hw1.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# hw1: getting started with Gaussian Processes (due noon Monday 21 Sep)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "###Problem 1 of 3 (40 points).  Get your computing infrastructure set up.\n",
    "\n",
    "- Options:\n",
    "     1. python+GPy+GitHub: \n",
    "          1. See [these instructions](getting_started.ipynb)\n",
    "          2. Fork this repository to get this notebook\n",
    "          3. Make sure you can run the commands already in this notebook\n",
    "     2. matlab: \n",
    "          1. Choose [gpml](http://www.gaussianprocess.org/gpml/code/matlab/doc/) or [gpstuff](http://becs.aalto.fi/en/research/bayes/gpstuff/).  I recommend gpml, but only modestly.\n",
    "          2. Look at the html version of this and future notebooks.\n",
    "     3. R: \n",
    "          0. Seriously reconsider using either python or matlab.\n",
    "          1. Apparently [gpstuff](http://becs.aalto.fi/en/research/bayes/gpstuff/) can be used in R, but I can not speak to that.\n",
    "          2. Look at the html version of this and future notebooks.\n",
    "      \n",
    "      \n",
    " - Help me choose:\n",
    "     1. You should choose the python+GitHub option:\n",
    "         - PRO: \n",
    "             - once you understand and get through the first step, the rest of this homework will be extremely easy\n",
    "             - you will learn a modern computing infrastructure, which you should want to do\n",
    "             - knowing these things will increase your employability and usefulness as a statistician, data scientist, computer scientist,...\n",
    "             - you will need to invest a few hours up front, but you will recoup it many times over by the end of the semester\n",
    "         - CON: \n",
    "             - python and git may be new to you.  They can be confusing, and some effort is required.\n",
    "     2. You should choose the matlab option:\n",
    "         - PRO: \n",
    "             - much of the research literature is implemented and availale in matlab, so some topics will be correspondingly easier to consider empirically \n",
    "             - the GPy package is not as well commented as gpml\n",
    "             - implementing something like hw1 is also quite easy in matlab\n",
    "         - CON: \n",
    "             - matlab can pigeonhole you into academic machine learning only (not real world heavy duty data analysis)  \n",
    "     2. The only reasons to choose a different option:\n",
    "         - New technologies can be uncomfortable and scary.  \n",
    "         - You already know that you will never need to do anything but R for the rest of your life.  \n",
    "        "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "###Problem 2 of 3 (40 points).  Run a simple GP regression on toy data.\n",
    " Notes: this is a modification of this [GPy tutorial](http://nbviewer.ipython.org/github/SheffieldML/notebook/blob/master/GPy/basic_gp.ipynb).  All you are expected to do is to run the commands below.  You should tweak them in small ways to demonstrate your understanding (small changes to the toy data, figure colors, or something like that).  Note that, if you chose the python+git option, this should take about 5 minutes; otherwise this should take a few hours.\n",
    "\n",
    "\n",
    " - Import relevant libraries (it's good practice to do this in a block at the top of the code)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import matplotlib\n",
    "from matplotlib import pyplot as plt\n",
    "import numpy as np\n",
    "import GPy as gpy\n",
    "from IPython.display import display"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " - Format figures."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# (python does not typically show plots until you ask it, so this inline call gives more 'natural' behavior)\n",
    "%matplotlib inline  \n",
    "%config InlineBackend.figure_format = 'svg'\n",
    "matplotlib.rcParams['figure.figsize'] = (8,5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " - Generate and plot simple toy data for regression."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x10a955450>]"
      ]
     },
     "execution_count": 48,
     "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=\"311pt\" version=\"1.1\" viewBox=\"0 0 494 311\" width=\"494pt\" 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 311.917\n",
       "L494.43 311.917\n",
       "L494.43 0\n",
       "L0 0\n",
       "L0 311.917\" style=\"fill:none;\"/>\n",
       "  </g>\n",
       "  <g id=\"axes_1\">\n",
       "   <g id=\"patch_2\">\n",
       "    <path d=\"\n",
       "M33.7594 291.039\n",
       "L480.159 291.039\n",
       "L480.159 12.0391\n",
       "L33.7594 12.0391\n",
       "L33.7594 291.039\" style=\"fill:none;\"/>\n",
       "   </g>\n",
       "   <g id=\"line2d_1\">\n",
       "    <defs>\n",
       "     <path d=\"\n",
       "M-3 3\n",
       "L3 -3\n",
       "M-3 -3\n",
       "L3 3\" id=\"m7bb187e4e2\" style=\"stroke:#000000;stroke-width:1.5;\"/>\n",
       "    </defs>\n",
       "    <g clip-path=\"url(#pbdbbb85bc5)\">\n",
       "     <use style=\"stroke:#000000;stroke-width:1.5;\" x=\"121.097808533\" xlink:href=\"#m7bb187e4e2\" y=\"201.795059663\"/>\n",
       "     <use style=\"stroke:#000000;stroke-width:1.5;\" x=\"270.783539396\" xlink:href=\"#m7bb187e4e2\" y=\"84.5991774242\"/>\n",
       "     <use style=\"stroke:#000000;stroke-width:1.5;\" x=\"107.231062657\" xlink:href=\"#m7bb187e4e2\" y=\"162.62556543\"/>\n",
       "     <use style=\"stroke:#000000;stroke-width:1.5;\" x=\"457.357393497\" xlink:href=\"#m7bb187e4e2\" y=\"186.49621754\"/>\n",
       "     <use style=\"stroke:#000000;stroke-width:1.5;\" x=\"88.2852243045\" xlink:href=\"#m7bb187e4e2\" y=\"112.252617622\"/>\n",
       "     <use style=\"stroke:#000000;stroke-width:1.5;\" x=\"271.13193295\" xlink:href=\"#m7bb187e4e2\" y=\"78.0798906056\"/>\n",
       "     <use style=\"stroke:#000000;stroke-width:1.5;\" x=\"250.20983113\" xlink:href=\"#m7bb187e4e2\" y=\"111.820429523\"/>\n",
       "     <use style=\"stroke:#000000;stroke-width:1.5;\" x=\"368.510202825\" xlink:href=\"#m7bb187e4e2\" y=\"175.563969233\"/>\n",
       "     <use style=\"stroke:#000000;stroke-width:1.5;\" x=\"138.322256607\" xlink:href=\"#m7bb187e4e2\" y=\"215.960663735\"/>\n",
       "     <use style=\"stroke:#000000;stroke-width:1.5;\" x=\"434.215646513\" xlink:href=\"#m7bb187e4e2\" y=\"241.230359807\"/>\n",
       "     <use style=\"stroke:#000000;stroke-width:1.5;\" x=\"63.7950121487\" xlink:href=\"#m7bb187e4e2\" y=\"78.6797755492\"/>\n",
       "     <use style=\"stroke:#000000;stroke-width:1.5;\" x=\"60.9036997304\" xlink:href=\"#m7bb187e4e2\" y=\"60.1638160152\"/>\n",
       "     <use style=\"stroke:#000000;stroke-width:1.5;\" x=\"276.590542512\" xlink:href=\"#m7bb187e4e2\" y=\"67.2687319961\"/>\n",
       "     <use style=\"stroke:#000000;stroke-width:1.5;\" x=\"303.82086065\" xlink:href=\"#m7bb187e4e2\" y=\"63.7223466783\"/>\n",
       "     <use style=\"stroke:#000000;stroke-width:1.5;\" x=\"161.401560135\" xlink:href=\"#m7bb187e4e2\" y=\"247.519785359\"/>\n",
       "     <use style=\"stroke:#000000;stroke-width:1.5;\" x=\"179.167253711\" xlink:href=\"#m7bb187e4e2\" y=\"241.49951123\"/>\n",
       "     <use style=\"stroke:#000000;stroke-width:1.5;\" x=\"261.869819726\" xlink:href=\"#m7bb187e4e2\" y=\"101.543393963\"/>\n",
       "     <use style=\"stroke:#000000;stroke-width:1.5;\" x=\"38.8547153078\" xlink:href=\"#m7bb187e4e2\" y=\"56.7482534439\"/>\n",
       "     <use style=\"stroke:#000000;stroke-width:1.5;\" x=\"261.205919779\" xlink:href=\"#m7bb187e4e2\" y=\"90.6988713769\"/>\n",
       "     <use style=\"stroke:#000000;stroke-width:1.5;\" x=\"106.378413373\" xlink:href=\"#m7bb187e4e2\" y=\"156.07532356\"/>\n",
       "     <use style=\"stroke:#000000;stroke-width:1.5;\" x=\"390.317222779\" xlink:href=\"#m7bb187e4e2\" y=\"214.850436281\"/>\n",
       "     <use style=\"stroke:#000000;stroke-width:1.5;\" x=\"464.51993937\" xlink:href=\"#m7bb187e4e2\" y=\"196.130067863\"/>\n",
       "     <use style=\"stroke:#000000;stroke-width:1.5;\" x=\"434.905908571\" xlink:href=\"#m7bb187e4e2\" y=\"225.829918978\"/>\n",
       "     <use style=\"stroke:#000000;stroke-width:1.5;\" x=\"93.4406690536\" xlink:href=\"#m7bb187e4e2\" y=\"118.344929547\"/>\n",
       "     <use style=\"stroke:#000000;stroke-width:1.5;\" x=\"433.758304824\" xlink:href=\"#m7bb187e4e2\" y=\"238.750544904\"/>\n",
       "    </g>\n",
       "   </g>\n",
       "   <g id=\"patch_3\">\n",
       "    <path d=\"\n",
       "M33.7594 12.0391\n",
       "L480.159 12.0391\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_4\">\n",
       "    <path d=\"\n",
       "M480.159 291.039\n",
       "L480.159 12.0391\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_5\">\n",
       "    <path d=\"\n",
       "M33.7594 291.039\n",
       "L480.159 291.039\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_6\">\n",
       "    <path d=\"\n",
       "M33.7594 291.039\n",
       "L33.7594 12.0391\" 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_2\">\n",
       "      <defs>\n",
       "       <path d=\"\n",
       "M0 0\n",
       "L0 -4\" id=\"m93b0483c22\" style=\"stroke:#000000;stroke-width:0.5;\"/>\n",
       "      </defs>\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"33.759375\" xlink:href=\"#m93b0483c22\" y=\"291.0390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"line2d_3\">\n",
       "      <defs>\n",
       "       <path d=\"\n",
       "M0 0\n",
       "L0 4\" id=\"m741efc42ff\" style=\"stroke:#000000;stroke-width:0.5;\"/>\n",
       "      </defs>\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"33.759375\" xlink:href=\"#m741efc42ff\" y=\"12.0390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_1\">\n",
       "      <!-- −0.8 -->\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",
       "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",
       "       <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",
       "       <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(22.48984375 302.6375)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=\"xtick_2\">\n",
       "     <g id=\"line2d_4\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"83.359375\" xlink:href=\"#m93b0483c22\" y=\"291.0390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"line2d_5\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"83.359375\" xlink:href=\"#m741efc42ff\" y=\"12.0390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_2\">\n",
       "      <!-- −0.6 -->\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(72.0625 302.6375)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=\"xtick_3\">\n",
       "     <g id=\"line2d_6\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"132.959375\" xlink:href=\"#m93b0483c22\" y=\"291.0390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"line2d_7\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"132.959375\" xlink:href=\"#m741efc42ff\" y=\"12.0390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_3\">\n",
       "      <!-- −0.4 -->\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(121.628125 302.6375)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=\"xtick_4\">\n",
       "     <g id=\"line2d_8\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"182.559375\" xlink:href=\"#m93b0483c22\" y=\"291.0390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"line2d_9\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"182.559375\" xlink:href=\"#m741efc42ff\" y=\"12.0390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_4\">\n",
       "      <!-- −0.2 -->\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(171.4484375 302.6375)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-32\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_5\">\n",
       "     <g id=\"line2d_10\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"232.159375\" xlink:href=\"#m93b0483c22\" y=\"291.0390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"line2d_11\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"232.159375\" xlink:href=\"#m741efc42ff\" y=\"12.0390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_5\">\n",
       "      <!-- 0.0 -->\n",
       "      <g transform=\"translate(224.86953125 302.6375)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#BitstreamVeraSans-Roman-30\"/>\n",
       "       <use x=\"63.623046875\" xlink:href=\"#BitstreamVeraSans-Roman-2e\"/>\n",
       "       <use x=\"95.41015625\" xlink:href=\"#BitstreamVeraSans-Roman-30\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_6\">\n",
