{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Problems from Hughes and Hase"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import scipy as sp\n",
    "from scipy import stats\n",
    "\n",
    "import matplotlib as mpl       # As of July 2017 Bucknell computers use v. 2.x \n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# Following is an Ipython magic command that puts figures in the  notebook.\n",
    "# For figures in separate windows, comment out following line and uncomment\n",
    "# the next line\n",
    "# Must come before defaults are changed.\n",
    "%matplotlib notebook\n",
    "#%matplotlib\n",
    "\n",
    "# As of Aug. 2017 reverting to 1.x defaults.\n",
    "# In 2.x text.ustex requires dvipng, texlive-latex-extra, and texlive-fonts-recommended, \n",
    "# which don't seem to be universal\n",
    "# See https://stackoverflow.com/questions/38906356/error-running-matplotlib-in-latex-type1cm?\n",
    "mpl.style.use('classic')\n",
    "        \n",
    "# M.L. modifications of matplotlib defaults using syntax of v.2.0 \n",
    "# More info at http://matplotlib.org/2.0.0/users/deflt_style_changes.html\n",
    "# Changes can also be put in matplotlibrc file, or effected using mpl.rcParams[]\n",
    "plt.rc('figure', figsize = (6, 4.5))            # Reduces overall size of figures\n",
    "plt.rc('axes', labelsize=16, titlesize=14)\n",
    "plt.rc('figure', autolayout = True)             # Adjusts supblot parameters for new size"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Problem 2.2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Twelve data points given:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "data = sp.array([5.33,4.95,4.93,5.08,4.95,4.96,5.02,4.99,5.24,5.25,5.23,5.01])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### a) Calculating the mean: $\\quad\\mu = \\frac{1}{N}\\sum_i x_i$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "mean = 5.07833333333\n"
     ]
    }
   ],
   "source": [
    "print(\"mean =\",sum(data)/len(data))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "or"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "mean = 5.07833333333\n"
     ]
    }
   ],
   "source": [
    "print(\"mean =\",sp.mean(data))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### b) standard deviation: $\\quad\\sigma = \\sqrt{\\frac{1}{N-1} \\sum_i (x_i - \\mu)^2}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "standard deviation = 0.143579774046\n"
     ]
    }
   ],
   "source": [
    "print(\"standard deviation =\",sp.sqrt(sum((data-sp.mean(data))**2)/(len(data)-1)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "or"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "standard deviation = 0.137467167797\n"
     ]
    }
   ],
   "source": [
    "print(\"standard deviation =\",sp.std(data))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "These results do not agree!!  \n",
    "\n",
    "By default the scipy std method calculates $\\sigma_N$, which is similar to the\n",
    "$\\sigma_{N-1}$ given in Eq.(2.3) of H&H, except the denominator is $N$ instead of $N-1$.  The difference doesn't usually matter, and we won't go into this in any depth now. But if we set the 'ddof=1' option scipy will calculate $\\sigma_{N-1}$.\n",
    "\n",
    "Remember: you can see all the details of sp.std by typing sp.std?."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "standard deviation = 0.143579774046\n"
     ]
    }
   ],
   "source": [
    "print(\"standard deviation =\",sp.std(data,ddof=1))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### c) Standard error, or standard deviation of the  mean"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Use Eq.(2.7): $\\quad\\alpha = \\frac{\\sigma_{N-1}}{\\sqrt{N}}$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "standard error = 0.0414479105979\n"
     ]
    }
   ],
   "source": [
    "print(\"standard error =\",sp.std(data,ddof=1)/sp.sqrt(len(data)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### d) Formatted result"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$\\mbox{sensitivity} = 5.071 \\pm 0.041 $"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Sample $n$  random numbers from the normal distribution with mean $\\mu$, standard deviation $\\sigma$, and \n",
    "pdf\n",
    "\\begin{equation}\n",
    "p(x) = \\frac{1}{\\sqrt{2\\pi\\sigma^2}}\\exp\\left(-(x-\\mu)^2/\\sigma^2\\right)\n",
    "\\end{equation}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Problem 2.3"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The standard error, or standard deviation of the  mean, is given by Eq.(2.7):\n",
    "\n",
    "$$ \\alpha = \\frac{\\sigma_{N-1}}{\\sqrt{N}}. $$\n",
    "\n",
    "To decrease $\\alpha$ by a factor of 10, the denominator must be increased by the \n",
    "same factor, which means that  $N$ must increase by a factor of 100.  Translating to the described experiment, this means that data should be collected for 100 minutes (assuming that everything in the experiment is stable for that length of time).\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " ### Problem 2.6"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "(i) If the mean is $\\bar{\\delta} = 3.27346$, and the standard error (standard deviation of the mean) is $\\alpha = 0.01913$, I would report $\\delta = 3.27 \\pm 0.02$ (although some might report this as $\\delta = 3.273 \\pm 0.019)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Problem 3.2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import sympy as sym # import sympy for symbolic integration\n",
    "sym.init_printing() # for LaTeX formatted output\n",
    "\n",
    "a, x, mu  = sym.symbols('a x mu') # must declare symbolic variables in sympy\n",
    "                                  # I will use mu for x-bar"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Define the probability distribution function.<br>\n",
    "(The conditional will be incorporated in the limits of integration.)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "p = 1/a"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "a) A probability distribution is normalized if the integral over all space is one, i.e., $\\int_{-\\infty}^\\infty P_U(x;\\bar{x},a) \\, dx = \\int_{\\mu-a/2}^{\\mu+a/2}P_U(x;\\bar{x},a) \\, dx = 1$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAPoAAAAqBAMAAABo/FshAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nYII=\n",
      "text/latex": [
       "$$- \\frac{1}{a} \\left(- \\frac{a}{2} + \\mu\\right) + \\frac{1}{a} \\left(\\frac{a}{2} + \\mu\\right)$$"
      ],
      "text/plain": [
       "    a       a    \n",
       "  - ─ + μ   ─ + μ\n",
       "    2       2    \n",
       "- ─────── + ─────\n",
       "     a        a  "
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sym.integrate(p,(x,mu-a/2,mu+a/2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAAgAAAAPBAMAAAArJJMAAAAAHlBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAACGjDitAAAACXRSTlMAVO8Qq5l2zWYZcMvdAAAACXBIWXMAAA7EAAAOxAGV\nKw4bAAAAHUlEQVQIHWNgAANGZQYGk5DJQDYbqQSr03QPsBkAJYgIYEZbtZEAAAAASUVORK5CYII=\n",
      "text/latex": [
       "$$1$$"
      ],
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sym.simplify(_)   # The underscore \"_\" is like the Mathematica %\n",
    "                  # it refers to the previous output. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "b) The mean is just the first moment of the distribution given by Eq.(3.4):\n",
    "\n",
    "$$ \\bar{x} = \\int_{-\\infty}^\\infty P(x) x\\, dx     $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAOEAAAA1BAMAAABFMpFwAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nAElFTkSuQmCC\n",
      "text/latex": [
       "$$- \\frac{\\left(- \\frac{a}{2} + \\mu\\right)^{2}}{2 a} + \\frac{\\left(\\frac{a}{2} + \\mu\\right)^{2}}{2 a}$$"
      ],
      "text/plain": [
       "           2          2\n",
       "  ⎛  a    ⎞    ⎛a    ⎞ \n",
       "  ⎜- ─ + μ⎟    ⎜─ + μ⎟ \n",
       "  ⎝  2    ⎠    ⎝2    ⎠ \n",
       "- ────────── + ────────\n",
       "     2⋅a         2⋅a   "
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sym.integrate(p*x,(x,mu-a/2,mu+a/2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAAwAAAANBAMAAABvB5JxAAAALVBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAADAOrOgAAAADnRSTlMAMu92q4ndmc0QVLsiRAus\n9U8AAAAJcEhZcwAADsQAAA7EAZUrDhsAAABUSURBVAgdY2BgVGBgdmBgYE1gYCtgYOAoYJi3gAGE\n101gAOEKBgaGMgaGVE4GhmwGnlesDJzPGNjfSDFwPQ82MDVgYGkAyjMwMBmAqXMCYOoamAQAAh4P\nsS7zeAEAAAAASUVORK5CYII=\n",
      "text/latex": [
       "$$\\mu$$"
      ],
      "text/plain": [
       "μ"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sym.simplify(_)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "c) The square of the standard deviation, or variance,  is given by Eq.(3.5):\n",
    "\n",
    "$$ \\sigma^2 = \\int_{-\\infty}^\\infty P(x)(x-\\bar{x})^2\\, dx $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAEIAAAAwBAMAAABXkLERAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n32aYdI9K8GZJh7DR/FtgZIalWeRPRZKSXfCaO44AAAAASUVORK5CYII=\n",
      "text/latex": [
       "$$\\frac{\\sqrt{3} \\sqrt{a^{2}}}{6}$$"
      ],
      "text/plain": [
       "      ____\n",
       "     ╱  2 \n",
       "√3⋅╲╱  a  \n",
       "──────────\n",
       "    6     "
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sym.sqrt(sym.integrate(p*(x-0)**2,(x,-a/2,a/2)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Problem 3.5"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Normally distributed pasta bags with a mean weight of 502 g, and an s.d. of 14 g."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "mean = 502.\n",
    "sigma = 14."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "What is the probability that a bag contains less than 500 g?<br>\n",
    "This information is given directly by the cumulative distribution function (c.d.f.)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAIwAAAAPBAMAAADEyjp7AAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nPf4ABYHdd9UPJxEAAAAASUVORK5CYII=\n",
      "text/latex": [
       "$$0.443201503184$$"
      ],
      "text/plain": [
       "0.443201503184"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sp.stats.norm.cdf(500,mean,sigma)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In a sample of 1000 bags, how many are expected to contain at least 530 g?<br>\n",
