From 2a651f6c5bc4cf74d3130cf9ba88293d6e9b8345 Mon Sep 17 00:00:00 2001 From: Roger Labbe Date: Tue, 27 Jan 2015 10:18:25 -0800 Subject: [PATCH] Moved chapter 5 as part of reorg. --- 05_Kalman_Filters.ipynb | 2415 ++++++++++++++++ 05_Kalman_Filters/Kalman_Filters.ipynb | 2425 ----------------- 05_Kalman_Filters/README.md | 2 - .../05_dog_track.gif | Bin 184194 -> 183457 bytes .../05_volt_animate.gif | Bin .../Kalman_Filters_Animations.ipynb | 22 +- 6 files changed, 2426 insertions(+), 2438 deletions(-) create mode 100644 05_Kalman_Filters.ipynb delete mode 100644 05_Kalman_Filters/Kalman_Filters.ipynb delete mode 100644 05_Kalman_Filters/README.md rename 05_Kalman_Filters/dog_track.gif => animations/05_dog_track.gif (90%) rename 05_Kalman_Filters/volt_animate.gif => animations/05_volt_animate.gif (100%) rename {05_Kalman_Filters => animations}/Kalman_Filters_Animations.ipynb (99%) diff --git a/05_Kalman_Filters.ipynb b/05_Kalman_Filters.ipynb new file mode 100644 index 0000000..8f39ad8 --- /dev/null +++ b/05_Kalman_Filters.ipynb @@ -0,0 +1,2415 @@ +{ + "metadata": { + "name": "", + "signature": "sha256:fd5c9b799c18c3ea9b9d184177fe5d044cef5d0effd57570a21d613ebd67f799" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "[Table of Contents](http://nbviewer.ipython.org/github/rlabbe/Kalman-and-Bayesian-Filters-in-Python/blob/master/table_of_contents.ipynb)" + ] + }, + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "One Dimensional Kalman Filters" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#format the book\n", + "%matplotlib inline\n", + "import sys\n", + "sys.path.insert(0,'./code') # allow us to import book_format\n", + "import book_format\n", + "book_format.load_style()" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "html": [ + "\n", + "\n" + ], + "metadata": {}, + "output_type": "pyout", + "prompt_number": 1, + "text": [ + "" + ] + } + ], + "prompt_number": 1 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "One Dimensional Kalman Filters" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now that we understand the histogram filter and Gaussians we are prepared to implement a 1D Kalman filter. We will do this exactly as we did the histogram filter - rather than going into the theory we will just develop the code step by step." + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Tracking A Dog" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "As in the histogram chapter we will be tracking a dog in a long hallway at work. However, in our latest hackathon someone created an RFID tracker that provides a reasonable accurate position for our dog. Suppose the hallway is 100m long. The sensor returns the distance of the dog from the left end of the hallway. So, 23.4 would mean the dog is 23.4 meters from the left end of the hallway.\n", + "\n", + "Naturally, the sensor is not perfect. A reading of 23.4 could correspond to a real position of 23.7, or 23.0. However, it is very unlikely to correspond to a real position of say 47.6. Testing during the hackathon confirmed this result - the sensor is reasonably accurate, and while it had errors, the errors are small. Furthermore, the errors seemed to be evenly distributed on both sides of the measurement; a true position of 23m would be equally likely to be measured as 22.9 as 23.1.\n", + "\n", + "Implementing and/or robustly modeling an RFID system is beyond the scope of this book, so we will write a very simple model. We will start with a simulation of the dog moving from left to right at a constant speed with some random noise added. We will talk about this in great detail later, but we need to model two kinds of noise. The *process noise* is the noise in the physical process. Something moving at a notionally 'constant' velocity will never maintain a perfectly constant velocity. Undulations on the ground, wind, and a host of other factors mean that there will always be slight variations in the velocity. The second noise we want to model is the noise in the measurement as no measurement is perfect." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from __future__ import print_function, division\n", + "import matplotlib.pyplot as plt\n", + "import numpy.random as random\n", + "import math\n", + "\n", + "class DogSensor(object):\n", + " \n", + " def __init__(self, x0=0, velocity=1, \n", + " measurement_variance=0.0, process_variance=0.0):\n", + " \"\"\" x0 - initial position\n", + " velocity - (+=right, -=left)\n", + " measurement_variance - variance in measurement\n", + " process_variance - variance in process (m/s)^2\n", + " \"\"\"\n", + " self.x = x0\n", + " self.velocity = velocity\n", + " self.noise = math.sqrt(measurement_variance)\n", + " self.pnoise = math.sqrt(process_variance)\n", + " self.constant_vel = velocity\n", + "\n", + " def sense_position(self):\n", + " pnoise = abs(random.rand() * self.pnoise)\n", + " if self.velocity > self.constant_vel:\n", + " pnoise = -pnoise\n", + " self.velocity += pnoise\n", + " self.x = self.x + self.velocity\n", + " return self.x + random.randn() * self.noise" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 2 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The constructor `_init()__` initializes the DogSensor class with an initial position `x0`, velocity `vel`, and the variance in the measurement and noise. The `sense_position()` function has the dog move by the set velocity and returns its new position, with noise added. If you look at the code for `sense_position()` you will see a call to `numpy.random.randn()`. This returns a number sampled from a normal distribution with a mean of 0.0. and a standard deviation of 1.0. *Variance* is defined as the standard deviation squared, so in `__init()__` we take the square root of the variances to get the standard deviation. Therefore the expression `self.x + random.randn() * self.noise` computes a simulated measurement with the variance that we desire. \n", + "\n", + "Let's look at some example output for that." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "for i in range(20):\n", + " print('{: 5.4f}'.format(random.randn()), end='\\t')\n", + " if (i+1) % 5 == 0:\n", + " print ('')" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "-1.0017\t-1.5845\t-0.9908\t 0.9088\t-0.7612\t\n", + " 0.2126\t-0.3131\t 1.4439\t-0.5407\t 0.2265\t\n", + "-0.9048\t-0.5614\t 0.4823\t-0.6600\t 0.1101\t\n", + " 0.0350\t 1.2220\t 1.9535\t 0.3303\t-0.1984\t\n" + ] + } + ], + "prompt_number": 3 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "You should see a sequence of numbers near 0, some negative and some positive. Most are probably between -1 and 1, but a few might lie somewhat outside that range. This is what we expect from a normal distribution - values are clustered around the mean, and there are fewer values the further you get from the mean.\n", + "\n", + "Okay, so lets look at the output of the `DogSensor` class. We will start by setting the variance to 0 to check that the class does what we think it does. Zero variance means there is no noise in the signal, so the results should be a straight line." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import matplotlib.pyplot as plt\n", + "import matplotlib.pylab as pylab\n", + "\n", + "dog = DogSensor(measurement_variance=0.0)\n", + "xs = []\n", + "for i in range(10):\n", + " x = dog.sense_position()\n", + " xs.append(x)\n", + " print(\"%.4f\" % x, end=' '),\n", + "plt.plot(xs, label='dog position')\n", + "plt.legend(loc='best')\n", + "plt.show()" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "1.0000 2.0000 3.0000 4.0000 5.0000 6.0000 7.0000 8.0000 9.0000 10.0000 " + ] + }, + { + "metadata": {}, + "output_type": "display_data", + "png": 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zfFWAhlAUgII+qVzndnH2kAzMKqMT6XAKFCIiItLt7G4M8WyFn5eqAwS/aqM7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\nnGE2PTTWpcXj3boletD8rwIAAAADhuXfZfsDhv5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+ "text": [ + "" + ] + } + ], + "prompt_number": 4 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The constructor initialized the dog at position 0 with a velocity of 1 (move 1.0 to the right). So we would expect to see an output of 1..10, and indeed that is what we see. If you thought the correct answer should have been 0..9 recall that `sense()` returns the dog's position *after* updating his position, so the first position is 0.0 + 1, or 1.0.\n", + "\n", + "Now let's inject some noise in the signal." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "def test_sensor(measurement_var, process_var=0.0):\n", + " dog = DogSensor(measurement_variance=measurement_var, \n", + " process_variance=process_var)\n", + "\n", + " xs = []\n", + " for i in range(100):\n", + " x = dog.sense_position()\n", + " xs.append(x)\n", + "\n", + " plt.plot(xs, label='sensor')\n", + " plt.plot([0, 99], [1, 100], 'r--', label='ideal')\n", + " plt.xlabel('time')\n", + " plt.ylabel('pos')\n", + " plt.ylim([0,100])\n", + " plt.title('variance = {}, process variance = {}'.format(\n", + " measurement_var, process_var))\n", + " plt.legend(loc='best')\n", + " plt.show()\n", + " \n", + "test_sensor(measurement_var=4.0)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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KyqJPnz4WZe/lXsvr881Lz549Wb16NWFhYTzxxBMEBATg5OSEUooFCxbc0T0Npvv6Xu/p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+ "text": [ + "" + ] + } + ], + "prompt_number": 5 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "> **Note**: numpy uses a random number generator to generate the normal distribution samples. The numbers I see as I write this are unlikely to be the ones that you see. If you run the cell above multiple times, you should get a slightly different result each time. I could use `numpy.random.seed(some_value)` to force the results to be the same each time. This would simplify my explanations in some cases, but would ruin the interactive nature of this chapter. To get a real feel for how normal distributions and Kalman filters work you will probably want to run cells several times, observing what changes, and what stays roughly the same.\n", + "\n", + "So the output of the sensor should be a wavering blue line drawn over a dotted red line. The dotted red line shows the actual position of the dog, and the blue line is the noise signal produced by the simulated RFID sensor. Please note that the red dotted line was manually plotted - we do not yet have a filter that recovers that information! \n", + "\n", + "If you are running this in an interactive IPython Notebook, I strongly urge you to run the script several times in a row. You can do this by putting the cursor in the cell containing the Python code and pressing Ctrl+Enter. Each time it runs you should see a different jagged blue line wavering over the top of the dotted red line.\n", + "\n", + "I also urge you to adjust the noise setting to see the result of various values. However, since you may be reading this in a read only notebook, I will show several examples. The first plot shows the noise set to 100.0, and the second shows noise set to 0.5." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "test_sensor(measurement_var=100.0)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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h9D0VJALQ6sgOKNavAgAcfqYzWn/2AYRiBicepkoLeo4dO4ZOnToBMMzTmT17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yhKaJiBUeK2uztzx1UbKowJbi5fKFBNZoiBoVrK24QQQiRJgh4hRFKMi1KAbW2upI8LZXqS7Ocx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\nr0Crtduf6SkcZE8PRJ7g1mD19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GCU8JxpGef2HCU7Lx8yMiIiJ6fvuOXkbczE+xbd8PsFFn6gtPnDBvUIWISQ8R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\noNQ+AH7zyHqlQhCrAAAAAElFTkSuQmCC\n", + "text": [ + "" + ] + } + ], + "prompt_number": 7 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now lets see the effect of the process noise. My simulation is not meant to exactly model any given physical process. On each call to `sense_position()` I modify the current velocity by randomly generated process noise. However, I strive to keep the velocity close to the initial value, as I am assuming that there is a control mechanism in place trying to maintain the same speed. In this case, the control mechanism would be the dog's brain! For an automobile it could be a cruise control or the human driver.\n", + "\n", + "So let's first look at the plot with some process noise but no measurement noise to obscure the results." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import numpy as np\n", + "np.random.seed(1234)\n", + "test_sensor(measurement_var=0, process_var=0.5)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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cGRToTjV3u0dv8OWX4fRpGDsW6tXL93gfRbFYp6eg3ds9JsPbRH6TLn1REOS8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+ "text": [ + "" + ] + } + ], + "prompt_number": 8 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can see that the position wanders slightly from the ideal track. You may have thought that the track would have wandered back and forth the ideal path like the measurement noise did, but recall that we are modifying velocity on each, not the position. So once the track has deviated, it will stay there until the random changes in velocity happen to result in the track going back to the original track. \n", + "\n", + "Finally, let's look at the combination of measurement noise and process noise." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "test_sensor(measurement_var=1, process_var=0.5)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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VlsXQlAhc2rUG26J7nlLU9++lciADIYQQQgghRNEwZJvIzDHdtkxMWhbDNl/l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8AAAH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\nqbHpISIiIiIip/Z/z8oeNKVh2dIAAAAASUVORK5CYII=\n", + "text": [ + "" + ] + } + ], + "prompt_number": 9 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Math with Gaussians" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's say we believe that our dog is at 23m, and the variance is 5, or $pos_{dog}=\\mathcal{N}(23,5)$). We can represent that in a plot:" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import stats\n", + "stats.plot_gaussian(mean=23, variance=5)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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1NfWU9ysoKOjOmNJOGpfQozELXjUtFu7/Mpa6Zitj4n2MbtoPFo1ZqLmxF3h8Nj6rh3//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\n8M6BSmw8VYfthXY8NsiIh/qFQiHjdUMgYaSkq0oQBHx7ug7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+ "text": [ + "" + ] + } + ], + "prompt_number": 10 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This corresponds to a fairly inexact belief. While we believe that the dog is at 23, note that roughly 21 to 25 are quite likely as well. Let's assume for the moment our dog is standing still, and we query the sensor again. This time it returns 23.2 as the position. Can we use this additional information to improve our estimate of the dog's position?\n", + "\n", + "Intuition suggests 'yes'. Consider: if we read the sensor 100 times and each time it returned a value between 21 and 25, all centered around 23, we should be very confident that the dog is somewhere very near 23. Of course, a different physical interpretation is possible. Perhaps our dog was randomly wandering back and forth in a way that exactly emulated a normal distribution. But that seems extremely unlikely - I certainly have never seen a dog do that. So the only reasonable assumption is that the dog was mostly standing still at 23.0.\n", + "\n", + "Let's look at 100 sensor readings in a plot:" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "dog = DogSensor(x0=23, velocity=0, \n", + " measurement_variance=5, process_variance=0.0)\n", + "xs = range(100)\n", + "ys = []\n", + "for i in xs:\n", + " ys.append(dog.sense_position())\n", + " \n", + "plt.plot(xs,ys, label='dog position')\n", + "plt.legend(loc='best')\n", + "plt.show()" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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03Hrrrdi+fTu2bdumpMAFQZrUvvjFL+Lmm28GAJx++uno7u7GI488gs9//vNp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\ni/zkVb143wWd+Osbh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+ "text": [ + "" + ] + } + ], + "prompt_number": 11 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Eyeballing this confirms our intuition - no dog moves like this. However, noisy sensor data certainly looks like this. So let's proceed and try to solve this mathematically. But how?\n", + "\n", + "\n", + "Recall the histogram code for adding a measurement to a preexisting belief:\n", + "\n", + " def update(pos, measure, p_hit, p_miss):\n", + " q = array(pos, dtype=float)\n", + " for i in range(len(hallway)):\n", + " if hallway[i] == measure:\n", + " q[i] = pos[i] * p_hit\n", + " else:\n", + " q[i] = pos[i] * p_miss\n", + " normalize(q)\n", + " return q\n", + " \n", + "Note that the algorithm is essentially computing:\n", + "\n", + " new_belief = old_belief * measurement * sensor_error\n", + " \n", + "The measurement term might not be obvious, but recall that measurement in this case was always 1 or 0, and so it was left out for convenience. \n", + " \n", + "If we are implementing this with gaussians, we might expect it to be implemented as:\n", + "\n", + " new_gaussian = measurement * old_gaussian\n", + " \n", + "where measurement is a Gaussian returned from the sensor. But does that make sense? Can we multiply gaussians? If we multiply a Gaussian with a Gaussian is the result another Gaussian, or something else?" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "It is not particularly difficult to perform the algebra to derive the equation for multiplying two gaussians, but I will just present the result:\n", + "$$\n", + "N(\\mu_1, \\sigma_1^2)*N(\\mu_2, \\sigma_2^2) = N(\\frac{\\sigma_1^2 \\mu_2 + \\sigma_2^2 \\mu_1}{\\sigma_1^2 + \\sigma_2^2},\\frac{1}{\\frac{1}{\\sigma_1^2} + \\frac{1}{\\sigma_2^2}}) $$ \n", + "\n", + "In other words the result is a Gaussian with \n", + "\n", + "$$\\begin{aligned}\n", + "\\mu &=\\frac{\\sigma_1^2 \\mu_2 + \\sigma_2^2 \\mu_1} {\\sigma_1^2 + \\sigma_2^2}, \\\\\n", + "\\sigma^2 &= \\frac{1}{\\frac{1}{\\sigma_1^2} + \\frac{1}{\\sigma_2^2}}\n", + "\\end{aligned}$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Without doing a deep analysis we can immediately infer some things. First and most importantly the result of multiplying two Gaussians is another Gaussian. The expression for the mean is not particularly illuminating, except that it is a combination of the means and variances of the input. But the variance of the result is merely some combination of the variances of the variances of the input. We conclude from this that the variances are completely unaffected by the values of the mean!\n", + "\n", + "Let's immediately look at some plots of this. First, let's look at the result of multiplying $N(23,5)$ to itself. This corresponds to getting 23.0 as the sensor value twice in a row. But before you look at the result, what do you think the result will look like? What should the new mean be? Will the variance by wider, narrower, or the same?" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from __future__ import division\n", + "import numpy as np\n", + "\n", + "def multiply(mu1, var1, mu2, var2):\n", + " if var1 == 0.0:\n", + " var1=1.e-80\n", + " \n", + " if var2 == 0:\n", + " var2 = 1e-80\n", + " \n", + " mean = (var1*mu2 + var2*mu1) / (var1+var2)\n", + " variance = 1 / (1/var1 + 1/var2)\n", + " return (mean, variance)\n", + "\n", + "xs = np.arange(16, 30, 0.1)\n", + "\n", + "mean1, var1 = 23, 5\n", + "mean, var = multiply(mean1, var1, mean1, var1)\n", + "\n", + "ys = [stats.gaussian(x, mean1, var1) for x in xs]\n", + "plt.plot (xs, ys, label='original')\n", + "\n", + "ys = [stats.gaussian(x, mean, var) for x in xs]\n", + "plt.plot (xs, ys, label='multiply')\n", + "\n", + "plt.legend(loc='best')\n", + "plt.show()" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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kZGOnP+d0HBGRgKdyIiISAOKWvJP76OB212EaXup0HPkNc/u9EBKKXbEI+/3X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+ "text": [ + "" + ] + } + ], + "prompt_number": 12 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The result is either amazing or what you would expect, depending on your state of mind. I must admit I vacillate freely between the two! Note that the result of the multiplication is taller and narrow than the original Gaussian but the mean is the same. Does this match your intuition of what the result should have been?\n", + "\n", + "If we think of the Gaussians as two measurements, this makes sense. If I measure twice and get the same value, I should be more confident in my answer than if I just measured once. If I measure twice and get 23 meters each time, I should conclude that the length is close to 23 meters. So the mean should be 23. I am more confident with two measurements than with one, so the variance of the result should be smaller. \n", + "\n", + "\"Measure twice, cut once\" is a useful saying and practice due to this fact! The Gaussian is just a mathematical model of this physical fact, so we should expect the math to follow our physical process. \n", + "\n", + "Now let's multiply two gaussians (or equivalently, two measurements) that are partially separated. In other words, their means will be different, but their variances will be the same. What do you think the result will be? Think about it, and then look at the graph." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "xs = np.arange(16, 30, 0.1)\n", + "\n", + "mean1, var1 = 23, 5\n", + "mean2, var2 = 25, 5\n", + "mean, var = multiply(mean1, var1, mean2, var2)\n", + "\n", + "ys = [stats.gaussian(x, mean1, var1) for x in xs]\n", + "plt.plot(xs, ys, label='measure 1')\n", + "\n", + "ys = [stats.gaussian(x, mean2, var2) for x in xs]\n", + "plt.plot(xs, ys, label='measure 2')\n", + "\n", + "ys = [stats.gaussian(x, mean, var) for x in xs]\n", + "plt.plot(xs, ys, label='multiply')\n", + "plt.legend()\n", + "plt.show()" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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q1Ljl72NsbCweHh6UKlXqlq/NDUpORERERCQb+/3186xt68LtedJuREQEn3zyCQBDhgwh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2v+y9HjWQD0aDOQUb3H4+1pcmHUkiRJ0qWiKApdWvSlRZOOzP/1MzbvW82idV8QHfob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\n4lge5OUgCnKdw7IKc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+ "text": [ + "" + ] + } + ], + "prompt_number": 13 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Another beautiful result! If I handed you a measuring tape and asked you to measure the distance from table to a wall, and you got 23m, and then a friend make the same measurement and got 25m, your best guess must be 24m. \n", + "\n", + "That is fairly counter-intuitive, so let's consider it further. Perhaps a more reasonable assumption would be that either you or your coworker just made a mistake, and the true distance is either 23 or 25, but certainly not 24. Surely that is possible. However, suppose the two measurements you reported as 24.01 and 23.99. In that case you would agree that in this case the best guess for the correct value is 24? Which interpretation we choose depends on the properties of the sensors we are using. Humans make galling mistakes, physical sensors do not. \n", + "\n", + "This topic is fairly deep, and I will explore it once we have completed our Kalman filter. For now I will merely say that the Kalman filter requires the interpretation that measurements are accurate, with Gaussian noise, and that a large error caused by misreading a measuring tape is not Gaussian noise.\n", + "\n", + "For now I ask that you trust me. The math is correct, so we have no choice but to accept it and use it. We will see how the Kalman filter deals with movements vs error very soon. In the meantime, accept that 24 is the correct answer to this problem.\n", + "\n", + "One final test of your intuition. What if the two measurements are widely separated? " + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "xs = np.arange(0, 60, 0.1)\n", + "\n", + "mean1, var1 = 10, 5\n", + "mean2, var2 = 50, 5\n", + "mean, var = multiply(mean1, var1, mean2, var2)\n", + "\n", + "ys = [stats.gaussian(x, mean1, var1) for x in xs]\n", + "plt.plot (xs, ys, label='measure 1')\n", + "\n", + "ys = [stats.gaussian(x, mean2, var2) for x in xs]\n", + "plt.plot (xs, ys, label='measure 2')\n", + "\n", + "ys = [stats.gaussian(x, mean, var) for x in xs]\n", + "plt.plot(xs, ys, label='multiply')\n", + "plt.legend()\n", + "plt.show()" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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v3x6US7pAwYmIiHjBoVznP+4p7Tqf5syarBYryfHOvihZR/ed5mwRkdqdLnjo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+ "text": [ + "" + ] + } + ], + "prompt_number": 14 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This result bothered me quite a bit when I first learned it. If my first measurement was 10, and the next one was 50, why would I choose 30 as a result? And why would I be *more* confident? Doesn't it make sense that either one of the measurements is wrong, or that I am measuring a moving object? Shouldn't the result be nearer 50? And, shouldn't the variance be larger, not smaller?\n", + "\n", + "Well, no. Recall the g-h filter chapter. In that chapter we agreed that if I weighed myself on two scales, and the first read 160lbs while the second read 170lbs, and both were equally accurate, the best estimate was 165lbs. Furthermore I should be a bit more confident about 165lbs vs 160lbs or 170lbs because I know have two readings, both near this estimate, increasing my confidence that neither is wildly wrong. \n", + "\n", + "Let's look at the math again to convince ourselves that the physical interpretation of the Gaussian equations makes sense.\n", + "\n", + "$$\n", + "\\mu=\\frac{\\sigma_1^2 \\mu_2 + \\sigma_2^2 \\mu_1} {\\sigma_1^2 + \\sigma_2^2}\n", + "$$\n", + "\n", + "If both scales have the same accuracy, then $\\sigma_1^2 = \\sigma_2^2$, and the resulting equation is\n", + "\n", + "$$\\mu=\\frac{\\mu_1 + \\mu_2}{2}$$\n", + "\n", + "which is just the average of the two weighings. If we look at the extreme cases, assume the first scale is very much more accurate than than the second one. At the limit, we can set \n", + "$\\sigma_1^2=0$, yielding\n", + "\n", + "$$\n", + "\\begin{aligned}\n", + "\\mu&=\\frac{0*\\mu_2 + \\sigma_2^2 \\mu_1} { \\sigma_2^2}, \\\\\n", + "\\text{or just}\\\\\n", + "\\mu&=\\mu_1\n", + "\\end{aligned}\n", + "$$\n", + "\n", + "Finally, if we set $\\sigma_1^2 = 9\\sigma_2^2$, then the resulting equation is\n", + "\n", + "$$\n", + "\\begin{aligned}\n", + "\\mu&=\\frac{9 \\sigma_2^2 \\mu_2 + \\sigma_2^2 \\mu_1} {9 \\sigma_2^2 + \\sigma_2^2} \\\\\n", + "\\text{or just}\\\\\n", + "\\mu&= \\frac{1}{10} \\mu_1 + \\frac{9}{10} \\mu_2\n", + "\\end{aligned}\n", + "$$\n", + "\n", + "This again fits our physical intuition of favoring the second, accurate scale over the first, inaccurate scale." + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Implementing the Update Step" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Recall the histogram filter uses a numpy array to encode our belief about the position of our dog at any time. That array stored our belief of our dog's position in the hallway using 10 discrete positions. This was very crude, because with a 100m hallway that corresponded to positions 10m apart. It would have been trivial to expand the number of positions to say 1,000, and that is what we would do if using it for a real problem. But the problem remains that the distribution is discrete and multimodal - it can express strong belief that the dog is in two positions at the same time.\n", + "\n", + "Therefore, we will use a single Gaussian to reflect our current belief of the dog's position. In other words, we will use $dog_{pos} = \\mathcal{N}(\\mu,\\sigma^2)$. Gaussians extend to infinity on both sides of the mean, so the single Gaussian will cover the entire hallway. They are unimodal, and seem to reflect the behavior of real-world sensors - most errors are small and clustered around the mean. Here is the entire implementation of the update function for a Kalman filter:" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "def update(mean, variance, measurement, measurement_variance):\n", + " return multiply(mean, variance, measurement, measurement_variance)" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 15 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Kalman filters are supposed to be hard! But this is very short and straightforward. All we are doing is multiplying the Gaussian that reflects our belief of where the dog was with the new measurement. Perhaps this would be clearer if we used more specific names:\n", + "\n", + " def update_dog(dog_pos, dog_variance, measurement, measurement_variance):\n", + " return multiply(dog_pos, dog_sigma, measurement, measurement_variance)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "That is less abstract, which perhaps helps with comprehension, but it is poor coding practice. We are writing a Kalman filter that works for any problem, not just tracking dogs in a hallway, so we don't use variable names with 'dog' in them. Still, the `update_dog()` function should make what we are doing very clear. \n", + "\n", + "Let's look at an example. We will suppose that our current belief for the dog's position is $N(2,5)$. Don't worry about where that number came from. It may appear that we have a chicken and egg problem, in that how do we know the position before we sense it, but we will resolve that shortly. We will create a `DogSensor` object initialized to be at position 0.0, and with no velocity, and modest noise. This corresponds to the dog standing still at the far left side of the hallway. Note that we mistakenly believe the dog is at position 2.0, not 0.0." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "dog = DogSensor(velocity=0., measurement_variance=5, process_variance=0.0)\n", + "\n", + "pos,s = 2, 5\n", + "for i in range(20):\n", + " pos,s = update(pos, s, dog.sense_position(), 5)\n", + " print('time:', i, \n", + " '\\tposition =', \"%.3f\" % pos, \n", + " '\\tvariance =', \"%.3f\" % s)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "time: 0 \tposition = 3.566 \tvariance = 2.500\n", + "time: 1 \tposition = 2.147 \tvariance = 1.667\n", + "time: 2 \tposition = 2.152 \tvariance = 1.250\n", + "time: 3 \tposition = 1.261 \tvariance = 1.000\n", + "time: 4 \tposition = 0.745 \tvariance = 0.833\n", + "time: 5 \tposition = 0.796 \tvariance = 0.714\n", + "time: 6 \tposition = 0.638 \tvariance = 0.625\n", + "time: 7 \tposition = 0.722 \tvariance = 0.556\n", + "time: 8 \tposition = 0.871 \tvariance = 0.500\n", + "time: 9 \tposition = 0.973 \tvariance = 0.455\n", + "time: 10 \tposition = 0.898 \tvariance = 0.417\n", + "time: 11 \tposition = 0.817 \tvariance = 0.385\n", + "time: 12 \tposition = 0.965 \tvariance = 0.357\n", + "time: 13 \tposition = 0.445 \tvariance = 0.333\n", + "time: 14 \tposition = 0.360 \tvariance = 0.312\n", + "time: 15 \tposition = 0.384 \tvariance = 0.294\n", + "time: 16 \tposition = 0.470 \tvariance = 0.278\n", + "time: 17 \tposition = 0.445 \tvariance = 0.263\n", + "time: 18 \tposition = 0.292 \tvariance = 0.250\n", + "time: 19 \tposition = 0.457 \tvariance = 0.238\n" + ] + } + ], + "prompt_number": 16 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Because of the random numbers I do not know the exact values that you see, but the position should have converged very quickly to almost 0 despite the initial error of believing that the position was 2.0. Furthermore, the variance should have quickly converged from the initial value of 5.0 to 0.238.\n", + "\n", + "By now the fact that we converged to a position of 0.0 should not be terribly surprising. All we are doing is computing `new_pos = old_pos * measurement` and the measurement is a normal distribution around 0, so we should get very close to 0 after 20 iterations. But the truly amazing part of this code is how the variance became 0.238 despite every measurement having a variance of 5.0. \n", + "\n", + "If we think about the physical interpretation of this is should be clear that this is what should happen. If you sent 20 people into the hall with a tape measure to physically measure the position of the dog you would be very confident in the result after 20 measurements - more confident than after 1 or 2 measurements. So it makes sense that as we make more measurements the variance gets smaller.\n", + "\n", + "Mathematically it makes sense as well. Recall the computation for the variance after the multiplication: $\\sigma^2 = 1/(\\frac{1}{{\\sigma}_1^2} + \\frac{1}{{\\sigma}_2^2})$. We take the reciprocals of the sigma from the measurement and prior belief, add them, and take the reciprocal of the result. Think about that for a moment, and you will see that this will always result in smaller numbers as we proceed." + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Implementing Predictions" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "That is a beautiful result, but it is not yet a filter. We assumed that the dog was sitting still, an extremely dubious assumption. Certainly it is a useless one - who would need to write a filter to track non-moving objects? The histogram used a loop of sense and update functions, and we must do the same to accommodate movement.\n", + "\n", + "How how do we perform the predict function with gaussians? Recall the histogram method:\n", + "\n", + " def predict(pos, move, p_correct, p_under, p_over):\n", + " n = len(pos)\n", + " result = array(pos, dtype=float)\n", + " for i in range(n):\n", + " result[i] = \\\n", + " pos[(i-move) % n] * p_correct + \\\n", + " pos[(i-move-1) % n] * p_over + \\\n", + " pos[(i-move+1) % n] * p_under \n", + " return result\n", + " \n", + " \n", + "In a nutshell, we shift the probability vector by the amount we believe the animal moved, and adjust the probability. How do we do that with gaussians?\n", + "\n", + "It turns out that we just add gaussians. Think of the case without gaussians. I think my dog is at 7.3m, and he moves 2.6m to right, where is he now? Obviously, $7.3+2.6=9.9$. He is at 9.9m. Abstractly, the algorithm is `new_pos = old_pos + dist_moved`. It does not matter if we use floating point numbers or gaussians for these values, the algorithm must be the same. \n", + "\n", + "How is addition for gaussians performed? It turns out to be very simple:\n", + "$$ N({\\mu}_1, {{\\sigma}_1}^2)+N({\\mu}_2, {{\\sigma}_2}^2) = N({\\mu}_1 + {\\mu}_2, {{\\sigma}_1}^2 + {{\\sigma}_2}^2)$$\n", + "\n", + "All we do is add the means and the variance separately! Does that make sense? Think of the physical representation of this abstract equation.\n", + "${\\mu}_1$ is the old position, and ${\\mu}_2$ is the distance moved. Surely it makes sense that our new position is ${\\mu}_1 + {\\mu}_2$. What about the variance? It is perhaps harder to form an intuition about this. However, recall that with the `update()` function for the histogram filter we always lost information - our confidence after the update was lower than our confidence before the update. Perhaps this makes sense - we don't really know where the dog is moving, so perhaps the confidence should get smaller (variance gets larger). I assure you that the equation for gaussian addition is correct, and derived by basic algebra. Therefore it is reasonable to expect that if we are using gaussians to model physical events, the results must correctly describe those events.\n", + "\n", + "I recognize the amount of hand waving in that argument. Now is a good time to either work through the algebra to convince yourself of the mathematical correctness of the algorithm, or to work through some examples and see that it behaves reasonably. This book will do the latter.\n", + "\n", + "So, here is our implementation of the predict function:" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "def predict(pos, variance, movement, movement_variance):\n", + " return (pos + movement, variance + movement_variance)" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 17 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "What is left? Just calling these functions. The histogram did nothing more than loop over the `update()` and `predict()` functions, so let's do the same. " + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# assume dog is always moving 1m to the right\n", + "movement = 1\n", + "movement_variance = 2\n", + "sensor_variance = 10\n", + "pos = (0, 500) # gaussian N(0,500)\n", + "\n", + "dog = DogSensor(pos[0], velocity=movement, \n", + " measurement_variance=sensor_variance, \n", + " process_variance=sensor_variance)\n", + "\n", + "zs = []\n", + "ps = []\n", + "\n", + "for i in range(10):\n", + " pos = predict(pos[0], pos[1], movement, movement_variance)\n", + " print('PREDICT: {: 10.4f} {: 10.4f}'.format(pos[0], pos[1]),end='\\t')\n", + " \n", + " Z = dog.sense_position()\n", + " zs.append(Z)\n", + " \n", + " pos = update(pos[0], pos[1], Z, sensor_variance)\n", + " ps.append(pos[0])\n", + " \n", + " print('UPDATE: {: 10.4f} {: 10.4f}'.format(pos[0], pos[1]))\n", + "\n", + " \n", + "plt.plot(ps, label='filter')\n", + "plt.plot(zs, c='r', linestyle='dashed', label='measurement')\n", + "plt.legend(loc='best')\n", + "plt.show()" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "PREDICT: 1.0000 502.0000\tUPDATE: 4.0880 9.8047\n", + "PREDICT: 5.0880 11.8047\tUPDATE: 4.1639 5.4138\n", + "PREDICT: 5.1639 7.4138\tUPDATE: 6.8504 4.2574\n", + "PREDICT: 7.8504 6.2574\tUPDATE: 10.4530 3.8490\n", + "PREDICT: 11.4530 5.8490\tUPDATE: 9.5694 3.6904\n", + "PREDICT: 10.5694 5.6904\tUPDATE: 9.2446 3.6267\n", + "PREDICT: 10.2446 5.6267\tUPDATE: 10.7525 3.6007\n", + "PREDICT: 11.7525 5.6007\tUPDATE: 8.3439 3.5900\n", + "PREDICT: 9.3439 5.5900\tUPDATE: 8.8032 3.5856\n", + "PREDICT: 9.8032 5.5856\tUPDATE: 7.2800 3.5838\n" + ] + }, + { + "metadata": {}, + "output_type": "display_data", + "png": 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gKsruSESkDlBCIVJXGAZ8+il8+SVcdJHd0dQ/rVtb61IUF1tJhYhUn2lapZlF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+ "text": [ + "" + ] + } + ], + "prompt_number": 18 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "There is a fair bit of arbitrary constants code above, but don't worry about it. What does require explanation are the first few lines:\n", + "\n", + " movement = 1 \n", + " movement_variance = 2\n", + " \n", + "For the moment we are assuming that we have some other sensor that detects how the dog is moving. For example, there could be an inertial sensor clipped onto the dog's collar, and it reports how far the dog moved each time it is triggered. The details don't matter. The upshot is that we have a sensor, it has noise, and so we represent it with a Gaussian. Later we will learn what to do if we do not have a sensor for the `predict()` step.\n", + "\n", + "For now let's walk through the code and output bit by bit.\n", + "\n", + " movement = 1\n", + " movement_variance = 2\n", + " sensor_variance = 10\n", + " pos = (0, 500) # gaussian N(0,500)\n", + " \n", + " \n", + "The first lines just set up the initial conditions for our filter. We are assuming that the dog moves steadily to the right 1m at a time. We have a relatively low error of 2 for the movement sensor, and a higher error of 10 for the RFID position sensor. Finally, we set our belief of the dog's initial position as $N(0,500)$. Why those numbers. Well, 0 is as good as any number if we don't know where the dog is. But we set the variance to 500 to denote that we have no confidence in this value at all. 100m is almost as likely as 0 with this value for the variance. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Next we initialize the RFID simulator with\n", + "\n", + " dog = DogSensor(pos[0], velocity=movement, \n", + " measurement_variance=sensor_variance, \n", + " process_variance=sensor_variance)\n", + "\n", + "It may seem very 'convenient' to set the simulator to the same position as our guess, and it is. Do not fret. In the next example we will see the effect of a wildly inaccurate guess for the dog's initial position.\n", + "\n", + "The next code allocates an array to store the output of the measurements and filtered positions. \n", + "\n", + " zs = []\n", + " ps = []\n", + " \n", + "This is the first time that I am introducing standard nomenclature used by the Kalman filtering literature. It is traditional to call our measurement $Z$, and so I follow that convention here. As an aside, I find the nomenclature used by the literature very obscure. However, if you wish to read the literature you will have to become used to it, so I will not use a much more readable variable name such as $m$ or $measure$." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now we just enter our `update() ... predict()` loop.\n", + "\n", + " for i in range(10):\n", + " pos = predict(pos[0], pos[1], movement, sensor_variance)\n", + " print 'PREDICT:', \"%.4f\" %pos[0], \", %.4f\" %pos[1]\n", + "\n", + "Wait, why `predict()` before `update()`? It turns out the order does not matter once, but the first call to `,DogSensor.sense()` assumes that the dog has already moved, so we start with the update step. In practice you will order these calls based on the details of your sensor, and you will very typically do the `sense()` first.\n", + "\n", + "So we call the update function with the gaussian representing our current belief about our position, the another gaussian representing our belief as to where the dog is moving, and then print the output. Your output will differ, but when writing this I get this as output:\n", + "\n", + " PREDICT: 1.000 502.000\n", + "\n", + "What is this saying? After the prediction, we believe that we are at 1.0, and the variance is now 502.0. Recall we started at 500.0. The variance got worse, which is always what happens during the prediction step.\n", + "\n", + " Z = dog.sense_position()\n", + " zs.append(Z)\n", + " \n", + "Here we sense the dog's position, and store it in our array so we can plot the results later.\n", + "\n", + "Finally we call the update function of our filter, save the result in our *ps* array, and print the updated position belief:\n", + "\n", + " pos = update(pos[0], pos[1], Z, movement_variance)\n", + " ps.append(pos[0])\n", + " print 'UPDATE:', \"%.4f\" %pos[0], \", %.4f\" %pos[1]\n", + " \n", + "Your result will be different, but I get\n", + "\n", + " UPDATE: 1.6279 , 9.8047\n", + " \n", + "as the result. What is happening? Well, at this point the dog is really at 1.0, however the predicted position is 1.6279. What is happening is the RFID sensor has a fair amount of noise, and so we compute the position as 1.6279. That is pretty far off from 1, but this is just are first time through the loop. Intuition tells us that the results will get better as we make more measurements, so let's hope that this is true for our filter as well. Now look at the variance: 9.8047. It has dropped tremendously from 502.0. Why? Well, the RFID has a reasonably small variance of 2.0, so we trust it far more than our previous belief. At this point there is no way to know for sure that the RFID is outputting reliable data, so the variance is not 2.0, but is has gotten much better.\n", + "\n", + "Now the software just loops, calling `predict()` and `update()` in turn. Because of the random sampling I do not know exactly what numbers you are seeing, but the final position is probably between 9 and 11, and the final variance is probably around 3.5. After several runs I did see the final position nearer 7, which would have been the result of several measurements with relatively large errors.\n", + "\n", + "Now look at the plot. The noisy measurements are plotted in with a dotted red line, and the filter results are in the solid blue line. Both are quite noisy, but notice how much noisier the measurements (red line) are. This is your first Kalman filter shown to work!" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In this example I only plotted 10 data points so the output from the print statements would not overwhelm us. Now let's look at the filter's performance with more data. This time we will plot both the output of the filter and the variance." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "%precision 2\n", + "# assume dog is always moving 1m to the right\n", + "movement = 1\n", + "movement_variance = 2\n", + "sensor_variance = 4.5\n", + "pos = (0, 100) # gaussian N(0,100)\n", + "\n", + "dog = DogSensor(pos[0], velocity=movement, \n", + " measurement_variance=sensor_variance, \n", + " process_variance=0.5)\n", + "\n", + "zs, ps, vs = [], [], []\n", + "for i in range(50):\n", + " pos = predict(pos[0], pos[1], movement, movement_variance) \n", + " Z = dog.sense_position()\n", + " zs.append(Z)\n", + " vs.append(pos[1])\n", + " \n", + " pos = update(pos[0], pos[1], Z, sensor_variance)\n", + " ps.append(pos[0])\n", + " \n", + "#plt.subplot(121) \n", + "plt.plot(zs, linestyle='dashed', label='measurement')\n", + "plt.plot(ps, label='filter')\n", + "plt.legend(loc=2)\n", + "plt.show()\n", + "\n", + "plt.plot(vs)\n", + "plt.title('Variance')\n", + "plt.show()\n", + "\n", + "for i in range(0,len(vs), 5):\n", + " print('{:.4f} {:.4f} {:.4f} {:.4f} {:.4f}'.format(*[v for v in vs[i:i+5]]))" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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XevLy8vB6vX49p4iIiIjIUQoaFeD222+nY8eOANxxxx04jkPPnj0ZO3bscWM0fmnbtm3E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\nERERERFp7jQYvB7dvWw/kUFufnZGPIlh/j9qO/evUFwAvQdhzr2gkSs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+ "text": [ + "" + ] + }, + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "102.0000 6.3099 4.6267 4.2812 4.1939\n", + "4.1708 4.1646 4.1629 4.1624 4.1623\n", + "4.1623 4.1623 4.1623 4.1623 4.1623\n", + "4.1623 4.1623 4.1623 4.1623 4.1623\n", + "4.1623 4.1623 4.1623 4.1623 4.1623\n", + "4.1623 4.1623 4.1623 4.1623 4.1623\n", + "4.1623 4.1623 4.1623 4.1623 4.1623\n", + "4.1623 4.1623 4.1623 4.1623 4.1623\n", + "4.1623 4.1623 4.1623 4.1623 4.1623\n", + "4.1623 4.1623 4.1623 4.1623 4.1623\n" + ] + } + ], + "prompt_number": 19 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here we can see that the variance converges very quickly to roughly 4.1623 in 10 steps. We interpret this as meaning that we become very confident in our position estimate very quickly. The first few measurements are unsure due to our uncertainty in our guess at the initial position, but the filter is able to quickly determine an accurate estimate." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "> Before I go on, I want to emphasize that this code fully implements a 1D Kalman filter. If you have tried to read the literature, you are perhaps surprised, because this looks nothing like the complex, endless pages of math in those books. To be fair, the math gets a bit more complicated in multiple dimensions, but not by much. So long as we worry about *using* the equations rather than *deriving* them we can create Kalman filters without a lot of effort. Moreover, I hope you'll agree that you have a decent intuitive grasp of what is happening. We represent our beliefs with Gaussians, and our beliefs get better over time because more measurement means more data to work with. \"Measure twice, cut once!\"" + ] + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "Animating the Tracking" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "If you are reading this in IPython Notebook you will be able to see an animation of the filter tracking the dog directly below this sentence.\n", + "" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The top plot shows the output of the filter in green, and the measurements with a dashed red line. The bottom plot shows the Gaussian at each step. \n", + "\n", + "When the track first starts you can see that the measurements varies quite a bit from the initial prediction. At this point the Gaussian probability is small (the curve is low and wide) so the filter does not trust its prediction. As a result, the filter adjusts its estimate a large amount. As the filter innovates you can see that as the Gaussian becomes taller, indicating greater certainty in the estimate, the filter's output becomes very close to a straight line. At `x=15` and greater you can see that there is a large amount of noise in the measurement, but the filter does not react much to it compared to how much it changed for the firs noisy measurement." + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Implementation in a Class" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "For many purposes the code above suffices. However, if you write enough of these filters the functions will become a bit annoying. For example, having to write\n", + "\n", + " pos = predict(pos[0], pos[1], movement, movement_variance) \n", + " \n", + "is a bit cumbersome and error prone. Let's investigate how we might implement this in a form that makes our lives easier.