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{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Compute and plot EMD"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pylab as pl\n",
    "import ot\n",
    "from ot.datasets import get_1D_gauss as gauss"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Generate data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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EwzCM70VVyU4twlHhbOiq1Lsm1WRkGIbRkDITC1j7wWHSj+YTGhnAiGld6dg/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YVw/XwGT5zA2ea94O/tMtPpdLHWaKLuYhfWfm/u/q6iFgbsLlalm6g6fQK7RYGXX/QxksuGO+0W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\n7yOw6hNkxFBWLpzE863vEdWjXDfmOm4cf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vdbW4vIYOA2YLJSagxGhoMF9E9b/xm4oNe6\no9n2QoyUQMMxskI/8a9suF87BIzCPKVKqf1KqTDwMtC3gHA/QClVo5TabP7dgXGCGIyh7wum2AvA\nf5ycHp4YRCQHmAc8ay4LcB6w3BTpjzonAzMxUsaglAorpVrp57bGSLXjNhNoeoAa+qGtlVKfYKQA\n6snRbDsfeFEZrAVSROS4c/33d4dwpFoOg48i228QkQJgIrAOyFJK1Zgf1QJZR/navyv/A/wMzFzV\nRh2OVqVU1FzujzYvBBqA582hsmdFxEs/trVSqgr4f0AFhiNoAzbR/23dzdFs+7We4/q7QzjlEBEf\n8L/AHUqp9p6fmRlo+02csYhcBNQrpTad7L58w9iBIuAJpdREIECv4aF+aOtUjKvhQoxyvF76Dquc\nEpxI2/Z3h3AstRz6DSLiwHAGS5VSr5mr67pvIc33+pPVvxPADOASETmAMRx4HsbYeoo5rAD90+aV\nQKVSap25vBzDQfRnW88GypRSDUqpCPAahv37u627OZptv9ZzXH93CKdM3QVz7Pw5oEQp9YceH/Ws\nVfED4M1vum8nCqXU3UqpHKVUAYZtP1ZKfRdYiVGXA/qZzgBKqVrgoIiMMFfNwkgx329tjTFUNE1E\nPOax3q1zv7Z1D45m27eA75vRRtOAth5DS/88Rhm5/vsC5gJ7gH3AL052f06gnmdh3EZuA7aar7kY\nY+orgL3AR0Daye7rCdL/HOAd8+8hGIWYSoFXAdfJ7t8J0HcCsNG09xtAan+3NXAvsAvYAfwFcPVH\nWwPLMJ6TRDDuBq8/mm0xipY+Zp7ftmNEYR33tq3UFRYWFhYWQP8fMrKwsLCwOEYsh2BhYWFhAVgO\nwcLCwsLCxHIIFhYWFhaA5RAsLCwsLEwsh2BhYWFhAVgOwcLCwsLC5P8DfMl6OzAFEe8AAAAASUVO\nRK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f2b0307b850>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "n=100 # nb bins\n",
    "n_target=25 # nb target distributions\n",
    "\n",
    "\n",
    "# bin positions\n",
    "x=np.arange(n,dtype=np.float64)\n",
    "\n",
    "lst_m=np.linspace(20,90,n_target)\n",
    "\n",
    "# Gaussian distributions\n",
    "a=gauss(n,m=20,s=5) # m= mean, s= std\n",
    "\n",
    "B=np.zeros((n,n_target))\n",
    "\n",
    "for i,m in enumerate(lst_m):\n",
    "    B[:,i]=gauss(n,m=m,s=5)\n",
    "    \n",
    "\n",
    "# loss matrix and normalization\n",
    "M=ot.dist(x.reshape((n,1)),x.reshape((n,1)),'euclidean')\n",
    "M/=M.max()\n",
    "\n",
    "\n",
    "M2=ot.dist(x.reshape((n,1)),x.reshape((n,1)),'sqeuclidean')\n",
    "M2/=M2.max()\n",
    "\n",
    "\n",
    "# plot the distributions\n",
    "\n",
    "pl.figure(1)\n",
    "pl.subplot(2,1,1)\n",
    "pl.plot(x,a,'b',label='Source distribution')\n",
    "pl.xticks([])\n",
    "pl.title('Source distribution')\n",
    "pl.subplot(2,1,2)\n",
    "pl.plot(x,B,label='Target distributions')\n",
    "pl.title('Target distributions')\n",
    "pl.show()    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Compute EMD and sinkhorn distances "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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8atatW9dYjC2l7HJYWBj29vaMHTsWR0dHunfvnuHO2aSkJEaNGsX06dONj2VW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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f2b49fa7650>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "d_emd=ot.emd2(a,B,M) # direct computation of EMD\n",
    "d_emd2=ot.emd2(a,B,M2)  # direct computation of EMD with loss M2\n",
    "\n",
    "reg=1e-2\n",
    "d_sinkhorn=ot.sinkhorn(a,B,M,reg) # sinkhorn returns a list of distance if B is a matrix\n",
    "d_sinkhorn2=ot.sinkhorn(a,B,M2,reg)\n",
    "\n",
    "pl.figure(2)\n",
    "pl.clf()\n",
    "pl.plot(d_emd,label='Euclidean EMD')\n",
    "pl.plot(d_emd2,label='Squared Euclidean EMD')\n",
    "pl.plot(d_sinkhorn,'+',label='Euclidean Sinkhorn')\n",
    "pl.plot(d_sinkhorn2,'+',label='Squared Euclidean Sinkhorn')\n",
    "pl.title('EMD distances')\n",
    "pl.legend()\n",
    "pl.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.12"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}