    "This information is given indirectly by the c.d.f.  The probability of one bag containing \n",
    "more than 530 is (1 - c.d.f), and we must multiply by the number of bags."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAH8AAAAPBAMAAAA/sQ3hAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\ndaDF89K/2h4AAAAASUVORK5CYII=\n",
      "text/latex": [
       "$$22.7501319482$$"
      ],
      "text/plain": [
       "22.7501319482"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "1000*(1-sp.stats.norm.cdf(530,mean,sigma))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Problem 3.7\n",
    "\n",
    "Radioactive decays recorded during 58 successive one-second experiments."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "data = sp.array([[1,1],[2,0],[3,2],[4,3],[5,6],[6,9],[7,11],[8,8],[9,8],\\\n",
    "                 [10,6],[11,2],[12,1],[13,1]])\n"
   ]
  },
  {
   "cell_type": "raw",
   "metadata": {},
   "source": [
    "For fun, let's reproduce Fig.3.8 from Hughes & Hase."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/javascript": [
       "/* Put everything inside the global mpl namespace */\n",
       "window.mpl = {};\n",
       "\n",
       "\n",
       "mpl.get_websocket_type = function() {\n",
       "    if (typeof(WebSocket) !== 'undefined') {\n",
       "        return WebSocket;\n",
       "    } else if (typeof(MozWebSocket) !== 'undefined') {\n",
       "        return MozWebSocket;\n",
       "    } else {\n",
       "        alert('Your browser does not have WebSocket support.' +\n",
       "              'Please try Chrome, Safari or Firefox ≥ 6. ' +\n",
       "              'Firefox 4 and 5 are also supported but you ' +\n",
       "              'have to enable WebSockets in about:config.');\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure = function(figure_id, websocket, ondownload, parent_element) {\n",
       "    this.id = figure_id;\n",
       "\n",
       "    this.ws = websocket;\n",
       "\n",
       "    this.supports_binary = (this.ws.binaryType != undefined);\n",
       "\n",
       "    if (!this.supports_binary) {\n",
       "        var warnings = document.getElementById(\"mpl-warnings\");\n",
       "        if (warnings) {\n",
       "            warnings.style.display = 'block';\n",
       "            warnings.textContent = (\n",
       "                \"This browser does not support binary websocket messages. \" +\n",
       "                    \"Performance may be slow.\");\n",
       "        }\n",
       "    }\n",
       "\n",
       "    this.imageObj = new Image();\n",
       "\n",
       "    this.context = undefined;\n",
       "    this.message = undefined;\n",
       "    this.canvas = undefined;\n",
       "    this.rubberband_canvas = undefined;\n",
       "    this.rubberband_context = undefined;\n",
       "    this.format_dropdown = undefined;\n",
       "\n",
       "    this.image_mode = 'full';\n",
       "\n",
       "    this.root = $('<div/>');\n",
       "    this._root_extra_style(this.root)\n",
       "    this.root.attr('style', 'display: inline-block');\n",
       "\n",
       "    $(parent_element).append(this.root);\n",
       "\n",
       "    this._init_header(this);\n",
       "    this._init_canvas(this);\n",
       "    this._init_toolbar(this);\n",
       "\n",
       "    var fig = this;\n",
       "\n",
       "    this.waiting = false;\n",
       "\n",
       "    this.ws.onopen =  function () {\n",
       "            fig.send_message(\"supports_binary\", {value: fig.supports_binary});\n",
       "            fig.send_message(\"send_image_mode\", {});\n",
       "            if (mpl.ratio != 1) {\n",
       "                fig.send_message(\"set_dpi_ratio\", {'dpi_ratio': mpl.ratio});\n",
       "            }\n",
       "            fig.send_message(\"refresh\", {});\n",
       "        }\n",
       "\n",
       "    this.imageObj.onload = function() {\n",
       "            if (fig.image_mode == 'full') {\n",
       "                // Full images could contain transparency (where diff images\n",
       "                // almost always do), so we need to clear the canvas so that\n",
       "                // there is no ghosting.\n",
       "                fig.context.clearRect(0, 0, fig.canvas.width, fig.canvas.height);\n",
       "            }\n",
       "            fig.context.drawImage(fig.imageObj, 0, 0);\n",
       "        };\n",
       "\n",
       "    this.imageObj.onunload = function() {\n",
       "        this.ws.close();\n",
       "    }\n",
       "\n",
       "    this.ws.onmessage = this._make_on_message_function(this);\n",
       "\n",
       "    this.ondownload = ondownload;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_header = function() {\n",
       "    var titlebar = $(\n",
       "        '<div class=\"ui-dialog-titlebar ui-widget-header ui-corner-all ' +\n",
       "        'ui-helper-clearfix\"/>');\n",
       "    var titletext = $(\n",
       "        '<div class=\"ui-dialog-title\" style=\"width: 100%; ' +\n",
       "        'text-align: center; padding: 3px;\"/>');\n",
       "    titlebar.append(titletext)\n",
       "    this.root.append(titlebar);\n",
       "    this.header = titletext[0];\n",
       "}\n",
       "\n",
       "\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_canvas = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var canvas_div = $('<div/>');\n",
       "\n",
       "    canvas_div.attr('style', 'position: relative; clear: both; outline: 0');\n",
       "\n",
       "    function canvas_keyboard_event(event) {\n",
       "        return fig.key_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    canvas_div.keydown('key_press', canvas_keyboard_event);\n",
       "    canvas_div.keyup('key_release', canvas_keyboard_event);\n",
       "    this.canvas_div = canvas_div\n",
       "    this._canvas_extra_style(canvas_div)\n",
       "    this.root.append(canvas_div);\n",
       "\n",
       "    var canvas = $('<canvas/>');\n",
       "    canvas.addClass('mpl-canvas');\n",
       "    canvas.attr('style', \"left: 0; top: 0; z-index: 0; outline: 0\")\n",
       "\n",
       "    this.canvas = canvas[0];\n",
       "    this.context = canvas[0].getContext(\"2d\");\n",
       "\n",
       "    var backingStore = this.context.backingStorePixelRatio ||\n",
       "\tthis.context.webkitBackingStorePixelRatio ||\n",
       "\tthis.context.mozBackingStorePixelRatio ||\n",
       "\tthis.context.msBackingStorePixelRatio ||\n",
       "\tthis.context.oBackingStorePixelRatio ||\n",
       "\tthis.context.backingStorePixelRatio || 1;\n",
       "\n",
       "    mpl.ratio = (window.devicePixelRatio || 1) / backingStore;\n",
       "\n",
       "    var rubberband = $('<canvas/>');\n",
       "    rubberband.attr('style', \"position: absolute; left: 0; top: 0; z-index: 1;\")\n",
       "\n",
       "    var pass_mouse_events = true;\n",
       "\n",
       "    canvas_div.resizable({\n",
       "        start: function(event, ui) {\n",
       "            pass_mouse_events = false;\n",
       "        },\n",
       "        resize: function(event, ui) {\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "        stop: function(event, ui) {\n",
       "            pass_mouse_events = true;\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "    });\n",
       "\n",
       "    function mouse_event_fn(event) {\n",
       "        if (pass_mouse_events)\n",
       "            return fig.mouse_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    rubberband.mousedown('button_press', mouse_event_fn);\n",
       "    rubberband.mouseup('button_release', mouse_event_fn);\n",
       "    // Throttle sequential mouse events to 1 every 20ms.\n",
       "    rubberband.mousemove('motion_notify', mouse_event_fn);\n",
       "\n",
       "    rubberband.mouseenter('figure_enter', mouse_event_fn);\n",
       "    rubberband.mouseleave('figure_leave', mouse_event_fn);\n",
       "\n",
       "    canvas_div.on(\"wheel\", function (event) {\n",
       "        event = event.originalEvent;\n",
       "        event['data'] = 'scroll'\n",
       "        if (event.deltaY < 0) {\n",
       "            event.step = 1;\n",
       "        } else {\n",
       "            event.step = -1;\n",
       "        }\n",
       "        mouse_event_fn(event);\n",
       "    });\n",
       "\n",
       "    canvas_div.append(canvas);\n",
       "    canvas_div.append(rubberband);\n",
       "\n",
       "    this.rubberband = rubberband;\n",
       "    this.rubberband_canvas = rubberband[0];\n",
       "    this.rubberband_context = rubberband[0].getContext(\"2d\");\n",
       "    this.rubberband_context.strokeStyle = \"#000000\";\n",
       "\n",
       "    this._resize_canvas = function(width, height) {\n",
       "        // Keep the size of the canvas, canvas container, and rubber band\n",
       "        // canvas in synch.\n",
       "        canvas_div.css('width', width)\n",
       "        canvas_div.css('height', height)\n",
       "\n",
       "        canvas.attr('width', width * mpl.ratio);\n",
       "        canvas.attr('height', height * mpl.ratio);\n",
       "        canvas.attr('style', 'width: ' + width + 'px; height: ' + height + 'px;');\n",
       "\n",
       "        rubberband.attr('width', width);\n",
       "        rubberband.attr('height', height);\n",
       "    }\n",
       "\n",
       "    // Set the figure to an initial 600x600px, this will subsequently be updated\n",
       "    // upon first draw.\n",
       "    this._resize_canvas(600, 600);\n",
       "\n",
       "    // Disable right mouse context menu.\n",
       "    $(this.rubberband_canvas).bind(\"contextmenu\",function(e){\n",
       "        return false;\n",
       "    });\n",
       "\n",
       "    function set_focus () {\n",
       "        canvas.focus();\n",
       "        canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    window.setTimeout(set_focus, 100);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>')\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items) {\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) {\n",
       "            // put a spacer in here.\n",
