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      "from __future__ import division, print_function\n",
      "%matplotlib inline\n",
      "import sys\n",
      "sys.path.insert(0,'../code') # allow us to format the book\n",
      "\n",
      "# use same formatting as rest of book so that the plots are\n",
      "# consistant with that look and feel.\n",
      "import book_format\n",
      "book_format.load_style()"
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     "source": [
      "This notebook creates the animations for the Multivariate Kalman Filter chapter. It is not really intended to be a readable part of the book, but of course you are free to look at the source code, and even modify it. However, if you are interested in running your own animations, I'll point you to the examples subdirectory of the book, which contains a number of python scripts that you can run and modify from an IDE or the command line. This module saves the animations to GIF files, which is quite slow and not very interactive. "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import stats\n",
      "import numpy as np\n",
      "from matplotlib.patches import Ellipse\n",
      "import matplotlib.pyplot as plt\n",
      "from matplotlib import cm\n",
      "from mpl_toolkits.mplot3d import Axes3D\n",
      "\n",
      "# this code lets me animate the 3d covariance. to be honest I do not find it\n",
      "# very instructive or compelling so I am not using it for now.\n",
      "def plot_3d_covariance(ax, mean, cov):\n",
      "    \"\"\" plots a 2x2 covariance matrix positioned at mean. mean will be plotted\n",
      "    in x and y, and the probability in the z axis.\n",
      "\n",
      "    Parameters\n",
      "    ----------\n",
      "    mean :  2x1 tuple-like object\n",
      "        mean for x and y coordinates. For example (2.3, 7.5)\n",
      "\n",
      "    cov : 2x2 nd.array\n",
      "       the covariance matrix\n",
      "\n",
      "    \"\"\"\n",
      "\n",
      "    # compute width and height of covariance ellipse so we can choose\n",
      "    # appropriate ranges for x and y\n",
      "    o,w,h = stats.covariance_ellipse(cov,3)\n",
      "    # rotate width and height to x,y axis\n",
      "    wx = abs(w*np.cos(o) + h*np.sin(o))*1.2\n",
      "    wy = abs(h*np.cos(o) - w*np.sin(o))*1.2\n",
      "\n",
      "\n",
      "    # ensure axis are of the same size so everything is plotted with the same\n",
      "    # scale\n",
      "    if wx > wy:\n",
      "        w = wx\n",
      "    else:\n",
      "        w = wy\n",
      "\n",
      "    minx = mean[0] - w\n",
      "    maxx = mean[0] + w\n",
      "    miny = mean[1] - w\n",
      "    maxy = mean[1] + w\n",
      "    #print (minx, maxx, miny, maxy)\n",
      "    \n",
      "    minx = -9.57238091319 \n",
      "    maxx= 13.5723809132 \n",
      "    miny = -4.57238091319 \n",
      "    maxy = 18.5723809132\n",
      "\n",
      "    xs = np.arange(minx, maxx, (maxx-minx)/40.)\n",
      "    ys = np.arange(miny, maxy, (maxy-miny)/40.)\n",
      "    xv, yv = np.meshgrid (xs, ys)\n",
      "\n",
      "    zs = np.array([100.* stats.multivariate_gaussian(np.array([x,y]),mean,cov) \\\n",
