Lecture2.ipynb

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   "cell_type": "markdown",
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   "source": [
    "# Lecture 2, Solving ODE's\n",
    "\n",
    "There are a number of question marks \"?\" throughout the markdown section of this notebook. You are responsible for filling those sections in. \n",
    "\n",
    "**MORE TESTS**\n",
    "**Overview:**\n",
    "* Solving initial value problems, a simple example\n",
    "* Survey of methods.\n",
    "* Errors and numerical stability\n",
    "    * Reading: Newman chapter 4.\n",
    "\n",
    "**Next Lecture:** Solving systems of coupled ODE's and Newtons 2nd law.\n",
    "\n",
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Simple Example, an RC circuit. \n",
    "We have a simple RC circuit, as shown below. After a long charge with the switch in position 1 it is flipped to position 2. What is the time dependence of the charge across $C$?\n",
    "\n",
    "$$Q(t)=CVe^{-t/RC}$$\n",
    "\n",
    "![RC circuit](./figs/Lecture2_circuit.png)\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Using Kirchoff's laws, determine the 1st order ODE we need to solve for $Q(t)$:\n",
    "\n",
    "$$\\frac{dQ}{dt} = \\frac{Q}{RC} $$\n",
    "\n",
    "What is the closed form solution of this equation:\n",
    "$$ Q(t) = CVe^{-t/RC} $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this case the problem was easy to solve. However, there are many cases of such problems, formulated as ordinary differential equations, where the solution is not so easy (or even impossible) to find. So how might we approximate the solution to this problem and solve numerically?\n",
    "\n",
    "An obvious thing to try is to Taylor expand $Q(t)$ for small $\\Delta t$ around $t=0$\n",
    "\n",
    "$$ Q(\\Delta t) = Q(0) + \\frac{dQ}{dt}\\Delta t + \\frac{1}{2}\\frac{d^2Q}{dt^2}(\\Delta t)^2 + \\dots $$\n",
    "\n",
    "If $\\Delta t$ is very small, then it is usually a good approximation to ignore terms that involve second and higher powers of $\\Delta t$\n",
    "\n",
    "$$ Q(\\Delta t) \\approx Q(0) + \\frac{dQ}{dt}\\Delta t$$\n",
    "\n",
    "and we know the functional form of the derivative. It is given by the original ODE! We now have:\n",
    "\n",
    "$$ Q(t + \\Delta t) \\approx Q(t) - Q'(t) \\Delta t $$\n",
    "\n",
    "This is the general strategy for solving ODE's on a computer. By Taylor expanding we have taken a problem defined on a continuous variable $t$, and transformed it to an approximate problem defined on a discrete variable $\\Delta t$. This is always necessary since computers only operate on discrete quantities.\n",
    "\n",
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Methods for ODE's\n",
    "\n",
    "To understand our approximate methods, we work with a single ordinary differential equation.\n",
    "$$\\frac{dx}{dt}=g(x,t)$$\n",
    "where $x(t)$ is the solution we seek and $g(x,t)$ is a well-behaved but otherwise arbitrary function.\n",
    "\n",
    "If we know $x(t)$ we could determine $g(t+\\Delta t)$ from the Taylor series:\n",