       "            continue;\n",
       "        }\n",
       "        var button = $('<button/>');\n",
       "        button.addClass('ui-button ui-widget ui-state-default ui-corner-all ' +\n",
       "                        'ui-button-icon-only');\n",
       "        button.attr('role', 'button');\n",
       "        button.attr('aria-disabled', 'false');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "\n",
       "        var icon_img = $('<span/>');\n",
       "        icon_img.addClass('ui-button-icon-primary ui-icon');\n",
       "        icon_img.addClass(image);\n",
       "        icon_img.addClass('ui-corner-all');\n",
       "\n",
       "        var tooltip_span = $('<span/>');\n",
       "        tooltip_span.addClass('ui-button-text');\n",
       "        tooltip_span.html(tooltip);\n",
       "\n",
       "        button.append(icon_img);\n",
       "        button.append(tooltip_span);\n",
       "\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    var fmt_picker_span = $('<span/>');\n",
       "\n",
       "    var fmt_picker = $('<select/>');\n",
       "    fmt_picker.addClass('mpl-toolbar-option ui-widget ui-widget-content');\n",
       "    fmt_picker_span.append(fmt_picker);\n",
       "    nav_element.append(fmt_picker_span);\n",
       "    this.format_dropdown = fmt_picker[0];\n",
       "\n",
       "    for (var ind in mpl.extensions) {\n",
       "        var fmt = mpl.extensions[ind];\n",
       "        var option = $(\n",
       "            '<option/>', {selected: fmt === mpl.default_extension}).html(fmt);\n",
       "        fmt_picker.append(option)\n",
       "    }\n",
       "\n",
       "    // Add hover states to the ui-buttons\n",
       "    $( \".ui-button\" ).hover(\n",
       "        function() { $(this).addClass(\"ui-state-hover\");},\n",
       "        function() { $(this).removeClass(\"ui-state-hover\");}\n",
       "    );\n",
       "\n",
       "    var status_bar = $('<span class=\"mpl-message\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.request_resize = function(x_pixels, y_pixels) {\n",
       "    // Request matplotlib to resize the figure. Matplotlib will then trigger a resize in the client,\n",
       "    // which will in turn request a refresh of the image.\n",
       "    this.send_message('resize', {'width': x_pixels, 'height': y_pixels});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_message = function(type, properties) {\n",
       "    properties['type'] = type;\n",
       "    properties['figure_id'] = this.id;\n",
       "    this.ws.send(JSON.stringify(properties));\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_draw_message = function() {\n",
       "    if (!this.waiting) {\n",
       "        this.waiting = true;\n",
       "        this.ws.send(JSON.stringify({type: \"draw\", figure_id: this.id}));\n",
       "    }\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    var format_dropdown = fig.format_dropdown;\n",
       "    var format = format_dropdown.options[format_dropdown.selectedIndex].value;\n",
       "    fig.ondownload(fig, format);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_resize = function(fig, msg) {\n",
       "    var size = msg['size'];\n",
       "    if (size[0] != fig.canvas.width || size[1] != fig.canvas.height) {\n",
       "        fig._resize_canvas(size[0], size[1]);\n",
       "        fig.send_message(\"refresh\", {});\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_rubberband = function(fig, msg) {\n",
       "    var x0 = msg['x0'] / mpl.ratio;\n",
       "    var y0 = (fig.canvas.height - msg['y0']) / mpl.ratio;\n",
       "    var x1 = msg['x1'] / mpl.ratio;\n",
       "    var y1 = (fig.canvas.height - msg['y1']) / mpl.ratio;\n",
       "    x0 = Math.floor(x0) + 0.5;\n",
       "    y0 = Math.floor(y0) + 0.5;\n",
       "    x1 = Math.floor(x1) + 0.5;\n",
       "    y1 = Math.floor(y1) + 0.5;\n",
       "    var min_x = Math.min(x0, x1);\n",
       "    var min_y = Math.min(y0, y1);\n",
       "    var width = Math.abs(x1 - x0);\n",
       "    var height = Math.abs(y1 - y0);\n",
       "\n",
       "    fig.rubberband_context.clearRect(\n",
       "        0, 0, fig.canvas.width, fig.canvas.height);\n",
       "\n",
       "    fig.rubberband_context.strokeRect(min_x, min_y, width, height);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_figure_label = function(fig, msg) {\n",
       "    // Updates the figure title.\n",
       "    fig.header.textContent = msg['label'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_cursor = function(fig, msg) {\n",
       "    var cursor = msg['cursor'];\n",
       "    switch(cursor)\n",
       "    {\n",
       "    case 0:\n",
       "        cursor = 'pointer';\n",
       "        break;\n",
       "    case 1:\n",
       "        cursor = 'default';\n",
       "        break;\n",
       "    case 2:\n",
       "        cursor = 'crosshair';\n",
       "        break;\n",
       "    case 3:\n",
       "        cursor = 'move';\n",
       "        break;\n",
       "    }\n",
       "    fig.rubberband_canvas.style.cursor = cursor;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_message = function(fig, msg) {\n",
       "    fig.message.textContent = msg['message'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_draw = function(fig, msg) {\n",
       "    // Request the server to send over a new figure.\n",
       "    fig.send_draw_message();\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_image_mode = function(fig, msg) {\n",
       "    fig.image_mode = msg['mode'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Called whenever the canvas gets updated.\n",
       "    this.send_message(\"ack\", {});\n",
       "}\n",
       "\n",
       "// A function to construct a web socket function for onmessage handling.\n",
       "// Called in the figure constructor.\n",
       "mpl.figure.prototype._make_on_message_function = function(fig) {\n",
       "    return function socket_on_message(evt) {\n",
       "        if (evt.data instanceof Blob) {\n",
       "            /* FIXME: We get \"Resource interpreted as Image but\n",
       "             * transferred with MIME type text/plain:\" errors on\n",
       "             * Chrome.  But how to set the MIME type?  It doesn't seem\n",
       "             * to be part of the websocket stream */\n",
       "            evt.data.type = \"image/png\";\n",
       "\n",
       "            /* Free the memory for the previous frames */\n",
       "            if (fig.imageObj.src) {\n",
       "                (window.URL || window.webkitURL).revokeObjectURL(\n",
       "                    fig.imageObj.src);\n",
       "            }\n",
       "\n",
       "            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
       "                evt.data);\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "        else if (typeof evt.data === 'string' && evt.data.slice(0, 21) == \"data:image/png;base64\") {\n",
       "            fig.imageObj.src = evt.data;\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        var msg = JSON.parse(evt.data);\n",
       "        var msg_type = msg['type'];\n",
       "\n",
       "        // Call the  \"handle_{type}\" callback, which takes\n",
       "        // the figure and JSON message as its only arguments.\n",
       "        try {\n",
       "            var callback = fig[\"handle_\" + msg_type];\n",
       "        } catch (e) {\n",
       "            console.log(\"No handler for the '\" + msg_type + \"' message type: \", msg);\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        if (callback) {\n",
       "            try {\n",
       "                // console.log(\"Handling '\" + msg_type + \"' message: \", msg);\n",
       "                callback(fig, msg);\n",
       "            } catch (e) {\n",
       "                console.log(\"Exception inside the 'handler_\" + msg_type + \"' callback:\", e, e.stack, msg);\n",
       "            }\n",
       "        }\n",
       "    };\n",
       "}\n",
       "\n",
       "// from http://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas\n",
       "mpl.findpos = function(e) {\n",
       "    //this section is from http://www.quirksmode.org/js/events_properties.html\n",
       "    var targ;\n",
       "    if (!e)\n",
       "        e = window.event;\n",
       "    if (e.target)\n",
       "        targ = e.target;\n",
       "    else if (e.srcElement)\n",
       "        targ = e.srcElement;\n",
       "    if (targ.nodeType == 3) // defeat Safari bug\n",
       "        targ = targ.parentNode;\n",
       "\n",
       "    // jQuery normalizes the pageX and pageY\n",
       "    // pageX,Y are the mouse positions relative to the document\n",
       "    // offset() returns the position of the element relative to the document\n",
       "    var x = e.pageX - $(targ).offset().left;\n",
       "    var y = e.pageY - $(targ).offset().top;\n",
       "\n",
       "    return {\"x\": x, \"y\": y};\n",
       "};\n",
       "\n",
       "/*\n",
       " * return a copy of an object with only non-object keys\n",
       " * we need this to avoid circular references\n",
       " * http://stackoverflow.com/a/24161582/3208463\n",
       " */\n",
       "function simpleKeys (original) {\n",
       "  return Object.keys(original).reduce(function (obj, key) {\n",
       "    if (typeof original[key] !== 'object')\n",
       "        obj[key] = original[key]\n",
       "    return obj;\n",
       "  }, {});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.mouse_event = function(event, name) {\n",
       "    var canvas_pos = mpl.findpos(event)\n",
       "\n",
       "    if (name === 'button_press')\n",
       "    {\n",
       "        this.canvas.focus();\n",
       "        this.canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    var x = canvas_pos.x * mpl.ratio;\n",
       "    var y = canvas_pos.y * mpl.ratio;\n",
       "\n",
       "    this.send_message(name, {x: x, y: y, button: event.button,\n",
       "                             step: event.step,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "\n",
       "    /* This prevents the web browser from automatically changing to\n",
       "     * the text insertion cursor when the button is pressed.  We want\n",
