{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h1 style=\"text-align:center\">Eigenvalue/Eigenvector Analysis <br>for Undamped Systems</h1>\n",
    "<h3 style=\"text-align:center\">MCHE 485: Mechanical Vibrations</h3> \n",
    "<p style=\"text-align:center\">Dr. Joshua Vaughan <br>\n",
    "<a href=\"mailto:joshua.vaughan@louisiana.edu\">joshua.vaughan@louisiana.edu</a><br>\n",
    "http://www.ucs.louisiana.edu/~jev9637/   </p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p style=\"text-align:center\">\n",
    "\t<img src=\"http://shared.crawlab.org/TwoMass_3spring.png\" alt=\"A Two-Mass-Spring System\" width=50%/></a><br>\n",
    "    <strong> Figure 1: A Two-Mass-Spring System</strong>\n",
    "</p>\n",
    "\n",
    "This notebook demonstrates the eigenvalue/eigenvector problem using a two-mass-spring-damper system shown in Figure 1. We'll just look at one example set of parameters. The same techniques apply for other parameters and for larger matrices. \n",
    "\n",
    "The equations of motion for the system are:\n",
    "\n",
    "$ \\quad m_1 \\ddot{x}_1 + (k_1+k_2)x_1 - k_2 x_2 = 0 $\n",
    "\n",
    "$ \\quad m_2 \\ddot{x}_2 -k_2 x_1 +(k_2 + k_3)x_2 = 0 $\n",
    "\n",
    "We could also write these equations in matrix form:\n",
    "\n",
    "$ \\quad \\begin{bmatrix}m_1 & 0 \\\\ 0 & m_2\\end{bmatrix}\\begin{bmatrix}\\ddot{x}_1 \\\\ \\ddot{x}_2\\end{bmatrix} + \\begin{bmatrix}k_1 + k_2 & -k_2 \\\\ -k_2 & k_2 + k_3\\end{bmatrix}\\begin{bmatrix}x_1 \\\\ x_2\\end{bmatrix} = \\begin{bmatrix}0 \\\\ 0\\end{bmatrix}$\n",
    "\n",
    "Define\n",
    "\n",
    "$ \\quad M = \\begin{bmatrix}m_1 & 0 \\\\ 0 & m_2\\end{bmatrix} $\n",
    "\n",
    "and \n",
    "\n",
    "$ \\quad K = \\begin{bmatrix}k_1 + k_2 & -k_2 \\\\ -k_2 & k_2 + k_3\\end{bmatrix} $\n",
    "\n",
    "Using $M$ and $K$, we want to solve:\n",
    "\n",
    "$ \\quad \\left[K - \\omega^2 M\\right]\\bar{X} = 0 $ \n",
    "\n",
    "for $\\bar{X}$. This is an eigenvalue problem.\n",
    "\n",
    "For information on how to obtain these equations, you can see the lectures at the [class website](http://www.ucs.louisiana.edu/~jev9637/MCHE485.html).\n",
    "\n",
    "We'll use the [Scipy version of the linear algebra module](http://docs.scipy.org/doc/scipy-0.13.0/reference/generated/scipy.linalg.eigh.html). It allows us to solve the \"general\" eignevalue problem."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# We want our plots to be displayed inline, not in a separate window\n",
    "%matplotlib inline \n",
    "\n",
    "# Import the plotting functions \n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Let's also improve the printing of NumPy arrays.\n",
    "np.set_printoptions(precision=3, suppress=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To see how to solve this eigenvalue problem, we will use the parameters from the example in the book, set up below. All three spring constants are equal and the two masses are equal."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Define the matrices\n",
    "m1 = 1.0\n",
    "m2 = 1.0\n",
    "\n",
    "k1 = 2 * np.pi**2 \n",
    "k2 = 4.0\n",
    "k3 = 4.0\n",
    "\n",
    "M = np.asarray([[m1, 0],\n",
    "                [0,  m2]])\n",
    "\n",
    "K = np.asarray([[k1, -k1],\n",
    "                [-k1,      k1]])\n",
    "\n",
    "# M = np.asarray([[m1, 0],\n",
    "#                 [0,  m2]])\n",
    "\n",
    "# K = np.asarray([[k1, k2],\n",
    "#                 [k1*m2/m1 - k3,      (k2 + k3 - k2*m2/m1)]])\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# We'll use the scipy version of the linear algebra\n",
    "from scipy import linalg\n",
    "\n",
