segment-recommender.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Populating the interactive namespace from numpy and matplotlib\n"
     ]
    }
   ],
   "source": [
    "%pylab inline\n",
    "%config InlineBackend.figure_format = 'svg'"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Strava segment recommender"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import stravalib\n",
    "from mpl_toolkits.basemap import Basemap"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Get data from Strava Public API"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 294,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "client = stravalib.Client(access_token='ea571a903a95d27a567aadfaeb85d8e76aeafee3')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Get IDs of popular Bay Area segments"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`Client.explore_segments` is limited to returning only 10 (of the most popular) segments per request. To get the most popular segments over a large area of the map, we can place a grid on the desired map area and make a request for each square of the grid."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 295,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# lat/lon bounds for the whole region of interest (South SF Bay Area)\n",
    "bounds = dict(llcrnrlat=36.8, llcrnrlon=-122.6, \n",
    "              urcrnrlat=38.0, urcrnrlon=-121.6)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, define the grid..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 296,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "gridlines = 15 # number of grid lines to use\n",
    "gridlat = linspace(bounds['llcrnrlat'], bounds['urcrnrlat'], gridlines)\n",
    "gridlon = linspace(bounds['llcrnrlon'], bounds['urcrnrlon'], gridlines)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/svg+xml": [
       "<?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?>\n",
       "<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n",
       "  \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n",
       "<!-- Created with matplotlib (http://matplotlib.org/) -->\n",
       "<svg height=\"237pt\" version=\"1.1\" viewBox=\"0 0 200 237\" width=\"200pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
       " <defs>\n",
       "  <style type=\"text/css\">\n",
       "*{stroke-linecap:butt;stroke-linejoin:round;}\n",
       "  </style>\n",
       " </defs>\n",
       " <g id=\"figure_1\">\n",
       "  <g id=\"patch_1\">\n",
       "   <path d=\"\n",
       "M1.42109e-14 237.6\n",
       "L200.4 237.6\n",
       "L200.4 0\n",
       "L1.42109e-14 0\n",
       "L1.42109e-14 237.6\" style=\"fill:none;\"/>\n",
       "  </g>\n",
       "  <g id=\"axes_1\">\n",
       "   <g id=\"patch_2\">\n",
       "    <path d=\"\n",
       "M7.2 230.4\n",
       "L193.2 230.4\n",
       "L193.2 7.2\n",
       "L7.2 7.2\n",
       "z\n",
       "\" style=\"fill:#00ffff;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_3\">\n",
       "    <path clip-path=\"url(#pdd855eeb13)\" d=\"\n",
       "M157.526 230.4\n",
       "L157.809 229.014\n",
       "L144.179 205.93\n",
       "L131.769 197.381\n",
       "L123.904 201.72\n",
       "L116.294 199.855\n",
       "L109.278 202.98\n",
       "L93.5037 199.431\n",
       "L76.7899 188.633\n",
       "L64.0751 173.288\n",
       "L56.7953 172.668\n",
       "L50.357 161.275\n",
       "L43.0771 156.625\n",
       "L40.2929 146.7\n",
       "L44.3231 126.705\n",
       "L33.9327 102.681\n",
       "L29.8202 99.8225\n",
       "L25.3303 101.208\n",
       "L21.8479 93.8454\n",
       "L21.6875 82.6901\n",
       "L25.712 81.3009\n",
       "L26.7976 72.4601\n",
       "L22.9221 47.8194\n",
       "L27.9598 46.3379\n",
       "L29.8202 42.6228\n",
       "L41.4452 42.1516\n",
       "L46.7979 45.9491\n",
       "L47.252 54.0094\n",
       "L52.5324 57.7358\n",
       "L45.8628 61.6042\n",
       "L48.0481 68.2795\n",
       "L45.5577 69.3552\n",
       "L49.2771 70.1413\n",
       "L45.8727 73.7003\n",
       "L46.5652 76.0986\n",
       "L51.1374 76.4845\n",
       "L52.2174 80.0549\n",
       "L48.5079 80.3643\n",
       "L51.3702 82.9229\n",
       "L71.0555 86.9473\n",
       "L72.6051 90.5134\n",
       "L76.3968 90.5901\n",
       "L74.6202 94.5379\n",
       "L77.7152 91.748\n",
       "L76.4848 93.7716\n",
       "L82.2874 93.3743\n",
       "L78.6503 99.5018\n",
       "L81.5949 95.6278\n",
       "L87.8005 100.587\n",
       "L93.3746 98.7228\n",
       "L96.3872 105.785\n",
       "L101.59 109.274\n",
       "L112.89 109.572\n",
       "L112.13 107.718\n",
       "L117.137 106.864\n",
       "L109.34 106.787\n",
       "L109.955 101.523\n",
       "L98.5627 100.36\n",
       "L90.9778 84.2397\n",
       "L88.3426 68.5803\n",
       "L83.3772 62.2357\n",
       "L81.4345 60.7528\n",
       "L78.9597 63.0772\n",
       "L73.5403 59.6672\n",
       "L70.0479 54.9403\n",
       "L74.1448 53.6234\n",
       "L65.0046 50.9924\n",
       "L63.1555 48.0422\n",
       "L57.028 47.8151\n",
       "L58.8927 43.6303\n",
       "L55.0172 43.3209\n",
       "L60.753 40.6843\n",
       "L57.1827 39.9052\n",
       "L63.3826 38.516\n",
       "L60.4366 37.5851\n",
       "L63.0675 36.8103\n",
       "L58.8827 31.0701\n",
       "L61.3732 31.0744\n",
       "L58.2725 27.6601\n",
       "L60.2777 26.7349\n",
       "L49.8248 21.3878\n",
       "L51.1999 24.7979\n",
       "L45.1703 24.7979\n",
       "L46.7923 22.086\n",
       "L40.1269 17.1193\n",
       "L38.9704 13.4723\n",
       "L44.7048 15.9627\n",
       "L44.2351 12.8621\n",
       "L50.5074 11.2358\n",
       "L50.5599 7.2\n",
       "L193.2 7.2\n",
       "L193.2 230.4\n",
       "z\n",
       "\" style=\"fill:#ff7f50;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_4\">\n",
       "    <path clip-path=\"url(#pdd855eeb13)\" d=\"\n",
       "M31.6011 7.2\n",
       "L35.4724 9.36975\n",
       "L25.4027 12.7854\n",
       "L29.6755 17.9778\n",
       "L23.3975 18.0559\n",
       "L37.1866 29.2097\n",
       "L32.6825 30.9155\n",
       "L33.5453 32.8567\n",
       "L27.8051 26.9619\n",
       "L25.0976 26.7292\n",
       "L26.2598 29.9178\n",
       "L21.4548 27.277\n",
       "L29.7422 33.3903\n",
       "L30.9824 38.2095\n",
       "L20.5197 41.5272\n",
       "L13.5449 34.4035\n",
       "L7.20028 30.9566\n",
       "L7.20028 7.2\n",
       "z\n",
       "\" style=\"fill:#ff7f50;\"/>\n",
       "   </g>\n",
       "   <g id=\"LineCollection_1\">\n",
       "    <path clip-path=\"url(#pdd855eeb13)\" d=\"\n",
       "M157.526 230.4\n",
       "L157.809 229.014\n",
       "L144.179 205.93\n",
       "L131.769 197.381\n",
       "L123.904 201.72\n",
       "L116.294 199.855\n",
       "L109.278 202.98\n",
       "L93.5037 199.431\n",
       "L76.7899 188.633\n",
       "L64.0751 173.288\n",
       "L56.7953 172.668\n",
       "L50.357 161.275\n",
       "L43.0771 156.625\n",
       "L40.2929 146.7\n",
       "L44.3231 126.705\n",
       "L33.9327 102.681\n",
       "L29.8202 99.8225\n",
       "L25.3303 101.208\n",
       "L21.8479 93.8454\n",
       "L21.6875 82.6901\n",
       "L25.712 81.3009\n",
       "L26.7976 72.4601\n",
       "L22.9221 47.8194\n",
       "L27.9598 46.3379\n",
       "L29.8202 42.6228\n",
       "L41.4452 42.1516\n",
       "L46.7979 45.9491\n",
       "L47.252 54.0094\n",
       "L52.5324 57.7358\n",
       "L45.8628 61.6042\n",
       "L48.0481 68.2795\n",
       "L45.5577 69.3552\n",
       "L49.2771 70.1413\n",
       "L45.8727 73.7003\n",
       "L46.5652 76.0986\n",
       "L51.1374 76.4845\n",
       "L52.2174 80.0549\n",
       "L48.5079 80.3643\n",
       "L51.3702 82.9229\n",
       "L71.0555 86.9473\n",
       "L72.6051 90.5134\n",
       "L76.3968 90.5901\n",
       "L74.6202 94.5379\n",
       "L77.7152 91.748\n",
       "L76.4848 93.7716\n",
       "L82.2874 93.3743\n",
       "L78.6503 99.5018\n",
       "L81.5949 95.6278\n",
       "L87.8005 100.587\n",
       "L93.3746 98.7228\n",
       "L96.3872 105.785\n",
       "L101.59 109.274\n",
       "L112.89 109.572\n",
       "L112.13 107.718\n",
       "L117.137 106.864\n",
       "L109.34 106.787\n",
       "L109.955 101.523\n",
       "L98.5627 100.36\n",
       "L90.9778 84.2397\n",
       "L88.3426 68.5803\n",
       "L83.3772 62.2357\n",
       "L81.4345 60.7528\n",
       "L78.9597 63.0772\n",
       "L73.5403 59.6672\n",
       "L70.0479 54.9403\n",
       "L74.1448 53.6234\n",
       "L65.0046 50.9924\n",
       "L63.1555 48.0422\n",
       "L57.028 47.8151\n",
       "L58.8927 43.6303\n",
       "L55.0172 43.3209\n",
       "L60.753 40.6843\n",
       "L57.1827 39.9052\n",
       "L63.3826 38.516\n",
       "L60.4366 37.5851\n",
       "L63.0675 36.8103\n",
       "L58.8827 31.0701\n",
       "L61.3732 31.0744\n",
       "L58.2725 27.6601\n",
       "L60.2777 26.7349\n",
       "L49.8248 21.3878\n",
       "L51.1999 24.7979\n",
       "L45.1703 24.7979\n",
       "L46.7923 22.086\n",
       "L40.1269 17.1193\n",
       "L38.9704 13.4723\n",
       "L44.7048 15.9627\n",
       "L44.2351 12.8621\n",
       "L50.5074 11.2358\n",
       "L50.5596 7.2\" style=\"fill:none;stroke:#000000;\"/>\n",
       "    <path clip-path=\"url(#pdd855eeb13)\" d=\"\n",
       "M31.6013 7.2\n",
       "L35.4724 9.36975\n",
       "L25.4027 12.7854\n",
       "L29.6755 17.9778\n",
       "L23.3975 18.0559\n",
       "L37.1866 29.2097\n",
       "L32.6825 30.9155\n",
       "L33.5453 32.8567\n",
       "L27.8051 26.9619\n",
       "L25.0976 26.7292\n",
       "L26.2598 29.9178\n",
       "L21.4548 27.277\n",
       "L29.7422 33.3903\n",
       "L30.9824 38.2095\n",
       "L20.5197 41.5272\n",
       "L13.5449 34.4035\n",
       "L7.2 30.9565\" style=\"fill:none;stroke:#000000;\"/>\n",
       "   </g>\n",
       "   <g id=\"line2d_1\">\n",
       "    <path clip-path=\"url(#pdd855eeb13)\" d=\"\n",
       "M7.2 230.4\n",
       "L193.2 230.4\n",
       "L193.2 230.4\" style=\"fill:none;stroke:#000000;stroke-dasharray:1.000000,1.000000;stroke-dashoffset:0.0;\"/>\n",
       "   </g>\n",
       "   <g id=\"line2d_2\">\n",
       "    <path clip-path=\"url(#pdd855eeb13)\" d=\"\n",
       "M7.2 214.457\n",
       "L193.2 214.457\n",
       "L193.2 214.457\" style=\"fill:none;stroke:#000000;stroke-dasharray:1.000000,1.000000;stroke-dashoffset:0.0;\"/>\n",
       "   </g>\n",
       "   <g id=\"line2d_3\">\n",
       "    <path clip-path=\"url(#pdd855eeb13)\" d=\"\n",
       "M7.2 198.514\n",
       "L193.2 198.514\n",
       "L193.2 198.514\" style=\"fill:none;stroke:#000000;stroke-dasharray:1.000000,1.000000;stroke-dashoffset:0.0;\"/>\n",
       "   </g>\n",
       "   <g id=\"line2d_4\">\n",
       "    <path clip-path=\"url(#pdd855eeb13)\" d=\"\n",
       "M7.2 182.571\n",
       "L193.2 182.571\n",
       "L193.2 182.571\" style=\"fill:none;stroke:#000000;stroke-dasharray:1.000000,1.000000;stroke-dashoffset:0.0;\"/>\n",
       "   </g>\n",
       "   <g id=\"line2d_5\">\n",
       "    <path clip-path=\"url(#pdd855eeb13)\" d=\"\n",
       "M7.2 166.629\n",
       "L193.2 166.629\n",
       "L193.2 166.629\" style=\"fill:none;stroke:#000000;stroke-dasharray:1.000000,1.000000;stroke-dashoffset:0.0;\"/>\n",
       "   </g>\n",
       "   <g id=\"line2d_6\">\n",
       "    <path clip-path=\"url(#pdd855eeb13)\" d=\"\n",
       "M7.2 150.685\n",
       "L193.2 150.685\n",
       "L193.2 150.685\" style=\"fill:none;stroke:#000000;stroke-dasharray:1.000000,1.000000;stroke-dashoffset:0.0;\"/>\n",
       "   </g>\n",
       "   <g id=\"line2d_7\">\n",
       "    <path clip-path=\"url(#pdd855eeb13)\" d=\"\n",
       "M7.2 134.743\n",
       "L193.2 134.743\n",
       "L193.2 134.743\" style=\"fill:none;stroke:#000000;stroke-dasharray:1.000000,1.000000;stroke-dashoffset:0.0;\"/>\n",
       "   </g>\n",
       "   <g id=\"line2d_8\">\n",
       "    <path clip-path=\"url(#pdd855eeb13)\" d=\"\n",
       "M7.2 118.8\n",
       "L193.2 118.8\n",
       "L193.2 118.8\" style=\"fill:none;stroke:#000000;stroke-dasharray:1.000000,1.000000;stroke-dashoffset:0.0;\"/>\n",
       "   </g>\n",
       "   <g id=\"line2d_9\">\n",
       "    <path clip-path=\"url(#pdd855eeb13)\" d=\"\n",
       "M7.2 102.857\n",
       "L193.2 102.857\n",
       "L193.2 102.857\" style=\"fill:none;stroke:#000000;stroke-dasharray:1.000000,1.000000;stroke-dashoffset:0.0;\"/>\n",
       "   </g>\n",
       "   <g id=\"line2d_10\">\n",
       "    <path clip-path=\"url(#pdd855eeb13)\" d=\"\n",
       "M7.2 86.914\n",
       "L193.2 86.914\n",
       "L193.2 86.914\" style=\"fill:none;stroke:#000000;stroke-dasharray:1.000000,1.000000;stroke-dashoffset:0.0;\"/>\n",
       "   </g>\n",
       "   <g id=\"line2d_11\">\n",
       "    <path clip-path=\"url(#pdd855eeb13)\" d=\"\n",
       "M7.2 70.9715\n",
       "L193.2 70.9715\n",
       "L193.2 70.9715\" style=\"fill:none;stroke:#000000;stroke-dasharray:1.000000,1.000000;stroke-dashoffset:0.0;\"/>\n",
       "   </g>\n",
       "   <g id=\"line2d_12\">\n",
       "    <path clip-path=\"url(#pdd855eeb13)\" d=\"\n",
       "M7.2 55.0282\n",
       "L193.2 55.0282\n",
       "L193.2 55.0282\" style=\"fill:none;stroke:#000000;stroke-dasharray:1.000000,1.000000;stroke-dashoffset:0.0;\"/>\n",
       "   </g>\n",
       "   <g id=\"line2d_13\">\n",
       "    <path clip-path=\"url(#pdd855eeb13)\" d=\"\n",
       "M7.2 39.0857\n",
       "L193.2 39.0857\n",
       "L193.2 39.0857\" style=\"fill:none;stroke:#000000;stroke-dasharray:1.000000,1.000000;stroke-dashoffset:0.0;\"/>\n",
       "   </g>\n",
       "   <g id=\"line2d_14\">\n",
       "    <path clip-path=\"url(#pdd855eeb13)\" d=\"\n",
       "M7.2 23.1425\n",
       "L193.2 23.1425\n",
       "L193.2 23.1425\" style=\"fill:none;stroke:#000000;stroke-dasharray:1.000000,1.000000;stroke-dashoffset:0.0;\"/>\n",
       "   </g>\n",
       "   <g id=\"line2d_15\">\n",
       "    <path clip-path=\"url(#pdd855eeb13)\" d=\"\n",
       "M7.2 7.2\n",
       "L193.2 7.2\n",
       "L193.2 7.2\" style=\"fill:none;stroke:#000000;stroke-dasharray:1.000000,1.000000;stroke-dashoffset:0.0;\"/>\n",
       "   </g>\n",
       "   <g id=\"line2d_16\">\n",
       "    <path clip-path=\"url(#pdd855eeb13)\" d=\"\n",
       "M7.20028 230.4\n",
       "L7.20028 7.2\n",
       "L7.20028 7.2\" style=\"fill:none;stroke:#000000;stroke-dasharray:1.000000,1.000000;stroke-dashoffset:0.0;\"/>\n",
       "   </g>\n",
       "   <g id=\"line2d_17\">\n",
       "    <path clip-path=\"url(#pdd855eeb13)\" d=\"\n",
       "M20.4856 230.4\n",
       "L20.4856 7.2\n",
       "L20.4856 7.2\" style=\"fill:none;stroke:#000000;stroke-dasharray:1.000000,1.000000;stroke-dashoffset:0.0;\"/>\n",
       "   </g>\n",
       "   <g id=\"line2d_18\">\n",
       "    <path clip-path=\"url(#pdd855eeb13)\" d=\"\n",
       "M33.7709 230.4\n",
       "L33.7709 7.2\n",
       "L33.7709 7.2\" style=\"fill:none;stroke:#000000;stroke-dasharray:1.000000,1.000000;stroke-dashoffset:0.0;\"/>\n",
       "   </g>\n",
       "   <g id=\"line2d_19\">\n",
       "    <path clip-path=\"url(#pdd855eeb13)\" d=\"\n",
       "M47.0576 230.4\n",
       "L47.0576 7.2\n",
       "L47.0576 7.2\" style=\"fill:none;stroke:#000000;stroke-dasharray:1.000000,1.000000;stroke-dashoffset:0.0;\"/>\n",
       "   </g>\n",
       "   <g id=\"line2d_20\">\n",
       "    <path clip-path=\"url(#pdd855eeb13)\" d=\"\n",
       "M60.3429 230.4\n",
       "L60.3429 7.2\n",
       "L60.3429 7.2\" style=\"fill:none;stroke:#000000;stroke-dasharray:1.000000,1.000000;stroke-dashoffset:0.0;\"/>\n",
       "   </g>\n",
       "   <g id=\"line2d_21\">\n",
       "    <path clip-path=\"url(#pdd855eeb13)\" d=\"\n",
       "M73.6282 230.4\n",
       "L73.6282 7.2\n",
       "L73.6282 7.2\" style=\"fill:none;stroke:#000000;stroke-dasharray:1.000000,1.000000;stroke-dashoffset:0.0;\"/>\n",
       "   </g>\n",
       "   <g id=\"line2d_22\">\n",
       "    <path clip-path=\"url(#pdd855eeb13)\" d=\"\n",
       "M86.915 230.4\n",
       "L86.915 7.2\n",
       "L86.915 7.2\" style=\"fill:none;stroke:#000000;stroke-dasharray:1.000000,1.000000;stroke-dashoffset:0.0;\"/>\n",
       "   </g>\n",
       "   <g id=\"line2d_23\">\n",
       "    <path clip-path=\"url(#pdd855eeb13)\" d=\"\n",
       "M100.2 230.4\n",
       "L100.2 7.2\n",
       "L100.2 7.2\" style=\"fill:none;stroke:#000000;stroke-dasharray:1.000000,1.000000;stroke-dashoffset:0.0;\"/>\n",
       "   </g>\n",
       "   <g id=\"line2d_24\">\n",
       "    <path clip-path=\"url(#pdd855eeb13)\" d=\"\n",
       "M113.486 230.4\n",
       "L113.486 7.2\n",
       "L113.486 7.2\" style=\"fill:none;stroke:#000000;stroke-dasharray:1.000000,1.000000;stroke-dashoffset:0.0;\"/>\n",
       "   </g>\n",
       "   <g id=\"line2d_25\">\n",
       "    <path clip-path=\"url(#pdd855eeb13)\" d=\"\n",
       "M126.771 230.4\n",
       "L126.771 7.2\n",
       "L126.771 7.2\" style=\"fill:none;stroke:#000000;stroke-dasharray:1.000000,1.000000;stroke-dashoffset:0.0;\"/>\n",
       "   </g>\n",
       "   <g id=\"line2d_26\">\n",
       "    <path clip-path=\"url(#pdd855eeb13)\" d=\"\n",
       "M140.058 230.4\n",
       "L140.058 7.2\n",
       "L140.058 7.2\" style=\"fill:none;stroke:#000000;stroke-dasharray:1.000000,1.000000;stroke-dashoffset:0.0;\"/>\n",
       "   </g>\n",
       "   <g id=\"line2d_27\">\n",
       "    <path clip-path=\"url(#pdd855eeb13)\" d=\"\n",
       "M153.343 230.4\n",
       "L153.343 7.2\n",
       "L153.343 7.2\" style=\"fill:none;stroke:#000000;stroke-dasharray:1.000000,1.000000;stroke-dashoffset:0.0;\"/>\n",
       "   </g>\n",
       "   <g id=\"line2d_28\">\n",
       "    <path clip-path=\"url(#pdd855eeb13)\" d=\"\n",
       "M166.628 230.4\n",
       "L166.628 7.2\n",
       "L166.628 7.2\" style=\"fill:none;stroke:#000000;stroke-dasharray:1.000000,1.000000;stroke-dashoffset:0.0;\"/>\n",
       "   </g>\n",
       "   <g id=\"line2d_29\">\n",
       "    <path clip-path=\"url(#pdd855eeb13)\" d=\"\n",
       "M179.915 230.4\n",
       "L179.915 7.2\n",
       "L179.915 7.2\" style=\"fill:none;stroke:#000000;stroke-dasharray:1.000000,1.000000;stroke-dashoffset:0.0;\"/>\n",
       "   </g>\n",
       "   <g id=\"line2d_30\">\n",
       "    <path clip-path=\"url(#pdd855eeb13)\" d=\"\n",
       "M193.2 230.4\" style=\"fill:none;stroke:#000000;stroke-dasharray:1.000000,1.000000;stroke-dashoffset:0.0;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_5\">\n",
       "    <path d=\"\n",
       "M7.2 7.2\n",
       "L193.2 7.2\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_6\">\n",
       "    <path d=\"\n",
       "M7.2 230.4\n",
       "L7.2 7.2\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_7\">\n",
       "    <path d=\"\n",
       "M193.2 230.4\n",
       "L193.2 7.2\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_8\">\n",
       "    <path d=\"\n",
       "M7.2 230.4\n",
       "L193.2 230.4\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;\"/>\n",
       "   </g>\n",
       "   <g id=\"matplotlib.axis_1\"/>\n",
       "   <g id=\"matplotlib.axis_2\"/>\n",
       "  </g>\n",
       " </g>\n",
       " <defs>\n",
       "  <clipPath id=\"pdd855eeb13\">\n",
       "   <rect height=\"223.2\" width=\"186.0\" x=\"7.2\" y=\"7.2\"/>\n",
       "  </clipPath>\n",
       " </defs>\n",
       "</svg>\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fce89c86e10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "mp = Basemap(resolution='i', **bounds)\n",
    "mp.fillcontinents(color='coral', lake_color='aqua')\n",
    "mp.drawmapboundary(fill_color='aqua')\n",
    "mp.drawcoastlines()\n",
    "mp.drawparallels(gridlat)\n",
    "mp.drawmeridians(gridlon);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 297,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "gridsquares = [(south, west, north, east)\n",
    "               for (south, north) in zip(gridlat[:-1], gridlat[1:])\n",
    "               for (west, east) in zip(gridlon[:-1], gridlon[1:])]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "segments = [(segment.id, segment.name)\n",
    "            for gridsquare in gridsquares\n",
    "            for segment in client.explore_segments(gridsquare)]\n",
    "\n",
    "segments = pd.DataFrame.from_records(segments, columns=['id','name'], index='id')\n",
    "segments.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 361,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#segments.to_csv('segments.csv')\n",
    "segments = pd.read_csv('segments.csv').set_index('id')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 362,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>name</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>id</th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>4236635</th>\n",
       "      <td>Pacific Coast Bike Route: Thurwachter to Jensen</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>658876</th>\n",
       "      <td>Trafton</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5086842</th>\n",
       "      <td>Hilltop Rd Salinas to Jenson</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4236698</th>\n",
       "      <td>Pacific Coast Bike Route: Jensen to Thurwachter</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>998126</th>\n",
       "      <td>Trafton Road Bump</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                                                    name\n",
       "id                                                      \n",
       "4236635  Pacific Coast Bike Route: Thurwachter to Jensen\n",
       "658876                                           Trafton\n",
       "5086842                     Hilltop Rd Salinas to Jenson\n",
       "4236698  Pacific Coast Bike Route: Jensen to Thurwachter\n",
       "998126                                 Trafton Road Bump"
      ]
     },
     "execution_count": 362,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "segments.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Get segment leaderboards"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "leaderboards = [client.get_segment_leaderboard(segment_id, top_results_limit=100) \n",
    "                for segment_id in segments['id']]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "len(leaderboards)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "columns = ['activity_id','athlete_id','average_hr',\n",
    "           'average_watts','effort_id','elapsed_time',\n",
    "           'moving_time','rank','start_date']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def leaderboard_to_df(leaderboard, fields):\n",
    "\n",
    "    records = [[entry.__getattribute__(x) for x in fields]\n",
    "               for entry in leaderboard]\n",
    "    \n",
    "    df = pd.DataFrame.from_records(records, columns=fields)\n",
    "    return df.convert_objects().set_index('athlete_id')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "leaders = [leaderboard_to_df(lb, columns) for lb in leaderboards]\n",
    "leaders = pd.concat(leaders, keys=segment_ids, names=['segment_id'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 353,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th>activity_id</th>\n",
       "      <th>average_hr</th>\n",
       "      <th>average_watts</th>\n",
       "      <th>effort_id</th>\n",
       "      <th>elapsed_time</th>\n",
       "      <th>moving_time</th>\n",
       "      <th>rank</th>\n",
       "      <th>start_date</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>segment_id</th>\n",
       "      <th>athlete_id</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th rowspan=\"5\" valign=\"top\">98</th>\n",
       "      <th>241840</th>\n",
       "      <td>301272007</td>\n",
       "      <td>NaN</td>\n",
       "      <td>376.9</td>\n",
       "      <td>7087798624</td>\n",
       "      <td>00:10:39</td>\n",
       "      <td>00:09:06</td>\n",
       "      <td>1</td>\n",
       "      <td>2015-05-09 19:25:05</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>637337</th>\n",
       "      <td>84869449</td>\n",
       "      <td>NaN</td>\n",
       "      <td>377.9</td>\n",
       "      <td>1743456704</td>\n",
       "      <td>00:10:41</td>\n",
       "      <td>00:10:41</td>\n",
       "      <td>2</td>\n",
       "      <td>2013-09-25 15:04:41</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>31292</th>\n",
       "      <td>324702550</td>\n",
       "      <td>NaN</td>\n",
       "      <td>332.7</td>\n",
       "      <td>7679192006</td>\n",
       "      <td>00:11:13</td>\n",
       "      <td>00:11:13</td>\n",
       "      <td>3</td>\n",
       "      <td>2015-06-13 17:12:40</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8777</th>\n",
       "      <td>73686159</td>\n",
       "      <td>169.4</td>\n",
       "      <td>245.5</td>\n",
       "      <td>1456747437</td>\n",
       "      <td>00:11:52</td>\n",
       "      <td>00:11:52</td>\n",
       "      <td>4</td>\n",
       "      <td>2013-08-10 18:38:09</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1689588</th>\n",
       "      <td>42595690</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>716076628</td>\n",
       "      <td>00:12:02</td>\n",
       "      <td>00:12:02</td>\n",
       "      <td>5</td>\n",
       "      <td>2013-02-28 20:06:25</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                       activity_id  average_hr  average_watts   effort_id  \\\n",
       "segment_id athlete_id                                                       \n",
       "98         241840        301272007         NaN          376.9  7087798624   \n",
       "           637337         84869449         NaN          377.9  1743456704   \n",
       "           31292         324702550         NaN          332.7  7679192006   \n",
       "           8777           73686159       169.4          245.5  1456747437   \n",
       "           1689588        42595690         NaN            NaN   716076628   \n",
       "\n",
       "                       elapsed_time  moving_time  rank          start_date  \n",
       "segment_id athlete_id                                                       \n",
       "98         241840          00:10:39     00:09:06     1 2015-05-09 19:25:05  \n",
       "           637337          00:10:41     00:10:41     2 2013-09-25 15:04:41  \n",
       "           31292           00:11:13     00:11:13     3 2015-06-13 17:12:40  \n",
       "           8777            00:11:52     00:11:52     4 2013-08-10 18:38:09  \n",
       "           1689588         00:12:02     00:12:02     5 2013-02-28 20:06:25  "
      ]
     },
     "execution_count": 353,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "leaders.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 352,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "#leaders.to_hdf('leaders.h5', 'leaders')\n",
    "leaders = pd.read_hdf('leaders.h5', 'leaders')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Building a recommender system"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 186,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "leaders = leaders.groupby(level='athlete_id').filter(lambda x: len(x) > 3)\n",
    "leaders = leaders.groupby(level='segment_id').filter(lambda x: len(x) > 3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 187,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "segment_id  athlete_id\n",
       "98          637337        2\n",
       "            31292         3\n",
       "            8777          4\n",
       "            1689588       5\n",
       "            2507490       6\n",
       "Name: rank, dtype: float64"
      ]
     },
     "execution_count": 187,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "leaders['rank'].head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 188,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "norm_rank = (leaders['rank'].groupby(level='segment_id')\n",
    "                            .transform(lambda x: (x-1)/(len(x)-1)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 190,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "score = (norm_rank.groupby(level='athlete_id')\n",
    "                  .transform(lambda x: (x - x.mean())/x.std())\n",
    "                  .sortlevel())\n",
    "\n",
    "score.name = 'score'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 192,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "segment_id  athlete_id\n",
       "98          8             1.011239\n",
       "            45           -0.540634\n",
       "            2519          1.972199\n",
       "            5349          0.733317\n",
       "            5580          0.373971\n",
       "Name: score, dtype: float64"
      ]
     },
     "execution_count": 192,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "score.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 282,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "df = score.reset_index()\n",
    "df['segment'] = df.segment_id.rank(method='dense')\n",
    "df['athlete'] = df.athlete_id.rank(method='dense')\n",
    "df = df.reindex(permutation(df.index)).reset_index(drop=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 284,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>segment_id</th>\n",
       "      <th>athlete_id</th>\n",
       "      <th>score</th>\n",
       "      <th>segment</th>\n",
       "      <th>athlete</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>642780</td>\n",
       "      <td>165048</td>\n",
       "      <td>-0.117106</td>\n",
       "      <td>202</td>\n",
       "      <td>2485</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>3564552</td>\n",
       "      <td>3804864</td>\n",
       "      <td>-1.048239</td>\n",
       "      <td>812</td>\n",
       "      <td>6734</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>3005325</td>\n",
       "      <td>10648</td>\n",
       "      <td>0.049176</td>\n",
       "      <td>740</td>\n",
       "      <td>759</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1850319</td>\n",
       "      <td>1834251</td>\n",
       "      <td>-1.050982</td>\n",
       "      <td>622</td>\n",
       "      <td>5864</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1494737</td>\n",
       "      <td>806075</td>\n",
       "      <td>-0.022325</td>\n",
       "      <td>553</td>\n",
       "      <td>4786</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   segment_id  athlete_id     score  segment  athlete\n",
       "0      642780      165048 -0.117106      202     2485\n",
       "1     3564552     3804864 -1.048239      812     6734\n",
       "2     3005325       10648  0.049176      740      759\n",
       "3     1850319     1834251 -1.050982      622     5864\n",
       "4     1494737      806075 -0.022325      553     4786"
      ]
     },
     "execution_count": 284,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Collaborative filtering"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 285,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import scipy.sparse as sparse\n",
    "from cofi import roll_params, unroll_params\n",
    "from scipy.optimize import fmin_cg"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 415,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "X = df[['segment','athlete']].values.astype(int) - 1\n",
    "y = df.score.values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 416,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "Y = sparse.coo_matrix((y, (X[:,0], X[:,1]))).todense()\n",
    "R = sparse.coo_matrix((ones_like(y), (X[:,0], X[:,1]))).todense()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 417,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1431, 7238)"
      ]
     },
     "execution_count": 417,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Y.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 199,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.011311910950610269"
      ]
     },
     "execution_count": 199,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sum(Y != 0) / Y.size"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 200,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x7fce773a60b8>"
      ]
     },
     "execution_count": 200,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/svg+xml": [
       "<?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?>\n",
       "<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n",
       "  \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n",
       "<!-- Created with matplotlib (http://matplotlib.org/) -->\n",
       "<svg height=\"256pt\" version=\"1.1\" viewBox=\"0 0 277 256\" width=\"277pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
       " <defs>\n",
       "  <style type=\"text/css\">\n",
       "*{stroke-linecap:butt;stroke-linejoin:round;}\n",
       "  </style>\n",
       " </defs>\n",
       " <g id=\"figure_1\">\n",
