1 files changed, 92 insertions, 2 deletions
diff --git a/docs/source/auto_examples/plot_optim_OTreg.ipynb b/docs/source/auto_examples/plot_optim_OTreg.ipynb
index 5ded922..333331b 100644
--- a/docs/source/auto_examples/plot_optim_OTreg.ipynb
+++ b/docs/source/auto_examples/plot_optim_OTreg.ipynb
@@ -15,7 +15,7 @@
     }, 
     {
       "source": [
-        "\n# Regularized OT with generic solver\n\n\n\n\n"
+        "\n# Regularized OT with generic solver\n\n\nIllustrates the use of the generic solver for regularized OT with\nuser-designed regularization term. It uses Conditional gradient as in [6] and\ngeneralized Conditional Gradient as proposed in [5][7].\n\n\n[5] N. Courty; R. Flamary; D. Tuia; A. Rakotomamonjy, Optimal Transport for\nDomain Adaptation, in IEEE Transactions on Pattern Analysis and Machine\nIntelligence , vol.PP, no.99, pp.1-1.\n\n[6] Ferradans, S., Papadakis, N., Peyr\u00e9, G., & Aujol, J. F. (2014).\nRegularized discrete optimal transport. SIAM Journal on Imaging Sciences,\n7(3), 1853-1882.\n\n[7] Rakotomamonjy, A., Flamary, R., & Courty, N. (2015). Generalized\nconditional gradient: analysis of convergence and applications.\narXiv preprint arXiv:1510.06567.\n\n\n\n\n"
       ], 
       "cell_type": "markdown", 
       "metadata": {}
@@ -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\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)\not.plot.plot1D_mat(a,b,G0,'OT matrix G0')\n\n#%% Example with Frobenius norm regularization\n\ndef f(G): return 0.5*np.sum(G**2)\ndef df(G): return G\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\ndef f(G): return np.sum(G*np.log(G))\ndef df(G): return np.log(G)+1\n\nreg=1e-3\n\nGe=ot.optim.cg(a,b,M,reg,f,df,verbose=True)\n\npl.figure(4)\not.plot.plot1D_mat(a,b,Ge,'OT matrix Entrop. reg')\n\n#%% Example with Frobenius norm + entropic regularization with gcg\n\ndef f(G): return 0.5*np.sum(G**2)\ndef df(G): return G\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)\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\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": {