       "     <g id=\"line2d_12\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"281.759375\" xlink:href=\"#m93b0483c22\" y=\"291.0390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"line2d_13\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"281.759375\" xlink:href=\"#m741efc42ff\" y=\"12.0390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_6\">\n",
       "      <!-- 0.2 -->\n",
       "      <g transform=\"translate(274.63828125 302.6375)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#BitstreamVeraSans-Roman-30\"/>\n",
       "       <use x=\"63.623046875\" xlink:href=\"#BitstreamVeraSans-Roman-2e\"/>\n",
       "       <use x=\"95.41015625\" xlink:href=\"#BitstreamVeraSans-Roman-32\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_7\">\n",
       "     <g id=\"line2d_14\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"331.359375\" xlink:href=\"#m93b0483c22\" y=\"291.0390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"line2d_15\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"331.359375\" xlink:href=\"#m741efc42ff\" y=\"12.0390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_7\">\n",
       "      <!-- 0.4 -->\n",
       "      <g transform=\"translate(324.01796875 302.6375)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#BitstreamVeraSans-Roman-30\"/>\n",
       "       <use x=\"63.623046875\" xlink:href=\"#BitstreamVeraSans-Roman-2e\"/>\n",
       "       <use x=\"95.41015625\" xlink:href=\"#BitstreamVeraSans-Roman-34\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_8\">\n",
       "     <g id=\"line2d_16\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"380.959375\" xlink:href=\"#m93b0483c22\" y=\"291.0390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"line2d_17\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"380.959375\" xlink:href=\"#m741efc42ff\" y=\"12.0390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_8\">\n",
       "      <!-- 0.6 -->\n",
       "      <g transform=\"translate(373.65234375 302.6375)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#BitstreamVeraSans-Roman-30\"/>\n",
       "       <use x=\"63.623046875\" xlink:href=\"#BitstreamVeraSans-Roman-2e\"/>\n",
       "       <use x=\"95.41015625\" xlink:href=\"#BitstreamVeraSans-Roman-36\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_9\">\n",
       "     <g id=\"line2d_18\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"430.559375\" xlink:href=\"#m93b0483c22\" y=\"291.0390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"line2d_19\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"430.559375\" xlink:href=\"#m741efc42ff\" y=\"12.0390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_9\">\n",
       "      <!-- 0.8 -->\n",
       "      <g transform=\"translate(423.2796875 302.6375)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#BitstreamVeraSans-Roman-30\"/>\n",
       "       <use x=\"63.623046875\" xlink:href=\"#BitstreamVeraSans-Roman-2e\"/>\n",
       "       <use x=\"95.41015625\" xlink:href=\"#BitstreamVeraSans-Roman-38\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_10\">\n",
       "     <g id=\"line2d_20\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"480.159375\" xlink:href=\"#m93b0483c22\" y=\"291.0390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"line2d_21\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"480.159375\" xlink:href=\"#m741efc42ff\" y=\"12.0390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_10\">\n",
       "      <!-- 1.0 -->\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",
       "      </defs>\n",
       "      <g transform=\"translate(473.0890625 302.6375)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#BitstreamVeraSans-Roman-31\"/>\n",
       "       <use x=\"63.623046875\" xlink:href=\"#BitstreamVeraSans-Roman-2e\"/>\n",
       "       <use x=\"95.41015625\" 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_22\">\n",
       "      <defs>\n",
       "       <path d=\"\n",
       "M0 0\n",
       "L4 0\" id=\"m728421d6d4\" style=\"stroke:#000000;stroke-width:0.5;\"/>\n",
       "      </defs>\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"33.759375\" xlink:href=\"#m728421d6d4\" y=\"291.0390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"line2d_23\">\n",
       "      <defs>\n",
       "       <path d=\"\n",
       "M0 0\n",
       "L-4 0\" id=\"mcb0005524f\" style=\"stroke:#000000;stroke-width:0.5;\"/>\n",
       "      </defs>\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"480.159375\" xlink:href=\"#mcb0005524f\" y=\"291.0390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_11\">\n",
       "      <!-- −1.5 -->\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(7.409375 293.7984375)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-35\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_2\">\n",
       "     <g id=\"line2d_24\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"33.759375\" xlink:href=\"#m728421d6d4\" y=\"244.5390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"line2d_25\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"480.159375\" xlink:href=\"#mcb0005524f\" y=\"244.5390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_12\">\n",
       "      <!-- −1.0 -->\n",
       "      <g transform=\"translate(7.2 247.2984375)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_26\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"33.759375\" xlink:href=\"#m728421d6d4\" y=\"198.0390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"line2d_27\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"480.159375\" xlink:href=\"#mcb0005524f\" y=\"198.0390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_13\">\n",
       "      <!-- −0.5 -->\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-35\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_4\">\n",
       "     <g id=\"line2d_28\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"33.759375\" xlink:href=\"#m728421d6d4\" y=\"151.5390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"line2d_29\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"480.159375\" xlink:href=\"#mcb0005524f\" y=\"151.5390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_14\">\n",
       "      <!-- 0.0 -->\n",
       "      <g transform=\"translate(15.1796875 154.2984375)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#BitstreamVeraSans-Roman-30\"/>\n",
       "       <use x=\"63.623046875\" xlink:href=\"#BitstreamVeraSans-Roman-2e\"/>\n",
       "       <use x=\"95.41015625\" xlink:href=\"#BitstreamVeraSans-Roman-30\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_5\">\n",
       "     <g id=\"line2d_30\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"33.759375\" xlink:href=\"#m728421d6d4\" y=\"105.0390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"line2d_31\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"480.159375\" xlink:href=\"#mcb0005524f\" y=\"105.0390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_15\">\n",
       "      <!-- 0.5 -->\n",
       "      <g transform=\"translate(15.3890625 107.7984375)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#BitstreamVeraSans-Roman-30\"/>\n",
       "       <use x=\"63.623046875\" xlink:href=\"#BitstreamVeraSans-Roman-2e\"/>\n",
       "       <use x=\"95.41015625\" xlink:href=\"#BitstreamVeraSans-Roman-35\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_6\">\n",
       "     <g id=\"line2d_32\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"33.759375\" xlink:href=\"#m728421d6d4\" y=\"58.5390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"line2d_33\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"480.159375\" xlink:href=\"#mcb0005524f\" y=\"58.5390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_16\">\n",
       "      <!-- 1.0 -->\n",
       "      <g transform=\"translate(15.61875 61.2984375)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#BitstreamVeraSans-Roman-31\"/>\n",
       "       <use x=\"63.623046875\" xlink:href=\"#BitstreamVeraSans-Roman-2e\"/>\n",
       "       <use x=\"95.41015625\" xlink:href=\"#BitstreamVeraSans-Roman-30\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_7\">\n",
       "     <g id=\"line2d_34\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"33.759375\" xlink:href=\"#m728421d6d4\" y=\"12.0390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"line2d_35\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"480.159375\" xlink:href=\"#mcb0005524f\" y=\"12.0390625\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_17\">\n",
       "      <!-- 1.5 -->\n",
       "      <g transform=\"translate(15.828125 14.7984375)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#BitstreamVeraSans-Roman-31\"/>\n",
       "       <use x=\"63.623046875\" xlink:href=\"#BitstreamVeraSans-Roman-2e\"/>\n",
       "       <use x=\"95.41015625\" xlink:href=\"#BitstreamVeraSans-Roman-35\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "   </g>\n",
       "  </g>\n",
       " </g>\n",
       " <defs>\n",
       "  <clipPath id=\"pbdbbb85bc5\">\n",
       "   <rect height=\"279.0\" width=\"446.4\" x=\"33.759375\" y=\"12.0390625\"/>\n",
       "  </clipPath>\n",
       " </defs>\n",
       "</svg>\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10a2752d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "num_points = 25\n",
    "t = np.random.uniform(-1.,1.,(num_points,1))\n",
    "x = np.sin(t*2*np.pi) + 0.1*np.random.randn(num_points,1)\n",
    "plt.plot(t,x,'kx',markersize=6,markeredgewidth=1.5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "  - Instantiate a kernel for your GP (you should know what each of these arguments means)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "kernel = gpy.kern.RBF(input_dim=1, variance=1., lengthscale=.1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " - Do GP regression with your noisy data, and display the model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "<b>Model</b>: GP regression<br>\n",
       "<b>Log-likelihood</b>: -30.5469120044<br>\n",
       "<b>Number of Parameters</b>: 3<br>\n",
       "<br><b>Parameters</b>:\n",
       "<table>\n",
       "<tr>\n",
       "  <td><b>GP_regression.</b>\n",
       "  <td><b>Value</b></td>\n",
       "  <td><b>Constraint</b></td>\n",
       "  <td><b>Prior</b></td>\n",
       "  <td><b>Tied to</b></td>\n",
       "<tr><td>rbf.variance           </td><td align=\"right\">  1.0</td><td>   +ve    </td><td>     </td><td>       </td></tr>\n",
       "<tr><td>rbf.lengthscale        </td><td align=\"right\">  0.1</td><td>   +ve    </td><td>     </td><td>       </td></tr>\n",
       "<tr><td>Gaussian_noise.variance</td><td align=\"right\">  1.0</td><td>   +ve    </td><td>     </td><td>       </td></tr>\n",
       "</table>"
      ],
      "text/plain": [
       "<GPy.models.gp_regression.GPRegression at 0x10abebfd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "m = gpy.models.GPRegression(t,x,kernel)\n",
    "display(m)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    " - Plot this temporary result and notice that the hyperparameters (variance, lengthscale) describe the data poorly.  Note the log-likelihood above."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'dataplot': [<matplotlib.lines.Line2D at 0x10ab47b90>],\n",
       " 'gpplot': [[<matplotlib.lines.Line2D at 0x10ab3a750>],\n",
       "  [<matplotlib.patches.Polygon at 0x10acb9190>],\n",
       "  [<matplotlib.lines.Line2D at 0x10ab3afd0>],\n",
       "  [<matplotlib.lines.Line2D at 0x10ab47550>]]}"
      ]
     },
     "execution_count": 58,
     "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=\"307pt\" version=\"1.1\" viewBox=\"0 0 477 307\" width=\"477pt\" 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 307.078\n",
       "L477.681 307.078\n",
       "L477.681 0\n",
       "L0 0\n",
       "L0 307.078\" style=\"fill:none;\"/>\n",
       "  </g>\n",
       "  <g id=\"axes_1\">\n",
       "   <g id=\"patch_2\">\n",
       "    <path d=\"\n",
       "M24.0813 286.2\n",
       "L470.481 286.2\n",
       "L470.481 7.2\n",
       "L24.0813 7.2\n",
       "L24.0813 286.2\" style=\"fill:none;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_3\">\n",
       "    <path clip-path=\"url(#p0530076909)\" d=\"\n",
       "M24.0813 38.4187\n",
       "L26.3245 38.3977\n",
       "L28.5677 38.3674\n",
       "L30.8109 38.3246\n",
       "L33.0541 38.2651\n",
       "L35.2973 38.1837\n",
       "L37.5405 38.0746\n",
       "L39.7838 37.931\n",
       "L42.027 37.7459\n",
       "L44.2702 37.5125\n",
       "L46.5134 37.2249\n",
       "L48.7566 36.8791\n",
       "L50.9998 36.4742\n",
       "L53.2431 36.0132\n",
       "L55.4863 35.504\n",
       "L57.7295 34.9594\n",
       "L59.9727 34.397\n",
       "L62.2159 33.8372\n",
       "L64.4591 33.3016\n",
       "L66.7024 32.8097\n",
       "L68.9456 32.3763\n",
       "L71.1888 32.0083\n",
       "L73.432 31.7045\n",
       "L75.6752 31.4552\n",
       "L77.9184 31.2456\n",
       "L80.1617 31.0599\n",
       "L82.4049 30.8872\n",