       "     * to control all of the cursor setting manually through the\n",
       "     * 'cursor' event from matplotlib */\n",
       "    event.preventDefault();\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    // Handle any extra behaviour associated with a key event\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.key_event = function(event, name) {\n",
       "\n",
       "    // Prevent repeat events\n",
       "    if (name == 'key_press')\n",
       "    {\n",
       "        if (event.which === this._key)\n",
       "            return;\n",
       "        else\n",
       "            this._key = event.which;\n",
       "    }\n",
       "    if (name == 'key_release')\n",
       "        this._key = null;\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.which != 17)\n",
       "        value += \"ctrl+\";\n",
       "    if (event.altKey && event.which != 18)\n",
       "        value += \"alt+\";\n",
       "    if (event.shiftKey && event.which != 16)\n",
       "        value += \"shift+\";\n",
       "\n",
       "    value += 'k';\n",
       "    value += event.which.toString();\n",
       "\n",
       "    this._key_event_extra(event, name);\n",
       "\n",
       "    this.send_message(name, {key: value,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onclick = function(name) {\n",
       "    if (name == 'download') {\n",
       "        this.handle_save(this, null);\n",
       "    } else {\n",
       "        this.send_message(\"toolbar_button\", {name: name});\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onmouseover = function(tooltip) {\n",
       "    this.message.textContent = tooltip;\n",
       "};\n",
       "mpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home icon-home\", \"home\"], [\"Back\", \"Back to  previous view\", \"fa fa-arrow-left icon-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right icon-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Pan axes with left mouse, zoom with right\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
       "\n",
       "mpl.extensions = [\"eps\", \"jpeg\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\", \"tif\"];\n",
       "\n",
       "mpl.default_extension = \"png\";var comm_websocket_adapter = function(comm) {\n",
       "    // Create a \"websocket\"-like object which calls the given IPython comm\n",
       "    // object with the appropriate methods. Currently this is a non binary\n",
       "    // socket, so there is still some room for performance tuning.\n",
       "    var ws = {};\n",
       "\n",
       "    ws.close = function() {\n",
       "        comm.close()\n",
       "    };\n",
       "    ws.send = function(m) {\n",
       "        //console.log('sending', m);\n",
       "        comm.send(m);\n",
       "    };\n",
       "    // Register the callback with on_msg.\n",
       "    comm.on_msg(function(msg) {\n",
       "        //console.log('receiving', msg['content']['data'], msg);\n",
       "        // Pass the mpl event to the overriden (by mpl) onmessage function.\n",
       "        ws.onmessage(msg['content']['data'])\n",
       "    });\n",
       "    return ws;\n",
       "}\n",
       "\n",
       "mpl.mpl_figure_comm = function(comm, msg) {\n",
       "    // This is the function which gets called when the mpl process\n",
       "    // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
       "\n",
       "    var id = msg.content.data.id;\n",
       "    // Get hold of the div created by the display call when the Comm\n",
       "    // socket was opened in Python.\n",
       "    var element = $(\"#\" + id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm)\n",
       "\n",
       "    function ondownload(figure, format) {\n",
       "        window.open(figure.imageObj.src);\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy,\n",
       "                           ondownload,\n",
       "                           element.get(0));\n",
       "\n",
       "    // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n",
       "    // web socket which is closed, not our websocket->open comm proxy.\n",
       "    ws_proxy.onopen();\n",
       "\n",
       "    fig.parent_element = element.get(0);\n",
       "    fig.cell_info = mpl.find_output_cell(\"<div id='\" + id + \"'></div>\");\n",
       "    if (!fig.cell_info) {\n",
       "        console.error(\"Failed to find cell for figure\", id, fig);\n",
       "        return;\n",
       "    }\n",
       "\n",
       "    var output_index = fig.cell_info[2]\n",
       "    var cell = fig.cell_info[0];\n",
       "\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function(fig, msg) {\n",
       "    var width = fig.canvas.width/mpl.ratio\n",
       "    fig.root.unbind('remove')\n",
       "\n",
       "    // Update the output cell to use the data from the current canvas.\n",
       "    fig.push_to_output();\n",
       "    var dataURL = fig.canvas.toDataURL();\n",
       "    // Re-enable the keyboard manager in IPython - without this line, in FF,\n",
       "    // the notebook keyboard shortcuts fail.\n",
       "    IPython.keyboard_manager.enable()\n",
       "    $(fig.parent_element).html('<img src=\"' + dataURL + '\" width=\"' + width + '\">');\n",
       "    fig.close_ws(fig, msg);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.close_ws = function(fig, msg){\n",
       "    fig.send_message('closing', msg);\n",
       "    // fig.ws.close()\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.push_to_output = function(remove_interactive) {\n",
       "    // Turn the data on the canvas into data in the output cell.\n",
       "    var width = this.canvas.width/mpl.ratio\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] = '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Tell IPython that the notebook contents must change.\n",
       "    IPython.notebook.set_dirty(true);\n",
       "    this.send_message(\"ack\", {});\n",
       "    var fig = this;\n",
       "    // Wait a second, then push the new image to the DOM so\n",
       "    // that it is saved nicely (might be nice to debounce this).\n",
       "    setTimeout(function () { fig.push_to_output() }, 1000);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>')\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items){\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) { continue; };\n",
       "\n",
       "        var button = $('<button class=\"btn btn-default\" href=\"#\" title=\"' + name + '\"><i class=\"fa ' + image + ' fa-lg\"></i></button>');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = $('<span class=\"mpl-message\" style=\"text-align:right; float: right;\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = $('<div class=\"btn-group inline pull-right\"></div>');\n",
       "    var button = $('<button class=\"btn btn-mini btn-primary\" href=\"#\" title=\"Stop Interaction\"><i class=\"fa fa-power-off icon-remove icon-large\"></i></button>');\n",
       "    button.click(function (evt) { fig.handle_close(fig, {}); } );\n",
       "    button.mouseover('Stop Interaction', toolbar_mouse_event);\n",
       "    buttongrp.append(button);\n",
       "    var titlebar = this.root.find($('.ui-dialog-titlebar'));\n",
       "    titlebar.prepend(buttongrp);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(el){\n",
       "    var fig = this\n",
       "    el.on(\"remove\", function(){\n",
       "\tfig.close_ws(fig, {});\n",
       "    });\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(el){\n",
       "    // this is important to make the div 'focusable\n",
       "    el.attr('tabindex', 0)\n",
       "    // reach out to IPython and tell the keyboard manager to turn it's self\n",
       "    // off when our div gets focus\n",
       "\n",
       "    // location in version 3\n",
       "    if (IPython.notebook.keyboard_manager) {\n",
       "        IPython.notebook.keyboard_manager.register_events(el);\n",
       "    }\n",
       "    else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\n",
       "    }\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    var manager = IPython.notebook.keyboard_manager;\n",
       "    if (!manager)\n",
       "        manager = IPython.keyboard_manager;\n",
       "\n",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which == 13) {\n",
       "        this.canvas_div.blur();\n",
       "        // select the cell after this one\n",
       "        var index = IPython.notebook.find_cell_index(this.cell_info[0]);\n",
       "        IPython.notebook.select(index + 1);\n",
       "    }\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    fig.ondownload(fig, null);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.find_output_cell = function(html_output) {\n",
       "    // Return the cell and output element which can be found *uniquely* in the notebook.\n",
       "    // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n",
       "    // IPython event is triggered only after the cells have been serialised, which for\n",
       "    // our purposes (turning an active figure into a static one), is too late.\n",
       "    var cells = IPython.notebook.get_cells();\n",
       "    var ncells = cells.length;\n",
       "    for (var i=0; i<ncells; i++) {\n",
       "        var cell = cells[i];\n",
       "        if (cell.cell_type === 'code'){\n",
       "            for (var j=0; j<cell.output_area.outputs.length; j++) {\n",
       "                var data = cell.output_area.outputs[j];\n",
       "                if (data.data) {\n",
       "                    // IPython >= 3 moved mimebundle to data attribute of output\n",
       "                    data = data.data;\n",
       "                }\n",
       "                if (data['text/html'] == html_output) {\n",
       "                    return [cell, data, j];\n",
       "                }\n",
       "            }\n",
       "        }\n",
       "    }\n",
       "}\n",
       "\n",
       "// Register the function which deals with the matplotlib target/channel.\n",
       "// The kernel may be null if the page has been refreshed.\n",
       "if (IPython.notebook.kernel != null) {\n",