       "  <g id=\"patch_1\">\n",
       "   <path d=\"\n",
       "M0 256.006\n",
       "L277.243 256.006\n",
       "L277.243 0\n",
       "L0 0\n",
       "L0 256.006\" style=\"fill:none;\"/>\n",
       "  </g>\n",
       "  <g id=\"axes_1\">\n",
       "   <g id=\"patch_2\">\n",
       "    <path d=\"\n",
       "M34.8875 235.127\n",
       "L258.087 235.127\n",
       "L258.087 11.9275\n",
       "L34.8875 11.9275\n",
       "z\n",
       "\" style=\"fill:#ffffff;\"/>\n",
       "   </g>\n",
       "   <g clip-path=\"url(#pc4860fca7c)\">\n",
       "    <image height=\"224.0\" id=\"imaged5b391e96c\" width=\"224.0\" x=\"34.8875\" xlink:href=\"data:image/png;base64,\n",
       "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\" y=\"11.1274625\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_3\">\n",
       "    <path d=\"\n",
       "M34.8875 11.9275\n",
       "L258.087 11.9275\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_4\">\n",
       "    <path d=\"\n",
       "M34.8875 235.127\n",
       "L34.8875 11.9275\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_5\">\n",
       "    <path d=\"\n",
       "M258.087 235.127\n",
       "L258.087 11.9275\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_6\">\n",
       "    <path d=\"\n",
       "M34.8875 235.127\n",
       "L258.087 235.127\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;\"/>\n",
       "   </g>\n",
       "   <g id=\"matplotlib.axis_1\">\n",
       "    <g id=\"xtick_1\">\n",
       "     <g id=\"line2d_1\">\n",
       "      <defs>\n",
       "       <path d=\"\n",
       "M0 0\n",
       "L0 -4\" id=\"mc7db9fdffb\" style=\"stroke:#000000;stroke-width:0.5;\"/>\n",
       "      </defs>\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"34.9991\" xlink:href=\"#mc7db9fdffb\" y=\"235.1274625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"line2d_2\">\n",
       "      <defs>\n",
       "       <path d=\"\n",
       "M0 0\n",
       "L0 4\" id=\"m5a7d422ac3\" style=\"stroke:#000000;stroke-width:0.5;\"/>\n",
       "      </defs>\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"34.9991\" xlink:href=\"#m5a7d422ac3\" y=\"11.9274625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_1\">\n",
       "      <!-- 0 -->\n",
       "      <defs>\n",
       "       <path d=\"\n",
       "M31.7812 66.4062\n",
       "Q24.1719 66.4062 20.3281 58.9062\n",
       "Q16.5 51.4219 16.5 36.375\n",
       "Q16.5 21.3906 20.3281 13.8906\n",
       "Q24.1719 6.39062 31.7812 6.39062\n",
       "Q39.4531 6.39062 43.2812 13.8906\n",
       "Q47.125 21.3906 47.125 36.375\n",
       "Q47.125 51.4219 43.2812 58.9062\n",
       "Q39.4531 66.4062 31.7812 66.4062\n",
       "M31.7812 74.2188\n",
       "Q44.0469 74.2188 50.5156 64.5156\n",
       "Q56.9844 54.8281 56.9844 36.375\n",
       "Q56.9844 17.9688 50.5156 8.26562\n",
       "Q44.0469 -1.42188 31.7812 -1.42188\n",
       "Q19.5312 -1.42188 13.0625 8.26562\n",
       "Q6.59375 17.9688 6.59375 36.375\n",
       "Q6.59375 54.8281 13.0625 64.5156\n",
       "Q19.5312 74.2188 31.7812 74.2188\" id=\"BitstreamVeraSans-Roman-30\"/>\n",
       "      </defs>\n",
       "      <g transform=\"translate(32.47956875 246.7259)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#BitstreamVeraSans-Roman-30\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_2\">\n",
       "     <g id=\"line2d_3\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"79.6391\" xlink:href=\"#mc7db9fdffb\" y=\"235.1274625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"line2d_4\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"79.6391\" xlink:href=\"#m5a7d422ac3\" y=\"11.9274625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_2\">\n",
       "      <!-- 200 -->\n",
       "      <defs>\n",
       "       <path d=\"\n",
       "M19.1875 8.29688\n",
       "L53.6094 8.29688\n",
       "L53.6094 0\n",
       "L7.32812 0\n",
       "L7.32812 8.29688\n",
       "Q12.9375 14.1094 22.625 23.8906\n",
       "Q32.3281 33.6875 34.8125 36.5312\n",
       "Q39.5469 41.8438 41.4219 45.5312\n",
       "Q43.3125 49.2188 43.3125 52.7812\n",
       "Q43.3125 58.5938 39.2344 62.25\n",
       "Q35.1562 65.9219 28.6094 65.9219\n",
       "Q23.9688 65.9219 18.8125 64.3125\n",
       "Q13.6719 62.7031 7.8125 59.4219\n",
       "L7.8125 69.3906\n",
       "Q13.7656 71.7812 18.9375 73\n",
       "Q24.125 74.2188 28.4219 74.2188\n",
       "Q39.75 74.2188 46.4844 68.5469\n",
       "Q53.2188 62.8906 53.2188 53.4219\n",
       "Q53.2188 48.9219 51.5312 44.8906\n",
       "Q49.8594 40.875 45.4062 35.4062\n",
       "Q44.1875 33.9844 37.6406 27.2188\n",
       "Q31.1094 20.4531 19.1875 8.29688\" id=\"BitstreamVeraSans-Roman-32\"/>\n",
       "      </defs>\n",
       "      <g transform=\"translate(70.7937875 246.7259)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#BitstreamVeraSans-Roman-32\"/>\n",
       "       <use x=\"63.623046875\" xlink:href=\"#BitstreamVeraSans-Roman-30\"/>\n",
       "       <use x=\"127.24609375\" xlink:href=\"#BitstreamVeraSans-Roman-30\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_3\">\n",
       "     <g id=\"line2d_5\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"124.2791\" xlink:href=\"#mc7db9fdffb\" y=\"235.1274625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"line2d_6\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"124.2791\" xlink:href=\"#m5a7d422ac3\" y=\"11.9274625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_3\">\n",
       "      <!-- 400 -->\n",
       "      <defs>\n",
       "       <path d=\"\n",
       "M37.7969 64.3125\n",
       "L12.8906 25.3906\n",
       "L37.7969 25.3906\n",
       "z\n",
       "\n",
       "M35.2031 72.9062\n",
       "L47.6094 72.9062\n",
       "L47.6094 25.3906\n",
       "L58.0156 25.3906\n",
       "L58.0156 17.1875\n",
       "L47.6094 17.1875\n",
       "L47.6094 0\n",
       "L37.7969 0\n",
       "L37.7969 17.1875\n",
       "L4.89062 17.1875\n",
       "L4.89062 26.7031\n",
       "z\n",
       "\" id=\"BitstreamVeraSans-Roman-34\"/>\n",
       "      </defs>\n",
       "      <g transform=\"translate(115.3119125 246.7259)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#BitstreamVeraSans-Roman-34\"/>\n",
       "       <use x=\"63.623046875\" xlink:href=\"#BitstreamVeraSans-Roman-30\"/>\n",
       "       <use x=\"127.24609375\" xlink:href=\"#BitstreamVeraSans-Roman-30\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_4\">\n",
       "     <g id=\"line2d_7\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"168.9191\" xlink:href=\"#mc7db9fdffb\" y=\"235.1274625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"line2d_8\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"168.9191\" xlink:href=\"#m5a7d422ac3\" y=\"11.9274625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_4\">\n",
       "      <!-- 600 -->\n",
       "      <defs>\n",
       "       <path d=\"\n",
       "M33.0156 40.375\n",
       "Q26.375 40.375 22.4844 35.8281\n",
       "Q18.6094 31.2969 18.6094 23.3906\n",
       "Q18.6094 15.5312 22.4844 10.9531\n",
       "Q26.375 6.39062 33.0156 6.39062\n",
       "Q39.6562 6.39062 43.5312 10.9531\n",
       "Q47.4062 15.5312 47.4062 23.3906\n",
       "Q47.4062 31.2969 43.5312 35.8281\n",
       "Q39.6562 40.375 33.0156 40.375\n",
       "M52.5938 71.2969\n",
       "L52.5938 62.3125\n",
       "Q48.875 64.0625 45.0938 64.9844\n",
       "Q41.3125 65.9219 37.5938 65.9219\n",
       "Q27.8281 65.9219 22.6719 59.3281\n",
       "Q17.5312 52.7344 16.7969 39.4062\n",
       "Q19.6719 43.6562 24.0156 45.9219\n",
       "Q28.375 48.1875 33.5938 48.1875\n",
       "Q44.5781 48.1875 50.9531 41.5156\n",
       "Q57.3281 34.8594 57.3281 23.3906\n",
       "Q57.3281 12.1562 50.6875 5.35938\n",
       "Q44.0469 -1.42188 33.0156 -1.42188\n",
       "Q20.3594 -1.42188 13.6719 8.26562\n",
       "Q6.98438 17.9688 6.98438 36.375\n",
       "Q6.98438 53.6562 15.1875 63.9375\n",
       "Q23.3906 74.2188 37.2031 74.2188\n",
       "Q40.9219 74.2188 44.7031 73.4844\n",
       "Q48.4844 72.75 52.5938 71.2969\" id=\"BitstreamVeraSans-Roman-36\"/>\n",
       "      </defs>\n",
       "      <g transform=\"translate(160.0566 246.7259)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#BitstreamVeraSans-Roman-36\"/>\n",
       "       <use x=\"63.623046875\" xlink:href=\"#BitstreamVeraSans-Roman-30\"/>\n",
       "       <use x=\"127.24609375\" xlink:href=\"#BitstreamVeraSans-Roman-30\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_5\">\n",
       "     <g id=\"line2d_9\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"213.5591\" xlink:href=\"#mc7db9fdffb\" y=\"235.1274625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"line2d_10\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"213.5591\" xlink:href=\"#m5a7d422ac3\" y=\"11.9274625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_5\">\n",
       "      <!-- 800 -->\n",
       "      <defs>\n",
       "       <path d=\"\n",
       "M31.7812 34.625\n",
       "Q24.75 34.625 20.7188 30.8594\n",
       "Q16.7031 27.0938 16.7031 20.5156\n",
       "Q16.7031 13.9219 20.7188 10.1562\n",
       "Q24.75 6.39062 31.7812 6.39062\n",
       "Q38.8125 6.39062 42.8594 10.1719\n",
       "Q46.9219 13.9688 46.9219 20.5156\n",
       "Q46.9219 27.0938 42.8906 30.8594\n",
       "Q38.875 34.625 31.7812 34.625\n",
       "M21.9219 38.8125\n",
       "Q15.5781 40.375 12.0312 44.7188\n",
       "Q8.5 49.0781 8.5 55.3281\n",
       "Q8.5 64.0625 14.7188 69.1406\n",
       "Q20.9531 74.2188 31.7812 74.2188\n",
       "Q42.6719 74.2188 48.875 69.1406\n",
       "Q55.0781 64.0625 55.0781 55.3281\n",
       "Q55.0781 49.0781 51.5312 44.7188\n",
       "Q48 40.375 41.7031 38.8125\n",
       "Q48.8281 37.1562 52.7969 32.3125\n",
       "Q56.7812 27.4844 56.7812 20.5156\n",
       "Q56.7812 9.90625 50.3125 4.23438\n",
       "Q43.8438 -1.42188 31.7812 -1.42188\n",
       "Q19.7344 -1.42188 13.25 4.23438\n",
       "Q6.78125 9.90625 6.78125 20.5156\n",
       "Q6.78125 27.4844 10.7812 32.3125\n",
       "Q14.7969 37.1562 21.9219 38.8125\n",
       "M18.3125 54.3906\n",
       "Q18.3125 48.7344 21.8438 45.5625\n",
       "Q25.3906 42.3906 31.7812 42.3906\n",
       "Q38.1406 42.3906 41.7188 45.5625\n",
       "Q45.3125 48.7344 45.3125 54.3906\n",
       "Q45.3125 60.0625 41.7188 63.2344\n",
       "Q38.1406 66.4062 31.7812 66.4062\n",
       "Q25.3906 66.4062 21.8438 63.2344\n",
       "Q18.3125 60.0625 18.3125 54.3906\" id=\"BitstreamVeraSans-Roman-38\"/>\n",
       "      </defs>\n",
       "      <g transform=\"translate(204.68644375 246.7259)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#BitstreamVeraSans-Roman-38\"/>\n",
       "       <use x=\"63.623046875\" xlink:href=\"#BitstreamVeraSans-Roman-30\"/>\n",
       "       <use x=\"127.24609375\" xlink:href=\"#BitstreamVeraSans-Roman-30\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_6\">\n",
       "     <g id=\"text_6\">\n",
       "      <!-- 1000 -->\n",
       "      <defs>\n",
       "       <path d=\"\n",
       "M12.4062 8.29688\n",
       "L28.5156 8.29688\n",
       "L28.5156 63.9219\n",
       "L10.9844 60.4062\n",
       "L10.9844 69.3906\n",
       "L28.4219 72.9062\n",
       "L38.2812 72.9062\n",
       "L38.2812 8.29688\n",
       "L54.3906 8.29688\n",
       "L54.3906 0\n",
       "L12.4062 0\n",
       "z\n",
       "\" id=\"BitstreamVeraSans-Roman-31\"/>\n",
       "      </defs>\n",
       "      <g transform=\"translate(246.35535 246.7259)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#BitstreamVeraSans-Roman-31\"/>\n",
       "       <use x=\"63.623046875\" xlink:href=\"#BitstreamVeraSans-Roman-30\"/>\n",
       "       <use x=\"127.24609375\" xlink:href=\"#BitstreamVeraSans-Roman-30\"/>\n",
       "       <use x=\"190.869140625\" xlink:href=\"#BitstreamVeraSans-Roman-30\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "   </g>\n",
       "   <g id=\"matplotlib.axis_2\">\n",
       "    <g id=\"ytick_1\">\n",
       "     <g id=\"line2d_11\">\n",
       "      <defs>\n",
       "       <path d=\"\n",
       "M0 0\n",
       "L4 0\" id=\"md7965d1ba0\" style=\"stroke:#000000;stroke-width:0.5;\"/>\n",
       "      </defs>\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"34.8875\" xlink:href=\"#md7965d1ba0\" y=\"12.0390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"line2d_12\">\n",
       "      <defs>\n",
       "       <path d=\"\n",
       "M0 0\n",
       "L-4 0\" id=\"md9a1c1a7cd\" style=\"stroke:#000000;stroke-width:0.5;\"/>\n",
       "      </defs>\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"258.0875\" xlink:href=\"#md9a1c1a7cd\" y=\"12.0390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_7\">\n",
       "      <!-- 0 -->\n",
       "      <g transform=\"translate(25.8484375 14.7984375)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#BitstreamVeraSans-Roman-30\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_2\">\n",
       "     <g id=\"line2d_13\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"34.8875\" xlink:href=\"#md7965d1ba0\" y=\"56.6790625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"line2d_14\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"258.0875\" xlink:href=\"#md9a1c1a7cd\" y=\"56.6790625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_8\">\n",
       "      <!-- 200 -->\n",
       "      <g transform=\"translate(13.196875 59.4384375)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#BitstreamVeraSans-Roman-32\"/>\n",
       "       <use x=\"63.623046875\" xlink:href=\"#BitstreamVeraSans-Roman-30\"/>\n",
       "       <use x=\"127.24609375\" xlink:href=\"#BitstreamVeraSans-Roman-30\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_3\">\n",
       "     <g id=\"line2d_15\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"34.8875\" xlink:href=\"#md7965d1ba0\" y=\"101.3190625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"line2d_16\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"258.0875\" xlink:href=\"#md9a1c1a7cd\" y=\"101.3190625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_9\">\n",
       "      <!-- 400 -->\n",
       "      <g transform=\"translate(12.953125 104.0784375)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#BitstreamVeraSans-Roman-34\"/>\n",
       "       <use x=\"63.623046875\" xlink:href=\"#BitstreamVeraSans-Roman-30\"/>\n",
       "       <use x=\"127.24609375\" xlink:href=\"#BitstreamVeraSans-Roman-30\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_4\">\n",
       "     <g id=\"line2d_17\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"34.8875\" xlink:href=\"#md7965d1ba0\" y=\"145.9590625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"line2d_18\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"258.0875\" xlink:href=\"#md9a1c1a7cd\" y=\"145.9590625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_10\">\n",
       "      <!-- 600 -->\n",
       "      <g transform=\"translate(13.1625 148.7184375)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#BitstreamVeraSans-Roman-36\"/>\n",
       "       <use x=\"63.623046875\" xlink:href=\"#BitstreamVeraSans-Roman-30\"/>\n",
       "       <use x=\"127.24609375\" xlink:href=\"#BitstreamVeraSans-Roman-30\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_5\">\n",
       "     <g id=\"line2d_19\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"34.8875\" xlink:href=\"#md7965d1ba0\" y=\"190.5990625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"line2d_20\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"258.0875\" xlink:href=\"#md9a1c1a7cd\" y=\"190.5990625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_11\">\n",
       "      <!-- 800 -->\n",
       "      <g transform=\"translate(13.1421875 193.3584375)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#BitstreamVeraSans-Roman-38\"/>\n",
       "       <use x=\"63.623046875\" xlink:href=\"#BitstreamVeraSans-Roman-30\"/>\n",
       "       <use x=\"127.24609375\" xlink:href=\"#BitstreamVeraSans-Roman-30\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_6\">\n",
       "     <g id=\"text_12\">\n",
       "      <!-- 1000 -->\n",
       "      <g transform=\"translate(7.2 237.9984375)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#BitstreamVeraSans-Roman-31\"/>\n",
       "       <use x=\"63.623046875\" xlink:href=\"#BitstreamVeraSans-Roman-30\"/>\n",
       "       <use x=\"127.24609375\" xlink:href=\"#BitstreamVeraSans-Roman-30\"/>\n",
       "       <use x=\"190.869140625\" xlink:href=\"#BitstreamVeraSans-Roman-30\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "   </g>\n",
       "  </g>\n",
       " </g>\n",
       " <defs>\n",
       "  <clipPath id=\"pc4860fca7c\">\n",
       "   <rect height=\"223.2\" width=\"223.2\" x=\"34.8875\" y=\"11.9274625\"/>\n",
       "  </clipPath>\n",
       " </defs>\n",
       "</svg>\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fce8285d048>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "imshow(Y[:1000,:1000], interpolation='nearest', cmap=cm.gray);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 201,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def cofi_cost(params, Y, R, λ, num_users, num_items, num_features=30):\n",
    "    \n",
    "    \"\"\"Regularized cost function and gradient for collaborative filtering\"\"\"\n",
    "    \n",
    "    X, Θ = unroll_params(params, num_users, num_items, num_features)\n",
    "    \n",
    "    D = where(R, dot(X, Θ.T) - Y, 0)\n",
    "    J = 0.5*(sum(D**2) + λ*(sum(Θ**2) + sum(X**2)))\n",
    "    \n",
    "    return J\n",
    "\n",
    "\n",
    "def cofi_cost_grad(params, Y, R, λ, num_users, num_items, num_features=30):\n",
    "    \n",
    "    \"\"\"Gradient of regularized cost function for collaborative filtering\"\"\"\n",
    "    \n",
    "    X, Θ = unroll_params(params, num_users, num_items, num_features)\n",
    "    \n",
    "    D = where(R, dot(X, Θ.T) - Y, 0)\n",
    "    X_grad = dot(D, Θ) + λ*X\n",
    "    Θ_grad = dot(D.T, X) + λ*Θ\n",
    "    \n",
    "    return roll_params(X_grad, Θ_grad)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 202,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "num_features = 10         # analog of action, comedy, romance, etc.\n",
    "num_segments = Y.shape[0] # analog of movies\n",
    "num_athletes = Y.shape[1] # analog of users"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 203,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "num_params = (num_athletes + num_segments)*num_features\n",
    "params_test = rand(num_params)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 204,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "465620.35574790178"
      ]
     },
     "execution_count": 204,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cofi_cost(params_test, Y, R, 1, num_athletes, num_segments, num_features)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Gradient checking"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 205,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def cofi_cost_grad_check(params, eps, n=None, *args, **kw):\n",
    "    \n",
    "    grad = np.empty_like(params)\n",
    "    \n",
    "    if n is None:\n",
    "        n = len(params)\n",
    "    \n",
    "    for i in range(n):\n",
    "        params[i] -= eps\n",
    "        J0 = cofi_cost(params, *args, **kw)\n",
    "        params[i] += 2*eps\n",
    "        J1 = cofi_cost(params, *args, **kw)\n",
    "        params[i] -= eps\n",
    "        grad[i] = (J1 - J0)/(2*eps)\n",
    "        \n",
    "    return grad"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 206,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "grad = cofi_cost_grad(params_test, Y, R, 1, num_athletes, num_segments, num_features)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 207,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "check = cofi_cost_grad_check(params_test, 1e-6, 100,\n",
    "                             Y, R, 1, num_athletes, num_segments, num_features)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 208,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 208,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "allclose(grad[:100], check[:100])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Complete algorithm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 209,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from cofi import StatusPrinter # callback to print cost at each iteration\n",
    "from sklearn.base import BaseEstimator\n",
    "\n",
    "class CollaborativeFiltering(BaseEstimator):\n",
    "    \n",
    "    def __init__(self, num_users, num_items, \n",
    "                 num_features=10, lm=0, maxiter=100):\n",
    "        \n",
    "        self.num_users = num_users\n",
    "        self.num_items = num_items\n",
    "        self.num_features = num_features\n",
    "        self.lm = lm\n",
    "        self.maxiter = maxiter\n",
    "        \n",
    "        # arguments to pass to the cost function\n",
    "        self.args = (Y, R, self.lm, self.num_users, self.num_items, self.num_features)\n",
    "        \n",
    "    def fit(self, X, y, progress=False, **kw):\n",
    "        \n",
    "        # construct Y matrix\n",
    "        Y = sparse.coo_matrix((y, (X[:,0], X[:,1]))).todense()\n",
    "        R = sparse.coo_matrix((ones(X.shape[0]), (X[:,0], X[:,1]))).todense()\n",
    "        \n",
    "        # initialize parameters randomly\n",
    "        num_params = (self.num_users + self.num_items)*self.num_features\n",
    "        params_initial = randn(num_params)\n",
    "        \n",
    "        # set parameters for minimization routine\n",
    "        \n",
    "        params = dict(disp=False)\n",
    "        params.update(kw)\n",
    "        \n",
    "        if progress:\n",
    "            params['callback'] = StatusPrinter(cofi_cost, self.args)\n",
    "        \n",
    "         # minimize cost using conjugate gradient\n",
    "        \n",
    "        params_optimal = fmin_cg(cofi_cost, params_initial, \n",
    "                                 cofi_cost_grad, self.args, \n",
    "                                 maxiter=self.maxiter, **params)\n",
    "        \n",
    "        X, Θ = unroll_params(params_optimal, \n",
    "                             self.num_users, \n",
    "                             self.num_items, \n",
    "                             self.num_features)\n",
    "\n",
    "        self.H_ = dot(X, Θ.T)\n",
    "        return self\n",
    "        \n",
    "    def predict(self, X):\n",
    "        return self.H_[X[:,0], X[:,1]]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 210,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "est = CollaborativeFiltering(num_athletes, num_segments, num_features=10, lm=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 211,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "iteration 1, cost = 116221.38042518207\n",
      "iteration 2, cost = 78564.87806091682\n",
      "iteration 3, cost = 70467.53488570957\n",
      "iteration 4, cost = 65863.56743108822\n",
      "iteration 5, cost = 55913.06484426811\n",
      "iteration 6, cost = 46328.577856524236\n",
      "iteration 7, cost = 41400.63914117526\n",
      "iteration 8, cost = 36364.33919407551\n",
      "iteration 9, cost = 33576.79647888923\n",
      "iteration 10, cost = 31574.291760328506\n",
      "iteration 20, cost = 25620.037707604486\n",
      "iteration 30, cost = 24228.804787422418\n",
      "iteration 40, cost = 23579.794578627985\n",
      "iteration 50, cost = 23112.51706076857\n",
      "iteration 60, cost = 22821.85818596088\n",
      "iteration 70, cost = 22658.21766229917\n",
      "iteration 80, cost = 22430.154598118905\n",
      "iteration 90, cost = 22322.398844846364\n",
      "iteration 100, cost = 22229.21745005595\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "CollaborativeFiltering(lm=1, maxiter=100, num_features=10, num_items=1431,\n",
       "            num_users=7238)"
      ]
     },
     "execution_count": 211,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "est.fit(X, y, progress=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 217,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/svg+xml": [
       "<?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?>\n",
       "<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n",
       "  \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n",
       "<!-- Created with matplotlib (http://matplotlib.org/) -->\n",
       "<svg height=\"185pt\" version=\"1.1\" viewBox=\"0 0 388 185\" width=\"388pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
       " <defs>\n",
       "  <style type=\"text/css\">\n",
       "*{stroke-linecap:butt;stroke-linejoin:round;}\n",
       "  </style>\n",
       " </defs>\n",
       " <g id=\"figure_1\">\n",
       "  <g id=\"patch_1\">\n",
       "   <path d=\"\n",
       "M0 185.023\n",
       "L388.807 185.023\n",
       "L388.807 0\n",
       "L0 0\n",
       "L0 185.023\" style=\"fill:none;\"/>\n",
       "  </g>\n",
       "  <g id=\"axes_1\">\n",
       "   <g clip-path=\"url(#p971ba262fa)\">\n",
       "    <image height=\"153.0\" id=\"image58b34c1f5a\" width=\"153.0\" x=\"34.8875\" xlink:href=\"data:image/png;base64,\n",
       "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\" y=\"11.1447897727\"/>\n",
       "   </g>\n",
       "  </g>\n",
       "  <g id=\"axes_2\">\n",
       "   <g clip-path=\"url(#p0afb43c030)\">\n",
       "    <image height=\"153.0\" id=\"image58b34c1f5a\" width=\"153.0\" x=\"217.505681818\" xlink:href=\"data:image/png;base64,\n",
       "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\" y=\"11.1447897727\"/>\n",
       "   </g>\n",
       "  </g>\n",
       " </g>\n",
       " <defs>\n",
       "  <clipPath id=\"p971ba262fa\">\n",
       "   <rect height=\"152.181818182\" width=\"152.181818182\" x=\"34.8875\" y=\"11.9629715909\"/>\n",
       "  </clipPath>\n",
       "  <clipPath id=\"p0afb43c030\">\n",
       "   <rect height=\"152.181818182\" width=\"152.181818182\" x=\"217.505681818\" y=\"11.9629715909\"/>\n",
       "  </clipPath>\n",
       " </defs>\n",
       "</svg>\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fce75e164a8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = subplots(1, 2)\n",
    "ax[0].imshow(Y[:1000,:1000], interpolation='nearest', cmap=cm.gray)\n",
    "ax[1].imshow(est.H_[:1000,:1000], interpolation='nearest', cmap=cm.gray)\n",
    "ax[0].axis('off')\n",
    "ax[1].axis('off');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Taking advantage of sparseness\n",
    "\n",
    "The above code is a bit slow for the amount of data we're working with here. In fact the above code is pretty wasteful since it uses ordinary matrix multiplication when the matrices we're dealing with are very sparse. We can get major time and space savings by taking advantage of the sparse nature of the problem. For the remainder of this experiment I'll use a more efficient version of the code written in Cython ([here](https://github.com/mcwitt/segment-recommender/blob/master/cofi/cofi.pyx)) which substitutes loops over nonzero elements for matrix operations to take advantage of the sparseness of `Y`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 218,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from cofi import CollaborativeFiltering\n",
    "from cofi import cost as cofi_cost2\n",
    "from cofi import cost_grad as cofi_cost_grad2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 219,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10 loops, best of 3: 117 ms per loop\n"
     ]
    }
   ],
   "source": [
    "timeit cofi_cost(params_test, Y, R, 1, num_athletes, num_segments, num_features)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 220,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "100 loops, best of 3: 6.06 ms per loop\n"
     ]
    }
   ],
   "source": [
    "timeit cofi_cost2(params_test, X[:,0], X[:,1], y, len(y), 1, num_athletes, num_segments, num_features)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 221,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 221,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "allclose(cofi_cost(params_test, Y, R, 1, num_athletes, num_segments, num_features),\n",
    "         cofi_cost2(params_test, X[:,0], X[:,1], y, len(y), 1, num_athletes, num_segments, num_features))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 222,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 222,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "allclose(cofi_cost_grad(params_test, Y, R, 1, num_athletes, num_segments, num_features),\n",
    "         cofi_cost_grad2(params_test, X[:,0], X[:,1], y, len(y), 1, num_athletes, num_segments, num_features))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Cross-validation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Model selection: Regularization parameter"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 223,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from sklearn.learning_curve import learning_curve, validation_curve"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 251,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "est = CollaborativeFiltering(num_athletes, num_segments, num_features=10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 252,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "lm = linspace(6, 16, 20)\n",
    "\n",
    "train_scores, valid_scores =\\\n",
    "    validation_curve(est, X, y, 'lm', lm,\n",
    "                     scoring='mean_squared_error',\n",
    "                     cv=8, n_jobs=4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 253,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def plot_cv_scores(x, test_scores, train_scores=None, ax=None):\n",
    "    \n",
    "    if ax is None:\n",
    "        ax = gca()\n",
    "    \n",
    "    def _plot(x, scores, **kw):\n",
    "        score_mean = scores.mean(axis=1)\n",
    "        score_std = scores.std(axis=1)\n",
    "        ax.plot(x, score_mean, **kw)\n",
    "        \n",
    "        ax.fill_between(x, \n",
    "                        score_mean - score_std,            \n",
    "                        score_mean + score_std,\n",
    "                        alpha=0.3)\n",
    "        \n",
    "    if train_scores is not None:\n",
    "        _plot(x, train_scores, label='train', color='b', marker='o')\n",
    "        \n",
    "    _plot(x, valid_scores, label='test', color='g', marker='s')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 254,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/svg+xml": [
       "<?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?>\n",
       "<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n",
       "  \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n",
       "<!-- Created with matplotlib (http://matplotlib.org/) -->\n",
       "<svg height=\"270pt\" version=\"1.1\" viewBox=\"0 0 396 270\" width=\"396pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
       " <defs>\n",
       "  <style type=\"text/css\">\n",
       "*{stroke-linecap:butt;stroke-linejoin:round;}\n",
       "  </style>\n",
       " </defs>\n",
       " <g id=\"figure_1\">\n",
       "  <g id=\"patch_1\">\n",
       "   <path d=\"\n",
       "M0 270.795\n",
       "L396.039 270.795\n",
       "L396.039 0\n",
       "L0 0\n",
       "L0 270.795\" style=\"fill:none;\"/>\n",
       "  </g>\n",
       "  <g id=\"axes_1\">\n",
       "   <g id=\"patch_2\">\n",
       "    <path d=\"\n",
       "M48.5406 235.239\n",
       "L200.722 235.239\n",
       "L200.722 12.0391\n",
       "L48.5406 12.0391\n",
       "z\n",
       "\" style=\"fill:#ffffff;\"/>\n",
       "   </g>\n",
       "   <g id=\"PolyCollection_1\">\n",
       "    <defs>\n",
       "     <path d=\"\n",
       "M48.5406 -235.574\n",
       "L48.5406 -234.837\n",
       "L56.5502 -224.617\n",
       "L64.5598 -214.607\n",
       "L72.5693 -204.418\n",
       "L80.5789 -194.255\n",
       "L88.5885 -184.301\n",
       "L96.598 -174.531\n",
       "L104.608 -165.204\n",
       "L112.617 -156.099\n",
       "L120.627 -147.417\n",
       "L128.636 -139.345\n",
       "L136.646 -131.643\n",
       "L144.655 -124.497\n",
       "L152.665 -117.999\n",
       "L160.675 -112.192\n",
       "L168.684 -107.035\n",
       "L176.694 -102.524\n",
       "L184.703 -98.6248\n",
       "L192.713 -95.3236\n",
       "L200.722 -92.6334\n",
       "L200.722 -93.6653\n",
       "L200.722 -93.6653\n",
       "L192.713 -96.3659\n",
       "L184.703 -99.6811\n",
       "L176.694 -103.613\n",
       "L168.684 -108.167\n",
       "L160.675 -113.38\n",
       "L152.665 -119.192\n",
       "L144.655 -125.645\n",
       "L136.646 -132.609\n",
       "L128.636 -140.299\n",
       "L120.627 -148.473\n",