       "L84.6481 30.7255\n",
       "L86.8913 30.5843\n",
       "L89.1345 30.4837\n",
       "L91.3777 30.45\n",
       "L93.6209 30.5094\n",
       "L95.8642 30.6823\n",
       "L98.1074 30.9802\n",
       "L100.351 31.4069\n",
       "L102.594 31.9628\n",
       "L104.837 32.6524\n",
       "L107.08 33.4896\n",
       "L109.323 34.5\n",
       "L111.567 35.7183\n",
       "L113.81 37.1808\n",
       "L116.053 38.9157\n",
       "L118.296 40.9346\n",
       "L120.54 43.2258\n",
       "L122.783 45.7529\n",
       "L125.026 48.4581\n",
       "L127.269 51.2687\n",
       "L129.512 54.1071\n",
       "L131.756 56.8993\n",
       "L133.999 59.5833\n",
       "L136.242 62.1135\n",
       "L138.485 64.4626\n",
       "L140.728 66.6196\n",
       "L142.972 68.5873\n",
       "L145.215 70.3775\n",
       "L147.458 72.0069\n",
       "L149.701 73.4943\n",
       "L151.945 74.8575\n",
       "L154.188 76.1129\n",
       "L156.431 77.2752\n",
       "L158.674 78.3576\n",
       "L160.917 79.3728\n",
       "L163.161 80.3324\n",
       "L165.404 81.2463\n",
       "L167.647 82.1197\n",
       "L169.89 82.9511\n",
       "L172.134 83.728\n",
       "L174.377 84.4254\n",
       "L176.62 85.0038\n",
       "L178.863 85.4107\n",
       "L181.106 85.5833\n",
       "L183.35 85.4535\n",
       "L185.593 84.9552\n",
       "L187.836 84.0319\n",
       "L190.079 82.6453\n",
       "L192.322 80.7824\n",
       "L194.566 78.4602\n",
       "L196.809 75.7264\n",
       "L199.052 72.6573\n",
       "L201.295 69.3505\n",
       "L203.539 65.9162\n",
       "L205.782 62.4676\n",
       "L208.025 59.1118\n",
       "L210.268 55.9428\n",
       "L212.511 53.0372\n",
       "L214.755 50.4519\n",
       "L216.998 48.2245\n",
       "L219.241 46.3749\n",
       "L221.484 44.9073\n",
       "L223.727 43.812\n",
       "L225.971 43.067\n",
       "L228.214 42.6391\n",
       "L230.457 42.4845\n",
       "L232.7 42.5497\n",
       "L234.944 42.7728\n",
       "L237.187 43.0866\n",
       "L239.43 43.4216\n",
       "L241.673 43.7109\n",
       "L243.916 43.8939\n",
       "L246.16 43.9201\n",
       "L248.403 43.7512\n",
       "L250.646 43.362\n",
       "L252.889 42.7399\n",
       "L255.133 41.8855\n",
       "L257.376 40.8129\n",
       "L259.619 39.5524\n",
       "L261.862 38.1524\n",
       "L264.105 36.6795\n",
       "L266.349 35.2158\n",
       "L268.592 33.8513\n",
       "L270.835 32.6729\n",
       "L273.078 31.7524\n",
       "L275.321 31.1349\n",
       "L277.565 30.8319\n",
       "L279.808 30.8187\n",
       "L282.051 31.0398\n",
       "L284.294 31.4192\n",
       "L286.538 31.8755\n",
       "L288.781 32.3373\n",
       "L291.024 32.7569\n",
       "L293.267 33.1176\n",
       "L295.51 33.4343\n",
       "L297.754 33.7482\n",
       "L299.997 34.1167\n",
       "L302.24 34.6038\n",
       "L304.483 35.27\n",
       "L306.726 36.1662\n",
       "L308.97 37.3295\n",
       "L311.213 38.7808\n",
       "L313.456 40.5242\n",
       "L315.699 42.5467\n",
       "L317.943 44.8181\n",
       "L320.186 47.2921\n",
       "L322.429 49.9082\n",
       "L324.672 52.5949\n",
       "L326.915 55.2751\n",
       "L329.159 57.873\n",
       "L331.402 60.3206\n",
       "L333.645 62.5636\n",
       "L335.888 64.5651\n",
       "L338.132 66.3051\n",
       "L340.375 67.7783\n",
       "L342.618 68.9905\n",
       "L344.861 69.9556\n",
       "L347.104 70.6957\n",
       "L349.348 71.2435\n",
       "L351.591 71.6462\n",
       "L353.834 71.9686\n",
       "L356.077 72.2925\n",
       "L358.32 72.7111\n",
       "L360.564 73.3188\n",
       "L362.807 74.1964\n",
       "L365.05 75.3964\n",
       "L367.293 76.9295\n",
       "L369.537 78.7554\n",
       "L371.78 80.7815\n",
       "L374.023 82.8688\n",
       "L376.266 84.8481\n",
       "L378.509 86.5428\n",
       "L380.753 87.7968\n",
       "L382.996 88.5007\n",
       "L385.239 88.6087\n",
       "L387.482 88.1414\n",
       "L389.725 87.1726\n",
       "L391.969 85.8056\n",
       "L394.212 84.1455\n",
       "L396.455 82.2766\n",
       "L398.698 80.2488\n",
       "L400.942 78.0761\n",
       "L403.185 75.7457\n",
       "L405.428 73.234\n",
       "L407.671 70.5257\n",
       "L409.914 67.6286\n",
       "L412.158 64.5817\n",
       "L414.401 61.4529\n",
       "L416.644 58.3299\n",
       "L418.887 55.3065\n",
       "L421.13 52.4693\n",
       "L423.374 49.8874\n",
       "L425.617 47.6069\n",
       "L427.86 45.6493\n",
       "L430.103 44.014\n",
       "L432.347 42.6823\n",
       "L434.59 41.6236\n",
       "L436.833 40.8001\n",
       "L439.076 40.1721\n",
       "L441.319 39.7014\n",
       "L443.563 39.3537\n",
       "L445.806 39.0998\n",
       "L448.049 38.9161\n",
       "L450.292 38.7839\n",
       "L452.536 38.6892\n",
       "L454.779 38.6216\n",
       "L457.022 38.5734\n",
       "L459.265 38.5391\n",
       "L461.508 38.5148\n",
       "L463.752 38.4977\n",
       "L465.995 38.4857\n",
       "L468.238 38.4773\n",
       "L470.481 38.4716\n",
       "L470.481 254.245\n",
       "L468.238 254.25\n",
       "L465.995 254.258\n",
       "L463.752 254.269\n",
       "L461.508 254.283\n",
       "L459.265 254.303\n",
       "L457.022 254.328\n",
       "L454.779 254.359\n",
       "L452.536 254.396\n",
       "L450.292 254.438\n",
       "L448.049 254.483\n",
       "L445.806 254.524\n",
       "L443.563 254.553\n",
       "L441.319 254.559\n",
       "L439.076 254.525\n",
       "L436.833 254.431\n",
       "L434.59 254.255\n",
       "L432.347 253.975\n",
       "L430.103 253.571\n",
       "L427.86 253.034\n",
       "L425.617 252.364\n",
       "L423.374 251.581\n",
       "L421.13 250.723\n",
       "L418.887 249.851\n",
       "L416.644 249.045\n",
       "L414.401 248.392\n",
       "L412.158 247.98\n",
       "L409.914 247.878\n",
       "L407.671 248.122\n",
       "L405.428 248.705\n",
       "L403.185 249.577\n",
       "L400.942 250.65\n",
       "L398.698 251.819\n",
       "L396.455 252.984\n",
       "L394.212 254.067\n",
       "L391.969 255.034\n",
       "L389.725 255.893\n",
       "L387.482 256.687\n",
       "L385.239 257.476\n",
       "L382.996 258.316\n",
       "L380.753 259.229\n",
       "L378.509 260.194\n",
       "L376.266 261.148\n",
       "L374.023 261.995\n",
       "L371.78 262.627\n",
       "L369.537 262.95\n",
       "L367.293 262.897\n",
       "L365.05 262.441\n",
       "L362.807 261.594\n",
       "L360.564 260.407\n",
       "L358.32 258.96\n",
       "L356.077 257.345\n",
       "L353.834 255.657\n",
       "L351.591 253.983\n",
       "L349.348 252.392\n",
       "L347.104 250.933\n",
       "L344.861 249.641\n",
       "L342.618 248.538\n",
       "L340.375 247.637\n",
       "L338.132 246.951\n",
       "L335.888 246.484\n",
       "L333.645 246.234\n",
       "L331.402 246.183\n",
       "L329.159 246.294\n",
       "L326.915 246.512\n",
       "L324.672 246.764\n",
       "L322.429 246.965\n",
       "L320.186 247.028\n",
       "L317.943 246.866\n",
       "L315.699 246.407\n",
       "L313.456 245.591\n",
       "L311.213 244.38\n",
       "L308.97 242.758\n",
       "L306.726 240.734\n",
       "L304.483 238.342\n",
       "L302.24 235.64\n",
       "L299.997 232.707\n",
       "L297.754 229.642\n",
       "L295.51 226.551\n",
       "L293.267 223.538\n",
       "L291.024 220.694\n",
       "L288.781 218.084\n",
       "L286.538 215.74\n",
       "L284.294 213.662\n",
       "L282.051 211.821\n",
       "L279.808 210.175\n",
       "L277.565 208.681\n",
       "L275.321 207.315\n",
       "L273.078 206.073\n",
       "L270.835 204.982\n",
       "L268.592 204.098\n",
       "L266.349 203.492\n",
       "L264.105 203.241\n",
       "L261.862 203.418\n",
       "L259.619 204.076\n",
       "L257.376 205.243\n",
       "L255.133 206.922\n",
       "L252.889 209.088\n",
       "L250.646 211.699\n",
       "L248.403 214.694\n",
       "L246.16 218.003\n",
       "L243.916 221.545\n",
       "L241.673 225.237\n",
       "L239.43 228.99\n",
       "L237.187 232.72\n",
       "L234.944 236.347\n",
       "L232.7 239.801\n",
       "L230.457 243.029\n",
       "L228.214 245.99\n",
       "L225.971 248.66\n",
       "L223.727 251.028\n",
       "L221.484 253.093\n",
       "L219.241 254.864\n",
       "L216.998 256.354\n",
       "L214.755 257.578\n",
       "L212.511 258.556\n",
       "L210.268 259.311\n",
       "L208.025 259.872\n",
       "L205.782 260.27\n",
       "L203.539 260.546\n",
       "L201.295 260.743\n",
       "L199.052 260.904\n",
       "L196.809 261.07\n",
       "L194.566 261.27\n",
       "L192.322 261.519\n",
       "L190.079 261.817\n",
       "L187.836 262.144\n",
       "L185.593 262.465\n",
       "L183.35 262.737\n",
       "L181.106 262.912\n",
       "L178.863 262.944\n",
       "L176.62 262.796\n",
       "L174.377 262.44\n",
       "L172.134 261.862\n",
       "L169.89 261.057\n",
       "L167.647 260.033\n",
       "L165.404 258.8\n",
       "L163.161 257.373\n",
       "L160.917 255.764\n",
       "L158.674 253.983\n",
       "L156.431 252.038\n",
       "L154.188 249.934\n",
       "L151.945 247.678\n",
       "L149.701 245.281\n",
       "L147.458 242.762\n",
       "L145.215 240.149\n",
       "L142.972 237.48\n",
       "L140.728 234.8\n",
       "L138.485 232.155\n",
       "L136.242 229.592\n",
       "L133.999 227.147\n",
       "L131.756 224.843\n",
       "L129.512 222.685\n",
       "L127.269 220.663\n",
       "L125.026 218.752\n",
       "L122.783 216.919\n",
       "L120.54 215.137\n",
       "L118.296 213.39\n",
       "L116.053 211.68\n",
       "L113.81 210.036\n",
       "L111.567 208.505\n",
       "L109.323 207.152\n",
       "L107.08 206.047\n",
       "L104.837 205.256\n",
       "L102.594 204.831\n",
       "L100.351 204.807\n",
       "L98.1074 205.199\n",
       "L95.8642 206.01\n",
       "L93.6209 207.234\n",
       "L91.3777 208.86\n",
       "L89.1345 210.871\n",
       "L86.8913 213.246\n",
       "L84.6481 215.95\n",
       "L82.4049 218.933\n",
       "L80.1617 222.129\n",
       "L77.9184 225.456\n",
       "L75.6752 228.821\n",
       "L73.432 232.132\n",
       "L71.1888 235.302\n",
       "L68.9456 238.259\n",
       "L66.7024 240.949\n",
       "L64.4591 243.341\n",
       "L62.2159 245.422\n",
       "L59.9727 247.195\n",
       "L57.7295 248.679\n",
       "L55.4863 249.9\n",
       "L53.2431 250.889\n",
       "L50.9998 251.68\n",
       "L48.7566 252.304\n",
       "L46.5134 252.79\n",
       "L44.2702 253.165\n",
       "L42.027 253.451\n",
       "L39.7838 253.667\n",
       "L37.5405 253.828\n",
       "L35.2973 253.947\n",
       "L33.0541 254.033\n",
       "L30.8109 254.096\n",
       "L28.5677 254.14\n",
       "L26.3245 254.171\n",
       "L24.0813 254.192\n",
       "z\n",
       "\" style=\"fill:#729fcf;opacity:0.3;stroke:#729fcf;stroke-linejoin:miter;stroke-width:0.5;\"/>\n",
       "   </g>\n",
       "   <g id=\"line2d_1\">\n",
       "    <path clip-path=\"url(#p0530076909)\" d=\"\n",
       "M24.0813 146.305\n",
       "L33.0541 146.149\n",
       "L39.7838 145.799\n",
       "L44.2702 145.339\n",
       "L48.7566 144.591\n",
       "L53.2431 143.451\n",
       "L55.4863 142.702\n",
       "L57.7295 141.819\n",
       "L59.9727 140.796\n",
       "L62.2159 139.629\n",
       "L64.4591 138.321\n",
       "L68.9456 135.317\n",
       "L73.432 131.918\n",
       "L82.4049 124.91\n",
       "L84.6481 123.338\n",
       "L86.8913 121.915\n",
       "L89.1345 120.677\n",
       "L91.3777 119.655\n",
       "L93.6209 118.872\n",
       "L95.8642 118.346\n",
       "L98.1074 118.09\n",
       "L100.351 118.107\n",
       "L102.594 118.397\n",
       "L104.837 118.954\n",
       "L107.08 119.768\n",
       "L109.323 120.826\n",
       "L111.567 122.112\n",
       "L113.81 123.608\n",
       "L116.053 125.298\n",
       "L118.296 127.162\n",
       "L122.783 131.336\n",
       "L127.269 135.966\n",
       "L133.999 143.365\n",
       "L140.728 150.71\n",
       "L145.215 155.263\n",
       "L149.701 159.388\n",
       "L154.188 163.024\n",
       "L158.674 166.17\n",
       "L163.161 168.853\n",
       "L167.647 171.076\n",
       "L169.89 172.004\n",
       "L172.134 172.795\n",
       "L174.377 173.433\n",
       "L176.62 173.9\n",
       "L178.863 174.177\n",
       "L181.106 174.247\n",
       "L183.35 174.095\n",
       "L185.593 173.71\n",
       "L187.836 173.088\n",
       "L190.079 172.231\n",
       "L192.322 171.151\n",
       "L194.566 169.865\n",
       "L196.809 168.398\n",
       "L201.295 165.047\n",
       "L208.025 159.492\n",
       "L214.755 154.015\n",
       "L219.241 150.62\n",
       "L225.971 145.863\n",
       "L234.944 139.56\n",
       "L241.673 134.474\n",
       "L250.646 127.53\n",
       "L255.133 124.404\n",
       "L257.376 123.028\n",
       "L259.619 121.814\n",
       "L261.862 120.785\n",
       "L264.105 119.96\n",
       "L266.349 119.354\n",
       "L268.592 118.975\n",