       "    IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<img src=\"data:image/png;base64,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\" width=\"480\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(1)\n",
    "n = data.T[0]   # get values for horizontal axis (use transform of data array)\n",
    "height = data.T[1]\n",
    "plt.title(\"Figure 3.8 of Hughes & Hase, p. 33\",fontsize=14)\n",
    "plt.xlabel(\"Number of Counts, $N$\")\n",
    "plt.ylabel(\"Occurence\")\n",
    "plt.bar(n,height,align='center',alpha=0.5)  # alpha sets opacity so data will \n",
    "                                            # data will be visible later\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "Check that we have the correct number of trials:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "58"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ntrials = sum(height)\n",
    "ntrials"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "That was good.  Now calculate the total number of counts recorded.  Remember that multiplication of scipy arrays is \"element by element.\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "423"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sum(n*height)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "or equivalently"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "423"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sp.dot(n,height)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The mean count rate is the total number of counts divided by the total number of trials:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAH8AAAAPBAMAAAA/sQ3hAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nRU5ErkJggg==\n",
      "text/latex": [
       "$$7.29310344828$$"
      ],
      "text/plain": [
       "7.29310344828"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mean = sp.dot(n,height)/ntrials\n",
    "mean"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The easiest way to determine the probability of 5 counts or fewer is to use the CDF:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAIwAAAAPBAMAAADEyjp7AAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nZrtAtGPKlvvat1PW/JfxB6SN5qB9pARcAAAAAElFTkSuQmCC\n",
      "text/latex": [
       "$$0.264848929955$$"
      ],
      "text/plain": [
       "0.264848929955"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "prob = sp.stats.poisson.cdf(5,mean)\n",
    "prob"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The expected number of occurrences is the probability $\\times$ the number of experiments:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAH8AAAAPBAMAAAA/sQ3hAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nbck8VsZ1UQAAAABJRU5ErkJggg==\n",
      "text/latex": [
       "$$15.3612379374$$"
      ],
      "text/plain": [
       "15.3612379374"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "prob*ntrials"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The expected number of occurrences 20 or more is (1 - c.d.f(19)):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAALgAAAAPBAMAAACl0hg5AAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nkj7Op1RzUoChuxk+N8az4d26YGP2f+M/jRMBqZCNMW8AAAAASUVORK5CYII=\n",
      "text/latex": [
       "$$7.67424359367e-05$$"
      ],
      "text/plain": [
       "7.67424359367e-05"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "prob2 = 1 - sp.stats.poisson.cdf(19,mean)\n",
    "prob2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The expected number of occurrences 20 or more is the probability $\\times$ the number of experiments:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAKAAAAAPBAMAAACRq9klAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n",
      "text/latex": [
       "$$0.00445106128433$$"
      ],
      "text/plain": [
       "0.00445106128433"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "prob2*ntrials"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "CONCLUSION: We're not going to observe any runs with 20 or more counts.  If the mean is 7, that implies that $\\sigma=\\sqrt{7}$.  A detection of 20 counts would be $(20-7)/\\sqrt{7} = 4.9$\n",
    "standard deviations away from the mean."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x7f49edc1b828>"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y = sp.stats.poisson.pmf(n,mean)*ntrials\n",
    "plt.scatter(n,y,c='r')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Problem 3.8\n",
    "Another radioactive decay problem $\\implies$ another Poisson distribution problem.<br>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Use counts/min as units.  Then the mean count rate is just 270 (only 1 trial).\n",
    "So  \n",
    "\\begin{eqnarray*}\n",
    "\\overline{n} &=& 270 \\\\\n",
    "\\sigma &=& \\sqrt{270} \\\\\n",
    "\\alpha &=&\\frac{\\sigma}{\\sqrt{N}} = \\frac{\\sqrt{270}}{\\sqrt{1}} = 16.4\n",
    "\\end{eqnarray*}\n",
    "So the error in the mean count rate is $\\alpha = 16.4$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The fractional error is:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAIwAAAAPBAMAAADEyjp7AAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n",
      "text/latex": [
       "$$0.060858061945$$"
      ],
      "text/plain": [
       "0.060858061945"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sp.sqrt(270)/270"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Counting for 15 minutes should yield a count rate of $15\\times 270\\pm \\sqrt{15\\times 270}$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAANUAAAAUBAMAAADo2mWhAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nSUVORK5CYII=\n",
      "text/latex": [
       "$$\\left ( 4050, \\quad 63.6396103068\\right )$$"
      ],
      "text/plain": [
       "(4050, 63.6396103068)"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "15*270,sp.sqrt(15*270)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The mean of the distribution should be 4050.  The probability of getting exactly this value is given by the pmf:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAKAAAAAPBAMAAACRq9klAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAEJmJZjLNVN0i77ur\nRHZ72Yd1AAAACXBIWXMAAA7EAAAOxAGVKw4bAAACpUlEQVQ4Ea2UT0hUURTGf2/ejE/njw4JIRI6\nJLQog8HRVaATQRBEDbUNHKFoEcEsaudiIKiFQkNE0KpxJWHBFLSoFg2lBGI5bapVikJQC8uysdSa\nzjlXdy17MN/5zp/7vXvfOXdgV/8A+ph1TmY5x40DjyToDw7grfTVHJPAKS01UKJpiKSIjPdkMnQt\nHxT3PB0lTZo12F0L5b0qQzW8i+wjBC8dk6oxLVUIJtgJNlcINxqNLVLEC4TL+HkpMOuch8Qq8STR\nMrEUT7kEtxyD1ikpVdjTu8pO8HOFkOypGmRpyROrEkjOWXMSv8SNFon/YEH3fgg6HIObFyRg0CqL\nLE3L0Qq+HD/nV/CKtFVJrEuVWYNYWdymVRV8IoyFB/Q7BmkVNFBBS+M3VbTsA4nNpJ+lO0Xij/hm\nDdrODeq3pXmV+umlGvHGkaxjhEsiaIAKWppjTlBU59f64U6ayHdZbtag+yzRgkQW0l49yyQM1ZPb\nrAsRNFBBF/QWTVD2ht8YESHpuQmqNad7ldCECI7jNZLsTwavrt93jLQKGpigpX1MsFtWjL7fqP3r\nyEXCvyGUgp9wsnac1o2ksSAnggbSajmyBS87wY/yLap8mdBmBNtNCdbNac4TXoMleeVVEczeheGC\nsXZE0MAJavBw2gmOyWSUiKzLyBGWlzlrTrysOwxS3GZWVrz5CvGsstro3NzGawMnqMF3c3Pz9xbx\ntqSvIjOtAx3KCzNrEJFvWNbr9Ylh+YbIDmMlY1I2JT8DPfJ2MCoNjnyzHfIYrtGZ8+rOmsMLOgst\nVzK9Mttpb5K3SU44JlqbKqiggpaWERbBQAQTI4QXoX1lRjvqrDn+3hma5HIWoa83R+S5/jkok1vT\nmHYQmq0Ls6D/bEvunIwXZ3psgIX9x+cvt/4EK+mfM88AAAAASUVORK5CYII=\n",
      "text/latex": [
       "$$0.00626864416478$$"
      ],
      "text/plain": [
       "0.00626864416478"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sp.stats.poisson.pmf(4050,4050)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Problem 3.9\n",
    "\n",
    "Comparing Poisson distribution with mean of 35 to a normal distribution with a mean of 35 and a standard deviation of $\\sqrt{35}$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [],
   "source": [
    "mean = 35\n",
    "upper = 2*mean  # limit for graphs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/javascript": [
       "/* Put everything inside the global mpl namespace */\n",
       "window.mpl = {};\n",
       "\n",
       "\n",
       "mpl.get_websocket_type = function() {\n",
       "    if (typeof(WebSocket) !== 'undefined') {\n",
       "        return WebSocket;\n",
       "    } else if (typeof(MozWebSocket) !== 'undefined') {\n",
       "        return MozWebSocket;\n",
       "    } else {\n",
       "        alert('Your browser does not have WebSocket support.' +\n",
       "              'Please try Chrome, Safari or Firefox ≥ 6. ' +\n",
       "              'Firefox 4 and 5 are also supported but you ' +\n",
       "              'have to enable WebSockets in about:config.');\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure = function(figure_id, websocket, ondownload, parent_element) {\n",
       "    this.id = figure_id;\n",
       "\n",
       "    this.ws = websocket;\n",
       "\n",
       "    this.supports_binary = (this.ws.binaryType != undefined);\n",
       "\n",
       "    if (!this.supports_binary) {\n",
       "        var warnings = document.getElementById(\"mpl-warnings\");\n",
       "        if (warnings) {\n",
       "            warnings.style.display = 'block';\n",
       "            warnings.textContent = (\n",
       "                \"This browser does not support binary websocket messages. \" +\n",
       "                    \"Performance may be slow.\");\n",
       "        }\n",
       "    }\n",
       "\n",
       "    this.imageObj = new Image();\n",
       "\n",
       "    this.context = undefined;\n",
       "    this.message = undefined;\n",
       "    this.canvas = undefined;\n",
       "    this.rubberband_canvas = undefined;\n",
       "    this.rubberband_context = undefined;\n",
       "    this.format_dropdown = undefined;\n",
       "\n",
       "    this.image_mode = 'full';\n",
       "\n",
       "    this.root = $('<div/>');\n",
       "    this._root_extra_style(this.root)\n",
       "    this.root.attr('style', 'display: inline-block');\n",
       "\n",
       "    $(parent_element).append(this.root);\n",
       "\n",
       "    this._init_header(this);\n",
       "    this._init_canvas(this);\n",
       "    this._init_toolbar(this);\n",
       "\n",
       "    var fig = this;\n",
       "\n",
       "    this.waiting = false;\n",
       "\n",
       "    this.ws.onopen =  function () {\n",
       "            fig.send_message(\"supports_binary\", {value: fig.supports_binary});\n",
       "            fig.send_message(\"send_image_mode\", {});\n",
       "            if (mpl.ratio != 1) {\n",