       "L112.617 -156.948\n",
       "L104.608 -165.846\n",
       "L96.598 -175.429\n",
       "L88.5885 -184.933\n",
       "L80.5789 -194.833\n",
       "L72.5693 -205.242\n",
       "L64.5598 -215.287\n",
       "L56.5502 -225.446\n",
       "L48.5406 -235.574\n",
       "z\n",
       "\" id=\"m9bc27e4d43\" style=\"stroke:#000000;stroke-opacity:0.3;\"/>\n",
       "    </defs>\n",
       "    <g clip-path=\"url(#p6f87c8219a)\">\n",
       "     <use style=\"fill:#0000ff;fill-opacity:0.3;stroke:#000000;stroke-opacity:0.3;\" x=\"0.0\" xlink:href=\"#m9bc27e4d43\" y=\"270.7953125\"/>\n",
       "    </g>\n",
       "   </g>\n",
       "   <g id=\"PolyCollection_2\">\n",
       "    <defs>\n",
       "     <path d=\"\n",
       "M48.5406 -74.6392\n",
       "L48.5406 -67.1777\n",
       "L56.5502 -71.6132\n",
       "L64.5598 -77.5858\n",
       "L72.5693 -79.6848\n",
       "L80.5789 -83.6597\n",
       "L88.5885 -85.8501\n",
       "L96.598 -87.3885\n",
       "L104.608 -88.7274\n",
       "L112.617 -89.3478\n",
       "L120.627 -89.8921\n",
       "L128.636 -90.1109\n",
       "L136.646 -90.0727\n",
       "L144.655 -89.6017\n",
       "L152.665 -89.1652\n",
       "L160.675 -88.6447\n",
       "L168.684 -88.0828\n",
       "L176.694 -87.4736\n",
       "L184.703 -86.8585\n",
       "L192.713 -86.2914\n",
       "L200.722 -85.7645\n",
       "L200.722 -91.7185\n",
       "L200.722 -91.7185\n",
       "L192.713 -92.2853\n",
       "L184.703 -92.8794\n",
       "L176.694 -93.5024\n",
       "L168.684 -94.1447\n",
       "L160.675 -94.8404\n",
       "L152.665 -95.4297\n",
       "L144.655 -95.8818\n",
       "L136.646 -96.25\n",
       "L128.636 -96.5846\n",
       "L120.627 -96.5826\n",
       "L112.617 -96.4002\n",
       "L104.608 -94.8823\n",
       "L96.598 -94.1829\n",
       "L88.5885 -92.6201\n",
       "L80.5789 -90.5838\n",
       "L72.5693 -88.0044\n",
       "L64.5598 -84.9392\n",
       "L56.5502 -80.56\n",
       "L48.5406 -74.6392\n",
       "z\n",
       "\" id=\"ma0902e86bf\" style=\"stroke:#000000;stroke-opacity:0.3;\"/>\n",
       "    </defs>\n",
       "    <g clip-path=\"url(#p6f87c8219a)\">\n",
       "     <use style=\"fill:#0000ff;fill-opacity:0.3;stroke:#000000;stroke-opacity:0.3;\" x=\"0.0\" xlink:href=\"#ma0902e86bf\" y=\"270.7953125\"/>\n",
       "    </g>\n",
       "   </g>\n",
       "   <g id=\"line2d_1\">\n",
       "    <path clip-path=\"url(#p6f87c8219a)\" d=\"\n",
       "M48.5406 35.5901\n",
       "L56.5502 45.7639\n",
       "L64.5598 55.8485\n",
       "L72.5693 65.9652\n",
       "L80.5789 76.251\n",
       "L88.5885 86.1782\n",
       "L96.598 95.8155\n",
       "L104.608 105.27\n",
       "L112.617 114.272\n",
       "L120.627 122.851\n",
       "L128.636 130.973\n",
       "L136.646 138.669\n",
       "L144.655 145.724\n",
       "L152.665 152.2\n",
       "L160.675 158.009\n",
       "L168.684 163.194\n",
       "L176.694 167.727\n",
       "L184.703 171.642\n",
       "L192.713 174.951\n",
       "L200.722 177.646\" style=\"fill:none;stroke:#0000ff;stroke-linecap:square;\"/>\n",
       "    <defs>\n",
       "     <path d=\"\n",
       "M0 3\n",
       "C0.795609 3 1.55874 2.6839 2.12132 2.12132\n",
       "C2.6839 1.55874 3 0.795609 3 0\n",
       "C3 -0.795609 2.6839 -1.55874 2.12132 -2.12132\n",
       "C1.55874 -2.6839 0.795609 -3 0 -3\n",
       "C-0.795609 -3 -1.55874 -2.6839 -2.12132 -2.12132\n",
       "C-2.6839 -1.55874 -3 -0.795609 -3 0\n",
       "C-3 0.795609 -2.6839 1.55874 -2.12132 2.12132\n",
       "C-1.55874 2.6839 -0.795609 3 0 3\n",
       "z\n",
       "\" id=\"mdb00ba95ec\" style=\"stroke:#000000;stroke-width:0.5;\"/>\n",
       "    </defs>\n",
       "    <g clip-path=\"url(#p6f87c8219a)\">\n",
       "     <use style=\"fill:#0000ff;stroke:#000000;stroke-width:0.5;\" x=\"48.540625\" xlink:href=\"#mdb00ba95ec\" y=\"35.5900994478\"/>\n",
       "     <use style=\"fill:#0000ff;stroke:#000000;stroke-width:0.5;\" x=\"56.550194378\" xlink:href=\"#mdb00ba95ec\" y=\"45.7639339037\"/>\n",
       "     <use style=\"fill:#0000ff;stroke:#000000;stroke-width:0.5;\" x=\"64.559763756\" xlink:href=\"#mdb00ba95ec\" y=\"55.8485490816\"/>\n",
       "     <use style=\"fill:#0000ff;stroke:#000000;stroke-width:0.5;\" x=\"72.569333134\" xlink:href=\"#mdb00ba95ec\" y=\"65.9651518223\"/>\n",
       "     <use style=\"fill:#0000ff;stroke:#000000;stroke-width:0.5;\" x=\"80.578902512\" xlink:href=\"#mdb00ba95ec\" y=\"76.2509974163\"/>\n",
       "     <use style=\"fill:#0000ff;stroke:#000000;stroke-width:0.5;\" x=\"88.58847189\" xlink:href=\"#mdb00ba95ec\" y=\"86.178190176\"/>\n",
       "     <use style=\"fill:#0000ff;stroke:#000000;stroke-width:0.5;\" x=\"96.5980412679\" xlink:href=\"#mdb00ba95ec\" y=\"95.8155210291\"/>\n",
       "     <use style=\"fill:#0000ff;stroke:#000000;stroke-width:0.5;\" x=\"104.607610646\" xlink:href=\"#mdb00ba95ec\" y=\"105.270280786\"/>\n",
       "     <use style=\"fill:#0000ff;stroke:#000000;stroke-width:0.5;\" x=\"112.617180024\" xlink:href=\"#mdb00ba95ec\" y=\"114.271601658\"/>\n",
       "     <use style=\"fill:#0000ff;stroke:#000000;stroke-width:0.5;\" x=\"120.626749402\" xlink:href=\"#mdb00ba95ec\" y=\"122.850500469\"/>\n",
       "     <use style=\"fill:#0000ff;stroke:#000000;stroke-width:0.5;\" x=\"128.63631878\" xlink:href=\"#mdb00ba95ec\" y=\"130.972906976\"/>\n",
       "     <use style=\"fill:#0000ff;stroke:#000000;stroke-width:0.5;\" x=\"136.645888158\" xlink:href=\"#mdb00ba95ec\" y=\"138.669418868\"/>\n",
       "     <use style=\"fill:#0000ff;stroke:#000000;stroke-width:0.5;\" x=\"144.655457536\" xlink:href=\"#mdb00ba95ec\" y=\"145.723975091\"/>\n",
       "     <use style=\"fill:#0000ff;stroke:#000000;stroke-width:0.5;\" x=\"152.665026914\" xlink:href=\"#mdb00ba95ec\" y=\"152.199720251\"/>\n",
       "     <use style=\"fill:#0000ff;stroke:#000000;stroke-width:0.5;\" x=\"160.674596292\" xlink:href=\"#mdb00ba95ec\" y=\"158.009224572\"/>\n",
       "     <use style=\"fill:#0000ff;stroke:#000000;stroke-width:0.5;\" x=\"168.68416567\" xlink:href=\"#mdb00ba95ec\" y=\"163.194487947\"/>\n",
       "     <use style=\"fill:#0000ff;stroke:#000000;stroke-width:0.5;\" x=\"176.693735048\" xlink:href=\"#mdb00ba95ec\" y=\"167.726870078\"/>\n",
       "     <use style=\"fill:#0000ff;stroke:#000000;stroke-width:0.5;\" x=\"184.703304426\" xlink:href=\"#mdb00ba95ec\" y=\"171.642371647\"/>\n",
       "     <use style=\"fill:#0000ff;stroke:#000000;stroke-width:0.5;\" x=\"192.712873804\" xlink:href=\"#mdb00ba95ec\" y=\"174.950576179\"/>\n",
       "     <use style=\"fill:#0000ff;stroke:#000000;stroke-width:0.5;\" x=\"200.722443182\" xlink:href=\"#mdb00ba95ec\" y=\"177.645960353\"/>\n",
       "    </g>\n",
       "   </g>\n",
       "   <g id=\"line2d_2\">\n",
       "    <path clip-path=\"url(#p6f87c8219a)\" d=\"\n",
       "M48.5406 199.887\n",
       "L56.5502 194.709\n",
       "L64.5598 189.533\n",
       "L72.5693 186.951\n",
       "L80.5789 183.674\n",
       "L88.5885 181.56\n",
       "L96.598 180.01\n",
       "L104.608 178.99\n",
       "L112.617 177.921\n",
       "L120.627 177.558\n",
       "L128.636 177.448\n",
       "L136.646 177.634\n",
       "L144.655 178.054\n",
       "L152.665 178.498\n",
       "L160.675 179.053\n",
       "L168.684 179.682\n",
       "L176.694 180.307\n",
       "L184.703 180.926\n",
       "L192.713 181.507\n",
       "L200.722 182.054\" style=\"fill:none;stroke:#008000;stroke-linecap:square;\"/>\n",
       "    <defs>\n",
       "     <path d=\"\n",
       "M-3 3\n",
       "L3 3\n",
       "L3 -3\n",
       "L-3 -3\n",
       "z\n",
       "\" id=\"m45eb232605\" style=\"stroke:#000000;stroke-linejoin:miter;stroke-width:0.5;\"/>\n",
       "    </defs>\n",
       "    <g clip-path=\"url(#p6f87c8219a)\">\n",
       "     <use style=\"fill:#008000;stroke:#000000;stroke-linejoin:miter;stroke-width:0.5;\" x=\"48.540625\" xlink:href=\"#m45eb232605\" y=\"199.886845931\"/>\n",
       "     <use style=\"fill:#008000;stroke:#000000;stroke-linejoin:miter;stroke-width:0.5;\" x=\"56.550194378\" xlink:href=\"#m45eb232605\" y=\"194.708718653\"/>\n",
       "     <use style=\"fill:#008000;stroke:#000000;stroke-linejoin:miter;stroke-width:0.5;\" x=\"64.559763756\" xlink:href=\"#m45eb232605\" y=\"189.53280283\"/>\n",
       "     <use style=\"fill:#008000;stroke:#000000;stroke-linejoin:miter;stroke-width:0.5;\" x=\"72.569333134\" xlink:href=\"#m45eb232605\" y=\"186.950708872\"/>\n",
       "     <use style=\"fill:#008000;stroke:#000000;stroke-linejoin:miter;stroke-width:0.5;\" x=\"80.578902512\" xlink:href=\"#m45eb232605\" y=\"183.673589047\"/>\n",
       "     <use style=\"fill:#008000;stroke:#000000;stroke-linejoin:miter;stroke-width:0.5;\" x=\"88.58847189\" xlink:href=\"#m45eb232605\" y=\"181.560199452\"/>\n",
       "     <use style=\"fill:#008000;stroke:#000000;stroke-linejoin:miter;stroke-width:0.5;\" x=\"96.5980412679\" xlink:href=\"#m45eb232605\" y=\"180.009590772\"/>\n",
       "     <use style=\"fill:#008000;stroke:#000000;stroke-linejoin:miter;stroke-width:0.5;\" x=\"104.607610646\" xlink:href=\"#m45eb232605\" y=\"178.990463569\"/>\n",
       "     <use style=\"fill:#008000;stroke:#000000;stroke-linejoin:miter;stroke-width:0.5;\" x=\"112.617180024\" xlink:href=\"#m45eb232605\" y=\"177.921294982\"/>\n",
       "     <use style=\"fill:#008000;stroke:#000000;stroke-linejoin:miter;stroke-width:0.5;\" x=\"120.626749402\" xlink:href=\"#m45eb232605\" y=\"177.557953102\"/>\n",
       "     <use style=\"fill:#008000;stroke:#000000;stroke-linejoin:miter;stroke-width:0.5;\" x=\"128.63631878\" xlink:href=\"#m45eb232605\" y=\"177.44757515\"/>\n",
       "     <use style=\"fill:#008000;stroke:#000000;stroke-linejoin:miter;stroke-width:0.5;\" x=\"136.645888158\" xlink:href=\"#m45eb232605\" y=\"177.633936992\"/>\n",
       "     <use style=\"fill:#008000;stroke:#000000;stroke-linejoin:miter;stroke-width:0.5;\" x=\"144.655457536\" xlink:href=\"#m45eb232605\" y=\"178.053575212\"/>\n",
       "     <use style=\"fill:#008000;stroke:#000000;stroke-linejoin:miter;stroke-width:0.5;\" x=\"152.665026914\" xlink:href=\"#m45eb232605\" y=\"178.497852102\"/>\n",
       "     <use style=\"fill:#008000;stroke:#000000;stroke-linejoin:miter;stroke-width:0.5;\" x=\"160.674596292\" xlink:href=\"#m45eb232605\" y=\"179.05273931\"/>\n",
       "     <use style=\"fill:#008000;stroke:#000000;stroke-linejoin:miter;stroke-width:0.5;\" x=\"168.68416567\" xlink:href=\"#m45eb232605\" y=\"179.68156768\"/>\n",
       "     <use style=\"fill:#008000;stroke:#000000;stroke-linejoin:miter;stroke-width:0.5;\" x=\"176.693735048\" xlink:href=\"#m45eb232605\" y=\"180.307321775\"/>\n",
       "     <use style=\"fill:#008000;stroke:#000000;stroke-linejoin:miter;stroke-width:0.5;\" x=\"184.703304426\" xlink:href=\"#m45eb232605\" y=\"180.926363878\"/>\n",
       "     <use style=\"fill:#008000;stroke:#000000;stroke-linejoin:miter;stroke-width:0.5;\" x=\"192.712873804\" xlink:href=\"#m45eb232605\" y=\"181.506974726\"/>\n",
       "     <use style=\"fill:#008000;stroke:#000000;stroke-linejoin:miter;stroke-width:0.5;\" x=\"200.722443182\" xlink:href=\"#m45eb232605\" y=\"182.053816819\"/>\n",
       "    </g>\n",
       "   </g>\n",
       "   <g id=\"patch_3\">\n",
       "    <path d=\"\n",
       "M48.5406 12.0391\n",
       "L200.722 12.0391\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_4\">\n",
       "    <path d=\"\n",
       "M48.5406 235.239\n",
       "L48.5406 12.0391\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_5\">\n",
       "    <path d=\"\n",
       "M200.722 235.239\n",
       "L200.722 12.0391\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_6\">\n",
       "    <path d=\"\n",
       "M48.5406 235.239\n",
       "L200.722 235.239\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;\"/>\n",
       "   </g>\n",
       "   <g id=\"matplotlib.axis_1\">\n",
       "    <g id=\"xtick_1\">\n",
       "     <g id=\"line2d_3\">\n",
       "      <defs>\n",
       "       <path d=\"\n",
       "M0 0\n",
       "L0 -4\" id=\"mc7db9fdffb\" style=\"stroke:#000000;stroke-width:0.5;\"/>\n",
       "      </defs>\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"48.540625\" xlink:href=\"#mc7db9fdffb\" y=\"235.2390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"line2d_4\">\n",
       "      <defs>\n",
       "       <path d=\"\n",
       "M0 0\n",
       "L0 4\" id=\"m5a7d422ac3\" style=\"stroke:#000000;stroke-width:0.5;\"/>\n",
       "      </defs>\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"48.540625\" xlink:href=\"#m5a7d422ac3\" y=\"12.0390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_1\">\n",
       "      <!-- 6 -->\n",
       "      <defs>\n",
       "       <path d=\"\n",
       "M33.0156 40.375\n",
       "Q26.375 40.375 22.4844 35.8281\n",
       "Q18.6094 31.2969 18.6094 23.3906\n",
       "Q18.6094 15.5312 22.4844 10.9531\n",
       "Q26.375 6.39062 33.0156 6.39062\n",
       "Q39.6562 6.39062 43.5312 10.9531\n",
       "Q47.4062 15.5312 47.4062 23.3906\n",
       "Q47.4062 31.2969 43.5312 35.8281\n",
       "Q39.6562 40.375 33.0156 40.375\n",
       "M52.5938 71.2969\n",
       "L52.5938 62.3125\n",
       "Q48.875 64.0625 45.0938 64.9844\n",
       "Q41.3125 65.9219 37.5938 65.9219\n",
       "Q27.8281 65.9219 22.6719 59.3281\n",
       "Q17.5312 52.7344 16.7969 39.4062\n",
       "Q19.6719 43.6562 24.0156 45.9219\n",
       "Q28.375 48.1875 33.5938 48.1875\n",
       "Q44.5781 48.1875 50.9531 41.5156\n",
       "Q57.3281 34.8594 57.3281 23.3906\n",
       "Q57.3281 12.1562 50.6875 5.35938\n",
       "Q44.0469 -1.42188 33.0156 -1.42188\n",
       "Q20.3594 -1.42188 13.6719 8.26562\n",
       "Q6.98438 17.9688 6.98438 36.375\n",
       "Q6.98438 53.6562 15.1875 63.9375\n",
       "Q23.3906 74.2188 37.2031 74.2188\n",
       "Q40.9219 74.2188 44.7031 73.4844\n",
       "Q48.4844 72.75 52.5938 71.2969\" id=\"BitstreamVeraSans-Roman-36\"/>\n",
       "      </defs>\n",
       "      <g transform=\"translate(46.0234375 246.8375)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#BitstreamVeraSans-Roman-36\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_2\">\n",
       "     <g id=\"line2d_5\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"78.9769886364\" xlink:href=\"#mc7db9fdffb\" y=\"235.2390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"line2d_6\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"78.9769886364\" xlink:href=\"#m5a7d422ac3\" y=\"12.0390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_2\">\n",
       "      <!-- 8 -->\n",
       "      <defs>\n",
       "       <path d=\"\n",
       "M31.7812 34.625\n",
       "Q24.75 34.625 20.7188 30.8594\n",
       "Q16.7031 27.0938 16.7031 20.5156\n",
       "Q16.7031 13.9219 20.7188 10.1562\n",
       "Q24.75 6.39062 31.7812 6.39062\n",
       "Q38.8125 6.39062 42.8594 10.1719\n",
       "Q46.9219 13.9688 46.9219 20.5156\n",
       "Q46.9219 27.0938 42.8906 30.8594\n",
       "Q38.875 34.625 31.7812 34.625\n",
       "M21.9219 38.8125\n",
       "Q15.5781 40.375 12.0312 44.7188\n",
       "Q8.5 49.0781 8.5 55.3281\n",
       "Q8.5 64.0625 14.7188 69.1406\n",
       "Q20.9531 74.2188 31.7812 74.2188\n",
       "Q42.6719 74.2188 48.875 69.1406\n",
       "Q55.0781 64.0625 55.0781 55.3281\n",
       "Q55.0781 49.0781 51.5312 44.7188\n",
       "Q48 40.375 41.7031 38.8125\n",
       "Q48.8281 37.1562 52.7969 32.3125\n",
       "Q56.7812 27.4844 56.7812 20.5156\n",
       "Q56.7812 9.90625 50.3125 4.23438\n",
       "Q43.8438 -1.42188 31.7812 -1.42188\n",
       "Q19.7344 -1.42188 13.25 4.23438\n",
       "Q6.78125 9.90625 6.78125 20.5156\n",
       "Q6.78125 27.4844 10.7812 32.3125\n",
       "Q14.7969 37.1562 21.9219 38.8125\n",
       "M18.3125 54.3906\n",
       "Q18.3125 48.7344 21.8438 45.5625\n",
       "Q25.3906 42.3906 31.7812 42.3906\n",
       "Q38.1406 42.3906 41.7188 45.5625\n",
       "Q45.3125 48.7344 45.3125 54.3906\n",
       "Q45.3125 60.0625 41.7188 63.2344\n",
       "Q38.1406 66.4062 31.7812 66.4062\n",
       "Q25.3906 66.4062 21.8438 63.2344\n",
       "Q18.3125 60.0625 18.3125 54.3906\" id=\"BitstreamVeraSans-Roman-38\"/>\n",
       "      </defs>\n",
       "      <g transform=\"translate(76.4769886364 246.8375)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#BitstreamVeraSans-Roman-38\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_3\">\n",
       "     <g id=\"line2d_7\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"109.413352273\" xlink:href=\"#mc7db9fdffb\" y=\"235.2390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"line2d_8\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"109.413352273\" xlink:href=\"#m5a7d422ac3\" y=\"12.0390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_3\">\n",
       "      <!-- 10 -->\n",
       "      <defs>\n",
       "       <path d=\"\n",
       "M12.4062 8.29688\n",
       "L28.5156 8.29688\n",
       "L28.5156 63.9219\n",
       "L10.9844 60.4062\n",
       "L10.9844 69.3906\n",
       "L28.4219 72.9062\n",
       "L38.2812 72.9062\n",
       "L38.2812 8.29688\n",
       "L54.3906 8.29688\n",
       "L54.3906 0\n",
       "L12.4062 0\n",
       "z\n",
       "\" id=\"BitstreamVeraSans-Roman-31\"/>\n",
       "       <path d=\"\n",
       "M31.7812 66.4062\n",
       "Q24.1719 66.4062 20.3281 58.9062\n",
       "Q16.5 51.4219 16.5 36.375\n",
       "Q16.5 21.3906 20.3281 13.8906\n",
       "Q24.1719 6.39062 31.7812 6.39062\n",
       "Q39.4531 6.39062 43.2812 13.8906\n",
       "Q47.125 21.3906 47.125 36.375\n",
       "Q47.125 51.4219 43.2812 58.9062\n",
       "Q39.4531 66.4062 31.7812 66.4062\n",
       "M31.7812 74.2188\n",
       "Q44.0469 74.2188 50.5156 64.5156\n",
       "Q56.9844 54.8281 56.9844 36.375\n",
       "Q56.9844 17.9688 50.5156 8.26562\n",
       "Q44.0469 -1.42188 31.7812 -1.42188\n",
       "Q19.5312 -1.42188 13.0625 8.26562\n",
       "Q6.59375 17.9688 6.59375 36.375\n",
       "Q6.59375 54.8281 13.0625 64.5156\n",
       "Q19.5312 74.2188 31.7812 74.2188\" id=\"BitstreamVeraSans-Roman-30\"/>\n",
       "      </defs>\n",
       "      <g transform=\"translate(103.932102273 246.8375)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#BitstreamVeraSans-Roman-31\"/>\n",
       "       <use x=\"63.623046875\" xlink:href=\"#BitstreamVeraSans-Roman-30\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_4\">\n",
       "     <g id=\"line2d_9\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"139.849715909\" xlink:href=\"#mc7db9fdffb\" y=\"235.2390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"line2d_10\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"139.849715909\" xlink:href=\"#m5a7d422ac3\" y=\"12.0390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_4\">\n",
       "      <!-- 12 -->\n",
       "      <defs>\n",
       "       <path d=\"\n",
       "M19.1875 8.29688\n",
       "L53.6094 8.29688\n",
       "L53.6094 0\n",
       "L7.32812 0\n",
       "L7.32812 8.29688\n",
       "Q12.9375 14.1094 22.625 23.8906\n",
       "Q32.3281 33.6875 34.8125 36.5312\n",
       "Q39.5469 41.8438 41.4219 45.5312\n",
       "Q43.3125 49.2188 43.3125 52.7812\n",
       "Q43.3125 58.5938 39.2344 62.25\n",
       "Q35.1562 65.9219 28.6094 65.9219\n",
       "Q23.9688 65.9219 18.8125 64.3125\n",
       "Q13.6719 62.7031 7.8125 59.4219\n",
       "L7.8125 69.3906\n",
       "Q13.7656 71.7812 18.9375 73\n",
       "Q24.125 74.2188 28.4219 74.2188\n",
       "Q39.75 74.2188 46.4844 68.5469\n",
       "Q53.2188 62.8906 53.2188 53.4219\n",
       "Q53.2188 48.9219 51.5312 44.8906\n",
       "Q49.8594 40.875 45.4062 35.4062\n",
       "Q44.1875 33.9844 37.6406 27.2188\n",
       "Q31.1094 20.4531 19.1875 8.29688\" id=\"BitstreamVeraSans-Roman-32\"/>\n",
       "      </defs>\n",
       "      <g transform=\"translate(134.537215909 246.8375)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#BitstreamVeraSans-Roman-31\"/>\n",
       "       <use x=\"63.623046875\" xlink:href=\"#BitstreamVeraSans-Roman-32\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_5\">\n",
       "     <g id=\"line2d_11\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"170.286079545\" xlink:href=\"#mc7db9fdffb\" y=\"235.2390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"line2d_12\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"170.286079545\" xlink:href=\"#m5a7d422ac3\" y=\"12.0390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_5\">\n",
       "      <!-- 14 -->\n",
       "      <defs>\n",
       "       <path d=\"\n",
       "M37.7969 64.3125\n",
       "L12.8906 25.3906\n",
       "L37.7969 25.3906\n",
       "z\n",
       "\n",
       "M35.2031 72.9062\n",
       "L47.6094 72.9062\n",
       "L47.6094 25.3906\n",
       "L58.0156 25.3906\n",
       "L58.0156 17.1875\n",
       "L47.6094 17.1875\n",
       "L47.6094 0\n",
       "L37.7969 0\n",
       "L37.7969 17.1875\n",
       "L4.89062 17.1875\n",
       "L4.89062 26.7031\n",
       "z\n",
       "\" id=\"BitstreamVeraSans-Roman-34\"/>\n",
       "      </defs>\n",
       "      <g transform=\"translate(164.753267045 246.8375)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#BitstreamVeraSans-Roman-31\"/>\n",
       "       <use x=\"63.623046875\" xlink:href=\"#BitstreamVeraSans-Roman-34\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_6\">\n",
       "     <g id=\"line2d_13\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"200.722443182\" xlink:href=\"#mc7db9fdffb\" y=\"235.2390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"line2d_14\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"200.722443182\" xlink:href=\"#m5a7d422ac3\" y=\"12.0390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_6\">\n",
       "      <!-- 16 -->\n",
       "      <g transform=\"translate(195.224005682 246.8375)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#BitstreamVeraSans-Roman-31\"/>\n",
       "       <use x=\"63.623046875\" xlink:href=\"#BitstreamVeraSans-Roman-36\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"text_7\">\n",
       "     <!-- $\\lambda$ -->\n",
       "     <defs>\n",
       "      <path d=\"\n",
       "M5.07812 1.70312\n",
       "Q5.07812 3.17188 6.39062 4.5\n",
       "L34.5156 32.0781\n",
       "L24.6094 59.9062\n",
       "Q23.4375 63.0938 22.1406 64.9375\n",
       "Q20.8438 66.7969 18.4062 66.7969\n",
       "Q17.2812 66.7969 17.2812 68.1094\n",
       "Q17.3906 68.7031 17.7812 69.0469\n",
       "Q18.1719 69.3906 18.7969 69.3906\n",
       "Q29.2969 69.3906 31.5 63.1875\n",
       "L51.8125 6.5\n",
       "Q53.125 2.25 54.5 0.78125\n",
       "Q54.9844 0.046875 54.9844 -0.203125\n",
       "Q54.9844 -1.125 54.2031 -1.125\n",
       "L48.7812 -1.125\n",
       "Q46.2969 -0.390625 44.8281 3.21875\n",
       "L35.6875 28.8125\n",
       "L11.5312 0.390625\n",
       "Q9.71875 -1.3125 8.29688 -1.3125\n",
       "Q7.03125 -1.3125 6.04688 -0.4375\n",
       "Q5.07812 0.4375 5.07812 1.70312\" id=\"Cmmi10-b8\"/>\n",
       "     </defs>\n",
       "     <g transform=\"translate(121.681534091 261.515625)scale(0.1 -0.1)\">\n",
       "      <use transform=\"translate(0.0 0.609375)\" xlink:href=\"#Cmmi10-b8\"/>\n",
       "     </g>\n",
       "    </g>\n",
       "   </g>\n",
       "   <g id=\"matplotlib.axis_2\">\n",
       "    <g id=\"ytick_1\">\n",
       "     <g id=\"line2d_15\">\n",
       "      <defs>\n",
       "       <path d=\"\n",
       "M0 0\n",
       "L4 0\" id=\"md7965d1ba0\" style=\"stroke:#000000;stroke-width:0.5;\"/>\n",
       "      </defs>\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"48.540625\" xlink:href=\"#md7965d1ba0\" y=\"235.2390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"line2d_16\">\n",
       "      <defs>\n",
       "       <path d=\"\n",
       "M0 0\n",
       "L-4 0\" id=\"md9a1c1a7cd\" style=\"stroke:#000000;stroke-width:0.5;\"/>\n",
       "      </defs>\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"200.722443182\" xlink:href=\"#md9a1c1a7cd\" y=\"235.2390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_8\">\n",
       "      <!-- −1.1 -->\n",
       "      <defs>\n",
       "       <path d=\"\n",
       "M10.5938 35.5\n",
       "L73.1875 35.5\n",
       "L73.1875 27.2031\n",
       "L10.5938 27.2031\n",
       "z\n",
       "\" id=\"BitstreamVeraSans-Roman-2212\"/>\n",
       "       <path d=\"\n",
       "M10.6875 12.4062\n",
       "L21 12.4062\n",
       "L21 0\n",
       "L10.6875 0\n",
       "z\n",
       "\" id=\"BitstreamVeraSans-Roman-2e\"/>\n",
       "      </defs>\n",
       "      <g transform=\"translate(22.240625 237.9984375)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#BitstreamVeraSans-Roman-2212\"/>\n",
       "       <use x=\"83.7890625\" xlink:href=\"#BitstreamVeraSans-Roman-31\"/>\n",
       "       <use x=\"147.412109375\" xlink:href=\"#BitstreamVeraSans-Roman-2e\"/>\n",
       "       <use x=\"179.19921875\" xlink:href=\"#BitstreamVeraSans-Roman-31\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_2\">\n",
       "     <g id=\"line2d_17\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"48.540625\" xlink:href=\"#md7965d1ba0\" y=\"203.353348214\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"line2d_18\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"200.722443182\" xlink:href=\"#md9a1c1a7cd\" y=\"203.353348214\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_9\">\n",
       "      <!-- −1.0 -->\n",
       "      <g transform=\"translate(21.98125 206.112723214)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#BitstreamVeraSans-Roman-2212\"/>\n",
       "       <use x=\"83.7890625\" xlink:href=\"#BitstreamVeraSans-Roman-31\"/>\n",
       "       <use x=\"147.412109375\" xlink:href=\"#BitstreamVeraSans-Roman-2e\"/>\n",
       "       <use x=\"179.19921875\" xlink:href=\"#BitstreamVeraSans-Roman-30\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_3\">\n",
       "     <g id=\"line2d_19\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"48.540625\" xlink:href=\"#md7965d1ba0\" y=\"171.467633929\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"line2d_20\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"200.722443182\" xlink:href=\"#md9a1c1a7cd\" y=\"171.467633929\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_10\">\n",
       "      <!-- −0.9 -->\n",
       "      <defs>\n",
       "       <path d=\"\n",
       "M10.9844 1.51562\n",
       "L10.9844 10.5\n",
       "Q14.7031 8.73438 18.5 7.8125\n",
       "Q22.3125 6.89062 25.9844 6.89062\n",
       "Q35.75 6.89062 40.8906 13.4531\n",
       "Q46.0469 20.0156 46.7812 33.4062\n",
       "Q43.9531 29.2031 39.5938 26.9531\n",
       "Q35.25 24.7031 29.9844 24.7031\n",
       "Q19.0469 24.7031 12.6719 31.3125\n",
       "Q6.29688 37.9375 6.29688 49.4219\n",
       "Q6.29688 60.6406 12.9375 67.4219\n",
       "Q19.5781 74.2188 30.6094 74.2188\n",
       "Q43.2656 74.2188 49.9219 64.5156\n",
       "Q56.5938 54.8281 56.5938 36.375\n",
       "Q56.5938 19.1406 48.4062 8.85938\n",
       "Q40.2344 -1.42188 26.4219 -1.42188\n",
       "Q22.7031 -1.42188 18.8906 -0.6875\n",
       "Q15.0938 0.046875 10.9844 1.51562\n",
       "M30.6094 32.4219\n",
       "Q37.25 32.4219 41.125 36.9531\n",
       "Q45.0156 41.5 45.0156 49.4219\n",
       "Q45.0156 57.2812 41.125 61.8438\n",
       "Q37.25 66.4062 30.6094 66.4062\n",
       "Q23.9688 66.4062 20.0938 61.8438\n",
       "Q16.2188 57.2812 16.2188 49.4219\n",
       "Q16.2188 41.5 20.0938 36.9531\n",
       "Q23.9688 32.4219 30.6094 32.4219\" id=\"BitstreamVeraSans-Roman-39\"/>\n",
       "      </defs>\n",
       "      <g transform=\"translate(22.0203125 174.227008929)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#BitstreamVeraSans-Roman-2212\"/>\n",
       "       <use x=\"83.7890625\" xlink:href=\"#BitstreamVeraSans-Roman-30\"/>\n",
       "       <use x=\"147.412109375\" xlink:href=\"#BitstreamVeraSans-Roman-2e\"/>\n",
       "       <use x=\"179.19921875\" xlink:href=\"#BitstreamVeraSans-Roman-39\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_4\">\n",
       "     <g id=\"line2d_21\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"48.540625\" xlink:href=\"#md7965d1ba0\" y=\"139.581919643\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"line2d_22\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"200.722443182\" xlink:href=\"#md9a1c1a7cd\" y=\"139.581919643\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_11\">\n",
       "      <!-- −0.8 -->\n",
       "      <g transform=\"translate(22.0015625 142.341294643)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#BitstreamVeraSans-Roman-2212\"/>\n",
       "       <use x=\"83.7890625\" xlink:href=\"#BitstreamVeraSans-Roman-30\"/>\n",
       "       <use x=\"147.412109375\" xlink:href=\"#BitstreamVeraSans-Roman-2e\"/>\n",
       "       <use x=\"179.19921875\" xlink:href=\"#BitstreamVeraSans-Roman-38\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_5\">\n",
       "     <g id=\"line2d_23\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"48.540625\" xlink:href=\"#md7965d1ba0\" y=\"107.696205357\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"line2d_24\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"200.722443182\" xlink:href=\"#md9a1c1a7cd\" y=\"107.696205357\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_12\">\n",
       "      <!-- −0.7 -->\n",
       "      <defs>\n",
       "       <path d=\"\n",
       "M8.20312 72.9062\n",
       "L55.0781 72.9062\n",
       "L55.0781 68.7031\n",
       "L28.6094 0\n",
       "L18.3125 0\n",
       "L43.2188 64.5938\n",
       "L8.20312 64.5938\n",
       "z\n",
       "\" id=\"BitstreamVeraSans-Roman-37\"/>\n",
       "      </defs>\n",
       "      <g transform=\"translate(22.171875 110.455580357)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#BitstreamVeraSans-Roman-2212\"/>\n",
       "       <use x=\"83.7890625\" xlink:href=\"#BitstreamVeraSans-Roman-30\"/>\n",
       "       <use x=\"147.412109375\" xlink:href=\"#BitstreamVeraSans-Roman-2e\"/>\n",
       "       <use x=\"179.19921875\" xlink:href=\"#BitstreamVeraSans-Roman-37\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_6\">\n",
       "     <g id=\"line2d_25\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"48.540625\" xlink:href=\"#md7965d1ba0\" y=\"75.8104910714\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"line2d_26\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"200.722443182\" xlink:href=\"#md9a1c1a7cd\" y=\"75.8104910714\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_13\">\n",
       "      <!-- −0.6 -->\n",
       "      <g transform=\"translate(21.946875 78.5698660714)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#BitstreamVeraSans-Roman-2212\"/>\n",
       "       <use x=\"83.7890625\" xlink:href=\"#BitstreamVeraSans-Roman-30\"/>\n",
       "       <use x=\"147.412109375\" xlink:href=\"#BitstreamVeraSans-Roman-2e\"/>\n",
       "       <use x=\"179.19921875\" xlink:href=\"#BitstreamVeraSans-Roman-36\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_7\">\n",
       "     <g id=\"line2d_27\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"48.540625\" xlink:href=\"#md7965d1ba0\" y=\"43.9247767857\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"line2d_28\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"200.722443182\" xlink:href=\"#md9a1c1a7cd\" y=\"43.9247767857\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_14\">\n",
       "      <!-- −0.5 -->\n",
       "      <defs>\n",
       "       <path d=\"\n",
       "M10.7969 72.9062\n",
       "L49.5156 72.9062\n",
       "L49.5156 64.5938\n",
       "L19.8281 64.5938\n",
       "L19.8281 46.7344\n",
       "Q21.9688 47.4688 24.1094 47.8281\n",
       "Q26.2656 48.1875 28.4219 48.1875\n",
       "Q40.625 48.1875 47.75 41.5\n",
       "Q54.8906 34.8125 54.8906 23.3906\n",
       "Q54.8906 11.625 47.5625 5.09375\n",
       "Q40.2344 -1.42188 26.9062 -1.42188\n",
       "Q22.3125 -1.42188 17.5469 -0.640625\n",
       "Q12.7969 0.140625 7.71875 1.70312\n",
       "L7.71875 11.625\n",
       "Q12.1094 9.23438 16.7969 8.0625\n",
       "Q21.4844 6.89062 26.7031 6.89062\n",
       "Q35.1562 6.89062 40.0781 11.3281\n",
       "Q45.0156 15.7656 45.0156 23.3906\n",
       "Q45.0156 31 40.0781 35.4375\n",
       "Q35.1562 39.8906 26.7031 39.8906\n",
       "Q22.75 39.8906 18.8125 39.0156\n",
       "Q14.8906 38.1406 10.7969 36.2812\n",
       "z\n",
       "\" id=\"BitstreamVeraSans-Roman-35\"/>\n",
       "      </defs>\n",
       "      <g transform=\"translate(22.190625 46.6841517857)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#BitstreamVeraSans-Roman-2212\"/>\n",
       "       <use x=\"83.7890625\" xlink:href=\"#BitstreamVeraSans-Roman-30\"/>\n",
       "       <use x=\"147.412109375\" xlink:href=\"#BitstreamVeraSans-Roman-2e\"/>\n",
       "       <use x=\"179.19921875\" xlink:href=\"#BitstreamVeraSans-Roman-35\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_8\">\n",