    "$$x(t+\\Delta t) = x(t) + \\frac{dx}{dt}\\Delta t + \\frac{d^2x}{dt^2}\\frac{(\\Delta t)^2}{2!} + \\frac{d^3x}{dt^3}\\frac{\\Delta t^2}{3!} + \\dots$$\n",
    "\n",
    "## Euler's method\n",
    "\n",
    "$$x(t_{n+1}) = x(t_{n}) + g(x_n,t_n)\\Delta t +O[(\\Delta t)^2].$$\n",
    "\n",
    "where $x_n$ is the the value of our solution at time point $t_n$ and discrete step $n$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Improved accuracy: Runge-Kutta methods\n",
    "\n",
    "### RK2:\n",
    "\n",
    "$$\n",
    "\\begin{align}\n",
    "k_1 &= g(x_n, t_n)\\,\\Delta t\\\\\n",
    "k_2 &= g(x_n+\\tfrac{1}{2}k_1, t_n+\\tfrac{1}{2}\\Delta t)\\,\\Delta t \\\\\n",
    "x(t_{n+1}) &= x(t_n) + k_2\n",
    "\\end{align}\n",
    "$$\n",
    "\n",
    "\n",
    "### RK4:\n",
    "\n",
    "$$\n",
    "\\begin{align}\n",
    "k_1 &= g(x_n, t_n)\\,\\Delta t \\\\\n",
    "k_2 &= g(x_n+\\tfrac{1}{2}k_1, t_n+\\tfrac{1}{2}\\Delta t)\\,\\Delta t \\\\\n",
    "k_3 &= g(x_n+\\tfrac{1}{2}k_2, t_n+\\tfrac{1}{2}\\Delta t)\\,\\Delta t\\\\\n",
    "k_4 &= g(x_n+k_3, t_n+\\Delta t)\\,\\Delta t\\\\\n",
    "x(t_{n+1}) &= x(t_n) + \\tfrac{1}{6}(k_1+2k_2+2k_3+k_4)\n",
    "\\end{align}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "***\n",
    "## Pseudocode (for all methods):\n",
    "### Initialization\n",
    "* Assign initial values and constants: $x\\left(0\\right)$, $\\Delta t$, any constants in $g(x,t)$.\n",
    "* Set the number of time steps and the initial value of time.\n",
    "\n",
    "### Calculation\n",
    "* At time step $x_i$, calculate $x_{i+1}$ and $t_{i+1}$ at step $i+1$.\n",
    "* Increase to $t_i$ to the next time step $t_{i+1} = t_i + \\Delta t$.\n",
    "* repeat for $n-1$ time steps.\n",
    "\n",
    "### Analysis\n",
    "* store the values for $x_i$ and $t_i$ in a file. \n",
    "* plot results or use in subsequent calculation.\n",
    "\n",
    "***"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Exercise\n",
    "\n",
    "1. Define a function for the exact solution of our simple RC circuit, $Q(t)$. This will be used to test the accuracy of our numerical methods. \n",
    "\n",
    "2. Define another function to find the solution of our differential equation numerically using an RK2 method.\n",
    "\n",
    "3. Using the functions in 1 and 2, plot the exact and approximate solutions over-top of each other for the range of time from $t$ = 0 to 10, and using the parameters: $R=1$, $C=1$, $Q_0=1$, and $\\Delta t$ = 0.1 .\n",
    "\n",
    "4. Finally, create a function to calculate and then plot the total cumulative error of our approximation as a function of the step size $\\Delta t$ from $\\Delta t$ = 0.001 to 10 over a time from $t$ = 0 to 10. How does this plot change with increasing final time?\n",
    "\n",
    "\n",
    "\n",
    "**You will find some starter code in the cells below**\n"
   ]
  },
  {
   "cell_type": "code",
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   "execution_count": 5,
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   "execution_count": 9,