       "                fig.send_message(\"set_dpi_ratio\", {'dpi_ratio': mpl.ratio});\n",
       "            }\n",
       "            fig.send_message(\"refresh\", {});\n",
       "        }\n",
       "\n",
       "    this.imageObj.onload = function() {\n",
       "            if (fig.image_mode == 'full') {\n",
       "                // Full images could contain transparency (where diff images\n",
       "                // almost always do), so we need to clear the canvas so that\n",
       "                // there is no ghosting.\n",
       "                fig.context.clearRect(0, 0, fig.canvas.width, fig.canvas.height);\n",
       "            }\n",
       "            fig.context.drawImage(fig.imageObj, 0, 0);\n",
       "        };\n",
       "\n",
       "    this.imageObj.onunload = function() {\n",
       "        this.ws.close();\n",
       "    }\n",
       "\n",
       "    this.ws.onmessage = this._make_on_message_function(this);\n",
       "\n",
       "    this.ondownload = ondownload;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_header = function() {\n",
       "    var titlebar = $(\n",
       "        '<div class=\"ui-dialog-titlebar ui-widget-header ui-corner-all ' +\n",
       "        'ui-helper-clearfix\"/>');\n",
       "    var titletext = $(\n",
       "        '<div class=\"ui-dialog-title\" style=\"width: 100%; ' +\n",
       "        'text-align: center; padding: 3px;\"/>');\n",
       "    titlebar.append(titletext)\n",
       "    this.root.append(titlebar);\n",
       "    this.header = titletext[0];\n",
       "}\n",
       "\n",
       "\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_canvas = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var canvas_div = $('<div/>');\n",
       "\n",
       "    canvas_div.attr('style', 'position: relative; clear: both; outline: 0');\n",
       "\n",
       "    function canvas_keyboard_event(event) {\n",
       "        return fig.key_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    canvas_div.keydown('key_press', canvas_keyboard_event);\n",
       "    canvas_div.keyup('key_release', canvas_keyboard_event);\n",
       "    this.canvas_div = canvas_div\n",
       "    this._canvas_extra_style(canvas_div)\n",
       "    this.root.append(canvas_div);\n",
       "\n",
       "    var canvas = $('<canvas/>');\n",
       "    canvas.addClass('mpl-canvas');\n",
       "    canvas.attr('style', \"left: 0; top: 0; z-index: 0; outline: 0\")\n",
       "\n",
       "    this.canvas = canvas[0];\n",
       "    this.context = canvas[0].getContext(\"2d\");\n",
       "\n",
       "    var backingStore = this.context.backingStorePixelRatio ||\n",
       "\tthis.context.webkitBackingStorePixelRatio ||\n",
       "\tthis.context.mozBackingStorePixelRatio ||\n",
       "\tthis.context.msBackingStorePixelRatio ||\n",
       "\tthis.context.oBackingStorePixelRatio ||\n",
       "\tthis.context.backingStorePixelRatio || 1;\n",
       "\n",
       "    mpl.ratio = (window.devicePixelRatio || 1) / backingStore;\n",
       "\n",
       "    var rubberband = $('<canvas/>');\n",
       "    rubberband.attr('style', \"position: absolute; left: 0; top: 0; z-index: 1;\")\n",
       "\n",
       "    var pass_mouse_events = true;\n",
       "\n",
       "    canvas_div.resizable({\n",
       "        start: function(event, ui) {\n",
       "            pass_mouse_events = false;\n",
       "        },\n",
       "        resize: function(event, ui) {\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "        stop: function(event, ui) {\n",
       "            pass_mouse_events = true;\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "    });\n",
       "\n",
       "    function mouse_event_fn(event) {\n",
       "        if (pass_mouse_events)\n",
       "            return fig.mouse_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    rubberband.mousedown('button_press', mouse_event_fn);\n",
       "    rubberband.mouseup('button_release', mouse_event_fn);\n",
       "    // Throttle sequential mouse events to 1 every 20ms.\n",
       "    rubberband.mousemove('motion_notify', mouse_event_fn);\n",
       "\n",
       "    rubberband.mouseenter('figure_enter', mouse_event_fn);\n",
       "    rubberband.mouseleave('figure_leave', mouse_event_fn);\n",
       "\n",
       "    canvas_div.on(\"wheel\", function (event) {\n",
       "        event = event.originalEvent;\n",
       "        event['data'] = 'scroll'\n",
       "        if (event.deltaY < 0) {\n",
       "            event.step = 1;\n",
       "        } else {\n",
       "            event.step = -1;\n",
       "        }\n",
       "        mouse_event_fn(event);\n",
       "    });\n",
       "\n",
       "    canvas_div.append(canvas);\n",
       "    canvas_div.append(rubberband);\n",
       "\n",
       "    this.rubberband = rubberband;\n",
       "    this.rubberband_canvas = rubberband[0];\n",
       "    this.rubberband_context = rubberband[0].getContext(\"2d\");\n",
       "    this.rubberband_context.strokeStyle = \"#000000\";\n",
       "\n",
       "    this._resize_canvas = function(width, height) {\n",
       "        // Keep the size of the canvas, canvas container, and rubber band\n",
       "        // canvas in synch.\n",
       "        canvas_div.css('width', width)\n",
       "        canvas_div.css('height', height)\n",
       "\n",
       "        canvas.attr('width', width * mpl.ratio);\n",
       "        canvas.attr('height', height * mpl.ratio);\n",
       "        canvas.attr('style', 'width: ' + width + 'px; height: ' + height + 'px;');\n",
       "\n",
       "        rubberband.attr('width', width);\n",
       "        rubberband.attr('height', height);\n",
       "    }\n",
       "\n",
       "    // Set the figure to an initial 600x600px, this will subsequently be updated\n",
       "    // upon first draw.\n",
       "    this._resize_canvas(600, 600);\n",
       "\n",
       "    // Disable right mouse context menu.\n",
       "    $(this.rubberband_canvas).bind(\"contextmenu\",function(e){\n",
       "        return false;\n",
       "    });\n",
       "\n",
       "    function set_focus () {\n",
       "        canvas.focus();\n",
       "        canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    window.setTimeout(set_focus, 100);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>')\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items) {\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) {\n",
       "            // put a spacer in here.\n",
       "            continue;\n",
       "        }\n",
       "        var button = $('<button/>');\n",
       "        button.addClass('ui-button ui-widget ui-state-default ui-corner-all ' +\n",
       "                        'ui-button-icon-only');\n",
       "        button.attr('role', 'button');\n",
       "        button.attr('aria-disabled', 'false');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "\n",
       "        var icon_img = $('<span/>');\n",
       "        icon_img.addClass('ui-button-icon-primary ui-icon');\n",
       "        icon_img.addClass(image);\n",
       "        icon_img.addClass('ui-corner-all');\n",
       "\n",
       "        var tooltip_span = $('<span/>');\n",
       "        tooltip_span.addClass('ui-button-text');\n",
       "        tooltip_span.html(tooltip);\n",
       "\n",
       "        button.append(icon_img);\n",
       "        button.append(tooltip_span);\n",
       "\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    var fmt_picker_span = $('<span/>');\n",
       "\n",
       "    var fmt_picker = $('<select/>');\n",
       "    fmt_picker.addClass('mpl-toolbar-option ui-widget ui-widget-content');\n",
       "    fmt_picker_span.append(fmt_picker);\n",
       "    nav_element.append(fmt_picker_span);\n",
       "    this.format_dropdown = fmt_picker[0];\n",
       "\n",
       "    for (var ind in mpl.extensions) {\n",
       "        var fmt = mpl.extensions[ind];\n",
       "        var option = $(\n",
       "            '<option/>', {selected: fmt === mpl.default_extension}).html(fmt);\n",
       "        fmt_picker.append(option)\n",
       "    }\n",
       "\n",
       "    // Add hover states to the ui-buttons\n",
       "    $( \".ui-button\" ).hover(\n",
       "        function() { $(this).addClass(\"ui-state-hover\");},\n",
       "        function() { $(this).removeClass(\"ui-state-hover\");}\n",
       "    );\n",
       "\n",
       "    var status_bar = $('<span class=\"mpl-message\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.request_resize = function(x_pixels, y_pixels) {\n",
       "    // Request matplotlib to resize the figure. Matplotlib will then trigger a resize in the client,\n",
       "    // which will in turn request a refresh of the image.\n",
       "    this.send_message('resize', {'width': x_pixels, 'height': y_pixels});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_message = function(type, properties) {\n",
       "    properties['type'] = type;\n",
       "    properties['figure_id'] = this.id;\n",
       "    this.ws.send(JSON.stringify(properties));\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_draw_message = function() {\n",
       "    if (!this.waiting) {\n",
       "        this.waiting = true;\n",
       "        this.ws.send(JSON.stringify({type: \"draw\", figure_id: this.id}));\n",
       "    }\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    var format_dropdown = fig.format_dropdown;\n",
       "    var format = format_dropdown.options[format_dropdown.selectedIndex].value;\n",
       "    fig.ondownload(fig, format);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_resize = function(fig, msg) {\n",
       "    var size = msg['size'];\n",
       "    if (size[0] != fig.canvas.width || size[1] != fig.canvas.height) {\n",
       "        fig._resize_canvas(size[0], size[1]);\n",
       "        fig.send_message(\"refresh\", {});\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_rubberband = function(fig, msg) {\n",
       "    var x0 = msg['x0'] / mpl.ratio;\n",
       "    var y0 = (fig.canvas.height - msg['y0']) / mpl.ratio;\n",
       "    var x1 = msg['x1'] / mpl.ratio;\n",
       "    var y1 = (fig.canvas.height - msg['y1']) / mpl.ratio;\n",
