2016-08-10-notes/2016-08-10-notes.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# UBC Scientific Software Seminar\n",
    "\n",
    "## August 10, 2016\n",
    "\n",
    "Today's Agenda:\n",
    "\n",
    "A tour of the SciPy stack:\n",
    "\n",
    "1. Plotting with NumPy arrays and matplotlib\n",
    "2. Linear algebra in SciPy\n",
    "3. Data analysis in pandas"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### The SciPy Stack\n",
    "\n",
    "Scientific computing in Python is built a collection of Python packages known as the SciPy stack:\n",
    "\n",
    "* [NumPy](http://www.numpy.org/) provides fast array computations\n",
    "* [matplotlib](http://matplotlib.org/) is a plotting library\n",
    "* [SciPy](http://scipy.org/) is a library of common mathematical/statistical functions and objects\n",
    "* [pandas](http://pandas.pydata.org/) provides essential datatypes and tools for data analysis\n",
    "\n",
    "Let's begin with NumPy and matplotlib. Recall, when using a package, we [import](https://docs.python.org/3/reference/import.html) it with the `import` keyword and access its functions/objects with the dot syntax."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1. Plotting functions with NumPy arrays and matplotlib\n",
    "\n",
    "#### EXAMPLE\n",
    "\n",
    "Plot the function $y = e^{-0.1 x^2} \\cos(10x)$ on the interval $[-10,10]$.\n",
    "\n",
    "See the [pyplot API documentation](http://matplotlib.org/api/pyplot_summary.html) to see a summary of the pyplot commands."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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wzlUDNY26V8aYnNhfxnLMKYZ/vgJTZ4VfRGLxKr1QP3Z0w3VnToAXPgjeRnWN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\ntSt2nE8AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fe8546ebb38>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.linspace(-10,10,1000)\n",
    "y = np.exp(-0.1*x**2) * np.cos(10*x)\n",
    "\n",
    "plt.figure(figsize=(15,3)) # Specifiy the size of the figure\n",
    "plt.plot(x,y,color=(0.2,0.4,1)) # Specify the color as RGB tuple\n",
    "plt.grid('on'), plt.xlim([-10,10]), plt.ylim([-2,2]) # Turn on the grid and set the x and y display limits\n",
    "plt.xlabel('x values'), plt.ylabel('y values'), plt.title('Decaying Cosine Wave'); # Add labels and a title"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### EXAMPLE\n",
    "\n",
    "Plot the parametric curve $x(t) = \\cos 3t$ and $y(t) = \\sin(2t)$ for $t \\in [0,2 \\pi]$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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b8wgj8PnnzFHv39/okQjZpVw5+pyjo7mK6dSJx4YN7iGja1a0Zqphhw6sRG3U\niP+DTz+liKDgWbz6Kqv2v/nG8e/t9u6g6GigSRO6gSpWNG5cgmNITGS++WefcVU6fDgFtETuwzEk\nJrLF6Bdf0BCMGEFZFZH98HwiIugW2rcPKFPm1p+ZOibQuzdXMaNHGzgoweFYLIwXfP45fdXvvMPg\nV6FCRo/MM7l8mTUc33zDAq9hw5hJJ8Fec/Hee+wO+PPPtz5vWiOwYwdXiZGRVAgVzElICFeuq1ez\nSvWddyT2k1UOH2asbNYs1s0MHUojIJiTa9dYsb9u3a3/Z9MGhkePBsaOFQNgdho14iS2Zw9Xrg0a\n0IUhjW4yRms2cOnZE2jenCm4YWFs3SgGwNwULkzxvg8+cNx7uu1OYNs24Lnn6AcTjXLvIiYG+Okn\nKlZWqEDXRrduUhuSkkI5gcBAun+GDOHO6YEHjB6Z4Eri45kos2EDULMmnzOlO6hPH7Y+fOsto0ck\nGEVKCoXrAgMpZ2Cd9AoUMHpkruXGDfqAp05lQHDYMKns9XY++YRu8t9+42PTGYHoaI3GjYFjx0Qh\nVLC5PwIDga1bgUGDgMGDzS8eeOoUNbJ++YUtP4cOZYWvIFy7xmzJw4fZr9h0MYEZM1jcIgZAABgn\naNWK0rpbtgBXrrDQaeBA16gsupo9e+gKrVuXMs4hIcDcuWIABBuFCwNPPsl0a3txSyPw55+sLhWE\n26laFfj2W66AqlRhGmTHjsCaNZ5dfGaxAMuWAW3b0tVTrx5rZKZMkfoYIWMGDrwzVTQnuKU7qGpV\njYgIyXEW7k1iIjOLvviC58vQodxFeoqCaXw85TWmTGEW3LBhwNNPS/GccG8sFqBsWWoKVatmMneQ\nv78YACFr5MtHgbr9+1l4Nns2MycmTGAGjbty4QK14itWZH/sb78Fdu2iBLcYACEr5MrFrLnly+18\nH8cMx7F07Gj0CARPQyngiSdYcLZ6Nd1FPj7Am2/yvrtw6BAD29WqAWfOcBVndQPJwkfILt268fyx\nB7c0Ai1bGj0CwZOpU4eFU2FhDKA1b87Cqk2bjIkbaA388w8v2DZtKOAWEQH88IMoeQr20bo12+3a\ng1vGBNxtTIJnExsL/P47/e5FitDv3ru384sQk5KY1fPFF0BCAuscBgyQCnjBsVSvDkREmKxOwN3G\nJJiD1FRunQMDgePHqVH08suOF627ehWYPh34+mu6fYYNo3y29F4WnMGAAcCff5osMCwIziB3biYd\n/PsveyKy1gAsAAAgAElEQVTv3AlUrsxJ+vhx+9//yBFWuFeuTFfUsmVshdqlixgAwXlUrWrf7zvk\n1FRKdVJKHVJKRSql3svkNdOUUlFKqb1KqfqO+FxByCmNGzOTyCpa9+ijFK3Lrn9Vaxaw9erFYq6C\nBVnANmMGUF/OcsEFVKpk3+/bbQSUUrkAfA2gI4BaAPopparf9prOAKporasCeA3A9/Z+riA4gvLl\nbT0NmjZljn6rVsDChXdv5ZeSAsybx6DzCy8A7dpR5mTixDsbfgiCM7G3d7cjdgJNAERprY9rrZMB\nzAHgf9tr/AHMAACt9Q4AhZRSJR3w2YLgEB56iIHbw4fp0vn0U/rzv/4auHnT9rqYGAaYfXyAr75i\nk4+ICGoZicyJYAQPPmjf7zvCCJQBcDLd41Npz93tNaczeI0gGE6ePNwNbN/OjKJ//mFB13PPscd1\npUr82bx5TDnt2VPUPAVjsTfe5JZK/QEBAf+/7+fnBz8/P8PGIngnSrGfa758wMmTNqGuVq3Y7Ej8\n/YKRBAUFISgoCADVZu3B7hRRpVQzAAFa605pj0cB0FrrSele8z2Af7TWc9MeHwLQRmt9PoP3kxRR\nwVAySyW1WFjg9dVXdBUNHQp07iyZP4KxhIUBtWoZmyK6E4CPUqqCUiovgL4Altz2miUAngf+bzSu\nZWQABMFIYmOp4VO9OjB+PPDGG0z7HDqUtQRFijAGEB1NvaIPPgBq1aJhiI83evSCt2KvRpbdRkBr\nnQpgMIA1AA4CmKO1DldKvaaUGpT2mhUAjiqlDgOYDuANez9XEBzF2bPA++/T9792LSUngoOZMppR\nVXHevIwR7N5No7F0KX937FgKwwmCK7l40b7fd0hMQGu9CkC1256bftvjwY74LEFwFPv2MdNn8WKq\nd27bxqyfrKIUhd/atqUw3Jdf0k3Uuzd3D9b+r4LgTE6ftu/3xZspeBVaAytXshlN586ctI8cYSpo\ndgzA7VSvDnz/Pfu+VqjAuoHOnYF16zy72Y3g/oSF2ff7oh0keAUJCexYN2UKXTzDhtHdkzev8z7P\n2uwmd27uDPr29ZxmN4Ln0Lo1sGmTyQTkLBYt2uqCQ7h4kX77774DGjbkZNyuneu0+7Vm68vAQMpJ\nDB4MvPYa8PDDrvl8wdykpPBciokxmYBcRITRIxA8nfBwNm/x9WUe9YYN7MDUvr1rm7coZeuBvHo1\nEBVla3YTFeW6cQjmJCSE7kd7cEsjsG6d0SMQPBGtOdl37Qr4+VHDJyIC+PFH9wjSpm92U7Qoi9F6\n9KCqqZttyAUP4Z9/mJhgD25pBBYtMnoEgieRlMRm7Y8+SndLz54Ucxs7FihRwujR3ckjjwDjxnGM\nHTsCr7wCNGlCVdPkZKNHJ3gSixczAcEe3DIm8NBDGtHR4jcV7s6VK7YK3ho16O/3xOYtFgtdVYGB\nLER7+23g1Vcd3+xGMBfHjlES/cwZIG9ek8UEOnfmqkgQMsLavMXHh77/5cvpQvTU5i25cgFPPsmm\n8wsXssdBpUpUNT12zOjRCe7K3LnsY3Hfffa9j1teMoMGsT2fm21SBANJ37ylWTPK54aGUunTTGJu\nDRtSrG7fPl7cDRvaVE0FwUpqKufIgQPtfy+3NAJt29LPu3Wr0SMRjMbavKVZMzZvad+eq+NPPgFK\nlzZ6dM6jXDlg8mT+rS1aAP368Xb+/Ls3uxG8gxUrgGLF2AjJXtwyJqC1xrffsrJz6VKjRyQYQUwM\n8NNPwNSpTIEbOpQuE2/V7k9JYcLEF18A584B777LVaA0svFO2rWjiOGAAXyslMliAgBP8N276R8V\nvIcTJ4Dhw+kTDw4G/vqLKZQ9enivAQBY5dynD3fHM2eyoU3FilQ1tVdPXvAsgoJ4nfTt65j3c1sj\nkD8/MHIk0/wE87NzJ10eDRrw8e7dwJw5TJ0UbqV5cxrH4GAgMRGoW9emaiqYG62Bjz7iYW9A2Irb\nGgGA5fWhocD69UaPRHAGqal0cbRqBTz1FCf8o0fZ+N3eKkhvoHJlKpdGRwP16gH+/oynLVvGtFPB\nfCxbRimU/v0d955uGxOwsmABdwN79mSs7S54HrGxwG+/cQIrUoRibr17y//XXpKTuUMIDOR3PGQI\nfcYFChg9MsERxMezidH06VTBTY8pYwJWevYEihdnQZDg2Zw5A4wZQ1/2+vWUUNixA3jmGTEAjuC+\n+7hCDAnhRLFiBb/rDz9kMFnwbCZPZlX87QbAXtzeCCjFE3rCBODwYaNHI+SE/fuZ3lm7NnDjBnPe\nFywAWrZ0rZibt6AU0KYNJQU2b2b7wRo1WIUs4oyeyYED7HnxxReOf2+3NwIAULUq2/8NHCi+Tk9B\na4pbde5MKYfq1WnEv/oKqFLF6NF5D76+lNKOjKSgXqtW3F1v22b0yISskpQEPP888OmnQPnyjn9/\nt48JWElNZdCrc2dg9GgDBiZkidRUSh9Mnsxc/xEjmLkizVTcg7g4uuECA2kURo6k6qonym14Cx98\nAOzdy5qpzHbO9sQEPMYIAMyHbtSIwa9WrVw8MOGuxMdTwuHzzxnDee89oHt3mVzclZQUVh9PmsQu\naCNGMJ4gxtq9WLWKKrMhIUCpUpm/zmuMAMBg12uvAbt2uadMsLdx5QrdDV9/zRTPkSMpbyC+fs/A\n2oNh8mSmY7/7LrW7RMHUeE6c4DWVlUWvqbODbqdLF+DFFykklpho9Gi8lxMnmILo40NVzw0bgCVL\nJNjraShFPabVq6nGuncv6w/ee4/ZXIIxxMUxbXr4cOd7PTzOCADAxx9zazRokCiNupr9+5l73qAB\n0zr376eP2R06dwn2Ub8+JSl27aKLqHZt4OWXKdctuA6LhddYjRqsoXE2HmkEcuWi//nAAapJCs5F\na+qVWDN9atfm6v+zz4CyZY0eneBoKlakcF9UFO/7+bEaecsWgwfmJYwaBVy6xLaorthVe1xMID1n\nztD9MGoUdwWCY0mf6XP9ui3TJ39+o0cmuJL4eFZ4BwYCJUsy7vPkkxL0dwZTpgDff0+hwOx0VvSq\nwPDtHD7MwpipU6myKNhPfDwwYwYzfYoVk0wfgVgXBZMmsehv+HC6LSSjyDH8/DN7T//7b/brAbza\nCADswvTEE+w36+/vpIF5AdevM9Nn6lT2Lh05UgK9wp1Y3YOTJgEHD9Jv/eqrwAMPGD0yz2XuXCZa\nBAWxwC+7eFV2UEbUq8fMhkGDuFIRsseFC6zIrlIFCAtjv96lS5mVIAZAuB2lWLi5ahVVYDdvZkbR\nuHHA1atGj87zmDmTqbmrVuXMANiLKYwAwCKylSuB119nEYxwb06eBN55h5IOV65Qn/6PPxj4FYSs\n0LAh8PffwMaNlLT28aH7UATrssYvv3DHvW4d+0IYgWmMAECFvdWrgbfeYmtCIWMiI5n6V68ekDcv\ni4S++46rOUHICdWrM1V4zx7GlGrWBN54g/0hhIz5+msgIIAaW7VqGTcOUxkBgLnOGzcydXTCBKkj\nSM/evZRtbtGCgaeoKKZ5mrlhu+BaypcHpk0DDh0CChdmbGnAAMYOBKI19c+++opBYCNcQOkxnREA\nqDq6ZQswbx7w5ptstuHNbNlCkbAuXViGHh3NRj3ZSUEThOxQogQXYkeOcFfQvj3VS4ODjR6ZsSQn\nU1Y9KIjXZcWKRo/IpEYAAB55hFb22DEWOV25YvSIXIvWdI21acOVWPfunPyHDQMefNDo0QneQqFC\nXPVGR9MQPPUU0KEDZUa8bZd++TLQsSNw7RqbKhUrZvSIiGmNAMATcOlSuoiaNuUW1exYLAyMN2oE\nDB3K1L3ISIruSZGXYBQFCgCDB9MF+dxzjBc0a0a9KW8wBmFhnIMaNWIGozu1/DRFnUBW+PVXZi3M\nmEHpA7ORksJc4/HjudIfM0YKvAT3JTWV6aXjx/Pxhx8CPXqY83xdupSJGJ9/zuYwzsDri8WyyubN\n3I6+8w7TssxwwqWkALNm8WIqUQL46CP2IJX8fsET0BpYtgz4738pWvfhh1TPzJ3b6JHZT3IyG8LM\nns0FWvPmzvssMQLZ4ORJoF8/oGBB7go8tSdBcjLw55/MgCpThoHetm1l8hc8E61ZLPXxx+xI98EH\nzGTzVGNw+jTQty+rqP/4g42WnInXVwxnh3LlmJfboAHrCjZuNHpE2SMpiTUQ1arRCPz8M/+Gdu3E\nAAiei1JM4Ni2jbIl337LrKIZM7jb9STWrKHvv1MnNsFytgGwF6/bCaRn1SrgpZcYpBozxr1XHYmJ\nVHKcOJF5xR99RF0fQTAjVn2ijz9mW9n332dA+b77jB5Z5iQn0631yy9coLVt67rPFneQHZw5w96q\nAIPHlSq57KOzREICT6pPP2VV4UcfOde3KAjuxr//Upfo8GEu1l54gZXu7kRYGIO+xYtzHrlbP2Bn\nIO4gOyhdmjm7XbuykGr6dPdIWUtIYEWhjw+3lH//TW0kMQCCt9G6NbB2LYXWFixgMehPP7lHEajF\nwh4AbdpQwHLFCtcbAHvx+p1AesLCuMooWpQnWblyrh9DUhJXEhMmsL5h7FiKdAmCQLZtYxbRsWPc\nGT/7rDGu3GPH2O88NZWu2ipVXD8GK7ITcBA1a7KjT6tWDBr/9pvrdgUpKWyZWb06Vzt//81CGjEA\ngnArzZtTdfPnn7lYq1WLKZgWi2s+32Jh96/GjelBCAoy1gDYi+wEMmHfPu4KSpYEvvmGbhlnYLFQ\n4ygggOmq48dz+ysIwr3Rmgbhww+BuDgGknv0cF6mXGgo3T5K0XXsLrLrshNwAvXqATt3smNZs2YM\nTCUmOu79tWbFZP369Cl+9RVTPcUACELWUYrFkdu2UbBu3DimZ65Y4dhdfHw8g9Lt2nFxuGmT+xgA\ne5GdQBY4cYJVxmFh1N1v1y7n72UVdvvwQ7qAxo3jllJy/AXBfiwWLq4++ojyKePGUbjOnutrzRrg\nP/+h++fLL90z8Cspoi5iyRI2rGndmjr82T0ZgoJYCXn1KretvXqZQ7pCENyN1FSbm/WRR7hLeOyx\n7L3HsWOUl9m5k8VrnTs7Y6SOwTB3kFKqiFJqjVIqQim1WilVKJPXHVNK7VNK7VFKeayiePfubI5R\nujS3ghMnMpXzXuzZQwnZV17himL/fqBPHzEAguAscuemPMzBg3Tf9OvHWEFY2L1/9+ZN7tQbNgTq\n1OHvuLMBsBd7p6FRANZprasB2ABgdCavswDw01o30Fo3sfMzDaVgQWDSJGD7dq4QatQA/vorY/9j\ndDTT17p25QkYHm5cOpsgeCN58lAVICKCWX9+fsDAgdQQux2LhTo/1avz2t27l8bg/vtdPmyXYq8R\n8Afwe9r93wH0yOR1ygGf5Vb4+DCV89dfudVs3RoICeHPLl5kDKFJE55QkZHcAbhzybsgmJn8+dlQ\nKSqK7qH69YERI2zNprZvp7to2jS6kWbONKZOyAjsigkopa5orYtm9jjd89EArgFIBfCD1vrHu7yn\n28YEMsNaLDJkCHDjBp97+23qnXiqSqkgmJkzZ6jzM306Hxcpwiy9AQM8001rT0wgTxbefC2Akumf\nAqABfJDByzObvVtorc8qpYoDWKuUCtdab87sMwMCAv5/38/PD35+fvcapqFYLKz0TW+7LBbXFa8I\ngpA9UlPvlJ1ISXEPyZisEBQUhKCgIMe8mdY6xweAcAAl0+6XAhCehd8ZC2DoXX6uPQWLReslS7T2\n9dW6Qwetd+3i8xcuaD1kiNZFi2o9erTWV64YO05BEMilS1oPG3bntbljh9YtW2pdr57W69YZO8ac\nkDZv5mget3fjswTAi2n3XwCw+PYXKKUKKKUKpt1/AMATAELt/FzD2b+fRSojR3IbuWYNpSYAKgl+\n8QUDS5cuUfr5k0+A2FhjxywI3sq1a3T/VKvG6/DAAV6TRYrw502aUK30ww9ZEdy9O4PJ3oC9RmAS\ngMeVUhEA2gP4FACUUo8opZalvaYkgM1KqT0AtgNYqrVeY+fnGsb58zxJHn8c6NmTxqBLl4yLUcqV\nA374Adiyha+rUoWZRda4gSAIzuXqVdYK+PgAR46wsvi775jmfTtKsbVlWBhVQVu2ZF3QpUsuH7ZL\nscsIaK2vaK07aK2raa2f0FpfS3v+rNa6W9r9o1rr+prpoXW01p86YuCuJiHBpun/4IPAoUPAm29m\nLePH1xeYM4eS1fv20RiMG8fViSAIjufyZRZm+viw4n/7dgo0Vq1679/Nl4+ZROHhfFyjBhAY6FjZ\nGHfCA+PgrkVr1gHUqAEEB3MlERho20Zmh1q12BR+82auSnx8eKKafaUhCK7i4kVg9GguvM6fZy3P\nL7/kTACyWDFqem3axGr/2rWpSWQ2xAjchfBwoEMHKnv++qutoYW9+PoypTQ4GLhwgY9HjGBzakEQ\nss/Ro3Td+PrSBbR7N/Djj0Dlyva/d/XqwNKlNAjvvst4QXS0/e/rLogRyIAbNxjwbd0a8PcHdu1i\npaGjqVyZMYO9e5liWqcOm1QcOOD4zxIEM7JrF9C3L5VDCxakP//774EKFRz/WZ068dp87DEGkseO\npXy1pyNGIB1aszlFzZrcSh44wKKvPPesprCP8uWBqVPZQ9XXl/LVnToxhuApecuC4CqsSrzt21OO\npXFj7gQmTmQ1sDPJlw8YNYp6YIcOca5YuNCzr1NREU0jPBwYPJj++W++YWaAUSQmsmz988950g0f\nDjz9tMhOCN5NQgIXaVOmsNhrxAjuAoxsOr9hA91QZcvSXeTra8w4pKmMHVibRbRuzVXFrl3GGgCA\nE//AgexiNH48fZuVKvH++fPGjk0QXM3p00ygqFCBWXYTJzLl+vnnjTUAAHuL7N3L3ftjj7H24PZK\nZHfHq43Axo3sIHb4MF0/b73lfNdPdsiVy9bDdPly4PhxBqkGDGBQWRDMitasr+nbl7Gy69dZzLVy\nJWWd3akJ0333MaU0JISZRA0bAjt2GD2qrOOV7qDr1xn4Xb6crh9/f6d+nEO5coUpb998Q3G6wYPp\nKsqXz+iRCYL9xMdTxXPaNCAmhguzF18EHnrI6JFlDa2B2bOBoUOBZ57h7v3BB53/ueIOygaLFzNf\nH2DDCU8yAABQtChjBIcPc4v855/cJo8ZY660NcG7CA9n+mW5cnT5jBtH2Ya33/YcAwBwh9K/P+eW\n69dZW7B8udGjujtesxO4cIGr5r176WNv08bhH2EYERFMNf3jD7q3Bg2icTPaXyoIdyMhAZg/n3LO\nUVGMg73yCuNfZmHtWuD114HmzRk4zkmRaVaQncA9WLyYk2OlSpRtMJMBACiKFRjIbkkvv0xtlHLl\ngPfe48UlCO7EoUN0l5QrRymHd96htMOECeYyAAA1xvbvBwoXBurWpdCku2HqnUBMDLeYGzcCM2YA\nLVo45G09gshI4KefeJHVqsUVVo8eQIECRo9M8EZiYii/8uuvdGW+9BLPySpVjB6Z61i3jrudbt2A\nzz4DHnjAce8tO4EM+Pdfrv7z5KELyJsMAMB85cmTucJ6/XW6isqW5YW3ebNnF7cInoHFwjz6559n\nQeSyZcztP3mSaZ7eZAAAStDs308p6/r1qWvkDphuJ5Cayoj899/T99+tmwMH5+GcOcNA8m+/Uabi\n+ed5VKxo9MgEM3H0KM+x338HChXiqr9/f2m1mp6//wbeeIMu2yFD7G9pac9OwFRG4Nw54NlnuQKZ\nNcv5JeSeitbMaf79d2Zi1KkDvPAC0KuXZ2ViCO7DlSuc2GbOpH5P//5M7WzQwOiRuS/HjrEO4uGH\naTSLF8/5e4k7CPS3Pfoo0KoV74sByBylqLfy9desxhw8mPon5coBTz3F+wkJRo9ScHfi4ijj0L07\nA7rr1zPge+oUtbDEANydihVZXFa7Nr+rTZuMGYfH7wS0pu976lT6vdu3d+LgTM6VK0zZmz2bcZQe\nPbiia9sWyJ3b6NEJ7kBKCif7mTMpr9ykCc+Rnj1lF2kPK1dy5xQQwBhediuivdYdFB/PQGdEBLBo\nEQOfgmM4fZqrvNmzubJ7+mluXZs2td9/KXgWqalcpc6bx0VChQp0uz7zDFCqlNGjMw+HD3Ph1bw5\nd+nZUQHwSiNw6hS/sGrVmAp5//0uGJyXEhlJYzB3Lnst9OnDo3lzMQhmJf3Ev2AB3atPPcXDEY2V\nhIy5cYM7gjNnuLAtWTJrv+d1RuDAATZ3HzyYGkDuJCZldsLCGAD86y+6j3r14sTQooW4jDyd2yf+\n0qVtE39O2jMKOUNruoVmzgRWrcrad+9VRmDTJq5Cp06le0IwjkOH6B746y9mZvXqxaNNG+l94Ckk\nJDCRYvFi+vhLl6brr08fmfiN5scfgY8+4v+mSZO7v9ZrjMCSJYwBzJzJcmzBfYiK4g5h0SLe79SJ\nWSOdOzNXXHAfrlyhqNmiRTQA9evTterv75ievILjWLqUVcazZt19zvMKI7BoEaPmy5axn6jgvpw9\ny5N38WLu3Jo1o0Ho3p2Vo4LrOXaM/49Fi9g4qX17TvrdugHFihk9OuFubN7MHfacOWxikxGmNwKr\nVrGydeVKNmwQPIebNymatXgxV5/ly9MY+PtzBSrxHOegNfvgLl7M48wZTvg9elC+QDSkPIt//6WL\n7q+/MhbANLUR2LiRgalFi9i+TfBcUlKArVvp1lu8mL2Uu3Wjy6htW6BgQaNH6Nlcu0bp4pUruXB6\n4AEaW39/XjsSuPdsgoIYr1m1ioWx6TGtETh6lGmIf/7J1YtgHrRmI5EVKzhpBQezBqFTJxqFmjVl\nl3AvtKYgmfU73LOH/bE7d+YhqZzmY8ECSm8HB9+qimBKIxAby9XLyy+zu5Bgbm7epOLkypU8LBYa\nhE6duACQalRy/TqDudbv6f77OeF36UI3gbh5zM+ECdxJb9xoq48ypRF47jmmGf7yi6wIvQ2tWQW+\nahUnuq1bGQuyGoW6db2nSC01lYHcdesYW9m1izUZ1olfVvveh9ZMjy9WjL3GARMagfnzNUaNon6N\nrGyEuDj6Q1et4nH1KmMI7dvzqFLFPAsFqwFct44aPUFBlEPp0IFH27ZyTQiM/9Srx7ayHTua0AiU\nKaMxZw79m4JwOydPcoLcsIG3efLYDEK7dp6nIHvmDP8O68SfK5dt0m/XTvR5hIxZtQp46y0gNBTI\nn99kRuDppzXmzjV6JIInYF05r19vWzk/8ojNKLRpw/6u7sTly8z9tk78585xsu/QgWP28THPzkZw\nLt26AU88AbzzjsmMQFiYRo0aRo9E8ERSU5klYzUK27ZRZLB1a/aaaNXK9cVR584xz9t6HDvGrDfr\nxF+/vqRvCjljxw7GB44dM5kRcLcxCZ5LYiK7qFkn4K1b6WNv1cpmGMqVc+xnHj9+66R/8SJdm61b\nc2fSoAFdWILgCBo3BkJCxAgIQpZISWFuvXWC3rSJRWpWg9C6NTNusuqOsVgotb15M99v40aKsrVu\nbTvq1PGebCbB9UyYAHzwgRgBQcgRWlMNNf3KPSmJ7prmzal71KgRq28B6r3v2EE307ZtwPbtFMh7\n7DGu8lu3pvtJfPqCq1i7FnjiCTECguAQtAZOnLBN8n/8wZTU9JQqBTz3nM1QeFo2kmAuwsOBmjVz\nbgTEMykIaVy9yvjBzp22VX7BgnQT5c/P1yQksGDrt9+4gzh0iIagUSPgwQcNHb7gpSQn2/f7shMQ\nvJIbN4Ddu22TfkgIcP48g7aNG9MN1Lx55n2rT52yGYpt24B9+9h7t2FDGoRGjZj1Y3UjCYKzmDMH\n6NdP3EGCkCnx8aw+Tz/hHz9O+YlGjTjpN2pEX35OUzWTk4GDB7lLCAnhcfAgm7RYjUKjRqzylH7Y\ngiN55hlg3jyTGYEjR7R0OBJyxKVLXJXv3Wu7PXyYqqTWibhxYz52dgvMpCRWc4aE2IxDeDizjxo2\n5K6jbl0aBncraBM8g4MHAT8/4NIlkxmBVq001q0D8uY1ejSCu2KxcHK/fcK/eZMTa/36POrVA2rX\nBvLlM3rEJDEROHCABsE67tBQoGhRjjX9UaWKpJYKmRMXx3jVyy8Db75pMiPQs6dG7tzsI+AuF69g\nHBcuAGFhXPWEhnLiPHCAlb/Wid56W7Gi56VnWizAkSP8u9IfV67QgFmNQp06QK1aQJEiRo9YMJq4\nOHYaK1qUGWy5cpnMCMTFUUr64kU2WM4sOCeYi4sXOdFbJ3zrkZLCyc961K/P1b7ZXShXr7KwzWoU\nDhygO6lgQbqzatXirfWQXsHeQXQ00K8f4OtLqf377jOhiqjWGhYL8MknwLRpwLhx3PJIqb3nY7FQ\nBTQykkd4uG2yT0q6dbK3TnKPPOJ5q3tnoTUzk6zG0nocPMg01vRGoWZNThSlS8v3ZwaSk9k/YMIE\nYMwYdhizugtNaQSs7N0LvPsuV4ljxrDHprMDeoJ9aM0ArXWiT38cOcItrK8vj+rVbZO9TFY5R2tK\nUqc3DGFhQFQU4yQ+PgxI+/reelusmHzn7k5SEl3jn34KVKoEfPkl7hDYNLURAHiCr1oFTJ7MYODz\nzwPPPsuJQzCGlBSu6I8evfU4fJiTPcCUS+tkbz18fKShvKuJiaExiIzkrfW+9f+U3ihUqsSjYkUa\nZVE3NY4DB1iUOHMm3Z+jRzMTKCOjbZgRUEr1ARAAoAaAxlrr3Zm8rhOALwHkAvCz1nrSXd7zrnUC\n+/bRKs6eDRQvDvTqBTz+OFP/xF3kOFJTWTx14gQn9+joWyf706eBEiVsk0blyrytUoWT/8MPywrT\n3dGavQ3SG4Zjx2z/48uXqbBqNQq335YqJf9jR5KSwuLDVauAZcuYGDBgABe91ard/XeNNALVAFgA\nTAcwPCMjoJTKBSASQHsAZwDsBNBXa30ok/fMUrFYairFvpYto4DSyZNsvdeiBQ1CgwbSnDwoKAh+\nfn53PJ+SQo37U6d4nDxpu299fO4cs1DKl7dN9Okn/PLlvS9zK7Pv06wkJLCoLr1hSH//xg3uFsqW\nBX1PkmYAAAYwSURBVMqU4W36+2XKMJ6T2eLM277P24mJYfFicDBFCTdu5PVl7aXdokXWd2L2GAG7\n1s5a64i0Adztw5sAiNJaH0977RwA/gAyNAJZJXduTvpt2/LxuXNsIrJjBzB/PncM5coxta5atVtd\nE4UK2fPJ7klKCv3w58/zuHABmDEjCCtW+N3y3PnzjK8UL267aK1Ho0a2+6VLe98kfy+8bdLKn992\n7WREXBx3hKdPc/Fw+jTdgRs32hYUly4x7lCmDHcOJUrYjk2bgpCc7Pf/x8WKmS/epzVw/Tq/l/Bw\nak2FhzNec+oUM92aNmW2z3ffGSNG6AoHShkAJ9M9PgUaBodSqhTjBM8+y8cpKfyiDxzgNnfpUpsf\n9L777lyxlCpFF0bRorceBQs6v2DHYqG0QWwsj7g43t68yTTBrBzXr3O8JUoAJUvyuHGDf1PNmrc+\nX7Kk+S42wfUUKMA4QtWqmb8mOZkLtNOnuQixHseP0wU1aZLtucuXuXsvXpy70CJFmAZcuHDm9wsW\n5DisR/78zr9eU1J4fV6/zjFfusTDev/0abpRT57kAdBNWqMGEyH69uVtjRrucR3e0wgopdYCKJn+\nKQAawPta66XOGpi95MnDYErdurc+b/WD3r6C2buXPrj0x+XLnJDz5aMQmPVEe+AB/vPy5OGOxHqb\nOzdPwNRUnijW29vvp6TYJvrYWG678+fn+1o/x3rfejFYjzJlONnf/nzRonduHQMCgPfec9lXLgh3\ncN993JFn1L0tIICHFYuF192FC8C1azyuXrXdnj/PftLpn7MumqxHYiKvpfSG4f77eY3mymW7Tq3X\navrHqak0Wikpt94mJtoWZbGxfK5gQRqsYsW40LLePvwwd9Q9e9r+7kKF3Dt24pDsIKXUPwCGZRIT\naAYgQGvdKe3xKAA6s+CwUsq90pUEQRA8AHfoJ5DZAHYC8FFKVQBwFkBfAP0ye5Oc/iGCIAhC9rHL\ne6aU6qGUOgmgGYBlSqmVac8/opRaBgBa61QAgwGsAXAQwBytdbh9wxYEQRAcgdsViwmCIAiuw1Ch\nWqVUH6VUqFIqVSn16F1e10kpdUgpFamUklBnJiiliiil1iilIpRSq5VSGSbDKqWOKaX2KaX2KKWC\nXT1Odycr55tSappSKkoptVcpVd/VY/QU7vVdKqXaKKWuKaV2px0fGDFOT0Ep9bNS6rxSav9dXpOt\nc9NotfIDAHoC2JjZC9KKzb4G0BFALQD9lFLVXTM8j2MUgHVa62oANgAYncnrLAD8tNYNtNYOT9f1\nZLJyvimlOgOoorWuCuA1AN+7fKAeQDau3X+11o+mHeNdOkjP41fw+8yQnJybhhoBrXWE1joKmQeV\ngXTFZlrrZADWYjPhTvwB/J52/3cAPTJ5nYLxCwB3JSvnmz+AGQCgtd4BoJBSqiSE28nqtSvJIFlE\na70ZwNW7vCTb56YnTAQZFZuVMWgs7k4JrfV5ANBanwNQIpPXaQBrlVI7lVKvumx0nkFWzrfbX3M6\ng9cIWb92m6e5LpYrpUQW0j6yfW46vWLYU4vN3JW7fJ8Z+VIzi/q30FqfVUoVB41BeNoKQxBczS4A\n5bXWcWmujEUAfA0ek1fhdCOgtX7czrc4DaB8usdl057zSu72faYFjEpqrc8rpUoBuJDJe5xNu72o\nlFoIbtvFCJCsnG+nAZS7x2uELHyXWuub6e6vVEp9q5QqqrW+4qIxmo1sn5vu5A66Z7GZUiovWGy2\nxHXD8iiWAHgx7f4LABbf/gKlVAGlVMG0+w8AeAJAqKsG6AFk5XxbAuB54P8V8desbjjhFu75Xab3\nVyulmoBp62IA7o5C5vNlts9NQxX4lVI9AHwFoBhYbLZXa91ZKfUIgB+11t201qlKKWuxmbUfgRSb\nZcwkAPOUUgMBHAfwNMDiPaR9n6AraWGaPEceADO11muMGrC7kdn5ppR6jT/WP2itVyiluiilDgOI\nBfCSkWN2V7LyXQLoo5T6D4BkAPEAnjFuxO6PUmoWAD8ADyulTgAYCyAv7Dg3pVhMEATBi3End5Ag\nCILgYsQICIIgeDFiBARBELwYMQKCIAhejBgBQRAEL0aMgCAIghcjRkAQBMGLESMgCILgxfwPNpGS\nKJZhs0MAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fe85468d550>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "t = np.linspace(0,2*np.pi,1000)\n",
    "x = np.cos(3*t)\n",
    "y = np.sin(2*t)\n",
    "plt.plot(x,y);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### EXAMPLE\n",
    "\n",
    "Plot the [butterfly curve](https://en.wikipedia.org/wiki/Butterfly_curve_%28transcendental%29) with variable parameters:\n",
    "\n",
    "![x coordinate butterfly curve](https://wikimedia.org/api/rest_v1/media/math/render/svg/6a17a33d739ede62a269949b5bf551a875397102)\n",
    "![y coordinate butterfly curve](https://wikimedia.org/api/rest_v1/media/math/render/svg/92e1ec07900777c282b5c379b0877906f4594727)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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7sWkT/fEB+tMnF8o2KUmkRg1O6y9RgmME58/zfOHh7Jkrl0VNxrJ8+XKbViI9\nzSwAcgFYCOBVH2XS/CZoUsawYRTSK1dMEYuIoNju25d8vQMH6LusREtNNClZ0r/d9803Wcf6Sq8m\n87ibUzZtotiofYHYcw8dMuu1bMltypRSvDh950UYl6ZpU7Ncq1ZmvVy5nJ9PROTiRda76y5+Tptm\n7lPjE+4Pyv37uX3ZsuSPu3Sp2abXXhNZsMBcf/BB37Hof/qJwdOqVuVEseho2sybNaO4b94c2DVq\n0o/0FvMZAMb7KZPW16xJIS4Xe4v3389JLXfeyb+Mrl3Za/Mlnpcv0+NEiUqBArTnhoaKbN2afL3j\nx1le2W0V585xe5489vZZxXzv3sCuTdUrUsS0iw8YwBmSiv37zcHKevXsPetAZ0CqtwF1H9Ws0fh4\n85juVK/u+0G1YoVZd8gQvlGp9WnTfP9G0dH0qMmfn4PbiYl8WDdqxN9pwYLArk+TvqSbmAO4G0AS\ngK0AtgDYDKCNl3Lpcd2aFJKQwOn8Tz1l9wKpUEHks898101MFHn9dbsAfvEFBxWVy583AA7gubN6\ntXgMOvbubR57/PjAri0igvWKFeObBiDy+OO8XsWVKzQvKdG3mlhmzw7sfMqVEmBvWKEE++pVe/nr\n17n93Xe9H2/NGvN4o0czpK1a37LFf3vU4HZYGIW9d28+sCpW1CFtswLp2jN3dCIt5pme69cZs6N/\nf5EdO0zBCAlx5nr42Wd2QZ88mfGzk4v/rVKoefPfVnZldd7Vq3ksgOaRQPjwQ/nPo+Wbb/i9TRv6\nuytcLr5VWNtfoQI/A7ElK5dE9Sbx+efcPnMm13/5heK8aJHZm37jDe6LjfU83qZNZnsmTOBDSN0D\nJ95DX37J8vnz0yw2ZgxNLbVrm2MImsyNFnNNijh3jnbwSZNoLlFC0rmzM1v1n3/aBXHUKPa+vU2Y\nUWaHhx7yfiyrScLlsrtEuvdufbFhA+uULy/y6qv83qQJ3yasqJ64+xKIjV4NIqtByYsXOdAI8EG5\neDH33XYbBzCVGahxY89jbd9utmHsWNMGX7cufyd/bN9u+sn/+CP90suUYdCwRx9Nn/g6mtSjxVyT\nYo4cYc9y1ixOOrG+4jvh8GFOKlL1Bgxgb1ANNlp58UWWUQGorl9nIuqoKE52sQ4gqsFZILAkCypB\nRNGinPgE0MPE3ayhxNK6uHui+EN55KgHhtVm/8cfFPKVK3nuvn3NiUInTtiPs3u3iGFw39Ch5kBz\nmzbOZqKyBKccAAAgAElEQVReuWLWeeUVDp4WK0ZTT/v23t8CNJkTLeaaVLFlC4Vn2TJzxiTgPBRt\nVJRpIwYo2jVreoaQVZEFe/Tg+jff0GZdr57IP/+YXiXXr1PglCnkjjsCux5Vr2hRs5c+ebK9jDVS\npFreecf5OWJj7XW//Vbkf//j9//7P97PpUtZtmlTc2KR+7/G/v1me1991TT3dOvmbEKPy2WaY+68\nk28mxYrRa0ULedZDi7km1fzxB70drJ4UgHM3tpgYcwYkwNCq9et75iR98knuj4/n9ylTKIIVK5qm