plot1D_mat(a, b, Gel2, 'OT entropic + matrix Frob. reg')\npl.show()"
+        "import numpy as np\nimport matplotlib.pylab as pl\nimport ot"
+      ], 
+      "outputs": [], 
+      "metadata": {
+        "collapsed": false
+      }
+    }, 
+    {
+      "source": [
+        "Generate data \n#############################################################################\n\n"
+      ], 
+      "cell_type": "markdown", 
+      "metadata": {}
+    }, 
+    {
+      "execution_count": null, 
+      "cell_type": "code", 
+      "source": [
+        "#%% parameters\n\nn = 100  # nb bins\n\n# bin positions\nx = np.arange(n, dtype=np.float64)\n\n# Gaussian distributions\na = ot.datasets.get_1D_gauss(n, m=20, s=5)  # m= mean, s= std\nb = ot.datasets.get_1D_gauss(n, m=60, s=10)\n\n# loss matrix\nM = ot.dist(x.reshape((n, 1)), x.reshape((n, 1)))\nM /= M.max()"
+      ], 
+      "outputs": [], 
+      "metadata": {
+        "collapsed": false
+      }
+    }, 
+    {
+      "source": [
+        "Solve EMD \n#############################################################################\n\n"
+      ], 
+      "cell_type": "markdown", 
+      "metadata": {}
+    }, 
+    {
+      "execution_count": null, 
+      "cell_type": "code", 
+      "source": [
+        "#%% EMD\n\nG0 = ot.emd(a, b, M)\n\npl.figure(3, figsize=(5, 5))\not.plot.plot1D_mat(a, b, G0, 'OT matrix G0')"
+      ], 
+      "outputs": [], 
+      "metadata": {
+        "collapsed": false
+      }
+    }, 
+    {
+      "source": [
+        "Solve EMD with Frobenius norm regularization\n#############################################################################\n\n"
+      ], 
+      "cell_type": "markdown", 
+      "metadata": {}
+    }, 
+    {
+      "execution_count": null, 
+      "cell_type": "code", 
+      "source": [
+        "#%% Example with Frobenius norm regularization\n\n\ndef f(G):\n    return 0.5 * np.sum(G**2)\n\n\ndef df(G):\n    return G\n\n\nreg = 1e-1\n\nGl2 = ot.optim.cg(a, b, M, reg, f, df, verbose=True)\n\npl.figure(3)\not.plot.plot1D_mat(a, b, Gl2, 'OT matrix Frob. reg')"
+      ], 
+      "outputs": [], 
+      "metadata": {
+        "collapsed": false
+      }
+    }, 
+    {
+      "source": [
+        "Solve EMD with entropic regularization\n#############################################################################\n\n"
+      ], 
+      "cell_type": "markdown", 
+      "metadata": {}
+    }, 
+    {
+      "execution_count": null, 
+      "cell_type": "code", 
+      "source": [
+        "#%% Example with entropic regularization\n\n\ndef f(G):\n    return np.sum(G * np.log(G))\n\n\ndef df(G):\n    return np.log(G) + 1.\n\n\nreg = 1e-3\n\nGe = ot.optim.cg(a, b, M, reg, f, df, verbose=True)\n\npl.figure(4, figsize=(5, 5))\not.plot.plot1D_mat(a, b, Ge, 'OT matrix Entrop. reg')"
+      ], 
+      "outputs": [], 
+      "metadata": {
+        "collapsed": false
+      }
+    }, 
+    {
+      "source": [
+        "Solve EMD with Frobenius norm + entropic regularization\n#############################################################################\n\n"
+      ], 
+      "cell_type": "markdown", 
+      "metadata": {}
+    }, 
+    {
+      "execution_count": null, 
+      "cell_type": "code", 
+      "source": [
+        "#%% Example with Frobenius norm + entropic regularization with gcg\n\ndef f(G):\n    return 0.5 * np.sum(G**2)\n\n\ndef df(G):\n    return G\n\n\nreg1 = 1e-3\nreg2 = 1e-1\n\nGel2 = ot.optim.gcg(a, b, M, reg1, reg2, f, df, verbose=True)\n\npl.figure(5, figsize=(5, 5))\not.plot.plot1D_mat(a, b, Gel2, 'OT entropic + matrix Frob. reg')\npl.show()"
       ], 
       "outputs": [], 
       "metadata": {
diff --git a/docs/source/auto_examples/plot_optim_OTreg.py b/docs/source/auto_examples/plot_optim_OTreg.py
index 276b250..d36b269 100644
--- a/docs/source/auto_examples/plot_optim_OTreg.py
+++ b/docs/source/auto_examples/plot_optim_OTreg.py
@@ -12,6 +12,10 @@ import matplotlib.pylab as pl
 import ot
 