\n", + "\n", + "First, values for the movement error and the measurement errors are typically constant for a given problem, so we only want to specify them once. We can store them in instance variables in the class. Second, it is annoying to have to pass in the state (pos in the code snippet above) and then remember to assign the output of the function back to that state, so the state should also be an instance variable. Our first attempt might look like:\n", + "\n", + " class KalmanFilter1D:\n", + " def __init__(self, initial_state, measurement_variance, movement_variance):\n", + " self.state = initial_state\n", + " self.measurement_variance = measurement_variance\n", + " self.movement_variance = movement_variance\n", + "\n", + "That works, but I am going to use different naming. The Kalman filter literature has settled on one letter notations for each of these concepts, and so you might as well start getting exposed to it now. At first it seems impossiblely terse, but as you become familiar with the nomenclature you'll see that the math formulas in the textbooks will have an exact one-to-one correspondance with the code. Unfortunately there is not a lot of meaning behind the names chosen; you will just have to memorize them. If you do not make this effort you will never be able to read the Kalman filter literature.\n", + "\n", + "So, we use `x` for the state (estimated value of the filter) and `P` for the variance of the state. `R` is the measurement error, and `Q` is the movement error. This gives us:\n", + "\n", + " class KalmanFilter1D:\n", + " def __init__(self, x0, R, Q):\n", + " self.x = x0\n", + " self.R = R\n", + " self.Q = Q\n", + " \n", + "Now we can implement the `update()` and `predict()` function. In the literature the measurement is usually named either `z` or `y`; I find `y` is too easy to confuse with the y axis of a plot, so I like `z`. I like to think I can hear a `z` in *measurement*, which helps me remember what `z` stands for. So for the update method we might write:\n", + "\n", + " def update(z):\n", + " self.x = (self.P * z + self.x * self.R) / (self.P + self.R)\n", + " self.P = 1 / (1/self.P + 1/self.R)\n", + "\n", + "Finally, the movement is usually called `u`, and so we will use that. So for the predict function we might write:\n", + "\n", + " def predict(self, u):\n", + " self.x += u\n", + " self.P += self.Q\n", + " \n", + "That give us the following code. Production code would require signficant comments. However, in the next chapter we will develop Kalman filter code that works for any dimension, including 1, so this class will never be more than a stepping stone for us, since we can, and will use the class developed in the next chapter in the rest of the book." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "class KalmanFilter1D:\n", + " def __init__(self, x0, P, R, Q):\n", + " self.x = x0\n", + " self.P = P\n", + " self.R = R\n", + " self.Q = Q\n", + " \n", + " def update(self, z):\n", + " self.x = (self.P * z + self.x * self.R) / (self.P + self.R)\n", + " self.P = 1. / (1./self.P + 1./self.R)\n", + "\n", + "\n", + " def predict(self, u=0.0):\n", + " self.x += u\n", + " self.P += self.Q" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 20 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Relationship to the g-h Filter" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In the first chapter I stated that the Kalman filter is a form of g-h filter. However, we have been reasoning about the probability of Gaussians, and not used any of the reasoning or equations of the first chapter. A trivial amount of algebra will reveal the relationship, so let's do that now. It's not particularly illuminating algebra, so feel free to skip to the bottom to see the final equation that relates *g* and *h* to the variances.\n", + "\n", + "The equation for our estimate is:\n", + "\n", + "$$\n", + "\\mu_{x'}=\\frac{\\sigma_1^2 \\mu_2 + \\sigma_2^2 \\mu_1} {\\sigma_1^2 + \\sigma_2^2}\n", + "$$\n", + "\n", + "which I will make more friendly for our eyes as:\n", + "\n", + "$$\n", + "\\mu_{x'}=\\frac{ya + xb} {a+b}\n", + "$$\n", + "\n", + "We can easily put this into the g-h form with the following algebra\n", + "\n", + "$$\n", + "\\begin{aligned}\n", + "\\mu_{x'}&=(x-x) + \\frac{ya + xb} {a+b} \\\\\n", + "\\mu_{x'}&=x-\\frac{a+b}{a+b}x + \\frac{ya + xb} {a+b} \\\\ \n", + "\\mu_{x'}&=x +\\frac{-x(a+b) + xb+ya}{a+b} \\\\\n", + "\\mu_{x'}&=x+ \\frac{-xa+ya}{a+b} \\\\\n", + "\\mu_{x'}&=x+ \\frac{a}{a+b}(y-x)\\\\\n", + "\\end{aligned}\n", + "$$\n", + "\n", + "We are almost done, but recall that the variance of estimate is given by \n", + "\n", + "$${\\sigma_{x'}^2} = \\frac{1}{ \\frac{1}{\\sigma_1^2} + \\frac{1}{\\sigma_2^2}}\\\\\n", + "= \\frac{1}{ \\frac{1}{a} + \\frac{1}{b}}\n", + "$$\n", + "\n", + "We can incorporate that term into our equation above by observing that\n", + "$$ \n", + "\\begin{aligned}\n", + "\\frac{a}{a+b} &= \\frac{a/a}{(a+b)/a} = \\frac{1}{(a+b)/a}\\\\\n", + " &= \\frac{1}{1 + \\frac{b}{a}} = \\frac{1}{\\frac{b}{b} + \\frac{b}{a}}\\\\\n", + " &= \\frac{1}{b}\\frac{1}{\\frac{1}{b} + \\frac{1}{a}} \\\\\n", + " &= \\frac{\\sigma^2_{x'}}{b}\n", + " \\end{aligned}\n", + "$$\n", + "\n", + "We can tie all of this together with\n", + "\n", + "$$\n", + "\\begin{aligned}\n", + "\\mu_{x'}&=x+ \\frac{a}{a+b}(y-x)\\\\\n", + "&= x + \\frac{\\sigma^2_{x'}}{b}(y-x) \\\\\n", + "&= x + g_n(y-x)\\\\\n", + "\\blacksquare\n", + "\\end{aligned}\n", + "$$\n", + "\n", + "where\n", + "\n", + "$$g_n = \\frac{\\sigma^2_{x'}}{\\sigma^2_{y}}$$\n", + "\n", + "The end result is multipying the residual of the two measurements by a constant and adding to our previous value, which is the *g* equation for the g-h filter. *g* is the variance of the new estimate divided by the variance of the measurement. Of course in this case g is not truly a constant, as it varies with each time step as the variance changes, but it is truly the same formula. We can also derive the formula for *h* in the same way but I don't find this a particularly interesting derivation. The end result is\n", + "\n", + "$$h_n = \\frac{COV (x,\\dot{x})}{\\sigma^2_{y}}$$\n", + "\n", + "The takeaway point is that *g* and *h* are specified fully by the variance and covariances of the measurement and preditions at time *n*. In other words, we are just picking a point between the measurement and prediction by a scale factor determined by the quality of each of those two inputs. That is all the Kalman filter is. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#####Exercise:\n", + "Modify the values of `movement_variance` and `sensor_variance` and note the effect on the filter and on the variance. Which has a larger effect on the value that variance converges to. For example, which results in a smaller variance:\n", + "\n", + " movement_variance = 40\n", + " sensor_variance = 2\n", + " \n", + "or:\n", + "\n", + " movement_variance = 2\n", + " sensor_variance = 40" + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Introduction to Designing a Filter" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "So far we have developed our filter based on the dog sensors introduced in the Discrete Bayesian filter chapter. We are used to this problem by now, and may feel ill-equipped to implement a Kalman filter for a different problem. To be honest, there is still quite a bit of information missing from this presentation. The next chapter will fill in the gaps. Still, lets get a feel for it by designing and implementing a Kalman filter for a thermometer. The sensor for the thermometer outputs a voltage that corresponds to the temperature that is being measured. We have read the manufacturer's specifications for the sensor, and it tells us that the sensor exhibits white noise with a standard deviation of 2.13.\n", + "\n", + "We do not have a real sensor to read, so we will simulate the sensor with the following function. " + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "def volt(voltage, temp_variance):\n", + " return random.randn()*temp_variance + voltage" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 21 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We generate white noise with a given variance using the equation `random.randn() * variance`. The specification gives us the standard deviation of the noise, not the variance, but recall that variance is just the square of the standard deviation. Hence we raise 2.13 to the second power.\n", + "\n", + "> **Sidebar**: spec sheets are just what they sound like - specifications. Any individual sensor will exhibit different performance based on normal manufacturing variations. Numbers given are often maximums - the spec is a guarantee that the performance will be at least that good. So, our sensor might have standard deviation of 1.8. If you buy an expensive piece of equipment it often comes with a sheet of paper displaying the test results of your specific item; this is usually very trustworthy. On the other hand, if this is a cheap sensor it is likely it received little to no testing prior to being sold. Manufacturers typically test a small subset of their output to verify that everything falls within the desired performance range. If you have a critical application you will need to read the specification sheet carefully to figure out exactly what they mean by their ranges. Do they guarantee their number is a maximum, or is it, say, the $3\\sigma$ error rate? Is every item tested? Is the variance normal, or some other distribution. Finally, manufacturing is not perfect. Your part might be defective and not match the performance on the sheet.\n", + "\n", + "> For example, I just randomly looked up a data sheet for an airflow sensor. There is a field *Repeatability*, with the value $\\pm 0.50\\%$. Is this a Gaussian? Is there a bias? For example, perhaps the repeatability is nearly 0.0% at low temperatures, and always nearly +0.50 at high temperatures. Data sheets for electrical components often contain a section of \"Typical Performance Characteristics\". These are used to capture information that cannot be easily conveyed in a table. For example, I am looking at a chart showing output voltage vs current for a LM555 timer. There are three curves showing the performance at different temperatures. The response is ideally linear, but all three lines are curved. This clarifies that errors in voltage outputs are probably not Gaussian - in this chip's case higher temperatures leads to lower voltage output, and the voltage output is quite nonlinear if the input current is very high. \n", + "\n", + "> As you might guess, modeling the performance of your sensors is one of the harder parts of creating a Kalman filter that performs well. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now we need to write the Kalman filter processing loop. As with our previous problem, we need to perform a cycle of predicting and updating. The sensing step probably seems clear - call `volt()` to get the measurement, pass the result into `update()` function, but what about the predict step? We do not have a sensor to detect 'movement' in the voltage, and for any small duration we expect the voltage to remain constant. How shall we handle this?\n", + "\n", + "As always, we will trust in the math. We have no known movement, so we will set that to zero. However, that means that we are predicting that the temperature will never change over time. If that is true, then over time we should become extremely confident in our results. Once the filter has enough measurements it will become very confident that it can predict the subsequent temperatures, and this will lead it to ignoring measurements that result due to an actual temperature change. This is called a *smug* filter, and is something you want to avoid. So we will add a bit of error to our prediction step to tell the filter not to discount changes in voltage over time. In the code below I set `movement_variance = .2`. This is just the expected variance in the change of voltage over each time step. I chose this value merely to be able to show how the variance changes through the update and predict steps. For an real sensor you would set this value for the actual amount of change you expect. For example, this would be an extremely small number if it is a thermometer for ambient air temperature in a house, and a high number if this is a thermocouple in a chemical reaction chamber. We will say more about selecting the actual value in the next chapter. \n", + "\n", + "Let's see what happens. " + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "variance = 2.13**2\n", + "movement_variance = .2\n", + "actual_voltage = 16.3\n", + "\n", + "N=50\n", + "zs = [volt(actual_voltage, variance) for i in range(N)]\n", + "ps = []\n", + "estimates = []\n", + "\n", + "kf = KalmanFilter1D(x0=25, # initial state\n", + " P = 1000, # initial variance \n", + " # large says 'who knows?'\n", + " R=variance, # sensor noise\n", + " Q=movement_variance) # movement noise\n", + "\n", + "for i in range(N):\n", + " kf.predict(movement)\n", + " kf.update(zs[i])\n", + "\n", + " # save for latter plotting\n", + " estimates.append(kf.x)\n", + " ps.append(kf.P)\n", + "\n", + "# plot the filter output and the variance\n", + "plt.scatter(range(N), zs, marker='+', s=64, color='r', label='measurements')\n", + "p1, = plt.plot(estimates, label='filter')\n", + "plt.legend(loc='best', scatterpoints=1)\n", + "plt.xlim((0,N));plt.ylim((0,30))\n", + "plt.show()\n", + "plt.plot(ps)\n", + "plt.title('Variance')\n", + "plt.show()\n", + "print('Variance converges to {:.3f}'.format(ps[-1]))" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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0Ehsbe8FjAwMDyc/Pr/Bau3fvrtLvCC78dwgODgao8JwXM378eN577z0efvhhnn32WYYP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\n1Wn06NEaN26cli1bpjVr1igvL0+5ublavXq10tLSdN111wW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AEHAhEzw8XjPYJQAAAAAIkJAJHiUVnmCXAAAAACBAQiZ4nConeAAAAADhiuABAAAAIOAI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\nqUru4FDByQpN+9Nh/fFvJar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+ "text": [ + "" + ] + }, + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Variance converges to 0.858\n" + ] + } + ], + "prompt_number": 22 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The first plot shows the individual sensor measurements marked with '+'s vs the filter output. Despite a lot of noise in the sensor we quickly discover the approximate voltage of the sensor. In the run I just completed at the time of authorship, the last voltage output from the filter is $16.213$, which is quite close to the $16.4$ used by the `volt()` function. On other runs I have gotten up to around $16.9$ as an output and also as low as 15.5 or so.\n", + "\n", + "The second plot shows how the variance converges over time. Compare this plot to the variance plot for the dog sensor. While this does converge to a very small value, it is much slower than the dog problem. The section **Explaining the Results - Multi-Sensor Fusion** explains why this happens." + ] + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "Animation" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "For those reading this in IPython Notebook, here is an animation showing the filter working. The top plot in the animation draws a green line for the predicted next voltage, then a red '+' for the actual measurement, draws a light red line to show the residual, and then draws a blue line to the filter's output. You can see that when the filter starts the corrections made are quite large, but after only a few updates the filter only adjusts its output by a small amount even when the measurement is far from it. \n", + "\n", + "The lower plot shows the Gaussian belief as the filter innovates. When the filter starts the Gaussian curve is centered over 25, our initial guess for the voltage, and is very wide and short due to our inital uncertainty. But as the filter innovates, the Gaussian quickly moves to about 16.0 and becomes taller, reflecting the growing confidence that the filter has in it's estimate for the voltage. You will also note that the Gaussian's height bounces up and down a little bit. If you watch closely you will see that the Gaussian becomes a bit shorter and more spread out during the prediction step, and becomes taller and narrower as the filter incorporates another measurement (the innovation step)." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Think of this animation in terms of the g-h filter. At each step the g-h filter makes a prediction, takes a measurement, computes the residual (the difference between the prediction and the measurement, and then selects a point on the residual line based on the scaling factor *g*. The Kalman filter is doing exactly the same thing, except that the scaling factor *g* varies with time. As the filter becomes more confident in its state the scaling factor favors the filter's prediction over the measurement. \n", + "\n", + "> If this is not clear, I urge you to go back and review the g-h chapter. This is the crux of the algorithms in this book. " + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Exercise(optional):" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Write a function that runs the Kalman filter many times and record what value the voltage converges to each time. Plot this as a histogram. After 10,000 runs do the results look normally distributed? Does this match your intuition of what should happen?\n", + "\n", + "> use plt.hist(data,bins=100) to plot the histogram. " + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Your code here" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 23 + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "Solution\n" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "variance = 2.13**2\n", + "actual_voltage = 16.3\n", + "\n", + "\n", + "def VKF():\n", + " voltage=(14,1000)\n", + " for i in range(N):\n", + " Z = volt(actual_voltage, variance)\n", + " voltage = update(voltage[0], voltage[1], Z, variance)\n", + " return voltage[0]\n", + "\n", + "vs = []\n", + "for i in range (10000):\n", + " vs.append (VKF())\n", + "plt.hist(vs, bins=100, color='#e24a33') \n", + "plt.show()" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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OKog4HA5JktvtltPpDLS73e7ANofDIa/Xq/PnzwfdFXG5XCotLQ177jlz5oym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\n13PPPae/+Iu/0DvvvKO8vLx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+ "text": [ + "" + ] + } + ], + "prompt_number": 24 + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "Discussion" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The results do in fact look like a normal distribution. Each voltage is Gaussian, and the **Central Limit Theorem** guarantees that a large number of Gaussians is normally distributed. We will discuss this more in a subsequent math chapter." + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Explaining the Results - Multi-Sensor Fusion" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**author's note:** I am not overly keen about this explanation. It is true that multiple sensors improve results, but we get good results merely by having an accurate model of the process. I explain this much better in the next chapter. I'll leave this section here while I mull how best to explain this at this stage of learning. For now don't worry if this section is not entirely convincing; it does need work.\n", + "\n", + "So how does the Kalman filter do so well? I have glossed over one aspect of the filter as it becomes confusing to address too many points at the same time. We will return to the dog tracking problem. We used two sensors to track the dog - the RFID sensor that detects position, and the inertial tracker that tracked movement. However, we have focused all of our attention on the position sensor. Let's change focus and see how the filter performs if the inertial tracker is also noisy. This will provide us with an vital insight into the performance of Kalman filters." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "sensor_variance = 30\n", + "movement_sensor = 30\n", + "pos = (0,500)\n", + "\n", + "dog = DogSensor(0, velocity=movement, \n", + " measurement_variance=sensor_variance,\n", + " process_variance=0.5)\n", + "\n", + "zs = []\n", + "ps = []\n", + "vs = []\n", + "\n", + "for i in range(100):\n", + " Z = dog.sense_position()\n", + " zs.append(Z)\n", + " \n", + " pos = update(pos[0], pos[1], Z, sensor_variance)\n", + " ps.append(pos[0])\n", + " vs.append(pos[1])\n", + "\n", + " pos = predict(pos[0], pos[1], movement+ random.randn(), movement_variance)\n", + "\n", + "plt.plot(ps, label='filter')\n", + "plt.plot(zs, linestyle='dashed', c='r', label='measurement')\n", + "plt.legend()\n", + "plt.show()\n", + "plt.plot(vs)\n", + "plt.title('Variance')\n", + "plt.show()" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + 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GfPON+fkyISU+4QyP/nCETIdB99qBjGgSisMwcBjgdJrvOYaB0wnhfh5E+Ktz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\nX6bjpkyZwpQpU1x12/PLsmUwZox5PXiw+Vf5hg3Bz8/MTUlJgaCgmm1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NoSMjI0OSVFhYqKysrNDxwsLC0LkzycnJafU96oOmHtn7uYrrXeo94Ap19lmW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\nMQzJJckwJEMnzhuN55u2fHE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+ "text": [ + "" + ] + } + ], + "prompt_number": 25 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This result is worse than the example where only the measurement sensor was noisy. Instead of being mostly straight, this time the filter's output is distinctly jagged. But, it still mostly tracks the dog. What is happening here?\n", + "\n", + "This illustrates the effects of *multi-sensor fusion*. Suppose we get a position reading of -28.78 followed by 31.43. From that information alone it is impossible to tell if the dog is standing still during very noisy measurements, or perhaps sprinting from -29 to 31 and being accurately measured. But we have a second source of information, his velocity. Even when the velocity is also noisy, it constrains what our beliefs might be. For example, suppose that with the 31.43 position reading we get a velocity reading of 59. That matches the difference between the two positions quite well, so this will lead us to believe the RFID sensor and the velocity sensor. Now suppose we got a velocity reading of 1.7. This doesn't match our RFID reading very well - it suggests that the dog is standing still or moving slowly.\n", + "\n", + "When sensors measure different aspects of the system and they all agree we have strong evidence that the sensors are accurate. And when they do not agree it is a strong indication that one or more of them are inaccurate. \n", + "\n", + "We will formalize this mathematically in the next chapter; for now trust this intuitive explanation. We use this sort of reasoning every day in our lives. If one person tells us something that seems far fetched we are inclined to doubt them. But if several people independently relay the same information we attach higher credence to the data. If one person disagrees with several other people, we tend to distrust the outlier. If we know the people that might alter our belief. If a friend is inclined to practical jokes and tall tales we may put very little trust in what they say. If one lawyer and three lay people opine on some fact of law, and the lawyer disagrees with the three you'll probably lend more credence to what the lawyer says because of her expertise. In the next chapter we will learn how to mathematical model this sort of reasoning." + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "More examples" + ] + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "Example: Extreme Amounts of Noise" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "So I didn't put a lot of noise in the signal, and I also 'correctly guessed' that the dog was at position 0. How does the filter perform in real world conditions? Let's explore and find out. I will start by injecting a lot of noise in the RFID sensor. I will inject an extreme amount of noise - noise that apparently swamps the actual measurement. What does your intuition tell about how the filter will perform if the noise is allowed to be anywhere from -300 or 300. In other words, an actual position of 1.0 might be reported as 287.9, or -189.6, or any other number in that range. Think about it before you scroll down." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "sensor_variance = 30000\n", + "movement_variance = 2\n", + "pos = (0,500)\n", + "\n", + "dog = DogSensor(pos[0], velocity=movement, measurement_variance=sensor_variance)\n", + "\n", + "zs = []\n", + "ps = []\n", + "\n", + "for i in range(1000):\n", + " pos = predict(pos[0], pos[1], movement, movement_variance)\n", + " \n", + " Z = dog.sense_position()\n", + " zs.append(Z)\n", + " \n", + " pos = update(pos[0], pos[1], Z, sensor_variance)\n", + " ps.append(pos[0])\n", + "\n", + "\n", + "p1, = plt.plot(zs, c='r', linestyle='dashed', label='measurement')\n", + "p2, = plt.plot(ps, c='#004080', label='filter')\n", + "plt.legend(loc='best')\n", + "plt.show()" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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57fffSQR99hlQrRpte/lS+t3Li44TqaltxGvtisYwDMMwTC7h3Lmc7gGTWxA1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\nx4b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H68qNA1vYBOt/szM1q1ezZK1WLRpQZIYIueeeC/w3a+MWFqEIDa+SPyHUOTpxcTnX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\nREcDBQtyP44cAVau5OtLlhgxk1Vr5ipVgE2b/K/XcJP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+ "text": [ + "" + ] + } + ], + "prompt_number": 28 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In this example the noise is extreme yet the filter still outputs a nearly straight line! This is an astonishing result! What do you think might be the cause of this performance? If you are not sure, don't worry, we will discuss it latter." + ] + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "Example: Bad Initial Estimate" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "Now let's lets look at the results when we make a bad initial estimate of position. To avoid obscuring the results I'll reduce the sensor variance to 30, but set the initial position to 1000m. Can the filter recover from a 1000m initial error?" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "sensor_variance = 30\n", + "movement_variance = 2\n", + "pos = (1000,500)\n", + "\n", + "dog = DogSensor(0, velocity=movement, measurement_variance=sensor_variance)\n", + "\n", + "zs = []\n", + "ps = []\n", + "\n", + "for i in range(100):\n", + " pos = predict(pos[0], pos[1], movement, movement_variance)\n", + " \n", + " Z = dog.sense_position()\n", + " zs.append(Z)\n", + " \n", + " pos = update(pos[0], pos[1], Z, sensor_variance)\n", + " ps.append(pos[0])\n", + "\n", + "plt.plot(ps, label='filter')\n", + "plt.plot(zs, c='r', linestyle='dashed', label='measurement')\n", + "plt.legend(loc='best')\n", + "plt.show()" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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H6TkGGdkOMnIcJGU5mLH2KACPdQjh4ppO2qukGlEwEREREZGqZdo0eO89eO45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+ "text": [ + "" + ] + } + ], + "prompt_number": 29 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Again the answer is yes! Because we are relatively sure about our belief in the sensor ($\\sigma=30$) even after the first step we have changed our belief in the first position from 1000 to somewhere around 60.0 or so. After another 5-10 measurements we have converged to the correct value! So this is how we get around the chicken and egg problem of initial guesses. In practice we would probably just assign the first measurement from the sensor as the initial value, but you can see it doesn't matter much if we wildly guess at the initial conditions - the Kalman filter still converges very quickly." + ] + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "Example: Large Noise and Bad Initial Estimate" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "What about the worst of both worlds, large noise and a bad initial estimate?" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "sensor_variance = 30000\n", + "movement_variance = 2\n", + "pos = (1000,500)\n", + "\n", + "\n", + "dog = DogSensor(0, velocity=movement, measurement_variance=sensor_variance) \n", + "zs = []\n", + "ps = []\n", + "\n", + "for i in range(1000):\n", + " pos = predict(pos[0], pos[1], movement, movement_variance)\n", + " \n", + " Z = dog.sense_position()\n", + " zs.append(Z)\n", + " \n", + " pos = update(pos[0], pos[1], Z, sensor_variance)\n", + " ps.append(pos[0])\n", + "\n", + "plt.plot(zs, c='r', linestyle='dashed', label='measurement')\n", + "plt.plot(ps, c='#004080', label='filter')\n", + "plt.legend(loc='best')\n", + "plt.show()" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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R3bfyo0oV4JlngMaNgW3brC9sunYl97ZnnqE4D2sJm/zu27FjtBVZYydPJtcx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\nvPbNGnxeojo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RA1P7pqhjI0Shdm3WgFmpFXl7O54XVe63WTPKJcfFcXzWrWNKlztFylbF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\no6m7+OjResnlBQuMneG7d9fzUlQD10rYWHlsDh6kMCU2Xvz89P0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zv5tx44xhVdu26d4j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+ "text": [ + "" + ] + } + ], + "prompt_number": 30 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This time the filter does struggle. Notice that the previous example only computed 100 updates, whereas this example uses 1000. By my eye it takes the filter 400 or so iterations to become reasonable accurate, but maybe over 600 before the results are good. Kalman filters are good, but we cannot expect miracles. If we have extremely noisy data and extremely bad initial conditions, this is as good as it gets.\n", + "\n", + "Finally, let's make the suggest change of making our initial position guess just be the first sensor measurement." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "sensor_variance = 30000\n", + "movement_variance = 2\n", + "pos = None\n", + "\n", + "dog = DogSensor(0, velocity=movement, measurement_variance=sensor_variance)\n", + "\n", + "zs = []\n", + "ps = []\n", + "\n", + "for i in range(1000):\n", + " Z = dog.sense_position()\n", + " zs.append(Z)\n", + " if pos == None:\n", + " pos = (Z, 500)\n", + " \n", + " pos = update(pos[0], pos[1], Z, sensor_variance)\n", + " ps.append(pos[0])\n", + "\n", + " pos = predict(pos[0], pos[1], movement, movement_variance)\n", + "\n", + "plt.plot(zs, c='r', linestyle='dashed', label='measurement')\n", + "plt.plot(ps, c='#004080', label='filter')\n", + "plt.legend(loc='best')\n", + "plt.show()" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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AaCiJO2vx0Udkqdi5kybvmzYBn39Ok/xZs6R2crez5s3pviQkkEixsyMLiTzh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\nxUiCFXQDv1w5ICUF5wNCEf3eT1izIxZFXCnoe2Enfnq5Bc4uGow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ByeXL8nr2rG2vY0yl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+ "text": [ + "" + ] + } + ], + "prompt_number": 31 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This simple change significantly improves the results. On some runs it takes 200 iterations or so to settle to a good solution, but other runs it converges very rapidly. This all depends on whether the initial measurement $Z$ had a small amount or large amount of noise. \n", + "\n", + "200 iterations may seem like a lot, but the amount of noise we are injecting is truly huge. In the real world we use sensors like thermometers, laser rangefinders, GPS satellites, computer vision, and so on. None have the enormous error as shown here. A reasonable value for the variance for a cheap thermometer might be 10, for example, and our code is using 30,000 for the variance. " + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Exercise: Interactive Plots" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Implement the Kalman filter using IPython Notebook's animation features to allow you to modify the various constants in real time using sliders. Refer to the section **Interactive Gaussians** in the Gaussian chapter to see how to do this. You will use the `interact()` function to call a calculation and plotting function. Each parameter passed into `interact()` automatically gets a slider created for it. I have built the boilerplate for this; just fill in the required code." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from IPython.html.widgets import interact, interactive, fixed\n", + "import IPython.html.widgets as widgets\n", + "\n", + "\n", + "def plot_kalman_filter(start_pos, \n", + " sensor_noise, \n", + " movement, \n", + " movement_noise,\n", + " noise_scale):\n", + " # your code goes here\n", + " pass\n", + "\n", + "interact(plot_kalman_filter,\n", + " start_pos=(-10,10), \n", + " sensor_noise=widgets.IntSliderWidget(value=5, min=0, max=100), \n", + " movement=widgets.FloatSliderWidget(value=1, min=-2., max=2.), \n", + " movement_noise=widgets.FloatSliderWidget(value=5, min=0, max=100.),\n", + " noise_scale=widgets.FloatSliderWidget(value=1, min=0, max=2.))" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "pyout", + "prompt_number": 32, + "text": [ + "" + ] + } + ], + "prompt_number": 32 + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "Solution" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "One possible solution follows. We have sliders for the start position, the amount of noise in the sensor, the amount we move in each time step, and how much movement error there is. Movement error is perhaps the least clear - it models how much the dog wanders off course at each time step, so we add that into the dog's position at each step. I set the random number generator seed so that each redraw uses the same random numbers, allowing us to compare the graphs as we move the sliders." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "def plot_kalman_filter(start_pos, \n", + " sensor_noise, \n", + " movement,\n", + " movement_noise):\n", + " n = 20\n", + " zs = []\n", + " ps = []\n", + " \n", + " dog = DogSensor(start_pos, velocity=movement, measurement_variance=sensor_noise)\n", + " random.seed(303)\n", + " pos = (0., 1000.) # mean and variance\n", + "\n", + " for _ in range(n): \n", + " move_error = random.randn()*movement_noise\n", + " dog.x += move_error\n", + " \n", + " z = dog.sense_position()\n", + " zs.append(z)\n", + "\n", + " pos = update(pos[0], pos[1], z, sensor_noise)\n", + " ps.append(pos[0])\n", + "\n", + " pos = predict(pos[0], pos[1], movement, movement_noise)\n", + "\n", + " plt.plot(zs, c='r', linestyle='dashed', label='measurement')\n", + " plt.plot(ps, c='#004080', alpha=0.7, label='filter')\n", + " plt.legend(loc='best')\n", + " plt.show()\n", + "\n", + "interact(plot_kalman_filter,\n", + " start_pos=(-10, 10), \n", + " sensor_noise=widgets.FloatSliderWidget(value=5, min=0., max=100), \n", + " movement=widgets.FloatSliderWidget(value=1, min=-2., max=2.), \n", + " movement_noise=widgets.FloatSliderWidget(value=.1, min=0, max=.5))" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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N/doyrEdrfL31sdaV6L+GiIiIiFy8OgoYlVU2lm3I4rNlW9l3+AQAYcH+jOnf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\nRzN+/HieeeYZSkpKuOGGG9zx9CIiIiIi4kXcEjJmzZpFZWUlCxcupLi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+ "text": [ + "" + ] + } + ], + "prompt_number": 33 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Exercise - Nonlinear Systems" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Our equations are linear: \n", + "$$\\begin{aligned}new\\_pos &= old\\_pos+dist\\_moved\\\\\n", + "new\\_position &= old\\_position*measurement\\end{aligned}$$\n", + "\n", + "Do you suppose that this filter works well or poorly with nonlinear systems?\n", + "\n", + "Implement a Kalman filter that uses the following equation to generate the measurement value for i in range(100):\n", + "\n", + " Z = math.sin(i/3.) * 2\n", + " \n", + "Adjust the variance and initial positions to see the effect. What is, for example, the result of a very bad initial guess?" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#enter your code here." + ], + "language": "python", + "metadata": {}, + "outputs": [] + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "Solution" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "sensor_variance = 30\n", + "movement_variance = 2\n", + "pos = (100,500)\n", + "\n", + "zs, ps = [], []\n", + "\n", + "for i in range(100):\n", + " pos = predict(pos[0], pos[1], movement, movement_variance)\n", + "\n", + " Z = math.sin(i/3.)*2\n", + " zs.append(Z)\n", + " \n", + " pos = update(pos[0], pos[1], Z, sensor_variance)\n", + " ps.append(pos[0])\n", + "\n", + "plt.plot(zs, c='r', linestyle='dashed', label='input')\n", + "plt.plot(ps, c='#004080', label='filter')\n", + "plt.legend(loc='best')\n", + "plt.show()" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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7ga+ALjWzh7XB7GGtIRSJMeT3gzh165nc70HkLyAoEsH3Y1DZzBDzR7djHQ5M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\n7MJdDH3xtWb+yFZoVM16DxArnYO9LRaMolLdaauPYcrKw2a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MF0jdRcf79tEX9EuXANts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\na2iQFwR1d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+ "text": [ + "" + ] + } + ], + "prompt_number": 34 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "######Discussion\n", + "\n", + "Here we set a bad initial guess of 100. We can see that the filter never 'acquires' the signal. Note now the peak of the filter output always lags the peak of the signal by a small amount, and how the filtered signal does not come very close to capturing the high and low peaks of the input signal.\n", + "\n", + "If we recall the g-h filter chapter we can understand what is happening here. The structure of the g-h filter requires that the filter output chooses a value part way between the prediction and measurement. A varying signal like this one is always accelerating, whereas our process model assumes constant velocity, so the filter is mathematically guaranteed to always lag the input signal. \n", + "\n", + "Maybe we just didn't adjust things 'quite right'. After all, the output looks like a sin wave, it is just offset some. Let's test this assumption." + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Exercise - Noisy Nonlinear Systems" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Implement the same system, but add noise to the measurement." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#enter your code here" + ], + "language": "python", + "metadata": {}, + "outputs": [] + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "Solution" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "sensor_variance = 30\n", + "movement_variance = 2\n", + "pos = (100,500)\n", + "\n", + "zs, ps = [], []\n", + "\n", + "for i in range(100):\n", + " pos = predict(pos[0], pos[1], movement, movement_variance)\n", + "\n", + " Z = math.sin(i/3.)*2 + random.randn()*1.2\n", + " zs.append(Z)\n", + " \n", + " pos = update(pos[0], pos[1], Z, sensor_variance)\n", + " ps.append(pos[0])\n", + "\n", + "p1, = plt.plot(zs, c='r', linestyle='dashed', label='measurement')\n", + "p2, = plt.plot(ps, c='#004080', label='filter')\n", + "plt.legend(loc='best')\n", + "plt.show()" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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4ZkhNtWI5yZAm1Xv7BIWE49p9IVfuvaB73WLM71/nq9oS8jRRJIwvva7uPgkg\nd9vZRERGcW5xDwrmzJCA0X3coxeBVB2wikt3nuGcNS0HfmuHg72NKrGID/ua96x1+y/Q1n0znd2+\n4/efase7l/9FwGuqDlyF9/XHAJiZ6vi+cHZql8pN7VK5cXqzFpdI+mr0W8Qe74f0alCcOX3dErSt\ng963qT1kLa9DI+hWpygLBtRN0PaEOgzdA6IbPXr06G8+yxcICwuL/Vqv//RiOJZ6U1pVKYjPraec\nu/GEtft9UBSFLlO38tgviOJ5M7N/WvvYijDvcsyQGreSufE46suFW0/Zc+oGDcvlxeoTvRcRkVH0\nnb2LkcsOEh2t8FOTkqwY0vCTx3yOnbUFFQo5Usgpw0d7TsxMdZQrmI1lu7w5efkBBXKkxyW7VNL6\nGg8fPiRz5sxqhyGSmS+9rgbO38Mp34e0rFyAHxoUT8DIPs3a0pxm37uwx+sGl24/w+OfKzQom+eT\nE+FF4vrSayssPJK6w9YTEBzG6auPuHrfj/pl86DTfjoJeTf5yJnZjjxZ03H3aQA3Hvqz6+R1Zv11\nkvUHfLj1yJ90NpYfHPYskgbfu88ZsOAApiZa/hjVFFurhP19z54xNeUKZGXDwYucuPyAorkzfbYI\nj0h6vuT+PT6MOgGBmEW6mn7vwlP/YE5cfoCn921CwyNpWD4vW8a3/OTkygxpUtG4Qj62HbvKpTvP\n8DjqS+DrMLyvPeby3efceODH/WeveBbwmqf+wbQZ/xd/HrqEmamOxYPq8Uurcok2njFjmlSktjJn\n58nr7Dl1gxaVC8hNwlcwtgTk0YtANnhexCmzHXozo6r5IL7Al1xX1+6/oMuUrWg1Gv4c3Yy0Ks+9\nsNKb0ez7/Hh63+LirWdsOnKZumXyfHWvrjCsL33PWrj1NOsP+JAjU2qioqM5c/UR5248oWH5vJh8\npCfE71UI1QbFJB+5s6Th8IyO9Gtaih/qF6dgzvSYmep48DyQB88DOXbpPot3nCV/dnt5EJZE9Z+7\nm3M3ntDF7TtaVyuUKG1mz5iaVHozdp26waFzt+nsVlQ+85IZQycgRj0E612KouC+5gjjVx+hV4Pi\nTOxaNd7dzk/8gqj585rYbudPyZQ2FZt/bZ7ga4l8iKIoNBi+gS3/XqF0/iwcmtEBU5P4lSEWMYxp\nCNblO8+oPmg195+9wjlrWv4a0+y9oYIiafiS66r1uL9Yu/8CnWoVYcng+gkcWfwFBIXi9sta/r14\nj0xpU3HqA/5JAAAgAElEQVRgWnvyylNK1X3JtRUaHkmu1rN48DyQjaObki2DLTUGr8Y/MJSqxXLi\nMbb5ez32fq9CqDpwJWevxSQfB6d3+GDvRmRUNP/63GPFbm+W7vTGRKfFY2xzWU8mibl85xkFO80D\n4PqaPmTPmDrR2o6KiqZ832Ucu3jf6N7/xLdLUUOw3qXRaKhQyJFfWpajRolcX9QzkcrCjFZVCpIp\nTSqK5MpAYaeM5MtmT87Mdjiks8be1gobK3PK5M/KlvEtVVtIUKPRUN01J2v2XeDSnedERUdTpWhO\nVWJJqhKiByQqKpobD/1IY20R77LOJy7dp8rAVTzxD8bcVMdT/2CW7z5Hrsx2UuksCYrvdeVz6ym9\nZm7H1ETLpjHNjKoXU29mQvNK+Tl+6T4Xbj7l2MX7dKtTVNYfUtmXvGfN3+LFBs+LFMqZgRm9a5LF\n3ga3krn568hlLtx8yqFzd2hcIV/sk2e/VyFUG7gqNvnwnNb+o3OAtFoNjhlTU69MHoJCwvnH5x6b\nDl+mtEuWDw5zFsZHURRajfuLGw/9aVgyG90bGK70bnxotRrKFsjG4u1n8LryiLIFsuKUWeYVJReG\n7gExyipYn/K1JXVtrMzp07gkE7pWZU5fN1YMacBfvzZn32/tODGvC5eW9+Lv8S1UH/ea1taStcMb\no9VqmLD2KPtP31Q1npQuPCKKusPW4dx2Dm6/rOXGA7/PHrP75HUqD1iJ36sQ6pR25sGf/WlTrRCv\nQyNoMXYT/efuJiIyKhGiF4ltxFJPFAW61y2GYyI+eYyvVBZmbHNvRVobC85ce4TXlYdqhyTiKTQ8\nkglrYxamHN2hYuxDuII5M3B4ZkeyprfhH597VBmwkucBr2OTjzPXHpHL4dPJx7s0Gg1TelSjZz1X\nwiKiqDd8Pf9cuJugr00YxuYjvuw7fRM7az09a+ZRJYa82dIxqn1FALpO3SqV1sRHJbkEJCWoUNiR\nEW0roCjQxn0zT/2D1Q4pRYqKiqbN+L/YeeI6ALtOXqdAp3mMX334o6Wd1x/woe6wdbwOjaBd9cL8\n9WvMHICVQxowu08tTHRapm88TrWBq3giZVGTlVO+D/A46ouFuQnD2lRQO5yPstSb0qFmEQAWbjut\ncjQivhZuPc3D54EUyZWRBuXyxvmec9a0HJnZEafMdpy++oiKfZfHTT6mxy/5eEuj0TCnrxvtaxTm\ndWgEbkPWclqSVaP2OjSC/r/vBmBcp8qktvr64jnfamDzMnyXOyN3ngQwZNE+1eIQxk0SECM1vG0F\nyhfKxmO/IPrO2aV2OCmOoij0mL6NP99ZZ6ZNtUKEhkcyfIknRbou4KD37TjHzN18klbjNhERGc2A\nZqVZ9nP92Dk8Go2G3g1LcHB6ezKlTcWhc3co2n0hxy/dV+HViYQwfIknAD82LEHGD5TbNibd6hQD\nYN1+H14Fh31mb6G2kLCI//d+tK/4wWFzjhlTc2RWR/Jnt+fSnWecufYIp8x2eE5vT5avKL2s1WpY\nPKgeTSu68Co4jOqDV+Nz6+k3vxaRMCav/4c7TwIo7JSB7nWLqRqLqYmOpYPrY6LTMmfzKY6cv6Nq\nPMI4SQJipEx0WlYNaYi5qY71B3w4F48J9MIwFEVh0Py9LN5+Fr2ZCdvcW1KzRC5WDW3I/t/a4Zw1\nLb53n1Op3wravemhGrXMk96zdqIoMKlbVab0qPbBeUplC2bj9IJulCuYjYfPA6nQdxlLtp9R4VUK\nQzp87g57vG5gY2XO4BYJs+iXITlnTcv3RbITHBrB2v0X1A5HfMaCrad57BdE0dyZqFf240NrMqW1\n5uCMDlT6LjtFc2fi4IwOX5V8vGWi07J6WCPqlHaOmcw+YCVX77346vOJhHH78UsmrfsHgNl9an31\nUHVDKpIrI7+0inkv7DxlCyFhssiyiEv9q1R8lGPG1PSsH1MdZfhST5WjSTnc1xzhtz+OYaLT8tev\nzShfyDH2e5WL5uD84h782vF7zE11rNp7nmzNp/PrysNotRqWDKrH4JZlPzmxN1Naaw5Ma0ffxiWJ\niIym+7RtMhY/CVMUhWFLDgDQv2kp1cvuxle3OkWBmJvbRC6GKL7A69AIJr4z9+NzRQPS2VpyYFp7\nvBZ0/abk4y0zUx1/jm5KlaI5eOIfTJUBK7nz+OU3n1cYTv/fdxMaHkmrKgXjfF6pbXibCrg42nPt\nvh+jlx9UOxxhZCQBMXJDWpXHSm/KtmNXOXbxntrhJHtzNp9k+BJPNBpYM6wRtUrmfm8fczMTRrSr\niM+yH6ju6kRYRBTmpjo2jWlGJ7fv4tWOqYmOGb1r0q9JKaKiFTpO+vuj80qEcdt96gZHL9wlrY0F\n/ZokbtWZb9GwfD7S2ljgff0xp68+Ujsc8RHzt3jxxD8Y1zyZqfMFJXENWd1Mb2bC3+NaULZAVu4/\ne0WrcX8RHS1JqzHY63WDzUd8sdKbMrl7VbXDicPczISlg+uh1WqY+scxTvk+UDskYUQkATFy6e2s\n+KlJKYDYp6wiYazee54fZ+0EYEH/OjSrlP+T++dySMOuya3ZO7UtXgu6vTcxND7Gda5MLoc0+Nx6\nivuaI18Vt1CPoigMf/N7+XPLsthYmascUfzpzUxoX6MwAAu2eqkcjfiQ4JBwJq2PGVozpsP3qpZM\ntrIwY6t7SzKlTcW/F+8x7+9TqsUiYoRHRNFndswc0RHtKnxRoYHEUtIlC/2alCI6WqHzlC2ER0gF\nSBEjwRKQCRMmoNVq+fHHHxOqiRRjYPMypE6lx/PsbSnLm0D+PupLh4keAEzpUY2udeI3iU+j0VC1\nWM6vXtvDUm/KkkH1AHBfczRei2UK47Ht2FVOX31ExjSp6NWghNrhfDGZjG7c5m3x4ql/MCXzOVCr\nZC61w8HO2oI5fdwA+GXRfu49DfjMESIhzd58At+7z8mdJQ0/NS6ldjgf9WvHSuRySMOFm09lKJaI\nlSAJyPHjx1m0aBGFChWSRa4MIHUqPYNblAFg6OIDMl7bwP65cJfmv24kKlphWJvyDGxeJlHbr1DY\nkd4NixMZFU3HSX/LGiFJyMxNJwAY2Lw0lnpTlaP5cnmypaNiYUeCQyNYJ5PRjUpwSDiT3/R+jFa5\n9+NdjSrko1H5fASFhPPDjB3yeaSSRy8CGbPiEAAze9fE/M3ik8bIUm/Ksp/ro9VqmLjuKJ5nb6kd\nkjACBk9AAgICaNOmDcuWLcPOTlZPNZQ+jUqS3s6Kk74P2PrvVbXDSTauP/Cj/vD1hEVE0aNeMcZ2\nqqRKHBO6ViV7xtR4X38cW81EGDefW0/Zf+YWVnpTOrsVVTucr/a2F2ThNqnGZkzmepzi2cvXlHLJ\nQo3iTmqHE8fsPrWwtTJn27GrbPC8qHY4KdIvC/cT+DqcumWcPzhX0diUK5iN4W3KoyjQ1n0zLwJe\nqx2SUJnBE5Bu3brRtGlTKlasKE9GDMjKwoxhrcsDMHzpAZkAaAAvAl7j9ssaXrwKwa1kbmb3cVPt\nKWMqCzMWD6wLwK8rD3FR6u0bvVlvej/a1yhM6lR6laP5eo0q5CONrIxuVIJCwpmy4V9A/bkfH5I5\nnTVTelQDoM/snXIzmcj+9bnHyj3nMDfVMf2HGmqHE28j2lWkTP6sPHgeSNfftso9Ygpn0ARk0aJF\n3Lx5k3HjxgGGrcIhoHvdYmRNb8OFm0/Z4OmjdjhJWmh4JA1GbODafT+K5MrIhlFNMFG5dnqVYjnp\nVqcoEZHRdJz8N5FR0arGIz7uRcBrVu87D8CPjUqqHM230ZuZ0L56zGT0hVtlZXRj8LvHKZ4HvKZ0\n/ixUc82pdjgf1NmtKBULO/Ls5WsGzNujdjgpxmO/IFqN2wTAoBZlcHJIo3JE8Wei07JmeCNsrMzZ\nfMSXRdLrmqJpFAOloFeuXKF8+fIcPXoUZ+eYUoHff/89BQsWZPbs2bH7BQT8f9LatWvXDNF0ivL3\nybuM+/MCWdNZ8sfAiqrfNCdF0dEKI9d5s9v7Ielt9Sz7sSzpbY3jCXZQaAQtfjvMk5eh/OiWl3aV\njGvohYixwvMGc3b4UsrZntldk97k8/+6/TSIplMOYWGmY+eIqljpjXc8eXIXEh5JfXdP/IPDmdWl\nBKXz2Ksd0kfdfRZMy2mHCY+MZk7XEpR0Nt5Yk4Pg0Eh6zD+G74NXFMiWmnk9SqE31akd1hfb4/2Q\nYWvOYm6qZWXfcuTMYK12SCIecuf+/1A/W1vbbz6fwT5ljh07xvPnz8mf//+lS6Oiojhy5AgLFiwg\nODgYU9O4kzRdXV0N1XyKUeS7omw49oBr9/3weW5Cl9pJd+x5QvDy8vrsdTV8yQF2ez8klYUZe6a2\np3CujIkUXfysMLOn5s9rWLj3Gj80r0LebOnUDinFe/e6ioyKptGUmJLJIztVw9XV+Mdff44rUGH3\nbQ6fv8MVf1O61Y1fFTjx7f77njV1w7/4B4dTMp8DvVvVNOqRBK7AGH8dQxbt57dtV7mwpApWFmZq\nh5UsRURGUW/YenwfvCKXQxoOzOyEfWqrj+4fn89Ctbi6wtXn0azYfQ73zVc4/nsX9EY8iV7EeLcD\nwRAM9vi8YcOG+Pj4cO7cOc6dO4e3tzeurq60bNkSb2/v95IP8XVMdFp+7RgzUXrMikOEyuJ1X2Tp\njrOMX30EnVbDn6ObGl3yAVCjRC461ixCWEQUnSb/TZQMxTIqHkd9uff0Fc5Z01KjuPqlUQ3l3ZXR\nhTqC35n7Mar951c9NwYDmpWmSK6M3Hr0kpHLPNUOJ1lSFIWe07ez6+R10tlasnNS608mH0nB7D61\nyOWQhnM3njBk0T61wxEqMFgCYmtri4uLS+yf/PnzY2lpiZ2dHS4uLoZqRgDNvs9PoZwZuP/sFQu2\nyAJi8bXv9E26T9sGwNy+btQsYbw3j9N61SBT2lQcu3ifJTvOqh2OeMfb0rs/NiyBVmv8N4jx1bii\nC3bWes5ce8RpmYyuivlbY9b9KJHXwajfn95laqJj8cC6aLUaZmw6IatdJ4CxKw+zZMdZLMxN2Obe\nklxJaN7Hx1hbmrN2eCNMdFpmbDzBzhMyJD+lSdAJBBqNJkk8wUlqtFoN4zrH9IKMX3OEoJBwlSMy\nfhduPqHxqD+IjIpmUPMydK9nnF3Tb6VOpWfam+omE9YelbVBjMSZq484euEuNlbmsauIJxfvroy+\ncJv0giS216ERTF6ftHo/3iqWJzP9m8asdt1h4t9Sxc+Alu08y6jlB9FqNawf0YSSLlnUDslgiud1\niL2X6TDpb574BakckUhMCZqAeHp6MmvWrIRsIsWqU9qZ0vmz8Ozla6a+6bIXH7b75HXK91nGq+Aw\nmlR0YWK3qmqHFC9NK7qQJ2tabj9+ybr9UvXMGLzt/ehc6zusLc1Vjsbw3q4Jsna/D4GvZWX0xLTg\nTe+Ha57MRrHq+Zca06ESubOk4dKdZxTsPI8OEz248/il2mElabtPXqfr1K0AzOlTi3pl83z7SZ88\ngWXLIMo4HmoNal6Wyt/l4Kl/MO0nesgSAymIlFBKojQaDZO7x9Rhn7LhXx69CFQ5IuOjKAozNx7H\nbchaAoLDaFQ+HyuHNEgyw2Z0Oi2/tCoHxPSCyBuzup74BbHe0weNBno3TPqVrz4kn6M95QtlIygk\nnNHLD6odTooREpZ0ez/estSbcnRWJ3o1KI5Oq2XF7nM4t5tDv7m7eC7rhHyxs9ce0WT0n0RFK/zc\nsiw96xc3zIldXaFTp5gkxAhotRpWDmlAWhsLdp+6wfjVh9UOSSQSSUCSsHIFs9GgXF5eh0bIzcJ/\nhEdE0e23rfw0dzfR0Qoj2lbgz9FNsTBPWsUQWlctSLYMtvjefc7mI5fVDidFW7D1NOERUdQtnYec\nme3UDifB/NazOjqthml/HufAmVtqh5MiLNx6msd+QRRzzkTtUkm3qlp6Oyvm9HXDd0UvWlUpSHhE\nFDM2niBnq5mMXXlIhgvHk+/d57j9spagkHBaVSmIe5cqhjlxcDDcvx/z9alThjmnATjY27BmWCM0\nGhi1/CB7vW6oHZJIBJKAJHETu1ZBp9WweMdZLt1+pnY4Cepfn3t0nbqF1XvP8zIo9KP7PQ94TbWB\nq1i8/Sx6MxPWj2jMr50qJZmej3eZmugY3LwMEDPfR1aOVUdEZDTz3hR86Ns4aS88+DnF8zowsl1F\nADpM8vjk75r4dqERUUxa/w8AI9slzd6P/3JySMOa4Y04u6g7NUvkIvB1OCOXHcSp9SwOet9WOzyj\ndubqI8r3WcZjvyAqf5eDpYPrGe6za+/e/38daly/1zVK5GJU+4ooCrQcu4l7Tw1b8lUYH0lAkrg8\n2dLRrU4xoqMVfl6YvEvZ9Ru7lsXbz9LWfTPpG06h1s9rWLz9DM9eBsfuc/1xIMV7LOLw+TtkTmfN\nkVkdaV65gIpRf7tObt+Rwc6Ks9ces/uUPBlSw77zj3jsF0SBHOmp9F12tcNJcEPblKdEXgfuPX1F\n75k71A4nWfM4cZdHL4L4LndG6pZxVjscgyqSKyM7J7XGc3p7SuZz4Kl/ML1m7JAHKR9x9MJdKvVf\nwfOA19QskYut7i0xN+T6GBkzQsWK0LQpTJ5suPMayIi2FalR3IkXr0JoOvpPwiOMY56KSBiSgCQD\no9pXJJWFGduOXU22T5ee+AVx8mko5tGRfG8VQVS0wq43E/QyNv6NSv1WMHKpJ53n/MPtxy8pnjcz\np+Z1xTVPZrVD/2YW5qYMaFYagPGrj8T7uBcBr+WD3gAURWH90ZihSH0alUgWT6g/x0SnZdXQhljq\nTVmz7wIbDkgRhIQQGh7JSs+YhwrJpffjQ74vkp0jszqSOZ01l+48Y78M7XvP7pPXqT5oFa+Cw2ha\n0YW/x7XAUm/gIcOlSsHBg/DHH5Ahg2HPbQBarYbVwxqRNb0NJy4/YOC8PWqHJBKQJCDJQIY0qfi5\nZVkABs3fmywnK+94UyO8sv8tPIvA400DWDSwLjVL5EKn1XDQ+zZjVx3mdVgULSoX4NCMDmROZ61y\n1IbTo54rdtZ6jl64y+Fzdz65r6Io9Jm1k3QNplBt4CrOXH2USFEmT8cv3efSvQDS2FjQumohtcNJ\nNM5Z0/Jbz+oA9JyxnQfPXqkcUfKzePsZnr0Ko7BTBuobosKRETM10dHzTfnzWX+dUDka47Lp0CXq\nDltHSFgknWoVYd2IxpiZ6tQOSxXpbC3ZOLoZpiZaZm8+yXp5+JFsSQKSTPRrUopMaVPhdeUhGzyT\n3y/stmMxCUidF1fBxAT71FZ0qV2UnZNa83TzIFYNbUjzSvn5qU4+1g5vlOQmm3+OtaU5fRrFzD1w\nX/PxXhBFUeg3dzezN58EYP+ZWxTrvpC27pulJOZnKIrC84DXHLt4j1V7zjFyqSetxm6i5dhNQMxK\n4QZ/ImnkutcthlvJ3PgHhtJx8t/J8uGGWsLCI5m49iiQvHs/3tWtTjHMTHVsO3aVGw/81A7HKCzf\n5U2zXzcSERlNvyalWDyoHjpdyr41K5HPgRm9agLQZcqWZD+/VU2vQyPYd/omw5ccoGzvpQxbvD/R\n2tYoiTxGIyDg/xOLbG1tE7PpZG/J9jN0mbqV7BlT47uil2HHjqooLDySdA2mEBQSzu1j03Hs0gbm\nzPngvl5eXri6Gvcig1/L71UIji1mEBQSzqn57w8vUxSFwQv2MnXDMUxNtKz4pQGnrz5i9uaThEdE\nYW6qo0+jkgxtU57UqfQqvQrjc//ZK1qN28T5G08ICP7w2hdW5ib4rvqRLPY2iRyd+h77BVGg4++8\neBXCrB9r8mOj5D0JP7EMX3KA8auPkCujNVfW9EuSRTK+RoeJHqzYfY6fmpRk+pubzJRq1qYT9J2z\nC4DRHSoaNBFN6p+FiqLQZvxm1u6/QD7HdJyc15VUFmZqh5XkhYZH8s+Fu3h63+ag921O+j4gIjI6\n9vsl8jpwYl6XDx5r6Pv3lJ1mJzMdahYhf3Z7bj9+yVwP4ymx960On79DUEg4BdOY4aiLgBQ6ryGN\njUXsEIb/9oIoisLQxfuZuuEYJjotG0c3o2WVgkztWR3fFb1oWbkAYRFRTNnwL06tZzFj43GZ4PeG\n++ojHDl/l4DgMKwtzSiaOxPNK+VnWJvyLPu5PkdndWTrsMopMvkAyJgmFQsH1AVg8IJ9XL4jTyO/\n1YyNxxm/+gharYa+dfKlmOQDiO3JXbrTO0Uvdum++khs8jG9Vw1Gtf8+RfSCxZdGo2HhgDq4ONpz\n+c5zuk7dKnMav0FUVDRLtp/BqfUsqg5cxfjVR/jH5x5R0QrFnDMxoFlptrm3ZM+UNokWkyQgyYhO\np41dnHDc6sP4B4aoHJFhbD/+ZvhVzeIxdcznzlU5IvX0a1oKc1Mdm4/4xumWHrXsIBPX/oNOq2HD\nyCZxVszNkcmOtSMac3JeFyoWdsTvVQj95u6meI9FyeYa+VrPXgazbJc3AKfmdyVg2y+cXtiN9SOb\nMK5zZTrULELZgtmwtkhZQ6/+q1GFfHSoWYTQ8EjajN8syes3WLL9DP3m7o75elA9SuWxVzmixFXU\nORPlCmbjVXAYK3efUzscVUxad5RhSw6g0cRcAz81KZWwDU6eDPXrwz8x5Z754w/Ilw+GDk3Ydr+R\nlYUZm35tRioLM9Yf8GGD50W1Q0pyFEVhx/FrFO4yny5Tt/LweSD5HNMxoFlptrq35MXfg/Fa0I2p\nPatTu7Qztok4OkISkGSmVslcVP4uB/6BoZ+cK5BUKIrC1mNXAahTOnlP0oyPTGmt6ez2HRCzOjrA\n2JWHGLvqMDqthnUjGtOoQr4PHls8rwOe09uzZXwLcma24/zNJzQbs5GIyJR7M/n736cIDY+kdqnc\nuObJLE8gP2Fm75pkz5iaM9ceMWq5p9rhJEl/eF6k629bAZj1Y0061CyickTq6NOoBACzNp9McfOK\nfvvjX35ZuB+NBpb/3IBOb97PE9S6dbBlC7wzhAZfX7hs/Ivb5s2WjgldYxZiXLknZSasX8vrykOq\nDFhJ7SFruXj7Gdkzpmbt8Eb4LP2BqT2rU6e0s6rDsSUBSWY0Gg1TesT0gsz66yS3k/jE4yv3XnDz\noT9prcwo2b8LDBumdkiqG9yiLCY6Lev2X6Dv7J2MXHYQrVbDqqENafp9/k8eq9FoqFsmD/t/a0d6\nOyv2nb7Jj7N2psiu7ZCwCOZsjhmqOOjNYo/i42yszFk5pAFarYaJa/9h9d7zaoeUpOw4fo3W4/9C\nUWBc50opei5Nw/L5yGJvw9V7L9iTgla9nrnxOAPnxSwGuHhgPdrVKJzwjd65A97ekCoVVK4csy1n\nzpi/b95M+PYNoHml/Gi1GvadvikLo8bDrUf+tBq7ieI9FuF59jZ21nqm/fBmOHaVgkYz5FMSkGSo\nqHMmWlctSHhEVJKvo73tTe9Hrew26PbugVPJZ27L13LMmJrWVQsSFa0w66+Tb56k1adllYLxPkf2\njKnxGNscc1MdC7aeZtamlFcWc8XuczwPeI1rnsxUKOxo+AYCA2OGOLRqFffJYxJWvpAj03+oAUDn\nKVs+WxJaxDjkfZvGo/4gMiqaQc3LMLR1ebVDUpWJTkuvBsWBlFOSd+7mk/z0Zujdgv51EqfnA+Dv\nv2P+rlkT9G+edr9NQG7dShJzKu1TW1GhkCMRkdGx9wTiw/afvkm+9nNZd8AHc1Mdg1uU4caaPvRr\nWtroChNJApJMuXepQioLMzYdvpykFxF7+2ZTJ+ObMfhp0qgYjfEY0qocb0cLLRlUj7bVv/xJWun8\nWVn2c30A+s/bw/YU9MYeFRXNtD+PATCwWWnDDr1SlP+PsZ4wIWb4Q58+hju/yvo0LkmfRiUIj4ii\nwYj1XLn7XO2QjNrJyw+oM3QdoeGR9KhXjEndq8pQP6Br7aLozUzYeeJ6sr+GFm49Te9ZOwGY06cW\n3eoWS7zGPTxi/m7Q4P/b7OzA1jbmIcmLF4kXyzdo/GZo8abDxj9sTC0vAl7TdsJmwiKiaFrRhaur\nfmRS92rYWVuoHdoHSQKSTGXLYBu7iNgPM3fw2C9I5Yi+3MugUI5euItOq6FGqvCYjZaW8OABhIer\nG5zK8mRLxzb3Vuye3IaOtb7+SVrLKgUZ1b4i0dEKLcZu4sLNJwaM0nhtPXaVa/f9yJ4xNY0ruhj2\n5MuXQ/PmMddpsWJgYQGHDiWZD/r4mPZDDeqWccY/MJTaQ9by7GWw2iGpIjIqmuOX7nP43B3+9bnH\nKd8HnL32iAs3n+B79zmHz92h1i9rCAoJp1WVgsztW1uSjzfS2lrSplpMr+0cj5MqR5Nwlu44S/dp\n2wCY0asGvRqWSLzGQ0Lg7FkwMQE3t/9v12ggR46Yr5PIMKyG5fICsOvkdYJCUvbn/4coikLP6dt5\n9CKIMvmzsm5EY7JlMO6lLiQBSca61ilKjeJO+L0KodtvSa+E3e6T14mKVihfyJHUgf4xG5ctgyxZ\n4MIFdYMzAm6lclO9uNM3n2dU+4q0qFyAoJBw6gxdx5MkmKx+qSnr/wViFvA0MfSiXy1agKsrLFgA\nJ0/GTP48dw7SpjVsOyrS6bSsHd6YorkzceOhPw2GbyA0PFLtsBLVvacBVOy7nNK9llDxp+WU/XEp\nJXoupmi3hRTqPJ987edS8afl+L0KoV6ZPCz/pb7hx15HJu2f+Y8NY+bBLN91joBkOLZ/xS5vukzd\nAsDUntXom9DVrv7LwgIeP4ajR2N6Pd71xx/w9CkUL564MX0lB3sbyuTPSmh4JDveVMYU/7d23wX+\nPHSJVBZmrBraMEksZmn8EYqvptFoWDyoHrZW5mz992qSK3m47W353dK5we8/q+Ymo6fJatNoNCwd\nXI+S+Ry4+ySABiM2EBIWoXZYCeZfn3v8e/Eedtb6hBmHbWERk3h06wZaLVStGjPcIZlJZWHGVveW\nZE1vw78X79FhokeKqWi0/dhVinRdwL8X75HezopyBbNRyiULrnkyUyRXRgrkSE/ebOlwymxHh5pF\n2IStyT0AACAASURBVDCqCaYmOsMF8M8/YGMD1aoZ7pwqKOSUge+LZCcoJJzlb8phJxdeVx7SacoW\nFAUmdK3CgGYqFbowN4eSHyh4kDs32NtDEuqRk2FYH3b3SQC9Zu4AYnrZcma2+8wRxiF5JSBjxsCg\nQUliUlViyWJvw6wfawHQd84u7j97pXJE8RMVFc2OE28SkFLO8MMPsG1bzJAWgOfJe8xwYrMwN8Vj\nXAuyZbDl+KX7dJq8Jcn1mMXX1D9iej961nNNuJV1k9CH+rfInM6abe6tsLY0Y4PnRUYsPaB2SAkq\nIjKKwfP3UmfoOvxehVCzRC58lvbkyKyOHJvbmVPzu3J2UXcuLO3J5RW9uL6mD8t+ro/eUJM/fXzA\n3z8m+QgMhCdJf8hk38YxN8ezN58kKir6M3snHUMX7yc6WuHHhiX4pVU5tcNJFt6WmN9+/Gqyfkj2\nJaKjFTpM8iAgOIx6ZfIkXnEDA0g+CcjlyzB6NEydCg8fqh2NUWlbvRD1yuQhIDiMzknkxvL4pfv4\nvQohl0ManLOmjXlaU7s2lHrThS0JiMFlTJOKreNbxi76NGJp8lvr4dr9F3gc9cXMVEdvQ4zFvn07\nprcjBffIFXLKwJ+jmqLTanBfc5SlO86qHVKCuPskgIo/LWfKhn/RaTVM7FaF7RNaYZ/aKnECiIqC\nli1jxu7fuxez7fHjxGk7AdUt7YxjBltuPPRn58nraodjEJ5nb7HX6yY2VuaM7vC92uEkG9kzpqaY\ncyaCQyPYcyrllG/+lJmbjuN59jbp7axYNLBukppjlnwSkAULYv4uXRrSp1c3FiOj0WhYMKAOaWws\n2ON1g4VbT6sd0mdtO/528cHccX+h0qWL+VsSkARRyCkDG0Y2QafVMH71EX73SF5lj6f/eRxFgTZV\nC5IprfW3n3DZspjhDTNnxv+YsDD47bdkVUihRolc/P5TbQC6T9vGxkOXVI7IsLYdu8p33RZw7OJ9\nHNJZc3BGB35uWS5x6+mvXRvTA2JrC5UqgU4X0xuSxK8jnU4b+zAgOZTkVRSFoYtjegIHNS9DGhvj\nrECUVP2PvbOOiyJ/4/hnFxAQDBADu7DFwhb17D674+zu88zTu7Pj1J95Z3fH2Y2BLRZiYWKioohI\ns7u/Px7HBYRlZndmZ3b5vl8vXwPLzswjzM58n/o8rAxLT8Cz9xi/8hQAYNWvzZHNxUzBEJGwDgck\nKgpYv56+XrIEsLOT1x4FksPVGcuGkwrG6OXH8extqMwWGebQt/6PplWKJP5B9uxUt2ojYj01IxFN\nqnjg31HNAABDFh3GHiu50X/4HIG13+rMRavH5rKtOXPy36dDB+DXX4EpU8SxQSH0a14B4zpXR7xG\ni/Z/7sTSvdahbDRx1Sk0/1Zy1aSyB26tGoAapfOa14iYGGDyZPr6r7+oz4gLtL1/b15bJKB3k3JI\n72CHE35PsdHCp10fvBSIy/deIWvm9Bhh7qZzDo0GrkeO8MvMxsUBWsspfWtTk1QL9198iNg4jczW\nyEdMbDy6Tt+DmDgN+jYtj+bVisptkmCswwHZsQP4/JnUHMqXl9saxdKhTim0q1UCEdFx6Dl7n2Ib\nRoOCP+PO0/dwdkyHmp5JBsQNHEgPXCtbvCmN3k3LY2qvn6DTAZ2n7baKgXPL9l1DdGw8mlbxQIn8\nWcU5KOeA5MrFf58xY6g5ffZswNdXHDsUwow+dTG9dx3odMCQRUcwabWPRZR8psSBiw8xY/N52KhV\nmNO/Hg7M6AS3TOnNb8iKFVTuV6IE0LUrvZY9OwVirCAb7JLBEdN705TuX2bvw84zd2W2yDi0Wh0m\nrqbsx8Qu3tL1mKXGpUsoOHkyUC2VQIu3Nzmzz5+bxSwxKJInC0oXzIawiBicumEZEsJSMGXdGdx+\n8g4Fc7pg/uCGcptjFNbhgGi1FIHs319uSxTPspFNkc3FCWdvB2GJQiOUXPajYcVCSGfHMh1yMbGr\nNwa28EJMnAYtJm616BkhkdFxWLKXysnGdBBRjeb1a9oKyYBUrw6MH09iGd26AV8sQxiCDyqVChO6\nemPNby2+l/H1nXcA8RbYXBwZHYdhi48CAOYOqI8xHaubt+SKIyYGmD6dvp4xQ5/9PXuWyq/KljW/\nTRIwom2V7zOJOk/bgwMXH8ptkmC2+QTgztP3yJMtI/q38JLPEG74YLNmht+nVlNvkYXMAuFI62VY\nvv5BmLPtAtRqFTaObyWfo2si1uGA9OwJBAXRw5xhELdM6bHiW3nNiKVHUbjLIjQdtwUjlx7F8n3X\ncOr6U7z68EXW7Ii+/+Nb+dXXrxSp6dhRNpvSIiqVCouHNUZr7+IIi4hB47Gb8eJdmNxmGcWG47cR\nEhYJr6I5UbNMvtR34IsxJVgAZfAqVKD7FldaY0X0bFwO/03rCEd7W6w+fBOtJ29HZLRlqdbM3OKL\n58Gf4VkwO4a2TkbG1FzY25MC4IgRQIsW+tczZqQFpBUxpUctjOlQDfEaLdr+sdOiGo3j4jWYvJaE\nO/7oUVs85TOh6HTJTz9PjoIFafvsmbQ2iQxXhvXf+QcWGdwwhejYePScvQ86HTC+cw1UK5VHbpOM\nxnruXra2QDrL9ALNzc81iuG3jtWgUqnw5E0oDl95hIW7rmDQwsOo9+tG5Gm/ABmbzpQlQxIRFQuf\nG8+gUgGNKxWmFz9+pEFKFy6Y3Z60jo2NGpsntUZNz3x4HRKORmM34dOXKLnN4k3Y12hMXHUKo5Yd\nAwD82r6qeCohWi0NHPT0FC58YWcHzJ1LX9+zroZtjmZVi+DU393hmtERBy4Got6vG/AxLFJus3gR\n+PIj5nwbVrl8ZFPxh1UKxcsLWLDA6uWdVSoVZvevh6GtKiE2ToOWv2/D2VvP5TaLF2sO38STN6Eo\nkicLujcsI58hDx4AT54gLnPm1EuwOAfEwjIgJfNnRZE8WfDxS5RVlAcLYf6OS3jyJhQl82fF5O61\n5DbHJKzHAeFo355qYx9bh5yfVMzuXx8RRybg7tpB2PNXe8zqVxe9GpdFjdJ5kTVzekREx2Hk0mN4\n+MK89cWnbjxDTJwGlYrlQnZXZ3qRG0Lo6mpWWxiEQzpb7JveEaUKZMP9oBA0m7BF8dHs2DgNFu+5\ngsJdF2PG5vOIiolH9wZl0KZWCfFOolYDhw/TlHNjRBFq1AAiI4Hjx8WzSWFULZkH5xf1RN7smXDp\n7it4D1+r+CyaTqfDkEWHERunQc9GZS06wmiJqFQqLBzSCH2alkNUTDyaTdiKS3dfym2WQaJi4vDX\nxnMAgKk9f5LXYT1KZYNfqlZN/b5UoABtLcwBUalUaOPNlWFZZwAnOV5/+IIZm6lvcNHQxhZfom59\nDsinT9Sk/OiR3JYoHod0tiiRPytaeRfH2E41sPq3n+G7qCfe7x2D3k3KIV6jxejlwhZH0bHxmLzm\nNP636zLeh0YItulQ0vIr4EcHJDSU/r7x8YKPzzCOzM4OODK7C/Jky4hLd1+hw1+7EBOrvN+/TqfD\njtN3UeKXpRi2+ChCwiLh7ZkXl5b2xvrxLeWPZCfEzo4aQK2c4vmy4uLiXt8d2JrD1+JNSLjcZqXI\nrrP3cMLvKVwyOGB2/3pym5MmUatV+GdkM3SpVxpfo2LReOxm3Ah8K7dZKbJs3zW8CQlHOY8caCtm\nkMMYKlYE+vbFp7p1U38vlwGxwDlG3O95j+8DxQrqiM3YFScRER2H1t7FUad8AbnNMRkFPY2NIDl1\nlSLfFq6Bgea1xcqY3rsOMqRPh0OXH+GogOFQE1aewtSN5zBi6THkbPs3mo7bgm0+Abymlr79GI6D\n3xrQDTogZcvS3/nVK952MUwnd9aMODanK1wyOODgpUA0Hb8F4ZExcpv1nbO3nqPKoNXo8NcuPHkT\nimJ53bBvWkecXfgLqpTILbd5aZpcWTPCd1FPVCqWC0HvwtDwt00IDVdeKV94ZAxGLKVyvZl96ppv\nyKCxaLVWJWKQEBsbNdaNa4m2tUogLCIGDcZsRMAz5UkOf4mIwczN5wHQc1MWoYKE1KgBrFiBsFo8\nynMqVgTCwoCTJ6W3S2TKeeRA/hyZEfzpKy4qPEMmBhcDXmLzyTuwt7PBvIH15TZHFCzXAblxAyhV\nClizJvHrzAERheyuzt/rC0cuPYa4+NT1tk9df4oFuy7DRq1Cw4qFoFKpcPjKI3Sauhs52vyN3nP2\n4cyt54jXaBH48iO2+wRg/MqTaPTbJuRoPQ85287Hm5Bw5HLLgDKFsusPzDkgWbLQlg0jlI3i+bLC\nZ34PZHdxwqkbz1Bn1AaEyFjXr9XqcPBSIGoNX4faI9fj6oPXyOHqjH9HNcOdNQPRonpRi5oMa81k\ndnbA4VmdUTyfGwKevUfzCVsVV8r35/qzeBMSjorFcqJPUxkl3blhlWfOpPyehw+pQb2yjA3yEmNr\no8bmia3RrGoRfPwShYa/bVJcCd/8nZfw8UsUvD3zohHXt2gp2NmRmIEFolKpEqhhJV+GFREVizlb\nL6D2iHXwe/jGnOaJilarw7DFRwAAYzpWQwF3F5ktEgfLdUD+/ZeaN/39E7/OHBDRGNa6Mjxyu+LB\ni5BUJ2KHhkehxyxS3pjcvRaOzumKN7tGYdHQRvAqmhNfImKw5sgt/DRyPRwbTkfR7kvQcepuzNpy\nAceuPcG70AhkcrJHTc98WDq8SeJF488/Az4+wNCh9D3niDAHRBbKFs6BC4t7oYB7Zvg9fIMaQ9eY\nfVEQG6fBuqO3ULrXcjSfsBXn/IOQyckef/xSC482DUW/5hWUVW7FAABkyZQex+Z0RZ5sGXEh4CXa\n/7mTV3DDHAQ8e4+Fuy5DpQKWj2gKGzmvn7t3aVjlwIEpvydLFipDfWe58th8SGdng51/tEOtMvnw\nRmFCGCFhkfh7xyUAlP1gwQ7zwjkge3wfJJo3FB0bj//tuoxCXRZh7IqTOHs7CAPmH7TYmURrj9zE\n9cC3yJ01I8Z1qiG3OaIhk06ciXz5AmzeTF8nnf3h4UFb1oRuMunsbDB/UEM0n7AVU9adQed6pZMt\nSdDpdBi44BBeh4SjSoncmNDVGwCQNbMThraujKGtK+PBixBsPH4bm07ewYt3YcjllgHlPNxRrnAO\nlC2c43s6NdkbeI4c9I+DZUBkp1AuV1xY3AsNf9uEO0/fo/rQNTg+tyuK5xNpwF8KhH2NxoqD17Fw\n95XvfQS5s2bEiLaV0bdpBWR0spf0/Im4eFE/hyFzZuOP8/UrEBUFZJX2d6cU8mTLhONzu6HG0DU4\ndPkRes/Zj3XjWspauqLT6TBo4SFotDoM+tkLFYoKlFUWm5s3aWtoxoerKzUZh4ZSxsTejNe+mXFI\nZ4v/pnWE97C1CHj2Hi0mbsWJed3gaG8nq10zNvlSj0rlwvBOOjSXITmVi+dGTrcMePEuDH4P36BM\noRxYc+Qmpm08h9ffng9eRXPi5fswXA98i72+D9D6m9NiKXz+Go3xq04BAOb0rwcnC535kRyW6YBs\n2QJERAA1awLFk1xMBQoA9+/r1R0YJtG0igcaViyEY9eeYPLa01g+8sfBRltO3sH203fh5GCHjRNa\nJRt5LpbXDdP71MXUXnUQER2LDOlNeFgyB0QRuGfJgLMLf0HzCVtxIeAlvIetxeFZXVCpuICp4AmI\n12hxwu8Jgj99RXhkLMKjYmgbSdsvkTE4fes5vkRQ30mpAtkwpkM1dKxTSh41kN9/p8zcsWNAgwbG\nHWPjRqB7d5puvXGjuPYpmGJ53XB4VhfUGbUeG0/4wy1Tevw9qIFsEeSNx/3h6/8CWTOnx7RvE7ll\nhXNAypVL+T1qNSk+vnlDwit5rFutixPCqDp4NS4EvESX6Xuwc0o72TJV94M+YPHeq1Cp8H2KO8O8\nqNUqtPYuhiV7r2H8ylN48iYUz4M/AwDKFMqOv3r+hObVimD5Pj8M/t9hTFrjg5+rF5U3uymQv9af\nxYfPkahROi861ikltzmiYjl/BQ6dDvjnH/o6ucnntrZAsWJWHQ0yJyqVCvMHNYSNWoUVB2/g9uPg\nRD8PCv6Mwf87DABYOKQRCucyLJWrVqtMcz4AIHduIH9+NvdFAbhkcMTxud3QtIoHPn6JQp1R63Hy\nunBJx2dvQ1Fr+Do0GbcFvebsx/AlRzFp9WnM3noBy/b5YeMJf+y78BBfImJQu2x+HJ7VGf6rB6B7\nwzLySREaMwU9Kdy+QWlLyx4AKhXPhb1TO8DOVo0Fuy5j9lZ55vyEhkdhzL8nAADzBjSASwYFKJPx\ncUAAckAAIDjY8PushNxZM+Lo7C7I7OyAvb4PMGzxEVnKanQ6HYYtPop4jRZ9m5ZHOQ93s9vwA5s3\nA/XrA/v2Cd83KspiS/nafhtKeOrGMzwP/ozi+dyw8492uLGi//cewD5NyyN/jsy4HxSCLafuyGwx\nfxI6uYuGNrK6Ej/Lc0A+fgTi4igK3qaN3NakCUrkz4rBLStCq9VhxNJj32/4Go0WPWb9h7CIGLSo\nVhS9m6TysBSL336jya2DBpnnfAyDpHeww96pHdC1viciouPQZNzm76UJfNh8wh9l+/6Li3dfIqdb\nBnRvUAaDW1bEuM7VMb13HSwa2gjrxv6M3X+2x+1VA3B6QQ80ruwh/82Ym4Key7iMDwAg37eyjRcv\nTLfHAqnvVQibJrSGSgWMX3kKqw7dMOv5Y+M06DHrP7wPjYC3Z150a+Bp1vMni1ZLs2UAwyVYADkg\nzs5Wq4SVHCULZMP+6R1hb2eDZfv8MGvLebPbsPvcfZy8/hSuGR0xow8PuVtzsH8/qVkJVYc8ehRI\nnx745RdJzJKaGqXzonbZ/ChVIBs2TWiFO6sHom2tEolKOtPZ2eCPHiSqM2XdGcTGKaPvzBA6nQ4j\nlx5TlpMrMpZXguXmBgQE0AObZTnMxh+/1Mbmk3dw5tZz7Dl3H21qlcD8nZdw9nYQsrs4YdWY5vIv\nCBmyYWdrg/XjWsItkyMW7rqCiat9sHD3ZYzvXAMDWnglW6sd9jUagxYe/h6Rau1dHCtGN0OWTOnN\nbb5wwsPpn4ODaf0fXNnMq1fUUGxrebdkU2n/U0l8/BKJQQsPo//8g7j24DUmdPFGvhwm/F55EBev\nQcepu3DgYiBcMzpixWiF3MNiY4GJEynIklpf0P79pGSUxvD2zIfNE1uj3Z87MWGVD3JmyYAejVJx\n1kQiIioWo5aRVPP03nWUcb/SaIATlMVDw4bC9s39TaLcwoYRctjYqHF6QY9U39e1vidmb7uA+0Eh\nWH34Bgb+XNEM1hnPwUuBOHbtCTI52SujLFQCLC8DAgAqlT5yyDALLhkcMbXXTwCAX/85gSv3XmHi\nah8AwOoxLaTVy2/UCKhXTy/Hy1AkarUKCwY3wvG5XVGpWC58+ByJUcuOo3DXxVi+71qiqNOFOy9Q\ntu+/2HLqDtI72GHVr82x6892yniY8yFh9sOURau9PeDuTguIN5YrE2kqA3+uiBl96CG74uANFO66\nGH3n7cezt6GSnC9eo0XX6Xux1/cBMjs74MTcbiiW102ScwnGwQEYPx5YsSL196ZB54OjTa0SWDS0\nMQCg99z9OHQp0CzlWDM2++Ll+y8o7+GOvnJKNSfEz4/ECAoWBAoLlALm+mWfP6f7kJViY6PGXz1p\nDTN14zles8mkxP/JO/yz3w8rDlzH6kM3sPbITWw4dhubT/hjm08ARn6bR/TnL7WVP4/ISKw73BYe\nDmTIILcVVkPfZhWwfL8f7jx9j9oj1yMuXouBLbzQNOHQQCk4d45qVB0cpD0PQxTqexVCvQoFcejy\nI0xa7YPbT95h0MLDmL31AiZ3r4UX78MwdeM5aLU6VCjiji2T2qBInixymy0MtRpo1QrIls30YxUq\nRAvJ0FAgb17Tj2ehjO/ijdbexTFtky+2nLqDVYduYt3R2+jewBMTu9ZEwZziaN9rNFr8Mus/7Dhz\nFxmd7HFsTleUL2J95Q1pgSGtKuF1yBfM2nIBzSZshY1aBZcMjnDN6AjXDI7Iwm0zOaJK8dxoUsXD\npB7ER68+Yt432d0lwxsrp5n5GC1WBWc/AMDJiUr53r2jIIgVixm09i6O8h7uuPHoLZb+dw2/dqgm\nix1hX6NRa8Q6fP4abfB9JfJlxaCWys7UmIJ1OiAhIUDRoiRR+F55k1MtFVsbNRYOboS6ozcgOjYe\nRfJkwbyBRqr/8CUqiv7Z2wOOCmgOZfBCpVKhWdUiaFLZA3t872Py2tO4HxSC3nP3f/s5MK5zdfz5\ny0/yNZGbgocHsGePOMc6d860LIoVUTSvGzZOaIXfu9XE9E2+2HTSH2uO3ML6Y7fRrUEZjOlQDSXy\nGy9XrNXq0GfeAWw+eQfOjulwxATVNoYymNGnLmLjNFh56AbCI2MREhaZwnDUK7C3s0F9r0Jo7V0M\nzasVhZuAjKtOp8PwJUcRG6dBz0ZlUbWkghbqFy/S1hgHBKDMybt3VIZlxQ6IWq3C9D510HjsZszc\nch79mplZuv0by/f74fPXaBTNkwXennmh0eig0eqg1emg0Wih0epgo1ZhTMdqsLO1wOcjT1Q6M0tI\nhIXpB5ZlypSJ/45Cshk6HTXmRUZS2Y6LCZGzO3dIoaZBA1Jd8vGhYYdc3WQapMfM/7D3/H2c+rs7\nKhaT+OH9+jX9rnPkAN6+1b/+6hU5mmXKJFq8+fn5wcvLS1qbGILRaLTY6hOAvzacRWycBmvH/oyf\nyilEKvvlS6BdOxr81rZtsm9h15U8PH79CdM3+WLj8dvQaOlRVbZwDnSqUwod65RC3uz8nyFarQ79\n5x/AqkM3kd7BDkdnd1HE7AZ2bYlHXLwGn75E4VN4FD59icLHb1+/CQnHkauPcSHgBbgVj41ahVpl\n8qOVdzG0qlEMubIangi+/8JD/DxpGzI52SNw41Bkc1FQWUx8PHDtGlC6NK19IPC66tYNOH2aBjw3\nbSqhofKj0+lQc/g6nL/zAlN61MIfv9Q26/kjo+OQv9NCfPgciWNzuqJBxUJmPb8pGL1+TwHLcECu\nXwfq1AH++AMYOZLfPmXLkpLIlStApUrCDeUYMIA+lJMn0wf7t99It3/9euOPaeFotTrExWtgn84M\nCbQ7dwBPT6BECZoOzJEhAw1wCwsDMuofHOxhrmx0Oh10Osg6dO4HevYE1q2jr1O4HbLrSl6evP6E\nOdsuYPvpuwj7NgcGALw986JTnVJoV7ukwWi2TqfD4IWHsXy/HxzS2eLwrM6KcYBNvraioynQxlcO\n+vlzCtrkzk1VAmmI4E9fse/8A+zxfQCfm88Qr9ECIGekV+NymNStZrJObVRMHEr2XIZnbz9j0dBG\nGNq6srlNF4yg60qrpbLSNIKvfxBqDl+HDOnT4emW4YIyYaayZO9VDF10BBWKuOPaP32VIXzBE7Ed\nEFFXkDNnzsSePXsQGBgIe3t7VKlSBTNnzkTJkiWNP6hOBwwbRjKDQpo0ixQhByQw0HgHJD4e2L2b\nvm7ThmolJ00CNmwgmypUMO64Fo5arTKP8wHoG89dk8wXyZKFHJCQkEQOCEPZqFQq5VUbFbKcCFRa\npVAuV/w7ujkWDW2MI1cfY+upAOy/+BC+/i/g6/8CwxYfRU3PfHDN6AhbG3WCfyrY2qjxOiQcBy4G\nwt7OBvund1SM8/EDFy4Aq1cDLVoALVum/v5Pn+hemCkT8Pkzv3P8/juwaROwahXQu7dp9loYOVyd\n0b+FF/q38EJoeBQOXgrE7nP3ceBSIFYeuoH1x2+jf7MKGN+lBtyz6Csu5my7gGdvP8OzYHbFqycZ\nRRpyPgBSUWtUqTCOXn2M2VvPY+4AiUvJvxEbp8GcbTTvaEIXb4tyPqRA1FXk2bNnMWTIEFSsWBFa\nrRaTJ09GvXr1cO/ePbgYWwa1ZQvVN2bPTjdOvhT51hgdGGjceQFKSYaE0GDD0qUpajR0KPD338Do\n0fTzNH4BSU758pTFSipP6uZGpXEhIVS/ymAYy5gxwJQp9HVsrOUMuDx/nu5zYjTCWwj26WzRskYx\ntKxRDOGRMdh34SG2nLqD49eewOfmM4P7prOzwd6pHVDfS8EO55kzwNq15FDwcUAyZyYBg7AwyoTw\nEep49u33lMbvmy4ZHNGtQRl0a1AGD1+E4M/1Z7HtdAAW772KVYdvYEjLSvitU3WER8Zg1hZaNC4Z\n3hi2Smk8Z5jEtF4/4ejVx1iy9xpGtq2KnG7SCxZtOXUHL99/QbG8bmhZo5jk51M6ojogR48eTfT9\nxo0bkSlTJly8eBFNjakr/PqVSp4AYOZMYZFuDw9atJoyoGnHDtq2b693NCZNonKNs2dJg/3nn40/\nPiN1MmRIPoPl9k0yMyRE2vMHBJADmgbnM6QZ7O1Jfer5c2rCLMbjwbBlCy3+6tYVZx7Rhw/kUFeo\nwC+o4esL1KxJ2ZvHj00/vwWSIb09utb3RNf6nvjwOQIXA14iNl6DeI0W8Rot4uK137+O12hRu2x+\neBbKLrfZhuE7AZ1DrSYH9PVraiLmI0/PzXtI4w5IQormdcOW39tgfJcamLLuDPb6PsDc7RexfL8f\n8mXPhOjYeHSpV1oRPUMMcahQNCfa1CyO3efuY9jiIxjcsiI8cmdBziwZJCkR1mi034dmju9cQ1ll\nyDIh6arqy5cv0Gq1xmc/Zs6ksquKFYEeqQ+aSUTHjkCXLsYvHOPi9Co37dvrX8+cmaKlw4YBCxYw\nB0QusnyTbZXKAdHpgKVLgVGjqDl5xgxpzsNQBmPGUB100lK/5NDpaGpwXBwQESHO+YsUoRKad+/4\nZTROnqTtkydpdoBhQrJmdsLP1hBRvHWLtqlNQE9Ijhz8HZCoKBLzsLWl/d69o+oCBgCgdMHs2PNX\nB1x/+Aa/rz2NI1ce4+7zD3B2TIe5A+rLbd6P3L1L2bI0LIpjCn/1/Al7zz/A7nP3sfvcfQCAo70t\nCuV0hUduVxTO6YqiebKgdtn8KJSLx7PBAP+df4CHLz8iX/ZM6FS3lBjmWzySPrWGDx+OcuXKHmx4\njQAAIABJREFUoWrVqsYdoFMn4OpVYOpU4TWKpkYldTpg4UIq/0rawzJgAC0++vUz7RwM4ylYkBrT\nxYg+JyU8HOjbF9i+nb6PiKDrwZhyuw0baP+ff+bfJMowP4MG8X/vx4/0+c+cGUgvUvNivnzkgAQF\n8XNAOHlxW1taVLJ5R5ZPWBg5lPb2QPHi/PfjHIjg4NTf+/w5bePjydkuX56yaYxEVCiaE4dndcHF\ngJdYvt8PbWsWT9QTohjGjAGOHAF27aI+VVP48oWyYwUKkFOTBiiRPysOzeyMracC8Oj1Rzx+/Qkf\nPkci4Nl7BDxLPMKhWF43NK3igWZVi6B6qTyC5HF1Oh1mbKbsx28dq1u1tK4QJFPBGjVqFHbs2IHz\n588jf/78319P2EX/6NEjKU7NYBiNw+PHKDRuHByDgqBJnx7PJ01CaH3jI1/Fu3WD04MHeLBqFb6W\nKSOipQy5cAwMRMkuXRBVoADucmWaJlJo9Gi4nDuHJ7NmIbRu3VTfX7RPH2S4fRuBS5bgS2XlK/Iw\nUsf5xg0U698fEcWL4/6GDbz3yzdtGjL7+uLFb7+leu2kf/AA+aZPh8bJCRmvX4fG3h43z5xJ8xk0\nS0QVE4OydevCJiYGt48cQRxXlmwkHkOHItPly3g0fz7CvL1FstLy+BoVh5cfI/EyJAIvQyLw+G04\nLgd+wNfo+O/vcXawRZWiWVGjWDbUKJENmdIb7hu89PADhq26Cldne+yb8BMcLHH2FQAPD4/vXytO\nBYtj5MiR2LFjB06fPp3I+UgKk7VkiI3JkpZTp1IUulQp2OzahUJFixp/LK2WjgWgWKtW/Mp7GOYl\nMJD088uVo4xaCiS6rj58AAA4Fi4s3j2sTBng3DkUsrUF+Bxz5Ejg6lUUadcuTTWhWyPfr63ChYEc\nOeAEgc/GvXsBlQq8Wuu9vICuXenrwoVh8+QJvBwchJV8MZTByZNATAzg6YkyjRr98GPBz8KyZYHL\nl+FhY8PvHpSGiIvX4GLASxy6/AgHLwfiflAITt5+i5O33yKjkz1Wjm6O9j+lrPY6euM6AMDYzt6o\nUdVyA0YJEwhiILqcw/Dhw7F9+3b4+PigCKdExWAYS8+eQLVq+uZMqVm5khZ3V64ACZ2P+fOBVq2E\nNfwGBVF5TI4czPlQKkeP0oJs8WL++3By4GKW1HG1+98c1lTp0YN6lJj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8dDoqp+3dW9yZ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\na8xIaFlZ1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+ "text": [ + "" + ] + } + ], + "prompt_number": 35 + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "Discussion" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This is terrible! The output is not at all like a sin wave, except in the grossest way. With linear systems we could add extreme amounts of noise to our signal and still extract a very accurate result, but here even modest noise creates a very bad result.\n", + "\n", + "Very shortly after practitioners began implementing Kalman filters they recognized the poor performance of them for nonlinear systems and began devising ways of dealing with it. Much of the remainder of this book is devoted to this problem and its various solutions." + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Summary" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This information in this chapter takes some time to assimilate. To truly understand this you will probably have to work through this chapter several times. I encourage you to change the various constants and observe the results. Convince yourself that Gaussians are a good representation of a unimodal belief of something like the position of a dog in a hallway. Then convince yourself that multiplying Gaussians truly does compute a new belief from your prior belief and the new measurement. Finally, convince yourself that if you are measuring movement, that adding the Gaussians correctly updates your belief. That is all the Kalman filter does. Even now I alternate between complacency and amazement at the results. \n", + "\n", + "If you understand this, you will be able to understand multidimensional Kalman filters and the various extensions that have been make on them. If you do not fully understand this, I strongly suggest rereading this chapter. Try implementing the filter from scratch, just by looking at the equations and reading the text. Change the constants. Maybe try to implement a different tracking problem, like tracking stock prices. Experimentation will build your intuition and understanding of how these marvelous filters work." + ] + } + ], + "metadata": {} + } + ] +} \ No newline at end of file diff --git a/05_Kalman_Filters/Kalman_Filters.ipynb b/05_Kalman_Filters/Kalman_Filters.ipynb deleted file mode 100644 index 0ed555c..0000000 --- a/05_Kalman_Filters/Kalman_Filters.ipynb +++ /dev/null @@ -1,2425 +0,0 @@ -{ - "metadata": { - "name": "", - "signature": "sha256:b01859212b570d5ecf1bb56f51a3f9aad5c617170e84aa4e71d3cb44fae8051f" - }, - "nbformat": 3, - "nbformat_minor": 0, - "worksheets": [ - { - "cells": [ - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "[Table of Contents](http://nbviewer.ipython.org/github/rlabbe/Kalman-and-Bayesian-Filters-in-Python/blob/master/table_of_contents.ipynb)" - ] - }, - { - "cell_type": "heading", - "level": 1, - "metadata": {}, - "source": [ - "One Dimensional Kalman Filters" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "#format the book\n", - "%matplotlib inline\n", - "import sys\n", - "sys.path.insert(0,'../code') # allow us to import book_format\n", - "import book_format\n", - "book_format.load_style()" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "html": [ - "\n", - "\n" - ], - "metadata": {}, - "output_type": "pyout", - "prompt_number": 1, - "text": [ - "" - ] - } - ], - "prompt_number": 1 - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "One Dimensional Kalman Filters" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Now that we understand the histogram filter and Gaussians we are prepared to implement a 1D Kalman filter. We will do this exactly as we did the histogram filter - rather than going into the theory we will just develop the code step by step." - ] - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "Tracking A Dog" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "As in the histogram chapter we will be tracking a dog in a long hallway at work. However, in our latest hackathon someone created an RFID tracker that provides a reasonable accurate position for our dog. Suppose the hallway is 100m long. The sensor returns the distance of the dog from the left end of the hallway. So, 23.4 would mean the dog is 23.4 meters from the left end of the hallway.\n", - "\n", - "Naturally, the sensor is not perfect. A reading of 23.4 could correspond to a real position of 23.7, or 23.0. However, it is very unlikely to correspond to a real position of say 47.6. Testing during the hackathon confirmed this result - the sensor is reasonably accurate, and while it had errors, the errors are small. Furthermore, the errors seemed to be evenly distributed on both sides of the measurement; a true position of 23m would be equally likely to be measured as 22.9 as 23.1.\n", - "\n", - "Implementing and/or robustly modeling an RFID system is beyond the scope of this book, so we will write a very simple model. We will start with a simulation of the dog moving from left to right at a constant speed with some random noise added. We will talk about this in great detail later, but we need to model two kinds of noise. The *process noise* is the noise in the physical process. Something moving at a notionally 'constant' velocity will never maintain a perfectly constant velocity. Undulations on the ground, wind, and a host of other factors mean that there will always be slight variations in the velocity. The second noise we want to model is the noise in the measurement as no measurement is perfect." - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "from __future__ import print_function, division\n", - "import matplotlib.pyplot as plt\n", - "import numpy.random as random\n", - "import math\n", - "\n", - "class DogSensor(object):\n", - " \n", - " def __init__(self, x0=0, velocity=1, \n", - " measurement_variance=0.0, process_variance=0.0):\n", - " \"\"\" x0 - initial position\n", - " velocity - (+=right, -=left)\n", - " measurement_variance - variance in measurement\n", - " process_variance - variance in process (m/s)^2\n", - " \"\"\"\n", - " self.x = x0\n", - " self.velocity = velocity\n", - " self.noise = math.sqrt(measurement_variance)\n", - " self.pnoise = math.sqrt(process_variance)\n", - " self.constant_vel = velocity\n", - "\n", - " def sense_position(self):\n", - " pnoise = abs(random.rand() * self.pnoise)\n", - " if self.velocity > self.constant_vel:\n", - " pnoise = -pnoise\n", - " self.velocity += pnoise\n", - " self.x = self.x + self.velocity\n", - " return self.x + random.randn() * self.noise" - ], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 26 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The constructor `_init()__` initializes the DogSensor class with an initial position `x0`, velocity `vel`, and the variance in the measurement and noise. The `sense_position()` function has the dog move by the set velocity and returns its new position, with noise added. If you look at the code for `sense_position()` you will see a call to `numpy.random.randn()`. This returns a number sampled from a normal distribution with a mean of 0.0. and a standard deviation of 1.0. *Variance* is defined as the standard deviation squared, so in `__init()__` we take the square root of the variances to get the standard deviation. Therefore the expression `self.x + random.randn() * self.noise` computes a simulated measurement with the variance that we desire. \n", - "\n", - "Let's look at some example output for that." - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "for i in range(20):\n", - " print('{: 5.4f}'.format(random.randn()), end='\\t')\n", - " if (i+1) % 5 == 0:\n", - " print ('')" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - " 1.6843\t 1.2912\t 1.1466\t 0.4007\t 0.4046\t\n", - "-1.3402\t 1.7754\t-0.7792\t-0.5521\t 0.0399\t\n", - " 0.4786\t-0.1534\t 0.2983\t-0.7419\t-3.0835\t\n", - "-0.3109\t 0.9006\t 1.8374\t 0.3517\t-0.2178\t\n" - ] - } - ], - "prompt_number": 3 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "You should see a sequence of numbers near 0, some negative and some positive. Most are probably between -1 and 1, but a few might lie somewhat outside that range. This is what we expect from a normal distribution - values are clustered around the mean, and there are fewer values the further you get from the mean.\n", - "\n", - "Okay, so lets look at the output of the `DogSensor` class. We will start by setting the variance to 0 to check that the class does what we think it does. Zero variance means there is no noise in the signal, so the results should be a straight line." - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "import matplotlib.pyplot as plt\n", - "import matplotlib.pylab as pylab\n", - "\n", - "dog = DogSensor(measurement_variance=0.0)\n", - "xs = []\n", - "for i in range(10):\n", - " x = dog.sense_position()\n", - " xs.append(x)\n", - " print(\"%.4f\" % x, end=' '),\n", - "plt.plot(xs, label='dog position')\n", - "plt.legend(loc='best')\n", - "plt.show()" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "1.0000 2.0000 3.0000 4.0000 5.0000 6.0000 7.0000 8.0000 9.0000 10.0000 " - ] - }, - { - "metadata": {}, - "output_type": "display_data", - "png": 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zfFWAhlAUgII+qVzndnH2kAzMKqMT6XAKFCIiItLt7G4M8WyFn5eqAwS/aqM7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\nnGE2PTTWpcXj3boletD8rwIAAAADhuXfZfsDhv5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- "text": [ - "" - ] - } - ], - "prompt_number": 27 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The constructor initialized the dog at position 0 with a velocity of 1 (move 1.0 to the right). So we would expect to see an output of 1..10, and indeed that is what we see. If you thought the correct answer should have been 0..9 recall that `sense()` returns the dog's position *after* updating his position, so the first position is 0.0 + 1, or 1.0.\n", - "\n", - "Now let's inject some noise in the signal." - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "def test_sensor(measurement_var, process_var=0.0):\n", - " dog = DogSensor(measurement_variance=measurement_var, \n", - " process_variance=process_var)\n", - "\n", - " xs = []\n", - " for i in range(100):\n", - " x = dog.sense_position()\n", - " xs.append(x)\n", - "\n", - " plt.plot(xs, label='sensor')\n", - " plt.plot([0, 99], [1, 100], 'r--', label='ideal')\n", - " plt.xlabel('time')\n", - " plt.ylabel('pos')\n", - " plt.ylim([0,100])\n", - " plt.title('variance = {}, process variance = {}'.format(\n", - " measurement_var, process_var))\n", - " plt.legend(loc='best')\n", - " plt.show()\n", - " \n", - "test_sensor(measurement_var=4.0)" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "display_data", - "png": 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ClEJ7otLYHZ2Oq72OWa3KArDoSCLRqdkFPsbc/bH0jnTkcHBtfm/8GAs+W4fn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- "text": [ - "" - ] - } - ], - "prompt_number": 51 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "\n", - "> **Note**: numpy uses a random number generator to generate the normal distribution samples. The numbers I see as I write this are unlikely to be the ones that you see. If you run the cell above multiple times, you should get a slightly different result each time. I could use `numpy.random.seed(some_value)` to force the results to be the same each time. This would simplify my explanations in some cases, but would ruin the interactive nature of this chapter. To get a real feel for how normal distributions and Kalman filters work you will probably want to run cells several times, observing what changes, and what stays roughly the same.\n", - "\n", - "So the output of the sensor should be a wavering blue line drawn over a dotted red line. The dotted red line shows the actual position of the dog, and the blue line is the noise signal produced by the simulated RFID sensor. Please note that the red dotted line was manually plotted - we do not yet have a filter that recovers that information! \n", - "\n", - "If you are running this in an interactive IPython Notebook, I strongly urge you to run the script several times in a row. You can do this by putting the cursor in the cell containing the Python code and pressing Ctrl+Enter. Each time it runs you should see a different jagged blue line wavering over the top of the dotted red line.\n", - "\n", - "I also urge you to adjust the noise setting to see the result of various values. However, since you may be reading this in a read only notebook, I will show several examples. The first plot shows the noise set to 100.0, and the second shows noise set to 0.5." - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "test_sensor(measurement_var=100.0)" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "display_data", - "png": 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t2jWcOHEC/v7+qF27NqZOnYq33noLERERqF+/PhYsWABPT0+pLMLb2xtjx47F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\niOSLvMv0+NJkQ46v8VFYYLClxc/ejgCTs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4bmGWZWG329VTJyIiInId0hyGaV/tpcu7s1k1ogX9Nn6c3yHlGvX0/I0Snlub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\nAElFTkSuQmCC\n", - "text": [ - "" - ] - } - ], - "prompt_number": 62 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Now lets see the effect of the process noise. My simulation is not meant to exactly model any given physical process. On each call to `sense_position()` I modify the current velocity by randomly generated process noise. However, I strive to keep the velocity close to the initial value, as I am assuming that there is a control mechanism in place trying to maintain the same speed. In this case, the control mechanism would be the dog's brain! For an automobile it could be a cruise control or the human driver.\n", - "\n", - "So let's first look at the plot with some process noise but no measurement noise to obscure the results." - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "import numpy as np\n", - "np.random.seed(1234)\n", - "test_sensor(measurement_var=0, process_var=0.5)" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "display_data", - "png": 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cGRToTjV3u0dv8OWX4fRpGDsW6tXL93gfRbFYp6eg3ds9JsPbRH6TLn1REOS8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- "text": [ - "" - ] - } - ], - "prompt_number": 65 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "We can see that the position wanders slightly from the ideal track. You may have thought that the track would have wandered back and forth the ideal path like the measurement noise did, but recall that we are modifying velocity on each, not the position. So once the track has deviated, it will stay there until the random changes in velocity happen to result in the track going back to the original track. \n", - "\n", - "Finally, let's look at the combination of measurement noise and process noise." - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "test_sensor(measurement_var=1, process_var=0.5)" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "display_data", - "png": 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VlsXQlAhc2rUG26J7nlLU9++lciADIYQQQgghRNEwZJvIzDHdtkxMWhbDNl/l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- "text": [ - "" - ] - } - ], - "prompt_number": 66 - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "Math with Gaussians" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Let's say we believe that our dog is at 23m, and the variance is 5, or $pos_{dog}=\\mathcal{N}(23,5)$). We can represent that in a plot:" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "import stats\n", - "stats.plot_gaussian(mean=23, variance=5)" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "display_data", - "png": 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N08AbX9aaHUdEeggVHyLSYxxtaGHFsTnu87JdOGx6CZSeK8FhY+bo1r1tlmwr\no745YHIiEekJ9M4rIj3GY4Xl1DYHyOkdzRV9Y8yOI2K6a8+L54IUB2UNfp7aqcXnItL1VHyISI+w\n29vIq19UE2GFu8akYrGota6I1WLhPy9OA+C5PZUcqvGZnEhEwp2KDxEJewHD4HcfHcEAfnR+Ev3j\n7WZHEgkaw11R/L9z42gOGDy8zWt2HBEJcyo+RCTsvVZcw67yJlxOG7eMSDY7jkjQmTnahTPCwjuH\n6thSWm92HBEJYyo+RCSs1fj8PLq99dvc2Re5iInUy57IP0uLjmDa8NbCfHFBGS0Btd4Vka6hd2ER\nCWv/9clRjjb6GZkaxXcGxJkdRyRo/WhYIn1iI/ii0sfaz6vMjiMiYUrFh4iErQPVPl74tBILcLcW\nmYu0yWGzMicrFYDlheVUNflNTiQi4UjFh4iErYe3eWkx4N/Oi+f8lCiz44gEvasyYxiT7qTKF+CJ\nHeVmxxGRMKTiQ0TC0pbSet49XEd0hIXbRqWYHUckJFgsFu4Yk4rVAi/trWJfZZPZkUQkzKj4EJGw\n4w8YPLStDICbhyfjckaYnEgkdAxOcvC9QQn4DVhc4MUwtPhcRDqPig8RCTuv7qvm8wofGTER/GhY\notlxRELOjJHJxNmtfFhaz3uH68yOIyJhRMWHiISVWp+fxwtb56rPusiFw6aXOZFvKjkqgukXtrbe\nfWibl2a/fv0Qkc7R7nfl5cuXM2DAAJxOJ9nZ2WzcuPG05zY1NZGfn8/IkSOx2+2MHz/+pHPWrl1L\nbm4uaWlpxMfHc+mll/LXv/61Y1chInLMyl0Vx1vr5vaPNTuOSMi6YUgiA+IjOVTTzH9/Wml2HBEJ\nE+0qPtasWcPs2bNZsGABhYWF5OTkMHHiRA4dOnTK8/1+P06nk5kzZ5KXl3fK9pbvvfceEyZMYN26\ndRQWFvKd73yH6667rs2iRkSkLYdrmnluT+uHpDuz1VpX5GxEWi3My25tvftfO49S3tBiciIRCQft\nKj6WLFnC1KlTmTZtGkOGDGHp0qVkZGSwYsWKU54fHR3NihUruOWWW+jTp88pF6s98sgj3HXXXWRn\nZ3Puuedyzz33kJWVxSuvvHJ2VyQiPdaj2700Bwzyzo3jApda64qcrcv6xHB5n2jqmgMsK1TrXRE5\ne2csPnw+H9u3byc3N/eE47m5uWzatKlTw1RXV5OcnNypjykiPcM2TwNvHqwlymZhplrrinSauVmp\nRFjg1S8vj2xpAAAgAElEQVSq2VPeaHYcEQlxZyw+vF4vfr+f9PT0E46npaXhdrs7Lcjjjz9OSUkJ\nU6ZM6bTHFJGeIWAYPFTQ2lo3/4Ik0mMiTU4kEj7OSbDzw6GJGMCDBWVqvSsiZyUomt//+c9/5q67\n7uLFF18kMzPztOcVFBR0YyppL41L6Am3MdtUGcmeo9EkRgQY3rSfgoL9ZkfqdOE2Zj1BOI3ZGD+8\naovj4yONPPHOJ4yJbzY7UpcIpzHrCTRewWnQoEFt3n7G4sPlcmGz2fB4PCcc93g8ZGRknF064OWX\nX+YnP/kJzzzzDHl5eW2em52dfdbPJ52roKBA4xJiwm3M6psDzH/1S8DPvEsyuOzcIWZH6nThNmY9\nQTiO2aykKhZuOcJfK+O5+Yr+YdfGOhzHLJxpvIJXVVVVm7ef8ZXDbreTlZXF+vXrTzi+YcMGcnJy\nzirciy++yI9//GOefvppvve9753VY4lIz7R6dwXeBj8XpDj4zoA4s+OIhK1rz4tnUKKd0roWni1S\n610R6Zh2fW0xd+5cVq9ezcqVK9mzZw+zZs3C7XYzffp0AObPn8+ECRNOuE9RURGFhYV4vV5qa2vZ\nsWMHhYWFx29/4YUXuOmmm1i0aBHjxo3D7Xbjdrs5evRoJ16eiISz0rpm/lRUAcAd2alY1VpXpMvY\nrBbmHmu9+8ddar0rIh3TrjUfkyZNory8nIULF1JaWsqIESNYt27d8fUZbreb4uLiE+6Tl5fHgQMH\nALBYLIwePRqLxYLf7wfgySefJBAIMGvWLGbNmnX8fldeeSVvv/12p1yciIS3x7aX0+Q3yO0fy6g0\np9lxRMLepRnRfKtPDO99VcfywnJ+OTb9zHcSEfkH7V5wPmPGDGbMmHHK21atWnXSsf37217w+c47\n77T3qUVETvJJWQN/+7IGu9XCrItcZscR6THmZLnYVFLHK/uq+cHQRAYnOcyOJCIhJLxWi4lIj2AY\nBosLvABMGZZI71i11hXpLuck2Pn+4AQCBjyk1rsi8g2p+BCRkPP6l7Xs9DbictqYOlwbk4p0t1tH\nphBvt/KRu4H3DteZHUdEQoiKDxEJKQ0tAZZub/3V46cjU4iJ1MuYSHdLdNj4jwtbC/+Ht3tp9uvX\nDxFpH71ri0hIebaoEnd9C0OSHHx3YLzZcUR6rEmDE+kXF8mB6mZe2qvWuyLSPio+RCRkHKlv4Y+7\nWttx35HtwmZVa10Rs0TaLMzJam328OQnR6lq8pucSERCgYoPEQkZjxd6afQbXJUZQ3avaLPjiPR4\nV/SN4eJeTqp9Af7rE+3TJSJnpuJDREJCUXkjf9lXQ4QVtdYVCRIWi4W5WalYgBc/q+TLKp/ZkUQk\nyKn4EJGg19patwyAyUMT6RdvNzmRiHxtSLKDfzsvnhajdfG5iEhbVHyISNB762AtHx9pJNFh45YR\naq0rEmxuG5VCdISF9w7XsaW03uw4IhLEVHyISFBr8gd45Ni3qTNGJhNnt5mcSET+mcsZwc3H9tx5\naFsZ/oBa74rIqan4EJGg9t+fVvJVbQsDE+x8b1CC2XFE5DRuOj+RXjERfF7h49V91WbHEZEgpeJD\nRIJWeUMLf9hZAcC8bBcRaq0rErSiIqzMGt3aDOLxwnJqfWq9KyInU/EhIkFrxY5y6poDXN4nmrG9\nY8yOIyJncM05sYxwRXG00c+q3RVmxxGRIKTiQ0SC0t6KJv7ni2oiLDAnK9XsOCLSDhaLhTuyW3/9\neLaokpLaZpMTiUiwUfEhIkHHMAweKigjYMANQxIZkKDWuiKh4sJUJ/9yTiy+gMGjar0rIv9ExYeI\nBJ33DtfxkbuBeLuVWy9Ua12RUHP7RS4cNgvrD9RSeKTB7DgiEkRUfIhIUGn2GyzZ1vpt6a0XJpPg\nUGtdkVCTERPJlPMTAY79iqnWuyLSSsWHiASVF/dWcrCmmXPiI7lhSKLZcUSkg6YOT8bltLGrvInX\n99eYHUdEgoSKDxEJGpVNfp785CgAc7JcRKq1rkjIio60ctuoFACWflxOQ0vA5EQiEgxUfIhI0Hhi\nRzk1vgCXZkRzeR+11hUJdf96bjxDkhx46lt4pkitd0VExYeIBIl9lU28vLcKqwXmZbmwWPSrh0io\ns1ktzDvWenfVrgqO1LeYnEhEzKbiQ0SCwsPbvPgN+N6gBM5LcpgdR0Q6yZhe0VzZN4ZGv8HywnKz\n44iIyVR8iIjpPviqjg9K6omNtDJjpFrrioSb2VkuIqzwl33V7ClvNDuOiJhIxYeImKol8H+tdW8Z\nkUxyVITJiUSks/WPt/ODIYkYwEPbvBhqvSvSY6n4EBFTrf28iuIqH31jI7lxaILZcUSki/zHiGQS\nHVa2eRp451Cd2XFExCQqPkTENNVNflbsaJ0DPjvLhd2mlySRcBXvsDF9ZGvr3Ye3efH51XpXpCfS\nO72ImOapnUepbAqQle7kqky11hUJd9cPSuDcBDuHa5v570+rzI4jIiZQ8SEipjhQ7eOFzyqxAHdk\nq7WuSE8Q8Q+td5/aeZTyBrXeFelpVHyIiCke2ealJQDfHRjP0OQos+OISDfJ6R3DuD7R1DUHjk+7\nFJGeo13Fx/LlyxkwYABOp5Ps7Gw2btx42nObmprIz89n5MiR2O12xo8ff8rz3n33XbKysnA6nQwc\nOJAnn3yyY1cgIiFnS2k9fz9cR3SEhdtGpZgdR0S62ZysVGwW+J8vqtlb0WR2HBHpRmcsPtasWcPs\n2bNZsGABhYWF5OTkMHHiRA4dOnTK8/1+P06nk5kzZ5KXl3fKqRT79+/nO9/5DuPGjaOwsJD58+cz\nc+ZM1q5de/ZXJCJBzR8weKigDICbhyeTGq3WuiI9zbkJdm4YnEDAgIcKytR6V6QHOWPxsWTJEqZO\nncq0adMYMmQIS5cuJSMjgxUrVpzy/OjoaFasWMEtt9xCnz59TvmC8sQTT9C3b18effRRhgwZwi23\n3MJPfvITFi9efPZXJCJB7ZUvqvm80kdGTAQ/GpZodhwRMcmtI1OIt1v5yN3Au4fVelekp2iz+PD5\nfGzfvp3c3NwTjufm5rJp06YOP+nmzZtP+ZgFBQX4/f4OP66IBLcan5/HC1vneM/JcuFQa12RHivR\nYePWC1unXS7Z5qXZr18/RHqCNt/5vV4vfr+f9PT0E46npaXhdrs7/KQej+ekx0xPT6elpQWv19vh\nxxWR4LZyZwUVTX5Gp0UxoV+s2XFExGQ3DEngnPhIDtU088JnlWbHEZFuEFKTrQsKCsyOIKegcQk9\nZozZEZ+VZ/fFYgHyosvYts3T7RlCmf7OQo/GrH2+mxDB0uoYVnxcRt/qYuIizPsFRGMWWjRewWnQ\noEFt3t5m8eFyubDZbHg8J35I8Hg8ZGRkdDhUr169TvrlxOPxEBERgcvlOu39srOzO/yc0jUKCgo0\nLiHGrDGb9/cS/NTx3YFxXJ8zuNufP5Tp7yz0aMzaL8swKHi7hE0l9XxoyWR+dpopOTRmoUXjFbyq\nqtreQLTNaVd2u52srCzWr19/wvENGzaQk5PT4VBjx45lw4YNJz3mmDFjsNlsHX5cEQlOW931vH2o\nDmeEhdtGnf4LBhHpeSwWC3OzXNgs8PLnVXyh1rsiYe2Mqz3nzp3L6tWrWblyJXv27GHWrFm43W6m\nT58OwPz585kwYcIJ9ykqKqKwsBCv10ttbS07duygsLDw+O3Tp0/nq6++Ys6cOezZs4c//OEPPP30\n09xxxx2dfHkiYjZ/wGDxsda6Uy9IJk2tdUXknwxMdHD9oGOtd7d51XpXJIyd8VPApEmTKC8vZ+HC\nhZSWljJixAjWrVtHZmYmAG63m+Li4hPuk5eXx4EDB4DWbzRGjx6NxWI53snqnHPOYd26dcyZM4cV\nK1bQp08fHnvsMa677rrOvj4RMdmr+6rZW+GjV3QEU9RaV0ROY/rIFNbtr+HD0no2flXP5X1jzI4k\nIl2gXV9BzpgxgxkzZpzytlWrVp10bP/+/Wd8zG9961ts27atPU8vIiGq9h9a6866yEVUhFrrisip\nJUXZuPXCZB7a5mXJtjIu7R1NpPXkjYpFJLTpk4CIdJmVuyo42ujnwtQorjlHrXVFpG0/GJJIv7hI\nvqxu5qXP2l60KiKhScWHiHSJwzXNPLentW//ndmpWCz6BlNE2hZpa118DvDkJ+VUNmnjYZFwo+JD\nRLrEI9u9NAcM8s6NY7gryuw4IhIivtU3hkt6Oan2BXhyR7nZcUSkk6n4EJFOV+Cp562DtUTZLMwc\nlWJ2HBEJIRaLhXnZqVgt8NLeKoqrfGZHEpFOpOJDRDqVP2DwUIEXgPzhSaTHRJqcSERCzaAkB9ed\nF4/fgCXHWnWLSHhQ8SEineqvxdV8erSJ9OgIfjwsyew4IhKifjoyhdhIKx+U1PPBV3VmxxGRTqLi\nQ0Q6TV1zgGUff91aNwWnWuuKSAclOyP49xHJQOvGgy0BbTwoEg70yUBEOs0fdx2lvNHPCFcU/3JO\nnNlxRCTE/XBoAplxkeyv8vHnz9V6VyQcqPgQkU7xVU0zzxa1tta9I9ul1roictbsNitzLmptvbui\nsJxqtd4VCXkqPkSkUyzZXoYvYDDxnDguTHWaHUdEwsSVmTGMSXdS5QvwX58cNTuOiJwlFR8ictY+\nKq3n7YN1RNkszLpIrXVFpPN83XrXAqz5rFKtd0VCnIoPETkrLQGD329tbYV5y4hktdYVkU43JNnB\n9wbF02LA4q1lGIYWn4uEKhUfInJWXtpbxb4qH31jI/nRsESz44hImPrpqBTi7FY2l9bz7mG13hUJ\nVSo+RKTDKhr9rNjR2lp3bpYLh00vKSLSNZKjIpgxsnVa50MFXpr8AZMTiUhH6JOCiHTY8h3l1PgC\nXJoRzZWZMWbHEZEwd8PgBAYm2Dlc+3/d9UQktKj4EJEO+exoE3/eW4XNota6ItI9IqwW7hqTCsAf\ndh7FU9dsciIR+aZUfIjIN2YYBou2HsEAfjAkkYGJDrMjiUgPcXFGNN/uF0uj3+DR7eVmxxGRb0jF\nh4h8Y+sP1PLxkUYSHTamj0w2O46I9DCta8ws/O3LGj4+0mB2HBH5BlR8iMg30tAc4JFtXgBmjk4h\nzm4zOZGI9DS9YyPJvyAJgEUfleEPqPWuSKhQ8SEi38iq3RW461sYmuzg3wbGmx1HRHqon1yQRK+Y\nCD6raOJ/vqg2O46ItJOKDxFpt5LaZv5UVAHA3WNSsVm1yFxEzOGMsDI3ywXA44Veqpr8JicSkfZQ\n8SEi7bZkm5cmv8HEc+IYleY0O46I9HAT+sWSne6ksilwfM8hEQluKj5EpF0+Kq3nrYO1OCMszD72\nbaOIiJksltbWu1YLvLy3is8rmsyOJCJnoOJDRM6oJWDwYEEZANOGJ5MWHWFyIhGRVoOSHNwwOAG/\nAQ9uLcMwtPhcJJip+BCRM3ppbxVfVProGxvJj4Ylmh1HROQEM0amkOiwstXTwJsHa82OIyJtUPEh\nIm0qb2hheWHrXOq52S4cNr1siEhwSXDYuG1U63TQJdu8NLQETE4kIqejTxEi0qZHtnupbQ4wrk80\nV/aNMTuOiMgpXXdePEOSHLjrWli9u8LsOCJyGio+ROS0Pj7SwGvFNditrYs6LRa11hWR4GQ79joF\nsHpXBYdqfCYnEpFTaVfxsXz5cgYMGIDT6SQ7O5uNGze2ef7OnTu54ooriI6Opm/fvtx3330nnfPM\nM88wcuRIYmJiyMjIYMqUKXg8no5dhYh0upaAwQMfHQEgf3gSmXF2kxOJiLTtonQneQPi8AUMfq/F\n5yJB6YzFx5o1a5g9ezYLFiygsLCQnJwcJk6cyKFDh055fnV1NVdffTUZGRkUFBTw6KOP8uCDD7Jk\nyZLj57z77rvk5+dz8803U1RUxCuvvMKePXu46aabOu/KROSsvPhZFZ9X+OgdE8HUC5LMjiMi0i6z\ns1zERlrZ+FU9fz9cZ3YcEfknZyw+lixZwtSpU5k2bRpDhgxh6dKlZGRksGLFilOe/9xzz9HY2MjT\nTz/NsGHDuP7667n77rtPKD62bt1KZmYms2bNon///lxyySXcdtttbNmypfOuTEQ6rLyh5fiGXXeO\nSSUqQjM0RSQ0uJwR/HRUCtDaeleLz0WCS5ufKHw+H9u3byc3N/eE47m5uWzatOmU99m8eTOXX345\nDofjhPNLSko4cOAAAFdffTVlZWW89tprGIaB1+vlhRdeIC8v72yvR0Q6wT8uMr9Ci8xFJMTcMDiB\nIUkOSuta+OPOo2bHEZF/0Gbx4fV68fv9pKenn3A8LS0Nt9t9yvu43e6Tzv/631/fZ+TIkTz77LPc\neOONOBwO0tLSAFi9enWHLkJEOo8WmYtIqIuwWvjPi1sXnz9dVMmBai0+FwkWnb5NcXs+qHz44Yfk\n5+dz7733cs0111BSUsKdd97JrbfeytNPP33a+xUUFHRmVOkkGpfQc7ox8xuwcH8sYCM3uQHPZ5+g\nNhDBQX9noUdjZr7LEpx8UGXn529+wezMes70EUVjFlo0XsFp0KBBbd7eZvHhcrmw2WwndaHyeDxk\nZGSc8j69evU66VeRr+/fq1cvAB5++GEmTJjAvHnzABg+fDgxMTFcfvnlPPDAA/Tu3fuUj52dnd3m\nxUj3Kygo0LiEmLbG7Pk9lRxuKqN3TAS/uPoCrfUIEvo7Cz0as+BwbmML1756gKK6SKrShjChf9xp\nz9WYhRaNV/Cqqqpq8/Y2P1nY7XaysrJYv379Ccc3bNhATk7OKe8zduxY3n//fZqamk44v0+fPvTv\n3x8AwzCwWk986q//HQhoYZiIGbTIXETCTXJUBD87tvh8cYGX+mZ9xhAx2xk/XcydO5fVq1ezcuVK\n9uzZw6xZs3C73UyfPh2A+fPnM2HChOPnT548mejoaPLz89m9ezdr165l0aJFzJ079/g51157La++\n+ipPPPEExcXFfPDBB9x+++1kZWXRt2/fLrhMETkTLTIXkXB0/aAEhqU48NS38JQWn4uY7oxrPiZN\nmkR5eTkLFy6ktLSUESNGsG7dOjIzM4HWReTFxcXHz4+Pj2fDhg3cdtttZGdnk5yczB133MGcOXOO\nnzN58mSqqqpYtmwZ8+bNIzExkauuuopFixZ1wSWKyJlokbmIhCub1cLPL05jyt8O8WxRBf86MJ5z\nE7RpqohZ2rXgfMaMGcyYMeOUt61ateqkY8OHD+fdd9/t8GOKSPdpDhjcv0U7mYtI+LrAFcX3BsXz\n58+r+d2WIzx5dR99ySJiEk3qFunhnttTwReVPvrGRmoncxEJWz8b7SLRYWWrp4E3vqw1O45Ij6Xi\nQ6QHK6lt5skdrXOg51+iReYiEr4SHTZmjnYB8NC2Mmp8fpMTifRM+qQh0kMZhsHvPjpCo98gt38s\nOb21yFxEwtu158UzwhWFt8HP44XlZscR6ZFUfIj0UG8drOX9r+qJjbRyR3aq2XFERLqc1WJhwaVp\n2Czw4mdV7PI2mh1JpMdR8SHSA9X6/Px+axkAM0enkBrdrt4TIiIhb3CSgynDkjCA+z700BIwzI4k\n0qOo+BDpgZbvOEpZg5/hKQ6uH5RgdhwRkW71HyOS6R0Twd4KH89/Wml2HJEeRcWHSA9zoMHKms8q\nsVlgwaXp2KxqNykiPYsz0sr8S9IAWFFYTklts8mJRHoOFR8iPYg/YPCM20nAgBuHJjIk2WF2JBER\nU4zrE0Nu/1ga/a3NNwzNvhLpFio+RHqQF/dWcaAxgl7REcwYmWJ2HBERU92RnUpspJX3v6pne43W\nvol0BxUfIj3EkfqW460l77o4lehI/fmLSM+WGh3BzNGtX8T8t8epvT9EuoE+fYj0EA9uLaOuOcCo\n2GbGZ8aaHUdEJCh8f3ACI1xRVLVYtfeHSDdQ8SHSA7x3uJY3D9bijLBwY68Gs+OIiASNr/f+sGJo\n7w+RbqDiQyTM1fr83L+ldU+P20alkBypVZUiIv9ocJKDq1N82vtDpBuo+BAJc0s/LsdT38LwFAc/\nHJJodhwRkaD0r67G43t/PLdHe3+IdBUVHyJh7OMjDby0t4oIC9wzVnt6iIicjsPK/+39saOcg9U+\nkxOJhCcVHyJhqskf4DebPQBMHZ7MoCTt6SEi0pZxfWLIGxBHk9/gNx8eIaDNP0Q6nYoPkTD1h0+O\n8mV1MwPiI7llRJLZcUREQsK87FSSHDa2eRr4n8+rzY4jEnZUfIiEob0VTazeXYGF1ulWdpv+1EVE\n2iMpysbdF6cC8Mh2L566ZpMTiYQXfSIRCTP+gMFvNntoMWDSkARGpTnNjiQiElJy+8dyZd8YapsD\n3L+lDEPTr0Q6jYoPkTDz/KeV7C5vIj06gpmjXWbHEREJORaLhfmXpBEbaeW9r+p448tasyOJhA0V\nHyJh5HBNM8uP7dD7i0vSiInUn7iISEekRUcwJ6v1C5xFW8uoaPSbnEgkPOiTiUiYMAyDhR96aPQb\n/Ms5sVzeN8bsSCIiIe268+IZk+6kssnP4oIys+OIhAUVHyJhYu3n1WxxN5DosHJndqrZcUREQp7F\nYuGXY9OIsllYt7+G9w/XmR1JJOSp+BAJAyW1zSzZ1vqt3H9enEayM8LkRCIi4SEzzs5PR6UA8Nst\nR6j1afqVyNlQ8SES4gzD4NebPdS3GHy7Xyy5/WPNjiQiElYmD01keIoDT30LS7Z5zY4jEtJUfIiE\nuJc/r+IjdwOJDhs/vzgVi8VidiQRkbBis1q4NyedSKuF//mimo1fafqVSEep+BAJYSW1zTxy7Fu4\n+RenarqViEgXGZjo4KejkgH4zWYP1U2afiXSESo+REJU4B+mW03oF0vuOXFmRxIRCWtTzk/iwtQo\nyhr8PKjuVyIdouJDJES9vLd1ulWSw8b8S9TdSkSkq9msFn6Tk47DZuG14hr+fkibD4p8U+0qPpYv\nX86AAQNwOp1kZ2ezcePGNs/fuXMnV1xxBdHR0fTt25f77rvvpHN8Ph/33HMP5557LlFRUfTv35/H\nHnusY1ch0sN8VdPMI9uPTbe6JJXkKE23EhHpDv3j7cwc3dr9auGHR6jU9CuRb+SMn1jWrFnD7Nmz\nWbFiBePGjePxxx9n4sSJFBUVkZmZedL51dXVXH311Vx55ZUUFBSwZ88epk6dSkxMDHPnzj1+3g9/\n+ENKSkp46qmnGDRoEB6Ph/r6+s69OpEwFDAM7t3soaHFILd/LFf313QrEZHudOPQRN4+WMf2Iw08\nsOUIi76VYXYkkZBxxuJjyZIlTJ06lWnTpgGwdOlSXn/9dVasWMH9999/0vnPPfccjY2NPP300zgc\nDoYNG8ann37KkiVLjhcf69ev5+2336a4uJjk5NbFW/369evM6xIJWy/traLA0zrd6u6LNd1KRKS7\nWS0Wfp2TzqTXDrD+QC0TDtToiyCRdmpz2pXP52P79u3k5uaecDw3N5dNmzad8j6bN2/m8ssvx+Fw\nnHB+SUkJBw4cAOCVV15hzJgxLF68mMzMTAYPHsysWbOoq1PrOpG2fFnlO97d6ueabiUiYpq+cZHM\nvsgFwP1bjlDe0GJyIpHQ0Gbx4fV68fv9pKenn3A8LS0Nt9t9yvu43e6Tzv/631/fp7i4mI0bN7Jz\n507Wrl3LsmXLeP3118nPz+/odYiEveaAwYIP3DT6DfLOjWOCvmUTETHV9wcncHEvJ5VNAX675QiG\nYZgdSSTodfrXpu3Z4CwQCGC1Wnn++eeJi2v9ALVs2TKuueYaysrKSE099VSSgoKCTs0qnUPj0j1e\nLXOwuzyK5IgAuRGHKSg43OHH0piFHo1Z6NGYhZ6OjNn3Yi18Yo3jnUN1LH3rEy5LbO6CZHIq+hsL\nToMGDWrz9jaLD5fLhc1mw+PxnHDc4/GQkXHqxVW9evU66VeRr+/fq1cvADIyMujdu/fxwgNg6NCh\nABw8ePC0xUd2dnZbccUEBQUFGpdu8ElZA3/79DAWYNFVmWSnR3f4sTRmoUdjFno0ZqHnbMasKa2a\nX23y8GJZDNdf0p++cZGdnE7+mf7GgldVVVWbt7c57cput5OVlcX69etPOL5hwwZycnJOeZ+xY8fy\n/vvv09TUdML5ffr0oX///gCMGzeOkpKSE9Z47N27F+D4OSLSqr45wIIPPPgNmDIs8awKDxER6Xz/\nem4cE/rFUt/SOj22JaDpVyKnc8Z9PubOncvq1atZuXIle/bsYdasWbjdbqZPnw7A/PnzmTBhwvHz\nJ0+eTHR0NPn5+ezevZu1a9eyaNGiE9rsTp48mZSUFKZOnUpRUREffPABs2bN4oYbbsDlcnXBZYqE\nriXbyjhU08ygRDu3jUoxO46IiPwTi8XCLy5NI9VpY0dZI6t2VZgdSSRonbH4mDRpEo888ggLFy5k\n9OjRbNq0iXXr1h3f48PtdlNcXHz8/Pj4eDZs2EBJSQnZ2dnMnDmTO+64gzlz5hw/JyYmhjfffJOq\nqirGjBnDD37wA8aPH88f//jHLrhEkdD1/uE6/vx5NZFWCwvH9cJua9e+oCIi0s0SHTZ+c1nr9PIn\nPylnl7fR5EQiwaldC85nzJjBjBkzTnnbqlWrTjo2fPhw3n333TYfc/DgwbzxxhvteXqRHuloYwu/\n3ty6Xupno1IYnOQ4wz1ERMRMl2ZEc9P5iTy3p5JfbHTzQl4/nJH60kjkH+kvQiQIGYbBfZuPUN7o\nJzvdyY+GJZodSURE2mHm6BQGJdo5WNPMQ9vKzI4jEnRUfIgEoZf2VvH3w3XERlr5dU461na0sBYR\nEfM5bFZ+O64XkVYLf/68mr8fqjU7kkhQUfEhEmQ+r2jioYLWXczvGZtG71i1bBQRCSWDkhzcPrq1\nQcivNx+hrF67n4t8TcWHSBBpaAnwn++78f3/9u48vqkyXwP4k31pkrahTbq3iGxFFqWo7KilAjpc\nl1Gv6Hjp4AjCOJSKKCM6jCJeBmXEDXVGhyo4wnUYF0SkyC6IVClCSwFZSreke9OmadZz/yh0KJS2\nLGPmbJIAACAASURBVO1p0uf7+eRTOHlP+MW3mTlPzrv4BNxzrQHjuYs5EZFfmtI/BDdFaFDt9GLB\ndxZ4ufwuEQCGD6Iu5dWsMpyocaFnsBJzh7W82SYREXV9UknjKoVGtQw/WBxYmcPld4kAhg+iLmNz\nfi3+dcwGpVSCl0dFQCPnx5OIyJ+FaeR4caQZALDiQAWySx0iV0QkPl7dEHUBJXY3Xvi+FAAwZ2gY\n+hq5rC4RUSAYERWEqQNC4RWA+bssqHF6xS6JSFQMH0Qi8/gE/HGnBbUuH8bEBOGBvsFil0RERFfR\nzCE9MDBMDYu9cf8mQeD8D+q+GD6IRPbez5XILmtAuEaGhcPNkHBZXSKigKI4M5xWp5Bia4Eda4/W\niF0SkWgYPohEtKfYjr8frIQEwEujIhCqloldEhERdYBovQLPDzcBAF7NKseRSqfIFRGJg+GDSCRW\nuxt/3GWFAGD6YCOGRWjFLomIiDrQ+Hg97u1tgNsn4OmdJbC7fWKXRNTpGD6IRND4fzwWVDu9GB6p\nxe8GGsUuiYiIOsGTSeG4NkSJfJsbL3D+B3VDDB9EInhjfzkOlDXApJVj0SgzpJznQUTULWjkUiwd\nEwmtXIJN+XX45Ajnf1D3wvBB1Mm2FtTho9xqyCTAktERMKrlYpdERESdKCFYiYUjGvf/WPZjGX4u\n4/4f1H0wfBB1osJaN57/zgoA+MMNYRhi0ohcERERiWF8vB5T+oXA4wPm7bCgssEjdklEnYLhg6iT\nOL0+zNtRgjq3D+NigvCb/iFil0RERCJKuyEMg8LVsNZ78OwuK7w+zv+gwMfwQdRJlu4rw+FKJ6J1\ncrwwkvt5EBF1dwqZBH8ZHYEQlQzfl9TjvYOVYpdE1OEYPog6wbpjNfjXMRuUUgn+MiYSeiX38yAi\nIsAcpMDLoyMgAfC3nyvxXZFd7JKIOhTDB1EH+7nMgf/9oQwA8OzNJiT2UItcERERdSU3R2rx+OAe\nEAA8u8uColq32CURdRiGD6IOVO7wYO72Erh9Ah7oG4zJvQxil0RERF3QtIGhGB2tRY3Lhznbi+Hg\nBoQUoBg+iDqI2yvgqe0lKHN4cb1JjSeTwsUuiYiIuiipRIKXRkUg3qDAsSoX/sQNCClAMXwQdZBX\nssqQXdYAs1aOpWMioZBygjkREV2cXinDX8dFQaeQIjO/Dh8cqhK7JKKrjuGDqAN89ksN1h6tgVIq\nwatjI9FDw40EiYiobT2DlXhplBkSAG9lV2BHYZ3YJRFdVQwfRFfZofIGLN77nwnmA8I4wZyIiNpv\nTIwOM4c0TkD/4y4rTta4xC6J6Kph+CC6iqx2N+ZsK+YEcyIiuiLTrgtFcpwOdrcPc7YVo9blFbsk\noquC4YPoKnG4fUjbVoJyhxdJZg2eHMoJ5kREdHkkEgn+PMKM3qFK5Nvc+OMuC3dAp4DA8EF0FfgE\nAc9+Z0FepRNxegVeGRsJhYwTzImI6PJpFVL8dWwUQlRS7Cqqx19/LBe7JKIrxvBBdBW8sb8CWwvs\n0CuleP3WKASruIM5ERFduWi9AkvHRkIuBVbnVWPtkWqxSyK6IgwfRFfoi+M2rMypgkwCLB0TiXiD\nUuySiIgogCSZtXj+ZjMA4C/7yvBdkV3kioguX7vCx9tvv42ePXtCo9EgKSkJu3btarX9wYMHMXbs\nWGi1WsTExODFF1+8aNtdu3ZBLpdj4MCBl1Y5URfwo9WBF7+3AgDm32jCTZFakSsiIqJA9KteBjw6\n0AivADy904JjVU6xSyK6LG2GjzVr1iAtLQ0LFixAdnY2RowYgYkTJ6KgoKDF9jabDePHj0dkZCSy\nsrKwfPlyLF26FMuWLbugbVVVFR555BEkJydDIuH4ePIvp20uPLmtGB4f8FC/ENzbJ1jskoiIKIA9\nPtiIlPjGFbD+sKUY5Q6P2CURXbI2w8eyZcuQmpqKadOmoW/fvnj99dcRGRmJFStWtNh+9erVaGho\nQEZGBhITE3Hvvffi6aefbjF8TJs2DampqRg+fDgEgSs4kP+oavDiD1uLUePyYVS0FnOGholdEhER\nBTipRIIXRpoxKFwNS70HaVuL4fD4xC6L6JK0Gj5cLhd++uknpKSkNDuekpKC3bt3t3jOnj17MHr0\naKhUqmbti4uLkZ+f33Ts7bffRllZGRYsWMDgQX7F4fEhbVsx8m1u9A5V4uVREZBJeeeOiIg6nkom\nxV/HRiJaJ0dOhRMLvrPAx+so8iOtho/y8nJ4vV6YzeZmx00mEywWS4vnWCyWC9qf/fvZcw4ePIgX\nXngBq1at4nAr8iten4Bnd1nwc1kDIoLkePPWaOiUXNmKiIg6j1Ejx/JboqBTSLHltB1L95Xxi1zy\nG/Kr/YJthQmn04kHHngAr7zyCuLj4y/ptbOysq6kNOog3aVfBAH42KrGtioVtFIBj5urcDq3AqfF\nLuwydJc+CyTsM//DPvM//tZn0yNlWF4QhE+O1MBVacHEMJfYJXUqf+uv7qJ3796tPt9q+AgLC4NM\nJoPVam123Gq1IjIyssVzIiIiLrgrcvb8iIgIlJSUIC8vD6mpqUhNTQUA+Hw+CIIAhUKBr7/+GsnJ\nyS2+dlJSUqtvhjpfVlZWt+mXDw5VYltVBZRSCd5IjsENZo3YJV2W7tRngYJ95n/YZ/7HH/ssCYDp\nVC2e2WnBujINBvdOwOReBrHL6hT+2F/dRU1NTavPtzrsSqlUYujQodi0aVOz45mZmRgxYkSL5wwf\nPhw7d+6E0+ls1j46Ohrx8fGIiYnBoUOHcODAgabHjBkzcO211+LAgQMYPnx4e98bUaf56oQNb+yv\ngATAolFmvw0eREQUWFIS9HhqWDgA4IU9VuziHiDUxbW52lV6ejpWrlyJ999/H4cPH8bs2bNhsVgw\nY8YMAMD8+fOb3amYMmUKtFotpk6dipycHKxbtw5LlixBeno6AEAulyMxMbHZIzw8HCqVComJiQgK\nCuqgt0p0eXYW2bFwd+Pdu7lJ4Rgfrxe5IiIiov94sF8IUgeEwisAT20vwaHyBrFLIrqoNud83H//\n/aioqMCiRYtQUlKCgQMHYsOGDYiNjQXQOIn8xIkTTe0NBgMyMzMxa9YsJCUlwWg0Yu7cuZgzZ85F\n/w2JRMKJ59Ql/Wh14KntJfAIwNQBoZjSP0TskoiIiC7wxPU9UObwYP2JWjyxpRj/uD0GCcFKscsi\nuoBE6OLLI5w7biw4mJu4dTWBPObycEUDHsssQp3bh3t7G/DsTaaACMmB3GeBin3mf9hn/icQ+szt\nEzBnazG+K66HWSvHB7fHIEqnELusDhEI/RWo2rp2b3PYFVF3dLLGhZnfFqPO7UNKvA7zbwyM4EFE\nRIFLIZVg6ZhIXG9Sw1rvwYzNRSir5y7o1LUwfBCdp7jOjcc3F6Ha6cWIKC0WjeQmgkRE5B80CimW\n3xKF/kYVCmrdmLG5CFUNXrHLImrC8EF0jnKHB49vLoK13oMh4Wq8MjYSChmDBxER+Q+9Uoa3bovG\nNcFKnKhxYda3Rah1MYBQ18DwQXRGpcODxzKLcLrWjT6hSrx+axQ0cn5EiIjI/4SqZXgnORqxegUO\nVzrxhy3FcLh9YpdFxPBBBACVDR5M31yEkzUu9ApWYkVyNPRKmdhlERERXbZwrRzvJEfDrJUju6wB\naduK4fAwgJC4GD6o26tq8GLG5iL8Uu1Cz2Al3h0fDaO6zVWoiYiIurwonQLvJEejh1qGHywOpG1l\nACFxMXxQt1bj9OLxzUU4VuVCgkGB98ZHo4eGwYOIiAJHQrASf0uJYQChLoHhg7ot25ngcaTKiTi9\nAu+Oj0EYgwcREQWgngwg1EUwfFC3VNXgxfTNRThc6USsvvGOh0nL4EFERIGLAYS6AoYP6nbK6j34\n3aZC5J0JHu+Oj4Y5KDB3gCUiIjrX+QFk9pZi1HMVLOpEDB/UrVjsbjy6qRDHa1y4JliJ91NiEMng\nQURE3cjZABKmkWGf1YEZm4tgc3IfEOocDB/UbRTWuvHbbwpxutaNvqEq/C0lGuEcakVERN1Qz6Yv\n4OQ4WN6A32UWotLhEbss6gYYPqhbOFnjwm+/KUCJ3YOBYWq8x+V0iYiom4szKPHB7TGINyhwtMqF\n324qhMXuFrssCnAMHxTwcsob8NtvClHm8OIGkwYrkqNhUHEDQSIiooggBT5IiUGfUCXybW6kflOI\nfJtL7LIogDF8UEDbXWzH7zILUe30YmSUFm/eFoUgBX/tiYiIzjJq5Pjb+BgMClfDYvdg2jeFyKts\nELssClC8CqOA9dUJG2ZvKYbDI+DOa/T46y1R0Mj5K09ERHQ+g0qGFbdF48YIDSoavHh0UxG+L7aL\nXRYFIF6JUUD6MLcKC76zwiMAUweE4oURZiikErHLIiIi6rK0CineuDUKExJ0sLt9eGJLMdafsIld\nFgUYhg8KKD5BwLIfy/DXH8sBAE8ODcPsG8IgkTB4EBERtUUpk+KlURF4JDEEHgF47jsrPjhUCUEQ\nxC6NAgTDBwUMh8eHp3aU4KPcasglwEsjzXg4MVTssoiIiPyKVCLBnKHheCopDBIAb+yvwP/+UAav\njwGErhzDBwWEsnoPHt1UiC2n7dAppHjjtmhMusYgdllERER+a0r/UCwZEwGFVIK1R2uQvq0Edu6G\nTleI4YP83tEqJx75ugC5FU5E6+RYOSEGN0dqxS6LiIjI742P12NFcjSClVLsKLJj6sYCFNdxLxC6\nfAwf5Nd2FtmRurEAlnoPBoWr8eGEWPQKUYldFhERUcAYatbgw4mx6GlQ4JdqFx7eUIDsUofYZZGf\nYvggvyQIAj7MrULa1mLUewTcnqBr3LVcw13LiYiIrrY4gxIZE2MxPFKLKqcXj2UW4cvjXAmLLh3D\nB/kdh8eHP+6y4K8/lsMnAI8NMuLlURFQyfjrTERE1FH0ShlevzUKD/QNhtsn4PndVrz2Yzk8nIhO\nl4BXa+RXimrdmLqxABtP1UErl+CVsZF4fHAPLqVLRETUCeRSCZ650YT5N4ZDJgEycqsw69siVDZ4\nxC6N/ATDB/mN74vteGjDaRytciFOr8CHE2NxW5xO7LKIiIi6nfv7huDd8THooZbhB4sDU74qwKHy\nBrHLIj/A8EFdnk8Q8MGhSszaUowalw+jorVYNYkTy4mIiMQ01KzBx3fEYVC4GtZ6D377TSH+dbSG\nGxJSqxg+qEurbPDgiS3FeGN/BXwC8OhAI5bfEgW9UiZ2aURERN2eSSvH38fHNM0DWbS3FH/eUwoH\n9wOhi2D4oC7rJ6sD/73+NHYX1yNEJcXrt0Zh1pAekHJ+BxERUZehkDXOA3lxpBkqmQSfH7fhoa8L\ncKzKKXZp1AW1O3y8/fbb6NmzJzQaDZKSkrBr165W2x88eBBjx46FVqtFTEwMXnzxxWbPr1u3Dikp\nKTCZTDAYDLj55pvx5ZdfXt67oIDiEwS8f7ASv8ssRJnDiyHhavzzjjiMjg4SuzQiIiK6iDuvMeCj\nibHoGazEyRoXfvN1AT7lMCw6T7vCx5o1a5CWloYFCxYgOzsbI0aMwMSJE1FQUNBie5vNhvHjxyMy\nMhJZWVlYvnw5li5dimXLljW12bFjB5KTk7FhwwZkZ2dj0qRJuPvuu9sMNRTYSus9mPVtMd7Mbhxm\nlTogFO+lxCAiSCF2aURERNSG3qEqrJ4Yi7uuNcDpFfDS3lI8tcOCWpdX7NKoi2jXjmzLli1Damoq\npk2bBgB4/fXXsXHjRqxYsQKLFy++oP3q1avR0NCAjIwMqFQqJCYmIi8vD8uWLUN6ejoA4LXXXmt2\nzvPPP4+vvvoKn332GUaNGnWl74v8UGZ+LRZ9Xwqby4cQlQwvjjRjFO92EBER+RWNQoo/DTfjpggt\nFu0txben65Bb0YAXRpqRZNaKXR6JrM07Hy6XCz/99BNSUlKaHU9JScHu3btbPGfPnj0YPXo0VCpV\ns/bFxcXIz8+/6L9ls9lgNBrbWzsFiFqXFwu+s2DeDgtsLh9GRmmx9s44Bg8iIiI/NqGnHv+8IxYD\neqhQYvfgsU1FeDWrDE4vJ6N3Z22Gj/Lycni9XpjN5mbHTSYTLBZLi+dYLJYL2p/9+8XOeeutt1Bc\nXIzf/OY37SqcAsOPVgfuX38aX52ohVomwfwbw/HGrVEI17brphwRERF1YbF6Jf4xIRaPDTJCKgFW\nHa7Gg18VIKeCe4J0Vx1yhXepu03/61//wrx587B27VrExsZetF1WVtaVlkYd4HL6pcEHrCtVY1uV\nEgIkiFd78GiUAxG11fjxxw4okprhZ8n/sM/8D/vM/7DPOs4wAGHxMnxQrMHJGhce2XAad4Q5MSnM\nCfllLmLJ/uqaevfu3erzbYaPsLAwyGQyWK3WZsetVisiIyNbPCciIuKCOxxnz4+IiGh2/NNPP8X/\n/M//4KOPPsIdd9zRai1JSUltlUudLCsr65L75ftiOxZ/X4oSuwdyCZB6nRG/G2SEQsoldDvD5fQZ\niYt95n/YZ/6HfdbxkgD8yuPDG/sr8HFeNb4sV+OI14DnbzZjQJj6kl6L/dV11dTUtPp8m8OulEol\nhg4dik2bNjU7npmZiREjRrR4zvDhw7Fz5044nc5m7aOjoxEfH990bO3atXjkkUeQkZGBe+65p61S\nyM/ZnF4s3G3F498Wo8TuQX+jCqsmxWHmkB4MHkRERN2AWi7FU8PC8d74aETr5Dha5cIjGwvwSlYZ\nNybsJtq11G56ejpWrlyJ999/H4cPH8bs2bNhsVgwY8YMAMD8+fORnJzc1H7KlCnQarWYOnUqcnJy\nsG7dOixZsqRppSsA+OSTT/DQQw9hyZIlGDVqFCwWCywWCyorK6/yWySxCYKAb07V4t4v8/H5cRuU\nUgmeuL4HPpwYi75GVdsvQERERAFlWIQW/3dnPH6TGAIAWH24Gr/+Mh+7i+0iV0YdrV1zPu6//35U\nVFRg0aJFKCkpwcCBA7Fhw4am+RkWiwUnTpxoam8wGJCZmYlZs2YhKSkJRqMRc+fOxZw5c5ravPvu\nu/D5fJg9ezZmz57ddHzcuHHYsmXL1Xp/JLJTNS787w+l2GtxAACGhKvxp+FmJAQrRa6MiIiIxKRR\nSJE+NBwTEvR4YU8pjlQ5MevbYkxI0GHO0HCYuPhMQGp3rz7++ON4/PHHW3zuH//4xwXHrrvuOmzf\nvv2ir7d169b2/tPkhxweH/5+sBIf5lbB4wOClVL84YYw3HWtAdJLXJCAiIiIAldiDzU+mhSL1Yer\n8M6BSmw8VYfthXY8NsiIh/qFQiHjdUMgYaSkq0oQBHx7ug7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- "text": [ - "" - ] - } - ], - "prompt_number": 12 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "This corresponds to a fairly inexact belief. While we believe that the dog is at 23, note that roughly 21 to 25 are quite likely as well. Let's assume for the moment our dog is standing still, and we query the sensor again. This time it returns 23.2 as the position. Can we use this additional information to improve our estimate of the dog's position?