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   "cells": [
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "A basic example of ROOT's RooFit statistical modeling language in iPython notebook"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "License: [BSD](http://opensource.org/licenses/BSD-3-Clause) (C) 2014, Kyle Cranmer. Feel free to use, distribute, and modify with the above attribution."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Particle physicisits primarily use [ROOT](http://root.cern.ch) for the data analysis framework.  Part of that framework is a package called [RooFit](http://root.cern.ch/drupal/content/users-guide#roofit) statistical modeling and fitting package.  I have contributed to this package and added a layer on top called [RooStats](https://twiki.cern.ch/twiki/bin/view/RooStats/WebHome) that provides with statistical inference in both frequentist and Bayesian paradigms based on statistical models made with RooFit. These are the tools that were used to claim the discover the Higgs boson, and those [statistical models get pretty complicated](http://blogs.discovermagazine.com/cosmicvariance/2011/12/08/making-the-higgs-sausage/?utm_source=feedburner&utm_medium=feed&utm_campaign=Feed%3A+CosmicVariance+%28Cosmic+Variance%29#.UxFW0NyrvlI).\n",
      "\n",
      "Here I demonstrate a simple example of RooFit's ability to create a statistical model, generate some simulated data, fit that data, create the profile likelihood, and provide a covariance matrix from the likelihood fit.  \n",
      "\n",
      "ROOT is a C++ library, but it has python bindings known as PyROOT.  "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import ROOT\n",
      "import rootnotes #for plotting with iPython\n",
      "c1 = rootnotes.default_canvas()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Here we create a \"workspace\" object that provides a factory with a convenient syntax for statistical models and variables. The workspace also provides an I/O mechanism to read/write statistical models and data to/from files.\n",
      "\n",
      "In this example, we create a mixture model of a falling exponential distribution and a Gaussian for a variable x.  \n",
      "This is really a marked Poisson process, because in addition to the pdf on x, we also encode that we expect s=50 events from the Gaussian and b=100 events from the falling exponential."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "w = ROOT.RooWorkspace()\n",
      "w.factory('Gaussian::g(x[-5,5],mu[-3,3],sigma[1])')\n",
      "w.factory('Exponential::e(x,tau[-.5,-3,0])')\n",
      "w.factory('SUM::model(s[50,0,100]*g,b[100,0,1000]*e)')\n",
      "w.Print() #this isn't displaying in iPython"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stderr",
       "text": [
        "TClass::TClass:0: RuntimeWarning: no dictionary for class stack<RooAbsArg*,deque<RooAbsArg*> > is available\n"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Now that we have made the mdoel, we can generate some fake data, make a plot of the data, fit the model to that data, and overlay the fitted model in the plot"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "x = w.var('x')\n",
      "pdf = w.pdf('model')\n",
      "frame = x.frame()\n",
      "data = pdf.generate(ROOT.RooArgSet(x))\n",
      "data.plotOn(frame)\n",
      "fitResult = pdf.fitTo(data,ROOT.RooFit.Save())\n",
      "pdf.plotOn(frame)\n",
      "frame.Draw()\n",
      "c1"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
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DKNlGJZf3NVC9eYXBn3vf6jcAoEe+3XTMdv9Np9Nyi9R8Phf9TamQ1uslPQAAYBhMBVUy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\n",
       "prompt_number": 3,
       "text": [
        "<ROOT.TCanvas object (\"icanvas\") at 0x7fd6bb865050>"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We can check the value of the parameters after the fit"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "mu = w.var('mu')\n",
      "print 'best fit value of mean for Gaussian is', mu.getVal(), '\u00b1', mu.getError()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "best fit value of mean for Gaussian is 0.324840840875 \u00b1 0.158716435359\n"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "And make a plot of the log(profile likelihood Ratio) as a function of the signal rate"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "s=w.var('s')\n",
      "sframe=s.frame()\n",
      "lnL = pdf.createNLL(data)\n",
      "lnProfileL = lnL.createProfile(ROOT.RooArgSet(s))\n",
      "lnProfileL.plotOn(sframe)\n",
      "sframe.Draw()\n",
      "c1"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "png": 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uAoBHzHX2X8g3Z7fhC5WqCQNQW/oa3qfC1bjuaYAAwCNmbKlQFMXxeAy7AXbb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\nrklPJCpuIVTBugxzlWgFc7v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       "prompt_number": 5,
