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      "[Table of Contents](http://nbviewer.ipython.org/github/rlabbe/Kalman-and-Bayesian-Filters-in-Python/blob/master/table_of_contents.ipynb)"
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      "Multivariate Kalman Filters"
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      "#format the book\n",
      "%matplotlib inline\n",
      "from __future__ import division, print_function\n",
      "import matplotlib.pyplot as plt\n",
      "import sys\n",
      "sys.path.insert(0, '../code') # allow us to import book_format\n",
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     "source": [
      "Introduction"
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     "source": [
      "**author's note**: In this chapter there is some duplication in my discussion of the Kalman filter code, and information about Q is strewn in a few different places. If it seems like I am repeating what I said, I am; this requires a copy edit.\n",
      "\n",
      "The techniques in the last chapter are very powerful, but they only work in one dimension. The gaussians represent a mean and variance that are scalars - real numbers. They provide no way to represent multidimensional data, such as the position of a dog in a field. You may retort that you could use two Kalman filters for that case, one tracks the x coordinate and the other tracks the y coordinate. That does work in some cases, but put that thought aside, because soon you will see some enormous benefits to implementing the multidimensional case.\n",
      "\n",
      "In this chapter I am purposefully glossing over many aspects of the mathematics behind Kalman filters. If you are familiar with the topic you will read statements that you disagree with because they contain simplifications that do not necessarily hold in more general cases. If you are not familiar with the topic, expect some paragraphs to be somewhat 'magical' - it will not be clear how I derived a certain result. I prefer that you develop an intuition for how these filters work through several worked examples. If I started by presenting a rigorous mathematical formulation you would be left scratching your head about what all these terms mean and how you might apply them to your problem. In later chapters I will provide a more rigorous mathematical foundation, and at that time I will have to either correct approximations that I made in this chapter or provide additional information that I did not cover here. \n",
      "\n",
      "To make this possible we will restrict ourselves to a subset of problems which we can describe with Newton's equations of motion. In the literature these filters are called \n",
      "*discretized continuous-time kinematic filters*. In the next chapter we will develop the math required for solving any kind of dynamic system. \n",
      "\n",
      "\n",
      "In this chapter we are dealing with a simpler form that we can discuss in terms of Newton's equations of motion: given a constant velocity v we can compute distance exactly with:\n",
      "\n",
      "$$ x = vt + x_0$$\n",
      "\n",
      "If we instead assume constant acceleration we get\n",
      "\n",
      "$$ x = \\frac{a}{2}t^2 + v_0 t + x_0$$\n",
      "\n",
      "And if we assume constant jerk we get\n",
      "\n",
      "$$ x = \\frac{j}{3}t^3 +  \\frac{a_0}{2}t^2 + v_0 t + x_0$$\n",
      "\n",
      "As a reminder, we can generate these equations using basic calculus. Given a constant velocity v we can compute the distance travelled over time with the equation\n",
      "\n",
      "$$ v = \\frac{dx}{dt}\\\\\n",
      "x = \\int v \\, \\mathrm{d}t\\\\ x = vt + x_0$$"
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     "source": [
      "Multivariate Normal Distributions"
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     "source": [
      "What might a *multivariate normal distribution* look like? In this context, multivariate just means multiple variables. Our goal is to be able to represent a normal distribution across multiple dimensions. Consider the 2 dimensional case. Let's say we believe that $x = 2$ and $y = 17$. Therefore we can see that for $N$ dimensions, we need $N$ means, like so:\n",
      "\n",
      "$$\n",
      "\\mu = \\begin{bmatrix}{\\mu}_1\\\\{\\mu}_2\\\\ \\vdots \\\\{\\mu}_n\\end{bmatrix}\n",
      "$$\n",
      "\n",
      "Therefore for this example we would have\n",
      "\n",
      "$$\n",
      "\\mu = \\begin{bmatrix}2\\\\17\\end{bmatrix} \n",
      "$$\n",
      "\n",
      "The next step is representing our variances. At first blush we might think we would also need N variances for N dimensions. We might want to say the variance for x is 10 and the variance for y is 4, like so. \n",
      "\n",
      "$$\\sigma^2 = \\begin{bmatrix}10\\\\4\\end{bmatrix}$$ \n",
      "\n",
      "While this is possible, it does not consider the more general case. For example, suppose we were tracking house prices vs total $m^2$ of the floor plan. These numbers are *correlated*. It is not an exact correlation, but in general houses in the same neighborhood are more expensive if they have a larger floor plan. We want a way to express not only what we think the variance is in the price and the $m^2$, but also the degree to which they are correlated. It turns out that we use the following matrix to denote *covariances* with multivariate normal distributions. You might guess, correctly, that *covariance* is short for *correlated variances*."
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      "$$\n",
      "\\Sigma = \\begin{bmatrix}\n",
      "  \\sigma_1^2 & \\sigma_{12} & \\cdots & \\sigma_{1n} \\\\\n",
      "  \\sigma_{21} &\\sigma_2^2 & \\cdots & \\sigma_{2n} \\\\\n",
      "  \\vdots  & \\vdots  & \\ddots & \\vdots  \\\\\n",
      "  \\sigma_{n1} & \\sigma_{n2} & \\cdots & \\sigma_n^2\n",
      " \\end{bmatrix}\n",
      "$$\n",
      "\n",
      "If you haven't seen this before it is probably a bit confusing at the moment. Rather than explain the math right now, we will take our usual tactic of building our intuition first with various physical models. At this point, note that the diagonal contains the variance for each state variable, and that all off-diagonal elements (covariances) are represent how much the $i$th (row) and $j$th (column) state variable are linearly correlated to each other. In other words, it is a measure for how much they change together. No correlation will have a covariance of 0. So, for example, if the variance for x is 10, the variance for y is 4, and there is no linear correlation between x and y, then we would say\n",
      "\n",
      "$$\\Sigma = \\begin{bmatrix}10&0\\\\0&4\\end{bmatrix}$$\n",
      "\n",
      "If there was a small amount of correlation between x and y we might have\n",
      "\n",
      "$$\\Sigma = \\begin{bmatrix}10&1.2\\\\1.2&4\\end{bmatrix}$$\n",
      "\n",
      "where 1.2 is the covariance between x and y. Note that this is always symmetric - the covariance between x and y is always equal to the covariance between y and x. That is, $\\sigma_{xy}=\\sigma_{yx}$ for any x and y."
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      "Now, without explanation, here is the full equation for the multivariate normal distribution in $n$ dimensions.\n",
      "\n",
      "$$\\mathcal{N}(\\mu,\\,\\Sigma) = (2\\pi)^{-\\frac{n}{2}}|\\Sigma|^{-\\frac{1}{2}}\\, e^{ -\\frac{1}{2}(\\mathbf{x}-\\mu)'\\Sigma^{-1}(\\mathbf{x}-\\mu) }$$\n",
      "\n",
      "I urge you to not try to remember this function. We will program it in a Python function and then call it when we need to compute a specific value. However, if you look at it briefly you will note that it looks quite similar to the *univariate normal distribution*  except it uses matrices instead of scalar values, and the root of $\\pi$ is scaled by $n$. Here is the *univariate* equation for reference:\n",
      "\n",
      "$$ \n",
      "f(x, \\mu, \\sigma) = \\frac{1}{\\sigma\\sqrt{2\\pi}} e^{{-\\frac{1}{2}}{(x-\\mu)^2}/\\sigma^2 }\n",
      "$$\n",
      "\n",
      "If you are reasonably well-versed in linear algebra this equation should look quite manageable; if not, don't worry! Let's just plot it and see what it looks like."
     ]
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     "cell_type": "code",
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     "input": [
      "import mkf_internal\n",
      "import numpy as np\n",
      "mkf_internal.plot_3d_covariance((2, 17), np.array([[10., 0], [0, 4.]]))"
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P5qz7pcwrMPx7cx4npf01hnd33sey1Vp054m8+4RS38GPJ0g6byfo3ZpzP41B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\n8Lw9JONa0X8+hFW5Eu6ZRVSRYPe3cY/pmXYdzbKVCfWYgL//X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YP4hrX/Q6cto1wVwt3H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7Y4n332xPZaqoprxAiMrCxsU6diJCUR6NGj2oLKakXdtw/zd99hWbgQz/33o3Xq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\nrEokEolEIpFIGiz/DzG3IC9iRyRUAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f1a474cbf60>"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Here we have plotted a two dimensional multivariate Gaussian with a mean of $\\mu=[\\begin{smallmatrix}2\\\\17\\end{smallmatrix}]$ and a covariance of $\\Sigma=[\\begin{smallmatrix}10&0\\\\0&4\\end{smallmatrix}]$. The three dimensional shape shows the probability of for any value of (x,y) in the z-axis. I have projected just the variance for x and y onto the walls of the chart - you can see that they take on the normal Gaussian bell curve shape. You can also see that, as we might hope, that the curve for x is wider than the curve for y, which is explained by $\\sigma_x^2=10$ and $\\sigma_y^2=4$. Also, the highest point of the curve is centered over (2,17), the means for x and y. I hope this demystifies the equation for you. Any multivariate Gaussian will create this sort of shape. If we think of this as a the Gaussian for our dog's position in a two dimensional field, the z-value at each point of (x,y) is the probability density forthe dog being at that position. So, he has the highest probability of being near (2,17), a modest probability of being near (5,14), and a very low probability of being near (10,10).\n",
      "\n",
      "We will discuss the mathematical description of covariances in the Kalman Filter math chapter. For this chapter we just need to understand the following.\n",
      "\n",
      "1. The diagonal of the matrix contains the variance for each variable. \n",
      "\n",
      "2. Each off-diagonal element contains $\\sigma_{ij}$ - the covariance between *i* and *j*. This tells us how much linear correlation there is between the two variables. 0 means no correlation, and as the number gets higher the correlation gets greater.\n",
      "\n",
      "3. $\\sigma_{ij} = \\sigma_{ji}$\n",
      "\n",
      "4. The covariance between x and itself is just the variance of x: $\\sigma_{xx} = \\sigma_x^2$.\n",
      "\n",
      "5. This chart only shows a 2 dimensional Gaussian, but the equation works for any number of dimensions >= 1. It's kind of hard to show a chart for the higher dimensions."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "I have programmed the multivariate Gaussian equation and saved it in the file `stats.py` with the function name `multivariate_gaussian`. I am not showing the code here because I have taken advantage of the linear algebra solving apparatus of numpy to efficiently compute a solution - the code does not correspond to the equation in a one to one manner. If you wish to view the code, I urge you to either load it in an editor, or load it into this worksheet by putting `%load -s multivariate_gaussian stats.py` in the next cell and executing it with ctrl-enter. \n",
      "\n",
      "However, please note that the Kalman filter equations incorporate this computation automatically; you will not be using this function very often in this book, so I would not spend a lot of time mastering this function unless it interests you."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      ">As of version 0.14 scipy.stats has implemented the multivariate normal equation with the function `multivariate_normal()`. It implements a 'frozen' form where you set the mean and covariance once, and then calculate the probability for any number of values for x over any arbitrary number of calls. This is much more efficient then recomputing everything in each call. So, if you have version 0.14 or later you may want to substitute my function for the built in version. Use `scipy.version.version` to get the version number. I deliberately named my function `multivariate_gaussian()` to ensure it is never confused with the built in version. I will say that for a single call, where the frozen variables do not matter, mine consistently runs faster as measured by the `timeit` function.\n",
      "\n",
      "> The <a href=\"http://docs.scipy.org/doc/scipy/reference/tutorial/stats.html\">tutorial</a>[1] for the `scipy.stats` module explains 'freezing' distributions and other very useful features. As of this date, it includes an example of using the multivariate_normal function, which does work a bit differently from my function."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from stats import gaussian, multivariate_gaussian"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 3
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Let's use it to compute a few values just to make sure we know how to call and use the function, and then move on to more interesting things.\n",
      "\n",
      "First, let's find the probability density for our dog being at (2.5, 7.3) if we believe he is at (2, 7) with a variance of 8 for $x$ and a variance of 4 for $y$.\n",
      "\n",
      "Start by setting $x$ to (2.5, 7.3):"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "x = [2.5, 7.3]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 52
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Next, we set the mean of our belief:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "mu = [2.0, 7.0]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 53
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Finally, we have to define our covariance matrix. In the problem statement we did not mention any correlation between $x$ and $y$, and we will assume there is none. This makes sense; a dog can choose to independently wander in either the $x$ direction or $y$ direction without affecting the other. If there is no correlation between the values you just fill in the diagonal of the covariance matrix with the variances. I will use the seemingly arbitrary name $\\textbf{P}$ for the covariance matrix. The Kalman filters use the name $\\textbf{P}$ for this matrix, so I will introduce the terminology now to avoid explaining why I change the name later. "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "P = [[8.,  0.], \n",
      "     [0., 4.]]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 54
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Now just call the function"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print('{:.4}'.format(multivariate_gaussian(x, mu, P)))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "0.02739\n"
       ]
      }
     ],
     "prompt_number": 55
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "> Note that the function can accept lists, np.array, or np.matrix as arguments, or even scalars. Type `multivariate_gaussian?` in a cell and press ctrl-enter to get the help for this function. \n"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "These numbers are not easy to interpret. Let's plot this in 3D, with the $z$ (up) coordinate being the probability."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import mkf_internal\n",
      "mkf_internal.plot_3d_covariance((2, 7), np.array([[8., 0], [0, 4.]]))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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8s9XupnuilkJQP1FGmmEe7fkpiUDWdTF8DYQPnoNKW8bsqa2diaH8NfvzUGqz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WTUz14hetRoQudcj96zmZCbchZ1mZ+ihL/BXfckSmQJvoZH8fgnEXWfju4ciO7oj670AaeXyNBx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\n05YtyIWyW3q9ethnzUL56acS1f3L7W1D/fpZL/8FBTji4oiNj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rj3kxQ89xxiZobVuRFE\nxOPHEbxehOxsbEuWYFtiaRgbQKRrVyKdO2MGAii7d2PUqGElo4MHI0SjiPv2of76K+KmTYQfewzt\n5ptR/v1vq+1dqF1rut3Frfxx4yyh/goVMAHpzBnk9eutl1ooEvtX1q617lVjx0JaGurkyRa5q2FD\nwr16YaSmFqsV6DoEAhhpaSgrVlhKBYWyWywv2YnQGjYkMGUKZmIi8qlTFkZ10iQrAfX5LLLYunWI\ne/YQfOMNzAoVcIwahbK5JJ74koGB1ry55cYVDEI4DJpG9IYbQFUt1YK9exHz8xG3brUUYh54AGXr\nVhyTJ4PXi1mpkqUfe/vt6E8+aRmexMZiJiRY994FC1AXLUIutNIWMzOLqroGWJXpJk2wffqpZZ7Q\nqhV6jRqWfmx8PDfHxnJDjSrobndJ/dhAAbszj3M6kEtuKIiPfMIiaIKAIQhIZZCUDcP4X0Gi/v9b\nXEtW/w/Hf+Iw9dv4w4neZWE/9jFK3jaIglngIHCXxTR25k9AiWxHl6oQOtOO2Ne7IISDhO58lEDv\nkZft24fTOQG7/RMEwcDMdsETQaTlZzBlmWCPLgSff94S6f4TQsjNRTl4EOXbbzGTkjCqV8c3fbql\niaqqlhbpsWNoLVtalZH330cePbrMRCvcti3hXr2Qt23DNvdT6+aZkoJWvz7Ru+/GiE9Ab9DAEvXP\nz4doBL1SJXzvvGNVUQQRE9OqErvdiOfPYzqdBCZOAgpZwRUqIPj9iPl54PMReeJpxFMn0ZpchxkT\ng/uZp5BPWIlt+JZb8S5ahph5HqNaLdRvlkJBAXqr1rhGDMR0OAk89xLRW+9G/Wk5jplTESLWg8r3\n4XxcY57DFEUCz49Fr1EXQRRxTJ+AbVVxO9wAtFY34/hnSZa8kVAR7cY7Maul4Zj6GvLhvcXXqecg\n3K/0KnX9DNWOmH8BQS+NrzRsDsS8zPJlnCqmIJ4rW0TfqJCCmH0GU3VgKiqodkzFBooNU7WhNbwZ\nMfssRnwywsULpVr5hisOMTejzLUvxe/BqxIJXzHhBTCSqiGePnTFOabDjRAO4Jo8BN9rn+FYOKYU\nwQgsnK0ZKTtB/22E7+qCc9JzEA7im/IlQtCHcnRbmXNDD/bH+WlpbVxR03BOHYKv//u43+5e9F2F\nHnoG+/x3ylzL+cUkvG8sRd65EvkyDVtTkgn9YwjuIW0BUHavJ3r9PYT/3h7bmtKOXUIkhGP+ZAKD\npuN+b2DxOqodvW4rtLRm2L54F8+s4t9p+P7H0Wo3xTXNgn8EuwzG+/p8pIyT6E3rY/98Kr69uzCz\nchGcLoQL2TiHPo9a6CxniiJG9epozZoTHPai1S2pUtV6aXW5kLdtw927dwkr5KLj8niI3HSTZcWa\nlWV1VaJRtHvuwV+vHsqGDRbBKysLedcuDJeLSJs2SIcO4XjqKYQLFyyFgPr1iTz0EMbAgZZ5gctl\nJWsxMajffIOrb98iRzzpxAnUfxVXzUNduhDp1All/XqElSvRmzbFV6gLjc2GcPEi0p49iCdOEOna\nFen0adzdu5c6HxMwExLQmjTB/+abSJmZEAyCKBIcPpxQRgbKtm3F1rZ5eUSaNyf6wAPYZ81CnTcP\nwTSt+1vlymj16hG97z70/v3R09LAZrMMDLZtQ9q/HyM2FsnrtYxRMjLg118t5ZepU5FycrC/+CKC\nplnyXd27E0pNLbK3NU0TFAWzUiXsU6fiHDOm6Hdq++GHEucVfvhhwgMGIG/YgOFwYKSkYMTF4YiP\nJ9mTgp7asJQRwtn8LMJlQIHy8/OJj48vtf1a/NfiWrL6F8efUVn9Tx2m/syQvEdx7S30PT4FwZsH\nYrqTsBfMxFkwHRORUGZvYl7rixCNELq/G75BbxU6VJnYbEtwOl+3xP11AXOqgPCqHzMkEurUicDQ\noRg1avw5x3r2LPLOnTgmTy4huH15RFu3trCn4TDqzz9j1K5NqFs3eOopK5mVZcjLsyRhatdGWbkS\nd5fHES8jS1AoURXq2g2tYwfU5cuxf/hBcfWiMLRq1QhMmoyckY5jyGCEvDzLLjEaxQRCw0agtWiB\nc9gLKNuKSR1a/YYEJryBsvZXCAYIjhiF6XJjpKYiHz6A6/n+yFs3IZgmgWeHYlSogLx/F95PliBm\nZWK63djnfYJ9QXFlK/j0YKTNvxDsNwLTHYd97kykI1Pxj51SIlEFCPcahG35F0U3fK3edYR6DEZL\nqYHt85k4Fn9SYr7hdCNczEEIlNRcBQh1H4z6w/wyv4tw+6dRV39V5tglJr9RsQp6ldrotZqip9bG\ntLssIlBCJYRoGN/zcyAahkgEIRyCcBAhECB6413Iuzbg7zoeMzbOgmLoUYv5r0UwE5IRL5xFq9EI\n6fTBMnGpV8Or6hWrIqWXj7ctOo+LOVclBUb+3hb134sQs8/jHvAw/nFz0epcj3359BKfDf/tURzL\nS+OIfxumJFsEsnAQAPeLHfFN/RphznDkMyVlh0ywlBvOHC5zLfnsUZS1PxDsNBLnwnGYgki0/s04\nZpcv+eUa0xPfa5/hGd+x6BoGHx2ObcGMElVSx+yx+CYsQtn1C2JBTql1lN1riNzegWjt5ihHdxBt\ncAPBLiNxTH8V56mX8b65AHXNv4qMBmw/zEcb0JjQPY9i/3ExjnnvYlSsjHhkP0JGOqFHeqH+sIDo\nfZ0Qv1iA/ddfiN56G+Fu3THdbgRFQTh0COnMGfSq1RAEAWXlSmzzvgC73aqGDhuGUSERnC6QZYST\nJxGzsojedBPy6dO4evZEPn68+PrKsoXfbNqUwLPPot12m1V5VFXEU6cQz53DqFoV8cIFxPPnUc+f\nR125EiMx0erEeL3Y33gD0e8v4cKF01lUASUate5X8+bhad++iLz02+85etttBEeORDp0CDEjAyMh\nAd/06aAoiJeY/WvXImZn458wAZxO3IMHI+/aVbyOIGCkplqJY/v2RB55BKGgwGrz+/1Er7sOQiGU\nX39FzM5GKDynqNdL9JZbUDZswDFlimUFe8nA4MknMSpXtshiHg9mXBzExGCfORN14cIieUDp5Mki\nUwYDCL38MlrLltg+/xwUBa15c3z33FN8bUIhpH37oKCA6L33ov76K562bRHKeOEzPR60Zs3wT5lC\nNCGBqMOydK0Sl1Tmbzw3N/dasvrfENcwq39xCIKAoih/+HN/hsNUWfEf4T0NjdhfHraqqjmgF9Qg\nb+AqbNFleHKeAyB4oTf20Z8h6BrBR57E328CiCKStAu3+yUUxUrCzE0CQl8Tc49IuGNHAs8/X6ZV\n55XCNE20Qga0LMvWdYhGkY8dQ9mwATQNIzGx6EaFYSCdOIG8ZQt6cjLavfcib9uGY9q0sgW87XYC\nEyZgVq2KungxmCZ6rZqYlVMwHA6w2zBUFbNyCqgKgmEiHtiPeCEHITsLKSMDISsTolGCQ55H9Ppw\nTHvbYv+bpuUiZRiEHm5DpPeTyDu3I548ad2kEytgxMRiJlW0HKiyspDOnkFevwbp6FECb01F/Xox\ntqWWjakB+KfNwmjYCPHYEdRvv0T98TtC3Z7ArJSM8+1ir/tokxb435qJdGAvjplvIx+0ku2Cjxfj\nHjMYMatkS7ngoy/xPNuRyF3tiDzQCSEjA+fEV/BN/wzPwI6lHoS+l97C9q/PUQ7u5LdR8N6XeIZ1\nLFN/s2DKUjyjO1tQBVHEqFaPSKu70Gs3RUuujoCJdOoY0sG9KHs3Ix7cVcSAL3hvKZ7nOpSbBHon\nz8MzrEs5o3DxnaU4Z08icmdb9LR6CNEgoi8Xee8alD1rMFTbVfGq/p5jUNd8jXK4fIxp6M7HEaJR\nbCuXlDsHwPvKp7hG9yqRyAUfH4zeqDGumYMRolYy5h0yF8/4sp2+Lo/wjQ9hJNTAsXhG0TZDlvFN\nXYbz/WdKVDyj9W4g0vxhXB+NuuKavqEzULd/g+mOxzRd2L/95Irzwzc+gN7yFpxzR6JXSMX/5NvE\nvFQaDmIkVsL30kxiXimNCQQwbQ68ry9CPL4b052Ea2zfIikurWodgs9NxDO0Q/F8QcA37jPLJe30\nEUzA//onqEtmIx/dj2/KPAxPDDhjMA0D8UIeRKJgGIhZmQheL+KZMxjVqhXJ0glZWSirVqGuWIGY\nb8FLtCZNCLw4DEFVkXbswExMKLz/FCaxp0+hrF2HsnIlRCIExozBrFYN9auvUBctAl0vxqS2bo1e\nu7bVuUlMtDSk3W5ss2Zhmz+/KFkrcd2A0PDhaDfeiLp8uUX8rFevyIVLUJQiuSwhN5fwk08iHTiA\nY9KkUutdMh64ZBktnTxpHZ+iFBOr1q+3Wvn5+Ra5a/BgonfcgW3+fNTFi61Kqs1WJLulNW9uVaar\nV7cqqQ4H8ooVKKtWIW/YgBgMljyfwkqqoGnYp0wBSUJr1gy9aVOM+Pji+7rPZ1VSU1OxTZmC7dtv\ny70PhNu0ITxgANL27WC3W5CCQvkuITcXedcuC+Zw7BjBYcOI3H03kcuKJ5eewb/9P8CmTZtYvXo1\nw4eXLbt3La4c1zCr/0vij1ZW/yhh6o/GfwIDcByZYSWqETAz7BQ8/Smq9jPunOcBCJ9vi32sBZwP\ndBxI4MnRCOIFXK43sNk+RxBMzAwQhgNfQKj9owRnPo9eu/Z/6RwAKChAPnwY+4IF2ObNQyhDxseI\nicH/9tuEe/VCOnAAMSMDvU4dvB99BIqCkJ+PdOgQ0pEjhNu3RzAM7NPfQ9laWqDeEEWCI0diNm2K\nfdo7qN8ss26eMRZr2IyNRatfn9BrryPt34+ybSsIApGHH4/HcmsAACAASURBVAFRAAT0mjUxqldH\n3rQR24J5iOnpSOnpCHm5aM2aE+7SDeeIoShbi9u/0Rat8L/zHo63xqO1uJ6C2fNBEDGq18T27RLs\nI59H8FsVzcgd96A3uQ7XSwMw4hMJDByOXiMNEivgfvJR5LPFCUr47geR9+8olagGeg4A1Y73nSWo\nq3/E1acTIhC+pw3K+p/LrthUqV5momq4YxAvnC8zUdXjKmDGJeIf/DamJx5TdSCeOIptxVfYPpyO\nb8ZSPM93LlMD1UioiJR+qtwHlNawBdKhXeWMFuJZfQUouzeh7N5UvF21E7ntIfxdx6FXr410MZvw\n9Q+ibltRJoxBr9EIec5r5e4HIPK3tnjeuLIgvykrmE5PKaKRY/67ROs1wztiEc5ZzyLlnPv/2Dvv\nKCnq7O1/KnaeYYABhjwkCaIgoIIZ86qACigIEgwEyUmS5JwlSQYBySKYV9ZAUImiCEiQHAUJM527\nq6veP74TGLoH3d3f7nrOyz3Ho3bFru6pfureJ4DNdcN95Rz3/udxDc/r/SobBu7eTfCNX417Slvk\nq8IuLPxYG5yTbmxRBeCa8Abe8etBlnH3fOYP17dt/Qzv/Q2JVH+A8JOv4R7dPuF68qXz2D5ZjP+1\nkbjmDohfwRAdcaNUNQp0ywto1VOH0T9bjq/rONxvi9ARybJwj2iPd8xy3D2aIEdCuIa3xzfmPeTx\nfXH3eBHfuKVYAT9WanHMggXg573ovx7GLFkKMzUVKykJbcMX6Os+QPL5BJC75z68az8QXsoZGZCc\njLrhC2wrViLv25vn87MUBTM9nVDr1oT69EE+flxw3y2LaN26YFloX38t+O5ZnNRI/fqEOnVC3bcP\n+7RpkNXpCw4YIABs1iify5eFpV7hwtimTMEzdmzCvwVLUQg3bUr41VdRDhxAvnhRUKLmzRMA9NAh\ntG+/Rf32W1BVAoMHA+B++eUcz1cQwqpYuXLEbruNQL9+GA88gJyRIUIgzp4lVro0Rt26QlgVDot7\n6sGDSKdOEerbF+3bb0UnVZZzeK3X2m5ZDgdWUhJ4PDhGjED76KOch5HsoBXIAud9+ghwvmYNVnIy\nsUcewffssyKJS9PEQ8Xu3VgZGUSaNUPbuhVPo0Z5bMQgi+ZQtChGjRr45s3D0jQiReI7qNm/Odf/\n9l65coUFCxbgdDoTXPmb9e/Uzc7q/6B0Xf/Ddf5bgqlru5J/puOrZOyjwFePIFkGHAbv4zMxbylI\n0oWWSESJ7r8N7e09AARe6k2gRQccztk4bVOR1CBWFKS3wRolE360McHu3f9lkJqnzp5F378f+cIF\nYdqdrea/fBl1zx7B1Tp3TiRIqSr2d95B+y7e9zF7JBYaMEAIKi5dwkpJETdOmw6a+OykCxewihbF\nLFkS23tLsS1ZHNeVMFNT8U+cjOTNxDliOPL5c3HLfW9PQzl+FOeokUiBXAsj0+nEP2suyuFD2MeN\nxCpajNitt2FUu5XofQ+Ay4186iTy2VNoX/0Dded2/NNno3/0PraPcnl+RqXKBN4aiXL4F5Fadeok\ntmWLCLXvgm35AvQduX6jJuBbsh5Ph+eRDANTVQm3eIPIXQ9ASkEc4waib8/ro5q5YB2ezk3iwGP4\n3scwK1TEsWwG15e/63D0zR+h7duO5fQQqVOfaN3HMAsUxipQGO37r7HPm4AczvtDYtqdBN6ajHtQ\nuwRfAPD1Hoftk/fQ8gGk3pGLcE3pi/x7Yk5q6G/NkEwT2+crEy4HyJzyPu5eLxJu/BrRex5B9l9G\n27wG/Yd/5ABXb+9FeEa3zncfAN4B7+EZ8tIN1wnX/Rtmalkcq/Pxk7U78Y1einLxKPLJo/n6zmaX\npdnwDlhGUu/nEy43k1LwjVyCe0JLpHAAb+9lJPVLvO71FanzCIG2Q0ju8URc1G7CYwHe6V8h79uB\nZ9qNO1C+nlOxfbkU7ZfchzVLkvC/OR999bvEKt8GqoZj6aS4bf2dRqLu3Y5tY64nsFGyPIHuE0jq\n9qzYl9ODd+wy3L1bgmXiG7sY2+p3CbfsSCytFOg2uJqRo5A3U1MhKQkpI0N0GD0etPffxz5jOkpG\nhhgb31qd6H33YpavgOVyi9Hz+fNYWUBM37QJ+7x5OZMcMUEojVGjhuimFi2KWbUqxGJIsoy+bBna\n55+jHjkS9x7NpCT8Y8dCcjL6unWYZcoQS0/PsagChLfp999j6jrRFi1Qt27FMXWqoB1cU5bLRaxc\nOaIPPkj45ZdRjh4VvtKKgnTlSm7H8ccfkU1TAMXevTHuvhvbkiXo69aJ/RQsKABorVrEKlcWbgUl\nSuSAR9vSpWgbNghe6/XvJyUF/6RJ4m8xC5xHa9XCrFAh13ZLVeH0adEVLV0a+zvvoOfTSbUkiUij\nRoTeeAP155+FV3YWrxVZRj5xAm3bNrQtW5CuXiXQqxeRJ58kkp4u/ML/RGVmZjJnzhw2btzIq6++\nyhNPPPF/F1Dz/1nl11m9CVb/B5UfWP2/EEz9s5VwhJ5fmREKfPkwqvcAXIRgWlsijz5J0sWXkawg\nsR2pKPMuYul2fF3GIj0dwamNQrZlKZg/AetNhXDNZgS6dMFMT//3Tj4WQzl2DO3773GOH498Li8Y\ntACrWDHCjRsTeeEF5KwbfbagisxM1IMHBR9r2zai9eqJ1Jp9+7BPnJgz1stzCdxu/BMngseD7b2l\nwjewZCnMYsUESNZ1rCQPZqlSSJle8eRuRLNEVRJSJIIZCkHWiF8+LnxXLU3LClIwMZOSxWd96RKS\n34cUDCJfvIB08iTRZi+hr1qGbenCnBuzKcv4lq3BPnsq+pZvhBDq/vqEGzXFrFAJ5eB+bCuWoO7a\nhgQEm7fBKloY54zxed6bb+gk9K/XYzlcRJ5vAz4v+vrVRO9/GP3rT9C/y2vDFLnrfoy77sY5e1zc\ndcqcuQZP35eRQnlTpCxNJ3Pe31EP/ohZqBiWJaF/9Rn6JyuRQyEyZ6/F06VJwk6tv/Ng9O83oO1O\nbC6fOW1NQous7PJOWIGn94v5LAXvpNW4+72MFA4mXG66kwh0GYl7ZOfc13SdcNN2ROs+hOy9hPLr\nTrAn41gef02yyyhahvATr+CaNyjfdQB8fWbjHNMZOXpj4dTV2V+hHtyOa16/PH6911f4waZYpo79\ns6X5rmMWSsM3aBb6zk/h9yvYv1x1w2Nnl/etJdjfGUmoyzDcQ5sn7DhfW5askDlqLRIK7v6Nc7il\nCdfVbHhHr8Y9uDGyERHj++4z0b75HNvXwpXBN2AG+t9XoO++ztdTkvCNXo5zSi+U33K9asP3PkX0\nnidxjxICrVjhNPyD5+Lu1AjJ5sA7ZjGOaSMIdeiHUbEaKAqoGlz4DeXkCVBU5FOnsS9agBSNEHn4\nUWK33ipoBIjEJ331aqwiRYTdnseDcuIkys8/E7v9dsyCBbFcLpE8tWcP2oYNKDt2YJUoQWD4cLDZ\n0JcvR//0UyFEqlYN4847MUuVyhUQRaNYRYogRaM4e/RAy4ePb9ntBHv0EJ3Pw4fFtlmOJlJGhgCg\nmzcj//ADFC+Of/x4JK8X+6hRqFnWVxZgFSlCrFIljFq1MCpWJFarluDFqirKTz+hbd+OumkTyum8\nnsCRevUI9eqVQ7UyCxQgVqUKRq1aglKR/X4UBZKTwW4X7+eaEIZrKwcg33MP2qefiqZB8eIiwCCb\n5pXl+2oGAkQ6d0b94QcckyYhBa6/H2mYZcsSrVWLUP/+WJYlOql/8nfW7/czf/58/v73v9OmTRsa\nNGhw01/136ybYPUvVJqm5QGF/2vBVDTLOuWGYNUyce/qhv3kcghDNLMG4aaNcGUOQ8LE2qojLYwQ\nK1aa4LCXcVSYj5KUBR63gzVQI1SqJcFOnTBLlfr3TtjvR/31V2GobbOJGxQgHzmClpWMIl26RLht\nWyLPPIO6YweOadPy8FGzVa2x9HSCffpASopIjlFVMZZTVeGbeOgQ6o8/Ih09SmjQW2CBY9LEPGOo\n7DI9HvyTpyAB9lEj4tJdLEki2L0HRr16ON6ejHLooBAARSIQDmMVKoR/xizUzRuxz5yWB3hEb7ud\n4JDhOAf2Rj2UO4oznU68q9aj7NmNWaK0uA6ZGcgHfiH62BN4XmuOfCXXF9YoW47ggKG432iZV6Dz\n4GME3xyGcuIY6uavsb//HlLAj1mwEP4Rk/B0i+dDZs5fi6fHSyLS9drrkFSAQJ/RuId1EKlKpSsQ\nfrwJsfJVMVNSkS+cwzWsO3Jm3oeBWPFShNp0wTW2d8KPPXPm+3g6J+ajmqlpBNv2wDUh8bZG+apE\nHnse56zhCZebgH/UYjz9X064HMDffpAAyz9+n3gfuk7mO58gRwKoB7fjeH9qwgQrX/ux2D9ZnNBD\nNrssScI7cg1JPW/c2bRUDe/oleifriD6eEPck9rna7zv7fcuroGt/jAJyyiRjm/0CpI61Ue+LrAg\n4frF0wm2GIhn0CtE7riPyLMtcY19/YbiseAL3ZCPHEM5vJfAm5Nw92l4w/MyylYm8PoQkoa+iL/9\nOJR9e7B/lAu6LUXFO2El7lEd41LPTHcyvlFLcXdvmCdeNtCmL9Ll33GsFcI0o3w1Ap1G4O70LJLD\nhXfsYpyTBhN+vhXRO+phqToUSAF/QFBYMjPBMKBgQaSMDOT9+yHgh/RyWIqClJEhrKbcbsjIRN+0\nEX3dOuRLuYIxy+UiWr06wUGDBHi8fEXwJn//XfiKfvFFXDc1mxagHDuGtn49sRo1iFWqlBMDC6Ac\nPoy6ZQtG1arE7rlHeJouWZLnIdCCHG5s5KmnMOrXRz55Upy7aSJldxw3bhT8evLaQNnnz0f7/HOR\ntlWmjDhW7dq5gqjUVCyXS9wPJ0xA+/JLZF98190sUCC3kzp3bk6H2UxNFRSHrEQwef9+rAIFRHTr\nwoXo69Yl7qQ6ncKt5fXXUQ4dwpJlQc2y28HnQ923T1gMbt+OJEkEu3Yl3LAhkfLl/zRIDQQCLFq0\niI8//piWLVvy3HPP3eyk/h/VTbD6F6psUPifEEz9K/WHYNUycf3QA8eJ98AE81QykUYPYpfFaM36\nBKSPIFrnVuQ+F1HKZv1YHAZzhINQwdcJvvY6VgLuzz9T8sWLqL/8Ikb412dM2+2Y6elEatUi3Lkz\n8vnzQmEPSJEI8uHDaNu2CQL/lSuYuk5g+HCs9HT0lSvR167NAw4tWcYqWpRo3bqEuncXlIBgIKcr\na2m66Lb4vMhnzxGrVhVSUrBNnIi+8RvkjIw85x6pX59Q567YVq9AX7E83qe0Vx9i1W/D1beX8Ha8\npvw9ehO7805sH63DqFQZs2w6ls0uurEuF+ruXWhffoG2YxuS34fpdOJbuhpXl1dRfsvtNpuyjG/5\nh3g6NMOSFUIvvYpRu67g3pUug7tjS5Qzp/IcO3PuSlwjeqCcy2sGbtxei8hjz+CcOiTuc/INnYF8\n5TfMoiUxkwoinzuLfckc1IN7yZy9CveAdsgZ8X6h3vELcE4djHLuVNyyWFopQi93wjUh8cjY138y\n9jVzUI/8knC5d9g8nO8MQTmfOAkqfP9TWAWLYF8X7wGaXZlT1grx1g26l94JK/H0eIFo9TqEXu+D\nlPkb9lWTUM/mqsAzh67B0z//DjBAtNrdRGo/hmvOsBusBeH6z2E5UrB/MF/E4Q6YgnNWT9TrFPyW\nw42v90I8bza54f4AYsVK4+86CVQZz/CWcQlb15ev10ycU95CvipAWOjpFsQqVcE1JwHPNOtcvG8t\nIamzGMNH7nqYcIOXcmJn86tgkzeI1qmPtvUbHO9Ni1tuFiiEb+S7uLs1yANKAYxbahBo04ekfrni\nOgvwD56Pbdl0tAO7c8/lqZZ4+rXGsjvxjV2MfcpQYtVrEanfAIIBYnfeK8I8fj2EbFrCJzUYRP/4\nQ2IVK2GWLC3sl3buxL74XeTz5zALFsSoU4foAw9hpqVhejxImobp9iCfPYN9wUK0r7/KNcgvXFiI\nke6ui1mmDGb2GN1uRz53Dlfv3iiHDye8TmZSEr6pU5GSk4VQM0sMhs0muJvZ6VlHjmBUrUpw6FDk\nkydxjBmDfPGiuDZZHUejenViNWtipKVhVasmPFKjUbSvvkLbsgVl2zbk6xT0kQcfJNStG+q2bdjn\nzhWWftmCqCwaBDYbZGRglSgBsRjOrl3R8ns/QKhfP4x69VA3b8ZKS8tJFMsOY1B370bbskVYHg4c\niPrzzzjGj8/10M7eV7bv6913E27fHiscJlKsWJZLzR9XKBRi6dKlvP/++zRr1oymTZv+S4Lpm5V/\n3QSrf6GSZTkOoP4nR/1/VIZhYFkWiqIgX/9Ha1m4dvXAcXIpmGAdtxGrn45a6ABWVEJaaGHtluBF\nJ1I3P8jACTCneQh6OhNq+Yogyf+rZVmox48Lo31FEdypq1dRf/xRcKd++AEZkdUdGDUKDEOA2WvM\nqS2Ph1iWRUy0Xj1id92FfPassKPy+ZCPH0f76SchBDh8GBkwbr2V4JAhSKdP4xw7RoDf68p0OvHP\nmAGqim3VKsykZMyiRUWKjNuFpelYRYuKlJrLlyAcQkLCgpybo+V2C2FGOIx09QqYJlLMBDMmeGwV\nKqDu/Rn55EmUX/ajHD6IcvoURsVbCL7ZH3fHV4QPa/Y5qSq+letw9umEevJ47uuyjHf5R+LoPh/K\n+bPoH69D3f4d/iFj0L79Cts/8lpVRe68B+ORJ3BOiFeDZ85bi6dPKyS/F0vTMWrWJfJIA2KpaViF\nimBbMgf9kzV5QINZKJVA76G43+oYfy0B/9RleHokVup7h8/COW8syunEllCZU1eT1D1/IOaduBJP\nr8QBBACZE1biGfwqkj9xV9J0ugn0GIt7+BsJlwMYFW4lUr8hzlkjc7crmIq/5yhwO7F9thB191cE\neszG/QfiKn+3t3HMGIzsu3GAgXfYu7j65nZLTV3HP34Z+tfL8niUhv7WFun8BWyb84+hzTl290k4\n5k3AdLgI9BmLZ/jL+fJQTU8Kvl6zSOqZ99r62w1EDl7GsTaeR+vvMBbbuvdQD+3JeS3YpB1WairO\nhfn714Yfep5Q0644Zg5G3544GSxa5Q5CbXrh6Rf/PQo1bEssNQ3XfPH5WIpCtO7jBNsNQTr6i3gI\nkWXMoiUhHEE5cwz53Emi9RvgGNULKRQi2G0o2ufriTzbHMsCXB4sw0A5fQrpzGms4iWRL/yGfdpU\nrEKFiDz1DLHSpbFSCiKdPQsejxhTX7iA9vfPsWQF4957MYsWE13ISBj1+63oH65HOXUKo+YdBPr0\nQQqFsC1dgnrgQA6IjRUvDm4Xls0uXEJ++olovXrIgH36dLRt2/K8f0uShF9rtWqEmzXDrFAB6cIF\n4QUdCCAfOCCEVd99l2PJZ6oqgTFjsEqWxD5zJtqmTSIFqmJFMcavUkWEojidxJKTISUF+fJlnG++\nifzzzwm75deq+/WVK4lVqZKTwmXZ7UiqinT6NOqOHRilSmHeeSe2ZcvQ16yJe8CzACstjXCDBkRe\neklQvRRFcIQVBenkSbTt24Vd1tmzWKpKqEMHQk2aEC1fXvym/ImKRCIsW7aMlStX0rhxY5o1a4Yt\na6J3s/5v66YbwF+orgWq/01v1H+6LAvXru44TmZ1VE87serbUQsdgMsgzbTEyGhRDKr64RTE5hUh\nkNqHcPcXxdPzv1rBIOqvv6L//e84rkmZyuFO3XIL0QceIDJypIjkCwaRDAP5118xy5cndvZsDndK\n8npBVYk2aoT022+4GzdGPX5c7C+LoB+rVIlIkyZE77sPHA6xjWFAaiqBrl3R9u1H2fMT8r59oGn4\nJ00Gt0t4tybIBzdTUvBPnYZ8/BjOV1rH8V9NWcY/bQbyxQu4BvaPs8yKPPAQoa7dcLd9GfVIXgP8\nUNMXMR55DE/rF/P4ApqShG/5WuxjhxKrUZtglz5YRYoiBYKY5cqhffEp9vnvIF/OHUNG7qyHpEhx\nQBUg1KUPng7xAC9asQqSESH4Sg9ipSuAzYG67Vsc40YQ6NIf28J30LZvjtvOP2AMjumJwUikSRv0\nDYm9VQFILpAvUI2llUI5kTgkAMAoVR7l2I3N9yUjki9QBQg174Tt0/yFVwDB1j1xTc6bay9fvohn\nwGuYskzo9b4Em/dFObZfKKYTuCGA+I7HUkv8IVC1nB7hlnDt8SIRPF0b4+szkViF23EsGoJkWURr\n1Mc9oMUN9weCUxxLK4t84Swy4BzTG++gJQKwJqA0BJv1xDkjPi7WNXsE3oHvEL6vIbbNueIms3Bx\nYkXK5AGqAI7Vs/H3HEf4geewbYwPAogVKUn48ZYkvVwf34SlyBfPoR47ELee9ssPxDZ/hv+NEbhm\nDMyzzL5+Af4+U/C36oVVqhJmcmHUHVtwv9oQ/8hZOAd1yunqhx9rRPiZZtjenYPkDRFq3QPL6US5\n/BvhVh2wTxyKcf9jmCmFIGpgpZUUlk4lSxIrVJjg4KFC0V6sONLlS2gbvkA98itGzTuIlSlLrERJ\nrCeexLZmNY5+fXMfNpKTiTR6Fu/7a8XoPcuGTz58SPg1nzuHfuYM+jWm9pF77yPUpw+maaIdOUKs\neHFCXboQtNuFKGrXLjGCP3SIaK1ahNu0Qd2xA3enTkh+0TW3PB5i5csTrVWL6DPPECtcGLNCBbAs\n5N9+EyP3U+LayBkZyDt35rijhJ94gnD79ti++gp99WpxL336acyOHXOFTJaFfPIkRuXKyBkZON96\nK5cmtWFDns/JUhQCgwYRadZMBBVcuECkQQPCL7wAhiHcCrZuRf32W8zSpQkMHYpy4ABJTz2Vl+ql\nqoKeUK0awQ4diDZoIDqpxYuL360/8ZsbjUZZvXo1S5cupWHDhqxevRpHFtXiZv1362Zn9X9Q1wLU\nvwJITdhZtUzcO7pjP71MANVzNuQHwpAM/ArWPJBeAFoB5yC2Kh1fycFE6z/5p0cqiUq6dAn111/F\ndQkEkLMEVNrGjciXBffSBEI9emDcey/axo3Y58xBCgbFzal0acGdqlULMy2NWOXKIi7R5UL5/nu0\nzZvRvvsuTowVat6cSNOmaFu2YJ8xI0cla7mF6X4sPR2jZk0ijRujHDsGkQiWLAnRhWUhXb6EfOoU\n8tGjRB97XNitvNkL7Vg8wAo3bES4VWscY0ah7bgunhAITJqCZERxDuqfE8WYXf4Bg7EcduwrlhKr\nWg3jlqqYpUpjJheAgoWQz5wUSTjbvkPduR359ClCzVthVSiPc1ReQY+p6/gWr8HzSuM4M+xgu27I\nl89jW78C051E5JkXiNZ7CEuSMUuXQfv2G2xL56EeP5Jnf/5p7+J5o1ncezZVFf+UhXi6t4xbBghh\nVdemCa3GojXvxqhVD8fCeLU3gO+t6djfexv1ROIxou+td3AsHIdyJjHYjdR+gFjFW3Esj3cuyDm/\nKe/j6d4kX4AJWR6uPfP3cAXwvr0GdePnRB99CtuXK9H/sSKuW2SUqUyoQTvcE7rfcF/Bxh2Qjx3B\n9v0XCZeHnniB6GPP4JzTF//r40nqH/+5xG3ToC1cvop9wzWOEiXKEBjwtqAEXANYLc2Gd8hykro+\nl+/+MieuwrF8PNoBIZbx9Z2Hc0I/5CsX49YVYqglOBaPQj2WKxayFBXvqNW4e7dC9mViOVx4Jy3H\nPfiVhPsB8Hcbg/rz99i+ucYFIL0KgTdGgGrDNnM0tl25ThiW24N34hKcI3uinhDf6egddQl26Ie7\nnfj7CHZ8k1j6LSg/7cS472ExhrbASimE7d05GHffCxYo+/YSq1kLMr04Zs8kWqsOxt31sJKSUHft\nwj53NtKlS5jp5Yg8+hjGHbWJ3VJJ0JbcLtQt3+KYNk14miIEobFbbiF6z73Eqt+K5UnCdDpAt2EV\nLoz25Zc4R4+OG3ln2zBFq1Uj1KePuKdmZopOajCIsmcP2qZNYqKUTT/IsvVD17FPmoS6Zw9myZLE\nqlbFqF1bCLyy+J+Ww4FZpAja/v04u3fPSc+6vsxChfC9/TZyKIT6zTfEqlUT4QUORy6PNCu+NXLH\nHcQeeQRbVnxqXCfV5SKWnk6kYUOiTz2FfPRojs5AunpVxMBu2YKyaxeyaWLJMuG2bQk2b064QgWs\nfHil27ZtIyUlhSJFipCcnAzA2rVrWbRoEU8++SStWrW6aUf1X6qbNIC/UMmy/JciY8diMUzTRJZl\nwZcNXSRpc3M0749i9H9BQnrIAg34CPgNGABWGIx/1MJfZTjG7XX+rXNQTpxA3b1bdCoPCb6dpeuY\n6ekYt9+OUbMmsVKlMMuXFwAuHEb/9FMx3tm9O++4WZYJ9u+PWaMG6mefYV+8WIgA0tMFkL39dswi\nRTBdLmFMrWlIfj+2ZctQt25F3r8/T7cq5wauqjgmTogTV1mahplaRHBgCySjbdokLGoKFMDSbVia\nCpqGmZwMBQtCIJDbAZCknH8smw2rQAGkYADpaoYA2ZagBViWiVm+AsrhQ0iZGcinT6P8egjlmLDX\n8s+YjXPEINSfduc5t8g99xNp1hxXt/ZxN37v/GU4Jg5DPZzboTIBo2YdAuNmIJ8+JYQNF86jfbMB\nbdu3hJ9siJWSgmN+PGfQN3oatpUL0Pbujlvm7zsS/ZtP0HbFK/n/UFg1ZTnuYR0T8lwBMt9eRVKP\npgmXAWROWkVSz/yXe8cuxTWqC3LG5YTLTd1OoO8U3EMT+4ECRKvfhXHHvTgWTsx3HVPXCQycibv/\nqwAEW3Qkev+j2D5bhL55fc7n4283CtuqWajnT+a7LwDvqOV4et0YgBqlK+If+y62FdOx/33ZDdcV\n+1yJp3t8Nz2WVgr/oOm4R7yM7BN87GDjzsiHDmP77vO49bPLBHwzPsI5uRN4Ugg+1Q7P8A75rm/Z\nnXgnrMA99OWczrK/ywS0Lz5C374xd78phfGNWYS7R2InAUuS8I1dhmPmQJTzpwi0G4xZuBSu/q8j\nmSa+Ce9inz8JbU+u4txyugVgHfsm6jFxDzLKViQwp7GcXwAAIABJREFUaAruLi2Rr14mcs/DhF7p\nirtLK2IVqxLs0g/pzCmskmWw3EkQCWMlF0A6dxZtw2cY9z6IlZKCunkz+qrlRJ99nkiDZ0UYSCgE\nsoKy92f0LZtRt35PrGIlog/VxyyWhuV2If3+u7jPff45ciRC5KGHCHfoCD4vthUrQFUx6tYllr2+\nqiEdP47+9dcoW7cKD+jixdGXLUP/8MMcvrWZnCyU/XfeKcbwxYphFSuGpGnIe/eir1sn7q3Xce8B\nQo0bE3npJcFb3bQJ4447iFWvLoz1s7mxv/+Osn8/kXvuQcnIwDFyZM40K+47UrAggYEDMStXRj52\nLAcMS5qGdO4c6s6dqJs2oR47hlGxIsFRo5CPHsUxenTOxMoCrMKFc+gJscqVMe66C8swiJQogaVp\n+XqJh8Nh+vTpk/P/qqri9/spWLAgtWvXpkSJEhQpUoQiRYrcBKz/hboJVv9C9VcGq/bfviJp6ytI\nBMEAMoAHgZPAZ8CLYBWRiOx+An/tETkK9H+lrFAI7ehRJMsSkX47d4oOahYPNbuMmjUJ9uuHdOkS\n9smThcIzO+Gldu3chJfkZKyUFHC70b75BvuUKXE2KiC4poHRo7GKFkVfvFjEq5YsSaxCBWK33SY4\nZi6XSEcpXFiIGn76Ef2bb1B+/EmkU10DjoPduhO97z7ss99Bv26kBVm8rylvg67jHNg/R8RwbfmH\nDMUqXhznm73ifiDMtOL43pmDY/Sw+E5sUhK+xctx9u2OejivqMZIL09w2Cjcr70U17EMtnoNq1AK\nyrEjRO99CLNIGlIohOTzEatcBcfIgWjbv8uznamq+BauwtM2XmRkOt34x8/E0zWxmt47dzWejok5\npTcSVpmAf+JSPH0Sj7CNkuWINGmDc2rilKVYWilCL3bENaVfwuUA3nE3TrUKtO6Fun8X+rbEPEkA\n75gluEZ3R74Snw2fs5/X+6Pt/BbtWtAFhF7thVGnLvb1s9G3f4F3+Eo8ffLn10JWulOXcST1y9+9\nAMSPuHfy+4CF7avV2DbkT2Uwyt9K6JnXcI/umnB5rGhJ/ENm4B7RCsmfgXfk+yR1yb+rmnOudie+\nSasgGsHd68U4QU7ccVKL4x86F3evp4k++BxGhdq4JsZ/fkaZigT6TsTdpUFCbqTl8pA5cTXEDBwz\nx6LvyKWmWJqeBVgnou3JDfuw7E58kxbjmDwE9ZB4KDULFcE3Zh7OId1RTxwhViQN/6iZ2GdNQtu1\njUCfYZiFUnEOH0Cwe3/MYsWxrVhC9KHHiFWrjnz8OMrxY5glSxErUwblyBHsUyYhZ2QQqf8wxr33\nYRZIQfIKAKp+uQERSg1WiRIE3+hE9OFHkc+dw0pOQvnlAPpHH6Ju2BB3LS1FIfLkk4R69UY+fVpQ\nE2w2kR54+DDaxo2oGzfmcFKNypUJDBuGfOFCjsDKLFdO+L3WrCkstrIFUZJErHhx9A0bcAwdmpMa\nF/d5FymCb+ZM5CtXBC2rbNkck3/Icm3JmnKFmzYl+vjj2FauFJ3U60SuZsmSIr71qaeI1akjHFtk\nGSKRHHuq7PQsEA8p4WbNCL3yCpGKFYWzS6LvxjXH8Xq9fPjhh5w7d45Lly7h9ycWFKalpd1Mpfov\n1E2w+heqfzVy9T9VsVgM04hQYGdv7OdXCrtPL0geoArwOVAZzGIOwr+/hL9uf3B7/uXjSZcvox44\ngH3xYvQPPkAyTcyCBcXTcO3axCpVEurXsmWF4l6WsU+fjv7ppwm9T43bbyc4YADSxYvYp05FMgyM\natWI1awp/Peyx1YAKSlYdjvOt95C/zox+DDKlCEwZgzy1avYx45FuXRJ3DTLlRNdiNKlsZxOYpUq\niS6voiCfPo10/hzK0aMohw+jHDiAdOY04VdeJfrk33CMGxMHNAGM8uUJTJiE7d1F2D6M52yGn2lA\npNlLuDq3jxuzmUWK4pszH1fndihn86r1zeQCeOctxj3kTYxKVTCq18AsU05cB6cTybJQDv6CunMb\n6q7tyKdOIlkWwQ5dwIjgWDgr7ly8U+biWDQDdW98KpV38jwcs8ej/hrPDQ292BYpEsD20Yq4ZX8k\nrAo1bIFkGdg+id8WwDt0Fs55o1HOnki43NfvbewrZqIeT8xZNarVInrnwzgW5u+LmjllLZ4eib1f\nc85j7FI8vW/MCc2cuhbPG4ndBEwg2GUQseo1IRoh6c0bg9XAqwPR/7Ee9VA8X/raila/i8gDDXBN\nHIC/92jQJZwz+yekM/j6zcI5rg+yLz7CM+c8ixTHN2wW+qYPsCQXjhXTb3j87Ao1eJlg0zfw9GqK\nei7xZ5XnvG+tQ/C1foBEUsdn810vUvMeQi3eIKlvAkHV35oRvb8BlisJd9dmce8rB7DOm4D2867c\n1+0O8fqM0Wj7xZTAcnnwjVuAbfZE9B+2Yqka/kETkS+cxzllFNHqdxDsORjb/Jlov+wl0GcwlqLi\nHNSXyHNNMe59EPnXQzjGjCRWszbh55tgFktD2b8Px9QpyJcvYxZLI/y3vxF96GHM0mWFP7Mko7+/\nBvvyZcgXL2JJkvAFrXsPsTvrYKakYDld8PtFZJ+fWMWKaD/9hP3tt5F/z31wsmw2oYKvU4dYjRoY\n1aoJganDgbJtG/rnnwsQe50PqQmE33iD6COPoH/4oeCd1qkj/FHdbjHGz0q9Un/6ifBzzyF7vThG\njkQ5Ff/wadlsmOXKEejbF6toUQE+7facuFR1714xxt+5E9kwMMqVIzB2LMrJkzhGjsyhglkOB7H0\ndPFebrtNxLfecgumaRItUybHzvCPyrIsNmzYwMyZM6lTpw7t2rXDZrNx8eJFLl68yIULF3L+u1ix\nYrRo8ce875v179VNsPoXqr8aWFXOf0vS96+jWBfE4/xV4DbgGBCFWMkiBBw9Cddu/W/xUZVTp5Cj\nUeSDB9HXr0f75ps8noOQ1fUcORKrRAmRlb1+vSDJ16ghvPeujReUZWLFiqHu3YuzVy+UBCMrAKNW\nLYL9+iGfOYNt6VJi5cuLG1yhQuByiRtbLIb8++8YVauiHDuGq3//HG/B6yvUpg2RBg2wrX0f/b33\nxEjP48EsVoxYWhpmuXJEH34Es2RJ5GNHAQk0VXCrFAVkBQsLPG6sgoVRt21FunoVKeBH8nmRAgEk\nv5/w089AocLYli8VNlWaJqgCug2zUEGMhx9DOfgLlm4ToD4WE6IwRcFKTUU5fAj53FmUX/ahHD6I\nfOok6DZ878zD06YZUjDvD5NRviKhXv1wdW4bz6OsfCvhVq/ieqtb3PUwCxYiMGgs7l6vJrxemQs+\nEKlYCQBSqHFrpEgQ/asPsZJSsJKSMZNSMFPTMFOLEXmmOeqerYCEpagiolYSAQsiprEqyuG9Iukn\nGkbye4VQypeB7M0g1OQ13MM7Iv92BinBuNg74sapVqauE+g3DfeQxKlZAJG76hMrWxnH8vwTpGJp\npQg174Rr7I07M1cnr0C5ehmSnDhmDcqXCpA5dhVJ3fOnNmSXd9h8XIPeyEkDCz/0FJEmrXCNboec\nmfvwYznc+AYtwtOt8R/u0yycRub0tbi7PY968Y9/IyxFwTvxfdzdW+KbuATn5N6oJxPzi3O2kSS8\n0z+CS7+T1K/1DdcNP/Y80bsfwj26U85rwRZdiRVNxz20G7GiJfCPnoO7Z4s4Kkm+gFW35VIFfhQP\nmZaq4Rs9B/2Lj7B9Jji9oWavEr2nPq6OLZBkmWC3AcTKVMTV7VXM4qUI9hyI5PXi7NeDWPWahNu8\nhun24JwwFvnIr4RbtibcvKXgq1oW0tUM1D0/ipCAE8eJ3ne/sK9KTgZJQtu8GdvKFTn3TeOOWgR7\n9hThAt99h1k2PcefVDJNlB9/RP/sM+SfRKpbpF07Ik88Ibj577wDsZi4X9WqJR7uU1LE/VVVsVQV\nq1gxbHPnYl+wIF/LtlilSvinTBEP7F6vsKfKpgNcvIj2ww+omzYhHzhAuF070UldtQp95co8+zQL\nFhRj/Nq1Me6+G7NcOaTMTCEwO3EiDx0g53MCIs89R7B9e6K33IL5T4DUb775hqlTp3LbbbfRsWNH\nChcu/Ke2vVn/2boJVv9i9WciV//TJQXOkbSxDWpgl/BCjgAK4ATrKhiFK+OvOBqj3L3/8jGscBjt\nyBG0r77CMWUKkt8vuKO33SasT1JTweUSvnkuF7jdOMaPR1u1KrHtia4THDoUs0IFtI8/Rj5xgljt\n2sTKl887ajp6FMJhYjVrom3bJqIFvYnV3uFHHyWcFcWn7NkjBABFi4qIVbtdBAT8/juSZWFUq4rt\nvWXY585JePM2KlQkMHYs6o8/4JgwIS57GiDyUH1C3bphmzMbdc9PYLOLKNesf8fKlSfc9lX0D9Yg\nnz4jVMDRiAgQiEaJ1n+Y2K234hw5TKRcZVzNEUiZhVPxzVuYuNuq6/hWrMXdoQ3y73mpCCbgW/0R\nnteaI/nir1PmsvV4OryE5I+3MPLOWIxj3EDUM3mBlanrhBq9hFn7LrQtG4iVKodVrASmPUscoulY\nqcWQMrPOP+Mq8uVLyOfOIv92DkvXMe64E+f4IRAKxI0dQ42agcuBffkCcTybDQoUwkwphJlSEKPG\nncSq3YZ06QJmWklQZDAiAtSGQ8hXLmLcdheuoe2Qz55I6HsafKkLytED6N8lFjEBZE5YgXvQ6zfs\nSHqHzMYxeyzqqaP5rmPqOv5hc/D0ao2ZnIJ/xHTky+dwzhmaR9hklLmFUNNOeZK0Eu4vKQXfW7NI\n6pK3S2sWLY5v1Bwc84ai7ReczWDz7ig/7kTfFe/icH1F6j5CpPbDmFWq45zaH/XwnhuuH2zeBenU\naeyfr83ihS7GOWMg6tHEiUsAgVf7Ih86jGRaRB5tgKd/6xsfo0VnzKQknHNHEugyEinDh3PG6Nz3\nXLgovnHzcfdpg3w573ff0nR8Exdjnz0Obd8PeV8ftxDbslkoZ05i1LgLo2ZdonXuhUsXkTOF6T92\nB5bNCVhIGVfA6cKyOcDpRjqwD0nTsZwOzOLi4VXyepEQ9B7L5cY+dQra999heTyEn29MrEo1cDhQ\nt2zBtmhBToyz5XIRvetuwi1aEqtaDSkQwNJ1HFMmo61dG/f3YbndGFWrEnnscaKNGiGfP4/lcAjP\n6S1b0DdsiLPkM3VdWFWVKIG+bBkoirhPFymSa9B/+TLazp1IBw8Sat8e5cIFnKNGxe0rxyqrcmVC\nPXuKFzMyxIO1ZYkx/nff5Rnjx0qVwj9hAsq5c6KTevGioAOUKiVSr2rXxixZUtC00tKwZJloejrm\nP6HQ37JlC1OmTKFSpUp06tSJokWL/ultb9Z/vm6C1b9Y/U/BaiyMe0sXbBfWIimIx1MfUBAsH0QK\nP4KvzkSsAom/NH+mpKtXUTIykH/9FceECWKsk2C9UNOmwqJk/37sixYRK1lSjJnKlhVjJocDKRZD\nOnaMWNWqSJmZOGbORPs+nxQhVSU4bBixatXQNm/GLFRIKE+dTuG9Fwig7NuH9t13RG+5BeOpp9A2\nbcL+zjsJgaUJhLt2Jfrww2iffAKWhVmxIlZyship6zroGvgDmCVLICHhHDQIZUe8WbaZkoLvnVmo\ne/fiGDcmTukPEOjRE7N6dZw9uiWkPPhGjUWKGTiHDIwDy7ESJfFPfwd3uzbIl/JyJ03At2odzkFv\noh6OH4l7Z8zHvmQO2s5tccuCHbohX76I7f33cvZFkTSMylWJ1qhD9PFnUM6cwlJU8Z4iEQiFkAN+\norffgf7V5yhHDqEcOoh85GDOj2rohZexbDYcS+fGHRPAu2ANrh6vCFCQoDIXfYDntcb5jue9c9fg\n7tEmIfgGCDZuSazOvRCLYhZLQwoHkHyZqL/sQvvhW+STh/FOXI2n5wv5xoeagH9M/pzanHOZuAJP\n1/yjXgH8bwxE37oJbdumnNeMSrcS6DMc7YeN2FdNQ4rF8HefgGP+ROTfz91gbxBoNxD9H5+g7o8X\nvJmyjH/Cu6j7vse+ZibesWtI6vLHXVWAzMmrcbdvAqqKb8ZK7O/PzhfMWw433lFLSXq9Ue5rdie+\nie9inzsC7dBPcdsYFW4l2KYvnq7imoYffppIgxf/8Br7u48iVqEK2ufrcaxZFP+eCxbGN34h7v6v\nI1+8Lpo5u8M6Zzzavh+wAKN6bcLNXidWIh3MGPZFs9C++QdywEf4iYaEm7+Cq3cHlHNnsBSFYOc+\nGNXvwN3tdaSrV4g8+iThl19D27wRx8y3McqWI/xGN2JpJbDPnIq+eSNGhYqEX26LWaEi0skTOMeP\nQ77wG5auE613D9FnGmGkFQNNx1JVZL8fdd9+bEveRT55EjM9nej9D2DUqZNzT5IP/4rt44+wogbh\nnj2RLl/GPm0a6t69OTxY4/bbhTArLS3XXsrtxnK7cQ4ciP7ll4k/TyB6//0EBw1COXpUcGKzt4/F\nUH75BW3LFtTvvoNQiHCnTkTr1xfq/tWrc+5Zlt0uaFU1a2Lcfjux9HSstDQwTaFfyEoivF48awGR\nv/2NUOfORCpX/qdA6rZt25g8eTKlS5emc+fO+YKim/W/rZtg9S9W10eu/lcqFsH1XU/sZ1YgZWNl\nP2AHM6oQKNGG0D3DhB3Tv1jKyZOoe/bgmDgR+ezZnKfhWKVKOeDTAtA0SE1FW7YMx9y5CYEbQPiR\nRwh36oRy5AjK/v0ifzs5WXirahrS2bOo27ej/Pwzoa5dQdOwz52LumlTwk5ZLDWVwPjxWIUKiWhB\nh0N0Y3UdKSMDZe9etO+/R965k3Dv3hh33CEMqdeuTRzzmZKCb8oU5HAY28IFmEWLYpavgFmyJKZL\n0BVMXYcSJcFmQz55Aun4MZTTp5FPnkA5fgL56BHQNHxz56N/9CH2xYvij6Oq+JYux7Z2DbY18SIZ\no0JFAmPG4369VUIFr3feYmxLF6Jvjufphp57gVjFCthXLCZWthxW6bIYJUpjFk3DLJQKxYohnTsr\nup+RiHAIuPw78onjhJs0w9WvG8qJ43G0gkDX3iinT2BbF58vbwK+JR/gaf1c4g71LdUIv9AS14i+\nCa46hO9/BLNqdRxzJidcbhYtTrDTm7gGJRYLQVZcbIdmSJFw7naqinH3A0TqP4FZrgKW24N64Ef0\nL9eh/rQ1DrSGH2qAlVQI+wf5J19Fat9HrHItHIum5LsOQOb09/G0TxwnG378WcIvtMa2fj7hBq3/\nUNhkSRLeye+T1OHG6wVe7UXsznrIB3/GNW3wDdcFQXmI1nwQ1+RcGzTvuPloe77Fvm5B3Pr+rmOw\nfbAC9Ze8PGfLZhfgcOlEtJ+vCfBQVLyT38fdvkmeh73I/Y8TatoGd88XE4upAP9b0zGTCqP+vAPn\n3MSuDGZyCr6J7+Ia1DEuzczSbfgmLUG6cB6zSBrKkcM4Jo9CCvgIvdIJ4467cXV6OdfmKaUg/hFv\no+7cimO+sD2LpZUgMGgMyqGDOCeMEOCqYWPCTV5C//hD7EsXYjldhNq+TrTufag7tmOfPA7JNIlV\nrUb45bYYZcsiX7yMKUtIyclIGRmo27chhcMYdethpqQgRaJon3+KvnZtjlhKvL9k/JMmYxUtJgRZ\nTieWriOfPo3+xReoX36ZZ32jalUCgwcjX76MbcECQbmqXRuzcGEx6craVtuyBS5dIvzGGyiHDuEY\nOzbuYdpyu4mVL0+kdm0ibduK+1A0CoaBfO4c6o4dcWP8WMmS+CdMQL54EeeIEUi//ZZQPGs5HOBw\nYOo60UqVMP8JVf4PP/zAxIkTSU1NpVu3bpT6d+O+b9Z/tG6C1b9Y/VfBqhHG82UL9Cvf5ILUsKBa\nmnIy3tvHEazwTM55/bNlhcOoly6hHD+Oq0sXlBOJBRRGejrB4cMhGsW2YoXgeGZF8OFyYWmaeKre\nvh2jXDnMGjXy+KjGHVeWiTRsSLhTJ+Tjx8VTftboXgqHBfD89luUbdvA5cI/fjzY7djnzIkDs9lh\nA9GqVQkNGSI4pBkZgitqtyP5fMiHDqHt3Im6dSuYJv4pU5AsE/uIEfnasgTbtiX69DMiUWbjN8LO\nKqvba5YsiVmiBOHnnke58BtcuiRGZIoCioqlyILf6nZBcjL4/UiBgOBnxmIQMyBqYNptWOUqoBw6\nIOyuVAXkLH6sImMVToVoBOnKZbE8FhMpWTEDK6UgKArK0SPCK/bsGeQzp5HPn4MrlwlMm427Yxvk\nixfi3pt/0EjU3TuwfbIubpmZVAD/5Jm4X2+eEHz53xyCtnMr+teJbY+8C9fg6v4HXdUOzZDC8d1w\ngMxpi3GP6od8/kzC5UbFKoSfa4FrbOJIUADv6Bk4FsxAvvgboWavYNS+EykUQDl+ANuGtcjHDuCb\ntAp3vzZIwfwjSTMnrcTd/7Ub0gSit99FtM6DOGeNzXcdE/DOXAnJKbhGd0loip9d4fufwixZEcfC\nGwNkgIx31oMi4ZrQC/X4oRuumzlpFe43XoyLM/X3GYVkBHDMGZHzeZuF0/D1nkxSp8QdZUvT8Y1f\nhG3NO+g/CPqBv/NItE1foX8b39mL1KtPqEUH3N2bxAHWQLfhSEeP41g+n0D73phFi+Ie2SvhcU1P\nMr5Ji3GO6IZ6SgAnS5IINWtH9P4nkK5cRd37I465ea+dcWsNAn1H4BzYHfWY4NxaQOjldkTvfwR3\n5zbIWTSZ8FPPEm7WGse4YWi7dwmV+outiDzdCH3ZYuzr12IB4RZtCL3WETIzkUJB5CtXkTKuovy8\nB7NCRcxSpSEcxrZkMeqX/8gND0hJIfrAg8LmqnBhrIIFsRxOEZs6eRLqrl05n4MlSYJ6dXddMbVK\nScEsUUJMrQwDZ48eaLt2kagsWSbcqhXhFi1QDh8WPNbsmNOLF0V069dfox49Kpwt+vTBuOsubEuW\niCABrlH1X+PVGitaVNj4ORwoGzeif/aZoAMkok09/DDBHj1EJ9XlSnieiWrPnj1MnDgRj8dDt27d\nSE9P/9Pb3qz/Xd0Eq3+xUlU1Ptr0/7rCmRT4+HGU6K95QaoBMXtZMuuvwCxUHsuyMLJGs6qq/mkQ\nLV25gnrwIPalS1H37Mm1OylcOKdbKZ8/j3T1Ksbtt6Pu24dj8uSE0aUAZtGiItMaYW9iFi4sQKzd\njuT1ivznTZuQdu8m+sorRJ5+GnXHDhzTpsXxUc2kJJGk8txzGPXrIx8/LoAnIJ8/n0vWPyIMwM2U\nFAFmdV0Ay+3XWUQVKCBGbvfcQ7h1a5QjR0QkqqIiKQpcuIC6fx/q7t0ou3Zh1K1HqGtX9HUfYHv3\n3YTdw2jNOwgOGYxt6VJsa1YnvCb+USOxChTE9WYvJL8fS5KEijfrn2DHTpjp6TiHDYFIGAwDycgC\nsoaBb8ZstO82Y1+yKG7fRtl0AmMm4Gn7UkIKhHfeYuzzZ6Jt3xq/bbXqhF5tj7tn4vjRzAUrcA7t\ng3o6XiBk2u34ZyzC81piEGNUvpVwk5dwjUxsN2XcWpPIkw1xThyScLnpcOIfPQNP9zYJlwNkvrMC\nd/83kK9cSrhcJIwtxdMxXmVuVKxCqPkrmGXTsQoUxL7kbfRNn+Xp0ObZz8iFeHq3yvdcALxvr8LV\n91Vkb/6AFsA7ay2uzi3xj56BHMzAMf2thCDYO2Yprp4vx4HKuPdS+XZCTV/DObwXvinvom/7B/Y1\niWkZ0ToPEKnzCK6JiW3Cgi+1J1b1Vlxjuwgv0yHzcI4dgPx7YqEiiJQh39gF2D5ZjOTLJPTs63je\nTCzUA4jUuY/Qq91wd3k+B7gFW3XDUh04p+ZyVEPPtSB6/yO4erXO19bKO2kxznFvYnkKEOzQF/3T\nddhXLhb7bNMRo3ZdXJ1b5R1Du9z4R09H2fEdjsVzcl43SpUlMHQithXvYvv8Q7Gu3UHgzSHEUouh\nf7CKWI1amJWqiNQrwPIko332MVpWeEfk2SYY1aoh//47jnGjc9T0Zmoq4YbPXhMssBPb7FlE73uA\naPPmEAigf/4Z0tlzGI88QqxkSSy3GykjE+2Lv6N//DFyICD4/oMGY95yC+oXX2D7+COMKlUw6t1D\nrHQpLJdbTH/OnEHbuJFYUhJGw4aiYXAdTSqHTlCtGtG77sJ4+mmkS5ewFAX5wgVhzn9d4ABkdVLH\nj0e5eBHHyJFIgYAQvGZ7tWaLszQN+fJljGLFiFapgul25/uduL5++eUXJkyYgKqqdO/enYoVK/7p\nbW/W/75ugtW/WP0nwap88ScKfNEISfMhZdu5ZoHUSMHH8D6xEJS8nNlo1hj+z4BV5cIF5F9/xTVg\nQJxBfnaZqkpw0CDM225D3bw5JwkqRwTl9aL99BPaxo2Yuk64Vy+k334TqSlHjuTZlwVYhQoRrVmT\nYNbISvL7RRqJZQn/wG+/Rd28GTkrxSXcqBHhVq1Q9+7FPnlyruWJLItEqqpVMWrVwqhZE6t4cWHU\nHw6j7NmDun072ubNeZwKzLQ0/OPHIwUC2MeMQT2aK5SxFAUzLQ0zPZ1Io0YYd90pBF6SLACyroHP\nLygS+/YhHTxAsGs31N/O4xw6JGHXOFaqFP7pM7AtnI/tw/Vxy03AP38R6o8/YJ8+Na57aQK+ZSux\nvbcE22fxefBmsTR8M2bhadMiIacz0OtNpIyrOBbMTnhs3+qP8LR+IW70DxC5vz5Gvftwjo+P4QTw\nTpqNY/4M1F8SC3MyF63F3bV1vsDNO38N7u75c1F9w6ZgW/1uwnACALNACoF+o3G/mb/Jf6DrQNSd\n36NvSczdA/C9NQ79s/WY5SsRefxppEAm+sZP0L/5OKfjG3qhHdL589i+jP8Mc87H7iTw1lTcNwBp\nIJT8ZomyOBaJkbNRrhKBt8ai7fwa+7LpOW4LZtES+DuNxNOn9Q33B+Ad/y6uPu1yOlrB13oQq1oV\n1+iucd3izImrcHeK76rmOcf7nyDy/9h7zygpym/t+1ehq/MwpBlyzlEREOUPGFDMERAkSk4SJOec\nQVCSgJIFFFFBRVAkCBJEVIKCgOScmenc1VUFxfFdAAAgAElEQVTPh3umh7G7Uc9z3udw1stey+Va\ndPVd1dU9VVftfYVGLbB9NIvA0y1xD0l8jjPLVBS84+ajFyhMUosGfwuww/fXwt9lAK7urxB6vhl6\n6ftwjewds12oTn0Crbrg6tIw7ppGci7SF3yJdPECrnaNYrYJV30Af9+ROPt3RjmXZcNkAv6OvdAr\n3Y+re+vo+0xZxt9rCJGyFVF+3IlRrgKm04VptYFugCLj7NEF5dJFTEki9NSzhBo3hVAYx6ihUXCq\nlyxFsHVbwWM9eRLH5InIV6+I62SbdoRfeEkAwwzdg2XrVqzLlsZa2+XLR/jhhwk2fg2zUGEIh5Fu\n3MC6dAmWDRuQ4/iJGrKMb+IkjPLlkf/8U/BRnU4kVUU6eVIkAG7ejJyWJsJXxowhUqoUtvnzsXz7\nrRCOJScLVX+NGhjlymEkJQkXl6QkcDiwzZ2L9tlnMU4w0fNepw6+vn0JlS+P4f7nFolHjhxh6tSp\n6LpOr169KF++/D9+7726e+oeWL3LSlEUFEX5b11T+3U27gOjwBYRwinADAC6jKfiQIIPxNoOZdbf\ngdWoqn/LFizbt2d57TmdYpwUCKDs34/y228EXnsN2TSxvf8+6rZt8bmjuXMLMFuhguh6ZnrtmSbK\nH38Ikv62bch+P3rJkvhHjYJAANusWVh+vk2xm0HU16tVE53dOnWQb94UqtdDh0SG9G0d1MwKPfoo\ngTffRDl6FHsGZ8q02cS4rHJl9KpVhXdf/vyQcZFVdu5E27ABdceOmBuDXrUqvuHDUQ8ewD55crbo\nQxMwk5OJFCpEYOQoTMNAPn8uo/tsxdQsoFqQZBlu3hD2TcWK4pgwHnn/r8inTmVP6Mqbguf9Bdgn\njsOyMzYRSqj+P8E+eRyW3bFdUSNHMp5Fy3C1a4l8Iza1KVTvMUIvvIirX3y+Z/q787AtX4jlx1iR\nmwF4Vq7F3frVuDxkI28qviFjcfWKD8z0CpUJvtIU57hB8V8vUpxgm644RyUY8QLeuR/h7pTYpzR9\n4lzsc6eiHk888k6fvxpXu/j80cz9eOZ+TFKHLPsoQ5YJvdKM8DMvgt+Dtn09wadfw90tsQgMwNt7\nPNr6z7Dsi/Xhvb3S5n6Gu3OTmA5u4LlGhBo1w/bhDLTd3+HtPRnbwnfjhizcXnrJcvhbvYW7f4fs\n/16qHL5hk7HPHoHlNzEeDlevS6hWA5yTE9Mmou8vUwnvpPexjeiO9W8+U2Z5B08jkpQL5fxJnNP+\nnjsbrvQAvv7jkC6eJ+kOHXS9QlV8/cfh6t4E2Xubo0LBovhGvItt2njCLzSCcChuJ99IyoF30ntY\nvvoU2xfZpx/h+6rj7z0Cx6h+REqVJfz40xg5cyOfOYORvwDykcM4xgyLdnb1MuUI9OiLIau4BvWJ\nOnJEChYi0LUHkRIl0VZ9hG2V4KQLvuvL+PsPRkpLw0xOxvrB+9g+eD/q/mHabIQfeojwU89g5C8A\nVivKnh/Rln9IqOnr6LVqof66D9vsWSLitXBh9Fq1hB1W7twCiHo8KLt2oVepgpQrF9rixWhff52d\nJqUoIizggQcI16yJXqcO0rVroKpRupVl8+Zs3q6Q4Vk9aRLKxYvYJ03CdDqjiYRG3rxC+GqzCb3A\noUOE69QhXKECkX/RST1x4gRTp04lPT2dXr16Ubly5X/83nt199U9sHqX1X8bWDUM3OteQru5E+zC\nfhLA9INhurn1+GqM/Pf/7TK6rmOaJoqiZOv4SrduoRw+jH3pUrRPPkl40w02akSgfXuUI0dEdGgm\nKR5E53P7dtStW0FV8Y0bh5k3L9pHHwle0+1jNrtdjIWqVyf02msCCHu9QiV6/LhIPtmyJRuVwMid\nG+/48eB0Yl20CMu334IkZXVQq1fHKFJExKsWEkInKRgU0a6bNsXnSdWqRaBfPwFmJ09GCgaJFCtG\npHJl9MqVhUerwyESXlwuQR+YOxfLdxvjmmH727cn/PTT2GbPRtu4Me45DNWqRWDIULSPP0I+fw6j\nUGERapA3b9R5wCheQvBPPR5BOpZlpIAf0tORbt6AtHT0F1/C+vFylH37hAji5nUBrtPSwGbDs3I1\nzq7tUS7E/n0bqfnwTpuJ640mMalXAMHHnyRSuy6OMUPifgbPyIlo329E2xKb5AWQ9v5KXMPeQr4Y\n/9qStnA1rp5vJOyqps1diWvIm8jX4mfC+zq9hfLnEawbY7vJkDGWf3cp7m7N4r4OEHi1OcgKto8X\nJ9zG9+ZAlIO/Yt30dfz9AIFOvQjXfxbl3Emsny1B3RNf9Jc+YxWuzo0SAmMAvXxVQg1exTFlWNzX\nDcA3eAJmwQKYjiSSOr0Ud7ts+52wAOfQnnFpBIYs43l7IeqJg9gXTCZ96ke4ujX9264nQODVVhjO\nnBglyyGfP4FjXmIeLkCo9uOEHnke15CeBBq1JFz/KZw9m99xX3rpivj6jQckHKN73/HBI5K/IN4J\nc3EO7ohy8RzBJ14k+GprXJ1bIPsyJjHPNyT4ajNcXbP+LbNMScLfezhGck5cQ7Ie4MJVHiDQ6S2M\n5FwQMXA1exnldlHYY08SaNsJy6ZvsL+fFbKhFylKoNcAjBzJOIf0i14vTIuFQMs2BFu2EULGmzex\n/Lgb66qPkY8ewShZimDj14iUKw9WK5YN69GWLc0mRAvXrYd/4GCkq1fBNDBtdqQrl7MiW//yAKkX\nL45v8mSkdA/K2bMidtXlEp3U48fRNm1C3bwZORgUsdNTpwre//TpWPbuFSA20we7enXh8ep0iut/\ncjKSLOPo2xd1586Ev+/wQw/hGzmScLFiRJKSEn6Pf63Tp08zbdo0rly5Qo8ePahWrdo/fu+9unvr\nHli9y+r/OnI17TQ5v3gCWbqOZMv4N0N0UnV7OW69sBEs/8wgGbLAqizL4tjOnkXdtw91716MMmWE\nD6rdLmL7jh3Dsm0byo4dBLp1E16mmzdje//9GO6jabMJhWjjxoSfeiqLO2qaQmW6c6d4Is8w4Ddk\nGf+gQWLNjRuFGXUwKC6KRYqgV6kifFVTUzGKFAG7HdPpxPLNN1hXrEA+cCCGo2ZYrfhGjcIsVgxt\n9Wos69eLLkEmTyopSYgGLBYwDCKFCmH56SccAwfGHZUBhB56iEDfvqi//YZt1izMnDnRy5UTgrF8\n+QTdwWoV4rHkZOQLF7DNeBd1z54oVSF6fElJeOe8h3zyJI4xo+JbaCUl4Zn/AZZdO7G9My3LAgbA\n6cJMSiL44kuEn3wS2/x5mE4HpjsJ0+3CdLkFDSMlFaN4CZQ/DokHCkkWPpGyMNg3bTbMlBTkCxcE\nEAbx9COBiYTpsIM7CenqFSQTzMy7T8YTkulyiweB69cQdyYp2/8NpxvJYRevmyZSOIQZCmf4ngYx\nHHbMQkXRvlgl3AauXEa6fBH50gVknwcjd158/UfhGpA4Wz7tg09xt3sl4Y3R23MYlj3b0X7YdIc1\n7myJFd1Pm8T7AREx6+zTEfw+/F37EKlyP8rxw9iXz44Kv0IPPUakVCXsC9+9w0qQPmsVzr7tEgrO\nMuvW1AWQMxfqqSM4ZoxC8sX64gLoRUri7zQYd+82d1wv0LAloRcaIZ09jXtYfH7y7WU63aRPW0ZS\nyxfF+5u1I1SvvjDkj/PwYzrdpE//EFfzrMhUvdL9+AaMwTWgXYzFFICRMzeeqYtxtXwJSbPimTgH\ndccm7KsWJTwuI0cynqkLka5eQPL6cQ2LpQ1EChXBO/ZdbLOnoP24Peb1UP1nCLToiLJpA8Z/HhFW\nU+OGI/t8hGs+hL97X7Sv1mBbnvWQYwKhxs0IvtQI67KFWL/KooMYKan43hpIpHQZSBPeq/Kli2jr\nvkI5dZJg0+boZcsi3byJfdpU1CNZgNy02wk9Xp/wU88QKVAQ7DZQLVi++hLbB+9HHUFMwChUiHDd\nR9BrPYiZMxemzYp08yaRwkVQ9+3DMWVKTACKqaoYpUoRfvBBwvXqCdtAj0dM0HbtQtuyBWXHjpgH\nCr1MGfxjxyKfOoVt3jwiRYqg16yJUbhw1hQuFEL57TfkI0cINW9OqGJFIv9i3H/u3DneeecdTp8+\nTY8ePahZs+Y/fu+9uvvrHli9y+q/Cla1/XNx/zpcjPoz3m7qQEDCX7wtvjrj7/j+RKXrOoRCWE+c\nQNuyBfv06XF9Pk2rFf3hh/GNGCG6m36/8NjLUPJHO58XxE0m0KoVoZdeQv31V2zvvhsdn0efyKtW\nFRYlJUtiFC0qRsceD9oXXwgQe/hwDPgMtGhB6JVXUH/5Bds774CmoZcvT6RGDREOkBEDaMoy5MwJ\nioJ96FC0bfENz29XsVo2bEA5eVIYYRcunBUpmGFiLaWnE374YSy7domQA18sZxMg+OyzBNu3x7J5\nM9ZPPhH+sZUqiUjA5GSw2TBsVkhJxXS5sGzZjGXTJtRffxVK/NvK3/oN9Kefxt6/L2ocpwUD8L07\nE+nWTRwjhsVNigo9XJtAz964OreL8nezrZEvP56583F2ao9yMQ5AyJGMZ/EyXG1bxFAgoq9/sAR3\nyyZxeayGy4VnwYe4WzWOPnygWUUYgmbFsNvxTZ+DY8QgDKcTM09ejNx5MHPmxsxI1dHvr4F8+TyS\nzyu6y6EgUvot5PNnUU4fRy9eBsmiYps7NSGITJ//Ca72DRO+Hqr+MPqDdXHMnJBgCwg074CUnob1\n8/gRsAB6yTIEm7XHOaJv9n8vVgp/70Fgs2P54VtCjz2Hu2eLO7oJGHnz4+s6CNeQvwkBSM6Jb/AU\nXL3aopevjG/gaCw7vsW2fE7Mb8Iz7n0co/rGJDr9tUxJIm3+Z0iXLyF7buCYNCCuYCmzvMOmY100\nD/VIluG/XqYivqETcEzsh/rnoezHMWYuttlTUf/M3hk1knPhnTIX64dz0HZkPViYFo30mStx9emM\nfEUALBPwdx9ApEgxnAM6xRdUWSx4Js7D1BwoJ/7AOSF+h9q0WPANmwTedJwTs7YRSUmvE3y5KQSD\nKPv3YZ88Otu+TEki0LId4QbP4hg7HPVgloesqaoE2ncjXOcRrG9PwCxVhvBTz4E/gLr3J2Hgf9/9\nyKdO4hg/FvlW1rU3UqQIwZZvEClbHjwe7NPfRv7zGIEevdBrPohy8iTaxx+hV3sAvVo1zBw5kDzp\naJ9/LoJTMrnMioK//0Ai1aph+X4rhHVhBZiUBDabsLf69lvUjRuRAwH0cuXwjRqFfOkSjgkTkM+d\nE2P8smXRH3yQSIUKmBlNDFNVMVNTkS9exNm5M8rlWPeQzAo9+SS+kSPR8+T5VyD10qVLvPvuuxw5\ncoQ333yT2rVr/+P33qv/PXUPrN5l9W8jV91fvIB26y+j/iCYup2bj67EKPTwf/1YbtxAPXxY2I/k\nyJGlxvwL+Aw9/jiBLl2EPcrUqShns3wKTVkW4LNKFcK1awsF/qVLmA4H8okTqHv2xAWfof/8h0Cv\nXijnzmGdOhXl1CnMfPmESvXBBzGKFhVdQadTEPRz5sTy7bfYR4yIO77PtuaZM1hXrBBANkNpSqbv\n4PnzyD//jF6rFlJSEtbFi7GsX58QxPg7dSL83HOou3djOhxRGoCZQSmQDx/GsmsXEaeT8BtvCAXt\nrFlRblnMehlm2ba576EeOIBRsBB62bIYZcsINwWbHSN3LsiRLHhh+35FPv4n6qHDKL8dQDpzBplM\nkDkP28x30TbGH737O3YmUrUqzp5vxuWR6sWL45v6Dq72reMDWYcDz4pVODu3iw9kJQnP6i9wdusQ\nl1oAkLbyMxwDeqKejm9rlj7rfWyL5mH5KT7HMfBiQ4wSJXFMzz5SNpKSiZQpS6RUGYLNWyOdOwsu\nlwCzQb8IgTh9HOXQfiKlyiH5fdhWxvqBRo9z/mrc3VsKQJyg0hd8jqvNywnjJwHS3/8E51vtkW8m\nBoP+1p0JvdAQ5c/D2JbMQD0W34oqbepinBMGo1w4G/f16HbTl+CYMBT1bNY5Drz0GqFXmmL7cBba\nD+L3oRcogq/XWJK6t7jjegD+Zh2Q/EFsKxcTfOJZgq06ZoDO2GPVy1XB37I77rdi+cimw4l33AyU\ngz9h/1DE0gafehW9VBWck+NzVE1FwTdiCtL1yzhmjxdeqhPfx7p4HpafY38noTqPE+jQA1evVtnO\nu+lw4pm6AOvs6Wh7dhJ8/hWCTVrh6tMJ+XL8YIXgS00IvtgYV9fmRMpXwt+1vzD3nys64MFnXiDY\noi222dNjvItNhxNf/2EYBQvh7NUVOe1mxud9jmDzNkj+AEaePMIpZP6cbNfDcJX7CLZph5G/ANoX\na9CWLs6yqwKCnbsRavga0vXrmC4n1pUr0JZ/GHMtNFJTCT1eH732f4gULITpdoPTiX3yZLRVH8dc\n5zLtrcIPPUyocWNxrdV1pGvXsOzYgWXDBtTDcb7zBx7AN3gwyqFDaJ9/Lh7yK1TAcLvFtOq2SRxe\nL4FevQhVqPCvxv1Xrlxh1qxZ7N+/n27dulG3bt3/9x7ld6gDBw6wceNGzp07R7Vq1Xj9deEg8vXX\nX/Ptt99G7/Mul4uhQ+M7adyrrLoHVu+y+kdg9foxcn79NLJ0MzrqN03AD7pWklsvbQHNdqcV7ljK\nmTOo+/Zhnzo1RtWfCT7D991H4K23xOg6KIQd0pUrwm9082bkI0eyxndlywqDab8f6+zZgtMEAnxW\nqCDGQcWKYbhcWdxRvx/HmDEoW7bE5ajpRYviHzsWwmFs8+dDKIReo4Z4qne7o9QE6fhxZElCL1cO\nbds2bLNnC65rnNJLlcI3dSry9esiBSZ//ujYXgoEorYr8s8/ExgwgEjVqlg/+URkWcc5RtPtxt+j\nB3q9eshHjwqVrt2elZh1+DDq7t2ou3YReu45Qk2bYl2xHO3j2JsGZMRuzpwlkqqGDkVKSxNhAwUK\nEClVGqNkSYyUvKITc+MGBPwgSUi6jnTliggbOHYU5egRfJ26oJ49i33KxLj7CleqjH/YCNxtW8dV\n1xuqiueTNTh6dUU9dTLu+UxfvALbzLex/LQn7uuesZOx/LgD6xefxX09+OwLRKrcj2NCfPcAw+HA\nM38p7hYNEwJEz+SZaJ+uRNuZfXxryDJGhcqEq9ck2LgZ8vWrEA4i+bwoZ0+i/vgD6qH9yLduoBcu\nTrB1YvEWQOCZVzBzp2Bf8l7CbfQyFQg2boVzVP+E2wCkfbAaV6/2YJr4Bo3GTEnBsnU91s+XIYUz\n4nNtNryj38Pdq/Ud1zJSC+B7cwiuAV1iXwP8A8dgFC+O/Z3hBNr2xjF5xB0tpQARjfruMpJa3pY+\n5XThHT4Jgj4c4/tE//ZNIH3Oalwdm8Ykt3HbNoF2PdDvr45jXC+84z+I0gXuVIHm7Qk/VBf51DHk\nU6ewr1yUcNtIan68E2Zje/9ttN3bMJJz4Zm6AMfwfqjHsrq3Ru48eMe/g7pzW8LvMlz5fryT30O6\nfBl385dj40w1DX/PAegVKuHq0zUmwlgvXBTf+GkYScnIV6+gbdyA9aOVSH4fpqIQeqkhoRdfglu3\ncI4Ymu39psVC6LkXCT3/IobLjSkrKGm30NZ/jfbpaqRAANPpJPTo44QbNMDIkwfJ58W6fHnUjzXw\n8iuEmjVHOX5cjOQLFxa+rAVFzKvk9WLZuBHti7XIaWkEXn+dUMNGqDt3Yp85E8nnw8iZk0ilSoRr\n18YoXjxr0hQMYhQujLpnD85hw7IJSrOdI6uVYLNmBHr2JOxw/CsLquvXrzNnzhx+/PFHOnfuTP36\n9e8qkJpZx44dw+fzceTIEUKhUBSsrl+/nqtXr9K8+Z2T1+5V9roHVu/CShS5qu2djvv38WA1Ykb9\nvuJt8f8XR/2QpepXTp8W3FGLBenqVQE+v/suaslk5M+Pd+xY0DTRdcywJTEBM39+AT4ffFDwSMuX\nFyDO6cSyYQOWtWtR9u6NAZ9GcrIQQiUno61YgeX774XFSc2aRMqXzwKfgJSWRqRECZQDB3BOmBCl\nFfy1DIcD38SJmPnzo27bhlGwoFC5OhwilerSJSw//oi6eTNGyZIEMtKw7HF4WpnHGK5WDf/IkSiX\nLoHPJ0CnoiCdOYNl924sW7ciX7ggOh1duhB+4gksX32FbeHCGJ5jpj+rv0sXjJIlkc+cAVUVa4bD\nyH/+ibr3J5GadekSvr790KtXxzFmDOqB+NZOesVK+MaNxfrRR2grlmeZf9vtQuCQkkr4oVqEXm2E\ncmC/CBjIiIU1LRbh0WqagIlRrDjWJYtQ/jyGfOoE8smTUbAhOqZrcAwdgHoofo67Z8IULD//hHVV\n/JF4sMEz6P+pg3N4fM9UI0cyntkf4G7ZKO6DAEDawpU4xgxBPX4s/vmoUJlA6/a4+nWP+zqAZ+I7\naGs+QduRRQXRS5Ym/FgDwtVrgsOGkZIP9fgRLOs+w/LTD9lGsdFjWfAZ7vaN4orPMit9/p0DDQBC\nNWuj16mPY1J2gB54sRGhhk1RLpzGuuhdAq27Y/04sQ1X9LhmrcQ1pEd0NB6vDIeL9NlLISkHzgEd\no8b2ico7dCrW5YtQDx2IPf5HGxBo2w3HlIGoRw7if70j+ELYVyZO8sqscNXq+EZNw/72KLSt8acB\nfy1f7+GEaz+OY1hPLAd+vuO2psWCd8RUzKAfs2wlXN3axD0vJhBo24Vw7Udw9XgD+bZuemacqqNv\nd8INniX8aH0cowah/nEoZh0jNT/e4eORrlzCMbw/MhCq+TCBbr1RTp3C8s3XBJs0w5RlnMMGoZzL\n3iHXS5Um0KU7RoGCWOe/h3XjNxg5kvENHIJRpKgw+Pf50B+oDg6H8E5dsjg2zjk1n4ivbt4SKS0N\nFAXb229j+fKL+NZdefMSql2bQL/+yDdvYCoq8oULWLZvR/vqK+Q49//gc88RbNsWddcukShYs6YQ\nZTmdwqP14kXUHTvQNm0iUrIkvr59CZcv/686qbdu3WLu3Lls27aNDh068PTTT9+VIPWvtW7dOm7e\nvJmts3rt2rV7YPVf1j2wehdWNrAaDpH01XNY0n8Bx19G/REH1x/9CArW+i/vK3PUb/vww2yqfhMw\nCxRAr1QJvWZNwnXqQAZHU7p2Dcv27YIG8Msv2cZVhqbhHzECo3RpLF9/jXXpUkyHg0i5coLPVLZs\nVryqpmHmzo0UDOLo0wfLr7/GPUZDlrO4o1u2IN24QaRqVYycOcHhAFVFyqAmcOIEoR49kPx+rDNm\nxF3TlCQiBQviHzkSs3Bh5LNnxbHYbKLjuW+fMK7OANZ6yZL4xoxBTk/HNm0a6qGsG5OpqoLmULky\n4erV0Z98EvnaNZHXfelSVlrWrl3ZFLeB118n1LgxlvXrhQDtNpBjulxEihYlUqkSgdathXXVjesg\nKwIcX7yIcvAAlj17kPcJ/pt3zhxkjxfHsCEJuxm+QUMwSpbA0futuLxjAM+Ut5EwsC5aiJE7D0bh\nDOeB1FQBep0uzGLFkC5fBtMARREUguvXka9cRjl7Gr1kaXA4cAzsHVc8Y6Sk4p02C1erxomB6Ier\ncfbrjnI+ftJUoGFTjAIFcMxIEJ9JhlVWm6YJR/d6mXIEOr6ZMMAAIPjkM0Tuq4btvZmEXniF8COP\nYWoWJG866h+/YdmyASNvPvSq1XHMmpRwHb1cJYIvJw40yKy0xZ/jbtskYQKXkZofz5AxmCVKY1s0\nE23d6oSCL71EaYLNOuEcHisait3vWly9OuLv0R8jNQXnyF5xO6x6sVL4ewzH3TUxVcB0OPEOnYCp\nSkRSC5Lc+uW/3T+Av+NbmP4gZolSGA47zgFd7qj8D99fk0D7nri6tcU3dCyG3Y5zYNc7uwUUL4V3\n8lwkj1ckTp38M/G2RYvjGzUV64oP0H7YgnfEVKTr13COzLLpMt1ufINGEcmVG1fvLtGkqtsrVPcx\nfP2HgqyirfsC+3uzsv0mjQIF8ffsQ6RQEWwzpqHtyD4FMO0OPO/MFmETTif2cWOxrsk+jTBtNiGs\nevY5jDx5kf88hn3GDMyUFHz9ByDfuoX1vTmoP/+MWbAgocceR3/oIRFRrShYduzA+tFH4PHgmzAB\nM1durAsXZHmk5smDfv/9hOvUFRMnt0tMrtI9GMWLY/n8c+xz5sSlN5mShFGoEMFOnQg2akRElv+V\nBZXH42H+/Pl89913tGnThueff/7/++Cc/8b66quvuHXrVrbO6pYtW1AUheTkZJ555hkqVqz4P3yU\nd3/dA6t3YVksFqSrv5FrwwtIcnrsqN9ejlsvfAeW+B3Yf1LKmTMoZ88KUHXxIurPP2PZtAn599+z\nuFCSRKB3byIPP4y6fTu2uXORvF6MXLmIlC8vOp+lSwvuaHKyINUnJWFbvBjrrFnxgQoQat2a0Asv\noO7bh/bFF+j33ZctpURSVaRTp1B+/ZXQo48iW62ii/vNN3FH1qaiEGjfnlCjRijHjgkBVaZP340b\nqHv3RnmxuFzCIislBW3FCrS1a7ONkI2cOUX+dI0ahJ5+WoDhYFDQAH7/PcvnNS3L1sdISsI7aRK4\n3djmz0fdsiW7CXa1ahjlyxPJkQOjRAkB8HQd7cMPRTf2NspEZgUaNiTUvDna2rVYFy2KgjpTUcTY\nv0QJIlWqEGzSRHii+vxCwR+JIJ85jWXfPpRffkb+/XfMgoXwzpqFdfmHWD/+OO7vwcidG88HC7B+\n8D7WL7+Iu41eoQK+cRNw9OqeLUbWtNsxc+XCyJkLf/eeSBEd+dSpLGstq1V0bS0WDE3DzJ8f+exZ\n5DMnUU6fRDlxAvnYEdHBNQx8bw1AvngO24ql8Y/V5cLz3iLRdU1wmfIOH4e6czvWb9bFfR0gbeUa\n3O3ihx9ABtVhySpBM/gLIDSBSNVqBF9uhP7Ag0jXriDpISwb1qCt/zzmt5/2/mrRpbtDElWgYXNM\nmwP74nkJtwFIn7kI27tTiNSoReipZ1COHsL+wfQY2670eX/PjwXw9h6Gun8f1nVCkW7kL4iv/whM\nVcI5rDtyIEsYlz5zOc6eHWJsnOJV2rKTDgAAACAASURBVIqvRYTyRwuxfh2f6pFZ4SrVCLTrhbuT\nAMHhajXx9xmCdfEsrJs3xGwfyVcQ76S5uJo8F/3bCdeohb/XIGyzJ6PtjhVN6qXL4xs+GVeLhqBZ\n8Q0fD6aBY2D3hADXlGU8MxcSKVEax8DeaHtiPYRBdOP9g0YiHz2MfeKo6DGFHqpDoFtvLN9uQPJ4\nCD/3IvLh37GPHxVLH3A4CXToQrjWw2gbv8Hy4WL8g4ZjFi+B+t132JYuwsiXn2DLVkTKlAOfF/s7\n01EPZu9wG4Bv/AQi9z2AlJ4GsoL6w3Zsy5bGnRqZDgfBF14g2LMX0pkzYLUhXbmMZcsWtC++iA0V\nAIKdMyZH69eDJBGpVElMwBwOpEBA3E++/Rb54EH0xx7D36uXiEX9F8Ipr9fLwoULWbduHa1ateLl\nl1/+b/cg/39Rf+2sXrp0CZfLhd1u5+DBgyxbtow+ffqQkpLyP3ykd3fdA6t3WTn3TCDp+Kw4o34Z\nb5muBGrFV6v+k7rdwN8+bZowyQfMvHmzxvclShDJmxdSUzE1DeXIEWwzZ8bE42VW8NlnCbZti3Ls\nGLY5czBz5CBcsyZGxYpZ1k+yjHTiBGb+/JguF7aPPxa8zAQdofBDD+EfMgT5zBmkmzeFsOj23Ond\nu4UP6pkzBAYMQH/ggWx2VtHPSxYvNvTii0Rq1UI6d07QAG7dEhzUrVtRdu/OUsYCwW7dCD/+uBBD\nzZ2L5PcLu6kSJdDvv18YV+fKhZGSgpkjh6A5fPUV1sWLY0IGIMN2a/BgIvfdh/Xjj9E++QQjf37h\n9VqtmhCLZYBrMykJM3dulCNHcPTti5KA5hBo0oRQkyZYly5B+/TT7CP/QoWIlCqFXqkyocaNkU+e\nBD0MigqmgXz2HOpvB4XDwIH9hJ9/gVDTpji7d4t7MwPwt2iF/tijuLp1Seh04Jn2DsqZ09inJeh2\nulx4PlyJo18f5EsXMfOmEElJxShaVPjdpqQSKV0WKRKG9DTxMCZJSNevopw+hXLkEMrh3/ENG4tj\naF/U0yfj7kcvUoxA38G43mwf93UAb79hqIcPYl37acJt0me8j33eTNQD8Tv+AN6hY1F/2o113VqM\n5JyEH3uScL1HMXLlQvL5sH7xEdLF84ReaIxzXGLjfAPwLPoMd8tX7ijQ0ivfT7Dh6ziHZrkJ6GXK\n4e83FCJhbCsXoO7+nkjlaoQavIxjwp2FG0bO3HhHTY+CxGz7KlMOf+8hQsg0tg/hx59DL1cV59TR\nd1wTwDtoLOren9C+XkugY3fCD9fFMaZfXIqB6XSRPmcFrtdfzB5hqqr4ew0iUrYczt7tkTOcEUyH\nU2zfvnmMF6ypafj6j8DIlx9nn/ZRQKiXr4Jv0Fhcr2fnmIZrPoS/Z3+sHy6IxqFG1wICnXqiV7wP\n29jhBAcOxwyGcA7onpB/G2zwHMHW7VG/+RL9sadQf/0F+ztTorZzJqD/py6BNh3A78c5uF/Mw0Sk\nYCE88xeLqGirFfuYkVh2xQnxKFCQQPOWRCpXhnAYbekSwq80xExORvv4Y7S1a5AMA1PT0GvWJPTM\ns8LJxGZH/WUv1sVLiBQuRKB3X5RTp7BPmRylVRkpKYRrCJN/I1+quD75fEiGiZmSgm3RIjGJi/Nb\nNXLkEFOhXr1E7KqqEnE6s43s7zS+9/v9LFmyhM8//5xmzZrRsGHDfyU6vtvqr53Vv9a8efMoV64c\ndevW/X98ZP+76h5YvRsqHCL310+jBQ5nV/UHwDTcXK//KeS777+8vHTjBsrFi0iRCNratVg2bozr\nOxqqXZtAr17C+3P6dOSrV4mUKSPG9+XKRZ+cTcNAUhSMlBS01auxv/deNpB4e+llyuAfPRp8Pizb\nthEpX14Y5jscSBYL0vnzWHbsQN28mfALLxB6+mnUn37CPmOGuFjfVmaGoX+4Th2h6j91CtM0Racy\nPR31l18ENWHfvuhni4LpP/7A/vbbyFdE98lISop2UDOPyShWTKx1+bIw8t+6Ncb7FDJcBd56C+X4\ncexTp4Iso1esKNK7Mn0DbTYIhUQwQI4c2MaPR9uwIaGrQKBVK0Ivv4zlm2/QNm9Gr1CByH33YaSm\nZom8wmG4dYtIxYpoa9Zgnz4t4Rjd364d4aefwT5lsqBHZJ5Dm02A2czUmZdeQj56DEwT06ohyQpc\nvYJy9Cjq/n2ov/6Cb9hw5EuXsI8fG1/4BXiXLUdb8xnWT1bF2QKMXLnwLFyC880uKKdPx90mWP8J\nQk1ex9WxbbZOspmSipEvH5ESJQm07yg4c+EQ2OzC4so0kS+cRz10EPXAL3j7DcPdsWVCbqiRmh/v\nyPG4O7VO8G1AqOZDhJ99EefwAQm30UuWJtC9D67uHePvJyWV0BNPE2zWGunWDeTTx7EtnB139Ozt\nMxzLT7vRvlufcH8AacvW4G7bNL4NmKbhf2sQkUqVMfLmw921OcrpE3deb97HOAf3Ski3AAjXfBhf\nt94YqflIerY2f9fbCleoSrBFB1x9sugVRo5kfINHY7qcOAd2iarUTcA7bQG2aROyCZ1uL714KXzD\nx2PZ8jW2lYvwzFyKfdJo1CPxXRIA9EpV8Q0ciXXZfOTLF/D3HoGr+SvxPV0VBX+33kQeqImzT2fk\na1cwbXa8k2ai7N2Lff7srHUrV8X/1gDkE39iHzMk1rtZVfFOnwsWDdOdhLb+K7QF8+LaZuklSxPo\n0RsjOSeOMcNBlvEPHoF84QL2KZNEAEju3ARbtEKvXgMzGMLxztuo+/dlX6dcOXxjxiPfvIUpy5hO\nJ8rB37B9MD9uEIlpseAfOIhwvUeEM4vVinT5MtqG9Vi+/jrWQUBV8Y0ajVGqFNq6dRjFixPJaDxI\nFgvS0aNo332HunUrUjhM6Nln8XftSqhMGSIOR8LvaPv27Zw9e5aUlBRSU1PJmTMnGzZs4JNPPqFx\n48Y0adIkoX7jf1P9tbP617oHVv9Z3QOr/8OVvKk99hvrkDJ8+k0T8EHYVZW059b93436T59G3b8/\nquo3cucW4/sHH4z6jhoOB7jdGMnJWA4cwPHWW9lG3LeXUaAA3nHjQFGwfvwxRt68wuw+c3yvKEgn\nTmD54QciDgd6o0Yohw6JLu6V2GQhU5aJVKiAb/JkMWq/di1LLX/tWtRZQD0qujHhGjUI9OuHdOkS\ntqlTUU9k3Yijn61mTfTSpYncf7/oANpsqN9+i7ZxI8rOnTE3K71YMeEqEAximzED9fffMUqUIPzA\nA4IXmwGssVoxDQOjQAG077/HMXp0QlcBI39+PBMnIkUiWFesIFK8uLBtyfAelFQV6cwZ1N270YsW\nxXjwQbTPP8e6bFlC8Bl6/HEC3buj7tqFfOaMoE3kyhW13JJCIeQ//kC6fJnws89g/fRTQR9I8Nvw\nDRxEpFIl7IMHZR/pyzJmvnxEChcm9OST