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diff --git a/notebooks/plot_stochastic.ipynb b/notebooks/plot_stochastic.ipynb
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-{
- "cells": [
-  {
-   "cell_type": "code",
-   "execution_count": 1,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [],
-   "source": [
-    "%matplotlib inline"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "\n",
-    "# Stochastic examples\n",
-    "\n",
-    "\n",
-    "This example is designed to show how to use the stochatic optimization\n",
-    "algorithms for descrete and semicontinous measures from the POT library.\n",
-    "\n",
-    "\n"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 2,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [],
-   "source": [
-    "# Author: Kilian Fatras <kilian.fatras@gmail.com>\n",
-    "#\n",
-    "# License: MIT License\n",
-    "\n",
-    "import matplotlib.pylab as pl\n",
-    "import numpy as np\n",
-    "import ot\n",
-    "import ot.plot"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "COMPUTE TRANSPORTATION MATRIX FOR SEMI-DUAL PROBLEM\n",
-    "############################################################################\n",
-    "############################################################################\n",
-    " DISCRETE CASE:\n",
-    "\n",
-    " Sample two discrete measures for the discrete case\n",
-    " ---------------------------------------------\n",
-    "\n",
-    " Define 2 discrete measures a and b, the points where are defined the source\n",
-    " and the target measures and finally the cost matrix c.\n",
-    "\n"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 3,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [],
-   "source": [
-    "n_source = 7\n",
-    "n_target = 4\n",
-    "reg = 1\n",
-    "numItermax = 1000\n",
-    "\n",
-    "a = ot.utils.unif(n_source)\n",
-    "b = ot.utils.unif(n_target)\n",
-    "\n",
-    "rng = np.random.RandomState(0)\n",
-    "X_source = rng.randn(n_source, 2)\n",
-    "Y_target = rng.randn(n_target, 2)\n",
-    "M = ot.dist(X_source, Y_target)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Call the \"SAG\" method to find the transportation matrix in the discrete case\n",
-    "---------------------------------------------\n",
-    "\n",
-    "Define the method \"SAG\", call ot.solve_semi_dual_entropic and plot the\n",
-    "results.\n",
-    "\n"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 4,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "[[2.55553509e-02 9.96395660e-02 1.76579142e-02 4.31178196e-06]\n",
-      " [1.21640234e-01 1.25357448e-02 1.30225078e-03 7.37891338e-03]\n",
-      " [3.56123975e-03 7.61451746e-02 6.31505947e-02 1.33831456e-07]\n",
-      " [2.61515202e-02 3.34246014e-02 8.28734709e-02 4.07550428e-04]\n",
-      " [9.85500870e-03 7.52288517e-04 1.08262628e-02 1.21423583e-01]\n",
-      " [2.16904253e-02 9.03825797e-04 1.87178503e-03 1.18391107e-01]\n",
-      " [4.15462212e-02 2.65987989e-02 7.23177216e-02 2.39440107e-03]]\n"
-     ]
-    }
-   ],
-   "source": [
-    "method = \"SAG\"\n",
-    "sag_pi = ot.stochastic.solve_semi_dual_entropic(a, b, M, reg, method,\n",
-    "                                                numItermax)\n",
-    "print(sag_pi)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "SEMICONTINOUS CASE:\n",
-    "\n",
-    "Sample one general measure a, one discrete measures b for the semicontinous\n",
-    "case\n",
-    "---------------------------------------------\n",
-    "\n",
-    "Define one general measure a, one discrete measures b, the points where\n",
-    "are defined the source and the target measures and finally the cost matrix c.\n",
-    "\n"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 5,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [],
-   "source": [
-    "n_source = 7\n",
-    "n_target = 4\n",
-    "reg = 1\n",
-    "numItermax = 1000\n",
-    "log = True\n",
-    "\n",
-    "a = ot.utils.unif(n_source)\n",
-    "b = ot.utils.unif(n_target)\n",
-    "\n",
-    "rng = np.random.RandomState(0)\n",
-    "X_source = rng.randn(n_source, 2)\n",
-    "Y_target = rng.randn(n_target, 2)\n",
-    "M = ot.dist(X_source, Y_target)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Call the \"ASGD\" method to find the transportation matrix in the semicontinous\n",
-    "case\n",
-    "---------------------------------------------\n",
-    "\n",
-    "Define the method \"ASGD\", call ot.solve_semi_dual_entropic and plot the\n",
-    "results.\n",