       "L270.835 118.828\n",
       "L273.078 118.912\n",
       "L275.321 119.225\n",
       "L277.565 119.757\n",
       "L279.808 120.497\n",
       "L282.051 121.43\n",
       "L284.294 122.541\n",
       "L286.538 123.808\n",
       "L291.024 126.726\n",
       "L295.51 129.993\n",
       "L306.726 138.45\n",
       "L311.213 141.58\n",
       "L315.699 144.477\n",
       "L320.186 147.16\n",
       "L326.915 150.893\n",
       "L333.645 154.399\n",
       "L340.375 157.708\n",
       "L349.348 161.818\n",
       "L371.78 171.704\n",
       "L374.023 172.432\n",
       "L376.266 172.998\n",
       "L378.509 173.369\n",
       "L380.753 173.513\n",
       "L382.996 173.408\n",
       "L385.239 173.043\n",
       "L387.482 172.414\n",
       "L389.725 171.533\n",
       "L391.969 170.42\n",
       "L394.212 169.106\n",
       "L398.698 166.034\n",
       "L409.914 157.753\n",
       "L414.401 154.923\n",
       "L418.887 152.579\n",
       "L423.374 150.734\n",
       "L427.86 149.342\n",
       "L432.347 148.329\n",
       "L436.833 147.615\n",
       "L441.319 147.13\n",
       "L448.049 146.699\n",
       "L457.022 146.451\n",
       "L470.481 146.358\n",
       "L470.481 146.358\" style=\"fill:none;stroke:#204a87;stroke-linecap:square;stroke-width:2;\"/>\n",
       "   </g>\n",
       "   <g id=\"line2d_2\">\n",
       "    <path clip-path=\"url(#p0530076909)\" d=\"\n",
       "M24.0813 38.4187\n",
       "L33.0541 38.2651\n",
       "L39.7838 37.931\n",
       "L44.2702 37.5125\n",
       "L48.7566 36.8791\n",
       "L53.2431 36.0132\n",
       "L59.9727 34.397\n",
       "L66.7024 32.8097\n",
       "L71.1888 32.0083\n",
       "L75.6752 31.4552\n",
       "L84.6481 30.7255\n",
       "L89.1345 30.4837\n",
       "L93.6209 30.5094\n",
       "L95.8642 30.6823\n",
       "L98.1074 30.9802\n",
       "L100.351 31.4069\n",
       "L102.594 31.9628\n",
       "L104.837 32.6524\n",
       "L107.08 33.4896\n",
       "L109.323 34.5\n",
       "L111.567 35.7183\n",
       "L113.81 37.1808\n",
       "L116.053 38.9157\n",
       "L118.296 40.9346\n",
       "L120.54 43.2258\n",
       "L122.783 45.7529\n",
       "L127.269 51.2687\n",
       "L131.756 56.8993\n",
       "L136.242 62.1135\n",
       "L138.485 64.4626\n",
       "L140.728 66.6196\n",
       "L142.972 68.5873\n",
       "L145.215 70.3775\n",
       "L147.458 72.0069\n",
       "L151.945 74.8575\n",
       "L156.431 77.2752\n",
       "L160.917 79.3728\n",
       "L165.404 81.2463\n",
       "L169.89 82.9511\n",
       "L174.377 84.4254\n",
       "L176.62 85.0038\n",
       "L178.863 85.4107\n",
       "L181.106 85.5833\n",
       "L183.35 85.4535\n",
       "L185.593 84.9552\n",
       "L187.836 84.0319\n",
       "L190.079 82.6453\n",
       "L192.322 80.7824\n",
       "L194.566 78.4602\n",
       "L196.809 75.7264\n",
       "L199.052 72.6573\n",
       "L203.539 65.9162\n",
       "L208.025 59.1118\n",
       "L210.268 55.9428\n",
       "L212.511 53.0372\n",
       "L214.755 50.4519\n",
       "L216.998 48.2245\n",
       "L219.241 46.3749\n",
       "L221.484 44.9073\n",
       "L223.727 43.812\n",
       "L225.971 43.067\n",
       "L228.214 42.6391\n",
       "L230.457 42.4845\n",
       "L232.7 42.5497\n",
       "L237.187 43.0866\n",
       "L241.673 43.7109\n",
       "L243.916 43.8939\n",
       "L246.16 43.9201\n",
       "L248.403 43.7512\n",
       "L250.646 43.362\n",
       "L252.889 42.7399\n",
       "L255.133 41.8855\n",
       "L257.376 40.8129\n",
       "L259.619 39.5524\n",
       "L264.105 36.6795\n",
       "L268.592 33.8513\n",
       "L270.835 32.6729\n",
       "L273.078 31.7524\n",
       "L275.321 31.1349\n",
       "L277.565 30.8319\n",
       "L279.808 30.8187\n",
       "L282.051 31.0398\n",
       "L286.538 31.8755\n",
       "L291.024 32.7569\n",
       "L302.24 34.6038\n",
       "L304.483 35.27\n",
       "L306.726 36.1662\n",
       "L308.97 37.3295\n",
       "L311.213 38.7808\n",
       "L313.456 40.5242\n",
       "L315.699 42.5467\n",
       "L317.943 44.8181\n",
       "L322.429 49.9082\n",
       "L329.159 57.873\n",
       "L331.402 60.3206\n",
       "L333.645 62.5636\n",
       "L335.888 64.5651\n",
       "L338.132 66.3051\n",
       "L340.375 67.7783\n",
       "L342.618 68.9905\n",
       "L344.861 69.9556\n",
       "L347.104 70.6957\n",
       "L349.348 71.2435\n",
       "L353.834 71.9686\n",
       "L358.32 72.7111\n",
       "L360.564 73.3188\n",
       "L362.807 74.1964\n",
       "L365.05 75.3964\n",
       "L367.293 76.9295\n",
       "L369.537 78.7554\n",
       "L376.266 84.8481\n",
       "L378.509 86.5428\n",
       "L380.753 87.7968\n",
       "L382.996 88.5007\n",
       "L385.239 88.6087\n",
       "L387.482 88.1414\n",
       "L389.725 87.1726\n",
       "L391.969 85.8056\n",
       "L394.212 84.1455\n",
       "L396.455 82.2766\n",
       "L400.942 78.0761\n",
       "L403.185 75.7457\n",
       "L405.428 73.234\n",
       "L407.671 70.5257\n",
       "L412.158 64.5817\n",
       "L418.887 55.3065\n",
       "L421.13 52.4693\n",
       "L423.374 49.8874\n",
       "L425.617 47.6069\n",
       "L427.86 45.6493\n",
       "L430.103 44.014\n",
       "L432.347 42.6823\n",
       "L434.59 41.6236\n",
       "L436.833 40.8001\n",
       "L439.076 40.1721\n",
       "L441.319 39.7014\n",
       "L445.806 39.0998\n",
       "L450.292 38.7839\n",
       "L457.022 38.5734\n",
       "L470.481 38.4716\n",
       "L470.481 38.4716\" style=\"fill:none;stroke:#204a87;stroke-linecap:square;stroke-width:0.2;\"/>\n",
       "   </g>\n",
       "   <g id=\"line2d_3\">\n",
       "    <path clip-path=\"url(#p0530076909)\" d=\"\n",
       "M24.0813 254.192\n",
       "L33.0541 254.033\n",
       "L39.7838 253.667\n",
       "L44.2702 253.165\n",
       "L48.7566 252.304\n",
       "L50.9998 251.68\n",
       "L53.2431 250.889\n",
       "L55.4863 249.9\n",
       "L57.7295 248.679\n",
       "L59.9727 247.195\n",
       "L62.2159 245.422\n",
       "L64.4591 243.341\n",
       "L66.7024 240.949\n",
       "L68.9456 238.259\n",
       "L71.1888 235.302\n",
       "L75.6752 228.821\n",
       "L80.1617 222.129\n",
       "L82.4049 218.933\n",
       "L84.6481 215.95\n",
       "L86.8913 213.246\n",
       "L89.1345 210.871\n",
       "L91.3777 208.86\n",
       "L93.6209 207.234\n",
       "L95.8642 206.01\n",
       "L98.1074 205.199\n",
       "L100.351 204.807\n",
       "L102.594 204.831\n",
       "L104.837 205.256\n",
       "L107.08 206.047\n",
       "L109.323 207.152\n",
       "L111.567 208.505\n",
       "L116.053 211.68\n",
       "L122.783 216.919\n",
       "L127.269 220.663\n",
       "L131.756 224.843\n",
       "L136.242 229.592\n",
       "L140.728 234.8\n",
       "L147.458 242.762\n",
       "L151.945 247.678\n",
       "L156.431 252.038\n",
       "L158.674 253.983\n",
       "L160.917 255.764\n",
       "L163.161 257.373\n",
       "L165.404 258.8\n",
       "L167.647 260.033\n",
       "L169.89 261.057\n",
       "L172.134 261.862\n",
       "L174.377 262.44\n",
       "L176.62 262.796\n",
       "L178.863 262.944\n",
       "L181.106 262.912\n",
       "L185.593 262.465\n",
       "L194.566 261.27\n",
       "L205.782 260.27\n",
       "L208.025 259.872\n",
       "L210.268 259.311\n",
       "L212.511 258.556\n",
       "L214.755 257.578\n",
       "L216.998 256.354\n",
       "L219.241 254.864\n",
       "L221.484 253.093\n",
       "L223.727 251.028\n",
       "L225.971 248.66\n",
       "L228.214 245.99\n",
       "L230.457 243.029\n",
       "L232.7 239.801\n",
       "L237.187 232.72\n",
       "L246.16 218.003\n",
       "L248.403 214.694\n",
       "L250.646 211.699\n",
       "L252.889 209.088\n",
       "L255.133 206.922\n",
       "L257.376 205.243\n",
       "L259.619 204.076\n",
       "L261.862 203.418\n",
       "L264.105 203.241\n",
       "L266.349 203.492\n",
       "L268.592 204.098\n",
       "L270.835 204.982\n",
       "L273.078 206.073\n",
       "L277.565 208.681\n",
       "L279.808 210.175\n",
       "L282.051 211.821\n",
       "L284.294 213.662\n",
       "L286.538 215.74\n",
       "L288.781 218.084\n",
       "L291.024 220.694\n",
       "L295.51 226.551\n",
       "L302.24 235.64\n",
       "L304.483 238.342\n",
       "L306.726 240.734\n",
       "L308.97 242.758\n",
       "L311.213 244.38\n",
       "L313.456 245.591\n",
       "L315.699 246.407\n",
       "L317.943 246.866\n",
       "L320.186 247.028\n",
       "L322.429 246.965\n",
       "L331.402 246.183\n",
       "L333.645 246.234\n",
       "L335.888 246.484\n",
       "L338.132 246.951\n",
       "L340.375 247.637\n",
       "L342.618 248.538\n",
       "L344.861 249.641\n",
       "L347.104 250.933\n",
       "L349.348 252.392\n",
       "L353.834 255.657\n",
       "L358.32 258.96\n",
       "L360.564 260.407\n",
       "L362.807 261.594\n",
       "L365.05 262.441\n",
       "L367.293 262.897\n",
       "L369.537 262.95\n",
       "L371.78 262.627\n",
       "L374.023 261.995\n",
       "L378.509 260.194\n",
       "L382.996 258.316\n",
       "L394.212 254.067\n",
       "L398.698 251.819\n",
       "L403.185 249.577\n",
       "L405.428 248.705\n",
       "L407.671 248.122\n",
       "L409.914 247.878\n",
       "L412.158 247.98\n",
       "L414.401 248.392\n",
       "L416.644 249.045\n",
       "L427.86 253.034\n",
       "L430.103 253.571\n",
       "L432.347 253.975\n",
       "L436.833 254.431\n",
       "L441.319 254.559\n",
       "L450.292 254.438\n",
       "L463.752 254.269\n",
       "L470.481 254.245\n",
       "L470.481 254.245\" style=\"fill:none;stroke:#204a87;stroke-linecap:square;stroke-width:0.2;\"/>\n",
       "   </g>\n",
       "   <g id=\"line2d_4\">\n",
       "    <defs>\n",
       "     <path d=\"\n",
       "M-3 3\n",
       "L3 -3\n",
       "M-3 -3\n",
       "L3 3\" id=\"m7bb187e4e2\" style=\"stroke:#000000;stroke-width:1.5;\"/>\n",
       "    </defs>\n",
       "    <g clip-path=\"url(#p0530076909)\">\n",
       "     <use style=\"stroke:#000000;stroke-width:1.5;\" x=\"149.459303316\" xlink:href=\"#m7bb187e4e2\" y=\"167.380387111\"/>\n",
       "     <use style=\"stroke:#000000;stroke-width:1.5;\" x=\"261.585833207\" xlink:href=\"#m7bb187e4e2\" y=\"118.330923691\"/>\n",
       "     <use style=\"stroke:#000000;stroke-width:1.5;\" x=\"139.072006631\" xlink:href=\"#m7bb187e4e2\" y=\"150.986955551\"/>\n",
       "     <use style=\"stroke:#000000;stroke-width:1.5;\" x=\"401.344504311\" xlink:href=\"#m7bb187e4e2\" y=\"160.977431796\"/>\n",
       "     <use style=\"stroke:#000000;stroke-width:1.5;\" x=\"124.880065301\" xlink:href=\"#m7bb187e4e2\" y=\"129.904593153\"/>\n",
       "     <use style=\"stroke:#000000;stroke-width:1.5;\" x=\"261.846807717\" xlink:href=\"#m7bb187e4e2\" y=\"115.602436015\"/>\n",
       "     <use style=\"stroke:#000000;stroke-width:1.5;\" x=\"246.174487706\" xlink:href=\"#m7bb187e4e2\" y=\"129.72371142\"/>\n",
       "     <use style=\"stroke:#000000;stroke-width:1.5;\" x=\"334.790884784\" xlink:href=\"#m7bb187e4e2\" y=\"156.402007274\"/>\n",
       "     <use style=\"stroke:#000000;stroke-width:1.5;\" x=\"162.361786276\" xlink:href=\"#m7bb187e4e2\" y=\"173.309053422\"/>\n",
       "     <use style=\"stroke:#000000;stroke-width:1.5;\" x=\"384.009493352\" xlink:href=\"#m7bb187e4e2\" y=\"183.885065219\"/>\n",
       "     <use style=\"stroke:#000000;stroke-width:1.5;\" x=\"106.534946568\" xlink:href=\"#m7bb187e4e2\" y=\"115.853503152\"/>\n",
       "     <use style=\"stroke:#000000;stroke-width:1.5;\" x=\"104.36912337\" xlink:href=\"#m7bb187e4e2\" y=\"108.104102213\"/>\n",
       "     <use style=\"stroke:#000000;stroke-width:1.5;\" x=\"265.935740875\" xlink:href=\"#m7bb187e4e2\" y=\"111.077690618\"/>\n",
       "     <use style=\"stroke:#000000;stroke-width:1.5;\" x=\"286.333417146\" xlink:href=\"#m7bb187e4e2\" y=\"109.593437983\"/>\n",
       "     <use style=\"stroke:#000000;stroke-width:1.5;\" x=\"179.650022115\" xlink:href=\"#m7bb187e4e2\" y=\"186.517350096\"/>\n",
       "     <use style=\"stroke:#000000;stroke-width:1.5;\" x=\"192.957941048\" xlink:href=\"#m7bb187e4e2\" y=\"183.997711948\"/>\n",
       "     <use style=\"stroke:#000000;stroke-width:1.5;\" x=\"254.908747494\" xlink:href=\"#m7bb187e4e2\" y=\"125.422510131\"/>\n",
       "     <use style=\"stroke:#000000;stroke-width:1.5;\" x=\"87.8526785714\" xlink:href=\"#m7bb187e4e2\" y=\"106.674602232\"/>\n",
       "     <use style=\"stroke:#000000;stroke-width:1.5;\" x=\"254.411433576\" xlink:href=\"#m7bb187e4e2\" y=\"120.883801059\"/>\n",
       "     <use style=\"stroke:#000000;stroke-width:1.5;\" x=\"138.433304432\" xlink:href=\"#m7bb187e4e2\" y=\"148.245512397\"/>\n",
       "     <use style=\"stroke:#000000;stroke-width:1.5;\" x=\"351.12607893\" xlink:href=\"#m7bb187e4e2\" y=\"172.844394938\"/>\n",
       "     <use style=\"stroke:#000000;stroke-width:1.5;\" x=\"406.709821429\" xlink:href=\"#m7bb187e4e2\" y=\"165.009443672\"/>\n",