      "                   for x,y in zip(np.ravel(xv), np.ravel(yv))])\n",
      "    zv = zs.reshape(xv.shape)\n",
      "\n",
      "    ax.plot_surface(xv, yv, zv, rstride=1, cstride=1, cmap=cm.autumn)\n",
      "\n",
      "    ax.set_xlabel('X')\n",
      "    ax.set_ylabel('Y')\n",
      "    ax.set_zlim([0,10])\n",
      "    #ax.set_ylim([-5,20])\n",
      "    #ax.set_xlim([-10,10])\n",
      "\n",
      "    ax.contour(xv, yv, zv, zdir='x', offset=minx-1, cmap=cm.autumn)\n",
      "    ax.contour(xv, yv, zv, zdir='y', offset=maxy, cmap=cm.BuGn)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 3
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import numpy as np\n",
      "import mkf_internal\n",
      "import matplotlib.pyplot as plt\n",
      "from gif_animate import animate\n",
      "import stats\n",
      "def mkf_animate(frame):\n",
      "    global ax\n",
      "    plt.cla()\n",
      "    var = (31-frame) / 3\n",
      "    plot_3d_covariance(ax, (2,7), np.array([[var,0],[0,4.]]))\n",
      "    \n",
      "    \n",
      "def ellipse_animate(frame):\n",
      "    \n",
      "    plt.cla()\n",
      "    cov = frame/15.\n",
      "    P = np.array([[2,cov],[cov,2]])\n",
      "    stats.plot_covariance_ellipse((2,7), cov=P, facecolor='g', alpha=0.2, \n",
      "                              title='|2.0 {:.1f}|\\n|{:.1f} 2.0|'.format(cov, cov))\n",
      "\n",
      "fig = plt.figure()\n",
      "#ax = fig.add_subplot(111, projection='3d')\n",
      "animate('ellipse.gif', ellipse_animate, 30, 125)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
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       "output_type": "display_data",
       "text": [
        "<matplotlib.figure.Figure at 0x7f34310bbd68>"
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oSoKIUKyMbn0XvDYTDNrmvu/USnhmQ9RmJsY4G0v7oNVW4HFOP4tusxFFCf5I\nAVa1HS6zGQ5za7yuVsGwIWoj/lgWo9EE/FkfzKYOdBrV9S6pakLxIjQyA5xGK3o4wGbDYdgQtQFJ\nkjAaycCfSMCX9TX1GGfTSaTLKBUV6Dd3oY8DbDak1vm0EdG0RFHCcCiFQCqOUC4Il00JvaZ1Dv18\nsYJYSkCPoRdeh5EdNxsUfytELUyoiONjnKWiiBXD6Haom25WzZmUBRGBaBEuXTe6O42w6FvnsmCr\nYdgQtaiSUMGJQBK+dBjpcrxl+tBMEEUJvkgBnSobXCYLuq3suNnIGDZELShfFHAimIQvHURBTKPH\nqYVc3lr3MXyRPLQdJriMNvQ5jey42eAYNkQtZqKz5mjaB0legNfZnNM3zyQUK0AsqdCtN6PfZYa8\no3XO2FoVw4aohcQzBQyHkhjL+KBSCXBa1S33F38qW0a5oka/xQunvgNqZevcg2plDBuiFhFO5jAS\nGQ8avU6C3dJ6N8vzxfEpA/6fx4t+lwUyIV/vkmiOeO5J1AJ80QyGQnGMpEdhNgJ2S+sN01J6s+VZ\nl64bXpsFdo4Q0FR4ZkPUxCRJwkg4DX9yfB4aR6cSRl3rHdYVUYI/XIBV7UCX2QKvw1TvkmieWu9T\nSdQmRFHCUCiFQDKGcD6ELpuqJeaheStJGp8ETSc3w2WwotfBoWiaEcOGqAkJFREnAkkEUlHEShG4\nHRqoVa15VTycKAEVNbrNTvR3cSiaZsWwIWoyxfJ4Z01/OoSMkIDXqWnZOVsSmTLy+Q70mbrR7zRB\npWi9M7d2wbAhaiK5Qhkngin40gGUkIG3BTtrTsgWBMSTFXgNPehxmKDTKOtdEi0Cw4aoSaRzJZwI\nJjCW8UMmL8Jja73OmhNKZRGhaBndejc8NhM6DZp6l0SLxLAhagKxdAHD4QR8GT9UagHOztbrrDmh\nUhkf88ymccJlNqOrk2OetQKGDVGDCyXGO2v6MmMwGACbufU6a06QpPHZNo0KC7pMnAStlTBsiBrY\n+MyacfiyPnSa5bAYWvu+RShWglzSocvg5CRoLYZhQ9SgxiIZ+OIJjGXHWraz5qliqRJKJQV6jC70\nd5latoVdu2rtTy9RkxoJp+FLJODP+uCyKqHXtvahmskJSKYl9Bi70Oc0Q8vZNlsOf6NEDUSSJJwM\np+FLxBHKBVp2VIBTFUsiQvEyPHoPvDYzzJxtsyXNGDY+nw9XXXXVlGX5fB4PP/wwLr/88jNu9+tf\n/xof+tAi0yMWAAAgAElEQVSHoNVqJ5ft3r0by5cvX2S5RK1LFCUMh1LwJ2MIF0LotqugUbd20AgV\nEf5oEU6tE10WM5wWDq7ZqmYMG7fbjVdeeWXy5+HhYVx99dW4+OKLZ92xy+XCwYMHF18hURsQRQkn\ngkn4kzFEiyG47a07/MwEUZTgjxRhUnbCZeqE126od0lUQ/O6jLZ7925s2rQJGg07WBFVS0UUcSKQ\ngj8ZQbwchcehgUrZ2kEDAMFYESro0WWwo89patl+QzRuzmEjiiKefvpp3HvvvXNaPxqNYsOGDdDp\ndLj22mvx0Y9+dNr1bDbbXEtoCErleNPTZqqbNS+d+dYtVET8aTSGtFRAWVPAX/Q7l7wVlkIx/jVg\ntpiX7DnD8QJ0Gh36LX1Y3WuHZp4NAtrl89EIJmperDn/hg8fPgyZTIaLLrpo1nVXrlyJ5557Dr29\nvXj99dexY8cOOBwOXHPNNaete/fdd0/+e2BgABs3bpxrSURNrVSuYHAshpFEAJlKHH1deijaoLlv\nPFVCOg30W7xY3t0576Ch2jt48CAOHToEAJDL5RgYGFj0PmVHjx6V5rLiLbfcgt7eXnzqU5+a95M8\n+uijePXVV/Hwww9PWT4yMoI1a9bMe3/1NPEXSTQarXMlc8eal85c6y6WKzjuT8KXDiIvpuBxaOo2\noObEGU0ykaz5c2VyAsJxAV5DD5a5OmE1LuySfKt/PhqJzWbD4cOH0dPTs6j9zOlPimQyiQMHDuCp\np55a1JMREZAvCTgRSGIsFUAZGXicGsjboKd8vliZbOLcYzcvOGioOc3pnP2ZZ57BWWedhRUrVpz2\n2NatW7Fz584py1544QX4fD4AwLFjx/Dkk0/ikksuqUK5RM0tXxRw3JfAaNIHoSMLt6M9gqZUFhGI\nltCl64a708Imzm1oTmc2e/bswdVXXz3tY2NjY/B6vVOWvfbaa7j11luRzWZhs9mwZcuWae/XELWT\nbKGME4EkRtM+QFGA29a6IzefSqiI8EWKsGuc6LZY4GET57Y0p7DZvXv3GR87cODAacu2b9+O7du3\nL7wqohbz57lofJArS3BZ2yNoKqKEsXABZqUNLmMneh0cxbldsRkIUY0ls8XJoFGpBbis7XGvQpIk\n+MMF6DrM6DbasayLfWnaGcOGqIbimQKGQgmMpX3Q6ipwWNpn3C9/tAiFpIPb5MKyLjPkHa3frJvO\njGFDVCMTs2uOpsdg0EstPenZW4XiRUiCCh5jN5ZxugACw4aoJsLJHE6GkxjLjMJs6kCnUVXvkpZM\nLFlCIS9Hr8mN/i4zO20SAIYNUdX5oxkMhSZm1+xo+dk1T5XMlJHKSOgxudHnNEOvaZ/XTjNj2BBV\n0Wg4hZFIDL7sGOwWBYz69jnEsnkBsWQFHoMXfQ4L56WhKdrnSCCqsdFwGhlRwlh6FI5OBQwtPo3z\nqQrFCoKxP0+AxtEB6K3a52ggqhFJkiancc7K0+h2aiAUhXqXtWRK5fEJ0Fy6bnRbzOjq1Ne7JGpA\nbCJCtAiSJGE4lMZYIoZgzg+3UwO9tn3+hhMqIsbCBVjVDnSbO+Flp006g/Y5KoiqTBQlDL05jXOk\nEES3Qw2dpn0OqYoowRcuwqyyottk4+gANKP2OTKIqqgdp3E+lSRJ8EcK0HQYJ0cH6GiDAUVp4Rg2\nRPM0ETS+ZBSxYhgepwaqNuu0GIgWIRd1cJs5OgDNDT8hRPNwatDES5G2DJpwvIhKWfnm6ABmqBTy\nepdETaC9jhKiRRBFCccDfw4at0PddkETT5eRz8vhMXjQ7zJBy9EBaI7a60ghWqCJoPGn2jdo0lkB\niZQIj9GNPpcZBm37DMFDi8c/S4hmURFFnAik4E9GEC9H4XGo225gyWxBQDhRhkfvRa/dDAtHB6B5\naq8jhmiepgZNpC2DplCqIBQtw613w2uzwGbS1rskakLtddQQzcPpQaNpu6ApCSL8kSKcOhe6LRZ0\nWzk6AC0ML6MRTWMiaHzJMBLlaFsGTVkQ4QsXYVU70GXqhNduqHdJ1MTa6+ghmgMGzfgwNL5wARbl\n+OgAfU5O6UyLwzMbolNURBHH/Un4UhEky1F4nRoo5O0VNBVRwli4AKPSim4TRweg6mivo4hoBqcG\nTapNg0YUJfjCBejlZriNDo4OQFXDMxsi/DloxlJhpMsxeNo1aCIFqGVGuI3jw9C023tAtcNPErW9\nU89o2jVoJEmCP1qEUtLDY+zC8m5z292notrip4na2lsvnbVj0ACAL5xHR0ULj6kby7s53hlVHy+j\nUduabHXW5kHjD+chlTXwGo1Y1mWGWsmgoepj2FBbOrV5c7u2OgOAULwItVKPfosXNi04sCbVTPsd\nXdT23tqPpl2DJpIooVhQoNfcg5UeK3QaZb1LohbWfkcYtTVRlCaHoJnosNmOQRNLlpDLdcBjcGOl\n28oRnKnm2u8oo7Y1OU1AG491BgCJdBnpDOAxurHMZYGJIzjTEmi/I43a0tSgac8haAAgmSm/OSeN\nB30OC8wMGloi7Xe0UduZMvFZm85HA4xPfhZLVuA2jAeN1aipd0nURtrviKO2IooSTgSnzrDZjkGT\nzY9PfubWe9Br55w0tPTa76ijtjERNL5k+07lDAC5QgXBWBkevQc9dgucFl29S6I21H5HHrWFU4Mm\nVgy3bdDkixUEoiW49W64rRZ0dXLyM6qPGY8+n8+Ht73tbVP+W716Nfbt2zfrjnft2oUNGzbgggsu\nwAMPPFC1golmI0kShkIp+JMxxIpheJyatgyaQqmCQKSELl033BYLPDZOfkb1M2N3YbfbjVdeeWXy\n5+HhYVx99dW4+OKLZ9zpkSNH8Mgjj+CJJ56AwWDABz/4QaxZswabN2+uTtVEMzgZTiOQjCFaDMHj\naM+gKZUnpnPugttigddhrHdJ1ObmdRTu3r0bmzZtgkYzcyuWvXv3YtOmTVixYgVcLheuu+46PPfc\nc4sqlGguRsJp+BJxhAtBuO0aqJRLHzQvv1TficZKgoixcAF2jQtdpk70MGioAcx5ICRRFPH000/j\n3nvvnXXdoaEhrF+/Ho899hgCgQDWrVuHZ555Ztp1bTbb3KttAErl+JAezVR3u9R8MpRERhSR68jg\n7BUOaNVLP86XQqHAq0dkOG+decmfGwAEQUQkkEW/YwV6Op1Y6emcdTrndvl8NIJmrHui5sWa89F4\n+PBhyGQyXHTRRbOum8/nodPpMDg4CJ/Ph4GBAeRyuWnXvfvuuyf/PTAwgI0bN861JKJJY5E0RqNx\n+DKj6HZq6hI0L78kw6tHZPjWf8ggVjpw3nkSzlsnLdnzCxURJ4M5dKoc8FocWOGePWiIpnPw4EEc\nOnQIACCXyzEwMLDofc75iNyzZw/e9773zWldrVaLXC6HO++8EwCwb98+6HTTN7fcsWPHlJ+j0ehc\nS6qLib9IGr3OU7V6zcF4DicjMYxlx+CyKiEUK0gWa13h6VasAM5bZ4ZY6cB118UBAMnE0jx3RZQw\nFipAr7DAoFTBohERj8fmtG2rfz4aSbPUvXbtWqxduxbAeM2HDx9e9D7ndEE7mUziwIEDeP/73z+n\nnfb39+P48eOTPw8ODmL58uULq5BoBpFkHiPRBHxZHxydSui19R8i/7zzlu5sBnhzOudwATq5CW6j\nA8u6zJB3tF+jCGpsc/pEPvPMMzjrrLOwYsWK0x7bunUrdu7cOWXZ5s2bsW/fPgwODiIYDGL37t1s\niUZVF0sXMBxOYCwzBptFDqOu/kEDYEkvnYmiBF+kALXMCLfRheVdlrYcxZoa35yOzj179uDqq6+e\n9rGxsTF4vd4py8455xzcfPPN2LZtGwRBwJYtWxg2VFXxzETQjKLT3AGTvv3mYpEkCf5oEUpJD4+p\nC8u7zW05FA81hzmFze7du8/42IEDB6Zdvm3bNmzbtm1hVRHNIJUrYTiUxGh6DCajDBZDewaNL1KE\nQtTBY+rGsi4TVApO50yNi38GUVPJ5EsYCiYwlvHBoJdgNbXfpF+SJMF/StAs7zJDw+mcqcExbKhp\nZAtlHA8kMJIeg0YjwGZu36DpqGgZNNRUGDbUFPJFAScCSYxlfFCpBTg622/Sr1ODxmt2M2ioqTBs\nqOEVSgKOB5IYTfvQoSjBZW3foJFVtPCY3FjGoKEmw7ChhlYsV3A8kMRYygfIC+iytWnQRMeDxmty\nY3m3GVoGDTUZhg01rLJQwYlAEr50EEJHDt12ddsNvzIZNAKDhpobw4YaklAR8afRGMZSQRSlNNx2\nTdsGDQQNvMZuBg01NYYNNZyKKGJwLIbRZBB5MQW3Q4OOjvYLmsCbQdNjdGN5t4VBQ02Nn15qKKIo\n4UQghbRUQEqIwePQQN6mQSMJGngngqYOo1gTVRPPbKhhSJKEE8Ek/Kko4qUIel06yOXtFTQAEIwV\nIQpqeI1urGDQUItg2FBDkCQJQ8EU/MkYYsUwelx6KNpwnK9AtIBKWY0eowfLu8wMGmoZ/CRTQzgZ\nTsOfjCFaDMHjqM90zvU0celMFP4cNDpN+435Rq2rvY5oakgj4TR8iTjC+RC67WoGDYOGWhDPbKiu\nxqIZ+BIJBHMBuO0qaFTtNXLxqY0BeniPhloYP9VUN/5YFr5YAv6sD102FTTq9gsa/1ubNzNoqEW1\n1/UKahjhZA6j0QTGsmNwWZXQaRg0DBpqZfx005KLZwoYiSThy/rgsCih17bXx3DKEDTGbgYNtQV+\nwmlJZfLjs2yOZXzoNHXAqG+vj+CpozdzrDNqJ7yMRksmXxQwFEzBl/FBpxNhMbZXiysGDbUzhg0t\niZJQwYlgEmNpPxSqMhyW9poqYMrEZwwaakMMG6o5oSJOThUgyvNtN/mZJEnwnTLD5goGDbUhhg3V\nlCiOD0PjS4dRENPotrXXnDSiOB40ClHHqZyprTFsqGYkScJwKAV/Kop0OQ5Pm00VIIrjrc4Uog4e\nUzeDhtoaw4ZqZjSSQSAVR6wYhtuhaasRnMfPaApQiHoGDRHY9JlqxB/Lwp9IIJgLwu1QQ9VGIzhX\nRAlj4QLUMiM8pi4s7zZDrWyvTqtEb8WwoaqLpvIYi4132nTZlG013pkgiBgJ5qDtMMFtdGF5txkq\nRfu8fqIzYdhQVSWyRZyMJOHLjMFuUUCvaZ+PWFkQcTKYg1lhhcGkwbIuM5RtdEZHNJP2+SagmssW\nyjgZSmIs7YPJKINJ3z6dNkuCCF+4iB5bN7wWJzo1EhRyBg3RBB4NVBX5koATgSRG02PQaiuwmlT1\nLmnJFEsixkIFdKrs6O10YZXHyqAhegue2dCilYTKm502/ZAry3B0aupd0pIplCrwR4qwa1zoNlux\n0mNtq+bdRHPFsKFFqYh/Hh1A6MjBY2ufoMkXKwhESnDqutBttqLPaWTQEJ0Bw4YWTBQlnAikEEhH\nkRdT8Dq1bTM6QLYgIBgto0vXDbfFgh6HsW1eO9FCMGxowU6G0wikYkiWY/A6NZC3yV/1mZyAULwM\nt94Nt8UCr8NY75KIGh7DhhZkNJyGPxlHtBiCx6Fpmxvi6ayASEKAR++Bx2qB22aod0lETYFhQ/MW\njOfgTyQRzAXgtquhUrZH0CQyZcSTItx6D3rtnXB16updElHTmPVbolAo4K677sKFF16I9evX4/Of\n//ysO/31r3+N1atX421ve9vkf8ePH69KwVRfsXQBI9HE+OgAViU06vboHR9Pl5FIivAavOh3MmiI\n5mvWM5t77rkHIyMjePbZZ2Gz2TA4ODinHbtcLhw8eHDRBVLjSGaLGA4n4MuMwWqWQ69tjxPjaLKE\nTFaGHlMP+hwWWI3t0+KOqFpm/LYoFAp4+umnsWfPHtjtdgDAqlWrlqQwaizZQhnDoSR8GT9MBhnM\nhvYYHSCcKCKfk8NrdKPfaUGngUFDtBAzXkYbGhqCTCbD/v37sWHDBlx11VXYv3//nHYcjUaxYcMG\nXH755fjGN75RlWKpPgolAUOBJMYyPqg1Aqzm9hgdIBgropBXwGv0YLmrk0FDtAgzntlkMhmUy2WM\njo7i+eefxyuvvIKbbroJP//5z+FwOM643cqVK/Hcc8+ht7cXr7/+Onbs2AGHw4FrrrnmtHVtNtvi\nX8USUirH/6JvproXU7NQEeE/GUFKloXJqobX2Vnt8qalUIx/NM0W85I836kkSYI/kodWZcBZDi9W\nuq0w6ec2lXW7fT7qpRlrBpqz7omaF2vGsNFoNKhUKrjhhhugUqlw4YUXYtmyZThy5Aguu+yyM25n\ns9km38zVq1fj+uuvx/PPPz9t2Nx9992T/x4YGMDGjRsX+lqoyiRJwjFfHL5UCGVZFr2O1r8pLkkS\nxsJ5oKxBn8WLlR4rDNr2OJMjmnDw4EEcOnQIACCXyzEwMLDofc4YNj09PTXvFb1jx44pP0ej0Zo+\n32JNhGij13mqhdZ8MpTCSDyKSCGIXpcWqWSqFuVNa+KMJplILtlzTkzjLK9o4TEaYdfJUMylUczN\nfR/t9Pmop2asGWieuteuXYu1a9cCGK/58OHDi97njPdszGYz1q9fj+9+97sQBAEvvvgiTpw4gXPP\nPXdyna1bt2Lnzp1TtnvhhRfg8/kAAMeOHcOTTz6JSy65ZNHF0tIJxnMIJJOI5ENw21t/SueKKMEX\nHp/G2Wt2Y7nbAq26PVrbES2FOTV9vuOOO7B+/Xq4XC7cf//9U+7XjI2Nwev1Ttnmtddew6233ops\nNgubzYYtW7ZMewmNGlMiW8RYLAl/1g+nVQm1qrU7bVYq49M4nzq7JqdxJqquWcPG6/Xie9/73hkf\nP3DgwGnLtm/fju3bty+uMqqLfFHAyTebOHeaWr8vjVARMRYuwCC3wG1yYlkXp3EmqoXW/iaheSkL\nIk4Ek/BlAtBoK7AY59YCq1mVhfGgMStt6DbaOY0zUQ0xbAjA+M3xoWASgUwIYkceDktr9ykplUX4\nIkV0Ku3oNtuxrMsEeQeDhqhWGDYE4M3pAtIxZIUkvK7WnpemUKzAHy3Cpnai22zFMpeZk54R1RjD\nhuCPZRFMJRErhuFp8XlpsnkBwVgZLl03us2d6HVwdk2ipcCwaXOxdOHNlmc+dNnUULXwPYtkpoxY\nsgKP3oNui5mTnhEtIYZNG8sWyjgZTsKf8cFmVkCnad1WWLFkCamMBI/Bix6bhVMEEC0xhk2bKpYr\nGAqm4M/6odNLMBtad0iWULyIQl6OHpObUwQQ1QnDpg1VRBHDwRT8mSBk8lLLtjyTpPHhZyRBhV6T\nG31OM8xzHFCTiKqLYdOGhkNpBNNR5MUUepzaepdTExVRgj9cgBJ6uI1d6O8yQ69pjzl4iBoRw6bN\njEUzCKYSiJUi8Do1LdkSa2JUAL3cjG6DC8u6TNCo+FEnqicegW0kmsrDF0simAvAbVe3ZG/5ic6a\nFqUNXRwVgKhhMGzaRCpbxMnIeBNnh0UJjbr1Wp7lixUEoiXYNU50mTrR7+KoAESNgmHTBgolAcf9\ncfgyfhgNMhj1rfdrz+QEhOJldOm60W2xoNdhbOlREIiaTet969AUQkXEMV8coykfFMoybObWa3mW\nyJQRf7OzprvTAo/dUO+SiOgtGDYtTJIkDIdSSIkFlJCFy9p6zX6jyRIyGcBr6EGP3QynhZ01iRoR\nw6aFjUUyCKbiKChz6OvWIZsR6l1SVQVjRZSKCnhN3eysSdTgePe0RYWTOfgTSYTyIXicWihaqEWW\n+OYUzkJJhR6jByu6rAwaogbHM5sWlMmXMBpNwZf1w9nZWi3PKhUJvkgBKhjgNnVhmcsEHTtrEjU8\nhk2LKQkVDIfS8Gf8MBlkMOha51dcFkT4wgUYFBZ0G8encFYrWydIiVpZ63wTESRJwslQGsFsCB2K\n1mp5ViyJ8EUKsKrs6DLZ0O9iZ02iZsKwaSG+aBahdBwZIYkeV+uMeZYrVBCMluDQuuBiZ02ipsSw\naRGxdAG++JsNAhytM9tmOicgHC+jW+9Gt9mMHnbWJGpKDJsWkC8KGI2kEMj6YbcooFa1xl/9sVQR\nkXgFHr0XHqsZbhs7axI1K4ZNk6uIIoZD43PTaHUSTPrWmAQtFCsgm5Whx+hFj90Mh5mdNYmaGcOm\nyQ2H0ghmohBkOXS1wCRooighECvCoDGgz+yBRS2h09D8r4uo3TFsmlggnkUolUSiFEWPS9P09zLK\nwniLM22HCcusvVje3YliLl3vsoioChg2TSqVK8EXSyGYC8BlU0Mhb+77NIViBf5oEZ0qG1xGG872\n2qBWKVDM1bsyIqoGhk0TKgkVnAyl4M8GYDHJodM0d8fGdFZAOFGGS9cNl8mCPqcRas6sSdRSeEQ3\nmYmOm4FsCHJlGZ1NPiZYNFlCOiPBo/fC3WmG26Zv+suBRHQ6hk2T8cXGO27mKin02Ju346YoSgjG\nihDKSvSYutFrN8Nmat7XQ0QzY9g0kUS2CH88hVA+BLdD3bQdN4WKCH+kCBX06DN1oc9pglHXGk22\niWh6DJsmUSxXMBpOI5ANwGpWQKNqzvs0xZIIf7QIk7ITXQY7+l0maHh/hqjl8ShvAuP3aVIIZENQ\nqgRYmrTfSSYnIBQvw6l1wmkcH+Os2VvREdHcMGyagC+aRSiTQL6J79PE02UkUiI8eg+6LGZ47QY2\nBCBqIwybBhfPFOBPpBB+c4DNjia7TyNJEkKxEkolBXqMbnhtZjgtHHqGqN0wbBpYoSRgNJyGP+uH\nzdx8A2xWKhL8kQLkkg49Rhf6nGaY9ep6l0VEdTDrt1ehUMBdd92FCy+8EOvXr8fnP//5Oe14165d\n2LBhAy644AI88MADiy603Yjin/vTaNQizIbmmvq4VBYxEspD22FGr9mDVR4rg4aojc16ZnPPPfdg\nZGQEzz77LGw2GwYHB2fd6ZEjR/DII4/giSeegMFgwAc/+EGsWbMGmzdvrkrR7cAfzyKUiaMgptHT\n2Vz3abIFAaFoGTaNE10mK/qcJs6qSdTmZgybQqGAp59+Gnv27IHdbgcArFq1atad7t27F5s2bcKK\nFSsAANdddx2ee+45hs0cZfIlBBNphAsheJvsPk0iU0Y8WUG33g2X2Yweu7Gp6iei2pgxbIaGhiCT\nybB//35s27YNFosF//iP/4jLLrtsxp0ODQ1h/fr1eOyxxxAIBLBu3To888wz065rs9kWXn0dKJXj\nl7NqVXelIsKfiiDXkUefxwqbZfGXnhSK8V+z2WJe9L7OZLwhQBGipMH/83jR47DAbTMueH+1fp9r\npRnrZs1Lpxnrnqh5sWYMm0wmg3K5jNHRUTz//PN45ZVXcNNNN+HnP/85HA7HGbfL5/PQ6XQYHByE\nz+fDwMAAcrnph++9++67J/89MDCAjRs3LvCltIaRcArBTBSVjgJsFn29y5mTiijBF8pBVtFimcWD\n/i4LrMbmuvRHRH928OBBHDp0CAAgl8sxMDCw6H3OGDYajQaVSgU33HADVCoVLrzwQixbtgxHjhyZ\n8exGq9Uil8vhzjvvBADs27cPOt30zV137Ngx5edoNDrf17CkJv4iqUWdyWwRf/JHMZoZgdelRjIh\nVGW/E2c0yUSyKvs7VUkQ4Q8XoJOb0W00waGTQSrlEI0ubm