\n", - "\n", - "Intuition suggests 'yes'. Consider: if we read the sensor 100 times and each time it returned a value between 21 and 25, all centered around 23, we should be very confident that the dog is somewhere very near 23. Of course, a different physical interpretation is possible. Perhaps our dog was randomly wandering back and forth in a way that exactly emulated a normal distribution. But that seems extremely unlikely - I certainly have never seen a dog do that. So the only reasonable assumption is that the dog was mostly standing still at 23.0.\n", - "\n", - "Let's look at 100 sensor readings in a plot:" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "dog = DogSensor(x0=23, velocity=0, \n", - " measurement_variance=5, process_variance=0.0)\n", - "xs = range(100)\n", - "ys = []\n", - "for i in xs:\n", - " ys.append(dog.sense_position())\n", - " \n", - "plt.plot(xs,ys, label='dog position')\n", - "plt.legend(loc='best')\n", - "plt.show()" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "display_data", - "png": 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zzzyDQCCAs88+G/v27UN7ezsuvPBC/TVutxtnn302NmzYUJCDJSIiIio3iqqyuZxGhYw7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\n+nfu184xQU48AEOIoPY+tIDo46T/69qWzj7HiyURFUnBYCJ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5rPg88QB0MbtdWrqbADmm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\n6fZO79q1S1OmTNGUKVPU1NSk1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- "text": [ - "" - ] - } - ], - "prompt_number": 69 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Eyeballing this confirms our intuition - no dog moves like this. However, noisy sensor data certainly looks like this. So let's proceed and try to solve this mathematically. But how?\n", - "\n", - "\n", - "Recall the histogram code for adding a measurement to a preexisting belief:\n", - "\n", - " def update(pos, measure, p_hit, p_miss):\n", - " q = array(pos, dtype=float)\n", - " for i in range(len(hallway)):\n", - " if hallway[i] == measure:\n", - " q[i] = pos[i] * p_hit\n", - " else:\n", - " q[i] = pos[i] * p_miss\n", - " normalize(q)\n", - " return q\n", - " \n", - "Note that the algorithm is essentially computing:\n", - "\n", - " new_belief = old_belief * measurement * sensor_error\n", - " \n", - "The measurement term might not be obvious, but recall that measurement in this case was always 1 or 0, and so it was left out for convenience. \n", - " \n", - "If we are implementing this with gaussians, we might expect it to be implemented as:\n", - "\n", - " new_gaussian = measurement * old_gaussian\n", - " \n", - "where measurement is a Gaussian returned from the sensor. But does that make sense? Can we multiply gaussians? If we multiply a Gaussian with a Gaussian is the result another Gaussian, or something else?" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "It is not particularly difficult to perform the algebra to derive the equation for multiplying two gaussians, but I will just present the result:\n", - "$$\n", - "N(\\mu_1, \\sigma_1^2)*N(\\mu_2, \\sigma_2^2) = N(\\frac{\\sigma_1^2 \\mu_2 + \\sigma_2^2 \\mu_1}{\\sigma_1^2 + \\sigma_2^2},\\frac{1}{\\frac{1}{\\sigma_1^2} + \\frac{1}{\\sigma_2^2}}) $$ \n", - "\n", - "In other words the result is a Gaussian with \n", - "\n", - "$$\\begin{aligned}\n", - "\\mu &=\\frac{\\sigma_1^2 \\mu_2 + \\sigma_2^2 \\mu_1} {\\sigma_1^2 + \\sigma_2^2}, \\\\\n", - "\\sigma^2 &= \\frac{1}{\\frac{1}{\\sigma_1^2} + \\frac{1}{\\sigma_2^2}}\n", - "\\end{aligned}$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Without doing a deep analysis we can immediately infer some things. First and most importantly the result of multiplying two Gaussians is another Gaussian. The expression for the mean is not particularly illuminating, except that it is a combination of the means and variances of the input. But the variance of the result is merely some combination of the variances of the variances of the input. We conclude from this that the variances are completely unaffected by the values of the mean!\n", - "\n", - "Let's immediately look at some plots of this. First, let's look at the result of multiplying $N(23,5)$ to itself. This corresponds to getting 23.0 as the sensor value twice in a row. But before you look at the result, what do you think the result will look like? What should the new mean be? Will the variance by wider, narrower, or the same?" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "from __future__ import division\n", - "import numpy as np\n", - "\n", - "def multiply(mu1, var1, mu2, var2):\n", - " if var1 == 0.0:\n", - " var1=1.e-80\n", - " \n", - " if var2 == 0:\n", - " var2 = 1e-80\n", - " \n", - " mean = (var1*mu2 + var2*mu1) / (var1+var2)\n", - " variance = 1 / (1/var1 + 1/var2)\n", - " return (mean, variance)\n", - "\n", - "xs = np.arange(16, 30, 0.1)\n", - "\n", - "mean1, var1 = 23, 5\n", - "mean, var = multiply(mean1, var1, mean1, var1)\n", - "\n", - "ys = [stats.gaussian(x, mean1, var1) for x in xs]\n", - "plt.plot (xs, ys, label='original')\n", - "\n", - "ys = [stats.gaussian(x, mean, var) for x in xs]\n", - "plt.plot (xs, ys, label='multiply')\n", - "\n", - "plt.legend(loc='best')\n", - "plt.show()" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "display_data", - "png": 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kZGOnP+d0HBGRgKdyIiISAOKWvJP76OB212EaXup0HPkNc/u9EBKKXbEI+/3X\nTscREQloKiciIn7ObtlI9MYvIDgEc/t9TseR3zGVq2J6DQDAN+U/YK3DiUREApfKiYiIH7PW5v7A\nC5iet2Ji4xxOJKdj+gyCCpXgh2+psHmt03FERAKWyomIiD9b/Sl8t4Hs8EhM3zudTiNnYDwRmFv/\nCEDc4rnY7CyHE4mIBCaVExERP2W9OfhOPjo4qX1PTESkw4nkbEynXlDzIkJTD2IXvu10HBGRgKRy\nIiLip+ySD2DPDoitzsEW7ZyOI+dg3G5ct90DgH3rVWz6CYcTiYgEHpUTERE/ZLMysbNfAsDcOgLr\nDnI4kRTI5R1Ii68LqYex7890Oo2ISMApUDl58cUXqVOnDh6Ph4SEBFasWHHGdZcuXUqvXr2Ii4sj\nIiKCZs2aMWXKlFPWW7ZsGa1atcLj8XDRRRfx0ksvXfhZiIiUMvbjtyAlCWrXx7Tr6nQcKSBjDHs7\n9gHAvvsG9ugRhxOJiASWc5aTOXPm8MADDzB27Fg2bNhAmzZt6NatG7t27Trt+qtXr6ZZs2bMnTuX\nTZs2MWLECIYNG8asWbPy1tm+fTvdu3enbdu2bNiwgTFjxjBy5EjmzZtXdGcmIhKgbHoa9u3XAHDd\ndi/GpUHuQHK8dkNo3hpOHMfOO/Uf50RE5MzO+R3v6aefZvDgwQwZMoSGDRvy3HPPUa1aNSZNmnTa\n9ceMGcM//vEPWrduTe3atRk+fDh9+vRh7ty5eetMnjyZ6tWr89///peGDRty1113MXDgQP79738X\n3ZmJiAQoO38GHD0CjZtDguaaBCLX7fcCYBfMwaYkO5xGRCRwnLWcZGVlsW7dOrp06ZJveZcuXVi1\nalWBD5Kamkp0dHTe16tXrz7tPteuXYvX6y3wfkVEShubegj77hsAuG4fiTHG4URyIUy9Jpg2nSEr\nEzvnZafjiIgEjLOWk5SUFLxeL7GxsfmWV6lShaSkpAId4IMPPmDx4sUMGzYsb1lycvIp+4yNjSUn\nJ4eUlJSCZhcRKXXs3Nch4wS0vApzcUun40ghmNv+CC439tP52D0/Ox1HRCQgFOvjX1auXMltt93G\nxIkTSUhIKNS+1q7VG3cDha5V4NC18i/BqQdp8uEcXMD3La8h/XfXR9crcPxyrWpc2oaYDZ9x8IXH\n2NFn2Dm2Eifoz1Vg0fXyf/Xr1y/U9mctJzExMbjdbpKT898vm5ycTLVq1c664xUrVtCjRw/++c9/\ncvfdd+flDU8qAAAgAElEQVT7rGrVqqeMvCQnJxMUFERMTMxp91fYciMlY+3atbpWAULXyv/4nh+H\n9eZg2l3Hxdf3yfeZrlfg+O21srVr4BtxAxU3r6HSXaMwdRs5nE5+S3+uAouuV2BITU0t1PZnva0r\nJCSEVq1asWjRonzLExMTadOmzRm3W758Od27d2fcuHHcd999p3zeunVrEhMTT9nnZZddhtvtPp/8\nIiKlgt23C7v4fXC5MbeMcDqOFBETE4vp1h8A3+zJDqcREfF/53xa16hRo5g6dSqvvfYa3333Hfff\nfz9JSUkMHz4cyH0617XXXpu3/tKlS+nWrRsjRozglltuISkpiaSkJA4cOJC3zvDhw9mzZw8PPvgg\n3333Ha+++irTpk3jz3/+czGcooiI/7NvvgI+L6bj9Zi4Wk7HkSJk+gyG0DD4chn2x01OxxER8Wvn\nLCf9+/fn2WefZfz48bRo0YJVq1axYMECatSoAUBSUhLbtm3LW3/atGlkZGTw1FNPUa1aNeLi4oiL\ni+OKK67IW6d27dosWLCA5cuX06JFCyZMmMDEiRPp3bt3MZyiiIh/s3t/xi77ENxBmH53OR1Hipip\nEI3pdhMAvtl64bCIyNkUaEL8iBEjGDHi9LcZ/P7t71OmTDntG+F/r3379nz11VcFObyISKmWO2ri\nw1x7A6ZqdafjSDEwve/AfvwmrP0Mu2UjpkFTpyOJiPglvXZYRMRBds8O7PKPTo6aDHU6jhQTExWN\n6f7L6InmnoiInInKiYiIg/JGTa65ARMb53QcKUbmD3dAWDisW4n9/mun44iI+CWVExERh9jd27Gf\nfQxBQZh+Q5yOI8XMlK+Iuf4WQHNPRETOROVERMQhds7LuaMmnXphqmjUpCwwvQaAJwI2rMZ+v8Hp\nOCIifkflRETEAXbXT9gVC3NHTW7UqElZYSKjfh09maW5JyIiv6dyIiLiADv7ZbAWc21vTOVqTseR\nEmR6DYDwcvD1F9hN65yOIyLiV1RORERKmN31E3ZVIgQFa9SkDDLlymN63gpo7omIyO+pnIiIlDD7\n1mu5oyade2NiYp2OIw4wPW/PHT359ks9uUtE5DdUTkRESpDd+3PuXBN3EKbPIKfjiENMuUhMj5sB\n8L35isNpRET8h8qJiEgJsnOn5D6hq+P1mmtSxpmet0KYJ/e9Jz9udjqOiIhfUDkRESkhNnkvdumH\n4HJj+t7pdBxxmClfEdO1HwC+t151OI2IiH9QORERKSF23uvgzcG074qpVsPpOOIHTK8BEBIKXyzB\n7tjidBwREcepnIiIlACbkoz99D0wRk/okjymYgymc28A7NuvOZxGRMR5KiciIiXAvjsNcrIxbTpj\nqtdxOo74EdN7EAQFYVcmYndvdzqOiIijVE5ERIqZPZyCXTQPANNPoyaSn4mJxVzTC6zV6ImIlHkq\nJyIixczOnwFZmXB5B0ztBk7HET9k+g4Glxu7/GPsvl1OxxERcYzKiYhIMbJHD2M/fhMAV/+hDqcR\nf2Vi4zEdeoDPi503xek4IiKOUTkRESlG9v3/QUY6tLwKU6+J03HEj5m+d4LLhV3yPvZAktNxREQc\nEeR0ABGR0sqeOI5dMAcAV7+7HE5T8qy1HMvysS8th2NZXtK9lowcHxk5lvQcHzk+CAsyeIIMYW4X\nYUGGsCAXMR43VcODCXYbp0+hRJn4WpirOmM/W4h9bwZmyJ+djiQiUuJUTkREion9+G1IOwYXt8Q0\nbu50nGKT6fXx45EsvjuYyZbDmexLy2bf8RySTuSQlu27oH0ayC0pEcFUiwiiZvkQGkeH0ig6lGoR\nQRhTOouL6T04t5wsmovtNwRTvqLTkURESpTKiYhIMbCZGdj3ZgDgKmXvNUlOy2b1vhNs2J/Bd4cy\n2HYkixx7+nU9QYZqEcFUCHXnjpAEnRwhcRuCXIbM342mnMixHDiRw/70HA6kezmQ7uXblPz7rBDq\nolF0GI2jQ7m8WjgtqoQR6i4ddymbug2h5VWwbiX2w9mYW0Y4HUlEpESpnIiIFAO7+D04chDqNoLm\nrZ2OUyjpOT7WJaezeu8JVu87wbbUrHyfG6BOVAhNokNpEB1Kjchg4iKCqRoRRPkQ1wWNcuT4LPtP\n5JCUlsO+tGy2peaOzHx3KIMjmT4+33eCz/edYMqmw4S5DS1jPbSuFk7ruHDqRoUE9MiKq++d+E6W\nE/uHgRhPuNORRERKjMqJiEgRs94c7DvTAHDdeGdA/qCc7bWs3JvGR9uPsXx3GhneX4dGwoMMCVXD\nuaKqhyaVwmhQMZTw4KIduQhyGeLKBRNXLhjw5C231pJ0IofvD2by9YEMVu9LY8vhLFbtPcGqvSfg\nK6gRGUzX2pF0rRNJ3aiQIs1VIpq0gEbN4PuvsYvmYnoNcDqRiEiJUTkRESli9rOFsH8vxNWCK65x\nOk6B+azlq+R0Ptp+jE93Hudo1q/zRRpHh9ImLpwr48JpFuNxbLK6Mbm3iVWLCKZjzXI8QAwp6Tl8\nse8Eq08WlF3Hsnnl20O88u0hGlYMpVudSLrWLkdsRLAjmc+XMSZ39OSx+7Hzp2O734QJDsCSJSJy\nAVRORESKkPX5sHNfB3JfrGfcbocTnduxLC/v/XSUOT+ksutYdt7y+hVD6FY7kutqR54cwfBPMZ4g\netQtT4+65fH6LGt/U7B+OJzJD4czeW59CldXj+DmhhW4rKrH/0ezWrWFmvVg54/YpR9iOvd2OpGI\nSIlQORERKUprlsGubVApFtO+u9NpzurHw5nM/uEIH247lnfbVtWIIK6vk3tL1EUVQh1OeP7cLsMV\n1cK5olo4D19RmZV7TvDRjmMs2XWcJbvSWLIrjTpRIdzcMIrr65Yv8tvRiopxuTB9B2OfeQT7zlTs\nNTcERNEVESkslRMRkSJircX39slRk953YIL9c7RhXXI6L39zkC+S0vOWXV7Vw82NKtA+PgK3y89H\nFQooxO2iY81ydKxZjpT0HOZuTeXtLalsT81iwpcHmLj+IP0bRnF744pUDPO/H/xN2y7YmS/A3p3w\nxWJo09npSCIixU7lRESkqHy7BrZuhPIV/PI2nLVJJ3jpm0OsTc4tJZ4gQ8+65enfMCogR0nOR4wn\niLsvrcSdTaNZvPM4s78/woYDGby+8TCzvj/CTQ0rMKBJBaLD/OfbonEHYf4wEPvyBHxvT8HV+lr/\nvx1NRKSQ/OdvYRGRAOd7+zUATM/bMKGec6xdctYknWDy14dYtz+3lJQLdnFb4wrc2qgC5UP9b8Sg\nOAW7DNednEfzzYF0Xv7mECv3nmDqpsPM/v4I/RtGMbBJRaI9/vHt0XS6ATvnJdj2HWz4HFoE9mOp\nRUTOxT9vthURCTD2x03wzZfgicB0u8npOAD8dCSTez/dw7DEPazbn05kiIvhzaJZ0Kc2w5tVKnPF\n5Pcurezh+U7xTO9Wg3bx4WR4LW9sPkLPd3fw2reHyMi5sLfbFyUTGoa54TYAfPOmOJxGRKT4+cc/\nDYmIBDjfvKkAmOv6YspFOprlUHoOk785xLytqXht7kjJHU0qckujKMqFlO1CcjpNY8J47pp4Nh/M\nYPLXB/lszwme33CQt7emcl+LGLrWLufo7VSmaz/s3Cnw7Rrslm8xDS5xLIuISHHTyImISCHZvT/D\n6k8hKDjvX7mdkOn1MXXTIXrN/5m3tqQC0L9BFPP/UIuhl0armJxDk0q5JWXytfHUrxhCUloOD69I\nYuDHu9mwP/3cOygmJiIS060fQN4DF0RESiuVExGRQrLvTgdrMR16YKKrOJJhTdIJbvpgJ/9dd5Dj\n2T7axocz5/qajLmiil9N8g4EV1QLZ1b3mvzflVWI8bj5NiWDwQt3M251MqmZXkcymetvheAQ+HIp\ndtdPjmQQESkJKiciIoVgDx3ALn4PjMH0Hljixz+c4eX/ViYxLHEPPx/Npk5UCC92imPiNfGl/glc\nxcntMvSuH8X8XrW5q2lFgl2Gd388Su/5P7Ng21GstSWax1SMwXTqBYA9eQuhiEhppHIiIlII9oP/\nQU42XNERE1+75I5rLe//dJQ+7+3g/W3HCHEZRjSLZnaPGrSOiyixHKVdeLCLe1rEMOf6mrSK9XA4\n08sjK5P546d72XUsq0SzmN4DweXGLv8Yu39viR5bRKSkqJyIiFwgm3YM+/HbALj6DCqx4+5Ly2bE\nJ3v4v1XJHMn0cVmshzd71mTYpZUIceuv9eJQJyqEVzrH82jrKkSFuPh83wn6vb+TNzYdxusrmVEU\nExuPadsFvDnY+dNL5JgiIiVN38VERC6QXTgXThyHpgkl8gQlay0fbDtK//d38kVSOhVCXYxrE8tL\nneOpVT6k2I9f1hlj6FUvinm9atGjbiSZXssz61IYlriHPceySyZDn8EA2MR3samHSuSYIiIlSeVE\nROQC2KxM7PszgZIZNTmWY/jz8n38bWUyx7N9XF09grk9a3HDReX11vASFh0WxPirqvJcxzgqhblZ\ntz+d/h/8zLs/phb7XBRTuz4ktIesDOwHs4r1WCIiTlA5ERG5AHbph3A4BWo3gBZtivVYy3cf59Ft\n5Vi8M42IYBePtq7CMx2q+c1bzMuqdtUjeKtnLTrVLMeJHMu41ft5cOk+juYUb1l09T05erJgDvbE\n8WI9lohISVM5ERE5T9brxb47DQDTZ1CxjVxken088eV+7l+yj6NeF61iPbx5fU161YvSaImfqBjm\n5qn2VRl/VSzlgl0s253Go9vKsXpvWrEd0zRuDk1aQNqx3FsLRURKEZUTEZHz9cUS2LsTYuMxV3Uu\nlkPsPJrFoI93M+eHVIJccGOVdF7uHE9cueBiOZ5cOGMMPeqW562eNbks1sMxr4t7Pt3LC+tTyCmm\nyfKuX+aevDcDm12yTw0TESlOKiciIufBWovvnakAmF4DMO6iv7Vq4Y5j3LpgF98fyiS+XBBTr6vB\ndZWycGm0xK9VjQhm0rXx3BCTgTHw6sbDDEvczf4TOUV/sFZtoXZ9OJyCXfpB0e9fRMQhKiciIufj\n2zWwdROUr4DpdEOR7jojx8f4z5P562dJpGX76FSzHLN61OTimLAiPY4UH7fL0LNyJi9dG0+Mx836\n/Rnc9MFOVu4p2tu8jDGY3idHT96ZhvU68+Z6EZGipnIiInIefCffzm2uvxUT6imy/e49ns3ghbuZ\nu/UowS7DXy+vzFPtqxIZ4i6yY0jJSagazpweNbmyWjhHMr3cu3gvk78+iK8In+Zl2naGKnG5txh+\nsaTI9isi4iSVExGRArLbvocNqyHMg+nWv8j2++W+E9y2YCffH8qkerlgpnWtzk0NK2jSe4CL9gTx\nQqc47mleCQO89M0hRi3dx7GsohnlMO4gzB/uAMD3ztRif4yxiEhJUDkRESkg+8tcky59MJFRhd+f\ntczYfJg/frqHI5k+2sSFM7N7DRpX0m1cpYXLGO66JJrnO8URGZL7NK87PtrF9tSimcRuOt0A5Svk\n3mr47Zoi2aeIiJNUTkRECsDu24VdmQjuIEzP2wu9v/QcH2NXJvOfr1LwWrizaUWe6xhH+VDdxlUa\ntYmLYGb3GtSrEMKOo9kM+GgXS3cV/h0lJtSD6XEL8OsthyIigUzlRESkAOz86eDzYa7ujqlctVD7\nSk7LZsjC3SzYfgxPkOHJ9lUZ2SIGt0u3cZVmNSJDmNa1Bp1rlSMt28eDS/fx8jcHC307lul+E4R5\nYMPq3FsPRUQCWIHKyYsvvkidOnXweDwkJCSwYsWKM66bmZnJoEGDaNasGSEhIXTs2PGUdZYuXYrL\n5Trl15YtWy78TEREiok9cgi7+D0ATO+BhdrX5oMZDPhoF98dyqRGZDBvdK1B51qRRRFTAkB4sIt/\ntavKfS1y56FM+voQY1cmk+n1XfA+TWQUpksfAOy8KUWUVETEGecsJ3PmzOGBBx5g7NixbNiwgTZt\n2tCtWzd27dp12vW9Xi8ej4eRI0fSo0ePs07o3Lx5M0lJSXm/6tWrd+FnIiJSTOyHsyArEy6/GlOj\n7gXvZ8nO4wxZuJsD6V5aVvHwRrca1KsYWoRJJRAYYxjcNJpnOlTDE2RYsP0YwxP3cCjjwt+HYnre\nDu4g7KpPsPtO//1ZRCQQnLOcPP300wwePJghQ4bQsGFDnnvuOapVq8akSZNOu354eDiTJk3irrvu\nIj4+/qzD1ZUrV6ZKlSp5v1wu3WUmIv7FpqdhF8wBwNVn0IXtw1re2HSYPy3bR4bX0rNuJJOvjaeC\n5peUaVfXKMeU62oQGx7EhgMZDPxoN9sucKK8qVwVc3V38Plyb0EUEQlQZ20DWVlZrFu3ji5duuRb\n3qVLF1atWlXogyckJBAXF8e1117L0qVLC70/EZGiZhfOhbRj0KQFplHz894+22cZ//l+nlmXggXu\nbV6JcW1iCXZrfolAw+hQpnerQePoUHYfz2bgR7v4fN+JC9rXL7cc2k/nY48cLMqYIiIl5qzlJCUl\nBa/XS2xsbL7lVapUISkp6YIPGhcXx+TJk5k3bx7z5s2jYcOGdOrU6axzWURESprNzsa+PxMAV5/B\n5719WraP+xfvZd6PRwl15058H3JJtN5fIvlUDg/itS7VuaZmBMezfYz8dA/v/3T0vPdjatSFyztA\ndhb2g1lFH1REpAQEOXHQBg0a0KBBg7yvr7zySnbs2MFTTz1F27ZtnYgkInIKu3wBHNwPNetBq/P7\nu+lgeg4jF+/lu0OZVAx189w1cTSN0ftL5PQ8wS6eal+N59YdZNrmw/zfqmQOpOcw+OKK51VmXX0G\n4ftyKXbBHGyfQZjwcsWYWkSk6J21nMTExOB2u0lOTs63PDk5mWrVqhVpkMsvv5w5c+ac8fO1a9cW\n6fGk+OhaBQ5dq7OwPhr/bzJhwI7m7Tn81VcF3jQ5y8V/d4ZzINtN5WAvD1Q/RsaOQ6zdUbhIul6B\n40KvVVsgMzaEOclhTFx/kI079nJzbAbn85Tp+jXqU27XVna99l/2t77ugnKUJfpzFVh0vfxf/fr1\nC7X9WctJSEgIrVq1YtGiRfTt2zdveWJiIv369SvUgX9vw4YNxMXFnfHzhISEIj2eFI+1a9fqWgUI\nXauzs58vwXcwCSpXpe4dwzFBwQXabmNKBv9evJcj2V6aVAplYsc4oj2FH6TW9Qochb1WCUDLn4/x\nyIpklhwOxRVZicfaxhLqLthDYywj8Y2/j/j1y6gx/CFMcMgFZynt9OcqsOh6BYbU1NRCbX/O75ij\nRo1iwIABXH755bRp04bJkyeTlJTE8OHDARgzZgxr1qzhk08+ydtm8+bNZGVlkZKSwvHjx/n666+x\n1tK8ee5k0meffZY6derQpEkTsrKymDFjBvPnz2fevHmFOhkRkaJgrcX3Tu77IkyvAQUuJp/tSWP0\nySdytYkL56n21QgP1lMI5fx1rhVJxTA3Dy7Zx6c7j3Pokxye7RBH+YI84a1VW6hVH37eil36IaZz\n7+IPLCJSRM5ZTvr378/BgwcZP348+/bt45JLLmHBggXUqFEDgKSkJLZt25Zvmx49evDzzz8Duc9z\nb9GiBcYYvF4vANnZ2Tz00EPs3r0bj8dD06ZNWbBgAV27di3q8xMROX+b18EP30JkBcy1BfvB7qPt\nR/m/lcnkWLjhokjGXhlLsN74LoWQEBvOlOuqc8/ivazfn8Fdibt5sVM8MecYiTPGYPoMwj7zCPbd\nN7CdemH0qH4RCRAF+ttqxIgRbN++nYyMDNasWZNv0vqUKVNOKSfbt2/H5/Ph8/nwer15//3FQw89\nxJYtWzhx4gQHDx5k2bJlKiYi4jd886YCYLrfhAnznHP9N384wiMrcovJoIsr8mhrFRMpGvUqhjKt\na3Vqlw9m6+Es7ly4m73Hs8+5nWnbBSpXgz074MulxZ5TRKSo6J9SRER+w+7YAl+tgJAwTI+bzr6u\ntbz27SEmfHkAC9zXohL3t4zRo4KlSFWNCOa166rTODqUXceyGbxwNz8dyTzrNsYdhOk1AADf3Cln\nfSGyiIg/UTkREfkN+840AEyX3pjyFc+8nrU8uy6F5zccxABjr6jC4KbRJZRSyprosCBe6hxPyyoe\n9p/I4a5Fu9l0MOOs25jOf4DyFWDrRthY8KfNiYg4SeVEROQkm7wX+9lCcLkxN9x+xvW8Pss/Pt/P\nG5uPEGRgQruq9G0QVYJJpSyKDHHzQqc42sWHcyTTx92Je1ibdOa3yZtQD6bHzQD45k0pqZgiIoWi\nciIicpJ9bzr4vJh2XTFVTv9o8xyfZezKJN798ShhbsMzHeO4rnZkCSeVsiosyMV/OsTRtXY50rJ9\n3Lt4L6v2pp1xfdPtJggNg/WrsNt+KMGkIiIXRuVERASwqYewie8CYHoPPO062V7LXz7bx8c7jhMe\nZHihUzxt4yNKMqYIwS7D+Kuq0qdeeTK9lgeW7GPZruOnXdeUr4DpkvueMvvO1BJMKSJyYVROREQA\n+8EsyMqAhHaY2qe+3TbT6+NPy/ayeGca5YJdTL62Oi1jz/0kL5Hi4HYZxl5ZhZsbRpHts/x52T4S\nfz522nXNDbeDOwi7chE2aXcJJxUROT8qJyJS5tkTx7EfzgbAdeOdp3yenuPjwSX7+GzPCaJCXLzc\nOZ5LKoeVdEyRfIwxjL6sMgObVCTHwl8/S2LBtqOnrle5KqZ9N/D5sPOnO5BURKTgVE5EpMyzH78N\nJ47DxS0xjZrn++xEto/7Fu9l9b4TRIe5eaVLdRpXUjER/2CM4f6WlRh6STQ+C2NXJvPuj6mnrtcn\n91ZF++l87JFDJR1TRKTAVE5EpEyzWZnY92cC4Oqbf9Qkd8LxHtYmpxPjcfNql+rUrxjqREyRMzLG\n8Mfmlbi3eSUsMG71fuZtzV9QTI2L4LL2kJWJ/XCWM0FFRApA5UREyjS7+D04nAJ1G0GLNnnL07J9\n3PvpHtbvzyA2PIjXulSnTlSIg0lFzm7IJdE82CoGgPGf72f+70ZQXH0HA2AXzMGmn/kJXyIiTlI5\nEZEyy3pzfn3pYp/BeW92/6WYbDiQW0xe6RJPzfIqJuL/7mhSkQdaxuSNoLz3069zUEyj5tC4BaQd\nwy6c61xIEZGzUDkRkTLLrkiE5D0QVxPTuhOQW0zuOVlMqp4sJjUiVUwkcAy8uCL3tci9xevRVcl8\n8JtJ8nmjJ+/PxGZnO5RQROTMVE5EpEyyPh927usAmN6DMG43x7O83PPpHr4+WUxeVjGRADW4aXTe\nHJS/r0rmo+0nC0qrtlCzHhzcj12+wNGMIiKno3IiImXT2s9g549QqQqmw/V5b9v+Om/EpLqKiQS0\nIZdEM6LZr0/x+nj7MYwxeS8ZtfOmYn0+h1OKiOSnciIiZY61Ft8voya9BpBh3Ny/JH8xqR4Z7HBK\nkcIbdmklhl+aW1AeWZnEoh3HMO2ug8pVYc8O+HKZ0xFFRPJRORGRsmfTV/DDNxAZRfY1f2DU0n18\nlZxOZY+blzrHq5hIqXJ3s1/fg/LwiiQ+2ZOB6TUAAN+8KVhrHU4oIvIrlRMRKXN8c6fk/rf7zTz0\nZSqfn3zB4kudq+upXFIqjWgWzZCmFfFaePizJJY17AyRFWDLt7BxrdPxRETyqJyISJlif/oO1q/C\nhnkYF92Rz/acICrExeRr4/UeEym1jDHc07wSgy+uSI6F0V8cYUf7GwHwvf2aw+lERH6lciIiZcov\nc01WXtyND/e7KBfsYtK18Xrzu5R6xhhGtqjEwCa5BWVoUBtywsLh6y+wWzY6HU9EBFA5EZEyxO7Z\nAas/JccdxPjYLoQHGV7sFE/jSmFORxMpEcYY7m9ZidsbV+BwUDn+V6sz8GtpFxFxmsqJiJQZvnlT\nwVreq3E1x8tVYuI18VxSWcVEyhZjDKNaxXBzwyhm1OtBpjsYvliC3fmT09FERFRORKRs8B1Iwrvk\nQ7wYZjXuxbMd42gZ63E6logjjDE8dFll2l1ck/m1rgHg8P9ecTiViIjKiYiUAdZa1r/6Cm5fDotr\ntGbU9S25olq407FEHOUyhr9dWYUd19xMjnFT7otEdvywzelYIlLGqZyISKk3bfV2Gq79EIDoW4fS\nNj7C4UQi/sHtMvy5ezPWNeqI2/r45pWX+PloltOxRKQMUzkRkVJt6qZDZLz3PzzeTFKaXMnlrZs7\nHUnErwS7DC2HD8eHofO2xTw8/1v2Hs92OpaIlFEqJyJSar29JZVXvtjNTT99DECV24c5nEjEP4XW\nugiuvIYQXw6dv3mX4Z/s4cCJHKdjiUgZpHIiIqXSx9uP8fgX++mzPZHy2WnQuAWmSQunY4n4raB+\nQwDot/0TjqYcYsQnezic4XU4lYiUNSonIlLqfLYnjb+tTCLEm8Xd23Pnmrj6DnY4lYh/Mxc1hpZt\nCMvJ4I+7Puan1Czu+XQPx7JUUESk5KiciEip8lVyOg8t20eOhcfTV+M5fhjqNoZWbZ2OJuL3XP2G\nAtB7ywIahmTx3aH/Z+++w6Mq0z6Of58zM+mFVFLpEKQjiICAoKGpaxddd62ooIAgVnbVXesqKHZA\nX1HsYkFdBaR3FIgI0jshnfReJnOe94+BKCudJDOT3J/ryrUyc8557tnJTOY3T6vk/qXplNtNF1cm\nhGgsJJwIIRqMHbkVTFiWTqVDc0MLHy5O+hIAY8RdKKVcXJ0Q7k+d1w06X4BRXsrbVauI8rOyKbuC\niSsyqHRIQBFC1D0JJ0KIBuFAYRX3LUmnxG4ypHkAj5b8DLmHoVkb6DXQ1eUJ4TGMEc7ek4CFn/N2\nvyaE+Vj4OaOMx1ZmUm1qF1cnhGjoJJwIITxeeomdexenUVDpoG+MH89eGAbfzAJAjbgLZchbnRCn\nrVNPOK8bFBcSt+ZbpifGEuRlsDy1lH//lIWpJaAIIeqO/MUWQni03PJq7l2cRlZZNd0jfXjp4mgs\nq+fD4XSIbYHqk+jqEoXwKEqpmt4T/d1HtPE1efOSWHytirn7i5m8IRstAUUIUUcknAghPFZxlYP7\nlmtQnr4AACAASURBVKRxqNhOQog3rw2KwUeZ6K9mAqCuH4myWFxcpRAeqFsfaNsRCvPRC7+mc4QP\nrw6MwctQzN5VyLRNua6uUAjRQEk4EUJ4pHK7ybil6ezOr6J5kI1pl8YQ6GVBr14IGSkQFY8aMMzV\nZQrhkZRSNSt36W8+QFdV0ivajxcGRGFR8O7WfD7Ylu/iKoUQDZGEEyGEx7E7NA+tzGBzdgVRflam\nJ8YS6mtFmyb6y3cBUNfdgbJYXVypEB7sggHQMgHyc9CLvwVgUHwAT/dtigJe3ZjDnD2Frq1RCNHg\nSDgRQngUh6n555pM1qaXEeJtYXpiLNH+NuedPy2B1AMQEYUaeIVrCxXCwx0z92TOLLTdDsBlrYJ4\nrFcEAM/+fJgFB4tdVqMQouGRcCKE8Bhaa55dd5hFySUE2AymJcbQItir5j7zy/8DQF17B8pmc2Wp\nQjQMFw5yLsedk4le+t+am0ckNGFstzA08PjqTFallbquRiFEgyLhRAjhEbTWvLIxh2/3FuFjUbx+\nSQztQ31+P2DdMji4B0IjUJde5bpChWhAlGGgbhgJgP5qZk3vCcCdnUK4vWMI1RoeXpHBL1nlripT\nCNGASDgRQniEmVvz+Wh7AVYFUy6Opnukb8192jQxP58BgLruTpSXt6vKFKLBUX0HQ1xLyM44pvdE\nKcX93cO4rm0QlQ7N+GXpbM+tcGGlQoiGQMKJEMLtzd5VwFubclHAs/2i6Bfrf+wBPy919pqERaIG\nX+OSGoVoqJTFgrppFAD6q3eP6T1RSjGpVyRDWwRQajcZsySNfQWVripVCNEASDgRQri1efuLeGF9\nNgCP945kaIvAY+539pq8DUiviRB1RfVJhPhWkJ2JXvLtMfdZDMUzF0XRP9aPgkqTexenkVZsP8GV\nhBDi5CScCCHc1oqUEp5cmwXAhPPDubZt8J8P+nkJHNoLYU2l10SIOqIsFtSNR3tP3kPbq46532Yo\nJg+I5vxIX7LLHYxenEZ2WbUrShVCeDgJJ0IIt7Qhs4xHVmbi0M6Jt7d1DPnTMc5ek3cAUNffibJ5\n1XeZQjQaqm/i7yt3Lf72T/f7WA1eGxTNeaHepJbYuXdxGgWVDhdUKoTwZBJOhBBuZ1tOBROWpVNl\nam5oF8zYbmHHPU6vXezsNQmPQiVeXc9VCtG4KMPAuOke4Pi9JwABXhbeujSWlsFe7CusYtySNErt\nZn2XKoTwYBJOhBBuZV9BJWOWpFFWrRnWIoDHekWglPrTcdrhQM8+MtfkhpHSayJEfeh9KbRoC7lZ\n6EXfHPeQEB8LMxJjifG3sjW3kgeWpVPpkIAihDg9Ek6EEG4jrdg5FKSwyqR/rB9PXxSFcZxgAqDX\nLoKU/c7d4C+RfU2EqA/KMDBq5p7MRFcdf2WuSD8rMwbHEu5rYUNWOY+uzMRu6vosVQjhoSScCCHc\nQnZZNfcuSSO73MH5kb5MHhCNzThBMHE40LOPzjW5S3aDF6I+XTjI2XuSl41eOOeEh8UHejH90liC\nvQxWpJby77VZmFoCihDi5CScCCFcrrDSwX1L0kgptnNeqDevDYrGx3ritye9eiGkHoCIaNQlV9Zj\npUII59yT0QDor99DV55448U2Id68eWksflbFvAPFvLg+Gy0BRQhxEqcVTqZNm0bLli3x9fWlZ8+e\nrF69+oTHVlZWcvvtt9O1a1e8vLwYNGjQcY9bsWIFPXr0wNfXl9atW/P222+f3SMQQni0UrvJ2CVp\n7C2oomWwF29dGkuAl+WEx+tqO/rz6QCoEXdLr4kQrnDhIGjVHvJz0PO/OOmhncJ9eHVQDF6G4ovd\nhby1KbeeihRCeKJThpPZs2czYcIEHn/8cTZt2kTfvn0ZPnw4KSkpxz3e4XDg6+vLuHHjuPzyy487\nkfXAgQNcdtll9OvXj02bNjFp0iTGjRvHnDkn7h4WQjQ8lQ6TicvT2ZpbSYy/lRmJsYT4nDiYAOhl\n30NGCsQ0Q13yl3qqVAjxR0opjJvvA0B//T66rOSkx18Q5cfkAVFYFMzcms+sbXn1UaYQwgOdMpxM\nnTqVO+64g5EjR5KQkMDrr79OdHQ006dPP+7xfn5+TJ8+nbvuuovY2Njjdt/OmDGDuLg4XnvtNRIS\nErjrrru47bbbeOmll879EQkhPILd1Dy2MpP1meWE+1qYnhhLpJ/1pOfoqkr00X1N/novynLy44UQ\ndahHPzivGxQXoL//5JSHXxwfwDMXNUUBr23M5avdhXVfoxDC45w0nFRVVbFx40aGDBlyzO1Dhgxh\n7dq1Z93oTz/9dNxrJiUl4XDIhk1CNHSm1jy1NovlqaUEeRlMuzSWZkGnXgpY//gV5GZBi7aoi4ac\n8nghRN1RSmH8bQwA+tuP0EUFpzxneMsgHusVAcDz6w4z/0BxndYohPA8Jw0nOTk5OBwOmjZteszt\nkZGRZGZmnnWjWVlZf7pm06ZNqa6uJicn56yvK4Rwf1prJm/IZu6BYnytijcviaVtiPepzysvQ389\nEwDj5jEoQ9bzEMLVVKee0K0PlJeiv/ngtM4ZkdCEcd3D0MCTazJZmXryIWFCiMbFY8ZEJCUluboE\ncZrkufIcrniuvjnszbxcH6xKc29MCZXJW0lKPvV5TVfPJaYwn9LYVuxWftAIf8/kteU5GtNz5Xv+\nJbTf9BOO7z/lt2YdqQ5scspzugDDwrz5MdeHh5anMz6+lAR/14ycaEzPVUMgz5f7a9u27Tmdf9Jw\nEh4ejsViISsr65jbs7KyiI6OPutGo6Ki/tTzkpWVhdVqJTw8/Ljn9OzZ86zbE/UnKSlJnisP4Yrn\n6oNt+czLzcGiYPLFMQyKDzit83RxIebUxQAEjn6Mnp0vqMsy3ZK8tjxH43uueuLY/hPGz0vpsicJ\n457HTuusHlrjv+4wX+8pYlp6IO8MjqNjuE8d13qsxvdceTZ5vjxDYeG5zSc76bgILy8vevTowcKF\nC4+5fdGiRfTt2/esG+3Tpw+LFi360zUvuOACLJaTr9QjhPBMX+8u5NWNzmGbT/VtetrBBEB/+wGU\nlUDXC1GNMJgI4e6Mm+8DpdALv0ZnpZ3WOUopJvWKZFiLAMqqNWOWpLGv4Pg7zgshGo9TDtqeOHEi\ns2bNYubMmezYsYPx48eTmZnJ6NHODZgmTZpEYmLiMeds376dTZs2kZOTQ0lJCZs3b2bTpk01948e\nPZq0tDQeeOABduzYwbvvvssHH3zAQw89VMsPTwjhDn48UMxz6w4D8FivCC5vFXTa5+r8HPQPnwFg\n/G1sndQnhDg3qllr1IDLoLoa/fnp71tmMRRPXxRF/1g/CqtMRi9OI7XYXoeVCiHc3SnnnIwYMYLc\n3FyeffZZMjIy6Ny5M/PmzSM+Ph6AzMxM9u/ff8w5l19+OcnJzkHkSim6d++OUqpmJa4WLVowb948\nHnjgAaZPn05sbCxvvPEG11xzTW0/PiGEi61KLeWJNZloYGy3MG5MOPV49D/SX82EygroNRDVrlPd\nFCmEOGfqplHo1QvQK+air70dFd/qtM6zGYrJA6IZtzSdpKxy7l2cxsyhcadcWlwI0TCd1nI39957\nLwcOHKCiooINGzbQr1+/mvvef//9P4WTAwcOYJompmnicDhq/vePBgwYwC+//EJFRQX79u3jnnvu\nqYWHI4RwJ0lZZTy8MoNqDbd3DOHOTiFndL7OTEUv+Ar+sOGbEMI9qeh41OCrwTQxP37zjM71sRq8\nOiiGjmHepJbYuW9xGgWVsrWAEI2RrMUphKgT23IrmLAsg0qH5rq2QdzfPQyl1BldQ3/yJlRXowZe\ngWpxbqt/CCHqnhpxD3j7wLpl6B2bTn3CH/jbDN68NJZWwV7sK6xi7JI0Su1mHVUqhHBXEk6EELVu\nX0FlzQeLoS0CmNQr8syDyZ5t6FULwOaFuvneOqpUCFGbVGgE6qpbADBnvYLW+ozOb+JtYXpiLLEB\nVrblVjJhWToV1RJQhGhMJJwIIWpVWrGdexenUVBp0j/Wj2cuisJinGEw0Rrzw9cAUFfcjIo4+6XL\nhRD1S11zGwSHwK7fYN2yMz4/0s/KjMQ4wn0tJGWV8+jKTOzmmYUcIYTnknAihKg12WXVjF6cRna5\ng/MjfZk8IBrbGQYTADaugS0bICAIdd0dtV+oEKLOKF9/1I2jADA/fB1dfearb8UF2piRGEuwl8HK\ntFKeXJOJQwKKEI2ChBMhRK0oqHRw35I0UkvsnBfqzWuDovGxnvlbjHY4MD840mty/UhUwOkvOyyE\ncA9qyLUQHQ/pyejF357VNVo38eatS2Pxsyp+PFjCCxuyz3iYmBDC80g4EUKcs+IqB/ctTmNvQRUt\ng71469JYArzObkNVvXwuHNoLEdGoy26s5UqFEPVBWW0Yt4wDQH/+Nrq87Kyu0zHch9cGxeBlKL7a\nXcgbv+bWZplCCDck4UQIcU5K7SZjlqSzI6+S+CNDMUJ8zjKYVFagP50GgPrbGJSXd22WKoSoT30S\noV1nKMhFf/fRWV+mZ5QfUy6Owqrg/W35vLc1rxaLFEK4GwknQoizVl5tcv/SdLbkVBDtb+XtwbHn\ntHGanvsZ5GZBywTUgOG1WKkQor4ppTBuGw+A/vYDdMHZ93oMiAvg6YuiUMAbv+by5e6CWqpSCOFu\nJJwIIc5KpcPkgWXpbDxcTqSfM5hE+9vO+nq6qAD91XsAGLdNQBny9iSEp1Mde8AFA6CiHP352+d0\nreEtA5l0YQQA/1mXzfwDRbVRohDCzchffyHEGbM7NA+tyGBdZjlhPhbeTowlPtDrnK6pP58BZSXQ\nrQ+qW+9aqlQI4WrGrfeDYUEvnIM+tO+crnVDuybc3z0MDTyxJosVKSW1U6QQwm1IOBFCnBG7qXls\nVQar08po4m0wIzGWFsHnGEwO7UP/+BUYBsYdE2upUiGEO1DxrVFDrwPTgTnzpXNeceuOTqHc0TEE\nh4ZHVmbyc8bZTbYXQrgnCSdCiNPmMDVPrMlkaUopgV4G0xNjaRNybpPWtdaY770MpgM19HpU8za1\nVK0Qwl2ov44G/0DY/DMkrTrn643rHsaIdsFUmZoJy9JZLwFFiAZDwokQ4rSYWvPUT1ksOFiCv81g\n2qWxtA/1OfcL/7IaNv0EfgHODzBCiAZHBYX8vjHj+1PR9jPfmPGY6ynFo70iuKZNEJUOzfhl6SRl\nSUARoiGQcCKEOCWtNc+vO8z3+4vxsSjeuCSGTuHnHkx0td3ZawKom0ahgkLO+ZpCCPekLhsBsS2c\nGzPO/+Kcr2coxeO9I7mqdRAVDs39S9P59XD5uRcqhHApCSdCiJPSWvNSUg5f7ynC26J4bVAM3SN9\na+fa876A9GSIaY4aLhsuCtGQKautZk6Znv02uij/nK9pKMUTvSO5olUg5dWasUvS2CQBRQiPJuFE\nCHFCWmte/zWXT3cWYDMUL18cTa9ov9q5dlE+erZzaVHjjoko29kvQyyE8BA9+kG3PlBajP5sRq1c\n0mIo/t2nKcNbBFJWrRm7NJ0t2RW1cm0hRP2TcCKEOC6tNW/8msusbflYFbw4IIqLYv1r7/qfzYDS\nYujaG3r2r7XrCiHcl1IK484HnUsLL/gKnby3Vq5rMRRPX9SUoS0CKLWb3LckjW05ElCE8EQSToQQ\nf3K0x+T9I8HkP/2jGBQfUHvXP7QPveDI0sF3PohSqtauLYRwb6pZa9Sw68E0Md8796WFj7Iaimcv\nimJw8wBK7Cb3LkljR64EFCE8jYQTIcQxtNa8ujGnpsfkhQHRJDYPrNXrm//3IpimLB0sRCOlbhp1\nZGnhdbBuWa1d12oonusXxSXx/hRXmYxenMauvMpau74Qou5JOBFC1NBaM/WXHD7cXoBVweQB0Vza\nrPZ6TAD06gWwZQMEBsvSwUI0UiooBPW3MQCYM6egK2pvErvNULzQP5qBcf4UVZmMXpzK7nwJKEJ4\nCgknQgjAGUxeTsrh4x0FWA2YfHE0g2o7mJSVoI8uHXzL/bJ0sBCNmBp6PbRqD9mZ6C/frdVr2yyK\nyQOiGRDrT0GlyahFaeyVgCKER5BwIoSoWS74k53OYDJlQHStzjGpaefztyE/B9p2QiVeXevXF0J4\nDmWxYIyaBID+7kN02sFavb7NophycRQXxfhRUOngnkVp0oMihAeQcCJEI6e1ZvKG7GOWCx5YF8Ek\neS/6h89AKYxRk1CGvP0I0diphC7OLyqqqzHfebHWJscf5WUxeHlgNH1j/MivdHDPwlSZJC+Em5NP\nB0I0YlprXtyQzee7CmuCyYC4OggmWmO+8x8wHahhN6DadKj1NoQQnkndMg4CgmDzz7B2ca1f39ti\n8MrAaAbE+VNYZXLPojR+y5aNGoVwVxJOhGikTA3/WZ/N7KPBZGA0/eNqbx+TP9Ir5sG2jRD8+yRY\nIYQAUMGhzoACzqWFy8tqvQ0vi8FLA6JJbHZkmeHFaWzMkoAihDuScCJEI2RqzaeZPny5uxAvQ/HK\nwGj61+IGi3+kS4rRs14BQN06ARUQVCftCCE8l0q8Btp0gNzD6Nnv1EkbNoviP/2janaSH7MkjR2l\nljppSwhx9iScCNHIOEzNcz8fZkWBtzOYDIqu1Z3f/5f+bBoU5EL7rqhBV9RZO0IIz+WcHP8PUAr9\n/SfoQ/vqpB2roXjmoqZc1TqICofm9RR/VqeV1klbQoizI+FEiEbEbmr+uSaTOXuLsCnNq4Oi6RtT\nh8Fk91b0/C+cO8HLJHghxEmoth1RQ64FRzXm9GfRplkn7VgMxZN9IrmhXTDVWvHA8nSWpZTUSVtC\niDMnnxSEaCQqqk0eXJ7OgoMl+FkV4+NL6VOXwaTajvnW086d4K/8O6plQp21JYRoGNQt90OTMNix\nCb3gqzprx1CKSb0iSAytpNqER1ZksPBgcZ21J4Q4fRJOhGgESu0m45amsyqtjGAvg3cGx5Hg76jT\nNvU3H0LyHmgaJzvBCyFOiwoIwrjnUQD0h6+jc7Lqri2lGBFZwR0dQ6jWMGl1Jj/sL6qz9oQQp0fC\niRANXEGlg1GLUknKKifc18K7Q+LoGO5Tp23qtGT0F85JrcZ9/0R5+9Zpe0KIBqRPIvQaCOWlmG8/\nX+t7n/yRUjCuexiju4RianhyTRZz9hTWWXtCiFOTcCJEA5ZdVs3dC1PZlltJjL+V94bG0SbEu07b\n1KaJOe0ZsFehLrkS1bV3nbYnhGhY1JGNWvELgA0r62Tvk/9tb1TXMO7vHoYGnvn5MJ/tLKjTNoUQ\nJybhRIgGKr3EzsiFqewtqKJlsBfvD4snPtCrztvVi7+Fbb9AcCjq9gfqvD0hRMOjwiJRt40HwHzn\nBXRx3fdm3NEplId7hgMweUM2b/+WW6e9NkKI45NwIkQDdKCwijsXpJJSbOe8UG/eHRJLpJ+1ztvV\neYd/39Pk7kdQQU3qvE0hRMOkBl8LHbpDYV7N+0pdu/m8EJ7oHYmhYMbmPKYk5WBKQBGiXkk4EaKB\n2ZlXwcgFqWSVVdM90oe3B8cS6lP3wQTAfOdFKCuBngNQFw2plzaFEA2TMgyMMU+C1YZe8h1687p6\naffatsG82D8Km6H4bGcBT67Nwm5KQBGivkg4EaIB2XS4nLsXppFf6aBvjB9vXRpLoFf97ICs1yyC\nn5eCj59zTxOl6qVdIUTDpWJboG68BwBz2jPo8rJ6aTexeSCvXxKDr1Uxd38xD63IoKK6bvZdEUIc\nS8KJEA3E2vRS7l2cRondJLFZAK8OjMHXWj8vcZ2fgznjeQDUbeNREVH10q4QouFTV98GLRMgKw09\na2q9tds72o+3E+MI8jJYmVrK2KXpFFfV7RLsQggJJ0I0CD/sL2L80nQqHJqrWgfxn/5R2Cz103Oh\ntcZ86xkoLoBufVDDbqiXdoUQjYOy2TDGP+Mc3rXga/TGNfXWducIH94bGkeEr4VfssoZuTCVw2XV\n9da+EI2RhBMhPJjWmlnb8nhiTRbVGm7vGMK/+kRiNepvSJVe8h0krQS/AIyx/5LhXEKIWqdatEXd\nfC8A5ptP1cvqXUe1buLNrGHxtAiysSe/itt+TOFAYVW9tS9EYyPhRAgPZWrNS0k5vLYxFwU83DOc\n8eeH12s40Fnp6HenAKDueQwV3rTe2hZCNC7qqluhfVfIy0a/80K9th0TYOP9YfF0Dvchs7SaO35M\nYXN2eb3WIERjIeFECA9U5TCZtCqTT3cWYDMU/+kfxc3nhdRrDdo0MV9/EirKoPclqIsvq9f2hRCN\ni7JYMMY/Dd4+6FU/OhfhqEdNvC28PTiWAbH+FFaZjF6UxsrUknqtQYjGQMKJEB6mqNLBmCXpLEwu\nwd9m8OYlMQxtEVjvdegfPqvZbNG4958ynEsIUedUdLOazV3NGc+j83PqtX1fq8HLA6O5uk0QFQ7N\nA8sz+Hp3/Q0xE6IxkHAihAdJK7Zz+48pJGWVE+5rYeaQOHpF+9V7HTr1APrjNwAwxjyBCg6t9xqE\nEI2TGnYDdOsDxQWYbz1T77u4Ww3Fk70jubtzKKaGZ9cd5rWNslmjELVFwokQHmJrTgW3/pjCgSI7\nrYO9+HB4PAmh3vVeh7ZXYU79B1RVoi65EtVrYL3XIIRovJRSGGP/BX4BkLQS/eOXLqnhvm5hPNk7\nEouCWdvyeWxVJpUO2QtFiHMl4UQID7DsUAl3L0wlr8LBhVG+vD8sjmh/m0tq0R+8Bvt3QtNY1MiH\nXFKDEKJxU+FNUff+EwD93svog7tdUsc1bYN545IY/G0Gi5JLGLUojfwK2QtFiHMh4UQIN6a15pMd\n+Ty4IqNmD5M36nHX9z/Vs345+odPwWLFePAFlH/9z3URQggAo/8wVOLVYK/CfOkxdIVrVs/qE+PP\n+0PjiPKzsjm7gtt+TCG5SJYaFuJsSTgRwk3ZTc3z67N5KSkHDYzpFsa/+kRiq8c9TP5I52RhvvFv\nANQt41DtOrmkDiGEOErd9QjEtYTUA+h3J7usjrYh3nwwPJ72od6kFNu5dX4K6zPKXFaPEJ5MwokQ\nbqiw0sHYJWl8tbsQL0PxfL+m3NU51GUrYmlHNebUSVBcCOf3RV35d5fUIYQQf6R8fDEeehFsXujF\n32KunO+yWiL9rMwcEseAOH+KqkzGHHkPF0KcGQknQriZg4VV3DI/hfWZ5YT5WHh3SBzDWwa5tCb9\nxbuw/VcICce4/xmUIW8dQgj3oFq0rZn/pqc/h85IcVktfjaDqRdHc3vHEKo1PLfuMC+uP0y1KSt5\nCXG6TusTxrRp02jZsiW+vr707NmT1atXn/T4LVu2cPHFF+Pn50dcXBzPPPPMMfcvX74cwzD+9LN7\nt2smtAnhLn5OL+WW+SmkFNtJCPHm48vi6Rzh49Ka9JYk9Jf/B0phTHgW1USWDRZCuBc19HrocymU\nl2K+/BjabndZLRZDMf78cJ7q2xSrAZ/vKuT+pekUV8lEeSFOxynDyezZs5kwYQKPP/44mzZtom/f\nvgwfPpyUlON/M1FUVMTgwYOJjo4mKSmJ1157jSlTpjB16tQ/Hbt9+3YyMzNrftq0aXPuj0gID6S1\n5tMdBYxdmk6J3eSS+CMTLF20IldNXQW5mK/8A0wTdf1IVNcLXVqPEEIcj1IKY8yTEBENe7ejP3jV\n1SVxZesg/m9wHCHeFn7KKOPW+SkcLJSJ8kKcyinDydSpU7njjjsYOXIkCQkJvP7660RHRzN9+vTj\nHv/JJ59QUVHBBx98QIcOHbjuuut49NFHjxtOIiIiiIyMrPkxZKiIaIQqqk2eXJvFlKRsHBpGdgph\nysXR+Npc+3rQ1XbMyQ9DXjac1x110yiX1iOEECejAoIwHnoBrFb0D59irnDd/JOjukX68vFl8bRt\n4sXBIju3zE9hZWqJq8sSwq2d9NNPVVUVGzduZMiQIcfcPmTIENauXXvcc3766Sf69++Pt7f3Mcen\np6eTnJx8zLE9e/YkJiaGxMREli9ffpYPQQjPlVFq584Fqfywvxgfi+KF/lGM7R6O4aKJ73+kZ73y\n+zyTRyajLFZXlySEECelErqg7nwYAP3W0+j9u1xcEcQE2Jg1LJ7EZgGU2E3GL8vg7d9yZUd5IU7g\npOEkJycHh8NB06ZNj7k9MjKSzMzM456TmZn5p+OP/vvoOTExMcyYMYM5c+YwZ84cEhISuPTSS085\nl0WIhiQps4yb56awI6+S2AArHwyPZ2gL99g3xFw+F/3DZ2C1Yjz6Eiok3NUlCSHEaVHDb0BdciVU\nVWC++CC62PUrZvnZDCYPiGJstzAUMGNzHg8uz6BE5qEI8Se1/lXo6Sx12q5dO9q1a1fz7969e3Pw\n4EGmTJlCv379jntOUlJSrdUo6pY8VyenNSzJ9+LLLB9MFB387dwTU0TRvlzq+/+54z1XvpmHaDfr\nBQzg0OCbyC2xgzynbkFeW55DnivXUr2G0W7HZvwykin41xj23XQ/nGDoeH0+V12BcfFW3k3zY3lq\nKTd8s4f74sqI9jbrrQZPJ68t99e2bdtzOv+k4SQ8PByLxUJWVtYxt2dlZREdHX3cc6Kiov7Uq3L0\n/KioqBO21atXL2bPnn3C+3v27HmyUoWbSEpKkufqJEqqHDz982EWZTnHHN/eMYSx3cKwuGBjxeM9\nV7qoAPOdf0G1HZV4NS3umUhLNxhiJuS15UnkuXIPuvV0zAdvJmj/Ns7fvR7j72P/dIwrnquewKVF\nVUxcnsG+wipeOBTEE72bMqyle/ScuzN5bXmGwsJz66086bAuLy8vevTowcKFC4+5fdGiRfTt2/e4\n5/Tp04dVq1ZRWVl5zPGxsbE0b978hG1t2rSJmJiYM6ldCI+yJ7+Sv89PYVFyCX5WxeQBUYw/P9wl\nweR4tMOB+fIkOJwObTui7nnMZZs+CiHEuVIR0c4NGg0D/dVM9M9LXV1SjWZBXnw4PJ6hLQIoq9ZM\nWp3JC+sPU+WQHhQhTrkc0MSJE5k1axYzZ85kx44djB8/nszMTEaPHg3ApEmTSExMrDn+5ptv4vTu\nqAAAIABJREFUxs/Pj9tvv51t27YxZ84cXnzxRSZOnFhzzKuvvsp3333Hnj172LZtG5MmTeK7775j\n7Ng/f6shREPw331F3Do/heQiO22aePHJZc0Y3Ny9viXTs16BzT9DcAjGIy+hvLxPfZIQQrgx1aUX\n6tbxAJivPu4WE+SP8rMZ/KdfFI/1isBqwOxdhYxckEp6iev2aBHCHZxyzsmIESPIzc3l2WefJSMj\ng86dOzNv3jzi4+MB5yT3/fv31xwfFBTEokWLGDNmDD179iQ0NJSHHnqIBx54oOYYu93Oww8/TGpq\nKr6+vnTq1Il58+YxbNiwOniIQrhORbXJ5A3ZfLO3CIArWgXyjwsj8bW617LZ5tzP0d9/4pwA/8gU\nVMSJh2AKIYQnUVfdAgd2oVfMw3zufozJH6HCIl1dFuCcp3tjQhM6hvnw8MoMtuZWcvPcQzzTL4r+\nsf6uLk8Il1Bau+9adn8csxYcHOzCSsTpkvGgv9tXUMljqzLZW1CFl6F4tFcE17QJcpuhUkefK520\nCvP5Cc6NFsc/gzHoCleXJo5DXlueQ54r96PtVZhPjoYdv0LLBIzn30P5+rnVc1VQ6eCJNZmsTisD\n4JYOTRjXLRybxT3+ZrgDd3q+xImd6+d39/r6VogGQGvN17sL+fu8FPYWVNEs0MYHw+O4tm2w2wST\no/T+XZgvPeoMJjeOkmAihGiQlM0LY9JUiGkGB3ZhvvwY2uFey/g28bbw2qAY5yIpCj7aXsBtP6Zw\nqEh2lReNi4QTIWpRcZWDR1dl8uy6w1Q4NH9pFchnlzejfaiPq0v7E1tRHuaz46CiHHXx5bIDvBCi\nQVNBTTAefx0CgyFpFXrmFOfa7m7EUIqRnUOZOTSOaH8rO/Iq+evcQ8zdX+Tq0oSoNxJOhKglmw6X\nc+MPh1iUXIK/zeC5i5ry9EVR+Nnc72Wmy0tpNftNyMuGDt1RY590u14dIYSobSqmOcakV8BqQ8+b\nTcSGJa4u6bi6Rvgy+4pmDGnuXM3r8TVZPLEmk1K7rOYlGj73+9QkhIexOzRv/prDyIWpZJRW0yHM\nm88uj+eyVkGuLu24tN2OOeUR/LJSIKYZxmNTUTYvV5clhBD1QnXojrr/KQBiF36BXrvYxRUdX6CX\nhRf6R/FE70h8LIof9hdz4w/J/Hq43NWlCVGnJJwIcQ72FVRy648pzNyaj9bOTRVnDY0nPtA9P+xr\nhwP96uOwcS12vwCMx19HBTVxdVlCCFGvjAHDUX8bg0JjTp2E/nWtq0s6LqUU17YN5pPLm9E+1Ju0\nkmpGLkjl9Y052B3uNSRNiNoi4USIs2BqzSc78rl5bgo78yqJ8bfy7pA4xp/vviuraK3RM55Dr1kI\nfgHs++sEVMyJN0YVQoiGTF0/ksO9EqG6GvM/D6J3bHJ1SSfUKtiLD4fFc1enEJSC97fl8/f5h9ib\nX3nqk4XwMBJOhDhD6SV27l2cxktJOVSZmqvbBPHFX5pzflNfV5d2Qlpr9PtT0Yu+AS8fjH++Rnm0\nBBMhROOllCJt8A2oS6+CqgrMZ8a51SaN/8tmUYzpHs7MIXHEBdjYnV/FzfNS+GBbPg5TelFEwyHh\nRIjTZGrN7F0FXP99MuszywnxtjB1YDT/6tMUfzec9P5H+st30f/92LnJ4mMvoTqe7+qShBDC9ZSB\nuu9x6HMplJVgPnUvOi3Z1VWdVLdI52T5a9sEYTc1r27M4fYfU9hXIL0oomFw709UQriJQ0VV3LMo\njRfWZ1NerRncPICv/tKMQfEBri7tlMwfPkN/Og0MA+OB51HnX+TqkoQQwm0oixVj4vPQvS8U5mP+\nazQ6O8PVZZ2Un83giT5NeeOSGJr6WdmaW8lf56Ywc0sedulFER5OwokQJ+EwnXNLbvzhEL9klRPq\nY2HKgCgmD4gm1Nfq6vJOyZw3G/3uZADUvY+jLhrs4oqEEML9KJsXxqMvwXndICcT8/F70IfTXV3W\nKfWL9efLv/zei/Lmplxum5/CrjzpRRGeS8KJECewK6+S235M4aWkHCocmstaBvL1lc1JbB7o6tJO\ni/nfj9HvvACAuuthjMHXuLgiIYRwX8rHF+Ofr0ObDpCVivnPkeiMFFeXdUqBXhae6NOU6YmxNRs3\n/n3eIV7fmEN5teyLIjyPhBMh/keZ3WTqL9n8bd4htuVWEuln5dWB0TzXL4om3hZXl3dazK/fQ7/3\nMgBq1CSMK252cUVCCOH+VEAgxlMzIKELZGdiPn4XOu2gq8s6Lb2j/fjqL825MSEYh3au6HXD98ms\nTit1dWlCnBEJJ0L8wYqUEq77bzIfbS9AAze3b8KcK5tzsQfMLQHnqlzm7LfRH70BSqHGPIkxfISr\nyxJCCI+h/AMx/j0NOp4PuYcx/3kXOmWfq8s6LX42g8d6RfLBsHjahniRVlLNuKXpPLoyg+yyaleX\nJ8RpkXAiBJBWbGfi8nQmLM8gs6ya80K9+XB4PA9fEOH2K3EdpbVGf/IW+rMZYBio+5+WoVxCCHEW\nlK8/xhNvQpdeUJCL+fjd6IO7XV3Waesc4cMnlzXjgfPD8bEoFiaXcO1/k/l0Rz7VMmFeuDnP+NQl\nRB0przaZvjmX675PZllKKX5WxcM9w/lweDwdw3xcXd5p0w4H+v9eRH81EwwLauLzGIOucHVZQgjh\nsZxzUF6D84+s4vX43ejtv7q6rNNmMxS3dgzh6yubMyDWnxK7yZSkHG764RAbMstcXZ4QJyThRDRK\nWmsWJRdz7X+Teee3PCodmuEtAvnmqhbcfF4IVsM9d3k/Hl1ZgTn5YfS82WC1YTwyGaPfUFeXJYQQ\nHk95+2BMegUuHAQlRc5lhtcudnVZZyQmwMarg6J5ZWA0cQE29hU6l8Z/ZGUGGaV2V5cnxJ9IOBGN\nzq68SkYvTuORlZlkllaTEOLNe0PjeL5/FJF+7r888B/ponzMJ0fBumXgH4jx1HRU70tcXZYQQjQY\nyuaF8chk1LAbwF6FOeURzO8/dXVZZ0QpxcD4AL66shljuoXhY1EsSi7h2u+SeXtzLuV2WdVLuA/P\n+iQmxDnIKrUzbXMu3+8rRgPBXgb3dQvjurbBWDyop+QonZmK+fQYSD8EEVEYT76Jim/t6rKEEKLB\nURYrjJoEEVHoj95Az5yCmZ2Buv0BlOE53/N6Wwzu6hzKFa0CeeWXHBYmlzDjtzy+2lPIfV3DuLJ1\nkEf+PRQNi4QT0eCV2k1mbcvn4+35VDg0VgNubNeEu7qEeszSwP9L79mG+ez9UJgHLdphPPkGKjTS\n1WUJIUSDpZRCXXcnZlhT9Jv/Rv/3Y8g9DOOfRnl5u7q8MxLlb+PFAdGMyCpn6i/ZbM+t5OmfD/PZ\nzgIm9Ainb4y/q0sUjZiEE9Fg2R2aOXsLeee3PPIqHAAkNgtgXPcwmgV5ubi6s2cun4ue9gxUVULX\n3hiPTkH5ecZSx0II4emMgZejQ8IxX3wIvWYh+nAaxqMvo8Kburq0M9ajqS8fDY9nwcES3vg1hz0F\nVYxZkk6faD/Gdg+jgwctDCMaDgknosGpNjXzDhQzY3MuGaXOdd07h/swsUc43SJ9XVzd2dPVdvQH\nr6G//wQAlXg1atQ/UDabiysTQojGRXW9EOP5mZjPTYA92zAfvNk5L6VjD1eXdsYMpRjeMpBLmvnz\n+c5C3t2Sx08ZZfyUUcYlzfy5r2sYrZt4Vs+Q8GwSTkSDYWrNkkMlTNuUy8Ei5wokrYK9uK9bGJfE\n+6OU546j1QV5mC89CluTwGpF3f0oash1Hv2YhBDCk6kW7TBe/gTzpcfgt/WYT45G3fkg6rIbPfK9\n2dticFvHEK5qE8Ssrfl8vquApYdKWXaolMtaBTK6SxhxgfJlmKh7Ek6ExzsaSt7dksfu/CoA4gJs\njO4ayrAWgR4/uU/v3Y75woOQkwkh4c5hXO27ubosIYRo9FRQCMa/3kJ/9Cb62w/Q//ci7N0Oo/+B\n8vbMIVFNvC1M6BHOzec1YeaWPObsLWTu/mIWHCjmitZB3NkphPhAzx0aLdyfhBPhsRymZmFyMe9u\nyWd/oTOURPpZubtzKFe1CcLm6aFEa/T8L9DvTwV7FSR0cQYTmfguhBBuQ1msqNsnYLZuj37jKfSy\n79EHd2NMfB4V38rV5Z21SD8rky6M5LaOIbz9Wy4/7C/m271FfL+viGEtAxnZKZSWwRJSRO2TcCI8\njt2hmX+wmJlb8jhU7By+FeVv5Y4j3dHeFs9Z1vFEdGEe5htPQdJKANTQ61B3PYKyyR8CIYRwR0b/\nYej4VpgvPAQHdmE++DfUyAc9fghuTICNp/pGcWenUN7fms/c/UXM3V/MvP3FDG4ewMjOobQLkTkp\novZIOBEeo7jKwZw9RXy6s4DDZc6J7nEBNu7sFMIVrYKwWTz3zf+P9K8/Yb7+JOTnODdWHPMEqu9g\nV5clhBDiFFSLdhhTP0X/34voZT+gpz+H3rgWY8yTqKAmri7vnDQP8uLffZtyT5dQ3tuax3f7iliY\nXMLC5BL6xvhxa4cQekX5enQQE+5Bwolwe1mldj7dWcDXe4ooPbKLbatgL27vGMLwloFYPXz41lHa\nXuXc3Ou/Hztv6Hg+xoTnUBFRri1MCCHEaVN+Aajxz2B274ue8TysW4a5ZyvGhGdRXXq5urxzFhNg\n4/HeTbm7cygfbC/gmz2FrE0vY216Ge1Dvbm1QwiDmwc0mL/Nov5JOBFuSWvNlpwKPt9ZyKLkYqq1\n8/YLmvpyS8cQ+sX4NahvZ/TOzZhvPQ0p+8GwoP56L+ra21EWz9wkUgghGjtjwHB0QlfMV/4BOzdj\nPjkKNewG1K33N4i9qZr623jkggju6RLKV7sL+WxnATvzKvnH6kxe/9XKiHbBXNM22GM3OxauI+FE\nuJVKh8mCgyXM3lXA9txKAAwFQ1sEcEuHEDo2sA2hdHmps7dk/hegNcQ0c3671q6zq0sTQghxjlTT\nGIzn3kV/ORP95bvoH79Eb1iBMeofqF4Xu7q8WtHE28JdnUO5pUMT5u4v5qPt+RwssvP6r7m8/Vse\nw1oEclP7YNqHNqy/36LuSDgRbiG12M43ewuZs6eIgkrnbu7BXgbXtA3mhnbBxAQ0vLXVddIqzBnP\nO5cINiyoa29DjbjbY5efFEII8WfKYkXdNArd+xJnD/merZjPT0BdNAR19yOoJmGuLrFWeFsMrm0b\nzNVtglibXsbnOwtYk17Gd/uK+G5fEd0ifLihXTCXNg9oEAvXiLoj4US4TJXDZHlKKXP2FLIus7zm\n9vah3tyUEMzQFoH4WBveG5jOzkR/+Cp61QLnDa3Pwxj7L1TLBNcWJoQQos6oFm0xXpiFnjcb/fEb\n6DUL0Zt/Rv19LGrwNShLw/hIZihFv1h/+sX6k1xUxZe7CvluXxGbsivYlF3BixuyuaJVENe2DZKd\n58VxNYxXgvAoe/Mr+e/+Ir7fV1zTS+JtUSQ2D+D6tsF0jfBpUPNJjtIV5ehvZqG/+RCqKsDLB/W3\n+1BX/LXB/FESQghxYspiQf3lZnSvgZgznoNf16JnPI+e/yXGnQ+iul7o6hJrVfMgLx66IIL7uoUx\n70Axc/YUsiOvkk93FvDpzgK6RPhwTZsgEpsFEOAlc1OEk3wiEvUit7yaHw8W88P+YnbmVdbc3jbE\ni2vbBHNZy0CCGuikOW2a6BXz0B+9DnnZAKh+Q1C3jEc1jXFxdUIIIeqbahqD8eSb8NNizFmvQvIe\nzH+Nhl4XY9z+ACqmuatLrFV+NoPr2wVzfbtgduRWMGdvEfMPFPNbdgW/ZVfw4vpsBsb7c0WrIC6M\n9pOVvho5CSeizpTZTVakljL/QBFr08twHFlxK9DLYEjzAK5uE0zHMO8G2UsCzhXH+G0d5sdvwp5t\nzhvbdMC48yFUh+6uLU4IIYRLKaWg72CMngPQ33+C/nImrF+BuXENatgI1HV3oELCXV1mrTsvzId/\nhvkw8fxwFiQ7v7T8JaucHw+W8OPBEsJ9LQxrEciwloF0CG24nxHEiUk4EbWq0oRFycUsPFjC6rRS\nKo4kEquCAXH+XNEqkAFx/g1+MpzekoT52TTY/qvzhpBw1C3jUAOvQBkN+7ELIYQ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- "text": [ - "" - ] - } - ], - "prompt_number": 72 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The result is either amazing or what you would expect, depending on your state of mind. I must admit I vacillate freely between the two! Note that the result of the multiplication is taller and narrow than the original Gaussian but the mean is the same. Does this match your intuition of what the result should have been?\n", - "\n", - "If we think of the Gaussians as two measurements, this makes sense. If I measure twice and get the same value, I should be more confident in my answer than if I just measured once. If I measure twice and get 23 meters each time, I should conclude that the length is close to 23 meters. So the mean should be 23. I am more confident with two measurements than with one, so the variance of the result should be smaller. \n", - "\n", - "\"Measure twice, cut once\" is a useful saying and practice due to this fact! The Gaussian is just a mathematical model of this physical fact, so we should expect the math to follow our physical process. \n", - "\n", - "Now let's multiply two gaussians (or equivalently, two measurements) that are partially separated. In other words, their means will be different, but their variances will be the same. What do you think the result will be? Think about it, and then look at the graph." - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "xs = np.arange(16, 30, 0.1)\n", - "\n", - "mean1, var1 = 23, 5\n", - "mean2, var2 = 25, 5\n", - "mean, var = multiply(mean1, var1, mean2, var2)\n", - "\n", - "ys = [stats.gaussian(x, mean1, var1) for x in xs]\n", - "plt.plot(xs, ys, label='measure 1')\n", - "\n", - "ys = [stats.gaussian(x, mean2, var2) for x in xs]\n", - "plt.plot(xs, ys, label='measure 2')\n", - "\n", - "ys = [stats.gaussian(x, mean, var) for x in xs]\n", - "plt.plot(xs, ys, label='multiply')\n", - "plt.legend()\n", - "plt.show()" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "display_data", - "png": 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q1Ljl72NsbCweHh6UKlXqlq/NDUpORERERCQb+/3186xt68LtedJuREQEn3zyCQBDhgwh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2v+y9HjWQD0aDOQUb3H4+1pcmHUkiRJ0qWiKApdWvSlRZOOzP/1MzbvW82idV8QHfob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\n4lge5OUgCnKdw7IKc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- "text": [ - "" - ] - } - ], - "prompt_number": 11 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Another beautiful result! If I handed you a measuring tape and asked you to measure the distance from table to a wall, and you got 23m, and then a friend make the same measurement and got 25m, your best guess must be 24m. \n", - "\n", - "That is fairly counter-intuitive, so let's consider it further. Perhaps a more reasonable assumption would be that either you or your coworker just made a mistake, and the true distance is either 23 or 25, but certainly not 24. Surely that is possible. However, suppose the two measurements you reported as 24.01 and 23.99. In that case you would agree that in this case the best guess for the correct value is 24? Which interpretation we choose depends on the properties of the sensors we are using. Humans make galling mistakes, physical sensors do not. \n", - "\n", - "This topic is fairly deep, and I will explore it once we have completed our Kalman filter. For now I will merely say that the Kalman filter requires the interpretation that measurements are accurate, with Gaussian noise, and that a large error caused by misreading a measuring tape is not Gaussian noise.\n", - "\n", - "For now I ask that you trust me. The math is correct, so we have no choice but to accept it and use it. We will see how the Kalman filter deals with movements vs error very soon. In the meantime, accept that 24 is the correct answer to this problem.\n", - "\n", - "One final test of your intuition. What if the two measurements are widely separated? " - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "xs = np.arange(0, 60, 0.1)\n", - "\n", - "mean1, var1 = 10, 5\n", - "mean2, var2 = 50, 5\n", - "mean, var = multiply(mean1, var1, mean2, var2)\n", - "\n", - "ys = [stats.gaussian(x, mean1, var1) for x in xs]\n", - "plt.plot (xs, ys, label='measure 1')\n", - "\n", - "ys = [stats.gaussian(x, mean2, var2) for x in xs]\n", - "plt.plot (xs, ys, label='measure 2')\n", - "\n", - "ys = [stats.gaussian(x, mean, var) for x in xs]\n", - "plt.plot(xs, ys, label='multiply')\n", - "plt.legend()\n", - "plt.show()" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "display_data", - "png": 