    "eigenvals, eigenvects = linalg.eigh(K,M)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "The linalg.eigh function returns two arrays, one of the eigenvalues and one of the eigenvectors. The eigenvalues are the square of the two natural frequencies. The eigenvectors are returned in normalized form, with each \"column\" of the array representing an eigenvector.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "\n",
      "The resulting eigenalues are 0.00 and 39.48.\n",
      "\n",
      "\n",
      "So the two natural frequencies are 0.00rad/s and 6.28rad/s.\n",
      "\n",
      "\n"
     ]
    }
   ],
   "source": [
    "print('\\n')\n",
    "print('The resulting eigenalues are {:.2f} and {:.2f}.'.format(eigenvals[0], eigenvals[1]))\n",
    "print('\\n')\n",
    "print('So the two natural frequencies are {:.2f}rad/s and {:.2f}rad/s.'.format(np.sqrt(eigenvals[0]), np.sqrt(eigenvals[1])))\n",
    "print('\\n')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "\n",
      "The first eigenvector is [-0.707 -0.707].\n",
      "\n",
      "\n",
      "The second eigenvector is [-0.707  0.707].\n",
      "\n",
      "\n"
     ]
    }
   ],
   "source": [
    "print('\\n')\n",
    "print('The first eigenvector is ' + str(eigenvects[:,0]) + '.')\n",
    "print('\\n')\n",
    "print('The second eigenvector is ' + str(eigenvects[:,1]) + '.')\n",
    "print('\\n')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Responses\n",
    "Now, let's look at the response and see how it reflects these two modes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Define the equations of motion\n",
    "\n",
    "# Define the system as a series of 1st order ODEs (beginnings of state-space form)\n",
    "def eq_of_motion(w, t, p):\n",
    "    \"\"\"\n",
    "    Defines the differential equations for the coupled spring-mass system.\n",
    "\n",
    "    Arguments:\n",
    "        w :  vector of the state variables:\n",
    "                  w = [x1, x1_dot, x2, x2_dot]\n",
    "        t :  time\n",
    "        p :  vector of the parameters:\n",
    "                  p = [m1, m2, k1, k2, k3]\n",
    "    \"\"\"\n",
    "    x1, x1_dot, x2, x2_dot = w\n",
    "    m1, m2, k1, k2, k3 = p\n",
    "\n",
    "    # Create sysODE = (x1', x1_dot', x2', x2_dot')\n",
    "    sysODE = [x1_dot,\n",
    "             (-(k1+k2)*x1 + k2*x2) / m1,\n",
    "             x2_dot,\n",
    "             (k2*x1 - (k2+k3)*x2) / m2]\n",
    "    \n",
    "    return sysODE"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Import the ODE solver\n",
    "from scipy.integrate import odeint  \n",
    "\n",
    "# Set up simulation parameters \n",
    "\n",
    "# ODE solver parameters\n",
    "abserr = 1.0e-9\n",
    "relerr = 1.0e-9\n",
    "max_step = 0.01\n",
    "stoptime = 10.0\n",
    "numpoints = 10001\n",
    "\n",
    "# Create the time samples for the output of the ODE solver\n",
    "t = np.linspace(0.0, stoptime, numpoints)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Mode 1\n",
    "Let's start by looking at the first mode. For this set of parameters ($m_1 = m_2$ and $k_1 = k_2 = k_3$), the two masses move identically. To excite only this mode, we'll choose initial conditions that exactly match the mode shape.\n",
    "\n",
    "Here, we'll choose:\n",
    "\n",
    "$ \\quad x_1(0) = x_2(0) = x_0$\n",
    "\n",
    "and \n",
    "\n",
    "$ \\quad \\dot{x}_1(0) = \\dot{x}_2(0) = 0$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Initial conditions\n",
    "x1_init = 0.5                       # initial x1 position\n",
    "x1_dot_init = 0.0                   # initial x1 velocity\n",
    "x2_init = 0.5                       # initial x2 position\n",