6PXroxw5IgRYmlXsK+BHPn0K9bffkA4fxj9iBI6J47Hs\nij8iNfIXwDNnLq72bZGvxPdZDD1en2DTZrg6tUvYcff2H4ikR3BMzc4NNa1WjAIFiRQrjr//IJRT\nJzGljLACTUO6cR31wD4sP+5APvArnqWf4OreAfna1bj7MQDPR1/gbtkw4UMYQNrKtbjbNYt5qMp2\nzMPGoP6yF23tZ0TKlif06mtESpbG1CxoG79A+3QFyDLemUtxt00cBQvge7MfyqmTWD+PT+XILH+n\nnphWu/geCxUWY/hvYqkdwUcbEKlcHcfUsXdcDyB90SdYvvyc0DMvoJw4gn3isPjiHFnGs3gN7taN\nRYLaX0ovVwF//+Eo+/fimD0Jf6vOgIp9/ow77t8EAm06E2r4OtqqD7EvTOy6EH2PopA+bxlmvkI4\nOzRHPRPfHi167Kn58Y6cAGk3MYqWwDlsIOrvB+NuG3rkcQLtu2D5/rsomA28/BqhV5vgGDsSdf+v\nmLJM6KVXCb3cEOn8ORwjByP7Y89JuNbD+EZNgHAIdc8e7ONGI8eZXhip+Qi0bkOkShVI96Du+IHw\n88+jHDqMfdpU5GvXxOeWZfSq9xF+6SUixYqLa+APO9CWLCL4Rhv02rWxrFuHbdEiJF3P0CeIJoD+\n8EMYuXKL69SpU5ipqSDL2GfMwLIjNsLZVFWM0qUJP/QQwXbtMDWNcO7cGHY7t0OIeHBi3rx5/Pbb\nb9n+TZIk8uTJQ2pqKikpKaSkpFCuXDmSk5MTf3F3aRmGQSQSYf369dy6dYsmTZogSRK//fYbpUqV\nwmazcejQIZYsWULv3r3v0QD+pu6B1f/h0k5tJPevrTLmzzK3yvYhWP2t/zI3xwwGUS9dQvZ4cAwa\nhPLDD3Gf6o3cuQXwdLvRVq5EPn8+S32fmUplmihHjggA9OijqKdOYfuLj2q2Ne12vNOmYRYsiHz8\neJaKX9OQL1xA3bkTbdMm5AsX0MuUEcbSXm+MECrqLFCxIuGaNQk/+6wAhqqKdOkS6k8/oW3Zgrx3\nb3Zx1+3xqhkcV1wuIqVLE65Rg0jFillm1W43ZnIycno6jm7dUI/FV5QbmoZ/5EiMkiWxrF2LfPOm\n6Mbmzy+Aot0e7epKZ84QatoU5fx57JMmIZ+L360ybDa806dDvnzIhw9ngU6bDXw+1IMHhcDrp58I\nP/EEwQ4dsGzfjm3mzITgKVynDr7Bg1H37xeRspnesZl+r0ePYtm9GyMcItS9B9bFi7B+Gn8EbgC+\n6dNAs+Ic0D+2w+12YxQsRKBZMyLVqiEfOyYAfUb0K7KMfPkSyh9/wJVLhJo0w92mZUJR1z8Bqv4u\nb2Lmzo1j9Ii4rwN4R45FPnMa+wdzs44VMPPlRy9Vmsh91Qi+/ArKhQuYkgSmgXL4N7St36Hs2RUF\nX55J76J9/gnaju8T72vEeNSdP2BdHz++FSBcqSrBNzrgeitWwGU6nISeaED48Qbo5SuhnPoT+7gh\nqGfjd50Ndw68U+bgav/6HdOxIgUK4Rs6DleHlsKlw2oj0LQF4cfqI188j2PycGRPWgbtYA3uVq/e\n0cEAwNetL/LVK9g+XARA6D/1CLbtjHThDI6xA7M9AKZPX4DtgzlYfo5vVwYZRvrPv0LgjY6YQPKr\nDe64/+jaMxegfbMe/YEHiRQoiGtIL+RL8WkyAP5mbTDKVcb+9gR8/Ydi5syJc2DPGCupbJ+1xwAi\npcuC04V85Hfs40Ym5rMCoUZNCTR+HdPpxvrlGmyz3on7wBm+vxqBTt1As2IfOQj11CkihQvjHTcV\n5eRJ7OPHIKWnoz/8H4JNX8dIScWyeRPW+e/FPGAHGr1G6PUWyCf+xMyVG6xW1K2bsS5eHDdZz3A6\n8X6wEFOzQiAAqop85Ai2VauQf/k5tjucnIx3ylTQNNRdu8Q9IUcOMQ27fl1wWdetQ75xQ5yDV18l\n0KEDobJlMWx/b5mYCS2OHTvGrl27onjC4/FwM841omPHjpQvX/5v173bavfu3axcmd0NpUGDBly8\neJHDhw9jmiZ58+blmWeeoUKFCv9DR/m/p+6B1bugcn39KtdrTYGcxQFQFOVfg9Woqn/ZMixbtogR\nd61aooOaMZaWgkHkixcJV6ggLpDTp2eL6ru9DFkmMHAgeq1aqHv3YubIgZEzZ1YH9fhxYQq9ZQum\ny4V33DgkwDZvHur27dluqKYkYRQujF6lCsEOHTCTkpBu3IiO3C179sR4sxoOB74xYzALFUJbvRpt\n1SokwxACqExngUxxV0qKAEtOJ7aZM9GWL4/LKTOAYM+ehOvVExfcb74R2dUZHNTMDqp84QLygQOE\n6tZF0XVsc+bE5YxBZsenDeHXXkP5/XdMqzUaH4hhoPzxB5Zt21C3bwebDe/EieByYZs9G8sPP8Qe\nY86cRMqUwd+zp4g4vXQJU1WRZBnp7Fksu3YJr9eMv0G9UiV8I0eiHDqEY+LEuF0+0+0m/Oij+Hv3\nRjl6VNwsMjvYkQjysWOoe37EsnMneqlSBAYOxPb222hbt8T/bagq3nnvo5w6iX3M6Fjxkapi5M+P\nv09fzLwpyGdOY+RIBnuW2Eq6dg3l6BGIRNCrV8fdpmVioNqiFUaFijgG9kvcKe7ZGywWHFMSJ0z5\nO3bBzJ0Hx7hR4jjtDvQyZdEfrEWkQkVMt5tI3rxI7iS0T5ajff0FytnYMapephyBzj1x9eyUcF+G\nLONZsQZ3y/gdxswKvNwYo1wFtE8/JvhaM4wSJUEPYV2+EG17lql82rzlOEYO/NvuYNryNbg6to4r\nqtIrVSXQvjNm7tyYAT+2Zdn3Ea/0UmUIvNkPV7dYQ/9wjVoEOnVHunEVx+h+hOs8QaTKAzgmjLjj\nmpnr+vuNQN2zi3C9x7CuXIz1q8QiLM/oqaj792FbvgQQXUbfwOEYTgeuAT2iBvuZ5W/bBaNgMRxD\ns34zkYKF8A8YjmlRcA7omU3sZgCe2Yuw7PkR+zzRKQ3Ve5Rg245IF87jGD4g7jXF374Leq3/YNm8\niXD9J5AuXcQxcmhCIZ2Rmg9v/8FEqt6HpEdwNW2MEmfaYKoqoScaEHrlVcykJLRPV2M6nYSffhbL\nuq+wLcqywzNtNsJ16hJ69jmM1FThhLL8Q5SdO/BPmISZIxnb7FnRzqgpy0TKlSP8ZAP0jAd4SQ+j\n7NpF6MFaqH4/tkmTYu4NmQ4x4erV0WvXRn/kEQxdRy9Y8B+B1MyKRCKsWbOGDz74gCeffJI33ngD\np9MJQDAY5MqVK1y+fJnLly9z5coVnn/++f+VndV79d9b98DqXVj/JnJVuXAB5ehRHMOHxxj4Z5YB\nBLt2Jfzkk6g//oh061YWBzUTVB0+HFWm+0eOBLsd65IlWOLwLE2LBaNECfzt2hF56CGh/LZaRUft\n/PlsHVQQ4MY/dChGxYqoGzZgW7wYKRSKDQYoXpxIgQLi4ulwoOzejW3hwpgOamYFmjcn9OqrIrJ1\n/nyMvHkJ16iBUamSSNxyOITt0+nTmIUKYWoatgUL0L78MqGIJVyrFv4hQ1BOnEC6fl1ws5xOsNmQ\nbt0SKtctW5B+/51gprjr66/FZ/pLCpTpcBApVYrQ888TfvFF5BMnBPA0zajVVqY3a/R76tWLcJ06\naF9+iXXx4qwbUqZFVqVKRB54gPB990GOHBCJIF25Ivi6P/wgxGK33VSN1FS806YhX76MfdSomCQq\n0+kkUrQo4Xr1CLVqhXz0KEiS4IIiIZ88geXnvag//IBy9iyhOnUJ9O6DY8Qw1ERWYzYbnkWLsXy/\nVYQw/PX3I0mYqfnwjhmNhIR09SpGzmSwO277HZ1DPXgAw+kkUqo0rp7dEqeINW+FUb48ziGJ+aXB\nl14h/J+6OPv0TLiOXqo0/lHjcHbvil6hInrdekQKFcJ0ukCWUPf/gmX9l/iHj8PdtllCFwGA9NkL\nsM2fjeXnnxJuY+QvgHf8NFytmmR3pMidh+ArjdBr1sJ0OZFOHUcOBHCOu7O40jtkLOrePVi//PyO\n24UeqS9AZiiIdO4MjsmjYsAeZAC4FV/ifqMJUhxLpswKV7kPf68BGEWLkdT0hYRUj+i6riQ885bh\nbi1sxUxVJdC6PeH6DdBWL8f2F5qDr8cACIVxvBsr3NOLlcDffwiEQzgH90QOBPB3eQszKSf20UPj\nftd6ydL4+w2GQADnoJ6gWfHMXYZt2mS0H2K76eHqNQl07g6edJxD+yJ7PBjJOfHMeh/Lt99ge39u\ndD96xUoEOnfDzJ0H67tvo+3KGp0bgH/EGIwixbGPH02kQiVCzzwHLheWVR+hrV4V9zrnb9Oe8Esv\nI129iul0oRw+hG3ee3H5qCDCTbzzPkC+cgXTYkG6eQPLunVoa9fGTfeLFCyId9p05OvXkW7cEDx5\npxMpFELdtQtt7dooz9yUJIKvv06gdWtCZcqIv9d/WIZh8OWXXzJ//nzq1atHu3btcP8Ld4B79f/v\nugdW78L6O7Bqmmb0PykSQbl+HTktTSQvXb2KfPKkMJM/cQJ/r16QMyfaypUxNk3R9RwOoS5v1Qr5\nxAkBVmw2ARr+/BNt2zbUDLGRIcsE+vRBr1VLqOXnzUPK4GGZshztoEZq1kQvUwajSBEB4tLSsK5d\nKwIG4ijmswmhpk2DUEh0UGvWzO7NapqgaZA7N9qiRdiWLEk4xtTLlsU3ejRyWhrq99+LvOtcuQT4\nzKQm7NqFtmkToQYNhJ3Wnj3xxV2AmZJCuGZN/IMHo5w/jxkOi+5wKITy229idL9rV3RsF6pbl0CP\nHijHjmGfOhU5IxfbVBQRmlC5MpEaNdALFMCoUEF4FIbDaGvWCKFYPBFcnToE3noL9cAB7JMnI6Wn\nC7FYmTLCWSCTG5szZzT6Vfv4Y7TVq1H+/DPm5m3YbHhnzEAyTRzDh2cLWTBtNgGQy5cnXKsWkcce\nQzp9GkwDSZIF7/aXvYJHe+yYMD3/Tx0BZvv3Tdy1t9vxLFmKtnYNtmWx9lSmqmIUKoRv1FikcEh8\nRrdLCKo0Den6NdSDB1B/3EUkNR/6U0/j7N4lIQgNPfwfQq3a4OzUNuFDipGSimfWPNytmsUFZqbd\njl6xEt4Jk1FOnhDHIoHlx51YP1+FfFucbPD5V4iUr4hjYmLVvAF4Vn2Jq12LGGug2yuSPz/eWR8g\nnz2NkTcvyrHD2N97N8bMXi9XiUC7rrh6dU64FiBA1uwFuFs0RgqHRYznGx0w8qWirfoQ25dZ1JD0\n6fOxLl2A9mN8LnJ0TVnGs2It9snjCL7WDDM1BduMKVj27o7/uVd8gbN7J5QL2WkypqIQaNmGcINn\n0dZ+gm3VMgKvtSRSunzC8Ijo569YGX/vARg5cqD++jPO0X/vmqJXrop32BiM1Hy42rXCcjh+wEV0\n+/IV8ffsg5EnL1LEwNm9c0JhmulyE2jfifCDD6H+8hPS0T8IN22B7b05aN9mt+IyHQ6CL79C+PEn\nMW1WrIsWYP1mA4GXXyXUrAXa2jVYlywWyn5JQq9SlfCrDYkUL46pqmhffYW2cjm43XinTEWKmNgm\nTkQ9Kv7+jDx5CNerh163nrgmWK0ov/yMum0bga5dkS9fwTF+XEzAipGUJNxP6j1CpGhRjNKlMQyD\ncLFi/wqkmqbJhg0bmDNnDrVq1aJDhw73OqX36l/XPbB6F1aiyFXTNDHuYHidbQ3TRL51CyU9Heny\nZeRr10SM6s6dqAcOIJ8+jWmaBN98U/BRd+3CPnt2NkN5U9MwSpZEr1aNUJ06RB54AOnqVXGxO3AA\nyw8/CP/Sv4inQvXqEejeXdihTJ2KdO6c6KBWrBhNtzKdTkHCd7kwc+VC27oV+5AhyAk4mZFChQTV\nwDSxrlxJpEABjMqVox3U24G1brejN2uG8vvvQtx1NVZIY0oSkVKlhLhLlsXnstmyvFl/+inqzSqT\nobgdMQL51i0RDHBbHrbpdqOXLYtevboQeVWvLqxq7HaUXbuwbN4sOqh/Ea4ZuXMLWoCmYZs9G3XX\nLsw8ecQaNWoQKVUqSikwnU6MPHlQjx3D+eabMR3S6JqpqXinTEHKGOVJoVCWRVbhwuJ8W60C9Fut\nkCcP9t690XbHAgvI4K9OnIhZoAD24cOiojbTYsEoXFjQTe67j0ix4kSqVEG6cQPJ7xed0Z8zgGzG\nOQQIV6+Of8hQHH16o/6ZgCdsseBZ+iHaV19iW7ok+/cGmKn5iJQqhb/nW4CJlJ6WIVyzIJ0/h/rT\nj1i2b0U5cwa9bDn8Q0bgeqN5wocaw+XCs/QjXG1aJDyvAJ53ZmHZvi2aymU6XejVqhF+7AnRgXW5\nMP1eKF4S94tPxhXTZFb6rA+wLl0YYwCf7bhkGc+qtbg6tkG+clnYHlW9n9BrTYkUKYbkTcM+fxby\ngV/wrPwSd6vXEgYgQJZwzPlmB5SL2YGJabMRbNSUcP0G4E1H/Wk3Zv6CCaNub6+0hR/hmDIBdZ9I\n0zLdbvwdu6FXr4G25Vu0BVk59+nzl2ObOQ3L3jtwWmWZ4OutCDRuCqqFpGcfQ76DnVdmeUZNRIoY\nGKn5wKZhHzsC9c/EaVz+Zq2J1K6Hdfa7BNt0wMybF+ucd9G2x+cqG5qGd94ilP37MXPlJlKyJOrO\nHdhmTo/rMgAQKVAQz/xFostps6Ft/AZtwfsJtzddbrwjRxOpVBlUFe3T1VgXLojrSgLiNxh4+WWC\nXd+M/u1pn65GW706rkgLQC9TFt+MGSIMRRL8aUwTdc+PaGvWZGsmmLJMsEULAi1aEipdWnDS/2GZ\npsmmTZuYOXMm999/P507dyZXrlz/+P336l7dXvfA6l1at1t2/BuQ+nclAfLNmyi3bgkPS0lC/f57\nLLt2of7yC/KJE9m4g+FatQj06YN08SK2t99GPX5cdAaLFhV8z+rVMVJSMJxOzHz5wOFAvngRZ//+\nKIfjW8sYefMKIZTNhrZ0KbLHIzqoZcpEwZkUDqMcPAhXrhB+6inUkyeF9dQdREu+yZMxSpQQ4q5M\n3qimIWeO3DdtQr50CaNAATwTJiAZBrb33svGRxVgKDXqOxuuX1+Y7QPS1asCxG7dirJnTzbhRVSI\nVaoU2qefon30EaiqAPu3ebOaDocANUlJSBYL9r590eJwV+E2+sbjj2P59lss27ejV6sWdWDIdAKQ\nz59HPnSI8GOPoVy+jGPs2MTnSZbxjxqFUbo02rJlmDlyiPVu4+xKN2+i7t+PoWnotR/G/u4MtM2b\nEv6m/F27En7kERyjRqMe2C9+H4UKESlbTnzuokUwHE6MkiWRZBnl119Qd+9C3fEDyvHj2TqieunS\n+KZOwzGgP+rvv8XdnwF435uP8sch7NPezvKYVRQBoCtURK9eA71aNbDawOsBTzqWX37GsnUT8sGs\njrWhqnhWrcHZrWNC4SCAZ/xE1CNHsC38IOE2Ro5k0pcsx7pi2f9h77yjoyr3r/85dUoqhEAChBqK\n9F6kiAgW7Ip67b0Cil4EUbAgvYSODRGUJvYC0kNvgiIC0gJI76EkkymnvH88M5MMmUH53ea9b/Za\nrruW13lyzsmB2c9+9ndvzBatTxASiwAAIABJREFUhIql6yi/bEL/bBbqAeE3LXjwUezSZXCPHhFz\nLYAL02bjzBqOtjl6jahZoSL+e+7Dd8NNSPl5OD6ejP7tl1GPkgEujP8Ax6ez0FfE/l0C+K7uhO+F\nl6EgH3XzJpwTRkU9PgbIGzoWbeVyHN8UH9azZRn/Tbfh73o30plT2KaJtmEdzs9mXfLnA/iuv5HA\nzXegffcN/q73gM9L3MD+EQp2xL2Nex9t/Tqc06YAYKWWpeD5npi1rkD/fBbOLyOtBXnDRiOfPI1r\n6MDC9ycuHu/jTxK4si3K1l9xjRwcttT427TD+3wv3K/1Qd0p/l6zJYnANZ3w3XMfxMXjeH8S+nLh\nARbB/CMhuRTuV/sgnzqFrWn4r72OwC23YZUuLTY+778TfrZGZg08g4aKbNaR4t0ItGtP4KabMMuW\nA68X58yZqIsXIiM2WfmjRoOs4Bo8CDUnB6t0aQLt2mNcfTVWmTLCg795M46ZMwDwDB2GcvgwrsGD\nIjbxdny8UGyv7oBZpQokJmLrDqyEhP8TSV25ciVjx46lTp06dOvWjdTU1D/9+RKUIBpKyOpfEBs2\nbGDjxo3UqFGDmjVrUqlSpT/tYf2/QpIk5PPnUc6dQzp9Gun0aezMTKSCAuJ690b5+eeoVXpWqVKC\neCYloc+Ygbp5M2a9emIAqmLFwon53Fykw4cxGjcWw11ZWRHRUxFrAt4+fTDat0fZvFlEa4UKBgBl\n1y4xtLRyJbhc5A8dCm43jqlTw/WAIdiyLI7cGzbEf889WBkZSGfOiOP7I0dEPNZF1gQL8P797yLi\nZfFinB9+iOTzieP2kDUh6PkNNXeRlIQ+axbO8eNjfrH7OnXC160byo4dOD/+GKN6dcxgskBRX6y8\nebM4cktLwzlrFvpXX8U8vjYaNcIzaJA44j9zBqtChXAuK/n5qMHiA3nzZrwDBmBWr45z4kT05cuj\nrmcD3kcfFQNjwcG6kAVDUhSkAwfQ1oshL7NCBQr6v47j88/Rp38S8xjed911+J59Due4sWjLlwtC\nWbu2UHsrZmDHubGdLuzkJKzSpXGNG4u+cEHUuDMrOZm8qR/jHDvm0gT6ue6Y9eoR1/N5JL8/2Lom\nNiBmZg2hVLvd2OnpqGtX4/xoCsrO36LeQ37ffsh5ebjGj4n586zERPI+nkncM0+hFCFUtq6LGKHr\nbsCsUgUrtSx2mTK4X38FdXl2TGKZN3AY2i+bccy5NLHLGzwC9bftOL78HP9Nt+C/+hrs5GTUjetw\nfvhueNCn4NGnseMTcI8decn1rLLlyBv/PgkP3QcFHjGdft8DWGXKoM/7Bn3Wx+FrLniqB7bD+Yek\nG+DCyHGQVh5bltC//BT9yzkx7913020Err2RuO5PhyfrzYxKeLu/gFmlKo7Zn+D4TgxjWUD+R7PR\nZ8/EMffbYmvZmobvvgcJXHc90v59uEYNxjNxCvqs6cUqS8OfAYw27fA+8rjwbvv8YhP4xmvFfOnh\nzyQk4H3wEYwr22DLClZiIu4Rw2K+o7aiELi6I/477sQsl4admIiyby9xL/eKmZphlS2L76abReVp\nterYLheuCePRp06N+SxtTcPf5Ua8ffqI0zRdQ8r3oK5ZjePrr4sd/duShO+BB0Xu82WSVIC1a9cy\nZswYqlSpQo8ePUhPT7+sz5egBLFQQlb/gjhz5gybN29m9+7d7Nq1iwMHDmAYBunp6dSsWTP8T9Wq\nVf/locmSJCHl5aGcPYucmyt8sSdPIv/2G0anTki5ubiGDkXduTPq5y3A/+STYT8ofj9WlSqFCqrH\ng/LLL+jZ2Ug5ORQMGoRdpgz6zJno331XjKTZTidm9er4//Y3Ap06ieEuXUeyLEGkVq0Sx/dBH2D4\n53fpgrp2bdjqEI7HqldPhPlXriyKAdLThRq2YweuMWOQfyoe7QJgNG5MwauvCsV5/HjQdWEDaNhQ\nWBNcLiRNgwMHkGwbs2ZN9CVLcL77brjNptizKlWK/AkTQJJQtmwRdokgUSQQQPntN7QVK1DXrsVo\n1w5vt26o27bhHDkS+VzxAHyrdGkCDRrgfestkcHo8YS/fOScHJHmsHJl+MvRd+ON+J58Em3RItHc\ndXEdpKZhVamC/9pr8d9/P3JODshyMHvVK3y7q1eJIa9AQFS4vvMO6ubNuIYPj+0trloVT9Zo9Lnf\no61ciVG/PkbjJlipZcAdh+10iMzcUycxmzQl/pGHUGMUC1hA/nsfoG7fjnPs6NjDVNWq4Rk9FteA\nt8DtItC6DVa1aoXJGSeOo61aiVG5MrKq4h4yMMZKQRvB9E+Je/apS4frN2uG96XeuF9/DX+HqzGb\nNsNKSkLy+dAW/iBUUZ8P770PYFXLxD3wzZhrAXh6vQJ+ERRfFLaiYLRuK4hQejoUFGC7XCQ+cNcl\nY6+s+HjypkW3Q9i6jv+W2/HfeJNotvtxDXbVGsS9GHvwLYT83q8imTbuEUOwHQ58d95F4NobsC0D\n94jBqLsL/+7w3tYV46prhAc5mr9e1wX57HwdHDmEWS0T96jhl7RThOC78y68Tz6DVOBF//gj9K8+\nj0nyAIwqVfFkTUDZvhWrchVRbzomK2b2qhUfT/6k91H27AFL/JnHttA/+Rht4YLiEVGAZ+gI7HLl\ncEz/hEDHa7AyMkDT0LKXos+YHnH8bwEFAwdhVamGc8Rw5HPn8He+FrNpE6zEJCTDQFuyBP2Lz5HP\nn8dKTyd/5CjkU6dwDRoY9sxbyckYzZoJL2qFCmKYKhBA3rmDQPurBEm9DE8qwMaNG8nKyiI9PZ0X\nXniBChUqXNbnS1CCP0IJWf0vgW3bHDt2jN27d4f/2bdvH36/n9TU1AgSW716dZyXESXyf4Xs9SKH\nSOzp08IXu22bGO46eJCCPn2wy5cX0VOffx41f9BKTsZ/0034nn22cLhL05AMA3n7dvTlyyPC/L33\n3ov/7rtFAsCYMWGSZqsqVpUq4si9aVPM9HSsmjXFtHxBAY7p09EWL0aJcjweznw9f16seexYuGAg\nFI9lO52CbHk8WNWqoa5cKYamYhUoOJ14Bg3CrlIFddkyrPLlRW1sXFyx2lgcDvHzc3NF2UGUzFc7\nPl54bF9+GTstDfnYMfGcglW22urVQkENkfTkZPJHjgRNwzluHNqmTYVrhapjg7FdRosWYBjCMrFz\nJ9qGDajLliHv3h2ZY1u+PHlZWSjHjuF6++1wCDkEKxZr1sRo2lQkFjRvLtT0QAB5317UDT+irVge\nMcEs8lzHgsOB+5U+UQk3BKOypk5FPnYcec8erCtqYyUGNwSqgrR/P9r6tSibNuEZM+4PVVfvnV0J\n3HY78c8+E3Wi3wasjAzyx09EOnsWTFOo+raN+stm9AXzkH/dIo5i3W7yZn5GXPdnYk5ngxg88z31\nDPFPPFrshMJKSSHQvgNG+6swatTETkrCMWc2jtnTkc+cjrpewSOPY1eugvvNS9epBuo3xNu3P8ov\nm8VpgKahf/81+hefRtpYVJW82V8T9/xzKAejbwRC8N10C75HnhC984qMY+pk9GXRn7enTz8wDNwj\nikeKWWnpeJ98BqNuPZTftiLvy8Fs0lIQ4D/wqFpp6cILun8fVtmyqGtW4XxnQswa1IIHHsa4+hri\nuz8Hlonvjq4EOl+LrWk4J78XPr4PX3fPXlhX1MH9Us/wn3GrQgW8Dz+CWbc+FHhwjRuNuvVXsf4T\nT2NcfQ2uvq+g7ttbeJ2lSuG7/Q6Mtu2wExLE0f/k9/Hffgf+27viHDcGfdmyiJ9tu1wE2rfHf0MX\nEUVlGHDuPFZaGq7x44r99+GflZREoE0b/LfcIvzjpomycxf655+jLl4Uvb0L8He9i4Jnn8VfvRq2\n4/K+NzZv3kxWVhbJycn07NmTypUrX9bnS1CCP4sSsvpfDtu2OX36NLt27QorsXv37sXn85GcnBxB\nYjMzM8N5dv9KSH4/yoULyHl5wk95+rQ4ul+7FmX79jDJ8d5xB/4HH0TZtk0MQhUhP3aRMH+jYUNB\nfs6dC7axrEZbtgx1xYpiQwRmRgaeIUMgEBBDSxs3Cv9kgwaCfKanQ5EcVKt8eZQdO3D37o0SZRAL\ngj7P117DatwYdYGY5LXq1AkrqEgSyp49aKtWIe/cief110Xm7MSJaBs2FFvPliTs8uUpeOIJjGuu\nESRd14VCGaqNDR7dy6Gf368fVsOGwg87a1ZhHammYVWtKohnkyYiV7d8eWxAPnQIfcEC0QIWxXIR\nrnhdsADn5MkQCGCXLy8G4Zo1w6pcWRyXJyRgJyVBQgKuIUNEOUKU41ALKHjrLczatXGNGoW2YUPY\nhmGG1gzWNJrlykFiIsr2bTgnT0bZsCHql6n37rvx/+1e3G++IQoPLn6WQbXX83Jv7LQ0pBPHBbHU\nQxuCtWjZS8NEMm/oCGSfF9ebr8dOBnC7yft4Oo5PPsbxTWEMlB0XJ55N23aYNWuJzUfZcsg7d+CY\nM1sc60e5B9911+O/62+i9OASAfzee+/HaHcVcb3/TqBpcwLXX4+VXh7b5ULZ+guOmZ+g7t+H78Zb\nCVzTibgXe1xS1Qw0a4H3+ZeIf/zhcJmEHReP/4YbCFzTGSslBWX3ThwfTMIzcjzuAW+gbi3+jCPu\npcvNBG69nbhnnkQyTazkZHz33IvRug22ruGYMQ1twTxkIP+V/kiBQFSiWhQ2kD9mAlZaeZBA3bgB\n56TxUQPuAfwtW+F9sTfxzzyBfOYMtiwT6NAR/113Y6WUQV/wA/q0D5EtSyjt498VmcDDhxZPw0hM\nxHf/gxitrwTLwjHlfbzde6J//z3OaR/FvGarfAW8Dz1MoGUr7JQU1C1bcHd79pJKra1peB9/Av/d\n9yBdyIOzuejffI3+zTcxB668Xbvif/BhtGXZWFWqYKWUEZvKX7fgmDMnYtDTio8nf8xYJGycAwag\nHDwo2vjatMVo3gw7WeRky0ePoi1cIIannn3uT4f5F8W2bdsYNWoUDoeDnj17kpmZeVmfL0EJLhcl\nZPV/GLm5uezZsydMZHfv3k1BQQHx8fFhP2ytWrWoUaMGiYmJ//LrCcdsnTsnPKMJCWhffSWOtrdu\nRTp6NOLLxCpfnrzBg5EkCed776GtWYPtcGBWr1545F6qlPBoJiZiJyUJj22PHqi//Rb1GiL8qEuX\nomzbJhIKqlYV6xSxJigbN+K7/36kuDgcH36ItnRpVHJgOxz4b78d77PPouzdKywGoVrVw4cjUhMs\nwP/00/ivvx5txQphCygyNV60EteoUwezXj2R0GDbqMuWFVOaQzCaNKHg1VeRDx4UR+7HjgniWa+e\nyLCtWFEMwTmdEEwW0BcuxPXGG7EnmTMyyB8+HDk3F9fo0VgJCYJw1q0bUR3L778j6TpmlSq4xo9H\nX7gw5jvgb9cOb69eaIsW4Zg5E7NaNbHmFVcUrqkocPQoZoMGaNnZuN8eEJtYpqeTN3GisC68807h\nsExwQ2DUr4/RoiVGrVrYFSuAz4984HehHi9ZVIzEG3Xr4Rk0GPdLL6LuLR6xFoLvhhvxP/Iocc93\nx05IJNC2LUaTJthJydhuN/Lxo2hLFmM5nZgdriau2zMxq3QBPL36YCcl4e73avFcWlXFaNiQQJeb\nCFzZFpxOlJ9+xDl7BupPm6Ku52/TDt8TzxD/ZHElN7wuolmpIGss0tGjYFnoc78ReZ9RNw73YrRt\nT9zz3aLei52QII74r+qAWaEicm4u8Q/eE/P9CiFvzEQR7zZutKgKbdMO3113Y6WliUGn8WOQzwmr\nSsETT2M2bExczx5R/aO2puG/oQv+m2/DSkrCKlsO98A3cSxedMlrACh46lkC13dByrsQjIT6Hn32\nzKjXLwaohkOpUriGDyfQrh2BNm1EK97+fTg/eD8ius1KTCR//CTkY0dxD3gLKS9PKOqdOhO46iqs\nUqWRAgG0uXPRv/oCo3ETvK+8grZwEc733o0YerU1DaN+AwLXX4eZmSlOGZKSICEed88X0WPUHoP4\nnfsefxxvj+cJJCVdNknduXMnI0cK3/OLL75IrVq1LuvzJSjB/xUlZPX/Q1y4cCHCTrB7924uXLiA\ny+UKk9jQ//47okYk2xbq6/nzSGfOIJ8+jV2hArhcuHv3Rl2zJipZCU/Ld+qEtmoV+ty5gpw0bVp4\n5K5pyMeOIf/0E0br1kjx8ejTp6PPnRtTlQpceSUFb76JfPAgeL2iPMHpRLIs5GCeqrp6NbJhFNoS\nNm7ENW5cRD6rLcvh1IRAy5bC43viBDid4frTaKqnUbkyBUOGIHk8IoFh+/YIpdmqWzes6toJCdil\nSokEhu7do9ocQBzzet5+G7t6ddHwdfy4iMcqkmEbqtdVdu7Ed+utKIcP4x4yBPn48ehrEhyEa90a\nbckSrLQ0rLJlhXLtcIgIsE2bRMuZbVMweHChfzWWb9ftJn/CBCTTRFu0CKNRI6zU1MI1z5xB27QR\ndflyvH+7FypXxt375ajDWCHk9++PVT2TuN4vI504IWLU6tfHaNUqOOAVh+0SVbF26RQSHn1I+A5j\nIG/YCCTDwN3vteikDbAqVSJ//ARRExwIYLvjkHLPoGUvQZ8/L8I+kjdytIh5Gxd7gEvcxxvgjsP9\n6itY1TPxd7kRo3497IREpPPncHzzJerC+RhXXY3v/oeJf+qxSyq5VqlS5H30Ce5+r4oUh/gE/Nde\nK1TXMinIJ0/hnPoB6s8/UfDok+JYvNeLl/a9AvmTp6L+uB75+HEC114v1srZg2vSeJTDhYkLliyT\nN30Ojhmf4Pjum+LPUZIwmrfAf+/9mBUqYMUnoG75hbhXXv5Dn6z39q7477ob/ZuvRdNS6RTkPbtw\nTZoYcQ0QLLH44CPUnzbhyhqFZNvYcXH4O3UmcP0NWGXKIB84gPPdSah7duNv3Rpv776iLW9R5MbM\nBqxatfF17YpZsxa224VtWUiqhrt3r6gZ00V/H7777sd/731Ip04hGQHkn37G8cXnEQpq0WddMGgQ\nVtVqOCdOxEpKwmjXTjT6JcQj+fyioOXbb1AOHSLQpi2ePn3wX3EFVnz8HzzBSOTk5JCVlYXH46Fn\nz57Uq1fvsj5fghL8oyghqyUIw+PxkJOTE2EpOHv2LLquU7169bCdoFatWpQpUwZJ+qOvjD9G6DWL\n9rrJkoRy9mwEiZWPHUNdvx6jTRusihVxzJiB/vXXsafla9bEM2KEGAo7cqTQBhAiPj/+GE4D8N16\nK75HHhFDS1lZ0dueatTA37o1gUcfFdms4sGh7N4tEgpWrIgciihXTqQlKIqoWF2/PlxbWFT1tOPi\nsFJTBcFWVdz9+6MuXhz1WNGCcD6utmgR+rJlxeKxCEVa/fwzgTZtkB0OYUtYG1t18V91Fd6+fUXk\nmGWJpAO3WyjEBw+irV+Plp0Nx49T0K8fZqNGOKZNE4NwF/9eEe1k/i5d8D3+OPKePaAowuoQCAg/\n8ooVYZXYkmU8Q4ZgV6yIa9Ag1O3FA9pDaxZ064bZsqUYrnM6sV1OJK8PZcsWtOXLUDZuRLYsoZIO\nHoRj6lQcX8Wu8jQqVcIzbhzavHkov/+O0fpK0aQWHwe6A/nwIbRVK1HWr8czdhyOqdNwfBu7Jcoq\nVYq8KVNxfFz4c8VAX3kCrVqJd7dMGaz4eOwyZVB27yKu98th9TDa7zv/o49FI9iU6NFZVnp5/J07\n43v4EfAHkHLPoGcvQf/8s6jrGjVr4hk6gvinn0I+EX0zYlapgv/2O/HfejuYJurKZTimTkH9PXrl\nq8irnYVz1Aj0lYVZpTZg1quP7+57sKpXB8tC/e4b/A88RFz/V6PaOyLWTUkh74OP0L/6Cqt6dcxq\nVbFlBf3br9E/nxPpvQXy3/8QZe9eXEMGh/9eCF/DPX/DrFYNybbQZ88Uns1HnsDdtzfq7uiZrDZg\n1axFwQMPYlx9NZJto33/Pc6pH8XcyAH4utyI76mn0L/5BjOzBlZFMcwk783B+emnEc18VmIieWPH\nIV+4gPvNN8WGXdcx6tcn0Llz0DufIFqlVq7ATC2L1aiRSPbIjl6ZayUlYTRpgu/ppzHq1sV0OjEv\nszHq999/Z9SoUeTm5tKzZ08aNWp0WZ8vQQn+WSghqyX4Q3i9Xvbt2xdhJzh58iSqqlK1atUIX2x6\nevqfIrFnz56Naj0IffZSa1wcsyWfOYN8/LjIQN20CTknB3/Hjvieeko0YmVlFVPeQmkAgXr18Pbt\nKzx9+fkgSXDhAtrPP4sWqV9+KfxCKVVKxGTFx0fYAkIDS4GmTTEbN8ZKTg5HSOF245g2DcfMmRGe\n3IjnG6qNXb8e5yefYFatGoxYyozInZW3bcOsUgU7ORnnjBno33wTm6RXrYpnzBjRaHbkiPCIhibd\nQ4pnsPQgcMst+B59VKjDY8dGFEMA4VzdQJMmeHv1Qj52TAxkSRLSmTOFa+3cGX5WRp06FAwYgLxv\nH67BgyNamuyEBIwaNYSVo25djBYthAIJKMHaWG3ZsmIRPoGmTSno1w8tOxvnxIkRR6NWUlI4Vsxo\n0ACzfn2k8+eRzp9H2Sriu9TVqyO8thbgGTESkpJw9+kdtUkqpI57+vXHTk1FOn0K2+kCVUHZuRNt\nyRLUVSvDR8W+m27G9/AjxD3fIyLC6mIEGjWm4K23cI7Owk5IFIpYaip2XDzShfNiGnzu92Bb5H08\nA+fwYeirL1EgAORPniL831mjICGBQJs2BK7pJOoz3W6U7dtwzJ6BVbESvkceI/7pJ8LPPeqaqkre\nxzPQf5iHY/onIoLrllsxq1XDdrtRf9qEc9pHyMeOCvI7bBRxz3cLV3PGgu/ue/Ddez/SyZPYSUnI\nR4/i/Pgj1J+L58n6br4F//0PEdejWwQxtBMS8F93PYFOnbFKl0Y+dBB10QL8z3TDNejtqF7xojAr\nVCDvkxnIR46IDdSpUzg+nSWa+qL89wVPPUOgY0fc/fuJDU3z5vi73Cg2mm43ypYtOD75GHXfPsxK\nlcjPGiOKVkZnRajbtiRh1ayF/4brMerVE0f4pZIhPoG47t0iBiGjoeCZZwjcdDPKjh3CAhUXJ8j/\nTz+hz50bsckzatfGM2AA/gYNMC+zMerQoUOMGTOGw4cP88ILL9C8efPL+vy/A7/++iuLFy/m8OHD\nNGnShPvuuw8A0zSZM2cOmzdvxu12c+utt5aQ7P8BlJDVEvyfEQgE+P333yOU2KNHjyLLMpUrV46w\nE2RkZCBJEjt37iQ7O5sdO3bw2muvUaZMGeDPkdQ/Qjhm6/x5ET6fk4N89CjK5s1o69ej7N4d9oda\niYmimSk5Gce0aWjz54fVQZHJeUWYMJqVKkFCArjdKKtX45gzR9SqRjkC9t5xB/4HHkD95Rec48dj\nJyeL4aemTcXxnNsNTiecOIHkcmGVLYtj1iwcM2dGkK+isFJTyc8S8UTqjz9iVa9efLgrWIlr1q9P\nQe/eIst2xAhBLIsgVHoQqFMHX69eoGlw9qzwEBcUBNXJyNIDKz6e/BEjIDER54QJYXU2HP8VTE6w\nqlQRgeIuF7hcaD/8gPbDD2J46qJnZQHefv0wGjXC8eGH6D/8AJpWmFLQtGlhiUJwwEvy+Yjv0SN2\n2YQsi99pWhqut99G3bUL2+3GzMwk0KJFROOZ7XZjp6WhffcdrhHDY7ZNhWK1tHlzcX7wQaEn1uEQ\ntoxWrTEbipIGq0oVUBQcn32GNm9uzLrZvCFDwB1HXJ/eUe0QVrlyBFq0xPfEE6A7wOtFyj2NtmwZ\n+vffFSPVVvny5L3zPs6hQ9DXRC+YsBUFo149PFmjkXNzRVXz+fNo875Hn/t9sSl6I7MGnpGjcfeN\nXs5gqypG02b4b76FQKtW4HCiZS/BMWVybOUV8Iwdj3z2HK43Xhf1oYBVrRr+227HqFcfOzEBZdcu\n9I8m4+v5EvLpM7jeeuOSfl8byHvvA4iPB58fOyEeec8enJ9Mi6rQe+97AP9tt+Hu2xd1j1BTzYw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lT/qqWqeEaMEJuat99GPnNGDA22bVu4+VBVpD17UJcvx9+lC1KpUuENUDTYmoZZuzae0aMx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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f1a23301518>"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The result is clearly a 3D bell shaped curve. We can see that the gaussian is centered around (2,7), and that the probability density quickly drops away in all directions. On the sides of the plot I have drawn the Gaussians for $x$ in greens and for $y$ in orange.\n",
      "\n",
      "As beautiful as this is, it is perhaps a bit hard to get useful information. For example, it is not easy to tell if $x$ and $y$ both have the same variance or not. So for most of the rest of this book we will display multidimensional Gaussian using contour plots. I will use some helper functions in `stats.py` to plot them. If you are interested in linear algebra go ahead and look at the code used to produce these contours, otherwise feel free to ignore it."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import stats\n",
      "\n",
      "P = np.array([[2, 0], [0, 2]])\n",
      "plt.subplot(131)\n",
      "stats.plot_covariance_ellipse((2, 7), cov=P, facecolor='g', alpha=0.2, \n",
      "                              title='|2 0|\\n|0 2|', axis_equal=False)\n",
      "plt.ylim((4, 10))\n",
      "plt.gca().set_aspect('equal', adjustable='box')\n",
      "\n",
      "plt.subplot(132)\n",
      "P = np.array([[2, 0], [0, 9]])\n",
      "plt.ylim((4, 10))\n",
      "plt.gca().set_aspect('equal', adjustable='box')\n",
      "stats.plot_covariance_ellipse((2, 7), P,  facecolor='g', alpha=0.2, \n",
      "                              axis_equal=False, title='|2 0|\\n|0 9|')\n",
      "\n",
      "plt.subplot(133)\n",
      "P = np.array([[2, 1.2], [1.2, 2]])\n",
      "plt.ylim((4, 10))\n",
      "plt.gca().set_aspect('equal', adjustable='box')\n",
      "stats.plot_covariance_ellipse((2, 7), P,  facecolor='g', alpha=0.2, \n",
      "                              axis_equal=False, title='|2 1.2|\\n|1.2 2|')\n",
      "\n",
      "plt.tight_layout()\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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lfsg1APMN0SjoRr5Zc0Gl6zruvvtuXH/99firv/orXH755TjttNNQLpcP+b4/\n+7M/O+TftVptrac8YQeq216cqx/OO6rn5nPuvm3bth28Kzs5OYlHH320J+d9qRPNNcBw55udiwb2\nVvdCz/swmvHBkRKjaXT1vEeS1rlH/TknicBK00UuzqKgRshq3d2DrJf5ph9yDdDf+Yafeb3F5zy8\n5+5GvllXNj733HPx4x//GED7f8AXvvAFnHnmmesOiojopUY914RRAsPxYEc2pgocnRpVsiyhmFdg\nBhbqVgkbJ4tphzSURj3fENHqrWtV8zPPPAPf99FoNPAXf/EXeMtb3oItW7Z0KjYiIgDMNXXLg+Vb\nyGclKNzId6SV8yos30TT9g9b70OdMer5hohWb10F1T333IMNGzbg5JNPRpIkuPPOOzsVFxHRQaOe\naxotD2ZooVTo7hQv6n9ZXQGUCJbvwHSCtMMZSqOeb4ho9db16XzjjTfixhtv7FQsRERHNMq5puUG\nsDwHkfBRyObTDof6QKWQgekYqFtlVArcj6zTRjnfENHacCMTIqI+Vrc8GIGJCkenaL9SXkUrbMF0\nfIRRknY4REQjjwUVEVGfipMEhu2jxel+9BKKIiGflWEGFhotL+1wiIhGHgsqIqI+1Wz5MIMWdE1C\nRmW6pheViyrMwETdYkFFRJQ2fkITEfWpuuXBDAyUOTpFL1PIqoiED8tzYHth2uEQEY00FlRERH3I\nDSKYrocg8VDMKWmHQ32oXFD370nFUSoiojSxoCIi6kN1y4MZmijmFEgS956iw7ULKhPNloc4YXMK\nIqK0sKAiIuozQoj2+infRLmQSTsc6lMZVUZWl2AGLTRbftrhEBGNLBZURER9xnQCWL4NVU2ga0zT\ndHTlfHuUqsGCiogoNfykJiLqM6YToBW2UMyzGQUdWyGnwI892F6AKOa0PyKiNLCgIiLqI0IImE4A\nO7RRYDMKOg5ZlpDVJLRCG6YTpB0OEdFIYkFFRNRHbC+EHTiQlRga956iE1DIKbCDFgyb0/6IiNLA\nT2sioj5iHJjul+N0PzoxxZwKO7bRcgMkiUg7HCKikcOCioioj5h2ADvgdD86cYoiQVcltEIHpstp\nf0REvcaCioioT7h+hJbvIpEiZDUWVHTiinkVdmjD5LQ/IqKeY0FFRNQnDMeHHdkocnSKVqmQU9AK\nWjCdEEJw2h8RUS+xoCIi6hOmfaC7H9dP0epkVBmqKuCEDlpumHY4REQjhQUVEVEf8MMYLd9DJHzk\ndKZmWr31iE0OAAAgAElEQVRiTkErbLF9OhFRj/FTm4ioD5iODzuwkdcVSJKUdjg0gAo5FXZgw3C4\njoqIqJdYUBER9QHDDtCKWuzuR2umazKEHMH2PTgep/0REfUKCyoiopSFUQLL9eHFHvJZFlS0doWc\nAjuyYXDaHxFRz7CgIiJKmeW2m1HkdBmyzOl+tHbFnLq/2x+n/RER9QoLKiKilDVtH3bIdum0fjld\nQSR8tDwfXhClHQ4R0UhgQUVElKIkEWg5AZzYRiHLdum0foWcCie0Ybmc9kdE1AssqIiIUuT4IbzY\nQ0aRoCic7kfrl9cVOJHL/aiIiHqEBRURUYpaXggncpHLMh1TZ+SyMpzIge1xyh8RUS/wE5yIKEUt\nN4QbOcjrXD9FnaEqMlRFwA1duD6LKiKibmNBRUSUkiQRcLwQXuQhy4KKOiiXVeBGLloe11EREXUb\nCyoiopQ4fgg39qBlJChsl04dlNMUuJHHdVRERD3AgoqIKCXt9VMOchydog576ToqIUTa4RARDTX2\n6KXDJIlAGCeI4qT9Z9T+M4xihHGCJBEQAhBo/1kxY0iSBMNoQoIESQJkWUJGkaEqMjLq/j/3/1tT\nFW5eSoT966dCB+MF3tuiznr5Oqp8NpN2SETUJUEUIwhj+Pv/O3Ctloj912vixb8DB/LDi9dlqiJB\nVWSUyjG0DG/wrQULqhEXRDEcP4LrR3CD9p9hHCNKIsRi/59JhEhEiJN4/58JBAQgBAQESkEJANCy\nWoAkQYIEWZKgSioUWUVGbv+pyioUSYEqq1BlBTldQU5TkdNV5PUMdL6JaYQcWD/lxz5yei7tcGgI\nvbiOKmRBRTQEkkTA9kLYfggviOGHEcIoQRCHCOIQYRIiTAKEcYQECYADhZTYfxM8AQAoL7keU2QF\nqtS+Lqu5CXKahsh3UMhmUMjy2uxEsaAaIXGSwHLDQ4onPwrgRR782IcX+/AjHwni9t0Kub0vjrp/\nfxxt/x0MWZYgSzKwf5BpbEyHEICR97C/zkKcCMRxiCgJEMYJvFggCgSiuP2fBBlZVYeu6NCVLLJK\nFrqqHVJklXIaVIV37mk42d6L66c4YkvdkNMVWGa7oJpJOxgiWrU4SWB7EVpuAMeP4Oz/3HAiB0EU\nIEgCREkIWQYyqoSMKiOjSyiqMmQJkCQJsgRAal+3SZICASCJBaI4QpSESGIBPxGwIwHbaEFBBrEX\nI6tkkc/kkMvoGC/pmCzlkFF5TXY0LKiGnB/GMB0fphO035CRAy/yDhZPkpxAz8jQNRljmgxdW30R\nc+ANpq3ijRbHon13JbBhhRaqXoIkkQ4WWe03ch7FrI5yXkM5ryGr8eVKw4Prp6jb8rqC5ciF44UQ\nQkCSWLgT9TvbC9Bs+di9rwEnCOFGLrzIhRO5CGIfWkZCTldQzLeXUGRUdfU35Y5yOVUZK8EPYiwu\nt2B7LdRaCWShomJXUGlUMFbMYqqcQ4Ej3ofhFeoQsr0QphPAdHzYvg87dNAKW/AiF1ldRnYdxVOn\nKIqEQk5F4SUzneJYwAtj+L4NM7Cw5CbI2lkUjAIKmSIKuo5SXkMlr/HNTAPP9vavnyryjh91R3uG\ngYAbelxHRdTHWm4Aww5gOD4yuRZM38JifRFB4kPfX0BNlhRktVzXZzTomoKxYgZjxXa+8PwYzVYD\nNbOGklvGijmGSi6H2fECynmtq7EMEhZUQ8ILIqwYDnbuqcEJXLQiG07oIBI+8rqCclnBXDbX162Z\nFUVCQVFRyLb/3V5jEsP2mmjYNch2BkWrgEKmgHwmj1OTDKYr+XSDJlqDQ9ZPaVw/Rd3DdVRE/cnx\nQjRtH03bh+27sEILdmCjUMmilM9gagLIarnUR5azuoI5XUEUJzBaDvbZJlbcHEx3BjOVIjZOFqDI\nvDHIgmqACSFgOgFqlgdUXTS9JvY29gJyjEJOwVRJRU4f3IJDliUU8yqK+fbL1PNjtNwWlrwmEluB\np/hYrI9DhD4my1mMFfTUEw/RieD6KeoVrqMi6h9xkqDZ8lE1XVieByu00PItCDlCKa9itqJgdqbd\n6Mto+ilHeyhVkTFZ0TBRzqDZirDH3A0nnETLncCmqSJKIz5axYJqAIVRgrrloW55MH0bhteElJNQ\nLqqYm1aR1fS0Q+yKrK4gqyuYgoYgTJDIFnYadURugpVWBWW9iIlSFpPlLDSV61Kof3H9FPUK11ER\npc8LItRMD42WB8O30PSbiISPYl7BbFlFVhucYkSSJIyXMijkFCzXarCaFpxgDrOVIk6aKo5sjmFB\nNUDcIMJy00Gz5cH0TTQDA5BCVIoZbDppEooswWgGaYfZE1pGRmUsi+lxHXvna6i1FlF1FFSdCirN\nMsYKOcxUcpziQn2J66eoVxRFgqq211E5fsT1p0Q9IoSA4QSomS4Mx4URmDA8A5omMF7JoJBLfzrf\nemiqjE2zOTSsEHvM3fDiGQRxglNmyiM584IF1QAIohhLDQdVy0bdbcAMDeR1GdMTGeSz7Sl9/bw2\nqptkWUKlmEGlmIHnxzBaTbxg1lF0S6i3xjFZKmB2LM8OgdQ3hBDtLQu4fop6JKe311E5fsiCiqjL\n4iRB1XhxFlHTa8KNbZTyCjbNatAyw3UjbbyUQV5XMF9dQiLaGwqfOlceuXVVvMrsY1GcYKnpoGo4\nqPsNNP0GygUFJ09muT/TERyYEhjHAs2Wg92WhYZXRqM1galSHrPjBe6hQKnzghhe5EFVMZJ38aj3\n9IwML/Dh+lHaoRANrQOF1IrhouE10fSb7VlEpQxm893vzpcmXZNx0kwW8ysrgCEgScCps5Whfs4v\nx4KqDyWJwIrhYsVwUHcbaPgN5LMStsxmWRCcAEWRMFnRUCkmqJst7DQNNP0J1FtjmCrnMTueH7k7\nJ9Q/3CCCF/vIcvd56hFdk9E0fbgBCyqiTnt5IdXw6sho4pBZRKNAU2WcNJ3FvpUaJEOGLEk4da6S\ndlg9w4Kqz9QtDwt1Gw3XQN2rQdMFNk5r0DUWAKulKjJmxnWMlRLUjSZ+1WzC8CZQt8YxO55jy3VK\nxYHpfnqO72nqDT0jI0x8+EGMJBEjddeYqFuOVkjNTmVGtuFQRpWxcUrHvpVlaFYG5byGyfJoTG1n\nQdUngijGnhULtZaFZWcFshJidkob2TdlJ2mqjLnJLLwgRs2oo9lsohXMwLDL2DRV5Poq6ik3aBdU\nJd4koR6RJAmaKsGPfXgBN/glWg8WUsemZWRMj2lYaiwhV8uimNOgj8CMDF5J9oGa6WKhbmPZWYEV\nGpga01DKj0ZF30tZTcFJ0wpsL8JSfR6tsAXHn8LceBEzYxytou4TQsALIgSxDy3D9zj1jq7J8OL2\ntD8WVERrU7c8LDZs1BwWUsdSzKtouR6WnSry1Qz+z4axtEPqOhZUKXrpqNSSvQQ9m2DLbA6KwukY\n3VTIqtgyp6DatPGCYcMJZ2E6HK2i7vPCGG7oQ1FGtzMnpUPXZPgOG1MQrYXthZivtVB3WljhLKIT\nMj2uY/eigWqriIqhY6oy3DcRefWYkpePSk2PayiO+C7TvaTIEmYndI5WUU8dXD81ZG1zqf9lMzKs\nmI0piFYjCGPsXjZRtWxUnSrcxOYsohOkyBKmxzQsN5aQr2cxVtSHukM1C6oei5MEu5ctrFgmR6X6\nQCGr4uQ5BVXDxs6XjFadPFNmR0XquAPrp/QsX1vUW1pGRhC7cP0IQoiB3lCUqNuSRGCh1sJivYXn\nawsw/CbGigpmSsPd/rzTinkVpu2h6ZuoW4WhvmHNgqqHvCDCrmUTi1YNzaDGUak+IcsSZsZ12Ln2\naJUbOQijBKfMlpHT+RahzmmPUHkYZ0MK6jFZlqCq2N+YImZuIzoKw/YxX7MRZQRW7GVEkoXNszpv\nsq5RpaSiVjdQM8cxXckN7c0cZtQeMZ0Au5dNLLQW4Qsbm2a4p1S/KWRVbJlVsFAzsMsIEMZz2Dxd\nxngxm3ZoNCS8IIYf+8iyIQWlIJtRDjamYEFFdKgwSrCv1sKKaWHFXUahomHDbBahx2uA9ShkVVQl\nB6Zvw3AKGCvoaYfUFcyoPbBiONhbMzHfWoCaCbFpIssh4z6lKBJOms5ipeljl7kHYbwRGyfK2DBR\nSDs0GnBeEMGLfMgyOMWXUqFrMnx3f2OKUtrREPWPA3uALjtVmH4TExUVWzYWAQCGl3JwQ6BSyqDZ\naqJqlFhQ0eoJIbBnxcKSYWLeXkClJGGizDsd/U6S2lMAm5kQe4zdCJMN8IIIW2ZKUGSOKtLaHFw/\nxel+lBJdk2G12JiC6IAwSrC3aqFqWVhylqFmImyeG+7mCWko51XUDRuG48INisgNYUfldb1ifvaz\nn+Hcc89FpVLB1q1b8Y1vfKNTcQ28MErw/IKB3fUq5u19mB5XMFHmeqlBMlbMYG5Sw5I7j72NFTw3\n34QfxmmHNZKGIdccWD+VZYc/Skm7MUV7c18hRNrh9K1hyDd0fHXLwzN763ihvoB5Zy/GK8DG6SyL\nqS6QZQmFnAI7bKHlBmmH0xXretVcffXVuPjii2EYBm677TZceeWVqNfrnYptYAVRjF8tNrGnuYh6\nsIyN0zqK+eGrxkdBPqtg00wWzaiKPcYinl9owuPd3Z4bhlzDESpKmyJLUBXADX14vDl0VMOQb+jo\n2tdoBp5frGKnsQu+ZGLzbBalAq/TuimvK3AjDy03TDuUrljXJ/uOHTvw+7//+wCACy+8ELlcDjt3\n7uxIYIMqCGP8asHAXmMJdmxg80yOF1ADLqPK2DyTQwAL+8wF/GrRgOsPZ0LoV8OQa1w/hh8FzAeU\nKl2T4cfc4PdYhiHf0JHVLQ/P7KljZ20e885eTIxJ2DjFUaleyGVluJEL2xvO3LOucvyiiy7C3Xff\njRtvvBEPPPAAyuUytm3bdsj3TE5OrivAtchkMqmcOxESfrVowBA21KLAq+ZmofSo+YSqtn+VlbFK\nT87XD+fu9XkrYwL7lh0YiYWdSyZeedJkz19jab22X3ruNJxIrgH6N98EYYxcwUUpyWNysjPdAPie\n761hec6xlEXkasgWSpicLB/ze9PKN2nmGqB/800/5P9Bfc5JIrBr2UDVDVETDeTHgVMmZo9ZSA3L\ne76fzt10LegFHfliGTn90Pd52q+x9VpXQfXJT34Sv/M7v4ObbroJ2WwWX//616Hrh3bv+OhHP3rw\n7+eddx7OP//89ZyybwVhewh5V2MffFjYMpdnJ78hI8sSNs3msW/Fxa7GHgDAqbOHJ4Vh8vDDD+OR\nRx4BACiKgvPOOy+VOE4k1wD9m2+8IEIQ+9C4fopSpmVkOK0QQZ9N+euXXAMMfr6hQzleiJ2LTSxa\nVdScFcxM6igXh7PTXL/LZ1U4oQvLDVK9dupGvpHEGlemuq6LM844A5/+9Kfx9re/Hd///vdx6aWX\n4vHHH8eWLVsAAA888ADOOOOMdQe5Wgeq21qt1pPzBVF7mp8hbPiwUNbDnhdTB+4mGE2jp+dN89xp\nnVcIgVaoQY5yqEglnDZXQbZHHWt6/dp++bkfffRRXHDBBT0974nkGqC/803NdPHL+Xn4ch0z4535\nIOd7vreG5TkHYYKF5QivnDwNWzdPHPN708o3aeUaoL/zTdr5P41zr/e8VcPF3pqJJXsZIRzMTenQ\nTnAP0GF5z/fTuU07hGNp+LXZk3HyzKEj5IOeb9Z8u/TnP/85LMvCO97xDkiShHPPPRennXYafvCD\nH6wroEETRgl2LhrYZy7BExY2z3JkathJkoSTpnOIZefgmip2/+ueYcg1XhgjiANu5k2py6gSQhEh\njBJ2+juCYcg3BERx+9rsV8tV7DZ3Q9U9bJ7NnnAxRd2hqfLB/DNs1vzKOvXUU+G6Lv77v/8bQgj8\n+Mc/xtNPP53KHeK0CCGwa9nEvLUCNzGxmdP8RoYkSThpJo9QsjFvLeGFJQNxMnwJoh8MQ64Jwhhh\nEiLDDX0pZZLU7vTnxwGCIbyoWa9hyDejzvZC/L99TexuLGPB2YfpCQXT4zokifk3bYoiIUpYUB1i\namoKX/nKV/DhD38YlUoFl19+OT796U/jzDPP7GR8fW1vtYUlqwErbOCk6WzPGlBQf5DldncgNzGx\nZNWwe9lKO6ShNAy5JojaBRXXUFE/yKgywiTkyPoRDEO+GWXLTQfPztfwgrEHdlzHppksCjm2Q+8X\nqiIhETGiePgKqnW9yrZv347t27d3KpaBsmI4WGwaqLrL2DidhcI7zyPpQFG1d7kGzdSR1VRsmCik\nHdbQGfRcE4QJoiRERuUHO6Uvo0qI4v5rTNEvBj3fjKIkEdhTtbBkGFiwF1Auypis5NIOi16mPUoo\nECUx4iSBIg/PTUZ+uq+B5QTYWzMxby9gejzDfWVGXEaVMTepY6G6ALWuIqspGC9m0w6L+oQfxgji\nELIMTjmhvqCpMvwwgB+xoKLBF0Qxdi2ZWLTqqHtVzExkOCrVx9SXTPtThuj6ma+4VfKCqL1uqrWA\nSlFCMc//hQTkdAWTFRUL5gK0FRW6qiCfHd526nTiDq6fUllMUX/IqBJsTvmjIWB7IXYtm1iwluHE\nBk6ayXJqdZ9TFAnxEE77YzWwCnGStN+4rSWomRATFY5C0IsqxQz80Md8axHqsoJXbhxnVzdqr5+K\nA37IU9/IqDKn/NHAq1sedq+0p/hBCbBpNse17ANAliQIJEiGrMkoP+FXYfeyhSWrBl+0MDvBTeHo\ncNNjGhLZxWJrGbuWTbYlpnbL9CRkcU19g63TaZAJIbCv1sLzizXsMfdAy4ZsDDZABAAJMobt18VP\n+BNUtzxULQuNoIYNUzrbo9MRSZKEDZNZtCIDKy0Dy0037ZAoZWyZTv2GrdNpUEVxgl8tGthdq2Kf\nvRfjYxKmx3iDe5CIRECSpKFbU8wpfycgiGLM11pYdJYwNabxTjMdk6JImBnXsVRbRq6RRbmgIafx\nrTaqXpzyx9cA9Y+Xtk7XM0ra4RAdlx/G2LloYKlVQzOoYeOUjqzO1+6gEQBkSJCHrKBiZXAC9lZb\nWHZWoGkxSmxCQScgn1VQzAMrThV7VyxOqxlRQoh2y3QRsSkF9RWNrdNpgLhBhOcXmthrLsKK6tg8\nm2UxNaAS0Z70N2T1FAuq42lP9TNhhQZmxjmsTCdusqLBTSxUbZNT/0ZUECVsmU59KaPK8BO2Tqf+\nZzk+np9vYo8xj1BqYdNMFqrCy9dBJQSGcsofX5HHcGCq35KzjKkxjZv30qrIcnvq37KzjIWGBTeI\n0g6JeuzA+il2+KN+k1Glg1P+iPpVw/LwzN4adpt7IGVcbOQa9oEnRLvT37BN+eP8tWM4dKofW6TT\n6uWzCgr5CCtOFYUVDa/YODZ0d2Xo6PywvX6K0/2o32QyMsI44JQ/6ls104URuNhj7oWejTA9zuuw\nYRAngCKpQ9eVkbdNj4JT/ahTpl4y9W/F4NS/UeJHbJlO/SmjSIhEzNbp1JcWGzZ2Ljewy9iFUklg\nmtdhQyGMEqiSAk1Vhm6kkZ/yR5AkAosNG8vOCqf60bodmPq34ixjuekM3e7gdHRRnCBKIqjMIdRn\nJEmCIgNhEiJkTqI+snfFwp5qA3tbezA5oWCSbdGHRhAlyCiZoZwGP3zPqANWDBd1x