 
+##############################################################################
+# Generate data 
+##############################################################################
+
 #%% parameters
 
 n = 100  # nb bins
@@ -27,6 +31,10 @@ b = ot.datasets.get_1D_gauss(n, m=60, s=10)
 M = ot.dist(x.reshape((n, 1)), x.reshape((n, 1)))
 M /= M.max()
 
+##############################################################################
+# Solve EMD 
+##############################################################################
+
 #%% EMD
 
 G0 = ot.emd(a, b, M)
@@ -34,6 +42,10 @@ G0 = ot.emd(a, b, M)
 pl.figure(3, figsize=(5, 5))
 ot.plot.plot1D_mat(a, b, G0, 'OT matrix G0')
 
+##############################################################################
+# Solve EMD with Frobenius norm regularization
+##############################################################################
+
 #%% Example with Frobenius norm regularization
 
 
@@ -52,6 +64,10 @@ Gl2 = ot.optim.cg(a, b, M, reg, f, df, verbose=True)
 pl.figure(3)
 ot.plot.plot1D_mat(a, b, Gl2, 'OT matrix Frob. reg')
 
+##############################################################################
+# Solve EMD with entropic regularization
+##############################################################################
+
 #%% Example with entropic regularization
 
 
@@ -70,8 +86,11 @@ Ge = ot.optim.cg(a, b, M, reg, f, df, verbose=True)
 pl.figure(4, figsize=(5, 5))
 ot.plot.plot1D_mat(a, b, Ge, 'OT matrix Entrop. reg')
 
-#%% Example with Frobenius norm + entropic regularization with gcg
+##############################################################################
+# Solve EMD with Frobenius norm + entropic regularization
+##############################################################################
 
+#%% Example with Frobenius norm + entropic regularization with gcg
 
 def f(G):
     return 0.5 * np.sum(G**2)
diff --git a/docs/source/auto_examples/plot_optim_OTreg.rst b/docs/source/auto_examples/plot_optim_OTreg.rst
index f417158..532d4ca 100644
--- a/docs/source/auto_examples/plot_optim_OTreg.rst
+++ b/docs/source/auto_examples/plot_optim_OTreg.rst
@@ -11,24 +11,104 @@ Regularized OT with generic solver
 
 
 
+.. code-block:: python
+
+
+    import numpy as np
+    import matplotlib.pylab as pl
+    import ot
+
+
+
+
+
+
+
 
-.. rst-class:: sphx-glr-horizontal
+Generate data 
+#############################################################################
 
 
-    *
 
-      .. image:: /auto_examples/images/sphx_glr_plot_optim_OTreg_003.png
-            :scale: 47
+.. code-block:: python
+
+
+    #%% parameters
+
+    n = 100  # nb bins
+
+    # bin positions
+    x = np.arange(n, dtype=np.float64)
+
+    # Gaussian distributions
+    a = ot.datasets.get_1D_gauss(n, m=20, s=5)  # m= mean, s= std
+    b = ot.datasets.get_1D_gauss(n, m=60, s=10)
+
+    # loss matrix
+    M = ot.dist(x.reshape((n, 1)), x.reshape((n, 1)))
+    M /= M.max()
+
+
+
+
+
+
+
+Solve EMD 
+#############################################################################
+
+
+
+.. code-block:: python
+
+
+    #%% EMD
+
+    G0 = ot.emd(a, b, M)
+
+    pl.figure(3, figsize=(5, 5))
+    ot.plot.plot1D_mat(a, b, G0, 'OT matrix G0')
+
+
 
-    *
 
-      .. image:: /auto_examples/images/sphx_glr_plot_optim_OTreg_004.png
-            :scale: 47
+.. image:: /auto_examples/images/sphx_glr_plot_optim_OTreg_003.png
+    :align: center
 
-    *
 
-      .. image:: /auto_examples/images/sphx_glr_plot_optim_OTreg_005.png
-            :scale: 47
+
+
+Solve EMD with Frobenius norm regularization
+#############################################################################
+
+
+
+.. code-block:: python
+
+
+    #%% Example with Frobenius norm regularization
+
+
+    def f(G):
+        return 0.5 * np.sum(G**2)
+
+
+    def df(G):
+        return G
+
+
+    reg = 1e-1
+
+    Gl2 = ot.optim.cg(a, b, M, reg, f, df, verbose=True)
+
+    pl.figure(3)
+    ot.plot.plot1D_mat(a, b, Gl2, 'OT matrix Frob. reg')
+
+
+
+
+.. image:: /auto_examples/images/sphx_glr_plot_optim_OTreg_004.png
+    :align: center
 