       "     <use style=\"stroke:#000000;stroke-width:1.5;\" x=\"384.52655459\" xlink:href=\"#m7bb187e4e2\" y=\"177.439588256\"/>\n",
       "     <use style=\"stroke:#000000;stroke-width:1.5;\" x=\"128.741903877\" xlink:href=\"#m7bb187e4e2\" y=\"132.454380955\"/>\n",
       "     <use style=\"stroke:#000000;stroke-width:1.5;\" x=\"383.666908015\" xlink:href=\"#m7bb187e4e2\" y=\"182.847199485\"/>\n",
       "    </g>\n",
       "   </g>\n",
       "   <g id=\"patch_4\">\n",
       "    <path d=\"\n",
       "M24.0813 7.2\n",
       "L470.481 7.2\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_5\">\n",
       "    <path d=\"\n",
       "M470.481 286.2\n",
       "L470.481 7.2\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_6\">\n",
       "    <path d=\"\n",
       "M24.0813 286.2\n",
       "L470.481 286.2\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_7\">\n",
       "    <path d=\"\n",
       "M24.0813 286.2\n",
       "L24.0813 7.2\" 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_5\">\n",
       "      <defs>\n",
       "       <path d=\"\n",
       "M0 0\n",
       "L0 -4\" id=\"m93b0483c22\" style=\"stroke:#000000;stroke-width:0.5;\"/>\n",
       "      </defs>\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"46.8815140217\" xlink:href=\"#m93b0483c22\" y=\"286.2\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"line2d_6\">\n",
       "      <defs>\n",
       "       <path d=\"\n",
       "M0 0\n",
       "L0 4\" id=\"m741efc42ff\" style=\"stroke:#000000;stroke-width:0.5;\"/>\n",
       "      </defs>\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"46.8815140217\" xlink:href=\"#m741efc42ff\" y=\"7.2\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_1\">\n",
       "      <!-- −1.0 -->\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",
       "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",
       "       <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",
       "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(35.6018265217 297.7984375)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",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_2\">\n",
       "     <g id=\"line2d_7\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"139.767386485\" xlink:href=\"#m93b0483c22\" y=\"286.2\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"line2d_8\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"139.767386485\" xlink:href=\"#m741efc42ff\" y=\"7.2\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_2\">\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(128.592386485 297.7984375)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-35\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_3\">\n",
       "     <g id=\"line2d_9\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"232.653258948\" xlink:href=\"#m93b0483c22\" y=\"286.2\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"line2d_10\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"232.653258948\" xlink:href=\"#m741efc42ff\" y=\"7.2\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_3\">\n",
       "      <!-- 0.0 -->\n",
       "      <g transform=\"translate(225.363415198 297.7984375)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#BitstreamVeraSans-Roman-30\"/>\n",
       "       <use x=\"63.623046875\" xlink:href=\"#BitstreamVeraSans-Roman-2e\"/>\n",
       "       <use x=\"95.41015625\" xlink:href=\"#BitstreamVeraSans-Roman-30\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_4\">\n",
       "     <g id=\"line2d_11\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"325.539131411\" xlink:href=\"#m93b0483c22\" y=\"286.2\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"line2d_12\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"325.539131411\" xlink:href=\"#m741efc42ff\" y=\"7.2\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_4\">\n",
       "      <!-- 0.5 -->\n",
       "      <g transform=\"translate(318.353975161 297.7984375)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#BitstreamVeraSans-Roman-30\"/>\n",
       "       <use x=\"63.623046875\" xlink:href=\"#BitstreamVeraSans-Roman-2e\"/>\n",
       "       <use x=\"95.41015625\" xlink:href=\"#BitstreamVeraSans-Roman-35\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_5\">\n",
       "     <g id=\"line2d_13\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"418.425003874\" xlink:href=\"#m93b0483c22\" y=\"286.2\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"line2d_14\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"418.425003874\" xlink:href=\"#m741efc42ff\" y=\"7.2\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_5\">\n",
       "      <!-- 1.0 -->\n",
       "      <g transform=\"translate(411.354691374 297.7984375)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#BitstreamVeraSans-Roman-31\"/>\n",
       "       <use x=\"63.623046875\" xlink:href=\"#BitstreamVeraSans-Roman-2e\"/>\n",
       "       <use x=\"95.41015625\" 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_15\">\n",
       "      <defs>\n",
       "       <path d=\"\n",
       "M0 0\n",
       "L4 0\" id=\"m728421d6d4\" style=\"stroke:#000000;stroke-width:0.5;\"/>\n",
       "      </defs>\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"24.08125\" xlink:href=\"#m728421d6d4\" y=\"263.115581774\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"line2d_16\">\n",
       "      <defs>\n",
       "       <path d=\"\n",
       "M0 0\n",
       "L-4 0\" id=\"mcb0005524f\" style=\"stroke:#000000;stroke-width:0.5;\"/>\n",
       "      </defs>\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"470.48125\" xlink:href=\"#mcb0005524f\" y=\"263.115581774\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_6\">\n",
       "      <!-- −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",
       "      </defs>\n",
       "      <g transform=\"translate(7.2 265.874956774)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#BitstreamVeraSans-Roman-2212\"/>\n",
       "       <use x=\"83.7890625\" xlink:href=\"#BitstreamVeraSans-Roman-33\"/>\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=\"24.08125\" xlink:href=\"#m728421d6d4\" y=\"224.192711695\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"line2d_18\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"470.48125\" xlink:href=\"#mcb0005524f\" y=\"224.192711695\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_7\">\n",
       "      <!-- −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(7.4 226.952086695)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#BitstreamVeraSans-Roman-2212\"/>\n",
       "       <use x=\"83.7890625\" xlink:href=\"#BitstreamVeraSans-Roman-32\"/>\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=\"24.08125\" xlink:href=\"#m728421d6d4\" y=\"185.269841617\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"line2d_20\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"470.48125\" xlink:href=\"#mcb0005524f\" y=\"185.269841617\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_8\">\n",
       "      <!-- −1 -->\n",
       "      <g transform=\"translate(7.321875 188.029216617)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#BitstreamVeraSans-Roman-2212\"/>\n",
       "       <use x=\"83.7890625\" xlink:href=\"#BitstreamVeraSans-Roman-31\"/>\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=\"24.08125\" xlink:href=\"#m728421d6d4\" y=\"146.346971539\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"line2d_22\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"470.48125\" xlink:href=\"#mcb0005524f\" y=\"146.346971539\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_9\">\n",
       "      <!-- 0 -->\n",
       "      <g transform=\"translate(15.0421875 149.106346539)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#BitstreamVeraSans-Roman-30\"/>\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=\"24.08125\" xlink:href=\"#m728421d6d4\" y=\"107.42410146\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"line2d_24\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"470.48125\" xlink:href=\"#mcb0005524f\" y=\"107.42410146\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_10\">\n",
       "      <!-- 1 -->\n",
       "      <g transform=\"translate(15.740625 110.18347646)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#BitstreamVeraSans-Roman-31\"/>\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=\"24.08125\" xlink:href=\"#m728421d6d4\" y=\"68.5012313819\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"line2d_26\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"470.48125\" xlink:href=\"#mcb0005524f\" y=\"68.5012313819\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_11\">\n",
       "      <!-- 2 -->\n",
       "      <g transform=\"translate(15.453125 71.2606063819)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#BitstreamVeraSans-Roman-32\"/>\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=\"24.08125\" xlink:href=\"#m728421d6d4\" y=\"29.5783613036\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"line2d_28\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"470.48125\" xlink:href=\"#mcb0005524f\" y=\"29.5783613036\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_12\">\n",
       "      <!-- 3 -->\n",
       "      <g transform=\"translate(15.2828125 32.3377363036)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#BitstreamVeraSans-Roman-33\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "   </g>\n",
       "  </g>\n",
       " </g>\n",
       " <defs>\n",
       "  <clipPath id=\"p0530076909\">\n",
       "   <rect height=\"279.0\" width=\"446.4\" x=\"24.08125\" y=\"7.2\"/>\n",
       "  </clipPath>\n",
       " </defs>\n",
       "</svg>\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10abfe410>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "m.plot()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " - Perform **model selection** in the sense of maximizing the log-likelihood of the data over the hyperparameters.  Because this problem is non-convex, we use multiple random restarts and choose the best. (note: GPy tends to be heavy on warnings, and if I run the optimization a few times, these typically go away)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimization restart 1/10, f = 2.4758480353\n",
      "Optimization restart 2/10, f = 27.1293364959\n",
      "Optimization restart 3/10, f = 2.47584803533\n",
      "Optimization restart 4/10, f = 2.4758480353\n",
      "Optimization restart 5/10, f = 2.4758480353\n",
      "Optimization restart 6/10, f = 2.4758480353\n",
      "Optimization restart 7/10, f = 27.1293364959\n",
      "Optimization restart 8/10, f = 27.1293364959\n",
      "Optimization restart 9/10, f = 27.1293364959\n",
      "Optimization restart 10/10, f = 2.47584803531\n"
     ]
    }
   ],
   "source": [
    "m.optimize_restarts(num_restarts = 10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " - Display and plot the optimized GP model, and note how much better it looks.  Note the difference in log-likelihood compared to previous.  You may also want to try ```m.plot?``` (then enter) and ```gpy.kern.``` (followed by tab) to see more options. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "<b>Model</b>: GP regression<br>\n",
       "<b>Log-likelihood</b>: -2.4758480353<br>\n",
       "<b>Number of Parameters</b>: 3<br>\n",
       "<br><b>Parameters</b>:\n",
       "<table>\n",
       "<tr>\n",
       "  <td><b>GP_regression.</b>\n",
       "  <td><b>Value</b></td>\n",
       "  <td><b>Constraint</b></td>\n",
       "  <td><b>Prior</b></td>\n",
       "  <td><b>Tied to</b></td>\n",
       "<tr><td>rbf.variance           </td><td align=\"right\">  0.87218366313</td><td>   +ve    </td><td>     </td><td>       </td></tr>\n",
       "<tr><td>rbf.lengthscale        </td><td align=\"right\"> 0.276588968132</td><td>   +ve    </td><td>     </td><td>       </td></tr>\n",
       "<tr><td>Gaussian_noise.variance</td><td align=\"right\">0.0156716588755</td><td>   +ve    </td><td>     </td><td>       </td></tr>\n",
       "</table>"
      ],
      "text/plain": [
       "<GPy.models.gp_regression.GPRegression at 0x10a060cd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "display(m)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'dataplot': [<matplotlib.lines.Line2D at 0x10a4b1190>],\n",
       " 'gpplot': [[<matplotlib.lines.Line2D at 0x10a495d10>],\n",
       "  [<matplotlib.patches.Polygon at 0x10a495f90>],\n",
       "  [<matplotlib.lines.Line2D at 0x10a4a45d0>],\n",
       "  [<matplotlib.lines.Line2D at 0x10a4a4b10>]]}"
      ]
     },
     "execution_count": 46,
     "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=\"307pt\" version=\"1.1\" viewBox=\"0 0 477 307\" width=\"477pt\" 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 307.078\n",
       "L477.559 307.078\n",
       "L477.559 0\n",
       "L0 0\n",