\nhhIlWLZ+ffN4gZg/+vYV2+BmoUJ8cERH043yyhWRl17yFPNAPD2sroKAyKlT/KxXj0KuPHeionh+\nNRhr9eg5etSc8dq9O91DAdq3nV7v1KnmPVu1igPRAP3qtZBnPbSYa4LCzJnsGf7+uylSOXOy1+yE\n2FgzkJcyEzRuTPFUxMSYvdBp0xh7W4RiW6oUe7UA426PHWsea9Mm59eh2l+smFl//nxOjipShAOD\n775r7suXj59ObNOKNm3s16kmOt1+u93XfN48TptX3jNKpC9cMMcFHnzQtHcHktBajQ8AFHL1dtS2\nbcYk59akHi3mmqDx0UecXagG9wCaTJzGSYmLow+7qtuwIUXUWl8lgDhzRqRwYVPsR4/mw0D1Vv/+\n24yt0ry582s4eZJ1rB4rK1bQy+PTTznAO2WKZ8/cKdYJT4DpPtioEYXd2qvu3p0LwMiOIhRaZbO/\n7z7zON99F/g1qt6+st+3aaOFPCujxVwTVD79lIOi1unxDz3k3CMiIUGkUyez7p13UuDVa79y6Rsy\nhML+1VfcnpTEGZkDBphC17KleRyn57cORKpl9mz2XA8c4NvHtGn2/WFhzu9PZKTn8QGaV6yDm8eP\n298O1DU+8oh5X9S+JUucn//iRXPAdOZMth0Qad1aC3lWR4u5Juh88QUnxIwfbwrOoEHO6yck0ISi\n6jZpwgeCylGpzDHffksRUpw4QZPFU09xv/LLVqYEp7gL7bhxbI/LRYEdPty+36n3johp97cuxYrx\nWqy8/jo9ZABzhqwKbaDixQNmnHEnXLtmTlSaPNkcsNZCnj3QYq5JE775hr7K/fubwvP1187rJyaa\nnhYAE1OocLsqUcOQIbRjWycq/fyzdz/w+vWdn7tLF3vd55/nQKsI3xKUqUctkZHOjuut1w+wt201\nr5w7Z/bKVbyXyZO5rrxslC3fKXFxpjll6FBOBtJCnr3QYq5JM77/nh4SL7xgClBy0fq8kZRk76FX\nqGC6CSoTSteunsGonnvOPpiqFqcRDT//3F6vSRP6eYvQddI9Jot1kNYX69d7tqlUKc/B06FDzf3/\n/MOgZO71nLp+ivDB2K4d6/XqZWY0UjF2NNkDLeaaNGX2bJo+rKLsHtLVFy6XaScG6II3b545K7R0\nabrWWVPSXbtm911Xy6JFzs65caO9XtWqZnKO/v3tIX0D+XN94gnPNv36q8jcuSIq0vOVK+YgbliY\nPd6KWgIZ7HS5mBEIoKCr+9KqlbPkFpqsgxZzTZozdy4F3RouduNG5/VdLjMIFkCx27CBoQQARmwc\nNoxl9+5lOrfNm+mjbRVBp+nklAukWkqXFtm5k/tUlh+1hIY6vwZ3UX7mGfqch4bymg4fFvngA3P/\n1q2edVT+VacMHCj/mZlUtEct5NkTLeaadOG33+ixYZ3GHkhsbJfLTJgM0B5/5Ii9x37hAl0HCxVi\nrBfrAKhanE6GsdbJn98MVjVxon3fq686O541IJn1TaFECboHFi5Ml0E1+cfqi64Wqw+6EyZMMB84\nauDzvvu0kGdXnIp5UNPGaW482rcHvv4aOH6cKckAoEEDYNs2Z/UNA1i2DChbluunTgHt2gHLl5v7\nx44Fzp0D3n+fqe5CQ4FSpezHWbDA2fnCwszvMTFMnwYAISH2cvfd5+x4ffva1199lWnYPv8c+Ocf\n4N57mebtwgXu377dXv6DD4AXXnB2LgD46ivg9df5/fp1pol76CGm4POXbk6TzXGi+MFYoHvm2Zo/\n/mBv1GoC2bHDeX0Vo0UtLVrweAA9QMaMYfzxw4cZV6V1a88erhOsszwBc+LS7Nn27cmF7bXiPlGo\nZEm6F37yCfeHh9NfPn9+z7YCgbl1ingfMH3pJdO1U5M9ge6Za9KTe+9lMuB8+YBChbitTh1g925n\n9fPkAa5cMdeXL2eCaAC4dImJh1euBPLmBebPZ3LmMmXsx7h2zf956te3r6verHvP3JpEOjkWLrSv\n33wzULcu8NxzwLFj7IVv28Y3AHeefx4YOdL/OaznevBB+7aRI4EpU5hsW6PRPXNNUFm5kj1Uq9/0\nnj3O6589670XmyMH/cDfe4/lRo407dBqUYkgfPH3395786tWBd7LV/FbrD1zFeZ35Ej7tHzrEhER\nWJAwa1x5tUyf7ry+JmsDhz1zg2XTHsMwJL3OpQkO0dHAxInA1atAXBx73I89BtSs6bvepk1Ax47A\n6dOAy8Vt+/YB1ao5O+/Ro0Dlyp7bGzUCzp8HDhwAEhOBhg2BHTuApCSzjL8/MREgRw77OsCeb9u2\nzo8TFQUULWquFywITJ4M9OjBN4wqVYDChYFDh+z16tRhb90wfB9fMX060KuXfduvvwIPPJB8HRHe\n71Wr+Dazbx/fZm66ydk5NZkLwzAgIn7/YrSZRZMsiYnA6NEU0I0bgRkzgFq1KEQTJtD84Y3bb6eQ\nVK1qbqteHTh40Nl5K1XyPoC6bh3bMn8+kDs38MUXdiEHgIsXfR87ORE9ccJZ2xRTptjXmzQBunfn\n93Hj2D53IQeAzZudC/mECZ5CvmaNdyEXoXA/8ggfVjVqAM8+C9x9N1CuHPDxx87Oqcm6BEXMDcOY\nbhjGGcMwtvsvrckqFC5Mz4n4eODwYaBkSdPL4403gOLFgXr1gEWLPEW1cmXgr7+Apk3NbVWr8jhO\nqFsXWLHCc/uVK8DAgTxfWBgwaJB9/9Chzq/PitW237ix//KDB9vXP/mEIn3uHPDhh/QycefqVSBX\nLmftGTqU99jKnj2ebUtM5Llz5ACaNeO4Rf78wIsv8n4bBh9UOXS3LfvjxBbjbwHQFEAYgO0+yqSp\nXUmTNly+TFtww4YMdKU4csRM+aaWqVM9p9bHxNhnegJMyuCUH37wbndWURVjYzmTMxB7t7eyVl93\nf9mF9u61H8Mab9ybDzzgPP67yyXSu7e9br58nvWvXhV56y2zTK5c9KJRfvOXL5tp4158MTAbvSZz\nAYc282AOcFbUYp492bRJJCSEfy0//GDfFx9Plzm1H+DgnzU0bVKSp8j99Zfz87u7E6oJMyr+yNq1\n9n179/o+nsq8Y/2TtNb351IZHm4vr1wDjx/3LuTbtjm7Tmu6N7XUqGEPafDPP0xcofY3aeKZLPva\nNTMjU69eOnFzVkeLuSaonDxpJmkeMMB7T+/oUSZjUEIzbZq9nPssy59+cn7+tm09RXL8eHP/66/b\n9/nCGj1RCZ03cfaGu2/59u3mvmef9WyjCuTlj6QkewIPwJ4d6OxZ+73t1o0P2fnz7fc4Jsacjdut\nmxby7ECmFPNhw4b9tyxXEYg0WYaYGNPdrmnT5KePnztnvuKr3rwSHGu2IncThS+SCzOreq2XL9u3\n+5rer8LOAmbiCKcPgpkzzXIFCpjb9+/3bJvTa0tIYIJqa90XX+SDIzbWPkGqZk2KdNWqNH/ly8c3\nAhHed5Vqrk8fPZkoq7J8+XKbVmZKMddkfVwuexIHX7bgo0ft5hcV3XD1artwvfSSs3MnJHgK5sCB\n5v4PPzS333138sf57Tez3MqVzNLjVMyt5Y4eNbdbsygB9vEFX8TFcUarte5773neZ4Ax3u+/n3lQ\nt27lvS9ThiF4f/3VLKdS0aU3SUk08Zw9q0PwBhOnYh40P3PDMCoB+FVE6iSzX4J1Lk3G88svQKdO\n/P7nn/SkUHzyCTBrFj1d6tYFihSxz17csYMzPhs3Nt0bw8OBpUv9e11cvgwUK2bfdvIkZ4PGx3OG\nqCK5P7dt28wYLV99BdSuTXdKf/UOHaL/uHu5devsXiblywN//+3/WqKjzdgwilmz6M9v9XkPCaHL\nYf/+pq/+/v1AmzbAE09wNuyiRSx36BC9joJJXBx91XfuNJfjx9l+6xIXR0+a/PnpbRQRATz1FNC8\nuZ6lmhqc+pkHRcwNw5gJIBzATQDOABgmIl+4ldFiHkR27QL+7/8opPnyAQUKeF/KluVElTp1PINT\npZZ//qFwAcBddwFLlvCcCxcCjz8ODBjAKe3LlgF33EGf54EDWb5qVQrQAw+YboGFCtFPPHdu/9de\nu7a5/sQTwDff8Psnn5iBq774wvT9tnLxojmBZuBABgZ7+GFzf3J/plb/8AMHKOyJiZ7tjY21P1S8\n4T7pCAB+/plBs6z06cNgXiqIGcCHR6dOQJcudIMEgP/9j2Lv1IfdG0lJfBhYRXvnToZSuOUW3nO1\nVKzIB5H1by1fPvP8p04B333H3+XcOfrXB/shc6OQrmLuBC3mwWHjRkbmO3qUsw07duQsS/deUnQ0\no+odO8ae8I4d7B3Vrm2Ke506nASkYqmkBBFOSHnpJa7Pncs23XEH0KED/aXj4znhaOxY9qpLl2bP\nHqDgb9sG/P67ecyrV/23aeZMirhiyxb2tkW8z/B0R4nOgw/yQdSvn+8658/bxUiVefxx4Icf7OX8\nzbQ8cMA+G9YwOFHqyBFz28CB/J1DQ+11f/uND6ibb+Y1A8DevZyUFShRUfTlX76cE4527+YDX/2N\n1KzJCUfFi9O///x5vhnVrs177cRn/q+/2Dvfv1/3zlOKUzEPms3c3wJtMw8KixczmuC1a4HVc7lo\nY120iDbXp5+m10OBAsyt2bEjE0FERjqPDW7lwgW6CwKMsb1zp8hddzHS4aVLLJOYyLRojRqZCRXU\nYvXzBkTOnPF/TvcMP2rAz5pwessW73XV/ltuMTP2+LKZW/crt8pt2+zbd+3y3+aFCz3t/tZl5Ejz\nflm5elXk5ZdFDMMs+8gjtLk75coVJs3o148DroUK0c2ySxd64vTowd+hRg3+jeXMyYiV1arxt+zY\nkfe8Vi3a79u3F/noI9/njIgQmTLFeRs1niC9B0D9nkiLedDo0MFMRJxaEhPplz1rFlOnNWzIf/J7\n72UiiDVrnOfYFLF7q0ydSq+KW281M9GL8MGyYgWvw5ewHTrk+1zuHi4qMbRIYOJcpIj5PSzMs2x0\ntOfx3M/9xRf+783o0clfa7duzLI0cSJ/Byt//OE5SLp6tf/zXbvGh/eAASKNG9PzpUQJPsDCwkRu\nv12kYEGKdZcufMgvWcKH0pkzvn/3M2c4uapSJe/7T5/mIHDlyoF3PDR2tJhnYw4eZMTASZM4accJ\n164xNVmLFux53X03oxB26yby2mv8x5w8mWK8davIL7/Qd7tePWbLadeO/+ybN/v3Xb52TeTOO03h\nGT+eImJNjXbpksiMGTyPtyTNalmxwve53FPBHT7M7VbhVO6HVpI7X48enmWtk4RmzOA2NSkH4MPP\nFy4X77W384WEiDz0EN+SbrqJv8vtt7NeVBSTWFvL9++f/P1PSGDO0cGDeRz3c+XMyVyhXbuKjBvH\nt7CoKN9t98Xzz4uMGOHZhkmT+Hv368c3Ck3qcCrm2maeRdmxgwNjx47RFt2+ffKDXytWcKCxeXPa\n2atXpxfJxYu0V8+fz4G8xERuP3aM9Zo3p5dGxYqMFX7kCO2rZ89yX8uWXGrU8H7uFStYDmC882PH\nOAg6dizt4rfcQs+HatU4aLh3r/f2T5oEvPJK8vfi1CkzUxFA6UpKstt03f/0rO2tUIHeGQCDZFlj\nooibDT4+noPOrVqZ21yu5O99XBzHCbzFNL/lFt7vzp1p/8+ZE+jaleMIt95q92ipUoXjJUWK2I8R\nEwMsXgzMmQP89JM9pnuePPy7uOceeuuEhbGthw/zt4yJ4W9buTK9gZzatK9eBd57D/jsM2DrVtrV\nAQYBe+klDuxOmcLxGE3q0TbzGwCXizMAb7uNk3mSmzZ+8SJfpT/91NwWF0d/5ptuoo9069a0i9au\nnXyvVZkhnnyS9tNWrfiaXaECzSmRkZ4TVeLj7TMjixShbX36dJGHH+ayYAHfAgoUSP68zZr5vhcq\nLybAKewiIkOGmNvc7dDFipn7nnzS/L5wob3ciBHmvr59Rc6ft7fLV8/Tvax1yZePbwGHD/N3nDiR\nk4BmzBB57DF7WfecqpcuiXzzDXv07sdt1EjkzTdpIpsyhfFbHn6Yv1HOnDSr1K1LW/bjjzMcQOnS\nnN374ou+73FSEttXtixNKGqOwZ49HHcoW1bk2291HJhgA21muXGIj+c/bmgohcw6mUWxbx/3z5vH\nfzaVjGHOHPMY06fzFT801BzMdLLUqkVRqFaNgtSrFwXaOpB6+bJnQKz69WmOqVaNA5XnztmDR3lb\nfA34Wcvt3Utzj1ovXdpe1hoDpUoV87uaTentmOfO2ddnz06+LTt3Jn8NXbuawcauXBF59FGas6wP\nDoDmCiWMJ08yPILVfAUwJV2nTjxmly6eCTO8mVqKF+c4htXO/+qrIkOHJn8969fT7n7HHRwAjomh\ncDdvLlKqFFPgpcZko0keLeY3IBcvsldWvDh7zd99Z5+Jt2IFBbVpU/ZAv/uO4rtgAXt/OXJQUFTv\nOjGRs/l27hRZtozT8seMMWN/JLcUKEA7e9GiFJnZs81BsMOHPcuXK0dRmjyZ4nX6NO34yR0/uVmn\n7oOSiYkcE1Dr1nsxaZL3Y1t7lQsWmNvbtqUNWK3nyJH87zB3rvdjP/ww76Vi5UrasK2hDwAOPkdH\nixw4IPL++54ZlcqVo/hb861al9atRd5+m2MUa9fa30ri4/lQevJJvs3Ex9MjpXhxT28cl0vkzz/5\nG5YuzYf9rl0caC5Rgn9js2YF5lGjCRwt5jcw0dGMIdKqFf9JX3pJZONG/nMmJLBHVaMGPVfefps9\nq/792bsvWVJk6VJn5zl9mgOYgwZRYPz14CMi+Jp+8SKFzFuZTp1onhDhwKV7mF21LF7svU1bt5pl\nwsMp/Gr9nnvMcuvXez+uFev2779PvpyVoUM9j9m0qd1F8vRpuoZ6O/+SJXQRTS4JtPvSqBFNLvv3\nO/M6io7mA7l4cYpy1ao00W3aZJY5cYImuCpVGAtm1CgKfrNm/FsZMMBZwmtNcNBirhERmlzeeYcu\nYnXqsDd29iztn7NmsYd30020dxYpwk+AphJ/oWDdSUqieeOTTzxNKu5Lq1YiH3/Mnqe3/R9/bL4h\nHD3qPWqi1RXRitVGv3Sp3a1P9bzj4nyL+cGD5jZrfBmAPVtv1+7tgfbNN+Y5ExP5wEyu1+7ufuht\nufdePoydxke3tm/GDJGbb+bvXawYxz/UQzEujp5M7dpx33PP8Xd8/XXdC89otJhrbCQl0VTy5JMU\n7YceYkCmmBja0Rs25OCYu3jccw973ykNpXroEHv/vgSqQwfv4n/zzbTtKxYt8l7fW3RA6/5ly8zv\n1sQTvsTcus06UcfdFU+Eg6Dux3nuObt5Y80a9nKd9LatS+XKtG272/KdkpjIwGLWB02lSnzIJCXR\n7PPGGxwjadyYJpXu3TlgesstuheeGdBirkmWy5fZ67r7btq2O3Xi+qJFfMX3JqyGQY+L1AxyXb/O\nB0jDhoEJWseOZk80Jsb7IKm7t0psbPLHU6h1q01axD5wmlxdhRpIti4bNpj7z50T6dkzsOvt3Vvk\n2LGU32eXi2a155+3H7drV3o/rV3Lh9Kdd4rkyWPa4AsX5t/E6NG0jWuvlMyBFnONI86d42v7E09Q\n1OrUoVhOnmwf8LMudevSC+b69ZSf1+US2b1b5IUXnIvc8OGmh8yBA5773W3969aZ+6wxwZX9Wq3n\nycPP0FBur1jR+/ndbdItW9r3WwePExJoKnJ6bWPGeJ/GHwiHDvFh7N6znzqVvfsePexZlgC+jXXu\nzMHSs2dTd35N2qDFXBMwiYk0BwwZQhfFokVpy+3dm706byIUEkL/dW925ECIimJcEifCN28e67hc\nFCnrvttusx/XPXuPtYftvu2tt5JPgrFypf0+ue8/dYr7kpL4cPR3DQUKiHz9deoeiCIUYGssGrX0\n6kXzSfPm9CHPm5duiQDNV71706MpJXF4NOmLFnNNqjl1imL5yCMU9vr16flgTV/mvrz7rv+YKv64\nfp1JJ/wJ4rp1LH/liuc+a5gDb3W9mWFWrfJMPwfY47Vs3GjfN2oUt7tcDCLmq72FC/ONJjWDiImJ\nvG5vD9c6dRiuwRprBqAbZcOGfHPYulWbT7IaWsw1QSU+nj7H/ftTNAoVom29QoXkxeu++9ijDSRQ\nlzsXLnjGJ3Ff1AzJJUvs21VmwuvXPes0aMDJTu4PgOR68SI0L1m3X7hAYbT6o3tbZs9OeQo3l4sm\nJXfziVoqVKA7qfv25s0Zo2XhQntCaE3WQ4u5Jk25eFHk99/pV92qFXudVq8Pb4vyjElpFL3jx+22\nb/dl2zbP1HJqco81VZxa3nnHvm71elHLxYs0nVi3hYfzmMl51wB0uUypgJ8/zzciXw9K96VlSwZC\nW7tWuw9mN5yKuQ60pQkKSUlMbrBmDRMSrF4NHDzou84ttwCDBjGZRYkSgZ3PmvrN274NG4Bevcxt\n8fEMPGXl1VeBiROTP8eiRUDhwkCTJua2NWuYEu7xxz3Ld+zI4FOBZtS5eJFZhsaM8X/PFE8+yVR7\nTZsyUFlqMgxpMjc605Amwzl/Hli7lgK4ciUXfwwfDjz9NKP5OREoEXumIysLFgDt2pnrS5cyeqMT\natZkdEAVTREA3n6b6dnc+esvu+D74upVPiSmTWM6PSdUrsw0cU2bMupk6dLO6mmyB1rMNZmOxETm\nBF2zBti0ib33/fv913vrLaYeq1nTd5Jkb3k104pRo5hqzle+0pgYhsv95BOm03NChQq81jvuYDLs\nypX9J4bWZG/SO6FzGwAfAsgBYLqIjPFSRov5DUxiIsUtJgZISGDy3/z5mfj42DEmad65k0Kv8oP6\nonFjxjhv394zxjcADB5MwQ02R4/yrcGduDgmsv76a8YVd0LDhsBjjzEHqTUXq69/Ey3sNx7pJuaG\nYeQAsB/AvQBOAtgA4HER2etWTot5NiEhgckN9u8H9u3jsmYNxTijue8+YMgQmiNy5gTOnEm9WaJc\nOdPccuQI8OuvwOzZwKpVqW9vaihUiOMGzZrxGkND+aC54w5nyZY1WYP0FPPGAIaJSNt/1weAo69j\n3MppMc/CREdzsHLBAg4Axsd770FWq8bMQ7fdRnEJCeEgYv78NEmcP88e7PnztB9fuQKcO8fsRTca\nOXIAN93Et5PcuXmPr1zxnpXISokS5oPKnTx5KPJt2gAdOvAzvUxPmrTBqZgH4/ldDoBlmAgnADQM\nwnE1mYTDhykM9erRhPDzz8CECcDrrwMPPcTeYEiI72Ps3Qu8/DJTnz3wAAcMixUDihc3l2LF2Lv/\n8EMOKorQMyRnTnPJlcv8bhh8KJw7lz73wRshIUCdOrwH5cvzOvLnZ9tiY+1LTIz5eegQTUulS9Pr\npk8f78dPSuJYwMWLwJYtwB9/8IEKMOVc0aLAiRNAZCQHVL/4gink9uwBxo8HRozgeTTZn3R9GRs+\nfPh/38PDwxEeHp6ep9ekkIsX+bllCz1C4uPZm1y50hyUrFDBt6AXKACUKmUe78IFfs+RgwKdOzeP\nmS8fFxHui41l3bx5+VmwID8BimKuXCznrZea1tSqxesvVYpvH4UK8SHjcvGzYEFuT0jg9SYk0LZ+\n6RLrqzeWevWSP0dsLMX60CHa6w2Dx376aY4VHDvG3+XgQeDkSf4O0dG8x1FR9MDRZC0iIyMRGRkZ\ncL1gmVmGi0ibf9e1mSUbIkIb8bRp7Blev85BTW+EhtILo1IlJgrOl88U6oQEenhcvEgzy7VrFB1/\npgWNc1q2BOrX5yBx587aBz2rk54285wA9oEDoKcArAfQRUT2uJXTYp6NUD7Y1mXHDppHMqKX7E5Y\nGF0aixShx0tqKFQI2LyZJqJPP6VJI6MpWxZo1AioXp09/OrVgQYNnPvna7IOGeGaOBGma+JoL2W0\nmGu8IkIBEjHNBuvWAZ9/7n9gtFgxYPRo4NFHzYG+q1c5AHvyZPDb2qMHMHUqzSMuF2e9zpgBjBvH\ndX/UrAl060YPlLp1aYrxhohprtHc2OhJQ5pMjctFO/DmzVz+/JMC7osqVYCRI+mh4e5bHhfHQcRP\nP027NrszdSrwwgt2328R4MABDkR++qk53uCLe+4BIiKA22+neaRw4bRrsybrocVck6k4c4bmiTVr\nKN5Opva/+CKn6deq5d10EB3NWZgffRT05gbM4sVAq1be94nwmsePB2bOdHa8zp05qahBA9q+1YQi\nzY2HFnNNhnL+PHvby5dz2b3bd/kiRYD33weeeCJ50wNAP+wBAzgQmxkpVw744QfO6kzOdi1CF8yJ\nE4Hp050dt04dBvJq0YLHzp8/eG3WZG60mGvSlUuXgBUrTPE+cIA+0vHxydcZMYL245tv9n3sixfZ\nA//8c899uXIl71WjuP9+9pxTwqBBqQsLMG0a7ex58yZfxuUC1q8H3nuPs0vdyZePLopWmjblbNcW\nLTgQ6uv4mqyNUzHX8cw1KSIqijHC+/ZloodChZiBKCyMacm8xdyuXp0p32Ji/B//6FFmOPJ2nEaN\n/CesUIuTPJzbtvnev2aN9+333MPcndZt7kmUrUv37iInTvi/9pgYkenTRXLlstdv0ULk6ac972+O\nHEwEMmqUyF9/2bMsabI+0MkpNMHm9GmRjz6iqBQsyM/nnhPp0oWZbbwJ2AMPiOzb5//YFy6ITJyY\nvBCWKycycybFSm0LDRVp1iz5OqtWiTz+uH8xF/Ff5uTJ5B8u338v0qGDuV6vHh8AyeVNBURq1mQC\nav7sws8AABrZSURBVH8p3K5eZU7RwoXt9QcNYs7UFi3MbQUL8p4ULizStq3ItGkiZ86k+mfXZDBa\nzDVBQQl4eDhzS3bpIvLdd9x2550ixYszA7xVaKpUEfnpJ989xKtXmdC4UqXkBS8sjEJ25Qoz/lSp\nYu5bv54ZedR6qVL2ukeOiHzyibl+5538LFCAn2rfc8+xPe7nVr1fq0hfucLk1cmd0z1t3Vtv8Trn\nzBFp2tT3w+LVV0W2bPGdYu/SJd53a72nnuIb0syZfHAVKyZyyy1McRcWxt+sZUst7FkZLeaaFHPq\nlMjUqRTwokXZw5wzhwI5dChFrFUrkSeeoGBYTQzeeuEuF1O+zZ4tcvvtvkWteXORGTPMvJWJifb8\nl19+STOEtdfrnkj50iV7D/7DD/nZsKG5bdAgfs6dy/Oo7WvX8rNYMXNbz57m9/h4swxAE0ePHvbz\njx9vX//5Z54jJoZp8/wJO0ATzg8/iJw96/03WrSIvXBVvnt3Ptzi49nj79OHv1OTJiJPPiny8MOm\nsH/8cfLH1WQ+tJhrAuLSJU8BnzuXArRxI3uARYtSsHftoq24Th2R4cNF8ucXGThQZPdukf37KVgD\nB4rcdpt/0QJE7r+fIn3pkr1NkZFmmQ4dmJh57FhzW79+Itu3248VFydy7Ji5PmMG7fmAyFdfeZ77\nwAGe6803uf7HH+a+SZP42bcve7tqu8tFm777caw5O+vV41iCWq9UiW85irg45lB1IuzqodG9O3vm\ns2eLrFghsnMnbeg5coi8/DLF+9tvzXPExnL9rrvYtsGDKeSPPUZTzL33amHPCmgx1zji1CmR/v1p\nLnnsMVPARdgrfvppCsHo0bRri1C0c+USeeklkRdesPdinS6tW3OQTx3TyunTFBprb/mbb8z1OnVY\nb8EC+zFdLgq+Wn/lFT4kAJEPPqDpARBZvNgsk5TEc86fz/VmzUSqVuX3H37gfQHsJh31p3zxon3b\nrl1cfF339OmedvKEBD5Eunf3LF+mjP972bUr29+xI3vr3gaYN20SeeYZPpCfeooPytmzTWF/+GGW\n0WQ+tJhrfHL4sMiLL/Kfu3dvmlCsJCVRXFq2FImOtu87d47i2K8fyzRqJFKihEjOnKbA3HyzSOnS\n7BUbBgcwe/Sgvf38+eTbtXCheYznnxeZNctcz5FDZMMGlrMOltarZ7ZZbatdm6JZsiTX4+PtQmz9\nLiLy99/mNmuv+8ABfnbpQk8Ua09bROTaNbuwLlzI7T/8YN/etq35hnDXXSKHDnm//sRECu3LL3uK\ndpUqIp07803h00/5ltKvn0i3bnw4du/uv5d9/jx/u/LlRV5/nQ+Sq1dpGipXjm9Jy5f7H5jVpB9a\nzDVe2bmTNtTixUUGDLC/+ltRJonXXmOvcdUqCvGYMRT/Dh1oLy9enD27Fi3oHte4sUiNGiIhISLt\n2tFevWuXf3GIi6NIqQHKWrXsQvbnnyyXmCjy7LPm9h49uN3lspdXA4mrVlGE584191kFWGGtL2J+\nv36dx1i6lNs3bjT3derEbbGx9nNPmsTtCQkUTrW9cGHarQE++MaP931fkpJEVq+mYFvHJtQSFibS\nqxdNL+vWeT50fXHhAsc9WrXiG4a6js8+45tJo0a8Z+rNRZNxaDHXePDFF+ypvveeOcCYHHFxFPGB\nA9mTbNyYrnl9+7JX/PPP9KAYOpTCXrgwbcQDBogsW0ZhcMq+fazbsaPdW6RQIQ70KcG7elXk7rvN\n/YMHc7u7kF+54nkO9dbw66+mJ8ubb9rLqPrR0XQdBDiO4I51wFUdIyHB3oZevUwhvHBB5O23zX23\n3caHU4MGNFU5Fczz52kaeeEF9qyt5ytcmGMXderQNDZpEh9CV68mf7yEBP6m1avzIalITOQbUYMG\nfKiqB5kmY3Aq5noG6A3CvHkMCrV8OSMKBoLLxWxDW7Zw2byZn7lzc3Zlq1acjViyZODtunKFAbS6\ndGGShx9+oDyNGMHp62pK/D//MKzt+fNc/+AD4M03WdYa6Or4cWb8sRIdbYYIEDETSKxezanxinr1\ngO3bOcW+Vi3GRFF13Bk5krlGAWDyZGZRco9y2KgRk3moc1+/Dnz5JWO0lCoFPPccg3FVqwZ89lng\neTuPHePx1QIwc1GxYmYGop07uV6kCAN4WT/j45nCb9Qo4NlnPY8vAsyfDzzzDPDNN/ytNemPns6v\n+Y+tW5mmbd48//+QiYlMOWYV7a1b+c9fvz4DP9Wvz6V8+dTHzv7qK6B7d8bnfvBBpqELD7cL9JYt\nPK/CKuT58pkhAzZvZrvcmTGDmXkA1lFtvnLFnh3pgw8YAz0sjOdU5c6e9f6g6tjRnH7/889svwjz\ncKoQAyEhTJlXtqxZLymJqd0++ADYtInr338PPPaY07vmiQh/tz/+oLD/+SfPWasWk4VUqsQlJITX\nHRXFEAGPPmpmgEqOVat4bd99x4e2Jn3RYq75jzNnmD5szhz+85Yrx3/mqCjzH1stx45RpK2iXb8+\nkwinBadOMUF0w4Z2AVcsWwbce6+5PmoUMHAgv5cqZcY7//VX5hb1hhLl2bOBTp34RgF49ri3baOQ\nq32qnvWcVlwu3svTp7m+aBEfliIUUrUdYI+/Th3PY0RH81PlDQ0WiYlMFrJjB8+tlvh4xlGvW5ft\nqVsXqF3bd3Cz2FigZ0/+FidP6uQX6Y0Wc40Hp08zzvb16+xpuy+FCzPolb/kzOnF/Pl2gR46FHjn\nHX6vWpV5LwFGH0wuIfL582av2uUCvv0WeOop5hG9ft1eVuU2BSjIH37IpNVq3RuxsfYIhqqHDjAf\n54kT5r516/jQykjOnDEFXn3u2cNE1AUL8k0nf34u6vvWrRT9sWNpEtOkL1rMNVma2bOBRx4x1996\nCxjzb1bZsDD2ogGOA/gKhzt1Ku3ZAAW5ShUmxejThw8Bd1Sv88QJmify5OH6/v18gHjjwgX7m8tX\nXzEapAgfkNeumfv+/JNZhjITiYnsccfEcImNNb/HxPAto0mTjG7ljYuOmqjJsrjP1Hz1VXNfkybm\n9vBwuxeGN1TZ116zr8+Z4728mrX68sv28u6eL+4cPGhv8+TJ3O7u5WL1RddonADtmqjJirgHkure\nndtdLruQlytHf3FfHDlilj992j6pKLlJO9aQtiIiDz1krvvzlXcPlTtiBLdHR3sKuorXotH4w6mY\nexlyCqj7/7BhGDsNw0gyDKOB/xoaTfKMHcs0cYq6dWnjT0hg2rQ1a8x969f7HrQDaB9XlCrFAWBF\npUre67jbtMeNM7/7y1HauDFt5oohQ+h1kz+/Zy7Qhx6iu59GEzScKH5yC4DqAKoCWAaggZ+yaf8I\n02RJXC57ZETrLM7Llz2379/v7JjWOiJmbJbcuZOvZ423EhnJbWq9Z09n1zNhgv3czzzD7dY3BbV8\n8omzY2puXJCeZhYAy7WYa1KCy8VZpfnzM/aKErkLFzzt0ABDAzhh82azzv/+x23u4pocqlyDBlwv\nWtT+gHFCnz72djdsyLrr1nG9Rg1z37hxzo6puTFxKuapMrNoNKnB5aJZ5ZtvOPvR5eL2rVu5uLvB\nbdkC1Kzp7NhWk8orr5jHBvy7B6pZoZs381O5QwJ2U48vJkygR4ti/Xr6t5crx3yme/aYJqW+fYF3\n303e/VGjcYLfCcSGYSwBYJ0jZgAQAINExEv62eQZPnz4f9/Dw8MRHh4eSHVNNiIxkdPE166liN19\nN6eWjxzJ2ZCjR9vLr1tnTuhxwtSp5veCBe3JoBv4Gd1p1Qr46y9+j47m7NFXX+X63LnAPff4P3+O\nHDxnXBxDFNx6K10iy5cHfvyRZT76CJg1iy6Yw4YBV68C77+vJ+Xc6ERGRiIyMjLwik667/4WaDOL\nJgCSkhi5sVEjppx7/XWRPHk8TSoAw+euWBHY8a2hakuV4jZ3W7wv5swxy44a5Vk/EBISRCIiWK9x\nYzM+eUgIP3v3ZvCvXLloy3/xRR1+VmMHGWBm0f0JjV9EaFY4fJjBoNq2ZbwPFcsEoKeJYdAssXix\ns56wlQULzO8jRtjNF2Fh/gNaqQBbADBokOf+Q4ectyVXLvbEO3TgW0jp0pwAdfUqzUiffMJAW99/\nz+v94Qegf3/nx9doFKl1TYwwDOM4gMYAfjMM4/fgNEuTXRkzhsGgWrQALl1iBMFTpziDcsoURk+8\ndInufHPmpCyw07x55vcuXYCvvzbXH3rIf/3SpT23tW1rfp8/P7D25M7NGa3t29Pu//PPPEaTJry+\nkyeBzp15L3LnprB/8EFg59BogmJmcbJAm1lueKZPZ4ae779nerOjR7k9IYHp69q2ZZzuwoUZtzsl\nxMR4mkSs68rd0B+9epl1Fi2yp6hr1izlbWvdWv6b9OTNM+fZZ+n5cvPNjD+v0UDPANVkJubNYxq5\nFSsoZAsWmPs2b6btvEMHivw336T8PL//bhdvd39zp9l4rDlHAYYNsK5HRaWsfdHRTMWXIwcThaxZ\nY98fG8uxhKeeor3/l19Sdh5N9sGpmGvXRE2as3IlQ6jOmcPIh888Y5otvvqKYWN79qQ74nvvAU88\nkfJzWU0ghsEY3IpGjewRDn3RvDk/VVje2Fj7/iVLUta+/PmBX34BmjalPf2BB+jFo8ibF/jpJ8Yk\nf+kl3pdVq1J2Ls0NhhPFD8YC3TO/Idm2jT3QxYsZfKpFC/ZyY2PpuVGtGs0JpUuL/N//pe5cLpdI\nxYpm7/nBB+296QEDAjtewYJm3aeesh/r6adT19YrV5iOr1493p+ZM+37V67k9o8+4tvKtm2pO58m\n6wJtZtFkNIcP06Ty/fdcb9mS5pZt22hKiIhgFvsSJbg9tezaxb/oSpX4+cYb/FSibDXtOKFHD/nP\nPVKJuHKhLFTIf8RGf0RF8T40a8b79Prr9typU6eK1K7NsYZy5Xg/NTceTsVcm1k0acKFC0Dr1sCA\nAUyHdvUqzS1vvEHTwqOPAhERnJ05bx5TsKWW336jWeTuu7k+fjw/lanEmu/TCcrU0qWLuU2Ex7l2\nDdiwIXXtLVyYJhbDYKz0vXs5O3XXLu5/8UVONrp2jffx/vvNzEoajTtazDVBR4S23vbtzcQQAIX8\n88+Bo0cZCXHoUCAyMnCRTY7ffmOWpJYtzW0zZvBBUr8+sykFghLzNWt4LQDt3Or4vwY0/9k7RYsy\n3Vzp0kzb98QTzIE6ZQr39+vHhNEvvcSHSvv2nFWq0bijMw1pgs7HHzPr/Jo1Zho2hctFUV+6lL3S\ncuWCc86LFznZKHduxkHZsIGTdIoX51T55DIL+aNiReZF3bmT1xMSwjR0997LEL0q41FqcbmYp3Xu\nXGDSJIbPLVkSGDyYae4mTeKg8cMPM7XfhAnBOa8m86MzDWkyhF27aAPfu9dzX2ysyKOP0kZ86VJw\nz/vddyI1a4qULWufDn/HHSJ586bcb/2pp2gnV5EXRUSuX+fU+6JFRY4fT1273ZkyhVP+//pLZOhQ\ntr9iRZGRI7n/wgWRChVEfvstuOfVZF6gbeaa9CY2lqaA0aOB6tXt+6Ki2LNMSqJZoWjR4J57xQom\noAgLMwNV7dgB/PMP83g2bZqy4zZvTtu21aRSoAADZpUtC6xenfq2W+ndmwG4Onak/XzDBpqlVFiB\n4sUZZbJnT86c1WgUWsw1QWPAAMYZeeYZ+/ZNm+jjXbMmY4/kyxf8c69ZQzG/5RZz2/TpQJ06FN5S\npZKv6wtlN9+5Ezh3ztx+221AsWJmdMVgEhHBh0fPnjRXudOsGRNZP/WUPbSv5sZGi7kmKPz+OycF\nffqp2TNOTARGjQLatWNM8ClTgJw5g3/u69eB/fs5wFm5MrfFxTFtXLFiQKdOKT/2rbeyZ1+5Mu3Z\niho12EtOCzEHGOxr5UqGxB08mG80VgYP5jXqGC4ahRZzTVCYMIHCUqwY1w8fZq922TL2zB97LO3O\nvXEjByNPnjR75vPmmQOUEREpP7Zh0IMkNJQx0tUY/m23MU767t2MeZ4WVK3Kh8XKlfRwOXjQ3Jcr\nFx9W48al3kVSkz3QYq5JNXFxNHPcfz/F7vPPaVZ5+GFOey9fPm3Pv2YNe7KHD5tiPn06/c2vXAHu\nvDN1x+/cmceJjaWwAuyZHz0K1K7Nh0laERoKLF/Oe9m4Md0UlWnl5ptpS588Oe3Or8k6aDHXpBqV\nEu3NN+nPPXEiBej1180JO2nJ2rUUuiNHaA75+2++DRgGe+WpbUOLFjTjPPQQXQQB9sz37mUYW6ep\n5FJKjhzMdPTXXwyP27IlH1wAr+/33z3NMJobDy3mmlRTvDjw+OPA7bfTFLFhA3us6YEIxfTWWzmw\nGhJCwX38cfqxP/hg6s+RJw9nrRYuzIfUsWOMv54rF98E0spu7k61avTa6dCBbz7vvUczUt68TKun\nubHRk4Y0WZojR2hOOXqUk2wmTeLg4Lx5TPxw5gzfGlLLvHl846hXjw+N//2PJpAFCzjAe+ZM+ubu\n3LuX4xQnTwKnTzOjUps26Xd+TfrhdNKQFnNNlmbmTIaM/ekneq0sXMje85YtNL9YswylhpgYoEwZ\nHr9DB/aQw8K4vWJFnrNKleCcS6Ox4lTMtZlFk6VR9nKAQbu++IKxXubODY6JRZE/Pwd4d+4Ehg+n\nrbx8edqz77or7e3mGo0//KS29Y1hGO8D6AAgDsAhAD1E5EowGqbROGHtWuCRR/hd5Qu9dImDsla/\n8GDQuTOTaSxYwDgwyiWwSRPazZ96Krjn02gCIbU988UAaolIGIADAN5OfZM0Gufs2+c52Prbb/RA\nKVgwuOdq145Zfy5fpu/58OHcXqcO26HRZCSpEnMR+UNE1ITitQDS2KNYozG5do2hdN3jvMyYYfbW\ng0lICCfv/PabfXv58sDx48E/n0YTCMG0mT8D4PcgHk+j8cmpUxyUtHqRbN/O5A5pIeYAk2q4D6qW\nLw+cOGHODtVoMgK/Ym4YxhLDMLZblh3/fnawlBkEIEFEZqZpazUaCydPMnKhlfHjmRAjT560Oecj\nj3AQ1BrHvGBBDpBevJg259RonOB3AFREWvnabxhGdwDtALT0VQ4AhisjI4Dw8HCEh4f7q6LRJMup\nU3YxP3mS/uCHDqXdOfPm5WzMDz5gKFqF6p3fdFPanVtzYxAZGYnIyMiA66XKz9wwjDYAxgFoJiIX\n/JTVfuaaoDJ+PG3VKuvOoEGMm65SrqUVUVGc+blpE71aAA6O9u5tppfTaIJFevmZTwZQCMASwzA2\nG4bxUSqPp9E4xmpmuX6d4Xdfey3tz1ukCNCrl5kwGjB75hpNRpEqP3MRqRqshmg0gWJNbDx9OrMJ\npdcszNdeA2rVYlLqEiVoXjl7Nn3OrdF4Q88A1WRZ7r/fTIoxcqTp950elCnDSUSjR3N982bGT9do\nMgodm0WTZYmOBkqXZk7O+fMZtTE9OXGCD5TmzZko4uhRRpDUaIKJDrSluSGYNg245570C7nrTlQU\nk1ifPs3euUYTbLSYazTpRFISMxGplHkaTTDRYq7RaDTZAB0CV6PRaG4gtJhrNBpNNkCLuUaj0WQD\ntJhrNBpNNkCLuUaj0WQDtJhrNBpNNkCLuUaj0WQDtJhrNBpNNkCLuUaj0WQDtJhrNBpNNkCLuUaj\n0WQDtJhrNBpNNkCLuUaj0WQDtJhrNBpNNiBVYm4YxruGYWwzDGOLYRgLDcMoHayGaTQajcY5qe2Z\nvy8i9USkPoD5AIYFoU1ZksjIyIxuQpqSna8vO18boK/vRiFVYi4i1yyrBQG4UtecrEt2/4PKzteX\nna8N0Nd3o5ArtQcwDGMkgG4ALgNokeoWaTQajSZg/PbMDcNYYhjGdsuy49/PDgAgIoNF5GYA3wJ4\nJa0brNFoNBpPgpYD1DCMCgAWiEidZPbrBKAajUaTApzkAE2VmcUwjCoicvDf1QgAe1LTGI1Go9Gk\njFT1zA3DmA2gGjjw+TeAF0TkVJDaptFoNBqHBM3MotFoNJqMI91ngBqG8YphGHv+HUgdnd7nT2sM\nw+hrGIbLMIziGd2WYGIYxvv//m5bDcP4yTCMwhndpmBgGEYbwzD2Goax3zCM/hndnmBiGEZ5wzCW\nGYax69//tz4Z3aZgYxhGDsMwNhuG8UtGtyXYGIZRxDCMWf/+3+0yDKORr/LpKuaGYYQD6ACgzr8D\npWPT8/xpjWEY5QG0Ak1O2Y3FAGqJSBiAAwDezuD2pBrDMHIAmAKgNYBaALoYhnFbxrYqqCQCeENE\nagFoAqB3Nrs+AHgVwO6MbkQaMRF0KqkBoB58jEn+f3v38xJFHIdx/P2ECkIdokOBYirhqUNFSSB1\nKIIwsGsQRHXqF3UKQvsDulV0i1IoigiJokOBUVdDI8PoEgShQYZdootoPB1mhEVwNnJ2hx0+r9PO\n7AzzzM7uh+/3Oz8W6t8yPwtcs70EYHu+ztuvtevA5aJD1ILtV7aXbwobB9qLzJOTXuCz7a+2F4FH\nwNGCM+XG9nfbU+nr3yTFoK3YVPlJG0/9wJ2is+Qt7fnusz0CYHvJ9q+sdepdzHuA/ZLGJb2RtLvO\n268ZSQPAjO3porPUwWngRdEhctAGzFRMz1KiYldJUiewA3hbbJJcLTeeynjirwuYlzSSDiPdltSa\ntcKa7wBdSdIYsLlyFsmHfTXd3kbbeyXtAR4D3XlnqJUq+zZIMsRS+V5Dydi/IdvP02WGgEXbDwuI\nGP6DpPXAKHBpxSM4GpakI8Cc7al0+Lbhfm9VNAG7gPO2JyXdAK6Q8fyr3Iu57UOrvSfpDPAkXW4i\nPVG4yfbPvHPUwmr7Jmk70Al8kCSSIYh3knpt/6hjxDXJOnYAkk6SdGsP1CVQ7X0DOiqm29N5pSGp\niaSQ37f9rOg8OeoDBiT1A63ABkn3bJ8oOFdeZkl6+pPp9CiQeYK+3sMsT0kLgaQeoLlRCnkW2x9t\nb7HdbbuL5EDsbKRCXo2kwyRd2gHbC0XnyckEsE3SVkktwDGgbFdFDAOfbN8sOkiebA/a7rDdTXLc\nXpeokGN7DphJ6yTAQaqc6M29ZV7FCDAsaRpYIHlAVxmZ8nX7bgEtwFjS+WDc9rliI62N7T+SLpBc\nqbMOuGs784qBRiKpDzgOTEt6T/K9HLT9sthk4R9dBB5Iaga+AKeyFo6bhkIIoQTib+NCCKEEopiH\nEEIJRDEPIYQSiGIeQgglEMU8hBBKIIp5CCGUQBTzEEIogSjmIYRQAn8BBWpqfLCEs48AAAAASUVO\nRK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fe85464d160>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "a = 12\n",