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   "metadata": {},
   "outputs": [],
   "source": [
    "# it is good practice to include all import statements in the first code cell at the top of your workbook or script.\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# this is a so called \"magic\" function that allows for interactive plotting, \n",
    "# you will see below when we plot the results\n",
    "%matplotlib notebook  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "#  Modify this function to output the exact solution for Q(t) from above\n",
    "# Q0 and t0 are the initial charge and time\n",
    "\n",
    "# Note the default argument for t0 = 0. Using this means we only have to pass a value for t0 to the function\n",
    "# if we want something different from 0\n",
    "\n",
    "def exact(t, R, C, Q0, t0 =0.0):\n",
    "    # !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! exact solution here  !!!!!!!!!!!!!!!!!!!!!!!!!!!!!\n",
    "    Q = Q0*np.exp(-t/R/C)\n",
    "    return Q"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Modify this function to implement an RK2 method for our RC circuit ODE\n",
    "\n",
    "# note the template here is for one way to do this, and not necessarily the best way.\n",
    "# I encourage you to try and think of a better and more general way to write this Euler method function.\n",
    "\n",
    "def approx_rk2(dt, t_final, R, C, Q0, t0=0.0):\n",
    "    \n",
    "    # initialize an empty list of Q values.\n",
    "    q_vals = np.array([Q0])\n",
    "    \n",
    "    # initialize time steps - not including t_final.\n",
    "    t_vals = np.arange(t0,t_final,dt)\n",
    "    \n",
    "    for t in t_vals:\n",
    "        q_prev = q_vals[-1] # define q_prev as the previous Q_n.\n",
    "        g1 = -q_prev/R/C # define g(x,t) for k1.       \n",
    "        k1 = g1*dt # k1 definition\n",
    "        \n",
    "        q_prev2 = q_prev + 0.5*k1 # define new input for k2.\n",
    "        g2 = -q_prev2/R/C # define g(x,t) for k2.\n",
    "        k2 = g2*dt\n",
    "        \n",
    "        q_new = q_prev + k2 # Define Q_{n+1}\n",
    "        q_vals = np.append(q_vals,q_new)\n",
    "    \n",
    "    # add final t_final value to t_vals.\n",
    "    t_vals = np.append(t_vals,t_final)\n",
    "   \n",
    "    return t_vals, q_vals"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Define our constants\n",
    "Q0, t0 = 10, 0.0\n",
    "t_final, dt = 10, 0.1\n",
    "R, C = 1, 1 \n",
    "\n",
    "#create an array with 1000 equally spaced points spanning t0 to _final to pass to our exact expression\n",
    "t = np.linspace(t0,t_final,1000) \n",
    "\n",
    "# Calculate the exact solution\n",
    "Q_exact = exact(t,R,C,Q0)\n",
    "\n",
    "#Call our  approximate function, this returns function values and time points \n",