       "L0 307.078\" style=\"fill:none;\"/>\n",
       "  </g>\n",
       "  <g id=\"axes_1\">\n",
       "   <g id=\"patch_2\">\n",
       "    <path d=\"\n",
       "M23.9594 286.2\n",
       "L470.359 286.2\n",
       "L470.359 7.2\n",
       "L23.9594 7.2\n",
       "L23.9594 286.2\" style=\"fill:none;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_3\">\n",
       "    <path clip-path=\"url(#pa00aa19272)\" d=\"\n",
       "M23.9594 65.9943\n",
       "L26.2026 69.05\n",
       "L28.4458 72.1763\n",
       "L30.689 75.3572\n",
       "L32.9322 78.5742\n",
       "L35.1755 81.8071\n",
       "L37.4187 85.0335\n",
       "L39.6619 88.2292\n",
       "L41.9051 91.3682\n",
       "L44.1483 94.4231\n",
       "L46.3915 97.3654\n",
       "L48.6348 100.165\n",
       "L50.878 102.793\n",
       "L53.1212 105.217\n",
       "L55.3644 107.407\n",
       "L57.6076 109.333\n",
       "L59.8508 110.965\n",
       "L62.094 112.275\n",
       "L64.3373 113.234\n",
       "L66.5805 113.817\n",
       "L68.8237 113.998\n",
       "L71.0669 113.755\n",
       "L73.3101 113.068\n",
       "L75.5533 111.919\n",
       "L77.7966 110.298\n",
       "L80.0398 108.199\n",
       "L82.283 105.632\n",
       "L84.5262 102.623\n",
       "L86.7694 99.2188\n",
       "L89.0126 95.4896\n",
       "L91.2559 91.5242\n",
       "L93.4991 87.4225\n",
       "L95.7423 83.2864\n",
       "L97.9855 79.2121\n",
       "L100.229 75.2849\n",
       "L102.472 71.5771\n",
       "L104.715 68.1473\n",
       "L106.958 65.0422\n",
       "L109.202 62.2971\n",
       "L111.445 59.9381\n",
       "L113.688 57.9832\n",
       "L115.931 56.4444\n",
       "L118.174 55.3288\n",
       "L120.418 54.6396\n",
       "L122.661 54.378\n",
       "L124.904 54.5429\n",
       "L127.147 55.1321\n",
       "L129.391 56.1421\n",
       "L131.634 57.5675\n",
       "L133.877 59.4005\n",
       "L136.12 61.6305\n",
       "L138.363 64.243\n",
       "L140.607 67.2192\n",
       "L142.85 70.5359\n",
       "L145.093 74.1652\n",
       "L147.336 78.0748\n",
       "L149.579 82.229\n",
       "L151.823 86.5892\n",
       "L154.066 91.1153\n",
       "L156.309 95.767\n",
       "L158.552 100.505\n",
       "L160.796 105.29\n",
       "L163.039 110.089\n",
       "L165.282 114.87\n",
       "L167.525 119.605\n",
       "L169.768 124.267\n",
       "L172.012 128.836\n",
       "L174.255 133.29\n",
       "L176.498 137.61\n",
       "L178.741 141.778\n",
       "L180.985 145.775\n",
       "L183.228 149.583\n",
       "L185.471 153.183\n",
       "L187.714 156.554\n",
       "L189.957 159.676\n",
       "L192.201 162.527\n",
       "L194.444 165.085\n",
       "L196.687 167.328\n",
       "L198.93 169.236\n",
       "L201.173 170.787\n",
       "L203.417 171.963\n",
       "L205.66 172.747\n",
       "L207.903 173.124\n",
       "L210.146 173.085\n",
       "L212.39 172.623\n",
       "L214.633 171.734\n",
       "L216.876 170.42\n",
       "L219.119 168.685\n",
       "L221.362 166.539\n",
       "L223.606 163.992\n",
       "L225.849 161.062\n",
       "L228.092 157.765\n",
       "L230.335 154.121\n",
       "L232.578 150.154\n",
       "L234.822 145.887\n",
       "L237.065 141.348\n",
       "L239.308 136.567\n",
       "L241.551 131.574\n",
       "L243.795 126.403\n",
       "L246.038 121.093\n",
       "L248.281 115.683\n",
       "L250.524 110.216\n",
       "L252.767 104.738\n",
       "L255.011 99.2954\n",
       "L257.254 93.9389\n",
       "L259.497 88.7189\n",
       "L261.74 83.6862\n",
       "L263.983 78.8912\n",
       "L266.227 74.3827\n",
       "L268.47 70.2073\n",
       "L270.713 66.4087\n",
       "L272.956 63.0267\n",
       "L275.2 60.0967\n",
       "L277.443 57.6495\n",
       "L279.686 55.7105\n",
       "L281.929 54.2996\n",
       "L284.172 53.4313\n",
       "L286.416 53.1142\n",
       "L288.659 53.3512\n",
       "L290.902 54.1398\n",
       "L293.145 55.4722\n",
       "L295.389 57.3352\n",
       "L297.632 59.711\n",
       "L299.875 62.5771\n",
       "L302.118 65.9067\n",
       "L304.361 69.6692\n",
       "L306.605 73.8305\n",
       "L308.848 78.3532\n",
       "L311.091 83.197\n",
       "L313.334 88.3196\n",
       "L315.577 93.6763\n",
       "L317.821 99.2214\n",
       "L320.064 104.908\n",
       "L322.307 110.689\n",
       "L324.55 116.516\n",
       "L326.794 122.344\n",
       "L329.037 128.125\n",
       "L331.28 133.815\n",
       "L333.523 139.371\n",
       "L335.766 144.751\n",
       "L338.01 149.915\n",
       "L340.253 154.827\n",
       "L342.496 159.451\n",
       "L344.739 163.754\n",
       "L346.982 167.707\n",
       "L349.226 171.282\n",
       "L351.469 174.454\n",
       "L353.712 177.201\n",
       "L355.955 179.504\n",
       "L358.199 181.347\n",
       "L360.442 182.719\n",
       "L362.685 183.611\n",
       "L364.928 184.02\n",
       "L367.171 183.95\n",
       "L369.415 183.41\n",
       "L371.658 182.415\n",
       "L373.901 180.989\n",
       "L376.144 179.162\n",
       "L378.388 176.969\n",
       "L380.631 174.453\n",
       "L382.874 171.655\n",
       "L385.117 168.622\n",
       "L387.36 165.397\n",
       "L389.604 162.018\n",
       "L391.847 158.521\n",
       "L394.09 154.932\n",
       "L396.333 151.269\n",
       "L398.576 147.54\n",
       "L400.82 143.744\n",
       "L403.063 139.871\n",
       "L405.306 135.908\n",
       "L407.549 131.84\n",
       "L409.793 127.655\n",
       "L412.036 123.35\n",
       "L414.279 118.93\n",
       "L416.522 114.406\n",
       "L418.765 109.8\n",
       "L421.009 105.137\n",
       "L423.252 100.445\n",
       "L425.495 95.7534\n",
       "L427.738 91.0901\n",
       "L429.981 86.4824\n",
       "L432.225 81.9554\n",
       "L434.468 77.5319\n",
       "L436.711 73.2324\n",
       "L438.954 69.0749\n",
       "L441.198 65.075\n",
       "L443.441 61.2458\n",
       "L445.684 57.5981\n",
       "L447.927 54.1404\n",
       "L450.17 50.8791\n",
       "L452.414 47.8183\n",
       "L454.657 44.9601\n",
       "L456.9 42.305\n",
       "L459.143 39.8515\n",
       "L461.387 37.5964\n",
       "L463.63 35.5351\n",
       "L465.873 33.6619\n",
       "L468.116 31.9695\n",
       "L470.359 30.45\n",
       "L470.359 225.1\n",
       "L468.116 222.685\n",
       "L465.873 220.123\n",
       "L463.63 217.423\n",
       "L461.387 214.595\n",
       "L459.143 211.65\n",
       "L456.9 208.605\n",
       "L454.657 205.479\n",
       "L452.414 202.292\n",
       "L450.17 199.068\n",
       "L447.927 195.834\n",
       "L445.684 192.62\n",
       "L443.441 189.455\n",
       "L441.198 186.374\n",
       "L438.954 183.41\n",
       "L436.711 180.6\n",
       "L434.468 177.98\n",
       "L432.225 175.587\n",
       "L429.981 173.458\n",
       "L427.738 171.63\n",
       "L425.495 170.137\n",
       "L423.252 169.013\n",
       "L421.009 168.287\n",
       "L418.765 167.985\n",
       "L416.522 168.127\n",
       "L414.279 168.725\n",
       "L412.036 169.779\n",
       "L409.793 171.278\n",
       "L407.549 173.196\n",
       "L405.306 175.49\n",
       "L403.063 178.108\n",
       "L400.82 180.987\n",
       "L398.576 184.059\n",
       "L396.333 187.258\n",
       "L394.09 190.519\n",
       "L391.847 193.786\n",
       "L389.604 197.006\n",
       "L387.36 200.136\n",
       "L385.117 203.136\n",
       "L382.874 205.973\n",
       "L380.631 208.616\n",
       "L378.388 211.039\n",
       "L376.144 213.216\n",
       "L373.901 215.121\n",
       "L371.658 216.728\n",
       "L369.415 218.01\n",
       "L367.171 218.939\n",
       "L364.928 219.486\n",
       "L362.685 219.624\n",
       "L360.442 219.327\n",
       "L358.199 218.572\n",
       "L355.955 217.342\n",
       "L353.712 215.623\n",
       "L351.469 213.41\n",
       "L349.226 210.702\n",
       "L346.982 207.508\n",
       "L344.739 203.841\n",
       "L342.496 199.725\n",
       "L340.253 195.187\n",
       "L338.01 190.261\n",
       "L335.766 184.989\n",
       "L333.523 179.417\n",
       "L331.28 173.593\n",
       "L329.037 167.573\n",
       "L326.794 161.412\n",
       "L324.55 155.169\n",
       "L322.307 148.904\n",
       "L320.064 142.677\n",
       "L317.821 136.549\n",
       "L315.577 130.578\n",
       "L313.334 124.822\n",
       "L311.091 119.334\n",
       "L308.848 114.166\n",
       "L306.605 109.366\n",
       "L304.361 104.978\n",
       "L302.118 101.039\n",
       "L299.875 97.5826\n",
       "L297.632 94.6375\n",
       "L295.389 92.225\n",
       "L293.145 90.3611\n",
       "L290.902 89.0556\n",
       "L288.659 88.3124\n",
       "L286.416 88.1297\n",
       "L284.172 88.5\n",
       "L281.929 89.411\n",
       "L279.686 90.8452\n",
       "L277.443 92.7814\n",
       "L275.2 95.1941\n",
       "L272.956 98.055\n",
       "L270.713 101.333\n",
       "L268.47 104.993\n",
       "L266.227 109.002\n",
       "L263.983 113.32\n",
       "L261.74 117.911\n",
       "L259.497 122.734\n",
       "L257.254 127.748\n",
       "L255.011 132.913\n",
       "L252.767 138.186\n",
       "L250.524 143.526\n",
       "L248.281 148.888\n",
       "L246.038 154.232\n",
       "L243.795 159.513\n",
       "L241.551 164.691\n",
       "L239.308 169.726\n",
       "L237.065 174.579\n",
       "L234.822 179.215\n",
       "L232.578 183.6\n",
       "L230.335 187.707\n",
       "L228.092 191.509\n",
       "L225.849 194.984\n",
       "L223.606 198.116\n",
       "L221.362 200.889\n",
       "L219.119 203.292\n",
       "L216.876 205.316\n",
       "L214.633 206.955\n",
       "L212.39 208.203\n",
       "L210.146 209.057\n",
       "L207.903 209.514\n",
       "L205.66 209.57\n",
       "L203.417 209.224\n",
       "L201.173 208.475\n",
       "L198.93 207.323\n",
       "L196.687 205.77\n",
       "L194.444 203.82\n",
       "L192.201 201.479\n",
       "L189.957 198.758\n",
       "L187.714 195.669\n",
       "L185.471 192.229\n",
       "L183.228 188.46\n",
       "L180.985 184.386\n",
       "L178.741 180.035\n",
       "L176.498 175.442\n",
       "L174.255 170.641\n",
       "L172.012 165.673\n",
       "L169.768 160.577\n",
       "L167.525 155.396\n",
       "L165.282 150.173\n",
       "L163.039 144.951\n",
       "L160.796 139.769\n",
       "L158.552 134.666\n",
       "L156.309 129.679\n",
       "L154.066 124.84\n",
       "L151.823 120.182\n",
       "L149.579 115.734\n",
       "L147.336 111.524\n",
       "L145.093 107.58\n",
       "L142.85 103.929\n",
       "L140.607 100.599\n",
       "L138.363 97.6156\n",
       "L136.12 95.0059\n",
       "L133.877 92.795\n",
       "L131.634 91.0055\n",
       "L129.391 89.6572\n",
       "L127.147 88.7651\n",
       "L124.904 88.3387\n",
       "L122.661 88.3807\n",
       "L120.418 88.8871\n",
       "L118.174 89.8466\n",
       "L115.931 91.2409\n",
       "L113.688 93.0463\n",
       "L111.445 95.2341\n",
       "L109.202 97.773\n",
       "L106.958 100.631\n",
       "L104.715 103.776\n",
       "L102.472 107.182\n",
       "L100.229 110.826\n",
       "L97.9855 114.695\n",
       "L95.7423 118.785\n",
       "L93.4991 123.105\n",
       "L91.2559 127.669\n",
       "L89.0126 132.501\n",
       "L86.7694 137.621\n",
       "L84.5262 143.041\n",
       "L82.283 148.754\n",
       "L80.0398 154.738\n",
       "L77.7966 160.95\n",
       "L75.5533 167.336\n",
       "L73.3101 173.836\n",
       "L71.0669 180.386\n",
       "L68.8237 186.926\n",
       "L66.5805 193.396\n",
       "L64.3373 199.744\n",
       "L62.094 205.921\n",
       "L59.8508 211.883\n",
       "L57.6076 217.594\n",
       "L55.3644 223.021\n",
       "L53.1212 228.136\n",
       "L50.878 232.92\n",
       "L48.6348 237.356\n",
       "L46.3915 241.432\n",
       "L44.1483 245.142\n",
       "L41.9051 248.484\n",
       "L39.6619 251.46\n",
       "L37.4187 254.077\n",
       "L35.1755 256.344\n",
       "L32.9322 258.273\n",
       "L30.689 259.879\n",
       "L28.4458 261.181\n",
       "L26.2026 262.198\n",
       "L23.9594 262.95\n",
       "z\n",
       "\" style=\"fill:#729fcf;opacity:0.3;stroke:#729fcf;stroke-linejoin:miter;stroke-width:0.5;\"/>\n",
       "   </g>\n",
       "   <g id=\"line2d_1\">\n",
       "    <path clip-path=\"url(#pa00aa19272)\" d=\"\n",
       "M23.9594 164.472\n",
       "L26.2026 165.624\n",
       "L28.4458 166.679\n",
       "L30.689 167.618\n",
       "L32.9322 168.423\n",
       "L35.1755 169.075\n",
       "L37.4187 169.555\n",
       "L39.6619 169.845\n",
       "L41.9051 169.926\n",
       "L44.1483 169.782\n",
       "L46.3915 169.399\n",
       "L48.6348 168.76\n",
       "L50.878 167.856\n",
       "L53.1212 166.677\n",
       "L55.3644 165.214\n",
       "L57.6076 163.464\n",
       "L59.8508 161.424\n",
       "L62.094 159.098\n",
       "L64.3373 156.489\n",
       "L66.5805 153.607\n",
       "L68.8237 150.462\n",
       "L71.0669 147.071\n",
       "L75.5533 139.628\n",
       "L80.0398 131.468\n",
       "L86.7694 118.42\n",
       "L93.4991 105.264\n",
       "L97.9855 96.9536\n",