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v3x6US7pAwYmIiHjBoVznP+4p7Tqf5syarBYryfHOvihZR/ed5mwRkdqdLnjo\n3t2ZpV2zZo37mN1u56WXXmrQ/SIjIzl69Gij5vTcc89Ve/z8889jsVgYNWrUaa/97W9/y6pVq3jq\nqafcu3gFI9WciIiIx53InJzRpOtT253BgZzdHMzd627MKCLSGLU1SDz5eN++fTn//POZPn06R48e\nJS4ujn/84x91Lus69X4ZGRl88skn/OUvf6FDhw4kJyfXuwtYaGgo//nPf7jxxhsZMmQIq1at4t13\n3+X222+vVotS17zHjh3LH/7wB5YuXcqECRMIDw+v9/UHKmVORETEo+z2SrKPHQCgfXynJt3DlXFx\nBTkiIrUxDKPWDElDj7/xxhsMHjyYWbNmMWvWLC699FJmzZpV49ra7vfXv/6V8847j4cffpjf/OY3\n/PnPf652/qmsVivLly8nLy+PadOm8Z///Idp06bxwgsv1BirNgkJCe6thIN1SRcocyIiIh52OO8g\ndkcl7WKSCQ+LaNI9XBmXg0catvZbRFqnP/3pT/zpT3+qcXzBggUsWLCgxvFTGzB27dqVFStW1Djv\n1OxJbfc688wz+fTTT2scv/jii2vNvpimSadOnfjoo49qvpCT1LfVcWhoKJ06deLiiy+u9x6BTJkT\nERHxqIPuepOmLelyXluVOcndW+cSBxGRQNLYAvpTHT58mA8++CCosyagzImIiHiYq4g9tQnF8C6x\nbROICGtDUWkhhcX5REfGemp6IiI+0dQvWvbs2cO6det49dVXCQkJ4X/+5388PDP/osyJiIh4lKve\nxLXjVlMYhkFS1fWH8w54ZF4iIr5SVw1MQ6xevZqbbrqJXbt28dprr5Gamurh2fkXBSciIuJRh49W\nBSdxTQ9OnNd3ACD76M/NnpOIiC8tWLCA4uKm9W26+eabcTgc7Nmzh+uuu87DM/M/Ck5ERMRjHA47\nh/MOApAY27xv95JcwckxZU5ERFoLBSciIuIxRwtzqLRXEBMZT0R4m2bdy5V5OazgRESk1VBwIiIi\nHuMKJFxLspojOd6VOdGyLhGR1kLBiYiIeEx2Vb1JUjOK4V0SYtpjMSwcLcihorK82fcTae20Lbd4\ngrd/jhSciIiIx7iyHJ7InIRYQ2kX0x7TdJCTd6jZ9xNpzcLCwigtLVWAIs1it9spLS0lLCzMa2Oo\nz4mIiHiMa1lXkgeCE+d9UsnJO8jhYwfcXeNFpPEsFgvh4eGUlZW1+NiFhYVERUW1+LjieYZhYLPZ\nmt1Qsj7YwS8FAAAgAElEQVQKTkRExGNy87MA55IsT0iMSal2XxFpOovFgs1ma/Fxf/zxRzIyMlp8\nXAlMWtYlIiIeUVFZTv7xo1gMC/FRiR65Z0KsM8hRcCIi0jooOBEREY84WnAYE5O46ESsVs8k5l0Z\nmCP52R65n4iI+DcFJyIi4hGeXtIF0C5GmRMRkdZEwYmIiHiEOziJ9lxwEh+VhIHBscIc7PZKj91X\nRET8k4ITERHxCHdwEuu54CQ0JJTYqAQcpoOjhTkeu6+IiPgnBSciIuIRuXmeX9Z18v20tEtEJPgp\nOBEREY/ILfBOcNIuJtl5fwUnIiJBT8GJiIg0m8N0uHfUauelzMkRBSciIkFPwYmIiDRb/vGjVNor\naBsRgy0swqP31rIuEZHWQ8GJiIg0mze2EXZxByd5Ck5ERIKdghMREWm2FglOCrIxTdPj9xcREf+h\n4ERERJrNVW/ijeCkja0tbcLbUl5RSmFxvsfvLyIi/kPBiYiINJs3epycTHUnIiKtg4ITERFpNlfQ\n0C462Sv3dwU9ufmHvHJ/ERHxDwpORESk2bydOXEFPcqciIgENwUnIiLSLMVlxykuLSQsJJzoNnFe\nGUPLukREWgcFJyIi0iwnmi8mYxiGV8Y4saxLwYmISDBTcCIiIs1ytOAwAPHRSV4bw7Ws61hBjtfG\nEBER31NwIiIizXK0KmCIj/JecBLTth2GYaGg6BiV9gqvjSMiIr6l4ERERJrlaKErc5LotTGsFiux\nkfGYmBwrzPXaOCIi4lsNCk7mzp1L165diYiIICMjg3Xr1tV57urVq7n66qtJTU0lMjKSAQMGsGDB\nghrnrVmzhvT0dCIiIujevTsvvvhi01+FiIj4zLFCZ+YkLsp7wQlAXFXw4xpPRESCz2mDk8WLF3PP\nPffw0EMPsWHDBgYPHszIkSPZv39/red/+eWXDBgwgHfffZdNmzYxZcoUbrvtNt566y33Obt372bU\nqFFceOGFbNiwgenTp3PXXXexdOlSz70yERFpEe5lXV6sOYETy8aOqu5ERCRohZzuhGeeeYYJEyYw\nceJEAJ577jmWL1/OvHnzmDlzZo3zp0+fXu3x5MmTWbVqFe+++y5jx44FYP78+XTs2JFnn30WgLS0\nNP773//y9NNP86tf/arZL0pERFrO0UJXzYl3MyeuZWOuZWQiIhJ86s2clJeX8+233zJixIhqx0eM\nGMEXX3zR4EHy8/OJj493P/7yyy9rvWdmZiZ2u73B9xUREd8qKy+huLSQEGsobdvEeHUs17Ix1ZyI\niASvejMnubm52O12kpOTqx1PSkoiK6the83/61//4rPPPqsWzGRnZ9e4Z3JyMpWVleTm5tZ4TkRE\n/NPRqkAhLioRi+HdPVZcy8aOFShzIiISrE67rKs5Pv/8c2688Uaef/55MjIymnWvzMxMD81KAoXe\n89ZH73ngOXBsBwBWM6xJ719jrskvdgZCh3J/1s9KgNP71/roPW89evTo0azr6w1OEhISsFqtZGdn\nVzuenZ1NSkpKvTdet24do0eP5s9//jO33357tefat29fI/OSnZ1NSEgICQkJtd6vucGNBJbMzEy9\n562M3vPAVPpDLmyGLh26N/r9a+x7Xl5Rxvvfzae4opBz0s/xeqZGvEN/1lsfveetS35+frOur/dv\n9rCwMNLT01mxYkW14ytXrmTw4MF1Xrd27VpGjRrFI488wt13313j+QsuuICVK1fWuOe5556L1Wpt\nzPxFRMSHXMXwcV7eqQsgLDScthEx2O2VFBbleX08ERFpeaf92mnq1Km89tpr/P3vf+enn37id7/7\nHVlZWUyePBlw7s41fPhw9/mrV69m5MiRTJkyhbFjx5KVlUVWVhY5OSe2fpw8eTIHDhzg3nvv5aef\nfuKVV15h4cKF/OEPf/DCSxQREW9x1X94e6cul7goZ3ZdO3aJiASn09acXH/99Rw5coTHHnuMQ4cO\n0b9/f5YtW0anTp0AyMrKYteuXe7zFy5cSGlpKbNnz2b27Nnu4126dHGf16VLF5YtW8a9997LvHnz\n6NChA88//zzXXHONp1+fiIh4kXsbYS92hz9ZfFQi+w/v5GhBDl1TerXImCIi0nIaVBA/ZcoUpkyZ\nUutzp3Z/X7BgQa0d4U81dOhQvvnmm4YMLyIifuqYu8eJ95d1wYnlY+oSLyISnFRNKCIiTWK3V5Jf\ndAwDg5i28ae/wANcy8eOKjgREQlKCk5ERKRJ8o4fwTQdRLeNJ8Qa2iJjupaPHStQcCIiEowUnIiI\nSJO4itJbqhgeIK5q+ZgK4kVEgpOCExERaZKjBa56k5YLTlyZk6OFOZim2WLjiohIy1BwIiIiTdKS\nPU5c2oS3JTzURll5CSVlRS02roiItAwFJyIi0iQt3eMEwDAM4qO1tEtEJFgpOBERkSY5VpgLnGiM\n2FLi2lY1YlRRvIhI0FFwIiIiTZJ3/AgAcS2YOTl5PNf4IiISPBSciIhIo5mmybHjzsxJbFS7Fh3b\nNZ6CExGR4KPgREREGq2kvIjyilLCQm1EhEW26NixVcu68qqWlYmISPBQcCIiIo2WV+jMWsS2bYdh\nGC06dmxbV+ZEwYmISLBRcCIiIo3mWlLlChRakqsA/5iCExGRoKPgREREGs1dDN+2ZXfqgpOWdR0/\nokaMIiJBRsGJiIg0Wp6PiuEBwkLDaWOLwm6v5HhJfouPLyIi3qPgREREGu3Esq6Wz5w4x9WOXSIi\nwUjBiYiINJprpyxf1JycPK6CExGR4KLgREREGs2XBfFwotblmLYTFhEJKgpORESk0XwdnKgRo4hI\ncArx9QREXOwOk+9zStmVX86RghDOKK4ksY1+REX8TUlZMaXlxYRaw2hji/LJHNSIUcS/maYJ2zdh\n7t1G7MEszE6pGMmpvp6WBAB98hO/8MXBImavz2FPQUXVkUj+/s89/LpHNHefk0BEiJJ8Iv4iv6gq\naxKV0OINGF3UiFHEf5nbfsTx8izYvgmAroDj/b9jDB2JccsfMKJjfTtB8Wv6xCc+9+ZPx7jz04Ps\nKaggJTKEK7tF0SeygkqHyT+25jNpxc8cKan09TRFpMrJ3eF9RY0YRfyTY90KHA9OdAYmMfEYw0aR\n32MAWCyYqz/CMe0mzIN7fT1N8WMKTsSnPthZwOzMXExg8lnxvP/LLvx5SHvu7VzMW6M706FtCJuP\nlPG7VQcpqXT4eroigu/rTZxjqxGjiL8xN3yF+cwMqCjHuPzXWF76F5Z7H2fXmDuxvPBP6NYLsvbj\neOQOzPyjvp6u+CkFJ+Izm46U8uevsgF4YFAitw9oR6jlxBKRtPhwFl7RidTIEDYdKePxrw77aqoi\nchJXtsKXwYkaMYr4F/PwQRxP3QcOO8Yvf4sx+UGM8Aj380b7jlge/zt07w3ZB3A8NQ3ToS8dpSYF\nJ+IT5XYHf/o8m0oHXN8zhjFpta8/bRcRwnO/SMVmNfhodyGr9h1v4ZmKyKny/SA4OXl87dgl4lum\naeL426NQfBwGDcO46e5a69GMiDZYHpwDse1g0zeYy/7hg9mKv1NwIj6xYNMxduaX0zkqlHvS6+8w\n3T02nLvOdp4z8+vDFFXomxYRX3LXnET5pju8S9xJS7tExHfMVR/C9/+FqFgs//NHDEvdHy+N+CQs\nUx50Xvd/z2PmZLXUNCVAKDiRFpdTXMlrPx4D4H8vSGrQTlw39Iqhf4KN3BI7/7f5mLenKCL18Iea\nk5PHVyNGEd8xy0owF70AgHHL7zFi4097jXHeJTB4OJSXYr4519tTlACj4ERa3Is/HKHUbnJxx0gy\nkts06BqLYTC1KsPyf5uOkVOs3btEfOVEcOLbzIkaMYr4nvnBm3A0B7r1xhg2qsHXWW76HYSEYK7+\nF+burV6coQQaBSfSorKLKnh/ZwEWA+4+p3EfbAYmRXBxx0hK7SZv/JTnpRmKSH3KKkopLjuO1RpC\n24hon85FjRhFfMssLcH8YBEAlt/+rt7lXKcy2nfEuOI6ME3MJa96a4oSgBScSIt6/ac8Kh0wvHNb\nusaENfr6SWc508XvbMujoMzu6emJyGnkn7Sky1cNGF3UiFHEt8wVS6EwD9L6w1mDGn298cvfOrMn\nX36i3ifipuBEWkxhuZ2l251bfk7oF9eke/RtZ+O89hEUV5q8s03bh4q0NFd9h6+XdIEaMYr4kmmv\nPJE1+dWEJn1ZYSQkYwwbDQ4H5vuve3qKEqAUnEiL+XBnASWVJoPaR9Ar3tbk+9zU1xnYLNmej92h\n5msiLclfiuGdc1AjRhGfWf8fyM2C1M5w7rAm38b45XgAzDXLMIsKPTU7CWAKTqRFmKbJ21WZjuvr\n6GnSUOentKFTVChZRZX850CRJ6YnIg3kT8GJGjGK+I7j328DYFxxXaNqTU5ldOoO/TKgtARz1b88\nNT0JYApOpEVkZpewt6CCpDYhDOsY2ax7WQyDa3vGAGhpl0gL86fgBNSIUcQXzEP74fuvIMyG8Yv/\n1+z7WUZd77zvx0uUBRUFJ9IyPtrlTNX+v25RhFiaX0R7VbdoQizw1aFiDmtbYZEW4yo+j/NxA0YX\nNWIUaXnm2mUAGBdcitHWA7v2DboYYuJg/y7Ysbn595OApuBEvK7M7uDTfccBGNnNM1uPxtmsDO0Q\nicOEf+/WGlWRluIvPU5c1IhRpGWZpom5djkAxrCRHrmnERKKMdTZI8Vc9aFH7imBS8GJeN26A8Uc\nr3DQKz6cbk3YPrguV3V3Bjof7ixQGlikhfjdsi41YhRpWTt/ggN7ICYeBpznsdsal1wFgPmf5ZgV\n5R67rwQeBSfidct2FwAwsmuUR+87pEMkseEWduaXsytff5GJeFt5ZRlFJQVYLFbatonx9XQANWIU\naWnuJV0XjsCwhnjsvka3NDijBxTmw/f/9dh9JfAoOBGvKiy385+fizGAK7p4NjgJtRhc3KktAJ9U\nLRsTEe/JP34UgNjIeCyGf/zzoUaMIi3HtNsx//MxAMawUR6/vzH4Uuc4X37q8XtL4PCPf10kaH26\n7zgVDpOM5AiS2njuGxaXSzs7g5NP9yo4EfE2VwDgL/UmoEaMIi3qx0w4lgvtO0GPfh6/vXHBcADM\nr9dg2rXZTWul4ES8anlVsbqnl3S5nNe+DW1DLWzPK2dvgZZ2iXiTu97ET3bqAjViFGlJ5n+qCuGH\nXtGkjvCn1akbdOgChXnw4zeev78EBAUn4jWF5Xa+yS7BasAvqjIcnhZqNdx9Uz7V0i4Rr8or9K9i\neFAjRpGWYtrtmOvXAGAMGeGVMQzDwLhAS7taOwUn4jWfHyim0oSBSRHEhFu9Ns6lZ1Qt7VJwIuJV\n/rZTl4saMYq0gO0/Qv4xSEqFzt29NowxuGpp11efYdrtXhtH/JeCE/GatT8XATC0mR3hT+eClDZE\nhBhsPlLGweMVXh1LpDU7UXOi4ESktTHXrwXAGDTMO0u6XLqmQXIHyDsCW7733jjitxSciFdUOEzW\nHXQGJ8O8HJzYQixc1ME5xmfKnoh4javo3J9qTuCkLvHaTljEa9zByblDvTpOtaVdX33m1bHEPyk4\nEa/4/nAJheUOukSHcka05xov1uXiTs7gZN2BIq+PJdJa5fthzQmoEaOIt5nZB2DfDmjTFvqke308\nY9DFznG/Wef1scT/KDgRr1jTQku6XM5PicQAvj1cSkmFo0XGFGlNKiorKCzJx2JYiG4T6+vpVOMK\nlrSdsIh3uAvhB16AERrq/QHT+kNkFBzci5n1s/fHE7+i4ES84kS9iXd26TpVnM1K33bhVDhMMrNL\nWmRMkdakoMjZgDEmMh6LxXsbXDTFydsJi4jnuZZ0MWhYi4xnWEMwBpzvHPvbL1pkTPEfCk7E4/bk\nl7OvsILoMAsDEm0tNu6QqrqTzw9qaZeIp7mK4WOi/GtJF5zInLiWnYmI55jFx2HTN2CxYJwzpOUG\nPmewc/zvPm+5McUvNCg4mTt3Ll27diUiIoKMjAzWrat7DWBZWRk333wzAwYMICwsjEsuuaTGOatX\nr8ZisdT4tW3btqa/EvEbX1QFB4NT2xBi8eKOHqcYnNqmavziFhtTpLXw122EofpuXWrEKOJhP6yH\nykpIOwsjuuWWdBpVwQkb12NWqMlya3La4GTx4sXcc889PPTQQ2zYsIHBgwczcuRI9u/fX+v5drud\niIgI7rrrLkaPHl3vdnObN28mKyvL/evMM89s+isRv/HfQ85lVRektky9iUvfdjZiwizsL6xQt3gR\nDztW6NpG2L926gIID4sgIjySCns5RaWFvp6OSFAxf/gvAMbA81t0XCM+Cbr0gNIS2Pxdi44tvnXa\n4OSZZ55hwoQJTJw4kbS0NJ577jlSUlKYN29eree3adOGefPmMWnSJDp06FDvt1iJiYkkJSW5f1ks\nWmUW6Jw1H87MxfkpbVp0bKvF4HxlT0S8wp8zJ3By9kRF8SKeZG74CsBdA9KSXMvIzG+1tKs1qTca\nKC8v59tvv2XEiBHVjo8YMYIvvmh+gVJGRgapqakMHz6c1atXN/t+4ns/5pZSXGnSNSaMpDYhLT7+\n4KpszReqOxHxKP8PTly9TlR3IuIpZs4hOLjXuYVwj74tPr5xdlVw8p2K4luTeoOT3Nxc7HY7ycnJ\n1Y4nJSWRlZXV5EFTU1OZP38+S5cuZenSpaSlpXHppZfWW8sigeGrQ86MxXntI3wyvqvuJDOrhDK7\nthQW8ZQTwYn/LesCiFOvExGPM793LumiXwaGteW/cKTXAIiIhH07MXOa/rlTAosPftKgZ8+e9OzZ\n0/34/PPPZ8+ePcyePZsLL7zQF1MSD3EFJy29pMslISKEHrFhbM8rZ2NuKRnJvpmHSLBxLZeK88Pd\nugBi3NsJa1mXiMd871rSdZ5PhjdCQ6FvOmSuxfxxPcYlV/lkHtKy6g1OEhISsFqtZGdnVzuenZ1N\nSkqKRycyaNAgFi9eXOfzmZmZHh1PPK/YDj/mRGMBLAe3kJl92kvq1dT3vLNhYzvhfPDtTkgsa94k\npEXpz7l/cjjsFBQdw8Bg+0+7sFj2euzennrP83KdhfA79mwlM0w/R/5Of9YDgOmg3zdfEApsCmlL\nWTPfs6a+54lx7ekI5K5azr4oz372FO/o0aNHs66vNzgJCwsjPT2dFStW8Otf/9p9fOXKlVx33XXN\nGvhUGzZsIDU1tc7nMzIyPDqeeN6q/cdxbDvEwEQbF53X8/QX1CMzM7PJ73nh/uN8uvoQP1tiycjo\n1Kx5SMtpznsu3nW0IAe+hOjIOAYN8tw3qJ58zyP3Wvlyx78ICde/F/5Of9YDg7lrK47iQmiXTL8R\n9e++ejrNec/N+CgcK9+m3aFdJKanN2se0jLy8/Obdf1pl3VNnTqV8ePHM2jQIAYPHsz8+fPJyspi\n8uTJAEyfPp3169fzySefuK/ZvHkz5eXl5Obmcvz4cb7//ntM02TgwIEAzJkzh65du9KnTx/Ky8tZ\ntGgR77//PkuXLm3WixHf+q+r3sRHS7pcMpIjsBiwMbeUkkoHESHaBU6kOVxLpfy1GB7UJV7E007e\nQtinAUGXHhAVAzlZkH0A2nf03VykRZw2OLn++us5cuQIjz32GIcOHaJ///4sW7aMTp2c30hnZWWx\na9euateMHj2avXudaX/DMDj77LMxDAO73Q5ARUUF9913Hz///DMRERH069ePZcuWccUVV3j69UkL\n+jrL2d/E18FJVJiVtLhwfjpaxveHSzi/hfutiAQbf9+pCyAuyhmcHDuei2ma+nZVpJlcwQlnDfLp\nPAyLxVl38tVnmBu/xlBwEvQaVBA/ZcoUpkyZUutzCxYsqHFs9+7d9d7vvvvu47777mvI0BIgjpRU\nsju/HJvVoF87m6+nw7ntI/jpaBnrsxWciDSXO3MS5Z87dQHYwiKwhbWhtLyY4rLjRNqifD0lkYBl\n2ith8wYAjP6+X4Jn9D8X86vPYGMmXPYrX09HvEzrXcQjvj3szJqclWgj1Or7byzPbe/M3qyvyuaI\nSNO5eof46zbCLu5GjOp1ItI8u7ZCaTGkdHJ2avcx46xzATA3rq+3ubcEBwUn4hHfZDuDgPRk3/Q3\nOdXZSRFYDdh8pJSiCvU7EWmOQFjWBeoSL+Ip5qZvADD6pvt4JlU6doPYdnAsFw7s8fVsxMsUnIhH\nfOsOTvyjr0hkqIW+CTbs5omsjog0TcAEJ1EqihfxBPNHZ3CCnwQnhmG4l5eZG9f7eDbibQpOpNny\nyuxszysnzGLQLyHc19NxO7cqi5OZVezjmYgEthM1J34enChzItJspt0Om78FwOjnH8EJAP2cS7vY\nqB45wU7BiTTbd1VZk34JNsKt/vMjdU5VcLIhp9THMxEJXHaHnfyiYwDERMb7eDb1c28nrJoTkabb\nux2Kj0NSKkai/zQ9NPqeA4C5ZYPqToKc/3ySlIDlb/UmLmcl2LBU1Z2UVqruRKQpCoqOYZoOotrE\nEmIN9fV06nUic6LgRKSpXEu6/KbexKVDF4iKhaM5cPigr2cjXqTgRJrNVdPhb8FJ2zArPWLDqXTA\npiNlvp6OSEAKlHoTqN7rRESaxqxa0oU/LenCWXdCb2czb3Pzdz6ejXiTghNplsJyO1uPlRFicW4j\n7G8GJjnntEFF8SJN4gpO4vy4x4nLyZkTLfsQaTzT4YBNVfUm/pY5AYw+Zzv/56cNvp2IeJWCE2mW\nDTmlOEzo285GRIj//TgNTHRmc75TcCLSJO5i+ADInNjC2hAeaqO8opSS8iJfT0ck8Py8GwrzoF0y\nJHfw9WxqMHoNAMD8SZmTYOZ/nyYloPxQ9aHfFQT4m7OrMiff55Rid+ibVJHGyq/KnMT4eQNGcC77\nUFG8SNOZW74HwOg9wLmMyt907w1h4bB/F2ZBnq9nI16i4ESa5Ydc505Y/rikCyA5MpSUyBCOVzjY\nmV/u6+mIBJxAqjkBbScs0ixbf3D+N22Ab+dRByM0DHr0dT6oCqQk+Cg4kSazO0x+rApO+if4Z3AC\nzm7xoLoTkaY4Vhg4y7pAjRhFmsOsCk6MtLN8PJO6Gb2ddSem6k6CloITabKd+eUUV5qkRIaQ2CbE\n19Opk6soXnUnIo0XsJkTLesSaRTzeIGz5iQ0DLqm+Xo6dTJcO3ap7iRoKTiRJtuY499LulzOTnRl\nTtSMUaQxHA47+UVHgQAMTrSsS6Rxtv/o/G/33hihftzTKG0AGAbs2IRZpn/Xg5GCE2myH3KdmYiz\nEvyzGN6lW2wYUWEWsoorOVRU4evpiASMwpJ8HA47bSNiCA0J8/V0GsQVnKjXiUjjmFv8f0kXgNE2\nCs44EyorYcdmX09HvEDBiTTZDwGSObEYBgMTXf1O9C2LSEO5lkYFStYETvRjUc2JSOOcqDfp7+OZ\nnJ677mSL6k6CkYITaZL8Mjt7CioItxqkxYX7ejqnNVBF8SKNFkg9TlzcWwkrOBFpMNPhgG0bnQ/8\ndKeuatx1JwpOgpGCE2mSjVW7dPWODyfU6od7oZ/CtWPXdzkKTkQayr1TVwB0h3eJCI8kLCScsvIS\nSsqKfT0dkcBwYDcUH4d2yRjtknw9m9NyZU74aYMzsJKgouBEmsS1pKu/ny/pcunTLpxQi8GOY+UU\nltt9PR2RgHCsMAeAuABowOjibMSooniRxgiUehMXI7E9JLaHokLYv8vX0xEPU3AiTeLKnJzlx/1N\nThZutdCnXTgmzm7xInJ6rqLyuADKnMDJO3ZpaZdIg7iWdPUKjOAEwOilLYWDlYITaTSHeaL54lmJ\n/r1T18kGVGV5XIGViNTPVRAfcMGJqyi+UJkTkYZwF8P39P9ieLdeVbUxWzf6dh7icQpOpNF25ZVz\nvMJB+zYhJPlx88VTubrYb1TmRKRBXJmTQKo5ARXFizSG6VoaFRIK3Xv7ejoN5tpVzNym4CTYKDiR\nRvshNzC2ED6VK8uzMbcUh2n6eDYi/s1ur6Tg+FEMDGIjA2e3LlCvE5FG2b4JTBO698IIDYx+RgCc\n0RPCwuHAHszCfF/PRjxIwYk0WqD0NzlVUpsQ2rcJ4XiFg9355b6ejohfyy86iolJdGQcVmvgZEhB\nNScijWFu/R4Ao2fg1JsAzi723fs4Hyh7ElQUnEijuTIn/QOkGP5k/VV3ItIggbiNsIurRiZfwYnI\nabnqTQiQnbpOpqVdwUnBiTRKYbmd3fnlhFoMesX7f/PFU7kCqh9UdyJSL9c2vIG0jbCLO3OigniR\nejmbL/4IBM42widzFfCbKooPKgpOpFHczRfbhRNmDbwfn7OUORFpkKMBnDlpY4si1BpGSXkxpeVq\nvCpSp4N74XgBxCdCQrKvZ9N4roBq20Y1YwwigffpUnzK3XwxAJd0AfSKDyfEAjvzyjmuZowidXJl\nHQJtG2FQI0aRhjp5SZdhGL6dTBMY7ZIgob2zu/2B3b6ejniIghNpFFfGYUCAFcO7hFst9IpzNmPc\ndKTM19MR8VvHAnhZF5zc60R1JyJ1qloOFYhLuly0tCv4KDiRBnOYZsBnTgD6V20prLoTkboFcuYE\ntGOXSEO4my8GcHBCVVG8mjEGDwUn0mC7853NF5PahNA+MtTX02mys1zNGHO1Fl2kLoHagNFFvU5E\n6mcWH4d9OyAkBLr18vV0msy9Y5driZoEPAUn0mCuJV1nBXDWBKoXxZtqxihSQ3lFGUUlBVgtIUS1\nifX1dJrEFZzkKzgRqZ2r+WLXNIzwAP53vVtvZ4C1f6cz4JKAp+BEGsy9pCtA601cUiJDaGezklfm\nYF9hha+nI+J3XEXksW3bYTEC858J1ZyI1C8olnQBRlg4dO3lDLS2b/L1dMQDAvNfHfGJYMmcGIah\nLYVF6hHIDRhdYqsK+VVzIlI7d+PCAA9OQM0Yg42CE2mQwnI7O/PKCbE4e5wEOldB/0YVxYvUEMgN\nGF1UcyJSN9M0T+zU1TPwgxN6qu4kmCg4kQbZlFuKCfSKCyc8AJsvnqq/MicidToa4Dt1AbSNiMZq\nDQ78NCcAACAASURBVKGkrIgyNWIUqe7gPijMg7gESErx9Wyazb00betG1ZIGgcD/lCkt4gfXkq6q\nbXgDXd94G1YDth0ro6RCXWVFTpYXBMu6qjViLDrq49mI+BdzW2A3X6whKRVi2zkDrqz9vp6NNJOC\nE2kQVzH8WQFeDO8SEWqhR1w4dhM2H1UzRpGTBXoDRhfX/F3BlohUcRXDVy2HCnSGYZy0tEt1J4FO\nwYmclsM03cufArn54qn6q9+JSK0CvQGji6so/piCE5FqzC3BsVPXyQx3M0bVnQQ6BSdyWvsKKigo\nd5AQYSUlMsTX0/EYV3CiTvEiJ5imybHCHADiohJ9PJvmcQVXrtcjImCWFDubL1pD4Mzevp6Ox7gK\n+5U5CXwKTuS0TtSb2IJjbWoVNWMUqamkvIiyilLCQm1EhEf6ejrNEh+dBMBRBSciJ+zYBA4HdOmB\nER4cdaQA9OgLFgvs2YZZphURgUzBiZzWDznOP+RnJQTRX2JA56hQYsIs5JbYOVRU6evpiPgF95Ku\ntgkB/2WEK/OjzInICcG4pAvAsEXAGT3AYYcdP/l6OtIMCk7ktE7OnAQTwzDcWwpraZeI04kGjO18\nPJPmcwcnBQpORFxO3qkr2LibMaruJKApOJF6FVU4nM0XDegdH/jNF091oihewYkInAhOAr3eBCA+\n2vkajh7PwWFqy3ARZ/PF4MycACd27FKn+ICm4ETq9WNuKQ4TesaHYwsJvh+XsxSciFQTDN3hXcJD\nbUTaorDbKzlenO/r6Yj4XtZ+KMiDmHhI7uDr2XjciWaMP6iWNIAF36dN8SjXh/azgmgL4ZP1TbBh\nAFuOllFu1zerIseCoAHjyVwZIBXFi5y0k1Va/4CvKatV6hnQNhqO5UJulq9nI02k4ETq5S6GD5LO\n8KeKCrPSLSaMCofJFjVjFAmaBowurqVdKooXIbiXdKFmjMFCwYnUyTyp+WKwZk4Ad1G8lnaJnLRb\nV3Tg15zASZkTFcWLuAvFgzU4gZOaMW5TUXygUnAiddpXWEFemYN2NiupbYOn+eKp1IxRxMlhOoIu\nc3JiO+HDPp6JiG+ZpSWwZztYrHBmX19Px2tONGNUcBKoGhSczJ07l65duxIREUFGRgbr1q2r89yy\nsjJuvvlmBgwYQFhYGJdcckmt561Zs4b09HQiIiLo3r07L774YtNegXiN68N6sDVfPJWK4kWcjhfn\nY7dXEmmLIiw0OHbni3fXnOT6eCYiPrZjk7MHSJcezp4gwapHP+d/d27BrCj37VykSU4bnCxevJh7\n7rmHhx56iA0bNjB48GBGjhzJ/v37az3fbrcTERHBXXfdxejRo2v9ULt7925GjRrFhRdeyIYNG5g+\nfTp33XUXS5cubf4rEo9x9TfpH8RLugC6xoQRGWrhUFElOcVqxiit15ECZ3bB1Vk9GJzodaLMibRu\nrWFJF4DRNgo6doXKCti91dfTkSY4bXDyzDPPMGHCBCZOnEhaWhrPPfccKSkpzJs3r9bz27Rpw7x5\n85g0aRIdOnSodSu3+fPn07FjR5599lnS0tKYNGkSv/3tb3n66aeb/4rEYza6MydB/A0LYLUY9Gvn\n/JZY2RNpzY4GYXByoiBemRNp3dwF4lUF48HMFYCpKD4w1RuclJeX8+233zJixIhqx0eMGMEXX3zR\n5EG//PLLWu+ZmZmJ3W5v8n3Fc4orHGzPK8NqQJ92wbG8oz79qwIwBSfSmrmCk3ZBFJy0jYgh1BpG\ncdlxSstLfD0dEZ+o1nyxV3BnTgBwZYdUFB+Q6g1OcnNzsdvtJCcnVzuelJREVlbT94/Ozs6ucc/k\n5GQqKyvJzdW3W/5g05Gq5otx4UQEYfPFU52loniRoMycGIZBXFXPlqNa2iWtVfYByD8K0bHQvpOv\nZ+N1hrYTDmgBswVTZmamr6fw/9u788Coq3v//8/P7JN9X4GwCGFHJKwqYkWq7a2tdat2Ub/t9erV\nXoTqT/nW+9PeUltraxcXqtartLdWay+tG63ggoigsgUwhDWBJJBMCJB9nfmc7x+zYGSHkDPzmffj\nXmoy+UzympwE5j3nvM+JK/9ocAMe8lSztu99f35dv98AUvj0QDsfr12H3br9/1FNfs/1qqzZCcAh\nX//93vfH17ETnP39ZMMaBmTIlsLRQH7X+1f6px8zGGjKHUTF+vVaMvTrmJsm411u7PX7KV3xDv6k\n1P772oLhw4ef1f1PWJxkZWVht9vx+Xy9bvf5fOTn55/xF83Lyztq5sXn8+FwOMjKOvb2lSUlJWf8\n9cTp++N7+4E2Zo8eRMnQlH7/+uvWrev3MR9Yt4fqlh5Sh41lZIa1NwGIRjrGXPT21tYXAJhywXQK\nsgaf86/XX2O+s/FjahsrycxLpWS8/IzpJr/r/c/c8DYKSJsyU8v3XseYB4onwJZPmOCxYcjPW79q\namo6q/ufcL2Oy+Vi0qRJLFu2rNfty5cvZ8aMGWf8RadPn87y5cuP+pyTJ0/Gbref8ecVfUMpFVne\nFD6gMB7I0i4Rz5RSkWVP6cnWWdYFRJZ1SVO8iFdHduqyfjN8WPixKuk7iTknbSaYP38+L7zwAs89\n9xzl5eXMnTuXuro6br/9dgAWLFjA7Nmze91n69atlJaW0tDQQGtrK5s2baK0tDTy8dtvv519+/Yx\nb948ysvL+f3vf8/ixYu55557+vjhiTNR09pDY1eAdLedAUlO3XH6zfhQIbZZmuJFHGppb6In0E2C\nJxmvO0F3nD4V7qGR7YRFPFJd4cMXbUfOAIkDsmNX7Dppz8n111/PwYMHWbhwIbW1tYwbN46lS5cy\ncGCwoaquro6Kiope9/nyl7/M3r17gWAz4sSJEzEMI7IT1+DBg1m6dCnz5s1j0aJFFBYW8vjjj3P1\n1Vf39eMTZ+CzsyZWPnzx88LnuWyRmRMRhw61hJvhszUn6XuRhvgW6TcRcWhXOQT8MHgEhtdaLzyc\n0IhQIbarDBXwY9hjps067p3SSN1xxx3ccccdx/zY888/f9RtlZWVJ/2cM2fOZL2mpixxYpGT4S1+\n+OLnnZfuxmM3qGoJzhyluWWJoYgfkW2ELbakC47MnMhuXSIexeOSLgAjNSO4M1ldNezdBUNH6o4k\nTpH194gVpy181seEOOo3AXDaDEbJYYwiToVPh0+30DbCYWlJWdgMG01th+jxd+uOI0S/UjtCy5os\nfjL8sUT6TrZL30kskeJE9NLRY7LjcBc2A0ZnxldxAjA+K3QYoyztEnHmsAUPYAyz2+ykJweXq8nS\nLhFPeh2+WDxBcxoNQuedsEP6TmKJFCeil7JDnQQUDE9zk+CMvx+P8O5kMnMi4o0VD2D8rHDRdbDJ\nd5IrhbCQ+lo43ADJqVAwSHeafndk5kSKk1gSf88+xQmFZwzGx9mSrrBwU/ynDZ2YSmlOI0T/ORhu\niLdgzwlAZmoeAAebpTgR8SOyje6IcXG1wU1E0QhwuWH/XlRzo+404hRJcSJ6iezUFWfN8GE5CQ7y\nEh209phUNsnadBEfPnvGiRV36wKZORFxKryka0R8NcOHGU4nDBsdfGfnp3rDiFMmxYmIUEpFzviI\n15kTkMMYRfxp7Wiix9+N152I152oO845kZmaC8jMiYgvkZ26RsZfM3yYNMXHHilORERNaw+HOoOH\nLw5Kjp/DFz8vct6J9J2IOGH1fhOQZV0i/qiuDqjYHjx8MU5nTuDIrJH0ncQOKU5ERGn9kS2E43Jt\naog0xYt4E97Byoo7dYXJsi4Rd3aWBQ9fLBqO4bXmjOgpCW+hvPNTlGnqzSJOiRQnImLTgQ4AJuTE\n75IugJEZbhw22N3YTWt3QHccIc65yMyJRZvhAZK8qbgcbjq62mjvatUdR4hzTm3bBIAxMg63EP4M\nIzMHMnOhvRX2nfyQcKGfFCciItxjMSHbqzmJXm67jZHpbhRQdrBLdxwhzrmG0GyClZd1GYZxpO+k\nSU6KF9antoV6LOK8OAFAthSOKVKcCABaugPsauzGYYPRoVPS49n4UIEmTfEiHjQ01QKQFerLsKrM\nlHBxUqc5iRDnVvDwxfDMyfma0+hnhJd2SVN8TJDiRADB/goFjMrw4LbLj0V4t7LwUjchrKwh9GQ9\nK83ixUlkxy6ZOREWt28PtDRBehbk5OtOo124OAkvdRPRTZ6FCgA2HTjSDC/g/EhxIocxCmsLBPwc\nbj6AgRGZWbCqyMyJ7NglLC7yJHzkhLje4CZi2ChwuqC6AtXSpDuNOAkpTgQAm+qDMwTn58R3v0lY\nbqKT/NBhjLsb5TBGYV2HWg5gKpPUpAycDpfuOOfUkZ4TKU6ExYWb4UfJki4Aw+mC4WOC78jsSdST\n4kTgN1Vk29zxcXoy/LGcH+o72VgvS7uEdUWWdFm83wQ+s52wzJwIi5Oduo4WLtRU+UbNScTJSHEi\n2N3YTbtfUZjkIDvBoTtO1Dg/58jSLiGsqqEx1AyfZv116eFlXYea6zGVnHcgrEk1N0JNJbjcMGSk\n7jhRwxg1EQBVLjMn0U6KExFp+j4/zrcQ/rzwEjeZORFWFk8zJ26XlyRvKv5AD81th3XHEeLc2BHa\nLve80RhOp94s0SS8Y9euMlSPLNeOZlKciMjMwHhphu9lWKqLJKeN2jY/vrYe3XGEOCfiqTgBOSle\nWJ8s6To2IzkVBg2Dnm7YvVV3HHECUpwISkMzA/F++OLn2W1GpGArlaVdwqLirjgJPU7pOxFWpcpL\nASlOjiV85ovaWqo5iTgRKU7iXH27n/1tfhKdNs5Ls/ZOPWdiYmhpV6ks7RIWpJSKzCBY/YyTsOzQ\n4zzQuF9zEiH6nvL3wM6y4DtSnBwt3BS/TYqTaCbFSZzbHOo3GZflwW6TvdA/73yZOREW1tx+mG5/\nFwmeZBLcSbrj9IvstAIADoQ2AhDCUvbsgO5OKCjCSEnXnSbqRLZWLt+EkjPMopYUJ3GuVA5fPKEx\nWR4cBuw43EVbj+zuI6yloTG+lnQBZId2JauXmRNhQeGdqGRJ13HkFkJ6FrQ0wr49utOI45DiJM5t\n8MnhiyfiddgYmeHGVLDlgCztEtYSb/0m0HvmRF45FVajytYH35DDF4/JMIwjS7vkvJOoJcVJHGvt\nDrD9cBcOAybI4YvHFS7cZGmXsJp4LE4SPcl43Yl0dXfQ0t6oO44QfUYpBVs3AGCMnaQ5TfQKn3eC\nnHcStaQ4iWOlBzoxFYzK9OB1yo/C8ch5J8Kq4rE4MQyDnMjsiSztEhZSUwHNjcFlS3kDdaeJWsao\n4JI3mTmJXvKMNI6Fl3RNypUlXScSborf0tCJ35RlIMI6IsVJnOzUFRZe2lUvTfHCQlTZkVkTw5AN\nbo5rSDF4vFBbjWo8qDuNOAYpTuLY+nopTk5FptfBwGQnHX7FjsNduuMI0WficeYEjjTFy45dwlLC\n/SZjZEnXiRh2BwwfF3ynXLYUjkZSnMSpDr/J1oZObMaRmQFxfBeElnaFZ5uEiHXtXa20dTTjdLhI\nSYyvLUePFCeyrEtYg1LqyMzJmAs0p4l+xuhg30n4eyaiixQncWrzgU78CorT3SS57LrjRL3w7NJa\nKU6ERdQfDj4xz0krwGbE1z8FctaJsJy6ajh0AFLSYMBQ3WminjG2BAD16VrNScSxxNe/SCJifehJ\n9gWypOuUlOQdmTkJSN+JsID6w/sAyM0YoDlJ/8tOD86cNDTWYio5v0jEPvVpaEnX6Auk3+RUFI8D\npwv27EQ1y6590UaKkzi1QfpNTkt+opMBSU5ae0y2S9+JsADfoRoActIKNSfpfwnuJBK9KXT7u2hq\nPaQ7jhBnT7YQPi2Gyw3F44PvhHt1RNSQ4iQOdQVMtoTO7Jgohy+esnAht06WdgkL8EVmTuKvOAFp\nihfWEp45MUZLcXKqjHHhpV3rNCcRnyfFSRwqa+ii21QMT3OR5pZ+k1M1ObS0a11du+YkQpy98LKu\nnPT4LE7krBNhFap+PxyohcRkKDpPd5yYEek72SLFSbSR4iQOSb/JmSnJDR/GKOediNgWMAORGYPw\nk/R4I03xwioiO06NmohhlxccT9mIceByQ9UuVJMs74wmUpzEIek3OTO5iU4GJof6Tg5J34mIXYea\n6wmYftKTsnC74vPvAdlOWFiG9JucEcPpguLgafHSdxJdpDiJMz2mYtOB0MyJ9JucthLpOxEWEGmG\nj9MlXfDZU+KlOBGxTYWeWBty+OJpCxd0kd3ORFSQ4iTObDvYRYdfMTjFSabXoTtOzDlSnEjfiYhd\n9Y3x3QwPkJMeLE4aGusIBPya0whxZtShA7C/CjwJMLRYd5yYY4ybDEhTfLSR4iTOfBJq5pYlXWem\nJC8BkL4TEdt8h+K7GR7A7fSQmZJLwPRzoEn6TkRsijRzjzofwy4vOJ624WPA5YGq3ahG6TuJFlKc\nxJlwcTI1P0FzktiUk+BgULKTth6TbdJ3ImJU5ADG9Pg7gPGz8jIGAlB3sFpzEiHO0OaPATAmTNUc\nJDYZTheMkr6TaCPFSRzp9JuU1ndiACW5UpycqfCWwmtlS2ERo3xxvo1wWF5msDirPSTFiYg9SinU\nplBxMl6KkzN1ZEvhtZqTiDApTuJI6YFOuk1FcYabdI9sN3imJoUKO2mKF7GorbOF1o4mXE4PaUmZ\nuuNoFZ458UlxImJRbRU01EFKGgwerjtNzJLDGKOPFCdx5OPa0JKuPJk1ORtHzjvpoEf6TkSMOXL4\nYgGGYWhOo1dexiBAlnWJ2BSZNRk3BcMmT+fO2LAx4PZATSXqcIPuNAIpTuLKkX4TaYY/G9kJDoak\nOOnwKz5t6NQdR4jTEm6Gz02L7yVdALkZwWVdvsZ9BMyA5jRCnJ5wcYL0m5wVw+mE0RcAoDZ/ojmN\nAClO4kZTV4Dyg104bQbny/kmZ21aQSIAq/dL34mILb7DcsZJmMflJT05m0DAT0NTne44QpwyFQhA\nqEdCmuHPnnH+tOAbG1frDSIAKU7ixtq6dhQwIduD1yHDframFwSXxn20v01zEiFOT23DXgAKsoo0\nJ4kO+bJjl4hFldugrQVyCzFy5YWGs2VMnAGAKv0IpWS5tm7yLDVOfFIXbN6WLYT7RkmOF4cNyg52\n0dQly0FE7Nh3MFic5GdKcQKQlxkqTqQpXsQQ2aWrjw0cChnZ0HgQ9u7UnSbuSXESJz4KNcNPyZMl\nXX3B67QxMduL4kgvjxDRrq2zhabWg7gcbrJSc3XHiQq5kZmTKs1JhDh1qjTcbzJFbxCLMAwD4/zp\nQHD2ROglxUkcqGruprqlhxSXjTGZHt1xLCO8tEv6TkSs2B9a0pWXOQibTbYTB8jPDO3YJTMnIkao\njjYo3wA2m8yc9KWJoeJE+k60k+IkDnwYevI8vSABuy2+tw7tS0f6TtpljaqICbUHpd/k83LTQzt2\nHd6HKTt2iViw+RPw+2H4WIyUNN1pLMOYMBUMA7ZuRHXJOWY6nVJx8tRTTzFkyBC8Xi8lJSWsWrXq\nhNdv2bKFSy65hISEBAYMGMCPf/zjXh9fsWIFNpvtqD87duw480cijuvDfcGm7QtDO0yJvjEi3U26\n205du589zT264whxUvsb9gBQIP0mEV53AmlJmfgDPRxsrtcdR4iTUhs+BMC44ELNSazFSEmHoSOh\npxu2btQdJ66dtDh5+eWXufvuu3nggQcoLS1lxowZXHnllVRXH3sKvLm5mcsvv5z8/HzWrVvHb37z\nGx599FEee+yxo67dunUrdXV1kT/nnXfe2T8i0Uun34ycZD6jQJrh+5LNMCKzJ2tk1y4RA/Y3BPsq\nCrIG6w0SZcInxddK34mIckqpI8XJJClO+lpk1y5Z2qXVSYuTxx57jFtvvZXvfve7FBcX89vf/pb8\n/HwWLVp0zOv/9Kc/0dnZyeLFixk9ejTXXHMN99133zGLk+zsbHJyciJ/bHLCaZ9b5+ugK6AYleEm\n0+vQHcdywsXJqn3SdyKim6lM9suyrmMKfz/2hWaWhIhaNRVwoA5SM2DoKN1pLMcI952s/1Bzkvh2\nwmqgu7ubDRs2MGfOnF63z5kzh9Wrj11Vrlmzhosvvhi3293r+v3797N3795e15aUlFBQUMDs2bNZ\nsWLFGT4EcSKRJV2FsqTrXLiwIBGDYBHY1mPqjiPEcR1qrqe7p5OUxHSSvCm640SVAdlDAaip3605\niRAnFn7SbEycjiEv6Pa9kRMgMRn27UHt33vy68U5ccKf7IaGBgKBALm5vbeczMnJoa7u2Kfp1tXV\nHXV9+P3wfQoKCvjd737HkiVLWLJkCcXFxVx22WUn7WURpy/cDH+hLOk6J9I9dsZne+gxVWS7ZiGi\nkfSbHN+AnFBxcqBScxIhTiy8pAvpNzknDLsj0suj1slzUl36fJ2PYZx8N6gRI0YwYsSIyPvTpk1j\nz549PProo1x00UXHvM+6dev6LGO8qO+2Ud2STILNpHtvGetibDl1rIz5UNxswsPfSveSWi87fJyN\nWBnzWLS5eg0ANr8nqr7P0ZDFVCYOm5PDLQdYtWYlHqe8mHOuRcO4xxpbdyfjyjZgGAab8RKIse9h\nrIx5euYABgPN777JroJi3XFi0vDhw8/q/icsTrKysrDb7fh8vl63+3w+8vPzj3mfvLy8o2ZVwvfP\ny8s77teaMmUKL7/88nE/XlJScqKo4hheLD8MNHDRwBSmTI6tX7B169bFzJinHe7ib29UUd7l5YJJ\no7GdQoEujhZLYx6LNvveBeCCsVMpGRUd3+doGvNVFUPZU7ed7MJUigdN0B3H0qJp3GOJ+ug9zIAf\niscxceYs3XFOSyyNuSoejvna8yRX72TSqGKMxGTdkWJOU1PTWd3/hMu6XC4XkyZNYtmyZb1uX758\nOTNmzDjmfaZPn84HH3xAV1dXr+sLCwspKjr+coLS0lIKCgpOJ7s4ifeqg/0mswYmaU5ibcPSXOQn\nOjjUGaCsoevkdxBCA2mGP7EjS7sqNCcR4tjUx+8BYEyZpTeIxRnJqTBqAgT8IKfFa3HSbqr58+fz\nwgsv8Nxzz1FeXs7cuXOpq6vj9ttvB2DBggXMnj07cv1NN91EQkICt9xyC2VlZSxZsoRHHnmE+fPn\nR6759a9/zauvvsrOnTspKytjwYIFvPrqq9x1113n4CHGp8auABvqO3DY4KJCWaJwLhmGwcwBwQ0H\nVu6TLYVF9Onu6eJAYy02w0Zu+kDdcaLSkaZ4KU5E9FEBP2rdSgCMqZdqTmN9RslMgMj3XPSvk/ac\nXH/99Rw8eJCFCxdSW1vLuHHjWLp0KQMHBv+Bq6uro6LiyF/mKSkpLF++nDvvvJOSkhIyMjK45557\nmDdvXuSanp4e7r33XmpqavB6vYwdO5alS5dyxRVXnIOHGJ9W1rRhKpial0Cyy647juXNHJDIy9ub\nWFnTyp3nZ+qOI0QvNQcqUMqkIGswTodTd5yoNCB7CCBN8SJKbS2FliYoHIwxYIjuNJZnTJ6JWvxr\n1PpVqEAAwy7Po/rTKTXE33HHHdxxxx3H/Njzzz9/1G1jx47l/fffP+7nu/fee7n33ntPMaI4Eyuq\nWwGYNVC2EO4Pk3K9eB0GOw53s7+1h4IkeQIoosfeup0ADMo9uyZFK8vPLMJms1N/eB9d3R24XV7d\nkYSIiCzpmjpLb5B4UTgY8gZCXTVs3wyjJ+pOFFdkk2wL6vCbrAltISz9Jv3DbbdxUegsmXerWjWn\nEaK3Kl+wOCnKk+LkeJwOJ/kZA1Eo9jXI+QYieiilPlOcyJKu/mAYBsa04PdarXlHc5r4I8WJBX1U\n205nQDEm001OgpwK319mDwoWgm9LcSKizF5feObkPM1Joluk70Sa4kU0qdwBB2ohPQuGj9WdJm4Y\nM4L91Gr12yhTDlnuT1KcWFB4SdelMmvSry4qTMRtN9h0oJP6dr/uOEIA0NbRTENTHU6Hi/yMQbrj\nRDXZsUtEo8isyeRL5FT4/jR8LGTlwUEf7CrTnSauyE+5xfQEFO9HthCWfpP+lOC0cWFBcGe0d2T2\nRESJqvrdAAzMHobdLjOpJyI7doloFF5WZEy5RHOS+GIYBsb0y4Dg7InoP1KcWMxHde00dZsMS3Ux\nLM2tO07cmV0UWtq1V4oTER321u0AZEnXqRiQPQSbYWN/wx66ejp1xxECtXcXVO2CpBSYME13nLjT\na2mXUprTxA8pTizmrT0tAHxxsJxoqsPFhYk4bQYb6zto6JClXUK/vdIMf8rcLi8F2YMxlRnZ4UwI\nndSqtwAwpl+G4ZRdIPtd8fhgr0/9fthdrjtN3JDixEI6/SYrQku6vjhY+k10SHLZmV6QgEJ27RL6\nKaWo8u0CZBvhUzU0fxQAlbXbNCcR8U4phfogVJxcLOfA6WDYbJ9Z2rVcc5r4IcWJhXy4v522HpPR\nmW4Gpbh0x4lb4V27/hmaxRJCl8MtDbS0N5LgTiIrNU93nJgwJH8kAJX75VVSodnurcFzNtIyYcwk\n3WniVmRp1wdvya5d/USKEwv5Z6Us6YoGXxiUhMdusLG+k30tPbrjiDgWPt9kUN5wDMPQnCY2DC0I\nFSd12zGVPBER+kRmTS68XE4o12n0BZCdF9zOuXyj7jRxQYoTi2jrMflgX3BJ15wiWdKlU6LTFtnG\n+c3KZs1pRDzb6ws2wxdJM/wpS0/OJi0pk46uNnyHanTHEXFKmSZq1TJAlnTpZthsGDO/BIB67w3N\naeKDFCcW8V51K10BxcQcD3mJ0jSn25eHBmev3qxokR0+hDa79wWXJoWXKolTM7Qg2HdSIUu7hC5b\nNwTP18jODzZlC62MWV8GQrt2dclOfueaFCcW8dqu4Cv0XxqSojmJAJian0Cmx05VSw+fNnTpjiPi\nUHdPF1X1uzAMmxQnpynSdyJN8UIT9c5rABiXfEmWZEYBY+BQGDYK2ltRa1fqjmN5UpxYQHVLN2t9\nHXjshuzSFSUcNoMrhoRmT2Rpl9BgT912TDNAYdZgvG45kPV0HGmKl+JE9D/V3hrZGcq47KuaNY1g\nvAAAHwpJREFU04gwY9a/AKBWvKk5ifVJcWIB4VmT2UVJJLukaS5a/Etoaddbe1roCcjSLtG/du/b\nCsCwwtGak8SewuwhuJweDjTV0tzWqDuOiDNq1TLo6oSxJRj5A3XHESHGxVeAzQ4bV6MaD+mOY2lS\nnMS4gKl4rSK4S9dXz5MlXdGkON3N8DQXjV0m71XLmSeif+3eHypOCqQ4OV12m53BoXNhZGmX6G/q\nnb8DMmsSbYy0DLjgQgj4Ue+9rjuOpUlxEuPW1LZT3+5nYLKTSTle3XHEZxiGwTUjUgF4ZUeT5jQi\nnvT4uyNLkmTm5MwMKxwDwM6aLZqTiHiiqnfD9i2QkIQx4zLdccTn2L54DQDqrf+VM0/OISlOYtyr\noSVdXx2WIk1zUejLQ5LxOgzW+TqoaOrWHUfEicrabfQEuinMGkxyQpruODFpxMDgDknbqzdpTiLi\niXr7VQCMi7+I4ZYXHKPOBRcGzzypq4ZNH+tOY1lSnMSw+nY/K6pbsRvwlWGypCsaJbnsXBk6FPN/\nZfZE9JPtVcEn1MWDJmhOErsG543A7fTgO1RDY+tB3XFEHFBdHah3QsXJ7Ks1pxHHYtjtGHOCsyfm\nW3/VnMa6pDiJYX/Z3ohfBU8kz0lw6I4jjuO64uDSrtcrmunwyzSwOPe2V28GYMRAKU7OlN3uiCzt\n2hH6fgpxLqkVS6G1GUaMwxg+RncccRzG7K+B3QGfvI86WK87jiVJcRKjOv0m/7sz+Er8TSNl2UY0\nG5nhYWymm5Zuk7f2tOiOIyyurbOF6vrd2G0O6Tc5S8Wh4m5bVanmJMLqlFKoN/8MgPEvN2pOI07E\nSM/CmHopmAHUsiW641iSFCcx6h+VLTR2mYzKcDMh26M7jjiJ64qDBeSL5Y1yYrw4p7bt3YhSJsMK\nRuF2yt8NZ2Nk0UQAyvduxDQDmtMIS9v8MVTthoxsjBmzdacRJ2FceT0A6p+vyInx54AUJzFIKcWf\ntwX33r9pVJo0wseAKwYnke21s7Oxmw/3t+uOIyysrHI9AKOHlGhOEvvyMgaQkZJDW0cze327dMcR\nFma+Hpo1ufJ6DIdTcxpxUmMnwdBR0HQIteIN3WksR4qTGLS2roOdjd1keuzMKZIT4WOBy27jm6PS\nAXih7LDmNMKqTDNA+d4NAIyR4uSsGYbBmMHB7+PWPes1pxFWpfbvhfU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- "text": [ - "" - ] - } - ], - "prompt_number": 12 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "This result bothered me quite a bit when I first learned it. If my first measurement was 10, and the next one was 50, why would I choose 30 as a result? And why would I be *more* confident? Doesn't it make sense that either one of the measurements is wrong, or that I am measuring a moving object? Shouldn't the result be nearer 50? And, shouldn't the variance be larger, not smaller?\n", - "\n", - "Well, no. Recall the g-h filter chapter. In that chapter we agreed that if I weighed myself on two scales, and the first read 160lbs while the second read 170lbs, and both were equally accurate, the best estimate was 165lbs. Furthermore I should be a bit more confident about 165lbs vs 160lbs or 170lbs because I know have two readings, both near this estimate, increasing my confidence that neither is wildly wrong. \n", - "\n", - "Let's look at the math again to convince ourselves that the physical interpretation of the Gaussian equations makes sense.\n", - "\n", - "$$\n", - "\\mu=\\frac{\\sigma_1^2 \\mu_2 + \\sigma_2^2 \\mu_1} {\\sigma_1^2 + \\sigma_2^2}\n", - "$$\n", - "\n", - "If both scales have the same accuracy, then $\\sigma_1^2 = \\sigma_2^2$, and the resulting equation is\n", - "\n", - "$$\\mu=\\frac{\\mu_1 + \\mu_2}{2}$$\n", - "\n", - "which is just the average of the two weighings. If we look at the extreme cases, assume the first scale is very much more accurate than than the second one. At the limit, we can set \n", - "$\\sigma_1^2=0$, yielding\n", - "\n", - "$$\n", - "\\begin{aligned}\n", - "\\mu&=\\frac{0*\\mu_2 + \\sigma_2^2 \\mu_1} { \\sigma_2^2}, \\\\\n", - "\\text{or just}\\\\\n", - "\\mu&=\\mu_1\n", - "\\end{aligned}\n", - "$$\n", - "\n", - "Finally, if we set $\\sigma_1^2 = 9\\sigma_2^2$, then the resulting equation is\n", - "\n", - "$$\n", - "\\begin{aligned}\n", - "\\mu&=\\frac{9 \\sigma_2^2 \\mu_2 + \\sigma_2^2 \\mu_1} {9 \\sigma_2^2 + \\sigma_2^2} \\\\\n", - "\\text{or just}\\\\\n", - "\\mu&= \\frac{1}{10} \\mu_1 + \\frac{9}{10} \\mu_2\n", - "\\end{aligned}\n", - "$$\n", - "\n", - "This again fits our physical intuition of favoring the second, accurate scale over the first, inaccurate scale." - ] - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "Implementing the Update Step" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Recall the histogram filter uses a numpy array to encode our belief about the position of our dog at any time. That array stored our belief of our dog's position in the hallway using 10 discrete positions. This was very crude, because with a 100m hallway that corresponded to positions 10m apart. It would have been trivial to expand the number of positions to say 1,000, and that is what we would do if using it for a real problem. But the problem remains that the distribution is discrete and multimodal - it can express strong belief that the dog is in two positions at the same time.\n", - "\n", - "Therefore, we will use a single Gaussian to reflect our current belief of the dog's position. In other words, we will use $dog_{pos} = \\mathcal{N}(\\mu,\\sigma^2)$. Gaussians extend to infinity on both sides of the mean, so the single Gaussian will cover the entire hallway. They are unimodal, and seem to reflect the behavior of real-world sensors - most errors are small and clustered around the mean. Here is the entire implementation of the update function for a Kalman filter:" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "def update(mean, variance, measurement, measurement_variance):\n", - " return multiply(mean, variance, measurement, measurement_variance)" - ], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 71 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Kalman filters are supposed to be hard! But this is very short and straightforward. All we are doing is multiplying the Gaussian that reflects our belief of where the dog was with the new measurement. Perhaps this would be clearer if we used more specific names:\n", - "\n", - " def update_dog(dog_pos, dog_variance, measurement, measurement_variance):\n", - " return multiply(dog_pos, dog_sigma, measurement, measurement_variance)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "That is less abstract, which perhaps helps with comprehension, but it is poor coding practice. We are writing a Kalman filter that works for any problem, not just tracking dogs in a hallway, so we don't use variable names with 'dog' in them. Still, the `update_dog()` function should make what we are doing very clear. \n", - "\n", - "Let's look at an example. We will suppose that our current belief for the dog's position is $N(2,5)$. Don't worry about where that number came from. It may appear that we have a chicken and egg problem, in that how do we know the position before we sense it, but we will resolve that shortly. We will create a `DogSensor` object initialized to be at position 0.0, and with no velocity, and modest noise. This corresponds to the dog standing still at the far left side of the hallway. Note that we mistakenly believe the dog is at position 2.0, not 0.0." - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "dog = DogSensor(velocity=0., measurement_variance=5, process_variance=0.0)\n", - "\n", - "pos,s = 2, 5\n", - "for i in range(20):\n", - " pos,s = update(pos, s, dog.sense_position(), 5)\n", - " print('time:', i, \n", - " '\\tposition =', \"%.3f\" % pos, \n", - " '\\tvariance =', \"%.3f\" % s)" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "time: 0 \tposition = -0.009 \tvariance = 2.500\n", - "time: 1 \tposition = 0.837 \tvariance = 1.667\n", - "time: 2 \tposition = -0.287 \tvariance = 1.250\n", - "time: 3 \tposition = 0.048 \tvariance = 1.000\n", - "time: 4 \tposition = -0.004 \tvariance = 0.833\n", - "time: 5 \tposition = 0.302 \tvariance = 0.714\n", - "time: 6 \tposition = -0.011 \tvariance = 0.625\n", - "time: 7 \tposition = -0.244 \tvariance = 0.556\n", - "time: 8 \tposition = -0.323 \tvariance = 0.500\n", - "time: 9 \tposition = -0.304 \tvariance = 0.455\n", - "time: 10 \tposition = -0.155 \tvariance = 0.417\n", - "time: 11 \tposition = -0.235 \tvariance = 0.385\n", - "time: 12 \tposition = -0.007 \tvariance = 0.357\n", - "time: 13 \tposition = 0.041 \tvariance = 0.333\n", - "time: 14 \tposition = 0.171 \tvariance = 0.312\n", - "time: 15 \tposition = -0.007 \tvariance = 0.294\n", - "time: 16 \tposition = -0.072 \tvariance = 0.278\n", - "time: 17 \tposition = -0.007 \tvariance = 0.263\n", - "time: 18 \tposition = 0.272 \tvariance = 0.250\n", - "time: 19 \tposition = 0.159 \tvariance = 0.238\n" - ] - } - ], - "prompt_number": 73 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Because of the random numbers I do not know the exact values that you see, but the position should have converged very quickly to almost 0 despite the initial error of believing that the position was 2.0. Furthermore, the variance should have quickly converged from the initial value of 5.0 to 0.238.\n", - "\n", - "By now the fact that we converged to a position of 0.0 should not be terribly surprising. All we are doing is computing `new_pos = old_pos * measurement` and the measurement is a normal distribution around 0, so we should get very close to 0 after 20 iterations. But the truly amazing part of this code is how the variance became 0.238 despite every measurement having a variance of 5.0. \n", - "\n", - "If we think about the physical interpretation of this is should be clear that this is what should happen. If you sent 20 people into the hall with a tape measure to physically measure the position of the dog you would be very confident in the result after 20 measurements - more confident than after 1 or 2 measurements. So it makes sense that as we make more measurements the variance gets smaller.\n", - "\n", - "Mathematically it makes sense as well. Recall the computation for the variance after the multiplication: $\\sigma^2 = 1/(\\frac{1}{{\\sigma}_1^2} + \\frac{1}{{\\sigma}_2^2})$. We take the reciprocals of the sigma from the measurement and prior belief, add them, and take the reciprocal of the result. Think about that for a moment, and you will see that this will always result in smaller numbers as we proceed." - ] - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "Implementing Predictions" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "That is a beautiful result, but it is not yet a filter. We assumed that the dog was sitting still, an extremely dubious assumption. Certainly it is a useless one - who would need to write a filter to track non-moving objects? The histogram used a loop of sense and update functions, and we must do the same to accommodate movement.\n", - "\n", - "How how do we perform the predict function with gaussians? Recall the histogram method:\n", - "\n", - " def predict(pos, move, p_correct, p_under, p_over):\n", - " n = len(pos)\n", - " result = array(pos, dtype=float)\n", - " for i in range(n):\n", - " result[i] = \\\n", - " pos[(i-move) % n] * p_correct + \\\n", - " pos[(i-move-1) % n] * p_over + \\\n", - " pos[(i-move+1) % n] * p_under \n", - " return result\n", - " \n", - " \n", - "In a nutshell, we shift the probability vector by the amount we believe the animal moved, and adjust the probability. How do we do that with gaussians?\n", - "\n", - "It turns out that we just add gaussians. Think of the case without gaussians. I think my dog is at 7.3m, and he moves 2.6m to right, where is he now? Obviously, $7.3+2.6=9.9$. He is at 9.9m. Abstractly, the algorithm is `new_pos = old_pos + dist_moved`. It does not matter if we use floating point numbers or gaussians for these values, the algorithm must be the same. \n", - "\n", - "How is addition for gaussians performed? It turns out to be very simple:\n", - "$$ N({\\mu}_1, {{\\sigma}_1}^2)+N({\\mu}_2, {{\\sigma}_2}^2) = N({\\mu}_1 + {\\mu}_2, {{\\sigma}_1}^2 + {{\\sigma}_2}^2)$$\n", - "\n", - "All we do is add the means and the variance separately! Does that make sense? Think of the physical representation of this abstract equation.\n", - "${\\mu}_1$ is the old position, and ${\\mu}_2$ is the distance moved. Surely it makes sense that our new position is ${\\mu}_1 + {\\mu}_2$. What about the variance? It is perhaps harder to form an intuition about this. However, recall that with the `update()` function for the histogram filter we always lost information - our confidence after the update was lower than our confidence before the update. Perhaps this makes sense - we don't really know where the dog is moving, so perhaps the confidence should get smaller (variance gets larger). I assure you that the equation for gaussian addition is correct, and derived by basic algebra. Therefore it is reasonable to expect that if we are using gaussians to model physical events, the results must correctly describe those events.\n", - "\n", - "I recognize the amount of hand waving in that argument. Now is a good time to either work through the algebra to convince yourself of the mathematical correctness of the algorithm, or to work through some examples and see that it behaves reasonably. This book will do the latter.\n", - "\n", - "So, here is our implementation of the predict function:" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "def predict(pos, variance, movement, movement_variance):\n", - " return (pos + movement, variance + movement_variance)" - ], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 74 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "What is left? Just calling these functions. The histogram did nothing more than loop over the `update()` and `predict()` functions, so let's do the same. " - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "# assume dog is always moving 1m to the right\n", - "movement = 1\n", - "movement_variance = 2\n", - "sensor_variance = 10\n", - "pos = (0, 500) # gaussian N(0,500)\n", - "\n", - "dog = DogSensor(pos[0], velocity=movement, \n", - " measurement_variance=sensor_variance, \n", - " process_variance=sensor_variance)\n", - "\n", - "zs = []\n", - "ps = []\n", - "\n", - "for i in range(10):\n", - " pos = predict(pos[0], pos[1], movement, movement_variance)\n", - " print('PREDICT: {: 10.4f} {: 10.4f}'.format(pos[0], pos[1]),end='\\t')\n", - " \n", - " Z = dog.sense_position()\n", - " zs.append(Z)\n", - " \n", - " pos = update(pos[0], pos[1], Z, sensor_variance)\n", - " ps.append(pos[0])\n", - " \n", - " print('UPDATE: {: 10.4f} {: 10.4f}'.format(pos[0], pos[1]))\n", - "\n", - " \n", - "plt.plot(ps, label='filter')\n", - "plt.plot(zs, c='r', linestyle='dashed', label='measurement')\n", - "plt.legend(loc='best')\n", - "plt.show()" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "PREDICT: 1.0000 502.0000\tUPDATE: 2.1518 9.8047\n", - "PREDICT: 3.1518 11.8047\tUPDATE: 5.0312 5.4138\n", - "PREDICT: 6.0312 7.4138\tUPDATE: 5.7636 4.2574\n", - "PREDICT: 6.7636 6.2574\tUPDATE: 5.5107 3.8490\n", - "PREDICT: 6.5107 5.8490\tUPDATE: 5.0846 3.6904\n", - "PREDICT: 6.0846 5.6904\tUPDATE: 6.8312 3.6267\n", - "PREDICT: 7.8312 5.6267\tUPDATE: 8.6453 3.6007\n", - "PREDICT: 9.6453 5.6007\tUPDATE: 10.8448 3.5900\n", - "PREDICT: 11.8448 5.5900\tUPDATE: 13.2680 3.5856\n", - "PREDICT: 14.2680 5.5856\tUPDATE: 12.3199 3.5838\n" - ] - }, - { - "metadata": {}, - "output_type": "display_data", - "png": 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+K/alsAIInLeRq+qG0nlvCp1r+VEnsHIvI6uCQkRERKQ8GAbcdBN89hkEBJhL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\nA+zZA2vXQvfucPvtZsJyIMyaEeOZZ2DbNuja1fz/ExERqQM+X6HwGxM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- "text": [ - "" - ] - } - ], - "prompt_number": 76 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "There is a fair bit of arbitrary constants code above, but don't worry about it. What does require explanation are the first few lines:\n", - "\n", - " movement = 1 \n", - " movement_variance = 2\n", - " \n", - "For the moment we are assuming that we have some other sensor that detects how the dog is moving. For example, there could be an inertial sensor clipped onto the dog's collar, and it reports how far the dog moved each time it is triggered. The details don't matter. The upshot is that we have a sensor, it has noise, and so we represent it with a Gaussian. Later we will learn what to do if we do not have a sensor for the `predict()` step.\n", - "\n", - "For now let's walk through the code and output bit by bit.\n", - "\n", - " movement = 1\n", - " movement_variance = 2\n", - " sensor_variance = 10\n", - " pos = (0, 500) # gaussian N(0,500)\n", - " \n", - " \n", - "The first lines just set up the initial conditions for our filter. We are assuming that the dog moves steadily to the right 1m at a time. We have a relatively low error of 2 for the movement sensor, and a higher error of 10 for the RFID position sensor. Finally, we set our belief of the dog's initial position as $N(0,500)$. Why those numbers. Well, 0 is as good as any number if we don't know where the dog is. But we set the variance to 500 to denote that we have no confidence in this value at all. 100m is almost as likely as 0 with this value for the variance. " - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Next we initialize the RFID simulator with\n", - "\n", - " dog = DogSensor(pos[0], velocity=movement, \n", - " measurement_variance=sensor_variance, \n", - " process_variance=sensor_variance)\n", - "\n", - "It may seem very 'convenient' to set the simulator to the same position as our guess, and it is. Do not fret. In the next example we will see the effect of a wildly inaccurate guess for the dog's initial position.\n", - "\n", - "The next code allocates an array to store the output of the measurements and filtered positions. \n", - "\n", - " zs = []\n", - " ps = []\n", - " \n", - "This is the first time that I am introducing standard nomenclature used by the Kalman filtering literature. It is traditional to call our measurement $Z$, and so I follow that convention here. As an aside, I find the nomenclature used by the literature very obscure. However, if you wish to read the literature you will have to become used to it, so I will not use a much more readable variable name such as $m$ or $measure$." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Now we just enter our `update() ... predict()` loop.\n", - "\n", - " for i in range(10):\n", - " pos = predict(pos[0], pos[1], movement, sensor_variance)\n", - " print 'PREDICT:', \"%.4f\" %pos[0], \", %.4f\" %pos[1]\n", - "\n", - "Wait, why `predict()` before `update()`? It turns out the order does not matter once, but the first call to `,DogSensor.sense()` assumes that the dog has already moved, so we start with the update step. In practice you will order these calls based on the details of your sensor, and you will very typically do the `sense()` first.\n", - "\n", - "So we call the update function with the gaussian representing our current belief about our position, the another gaussian representing our belief as to where the dog is moving, and then print the output. Your output will differ, but when writing this I get this as output:\n", - "\n", - " PREDICT: 1.000 502.000\n", - "\n", - "What is this saying? After the prediction, we believe that we are at 1.0, and the variance is now 502.0. Recall we started at 500.0. The variance got worse, which is always what happens during the prediction step.\n", - "\n", - " Z = dog.sense_position()\n", - " zs.append(Z)\n", - " \n", - "Here we sense the dog's position, and store it in our array so we can plot the results later.\n", - "\n", - "Finally we call the update function of our filter, save the result in our *ps* array, and print the updated position belief:\n", - "\n", - " pos = update(pos[0], pos[1], Z, movement_variance)\n", - " ps.append(pos[0])\n", - " print 'UPDATE:', \"%.4f\" %pos[0], \", %.4f\" %pos[1]\n", - " \n", - "Your result will be different, but I get\n", - "\n", - " UPDATE: 1.6279 , 9.8047\n", - " \n", - "as the result. What is happening? Well, at this point the dog is really at 1.0, however the predicted position is 1.6279. What is happening is the RFID sensor has a fair amount of noise, and so we compute the position as 1.6279. That is pretty far off from 1, but this is just are first time through the loop. Intuition tells us that the results will get better as we make more measurements, so let's hope that this is true for our filter as well. Now look at the variance: 9.8047. It has dropped tremendously from 502.0. Why? Well, the RFID has a reasonably small variance of 2.0, so we trust it far more than our previous belief. At this point there is no way to know for sure that the RFID is outputting reliable data, so the variance is not 2.0, but is has gotten much better.\n", - "\n", - "Now the software just loops, calling `predict()` and `update()` in turn. Because of the random sampling I do not know exactly what numbers you are seeing, but the final position is probably between 9 and 11, and the final variance is probably around 3.5. After several runs I did see the final position nearer 7, which would have been the result of several measurements with relatively large errors.\n", - "\n", - "Now look at the plot. The noisy measurements are plotted in with a dotted red line, and the filter results are in the solid blue line. Both are quite noisy, but notice how much noisier the measurements (red line) are. This is your first Kalman filter shown to work!" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "In this example I only plotted 10 data points so the output from the print statements would not overwhelm us. Now let's look at the filter's performance with more data. This time we will plot both the output of the filter and the variance." - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "%precision 2\n", - "# assume dog is always moving 1m to the right\n", - "movement = 1\n", - "movement_variance = 2\n", - "sensor_variance = 4.5\n", - "pos = (0, 100) # gaussian N(0,100)\n", - "\n", - "dog = DogSensor(pos[0], velocity=movement, \n", - " measurement_variance=sensor_variance, \n", - " process_variance=0.5)\n", - "\n", - "zs, ps, vs = [], [], []\n", - "for i in range(50):\n", - " pos = predict(pos[0], pos[1], movement, movement_variance) \n", - " Z = dog.sense_position()\n", - " zs.append(Z)\n", - " vs.append(pos[1])\n", - " \n", - " pos = update(pos[0], pos[1], Z, sensor_variance)\n", - " ps.append(pos[0])\n", - " \n", - "#plt.subplot(121) \n", - "plt.plot(zs, linestyle='dashed', label='measurement')\n", - "plt.plot(ps, label='filter')\n", - "plt.legend(loc=2)\n", - "plt.show()\n", - "\n", - "plt.plot(vs)\n", - "plt.title('Variance')\n", - "plt.show()\n", - "\n", - "for i in range(0,len(vs), 5):\n", - " print('{:.4f} {:.4f} {:.4f} {:.4f} {:.4f}'.format(*[v for v in vs[i:i+5]]))" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "display_data", - "png": 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o10vaWT3YmVsMh/os1qpB7sBHyF82jzpzphH8y3K8Q24gveXp7OzWm8IatQEI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\nIkP1iJaIiIhIQ2kS/+37/bkm35Wbm9uIlUhDa++DduHRnJF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- "text": [ - "" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "102.0000 6.3099 4.6267 4.2812 4.1939\n", - "4.1708 4.1646 4.1629 4.1624 4.1623\n", - "4.1623 4.1623 4.1623 4.1623 4.1623\n", - "4.1623 4.1623 4.1623 4.1623 4.1623\n", - "4.1623 4.1623 4.1623 4.1623 4.1623\n", - "4.1623 4.1623 4.1623 4.1623 4.1623\n", - "4.1623 4.1623 4.1623 4.1623 4.1623\n", - "4.1623 4.1623 4.1623 4.1623 4.1623\n", - "4.1623 4.1623 4.1623 4.1623 4.1623\n", - "4.1623 4.1623 4.1623 4.1623 4.1623\n" - ] - } - ], - "prompt_number": 92 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Here we can see that the variance converges very quickly to roughly 4.1623 in 10 steps. We interpret this as meaning that we become very confident in our position estimate very quickly. The first few measurements are unsure due to our uncertainty in our guess at the initial position, but the filter is able to quickly determine an accurate estimate." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "> Before I go on, I want to emphasize that this code fully implements a 1D Kalman filter. If you have tried to read the literature, you are perhaps surprised, because this looks nothing like the complex, endless pages of math in those books. To be fair, the math gets a bit more complicated in multiple dimensions, but not by much. So long as we worry about *using* the equations rather than *deriving* them we can create Kalman filters without a lot of effort. Moreover, I hope you'll agree that you have a decent intuitive grasp of what is happening. We represent our beliefs with Gaussians, and our beliefs get better over time because more measurement means more data to work with. \"Measure twice, cut once!\"" - ] - }, - { - "cell_type": "heading", - "level": 3, - "metadata": {}, - "source": [ - "Animating the Tracking" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "If you are reading this in IPython Notebook you will be able to see an animation of the filter tracking the dog directly below this sentence.\n", - "\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The top plot shows the output of the filter in green, and the measurements with a dashed red line. The bottom plot shows the Gaussian at each step. \n", - "\n", - "When the track first starts you can see that the measurements varies quite a bit from the initial prediction. At this point the Gaussian probability is small (the curve is low and wide) so the filter does not trust its prediction. As a result, the filter adjusts its estimate a large amount. As the filter innovates you can see that as the Gaussian becomes taller, indicating greater certainty in the estimate, the filter's output becomes very close to a straight line. At `x=15` and greater you can see that there is a large amount of noise in the measurement, but the filter does not react much to it compared to how much it changed for the firs noisy measurement." - ] - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "Implementation in a Class" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "For many purposes the code above suffices. However, if you write enough of these filters the functions will become a bit annoying. For example, having to write\n", - "\n", - " pos = predict(pos[0], pos[1], movement, movement_variance) \n", - " \n", - "is a bit cumbersome and error prone. Let's investigate how we might implement this in a form that makes our lives easier.\n", - "\n", - "First, values for the movement error and the measurement errors are typically constant for a given problem, so we only want to specify them once. We can store them in instance variables in the class. Second, it is annoying to have to pass in the state (pos in the code snippet above) and then remember to assign the output of the function back to that state, so the state should also be an instance variable. Our first attempt might look like:\n", - "\n", - " class KalmanFilter1D:\n", - " def __init__(self, initial_state, measurement_variance, movement_variance):\n", - " self.state = initial_state\n", - " self.measurement_variance = measurement_variance\n", - " self.movement_variance = movement_variance\n", - "\n", - "That works, but I am going to use different naming. The Kalman filter literature has settled on one letter notations for each of these concepts, and so you might as well start getting exposed to it now. At first it seems impossiblely terse, but as you become familiar with the nomenclature you'll see that the math formulas in the textbooks will have an exact one-to-one correspondance with the code. Unfortunately there is not a lot of meaning behind the names chosen; you will just have to memorize them. If you do not make this effort you will never be able to read the Kalman filter literature.\n", - "\n", - "So, we use `x` for the state (estimated value of the filter) and `P` for the variance of the state. `R` is the measurement error, and `Q` is the movement error. This gives us:\n", - "\n", - " class KalmanFilter1D:\n", - " def __init__(self, x0, R, Q):\n", - " self.x = x0\n", - " self.R = R\n", - " self.Q = Q\n", - " \n", - "Now we can implement the `update()` and `predict()` function. In the literature the measurement is usually named either `z` or `y`; I find `y` is too easy to confuse with the y axis of a plot, so I like `z`. I like to think I can hear a `z` in *measurement*, which helps me remember what `z` stands for. So for the update method we might write:\n", - "\n", - " def update(z):\n", - " self.x = (self.P * z + self.x * self.R) / (self.P + self.R)\n", - " self.P = 1 / (1/self.P + 1/self.R)\n", - "\n", - "Finally, the movement is usually called `u`, and so we will use that. So for the predict function we might write:\n", - "\n", - " def predict(self, u):\n", - " self.x += u\n", - " self.P += self.Q\n", - " \n", - "That give us the following code. Production code would require signficant comments. However, in the next chapter we will develop Kalman filter code that works for any dimension, including 1, so this class will never be more than a stepping stone for us, since we can, and will use the class developed in the next chapter in the rest of the book." - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "class KalmanFilter1D:\n", - " def __init__(self, x0, P, R, Q):\n", - " self.x = x0\n", - " self.P = P\n", - " self.R = R\n", - " self.Q = Q\n", - " \n", - " def update(self, z):\n", - " self.x = (self.P * z + self.x * self.R) / (self.P + self.R)\n", - " self.P = 1. / (1./self.P + 1./self.R)\n", - "\n", - "\n", - " def predict(self, u=0.0):\n", - " self.x += u\n", - " self.P += self.Q" - ], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 89 - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "Relationship to the g-h Filter" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "In the first chapter I stated that the Kalman filter is a form of g-h filter. However, we have been reasoning about the probability of Gaussians, and not used any of the reasoning or equations of the first chapter. A trivial amount of algebra will reveal the relationship, so let's do that now. It's not particularly illuminating algebra, so feel free to skip to the bottom to see the final equation that relates *g* and *h* to the variances.\n", - "\n", - "The equation for our estimate is:\n", - "\n", - "$$\n", - "\\mu_{x'}=\\frac{\\sigma_1^2 \\mu_2 + \\sigma_2^2 \\mu_1} {\\sigma_1^2 + \\sigma_2^2}\n", - "$$\n", - "\n", - "which I will make more friendly for our eyes as:\n", - "\n", - "$$\n", - "\\mu_{x'}=\\frac{ya + xb} {a+b}\n", - "$$\n", - "\n", - "We can easily put this into the g-h form with the following algebra\n", - "\n", - "$$\n", - "\\begin{aligned}\n", - "\\mu_{x'}&=(x-x) + \\frac{ya + xb} {a+b} \\\\\n", - "\\mu_{x'}&=x-\\frac{a+b}{a+b}x + \\frac{ya + xb} {a+b} \\\\ \n", - "\\mu_{x'}&=x +\\frac{-x(a+b) + xb+ya}{a+b} \\\\\n", - "\\mu_{x'}&=x+ \\frac{-xa+ya}{a+b} \\\\\n", - "\\mu_{x'}&=x+ \\frac{a}{a+b}(y-x)\\\\\n", - "\\end{aligned}\n", - "$$\n", - "\n", - "We are almost done, but recall that the variance of estimate is given by \n", - "\n", - "$${\\sigma_{x'}^2} = \\frac{1}{ \\frac{1}{\\sigma_1^2} + \\frac{1}{\\sigma_2^2}}\\\\\n", - "= \\frac{1}{ \\frac{1}{a} + \\frac{1}{b}}\n", - "$$\n", - "\n", - "We can incorporate that term into our equation above by observing that\n", - "$$ \n", - "\\begin{aligned}\n", - "\\frac{a}{a+b} &= \\frac{a/a}{(a+b)/a} = \\frac{1}{(a+b)/a}\\\\\n", - " &= \\frac{1}{1 + \\frac{b}{a}} = \\frac{1}{\\frac{b}{b} + \\frac{b}{a}}\\\\\n", - " &= \\frac{1}{b}\\frac{1}{\\frac{1}{b} + \\frac{1}{a}} \\\\\n", - " &= \\frac{\\sigma^2_{x'}}{b}\n", - " \\end{aligned}\n", - "$$\n", - "\n", - "We can tie all of this together with\n", - "\n", - "$$\n", - "\\begin{aligned}\n", - "\\mu_{x'}&=x+ \\frac{a}{a+b}(y-x)\\\\\n", - "&= x + \\frac{\\sigma^2_{x'}}{b}(y-x) \\\\\n", - "&= x + g_n(y-x)\\\\\n", - "\\blacksquare\n", - "\\end{aligned}\n", - "$$\n", - "\n", - "where\n", - "\n", - "$$g_n = \\frac{\\sigma^2_{x'}}{\\sigma^2_{y}}$$\n", - "\n", - "The end result is multipying the residual of the two measurements by a constant and adding to our previous value, which is the *g* equation for the g-h filter. *g* is the variance of the new estimate divided by the variance of the measurement. Of course in this case g is not truly a constant, as it varies with each time step as the variance changes, but it is truly the same formula. We can also derive the formula for *h* in the same way but I don't find this a particularly interesting derivation. The end result is\n", - "\n", - "$$h_n = \\frac{COV (x,\\dot{x})}{\\sigma^2_{y}}$$\n", - "\n", - "The takeaway point is that *g* and *h* are specified fully by the variance and covariances of the measurement and preditions at time *n*. In other words, we are just picking a point between the measurement and prediction by a scale factor determined by the quality of each of those two inputs. That is all the Kalman filter is. " - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "#####Exercise:\n", - "Modify the values of `movement_variance` and `sensor_variance` and note the effect on the filter and on the variance. Which has a larger effect on the value that variance converges to. For example, which results in a smaller variance:\n", - "\n", - " movement_variance = 40\n", - " sensor_variance = 2\n", - " \n", - "or:\n", - "\n", - " movement_variance = 2\n", - " sensor_variance = 40" - ] - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "Introduction to Designing a Filter" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "So far we have developed our filter based on the dog sensors introduced in the Discrete Bayesian filter chapter. We are used to this problem by now, and may feel ill-equipped to implement a Kalman filter for a different problem. To be honest, there is still quite a bit of information missing from this presentation. The next chapter will fill in the gaps. Still, lets get a feel for it by designing and implementing a Kalman filter for a thermometer. The sensor for the thermometer outputs a voltage that corresponds to the temperature that is being measured. We have read the manufacturer's specifications for the sensor, and it tells us that the sensor exhibits white noise with a standard deviation of 2.13.