    "k = 2\n",
    "t = np.linspace(0,25,1000)\n",
    "x = np.sin(t) * (np.exp(np.cos(t)) - 2*np.cos(a*t) - np.sin(t/12)**k)\n",
    "y = np.cos(t) * (np.exp(np.cos(t)) - 2*np.cos(a*t) - np.sin(t/12)**k)\n",
    "plt.plot(x,y)\n",
    "plt.axis('equal')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### EXAMPLE\n",
    "\n",
    "Plot the degree 1, 3, and 5 Taylor series of $\\sin x$ on the interval $[-3,3]$. Recall, the Taylor series of $\\sin x$ is\n",
    "\n",
    "$$\n",
    "\\sin x = x - \\frac{x^3}{3!} + \\frac{x^5}{5!} - \\cdots\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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ZQxn+m07+Lk3k1/Lz4Y473Ofgu+/WuBZBycnw1FNuDf3557uL86uj04OC1LEU\nFcE550CrVm5FWw0Y2hSRwJSancrdrzzM6oIYNrXpwahlKdx98Xl07nqyv0sTObF333VdMadNc82r\na9jn4cGD8OyzbsZy0CC3lr53b+8dX0HqeNLTXbPOa691VzKIiFRAanYqU//1MKvCG7Hz5HacvTKV\n+/7wW5q10pIBqWE2bXK3l+nQAaZPr/q9W/wgO9s19/zHP1zLhLvuguHDq54LFaROZPt26N/fvftn\nneXvakSkBtibsZcp/3yEFQ1bcTAhkXN/zOavN1xGvYbR/i5NpPLy8tygwnffwccfQ5s2/q6oUgoK\n3FLoRx5xeXDqVDf1V8Fb7B2mIFUeCxa4d/nrrwPqztkiElh27U/hrqf/wQ+tOlIUHM6Fuw333XoZ\nEZFaZym1yHPPuWm+//4XRozwdzWV5vHARx/BQw9BRoZbQ3XFFRVv8K4gVV5vvgn/93+waBE0buzv\nakQkgGzfu5upzz3F4nZdiMrN57dZsdx90yUE6wo8qa3mznWtxadOdaNUNWzd1JGshTlzXKDatMkF\nqj/8ASIiyvd8BamKmDbNXb3wzTcQrSF6kbpu695d3PHCcyzs1JWT9+zjspBm3D7pfEwN/lARKbft\n2+G889xtZZ57DsLD/V1RlS1a5FpoLV8Od97plkhHRR3/OQpSFWGti6n79sGHH6otgkgdtXnPTu6c\n/gLfd+5Om+SdXBnZmuuvP9/fZYn4XlYW/P73sH+/+1z0x52Eq8GyZfDAA25lz+23u9sRxsSUva+C\nVEUVFrr1UomJ8MorNXo4U0QqZlPKDv700gssOK0H7bYlMz62Lddde56/yxLxL4/H9Zv6/HP47DNo\n2dLfFXnN6tWuwfucOW4G86ab3K1ojqQgVRnZ2e6ayREj3DssIrXaj7uSmfLKdBZ06UnHLVv5XUIH\nrrnmHH+XJRJYnnoKHnvMXdFXw5p3nsiGDfDgg251zw03uFvQlN74REGqsvbvdz2mbroJbrzR39WI\nSDXYsGM7U157mQVdetB50xYmNOzMVRPO9ndZIoHrf/+DSZPcTY9Hj/Z3NV63ZYtblP7BB2791O23\nQ2KiglTlbdsGAwfCk0/CJZf4uxoR8ZK127dx1+uvsqBrD077cSMTmnbh9+PVR06kXBYsgAsvdI2a\nfv97f1dTLZKT3ct76y04dEhBqmpWrIBRo9zNfMaM8Xc1IlIFq7du5f/++28WdO1J1/UbuLp5d668\novb9q1pBP61AAAAgAElEQVSk2m3YACNHukvfbrrJ39VUm927oVkzBamq+/57dwnoO+/A0KH+rkZE\nKmjVli3835uvs6BrT7qvW8fElr0Yd/lIf5clUrMlJ7u1xFdd5fow1tKLs3y6RsoYMxp4EggCXrbW\nPlLGPjUvSAEkJbn7EH38MfTr5+9qRKQcVmzczN3vvMHCLj3osXYNE9v25dLf1txOzSIB56ef3MjU\nmDFuLqwWhimfBSljTBCwEfgNkAIsAS6z1m44ar+aGaTAXfZ51VXuEtAePfxdjYgcw7INm/jLu2/y\nfbfu9Fy9huva9+WSSxSgRKrFgQMuSPXsCc8+C8HB/q7Iq8obpLxxn4PTgU3W2mRrbSHwFlC7GrCM\nGeO6u551Fqxb5+9qROQoP6z9kbMeuJ8RG9dRaIJ4qTiOr+6+WyFKpDo1aODuVbthg2tqXVzs74r8\nwhtB6mRg5xE/7yp5rHa58EL4+9/hzDNh7Vp/VyMiwOLVGxjzwP2cufVHii28Qjxf/PkvXHjBMH+X\nJlI3xMbCrFmwYwdcc41r4lnHhPjyZNOmTTv8/dChQxla0xZwX3GF+zpiBMyeDV27+rcekTpq4ar1\n3Pfxuyzs1p2+HsvrJoFz/nKPv8sSqZuio2HmTDdrc+218OKLEFTzbuydlJREUlJShZ/njTVS/YBp\n1trRJT9PBezRC85r9Bqpo73zjusp/9lnWjMl4kMLlq/l/ln/Y1G3bvRdvowb+/yGsWMG+bssEQF3\nf76zzoIOHeCFF2pkmDqSLxebBwM/4hab/wQsBsZZa9cftV/tCVIA77/v7nY4axb07u3vakRqtW+X\nruGvn33I4m5d6bdsGTefcSZjRg7wd1kicrSsLNf5/NRT3driGhym/NH+4Cl+bn/wcBn71K4gBa4l\nwjXXqDWCSDWZt2gVf/vyIxZ360a/5Uu5pf8oRo/o7++yROR4MjNdmOrVy92nr4a2RtC99nzl009d\na4T//tctRBeRKpv7/Uoe/PoTFnfryhnLlnLroDGMHK5/rIjUGGlpMGyYa2p9xPromkRBypfmz4eL\nL4ann3bNO0WkUubMW84j82exuKsLULcPPYsRQ/r6uywRqYy9e2HQILjhBrjlFn9XU2HlDVI+vWov\nNxciI315Rh8ZNAi+/NItstu/362dEpFy+yppKY99+5lbA1VUwPsNmjD83vv8XZaIVEXjxu6zcdAg\nqFcPfvc7f1dULXwapE45Bf74R5g0CWJifHlmH+ja1Y1MjRwJ+/bBvffW2HlhEV/54usl/P37L1jS\nrQv9PAV8kHgyQ+89199liYi3tGzp2gUNHw4JCXBu7fvv26fL6WfPhiVLoE0bePBBSE/35dl9oHVr\n+PZbt/h88mQoKvJ3RSIB6bPPFzLqgQe4LDuFYE8+H53UnM/uuZ+hfXv5uzQR8bZOneCTT9zFWZXo\n0xTo/LJGav16eOgh14Zp8mQ3dVq/vk/K8I2MDLdWyhh4+22Ii/N3RSIB4eNPFvD0qiSWdjmVfit+\n4O5zLmZAj27+LktEfGHOHBg3Dr75Bjp39nc1J+TLe+1VWKdO8PrrsHAh7N4N7drB1KluRqxWiItz\nXV5bt4YBAyA52d8VifjVOx9+y5BHH2OCJ5XwohxmtmrNp/f8VSFKpC4ZPtzdau3ss+Gnn/xdjdf4\ntVNWmzbw0kuwbJlrO9GxI9x+O6Sk+LMqLwkJcXfDvvpqOOMMWLTI3xWJ+Nxrb82h/xNPcqPdR72s\n/cxu14aZ9z5Af91eSaRuGj/efS6OHeuad9YCAdX+ICUFHnsMXnvNjf5NmQItWvikvOr1ySfuztjP\nPqv2CFInPPvSp/w7dyu7T0qk/8pF/Hn8NXTv0MnfZYlIILAWJk50o1IffeQGHgJQje4jtW8fPP44\nTJ8OF1zgpv3atq3mAqvbihWuMdm4cfDAAwH7F0eksjzFHv7+zEfMCNvLwYRYTl+3lPuumUTnlu39\nXZqIBJrCQjjnHGjVyt1KJgCvcq/RQarUgQOuu/xzz7mp1SlToGfPairQF1JTXZAyBmbMgIYN/V2R\nSJUV5hfx4BPv8U7DbPLDg+m1ZQUPXH8z7Rqf4u/SRCSQZWTA4MFwxRVw553+ruZXakWQKpWZ6Uan\nHn/cLfSfMsUFqwAMsCdWVAR33+2u5nv/fXcvIpEaKCsjj/ufeocPW0BwcS7ddq/noetvpXXDVv4u\nTURqil27oG9feOEFt24qgNSqIFWqoMDd0u7RRyE62k35XXABBAd7qUhfeu89uP56eOQRmDChhqZC\nqYv27sngnunv80nHGBqn7qJjxnYevvZ2WtZv6e/SRKQmWrjQNer85hs49VR/V3NYrQxSpTwe1/Py\nkUfc9N8dd7jO8xERXjm876xf7+7R16MH/Otf6jclAW3Nqt08+MGnzO6eSMdNy2lj9/G3a++ieXxz\nf5cmIjXd66/D/fe7K9wbNPB3NUAtD1KlrHV3ZXn4YbeW+5Zb3O1n4uO9eprqlZPjej589ZVbN9Wn\nj78rEvmFrz9fw5NLvuXbbifTbfU3tInNYdrv71aAEhHvuvNO1w/p888hNNTf1dSNIHWkVavclN9n\nn7lOAzfdVMNaJ7z3nmvzfued7oaEQX5t8SV1nPVY/vvv+by8fz2r2zemy4qZtG0Zyj0X/p8ClIhU\nj+JidyXfKafAM8/4u5q6F6RKbd8OTz8N//43jBjhBnv69q3203pHcrK7eiEqCl5+GZrrA0t8qyCv\nkMef/pR3o/azr2EMp6z5Hx27NODPozSFJyI+kJ4O/frBbbfBtdf6tZQ6G6RKZWTAK6/AP/8JJ53k\n/kwuuKAGtG8qKnJzlU895b7+4Q9aiC7VbteOQzz82md81C6UeumHiN35AV37tOb/hipAiYiPbdwI\nAwfCrFl+Xe5S54NUqeJi1zj18cfdVZY33+y60wf8OqpVq+Cqq6BxY9f7oVkzf1cktdDcL9byz4Xf\nM6d7Y7qt30B2+tv0GdCXuwZOVYASEf/54AO49VZYutRvPRcVpMqwZAk88YRbx/a737l1VG3a+LWk\n4ysshIcecnOVapMgXuIpKubF57/izbwdrGvbmH4rl/Gj5z+MPH00UxWgRCRQTJkCy5e7xc9+6HMU\nkEHqkjVrSAwNpVFYGImhoSSGhdEiPJyWERE0Cg3F+Cgk7Nzp1rG9+qrrhzl5Mpx1VgD3o1q50g2j\nRUe7NgkB1GdDao49uw7xj+mzmNnCUhAaSs9tK5kf+goXdbtYAUpEAk9REYwcCQMGwF//6vPTB2SQ\nmrFnD/sKC0ktLGRfQQF7CwrYkZ9Pcl4eeR4PLSIiaBkeTpvISDpGRdEpKoqOUVGcHB5eLSErNxfe\necdlk337XOuEP/wBGjXy+qmqrrgYnn8epk1zRd5zjwtWIifw5czlPL9sKd90a8ypm/fRyv7IzKLp\nXN7lcgUoEQlse/dC797ug/qcc3x66oAMUsc7V2ZREcl5eSTn57M5N5cNOTlsyMlhfXY22R4PHaOi\n6BwVRfeYGHrExNAtJoZ6Xuwz8cMP7s/pgw/cn9Xkye5qv4CbSduzx3UgnT8fnnwSzj8/AIsUf8s6\nmMVTL3zKRzFZJDetz/BVqdRruYG3Ul9l3GnjFKBEpOZYsMB91n3/vU/X49S4IHU8hwoL+TEnhzXZ\n2azIymJ5VharsrNpGBp6OFj1iInh9Lg4GoeFVanOAwfclN9zz0FCAlx3HVx2WQA2Hf/mG7jxRkhM\nhL//XffsEwAWfr6K579dwOc9GnPyT5mMzo0ir/NiXl3zkgKUiNRcpX2NFiyA8HCfnLJWBamyeKxl\nc27u4WC1LDOTJZmZxIeE0Dc2ln5xcfSLi6NHbCzhlWhu6fHA7Nnw0kvw9deudcI110D//gE0AFRU\n5Ho83Huva5r1t7/VsC6k4g1ZBzN59sXPmRV6kDXtmjJ4dRpX9OrID8HvMX3ZdAUoEan5rIULL4RW\nrdxVYz5Q64NUWTzWsik3l4UZGSzKyGBhRgY/5uRwWnQ0/eLi6B8fz6D4eJpWMM3u3Qv/+Y8LVeAC\n1e9+5waDAkJmJjz2GDz7LEyc6LqjB8i9iqSaeDx8NmM+r/+4lq96nEyLXWmMLmjI7y/vxstrnlaA\nEpHa5+BBd2/aZ57xyXqpOhmkypJTXMzSzEwWZmTwXXo689PTSQgJYXBCAoNKglXbyMhyLWa31o0q\nvvQSfPghDB/u1n2PHBkQtwWC3bvhvvvg/ffdyvnbb1egqmW2L93Cv97/mtktQ9lXL4GhP+YycegA\nuvSM4u8L/q4AJSK123ffwUUXuYXN1dxfUUHqGDzWsj4nh/lpacwrCVZF1h4OVYPi4+kSE0PwCYJV\nRga89Ra89hps3gyXXgpXXumasPp96m/7dnjwQQWqWiJn7wFefuVLPitO5bvup9B9w0EuaNieyVf0\nIb3ggAKUiNQtDz7oGkLOmVOttytRkConay3JeXmHQ9W8tDT2FRbSPy6OIQkJDI6Pp1dsLKHHWWe1\nZQv897/wxhvu5yuvdLfM83uzz9JA9d57bi7yllugdWs/FyXlUZSWwTuvfMGHabuZ07MVTVOyGZIT\nz23jhnDKyTGkZqcqQIlI3VRcDKNGudvITJtWbadRkKqCvQUFh0es5qWlsSUvj35xcQyOj2dIQgKn\nx8YSUUb3Tmtd9/Q33nCjVW3bwrhxbn3cySf74YWU2rXLXfHw8sswbJgboTrjDD8WJGWxObl8/sps\n3tu5ha96NCMoP4iBKaFcM3IAQ3q55mYKUCIiuFZAPXvCm2/C0KHVcgoFKS86WFjId+npzEtPZ25a\nGuuys+kZG3t4xOqMuDhijhpeLCyEL75wDT8/+QQ6d4aLL3ZTu8399bmXleWu8nvySXcPv0mT4JJL\nICrKTwWJ58BBvvzvl3ywawdzOzfmYFQ8/bd5+H3/Ppw/6Of5fwUoEZGjfP45XHutuzdtQoLXD68g\nVY0yi4pYkJHBvJJRq+WZmZwWHc3ghASGJCQwIC6OhCNWn+fnuxYK774LH38M7du7/HLRRdCypR9e\nQHExzJwJL74ICxe6RlkTJ0L37n4opu4p3rqdj9/4kk8zU5nTvTU5QVH0TrZc3LM7V45oSXDQz//d\nKkCJiBzHjTfCoUNufY2XKUj5UG5xMYsyMg6PWC3KyKBdVBRD4uMPXx3YqKRRaEGBWx/33nvuyr8W\nLWDsWHclZ69eUImWV1Wzc6cbpXr5ZdfP4corXcrz61xkLVNQQOa8Bbw3exnzTBZf9uoMhaH03hvO\npX17cmn/RgQF/fK/VQUoEZFyyMlxH5733usGBbxIQcqPCjwefsjMPDxi9V16Os3CwxlcMhU4JCGB\npuHhFBW5dgozZ7rpv7Q0OPtsF6xGjICYGB8WXVzshs1mzICPPoKuXd1fyosuCtCbDwa4zZtZ98Ec\nPtqSzILmsSR178ZJu/PpmVeP3w/rzpjT4spsuaEAJSJSQT/84D48ly71aksEBakAUuTxsDI7m3lp\nacxNS2N+ejr1SnpZla6zahURwZYthlmzXLBatAj69XOBasQIN+vms9GqvDzX1v2tt+DTT6FbN5fu\nxo6FTp0CoL9DgLEWtmwha848Pv9hI9+HFPJlj9PYelJTOmz10L9BWyYPb0mnpse+fZEClIhIFTzw\nACQlucXJXvqwVJAKYB5rWZedzdySqwLnpqURGhREv7g4+sbG0jcujnbEsmhuMF99BV99Bfv3uwag\npcHKZ10McnPdff1KE15QkEv+v/kNDB5cN/tTFRbCmjUUzF/A/MXrWBBSyJwup7GwU0ca7immU359\nLuzWngmnxxMecvz/oBWgRES8oKjIfSZdeqlr9eMFClI1iC25b2DprW0WZWayNjubDlFRh4NVi5w4\nkudHMecrw1dfQWQkDBrk2mgMHAgdO/pgxMpaWLPGjVIlJbkOs61auUtPhwyB0093w6q1acSquBh+\n/BGWLCFvyVIWbU1hSWwYX3frw/zTOhOZaTglowHDmrXg2r4JnJJYvhb3ClAiIl62ZYubypk7110q\nX0UKUjVcXnExK7KyWJSZ6cJVRgYHCgvpGRtLt+gYGmfEkLsmhq3fRLFgfhBpae6GygMGuBZRPXpA\nXFw1F1lUBMuWuVA1bx4sXuxCVO/ebuvVC0491YWtMvpuBRSPxzUwXbvWbevWsffHrSwOC2ZOt9OZ\n06kHG1o3JvpAMC3yGjK0SSOu6ZXAaU0qdt9GBSgRkWo0fTq88IK7Ir2KXc99EqSMMRcD04BOQB9r\n7bLj7KsgVUWpBQUsy8piRVYWyzMzWZGVxY78fDpHRdE+OIao3bGkL4tme1I06xaF0rz5z3mmd28X\nrqp1Abu1rvnn0qVu8d/SpbB+Pezb57qTduzotlatXDOt0i06uhqLKlFQ4OrYs8ddqbhtG2zdCtu2\nYbdtY//+Ayzs0ot5p57OgpbtWXtyI7LiQ2mwN5bOQfUZeXI8V/SIo0X9yv2HqQAlIuID1sLo0W6m\n5K67qnQoXwWpDoAHeAG4Q0HK97KLi1lVEq5Kt/U5OUQFBdHcRhN7IIqiLVGk/hBN8rwomkSEcWpn\nw6mncnjr2NFNFVZfkdmwcSNs2OC25GQXZkq3yEjXeqF+fbfmqvRrdDSEh0NExM9baKibbjtyKypy\na7kyMtyWmem+pqfD3r0uPGVmQqNGZDRpztLWp7GwWSd+qN+M1Qn1SW4cTmGMISE1hjbFsZxeL5bz\nOsUwvH0UIUFVm6ZUgBIR8bEdO9wIQlKS+5CrJJ9O7RljvgH+qCAVGKy17M7PZ31ODutyclifne2+\nz84hr9hDw8JIIg9F4NkdScaPEexfHcFJNpIO8RG0bRlEmzZwyik/b9U6RWitW0m/fz8cOAAHD/78\nNSfHXUFYuuXnu5Gl4OCft5AQ9zUqCmJj8cTE8RPxLCee1TaGlSaODUER7Ai1pNfLwZNQQOSBSBJz\no2kfHkXfxtGM6RBNv+aRBHlxbZcClIiIH734Irz0kusxVMkpPgUpKdPBwkK25eWxNTeXrSVft+Tk\nsTErl5+K8oksDiEiO5ygg2EU/BRO5vYwQtPDaUAYjcNDaRobSvOEEFo1CKFZkyAaNnSd+Y/cQsu3\n3rrcCgogI8OScsDDtv1FbD1YwPbMAnbnFrCnsIDU4nwOmgIywwrIr5cHsUVEpIUTnxNJEyJoFxNJ\nt0YRDGsdTZ9mEce9AXVVKUCJiAQAa+HMM2HkSPjTnyp1CK8FKWPMl0DjIx8CLHC3tfaTkn0UpGqB\nYmvZV1BASkEBKfn5/FRQwO78fLZlFLA9K5/U/EIOFReRSSG5wUUEFwUTkhOCyQ7FZgVTnB1MYXYQ\nwUVBhBNMSHEQoZ4ggjGEBENwsCEkxF1daD3u73lxkIfiIEtxsIfiYA9FxkOh8VAYXExRRBHFkUUQ\n4zZjDSH5wUTkhRFbGEZ9TxiNgsNpGh5Gm3phnNo4nN7NImgVG+bV0aXyUIASEQkw27dDnz7uYqhO\nnSr89PIGqROOd1lrz6zw2Y9h2rRph78fOnQoQ6vpjs1SOcHG0CQ8nCbh4fSKjT3uvh5rySwu5mBh\nIQeLisgoKiLX4yGn2MOhnGIOZnvILPCQVVRMQZGlqBiKi6CwyF0gR5DFGAgzIUQEBRFmgogwQUSH\nBhEbEUS9yCAaR4fQJDaExMgQEkJCiAjAK/+ODlArJ61UgBIRCQStWsH998OECa5dzwk+Q5KSkkhK\nSqrwabw5tXeHtXbpcfbRiJTUGhqBEhGpATwe10D67LPhjjsq9FRfXbV3PvA00BBIA1ZYa8ccY18F\nKanxFKBERGqYLVugb19YsqRCtwVRQ04RL1KAEhGpwR5+2HU8//TTct99o7xByle3wRWpkVKzU5ny\n5RQ6PNOBrIIsVk5aybNnP6sQJSJSk/zxj7B7N7z1ltcPrREpkTJoBEpEpJZZuBAuuMDdBqx+/RPu\nrqk9kUpQgBIRqcVuvNE1d54+/YS7KkiJVIAClIj4UqtWrUhOTvZ3GQK0bNmS7du3/+pxr/WREqnN\n1AdKRPwhOTkZDS4EBlPFBs4KUlInKUCJiIg3KEhJnaIAJSIi3qQgJXWCApSIiFQH9ZGSWk19oERE\nvOOhhx7i2muvLff+69ato0+fPuXa9+KLL2b27NmVLc2vdNWe1Eq6Ck9EAlnJFWH+LqNaXXzxxVx6\n6aVccsklJ9x3yZIlXH/99fzwww8+qOyXjDHYnByIjPz14+psLnWNRqBERPxvz549JCUlcd5555Vr\n/z59+pCZmcmyZcuqubJjeOSRSj9VQUpqBQUoERHveeSRR2jWrBlxcXF06tSJb775hvvuu4/x48cD\nrn1DUFAQr7/+Oi1btiQxMZEHH3zw8PO//PJLevbsSVhYGABbt26lQYMGrFixAoCUlBQSExOZN2/e\n4ecMGTKEWbNm+fBVHuGZZ9zNjStBQUpqNAUoERHv2rhxI88++yxLly4lIyOD2bNn06pVK+DXPZe+\n++47Nm3axFdffcX999/Pjz/+CMDq1avp0KHD4f1OOeUUHn30Ua688kpyc3OZMGECEyZMYPDgwYf3\n6dSpEytXrqz+F1iWO++Em2+GSky3KkhJjaQAJSJSPYKDgykoKGDNmjUUFRXRokULWrdu/av9jDFM\nmzaNsLAwunbtSrdu3Q4HobS0NGJjY3+x/9VXX03btm3p27cve/fu5YEHHvjF72NjY0lLS6u+F3Y8\nt93mRqQ+/rjCT1WQkhpFAUpE6gpjqr5VRps2bXjyySeZNm0aiYmJXH755fz0009l7tu4cePD30dF\nRZGVlQVAvXr1yMzM/NX+11xzDWvXruWmm24iNDT0F7/LzMwkISGhckVXVViYm9677TbIy6vQUxWk\npEZQgBKRusbaqm+VddlllzF//nx27NgBwJQpUyr0/K5du7Jx48ZfPJadnc2tt97K1VdfzbRp0341\n+rR+/Xq6detW+aKrasQI6NYNnniiQk9TkJKApgAlIuJbGzdu5JtvvqGgoICwsDAiIyMJDg7+1X7H\na99w5plnsmzZMgoKCg4/dvPNN3P66afz4osvctZZZ3Hdddf94jlz585lzJgx3nshlfH3v8M//gEp\nKeV+ioKUBCQFKBER/8jPz2fq1Kk0atSIpk2bkpqaykMPPfSr/Y5eeH7kz4mJiQwfPpwPP/wQgI8/\n/pgvvviCf/3rXwA8/vjjLF++nBkzZgCuj1RsbCy9e/eurpdVPm3awMSJcNdd5X6KGnJKQFEjTRGp\nC+pCQ87169dz1VVXsWjRohPue/HFF3PNNdcwevRoH1T2S7/6s8jMhI4dMSkp5WrIqSAlAUEBSkTq\nkroQpGqKMv8sPvwQc8EFClIS+BSgRKQuUpAKHMf6syjvLWJCqqUqkRM4OkCtnLRSAUpERGocBSnx\nKQUoERGpTRSkxCcUoEREpDZSkJJqpQAlIiK1mYKUVAsFKBERqQsUpMSrFKBERKQuUZASr1CAEhGR\nuki3iJEq0a1cRERqn1atWhEVFUV8fDz169dn4MCBvPDCCzWm99U999xD165dCQ0N5f7776/WcylI\nSaUoQImI1F7GGGbNmkV6ejrJyclMnTqVRx55hKuvvrpazufxeLx6vHbt2vHYY48xduxYrx63LApS\nUiEKUCIidUPp6FNsbCxjx47l7bff5rXXXmPdunUAFBQUcMcdd9CyZUuaNGnC5MmTyc/PP/z8Rx99\nlKZNm9KsWTNefvllgoKC2Lp1KwATJkxg8uTJnH322cTGxpKUlHTC482cOZMePXpQr149Bg4cyOrV\nq49Z+/jx4xk1ahQxMTHV8db8goKUlIsClIhI3danTx+aNWvG/PnzAZgyZQqbN29m1apVbN68md27\ndx+eRvv888958sknmTNnDps3byYpKQljfnm3lRkzZvCXv/yFzMxMBgwYcNzjLV++nKuvvprp06dz\n8OBBrrvuOs4991wKCwt9+yaUQUFKjksBSkRESjVt2pSDBw8CMH36dJ544gni4+OJjo5m6tSpzJgx\nA4B3332XCRMm0LFjRyIiIpg2bdqvjnXeeefRr18/AMLDw497vOnTpzNp0iR69+6NMYbx48cTHh7O\nwoULffPCj0NX7UmZdBWeiIh/mftOeL/cE7L3endx+O7du6lfvz6pqank5OTQq1evw7/zeDyHpwNT\nUlLo06fP4d81b978VwvVmzf/+TPlRMdLTk7m9ddf5+mnn3avy1oKCwtJSUnx6uurDAUp+QUFKBGR\nwODtEFRVS5YsISUlhUGDBtGwYUOioqJYu3YtTZo0+dW+TZo0YdeuXYd/3rFjx6+m9o78+UTHa968\nOXfffTd33XWXF1+Rd2hqTwBN4YmISNkyMzOZOXMm48aNY/z48XTu3BljDBMnTuTWW28lNTUVcKNV\nX3zxBQC//e1vefXVV9mwYQM5OTk88MADxz3HiY43ceJEnn/+eRYvXgxAdnY2n376KdnZ2WUer6io\niLy8PDweD4WFheTn53v9ysBSClJ1nAKUiIiU5ZxzziE+Pp4WLVrw0EMPcccdd/DKK68c/v0jjzxC\n27Zt6devHwkJCYwcOZKNGzcCMHr0aG6++WaGDRtG+/btOeOMMwC3FupYjne8Xr16MX36dG688Ubq\n169P+/btee211455rIkTJxIVFcVbb73Fgw8+SFRUFG+88YY33pZfMb5qrmWMsTWlkVddcPQU3tSB\nUxWeRER8xBhTY5pbesOGDRvo0qUL+fn5BAUF1hjOsf4sSh4/4UK1Kr0aY8yjxpj1xpgVxpj3jTFx\nVTmeVD+NQImIiC98+OGHFBQUcOjQIaZMmcK5554bcCHKG6r6ir4ATrXWdgc2AYG3CkwABSgREfGt\nF154gcTERNq1a0doaCj/+te//F1StfDa1J4x5nzgImvt+GP8XlN7fqApPBGRwFPXpvYCWVWn9rzZ\n/uAPwFtePJ5UgdoYiIiIVL8TBiljzJdA4yMfAixwt7X2k5J97gYKrbVvHu9YR3Y2HTp0KEOHDq14\nxVLqC3UAAA3iSURBVHJcClAiIiIVl5SURFJSUoWfV+WpPWPMVcBEYLi1Nv84+2lqrxppCk9EpObQ\n1F7g8OvUnjFmNHAnMPh4IUqqj0agRERE/Keqa6SeBsKAL0tavS+01k6uclVyQgpQIiIi/lelIGWt\nbeetQqR8FKBEREQCR+3rjFVLqQ+UiIj4SqtWrYiKiiI+Pp769eszcOBAXnjhhRqzrmv48OEkJiaS\nkJBAjx49+Pjjj6vtXN5sfyDVQCNQIiLia8YYZs2axbBhw8jMzGTu3LncfPPNLFq06Bf32/MWj8fj\n1a7nTz31FB07diQ0NJTFixczYsQINm3aROPGjU/85ArSiFSA0giUiIj4U+noU2xsLGPHjuXtt9/m\ntddeY926dQAUFBRwxx130LJlS5o0acLkyZPJz//5urNHH32Upk2b0qxZM15++WWCgoLYunUrABMm\nTGDy5MmcffbZxMbGkpSUdMLjzZw5kx49elCvXj0GDhzI6tWrj1l7ly5dCA0NPfxzUVERO3fu9Or7\nU0pBKsAoQImISCDq06cPzZo1Y/78+QBMmTKFzZs3s2rVKjZv3szu3bu5//77Afj888958sknmTNn\nDps3byYpKYmSi9IOmzFjBn/5y1/IzMxkwIABxz3e8uXLufrqq5k+fToHDx7kuuuu49xzz6WwsPCY\n9Z5zzjlERkbSr18/hg0bRu/evavlfVGQChAKUCIiEuiaNm3KwYMHAZg+fTpPPPEE8fHxREdHM3Xq\nVGbMmAHAu+++y4QJE+jYsSMRERG/aMhd6rzzzqNfv34AhIeHH/d406dPZ9KkSfTu3RtjDOPHjyc8\nPJyFCxces9ZPPvmErKwsPvvsM84880wvvxM/0xopP9MaKBERKZM5YS/IE/Py4vDdu3dTv359UlNT\nycnJoVevXod/5/F4Dk8HpqSk0KdPn8O/a968+a8Wqjdv/vNn3YmOl5yczOuvv87TTz9d8rIshYWF\npKSkHLfe4OBgRo0axZNPPknbtm0ZO3ZsJV/5sSlI+YkClIiIHFeAXSG3ZMkSUlJSGDRoEA0bNiQq\nKoq1a9fSpEmTX+3bpEkTdu3adfjnHTt2/Gpq78ifT3S85s2bc/fdd3PXXXdVqvaioiK2bNlSqeee\niKb2fExTeCIiUpNkZmYyc+ZMxo0bx/jx4+ncuTPGGCZOnMitt95Kaur/t3f3MVWeZxzHv5ebo9Mq\nygwWy4t/IGtM2HTUDSNNZVstmxX7x2LaNS51Dakay/oHCzjb1RgXq/2jbUyMhDiD63S2XeI2ZQQX\nR8fW+JJNh9MiJY34wtoYdZFCCnRc++McHYq8yHnlnN8nMZznnOfcz/XcHOTivp/nuq8AgdGqhoYG\nAFasWMHu3btpaWmhu7ubzZs3D3uMkdorKytj586dHD9+HICuri7q6uro6uoa1Na5c+eor6/ns88+\n4/PPP+ett96iqamJRx99NGx9MpASqShRAiUiIuPJsmXLSE1NJTs7my1btlBRUXFb6YOtW7eSm5tL\nYWEh06ZNY8mSJbS2tgJQUlJCeXk5xcXF5OXlsXDhQiBwLdRQhmuvoKCAmpoa1q1bR1paGnl5edTW\n1t61HXdn48aNzJw5k/T0dLZv387bb7/NvHnzwtU1twl50eJRHyhJFy3WYsIiInKnZFu0uKWlhfz8\nfHp6esJaLyocQl20OL7OJoFoBEpERJLZgQMH6O3t5fr161RWVlJaWhp3SVQ4JN4ZxZgSKBEREaiu\nriY9PZ05c+YwceJEduzYEeuQIkJTe2GiKTwRERmtZJvai2ehTu2p/EGIVMZAREQkeSmRGiMlUCIi\nIqJE6h4pgRIREZGblEiNkhIoERERuZMSqREogRIREZGhKJEaghIoERERGYnqSN1BdaBERCTZzZ49\nm0mTJpGamkpaWhpFRUVUV1ePm5INN+OfOnUqU6dOpaSkJGLH0ohUkEagREREAsyMQ4cOUVxcTGdn\nJ++99x7l5eUcO3bstvX2wqW/vz+sVc8Hxh9pST8ipREoERGRwW6OPk2ZMoUnnniC/fv3U1tby9mz\nZwHo7e2loqKCnJwcMjIyWLt2LT09Pbfev23bNmbNmkVmZia7du1iwoQJfPTRRwCsWrWKtWvXsnTp\nUqZMmUJjY+OI7R08eJD58+czffp0ioqKOH369Kjij7SkTaSUQImIiIzeggULyMzMpKmpCYDKykra\n2tpobm6mra2Ny5cvs2nTJgDq6+t54403OHLkCG1tbTQ2NmJ2e5Hwffv28fLLL9PZ2cmiRYuGbe/k\nyZM899xz1NTUcO3aNZ5//nlKS0vp6+sbMt5nnnmGmTNnUlJSQnNzc4R6JQkTKSVQIiIiYzNr1iyu\nXbsGQE1NDa+//jqpqalMnjyZqqoq9u3bB8A777zDqlWreOihh7jvvvvYuHHjoLaWL19OYWEhACkp\nKcO2V1NTw+rVq3n44YcxM1auXElKSgpHjx69a5x79+7l/PnztLe3s3jxYh5//HFu3LgRgR5Jomuk\ndA2UiIiMJ9bYGHIbvnhxyG0MdPnyZdLS0rhy5Qrd3d0UFBTceq2/v//WdFpHRwcLFiy49VpWVtag\nqbasrP//Dh6pvfb2dvbs2cP27dsD5+VOX18fHR0dd41z4cKFtx5XVVVRW1tLU1MTS5cuHeupDynh\nEyklUCIiMh6FOwkK1YkTJ+jo6OCRRx5hxowZTJo0iTNnzpCRkTFo34yMDC5dunRr+8KFC4Om9gZu\nj9ReVlYWGzZsYP369WOKPZKLRCfs1J6m8ERERELX2dnJwYMHefrpp1m5ciVz587FzCgrK+PFF1/k\nypUrQGC0qqGhAYAVK1awe/duWlpa6O7uZvPmzcMeY6T2ysrK2LlzJ8ePHwegq6uLuro6urq6BrV1\n8eJF3n//ffr6+ujp6eG1117j6tWrLFq0KGx9MlDCJVJKoEREREK3bNkyUlNTyc7OZsuWLVRUVNxW\n+mDr1q3k5uZSWFjItGnTWLJkCa2trQCUlJRQXl5OcXExeXl5t6baUlJShjzecO0VFBRQU1PDunXr\nSEtLIy8vj9ra2ru209nZyZo1a0hLSyMzM5OGhgbq6+uZPn16uLrmNhat2wPNzCN5rDun8KqKqpQ8\niYhIXIrkVFM8amlpIT8/n56enrDWiwqHob4XweftLm+5TXydzRhoBEpERCT+HDhwgN7eXq5fv05l\nZSWlpaVxl0SFw7g9IyVQIiIi8au6upr09HTmzJnDxIkT2bFjR6xDiohxN7WnKTwRERnvkm1qL56F\nOrU3bsofqIyBiIiIxJu4T6SUQImIiEi8ittESgmUiIiIxLu4S6SUQImIiMh4ETeJlBIoERFJFjk5\nOYOWTJHYyMnJCen9ISVSZrYJWA70A58Az7r7x/fShhIoERFJNufPn491CBImodaR2ubuX3f3+cAh\n4JXRvlF1oCKvMQwrh8u9UZ9Hn/o8+tTn0ac+j18hJVLu/umAzckERqaGpQQqevSDF33q8+hTn0ef\n+jz61OfxK+RrpMxsM/Aj4D9A8XD7Vh6u1BSeiIiIJIwREykzOwzMHPgU4MAGd/+Du78EvGRmlcAL\nwMah2ro5AqUESkRERBJB2JaIMbMsoM7d84d4XbXwRUREZNyI+BIxZpbr7m3BzSeBD0IJRkRERGQ8\nCWlEyszeBfIIXGTeDqx293+HKTYRERGRuBa2qT0RERGRZBNqHal7YmabzOyfZnbSzOrN7IFoHj8Z\nmdk2M/vAzE6Z2W/NbGqsY0p0ZvYDM/uXmf3XzL4R63gSlZmVmFmLmbUGb3aRCDOzXWb2iZk1xzqW\nZGFmmWZ2xMzOmNlpMyuPdUyJzMxSzOxYME85bWYj1seM6oiUmd1/s/aUmb0AzHX3NVELIAmZ2XeB\nI+7eb2avAu7u62MdVyIzs68SmO6uBirc/R8xDinhmNkEoBX4DtABnACecveWmAaW4MysCPgU2OPu\nX4t1PMkgOODwgLufMrP7gb8Dy/VZjxwzm+Tu3Wb2BeBvQLm7Hx9q/6iOSI2lgKeExt3/5O43+/ko\nkBnLeJKBu59z9w8JlAqRyPgm8KG7t7t7H/AbAstVSQS5+1+B67GOI5m4+8fufir4+FMCN3U9GNuo\nEpu7dwcfphC4KW/YEaeoJlIQKOBpZheAHwI/j/bxk9yPgT/GOgiRMHgQuDhg+xL65SIJzsxmA/OA\nY7GNJLGZ2QQzOwl8DBx29xPD7R/2RMrMDptZ84B/p4NflwG4+0vung38mkABTwnRSH0e3GcD0Ofu\ne2MYasIYTZ+LiIRLcFrvXeAnd8zuSJi5e39wDeFM4FtmNne4/UNeIuYuATw2yl33AnUMUwldRmek\nPjezZ4HvA9+OSkBJ4B4+5xIZl4HsAduZwedEEo6ZfZFAEvUrd/9drONJFu5+w8z+DJQAZ4faL9p3\n7eUO2By2gKeEh5mVAD8FSt29J9bxJCFdJxUZJ4BcM8sxsy8BTwG/j3FMycLQ5zrafgmcdfc3Yx1I\nojOzGWaWGnz8ZeAxYNgL+6N9154KeEaZmX0IfAm4GnzqqLuvjWFICc/MngS2AzMILOZ9yt2/F9uo\nEk/wj4Q3CfxBuMvdX41xSAnPzPYCi4GvAJ8Ar7j77pgGleDMbBHwF+A0gYueHfiZu9fHNLAEZWb5\nQC2B/1cmAPvd/RfDvkcFOUVERETGJup37YmIiIgkCiVSIiIiImOkREpERERkjJRIiYiIiIyREikR\nERGRMVIiJSIiIjJGSqRERERExkiJlIiIiMgY/Q97nXPN9Fb8OgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fe8520787b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Degree 1 T1(x) = x\n",
    "# Degree 3 T3(x) = x - x^3 / 6\n",
    "# Degree 5 T3(x) = x - x^3 / 3! + x^5 / 5!\n",
    "x = np.linspace(-3,3,1000)\n",
    "y = np.sin(x)\n",
    "y1 = x\n",
    "y3 = y1 - x**3 / (3*2*1)\n",
    "y5 = y3 + x**5 / (5*4*3*2*1)\n",
    "\n",
    "plt.figure(figsize=(10,5))\n",
    "plt.plot(x,y,x,y1,x,y3,x,y5)\n",
    "plt.title('Taylor Polynomials of $\\sin x$')\n",
    "plt.legend(['sin(x)','Degree 1', 'Degree 3','Degree 5'],loc=4);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2. Linear algebra with SciPy\n",
    "\n",