       "    x0 = Math.floor(x0) + 0.5;\n",
       "    y0 = Math.floor(y0) + 0.5;\n",
       "    x1 = Math.floor(x1) + 0.5;\n",
       "    y1 = Math.floor(y1) + 0.5;\n",
       "    var min_x = Math.min(x0, x1);\n",
       "    var min_y = Math.min(y0, y1);\n",
       "    var width = Math.abs(x1 - x0);\n",
       "    var height = Math.abs(y1 - y0);\n",
       "\n",
       "    fig.rubberband_context.clearRect(\n",
       "        0, 0, fig.canvas.width, fig.canvas.height);\n",
       "\n",
       "    fig.rubberband_context.strokeRect(min_x, min_y, width, height);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_figure_label = function(fig, msg) {\n",
       "    // Updates the figure title.\n",
       "    fig.header.textContent = msg['label'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_cursor = function(fig, msg) {\n",
       "    var cursor = msg['cursor'];\n",
       "    switch(cursor)\n",
       "    {\n",
       "    case 0:\n",
       "        cursor = 'pointer';\n",
       "        break;\n",
       "    case 1:\n",
       "        cursor = 'default';\n",
       "        break;\n",
       "    case 2:\n",
       "        cursor = 'crosshair';\n",
       "        break;\n",
       "    case 3:\n",
       "        cursor = 'move';\n",
       "        break;\n",
       "    }\n",
       "    fig.rubberband_canvas.style.cursor = cursor;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_message = function(fig, msg) {\n",
       "    fig.message.textContent = msg['message'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_draw = function(fig, msg) {\n",
       "    // Request the server to send over a new figure.\n",
       "    fig.send_draw_message();\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_image_mode = function(fig, msg) {\n",
       "    fig.image_mode = msg['mode'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Called whenever the canvas gets updated.\n",
       "    this.send_message(\"ack\", {});\n",
       "}\n",
       "\n",
       "// A function to construct a web socket function for onmessage handling.\n",
       "// Called in the figure constructor.\n",
       "mpl.figure.prototype._make_on_message_function = function(fig) {\n",
       "    return function socket_on_message(evt) {\n",
       "        if (evt.data instanceof Blob) {\n",
       "            /* FIXME: We get \"Resource interpreted as Image but\n",
       "             * transferred with MIME type text/plain:\" errors on\n",
       "             * Chrome.  But how to set the MIME type?  It doesn't seem\n",
       "             * to be part of the websocket stream */\n",
       "            evt.data.type = \"image/png\";\n",
       "\n",
       "            /* Free the memory for the previous frames */\n",
       "            if (fig.imageObj.src) {\n",
       "                (window.URL || window.webkitURL).revokeObjectURL(\n",
       "                    fig.imageObj.src);\n",
       "            }\n",
       "\n",
       "            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
       "                evt.data);\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "        else if (typeof evt.data === 'string' && evt.data.slice(0, 21) == \"data:image/png;base64\") {\n",
       "            fig.imageObj.src = evt.data;\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        var msg = JSON.parse(evt.data);\n",
       "        var msg_type = msg['type'];\n",
       "\n",
       "        // Call the  \"handle_{type}\" callback, which takes\n",
       "        // the figure and JSON message as its only arguments.\n",
       "        try {\n",
       "            var callback = fig[\"handle_\" + msg_type];\n",
       "        } catch (e) {\n",
       "            console.log(\"No handler for the '\" + msg_type + \"' message type: \", msg);\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        if (callback) {\n",
       "            try {\n",
       "                // console.log(\"Handling '\" + msg_type + \"' message: \", msg);\n",
       "                callback(fig, msg);\n",
       "            } catch (e) {\n",
       "                console.log(\"Exception inside the 'handler_\" + msg_type + \"' callback:\", e, e.stack, msg);\n",
       "            }\n",
       "        }\n",
       "    };\n",
       "}\n",
       "\n",
       "// from http://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas\n",
       "mpl.findpos = function(e) {\n",
       "    //this section is from http://www.quirksmode.org/js/events_properties.html\n",
       "    var targ;\n",
       "    if (!e)\n",
       "        e = window.event;\n",
       "    if (e.target)\n",
       "        targ = e.target;\n",
       "    else if (e.srcElement)\n",
       "        targ = e.srcElement;\n",
       "    if (targ.nodeType == 3) // defeat Safari bug\n",
       "        targ = targ.parentNode;\n",
       "\n",
       "    // jQuery normalizes the pageX and pageY\n",
       "    // pageX,Y are the mouse positions relative to the document\n",
       "    // offset() returns the position of the element relative to the document\n",
       "    var x = e.pageX - $(targ).offset().left;\n",
       "    var y = e.pageY - $(targ).offset().top;\n",
       "\n",
       "    return {\"x\": x, \"y\": y};\n",
       "};\n",
       "\n",
       "/*\n",
       " * return a copy of an object with only non-object keys\n",
       " * we need this to avoid circular references\n",
       " * http://stackoverflow.com/a/24161582/3208463\n",
       " */\n",
       "function simpleKeys (original) {\n",
       "  return Object.keys(original).reduce(function (obj, key) {\n",
       "    if (typeof original[key] !== 'object')\n",
       "        obj[key] = original[key]\n",
       "    return obj;\n",
       "  }, {});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.mouse_event = function(event, name) {\n",
       "    var canvas_pos = mpl.findpos(event)\n",
       "\n",
       "    if (name === 'button_press')\n",
       "    {\n",
       "        this.canvas.focus();\n",
       "        this.canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    var x = canvas_pos.x * mpl.ratio;\n",
       "    var y = canvas_pos.y * mpl.ratio;\n",
       "\n",
       "    this.send_message(name, {x: x, y: y, button: event.button,\n",
       "                             step: event.step,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "\n",
       "    /* This prevents the web browser from automatically changing to\n",
       "     * the text insertion cursor when the button is pressed.  We want\n",
       "     * to control all of the cursor setting manually through the\n",
       "     * 'cursor' event from matplotlib */\n",
       "    event.preventDefault();\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    // Handle any extra behaviour associated with a key event\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.key_event = function(event, name) {\n",
       "\n",
       "    // Prevent repeat events\n",
       "    if (name == 'key_press')\n",
       "    {\n",
       "        if (event.which === this._key)\n",
       "            return;\n",
       "        else\n",
       "            this._key = event.which;\n",
       "    }\n",
       "    if (name == 'key_release')\n",
       "        this._key = null;\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.which != 17)\n",
       "        value += \"ctrl+\";\n",
       "    if (event.altKey && event.which != 18)\n",
       "        value += \"alt+\";\n",
       "    if (event.shiftKey && event.which != 16)\n",
       "        value += \"shift+\";\n",
       "\n",
       "    value += 'k';\n",
       "    value += event.which.toString();\n",
       "\n",
       "    this._key_event_extra(event, name);\n",
       "\n",
       "    this.send_message(name, {key: value,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onclick = function(name) {\n",
       "    if (name == 'download') {\n",
       "        this.handle_save(this, null);\n",
       "    } else {\n",
       "        this.send_message(\"toolbar_button\", {name: name});\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onmouseover = function(tooltip) {\n",
       "    this.message.textContent = tooltip;\n",
       "};\n",
       "mpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home icon-home\", \"home\"], [\"Back\", \"Back to  previous view\", \"fa fa-arrow-left icon-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right icon-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Pan axes with left mouse, zoom with right\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
       "\n",
       "mpl.extensions = [\"eps\", \"jpeg\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\", \"tif\"];\n",
       "\n",
       "mpl.default_extension = \"png\";var comm_websocket_adapter = function(comm) {\n",
       "    // Create a \"websocket\"-like object which calls the given IPython comm\n",
       "    // object with the appropriate methods. Currently this is a non binary\n",
       "    // socket, so there is still some room for performance tuning.\n",
       "    var ws = {};\n",
       "\n",
       "    ws.close = function() {\n",
       "        comm.close()\n",
       "    };\n",
       "    ws.send = function(m) {\n",
       "        //console.log('sending', m);\n",
       "        comm.send(m);\n",
       "    };\n",
       "    // Register the callback with on_msg.\n",
       "    comm.on_msg(function(msg) {\n",
       "        //console.log('receiving', msg['content']['data'], msg);\n",
       "        // Pass the mpl event to the overriden (by mpl) onmessage function.\n",
       "        ws.onmessage(msg['content']['data'])\n",
       "    });\n",
       "    return ws;\n",
       "}\n",
       "\n",
       "mpl.mpl_figure_comm = function(comm, msg) {\n",
       "    // This is the function which gets called when the mpl process\n",
       "    // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
       "\n",
       "    var id = msg.content.data.id;\n",
       "    // Get hold of the div created by the display call when the Comm\n",
       "    // socket was opened in Python.\n",
       "    var element = $(\"#\" + id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm)\n",
       "\n",