       "     <g id=\"line2d_29\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"48.540625\" xlink:href=\"#md7965d1ba0\" y=\"12.0390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"line2d_30\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"200.722443182\" xlink:href=\"#md9a1c1a7cd\" y=\"12.0390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_15\">\n",
       "      <!-- −0.4 -->\n",
       "      <g transform=\"translate(21.878125 14.7984375)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#BitstreamVeraSans-Roman-2212\"/>\n",
       "       <use x=\"83.7890625\" xlink:href=\"#BitstreamVeraSans-Roman-30\"/>\n",
       "       <use x=\"147.412109375\" xlink:href=\"#BitstreamVeraSans-Roman-2e\"/>\n",
       "       <use x=\"179.19921875\" xlink:href=\"#BitstreamVeraSans-Roman-34\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"text_16\">\n",
       "     <!-- score -->\n",
       "     <defs>\n",
       "      <path d=\"\n",
       "M30.6094 48.3906\n",
       "Q23.3906 48.3906 19.1875 42.75\n",
       "Q14.9844 37.1094 14.9844 27.2969\n",
       "Q14.9844 17.4844 19.1562 11.8438\n",
       "Q23.3438 6.20312 30.6094 6.20312\n",
       "Q37.7969 6.20312 41.9844 11.8594\n",
       "Q46.1875 17.5312 46.1875 27.2969\n",
       "Q46.1875 37.0156 41.9844 42.7031\n",
       "Q37.7969 48.3906 30.6094 48.3906\n",
       "M30.6094 56\n",
       "Q42.3281 56 49.0156 48.375\n",
       "Q55.7188 40.7656 55.7188 27.2969\n",
       "Q55.7188 13.875 49.0156 6.21875\n",
       "Q42.3281 -1.42188 30.6094 -1.42188\n",
       "Q18.8438 -1.42188 12.1719 6.21875\n",
       "Q5.51562 13.875 5.51562 27.2969\n",
       "Q5.51562 40.7656 12.1719 48.375\n",
       "Q18.8438 56 30.6094 56\" id=\"BitstreamVeraSans-Roman-6f\"/>\n",
       "      <path d=\"\n",
       "M56.2031 29.5938\n",
       "L56.2031 25.2031\n",
       "L14.8906 25.2031\n",
       "Q15.4844 15.9219 20.4844 11.0625\n",
       "Q25.4844 6.20312 34.4219 6.20312\n",
       "Q39.5938 6.20312 44.4531 7.46875\n",
       "Q49.3125 8.73438 54.1094 11.2812\n",
       "L54.1094 2.78125\n",
       "Q49.2656 0.734375 44.1875 -0.34375\n",
       "Q39.1094 -1.42188 33.8906 -1.42188\n",
       "Q20.7969 -1.42188 13.1562 6.1875\n",
       "Q5.51562 13.8125 5.51562 26.8125\n",
       "Q5.51562 40.2344 12.7656 48.1094\n",
       "Q20.0156 56 32.3281 56\n",
       "Q43.3594 56 49.7812 48.8906\n",
       "Q56.2031 41.7969 56.2031 29.5938\n",
       "M47.2188 32.2344\n",
       "Q47.125 39.5938 43.0938 43.9844\n",
       "Q39.0625 48.3906 32.4219 48.3906\n",
       "Q24.9062 48.3906 20.3906 44.1406\n",
       "Q15.875 39.8906 15.1875 32.1719\n",
       "z\n",
       "\" id=\"BitstreamVeraSans-Roman-65\"/>\n",
       "      <path d=\"\n",
       "M44.2812 53.0781\n",
       "L44.2812 44.5781\n",
       "Q40.4844 46.5312 36.375 47.5\n",
       "Q32.2812 48.4844 27.875 48.4844\n",
       "Q21.1875 48.4844 17.8438 46.4375\n",
       "Q14.5 44.3906 14.5 40.2812\n",
       "Q14.5 37.1562 16.8906 35.375\n",
       "Q19.2812 33.5938 26.5156 31.9844\n",
       "L29.5938 31.2969\n",
       "Q39.1562 29.25 43.1875 25.5156\n",
       "Q47.2188 21.7812 47.2188 15.0938\n",
       "Q47.2188 7.46875 41.1875 3.01562\n",
       "Q35.1562 -1.42188 24.6094 -1.42188\n",
       "Q20.2188 -1.42188 15.4531 -0.5625\n",
       "Q10.6875 0.296875 5.42188 2\n",
       "L5.42188 11.2812\n",
       "Q10.4062 8.6875 15.2344 7.39062\n",
       "Q20.0625 6.10938 24.8125 6.10938\n",
       "Q31.1562 6.10938 34.5625 8.28125\n",
       "Q37.9844 10.4531 37.9844 14.4062\n",
       "Q37.9844 18.0625 35.5156 20.0156\n",
       "Q33.0625 21.9688 24.7031 23.7812\n",
       "L21.5781 24.5156\n",
       "Q13.2344 26.2656 9.51562 29.9062\n",
       "Q5.8125 33.5469 5.8125 39.8906\n",
       "Q5.8125 47.6094 11.2812 51.7969\n",
       "Q16.75 56 26.8125 56\n",
       "Q31.7812 56 36.1719 55.2656\n",
       "Q40.5781 54.5469 44.2812 53.0781\" id=\"BitstreamVeraSans-Roman-73\"/>\n",
       "      <path d=\"\n",
       "M48.7812 52.5938\n",
       "L48.7812 44.1875\n",
       "Q44.9688 46.2969 41.1406 47.3438\n",
       "Q37.3125 48.3906 33.4062 48.3906\n",
       "Q24.6562 48.3906 19.8125 42.8438\n",
       "Q14.9844 37.3125 14.9844 27.2969\n",
       "Q14.9844 17.2812 19.8125 11.7344\n",
       "Q24.6562 6.20312 33.4062 6.20312\n",
       "Q37.3125 6.20312 41.1406 7.25\n",
       "Q44.9688 8.29688 48.7812 10.4062\n",
       "L48.7812 2.09375\n",
       "Q45.0156 0.34375 40.9844 -0.53125\n",
       "Q36.9688 -1.42188 32.4219 -1.42188\n",
       "Q20.0625 -1.42188 12.7812 6.34375\n",
       "Q5.51562 14.1094 5.51562 27.2969\n",
       "Q5.51562 40.6719 12.8594 48.3281\n",
       "Q20.2188 56 33.0156 56\n",
       "Q37.1562 56 41.1094 55.1406\n",
       "Q45.0625 54.2969 48.7812 52.5938\" id=\"BitstreamVeraSans-Roman-63\"/>\n",
       "      <path d=\"\n",
       "M41.1094 46.2969\n",
       "Q39.5938 47.1719 37.8125 47.5781\n",
       "Q36.0312 48 33.8906 48\n",
       "Q26.2656 48 22.1875 43.0469\n",
       "Q18.1094 38.0938 18.1094 28.8125\n",
       "L18.1094 0\n",
       "L9.07812 0\n",
       "L9.07812 54.6875\n",
       "L18.1094 54.6875\n",
       "L18.1094 46.1875\n",
       "Q20.9531 51.1719 25.4844 53.5781\n",
       "Q30.0312 56 36.5312 56\n",
       "Q37.4531 56 38.5781 55.875\n",
       "Q39.7031 55.7656 41.0625 55.5156\n",
       "z\n",
       "\" id=\"BitstreamVeraSans-Roman-72\"/>\n",
       "     </defs>\n",
       "     <g transform=\"translate(14.7984375 136.534375)rotate(-90.0)scale(0.1 -0.1)\">\n",
       "      <use xlink:href=\"#BitstreamVeraSans-Roman-73\"/>\n",
       "      <use x=\"52.099609375\" xlink:href=\"#BitstreamVeraSans-Roman-63\"/>\n",
       "      <use x=\"107.080078125\" xlink:href=\"#BitstreamVeraSans-Roman-6f\"/>\n",
       "      <use x=\"168.26171875\" xlink:href=\"#BitstreamVeraSans-Roman-72\"/>\n",
       "      <use x=\"207.125\" xlink:href=\"#BitstreamVeraSans-Roman-65\"/>\n",
       "     </g>\n",
       "    </g>\n",
       "   </g>\n",
       "   <g id=\"legend_1\">\n",
       "    <g id=\"patch_7\">\n",
       "     <path d=\"\n",
       "M124.933 56.8666\n",
       "L194.722 56.8666\n",
       "L194.722 18.0391\n",
       "L124.933 18.0391\n",
       "z\n",
       "\" style=\"fill:#ffffff;stroke:#000000;stroke-linejoin:miter;\"/>\n",
       "    </g>\n",
       "    <g id=\"line2d_31\">\n",
       "     <path d=\"\n",
       "M133.333 27.7572\n",
       "L150.133 27.7572\" style=\"fill:none;stroke:#0000ff;stroke-linecap:square;\"/>\n",
       "    </g>\n",
       "    <g id=\"line2d_32\">\n",
       "     <g>\n",
       "      <use style=\"fill:#0000ff;stroke:#000000;stroke-width:0.5;\" x=\"133.333068182\" xlink:href=\"#mdb00ba95ec\" y=\"27.7571875\"/>\n",
       "      <use style=\"fill:#0000ff;stroke:#000000;stroke-width:0.5;\" x=\"150.133068182\" xlink:href=\"#mdb00ba95ec\" y=\"27.7571875\"/>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"text_17\">\n",
       "     <!-- train -->\n",
       "     <defs>\n",
       "      <path d=\"\n",
       "M54.8906 33.0156\n",
       "L54.8906 0\n",
       "L45.9062 0\n",
       "L45.9062 32.7188\n",
       "Q45.9062 40.4844 42.875 44.3281\n",
       "Q39.8438 48.1875 33.7969 48.1875\n",
       "Q26.5156 48.1875 22.3125 43.5469\n",
       "Q18.1094 38.9219 18.1094 30.9062\n",
       "L18.1094 0\n",
       "L9.07812 0\n",
       "L9.07812 54.6875\n",
       "L18.1094 54.6875\n",
       "L18.1094 46.1875\n",
       "Q21.3438 51.125 25.7031 53.5625\n",
       "Q30.0781 56 35.7969 56\n",
       "Q45.2188 56 50.0469 50.1719\n",
       "Q54.8906 44.3438 54.8906 33.0156\" id=\"BitstreamVeraSans-Roman-6e\"/>\n",
       "      <path d=\"\n",
       "M9.42188 54.6875\n",
       "L18.4062 54.6875\n",
       "L18.4062 0\n",
       "L9.42188 0\n",
       "z\n",
       "\n",
       "M9.42188 75.9844\n",
       "L18.4062 75.9844\n",
       "L18.4062 64.5938\n",
       "L9.42188 64.5938\n",
       "z\n",
       "\" id=\"BitstreamVeraSans-Roman-69\"/>\n",
       "      <path d=\"\n",
       "M18.3125 70.2188\n",
       "L18.3125 54.6875\n",
       "L36.8125 54.6875\n",
       "L36.8125 47.7031\n",
       "L18.3125 47.7031\n",
       "L18.3125 18.0156\n",
       "Q18.3125 11.3281 20.1406 9.42188\n",
       "Q21.9688 7.51562 27.5938 7.51562\n",
       "L36.8125 7.51562\n",
       "L36.8125 0\n",
       "L27.5938 0\n",
       "Q17.1875 0 13.2344 3.875\n",
       "Q9.28125 7.76562 9.28125 18.0156\n",
       "L9.28125 47.7031\n",
       "L2.6875 47.7031\n",
       "L2.6875 54.6875\n",
       "L9.28125 54.6875\n",
       "L9.28125 70.2188\n",
       "z\n",
       "\" id=\"BitstreamVeraSans-Roman-74\"/>\n",
       "      <path d=\"\n",
       "M34.2812 27.4844\n",
       "Q23.3906 27.4844 19.1875 25\n",
       "Q14.9844 22.5156 14.9844 16.5\n",
       "Q14.9844 11.7188 18.1406 8.90625\n",
       "Q21.2969 6.10938 26.7031 6.10938\n",
       "Q34.1875 6.10938 38.7031 11.4062\n",
       "Q43.2188 16.7031 43.2188 25.4844\n",
       "L43.2188 27.4844\n",
       "z\n",
       "\n",
       "M52.2031 31.2031\n",
       "L52.2031 0\n",
       "L43.2188 0\n",
       "L43.2188 8.29688\n",
       "Q40.1406 3.32812 35.5469 0.953125\n",
       "Q30.9531 -1.42188 24.3125 -1.42188\n",
       "Q15.9219 -1.42188 10.9531 3.29688\n",
       "Q6 8.01562 6 15.9219\n",
       "Q6 25.1406 12.1719 29.8281\n",
       "Q18.3594 34.5156 30.6094 34.5156\n",
       "L43.2188 34.5156\n",
       "L43.2188 35.4062\n",
       "Q43.2188 41.6094 39.1406 45\n",
       "Q35.0625 48.3906 27.6875 48.3906\n",
       "Q23 48.3906 18.5469 47.2656\n",
       "Q14.1094 46.1406 10.0156 43.8906\n",
       "L10.0156 52.2031\n",
       "Q14.9375 54.1094 19.5781 55.0469\n",
       "Q24.2188 56 28.6094 56\n",
       "Q40.4844 56 46.3438 49.8438\n",
       "Q52.2031 43.7031 52.2031 31.2031\" id=\"BitstreamVeraSans-Roman-61\"/>\n",
       "     </defs>\n",
       "     <g transform=\"translate(163.333068182 31.9571875)scale(0.12 -0.12)\">\n",
       "      <use xlink:href=\"#BitstreamVeraSans-Roman-74\"/>\n",
       "      <use x=\"39.208984375\" xlink:href=\"#BitstreamVeraSans-Roman-72\"/>\n",
       "      <use x=\"80.322265625\" xlink:href=\"#BitstreamVeraSans-Roman-61\"/>\n",
       "      <use x=\"141.6015625\" xlink:href=\"#BitstreamVeraSans-Roman-69\"/>\n",
       "      <use x=\"169.384765625\" xlink:href=\"#BitstreamVeraSans-Roman-6e\"/>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"line2d_33\">\n",
       "     <path d=\"\n",
       "M133.333 45.3709\n",
       "L150.133 45.3709\" style=\"fill:none;stroke:#008000;stroke-linecap:square;\"/>\n",
       "    </g>\n",
       "    <g id=\"line2d_34\">\n",
       "     <g>\n",
       "      <use style=\"fill:#008000;stroke:#000000;stroke-linejoin:miter;stroke-width:0.5;\" x=\"133.333068182\" xlink:href=\"#m45eb232605\" y=\"45.3709375\"/>\n",
       "      <use style=\"fill:#008000;stroke:#000000;stroke-linejoin:miter;stroke-width:0.5;\" x=\"150.133068182\" xlink:href=\"#m45eb232605\" y=\"45.3709375\"/>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"text_18\">\n",
       "     <!-- test -->\n",
       "     <g transform=\"translate(163.333068182 49.5709375)scale(0.12 -0.12)\">\n",
       "      <use xlink:href=\"#BitstreamVeraSans-Roman-74\"/>\n",
       "      <use x=\"39.208984375\" xlink:href=\"#BitstreamVeraSans-Roman-65\"/>\n",
       "      <use x=\"100.732421875\" xlink:href=\"#BitstreamVeraSans-Roman-73\"/>\n",
       "      <use x=\"152.83203125\" xlink:href=\"#BitstreamVeraSans-Roman-74\"/>\n",
       "     </g>\n",
       "    </g>\n",
       "   </g>\n",
       "  </g>\n",
       "  <g id=\"axes_2\">\n",
       "   <g id=\"patch_8\">\n",
       "    <path d=\"\n",
       "M231.159 235.239\n",
       "L383.341 235.239\n",
       "L383.341 12.0391\n",
       "L231.159 12.0391\n",
       "z\n",
       "\" style=\"fill:#ffffff;\"/>\n",
       "   </g>\n",
       "   <g id=\"PolyCollection_3\">\n",
       "    <defs>\n",
       "     <path d=\"\n",
       "M231.159 -114.74\n",
       "L231.159 -71.2149\n",
       "L239.168 -97.0884\n",
       "L247.178 -131.929\n",
       "L255.188 -144.173\n",
       "L263.197 -167.359\n",
       "L271.207 -180.137\n",
       "L279.216 -189.111\n",
       "L287.226 -196.921\n",
       "L295.235 -200.541\n",
       "L303.245 -203.716\n",
       "L311.255 -204.992\n",
       "L319.264 -204.769\n",
       "L327.274 -202.021\n",
       "L335.283 -199.475\n",
       "L343.293 -196.439\n",
       "L351.302 -193.161\n",
       "L359.312 -189.607\n",
       "L367.321 -186.019\n",
       "L375.331 -182.711\n",
       "L383.341 -179.637\n",
       "L383.341 -214.37\n",
       "L383.341 -214.37\n",
       "L375.331 -217.676\n",
       "L367.321 -221.142\n",
       "L359.312 -224.775\n",
       "L351.302 -228.522\n",
       "L343.293 -232.581\n",
       "L335.283 -236.018\n",
       "L327.274 -238.655\n",
       "L319.264 -240.803\n",
       "L311.255 -242.755\n",
       "L303.245 -242.743\n",
       "L295.235 -241.679\n",
       "L287.226 -232.825\n",
       "L279.216 -228.745\n",
       "L271.207 -219.629\n",
       "L263.197 -207.75\n",
       "L255.188 -192.704\n",
       "L247.178 -174.824\n",
       "L239.168 -149.278\n",
       "L231.159 -114.74\n",
       "z\n",
       "\" id=\"m74f62c9c96\" style=\"stroke:#000000;stroke-opacity:0.3;\"/>\n",
       "    </defs>\n",
       "    <g clip-path=\"url(#pebf3d5afac)\">\n",
       "     <use style=\"fill:#0000ff;fill-opacity:0.3;stroke:#000000;stroke-opacity:0.3;\" x=\"0.0\" xlink:href=\"#m74f62c9c96\" y=\"270.7953125\"/>\n",
       "    </g>\n",
       "   </g>\n",
       "   <g id=\"line2d_35\">\n",
       "    <path clip-path=\"url(#pebf3d5afac)\" d=\"\n",
       "M231.159 177.818\n",
       "L239.168 147.612\n",
       "L247.178 117.419\n",
       "L255.188 102.357\n",
       "L263.197 83.2405\n",
       "L271.207 70.9124\n",
       "L279.216 61.8671\n",
       "L287.226 55.9222\n",
       "L295.235 49.6854\n",
       "L303.245 47.5659\n",
       "L311.255 46.9221\n",
       "L319.264 48.0092\n",
       "L327.274 50.4571\n",
       "L335.283 53.0487\n",
       "L343.293 56.2855\n",
       "L351.302 59.9537\n",
       "L359.312 63.6039\n",
       "L367.321 67.215\n",
       "L375.331 70.6019\n",
       "L383.341 73.7918\" style=\"fill:none;stroke:#008000;stroke-linecap:square;\"/>\n",
       "    <g clip-path=\"url(#pebf3d5afac)\">\n",
       "     <use style=\"fill:#008000;stroke:#000000;stroke-linejoin:miter;stroke-width:0.5;\" x=\"231.158806818\" xlink:href=\"#m45eb232605\" y=\"177.817799179\"/>\n",
       "     <use style=\"fill:#008000;stroke:#000000;stroke-linejoin:miter;stroke-width:0.5;\" x=\"239.168376196\" xlink:href=\"#m45eb232605\" y=\"147.612056726\"/>\n",
       "     <use style=\"fill:#008000;stroke:#000000;stroke-linejoin:miter;stroke-width:0.5;\" x=\"247.177945574\" xlink:href=\"#m45eb232605\" y=\"117.419214424\"/>\n",
       "     <use style=\"fill:#008000;stroke:#000000;stroke-linejoin:miter;stroke-width:0.5;\" x=\"255.187514952\" xlink:href=\"#m45eb232605\" y=\"102.356999667\"/>\n",
       "     <use style=\"fill:#008000;stroke:#000000;stroke-linejoin:miter;stroke-width:0.5;\" x=\"263.19708433\" xlink:href=\"#m45eb232605\" y=\"83.2404673555\"/>\n",
       "     <use style=\"fill:#008000;stroke:#000000;stroke-linejoin:miter;stroke-width:0.5;\" x=\"271.206653708\" xlink:href=\"#m45eb232605\" y=\"70.9123613884\"/>\n",
       "     <use style=\"fill:#008000;stroke:#000000;stroke-linejoin:miter;stroke-width:0.5;\" x=\"279.216223086\" xlink:href=\"#m45eb232605\" y=\"61.8671440838\"/>\n",
       "     <use style=\"fill:#008000;stroke:#000000;stroke-linejoin:miter;stroke-width:0.5;\" x=\"287.225792464\" xlink:href=\"#m45eb232605\" y=\"55.9222354048\"/>\n",
       "     <use style=\"fill:#008000;stroke:#000000;stroke-linejoin:miter;stroke-width:0.5;\" x=\"295.235361842\" xlink:href=\"#m45eb232605\" y=\"49.6854186458\"/>\n",
       "     <use style=\"fill:#008000;stroke:#000000;stroke-linejoin:miter;stroke-width:0.5;\" x=\"303.24493122\" xlink:href=\"#m45eb232605\" y=\"47.5659243456\"/>\n",
       "     <use style=\"fill:#008000;stroke:#000000;stroke-linejoin:miter;stroke-width:0.5;\" x=\"311.254500598\" xlink:href=\"#m45eb232605\" y=\"46.9220529603\"/>\n",
       "     <use style=\"fill:#008000;stroke:#000000;stroke-linejoin:miter;stroke-width:0.5;\" x=\"319.264069976\" xlink:href=\"#m45eb232605\" y=\"48.0091637022\"/>\n",
       "     <use style=\"fill:#008000;stroke:#000000;stroke-linejoin:miter;stroke-width:0.5;\" x=\"327.273639354\" xlink:href=\"#m45eb232605\" y=\"50.4570533173\"/>\n",
       "     <use style=\"fill:#008000;stroke:#000000;stroke-linejoin:miter;stroke-width:0.5;\" x=\"335.283208732\" xlink:href=\"#m45eb232605\" y=\"53.048668514\"/>\n",
       "     <use style=\"fill:#008000;stroke:#000000;stroke-linejoin:miter;stroke-width:0.5;\" x=\"343.29277811\" xlink:href=\"#m45eb232605\" y=\"56.2855105565\"/>\n",
       "     <use style=\"fill:#008000;stroke:#000000;stroke-linejoin:miter;stroke-width:0.5;\" x=\"351.302347488\" xlink:href=\"#m45eb232605\" y=\"59.9536760489\"/>\n",
       "     <use style=\"fill:#008000;stroke:#000000;stroke-linejoin:miter;stroke-width:0.5;\" x=\"359.311916866\" xlink:href=\"#m45eb232605\" y=\"63.6039082712\"/>\n",
       "     <use style=\"fill:#008000;stroke:#000000;stroke-linejoin:miter;stroke-width:0.5;\" x=\"367.321486244\" xlink:href=\"#m45eb232605\" y=\"67.2149872055\"/>\n",
       "     <use style=\"fill:#008000;stroke:#000000;stroke-linejoin:miter;stroke-width:0.5;\" x=\"375.331055622\" xlink:href=\"#m45eb232605\" y=\"70.6018838183\"/>\n",
       "     <use style=\"fill:#008000;stroke:#000000;stroke-linejoin:miter;stroke-width:0.5;\" x=\"383.340625\" xlink:href=\"#m45eb232605\" y=\"73.7917960292\"/>\n",
       "    </g>\n",
       "   </g>\n",
       "   <g id=\"patch_9\">\n",
       "    <path d=\"\n",
       "M231.159 12.0391\n",
       "L383.341 12.0391\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_10\">\n",
       "    <path d=\"\n",
       "M231.159 235.239\n",
       "L231.159 12.0391\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_11\">\n",
       "    <path d=\"\n",
       "M383.341 235.239\n",
       "L383.341 12.0391\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_12\">\n",
       "    <path d=\"\n",
       "M231.159 235.239\n",
       "L383.341 235.239\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;\"/>\n",
       "   </g>\n",
       "   <g id=\"matplotlib.axis_3\">\n",
       "    <g id=\"xtick_7\">\n",
       "     <g id=\"line2d_36\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"231.158806818\" xlink:href=\"#mc7db9fdffb\" y=\"235.2390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"line2d_37\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"231.158806818\" xlink:href=\"#m5a7d422ac3\" y=\"12.0390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_19\">\n",
       "      <!-- 6 -->\n",
       "      <g transform=\"translate(228.641619318 246.8375)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#BitstreamVeraSans-Roman-36\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_8\">\n",
       "     <g id=\"line2d_38\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"261.595170455\" xlink:href=\"#mc7db9fdffb\" y=\"235.2390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"line2d_39\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"261.595170455\" xlink:href=\"#m5a7d422ac3\" y=\"12.0390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_20\">\n",
       "      <!-- 8 -->\n",
       "      <g transform=\"translate(259.095170455 246.8375)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#BitstreamVeraSans-Roman-38\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_9\">\n",
       "     <g id=\"line2d_40\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"292.031534091\" xlink:href=\"#mc7db9fdffb\" y=\"235.2390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"line2d_41\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"292.031534091\" xlink:href=\"#m5a7d422ac3\" y=\"12.0390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_21\">\n",
       "      <!-- 10 -->\n",
       "      <g transform=\"translate(286.550284091 246.8375)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#BitstreamVeraSans-Roman-31\"/>\n",
       "       <use x=\"63.623046875\" xlink:href=\"#BitstreamVeraSans-Roman-30\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_10\">\n",
       "     <g id=\"line2d_42\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"322.467897727\" xlink:href=\"#mc7db9fdffb\" y=\"235.2390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"line2d_43\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"322.467897727\" xlink:href=\"#m5a7d422ac3\" y=\"12.0390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_22\">\n",
       "      <!-- 12 -->\n",
       "      <g transform=\"translate(317.155397727 246.8375)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#BitstreamVeraSans-Roman-31\"/>\n",
       "       <use x=\"63.623046875\" xlink:href=\"#BitstreamVeraSans-Roman-32\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_11\">\n",
       "     <g id=\"line2d_44\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"352.904261364\" xlink:href=\"#mc7db9fdffb\" y=\"235.2390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"line2d_45\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"352.904261364\" xlink:href=\"#m5a7d422ac3\" y=\"12.0390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_23\">\n",
       "      <!-- 14 -->\n",
       "      <g transform=\"translate(347.371448864 246.8375)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#BitstreamVeraSans-Roman-31\"/>\n",
       "       <use x=\"63.623046875\" xlink:href=\"#BitstreamVeraSans-Roman-34\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_12\">\n",
       "     <g id=\"line2d_46\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"383.340625\" xlink:href=\"#mc7db9fdffb\" y=\"235.2390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"line2d_47\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"383.340625\" xlink:href=\"#m5a7d422ac3\" y=\"12.0390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_24\">\n",
       "      <!-- 16 -->\n",
       "      <g transform=\"translate(377.8421875 246.8375)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#BitstreamVeraSans-Roman-31\"/>\n",
       "       <use x=\"63.623046875\" xlink:href=\"#BitstreamVeraSans-Roman-36\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "   </g>\n",
       "   <g id=\"matplotlib.axis_4\">\n",
       "    <g id=\"ytick_9\">\n",
       "     <g id=\"line2d_48\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"231.158806818\" xlink:href=\"#md7965d1ba0\" y=\"235.2390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"line2d_49\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"383.340625\" xlink:href=\"#md9a1c1a7cd\" y=\"235.2390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_25\">\n",
       "      <!-- −1.02 -->\n",
       "      <g transform=\"translate(198.574431818 237.9984375)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#BitstreamVeraSans-Roman-2212\"/>\n",
       "       <use x=\"83.7890625\" xlink:href=\"#BitstreamVeraSans-Roman-31\"/>\n",
       "       <use x=\"147.412109375\" xlink:href=\"#BitstreamVeraSans-Roman-2e\"/>\n",
       "       <use x=\"179.19921875\" xlink:href=\"#BitstreamVeraSans-Roman-30\"/>\n",
       "       <use x=\"242.822265625\" xlink:href=\"#BitstreamVeraSans-Roman-32\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_10\">\n",
       "     <g id=\"line2d_50\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"231.158806818\" xlink:href=\"#md7965d1ba0\" y=\"198.0390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"line2d_51\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"383.340625\" xlink:href=\"#md9a1c1a7cd\" y=\"198.0390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_26\">\n",
       "      <!-- −1.00 -->\n",
       "      <g transform=\"translate(198.236931818 200.7984375)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#BitstreamVeraSans-Roman-2212\"/>\n",
       "       <use x=\"83.7890625\" xlink:href=\"#BitstreamVeraSans-Roman-31\"/>\n",
       "       <use x=\"147.412109375\" xlink:href=\"#BitstreamVeraSans-Roman-2e\"/>\n",
       "       <use x=\"179.19921875\" xlink:href=\"#BitstreamVeraSans-Roman-30\"/>\n",
       "       <use x=\"242.822265625\" xlink:href=\"#BitstreamVeraSans-Roman-30\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_11\">\n",
       "     <g id=\"line2d_52\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"231.158806818\" xlink:href=\"#md7965d1ba0\" y=\"160.8390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"line2d_53\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"383.340625\" xlink:href=\"#md9a1c1a7cd\" y=\"160.8390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_27\">\n",
       "      <!-- −0.98 -->\n",
       "      <g transform=\"translate(198.257244318 163.5984375)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#BitstreamVeraSans-Roman-2212\"/>\n",
       "       <use x=\"83.7890625\" xlink:href=\"#BitstreamVeraSans-Roman-30\"/>\n",
       "       <use x=\"147.412109375\" xlink:href=\"#BitstreamVeraSans-Roman-2e\"/>\n",
       "       <use x=\"179.19921875\" xlink:href=\"#BitstreamVeraSans-Roman-39\"/>\n",
       "       <use x=\"242.822265625\" xlink:href=\"#BitstreamVeraSans-Roman-38\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_12\">\n",
       "     <g id=\"line2d_54\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"231.158806818\" xlink:href=\"#md7965d1ba0\" y=\"123.6390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"line2d_55\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"383.340625\" xlink:href=\"#md9a1c1a7cd\" y=\"123.6390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_28\">\n",
       "      <!-- −0.96 -->\n",
       "      <g transform=\"translate(198.202556818 126.3984375)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#BitstreamVeraSans-Roman-2212\"/>\n",
       "       <use x=\"83.7890625\" xlink:href=\"#BitstreamVeraSans-Roman-30\"/>\n",
       "       <use x=\"147.412109375\" xlink:href=\"#BitstreamVeraSans-Roman-2e\"/>\n",
       "       <use x=\"179.19921875\" xlink:href=\"#BitstreamVeraSans-Roman-39\"/>\n",
       "       <use x=\"242.822265625\" xlink:href=\"#BitstreamVeraSans-Roman-36\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_13\">\n",
       "     <g id=\"line2d_56\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"231.158806818\" xlink:href=\"#md7965d1ba0\" y=\"86.4390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"line2d_57\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"383.340625\" xlink:href=\"#md9a1c1a7cd\" y=\"86.4390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_29\">\n",
       "      <!-- −0.94 -->\n",
       "      <g transform=\"translate(198.133806818 89.1984375)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#BitstreamVeraSans-Roman-2212\"/>\n",
       "       <use x=\"83.7890625\" xlink:href=\"#BitstreamVeraSans-Roman-30\"/>\n",
       "       <use x=\"147.412109375\" xlink:href=\"#BitstreamVeraSans-Roman-2e\"/>\n",
       "       <use x=\"179.19921875\" xlink:href=\"#BitstreamVeraSans-Roman-39\"/>\n",
       "       <use x=\"242.822265625\" xlink:href=\"#BitstreamVeraSans-Roman-34\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_14\">\n",
       "     <g id=\"line2d_58\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"231.158806818\" xlink:href=\"#md7965d1ba0\" y=\"49.2390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"line2d_59\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"383.340625\" xlink:href=\"#md9a1c1a7cd\" y=\"49.2390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_30\">\n",
       "      <!-- −0.92 -->\n",
       "      <g transform=\"translate(198.574431818 51.9984375)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#BitstreamVeraSans-Roman-2212\"/>\n",
       "       <use x=\"83.7890625\" xlink:href=\"#BitstreamVeraSans-Roman-30\"/>\n",
       "       <use x=\"147.412109375\" xlink:href=\"#BitstreamVeraSans-Roman-2e\"/>\n",
       "       <use x=\"179.19921875\" xlink:href=\"#BitstreamVeraSans-Roman-39\"/>\n",
       "       <use x=\"242.822265625\" xlink:href=\"#BitstreamVeraSans-Roman-32\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_15\">\n",
       "     <g id=\"line2d_60\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"231.158806818\" xlink:href=\"#md7965d1ba0\" y=\"12.0390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"line2d_61\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"383.340625\" xlink:href=\"#md9a1c1a7cd\" y=\"12.0390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_31\">\n",
       "      <!-- −0.90 -->\n",
       "      <g transform=\"translate(198.236931818 14.7984375)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#BitstreamVeraSans-Roman-2212\"/>\n",
       "       <use x=\"83.7890625\" xlink:href=\"#BitstreamVeraSans-Roman-30\"/>\n",
       "       <use x=\"147.412109375\" xlink:href=\"#BitstreamVeraSans-Roman-2e\"/>\n",
       "       <use x=\"179.19921875\" xlink:href=\"#BitstreamVeraSans-Roman-39\"/>\n",
       "       <use x=\"242.822265625\" xlink:href=\"#BitstreamVeraSans-Roman-30\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "   </g>\n",
       "  </g>\n",
       " </g>\n",
       " <defs>\n",
       "  <clipPath id=\"p6f87c8219a\">\n",
       "   <rect height=\"223.2\" width=\"152.181818182\" x=\"48.540625\" y=\"12.0390625\"/>\n",
       "  </clipPath>\n",
       "  <clipPath id=\"pebf3d5afac\">\n",
       "   <rect height=\"223.2\" width=\"152.181818182\" x=\"231.158806818\" y=\"12.0390625\"/>\n",
       "  </clipPath>\n",
       " </defs>\n",
       "</svg>\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fce76f99dd8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, (axl, axr) = subplots(1, 2, sharex=True)\n",
    "plot_cv_scores(lm, valid_scores, train_scores, ax=axl)\n",
    "plot_cv_scores(lm, valid_scores, ax=axr)\n",
    "axl.set_xlabel('$\\lambda$')\n",
    "axl.set_ylabel('score')\n",
    "axl.legend();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 255,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "est = CollaborativeFiltering(num_athletes, num_segments, lm=10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Model selection: number of features"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 256,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "num_features = [1,2,4,8,16,32,64]\n",
    "\n",
    "train_scores, valid_scores =\\\n",
    "    validation_curve(est, X, y, 'num_features', num_features,\n",
    "                     scoring='mean_squared_error', \n",
    "                     cv=8, n_jobs=4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 257,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/svg+xml": [
       "<?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?>\n",
       "<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n",
       "  \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n",
       "<!-- Created with matplotlib (http://matplotlib.org/) -->\n",
       "<svg height=\"271pt\" version=\"1.1\" viewBox=\"0 0 406 271\" width=\"406pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
       " <defs>\n",
       "  <style type=\"text/css\">\n",
       "*{stroke-linecap:butt;stroke-linejoin:round;}\n",
       "  </style>\n",
       " </defs>\n",
       " <g id=\"figure_1\">\n",
       "  <g id=\"patch_1\">\n",
       "   <path d=\"\n",
       "M0 271.817\n",
       "L406.45 271.817\n",
       "L406.45 0\n",
       "L0 0\n",
       "L0 271.817\" style=\"fill:none;\"/>\n",
       "  </g>\n",
       "  <g id=\"axes_1\">\n",
       "   <g id=\"patch_2\">\n",
       "    <path d=\"\n",
       "M54.8 235.239\n",
       "L206.982 235.239\n",
       "L206.982 12.0391\n",
       "L54.8 12.0391\n",
       "z\n",
       "\" style=\"fill:#ffffff;\"/>\n",
       "   </g>\n",
       "   <g id=\"PolyCollection_1\">\n",
       "    <defs>\n",
       "     <path d=\"\n",
       "M54.8 -73.7571\n",
       "L54.8 -72.4969\n",
       "L77.7056 -94.9152\n",
       "L100.611 -129.305\n",
       "L123.517 -174.588\n",
       "L146.423 -215.956\n",
       "L169.328 -239.408\n",
       "L192.234 -245.123\n",
       "L192.234 -246.37\n",
       "L192.234 -246.37\n",
       "L169.328 -240.974\n",
       "L146.423 -217.586\n",
       "L123.517 -176.05\n",
       "L100.611 -131.15\n",
       "L77.7056 -96.4435\n",
       "L54.8 -73.7571\n",
       "z\n",
       "\" id=\"mf485ba0f32\" style=\"stroke:#000000;stroke-opacity:0.3;\"/>\n",
       "    </defs>\n",
       "    <g clip-path=\"url(#p2f9be9b7ad)\">\n",
       "     <use style=\"fill:#0000ff;fill-opacity:0.3;stroke:#000000;stroke-opacity:0.3;\" x=\"0.0\" xlink:href=\"#mf485ba0f32\" y=\"271.8171875\"/>\n",
       "    </g>\n",