-    "\n"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 6,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "[3.88833283 7.64041833 3.93000933 2.68489048 1.42837354 3.25840738\n",
-      " 2.80033951] [-2.50038759 -2.4083026  -0.96389053  5.87258072]\n",
-      "[[2.49326139e-02 1.01118047e-01 1.68018025e-02 4.67918477e-06]\n",
-      " [1.20543018e-01 1.29218840e-02 1.25860644e-03 8.13363473e-03]\n",
-      " [3.52425849e-03 7.83826265e-02 6.09501106e-02 1.47316769e-07]\n",
-      " [2.62727985e-02 3.49290291e-02 8.11998888e-02 4.55426386e-04]\n",
-      " [9.00986942e-03 7.15412954e-04 9.65318348e-03 1.23478677e-01]\n",
-      " [1.98446848e-02 8.60145164e-04 1.67017745e-03 1.20482135e-01]\n",
-      " [4.16774129e-02 2.77550575e-02 7.07529364e-02 2.67173611e-03]]\n"
-     ]
-    }
-   ],
-   "source": [
-    "method = \"ASGD\"\n",
-    "asgd_pi, log_asgd = ot.stochastic.solve_semi_dual_entropic(a, b, M, reg, method,\n",
-    "                                                           numItermax, log=log)\n",
-    "print(log_asgd['alpha'], log_asgd['beta'])\n",
-    "print(asgd_pi)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Compare the results with the Sinkhorn algorithm\n",
-    "---------------------------------------------\n",
-    "\n",
-    "Call the Sinkhorn algorithm from POT\n",
-    "\n"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 7,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "[[2.55535622e-02 9.96413843e-02 1.76578860e-02 4.31043335e-06]\n",
-      " [1.21640742e-01 1.25369034e-02 1.30234529e-03 7.37715259e-03]\n",
-      " [3.56096458e-03 7.61460101e-02 6.31500344e-02 1.33788624e-07]\n",
-      " [2.61499607e-02 3.34255577e-02 8.28741973e-02 4.07427179e-04]\n",
-      " [9.85698720e-03 7.52505948e-04 1.08291770e-02 1.21418473e-01]\n",
-      " [2.16947591e-02 9.04086158e-04 1.87228707e-03 1.18386011e-01]\n",
-      " [4.15442692e-02 2.65998963e-02 7.23192701e-02 2.39370724e-03]]\n"
-     ]
-    }
-   ],
-   "source": [
-    "sinkhorn_pi = ot.sinkhorn(a, b, M, reg)\n",
-    "print(sinkhorn_pi)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "PLOT TRANSPORTATION MATRIX\n",
-    "#############################################################################\n",
-    "\n"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Plot SAG results\n",
-    "----------------\n",
-    "\n"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 8,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "image/png": 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\n",
-      "text/plain": [
-       "<Figure size 360x360 with 3 Axes>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
-   "source": [
-    "pl.figure(4, figsize=(5, 5))\n",
-    "ot.plot.plot1D_mat(a, b, sag_pi, 'semi-dual : OT matrix SAG')\n",
-    "pl.show()"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Plot ASGD results\n",
-    "-----------------\n",
-    "\n"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 9,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "image/png": 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\n",
-      "text/plain": [
-       "<Figure size 360x360 with 3 Axes>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
-   "source": [
-    "pl.figure(4, figsize=(5, 5))\n",
-    "ot.plot.plot1D_mat(a, b, asgd_pi, 'semi-dual : OT matrix ASGD')\n",
-    "pl.show()"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Plot Sinkhorn results\n",
-    "---------------------\n",
-    "\n"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 10,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "image/png": "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\n",
-      "text/plain": [
-       "<Figure size 360x360 with 3 Axes>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
-   "source": [
-    "pl.figure(4, figsize=(5, 5))\n",
-    "ot.plot.plot1D_mat(a, b, sinkhorn_pi, 'OT matrix Sinkhorn')\n",
-    "pl.show()"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "COMPUTE TRANSPORTATION MATRIX FOR DUAL PROBLEM\n",
-    "############################################################################\n",
-    "############################################################################\n",
-    " SEMICONTINOUS CASE:\n",
-    "\n",
-    " Sample one general measure a, one discrete measures b for the semicontinous\n",
-    " case\n",
-    " ---------------------------------------------\n",
-    "\n",
-    " Define one general measure a, one discrete measures b, the points where\n",
-    " are defined the source and the target measures and finally the cost matrix c.\n",