       "text": [
        "<ROOT.TCanvas object (\"icanvas\") at 0x7fd6bb865050>"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "And finally, make a plot that encodes the correlation matrix between the four free parameters in the fit."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "corrMatrixHist = fitResult.correlationHist()\n",
      "corrMatrixHist.SetStats(False)\n",
      "corrMatrixHist.Draw('colz text')\n",
      "c1"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "png": 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P+oVSk7U2TdNWIarJvxRKWcaYLMvCfsYgVAEAgC7zIalZmvKPx4wA+hTV6r8n\nQhUAAOi41rpL40NVURStotSEC2ESqgAAwGoZH6padakwJWvP4b+OLP4JAAAW2ff3v8mtGNcLTriS\n5SjhskE/XX08QhUAAFhEB14FqZnGDhynnHP+ir89118IGP4DAAAd10pFe5avjDG9Xi9N06IoJr+z\nMKEKAAB0XGsBhfGhylpblmWWZc65fRW6CFUAAKDLWpf+aa9Qled5mqZ7TksfRKgCAABd5uNRkiTh\nqV8wPXQwxiRJ4pOW/9svud6y5zggE9UBAECX+SXR8zwPuWrM3PPQPrjk+p6jgdxQGR3BDZW7jRsq\ndxg3VO6w5g2Vj8/whsq3Bm6o7PmSlS87TeO4VKoAAMBKOMA0qX1hThUAAEAEhCoAAIAICFUAAAAR\nEKoAAAAiIFQBAABEQKgCAACIgFAFAAAQAaEKAAAgAkIVAABABIQqAACACAhVAAAAERCqAAAAIiBU\nAQAARECoAgAAiODIvE8AAAB03y39+xke7f/O8Fh9VKoAAAAiIFQBAABEQKgCAACIgFAFAAAQAaEK\nAAAgAkIVAABABIQqAACACAhVAAAAERCqAAAAIiBUAQAARECoAgAAiIBQBQAAEAGhCgAAIAJCFQAA\nQASEKgAAgAiOzPsEAAAAZsFaK8kYY4yZxv4JVQAAoOOstXme+8d5nqdp6pyLfhSG/wAAQJc553yi\nKoqiqqosy8qynEaxilAFAAC6zI/6FUXhg5S1Nk3TsiyjH4hQBQAAusznp2Zpyj+OPgJIqAIAAB2X\npmnzKaEKAAAggimFqpW7+u9WctAtq5/GPA/EllSvz/sUMEVVcmnep4BpSd6r5n0KmJ7mD90z+9/6\nzw9/Bj45TWkNhZaVC1VkIwAAlkP1nw+4YSONzSZOeQz/AQCAjmuN9E2pfEWoAgAAHddaQIFQBQAA\nsG+tS/9EqAIAADgAv/hnkiThaVmWg0nr8FZvojoAAFglxpgsy/I8D7lqSvf+S6pqha5lTZKEq/+6\niyUVuowlFTqMJRW67PF+zEj0X2Z33OTPh8YbX7IyxkzpkkAqVQAAYCX4UDU9zKkCAACIgFAFAAAQ\nAaEKAAAgAkIVAABABIQqAACACAhVAAAAERCqAAAAIiBUAQAARECoAgAAiIBQBQAAEAGhCgAAIAJC\nFQAAQASEKgAAgAiOzPsEAADAKnhkhsf68xkeq49KFQAAQASEKgAAgAgIVUjJCJEAABh9SURBVAAA\nABEQqgAAACIgVAEAAERAqAIAAIiAUAUAABABoQoAACACQhUAAEAEhCoAAIAICFUAAAAREKoAAAAi\nIFQBAABEQKgCAACIgFAFAAAQwZF5nwAAAMB8OOecc8YYY8wk/a21rQdNSVVV0U5t4SVJouqn8z4L\nTMnr8z4BTFGVXJr3KWBakvdW6MfQynm8HzMS/c7sjptcmiTeJEnSfFoUxZhoZa3N87zZkmVZK1ox\n/AcAAFaOT1RFUVRVVRSFpF6vN6qzc84nqmb/PM+dc81uhCoAALBafBjKssyXpowxWZZpxKBeaK+q\nKvT3lbBWf4b/0BkM/3UZw38dxvBfly3q8J8xpizLVp8kSdI0bRWfwkuSBvu3GpmoDgAAIEllWQ5t\n9+N9g9I0bT4lVAEAgNUyKjyNMjiB3be0hv8IVQAAYAbO7HuL5BemcBqH5ZzzU9rDlKyAUAUAABZS\n9b8OuOHuNNZcOmFwHYTJhTilEesvEKoAAECX+Sv7PJ+E0jTd7whgs0A1KpYRqgAAQJdNXppqTTwP\nfKIadW1gwDpVAABgtfiY1Qxb/vGoFdX9q+MTlVinCh3COlVdxjpVHcY6VV22a52qv5vdcZNf2DPe\nhBXVjTFhaC9s1SpN+c6DdSxjTDOZMfwHAABWTlVVSZI0b00zajGqYHAaVlmWhCoAALDqqqpyzjnn\njDGtgb9wI5rQc5IdMqdq4ZnTSu5Rco+2BhJ0eMle3tWe3NN/7Mq6jzldt9jLdYvfMHQIfwLf0+3v\n+gjsg/lTJZeUXNLWJ0NedbfVHPMy36k7J5fkbkuS3aqf2q26T2gx39m1k/EtAPbrotHjiR5P9Pdb\nQ1790OnxRBfNrsZmy3dtvfl37a5Nmn0GW8K2YSscmh+/GzWVar86EqqstQdedmKhmdMqP9D1v5Wk\n01/e9ZK9rPIDFe8rfVT5a/3GZiqS1HtM6aMq3lf5QZ298teUPlr/Mamk/tMmV9a7JVRNiflTlT/U\n9V+VpNN/tusld1t2S73doae8rfRo/cf3ybeUbSjbUL5Vx6x8S+lRZRsqb9eZqfcdpUdVvDiuBQsm\n2bsL5uqi0UelvnVdkr5+ekiHr/Uk6aNy1yah5UOnt3M9n+n5TG/n+tDVmzyc6o1CH5V158GWD50u\nmv4mWDxdCFVhUa/m6l4dUX6g9FFt9Opc1SpWZd+USWU3JcmV9Z8mn6LcdZlU1U/rnpLspuxm3W5S\nuety1+tXi/frPr3HlH1zev8yqPyh0p/TxvE6V7WKVT4ktZ66F2U35F6UOVpXp+yG7IYk2a1dfdKj\nKnf2YDdkdpJWXeJqtGCRWBLVUvio1MOpvrRR56pWseq7Vg/vns78oas3CR0kvWD1gq2f+pD0gtUj\nRu9Vuurqnr7l+ayfxrDYln5OlbU2TdNulqm8VgEp8BnIXq4rT77m5K7XLU2hdhWufOw9Vj8o3q83\n1E5Nyz+1l5U+KrvZ3hXi8jWnQeao3IuyW8p3f1iH0cDqiszRdiQyR1VdqR/7spY/hC9NlbdVvCiz\nU+UyR9u5DQvAzfsEMKmHh69mJElv53qv0uONePy1nt4o+mN2j5hdRSypX6zy3ij0iNHDaV2s+qjU\nG4WkOoQ9TvBeXEtfqbLWlmWZJEnEMdE5C3OeJh93Kz8Y92r2zbr+5KdV+ac+YIXJWP5YoZSVvyZ3\nfb8njr2FOU8HCDTZhqorKl6s9+MLVH5vTWEmlntR2klXPkv54lZ6VPmWkkuUqRaQk7I9O2Euwiyo\n8eWii0bP734PfeHqEdNvCdmoFY+ez+RXlwijh2FDJlEtiaWvVKkxe7/X6w29F8/yaVanRgWmEIPs\nZj3lPESiFt+ePlrvKnQLLdpJV3W5q5Qa9a38tXqUEFE0q1OTxxqzE4xCqUlSdUV2S+Zof/aVu13X\npdxO9tJOupLqupevgTVbAEyiWZ36aMQvvR+V+qjU23n99OJOUSrkp4tGV53eq/Rdq0dMnZ8eMXo7\nr8OWn2jlU1QYBww7xGLrQqXK16j8OOCeq50uAT/byU94Crnn8hVJ2ujJlXXByV6uR/HGFLRCSHJl\nPT0rXNAXWrzyg/4MKpOqeF/F+3VLGBPE4fkZUX5SVPpzKn8oSZcLSdo4Ljd65ri/9E87ccoP3iWX\n6ozl9yzV6crPuPJjfArRaifA+f3YjXpWO4BJvGB11emqqwfmfFT6H5cl6Usb9RRySW8U9R/vquu3\n+Ez2gq0v6wu1Kz9xSjvlqLfzdoGKqVTLY+krVdbaJEl8lirLsguhqmnzkk5/uS4abfqfqWW/4NR7\nrH7Jz38a5GNZmEHlR/Ty19otQzf0f/syFaZhs6fTf1ZHnM2eJLnbI2tXdkO9nVyVHq0jlHZSlB/g\na9Wfcqm6Ug/2+ZZso/47tIT9AJjcr2zq66fr4tOvbEo7U9GlXcN8XqslPPU1qpCffIHKV6R8zHo4\n7bc8z7DwcujIbWp8ltpz4G9Zb1OzVWijN/wlX6baM/e4clefCbdaMst5m5qtT7RxfNLOoUw1pmXU\nhq0+gy2LbXVuU2N9Hp73aczSst6m5u+39KVD/Fri60+tyPWh27tluSzwbWqmcthuhKoJLWuowkSW\nM1RhMqsTqlbQsoYqTGLFQtXSz6kCAABYBIQqAACACAhVAAAAERCqAAAAIiBUAQAARLD061QBAIBl\n8Mi8T2DqqFQBAABEQKgCAACIgFAFAAAQAaEKAAAgAkIVAABABIQqAACACAhVAAAAERCqAAAAIiBU\nAQAARECoAgAAiIBQBQAAEAGhCgAAIAJCFQAAQASEKgAAgAgIVQAAABEQqgAAwIpyzllrnXMH2Gqw\nPamqKsppLYUkSVT9dN5ngSl5fd4ngCmqkkvzPgVMS/LeCv0YWjmP92NGov83u+Mm90wSb5IkaT4t\nisIYM9Huk0TS4CGoVAEAgJXjg1FRFFVVFUUhqdfrTbLhmOBFqAIAAKvFj/dlWeYTkjEmyzJJQwf1\nWhuWZTnqVYb/0BkM/3UZw38dxvBfly3q8J8xpizLVp8kSdI0HT+/yveRNLi5qFQBAAB4Y6pQ2hn4\nG5O6CFUAAGC1jA9PQ1lry7L0s69GOXKIUwIAAJjM+/uPHI8ne/eZCedcnudhDtYohCoAALCQDjzf\nbncaay6dkGXZnrPRB/V6vTRN99yQUAUAALrMX9nn+VJTmqaTjwD6SVRlWYYyld92cIoVoQoAAHTZ\n5KUpf2XfKK0cNhjLmKgOAABWi49ZzbDlHw+dMmWMqXbz2cs/bvYkVAEAgNXiw1Oe537wzs9DVyNm\nOeeSJJnwrjUBw38AAGDlVFWVJEnz1jTjl0uYBKEKAACsoqqqnHPOOWNMqyjlh/xGbThq/U9CFQAA\nWFGDceowmFMFAAAQAaEKAAAgAkIVAABABIQqAACACAhVAAAAERCqAAAAIiBUAQAARECoAgAAiIBQ\nBQAAEAGhCgAAIAJCFQAAQASEKgAAgAgIVQAAABEQqgAAACI4Mu8TmLnknoNt91YV9zwQ2evzPgFM\nVfIe34GdVT2ezPsUMC273tp/mNdZzM7KhSqyEQAAmAaG/wAAACIgVAEAAERAqAIAAIiAUAUAABAB\noQoAACACQhUAAEAEhCoAAIAICFUAAAAREKoAAAAiIFQBAABEQKgCAACIgFAFAAAQAaEKAAAgAkIV\nAABABEfmfQIAAADz4ZxzzhljjDGT95dkrR18NamqKubZLbYkSd5aoX/uanl93ieAqbr1Pt+6nVU9\nnsz7FDAtiRRiRvLGDA/8WxPFmyTZ9X+vKIrx0arVP8uyVrRi+A8AAKwcn5CKoqiqqigKSb1eb1/9\n8zxv9SFUAQCA1eKH8LIs86UpY0yWZRoxqDe0v89Vrf4M/6EjGP7rNob/Oozhvw5b2OE/Y0xZlq0+\nSZKkaerz0yT9BzFRHQAAQJLKshzfHiLX0NlXhCoAALBaRoWnMdI09fWq0DI4UZ3hP3QEw3/dxvBf\nhzH812G7hv8e3//27x/8/8b4eONnnQ8O/43aMFz3568QdM75We2tCwapVAEAgIX02EF/m9qdxppL\nIQyWlyYXIpQxpqqqJEmstc05WIQqAADQZf7KPs+nojRNDzACODiPqrUTQhUAAOiyyUtTaZoe5kCs\nUwUAAFaLj1nNsOUfj1pR3de6BldbaIUwJqqjI5io3m1MVO8wJqp32GEnqh/Y+3vHm7BCenPiedjK\ntzSXrRran4nqAABg1fmZ5s1b0/hF0kcpiqLX67X6typbhCoAALCKqqpyzjnnjDGteOSv7xtsGdXf\nY/gPHcHwX7cx/NdhDP912CIP/00DE9UBAAAiIFQBAABEQKgCAACIgFAFAAAQAaEKAAAgAkIVAABA\nBIQqAACACAhVAAAAERCqAAAAIiBUAQAARECoAgAAiIBQBQAAEAGhCgAAIAJCFQAAQARH5n0CAABg\nBfzDvE9g+qhUAQAARECoAgAAiIBQBQAAEAGhCgAAIAJCFQAAQASEKgAAgAgIVYvrXauXEr2U6F07\n8qWrpm654dotzZ43XP30qqm73dgaaHG7no46NKK4Y3Ur0a1Ed+zwDp8a3XX147uu7vypae8kbB76\nNLt9auqWn2y1W0YdFzFdNHo80eOJ/n5ryKsfOj2e6KLZ1dhs+a6tN/+u3bVJs89gS9g2bAVgVpYj\nVCVJMu9TmLUbTtdync10NtO1vJ+KWi/dLOvc82ZPJ1N9tdDNclfSupZL0k0nSVeNbpb66nWdTPXm\n6UZLoZOp3uxJ0kmjk2n9B1Ny1+lOrvVM65nu5P3w5Pm8tV32Wz7raS3Veqbtsg5Md50+Nbu23XaS\ntJZqLdW9RpI+Ndou9fnrWkv1o9P1nrdLrWdaS4ccF5FdNPqo1LeuS9LXTw/p8LWeJH1U7toktHzo\n9Hau5zM9n+ntXB+6epOHU71R6KOy7jzY8qHTRdPfBAtm5X6YrZglCFXOufC3f2CtDU+bL7UeL7Vr\nVpLOWZ2z0k4qCk6m/ZeCs1anjE6murnzKf1mT2ezfoebpU6mOrWhi05vVXXL2UynjM5aSbrhdM7q\notPFncO1DoEofJVo3WrdSjt5KLjrtJbueho6r6V12GptErZat/qi29ltqbVUn9vQfZtD+gzdCWL6\nqNTDqb60UeeqVrHqu1YP7/7F5UNXbxI6SHrB6gVbP/Uh6QWrR4zeq3TV1T19y/NZP41hIVkS1QpY\nmlBlrZVkjPEPrLXGGN+h1+uFzs3HXdIMVaeMLjrdcHVFyuceX2oKlSdJ71qdTHXS7N5PuTOutxO2\n/J5boe2G6+8H09aqGIVUNEYIRk3bpT7r9Yf2Pn+9rmz96HSd0r7o6q18hzVzqNPG3h4eXe99O++n\nIu9rPb3R+JZ7xLQ3CcUqP97nnz6c6mu9ujTlN3/BtveMxeDmfQKYgSUIVT5F+WhljAmVqrIsx2+4\nIvzwn69C+Qjlq1zX8n7BqemtSidTXbssqR5AfCmpRwkDP5h4ykztpDGxZj3Jj+sNda/ReqZjVT20\nJ+lfL0s7A4LNwcQ7th58HLM3HFCYBTW+XHTR6PlsV4svXDWDlC9Q+b01PZ/pvUpqjB6GDZlEtdic\nlO3ZCUtuye79Z60lUUm64XTK6JTTVdPPQyFChTlYLyX9Fp+3zm7Wf795Wje2dM7qpKnLVGE/fls/\nIIi5WzPSzlszZhZUKG6tW33W012n7VL3ber+XJJuJfpxpvvzeqLVFwoS1dQ0q1MfjfiY+qjUR6Xe\nDt+6pu4Z8tNFo6tO71X6rtUjps5Pjxi9nddhy0+08ikq1KXe3v27EYCZW4JKVZOfsW6trapq8NXO\nTKiS6gx0w9URxz+9anTD6V2rN3t1e7NAVZesnCSdMvpqoa8W9ZwqP3EqFKj836c2dNXomtU529+q\nuQdMiQ80d10dksK88qGZyb/qB+z8NKmhwkV/vqffyheofpxJ0lpaT1RfS7XtdMcyUX0K/NDbVadH\njB5O66j0Py5L0pc26inkkt4o6j/eVddv8ZnsBVtf1hdqV37ilHbKUW/n7QIVU6mABbBMlarm5Kqh\n+alLocoHnTd7/ad+ntNN134pzE+/ltfVJj8Xqp+Kdn599QUqX76qS1ZWb/bqljCDqjW/CtGtW911\n+qy36+l2qW03vIDkLxK8ldSdh++z2SeTpM9f149O1y1+xrq/BnC7rMPW+tjxRBzWr2zq66fr4tOv\nbEo7U9E1bL5UqyU89TWqkJ98gcpXpHzMejjttzzP4BIwZ8nQks+iSZIkTVPnnH/gG8uyzLLMWuvL\nV769LMsx/6IkSd5agn9uny9HDS0aDX3JDwvusc8tndrY91aL7/V5n8B+NctUE/bfs/Ngn59s6XMb\nwzsvl1vvL9W3bvD3W/rSId4AX39qRa4P3d4tS6VqzRvrLivl0nL+Vz6gRAo/lJP/MMMD/5/5xJvl\nCFWSnHP+cr/mjHX/oNk4fidLF6owuaULVdiXZQ1VmMDqhKoVtPihyjnnA8aeEcILaxEM7b80oSoK\nQlWHEaq6jVDVYYSqDlvwUNVaWrwoijHRylqb57suBxnsv2QT1QEAAA7PJ6qiKKqqKopCY5e6dM75\nRDW+P6EKAACsFj9rKMsyX2oyxmRZpp3RvUG+PZSmRvUnVAEAgNUS7s7Sahm/jEBzsG/oQCGhCgAA\nQJJGLS0e5qe3WlqVqmVapwoAAODw9ntfFj/el+d5c267n1nVRKgCAABT95/+z743+Tst0JWhYWQw\nTVOfycJiTwGhCgAALKL/dNClUltprFle8suG73eHxpiyLJtrKIQVFpp7Y50qdATrVHUb61R1GOtU\ndVhznapfmOH7/He7400z95gdg7dg8dlraC4Kd3YZ359KFQAA6LLJS1PhVngHw9V/AABgtYxaUmHM\niupD57a3QhihCgAArBYfnvI89yN6YcH0ELOcc0mShIzll/oM9x32r4olFQAAAKqqSpKkeauZwSUS\nAh+e8jxv9g8LsgdMVEdHMFG925io3mFMVO+wBZmoPoZzzq+MMGbgrymMEg7tT6hCRxCquo1Q1WGE\nqg5b/FAVF3OqAAAAIiBUAQAARECoAgAAiIBQBQAAEAGhCgAAIAJCFQAAQASEKgAAgAgIVQAAABEQ\nqgAAACIgVAEAAERAqAIAAIiAUAUAABABoQoAACCCI/M+AQAA0H2PzPBYfzfDYzVRqQIAAIiAUAUA\nABABoQoAACACQhUAAEAEhCoAAIAICFUAAAAREKoAAAAiIFQBAABEQKgCAACIgFCFjriVzPsMMFWP\n8wZ3Fm8tOoNQBQAAEAGhCgAAIAJCFQAAQASEKgAAgAgIVQAAABEQqgAAACIgVAEAgJVmrY2yH0IV\nAABYXdbaPM+j7IpQBQAAVpRzLlaiknQk1o4AAACWhTGmLMu4+yRUAQCAlWOtdc5JolIFAABwcMYY\nY4wk51ysktXKhaqXuHVnd3FP5Y7jnsrdxVu7Cr5T7XuTJFmy/xqrFaqqav9vKQAAmIel+6nN1X8A\nAKDLkoZYS1INtVqVKgAAsGqyLAuP/TyqKSFUAQCALptqdaqJ4T8AAIAICFUAAAAREKq6xjk3szon\nZsMvTxfWqWu9xb5x8DGWlLWWb2FgSRGqOoifrB3T6/X8zMper5ckiXPOOReWb+n1es2eczlDxBLe\n1qVbngeDeBOXhXMu1toNTFTvJv9zNywXi2UXgnIoU/F53T3W2jRNKVN1Q6grhzW7W5/J4aXWYyw1\nKlUdVJalr1iECgc6gze0w6y1ZVn6dXR4o5ddGLWXZIzxD5rvLDXmTiJUdVNVVdbaqqqi34IbC4th\n3w6oqqooCkm9Xo83dKn5FOXfRGOMrzFHvMccFhOhqoPSNG0+5aN5RfBGLzs/Rd1XNdI05Q3tjPDO\nMmrfecyp6iB+E1o1SZK0kjSWkbXWX4ggqSxLQlVnJEmSZdmoXMUb3SWEqi4Llec5nwcOJ1yW0pzC\nHBqrquKN7gzeze5pTq4amp8IVV1CqOomX7ooy7J5wyN0FT+Au4R3s0v8bCrtflvDUmTUmLuHUNU1\nxhhfw+AaXQCYo1B3bBYgQ12KqmQnJbEWvAIAAFhlXP0HAAAQAaEKAAAgAkIVAABABIQqAACACAhV\nAAAAERCqAAAAIiBUAQAARECoAgAAiIBQBQAAEAGhCgAAIAJCFQAAQASEKgAAgAgIVQAAABEQqgAA\nACIgVAEAAERAqAIAAIiAUAUAABABoQoAACACQhUAAEAEhCoAAIAICFUAAAAREKoAAAAiIFQBAABE\nQKgCAACIgFAFAAAQAaEKAAAgAkIVAABABIQqAACACAhVAAAAERCqAAAAIiBUAQAARECoAgAAiIBQ\nBQAAEAGhCgAAIAJCFQAAQASEKgAAgAgIVQAAABEQqgAAACIgVAEAAERAqAIAAIjg/wPXZ7FhAZ+3\nTAAAAABJRU5ErkJggg==\n",
       "prompt_number": 6,
       "text": [
        "<ROOT.TCanvas object (\"icanvas\") at 0x7fd6bb865050>"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Visualize the model"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "% pylab inline\n",
      "import networkx as nx"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Populating the interactive namespace from numpy and matplotlib\n"
       ]
      }
     ],
     "prompt_number": 38
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "pdf.graphVizTree('expressionTree.dot')\n",
      "G = nx.DiGraph(nx.read_dot('expressionTree.dot'))\n",
      "nx.draw_graphviz(G,'dot')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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Wr16dnT9/nncshRAaGso0NDS+vLYtWrRgQqGQdyyZt3PnzhKf8ypVqrBNmzYx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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10f865e10>"
       ]
      }
     ],
     "prompt_number": 63
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import pydot\n",
      "g = pydot.graph_from_dot_file('expressionTree.dot')\n",
      "G2 = nx.from_pydot(g)\n",
      "nx.draw_graphviz(G2,'dot')\n",
      "\n",
      "\"\"\"\n",
      "print \"inspect networkx graph\"\n",
      "#iterate over networkx graph\n",
      "print G2.node\n",
      "for n in G2.nodes():\n",
      "    print n, G2.out_degree(n), G2.successors(n)\n",
      "\n",
      "print \"inspect pydot graph\"\n",
      "#iterate over pydot graph\n",
      "for n in g.get_node_list():\n",
      "    print n.get_label(), n.get_attributes(), n.get_layer()\n",
      "\"\"\"\n",
      "g.write_png('test.png')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 97,
       "text": [
        "True"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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XhoZGsdOs5s+fjzdv3nBKpLieP39e4il/Fy9eRNu2beHp6flx7ZdIEe/GJxVz\n7do11qVLl2LfWFHom+uVK1d4x1QqycnJzNDQsMjfeezYsbxjKbWkpCSmr69f5G/u6urKO5ZCEolE\nbPny5UxHR6fEz4x69eqxffv2MYlEwjuq0qLCVTDJycls3LhxTCAQlPimqVu3LtuxYwcTi8W8oyqd\nCRMmFPlbV6lShb18+ZJ3LKW3bNmyIn93NTU1dufOHd6xFNa///7L+vTpU+qX9R49erD79+/zjqmU\nqHAVRG5uLluzZk2xNawPP5qammz27NksPT2dd1SldOPGjWJfcvz8/HjHUgnZ2dmscePGRf72NjY2\ntCb2lY4ePcoaNmxY6ufJggULWFZWFu+YSoUKVwGEhoYyMzOzUr+R9urVi/3zzz+8YyotiUTCLC0t\ni/zNv/vuOyYSiXhHUxmHDh0q9ro/fPgw71gK7927d2zOnDlMQ0OjxM+WJk2asJCQEN4xlQYVrhx7\n+PAh69u3b6lFa2JiQm8GGdi/f3+xv/3x48d5x1IpEomE2djYFFkGjRs3Zjk5ObyjKYW4uDhmZWVV\n6mdNv3792NOnT3nHVHhUuHIoIyODzZ07l2lpaZX44jcwMGCrVq2iNSwZyMrKKrbZzcHBgTZncnDn\nzh0mFAqLLIvly5fzjqU0JBIJ27VrFzMyMirxc0dPT4/5+fmx3Nxc3lEVFhWuHJFIJGz37t2sfv36\npX7THD16NB2oI0NLliwp8vdXV1dncXFxvGOprClTphRZHvr6+iwpKYl3LKWSkpLCpkyZUuqBmebm\n5uz8+fO8YyokKlw5cf36dfbDDz+UWrTff/89i4mJ4R1TpTx9+pTp6uoWWQ4eHh68Y6m0//77j1Wr\nVq3IMhk5ciTvWErp6tWrrH379qV+Jo0aNYq9fv2ad0yFQoXL2ZdO86lTpw6d5sPJ0KFDiyyLmjVr\nsrdv3/KOpfLWrl1b7H1CX0alIz8/n/3222+lnh1RvXp1tmnTJvp8KiMqXE5yc3OZv79/qS9kDQ0N\nNmvWLDrNh5Po6Ohiy2TDhg28YxHGWF5eHmvRokWxLUC0X116Xr58yX7++efPboG7ceMG75hyjwqX\ng9OnT7PmzZuX+uJ1dnamE885EovFxTaltWrViuXn5/OORt47ffp0sffNrl27eMdSepGRkaWeoigU\nCpm7uztLS0vjHVNuUeHK0KNHj5iLi0upRdusWTN24sQJ3jFV3rZt24otmzNnzvCORT7x6WhJ9erV\nYxkZGbxczRP5AAAgAElEQVRjKb0PQ0R+enzDh5+6deuyvXv30haHElDhykBmZibz9vb+7Gk+fn5+\ndJqPHEhLSyt2WsRPP/3EOxYpwT///FPsClne3t68Y6mMLw0RaWdnx+7du8c7plyhwpUiiUTC9uzZ\nw7755pvPHun34sUL3lHJe7NmzSqyfLS0tNjjx495xyKloOXF39GjR5mxsXGJn2+ampps/vz5NETk\ne3QB+i9ISUnBjj/+wM2LF5H29i10dHXx7XffYcTYsTAzMyv1927cuAE3NzecP3++xNv/97//ITAw\nEB07dpRWdFIKsViMU6dO4dj+/Xjz4gUYY6hRpw4sOnfG1KlTkZeX9/G+3t7eWLJkCce05HMyMjLQ\nrFkzvHz58uO0nj17osv33yPhxg2kp6bCoEoVNGnZEqPGjSt2uT9SObKysrB06VL4+voWef980Lhx\nY6xbtw6Ojo4l/r5YLEZwcDBO/P033rx8CYFAgBp166JX//6wt7eHmpqatJ+CbHAufLkVGxvLxgwZ\nwgy1tdlgXV22BWAHALYTYLPV1VkdHR1m1b49O3jwYJF9Fa9fv2YTJkz47Gk+27dvp8PoOcjIyGAr\nfHxYo9q1WTt9fbYaYHvf//gDrJWaGtMFmPD9sqpfvz7LzMzkHZt8QeF97roA0wbYaA0Ntu39e/YP\