    "x2_dot_init = 0.0                   # initial x2 velocity\n",
    "\n",
    "# Pack the parameters and initial conditions into arrays \n",
    "p = [m1, m2, k1, k2, k3]\n",
    "x0 = [x1_init, x1_dot_init, x2_init, x2_dot_init]\n",
    "\n",
    "# Call the ODE solver.\n",
    "resp = odeint(eq_of_motion, x0, t, args=(p,), atol=abserr, rtol=relerr,  hmax=max_step)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
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/tLp8qRovHNVv2ljS1xmShhgAWObOhXnaVMjLl1Hz1A+5u7KNaDz///jHDag2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\nvcMAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11f3637f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Set the plot size - 3x2 aspect ratio is best\n",
    "fig = plt.figure(figsize=(6,4))\n",
    "ax = plt.gca()\n",
    "plt.subplots_adjust(bottom=0.17,left=0.17,top=0.96,right=0.96)\n",
    "\n",
    "# Change the axis units to serif\n",
    "plt.setp(ax.get_ymajorticklabels(),family='serif',fontsize=18)\n",
    "plt.setp(ax.get_xmajorticklabels(),family='serif',fontsize=18)\n",
    "\n",
    "ax.spines['right'].set_color('none')\n",
    "ax.spines['top'].set_color('none')\n",
    "\n",
    "ax.xaxis.set_ticks_position('bottom')\n",
    "ax.yaxis.set_ticks_position('left')\n",
    "\n",
    "# Turn on the plot grid and set appropriate linestyle and color\n",
    "ax.grid(True,linestyle=':',color='0.75')\n",
    "ax.set_axisbelow(True)\n",
    "\n",
    "# Define the X and Y axis labels\n",
    "plt.xlabel('Time (s)',family='serif',fontsize=22,weight='bold',labelpad=5)\n",
    "plt.ylabel('Position (m)',family='serif',fontsize=22,weight='bold',labelpad=10)\n",
    "\n",
    "plt.plot(t,resp[:,0],linewidth=2,label=r'$x_1$')\n",
    "plt.plot(t,resp[:,2],linewidth=2,linestyle=\"--\",label=r'$x_2$')\n",
    "\n",
    "# uncomment below and set limits if needed\n",
    "# plt.xlim(0,5)\n",
    "plt.ylim(-1,1.35)\n",
    "plt.yticks([-0.5,0,0.5,1.0],['$-x_0$','$0$','$x_0$','$2x_0$'])\n",
    "\n",
    "# Create the legend, then fix the fontsize\n",
    "leg = plt.legend(loc='upper right', fancybox=True)\n",
    "ltext  = leg.get_texts()\n",
    "plt.setp(ltext,family='serif',fontsize=18)\n",
    "\n",
    "# Adjust the page layout filling the page using the new tight_layout command\n",
    "plt.tight_layout(pad=0.5)\n",
    "\n",
    "# save the figure as a high-res pdf in the current folder\n",
    "# It's saved at the original 6x4 size\n",
    "# plt.savefig('FreeVibration_mode_1.pdf')\n",
    "\n",
    "fig.set_size_inches(9,6) # Resize the figure for better display in the notebook"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Mode 2\n",
    "Now, let's look at the second mode. For this set of parameters ($m_1 = m_2$ and $k_1 = k_2 = k_3$), the two masses move exactly opposite of one another in the second mode. To excite only this mode, we'll choose initial conditions that exactly match the mode shape.\n",
    "\n",
    "Here, we'll choose:\n",
    "\n",
    "$ \\quad x_1(0) = x_2(0) = x_0$\n",
    "\n",
    "and \n",
    "\n",
    "$ \\quad \\dot{x}_1(0) = \\dot{x}_2(0) = 0$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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EWXLX+QhpLxbSXyykv1hIf3GYRXtKU2rA6DSlJEmwWMg/FgFpLxbSXyykv1hIf3HkQHtK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6JHj2Z97dD3fwAeDKLoho3wNTbatMIEC6aW4ZqGWoRjEvadzp5TfKprGE8d6IDbxfC+q+ptWuFo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\nblAAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11f34f9e8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Initial conditions\n",