6AWr7PtdSMdbPmpdMsda9duxZr164F\nMF7z4cOHF73PGcOmp6dnQR3v+vv7cfz48cmfBwcHsXz58vlX10aEioixaAbBXBBWkwKqJrihni0I\nCMVKsKodcBms6O8yQaVozmF0iKi2ZvxGM5vNWL9+Pb773e9CEAS8+OKLOHHiBM4999zJdbZu3Yqd\nO3dO2W7z5s3Yt28fBgcHEQwGsXv3bjYOmMVYNINwNgaZvASLsfGbOcdSJYSiArp0HvR0OrDSbWHQ\nENEZzanp8x133IH169fD5XLh/vvvn3K/ZmxsDF6vd8o255xzDm6++WZs27YNgiBgy5YtDJsZxDMF\nhJJpJIoxeF2N3Rel8ubUAJWyEr0mL9ydJrg6OSIAEc1s1rDxer343ve+d8bHDxw4MO3ybdu2Ydu2\nbQuvrE2UBRFjkfHLZzaLoqH7oxRLIgLRArRyE3pMTvRyagAimiMOV1NnI5E0wrkIFCoBJn3jjuac\nzgkIx8uwa5xwGTvR5+L9GSKaO4ZNHUVTeUTTaaTKCfS4GjNoJElCJFFCNofJEZs9NgM7ahLRvDBs\n6qRYrsAXzSCQDcDeqWrIeV2EiohApIgOSYtekws9dhOnbiaiBWHY1MlIOI1QLgK1RmzI+x75YgWB\naBEmVSe69A70OY3QaRq/lRwRNSaGTR3E0gXEsmlkhCR6G3AytES6jFhKgEvXDafRjD4nZ9QkosVh\n2CyxiijCH8silAvDblFB3kD3Pk5t1txj6IXbakK3tTmGzCGixsawWWKBWA7RXAwdijKMusY5qymU\nxi+b6eQmeE1O9DiMnH+GiKqGYbOEcoUyQskMosUoepyN0/oskSkjlhTg1LrgNHai12lks2YiqiqG\nzRIai2YQzoVh1iugUtb/HkhFHJ8WoFxSwGvoQXenCW6rfkHj4RERzYRhs0SiqTyi2TTyYhZ9DdB8\n+NTRADxmJ7wOIyy8bEZENcKwWQJCZbxRQDgfhrNTVfcOkclMGdGkAIfWBafBgl6nCWolL5sRUe0w\nbJZAMJ5DNB+HUlmBXlu/ezWiKCEcL6FYlI9fNrOY4LbxshkR1R7DpsZKQgWRVA7xYgxeZ/0uU2Xz\nAoYDeegVJvSbnfDYDeg0NE4jBSJqbQybGgvGc4gV49BrOurSKEAUJQSjBWQyIpzabjgMZnjtBmhU\n/NUT0dLhN04NFUoCIuksEsU4eusw0GahWEEwVoTdbMayzm7oOipwWrS8bEZES45hU0PBRA6xfBwm\nnXxJ56mRJAmxVBnJTAVOrQsrbH3oc5mRz6aWrAYiolMxbGokXxQQTWeRLqfQa1u6ezXFkohgrAgF\ntOgzOdFlMWJ1rw0ymQz57JKVQUQ0BcOmRoKJHGKFOEx6+ZINYhlLlRBPC7BrHHDoO9HjMEKvUfKy\nGeb4yPgAAA2QSURBVBHVHcOmBsqCiGS2gHQ5hX5b7TtwlgQRoWgRMkmNXoMHXRYjuq36uvfnISKa\nwLCpgXimgFQpDZ26A3J5bb/wJ8Y1s6ltsOut8NoNDTk/DhG1N4ZNDcTSBSSLSdittZtsrCSICMWK\nkCoqeA09cJmNcNv0kHfUf8w1IqK3YthUWTpXQrqQgygrQafRVX3/oighni4jkRk/m7EZxs9mOB0A\nETUyhk2VxTMFJEspmPTVf2uzeQHhRAkamR59Rg+cJgO6rHrOoklEDY9hU2XZgoBcOQt3FS+hlQUR\n4UQJ5WIHnDo3bHojPDYDdJraXaYjIqomhk0VlQURhXIJIgSoFIu/rCWKEhKZMhLpCizqTngtVnR1\n6mE313+KAiKi+WDYVFGuWEahUoBatbjh+iVJQjIrIJ4qQ9OhR4/BDodJj26rYUlHIiAiqhaGTRXl\nSwIKlSI0qoUHQipbRixVhlKmhVvnQqfegK5OHQxaNmcmoubFsKk2ScJCetZkcgKiyRLkUMOl9aBT\na4CrU8dWZkTUEhg2VaSUd0AhU6AoSnNaX6iISGUFpLIC5FDDrulGp9YIV6eOc80QUUth2FSRRqWA\nRqFFLBdBxSxBPs1wMZIkIVesIJURkCuKMCpN6NaaYNTo4LTo/n879x8S9f3HAfx5Xz93nqdeer+0\noWV13FbrAucKt0jRQGjR+jkWhDWEsc2BtA0mrK1/GmNCk2Ct/mgy1pBtSUgbulYQnITVfmQG6wec\nziEa6jLNtPt93z/8et9u0/vx0fd97ur5gCCvz/t69uLy6edzn3sjNyude5kR0WOHZbOAMrVq5GZm\nYsK7CP1D49DrJEiSCiqo4PL64XYH4PYFoflPOvQaI/L12cjJ0sKQpeUWM0T0WGPZLLAlluzpW5Yf\nZuGB5wEeuvwIBoNIl7KRla5Fui4dGRoJuVla5GZpeXcZET0RWDYLTCOlwVaQi/FJHabcBvj8AQSC\nQWRoJGRoJOi0EvcvI6InDstGkEWZ6byTjIjof/gjNhERCRf1zKa6uhrd3d1IS5v+VHxVVRUaGhoi\nrrly5Qr27duHjIz/b6ty+vRpLF++fJ5xiYgoFcV0Ge3gwYPYtWtXXE+cl5cHh8MhKxQRET1eYrqM\nFgzG9iFFIiKi2cR0ZtPY2IjPPvsMq1atwoEDB7BixYqoa+7evYv169dDp9Nh165deOONN2Y9zmg0\nxpdYYWr19Lb+qZSbmRMnFXMzc+KkYu6ZzPMVtWzq6+ths9ng9/tx7Ngx1NbWoq2tDZI091Kr1Yr2\n9nYsWbIEt27dQm1tLcxmM3bs2PGvYw8dOhT6fVlZGcrLy2X+U4iIaCE4HA50dHQAANLS0lBWVjbv\n51Tdvn075mtkwWAQJSUl+O6772Cz2WL+S5qamnDt2jV8/vnnYY/39/dj5cqVsadNAjM/kdy9e1fh\nJLFj5sRJxdzMnDipmNtoNOLixYsoLCyc1/PEfeuzSqXiezhERBSXiGUzMTEBh8MBj8cDj8eDo0eP\nwmQywWq1ho6prq7G4cOHw9ZdvnwZg4ODAICenh58++23qKioEBCfiIhSQcT3bLxeL44cOYL9+/dD\nrVbDbrfj+PHjoc/cAMDAwAAKCgrC1t24cQPvvfceJicnYTQasXv37lnfryEioidDxLIxGAxobW2N\n+AQXLlz412M1NTWoqamZXzIiInpscLsaIiISjmVDRETCsWyIiEg4lg0REQnHsiEiIuFYNkREJBzL\nhoiIhGPZEBGRcCwbIiISjmVDRETCsWyIiEg4lg0REQnHsiEiIuFYNkREJBzLhoiIhGPZEBGRcCwb\nIiISjmVDRETCsWyIiEg4lg0REQnHsiEiIuFYNkREJBzLhoiIhGPZEBGRcCwbIiISjmVDRETCsWyI\niEg4lg0REQnHsiEiIuFYNkREJBzLhoiIhGPZEBGRcCwbIiISjmVDRETCsWyIiEi4qGVTXV2NNWvW\noLi4GMXFxaivr4/piU+ePIn169dj3bp1aGxsnHdQIiJKXTGd2Rw8eBBdXV3o6upCQ0ND1OO7u7vx\nxRdf4OTJk/jxxx/R1taGn376ad5hk8XNmzeVjhA3Zk6cVMzNzImTqrnnK6ayCQaDcT3p2bNnUVVV\nhRUrViAvLw+vvPIK2tvbZQVMRqn4YmHmxEnF3MycOKmae75iKpvGxkaUlpaipqYGPT09UY/v6+vD\nsmXL8PXXX6OhoQFWqxV//vnnvMMSEVFqkqIdUF9fD5vNBr/fj2PHjqG2thZtbW2QpLmXPnz4EDqd\nDk6nE4ODgygrK8PU1NSsxxqNRvnpFaBWq1FZWYmcnBylo8SMmRMnFXMzc+KkYm61Wr0gzxO1bFav\nXh36/bvvvovm5mb09vbCZrPNuSYjIwNTU1P48MMPAQDnz5+HTqeb9diLFy/Gm5mIiFJM1LL5J5VK\nFfU9nKKiIvT29oa+djqdWL58+b+OKywsjPevJyKiFBTxPZuJiQk4HA54PB54PB4cPXoUJpMJVqs1\ndEx1dTUOHz4ctm7Tpk04f/48nE4nhoaGcPr0aWzatEnMv4CIiJJexDMbr9eLI0eOYP/+/VCr1bDb\n7Th+/DjS0tJCxwwMDKCgoCBs3Zo1a/D2229j79698Pl82L17N8uGiOgJprp9+3Z89zUTERHFidvV\nEBGRcCwbIiISjmVDRETCxX3rc6zGx8fR0tKCgYEBmM1m7Ny5E3l5eVHXXbp0CQ6HA36/H2vXrkVV\nVZWoiLOSk7u3txdfffVV2Ief3nrrLZjNZtFxcfPmTXR0dODOnTuw2+3YuXNnTOuUnrOc3ErOGQD8\nfj9aW1vR09MDr9eLxYsXY8uWLbBYLFHXKjVvuZmVnnVLS0soc25uLjZu3IiVK1dGXaf061pObqVn\nPaOvrw9NTU3YunUrnn/++ajHxztrYWVz5swZ5Ofn47XXXsOlS5fw/fffo66uLuKa/v5+XLhwAa+/\n/jq0Wi1OnDiBp556KuyDpaLJyQ0A2dnZeP/99xOQMJxWq8WGDRvQ09MDj8cT05pkmLOc3IBycwam\n9wg0Go2oqqqCXq9HZ2cnmpub8c4770Rcp+S85WYGlJ31hg0bsH37dkiSBKfTiW+++QYHDhyARqOZ\nc00yvK7l5AaUnTUw/UPJuXPnYDaboVKpoh4vZ9ZCLqO5XC44nU6UlZVBkiS88MILGBsbw9DQUMR1\nf/zxB5599llYLBbo9XqUlJTg+vXrIiLOSm5uJS1btgyrVq1CRkZGzGuUnjMgL7fSJElCRUUF9Ho9\nAKC4uBijo6NzbsU0Q8l5y82stPz8fEiShGAwCL/fD41GE/WbYDK8ruXkTgaXL1/G008/jczMzJiO\nlzNrIWc2o6OjkCQJGo0GJ06cwLZt22AwGDAyMhLxktTff/+NoqIidHZ2Ynx8HEuXLk3oi0VubgCY\nnJzEp59+Co1Gg5KSEpSXlyco9bR4duZWes6PindHcaXn/Kj+/n5kZ2fPuRXTjGSad6yZAeVn/cMP\nP+Dq1auQJAl79+6NukdXssw53tyAsrOemJhAV1cX3nzzTTidzpjWyJm1kLLxeDzQaDRwu90YGRmB\ny+VCenp61MslM+tGRkYwNjYGm80W1yWW+ZKb22KxoK6uDkajEXfu3EFzczOys7Px3HPPJSg54vrp\nSek5Pyqe3Mkw5xkulwvt7e146aWXoh6bLPOOJ3MyzPrll1/G5s2b8euvv6KlpQV1dXURv3Eny5zj\nza30rM+ePYvy8vKImyv/k5xZC7mMptFo4PF4sGjRInzwwQcoLCyE2+1Genp6TOs2b96MPXv2wO12\nR73WuZDk5s7KygrtXr148WKUlpbi1q1biYgcEs8ZgtJzflQ8uZNhzgDg8/nQ3NwMu90e0/sByTDv\neDMny6zT0tJQWloKSZLC9lucTTLMeUY8uZWc9V9//YV79+7BbreHHovl/6ScWQs5szEYDPD5fLh/\n/z70ej18Ph9GR0dhMpkirjOZTBgZGQl9PTw8nNA7MuTmTgbxnCEoPedHpcL17EcFAgGcOnUKJpMJ\nGzdujGmN0vOWkznZxPINUOk5zybey8SJNjAwgP7+fnz00Uehx/r6+jA8PBzxDFjOrIWc2Wi1Wlit\nVnR0dMDr9aKzsxM5OTlh73t8+eWX+Pnnn8PWrV69Gjdu3MDw8DDu37+P33//PaxxRZObu7e3F2Nj\nYwCmh37lyhU888wzCckcCATg9XoRCAQQDAbh8/kQCAQi5lV6znJzKznnGWfOnIFKpcKWLVtm/fNk\nnLeczErO+sGDB/jtt9/gcrng9/vxyy+/YHJyMmyX+GScs9zcSs76xRdfxKFDh0K/ioqKsG3btrCi\nWahZC7v1eevWrWhpacEnn3wCs9mMV199NezPx8bGYDAYwh4rKChAZWUlmpqaEAgEsHbt2oTetgjI\nyz04OIhTp07B7XYjKysL69atS9j11mvXrqG1tTX0dXd3NyoqKlBZWTln3mSYs5zcSs4ZAO7du4er\nV69CrVbj448/Dj2+b98+LF26dM7cSs5bbmYlZ61SqXD9+nWcO3cOfr8fFosFe/bsCbupIdnmPJ/c\nSr+uo1moWXMjTiIiEo7b1RARkXAsGyIiEo5lQ0REwrFsiIhIOJYNEREJx7IhIiLhWDZERCQcy4aI\niIT7L6NdmT4PO7VdAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f34310bbe48>"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<img src='ellipse.gif'>"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import numpy as np\n",
      "from matplotlib.patches import Ellipse\n",