    "See the [SciPy documentation](http://docs.scipy.org/doc/scipy/reference/tutorial/linalg.html) for a summary of the linear algebra functions and objects provided by SciPy. As usual, we need to import the package before we use it:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import scipy.linalg as la"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Before we get started, we need to emphasize the [difference between NumPy arrays and NumPy matrices](http://docs.scipy.org/doc/scipy/reference/tutorial/linalg.html#numpy-matrix-vs-2d-numpy-ndarray). A NumPy array is an array of numbers and operations are always computed elementwise!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 2],\n",
       "       [3, 4]])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A = np.array([[1,2],[3,4]]) # Create a NumPy array\n",
    "A"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "numpy.ndarray"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "type(A)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1,  4],\n",
       "       [ 9, 16]])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A * A # Compute the square of each element in the array"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "matrix([[1, 2],\n",
       "        [3, 4]])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "M = np.matrix([[1,2],[3,4]]) # Create a NumPy matrix\n",
    "M"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "numpy.matrixlib.defmatrix.matrix"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "type(M)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "matrix([[ 7, 10],\n",
       "        [15, 22]])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "M * M # Compute matrix multiplication"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Always be aware of the dataype we're working with!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### EXAMPLE\n",
    "\n",
    "Find the determinant, eigenvalues and eigenvectors of the matrix $A = \\begin{bmatrix} 1 & 2 & 1 \\\\ 4 & 2 & -3 \\\\ 0 & -5 & -1 \\end{bmatrix}$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "matrix([[ 1,  2,  1],\n",
       "        [ 4,  2, -3],\n",
       "        [ 0, -5, -1]])"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A = np.matrix([[1,2,1],[4,2,-3],[0,-5,-1]])\n",
    "A"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "numpy.matrixlib.defmatrix.matrix"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "type(A)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-29.0"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "la.det(A) # Compute the determinant"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Eigenvalues of A: \n",
      "\n",
      " [ 5.43436462  1.16120709 -4.5955717 ]\n",
      "\n",
      "Eigenvectors of A: \n",
      "\n",
      " [[-0.21277719  0.61090902 -0.33351363]\n",
      " [-0.7715384  -0.31411793  0.55040399]\n",
      " [ 0.59954513  0.72671872  0.76539147]]\n"
     ]
    }
   ],
   "source": [
    "evals, evecs = la.eig(A) # Compute eigenvalues and eigenvectors\n",
    "print(\"Eigenvalues of A:\", \"\\n\\n\", np.real(evals))\n",
    "print()\n",
    "print(\"Eigenvectors of A:\", \"\\n\\n\", evecs)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's verify that $A v_1 = \\lambda_1 v_1$ for the first eigenpair $(\\lambda_1,v_1)$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "matrix([[-0.21277719,  0.61090902, -0.33351363],\n",
       "        [-0.7715384 , -0.31411793,  0.55040399],\n",
       "        [ 0.59954513,  0.72671872,  0.76539147]])"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "P = np.matrix(evecs) # The matrix of eigenvectors\n",
    "P"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "matrix([[-0.21277719],\n",
       "        [-0.7715384 ],\n",
       "        [ 0.59954513]])"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "v1 = P[:,0] # The first eigenvector\n",
    "v1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 5.43436462,  1.16120709, -4.5955717 ])"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s = np.real(evals) # The array of eigenvalues\n",
    "s"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5.4343646192384165"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s1 = s[0] # The first eigenvalue\n",
    "s1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Compute $A v_1$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "matrix([[-1.15630886],\n",
       "        [-4.19282097],\n",
       "        [ 3.25814686]])"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A * v1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now compute $\\lambda_1 v_1$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "matrix([[-1.15630886],\n",
       "        [-4.19282097],\n",
       "        [ 3.25814686]])"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s1 * v1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's see the diagonlization of $A$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "matrix([[ 5.43436462,  0.        ,  0.        ],\n",
       "        [ 0.        ,  1.16120709,  0.        ],\n",
       "        [ 0.        ,  0.        , -4.5955717 ]])"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "D = np.matrix(np.diag(np.real(evals)))\n",
    "D"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "matrix([[  1.00000000e+00,   2.00000000e+00,   1.00000000e+00],\n",
       "        [  4.00000000e+00,   2.00000000e+00,  -3.00000000e+00],\n",
       "        [ -7.52114818e-16,  -5.00000000e+00,  -1.00000000e+00]])"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "P * D * P**(-1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's round the result to see the matrix $A$ more clearly:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "matrix([[ 1.,  2.,  1.],\n",
       "        [ 4.,  2., -3.],\n",
       "        [-0., -5., -1.]])"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.round(P * D * P**(-1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "matrix([[ 1,  2,  1],\n",
       "        [ 4,  2, -3],\n",
       "        [ 0, -5, -1]])"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### EXAMPLE\n",
    "\n",
    "Suppose $M$ is a 2 by 2 matrix with random entries sampled uniformly from $[0,1]$. How are the (real) eigenvalues of the symmetric matrix $A = M M^T$ distributed? Compute a random sample of such matrices and plot the eigenvalues in a scatter plot."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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ruWcv3nYbsGNHCIEAvWfXXBPpZbPC8fXXgW3b+GPb6WvmZ3c3BZPtV2cnz1dX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\nD495BE/OPDw8PDw8PDzmEf5/cLTN/WjXXq4AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fe84fd26978>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ev1 = np.array([])\n",
    "ev2 = np.array([])\n",
    "\n",
    "for _ in range(0,10000):\n",
    "    M = np.matrix(np.random.random([2,2]))\n",
    "    A = M * M.T\n",
    "    evals, evecs = la.eig(A)\n",
    "    evals = np.real(evals)\n",
    "    ev1 = np.append(ev1,np.max(evals))\n",
    "    ev2 = np.append(ev2,np.min(evals))\n",
    "\n",
    "plt.figure(figsize=(10,3))\n",
    "plt.plot(ev1,ev2,'.',alpha=0.3)\n",
    "plt.axis('equal')\n",
    "plt.grid('on')\n",
    "plt.title('Distribution of Random Eigenvalues')\n",
    "plt.xlabel('Maximum eigenvalue'), plt.ylabel('Minimum eigenvalue');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3. Data analysis with pandas\n",
    "\n",
    "The main object we'll be dealing with in the pandas library is the [DataFrame](). The [documentation](http://pandas.pydata.org/) for pandas is extensive. Check it out!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "One of the great features of pandas is its robust I/O Tools. Check out the documentation for the [read_csv](http://pandas.pydata.org/pandas-docs/stable/io.html#io-read-csv-table) method. Let's import a `.csv` file containing weather data recorded at the Vancouver International Airport from 2010 to 2016."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "wind = pd.read_csv('wind.csv')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "pandas.core.frame.DataFrame"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "type(wind)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now that we have the `.csv` file loaded as a pandas DataFrame, let's look at the data. The `.head()`, `.tail()` and `.info()` are always a great first step in exploring a dataset."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Year</th>\n",
       "      <th>Month</th>\n",
       "      <th>Day</th>\n",
       "      <th>Hour</th>\n",
       "      <th>Pressure</th>\n",
       "      <th>Wind Direction</th>\n",
       "      <th>Wind Speed</th>\n",
       "      <th>Temperature</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>2010</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>100.87</td>\n",
       "      <td>E</td>\n",
       "      <td>22.0</td>\n",
       "      <td>5.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2010</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>100.81</td>\n",
       "      <td>E</td>\n",
       "      <td>19.0</td>\n",
       "      <td>5.4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2010</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>100.77</td>\n",
       "      <td>E</td>\n",
       "      <td>26.0</td>\n",
       "      <td>5.7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>2010</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>3</td>\n",
       "      <td>100.69</td>\n",
       "      <td>ESE</td>\n",
       "      <td>26.0</td>\n",
       "      <td>5.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>2010</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>4</td>\n",
       "      <td>100.58</td>\n",
       "      <td>ESE</td>\n",
       "      <td>26.0</td>\n",
       "      <td>5.8</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Year  Month  Day  Hour  Pressure Wind Direction  Wind Speed  Temperature\n",
       "0  2010      1    1     0    100.87              E        22.0          5.5\n",
       "1  2010      1    1     1    100.81              E        19.0          5.4\n",