    "x1_init = 0.5                       # initial x1 position\n",
    "x1_dot_init = 0.0                   # initial x1 velocity\n",
    "x2_init = -0.5                      # initial x2 position\n",
    "x2_dot_init = 0.0                   # initial x2 velocity\n",
    "\n",
    "# Pack the parameters and initial conditions into arrays \n",
    "p = [m1, m2, k1, k2, k3]\n",
    "x0 = [x1_init, x1_dot_init, x2_init, x2_dot_init]\n",
    "\n",
    "# Call the ODE solver.\n",
    "resp = odeint(eq_of_motion, x0, t, args=(p,), atol=abserr, rtol=relerr,  hmax=max_step)\n",
    "\n",
    "\n",
    "# Set the plot size - 3x2 aspect ratio is best\n",
    "fig = plt.figure(figsize=(6,4))\n",
    "ax = plt.gca()\n",
    "plt.subplots_adjust(bottom=0.17,left=0.17,top=0.96,right=0.96)\n",
    "\n",
    "# Change the axis units to serif\n",
    "plt.setp(ax.get_ymajorticklabels(),family='serif',fontsize=18)\n",
    "plt.setp(ax.get_xmajorticklabels(),family='serif',fontsize=18)\n",
    "\n",
    "ax.spines['right'].set_color('none')\n",
    "ax.spines['top'].set_color('none')\n",
    "\n",
    "ax.xaxis.set_ticks_position('bottom')\n",
    "ax.yaxis.set_ticks_position('left')\n",
    "\n",
    "# Turn on the plot grid and set appropriate linestyle and color\n",
    "ax.grid(True,linestyle=':',color='0.75')\n",
    "ax.set_axisbelow(True)\n",
    "\n",
    "# Define the X and Y axis labels\n",
    "plt.xlabel('Time (s)',family='serif',fontsize=22,weight='bold',labelpad=5)\n",
    "plt.ylabel('Position (m)',family='serif',fontsize=22,weight='bold',labelpad=10)\n",
    "\n",
    "plt.plot(t,resp[:,0],linewidth=2,label=r'$x_1$')\n",
    "plt.plot(t,resp[:,2],linewidth=2,linestyle=\"--\",label=r'$x_2$')\n",
    "\n",
    "# uncomment below and set limits if needed\n",
    "# plt.xlim(0,5)\n",
    "plt.ylim(-1,1.35)\n",
    "plt.yticks([-0.5,0,0.5,1.0],['$-x_0$','$0$','$x_0$','$2x_0$'])\n",
    "\n",
    "# Create the legend, then fix the fontsize\n",
    "leg = plt.legend(loc='upper right', fancybox=True)\n",
    "ltext  = leg.get_texts()\n",
    "plt.setp(ltext,family='serif',fontsize=18)\n",
    "\n",
    "# Adjust the page layout filling the page using the new tight_layout command\n",
    "plt.tight_layout(pad=0.5)\n",
    "\n",
    "# save the figure as a high-res pdf in the current folder\n",
    "# It's saved at the original 6x4 size\n",
    "# plt.savefig('FreeVibration_mode_2.pdf')\n",
    "\n",
    "fig.set_size_inches(9,6) # Resize the figure for better display in the notebook"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Both modes\n",
    "For any input that does not match a mode shape, both modes will be excited. \n",
    "\n",
    "Here, we'll choose:\n",
    "\n",
    "$ \\quad x_1(0) = x_0$, \n",
    "\n",
    "$ \\quad x_2(0) = 0$\n",
    "\n",
    "and \n",
    "\n",
    "$ \\quad \\dot{x}_1(0) = \\dot{x}_2(0) = 0$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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fHFFwL9OUsYbH4zEdQtwi7s0i/s0i/s0i/s1hFfeSjFmI0tJS0yHELeLeLOLfLOLfLOLf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\nIAiCIAhCIOSMEQRBEARBCOT/Aeceq1Tb55fBAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11ff7db00>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Initial conditions\n",
    "x1_init = 0.5                       # initial x1 position\n",
    "x1_dot_init = 0.0                   # initial x1 velocity\n",
    "x2_init = 0                       # initial x2 position\n",
    "x2_dot_init = 0.0                   # initial x2 velocity\n",
    "\n",
    "# Pack the parameters and initial conditions into arrays \n",
    "p = [m1, m2, k1, k2, k3]\n",
    "x0 = [x1_init, x1_dot_init, x2_init, x2_dot_init]\n",