 
 .. rst-class:: sphx-glr-script-out
@@ -258,6 +338,45 @@ Regularized OT with generic solver
     It.  |Loss        |Delta loss
     --------------------------------
       200|1.663543e-01|-8.737134e-08
+
+
+Solve EMD with entropic regularization
+#############################################################################
+
+
+
+.. code-block:: python
+
+
+    #%% Example with entropic regularization
+
+
+    def f(G):
+        return np.sum(G * np.log(G))
+
+
+    def df(G):
+        return np.log(G) + 1.
+
+
+    reg = 1e-3
+
+    Ge = ot.optim.cg(a, b, M, reg, f, df, verbose=True)
+
+    pl.figure(4, figsize=(5, 5))
+    ot.plot.plot1D_mat(a, b, Ge, 'OT matrix Entrop. reg')
+
+
+
+
+.. image:: /auto_examples/images/sphx_glr_plot_optim_OTreg_006.png
+    :align: center
+
+
+.. rst-class:: sphx-glr-script-out
+
+ Out::
+
     It.  |Loss        |Delta loss
     --------------------------------
         0|1.692289e-01|0.000000e+00
@@ -481,52 +600,17 @@ Regularized OT with generic solver
     It.  |Loss        |Delta loss
     --------------------------------
       200|1.607143e-01|-2.151971e-10
-    It.  |Loss        |Delta loss
-    --------------------------------
-        0|1.693084e-01|0.000000e+00
-        1|1.610121e-01|-5.152589e-02
-        2|1.609378e-01|-4.622297e-04
-        3|1.609284e-01|-5.830043e-05
-        4|1.609284e-01|-1.111580e-12
-
 
 
+Solve EMD with Frobenius norm + entropic regularization
+#############################################################################
 
-|
 
 
 .. code-block:: python
 
 
-    import numpy as np
-    import matplotlib.pylab as pl
-    import ot
-
-
-    #%% parameters
-
-    n = 100  # nb bins
-
-    # bin positions
-    x = np.arange(n, dtype=np.float64)
-
-    # Gaussian distributions
-    a = ot.datasets.get_1D_gauss(n, m=20, s=5)  # m= mean, s= std
-    b = ot.datasets.get_1D_gauss(n, m=60, s=10)
-
-    # loss matrix
-    M = ot.dist(x.reshape((n, 1)), x.reshape((n, 1)))
-    M /= M.max()
-
-    #%% EMD
-
-    G0 = ot.emd(a, b, M)
-
-    pl.figure(3, figsize=(5, 5))
-    ot.plot.plot1D_mat(a, b, G0, 'OT matrix G0')
-
-    #%% Example with Frobenius norm regularization
-
+    #%% Example with Frobenius norm + entropic regularization with gcg
 
     def f(G):
         return 0.5 * np.sum(G**2)
@@ -536,52 +620,35 @@ Regularized OT with generic solver
         return G
 
 
-    reg = 1e-1
-
-    Gl2 = ot.optim.cg(a, b, M, reg, f, df, verbose=True)
-
-    pl.figure(3)
-    ot.plot.plot1D_mat(a, b, Gl2, 'OT matrix Frob. reg')
-
-    #%% Example with entropic regularization
-
-
-    def f(G):
-        return np.sum(G * np.log(G))
-
-
-    def df(G):
-        return np.log(G) + 1.
-
-
-    reg = 1e-3
-
-    Ge = ot.optim.cg(a, b, M, reg, f, df, verbose=True)
+    reg1 = 1e-3
+    reg2 = 1e-1
 
-    pl.figure(4, figsize=(5, 5))
-    ot.plot.plot1D_mat(a, b, Ge, 'OT matrix Entrop. reg')
+    Gel2 = ot.optim.gcg(a, b, M, reg1, reg2, f, df, verbose=True)
 
-    #%% Example with Frobenius norm + entropic regularization with gcg
+    pl.figure(5, figsize=(5, 5))
+    ot.plot.plot1D_mat(a, b, Gel2, 'OT entropic + matrix Frob. reg')
+    pl.show()
 
 
-    def f(G):
-        return 0.5 * np.sum(G**2)
 
+.. image:: /auto_examples/images/sphx_glr_plot_optim_OTreg_008.png
+    :align: center
 
-    def df(G):
-        return G
 
+.. rst-class:: sphx-glr-script-out
 
-    reg1 = 1e-3
-    reg2 = 1e-1
+ Out::
 
-    Gel2 = ot.optim.gcg(a, b, M, reg1, reg2, f, df, verbose=True)
+    It.  |Loss        |Delta loss
+    --------------------------------
+        0|1.693084e-01|0.000000e+00
+        1|1.610121e-01|-5.152589e-02
+        2|1.609378e-01|-4.622297e-04
+        3|1.609284e-01|-5.830043e-05
+        4|1.609284e-01|-1.111580e-12
 
-    pl.figure(5, figsize=(5, 5))
-    ot.plot.plot1D_mat(a, b, Gel2, 'OT entropic + matrix Frob. reg')
-    pl.show()
 
-**Total running time of the script:** ( 0 minutes  2.720 seconds)
+**Total running time of the script:** ( 0 minutes  2.719 seconds)