       "   </g>\n",
       "   <g id=\"PolyCollection_2\">\n",
       "    <defs>\n",
       "     <path d=\"\n",
       "M54.8 -54.2977\n",
       "L54.8 -41.8368\n",
       "L77.7056 -44.653\n",
       "L100.611 -46.23\n",
       "L123.517 -47.0724\n",
       "L146.423 -50.8256\n",
       "L169.328 -54.2252\n",
       "L192.234 -55.6067\n",
       "L192.234 -69.7135\n",
       "L192.234 -69.7135\n",
       "L169.328 -68.5475\n",
       "L146.423 -64.6338\n",
       "L123.517 -60.0805\n",
       "L100.611 -58.6891\n",
       "L77.7056 -57.1703\n",
       "L54.8 -54.2977\n",
       "z\n",
       "\" id=\"mf0817f88bc\" style=\"stroke:#000000;stroke-opacity:0.3;\"/>\n",
       "    </defs>\n",
       "    <g clip-path=\"url(#p2f9be9b7ad)\">\n",
       "     <use style=\"fill:#0000ff;fill-opacity:0.3;stroke:#000000;stroke-opacity:0.3;\" x=\"0.0\" xlink:href=\"#mf0817f88bc\" y=\"271.8171875\"/>\n",
       "    </g>\n",
       "   </g>\n",
       "   <g id=\"line2d_1\">\n",
       "    <path clip-path=\"url(#p2f9be9b7ad)\" d=\"\n",
       "M54.8 198.69\n",
       "L77.7056 176.138\n",
       "L100.611 141.59\n",
       "L123.517 96.498\n",
       "L146.423 55.0464\n",
       "L169.328 31.6265\n",
       "L192.234 26.0708\" style=\"fill:none;stroke:#0000ff;stroke-linecap:square;\"/>\n",
       "    <defs>\n",
       "     <path d=\"\n",
       "M0 3\n",
       "C0.795609 3 1.55874 2.6839 2.12132 2.12132\n",
       "C2.6839 1.55874 3 0.795609 3 0\n",
       "C3 -0.795609 2.6839 -1.55874 2.12132 -2.12132\n",
       "C1.55874 -2.6839 0.795609 -3 0 -3\n",
       "C-0.795609 -3 -1.55874 -2.6839 -2.12132 -2.12132\n",
       "C-2.6839 -1.55874 -3 -0.795609 -3 0\n",
       "C-3 0.795609 -2.6839 1.55874 -2.12132 2.12132\n",
       "C-1.55874 2.6839 -0.795609 3 0 3\n",
       "z\n",
       "\" id=\"mdb00ba95ec\" style=\"stroke:#000000;stroke-width:0.5;\"/>\n",
       "    </defs>\n",
       "    <g clip-path=\"url(#p2f9be9b7ad)\">\n",
       "     <use style=\"fill:#0000ff;stroke:#000000;stroke-width:0.5;\" x=\"54.8\" xlink:href=\"#mdb00ba95ec\" y=\"198.690171802\"/>\n",
       "     <use style=\"fill:#0000ff;stroke:#000000;stroke-width:0.5;\" x=\"77.7056460337\" xlink:href=\"#mdb00ba95ec\" y=\"176.137818936\"/>\n",
       "     <use style=\"fill:#0000ff;stroke:#000000;stroke-width:0.5;\" x=\"100.611292067\" xlink:href=\"#mdb00ba95ec\" y=\"141.589990218\"/>\n",
       "     <use style=\"fill:#0000ff;stroke:#000000;stroke-width:0.5;\" x=\"123.516938101\" xlink:href=\"#mdb00ba95ec\" y=\"96.4980153067\"/>\n",
       "     <use style=\"fill:#0000ff;stroke:#000000;stroke-width:0.5;\" x=\"146.422584135\" xlink:href=\"#mdb00ba95ec\" y=\"55.0464318106\"/>\n",
       "     <use style=\"fill:#0000ff;stroke:#000000;stroke-width:0.5;\" x=\"169.328230169\" xlink:href=\"#mdb00ba95ec\" y=\"31.6265362264\"/>\n",
       "     <use style=\"fill:#0000ff;stroke:#000000;stroke-width:0.5;\" x=\"192.233876202\" xlink:href=\"#mdb00ba95ec\" y=\"26.0707827455\"/>\n",
       "    </g>\n",
       "   </g>\n",
       "   <g id=\"line2d_2\">\n",
       "    <path clip-path=\"url(#p2f9be9b7ad)\" d=\"\n",
       "M54.8 223.75\n",
       "L77.7056 220.906\n",
       "L100.611 219.358\n",
       "L123.517 218.241\n",
       "L146.423 214.088\n",
       "L169.328 210.431\n",
       "L192.234 209.157\" style=\"fill:none;stroke:#008000;stroke-linecap:square;\"/>\n",
       "    <defs>\n",
       "     <path d=\"\n",
       "M-3 3\n",
       "L3 3\n",
       "L3 -3\n",
       "L-3 -3\n",
       "z\n",
       "\" id=\"m45eb232605\" style=\"stroke:#000000;stroke-linejoin:miter;stroke-width:0.5;\"/>\n",
       "    </defs>\n",
       "    <g clip-path=\"url(#p2f9be9b7ad)\">\n",
       "     <use style=\"fill:#008000;stroke:#000000;stroke-linejoin:miter;stroke-width:0.5;\" x=\"54.8\" xlink:href=\"#m45eb232605\" y=\"223.74994318\"/>\n",
       "     <use style=\"fill:#008000;stroke:#000000;stroke-linejoin:miter;stroke-width:0.5;\" x=\"77.7056460337\" xlink:href=\"#m45eb232605\" y=\"220.905560349\"/>\n",
       "     <use style=\"fill:#008000;stroke:#000000;stroke-linejoin:miter;stroke-width:0.5;\" x=\"100.611292067\" xlink:href=\"#m45eb232605\" y=\"219.357656159\"/>\n",
       "     <use style=\"fill:#008000;stroke:#000000;stroke-linejoin:miter;stroke-width:0.5;\" x=\"123.516938101\" xlink:href=\"#m45eb232605\" y=\"218.240713729\"/>\n",
       "     <use style=\"fill:#008000;stroke:#000000;stroke-linejoin:miter;stroke-width:0.5;\" x=\"146.422584135\" xlink:href=\"#m45eb232605\" y=\"214.08752281\"/>\n",
       "     <use style=\"fill:#008000;stroke:#000000;stroke-linejoin:miter;stroke-width:0.5;\" x=\"169.328230169\" xlink:href=\"#m45eb232605\" y=\"210.43081424\"/>\n",
       "     <use style=\"fill:#008000;stroke:#000000;stroke-linejoin:miter;stroke-width:0.5;\" x=\"192.233876202\" xlink:href=\"#m45eb232605\" y=\"209.157058421\"/>\n",
       "    </g>\n",
       "   </g>\n",
       "   <g id=\"patch_3\">\n",
       "    <path d=\"\n",
       "M54.8 12.0391\n",
       "L206.982 12.0391\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_4\">\n",
       "    <path d=\"\n",
       "M54.8 235.239\n",
       "L54.8 12.0391\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_5\">\n",
       "    <path d=\"\n",
       "M206.982 235.239\n",
       "L206.982 12.0391\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_6\">\n",
       "    <path d=\"\n",
       "M54.8 235.239\n",
       "L206.982 235.239\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;\"/>\n",
       "   </g>\n",
       "   <g id=\"matplotlib.axis_1\">\n",
       "    <g id=\"xtick_1\">\n",
       "     <g id=\"line2d_3\">\n",
       "      <defs>\n",
       "       <path d=\"\n",
       "M0 0\n",
       "L0 -4\" id=\"mc7db9fdffb\" style=\"stroke:#000000;stroke-width:0.5;\"/>\n",
       "      </defs>\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"54.8\" xlink:href=\"#mc7db9fdffb\" y=\"235.2390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"line2d_4\">\n",
       "      <defs>\n",
       "       <path d=\"\n",
       "M0 0\n",
       "L0 4\" id=\"m5a7d422ac3\" style=\"stroke:#000000;stroke-width:0.5;\"/>\n",
       "      </defs>\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"54.8\" xlink:href=\"#m5a7d422ac3\" y=\"12.0390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_1\">\n",
       "      <!-- $\\mathdefault{10^{0}}$ -->\n",
       "      <defs>\n",
       "       <path d=\"\n",
       "M12.4062 8.29688\n",
       "L28.5156 8.29688\n",
       "L28.5156 63.9219\n",
       "L10.9844 60.4062\n",
       "L10.9844 69.3906\n",
       "L28.4219 72.9062\n",
       "L38.2812 72.9062\n",
       "L38.2812 8.29688\n",
       "L54.3906 8.29688\n",
       "L54.3906 0\n",
       "L12.4062 0\n",
       "z\n",
       "\" id=\"BitstreamVeraSans-Roman-31\"/>\n",
       "       <path d=\"\n",
       "M31.7812 66.4062\n",
       "Q24.1719 66.4062 20.3281 58.9062\n",
       "Q16.5 51.4219 16.5 36.375\n",
       "Q16.5 21.3906 20.3281 13.8906\n",
       "Q24.1719 6.39062 31.7812 6.39062\n",
       "Q39.4531 6.39062 43.2812 13.8906\n",
       "Q47.125 21.3906 47.125 36.375\n",
       "Q47.125 51.4219 43.2812 58.9062\n",
       "Q39.4531 66.4062 31.7812 66.4062\n",
       "M31.7812 74.2188\n",
       "Q44.0469 74.2188 50.5156 64.5156\n",
       "Q56.9844 54.8281 56.9844 36.375\n",
       "Q56.9844 17.9688 50.5156 8.26562\n",
       "Q44.0469 -1.42188 31.7812 -1.42188\n",
       "Q19.5312 -1.42188 13.0625 8.26562\n",
       "Q6.59375 17.9688 6.59375 36.375\n",
       "Q6.59375 54.8281 13.0625 64.5156\n",
       "Q19.5312 74.2188 31.7812 74.2188\" id=\"BitstreamVeraSans-Roman-30\"/>\n",
       "      </defs>\n",
       "      <g transform=\"translate(45.15 247.859375)scale(0.1 -0.1)\">\n",
       "       <use transform=\"translate(0.0 0.546875)\" xlink:href=\"#BitstreamVeraSans-Roman-31\"/>\n",
       "       <use transform=\"translate(63.623046875 0.546875)\" xlink:href=\"#BitstreamVeraSans-Roman-30\"/>\n",
       "       <use transform=\"translate(127.24609375 53.046875)scale(0.7)\" xlink:href=\"#BitstreamVeraSans-Roman-30\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_2\">\n",
       "     <g id=\"line2d_5\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"130.890909091\" xlink:href=\"#mc7db9fdffb\" y=\"235.2390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"line2d_6\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"130.890909091\" xlink:href=\"#m5a7d422ac3\" y=\"12.0390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_2\">\n",
       "      <!-- $\\mathdefault{10^{1}}$ -->\n",
       "      <g transform=\"translate(121.240909091 247.759375)scale(0.1 -0.1)\">\n",
       "       <use transform=\"translate(0.0 0.46562500000000284)\" xlink:href=\"#BitstreamVeraSans-Roman-31\"/>\n",
       "       <use transform=\"translate(63.623046875 0.46562500000000284)\" xlink:href=\"#BitstreamVeraSans-Roman-30\"/>\n",
       "       <use transform=\"translate(127.24609375 52.965625)scale(0.7)\" xlink:href=\"#BitstreamVeraSans-Roman-31\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_3\">\n",
       "     <g id=\"line2d_7\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"206.981818182\" xlink:href=\"#mc7db9fdffb\" y=\"235.2390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"line2d_8\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"206.981818182\" xlink:href=\"#m5a7d422ac3\" y=\"12.0390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_3\">\n",
       "      <!-- $\\mathdefault{10^{2}}$ -->\n",
       "      <defs>\n",
       "       <path d=\"\n",
       "M19.1875 8.29688\n",
       "L53.6094 8.29688\n",
       "L53.6094 0\n",
       "L7.32812 0\n",
       "L7.32812 8.29688\n",
       "Q12.9375 14.1094 22.625 23.8906\n",
       "Q32.3281 33.6875 34.8125 36.5312\n",
       "Q39.5469 41.8438 41.4219 45.5312\n",
       "Q43.3125 49.2188 43.3125 52.7812\n",
       "Q43.3125 58.5938 39.2344 62.25\n",
       "Q35.1562 65.9219 28.6094 65.9219\n",
       "Q23.9688 65.9219 18.8125 64.3125\n",
       "Q13.6719 62.7031 7.8125 59.4219\n",
       "L7.8125 69.3906\n",
       "Q13.7656 71.7812 18.9375 73\n",
       "Q24.125 74.2188 28.4219 74.2188\n",
       "Q39.75 74.2188 46.4844 68.5469\n",
       "Q53.2188 62.8906 53.2188 53.4219\n",
       "Q53.2188 48.9219 51.5312 44.8906\n",
       "Q49.8594 40.875 45.4062 35.4062\n",
       "Q44.1875 33.9844 37.6406 27.2188\n",
       "Q31.1094 20.4531 19.1875 8.29688\" id=\"BitstreamVeraSans-Roman-32\"/>\n",
       "      </defs>\n",
       "      <g transform=\"translate(197.331818182 247.859375)scale(0.1 -0.1)\">\n",
       "       <use transform=\"translate(0.0 0.546875)\" xlink:href=\"#BitstreamVeraSans-Roman-31\"/>\n",
       "       <use transform=\"translate(63.623046875 0.546875)\" xlink:href=\"#BitstreamVeraSans-Roman-30\"/>\n",
       "       <use transform=\"translate(127.24609375 53.046875)scale(0.7)\" xlink:href=\"#BitstreamVeraSans-Roman-32\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_4\">\n",
       "     <g id=\"line2d_9\">\n",
       "      <defs>\n",
       "       <path d=\"\n",
       "M0 0\n",
       "L0 -2\" id=\"mc21db286a6\" style=\"stroke:#000000;stroke-width:0.5;\"/>\n",
       "      </defs>\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"77.7056460337\" xlink:href=\"#mc21db286a6\" y=\"235.2390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"line2d_10\">\n",
       "      <defs>\n",
       "       <path d=\"\n",
       "M0 0\n",
       "L0 2\" id=\"ma9c915e141\" style=\"stroke:#000000;stroke-width:0.5;\"/>\n",
       "      </defs>\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"77.7056460337\" xlink:href=\"#ma9c915e141\" y=\"12.0390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_5\">\n",
       "     <g id=\"line2d_11\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"91.1045900182\" xlink:href=\"#mc21db286a6\" y=\"235.2390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"line2d_12\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"91.1045900182\" xlink:href=\"#ma9c915e141\" y=\"12.0390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_6\">\n",
       "     <g id=\"line2d_13\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"100.611292067\" xlink:href=\"#mc21db286a6\" y=\"235.2390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"line2d_14\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"100.611292067\" xlink:href=\"#ma9c915e141\" y=\"12.0390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_7\">\n",
       "     <g id=\"line2d_15\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"107.985263057\" xlink:href=\"#mc21db286a6\" y=\"235.2390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"line2d_16\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"107.985263057\" xlink:href=\"#ma9c915e141\" y=\"12.0390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_8\">\n",
       "     <g id=\"line2d_17\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"114.010236052\" xlink:href=\"#mc21db286a6\" y=\"235.2390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"line2d_18\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"114.010236052\" xlink:href=\"#ma9c915e141\" y=\"12.0390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_9\">\n",
       "     <g id=\"line2d_19\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"119.104278136\" xlink:href=\"#mc21db286a6\" y=\"235.2390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"line2d_20\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"119.104278136\" xlink:href=\"#ma9c915e141\" y=\"12.0390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_10\">\n",
       "     <g id=\"line2d_21\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"123.516938101\" xlink:href=\"#mc21db286a6\" y=\"235.2390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"line2d_22\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"123.516938101\" xlink:href=\"#ma9c915e141\" y=\"12.0390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_11\">\n",
       "     <g id=\"line2d_23\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"127.409180036\" xlink:href=\"#mc21db286a6\" y=\"235.2390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"line2d_24\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"127.409180036\" xlink:href=\"#ma9c915e141\" y=\"12.0390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_12\">\n",
       "     <g id=\"line2d_25\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"153.796555125\" xlink:href=\"#mc21db286a6\" y=\"235.2390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"line2d_26\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"153.796555125\" xlink:href=\"#ma9c915e141\" y=\"12.0390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_13\">\n",
       "     <g id=\"line2d_27\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"167.195499109\" xlink:href=\"#mc21db286a6\" y=\"235.2390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"line2d_28\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"167.195499109\" xlink:href=\"#ma9c915e141\" y=\"12.0390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_14\">\n",
       "     <g id=\"line2d_29\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"176.702201158\" xlink:href=\"#mc21db286a6\" y=\"235.2390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"line2d_30\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"176.702201158\" xlink:href=\"#ma9c915e141\" y=\"12.0390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_15\">\n",
       "     <g id=\"line2d_31\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"184.076172148\" xlink:href=\"#mc21db286a6\" y=\"235.2390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"line2d_32\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"184.076172148\" xlink:href=\"#ma9c915e141\" y=\"12.0390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_16\">\n",
       "     <g id=\"line2d_33\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"190.101145143\" xlink:href=\"#mc21db286a6\" y=\"235.2390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"line2d_34\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"190.101145143\" xlink:href=\"#ma9c915e141\" y=\"12.0390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_17\">\n",
       "     <g id=\"line2d_35\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"195.195187227\" xlink:href=\"#mc21db286a6\" y=\"235.2390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"line2d_36\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"195.195187227\" xlink:href=\"#ma9c915e141\" y=\"12.0390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_18\">\n",
       "     <g id=\"line2d_37\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"199.607847192\" xlink:href=\"#mc21db286a6\" y=\"235.2390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"line2d_38\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"199.607847192\" xlink:href=\"#ma9c915e141\" y=\"12.0390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_19\">\n",
       "     <g id=\"line2d_39\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"203.500089127\" xlink:href=\"#mc21db286a6\" y=\"235.2390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"line2d_40\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"203.500089127\" xlink:href=\"#ma9c915e141\" y=\"12.0390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"text_4\">\n",
       "     <!-- number of features -->\n",
       "     <defs>\n",
       "      <path d=\"\n",
       "M56.2031 29.5938\n",
       "L56.2031 25.2031\n",
       "L14.8906 25.2031\n",
       "Q15.4844 15.9219 20.4844 11.0625\n",
       "Q25.4844 6.20312 34.4219 6.20312\n",
       "Q39.5938 6.20312 44.4531 7.46875\n",
       "Q49.3125 8.73438 54.1094 11.2812\n",
       "L54.1094 2.78125\n",
       "Q49.2656 0.734375 44.1875 -0.34375\n",
       "Q39.1094 -1.42188 33.8906 -1.42188\n",
       "Q20.7969 -1.42188 13.1562 6.1875\n",
       "Q5.51562 13.8125 5.51562 26.8125\n",
       "Q5.51562 40.2344 12.7656 48.1094\n",
       "Q20.0156 56 32.3281 56\n",
       "Q43.3594 56 49.7812 48.8906\n",
       "Q56.2031 41.7969 56.2031 29.5938\n",
       "M47.2188 32.2344\n",
       "Q47.125 39.5938 43.0938 43.9844\n",
       "Q39.0625 48.3906 32.4219 48.3906\n",
       "Q24.9062 48.3906 20.3906 44.1406\n",
       "Q15.875 39.8906 15.1875 32.1719\n",
       "z\n",
       "\" id=\"BitstreamVeraSans-Roman-65\"/>\n",
       "      <path d=\"\n",
       "M37.1094 75.9844\n",
       "L37.1094 68.5\n",
       "L28.5156 68.5\n",
       "Q23.6875 68.5 21.7969 66.5469\n",
       "Q19.9219 64.5938 19.9219 59.5156\n",
       "L19.9219 54.6875\n",
       "L34.7188 54.6875\n",
       "L34.7188 47.7031\n",
       "L19.9219 47.7031\n",
       "L19.9219 0\n",
       "L10.8906 0\n",
       "L10.8906 47.7031\n",
       "L2.29688 47.7031\n",
       "L2.29688 54.6875\n",
       "L10.8906 54.6875\n",
       "L10.8906 58.5\n",
       "Q10.8906 67.625 15.1406 71.7969\n",
       "Q19.3906 75.9844 28.6094 75.9844\n",
       "z\n",
       "\" id=\"BitstreamVeraSans-Roman-66\"/>\n",
       "      <path d=\"\n",
       "M8.5 21.5781\n",
       "L8.5 54.6875\n",
       "L17.4844 54.6875\n",
       "L17.4844 21.9219\n",
       "Q17.4844 14.1562 20.5 10.2656\n",
       "Q23.5312 6.39062 29.5938 6.39062\n",
       "Q36.8594 6.39062 41.0781 11.0312\n",
       "Q45.3125 15.6719 45.3125 23.6875\n",
       "L45.3125 54.6875\n",
       "L54.2969 54.6875\n",
       "L54.2969 0\n",
       "L45.3125 0\n",
       "L45.3125 8.40625\n",
       "Q42.0469 3.42188 37.7188 1\n",
       "Q33.4062 -1.42188 27.6875 -1.42188\n",
       "Q18.2656 -1.42188 13.375 4.4375\n",
       "Q8.5 10.2969 8.5 21.5781\" id=\"BitstreamVeraSans-Roman-75\"/>\n",
       "      <path d=\"\n",
       "M48.6875 27.2969\n",
       "Q48.6875 37.2031 44.6094 42.8438\n",
       "Q40.5312 48.4844 33.4062 48.4844\n",
       "Q26.2656 48.4844 22.1875 42.8438\n",
       "Q18.1094 37.2031 18.1094 27.2969\n",
       "Q18.1094 17.3906 22.1875 11.75\n",
       "Q26.2656 6.10938 33.4062 6.10938\n",
       "Q40.5312 6.10938 44.6094 11.75\n",
       "Q48.6875 17.3906 48.6875 27.2969\n",
       "M18.1094 46.3906\n",
       "Q20.9531 51.2656 25.2656 53.625\n",
       "Q29.5938 56 35.5938 56\n",
       "Q45.5625 56 51.7812 48.0938\n",
       "Q58.0156 40.1875 58.0156 27.2969\n",
       "Q58.0156 14.4062 51.7812 6.48438\n",
       "Q45.5625 -1.42188 35.5938 -1.42188\n",
       "Q29.5938 -1.42188 25.2656 0.953125\n",
       "Q20.9531 3.32812 18.1094 8.20312\n",
       "L18.1094 0\n",
       "L9.07812 0\n",
       "L9.07812 75.9844\n",
       "L18.1094 75.9844\n",
       "z\n",
       "\" id=\"BitstreamVeraSans-Roman-62\"/>\n",
       "      <path d=\"\n",
       "M44.2812 53.0781\n",
       "L44.2812 44.5781\n",
       "Q40.4844 46.5312 36.375 47.5\n",
       "Q32.2812 48.4844 27.875 48.4844\n",
       "Q21.1875 48.4844 17.8438 46.4375\n",
       "Q14.5 44.3906 14.5 40.2812\n",
       "Q14.5 37.1562 16.8906 35.375\n",
       "Q19.2812 33.5938 26.5156 31.9844\n",
       "L29.5938 31.2969\n",
       "Q39.1562 29.25 43.1875 25.5156\n",
       "Q47.2188 21.7812 47.2188 15.0938\n",
       "Q47.2188 7.46875 41.1875 3.01562\n",
       "Q35.1562 -1.42188 24.6094 -1.42188\n",
       "Q20.2188 -1.42188 15.4531 -0.5625\n",
       "Q10.6875 0.296875 5.42188 2\n",
       "L5.42188 11.2812\n",
       "Q10.4062 8.6875 15.2344 7.39062\n",
       "Q20.0625 6.10938 24.8125 6.10938\n",
       "Q31.1562 6.10938 34.5625 8.28125\n",
       "Q37.9844 10.4531 37.9844 14.4062\n",
       "Q37.9844 18.0625 35.5156 20.0156\n",
       "Q33.0625 21.9688 24.7031 23.7812\n",
       "L21.5781 24.5156\n",
       "Q13.2344 26.2656 9.51562 29.9062\n",
       "Q5.8125 33.5469 5.8125 39.8906\n",
       "Q5.8125 47.6094 11.2812 51.7969\n",
       "Q16.75 56 26.8125 56\n",
       "Q31.7812 56 36.1719 55.2656\n",
       "Q40.5781 54.5469 44.2812 53.0781\" id=\"BitstreamVeraSans-Roman-73\"/>\n",
       "      <path d=\"\n",
       "M34.2812 27.4844\n",
       "Q23.3906 27.4844 19.1875 25\n",
       "Q14.9844 22.5156 14.9844 16.5\n",
       "Q14.9844 11.7188 18.1406 8.90625\n",
       "Q21.2969 6.10938 26.7031 6.10938\n",
       "Q34.1875 6.10938 38.7031 11.4062\n",
       "Q43.2188 16.7031 43.2188 25.4844\n",
       "L43.2188 27.4844\n",
       "z\n",
       "\n",
       "M52.2031 31.2031\n",
       "L52.2031 0\n",
       "L43.2188 0\n",
       "L43.2188 8.29688\n",
       "Q40.1406 3.32812 35.5469 0.953125\n",
       "Q30.9531 -1.42188 24.3125 -1.42188\n",
       "Q15.9219 -1.42188 10.9531 3.29688\n",
       "Q6 8.01562 6 15.9219\n",
       "Q6 25.1406 12.1719 29.8281\n",
       "Q18.3594 34.5156 30.6094 34.5156\n",
       "L43.2188 34.5156\n",
       "L43.2188 35.4062\n",
       "Q43.2188 41.6094 39.1406 45\n",
       "Q35.0625 48.3906 27.6875 48.3906\n",
       "Q23 48.3906 18.5469 47.2656\n",
       "Q14.1094 46.1406 10.0156 43.8906\n",
       "L10.0156 52.2031\n",
       "Q14.9375 54.1094 19.5781 55.0469\n",
       "Q24.2188 56 28.6094 56\n",
       "Q40.4844 56 46.3438 49.8438\n",
       "Q52.2031 43.7031 52.2031 31.2031\" id=\"BitstreamVeraSans-Roman-61\"/>\n",
       "      <path d=\"\n",
       "M52 44.1875\n",
       "Q55.375 50.25 60.0625 53.125\n",
       "Q64.75 56 71.0938 56\n",
       "Q79.6406 56 84.2812 50.0156\n",
       "Q88.9219 44.0469 88.9219 33.0156\n",
       "L88.9219 0\n",
       "L79.8906 0\n",
       "L79.8906 32.7188\n",
       "Q79.8906 40.5781 77.0938 44.375\n",
       "Q74.3125 48.1875 68.6094 48.1875\n",
       "Q61.625 48.1875 57.5625 43.5469\n",
       "Q53.5156 38.9219 53.5156 30.9062\n",
       "L53.5156 0\n",
       "L44.4844 0\n",
       "L44.4844 32.7188\n",
       "Q44.4844 40.625 41.7031 44.4062\n",
       "Q38.9219 48.1875 33.1094 48.1875\n",
       "Q26.2188 48.1875 22.1562 43.5312\n",
       "Q18.1094 38.875 18.1094 30.9062\n",
       "L18.1094 0\n",
       "L9.07812 0\n",
       "L9.07812 54.6875\n",
       "L18.1094 54.6875\n",
       "L18.1094 46.1875\n",
       "Q21.1875 51.2188 25.4844 53.6094\n",
       "Q29.7812 56 35.6875 56\n",
       "Q41.6562 56 45.8281 52.9688\n",
       "Q50 49.9531 52 44.1875\" id=\"BitstreamVeraSans-Roman-6d\"/>\n",
       "      <path id=\"BitstreamVeraSans-Roman-20\"/>\n",
       "      <path d=\"\n",
       "M54.8906 33.0156\n",
       "L54.8906 0\n",
       "L45.9062 0\n",
       "L45.9062 32.7188\n",
       "Q45.9062 40.4844 42.875 44.3281\n",
       "Q39.8438 48.1875 33.7969 48.1875\n",
       "Q26.5156 48.1875 22.3125 43.5469\n",
       "Q18.1094 38.9219 18.1094 30.9062\n",
       "L18.1094 0\n",
       "L9.07812 0\n",
       "L9.07812 54.6875\n",
       "L18.1094 54.6875\n",
       "L18.1094 46.1875\n",
       "Q21.3438 51.125 25.7031 53.5625\n",
       "Q30.0781 56 35.7969 56\n",
       "Q45.2188 56 50.0469 50.1719\n",
       "Q54.8906 44.3438 54.8906 33.0156\" id=\"BitstreamVeraSans-Roman-6e\"/>\n",
       "      <path d=\"\n",
       "M18.3125 70.2188\n",
       "L18.3125 54.6875\n",
       "L36.8125 54.6875\n",
       "L36.8125 47.7031\n",
       "L18.3125 47.7031\n",
       "L18.3125 18.0156\n",
       "Q18.3125 11.3281 20.1406 9.42188\n",
       "Q21.9688 7.51562 27.5938 7.51562\n",
       "L36.8125 7.51562\n",
       "L36.8125 0\n",
       "L27.5938 0\n",
       "Q17.1875 0 13.2344 3.875\n",
       "Q9.28125 7.76562 9.28125 18.0156\n",
       "L9.28125 47.7031\n",
       "L2.6875 47.7031\n",
       "L2.6875 54.6875\n",
       "L9.28125 54.6875\n",
       "L9.28125 70.2188\n",
       "z\n",
       "\" id=\"BitstreamVeraSans-Roman-74\"/>\n",
       "      <path d=\"\n",
       "M30.6094 48.3906\n",
       "Q23.3906 48.3906 19.1875 42.75\n",
       "Q14.9844 37.1094 14.9844 27.2969\n",
       "Q14.9844 17.4844 19.1562 11.8438\n",
       "Q23.3438 6.20312 30.6094 6.20312\n",
       "Q37.7969 6.20312 41.9844 11.8594\n",
       "Q46.1875 17.5312 46.1875 27.2969\n",
       "Q46.1875 37.0156 41.9844 42.7031\n",
       "Q37.7969 48.3906 30.6094 48.3906\n",
       "M30.6094 56\n",
       "Q42.3281 56 49.0156 48.375\n",
       "Q55.7188 40.7656 55.7188 27.2969\n",
       "Q55.7188 13.875 49.0156 6.21875\n",
       "Q42.3281 -1.42188 30.6094 -1.42188\n",
       "Q18.8438 -1.42188 12.1719 6.21875\n",
       "Q5.51562 13.875 5.51562 27.2969\n",
       "Q5.51562 40.7656 12.1719 48.375\n",
       "Q18.8438 56 30.6094 56\" id=\"BitstreamVeraSans-Roman-6f\"/>\n",
       "      <path d=\"\n",
       "M41.1094 46.2969\n",
       "Q39.5938 47.1719 37.8125 47.5781\n",
       "Q36.0312 48 33.8906 48\n",
       "Q26.2656 48 22.1875 43.0469\n",
       "Q18.1094 38.0938 18.1094 28.8125\n",
       "L18.1094 0\n",
       "L9.07812 0\n",
       "L9.07812 54.6875\n",
       "L18.1094 54.6875\n",
       "L18.1094 46.1875\n",
       "Q20.9531 51.1719 25.4844 53.5781\n",
       "Q30.0312 56 36.5312 56\n",
       "Q37.4531 56 38.5781 55.875\n",
       "Q39.7031 55.7656 41.0625 55.5156\n",
       "z\n",
       "\" id=\"BitstreamVeraSans-Roman-72\"/>\n",
       "     </defs>\n",
       "     <g transform=\"translate(82.9690340909 262.5375)scale(0.1 -0.1)\">\n",
       "      <use xlink:href=\"#BitstreamVeraSans-Roman-6e\"/>\n",
       "      <use x=\"63.37890625\" xlink:href=\"#BitstreamVeraSans-Roman-75\"/>\n",
       "      <use x=\"126.7578125\" xlink:href=\"#BitstreamVeraSans-Roman-6d\"/>\n",
       "      <use x=\"224.169921875\" xlink:href=\"#BitstreamVeraSans-Roman-62\"/>\n",
       "      <use x=\"287.646484375\" xlink:href=\"#BitstreamVeraSans-Roman-65\"/>\n",
       "      <use x=\"349.169921875\" xlink:href=\"#BitstreamVeraSans-Roman-72\"/>\n",
       "      <use x=\"390.283203125\" xlink:href=\"#BitstreamVeraSans-Roman-20\"/>\n",
       "      <use x=\"422.0703125\" xlink:href=\"#BitstreamVeraSans-Roman-6f\"/>\n",
       "      <use x=\"483.251953125\" xlink:href=\"#BitstreamVeraSans-Roman-66\"/>\n",
       "      <use x=\"518.45703125\" xlink:href=\"#BitstreamVeraSans-Roman-20\"/>\n",
       "      <use x=\"550.244140625\" xlink:href=\"#BitstreamVeraSans-Roman-66\"/>\n",
       "      <use x=\"585.44921875\" xlink:href=\"#BitstreamVeraSans-Roman-65\"/>\n",
       "      <use x=\"646.97265625\" xlink:href=\"#BitstreamVeraSans-Roman-61\"/>\n",
       "      <use x=\"708.251953125\" xlink:href=\"#BitstreamVeraSans-Roman-74\"/>\n",
       "      <use x=\"747.4609375\" xlink:href=\"#BitstreamVeraSans-Roman-75\"/>\n",
       "      <use x=\"810.83984375\" xlink:href=\"#BitstreamVeraSans-Roman-72\"/>\n",
       "      <use x=\"849.703125\" xlink:href=\"#BitstreamVeraSans-Roman-65\"/>\n",
       "      <use x=\"911.2265625\" xlink:href=\"#BitstreamVeraSans-Roman-73\"/>\n",
       "     </g>\n",
       "    </g>\n",
       "   </g>\n",
       "   <g id=\"matplotlib.axis_2\">\n",
       "    <g id=\"ytick_1\">\n",
       "     <g id=\"line2d_41\">\n",
       "      <defs>\n",
       "       <path d=\"\n",
       "M0 0\n",
       "L4 0\" id=\"md7965d1ba0\" style=\"stroke:#000000;stroke-width:0.5;\"/>\n",
       "      </defs>\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"54.8\" xlink:href=\"#md7965d1ba0\" y=\"235.2390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"line2d_42\">\n",
       "      <defs>\n",
       "       <path d=\"\n",
       "M0 0\n",
       "L-4 0\" id=\"md9a1c1a7cd\" style=\"stroke:#000000;stroke-width:0.5;\"/>\n",
       "      </defs>\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"206.981818182\" xlink:href=\"#md9a1c1a7cd\" y=\"235.2390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_5\">\n",
       "      <!-- −0.95 -->\n",
       "      <defs>\n",
       "       <path d=\"\n",
       "M10.7969 72.9062\n",
       "L49.5156 72.9062\n",
       "L49.5156 64.5938\n",
       "L19.8281 64.5938\n",
       "L19.8281 46.7344\n",
       "Q21.9688 47.4688 24.1094 47.8281\n",
       "Q26.2656 48.1875 28.4219 48.1875\n",
       "Q40.625 48.1875 47.75 41.5\n",
       "Q54.8906 34.8125 54.8906 23.3906\n",
       "Q54.8906 11.625 47.5625 5.09375\n",
       "Q40.2344 -1.42188 26.9062 -1.42188\n",
       "Q22.3125 -1.42188 17.5469 -0.640625\n",
       "Q12.7969 0.140625 7.71875 1.70312\n",
       "L7.71875 11.625\n",
       "Q12.1094 9.23438 16.7969 8.0625\n",
       "Q21.4844 6.89062 26.7031 6.89062\n",
       "Q35.1562 6.89062 40.0781 11.3281\n",
       "Q45.0156 15.7656 45.0156 23.3906\n",
       "Q45.0156 31 40.0781 35.4375\n",
       "Q35.1562 39.8906 26.7031 39.8906\n",
       "Q22.75 39.8906 18.8125 39.0156\n",
       "Q14.8906 38.1406 10.7969 36.2812\n",
       "z\n",
       "\" id=\"BitstreamVeraSans-Roman-35\"/>\n",
       "       <path d=\"\n",
       "M10.9844 1.51562\n",
       "L10.9844 10.5\n",
       "Q14.7031 8.73438 18.5 7.8125\n",
       "Q22.3125 6.89062 25.9844 6.89062\n",
       "Q35.75 6.89062 40.8906 13.4531\n",
       "Q46.0469 20.0156 46.7812 33.4062\n",
       "Q43.9531 29.2031 39.5938 26.9531\n",
       "Q35.25 24.7031 29.9844 24.7031\n",
       "Q19.0469 24.7031 12.6719 31.3125\n",
       "Q6.29688 37.9375 6.29688 49.4219\n",
       "Q6.29688 60.6406 12.9375 67.4219\n",
       "Q19.5781 74.2188 30.6094 74.2188\n",
       "Q43.2656 74.2188 49.9219 64.5156\n",
       "Q56.5938 54.8281 56.5938 36.375\n",
       "Q56.5938 19.1406 48.4062 8.85938\n",
       "Q40.2344 -1.42188 26.4219 -1.42188\n",
       "Q22.7031 -1.42188 18.8906 -0.6875\n",
       "Q15.0938 0.046875 10.9844 1.51562\n",
       "M30.6094 32.4219\n",
       "Q37.25 32.4219 41.125 36.9531\n",
       "Q45.0156 41.5 45.0156 49.4219\n",
       "Q45.0156 57.2812 41.125 61.8438\n",
       "Q37.25 66.4062 30.6094 66.4062\n",
       "Q23.9688 66.4062 20.0938 61.8438\n",
       "Q16.2188 57.2812 16.2188 49.4219\n",
       "Q16.2188 41.5 20.0938 36.9531\n",
       "Q23.9688 32.4219 30.6094 32.4219\" id=\"BitstreamVeraSans-Roman-39\"/>\n",
       "       <path d=\"\n",
       "M10.5938 35.5\n",
       "L73.1875 35.5\n",
       "L73.1875 27.2031\n",
       "L10.5938 27.2031\n",
       "z\n",
       "\" id=\"BitstreamVeraSans-Roman-2212\"/>\n",
       "       <path d=\"\n",
       "M10.6875 12.4062\n",
       "L21 12.4062\n",
       "L21 0\n",
       "L10.6875 0\n",
       "z\n",
       "\" id=\"BitstreamVeraSans-Roman-2e\"/>\n",
       "      </defs>\n",
       "      <g transform=\"translate(22.0875 237.9984375)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#BitstreamVeraSans-Roman-2212\"/>\n",
       "       <use x=\"83.7890625\" xlink:href=\"#BitstreamVeraSans-Roman-30\"/>\n",
       "       <use x=\"147.412109375\" xlink:href=\"#BitstreamVeraSans-Roman-2e\"/>\n",
       "       <use x=\"179.19921875\" xlink:href=\"#BitstreamVeraSans-Roman-39\"/>\n",
       "       <use x=\"242.822265625\" xlink:href=\"#BitstreamVeraSans-Roman-35\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_2\">\n",
       "     <g id=\"line2d_43\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"54.8\" xlink:href=\"#md7965d1ba0\" y=\"203.353348214\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"line2d_44\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"206.981818182\" xlink:href=\"#md9a1c1a7cd\" y=\"203.353348214\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_6\">\n",