4CshOzqRx2R\nzyrQdIG628BS00k7HOqRMGp3+GNBRf1IVSTESYw45ggVpU8IgReWTOxp1LHP3ofZiQwqRS3tsKiD\nwkggI2vQ1eHr0MiC6mWiOMGK4aDu1TA5xjcydc5kWUPDb6BqOAjYWWskRHGCJIk5yk19SZElRCLi\nCBWl7kAxNd+sYdldwMYpDYUcb2gPmzBKoMkZ6BoLqqG33HTQcJvQNIEc9zigDtI1GfmshLrfwFKD\no1SjIIr3j1AN2VxxGg6KIiFKYk5DplQdLKaMOla8JWyc4h5TwyoMRXvKH0eohlsQxaiaDmpeHZMV\njk5R501UMjD8JqqWzTbqQy5JBKIkgYAYusW3NBxUZf8IVcSCitKRJAI79xdT1f3FlK7x0nRYtZtS\nZKBlWFANtaWGg5rXQD4HvqGpKzKqjFJBRs2tY7Fupx0OdVHIhhTU55T9a6g4QkVpEELgheX2NL+q\nt4STpllMDbMkEYhiQFe4hmqoeUGEqmWj6Tc4OkVdNVHS0ApN1FsObC9MOxzqkihOEIuY0/2ob6ny\n/oIqYUFFvSXE/pGpZg01fxknTWeHsvMbvcgLEmiKjnw2M5SzNvjq3W+56aDhNVDOK9wzhrpKUSSM\nFVXUvRo7/g2xME4QJxEbUlDfUjjlj1JwYM3UglFnMTVCPD9GXs0hrw9nsxG+gtG+k9xoeTACA+Pl\nTNrh0AiolDKwIxuG7cLjWqqhFEUJ4iTmlD/qW+0pfxGn/FHPCCGwa9k6uGaKxdTocPwYWTWHYm44\nZ4HxVQygbnkwAws5XYaq8H8JdZ8iSyjmZRiBibrlpR0OdUGUtDv8KUM4tYGGgypLiAXXUFHv7Fmx\nDq6Z2jjFYmpUCCHghwI5NYdCliNUQ6tmejB8A2NFjk5R71QKGRi+gbrlI0m4seawiaIEEfegoj7W\nXsfQ7kYZcx0Vddm+WgsLhoEVdxkbpnQ2oBghfpBAk3XktQwUeTh/78P5rFbBdAJYvg0hBchnh6/r\nCPUvXZORURNYgYWm7acdDnVYeGAPKhZU1MdURUKURIhi3tSh7lluOpivN7Fgz2NuSkN2CDd2paNz\n/BhZJYtCdngHLka+oKqZLgzfQIWjU5SCSjGDpt9EzXTTDoU6LIoTJCLhCBX1NYXT/qjL6paHPVUD\n8/Y8ZsYzyHHT3pHj+QlyahaF3PBea490QeWHMZq2CzuyUSoM55xO6m/FvIIg8WC4Lhy2UB8q3IeK\nBoGyf4QqZEFFXWA6AXatNDHf2ofxioJintdaoyZJBNwgQU7No6CzoBpKNdOFEZgo5GQuHKdUSJKE\nUl6F4RuosTnFUIljgZhNKajPqQc6/bF1OnWY44V4YamJ+dYCSkVwnfqIcrz2dL9STh/qbYmG95md\ngKbtw/JNVIq8Y0LpqRRVmIEJw2ZzimER7R+dkqV20UzUrw7uRcURKuogL4iwc9HAvtY89GyEicpw\ntsqm47PdGMVMCZXCcL8GRragcrwQtu9ByBEXR1KqMqoMLQO0AgctTvsbCgem+3H9FPW79ghVwjVU\n1DFBFGPnool91gIkNcDMuJ52SJQSIQRsL0YxU0A5P9yvg5EtqEw3gB3ZKLCzH/WBQlaBHdow2e1v\nKMRxglgknO5HfU+R2yNULKioE5JE4IVFE/PWEiLZwYbJ4b6IpmNzvBgZWUcxq0PPDPf19ugWVHYA\nO7RRyHG6H6WvkFNhhy2YbpB2KNQBcSKQiHj/Pj9E/UuWJQiRIBGcbkzrt3vFwlKrDic2sGEqyynP\nI85yIpQzJVQKw19Yj2RBFUQxbN9HmPjI6SP5v4D6jK7JEFIM2/fg+lHa4dA6JUIgEQIKLyaoz0nS\n/tcr12/SOi02bCyZBur+CjZMZzlCP+KSRMDxEhS1IsaKLKiGkmkHaIU28lmZd0+obxRzCuzIhuFw\n2t+gSxIBAQFpJDMsDRKOUFEnNG0f+2omFu0FzExo0Ia4mxudGNuLoSs5lHJZaOpwT/cDRrWgcvdP\n98tyuh/1j/a0PxumzWl/g649QpWA92uo38kSEIsEMUeoaI3cIMLuZQML9gLGywqvrQgAYNoRSpkS\nxkdgdAoYwYIqThK0nABu5CCfG/6KmQZHTpcRJj5s30cQxWmHQ+uQJECChFP+qO9JkgSBBAl7UtAa\nRHGCFxZNLLSWoGdjjJW41xQBQZTA94GKXhqJ6X7ACBZULTeEHTnQNYnze6mvSJKEnC7DDh20XLZP\nH2RxkiBJEkjMMdTnFFmCgIDglD9aJSEEXlgysWivIJYczIwP9z5DdOIMK0RFL2OilIMij0apMRrP\n8iXcIIIXe9x7ivpSTlfgxWxMMeiEAAQEWE/RoIhFwsYUtCrzNRvLVgNW2MTclM416QSgvYbYcmJU\n9Aomytm0w+mZ0Suo/Ah+5COrjdxTpwGgazL82IcbsKAaZHGSQIgEMi8waADIEtiYglalbnmYbxhY\ndpcxN6lBVXhNRW2WEyGnFFDO5ZDTRmc93ci9A9wggh/70FlQUR/SMzKC2IfrR5yCM8AS0b7jz3qK\nBoEsSwdb/RMdjxdE2Fttd/SbHstwxg8dotkKUdErmKrk0g6lp0aqqgiiGH4YQiBChi09qQ/JsgRV\nAbzIgxewMcWgSoSAQMKNfWkgtPeiitnpj44rSQR2L1tYspeRzQmUCqMzAkHH5/oxkGRQzhZQyY/W\nmrqRqipcv71+SufdFOpjuibD47S/gZYk7bv9rKdoECjS/sYULKjoOOZrLSy3GvBEC9Njo3XBTMdn\ntEKMaRVMlLIjt6ZutAqqIIIX+9AzI/W0acBkNaW9joqNKQZWu6DiCBUNBkmWuBcVHVfD8rBoWKh6\nK5ibyDK/0SHCKIHtJSjrZUyWRmu6HzBqBRUbUtAAYGOKwRcnAoJrqGhASGxKQcfhBxF2LTWxaC9i\nsqJyHTodpmGFGNPGMFHKjeSympF6xmxIQYOAjSkGXyIEYnb5owGhSGxKQUfX3m/KwEJrERktQqXI\nzXvpUGGUwHJijGfHMTOWTzucVIzMakIhBMIoQSxiZNTR2LWZBpMsS5BlIExCRLFARuVF+aBpF8IC\nI7KfIQ04SQZEzH2o6MgW6jYaQYhWZGBmgtdPdLgDo1OTpTz0zGj2KRiZj/swThAlEbhVAg0CRZYQ\nJzGiOEk7FFolsf9OvxBi5Bbl0mCSJQkJOEJFh7OcAItNC4v2AjZO56Bw3RS9DEen2kamvIiiBPH/\n3969x8p61fXjfz/3+zxzn307t7bWAseYVKMiSVtLUOItYBCiUW6ikGKMiFEUY0ASYqIhwYaQfBEk\nKCbGP2iUQAIitBRE4AtfsRRSf1Joz2XfZu+5zzzX9ftj9j6X9lz2nj0zz1zer/SkPefs6VprLp95\nPuLfxoIAACAASURBVM9a67NEDFVhMKDZpyoSYhEjYkI1d1IhkKTcP0XzQ5aAFCxKQddL0hQXdjvY\n7G6imFdhGUuzqImOgbNTQ0uTUF2ZoWJCRXNAUSTEnKGaS2kKnkFFc0WSJaQpl/zR9S7Xu9jt7gFy\niKLPpX70fJydumppEqo4SZGkCWeoaC5cmaGKmVDNGwEBrpyiecJvRXquTj/EVrODelDnvim6Kc5O\nXbU0CVWUpIhFDJV3jWkOKMpwD1UUJ1l3hUbEJX80TwQEeB+AgOE5ehd2O9jubyHvKdB5difdQMjZ\nqesszackjlPEacIlfzQXNEVCnHIPFRFNAb8W6RqX97vY6e4jlQIUc3rW3aEZVW+EKBhFzk4dWJqE\nKjycoWJCRXNAUSQkgnuo5pEQ4L1+IppL3UGErUYbu4MdVAtc6kc31hskCAIJZauIlYKTdXdmwsgJ\n1TPPPAPP8677JcsyPvGJT4yzf2OTpgKpSFnyk+bCsGx6zKpbB+Yt3gC86U9ziOFmLmPNuKSpwLM7\nbWz3dlBwVRj60txzp2PaaQQoW2VU8zY0le8T4AQJ1enTp9Fut6/8+uY3vwnXdfHyl798nP0bG8Fz\nYWiOSNLw2obFDYbmKd4cxhqiecFvxavmKdaM2+Z+F7vdBiL0UMhpWXeHZlSjE0GFiaLto+JbWXdn\nZowtrfzIRz6CX/mVX4FlzeaTy2U4NE8kSMMLc75nb2jW4w3RvOGNgBtblljTD2NsNTvYHeygVjR4\n85luKEkF9lsRymYFq0WH75NrjCWhStMUf//3f4/Xvva14/jfTYSAAIRg5a0J+cb/5RM7biy/fWPz\nEG8A8Lb/hDDWjB+/F29sbmLNGFyqd1Dv78FzZJg6CwwcYry53l4zhKPmUPJc+A732F1rLMdef+Yz\nn4EkSXjwwQef93elUmkcTRyLpmnPazvfTuEGHvy8PrESoKo6fDr9vD+R//8st/3//kvCvT823baz\nHvMk205SAa+twff9697HN3pvT8th21mb9XjTDyLkmwN0uw34eXdi7S7y+/9W7WYRaw7bBrIZ88Tb\nVUOosoF8oYBS6Wo7WcWbeYg1QHbPy7jb3W8PkChtSGaKcxuVG+41X+j3/y3a5rXNVUGYAE0Vd67c\nifNnqzD1saQQV8x7vBnLs/F3f/d3+I3f+I0b/t173vOeK/9933334f777x9HkyPjkobx+sb/lfD/\n/kvC335IQprIuPdegXt/jM/xSR2+T7O+c/zoo4/iscceAwAoioL77rsv2w5h9uMNl0BMBmPNYpu3\nWAPMRrw5KSEELu62sNXdRrlgsHDXAcab59veG6Bkl1EruGNPpqZtEvHmxM/I/v4+/uVf/gXf/OY3\nb/j3Dz300HW/r9frJ23ytg6z22vbajab6HQ6aDaUiVWuOczom43mRP7/s9j2nXcC9/6YjzSR8au/\nun/Qh+m0vcjPd5IIdDoBmkYT9frVj+mN3tuTdP78eZw/f/5K248//vhU2r2ZeYg3gzBGo9FEe9BG\nszG5g5kX+f1/I1nGGiC753sa7TY7EQZdEw1rH64aX/nzacabeYs1wPTjzSRej639Hr63vYVmuAvf\ntdBs9G/4c4v8/r8RXttc33a7G6PRBAp5BQaCibzX5z3enDiz+Md//Ef8yI/8CO65554Td2aSJGm4\n0Z8m4957l/vOzbgJDCtS8j17vXmJNwBYgnpCGGsmQ5Ikzq5eY65izYiiOMV2o4t6fxeVAg/wvRHG\nm+EN3t1miJpdxWrRgSKzTPqNnPhZ+ehHPzoXGzYPvyy45G8yln0qfNyEYE2DG5mHeMML08lirBk/\nPqPPNw+x5qQu73WwO9iDYQhYBgtR3AjjDbC9HyCn5VHyPBQ9M+vuzKwTL/n72te+No5+TJwsS5Al\nGYmY3BIconFJUgFZUqAqvDC/1rzEG4AXqTSHGG6umKdYM4ruIMJuu4tm0MCpGqu10Y11ejHCUMG6\nX8ZGeXJFlhbB0szbaYoMVVKRJLzModmXJAKqrEJVluYjujC4vJiIZt3lvS52e7vwXQWayu8Zer4k\nEdhpXF3qp6ucxbyVpfkUqYoMVVYQx0yoaPbFBwmVxoSKiCaNX4tLpdULsd/toJ92UfBmo0Q9zZ7d\nRghX9VFyPZRyi32w9TgszdWarg5nqOKU3xw0+5JEQJEVqLxzOLe4XZPmCUvgLI+t/S7qgz0UPA0y\ny6TTDXT7MQYDCVW7jI2yl3V35sLSXK2pigxFVhBzyR/NgTgVUCXOUM0jCVLm54cRHQe/FZdHqxei\n0esiSHvw3fk+S4gmI0kFdhoRqk4Nq0UXhsalfkexNFdrmiJDlbmHiuZDHAuosgKNa5bnjiwDEmRW\nFKW5IVIBWZI4W7EErp2dYjVSupHt+gC24qHkeCj7XOp3VEuTUKmqDEVSOUNFcyFOOEM1r2RpWFE0\nTbPuCdHRpAKQJQUKE6qFxtkpup1WJ8JgIB8s9WNVv+NYmk8UZ6honiTpwR4qJlRzR5IkKPLVc+94\nF5hmXSoENEiQ+V5daJydolsJ4xTNZoDT/hmUTBWmvjQpwlgszdWaJEnQVBmKrCKKeeuYZleaCqQp\noMkaz6GaU8OLFQmsgUPzQKSAJMlc8rfAODtFtyKEwOZugLJdRS3v8wDfESxNQgUApq7CUAwEIRMq\nml1BlEJXDJi6wruIc+rqsj9mVDT7UnGwh4rxZmFxdopuZbcRQoONmlfCmaqfdXfm0lIlVLahwlAN\nBBETKppdQZjCUAxYnG6fW4o8TKhYl4LmQSoOZqh4ob2Q2pydolvo9GJ0e0DNqeLcSp4z1SNaqoTK\n0lWYnKGiGXeYUNkmD1ycV7LMGSqaHyIVUCSZRSkWVL09QDNswXdVzk7RdaI4xU4jxIqzgo1Sjtcd\nJ7BcCZUxXPI3CJOsu0J0U4MogckZqrk2TKi4h4rmQyLE8Pw0JlQLJ4wTNLp9tMMWfIcXy3SVEAJb\n9QB5vYRqzmeJ9BNaqoRKVxUYqg4IhYUpaCalqUAcA6ZqwtR5BtW8kiWJZ1HR3BAsm76w6q0BWkEL\njiVDYZEjuka9GUESJqpOiSXSx2CpEipgOEtlqiaX/dFMYkGKxSBLgAyJZ1HRXBgmVCxKsWiEENhr\nD9AMmsi7nJ2iq9q9GJ2uwIpTw+mqxyNaxmDpnkEWpqBZxoIUi0GRZciygpQzVDQHklSwKMUCanQD\ntIIOJCWBaXDFAw0NwgQ7+xFWnVWcKvlwuG9qLJYuoRoWpjDRD7iPimbPIExYkGIBSBIg8RwqmiMK\nz6FaOPXWweyUxxt0NJQkApv1EFWritU8902N09IlVK6lwVYtBKFAwqsdmiFCCPQGKRzN5h2jOTec\noZIhGGNoxqXpQUEKzk4tlH4Qo9nrI0h7cC0mVDS8xri8O4Cn5VH1CljnvqmxWrqESpFluJYOU7XQ\nG3CWimZHP0ihyQZcw4ShcXnGPJNlQIbMGSqaeakQkCBDXrqrgcVWb/XRDBtwbYUzjwQA2N4PoQgb\nK04FZ2s53kQZs6UMob5twNVcdPtx1l0huqI7iOFoDjxbz7ordEKyJA2LUnAPFc24VIBnUC0YIQQa\n3RDtsMNS6QQAaHQiBAMFq24NZ2s5FqGYgKV8Rj1bh6PZ6AcpyxrTzOj2EziqDZ8J1dyTZQmSJEOw\n9g3NuJQFKRZOqxeiG/WgKCl0bSkv8+gavUGCvWaMVWcVp6s+LINLQCdhKT9phqbANUyokoF+wCse\nyl4YpUCqwDEsFqRYAIclqBPesKEZJwQgSdxDtUia3QDtsA3P4YXzsgvjFFt7AVadNayXcsg7RtZd\nWlhLmVABw1kqW7PRHXDZH2Wv049haw5yFmenFoEiS5AlBcynaNalqYDMJX8LI03FlYTKtbgXd5kl\nicClnQGKRgW1nI+VgpN1lxba0iZUvq3DVR10+yxMQdnr9RO4msv9UwtCUWQokow44Qw4zbYkFVAl\nhXsqFkS7H6IT9WBogKbyNV1WaSpwcWcATytgNVfC6YqXdZcW3tJ+2mxTg2NYQKogCHnRQ9mJ4hRh\nDDiaBY8zVAtBU2Sosook4RQVzbY4EVBkJlSLotkN0I26cGwu91tWQghcrgcwZQ9r3rCiHys9Tt5S\nR1DfMZAzfDS7UdZdoSXW6sZwNQ++YzDoLQj1IKFKBVj4hmZakgiokgqNCdXcE0Kg1YvQCTtwuNxv\naW3tBZATC2teDedWfN4smZKlfpZLnglfz6HdS3jIL2VCCIFWN0beyKOU44nli0RRJCiSythCM204\nQ6VC5fKwudfpR+hFPShqCp2v51La2Q8QhxrWvVWcW/Ghq0ysp2WpP3GmrsJ3LDiKg3aPxSlo+jr9\nBLpsImdacFjdb6FoigxFUhBz2R/NsCQVUGXOUC2CziBCN+7BMbncbxnttUL0+wo2vHWcW/Fh6Xwf\nTNPSR9CSZ8I382i2ueyPpq/ZieDrPso+Z6cWjarIUGSF+6hopiWJgCIprPK3ALqDCP2oB8tc+ku7\npdPqRmi1Bda9NZyp+rxBm4Gl/9TlbB05wwGEht6AFf9oeoIwRRTJyBk8G2IRaYoMVVI5Q0UzLT5I\nqFgRbr6lqUBvECFIApg6l3ktk24/Rr2RYM1dx+myD5/XE5lY+ggqSRKKnom87qPZ4SwVTU+zGyFn\n5FDwWIxiESmKDFVWuIeKZlaaCgASNEWBIi/95cBc6wURBskAmipxtnGJdPsxtvYirDlr2Cj53Iud\nIUZQAEXPRM7IoRekPDeGpiJNBTq9BL6eQ8kzs+4OTcDhDBWX/NGsitPh7BSrgM2/7iBGL+5zud8S\n6Q6GydS6s471Yp4H92aMnzwMD7/LuyZymo997qWiKWh0ItiKA9+2YHLj6EJSVRmyzKIUNLvSwwp/\nTKjmXmcQoh/3YXG531LoDRJs1YczU2vFPNZKbtZdWnqMogeqeRtFs4B2N0UUc5aKJidJBRrtGEWr\nhFrezro7NCE83JdmXXxwBhUTqvkmhEA/iDGI+7AMJlSLrjdIsFkPseasYb1QwDqTqZnAKHrA0lWU\nPBu+7mOvxVkqmpz9VgRXy6HoOnAtPevu0ISoh2XTuYeKZlScCiiywpLpc24QJuhHA6jq8Pw7Wlzd\nQYzNeojVw2SqzGRqVjCKXqNWcFA0i+j2U4QRZ6lo/OIkRauboGgWsMr1zgvtcIaKS/5oViXJMKHi\nDNV8G0QxgiSEofF1XGTdQXxlmd8Gk6mZw0/fNQxNQdm3UTSK2G2GWXeHFlC9eXDulOfAMrh3apHJ\nsgRVliFBOqimRjRbDpf8sWT6fAuiBJGI+DousG7/ajK1XmQyNYv46XuOWt5G0SogCCQMAp5LReMT\nRim6/RQFs4AaZ6eWApf90SxLUgGVM1RzL4wSxEkETeVyv0XU7l1bzY97pmYVo+hzqIqMsm+haHKW\nisar3gxRMIqo5BwYGjcOLwNVkaGwMAXNqOSwKAXPLZprYZwiTCPonKFaOI1OhN39+EppdCZTs4uf\nvhuo+BaKVh5JrKLTi7PuDi2AfpBgEEgomnlUWdlvaWjq8Cwq7qOiWRQnArKkQOWF+FwbhAnCJOSS\nvwVTb4ZoNgU23FM4UymyNPqM46fvBhRZxkrBRtWuYqcRIuFyHTqBNBXY3gtQtSuo5h1+6S0RlYUp\naEYJIZCkgCarrPI3x+IkRZTEAFJW+Fsgl3f76PUUbOQ2cK5W4I3YOcAoehOlnIWy68FVfezsB1l3\nh+ZYvRXClF2UbB/VvJV1d2iKDFWBLms8245mTpQIqJICXVMgSbwQn1dhlCBOWZBiUaSpwIXtHpLA\nwClvHXeuFFH0zKy7RUfAT+AtbJQ9VO0ygoHMpX80kn6QoNMVqNgVnKp4vHBZMoamQFU0RDFnqGi2\nRHEKTdGhcz/nXItTgVjEUDk7NfeSVODSzgBybONM/hTuWi0gZ/OsynnBhOoWDE3BatFF1alx6R8d\n29WlflWsFFyWSV9CuqZAl3Wea0czJ4oENFmDoTKhmmepEEiFAO/Vzbc4SXFhuw9DyuFsYQM/fKoE\n29Sy7hYdAxOq2yj7XPpHo6m3QhiSg5Lto8b1z0tJV2XoioYkHe5ZIZoVUZxClzVWHJ1zQggIISAz\no5pbQZjiwnaAnFrCKX8FP3yqBFPnDdh5w4TqCLj0j47rcKlf1alyqd8SkyQJmipDk1Qu+6OZEsWC\nS/4WgBCAgIDEq7m51OnFuLQToGRUse5XcOeaD42zxnOJKfARHC7968c1XG5chGnIPAiRbipJBbb2\nAlSsGpf60TX7qBLoGuMGzYYwTqHpGs8umnNpKiBECt6ymz97zRDNjsCas46VvI+Nssubr3OMkfSI\nyr6FspeDrxdxeTfg8h26qc16AEfxUXHzXOpHV/dRcYaKZoQQAnECLvlbAKkQEAAvxOdImgpc3h2g\n21NwOncKZ6tFrmRZAEyojuF0xcOKW4YmbGzvhVl3h2bQTiMAEh2rXhVnajkGSGLpdJo5LJm+OIQA\nUqQsSjEnojjFhe0B5MTBmdwp3LVSRMXnjddFwITqGFRFxplaDmveKsJQxX47yrpLNENa3Qi9roRV\nZxVnqjnoXAdNYOl0mj1RxJLpi0KWARkyUq6amXn9IMGF7QFyahGn86v4ofUCPJZFXxjc3HFMlq7i\nVMVDmKzg2daz0DUJjsmncdkNggS7jRjrzgZOV3w4LHdKB1g6nWZNFLNk+qJQFRmKpCBImFDNsmYn\nQr0ZY8VeQy3n43TVgyJzTmORMBMYge8YWC/6iNMYl+uXsF6Vudl8icVJisv1ADV7FWtFn6ea03UO\nS6enB6XTucSKssaS6YtDlWWosoqEBYhnUpoK7DRCDAYyNtxTWC/6WC06WXeLJuBEWUC/38eb3/xm\nlEolFAoFvPWtbx1Xv2ZerWCj5vsommVc3h3w0N8lNdxcGiCvl1DL5bHGQDkR8xxrDkunqyydTjMi\nZMn0W5qneKOqwxmqOOEM+KwJwhTPbvWByMaZ3CncuVJkMrXATjRD9ba3vQ3f+9738OSTT6JareLJ\nJ58cV7/mwqmyhzBKEDVDXNppIZ8XkGXefV4WQghcrgfQ4aDmlnCmyio9kzLvscbQFGiKjiiOOZtN\nmYtYMv2W5ineaIoMVVaQcMnfTGl0Iuw1Y5TNKqpuAaerHg/rXXAjv7r9fh8f+9jH8I1vfAO1Wg0A\n8KIXvWhsHZsHsizhbM1HkgpcaAlc2O5ho8pqLctACIGLO33IiYV1fxVnazmuh56QRYg1uqZAkzWE\ncQTen6QsHZZMNxSdS/5uYN7ijaoMl/ylgkuKZ0GSCmzvBYhCFRvuKazmc1gtOrzZvgRGvgJ86qmn\nIEkSPvGJT2BlZQUvetGL8Mgjj4yzb3NBU2Xcsepj3VuBJlxc3O7xjKolcGmnD0QmNnJrOLfi887T\nBC1CrDE1lk6n2RAlApqkQlNlXnzfwDzGG02VoUkawojXHlkaBAme2exDTT2c9U/jrtUS1ssuk6kl\nMfJVYKvVQhiGePrpp/HMM8/gy1/+Mn7pl34J//M//4OVlZUrP1cqlcbS0ePQNG3qbRcLRXxvs4Uf\n7D+LdtDCetWe6odIVYcvpZ/3p9Zm1m1n0a4QApd2+pBTB2dKp3DHig97ihX9snhvP7ftaTtqrAFm\nN95oZoDtXoB6FMLPj2eOip/56VqUMXd6EYp5BbVKCaVS8ZY/m1W8ySrWALMdb272eqxHChqiA80M\n4OcmU4Z7Ud7/k2q73gjQHsS4q3oWNb+Acyv5kfcozsL3/DK1Pa54M3JCZds2kiTB29/+dui6jgce\neAB33303vvKVr+AVr3jFlZ97z3vec+W/77vvPtx///0n6/GMMnQVd58avgm+V/8BLmx3sDHlpIom\n63CZHyITZ0qncPdGCbq62K/vo48+isceewwAoCgK7rvvvqn34aixBpjdeGPqKnTFQNDjDBVlK4xS\n6IoJY8Zm1Wch1gDzGW9cS4ej2WgPuihMKKGiG4viFJd3+0Bs4Kx/CutlH2sll7O/M24S8WbkiHrH\nHXcc6Q3z0EMPXff7er0+apNHdpjdTqOt57Z7x0oO9bqLi60OnmxuYa1iQplCUnV4B6XZaE68rVlp\ne5rtpumwAIWSWFjP5XDHig9dlTJ5jwHTe2+fP38e58+fv9L2448/PpV2r3XUWAPMdrzpd3toNbuo\n2zFU5eT77fiZn65FGfNOfQAbKgbdNuryrQ+nn2a8mYVYA8x2vLnZ6xGEMcJuhJ1uE65+69d0VIvy\n/h9n2412hL1WjIJRRMXJo+ooMKUQe3t7J2o3q2vYZWp7EvFm5G/1QqGA+++/H+973/sQxzG++MUv\n4qmnnsJP/dRPnbhT88zQVdy55mMjtwJTyuHCVh8h903MtThJcWF7ADV1sOGv4Y7V6S7zW3aLEmss\nQ4GpGgh4wC9lKAhTGIoBy5itGapZMY/xxtRVWLoOCIXXG1MQxikubPXR6QzPljpXquHu9QI8m7OD\ny+xEEfUjH/kIXv/61yOfz2NjYwP/8A//8Lw1xstIVxXcsepDkSVstnVc3NpFtaTBMfkFNm8GQYLL\n9YNzptwSztZyLECRgUWINZauwlAMBGEXDs9+pgyk6bDCn6kaMFnh76bmMd44pgZbtdAfBNBdVpyd\nlP12hP1WjJJRQilXwEbZQ46JFOGECdXZs2fxhS98YUxdWSy6quDO1eGmRKOp43L9MvI5gYLHmY15\n0epG2GlEWLFXUcvlcabqsTR6RhYh1liGCkMx0QnbWXeFllQQpdAVA6aucI/HLcxjvPEsHY7moNHt\nwnd5nTFuQZhiez+ALAycctdQ812slhxeE9AVvNU+QbIs4Uw1B1NTocoqLrUvIwwDVIs6v8xm3E4j\nQK8r4ZR7GquFHNZLbtZdojl3OENVD7gkh7IxXO5nweIs+8LJOwZyRg67/V0MwgSmzhnIcRBCYK8Z\nYr8To2xWULYL2Ci7XN5Hz8OoOgW1gg1TV6BuK9jsbOHCdg+rZWMsG9NpvJJUYLMeAImBU7kVnK74\nKHpcn0UnZ+oqTFVHkgzfZ9MoVkN0rSBMYXL/1EKSZQlFz0C9n0ez3YBZYkJ1Uu1uhO39AaK+gTPe\nOmq+x0N66aYYVafEdwz80HoR2qaKre4unt3aQ7Wgw7H4EsyKfpBgay+Ao/hY9as4U83BYfEJGiPz\nyj6qFLbJCx6arkGUIG8anKFaUGXfwnYzh6ebdZQTAUXhhf8ogjDFbjOEZZpYtTegaALrZZfXA3RL\njKpTZOkqfmg9D31bhtWxsLW3iY6ZoFzQebc6Q2kqUG+GaHcFas4Kyo6PM7UcdJUXvDReh/uogqjH\nhIqmSgiBOAYr/C0wXVWQdyx4/RyanR6KPpelHUeSDpf3tXspSkYJd5TOYrXoQU76WXeN5gCj6pSp\niow7V/PINXVYewa2e7t4dquNSl7jbFUGDmelLNnFWb+C1YKHat7iHjeaiMN9VL2wDYB3O2l6giiF\nJuswdZXxbYFVfAu77TwudNpwnRS6yq0FR9HoRNhvRXDUHM7mSqj4Dl50pgJFkVGvM6Gi2+MVfEYq\nvo2cbcDe0VHvtjlbNWU3mpXaqHhcCkMTNZyhMrDfZ2EKmq5hQQqTs1MLzjE1VHMuelER23t72Kha\nWXdppnX7MXabIVSYWLNXUPJcrBUdmLoKhfvc6RgYWTNkaAruWsvD52zVVHFWirJiagoszUDcGSb1\n3NxM0xJEBwUpeNNo4a2VXHQGEdqNDhqdCHmWUX+ebj/GXiuCSDSUrRUUrBzWSi7PlKKRMbLOgOfO\nVm3vbaGhD1DyNZY+HaMwGm40DQIJVZuzUjR9kiTB1FXoioEgSmEZ/HzTdARhipzB/VPLQFVkrJdc\n9MIaLjSfhW0qXPp34NpEqmhWkc/lUPVtlHImb6rSiTCyzojD2ap804Czb2N/0MDlnT2YRoRSXmcw\nPIEoTrHXitDtpygaRaz7eVTzDmelKBPWlUp/fSZUNBVCCISxgGGbvIG0JHzHuLL0b3N3DxtVc6ln\nxG+WSBW95X5eaHwYWWdM2bdQ8AxsN0zsNnOoD/ZxYWsfri2jmNN4dtUxJInAXjtEu5vC132cyxVR\n9m3U8jafR8rM4T6qQdjNuiu0JMJIQJWGKx548bg81ssuekGMsBXh0m4b65Xlm4Xp9GLst5lI0eQx\noZpBiixjteignLOwtW9it+1jb7CHZzZbyDkKCp7G8yVuIUkFmp0IjXYMV8vhjFdEybNRKzgwNM4I\nULYsXYWpGGgMkqy7QksiiBLun1pCiizjjlUfQgAXWiku7fawWjIWPpFIEoFmN0KrG0OBgYLBRIom\nj9F1hmmqjI2Kh7JvYathod7OY2+wjx9stuGYMnxXhcklQ1cEYYpmN0Knl8JRHWy4RZRcBytFhxcS\nNDNMXYGhGIhjFqag6RhW+OP+qWWkqwrOreQgIHCxtYlLOx2sVsyFrCY8CBM02zG6gxSO6mLV8uGZ\nNso5i4kUTRyj6xwwdRVnqsO7K1sNB41uH62gha3dJiQlhO+q8HLLeWEmhEC7G6PZiRDFMnzDxxkv\nB9+xUMvbPNmcZo4kSbBNDXrHwCBMecAvTVwvSLBiWrANxsNlZOoq7lzNQ4KEy50tPLvVQqWgwTHn\n/xJQCIF2L0azEyOJZfhGHpVcDr5topyz4LFqH03J/H+alohlqDhbyyGMHdRbLvbaRbSCDpqdJv73\n2Q5yrgY5TaFri78/KIpT7OwP0GxHCHsyCkYNnuuh6BkoeiZMzkjRDHNMDbZqoR90mFDRRCWJQBwD\nlmbC5gzV0josfKVty9jtONiub6FjJSjn5/Psy36QoN2L0e0n0GULRaOEnOeh6Jko5UzoKuMqTRej\n6xzSVQWrRQcrBRuNroN6y4ekGdgf7OPCbhOKmsK1VDiWslBl14MwRbcfoztIEEbARrmM07kCYIYo\n5SzkncVfG06LwTE1WKqNvUET8LPuDS2yfpDAVC3YprZ0BQnoepoqXzn70t4z5+7sy0GQoN2PQ3fW\nfAAAHoxJREFU0eklUKDD0/PYcFzkLBOlnIWCa/A9TpmZ/U8Q3ZQkSSi4JgquCdvNYafpwUwM9KIe\nOmEHW90eUgSwTQWupcAy5qvCkxACvSBBr5+g008gCxW25qBsuHBcC2dWaqjkbQy67ay7SnQs7sEM\n1eWu4D4qmqh+kMBWPbhc/kwHKr4Nz9Jh7+rY7bSws7+D3WYPeVeDZ6szE4+EEOj2Y7R7ETa3epCh\nwdVzWLNdeKYF3zGQd1lshWYD34ULwjI0nK76sOUI3YGHZq+Adi9EJxigF3Wx3+hgM+3DMmSYugxD\nl2HqykxN9SepQBCmCKIUgyBBP0ihyQZcLY8124ZjmPBtA56tw7M0lMt5AMCA1adpzsjycB+V0THQ\nD5OF2MtAs+lw/xT3k9K1TF29cvZlrumgNeii0Wlgr9WDZ6vwXRXalM+/TFOBfphgEKToDxIMIoFK\n3oGr57Hu5ODoJnxHR94xYPP9TDOG3+ILRpIkuJYO19KBEtAPY7R7IVq9EO1+gF7cw2AwwH53gCDp\nQ1EAQxsmWNNMsq5NnoIwQRCmiBNAVwwYigVHMVH1bLjmMIHybVaoosXimBoszUZ/0IZjZt0bWkTc\nP0W3U/YtlHLmwfaBHJq9PhpBA89stqCqApYxXN3iuCnUMSZYaSoQxQJhnGJwkESFkRhWo1RdFHUb\nlm1irVpBzjGQBj1eA9BM47tzwVm6CktXUc3biOIUnUGIXhCjH8QYhDEGcYggCa5LsiRJQFEkqIoM\nVZYO/vuaf8sSMPwHkgTESQqIYaEIABAA0kQgTgTiVBx8qQ//O05SJImAEBJ0xYCp2LAVAwXLgKUZ\nMA/6axkqXEvjxlJaWK6pwVIs7AWNrLtCC6oXJLBUm/un6Jau3T7QGziot100uwH60QD9uI92q49+\n2IespoiDwY2vD2QJAgKpACCAVAgIAQhxkDwlAmGUIopTRLFAmgKqrEGTNZiqi7JhwbJN2KYG58ov\nFdVKGQBQr4fZPklEt8GEaoloqnwQNK/+2SCMhwlWeDXJipIEcRojFjHiNEYSJwjDGEmaIBYx0jSG\ngIDAcI2z1xkAADqdaJhkQYIsK1AlDYqsQJVVmJICVVWhasPfa4p6XfJkGSpMTeGXPi0Nh/uoaMK4\nf4qOyzY12KaGjbKLfhCjM4jQHUTQTAf9aICtYBtJnCAOYwRpjAQJ4jRBkiaQJOngRqsMWRrOZsmS\nBAnKMHFSdHiaBs3QoCsadE2GriqwjWHyZBsa4yDNLSZUS87U1eeVGI+TFFGSIo4P/p1c8+84RZKm\nV+48CQjk/eFepqbehCQNZ60UWYaqyNCUg3+rB/+tXv0zomXGfVQ0af0ggW9aTKjo2A7Pyzvcq1Qq\nldAbRLhoqkjS4bXAtdcGcSIgScMESpakg2sBCbI8/L2uyjA0BbqqwNAVrj6hhcNvcHoe9TDhOeJ5\neKVSCQBQrzNAEh0H91HRpAyXWkuwNJN7T2gsbFND0WOgIroRThMQEWVkWD7dRj9Isu4KLZjh/ime\nP0VENA1MqIiIMuKYGizFRBgN91ERjctw/xSX+xERTQMTKiKijFzZR6UM91ERjUt/MJyhYkJFRDR5\nTKiIiDLkWof7qNKsu0ILYlgkQIKlWdw/RUQ0BUyoiIgy5BjcR0Xj1Q9SWKoFx1S5f4qIaAqYUBER\nZejafVQJ91HRGPQGCRzVhsPlfkREU8GEiogoQ7IswbV1WKqNXp+zVHRyvUECW3Pg2Uc8+4KIiE6E\nCRURUcZ8W4ejOej046y7QnOuHyRQoMMxDFg6908REU0DEyoioozlbAOu5qIXpCyfTifS6cdwdAc5\nzk4REU0NEyoiooxpqgzPMmDIBotT0Il0+wlc1YHvGFl3hYhoaTChIiKaATlbh6d56HAfFY0oCFMg\nVeAYFgtSEBFNERMqIqIZkLN1OLqDLvdR0Yi6/RiO5iJncbkfEdE0MaEiIpoBpq7CMQxossllfzSS\nTj+Bq7vIcbkfEdFUMaEiIpoROdtgtT8aSRSniGMJjmbDs7jcj4homphQERHNCN/W4agOOj3OUNHx\ndPsJHM2BZ2uQJCnr7hARLRUmVEREM8I2NTiGCVmowwIDREfU6cdwWS6diCgTTKiIiGaIbxtwdC77\no6NLEoEgEnBUJlRERFlgQkVENENytg5Xc5lQ0ZF1BzFsxYFr61Bkfq0TEU0bIy8R0QxxLQ22ZiOJ\nZYQxl/3R7XUO9k/lWd2PiCgTTKiIiGaIJEnI2Rpc3UWXh/zSbaSpQD9IhwUpeP4UEVEmmFAREc2Y\nnHNQPr3HZX90a91BAlMx4VkGNJVf6UREWWD0JSKaMTlLh6e7iGMZYcRlf3RzrW6MnO6j4HK5HxFR\nVphQERHNGFmWUHAN5HQPzW6UdXdoRkVxiiAUyOku8kyoiIgyw4SKiGgGFT0TOd1Hp5dACJF1d2gG\ntbsxXM2D7xis7kdElCFGYCKiGWQZKjzThCYZLE5BN9TqxfD1HIqemXVXiIiWGhMqIqIZdThL1eqy\nOAVdrzdIIAsdnmnDZXU/IqJMMaEiIppRBc+Ab3johynihMUp6KpWN4Kv51BwOTtFRJQ1JlRERDNK\nkWX4jgFPy3GWiq5IUoHeQMAzPBQ8FqMgIsoaEyoiohlWcE34OhMquqrdi2ErNnzbhK4qWXeHiGjp\nnSiheuCBB2BZFjzPg+d5eN3rXjeufhERXWdZ441n63ANG7LQ0RuwOAUBrU6MnOGjwGIUE7GssYaI\nRqee5MGSJOEDH/gA3vjGN46rP0REN7TM8abomdjt5tDq7sE2OSOxzAZhgjSR4RkOfJvFKCZhmWMN\nEY3mxEv+eD4KEU3LssabgmfAMzz0BgJJupzPAQ21ugezU64BSZKy7s7CWtZYQ0SjOXFC9Sd/8ieo\nVCr42Z/9WXz3u98dR5+IiG5oWeONrirI2SZsxUa7x71Uy0oIgU4vQU73uNxvwpY11hDRaE605O+v\n//qvcf78eSRJgve85z345V/+ZTz55JNQ1av/21KpdOJOHpemaZm0nVW7y9o2xzxdh21nZdnjjaw7\nCCCwHVyEn3evjNvP+xNt90ayanvZx9zqRKjkczhdXcXG6uTf61nHuawcJdYAyxn/OebFbXdZ2x5X\nvJHEmOa1hRDwfR9f/vKXcf78eQDA5z73OXz+85+/8jP33Xcf7r///nE0d0uHT04URRNvaxbaXda2\nOebJe/TRR/HYY48BABRFwX333YeXvvSlU2n7VpYx3ggh8N9Pb+Op3f8PqzUNnjOcoYjj6c9YHV5Y\nTrvtrNrNsu1r2/3B5S6K2gpedGodZd+eeNvTjDfzFGuAbOINv/Omi2Ne3LYnEW9ONEP1XJIkPW/d\n8UMPPXTd7+v1+jibvKHD7HYabc1Cu8vaNsc8eefPn79yEVEqlfD4449Ppd2jWMZ4IycBlFDBD56t\n4567agCAZqM58Xaf63CWZtptZ9Vulm0ftru1tYfGXoxSQUCEPdTr/Ym3Pc339rzFGmD68YbfedPF\nMS9u25OINyPvoWo2m/j0pz+NIAgQBAHe/e53o1ar4YUvfOGJO0VEdC3Gm6FyzoJv+OgHAmGUZt0d\nmqL9doSCUUApZ0KWWYxiUhhriGgUIydUURThne98J8rlMlZXV/GVr3wF//qv/wpFYUlfIhovxpsh\nTZVR8iz4uo/9Vph1d2hKwihFPxDwzRxKnpV1dxYaYw0RjWLkJX/lchnf+MY3xtkXIqIbYry5quxb\n2GnlUe/UUcpzlmoZ7LUC+LqPomtBU09cnJdugbGGiEbByExENEdMXUXeseDqHhrt6W8cpumKkxTt\nToK8kUfZ5+wUEdEsYkJFRDRnKr6FklVEsx3xANIF12hH8PQcCq4NUx9rHSkiIhoTJlRERHPGtXQU\nHBeGbKPZ4UG/iypNBRqtEEWriApnp4iIZhYTKiKiOVQrOCjbZexzlmphNToRbNVDyXXhmNkedktE\nRDfHhIqIaA7lXRMF24UuW2h1OUu1aNJUoNmJUbZLWCk6WXeHiIhugQkVEdGcWim6KJlFzlItoFY3\nhik7KDguPNvIujtERHQLTKiIiOZUwTPhWw40yUS7x1mqRSGEwH47QtEscHaKiGgOMKEiIppj1byN\nolnCfosl1BdFsxvDkG3kbQe+Y2bdHSIiug0mVEREc6zgmvBNBwoMNDtMquZdmgrstyKUzCKqeTvr\n7hAR0REwoSIimnMrRQcVq4K9VoQk5V6qebbXimArLgqOC9/h3ikionnAhIqIaM7lHQMFx4WteNhr\nhVl3h0YUxila3QQlq4T1kpt1d4iI6IiYUBERLYD1kouyXUKrmyCM06y7QyOoN0LkjQIqOReWoWbd\nHSIiOiImVEREC8AyVFQ8B0WjhN0GZ6nmTW+QIAgklK0iVgqs7EdENE+YUBERLYiVooOSVUAUyOgO\nWEZ9nuw0ApStMqp5G5rKr2YionnCqE1EtCBURUatYKNsl7HbCHnY75xodiIowkDR9lHxray7Q0RE\nx8SEiohogZRzFgpWDipMNLucpZp1SSqw14pQsSpYLTqQJCnrLhER0TExoSIiWiCSJGG16KBsVrDP\nMuozb68VwlFzKLosk05ENK+YUBERLRjfMVDyXDhqDntNFqiYVWF0WCa9iDWWSScimltMqIiIFtBq\n0UHZKqHdSxFGLKM+i3YbIUpGCdWcC0tnmXQionnFhIqIaAFZuopKzkHJKGF7P8i6O/Qc3X6MKJRR\ntAqoFeysu0NERCfAhIqIaEHVCjZKTgEi0bHfjrLuDh1IEoHt/RA1p4aVggNV4VcxEdE8YxQnIlpQ\nqiJjo+xhxV7BfitGEHLp3yzY2guQ0/IoezmUWSadiGjuMaEiIlpgOVvHSt5D2axgc2/As6ky1uhE\nSGINVaeCU2Uv6+4QEdEYMKEiIlpwq0UHFTcPAw52G6z6l5UwSrHXjFGza9gou9BUfgUTES0CRnMi\nogUnyxJOV3KoOlV0ekB3wAN/p00Igc16gJJZxorv8cwpIqIFwoSKiGgJWIaK9ZKHFWcF23shkoRL\n/6ap3oygwUbFKfDMKSKiBcOEiohoSVR8G2XXg6f52GIp9anpDRK0uylqThWnKx5kWcq6S0RENEZM\nqIiIlsipioeqXUEcqmh2WEp90pJ0WCK9atewWvBgm1rWXSIiojFjQkVEtER0VcFGxUPNrqHejBHG\nLKU+Sdt7ARwlh4rr8wBfIqIFxYSKiGjJ5B0DK/kcSmYZm7sB0pT7qSah0YkQhgpqTgWnqyyRTkS0\nqJhQEREtobWSg6pbgCl7uFwPeD7VmHV6MfabCdacNayXXeiqknWXiIhoQphQEREtIUWWcW7Fx5pX\ng5SY2N7j+VTjMggSbO9HWHPWsFHyUXDNrLtEREQTxISKiGhJ6aqCczUfa+4KwlBFvcmk6qTCOMXl\neoCavYLVPPdNEREtAyZURERLzDJUnK3lseauotMBK/+dQJIIXNoZoGhUsJLLY6PCfVNERMtAzboD\nRESUrZyt40wljyRNcbF5AaoiwbH49XAcaSpwaXcATytgNVfCmWou6y4REdGU8BuTiIhQ9EyEsQ8h\nUlzcu4i1igRTZyGFo9qsB9DhYtWt4Gwtx8N7iYiWCBMqIiICAKwUHERxiljEuLy7ifWqCV3lyvDb\n2d4PIBIDa7kVnFvxoSp8zoiIlgkTKiIiumKj7CJKUsRpgss7O1ivmkwQbmGvGWLQV3A6t4pztRwM\njbN6RETLhgkVERFdIUkSzlZzSJIUaSvFhe09rJUN6BqTqufa3g8w6CtY99ZwpurDNrWsu0RERBlg\nQkVERNeRZQnnVnxIkgSlpeDi9g5Wyjosg7MvwLAAxeZeABHrOJ0bJlO+Y2TdLSIiyggTKiIieh5V\nkXHnqg9NlaE2VFzevYxKQYNnL/fXRpIMq/npcId7pmo5zkwRES255f5mJCKim5IkCWeqOWiKDEVS\ncGn/EuJEwM9n3bNshFGKZ7f7w9LobgXnVnzumSIiIiZURER0a2slF7qqQK0ruNi+hM16HyslK+tu\nTVU/iHFxq4+CXsFqroSztRyLdRAREQAmVEREdARl34KmylAkGa1+Bxe2e3BUsRT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       "text": [
        "<matplotlib.figure.Figure at 0x7f1a22fbf7b8>"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "And for those of you viewing this online or in IPython Notebook on your computer, here is an animation.\n",
      "<img src='ellipse.gif'>"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "From a mathematical perspective these display the values that the multivariate gaussian takes for a specific standard deviation (in this case $\\sigma=1$). \n",
      "\n",
      "Thinking about the physical interpretation of these plots clarifies their meaning. The first plot uses the mean and covariance matrices of\n",
      "$$\n",
      "\\begin{aligned}\n",
      "\\mathbf{\\mu} &= \\begin{bmatrix}2\\\\7\\end{bmatrix} \\\\\n",
      "\\Sigma &= \\begin{bmatrix}2&0\\\\0&2\\end{bmatrix}\n",
      "\\end{aligned}\n",
      "$$ \n",
      "\n",
      "Let this be our current belief about the position of our dog in a field. In other words, we believe that he is positioned at (2,7) with a variance of $\\sigma^2=2$ for both x and y. The contour plot shows where we believe the dog is located with the '+' in the center of the ellipse. The ellipse shows the boundary for the $1\\sigma$ probability, where $1\\sigma$ is one *standard deviation*. In other words, for this Gaussian 68% of the data will fall within this ellipse. Recall from the Gaussians chapter the the 68-95-99.7 rule - 68% of all values will fall within 1 standard deviation ($1\\sigma$), 95% within $2\\sigma$, and 99.7% within $3\\sigma$. The dog could be at (356443,58483), but the chances for values that far away from the mean are infitestimally small.\n",
      "\n",
      "An equivalent way of thinking about this is the circle/ellipse shows us the amount of error in our belief. A tiny circle would indicate that we have a very small error, and a very large circle indicates a lot of error in our belief. We will use this throughout the rest of the book to display and evaluate the accuracy of our filters at any point in time. "
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The second plot uses the mean and covariance matrices of\n",
      "\n",
      "$$\n",
      "\\begin{aligned}\n",
      "\\mu &=\\begin{bmatrix}2\\\\7\\end{bmatrix} \\\\\n",
      "\\Sigma &= \\begin{bmatrix}2&0\\\\0&9\\end{bmatrix}\n",
      "\\end{aligned}\n",
      "$$\n",
      "\n",
      "This time we use a different variance for $x$ (2) vs $y$ (9). The result is an ellipse. When we look at it we can immediately tell that we have a lot more uncertainty in the $y$ value vs the $x$ value. Our belief that the value is (2,7) is the same in both cases, but errors are different. In this case the standard deviation in $x$ is $\\sigma_x = \\sqrt{2}=1.414$ and the standard deviation for $y$ is $\\sigma_y = \\sqrt{9}=3$. This sort of thing happens naturally as we track objects in the world - one sensor has a better view of the object, or is closer, than another sensor, and so we end up with different error rates in the different axis."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The third plot uses the mean and covariance matrices of:\n",
      "$$\n",
      "\\begin{aligned}\n",
      "\\mu &=\\begin{bmatrix}2\\\\7\\end{bmatrix} \\\\\n",
      "\\Sigma &= \\begin{bmatrix}2&1.2\\\\1.2&2\\end{bmatrix}\n",
      "\\end{aligned}\n",
      "$$\n",
      "\n",
      "This is the first contour that has values in the off-diagonal elements of $cov$, and this is the first contour plot with a slanted ellipse. This is not a coincidence. The two facts are telling use the same thing. A slanted ellipse tells us that the $x$ and $y$ values are somehow **correlated**. We denote that in the covariance matrix with values off the diagonal. What does this mean in physical terms? Think of trying to park your car in a parking spot. You can not pull up beside the spot and then move sideways into the space because most cars cannot go purely sideways. $x$ and $y$ are not independent. This is a consequence of the steering system in a car. When your tires are turned the car rotates around its rear axle while moving forward. Or think of a horse attached to a pivoting exercise bar in a corral. The horse can only walk in circles, he cannot vary $x$ and $y$ independently, which means he cannot walk straight forward to to the side. If $x$ changes, $y$ must also change in a defined way. \n",
      "\n",
      "So when we see this ellipse we know that $x$ and $y$ are correlated, and that the correlation is \"strong\". The size of the ellipse shows how much error we have in each axis, and the slant shows how strongly correlated the values are.\n",
      "\n",
      "A word about **correlation** and **independence**. If variables are **independent** they can vary separately. If you walk in an open field, you can move in the $x$ direction (east-west), the $y$ direction(north-south), or any combination thereof. Independent variables are always also **uncorrelated**. Except in special cases, the reverse does not hold true. Variables can be uncorrelated, but dependent. For example, consider the pair$(x,y)$ where $y=x^2$. Correlation is a linear measurement, so $x$ and $y$ are uncorrelated. However, they are obviously dependent on each other. "
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Unobserved Variables"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Let's say we are tracking an aircraft and we get the following data for the $x$ coordinate at time $t$=1,2, and 3 seconds. What does your intuition tell you the value of $x$ will be at time $t$=4 seconds?"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import mkf_internal\n",
      "mkf_internal.show_position_chart()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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nzm3/ecKECTFx4sTuHgkAgEPYihUrYuXKle2PzzzzzE737ZFnkGfPnt3hcUNDQ3eOAx2U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\nRK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f1a23b46b38>"
       ]
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "It appears that the aircraft is flying in a straight line because we can draw a line between the three points, and we know that aircraft cannot turn on a dime. The most reasonable guess is that $x$=4 at $t$=4. I will depict that with a green arrow."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "mkf_internal.show_position_prediction_chart()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAskAAAGDCAYAAADZHo16AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n9sSmrTF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4MJ555pnYt29fm20Pe/bsiVwuF01NTRHxx5v9IiL69OnTZu/yqaeeGj/96U9j\ny5Ytceqpp0YmkyncvNfU1BTNzc2xZ8+eiIh48803Y/fu3VFdXR39+/eP2tra+Iu/+Iu4//77Y/Dg\nwdG/f/+477774uSTT45x48YV448LoGyIZIATVFVVdcTjn/rUp2LJkiXx5S9/OSIizj///Dbvn1xb\nWxsvvvhirFq1KpqammLYsGHxiU98IhoaGgrnfOELX2iz7/fgW7ldfvnlcdlllxWev/jii2PTpk3x\nla98Jfbu3dvmLeDuvffeNm8T9y//8i8R0fZt4ubNmxdLly6NW265JQ4cOBDnnHNOXHvttUfcXnG0\n3z9AJfKJewAAkLAnGQAAEiIZAAASIhkAABIiGQAAEiIZAAASIhkAABIiGQAAEiIZAAASIhkAABL/\nD+qKaqgV54igAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f1a23058668>"
       ]
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "If this is data from a Kalman filter, then each point has both a mean and variance. Let's try to show that by showing the approximate error for each point. Don't worry about why I am using a covariance matrix to depict the variance at this point, it will become clear in a few paragraphs. The intent at this point is to show that while we have $x$=1,2,3 that there is a lot of error associated with each measurement."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "mkf_internal.show_x_error_chart()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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8vgp2m4T+0RhSmdzC3zjROeDk4BQAYFVzDQA9fqxMGwuibOqVY0rZlCRJOK9J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\nyDhpFa/R9HIHg2eSirRXPQNlGXq7D5GXXkp/q0ndZYoERK/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cOXKk18shGcHgmRBCliBR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\nTAghhBBCSJv8PznVxn99mBU/AAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f1a23076550>"
       ]
      }
     ],
     "prompt_number": 12