       "L102.472 89.3795\n",
       "L104.715 85.9618\n",
       "L106.958 82.8365\n",
       "L109.202 80.0351\n",
       "L111.445 77.5861\n",
       "L113.688 75.5147\n",
       "L115.931 73.8427\n",
       "L118.174 72.5877\n",
       "L120.418 71.7634\n",
       "L122.661 71.3793\n",
       "L124.904 71.4408\n",
       "L127.147 71.9486\n",
       "L129.391 72.8997\n",
       "L131.634 74.2865\n",
       "L133.877 76.0977\n",
       "L136.12 78.3182\n",
       "L138.363 80.9293\n",
       "L140.607 83.909\n",
       "L142.85 87.2326\n",
       "L145.093 90.8727\n",
       "L147.336 94.7995\n",
       "L151.823 103.386\n",
       "L156.309 112.723\n",
       "L163.039 127.52\n",
       "L169.768 142.422\n",
       "L174.255 151.966\n",
       "L178.741 160.907\n",
       "L183.228 169.022\n",
       "L185.471 172.706\n",
       "L187.714 176.112\n",
       "L189.957 179.217\n",
       "L192.201 182.003\n",
       "L194.444 184.452\n",
       "L196.687 186.549\n",
       "L198.93 188.279\n",
       "L201.173 189.631\n",
       "L203.417 190.593\n",
       "L205.66 191.158\n",
       "L207.903 191.319\n",
       "L210.146 191.071\n",
       "L212.39 190.413\n",
       "L214.633 189.345\n",
       "L216.876 187.868\n",
       "L219.119 185.988\n",
       "L221.362 183.714\n",
       "L223.606 181.054\n",
       "L225.849 178.023\n",
       "L228.092 174.637\n",
       "L230.335 170.914\n",
       "L232.578 166.877\n",
       "L234.822 162.551\n",
       "L239.308 153.146\n",
       "L243.795 142.958\n",
       "L250.524 126.871\n",
       "L257.254 110.844\n",
       "L261.74 100.799\n",
       "L263.983 96.1058\n",
       "L266.227 91.6922\n",
       "L268.47 87.6004\n",
       "L270.713 83.8707\n",
       "L272.956 80.5408\n",
       "L275.2 77.6454\n",
       "L277.443 75.2154\n",
       "L279.686 73.2778\n",
       "L281.929 71.8553\n",
       "L284.172 70.9657\n",
       "L286.416 70.6219\n",
       "L288.659 70.8318\n",
       "L290.902 71.5977\n",
       "L293.145 72.9167\n",
       "L295.389 74.7801\n",
       "L297.632 77.1743\n",
       "L299.875 80.0799\n",
       "L302.118 83.4726\n",
       "L304.361 87.3234\n",
       "L306.605 91.5983\n",
       "L308.848 96.2596\n",
       "L311.091 101.265\n",
       "L315.577 112.127\n",
       "L320.064 123.793\n",
       "L331.28 153.704\n",
       "L335.766 164.87\n",
       "L338.01 170.088\n",
       "L340.253 175.007\n",
       "L342.496 179.588\n",
       "L344.739 183.798\n",
       "L346.982 187.607\n",
       "L349.226 190.992\n",
       "L351.469 193.932\n",
       "L353.712 196.412\n",
       "L355.955 198.423\n",
       "L358.199 199.959\n",
       "L360.442 201.023\n",
       "L362.685 201.617\n",
       "L364.928 201.753\n",
       "L367.171 201.445\n",
       "L369.415 200.71\n",
       "L371.658 199.572\n",
       "L373.901 198.055\n",
       "L376.144 196.189\n",
       "L378.388 194.004\n",
       "L380.631 191.534\n",
       "L382.874 188.814\n",
       "L387.36 182.766\n",
       "L391.847 176.154\n",
       "L405.306 155.699\n",
       "L409.793 149.467\n",
       "L414.279 143.827\n",
       "L416.522 141.266\n",
       "L418.765 138.892\n",
       "L421.009 136.712\n",
       "L423.252 134.729\n",
       "L425.495 132.945\n",
       "L427.738 131.36\n",
       "L429.981 129.97\n",
       "L432.225 128.771\n",
       "L434.468 127.756\n",
       "L436.711 126.916\n",
       "L438.954 126.242\n",
       "L441.198 125.724\n",
       "L443.441 125.35\n",
       "L445.684 125.109\n",
       "L450.17 124.974\n",
       "L454.657 125.219\n",
       "L459.143 125.751\n",
       "L465.873 126.893\n",
       "L470.359 127.775\n",
       "L470.359 127.775\" style=\"fill:none;stroke:#204a87;stroke-linecap:square;stroke-width:2;\"/>\n",
       "   </g>\n",
       "   <g id=\"line2d_2\">\n",
       "    <path clip-path=\"url(#pa00aa19272)\" d=\"\n",
       "M23.9594 65.9943\n",
       "L28.4458 72.1763\n",
       "L44.1483 94.4231\n",
       "L48.6348 100.165\n",
       "L50.878 102.793\n",
       "L53.1212 105.217\n",
       "L55.3644 107.407\n",
       "L57.6076 109.333\n",
       "L59.8508 110.965\n",
       "L62.094 112.275\n",
       "L64.3373 113.234\n",
       "L66.5805 113.817\n",
       "L68.8237 113.998\n",
       "L71.0669 113.755\n",
       "L73.3101 113.068\n",
       "L75.5533 111.919\n",
       "L77.7966 110.298\n",
       "L80.0398 108.199\n",
       "L82.283 105.632\n",
       "L84.5262 102.623\n",
       "L86.7694 99.2188\n",
       "L89.0126 95.4896\n",
       "L93.4991 87.4225\n",
       "L97.9855 79.2121\n",
       "L102.472 71.5771\n",
       "L104.715 68.1473\n",
       "L106.958 65.0422\n",
       "L109.202 62.2971\n",
       "L111.445 59.9381\n",
       "L113.688 57.9832\n",
       "L115.931 56.4444\n",
       "L118.174 55.3288\n",
       "L120.418 54.6396\n",
       "L122.661 54.378\n",
       "L124.904 54.5429\n",
       "L127.147 55.1321\n",
       "L129.391 56.1421\n",
       "L131.634 57.5675\n",
       "L133.877 59.4005\n",
       "L136.12 61.6305\n",
       "L138.363 64.243\n",
       "L140.607 67.2192\n",
       "L142.85 70.5359\n",
       "L145.093 74.1652\n",
       "L147.336 78.0748\n",
       "L151.823 86.5892\n",
       "L156.309 95.767\n",
       "L172.012 128.836\n",
       "L176.498 137.61\n",
       "L180.985 145.775\n",
       "L185.471 153.183\n",
       "L187.714 156.554\n",
       "L189.957 159.676\n",
       "L192.201 162.527\n",
       "L194.444 165.085\n",
       "L196.687 167.328\n",
       "L198.93 169.236\n",
       "L201.173 170.787\n",
       "L203.417 171.963\n",
       "L205.66 172.747\n",
       "L207.903 173.124\n",
       "L210.146 173.085\n",
       "L212.39 172.623\n",
       "L214.633 171.734\n",
       "L216.876 170.42\n",
       "L219.119 168.685\n",
       "L221.362 166.539\n",
       "L223.606 163.992\n",
       "L225.849 161.062\n",
       "L228.092 157.765\n",
       "L230.335 154.121\n",
       "L232.578 150.154\n",
       "L234.822 145.887\n",
       "L239.308 136.567\n",
       "L243.795 126.403\n",
       "L250.524 110.216\n",
       "L257.254 93.9389\n",
       "L261.74 83.6862\n",
       "L263.983 78.8912\n",
       "L266.227 74.3827\n",
       "L268.47 70.2073\n",
       "L270.713 66.4087\n",
       "L272.956 63.0267\n",
       "L275.2 60.0967\n",
       "L277.443 57.6495\n",
       "L279.686 55.7105\n",
       "L281.929 54.2996\n",
       "L284.172 53.4313\n",
       "L286.416 53.1142\n",
       "L288.659 53.3512\n",
       "L290.902 54.1398\n",
       "L293.145 55.4722\n",
       "L295.389 57.3352\n",
       "L297.632 59.711\n",
       "L299.875 62.5771\n",
       "L302.118 65.9067\n",
       "L304.361 69.6692\n",
       "L306.605 73.8305\n",
       "L308.848 78.3532\n",
       "L311.091 83.197\n",
       "L315.577 93.6763\n",
       "L320.064 104.908\n",
       "L333.523 139.371\n",
       "L338.01 149.915\n",
       "L340.253 154.827\n",
       "L342.496 159.451\n",
       "L344.739 163.754\n",
       "L346.982 167.707\n",
       "L349.226 171.282\n",
       "L351.469 174.454\n",
       "L353.712 177.201\n",
       "L355.955 179.504\n",
       "L358.199 181.347\n",
       "L360.442 182.719\n",
       "L362.685 183.611\n",
       "L364.928 184.02\n",
       "L367.171 183.95\n",
       "L369.415 183.41\n",
       "L371.658 182.415\n",
       "L373.901 180.989\n",
       "L376.144 179.162\n",
       "L378.388 176.969\n",
       "L380.631 174.453\n",
       "L382.874 171.655\n",
       "L385.117 168.622\n",
       "L389.604 162.018\n",
       "L394.09 154.932\n",
       "L400.82 143.744\n",
       "L405.306 135.908\n",
       "L409.793 127.655\n",
       "L414.279 118.93\n",
       "L421.009 105.137\n",
       "L429.981 86.4824\n",
       "L434.468 77.5319\n",
       "L438.954 69.0749\n",
       "L443.441 61.2458\n",
       "L447.927 54.1404\n",
       "L450.17 50.8791\n",
       "L452.414 47.8183\n",
       "L454.657 44.9601\n",
       "L456.9 42.305\n",
       "L459.143 39.8515\n",
       "L461.387 37.5964\n",
       "L463.63 35.5351\n",
       "L465.873 33.6619\n",
       "L468.116 31.9695\n",
       "L470.359 30.45\n",
       "L470.359 30.45\" style=\"fill:none;stroke:#204a87;stroke-linecap:square;stroke-width:0.2;\"/>\n",
       "   </g>\n",
       "   <g id=\"line2d_3\">\n",
       "    <path clip-path=\"url(#pa00aa19272)\" d=\"\n",
       "M23.9594 262.95\n",
       "L26.2026 262.198\n",
       "L28.4458 261.181\n",
       "L30.689 259.879\n",
       "L32.9322 258.273\n",
       "L35.1755 256.344\n",
       "L37.4187 254.077\n",
       "L39.6619 251.46\n",
       "L41.9051 248.484\n",
       "L44.1483 245.142\n",
       "L46.3915 241.432\n",
       "L48.6348 237.356\n",
       "L50.878 232.92\n",
       "L53.1212 228.136\n",
       "L55.3644 223.021\n",
       "L59.8508 211.883\n",
       "L64.3373 199.744\n",
       "L71.0669 180.386\n",
       "L77.7966 160.95\n",
       "L82.283 148.754\n",
       "L86.7694 137.621\n",
       "L89.0126 132.501\n",
       "L91.2559 127.669\n",
       "L95.7423 118.785\n",
       "L100.229 110.826\n",
       "L102.472 107.182\n",
       "L104.715 103.776\n",
       "L106.958 100.631\n",
       "L109.202 97.773\n",
       "L111.445 95.2341\n",
       "L113.688 93.0463\n",
       "L115.931 91.2409\n",
       "L118.174 89.8466\n",
       "L120.418 88.8871\n",
       "L122.661 88.3807\n",
       "L124.904 88.3387\n",
       "L127.147 88.7651\n",
       "L129.391 89.6572\n",
       "L131.634 91.0055\n",
       "L133.877 92.795\n",
       "L136.12 95.0059\n",
       "L138.363 97.6156\n",
       "L140.607 100.599\n",
       "L142.85 103.929\n",
       "L145.093 107.58\n",
       "L147.336 111.524\n",
       "L149.579 115.734\n",
       "L154.066 124.84\n",
       "L158.552 134.666\n",
       "L165.282 150.173\n",
       "L172.012 165.673\n",
       "L176.498 175.442\n",
       "L180.985 184.386\n",
       "L183.228 188.46\n",
       "L185.471 192.229\n",
       "L187.714 195.669\n",
       "L189.957 198.758\n",
       "L192.201 201.479\n",
       "L194.444 203.82\n",
       "L196.687 205.77\n",
       "L198.93 207.323\n",
       "L201.173 208.475\n",
       "L203.417 209.224\n",
       "L205.66 209.57\n",
       "L207.903 209.514\n",
       "L210.146 209.057\n",
       "L212.39 208.203\n",
       "L214.633 206.955\n",
       "L216.876 205.316\n",
       "L219.119 203.292\n",
       "L221.362 200.889\n",
       "L223.606 198.116\n",
       "L225.849 194.984\n",
       "L228.092 191.509\n",
       "L230.335 187.707\n",
       "L232.578 183.6\n",
       "L234.822 179.215\n",
       "L239.308 169.726\n",
       "L243.795 159.513\n",
       "L259.497 122.734\n",
       "L263.983 113.32\n",
       "L266.227 109.002\n",
       "L268.47 104.993\n",
       "L270.713 101.333\n",
       "L272.956 98.055\n",
       "L275.2 95.1941\n",
       "L277.443 92.7814\n",
       "L279.686 90.8452\n",
       "L281.929 89.411\n",
       "L284.172 88.5\n",
       "L286.416 88.1297\n",
       "L288.659 88.3124\n",
       "L290.902 89.0556\n",
       "L293.145 90.3611\n",
       "L295.389 92.225\n",
       "L297.632 94.6375\n",
       "L299.875 97.5826\n",
       "L302.118 101.039\n",
       "L304.361 104.978\n",
       "L306.605 109.366\n",
       "L308.848 114.166\n",
       "L311.091 119.334\n",
       "L315.577 130.578\n",
       "L320.064 142.677\n",
       "L331.28 173.593\n",
       "L335.766 184.989\n",
       "L338.01 190.261\n",
       "L340.253 195.187\n",
       "L342.496 199.725\n",
       "L344.739 203.841\n",
       "L346.982 207.508\n",
       "L349.226 210.702\n",
       "L351.469 213.41\n",
       "L353.712 215.623\n",
       "L355.955 217.342\n",
       "L358.199 218.572\n",
       "L360.442 219.327\n",
       "L362.685 219.624\n",
       "L364.928 219.486\n",
       "L367.171 218.939\n",
       "L369.415 218.01\n",
       "L371.658 216.728\n",
       "L373.901 215.121\n",
       "L376.144 213.216\n",
       "L378.388 211.039\n",
       "L380.631 208.616\n",
       "L382.874 205.973\n",
       "L387.36 200.136\n",
       "L391.847 193.786\n",
       "L398.576 184.059\n",
       "L400.82 180.987\n",
       "L403.063 178.108\n",
       "L405.306 175.49\n",
       "L407.549 173.196\n",
       "L409.793 171.278\n",
       "L412.036 169.779\n",
       "L414.279 168.725\n",
       "L416.522 168.127\n",
       "L418.765 167.985\n",
       "L421.009 168.287\n",
       "L423.252 169.013\n",
       "L425.495 170.137\n",
       "L427.738 171.63\n",
       "L429.981 173.458\n",
       "L432.225 175.587\n",
       "L434.468 177.98\n",
       "L436.711 180.6\n",
       "L441.198 186.374\n",
       "L445.684 192.62\n",
       "L456.9 208.605\n",
       "L461.387 214.595\n",
       "L465.873 220.123\n",
       "L470.359 225.1\n",
       "L470.359 225.1\" style=\"fill:none;stroke:#204a87;stroke-linecap:square;stroke-width:0.2;\"/>\n",
       "   </g>\n",
       "   <g id=\"line2d_4\">\n",
       "    <defs>\n",
       "     <path d=\"\n",