ngE3V1GTVtbVZb2trFhERwTuy0oqPj//iEJGJiYkf75+amsqWLl7MGtSowb43MGD+hd6TqwHWTl+f\nNapdm61Ytkwp9s9T4ZbgyJEjrKauLvtVTY29BBgr4Uf0/kVhpqfHpowdy3JyclhgYCCrWrVqqaf5\nzJw5k07z4eT58+eszXffsX7a2iymlGXKAHYNYC7vP7j9/f15xyZlIBaLWaMGDZjB+y9OqaUs20yA\nbQbYt7q6bNnixXRQj5R8GDHvc0NE+vr6sgcPHrAWxsZssLY2u1bKMpMA7DLA+mlrM4tmzdjz5895\nP72vQoX7iRMnTjAjHZ0iH8oNARZWygsiFWBdtbSYUSnn0wJgPXv2pIMHOHrz5g0z+fZbtkRdnUk+\nU7aF3+TLAda4Th326tUr3vHJF2zasIE11NJi/5Rh2TKAPQNYy/elS6QnJSWFubq6Fhv/+sNPFXV1\n5isUlmmZSQC2WF2dmTZowN68ecP7qVUYFW4hSUlJrKaeHov+ZGEbAyz8My+GNIA1KeEF1axZMxYc\nHMz7aam83jY2zEtTs0xv7MI/3hoazPb773nHJ59x48YNVltHh90r57J99n5NlzYvS9/Vq1dZhw4d\niq7lAmxmOZcZA5iXpibrbWPD+ylVGBVuIYvmz2cTtbWLLeQvFS4DWCjA9PH/p/n4+vrSaT5y4P79\n+6yWtjbLrsCbOxdg9XR02O3bt3k/DVKK0YMHs2VlXEv69GczwHpbW/N+CiohPz+frV+//uMut6rv\n31/lXWbZAKulra2w1/8WSuE4LIWUl5eHTevWYVJOTom3xwBoAaA6gNEARJ/cbgPAAICjoyPu37+P\n6dOnQ1NTU5qRSRlsCAzEKLEY2iXclgSgH4DaABoDWPvJ7RoAxuflYf2aNVJOSSri7du3OHjoEEZL\nJCXefh2ABYAqAAYAGAhgfqHbBwM4f+ECnjx5Iu2oKk9NTQ0TJ05EQkICWjRpAlcUvL8+tQLANyhY\nZqYAIj65XRvAKLEYGwICpBtYSqhw3zt16hSM8/PRqoTbGIA9AEIBPARwH8Cvn9xHCGCaQAAjAwPU\nqVNHumFJmYjFYvyxbRsmlHCaggRALxR8ICcBCAfgj4JlXNi4/Hz8uXcvckr5Ikb42bNnD5wEAtQu\n4bZcAC4o+HKcgoJyPQxAUOg+egCGSSTYtnmz1LOSAoaGhnj2/DkmlXDbPQBBAK4CSEfBe9G4hPtN\nzMvDH9u2QSwWSy+olFDhvvfgwQO0E3263lpAAMAVQH0A1QDMA/BnCfdrzxgexsdLLSMpn5SUFCA/\nH41LuO0KgP8AeANQB9AIwFgAez+5Xz0A+kIhkpOTpZqVlN/D+Hi0y84u8bZLAMQApgJQQ0H5lnTG\ne7vcXDyMjZVaRlJUcnIyDIRC1CvhNjUUbDmMBZAHoAFQ4nu3EQCWn1/w/lYwVLjvZWZmQi8/v9Tb\nvy307wYoWCv6lAGA9MzMSk5GKiozMxN66uol3vYEBcuwWqGfZQBKqlV9oRAZGRnSikkqKDM1FXql\n3JaEgi/IhX2Lgq1VhekDyEhNrexopBQZGRnQL2UQi6Yo2Mr0CwAjFGyVeFHK4+irqyvke5IK9z0D\nAwNkapS0V6FA4if/LukbWjoAQwODSk5GKsrAwACZpXyJaoCCb8ophX7SARwv4b4ZYjGqVKkirZik\nggyqVUNpX2/rAnj+ybREFN2kDAAZAKpUq1bZ0UgpqlSpgozPbAoeDOAcCr4QCwDMKuV+Gfn5Cvme\npMJ9z9TUFBdLOciJoWDfwnMAbwEsBTCohPtdEgph0qqkvcCEh2rVqkFTSwsJJdzWEQVbJFYCyEbB\n5se7KNh/VNgTADkCAYyMjKSalZSfaatWuKhX8jpuZxRsolwHIB/AERTsRvjUJW1tmLRpI7WMpCgj\nIyNkA/i3hNvuo+AgKREALRQcIFXSuvA9AJpaWqhataq0YkoNFe57tra2eKOjU+KbUgBgKIAeAJoA\n+A4F+/4KEwPYoK2NCR4e0g1KykwoFGLMhAnYUMIXKSEK1mZvomA/US0A41GwllvYRg0NDB8xgo44\nl0ODBg1ChERS4u4dDQAHAWxFwe6C3QCcARReiukA9jKGUWPHSj0rKaCpqYnhI0ZgUwm7ekQA5qDg\nvVgXBcdYLCvhMdZramLsxIkKOb4yXbygkJXLliFhyRL8XsqBGJ9zHMASMzNcjour/GCkwp48eYK2\npqZIzMkpdX9faUQAGujo4NzNm2jWrJk04pGvNHn0aBjt3ImFnzn+4oP/AZgMYMT7/wcJBIhydMRf\nwcHSjEg+ce/ePXRr0waJOTnQKufvvgPQQFsbN+7dU8gLUdAabiGjx43DCQ2NYqeGfMl/ALx0dTF9\n0SJpxCJfoWHDhrC3t4e7tnaxA2Y+hwGYoaWFTl26UNnKsakzZmCdpiZulnDbWQAvUbBJeTsKdhk4\nvL/tIYBfdXTg6f3ptioibSYmJuj0ww+YoalZ7veku7Y27Hv0UMiyBahwi6hZsyYOBAdjmK4uwsv4\nO8kAHHV18eOECejfv78045EK2rRrFy7VqQNXFJx/+yUMwDwNDUTUq4c/9u+XcjryNczMzNBn0CBY\nCwTFSvcegDYo2KS8BsABFBz9+gBAV4EAHa2s0KlTJ9kGJgCAP/bvR0S9evDW0ChT6UoATNPUxI2G\nDbFp925px5MaKtxP/PDDD9h/4gSGGBhgmoYGHpRyvwwA6wF01NWFk5sblq1aJcOUpDxev36NNzk5\nONe4MXro6uIUSi5eBiAMgJOuLiJMTHDm8mWFPDBDlaxZswbhERFYHBCAHrq6WKSm9nGf7jgUrOFm\noGBffQcAK4VC/KCrC08fH/zz6BG8vb1Be9Vkr2rVqjgTE4NwExM4vV/BKWkpSACcBNBDVxfXzM0R\ndvEi9PX1ZRu2MnEeWlJuPXnyhM308GC19PWZvb4+WwmwTSi4/NcELS1WTVub/eTgwCIjI3lHJZ+R\nnJzMvvvuO7Z27VqWk5PDtmzZwiyaNmVN9PSYt0DAggD2G8DmA6yZnh4zNzZmG9avZ1lZWbyjky9Y\ntmwZa9KkCfv3338ZY4zFxcWxSaNGsWo6OuwnPT3m9/49uxpgw3R0WFVtbTZq4EB2/fp1xhhjr169\nYq1atWLTp0+nS/VxkpWVxTasX8/MjY2Zib4+WygQsN8AFgSw+QIBa6KnxyyaNmVbtmxhOTk5vON+\nNTpo6gtycnJw4MAB3IiJQdrr19CtUgXfNG6MocOGoX79T0+tJ/IkMzMTVlZWcHBwwJIlSz5OZ4wh\nJiYGRw8dwpsXL/Do0SM8f/0am7ZuRefOnSEQfHq2JpEnjDEsXrwYf/75J8LDw4u9D9PT0/Hnn38i\n4fZtpL95g1379sEvIABDhw1D9erVi9z3zZs3sLe3R+fOnREQEEDLnhPGGKKjo3Hi2DG8ffkSAFCj\nbl30dnFBx44dlWa5UOESpZSbm4tevXqhQYMG2LRp02ffsBcuXICXlxcuXbokw4SkIhhjmDdvHo4d\nO4awsLAynR8tEAg+u9k4NTUVjo6OaNWqFdavXw+hkPa0EemgVxZROhKJBKNGjYK2tjbWr1//xW/H\nxsbG+Pfff2UTjlQYYwzTpk1DSEgIzpw5U2mDkVStWhWhoaGIj4/H6NGjFXJQfKIYaA2XKBXGGLy8\nvHD16lWEhoZCR0fni78jkUigq6uLlJSUMt2fyJ5EIoGrqyuuXr2KU6dOoVo5hmP80hruB+/evUPv\n3r1Ru3Zt7NixAxqfGeqVkIqgNVyiVHx9fXH69GkcPXq0zOUpFArRoEEDui6qnBKLxRg/fjxu3bqF\n06dPl6tsy0NPTw/Hjx9HamoqBg0ahNzcXKnMh6guKlyiNLZv347ffvut3GtAAG1Wllf5+fkYOXIk\nHj58iFOnTsHQ0FCq89PR0cHhw4eRn5+PH3/8ka6DTCoVFS5RCsHBwZg1axZOnjxZoaPHqXDlT15e\nHoYMGYJXr14hODhYZudfamlp4cCBA9DV1UWfPn2QlZUlk/kS5UeFSxTepUuXMHLkSBw+fBimpqYV\negwqXPkiEonQv39/ZGVl4ejRo9DV1ZXp/DU0NLBnzx7UqlULzs7OyKTrXJNKQIVLFFp8fDz69u2L\n7du34/vvv6/w41Dhyo/s7Gy4uLhAKBTi4MGD0NbW5pJDXV0d27dvR6NGjeDg4ID09E+vJUVI+VDh\nEoX17NkzODo6YuXKlXBycvqqx6LClQ8fjhQ2NDTEvn37uF8WUU1NDZs3b0arVq1gZ2eHlJQUrnmI\nYqPCJQopJSUFDg4OmDx5MoYPH/7Vj0eFy19GRgacnJxQv3597Nq1S25OyxEKhQgKCkLnzp1hY2OD\n//77j3ckoqCocInCyc7ORq9evdCjRw/MmDGjUh6zTp06SEtLowNkOElNTUWPHj1gYmKC33//Xe4u\nLi4QCLB69WrY29vDysoKr1694h2JKCAqXKJQ8vPzMWjQIDRs2BB+fn6VNsYqnYvLz9u3b2Fra4v2\n7dtj48aNcju0okAggI+PD3766SdYWlri+fPnvCMRBSOfr2xCSsAYw6RJk5CTk4Nt27ZV+gczbVaW\nvdevX8PKygrdu3dHYGCg3A9SLxAIsHDhQowYMQKWlpZITEzkHYkoEHXeAQgpqwULFuDWrVuIiIiQ\nysE0VLiy9eLFC9ja2sLFxQVLliyR+7ItbM6cOdDW1oalpSXCw8PRuHFj3pGIAqDCJQph3bp12Ldv\nH6Kjo6U2AAIVruw8e/YMNjY2+Pnnn+Ht7c07ToV4enpCS0sL3bt3R1hYGJo1a8Y7EpFzVLhE7v31\n119Yvnw5zp07h1q1akltPsbGxjh8+LDUHp8U+Pfff2FjY4OJEydW2kFvvEyePBlaWlqwsrLC6dOn\n0bx5c96RiByjwiVyLSIiAq6urjh9+jQaNWok1XnRGq70PXjwALa2tpg2bRqmTp3KO06lGDNmDLS0\ntGBjY4OTJ0+idevWvCMROUWFS+TWjRs3MGjQIOzfv18mH2JUuNKVkJAAOzs7zJ8/H+PHj+cdp1IN\nGzYMWlpa6NGjB4KDg9G+fXvekYgcosIlcunhw4fo2bMn1q9fD0tLS5nM08jICOnp6cjKypL52L3K\n7u7du+jRoweWLVuGESNG8I4jFf3794empiacnJxw5MgRdOrUiXckImfotCAid169egV7e3ssWLAA\n/fr1k9l86Vxc6bhx4wZsbW2xatUqpS3bD/r06YPt27ejT58+OHv2LO84RM5Q4RK58mF4v2HDhmHi\nxIkyn7+xsTEeP34s8/kqq5iYGDg4OCAoKAiDBw/mHUcmHB0d8eeff6Jfv34IDw/nHYfIESpcIjdE\nIhFcXFzQoUMHLFy4kEuGRo0a0X7cShIdHQ1nZ2ds2bJFplsq5IGNjQ3+/vtvDB48GCEhIbzjEDlB\nhUvkgkQiwYgRI2BoaIigoCBugyDQgVOVIzIyEn379sXOnTvRq1cv3nG46NatG44cOYIRI0bgyJEj\nvOMQOUAHTRHuGGPw9PTEixcvcOrUKa4D1xsbG+P69evc5q8MQkNDMXToUPz111+wsrLiHYerTp06\n4cSJE+jZsydyc3PRv39/3pEIR1S4hLsVK1bgzJkzOHv2LLeLjX9Aa7hf5/jx4xg9ejQOHTqEH374\ngXccudC+fXuEhobCwcEBIpEIw4YN4x2JcEKFS7jatm0bNm7ciOjoaFStWpV3HCrcr3Dw4EFMmjQJ\nx48fR8eOHXnHkSutW7dGeHg47OzskJubi9GjR/OORDigwiXcHDt2DHPnzkVUVBTq1avHOw6AgnNx\nMzIy8O7dO+jp6fGOozD27t0LDw8PhISEoG3btrzjyKXmzZvjzJkzsLW1hUgkwqRJk3hHIjJGhUu4\nuHDhAkaPHo3g4GC5GvRdIBCgYcOGePLkCY2LW0bbt2/HnDlzcPr0aZibm/OOI9eaNWuGyMhI2NjY\nICcnB56enrwjERmio5SJzMXGxsLFxQU7d+6Uy02PtFm57DZv3ox58+YhIiKCyraMGjdujKioKAQF\nBWH58uW84xAZojVcIlNPnz6Fo6MjVq1aBQcHB95xSkSFWzbr1q2Dr68vIiMj0bRpU95xFEqDBg0Q\nFRUFGxsbiEQiLFiwQKGuB0wqhgqXyMzbt29hb28PDw8PuT5Skwr3y1atWoWgoCBERUXB2NiYdxyF\nVL9+fURFRX3cp7t06VIqXSVHm5SJTGRlZcHZ2RnOzs7w8vLiHeezaHjHz1u6dCk2btxIZVsJjIyM\ncObMGYSEhGDatGlgjPGORKSICpdIXX5+PgYOHIimTZsqxD4rGt6xZIwxzJ8/H7t370ZUVBS+/fZb\n3pGUQs2aNREREYHz589jypQpkEgkvCMRKaHCJVLFGMP48eMhFouxdetWCIXy/5KjTcrFMcYwa9Ys\nHD16FJGRkahbty7vSEqlWrVqCAsLw+3btz++X4jykf9PP6LQ5s2bh9jYWOzfvx8aGhq845RJ7dq1\n8e7dO2RmZvKOIhcYY3B3d0dERAQiIiJQu3Zt3pGUUpUqVXDy5Ek8fPgQI0eORH5+Pu9IpJJR4RKp\nCQgIwMGDBxEcHKxQg0gUPhdX1UkkEkycOBFXrlxBWFgYatSowTuSUtPX10dwcDCSk5MxZMgQ5OXl\n8Y5EKhEVLpGKvXv3ws/PD6dOnULNmjV5xyk32qwMiMVijBkzBvHx8QgNDZWLoTdVga6uLo4cOYLs\n7Gz0798fIpGIdyRSSahwSaULCwuDu7s7Tpw4gYYNG/KOUyGqXrj5+fn4+eefkZiYiJCQEBgYGPCO\npFK0tbXx999/Q01NDS4uLsjOzuYdiVQCKlxSqa5du4YhQ4bgwIEDCj3ykCoXbm5uLgYNGoSUlBQc\nP35coXYHKBNNTU3s3bsXhoaG6N27N969e8c7EvlKVLik0vzzzz/o1asXNm3ahK5du/KO81VUtXBz\ncnLQr18/5OXl4fDhw9DR0eEdSaVpaGhg165dqF+/PpycnJCRkcE7EvkKVLikUrx8+RIODg5YtGgR\n+vbtyzvOV1PFws3KykKfPn2go6ODAwcOQEtLi3ckAkBNTQ2///47TExM0KNHD6SmpvKORCqICpd8\ntfT0dDg6OmLkyJEYN24c7ziVQtUKNzMzE87OzqhVqxb27NmjMKdwqQqhUIiNGzeiQ4cOsLW1xdu3\nb3lHIhUgYDSWGPkKIpEIjo6OMDMzw7p165RmLFjGGPT09JCcnAx9fX3ecaQqPT0dTk5OMDExwaZN\nm6CmpsY7UqUSCARKM2QiYwwzZ85EaGgowsLCUKtWLd6RSDnQGi6pMLFYjGHDhqFGjRoIDAxUmrIF\nCj6kVWEtNyUlBXZ2dmjVqhU2b96sdGWrbAQCAVauXInevXuje/fuePnyJe9IpByocEmFfBh96M2b\nN9i1a5dSflAre+G+efMGNjY26Ny5M4KCghRi2E1SULpLlizB4MGDYWlpiWfPnvGORMqILs9HKsTH\nxwfnz59HVFSU0h5co8yF++rVK9jZ2aFnz57w8fFRqq0TqsLb2xva2tqwtLREeHg4XblJAVDhknLb\nsmULfv/9d5w/fx6Ghoa840iNshZuUlISbGxsMHDgQCxcuJDKVoFNnz4dWlpa6N69O8LCwtC0aVPe\nkchnUOGScjly5AgWLFiAqKgopb9ijLGxMWJiYnjHqFSJiYmwsbHB6NGjMWfOHN5xSCWYOnUqtLS0\nYGVlhdOnT8PU1JR3JFIKKlxSZufPn8e4ceMQEhKC7777jnccqVO2NdzHjx/D2toabm5u8PT05B2H\nVKLx48dDS0sL1tbWCA0NRcuWLXlHIiWgwiVlcvfuXfTr1w+7d+9Gu3bteMeRCWUq3Pv378PW1haz\nZ8/G5MmTecchUjBixAhoamrC1tYWISEhsLCw4B2JfIIKl3zRkydP4OjoiICAANjZ2fGOIzO1atVC\nVlYWMjIyFHrw/ri4ONjZ2WHx4sUYM2YM7zhEigYPHgwtLS04ODjg2LFj6NixI+9IpBA6D4B81n//\n/QcHBwdMnz4dgwYN4h1Hpj6ci6vI18W9ffs2bG1tsWLFCipbFfHjjz9i69atcHZ2RnR0NO84pBAq\nXFKqd+/ewdnZGX379oW7uzvvOFwYGxvj8ePHvGNUyLVr19CjRw8EBARg2LBhvOMQGXJ2dsauXbvg\n4uKCyMhI3nHIe1S4pER5eXno378/mjdvDh8fH95xuGnUqJFC7se9dOkSnJycsHHjRvTv3593HMJB\njx498Ndff2HAgAEIDQ3lHYeACpeUgDGGsWPHQigUYtOmTSp9nqYiHjh17tw59O7dG3/88Qf69OnD\nOw7hqHv37jh06BCGDRuG48eP846j8qhwSTGzZ8/G/fv38ddff0FdXbWPq1O0wg0PD8ePP/6IPXv2\nwNHRkXccIge6dOmC48ePY8yYMTh48CDvOCpNtT9NSTGrV6/GsWPHcO7cOejq6vKOw50iFW5ISAhG\njBiBv//+G926deMdh8iRjh07IiQkBE5OTsjNzVW5AyDlBRUu+Wj37t3w9/dHdHQ0atSowTuOXFCU\nwj169CjGjh2LI0eOoFOnTrzjEDnUtm1bnD59Gvb29hCJRBgxYgTvSCqHCpcAAEJDQzFt2jSEh4fj\n22+/5R1HbtSsWRM5OTlIT09HlSpVeMcp0YEDB+Dq6ooTJ06gffv2vOMQOWZubo6IiAjY2dkhNzcX\n48aN4x1JpVDhEly5cgXDhg3D4cOH0aJFC95x5Erhc3HNzc15xylm9+7dmD59Ok6dOoXWrVvzjkMU\ngKmpKc6cOQNbW1uIRCK4urryjqQy6KApFXf//n307t0bW7duRefOnXnHkUvyuln5999/x8yZMxEe\nHk5lS8qladOmiIyMxJo1a7Bq1SrecVQGreGqsBcvXsDe3h5Lly5Fr169eMeRW/JYuBs2bICPjw/O\nnDmDZs2a8Y5DFJCxsTGioqJgbW2NnJwczJs3j3ckpUeFq6LS0tLg4OCA8ePHY/To0bzjyDV5K1x/\nf38EBAQgMjISjRs35h2HKLBvvvkGUVFRsLW1RU5ODhYvXqzS591LG21SVkE5OTno06cPLC0tMXv2\nbN5x5F6jRo3kZnjHFStWYN26dYiKiqKyJZWibt26iIyMxNGjRzFr1iwwxnhHUlpUuCpGLBZj6NCh\nMDIygr+/P32bLQN5WMNljGHx4sXYtm0boqKi0KBBA655iHKpVasWIiIiEBERAQ8PDypdKaHCVSGM\nMbi6uiItLQ07duyAUEiLvyx4Fy5jDN7e3ti/fz+ioqJQv359blmI8qpRowbCwsIQExODSZMmQSKR\n8I6kdOgTVwUkJiYCAJYsWYKYmBgcPHgQWlpanFMpjho1aiA3NxdpaWkym6dIJEJsbCwYY5g+fTpO\nnDiBM2fOwMjISGYZiOqpWrUqQkNDERcXhzFjxkAsFuOff/5BZmYm