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We can see that there is a lot of error associated with each value of $x$. We could write a 1D Kalman filter as we did in the last chapter, but suppose this is the output of that filter, and not just raw sensor measurements. Are we out of luck?\n",
      "\n",
      "Let us think about how we predicted that $x$=4 at $t$=4. In one sense we just drew a straight line between the points and saw where it lay at $t$=4. My constant refrain: what is the physical interpretation of that? What is the difference in $x$ over time? In other words, what is $\\frac{\\partial x}{\\partial t}$? The derivative, or difference in distance over time is *velocity*. \n",
      "\n",
      "This is the **key point** in Kalman filters, so read carefully! Our sensor is only detecting the position of the aircraft (how doesn't matter). It does not have any kind of sensor that provides velocity to us. But based on the position estimates we can compute velocity. In Kalman filters we would call the velocity an *unobserved variable*. Unobserved means what it sounds like - there is no sensor that is measuring velocity directly. Since the velocity is based on the position, and the position has error, the velocity will have error as well. What happens if we draw the velocity errors over the positions errors?"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "mkf_internal.show_x_with_unobserved()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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4ypepy+cLSKZPX6mgdGSkhkuC0QzTep7PMNE6nsyctnmUtutlMKq1TZYVUaVh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\nIrKIwTMRERERkUUMnomIiIiILPp/xetSStXj64YAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f1a232bfba8>"
       ]
      }
     ],
     "prompt_number": 13
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Think about what this plot means. We have a lot of error in our position estimates. We therefore have a lot of error in our velocity estimates. But look at the intersections between the velocity and the positions. Take the intersection at $t$=2. The intersection between the velocity and the position is where our aircraft is most likely to be, which I have roughly depicted with a red ellipse ('roughly' because I set the size via eyeball, not via math). The size of the error is much smaller than the error of the positions, despite the fact that velocity was derived from position. \n",
      "\n",
      "What makes this possible? Imagine for a moment that we superimposed the velocity from a *different* airplane over the position graph. Clearly the two are not related, and there is no way that combining the two could possibly yield any additional information. In contrast, the velocity of the this airplane tells us something very important - the direction and speed of travel. So long as the aircraft does not alter its velocity the velocity allows us to predict where the next position is. After a relatively small amount of error in velocity the probability that it is a good match with the position is very small. Think about it - if you suddenly change direction your position is also going to change a lot. If the position measurement is not in the direction of the assumed velocity change it is very unlikely to be true. The two are correlated, so if the velocity changes so must the position, and in a predictable way.  "
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Kalman Filter Algorithm"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "So in general terms we can show how a multidimensional Kalman filter works. In the example above, we compute velocity from the previous position measurements using something called the *measurement function*. Then we predict the next position by using the current estimate and something called the *state transition function*. In our example above,\n",
      "\n",
      "$$new\\_position = old\\_position + velocity*time$$ \n",
      "\n",
      "Next, we take the measurement from the sensor, and compare it to the prediction we just made. In a world with perfect sensors and perfect airplanes the prediction will always match the measured value. In the real world they will always be at least slightly different. We call the difference between the two the *residual*. Finally, we use something called the *Kalman gain* to update our estimate to be somewhere between the measured position and the predicted position. I will not describe how the gain is set, but suppose we had perfect confidence in our measurement - no error is possible. Then, clearly, we would set the gain so that 100% of the position came from the measurement, and 0% from the prediction. At the other extreme, if he have no confidence at all in the sensor (maybe it reported a hardware fault), we would set the gain so that 100% of the position came from the prediction, and 0% from the measurement. In normal cases, we will take a ratio of the two: maybe 53% of the measurement, and 47% of the prediction. The gain is updated on every cycle based on the variance of the variables (in a way yet to be explained). It should be clear that if the variance of the measurement is low, and the variance of the prediction is high we will favor the measurement, and vice versa. "
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The chart shows a prior estimate of $x=2$ and a velocity $\\dot{x}=1$. \n",
      "\n",
      "> We use the familar dot notation $\\dot{x}$ to denote the derivative of x.\n",
      "\n",
      "\n",
      "Therefore we predict $x= 2+1 = 3$.\n",
      "\n",
      "However, the new measurement is $z=2.3$, giving a residual $r=0.7$. Finally, the Kalman filter gain $K$ gives us a new estimate of $x=2.8$.\n",
      "\n",
      "> We use the notation $z$ to denote a measurement. I will address notation in more detail later. It is an unfortunate reality that nearly every text on Kalman filtering uses different notation and variables - there is almost no agreement across texts. Be sure to read the introductory material very carefully to avoid being led astray."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from mkf_internal import *\n",
      "show_residual_chart()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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fQWGVvz4znftx91EGHOtblWUXivQwLRPW5iYwqvPPdTs7WzM8SHuqfmxjYaL+\n2aiODNn5rh4TlVaJgbhdu3YA8t6+yM7OhqWlZYmfBP3+++8xdOhQuLm5AQDGjh2Lb775hoGYiIio\nGLdu5QAAzHTIow9SM9U/P0zLxIvu9urHclnhv9P2CgtMHdwBkwe2L7SugY2ZOlCr6tOVfT1LnL+R\nVGwZCaW7g0R9GzM8fpqF7JxcGNeRA8jb3wY2RV+MIyoPneYQT5w4EWZmZggKCsLevXthVsKZmpCQ\ngNatW+OTTz7Be++9B3d3d1y+fLlCOkxERKSPzpyxgKenGTw9zXDmjEWxZYUAdkRdQnpmNs5efYA/\nrjyAdzvH/1+nfa7Da14u+CoyHhduJEEIgaS0TET8chUA4PWCI/68+hBnrz5AemY2voqML7bt/Aa/\n2BLR527h5z8SkatU4vq9NPz2/x+kU7GzNcOlm4+K36d8kyeaNrBCy8a22PzTeeTkKrHrxP/wPDcX\nHVo2KHIfhdbJF0S60ekuE5s2bcK6deuwefNmBAUFIS4uDqampkWWz8jIgKWlJeLi4pCYmIh+/foh\nPT1da1mFQlG2nlO5GBkZAeDx11ccX/3FsdVPt27lICTEDPfu5V2nCgmxwokTdeDoqP3PtFwuh5dH\nc/jO3gWZTIZ177yMdi5OAABTU1OYm5sVeo70USiwMkeOmVtO4sa9NNhYmmC4jzsUCgUUCgU+ndof\nb284hpwcJUb1eQHhkRehUCiQm6uE3dA1kCQJmVnP8ebqnyGXybDq7Zcwpk87KBQKfP/hMHywJQrv\nfhqNxgpLbHy3r0b7S97yxfztMZj/1S9446W2WBzsjei/EjF00S4IISBJEtzHfwVJAn7Z8CZa2tdF\n+AdDMPGTg/j0p3No3sgW38wfCofGDbXuo5GRESwtLWv0ecFzt2aTRCm/GsbNzQ0rV67EgAEDiiwz\naNAgeHl5YcaMGQCA3bt3Y/78+bhw4YJGucjISBw7dkz92MvLC97evG1KVVCdmM+fP6/mnlBl4Pjq\nL46tfrp1Kweenv8E4kaNlDhxIrPIQNx6zKf4bFo/+LZvVoW9pPLguVv1oqOjERMTo37s6+sLf39/\nrWVLfR9iXfKzi4sLLl26pH4cFxcHV1dXrWUnTpyo8Tg5Obm0XaIyUL1C5fHWTxxf/cWx1U9mZsDm\nzTkICcn7cNrmzU9gZpaBooZZqczF48eP+TyoRXjuVr22bduibdu26sfx8UVPBSp2DvH9+/exZcsW\nPH78GDmtH4cfAAAgAElEQVQ5Odi8eTMePHiAHj3+uYegj48P5syZo7FdYGAgfvjhB8TFxeH27dsI\nDQ3F8OHDy7o/REREeq9z5wycOJGJEycy0blzRskbEFGFKfYKsVwuR3h4OObMmYPs7Gy4u7sjIiIC\n9erVU5dJTExEixYtNLbr2rUrFi5cCF9fXzx//hwTJkzgHSaIiIiQ907r+RtJWLfnT/x1/SF2zOmP\nVva2AAB726eQzC3xKKX4On5Z+3oV9JTIcBQbiOvXr4/IyMhiK7h+/brW5VOmTMGUKVPK3jMiIiI9\noQrBe3+5hn2nr+Pmwyfqdccv3EYre1uIRw+RNC8Epr79gdfGVmNviQxPqecQExERUel8/P3v+GTP\n2ULLjerIMMKndd6DpPtATg5ybydWce+ISKf7EBMREVHZ1bMyRcvGNvB+wVHjKyoGdGkOM2NemyKq\nbjwLiYiIKtnYvm3RwMYMkzcegwDQ0NYc91Of4tXuLUrclogqH68QExERVbIfY69i8sZjUAqBt15u\ng/upT2FhaqT+djkiql4MxERERJUofxiePqQjXunaHADwSjdOlyCqKXgmEhERVZKCYXjG0E4AgIhF\nA+HapF4JWxNRVWEgJiIiqgRFhWEA6OTcsBp7RkQFccoEERFRBSsuDBNRzcNATEREVIEYholqHwZi\nIiKiCsIwTFQ7MRATERFVAIZhotqLgZiIiKicGIaJajcGYiIionJgGCaq/RiIiYiIyohhmEg/MBAT\nERGVAcMwkf5gICYiIiolhmEi/cJATEREVAoMw0T6h4GYiIhIRwzDRPqJgZiIiEgHDMNE+ouBmIiI\nqAQMw0T6jYGYiIioGAzDRPqPgZiIiKgIDMNEhoGBmIiISAuGYSLDwUBMRERUAMMwkWFhICYiIsqH\nYZjI8DAQExER/T+GYSLDxEBMREQEhmEiQ8ZATEREBo9hmMiwMRATEZFBYxgmIgZiIiIyWAzDRAQw\nEBMRkYFiGCYiFQZiIiIyOAzDRJQfAzERERkUhmEiKoiBmIiIDAbDsH66ffs2XFxcIISo7q5QLcVA\nTEREBoFhuHZzdHREYmKi1nUODg5ISEiAJElV1ibpFwZiIiLSewzDtZvqym9VXgGujjap+jAQExGR\nXmMYLqxbt25YtWoVevbsiTZt2uCrr75Sr1MqlVi9ejW6d++O9u3bY8GCBcjJyUF4eDjefvvtQnVt\n3rwZM2fOLLHNlJQUvPPOO2jfvj169OiB8PBw9brMzExMnDgRbdq0Qdu2bTFu3Dj1uqCgILRu3RoA\n0Lt3b7i4uGDRokXq9QMHDoSzszMcHR2hVCrVy7/99lv069cPnTp1woQJEzBmzBh06NABly5dAgAc\nPXoUvXv3RuvWrdG+fXssX75c5zbj4+MxbNgwtGnTBi+//DJ+//33EvefarZiA3FOTg5Gjx4Ne3t7\n2Nraws/PD3FxcTpVPH/+fNjb26N+/foYOXIknjx5UiEdJiIi0hXDsHaSJOHPP/9EZGQkVq1ahaVL\nl6rD5ObNm3H48GH8+OOPOHnyJBISErBlyxZ06tQJ586dK1TX+fPn0alTycd1ypQpMDY2xunTp/HN\nN99g1apV6vq+//57JCYm4syZMzh79ixGjRql3i4sLAwJCQkAgCNHjiAhIUEjnEZERODYsWNa2zQx\nMcGxY8dw+PBhBAcHY8SIEYiIiACQd+V32bJliIuLQ0REBMLDw/Hzzz+X2GZ6ejpGjhyJIUOG4MKF\nC5g9ezbGjRuHzMzMEo8B1VzFBuLc3Fw4OzvjzJkzSE1NxcCBAzF48OASK92zZw++/PJL/P7777h5\n8yYePXqEJUuWVFiniYiISsIwXLzhw4fD1NQUfn5+SE9Px4MHDwAA4eHhmDZtGho2bAgLCwuMGTMG\nBw4cgIuLC1JSUpCWloZNmzZh0qRJAIBz586hY8eOxbZ1//59REVFYcGCBTAxMYGTkxMGDBiAAwcO\nAADkcjnS09Nx/fp1GBkZwcvLq1T7UtS0BicnJ1hbW6Nu3bpo2bIlmjZtiqSkJACAv78/unTpArlc\njqZNm+LFF1/ExYsXS2zryJEjsLOzw8iRIyFJEvz8/KBQKPDbb7+Vqs9Us9QpbqWJiQnmz5+vfhwc\nHIzp06cjOTkZCoWiyO0uXbqEF198EY0bNwYADBgwAIcOHaqgLhMRERVPn8Pw6dOn4erqChsbm3LV\nY2trCwAwNjYGAGRlZQEA7ty5gylTpkAmy7tmplQqYWdnB0mS0K5dO5w7dw6xsbFIT09HamoqkpKS\n4OLiUmxbd+7cAQD06NFDvSwnJ0d9kW3YsGG4desWJk2ahKSkJAQFBWH27Nnl2j8A6n2oU6cOZDIZ\nZDIZcnJyAABnz57F0qVLkZCQgJycHGRmZqJly5Yl1nnnzh0kJCTA3d1dvez58+d4+PBhuftL1afY\nQFxQbGwsHBwcig3DAPDSSy/hiy++wK1bt2Bra4t9+/YhICCgXB0lIiLSRW0Pw1lZAkZalt+4cQPb\nt29Hhw4d0LVr10pr38HBAWvXrtV61bdjx47qK6Fdu3ZFeHg4PDw8SqzT3t4eJiYmuHjxotY7QRgb\nG2PWrFmYNWsWLl68iEGDBuHVV1/VCJ0VdQcJ1dXkSZMm4V//+he+/fZbyOVyjBs3rtCVZm1tOjg4\n4MUXX8TXX39dIf2hmkHnD9WlpaVh6tSpWL16dYllO3fujNdffx1NmzaFra0tjIyMNCbIExERVYba\nHIYvXTIDAPz1pwxnzliolz9+/Bhr1qzBzz//jJkzZ8LPzw/37t3DlStXcPbsWRw/fhwHDx7Ed999\nh23btmHDhg1YtWoVvvzyyzL1Y8SIEfj4449x//59CCFw9epVxMTEAMgLxGFhYejevTu8vLzwxRdf\nlDhdAgAaNmyIHj16YOnSpXj69CmeP3+O3377Tf25pNOnT+PSpUsQQkAmk0EIAUtLS4067Ozs1B+I\nK0pp7giRkZGBunXrQiaT4dSpU4iKiipURlub/v7+uHTpEvbt24ecnBw8ffoU+/fvR1pams5tU82j\n0xXirKwsBAQEYMSIEQgMDCyx/MaNG3H8+HEkJSXBxMQEY8eOxZQpU7Bx48ZCZUu62kyVw8go7/oD\nj79+4vjqL45t0XZGxWHyprwwPO+Nnpg/qld1d0lnt27lYNUqM2x2AbKfS3gnxAonTtSBo2MdDBo0\nCPXq1UOnTp2wfft2WFpawtLSEtbW1rCysoJCoUDz5s1haWkJKysrWFtbw8TEpNgrqjKZDNbW1urn\nkSRJsLW1hUKhwNy5c7F8+XIMHToUycnJaNKkCWbOnAmFQgF/f388fPgQAwcOhLu7OzIyMuDj46PT\n8zEsLAyzZs2Cl5cXMjMz0bZtW6xcuRIKhQJZWVmYMGEC7t69i7p162L58uXo0KGDxvZLlizB/Pnz\nMX/+fLzxxhtYvHgxoqOjMXToUAghIEkS3N3dIUkSYmNjYWVlBVNTUygUCshkMtStW1dj2fr16zF7\n9mzMnTsXvXv3Rv/+/WFmZqaxL9raVCgU2LdvH2bOnIn3338fcrkcnp6eGDRoEKytrYvcf567NZsk\nSng5lZubi8DAQNjZ2eGzzz7TqdJXXnkFffv2xeTJkwEAP/30E2bMmFHoVVZkZKTGJ0O9vLzg7e1d\n2n2gMlCdmM+fP6/mnlBl4PjqL46tdjuj4hC8Yi+UytoXhoG8QPxO33hsdpmA04864J0bm3HiRCYc\nHfOuW/3222/48ccf0aBBA4waNQr16tWr5h5TafHcrXrR0dHqdzcAwNfXF/7+/lrLlhiIx44di9TU\nVOzcuVM9OT0/Hx8fdO/eHR999JF62cyZM/H777/jhx9+gKmpKUJCQpCeno5du3ZpbBsZGQk3N7dS\n7RxVDNUr1OTk5GruCVUGjq/+4tgWVpunSeQXH3EVLnun4eyT9sB7q9C5c0ahMnfv3sXOnTvh7++P\ntm3bVkMvqax47la/+Pj4IgNxsXOIExMTERoaioMHD8LGxgZWVlawsrLCyZMnNcqobtWisnDhQjRp\n0gQuLi5wcHBAamoq1q9fXwG7QkRE9A99CcMA4Oqadx9bj/ZKrWEYABo3box3332XYZioghU7h9jJ\nyUnjW1+0uX79eqFllpaW2L59e/l6RkREVAx9CsP5mZhIKP4vLxFVNH51MxER1Tr6GoaJqHowEBMR\nUa3CMExEFY2BmIiIag2GYSKqDAzERERUKzAME1FlYSAmIqIaj2GYiCoTAzEREdVoDMNEVNkYiImI\nqMZiGCaiqsBATERENRLDMBFVFQZiIiKqcRiGiagqMRATEVGNwjBMRFWNgZiIiGoMhmEiqg4MxERE\nVCMwDBNRdWEgJiKiascwTETViYGYiIiqFcMwEVU3BmIiIqo2DMNEVBMwEBMRUbVgGCaimoKBmIiI\nqhzDMBHVJAzERERUpRiGiaimYSAmIqIqwzBMRDURAzEREVUJhmEiqqkYiImIqNIxDBNRTcZATERE\nlYphmIhqOgZiIiKqNAzDRFQbMBATEVGlYBgmotqCgZiIiCocwzAR1SYMxEREVKEYhomotmEgJiKi\nCsMwTES1EQMxERFVCIZhIqqtGIiJiKjcGIaJqDZjICYionJhGCai2o6BmIiIyoxhmIj0AQMxERGV\nCcMwEekLBmIiIio1hmEi0icMxEREVCoMw0SkbxiIiYhIZwzD+kskP0Tu5OEQQhRbLnf8IIiH98rV\nlvK348idPBy5E4ZAuSesXHURVQQGYiIi0gnDsH6TFA0g3/AtJEmq9LZkXXrltdXNG6iC9ohKwkBM\nREQlYhimSlPCFWmiqlCnujtAREQ1G8NwzZM7ZyyklwMgThwB7t8G3Dwge/t9iH3fQpyKBJ5nQ+rS\nC1LgW5DkcgCA8qedEMf2A9nPADt7yCbPg2SryKvvo1nArRtAdhZkn+2GJPvnepm4eQ3KbZ8ASQ8g\nvRyg0Q9l6FqgXn3IBgfl1fPxXEjdfSDr1Qfi4T0ot68H/r4OCCUk9w6QRk+GZG5RNQeJqBSKvUKc\nk5OD0aNHw97eHra2tvDz80NcXJxOFR85cgQeHh6wtLREq1atcO7cuQrpMBERVR2G4ZpLxByCbOx0\nyNZ9A1m/YRCH90Cc+w2yOSsgW7oZ4s5NiMi9eWXv3YLY/x1k76+AfN03kAW9DdQxUtcln7MCsg83\nFG5DCCi/WAXpRX/I1oQB6U80C0iS5pSH/I9zcyB594VsxVbIVoRCZDyB2PtNhR8HoopQbCDOzc2F\ns7Mzzpw5g9TUVAwcOBCDBw8usdIbN25g6NCh+OCDD/D48WOcPHkSjRs3rrBOExFR5WMYrtkkr5ch\nNW4CSSaD1KI1xInDkL0yHJJtPUimZpD59Ic4G6sqDSiVwN2/IXJyIDVzhmRprVmhtqkLD+8BD+9B\n8hsASS6H1HtQ4TJFTHmQGjlC1qUXJBMTSKbmkDq9CHHrenl2majSFDtlwsTEBPPnz1c/Dg4OxvTp\n05GcnAyFQlHkdtu2bUO/fv0QGBgIAGjYsGEFdZeIiKoCw3DNJ9nZay549BDK0DX/XKEVArCpm1e2\nkQOkUROh/GknsHkFpDYdIQW/A8nUvPhGnqQB5haQZHnTLmBto3P/xONUiG8+h/hfXN40jZwcoFkr\nLTvCD9VR9SvVHOLY2Fg4ODgUG4YB4Ny5c2jYsCG6d++OGzduwN/fH59++imsra2L3Y6IiKofw3At\nISvwJm+9BpC9ORVSi9bai7/oD7zoD/EkDcrVC4ATRyC9NLD4NqxtgacZELm5eXORH6dqrjcyApS5\n/zzOfKr+UfzwJSDJIFuyCZKpGZSReyHOnNTcvk4dIDcXRNVN50CclpaGqVOnYvXq1TqVjY6OxtGj\nR+Hs7Izhw4djwYIFWLt2baGyJYVrqhxGRnlzx3j89RPHV39V9tjujIrD5E15YXjeGz0xf1SvSmmH\nCsu2tkEqAEmSShzfJLkc1jY2MM5XLqP3IGTv3wnrdz6ArK4CuXf/hvLBPRi374rce7eR+/AejFzb\nQRgbIUUug3kDO5jl2z43NxvJABT16qk/iCfq1cOjxo4w+zUKZn2HID3ia2QCqGtrC7lCgafNnZH1\nRyzqKhTIuXMTj+4kwtLSEmYKBdKEEpKtLawa20P58B5STx6GzNIadfO1+bSFC7LOnICtra26TX3F\n38s1m06BOCsrCwEBARgxYoR6GkRxLCws0KdPH3h4eAAAxo8frzH1Ir8lS5aof/by8oK3t7cuXSIi\nogq2MyoOwSv2QqlkGK6NzAeOAJ5nI2Xe2xBP0iCr3xAWQ0YBAERODtLDPkPurRuAkTFMunvD1Lsv\nACD7wh9IWzYrrxJJQtKolwFJQt2VW1GnsSNspi3C4/X/RsY3W2A+JEhjioOpX39k/RqD5HffgFEL\nV9Rp6apeZzH8LTxetwRJQX0gd2wGky6eeH7pvEafTV96Fdl/nkbSqJchb9Ic9ZZ/XrkHiQxKdHQ0\nYmJi1I99fX2LLCuJEr6SJjc3F4GBgbCzs8Nnn32mUwemTZuGe/fuYceOHQCAiIgIzJ8/H3/99ZdG\nucjISLi5uelUJ1Us1SvU5OTkau4JVQaOr/6qrLHlNInqJxIuQPnxXBi5e0A5bUnJG1Ctwt/L1S8+\nPh7+/v5a15X4xRwhISGQyWTYtGmT1vU+Pj6YM2eOxrKAgADs378fFy5cwLNnz7Blyxb4+fmVoetE\nRFTZGIaJyNAVG4gTExMRGhqKgwcPwsbGBlZWVrCyssLJkyc1yjx48EBjOy8vLyxYsAC9e/eGg4MD\nLCwssHjx4srZAyIiKjOGYSKiEuYQOzk5QalUFlvB9eva7yk4Y8YMzJgxo+w9IyKiSsUwTESUp8Qp\nE0REpH8YhomI/sFATERkYBiGiYg0MRATERkQhmEiosIYiImIDATDMBGRdgzEREQGgGGYiKhoDMRE\nRHqOYZiIqHgMxEREeoxhmIioZAzERER6imGYiEg3DMRERHqIYZiISHcMxEREeoZhmIiodBiIiYj0\nCMMwEVHpMRATEekJhmEiorJhICYi0gMMw0REZcdATERUyzEMExGVDwMxEVEtxjBMRFR+DMRERLUU\nwzARUcVgICYiqoUYhomIKg4DMRFRLbMzKo5hmIioAjEQExHVIjuj4hC8Yi/DMBFRBapT3R0gIiLd\n/Bh7FZM3HYNSyTBMRFSRGIiJiGqB/HOG573RExP7u1d3l4iI9AanTBAR1XAFw/D8Ub2qu0tERHqF\ngZiIqAYreDcJhmEioorHQExEVEPx1mpERFWDgZiIqAZiGCYiqjoMxERENQzDMBFR1WIgJiKqQRiG\niYiqHgMxEVENwTBMRFQ9GIiJiGoAhmEiourDQExEVM0YhomIqhcDMRFRNWIYJiKqfgzERETVhGGY\niKhmYCAmIqoGDMNERDUHAzERURVjGCYiqlkYiImIqhDDMBFRzcNATERURRiGiYhqJgZiIqIqwDBM\nRFRzMRATEVUyhmEiopqt2ECck5OD0aNHw97eHra2tvDz80NcXFypGnjppZfQpEmTcnWSiKi2Yhgm\nIqr5ig3Eubm5cHZ2xpkzZ5CamoqBAwdi8ODBOlf+7bff4smTJ5AkqdwdJSKqbRiGiYhqh2IDsYmJ\nCebPnw97e3sAQHBwMK5cuYLk5OQSK05PT8fy5csxb948CCEqprdERLUEwzARUe1RqjnEsbGxcHBw\ngEKhKLHs4sWLERISAmtr6zJ3joioNmIYJiKqXeroWjAtLQ1Tp07F6tWrSywbHx+PyMhILF++HNHR\n0cWW1SVcU8UzMjICwOOvrzi+1WdnVBwmb8oLw/Pe6In5o3pVaP0cW/2VbW2DVACSJHF89RDP3ZpN\np0CclZWFgIAAjBgxAoGBgSWWnzJlCpYtW6bT3OElS5aof/by8oK3t7cuXSIiqnF2RsUheMVeKJWV\nE4aJiEh30dHRiImJUT/29fUtsmyJgTg3Nxevv/46XFxc8OGHH+rUgTNnzqBfv34ay+RyOVJSUgpN\noZg4caLGY13mJ1P5qV6h8njrJ45v1Ss4TWJif/dKOf4cW/0lHqfl/S8Ex1cP8dytem3btkXbtm3V\nj+Pj44ssW+Ic4pCQEMhkMmzatEnreh8fH8yZM0djWUpKCpRKJZRKJY4dOwYHBwfk5uZyPjER6SXO\nGSYiqt2KvUKcmJiI0NBQmJubw8bGRr384MGD6Nmzp7pMixYtiqxDCMHbrhGR3mIYJiKq/YoNxE5O\nTlAqlcVWcP369WLX+/j44ObNm6XvGRFRDccwTESkH/jVzUREZcAwTESkPxiIiYhKiWGYiEi/MBAT\nEZUCwzARkf5hICYi0hHDMBGRfmIgJiLSAcMwEZH+YiAmIioBwzARkX5jICYiKgbDMBGR/mMgJiIq\nAsMwEZFhYCAmItKCYZiIyHAwEBMRFcAwTERkWBiIiYjyYRgmIjI8DMRERP+PYZiIyDAxEBMRgWGY\niMiQMRATkcFjGCYiMmwMxERk0BiGqcaoWx+QJMgbNK7unhAZHAZiIjJYDMNUk0gNGkGx+QdYTZxT\n3V3RS46OjkhMTKzublANVae6O0BEVB0YhqkmuvusHvAMMDOr7p7oFyGExv9EBfEKMREZHIZhqonO\nnLGAp6cZPD3NcOaMhc7bffvtt+jXrx86deqECRMmYMyYMejQoQMuXboEpVKJ1atXo3v37mjfvj0W\nLFiAnJwcAMDNmzcRGBiINm3awNXVFSEhIXj8+LG63sOHD6NXr15o3bo1PD09ER0drV7XrVs3HD9+\nXP244NXXqVOnYsGCBRg3bhxcXFzQrVs3ZGRkAAD2798PPz8/tGnTBqNGjcKDBw/U2wwbNgzt2rXD\nkiVL4O3tjX79+iEzMxMAkJKSgnfeeQft27dHjx49EB4ertHejBkzEBAQgNatW2PGjBnqdUFBQWjd\nujUAoHfv3nBxccGiRYt0Pr5kGBiIicigMAxTTfTokTFCQqxw754M9+7JEBJihUePjHXe3sTEBMeO\nHcPhw4cRHByMESNGICIiAps3b8bhw4fx448/4uTJk0hISMCWLVsAANnZ2QgKCsKZM2dw5swZpKSk\nYPXq1eo6Z82ahVmzZuHy5cv45ptv0KhRI/U6SZIgSVKxfdq1axeGDx+Oy5cvIzQ0FHK5HGfPnsXM\nmTOxZs0anD9/Hm3btsWsWbPUdXbu3Bnr16/H1q1bERERAVNTU5w5cwYAMGXKFBgbG+P06dP45ptv\nsGrVKpw7d07dXkxMDDZu3IijR49i3759+PPPPwEAYWFhSEhIAAAcOXIECQkJDMRUCAMxERkMhmHS\nV05OTrC2tkbdunXRokULNG3aFElJSdixYwemTZuGhg0bwsLCAmPGjMGBAwcAAK1atcKgQYNgZmYG\nS0tLDBgwAHFxceo6ZTIZbty4gSdPnsDR0VF9lVVXPXv2xEsvvQRJktCmTRuYmppix44dCAwMhIeH\nB2QyGUJCQhAZGYns7GwAQPPmzdG0aVMoFArY2NjA0dERycnJuH//PqKiorBgwQKYmJjAyckJAwYM\nUO8LAPTp0wf29vZwcHCAq6srrl27VgFHlgwF5xATkUFgGKaarF69bGze/AQhIVYAgM2bn6BevWyd\nt5fJ8q5v1alTB3K5HHK5HDk5Obhz5w6mTJmiXq9UKmFnZwcASEpKwvz58/Hrr78iMzMT2dnZ8PDw\nUNe5efNmbNiwAZ9++ilatmyJlStX6hyKJUlC8+bNCy2/e/cuYmNjsXPnTvUyY2Nj9bQJmUym3gfV\n/jx//hx3794FAPTo0UO9XU5ODgYPHqxuz8bGRr3OyMhIHbKJdMFATER6j2GYaoPOnTNw4kTen2Uz\ns4xy1yeEgIODA9asWYOOHTsWWv+f//wHcrkcMTExsLCwwJYtW7Bv3758/emMbdu2ITs7G7Nnz8aK\nFSvU0y1MTEyQm5sLAHjy5InW9lWhNj97e3tMnToVkydPLtW+2Nvbw8TEBBcvXixxqkZRyrodGQZO\nmSAivcYwTLWJo2MdODqW/1qV6m4Kw4cPx8cff4z79+9DCIGrV68iJiYGAJCRkQELCwuYmZnh5s2b\nCAsL09h+165dyMjIgCRJEELAyspKvb558+b4448/AAA//fRTke0X9Nprr+Grr77ChQsXIIRAUlIS\nIiIiitxO9djOzg49evTA0qVL8fTpUzx//hy//fabeoqHtvYKLrOzs8OlS5eKOGJk6BiIiUhvMQyT\nISj4ATfVY0mSEBISgq5duyIgIABubm4YP348kpOTAQDTp0/HuXPn4Orqirfffht9+vRR1yOEwO7d\nu9GlSxe0a9cODx8+xOzZs9VtTJs2Dbt27cKAAQNw//79Qldfi/rQXadOnbBw4UJMmzYNbm5u6N+/\nPy5cuKC176rHKuvWrUNSUhI8PT3h4eGBjz76CEqlssj2Cj6ePXs25s2bh06dOuGjjz7S/QCTQZBE\nNd6ULzIyEm5ubtXVvEFTKBQAoP7FSPqF46u/YZhjq984vvqLY1v94uPj4e/vr3UdrxATkd7R1zBM\nRESVg4GYiPQKwzAREZUWAzER6Q2GYSIiKgsGYiLSCwzDRERUVgzERFTrMQwTEVF5MBATUa3GMExE\nROXFQExEtRbDMBERVQQGYiKqlRiGiYioojAQE1GtwzBMREQViYGYiGoVhmEiIqpoDMREVGswDBMR\nUWVgICaiWoFhmIiIKgsDMRHVeAzDRERUmUoMxDk5ORg9ejTs7e1ha2sLPz8/xMXFlVjx/v370aVL\nF9jY2KBp06ZYunRphXSYiAwLwzAREVW2EgNxbm4unJ2dcebMGaSmpmLgwIEYPHhwiRVnZGRg+fLl\nSEpKwi+//IKwsDB8/fXXFdJpIjIMDMNERFQVSgzEJiYmmD9/Puzt7QEAwcHBuHLlCpKTk4vdLjAw\nEH5+fjAyMoK9vT369u2L2NjYiuk1Eek9hmEiIqoqpZ5DHBsbCwcHBygUilJv5+HhUdrmiMgAMQwT\nEX7KtpoAABNFSURBVFFVqlOawmlpaZg6dSpWr15dqkY2btyI7OxsBAcHF1pX2mBNFcPIyAgAj7++\nqs3juzMqDpM35YXheW/0xPxRvaq7SzVKbR5bKhnHV39xbGs2nQNxVlYWAgICMGLECAQGBurcwP79\n+7Fy5UocP35c/WTIb8mSJeqfvby84O3trXPdRKRfdkbFIXjFXiiVDMNERFQ+0dHRiImJUT/29fUt\nsqwkhBAlVZibm4vAwEDY2dnhs88+07kjp06dwvDhw3Ho0CG4u7sXWh8ZGQk3Nzed66OKo3qFWtJc\ncKqdauP4cpqEbmrj2JLuOL76i2Nb/eLj4+Hv7691nU5ziENCQiCTybBp0yat6318fDBnzhyNZefO\nnUNgYCB27typNQwTEakwDBMRUXUqMRAnJiYiNDQUBw8ehI2NDaysrGBlZYWTJ09qlHnw4IHGdmvX\nrsXDhw/Rp08f9TYDBgyo+D0golqNYZiIiKpbiXOInZycoFQqiy1z/fr1QstCQ0MRGhpa9p4Rkd5j\nGCYiopqAX91MRNWCYZiIiGoKBmIiqnIMw0REVJMwEBNRlWIYJiKimoaBmIiqDMMwERHVRAzERFQl\nGIaJiKimYiAmokrHMExERDUZAzERVSqGYSIiqukYiImo0jAMExFRbcBATESVgmGYiIhqCwZiIqpw\nDMNERFSbMBATUYViGCYiotqGgZiIKgzDMBER1UYMxERUIRiGiYiotmIgJqJyYxgmIqLajIGYiMqF\nYZiIiGo7BmIiKjOGYSIi0gcMxERUJgzDRESkLxiIiajUGIaJiEifMBATUakwDBMRkb5hICYinTEM\nExGRPmIgJiKdMAwTEZG+YiAmohIxDBMRkT5jICaiYjEMExGRvmMg/r/27j0o6ur/4/hrMeSmYZDK\nzVvGKumoCKKIiVKW3SxKNK00S6UcY7AmZGzUtMm8ZRIao42O000nL1iZ2ViZZBfTsq8RKuV4CW+A\nqAkKCLu/Pxz31wayK4LAfp6Pv9j9nHM+bz5nj7z8ePwA4KoIwwAAIyAQA6gWYRgAYBQEYgBVEIYB\nAEZCIAZghzAMADAaAjEAG8IwAMCICMQAJBGGAQDGRSAGQBgGABgagRgwOMIwAMDoCMSAgRGGAQAg\nEAOGRRgGAOAyAjFgQIRhAAD+H4EYMBjCMAAA9gjEgIEQhgEAqIpADBgEYRgAgOoRiAEDIAwDAHB1\nNQbiiooKjRkzRkFBQWrVqpXi4uKUk5Pj1MBvv/22AgIC5Ofnp2nTptVJsQCuHWEYAICa1RiIKysr\nFRoaqt27d+vs2bMaNmyYHnnkEYeD7ty5U7NmzdK2bduUnZ2tNWvWaO3atXVWNADnEIYBAHCsxkDs\n4eGh6dOnKygoSJL09NNP66+//tLp06drHHTdunV67LHHFBYWpqCgII0fP15r1qypu6oB1Cgvr0I7\n/3eaMAwAgBNuupbGP/74o4KDg+Xv719ju9zcXA0cOFBpaWn6+++/NWDAAH300UfXVSgA5+ze7aPE\nRC9Z3NzUY0g7DRsQqMT7ezR0WQAANFpOB+Jz584pOTlZixYtcti2pKRELVq0UE5Ojo4cOaL77rtP\nxcXF1bZ1FK5RP9zd3SVx/V1NXl6FEhO9dPKkmyQvuX05VmOmX5S//zX93ReNGGvXtTG/rou5bdyc\n+ilZVlam+Ph4Pf7440pISHDY3sfHR8XFxUpLS5MkZWZmqkWLFtW2fe2112xfDxw4ULGxsc6UBAAA\nAFzV9u3blZWVZXs9ePDgq7Z1GIgrKys1atQomc1mzZo1y6kCzGaz9u/fb3udk5Ojrl27Vtt20qRJ\ndq8d7U9G3bjyN1Sut2vx8pKWLatQYmJLSdKyZefl5VUiptl1sHZdG/PrupjbG6979+7q3r277fW+\nffuu2tbhc4gTExPl5uamd955p9rjgwYNUmpqqt17CQkJ2rBhg3JycnTs2DGtXLlSI0eOdLZ+ANch\nMrJEO3Zc1I4dFxUZWdLQ5QAA0OjVeIf4yJEjWrlypby9veXr62t7f8uWLYqJibG1ue222+z6RUVF\naebMmRo8eLAuXbqk5557zqmtFgDqRkjI5aXNjQgAAByrMRB36NBBFoulxgEOHTpU7ftJSUlKSkqq\nfWUAAADADcCvbgYAAIChEYgBAABgaARiAAAAGBqBGAAAAIZGIAYAAIChEYgBAABgaARiAAAAGBqB\nGAAAAIZGIAYAAIChEYgBXNWGDRs0evTohi6jTqSmpmrx4sUNXQYAoBGq8Vc3AzC2Rx99VI8++mhD\nl+GUN998U4cPH1Z6enq1x+fOnXvDzwkAaBq4QwwAAABDIxADLqxv376aM2eOIiIiFBUVpfXr19sd\nT05O1owZMzRhwgSZzWb17dtXJSUl+ueffxQaGqrOnTsrPj6+yrhffvmlBg4cqG7dumns2LEqKCio\nct5Vq1Zp6NChCg0N1bhx45yqd/PmzYqLi1O3bt301FNPKT8/33Zs69atuvPOO9WlSxcNGDBA27dv\nlyTt3LlTZrNZS5Ys0WeffSaz2awuXbqoqKjI1s9sNqtjx46aP39+lTqfeuophYeHa968eQoPD1dK\nSort+PPPP69evXopNDRUw4YN0759+5w6p8Vi0aJFi9SvXz/16tVLM2bMUEVFhVPXAABw4xGIARdm\nMpm0a9cuZWVl6d1331VqaqqOHz9u12b9+vUaOXKkDhw4oJUrV6pZs2a6+eab9eeff+qNN96oMubJ\nkyc1efJkzZs3T7/99psCAwOVmppa5bwffPCB0tPTdeDAASUlJTmsdc+ePXr55Zf11ltv6ffff1f3\n7t3twmlKSopSUlJ04MABrVmzRgEBAZIuh9rc3Fy98MILGjZsmHJzc3XgwAH5+flJkoYMGaLc3FzF\nx8fLZDJVqXPChAkaMWKEduzYoaysLGVmZqq8vFyS1KNHD33zzTfKzc1Vv379lJyc7NQ5ly1bpq1b\nt+qTTz7R999/r9zcXK1YscLhNQAANAwCMeDinnjiCfn4+Khnz56KiIjQt99+a3c8JiZGd999t0wm\nk7p16yZPT0/bMavVWmW87du3q2fPnoqOjpa7u7smTZqkr776ShaLxa7dk08+qdDQULm5uSk8PNxh\nnatXr1ZCQoJ69uwpNzc3JSYm6uuvv9alS5ckSW5ubjp8+LDOnz+vkJAQdenSxa6/1Wqttt7/tvmv\nDh06qGPHjrrtttvUsmVL+fr66syZM5Iu3yH28/OTyWRSQkKC7Q6xo3OuXr1aU6ZMUdu2beXj46Ox\nY8fqiy++cHgNAAANg/9UB7i4W2+91e7rf29vMJlM6tSp0zWNV1BQYDdm69atVVlZqaKiIrv3r3Xc\nEydO6Mcff9THH39se6958+bKz89XcHCwli1bpiVLligjI0OdO3fWwoULq4Ti2mjWrJnc3Nzk5nb5\n/sBNN92kiooKVVZWav78+dq0aZPOnDkji8ViC8D/vdP8X8eOHVNSUpJtTIvFojZt2lx3rQCA+kEg\nBlzcv/fhFhQUqH///nbHmzVrdtW+1QW/1q1b24Xq/Px8NWvWzLZdwJlxqxMUFKTk5GRNnjy52uOR\nkZFatWqVysvLNXXqVM2fP99uG8KV8FkTR0H23zIzM7VlyxatXbtWQUFBysnJ0T333GMXiK92zuDg\nYC1evFi9e/d2+nwAgIbDlgnAhVmtVq1evVrFxcXas2ePfv31V8XGxtodd9T/v2JjY7V371798MMP\nKi8v1zvvvKPBgwc7FUhrMmLECL3//vvKzs6W1WpVYWGhPv30U1sd69evV0lJiUwmk6xWq1q2bGnX\nv02bNjp48KAqKyuv+r04+n7/3bakpESenp7y9fVVcXFxtY9Wu9o5H3/8cS1YsECnTp2S1WrVwYMH\nlZWV5dS5AQA3HoEYcGEmk0l9+vRRbGysJk6cqDlz5ig4ONjueHV3Td966y2ZzWZNmzZNv/76q8xm\ns2JiYiRJAQEBevvtt5WamqpevXrp+PHjdfKM34iICM2cOVNTpkxRWFiY7r//fmVnZ9uOZ2Zmqk+f\nPurRo4cKCgo0depUu/4PPfSQWrRooYiICPXp08f2xIdRo0bJbDZr48aNysjIkNls1osvvljlGvz7\nOlzZMxwcHKzevXvr3nvvVURERJVrdbVzJiYmKioqSvHx8QoLC9PEiRN1+vTp675GAID6YbI6e8uk\nHnz99dcKCwtrqNMbmr+/vyTxQ9pFXZnf0NBQLVy4UAMGDGjgilBXWLuujfl1Xcxtw9u3b5/uuuuu\nao9xhxgAAACGRiAGAACAofGUCcCF/fTTTw1dAgAAjR53iAEAAGBoBGIAAAAYGoEYAAAAhkYgBgAA\ngKERiAEAAGBoBGIAAAAYGoEYAAAAhkYgBgAAgKERiAEAAGBoBGIAAAAYGoEYAAAAhkYgBgAAgKER\niAEAAGBoBGIAAAAYGoEYAAAAhuYwEH/yySeKjo6Wp6enxo0b5/TA06dPV1BQkG699VaNHj1a58+f\nv65CAQAAgPrgMBC3atVKKSkpevbZZ50edOPGjXrvvff0yy+/6OjRoyoqKtJrr712XYWi7u3bt6+h\nS0A9Yn5dF3Pr2phf18XcNl4OA3FsbKzi4+Pl5+fn9KD79+9X//79FRgYKG9vbz3wwAPKycm5rkJR\n91iYro35dV3MrWtjfl0Xc9t4Ob2H2Gq1Oj3o3XffrV27dikvL0/FxcXatGmTHnzwwVoVCAAAANSn\nm5xtaDKZnB40MjJSo0aNUvv27eXm5qahQ4dqwoQJ1bb19/d3elzUHXd3d8XFxalVq1YNXQrqAfPr\nuphb18b8ui7mtnFzOhBfyx3ipUuX6rvvvlNhYaE8PDw0fvx4JSUlaenSpVXa7tixw+lxAQAAgLpW\nL3eIv/jiCw0fPty27/jJJ5/USy+9VKXdXXfd5fSYAAAAQH1wuIfYYrGotLRUFRUVqqysVFlZmSor\nK23HBw0apNTUVLs+YWFh2rBhg86ePavS0lJ9/PHH6tatW91XDwAAAFwnh4H4vffek7e3t+bNm6cP\nPvhAXl5eev31123Hjxw5ovz8fLs+M2fOVLt27WQ2mxUcHKyzZ88qPT297qsHAAAArpPJei2bgwEA\nAAAXw69uBgAAgKERiAEAAGBoTj9lAk3L6dOnlZ6eroMHDyooKEiTJ09Wu3btauzzxx9/aPbs2fLw\n8LC9N3fuXAUFBdV3ubgGu3bt0saNG3X48GHFxMRo0qRJTvXbvHmzMjMzVVFRoSFDhmj06NH1XClq\nozbzy9ptGiorK5WRkaHff/9dZWVl6tSpk5599lmFhIQ47Mv6bdxqO7es3caDQOyili9frvbt2+uV\nV17R5s2btXjxYr355psO+/n5+SkjI+MGVIja8vHx0cMPP6y9e/eqvLzcqT5//vmn1q1bp9mzZ8vb\n21szZsxQp06dFB0dXc/V4lrVZn4l1m5TYLFYFBAQoNGjR8vPz0+ff/65FixYoLS0tBr7sX4bv9rO\nrcTabSzYMuGCLly4oL179+qRRx6Ru7u7HnjgARUUFOjo0aMNXRrqwB133KGoqCi1aNHC6T4//fST\n+vbtq5CQEPn5+SkuLk7ff/99PVaJ2qrN/KJpcHd3t3tG/6BBg3Ty5EmdP3++xn6s38avtnOLxoM7\nxC7o5MmTcnd3l6enp2bMmKHnnntObdu21fHjx9W+ffsa+547d04TJkyQp6en4uLiFB8ff4OqRn06\nceKEwsLCtHnzZhUWFqpr1678QHUxrN2mJzc3V35+fmrZsmWN7Vi/TY+zcyuxdhsLArELKisrk6en\npy5evKhjx46puLhYXl5eKi0trbFfSEiIFi1apICAAB0+fFgLFizQLbfcokGDBt2YwlFvrnwm8vLy\nVFBQoPDwcIefBzQdrN2m58KFC1q1apXGjBnjsC3rt2m5lrll7TYeBGIX5OHhodLSUvn7+2vFihWS\npIsXL8rT07PGfr6+vvL19ZUkdezYUffee692797NwnQBVz4T48aNkyT9/PPPDj8PaDpYu03LpUuX\ntGDBAsXExDi1D5j123Rc69yydhsP9hC7oICAAJWXl6uoqEiSVFFRoVOnTvG/Vg0sMDBQx44ds73O\ny8vj8wA0AIvForS0NAUGBmrEiBFO9WH9Ng21mVs0HgRiF+Tt7a2ePXtq48aNKi8v16ZNm9S6dWu7\n/cOvvvqqPvzwQ7t+2dnZKiwslHT5D9ytW7cqMjLyhtYOxywWi8rLy2WxWGSxWHTp0iVZLBbb8erm\nNjo6Wj///LPy8vJUVFSkbdu2qX///je6dDihNvPL2m06li9fLpPJpPHjx1d7nPXbdNVmblm7jQdb\nJlzUxIkTlZ6ermeeeUbBwcFKTk62O15QUKA2bdrYvXfo0CGlpaWptLRUvr6+GjJkCP9s0whlZWXZ\nPaLnu+++U0JCgoYPHy6p+rm9/fbbNXz4cM2aNcv2HFMe2dQ41WZ+WbtNQ0FBgbZt26bmzZvr6aef\ntr0/bdo0de3a1daG9dv01HZuWbuNh8lqtVobuggAAACgobBlAgAAAIZGIAYAAIChEYgBAABgaARi\nAAAAGBqBGAAAAIZGIAYAAIChEYgBAABgaARiAAAAGBqBGAAAAIb2f/eMOX85zhxvAAAAAElFTkSu\nQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f1a232cab70>"
       ]
      }
     ],
     "prompt_number": 14
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## A Visualization"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "The Equations"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The brilliance of the Kalman filter is taking the insights of the chapter up to this point and finding an optimal mathematical solution. The Kalman filter finds what is called a *least squared fit* to the set of measurements to produce an optimal output. We will not trouble ourselves with the derivation of these equations. It runs to several pages, and offers a lot less insight than the words above, in my opinion. Furthermore, to create a Kalman filter for your application you will not be manipulating these equations, but only specifying a number of parameters that are used by them. It would be going too far to say that you will never need to understand these equations; but to start we can pass them by and I will present the code that implements them. So, first, let's see the equations. \n",
      "> Kalman Filter Predict Step:\n",
      "\n",
      "> $$\n",
      "\\begin{aligned}\n",
      "\\hat{\\textbf{x}}^-_{k+1} &= \\mathbf{F}_{k}\\hat{\\textbf{x}}_{k} + \\mathbf{B}_k\\mathbf{u}_k\\;\\;\\;&(1) \\\\\n",
      "\\textbf{P}^-_{k+1} &=  \\mathbf{F}_k \\textbf{P}_k\\mathbf{F}_k^\\mathsf{T} + \\textbf{Q}_{k}\\;\\;\\;&(2)\n",
      "\\end{aligned}\n",
      "$$\n",
      "\n",
      "> Kalman Filter Update Step:\n",
      "\n",
      ">$$\n",
      "\\begin{aligned}\n",
      "\\textbf{y}_k &= \\textbf{z}_k - \\textbf{H}_k\\hat{\\textbf{}x}^-_k\\;\\;\\;&(3) \\\\\n",
      "\\mathbf{S}_k &= \\textbf{H}_k\\textbf{P}^-_k\\textbf{H}_k^\\mathsf{T} + \\textbf{R}_k \\;\\;\\;&(4) \\\\\n",
      "\\textbf{K}_k &= \\textbf{P}^-_k\\textbf{H}_k^\\mathsf{T}\\mathbf{S}_k^{-1}\\;\\;\\;&(5) \\\\\n",
      "\\hat{\\textbf{x}}_k  &= \\hat{\\textbf{x}}^-_k +\\textbf{K}_k\\textbf{y} \\;\\;\\;&(6)\\\\\n",
      "\\mathbf{P}_k &= (\\mathbf{I}-\\mathbf{K}_k\\mathbf{H}_k)\\mathbf{P}^-_k\\;\\;\\;&(7)\n",
      "\\end{aligned}\n",
      "$$\n",
      "\n",
      "Dash off, wipe the blood out of your eyes, and we'll disuss what this means. "
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "These are nothing more than linear algebra equations that implement the algorithm we used in the last chapter, but using multidimensional Gaussians instead of univariate Gaussians, and optimized for a least squares fit.\n",
      "\n",
      "\n",
      "Different texts use different notation and variable names for the Kalman filter. Later we will expose you to these different forms to prepare you for reading the original literature. In the equations above I have adopted the variable names used by the Wikipedia article[2] on Kalman filters. Each bold letter denotes a matrix or vector. The subscripts indicate which time step the data comes from; $k$ is now, $k+1$ is the next step. The caret (^) indicates that the value is an estimate. Finally, I particularly like how Brown [3] uses a raised $^-$ to denote a prediction, and so I have adopted that approach. For a matrix $\\mathbf{A}$, $\\mathbf{A}^\\mathsf{T}$ signifies its transpose, and $\\mathbf{A}^{-1}$ its inverse. So, taken together, $\\hat{\\mathbf{x}}^-_{k+1}$ represents the prediction for the estimate of $\\mathbf{x}$ at time step $k+1$, where $\\mathbf{x}$ is some vector in the form $\\mathbf{x} = \\begin{bmatrix}x_1&x_2&..&x_n\\end{bmatrix}^\\mathsf{T}.$ The notation does not specify that $\\mathbf{x}$ is a column vector - we will learn the shapes and sizes of all of the variables later in the chapter."