    "t_approx, Q_approx = approx_rk2(dt,t_final,R,C,Q0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Capacitor Charge as Function of Time')"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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JTJw4kfPOO49rr72WY8eOcd1113H66aczYMAA5s6dC8Cjjz7K9ddfD8Dq1avp06cPR44cYfr06dx6660ATJgwgZtvvpnRo0fTuXNn5s+fz/XXX89pp53GhAkTTsR98803k52dTe/evZk0aRLgDIq3bds2Ro8ezejRowF49913GTJkCAMHDuSSSy7h0KEofKFV1Vr/M2jQIK2WLZ/osUkZGpjURPXXrVS3fFK94xljdO3atZV7wpZPnP+/yU1r9P9wz549qqp65MgR7d27t+7evVsBff7551VV9f7779cf/ehHqqo6cuRIveGGG1RVdf78+dq7d29VVZ00aZIOHDhQjxw5oqqqjzzyiE6YMEFVVdetW6eZmZl69OhRDQaDOnz4cJ09e7YOGjRIP/zwQ1VVnTZt2okyxo8fr5dddpmGQiH95z//qenp6frZZ59pMBjUgQMH6sqVK0+KOxAI6MiRI/XTTz9VVdWOHTtqYWGhqqoWFhbq8OHD9dChQ6qqOmXKFL3//vvLfB/K+jyAZRrBOTYhrgjIXUgSxfgJoTZtpTHeyF3oTBurwRqdPvbxxx+nX79+DB48+MTQ0j6f78SYQVdffTUffvjhif2vuMIZGHnEiBEcOHCAffv2AU71Tv369QH48MMPueaaawDo2bMnHTt2ZMOGDfh8PqZPn84111zDyJEjGTZsWJkxXXjhhYgIp59+Oq1ateL000/H5/PRu3dvcnNzAXj55ZcZOHAgAwYMYM2aNaxdu/Ybx1m8eDFr165l2LBh9O/fnxkzZpCXl1cj71u4WE9M442s4agvhUCwCF9SMmLTVhoTe1nDwZ/iJIEamj62vKGlSwsfZrr0kNMl6w0bNjzxmFbQ1Xzjxo2kpaWxbdu2cvepV68eAD6f78RyyXogEGDz5s088sgjLF26lKZNmzJhwoQy41ZVzj33XF544YVyy6oJiXFFkJnDhrGzeDRwCStHzbRpK43xQmYOjJ8DZ//S+V0D/4flDS0dCoV49dVXAfj73//OWWeddeI5L730EuB862/cuDGNGzf+xnFHjBjBrFmzANiwYQNbtmyhR48e7N+/n9tuu40FCxawZ8+eE2VU1oEDB2jYsCGNGzdm586dvP322ye2hQ9/PXjwYBYtWsSmTZsAZ56FDRs2VKnMiiTGFQHQ7vSRPDH7OOmBrgzyOhhjElVmTo1+ERs7dixPPvkkffv2pUePHieGlm7YsCFr1qxh0KBBNG7c+MTJH6Bp06YMHTqUAwcO8Oyzz5Z53FtuuYWbbrqJ008/naSkJKZPn069evW4+eabueWWW+jevTvPPPMMo0ePZsSIEZWOu1+/fgwYMIDevXvTuXPnk6qYJk6cyPnnn0+bNm2YO3cu06dP54orruD4cec+qAcffJDu3btXusyKxP0w1OGGPvQBZ3Rqxp8uH1ADURmT2GrzMNRpaWll9q4ZNWoUjzzyCNnZpxyZuc6xYagj1KN1Ov/dYcNRG2NMuISpGgLo0boRH27aTXEwRLI/oXKgMQmlvL728+bNi20gdURCnQ17tk6nOKh8WXjY61CMiQt1oWo5EVT3c0ioRNCjdToA63cc8DgSY+q+1NRU9uzZY8nAY6rKnj17SE1NrfIxEqpqqEtGGkk+sXYCY2pA+/btKSgoODF8g/FOamoq7du3r/LzEyoRpCT56JKRZonAmBqQnJxMp06dvA7D1ICEqhoCp3povSUCY4w5ISETwdZ9RzlwrNjrUIwxplZIuETQ020w3mBXBcYYAyRgIjitTSMA1m63nkPGGAMJmAjaNE5lVIPNZKz6i01SY4wxJGAikIKl/E0f4LydT8OMcZYMjDEJL+ESAbkLSVabpMYYY0p4kghE5A4RWSMin4vICyJS9VviKitrOOpPIaA+1JdcI5NjGGNMXRbzRCAi7YCfANmq2gfwA5fHLIDMHHZc/BKPBi5h7plP2yQ1xpiE59WdxUlAfREpBhoA5c/5FgVteo9khv8Yh4+2Z0wsCzbGmFrolIlARHxAP6AtcBRYo6o7q1qgqm4VkUeALe7x3lXVd8sodyIwEaBDhw5VLa5MPp/Qq20jPt9mXUiNMabcqiER6SIiU4FNwBTgCuAW4D0RWSwi17lJolJEpClwEdAJJ7k0FJGrS++nqlNVNVtVszMyMipbzCn1btuYddsPEAzZyInGmMRW0Yn8QeB5oIuqfktVr1bV76tqX2Ac0Bi4pgplngNsVtVCVS0GZgNDq3CcaundthFHioLk7rG5CYwxia3cqiFVvaKCbbuAx6pY5hZgsIg0wKkaGgNUf0LiSurdtjEAn2/dT5eMtFgXb4wxtcYpq3ZE5BIRSXeX7xOR2SIysKoFquonwKvACmC1G8PUqh6vqrq1SiPF72OttRMYYxJcJHX8v1LVgyJyFvAtYAbw1+oUqqqTVLWnqvZR1WtU9Xh1jlcVyX4fPVqns8YSgTEmwUWSCILu728Df1XV14GU6IUUO73bNuLzbfttqj1jTEKLJBFsFZG/AZcCb4lIvQifV+v1adeYfUeKKfjqqNehGGOMZyI5oV8K/BsYq6r7gGbA3VGNKkb6ZzYB4NOCfR5HYowx3okkEfxNVWer6kYAVd1O1bqN1jo9WqeTk7SJhp/8yUYhNcYkrEgSQe/wFRHxA4OiE05sJW9bxnNJDzJi61QbktoYk7AqurP45yJyEOgrIgfcn4PALuD1mEUYTbkLSSZgQ1IbYxJauYlAVR9S1XTgYVVt5P6kq2pzVf15DGOMnqzhhHw2JLUxJrGVe2exiPRU1fXAK2XdQKaqK6IaWSxk5lD4nZd57sVZDBh6AefakNTGmARU0eijd+KM/vmHMrYpcHZUIoqx1n1GMCvlOF8dbs25XgdjjDEeqGisoYnu79GxCyf2RIR+mU1Ylb/f61CMMcYTEU1MIyJDgazw/VV1ZpRiirn+7Rvzl3lfcKQoQIMUr+bqMcYYb0QyMc1zQBdgFV8PN6FA3CSCfplNCIaUNdsOcEZWM6/DMcaYmIrk62820EvjeECevu3dO4zz91kiMMYknEhuKPscaB3tQLyUkV6Pdk3qszLfhpowxiSeSK4IWgBrRWQJcGK4aFUdF7WoPNC/QxNW5n3ldRjGGBNzkSSCydEOojbI7tiUf322nW37jtK2SX2vwzHGmJg5ZSJQ1fmxCMRr2R2dtoFleV8xzhKBMSaBRDJV5cGwsYaOiUhQROJuWq/T2qQzJOULGix+zAafM8YklEiuCNLD10XkYiDuxmJI2raM6f4HSdpeDDNmwvg5YENOGGMSQKVnGlPVfxInw0ucJHchyVpsI5EaYxJOJDeUfTds1YdzX0H83VOQNRz1pxAIFCH+ZPw2EqkxJkFE0mvowrDlAJALXBSVaLyUmcOxK1/jiWnT6dDvPC6zaiFjTIKIpI3gulgEUhs07DKU/2QEafFVCpd5HYwxxsRIRTOU3Sci5Y63ICJni8gF0QnLO9kdm7Ii7ysCwZDXoRhjTExUdEWwGnhDRI4BK4BCIBXoBvQH3gd+G/UIYyw7qynPLc5j/Y6D9GnX2OtwjDEm6iqaj+B14HUR6QYMA9oAB4DngYmqejQ2IcbWoI5NAVie95UlAmNMQoikjWAjsDEGsdQK7ZrUp12T+nyyeQ/jh2Z5HY4xxkRdpe8jiHciwpmdm7H4y73E8cjbxhhzgiWCMgzp3Jy9h4vYsPOQ16EYY0zUWSIow+DOzQH4+IvdHkdijDHRF8mgc91F5AMR+dxd7ysi91WnUBFpIiKvish6EVknIkOqc7yaltmsAd9qlEfj5X+2AeiMMXEvkiuCp4CfA8UAqvoZcHk1y/0T8I6q9gT6Aeuqebyalb+EPxdP5sK909AZ4ywZGGPiWiSJoIGqlj4TBqpaoIg0AkYAzwCoapGq1q45InMXkqTFJBECG4DOGBPnIkkEu0WkC+5AcyLyfWB7NcrsjHNz2jQRWSkiT4tIw9I7ichEEVkmIssKCwurUVwVZA2HpBQC6iMoSc66McbEqUgSwY+AvwE9RWQrcDtwczXKTAIGAn9V1QHAYeDe0jup6lRVzVbV7IyMjGoUVwWZOfjGv8GzKVfycOuHbV4CY0xci+SGsi+Bc9xv7T5VPVjNMguAAlX9xF1/lTISgecyc/iiRypvf76dn4UUv0+8jsgYY6IikvkI7iy1DrAfWK6qqypboKruEJF8Eemhqv8FxgBrK3ucWBjSpTkvLctn3fYDNtyEMSZuRVI1lA3cBLRzfyYCo4CnRORnVSz3x8AsEfkMZwC7Wjl43dCuzv0ECzbGuI3CGGNiKJJE0BwYqKp3qepdOIkhA6fnz4SqFKqqq9z6/76qerGqflWV40Rby/RUTmvTiAUbLBEYY+JXJImgA1AUtl4MdHRHHz0elahqkRHdWrA87ysOH69yj1ljjKnVIkkEfwcWi8gkEZkELAJecBuPa2Xdfk0a0T2D4qCy+Ms9XodijDFREUmvoV+LyFvAWYAAN6nqMnfzVdEMrjbIzmrKkOQv0AXzIe371pXUGBN3KkwEIuIDPlPVPsDy2IRUu9TbvpzpSQ+StL0YZsyE8XMsGRhj4kqFVUOqGgI+FZEOMYqn9sldSLIW4yeE2nATxpg4dMqqIZwpKteIyBKcu4ABUNVxUYuqNikZbqK4CHzJJNlwE8aYOBNJIrg/6lHUZpk5yLVzeHrmTPa3yuEeqxYyxsSZSBqL58cikNpMOpxJXq/6vPnpdu4Mhkj223w+xpj4EcnENINFZKmIHBKRIhEJisiBWARXm4zq0ZKDxwMs3bzX61CMMaZGRfLV9v+AK4CNQH3gBvexhDK8WwtSkny8t26n16EYY0yNiqiOQ1U3AX5VDarqNJyxhhJKg5QkhnVpzvvrdqKqXodjjDE1JpJEcEREUoBVIvJ7EbkD+MZEMongnF6tyN97lI27DnkdijHG1JhIEsE17n634nQfzQS+F82gaqsxPVsB8L5VDxlj4kgkvYby3MVjJHhX0taNU/l+y200Wvpv6HK13WFsjIkLkUxMMwyYDHQM319VO0cvrFoqfwkPHfolEixGZ7yEjH/DkoExps6L5IayZ4A7cMYaCkY3nFoudyFJGkAkRChQjOQutERgjKnzIkkE+1X17ahHUhdkDQd/CoHAcUKSRIoNN2GMiQPlJgIRGeguzhWRh4HZhE1Eo6orohxb7ZOZg4yfw7y3/8FTW9rybMuBidl9yhgTVyq6IvhDqfXssGUFzq75cOqAzBzSz+nCJ1MX85/1u7iwX1uvIzLGmGopNxGo6uhYBlKXZGc1IyO9Hm+t3m6JwBhT50Uy1tBvRaRJ2HpTEXkwumHVbn6fcH6f1sz97y6OFNlcxsaYui2SG8rOV9V9JSuq+hXwP9ELqW44v08bjhWHmLu+0OtQjDGmWiJJBH4RqVeyIiL1gXoV7J8Qcjo1Y3TDXALzH4H8JV6HY4wxVRZJ99HngQ9EZBpOI/H1wIyoRlUH+Lcu5W+h+/HtLkZnzEJsLmNjTB0VyRATvxeRz4BzAAF+rar/jnpktZ07l7Fzc1mR3VxmjKmzIrkiQFXfAd6Jcix1S9ZwSKpnN5cZY+o8m3Oxqtyby+a3ncjVxb9kX/P+XkdkjDFVYomgOjJzaPXtX7Ak0JV/rd7udTTGGFMlFSYCEfGLyPOxCqYu6t22Ed1apvHaiq1eh2KMMVVSYSJQ1SCQ4c5QZsogInxnYDuW5X3Flj1HvA7HGGMqLZLG4lxgkYjMwZmhDABVfTRaQdU1F/Vvx/v/foOCNxbRYczF1nvIGFOnRJIItrk/PiC9pgoWET+wDNiqqhfU1HG90O7gal6o9xBJucXojGftngJjTJ0SyX0E9wOISLqzqjU1c/ttwDqgUQ0dzzu5C0mmGB8hNFgEdk+BMaYOiWTQuT4ishL4HFgjIstFpHd1ChWR9sC3gaerc5xaI2s4klSPgPooJsm5x8AYY+qISLqPTgXuVNWOqtoRuAt4qprlPgb8DAiVt4OITBSRZSKyrLCwlg/s5t5T8H7rGxgfuI+DGQO8jsgYYyIWSSJoqKpzS1ZUdR5UfWIuEbkA2KWqyyvaT1Wnqmq2qmZnZGRUtbjYycyhzQW/5OPiLry+apvX0RhjTMQiSQRfisivRCQYQXuNAAAUJ0lEQVTL/bkP2FyNMocB40QkF3gRODte7lXo274xp7VpxAtLtngdijHGRCySRHA9kIEzZ/FsoAUwoaoFqurPVbW9qmYBlwP/UdWrq3q82kREuDInkzXbDrC6YL/X4RhjTEQiSQTnqOpPVHWg+3M7cG60A6urLhrQjsHJm9j65m9sngJjTJ0QSSL4eYSPVZqqzqvr9xCU1qhwJTOTfsM5259CZ1xoycAYU+uVex+BiJyPMyVlOxF5PGxTI8Am6i1P7kKSCbjzFBTbPAXGmFqvohvKtuHc+TsOCO/hcxC4I5pB1WlZwxF/CoHAcQL4Se5wFn6vYzLGmAqUmwhU9VPgUxGZpap2BRCpzBwYP4dNi9/iFysac/PhLGtQMcbUahVVDb2sqpcCK0VES29X1b5Rjawuy8yha9tsdmyay7RFmzm3VyuvIzLGmHJVVDV0m/s7rhpzYyXJ7+OaIVn87p31rN9xgJ6t6/6QSsaY+FRuryFV3R62z05VzVPVPGAXziT25hSuyMkkNdnHB+++CQv/YD2IjDG1UiTDUL8CDA1bD7qPnRGViOJIkwYp3NlzP9dsuA3dHET8KWBDVBtjaplI7iNIUtWikhV32WYsi9ClLXKd7qQahJIhqo0xphaJJBEUisi4khURuQjYHb2Q4kuTXmcT8iUTUB/qT7Yhqo0xtU4kVUM3AbNE5P9w2gbygWujGlU8ycxhx8Uv8+LLf6dD3/O43KqFjDG1TCQzlH0BDBaRNEBU9WD0w4ovHfqNYtOnacz6fC8XXBAgrV4k+dcYY2IjojOSiHwb6A2kijgdhlT1gSjGFXduGd2Vd9cu4r1/z+E7TTc7VUR2dWCMqQVOmQhE5EmgATAaZ2rJ7wPWD7KS+mc24QdZhYxdcTcq1oPIGFN7RNJYPFRVrwW+cieyHwJkRjes+HRj+60kq/UgMsbULpEkgqPu7yMi0hYoBjpFL6T41brfudaDyBhT60SSCN4UkSbAw8AKIBd4IZpBxS23B9GjwUt4rvufrVrIGFMrRNJr6Nfu4j9E5E0gVVVtHsYq6tBvFNvXN+HZ1dv51thjtGqU6nVIxpgEd8orAhFJFZE7RWQ28HfgehGxs1c13HFOd0IhePm1f9gYRMYYz0XSfXQmzmQ0f3bXrwCeAy6JVlDxrkPzBtzX9yCXrL0dzbUeRMYYb0WSCHqoar+w9bki8mm0AkoUl7bMI2ldANEQGiyyKS2NMZ6JpLF4pYgMLlkRkTOBRdELKTGkdh0JvhQC6iPksx5ExhjvRJIIzgQ+EpFcEckFPgZGishqEfksqtHFs8wcGP86M1Ov5hb/JI62GuR1RMaYBBVJ1dDYqEeRoJI6Dua0S7vxwFOL+cfrs7m69RYbesIYE3ORdB/NAxCRlkBq2ONbohhXwhjSpTl39tzH9z6/HV1rDcfGmNiLpPvoOBHZCGwG5uPcUPZ2lONKKDdkbiVZnKEn1IaeMMbEWCRtBL8GBgMbVLUTMAZrLK5RDbqPOtFwHBRrODbGxFYkiaBYVfcAPhHxqepcoH+U40osmTn4J8zhlUbXMiF4H1vTT/c6ImNMAokkEexzJ6VZgDNT2Z+AQHTDSjzS4UyGTXiIFdqNp2a9SGiB3XFsjImNSHoNXYQzAukdwFVAY8AmpYmCDs0b8MehRYz4+GfwnwAk1bOGY2NM1JV7RSAiXUVkmKoeVtWQqgZUdQawCmgSuxATy3kNNpIiAXyErOHYGBMTFVUNPYYzxlBpR9xtVSIimSIyV0TWicgaEbmtqseKR9JpOL6kFAL4OK5+jrcf6nVIxpg4V1EiyFLVb9w5rKrLgKxqlBkA7lLV03B6I/1IRHpV43jxJTMHGf8Gm0+/nSuP/4KZH+fZCKXGmKiqqI2goqGm61e1QFXdDmx3lw+KyDqgHbC2qseMO5k5dMvM4cLil7h83a2ENgTwWXuBMSZKKroiWCoiN5Z+UER+ACyvicJFJAsYAHxSxraJIrJMRJYVFhbWRHF1zjVt8q29wBgTdRVdEdwOvCYiV/H1iT8bSAG+U92C3S6p/wBuV9UDpber6lRgKkB2drZWt7y6KKnzCEILHyYQKCKgfoJth9DQ66CMMXGn3ESgqjuBoSIyGujjPvwvVf1PdQsVkWScJDBLVWdX93hxKzMH3/g32LLs3/x0WToD39vIvVs/xtfJBqYzxtScSAadmwvMrakCRUSAZ4B1qvpoTR03bmXmkJWZw/WprzN68Q2ww+4vMMbUrEjuLK5pw4BrgLNFZJX78z8exFGnnN9w04n2glDA2guMMTUnkjuLa5SqfghIrMut65z7C+oRDBynSP1s3p9Mr4V/sPkLjDHVFvNEYKooMwcZP4fApvk8vXQfNyz9NSoBxKqJjDHV5EXVkKmqzBzqjb6b6wc1JkUCiHUrNcbUAEsEdVDD7qOQsGEothc1sLuPjTFVZlVDdZHbrXTfmv/w5NKvuHPh/6Ji01waY6rGrgjqqswcmo29l5tzmpKETXNpjKk6SwR1XNNeZ58YrfRYyM/GgylWTWSMqRSrGqrr3Gqiw+vn8syK/fzwkwcIiQ1SZ4yJnF0RxIPMHNLPvYebcpqedNOZbrZqImPMqVkiiCOpXUc6N525vYleXHOY4nmPWDWRMaZCVjUUT9ybzmTzQj7OD3Lxhofx7QwQ+vBhfOPfsGoiY0yZ7Iog3mTm4BtxF2d38FNPAvjdaqKCuc9YI7Ixpkx2RRCvspyxiTRYRFCFjC9eJfhlCF9SPcQakY0xYSwRxKvMHBg/B8ldiP+rLfhWzMRHiEDgOAc+mk6ztgttwDpjDGCJIL5l5kBmDkn5S+Czlwi5VwcN175EaF0IsasDYwyWCBKDe3Xgy10Iu/NI+vS5E1cHhQum0aaDXR0Yk8gsESQK9+qgXv4SWPPyiauDZhteJrgxhCSlWM8iYxKU9RpKNCVXB2f/Ev/Aq0mWkNOzqLiIlW88wfG5D1vPImMSjKiq1zGcUnZ2ti5btszrMOJP/hKYMQ4NFhFQHyFV/BJCfcmEvvUQ9Yr2WZWRMXWYiCxX1exT7WdVQ4ksrGdR8v4CdPkMREMEgkX43r6bEGoNysYkAKsaSnSZOTD8Luh3hTOfgfjx+fz4CeEjRDBwnJVvPMHB935nVUbGxCmrGjJfy1/izGdQvzm8c+/JVUaECPmS2TZkEh1TjyGdrMrImNrOqoZM5bk9iwBo1eubVUahItot+hUhUdSXzJExv6FR6IC1IxhTx1kiMGUrSQr5S5BVL0CwCL9P0JBTZRQIFlH/3XsIiqK+FALn/ZbUYmtcNqYuskRgKuY2KJO7EKnfHHnnXggW4fMJhIL4UALB4/jfvvtEUig+77fUt6RgTJ1hicCcWqkqI3IX4gtrR/CJgH6dFJLcpBDyJbNz6GTapRy1NgVjajFLBKZyymhHkHKSggaLaLXwPicpSDIrTruHLulFNO91Nr6OZ37dOG1XDsZ4ynoNmZpRqscRwSJUwtoUEFR9CEpAkni5xY+4cu8T+EPFkJSCjP0dHN3jJAWwBGFMDbBeQya2yqg+Cm9T8ItAKIQQQgjQc+9cCBYjEiJQfBzevBNBUfHjE0E0CP4UZOwUSxDGRJklAlPzykkKJVcKfn8KOWOvQ9+5h1CwGBEQDeFDCYYUUEQgUHzMEoQxMWCJwERXGUmh5IQtbhtDeHWSz+9HFUKhIAgIIfxlJAh98058KCH8iIBPg6g/hd3D7qcxB6nXdQQi8nV5UPayJQ5jrI3A1BLhDcfwzfYGn5MgCAXR8CsIBFHFJxBQQXHaIYL4EBH8BE9KFiFJcpZDATQphcOjH6RBYD/+ziO+LreixBG+bEnE1HKRthF4kghEZCzwJ8APPK2qUyra3xJBAjtFgsDnRxEIBVAEUacdIoQAfCNZBFUQykgc4kNwEkcQPwL4CKL4oVQSkVAA9aewffAkUgP7CXYYRr1kH/W3fkxS5xH4fRFciZS37N7EV63nG+OqtYlARPzABuBcoABYClyhqmvLe44lAvMNESQI3ARRsqyhAOrzgwIadLar06vpG4kDxQeRJRF37EY/oa+XxVn+Orn4IDzRlCSXkxJNMu91vINzt/wRf6iYkPgRBNHASUnopITkc2p3S5LT5uz7SCnax+E2Q/D5oNGOTzjSdgh+ERruWMzx9kPwI9Tf9jHFmcPw+yCl4COKM4fhE0jO/4hgh2EIQlL+IoIdS5Y/RDucBQL+LYvQjmc5ryFvEbjLkvdh1ZJXJMvVTZB1fbmKCb429xrKATap6pcAIvIicBFQbiIw5hvC2x5K1uHkdgg4aVlyFyLlJA5fWOLwl1pWN4n4/H4nh4SCbsO1c/Xhc65J3ORx8jLgPua0cThpQp3kUmpZQ8Wkf/kWIsX4JISG9ETi0VBxmcvB4NfLgcBxOi6eVH5yqmA5uZzHxV32hT0OIUJhy5UtK4gPpKwEWfZygCQe8V3HT0PTSCIQ0XNKkrAvhstOrDW/HIvZA71IBO2A/LD1AuDM0juJyERgIkCHDh1iE5mp+8pLEOUtV5A4SpaljGUpJ4lEslw60ZQsJyWlMHzsD76+Oc//9ZWMs+wkIQlf9rnLGnly8moZnKRY2WUhwKUNVpJ8KOAOj171Y0V7WaKwrMFi5+8vzhKBlPHYN+qnVHUqMBWcqqFoB2USVGUTR/hyBEmk0suZOSfu2C5vPylvuRrJqTYv+/0pdB91FbyzOu5eWyTL4k/5+vOPEi/aCIYAk1X1W+76zwFU9aHynmNtBMZEKF7r0a2NgKqozY3FSTiNxWOArTiNxVeq6prynmOJwBhjKq/WNharakBEbgX+jdN99NmKkoAxxpjo8uTOYlV9C3jLi7KNMcaczCavN8aYBGeJwBhjEpwlAmOMSXCWCIwxJsHVidFHRaQQyKvi01sAu2swnLrAXnNisNcc/6r7ejuqasapdqoTiaA6RGRZJP1o44m95sRgrzn+xer1WtWQMcYkOEsExhiT4BIhEUz1OgAP2GtODPaa419MXm/ctxEYY4ypWCJcERhjjKmAJQJjjElwcZ0IRGSsiPxXRDaJyL1exxNNIpIpInNFZJ2IrBGR27yOKVZExC8iK0XkTa9jiQURaSIir4rIevfzHuJ1TNEmIne4f9efi8gLIpLqdUw1TUSeFZFdIvJ52GPNROQ9Edno/m4ajbLjNhGIiB/4C3A+0Au4QkR6eRtVVAWAu1T1NGAw8KM4f73hbgPWeR1EDP0JeEdVewL9iPPXLiLtgJ8A2araB2f4+su9jSoqpgNjSz12L/CBqnYDPnDXa1zcJgIgB9ikql+qahHwInCRxzFFjapuV9UV7vJBnJNDO2+jij4RaQ98G3ja61hiQUQaASOAZwBUtUhV93kbVUwkAfXdia0aANs8jqfGqeoCYG+phy8CZrjLM4CLo1F2PCeCdkB+2HoBCXBiBBCRLGAA8Im3kcTEY8DPgJDXgcRIZ6AQmOZWhz0tIg29DiqaVHUr8AiwBdgO7FfVd72NKmZaqep2cL7sAS2jUUg8JwIp47G47ysrImnAP4DbVfWA1/FEk4hcAOxS1eVexxJDScBA4K+qOgA4TJSqC2oLt178IqAT0BZoKCJXextVfInnRFAAZIattycOLyfDiUgyThKYpaqzvY4nBoYB40QkF6fq72wRed7bkKKuAChQ1ZKrvVdxEkM8OwfYrKqFqloMzAaGehxTrOwUkTYA7u9d0SgknhPBUqCbiHQSkRScxqU5HscUNSIiOPXG61T1Ua/jiQVV/bmqtlfVLJzP9z+qGtffFFV1B5AvIj3ch8YAaz0MKRa2AINFpIH7dz6GOG8gDzMHGO8ujwdej0YhnsxZHAuqGhCRW4F/4/QyeFZV13gcVjQNA64BVovIKvexX7jzQ5v48mNglvsF50vgOo/jiSpV/UREXgVW4PSOW0kcDjUhIi8Ao4AWIlIATAKmAC+LyA9wEuIlUSnbhpgwxpjEFs9VQ8YYYyJgicAYYxKcJQJjjElwlgiMMSbBWSIwxpgEZ4nAxA13VM5bwtbbut0Oo1HWxSLyv9V4/tMlgwKKyC8i2P9FEelW1fKMqYh1HzVxwx1j6U13hMpol/URME5Vd9fAsQ6patop9hkJXK2qN1a3PGNKsysCE0+mAF1EZJWIPCwiWSVju4vIBBH5p4i8ISKbReRWEbnTHbhtsYg0c/frIiLviMhyEVkoIj1LFyIi3YHjJUlARKaLyPfDth9yf48SkXlhcwfMcu+MxX08W0Sm4Iyqucrd3lBE/iUin7pj71/mHnYhcI47+qYxNcoSgYkn9