example+rst titles

1 files changed, 91 insertions, 1 deletions

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": {