    "\n",
    "# Call the ODE solver.\n",
    "resp = odeint(eq_of_motion, x0, t, args=(p,), atol=abserr, rtol=relerr,  hmax=max_step)\n",
    "\n",
    "\n",
    "# Set the plot size - 3x2 aspect ratio is best\n",
    "fig = plt.figure(figsize=(6,4))\n",
    "ax = plt.gca()\n",
    "plt.subplots_adjust(bottom=0.17,left=0.17,top=0.96,right=0.96)\n",
    "\n",
    "# Change the axis units to serif\n",
    "plt.setp(ax.get_ymajorticklabels(),family='serif',fontsize=18)\n",
    "plt.setp(ax.get_xmajorticklabels(),family='serif',fontsize=18)\n",
    "\n",
    "ax.spines['right'].set_color('none')\n",
    "ax.spines['top'].set_color('none')\n",
    "\n",
    "ax.xaxis.set_ticks_position('bottom')\n",
    "ax.yaxis.set_ticks_position('left')\n",
    "\n",
    "# Turn on the plot grid and set appropriate linestyle and color\n",
    "ax.grid(True,linestyle=':',color='0.75')\n",
    "ax.set_axisbelow(True)\n",
    "\n",
    "# Define the X and Y axis labels\n",
    "plt.xlabel('Time (s)',family='serif',fontsize=22,weight='bold',labelpad=5)\n",
    "plt.ylabel('Position (m)',family='serif',fontsize=22,weight='bold',labelpad=10)\n",
    "\n",
    "plt.plot(t,resp[:,0],linewidth=2,label=r'$x_1$')\n",
    "plt.plot(t,resp[:,2],linewidth=2,linestyle=\"--\",label=r'$x_2$')\n",
    "\n",
    "# uncomment below and set limits if needed\n",
    "# plt.xlim(0,5)\n",
    "plt.ylim(-1,1.35)\n",
    "plt.yticks([-0.5,0,0.5,1.0],['$-x_0$','$0$','$x_0$','$2x_0$'])\n",
    "\n",
    "# Create the legend, then fix the fontsize\n",
    "leg = plt.legend(loc='upper right', fancybox=True)\n",
    "ltext  = leg.get_texts()\n",
    "plt.setp(ltext,family='serif',fontsize=18)\n",
    "\n",
    "# Adjust the page layout filling the page using the new tight_layout command\n",
    "plt.tight_layout(pad=0.5)\n",
    "\n",
    "# save the figure as a high-res pdf in the current folder\n",
    "# It's saved at the original 6x4 size\n",
    "# plt.savefig('FreeVibration_BothModes.pdf')\n",
    "\n",
    "fig.set_size_inches(9,6) # Resize the figure for better display in the notebook"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<hr style=\"border: 0px;\n",
    "        height: 1px;\n",
    "        text-align: center;\n",
    "        background: #333;\n",
    "        background-image: -webkit-linear-gradient(left, #ccc, #333, #ccc); \n",
    "        background-image:    -moz-linear-gradient(left, #ccc, #333, #ccc); \n",
    "        background-image:     -ms-linear-gradient(left, #ccc, #333, #ccc); \n",
    "        background-image:      -o-linear-gradient(left, #ccc, #333, #ccc);\">"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Licenses\n",
    "Code is licensed under a 3-clause BSD style license. See the licenses/LICENSE.md file.\n",
    "\n",
    "Other content is provided under a [Creative Commons Attribution-NonCommercial 4.0 International License](http://creativecommons.org/licenses/by-nc/4.0/), CC-BY-NC 4.0.\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<script>\n",
       "    MathJax.Hub.Config({\n",
       "                        TeX: {\n",
       "                           extensions: [\"AMSmath.js\"]\n",
       "                           },\n",
       "                tex2jax: {\n",
       "                    inlineMath: [ ['$','$'], [\"\\\\(\",\"\\\\)\"] ],\n",
       "                    displayMath: [ ['$$','$$'], [\"\\\\[\",\"\\\\]\"] ]\n",
       "                },\n",
       "                displayAlign: 'center', // Change this to 'center' to center equations.\n",
       "                \"HTML-CSS\": {\n",
       "                    styles: {'.MathJax_Display': {\"margin\": 4}}\n",
       "                }\n",