       "      <!-- −0.90 -->\n",
       "      <g transform=\"translate(21.878125 206.112723214)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#BitstreamVeraSans-Roman-2212\"/>\n",
       "       <use x=\"83.7890625\" xlink:href=\"#BitstreamVeraSans-Roman-30\"/>\n",
       "       <use x=\"147.412109375\" xlink:href=\"#BitstreamVeraSans-Roman-2e\"/>\n",
       "       <use x=\"179.19921875\" xlink:href=\"#BitstreamVeraSans-Roman-39\"/>\n",
       "       <use x=\"242.822265625\" xlink:href=\"#BitstreamVeraSans-Roman-30\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_3\">\n",
       "     <g id=\"line2d_45\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"54.8\" xlink:href=\"#md7965d1ba0\" y=\"171.467633929\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"line2d_46\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"206.981818182\" xlink:href=\"#md9a1c1a7cd\" y=\"171.467633929\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_7\">\n",
       "      <!-- −0.85 -->\n",
       "      <defs>\n",
       "       <path d=\"\n",
       "M31.7812 34.625\n",
       "Q24.75 34.625 20.7188 30.8594\n",
       "Q16.7031 27.0938 16.7031 20.5156\n",
       "Q16.7031 13.9219 20.7188 10.1562\n",
       "Q24.75 6.39062 31.7812 6.39062\n",
       "Q38.8125 6.39062 42.8594 10.1719\n",
       "Q46.9219 13.9688 46.9219 20.5156\n",
       "Q46.9219 27.0938 42.8906 30.8594\n",
       "Q38.875 34.625 31.7812 34.625\n",
       "M21.9219 38.8125\n",
       "Q15.5781 40.375 12.0312 44.7188\n",
       "Q8.5 49.0781 8.5 55.3281\n",
       "Q8.5 64.0625 14.7188 69.1406\n",
       "Q20.9531 74.2188 31.7812 74.2188\n",
       "Q42.6719 74.2188 48.875 69.1406\n",
       "Q55.0781 64.0625 55.0781 55.3281\n",
       "Q55.0781 49.0781 51.5312 44.7188\n",
       "Q48 40.375 41.7031 38.8125\n",
       "Q48.8281 37.1562 52.7969 32.3125\n",
       "Q56.7812 27.4844 56.7812 20.5156\n",
       "Q56.7812 9.90625 50.3125 4.23438\n",
       "Q43.8438 -1.42188 31.7812 -1.42188\n",
       "Q19.7344 -1.42188 13.25 4.23438\n",
       "Q6.78125 9.90625 6.78125 20.5156\n",
       "Q6.78125 27.4844 10.7812 32.3125\n",
       "Q14.7969 37.1562 21.9219 38.8125\n",
       "M18.3125 54.3906\n",
       "Q18.3125 48.7344 21.8438 45.5625\n",
       "Q25.3906 42.3906 31.7812 42.3906\n",
       "Q38.1406 42.3906 41.7188 45.5625\n",
       "Q45.3125 48.7344 45.3125 54.3906\n",
       "Q45.3125 60.0625 41.7188 63.2344\n",
       "Q38.1406 66.4062 31.7812 66.4062\n",
       "Q25.3906 66.4062 21.8438 63.2344\n",
       "Q18.3125 60.0625 18.3125 54.3906\" id=\"BitstreamVeraSans-Roman-38\"/>\n",
       "      </defs>\n",
       "      <g transform=\"translate(22.0875 174.227008929)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#BitstreamVeraSans-Roman-2212\"/>\n",
       "       <use x=\"83.7890625\" xlink:href=\"#BitstreamVeraSans-Roman-30\"/>\n",
       "       <use x=\"147.412109375\" xlink:href=\"#BitstreamVeraSans-Roman-2e\"/>\n",
       "       <use x=\"179.19921875\" xlink:href=\"#BitstreamVeraSans-Roman-38\"/>\n",
       "       <use x=\"242.822265625\" xlink:href=\"#BitstreamVeraSans-Roman-35\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_4\">\n",
       "     <g id=\"line2d_47\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"54.8\" xlink:href=\"#md7965d1ba0\" y=\"139.581919643\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"line2d_48\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"206.981818182\" xlink:href=\"#md9a1c1a7cd\" y=\"139.581919643\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_8\">\n",
       "      <!-- −0.80 -->\n",
       "      <g transform=\"translate(21.878125 142.341294643)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#BitstreamVeraSans-Roman-2212\"/>\n",
       "       <use x=\"83.7890625\" xlink:href=\"#BitstreamVeraSans-Roman-30\"/>\n",
       "       <use x=\"147.412109375\" xlink:href=\"#BitstreamVeraSans-Roman-2e\"/>\n",
       "       <use x=\"179.19921875\" xlink:href=\"#BitstreamVeraSans-Roman-38\"/>\n",
       "       <use x=\"242.822265625\" xlink:href=\"#BitstreamVeraSans-Roman-30\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_5\">\n",
       "     <g id=\"line2d_49\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"54.8\" xlink:href=\"#md7965d1ba0\" y=\"107.696205357\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"line2d_50\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"206.981818182\" xlink:href=\"#md9a1c1a7cd\" y=\"107.696205357\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_9\">\n",
       "      <!-- −0.75 -->\n",
       "      <defs>\n",
       "       <path d=\"\n",
       "M8.20312 72.9062\n",
       "L55.0781 72.9062\n",
       "L55.0781 68.7031\n",
       "L28.6094 0\n",
       "L18.3125 0\n",
       "L43.2188 64.5938\n",
       "L8.20312 64.5938\n",
       "z\n",
       "\" id=\"BitstreamVeraSans-Roman-37\"/>\n",
       "      </defs>\n",
       "      <g transform=\"translate(22.0875 110.455580357)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#BitstreamVeraSans-Roman-2212\"/>\n",
       "       <use x=\"83.7890625\" xlink:href=\"#BitstreamVeraSans-Roman-30\"/>\n",
       "       <use x=\"147.412109375\" xlink:href=\"#BitstreamVeraSans-Roman-2e\"/>\n",
       "       <use x=\"179.19921875\" xlink:href=\"#BitstreamVeraSans-Roman-37\"/>\n",
       "       <use x=\"242.822265625\" xlink:href=\"#BitstreamVeraSans-Roman-35\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_6\">\n",
       "     <g id=\"line2d_51\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"54.8\" xlink:href=\"#md7965d1ba0\" y=\"75.8104910714\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"line2d_52\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"206.981818182\" xlink:href=\"#md9a1c1a7cd\" y=\"75.8104910714\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_10\">\n",
       "      <!-- −0.70 -->\n",
       "      <g transform=\"translate(21.878125 78.5698660714)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#BitstreamVeraSans-Roman-2212\"/>\n",
       "       <use x=\"83.7890625\" xlink:href=\"#BitstreamVeraSans-Roman-30\"/>\n",
       "       <use x=\"147.412109375\" xlink:href=\"#BitstreamVeraSans-Roman-2e\"/>\n",
       "       <use x=\"179.19921875\" xlink:href=\"#BitstreamVeraSans-Roman-37\"/>\n",
       "       <use x=\"242.822265625\" xlink:href=\"#BitstreamVeraSans-Roman-30\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_7\">\n",
       "     <g id=\"line2d_53\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"54.8\" xlink:href=\"#md7965d1ba0\" y=\"43.9247767857\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"line2d_54\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"206.981818182\" xlink:href=\"#md9a1c1a7cd\" y=\"43.9247767857\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_11\">\n",
       "      <!-- −0.65 -->\n",
       "      <defs>\n",
       "       <path d=\"\n",
       "M33.0156 40.375\n",
       "Q26.375 40.375 22.4844 35.8281\n",
       "Q18.6094 31.2969 18.6094 23.3906\n",
       "Q18.6094 15.5312 22.4844 10.9531\n",
       "Q26.375 6.39062 33.0156 6.39062\n",
       "Q39.6562 6.39062 43.5312 10.9531\n",
       "Q47.4062 15.5312 47.4062 23.3906\n",
       "Q47.4062 31.2969 43.5312 35.8281\n",
       "Q39.6562 40.375 33.0156 40.375\n",
       "M52.5938 71.2969\n",
       "L52.5938 62.3125\n",
       "Q48.875 64.0625 45.0938 64.9844\n",
       "Q41.3125 65.9219 37.5938 65.9219\n",
       "Q27.8281 65.9219 22.6719 59.3281\n",
       "Q17.5312 52.7344 16.7969 39.4062\n",
       "Q19.6719 43.6562 24.0156 45.9219\n",
       "Q28.375 48.1875 33.5938 48.1875\n",
       "Q44.5781 48.1875 50.9531 41.5156\n",
       "Q57.3281 34.8594 57.3281 23.3906\n",
       "Q57.3281 12.1562 50.6875 5.35938\n",
       "Q44.0469 -1.42188 33.0156 -1.42188\n",
       "Q20.3594 -1.42188 13.6719 8.26562\n",
       "Q6.98438 17.9688 6.98438 36.375\n",
       "Q6.98438 53.6562 15.1875 63.9375\n",
       "Q23.3906 74.2188 37.2031 74.2188\n",
       "Q40.9219 74.2188 44.7031 73.4844\n",
       "Q48.4844 72.75 52.5938 71.2969\" id=\"BitstreamVeraSans-Roman-36\"/>\n",
       "      </defs>\n",
       "      <g transform=\"translate(22.0875 46.6841517857)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#BitstreamVeraSans-Roman-2212\"/>\n",
       "       <use x=\"83.7890625\" xlink:href=\"#BitstreamVeraSans-Roman-30\"/>\n",
       "       <use x=\"147.412109375\" xlink:href=\"#BitstreamVeraSans-Roman-2e\"/>\n",
       "       <use x=\"179.19921875\" xlink:href=\"#BitstreamVeraSans-Roman-36\"/>\n",
       "       <use x=\"242.822265625\" xlink:href=\"#BitstreamVeraSans-Roman-35\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_8\">\n",
       "     <g id=\"line2d_55\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"54.8\" xlink:href=\"#md7965d1ba0\" y=\"12.0390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"line2d_56\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"206.981818182\" xlink:href=\"#md9a1c1a7cd\" y=\"12.0390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_12\">\n",
       "      <!-- −0.60 -->\n",
       "      <g transform=\"translate(21.878125 14.7984375)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#BitstreamVeraSans-Roman-2212\"/>\n",
       "       <use x=\"83.7890625\" xlink:href=\"#BitstreamVeraSans-Roman-30\"/>\n",
       "       <use x=\"147.412109375\" xlink:href=\"#BitstreamVeraSans-Roman-2e\"/>\n",
       "       <use x=\"179.19921875\" xlink:href=\"#BitstreamVeraSans-Roman-36\"/>\n",
       "       <use x=\"242.822265625\" xlink:href=\"#BitstreamVeraSans-Roman-30\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"text_13\">\n",
       "     <!-- score -->\n",
       "     <defs>\n",
       "      <path d=\"\n",
       "M48.7812 52.5938\n",
       "L48.7812 44.1875\n",
       "Q44.9688 46.2969 41.1406 47.3438\n",
       "Q37.3125 48.3906 33.4062 48.3906\n",
       "Q24.6562 48.3906 19.8125 42.8438\n",
       "Q14.9844 37.3125 14.9844 27.2969\n",
       "Q14.9844 17.2812 19.8125 11.7344\n",
       "Q24.6562 6.20312 33.4062 6.20312\n",
       "Q37.3125 6.20312 41.1406 7.25\n",
       "Q44.9688 8.29688 48.7812 10.4062\n",
       "L48.7812 2.09375\n",
       "Q45.0156 0.34375 40.9844 -0.53125\n",
       "Q36.9688 -1.42188 32.4219 -1.42188\n",
       "Q20.0625 -1.42188 12.7812 6.34375\n",
       "Q5.51562 14.1094 5.51562 27.2969\n",
       "Q5.51562 40.6719 12.8594 48.3281\n",
       "Q20.2188 56 33.0156 56\n",
       "Q37.1562 56 41.1094 55.1406\n",
       "Q45.0625 54.2969 48.7812 52.5938\" id=\"BitstreamVeraSans-Roman-63\"/>\n",
       "     </defs>\n",
       "     <g transform=\"translate(14.7984375 136.534375)rotate(-90.0)scale(0.1 -0.1)\">\n",
       "      <use xlink:href=\"#BitstreamVeraSans-Roman-73\"/>\n",
       "      <use x=\"52.099609375\" xlink:href=\"#BitstreamVeraSans-Roman-63\"/>\n",
       "      <use x=\"107.080078125\" xlink:href=\"#BitstreamVeraSans-Roman-6f\"/>\n",
       "      <use x=\"168.26171875\" xlink:href=\"#BitstreamVeraSans-Roman-72\"/>\n",
       "      <use x=\"207.125\" xlink:href=\"#BitstreamVeraSans-Roman-65\"/>\n",
       "     </g>\n",
       "    </g>\n",
       "   </g>\n",
       "   <g id=\"legend_1\">\n",
       "    <g id=\"patch_7\">\n",
       "     <path d=\"\n",
       "M60.8 56.8666\n",
       "L130.589 56.8666\n",
       "L130.589 18.0391\n",
       "L60.8 18.0391\n",
       "z\n",
       "\" style=\"fill:#ffffff;stroke:#000000;stroke-linejoin:miter;\"/>\n",
       "    </g>\n",
       "    <g id=\"line2d_57\">\n",
       "     <path d=\"\n",
       "M69.2 27.7572\n",
       "L86 27.7572\" style=\"fill:none;stroke:#0000ff;stroke-linecap:square;\"/>\n",
       "    </g>\n",
       "    <g id=\"line2d_58\">\n",
       "     <g>\n",
       "      <use style=\"fill:#0000ff;stroke:#000000;stroke-width:0.5;\" x=\"69.2\" xlink:href=\"#mdb00ba95ec\" y=\"27.7571875\"/>\n",
       "      <use style=\"fill:#0000ff;stroke:#000000;stroke-width:0.5;\" x=\"86.0\" xlink:href=\"#mdb00ba95ec\" y=\"27.7571875\"/>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"text_14\">\n",
       "     <!-- train -->\n",
       "     <defs>\n",
       "      <path d=\"\n",
       "M9.42188 54.6875\n",
       "L18.4062 54.6875\n",
       "L18.4062 0\n",
       "L9.42188 0\n",
       "z\n",
       "\n",
       "M9.42188 75.9844\n",
       "L18.4062 75.9844\n",
       "L18.4062 64.5938\n",
       "L9.42188 64.5938\n",
       "z\n",
       "\" id=\"BitstreamVeraSans-Roman-69\"/>\n",
       "     </defs>\n",
       "     <g transform=\"translate(99.2 31.9571875)scale(0.12 -0.12)\">\n",
       "      <use xlink:href=\"#BitstreamVeraSans-Roman-74\"/>\n",
       "      <use x=\"39.208984375\" xlink:href=\"#BitstreamVeraSans-Roman-72\"/>\n",
       "      <use x=\"80.322265625\" xlink:href=\"#BitstreamVeraSans-Roman-61\"/>\n",
       "      <use x=\"141.6015625\" xlink:href=\"#BitstreamVeraSans-Roman-69\"/>\n",
       "      <use x=\"169.384765625\" xlink:href=\"#BitstreamVeraSans-Roman-6e\"/>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"line2d_59\">\n",
       "     <path d=\"\n",
       "M69.2 45.3709\n",
       "L86 45.3709\" style=\"fill:none;stroke:#008000;stroke-linecap:square;\"/>\n",
       "    </g>\n",
       "    <g id=\"line2d_60\">\n",
       "     <g>\n",
       "      <use style=\"fill:#008000;stroke:#000000;stroke-linejoin:miter;stroke-width:0.5;\" x=\"69.2\" xlink:href=\"#m45eb232605\" y=\"45.3709375\"/>\n",
       "      <use style=\"fill:#008000;stroke:#000000;stroke-linejoin:miter;stroke-width:0.5;\" x=\"86.0\" xlink:href=\"#m45eb232605\" y=\"45.3709375\"/>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"text_15\">\n",
       "     <!-- test -->\n",
       "     <g transform=\"translate(99.2 49.5709375)scale(0.12 -0.12)\">\n",
       "      <use xlink:href=\"#BitstreamVeraSans-Roman-74\"/>\n",
       "      <use x=\"39.208984375\" xlink:href=\"#BitstreamVeraSans-Roman-65\"/>\n",
       "      <use x=\"100.732421875\" xlink:href=\"#BitstreamVeraSans-Roman-73\"/>\n",
       "      <use x=\"152.83203125\" xlink:href=\"#BitstreamVeraSans-Roman-74\"/>\n",
       "     </g>\n",
       "    </g>\n",
       "   </g>\n",
       "  </g>\n",
       "  <g id=\"axes_2\">\n",
       "   <g id=\"patch_8\">\n",
       "    <path d=\"\n",
       "M237.418 235.239\n",
       "L389.6 235.239\n",
       "L389.6 12.0391\n",
       "L237.418 12.0391\n",
       "z\n",
       "\" style=\"fill:#ffffff;\"/>\n",
       "   </g>\n",
       "   <g id=\"PolyCollection_3\">\n",
       "    <defs>\n",
       "     <path d=\"\n",
       "M237.418 -139.942\n",
       "L237.418 -67.2536\n",
       "L260.324 -83.6814\n",
       "L283.229 -92.8806\n",
       "L306.135 -97.795\n",
       "L329.041 -119.688\n",
       "L351.946 -139.52\n",
       "L374.852 -147.578\n",
       "L374.852 -229.868\n",
       "L374.852 -229.868\n",
       "L351.946 -223.066\n",
       "L329.041 -200.236\n",
       "L306.135 -173.675\n",
       "L283.229 -165.559\n",
       "L260.324 -156.699\n",
       "L237.418 -139.942\n",
       "z\n",
       "\" id=\"m52358fb8bd\" style=\"stroke:#000000;stroke-opacity:0.3;\"/>\n",
       "    </defs>\n",
       "    <g clip-path=\"url(#pbb8d73d0c2)\">\n",
       "     <use style=\"fill:#0000ff;fill-opacity:0.3;stroke:#000000;stroke-opacity:0.3;\" x=\"0.0\" xlink:href=\"#m52358fb8bd\" y=\"271.8171875\"/>\n",
       "    </g>\n",
       "   </g>\n",
       "   <g id=\"line2d_61\">\n",
       "    <path clip-path=\"url(#pbb8d73d0c2)\" d=\"\n",
       "M237.418 168.219\n",
       "L260.324 151.627\n",
       "L283.229 142.598\n",
       "L306.135 136.082\n",
       "L329.041 111.855\n",
       "L351.946 90.5243\n",
       "L374.852 83.094\" style=\"fill:none;stroke:#008000;stroke-linecap:square;\"/>\n",
       "    <g clip-path=\"url(#pbb8d73d0c2)\">\n",
       "     <use style=\"fill:#008000;stroke:#000000;stroke-linejoin:miter;stroke-width:0.5;\" x=\"237.418181818\" xlink:href=\"#m45eb232605\" y=\"168.219199797\"/>\n",
       "     <use style=\"fill:#008000;stroke:#000000;stroke-linejoin:miter;stroke-width:0.5;\" x=\"260.323827852\" xlink:href=\"#m45eb232605\" y=\"151.626966618\"/>\n",
       "     <use style=\"fill:#008000;stroke:#000000;stroke-linejoin:miter;stroke-width:0.5;\" x=\"283.229473886\" xlink:href=\"#m45eb232605\" y=\"142.597525511\"/>\n",
       "     <use style=\"fill:#008000;stroke:#000000;stroke-linejoin:miter;stroke-width:0.5;\" x=\"306.135119919\" xlink:href=\"#m45eb232605\" y=\"136.082028004\"/>\n",
       "     <use style=\"fill:#008000;stroke:#000000;stroke-linejoin:miter;stroke-width:0.5;\" x=\"329.040765953\" xlink:href=\"#m45eb232605\" y=\"111.855080974\"/>\n",
       "     <use style=\"fill:#008000;stroke:#000000;stroke-linejoin:miter;stroke-width:0.5;\" x=\"351.946411987\" xlink:href=\"#m45eb232605\" y=\"90.5242809824\"/>\n",
       "     <use style=\"fill:#008000;stroke:#000000;stroke-linejoin:miter;stroke-width:0.5;\" x=\"374.85205802\" xlink:href=\"#m45eb232605\" y=\"83.0940387054\"/>\n",
       "    </g>\n",
       "   </g>\n",
       "   <g id=\"patch_9\">\n",
       "    <path d=\"\n",
       "M237.418 12.0391\n",
       "L389.6 12.0391\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_10\">\n",
       "    <path d=\"\n",
       "M237.418 235.239\n",
       "L237.418 12.0391\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_11\">\n",
       "    <path d=\"\n",
       "M389.6 235.239\n",
       "L389.6 12.0391\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_12\">\n",
       "    <path d=\"\n",
       "M237.418 235.239\n",
       "L389.6 235.239\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;\"/>\n",
       "   </g>\n",
       "   <g id=\"matplotlib.axis_3\">\n",
       "    <g id=\"xtick_20\">\n",
       "     <g id=\"line2d_62\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"237.418181818\" xlink:href=\"#mc7db9fdffb\" y=\"235.2390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"line2d_63\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"237.418181818\" xlink:href=\"#m5a7d422ac3\" y=\"12.0390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_16\">\n",
       "      <!-- $\\mathdefault{10^{0}}$ -->\n",
       "      <g transform=\"translate(227.768181818 247.859375)scale(0.1 -0.1)\">\n",
       "       <use transform=\"translate(0.0 0.546875)\" xlink:href=\"#BitstreamVeraSans-Roman-31\"/>\n",
       "       <use transform=\"translate(63.623046875 0.546875)\" xlink:href=\"#BitstreamVeraSans-Roman-30\"/>\n",
       "       <use transform=\"translate(127.24609375 53.046875)scale(0.7)\" xlink:href=\"#BitstreamVeraSans-Roman-30\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_21\">\n",
       "     <g id=\"line2d_64\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"313.509090909\" xlink:href=\"#mc7db9fdffb\" y=\"235.2390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"line2d_65\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"313.509090909\" xlink:href=\"#m5a7d422ac3\" y=\"12.0390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_17\">\n",
       "      <!-- $\\mathdefault{10^{1}}$ -->\n",
       "      <g transform=\"translate(303.859090909 247.759375)scale(0.1 -0.1)\">\n",
       "       <use transform=\"translate(0.0 0.46562500000000284)\" xlink:href=\"#BitstreamVeraSans-Roman-31\"/>\n",
       "       <use transform=\"translate(63.623046875 0.46562500000000284)\" xlink:href=\"#BitstreamVeraSans-Roman-30\"/>\n",
       "       <use transform=\"translate(127.24609375 52.965625)scale(0.7)\" xlink:href=\"#BitstreamVeraSans-Roman-31\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_22\">\n",
       "     <g id=\"line2d_66\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"389.6\" xlink:href=\"#mc7db9fdffb\" y=\"235.2390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"line2d_67\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"389.6\" xlink:href=\"#m5a7d422ac3\" y=\"12.0390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_18\">\n",
       "      <!-- $\\mathdefault{10^{2}}$ -->\n",
       "      <g transform=\"translate(379.95 247.859375)scale(0.1 -0.1)\">\n",
       "       <use transform=\"translate(0.0 0.546875)\" xlink:href=\"#BitstreamVeraSans-Roman-31\"/>\n",
       "       <use transform=\"translate(63.623046875 0.546875)\" xlink:href=\"#BitstreamVeraSans-Roman-30\"/>\n",
       "       <use transform=\"translate(127.24609375 53.046875)scale(0.7)\" xlink:href=\"#BitstreamVeraSans-Roman-32\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_23\">\n",
       "     <g id=\"line2d_68\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"260.323827852\" xlink:href=\"#mc21db286a6\" y=\"235.2390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"line2d_69\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"260.323827852\" xlink:href=\"#ma9c915e141\" y=\"12.0390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_24\">\n",
       "     <g id=\"line2d_70\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"273.722771836\" xlink:href=\"#mc21db286a6\" y=\"235.2390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"line2d_71\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"273.722771836\" xlink:href=\"#ma9c915e141\" y=\"12.0390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_25\">\n",
       "     <g id=\"line2d_72\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"283.229473886\" xlink:href=\"#mc21db286a6\" y=\"235.2390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"line2d_73\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"283.229473886\" xlink:href=\"#ma9c915e141\" y=\"12.0390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_26\">\n",
       "     <g id=\"line2d_74\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"290.603444875\" xlink:href=\"#mc21db286a6\" y=\"235.2390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"line2d_75\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"290.603444875\" xlink:href=\"#ma9c915e141\" y=\"12.0390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_27\">\n",
       "     <g id=\"line2d_76\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"296.62841787\" xlink:href=\"#mc21db286a6\" y=\"235.2390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"line2d_77\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"296.62841787\" xlink:href=\"#ma9c915e141\" y=\"12.0390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_28\">\n",
       "     <g id=\"line2d_78\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"301.722459954\" xlink:href=\"#mc21db286a6\" y=\"235.2390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"line2d_79\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"301.722459954\" xlink:href=\"#ma9c915e141\" y=\"12.0390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_29\">\n",
       "     <g id=\"line2d_80\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"306.135119919\" xlink:href=\"#mc21db286a6\" y=\"235.2390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"line2d_81\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"306.135119919\" xlink:href=\"#ma9c915e141\" y=\"12.0390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_30\">\n",
       "     <g id=\"line2d_82\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"310.027361855\" xlink:href=\"#mc21db286a6\" y=\"235.2390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"line2d_83\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"310.027361855\" xlink:href=\"#ma9c915e141\" y=\"12.0390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_31\">\n",
       "     <g id=\"line2d_84\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"336.414736943\" xlink:href=\"#mc21db286a6\" y=\"235.2390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"line2d_85\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"336.414736943\" xlink:href=\"#ma9c915e141\" y=\"12.0390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_32\">\n",
       "     <g id=\"line2d_86\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"349.813680927\" xlink:href=\"#mc21db286a6\" y=\"235.2390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"line2d_87\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"349.813680927\" xlink:href=\"#ma9c915e141\" y=\"12.0390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_33\">\n",
       "     <g id=\"line2d_88\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"359.320382977\" xlink:href=\"#mc21db286a6\" y=\"235.2390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"line2d_89\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"359.320382977\" xlink:href=\"#ma9c915e141\" y=\"12.0390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_34\">\n",
       "     <g id=\"line2d_90\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"366.694353966\" xlink:href=\"#mc21db286a6\" y=\"235.2390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"line2d_91\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"366.694353966\" xlink:href=\"#ma9c915e141\" y=\"12.0390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_35\">\n",
       "     <g id=\"line2d_92\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"372.719326961\" xlink:href=\"#mc21db286a6\" y=\"235.2390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"line2d_93\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"372.719326961\" xlink:href=\"#ma9c915e141\" y=\"12.0390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_36\">\n",
       "     <g id=\"line2d_94\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"377.813369045\" xlink:href=\"#mc21db286a6\" y=\"235.2390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"line2d_95\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"377.813369045\" xlink:href=\"#ma9c915e141\" y=\"12.0390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_37\">\n",
       "     <g id=\"line2d_96\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"382.22602901\" xlink:href=\"#mc21db286a6\" y=\"235.2390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"line2d_97\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"382.22602901\" xlink:href=\"#ma9c915e141\" y=\"12.0390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_38\">\n",
       "     <g id=\"line2d_98\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"386.118270946\" xlink:href=\"#mc21db286a6\" y=\"235.2390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"line2d_99\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"386.118270946\" xlink:href=\"#ma9c915e141\" y=\"12.0390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "   </g>\n",
       "   <g id=\"matplotlib.axis_4\">\n",
       "    <g id=\"ytick_9\">\n",
       "     <g id=\"line2d_100\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"237.418181818\" xlink:href=\"#md7965d1ba0\" y=\"235.2390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"line2d_101\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"389.6\" xlink:href=\"#md9a1c1a7cd\" y=\"235.2390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_19\">\n",
       "      <!-- −0.95 -->\n",
       "      <g transform=\"translate(204.705681818 237.9984375)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#BitstreamVeraSans-Roman-2212\"/>\n",
       "       <use x=\"83.7890625\" xlink:href=\"#BitstreamVeraSans-Roman-30\"/>\n",
       "       <use x=\"147.412109375\" xlink:href=\"#BitstreamVeraSans-Roman-2e\"/>\n",
       "       <use x=\"179.19921875\" xlink:href=\"#BitstreamVeraSans-Roman-39\"/>\n",
       "       <use x=\"242.822265625\" xlink:href=\"#BitstreamVeraSans-Roman-35\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_10\">\n",
       "     <g id=\"line2d_102\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"237.418181818\" xlink:href=\"#md7965d1ba0\" y=\"198.0390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"line2d_103\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"389.6\" xlink:href=\"#md9a1c1a7cd\" y=\"198.0390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_20\">\n",
       "      <!-- −0.94 -->\n",
       "      <defs>\n",
       "       <path d=\"\n",
       "M37.7969 64.3125\n",
       "L12.8906 25.3906\n",
       "L37.7969 25.3906\n",
       "z\n",
       "\n",
       "M35.2031 72.9062\n",
       "L47.6094 72.9062\n",
       "L47.6094 25.3906\n",
       "L58.0156 25.3906\n",
       "L58.0156 17.1875\n",
       "L47.6094 17.1875\n",
       "L47.6094 0\n",
       "L37.7969 0\n",
       "L37.7969 17.1875\n",
       "L4.89062 17.1875\n",
       "L4.89062 26.7031\n",
       "z\n",
       "\" id=\"BitstreamVeraSans-Roman-34\"/>\n",
       "      </defs>\n",
       "      <g transform=\"translate(204.393181818 200.7984375)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#BitstreamVeraSans-Roman-2212\"/>\n",
       "       <use x=\"83.7890625\" xlink:href=\"#BitstreamVeraSans-Roman-30\"/>\n",
       "       <use x=\"147.412109375\" xlink:href=\"#BitstreamVeraSans-Roman-2e\"/>\n",
       "       <use x=\"179.19921875\" xlink:href=\"#BitstreamVeraSans-Roman-39\"/>\n",
       "       <use x=\"242.822265625\" xlink:href=\"#BitstreamVeraSans-Roman-34\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_11\">\n",
       "     <g id=\"line2d_104\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"237.418181818\" xlink:href=\"#md7965d1ba0\" y=\"160.8390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"line2d_105\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"389.6\" xlink:href=\"#md9a1c1a7cd\" y=\"160.8390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_21\">\n",
       "      <!-- −0.93 -->\n",
       "      <defs>\n",
       "       <path d=\"\n",
       "M40.5781 39.3125\n",
       "Q47.6562 37.7969 51.625 33\n",
       "Q55.6094 28.2188 55.6094 21.1875\n",
       "Q55.6094 10.4062 48.1875 4.48438\n",
       "Q40.7656 -1.42188 27.0938 -1.42188\n",
       "Q22.5156 -1.42188 17.6562 -0.515625\n",
       "Q12.7969 0.390625 7.625 2.20312\n",
       "L7.625 11.7188\n",
       "Q11.7188 9.32812 16.5938 8.10938\n",
       "Q21.4844 6.89062 26.8125 6.89062\n",
       "Q36.0781 6.89062 40.9375 10.5469\n",
       "Q45.7969 14.2031 45.7969 21.1875\n",
       "Q45.7969 27.6406 41.2812 31.2656\n",
       "Q36.7656 34.9062 28.7188 34.9062\n",
       "L20.2188 34.9062\n",
       "L20.2188 43.0156\n",
       "L29.1094 43.0156\n",
       "Q36.375 43.0156 40.2344 45.9219\n",
       "Q44.0938 48.8281 44.0938 54.2969\n",
       "Q44.0938 59.9062 40.1094 62.9062\n",
       "Q36.1406 65.9219 28.7188 65.9219\n",
       "Q24.6562 65.9219 20.0156 65.0312\n",
       "Q15.375 64.1562 9.8125 62.3125\n",
       "L9.8125 71.0938\n",
       "Q15.4375 72.6562 20.3438 73.4375\n",
       "Q25.25 74.2188 29.5938 74.2188\n",
       "Q40.8281 74.2188 47.3594 69.1094\n",
       "Q53.9062 64.0156 53.9062 55.3281\n",
       "Q53.9062 49.2656 50.4375 45.0938\n",
       "Q46.9688 40.9219 40.5781 39.3125\" id=\"BitstreamVeraSans-Roman-33\"/>\n",
       "      </defs>\n",
       "      <g transform=\"translate(204.633806818 163.5984375)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#BitstreamVeraSans-Roman-2212\"/>\n",
       "       <use x=\"83.7890625\" xlink:href=\"#BitstreamVeraSans-Roman-30\"/>\n",
       "       <use x=\"147.412109375\" xlink:href=\"#BitstreamVeraSans-Roman-2e\"/>\n",
       "       <use x=\"179.19921875\" xlink:href=\"#BitstreamVeraSans-Roman-39\"/>\n",
       "       <use x=\"242.822265625\" xlink:href=\"#BitstreamVeraSans-Roman-33\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_12\">\n",
       "     <g id=\"line2d_106\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"237.418181818\" xlink:href=\"#md7965d1ba0\" y=\"123.6390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"line2d_107\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"389.6\" xlink:href=\"#md9a1c1a7cd\" y=\"123.6390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_22\">\n",
       "      <!-- −0.92 -->\n",
       "      <g transform=\"translate(204.833806818 126.3984375)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#BitstreamVeraSans-Roman-2212\"/>\n",
       "       <use x=\"83.7890625\" xlink:href=\"#BitstreamVeraSans-Roman-30\"/>\n",
       "       <use x=\"147.412109375\" xlink:href=\"#BitstreamVeraSans-Roman-2e\"/>\n",
       "       <use x=\"179.19921875\" xlink:href=\"#BitstreamVeraSans-Roman-39\"/>\n",
       "       <use x=\"242.822265625\" xlink:href=\"#BitstreamVeraSans-Roman-32\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_13\">\n",
       "     <g id=\"line2d_108\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"237.418181818\" xlink:href=\"#md7965d1ba0\" y=\"86.4390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"line2d_109\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"389.6\" xlink:href=\"#md9a1c1a7cd\" y=\"86.4390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_23\">\n",