       "    function ondownload(figure, format) {\n",
       "        window.open(figure.imageObj.src);\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy,\n",
       "                           ondownload,\n",
       "                           element.get(0));\n",
       "\n",
       "    // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n",
       "    // web socket which is closed, not our websocket->open comm proxy.\n",
       "    ws_proxy.onopen();\n",
       "\n",
       "    fig.parent_element = element.get(0);\n",
       "    fig.cell_info = mpl.find_output_cell(\"<div id='\" + id + \"'></div>\");\n",
       "    if (!fig.cell_info) {\n",
       "        console.error(\"Failed to find cell for figure\", id, fig);\n",
       "        return;\n",
       "    }\n",
       "\n",
       "    var output_index = fig.cell_info[2]\n",
       "    var cell = fig.cell_info[0];\n",
       "\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function(fig, msg) {\n",
       "    var width = fig.canvas.width/mpl.ratio\n",
       "    fig.root.unbind('remove')\n",
       "\n",
       "    // Update the output cell to use the data from the current canvas.\n",
       "    fig.push_to_output();\n",
       "    var dataURL = fig.canvas.toDataURL();\n",
       "    // Re-enable the keyboard manager in IPython - without this line, in FF,\n",
       "    // the notebook keyboard shortcuts fail.\n",
       "    IPython.keyboard_manager.enable()\n",
       "    $(fig.parent_element).html('<img src=\"' + dataURL + '\" width=\"' + width + '\">');\n",
       "    fig.close_ws(fig, msg);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.close_ws = function(fig, msg){\n",
       "    fig.send_message('closing', msg);\n",
       "    // fig.ws.close()\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.push_to_output = function(remove_interactive) {\n",
       "    // Turn the data on the canvas into data in the output cell.\n",
       "    var width = this.canvas.width/mpl.ratio\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] = '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Tell IPython that the notebook contents must change.\n",
       "    IPython.notebook.set_dirty(true);\n",
       "    this.send_message(\"ack\", {});\n",
       "    var fig = this;\n",
       "    // Wait a second, then push the new image to the DOM so\n",
       "    // that it is saved nicely (might be nice to debounce this).\n",
       "    setTimeout(function () { fig.push_to_output() }, 1000);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>')\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items){\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) { continue; };\n",
       "\n",
       "        var button = $('<button class=\"btn btn-default\" href=\"#\" title=\"' + name + '\"><i class=\"fa ' + image + ' fa-lg\"></i></button>');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = $('<span class=\"mpl-message\" style=\"text-align:right; float: right;\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = $('<div class=\"btn-group inline pull-right\"></div>');\n",
       "    var button = $('<button class=\"btn btn-mini btn-primary\" href=\"#\" title=\"Stop Interaction\"><i class=\"fa fa-power-off icon-remove icon-large\"></i></button>');\n",
       "    button.click(function (evt) { fig.handle_close(fig, {}); } );\n",
       "    button.mouseover('Stop Interaction', toolbar_mouse_event);\n",
       "    buttongrp.append(button);\n",
       "    var titlebar = this.root.find($('.ui-dialog-titlebar'));\n",
       "    titlebar.prepend(buttongrp);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(el){\n",
       "    var fig = this\n",
       "    el.on(\"remove\", function(){\n",
       "\tfig.close_ws(fig, {});\n",
       "    });\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(el){\n",
       "    // this is important to make the div 'focusable\n",
       "    el.attr('tabindex', 0)\n",
       "    // reach out to IPython and tell the keyboard manager to turn it's self\n",
       "    // off when our div gets focus\n",
       "\n",
       "    // location in version 3\n",
       "    if (IPython.notebook.keyboard_manager) {\n",
       "        IPython.notebook.keyboard_manager.register_events(el);\n",
       "    }\n",
       "    else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\n",
       "    }\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    var manager = IPython.notebook.keyboard_manager;\n",
       "    if (!manager)\n",
       "        manager = IPython.keyboard_manager;\n",
       "\n",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which == 13) {\n",
       "        this.canvas_div.blur();\n",
       "        // select the cell after this one\n",
       "        var index = IPython.notebook.find_cell_index(this.cell_info[0]);\n",
       "        IPython.notebook.select(index + 1);\n",
       "    }\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    fig.ondownload(fig, null);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.find_output_cell = function(html_output) {\n",
       "    // Return the cell and output element which can be found *uniquely* in the notebook.\n",
       "    // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n",
       "    // IPython event is triggered only after the cells have been serialised, which for\n",
       "    // our purposes (turning an active figure into a static one), is too late.\n",
       "    var cells = IPython.notebook.get_cells();\n",
       "    var ncells = cells.length;\n",
       "    for (var i=0; i<ncells; i++) {\n",
       "        var cell = cells[i];\n",
       "        if (cell.cell_type === 'code'){\n",
       "            for (var j=0; j<cell.output_area.outputs.length; j++) {\n",
       "                var data = cell.output_area.outputs[j];\n",
       "                if (data.data) {\n",
       "                    // IPython >= 3 moved mimebundle to data attribute of output\n",
       "                    data = data.data;\n",
       "                }\n",
       "                if (data['text/html'] == html_output) {\n",
       "                    return [cell, data, j];\n",
       "                }\n",
       "            }\n",
       "        }\n",
       "    }\n",
       "}\n",
       "\n",
       "// Register the function which deals with the matplotlib target/channel.\n",
       "// The kernel may be null if the page has been refreshed.\n",
       "if (IPython.notebook.kernel != null) {\n",
       "    IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<img src=\"data:image/png;base64,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\" width=\"480\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x1 = sp.linspace(0,upper,upper+1)\n",
    "y1 = sp.stats.poisson.pmf(x1,mean)\n",
    "x2 = sp.linspace(0,upper,500)\n",
    "y2 = sp.stats.norm.pdf(x2,mean,sp.sqrt(mean))\n",
    "plt.figure(2)\n",
    "plt.xlim(0,upper)\n",
    "plt.axhline(0)\n",
    "plt.scatter(x1,y1)\n",
    "plt.plot(x2,y2);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "### Version details\n",
    "\n",
    "`version_information` is from J.R. Johansson (jrjohansson at gmail.com)<br>\n",
    "See Introduction to scientific computing with Python:<br>\n",
    "http://nbviewer.jupyter.org/github/jrjohansson/scientific-python-lectures/blob/master/Lecture-0-Scientific-Computing-with-Python.ipynb <br>\n",
    "for more information and instructions for package installation.<br>\n",
    "\n",
    "If `version_information` has been installed system wide (as it has been on linuxremotes), continue with next cell as written.  If not, comment out top line in next cell and uncomment the second line."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Loading extensions from ~/.ipython/extensions is deprecated. We recommend managing extensions like any other Python packages, in site-packages.\n"
     ]
    }
   ],
   "source": [
    "%load_ext version_information\n",
    "\n",
    "#%install_ext http://raw.github.com/jrjohansson/version_information/master/version_information.py"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/json": {
       "Software versions": [
        {
         "module": "Python",
         "version": "3.6.1 64bit [GCC 4.4.7 20120313 (Red Hat 4.4.7-1)]"
        },
        {
         "module": "IPython",
         "version": "6.1.0"
        },
        {
         "module": "OS",
         "version": "Linux 3.10.0 327.36.3.el7.x86_64 x86_64 with redhat 7.2 Maipo"
        },
        {
         "module": "scipy",
         "version": "0.19.1"
        },
        {
         "module": "matplotlib",
         "version": "2.0.2"
        },
        {
         "module": "sympy",
         "version": "1.1"
        }
       ]
      },
      "text/html": [
       "<table><tr><th>Software</th><th>Version</th></tr><tr><td>Python</td><td>3.6.1 64bit [GCC 4.4.7 20120313 (Red Hat 4.4.7-1)]</td></tr><tr><td>IPython</td><td>6.1.0</td></tr><tr><td>OS</td><td>Linux 3.10.0 327.36.3.el7.x86_64 x86_64 with redhat 7.2 Maipo</td></tr><tr><td>scipy</td><td>0.19.1</td></tr><tr><td>matplotlib</td><td>2.0.2</td></tr><tr><td>sympy</td><td>1.1</td></tr><tr><td colspan='2'>Tue Aug 01 11:08:17 2017 EDT</td></tr></table>"
      ],
      "text/latex": [
       "\\begin{tabular}{|l|l|}\\hline\n",
       "{\\bf Software} & {\\bf Version} \\\\ \\hline\\hline\n",
       "Python & 3.6.1 64bit [GCC 4.4.7 20120313 (Red Hat 4.4.7-1)] \\\\ \\hline\n",
       "IPython & 6.1.0 \\\\ \\hline\n",
       "OS & Linux 3.10.0 327.36.3.el7.x86\\_64 x86\\_64 with redhat 7.2 Maipo \\\\ \\hline\n",
       "scipy & 0.19.1 \\\\ \\hline\n",
       "matplotlib & 2.0.2 \\\\ \\hline\n",
       "sympy & 1.1 \\\\ \\hline\n",
       "\\hline \\multicolumn{2}{|l|}{Tue Aug 01 11:08:17 2017 EDT} \\\\ \\hline\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "Software versions\n",
       "Python 3.6.1 64bit [GCC 4.4.7 20120313 (Red Hat 4.4.7-1)]\n",
       "IPython 6.1.0\n",
       "OS Linux 3.10.0 327.36.3.el7.x86_64 x86_64 with redhat 7.2 Maipo\n",
       "scipy 0.19.1\n",
       "matplotlib 2.0.2\n",
       "sympy 1.1\n",
       "Tue Aug 01 11:08:17 2017 EDT"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "version_information scipy, matplotlib, sympy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}