wJfqGp/Vb27jO19gCtxhij/DXDEHbjtY+Bad5+pwI9VdRDwU+CJMo4zDOcu10gMAG7HmROjs/vcE1T1XuCoG/NVOOPRb1PVfu6VzTvufiFgE878A8bUKEsEJpHMVdWDqloI7AfecB9fDWS5I7cOBV5xh+n4G9CmjOO0wRkKOhJLVLXAPZGvArJOsf9qnG/+vxOR4aq6P2zbLpzRN42pUXaZaRLJ8bDlUNh6COd/wQfsU9X+pzjOUaBx2HrAfW7J4H8p5ZQZ5BT/c6q6QUQGAf8DPCQi76rqA+7mVLdsY2qUXRGYeHIQSK/qk935GzaLyCXgnNRFpKyqmHVA17D1XGCQu3wRkFzJoovdIcQRkbY4VVbP40zGEj7EdHcgngdONB6xRGDihqruARa5jawPV/EwVwE/EJFPcU66ZU1vugAYUNLwCzwFjBSRJcCZOJPFVMZU4DMRmQWcDixxq6Z+CTwIICKtcNoStlf2BRlzKtZ91JgqEJE/AW+o6vsxKu8O4ICqPhOL8kxisSsCY6rmtziTqMfKPr6exNyYGmVXBMYYk+DsisAYYxKcJQJjjElwlgiMMSbBWSIwxpgEZ4nAGGMS3P8DEJax++VIH2EAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Generate plots \n",
    "fig = plt.figure()\n",
    "ax = fig.add_subplot(111)\n",
    "ax.plot(t, Q_exact, '-', label = \"exact\")\n",
    "\n",
    "# plot approximate solution (use discrete points with no connecting line)\n",
    "ax.plot(t_approx, Q_approx, '.', label=\"approximate\")\n",
    "\n",
    "plt.legend()\n",
    "plt.xlabel(\"time (units)\")\n",
    "plt.ylabel(\"Capacitor charge (units)\")\n",
    "plt.title(\"Capacitor Charge as Function of Time\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Write a function to calculate the cumulative error\n",
    "# hint, try reading the help file on np.sum\n",
    "\n",
    "def cumulative_error(dt, t_final, R, C, Q0):\n",
    "    # error = abs(approximate - exact)\n",
    "    \n",
    "    t_vals, q_approx = approx_rk2(dt, t_final, R, C, Q0)\n",
    "    q_exact = exact(t_vals, R, C, Q0)\n",
    "    \n",
    "    q_error = abs(q_approx-q_exact)\n",
    "    return t_vals, q_error"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Cumulative Error of RK2 Method')"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "t_vals, q_error = cumulative_error(dt, t_final, R, C, Q0)\n",
    "plt.plot(t_vals,q_error)\n",
    "plt.xlabel('Time')\n",
    "plt.ylabel('Charge Difference')\n",
    "plt.title('Cumulative Error of RK2 Method')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "a = np.array([1,2,3,4])\n",
    "b = np.sum(a)\n",
    "print(b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "? np.sum"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "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",
       "        fig.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 overridden (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",
       "        event.shiftKey = false;\n",
       "        // Send a \"J\" for go to next cell\n",
       "        event.which = 74;\n",
       "        event.keyCode = 74;\n",
       "        manager.command_mode();\n",
       "        manager.handle_keydown(event);\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"
    },
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\" width=\"640\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure()\n",
    "plt.plot([1,2,3],[1,2,3])\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
<<<<<<< HEAD
   "version": "3.6.7"
=======
   "version": "3.6.6"
>>>>>>> upstream/master
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}