72hKgQpXya1duxYmJiaYPHky\nduzYgRMnTsjtAA7ySiAQoGHDhrh69SoSEhKkPr/s7Gy4uLigS5cuGDBgAM6dO4eIiAjUrFlT6vMm\nxMDAACEhIXj69Cn69OmDrl27wsHBAenp6byjKTwBo431Smvfvn0YPHjwx/0xPj4+mDNnDudUiuXe\nvXvo3bs3Hjx4AIlEAnNzc9y+fVtq83v37h369u2LsLAwAIC6ujqioqLoHOkK+PT4BPqoK5/Y2Fi0\na9cOIpEIQMF4zCdPnkS1atU4J1NcVLhKKiwsDE5OTsjLy/s4TU9PDw8ePECdOnU4JlMsycnJRTbj\nGhgYIC0tTSoHm2VkZMDZ2Rlnz54tMr1r166IioqiA9zKiQr36/Tr16/Y1YUsLCwQGhpKW1sqiDYp\nK6Hr16/DxcWlSNmqq6vj77//prItp1q1akFHR+fj/zMyMpCSklLp80lLS4O9vX2xsm3ZsiX2799P\nZUtkbuvWrfj++++LTLtx4wasra3x6tUrTqkUGxWuknn48CEcHR2LHeSwbds22Nvbc0qluD6MpVxY\nZR+x/PbtW9ja2uLixYtFprdp04YOlCLcfDiAqmvXrkWm37lzB927d0dSUhKnZIqLCleJvHr1Cj16\n9EBycnKR6atWrcKwYcM4pVJ80izc169fw9raGlevXi0yvUOHDnSgFOHuwwFU1tbWRaYnJCSgW7du\nH8+AIGVDhask0tPT4ejoiEePHhWZPmPGDHh5eXFKpRykVbgvX75E9+7dcevWrSLTO3fujNOnT9PB\nKUQu6Onp4fjx43BwcCgy/eHDh7C0tJSbUdgUARWuEhCJRHBxccGNGzeKTP/555+xfPlyTqmUhzQK\n965ZGs0AABAfSURBVNmzZ7C0tERcXFyR6d27d8epU6dgaGj41fMgpLLo6Ojg8OHD6N27d5Hp//77\nL7p164b79+9zSqZYqHAVnEQiwfDhwxEREVFkuqOjI7Zu3UqjSVWCyi7c0j6k7OzsEBwcDH19/a96\nfEKkQUtLCwcOHED//v2LTC/tyyMpjj6NFRhjDO7u7vjrr7+KTO/YsSP2798PDQ0NTsmUS2UWbmmb\n4Xr27ImjR49CV1e3wo9NiLRpaGhgz549GDp0aJHpH3aPSPMcdWVAhavAli1bhnXr1hWZZmJiguDg\nYOjp6XFKpXxKKtyKnNN57969Eg80cXFxwcGDB6Gtrf01MQmRCXV1dWzfvr3YZT1fv34NKysrXLt2\njVMy+UcDXyioLVu2YNy4cUWm1atXDxcuXEDDhg05pVJOjDHo6ekhOzv747Q3b96gevXqZX6Mu3fv\nwtbWttj5i4MGDcKOHTtoa4QU0MAX0iWRSODq6or169cXmW5oaIiTJ08WO4eX0BquQjp69CgmTJhQ\nZNqHFzmVbeX72nNxb9y4ge7duxcr2+HDh2PXrl1UtkQhCYVCBAUFwcPDo8j0tLQ02NnZ4dy5c5yS\nyS8qXAUTHR2NgQMHFrl0lpaWFo4dOwZzc3OOyZRbRQv3ypUrsLa2xps3b4pMHzt2LLZt2wY1NbVK\nSkiI7AkEAqxevRqzZs0qMj0zMxMODg4IDw/nlEw+UeEqkNjYWDg7OyMnJ+fjNKFQiL179xYbDYZU\nrk8LtyznHkZHR8PGxgapqalFpru6umLjxo10BDlRCgKBAMuWLcPChQuLTM/KykLPnj0REhLCKZn8\noXe8gkhMTIS9vX2xD+8NGzagb9++nFKpjkaNGhX5/5fWcCMjI2Fvb4+MjIwi06dNm4bAwEAqW6JU\nBAIBfvnlF/j4+BSZLhKJ0LdvXxw5coRTMvlC73oF8ObNG9jb2+P58+dFpi9evLjYgVNEOsqzSfn0\n6dNwcnLCu3fvikyfN28efH196UIERGnNmTMHq1evLjItNzcXP/30E/bv388plfxQ5x2AFGyefPz4\nMd69e4cqVaqgWbNmqFu3LoCC66M6OzsXu/D55MmT4e3tzSOuSvq0cO/cuYOYmBhYWFgUOegpODgY\n/fr1+3gN0Q+WLFlCy0uGPv1ySmTH09MTWlpamDJlysdp+fn5GDRoEHJzc4ucwysWi3Hr1i28fv0a\nYrEY1apVQ5s2bYpcoUupMMJFbm4u279/P7Nq357V1tFhloaGzKlKFdbV0JBV09ZmLnZ27OTJk8zJ\nyYkBKPLz008/sfz8fN5PQWUkJiYyr6lTmQ7AGgHsf+9/zA0MWL2qVdkv3t4sKSmJHTx4kGloaBRb\nXitXruT9FFSCWCxmISEhrJeVFauurc3MAdYFYK0Bpg8wu++/Z4cOHWJ5eXm8o6qELVu2MIFAUOS9\nIBAI2NatW9nr16/ZimXLWKPatZmpvj6zMzRkDoaGrF2VKqymvj6b7ubGHjx4wPspVDoqXA5u3brF\njI2MWDcDA7YXYCKAsUI/6QD7DWDfqasz3U8+vK2srFhOTg7vp6ASJBIJWzB7Nquurc1ctbRY7CfL\niQHsFsAmamuzKhoaTOOTDxcALCAggPfTUAlPnjxhrZs2ZW309dlmgGV+spxyALYLYJ0MDFjTevVY\nfHw878gqYefOnUwoFBYtXYAZaGiwkTo6LKaE99QDgM3Q0GA1tbXZ1PHjlWrlggpXxi5fvsxq6euz\nP0t4oX36IwHYIoDpvH+htvm/9u49tsr6juP4+5zTc+9FSksFioJlXlAZ3q/DTcQJBHFYmc0smUgY\ngkYxA6aJs7opds2UGakG1AqJgkNlXgpCIoExswWNxCXEAF5wE1EEDvR+evvuj6fUYynSup7nVM7n\nlZw/ntPntN8nvz7P5+nv+fX3GzPGDh06lOpDSAvt7e32m+nT7eJIxL7qQVvtAfsRWDDhwvL000+n\n+jDSwq5du2xobq495vNZew/a6nmPxwZlZdm2bdtSXXpaeOmll8zn8xlgGWBDwXb1oJ0OgY2LRKx4\n4sQTJnQVuC7avXu3nZyTY6/34Jct8fUnsOyMjBOyi6W/eqSszC6IRKy2F+0U6+hy9oFVVVWl+hDS\nQiwWs5FDhthTXm+vzqm/gg3NzbU9e/ak+hBOaI888ojNnDnT1qxZYxlerxWA7e1FO8XBro5EbN7t\nt6f6UPqEpnZ0UXZWFpMaGliZMGlFTxhwQyjEtRUVzL3jjuQUJ50OHTrEiMGD+XdTE8N6+dmPgQsC\nAfYcPKj5rF1QUV7Otgcf5MWEaTd76i6/n9DcuZQ//ngSKpNEra2tFObm8kZtLRf18rMxoCgY5INd\nuxg2rLdnZP+ifwtySV1dHfX19UzpZdgCeIB5TU1UVlRoPlgXrFi+nOu83l6HLUARcFUgwKpVq/q6\nLOmivb2dpx57jLu/R9gC3NnSQtUzz3xrIhlJjurqaoqg12ELMAD4FbCssrJvi0oBBa5Lrhk3jnYz\nZgBZQAVwEzAYOAm4CkhcTfKnwLMJ258Cn37+OZs3b3an4DRlZlRWVDCnoeGor30MDAS2dWx/AeQD\nf++y35y6OpY8+mhS6xRYv349e77+ms3AaJzz6jbgK2ACkAOMBw4Bm+CoG6hrgFNbW49a3lK+n/Ly\ncgoLC8nOzubMM89k48aNlJWVUVpaSmV5OXNqa1kBnArkAX8EhgNHVvIuw7kmlgLZOG26C1gErIzH\nebi8nLVr13b+vKqqKkaNGkV2djZFRUUsXbrUrUP93hS4Ljlt0CDygDeBWmA+MAn4CPgaOB/nLu4I\nT8crcXtgezubN21ypd50tW/fPvYfOMCV3XytCCgHbgEagVs7XmO77Dce2LF7NzU1NUmtNd1t3riR\niBlrgLeBHTjn1wTgUWAf0A48wbfPpSM8wJVNTWxOuIjL97Njxw6WLFnCe++9R01NDRs2bGD48OGd\nk7xs2rqVM4C5wEpgL3AY56Y10ZvAdJxu5PNwziVwbqLyAwFmzZrVuW9BQQHV1dXU1NRQVVXFvHnz\n2LZtG/2ZAtclsQMH6DpN/a+BKOAHHgA+wAnjY/EDsS4rzkjfOnjwIAP9/m4v0AAzgZHAxTgXgYe7\n2ccL5AaDxGKxJFUpALEvv8QH3InT0zAE+AlwGfBjIAj8gm96JLqTDcT2709ypSc+n89HPB5n+/bt\ntLS0cMopp3DaaadhZrS2tuIB1gLXA5fjXMse4ugbobE4IesDioEDwO86tocHg3zxxRedN7ITJ07s\nnHJ17NixXHvttf1+hSIFrkv8fj+JT1/bcH6RRuJ0fR2Zqfe7Tn0DAlqkPKn8fj+tx3lOPhPYjnOh\nP9bCei3t7QQCgT6uThL5AwEMKEh4L9xlOwTUfcf3aAO1Ux8YOXIkixcvpqysjIKCAkpKSti7dy/g\nLLDSZsYeoDDhM2GcRzSJBnX5eh7fhPKR0S91dU6Lrlu3jksvvZSBAwcyYMAA1q5de9SqXP2NAtcl\ngwoLaUvYfhF4Hacr7DDOM1qgM5SjQOJMvF8CTR4P+UOGJLvUtJafn8++eJxjDcOpA+7GCd0HcLq+\nuqoFalpbGTBgQJKqFIBBw4bR2s373d0uRYHEp/JtOI9yvgLyCwu7+YT0VklJCVu2bOGzzz7D4/Gw\ncOFCPB4PXq+XzGCQLODzhP0bcf6C7Yk24D/NzZ3b8XicG2+8kQULFrBv3z5isRgTJ07s94NKFbgu\nuWn6dBq9Xj7q2K7F6fLKxQnW+7rsPwZ4FeeX8iPgGZy/fouLi90pOE3l5ORwxUUXcaxp1u/C6U5e\nivMMfnY3+7wATLj6akLqjUiq4mnTqPd4aOnBvqcDTTjdmi04A3biwFuhENNKS5NYZXrYuXMnGzdu\nJB6PEwwGCYVC31rreVpxMXGvlzeAfwLNOIOkehqP64GhCf8S1NzcTHNzM3l5eXi9XtatW8eGDRv6\n7HiSRYHrkvHjx5OTk8PvcYa5x3BG6w0FzsF57pT4PGMeEMDpHru1Y5/s7OyjlomTvjdn4UIqs7KO\nev81YAPwVMf2Y8D7OINAjjCgMjOTOfPnJ7vMtDdq1Cj8fj//6PJ+18GGHpxntZU4PROFQCZOd6U/\nJ4crr+xuiJz0Rjwe59577yU/P5/Bgwezf/9+Fi1aBDhL991+zz38LRRiMXAzzvP2LJwu5GDH9+g6\nUJSE7crMTGbPn985CCsrK4snnniCadOmkZuby8qVK5kyZUqSj7IPpHLWjXTz54oKuy4cttZezjRV\nBzYqGrXq6upUH0JaaG1ttVPy8uytXraTgb0KdkZhobW3t6f6MNLC6tWr7bxo1Bp62U4tYD+LROyp\nyspUH0LauHz0aFvq8XS2QW3HVI+7j9NWW8EGRqNWX1+f6kP4v+kvXBfNvfNOGs8+m7sDAXo6/UUT\n8MtwmIsnT2bChAnJLE86+Hw+Vrz8MqXhMO/34nP/AmZFIjy/erXWvHXJ1KlTOX3cOG4Jh2k+/u6A\nM/jm9mCQwPnnc9vMmcksTxIsW7mS+cEgr+E8Rvstzv/anvodn9kJ3BAO8+wLLxCJRNwoM7lSnfjp\n5uDBg3bpuedaSSh03DlFd4GNjUateNIka25uTnXpaefVV16x/EjEVsF39kq0gK0Ay4tE1AuRAo2N\njTZ53Di7JhKxT45zTu0BmxoO29gLL7SamppUl552Jk+ebB6cBVmuBtt5jHZqA3sTrCActmeXLUt1\n2X1GgZsCDQ0NNnfGDDspFLKbIxHbhDPxfQvYAbDXwH6emWn5mZn2h/vvt7a2tlSXnLbeeecdu/is\ns+zUSMQWeb22G6wRrAHsE7CHfD4rjETsitGjbevWrakuN221tLTY/QsW2MBo1CZlZlp1x7nU0nFu\nvQ12YzRqJ4XDdvfs2VriMoW2b99u4y65xArCYbsvI8N2gNXjLKH4X7DHPR47PRq1c0eMsPXr16e6\n3D6lwE2hWCxmf1m82EaPGGFZwaB5PR47KRy2y845x5YvX26NjY2pLlE6vPvuuzajpMROzsmxgM9n\nAZ/PBufk2KzSUi3z1o/U19fbc889Z5ecdZblhELm9XgsOxSyMUVFtuTJJ+3w4cOpLlE6fPjhh3bX\n7NlWmJtroYwMy/B6LT8ry26+/nrbsmXLCTkOQqsF9SNmpmd/PwBHThm1Vf+nc+qHIx3aSoErIiLi\nAo1SFhERcYECV0RExAUKXBERERcocEVERFygwBUREXGBAldERMQFClwREREXKHBFRERcoMAVERFx\ngQJXRETEBQpcERERFyhwRUREXKDAFRERcYECV0RExAUKXBERERcocEVERFygwBUREXGBAldERMQF\nClwREREXKHBFRERcoMAVERFxgQJXRETEBQpcERERFyhwRUREXKDAFRERcYECV0RExAUKXBERERco\ncEVERFygwBUREXGBAldERMQFClwREREXKHBFRERcoMAVERFxgQJXRETEBQpcERERFyhwRUREXKDA\nFRERcYECV0RExAUKXBERERcocEVERFygwBUREXHB/wB6OxWDsXUlagAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10e3975d0>"
       ]
      }
     ],
     "prompt_number": 97
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Display the image generated via graphviz above that has the styling attributes\n",
      "\n",
      "![](files/test.png)"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "!cat expressionTree.dot"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "digraph model{\r\n",
        "\"model\" [ color=red, label=\"RooAddPdf\r\n",
        "model\"];\r\n",
        "\"g\" [ color=red, label=\"RooGaussian\r\n",
        "g\"];\r\n",
        "\"x\" [ color=blue, label=\"RooRealVar\r\n",
        "x\"];\r\n",
        "\"mu\" [ color=blue, label=\"RooRealVar\r\n",
        "mu\"];\r\n",
        "\"sigma\" [ color=blue, label=\"RooRealVar\r\n",
        "sigma\"];\r\n",
        "\"s\" [ color=blue, label=\"RooRealVar\r\n",
        "s\"];\r\n",
        "\"e\" [ color=red, label=\"RooExponential\r\n",
        "e\"];\r\n",
        "\"tau\" [ color=blue, label=\"RooRealVar\r\n",
        "tau\"];\r\n",
        "\"b\" [ color=blue, label=\"RooRealVar\r\n",
        "b\"];\r\n",
        "\"g\" -> \"x\";\r\n",
        "\"g\" -> \"mu\";\r\n",
        "\"g\" -> \"sigma\";\r\n",
        "\"e\" -> \"x\";\r\n",
        "\"e\" -> \"tau\";\r\n",
        "\"model\" -> \"g\";\r\n",
        "\"model\" -> \"e\";\r\n",
        "\"model\" -> \"s\";\r\n",
        "\"model\" -> \"b\";\r\n",
        "}\r\n"
       ]
      }
     ],
     "prompt_number": 77
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print \"inspect networkx graph\"\n",
      "#iterate over networkx graph\n",
      "print G2.node\n",
      "for n in G2.nodes():\n",
      "    print n, G2.out_degree(n), G2.successors(n)\n",
      "G2"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "inspect networkx graph\n",
        "{'tau': {'color': 'blue', 'label': '\"RooRealVar\\ntau\"'}, 'b': {'color': 'blue', 'label': '\"RooRealVar\\nb\"'}, 'e': {'color': 'red', 'label': '\"RooExponential\\ne\"'}, 'g': {'color': 'red', 'label': '\"RooGaussian\\ng\"'}, 'mu': {'color': 'blue', 'label': '\"RooRealVar\\nmu\"'}, 's': {'color': 'blue', 'label': '\"RooRealVar\\ns\"'}, 'x': {'color': 'blue', 'label': '\"RooRealVar\\nx\"'}, 'model': {'color': 'red', 'label': '\"RooAddPdf\\nmodel\"'}, 'sigma': {'color': 'blue', 'label': '\"RooRealVar\\nsigma\"'}}\n",
        "tau 0 []\n",
        "b 0 []\n",
        "e 2 ['tau', 'x']\n",
        "g 3 ['mu', 'x', 'sigma']\n",
        "mu 0 []\n",
        "s 0 []\n",
        "x 0 []\n",
        "model 4 ['s', 'b', 'e', 'g']\n",
        "sigma 0 []\n",
        "{}\n"
       ]
      }
     ],
     "prompt_number": 107
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "This post was created entirely in IPython notebook. Download the raw notebook [here](https://raw.github.com/cranmer/play/raw/master/iPythonROOT/BasicRooFitExample.ipynb), or see a static view on [nbviewer](http://nbviewer.ipython.org/url/github.com/cranmer/play/raw/master/iPythonROOT/BasicRooFitExample.ipynb)."
     ]
    }
   ],
   "metadata": {}
  }
 ]
}