     ]
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Kalman Equations Expressed as an Algorithm"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "However, I still find  the notation to be a bit dense, and unnecessarily complicated for writing code. The subscripts indicate the time step, but when we write code it is very clear what is being calculated at each time step. For most of this book I'm going to use the following simplified equations, which express an algorithm.\n",
      "\n",
      "$$\n",
      "\\begin{aligned}\n",
      "\\text{Predict Step}\\\\\n",
      "\\mathbf{x^-} &= \\mathbf{F x} + \\mathbf{B u}\\;\\;\\;&(1) \\\\\n",
      "\\mathbf{P^-} &= \\mathbf{FP{F}}^\\mathsf{T} + \\mathbf{Q}\\;\\;\\;&(2) \\\\\n",
      "\\\\\n",
      "\\text{Update Step}\\\\\n",
      "\\textbf{y} &= \\mathbf{z} - \\mathbf{H x^-} \\;\\;\\;&(3)\\\\\n",
      "\\textbf{S} &= \\mathbf{HP^-H}^\\mathsf{T} + \\mathbf{R} \\;\\;\\;&(4)\\\\\n",
      "\\mathbf{K} &= \\mathbf{P^-H}^\\mathsf{T} \\mathbf{S}^{-1}\\;\\;\\;&(5) \\\\\n",
      "\\mathbf{x} &=\\mathbf{x^-} +\\mathbf{K\\textbf{y}} \\;\\;\\;&(6)\\\\\n",
      "\\mathbf{P} &= (\\mathbf{I}-\\mathbf{KH})\\mathbf{P^-}\\;\\;\\;&(7)\n",
      "\\end{aligned}\n",
      "$$"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "What do all of the variables mean? What is $\\mathbf{P}$, for example? Don't worry right now. Instead, I am just going to design a Kalman filter, and introduce the names as we go. Then we will just pass them into Python function that implement the equations above, and we will have our solution. Later sections will then delve into more detail about each step and equation. I think learning by example and practice is far easier than trying to memorize a dozen abstract facts at once.  "
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Implementation in Python"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Before we go any further let's gain some familiarity with the equations by programming them in Python. I have written a production quality implementation of the Kalman filter equations in my `FilterPy` library, and we will be using that later in the chapter and the remainder of the book. We could just look at that code, but it contains a significant amount of code to ensure that the computations are numerically stable, that you do not pass in bad data, and so on. Let's just try to program this.\n",
      "\n",
      "The filter equations are *linear algebra* equations, so we will use the Python library that implements linear algebra - numpy. In the filter equations a **bold** variable denotes a matrix. Numpy provides two types to implement matrices: `numpy.array` and `numpy.matrix`. You might suspect that the latter is the one we want to use. As it turns out `numpy.matrix` does support linear algebra well, except for one problem - most of the rest of `numpy` uses `numpy.array`, not `numpy.matrix`. You can pass a `numpy.matrix` into a function, and get a `numpy.array` back as a result. Hence, the standard advice is that `numpy.matrix` is deprecated, and you should always use `numpy.array` even when `numpy.matrix` is more convienient. I ignored this advice in a early version of this code and ended up regretting that choice, and so now I use 'numpy.array' only.\n",
      "\n",
      "`numpy.array` implements a any-dimensional array. You can construct it with any list like object. The following constructs a 1-D array from a list:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import numpy as np\n",
      "x = np.array([1, 2, 3])\n",
      "print(x)\n",
      "print(type(x))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[1 2 3]\n",
        "<class 'numpy.ndarray'>\n"
       ]
      }
     ],
     "prompt_number": 15
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "You can create a 2D array with nested lists:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "x = np.array([[1, 2 ,3],\n",
      "              [4, 5, 6]])\n",
      "print(x)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[[1 2 3]\n",
        " [4 5 6]]\n"
       ]
      }
     ],
     "prompt_number": 16
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "You can create arrays of 3 or more dimensions, but we have no need for that here, and so I will not elaborate.\n",
      "\n",
      "By default the arrays use the data type of the values in the list; if there are multiple types than it will choose the type that most accurately represents all the values. So, for example, if your list contains a mix of `int` and `float` the data type of the array would be of type `float`. You can override this with the `dtype` parameter."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "x = np.array([1, 2, 3], dtype=float)\n",
      "print(x)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[ 1.  2.  3.]\n"
       ]
      }
     ],
     "prompt_number": 17
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "You can perform matrix addition with the `+` operator, but matrix multiplication requires the `dot` method or function. The `*` operator performs element-wise multiplication, which is **not** what you want for linear algebra."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "x = np.array([[1, 2],\n",
      "              [3, 4]], dtype=float)\n",
      "print('addition:\\n', x+x)\n",
      "print('\\nelement-wise multiplication\\n', x*x)\n",
      "print('\\nmultiplication\\n', np.dot(x,x))\n",
      "print('\\ndot is also a member\\n', x.dot(x))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "addition:\n",
        " [[ 2.  4.]\n",
        " [ 6.  8.]]\n",
        "\n",
        "element-wise multiplication\n",
        " [[  1.   4.]\n",
        " [  9.  16.]]\n",
        "\n",
        "multiplication\n",
        " [[  7.  10.]\n",
        " [ 15.  22.]]\n",
        "\n",
        "dot is also a member\n",
        " [[  7.  10.]\n",
        " [ 15.  22.]]\n"
       ]
      }
     ],
     "prompt_number": 18
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "You can get the transpose with `.T`, and the inverse with `numpy.linalg.inv`."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print('transpose\\n', x.T)\n",
      "print('\\ninverse\\n', np.linalg.inv(x))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "transpose\n",
        " [[ 1.  3.]\n",
        " [ 2.  4.]]\n",
        "\n",
        "inverse\n",
        " [[-2.   1. ]\n",
        " [ 1.5 -0.5]]\n"
       ]
      }
     ],
     "prompt_number": 19
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Finally, there are helper functions like `zeros` to create a matrix of all zeros, `ones` to get all ones, and `eye` to get the identity matrix."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print('zeros\\n', np.zeros((3, 2)))\n",
      "print('\\neye\\n', np.eye(3))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "zeros\n",
        " [[ 0.  0.]\n",
        " [ 0.  0.]\n",
        " [ 0.  0.]]\n",
        "\n",
        "eye\n",
        " [[ 1.  0.  0.]\n",
        " [ 0.  1.  0.]\n",
        " [ 0.  0.  1.]]\n"
       ]
      }
     ],
     "prompt_number": 20
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "There is a lot of useful functionality in `numpy`, but let's move on to implementing the Kalman filter. Let's start with the prediction equations.\n",
      "\n",
      "$$\n",
      "\\begin{aligned}\n",
      "\\mathbf{x^-} &= \\mathbf{F x} + \\mathbf{B u}\\;\\;\\;&(1) \\\\\n",
      "\\mathbf{P^-} &= \\mathbf{FPF}^\\mathsf{T} + \\mathbf{Q}\\;\\;\\;&(2) \\\\\n",
      "\\end{aligned}\n",
      "$$\n",
      "\n",
      "Those are linear algebra equations using matrix multiplication and addition. Assuming each variable is already defined somewhere, we can implement these equations in Python and numpy with:\n",
      "\n",
      "    x = dot(F, x) + dot(B, u)\n",
      "    P = dot(F, P).dot(F.T) + Q\n",
      "\n",
      "That is all there is to it! Okay, we need to put these in a function or a class somehow, but that is the 'hard' code, which is actually pretty easy.\n",
      "\n",
      "Now let's do the update step. Again, they consist of matrix multiplication and addition.\n",
      "\n",
      "$$\n",
      "\\begin{aligned}\n",
      "\\textbf{y} &= \\mathbf{z} - \\mathbf{H x} \\;\\;\\;&(3)\\\\\n",
      "\\textbf{S} &= \\mathbf{HP^-H}^\\mathsf{T} + \\mathbf{R} \\;\\;\\;&(4)\\\\\n",
      "\\mathbf{K} &= \\mathbf{P^-H}^\\mathsf{T} \\mathbf{S}^{-1}\\;\\;\\;&(5) \\\\\n",
      "\\mathbf{x}&=\\mathbf{x^-} +\\mathbf{K\\textbf{y}} \\;\\;\\;&(6)\\\\\n",
      "\\mathbf{P}&= (\\mathbf{I}-\\mathbf{KH})\\mathbf{P^-}\\;\\;\\;&(7)\n",
      "\\end{aligned}\n",
      "$$\n",
      "\n",
      "\n",
      "In Python we would write:\n",
      "\n",
      "    y = z - dot(H, x)\n",
      "    S = dot(H, P).dot(H.T) + R\n",
      "    K = dot(P, H.T).dot(np.linalg.inv(S))\n",
      "    x = x + dot(K,y)\n",
      "    P = (I - dot(K, H)).dot(P)\n",
      "    \n",
      "And that is it, we have implemented a Kalman filter!\n",
      "\n",
      "Well, you probably do not want to cut and paste that code into every project that uses a Kalman filter. So let's put this into a class. I don't intend to teach you how to program here, so I will instead point you to my `KalmanFilter` class from my FilterPy module, available on github [4]. However, I have written a simplified version of that class below for your inspection."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "    import numpy as np\n",
      "    import scipy.linalg as linalg\n",
      "    import matplotlib.pyplot as plt\n",
      "    import numpy.random as random\n",
      "    from numpy import dot\n",
      "\n",
      "    class KalmanFilter:\n",
      "\n",
      "        def __init__(self, dim_x, dim_z, dim_u=0):\n",
      "            \"\"\" Create a Kalman filter. You are responsible for setting \n",
      "            the various state variables to reasonable values; the defaults \n",
      "            below will not give you a functional filter.\n",
      "\n",
      "            **Parameters**\n",
      "\n",
      "            dim_x : int\n",
      "                Number of state variables for the Kalman filter. For \n",
      "                example, if you are tracking the position and velocity \n",
      "                of an object in two dimensions, dim_x would be 4.\n",
      "\n",
      "                This is used to set the default size of P, Q, and u\n",
      "\n",
      "            dim_z : int\n",
      "                Number of of measurement inputs. For example, if the sensor\n",
      "                provides you with position in (x,y), dim_z would be 2.\n",
      "\n",
      "            dim_u : int (optional)\n",
      "                size of the control input, if it is being used.\n",
      "                Default value of 0 indicates it is not used.\n",
      "            \"\"\"\n",
      "\n",
      "            self.x = np.zeros((dim_x,1)) # state\n",
      "            self.P = np.eye(dim_x)       # uncertainty covariance\n",
      "            self.Q = np.eye(dim_x)       # process uncertainty\n",
      "            self.u = np.zeros((dim_x,1)) # motion vector\n",
      "            self.B = 0                   # control transition matrix\n",
      "            self.F = 0                   # state transition matrix\n",
      "            self.H = 0                   # Measurement function\n",
      "            self.R = np.eye(dim_z)       # state uncertainty\n",
      "\n",
      "            # identity matrix. Do not alter this. \n",
      "            self._I = np.eye(dim_x)\n",
      "\n",
      "            if use_short_form:\n",
      "                self.update = self.update_short_form\n",
      "\n",
      "\n",
      "        def update(self, Z, R=None):\n",
      "            \"\"\"\n",
      "            Add a new measurement (Z) to the kalman filter. If Z is\n",
      "            None, nothing is changed.\n",
      "\n",
      "            **Parameters**\n",
      "\n",
      "            Z : np.array\n",
      "                measurement for this update.\n",
      "\n",
      "            R : np.array, scalar, or None\n",
      "                Optionally provide R to override the measurement noise \n",
      "                for this one call, otherwise  self.R will be used.\n",
      "            \"\"\"\n",
      "\n",
      "            if Z is None:\n",
      "                return\n",
      "\n",
      "            if R is None:\n",
      "                R = self.R\n",
      "            elif np.isscalar(R):\n",
      "                R = np.eye(self.dim_z) * R\n",
      "\n",
      "            # error (residual) between measurement and prediction\n",
      "            y = Z - dot(H, x)\n",
      "\n",
      "            # project system uncertainty into measurement space \n",
      "            S = dot(H, P).dot(H.T) + R\n",
      "\n",
      "            # map system uncertainty into kalman gain\n",
      "            K = dot(P, H.T).dot(linalg.inv(S))\n",
      "\n",
      "            # predict new x with residual scaled by the kalman gain\n",
      "            self.x += dot(K, y)\n",
      "\n",
      "            I_KH = self._I - dot(K, H)\n",
      "            self.P = dot(I_KH).dot(P).dot(I_KH.T) + dot(K, R).dot(K.T)\n",
      "\n",
      "\n",
      "        def predict(self, u=0):\n",
      "            \"\"\" Predict next position.\n",
      "\n",
      "            **Parameters**\n",
      "\n",
      "            u : np.array\n",
      "                Optional control vector. If non-zero, it is multiplied\n",
      "                by B to create the control input into the system.\n",
      "            \"\"\"\n",
      "\n",
      "            self.x = dot(self.F, self.x) + dot(self.B, u)\n",
      "            self.P = self.F.dot(self.P).dot(self.F.T) + self.Q"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We will see how to use this class in the rest of the chapter, so I will not belabor its use here. There are several additions to the version in `FilterPy` that make it more usable. For example, instead of using variables for the $R$, $P$, and so on, the `FilterPy` version uses properties. This allows you to write something like:\n",
      "\n",
      "    dog_filter.R = 3\n",
      "    \n",
      "and the class will recognize that $R$ is actually supposed to be a matrix and convert the $3$ into an appropriate matrix (we don't yet know what an 'appropriate' matrix for $R=3$ would be, but we will learn that soon).\n",
      "\n",
      "You can import the class from `FilterPy` using the following import statement, and that is what we will do in the rest of this chapter and book:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from filterpy.kalman import KalmanFilter"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 21
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Tracking a Dog"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Let's go back to our tried and true problem of tracking our dog. This time we will include the fundamental insight of this chapter - that of using *unobserved variables* to improve our estimates. In simple terms, our algorithm is:\n",
      "\n",
      "    1. predict the next value for x with \"x + vel*time\"\n",
      "    2. get measurement for x\n",
      "    3. compute residual as: \"x - x_prediction\"\n",
      "    4. compute kalman gain based on noise levels\n",
      "    5. compute new position as \"residual * kalman gain\"\n",
      "    \n",
      "That is the entire Kalman filter algorithm. It is both what we described above in words, and it is what the rather obscure Kalman Filter equations do. The Kalman filter equations just express this algorithm by using linear algebra. \n",
      "\n",
      "As I mentioned above, there is actually very little programming involved in creating a Kalman filter. We will just be defining several matrices and parameters that get passed into  the Kalman filter algorithm code. Rather than try to explain each of the steps ahead of time, which can be a bit abstract and hard to follow, let's just do it for our by now well known dog tracking problem. Naturally this one example will not cover every use case of the Kalman filter, but we will learn by starting with a simple problem and then slowly start addressing more complicated situations."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "##### **Step 1:** Choose the State Variables and Set Initial Conditions\n",
      "\n",
      "\n",
      "In the previous chapter we tracked a dog in one dimension by using a Gaussian. The mean $(\\mu)$ represented the most likely position, and the variance ($\\sigma^2$) represented the probability distribution of the position. In that problem the position is the *state* of the system, and we call $\\mu$ the *state variable*.\n",
      "\n",
      "In this chapter we will be tracking both the position and velocity of the dog, so we have two state variables. It is important to understand that this is a design choice with implications and assumptions that we are not yet prepared to explore. For example, we could optionally also track acceleration, or even acceleration and jerk. For now I will only state that the decision to track position and velocity contains an assumption that acceleration is zero, which of course often not true. If the object being tracked *is* accelerating, then the performance of the filter will be suboptimal, or even diverge. However, this is a good way to introduce the concept of Kalman filtering without getting bogged down into too many details, or having to deal with large matrices.\n",
      "\n",
      "State variables can either be *observed variables* - directly measured by a sensor, or *unobserved variables* - inferred from the observed variables. For our dog tracking problem, our observed state variable is position, and the unobserved variable is velocity. \n",
      "\n",
      "In the previous chapter would denote the dog's position being 3.2 meters as:\n",
      "$$\\mu = 3.2$$\n",
      "\n",
      "In this chapter we will use the multivariate Gaussian as described at the beginning of this chapter. For example, if we wanted to specify a position of 10.0 m and a velocity of 4.5 m/s, we would write:\n",
      "\n",
      "$$\\mu = \\begin{bmatrix}10.0\\\\4.5\\end{bmatrix}$$\n",
      "\n",
      "The Kalman filter is implemented using linear algebra. We use an $n\\times 1$ matrix to store  $n$ state variables. For the dog tracking problem, we use $x$ to denote position, and the first derivative of $x$, $\\dot{x}$, for velocity. The Kalman filter equations use $\\mathbf{x}$ for the state, so we define $\\mathbf{x}$ as:\n",
      "\n",
      "$$\\mathbf{x} =\\begin{bmatrix}x \\\\ \\dot{x}\\end{bmatrix}$$\n",
      "\n",
      "We use $\\mathbf{x}$ instead of $\\mu$, but recognize this is just the mean of the multivariate Gaussian.\n",
      "\n",
      "The other half of the Gaussian is the covariance $\\Sigma$. The Kalman filter equations use the alternative symbol $\\mathbf{P}$, but it means the same thing. In the one dimensional Kalman filter we specified an initial value for $\\sigma^2$, and then the filter took care of updating it's value as measurements were added to the filter. The same thing happens in the multidimensional Kalman filter.\n",
      "\n",
      "In the last chapter we initialized the dog's position at 0.0 m, and set the $\\sigma^2=500$ to indicate that we were very unsure about this initial value. We need to do the same thing for the multidimensional Kalman filter. We will set the initial position to 0.0 m, the initial velocity to 0.0 m/s, and then set $\\sigma^2$ to a 500 for both the position and velocity to reflect our uncertainty. \n",
      "\n",
      "Recall that the diagonals of the covariance matrix contains the variance of each variable. So to initialize the Kalman filter to the values in the previous paragraph we would write:\n",
      "\n",
      "$$\n",
      "\\begin{aligned}\n",
      "\\mathbf{x} &= \\begin{bmatrix}0 \\\\ 0\\end{bmatrix} \\\\\n",
      "\\mathbf{P} &= \\begin{bmatrix}500 & 0 \\\\ 0&500\\end{bmatrix} \\\\\n",
      "\\end{aligned}\n",
      "$$\n",
      "\n",
      "I am often frustrated when books use the same value for multiple variables in an example as it can be unclear which value corresponds to which variable. To ensure that there is no confusion let's look at the example of setting the initial position to 1 m, the initial velocity to 2.3 m/s, the $\\sigma^2$ of the position to 500, and the $\\sigma^2$ of the velocity to 400. In that case we would write:\n",
      "\n",
      "$$\n",
      "\\begin{aligned}\n",
      "\\mathbf{x} &= \\begin{bmatrix}1 \\\\ 2.3\\end{bmatrix} \\\\\n",
      "\\mathbf{P} &= \\begin{bmatrix}500 & 0 \\\\ 0&400\\end{bmatrix} \\\\\n",
      "\\end{aligned}\n",
      "$$\n",
      "\n",
      "We have chosen our state variables and set our initial conditions, so this step is complete."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "##### **Step 2:** Design the State Transition Function\n",
      "\n",
      "\n",
      "The next step in designing a Kalman filter is telling it how to predict the next state from the current state by providing it with equations that describe the physical model of the system. For example, for our dog tracking problem we are tracking a moving object, so we just need to provide it with the Newtonian equations for motion. If we were tracking a thrown ball we would have to provide equations for how a ball moves in a gravitational field, and perhaps include the effects of things like air drag. If we were writing a Kalman filter for a rocket we would have to tell it how the rocket responds to its thrusters and main engine. A Kalman filter for a bowling ball would incorporate the effects of friction and ball rotation. You get the idea. \n",
      "\n",
      "In the language of Kalman filters the physical model is call the *process model*. That is probably a better term than *physical model* because the Kalman filter can be used to track non-physical things like stock prices. We describe the process model with a set of equations we call the *State Transition Function.* \n",
      "\n",
      "\n",
      "We know from elementary physics how to compute a future position given our current position and velocity. Let $x$ be our current position, and $\\Delta t$ be the amount of time in the future. The velocity is then the derivative of $x$ with respect to time, which we notate as $\\dot{x}$. We can then write \n",
      "\n",
      "$$x_t = \\dot{x}_{t-1}\\Delta t + x_{t-1}$$\n",
      "\n",
      "However, to avoid subscripts we will adopt the notation that uses $x^-$ to denote our predicted position, and write\n",
      "\n",
      "$$x^- = \\dot{x}\\Delta t + x$$\n",
      "\n",
      "Equation (1) of the Kalman filter $\\mathbf{x^-} = \\mathbf{Fx} + \\mathbf{B u}$ implements the *state transition function* that we are discussing. This requires us to formulate the motion equation above with matrices, so let's learn how to do that now. For the moment we will ignore the $\\mathbf{B u}$ term, as for our problem it turns out that it is equal to zero. This will be explained in step 3. Thus, we must express our equations in the form \n",
      "$\\mathbf{x}^- = \\mathbf{Fx}.$\n",
      "\n",
      "A quick review on how to represent linear equations with matrices. Take the following two equations:\n",
      "$$2x+3y = 8\\\\3x-y=1$$\n",
      "\n",
      "We can put this in matrix form by writing:\n",
      "\n",
      "$$\n",
      "\\begin{bmatrix}2& 3 \\\\ 3& -1\\end{bmatrix}\\begin{bmatrix}x\\\\y\\end{bmatrix}=\\begin{bmatrix}8\\\\1\\end{bmatrix}$$\n",
      "If you perform the matrix multiplication in this equation the result will be the two equations above.\n",
      "\n",
      "So, given that $\\mathbf{x} = \\begin{bmatrix}x \\\\ \\dot{x}\\end{bmatrix}$ we can write:\n",
      "\n",
      "$$\n",
      "\\begin{aligned}\n",
      "\\mathbf{x}^- &= \\mathbf{Fx} \\\\\n",
      "\\begin{bmatrix}x \\\\ \\dot{x}\\end{bmatrix}^- &= \\mathbf{F}\\begin{bmatrix}x \\\\ \\dot{x}\\end{bmatrix}\n",
      "\\end{aligned}\n",
      "$$\n",
      "\n",
      "Since $\\mathbf{x}$ is a $2{\\times}1$ matrix $\\mathbf{F}$ must be a $2{\\times}2$ matrix to yield another $2{\\times}1$ matrix as a result. The first row of the F is easy to derive:\n",
      "\n",
      "$$\n",
      "\\begin{aligned}\n",
      "{\\begin{bmatrix}x\\\\\\dot{x}\\end{bmatrix}}^- &=\\begin{bmatrix}1&\\Delta t \\\\ ?&?\\end{bmatrix} \\begin{bmatrix}x \\\\ \\dot{x}\\end{bmatrix}\n",
      "\\end{aligned}\n",
      "$$\n",
      "\n",
      "When we multiply the first row of $\\mathbf{F}$ that out we get:\n",
      "\n",
      "$$ \n",
      "\\begin{aligned}\n",
      "x^- &= 1  x + \\Delta t \\dot{x} \\mbox{, or} \\\\\n",
      "x^- &= \\dot{x}\\Delta t + x\n",
      "\\end{aligned}\n",
      "$$\n",
      "\n",
      "which is our equation for computing the new position based on velocity, time, and the previous position.\n",
      "\n",
      "Now we have to account for the second row. I've left it somewhat unstated up to now, but we are assuming constant velocity for this problem. Naturally this assumption is not true; if our dog moves it must accelerate and decelerate. If you cast your mind back to the *g-h Filter* chapter we explored the effect of assuming constant velocity. So long as the acceleration is small compared to $\\Delta t$ the filter will still perform well. \n",
      "\n",
      "Therefore we will assume that\n",
      "\n",
      "$$\\dot{x}^- = \\dot{x}$$\n",
      "\n",
      "which gives us the second row of $\\mathbf{F}$ as follows, once we set $\\Delta t = 1$:\n",
      "\n",
      "\n",
      "$$\n",
      "{\\begin{bmatrix}x\\\\\\dot{x}\\end{bmatrix}}^- =\\begin{bmatrix}1&1 \\\\ 0&1\\end{bmatrix} \\times \\begin{bmatrix}x \\\\ \\dot{x}\\end{bmatrix}\n",
      "$$\n",
      "\n",
      "Which, when multiplied out, yields our desired equations:\n",
      "\n",
      "$$\n",
      "\\begin{aligned}\n",
      "x^- &= x + \\dot{x} \\\\\n",
      "\\dot{x}^- &= \\dot{x}\n",
      "\\end{aligned}\n",
      "$$\n",
      "\n",
      "In the vocabulary of Kalman filters we call this *transforming the state matrix*. We take our state matrix, which for us is $(\\begin{smallmatrix}x \\\\ \\dot{x}\\end{smallmatrix})$, and multiply it by a matrix we will call $\\mathbf{F}$ to compute the new state. In this case, $\\mathbf{F}=(\\begin{smallmatrix}1&1\\\\0&1\\end{smallmatrix})$. \n",
      "\n",
      "\n",
      "You will do this for every Kalman filter you ever design. Your state matrix will change depending on how many state random variables you have, and then you will create $\\mathbf{F}$ so that it updates your state based on whatever the physics of your problem dictates. $\\mathbf{F}$ is always a matrix of constants. Each row in $\\mathbf{F}$ is  If this is not fully clear, don't worry, we will do this many times in this book."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "##### **Step 3**: Design the Motion Function\n",
      "\n",
      "The Kalman filter does not just filter data, it allows us to incorporate control inputs for systems like robots and airplanes. Consider the state transition function we wrote for the dog:\n",
      "\n",
      "$$x_t = \\dot{x}(\\Delta t) + x_{t-1}$$\n",
      "\n",
      "Suppose that instead of passively tracking our dog we were actively controlling a robot. At each time step we would send control signals to the robot based on its current position vs desired position. Kalman filter equations incorporate that knowledge into the filter equations, creating a predicted position based both on current velocity *and* control inputs to the drive motors. \n",
      "\n",
      "We will cover this use case later, but for now passive tracking applications we set those terms to 0. In step 2 there was the unexplained term $\\mathbf{Bu}$ in equation (1):\n",
      "\n",
      "$$\\mathbf{x^-} = \\mathbf{Fx} + \\mathbf{Bu}$$.\n",
      "\n",
      "Here $\\mathbf{u}$ is the control input, and $\\mathbf{B}$ is its transfer function. For example, $\\mathbf{u}$ might be a voltage controlling how fast the wheel's motor turns, and multiplying by $\\mathbf{B}$ yields $[\\begin{smallmatrix}x\\\\\\dot{x}\\end{smallmatrix}]$. Since we do not need these terms we will set them both to zero and not concern ourselves with them for now.\n"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "##### **Step 4**: Design the Measurement Function\n",
      "\n",
      "The Kalman filter computes the update step in what we call *measurement space*. We mostly ignored this issue in the previous chapter because of the complication it adds. In the last chapter we tracked our dog's position using a sensor that reported his position. Computing the *residual* was easy - subtract the filter's predicted position from the measurement:\n",
      "\n",
      "$$ residual = measurement - position$$\n",
      "\n",
      "However, consider what would happen if we were trying to track temperature using a thermometer that varies a voltage output depending on the temperature. The equation for the residual computation would be nonsense; you can't subtract a temperature from a voltage.\n",
      "\n",
      "$$ residual = z_{volts} - temp_C\\;\\;\\;(BAD!)$$\n",
      "\n",
      "The Kalman filter generalizes this problem by having you supply a *measurement function*. It is somewhat counterintuitive at first. As I already stated the Kalman filter performs its calculations in *measurement space.*  It needs to do that because it only really makes sense to talk about the residual of the measurement in terms of the measurement. So it does something like this:\n",
      "\n",
      "    residual = measurement - convert_to_measurement(predicted state)\n",
      "\n",
      "In other words, for the thermometer tracking problem, it would take the filter's current prediction of temperature, convert that to whatever voltage would represent that temperature, and then subtract it from the current thermometer voltage output. This gives it a residual in the correct units (volts).\n",
      "\n",
      "It does this with a *measurement function* matrix that you provide. At first it might seem counterintuitive: to use the thermometer we need to know how to convert the output voltage into a temperature, but we tell the Kalman filter how to convert a temperature into a voltage!.  But if you think about it, what you are really telling the filter is how your sensor works. Your sensor converts temperature into voltage, and you are just telling the Kalman filter how it does it. The Kalman filter equations can take that information and figure out how to perform the inverse operation without you explicitly telling it the computation.\n",
      "\n",
      "The Kalman filter equation that performs this step is:\n",
      "\n",
      "$$\\textbf{y} = \\mathbf{z} - \\mathbf{H x^-} \\;\\;\\;(3)$$\n",
      "\n",
      "where $\\textbf{y}$ is the residual, $\\mathbf{x^-}$ is the predicted value for $\\mathbf{x}$, $\\textbf{z}$ is the measurement, and $\\textbf{H}$ is the measurement function. It is just a matrix that we multiply the state into to convert it into a measurement.\n",
      "\n",
      "For our dog tracking problem we have a sensor that measures position, but no sensor that measures velocity. So for a given state $\\mathbf{x}=\\begin{bmatrix}x & \\dot{x}\\end{bmatrix}^\\mathsf{T}$ we will want to multiply the position $x$ by 1 to get the corresponding measurement of the position, and multiply the velocity $\\dot{x}$ by 0 to get the corresponding measurement of velocity (of which there is none).\n",
      "\n",
      "We only have 1 measurement in this example, so the dimension of the residual matrix needs to be $1\\times 1$. $\\mathbf{x}$ is $2\\times 1$, so $\\mathbf{H}$ needs to be $1\\times 2$ to get the right result. If we put this in linear algebra terms we get:\n",
      "\n",
      "$$\n",
      "\\begin{aligned}\n",
      " \\textbf{y} &= \\mathbf{z} - &\\begin{bmatrix}1&0\\end{bmatrix} &\\begin{bmatrix}x \\\\ \\dot{x}\\end{bmatrix}, or \\\\\n",
      "\\textbf{y} &= \\mathbf{z} - &\\textbf{H}&\\begin{bmatrix}x \\\\ \\dot{x}\\end{bmatrix}\n",
      "\\end{aligned}\n",
      "$$\n",
      "\n",
      "And so, for our Kalman filter we set\n",
      "\n",
      "$$\\mathbf{H}=\\begin{bmatrix}1&0\\end{bmatrix}$$\n",
      "\n",
      "Believe it or not, we have designed the majority of our Kalman filter!! All that is left is to model the noise in our sensors."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "##### **Step 5**: Design the Measurement Noise Matrix\n",
      "\n",
      "The *measurement noise matrix* is a matrix that models the noise in our sensors as a covariance matrix. This can be admittedly a very difficult thing to do in practice. A complicated system may have many sensors, the correlation between them might not be clear, and usually their noise is not a pure Gaussian. For example, a sensor might be biased to read high if the temperature is high, and so the noise is not distributed equally on both sides of the mean. Later we will address this topic in detail. For now I just want you to get used to the idea of the measurement noise matrix so we will keep it deliberately simple.\n",
      "\n",
      "In the last chapter we used a variance of 5 meters for our position sensor. Let's use the same value here.  The Kalman filter equations uses the symbol $R$ for this matrix. In general the matrix will have dimension $m{\\times}m$, where $m$ is the number of sensors. It is $m{\\times}m$ because it is a covariance matrix, as there may be correlations between the sensors. We have only 1 sensor here so we write:\n",
      "\n",
      "$$R = \\begin{bmatrix}5\\end{bmatrix}$$\n",
      "\n",
      "If we had two position sensors, the first with a variance of 5 meters, the second with a variance of 3 meters, we would write\n",
      "\n",
      "$$R = \\begin{bmatrix}5&0\\\\0&3\\end{bmatrix}$$\n",
      "\n",
      "We put the variances on the diagonal because this is a *covariance* matrix, where the variances lie on the diagonal, and the covariances, if any, lie in the off-diagonal elements. Here we assume there is no correlation in the noise between the two sensors, so the covariances are 0."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "##### **Step 6**: Design the Process Noise Matrix\n",
      "\n",
      "What is *process noise*? Consider the motion of a thrown ball. In a vacuum and with constant gravitational force it moves in a parabola. However, if you throw the ball on the surface of the earth you will also need to model factors like rotation and air drag. However, even when you have done all of that there is usually things you cannot account for. For example, consider wind. On a windy day the ball's trajectory will differ from the computed trajectory, perhaps by a significant amount. Without wind sensors, we may have no way to model the wind. The Kalman filter models this as *process noise*, and calls it $\\mathbf{Q}$.\n",
      "\n",
      "Astute readers will realize that we can inspect the ball's path and extract wind as an unobserved state variable, but the point to grasp here is there will always be some unmodeled noise in our process, and the Kalman filter gives us a way to model it.\n",
      "\n",
      "Designing the process noise matrix can be quite demanding, and we will put it off until the Kalman math chapter. In this chapter we will focus on building an intuitive understanding on how modifying this matrix alters the behavior of the filter. \n",
      "\n",
      "We think of the the underlying system as behaving as\n",
      "\n",
      "$$f(x) = \\mathbf{F}x + w$$\n",
      "\n",
      "where $\\mathbf{F}x$ is the state transition and $w$ is the process noise. In other words $\\mathbf{F}x$ is the 'true' behavior of the process as we understand it, and $w$ is things like winds, control surface fluctuations, maybe circuit noise - whatever affects our process that is not modelled.\n",
      "\n",
      "\n",
      "As you might expect, the Kalman filter uses the process noise matrix during the prediction step because the prediction step is the step that uses the process model to predict the next state. It is used in equation (2) from the Kalman filter equations:\n",
      "\n",
      "$$\\mathbf{P} = \\mathbf{FP{F}}^\\mathsf{T} + \\mathbf{Q}$$\n",
      "\n",
      "If you look back at step one you will recall that $\\mathbf{P}$ is the covariance matrix. It will be of size $n\\times n$ where $n$ is the number of state variables. $\\mathbf{FP{F}}^\\mathsf{T}$ is just some linear algebra 'magic' that switches $\\mathbf{P}$ into state space. We will cover this in detail in the Kalman math chapter; for now I will just say that when the Kalman filter performs the math for Step 4 above it needed to convert $\\mathbf{P}$ into measurement space to compute the residual and Kalman gain, so here it it converted back into state space to perform the state prediction.\n",
      "\n",
      "In pseudocode we might express this equation as:\n",
      "    \n",
      "    P = to_state_space(P_in_measurement_space) + process_noise\n",
      "\n",
      "This is the multidimensional linear algebra analogue of the predict step in the one dimensional case, where we added the variance of the filter to the variance of the movement:\n",
      "\n",
      "    sigma = sigma + movement_sigma\n",
      "    \n",
      "$\\mathbf{P}$ is dimensioned $n\\times n$, so $\\mathbf{Q}$ must have the same dimensions. We are just adding matrices, so hopefully it is clear that each element in $\\mathbf{Q}$  specifies how much uncertainty is added to the system due to the process noise. \n",
      "\n",
      "We have not given the math for this yet, but if you suspect the math is sometimes difficult you would be correct. One of the problems is that we are usually modelling a *continuous* system - the behavior of the system is changing at every instant, but the Kalman filter is *discrete*. That means that we have to somehow convert the continuous noise of the system into a discrete value, which usually involves calculus. There are other difficulties I will not mention now."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "However, for the class of problems we are solving in this chapter (*discretized continuous-time kinematic filters*), where we can directly compute the state equations for moving objects by using Newton's equations.\n",
      "\n",
      "For these kinds of problems we can rely on precomputed forms for $\\mathbf{Q}$. We will learn how to derive these matrices in the next chapter. For now I present them without proof. If we assume that for each time period the acceleration due to process noise is constant and uncorrelated, we get the following.\n",
      "\n",
      "For constant velocity the form is\n",
      " $$\\begin{bmatrix}\n",
      " \\frac{1}{4}{\\Delta t}^4 & \\frac{1}{2}{\\Delta t}^3 \\\\\n",
      " \\frac{1}{2}{\\Delta t}^3 & \\Delta t^2\n",
      " \\end{bmatrix}\\sigma^2\n",
      " $$\n",
      "\n",
      "and for constant acceleration we have\n",
      "\n",
      " $$\\begin{bmatrix}\n",
      " \\frac{1}{4}{\\Delta t}^4 & \\frac{1}{2}{\\Delta t}^3 & \\frac{1}{2}{\\Delta t}^2 \\\\\n",
      " \\frac{1}{2}{\\Delta t}^3 & {\\Delta t}^2 & \\Delta t \\\\\n",
      " \\frac{1}{2}{\\Delta t}^2 & \\Delta t & 1\n",
      " \\end{bmatrix} \\sigma^2\n",
      " $$\n"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "It general it is not true that acceleration will be constant and uncorrelated, but this is still a useful approximation for moderate time period, and will suffice for this chapter. Fortunately you can get a long way with approximations and simulation. Let's think about what these matrices are implying. We are trying to model the effects of *process noise*, such as the wind buffeting the flight of a thrown ball. Variations in wind will cause changes in acceleration, and so the effect on the acceleration is large. However, the effects on velocity and position are proportionally smaller. In the matrices, the acceleration term is in the lower right, and this is the largest value. **A good rule of thumb is to set $\\sigma$ somewhere from $\\frac{1}{2}\\Delta a$ to $\\Delta a$, where $\\Delta a$ is the maximum amount that the acceleration will change between sample periods**. In practice we pick a number, run simulations on data, and choose a value that works well. \n",
      "\n",
      "The filtered result will not be optimal, but in my opinion the promise of optimal results from Kalman filters is mostly wishful thinking. Consider, for example, tracking a car. In that problem the process noise would include things like potholes, wind gusts, changing drag due to turning, rolling down windows, and many more factors. We cannot realistically model that analytically, and so in practice we work out a simplified model, compute $\\mathbf{Q}$ based on that simplified model, and then add *a bit* to  $\\small\\mathbf{Q}$ in hopes of taking the incalculable factors into account. Then we use a lot of simulations and trial runs to see if the filter behaves well; if it doesn't we adjust $\\small\\mathbf{Q}$ until the filter performs well. In this chapter we will focus on forming an intuitive understanding on how adjusting $\\small\\mathbf{Q}$ affects the output of the filter. In the Kalman Filter Math chapter we will discuss the analytic computation of $\\small\\mathbf{Q}$, and also provide code that will compute it automatically for you.\n",
      "\n",
      "For now we will just import the code from the `FilterPy` module, where it is already implemented. I will import it and call help on it so you can see the documentation for it."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from filterpy.common import Q_discrete_white_noise\n",
      "help(Q_discrete_white_noise)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Help on function Q_discrete_white_noise in module filterpy.common.discretization:\n",
        "\n",
        "Q_discrete_white_noise(dim, dt=1.0, var=1.0)\n",
        "    Returns the Q matrix for the Discrete Constant White Noise\n",
        "    Model. dim may be either 2 or 3, dt is the time step, and sigma is the\n",
        "    variance in the noise.\n",
        "    \n",
        "    **Paramaeters**\n",
        "    \n",
        "    dim : int (2 or 3)\n",
        "        dimension for Q, where the final dimension is (dim x dim)\n",
        "    \n",
        "    dt : float, default=1.0\n",
        "        time step in whatever units your filter is using for time. i.e. the\n",
        "        amount of time between innovations\n",
        "    \n",
        "    var : float, default=1.0\n",
        "        variance in the noise\n",
        "\n"
       ]
      }
     ],
     "prompt_number": 22
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "Q = Q_discrete_white_noise(dim=2, dt=0.1, var=2.35)\n",
      "Q"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 23,
       "text": [
        "array([[  5.87500000e-05,   1.17500000e-03],\n",
        "       [  1.17500000e-03,   2.35000000e-02]])"
       ]
      }
     ],
     "prompt_number": 23
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Implementing the Kalman Filter"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "As we already explained, the Kalman filter equations are already implemented for you in the `FilterPy` library, so let's start by importing it and creating a filter."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import numpy as np\n",
      "from filterpy.kalman import KalmanFilter\n",
      "\n",
      "dog_filter = KalmanFilter(dim_x=2, dim_z=1)\n",
      "help(KalmanFilter.__init__)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Help on function __init__ in module filterpy.kalman.kalman_filter:\n",
        "\n",
        "__init__(self, dim_x, dim_z, dim_u=0)\n",
        "    Create a Kalman filter. You are responsible for setting the\n",
        "    various state variables to reasonable values; the defaults below will\n",
        "    not give you a functional filter.\n",
        "    \n",
        "    **Parameters**\n",
        "    \n",
        "    dim_x : int\n",
        "        Number of state variables for the Kalman filter. For example, if\n",
        "        you are tracking the position and velocity of an object in two\n",
        "        dimensions, dim_x would be 4.\n",
        "    \n",
        "        This is used to set the default size of P, Q, and u\n",
        "    \n",
        "    dim_z : int\n",
        "        Number of of measurement inputs. For example, if the sensor\n",
        "        provides you with position in (x,y), dim_z would be 2.\n",
        "    \n",
        "    dim_u : int (optional)\n",
        "        size of the control input, if it is being used.\n",
        "        Default value of 0 indicates it is not used.\n",
        "\n"
       ]
      }
     ],
     "prompt_number": 24
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "That's it. We import the filter, and create a filter that uses 2 state variables. We specify the number of state variables with the 'dim=2' expression (dim means dimensions).\n",
      "\n",
      "The Kalman filter class contains a number of variables that you need to set. x is the state, F is the state transition function, and so on. Rather than talk about it, let's just do it!"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "dog_filter.x = np.array([0., 0.])        # state (location and velocity)\n",
      "dog_filter.F = np.array([[1, 1], [0, 1]])  # state transition matrix\n",
      "dog_filter.H = np.array([[1, 0]])          # Measurement function\n",
      "dog_filter.R *= 5                          # measurement noise\n",
      "dog_filter.Q = Q_discrete_white_noise(2, dt=0.1, var=0.1) # process noise\n",
      "dog_filter.P *= 500.                       # covariance matrix "
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 25
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Let's look at this line by line. \n",
      "\n",
      "**1**: We just assign the initial value for our state. Here we just initialize both the position and velocity to zero. \n",
      "\n",
      "**2**: We set $\\textbf{F}=\\begin{bmatrix}1&1\\\\0&1\\end{bmatrix}$, as in design step 2 above. \n",
      "\n",
      "**3**: We set $\\textbf{H}=\\begin{bmatrix}1&0\\end{bmatrix}$, as in design step 3 above.\n",
      "\n",
      "**4**: We set $\\textbf{R} = \\begin{bmatrix}5\\end{bmatrix}$. $\\textbf{R}$ is initialized to the identity matrix, so multiplying by 5 performs this assignment for us.\n",
      "\n",
      "**5** We use the `Q_discrete_white_noise()` method to set $\\mathbf{Q}$'s variance to 0.1.\n",
      "\n",
      "**5**: $\\mathbf{P}$ is initialized to the identity matrix of size $n{\\times}n$, so multiplying by 500 assigns a variance of 500 to $x$ and $\\dot{x}$. So $\\verb,f.P,$ contains\n",
      "\n",
      "$$\\begin{bmatrix} 500&0\\\\0&500\\end{bmatrix}$$\n",
      "\n",
      "All that is left is to run the code! The `DogSensor` class from the previous chapter has been placed in `DogSensor.py`."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import numpy as np\n",
      "from DogSensor import DogSensor\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., 0.])    # (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_discrete_white_noise(dim=2, dt=0.1, var=Q)\n",
      "    else:\n",
      "        dog_filter.Q = Q\n",
      "    return dog_filter\n",
      "\n",
      "\n",
      "def filter_dog(noise_var=0, count=0, R=0, Q=0, P=500., data=None, \n",
      "               initial_x=None):\n",
      "    \"\"\" Kalman filter 'count' readings from the DogSensor.\n",
      "    'noise_var' is the variance of the noise from the measurements.\n",
      "    'data' provides the measurements. If set, noise will\n",
      "    be ignored and data will not be generated for you.\n",
      "    \n",
      "    returns a tuple of (positions, measurements, covariance)\n",
      "    \"\"\"\n",
      "    if data is None:    \n",
      "        dog = DogSensor(velocity=1, noise_var=noise_var)\n",
      "        zs = [dog.sense() for t in range(count)]\n",
      "    else:\n",
      "        zs = data\n",
      "\n",
      "    dog_filter = dog_tracking_filter(R=R, Q=Q, cov=P)\n",
      "    if initial_x is not None:\n",
      "        dog_filter.x = initial_x\n",
      "\n",
      "    pos = [None] * count\n",
      "    cov = [None] * count\n",
      "    \n",
      "    for t in range(count):\n",
      "        z = zs[t]\n",
      "        pos[t] = dog_filter.x[0]\n",
      "        cov[t] = dog_filter.P\n",
      "    \n",
      "        # perform the kalman filter steps\n",
      "        dog_filter.update(z)\n",
      "        dog_filter.predict()\n",
      "        \n",
      "    return (pos, zs, cov)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 26
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "This is the complete code for the filter, and most of it is just boilerplate. The first function `dog_tracking_filter()` is a helper function that creates a `KalmanFilter` object with specified $\\mathbf{R}$, $\\mathbf{Q}$ and $\\mathbf{P}$ matrices. We've shown this code already, so I will not discuss it more here. \n",
      "\n",
      "The function `filter_dog()` implements the filter itself.  Lets work through it line by line. The first line creates the simulation of the DogSensor, as we have seen in the previous chapter.\n",
      "\n",
      "    dog = DogSensor(velocity=1, noise=noise)\n",
      "\n",
      "The next line uses our helper function to create a Kalman filter.\n",
      "\n",
      "    dog_filter = dog_tracking_filter(R=R, Q=Q, cov=500.)\n",
      "    \n",
      "We will want to plot the filtered position, the measurements, and the covariance, so we will need to store them in lists. The next three lines initialize empty lists of length *count* in a pythonic way.\n",
      "\n",
      "    pos = [None] * count\n",
      "    zs  = [None] * count\n",
      "    cov = [None] * count\n",
      "    \n",
      "Finally we get to the filter. All we need to do is perform the update and predict steps of the Kalman filter for each measurement. The `KalmanFilter` class provides the two functions `update()` and `predict()` for this purpose. `update()` performs the measurement update step of the Kalman filter, and so it takes a variable containing the sensor measurement. \n",
      "\n",
      "Absent the bookkeeping work of storing the filter's data, the for loop reads:\n",
      "\n",
      "    for t in range (count):\n",
      "        z = dog.sense()\n",
      "        dog_filter.update (z)\n",
      "        dog_filter.predict()\n",
      "    \n",
      "It really cannot get much simpler than that. As we tackle more complicated problems this code will remain largely the same; all of the work goes into setting up the `KalmanFilter` variables; executing the filter is trivial.\n",
      "\n",
      "Now let's look at the result. Here is some code that calls `filter_track()` and then plots the result. It is fairly uninteresting code, so I will not walk through it."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def plot_track(noise_var=None, count=0, R_var=0, Q_var=0, P=500., \n",
      "               initial_x=None,data=None, plot_P=True, \n",
      "               title='Kalman Filter'):\n",
      "    \n",
      "    ps, zs, cov = filter_dog(noise_var=noise_var, data=data, count=count,\n",
      "                             R=R_var, Q=Q_var, P=P, initial_x=initial_x)\n",
      "    \n",
      "    cov = np.asarray(cov)\n",
      "    std3 = cov[:,0,0]*1\n",
      "    std3_top = np.minimum(ps+std3, [count+10])\n",
      "    std3_btm = np.maximum(ps-std3, [-50])\n",
      "\n",
      "    plt.plot([0, count],[0, count], label='actual')\n",
      "    plt.plot(range(1, count+1), zs, linestyle='dashed', label='measurement')\n",
      "    plt.plot(range(1, count+1), ps, label='filter')\n",
      "    plt.plot(range(count), ps+std3, linestyle='--', c='k')\n",
      "    plt.plot(range(count), ps-std3, linestyle='--', c='k')\n",
      "    plt.fill_between(range(count), std3_btm, std3_top,\n",
      "                     facecolor='yellow', alpha=0.2)\n",
      "    plt.legend(loc=4)\n",
      "    plt.ylim((-50, count+10))\n",
      "    plt.title(title)\n",
      "    plt.show()\n",
      "    \n",
      "    \n",
      "    if plot_P:\n",
      "        ax = plt.subplot(121)\n",
      "        ax.set_title(\"$\\sigma^2_x$\")\n",
      "        plot_covariance(cov, (0, 0))\n",
      "        ax = plt.subplot(122)\n",
      "        ax.set_title(\"$\\sigma^2_y$\")\n",
      "        plot_covariance(cov, (1, 1))      \n",
      "        plt.show()\n",
      "    \n",
      "def plot_covariance(P, index=(0, 0)):\n",
      "    ps = []\n",
      "    for p in P:\n",
      "        ps.append(p[index[0], index[1]])\n",
      "    plt.plot(ps)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 27
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Finally, call it. We will start by filtering 50 measurements with a noise variance of 10 and a process variance of 0.01."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plot_track(noise_var=10, R_var=10., Q_var=0.01, count=50)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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VSjLK3mDL7insyW+iRW/s1a6TvZbx0X6kxAX2mnSnNzXwfelTGK024nyuJdJz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cAAAc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\nYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f1a22f8df28>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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y8wUAG7F8UGa7IQAwh9fDiDIA+7B8UI5Mvej0U3QBwOq8CV2L+Th0BIAdGBCU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\ndys1NVV33313dMWx6Y4eParnn39eiYm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       "text": [
        "<matplotlib.figure.Figure at 0x7f1a22fa6828>"
       ]
      }
     ],
     "prompt_number": 28
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "There is still a lot to learn, but we have implemented our first, full Kalman filter using the same theory and equations as published by Rudolf Kalman! Code very much like this runs inside of your GPS and phone, inside every airliner, inside of robots, and so on. \n",
      "\n",
      "The first plot plots the output of the Kalman filter against the measurements and the actual position of our dog (drawn in green). After the initial settling in period the filter should track the dog's position very closely. The yellow shaded portion between the black dotted lines shows 1 standard deviations of the filter's variance, which I explain in the next paragrah.\n",
      "\n",
      "The next two plots show the variance of $x$ and of $\\dot{x}$. If you look at the code, you will see that I have plotted the diagonals of $\\mathbf{P}$ over time. Recall that the diagonal of a covariance matrix contains the variance of each state variable. So $\\mathbf{P}[0,0]$ is the variance of $x$, and $\\mathbf{P}[1,1]$ is the variance of $\\dot{x}$. You can see that despite initializing $\\mathbf{P}=(\\begin{smallmatrix}500&0\\\\0&500\\end{smallmatrix})$ we quickly converge to small variances for both the position and velocity. We will spend a lot of time on the covariance matrix later, so for now I will leave it at that. For now we can look at the top plot and see that the filter's output stays within the 3 standard deviation lines, so we should feel confident that the filter is performing well."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "In the previous chapter we filtered very noisy signals with much simpler code than the code above. However, realize that right now we are working with a very simple example - an object moving through 1-D space and one sensor. That is about the limit of what we can compute with the code in the last chapter. In contrast, we can implement very complicated, multidimensional filter with this code merely by altering are assignments to the filter's variables. Perhaps we want to track 100 dimensions in financial models. Or we have an aircraft with a GPS, INS, TACAN, radar altimeter, baro altimeter, and airspeed indicator, and we want to integrate all those sensors into a model that predicts position, velocity, and accelerations in 3D (which requires 9 state variables). We can do that with the code in this chapter."
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Compare to Univariate Kalman Filter"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The equations in this chapter look very different from the equations in the last chapter, yet I claimed the last chapter implemented a full 1-D (univariate) Kalman filter. \n",
      "\n",
      "Recall that the univariate equations for the update step are:\n",
      "$$\n",
      "\\begin{aligned}\n",
      "\\mu &=\\frac{\\sigma_1^2 \\mu_2 + \\sigma_2^2 \\mu_1} {\\sigma_1^2 + \\sigma_2^2}, \\\\\n",
      "\\sigma^2 &= \\frac{1}{\\frac{1}{\\sigma_1^2} + \\frac{1}{\\sigma_2^2}}\n",
      "\\end{aligned}\n",
      "$$\n",
      "\n",
      "and that the 1-D equations for the predict step are:\n",
      "$$\n",
      "\\begin{aligned}\n",
      "\\mu &= \\mu_1+\\mu_2, \\\\ \\sigma^2 &= \\sigma_1^2 + \\sigma_2^2\n",
      "\\end{aligned}\n",
      "$$\n",
      "\n",
      "Let's implement a simple 1-D kalman filter using the Kalman filter from this chapter, and compare its output to the kalman filter from the previous chapter by plotting it. We will use a simple model of tracking an object that starts at x=0 and moves by 1 at each step. We will assume the arbitrary value 5 for the measurement noise and .02 for the process noise.\n",
      "\n",
      "First, let's implement the filter from the last chapter:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from __future__ import division\n",
      "import numpy as np\n",
      "from numpy.random import randn\n",
      "from filterpy.kalman import KalmanFilter\n",
      "\n",
      "# 1-D Kalman filter equations\n",
      "def predict(pos, variance, movement, movement_variance):\n",
      "    return (pos + movement, variance + movement_variance)\n",
      "\n",
      "\n",
      "def update (mu1, var1, mu2, var2):\n",
      "    mean = (var1*mu2 + var2*mu1) / (var1+var2)\n",
      "    variance = 1 / (1/var1 + 1/var2)\n",
      "    return (mean, variance)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 29
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Now, let's implement the same thing using the kalman filter. I will implement it as a function that returns a KalmanFilter object so that you can run the analysis code several times with the KalmanFilter initialized to the same starting conditions each time."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from filterpy.kalman import KalmanFilter\n",
      "\n",
      "def mkf_filter(R, Q):\n",
      "    f = KalmanFilter(dim_x=1, dim_z=1, dim_u=1)\n",
      "    f.P = 500.\n",
      "    f.H = np.array([[1.]])\n",
      "    f.F = np.array([[1.]])\n",
      "    f.B = np.array([[1.]])\n",
      "    f.Q = Q\n",
      "    f.R = R\n",
      "    \n",
      "    return f"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 30
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Finally, let's compare the two. I will plot the data from the 1-D Kalman filter as a blue line, and the output of the filter from this chapter as red dots. I wrote it as a function so you can easily modify the parameters and regenerate the plots."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def plot_kf_compare(x0, p0, R, Q, move):\n",
      "    # storage for filter output\n",
      "    x1,x2 = [], []\n",
      "    p1, p2 = [], []\n",
      "\n",
      "    # initialize the filters\n",
      "    f = mkf_filter(R, Q)\n",
      "    f.x[0] = 0.\n",
      "    f.P[0, 0] = p0\n",
      "    pos = (x0, p0)\n",
      "    for i in range(50):\n",
      "        z = i*move + randn()\n",
      "        pos = update(pos[0], pos[1], z, R)\n",
      "        f.update(z)\n",
      "\n",
      "        x1.append(pos[0])\n",
      "        x2.append(f.x[0])\n",
      "\n",
      "        p1.append(pos[1])\n",
      "        p2.append(f.P[0, 0])\n",
      "\n",
      "        u = move + randn()\n",
      "        pos = predict(pos[0], pos[1], u, Q)\n",
      "        f.predict(u=u)\n",
      "\n",
      "    plt.scatter(range(len(x2)), x2, c='r')\n",
      "    plt.title('State')\n",
      "    plt.plot(x1)\n",
      "    plt.xlim([0, 50])\n",
      "\n",
      "    plt.figure()\n",
      "    plt.plot(p1)\n",
      "    plt.scatter(range(len(x2)), p2, c='r')\n",
      "    plt.title('Variance')\n",
      "    plt.xlim([0, 50])\n",
      "    plt.show()\n",
      "    \n",
      "plot_kf_compare(x0=0., p0=500., R=5., Q=.2, move=1.)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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h5SmDib84sqFLqzMFZRERERGpFafTydZ9+fxn2RaWLN/MsYirAbjKeoC/PzuZkA5tGrhC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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f1a2338e898>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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YsWzglaTKQYNU+uGHGvvqU3p91vVqn5OutdsO6tp7X9f6HXyQDQAAoCWwdOCV\namd6PTk5uqBHW737p3EafE47HThapX/741t6Zdm/4l0eAAAAoszygfdUbbPS9MrdY3TLlf3k8QX0\nm2eW696/rpTXF4h3aQAAAIiSFhV4JSk5ya4Hbh2ih38yVA67Tc99sEk/fugdlRxzx7s0AAAAREGL\nC7x1bvz+ufrnvWPVLjtNq7Z8o2t+v1hf7ToS77IAAAAQYS028ErSoN7t9M6fxuminrkqKqnQuD++\nqdc/2R7vsgAAABBBLTrwSlJe63S9eu9Y3TCsj6o9fk2fv1SzX/5UtsNH2KgCAADAAlp84JWkFIdd\nj/w0X/938hAl2Q0teHuDbvrpXJmjxrIlMQAAQDNH4D3BMAxNvqqfXp0+VG19bn2U3lm9evxYD/7+\nWZXtLo53eQAAAAgTgfdbLu/VVp/t/qeuLN2hY0lO/T/XxRo4613ds+gT7T98PN7lAQAAoIkIvN/i\nyclR9lNz9P6hD7Vy92u6tmeWqr0BLfpws4bc8Yr+Y8HH2lZ0NN5lAgAAoJGS4l1AIqocNEjeDz9U\nb0l/zsnR1/tK9dRbX+qNVTv0zxXb9GrhNo0e2E3Tr7tQF/ZsG+9yAQAAcAbM8H6Hui2JJenczjma\nN+37Knz0R7r5yr5KTrLr3bW7Nea+xbrhwXdUuKlIpmkqubSUJzsAAAAkGAJvE3TJbaUHb71Cqx+/\nQdPGDlCG06EVG4s08YF3NO7Ol7Vi/E+VfdVVPNkBAAAggRB4w5CbnaZ7fnyJPp37Y/3nDwfKlZGs\ntQeq9G+dRqtflwn60++f12ef/kteXyDepQIAALR4rOE9C9npKZox/mL94tJOev2mu/RoVn9tS3Pp\nkTSXHpm7XK3SVmvY+Z008qLOGnFBZ7lapca7ZAAAgBanwRneN954Q5dddpmcTqduvfXWWNTU7Dja\n5+rWh6Zr++5X9NHeNzV9YK56dcjWsSqP3vp0p2YsWKYLpv1NY+97Q4+9vk5f7Toi0zSD17P2FwAA\nIHoanOHNzs7WXXfdpY8++khVVVWxqKlZqn2yw/u6QFLfnBz9TtKeQ8dUsH6vCr7Yp1VbvtH6HYe0\nfschPfLPz9UuO00jLuysazM9+sGjv1dmwKvjCxeqctCgeP9WAAAALKXBwDts2DBJ0rp16wi8Dah7\nqkOdrrmtNGVUf00Z1V9V1V4VbirWR1/sVcH6fTpwtFL//fG/9N+SHL0m67zKQ7rg/v9W79v8Oufc\nzurX1aUKEg1AAAAPmUlEQVTs9JT4/EYAAAAspNFreE/9L3g0XZrToasHdtXVA7vKNE1t3luqj1f+\nSx//vUCrU3P1RWZ7faH20qsbJG2QJHVqk6F+XVw6r6tL53XNUb+uLnVpmynDMIJLIL4dsgEAAFBf\nowOvYRhnfN/lcp11MS1Jfps2GnpRb/3u3FT5f3a7NqS4tHbKr7TR0Vobdh7Sxt2Htf9IhfYfqdAH\n6/YEr2uVlqzzWifr4o2r1LemTLm336ruV+Wra7sstTrDjLBpmvIXFUmS7B07Nvj3ebYcDock+gL1\n0RcIhb5AKPQFQqnri6aK2Azv7Nmzg6/z8/ODSyHw3QzDUNLIkTKWL9XFkr53ShD1+QPaXlSqL3cc\n0oadB7Vh5yFt2HlIB49WalWVR6tan197k9e31/6SlJ2Roi65WeqS26r2a7var53aZqrjvzao63/c\nLkNS1V/+UjtuI0JvrIMyAADAqZYtW6bly5dLkux2u/Lz85t8D8Ns5FqFe++9V/v379fzzz9/2nsF\nBQXq27dvkwdH0x3dXay9N9+uDZ4UbU/N0e6sXO3q3ldFR92q9vrPeK3T71XnmmNqK69aXXKRWrta\nKSfTqZxMp1pnOOVq5Qx+78p0KiPVoYzPP1fm1KmS1KQP1WW53ZKk8tSmPYqNpRrWVjdTU1JSEudK\nkEjoC4RCXyAUl8ulwsJCjRw5sknXNTjDGwgE5PF45PP55Pf7VVNTo6SkJNnt9rCLRfhad+ugTnPu\n1aipUyXvDh1/uDaEmqapkmPVJ5ZBHNf+IxUqOrEkovhQmYr2HNRRu1Pb0lzaJklffSPpmzOO5bAb\nalNdoTadxivbV62M2YuVkn9Y6VkZSnc6lJHqULrToczU5FNeO9Rm5zbl/fF+ZQS88j/2qAKXfE+O\npIb3OElfuzascB1OSA43WMdqrESvL9zrfPv3175owg9CVv2zsGJ94V5HX8T+mliOFW59VuyLRK8v\nlmPFeoKrwRneRYsWacqUKfWOzZo1S/fdd1/we2Z4Y6+pjZK+dq3M26erKClde2feq+KOXVVyvFql\nJ36VHKvW0ePVKq04+X1VjS9i9dpthpzJSXIm25XisNe+rvuabFeaTLVa/YnSqiqUbPrlcKYoMO46\n2TPS5UiyKdlukyPJLkeSTQ67rfZYkl0Z+/ao1bN/kcP0yzttmnzn9FGS3ZDdZqv9arfJbjOUZLPJ\nbq/9mrllk7Lu/b2STFNVDz2omgsvlN1myFb3yzBOfl/32jCUua7ps93hhPhwg78Vx0r0+mI5VqLX\nF8uxEr2+WI5Ffc1nrESvL5ZjhVufFP4Mb6OXNJwJgbd5aGpIdnt8qvlkjdz3zNIxW7IO/erXOtKx\nqyqqvaqs9uq426MK98nXlW6vKivccm/equOmTRX2ZLmTkuW2OxSwyEM+7GZANtOUTaaMlGQZNpts\nhiGbIdkMQ4ZhyDBUG5ZNU0mlpTICftlMU4bdJjO3nWS31Z5z4nxJMozaNd32QEBJe/fI8PlkSDLs\ndgV6dJeZVPufMYYUHMNQ7VdJsvn9cvzrXzK8HhmS5HDI37evAklJwXMMnRxLkmw+nxwbN8rweGqP\nJzvkHTBA+o4PBNRdZ/f55Fi/XvKcGCs5Wd6LLlLgxHXfXudtSLL5vEr6/HMZNbVjKTlZ3kEDZX5r\nrFOvNbxeOT77LFifkpPl/d73TrvmtDrrrqupkSHJTEmRd/D3ZDqSz3CNR441tddIklKS5R18iQLJ\nZx7L5vHKsebT+mNdcknwzyLkNV6vHJ9+GhwrnGuUkizvpZcqcIbfU+11HjlWr5ZRfWIsZ0qD14Vz\nTSzHSvT6YjkW9TWfsRK9vliO9e1rfu7erksWP9fobELgRdSEM5v87Z/cvL6Aqj0+VXt9qvb4a1/X\nffXWftXXW2X++Tl5DJsq/s8kVXTsLK/PL48vIK8vcPK1v/arv9It2wcfylPjlc+wyZuaKvf3LpHX\nniSfPyB/ICCf3zz51R+Q3+uT9u2Tz2/Ka9gUsCfJm5OjgGHIHzBlBkz5A6b85imvA6YCPJYPAICI\ne+rAcv3oH09EPfA2+ikNaLmaur6mctAgJRUW1r4+sfbKkWSTIylZmTrDT5gXd1Xy6IFNGjP98pyY\n/VdK6mefKe3n02RKKn/qKVVcdLFMszYMB0zVfj0xlR04EZKdX3yptJkzFZCh4w8+qKrzz5dpmjIl\nmSeuMU1TdXnaNE2lfLVRaX/4g0zDUMW996mqX78T70lS7bmmTr2m9nvn5i1KfeghSVLlzN/K3ffc\n4Dl1L05+W/sq5et/Ke2RR2RKqrrzDrn7nBP8/Z6a8c0TV9YdS926Vc7HHpMkuWfMkPucc06/6Fvf\nOrdtVerjT8g0JPev/kPVfXp/57knr9mm1LlzZUpy//KXqu7d5/STQnBu2yrnvCdr6/vldFX37t3A\nFSfGmvdk7VjTG3dN3XXOJ0+MNX26qnv1avia7duVGuY1pmHIPe0Xqu7d8DW19W1X6vynasdq5HXh\nXBPLsRK9vliORX3NZ6xEry+WY516Tff77ojJOl5meBEVsfx0LYv5m89Y4Ty9w6p/FlasL9zr6IvY\nXxPLscKtz4p9kej1xXKscOtjSQMSCo+TQSj0BUKhLxAKfYFQwg28DT8rCgAAAGjGCLwAAACwNAIv\nAAAALI3ACwAAAEsj8AIAAMDSCLwAAACwNAIvAAAALI3ACwAAAEsj8AIAAMDSCLwAAACwNAIvAAAA\nLI3ACwAAAEsj8AIAAMDSCLwAAACwNAIvAAAALI3ACwAAAEsj8AIAAMDSCLwAAACwNAIvAAAALI3A\nCwAAAEsj8AIAAMDSCLwAAACwNAIvAAAALI3ACwAAAEsj8AIAAMDSCLwAAACwNAIvAAAALI3ACwAA\nAEsj8AIAAMDSCLwAAACwNAIvAAAALI3ACwAAAEsj8AIAAMDSCLwAAACwNAIvAAAALI3ACwAAAEsj\n8AIAAMDSCLwAAACwNAIvAAAALI3ACwAAAEsj8AIAAMDSGhV49+/fr+HDhys9PV0DBw7Upk2bol0X\nAAAAEBGNCrw/+9nPNGDAAJWWlmrixImaOHFitOsCAAAAIqLBwHvs2DF9+OGH+u1vf6uUlBTNmDFD\ne/bs0caNG2NRH5qxLVu2xLsEJCD6AqHQFwiFvkCkNBh4t2/fLqfTqfT0dA0dOlS7du1Sz5499fXX\nX8eiPjRj/EOFUOgLhEJfIBT6ApHSYOCtrKxURkaGjh8/ri1btujo0aPKzMxUZWVlLOoDAAAAzkpS\nQyekp6eroqJCnTp10pEjRyRJx48fV0ZGRr3zXC5XdCpEs+RwODRixAhlZ2fHuxQkEPoCodAXCIW+\nQCgOhyOs6xoMvL169ZLb7VZRUZE6duwoj8ejHTt26Jxzzql3XmFhYVgFAAAAANFkmKZpNnTSmDFj\n1KNHDz388MN64okn9OKLL/KhNQAAADQLjXos2cKFC/XVV18pJydHf//73/XKK69Euy4AAAAgIho1\nwwsAAAA0V2wtDAAAAEsj8AIAAMDSCLwAAACwtAYfS3YmJSUlmjdvnnbs2KEOHTpo+vTp6ty5c6Rq\nQzPx2WefafHixdq9e7eGDBm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       "text": [
        "<matplotlib.figure.Figure at 0x7f1a2312a0b8>"
       ]
      }
     ],
     "prompt_number": 31
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "##### Discussion\n",
      "\n",
      "As you can see, both filters produce the same results. Feel free to vary the initial guess, the measurement noise, and the process noise; so long as you make the same changes to both filters the output should be the same. This is a solid demonstration, albeit not a rigorous proof, that both filters in fact implement the same math for the 1-D case. "
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Converting the Multivariate Equations to the Univariate Case"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "\n",
      "As it turns out the Kalman filter equations are quite easy to deal with in one dimension, so let's do the mathematical proof. \n",
      "\n",
      "> **Note:** This section will provide you with a strong intuition into what the Kalman filter equations are actually doing. While this section is not strictly required, I recommend reading this section carefully as it should make the rest of the material easier to understand. It is not merely a proof of correctness that you would normally want to skip past! The equations look complicated, but they are actually doing something quite simple.\n",
      "\n",
      "Let'start with the predict step, which is slightly easier. Here are the multivariate equations. \n",
      "$$\n",
      "\\begin{aligned}\n",
      "\\mathbf{x}^- &= \\mathbf{F x} + \\mathbf{B u} \\\\\n",
      "\\mathbf{P^-} &= \\mathbf{FP{F}}^\\mathsf{T} + \\mathbf{Q}\n",
      "\\end{aligned}\n",
      "$$\n",
      "\n",
      "The state $\\mathbf{x}$ only has one variable, so it is a $1\\times 1$ matrix. Our motion $\\mathbf{u}$ is also be a $1\\times 1$ matrix. Therefore, $\\mathbf{F}$ and $\\mathbf{B}$ must also be $1\\times 1$ matrices. That means that they are all scalars, and we can write\n",
      "\n",
      "$$x = Fx + Bu$$\n",
      "\n",
      "Here the variables are not bold, denoting that they are not matrices or vectors. \n",
      "\n",
      "Our state transition is simple - the next state is the same as this state, so $F=1$. The same holds for the motion transition, so, $B=1$. Thus we have\n",
      "$$x = x + u$$\n",
      "\n",
      "which is equivalent to the Gaussian equation from the last chapter\n",
      "\n",
      "$$ \\mu = \\mu_1+\\mu_2$$\n",
      "\n",
      "Hopefully the general process is clear, so now I will go a bit faster on the rest. Our other equation for the predict step is\n",
      "\n",
      "$$\\mathbf{P}^- = \\mathbf{FP{F}}^\\mathsf{T} + \\mathbf{Q}$$\n",
      "\n",
      "Again, since our state only has one variable $\\mathbf{P}$ and $\\mathbf{Q}$ must also be $1\\times 1$ matrix, which we can treat as scalars, yielding  \n",
      "$$P^- = FPF^\\mathsf{T} + Q$$\n",
      "\n",
      "We already know $F=1$. The transpose of a scalar is the scalar, so $F^\\mathsf{T} = 1$. This yields\n",
      "\n",
      "$$P^- = P + Q$$\n",
      "\n",
      "which is equivalent to the Gaussian equation of \n",
      "$$\\sigma^2 = \\sigma_1^2 + \\sigma_2^2$$\n",
      "\n",
      "This proves that the multivariate equations are performing the same math as the univariate equations for the case of the dimension being 1."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Here our our multivariate Kalman filter equations for the update step.\n",
      "$$\n",
      "\\begin{aligned}\n",
      "\\textbf{y} &= \\mathbf{z} - \\mathbf{H x^-}\\\\\n",
      "\\mathbf{K}&= \\mathbf{P^-H}^\\mathsf{T} (\\mathbf{HP^-H}^\\mathsf{T} + \\mathbf{R})^{-1} \\\\\n",
      "\\mathbf{x}&=\\mathbf{x}^- +\\mathbf{K\\textbf{y}} \\\\\n",
      "\\mathbf{P}&= (\\mathbf{I}-\\mathbf{KH})\\mathbf{P^-}\n",
      "\\end{aligned}\n",
      "$$\n",
      "\n",
      "As above, all of the matrices become scalars. $H$ defines how we convert from a position to a measurement. Both are positions, so there is no conversion, and thus $H=1$. Let's substitute in our known values and convert to scalar in one step. One final thing you need to know - division is scalar's analogous operation for matrix inversion, so we will convert the matrix inversion to division.\n",
      "\n",
      "$$\n",
      "\\begin{aligned}\n",
      "y &= z - x^-\\\\\n",
      "K &=P^- / (P^- + R) \\\\\n",
      "x &=x +Ky \\\\\n",
      "P &= (1-K)P^-\n",
      "\\end{aligned}\n",
      "$$\n",
      "\n",
      "Before we continue with the proof, I want you to look at those equations to recognize what a simple concept these equations implement. The residual $y$ is nothing more than the measurement minus the previous state. The gain $K$ is scaled based on how certain we are about the last prediction vs how certain we are about the measurement. We choose a new state $x$ based on the old value of $x$ plus the scaled value of the residual. Finally, we update the uncertainty based on how certain we are about the measurement. Algorithmically this should sound exactly like what we did in the last chapter.\n",
      "\n",
      "So let's finish off the algebra to prove this. It's straightforward, and not at all  necessary for you to learn unless you are interested. Feel free to skim ahead to the last paragraph in this section if you prefer skipping the algebra.\n",
      "\n",
      "Recall that the univariate equations for the update step are:\n",
      "$$\n",
      "\\begin{aligned}\n",
      "\\mu &=\\frac{\\sigma_1^2 \\mu_2 + \\sigma_2^2 \\mu_1} {\\sigma_1^2 + \\sigma_2^2}, \\\\\n",
      "\\sigma^2 &= \\frac{1}{\\frac{1}{\\sigma_1^2} + \\frac{1}{\\sigma_2^2}}\n",
      "\\end{aligned}\n",
      "$$\n",
      "\n",
      "Here we will say that $\\mu_1$ is the state $x$, and $\\mu_2$ is the measurement $z$. That is entirely arbitrary, we could have chosen the opposite assigment. \n",
      "Thus it follows that that $\\sigma_1^2$ is the state uncertainty $P$, and $\\sigma_2^2$ is the measurement noise $R$. Let's substitute those in.\n",
      "\n",
      "$$ \\mu = \\frac{Pz + Rx}{P+R} \\\\\n",
      "\\sigma^2 = \\frac{1}{\\frac{1}{P} + \\frac{1}{R}}\n",
      "$$\n",
      "\n",
      "I will handle $\\mu$ first. The corresponding equation in the multivariate case is\n",
      "\n",
      "$$\n",
      "\\begin{aligned}\n",
      "x &= x + Ky \\\\\n",
      " &= x + \\frac{P}{P+R}(z-x) \\\\\n",
      " &= \\frac{P+R}{P+R}x + \\frac{Pz - Px}{P+R} \\\\\n",
      " &= \\frac{Px + Rx + Pz - Px}{P+R} \\\\\n",
      " &= \\frac{Pz + Rx}{P+R} \\quad \\blacksquare\n",
      "\\end{aligned}\n",
      "$$"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Now let's look at $\\sigma^2$. The corresponding equation in the multivarate case is\n",
      "\n",
      "$$ \n",
      "\\begin{aligned}\n",
      "P &= (1-K)P \\\\\n",
      " &= (1-\\frac{P}{P+R})P \\\\\n",
      " &= (\\frac{P+R}{P+R}-\\frac{P}{P+R})P \\\\\n",
      "  &= (\\frac{P+R-P}{P+R})P \\\\\n",
      "  &= \\frac{RP}{P+R}\\\\\n",
      "  &= \\frac{1}{\\frac{P+R}{RP}}\\\\\n",
      "  &= \\frac{1}{\\frac{R}{RP} + \\frac{P}{RP}} \\\\\n",
      "  &= \\frac{1}{\\frac{1}{P} + \\frac{1}{R}}\n",
      " \\quad\\blacksquare\n",
      "\\end{aligned}\n",
      "$$\n",
      "\n",
      "So we have proven that the multivariate equations are equivalent to the univariate equations when we only have one state variable. I'll close this section by recognizing one quibble - I hand waved my assertion that $H=1$ and $F=1$. In general we know this is not true. For example, a digital thermometer may provide measurement in volts, and we need to convert that to temperature, and we use $H$ to do that conversion. I left that issue out of the last chapter to keep the explanation as simple and streamlined as possible. It is very straightforward to add that generalization to the equations of the last chapter, redo the algebra above, and still have the same results. In practice we do not use the equations in the last chapter to perform Kalman filtering due to the material in the next section which demonstrates how much better the Kalman filter performs when we include unobserved variables. So I prefer to leave the equations from the last chapter in their simplest form so that they economically represent our central ideas without any extra complications."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "##### Exercise: Compare to a Filter That Incorporates Velocity\n",
      "\n",
      "The last example did not use one of the fundamental insights of this chapter, unobserved variables. In this example velocity would the the unobserved variable. Write a Kalman filter that uses the state $\\mathbf{x}=\\begin{bmatrix}x & \\dot{x}\\end{bmatrix}^\\mathsf{T}$ and compare it against the filter in the last exercise which used the state $\\mathbf{x}=\\begin{bmatrix}x\\end{bmatrix}$."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# your code here"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 32
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "##### Solution\n",
      "\n",
      "We've already implemented a Kalman filter for position and velocity, so I will provide the code without much comment, and then plot the result."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def pos_vel_filter(R,Q):\n",
      "    f = KalmanFilter(dim_x=2, dim_z=1)\n",
      "    f.R = R\n",
      "    f.Q = Q_discrete_white_noise(dim=2, dt=0.1, var=Q)\n",
      "   \n",
      "    f.F = np.array([[1, 1],\n",
      "                    [0, 1]])  # state transition matrix\n",
      "    f.H = np.array([[1, 0]])  # Measurement function\n",
      "    return f\n",
      "\n",
      "def plot_compare_pos_vel(x0, p0, R, Q, move):\n",
      "    # storage for filter output\n",
      "    x1, x2 = [], []\n",
      "\n",
      "    # initialize the filters\n",
      "    f1 = mkf_filter(R, Q)\n",
      "    f1.x[0] = 0.\n",
      "    f1.P[0, 0] = p0\n",
      "    \n",
      "    f2 = pos_vel_filter(R, Q)\n",
      "    f2.x[0] = 0.\n",
      "    f2.x[1] = 1.\n",
      "    f2.P *= p0\n",
      "    \n",
      "    for i in range(50):\n",
      "        u = move + randn()\n",
      "        f1.predict(u=u)\n",
      "        f2.predict(u=u)\n",
      "        \n",
      "        z = i*move + randn()\n",
      "        f1.update(z)\n",
      "        f2.update(z)\n",
      "        \n",
      "        x1.append(f1.x[0, 0])\n",
      "        x2.append(f2.x[0, 0])\n",
      "\n",
      "    plt.plot(x1, label='1D Filter')\n",
      "    plt.scatter(range(len(x2)), x2, c='r', label='2D Filter')\n",
      "    plt.title('State')\n",
      "    plt.legend(loc=4)\n",
      "    plt.xlim([0,50])\n",
      "    plt.show()\n",
      "    \n",
      "plot_compare_pos_vel(x0=0., p0=500., R=5., Q=.2, move=1.)    "
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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j7sC8pk5BWURERERq2OwO/vDPb3lr6fcA3NS/I688mExwgE8j9+zSU1AWEREREQBy80/x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\njdllEREREbcpKMt5nTmDBYAlJYWtCz9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       "text": [
        "<matplotlib.figure.Figure at 0x7f1a233b4ba8>"
       ]
      }
     ],
     "prompt_number": 33
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "##### Discussion\n",
      "\n",
      "The output of the filter that incorporates velocity into the state produces much better output than the filter that only tracks position - the output is much closer to a straight line. We've already discussed why unobserved variables increase the precision of the filter, so I will not repeat that explanation here. But the last exercise and this one is intended to trigger a train of thought:\n",
      "\n",
      "1. The equations in this chapter are mathematically equivalient to the equations in the last chapter when we are only tracking one state variable.\n",
      "    \n",
      "2. Therefore, the simple Bayesian reasoning we used in the last chapter applies to this chapter as well.\n",
      "\n",
      "3. Therefore, the equations in this chapter might 'look ugly', but they really are just implementing multiplying and addition of Gaussians.\n",
      "\n",
      "> The above might not seem worth emphasizing, but as we continue in the book the mathematical demands will increase significantly. It is easy to get lost in a thicket of linear algebra equations when you read a book or paper on optimal estimation. Any time you start getting lost, just go back to the basics of the predict/update cycle based on residuals between measurements and predictions and the meaning of the math will usually be much clearer. The math *looks* daunting, and can sometimes be very hard to solve analytically, but the concepts are quite simple."