       "        });\n",
       "</script>\n",
       "\n",
       "<style>\n",
       "    @font-face {\n",
       "        font-family: \"Computer Modern\";\n",
       "        src: url('http://mirrors.ctan.org/fonts/cm-unicode/fonts/otf/cmunss.otf');\n",
       "    }\n",
       "    @font-face {\n",
       "        font-family: \"Computer Modern\";\n",
       "        src: url('http://mirrors.ctan.org/fonts/cm-unicode/fonts/otf/cmunsx.otf');\n",
       "        font-weight: bold;\n",
       "    }\n",
       "    @font-face {\n",
       "        font-family: \"Computer Modern\";\n",
       "        src: url('http://mirrors.ctan.org/fonts/cm-unicode/fonts/otf/cmunsi.otf');\n",
       "        font-style: oblique;\n",
       "    }\n",
       "    @font-face {\n",
       "        font-family: \"Computer Modern\";\n",
       "        src: url('http://mirrors.ctan.org/fonts/cm-unicode/fonts/otf/cmunso.otf');\n",
       "        font-weight: bold;\n",
       "        font-style: oblique;\n",
       "    }\n",
       "\n",
       "    div.cell {\n",
       "        max-width: 1100px;\n",
       "    }\n",
       "    \n",
       "    h1 {\n",
       "        font-family: Computer Modern;\n",
       "    }\n",
       "    \n",
       "    h4 {\n",
       "        margin-top: 12px;\n",
       "        margin-bottom: 3px;\n",
       "    }\n",
       "\n",
       "    div.text_cell_render {\n",
       "        font-family: Computer Modern, \"Helvetica Neue\", Arial, Helvetica, Geneva, sans-serif;\n",
       "        line-height: 145%;\n",
       "        font-size: 130%;\n",
       "        width: 100%;\n",
       "        max-width: 1100px;\n",
       "    }\n",
       "    \n",
       "    .CodeMirror {\n",
       "        font-family: \"Source Code Pro\", source-code-pro, Consolas, monospace;\n",
       "    }\n",
       "    \n",
       "    .warning {\n",
       "        color: rgb( 240, 20, 20 )\n",
       "    }  \n",
       "  \n",
       "   \n",
       "    hr.style-end {\n",
       "        border: 0px !important;\n",
       "        height: 1px !important;\n",
       "        text-align: center !important;\n",
       "        background: #333 !important;\n",
       "        background-image: -webkit-linear-gradient(left, #ccc, #333, #ccc) !important; \n",
       "        background-image:    -moz-linear-gradient(left, #ccc, #333, #ccc) !important; \n",
       "        background-image:     -ms-linear-gradient(left, #ccc, #333, #ccc) !important; \n",
       "        background-image:      -o-linear-gradient(left, #ccc, #333, #ccc) !important; \n",
       "    }\n",
       "\n",
       "    hr.style-end:after {\n",
       "        content: &#x269C !important;\n",
       "        left: 50% !important;\n",
       "        position: absolute !important;\n",
       "        /* Controls the whitespace around the symbol */\n",
       "        padding: 0px !important;\n",
       "        background: #fff !important;\n",
       "    }\n",
       "    \n",
       "/*  Center figures, etc\n",
       "    .ui-wrapper {\n",
       "        margin-left: auto !important;\n",
       "        margin-right: auto !important;\n",
       "    }\n",
       "*/\n",
       "    \n",
       "</style>\n"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# This cell will just improve the styling of the notebook\n",
    "from IPython.core.display import HTML\n",
    "import urllib.request\n",
    "response = urllib.request.urlopen(\"https://cl.ly/1B1y452Z1d35\")\n",
    "HTML(response.read().decode(\"utf-8\"))"
   ]
  }
 ],
 "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": "3.6.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}