       "M-3 3\n",
       "L3 -3\n",
       "M-3 -3\n",
       "L3 3\" id=\"m7bb187e4e2\" style=\"stroke:#000000;stroke-width:1.5;\"/>\n",
       "    </defs>\n",
       "    <g clip-path=\"url(#pa00aa19272)\">\n",
       "     <use style=\"stroke:#000000;stroke-width:1.5;\" x=\"388.835260122\" xlink:href=\"#m7bb187e4e2\" y=\"175.026507638\"/>\n",
       "     <use style=\"stroke:#000000;stroke-width:1.5;\" x=\"201.105508504\" xlink:href=\"#m7bb187e4e2\" y=\"191.341218689\"/>\n",
       "     <use style=\"stroke:#000000;stroke-width:1.5;\" x=\"120.722721271\" xlink:href=\"#m7bb187e4e2\" y=\"56.8946356821\"/>\n",
       "     <use style=\"stroke:#000000;stroke-width:1.5;\" x=\"153.493843064\" xlink:href=\"#m7bb187e4e2\" y=\"107.914176261\"/>\n",
       "     <use style=\"stroke:#000000;stroke-width:1.5;\" x=\"87.7308035714\" xlink:href=\"#m7bb187e4e2\" y=\"120.531988232\"/>\n",
       "     <use style=\"stroke:#000000;stroke-width:1.5;\" x=\"244.939270053\" xlink:href=\"#m7bb187e4e2\" y=\"147.176941374\"/>\n",
       "     <use style=\"stroke:#000000;stroke-width:1.5;\" x=\"257.75636402\" xlink:href=\"#m7bb187e4e2\" y=\"102.758441753\"/>\n",
       "     <use style=\"stroke:#000000;stroke-width:1.5;\" x=\"361.472031678\" xlink:href=\"#m7bb187e4e2\" y=\"204.079201617\"/>\n",
       "     <use style=\"stroke:#000000;stroke-width:1.5;\" x=\"377.588164077\" xlink:href=\"#m7bb187e4e2\" y=\"203.353549159\"/>\n",
       "     <use style=\"stroke:#000000;stroke-width:1.5;\" x=\"137.473126078\" xlink:href=\"#m7bb187e4e2\" y=\"75.474622676\"/>\n",
       "     <use style=\"stroke:#000000;stroke-width:1.5;\" x=\"277.487362073\" xlink:href=\"#m7bb187e4e2\" y=\"75.4903730327\"/>\n",
       "     <use style=\"stroke:#000000;stroke-width:1.5;\" x=\"294.37459844\" xlink:href=\"#m7bb187e4e2\" y=\"65.2526921792\"/>\n",
       "     <use style=\"stroke:#000000;stroke-width:1.5;\" x=\"324.755726031\" xlink:href=\"#m7bb187e4e2\" y=\"135.182646352\"/>\n",
       "     <use style=\"stroke:#000000;stroke-width:1.5;\" x=\"251.593229268\" xlink:href=\"#m7bb187e4e2\" y=\"131.324048872\"/>\n",
       "     <use style=\"stroke:#000000;stroke-width:1.5;\" x=\"130.613987825\" xlink:href=\"#m7bb187e4e2\" y=\"84.0846668249\"/>\n",
       "     <use style=\"stroke:#000000;stroke-width:1.5;\" x=\"239.790000156\" xlink:href=\"#m7bb187e4e2\" y=\"144.584557877\"/>\n",
       "     <use style=\"stroke:#000000;stroke-width:1.5;\" x=\"227.598323267\" xlink:href=\"#m7bb187e4e2\" y=\"178.899151701\"/>\n",
       "     <use style=\"stroke:#000000;stroke-width:1.5;\" x=\"160.391456219\" xlink:href=\"#m7bb187e4e2\" y=\"116.207809868\"/>\n",
       "     <use style=\"stroke:#000000;stroke-width:1.5;\" x=\"406.587946429\" xlink:href=\"#m7bb187e4e2\" y=\"154.659586876\"/>\n",
       "     <use style=\"stroke:#000000;stroke-width:1.5;\" x=\"92.9891461657\" xlink:href=\"#m7bb187e4e2\" y=\"104.846686571\"/>\n",
       "     <use style=\"stroke:#000000;stroke-width:1.5;\" x=\"301.01488601\" xlink:href=\"#m7bb187e4e2\" y=\"88.8853247724\"/>\n",
       "     <use style=\"stroke:#000000;stroke-width:1.5;\" x=\"374.361075543\" xlink:href=\"#m7bb187e4e2\" y=\"192.960791289\"/>\n",
       "     <use style=\"stroke:#000000;stroke-width:1.5;\" x=\"120.271805855\" xlink:href=\"#m7bb187e4e2\" y=\"76.7434729636\"/>\n",
       "     <use style=\"stroke:#000000;stroke-width:1.5;\" x=\"160.215657255\" xlink:href=\"#m7bb187e4e2\" y=\"126.005661802\"/>\n",
       "     <use style=\"stroke:#000000;stroke-width:1.5;\" x=\"219.815869197\" xlink:href=\"#m7bb187e4e2\" y=\"182.257781724\"/>\n",
       "    </g>\n",
       "   </g>\n",
       "   <g id=\"patch_4\">\n",
       "    <path d=\"\n",
       "M23.9594 7.2\n",
       "L470.359 7.2\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_5\">\n",
       "    <path d=\"\n",
       "M470.359 286.2\n",
       "L470.359 7.2\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_6\">\n",
       "    <path d=\"\n",
       "M23.9594 286.2\n",
       "L470.359 286.2\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_7\">\n",
       "    <path d=\"\n",
       "M23.9594 286.2\n",
       "L23.9594 7.2\" 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_5\">\n",
       "      <defs>\n",
       "       <path d=\"\n",
       "M0 0\n",
       "L0 -4\" id=\"m93b0483c22\" style=\"stroke:#000000;stroke-width:0.5;\"/>\n",
       "      </defs>\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"85.9221623623\" xlink:href=\"#m93b0483c22\" y=\"286.2\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"line2d_6\">\n",
       "      <defs>\n",
       "       <path d=\"\n",
       "M0 0\n",
       "L0 4\" id=\"m741efc42ff\" style=\"stroke:#000000;stroke-width:0.5;\"/>\n",
       "      </defs>\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"85.9221623623\" xlink:href=\"#m741efc42ff\" y=\"7.2\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_1\">\n",
       "      <!-- −1.0 -->\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",
       "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",
       "       <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",
       "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(74.6424748623 297.7984375)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",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_2\">\n",
       "     <g id=\"line2d_7\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"166.702425318\" xlink:href=\"#m93b0483c22\" y=\"286.2\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"line2d_8\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"166.702425318\" xlink:href=\"#m741efc42ff\" y=\"7.2\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_2\">\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(155.527425318 297.7984375)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-35\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_3\">\n",
       "     <g id=\"line2d_9\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"247.482688274\" xlink:href=\"#m93b0483c22\" y=\"286.2\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"line2d_10\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"247.482688274\" xlink:href=\"#m741efc42ff\" y=\"7.2\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_3\">\n",
       "      <!-- 0.0 -->\n",
       "      <g transform=\"translate(240.192844524 297.7984375)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#BitstreamVeraSans-Roman-30\"/>\n",
       "       <use x=\"63.623046875\" xlink:href=\"#BitstreamVeraSans-Roman-2e\"/>\n",
       "       <use x=\"95.41015625\" xlink:href=\"#BitstreamVeraSans-Roman-30\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_4\">\n",
       "     <g id=\"line2d_11\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"328.26295123\" xlink:href=\"#m93b0483c22\" y=\"286.2\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"line2d_12\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"328.26295123\" xlink:href=\"#m741efc42ff\" y=\"7.2\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_4\">\n",
       "      <!-- 0.5 -->\n",
       "      <g transform=\"translate(321.07779498 297.7984375)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#BitstreamVeraSans-Roman-30\"/>\n",
       "       <use x=\"63.623046875\" xlink:href=\"#BitstreamVeraSans-Roman-2e\"/>\n",
       "       <use x=\"95.41015625\" xlink:href=\"#BitstreamVeraSans-Roman-35\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_5\">\n",
       "     <g id=\"line2d_13\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"409.043214186\" xlink:href=\"#m93b0483c22\" y=\"286.2\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"line2d_14\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"409.043214186\" xlink:href=\"#m741efc42ff\" y=\"7.2\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_5\">\n",
       "      <!-- 1.0 -->\n",
       "      <g transform=\"translate(401.972901686 297.7984375)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#BitstreamVeraSans-Roman-31\"/>\n",
       "       <use x=\"63.623046875\" xlink:href=\"#BitstreamVeraSans-Roman-2e\"/>\n",
       "       <use x=\"95.41015625\" 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_15\">\n",
       "      <defs>\n",
       "       <path d=\"\n",
       "M0 0\n",
       "L4 0\" id=\"m728421d6d4\" style=\"stroke:#000000;stroke-width:0.5;\"/>\n",
       "      </defs>\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"23.959375\" xlink:href=\"#m728421d6d4\" y=\"256.862543408\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"line2d_16\">\n",
       "      <defs>\n",
       "       <path d=\"\n",
       "M0 0\n",
       "L-4 0\" id=\"mcb0005524f\" style=\"stroke:#000000;stroke-width:0.5;\"/>\n",
       "      </defs>\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"470.359375\" xlink:href=\"#mcb0005524f\" y=\"256.862543408\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_6\">\n",
       "      <!-- −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(7.278125 259.621918408)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#BitstreamVeraSans-Roman-2212\"/>\n",
       "       <use x=\"83.7890625\" xlink:href=\"#BitstreamVeraSans-Roman-32\"/>\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=\"23.959375\" xlink:href=\"#m728421d6d4\" y=\"195.738178139\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"line2d_18\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"470.359375\" xlink:href=\"#mcb0005524f\" y=\"195.738178139\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_7\">\n",
       "      <!-- −1 -->\n",
       "      <g transform=\"translate(7.2 198.497553139)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#BitstreamVeraSans-Roman-2212\"/>\n",
       "       <use x=\"83.7890625\" xlink:href=\"#BitstreamVeraSans-Roman-31\"/>\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=\"23.959375\" xlink:href=\"#m728421d6d4\" y=\"134.61381287\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"line2d_20\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"470.359375\" xlink:href=\"#mcb0005524f\" y=\"134.61381287\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_8\">\n",
       "      <!-- 0 -->\n",
       "      <g transform=\"translate(14.9203125 137.37318787)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#BitstreamVeraSans-Roman-30\"/>\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=\"23.959375\" xlink:href=\"#m728421d6d4\" y=\"73.4894476002\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"line2d_22\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"470.359375\" xlink:href=\"#mcb0005524f\" y=\"73.4894476002\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_9\">\n",
       "      <!-- 1 -->\n",
       "      <g transform=\"translate(15.61875 76.2488226002)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#BitstreamVeraSans-Roman-31\"/>\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=\"23.959375\" xlink:href=\"#m728421d6d4\" y=\"12.3650823307\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"line2d_24\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.5;\" x=\"470.359375\" xlink:href=\"#mcb0005524f\" y=\"12.3650823307\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_10\">\n",
       "      <!-- 2 -->\n",
       "      <g transform=\"translate(15.33125 15.1244573307)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#BitstreamVeraSans-Roman-32\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "   </g>\n",
       "  </g>\n",
       " </g>\n",
       " <defs>\n",
       "  <clipPath id=\"pa00aa19272\">\n",
       "   <rect height=\"279.0\" width=\"446.4\" x=\"23.959375\" y=\"7.2\"/>\n",
       "  </clipPath>\n",
       " </defs>\n",
       "</svg>\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10a79f610>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "m.plot()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "###Problem 3 of 3 (20 points).  Submit your homework in an allowable format.\n",
    "\n",
    "1. If you chose the python+git option, again this should take about 5 minutes:\n",
    "    A. You tweaked the commands in the above notebook in small ways to demonstrate you understand its workings.\n",
    "    B. Just run the notebook and save it.\n",
    "    C. Submit the notebook (ipynb format) to [courseworks](courseworks.columbia.edu)\n",
    "    \n",
    "2. If you chose a different option, this should take a while:\n",
    "    A. You ported the commands above to your platform of choice.  \n",
    "    B. Write latex that includes what you did, along with your output tables and figures.  \n",
    "    C. Submit a pdf of that file to [courseworks](courseworks.columbia.edu).\n",
    "         \n",
    "3. If you do not adhere to one of these above two options, you will get a 0 for the assignment."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.9"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}