       "2  2010      1    1     2    100.77              E        26.0          5.7\n",
       "3  2010      1    1     3    100.69            ESE        26.0          5.5\n",
       "4  2010      1    1     4    100.58            ESE        26.0          5.8"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "wind.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Year</th>\n",
       "      <th>Month</th>\n",
       "      <th>Day</th>\n",
       "      <th>Hour</th>\n",
       "      <th>Pressure</th>\n",
       "      <th>Wind Direction</th>\n",
       "      <th>Wind Speed</th>\n",
       "      <th>Temperature</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>54774</th>\n",
       "      <td>2016</td>\n",
       "      <td>4</td>\n",
       "      <td>1</td>\n",
       "      <td>7</td>\n",
       "      <td>102.15</td>\n",
       "      <td>ENE</td>\n",
       "      <td>4.0</td>\n",
       "      <td>8.7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>54775</th>\n",
       "      <td>2016</td>\n",
       "      <td>4</td>\n",
       "      <td>1</td>\n",
       "      <td>8</td>\n",
       "      <td>102.15</td>\n",
       "      <td>ESE</td>\n",
       "      <td>17.0</td>\n",
       "      <td>10.1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>54776</th>\n",
       "      <td>2016</td>\n",
       "      <td>4</td>\n",
       "      <td>1</td>\n",
       "      <td>9</td>\n",
       "      <td>102.15</td>\n",
       "      <td>ESE</td>\n",
       "      <td>11.0</td>\n",
       "      <td>11.7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>54777</th>\n",
       "      <td>2016</td>\n",
       "      <td>4</td>\n",
       "      <td>1</td>\n",
       "      <td>10</td>\n",
       "      <td>102.15</td>\n",
       "      <td>SE</td>\n",
       "      <td>10.0</td>\n",
       "      <td>13.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>54778</th>\n",
       "      <td>2016</td>\n",
       "      <td>4</td>\n",
       "      <td>1</td>\n",
       "      <td>11</td>\n",
       "      <td>102.15</td>\n",
       "      <td>SSW</td>\n",
       "      <td>13.0</td>\n",
       "      <td>13.4</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       Year  Month  Day  Hour  Pressure Wind Direction  Wind Speed  \\\n",
       "54774  2016      4    1     7    102.15            ENE         4.0   \n",
       "54775  2016      4    1     8    102.15            ESE        17.0   \n",
       "54776  2016      4    1     9    102.15            ESE        11.0   \n",
       "54777  2016      4    1    10    102.15             SE        10.0   \n",
       "54778  2016      4    1    11    102.15            SSW        13.0   \n",
       "\n",
       "       Temperature  \n",
       "54774          8.7  \n",
       "54775         10.1  \n",
       "54776         11.7  \n",
       "54777         13.5  \n",
       "54778         13.4  "
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "wind.tail()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "RangeIndex: 54779 entries, 0 to 54778\n",
      "Data columns (total 8 columns):\n",
      "Year              54779 non-null int64\n",
      "Month             54779 non-null int64\n",
      "Day               54779 non-null int64\n",
      "Hour              54779 non-null int64\n",
      "Pressure          54776 non-null float64\n",
      "Wind Direction    53180 non-null object\n",
      "Wind Speed        54777 non-null float64\n",
      "Temperature       54777 non-null float64\n",
      "dtypes: float64(3), int64(4), object(1)\n",
      "memory usage: 3.3+ MB\n"
     ]
    }
   ],
   "source": [
    "wind.info()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can select the columns of a DataFrame by the bracket notation `[ ]` with the column name."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0    22.0\n",
       "1    19.0\n",
       "2    26.0\n",
       "3    26.0\n",
       "4    26.0\n",
       "5    19.0\n",
       "6    13.0\n",
       "7    19.0\n",
       "8    22.0\n",
       "9    30.0\n",
       "Name: Wind Speed, dtype: float64"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "wind['Wind Speed'].head(10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### EXAMPLE\n",
    "\n",
    "Plot the hourly temperature from April 2015 as line plot and the wind speed as a historgram.\n",
    "\n",
    "As a first step, we can select the data from April 2015 with Boolean indexing:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "april_wind = wind[(wind['Year'] == 2015) & (wind['Month'] == 4)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Year</th>\n",
       "      <th>Month</th>\n",
       "      <th>Day</th>\n",
       "      <th>Hour</th>\n",
       "      <th>Pressure</th>\n",
       "      <th>Wind Direction</th>\n",
       "      <th>Wind Speed</th>\n",
       "      <th>Temperature</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>45983</th>\n",
       "      <td>2015</td>\n",
       "      <td>4</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>102.03</td>\n",
       "      <td>W</td>\n",
       "      <td>13.0</td>\n",
       "      <td>8.3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>45984</th>\n",
       "      <td>2015</td>\n",
       "      <td>4</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>102.08</td>\n",
       "      <td>NNW</td>\n",
       "      <td>8.0</td>\n",
       "      <td>7.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>45985</th>\n",
       "      <td>2015</td>\n",
       "      <td>4</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>102.11</td>\n",
       "      <td>WNW</td>\n",
       "      <td>17.0</td>\n",
       "      <td>6.8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>45986</th>\n",
       "      <td>2015</td>\n",
       "      <td>4</td>\n",
       "      <td>1</td>\n",
       "      <td>3</td>\n",
       "      <td>102.14</td>\n",
       "      <td>WNW</td>\n",
       "      <td>16.0</td>\n",
       "      <td>6.7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>45987</th>\n",
       "      <td>2015</td>\n",
       "      <td>4</td>\n",
       "      <td>1</td>\n",
       "      <td>4</td>\n",
       "      <td>102.17</td>\n",
       "      <td>WNW</td>\n",
       "      <td>13.0</td>\n",
       "      <td>5.5</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       Year  Month  Day  Hour  Pressure Wind Direction  Wind Speed  \\\n",
       "45983  2015      4    1     0    102.03              W        13.0   \n",
       "45984  2015      4    1     1    102.08            NNW         8.0   \n",
       "45985  2015      4    1     2    102.11            WNW        17.0   \n",
       "45986  2015      4    1     3    102.14            WNW        16.0   \n",
       "45987  2015      4    1     4    102.17            WNW        13.0   \n",
       "\n",
       "       Temperature  \n",
       "45983          8.3  \n",
       "45984          7.2  \n",
       "45985          6.8  \n",
       "45986          6.7  \n",
       "45987          5.5  "
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "april_wind.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Plotting the temperature and wind speed over April 2015 is as simple as as selecting the column and then chaining the `.plot()` method (which is built on top of matplotlib):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7fe84dce3b38>"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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dN8KP3Wbby97Flk6z/UchpX7L4YenCb4IWqMFf8oUrk+Twuc/z/MX9tmHc+xj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\nAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fe84dcda358>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "april_wind['Temperature'].plot(title='April 2015 Temperature (Deg C)')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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MbMwl/QoEt2427tbFxn7/3bqxfvj76M3MrMSFviRLHaBCljpAhSx1gApZ6gAV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\nCgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fe85c569b70>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "april_wind['Wind Speed'].hist(bins=15)\n",
    "# .hist creates a matplotlib figure\n",
    "# and so we can use pyplot commands on the current figure\n",
    "plt.title('Hourly Wind Speed Distribution');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### EXAMPLE\n",
    "\n",
    "Plot a bar chart showing the number of hourly wind direction measurements (in the entire DataFrame) for each direction: E, ESE, SE, SSE, S, etc."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array(['E', 'ESE', 'SE', 'SSE', 'S', 'ENE', 'NNW', 'WNW', 'SW', 'SSW', nan,\n",
       "       'W', 'NW', 'N', 'WSW', 'NE', 'NNE'], dtype=object)"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "wind['Wind Direction'].unique()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The [groupby](http://pandas.pydata.org/pandas-docs/stable/groupby.html) method splits the DataFrame into sub-DataFrames acording to the values in the specified column and then we can apply a function. For example, to simply count the number of measurements (rows) in each direction, we can enter:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7fe8545f9a90>"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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XegNl20+5yu57O4JqTaMf7wNlMoqI50nDlG8CkPR6UmA5Dfg4cHXfa/dpY0mj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\nVmH/H98f1Jpm2EGiAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fe84fd2ab00>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "wind.groupby('Wind Direction').size().plot(kind='bar',title='Hourly Wind Direction Measurements')"
   ]
  }
 ],
 "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",
   "version": "3.5.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}