      "import matplotlib.pyplot as plt\n",
      "from matplotlib import cm\n",
      "from mpl_toolkits.mplot3d import Axes3D\n",
      "from gif_animate import animate\n",
      "import numpy.random as random\n",
      "from DogSensor import DogSensor\n",
      "import stats\n",
      "from filterpy.common import Q_DWPA\n",
      "from filterpy.kalman import KalmanFilter\n",
      "\n",
      "def dog_tracking_filter(R,Q=0,cov=1.):\n",
      "    dog_filter = KalmanFilter (dim_x=2, dim_z=1)\n",
      "    dog_filter.X = np.array([[0], \n",
      "                             [0]])   # initial state (location and velocity)\n",
      "    dog_filter.F = np.array([[1,1],\n",
      "                             [0,1]])  # state transition matrix\n",
      "    dog_filter.H = np.array([[1,0]])  # Measurement function\n",
      "    dog_filter.R *= R                 # measurement uncertainty\n",
      "    dog_filter.P *= cov               # covariance matrix \n",
      "    if np.isscalar(Q):\n",
      "        dog_filter.Q = Q_DWPA(2, var=Q)\n",
      "    else:\n",
      "        dog_filter.Q = Q\n",
      "    return dog_filter\n",
      "\n",
      "\n",
      "R = 5\n",
      "Q = .01\n",
      "noise = 2.\n",
      "P=20.\n",
      "dog = DogSensor(velocity=1, noise=noise)\n",
      "f = dog_tracking_filter(R=R, Q=Q, cov=P)\n",
      "random.seed(200)\n",
      "zs = []\n",
      "xs = []\n",
      "def animate_track(frame):\n",
      "    if frame > 30: return\n",
      "    \n",
      "    plt.gca().set_xlim(-100,100)\n",
      "    if frame == 0:\n",
      "        stats.plot_covariance_ellipse ((0, f.X[0,0]), cov=f.P, axis_equal=True, \n",
      "                                       facecolor='g', edgecolor=None, alpha=0.2)\n",
      "        xs.append (f.X[0,0])\n",
      "        \n",
      "    z = dog.sense()\n",
      "    zs.append(z)\n",
      "    f.update(z)\n",
      "    xs.append (f.X[0,0])\n",
      "    \n",
      "    stats.plot_covariance_ellipse ((frame+1, f.X[0,0]), cov=f.P, axis_equal=True, \n",
      "                                       facecolor='g', edgecolor=None, alpha=0.5,\n",
      "                                       xlim=(-5,30), ylim=(-5,30))\n",
      "    \n",
      "    plt.plot(zs, c='r', linestyle='dashed')\n",
      "    plt.plot(xs, c='b')\n",
      "    f.predict()\n",
      "\n",
      "animate('track1.gif', animate_track, 37, 200, figsize=(10.5, 10.5))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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ppdG1/qXwJiIiMkh5fj8UCriJxA61z150Eesuvpj6gw/G19RE6+23Ma2QpuAW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\nPlFeQNBxxx07fJ4zzxxFKbj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NwyNdSJPMF/do67Q7ixvr2pniJrt2hhsvnsHy1yaWWgMw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/8HqfYWHv6HO9k9sps73vq/eODeD896jmZ/M+3Bdpp8TTLOTQghhDiFhDemqm2DyUGS2eSi9vWs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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f342966a048>"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<img src='track1.gif'>"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "\n"
     ]
    }
   ],
   "metadata": {}
  }
 ]
}