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Adjusting the Filter"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Your results will vary slightly depending on what numbers your random generator creates for the noise component of the noise, but the filter in the last section should track the actual position quite well. Typically as the filter starts up the first several predictions are quite bad, and varies a lot. But as the filter builds its state the estimates become much better. \n",
      "\n",
      "Let's start varying our parameters to see the effect of various changes. This is a *very normal* thing to be doing with Kalman filters. It is difficult, and often impossible to exactly model our sensors. An imperfect model means imperfect output from our filter. Engineers spend a lot of time tuning Kalman filters so that they perform well with real world sensors. We will spend time now to learn the effect of these changes. As you learn the effect of each change you will develop an intuition for how to design a Kalman filter. As I wrote earlier, designing a Kalman filter is as much art as science. The science is, roughly, designing the ${\\mathbf{H}}$ and ${\\mathbf{F}}$ matrices - they develop in an obvious manner based on the physics of the system we are modeling. The art comes in modeling the sensors and selecting appropriate values for the rest of our variables.\n",
      "\n",
      "Let's look at the effects of the noise parameters ${\\mathbf{R}}$ and ${\\mathbf{Q}}$. We will want to see the effect of different settings for ${\\mathbf{R}}$ and ${\\mathbf{Q}}$, so I have hard coded our measurements in `zs` based on a variance of 50 meters. That is very large, but it magnifies the effects of varius design choices on the graphs, making it easier to recognize what is happening. "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# dog = DogSensor(velocity=1, noise_var=50)\n",
      "# zs = [dog.sense() for t in range(50)]\n",
      "# I've hard coded zs to ensure we are all looking at the same data\n",
      "zs = [3.59, 1.73, -2.575, 4.38, 9.71, 2.88, 10.08, 8.97, 3.74,\n",
      "      12.81, 11.15, 9.25, 3.93, 11.11, 19.29,  16.20, 19.63,\n",
      "      9.54, 26.27, 23.29, 25.18, 26.21, 17.1, 25.27, 26.86,\n",
      "      33.70, 25.92, 28.82, 32.13, 25.0, 38.56, 26.97, 22.49,\n",
      "      40.77, 32.95, 38.20, 40.93, 39.42, 35.49, 36.31, 31.56,\n",
      "      50.29, 40.20, 54.49, 50.38, 42.79, 37.89, 56.69, 41.47, 53.66]\n",
      "    \n",
      "plot_track(data=zs, R_var=50, Q_var=20, count=50, plot_P=False, \n",
      "           title='R_var = 50 m, Q_var = 20 m')\n",
      "\n",
      "plot_track(data=zs, R_var=50, Q_var=.02, count=50, plot_P=False, \n",
      "           title='R_var = 50 m, Q_var = 0.02 m')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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MyNK1Pz2WJRVtvLqy5+IGjqbvodRsoJtf/yaZLJstJrKL0wDwdPC9Ide8kLeT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SqOFSs+omvXv6BpZuCPpVEff/zxfYtLCCGqM0mUy4FNyeOXc2vJsWVRy7Uubfx7FnueqmqcvpRT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\nahXhfjgapAAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f1a23381630>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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5t956a1eHJEmSJEmXBZO1iDpbJardHUu1nqyKHzBZSzhRs4cwYxIAn366lHnz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\nZf31VK3Wod+Wbmpq4je/+Q0vvfQSvb29HD26l7fe+j9j+XC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bv6BsqIVyetXArNglIzp/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\nRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f1a23381898>"
       ]
      }
     ],
     "prompt_number": 34
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The filter in the first plot should follow the noisy measurement almost exactly. In the second plot the filter should vary from the measurement quite a bit, and be much closer to a straight line than in the first graph. \n",
      "\n",
      "In the Kalman filter ${\\mathbf{R}}$ is the *measurement noise* and ${\\mathbf{Q}}$ is the *process uncertainty*. ${\\mathbf{R}}$ is the same in both plots, so ignore it for the moment. Why does ${\\mathbf{Q}}$ affect the plots this way?\n",
      "\n",
      "Let's remind ourselves of what the term *process uncertainty* means. Consider the problem of tracking a ball. We can accurately model its behavior in static air with math, but if there is any wind our model will diverge from reality. \n",
      "\n",
      "In the first case we set `Q_var=20 m`, which is quite large. In physical terms this is telling the filter \"I don't trust my motion prediction step\" as we are saying that the variance in the velocity is 10. Strictly speaking, we are telling the filter there is a lot of external noise that we are not modeling with $\\small{\\mathbf{F}}$, but the upshot of that is to not trust the motion prediction step. So the filter will be computing velocity ($\\dot{x}$), but then mostly ignoring it because we are telling the filter that the computation is extremely suspect. Therefore the filter has nothing to use but the measurements, and thus it follows the measurements closely. \n",
      "\n",
      "In the second case we set `Q_var=0.02 m`, which is quite small. In physical terms we are telling the filter \"trust the motion computation, it is really good!\". Again, more strictly this actually says there is very small amounts of process noise (variance 0.02 m), so the motion computation will be accurate. So the filter ends up ignoring some of the measurement as it jumps up and down, because the variation in the measurement does not match our trustworthy velocity prediction."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Now let's set `Q_var=0.2 m`, and bump `R_var` up to 10,000 m. This is telling the filter that the measurement noise is very large. "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plot_track(data=zs, R_var=10000., Q_var=.2, count=50, plot_P=False, \n",
      "           title='R_var = 10000 m, Q_var = 0.2 m')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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ykf2BjIAEZSGEEEKIcQoLjuKW2V/GGhQxputbexpwehyEBtiIComb4Nb5U512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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f1a22f8d2b0>"
       ]
      }
     ],
     "prompt_number": 35
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The effect of this can be subtle. We have created an suboptimal filter because the actual measurement noise variance is 30 m, not 10,000 m. By setting the filter's noise variance so high we force the filter to favor the prediction over the measurement. This can lead to apparently very smooth and good looking results. In the chart above the track may look extremely good to you since it follows the ideal path very closely. But, the 'great' behavior at the start should give you pause - the filter has not converged yet ($\\mathbf{P}$ is still large) so it should not be able to be so close to the actual position. We can see that $\\mathbf{P}$ has not converged because the entire chart is colored with the yellow background denoting the size of $\\mathbf{P}$. Let's make $\\mathbf{R}$ larger yet. Let's see the result of a bad initial guess for the position by guessing the initial position to be 20 m and the initial velocity to be 1 m/s."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plot_track(data=zs, R_var=10000., Q_var=.2, count=50, \n",
      "           initial_x=np.array([20., 1.]), plot_P=False, \n",
      "           title='R_var = 10000 m, Q_var = 0.2 m')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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z9h0MWLrR13wzDleKOFZjxJDZ6dHOn6S76aBTZ+Jc7zG0GxqwVLdmxs47igJl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\nSUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f1a230653c8>"
       ]
      }
     ],
     "prompt_number": 36
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Here we can see that the filter cannot acquire the actual track at all. This happens because even though the filter is getting reasonable good measurements it assumes that the measurements are bad, and eventually just predicts forward from a bad position at each step. If you think that perhaps that bad initial position would give similar results for a smaller measurement noise, let's set it back to the correct value of 50 m."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plot_track(data=zs, R_var=30, Q_var=.2, count=50, \n",
      "           initial_x=np.array([20., 1.]), plot_P=False, \n",
      "           title='R_var = 30 m, Q_var = 0.2 m')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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lK1ucKBcXF/PBBx/gcDiYNGk0zz//AD17nr0gR2voVQNDQ+JJOv4de/M20d27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IIdH1NhGYhhpGJ0bI/lhkuwXX0h7lWbcC1cVdl+usKB0aUj9jtHY4k8ccm402WaJt/umsXh0lxc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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f1a22f86390>"
       ]
      }
     ],
     "prompt_number": 37
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Here we see that the filter initially struggles for several iterations to acquire the track, but then it accurately tracks our dog. In fact, this is nearly optimum - we have not designed $\\mathbf{Q}$ optimally, but $\\mathbf{R}$ is optimal, and thus will yield optimal results. Recall that our rule of thumb for the variance of $\\mathbf{Q}$ was to set it between $\\frac{1}{2}\\Delta a$ to $\\Delta a$, where $\\Delta a$ is the maximum amount that the acceleration will change between sample period. This only applies for the assumption we are making in this chapter - that acceleration is constant and uncorrelated between each time period. In the Kalman Math chapter we will discuss several different ways of designing $\\mathbf{Q}$.\n",
      "\n",
      "To some extent you can get similar looking output by varying either ${\\mathbf{R}}$ or ${\\mathbf{Q}}$, but I urge you to not 'magically' alter these until you get output that you like. Always think about the physical implications of these assignments, and vary ${\\mathbf{R}}$ and/or ${\\mathbf{Q}}$ based on your knowledge of the system you are filtering."
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "A Detailed Examination of the Covariance Matrix"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "So far I have not given a lot of coverage of the covariance matrix $\\mathbf{P}$. It is nothing more than the variance of our state - such as the position and velocity of our dog. It has many elements in it, but don't be daunted; we will learn how to interpret a very large $9{\\times}9$ covariance matrix, or even larger.\n",
      "\n",
      "Recall the beginning of the chapter, where we provided the equation for the covariance matrix. It read:\n",
      "\n",
      "$$\n",
      "\\Sigma = \\begin{pmatrix}\n",
      "  \\sigma_1^2 & \\sigma_{12} & \\cdots & \\sigma_{1n} \\\\\n",
      "  \\sigma_{21} &\\sigma_2^2 & \\cdots & \\sigma_{2n} \\\\\n",
      "  \\vdots  & \\vdots  & \\ddots & \\vdots  \\\\\n",
      "  \\sigma_{n1} & \\sigma_{n2} & \\cdots & \\sigma_n^2\n",
      " \\end{pmatrix}\n",
      "$$\n",
      "\n",
      "(The Kalman filter literature uses $\\mathbf{P}$ for $\\Sigma$; they both denote the same thing.)\n",
      "\n",
      "The diagonal contains the variance of each of our state variables. So, if our state variables are\n",
      "\n",
      "$$\\textbf{x}=\\begin{bmatrix}x\\\\\\dot{x}\\end{bmatrix}$$\n",
      "\n",
      "and the covariance matrix happens to be\n",
      "$$\\textbf{P}=\\begin{bmatrix}2&0\\\\0&6\\end{bmatrix}$$\n",
      "\n",
      "we know that the variance of $x$ is 2 m, and the variance of $\\dot{x}$ is 6 m/s. The off diagonal elements are all 0, so we also know that $x$ and $\\dot{x}$ are not correlated. Recall the ellipses that we drew of the covariance matrices. Let's look at the ellipse for the matrix."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "P = np.array([[2., 0.], \n",
      "              [0., 6.]])\n",
      "stats.plot_covariance_ellipse((0, 0), P,  facecolor='g', alpha=0.2,\n",
      "                              title='|2 0|\\n|0 6|')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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6yjKNBwMwbRAAzowADKCvun64OgNMCwT6yLZXD8TwAmaAAZwZdyQAfeX5ofyw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\nhQAMAAAAqxCAAQAAYBUCMAAAAKzyA4boEebcIq5vAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f1a230e2c18>"
       ]
      }
     ],
     "prompt_number": 38
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Of course it is unlikely that the position and velocity of an object remain uncorrelated for long. Let's look at a more typical covariance matrix"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "P = np.array([[2.0, 2.4],\n",
      "              [2.4, 6.0]])\n",
      "stats.plot_covariance_ellipse((0, 0), P,  facecolor='g', alpha=0.2, \n",
      "                              title='|2.0  2.4|\\n|2.4  6.0|')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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RyPyvFBk/f2L8lm+iWJMVkhKZsDaO51as9zccnp+ac/nciryeX5leS8OhrMbH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\nSUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f1a2328f630>"
       ]
      }
     ],
     "prompt_number": 39
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Here the ellipse is slanted, signifying that $x$ and $\\dot{x}$ are correlated (and, of course, dependent - all correlated variables are dependent). You may or may not have noticed that the off diagonal elements were set to the same value, 2.4. This was not an accident. Let's look at the equation for the covariance for the case where the number of dimensions is two.\n",
      "\n",
      "$$\n",
      "\\mathbf{P} = \\begin{pmatrix}\n",
      "  \\sigma_1^2 & \\sigma_{1,2} \\\\\n",
      "  \\sigma_{2,1} &\\sigma_2^2 \n",
      " \\end{pmatrix}\n",
      "$$\n",
      "\n",
      "Here the notation $\\sigma_{1,2}$ means the covariance of variables 1 and 2 where that is defined as\n",
      "\n",
      "$$\\sigma_{i,j}\n",
      "= \\mathrm{cov}(X_i, X_j) = \\mathrm{E}\\begin{bmatrix}\n",
      "(X_i - \\mu_i)(X_j - \\mu_j)\n",
      "\\end{bmatrix}$$\n",
      "\n",
      "\n",
      "We can rearrange the terms to get\n",
      "\n",
      "$$\\begin{aligned}\n",
      "\\sigma_{i,j} &= \\mathrm{E}\\begin{bmatrix}(X_i - \\mu_i)(X_j - \\mu_j)\\end{bmatrix} \\\\ \n",
      "&= \\mathrm{E}\\begin{bmatrix} (X_j - \\mu_j)(X_i - \\mu_i)\\end{bmatrix} \\\\ \n",
      "&= \\sigma_{j,i}\n",
      "\\end{aligned}$$\n",
      "\n",
      "\n",
      "In general, we can state that $\\sigma_{i,j}=\\sigma_{j,i}$."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Let's get back to concrete terms. Let's start by revisiting plotting a track. I will hard code the data and noise to avoid being at the mercy of the random number generator, which might generate data that does not illustrate what I want to talk about. I will start with `P=500`."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# guarantee the noise is the same each time so I can be sure of\n",
      "# what the graphs look like.\n",
      "zs = [-6.947, 12.467, 6.899, 2.643, 6.980, 5.820, 5.788, 10.614, 5.210, \n",
      "      14.338, 11.401, 19.138, 14.169, 19.572, 25.471, 13.099, 27.090,\n",
      "      12.209, 14.274, 21.302, 14.678, 28.655, 15.914, 28.506, 23.181, \n",
      "      18.981, 28.197, 39.412, 27.640, 31.465, 34.903, 28.420, 33.889, \n",
      "      46.123, 31.355, 30.473, 49.861, 41.310, 42.526, 38.183, 41.383, \n",
      "      41.919, 52.372, 42.048, 48.522, 44.681, 32.989, 37.288, 49.141, \n",
      "      54.235, 62.974, 61.742, 54.863, 52.831, 61.122, 61.187, 58.441, \n",
      "      47.769, 56.855, 53.693, 61.534, 70.665, 60.355, 65.095, 63.386]\n",
      "\n",
      "plot_track(data=zs, R_var=50., Q_var=.2, P=500., count=len(zs), \n",
      "           plot_P=False, title='P=500 m')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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g26i9XFoiTpOgPEjS0hJISorh6NFK8vPzmThxoreHJIQQQpyVvaOS/DX1/OX5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IAAAg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\nUoH/D7r4NwUnkvkQAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f1a23270a90>"
       ]
      }
     ],
     "prompt_number": 40
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Looking at the output we see a very large spike in the filter output at the beginning. If you look at the data (dotted red line) you will see a corresponding, smaller spike in the beginning of the data. We set `P=500 m`, which corresponds to $\\text{P}=[\\begin{smallmatrix}500&0\\\\0&500\\end{smallmatrix}]$. We now have enough information to understand what this means, and how the Kalman filter treats it. The 500 in the upper left hand corner corresponds to $\\sigma^2_x$; therefore we are saying the standard deviation of `x` is $\\sqrt{500}$, or roughly 22.36 m. If we recall how standard deviations work, roughly 99% of the samples occur withing $3\\sigma$, therefore `P=500` is telling the Kalman filter that the initial estimate could be up to 67 meters off. That is a pretty large error, so when the measurement spikes the Kalman filter distrusts its own estimate and jumps wildly to try to incorporate the measurement. Then, as the filter evolves $\\mathbf{P}$ quickly converges to a more realistic value.\n",
      "\n",
      "Now let us see the effect of a smaller initial value for `P`."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plot_track(data=zs, R_var=50., Q_var=.2, P=1., count=len(zs), \n",
      "           plot_P=False, title='P=1 m')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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1DoMhHjh1HV9feOmll8Y1fnFxSFAWQgghzqK2tpaIiAj8/f0BD4oygKIMoiiD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\nH1nWkJDO2ScRQ63/Pn68nptu+gG1tc1ERETw6KOPcvPNN4tPSgRBEIR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R+Na3vkV9fT2z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\nVrlnhF5/AAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f1a2326c588>"
       ]
      }
     ],
     "prompt_number": 41
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "This *looks* fantastic at first blush. The plot does not have the spike that the former plot did; the filter starts tracking the measurements and doesn't take any time to settle to the signal. However, if we look at the plots for P you can see that there is an initial spike for the variance in position, and that it never really converges. Poor design leads to a long convergence time, and suboptimal results. \n",
      "\n",
      "So despite the filter tracking very close to the actual signal we cannot conclude that the 'magic' is to just use a small $\\text{P}$. Yes, this will avoid having the Kalman filter take time to accurately track the signal, but if we are truly uncertain about the initial measurements this can cause the filter to generate very bad results. If we are tracking a living object we are probably very uncertain about where it is before we start tracking it. On the other hand, if we are filtering the output of a thermometer, we are just as certain about the first measurement as the 1000th. For your Kalman filter to perform well you must set $\\text{P}$ to a value that truly reflects your knowledge about the data. \n",
      "\n",
      "Let's see the result of a bad initial estimate coupled with a very small $\\text{P}$ We will set our initial estimate at 100m (whereas the dog starts at 0m), but set `P=1 m`."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "x = np.array([100., 0.]).T\n",
      "plot_track(data=zs, R_var=50., Q_var=.2, P=1., initial_x=x,\n",
      "           count=len(zs), plot_P=False, title='P=1 m')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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RtFAcjmi0qDj0Y4fRS4tQRruntI4QQghxsVIVA1cn/RKTofeL3c7V3NzM888/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0lOjcuuY/t8FsbGRLCYMY8dhtYgpszjGUYYul6V6GgnBilJknSTq3SJst0oxFOrQmZWIM99vqJM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\ngg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f1a232d2ac8>"
       ]
      }
     ],
     "prompt_number": 42
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We can see that the initial estimates are terrible and that it takes the filter a long time to start converging onto the signal . This is because we told the Kalman filter that we strongly believe in our initial estimate of 100m and were incorrect in that belief.\n",
      "\n",
      "Now, let's provide a more reasonable value for P and see the difference."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "x = np.array([100, 0]).T\n",
      "plot_track(data=zs, R_var=50, Q_var=.02, P=500., initial_x=x,\n",
      "           count=len(zs), plot_P=False, title='P=500')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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WYxDh/qlYTX1Xrmhvb+fdd9/lpZdeorS0FIBPP32dBQt6l2szqiayoy9hc+UX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QwePNjqkEREREQsp0JZiIpqzQcfzObYsQx69epldTgiIiIiNYIK5XrMNMHrbYDHE4OW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\n799Po0aNuPTSSwGIj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       "text": [
        "<matplotlib.figure.Figure at 0x7f1a230032e8>"
       ]
      }
     ],
     "prompt_number": 43
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "In this case the Kalman filter is very uncertain about the initial state, so it converges onto the signal much faster. It is producing good output after only 5 to 6 evolutions. With the theory we have developed so far this is about as good as we can do. However, this scenario is a bit artificial; if we do not know where the object is when we start tracking we do not initialize the filter to some arbitrary value, such as 0 m or 100 m. Instead, we would normally take the first measurement, use that to initialize the Kalman filter, and proceed from there. But this is an engineering decision. You really need to understand the domain in which you are working and initialize your filter on the best available information. For example, suppose we were trying to track horses in a horse race. The initial measurements might be very bad, and provide you with a position far from the starting gate. We know that the horse must start at the starting gate; initializing the filter to the initial measurement would lead to suboptimal results. In this scenario we would want to always initialize the Kalman filter with the starting gate position. \n",
      "\n",
      "If we have the luxury of not needing to perform the filtering in real time, as the data comes in, we can take advantage of other techniques. We can 'eyeball' the data and see that  the initial measurements are giving us reasonable values for the dog's position because we can see all of the data at once. A *fixed lag smoother* will look N steps ahead before computing the state, and other filters will do things like first run forwards, than backwards over the data. This will be the subject of the Smoothing chapter. It is worthwhile to keep in mind that whenever possible we should prefer this sort of batch processing because it takes advantage of all available information. It does incur cost of additional processing time and increased storage due to the requirement to store some or all of the measurements. And, of course, batch processing does not work if we need real time results, such as when using GPS in our car."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Lets do another Kalman filter for our dog, and this time plot the covariance ellipses on the same plot as the position."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def plot_track_ellipses(noise, count, R, Q=0, P=20., plot_P=True, \n",
      "                        title='Kalman Filter'):\n",
      "    dog = DogSensor(velocity=1, noise_var=noise)\n",
      "    f = dog_tracking_filter(R=R, Q=Q, cov=P)\n",
      "\n",
      "    ps = []\n",
      "    zs = []\n",
      "    cov = []\n",
      "    for t in range (count):\n",
      "        z = dog.sense()\n",
      "        f.update(z)\n",
      "        ps.append(f.x[0])\n",
      "        cov.append(f.P)\n",
      "        zs.append(z)\n",
      "        f.predict()\n",
      "\n",
      "    plt.plot([0, count], [0, count], 'g', label='actual')\n",
      "    plt.plot(range(1,count+1), zs, c='r', linestyle='dashed', \n",
      "             label='measurement')\n",
      "    plt.plot(range(1,count+1), ps, c='b', label='filter')\n",
      "    plt.legend(loc='best')\n",
      "    plt.title(title)\n",
      "\n",
      "    for i,p in enumerate(cov):\n",
      "        stats.plot_covariance_ellipse(\n",
      "              (i+1, ps[i]), cov=p, axis_equal=False, \n",
      "               facecolor='g', edgecolor=None, alpha=0.2)\n",
      "\n",
      "        if i == len(cov)-1:\n",
      "            s = ('$\\sigma^2_{pos} = %.2f$' % p[0,0])\n",
      "            plt.text (20, 10, s, fontsize=18)\n",
      "            s = ('$\\sigma^2_{vel} = %.2f$' % p[1,1])\n",
      "            plt.text (20, 5, s, fontsize=18)\n",
      "    plt.show()\n",
      "\n",
      "\n",
      "plot_track_ellipses(noise=5, R=5, Q=.2, count=20, title='R = 5 m')\n",
      "plot_track_ellipses(noise=5, R=.5, Q=.2, count=20, title='R = 0.5 m')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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yMti0aRMAo0ePJjQ0tMDzc6cak4rDfvo/Wrp3FZPuX8Wle1ex6f5VLKZp8uOh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\nSUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f1a23299b38>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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6mjcn4cMPc9ojbDYMw8DhdpDtySY9w8X//ufFN1/7sGtHAN/vDCQzwwpAWEQ2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\nr82b2d/vPUZnr+c7moATGjV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p3jeOh/vHERjkIdm0kZFlx8vqhbfVmyCvoJJ7QyLFqF27\ndsyfPz/39alTp2jRokUJViRXSkFZRESuyKVaK8J9wrmvyn10qdaF26Zv5JOFQTzFbI6R82AQby83\ngaFOHh+UTIsWNm6reCs2I++vH9M0NZssNyy73U7t2rUB2Lt3L0lJScTExJRYPRs3bmTlypXUqFGD\nAwcO0Lp1ax566KEr3v/QoUNMmDCBESNG0LRp0zzrvv76a55++mmaNGlCaGgoqampHDlyhClTplC3\nbt2ifivFTkFZREQu6VKtFXaLnY6VOtK9ZnfaVmzLwR99eX9GAH0+jiYLKwCVKzsZMCCDHj0ymDvX\nn6GD3YABWBWKpUzKzMxk+vTpfPTRR/j6+pZIDdu3b2fkyJFs2bKF4OBgMjIyaNWqFX5+ftx3332X\n3fezzz5jzZo1BAYGsmnTJp566qmLtvF4PGRmZrJu3TpsNhstW7bk1VdfpVq1asX1loqVgrKIiFzk\nUq0Vt0XcRu8KXYg5HgJtH2H9eh96/t2fbdu8c7dp2zaLAQPSadMmO/cuFo0a6Z7IIjNnzmTKlClE\nRkby888/U6VKlWteQ2xsLPfeey/BwcEA+Pn5ER0dzWuvvfanQblDhw506NCBuLg45syZk+82hmEw\nbtw4unfvXuS1lwQFZRERAS7dWhHhG8ED1R/gUVtzGnzyJZlj5vJ+RgxvvBRK3G85s2L+/h569Mig\nX790qld3XzT2nXcqKEvZNnfuXNq3b4/dbufUqVN8+eWX1zwoZ2dns3XrVsaPH59nea1atfjXv/7F\n2bNnCQsL+9Nx/uwvQjfSX4wUlEVEyrAraa3oeNybkDff5cB/tzGKp5jPLLLwhd9y7oE8YEA6PXpk\nEBh44/xyFLkSDoeDN998k0WLFnHy5Mk867y8vNi1axfBwcF8++23/OMf/8Dj8eSuf+edd651uRw/\nfhyXy0VAQECe5YGBgbnrryQo/5kjR47w4osvEhAQwM8//0z79u3p2rVrocctCQrKIiJl0OVaK3rU\n6EG36t0I8wnD5YINL3/G7P+O5wva5m7Xpk1Oe0Xbttl6SIiUSQ6Hg969e+Pl5cVbb72FYRiMHj2a\n5s2bM3z4cHx9fXPbG5o2bcqxY8dKuGJITEwEctotznfu9bn1hXXw4EHee+89DMMgLS2Nu+66C29v\nbzp27Fgk419LCsoiImXEn7VWdK/RnbrhOVelJyYavDXHnw8+8OPEiUcB8Pdz0+PhzEu2V4iUJdOm\nTSMjI4OFCxditeZcwNqvXz8WL15MZGRksR57xIgRJCQkXNG2YWFhvP766wDYbDmx71y95zidTgBc\nLleha7vtttt47bXXMH5/Dn1AQADNmzfnlVdeUVAWEZHryxXdtSKqDf7bvsV36gfMvuN1vvnWm+XL\n/cjKyvlFV6WKi/790+nRI5OgIN3GTSQlJYXZs2fzzjvv5Amd2dnZRRI2/8zMmTOvar+IiAiAPC0g\nAGlpaQC5M+CFcWFbB4Cvry8HDhwgOTm5SI5xLRUqKK9cuZKXX36ZXbt20bNnT95//30g518mgwcP\nZunSpYSGhjJt2rQb5upHEZHS4LKtFTVzWitCbIF4ffp/+D0Rzfo9VXiDp/hiwR/9iXfenUJM3zO0\naJWM1WKQaRiY2T4EewcrLEuZ9s033+DxeLj77rvzLN+xYwe33357CVX152666SZ8fX2Jj4/Ps/xc\ny0XVqlULNX5aWhrt27enY8eOTJw4Mc9ywzCwl8Jn1RcqKIeEhDBmzBg2bNhARkZG7vLY2Fj27dtH\nXFwcu3btolOnTrRo0YKoqKhCFywiIvm7XGtFt2rd6Fi5I1WCq+D0OLF+sgJz+hLmnLiff/FJ7sNB\nrFY3jZon0qNXPB3+moXNsGG3+mM37HjZvLAaugeySFZWFmFhYXh5eeUuO3XqFJs3b+bTTz8t9uNf\nbeuFl5cXrVq14sCBA3m22bNnD/Xr1yc8PLxQdVksFhwOx0X3TD5y5AiNGjW6qDe6NChUUG7dujUA\nO3fuzBOUly5dyqhRowgKCqJ169a0aNGCFStW5HtjahERuXpX0lrR7tZ22C12nB4npmmyd6+d1xd0\nYfmJp3PuXgFUqeSk/2MZuN0GTzzhBIKBi2eOFZJFoEWLFmRlZZGYmEhoaCgOh4Onn36a5557jho1\nahT78a+29QKgd+/ejBgxgmeffZbAwEDOnj3L2rVrmTFjRu42n3/+OSNGjGDWrFm0atXqojHOtW64\n3XmvVfDz86N79+7cdddduct27drF0aNHWbFixVXXXJKKpEf5wh+cBw4coFatWvTu3ZvOnTtTt25d\nfvrpp6I4lPz/9u48PKryfOP498yaTFaSsC8CyiqoaMW6AaKIolVBEEsRd+uORe2vIFUE14IKqFBx\nrYiCqLghggWEUlCURbEgi4jskH2bzHrO748xEUiABDKZBO7PdfUqmZlzzju+nJk7h+c8r4gIle9a\nUduw9YIAACAASURBVCoQsJgzJ5HXX09g+XI30ASAnj1KuPFmb9niIEuXuhSGRQ4jIyODSZMmMXLk\nSFq1asXu3bu54YYb6NWr136v27NnD5988gnbtm3jlFNOIRgMsn37dh544AH8fj8vvvgiTZs2Zdeu\nXZx99tmcddZZmKbJm2++Sb169dixYwdDhgypsO73SF1wwQU89NBDPPjgg3Ts2JG1a9cyevRoevfu\nvd/rwuFwuSD8zTff8Oqrr/LDDz9gGAb33XcfXbp0oV+/fmU36t1///08//zzZGZm4nK5yM7O5uOP\nP+bkk0+utvdQkwyrGj4R//73v7N9+/ayGmWHw8H//vc/Bg4cyPXXX09OTg7btm3jjTfeKLft/Pnz\nOe+88452CFLDSuuMSu+UlbpF81c3+UI+5myew7++/xfzfppXVlrRwNOAP578RwZ3HkznBp3LXm+s\nX0/WxOlMafwIr7zuYseOyM15yckWQ4aEuf12k5NOUiiuSTr36raqzt/bb7/N1VdfTceOHVm1alXZ\nv7S/++67DB06lNtuu42ePXuWLSP97bffMm/ePNasWcP999/P/fffz6233kr79u2j+baOC06nk4UL\nF3LhhRdWabuoXFFOSEiguLiY1atXA5FamtJm1hUZM2ZM2Z+7detWVtIhInK8syyLb3d9y9Q1U3l3\n7bvk+fOASGnFFW2u4LrO13Fx64tx2n+7Scb4+mtWjvyISf85lRk8QoDI8tLt25vccUeYQYNMDvGR\nLCLV5IorrmDVqlV069aN5ORkAHbu3MnmzZvZunUrPXv2BCAnJ6dswZKMjAzGjRvH0qVLueuuuxSS\nj8KiRYtYvHgxEGmJV1EZyeFUS1Au7ZVXqm3btqxbt47TTz8dgLVr1x5yRZY777xzv58rW6AusVNa\n8K+5qps0f7XfwUorujTswnWdr6NX415lpRUFeQWRJ5d+yxfDVzB506V8zTMAGJj0Pi+HG+4yOf/8\nAIYBgQBo6mND517ddiTzt2DBAk477TSys7PZtm0bPp+PBQsWcOaZZ5bt59NPP+Wss84iOzubE044\ngblz5/LZZ59x++23s2zZsqi8l+NBp06d6NSpExCZuyVLllR5H0cVlE3TJBAIEAqFCIfD+P1+7HY7\n11xzDRMnTuTyyy9n1apVfPXVVxWWXYiIyG8O1bXi6pOuZkDbAZzXJlKqtu8X9Z49Nt56K4Fpr17E\nnvwrAEh1e/njwCKG3GHRooUWBxGJlZUrV3LDDTcAMHXqVIYNG0Z8fDyFhYVApPfy22+/zXPPPcey\nZct44YUXmDZtGrfeeivff/99DEcucJRB+c033+Smm24q+/mtt95i1KhRjBgxgh9//JHmzZtTr149\nXnvttaivUiMiUhcdrmvFNW2voUfzHjhtzgO2gxUrnLz+egKffhpPKBT5l72OjfZy450mfQdZxMer\n/lgk1jZu3MimTZvYsGEDaWlpDBkyBNM0efrpp5kxYwa//PILTzzxBC1btsTlcnHBBRfw3nvvkZWV\nxdChQ2M9/ONetdzMdzTmz59Phw4dYjkEOQL658O6TfMXe5XuWmGa2AoLseXmYsvLw1kU4pUXgryZ\n04fv/xdp7WazWfS+xMuQGwo46/d+bIaBw+bAZtjUwaKW0blXt1V1/nbu3MnQoUOZOXNmNIcllVBa\nehGTm/lEROTwfCEfi797n6++ncnPW74l1WtxkRduDHmw9ejF7/5wDx3TO2JaJoFwgKJgERkj/k7a\n2++ygTZM4TZe50ZyiHxZp6QGubz/Lq4cuItGTQM4bA6yfU5cdhceh4cEZ0Js37DIcW7FihWcdtpp\nsR6GHAUFZRGR6mRZOFeuxGzYkHCzZuVKK/7+ST7/LHdvjpeC351McXpHskuyCZgBLMsiGDBYlNWD\nd+x3sDDco+zVrR2b6XF+Lr3vaUDXM03stiY4jP0/zi3L0tVkkRhav349L7/8Mh6Ph59//plWrVrF\nekhyBBSURUSqgf2XX4j/4AM877+P4+ef2X3r9Uzq26xcaYW/WWN2t7ZIbNACe3p9zNRUzHr1CJxx\nBpZlkR6fzrZtdqZN8/DOO/FkZka6B8XHm/Tt6+OOO2wsXtyMG26IKz0yoBXzRGqbdu3a8fHHH8d6\nGHKUFJRFRI6Cc80akh9+GPfy5WWPZae4mPDzmzy1PBJe9+1a0eHWDphAwQH7CYVgwTw3U6cmsHCh\nG8uK3JzXvn2Q664rpl+/EpKTLdLT0/F6a+jNiYgc5xSURUSOQjg5Gffy5fjdDj7sYPBapyDzWwWw\nOZ30adHroF0rSu3aZWP6dA/TpiWwa1fk6rDbbXHZZV6GDPHyu99Feh/vq3t3S32QRURqgIKyiMjh\nWBbONWsIdu5MaWrdt2tFm0Gw+IQQRe5I14pR+3atqIBpwuLFbqZO9fDFF3GEw5F9tmoV4rrrihkw\nwEtamkopRERiTUFZROQg7Fu3Ev/++3g++ADH5s3s+GAmn2RklVsQJPfUDP5UWlqRdvB2l1lZNmbM\n8DBtmodffol8/DocFpdfXsJ11xVz7rnlrx6LiEjsKCiLiBwgbu5cEv75z/3qjvNS4hj+3vVMbRsp\nED7cgiClLAuWLXMxdWoCc+bEEQxGknCzZiH+9Ccv117rpUEDM/pvSkREqkxBWUTkAPZffsG9fDkB\nt4PPO8UzqX0h/27tI2yvYEGQfRj7XA7OyzMYPz6R+fPj+OmnyEetzWZxUS8vf7qukPO7lWC3g8Pm\nwDDs6lohIlILKSiLiPzKF/Ix75d5/DtlPkl9Dd5rH6LIXUhGfAa37FNaURqISxcGCZpBgmaQsBWm\nxB9i+tR0XnmhKUWFkY/Y9Pp+Lu+/m8uv3k3DJpGFQXIDWhhERKS2U1AWkeNTOIznrbcoHjSI1bk/\nlC0Ikh/IB8DZxUmvCrpWGIZBcbCYfH8+YSuMhYVBJDgvW5TK+KdasGVzpMdxQrKfK64qoN/VxZze\nxcRha1yuREMLg4iI1F4KyiJy/LEsnA/eR+qMD/jygyfpe3lh2VOHKq2IbGqR4EzY7yrwpk12Hn00\nmfnzIwG5VasQDz+cz+bNTm6/PQi49tteRETqBgVlETlulJZWxI97mus/3kKJA8Z1Ltx/QZBDdK0o\nVRp28/MNxo9P4rXXEgiFDBITTf7yl0JuvLEYtxuWLlUoFhGpyxSUReSYZlkWqzNXl5VW/PG/+Uye\nDWEDxt51BrcOvOeQXSsqEg7DO+94ePrpJHJy7BiGxaBBxfz1r4XUr/9bB4tzzglE4y2JiEgNUVAW\nkWPSvguCbMzbCEDvjfDiZ78+//gobrn+1irvd+lSF488ksLatZFg3bWrn9GjC+jcOVhtYxcRkdpB\nQVlEjhmlpRUHLghSWlpxbe8+BLf8A/+552JUMSRv22ZnzJhkZs+OB6Bp0xAjRxbwhz/4tEiIiMgx\nSkFZROq0A0sryrpWHGRBkOxp08BR+Y++4mKDF15I5KWXEvH7DeLiTO6+u4jbby8iPj4qb0lERGoJ\nBWURqZMqKq2Aw3etwFm5WmTThFmz4nniiWR277YD0Levl+HDC2jaVCvpiYgcDxSURaTOOFxpRWW7\nVhzOypVOHn44hVWrIm3dTj01wKOP5nPmmapDFhE5nigoi0itVtXSilJGcTGJL75I4dCh4HZX6li7\nd9t48slk3nvPA0CDBmGGDy+gf/8SbLbqfV8iIlL7KSiLSK10xKUVAIEA9W69lbhFi7Dv3k3es88e\n8lg+H0yZksjzzyfi9dpwuSxuu62Ie+4pIjFRvZBFRI5XCsoiUmtUS2mFaZI6bBhxixYRTk+n8J57\n9nva2KdFhWXBZ5+5GTkymT17Ih+HvXoX8dcRmTQ/IYAFFAQsDMPAbtjLVuPT6noiUlWfffYZ27dv\nZ9WqVbRp04Zhw4bFekhSCQrKIhJTR1pacZCdkTx6NJ5ZszATEsiZNo1gqxMIhH0EzSCBcICQGSJk\nhsjKNnh6VEsWzYtclW7Vpph7/vYTZ/w+D5thI9fnwGlz4rQ7ibPHlR1fIVlEqmrLli0UFBRw2223\n4fP56NatG61ataJv376xHpochoKyiMTEUZVWHET8Bx+Q+PLLWE4nmVP+yY4T6xMq2ln2vIGBzbCx\neH4aj488gdwcBy63Sf1GJdx4Uz4nNU6ndWoadsO+335Lw7FCsogcifXr1zNu3DiuvfZa4uLiOO20\n0/jmm28UlOsABWURqTHR7lrh69OHktmzKbnySswLLqTxAc/n5xv8/e+/3ax3zjl+nn02j08+iefm\nIQAGYCgQi0i16tmzJ2+99VbZz7t27eLss8+O4YikshSUReoI5/ffE+zQodJ9gGuLai2tONyx4uPJ\nffVVMIxIAfI+Fi1yM2xYKrt324mLM3nooUJuuKEYmw1OOy1w1McWETkYp9NJ+/btAfjhhx/Iy8vj\n2muvrfFxzJ8/n48++og2bdqwYcMGunfvTv/+/attu02bNvHII48wdOhQunbtGo23UOMUlEVqG8si\nccIEvAMGYDZtCoBj7VrS+/UjeNpp5E6ejFm/fowHeXjRKK2olAPWky4uNhgzJpmpUyM34p1+eoDx\n43M58cRw2WvOOUdBWUSir6SkhGeeeYa3336b+Bpe2vObb77hvvvuY8mSJaSkpOD1eunWrRsej4c+\nffoc1XZffPEFn332GUlJSSxatIh7DriJui5TUBapZeI+/5zksWPxTJ/O3v/+F+x2DL8fKzkZ97Jl\n1L/kEnJeeYVgly6xHmo5NbUgSGV99ZWLv/wlla1bHTidFg88UMjttxdVZQVrEZFqM2HCBB577DGa\nNm3Kzz//TKtWrWrs2M899xyXXnopKSkpAHg8Hvr27cv48eMPGZQrs12vXr3o1asX27dv57XXXov+\nm6lBaqEvUpuEwySNHQtA0e23gz1yU1mwSxcy58wh8LvfYd+9m4x+/fC8884RH8Y0TUzTxDAMDMPA\nxCRoBvGH/ZSESigKFlEYLKQgUEBRsAhfyLdfW7V9WZbFqr2rGL5kOKdPO507FtzBgm0LsBt2+rTs\nwxsXv8G3g77l4d8/XK0h2bZrFykPPojh9ZZ7rqQERo1Kpn//dLZudXDyyUHmzMnk7rsVkkUkNt58\n800uuuginE4nu3bt4j//+U+NHdvv97N06VLatWu33+Pt2rVj7dq15OTkVMt2x+L9HfrKEKlF4j/6\nCOf69YSaNcM7aNB+z5kNG5L93nskP/IICf/6FykjR+Lv3p1Qk8aYmNiwYTMiv/uWflgZhkEoBFlZ\nBrv2muzaa7Jnj0Gx10u9BkWcd8EuQmYI0zKxsDDYPwzbDBtxjjhS3Cnlxhqz0grAyMsjffBgnD/+\nCE4n+U88UfbcqlVO7rsvlU2bnNjtFvfcU8jQoYW4XFEZiogcxwKBAC+88ALTp09n586d+z3ncrlY\ntWoVKSkpLF++nJEjR2KaZtnzU6ZMqbFxbtu2jVAoRGJi4n6PJyUllT2fllb+8/pItzuWKCiL1BbB\nIEnPPANA0bBhGG43pmUSCAcImIGyHsDbR9xFSpsWZAYSWb/VIHdVDjlZLvJy3OTluCnMSSAny8He\nTBtZmXbych1YVvmrwYaRxqBbLK6/8xdcrkgodtqcuO1u4hxxxNnjcNvdGEakC4RlWbWjtKKkhLQb\nb8T5448E27Sh4MEHAQgEYPz4JF54IZFw2OCkk4JMmJDHaacFozseETkuBQIBBg8ejMvlYtKkSRiG\nwbBhw/j973/PvffeS3x8fFm5QteuXdm6dWvMxpqbmwtEyib2Vfpz6fPVtd2xREFZJMZKSxps3y7H\nvm0bvtYt2XTJ2eTt/IXXpzQgHHCQk51MTpaL3GwXOVkuCvJ+h2lWXApRfv8WqWkB0jICpKUHcbpM\niotcfL8ikWkvt+S//27CP1/KovPJv41l338+M02zxrpWHFYoRL2778a9fDnhxo3JnjYNq1491q51\nMHRoPdaudWIYFn/+cxEPPlhADd8rIyLHkXHjxuH1ennnnXew/1omd8MNNzBjxgya/nojdnUbOnQo\n2dnZlXptWloaEydOBMDxa81Z6ThLBYORCwmhUKjCfRzpdseSqAblHj168PXXX5f9h+7Xrx//+te/\nonlIkVqvNIz6w368QS/ekBdf2Ee4QwN+/uh1HDm5ZPsLGX5XF1Z9nXHQ/aTWC5KeEaZhA5MGDaBe\nuo+09BDp9UPUzwhTv74Z+V8GuJw2HDZHWWlGaqqHYcNCzJljsOVnF1dc3pgHHyzkz38uKi2Ljmlp\nxcEk/OtfxH/+OWZqKtnTphFo2JTJzyfyzDNJBIMGJ5wQ4rnn8jjrLHWxEJHoKSgo4NVXX2XKlCn7\nhUi/3x/V8DhhwoQj2i4jI/Jdsm/pB0BRURFA2ZXv6truWBLVoGwYBi+++CI33XRTNA8jUicYhoE/\n7C+7QS4YDhI2w4TNcFkJg795Q2wtGvPCEyey6usM7I4Q5/XaRZs2YU49NUzjhgZNGthp3MCB27V/\nPTJA/IwZuJcuJe+pp6jocmrpa202G337WgwbllXWOu3xx5P5fK6LK+//gC+9r9aKrhUHKr7uOhxr\n1+K99lp+tHfkvqvqsWpVpPh4yJBiRo4sICHh2LuZRERql6+//hrTNDn//PP3e/zbb7/ljDPOOKp9\nz5o1i5EjR/L555/TvHnzo9pXqYYNGxIfH09WVtZ+j5eWTrRu3bpatzuWRL304li8A1KkqgzDINeX\nS1bJPh82Ftht9siVXpsNhxG54vu/VfWYM7MlANddX8Tjo+0YRuRU3fd8OvDcMoqKSBk9GlteHo71\n68l95RXCzZoddEzdu1tkZ1s8+WQeJ3b9H08/3IYV39ZjxZAroPeXOM78D5e0rOHSisNxucgd+wyv\nvZbAk08m4/MZNGoU5tln8+je3R/r0YnIccLn85GWloZrn7uEd+3axeLFi5k9e/ZR7btPnz6MGzeu\nwpB8pKUXLpeLbt26sWHDhv1es2bNGjp16kR6enqF+zjS7Y4lUQ/Kw4cP529/+xtdunRh4sSJZSvT\niBxPLMuiXlw9El2JkQ4TloVhGNiMSEAuLcfIyTF46C/1CYcN7ryzkAsvDJVtf9hjJCaSNXMmabfc\ngmvNGjIuvZTcyZMJnHdeha/fWbiTV7979bfSilvrwWcvwA+D4NMp/L7wGcY8W0yjRmaF28fC1q12\nhg1LZdkyNwD9+3sZPTqflBT9Qi4iNefss8/G5/ORm5tLvXr1CAQCPPDAA4wYMYI2bdoc1b5Xr17N\nqaeeWuFzR1p6ATB48GCGDh3K8OHDSUpKIicnhzlz5vDss8+WvWbBggUMHTqUF198kW7dulV6u1Kl\nJRrhcLjcc3WVYUXxku+KFSvo1KkT4XCYMWPG8P7777N27dqymmWILIt43kG+yKX2cv66jHJpQb8c\nXoWnmmXBr72MLQv693cwe7ads84y+fe/g0e2WnVODs4bbsA2bx6WzUZo8mTM668HIguCfLrxU976\n31vM+2leWWlFA08DBnUaxOBOg1m36BTuvddBbq5BvXoWEyeGGDCgZsLywa6YWxaMGmVn8mQnRUUG\n9eubjHuuiEsu82Fhlb0PiHTvSHIlRX4RsR17reJ17tVtmr+6bd/5++KLL5g6dSonnXQSO3fu5Ior\nrii3cEdJSQnTpk1j4cKFvPHGG6xdu5ahQ4fy5Zdfkpuby/PPP0/btm1Zu3Yt9957LxkZGTz55JNk\nZGRw6623Vvv433zzTebNm0fnzp1Zs2YNffr0YdA+rUjnzp3L9ddfz5tvvsnFF19c6e2WLl3KpEmT\nWL16NZs3b6ZJkyZ07dqVa6+9liuuuKLa38eRcDqdLFy4kAsvvLBK20U1KO/LsixSUlJYunQpnTp1\nKnt8/vz5LFy4sOznbt260b1795oYkhwFfdhXD/uoURg//kj4sceYOKcdDz7oIDXV4uuvA5xwwlHs\nOBzGPno09kmTCHz5Jd/U8zJ1zVTeXfsuef48INK14rKTLmPIKUPo1aoXTvtvqXznTrjjDgdz50Zu\nUhkwIMyECSGqu11madu5UsFwZNGToBkkGA7y0/wdvP+flnz8aQbbf4n8E+eFl+Yy/Ilt1EuPXG23\nYcNld+F0OImzxxHniCPRlVi2mMqxRude3ab5q9uqOn/vv/8+f/jDHzj99NNZvnw5DoeDvn378skn\nn9CzZ09efvll2rRpw0svvUTv3r1p2bIll112GWPHjqVjx47RfCvHhUWLFrF48WIg0rmjW7duVQ7K\nNdoerrQf64HuvPPO/X6ubP2NxE5pXZLm6sjZsrJoMHEiNq+XBef/hREjIqH0mWdySUz0cbT/aXff\nfA3zOvt47T/XlutaceNpN3JNx2swSiJBsiCvYL9t3W549VWYNs3Do48mM3OmncWLYdy4PHr2rL5a\nYBOTHF8OvpCPQDiAaZlkZzpZMKcB//60Pj/+77ffFpyuEFf0z+SaPxbSvF4cDsuBw+74rXY6DFbI\nIugPklt87Pb21LlXt2n+6raqzt+ZZ57JokWLaN26NSUlJQD07NmTGTNmkJ+fz5IlS5gzZw6dOnUi\nKSmJ3bt3s27dOho2bKi/I9WgU6dOZRdn09PTWbJkSZX3EbWgnJ+fz9KlS+nZsycATz75JA0bNtRv\nSCK/Snz+eWxeL3t6XMGtE88hGDS46aYiLrnEd8T7rOyCIGUf9iUH/yA2DBg82Mt55/n5y19SWb7c\nzXXXpTN4cDEPP1w93SXshp20uDQKCi3mzYtn1qwElvwnrqxHdDL59E34nMv+eT5rf0rkttvAsvZf\nIUo3DItIbZWQkMCCBQvo1asXAIWFhaSmpvLTTz/RvXv3cmUJq1ev5uSTT6akpIR4NYKvFaIWlIPB\nIA899BAbN27E6XTStWtXPvnkk3JNq0WOR7adO0mYOhULuM18iV9+cdC5c4CRIwsOu+2BLMuq8oIg\nts8+w7zkkkrtv2XLMO+9l82UKQn84x/JvPVWAv/5j5vx4/Po2vXI+xUHg7BokYtZs+L5/PM4fL5I\nPbHTadGrWx43fnUPV/jew/vCZPw9wYgLKBSLSJ2Tm5tLly5dAJg3bx6XXnopS5YsIS8vr+w1a9as\nwePxsGrVKs4880w+/vhjBg4cGKshyz6iFpQzMjJYuXJltHYvUqcljR+P4ffzfOcX+HhxIxISTCZN\nysXtrvw+jnRBEM9bb+H8v/8jPGQIPPFE5NLxYdjtcMcdxfTo4efeeyMr4PXrl84ddxTxwAOFlR63\nZcHKlU4++MDDxx/HkZPz2y/OXbv66devhMsuK6H1w3fh8c3C16sX/l9vKDnnHC0iIiJ1z8CBA5kx\nYwZZWVmceOKJeDweLr74YlasWMHMmTOxLIuGDRvSuXNnsrKy+OCDD+jQIXb96mV/WsJaJAbMjAxW\nx5/FX9ffDsA//pFP69aHb6dT2dKKQwk3aYKVkID9zTfxdOqE909/qvS4O3QIMXt2Js8+m8SLLyYy\naVISCxfGMX58Lp06HXw1qp9+sjNrlodZs+LZsuW3j502bYL061dC374lNG8eef+O9evxzJqFGRdH\n/ujRlR6biEhtdMopp3DKKaeUe3z48OHlHjvrrLM466yzamJYUkkKyiIxsPuu/2PAJ+n4NtsZNKiY\nq64qOehrj6S04lD8PXsSev55nDfdRMrDDxPo0oVQFe4dcLngb38r5KKLfNx3Xz3WrXNy+eX1uf/+\nQu64o4jS7o+ZmTY++iieWbPiWb36t6b8DRuGueqqEvr1K+Hkk4PlLmiH2rUja/p0HNu3E27RotLj\nEhERqW4KyiIx8NBDKWza7KJduyCjR1dcl3ykpRWVYQ4aRHjxYuxvvEHan/9M5pw5WImJh99wH7/7\nXZB58zJ5/PFk3ngjgaeeSmbevDjOOc/L99+5+O+SeMLhSApOSAxzYe98+lyZwxldC7HZLQwMglY9\nXIar3L4D55+PCi1ERCTWFJRFatjMmfHMnOkhLs5k8uRc4uN/u0GtOkorKiv07LOYX32FUVKCbc8e\nwocJyqU9iU3LJBAOEDAD+G1+7nloF13O9/DYiFasXOlm5cpI8LU7TM69IJuLLt/LuT1yiPeAy+bC\n5YjDbXcT74jHaXPqBj0REam1FJRFatCmTQ5GjEgB4PHH82nXLlTtpRWV5vGQ8/rrmKmpWMnJh3xp\nYbCQ4mBxZDGQcPlG+6f9voiHny3ijRdbsmGdh24XFNKvfwHnnmPiNOJw2FvsN/7ScKyQLCIitZmC\nskgNCS1fw+0jeuL12ujb10v3y39m0nfRKa2orMrWANsNO4muRBJJxMDAhg2bYYssE23YcBgO2lxg\ncPUFQV59NcTNN5tYVsJ++zhkKPb7qVLLDxERkRqgoCxSA1xff81j/Xaxjt7Ub5pH9oWD6Tp9TlRL\nK6qTx+E57GtKg3D79lXsd1xSQv3evfFfdBEFDz4IarIvIiK1hIKySJRZpsnHw/7DZJ7FbvjJvPwC\nMrNWR7+0Ikaq2u84adIknD/9BA4HVNAuSUREJFYUlEWipLRrxfqp85m35XMAHBfdT8fOYa5pM6ZG\nSiuqzOcjZfRoAqecQsm110b9cPYtW0h88UUA8p98EpzHxi8LIiJybFBQllrF2Kepbl280atc14qg\nnY7vLaGAFM5q/iWPPdOXjukjYj3Mg4pbuJCEf/2L+Lg4gl26EGrXLnoHsyxS/v53DL8fb//+BNRk\nX0REahkFZak1CoOFeINewlYYm2EjwZlAkjMp1sM6rEN1rfj97NdYGuzKCbatvP7hCaSk1+4b1nyX\nXop3wAA8M2dS789/Juuzz7A8h69PPhJxn39O3IIFmMnJFIwcGZVjiIiIHA0FZYm5/EA+uf5c/CE/\nITMEv15Izrfn43a4qeeuR4orJbaDrMDhFgSpt/U67l51Ag5bmCn3LCWlUbcYjrby8p94Aufq1Tg3\nbiRlxAjyxo+PynECXbrgvfJKAl27YtavH5VjiIiIHA0FZYmp3d7d5PvzCYaDZR0gSoVDYQLhizT0\nBwAAGzZJREFUAP6QH2/QS+OExjEa5W8quyDIzp02eg1sAMDfRhTR6Y66EZIBLI+H3JdeIqNPHzwz\nZ+K74AJ8V15Z7ccxGzUib9IkqIMlNiIicnxQUJaY2e3dTb4vH3/Yf9DXWJaFP+SnwIos8xyLsFzV\nBUFCIbjrrnrk5dno2dPHn/9cXONjPlqhdu3If+IJ4ubPx3/BBdE92D516SIiIrWJgrLUOMMw2FW8\n67AheV/+sJ8CfyQsN0lsUu03+hkHhDXLsthZvJMPN31Y5QVBnn02ieXL3TRqFGb8+Dxstmodao0p\nueYaSq65RkFWRESOWwrKUqMMw6AgUECBv6DSIbmUP+ynMFBIvj+fFHfKUYXl0mAcCAcoCZXgC/sI\nhoN4Q14WbV/EZz9/xje7v8EkUlqRHpdO/7b9GdDm0AuCLF7sYuLERGw2ixdeyCU93Tzoa2s9BWQR\nETnOKShLjQpbYbJKsqockkv5Q36yfFkkuBKwY6/StoZhYFkWxaFivEEvxcFigmaQUDjEupx1zP1l\nLl9u/5KiYBEADsPB2Y3OpnfL3pzb9FxOTDnxkIuCZGbauPfeeliWwf/1Wc45v29KGItgOEjIChE2\nw1hYGBgYhoHTcBLvjK+TbfCOhFFQQOoDD1A4bBih9u1jPRwREZHDUlCWGmMYBpnFmfhCviMOhxaR\nmuVMbyaNExpXaj+GYRAIB8gP5FMQKCAYDhI2w+wt3sv87fP5YusXbCvcVvb6k1JO4qIWF9GjWQ9S\n3JFuG4Zl4A/7ywXl0ivT4bDFXXenkJlpp4djMY/NvoB1n48j++zTsSwLC2u/sRoY2G12GiY0rBMt\n8Mr4fNiyszGbNq3ypknjxhE/eza27Gyy338/CoMTERGpXgrKUmNKgiVlQfVoBMNBCgOFpLhSiHfE\nH/R1hmFQFCwiz5eHN+QlFA5RHCzmq91f8cXWL1i5Z2VZaUWqO5WezXtyUfOLaJXSqty+7HY7cY64\nsv2alok35I2UbYR8vDKpAf9dEk9afAHTSq6lsHNbtp/RHoIl5fdl2HE5XCS6EutUSLbt2EHaTTdh\nhEJkffopVvzB/9sfyPHDDyS8/jqWzUb+o49GcZQiIiLVR0FZaoRhGGT7sgmEAtWyv0AoQLYvm+ZJ\nzSu8qpznzyM/kI8/5CcQCrAudx1fbP2CRdsXlSut6HVCL85ocAYOW/nTwcAg3hlP/fj6ZfstChZF\n6qWLTPbudrJ+bSKvPt8CgDcZQhN2sfzue/ar8TUwcNgcOOwO4h3xZMRl1LmyCyslBZvXi2PzZpL/\n/nfyx42r3IamSeqIERimSdHNNxPq1Cm6AxUREakmCspSI/xhP95QZNW96hC2wpSESvCH/bhsLiAS\nxgsDhWT5svAH/ewu3s2/t/27UqUV+zJNKMqPIy8zkdxMD3v3OMnN9LB7t43MPQ3J3NOCrD1uiov2\nL8O47ZSPuOz7j8g+81RyzupSVl7hsDlw2SNXkJNdybjt7kg5Rh0KyQBWYiI5L71E/T/8gYR33iFw\n9tmUXH31YbeLf/ddXCtWEG7QgMIHHqiBkYqIiFQPBWWJOsMwyhYVqU7BcJA8fx6NEhrhC/nY691L\nni+PRdsXMW/rvApLK5oUXsbpzU/E99UefljRlF3eNLIz48ne6yZ7bxzZmXFk73UTCh2+p5vDaZKU\n4sfhDpCZ52XY7ocA2HzvzcQ54nDanXgcHpJdyXickWWg62JA3leoY0fyH32U1P/7P1L+9jeCp55K\n6KSTDrmNEQ5jJiRQ8PDDWMnJNTRSERGRo6egLFFnWRaFwcLI8tTVyLRMgmaQvcV7WbZrGbM3z2bh\n9oUVllY0C53HE8PO5IMNlQtqCcl+0uv7aNAoQHoDH+n1/aQ38JHRIPL/6Q18pKaFcNjs2Awbn37i\nYe/lz8PyNXjO7UmGw1NW01zXw/GBvH/6E65ly/B8+CHxM2dSOHz4YV/vu/hizIyMGhqhiIhI9VBQ\nlqgrDBYSDFXv1WS7YSc/kM/bP77Ngu0LDllakZfj5J4bfk/W7gTAIjGhhHah9bQwt9Ii+DNN2UFT\ndpCR4WP9y7eQnF5MSoKTBGcClmXhyi2g8/An8TVphK+gEf6SxgRDTQjZm2Nr0gy33U2PUxM5Md2B\n0ad9WSg+lsLxfgyD/Kefxt+tW2RBkkow69eP8qBERESqn4KyRFVp3XB1XU0OhAN8s+cb5m2dxze7\nv8EiEkYP1rUitLOYRx68kKzdCbRuW8AZvddw082Fvz7rxu49gfid8STsSiHBcBLfLgm3PaOs5zJA\nUtZu0petLDeW0Eknkbl4MZZl8bvTIo8ds+H4AFZiIiUDB8Z6GCIiIlGloCxRZVkWvpDvqG7isyyL\nDXkbynWtsBt2OqV3olvTblx8wsXlulZ4Vm3ksZvbs8FMpVFTL2NeXMG2XfuvlGclJBBq345A59NI\niavPSc7yLc+Mk5PJmToV29atOLZvx75tG/YdOwi1bHncBGMREZHjkYKyRFVJqOSIryZnl2SzYPuC\ncl0rWiW3omujrpyacSqJrkRcdhchK4Rjn7/O7q27mPznBnxh9iLdlcdjL35HWn0/ab9WADhsDhw2\nB3GOOOrF1SPZlXzQWmIrORlfz55H9B6OR7bMTNyLF1PSr5+WwRYRkTpNQVmixjAMikPFhM3KX00O\nhAMHXRCkV4te9GjWg3hnPEWBorJtwmYYX9hHvCPSl9iZV8CsPwWYHrgRj83LIy+voWnLkkgvY7sD\np91JojORFFcKHqfnmLvZLlbsP/9M3Ny5ONetw/Peezg2bDjsjX4iIiK1mYKyRJU3ePjeyQcrrThw\nQZAEVwK5vlz2evfut71pmfhCPnCDzR/gv4N+4fnCB3ES4OFnVtKhix+7zY3L7iLJlUSqOxWnzamA\nXI0Mr5eMK6/Enp0NgOV247322hiPSkRE5OgoKEvUBM0ggXAA0zIrfP5gpRUHXRDEipRMuB1uwsFw\n2X4tLAJmgJAVYtm0ZB7f+SAADz20ivMvsZHgrE+CMwGPw1N2k54CcvWyPB4Khw0j9aFIL+miu+4i\n3Kr8UuAiIiJ1iYKyRI0v7CtXdnGo0oqKulbst60ZINkV6YMcZ48jZIUwLRObYcNlc/H90mY89eIp\nAIy8fQ3X394Qt90NcOy3bKsFvNdfj+Pnn7Fv20bhnXfGejgiIiJHTUFZoiYQilxNrmxpxYFdKw5k\nWRb+kJ8kZ6R8wrRMQmYIu83OxjXpjLm/E+Gwwd13F3HH8PSybaSGGAYFjz4a61GIiIhUm6gG5e3b\ntzN48GC++eYb2rdvz5tvvsnJJ58czUNKLWEYBjuKdvDehveYu3Vu5UorKsHCwh/2QxgMDAzD4OcN\ncTxwe3tKSmwMHOjlb38rqO63IyIiIsehqAbl2267jVNOOYW5c+cyYcIEBg4cyA8//BDNQ0qM+UI+\n5v0yj5kbZ/Ll9i/L6ogrU1pRVRYWORuDPHT3+RTmuzi3Rw5jx/rVkUxERESqRdSCckFBAV988QWv\nvPIKbreb++67jzFjxvDDDz/QqVOnaB1WYsCyLFZnrubdDe/y0U8fkR/IByI33lWltKKqQuuyeGzw\nGWSG4+lwSi4Pj1uL3d66Wo8hIiIix6+oBeVNmzYRFxdHQkIC559/Pq+88gonnngiP/74o4LyMWJn\n4U5e/e5V3t3wLhvzNpY93jmjM/1O6keX+l3KbqarbubuIp64oS1rwx1oG7+Z0c9twhXnwh/2R+2Y\nIiIicnyJWlAuLi4mMTGRwsJC1q1bR25uLklJSRQXF5d7bXp6erSGIVEQMkP0e78fn2/6vKy0ooGn\nAYM6DWJwp8GcXP9kckty2VG4g6AVrPbjm0UBnhjoZpm/K00duxj78Q7qn5iEw3DgTnSTFp+GofqL\nQ3I6nYDOvbpIc1e3af7qNs1f3VU6d1UVtaCckJBAUVERzZo1IysrC4DCwkISExPLvXbMmDFlf+7W\nrRvdu3eP1rCkGjhsDvwhP3bDzhVtrmDIKUPo1aoXTnvkL6FlWQTNIBbV33HCCptMvqSIz/Ivo56R\ny3NT11G/TXzkOSxCZgjLshSURUREjnOLFi1i8eLFANjtdrp161blfRhWlPpnFRQUkJaWxi+//ELT\npk0JBAKkp6ezbNmy/Uov5s+fT4cOHaIxBImibLIjV25LygdSwzDILMlkb/FeQmaoWo877ammvDW9\nM/F4efaxz2l5uafsOYfNQYOEBtSPr6+2cIdRejUk+9eV9KTu0NzVbZq/uk3zV3elp6ezZMkSLrzw\nwiptZ4vSeEhOTqZ379489dRT+Hw+nnvuOU444QTVJx8j2qa3JcOTcdDnw2a42q8of/ROC96a3hmb\nzWT00P1DMkSuZFd3MBcREZHjV1Tbw7300ksMHjyYtLQ0OnTowIwZM6J5OKlFwla4Wq/qLprbiJf+\nEfmXh/se+R+drvSUe42FVW4lQBEREZEjFdWg3KxZM7788stoHkJqqbBVfVeUV32VzriHTsGyDG68\ndz29rtxR4essyypbEltERETkaEWt9EKOb2EzTHXk5M0rXYwZ1oVQyMaVg7Yw4MafD/ra0pv5RERE\nRKpDVK8oy/GrOq4o7/0hzKhbOlNiOuhxyU5ue+DHw666V9quTkRERORoKShLtbMs66jrk/N2wCM3\ndSbTrE8PzxIeHJGNzXb4hUSq49giIiIioNILqYWKC2w8PrA1WwIt6OJYzQNv78CWXPnV9qLRv1lE\nRESOPwrKUu2OJqgGAgbPXNOYH4racpKxiUdfWo29ZUqNHV9ERESklEovpFaZPKoty3a3ohG7GPv4\nFzjPaFWl7RWSRUREpLroirLUKm3P2UtqaiEnJS3gvZyT+e77qq3NbqClq0VERKR66IqyVLujCauX\nXp7LxZf+l3feac7gwd4aP76IiIhIKV1RllrHbofOpwSPeHsFZREREakOCspS7YzDNTuuhFOPIiiL\niIiIVAcFZYkKmy02f7VsNlu1BHURERERBWWJCofhqPESCAMDu2Gv0WOKiIjIsUtBWaLCZtT8lV3D\nUFAWERGR6qOgLFHhsOmKsoiIiNRtCsoSFXbDHpMryg6bOh6KiIhI9VBQlmpnWVYkKMegTZvNsGFZ\nWp1PREREjp6CskSF3VbzV5Rthk1XlEVERKTaKChLVLhsLmxGzf71MgwDl81Vo8cUERGRY5eCskSF\ny+GKyRVlp91Zo8cUERGRY5eCskSFw3DUeBmE3WbHaVNQFhERkeqhoCxRU5PlFzbDprILERERqVYK\nyhI1boe7RoNynCOuRo4lIiIixwcFZYkKy7Jq/Iqy0+ZUazgRERGpNgrKEjVuu7vGVsqzGTbcdneN\nHEtERESODwrKEjVxjjgc9ppZytphdxDviI/6cUREROT4oaAsURXviMdui+5VZbvNjsfhieoxRERE\n5PijoCxRY1kWCc6EqJdf2A07Cc4E1SeLiIhItVJQlqjyOD01ckVZZRciIiJS3RSUJaochiOqbeIM\nw8Btd2uhEREREal2CsoSdR5H9K4qO2wOPE7VJ4uIiEj1U1CWqLIsi2RXctSWs3bYHCS7klWfLCIi\nItVOQVmizmV3RbpfVPNNfXYjUpus/skiIiISDVELyqNGjcLpdJKUlERSUhKtW7eO1qGklrMsi1R3\nKg579V5VdtgdpLhTdDVZREREoiJqQdkwDP74xz9SWFhIYWEhmzdvjtahpA5IdCbidrgxjOpZfMQg\nchNfkjOpWvYnIiIicqCoBWXLsnSlT8oYhkGqKxWXzVUt+3PZXaS6U6steIuIiIgcKKpXlD/55BMy\nMjLo0qULn376abQOJXVAaflFvPPoa5Xthp04Zxyp7lT9MiYiIiJRE51WBMDAgQO55557SElJ4eOP\nP+baa69l5cqVtG3bttxr09PTozUMiRKnM9K3uCpzZ1kWrgQXWwu24jf9R3xsl81Fi+QWJLmTdEX5\nCB3J/EntoLmr2zR/dZvmr+4qnbuqOqqgPGrUKEaPHl3u8auuuooPPvig7Oe+ffvSo0cP5s6dW2FQ\nHjNmTNmfu3XrRvfu3Y9mWFJLGYZBgiuBFHcKOb4cQlaoyvtwGJEb+BJdiVEYoYiIiBwrFi1axOLF\niwGw2+1069atyvswrBr6t+vLL7+c3r17c8899+z3+Pz58+nQoUNNDEGqUelv09nZ2VXe1sTkl4Jf\n8Aa8hK1wpbezG3Y8Lg8nJJ+ATZ0Nj8rRzJ/EluaubtP81W2av7orPT2dJUuWcOGFF1Zpu6iljVmz\nZpGXl4dpmsyePZtFixbRu3fvaB1O6hAbNpomNsXj8lS6Xrk0JDdNbKqQLCIiIjUiajXK06dP58Yb\nbyQcDtOmTRtmzJhRYdmFHJ9cNhdNE5uyo2gHJcESQubByzDsNjseZyQkV1fXDBEREZHDiVpQnjFj\nRrR2LccIl81Fs8Rm7PHuwRv0EgwH9yvFsBt2nHYnHqeHBp4GCskiIiJSo6IWlEUqw2lz0jypOcXB\nYnJ8OfhCPiwsDAziHHGkxaWR4ExQGzgRERGpcQrKEnOWZeFxeEhIigTiMGHs2DEMQwvXiIiISMzo\nriipNUoDsR37fj+LiIiIxIKCsoiIiIhIBRSURUREREQqoKAsIiIiIlIBBWURERERkQooKIuIiIiI\nVEBBWURERESkAgrKIiIiIiIVUFAWEREREamAgrKIiIiISAUUlEVEREREKqCgLCIiIiJSAQVlERER\nEZEKKCiLiIiIiFRAQVlEREREpAIKyiIiIiIiFVBQFhERERGpgIKyiIiIiEgFFJRFRERERCqgoCwi\nIiIiUgEFZRERERGRCigoi4iIiIhUQEFZRERERKQCCsoiIiIiIhVQUBYRERERqYCCsoiIiIhIBRSU\nRUREREQqoKAsIiIiIlIBBWURERERkQoccVBev349l1xyCfXq1aNVq1blnp84cSKNGjUiLS2NESNG\nHNUgRURERERq2hEHZafTyaBBgxg7dmy5577++mseffRRFi5cyA8//MD06dOZOXPmUQ1URERERKQm\nHXFQbt26NUOGDKFly5blnnvvvfe4+uqr6dChA02aNOGWW25h+vTpRzNOqYXWrVsX6yHIUdD81V2a\nu7pN81e3af6OL1GpUd6wYQPt2rVjwoQJPPDAA3Ts2JH169dH41ASQ/qwqNs0f3WX5q5u0/zVbZq/\n40tUgnJxcTGJiYls3ryZTZs2kZSURFFRUTQOJSIiIiISFY5DPTlq1ChGjx5d7vGrrrqKDz744KDb\nJSQkUFRUxIQJEwCYNWsWiYmJB319enp6ZccrtYTT6aRnz56kpqbGeihyBDR/dZfmrm7T/NVtmr+6\ny+l0HtF2hw3Ko0aNqvJO27Zty48//lj289q1a2nfvv1BX79kyZIqH0NEREREJJoOGZQPx+fzEQwG\nsSwLv9+PYRi4XC4GDBjApZdeyl/+8hdSUlJ47bXXeOqppyrcx4UXXng0QxARERERiYojDspbtmyh\ndevWABiGQXx8PD169GDBggV07dqVRx55hAsuuIBgMMjtt9/OgAEDqm3QIiIiIiLRZliWZcV6ECIi\nIiIitY2WsBYRERERqYCCsoiIiIhIBRSURUREREQqcFRdL6rDu+++y6xZs8r62yUnJ/PCCy/EeFRy\nKNnZ2Tz//PP89NNPNGnShLvvvpvmzZvHelhSSaNGjWLjxo3Y7XYAunbtyt133x3jUUlFvvnmGz78\n8EO2bNnCueeey5133glAKBTi5Zdf5quvviIhIYHrrruOs88+O8ajlQMdbP70vVf7hcNhJk+ezJo1\na/D7/bRq1Yqbb76ZZs2a6fyrAw41f1U9/2IelA3D4Nxzz9UXdR0yZcoUWrRowUMPPcRnn33G+PHj\neeaZZ2I9LKkkwzC4+eab6dmzZ6yHIoeRkJDAlVdeyffff08gECh7fPbs2Wzfvp3JkyezZcsWnnrq\nKdq2bavFm2qZg82fvvdqP9M0adSoEYMGDSItLY3Zs2czduxYJkyYoPOvDjjU/AFVOv9iXnphWRZq\nvFF3eL1evv/+e6666iqcTieXXXYZmZmZbN26NdZDEznmdOzYka5du5Zb2fSrr77i0ksvxePx0LFj\nR9q2bcvy5ctjNEo5mIPNn773aj+n00n//v1JS0sDoEePHuzevZuCggKdf3XAoeYPqNL5F/OgbBgG\nK1as4Oabb+avf/0rK1asiPWQ5BB2796N0+kkLi6Ohx9+mL1799KwYUN27twZ66FJFbz99tvcfPPN\nPPbYY+zYsSPWw5Eq2rlzJ02aNGHixIksXbqUZs2a6RysQ/S9V/ds2LCBtLQ0kpKSdP7VQfvOH1Cl\n8y/mpRfnnHNO2W9m3377LePHj+fpp5+mSZMmsR6aVMDv9xMXF0dJSQk7duygqKiI+Ph4fD5frIcm\nlXTdddfRvHlzTNPk/fff5x//+AfPPvtsWc2y1H6l5+G2bdto3bo1cXFxZGdnx3pYUkn63qtbvF4v\nb7zxBkOGDMEwDJ1/dcyB83fuuefSp0+fSp9/NRKU3333Xd5///1yj5955pk88MADZT937dqVk08+\nme+++04fGLWU2+3G5/ORnp7Oq6++CkBJSQlxcXExHplUVumKmgB//OMfmTt3Ljt27KBFixYxHJVU\nRel5OHbsWABef/114uPjYzwqqaymTZuW/Vnfe7VbMBhk7NixnHvuuWU37On8qzsqmr+qnn81EpSv\nueYarrnmmpo4lERZo0aNCAQC5OTkkJaWRigUYs+ePfqAF6lBTZo0YceOHWW/9Gzfvp0zzzwzxqMS\nObaYpsmECRNo3LjxfhlG51/dcLD5q6qY1ygvX76c4uJiTNNk5cqVrF27llNPPTXWw5KD8Hg8nHrq\nqXz44YcEAgE+/fRT6tevr6uRdYTX62XVqlUEg0GCwSAzZ84kNTWVZs2axXpoUgHTNAkEApimiWma\nBINBwuEwZ599NnPmzMHr9fK///2PjRs30rVr11gPVw5wsPnT917dMGXKFAzD4JZbbtnvcZ1/dcPB\n5q+q559hxfjW2+eee47vvvsO0zRp3LgxAwcO5PTTT4/lkOQwSvsob9q0iaZNm6qPch1SUFDA448/\nzq5du7Db7Zx00knceOON+heBWurLL79k8uTJ+z02YMAA+vbty5QpU9THtZaraP769+/P9u3b9b1X\ny2VmZnL33XfjcrkwDKPs8REjRtCmTRudf7VcRfNnGAbDhw9nzpw5VTr/Yh6URURERERqo5iXXoiI\niIiI1EYKyiIiIiIiFVBQFhERERGpgIKyiIiIiEgFFJRFRERERCqgoCwiIiIiUgEFZRERERGRCigo\ni4iIiIhUQEFZRERERKQC/w8kULFnealSggAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f1a2329eac8>"
       ]
      }
     ],
     "prompt_number": 44
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "If you are viewing this in IPython Notebook or on the web, here is an animation of the filter filtering the data. I've tuned the filter parameters such that it is easy to see a change in $\\mathbf{P}$ as the filter progresses.\n",
      "<img src='track1.gif'>"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The output on these is a bit messy, but you should be able to see what is happening. In both plots we are drawing the covariance matrix for each point. We start with the covariance $\\mathbf{P}=(\\begin{smallmatrix}50&0\\\\0&50\\end{smallmatrix})$, which signifies a lot of uncertainty about our initial belief. After we receive the first measurement the Kalman filter updates this belief, and so the variance is no longer as large. In the top plot the first ellipse (the one on the far left) should be a slightly squashed ellipse. As the filter continues processing the measurements the covariance ellipse quickly shifts shape until it settles down to being a long, narrow ellipse tilted in the direction of movement.\n",
      "\n",
      "Think about what this means physically. The x-axis of the ellipse denotes our uncertainty in position, and the y-axis our uncertainty in velocity. So, an ellipse that is taller than it is wide signifies that we are more uncertain about the velocity than the position. Conversely, a wide, narrow ellipse shows high uncertainty in position and low uncertainty in velocity. Finally, the amount of tilt shows the amount of correlation between the two variables. \n",
      "\n",
      "The first plot, with `R=5 m`, finishes up with an ellipse that is wider than it is tall. If that is not clear I have printed out the variances for the last ellipse in the lower right hand corner. The variance for position is 3.85 m, and the variance for velocity is 3.0 m. \n",
      "\n",
      "In contrast, the second plot, with `R=0.5 m`, has a final ellipse that is taller than wide. The ellipses in the second plot are all much smaller than the ellipses in the first plot. This stands to reason because a small $\\small\\mathbf{R}$ implies a small amount of noise in our measurements. Small noise means accurate predictions, and thus a strong belief in our position. "
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Question: Explain Ellipse Differences"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Why are the ellipses for $\\mathbf{R}=5 m$ shorter, and more tilted than the ellipses for $\\mathbf{R}=0.5 m$. Hint: think about this in the context of what these ellipses mean physically, not in terms of the math. If you aren't sure about the answer,change $\\mathbf{R}$ to truly large and small numbers such as 100 m and 0.1 m, observe the changes, and think about what this means. "
     ]
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Solution"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The $x$ axis is for position, and $y$ is velocity. An ellipse that is vertical, or nearly so, says there is no correlation between position and velocity, and an ellipse that is diagonal says that there is a lot of correlation. Phrased that way, it sounds unlikely - either they are correlated or not. But this is a measure of the *output of the filter*, not a description of the actual, physical world. When $\\mathbf{R}$ is very large we are telling the filter that there is a lot of noise in the measurements. In that case the Kalman gain $\\mathbf{K}$ is set to favor the prediction over the measurement, and the prediction comes from the velocity state variable. So, there is a large correlation between $x$ and $\\dot{x}$. Conversely, if $\\mathbf{R}$ is small, we are telling the filter that the measurement is very trustworthy, and $\\mathbf{K}$ is set to favor the measurement over the prediction. Why would the filter want to use the prediction if the measurement is nearly perfect? If the filter is not using much from the prediction there will be very little correlation reported. \n",
      "\n",
      "**This is a critical point to understand!**. The Kalman filter is just a mathematical model for a real world system. A report of little correlation *does not mean* there is no correlation in the physical system, just that there was no *linear* correlation in the mathematical model. It's just a report of how much measurement vs prediction was incorporated into the model.  \n",
      "\n",
      "Let's bring that point home with a truly large measurement error. We will set $\\mathbf{R}=500 m$. Think about what the plot will look like before scrolling down. To emphasize the issue, I will set the amount of noise injected into the measurements to 0, so the measurement will exactly equal the actual position. "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plot_track_ellipses(noise=0., R=500., Q=.2, count=7, title='R = 500 m')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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waFuOBTiIq9o3pSLLhS//4sMtdFkXPwdz3Jzng6GDCBmhdN/djMLtEDlqDgr1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\nG9346Gf+M09z4BVdoMaiEbEiYvQyn97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qDiQmNSmujl83UQD7FB98ik88JodrhKsLRXLH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\nOPnkk/HNN9/g5Zdfxrnnnttja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Ja88cYbeOihh1Juu+SSSzB//nysXbuW+qxmWU/n/+KL\nL0ZDQwP93s+ypqYmLFmyBJIkgTHm375s2TKceOKJdP1nWU/nnzGGn/70p9i4cWNa139WwjAhhBBC\nCCHFgLZjJoQQQgghwxaFYUIIIYQQMmxRGCaEEEIIIcMWhWFCCCGEEDJsURgmhBBCCCHDFoVhQggh\nhBAybFEYJoQQQgghwxaFYUIIIYQQMmxRGCaEEEIIIcPW/wOmUfEbtmBS0QAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f1a232e3b70>"
       ]
      }
     ],
     "prompt_number": 45
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "I hope the result was what you were expecting. The ellipse quickly became very wide and not very tall. It did this because the Kalman filter mostly used the prediction vs the measurement to produce the filtered result. We can also see how the filter output is slow to acquire the track. The Kalman filter assumes that the measurements are extremely noisy, and so it is very slow to update its estimate for $\\dot{x}$. "
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Keep looking at these plots until you grasp how to interpret the covariance matrix $\\mathbf{P}$. When you start dealing with a, say, $9{\\times}9$ matrix it may seem overwhelming - there are 81 numbers to interpret. Just break it down - the diagonal contains the variance for each state variable, and all off diagonal elements are the product of two variances and a scaling factor $p$. You will not be able to plot a $9{\\times}9$ matrix on the screen because it would require living in 10-D space, so you have to develop your intution and understanding in this simple, 2-D case. \n",
      "\n",
      "> **sidebar**: when plotting covariance ellipses, make sure to always use *plt.axis('equal')* in your code. If the axis use different scales the ellipses will be drawn distorted. For example, the ellipse may be drawn as being taller than it is wide, but it may actually be wider than tall."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Batch Processing\n",
      "\n",
      "The Kalman filter is designed as a recursive algorithm - as new measurements come in we immediately create a new estimate. But it is very common to have a set of data that have been already collected which we want to filter. Kalman filters can always be run in a *batch* mode, where all of the measurements are filtered at once. We have implemented this in `KalmanFilter.batch_filter()`. Internally, all the function does is loop over the measurements and collect the resulting state and covariance estimates in arrays. It may seem a bit trivial, but you will almost always want to do this if you can for several reasons. First, it will execute a bit quicker than if you implement the loop yourself. Second, the logic in your code will be a bit cleaner, and you will have a reduced chance of bugs. Third, and most importantly, it you batch process your data you can then use an extremely powerful techique to generate far smoother results than you have seen so far. We will present that technique in the next section; here I will show you how to use `KalmanFilter.batch_filter()`.\n",
      "\n",
      "All you have to do is collect your measurements into an array or list. Maybe it is in a CSV file, for example.\n",
      "\n",
      "    zs = read_altitude_from_csv()\n",
      "\n",
      "Or maybe you will generate it using a generator:\n",
      "\n",
      "    zs = [some_func(i) for i in range(1000)]\n",
      "    \n",
      "Just do whatever it takes to get your measurements in an array.\n",
      "\n",
      "Now we will just call the `batch_filter()` method.\n",
      "\n",
      "    Xs, Ps, Xs_pred, Ps_pred = kfilter.batch_filter(zs)\n",
      "    \n",
      "The funtion takes the list/array of measurements, filters it, and returns a list of state estimates (Xs), covariance matrices (Ps), and the predictions for the same (Xs_pred, Ps_pred).\n",
      "\n",
      "Here is a complete example drawing from the code above"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "dog = DogSensor(velocity=1, noise_var=10.)\n",
      "f = dog_tracking_filter(R=3., Q=.02, cov=P)\n",
      "count = 50\n",
      "zs = [dog.sense() for t in range(count)]\n",
      "Xs, _, _, _ = f.batch_filter(zs)\n",
      "\n",
      "plt.plot([0, count], [0, count], 'g', label='actual')\n",
      "plt.plot(range(1,count+1), zs, c='r', linestyle='dashed', \n",
      "         label='measurement')\n",
      "plt.plot(range(1,count+1), Xs[:,0], c='b', label='filter')\n",
      "plt.legend(loc='best')\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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7SuaB0J/w/b8nGdg6gkHhG0psh7jiVqJh2Gw2ExQUxOnTp7UpRDnidm6/8ty2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TAAAB\njElEQVTAV77vy/d9cmGol5cX9Xo9WZYly7LU6XR0eXmp6+trMoFv5n1XLKQMr66uand3V9VqVY7j\nqFarKRwOK5FILGI5/GCe58lxHHmeJ8/z5LquptOp9vb2VK/XZdu22u22+v2+UqnU335c/EFXV1cK\nBAI6Pj7+bU42zDUajdRsNmXbtqbTqRqNhsbjsXZ2dsiFoTKZjO7u7mZXMpnUycmJcrkcmTCYbdt6\nenqS67pyXVeVSkUbGxuKx+Nz5WJhW6sVCgVdXFwon88rFovp9PR0UUvhB3t4eFC5XJ7dt1otHR4e\n6uDgQIPBQMViUWtrayoWi7OdBfD/Gw6Hur+/1/LysnK53Gx+dnam/f19smGopaUlPT4+6ubmRpPJ\nRPF4XKVSSevr6+QC35AJc00mE93e3urt7U3BYFDb29sqlUoKBoNz5SLgf/0BBwAAADAIxzEDAADA\nWJRhAAAAGIsyDAAAAGNRhgEAAGAsyjAAAACMRRkGAACAsSjDAAAAMBZlGAAAAMaiDAMAAMBYn/CR\ncjJSi4ynAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f1a23298a90>"
       ]
      }
     ],
     "prompt_number": 46
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Smoothing the Results\n",
      "\n",
      "I have an entire chapter on using the Kalman filter to smooth data; I will not repeat the chapter's information here. However, it is so easy to use, and offers such a profoundly improved output that I will tease you will a few examples. The smoothing chapter is not especially difficult; you are sufficiently prepared to read it now.\n",
      "\n",
      "Briefly, the recursive form of Kalman filtering that we have been using up to now use information from the past to generate the current estimate. Recall the last section, where we used batch processing to filter a collection of measurements. This implies that we know now only the past, but the future! This is a key insight.\n",
      "\n",
      "Let's assume that  we are tracking a car. Suppose we get a noisy measurement that implies that the car is starting to turn to the left, but the state function has predicted that the car is moving straight. The Kalman filter has no choice but to move the state estimate somewhat towards the noisy measurement, as it cannot judge whether this is just a particularly noisy measurement or the true start of a turn. \n",
      "\n",
      "However, if we have measurements from the future we can often figure out if a turn was made or not. Suppose the subsequent measurements all continue turning left. We can then be sure that the measurement was not very noisy, but instead a true indication that a turn was initiated. On the other hand, if the subsequent measurements continued on in a straight line we would know that the measurement was noisy and should be mostly ignored.\n",
      "\n",
      "We will not develop the math or algorithm here, I will just show you how to call the algorithm in `filterpy`. The algorithm that we have implemented is called an *RTS smoother*, after the three inventors of the algorithm: Rauch, Tung, and Striebel. The routine is `KalmanFilter.rts_smoother()`. Using it is trivial; we pass in the means and covariances computed from the `batch_filter` step, and receive back the smoothed means, covariances, and Kalman gain."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from numpy.random import seed\n",
      "dog = DogSensor(velocity=1, noise_var=40.)\n",
      "f = dog_tracking_filter(R=3., Q=.2, cov=P)\n",
      "count = 50\n",
      "seed(8923)\n",
      "zs = [dog.sense() for t in range(count)]\n",
      "Xs, Covs, _, _ = f.batch_filter(zs)\n",
      "Ms, Ps, _ = f.rts_smoother(Xs, Covs)\n",
      "\n",
      "#plt.plot([0, count], [0, count], 'g', label='actual', alpha=.7)\n",
      "plt.plot(range(1,count+1), zs, c='r', linestyle='dashed', \n",
      "         alpha=.5, label='measurement')\n",
      "plt.plot(range(1,count+1), Xs[:,0], c='b', label='filter', alpha=.5)\n",
      "plt.plot(range(1,count+1), Ms[:,0], c='k', label='RTS')\n",
      "plt.legend(loc='best')\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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ll1+yePFiTCZTw92wEEIIIUQTs9mgqEghK0vLrl2FPPPMG3UaxyOpF+5eSFu/fj3Lli0j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BQ8mZlQMjKCXQoREREF2IyePCHevAmx/DyaPmwDBAHZ2e6vflGo0TSY3n8fcn09NKMRzuLiYFcU\n2kQR7vvv9+4mQkRERCFtRgdlqbUVTT1WDEXOxpw5CmbPDv1lF340DaZTp2CsroZmMMCxeTPUpKRg\nV0VEREQUEmZ2UG5pwcXOBKjR0cjJCZNlF7cx1NXB+Mkn0EQRjo0boYTgvtFEREREwTJz1yhrGoSW\n67jUVQAtJSZ81iffxpObC3dzMzxZWVDS04NdDhEREVFImbFBWejpwdVWIwYRiVlJRsTFDQa7pKkn\nSRhavz7YVRARERGFpBkblDWTCTXz1sPjiEZ2jmfERhBERERERBMxc4OyOQL1njlQk0RkZw8Euxwi\nIiIiCjEz9ma+1lYJAwMiYmJUJCSowS6HiIiIiELMjA3KDQ1fjqzmsgsiIiIimmwBDcrXrl3DmjVr\nYLFYcP/99+PChQuTcl5NAy5dGg7KYThkhIiIiIgCLqBBeceOHcjPz4fdbkdpaSlKS0sn5bw3bojo\n6xNhsahITuayCyIiIiKafAELyr29vThx4gR+/OMfw2QyYffu3bhy5QpqamomfO4rRythqK9HTlI3\nl10QERERUUAELCg3NjbCbDbDYrFg1apVuHz5MubPn4/6+voJnVfzKGi8oEK025GdF2Yjq4mIiIho\nygRse7iBgQFERUWhr68PdXV16OrqQnR0NAYGRm7lFhcXd8/nbfvsBvpd0YiZIyO/KAnijL0dkUYj\nyzKAsfUFhTb2BOlhX5Ae9gXpGe6LsQpYULZYLOjv74fNZkNHRwcAoK+vD1FRUSOOffHFF32fr169\nGg8++OCo5714tgsAkLtQZEgmIiIiIl0ffvghTp8+DQCQJAmrV68e8zkCFpSzsrLgcDjQ0tKClJQU\nuFwufP7558jNzR1x7LPPPuv3dWdn56jn/bS8D263Gyl58l2Po5lr+CoA///SMPYE6WFfkB72BQ1b\nvHgxFi9eDMDbF2fOnBnzOQJ2TTYmJgYPP/ww9u3bh6GhIfzmN7/BvHnzfAWPR3e3gM7rCswGD2zL\nZk9itURERERE/gI6wvqll17Ck08+CavVigULFuC1116b0PlmzdLw3/8zHz2NXRDmMCgTERERUeAE\nNCjbbDZ88MEHk3rOuEQJcYlzJvWcRERERER34u1wREREREQ6GJSJiIiIiHQwKBMRERER6WBQJiIi\nIiLSwaBMRERERKSDQZmIiIiISAeDMhERERGRDgZlIiIiIiIdDMpERERERDoYlImIiIiIdDAoExER\nERHpYFAmIiIiItLBoExEREREpINBmYiIiIhIB4MyEREREZEOBmUiIiIiIh0MykREREREOhiUiYiI\niIh0MCgTEREREelgUCYiIiIi0sGgTERERESkg0GZiIiIiEgHgzIRERERkQ4GZSIiIiIiHQzKRERE\nREQ6GJSJiIiIiHQwKBMRERER6WBQJiIiIiLSwaBMRERERKSDQZmIiIiISAeDMhERERGRDgZlIiIi\nIiIdDMpERERERDoYlImIiIiIdDAoExERERHpYFAmIiIiItLBoExEREREpINBmYiIiIhIx7iD8sWL\nF7F+/XrMnj0bGRkZI54/ePAgEhMTYbVa8cILL0yoSCIiIiKiqTbuoCzLMp544gns379/xHPl5eX4\n+c9/jlOnTqGmpgbHjh3D8ePHJ1QohZe6urpgl0DTDHuC9LAvSA/7gibLuINyZmYmtm7divT09BHP\nvf7663j88cexYMECJCcnY/v27Th27NhE6qQww19ydCf2BOlhX5Ae9gVNloCsUW5oaEBubi4OHDiA\n559/HgsXLsTFixcD8a2IiIiIiALCEIiTDgwMICoqCrW1tbhy5QoeeeQR9Pf3j3p8XFxcIMqgGUqW\nZaxbtw6zZs0Kdik0TbAnSA/7gvSwL0iPLMvjet1dg/LevXvxi1/8YsTjmzZtwhtvvDHq6ywWC/r7\n+3HgwAEAwN///ndERUWNevyZM2futV4iIiIioinxlUF57969Yz5pTk4O6uvrfV/X1tYiLy9P99iH\nHnpozOcnIiIiIgq0Ca1RHhoagtvthqZpcDqdcLlcAIAtW7bgjTfeQG1tLVpaWvDyyy+jtLR0Ugom\nIiIiIpoK416j3NTUhMzMTACAIAiIiIjAmjVrcPLkSRQWFuJnP/sZ1q5dC7fbje9///vYsmXLpBVN\nRERERBRogqZpWrCLICIiIiKabjjCmoiIiIhIB4MyEREREZGOgOyjfC86Oztx6NAhfP7550hOTsZz\nzz2H1NTUYJVDQVBZWYk333wTTU1NWLlyJZ599lkAgMfjwR/+8AeUlZXBYrHgqaeeQnFxcZCrpami\nKAoOHz6M6upqOJ1OZGRkYNu2bbDZbOyNMHfw4EHU1NTA6XQiPj4epaWlWL58OfuCAHin8e3duxc7\nd+7EunXr2Bdhbu/evbh06RIkSQIAFBYW4rnnnhtzXwQtKB85cgRpaWn4yU9+gnfeeQe//e1v8etf\n/zpY5VAQWCwWbNy4EVVVVb4dUwDg7bffxrVr13D48GE0NTVh3759yMnJ4WCaMKGqKhITE/HEE0/A\narXi7bffxv79+3HgwAH2RpjbuHEjdu3aBVmWUVVVhX379uHll1/Ge++9x74Ic4qi4NVXX0VKSorv\nMf6+CG+CIGDbtm1Yt26d3+Nj7YugLL0YHBxEVVUVNm3aBFmW8dhjj6G9vR3Nzc3BKIeCZOHChSgs\nLBwxjKasrAyPPPIIIiMjsXDhQuTk5KCioiJIVdJUk2UZ3/rWt2C1WgEAa9aswY0bN9Db28veCHPz\n5s2DLMvQNA0ejwdmsxmCILAvCO+++y6WLVuG2NhY32PsC9Iz1r4ISlC+ceMGZFmG2WzGT3/6U9y8\neRMJCQlobW0NRjk0zbS2tiI5ORkHDx7E2bNnYbPZ2BthrKGhAVarFdHR0ewNwh//+Ec8+eSTOHTo\nEPbs2QOTycS+CHPd3d348MMPsWHDBr/H2Rf06quvYtu2bfjlL3+JlpYWAGPvi6AEZafTCbPZDIfD\ngZaWFvT39yMiIgJDQ0PBKIemmeH+uHr1Kux2O8xmM3sjTA0ODuKVV17B1q1bIQgCe4Owfft2HD16\nFKWlpTh06BBcLhf7IswdPXoUmzdvhizLfo+zL8LbU089hcOHD+P3v/89MjMz8atf/QqKooy5L4IS\nlE0mE4aGhhAXF4c//elPyMnJgcPhgNlsDkY5NM0M98f+/fuxYcMGOBwOREREBLssmmJutxv79+/H\nypUrfTdasDcIACRJwvr16yHLMmpqatgXYay+vh7t7e0oKSkBANw+GoJ9Ed4yMzMhyzJMJhO++93v\noru7Gy0tLWPui6AE5cTERLhcLtjtdgDeXQ7a2tqQnJwcjHJomklOTva9RQIA165dY2+EGVVVceDA\nASQlJeHb3/6273H2Bt1O0zRomsa+CGNffPEFGhoaUFpaitLSUtTV1eGll17CK6+8wr6gEcbz+yIo\nQTkyMhJLly7Fm2++CZfLhbfeegtz585FWlpaMMqhIFFVFS6XC6qqQlVVuN1uKIqC4uJivPvuuxgc\nHMSFCxdw6dIlFBYWBrtcmkJHjhyBIAjYvn273+PsjfDV3d2NkydPYnBwEIqi4MSJE+jp6UFubi77\nIow9+uijeO2113wfCxcuxM6dO/HMM8+wL8LY4OAgPvnkE7jdbrjdbhw/fhyzZs2CzWYbc18EbXu4\nHTt24NChQ/je976HlJQU7N69O1ilUJCcPn0ahw8f9n3973//G1u2bMHmzZvR0tKCXbt2wWKxYNeu\nXb4dECj0tbe349SpUzAajXjmmWd8j7/wwgt47LHH2BthShRFnDlzBn/961/h8Xhgs9mwZ88eREVF\nsS9IF/sifHk8Hhw7dgzXr1+HJEnIysrCnj17IEnSmPtC0G5f0ENERERERAA4wpqIiIiISBeDMhER\nERGRDgZlIiIiIiIdDMpERERERDoYlImIiIiIdDAoExERERHpYFAmIiIiItLBoExEREREpINBmYiI\niIhIx/8DuLLYeQnXUc0AAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f1a23298518>"
       ]
      }
     ],
     "prompt_number": 47
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "This output is fantastic!. Two things are very apparent to me in this chart. First, the RTS output is much, much smoother than the KF output. Second, it is almost always more accurate than the KF output (we will examine this claim in detail in the **Smoothing** chapter).\n",
      "\n",
      "While you can usually find isolated sections where the KF produces a more accurate estimate than the RTS smoother, the RTS almost always significantly outperforms the KF. If you are able to batch process your data, there is no reason to not use the RTS algorithm.\n",
      "\n",
      "We cannot always wait to collect all of our data before we filter it. If so, that means that we cannot use the RTS filter, but we may still have options. The **Smoothing** chapter discusses various strategies that you can use, and it is a mandatory (and easy) chapter if you want to achieve the best possible results from your filtering.\n",
      "\n",
      "Let's wrap this up by looking at the velocity estimates of the two filters."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "dog = DogSensor(velocity=1, noise_var=40.)\n",
      "f = dog_tracking_filter(R=3., Q=.2, cov=P)\n",
      "count = 50\n",
      "seed(8923)\n",
      "zs = [dog.sense() for t in range(count)]\n",
      "Xs, Covs, _, _ = f.batch_filter(zs)\n",
      "Ms, Ps, _ = f.rts_smoother(Xs, Covs)\n",
      "plt.plot(Xs[:,1], c='b', label='filter', alpha=.5)\n",
      "plt.plot(Ms[:,1], c='k', linestyle=':', label='RTS')\n",
      "plt.legend(loc='best')\n",
      "plt.gca().axhline(1, c='k')\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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WMlGlt8/wha8TFcX2akREREQUOCEUDF+6TMK3vRo7ShARERGRf0ImGPbUDF+sTAJg3TAR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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f1a22ef1f98>"
       ]
      }
     ],
     "prompt_number": 48
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The improvement in the velocity, which is an unobserved variable, is even more dramatic. \n",
      "\n",
      "Since we are plotting velocies let's look at what the the 'raw' velocity is, which we can compute by subtracting subsequent measurements. We see below that the noise swamps the signal, causing the computed values to be essentially worthless. I show this to reiterate the importance of using Kalman filters to compute velocities, accelerations, and even higher order values. I use a Kalman filter even when my measurements are so accurate that I am willing to use them unfiltered if I am also interested in the velocities and/or accelerations. Even a very small error in a measurement gets magnified when computing velocities. "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "dx = np.diff(zs, axis=0)\n",
      "plt.plot(range(1,count), dx, c='r',ls='--', label='raw velocity')\n",
      "plt.plot(Xs[:,1], c='b', label='filter', alpha=.5)\n",
      "plt.plot(Ms[:,1], c='k', linestyle=':', label='RTS')\n",
      "plt.legend(loc='best')\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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WdV2Gaoik+M46i4Zf/Qr/zJl2h2IpSZQt5HnrLQD00tKExrVaRlVpfOQRav/6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\nIiKyg4kyEREREZEdTJSJiIiIiOz4/yiDf6gpakN9AAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f1a22fd5898>"
       ]
      }
     ],
     "prompt_number": 49
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Walking Through the KalmanFilter Code (Optional)"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "** author's note: this code is somewhat old. This section needs to be edited; I would not pay a lot of attention to it right now. **\n",
      "\n",
      "The kalman filter code that we are using is implemented in my Python library `FilterPy`. If you are interested in the full implementation of the filter you should look in `filterpy\\kalman\\kalman_filter.py`. In the following I will present a simplified implementation of the same code. The code in the library handles issues that are beyond the scope of this chapter, such as numerical stability and support for the extended Kalman filter, subject of a later chapter. \n",
      "\n",
      "The code is implemented as the class `KalmanFilter`. Some Python programmers are not a fan of object oriented (OO) Python, and eschew classes. I do not intend to enter into that battle other than to say that I have often seen OO abused. Here I use the class to encapsulate the data that is pertinent to the filter so that you do not have to store and pass around a half dozen variables everywhere.\n",
      "\n",
      "The method `__init__()` is used by Python to create the object. Here is the method \n",
      "\n",
      "    def __init__(self, dim_x, dim_z):\n",
      "        \"\"\" Create a Kalman filter. You are responsible for setting the \n",
      "        various state variables to reasonable values; the defaults below will\n",
      "        not give you a functional filter.\n",
      "        \n",
      "        Parameters\n",
      "        ----------\n",
      "        dim_x : int\n",
      "            Number of state variables for the Kalman filter. For example, if\n",
      "            you are tracking the position and velocity of an object in two\n",
      "            dimensions, dim_x would be 4.\n",
      "            \n",
      "            This is used to set the default size of P, Q, and u\n",
      "           \n",
      "        dim_z : int\n",
      "            Number of of measurement inputs. For example, if the sensor\n",
      "            provides you with position in (x,y), dim_z would be 2.            \n",
      "        \"\"\"\n",
      "        \n",
      "        self.dim_x = dim_x\n",
      "        self.dim_z = dim_z\n",
      "\n",
      "        self.x = np.zeros((dim_x,1)) # state\n",
      "        self.P = np.eye(dim_x)       # uncertainty covariance\n",
      "        self.Q = np.eye(dim_x)       # process uncertainty\n",
      "        self.u = 0                   # control input vector\n",
      "        self.B = np.zeros((dim_x,1))\n",
      "        self.F = 0                   # state transition matrix\n",
      "        self.H = 0                   # Measurement function\n",
      "        self.R = np.eye(dim_z)       # state uncertainty\n",
      "\n",
      "        # identity matrix. Do not alter this.\n",
      "        self._I = np.eye(dim_x)\n",
      "\n",
      "More than anything this method exists to document for you what the variable names are in the filter. To do anything useful with this filter you will have to modify most of these values. Some are set to useful values. For example, `R` is set to an identity matrix; if you want the diagonals of `R` to be 10. you may write (as we did earlier in this chapter) `my_filter.R += 10.`.\n",
      "\n",
      "The names used for each variable matches the math symbology used in this chapter. Thus, `self.P` is the covariance matrix, `self.x` is the state, and so on.\n",
      "\n",
      "The predict function implements the predict step of the Kalman equations, which are \n",
      "\n",
      "$$\n",
      "\\begin{aligned}\n",
      "\\mathbf{x}^- &= \\mathbf{F x} + \\mathbf{B u} \\\\\n",
      "\\mathbf{P}^- &= \\mathbf{FP{F}}^\\mathsf{T} + \\mathbf{Q} \n",
      "\\end{aligned}\n",
      "$$\n",
      "\n",
      "The corresponding code is\n",
      "\n",
      "    def predict(self):        \n",
      "        self.x = self.F.dot(self.x) + self.B.dot(self.u)\n",
      "        self.P = self.F.dot(self.P).dot(self.F.T) + self.Q\n",
      "\n",
      "I haven't discussed the use of numpy much until now, but this method illustrates the power of that package. We use numpy's `array` class to store our data and perform the linear algebra for our filters. `array` implements matrix multiplication using the `.dot()` method; if you use `*` you will get element-wise multiplication. As a heavy user of linear algebra this design is somewhat distressing as I use matrix multiplication far more often than element-wise multiplication. However, this design is due to historical developments in the library and we must live with it. The Python community has recognized this problem, and in Python 3.5 we will have the `@` operator to implement matrix multiplication. \n",
      "\n",
      "With that in mind, the Python code `self.F.dot(self.x)` implements the math expression $\\mathbf{F x}$.\n",
      "\n",
      "Numpy's `array` implements matrix transposition by using the `.T` property. Therefore, `F.T` is the python implementation of $\\mathbf{F}^\\mathsf{T}$.\n",
      "\n",
      "The `update()` method implements the update equations of the Kalman filter, which are\n",
      "\n",
      "$$\n",
      "\\begin{aligned}\n",
      "\\mathbf{y} &= \\mathbf{z} - \\mathbf{H}\\mathbf{x^-} \\\\\n",
      "\\mathbf{K} &= \\mathbf{P} \\mathbf{H}^\\mathsf{T} (\\mathbf{H} \\mathbf{P^-} \\mathbf{H}^\\mathsf{T} +\\mathbf{R})^{-1} \\\\\n",
      "\\mathbf{x} &= \\mathbf{x}^- + \\mathbf{K} \\mathbf{y} \\\\\n",
      "\\mathbf{P} &= (\\mathbf{I} - \\mathbf{K} \\mathbf{H})\\mathbf{P^-}\n",
      "\\end{aligned}\n",
      "$$\n",
      "\n",
      "The corresponding code is:\n",
      "\n",
      "    def update(self, Z, R=None):\n",
      "        \"\"\"\n",
      "        Add a new measurement (Z) to the kalman filter. If Z is None, nothing\n",
      "        is changed.\n",
      "\n",
      "        Optionally provide R to override the measurement noise for this\n",
      "        one call, otherwise  self.R will be used.\n",
      "\n",
      "        self.residual, self.S, and self.K are stored in case you want to\n",
      "        inspect these variables. Strictly speaking they are not part of the\n",
      "        output of the Kalman filter, however, it is often useful to know\n",
      "        what these values are in various scenarios.\n",
      "        \"\"\"\n",
      "\n",
      "        if Z is None:\n",
      "            return\n",
      "\n",
      "        if R is None:\n",
      "            R = self.R\n",
      "        elif np.isscalar(R):\n",
      "            R = np.eye(self.dim_z) * R\n",
      "\n",
      "        # error (residual) between measurement and prediction\n",
      "        self.residual = Z - self.H.dot(self.x)\n",
      "\n",
      "        # project system uncertainty into measurement space\n",
      "        self.S = self.H.dot(self.P).dot(self.H.T) + R\n",
      "\n",
      "        # map system uncertainty into kalman gain\n",
      "        self.K = self.P.dot(self.H.T).dot(linalg.inv(self.S))\n",
      "\n",
      "        # predict new x with residual scaled by the kalman gain\n",
      "        self.x += self.K.dot(self.residual)\n",
      "\n",
      "        KH = self.K.dot(self.H)\n",
      "        I_KH = self._I - KH\n",
      "        self.P = (I_KH.dot(self.P.dot(I_KH.T)) +\n",
      "                 self.K.dot(self.R.dot(self.K.T)))\n",
      "\n",
      "There are a few more complications in this piece of code compared to `predict()` but it should still be quite clear. \n",
      "\n",
      "The first complication are the lines:\n",
      "\n",
      "        if Z is None:\n",
      "            return\n",
      "            \n",
      "This just lets you deal with missing data in a natural way. It is typical to use `None` to indicate the absence of data. If there is no data for an update we skip the update equations. This bit of code means you can write something like:\n",
      "\n",
      "    z = read_sensor()    # may return None if no data\n",
      "    my_kf.update(z)\n",
      "    \n",
      "instead of:\n",
      "    z = read_sensor()\n",
      "    if z is not None:\n",
      "        my_kf.update(z)\n",
      "        \n",
      "Reasonable people will argue whether my choice is cleaner, or obscures the fact that we do not update if the measurement is `None`. Having written a lot of avionics code my proclivity is always to do the safe thing. If we pass 'None' into the function I do not want an exception to occur; instead, I want the reasonable thing to happen, which is to just return without doing anything. If you feel that my choice obscures that fact, go ahead and write the explicit `if` statement prior to calling `update()` and get the best of both worlds.\n",
      "\n",
      "The next bit of code lets you optionally pass in a value to override `R`. It is common for the sensor noise to vary over time; if it does you can pass in the value as the optional parameter `R`.\n",
      "\n",
      "        if R is None:\n",
      "            R = self.R\n",
      "        elif np.isscalar(R):\n",
      "            R = np.eye(self.dim_z) * R\n",
      "            \n",
      "This code will use self.R if you do not provide a value for `R`. If you did provide a value, it will check if you provided a scalar (number); if so it constructs a matrix of the correct dimension for you. Otherwise it assumes that you passed in a matrix of the correct dimension.\n",
      "\n",
      "The rest of the code implements the Kalman filter equations, with one exception. Instead of implementing \n",
      "\n",
      "$$\\mathbf{P} = (\\mathbf{I} - \\mathbf{KH})\\mathbf{P}^-$$\n",
      "\n",
      "it implements the somewhat more complicated form \n",
      "\n",
      "$$\\mathbf{P} = (\\mathbf{I} - \\mathbf{KH})\\mathbf{P}^-(\\mathbf{I} - \\mathbf{KRK})^\\mathsf{T} + \\mathbf{KRK}^\\mathsf{T}$$.\n",
      "\n",
      "The reason for this altered equation is that it is more numerically stable than the former equation, at the cost of being a bit more expensive to compute. It is not always possible to find the optimal value for $\\text{K}$, in which case the former equation will not produce good results because it assumes optimality. The longer reformulation used in the code is derived from more general math that does not assume optimality, and hence provides good results for non-optimal filters (such as when we can not correctly model our measurement error).\n",
      "\n",
      "Various texts differ as to whether this form of the equation should always be used, or only used when you know you need it. I choose to expend a bit more processing power to ensure stability; if your hardware is very constrained and you are able to prove that the simpler equation is correct for your problem then you might choose to use it instead. Personally, I find that a risky approach and do not recommend it to non-experts. Brown's *Introduction to Random Signals and Applied Kalman Filtering* [3] discusses this issue in some detail, if you are interested."
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "References"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "- [1] http://docs.scipy.org/doc/scipy/reference/tutorial/stats.htmly\n",
      "\n",
      "- [2] https://en.wikipedia.org/wiki/Kalman_filter\n",
      "\n",
      "- [3] Brown, Robert Grover. *Introduction to Random Signals and Applied Kalman Filtering* John Wiley & Sons, Inc. 2012\n",
      "\n",
      "- [4] `FilterPy` library. Roger Labbe.\n",
      "https://github.com/rlabbe/filterpy"
     ]
    }
   ],
   "metadata": {}
  }
 ]
}