-    "\n"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 11,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [],
-   "source": [
-    "n_source = 7\n",
-    "n_target = 4\n",
-    "reg = 1\n",
-    "numItermax = 100000\n",
-    "lr = 0.1\n",
-    "batch_size = 3\n",
-    "log = True\n",
-    "\n",
-    "a = ot.utils.unif(n_source)\n",
-    "b = ot.utils.unif(n_target)\n",
-    "\n",
-    "rng = np.random.RandomState(0)\n",
-    "X_source = rng.randn(n_source, 2)\n",
-    "Y_target = rng.randn(n_target, 2)\n",
-    "M = ot.dist(X_source, Y_target)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Call the \"SGD\" dual method to find the transportation matrix in the\n",
-    "semicontinous case\n",
-    "---------------------------------------------\n",
-    "\n",
-    "Call ot.solve_dual_entropic and plot the results.\n",
-    "\n"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 12,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "[0.92524245 2.75994495 1.08144666 0.02747421 0.60913832 1.8156535\n",
-      " 0.11738177] [0.33905828 0.46705197 1.56941919 4.96075241]\n",
-      "[[2.20327995e-02 9.26244184e-02 1.09321230e-02 9.71212784e-08]\n",
-      " [1.56579562e-02 1.73985799e-03 1.20373178e-04 2.48153271e-05]\n",
-      " [3.49227454e-03 8.05110304e-02 4.44694627e-02 3.42874458e-09]\n",
-      " [3.15181548e-02 4.34346087e-02 7.17227024e-02 1.28326090e-05]\n",
-      " [6.79336320e-02 5.59136813e-03 5.35899879e-02 2.18675752e-02]\n",
-      " [8.02083959e-02 3.60364770e-03 4.97032746e-03 1.14377502e-02]\n",
-      " [4.87374362e-02 3.36433325e-02 6.09190548e-02 7.33833971e-05]]\n"
-     ]
-    }
-   ],
-   "source": [
-    "sgd_dual_pi, log_sgd = ot.stochastic.solve_dual_entropic(a, b, M, reg,\n",
-    "                                                         batch_size, numItermax,\n",
-    "                                                         lr, log=log)\n",
-    "print(log_sgd['alpha'], log_sgd['beta'])\n",
-    "print(sgd_dual_pi)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Compare the results with the Sinkhorn algorithm\n",
-    "---------------------------------------------\n",
-    "\n",
-    "Call the Sinkhorn algorithm from POT\n",
-    "\n"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 13,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "[[2.55535622e-02 9.96413843e-02 1.76578860e-02 4.31043335e-06]\n",
-      " [1.21640742e-01 1.25369034e-02 1.30234529e-03 7.37715259e-03]\n",
-      " [3.56096458e-03 7.61460101e-02 6.31500344e-02 1.33788624e-07]\n",
-      " [2.61499607e-02 3.34255577e-02 8.28741973e-02 4.07427179e-04]\n",
-      " [9.85698720e-03 7.52505948e-04 1.08291770e-02 1.21418473e-01]\n",
-      " [2.16947591e-02 9.04086158e-04 1.87228707e-03 1.18386011e-01]\n",
-      " [4.15442692e-02 2.65998963e-02 7.23192701e-02 2.39370724e-03]]\n"
-     ]
-    }
-   ],
-   "source": [
-    "sinkhorn_pi = ot.sinkhorn(a, b, M, reg)\n",
-    "print(sinkhorn_pi)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Plot  SGD results\n",
-    "-----------------\n",
-    "\n"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 14,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "image/png": 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\n",
-      "text/plain": [
-       "<Figure size 360x360 with 3 Axes>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
-   "source": [
-    "pl.figure(4, figsize=(5, 5))\n",
-    "ot.plot.plot1D_mat(a, b, sgd_dual_pi, 'dual : OT matrix SGD')\n",
-    "pl.show()"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Plot Sinkhorn results\n",
-    "---------------------\n",
-    "\n"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 15,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "image/png": 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\n",
-      "text/plain": [
-       "<Figure size 360x360 with 3 Axes>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
-   "source": [
-    "pl.figure(4, figsize=(5, 5))\n",
-    "ot.plot.plot1D_mat(a, b, sinkhorn_pi, 'OT matrix Sinkhorn')\n",
-    "pl.show()"
-   ]
-  }
- ],
- "metadata": {
-  "kernelspec": {
-   "display_name": "Python 3",
-   "language": "python",
-   "name": "python3"
-  },
-  "language_info": {
-   "codemirror_mode": {
-    "name": "ipython",
-    "version": 3
-   },
-   "file_extension": ".py",
-   "mimetype": "text/x-python",
-   "name": "python",
-   "nbconvert_exporter": "python",
-   "pygments_lexer": "ipython3",
-   "version": "3.6.7"
-  }
- },
- "nbformat": 4,
- "nbformat_minor": 0
-}