       "      <!-- −0.91 -->\n",
       "      <g transform=\"translate(204.755681818 89.1984375)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#BitstreamVeraSans-Roman-2212\"/>\n",
       "       <use x=\"83.7890625\" xlink:href=\"#BitstreamVeraSans-Roman-30\"/>\n",
       "       <use x=\"147.412109375\" xlink:href=\"#BitstreamVeraSans-Roman-2e\"/>\n",
       "       <use x=\"179.19921875\" xlink:href=\"#BitstreamVeraSans-Roman-39\"/>\n",
       "       <use x=\"242.822265625\" xlink:href=\"#BitstreamVeraSans-Roman-31\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_14\">\n",
       "     <g id=\"line2d_110\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"237.418181818\" xlink:href=\"#md7965d1ba0\" y=\"49.2390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"line2d_111\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"389.6\" xlink:href=\"#md9a1c1a7cd\" y=\"49.2390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_24\">\n",
       "      <!-- −0.90 -->\n",
       "      <g transform=\"translate(204.496306818 51.9984375)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#BitstreamVeraSans-Roman-2212\"/>\n",
       "       <use x=\"83.7890625\" xlink:href=\"#BitstreamVeraSans-Roman-30\"/>\n",
       "       <use x=\"147.412109375\" xlink:href=\"#BitstreamVeraSans-Roman-2e\"/>\n",
       "       <use x=\"179.19921875\" xlink:href=\"#BitstreamVeraSans-Roman-39\"/>\n",
       "       <use x=\"242.822265625\" xlink:href=\"#BitstreamVeraSans-Roman-30\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_15\">\n",
       "     <g id=\"line2d_112\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"237.418181818\" xlink:href=\"#md7965d1ba0\" y=\"12.0390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"line2d_113\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"389.6\" xlink:href=\"#md9a1c1a7cd\" y=\"12.0390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_25\">\n",
       "      <!-- −0.89 -->\n",
       "      <g transform=\"translate(204.535369318 14.7984375)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#BitstreamVeraSans-Roman-2212\"/>\n",
       "       <use x=\"83.7890625\" xlink:href=\"#BitstreamVeraSans-Roman-30\"/>\n",
       "       <use x=\"147.412109375\" xlink:href=\"#BitstreamVeraSans-Roman-2e\"/>\n",
       "       <use x=\"179.19921875\" xlink:href=\"#BitstreamVeraSans-Roman-38\"/>\n",
       "       <use x=\"242.822265625\" xlink:href=\"#BitstreamVeraSans-Roman-39\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "   </g>\n",
       "  </g>\n",
       " </g>\n",
       " <defs>\n",
       "  <clipPath id=\"p2f9be9b7ad\">\n",
       "   <rect height=\"223.2\" width=\"152.181818182\" x=\"54.8\" y=\"12.0390625\"/>\n",
       "  </clipPath>\n",
       "  <clipPath id=\"pbb8d73d0c2\">\n",
       "   <rect height=\"223.2\" width=\"152.181818182\" x=\"237.418181818\" y=\"12.0390625\"/>\n",
       "  </clipPath>\n",
       " </defs>\n",
       "</svg>\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fce76042f28>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, (axl, axr) = subplots(1, 2, sharex=True)\n",
    "plot_cv_scores(num_features, valid_scores, train_scores, ax=axl)\n",
    "plot_cv_scores(num_features, valid_scores, ax=axr)\n",
    "axl.set_xscale('log')\n",
    "axr.set_xscale('log')\n",
    "axl.set_xlabel('number of features')\n",
    "axl.set_ylabel('score')\n",
    "axl.legend(loc=2);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 246,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "est = CollaborativeFiltering(num_athletes, num_segments, num_features=10, lm=10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Learning curves"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "learning_curve()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 258,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "train_sizes, train_scores, valid_scores =\\\n",
    "    learning_curve(est, X, y,\n",
    "                   train_sizes=logspace(-2,0,20),\n",
    "                   scoring='mean_squared_error', \n",
    "                   cv=8, n_jobs=4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 259,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/svg+xml": [
       "<?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?>\n",
       "<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n",
       "  \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n",
       "<!-- Created with matplotlib (http://matplotlib.org/) -->\n",
       "<svg height=\"271pt\" version=\"1.1\" viewBox=\"0 0 391 271\" width=\"391pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
       " <defs>\n",
       "  <style type=\"text/css\">\n",
       "*{stroke-linecap:butt;stroke-linejoin:round;}\n",
       "  </style>\n",
       " </defs>\n",
       " <g id=\"figure_1\">\n",
       "  <g id=\"patch_1\">\n",
       "   <path d=\"\n",
       "M0 271.817\n",
       "L391.772 271.817\n",
       "L391.772 0\n",
       "L0 0\n",
       "L0 271.817\" style=\"fill:none;\"/>\n",
       "  </g>\n",
       "  <g id=\"axes_1\">\n",
       "   <g id=\"patch_2\">\n",
       "    <path d=\"\n",
       "M40.1219 235.239\n",
       "L374.922 235.239\n",
       "L374.922 12.0391\n",
       "L40.1219 12.0391\n",
       "z\n",
       "\" style=\"fill:#ffffff;\"/>\n",
       "   </g>\n",
       "   <g id=\"PolyCollection_1\">\n",
       "    <defs>\n",
       "     <path d=\"\n",
       "M41.3187 -70.0514\n",
       "L41.3187 -44.6534\n",
       "L53.0611 -51.3744\n",
       "L64.8026 -49.2732\n",
       "L76.5638 -54.8054\n",
       "L88.3159 -64.2721\n",
       "L100.058 -73.1285\n",
       "L111.81 -86.9599\n",
       "L123.55 -75.3696\n",
       "L135.299 -79.7147\n",
       "L147.05 -81.837\n",
       "L158.798 -79.5305\n",
       "L170.546 -80.5769\n",
       "L182.295 -82.2475\n",
       "L194.042 -78.9251\n",
       "L205.789 -80.4364\n",
       "L217.537 -86.904\n",
       "L229.285 -117.805\n",
       "L241.032 -163.389\n",
       "L252.78 -210.824\n",
       "L264.527 -251.979\n",
       "L264.527 -253.913\n",
       "L264.527 -253.913\n",
       "L252.78 -213.264\n",
       "L241.032 -166.424\n",
       "L229.285 -119.886\n",
       "L217.537 -89.9763\n",
       "L205.789 -86.2812\n",
       "L194.042 -80.6919\n",
       "L182.295 -85.1666\n",
       "L170.546 -84.054\n",
       "L158.798 -81.0225\n",
       "L147.05 -90.1296\n",
       "L135.299 -81.1436\n",
       "L123.55 -79.1333\n",
       "L111.81 -88.0844\n",
       "L100.058 -79.3619\n",
       "L88.3159 -84.9333\n",
       "L76.5638 -82.7954\n",
       "L64.8026 -74.8987\n",
       "L53.0611 -67.3651\n",
       "L41.3187 -70.0514\n",
       "z\n",
       "\" id=\"me8aa2f63a1\" style=\"stroke:#000000;stroke-opacity:0.3;\"/>\n",
       "    </defs>\n",
       "    <g clip-path=\"url(#pafb01ba72a)\">\n",
       "     <use style=\"fill:#0000ff;fill-opacity:0.3;stroke:#000000;stroke-opacity:0.3;\" x=\"0.0\" xlink:href=\"#me8aa2f63a1\" y=\"271.8171875\"/>\n",
       "    </g>\n",
       "   </g>\n",
       "   <g id=\"PolyCollection_2\">\n",
       "    <defs>\n",
       "     <path d=\"\n",
       "M41.3187 -89.3094\n",
       "L41.3187 -75.7692\n",
       "L53.0611 -75.7692\n",
       "L64.8026 -75.7692\n",
       "L76.5638 -75.7691\n",
       "L88.3159 -75.7684\n",
       "L100.058 -75.7692\n",
       "L111.81 -75.7692\n",
       "L123.55 -75.7692\n",
       "L135.299 -75.7669\n",
       "L147.05 -75.7692\n",
       "L158.798 -75.7692\n",
       "L170.546 -75.7692\n",
       "L182.295 -75.7692\n",
       "L194.042 -75.7692\n",
       "L205.789 -75.7963\n",
       "L217.537 -75.9118\n",
       "L229.285 -77.6455\n",
       "L241.032 -80.9423\n",
       "L252.78 -83.71\n",
       "L264.527 -87.5023\n",
       "L264.527 -102.863\n",
       "L264.527 -102.863\n",
       "L252.78 -98.8228\n",
       "L241.032 -96.0281\n",
       "L229.285 -91.7169\n",
       "L217.537 -89.6225\n",
       "L205.789 -89.3163\n",
       "L194.042 -89.3117\n",
       "L182.295 -89.3109\n",
       "L170.546 -89.3109\n",
       "L158.798 -89.3108\n",
       "L147.05 -89.3108\n",
       "L135.299 -89.3087\n",
       "L123.55 -89.3108\n",
       "L111.81 -89.3108\n",
       "L100.058 -89.3108\n",
       "L88.3159 -89.3109\n",
       "L76.5638 -89.3107\n",
       "L64.8026 -89.3108\n",
       "L53.0611 -89.3108\n",
       "L41.3187 -89.3094\n",
       "z\n",
       "\" id=\"m8e42443b27\" style=\"stroke:#000000;stroke-opacity:0.3;\"/>\n",
       "    </defs>\n",
       "    <g clip-path=\"url(#pafb01ba72a)\">\n",
       "     <use style=\"fill:#0000ff;fill-opacity:0.3;stroke:#000000;stroke-opacity:0.3;\" x=\"0.0\" xlink:href=\"#m8e42443b27\" y=\"271.8171875\"/>\n",
       "    </g>\n",
       "   </g>\n",
       "   <g id=\"line2d_1\">\n",
       "    <path clip-path=\"url(#pafb01ba72a)\" d=\"\n",
       "M41.3187 214.465\n",
       "L53.0611 212.447\n",
       "L64.8026 209.731\n",
       "L76.5638 203.017\n",
       "L88.3159 197.214\n",
       "L100.058 195.572\n",
       "L111.81 184.295\n",
       "L123.55 194.566\n",
       "L135.299 191.388\n",
       "L147.05 185.834\n",
       "L158.798 191.541\n",
       "L170.546 189.502\n",
       "L182.295 188.11\n",
       "L194.042 192.009\n",
       "L205.789 188.458\n",
       "L217.537 183.377\n",
       "L229.285 152.972\n",
       "L241.032 106.911\n",
       "L252.78 59.773\n",
       "L264.527 18.8708\" style=\"fill:none;stroke:#0000ff;stroke-linecap:square;\"/>\n",
       "    <defs>\n",
       "     <path d=\"\n",
       "M0 3\n",
       "C0.795609 3 1.55874 2.6839 2.12132 2.12132\n",
       "C2.6839 1.55874 3 0.795609 3 0\n",
       "C3 -0.795609 2.6839 -1.55874 2.12132 -2.12132\n",
       "C1.55874 -2.6839 0.795609 -3 0 -3\n",
       "C-0.795609 -3 -1.55874 -2.6839 -2.12132 -2.12132\n",
       "C-2.6839 -1.55874 -3 -0.795609 -3 0\n",
       "C-3 0.795609 -2.6839 1.55874 -2.12132 2.12132\n",
       "C-1.55874 2.6839 -0.795609 3 0 3\n",
       "z\n",
       "\" id=\"mdb00ba95ec\" style=\"stroke:#000000;stroke-width:0.5;\"/>\n",
       "    </defs>\n",
       "    <g clip-path=\"url(#pafb01ba72a)\">\n",
       "     <use style=\"fill:#0000ff;stroke:#000000;stroke-width:0.5;\" x=\"41.3186583777\" xlink:href=\"#mdb00ba95ec\" y=\"214.464792354\"/>\n",
       "     <use style=\"fill:#0000ff;stroke:#000000;stroke-width:0.5;\" x=\"53.0611335464\" xlink:href=\"#mdb00ba95ec\" y=\"212.447405265\"/>\n",
       "     <use style=\"fill:#0000ff;stroke:#000000;stroke-width:0.5;\" x=\"64.8025857301\" xlink:href=\"#mdb00ba95ec\" y=\"209.731232119\"/>\n",
       "     <use style=\"fill:#0000ff;stroke:#000000;stroke-width:0.5;\" x=\"76.5638136064\" xlink:href=\"#mdb00ba95ec\" y=\"203.016820079\"/>\n",
       "     <use style=\"fill:#0000ff;stroke:#000000;stroke-width:0.5;\" x=\"88.3158937\" xlink:href=\"#mdb00ba95ec\" y=\"197.2144796\"/>\n",
       "     <use style=\"fill:#0000ff;stroke:#000000;stroke-width:0.5;\" x=\"100.058121734\" xlink:href=\"#mdb00ba95ec\" y=\"195.571987706\"/>\n",
       "     <use style=\"fill:#0000ff;stroke:#000000;stroke-width:0.5;\" x=\"111.809873822\" xlink:href=\"#mdb00ba95ec\" y=\"184.295047325\"/>\n",
       "     <use style=\"fill:#0000ff;stroke:#000000;stroke-width:0.5;\" x=\"123.550370362\" xlink:href=\"#mdb00ba95ec\" y=\"194.565729675\"/>\n",
       "     <use style=\"fill:#0000ff;stroke:#000000;stroke-width:0.5;\" x=\"135.29946829\" xlink:href=\"#mdb00ba95ec\" y=\"191.38800482\"/>\n",
       "     <use style=\"fill:#0000ff;stroke:#000000;stroke-width:0.5;\" x=\"147.049593205\" xlink:href=\"#mdb00ba95ec\" y=\"185.833877062\"/>\n",
       "     <use style=\"fill:#0000ff;stroke:#000000;stroke-width:0.5;\" x=\"158.798255227\" xlink:href=\"#mdb00ba95ec\" y=\"191.540662999\"/>\n",
       "     <use style=\"fill:#0000ff;stroke:#000000;stroke-width:0.5;\" x=\"170.54591902\" xlink:href=\"#mdb00ba95ec\" y=\"189.501744933\"/>\n",
       "     <use style=\"fill:#0000ff;stroke:#000000;stroke-width:0.5;\" x=\"182.294683009\" xlink:href=\"#mdb00ba95ec\" y=\"188.110159493\"/>\n",
       "     <use style=\"fill:#0000ff;stroke:#000000;stroke-width:0.5;\" x=\"194.042251298\" xlink:href=\"#mdb00ba95ec\" y=\"192.008730177\"/>\n",
       "     <use style=\"fill:#0000ff;stroke:#000000;stroke-width:0.5;\" x=\"205.788802408\" xlink:href=\"#mdb00ba95ec\" y=\"188.458405435\"/>\n",
       "     <use style=\"fill:#0000ff;stroke:#000000;stroke-width:0.5;\" x=\"217.536571768\" xlink:href=\"#mdb00ba95ec\" y=\"183.377074157\"/>\n",
       "     <use style=\"fill:#0000ff;stroke:#000000;stroke-width:0.5;\" x=\"229.284834572\" xlink:href=\"#mdb00ba95ec\" y=\"152.97178035\"/>\n",
       "     <use style=\"fill:#0000ff;stroke:#000000;stroke-width:0.5;\" x=\"241.032027624\" xlink:href=\"#mdb00ba95ec\" y=\"106.910749898\"/>\n",
       "     <use style=\"fill:#0000ff;stroke:#000000;stroke-width:0.5;\" x=\"252.779786894\" xlink:href=\"#mdb00ba95ec\" y=\"59.7730085228\"/>\n",
       "     <use style=\"fill:#0000ff;stroke:#000000;stroke-width:0.5;\" x=\"264.527168955\" xlink:href=\"#mdb00ba95ec\" y=\"18.870808637\"/>\n",
       "    </g>\n",
       "   </g>\n",
       "   <g id=\"line2d_2\">\n",
       "    <path clip-path=\"url(#pafb01ba72a)\" d=\"\n",
       "M41.3187 189.278\n",
       "L53.0611 189.277\n",
       "L64.8026 189.277\n",
       "L76.5638 189.277\n",
       "L88.3159 189.278\n",
       "L100.058 189.277\n",
       "L111.81 189.277\n",
       "L123.55 189.277\n",
       "L135.299 189.279\n",
       "L147.05 189.277\n",
       "L158.798 189.277\n",
       "L170.546 189.277\n",
       "L182.295 189.277\n",
       "L194.042 189.277\n",
       "L205.789 189.261\n",
       "L217.537 189.05\n",
       "L229.285 187.136\n",
       "L241.032 183.332\n",
       "L252.78 180.551\n",
       "L264.527 176.635\" style=\"fill:none;stroke:#008000;stroke-linecap:square;\"/>\n",
       "    <defs>\n",
       "     <path d=\"\n",
       "M-3 3\n",
       "L3 3\n",
       "L3 -3\n",
       "L-3 -3\n",
       "z\n",
       "\" id=\"m45eb232605\" style=\"stroke:#000000;stroke-linejoin:miter;stroke-width:0.5;\"/>\n",
       "    </defs>\n",
       "    <g clip-path=\"url(#pafb01ba72a)\">\n",
       "     <use style=\"fill:#008000;stroke:#000000;stroke-linejoin:miter;stroke-width:0.5;\" x=\"41.3186583777\" xlink:href=\"#m45eb232605\" y=\"189.277895716\"/>\n",
       "     <use style=\"fill:#008000;stroke:#000000;stroke-linejoin:miter;stroke-width:0.5;\" x=\"53.0611335464\" xlink:href=\"#m45eb232605\" y=\"189.277189265\"/>\n",
       "     <use style=\"fill:#008000;stroke:#000000;stroke-linejoin:miter;stroke-width:0.5;\" x=\"64.8025857301\" xlink:href=\"#m45eb232605\" y=\"189.277189265\"/>\n",
       "     <use style=\"fill:#008000;stroke:#000000;stroke-linejoin:miter;stroke-width:0.5;\" x=\"76.5638136064\" xlink:href=\"#m45eb232605\" y=\"189.277283361\"/>\n",
       "     <use style=\"fill:#008000;stroke:#000000;stroke-linejoin:miter;stroke-width:0.5;\" x=\"88.3158937\" xlink:href=\"#m45eb232605\" y=\"189.277565609\"/>\n",
       "     <use style=\"fill:#008000;stroke:#000000;stroke-linejoin:miter;stroke-width:0.5;\" x=\"100.058121734\" xlink:href=\"#m45eb232605\" y=\"189.277189265\"/>\n",
       "     <use style=\"fill:#008000;stroke:#000000;stroke-linejoin:miter;stroke-width:0.5;\" x=\"111.809873822\" xlink:href=\"#m45eb232605\" y=\"189.277189265\"/>\n",
       "     <use style=\"fill:#008000;stroke:#000000;stroke-linejoin:miter;stroke-width:0.5;\" x=\"123.550370362\" xlink:href=\"#m45eb232605\" y=\"189.277184426\"/>\n",
       "     <use style=\"fill:#008000;stroke:#000000;stroke-linejoin:miter;stroke-width:0.5;\" x=\"135.29946829\" xlink:href=\"#m45eb232605\" y=\"189.279379905\"/>\n",
       "     <use style=\"fill:#008000;stroke:#000000;stroke-linejoin:miter;stroke-width:0.5;\" x=\"147.049593205\" xlink:href=\"#m45eb232605\" y=\"189.277180794\"/>\n",
       "     <use style=\"fill:#008000;stroke:#000000;stroke-linejoin:miter;stroke-width:0.5;\" x=\"158.798255227\" xlink:href=\"#m45eb232605\" y=\"189.277158342\"/>\n",
       "     <use style=\"fill:#008000;stroke:#000000;stroke-linejoin:miter;stroke-width:0.5;\" x=\"170.54591902\" xlink:href=\"#m45eb232605\" y=\"189.277149845\"/>\n",
       "     <use style=\"fill:#008000;stroke:#000000;stroke-linejoin:miter;stroke-width:0.5;\" x=\"182.294683009\" xlink:href=\"#m45eb232605\" y=\"189.277142566\"/>\n",
       "     <use style=\"fill:#008000;stroke:#000000;stroke-linejoin:miter;stroke-width:0.5;\" x=\"194.042251298\" xlink:href=\"#m45eb232605\" y=\"189.276750168\"/>\n",
       "     <use style=\"fill:#008000;stroke:#000000;stroke-linejoin:miter;stroke-width:0.5;\" x=\"205.788802408\" xlink:href=\"#m45eb232605\" y=\"189.260901838\"/>\n",
       "     <use style=\"fill:#008000;stroke:#000000;stroke-linejoin:miter;stroke-width:0.5;\" x=\"217.536571768\" xlink:href=\"#m45eb232605\" y=\"189.050047387\"/>\n",
       "     <use style=\"fill:#008000;stroke:#000000;stroke-linejoin:miter;stroke-width:0.5;\" x=\"229.284834572\" xlink:href=\"#m45eb232605\" y=\"187.135978931\"/>\n",
       "     <use style=\"fill:#008000;stroke:#000000;stroke-linejoin:miter;stroke-width:0.5;\" x=\"241.032027624\" xlink:href=\"#m45eb232605\" y=\"183.331986821\"/>\n",
       "     <use style=\"fill:#008000;stroke:#000000;stroke-linejoin:miter;stroke-width:0.5;\" x=\"252.779786894\" xlink:href=\"#m45eb232605\" y=\"180.550799284\"/>\n",
       "     <use style=\"fill:#008000;stroke:#000000;stroke-linejoin:miter;stroke-width:0.5;\" x=\"264.527168955\" xlink:href=\"#m45eb232605\" y=\"176.634673961\"/>\n",
       "    </g>\n",
       "   </g>\n",
       "   <g id=\"patch_3\">\n",
       "    <path d=\"\n",
       "M40.1219 12.0391\n",
       "L374.922 12.0391\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_4\">\n",
       "    <path d=\"\n",
       "M40.1219 235.239\n",
       "L40.1219 12.0391\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_5\">\n",
       "    <path d=\"\n",
       "M374.922 235.239\n",
       "L374.922 12.0391\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_6\">\n",
       "    <path d=\"\n",
       "M40.1219 235.239\n",
       "L374.922 235.239\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;\"/>\n",
       "   </g>\n",
       "   <g id=\"matplotlib.axis_1\">\n",
       "    <g id=\"xtick_1\">\n",
       "     <g id=\"line2d_3\">\n",
       "      <defs>\n",
       "       <path d=\"\n",
       "M0 0\n",
       "L0 -4\" id=\"mc7db9fdffb\" style=\"stroke:#000000;stroke-width:0.5;\"/>\n",
       "      </defs>\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"40.121875\" xlink:href=\"#mc7db9fdffb\" y=\"235.2390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"line2d_4\">\n",
       "      <defs>\n",
       "       <path d=\"\n",
       "M0 0\n",
       "L0 4\" id=\"m5a7d422ac3\" style=\"stroke:#000000;stroke-width:0.5;\"/>\n",
       "      </defs>\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"40.121875\" xlink:href=\"#m5a7d422ac3\" y=\"12.0390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_1\">\n",
       "      <!-- $\\mathdefault{10^{3}}$ -->\n",
       "      <defs>\n",
       "       <path d=\"\n",
       "M40.5781 39.3125\n",
       "Q47.6562 37.7969 51.625 33\n",
       "Q55.6094 28.2188 55.6094 21.1875\n",
       "Q55.6094 10.4062 48.1875 4.48438\n",
       "Q40.7656 -1.42188 27.0938 -1.42188\n",
       "Q22.5156 -1.42188 17.6562 -0.515625\n",
       "Q12.7969 0.390625 7.625 2.20312\n",
       "L7.625 11.7188\n",
       "Q11.7188 9.32812 16.5938 8.10938\n",
       "Q21.4844 6.89062 26.8125 6.89062\n",
       "Q36.0781 6.89062 40.9375 10.5469\n",
       "Q45.7969 14.2031 45.7969 21.1875\n",
       "Q45.7969 27.6406 41.2812 31.2656\n",
       "Q36.7656 34.9062 28.7188 34.9062\n",
       "L20.2188 34.9062\n",
       "L20.2188 43.0156\n",
       "L29.1094 43.0156\n",
       "Q36.375 43.0156 40.2344 45.9219\n",
       "Q44.0938 48.8281 44.0938 54.2969\n",
       "Q44.0938 59.9062 40.1094 62.9062\n",
       "Q36.1406 65.9219 28.7188 65.9219\n",
       "Q24.6562 65.9219 20.0156 65.0312\n",
       "Q15.375 64.1562 9.8125 62.3125\n",
       "L9.8125 71.0938\n",
       "Q15.4375 72.6562 20.3438 73.4375\n",
       "Q25.25 74.2188 29.5938 74.2188\n",
       "Q40.8281 74.2188 47.3594 69.1094\n",
       "Q53.9062 64.0156 53.9062 55.3281\n",
       "Q53.9062 49.2656 50.4375 45.0938\n",
       "Q46.9688 40.9219 40.5781 39.3125\" id=\"BitstreamVeraSans-Roman-33\"/>\n",
       "       <path d=\"\n",
       "M12.4062 8.29688\n",
       "L28.5156 8.29688\n",
       "L28.5156 63.9219\n",
       "L10.9844 60.4062\n",
       "L10.9844 69.3906\n",
       "L28.4219 72.9062\n",
       "L38.2812 72.9062\n",
       "L38.2812 8.29688\n",
       "L54.3906 8.29688\n",
       "L54.3906 0\n",
       "L12.4062 0\n",
       "z\n",
       "\" id=\"BitstreamVeraSans-Roman-31\"/>\n",
       "       <path d=\"\n",
       "M31.7812 66.4062\n",
       "Q24.1719 66.4062 20.3281 58.9062\n",
       "Q16.5 51.4219 16.5 36.375\n",
       "Q16.5 21.3906 20.3281 13.8906\n",
       "Q24.1719 6.39062 31.7812 6.39062\n",
       "Q39.4531 6.39062 43.2812 13.8906\n",
       "Q47.125 21.3906 47.125 36.375\n",
       "Q47.125 51.4219 43.2812 58.9062\n",
       "Q39.4531 66.4062 31.7812 66.4062\n",
       "M31.7812 74.2188\n",
       "Q44.0469 74.2188 50.5156 64.5156\n",
       "Q56.9844 54.8281 56.9844 36.375\n",
       "Q56.9844 17.9688 50.5156 8.26562\n",
       "Q44.0469 -1.42188 31.7812 -1.42188\n",
       "Q19.5312 -1.42188 13.0625 8.26562\n",
       "Q6.59375 17.9688 6.59375 36.375\n",
       "Q6.59375 54.8281 13.0625 64.5156\n",
       "Q19.5312 74.2188 31.7812 74.2188\" id=\"BitstreamVeraSans-Roman-30\"/>\n",
       "      </defs>\n",
       "      <g transform=\"translate(30.471875 247.859375)scale(0.1 -0.1)\">\n",
       "       <use transform=\"translate(0.0 0.546875)\" xlink:href=\"#BitstreamVeraSans-Roman-31\"/>\n",
       "       <use transform=\"translate(63.623046875 0.546875)\" xlink:href=\"#BitstreamVeraSans-Roman-30\"/>\n",
       "       <use transform=\"translate(127.24609375 53.046875)scale(0.7)\" xlink:href=\"#BitstreamVeraSans-Roman-33\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_2\">\n",
       "     <g id=\"line2d_5\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"151.721875\" xlink:href=\"#mc7db9fdffb\" y=\"235.2390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"line2d_6\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"151.721875\" xlink:href=\"#m5a7d422ac3\" y=\"12.0390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_2\">\n",
       "      <!-- $\\mathdefault{10^{4}}$ -->\n",
       "      <defs>\n",
       "       <path d=\"\n",
       "M37.7969 64.3125\n",
       "L12.8906 25.3906\n",
       "L37.7969 25.3906\n",
       "z\n",
       "\n",
       "M35.2031 72.9062\n",
       "L47.6094 72.9062\n",
       "L47.6094 25.3906\n",
       "L58.0156 25.3906\n",
       "L58.0156 17.1875\n",
       "L47.6094 17.1875\n",
       "L47.6094 0\n",
       "L37.7969 0\n",
       "L37.7969 17.1875\n",
       "L4.89062 17.1875\n",
       "L4.89062 26.7031\n",
       "z\n",
       "\" id=\"BitstreamVeraSans-Roman-34\"/>\n",
       "      </defs>\n",
       "      <g transform=\"translate(142.071875 247.759375)scale(0.1 -0.1)\">\n",
       "       <use transform=\"translate(0.0 0.46562500000000284)\" xlink:href=\"#BitstreamVeraSans-Roman-31\"/>\n",
       "       <use transform=\"translate(63.623046875 0.46562500000000284)\" xlink:href=\"#BitstreamVeraSans-Roman-30\"/>\n",
       "       <use transform=\"translate(127.24609375 52.965625)scale(0.7)\" xlink:href=\"#BitstreamVeraSans-Roman-34\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_3\">\n",
       "     <g id=\"line2d_7\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"263.321875\" xlink:href=\"#mc7db9fdffb\" y=\"235.2390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"line2d_8\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"263.321875\" xlink:href=\"#m5a7d422ac3\" y=\"12.0390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_3\">\n",
       "      <!-- $\\mathdefault{10^{5}}$ -->\n",
       "      <defs>\n",
       "       <path d=\"\n",
       "M10.7969 72.9062\n",
       "L49.5156 72.9062\n",
       "L49.5156 64.5938\n",
       "L19.8281 64.5938\n",
       "L19.8281 46.7344\n",
       "Q21.9688 47.4688 24.1094 47.8281\n",
       "Q26.2656 48.1875 28.4219 48.1875\n",
       "Q40.625 48.1875 47.75 41.5\n",
       "Q54.8906 34.8125 54.8906 23.3906\n",
       "Q54.8906 11.625 47.5625 5.09375\n",
       "Q40.2344 -1.42188 26.9062 -1.42188\n",
       "Q22.3125 -1.42188 17.5469 -0.640625\n",
       "Q12.7969 0.140625 7.71875 1.70312\n",
       "L7.71875 11.625\n",
       "Q12.1094 9.23438 16.7969 8.0625\n",
       "Q21.4844 6.89062 26.7031 6.89062\n",
       "Q35.1562 6.89062 40.0781 11.3281\n",
       "Q45.0156 15.7656 45.0156 23.3906\n",
       "Q45.0156 31 40.0781 35.4375\n",
       "Q35.1562 39.8906 26.7031 39.8906\n",
       "Q22.75 39.8906 18.8125 39.0156\n",
       "Q14.8906 38.1406 10.7969 36.2812\n",
       "z\n",
       "\" id=\"BitstreamVeraSans-Roman-35\"/>\n",
       "      </defs>\n",
       "      <g transform=\"translate(253.671875 247.759375)scale(0.1 -0.1)\">\n",
       "       <use transform=\"translate(0.0 0.46562500000000284)\" xlink:href=\"#BitstreamVeraSans-Roman-31\"/>\n",
       "       <use transform=\"translate(63.623046875 0.46562500000000284)\" xlink:href=\"#BitstreamVeraSans-Roman-30\"/>\n",
       "       <use transform=\"translate(127.24609375 52.965625)scale(0.7)\" xlink:href=\"#BitstreamVeraSans-Roman-35\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_4\">\n",
       "     <g id=\"line2d_9\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"374.921875\" xlink:href=\"#mc7db9fdffb\" y=\"235.2390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"line2d_10\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"374.921875\" xlink:href=\"#m5a7d422ac3\" y=\"12.0390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_4\">\n",
       "      <!-- $\\mathdefault{10^{6}}$ -->\n",
       "      <defs>\n",
       "       <path d=\"\n",
       "M33.0156 40.375\n",
       "Q26.375 40.375 22.4844 35.8281\n",
       "Q18.6094 31.2969 18.6094 23.3906\n",
       "Q18.6094 15.5312 22.4844 10.9531\n",
       "Q26.375 6.39062 33.0156 6.39062\n",
       "Q39.6562 6.39062 43.5312 10.9531\n",
       "Q47.4062 15.5312 47.4062 23.3906\n",
       "Q47.4062 31.2969 43.5312 35.8281\n",
       "Q39.6562 40.375 33.0156 40.375\n",
       "M52.5938 71.2969\n",
       "L52.5938 62.3125\n",
       "Q48.875 64.0625 45.0938 64.9844\n",
       "Q41.3125 65.9219 37.5938 65.9219\n",
       "Q27.8281 65.9219 22.6719 59.3281\n",
       "Q17.5312 52.7344 16.7969 39.4062\n",
       "Q19.6719 43.6562 24.0156 45.9219\n",
       "Q28.375 48.1875 33.5938 48.1875\n",
       "Q44.5781 48.1875 50.9531 41.5156\n",
       "Q57.3281 34.8594 57.3281 23.3906\n",
       "Q57.3281 12.1562 50.6875 5.35938\n",
       "Q44.0469 -1.42188 33.0156 -1.42188\n",
       "Q20.3594 -1.42188 13.6719 8.26562\n",
       "Q6.98438 17.9688 6.98438 36.375\n",
       "Q6.98438 53.6562 15.1875 63.9375\n",
       "Q23.3906 74.2188 37.2031 74.2188\n",
       "Q40.9219 74.2188 44.7031 73.4844\n",
       "Q48.4844 72.75 52.5938 71.2969\" id=\"BitstreamVeraSans-Roman-36\"/>\n",
       "      </defs>\n",
       "      <g transform=\"translate(365.271875 247.859375)scale(0.1 -0.1)\">\n",
       "       <use transform=\"translate(0.0 0.546875)\" xlink:href=\"#BitstreamVeraSans-Roman-31\"/>\n",
       "       <use transform=\"translate(63.623046875 0.546875)\" xlink:href=\"#BitstreamVeraSans-Roman-30\"/>\n",
       "       <use transform=\"translate(127.24609375 53.046875)scale(0.7)\" xlink:href=\"#BitstreamVeraSans-Roman-36\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_5\">\n",
       "     <g id=\"line2d_11\">\n",
       "      <defs>\n",
       "       <path d=\"\n",
       "M0 0\n",
       "L0 -2\" id=\"mc21db286a6\" style=\"stroke:#000000;stroke-width:0.5;\"/>\n",
       "      </defs>\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"73.7168225161\" xlink:href=\"#mc21db286a6\" y=\"235.2390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"line2d_12\">\n",
       "      <defs>\n",
       "       <path d=\"\n",
       "M0 0\n",
       "L0 2\" id=\"ma9c915e141\" style=\"stroke:#000000;stroke-width:0.5;\"/>\n",
       "      </defs>\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"73.7168225161\" xlink:href=\"#ma9c915e141\" y=\"12.0390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_6\">\n",
       "     <g id=\"line2d_13\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"93.3686070267\" xlink:href=\"#mc21db286a6\" y=\"235.2390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"line2d_14\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"93.3686070267\" xlink:href=\"#ma9c915e141\" y=\"12.0390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_7\">\n",
       "     <g id=\"line2d_15\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"107.311770032\" xlink:href=\"#mc21db286a6\" y=\"235.2390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"line2d_16\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"107.311770032\" xlink:href=\"#ma9c915e141\" y=\"12.0390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_8\">\n",
       "     <g id=\"line2d_17\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"118.126927484\" xlink:href=\"#mc21db286a6\" y=\"235.2390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"line2d_18\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"118.126927484\" xlink:href=\"#ma9c915e141\" y=\"12.0390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_9\">\n",
       "     <g id=\"line2d_19\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"126.963554543\" xlink:href=\"#mc21db286a6\" y=\"235.2390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"line2d_20\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"126.963554543\" xlink:href=\"#ma9c915e141\" y=\"12.0390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_10\">\n",
       "     <g id=\"line2d_21\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"134.434816266\" xlink:href=\"#mc21db286a6\" y=\"235.2390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"line2d_22\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"134.434816266\" xlink:href=\"#ma9c915e141\" y=\"12.0390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_11\">\n",
       "     <g id=\"line2d_23\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"140.906717548\" xlink:href=\"#mc21db286a6\" y=\"235.2390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"line2d_24\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"140.906717548\" xlink:href=\"#ma9c915e141\" y=\"12.0390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_12\">\n",
       "     <g id=\"line2d_25\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"146.615339053\" xlink:href=\"#mc21db286a6\" y=\"235.2390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"line2d_26\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"146.615339053\" xlink:href=\"#ma9c915e141\" y=\"12.0390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_13\">\n",
       "     <g id=\"line2d_27\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"185.316822516\" xlink:href=\"#mc21db286a6\" y=\"235.2390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"line2d_28\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"185.316822516\" xlink:href=\"#ma9c915e141\" y=\"12.0390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_14\">\n",
       "     <g id=\"line2d_29\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"204.968607027\" xlink:href=\"#mc21db286a6\" y=\"235.2390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"line2d_30\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"204.968607027\" xlink:href=\"#ma9c915e141\" y=\"12.0390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_15\">\n",
       "     <g id=\"line2d_31\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"218.911770032\" xlink:href=\"#mc21db286a6\" y=\"235.2390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"line2d_32\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"218.911770032\" xlink:href=\"#ma9c915e141\" y=\"12.0390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_16\">\n",
       "     <g id=\"line2d_33\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"229.726927484\" xlink:href=\"#mc21db286a6\" y=\"235.2390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"line2d_34\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"229.726927484\" xlink:href=\"#ma9c915e141\" y=\"12.0390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_17\">\n",
       "     <g id=\"line2d_35\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"238.563554543\" xlink:href=\"#mc21db286a6\" y=\"235.2390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"line2d_36\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"238.563554543\" xlink:href=\"#ma9c915e141\" y=\"12.0390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_18\">\n",
       "     <g id=\"line2d_37\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"246.034816266\" xlink:href=\"#mc21db286a6\" y=\"235.2390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"line2d_38\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"246.034816266\" xlink:href=\"#ma9c915e141\" y=\"12.0390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_19\">\n",
       "     <g id=\"line2d_39\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"252.506717548\" xlink:href=\"#mc21db286a6\" y=\"235.2390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"line2d_40\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"252.506717548\" xlink:href=\"#ma9c915e141\" y=\"12.0390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_20\">\n",
       "     <g id=\"line2d_41\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"258.215339053\" xlink:href=\"#mc21db286a6\" y=\"235.2390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"line2d_42\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"258.215339053\" xlink:href=\"#ma9c915e141\" y=\"12.0390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_21\">\n",
       "     <g id=\"line2d_43\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"296.916822516\" xlink:href=\"#mc21db286a6\" y=\"235.2390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"line2d_44\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"296.916822516\" xlink:href=\"#ma9c915e141\" y=\"12.0390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_22\">\n",
       "     <g id=\"line2d_45\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"316.568607027\" xlink:href=\"#mc21db286a6\" y=\"235.2390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"line2d_46\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"316.568607027\" xlink:href=\"#ma9c915e141\" y=\"12.0390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_23\">\n",
       "     <g id=\"line2d_47\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"330.511770032\" xlink:href=\"#mc21db286a6\" y=\"235.2390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"line2d_48\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"330.511770032\" xlink:href=\"#ma9c915e141\" y=\"12.0390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_24\">\n",
       "     <g id=\"line2d_49\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"341.326927484\" xlink:href=\"#mc21db286a6\" y=\"235.2390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"line2d_50\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"341.326927484\" xlink:href=\"#ma9c915e141\" y=\"12.0390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_25\">\n",
       "     <g id=\"line2d_51\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"350.163554543\" xlink:href=\"#mc21db286a6\" y=\"235.2390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"line2d_52\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"350.163554543\" xlink:href=\"#ma9c915e141\" y=\"12.0390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_26\">\n",
       "     <g id=\"line2d_53\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"357.634816266\" xlink:href=\"#mc21db286a6\" y=\"235.2390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"line2d_54\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"357.634816266\" xlink:href=\"#ma9c915e141\" y=\"12.0390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_27\">\n",
       "     <g id=\"line2d_55\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"364.106717548\" xlink:href=\"#mc21db286a6\" y=\"235.2390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"line2d_56\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"364.106717548\" xlink:href=\"#ma9c915e141\" y=\"12.0390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_28\">\n",
       "     <g id=\"line2d_57\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"369.815339053\" xlink:href=\"#mc21db286a6\" y=\"235.2390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"line2d_58\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"369.815339053\" xlink:href=\"#ma9c915e141\" y=\"12.0390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"text_5\">\n",
       "     <!-- training set size -->\n",
       "     <defs>\n",
       "      <path d=\"\n",
       "M56.2031 29.5938\n",
       "L56.2031 25.2031\n",
       "L14.8906 25.2031\n",
       "Q15.4844 15.9219 20.4844 11.0625\n",
       "Q25.4844 6.20312 34.4219 6.20312\n",
       "Q39.5938 6.20312 44.4531 7.46875\n",
       "Q49.3125 8.73438 54.1094 11.2812\n",
       "L54.1094 2.78125\n",
       "Q49.2656 0.734375 44.1875 -0.34375\n",
       "Q39.1094 -1.42188 33.8906 -1.42188\n",
       "Q20.7969 -1.42188 13.1562 6.1875\n",
       "Q5.51562 13.8125 5.51562 26.8125\n",
       "Q5.51562 40.2344 12.7656 48.1094\n",
       "Q20.0156 56 32.3281 56\n",
       "Q43.3594 56 49.7812 48.8906\n",
       "Q56.2031 41.7969 56.2031 29.5938\n",
       "M47.2188 32.2344\n",
       "Q47.125 39.5938 43.0938 43.9844\n",
       "Q39.0625 48.3906 32.4219 48.3906\n",
       "Q24.9062 48.3906 20.3906 44.1406\n",
       "Q15.875 39.8906 15.1875 32.1719\n",
       "z\n",
       "\" id=\"BitstreamVeraSans-Roman-65\"/>\n",
       "      <path id=\"BitstreamVeraSans-Roman-20\"/>\n",
       "      <path d=\"\n",
       "M54.8906 33.0156\n",
       "L54.8906 0\n",
       "L45.9062 0\n",
       "L45.9062 32.7188\n",
       "Q45.9062 40.4844 42.875 44.3281\n",
       "Q39.8438 48.1875 33.7969 48.1875\n",
       "Q26.5156 48.1875 22.3125 43.5469\n",
       "Q18.1094 38.9219 18.1094 30.9062\n",
       "L18.1094 0\n",
       "L9.07812 0\n",
       "L9.07812 54.6875\n",
       "L18.1094 54.6875\n",
       "L18.1094 46.1875\n",
       "Q21.3438 51.125 25.7031 53.5625\n",
       "Q30.0781 56 35.7969 56\n",
       "Q45.2188 56 50.0469 50.1719\n",
       "Q54.8906 44.3438 54.8906 33.0156\" id=\"BitstreamVeraSans-Roman-6e\"/>\n",
       "      <path d=\"\n",
       "M5.51562 54.6875\n",
       "L48.1875 54.6875\n",
       "L48.1875 46.4844\n",
       "L14.4062 7.17188\n",
       "L48.1875 7.17188\n",
       "L48.1875 0\n",
       "L4.29688 0\n",
       "L4.29688 8.20312\n",
       "L38.0938 47.5156\n",
       "L5.51562 47.5156\n",
       "z\n",
       "\" id=\"BitstreamVeraSans-Roman-7a\"/>\n",
       "      <path d=\"\n",
       "M18.3125 70.2188\n",
       "L18.3125 54.6875\n",
       "L36.8125 54.6875\n",
       "L36.8125 47.7031\n",
       "L18.3125 47.7031\n",
       "L18.3125 18.0156\n",
       "Q18.3125 11.3281 20.1406 9.42188\n",
       "Q21.9688 7.51562 27.5938 7.51562\n",
       "L36.8125 7.51562\n",
       "L36.8125 0\n",
       "L27.5938 0\n",
       "Q17.1875 0 13.2344 3.875\n",
       "Q9.28125 7.76562 9.28125 18.0156\n",
       "L9.28125 47.7031\n",
       "L2.6875 47.7031\n",
       "L2.6875 54.6875\n",
       "L9.28125 54.6875\n",
       "L9.28125 70.2188\n",
       "z\n",
       "\" id=\"BitstreamVeraSans-Roman-74\"/>\n",
       "      <path d=\"\n",
       "M44.2812 53.0781\n",
       "L44.2812 44.5781\n",
       "Q40.4844 46.5312 36.375 47.5\n",
       "Q32.2812 48.4844 27.875 48.4844\n",
       "Q21.1875 48.4844 17.8438 46.4375\n",
       "Q14.5 44.3906 14.5 40.2812\n",
       "Q14.5 37.1562 16.8906 35.375\n",
       "Q19.2812 33.5938 26.5156 31.9844\n",
       "L29.5938 31.2969\n",
       "Q39.1562 29.25 43.1875 25.5156\n",
       "Q47.2188 21.7812 47.2188 15.0938\n",
       "Q47.2188 7.46875 41.1875 3.01562\n",
       "Q35.1562 -1.42188 24.6094 -1.42188\n",
       "Q20.2188 -1.42188 15.4531 -0.5625\n",
       "Q10.6875 0.296875 5.42188 2\n",
       "L5.42188 11.2812\n",
       "Q10.4062 8.6875 15.2344 7.39062\n",
       "Q20.0625 6.10938 24.8125 6.10938\n",
       "Q31.1562 6.10938 34.5625 8.28125\n",
       "Q37.9844 10.4531 37.9844 14.4062\n",
       "Q37.9844 18.0625 35.5156 20.0156\n",
       "Q33.0625 21.9688 24.7031 23.7812\n",
       "L21.5781 24.5156\n",
       "Q13.2344 26.2656 9.51562 29.9062\n",
       "Q5.8125 33.5469 5.8125 39.8906\n",
       "Q5.8125 47.6094 11.2812 51.7969\n",
       "Q16.75 56 26.8125 56\n",
       "Q31.7812 56 36.1719 55.2656\n",
       "Q40.5781 54.5469 44.2812 53.0781\" id=\"BitstreamVeraSans-Roman-73\"/>\n",
       "      <path d=\"\n",
       "M34.2812 27.4844\n",
       "Q23.3906 27.4844 19.1875 25\n",
       "Q14.9844 22.5156 14.9844 16.5\n",
       "Q14.9844 11.7188 18.1406 8.90625\n",
       "Q21.2969 6.10938 26.7031 6.10938\n",
       "Q34.1875 6.10938 38.7031 11.4062\n",
       "Q43.2188 16.7031 43.2188 25.4844\n",
       "L43.2188 27.4844\n",
       "z\n",
       "\n",
       "M52.2031 31.2031\n",
       "L52.2031 0\n",
       "L43.2188 0\n",
       "L43.2188 8.29688\n",
       "Q40.1406 3.32812 35.5469 0.953125\n",
       "Q30.9531 -1.42188 24.3125 -1.42188\n",
       "Q15.9219 -1.42188 10.9531 3.29688\n",
       "Q6 8.01562 6 15.9219\n",
       "Q6 25.1406 12.1719 29.8281\n",
       "Q18.3594 34.5156 30.6094 34.5156\n",
       "L43.2188 34.5156\n",
       "L43.2188 35.4062\n",
       "Q43.2188 41.6094 39.1406 45\n",
       "Q35.0625 48.3906 27.6875 48.3906\n",
       "Q23 48.3906 18.5469 47.2656\n",
       "Q14.1094 46.1406 10.0156 43.8906\n",
       "L10.0156 52.2031\n",
       "Q14.9375 54.1094 19.5781 55.0469\n",
       "Q24.2188 56 28.6094 56\n",
       "Q40.4844 56 46.3438 49.8438\n",
       "Q52.2031 43.7031 52.2031 31.2031\" id=\"BitstreamVeraSans-Roman-61\"/>\n",
       "      <path d=\"\n",
       "M45.4062 27.9844\n",
       "Q45.4062 37.75 41.375 43.1094\n",
       "Q37.3594 48.4844 30.0781 48.4844\n",
       "Q22.8594 48.4844 18.8281 43.1094\n",
       "Q14.7969 37.75 14.7969 27.9844\n",
       "Q14.7969 18.2656 18.8281 12.8906\n",
       "Q22.8594 7.51562 30.0781 7.51562\n",
       "Q37.3594 7.51562 41.375 12.8906\n",
       "Q45.4062 18.2656 45.4062 27.9844\n",
       "M54.3906 6.78125\n",
       "Q54.3906 -7.17188 48.1875 -13.9844\n",
       "Q42 -20.7969 29.2031 -20.7969\n",
       "Q24.4688 -20.7969 20.2656 -20.0938\n",
       "Q16.0625 -19.3906 12.1094 -17.9219\n",
       "L12.1094 -9.1875\n",
       "Q16.0625 -11.3281 19.9219 -12.3438\n",
       "Q23.7812 -13.375 27.7812 -13.375\n",
       "Q36.625 -13.375 41.0156 -8.76562\n",
       "Q45.4062 -4.15625 45.4062 5.17188\n",
       "L45.4062 9.625\n",
       "Q42.625 4.78125 38.2812 2.39062\n",
       "Q33.9375 0 27.875 0\n",
       "Q17.8281 0 11.6719 7.65625\n",
       "Q5.51562 15.3281 5.51562 27.9844\n",
       "Q5.51562 40.6719 11.6719 48.3281\n",
       "Q17.8281 56 27.875 56\n",
       "Q33.9375 56 38.2812 53.6094\n",
       "Q42.625 51.2188 45.4062 46.3906\n",
       "L45.4062 54.6875\n",
       "L54.3906 54.6875\n",
       "z\n",
       "\" id=\"BitstreamVeraSans-Roman-67\"/>\n",
       "      <path d=\"\n",
       "M41.1094 46.2969\n",
       "Q39.5938 47.1719 37.8125 47.5781\n",
       "Q36.0312 48 33.8906 48\n",
       "Q26.2656 48 22.1875 43.0469\n",
       "Q18.1094 38.0938 18.1094 28.8125\n",
       "L18.1094 0\n",
       "L9.07812 0\n",
       "L9.07812 54.6875\n",
       "L18.1094 54.6875\n",
       "L18.1094 46.1875\n",
       "Q20.9531 51.1719 25.4844 53.5781\n",
       "Q30.0312 56 36.5312 56\n",
       "Q37.4531 56 38.5781 55.875\n",
       "Q39.7031 55.7656 41.0625 55.5156\n",
       "z\n",
       "\" id=\"BitstreamVeraSans-Roman-72\"/>\n",
       "      <path d=\"\n",
       "M9.42188 54.6875\n",
       "L18.4062 54.6875\n",
       "L18.4062 0\n",
       "L9.42188 0\n",
       "z\n",
       "\n",
       "M9.42188 75.9844\n",
       "L18.4062 75.9844\n",
       "L18.4062 64.5938\n",
       "L9.42188 64.5938\n",
       "z\n",
       "\" id=\"BitstreamVeraSans-Roman-69\"/>\n",
       "     </defs>\n",
       "     <g transform=\"translate(167.9046875 262.5375)scale(0.1 -0.1)\">\n",
       "      <use xlink:href=\"#BitstreamVeraSans-Roman-74\"/>\n",
       "      <use x=\"39.208984375\" xlink:href=\"#BitstreamVeraSans-Roman-72\"/>\n",
       "      <use x=\"80.322265625\" xlink:href=\"#BitstreamVeraSans-Roman-61\"/>\n",
       "      <use x=\"141.6015625\" xlink:href=\"#BitstreamVeraSans-Roman-69\"/>\n",
       "      <use x=\"169.384765625\" xlink:href=\"#BitstreamVeraSans-Roman-6e\"/>\n",
       "      <use x=\"232.763671875\" xlink:href=\"#BitstreamVeraSans-Roman-69\"/>\n",
       "      <use x=\"260.546875\" xlink:href=\"#BitstreamVeraSans-Roman-6e\"/>\n",
       "      <use x=\"323.92578125\" xlink:href=\"#BitstreamVeraSans-Roman-67\"/>\n",
       "      <use x=\"387.40234375\" xlink:href=\"#BitstreamVeraSans-Roman-20\"/>\n",
       "      <use x=\"419.189453125\" xlink:href=\"#BitstreamVeraSans-Roman-73\"/>\n",
       "      <use x=\"471.2890625\" xlink:href=\"#BitstreamVeraSans-Roman-65\"/>\n",
       "      <use x=\"532.8125\" xlink:href=\"#BitstreamVeraSans-Roman-74\"/>\n",
       "      <use x=\"572.021484375\" xlink:href=\"#BitstreamVeraSans-Roman-20\"/>\n",
       "      <use x=\"603.80859375\" xlink:href=\"#BitstreamVeraSans-Roman-73\"/>\n",
       "      <use x=\"655.908203125\" xlink:href=\"#BitstreamVeraSans-Roman-69\"/>\n",
       "      <use x=\"683.69140625\" xlink:href=\"#BitstreamVeraSans-Roman-7a\"/>\n",
       "      <use x=\"736.181640625\" xlink:href=\"#BitstreamVeraSans-Roman-65\"/>\n",
       "     </g>\n",
       "    </g>\n",
       "   </g>\n",
       "   <g id=\"matplotlib.axis_2\">\n",
       "    <g id=\"ytick_1\">\n",
       "     <g id=\"line2d_59\">\n",
       "      <defs>\n",
       "       <path d=\"\n",
       "M0 0\n",
       "L4 0\" id=\"md7965d1ba0\" style=\"stroke:#000000;stroke-width:0.5;\"/>\n",
       "      </defs>\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"40.121875\" xlink:href=\"#md7965d1ba0\" y=\"235.2390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"line2d_60\">\n",
       "      <defs>\n",
       "       <path d=\"\n",
       "M0 0\n",
       "L-4 0\" id=\"md9a1c1a7cd\" style=\"stroke:#000000;stroke-width:0.5;\"/>\n",
       "      </defs>\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"374.921875\" xlink:href=\"#md9a1c1a7cd\" y=\"235.2390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_6\">\n",
       "      <!-- −1.00 -->\n",
       "      <defs>\n",
       "       <path d=\"\n",
       "M10.5938 35.5\n",
       "L73.1875 35.5\n",
       "L73.1875 27.2031\n",
       "L10.5938 27.2031\n",
       "z\n",
       "\" id=\"BitstreamVeraSans-Roman-2212\"/>\n",
       "       <path d=\"\n",
       "M10.6875 12.4062\n",
       "L21 12.4062\n",
       "L21 0\n",
       "L10.6875 0\n",
       "z\n",
       "\" id=\"BitstreamVeraSans-Roman-2e\"/>\n",
       "      </defs>\n",
       "      <g transform=\"translate(7.2 237.9984375)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#BitstreamVeraSans-Roman-2212\"/>\n",
       "       <use x=\"83.7890625\" xlink:href=\"#BitstreamVeraSans-Roman-31\"/>\n",
       "       <use x=\"147.412109375\" xlink:href=\"#BitstreamVeraSans-Roman-2e\"/>\n",
       "       <use x=\"179.19921875\" xlink:href=\"#BitstreamVeraSans-Roman-30\"/>\n",
       "       <use x=\"242.822265625\" xlink:href=\"#BitstreamVeraSans-Roman-30\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_2\">\n",
       "     <g id=\"line2d_61\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"40.121875\" xlink:href=\"#md7965d1ba0\" y=\"198.0390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"line2d_62\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"374.921875\" xlink:href=\"#md9a1c1a7cd\" y=\"198.0390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_7\">\n",
       "      <!-- −0.95 -->\n",
       "      <defs>\n",
       "       <path d=\"\n",
       "M10.9844 1.51562\n",
       "L10.9844 10.5\n",
       "Q14.7031 8.73438 18.5 7.8125\n",
       "Q22.3125 6.89062 25.9844 6.89062\n",
       "Q35.75 6.89062 40.8906 13.4531\n",
       "Q46.0469 20.0156 46.7812 33.4062\n",
       "Q43.9531 29.2031 39.5938 26.9531\n",
       "Q35.25 24.7031 29.9844 24.7031\n",
       "Q19.0469 24.7031 12.6719 31.3125\n",
       "Q6.29688 37.9375 6.29688 49.4219\n",
       "Q6.29688 60.6406 12.9375 67.4219\n",
       "Q19.5781 74.2188 30.6094 74.2188\n",
       "Q43.2656 74.2188 49.9219 64.5156\n",
       "Q56.5938 54.8281 56.5938 36.375\n",
       "Q56.5938 19.1406 48.4062 8.85938\n",
       "Q40.2344 -1.42188 26.4219 -1.42188\n",
       "Q22.7031 -1.42188 18.8906 -0.6875\n",
       "Q15.0938 0.046875 10.9844 1.51562\n",
       "M30.6094 32.4219\n",
       "Q37.25 32.4219 41.125 36.9531\n",
       "Q45.0156 41.5 45.0156 49.4219\n",
       "Q45.0156 57.2812 41.125 61.8438\n",
       "Q37.25 66.4062 30.6094 66.4062\n",
       "Q23.9688 66.4062 20.0938 61.8438\n",
       "Q16.2188 57.2812 16.2188 49.4219\n",
       "Q16.2188 41.5 20.0938 36.9531\n",
       "Q23.9688 32.4219 30.6094 32.4219\" id=\"BitstreamVeraSans-Roman-39\"/>\n",
       "      </defs>\n",
       "      <g transform=\"translate(7.409375 200.7984375)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#BitstreamVeraSans-Roman-2212\"/>\n",
       "       <use x=\"83.7890625\" xlink:href=\"#BitstreamVeraSans-Roman-30\"/>\n",
       "       <use x=\"147.412109375\" xlink:href=\"#BitstreamVeraSans-Roman-2e\"/>\n",
       "       <use x=\"179.19921875\" xlink:href=\"#BitstreamVeraSans-Roman-39\"/>\n",
       "       <use x=\"242.822265625\" xlink:href=\"#BitstreamVeraSans-Roman-35\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_3\">\n",
       "     <g id=\"line2d_63\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"40.121875\" xlink:href=\"#md7965d1ba0\" y=\"160.8390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"line2d_64\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"374.921875\" xlink:href=\"#md9a1c1a7cd\" y=\"160.8390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_8\">\n",
       "      <!-- −0.90 -->\n",
       "      <g transform=\"translate(7.2 163.5984375)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#BitstreamVeraSans-Roman-2212\"/>\n",
       "       <use x=\"83.7890625\" xlink:href=\"#BitstreamVeraSans-Roman-30\"/>\n",
       "       <use x=\"147.412109375\" xlink:href=\"#BitstreamVeraSans-Roman-2e\"/>\n",
       "       <use x=\"179.19921875\" xlink:href=\"#BitstreamVeraSans-Roman-39\"/>\n",
       "       <use x=\"242.822265625\" xlink:href=\"#BitstreamVeraSans-Roman-30\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_4\">\n",
       "     <g id=\"line2d_65\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"40.121875\" xlink:href=\"#md7965d1ba0\" y=\"123.6390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"line2d_66\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"374.921875\" xlink:href=\"#md9a1c1a7cd\" y=\"123.6390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_9\">\n",
       "      <!-- −0.85 -->\n",
       "      <defs>\n",
       "       <path d=\"\n",
       "M31.7812 34.625\n",
       "Q24.75 34.625 20.7188 30.8594\n",
       "Q16.7031 27.0938 16.7031 20.5156\n",
       "Q16.7031 13.9219 20.7188 10.1562\n",
       "Q24.75 6.39062 31.7812 6.39062\n",
       "Q38.8125 6.39062 42.8594 10.1719\n",
       "Q46.9219 13.9688 46.9219 20.5156\n",
       "Q46.9219 27.0938 42.8906 30.8594\n",
       "Q38.875 34.625 31.7812 34.625\n",
       "M21.9219 38.8125\n",
       "Q15.5781 40.375 12.0312 44.7188\n",
       "Q8.5 49.0781 8.5 55.3281\n",
       "Q8.5 64.0625 14.7188 69.1406\n",
       "Q20.9531 74.2188 31.7812 74.2188\n",
       "Q42.6719 74.2188 48.875 69.1406\n",
       "Q55.0781 64.0625 55.0781 55.3281\n",
       "Q55.0781 49.0781 51.5312 44.7188\n",
       "Q48 40.375 41.7031 38.8125\n",
       "Q48.8281 37.1562 52.7969 32.3125\n",
       "Q56.7812 27.4844 56.7812 20.5156\n",
       "Q56.7812 9.90625 50.3125 4.23438\n",
       "Q43.8438 -1.42188 31.7812 -1.42188\n",
       "Q19.7344 -1.42188 13.25 4.23438\n",
       "Q6.78125 9.90625 6.78125 20.5156\n",
       "Q6.78125 27.4844 10.7812 32.3125\n",
       "Q14.7969 37.1562 21.9219 38.8125\n",
       "M18.3125 54.3906\n",
       "Q18.3125 48.7344 21.8438 45.5625\n",
       "Q25.3906 42.3906 31.7812 42.3906\n",
       "Q38.1406 42.3906 41.7188 45.5625\n",
       "Q45.3125 48.7344 45.3125 54.3906\n",
       "Q45.3125 60.0625 41.7188 63.2344\n",
       "Q38.1406 66.4062 31.7812 66.4062\n",
       "Q25.3906 66.4062 21.8438 63.2344\n",
       "Q18.3125 60.0625 18.3125 54.3906\" id=\"BitstreamVeraSans-Roman-38\"/>\n",
       "      </defs>\n",
       "      <g transform=\"translate(7.409375 126.3984375)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#BitstreamVeraSans-Roman-2212\"/>\n",
       "       <use x=\"83.7890625\" xlink:href=\"#BitstreamVeraSans-Roman-30\"/>\n",
       "       <use x=\"147.412109375\" xlink:href=\"#BitstreamVeraSans-Roman-2e\"/>\n",
       "       <use x=\"179.19921875\" xlink:href=\"#BitstreamVeraSans-Roman-38\"/>\n",
       "       <use x=\"242.822265625\" xlink:href=\"#BitstreamVeraSans-Roman-35\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_5\">\n",
       "     <g id=\"line2d_67\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"40.121875\" xlink:href=\"#md7965d1ba0\" y=\"86.4390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"line2d_68\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"374.921875\" xlink:href=\"#md9a1c1a7cd\" y=\"86.4390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_10\">\n",
       "      <!-- −0.80 -->\n",
       "      <g transform=\"translate(7.2 89.1984375)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#BitstreamVeraSans-Roman-2212\"/>\n",
       "       <use x=\"83.7890625\" xlink:href=\"#BitstreamVeraSans-Roman-30\"/>\n",
       "       <use x=\"147.412109375\" xlink:href=\"#BitstreamVeraSans-Roman-2e\"/>\n",
       "       <use x=\"179.19921875\" xlink:href=\"#BitstreamVeraSans-Roman-38\"/>\n",
       "       <use x=\"242.822265625\" xlink:href=\"#BitstreamVeraSans-Roman-30\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_6\">\n",
       "     <g id=\"line2d_69\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"40.121875\" xlink:href=\"#md7965d1ba0\" y=\"49.2390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"line2d_70\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"374.921875\" xlink:href=\"#md9a1c1a7cd\" y=\"49.2390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_11\">\n",
       "      <!-- −0.75 -->\n",
       "      <defs>\n",
       "       <path d=\"\n",
       "M8.20312 72.9062\n",
       "L55.0781 72.9062\n",
       "L55.0781 68.7031\n",
       "L28.6094 0\n",
       "L18.3125 0\n",
       "L43.2188 64.5938\n",
       "L8.20312 64.5938\n",
       "z\n",
       "\" id=\"BitstreamVeraSans-Roman-37\"/>\n",
       "      </defs>\n",
       "      <g transform=\"translate(7.409375 51.9984375)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#BitstreamVeraSans-Roman-2212\"/>\n",
       "       <use x=\"83.7890625\" xlink:href=\"#BitstreamVeraSans-Roman-30\"/>\n",
       "       <use x=\"147.412109375\" xlink:href=\"#BitstreamVeraSans-Roman-2e\"/>\n",
       "       <use x=\"179.19921875\" xlink:href=\"#BitstreamVeraSans-Roman-37\"/>\n",
       "       <use x=\"242.822265625\" xlink:href=\"#BitstreamVeraSans-Roman-35\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_7\">\n",
       "     <g id=\"line2d_71\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"40.121875\" xlink:href=\"#md7965d1ba0\" y=\"12.0390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"line2d_72\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"374.921875\" xlink:href=\"#md9a1c1a7cd\" y=\"12.0390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_12\">\n",
       "      <!-- −0.70 -->\n",
       "      <g transform=\"translate(7.2 14.7984375)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#BitstreamVeraSans-Roman-2212\"/>\n",
       "       <use x=\"83.7890625\" xlink:href=\"#BitstreamVeraSans-Roman-30\"/>\n",
       "       <use x=\"147.412109375\" xlink:href=\"#BitstreamVeraSans-Roman-2e\"/>\n",
       "       <use x=\"179.19921875\" xlink:href=\"#BitstreamVeraSans-Roman-37\"/>\n",
       "       <use x=\"242.822265625\" xlink:href=\"#BitstreamVeraSans-Roman-30\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "   </g>\n",
       "   <g id=\"legend_1\">\n",
       "    <g id=\"patch_7\">\n",
       "     <path d=\"\n",
       "M46.1219 56.8666\n",
       "L115.911 56.8666\n",
       "L115.911 18.0391\n",
       "L46.1219 18.0391\n",
       "z\n",
       "\" style=\"fill:#ffffff;stroke:#000000;stroke-linejoin:miter;\"/>\n",
       "    </g>\n",
       "    <g id=\"line2d_73\">\n",
       "     <path d=\"\n",
       "M54.5219 27.7572\n",
       "L71.3219 27.7572\" style=\"fill:none;stroke:#0000ff;stroke-linecap:square;\"/>\n",
       "    </g>\n",
       "    <g id=\"line2d_74\">\n",
       "     <g>\n",
       "      <use style=\"fill:#0000ff;stroke:#000000;stroke-width:0.5;\" x=\"54.521875\" xlink:href=\"#mdb00ba95ec\" y=\"27.7571875\"/>\n",
       "      <use style=\"fill:#0000ff;stroke:#000000;stroke-width:0.5;\" x=\"71.321875\" xlink:href=\"#mdb00ba95ec\" y=\"27.7571875\"/>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"text_13\">\n",
       "     <!-- train -->\n",
       "     <g transform=\"translate(84.521875 31.9571875)scale(0.12 -0.12)\">\n",
       "      <use xlink:href=\"#BitstreamVeraSans-Roman-74\"/>\n",
       "      <use x=\"39.208984375\" xlink:href=\"#BitstreamVeraSans-Roman-72\"/>\n",
       "      <use x=\"80.322265625\" xlink:href=\"#BitstreamVeraSans-Roman-61\"/>\n",
       "      <use x=\"141.6015625\" xlink:href=\"#BitstreamVeraSans-Roman-69\"/>\n",
       "      <use x=\"169.384765625\" xlink:href=\"#BitstreamVeraSans-Roman-6e\"/>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"line2d_75\">\n",
       "     <path d=\"\n",
       "M54.5219 45.3709\n",
       "L71.3219 45.3709\" style=\"fill:none;stroke:#008000;stroke-linecap:square;\"/>\n",
       "    </g>\n",
       "    <g id=\"line2d_76\">\n",
       "     <g>\n",
       "      <use style=\"fill:#008000;stroke:#000000;stroke-linejoin:miter;stroke-width:0.5;\" x=\"54.521875\" xlink:href=\"#m45eb232605\" y=\"45.3709375\"/>\n",
       "      <use style=\"fill:#008000;stroke:#000000;stroke-linejoin:miter;stroke-width:0.5;\" x=\"71.321875\" xlink:href=\"#m45eb232605\" y=\"45.3709375\"/>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"text_14\">\n",
       "     <!-- test -->\n",
       "     <g transform=\"translate(84.521875 49.5709375)scale(0.12 -0.12)\">\n",
       "      <use xlink:href=\"#BitstreamVeraSans-Roman-74\"/>\n",
       "      <use x=\"39.208984375\" xlink:href=\"#BitstreamVeraSans-Roman-65\"/>\n",
       "      <use x=\"100.732421875\" xlink:href=\"#BitstreamVeraSans-Roman-73\"/>\n",
       "      <use x=\"152.83203125\" xlink:href=\"#BitstreamVeraSans-Roman-74\"/>\n",
       "     </g>\n",
       "    </g>\n",
       "   </g>\n",
       "  </g>\n",
       " </g>\n",
       " <defs>\n",
       "  <clipPath id=\"pafb01ba72a\">\n",
       "   <rect height=\"223.2\" width=\"334.8\" x=\"40.121875\" y=\"12.0390625\"/>\n",
       "  </clipPath>\n",
       " </defs>\n",
       "</svg>\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fce77f45f60>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_cv_scores(train_sizes, valid_scores, train_scores)\n",
    "xscale('log')\n",
    "xlabel('training set size')\n",
    "legend(loc=2);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Find similar segments"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 363,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>name</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>id</th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>646647</th>\n",
       "      <td>Mt Charlie Climb</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4102842</th>\n",
       "      <td>Mount Charlie Descent</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                          name\n",
       "id                            \n",
       "646647        Mt Charlie Climb\n",
       "4102842  Mount Charlie Descent"
      ]
     },
     "execution_count": 363,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "segments[segments.name.str.contains('Charlie')]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 365,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "222.0"
      ]
     },
     "execution_count": 365,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df[df.segment_id == 646647].segment.iloc[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 465,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "est = CollaborativeFiltering(num_athletes, num_segments, num_features=30, lm=10, maxiter=10000)\n",
    "segment_features = est.fit(X, y).X_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 481,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "segment_features_normed = (segment_features / \n",
    "                           tile(sqrt(sum(segment_features**2, axis=1)), (segment_features.shape[1],1)).T)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 482,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "charlie_vec = segment_features[222,:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 488,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1431, 1431)"
      ]
     },
     "execution_count": 488,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dot(segment_features, segment_features.T).shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 483,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "similarity = dot(segment_features, charlie_vec)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 484,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "similar_segments = [(df[df.segment == segment].segment_id.iloc[0], similarity[segment])\n",
    "                    for segment in argsort(similarity)[::-1][:10]]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 485,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>id</th>\n",
       "      <th>name</th>\n",
       "      <th>similarity</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>646647</td>\n",
       "      <td>Mt Charlie Climb</td>\n",
       "      <td>1.384699</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>630146</td>\n",
       "      <td>Tassajara Lump</td>\n",
       "      <td>0.651514</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>953502</td>\n",
       "      <td>Carpenteria- San Juan to Seely</td>\n",
       "      <td>0.630642</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>781767</td>\n",
       "      <td>Sycamore Valley Rd Headwind Pull from Tassjara...</td>\n",
       "      <td>0.615667</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>3418564</td>\n",
       "      <td>from the parking lot of the county park</td>\n",
       "      <td>0.603940</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>4554906</td>\n",
       "      <td>to bay test</td>\n",
       "      <td>0.582470</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>1462453</td>\n",
       "      <td>XXXDH</td>\n",
       "      <td>0.569239</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>6512075</td>\n",
       "      <td>S. White Rd - Quimby to Aborn</td>\n",
       "      <td>0.537080</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>6790429</td>\n",
       "      <td>New Bike Path Sprint</td>\n",
       "      <td>0.533637</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>617863</td>\n",
       "      <td>Clayton Rd</td>\n",
       "      <td>0.531442</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        id                                               name  similarity\n",
       "0   646647                                   Mt Charlie Climb    1.384699\n",
       "1   630146                                     Tassajara Lump    0.651514\n",
       "2   953502                     Carpenteria- San Juan to Seely    0.630642\n",
       "3   781767  Sycamore Valley Rd Headwind Pull from Tassjara...    0.615667\n",
       "4  3418564            from the parking lot of the county park    0.603940\n",
       "5  4554906                                        to bay test    0.582470\n",
       "6  1462453                                              XXXDH    0.569239\n",
       "7  6512075                      S. White Rd - Quimby to Aborn    0.537080\n",
       "8  6790429                               New Bike Path Sprint    0.533637\n",
       "9   617863                                         Clayton Rd    0.531442"
      ]
     },
     "execution_count": 485,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.DataFrame.from_records([(sid, segments.name.loc[sid], similarity) \n",
    "                           for sid, similarity in similar_segments if sid in segments.index],\n",
    "                          columns=['id','name','similarity'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "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": "3.4.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}