\n", - "\n", - "We do not have a real sensor to read, so we will simulate the sensor with the following function. " - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "def volt(voltage, temp_variance):\n", - " return random.randn()*temp_variance + voltage" - ], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 19 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "We generate white noise with a given variance using the equation `random.randn() * variance`. The specification gives us the standard deviation of the noise, not the variance, but recall that variance is just the square of the standard deviation. Hence we raise 2.13 to the second power.\n", - "\n", - "> **Sidebar**: spec sheets are just what they sound like - specifications. Any individual sensor will exhibit different performance based on normal manufacturing variations. Numbers given are often maximums - the spec is a guarantee that the performance will be at least that good. So, our sensor might have standard deviation of 1.8. If you buy an expensive piece of equipment it often comes with a sheet of paper displaying the test results of your specific item; this is usually very trustworthy. On the other hand, if this is a cheap sensor it is likely it received little to no testing prior to being sold. Manufacturers typically test a small subset of their output to verify that everything falls within the desired performance range. If you have a critical application you will need to read the specification sheet carefully to figure out exactly what they mean by their ranges. Do they guarantee their number is a maximum, or is it, say, the $3\\sigma$ error rate? Is every item tested? Is the variance normal, or some other distribution. Finally, manufacturing is not perfect. Your part might be defective and not match the performance on the sheet.\n", - "\n", - "> For example, I just randomly looked up a data sheet for an airflow sensor. There is a field *Repeatability*, with the value $\\pm 0.50\\%$. Is this a Gaussian? Is there a bias? For example, perhaps the repeatability is nearly 0.0% at low temperatures, and always nearly +0.50 at high temperatures. Data sheets for electrical components often contain a section of \"Typical Performance Characteristics\". These are used to capture information that cannot be easily conveyed in a table. For example, I am looking at a chart showing output voltage vs current for a LM555 timer. There are three curves showing the performance at different temperatures. The response is ideally linear, but all three lines are curved. This clarifies that errors in voltage outputs are probably not Gaussian - in this chip's case higher temperatures leads to lower voltage output, and the voltage output is quite nonlinear if the input current is very high. \n", - "\n", - "> As you might guess, modeling the performance of your sensors is one of the harder parts of creating a Kalman filter that performs well. " - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Now we need to write the Kalman filter processing loop. As with our previous problem, we need to perform a cycle of predicting and updating. The sensing step probably seems clear - call `volt()` to get the measurement, pass the result into `update()` function, but what about the predict step? We do not have a sensor to detect 'movement' in the voltage, and for any small duration we expect the voltage to remain constant. How shall we handle this?\n", - "\n", - "As always, we will trust in the math. We have no known movement, so we will set that to zero. However, that means that we are predicting that the temperature will never change over time. If that is true, then over time we should become extremely confident in our results. Once the filter has enough measurements it will become very confident that it can predict the subsequent temperatures, and this will lead it to ignoring measurements that result due to an actual temperature change. This is called a *smug* filter, and is something you want to avoid. So we will add a bit of error to our prediction step to tell the filter not to discount changes in voltage over time. In the code below I set `movement_variance = .2`. This is just the expected variance in the change of voltage over each time step. I chose this value merely to be able to show how the variance changes through the update and predict steps. For an real sensor you would set this value for the actual amount of change you expect. For example, this would be an extremely small number if it is a thermometer for ambient air temperature in a house, and a high number if this is a thermocouple in a chemical reaction chamber. We will say more about selecting the actual value in the next chapter. \n", - "\n", - "Let's see what happens. " - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "variance = 2.13**2\n", - "movement_variance = .2\n", - "actual_voltage = 16.3\n", - "\n", - "N=50\n", - "zs = [volt(actual_voltage, variance) for i in range(N)]\n", - "ps = []\n", - "estimates = []\n", - "\n", - "kf = KalmanFilter1D(x0=25, # initial state\n", - " P = 1000, # initial variance \n", - " # large says 'who knows?'\n", - " R=variance, # sensor noise\n", - " Q=movement_variance) # movement noise\n", - "\n", - "for i in range(N):\n", - " kf.predict(movement)\n", - " kf.update(zs[i])\n", - "\n", - " # save for latter plotting\n", - " estimates.append(kf.x)\n", - " ps.append(kf.P)\n", - "\n", - "# plot the filter output and the variance\n", - "plt.scatter(range(N), zs, marker='+', s=64, color='r', label='measurements')\n", - "p1, = plt.plot(estimates, label='filter')\n", - "plt.legend(loc='best', scatterpoints=1)\n", - "plt.xlim((0,N));plt.ylim((0,30))\n", - "plt.show()\n", - "plt.plot(ps)\n", - "plt.title('Variance')\n", - "plt.show()\n", - "print('Variance converges to {:.3f}'.format(ps[-1]))" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "display_data", - "png": 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7UKs6a7tcLjp27Mirr756yvXi4uIAOHz4MEOGDKFDhw688sortGjRAr1ez59//skTTzxR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\nMzHazQIA8wgZI4PnkQDATcV8yLjQ5ddj7zXqVGu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AEHAhEzw8XjPYJQAAAAAIkJAJHiUVnmCXAAAAACBAQiZ4nConeAAAAADhiuABAAAAIOAI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\nqUru4FDByQpN+9Nh/fFvJar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- "text": [ - "" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "Variance converges to 0.858\n" - ] - } - ], - "prompt_number": 20 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The first plot shows the individual sensor measurements marked with '+'s vs the filter output. Despite a lot of noise in the sensor we quickly discover the approximate voltage of the sensor. In the run I just completed at the time of authorship, the last voltage output from the filter is $16.213$, which is quite close to the $16.4$ used by the `volt()` function. On other runs I have gotten up to around $16.9$ as an output and also as low as 15.5 or so.\n", - "\n", - "The second plot shows how the variance converges over time. Compare this plot to the variance plot for the dog sensor. While this does converge to a very small value, it is much slower than the dog problem. The section **Explaining the Results - Multi-Sensor Fusion** explains why this happens." - ] - }, - { - "cell_type": "heading", - "level": 3, - "metadata": {}, - "source": [ - "Animation" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "For those reading this in IPython Notebook, here is an animation showing the filter working. The top plot in the animation draws a green line for the predicted next voltage, then a red '+' for the actual measurement, draws a light red line to show the residual, and then draws a blue line to the filter's output. You can see that when the filter starts the corrections made are quite large, but after only a few updates the filter only adjusts its output by a small amount even when the measurement is far from it. \n", - "\n", - "The lower plot shows the Gaussian belief as the filter innovates. When the filter starts the Gaussian curve is centered over 25, our initial guess for the voltage, and is very wide and short due to our inital uncertainty. But as the filter innovates, the Gaussian quickly moves to about 16.0 and becomes taller, reflecting the growing confidence that the filter has in it's estimate for the voltage. You will also note that the Gaussian's height bounces up and down a little bit. If you watch closely you will see that the Gaussian becomes a bit shorter and more spread out during the prediction step, and becomes taller and narrower as the filter incorporates another measurement (the innovation step)." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Think of this animation in terms of the g-h filter. At each step the g-h filter makes a prediction, takes a measurement, computes the residual (the difference between the prediction and the measurement, and then selects a point on the residual line based on the scaling factor *g*. The Kalman filter is doing exactly the same thing, except that the scaling factor *g* varies with time. As the filter becomes more confident in its state the scaling factor favors the filter's prediction over the measurement. \n", - "\n", - "> If this is not clear, I urge you to go back and review the g-h chapter. This is the crux of the algorithms in this book. " - ] - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "Exercise(optional):" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Write a function that runs the Kalman filter many times and record what value the voltage converges to each time. Plot this as a histogram. After 10,000 runs do the results look normally distributed? Does this match your intuition of what should happen?\n", - "\n", - "> use plt.hist(data,bins=100) to plot the histogram. " - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "#Your code here" - ], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 21 - }, - { - "cell_type": "heading", - "level": 3, - "metadata": {}, - "source": [ - "Solution\n" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "variance = 2.13**2\n", - "actual_voltage = 16.3\n", - "\n", - "\n", - "def VKF():\n", - " voltage=(14,1000)\n", - " for i in range(N):\n", - " Z = volt(actual_voltage, variance)\n", - " voltage = update(voltage[0], voltage[1], Z, variance)\n", - " return voltage[0]\n", - "\n", - "vs = []\n", - "for i in range (10000):\n", - " vs.append (VKF())\n", - "plt.hist(vs, bins=100, color='#e24a33') \n", - "plt.show()" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "display_data", - "png": 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- "text": [ - "" - ] - } - ], - "prompt_number": 22 - }, - { - "cell_type": "heading", - "level": 3, - "metadata": {}, - "source": [ - "Discussion" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The results do in fact look like a normal distribution. Each voltage is Gaussian, and the **Central Limit Theorem** guarantees that a large number of Gaussians is normally distributed. We will discuss this more in a subsequent math chapter." - ] - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "Explaining the Results - Multi-Sensor Fusion" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "**author's note:** I am not overly keen about this explanation. It is true that multiple sensors improve results, but we get good results merely by having an accurate model of the process. I explain this much better in the next chapter. I'll leave this section here while I mull how best to explain this at this stage of learning. For now don't worry if this section is not entirely convincing; it does need work.\n", - "\n", - "So how does the Kalman filter do so well? I have glossed over one aspect of the filter as it becomes confusing to address too many points at the same time. We will return to the dog tracking problem. We used two sensors to track the dog - the RFID sensor that detects position, and the inertial tracker that tracked movement. However, we have focused all of our attention on the position sensor. Let's change focus and see how the filter performs if the inertial tracker is also noisy. This will provide us with an vital insight into the performance of Kalman filters." - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "sensor_variance = 30\n", - "movement_sensor = 30\n", - "pos = (0,500)\n", - "\n", - "dog = DogSensor(0, velocity=movement, \n", - " measurement_variance=sensor_variance,\n", - " process_variance=0.5)\n", - "\n", - "zs = []\n", - "ps = []\n", - "vs = []\n", - "\n", - "for i in range(100):\n", - " Z = dog.sense_position()\n", - " zs.append(Z)\n", - " \n", - " pos = update(pos[0], pos[1], Z, sensor_variance)\n", - " ps.append(pos[0])\n", - " vs.append(pos[1])\n", - "\n", - " pos = predict(pos[0], pos[1], movement+ random.randn(), movement_variance)\n", - "\n", - "plt.plot(ps, label='filter')\n", - "plt.plot(zs, linestyle='dashed', c='r', label='measurement')\n", - "plt.legend()\n", - "plt.show()\n", - "plt.plot(vs)\n", - "plt.title('Variance')\n", - "plt.show()" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "display_data", - "png": 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fNrdNmoCLS8m15wakIEVERESkmBhz52IBJla/hYR0B9FlPLivdiAdKvvglsdQ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- "text": [ - "" - ] - } - ], - "prompt_number": 91 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "This result is worse than the example where only the measurement sensor was noisy. Instead of being mostly straight, this time the filter's output is distinctly jagged. But, it still mostly tracks the dog. What is happening here?\n", - "\n", - "This illustrates the effects of *multi-sensor fusion*. Suppose we get a position reading of -28.78 followed by 31.43. From that information alone it is impossible to tell if the dog is standing still during very noisy measurements, or perhaps sprinting from -29 to 31 and being accurately measured. But we have a second source of information, his velocity. Even when the velocity is also noisy, it constrains what our beliefs might be. For example, suppose that with the 31.43 position reading we get a velocity reading of 59. That matches the difference between the two positions quite well, so this will lead us to believe the RFID sensor and the velocity sensor. Now suppose we got a velocity reading of 1.7. This doesn't match our RFID reading very well - it suggests that the dog is standing still or moving slowly.\n", - "\n", - "When sensors measure different aspects of the system and they all agree we have strong evidence that the sensors are accurate. And when they do not agree it is a strong indication that one or more of them are inaccurate. \n", - "\n", - "We will formalize this mathematically in the next chapter; for now trust this intuitive explanation. We use this sort of reasoning every day in our lives. If one person tells us something that seems far fetched we are inclined to doubt them. But if several people independently relay the same information we attach higher credence to the data. If one person disagrees with several other people, we tend to distrust the outlier. If we know the people that might alter our belief. If a friend is inclined to practical jokes and tall tales we may put very little trust in what they say. If one lawyer and three lay people opine on some fact of law, and the lawyer disagrees with the three you'll probably lend more credence to what the lawyer says because of her expertise. In the next chapter we will learn how to mathematical model this sort of reasoning." - ] - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "More examples" - ] - }, - { - "cell_type": "heading", - "level": 3, - "metadata": {}, - "source": [ - "Example: Extreme Amounts of Noise" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "So I didn't put a lot of noise in the signal, and I also 'correctly guessed' that the dog was at position 0. How does the filter perform in real world conditions? Let's explore and find out. I will start by injecting a lot of noise in the RFID sensor. I will inject an extreme amount of noise - noise that apparently swamps the actual measurement. What does your intuition tell about how the filter will perform if the noise is allowed to be anywhere from -300 or 300. In other words, an actual position of 1.0 might be reported as 287.9, or -189.6, or any other number in that range. Think about it before you scroll down." - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "sensor_variance = 30000\n", - "movement_variance = 2\n", - "pos = (0,500)\n", - "\n", - "dog = DogSensor(pos[0], velocity=movement, variance=sensor_variance)\n", - "\n", - "zs = []\n", - "ps = []\n", - "\n", - "for i in range(1000):\n", - " pos = predict(pos[0], pos[1], movement, movement_variance)\n", - " \n", - " Z = dog.sense_position()\n", - " zs.append(Z)\n", - " \n", - " pos = update(pos[0], pos[1], Z, sensor_variance)\n", - " ps.append(pos[0])\n", - "\n", - "\n", - "p1, = plt.plot(zs, c='r', linestyle='dashed', label='measurement')\n", - "p2, = plt.plot(ps, c='#004080', label='filter')\n", - "plt.legend(loc='best')\n", - "plt.show()" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "display_data", - "png": 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H2rVro0+fPvD29kZYWBgOHDiA1157Dd9++63Z1yEz/u///g979uxBly5dMGjQINSpUwcJ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G59/73nfq1Ceqw+a9aMRE0S/TMzke5wYcHKnfhywDjMXbkTuGKDOtxu1E0+jeZJR9GqXCGU+X0T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\nsy+cA8S21c7+8AdrzxvnIN1ZycybDS/dOROMu+7y7rrbt1sH3c5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- "text": [ - "" - ] - } - ], - "prompt_number": 24 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "In this example the noise is extreme yet the filter still outputs a nearly straight line! This is an astonishing result! What do you think might be the cause of this performance? If you are not sure, don't worry, we will discuss it latter." - ] - }, - { - "cell_type": "heading", - "level": 3, - "metadata": {}, - "source": [ - "Example: Bad Initial Estimate" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "\n", - "Now let's lets look at the results when we make a bad initial estimate of position. To avoid obscuring the results I'll reduce the sensor variance to 30, but set the initial position to 1000m. Can the filter recover from a 1000m initial error?" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "sensor_variance = 30\n", - "movement_variance = 2\n", - "pos = (1000,500)\n", - "\n", - "dog = DogSensor(0, velocity=movement, variance=sensor_variance)\n", - "\n", - "zs = []\n", - "ps = []\n", - "\n", - "for i in range(100):\n", - " pos = predict(pos[0], pos[1], movement, movement_variance)\n", - " \n", - " Z = dog.sense_position()\n", - " zs.append(Z)\n", - " \n", - " pos = update(pos[0], pos[1], Z, sensor_variance)\n", - " ps.append(pos[0])\n", - "\n", - "plt.plot(ps, label='filter')\n", - "plt.plot(zs, c='r', linestyle='dashed', label='measurement')\n", - "plt.legend(loc='best')\n", - "plt.show()" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "display_data", - "png": 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R1adYF1ofW4d2TOsUhs1Vj+j6BkRERESkdP3xB8yYYQ7BW9pq1DA7y993Hyxe\nDN7eGIbBS+tOsvpoKv7uVl7rHJFnZnfXJo0BeNrnBFM7hXFjiI2kTAevboyn55cH+PDvBNKyc4eV\n/UmZDF92hPh0Oy1DPZkWE66Aco6+BREREREpXYGB5vKbb0q3HABVq8Jvv5mTKrq7A/DB3wl8tisJ\nd6uF6THh1PR3z3tco0YAWP/+m5hqPrzXrSpvdImgcWUbiRl2pv15itu/PMDH2xNIz3aYAeWHCwFl\nekw4ngooOfRNiIiIiEjpuv12c7lkCZSFofrDw8FqPiYv3Z/CzI3xWIDn21XhhhDP/I9p2hQaNjRD\nDuZgOa3CvJhza1Ve6xxOVJAH8el2Xl5/ijsWHeDhZUc4lWbnpioKKPkp9x3nRURERKScu/lmqFwZ\n9u835wuJji6Z6xqG+bLmHxDWx51lwpo4AJ5sXpmuNS4zOmizZhcmZLyIxWKhbYQ3bcK9WH0klTf+\nOs3OBHNk2hZVPJnRKUwBJR/6RkRERESkdLm4QM+e5vslS0ruuv/+N4wdm6f2xjAMvtufwpMrYsly\nGPRvEMDAhgFFupTFYqFjNR/m9azGKx3DeLRpJWbGhOO58FOz5ubZZ4t0/uuNalJEREREpORlZUFC\nAoSEmD/ffjusW3ehf0pxi4+HmTMhIwNGjIA6dQBzosYX/zjBH8fTAOhS3YcxzSs7bY4zq8VC5+o+\ndK7uY67Ytg1iYyE7+/IHVjAKKSIiIiJS8pYuhbvvhscfh6lT4a67zJ9LyocfmgGle3eoU4e0bAez\nt5zmg20JZDvA393KE80qc2cdP6zFOQnz+SZiUVHFd41ySCFFREREREre+++btQehoebPxRkELmUY\n8NZb5vtHHuHnI6lM/uMEx1LN2ozedfz4fzdWJtB25YkYi+zcbPM0bFj81ypHFFJEREREpGSdOAFf\nf232RXnggZK//urVsHMn9tAw/u3bjOUrjgFQN9CdcS1DCh7B60qys83JIPfvhyFDrrx/Zibs3m0G\ntPr1r+2a1ymFFBEREREpWR9/bD7Q9+wJYWElfvmzy5bjBXxwcx+Wx2bi5Wrh0aZB3NcgAFdrEWp0\nHA7o2tXsb3PPPeDtffn9Dxwwj6lVCzyvMRhdpxRSRERERKTkGIbZ1Atg6NCin89uN2tkCiExw86c\nvxOYHz2IiEk3k+QTyG21fHmiWWVCvJzwWOzubtaIbN1q9jW56abL71+vHqSmQlxc0a99nVFIERER\nEZGSk5F9bqg6AAAgAElEQVQBbdpAWhr06pV3+6FD8N574OcHY8Zc/lxr18LAgTB58mU73Z/JtPPx\n9kTmbk/kTJYDgOqtb+TRpkHUDfQoyqfJq1EjM6Rs2XLlkAJmDUrNms4tw3VAIUVERERESo7NBm++\naTZzym8SxdhYeO45qFEDRo8usEO94XBwZsy/8d2zh88/Wc4iz5vwcXfB282Kj5sVH3crvm5WshwG\nn+9OIjHDDCetw7wYeUMQ0ZVtxfP5GjeG+fPNoCLXTCFFREREREpeAbO8c9NNUKUKHDxoPug3bpxr\nc1q2g6X7U9g2fwnjf11FspcfM7oMJSU+47KXuyHYxsgbg2hRxctZnyB/jRqZS4WUIlFIEREREZGy\nw2o1O9TPnm3OPn8upBxNyWLBrkQW7UkmOcPOx7OnALB12BO8dU8jMh0GqVkOzmQ6OJN17pXpIC3b\nQaswL9qEezltQsbLuuEG6NsX2rYt/mtdxxRSRERERKTUGIbBwt1JrDycCoAFaFqjDQ8zmwMff87M\nNkM4k+lgfVwaxrljhuxYTtSBrRhhYbR58T/gda7pVmam2ZRs0CAIuGTm+hMn4PnnYfjwC7UdxaF6\ndfjssyvvl5YG6ekQGHjlfSsghRQRERERKZqsLHMG9+bNzZqE/BhGnv4lhmHw6sZ43v87Idf6DeEt\nGOTmTvXtG9n09yES/IJws1roVsOH+xoE0KhKJHxRH8uoUeB1UfOtESPMkcP27oUZM3Jf/4MP4NVX\nzTlMlixxwocuoh9+gDvvNIcqXrCgtEtT5iikiIiIiEjRbNsGw4ZBZCTs2ZN7W3w8BAXBlCmwdCk8\n+yx06oRhGLy8/hTzdiTiaoExLYKp5uuGAzO87Jn+DmfqRTG+bn2wWGgabCPI89yja7du+ff5eOIJ\nmDMHXn8dHn74Qo2JwwFvv22+HzGi2L6Gq3J+pvnw8NItRxmlkCIiIiJS0rZsMR+oX30VoqNLuzRF\n9+ef5rJ589zr4+PN4HLrrbBuHezbB2lpOAyDF/84ycJdSbhZLUzpEEpMNZ/cx/5j0OWv6ZrPY2zT\npvDoo2ZIefxx+Okns/bmp5/M2pXq1c2ylAXbtpnLhg1LtxxlVAHDKoiIiIhIsXnsMVix4sKkhuXd\nhg3mslmz3OvXrDH7XXz6qRlQwsOxd+nKs7/FsXBXEh4uFqZ1CssbUIriuefMmpuVKy/0DXnzTXM5\nbFihJ350ihMnzOGI83O+JiUqquTKU44opIiIiIiUNG9vc9muXemWw1nOh5RLa1Juvx127zY7q3t6\nYv/3vxn/+0kW703B5mJhZkw4bSO8nVuWSpVg0iTz/eLFkJQE33xjhpOHHnLutS7H4YABA6B/f7OJ\nWXr6hW2GoZqUK1BIERERESlp5/tt1K1buuVwhuxs+Osv8/2lNSkA1arBW2+RlZLK2KZ9+e7AGbzd\nrMzqEkHLsKuYs2T1akhNLdy+Dz0EX38NH30E/v5mUJo7t2T7f1gscN994OEBb71lBtIDB8xtp0+b\nZQkNhcqVS65M5YhCioiIiEhJys42R5gCqF27dMviDGlpZv+PAQPMWox8JGbYGbPqGD8dSsXX3cqb\nXSK4McSzcOc3DLNPyW23QZ06cPLklY9xcTHnWjk/mljVqmZgKEkWi9m8bM0aqFXLrG1q1sys1QkK\ngl274PDhki1TOaKO8yIiIiIl6eBBM6hUrQqehXxQL8t8fc2Ru/Jx4mw2H21L4PPdSaRlGwR4WHmj\nSwQNKtkKf/62beG338z3nTpBcHDRy1ySmjUzA8rgwebQx2vWmAEK8u/8L4BCioiIiEjJcnEx+2j4\nOLGzeBlzOCWTOX8nsHhvClkOcwrGNuFejGkRTG1/96s7WfXqF0LK+b4m5U1gICxaBPPmmX1U5IoU\nUkRERERKUs2aZh+FzEx4+WVzvo/3388z0WF5tDshg/e3JvD9wRQchjl7fJfqPgxtFEjDoKuoPbnY\niBHm6GBDh0KTJk4tb4myWmHgwNIuRbmhkCIiIiJSGtzczGZSp07BhAlmvwVnee89GDvW7PsQFGT2\nFQkKgh49iuUv+alZDl5ce4Jv9qcA4GqBXpG+DImuRK2rrTm5VKdOZh+eatWKXlApNxRSREREREqD\nxQKtWpmjUP3+u3NDysmT5ghSp0+bI1udFxLi9JCyNzGDf66K5UByFh4uFnrX8WNQVCDhPm7Ou0jN\nms47l5QLCikiIiIipeXikOLM8PDPf5rD8MbHm0ElPt58FTAnR8ann7E7JZvF9duBuwf3NQgoVN+R\nPz5cxJ75SwhsdguuN7fl5Y5h1PArYs2JCE4cgjg7O5tx48ZRu3ZtPD09qV27Nv/973+x2+259ps4\ncSIRERF4eXkRExPDtvMT2YiIiIhUNK1amcvff3fueV1dzVGwGjSANm3MSRWHDIGbb87ZJTY1iwU7\nE3nsxyOceOJfNHp4AI/2bIpt+lT6Lj7I2NWx7Dydke/pM+0OJq09wa55XzFg6Wz6n9jMh7dWU0AR\np3FaTcqkSZN46623+PDDD2ncuDF//fUXQ4YMwcPDg/HjxwMwZcoUpk6dypw5c6hXrx7PPfccXbt2\nZefOnfhcxyNciIiIiAAQFwfvvANNm5rB4aabzGZfGzeaM5LbrrFzeWEvn5rFwt3JfLfPhyPbDwDg\nmp3JZ53v4941X1L14C5Gz5/Cuqbt+YF6/HDwDB2qevNw40o0qmyW7diZLMaujuXv+AxmH9gKQJc+\nHbG4afo9cR6nhZR169Zxxx130PPcuM/Vq1enV69erF27FgDDMJg+fTpPPfUUffr0AWDOnDmEhIQw\nb948hg8f7qyiiIiIiJRNW7bAf/8LHTqYIcXPD958E+rVM4cmvlbZ2eYs9g0a5Lv5eGoWs7cmsGhP\n8rkhgV3wdLXQOsyLDlVDaHff8wTZXoQHH4Q5c3gndR1vNmjJ57uTWH0kldVHUmkd5kWnat7M2hRP\nUqaDcE8rTY7sAMDSvPm1l10kH06LvD169OCnn35i586dAGzbto0VK1bkhJb9+/cTFxdHt27dco6x\n2Wx06NCBNWvWOKsYIiIiImXX+U7sdepcWDd8uDmClVsROpp//bXZ3+Shh3Ktjk3N4oW1J7h90QE+\n25VEtsOgaw0fnqiWysp7a/NKp3DurONPkKerWaPTty8APj98xz9vCuabPjUZEh2Il6uF32LP8uIf\nJ0nKdNAuwov59dJxST1jTkoZEnLtZRfJh9NqUv7xj39w5MgRGjZsiKurK9nZ2YwfP54RI0YAcPz4\ncQCqVKmS67iQkBCOHTvmrGKIiIiIlF179pjLi0OKM7zxhrmMjgbMJlmzt57mq73JZDvM+Uq61fBh\neJNKRAZ4sH79Udxd8vlbdZcu8Pnn0L07AJU8XXmiWWWGRAfyyY5Elu5P4Y5IPx5sFIh13krzGNWi\nSDFwWkiZOXMm77//PvPnzyc6OpqNGzfyxBNPULNmTYYOHXrZYy2Xmbxo/fr1ziqiSA7dV1IcdF9J\ncdB9dX2JXL+eQGCv1UqCk/5tPQ4fpvGyZTg8PFjbqCmffb2V1Qnu2LFgwaClXxY9K2cQ7pFEwp6j\nnL9qgfdW9eqwfXue1S2AFlWBjFP8uQHcAgPxmziRrEqVSNZ9WuHVrVvXqedzWkh54YUXGD9+PPfe\ney8A0dHRHDx4kBdffJGhQ4cSGhoKQFxcHFWrVs05Li4uLmdbflq0aOGsIooA5i9l3VfibLqvpDjo\nvroOnToFQGT37nDDDc4556efmqe+oy/PpdTm+NlsrBa4raYvwxrnP5mi0+6t224r+jnkupCUlOTU\n8zmtT4phGFituU9ntVoxDAOAWrVqERoayrJly3K2p6en88svv9CmTRtnFUNERESk7HrsMRg5EiIj\n899+7rmp0NLTcbz/PgBjonpz/Gw2DSt5ML9ndV5oF1r02d5FSonTalJ69+7N5MmTqVWrFlFRUWzc\nuJFp06YxePBgwGzSNWrUKCZNmkSDBg2oW7cuzz//PL6+vgwYMMBZxRAREREpux59NP/1ixbB+PHQ\nqxdMnlzo0/1+IIF9nfpTbc8WdtZpyuM3BDEoKhBXa8FN6UXKA6eFlGnTpuHn58fIkSOJi4sjLCyM\n4cOH88wzz+TsM3bsWNLS0hg5ciQJCQm0atWKZcuW4e3t7axiiIiIiJQ/7u7w999QqVKhdk/JtPPK\n+lN8tfcM3Pn/aBTkwSdtqhAZ4OG8MqWkwJ9/QseOzjunSCFZDONq6xWL38Vt2vz9/UuxJHI9Uhtv\nKQ66r6Q46L66fu1LyuT9racJ8HAhwseNGtnJtG5cA8PTE0tSUq7hiM9k2jmUksXhlCwOJWdxKCWT\ntbFnOZlmx91q4dEbKjGw4dXVnlzx3kpJgSpVwG6HkyfN+VxELsPZz+9Oq0kRERERqVAyM2H/fnMi\nxsuMVHqpk2ezGfnjUY6fzc61flGVmtSIO8DIqd9ytmkzDOBQchYJGfZ8z9O4so2JbapQuzj6nfj6\nQosW8PPP8O23cN99ubf36wfJyTB9OtSv7/zrS4WnkCIiIiJytX780ewEv3MnzJ0L999fqMPSshyM\nWnmM42ezaVzZRkw1b46eyeJIShZ7GzajRtwBqm77kwXhUTnHeLhYqObrRjVfN6r7ulPN142a/u7c\nEGzDpTj7nvTpY4aUL7/MHVIMA77/HpKSwMen+K4vFZpCioiIiEhhHT4MY8bAZ59dWPfFF4UKKY5/\n/Yuf47I50noAVUODmR4TRiXbRY9ie7rAyi943CueW7pEYLFAdV83gr1csV5aU3PiBFhsTvpQBejT\nB0aPNmtS0tPBdu56+/aZAaVKFQgPL94ySIWlkCIiIiJSWNOnmwHFywtjyBCyakXi3rPHlY9zOLC/\n+jrdMtKYFjOYmZ3DcwcUMGsr7rwTn/BwWl7uXIYBt9xivv/yS+fPXn9ezZrmXC6bNsHy5dCzp7l+\nwwZz2bz5VTVzE7kaCikiIiIihfXMMzgSE1n14BjeSvRhZ0IGbY958WRYxmVH1vr61530ykjjtG8l\nnr21Xv7zlwQGmq8rWbUKtm6FkBBzdvjiNGgQREebtSbnXRxSRIqJQoqIiIhUXMeOQe/ecPYsWK3g\n4mIurVZ4/nno3j1n17RsB1/FGnzUczzH9mcDGQD8euwsv8ce4u66/oxoGkSgzSXXJdYcS2Xxd3/S\nC6BOHVqGeV17effuhf79zfePPGIOXVycnnwy77pNm8ylQooUI4UUERERqbjCw+GJJ2DgwLzbEhLM\nRbqdBTsTmb8zkcQMB2D2FRkUFUibCC9mb03gi91JLNiVxLf7U3i4SSX61w/AzcXC7oQMxq4+Tte4\ngwBUalSEkbBiY6FbNzh+HDp3hnHjrv1cRfHVV7BlizmqmUgxUUgRERGRiu2228yHbofDnBfk3PJQ\ncDXm/XGCr/Ykk243p5VrFOTBkEaV6FTVO2dkradvDqFfPX+mbjjFb7FnmbbhFAt3JTGscSXe+Cue\n1CwH7dNjzWsVpf/I4sVmp/UWLcwZ6m3F3HG+IDYb3HRT6VxbKgyFFBERESk/HA6zs7YzO2xf1BfE\n7jD4+Wgqn+5M4vedZ3J2aRfhxeDoQJqHeGLJ59p1Atx5vWMIv5zIZNr6k+xPzmLCmjjAnM+k7ZND\noW0UtLxsl3hTVhZs3mx2Wne5qOnYI4+Ap6cZqnx9i/aZRco4hRQREREpuxwOWL0a2rSBZcvgqafg\nhRfgjjuu7XyGkW/AScyws2hPEgt2JhGbak6yaHOx0LO2L/3qB1A3sOBO8cyYAVOmYJk4kfbDh9Mq\nzIsvdifx5l/xBHi4ML1TGB6e1aD5jYUrY5MmsGOHGVQaN869bdCgwn5SkXLNWtoFEBERESnQxo0Q\nEwPNmpmdxrduheeeM8PG1Tp50gw7v/6as+pgciYT18Rx6+f7mfFnPLGp2VT1cWN088p8f3ctxreq\ncvmAAuDqavYXWbUKADerhX71A/ihb20W3F6DSp5X+Tfhpk3N5e+/X91xxWnNGujVyxxMQKQEKKSI\niIhI2fXdd+ayXTt4+GFzKNwNG8wJBq9GSgr06GE++P/zn5w+m8WLa09w9+KDfLU3mQy7QdtwL2Z2\nDuer3jV4ICoQPw+XK58XoGNHc7lqVa7w5Gq14HYtM8K3amUuFy+++mOLy5kz8M038PrrpV0SqSAU\nUkRERKTsWrrUXN56K3h5wb/+Zf58NbUp6enmMMMbNuCoXZu5L8zm9q8OsmBXEgbQu44fi+6swWu3\nRNA+wjvv7O5XEhUFQUFw9KjZsb2ozoeUr782O/SXBZ06mcvjxyEgoFSLIhWDQoqIiIiUTQkJ8Ntv\nZnOqzp3NdSNGQHAw/PGH2UflSrKzzeGFf/qJ9MohPPjku7xy1JWz2QbtI7xY0Ks6E1pXoYZfEeYb\nsVqhQwfz/bkmX0Vy443g52e+P3Cg6OdzBnd3c7hmgKSk0i2LVAgKKSIiIlI2LV9udpxv2/bCQ7u3\nN/zzn1C7tjlc8BXY1/6BsWgRqd6+DB71Dpv9q9Kwkgdvd41gZueIy84Sf1U6djTDysGDebfNmgV9\n+8IPPxTuXB4eZthZtw5uv9055XOGzz4DHx+YPbu0SyIVgEb3EhERkbIpKMh8SL/lltzrn3gCRo82\na1gKcOxMFov3JvPV8TAaPDaTBL8gUho2ZtKNQXSv6Xv1TbquZMgQePDBC2HqYqtWweefm03OCuuG\nG5xWNKdp08bs2yNSAhRSREREpGyKiTFfl/LIv/Yjy26w8sgZFu1J5rdjZznfY8W1423cW9+fe+v7\n4+FSTI1I/P0L3rZnj7ksykSOIhWMQoqIiIiUW8kZdradzuC3Y6ks2ZtCQobZBMzNauGW6t70qeNP\ni1BP59ecFJZhKKSIXAOFFBERESkXUrMcbD+dzrb4DLbFm8vDKVkXdjAMWmecoF27aG6r7UdAYYcQ\nLk4nT0JyslnTEhRU2qURKTcUUkREROTqGIbZz6Jdu8v2C3GWY2eyGP/rcTadSOfSQYfdrRaifaGF\ny1nuXrmAkFnTsCxeDA1vyfdcJe7iWpTSqs0RKYcUUkREROTK3n4b6tc3h9odMgQ+/BA++AAGDy7W\ny249lc4TK45xOt2OqxXqBngQFeRBVJCN6CAbkTs34npPX3Okr+PHzRG2Tp8u1jJdVkqKOaP9TTeZ\nNSeNG8PKlYUaiUxELlBIERERkcuLj4dRoyAtDXbuNOcs+fBD+N//4P77nV+b8uOP8OGHbOzel39Y\noki3G7QM9eT/OoTlnQW+fj2zOVVKillTMWcO3HOPc8tzNfr1MyegnDcP+vcHX98LM9KLSKFpnhQR\nERG5vDfeMANKjx5Qr54ZTOrWhb174aOPnH454/PP4aOPWPv5j6TbDXrX8eO1WyLyBhSASpVg/Hhz\nssF33zUnbixNzpzUUaQCU0gRERGRgqWnw2uvme/HjDGXrq7wzDPm+//9D7Ky8j/2GmTbHSR99Q0A\nvzbpwOM3BvFMqxDcrJfpzzF2LJw5A0OHOq0c10whRcQpFFJERKRi+/RT+OQTs0mT5PXxxxAXZ04u\n2LnzhfX9+5t9VPbvN/dxgjOZdl6Y+ysBsYdJ9AnkgQe6MLRRJSyF6XDu5uaUMhRZixbg6Qk7dpjf\nm4hcE/VJERGRiu2552DbNujTx+xP0K9faZeobJk921yOGZN7dCoXF5g82Wzyde+9V3XKLLtBUqad\npAw7KZkOkjLsJGU6mLstgRY/LgPA6NqVbpEBzvoUJcfd3ZyZffly+Pln6Nu3tEskUi4ppIiISMXl\ncMC+feb7L7+EjAyFlEt9/73Z7yS/76V37wIPy3IYHErOZE/iuVdCBnuTMjmVlk1a9qUDCV8wdvuv\nAAT27lnkopea3r2hcmU4cgSiouDWW2Hq1NIulUi5opAiIiIVV2ys2efivF9/NYeKdSkDkwCWFT4+\n8OijBW42DIOTaXZ2JWSwOyGDPYmZ7E7M4EBSFlmO/MOIiwX83F3w97Di5+GCv7u5DPN2o+63C+GX\nlRf6dpRHjz1mvj7+GLZvh0aNSrtEIuWOQoqIiFRce/eay1atzMBy8CBs3QpNm5Zuucqw/UmZbDqR\nxu7ETHafCyZJmY58943wcSUywIO6Ae5EBnhQJ8CdMG9XvN2sl+9nctddxVT6EnbxRI4iclUUUkRE\npOI6H1IiI80HyYMHzX4ECil5GIbB7K0JvL4pPs+s737uVuoFelA30AwidQM8qB3gjrdbBR+fZ/du\nc6mQInLVFFJERKTiql/fbJbTqhWkpsLcuWZIeeyx0i5Z8XnnHXNEsyeegNtvL9QhaVkOJv4Wx7KD\nZ7AAXWv40LCSGUrqBXoQ7OmCxeGABQvMpnLnO9I7HGZn+8KMznU9Uk2KyDVTSBERkYqrTRvzBWYt\nyrRpuYfZvR4tXmyOPHX//Xm3ZWWZQ/nOmgVBQXD33RxLNxi9MpadCRl4u1l5oW0VOlbzyXvsd9/B\ngAFQpQp88YU5BO+uXfDnn9CgQd79+/Qx+7vceit07252NL/enA8pdeuWbjlEyiGFFBEREYAaNWDU\nqNIuRfHKzIQVK8z33brl3rZiBTz0kDk541NPQXIy25b9ysiEUBIz7FTzdWN6TDi1/d3zP3ePHmYz\nub/+MmtqztuzJ29ISUw0w5LDYdZeWSwQEWGGm5tuct7nLW3btplNvkJDS7skIuWOQoqIiEhpOH0a\nBg6EBx4wJ0YsCb/9ZjZri442Q8HF3n7bnJhx4EAATrRsx+C4YLINO63DvJjcPhQ/j8uMema1muFk\nwQIz8DVoYDan8/fPu6+/vzlAwdKlZg3MqlXmcL3t2sGiRWbguR6EhJgvEblqCikiIiKl4b33zIf0\npUvNJk+BgcV/ze+/N5eX1qKAORdK+/YY//0vltOnmdjhQbINGBQVwOM3VsbVWoh+JfXrw3//e+X9\nLBZo2NB8jR5tBqeVK+HoUeja9ao+kohcnxRSRERESsOaNRfep6WVTEj57Tdz2b17nk0nMuHLdv34\nYVpbjKNHOVK9Hs+3DqFnbb/iL5e3N/Qsx5M3iojTKaSIiEjF9Pvv8M03Zkf5mJi82w2j+Ealys6+\n0DfkwAEIDy+e61zqxx9h/Xpo0gQAu8Pgt9izfL4riZ+PpmI3AIsXNaKimN02lOjKtpIpl4jIJRRS\nRESkYlqxAp5/3qzFuDikvPSSObrVK6/A3XcXz7U3bICkJHNo2ho1iuca+XFxgZtv5uTZbL7acpov\ndicRm5oNgKvFHFr47rr+3BTqibWiDhssImWCQoqIiFRMF0/keLG0tAuTOhZXSImOhq++Mq9VghyG\nwcfbE3ltYzyZDnNKxggfV+6q68+dkX4EeeqxQETKBv02EhGRiqmgkNKunbn8+efiu7aPD9xxR/Gd\nPx/HzmQxYU0c6+PMYNSpqjf31vfn5jAv1ZqISJljdebJYmNjGTx4MCEhIXh6ehIdHc3q1atz7TNx\n4kQiIiLw8vIiJiaGbdu2ObMIIiIihVNQSGnVClxdYdMmSE6+8nlOnIB3373QKb0otm83R7hyIsMw\nWLw3mX5fH2J9XBpBNhdmxIQxLSac1uHeCigiUiY5rSYlMTGRtm3b0qFDB7799luCg4PZt28fIReN\nDz5lyhSmTp3KnDlzqFevHs899xxdu3Zl586d+PjkM3utiIhIccjIMOflcHGB6tVzb/P2hmbN4I8/\nzOCRz0hYZGebIad+fTOgPP00DBkCrVtfVTEchkFShoPT6dlY33mHmv95gr19BvDtuGmcTrdz9IQn\n32bF4eNuxcfNio+bCz7uVnzdrPi6Wwn3cSPM2xVLAUHjdHo2L/x+goO/bcTb05eWN9bh6ZtDqGRT\nQwoRKduc9lvqpZdeIiIigg8++CBnXY2LOgMahsH06dN56qmn6NOnDwBz5swhJCSEefPmMXz4cGcV\nRURE5PLsdnj9dYiPBze3vNvbt4d162DHjvxDyty5MHQo/Oc/5mSMTz8NS5aY4cX1yv9rNQyDL/ck\nM+PPUyRnOgCoTn0+x0LNLz9h+c2DOBRaE3Bnfcrla3N83KxEBrhTJ8CduoEe1AnwoG6AOxtPpPHc\n7yc4nW7nzflTuHnzzxiff47FdlchviARkdLltJCyaNEievToQb9+/Vi5ciXh4eEMGzaMkSNHArB/\n/37i4uLodtEEUjabjQ4dOrBmzRqFFBERKTleXvDoowVv/9e/zOCR39wl2dnmqGCGYU5G2KAB1KsH\nu3bBL79Ap06XvfTJ02f436Ykfj56FgBfdytBNhcqhTTkzx730vKbT3h55dtsmf4usYcOUKVaTc5k\n2TmT6eBMloMzmQ5SshykZNo5kJRFQoadv06m89fJ9Hyv1yrQQstd6wCwtG1bqK9HRKS0OS2k7Nu3\nj1mzZjF69GjGjRvHxo0befzxxwEYOXIkx48fB6BKlSq5jgsJCeHYsWPOKoaIiEjRXfL/qlw+/ths\n6lWnDvTvb86l0qcPTJkCX3552ZCyYuMB2t5cn/71b2LT0x/w1M0h3FrT90JzrQYvwrKF1F36OXVf\nmsh6/yxa1PO/bFHj07LZnZjJnoQM9iRmsjsxg32JmQCMvCGIAUfXY0lPhxtuuPznEhEpQ5wWUhwO\nBy1btuSFF14AoGnTpuzevZvXX389pzalIAW1pQVYv369s4ookkP3lRQH3VcVQHY2jf77X2zA/oED\nObxhE2uT3KkZEc09QMaCBWwZODDPJJCpdgvzjtvw+/EnYrIy8bVkM75GEpXiE9kQn/sS1Xv3JuSz\nzzj95JMwaVKh7itXoAHQwB0IAUcwOADXs4mc+PBDQoHYJk04qntULqLfWeJMdevWder5nBZSwsPD\niYqKyrWuQYMGHDp0CIDQ0FAA4uLiqFq1as4+cXFxOdvy06JFC2cVUQQwfynrvhJn031VzLZvN5cN\nGhTfLPCF8eGHcPgw1KnDoUFP8MKG05xMs2Pxa8nZHg/x943tyUwOo3GIF02DbUQH2dh4Mo0X1sRx\nMn6Z4X0AACAASURBVM3OM9vWABDd73YatW6e/zWmT4ewMCr95z/sO3q06PfV5s0AhA0eTJjuUTlH\nv7PE2ZKSkpx6PqeFlLZt27Jjx45c63bt2kXNmjUBqFWrFqGhoSxbtozmzc1fzOnp6fzyyy+8/PLL\nziqGiIhcj/73P/jkE3jrLbPDeiE6pxeLLl1IH/k4XwbW56VfTgIQHeRBZU9X5gwZR0KGHY6lseqY\nOReJiwXs5pyJNA220Wv/HwBYunYt+Brh4TBjhvm+qMMROxxwyy3m96X+KCJSjjjtt/yTTz5JmzZt\nmDRpEvfeey8bN27k1Vdf5cUXXwTMJl2jRo1i0qRJNGjQgLp16/L888/j6+vLgAEDnFUMEfn/7N13\neJRV+v/x98xk0ntCCoQSepcuRUA6iL2g61pX197b96eu4oqK2NbuuuAKay9gFwUVEEREqnSkl5Ae\n0idt5vfHIUAgCUmYJDPk87quuZ7JU85zBoYw95xz7lvkVONyHSmseOON8PLLsH593dtzOs1aksRE\neOopsFZTMqygwKQiHjYMl8XCN45gnht6J9nFTvxtFm7vHcWlncKxWS24XC725ZXwR5qDdekO/khz\nsDWrCLvVwi29IrkyIBvbzh0QFgZ9qxhFcTerFV54oWHuJSLiRm4LUvr168fnn3/OQw89xJQpU2jd\nujVPPPEENx+VPeWBBx6gsLCQW2+9laysLAYOHMi8efMICgpyVzdERORUs3u3qWkSEAAOh5n6VVho\nfq6L/fvh44/NIvKnn67+3J49Yft20pat4LG8OJYmmYxcA+MD+cfpMbQIOZK+2GKx0DLEl5Yhvkxs\nGwpAYYkTLBDgY4UfV0NUFAwbZuqz1NbPP5v+hIfX/loRES/j1vHys846i7POOqvacyZPnszkyZPd\neVsRETmVlY+ijB4N27aZIGXDBqjrfPqqKs0fo7DESX7PvkRv386sN79m6YjLCfG1cl+/ZpzTNqTa\npC/lAuxHjdKMGmWq0x88WPs+Z2TAeeeZ4Oaf/zQjSo015U1EpAFUM8YtIiLiAcqDlKFD4bTTzPO1\na+veXhVBSkGJk6VJ+by8Kp2rv9vLsI+282ZYNwC6b/qdUa2CmXNua85tF3riAKWqBaRWK0RG1r7P\n2dlmFCUjA267zTyfO7f27YiIeAkFKSIi4tm6doVBg0z9kXoIUg7kl/D3efsY9tF2bv0xibc3ZPFH\nmgMnkD1gMADjl33Dc8PiiA44weiFywVjx0KzZpCSUvc+HqttW1i4EGbPNs83bYKzzjIV70VETkEK\nUkRExLPddRcsXQr9+x8JUk4m69VRQYrL5eKxpSmsSDHZuLpH+XF11wheHtmchZPa8syNI49cN3v2\nidu2WMBuh5IS+OqruvexqrYvvBA2boTnnoOICLj44qrPv+suMzUsPd29/RARaQCa0CoiIt5jxAjz\noTsqqu5tPPCAGe044wy+3J7D8uRCwv2sfHx2a5oFVvLf4gcfwMqVZk1ITVxwAXz7rak+f/31de9n\nVfz84N574aaboKrEM/n58MYbJli67Tb390FEpJ4pSBEREe/h728eJ6NvX+jbl/TCUp7/cjcA9/Vr\nVnmAAnDZZeZRU+ecY0Y9fvgBcnNNUDFzpln437btyfX9aFUFKMnJpiBkcbEZfTqZgE5EpJFoupeI\niDRJz/yeRm6xk8HNAzkrMcR9DcfGwuDBJkiYOxeWLTPZuM491333qM4//gHTppnnY8c2zD1FRNxM\nQYqIiDQ5C/bmMX93HgE+Fh4+PaZG6YRr5YILIC4O8vLMiAqYkZSG0L27KRhptZp+iIh4IQUpIiLi\nmZYvN+tHlixxa7O5xWVM/S0VgNt6RdE82H6CK+rg1lvN4v6//a3hg5S77oKdO80C+4aqbC8i4mZa\nkyIiIp7pq6/g2WehrIySQUOY9nsq+/NKuaprOAMjrFi2bYMePWrd7Eur0kkrLKNHtD+Xdqqn6u3l\n62ays02wZbPB8OH1c6/KRESYh4iIl/L4IMXpcmF19zC8iIh4vkNFHIuHnME9C5P4JakAgOX7c1l6\nYx/8igpxZWdjCQ2tcZNJ9z7E0J+WsfPcG3nonPOxWev5/5dFi6CsDIYMgRA3rnsRETnFefx0r4NF\nZY3dBRERaWhFRfDbbwDc72zPL0kFhPvZuL57BKEBvuyMbQPAlOk/smR/Pi6X68RNljnJ/P5Hhq9Z\nwPnxPrQL96vPV2C0awf33QdXX13/9xIROYV4/EhKZmEZkf4e300REXGnlSvB4WBfqw78XOhPswAb\nb4xuQbtwP67tHknSB71gzyZ81v3B7THd6R7lxw09oxgYH4jdVvnoyH/+yGRSkkk5PG7UaQ3zOrp1\nM1PWRESkVjz+03+mQyMpIiJNTf5PiwgClrXrS/MgH94ck0BCiFngHmi30n74APj8Ay4u2MmP/jbW\nZxRxx4IkrBaIC/QhIcROyxA7CSF2EoLt2KwWPlx9gNuzUnD5+OCb2KYxX56IiJyAxwcpGQpSRORU\n9913sHu3qaUhpOSX8EjMUBKunUJBpy78d1wCsUHHZOA6zYyEdNyzma/Pb8Mnf2bz6dZs9uWWkJRf\nSlJ+KcuTCytc0jZ1HwCW1q3Bx+P/+xMRadI8/rd0pqO0sbsgIlJ/1q2DCRNMNqjx46F168buUUUO\nh6mYfiiBSUmZiw0ZDnysFrpF+bm9vsje3GJumr+fpIBYsi+8kjdGtSAyoJL/qk47zdQhadGCALuV\nq7pGcFXXCIrLnCTllbI3r4T9uSXsyy1hb57ZnrnjgLm2XTu39llERNzP44OUjEKNpIiIByssNIu8\n66pHD7jsMvjwQ7PA+pNP3Nc3N3BNnUrZf6aze/AoFvUYxoct+5HmGwxAYqid8zuEcXbbkBOuHXSU\nOlmeXMDCvfnszysBoDy8KQ90LMCWrCIyHSY98KsjmxPqZ6u8wchIOHDguN2+NittwnxpE+Z7/DUj\nLoExnTWKIiLiBTz+N7XWpIiIR5s7Fy66iLZjxsC8eXVr45ln4Isv4NNPYcECGDHCvX2siS1boFMn\nAApLnSzam8+yAwWc9fXPDEg+QLs579JuzrtcafNhS5e+fDr+ar7oOZp/rUznldXpjGwZzAUdwhgQ\nF3A4bXxOURmL9+ezYG8+S5PyKSxx8tILNxKXeYDb7ptBWkRspV3pFxvAiyOaE2R3cwLKkBAYPNi9\nbYqISL3wgiBF071ExIP9+ScAJdHRtb92xgwIDYWzzoKHHoJHHoE774RVqxru2/7kZLjtNvjyS9KX\n/MZ7Pi2Z82c2OcVOAL648036pfzJRduW0n/1QiJX/UZ3Vx5dWpUyfFgcc7bnsDSpgHm785i3O48W\nwT6MahXM5swiVqYUUnZUZuD+9kKGrV0IwOev38CG2d9TGhEJQPlpvjYLvZoF4FPf9UtERMSjeXyQ\nooXzIuLRDgUpjpYta3edywX33gs5OZCaap6/9RYcPAi7dkH79u7v67H3nzUL1913Yzl4kKKAIJ55\n7xfm9xsHQPcoP0a3DmFgfCAdIjpgtUw01x08CJmZ2Nq2ZQQwonUIyfklfLEth8+35bA/r5T/bTwI\ngM0CA+ICGNEymOEtg4gPssPYdOjcmcAtm+h/3SXwww8QHFyxXyIi0uR5fJCSqTUpIuLJtm4FwNGq\nVe2uS001AUp4OERHm4XpX38NiYkQGFgPHT3Ktm04/3oF1uW/YQGW9BzGk9c8Tnqz5oxrHczlncPp\n2Syg8mvDw83jKHFBdm48LYrre0Sy7EAByw4U0DnSjzNaBBF27JqSqChYswbOOMMUazz/fPO6/f3N\n8R07YNAgOO88mD7d/a9dRES8gucHKY4yXC6X2zPIiIi4xaGRlBb//jesXw9vvFGz6w4FN3TseDhz\nFt261UMHK9qSWcR3+2zcsnIVOUHhPHvFwywdcT4XdQxnUqdwYgLr/t+CzWphSIsghrQIqv7EFi1g\n/nwTqERFgfWotSeLF0NamnnUxIYNpvDjeedBWFid+y4iIp7F44OUYqeLvBInIb5VZHgREWksRUUQ\nZD6QB69fD9nZNb/26CDFXbKzTdBU/li3Dt5+m0ybP9/uzOWrHTlszSoGYN0D/6X4tF6c36cljySG\n4O/j5kXqJ9K+vRlJSUgA21G/3xcvNtuhQ2vWznXXmXZ+/BFGjqz6vIUL4frrTTDz/PN17raIiDQM\njw9SwIymKEgREY/j5wfbtkFREc7gYKx790JeXsU1FlVxd5AyZoxZ33GMGT0n8O/EoYcXsIf6WpmQ\nGMI5Ey6mqzvqnJSWgtMJvpWk/D2RymrC1DZIOe00E6SsXVt9kLJ1K2zfDunpte+niIg0OK8JUlqH\nNnYvRESq4OdHUcuWBOzcaT4M9+lz4muGDjUBTXUfxh0Os0aja1dTj2XhQvO8sg/30dEQEEBxYjt2\nx7ZmRWgCm5u1YWm4SSs8LCGIc9qGMCwhCF+bm0ZN3nwTHnsMpk2Dq66q+rwPPoDVq+GGG6pPCJCc\nbEaAAgOhd++a9eFQ5XnWrq3+vB07zFaFHEVEvIJXBCkZhUpDLCKezdGmjQlStmypWZBy9tnmUZVd\nu2DUKBOo9OljpjMVFsKTT5p0xUffu9TJwoee59OrprEy/UhhyQ7hvlzdLpQJiSFEVVa1/WRZrSaw\nmDmz+iDllVfg119NQFFdkLJhg0m9PGgQ2O0160NNg5Tt2822vrOmiYiIW3hFkKKCjiLi6Rxt2pgn\nmze7p8GWLc1C8B07ICnJ7OvTB+LiDp+y/WARn27N5pudueQeqmsS4GNhXJsQLmwfRvdoN0znqs6k\nSaauy4IFsHOnyUx2rK1bTYASHGwyeVVn1Cizrqami+YBevY0240boaSk8uCmrMwsrgeNpIiIeAmv\nCFJUK0VEPF36WWcRf+WV0KOHexq02eD99+Gll6B/fxg/Hpo3B2B1aiFvr89k8f6Cw6d3jfLjwvZh\njGsTTHBDreELC4MLL4T33oP//Q8mTz7+nHfeMduLLz6cZKBagYGVT2erSkgIXHEFxMRAQUHlGb4y\nMswITXh4g2RQExGRk+cVQYpGUkTEIy1bZqYPRUVR1KYN9Ovn3vY7dz6c0tjpcrFkXx5vr89iTZoD\nAH+bhbPbhXJRh1A6R/q79941dc01JkiZNQseeaRiOmGn80iQUt10sJNVfo+qxMTAkiVmVKomSQ1E\nRKTReUeQojUpIuJpMjLM2ongYFOUsZ6UOF3M25XLzA1ZbDto0geH+lq5tFM4l3UOI9K/kX+Njxxp\nRj5atzZ/Js2aHTm2Zg3s3g2tWsHw4Y3XRzCBSkxM4/ZBRERqzCuCFE33EhGPc6iIIx06HCnGWFOz\nZpk1HJdeCl26VHpKidPFl9tyeGt9JgfyzRc1MYE+XNElnAs7hBFkb+C6JlWxWk0Ry8pGKPr0MaMX\nu3ZVHGERERE5Aa8IUjTdS0Q8zsnUOfngA/j+e+jb97ggpczp4rtdubz5RyZ7c0sAaBNq55puEZyV\nGIrdVo8L4euquilUiYmVL6ivT9u2mQXy9Zk0QERE6pWCFBGRujh6JKW2KglwXC4XP+3N5401GWzP\nNtO6Wofaufm0KMa0DsaqD9w1s3IlnHkmXH45vP56xWr2IiLiNTw+SLFbLeSXOHGUOvH30XQBEfEQ\nlY2kfPMN/N//mVS6L71U+XVFRWb6k80GiYm4XC6WJhXw2poMNmWaGifxQT7c2DOSiW1D8bEqOKmR\nn36CV1+Fzz4zP+flaSRFRMSLeXyQEuVvI7mglExHGc2DFaSIiIdISDBTtTp3PrLPbjcFCaOjq75u\n+3ZwuSAxkUKLD/f+mMSvB0wq4egAG9f3iOSC9qHuqwrfVHz66ZEAZdw4ePttrYMREfFiHv8bPMLf\nDNVnFGrKl4h4kOefNwUE+/c/sq88YKmuoOOhERhXx448/Esyvx4oIMzXyl19ovny/DZc2incewOU\nzZvhxhth7FhTwNHlarh7l2cP69YNZs8GX9+Gu7eIiLid54+kBJggJdOhNMQi4uESEkwxwpQUyMqC\niIjjzzntNHj1Vb4uCGLB3nxCfK3MHN+SNmGnwIfqAwfgP/8xz+fPN9PfzjqrYe59ySUm/fHAgebv\nQEREvJrHf10XdagGgNIQi4jHs1qhUyfzfMuWys9JTGTO2Ct4NG4IPhZ4blj8qRGgwPG1UEaPbrh7\nW62mZosCFBGRU4LHBymR/uUjKQpSRMQLlE/5Kl9Yf4xlBwqY+lsqAA+dHsOA+FPoQ7XVCg8/bJ7f\neKOmXImISJ15TZCSoarzIp6hsNDU97j55oZdc+DBFu/PZ1O+DZfLBU8/DcnJcOWVx523I7uY+xcd\noNQF13SL4IIOYY3Q23o2eTJ8/DH861+N3RMREfFiXrQmRSMpIh5hzRpYtQpKSppuitf5880oQb9+\nzE118tCSZCCYr77Zw1VdIxiXEIL9mD+bTEcpd/6URF6Jk5Gtgri9d1Tj9L2+2e1mfYiIiMhJqLeR\nlKlTp2K1Wrn99tsr7H/sscdo0aIFgYGBjBgxgo0bN1bbTuShNSkKUkQ8xPLlZnt0VqtTwYEDMGsW\nJCWd+Ny774Yzz2TvinU8/msKAIFWJ39mFfPILymc+9ku3tmYRX6JE4CiMif3LjzAvrwSukb58cSQ\nOBVnFBERqUa9BCnLli1j+vTp9OzZE8tR/xFPmzaNF154gVdffZXff/+dmJgYxowZQ15eXpVtRZVP\n91KQIuIZfv/dbMuDlFNlytdtt8E118CXX1Z/ntMJ27YBcP+BYBxlLia2DeG5Drk8NiiGxDBfkgtK\neWFlOuNn7+TlVek8+ksKa9IcTNy8hP/OuIeATz6q/9cjIiLixdwepGRnZ3PFFVfw9ttvE3FU+k2X\ny8WLL77Igw8+yAUXXEC3bt2YNWsWubm5vP/++1W2d3jhvNakiHiG8iAlMREuuAB69/aMQKW4GG69\nFR59FHJzT3z+6tVmfU258ePN9vvvq79u714oKiI3ohlbSvzoEO7Lw6fHYLfCee3D+PScVrw0Ip7e\nMf7klTh5e0MW83bnEehj4a7S7fh9NhvWrav76xQREWkC3B6k3HDDDVxyySUMHz7cLCI9ZOfOnaSk\npDB27NjD+/z9/Rk2bBhLly6tsr0wPxtWC2QXOylxesAHIZGmLDvbZK3y9YVhw2DxYli7FjZtauye\nwVdfweuvw5QpJg3wV19Vfe7y5ab/EyZAfr7ZN26c2f74o1lvU5U//zSbmNYE2608OzyeAJ8jv0qt\nFgvDEoL578g4/jcskpGtgogOsPH0sHii9+4wJ3XseDKvVERE5JTn1iBl+vTp7NixgyeeeAKgwlSv\n5ORkAGJjYytcExMTc/hYZWxWCxF+ZjQlS1O+RBpXaCjs2QNz50JAAEycaPZ/8UXj9gvgk0/MNirK\nrC/x96/8vHXrzKhJXh40b37kvFatoEsXMwrz669V3mbPivVmG9uGfw6OpXVoJWl2n3wSAgPp8eEM\nnh/enPkXt2Voi6AjaYkVpIiIiFTLbdm9tmzZwsMPP8ySJUuw2UxQ4XK5KoymVMVSzQLSFStWEOAK\nBmwsWfUHrfyd7uqyNGErVqxo7C54t9BQWLGC8G7daA/kffABm8eMabTuWBwOen35JTbgjxkz8Nu/\nn9yICDjm79lvzx46//3v2LOyODh0KNvvuAPX6tUApBdb6NKzF603beLAzJnsr6QoYHaphfmZAYzu\nP46S3j0JTd3MitQjx8vfV83y8mhdWkr6L7+wq7wPLhe9N2/GBqwpKKBU70GpIf2+kvqi95a4U4cO\nHdzantuClF9//ZX09HS6det2eF9ZWRmLFy/mzTffZP168+1jSkoKCQkJh89JSUkhLi6uynb79etH\ni6x97EsuJDaxE/1aBLmry9JErVixgn79+jV2N04NnTvDo48SvH49/RISoJp/y/XK5YIFC2DpUnqe\nf37l5yQlwUUXQWYmjBxJ+Dff0NffnyxHGS+tSueL7Tn0an8Of51ox3nmRfTschpxQfbDl5c6Xdz0\nw35W9hhJ2qiJvDmmBT7WI1+wVHhf5eXB008TnZ5OdPm+5GQztSwigl6jRjXd9M1SK/p9JfVF7y1x\nt+zsbLe257Yg5YILLmDAgAGHf3a5XFx77bV07NiRhx56iA4dOhAXF8e8efPo27cvAA6HgyVLlvDc\nc89V23ZUgNIQi3ik4GAYPRoWLjTTqBorSLFY4PTTzaMqUVGmCGXz5vDFFzj9/PhyWzYvrkwnu9iJ\n3Wphc9f+3N/p0H/ac3bRq5k/Y1qHMLp1MB9sPsjKlEKiA2xMGxZXIUA5TnnV+c2bTQBlsUB4OPz0\nE2RlKUARERE5AbcFKWFhYYSFVayeHBgYSEREBF27dgXgrrvu4qmnnqJz58506NCBJ554gpCQEC6/\n/PJq2z6c4UtBiojn+fe/ITq66jUgnsLPz1RCLyhgW4mdp+btY3WqA4ABcQE8dHoMMQE+LN6fz7zd\neSzZn8+aNAdr0hw8tyINF2CzwDPD4okOOMGvzthYMyUuKwvS0iAmxvz5jBhR/69TRETkFFCvFect\nFkuF9SYPPPAAhYWF3HrrrWRlZTFw4EDmzZtHUFD1U7jKq85nOJSGWKTR5OWZD9o+x/zaOGr6pqcr\ndFn5z7Zi3t2YQqnLfAFyX79oxrcJOfy7amybEMa2CaGgxMnP+/KZvzuXJfsLKHa6uLtvNL1jAk58\nI4vFjKZs2wb795sgRURERGqsXoOUBQsWHLdv8uTJTJ48uVbtHK46X6iRFJFG88wz8Pzz8OyzcMst\njd2bWilzupi3O49XVqdzIL8UCzCpYxi39Y4ixNdW6TWBdivjE0MYnxhCXnEZyfmltI/wq/lNFyyA\nShbfi4iIyInVa5DiLpruJeIBli+HggLPGhVwOMyC+LZtKz1c4nQxd2cu/12fye4cU/ukc6QfD58e\nQ/fomk9PC/a10d7XBj//DBs2wJlnmnTF1VGAIiIiUmduL+ZYH6L8Nd1LpFG5XEcqzffv37h9Odrc\nudCuHVxzTYXdxWVOZm/N5oIvdjF5aQq7c0poEezDIwNjeGdCyxMHKHPnmkDk2Wcr7v/oIzOK9N13\nbn0ZIiIiUpFXjKQou5dII9u506TubdbMFD2sTGYmfPst9OoF3bs3TL/KCzgeGtVwlDr5fFsOMzdk\nkVJgvtRoHWrnuu6RjE8MwV5dRq6jFRTAokUmOLv//iP7D1Wbr3Uxxl27TOHLIUPgP/+p3bUiIiJN\nkFcEKUdXnHe6XFiVvlOkYS1fbrb9+1edPnfqVHjuObjnHrN2pb4VFsJXX5nnl1zCmtRC/m9xMqmH\ngpN2Yb5c3yOSMa2DsdU0OCk3ahTYbLB0KeTkmExdcKRifG0LVm3ZAhs3mqxfIiIickJeMd3LbrMQ\n6mulzAXZRao4L9LgMjMhJKT6qV7nnmu2X3xhRiDq2/ffm4xjffrwaWkUf5+/j9SCUjpG+PL88Hg+\nPqcV4xNDah+ggKlpMnAglJaa2iZg1r/s2WOCl8TEmrVTXGyCk/Igr7YjMCIiIk2UVwQpcGRdSqbW\npYg0vFtugYMH4YEHqj5n8GBTL2X7dvPBvL4dmur144AJPPlbKqVOuLxzOO+e1YqRrYJPfsR13Diz\n/f57s92+3QRfiYlgt1d93dEmTYJu3eDVV83PClJERERqxGuClMhD61IylIZY5IiVK+H99xvmXlZr\n9RmrbDY4+2zz/Msv6707ee07kRLXihfbjcDXamHKkFju79+s5utOTmT8eLNdscJsQ0PhH/+A666r\neRudOpltaqrZKkgRERGpEa9YkwJKQyxyHJcL+vUzz+PjPaOa+XnnwcyZZsrXgw/W223WpBZyf48r\nSJ92GXFBdt4+M56uUW6ueN+3r8lo1qeP+bllS5gypXZtdO5c8WcFKSIiIjXihUGKpnuJABWnVA0d\n2nj9ONqYMXD99UfWp9SD2Vuzefp3M72rb1wgzwyNOzzS6lZW65EgsK7KR1ISEuCDD2q+lkVERKSJ\n85ogJepQ1fkMjaSIGOW1Oq68Enw85J9yUBBMn056YSlJaYVkOMrILCwjw1FKpqOMjEPPi8tcxAfZ\nSQixkxBsp0WInZbBdmKDfPCxWnC5XGQ5ytiVU8KunGJ25xSb59nF7Mk1RRkv6xTGPf3cOL2rPpQH\nKVlZJv2wMhOKiIjUiId8sjmxqIBDBR21JkXEmDvXbCdMqN/7zJtnUu62aVPth+zUglJ+2J3L97vz\n+CPNccJmN2QUHbfPxwKxQT7kFDvJLa48k1+Aj4X/NyCGc9uF1vglNJqoKLNwPirKpDIOC2vsHomI\niHgFrwlSIvyP1EoRafLy8mDxYhM0jBlTf/cpKjKL4UtLTXav0IqBQZajjB/35PH9rlxWphRSnnjY\n32ahbbgvUf42Iv19iAqwVXhut1pIyithX14J+3KPbNMKy9ifZ6Z0BtuttA610ybUl9ahvrQJs9M6\n1JdWIXb8fbwm5wesX9/YPRAREfE6XhOklKcgztCaFBEzveudd2DzZpP2t76sXQslJaai+1EByh9p\nhbz5Rya/HSig7FBk4mu1MKRFIOPahDCsRRAB9kOBxNatpsr6U0+Br+/hNnrFBBx3O0epkwP5pYT4\nWonyt2E5duSmqAhGDDfpgR980GQUawjz55v73XMPXH55w9xTRESkCfOiIEVrUkQO8/c3NTiOlpRk\nige2aeO++/z+u9keVcTxQH4Jt/2URG6xEx8LDGluApMzWwYR4ntM0OBymQ/1K1fCL7/Axx+bLFlV\n8PexkhjmW+Vx5s2DJUsgN9ekA24Iv/wCY8ea5x9/rCBFRESkAXjNnInD2b0Ky3A1RDVrEW8yY4bJ\nIPXEE+5tt7xS+oABAJQ5XfxjSQq5xU6GNA9k/iVteXVUC85pF3p8gAJmOtprr5nAZNkyk873hx/q\n1pfSUnj5ZfP8kkvq1kZdHBWgVVsnRkRERNzGa4KUALuVAB8LxU4X+SWVL6gVabIGDTKjFnPmV52k\n3wAAIABJREFUmOlZ7nLMSMrMDVmsSi0kOsDG40NiCferwXSr00+HVavMaER6utk+9VTt+uFywW23\nmQAnMhKuvrqWL+Qk+PoeWfDeo0fD3VdERKQJ85ogBTTlS6RK3bqZR1ZW3UcqjuVywciRJsg47TTW\npTl4Y20GAI8PjiXSvxazRaOj4dtv4dFHzc8hIbXryxtvwJtvgp+fqWafkFC760/WmjUmsLr33oa9\nr4iISBPlVUFKZICqzotQWkXyiEsvNduPPnLPfSwWePVVWLaMfKudh5YkU+aCv3YJZ1DzoNq3Z7PB\nP/8JGzbA7bfX7tpJk+CMM+D99029kYbWpo1ZOO9bzXoZERERcRuvClIOZ/gqVIYvaaIKCyE2FiZO\nPH5aV/lC+s8/N1mw3Gja8lT25ZXQMcKXO3pHnVxjXbrU/proaFi0CC688OTuLSIiIl7Ba7J7wVGL\n5zWSIk3VokWQmQnJyWC3VzzWqROMHw8dO0J+vpka5Qbf7czlqx25+NssTB0aj6+tnr7bKCurPqWw\n1au+UxEREZGT4FX/65fPgVeQIk3Wd9+Z7fjxlR+fOxdeesksLneDpLwSnvwtFYB7+kXTtrr0wCdj\n3TqzpmblyvppX0RERLyKVwUpUQHlBR0VpEgTVR6kTJhQ77cqdbr4xy/J5JU4OTMhiIs7hNXfzZ57\nDrZsgTPPNGtqJk92b5YyERER8SreOd1La1KkKdq503yQDwuDgQPr916ff86aeb9SEtOf6O59eHRQ\n7PHV391p+nSTEOD99+Gyy8y+7Gx48cX6u6eIiIh4LK8aSdF0L2nStmwxqXvHjAGf+vl+wely8du2\nVLKvv4l+bzxDQsoepgyJI8K/BvVQToavL7zzDtx3n/k5IeHIcxEREWlyvGok5XB2LwUp0hSNHw8Z\nGaYWipulFpTy+bZsPt+WwznvvcjpGSmsb9uDdjddxcD4BqqybrXCs8/CRRdB+/Ymo5eIiIg0Sd4V\npKhOijR1djvExJz4vI8/xvnCv9hzw+2kTzwfH4sFu9WCj9WCjxWztVj482ARn/2Zw5KkfJwuiD6Y\nyjXfzgCg+esvcv1pjRAo1PdUNhEREfF4XhWkBNut2K0W8kucOEqd+Pt41Ww1kXqVkl/C2jQHa9Mc\nxM1fz5W/LWObM4z77f1PeK2PFUa2DOa+754iwFEA559P5LiRDdBrERERkeN5VZBisViI9LeRUlBK\npqOM5sEKUqRpW5FSwCdbsvkjzUFywZGEErHdRnMlUxi2diGDgkvJ8w+m1Ok68nBBidNFqK+ViYmh\nnN02xCSmeMdm1odMm9aIr0pERESaOq8KUoBjghT7iS8QOUWtTi3klh+SKHG6ADPS2LOZP6c18+e0\nZi0o+2QIvkt/4fXC1XDB5TVrdMYMmDIF4uPrseciIiIi1fO6oYjDtVKUhrhp2rQJLrgAFi5s7J40\nnORkmDXLbA/ZnVPMPQtNgHJuuxA+ObsViy5ty2ujWnBDzyhOjw/Edtml5uQHH4Tt22t+PwUoIiIi\n0si8L0g5lIZYGb6aqCefhM8/h5Ejm06xv6++gmuugZtuAuBgURl3/JTEwSInZ7QI5JGBsbSP8MN6\nbB2Ta6+F00+HZs0gLq7h+y0iIiJSR1433au8XkOWgpSmp7DQBChgtvYmMt3vqCrzxWVO7lmYxJ7c\nEjpF+PH00Hh8rFUUWQwOhp9+grw8CApquP6KiIiInCQvHElRrRSPl5sLTqf72507F/LzoW9fOPdc\n97fviUpK4IcfAHCNG8djS1NZneogJtCHl0c2J8h+gn/CgYHVpyzOz4c1a9zYYREREZGT531Bitak\neL4HHjBTjD791L3tfvih2V52mXvb9WQ//gg5OdClC28cDGHurlwCfSy8PKI5MYEnMRBaUGBGpp5/\nHvr0gaeecl+fRURERE6S1033ig00U3y2ZhXhcrmwHDsPXxrfwoWQmQnNm7u33U6doGVLmDSp8uP/\n+pc51qKFe+/bWJxOuP9+ADaPu5Dp6zKxWuDpYfF0ivSre7tlZfDXv0JSEmzYAC4XDBnipk6LiIiI\nnDyvG0np0cyfSH8bu3JK2JhR1NjdkWOlpMDmzRAQACtWwJVXum+B+5QpsHs3tGp1/LH//hfuucdU\nK1+3zj33a2xWK8yZQ9plV3HtaX8B4P/6N2Noi5NcX3LgAKxaBcuXm+le550Hw4e7ocMiIiIi7uF1\nQYrdamFCmxAAvtqR08i9keP8/LPZDhkCr78O774Lq1e7r/2qRs7OO8/cc98+GDEC0tPdd89GUlTm\nZLYrhovOfxSHzZcruoQzqVP4yTeckAC//QaDBkF0tAo3ioiIiMfxuiAF4Jx2oQB8vyuXkjJXI/dG\nKli0yGyHD4czzjDPFy+u//tGRZkF5sOHQ0YGPPpo/d+znuQWl/HWukwmztnFE7+lklvsZFSrYO7u\nG+2+m8TFwdKlJqjr1Ml97YqIiIi4gVcGKR0jfOkQ7svBIidL9uc3dnfkaAUF4OtrgoWhQ82+hghS\nAPz9KXzxFVw2G6433yR/1ZrD1di9QWpBKS+sTGP87J28uiaDDEcZnSL8mHpGHNOGxh1fB8Ud/E5i\nbYuIiIhIPfG6hfMAFouFs9uF8q+V6Xy9I4cRrYIbu0tS7r//hddeMzVMyhewL1liFmfXY5KDA/kl\nvLfxIHO2BXDHiMtov+9Pnpp3gJ0bgvCxgL+PFX8fC4E+VoLKguhamkLLEF8SQuwkBNtpGWIn8ETp\nfOtBXnEZm7OK+Hp7Lt/szKHTn2spaNuTAfGBXNstgtPjA5UcQkRERJoctwUpU6dOZc6cOWzduhU/\nPz8GDhzI1KlT6datW4XzHnvsMaZPn05WVhann346r732Gl27dq31/Sa0CeGlVen8vD+fg0VlhPvZ\n3PVS5GQFBJhtYiLEx5uF2ps3Q5cutW8rNRXOOQcuvxzuvPO4w1uzivjfhiy+25VL+cy/96//B4VW\nO44ysJU6KXVBXomTvBKAMsCHTX8ev54pyt9Ghwg/zmgRyBktgmgd6lvjbmY6SslylOFvM8GQv48V\nP5ulQqHFzMJSNmcVsTnzyGNv7pGkAgM3/MIb064l+7yLCPvsk3oN6kREREQ8mduClEWLFnHbbbfR\nv39/nE4njz76KKNHj2bjxo1EREQAMG3aNF544QVmzZpFx44defzxxxkzZgxbtmwhOLh2oyHNAn0Y\nGB/I0qQCvt+Vy6XuWFAs7mWxwAsvQEQEtG5dtzZmzzZZqJo1OxykuFwufk8uZNbGLJYmFQBgs8D4\nNsFc3S2CzpH+hy93uVyUOsFR5qSw1EVeiZNFqzfiH9eGfbkl7M0tZl9uCfvySslwlJFxoIBlBwp4\nbkU6rULsDG0RxBkJQfSNCcBuM0FDQYmTTZlFbMhwsCHdwfp0B0n5ldft8bGCv82KjxUOFh1f4NJu\ntdA+3JfB9nxuvv9BAML6nqYARURERJo0twUp3333XYWf33nnHcLCwli6dCkTJ07E5XLx4osv8uCD\nD3LBBRcAMGvWLGJiYnj//fe54YYban3Pc9qGsjSpgK+25yhI8VQnW3jxmAKOmzIcTFmWyqZMk37a\n32bhgg5hXNElnObB9uMut1gs2G1gt9kI8YUYIDO4lH6dK75fypwuUgpKWZNayOL9+SxNKmBPbgnv\nbT7Ie5sPEmS30quZPykFpezILubYpS7+NgvxQT4UlblwlLlwlDpxlJkAKc9pgpNAHwudIv3oFOFH\nlyh/OkX40TbMF7sVOPdcSEk263geeujk/sxEREREvFy9rUnJycnB6XQeHkXZuXMnKSkpjB079vA5\n/v7+DBs2jKVLl9YpSDmzZRDBdisbMorYkV1M27CaT88RL7Bvn1l07+8P557Lgj15PLQkGUeZiwg/\nG3/pHM4lncLcMtXPZrXQPNhO82A7Z7UNpdTpYl26g8X78lm8P59tB4v55dCojY8FOkb60S3Kj+7R\n/nSL8icxzLfC1C6oOIpTVOYi0t9W+eL3V16Br7+G8HCTstmmqYsiIiLStNVbkHLnnXfSu3dvBg0a\nBEBycjIAsbGxFc6LiYkhKSmpTvfw97EypnUwn23L4ZsdOdze240pWqV21q2DHTtg2DAzvcsdPvkE\nXC5cEyfyzr4yXlyZggs4p20ID50eg79PDRe6JyXBvHlwzTU1vrWP1ULvmAB6xwRwR59oDuSXsDbV\nQXywD50i/I6/99NPw6ZNZnpbVBRwzChOVTdyueCLL8zz6dMrL1QpIiIi0sTUS5Byzz33sHTpUpYs\nWVKjzETVnbNixYpqr21fYgOC+WxzBqeX7sKqqfyNIuFf/yLu/fdJ+tvfSLr5Zre02fbrr4kE3m4/\nhFdWmuKMFzRzMME3m/Vr9tWoDWteHj3PPRdbXh4b7XYKD9UEOdH7qjLRQEkGrN9dcX/gpk10fdCs\nJylcvJiN776Ly7fmo3rWRx8l4owzyGjTBurQL/EcdXlfiZyI3ldSX/TeEnfq0KGDW9tze5By9913\n8/HHH7NgwQLatGlzeH9cXBwAKSkpJCQkHN6fkpJy+Fhl+vXrV+39+rpcvJ+xi/15pbgSutIvPvDk\nXoDUzebNADT/y19oXtXfWVlZraYy5X77PU/N+J6v/FriZ7MwZUgsY1pXOSZRteuugxdfpNv06bBg\nAStWrjzh+6pWHnnEbAMCCLj3XvoOHlz7NoYNI9F9PZJGsGLFCve+r0TQ+0rqj95b4m7Z2dlubc+t\nhSHuvPNOPvroI3766Sc6duxY4VhiYiJxcXHMmzfv8D6Hw8GSJUsYXJcPdYdYLBbObmsq0H+14/i0\nstIAsrNhzRpTG+XQ9L4Kdu2C/v2hFr8M9+YWc/V3+/gktCNBYcFMH5NQtwAFTPX5qChYtAjmzKlb\nG1VZvBi++w5CQuDPP+HWW93bvoiIiEgT5LYg5dZbb2XmzJm89957hIWFkZycTHJyMvn5piK8xWLh\nrrvuYtq0aXz22WesX7+ea665hpCQEC6//PKTuvfEtubD64+78ygoOT7Nq9SzJUvA6TSBSFDQ8cfj\n4uCPP0wgk5VVbVMlThdL9udz1dx97MwpoX24L/+b0JIezfyrva5aEREwZYp5ft99WIqK6t7WsXbt\nMgHK3XcfKV5ZnTlzwJ33FxERETkFuS1IeeONN8jLy2PUqFE0b9788OP5558/fM4DDzzA3Xffza23\n3kr//v1JSUlh3rx5BFX2wbYWWob40jvGH0eZix/35J3sS5HaWrTIbIcPP7wr02HS+SbllVBi94MB\nA8yBX36pcGlxmZPVqYXMWJfJzT/sZ/hH27n9pyQOFpUxuHkgb49LqDS1cK39/e/QvTsUFGB1OE6+\nvXJXXmkSBtx3X9XnbN9uFsg/8wxcdBFMmmR+FhEREZFKuW1NitNZsxGMyZMnM3nyZHfd9rCz24ay\nOtXB1ztyOKddqNvbl2oMH24qw0+YAMCa1EJu/mE/jkMl4C3A/c168BeW8NN7c1keM4BAHyvr0x38\nke6gqKziB/Y2oXbGtgnh7z0ij0vrW2c+PvCf/8DKlZSFhbmnzXLR1WSVW7cOzjgDOnWC3383RRrP\nPlvFGkVERESqUW8piBvamNbBTFuexu/JhRzILyE+qA7fvm/dCj//DFdfbdZXSM1MnGgewLasIu5Y\nkISjzEWrEDuOMhfphaUsbdubvwBRK37loy0VF1a1C/Olb2wAfWMD6BPtS/Rb/4ZuE8Ea5d5+Dhpk\nHpVlM9m61aT/9T+JaWWVSUqC0tIjAcp//1urVMgiIiIiTdEpE6SE+No4s2UQ83bn8e2OXK7rEVn7\nRt56y0zJWbQI3nnH/Z30NosWQXAw9O1bo9OT8kq45cf95BY7GdEyiGeGxeNjtVDqdJE5IhzXCzfS\nsTCDB3qFk1VmpVOkH71j/In0P+ptOHWqqbj+wgtmGlVDFDZ0OuH88816mf/3/+D228HqppmQ48bB\nwoUweTJcey1ccol72hURERE5hbk1u1djK5/m9fWOHFx1mfM/aZIZQXn3Xfj4Yzf3zsukpcGYMSYj\n148/nvD0TEcpt/y4n7TCMvrEBDB1aNzhqVo+VgsxLZph2b2bgL27+EuPZtzSK4p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- "text": [ - "" - ] - } - ], - "prompt_number": 25 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Again the answer is yes! Because we are relatively sure about our belief in the sensor ($\\sigma=30$) even after the first step we have changed our belief in the first position from 1000 to somewhere around 60.0 or so. After another 5-10 measurements we have converged to the correct value! So this is how we get around the chicken and egg problem of initial guesses. In practice we would probably just assign the first measurement from the sensor as the initial value, but you can see it doesn't matter much if we wildly guess at the initial conditions - the Kalman filter still converges very quickly." - ] - }, - { - "cell_type": "heading", - "level": 3, - "metadata": {}, - "source": [ - "Example: Large Noise and Bad Initial Estimate" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "What about the worst of both worlds, large noise and a bad initial estimate?" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "sensor_variance = 30000\n", - "movement_variance = 2\n", - "pos = (1000,500)\n", - "\n", - "\n", - "dog = DogSensor(0, velocity=movement, variance=sensor_variance) \n", - "zs = []\n", - "ps = []\n", - "\n", - "for i in range(1000):\n", - " pos = predict(pos[0], pos[1], movement, movement_variance)\n", - " \n", - " Z = dog.sense_position()\n", - " zs.append(Z)\n", - " \n", - " pos = update(pos[0], pos[1], Z, sensor_variance)\n", - " ps.append(pos[0])\n", - "\n", - "plt.plot(zs, c='r', linestyle='dashed', label='measurement')\n", - "plt.plot(ps, c='#004080', label='filter')\n", - "plt.legend(loc='best')\n", - "plt.show()" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "display_data", - "png": 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UOnD0HgBYFgGdPHkyPvnkEyQnJ6Ns2bJo0aIFXnzxxTx9Pnre3t7YvHkzPvjgA3z//fdY\nsGAB/P39ERYWhnHjxtkUJXBG7969MWrUKHz33Xf47rvvAEjVtJwGSERERERkn8lcSGc4q2FOAAyl\ndvWSk5MtJYuJChuevw+eqKgoNGnSpKCbQQ8YnlfkCjyvyBWc6b/nBefYEBERERFRocfAhoiIiIiI\nCj0GNkREREREVOgxsCEiIiIiokKPgQ0RERERERV6DGyIiIiIiKjQY2BDRERERESFHgMbIiIiIiIq\n9BjYEBERERFRocfAhoiIiIiICj0GNkREREREVOgxsCEiIiIiokKPgU0h9ueff6JVq1bw9/eHm5sb\nnnjiCbi5Gb/Stm3bol27dgXUQiIiIiKie8OjoBtAuZOZmYmIiAgAwLRp0+Dn54c//vgDJpPJsJ/J\nZDJsS0pKwpQpU9CuXTu0adPmnraZiIiIiMhVGNgUUpcvX8apU6cwY8YMDBkyBAAQERGBjz76yLCf\n2Ww2BDaJiYl499134ebmxsCGiIiIiB4YHIpWSF27dg0AEBAQYNnm7u4OLy8vp55vNpvztT2pqanI\nyMjI12MSERERETmLgU0hNGjQIDRp0gQA8K9//Qtubm5o164dJkyYYDPHRu/s2bMICQkBAEycOBFu\nbm5wc3PDv/71L8s+V65cwQsvvIDQ0FB4e3ujdu3a+OKLLwzH2bx5M9zc3LB48WJMmDABFSpUgK+v\nLy5duuSCd0tERERElD0ORSuEXnzxRVSrVg3jxo3DsGHD0KpVK5QqVQrbtm3L8nkhISGYNWsWXnrp\nJfTu3Ru9e/cGAFStWhWAZIGaNm0Ks9mMESNGICQkBBs3bsTLL7+MGzdu4J133jEcb/LkyXB3d8dr\nr70Gs9kMPz8/17xhIiIiIqJsMLDRMbWb6NLjm38fny/Hadq0KTw8PDBu3Dg0a9YMffv2BYBsAxtf\nX188+eSTeOmll1C/fn3L85T//Oc/SEtLw8GDB1GiRAkAwNChQzF06FBMnjwZI0aMQGBgoGX/hIQE\nHD16FD4+PvnyvoiIiIiIcotD0QiAzLlZtmwZHn/8cZjNZly/ft3yr1OnTkhKSsLu3bsNzxkwYACD\nGiIiIiK6LzBjo5NfGZXCKCYmBrdu3cLcuXMxd+5cm8dNJhNiYmIM29QQNiIiIiKigsbAhgDIujgA\n0LdvXzz//PN296ldu7bhZ2ZriIiIiOh+wcDmH8Z6AU8lODgY/v7+SEtLQ/v27e9xq4iIiIiI8oZz\nbP5hfH19AQA3b940bHd3d8dTTz2FlStX4sCBAzbPsx6GRkRERER0P2HG5h9Avxinj48P6tSpgyVL\nliAsLAzFixdHlSpV8Mgjj+DDDz/E5s2b0axZMwwZMgS1a9dGbGws9u/fj5UrVyIpKakA3wURERER\nkWMMbAox62FlJpPJqW1z587FyJEj8frrryMlJQWDBg3CI488guDgYOzevRvvvfceVq5ciVmzZqF4\n8eKoXbs2pk2bluVrExEREREVJJNZfzm/EImLi7Pc16+topecnAxvb+971SSifMXz98ETFRWFJk2a\nFHQz6AHD84pcgecVuYIz/fe84BwbIiIiIiIq9BjYEBERERFRocfAhoiIiIiICj0GNkREREREVOgx\nsCEiIiIiInHnDnDqVEG3IlcY2BARERERkahTB6heHTh4sKBbkmMPfGBTSKtZ0z8cz1siIiIqEGfP\nyu1vvxVoM3LjgQ5svLy8kJycjIyMjIJuCpHTMjIykJycDC8vr4JuChEREf1T1atX0C3IMY+CboAr\nubm5wdvbG6mpqUhLSyvo5lAhcfv2bfj7+xfY65tMJnh7e8NkMhVYG4iIiOgfql49GYZWsmRBtyTH\nnA5stm7diqlTp2Lfvn24fPkyvvnmGwwcONDy+KBBgzB//nzDc5o2bYqdO3dafk5JScEbb7yBJUuW\nICkpCR06dMDMmTNRtmxZyz6xsbEYOXIk1qxZAwDo0aMHPvvss1yvTmoymVCkSJFcPZf+mQ4dOsTV\nlomIiOifKT1dbj0KX/7D6aFoiYmJqF+/PmbMmAEfHx+bq8kmkwmdOnXC1atXLf/Wrl1r2GfUqFFY\nsWIFlixZgm3btiE+Ph7dunVDZmamZZ++ffti//79WL9+PdatW4d9+/ahf//+eXybRERERESUrdWr\ngQMHgKpVC7olOeZ0KPbYY4/hscceAyDZGWtmsxleXl4ICQmx+/y4uDh8/fXX+Pbbb9GhQwcAwIIF\nC1CxYkVs3LgRnTt3xtGjR7F+/Xrs2LEDjz76KABg9uzZaNWqFU6cOIGwsLCcvj8iIiIiInJWtWoF\n3YJcy7fiASaTCdu3b0epUqVQo0YNDB06FDExMZbH9+7di7S0NHTu3NmyrVy5cqhVqxYiIyMBAJGR\nkShatCiaNWtm2ad58+bw8/Oz7ENERERERGQt3wKb8PBwLFiwAJs2bcInn3yCP/74A+3bt0dqaioA\n4OrVq3B3d0eJEiUMzytVqhSuXr1q2Sc4ONjwuMlkQkhIiGUfIiIiIiJykcmTgfBwYNu2gm5JjuXb\nrKCIiAjL/Tp16qBx48aoWLEifv75Z/Tq1cvh8/JjvY6oqKg8H4NIj+cUuQrPLXIFnlfkCjyv/pmq\n/P47im/ciL9bt0asj0++Hrt69er5ejxrLit3ULp0aZQrVw6nTp0CAISGhiIjIwM3btwwZG2io6PR\npk0byz764WuABD7Xrl1DaGiow9diBSvKT1FRUTynyCV4bpEr8LwiV+B59Q92d/RU1YoVgXw+B+Li\n4vL1eNZctkBnTEwMLl26hNKlSwMAGjduDE9PT2zYsMGyz8WLF3Hs2DE0b94cANCsWTMkJCQY5tNE\nRkYiMTHRsg8REREREbnId9/J7fXrBduOXHA6Y5OYmIiTJ08CADIzM3Hu3Dns378fJUqUQPHixTF+\n/Hg89dRTCA0NxdmzZzF27FiUKlXKMgwtMDAQgwcPxpgxYxASEoLixYtj9OjRaNCgATp27AgAqFWr\nFsLDwzFs2DDMmTMHZrMZw4YNQ/fu3V2euiIiIiIiorsyMgq6BTnmdMZmz549aNSoERo1aoTk5GSM\nHz8ejRo1wvjx4+Hu7o5Dhw6hZ8+eqFGjBgYNGmSpdubn52c5xvTp09GrVy9ERESgZcuWCAgIwJo1\nawxr4ixevBgNGjRAly5dEB4ejoYNG2LBggX5+66JiIiIiMixfJgHf685nbFp27atYSFNa+vWrcv2\nGF5eXvj000/x6aefOtwnKCiIgQwRERERUUHq3r2gW5BjLptjQ0REREREhYynp9xWqlSgzcgNBjZE\nRERERCTS0+XW3b1g25ELLiv3TEREREREhczBg1I4wK3w5T8Y2BARERERkahTp6BbkGuFLxQjIiIi\nIiKywsCGiIiIiIjEwoVAeDhQCKsUM7AhIiIiIiLx99/A+vXAyZMF3ZIcY2BDRERERETC4+4UfFUd\nrRBhYENERERERMDNm8B//iP3MzK07TExwLRp8vh9jFXRiIiIiIgISE3V7uszNr17A9u3A5s3A6tX\n3/NmOYsZGyIiIiIiMgYz+ozN9u1yu2nTvW1PDjGwISIiIiIiYzAzbJh2v0QJuQ0NvbftySEGNkRE\nREREpGVsKlcGatXSto8cKbd9+977NuUA59gQEREREZGWsfGwChFeeQUYMAAICrr3bcoBBjZERERE\nRARUrAgcOgS4uxu3Fysm//LiwgUgICBvx8gGAxsiIiIiIgKKFAHq1HHNsStWBGJjXXPsuzjHhoiI\niIiIXMdsBurXd/nLMLAhIiIiIiKxbRsQHg68/7627cQJIDISuH49d8c0mYD9+/OnfVlgYENERERE\nRCI6Gli/HvjzT23bxIlA8+ay/T7GwIaIiIiIiISqiKZfrHPxYrmdOPHetycHGNgQEREREREQFQX0\n6iX39YGNcuuW7bZevYDAQGDTJte2zQkMbIiIiIiICLh9W7uv1rTRM5lst61cCcTHG4euFRAGNkRE\nREREZMzS2MvYuGUROiQmZn3cexD4MLAhIiIiIsqLLVuARYsKuhV5p8/SfPCBdj8w0HibU7duAY0a\n5b5dTmJgQ0RERESUF23bAv36AadPF3RL8kYFNl27Ak2aaNunT5fbpk0dP9feMDXr47qYxz15FSIi\nIiKiB1XRokBCAuDtXdAtyRs1/Mzd3bj9ySclePP3z91xGdgQERERERUCvr4S2FgHBIVN+/bAoUOA\nn59xu7+/46CmYkXg3DmgWzfHx83MzL82ZoGBDRERERFRXqiOe1aT651hNgPDhgG1agGvvZb3duWU\nvz9Qp07OnrN2LXDnDlCzpuN9mLEhIiIiIioE8iuwOXcO+PJLCTAKIrDJjdq1s9/HwwNo0MDlTWHx\nACIiIiKivKhYEahc2f5QNLPZ+eMkJ8tt6dL5067cOHsWeOwxYMgQbdv+/cCuXcaSzkuWAK1bA7Nn\nZ3/MsmXlGC7GwIaIiIiIKC/27ZOKaEFBxu0DBsiwstRU546jAgdf3/xtX07cuQOsWwds365tGzQI\naNYMOHVK23b8OLBtG3Dx4j1voiMMbIiIiIiI8qJ7d6mI9ttvxu0LFkgAEBXl3HHu3JFb68n795LH\n3Zkq+gU6//pLbocO1bbFxMhtcPC9aZcTGNgQERERUcEZNgyoVw+IjCzoluReejqQkuI4M+NsoKIC\nm4LK2Hz/PVC/vty3N+H/5k3t/q+/yu2rr8rCnd995/r2ZYOBDREREREVnDNnpMTw7dvZ77tkCTB4\nMLB+vevblRNeXnJrHdhUrSq3RYs6d5yCDmxu3JAADTBmbBT9IpxXrmj34+OBCxdc2zYnMLAhIiIi\nooKjKok5UxJ41y7g66+BI0dc26ac8vSUW+vARr03Z9dx6d4d6NIFuH5dCzDuJX0wY+/70Ac21oFo\nVvOIEhOBP//MW9ucwMCGiIiIiAqOyr44UzUrKUlufXxc157cUNkK62Dk00+B5cuB0FDnjuPhAezc\nCezYUTCBjQpmwsKARYu07WooncpMAcDixc4f9/BhoFGjvLcvG1zHhoiIiIgKh4IequXIH3/IrSrX\nrISHa/e//RaIjpahdCVLOj6Wo2Ft94LK2HTvDrRtq21ftQro2BEICdG21a1rfK4+m2PtHi3QyYwN\nERERERW8rDrGyurVcpuTbMG9NGiQ48c++QR46y3j3BR7HA1ruxdUAGK9Hk/z5jIXSl8gICeLkd6j\nwIYZGyIiIiJyrVOngHLlpCSyNXd36fh26pT9ceLj5fbQofxtX17oF+DUBwR37gALF8raNs8843zA\nojI2aWn5205nDB4MdOsGFC9u3O7jA1SqZNwWFgZcuiSLb6rnOuLsHKM8YsaGiIiIiFxnxw6genWg\nRQv7j5cvL7fFimV/rGeflds6dfKnbflBBTYmkzHrdPOmlLIePVp+VpPn1XA6RwpyKFrJkvLZli6d\n/b6enkCZMjI3as+erIfXMWNDRERERIVebKzc+vvbf9zR8Ce9XbuAn34C2reXks/OdLzvFZWNsB6a\npSb/Fyli3J6Y6PhYI0dKdqt3b+cLDuRGZCTw++9As2ZAu3Z5O1aDBtnv4+fn3H55xIwNEREREbmO\nymI4mvB/5owEARUqOD5Gs2bA++/LBHzAuQxAejowZAiwbFmOmptjZjNQpQpQubJxuwpsTp+WYEXJ\nqu0qCOzZ03EgmB9+/x145x376wGZzcBjj8nQQJWN2rlTgksVxN28CTRtKsPWnPHII85VvcsjZmyI\niIiIyHWyy8i4u2edrdFTZZWdCWyWLQO++kr+6efB5DdPT+Dvv22368s137yp3a9SxfGx7lXVN7Vg\nqMoeLVgAnDwJDBgAVKsG/PqrfMbp6fL+2rSR+2lpkplKTgZ2776/MmdgxoaIiIiIXMleYPO//8kV\nf+tFHrPTvLlURHvllez3vXUrZ8fOi2nTZIL92LHaNv0cGf3ClzVrOj7OvQps1Lo0KrAZMAB47z1g\nyxb52eNu7iM9XYJC1X6VoVE/e2STI8nMvGeFAwAGNkRERETkSvYCmxEj5Ir/kiXAhAlAvXrAihWO\njzF2rAyNeuMNoE8fGZqWnYoV5VZVI3O15GRjlqZECe2+qnDm4ZF1Wet7Fdio+UCqypwycqQUD1Dv\nIy3NGJhJVyBAAAAgAElEQVRcuSIV6TZulJ8vXJD3ExgI/Pe/tq/TsKGsd+PKjJkOh6IRERERkes8\n9BAwYwZQtaq2rV07medRtaosbnnoEHDjhuNjTJ4stwMGSNWw2bOzH77m4yO3zZvnrf3OsFfJrFo1\nqQS3Y4cEd336ZL9Wz70KbFTGa/ly29c/ckT7OS3NOOwvMxOYOhWYN8/4vPh422pvZjNw4IB2HPUZ\nuRADGyIiIiJyndRUmaheowbw+OOyTQ1hUnM2gOznzaSlyVwQNzfgyy+zf92GDYHt27X5JK7kqESz\nem8eHs4tKrp1K/B//ydZrPHjgUcfzddmWlSpAhw8CHTvnvV+6enGYXQZGUBCgnOvoc/0JCQA585l\nPb8oH3AoGhERERG5jskkHVt9mWP9HI45c+R+duu7JCXJra9v9pkPQIZHtWjh+jLDGRnA+fNy3zqw\nefddyYrUquXcsXx8pIraL7/I4peuoiq4Pf+8/cfffRfYsEEWFwW0BTszM4HLl+X+M88Yn2M93EwF\nqh4ecqxGjfLe7mwwY0NERERErqMPYhQ170W/LbtgRQU2aojZ/eLWLSlFDdgGNm3bavc3bZKFLDt0\nAJo0cXw89dnoj3XsmARHJUoA16/nvc3qc3c0/6hnT6B+fe3nyEjJuGVmyn21Tc+6SIB+btU9KiDA\njA0RERERuY69wGbwYGD6dJlY7iyV0YmJASZOzL/25ZXqtPv5yVA5R1avBt56S4bHZUUNa1MFBwCt\netyNG/kTJKhjq8Dm6FGZD6PWErJeQ6dyZVlvaPNmbZv1PCB77Xr4YQninCnPnQ8Y2BARERGR66hJ\n/vrAplgxqYQWGqpt699fJqHv3Ws7rMnX1zg/Y9Om7F/39m2ppJbdPJK80gc2+oIGhw/LXKBdu+Rn\ne5kYe+ztp6+2pg94csvLSzJfKoiqWVO+j61bgb/+AsqWtW1TpUpAmTLavKEyZWTYnPLWW8bn+PhI\nYYjt2+9ZYMOhaERERETkOmrI0sWL2ra+feXnU6fkZ09PoGRJICJC5pasXQsEBGj7q2FoijMdZbNZ\nyhK7uniACmzcrPIFv/0GvPqqlLauWxf44QfZ7igwSUuTwMhexkYf2KSmAkWK5K3NP/1kf7sqkZ2V\nefMkCC1dWvZXgai3NxAXJ5+Dn5/x8+BQNCIiIiIq9GJi5HbQIG2b6rSreTVpaUDjxsD330t55P37\n7R+rRQu5dSawUcOmnK3ilVuOAhsVjBQpAly9KlXBAMcZm1mzJMtx4QLw449Aly7aY8nJ2n3r53/8\ncdZD4Bz5+GNg3LicZ1P0Qwvd3KQoQOPGsq1NGwlI//pLfq5bV7JzKSmuL+IABjZERERE5Eqq46/P\nnKhhaQEBcn/VKmDfPu1xRyva2xvW5khW6+LkJzc3GSan5qcoKrD55BPjRHtHGZtLlyRoad4ceOIJ\nrXKZ/ljWzz92DBgzRtb3yakJE4D33rNfje6112QY39Gjki3bvh348095LDBQbr//Hnj9dePzVDu9\nvCSLc+uW/OvWzXGwmo84FI2IiIiIXEdfHUvRT153d7fNdmQX2OQ0y2A2O1ci2p5//1uGzC1bZn9R\n0NKlgb//tt2uD0YuXNDut2pl/3VUZiskxPaxTp2kKllysvG96xfTzCk/PwlqEhOlWtuWLUD79pJ1\n+eMPYOdO4OZN+W5atQLCwoDjx4HHHgPWrJG5S8ePG4+p3nPdusC1a7n/vnKJGRsiIiIiytq77wIz\nZ+buufYCm/h4ud2xw7iPot9XX964UiVZ6PLDD21fJzUVOHFC+1k/ryOnczyOHQMeegjo1w+YOhVY\nuVI6/47s3y/DyB5+WNtmPS8GkOFYjz1m/xhquJl1tTFAqpQdOyZBVrlywO+/a8dTrAsuZEdl0E6f\nlhLU774rxQMA4wKqKjt24oT2emqbdQCqf88JCdr6PiweQEREREQF7sYNYPx4uf/yyzl/vr3ARjl8\nWLIZL75o3K46zMePS8UuAOjcWebptG5te5z0dKBOHcmsHDwoGQPV+a5WLefZmvh4mSeiJvI7ar/+\nseRk41yYRx7R7qvAxlEmCtCe6+3teJ8RI+T21VelPHPVqvLaGRnyfh2tS2Pt9m3tM9EHjuPGSQCj\nX2dIH5QcPiyLh6pKb6tWyXH8/IBXXjEGNiqoAZixISIiIiIXWbtWqpA991z2+6oFMXO7MGbHjsCM\nGUCPHtq20aPl1s1NG4KldO4sVbsSE4EVK7Tt48cDX30FzJ5t+xpLlmgV1lQJYtWZ7tTJdqhbdvQT\n/1VA89BDjvdXAZC+Y//UU8CTT8r9gACpBKcvCGBNBTbOfM7697NnjwQcWQVe1urV0z6nuDjjY1ev\naoGNPmMDyGfatSswZYrxOYmJMqzNz0/bpq9kx4wNEREREblERoZkYqw7tfbYW2AzJxo1Atq2leff\nuSNX+K0raykmE3DoELBhAzBwIFCqlPbYqVNa9a9hw4yvERys3VdDsnr1AurXNx7DWSrDorIh+jbb\n4+gzUsFG5cq267xY+/lned1166R4QNeuwNCh9vfVz8Np2DDr49qj5jgNHiwBrp6vrzZ0zzpjk5XM\nTKn8VrOmZNpUoFaypAR2f/5pXIvIBZixISIiInrQTZkChIfbrjjvTLCS18DGZJKr9/qJ7+qYJ08C\n77yj7Vu5srFtZcrI/S5dtGDD3nCrLl2A3r2N7SxdGmjZEqhePedt1lf3ev99qSDmaDhbaqpWytk6\nCBg9Gli+XCqdZcdkkgzRxYsyxMteFTGzWf6tX+/0W7FLnQfvv29cJBWQNkyYIK/x6KMS6FiXag4K\nAr77zrhNBUPq+1GBTXAwMH++BLguxowNERER0YNOZQt+/lmyAfrJ4dlRGRWzWTqvOR3WBRjngXh4\naK+vn5MCGOeJpKcbJ6mrturnvei1by+ZAeuyy7mhSkX/+qtkj7Jy6pRMvldt1nv0Ue3+yZPAZ59J\nIYDRo4ESJewfz94CndOmSWnl556TYX2Onuss1U5PT9tzwNtb1qW5dQtYvVoCxl27jEPkbt2yHY6m\nApv9++UcOXhQflbf/T3g9Jm5detW9OjRA+XKlYObmxvmzZtns8+ECRNQtmxZ+Pr6ol27djhiVYIu\nJSUFr7zyCoKDg1G0aFH07NkTly5dMuwTGxuL/v37IygoCEFBQRgwYADinEmTEhEREeW3PXvkin9e\nr5DfL2Jjgeefl3kngMyncEbTpkCzZrnvoKpARj0/PByYPl1rh5KRYQy6OneWssHz52sZmy++sC02\nAADDhwPffGOsTJZbasFJZ6gOfZUqwJkzjvc7elQCm8mTpdLaoUPAyJHA//5n3E8FdvqFOC9flttF\ni7TqbGYz8MILUkhADb9LSpIAKqt2AFow4+Eh822OHAHeeEO2qeIFAwfKvxEjJItz5oy02/oY1p+D\nu7tkn7y95buoW/f+C2wSExNRv359zJgxAz4+PjBZpeOmTJmCadOm4fPPP8eePXsQEhKCTp06IUG3\n2uuoUaOwYsUKLFmyBNu2bUN8fDy6deuGTF0Jvr59+2L//v1Yv3491q1bh3379qF///758FaJiIiI\ncuipp+SKfHh4Qbckf7RoIZ1/xZl1UK5dk/LK337rfNUta/rhbKmpUgq4cWOgSRNtn4gImVOiz9h4\neUmmoEIFYNQobd+VK5173QEDgHbttMDAWcWKyW2pUjIx/vvvJXthjwoqfH2N2aR166TYwfnz8vr6\nz65kSakG99lntsdVx9AHNvZKRyclAXPnAnPmaMPktm+X9WYczc1RfHzkn6en3NaqBfzf/0lFtAkT\nZJ+jR+V21y45fqVKMpxMZcTS0rRy3QEBEqjqhYXJejjffZfzctu55HRg89hjj2HSpEl48skn4WaV\ngjSbzZg+fTrGjh2LXr16oU6dOpg3bx5u376NxYsXAwDi4uLw9ddfY+rUqejQoQMaNmyIBQsW4MCB\nA9i4cSMA4OjRo1i/fj3mzJmDRx99FE2bNsXs2bPx008/4YS+LjkRERHRvaA600OGFGw78qpiRel8\nlitn3P7889k/d/NmmfyvnwuTEz/+qK1bk54uiz527ixBoxoSVa+eVDa7eFEyGc89J/M4AOnUJyYa\nj5ldBmDmTFnQ8scfpf3Wz8+OmvSfmSnlkCMitFLL1lSn3XqI3uefy3nz7rtA2bJSDEApWVKrIKba\npgIke0PR9EP2VGCjkgfJyVLqeu9ebQ2cO3eyfn/Xrsk++uFlAQGSnVTzmoYPl9vOnbV92rUDNm3S\n2te4sbzutm3S7hs37H/W91vGJitnzpxBdHQ0OuveuLe3N1q3bo2dO3cCAPbu3Yu0tDTDPuXKlUOt\nWrUQGRkJAIiMjETRokXRrFkzyz7NmzeHn5+fZR8iIiKie0YNy3Fzkw7sgQO5n0RfkM6elQpo1os/\nquAhK6qTbG/hSGds2ya3770HFC9unDejOrwHD0r25ssv5ecZM4Dy5SWomTxZO5Yql2zdUV67VjIX\nZ8/Kz1OnSvZBdf5z+p2pICUjQwtyHHXOHQU2KjD56y/b5wQHawtkqkCgeHE532rVkoBMX0VNn7HZ\nv18CQN2oKBw5Yvx+swtsAMkUTZxov0gBIHOBAFnzRk+ffStSRLI49evLZ1+ypASpSo8ekv36+2/b\nAgQukC+BzdW74zNLWZXTCwkJsTx29epVuLu7o4TVZKdSpUoZ9gnWl+sDYDKZDMchIiKiB1R6ugxn\ncWZ41L2iX8/j44+lc+boyn1hlJYGLF4sw6YcyWtgowKCokVlSJN+fkfDhvK9T54sV/4Vfed52jRt\nu8pqWAcqs2ZJCegDB+Rn6xLIzhRJ0FPBzM2bsmil/n1Y8/SU+TVlyxq3qzZGRdk+Z+NGbX7TlSty\nm5QkAUyVKlLgQQ3TmzVLK3MNSCWz554zBjaAZG5UBsaZwObHH2XY2b59to998YWUggZkSNr27TJ0\nDtCC/QsXZD/lbvB12ScQfx6/hPNXYrHjtgnrTSWwI/wZLJ+xOPs25ZHLq6JZz8WxZlYnaB5E2Tth\niPKA5xS5yv10bpX+6iv479uHK88/j9v6ce5U6NxP51VeBC9fjooffggAiFITpAtYiYsXURnA9atX\nEbhyJTwBYPZsRL3wQgG3LPf0v+03Tp5Eic8+Q2pICA78/LNhP3VelTp+HOUBXI2Px0XduWZKT0fF\nSZPglpKCM+PHw6w6vFYqXLmCEADnL13CtagoFDl/HvUAJGdm4tDdYCb08mXoB8ntO3AAmT4+MKWl\nQT+NPy4uDoEAMtLS8KeuLdVjYhAI4Mb//ocrSUkonZAA/aX0IwcO4I5+zoqSkYEKH3+M240aIVY3\nqsiUnIyyffvC9/hxBNydk5SWkoK/HP2uLV2qPjTLphqxsfC3vzdS589H6saNKAoA0dGI2rMHTe4G\nBlEHDxqyP41GjrTJRMQnJuLSnj2opdt26vBhmPbvR1UAOHEi278LFePiEAzg3MmTuL1sGYqvX4/k\n8uVxs2tXlNu2DaEA7lStihQfHxRr1QrRffrgwt2FVUsPGwa/ufPw2caj2HToC1yOTUJV70wkNRiI\nLUGVYH7xK9V6oEEj4NsDcDMdwM0fRzlqTr7Il8Am9G796+joaJTTjd2Mjo62PBYaGoqMjAzcuHHD\nkLWJjo5GmzZtLPvEWK0+azabce3aNctx7GnC/5ApH0VFRfGcIpe4786tjz4C9uxBwBtvGCfwUqGS\n5/PKbHa8Pse9ppvUft/8rtSvD7z+OkoWKSLrotx137Qvp/QXlIsUQYm7/TavYsUM78lwXq1dCwAI\nvXoVoXXralfsz5+X8tEAii9caLsQ5tmzMrfnbr+vQuXKqNCkiWVuifeFC2hy/LhkH6xKKjd6+GF5\nnblzDdsDixcHFi2Cu5eX8Tu4Oy+lxIYNKBEebrM2S+2wMPt/57ZvB5YvR8jy5cDbb2vbZ82SzGG1\napZMkqfJ5Ph7T0/Xhpap+TD6+StKvXrAwYPwKl8eXgEBsi0iAk3U8K0iRdDkkUeMzwkKknk+OgFB\nQQjo2lWG3w0fDqSloVq5coZhZdmeo3fn0lTcu1eKQwDA44+jyrhxluyT75Ah8E1OBjZvhucPK1E2\nci/++HoZpseGYt2jI3Hjhi9wIxoAcAIAilVGkcx0hCXewM3g0nCLu4WQlASgenWUr1Y+6/bkg3wZ\nila5cmWEhoZig+6kTE5Oxvbt29H87oJEjRs3hqenp2Gfixcv4tixY5Z9mjVrhoSEBMN8msjISCQm\nJlr2ISKifOJoXDj9cxw5Ih1Aq85jgclqZfeC4uUlcw28vLQhaN26FUxbqlWTzrPVUhlOuXQJ6N5d\nggi1yGNyslY9S01kt0ddtN60SRs2BRiHdyUlGZ9z9aosthkWpg3hUsO79JmdjRtlrod1YQJ1Lugn\nooeHS3njvn2l8ICefnK9qqam9OghhQTsUa9jHUxcuqTNZVGeeML+MQB5bykp8k8Fj9272+6nhvOl\npGhD1YYP19pvL+ulAiC9jAwJtIcMke8UkM/l2jW5rw/SrGVmynwc9fr66R4//wysWAF4esIM4O8V\nv+Cn49fRv2YvlGj5JspU6osn3l2BRddMuOHpi4a3r2DExd2Ye2wV5t/YjuWHluLqzqk4EDULF4NP\n4fzOaYjaOwdR/Wrhx/ciHLcpnzj9FyQxMREnT54EAGRmZuLcuXPYv38/SpQogfLly2PUqFGYPHky\natasierVq2PSpEnw9/dH3759AQCBgYEYPHgwxowZg5CQEBQvXhyjR49GgwYN0LFjRwBArVq1EB4e\njmHDhmHOnDkwm80YNmwYunfvjuq5WTWWiIgcU50NBjaukZQk1Yt8fXNfItfVXn1VOkIvvKCNpy9I\nzzwj63S0bHlvX/foUWD8eKB2ba3UrfLKK1Ky99NPZe2Uzp0NmZt7KiFBOvpdugD//a/tGjCOpKTI\n9/zTT1pW5fJlyUaphSizCmyefx744AMpe62f25JVYKPmupQpAzz7rKxl0qKFbKtcWdalGTBAjme9\nXmGfPsDs2cDjjxtfr3NnKfNcsiTQurXte1QyMoyBTKdOQGCg/femnlekiOPjARLUfP21/WMAkvVU\nBSYyMyXQeestCZA+/1zec6lSQKtWwO7d8rdBTcr397cf2JjN0g57bde3b+JEmSdz4ICU5AZsFzHV\nF0GIjtYqnwE2Vcz+ungLbx71RFSLMbjh6QtcARBaEgBQIu0OyifH4ZmYw2gWfxFtbp2FJd+bGQJk\npAHpd9+L/py436qi7dmzB40aNUKjRo2QnJyM8ePHo1GjRhg/fjwAYMyYMXjttdcwfPhwPPzww4iO\njsaGDRvgp/tFmT59Onr16oWIiAi0bNkSAQEBWLNmjWEezuLFi9GgQQN06dIF4eHhlrLQWUlMsjNm\nkoiIsqZfTI3y3zPPyBCSH38EfvhBK3d7P7l7YRGtWhVsO5QWLWTIjbNrlOSX6Gj5jn7/3faxpCSt\n01m6tLSxSpV72z5FdQ4PHzaW4M1OVJRUrgK0SeVublpQA2iBTXw8MHAg/K3nZ+gn8ytZBTbqdbZu\nldLLixdLVkStRq8/nvXFldhYyY5ZV6CLjJRJ9KdP275HfQYnPR04flwCt6VLgV69bPdXHAU2aj6O\nyr5YP26P+luqb7N6b2fOAG++qWX9UlKMgU1oqHy/Z87IEL9eveS5vr62RQIAY6GCChXk2Homk/b9\nDh4swdHNm/Kz/nv7v/+zLGiaCRN+Ll4dbddewvpYycgEpyaiU3oMRl7chX1RX+D6jo/w597ZGHt+\nO9rqgxpA/o7cvCkXSgDt96ZZM7lo8Oef2X6EeeV0YNO2bVtkZmYiMzMTGRkZlvtf66LX8ePH4/Ll\ny0hKSsLvv/+O2rVrG47h5eWFTz/9FNevX0diYiJWrVqFslYVJIKCgrBgwQLExcUhLi4O8+fPR4C9\nFJzO3LWu/6CIiB44HIrmWqqTM26cBDkvv1yw7bGneHG5DQuzfeyDD6Ts7Pz597ZNrnDnDrBsmf0O\nIqAFnVu32j6mOqnOZt3++ks+M0cldPMit1e99UGH6mxav5+//pIO7+TJwPz5qPHSS8bHcxrY6DMK\nu3fLz0lJxlLPALBmDdCvn/G56oJ3Wpq2/9ix2u+UdTYCkA66ql6Wni5zdg4ckGDKulqZngpgrI+p\n2t+kCTBpkvwOO5KUJOWM1eeh/57+9S9tbs+uXRJgjBghwUaNGvI7pjIybm4yLycpSQvuzWagZk25\nX7cuEBMj2374wdgG61LK48dLZuvyZck0JSYCq1bJY2lpMAOIrPEIZjbqjhnBDdGz7rPwa/U2utV/\nDrdSMtG9QVmc3jUdV3dOxYawJMwoeQsNE3RD1p5+WssOKer/FHVuqc8wOBiYMkULrl3oPhzMmnNf\nrInCK70fybYCGxER6ahOrdWkVMonquOm1oLIqnNVULLK2l27Bhw79mCcHy+/DMybJ51TVb1Kz7pT\nrqcvTeyM1aulg/3OO8BDD+W8rVmJjdXu60sgZ0f//tLSpOOtPz/NZpk7Ex4uw82UXbvk8Tp17Gcj\n9J+JWo1e0c95uX5dGwJnHdjo91NUfy493RhYqu/CUZDZsCEwaJB87mpfe0GQXmamDP+ynuivAp7f\nfpO5aFn1MXftAtq3137Wf0YPPSRzfKKi5D0HBgKffZZ1m6zf3+jRcl5duiTZujJlZCFNneTKVXGw\neCVccPPBX+264dCRc0gzuaPOJz8iuFEPZMZcR9HUkkhbsRt/Hz6N7Y2HYq9/GWCGFIZASQmeKiXF\nYljXh/DaW/1QZP4YINkMnDsnaxGVLq39PfjhB9vgSv09+ewz4H//k7k6GzbIuXOPhqI9EIHN0XPX\nEXn4IprXdX21BSKiB4Yay22vBCrlneoIqs/3fsyMlS4tK8rbm1ht7wp9YaWqsZZ30E/IKhuzfbvc\n9u9vm1mwJ6tJ4PmpZEnn9jt5UjrWeq+/Lp1OQIZDFSsm9zdtMgYCasF0s1kyAr6+8r7i4uT8qF/f\nWGXNWtGikiVLTtZ+D1QHt359WbPo0CGZw6SnD2zeeEPmNvn4aJPkhw2TTvW8eVJ5rUYN+f164glt\ngr8aDpVdpi08XOaoJCbKULemTeX1331XqvQdO6bNmXFEdeibNQM2b7Z9TeviCXrTpskcr7feAqpW\nlW3WwVjdunL7ww/Aa6/B/OooxL47Gee+Xow/Ig/hW6/y2HM5ARn1B8l+MQCCZdTUmn3XgYBGQACA\nJbr1avzLoGRmMno83hS+yET5Imb0/Xwcyp06DEzdBnh5aMMJf/tNPp+9e+X3wF5mU/85qPcZFCTD\n3KpXNxYocKEHIrABgC9/3sfAhogoJ1RHW/1nRPmrMAQ2PXrYdnoVdTX2xIl71x419MjTM38rpKmr\n8UFB9h/Xd0Sty1/rA7vhw2VY1YwZ2kR4azkNbFJT5Wp8+/ZaFtWRyZOl2pWXF+BstVh/3UoqoaHS\niR82zLiP/v0XKwa88AIuJCSg/IwZsu2PP2ToVMOG8r34+kqlNLVgoz0DB8q/cuUk03DrlmxPT5fh\nVKdPS1BdrpwENlWrSlARGioZArWvr6+cgxER2rkYGyvnZ/Xq8pm88YYsngrI37O339bml0yZIhPr\nx42T17OWnq7NT3n3XcnoPfOMtMvDQx7PyJChYamp8ph1gKKCO19fY1CycKGcD2qoo73AZtUqCRT6\n9tUCG+vAyNsbt++k4KermfihTgR++9MX8T0/uvtgEIDbcHMzoVaRDFTJTETlM0fRPP4Ckt08cP6D\n/+Li53OQmZCIzKefhveunah0/ABqJN1A+6olEDDmA+11nm4qgW758vKeevYEvv9eHrt9W7JyXbvK\nfKNff5XtX30lQWRYGLBkibHdHTrIuQNIQHQP3Id/ZXPn+82HEZdgJ51JRET2qY72PRoi8I/z3Xdy\ne+yY3Ba2Ig2qc6nan19iYmSyvr1M0KefSudw4MD8fU3r4U/W9Ot9WLfrxx/ltm5dWdtk717gtdcc\nv5aqBrZokXNt+9//ZL7CY49lv6+qZBURoXWCs6MfSvj007aFIj75xNiRjo4GJk1CbLt22rahQ4E2\nbWRCvpr8ry+DnBWVLVNBUHq6BIedO8twPfV5N2okn8XFi7JuzsCBcu7duSMT0u0F2Koj/fnn2rYf\nf5RgRvn5ZykK0aWL/TlW1kGEvmiC+p3NzJRsUd++9jPcjuYrjhkj5ZjVpP3x4+W966miDQkJlgDp\nSkIavizdCO9WbIMB/1mI8HdXIviJj9F39238GFwL8W5eKJqegjqJ19Dj+jEsyDyM+M2TcOTSj/hp\nwyf4DCfR59oh/CvmIMYPaosvvc5ibuI+fPNSe8x6+2m8eWEHnki9jICdVpmXMmUk++XrK8H90qXa\n/Dv12b35pgwvCw6Wn9u1k98JNX/n5k3binLA/VcV7X7W9qFKuJOchu82HSrophARFR76/7Qp/6l1\nMbp0kdv7IWNz4YJcRVbrxamhN6++6vg5+d3uNm3kqvzx47aPHTkit4sX5+9rZhfYlC6tdTCt53yo\nbI9a+wWQ4U+OqEDQ2eIBqhKburKdFZVxUtkPZ+iHDf3f/xkn/AMSeNgZruWmOvBVqmjfVZUq2po2\nzlqwQAvIFi2SMs3670N1eH/4QSbSL10q67a4ucmikS+/bFi4FTVqaMPwhgyR26eflnkdX3+treOi\nqO8jNRV4/33b9lmfE2pYHmC8+KP+XtrroDsKbNRn/eST2jbrSr9qUc+FC5HkWQT/7f4yqg6fh6E1\nemB85XZYsP0U1u/5G6npGWgV7IUZJ3/B+chpiN/+AQ7tmYlVh5ag36kd8MtMk2F9gCyKCgC//CK3\nO3fK736ZMhKIBAdLFmntWsngqeDdHtU+6+ycOme8vCQorVlTAtMSJYD//Efbb9QoyURu2WJb4MAF\n7oO/snk35HGpsjBz1R5kZmYx1pOIiDQciuZaqgMUESHDNapV067m58SKFXKVXb8wYm7t2iVDQtRE\n5xqI7VYAACAASURBVPh4uYJ89Kjtvqqk8Rtv5P119bKab5DVfI28yC6wAWQY0tSptp189bM+IMjq\nOPaGO2WlcmXn91WBzdmzWqng7Og74jExtoHNH3/YnWCf6eUlC0yWLCnBXvXq0kFVV+qdzUDWry9D\n2AAZFufmZizI0KeP/Nyvn3aOe3howcy8eRKMK+nptgt9RkcDI0dKJi2rTJZ10ANIZkL/fer3Ua8z\ndqw238ReYOPtLb8v1usbqfPuk08sm8ypaTj5yUz89Oq7WDJzGZ69WhxNG72AttfKoFzT1zA6oRSS\nUtIR/kg1vP5MM8z9dw8sr5mOi03SsdX3OEZe2o3yKfHGMsvWWUa1CKhqs9ks82Rat5Z1mlSVte+/\nl5/tBTa//y5ZtX375HPYssX4+OXL2n6KvnS22Syf1Z07MnTw1VddUynQygMR2PRuXQtlS/rj4Olr\nWMKsDRGRc06elE4GF0B2DdUBOnhQxqD37y9XLK0Ww8vWk0/KBPb33st7m9SV/uRk6XhklbVTneie\nPXPW+c6OGlKkJuXr5TbITkqSORaOMj0ffSRBnHUJY73Ro2VSvfXcGHuBTVYT0lVZ70cfzb7dgBZU\n6IdPOVKpknTcDx40rtuSFX1H/Pp1207wl1/Kd6ICsrulh1PLlpW5P88/L9tVBlKfuYiPlzVqBg3S\n5lxk1QbrymqenlpgoZ/X5O6une/DhxuPpQ9sVAc+JkZu4+OBuXMdt8Ne4JySYhv8Ka+8Irf6Kmb2\nApu2baXcsz6zpNoKIG3rNpzyKY4xVTqh3OkQhP0Ug+4HzOjzw2EsdS+N3QHlsAVBuOnpi8beaVj9\n/rP4ZcpzmBpeHc8nnUbvLyahzMeTpOx0mza2r9+9u9zWqiVZsTVr5GcV2PTuLWtWbdsmWVFVLESt\nB6QWC50wQbJkgAR4v/4qx+7a1fbCilobSL+wq6q+98UX8n/L669r39Wbb2ZfDS4fPBCBjbeXB8YP\nlC96+vJdBdwaIqJCIj5eOpLZrBVGuaQ6QNZXw5290m4tP5Y00M8xSE+XhQABY4lfRT+XQL+QY36x\nN98htxmb6GiZz/Dcc1IO19qSJZIxe+ednB+7UiWpAqaGyQFZZ2zUQo725hnY869/AcuXOy7ioFex\nogQSgPNBoDoPhw2TK/bWbVcdTzVcyrrssXrfvr4ydDE2FtizR67k//STBB7z5tkGqomJcq5nZDgO\nbJYskaBT305AK1AAyPAmvbQ02bZkiZShbt9eOvSKmuxur9S2vYU9339fO+9KldKGokVEAOvW2c5J\ncjBXxGw248+GrbCzRGXsWLsD6/44he8Cq6POwy/Dq804VH90JD6u0AKXMzxQMj0JbWPPoMvNU/j4\n7w34rW0xrPM9ib93zcCe5kXQvfndwGPdOi2AdXOTYYCbNxtfePhwCUh+/VW+A/3aMsePy/el/849\nPSWwKV5ce99Ll0rGaeJErYy4eo6HhwS4c+fKZ12hggRx9rKg6qKNWpfn4kWZf6OoYhQu9MBURevX\nqT7GzN6IPccu469TV9GgWmhBN4mI6P7GBTpdS3WArFcsV5OpndWggSyeOHhw3tsUF6fdT0nRChyo\nQgF6Q4ZIp3b27NwHY1mx1zF3dhFMa/qr7P362a5wnpwsV6D1799Z7u5a8D99uswZyGpNopwGNrVr\ny7/sJCTIMDA1B8i6gx0dLQFqaKhxOJbaz99f5tjs3ClDElVGqUsXmQxerpxkjbZtA0wmNAGk41uv\nnlzxX7BAsjs//qiVVNYPrbReC+i112T/2bNtA5tSpaRjffOmnIPt2xuzbbdu2Q8eAwJk/oZ6fUCG\nWJ04YXz+gAFAt27aoprPPCMBj71gWgXwkyfLkDP1sR05gt8uJcGtajAOlmuKr0o3hinAH6XeWw0/\nf18U9fZCmZL+yMjMRHJqOrb+dR5HgjpKkbKPN8pBqve0HC8oLQkt4i/gzSqeaHlgK0xnzsgDTZsC\n40dKZiw5Vr4/RV/RTn+BxMtL2t2hA/Dvf8t3V66c/L5uvPvaxYtLoFK/vvGzzMiQc/iNNyRg6Xm3\njarIREyMBC1qzST9ELQrV2Suzc8/a9nfp5+2LaiggsPly43bHVUlzEcPTGDjU8QTfdrXxazVUVj6\n+2EGNkRE2WFg41pz5kgnwXpcf06ro6nOuLoKmhfWgU1WRo6UK/SzZ+f9de2xl52ZNEnK6qrJ5s7S\nV/6yV20tq4nfgHTmP/tMrs6r4UfKww9LFmjXLukwN26cdVnm0FAZRhWay37I119L5/2334yZiPR0\nY2ED6/fy888S/A4aZBwSVaeOVBhr0kQ6/5s2aWuK1KmjZWRKlJCs161bkokB5Cr98eMyPMlkko6q\n/vPVD8+zDmxUW4sUkc+0Z09tCFTnzpJ5qF9fjqeGTCmtW0sQsnSpZCDUJPigIPkennpKgrwTJ6Sz\nbf3aGRnagqAAMGQIMr6aC7OvLzJS05GUmo609Az4fTwFpz//Bn+ENsS1+ZvxZ9QdXAopj1SYcLx4\nD8SXvBtMVFPHBQ4fdFwNLjAzFVUSb8C7Xh34lywGM8zocOssXvj2AwRkpMCzfj1g4HhgrG50kQpY\nVLZDtfv4cWOJZH1gExgof1sWLTK+z3nztPu+vhI4pqUZJ/4vXSpD1RITHS9e6u4uQ5UBraIboP1f\n8eqr2u+odVATGOj49yO/Kyza8cAENgDwVJvamLU6Csu3HcX7L7SHKT/S9kRED6qsVp3/p9m1S650\njh2bf5/HypUyGV2/3ojJlPNActEi6cTktLNvj354TkqKdGw3btSubFtzRWGJfv1kMriahK4XGmoM\nUpylz9jkJrA5d06qcnl52QY2d+5Ix9nNTa5Et2yZdVusq0LllMrMDRggQ74U67Zb/6w6mNad1ccf\nl3+AtiinCgTU+iqANldCf9wFC+SKfYcO2lX/4cPlSv/UqVkHNipw/u9/JRN38qQsQvnNNzLMS78A\nrPXvhNkswwbHjdOyFlWqyFCy+fMlAAZkaNPMmRKQDR8uE9mPHAEuXYL5wyk406IjvurwHLYsP40/\np+5GaloGMgxFptyBh1/WfrwJ4ObduSRuXiidchtBHkDV2MsY+FwHVOgZjvg7KUhMSkVcYgqu3LwN\nTzcTUk+dxhXfILw5/32U2b8b+HKfVjDhww+B9LufzcyZ8vdg/HjtNVWWculS+bxV3/XZZ42fif57\nDQuTog7WFwf0wwj1BQR27DDup7KKanimdbU4k0nmnK1YAYwYoW3Xf0/2/o61aCHD4ebPN8656t9f\n3ltO5xfmwgMV2LRuUBElA31x4sIN7D56CU1r57AkIRHRPwkzNhq1wnqlSs6tLu8M1ZneuVPbpha9\nzAlnF2J0xsCBwPr12lAf1ZmtV89231WrjEN+MjPz51xRHTR764HklrOBjaNATXXmFy2S4Vo1akiA\nExcHqCFDzg6TW75cOpM9ejifZbt+XUr1BgYCISGS5evc2X4bARmSpZ+0DWhBhqOr8IDW8VXZFP0Q\npaVLJSjTBytqGNKdO9q+165JJ3XSJONn7Shjc+2aceK5+t7V8Y4ds53Hojr36enaa3z0kRRmuHZN\n+y7UY5UrI3PoMKz86GtsmbsMZ68H4aBfKZzxKQZsNQ6zdHczwdvLA16e7oiLv4OqSbEIS7qB6ndu\noG7iNYQt/gruwcGo1qIRQuKvy9pK8cWAJ1oANe0MQZw+HfjPazJkVGU39N/VE0/IMLfbt+W9Nm8u\nf2N+/FECNX3xFv13Z11BTDdMzm7hDcAY2Kj71t+L/rFq1WRI2vvvS1nn/fu1NpQqpWVtFP1Fn7lz\nJejU/31Sv1/Wvyv2LmK4yAMV2Hi4u2Fw14aY8t0OfLxkJ5a/6+AKFBERyRj7qCjpeOsXKPwny88M\nhfUcgc8/N65nUVD0cxGyKr2sn1fToEH+FC8ApKzyG2/kTwZKadhQqjetWSMd89u3jfMTBgyQ2xUr\nbNcRAYzf++nTEtisXCmTn1Uw56hgwJ9/yjyVhg0laHzzTZlcfeKE84HNpk2SxXjySenkL18u2bXb\nt2WSfqtWWic+NNR+6W8VMKhO5bJlMv9i9WotcLXu7Kp9K1eWwOGzz7Q5F3p37tieI56e2tyjokWl\nbLOeytj4+xvb60zpbWXyZK2EsocHkJaGFJM7ft53HldTL8A71hvRFVri4K547N72GU5fjgXKNbU8\nPSAjBc1qlMarKz7FIzXLwnvjBhTx8oCHu3ynZpMJNmd1g0oy5C3+bubw6lXJCDn6LtXn8tdftu8R\nkNLKPXtKllK95zFj5J+z/v1vyaBkRx/YlC0rbVLfddGi2hwj/X6qMEiJEtkv+qq/sNGggXEYHKD9\nHkVEyGKmiru7BHWOArJ89MBdphvZ+1EU8XTHim1Hsff45YJuDhHR/UtdRXNFxavCRl01VSVt84N1\nRzA5WSbk5nQF7rQ06Vharz+SH6pUkVK1akE/PX3HMyQk/wKbsmVl7kh+zBlS2reXuUAPPSTDygIC\njCvV/z971x0eRfVFT7KbTYEkBEjovffeBEGUIkWKVBFEFCmCKOJPAcUuiqAUUQGxgTRBBJQiIIKA\n0kF6751AaOnt98fh+t7Mzm42IRRhz/fl22ybffPmzcw9t5wr0Q9RFDNDJzbx8UzxOXeOz6VeoHhx\na+KbkMCIkRRTi0Fvlo12hW7dKAcOGNeHzQY8+iiPz+zZ7kmojANQHvcOHdjvRhedkDGNG0fBAvHI\ny7GNjXWudwH4WvHiLHQX1KzJqFRqKglYy5bG7zgcjCqZj7MY/TlyMNohPVV06Gtt5kzg3DnENXwE\nCwPz44Gqz6LdyMXoN3YRnr2QHUOLNsKMY7E4fDoKBSJC8HrT0vhuz8/YsHkSLm77HEtaFUazSweR\nIywrskz4HPbcuf5NvbJc0fv2sa5KMHy4sc7EDL3uqW1bHn+z1Le7Y7diBRXrZs2y3n6BAko5Tkdq\nKuup+vRRKWlCWJ55hsenShXVYFNfj/r8FipEdcTffnO5i/9CZKQB68ignB/m+r3ffqNjp1q1tH/j\nJnHPEZu8OYPRvy1vTMOn3Xpm6IUXXnjxn4W3QaeC5H6b03tuBmYj5pVXaCSb0zuscP0606CSkqhg\nlCULxQgyG716sS5B964K9L4q0un9ViM+noZiRtZknjxGNTQ97U8iE64U6XSyKQQ0MZEESSd4Zcs6\nN+CU78r5JIaup8Rm0SIVHYuKIll46SWSbUljXLWKqlfR0a4LsMX4luMmhKFiRfWZ3r0Zvdq717op\nK8B6jE6dcEVPMZo+HRg6lGISYiifPOk+nXDBAq7jpk2NryclMaK1YQOjbJL62aIF0/9eeQUoWBBR\n9gCszFYYG2NseGvUHJRp9T5almyHLcF5kTc5Fs+d3ozH4k6i9+lN+GbvPGx4pzUOTRuA932Pofu5\nf1Dj2mnYU5KBL7/k9hcuZPQlMtJIRsx44AFGyQBFAJKTaZzPmKEIrEDfVmAgDX4fH5LBiROZ3uiO\n2OzcyXPbVTTDVfrn6tUUC5g4UY2zWDFGh6pUYR3Pli2qx42+jvXaHLud5EmEHdwhXz6St0aN1Pqe\nMIGP9eqpZp26+lyTJowIjh+v0jpvIe45YgMAL3eoA5uvDxb8tQ9nL1lI+3nhhRdeeOElNjpuBbHR\nC4R1eBKx6dSJ6TBLlqjjlN5Iz80gNVXl+D/2mOvGlxnBmTOMhlipovXsSeNQ69SebkhUQRS/9KaU\nrtKfHnlEeaDj41W05upVI1nat48ko3t39ZoYuutuKF2JoTtsmGfHTE/5u3yZfW1GjzZKQJcpQ+M1\nKEgRCzOefpqPAQH8jBCgK1dYsL97N8lO/frG7y1dqgrdAUZwe/VCjG7orlqljGedzHiyf2bPflIS\n0wEbN2aRuRybqlVxvfszWHDwMspv80P2eoPRsPLTqDliOd7deAFHfQJRLPYS3gy+iD2JazBp/y9Y\nkOMMJuz/FT3ObkONiAD42W3GyGZ0tFJUA1TkQ4iuNB91BUlnTElhOliXLs7S6Dqx0UnIlSuMprzy\nintiI2O5ft14LZb0wa++sh6blaPj4YeZQqkX/AOsHSxYUKX1CQHJCObOpTCARIc6dmSvmu++4/ly\n5QodIadOkXi99pqK4Jil728B7klikzdnMB57oBSSklPw3ZJtaX/BCy+88OJ+hJfYKOzaRUMwM/ss\nSKrfo48aX7cqbjdDDKH16+np1F+7GcyezVx/ybs/dozCCWZVNN049GS87lCjBo3ikSP5vFAh1olY\nefvFAEpP/YEZMvYJE0huvvzSmtgkJpJIzZtHT7eQlbg4JYcMUETB3MR261Z62s2phQEByls9cWLa\nktoJCca5lt4hAI3gAQP4/4ABjJi4gxiNcXFG9ak5c2jAL12q9ltHzpzO0aX4ePjoYw8NVdcLXVLY\nkzXZo4f6f906oG/ff499kq8NyUnJWJS9BNrN3YccL/+E1pfzYxeywC8lGRWvn0WZlGtoZ7uEn3bO\nwi5sxDsLxiFE+MHgwWrbS5bw0Wpd5TeJSb31FiMJnTsr9TDAWJelP09Odq2sp8+TTmxknu12RkY/\n/xyoWtV5bEL8vvvOGF0bN45RLz0tLiPIm5eRkvXrSUAuXFB9mC5fZs2bNOXMCMLCuF/FivHczpaN\n+543L6ODO3aoY+NO2CKTcE8SGwDo1ZKL56uFW5CSYuEV8sILL+4dbNzI3g9epA9eYqOQLx9TMTJT\nIU4MoFdeAT780Pl1d5A0IUmJATLnOPXrx5qOH39kVCI+nsamWYFJNw49SYGLj6f87759zu9t2sRH\naeboznutR3GsIjqeQAxKOZY2mzWxmTOHyk5t2/J5u3b06NeqRW+5GMOJic4qT8eO8TOPPWbcDzOR\nSYvYCAkKCWFU5vJlRnrGjaNRGBCgxiFrKDmZn5NI0ZdfMo1LGjPqeO45pgHJPOjzI5g+3Zm8xsUh\nrkgRZWjrxK5zZ3r/ZSxpIX/+f9PiLvo4sHr3KSw+n4ynSrdF0MoUBK13oEXFJzE3vCwSfO0oEhuF\nEbZjuL56OP7ZNAG7k/7GnFVf4PHIPfBf/7dxX/RxT5vGR1m7em3RihXO9R3LljEqFh3NSAfgHFGQ\n6NjQoUoAwbzPXbuq+qKICPW6jO3kSZJcm00V5y9dykjGlCnGPlf67z/0ENfXhQtKJltHes6P1FSu\nqY4dGa2Rc+PqVZK80aM935YrCEm3240ERr+WeCM2GUeT6sVQOHc2HD4dhe9/80ZtvPDinkbNmryJ\n/f33nR7JfwuLFvEG17z5nR7JnceOHTQydCJxsxADKCXFKNXqSQTk+HE+LlqkXnvtNUYXMmNMTz/N\n88VVmpsYI2FhNJrDwpha4grjxjFVx1wIrhtfISF8LgTNykusjyM9RO6rr2icRUXRkC9ZUhlXNhs9\nxlevGnvQiJEpioBNm3IfKldmFEMU7JKSnImN9H+5ehVo2ND1uNKStJY0tNBQ5dX+7juSlKlTWe+h\nrwGA9SlhYcqTv3MnP3PaJJhUtSpJqdS4uCI2o0YxAjV/viJ+8fGIbNNGkQVzxEq2dfo08OefTLmS\niJwJR85EYVxAcRSrNQA5X1uA+i9+h+aHgjA1dyUkpgIJickIcNgxKP4g/tn4JQ6vH4tXA87DMf9n\nbsDf39jbR//95GQW9+fOzfqX8+dV6pY+ZpvNWq47NZXERtaabnj7+ytRh3nzlKS4+fw9d44NTZs0\nMc6B/rm5c40pjTNnkkR3704BBf03zfjlF9ZN6dEpGbsV3n2Xc6KfSx98wKaaa9YYz+PMlF6XKKE5\nVVIn/reB2NxTcs86bDZfvP9MQ3Qd/jOGTl6B9g3KIjjo1k+oF154cQeREW97UhKLSv39nVOG7nWc\nOsUbej6L3gz3G37+mZ7LN96gQXjgAFPASpRwzlf3FGJYmNMvMqoulpxMQ0vvLZPRMQGMJoiQwUlT\nN3VdYevKFUYH3Kmy7dxp/bpeRGy3G8mK1LHo0H9DT/9JC8OHUwGsQAEew+rVlTyu3c40nE6dKJss\nogJpNe0UIz8xkQpra9cCzZo5jzcwkNceKyK2fj2jAsWLO78H8NxbuxY4eNDYsFKUxK5eVZK6IuBg\njrTK98z1Q1u20Pg1R8iCg53HmyULRQu6dCHBl7oRIXAhIVwjJ04A+fJh76QfkJqUhMCJ3+PX37fh\nt7Bi8PnnACKPfY1sWQNQv2IhFAiyYeZfB7Fw02GkZiN5DHTYUL5wOEKPH0aRw3sw6MIWZO/0OILH\nfoqAmtWB6HNqrEJM/viDKVQffaRS8159lT1tKlVifdTgwTyv1q1TKo963ZDdbk1sYmN5THfupIMn\nLIzz9txzwOOPM7Vq2jRGNP39+XnzetHXSadOvJb8+CPJtQ59vnW55Qce4DbmzLE2/KdM4aMe2QGo\naAgYr9+pqaq275lnGGXKlcu4NvR5kP/Pn+efHnFKL+Rc14nN0aM8doLChTO+fQ9xzxIbAOjSqALG\nz9uIdbtP4sNpazD8uUfu9JC88MKLW4GSJWl4ZKQ+IjqahmJICA24+wneBp0K5v4eJ04wCtGw4c0T\nG91YKV06Yznzjz5Kj/7N9n7Rvcjx8SpqYvbYBgWp4ndJU3EXaXKlAKY3zkxMNBqFVkRJN8DSU1Mk\nKV8dOvDxyBFVm/Tqq1S0OnfOKNubFrERoy8xkWSgUSM6QVq0UJ+ROXE4rJW2WrdmCpSk4/3+Ox0K\nDRuShNntNGwfeEARvbNnWQcF8JokcxIZyeMiBEfGLTUv//zDqMulS6qu5aWXVHqgzcZasrlzGbH7\n+mtGWxo0UKIZTz5JtbIePVAdAN5+G3jySZzKXwwjXpuMPTsP43T+Ytj9ryJ0XqCEtiZ3kSAvXn/w\n35ccdhuaXj2CRqd24fml38Je/0GSj4cfBvafAiZ8Brz+qrEPjE70ABKsZs3UeWp2QomzQL5TtSqJ\nmsBmM9bSAIzshIertf/JJ9bS03KMH32Ux9msrKc3C01K4noRctqrFyMuZ84YiY0+lrJlgbp1XRMb\nV0p+DRpwLTVurF7T72GTJpHkDBtmjF6lpvLPx8fodBFZ8/Ti+eeV8hxgFGAZM0YJjzz/PInTLb7P\n3tN3Mx8fH4zpxxDsp7P/xpEzUWl8wwsvvPhPwiy3mh6kp1ncvQYvsVEQw1yMU0/mZuZMppLoqks6\nfv2V3ls9QuNpBELIlBg18j1Pv+8K5oiNK4SEMKUlVy5F9twRjYYNabS88ILxdTOx0Y07K2Lz88+s\n3wgPzxixERQporafkmJNYvTX5s2jt11Xf8udm17x11+nJ99upzG+ejWNUH0f5s9XqWQCiazpHvIx\nY7hm9LQk83h0DB/OOWzRgt7u2Fh1zZJ9EUNx7lwSKX3NjhvHuejenQ4gX1+O888/+b7UF4nUcJMm\nQO7cSIYP9gfmwMjrYXgw+yMotNGGz077YHl2kprgIAfCswUhny0JD0UdwXd7fsbcs8uxaszTmP7G\n4+j9WDU8dnE/hh9ejhPT+mNBvwYY8GoX2I8fUxGVpUvVPpuPX+HCJFiffca5B6yv0Vu3UrFN6o3k\nM8nJRpJgt3O/ZT1mz85Uw549Vb+jwYOt1fhkvj/4gOd8mTLG9/WIjfw/fjzXyaBBwPvv8zVXERs/\nP47X4TA6CD74gCS2UCGej2PHGn+3cWPW3ehS7brohYzl2jWV2gooSW2AhH3gQOC99zJ+D9TFJAAV\n9blyxTjm26TqeM/fyWuVzY8nG1XAtOU7MGLGWkx4uWXaX/LCCy/+W5AbRkaMPi+xuT+JTXy8MnzW\nr1cpLmLEezI306fTGztlinW+++HDTGmpW1e9tmsX02c+/ZQpNK4ga/nJJ1UB8cKFN09snnhCFSHH\nxysv7UsvWX/eU3W0zp35Z0bu3PRaR0WxfiUggJ7kXr1cp7aZ5XQ9gTuS1qKFNbHJnp01G/nzU6zh\nxx9JZI4dI0koXJgpSCEhaqwBAazTOXGCz2VOmjThtnv3phH5/feUV543z0hs5PNWaVFWx/bMGdax\n/PorU9bq1VNedleGYkAADVap3+ndm8p3gGq+eewY17gWwTofFY3pv+/AXyml8Vu92rhqDwA2RQGI\ngt3mi/a5gG7LpyN7Uixq9mgPx+hPWDj/+406HJ/cQCU2en3iobLAoMdI6vftoKFfqxbrPACuFV9f\nXneTk53T+IKDmUrYogXJfVSU9ZwNHEhi88cfLLaXOfznH6B9ex7fnj0VOZJoQkwM5+enn9S25s/n\nOTtokPE30rpH6BEb+f1Vq/g3cKASYPj2W4oQFC9ujNg4HDzHpTGs4J13uO5OneL+e3Kdlv3Ux6vX\n8AjmzlUk7mYU0QBjQ9eiRRVp1q8X777rPK+3CPfFnfyNbvUx/fcd+HbJNgx98kEUzJWJ3Y698MKL\nO49OnZimYS5w9QReYnP/EZuDB1k706cPUyj0hnvpidgcPer+d8TIWbvW+Pr27UxrcqdqVKwYjdgH\nHuBnpUfKzRKbb75h/cmCBTToZXtSQK/jwAHl2QUyJvtcqBAVoXRkZsGywB2xiY+3JjYhITQeQ0KA\nL77gax99xGvJ5Mn0iEszTrNRffIkDVQhDAB/Q5oVAmotrV6tXtMlgM0ICqIRaiaZCxbw87Je/P05\n5jNnVHE7wLk+doxj1ce7apUaZ1AQPernzwNnzmBX0fL4Iz4IY/PXxsHHR/EzvrkBXyB/3BXUTI5C\nl3f6odGD5RH65WfArBtpbb8uAEZ/YiSn+vGU4+FwsPZi40ZjqlOdOiQ9fn78rLkeRaKckt7las7k\nPTm++mcWLuSjHlGQHj+BgcqJocNKjvjllxllcpUSJjUtmzYpiXfB0qXKaQIwolK8OAVvbDauRz29\nVI/uytyeO+f5NTpXLp7j4eEqEmWFzDz3dOgEVZ/L8HDnVMBbhPvibla6YE50algeCYnJeG2ShRyi\nF1548d/Ghx8yXzoj3dHdGRr3OqTjtzmV4L+GlBQWhJsL4F1BDG0xQvWeHxJdkRu/SLxaQVJqWHUm\nSAAAIABJREFUXMG8pn75hUQFcG0kCV54gQZxp0587k4iOb14/nmm5bRp4z7aqROZfv2A8uVv/rcB\npkvt3s1Umz//vPkUldRUesYHDLA2nuLjlRqaiCUAjKYUKcLv6QaZpJTZ7a6vD99+S4L8wAM8ruHh\nRpIBWNfcSB2NXqcj8PdnRKNyZePrY8awqaacp3nzqvSzr79Wn5P6EIfDSGyk+PwGrhcqis/y1cSD\nr89B+YLt8UKJ5jgYmB2OlCQ0v7gfk2K24Z+NX+LEutH4aeN3aJfHjtCsAcY1IkZrrlwkyA0akCQK\nZN4cDhUZTUjgXPXrxygSYB2FAVSq3m+/uSc2snbkvbAwY/NUM3x8GKk5f95IymTdmGtcZs7k57t3\nd12Dohf1m9NST51i5K9mTeM4H36Y+5WaqhqrmiGftar7cYcePSg/bZ6vZs1UfZ+7aPHNQD+P9LnM\njOuWh7gviA0AjOjVCAEOO2au2Inlmw/f6eF44YUXmYkhQ1gount3+r8rOc3Hj6fdc+Jeg6jqZCT1\n527CtGnsz1CunGefL1DA+FyITZcuNPoBlbIivVesEBnp/nfMN/OEBGXgyO94gqQkenmbN1f9QzIL\nZcvSKLVSQ9INo4gIz4yTkyedI1QAveNlypAcZcvG/ydM4G+n1XgyLfj4UDp37FjrBojx8arj+m+/\nqdfFsPXzMxpkQkhsWhf7yEh6+aUWRYhFtmxMxYmMVApiAl3MxCwnnJjI9KL69Rm90NN5XBG9X39V\n4zIjKEh9z8/PGDlKTUVqaioWrTuABwd8i9CgphhQojnWHLuMwOREtLuwGzN2z0H06uFYuGM6nos5\niIrR53C2a1dGNSWVKl8+Nf7du0nAevZkWt7KlVzTzZrxPEpK4v5ny6ZIUHw8De7x49V2hg+33lfd\n2799OwmhHtnYuJGk3xzJzJ2b6ZYCsxpd27ZcL/36KWn3KlVIjAFub+RIfqZXL0Z0X3uNKWquoBPY\nvn2N4xQ1QXeOiRMnOM/vvmt8ffNmbu+zz1z/tjuImp7Az4/EcuxYJayR2dDPI520vv02HQg32+zX\nA9w3xKZgrlD8rxM9Zc0HT8PKbUfv7IC88MKLzMOaNbxgp+VBt0Lu3Epa1So14V7GvdKgU4wbs2Hp\nChLZk5oQITa6mk+JEnw0kyAdEtXRC4F1mI2Yrl1VvruQhtRUVQuh4/Jl7k9KCnPgc+dmrxIpWj94\nkJ956y3k++wzo6xyevDmmzRKpUGh4MgRpmUJQkOZRnPmjGvjJC6O81WvnrOTwW4H9u41NvAU4/vj\nj9VrMTHcTkabc65ereY2IoIG8MyZaq3rBE4nNjqZEEPVbjfua1yc6kck6Yuhoa6jXg0aOKfd6VLd\n2bNzvOvWGVONnnrKWomvWTOu1QULjK/7+dFQL1sWqQAut2iN/bmKYOljT+HDgvUwJmdl1Hp+MloM\nmY41O47D19cHNa+exNd75+PQ+rGYs+tHdD6/E/bUG/tx/DhQpQrOdu9Ow17G1qkT09oE//xjXLsH\nDjDaNWOGqos5ftw69XD1avbq6dpVCRi8+SajPoMG8Txp1YpOi7AwZ2IdGcmaKIFOwkfdSKkrV85I\nZJOSVFT3iy9UZMffnzUnAI/lq6/y/+vXjX2e/vqLdWIdOhjPN53YBAQ4X09nzHBPbKKiGEUWGXJB\nxYocpzm9zVN06mSsa7HbSXYGDMhY2rYrSKSufXvjea+rrp0+TYJ2G9Ke7xtiA7DWplvjikhMSkHP\nkQsQde0+M2K88OJexc0a6Hr/iPsJrpozmlGvHo2EtCIUdwpiLHqaXiGGSEAAj7kVsdGlfl1BSIq5\nIZ38hrmYXm7yVasqItG7N40MXeoWoDc8NJTRNN0YSE4m6ShRglGI8eORZ8qUzI82HjjAXH2AHugX\nX+Tv5c3rrP4FkITpBM/c10Y/x06f5lpq0EC9L+dezZrczooVGTsfU1PV9zZs4LZy5DCmM33xBcmD\nGOl2OyN+Ig8sDo7r1/l36JDafnQ00xWXLuXz0FB1/sycqeoaZsyggSzGvDy+8YZ11E03zF95hVGD\nwYNVVBWgkW63I9bmh3lr9mJmRHm8V6g+nmw/DFUvF0PzwJoIrf86wuoNRqmh89D0WlEMLdoIA+2l\nsXHvaUSEBOCTvk0QtXAI1k/sjWfObkWehOskrCKTDfBYVq2KJCv5fPP5oF87DiqJZwMxlejMpk1q\nnfbqxRqm48fVsalWjcf/1ClGMSZMoCJdrVrO4wjVaqXr1zca6jLG8eON89e/v5LdFjRowEiJpFnq\njowjRxQRSUmh7PmoUXQuBAeTGA0dalwfvr5cW88+q87b0aPdExu51kRHZ5zQu4K+rnLnztxtC/r0\nYXRp2DDlmBB88w0bzgLcTy+xyVw4/GyY/L9WqFA0AodOR6H9W7ORmtmLyAsvvLj98NRAdwVd1eZ+\ngn7Tdod9++iJ27mTxtrd1u8nvcT0oYeoaLZ9Ow3fVq0oBDB0KD3xkyYpj6w7YtO3L6Mdv/zi/J6M\nJUsWZcCLgfe//6maD+mSPnmy8fuylt96i5/XITn9cXHpE79ISGCdxo8/Uu1r0CASjNq1jcpt8ll9\nX/R7pVWD0REjjM+FbG7axEaHukGTLx/Tf77/XpHCXbvUbwEUTMhIiqQu/f6//9FgXbzYOE/vvANM\nnUryAdBTXqGCqjkrXJhELi6O33/vPWU4P/YYPfcCndgAjOh88QWjKnoXep14WvX8MRu8AQHAhx8i\ndfx4nPAPwcLsJTAnOTtGT1uFYk+OQ9ths/BE2fZ4s8jDmH4mBVsPnMXi9QdxzdcPwUnxKBZ7CXUS\nItH31Eb0Pr0JYw8sxpFny+HljnWQNdDhXNhtLpq3qg8CWOQ/bZp6ru/7nj187NfPuEYk+imfb9mS\n0TuA54Qcm9atGZWaOVPV2Bw9apQqFgjpKl2aBFVPOZO1a67fsarnadmSBEvEC557TvUAat7ceG8x\nH6MpU1jfqcPXl+fC5MlKca1gQRLazz9nPZIZMvdHjhjrlDIDImwAUPr7ViAigs6amTNJnnSVtSef\n9MxJlIm476plHX42LPywC6o8NxErth7BonUH0KJOybS/6IUXXty9WLmSjxlNJbvfIzZpERuJ1DRs\nyMeYmFuXo50RpNVoUZrRCYoW5Z/0f1i7VhXwtm5No/TBB/nc3ZpwOIxRBx26gf3JJzR0JPXKapzm\nfHhJmZk3z/mzQpCKFlV9KzwhNteuORcqly5NuWvz98U4LFWKtR26YW5loJhfE2Nt40b2pjHDZqPX\ne9s2rj/xlOvzbTVPqakci6uGoFbpZTabkdiYO7jL+q5YkWlxpUqR7E6dyjTXxESmiy1a5FwLMWeO\n0VidO5fEpyl76CEggNEg3ag2j91m+3d9prw8CKlxcVjVYyDm/X0AC1fvwuE6L6vPTiGpKporBMX2\nbEXl62dRtHYlFLl4Cteq1kDF3xeg5IaV/GyLFkDZPIo0B2jkRSeavr7cZx2uIoARETxvvv6aUTX9\nGEkaUtmyxu8EBXH/ExOVEpjA35/qZcnJJI9yDbfZ3F+XhdjoioYCWbtmsmZFbOT35L2EBO5bjx6M\nIAmJHTqUSoWuULs2HUC6KIiMe8sW7kuNGur98+dZd2KzMXolsGrQeTMIDKRzJToa6NaNJHHiRM/r\nEdMDcQbpkW/AKM5yG3BfRWwEBSJCMeRJestG/fj3HR6NF154kWnI6AX0Xic2CQnKQ6pj7FgaNa56\nmJghykG6xO3dgOrVuX/igdexYAFrGVascH5PCvnLlCFZ++EHVb+wejXTrqToPL3QjepSpYzF3D/9\npIrQBblyMUVr1iyj4WdVfyPvJyerNbtmDSMjekNMQe/eTI+xqkFz1XxTjMNKleht1tXGrIxeK7Iz\nYoRrkYRjx1gDUKwYPfpi7KdFbPr3p7F25Ih67fx5EpIffiBJKleOxrV+DM6cYYqVnsIkRqa8VqoU\nozySkqZ7msuUYYRLjGWbjf+//TYbPerGvLwHMF3x+++NQgKTJxsamaba7Vix5Qg6vTMHWTcFwr4n\nAo+8Og2f/bwBhyOjERboh5pXT6LthT1oVbkA5r/TAQdnvYylO6fh40NL0aduETT9bQbaR+1HSYc2\nf+XLMyIoDgk94mCOuvXtSxItNRmuIjb6PgIkTwkJjGo5HIyePP648+f1Y6GnLAYEcCx2u9HBYre7\nvy7LMTMTm8REpkUB6SM28tnERI7nwQe55tu14+tbthjnTOZUsG4dx//aa+o1GXdkJAnv35q9ef48\n65fGjzdGADOb2ADq3J0xg06cW0U0hNiYU3NvU2NOwX1JbACgZ/OqCPS3Y+W2ozh46lLaX/DCCy/u\nflSrlv7vXLjA4tSaNa1rJe4WrFzJNImM3JR69aJhttwkd79nD2/GnsqJiuFxm/oReIygIBqlVmke\nPXrQ+NEN7HPnqIK0YQOf22w0ert1M363ffuMK3bphpw5GvLzzyrlJCGBxlTPniQRnTur2hZXEI9o\nSooiIC+/zO2aC8sBRhWmTlWfzZVLpZ5Jyk9qqjHdTJfrNef+p0VsRHTgzTfd74dOTqy2Y2UQSb8Z\nXSnqxAkalJ98Qo/0d9/RgNOjNOfOkUAJmQXUPLoyvKxSaPTooBxXu9249nx9/zVQo9dvwuFt+/DP\nwbM4cPIikpNTsCFrXkxr0g3vjZ2HN4d+hertPsQjg6bgx5W7EGvjbxYMD8bQJ+th9bgeuPDLYKy/\nvAJzd83C/H710apeafgA6nzUCYBuGI8YwSiKVX2HWQUvZ05GKxs35nOrY3zpEo3zPXuYVvXww1xT\nb7/N4zJxIlPCcudWqm+i9qYLLOgRq88/Z+ra0aPG42C3q/m/fJnzq6/BoCCmxP30k/F1PYXSLKku\n2ytSRL0mBK5OHa4h6Vsk6NlTRbf0ue3Rw7mmLzGRa97h4Dkg609Ik07cdHIXHq5IU2YSmytXeH6b\nr9euJLZvFlbEZu9eo8T6bcB9S2xCswagU0MWi437af0dHo0XXnhxU5ALd0aKI3fs4MU/S5aM9cG5\nXWjYkJ5ePW/fU4hX0lz8n94GnWIE3AqvYnqwcCELrGX8166RmFgZqEJoJO0MoKGkd+O2253Tg8qX\nZ066rqqUHujGpJVBqdcB2O00bOT46EXYAqmzaddOGQ76/ooinHQe//13jj0hwTndxm5XUTcp7AWM\nhlf58izcrlvXOQpklbqoG/+VKvFRZIJ16MXZVlEe3cvuztMr/TgAZYT7+3N+atRgJ3ohba1a0fg9\nd864L3LdSA+x0c6VFJsNqQAN2BvjTgWwMks+dDsdiqK1XkTYoTwoNnAmKj83ESW7jUdAk/dQ6/nJ\n6PrJIrz58za899cpbDl9FTlDg/Buj4dwdOdknP5rFA6XvoIPOtdCvQoFYbP5qrGUKGFMXdqyRa3l\ntWsZcZEeMQAjdbp8tSA83JnMAnSAOBzAsWPwMR+flSvZt+f11zmOMmX4ep48znMlDTkfecS4Xnx8\njEb9ggUkRadOGSMz27YZHQJXrhgjJj4+PKebNze+LvvocDg7OgID+ffMMxTrmDhR9Yl66CGSkUcf\nNX4nJUWNX3pQAYzofPCB8bNJSfxsYiL/ihenM0qEQvR50MlGSIiq68nMa+uqVax9qViR1wNBZhOb\n99/n/oiqm56KNmiQqrlp0iRzf9cF7ltiAwCDOvLC/tXCLbh4JSaNT3vhhRd3LfR6hvQiPcXXdwPc\nNYx0Bdk3swHnKbExp2O5qm+4XWjZkt55iU688gpTU6QQX4dV/Y25CNhuNxpb58/Tiwy4npuoKEZX\nrGR5ARKM338ncdBrv6S+w6zOBChvcdOmzoW+MmabjRGXbdu4/dq1+bpE8oQYdOxII+3qVWXYikFj\ns9HYGjrUaBTqc1SlCg2WFStYgwNQdCAmhqlG5vSgrFlpLE+dyvEnJFgbUPo8WxGbI0c4DxER1nMv\nZEmMasBIbGStt2jB1D6Bvg4kMif9RpKTWVfRqZORyEq606+/MnoHYPuhc+j36ld4rPd4BFcZgCwP\nvo7S/b5HIb8HEfTI2wirNxgNcz+KHy754UhgGJJ9fFDIkYIKRSOQJ0dWJKUAheIuo33NIujftgb6\nt62Bue92xLGZL2HYUw1QKCUGeRKuw/beu0ZJYT06ILUqAAu2pWh/zx4a+kOGKCWxzZs5F927e+b4\nKViQZGf/fmfSI2tL1rNezyTvHT7MWhMZu6yBzz5Ta1rWwLhx1uSyZEkqwvn7qzQtV1HiNWtowIuj\nwNW1DiAhi4lhamXFihSxGDXKfYNivQFonz5K1S81letHb1qbmKj2e8YMnpuTJiki6ipi43DwPPTz\ny9xrq8zFhQuMagoym9iMHm28xunpnosWqf9vU0rafU1syheJQNMaxRCXkITpv++408PxwgsvMgp3\n3dPTwq0kNnv3Omv7u8PKlfQCmusvdGTEo+cqV91TYlOhAh9r1WLPicySDV2wgJEDvV9KeiDGjqS7\nWBk/VsRGJ0B//MHUL11VKWdOZXi4mpvr11kP8/nnVDgz37T9/WmwNG9OpSczYiycaboMtYy7enVK\nCxcqxOd2O0nRCy+QNMmxle3J+rh0I8V6yxYaYX5+JB/duvEYNmvGtSYpaSNHWp8DOvlISuL+hoaS\nOOn7/MknJG25c3MMrVqp7VWvrtJ/KldW9V67dpGkiXqU4I8/GF2RdafDfL6mpBgjia6uAbLWk5OZ\nOjV5MgnAU09xTjZvJnE7dIhzNno0P//jj4iyB+D9mHBU6zUJlXpOwBcbTuHXfZGI8fVDrM0P+05f\nxvGoWMQmA1fsAcgfALzR7UFsruGDc3+NwtHqSdj+dV+cnjMIl3dNxJF1YzC7bCo+sx/FZy1Koe2D\nZRAUoJFOgf7/558rEQA9Crhtm/O+ZslirOkZNoxrRVcnc4XU1H+Peap5PUhEe8kSEkGd2Iix/Mgj\nTG0VlTuHg+dQ//6qrmjkSK7Xfv2MkZ5r1/i3bx8jIj4+SlTDFbFp25ZEWJQa9fM9LdXbDRuYpikS\n3VYwr7f9+0lomjVj9FF65gD8PXE8CdkE1DVkyRIVWdX3x8+PxzYhQSnzZQZkzOvWGUVDMvted0kr\n5wgMVMIrOvr1sxZCuQX4j7gobx2eaVYFv208hLE/rccTj1RAztC7LHfcCy+8SBvPPssbUEaIjdyc\nbwWxadyY6lYHD1obIGYsX05j8/33lRyw4OOP6TnXu2p7CpmXjBKbJ55gbUK3bkoWNTNw6hRvupK6\n5CmKFaMBKsayTmyuXaPhnCULC7qtiI3U1gDM/968WamQAcb0E1dzoxv8a9cqOdilSykl/cUX6rf1\n4mB30IlNvnxcA1L3INEHm40e2NWrSTDEMJSohblgWqRyAwMZBZkyxfi+zEudOtb7qhsjyclqrn/+\nmcfP3JMla1bOzaVLKmXuo484v08/TfKhe4zPnyf5/+EHqqQtW0ZS4ep8HDeO0TKJLFSpQtluwBix\nMUPWfkqKUsWLjKSxnyPHv0XzqYMHwyc0FGfOX8ZXbfthlW8YttUagEuxQcCBM8gS4IeO9UvjIf9Y\nPPLT18haugQ2d++HlCxZUbZQOM5cvIbKxXMzfezNlUBiDL33zz8P5MuH0PgbkbXvvqMjY+5co9rW\n8OFMXwJ4rGNiSPzsdmP0IEsWGsLLlvG1ESNU4bqfnzES9913KtUpLejRb/N60JX7Nm0yqo/JuvPx\n4XGRCGJaUTt5v1EjkiGzopo7pwWgjqucaz4+HHdKirEOygpCPtzVGNpsPCYyF9mz81GMeXPUUY8S\nCipXVv/HxTH1TJ+X4GDXv38zcLXvEqnMLFSpotI+XSls3sYa1vs6YgMAreqWQtlC4Th0OgrVek/C\ngZMZ6FzuhRde3Fl8+SW98HdbxEZu7uabtSu46r8AsMZizpyMKZK5iti8/TYf33jD/feffpqqRz/8\nQAMjI3U+VtAN+fTALOcqEbEOHUhSatakyhNA0rttG/uSCHRjpFcv4M8/1fPu3WmYiYF3/Lh1CoXZ\noJG5bdqUqS2ffuq8prZvV1GIokVpyM2YoZpzfvwxC6KLFCGhWb2aaXaAtXSx1OfoMBMbMciuXqXR\n9+STxvfdNQ7U8dVXjNLokSY9vUUgNT5CPkqWJOEoVIipe3XqsPZh925GcgSRkdzn8eMZDTDj8mUe\nx7JlSYRCQjgWITWvvELvvQtlw+QSJbEzSwQuwY7L1+OwbNMhbHjlXUyu8zi+eWcSPr0YhGYVnoSj\nykvIW6ATCtYeiLfOBWLFmThc8gtC7YAE/DL8CUTOfxXfdKuJpwZ1Rb6j+xD69UQ8vGM1GjWrjbyf\nf4pqpfKS1ABqjRw5osYp4xOJevPa79lTGbo2GyODTz3FehJR+7LZnFMZBw5U2zKvgVdftZwTS+hR\nGDN0wQE/P863pHX16cPXxbA1p6K5gv6+1TU4LWKjkz1Bjx6so0kLruSpdSxfzvlu2ZLPZX1fuMDI\nUr16xmNoFW3PlUtF0GScQgBTU43pbJkJ83y+9x5/TyeWmYH581U0zkxstm1jNNd83bmFuO+JTYDD\njmWjuqF6qbw4fu4KnvpwHpKTM9i93AsvvLgzGDmSqS/uUrhcQdKq1q61NtRuBpL6IfUaaUGkfXVl\nn8xAwYJMDzB718WTaO4S7wpJScylzqzxCfFbvTp93zMTG10S2UziLl3i+7rh7iqdb9IkGvCXL6u+\nHr//bky1EJgN6NmzjY0Lz51zJgtJScpA+/xzGgRduvA4DB/OyEyXLsp4EiQnM6Wtd2/uu4gL2O1A\n7dq4/OCDLCDv3t057dHHxxgRM/d6qlaNvXj0vHgrZM/O+da//8EHzuk+OrGJiaH0cvXqTBfy86OR\ns2ULa2R0IYH4eHWeWDWA/eMPeoaFsMq8CEaMoDFrsyHKHoAv81bHq0Ubo0nFbqhWrRdK1XoBFWo8\njxxlnkPYYyPQ5H8/oNaxHHiuVCs8u+kaBl3MhiU5SiDJ14Yz/sFI9fFBu7AkzK0egN0bxuOvktFo\nWackAhx2Y00PQCP+wgVnxUI9ZVPWrJkQN29OQq5DJ5s6SZGUKZ3cAkxf8vMzOkb02q/0nK/uiI1e\nFP7ZZ4ws167N9XWjBsmwnWzZ0o5G6EIIVsSmWjWef3qthmDIEHXu6+fa5Mkkx+btpaYyOhcRwWMo\n8+kuYjNjBiNhW7bwuX48JkzgeXzsmIqWSRqWWV0tLQfCwIF0wlilqGYU0lRWYHUdywwUKKAEAszE\nplIlKjZmxOmYQdz3xAYA8uYMxrJR3ZAvZzDW7T6JkbM8TBvwwgsv7g5s2sTu76dOpf+7devyJnT+\nvLUa1c3g6FE+Fi7s2eel18mwYZk7jqVLSR7MXk9PG3QK0mqEmV6IV3fLFt7YPR3Hzp1MbRIPsr5f\n69bxUY7lu+/S2JCUHUDttx4xALh/ixezCP7jj1XqjVUUwGygPv20MT++dGnnm/n776tCfL2BpPzG\n0aMs1j90iEaI5OP/9BMFHCZOZJrb4cN8PToaiI7G9QoVaER+/z0LqXUkJBhTiszj/uILRg/0YnyA\n23n/feP4zp41kv/Fi9VYBGLsJySQuOnNOc+c4b6JMaof7/j4f4n2mb83Y9eR8zh36TpOR17DmYvX\nkHAxCgcCs+NwlhyY/dxQjG83AEfPXv53jhPjE/DVr5tRvHAn5Kz7Kp4v2RIjC9bFsuzFsCU4Lw4F\nZocjJRmB/nb42X1RtUQeVPSLxyNRh9G2YBA6BV3HK8fX4uzakTi8bgzO/DUKc8qkoG22JJSJiYRP\nFos+PrKvrmr8XnxRkRb5jllSHKAyo44BA9hbSk/xAvhadDTrOmRNlilDwYbUVFUvlT07lQNFtSs9\nHd+lFsuVQqSuBLZtm1LyM5O6Rx8ludXJvuDaNRKVdevokBL1MitiY7ORLIeHO7+nR1o9ibhLiuSF\nC4yWyryYG0rqkHMnOZkRMyHWFSvynvPGG0a1STmnzdtMi9h8/z1r/TLaZNoKlSvTGSBYuzbztm2G\nzUaH0K0iT+nAfV9jI8iWNQBf/68VHn1tGoZ98wceqlwYtcta9ETwwgsv7j7oN5+M4FY06ExMpDGa\nmpr+Jo+Z7d1ylW7nybzFxlIyNEsW4LHH0v58RjFmDL3X0kfDHcxG1/LlTHXKn18VWIv6mJ62JZAU\nOHOUwmZTqV+//qoMLivDsFAhkgxdRhoA6tdnvnnu3Kwb0CFGamAgxQr0SFVSEmsh3nmH9R6ffELC\nFh3tXOsgTQkXLQIWLUJ4njyMugDKMOrTh0RZan8Ev/7Kx507STzKlmVKkRnLlxuJzfHj1utYyFdk\nJH9LjP2kJOfUStn/o0dp9CYn45I9EDuzROD6mQRcCMuGFaXbYGpUGaQ+86Xzb9UaAPxbwuCPF3p/\nizy1XkJwUjzin/4Sx87fGIuPLxolR6Jsk7qokicEpQuHI+XxdqgSlAzHqj+QOvR12POWA64fBZbN\nAPI2I/GolQs4HA3I4U5O5ty0amWsLRPZWjHm5Xz46COmGnbpQqN/xgwlgSvE5uuvua7efVdtz3xe\nfvih+l8/9kuXMs0yTx7nyIqPDw39b76h5//LL5UoQ2ws19bjjzt78c0IDOS6CgmxXvfm6I/su05s\nSpRwTofTcfgwldoqVmQaptU5KqhendHPrVudz3s9BcyTa+bUqer/8uWZ+miWdzZDtpuSwiiVKKht\n26aOzbJlitwWLkxCYU5vS4vYyBxkdrRe1l1EhHH/Mxs+PmlHfW8TvMRGQ9OaxfFS+1oYM2c9Or4z\nG1sn9UYOr5iAF17c/dBvPhnBrSA2fn6eCQboaNqUcrNW/T9On1ZkyZ3RYAVXN1VP5i05WRXjy/yY\nu5JLpMxup/HhKTHr148pRIKoKM++99NPNMzbt2eqky7xqqelAUZxiOhokoV33mH0QCIsHTsyQpMj\nhzFa5m5dhIVRVKFwYf5m06Y0CiVisn07jf3y5RmZOnpUHbf//Y/EyByxkeJa3Wtbv761Aa4TAAAg\nAElEQVRzql6TJlRku4FUm81ZIa5PHxqPFSo4y9n+9htw8SK9zZ0709g+f54GrRiP5n0WAgMw5at1\na74m6Y3t23PfV6zgd0WJDQDeew8XR4/HGr+cOJm3BjZ+ugjzph+Hb9a6uFavGpLgA+wBsGcXkJtR\nm6Kxl3A1ewT8ggIQl5CEy9dikS/uKmKzhqBK9FlEJaRic3BenHEE44wjGDh/FSUL5MBbtXKjzYAu\nCKpdA5izmobzggXA1RNAcD7u509z+CdYvJiPbdqo1158kcZguXJMSxQlN8A5Mqwfx969ue82G9eU\nQDdYzXU17qIN+rn0xRck/m3auHZW6GmM5rqT+vXTJjaASqeykiRv144kb8wY9qoxE5vq1fm6O/z4\nIx/NdUdW83DqFCOFVga/zOOvv6a/RtLh8EylS3f+6E1LdXGGlSuVAESVKso5ouOzz3gtcnXtluvW\n1q3pd4S5w7p1vF6Hhf13WhrcJO6PvUwHRvRqjHW7T2Hd7pP45Me/Mfy5R9L+khdeeHHnkJSk0h3u\nJmKTEbRvT6OzalXn96Tz9syZqqkcwHSI/fvpVXYl55pWxCYtYgPQcJEid53Y/PILf1tw8iQVvTxB\ngQK84QqhsYocWGH2bBr2pUrR8LRSfZP6DXnt0CEldyzKYEJsmjRRcsq6h9yqQaMZdeqQJABGg1Un\nk9OnM4VHflfGZCY28ntCTmJirOuPTJ5rS2JTqRLTbfr0MarAAYwWDBzI/xMSaEydPm08rrLPPXvS\nUJNID0ADTz/m2uePRSdhycKtSIiNQ5bcVXDCPwQr5x3FyqovOO/H9XjYfH1Rq1B2hIVmQWhYMCrl\nyoLHvh2F8utX8DdbtEBqaioSX3oZjnGqqWoqgB2//AG/CuVw5MxlBAX4oV6FgrD/uQpISTSm+kkd\nkN3u3iMeFkainS0baz8OHmT0zNXxP32adVm6Etb166y7kIaqANdc0aLquTti89FHTPcbOpTnkW5A\nA2os8fG8JhQrRoLw+us8F/QIhMNBojVxIp9nRiS4QgX+rVplTWzcpXUJzNfZ8+edI4sCOSesrs0y\nj2ZHiyukJf9sBbk2jRrlXOQfHs60tgce4P5HRFgTx/37KfVcokTax0BU1zILwcH8k1RFHx9eU8zr\n6h6Cl9iY4PCz4ZO+TVD3hW8w6dfNGNylHkKy3OEu21544YVr6De125mKFhtL7/Qjj7hW9Tp+nNEF\nHx/n4loruCMaclNescJIbL79lnUMhQu7JjZWEZvYWBpfWbIYezG4+q4O3RP9+efG99KrcKY3IfS0\ncZwcLzHycuSgR93Pj+lsFy4oL/zChXwUQ3PqVEUwAgM5DyKhPXs2C4EFefPSgEzLCJAIi642pM95\nnTpqHACPV/XqxshcdLRSm0srz968Tm029dv6d3fvpkFlhs1mrIWRdbFsmZIFlrktV45kWhT0AJyL\nTcLyZdtxMvIqrkbHw89uA1AYP1eviO2faDWqpVv/+29AciIqRp9D5etnEZiShB5ntiK5cGHkX/07\nIsKycH1fu0aC9usX/NKNOfTx8YEjm9Fg9AFQMZsdKBSOMsf3AqvXAXEPcv2VLUtlOUlHLFqUhC85\n2Si9XaUKz1EhplmzGhXEXBnVBQqQfOTJQ+KwZAnHPeYG8fL1VZ75Zs243mbPZmrgE0+w7iZHDoo9\nAEZiM2MGicpzzykHgZ7yKMelc2c6EUaOZDTw118ZQevcWW3L4eBv/vILyVdmprjKtt55hyT3yBFG\n8Z56Ku3vNmzIa4jUyPn4uI4muLs2p5fYZARVqlCSe/9+Z6n7TZt4nenRg6Tn/Hln0QCA5GjuXKYR\nusKcOXQcSWPVzMapU2rt38OkBvASG0vUKZcfdcrlx9+7TqLTu3Mwc1g7hGa9w522vfDCC2voJOCR\nDERYDx6kwdOokdGrmhZ69aL8ce/equjfatsvv8z/Bw5UheOuEBBAr3F65Dg9KeiXgs7du1UxaWIi\nU+WCg419FswwkyzdKAacDRJ3DUR37mTkpHVr3sjXr2dazezZ6ZOkNRucdrtSMRMPq3g+s2VTNSkA\niU9qKo+LkACZw5deMv5OpUo8bmn17gkOpiqQvu/u+uDs2cP0t8REEl7p+/HFDYPeHbHJnZtGlPTq\nABB4+DC9xoCSXQWM+63DbleG98qVilw+8wxQowa3r83tzqgEbMxdGetC8uPP0ELYeykcGP6zcZuO\nkoADyOpvQ9NaJZEjqz/Oz5qLfFcjUTz2Enqc2YrQ5HhFCgBg1zkg9MZav3KFaz8khIYvYFzTXbsa\n61IArufLl0nu587l+127MvWuSBEljS4d3fPkYb2GIDHRvbFvJtAC+Y4cW4dD1WPJ+7IWNm4kUenY\nkc8feojCEl26cK4PHVLRQv03dUP+iSeYJvjDD859W1JSjBFLPRXtySfpePBU0js9GDyYdTxnz/Lv\n999ZsyUOnJgYkubAQOdrQtOmdNCUL8/jtmIF638eftj5d44c4eP777N+SMeLL3Jeq1XzbMxyjNLT\nN6tNG6anlitnTEUDmIbZuzf/d7VWAM8i4+3a8S8zkZDAqK0IMNwn8BIbC/j4+OC719qgZt+vsGTD\nQTz2+gz8/slTN7xSXnjhxV0FuVmEhjrLGXuCefPo0Rw0KH03vBkz+DhrlmtiY7qh+6RVGNqli3Mx\nuhnmdApPiM1zzwFvvmmsE5B5i42lB3nPHs5F8eLG75q3azZSzJ93R2ykh8uOHUot6rffVM69J7h0\niYXQAI2I1FTWsgQFMfrUoQONV7mRjxlDxbLQUBrPYoCMUWlN/76mG37Vq7MZpMNBIuYOoaEqtWvb\nNqbpSEqY2Zh8+mmOX+pQ5Ld1o8kceStYkET6jTfoHS5Zktu1MpTateO2ly2j0WgFXUZYj5gBlFUu\nXx549FH84ZMdH20Hlh5wAKVV/UkAUvBQzZIoUzAnQrP6IyUlFfETJqHKkR1o+9s0OKrcOI+O/AZ8\naWoIWry4UVktOZmGn96vRK+ZEpijeZMns7mqGJayX4MHcz2NHs33Ae7P0qUqgiMwN/U1n1uuUhH1\nZpCyHX18OrGJjDRGOCdOJAnt0IGKZmY1OhnDmDEkMuaxdO9OIqGf9zJff/3F6JM0sD17lue+GNaZ\nSWwKFqSxv2sX15J5rsaOZTrd4MFGMQSA8ybkdc0akq8iRayJjcAqKuMuAmKFwEAS3PQ0qNSdJzVq\n8LyyUmhzl7aaXvXJzMLZs0xrLlBANdC8D+CVe3aBkgVyYOOE55AnR1as3n4cH03PQH8ML7y4XYiN\nNRqt9xP0TtkZQUYbdEqR+QsWtQMA00L0tCYAvp6mul24wOJ2T+AJsbGqQZGbbFISoye7djnLXcfH\nM/Kh11OYicvHH6tUHsAzAYDjx53H5il0ApCUxPSliAglzTx+PCNAkqYi60JIpc2mupMLzIbfunWq\nIZ+rdbVhA9N+hCANG0bP+qefMvKzdy890R9+aIycCCkDjEaQRGkKFWJqoJ5C5u/v7HXftImRgOef\nN47L4SBJaN7cuIYeflhFD202pi4OGYJYXzu+zV0Zwws+iI5lO6Ds0sso9uQ4FPzhIB7eZcfSAxfh\n5wO0P78LbxVMwYYRHXFpzktY/FEXfNqvKd7q/hDe6dEQH/mfQiechyPrjVofnbTpCAgw9neR/RJi\nExjIKFt4uPH7ZuLw7LOq6aHAblffEaIJcJ1cuqTmTs5dM7EZP95Y+K6TE2moCTA1b+1aJeOemEjy\nK1FHX18a6gJdAnfMGHUcrCDnqFkmWa+70+tRdGIDMBVs5042jpTf7tyZr2d2Y0ZdmU2I8tmzTNuS\ntedpg05XdUwSxbCKKicm8hzT0wvdoUEDnmdWPXFcQb8/SN8mM0EG3NcC3axqZ0ahR/9y5GA92Jw5\n7r9zD8AbsXGDEvlzYNrrj+Phl6fgval/onyRCLR9sEzaX/TCi9uNunXpkfnjD+sc33sZrnpIeIqM\nEpu0FMWWLHHqtpxmxOabb2gYvP46n8fFORMJV8pm7m6aVh5wq3GfPKn+v3qVkYgGDaiStGABXzdH\nLxwOo8F09KixQ7kV/P2ZFnTmDNOffv7ZWjDBCjqxqV5dPXdltOne9bAwpo116KD2f/FiGn1//qkI\nlzSjBIzEZtUqGo2NG5O0zprFvzlzGIXSlcMARqjCw10XBCckqN8Rj7QQMhm3zcZUq99+43O7ndGK\nKVNo3JtVlr791jqlsnRpFrGfP4+9Rcrho1n/4PeD4bhQbzDifbW1fz0FuE5ymjXQgYHta6PP0bXI\n+95soPUQoFVDRsTee4/krWdPXnP0niJ58nAdiziD1DIBjDgtWsToWkwMhRD++EPtd1CQkuzWoRvI\n8r852mSzOZ/HDgfnOS5ONbbs358Rh2zZaBRHRXFf1q3jmly+nMf5kUfYgHLdOuM8S/8jaT6ZlERC\n+uyzNHyLF2faU+PG9PCbe3ukpjKilDUrIyqeoH9/rrlRo7gf+nlvbj4bEGAsYv/sM89+I73Q5bzl\nmLz/PiM1MiZPiY0rp4+cO1ZSwpcv8xiFh1uTjcyAp/cHd6loMk8ivnK7INc4IZmerrX/OLzEJg00\nrFLkXwnoTu/Owfz3O6NZLRcFul54cacgYeZ58+4/YuPvzzQdT9R4vvuOF/lBg5ShossBpwdpeeEs\nbtRpEpuJE40KVhcvqrSJ778nuTD3XZCbpTsDwipvPy1iI17QVauYApWaSiNCUkh0BAYyLWTDBvfp\nFsWLMyqUM6e62R8/zr8OHWgMSTdwM0aM4P5LHUrx4vxNSWvS+6ds20ZDdd8+puQAlD7+8UfntKG9\ne40pPwCPqVWNzFdf0ZM+ZYrRmFy71nn+dYPTVdM63QgyE5vs2el1r1aNjgvxMtts7AOyejVrFcy/\n27OnYY1csgdiRVgRnL/oD9/jSVhXrh1+WLYdySk31o2vHUVio9CqTglUyu6PyjkcCAnPDjzwAPLm\nDEagvx8wYoPaJ4ms/PMPCV1EBIv1dTJrLk5+802Sl6VLFRmQuYmO5nGUCIe5iaxA38/p0/loJjZ6\nxEZ/TSc2AK8VPXtyvdesyQiSKPINHcroJcAUUythiOPHuU6LFqWxKAp8JUsa087k+Jpr6+LjGbXJ\nls3Z2HzhBV7PrCDXGn0fT5wg+Xr1Vf62VSrouHGsRdEjZZkB2T+9kagcexlrWsRGrgPDhvE6Y4ae\nomiGud7oVqBAAUZd05o7UYW7csX5PYkm327c7tS3uwReYuMBPn2+KQBgzJz1aDFkOua/3xmPPVDq\nDo/KCy80tGhB1aX69e/0SG4/QkKUnGlaGDKEnuSnnlKKQxmN2HToQI+8Xg8hHsRnnlE9SQSVKqWt\nRmMmPjpZe+opa8Uh+R139UVWqWjZsjG3vV8/9ZqeIqan0jRqxL8ffqCB17UrjXyr33AXOZKaB8Bo\nKGbNSmPdXYHr4MF8lFQuc6Tj1CmSnc2bmQsvqF4d2LKFv7Ftm3Nhvp6yVKMG6wZCQtR+nDhB4yoo\nSHmPL11yHqs5ZS0hwXlNSd+Xy5fpgNi4keS1Vi16/OfMUce8alWj1LOeipaUhMv2ADh87YhJtWNP\naEFc8MuCZWFFsS1rbth9cyOsfBh2ZInA0cAb4zwHYDSV2Wy+PujVsipeeLwWsterhdynj8F33mkS\nwYceYoSugxaBeeEFGuCBgWwcCqj9Hz2aBGPSJPV52e/s2WnsZ8tGQpw9uzrvNm4kqZAo15Ej3Hfz\neQOQVG/Zwv9r1VIkRO9Z1Lat85wByrDu2dN5Lps3Z6Rt2zb1mpAa2Q8rw3rePBau9+/P/R4yhCRz\n+HDj77hKr5JO9VbiDm3akNjkyOH8nm7Iv/MOycrkyfztJk1IbKxUCV98kalcmU1sBg5ktCs0VJ3P\noaHGZp1p9dxK65roCbG5lf1ZDh/mfJcu7f5ztWoxyqc7hwRyTlsd01uJAgW4xoV43yfwEhsP4OPj\ng0/6NoUPfDB6zjo8P2YR6lUoiLDgTM5X9cKLjEJuZrc7h/duwddfU5Hn2WfdF3qHh5PYXLigDKzS\npXkzXryYNwFPU6JKlHAu8h43jgbYli0qneaZZzg+AIlWDe906AYBoLzb7uCJ4pHDQe+/bvA7HM7S\noqJApP+23iwuJYVEwqqQ1xNio+PECZKI3bvVjd+TGiRJORHPtJ6aduiQs6G0aRN/q3hxKsLpBlL7\n9sac848/ZurdxYsqp3/qVMprt2hhJDZmA9ysmBQf73xMkpOVMTt/Pg1OIWrt2rnMfz99/gqWVWyM\nNV2zYveqq7gQk4JDdV+FfXkcklL9kVLlGeMXYgDkpPMtMDkRFaLPISg5EdmTYlEEcXhu0dcoVfBG\nL5xaVYBLhTif5l44gqAg/iUmqkiUTrrNaYBCJpYv5/nYpw+fT55M9atnniEZKFpUNbGtWpWk1Arx\n8STWDgfTwgQiRgGw/0vJks7kX48YVKjA1DA5dnqNiJV322azjtjIsZY1eOUKrynmNVCsGInbhx8y\nShkQ4Fwr4uPDKNEHH/C5u/NZf88caTaPqXFjYy2Jp81vPcXEiXR09OrFa8W77/J8WrqUxxbgddVV\nBE4g0s+uMH06r4tWEXnprWRFJjILS5aQsH7wASNjriDrx4qo3QpVOk/g42OUmb9P4CU2HsLX1wcj\n+zTGmp3HsXHvaTz5wVz88sETsNm8+gte3AVwl997P2DXLiqbpZWGJ+kyej52t25M5Rs9mgXCnhKb\nS5d4wwoNVV5JvcZCjsXJk4yMlCyZtuSmHtEAPBNESOumeeIEGyzGxLCnjqvtZ8vGwneBVZTHirxc\nv86i6zVrnN9LC0KQ0kNsihY1SvYmJ5NwSLrX9987f6d1a8rRAspoz5uXvW10MiGGbHg4DdnHHuO6\nknHpxCYtZaWWLZ2Pif5begNJgOvlyhWSYn9/XC5YFH8fuoDNx6Pw0Q9/IjpBPhsA2OjISEgBfJCK\n8lmB8BJF8NDcb1HvynHEvDYEB76ZgYdP70a5mAuwp2pGe3AwIKQGMCqnyXGIjmbK3ZEjFEQoVowp\nhHKdSUkxpjyZiY18bvduIzm/do3bkfNPJxPuepGYjfalS1nb1KgRZb737VNz+b//qShkyZKMNl25\nwjSnokWNaUE6sbFat3a7GpduoJvH46rOz7wWjx2jKt7168a1oIt2BAUxVdbKkB8zhiTAz48CBjJ2\ngNehBx9UZK91a0a6hg3j8cxsYnPuHEmpNCe1240RswEDqIyWFoTouarLCwhw3RtL0kxvJTwt/Bc1\nO6tr9p0iNvcpvMQmHbDZfPHjWx1QvfckLF5/EG9++wc+6JmBvhleeJHZePppeuSlqPVeRGqq67QF\nT+Q0o6OVspG50NRVE7jISBpPffsaZWUBep3nz6dhKKkxekQkOJgRnTNnmLLSpo0SBUgLhQopT3Za\ncHfTPH7c2CNj+HCmrDRvzucybxUrOhe2ZslCda9z5yhJW6KEEkPQb/LvvqsaS/bt67mU6oEDTPMA\nlAfdHbHZt4+kpEgRYyFxpUqMsAQFkZQMGGD9fbPxHRBgLcwg/UZiY42KTYsXK1nvqCimHE6fTo+1\nudajWDFGo8x9lfTogcMBJCfjkj0Qm4LzIjUuCDsmLsKKHxbiol8QdgflxHW7Gl+Nq6fwwNUTaB25\nFxEJ0cidcB2O1GSkwAcpD9ZB2KdvA5f+AL5fBfz4JTD7W2slKUnfio0lmbfZgNde42t6xOb77xnd\nqFmTqSx6dDI11ZhiNGIECYTdTgPVvJ/m/48doxNAX0e7dzMK0Ls35zM6musiSxaVoinHa88eCm1k\nyeJMtmUNvfACt+XjoyJBQUEkqtOmkbQKsVm2jASmVy9jSp3NxmtFfLxxrYiq2r59xt/u25f79uGH\n/M5bb/H1jz7iY6FCFHcAKLbQoAGcEBJi3TD34EGmOhUv7tRnCADrsHQBhyJFmCp25AjFA8aO5X0i\ns+AqQpsjB8foadqV7IenzXl1WAkKZDY8lWp217fKS2xuK7zhhnSicO5smPVme/j6+mD4tDV469s/\nkJh0n6b/eHH34NFHaTyn1Ujwv4o9exhR0NV9UlJopPfv75lX7exZ9b6nxOaPP2jwi4GiQ4wt3XCr\nXJl1Tr17kwTs36863nsibiARp/z5naVspcjevI/ubppr1xqfjx3LlKo336Tx6u6mnTUrDd8hQ1hg\nv3YtZZQB1yIE77+vGmWmBTHCSpZUZMgdsSlZkvMbGgr8/TdrDEQpDEhfnv3s2SSZQjzCwqjmVrWq\nsW5Dj1otWMB1CNAIv3KF0Yw1a5heBTC1LDWVRuiFC5yzVq3+JeRH4nzwZd7qeKTxKyjfcyLKnyuI\nfHVeRtNK3fBoQmn8b/F+LM5RAhtC8uG63R9loi+gS+pZLMl6GBu2fIUxB5eg4eWjKNe8AXIkxSI4\nOQGhyfFIlX3/9lv+1tatNKLnz+f4pGmiYN06rt/XX2eKTa9eJDDiAY+ONqY6XbjA/3PlIgnYulXt\ns6BwYdZwJCbynFm2jK+vXk3ye/SoOld+/plRxD//NIplvPkmH4cM4bZupHD+GyGR7wsBi41Vx0WI\nlx6FkZopkSPPkoXHbtYs1olJTVm/fhTLsNlUHUrHjlzLPj4kwVZOFYnm6OfkRx8xRSo1lYRv9Gjn\n7wHpr4cUB8qUG32BPK0vkYiZp44ST+GK2HTtSqeFHMu0cDN1MnLMO3dO/3c9hacptu6ITVgYm5lK\nuqEXtxReYpMBPFKtKMb1fxQ+PsC7U/5Eo0FTERN3n6YA/Vfh788bVdOm6rWYGKaYmJu0eXHn8fHH\n9PDq3vi9e2k8ff65KmR351XTb0zmdDNXxEZSj8qWdd6ebkAJSpWiipjesFPqZnRiI2vspZeMCkjS\nB8OqtqZQIf7p/TQA9icpVYrEDeAcyL66mo+RI2l0e+KNlG1duqRS2fS51A0Sd/VNv/1G47dNG0ax\nRI62QgUajidOMK3Fk/Pv77+Bt982Epu0vKF6X5D27RmJE4O3f3/ObUCAcd9kLImJKoWtQQMa9hId\nrVRJ/a+nzNzYTqKPLzZNnYcnHngWpacfwPMlW2JFYlbsOnoBu5IDEGfzQ+0rJ9AIUehavQCm7f4J\nf22ZjAPrx2HXxs8xbdUEND1maq5XsKAhEpeqS1qL8R8QQFJVt67z3EyapD6XkEBysHEj61PatGHK\nlqwzPz9FbMLDOW+VK/NPV/TSPe96DQhAx8Dx40YngM3G86tyZVWwf/48a5DMxqQ4ES5c4PhESCIm\nhtGx0qVVREUnZObvBwW5J8+JiTTIP/mE9UBppaWePs0ok5k0TJ9unN+01rT+/jffkGiZGyqa+734\n+dEBkisX56xlSxJtM25VFD+9NXWuULgwt2FOw/UEcszdpTHeLGRtmvsKmREezvPG6todHMw6Myvx\nFy8yHV5ik0H0a1sTKz7tjrw5g/Hn9mNo8NJ3OHPxWtpf9OLugNzopIHiiRM0PHPkSFuS925E3bq8\n0emFtfcSRGK4Wzf1mp5aJAXZ7gx0MWhKl3auxXFFbKz6vwiWL+djWopsoiK1Ywds167RmC5cmAbU\n2LEkZXJjFqKxZAnVleQ3dEhuvcDPjykxkkq2bZvKd9dT43TExTGd6tlnmWYk6TE61qyhuIC5mWCT\nJpRNFuiebHfk4tgx/s2fz/oCMeakLil/fnrLZXvTpgFduqgCYR1WNWUbNqi5qVKF269TR73/+efG\nbcixLlKEEQWA865HuUJDOT8BAaqIfNUq5/FoBebXYxPw++bD+PXQZfQp2RJZr1REjclbMdNRAAm+\ndjS+dAgTT/6ObZ2LYWm5JOw7NAN/b/0ay1aOxdTFn6LL+R2oc/Ukisdewr8zay7ATkx0bjAq86kb\n1IKJE41RG72hYkKCOganTzOaojeptNvpbQaYCqVDIpk5b9TsSPNT8+/LdnRiM2ECPe7Hj9NxINHm\nffvUOoqM5DHdsoWy14mJXD9STyXzPn8+yfq+fSRLZctyLcl5O3AgHQwffuhch1ipkvo/MZHpZC+/\n7F64Q65HSUk0WNu0MZ4Tvr7809fp6tXc5927XW8X4Br84gtnQ9+85qdMYf1ew4Ycx8KFKkqmo3Fj\nPqZVxJ9eyLVWrm83A1/fjKWiiSPhVhIbSXcTcu8Kn37KiGebNrduLF54BC+xuQk8VLkwlo/qhgIR\nIdi07zSe+nAekpPvT93w/yx0j+wN+JqVbf4LSEriX1rSmf9VWKUrWHlBO3RwvQ2rHhAAjbizZ5la\nY1YJ01ORUlOt1XckPckVpDD4778RvHEjiczx42xwKMdLDD6HQwkMfP21Z+kjZs+p7rHOl8+atAC8\nYa9fT+OgZk3n9yMjSRakjkAQFmY0UD312OrCCvv3U2nM/LqObduAGTOs59eqqV+JEqoTvBzjv/5y\nVi8bNIiP77/PR5HeBWj46khMZK1Jhw4qYiMkyMcHSckpmL1yF951lEDzDu+h8LYA5Gz9MRq9MhWP\nLTqBiXmrIwG+yJY1AN3O/oPtG7/A0u1T0evgalTq0w2NOzdFyaO7SQJGjTJKDevQo33Vq9Mzr5HI\nHIsX0zhs2NCa2ISGGpuE2u2qyWNqqrMEtg4/P9Z0APRK6xDDUmqMdOO0Zk2mPQpsNj7v21e9dvCg\nMkqlf1H37ur4ffYZ93XRIqrbmbF4MWtmxo9ntHP7dkZAd+1iNFQ/54OCOD/vvGPchk50PBVf0SNk\nAJ0sorKovy/rMyaG6np9+xrlqLdsoXT08OHqNVdOFjmeMkY92mol9CG4VfUdUlfoCleu0OGUliDI\nli2MmFo1ZU0LVauSiJuPaWZCnGAtW9663/AiU+ElNjeJMoXCsf6LnsgZGoTlmw+j2/CfvTU3dxM2\nbqQkpdk4E4hxrF18ff+LERt3+b33AqwasZmNkHLl3NcYuWrmNno0PdLt2hkNMcAYsdm4kWkv5jzp\ndHgafRMSVD1Jvnxq/YmB1LAhvdGSn24uSreCq7Qdh4MG8dNPqxQy3TAVdahLl3C0/vAAACAASURB\nVGgQDh7MNCOJkMj8mufLXHCvExt3XmGdwOh1LFYN7QBnD/X16zSCZ80Cnn9evRcTwyhYXBwLlp96\nSokjADR+dcj+COGzqqkBGAWdMkWRy9hYJPr44i97dnxUsB5eqdwOlZ6dgI7vzMFbvx/G4gvJOHY5\nDvGJyaiWzYZHUy6gw/ld+DvHMUT98hqm7P0ZFaLP07MrxlJCgvJW68farBBVqZJKY+nXj5EoK0NV\nT0VbsEA1WQWMx0m+a9VjRHcY1K/P9dqnDwmeOT3KnAqkOw3y5OE5JbDbmX5YrJhxGzKuV17h48CB\nisg1acLHmTOdPeaTJ/N3W7VS13d9TvTPlyvHNSOphzr06316iY1cbxMTjdcB87GJjlbvT5rE2j2A\nkcXWrVlsLxD1MrNDQqTYRdxAP+9l3q9cUQ1rBbeK2IgDxpVIQMeO/IxV1FnHoUOMpi5Zkv4x5MrF\nCImVYyazcDt65XiRqbhHraDbizw5gjHvvU4IDnJgxoqdqN77Kxw85aLTtBe3F99/z/QlqxA9oG7i\n2k3f578YsRFvZkZuDmlhxAh6JN9+O/O37SlcRVty51Ye+bRIXWioqq3Q4e7GlTUrFcOKF2dUJyGB\n9R2A6j+iK09NmMC6gw0bWC9w4IDBU+6jpxDVravGrUfaIiNVVCAjxMaq9kf2TZpuZs+u3r94kYbz\niBGURJaCatnOiRNGj6g5RWf4cKbOACQRrnLlXREbc2G7ecxyfIKDuQ71QuGkJJKPnDlZuF+8OM95\nfa2aDTo3Bl60rx+O+Ydi6ltfYETe2ni2VCs0/CsGrV+fiYfCGyOs4TDUXRqJIUUb4ZPQ8th97AKK\nhjowpEs9TK6fCwdC9+Jis2BsmjcMi//8HD9+/jxqD+nHY7plC9XHjh5V9Su6IS1z8vHHVKITxTiA\nBMJsoM6bR0Kq13P5+zMta+JEphnq0ZFBg4BmzYzbkJoufW58fJSowhtvkNj4+Rmb2gqCghhNmT+f\ntVJ6emhqqvGckv+DgoySy3J8P/qIdXO9enF9hofz3GvRghElPQUzIoL7J2lkch3Xj60uXb5nD9Mg\n5X1dDEQnfLNnG+fdFT75hKSxXj21DyVLqoixnONz5jDqlC+fIpFbthhFUMwQKXMzIXjtNaaVSV2Z\nFbEBnAmRnx/Qo4dSNMwsyNo1k+OkJM6hOATSatBprh262+AlNv85eI9UJqFuhYJYNrIb2r45C9sP\nn8MT7/2E1eN6IMDhneI7CldhfYEFsflPRmwEaTWAzAhiYm5tDrMn6NyZXm5d3rNUKRahb93KlIS0\nPJJFiypVLx3ublw7d5IMiHEFqKiElRLb4sX0lEvvBZNsq09iojJgxSst405MJEnQCcDNRmzMnxFv\nbt68ruuRZD50Q0MXTyhWjAZlaChVrfz9VY0FwDVoblwKGJuPyj5Wr86UPCvo6Wauiq9bt1Z1cq56\nXejrIiyMpFNPWZw4EQl16+GD6zkwMqwmYus8AKw6DyAYyFMViEwCIiXi64PSBXOiYeXCKLJ5DfIs\nX4QOiafhH1mK+7RjBzD/hgHu7881W6oU06z27CHRkHQ5wBgtkGMtRF0f97PPkmQAXKcDB9JAHjXK\nmGrncLCuStamvo0yZSiBnCOHKigfNsxIWkV++PHHSSry57eeU4DHeexYEvtBgxg5kXOkVSumiHXt\nqj4vZKZvX/5Vr04Z5mrV6DTIlUsp6vXvz9/v2lWtWT1lUNaDrGFJEdXPYSFZDzxAEhIXp+ajQwee\n15JeeugQI/tJSYx6zJrFa0uHDs5kDmAECFAOs8REng+DBvH4SgRBj1hZORrSgwIF2L9HoJ/3+nE2\nR1SDgylIkNmQtWuOWJ88aYzKpRXR9hIbLzIZ3iOViahVNj92fvM8qvaaiE37TqPeC9/g2eZV0KNZ\nFS/BuVNwRWw2bABOnVLF1XrE5mZVXu4kbsXYrTpv3274+jJFIzHRuU9Kjhz08rozwgTHjtFoKVhQ\nef7NHbx17N5Nb3TVqvwOoObBShVIlMnGj2eOv3k3EhI4zubNSQ5atFDbiYtzjorpxGbRItbdmOuA\npNGfkA+JOEq6i75vBQuSDCxZYl2UDzDyERNjJCtFi1IauHRpev1fftlYs9GhA2shZsxwTZhefZVz\ntXSp2rZOvqpWJUkdPpxRHEmf277del0PGMA8/xEj+Fw36LZvp8x21apKqa1KFZKBr75CXJ/nMT13\nFawNLYBffjyFC47GwI3d8UtJRq0CoQi/Gokc+3ahbYeGiGvyKIKDHChXOAJ5c96IWL24FDi3nf+v\njXRel/HxNJxlPho1cla008meEF6JzgQGMiIQEcFIlB6x+ecfksqrV617xrhKP2rWTEVt9M8BFB4J\nCeEYQ0OZmuiqaSJAoYEffmCdVv/+HLecG+bo6eOPKxllgX6+WdUGRkUZ06piY7mNs2dVxMW81vT9\nle3Lo05sUlJ4/h87Rln1iAiSrB07GAGTdK9q1ayJjaBaNUZoq1Xj81q1nM9PgX6c3Bn7HTvyPEjr\neivXhqgobq9IEaaruSL4mQ1XERv9ugGkPR4R6zCnjN4tqFGD1yRdZMKLuxqZmor29ttvw9fX1/CX\n13Sxf/vtt5EvXz4EBQWhYcOG2G1SCImPj8cLL7yA8PBwZM2aFa1bt8apU6cyc5i3FNlDAvHL8CcQ\nEZYFm/efwfNjFqFm36/w+2YPwtteZD5cEZsaNZibKzetcuXoEbx4EbF6vnNmIimJRlhm9xMAVN1H\nmTKZv23J+daNsNuNLVuYumVuvlivHg3XsWNV0zx3OHSIKR16Ez53HjmJVOmqWFOm0PjImZPRGelT\no39e36546LNlQ1JICBsDLlxIAtG5M7uFR0Y6q0gBRjndZs1IYnr2NH5GUldEqUnSiOx2ys4WLaoI\n0/r1wIoVTIeKinJWWBMMGUKvu6BYMRbblyypDJdLpnTbtORfS5Sg5/jkSdY7hIQY09qkt9DQofSw\ny3xXrGgdcRWDSuZ85EgSgEOHgLZtkbp0KbaO/w4T9l1DpwETMPDxV9Hx5a/x0E+HUKj2S3i2dGt8\nk6cqLiTzNlg6+gJWFr+OhKInsPqVRzA332V8tf8XNE86h8cr5Ebj6sUUqQGcPcyu+pyIEXvqlHE/\nHn+cEUGpH3n5ZZLuY8do1I4YwUJzs8S2zWaUVtbXrStiM3gwU7ukBkcK9eVz/v40yMuUIWno2jVt\nUQwhkgcOMIVMh552VqKEM6kBjGvPKtoqhnuhQnQS5MzJ63XFimqN68SmYkWVaqlvU+b/r7+Uqlty\nMoULSpVS9U4yF+Io0PfDFVq04LVk9mySI11+3IyaNdXxcbddGU+FCu5/u3ZtPp4+zeMq6mfmiM2t\nQlgYryv9+hlfz5LFSGbcEUNARU8lre9uQ5UqvB7qdXte3NXI9Bqb0qVL4+zZs//+7dix49/3RowY\ngU8//RTjx4/Hxo0bERERgcaNG+O65pV86aWXMHfuXMycOROrV6/G1atX0bJlS6Sk1fX1LkKForlw\nYOoLmDKkDYrlDcOOw+fR6JWpaPzKVJw476JQ9n7GwoXGPPHMxIIFfExLYtNup+df90JnNr77jgZG\nlSqZv225kaSlQJMRTJ/OR1cpQ7cDrmSX//mHRPHHH0lwXCmACazSx2rXpkE8a5ZzjZJObEQVC/g/\ne9cdHkW5vd/NpvcAAZKQ0HsvgvQiilhAmoDiBbHrVRRRQOFiQaxXuBYsP0QQEOw0CwgK0iVIUTqh\nJUASSA/pyfz+eHOYbyazm0KiKPs+zz6bzM7Oznzzzcx5z3nPOTRk3N1JUtReFyo5kRycp5+m5z4l\nBcnmh+Nrr5EYnT1bkthERVl3JjfDbMSqEq7kZHpx1TLgYtR6eZFUOULNmnqCcFkigSqxKa1vR8+e\nlPyo460ae489xugQQMmSlUxFDLjiCNXvfjXxa2IOPv75EPrUvAF1uk5Eh04P4qEFW/H5vnjMWX8Y\nX+yOw8ZcHyR6+qNlbjImN/bCnp3vIXnzK9i/cy56P/c451C9ejS0fH0dN1mUa03mlJUDLifHaOTJ\nfKpTh4RlwwZGumrWpGzp9ts5D/LzjaRP00jcoqNJAKWylrs7EB6O1J49KSmT+S/PSzknFy/qUq78\nfH2u2Wzsg6TOM5FalubIUD315uiCnMsPP2SkTy21PWCALksTaalVfpz8/vXX8xqdPJkEe+9efW6o\nZdtfecXYHFb2QY2OfPUVHQEtW+oRMumnJGOmEoOyJtynpJCcOrv/Dh6sj4Psm83Gl1pSvazJ/uZI\ns0Rq/yxi8+uvzPMyNzu22YzNha1IrYr27XntqBFmF1y4DFS6Psput6OmRfha0zTMmTMHU6dOxZDi\nMoELFy5EzZo18emnn+L+++9HWloa5s+fjwULFuC6Yo/MokWLULduXaxbtw43SIWUvwEC/bxw1w1t\nMbRnc7z19Q68unQL1u06jr5PLMSGOeNQJzTwr97FKwe3306jcfjwkmHsy4V4Ha+EMshVQToEValT\nvhJyjhyVM5WH+uHDJLFWuR1W21EN9Rkz6OkdO5YG5I036p+pxOaeezhXBw+mVCQujsZM9eq6YaYW\nnhCHjZV39vbbSWbEeBNj1mpfS4MjYpOfb9wfM6Qil+Dxxym3uPvukvvgqKKcYNkyJu0DwPjxlJWo\nfT3KAnWc0tONkbSCAhrcxeQy93Qcfk+8iNO/HMTJBE9833E81gUUSwWXRAPeNKbCcjPQJT0OHTPP\noeC55xHy5mtoHXsINfMvouXj98M2cwqw/E3gYo7x+AYOJBm89VbmilhdA3K+fHysScCkSdx31eg/\neZLvkhOizkPZ3kcf8T0khFErHx8aj40akQCplfvWrwfS0pAwciSCVc95UBAJhERwzcRBfsvbm9tQ\nIQbmzTczSjdxorUsSjWgzZ+rZMIc+UlK4vEkJpYkYCrUnCNz3tjJkyywUbcuPenffVeSfFevzghj\nly6MUublcX2xTyTPSwikGr0SlDWvwtlxqGjcmPcZKRwikHkBUNL45JOGBqyWUKN2su0ePUpKIqsK\nqal0KgnJVBEWRsngjh1lq9T5Z+2zC1cFKp3YHD9+HBEREfDy8kKXLl0wa9Ys1K9fHydOnEBCQoKB\nnHh7e6NXr17YunUr7r//fuzatQv5+fmGderUqYPmzZtj69atfytiI/Dz8cTUO3vivls6YuDkJYg+\nfBb9Ji7EhtnjjLKGqxlisFRFVO7mmxkRclR56c+EVM9ypMG+HPTuzUo7bdpU/rYXLaJX+dZbK3/b\nZYUVIcnOLtmY09kcOncO+Ppr6/UcSRbFq3vsGCUWfn66t3nsWL6npele39dfLznXJOqhYvt25g/I\nA131ogM0YnftcnwsKszERpoDFhUZo0xmqBXaatRgVOLiRRIb8do/9BCNxg4dKE174AHjNjSNcjkx\nxs37VA4U2N1RZLMj1isQqe7eiMoHzvjXhkdKHmIOJCLlqy1Yv34X0vOK8OsTy3AuSSL9NiAgCj5a\nAZplnod/YR7ujt+NLuln0CzrAtxQHD0a1wd46T4gtbhsrk9xJMVcprd9e10uKg6RnBwSYD8/RuBW\nraIx/8EHvL9IZLhnT0ZTHn2U1/kttxhLLg8aRKIgskErYiNliidM4H7Mn2+MNKq5ZMVlwf0ffFBf\nNmECK/e9/bZ+rzEb3PJbv/zC6lt9+jByAxjJ8LRpzJ+xIjZqxCYqijIseUZbyeMEMt6nTjmOThQV\n6UUh/PxKRiOSkhid6tBBlzqZ59yYMYz2eXsz9+vIEc7r//6XpduFOHh50VFRrRrvcbm5OtEor3Nh\n4ECe4xUrrNfr3bv0KGz9+iWKjljCLKF99lm+/iw4k542b141z3MXXCgDKpXYXHvttVi4cCGaNWuG\nhIQEzJw5E926dcP+/fsRX5xUW0st8wigZs2aOHv2LAAgPj4edrsd1U110WvVqoUE0ZH/TVEjyBdr\nXhuD/pM+we6j8eg3cSHeenQg+nWoD3f7VV51u6rq7KvbvhIqmsgDvirKSbdpUzWkBtD3uyrOT1nx\nzjt8VzuiqxWC5CHqzKDetQuYM8d6PXPDx+Rk5mp07cpoxOuvUzYGlJxLquE2bBgNF+lO/+qr1qRa\niIMYmHl5lG8MGkQj2ddXJ0tyfKdP8xxERhq3ZXX9eHrSGLeqqiYRkLw8YzK17Nf587oB+cILNA4H\nD2avHzUaL7IfNVoxbBjlPuWITh46fQFzl+/EgtrDkRGukIwCAJ26APP2Athb4nv1vYGW1b1R95rW\naFE3FCNfmoDqu7Y5/qHMTH08pk+nV7lnT0bOAEYqqlUzVt8SQpGayjwub28Smyee4Pw4fJiJ40Js\nfvlF/+7s2fxfxiQigttTO7Wr89BqzD7+mKVzpRBFUVHJ8w9AU8/9kSO8TtQcKLPXfM8e5nxs3EiJ\n6YsvMu/w+efZQFbN7XJ072zQwPj/gAG6BHHePB7vSy9xHNzdGYXw89Nlkc8/TwJRWFiy/1FKCvDW\nW/x7wgQ9+ifXmkr03nmH16a5eEh8PO+JERE6QfXz4zmR8wWQmH77Lf9u3Vong97eJRuSOoJ6Hleu\n5G/06lW271YUf3W1LmfEZsmSP3dfXHBBQaVeETcqEo5WrVqha9euqF+/PhYuXIguTrzUtsuUCUVX\nRYnbKsJrd7bGwx9cxOHYJAx4ejGiQv3w7PDW6NDAQZOrqwDt8vLgDmD3vn0oNPfIuEw0SU5GIIAj\nMTFIV+ZJm5tuguf587jYtCkOLl4MgKV43XJyYPPwqJI55R0Tg1YAstPSsP9vNGeDT5xAIwCpSUk4\nVkn7bcvLg+bhUWaJYMMzZyBxDzk3IYcOQYqKFrz7LtwBJMTHI9bBPgYfPgwpC3G6Vy8kKusFnzyJ\nRgBSzp9HTHQ0ai9ciDrvvIOkgQNRHUB+tWrYW7x+w4wMqDGY6L17jaTijTfQYtQo+MbEYH9UFLJN\n+3P4vffQVBoKFnvn84YPhz0jAwn/+hfCAWRdvIgDyvfcsrLQodjTe/Cjj3BRIbF1brsNQVu2IPaj\nj5DevTtQWIhGnTrBVliInNOnYXQlAWmdOyO1e3dkN26M7L170R5AQX4+9pRh3NTSwEl16+LErl1o\ncOECLmWmFSe65+zahT9M24t84w0E7N6NxNuG4HTz1tihBeGLrSex81hx00Q3kppaeZkIzbuIY4E1\nUcOtEPDzRZ1aQfB0d0O7+iEIDfJG/fNxGP3so7jYtg0OP07ZsldOBpwhcdw41Cx2sO1v2hSe58+j\n8ebN/GzYMJzNy0PB7t1ok5MDoarJ6emoBiDl5EmEACjw8sKe6Gi0AOALYP+uXdDc3dEKQE5UlOGY\na508iUgAiW5uSHnvPWju7sg0jUmLjAyISV+Yl4fd0dHw+vprtB46VF9p40ac6NsX9QEU5OXheFYW\nzG1oNbv90nXRMCsLIQCOHTiA1GLDPOL8eYQp66cuWoRjHTqgRnY26snCnTuR+tJLODZnDkInT0bd\n4mpzu/bt47VqhqahRePG8FX6Fqn3zYjYWP5mZiYwYwZ2d++OwqAgNG/eHH4HDyKxWTOclqiMSPOK\nYcvPR8fi49p18iRqxcQgEkDWunXI7dMHBUFBCEXxdSI5HqYCBp5nz6INgNzCQtizs+EOYM+RI6iX\nlIRgWCM7IwOxbdvC54knkN65M7LPntWJrwMEb9yIRqb8kHMff4wzzprVFqO46DZSUlIQUzx2QZs2\nIWjbNqR2787r2QHCAIQ0aoSzaWlIjY5G/WnT4J6ejuOzZqFQLQF+mXD0LJTnQkpS0qV9d8GFsqBx\naZLxy4VWxejbt6/28MMPa8ePH9dsNpsWHR1t+Pymm27Sxo0bp2mapq1fv16z2WzahQsXDOu0aNFC\ne+655wzLUlNTL73+bkhOz9JmfPyzVn/0HA19ntPQ5zntntdWaEfjkv7qXftr4OuraYCmZWRU/rb7\n9uW21683LqdvUdPCw/n/zz9fWnbyqae4bNEiTXvgAU3buLFy9iUzU9PWrtW0HTsqZ3sqGjfWNHd3\nTTt2rPK3/eOPHKexYytne+fOaVpYmKbdckvZv/PUUzw/r76qL/v0U/08yuvhh43fy8/XtJQU/v3V\nV1xnyJCS21+5kp/JPn3yCf+/4Qa+V6+ur/vLL5q2ZIn+m88+W3J7R45o2m+/aVpWFv9PSdG0PXu0\nvcuXa1r79iX322bj+8SJfI+I0LT77tO0Rx/l99PS9HVHjDD+1vvvc/l99/H/11/n/08+yd9Vf+f1\n1zVtwwaut2OHpvXooWlt22rapk0lj+GttzStSxdNGzzYuI1t2zRt6lSOwb59mjZ0qHbSK0h7s861\n2gNNbtHubjpYm1GvjzZr8S/am59v1d5bsVN766vt2pxed2h3NRui1ew26dJ9D32e03xvfEm7/42V\n2p6j57S88xe0IkDTAgI0bfNmTRs9mvthxrZt3Jf27TVtzx5Ny83VtJMnecwAr1tN07Tx40uONaBp\n+/dr2vLl/HvQIH27W7YY1xs7VtMiIznmgKbVqcP1rrmG/2/fznsLoGm9ehn3cdYsLn/66ZL7n5qq\naV9/rWmtWnHOye/dfrumFRVp2vDhxv34/HO++/tr2u+/lzieuPvv5/c0Tf/u55/rv5eermmdOunf\n+e9/ufybb4zb6tCByxct0pcVFpbcfxUBAfq6Kh5/3LjttDQuT0zUtPfe49g2aqRpa9ZYb9fLi9+L\nidG0unX5d0gI3xs04HvLllx3/nxNe+01TUtI0L9/7BjXqV+fx5CRwTG6/nrrOQFoWsOGzo/VCg8/\nzO9Onuz8nnD0KK/VH3/Ul8n6t92mL3v2WS574YXy7UfNmvxefHz5j8EBdu7c6fhDue+o90YXXCgD\nqtp+r9IYZk5ODg4ePIh+/fqhfv36qF27NtauXYuOxTXfc3JysHnzZrxRrCft2LEjPDw8sHbtWowe\nPRoAEBcXh0OHDqFbt25Vuat/KkICfPDcuD6YckcPvPLpZrz86WZ89N1uLFyzFzPG9sazY3pedhTr\nb4WqlKKNGkUpjaNETJFOKGV6LzXo/OUXyjI6dKgcWYGfn16Ss7KRn09pQlkSNcuL/v2tKz6VB/n5\n1I0XFtI7e+4c+6jk55fewA2wll3IstBQPS/BnAPSpw/7JMTFOU6AX72aVfPuu0/vaxRW7N8Wb7Aq\nE+rZUy9FDBgrjgnMHqnVq4G77kLEgAF63o6gTh3dY336NHNyfHw496pVoyRHlXuYpR9mSYjI2zw8\nKG9780296lJkJKVyKSm65KZXL+tSqydOMPm3uNlgns2Or0Ob44vvTuPg2Qjk7NiPjJw98CuKwqmu\nT5T8/ryfjP+7NQGKCyQFFeSgSVYS7mhWDeM+mIxg/+J8l6Ii9hIJDOR5W7qUL+m/I5A5s3s3c9ei\noykJk+tc5snMmZRbxcQo+zWPPX+kTPf+/fpn5kaG27cD33zDBPYvvtBzTeQ9O5sJ6u+/z2R1FXKe\nraLQsbEs99y8OaVLaWk87ytXMor54YdMyp45k+uL9z8zk+fuf/+jRKsYER9+yO/ExelyLTVnKyDA\nWPFRxi/YFLtoUhwLUhPoS7unqNeCigceYBEDifLJOQkNBR58kLk9x44ZG9KqCAigbPfECebbtGyp\nn6vjxe0T9u9nvtOsWdzWgAG6XFK9Z7i58RyOHq031bRCRYqvyLlRc+msnmW//srjHjWK91RZduaM\nsbJiaU2lHcFRgZWqwogRLI1tvue64MJfjEolNpMmTcKgQYMQGRmJxMREvPjii8jOzsbY4iTbxx9/\nHLNmzUKzZs3QuHFjzJw5EwEBAbjjjjsAAEFBQbjnnnvw9NNPo2bNmqhWrRomTpyItm3bor/cCP5B\n8PZ0x3Pj+uDWrk0w+8vt+HT975g+/2ccjk3CO48NRJC/d+kb+Segb1/e3NPTK78J5HXXkVAkJhq7\nIQuE2CgPg0vERnJhzMmvFcVvv9HI6tChbGV8ywPJkagKYlMZ2LeP/UkAY6+Jo0eNXe0dwYqUiBEi\nywYMKJlnJM3f1q7Vy+6ajY577uH8OHdOL01qJjaFhcBdd7E87/z5eg8J+aw0FBuKtvx83eB9+WX2\nR1D3p2lTGtAZGTTuhXCrv+GoKaGsY+4I/sQTLKLRtClzS0aONJZWjY0F9u2DdvAgUseMQ5xXIM7f\nMQ7VioqwI6wjMjwbYlfzSKys0RRZdk9gk1S58gQ8PXEBgG9hHq5rXAPtCtPh+/M6JHTvC8/ePZGT\nV4CcvALY3dyQ99XXaHHqIG5MPobmWedhA4D+TwPqfc7NDWjVin/v2KEvf/RRJrd7ejKZfd484xis\nXcuKbs2aAf/6l07awsKAzZv186mO13ff8f3EiZKfATQ+163jHJXKT2LEyn0qJ4fE1Gzc/fADzy9g\nzJUSCKFISyORkXuNkKCQEOa9CLEJCuIx7dhBw/exx/gb33/Pz9KK2wjUqKHfr1asIBmQoiXqHBLj\nWTXGx49nyWSA98yywlz2WtCsGfPLzMRGUJohHhjIfCf53Eyg5s1jT6dBg/TxVH9DxuTcuZL76ggV\nITbqXBBYlTuX63HZMub61apFR4o4UwQyH7/5xiD9LBVynGbHSVWhWjXnJNEFF/4iVCqxOXPmDEaP\nHo0LFy4gNDQUXbt2xfbt2xFZnOz49NNPIzs7G4888ghSUlJw7bXXYu3atfBTbqJz5syBu7s7Ro4c\niezsbPTv3x+LFy/+R0cwOjYNx+Jnh2Jk35YY9eJXWPzjPny58QCG926B/h3qY1S/VvDyvAKS36sK\nJ09SH52crFecqixs2MCH3/jxTAQ3Qx5AykPfJkaGGIiV1Rdg40Z6zidMqHxic/o03999V09yryw0\nbsyH5h9/6M0mywNN05NzAZZeveUWeltXrqTRaa4cdvo0yUPduqzwZFUEwtOT3tnAQCYKW5G6vn1p\nxEdFcf1hw0pWpRODSSXVUq3swgUmFPv58Tfi4ng8AQGcW3366EQjPp6JOT41ZAAAIABJREFU5ZGR\nTJo+fZoGa0TEpTlU7SclijFwIImNut9ubixyINp6mYsqmSlrxEYl5OZ1muhZGufOnMfygffgf036\n4XCPKVx4FAB8gabFlfCKL8sWdUMxdkBbXNuiDqoNG4SQ2BNIemQCop58DMEnjjIKcf48cPd1wAOm\n6OQn04A4U3NaZ9eWeq5jY60JguCZZ4Bu3RgRNUdFzUTWWWRYPnvuOUaOAJ6T0FBWIJNk8v79WQVM\n+lLVqkXyfs89/EwicOPHs9KWNLmVeS79W6Sqn7PoDsCxMEe2332XEZxTp/SKhV5eHIuaNXkfyM+n\ngQywAMbQobzfyjbatmVEsGFDYwNCGeuyKCVeeonVuNQy4QCvE3WsHREbR46BOnVIRGQ9ldgEBHCs\np07lfJP7uPp769bxXS2gIePety+vV3Mp6nPnSIhkvbJAyG52NqObv/5qndCvRqaPH3f8rJOea0oP\nwHLhxAnrEswuuHCVoFKt5aVLl5a6zowZMzBjxgyHn3t6euKtt97CW1IR5SrCrd2aYvu79+Cxt3/A\nhj0nsfjHfVj84z48/L/vMKpvS0we3QNNIv+BRQbEsKuK8pClhfUtiI2bmdhUVsRGlQhVFVavpiF+\n5gxwxx006C8XmZmsfFXRcXj6aWP50pAQeoZHjaJh4uXFqIKKvDwaGUI2/vMfeurVqlxjxvC1ahW9\ntlYGqyTRZmZSymTVkFJKIqvJvmJcSO+LDz5g7xlA3ydzs88LF1gaG2BUbvx4RiHXr7c24K0iSDNn\ncqxlDhYWcu6qjp3SiI3VvFWug6IiDXHeQTgeXA9z6lyLFTV0I8ijqBC18jLRICcF5wNrIDI1Ho2y\nk6ENH4HHHrwFzaKK+0wNGADE7AMARPTsAETUAua+pUsCrQw7q2vQGbEp73XiKFqpjm9wMA3xVatI\nqM+d4xysU4frDRrE9VTZlpsbyanqPZ80iRGVvXv1/Tx3jpK46GhG9wDd0B01itGLL77gcn9/bjcr\ni/cFkVZZlQYHWIHMLMeUyKdZTta4MeW35mNv357lmzdsMBBbPPpoyd+LimJUqFGjkp+Z8cwzejRW\n8MILLI995536MvP5keMZM8a4nkAqCwopVImN3LflmSHRGfV4pYfPbbfpy4Sw3HQTP5d+OocO6Q11\n8/OBuXN5HT3wQOkqArlvZGVxjvz0U8k+NYBxPjsj6RXF/ffz3EopcRdcuErxDw4D/D3RukEt/Dx7\nLI7EJmHxj/uwfMsh/H48EfO/34P53+/B4O5N8djQLujVtu4/p0z0n0FszBKDzZvZC0FyCxRj8VLp\nVKn2IxWsLheVTZSsUFhIrf3mzXz4P/xw+byPVhCJRUVlguaeDDk5jNg88gi9yhculMy1kblw/DjH\nLSRE1+Obcxmiopgf07p1yd8WYiMliVNSKGEJDKTRkp/PMbPbjb//wQf636tXcx/MkR0zoVANL7XE\ns4fHpTme0b49AlavpjGanEyJWFgYj7OoiOesuErfJeTmMlKwaxeN8uIcxUufSfnggQONY7du3aU8\nh5wiYHtwPfwU1AafjHgDp5KzgHbjLm2mW9ppPF4HGLJ6Ady14u+3aKETvMH/AYTUACwpLDCX4AWs\nG6UuWMCo36uv6p5y9Vq4807g009p6L79tl7iuzTcdReNZDUiu3o1x2XIEL3fUEAAz3/nziQYYrTH\nxOg5ZOo5dSbvTE/XpbNCRsQAB3RilJWlXz9ffql/brNxf9LSGK2RqIqcQ0H//px7AQGOcxEjI7F/\nyRK0lD40sv9W695zD1+lISqKeTwVhcU+VhhqPpPIA8eM4TJH/ajUv1VCLffCtDRjo1MAWL6cEbSM\nDN6bAM6t0u573btTdtipE/dPbfCroqzEpm9fkmNz+erS8MEHvH/8g9UtLrhQFriIzRWKJpHV8cL4\nvnhhfF8cPn0Br3+2FZ+u/x0rthzGii2H4eftgY5NwvHIbddgSM9m8HD/C3uMXC7+ioiN2aM2eDC9\nzR4eOHP0KMuU1qtHOYDaYK88SE+n4RkURANOyNWsWfTsVWb/AZFFVa+uGzXPPEP99uXmp4k3NDXV\nsUe5PBACIN76WbNYJlgt16pGJZKTOTd69GAOjKqZHz+eCeQLFlBWY8Y11/D3JHcmOZkRpAYNaPRb\nRWuAkvPF21vf72XLSMhuu41SOjFiHSVRu7uTyDRvjpzISASIzM3Xl709du3i9mVf7Hbk2uzYFFwX\nyY9NhLblKODujlMJ2djVZjSq+/ggYvEvqBXiD38UIiPeht+b34patroI/343Go99DL9tPomko0mo\nff1YbEQwNtRohAQhMslZqJ6fhXo5qWhcKxATN32KazLOAq3uAjTlGpwyhfkq6nikpBijGZs2lYwO\n/Oc/zOMxo2NHvsaO5bbffdc47kIMFi9mZEGV7TnDpEnMrXrkEcrD5s4loSko4HUxZgyJfkgIZVjS\nC6l2bZLlZcv0bXXuzP1r3lzPQzpzhlI41TgXIlSnjm5Iqsaqaox7O8iVHDqURO6LL2gYDxhQcg6r\nOQxOiqxkN2miz3Grdd9+m1GUf/+bkZSqhtzb7HaSXDXHSfDii3oEyxm8vDgP8/IYOYuP14u5qM8M\nPz+jE8cqh0fOkdzTVMiYqcSgLPfojh0pMZ49m3PGUc6gGj131tZA5oBVdLk0uEiNCy5cpcSmrJWY\nrhA0jaqBeU8Nwovj++KlxZuwNjoGR+OS8cu+U/hl3ymEVfdH52YRGNm3JUZfZ+G1vtJRlcTm44/5\nXlqDV09PJt6quPVWXbJSEQwcSFK0eTOJlBo1ysurXGIjxtM2U4NClQRUBFKQFKAUS22QWVZIg0KA\nRo481FVvvTkqphKbrCw98mKWYR09ymaDq1bRoO7Vi2RB8MQTRpmbWT4GMLqSnc1cA19f5mSZf0cl\nNocOMWeoRw/K/dT9tIKHB6NJBw7gVHQ01JZ/Rd8sR/p7HyJxxkwcgi92z/sMS2q3RWyjAOTYPYCN\nF4CNDrqYC5oWy6c+UgoC+LSG3qAEQHYh6mWnoF/qCYzp2gC9F/wPbt26Aqs3A27FETWzZzoigsbV\npk36eJijF9WqlZTUFRaW7jl+5RU9UV2gXg9qjkD9+sYEfzOEaJ07x+hLRobxXlK9Oo3N/fuNhOux\nxzg3Z8/Wc9TuuIOvzEwu8/Xleu+/b6yeJjk0qlf9xhspJezdWydFWVnWkUSARShWr2alrNtuM0qm\nrPDVV4w8lkUeJscv5yQnh5FRq4atVQF5vn7yCc+HVV8VkZWWFlG22UhOli0j6VUjwDfeCHz2Gf9+\n5RWj40Xmk3otjx/Pymhm+R6gj5m6jbIShQsXKGmzKhogaNKE25McPUeoyiqhLrhwFeDqIzavvkpv\n4dat1snkVzDCqgfgnQk3QdM0xCdn4ptNh/DW1ztwODbpUiTnjc+2oXPzcEy/qzfCa1Rus8sqQXY2\nDVPA6HGsLKxZw/eyVN4yw6psanlg9hiqibi5uSWjBJcDR0TdTGy2bNHld84ewgLJ9QAqTjznzWOl\nq8REGnEiJXOWX6H+Vna2bvyYIylivJw6xeiJWs1J02hUeXvr51LOSVERCwRkZFCSGB/PXJqoKBIb\nq4jNzp00VF9/nctiYxllEEPIWcQGQGpmDjYdSMCynWux8efd2J94EYVaIPJ6TAHWZwLIBOrr+vhW\nuIhmva+BDYAGIDM7D73aRMHP2xNnkzKQmHIRmWmZSPpuLTrlJwOPPYZTCWk4diYZdQ/tQbPYwzjr\nFYhmF8+jZ9ppXJNxBh5aETD4aW4xL89ouN1wA2UwxaX2kZNTcg6bjS11nOSzl15iRa7yJj87MuS+\n/pr5ISqWLmUkprBQH3/5/vz5JeeqSOrU/R0+nMe/bp1ObARTp1IKJ/kn6nUAWBMbNzcm0QMcu4kT\n6dC48UYa41aJ+OUxYtu1436o8+ydd4BTp+DVvbseOQPojFGrBFoR+qqESlId3ZvKc+zmCpVpaXRY\n1KrFc/T22yWPLSCAjhSJkAKM2DiSgcn3PTw4N5KSnBMQFWWpSllQADz0EM+fs2Nu0YJzR5WcuuCC\nC2XG1UdsphRX/Xn22bJLHa4w2Gw2hFUPwMO3XYOHBnfC5t9P45tNh/D+qmj8dvQcfjt6Dss3H8bq\nWaPRsWl46Rv8KyEPrMDAikdGnKFBA+YvqF78suJyiY1ZBnfLLfRSJiaWNJQuF5GRTFj/7TfjcpXY\nfP+9sfJRWeDtzeTnzp0rbhQFB7PKFMCxrFOHBGTyZMffad6cBsnZsyQTVhWU0tL0ZHUxLNTPMzJI\niPz9+ffhwxwD2Q/xsObmljzXZmKzfz8Nyxo1dEL2xhuUOkkUq0MHRghN1aG2x2dh2pOf4Oc9J1FU\npJBJmx2wsVRykI8nmgd7oNbvv+HmpCNok5+CVqcOwFaaYZWYCLw8hvv1wCp9ed++wIkN1t8R73l0\nNKVAbm4cv8GDOWc/+4z5Bjk57FVx6BBJz/PPl7yORoxgvk1gICV+vXqx/1NF5oqjCGZ4OCVjvr56\nYYV69bh/qam6g0C+L2WcraBKkITUqUZmURHzmZKTjZ/FxLBU9osv8v8BA0ikQ9X4m4L+/Unwfvut\nZBRRRXmMezM5mTaNvwHAo2lTfb1PP2V+zKhRerRStj97No3rqu78rV4/jhwY5qiSM5grVObk8Fqr\nWVOPmprnXNeuxlwwwf33834wdy5JcUYGZcPvvceopZdX2SRyKuS377mH95JFi0rmFXl6Un5ZGjp1\nMpJUF1xwoVz4h2SflwPFzeYqpeHiFQCbzYaeberizUcG4PinE/DV87ejT7t6iE/ORI/HPsaTc9dg\n56EzRoPqSkJVh92tygSXFZVFbNQHrrNt5uQw8lARhIbqSdKA7klWiY3S0K9cEGOirMbqjh3ssWFV\nBSsvj/kJcXGUhah9v1V4eOh9h7KyKAcCjM38XnpJlweZqyQBetK2SKVWrdINvYQE/Tu5ubpXWc5L\n7940DKUSVqdOuozHXHJaULcuMG4cMHgwMuyeWBvSEINvmYqur/6I9b+dgN3NhnZ1AvHsHd2xtqsv\nTm2bjd93zkXmplk4e20R1j/ZH5/2qYk7E39Ha1uWkdTk5TE/xByBc2QcOitQoUa1fvvNGMUCgIUL\nSQAGDWLxiSlTeO4TE42/U6+ebjimp9PY//BD/n/wIInesWOO98MMR9eolxfnQlgYZVgtW/IY3N1J\n6KwIihl16/KYZC7fdBMJQM+eJCgAnV2FhTqpMW9zlUIcw8MpVVX7GanQNBK8DRucRybLc/8zk3ul\naW6Rer7Pn6cz4uRJfZkaSZBCGlUJifo5In4Az11CQtkie+aIjSpfnjyZEblx48q2b8uXU9Ym0uDH\nH+f98v/+j1LFijyL5Jxs28Zqbps3l38bLrjgQqXg6iM2Immo7H4pVwBqV/PH0F7Nsea1MbjnpvbI\nySvAm19sR+eH5qHLw/Mw7aOfcODk+b96N42oamLjSELTti0NoogIfVlREZCeDrv0lggPpwGkdoUu\nD6wKF4iRYxWx6dmTxuK+fRX7PTH6n3mGXvcOHYx9Z6TxYXlRWr8JFWfP0tgbONC6uVx5KsN1707j\nOiiIUjEz5DwBei6VM2Kj7v8NNxjXMxPOiRMpd/rPf3SpkzKXNACnvILwtkc9rNxyGDsPncFPv53A\nm59vQ1Of3qjWfTIGtL0LKzO94OvtgWfu7IHEiddi9+KJmLlkJq4P90FUbhpaXUxko8q33mLxB5EZ\nmaVUR48y1yQ8XO/PATBSMm0al4uXOT+f595RdaZ69fRj8vUtmeMmch0zMXdzM15HZmmV3c7yx4Ld\nuynn+f57bs9mMx6jGe++ywiQoHFjRkkcJd+bYXUPufdeGpm7dzOHRaI5AwdSSrh5M8fugQc4JxyV\n0gbK17QyO5vj6e3t3KlSEWJjQWYNxMbKeaJu/8/I3ZC+PM6qf7m5MeJSlmex3C/l/qnO2dq1GeFV\ni1o4gxAaOS+S/1fRIjHnz+vlugXSGNgFF1z403H1SdFK62vyD4Cnhx3znhqEhwdfg7e+3oFV244g\n+vBZRB8+i1eXbsF1Hepj3I3tMKpfBQ3dysRfFbER8iAP4HnzWDIYQLP69fmgWr6cORcPPlix3xbZ\nk4qFC/lgVQmVIDqa72vW6Np4K+TkML9g6FBdhhEcrMtsZs1iNGPXLuP3Kloww8uLxp/aQ8YRVA+9\nlbe+PL18pHM7oJ8/afT5+uv0sAJ6Qi5gNEyF2MTFGeVRU6dSqrV2Lf+3kqLJ7hYUYk1wQ7jbUtHj\nYg6+2rkHb8fWxL4+M1CgAZrNBkxbhhJws6NjZAh6X9sUT43qjtrV/EleZL/M893Njcaw2pDzjTdY\nHnnKFCPRmTpVr3Tn60uyMHMmpTQjRpAM/vADx2r+fGOOwWuvsVLc3XcDb75J4lazJomw+ZyMH09P\nuMic7Hbu5yefcL/MjWDtdnZUVyE5THKdbdzoOCG7WjXg8895vX3wAb3nMTEk6lLS2hleeYXX7ebN\nwEcfcf8FnToZr4fq1fXrZdy4S5IubN9e8pgEVgnwjlBaw02A+1lQwJy3slwPZimaEoXR1KiQzGWZ\n/wDP93PPMcn9zyA24mRxRmxmz+acffxxRgadITGR73LM5rF44w3eA554ovTovPkedLlFa+Rc+/rq\nBUSqohCOCy64UCZcfcSmXz960czJqP9AdGgShgVTbkNaZg7W7IzB6m1HsHjdPqzZGYM1O2NwJDYJ\nk0Z2g6/3X1ghrqqJzSOP0IBxZJSIQaxUtLrUoHPRIkp/pk0r/++qBrbam8KqcZsZzgyoffvoeT5x\ngp5GITbmPj1WqCixadTIIHtxClUqJYbjtGk8v+3a6cSkvPtibk4ojTABGq07d9IwlkaBGRl6qWKA\nhquMvd1uNPqWLMHahp2w+LYpiC90h9czS9G1RR3sO56AH3cdR3LdW7je2HnKDtngrhWiZ+ppwMcH\naa3bI9DPC7Wr+WN4r+YY0LkR/H1MUSmRAu7YYewlIj1tABpEISE0iL//nnmAY8YYK/aV1qBTNdzC\nwkh6ZA4HBpJUq1GTrCySIzP27SMZEFmj/I40n7QiNmZJYUaGsb+L7JczPP8883WSk0nCABI2R7Iv\nQVgYo1GbN5c0bv/4Q/9bqhSKLHn9ep3YqHIzgOT65ZdJJssTsSkLsXn1VZ6rp58uWwRTxtEiCm2I\n2KilpgW+vrw+LlxwnuBeWWjcmOTamQwvOZmRyAsXSt/eBx/wPEkJZDmGtDRWlps6leNSmtw2P1+X\n4skcmTKFMsSK5GEC+ngHBLiIjQsuXAG4+ojN0KF8XUUI8vfG7X1b4va+LfHqA/0xd8VOzFy0CTMW\nbMAbn29F33b18dDgTujVpu6fT3KqV2cFmlOn6J2VvIrKwsMP00DcuJHJ+2aIIaZE8NzE6C2rbCo9\nnZ7t6dOZmDpihO559/bWPdQrVpCQ3HKL85KtzoiNVa8WwPggtYoGAcbjuO++sjVzS0ujUVRWIjJ0\nKMsDL1kCXH89f+Pll7l/d9+tS8bK26TUbMwNHapr82XZkCG6sfrKKyQQgsxMoLAQuTY71qfaUf1k\nMs5Xb4KjPtWwe+keLKqtAZCS2UewepuedNwwLw0oLESMTzW0z0vGo9PGYXDOGfgMHwKfogIa09ve\nK/0YIiMpfwoNZXPA557jSyWlXl46yZFCDzk5RjJjNprMxMY8b599li8PD0ZDxo83lqbOzORYennp\n0Rk1B0G2X5pBbLfrsiLxXlsRm9KcGLINlSTNnUsppZcXjeacHL1ogYoePTinzfcR9TfFoJUGvCpp\nV68HKXUt65WH2EjVNLNESYWaCF8WrF9PSaaMjxxTnTootOqh8803LPwgpbP/zDLCQUHMuXKG8khc\ne/Y09nXx9WXE9r77GKE0b9MR1PuYjP/Uqbx3qAUYygMpXqESSRexccGFvwxXH7H5J2LrVnqqu3dn\ndMDd3aF3M6x6AF64uy/aNKiFFxf9gt+PJ2Ll1sNYufUwPD3s6N+hAfp3rI8aQb4ICfDBDZ0awtOj\nCh+EPj40fHbupNFf2cTm5El6vNu3d05slIdruYlNo0Z6da5167hN2YbaG2T+fCYq16tnTWySkvhA\nLK2vg0Dt9aEaR45klj4+fL3zjlGm4wyTJrH55UcfGSMgghEj6NlfvJjedQ8PGpdSUjovj8dkt+ve\n64kT6VnNySH52LOH3+3SRTdMtmwh4e3Rg7kjZkmhOkZiWCiGd8F1/RH35lxEB4RjS2AkTqAuvM4E\nYUffyTj1hw344yTQWu9B4wYNz9zVC91bReFCWha27Y9Fg/AQDOrWFI3uuRM4chhZp8/AL8AXGPg/\nAO2B48d4LsWI+fhjEuixYyl1O3yY+9SgAY9rxQpk3H03Aj78kPIwGSP1fOXnMxI3dqzuWc7NNRpK\n5YnYmNcrKODrvvsoixS0aUNDWJCWpm8nO5sSMXPBFammNm8ez1VsLMk7wOiAEJuyeOStoEZdFi0y\nRumsjg9grswDD5RcbpVjsn498NRTlEQJJPdozBi9d07v3oxoqQ0WS0PnzvzOkCGO15HcobJWSOzX\nz/j/1Kk81vBwFKl9fnr14vn48ksWc3jzTS5ftIgk1pHj48/G5cjCPTx4jdx3H8loWcotC9LTub6s\na7MxR6eikHt8Vhbv68eOOXZAueCCC1WOq4/YPPMME0lnzvzn1IlPTKRB5e/P/AoxYBzAZrNhRJ+W\nGNarBQ6dvoDPfv4D3+04hl1HzuK7HUfx3Y6jl9ZtGB6C//37RtzctUnV7X9VNugs7eHpiNhoWskS\no45wXinIIN5D8d6pic+l5ZeUJfm1TRs9P8iRQZSQwIjFv//NOVFYyONv3Jhyi5tvLv13BIcP87uO\nSnEfP07PuaPIj4yDkCqAsqqoKM5ZVQIVG6vLnrKz6Z2W6MXixTTKxLgsJjanxtyDY41a45Ozgfjx\neG14jpoDm82GuMQ0FFz7uHFfYjIAeCI02BfVAnxQI8gXHbMTEfbjtxh8Q0c0H68bjmPyYoHUE4BP\nU2DND8CFC/ALDTUayGad/+bNJAshITzX4rFOTyepa98eh+fNQycp5SrfU+fm0qVMhlYrV6lV29Tv\nCUqL2Ajc3bmtwkI6QXx8jF5mlYSr5GDVKjayVJO8n3hCv15HjuQ8+/JL/XOJWPz736gwSosSlifq\np543+V6HDiQ3x49z3jVqpBORkBBGkAEut+pB4wy+vnqTTkeQe0NZIzZmREToJEUlNtWr01Hw5ZfG\n477S+rbJ+EpOYHkh8099bpSloWZZe9OUFR4e+jN3+nRGP8s7X1xwwYVKw9VHbH79lQ+ziRP/6j2p\nPEjJW8lfKGNpYzc3G1rUC8Xzd/fF83f3RWLKRcz79jecTkzDuaRMHDx9HkfjknHLM0vRNLI6PD3s\nyM4tgKe7HR2bhGHcje3Qp109uLmVsTuz4x3he1USG3MOyvr1NDilOpZiLBYEB8MjL08nDr/8Yqyi\n5Qxqp2/AaCyWpyKYI1hV/bLC1KmMykyaRH26itGjy1aJqKhIb2zoSKZRWpKwGM6+viW1/2bCqCbu\nFxVBA5C4aQfif9iE/PoNsX7lHtgKd0GrWxdHozNwsP14bIurAy0uFajdDigEkKD3KQnPTUfjnBT0\nT45BU498FLz/AQK8PTBwy0rYbdnAU/9mnsNHm4EQk9E3fTodINHRNBStZDxmQiHHNWeOMYne0fVY\nowZJZny8MbF92zbjejk5zE+KjdVL0wri4lgAANBL7ArWr+e+169v3I+8POaemauTqXPVDLNjQIgL\nULL5qRndu1POlZjIaKEjTJ9Oh9O115IUSM8YR3D0e1YSS1k3MbFkCeJduyhHO3OGkQ6A57Q8UYCK\nwFmFxMvF36F7/eU2C71S5F42G8mZhwevQavItgsuuPCn4eojNn+HG355kZRk/L8iPVsA1AzxwzNj\ndB1zfkEh3l2+EzMWbMDhWONvHDh1Hot+3IeoWkGYNqYnxt3YDh7uFRzTvyJiY5Z1PPkk8w+8vLD3\n0CF08vQkOXj5ZTa0E++iFbp318t7yrwKCaGRZrNRouDrq5OrG25gUnjfvtbbc4bQUFaxWrOGHaoF\nubkliYK7u3W/HBmT7dspOXKkhd+zh3MrPJznKC7OaFQDeuUzSZY2wypik5ODxJSLWLI9Duta34Fd\nAeFIdveB18NL4eXlAbvdDRkZ2XDr+Qwu2j2BV38CoDbTLT4XQVFwh4aOBcmo2TAKEx4dggbhISgs\n0hDhocGnVg0aG927Ay3aA9e1Lq5CNZnn6amnjMRLhblYgVpid+1ayq969aK0UDzvjsoYO4o8dOhA\nAjRpkpHYyByqV4+kRSRrdeoYoyIAZV5r1zKSJz16du0iAZoyha9GjRhVk2IOaWnMWQFYCEAkXmai\n3LUriev+/cbrRyUNc+boxyf7PXo0I0+CzEzg6685F501HpSS3tu3M2L1/vuO17XC55/zmh06lFXz\nVGzYQMIjUjMV69frfzdvTonTtdfqjVcTE3n9R0ZenlPCjHbt+L5nT+VtU2B+zn3zDfP/brtNryb4\nV2PcOM49tWpfeXClEBuABSBccMGFKwJXH7GRcp6bN5c0bv+uMFciqiCxuYT8fKB7d3jY7Xh80ybc\nfWM7nIhPhQ0sJZ2ZnYdvtx/F/O9343RCGu7/72q8snQLJgztgk5Nw9G8bg2EBDjx/ppRVcRG01gG\nVI7JGby9jbIxm42E5uWXS2/Q2aVLSWJTrRo9wO+9x6pXDz9s3Adzo0UzhFS0b2+UqP30k/X6VgaX\n3W4toxNDVKQpIpUyQ8pVd+1Koy44uGQiuGDlSmtpZ1AQ8PLLyPTyxSqvCOy68z84nFIdP4x4EwWF\nRUB1XeKYn1uAzFzFgLZ7Ijg/GxF+7sgNrYXmB3aiUXoitIceQuNDu9HEIx9t0s+i5pIFQLN7gRee\nYPPGWbM4l556ivs8dapujJvlY02bUn7UsiVlZDExzFMz5/SoJXZorgH+AAAgAElEQVRPnGDeT0iI\nUWqlJuSrcOZE2b+feSm33sp9XbRIJyB9+rDggjM4ctSoZOrYMb26WOvWuoGel0cjV4iNOZLRqBEl\nZvv3O/auV6tWskGmmSClpZWtGqB6H6tbV/97zBhKEUuDlxdlZWovHYGzHk5qROa66/jKyeFcv+km\nEp3UVEYvLycXw4zbbyfZ+Oyzyicb5l43eXkkwWqD278akidX0Z5ybm68bqSS3eOPO1/fBRdcuCpw\n9REbeej+8IMu4fi7w1GVpIoiN1f3Vp4/j6CwMLRrVNuwyjXNIjD9rl74fMN+PLdwI47EJmHCOz/w\n592YwxPg44lOTcNxTbNwtG/sIEcjJkaX0DWp5DyeoiLdYHCWxOsI5t4mYniZZS7//S8NlO+/Nx6D\nnAfxdo8cqcuMzPKTZctYeGDkSFYTe/JJkpgff9R7lgimTGEVuRkzjAUEBO7u/E273ZrwNGgAzc0N\n5z384K4VoZoVccvIIPmqVw9FN92E39ZuQ4jdDfUKi2C3uxmOoQg2pBW5wTevAIUtW2KbFogt3Qbi\naHo+anTvjPj8xli18TAu5vwB9gROgd3NhlvaRGD0srfQ5mICGmclIfeXTcht1QZ5K1Yh/8GHkGH3\nZAPLu+4CPplJ6VZSEtD/VWDKcB7jnXdyXxITSa7Upp0vvEAyWVioExTViH34YRrMc+eyCELz5qwi\npUqg5ByGhbH5KKDP17g4RhakWpZVR3dH+Ufbt+sljQHOMSG+UprY7LCwQlmIDaBHhPbu5f4IscnL\nY67TuXM0/ufN45hs2MDjEePTUY6aulyNDqhIS0OZoB6vjGV4OImXmdhYFQho3ZrvP/7I+VCWvkuA\n9f1y2TIWuBg7lnldqamVLxm7XPVAcjKr6oWF8Z6hokEDRmKlSImZ0F8JsGg0Wi48+iillm++SWn5\nlXRsLrjgwl+Gq4/YCMpiNPxdcPPNevM/QH8Il5b07giqoeukCIHd7obR17XGiD4tseynP/Bj9HHs\nO56AvTHxWPYTjbP/+/Y3AEBEjQB4e7rDbndDWDV/eusB3N08GAM9A5DTui0aVDaxkQedh4ex8lFZ\nYSY2hw6x2lHPnnoHc0G9evQeqgalWQY3YQK9vh9+WDIKtGkTK4999BHw2GMlIwUqvv2Wxu+kScbl\nx49zu23bAgUFKLS5YVe+Dw7UbofTXkFIdfdGjE8IDvnWwCnvYOS6ucO9qBBdp3+F669tihZ1Q+Hh\nbkfGuURkP/Y4sho3RezkD7D658M41PF+DsnAWfD38YSftwfsbm4o6D8d8XlAwWYAA16CPWIUCm1u\nQCwA2IHv9l3avW4tI3FTTTtqfbYIN7ePQtjke4G37rv0uZeXOxDsB4wz5YpIcQYxgETCA+iOCnMi\ncZcuesPTRx5hbkd0tDHJOiWFBE6MaCsS6O7OiEdGBosv+Pvr5+a770iCXnmF/7/wAon6/ffr32/c\nuOQ2AV6jmzYZc8DMc8Lc7NKM2bN1b7XZOHQkmRKSlZnJ94QEY7Wze+5hQvqGDVynXz+O3YQJzKMa\nN04nzgBw7716hb3160k4zDldKSllKy1udU+W6+ncOf5mYSHPhZWXv149/e/t241lgJ1BHbvjxymX\nU3vGSLGObduMc+9ycbnE5qWXgLff5t8qsbl4EXj3XY635HvIb3z1FaM2zhpn/lmwaDRaLixYwG3I\nvd1FbFxwwQVcjcRm1Ch64xwZHFcSfviBcqabbnJclQrQNcotWlBukJjIB3Pt2o6/4wyqZKoMjR/d\n7W4Yc30bjLm+DQDg0OkLWLszBgkpmdh15Bw27DmJMxf0HIwjSr7Olj9igW5sjDb8uS8w6fauaFEv\nFAG+FSRlKiwa2ZULZmJz+jSNPSvP7d69NKalWSRgJCevvw58+ilzIYCS25DO2gDPnTnaI4iL0z36\npnyBwqi62Hc8AWn3PY1VF4qweMxcJKb6AM1uszw878J85Ng9sOngOWw6aJLGNS02Cj9jhCmoIAf+\nhXk4g0Ak52cjOV3ySeyAGxDgpiELbigqtKFDxln08s5Fq5h9SJ7wJPyaNcGAaxqiYUQ1NtObsR6o\nfzPnrTMHQ8OGJApxccxLUsdI8NVXfBdCI8aNREIAXWL4/vskjoJly/gu50IlA7VrMwcqMJB5Cdu2\nUW7YrZtR6ql+p18/vmbPBg4eLCntUmHuDZOXx6hRixbMzVL3G6DMLSGB0aGaNUmM1AIopUVsAOsy\nv1alxfv25Rz08+N2JkwA/vc/3di/cIFzMCiIRF9yi665hsdvJjZnzpStWpXVXJCxLsu9zM1Nj0Q1\naFDy86Qk7kdwsNGYlryf7t15v1Pllur1d/p06ftQHlwusYmNtV7u4UFip85T9XivlNyUjh05pyt6\n/G5uHMORIxmdKktVSRdccOEfj6uP2PToQYPGnFOQkcGeGn37XjmFBV59lZ7T9eudE5uoKGD5chph\nY8Zw2eV4r5xFbETaoxpdJjSLqoFmIV58aN3aCun+wbiQloXCoiIUFBYhNjEd9m++xvELmZhxzgvn\nMkmevtx4AF9uZBWuyJqBuOv6NhjasxmaZCTCv01L2MqbuOvMcLjuOkq9PDyMx5uVBfekJBprXl4k\nlZL0fuoU31X9v6YxMVqaRarjrkZsnnkGAJD/+x844VMdR2KzcGZlNPIKCjGkZ3NUO5+EHcH1sDUw\nEmfPB8NWGICcpoPQY28CQoIOwd3uBg93O7LSM7Gx4QBsCK6HlCnLUSPEH+E1ApCdW4B9xxOQmHIR\ngL34dRH1agXh2oahqPX5YgQV5KBRdjKictJwTcZZ+BTl44KHLzZ9tgabzmZi7+5j8Ny3B9Uiw+C7\nfx98Qqsj5O670KtFOHp2awkvuw0X0y8iKzcfGVl5KCgsgseC+Qh77hl4T3gURa+8ilwfX/igiEQk\nfjfQOhi4+Rp9TMpSGe7mmxmVmj6dEqRmzXT5lyNIBE2MNlWSJnNVzk2tWpybAitis2iRLgE0k0x1\nPlkRiAcfJBkYOdLx/qoVygDm/G3eTHIgZZhVA/Tnn/U+TMuXA4MHs5hAXBwjUr//rjcszMkhKWzS\nhFK44GBdViU4epTkz4p8eXkZo73m6ygoSM+ZiYzkb8jnVjlgEREkJg0aMKdp/nzrMZk6laQpJobE\nECh/uejTpxmVs8qpadmS5/3sWeP9tEULRtk6dix538zPZxTro4/4Xpm4XGLjyOnk4UGjv6CA60g5\nYsGV8nzz8Ci7XNAKdjuPLzjY+fPRBRdcuKpw9REbR57wm2+mNGTOHBoBVwLEaCotahIYSEMHcHx8\n5YH6e+btNGtGg+j8eedFCgYNIinz90dgRgYC/XRDqXndUGDI/3DdmTO4d8kS5I/5F05164fnBz6I\nvTEJOBKXhNjEdMxashmzlmwGANSyfYUB13fC8N7N0a5RbUTWLEMTS3MCuAoxwORYp0yhYZicjLYA\nMua8je3bD2J5SGecqdcUif/+CJ6xZ3Cg21Own/FDyyc/QVj1AFT390LR2x8h1d0bPk1uQTN3Tww6\nkwzs2YPt87/Fwfr90DDBDQVhHbDbPwxLojohvdAGROcC0TTWH3v7B8DWG2jXm/siuddhNfHRj7HA\nj58Z9z2yOOn/fAZOnc/AriN6tCWiKBuBhXnoc1tv3H1LJ3RqGg5bQQEwa0zJMWjQAKEtW2Joj6YY\nGhpKY3D/fqA44ITavYHxfTmOYbUADw/4+XjCz8cTocHFeSWNI4FOHYDISLjl58GnqICGuUQCzPkV\npfXyAfQk/MhI5ksAzJ8BdONdRXCwTmSKimjsqxGbtDTKViT34/XXuT2pMCZyNiE2N99sjOiaZYHd\nu5PcnjrFPL3oaL0xJUDnQr9+3C9HMBuX06YxUpOVpXvX4+KYv7V7t1Hedu+9vN5DQrjO9ddTenTy\nJD/z8+M4ZGczyqVpRjIOWDeIVXH0KIlZq1a6E0jd5xMnWNVNJZB2OwtuWCE+nq+tWx0TmyZNKK37\n5Rc2xezZk0U0Ro4k0SyLY6NWLWuZ2pAhOpk13w86dNCjTKtXGz8rKOCce/tt5+WwK4LEREaQatSo\n2PcdFTWx2VjlLzOTc8DDw1iu/kohNitXUk57662c5+WFXCcpKYwoVqtmvE5ccMGFqxJXH7Fp25YS\njmuvNS7ftInvy5dfecTGKmry1lt8eJkNicvp5ixQvWiqhKGggBp0gA8TZ1KbQ4f4Llp+M4qPzZab\nC0+tEI3tuVj87FAAQGFhEb7ceAAL1+7Ftl1HkZYPJMADn6zdi0/WsuJRxyZhsLu5oVlUDYQEeKNJ\nnerIyStAQkomkjOyUbdWMNpFhsDnwan46aInPBZsQN929VAjyBfhNQJw0SsQ39RoBg029D4Wj+Dk\nLHzq3wILG7XDYd8awPIkAMXjcOawDAbg6QfkAfG/KbkadboYDm3imGLde4thfN+bo0u7ChmNahZV\nA1E1gxCfnIkfdx1HYV4+Wlw8j+tSjqNuZChyklJQkJ6BAwOHI7NaDRQUFqEgNw/46Wd0vhiP/khG\n5JnjuLDyexzKBtZNfhX/Sj2E/hmnYbt4Efj+ed0gdXc3Gv+CDz9k5EpQu7beEwnQvfZ2O+VEVhg1\nii9AJxNeXnr55I0bmaPQtSsJgRTscEZsZs+mEarmM8h8tprXjRqRXLRuzSp45k73n39u7J9itxsr\nd33+OTB5MnuYdOjAPBGVCJidBVFRNJQlB+bbb1klrXNnfq9atdJlMapxPWYMiyDMnMlru3p1Rpk8\nPHiOAF3eCOgES4iTXGPSiLWoiPvs7a03NC0vkpNJqNzdOSaA8V6Qm1tyPpkbAw8ZQrK1e3f5fvua\na5jX5O+vS9CmT3de2aw0HNWbDjs17HfsMP6/ciWdOJcTWXCEQ4dIOtWy7eWBM4eXj49ObAIDeU2K\nTK+q+vKUFxcv8rxIUY7yQojdp58y2levnovYuOCCC1chsena1XkHZicSqz8dIq8RCZQgK4ueroAA\nx8TmcqRo/v7WendVJ19ahaDSdNyyn82asaTtiRM0gNq3h93uhpH9WmFkv1bQlixB0Zi7cGT4v7B4\nwF3YcfAMtu6PvRSl+PWQA4P7EoqN84Ub8fzCjfrirkp+wn0fAKgONNCrj3nZNDTJSMStnhnoMGsq\nQoP9kPno42i+cwO0GjVwcNHXuJBTiKSEZGTNeB4agDybHQf9QrG5yTVwz85Cs3MxaNc4DOfadobH\nsk/RLCMB/UbfiM4zHjR4f3PzCoBvvobXqpXAkjVA6LXAhVNMmJ72qZ4bcf48MGc8Dd+aNYGcFDQM\n90eXqCiMPfSNMbFdPf82G4no/Pm6nCYigiTj4kU9yXrCBGNPj4QEnpeIiLJ5y4OD6YXOz6c0qk0b\nypRefZXztFUrXbbkbHtt25ZcJgaz+XshIfTuR0fTkO7VC3jtNY5Rfj4TpUeMYERDYLcbe8788QfH\n65FHrPdHxvSGG0gE163Tc10SE/nd22/nOmUtStKyJRPxFyzg/qjRWfP1boacW4mKSQ+hwkKdsFX0\nPibXuJA2Pz9ryZRVtEAlNidO0NB8663yExsfH0rpVGzaxPmzfTsjat266YUTygJ1351FmtV7XKNG\nJFhpaVVDbOQcOWu06wzNmzOiae4tBegFNw4d0iNYV1oPt8tVFzz/PPDssyzrDlx+mwMXXHDhHwHX\nnUBQvz4fxmKgXEkwkxQhFeJRX7CAr2HDSChq1qwagma36wndjnp2CEojVmLIBQZy3Q0b6Nlv396w\nms3TE3ZoaK5l4qV7GV1ITs/G78cTkJ6Vi/2j7wUAHBtzH/xqh6JWiD9CArwRczYFe47FI+ZsCvrs\n/hn+hXnY1HsQMrLzkJhyEVlZOeiTehJROWlY0aQrPLIuom5KPJ6P24T+54/Armlwg8YoQ+9ij+qa\nT2noxaWiQetwGs+JicC4X4zH9sdnNOanfAIMeBp4dgjQpICSmlc3A1MeMRAbL093YOTtwJDbWLrU\nz0+v8KQa8nLe1Z47ubnGDunOInbe3vzdO+/k+L/3njEhWiI8deowgvHoo8yL+OMPGuJmzJ/PktP3\n3st3Nzc9ihcezoRe6SPk46OXRQY4PgAbOZ45wwT9iAh9XJYuZcnr0aMpU5H5NGgQZYOvvMIIx+TJ\nrEYmx69pXCZjICWZhdgMG0aJm7kAgLPrRTWypRnuzJl6A1YVc+aUrZ9GUBDz/RYs4H6rxOa//2UZ\n3yef5BiuWWP8bmEhDf2mTdnrRohgYaFxjlwOxDA+eJARm7lzGdESqMTm448ZZTl7Vp9PcjxqLtPl\nQMb5668ZTTJLxkpDWXNM5P7Tvbvea6qqIhxy/65oGelp03jthYZynqvo2pUFL3btIvEH2Mi1qOjK\nIQCX64S7804SG8GVQthccMGFvxRXyB3uT8TYsXzYzp9v7HgsEqsrEWY9vJnYHD9OyU9gIElHhw4V\nl6CUBpEYOeqyLigtYqMacs4adFrkGVUL9EHvdvUAALd6JzIKcNf/Wfd0AQD3J/nwPLiSD9O8PBR4\n+8BdK/693UvprV//McmKpuyHmkTt40MjQqISQEnP9ZOs8HZpfLy9aZTdfjs99KJ5t4Knp+4Zlu2q\n64pnV03uzskxEhvZrzfe0MsQS7+SfftICv7zH0YxAKO+v2NHRj6koajAan9PnaJxHRfnuGmnOg4q\nsfHz0wnQHXfw/amnKLu67z6O79atNCwlR2f7dh5DcLBeDS4lhedT7YehFiew2ykNkxLPUVF6Xs0P\nPzDnIyyM27TZeF3l5jLytXQp1xs5kqRo3DhKzczGk91uNMzKSmwAowddxjgujq/MTB7LBx9wLGSc\n5HvDhpF8xMfr+1QZERvBSy/xPSGBZHvSJKO8To2AjRvH9w0b9GUdOjDPKCbm8vZDIPeIpCTn6zlC\nWYmNOBICA3X5ZVURm8uN2ISG6teRmdi0aUNio+YFXWkNqSXP0dz3qKwwPy8OH7ZezwUXXLiqcIWI\nbf9EbNxID2hlN1szIzaWXncxLisC8aB362Zcbq4sJV5RkWZcjkcuN5eNJs0Rmfx8dsgePx54+eXS\nu0XLQ9sq4XbnTr03RM2azpvHmUsuO/rcmd7cHMVwd4f7998xn6qggPsqv21O5N2yhcbt11/zfzPR\nMkujxGiSc+Lvr3+mnrfMzJKeeBXq9l95hcRI9P9eXkajSB7wYpwDekRkxQquHxDAZRJBkTwUNU8q\nIIDkpn59encFVrKxevUYbQCcG9FCbHx9dVKclWUt2ZLx+fBDPScmJoYa+tRUjsm2bYzinDmjl0Xu\n1ImEqH17I6EUmMn43LkcCzEGJVfl228ZSRk2jPLIMWP0eeFIxiP/C5l5+mnHY2FGZCRlVW3a8HqS\nyk5q3566dXm8cr1160bJnRjDBw+y75GXF8loXh7PV04OyZvkDpYVjvqbmCOA8fEl11EJQGIiZVwr\nVnC8hfA7M65nz+YcbtSI533GDP0zidhUtNeVnKdff3U+X1WSqDoMqgKXG7FxhitNdmYFabLqqOBE\nabhSyla74IILVxSuvojNn3XD37SJXu2pU1m1qGPH8m/DUQUpeRCeOEED1UxCLofYTJ1KA2PkSL3P\nB0Aj8oUXKAVSK0A5wnff8fitGtqJUXRzcS8TORdWD6o+fbgdVcakQsbGEfEBOB65ubpx5uZGiY9g\nwwYmzW/fDrRti4NLlqD5vZS4ITeXyeWff05j3ExsatakEfzxx/xfjuWOO/jd669nnodKnvLzKXU5\nfJgvNVE9IYESCzHCPTw4l777jnMoKopjtnIlf0sldkVFPIbevUv0uDGMBaAbz9u20buuri+SNjWv\n5dw5/kZERMlrZ88eytWskrvViI0ktOfkcLkQDoGcQ3X7Gzbw9cQTrJa1axeN02uKS0h/8w2bZA4e\nTGIj+RwqoQ4IAO66Sz/GmTN5PNIDR4iNRIeWLy85XmpU6OBBSsWaNNEJ74ABbIYofYrKgoED+RLI\nuZTjV8dB5v+CBazYJvPw7FlGl266SW/4mZvL8yoOkQceYA+fsuDcOUr3mjQhmbzxRhIks9Ohd28u\nv/tufZlVL52wMBquJ0/yWM3V2VRIQ9WYGL5EYgjoxO7xx7l/Q4aU7XgEL73EY4qMdL5enTo8j61b\n64U0qorY1KpFh0XTppW/bfNz7tdfeb+95pqSzYX/KrRuzWdXRavNuYiNCy64YIGrj9iIl3b5cno6\nqwrqw3DjxsolNipxycgo6f2uDA31Z5/Rez17Ng1QkYBI2d3S0K6d4y7d6el8F++wMyna99/TYz9s\nmFGOo2msqCPfzc+nQTdsGA3sV14h6Zs3T+8s7yhJdehQyprefBP47DO4CXHs18/Yl+PiResS3K1b\n63+LIdGzJ3DgAI3t++/XIyUAx7NlS0atZs5kOVnBtGl6An/DhjRcxbPbuLHjxHI55yJbFK+0KqUD\n9PGSiM306UyK79yZv5WaSmPU01MfLw8PGl8pKfxe9erGba5ZQ0NKSjOruOUWRoWk78m0adwH2Y+5\nc3XZW14et1Pc8+fSceTkkHRYafJTUkhmQkNJNgSqseTrC3zySckx8Pcniaxfn/9bEXZzNNHNjTke\nn39O4vDii/q6pvywckOInVUlQYn8XbzI81JQwCiGzLfffqPDYONG5l2opLE88i2JrEVFcS5IYrr5\n2pHxVfuBOWsSWq+enjfmCOr1L958gOdIym97eRkJT1mhVv9zhlatgIUL9R4wGRmOnQSXi0aNeJ+t\nCqhEHOD8vXDBuWz0r8DllND29WWp6J07Ofelz5MLLrhwVePqk6IJxMNeVVDzYpxFE5zh9Gl6OlWi\n8t57Rg9fXl5JQnA50Sh12x9+yMaAgFFSJ3kKZcHx4zwGdR+F2AQF0cv8wQc03MQLr+LAAXrFDxww\nLl+2jPu6axf/z8ujFO/bbykz0jQ+7KZO5ed33eV4XCQputj4cROZj68vE+gBEjovL1bcWrzY2An9\niScYKZk92+iBV6v+BASQwIiBLaQ6OpoSszFjmLegliuNiWFEojQ5ngpzE0kzsUlKIqFUk7rlOy++\nSMK1dKkx18DLy1qioyI/n0Z1jRr0Qm/fTu96QgKJSufOXO/ZZ3lOhHg99BDJDsD8HzMpF6MyLU3f\nh7g4PRIk68ucEph73aiQ7TRpwnMp5MRMbOx2XQLVpQuJ3zffGPejotd2fDyjHmpCvpBliQKpZXCn\nTWOTyDp1dBmaj49OuKQyGkDDXCU25jlQFgiRknE1ExurIhXm66u06m5m3Hor31u3NpKixYtZAezP\nxIEDnLerVxvlpH8XtG7NKKJUVHQm9/27Ys4cOllEdvtPOjYXXHChwrh6iY0a5dA0EoYbbmAjuMpA\np058sP/6q55cW16Eh1O6oVZeUpO6ARpWTzyh/+/jQ4Oookm2Zg+aGC7qwz02tuzba9uWHvEhQ1i4\n4exZY8RGEnRvusk6quVIOvjWW/rfW7bQe26Orsh327QhoVC9y1a/UWysZXTuzPyAuXP5O0VFNLpq\n1OC5HD5cL7Ur6NSJ66i5R2L8rVtHaZ+mkWABuvc6Npbkb8kSdp436/8LC8tHbMxNSa3yY1QjWP2O\nnOvvvtN7lBw5wvOkEhupPpaaymia7NvFi5x3GRk0DP/3v5JRnFmzGA147z19mb+/dW7H0KEki4CR\n2IwYoUurzFIxgRr1Efz0E0m5eK0zM433AXN+jGw7NpZSOw8PRoZk+enTJHO7d/P8qT2ASkN+PqV1\nat8UOb8iO1Ov6xEjmN9WowaPtV8/3h/+/W9+rt4nTp40EpuylOo2Q653+a75vqDObZuNr1q1gAcf\n1NcxV4wrDaNHc0w2b9aN1YreOy8XldEP7K/Ek09SKnj99fxfyLDaD+nvji++oDRTpNguYuOCCy7g\naiQ24h1WczbS0kgYfvyR+nlBYSFvmqVVAHOEqChGIVTvfnmwaxe9Ul9+qedEDB5sXCc/X0+oDQhg\nmc/Dh8vWOyI/n8aaavCbDRhVcrVmDSMLqkykNIhhsHIlyYWfn5HYlJbz5OhzyYEBKHPKy9NLwO7c\nScPMHL0obR+L1yvy9qYMTPT4NhsN4LQ0vqyqhKWlMUrXqZO+TDWAP/9czyEAmJvj4UEiICTCw6Mk\nsUlO1sl2WZKMAwNp1EtCblm89WruD8CoF0CjSPJPVGIjCArSI5MiBZTfdFTxKSmJREHNC5s82boB\naMeOek7GunXGRHjZvryrDRgdYfp0EgQhdq1bGx0AL7+sRw0AGtoA+2V07Kjn3phLRX/5Ja8LNTen\nNFj18Jg8mREtiVKp8yw9nYTlyBGel759eT0JSevUiWRy3jzmvajXcUUiNl9+yXP3ySfM13n5ZePn\nw4dTSqk2MxbCKteN9MIpK2w2SjgDA+kI+eMPRnP/CvzdiY0Z/0SjX6JQ3bpx7n/00V+7Py644MIV\ngauP2IgHa+tWnRBIDgZgfJB99RUN8X/968/bPxVffUWv7YgRuiTKnPyal8d9XL6c8qzy9AYQrX5m\npm5cO4rYAIxo3XknNe4bN8IpcnIopVIN27p1aQw//DCP6+hRvTpaeYmNOfpyqrihZViY3ind6rs5\nOTQGBwzQcxSkTGhxwrx7aiqrOqlQyy+r+VPnzlE6JJK4wkLm6oSElDQG1aiEmxuTeYcN05PWrfqp\nSC8NwDpPQNMoGZRxrF6didISfWjXjtu3anopMEdsBAMH6kaxaohHR5csR52TY01szGTMUd6Y2XnQ\nrBkJWni4tXZett+vH6MT5rwUK7mcHOdtt+nL1P1wc9MLILz0UsmCEFZE2cPDWCChrJDrND6eTRQB\nHu/Mmfp21GNYvJiRz6ZNGQWePl2vogbwHK9ezXtVx45Gx01FIjYBATyPNhtw7bUlCz1Ur05iKLkv\nAMd35Uo9oltaTk1paNmyYvteGZDz46za4t8JZW0c+3eC3Id9fSlVtGpU6oILLlx1uPqIjWqUiJdX\nNYpUQmCVKF4aDh6kPKS0xnSFhZRmjRnD/195pWTlItXoEoCoMhAAACAASURBVANT9uW225h42qgR\nH8KDB1POZeUJdlQ9Rl1HPOg332xMZjcbuxs2UCaydavz4+vdu2T/HTGuIyKYn7BwY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Nrb6G334j+vBDXNHq3t15UKfVAY1n11hnyXDmx66x3ipsevfGAE2eLUMEEVajBqyP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\nj8e8n/btsf2CBUS33Wb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- "text": [ - "" - ] - } - ], - "prompt_number": 26 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "This time the filter does struggle. Notice that the previous example only computed 100 updates, whereas this example uses 1000. By my eye it takes the filter 400 or so iterations to become reasonable accurate, but maybe over 600 before the results are good. Kalman filters are good, but we cannot expect miracles. If we have extremely noisy data and extremely bad initial conditions, this is as good as it gets.\n", - "\n", - "Finally, let's make the suggest change of making our initial position guess just be the first sensor measurement." - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "sensor_variance = 30000\n", - "movement_variance = 2\n", - "pos = None\n", - "\n", - "dog = DogSensor(0, velocity=movement, variance=sensor_variance)\n", - "\n", - "zs = []\n", - "ps = []\n", - "\n", - "for i in range(1000):\n", - " Z = dog.sense_position()\n", - " zs.append(Z)\n", - " if pos == None:\n", - " pos = (Z, 500)\n", - " \n", - " pos = update(pos[0], pos[1], Z, sensor_variance)\n", - " ps.append(pos[0])\n", - "\n", - " pos = predict(pos[0], pos[1], movement, movement_variance)\n", - "\n", - "plt.plot(zs, c='r', linestyle='dashed', label='measurement')\n", - "plt.plot(ps, c='#004080', label='filter')\n", - "plt.legend(loc='best')\n", - "plt.show()" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "display_data", - "png": 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0YNUqKjn98stAhw7AoUOAlxdQu7Z63dOngXLlKLSvgHjmhQ3DMAzDMMxzjaV+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41Tbw4YGkoyM3s2xyKpf6dO0Xv+ww/GdegFwS6XOpdPPGEsim/ThkZm5cr8HBFhbNIXGalSijIz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BJAhOERtZJtdpJ2J5nY9s/+STzLXPTVkKTEsjgdT7T2Rk0JzAW68fiUzYi7719R97zNrdPT3d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\nbzAeSd16/HGmFrndFDPvvMMfIa8//0zxI6lV0pBx40bvJDEwUG2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- "text": [ - "" - ] - } - ], - "prompt_number": 27 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "This simple change significantly improves the results. On some runs it takes 200 iterations or so to settle to a good solution, but other runs it converges very rapidly. This all depends on whether the initial measurement $Z$ had a small amount or large amount of noise. \n", - "\n", - "200 iterations may seem like a lot, but the amount of noise we are injecting is truly huge. In the real world we use sensors like thermometers, laser rangefinders, GPS satellites, computer vision, and so on. None have the enormous error as shown here. A reasonable value for the variance for a cheap thermometer might be 10, for example, and our code is using 30,000 for the variance. " - ] - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "Exercise: Interactive Plots" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Implement the Kalman filter using IPython Notebook's animation features to allow you to modify the various constants in real time using sliders. Refer to the section **Interactive Gaussians** in the Gaussian chapter to see how to do this. You will use the `interact()` function to call a calculation and plotting function. Each parameter passed into `interact()` automatically gets a slider created for it. I have built the boilerplate for this; just fill in the required code." - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "from IPython.html.widgets import interact, interactive, fixed\n", - "import IPython.html.widgets as widgets\n", - "\n", - "\n", - "def plot_kalman_filter(start_pos, \n", - " sensor_noise, \n", - " movement, \n", - " movement_noise,\n", - " noise_scale):\n", - " # your code goes here\n", - " pass\n", - "\n", - "interact(plot_kalman_filter,\n", - " start_pos=(-10,10), \n", - " sensor_noise=widgets.IntSliderWidget(value=5, min=0, max=100), \n", - " movement=widgets.FloatSliderWidget(value=1, min=-2., max=2.), \n", - " movement_noise=widgets.FloatSliderWidget(value=5, min=0, max=100.),\n", - " noise_scale=widgets.FloatSliderWidget(value=1, min=0, max=2.))" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "pyout", - "prompt_number": 28, - "text": [ - "" - ] - } - ], - "prompt_number": 28 - }, - { - "cell_type": "heading", - "level": 3, - "metadata": {}, - "source": [ - "Solution" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "One possible solution follows. We have sliders for the start position, the amount of noise in the sensor, the amount we move in each time step, and how much movement error there is. Movement error is perhaps the least clear - it models how much the dog wanders off course at each time step, so we add that into the dog's position at each step. I set the random number generator seed so that each redraw uses the same random numbers, allowing us to compare the graphs as we move the sliders." - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "def plot_kalman_filter(start_pos, \n", - " sensor_noise, \n", - " movement,\n", - " movement_noise):\n", - " n = 20\n", - " zs = []\n", - " ps = []\n", - " \n", - " dog = DogSensor(start_pos, velocity=movement, variance=sensor_noise)\n", - " random.seed(303)\n", - " pos = (0., 1000.) # mean and variance\n", - "\n", - " for _ in range(n): \n", - " move_error = random.randn()*movement_noise\n", - " dog.x += move_error\n", - " \n", - " z = dog.sense_position()\n", - " zs.append(z)\n", - "\n", - " pos = update(pos[0], pos[1], z, sensor_noise)\n", - " ps.append(pos[0])\n", - "\n", - " pos = predict(pos[0], pos[1], movement, movement_noise)\n", - "\n", - " plt.plot(zs, c='r', linestyle='dashed', label='measurement')\n", - " plt.plot(ps, c='#004080', alpha=0.7, label='filter')\n", - " plt.legend(loc='best')\n", - " plt.show()\n", - "\n", - "interact(plot_kalman_filter,\n", - " start_pos=(-10, 10), \n", - " sensor_noise=widgets.FloatSliderWidget(value=5, min=0., max=100), \n", - " movement=widgets.FloatSliderWidget(value=1, min=-2., max=2.), \n", - " movement_noise=widgets.FloatSliderWidget(value=.1, min=0, max=.5))" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "display_data", - "png": 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gs9mIi4vj3XffLXSepUuXYrVamTVrFi+88AKNGzfGx8eHo0ePVsCzFREREZHaTt2lKsGD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\nZ1B2er9fxdat8M03RP35z66uRJxA73e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NSO8bb5hrMxQyRESqHH2isFvHjrB1K+zcaS5m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\nhvXxTMAA84H4oYfM48mTPXOM2mLHDnjrLbNCU26u3dVYw+F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- "text": [ - "" - ] - }, - { - "metadata": {}, - "output_type": "pyout", - "prompt_number": 29, - "text": [ - "" - ] - } - ], - "prompt_number": 29 - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "Exercise - Nonlinear Systems" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Our equations are linear: \n", - "$$\\begin{aligned}new\\_pos &= old\\_pos+dist\\_moved\\\\\n", - "new\\_position &= old\\_position*measurement\\end{aligned}$$\n", - "\n", - "Do you suppose that this filter works well or poorly with nonlinear systems?\n", - "\n", - "Implement a Kalman filter that uses the following equation to generate the measurement value for i in range(100):\n", - "\n", - " Z = math.sin(i/3.) * 2\n", - " \n", - "Adjust the variance and initial positions to see the effect. What is, for example, the result of a very bad initial guess?" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "#enter your code here." - ], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 30 - }, - { - "cell_type": "heading", - "level": 3, - "metadata": {}, - "source": [ - "Solution" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "sensor_variance = 30\n", - "movement_variance = 2\n", - "pos = (100,500)\n", - "\n", - "zs, ps = [], []\n", - "\n", - "for i in range(100):\n", - " pos = predict(pos[0], pos[1], movement, movement_variance)\n", - "\n", - " Z = math.sin(i/3.)*2\n", - " zs.append(Z)\n", - " \n", - " pos = update(pos[0], pos[1], Z, sensor_variance)\n", - " ps.append(pos[0])\n", - "\n", - "plt.plot(zs, c='r', linestyle='dashed', label='input')\n", - "plt.plot(ps, c='#004080', label='filter')\n", - "plt.legend(loc='best')\n", - "plt.show()" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "display_data", - "png": 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7ga+ALjWzh7XB7GGtIRSJMeT3gzh165nc70HkLyAoEsH3Y1DZzBDzR7djHQ5M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\n7MJdDH3xtWb+yFZoVM16DxArnYO9LRaMolLdaauPYcrKw2a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MF0jdRcf79tEX9EuXANts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\ns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- "text": [ - "" - ] - } - ], - "prompt_number": 31 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "######Discussion\n", - "\n", - "Here we set a bad initial guess of 100. We can see that the filter never 'acquires' the signal. Note now the peak of the filter output always lags the peak of the signal by a small amount, and how the filtered signal does not come very close to capturing the high and low peaks of the input signal.\n", - "\n", - "If we recall the g-h filter chapter we can understand what is happening here. The structure of the g-h filter requires that the filter output chooses a value part way between the prediction and measurement. A varying signal like this one is always accelerating, whereas our process model assumes constant velocity, so the filter is mathematically guaranteed to always lag the input signal. \n", - "\n", - "Maybe we just didn't adjust things 'quite right'. After all, the output looks like a sin wave, it is just offset some. Let's test this assumption." - ] - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "Exercise - Noisy Nonlinear Systems" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Implement the same system, but add noise to the measurement." - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "#enter your code here" - ], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 32 - }, - { - "cell_type": "heading", - "level": 3, - "metadata": {}, - "source": [ - "Solution" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "sensor_variance = 30\n", - "movement_variance = 2\n", - "pos = (100,500)\n", - "\n", - "zs, ps = [], []\n", - "\n", - "for i in range(100):\n", - " pos = predict(pos[0], pos[1], movement, movement_variance)\n", - "\n", - " Z = math.sin(i/3.)*2 + random.randn()*1.2\n", - " zs.append(Z)\n", - " \n", - " pos = update(pos[0], pos[1], Z, sensor_variance)\n", - " ps.append(pos[0])\n", - "\n", - "p1, = plt.plot(zs, c='r', linestyle='dashed', label='measurement')\n", - "p2, = plt.plot(ps, c='#004080', label='filter')\n", - "plt.legend(loc='best')\n", - "plt.show()" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "display_data", - "png": 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FJjBixlbjInRBb0yRBb3ykRXpF4mNggqrHMnT2dvZ0DzYUJ4h7Xitw+27D9h7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R0jZrDi4+NFHU86JVi9epHiQ6NGqse8vSloEMMRXS6nWrlmzYD69fUbj2E5yGTAggW0EiSXk/cH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\nSjlwgLYnTriWPvXyy5R+/uKLyozLR3AAo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- "text": [ - "" - ] - } - ], - "prompt_number": 33 - }, - { - "cell_type": "heading", - "level": 3, - "metadata": {}, - "source": [ - "Discussion" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "This is terrible! The output is not at all like a sin wave, except in the grossest way. With linear systems we could add extreme amounts of noise to our signal and still extract a very accurate result, but here even modest noise creates a very bad result.\n", - "\n", - "Very shortly after practitioners began implementing Kalman filters they recognized the poor performance of them for nonlinear systems and began devising ways of dealing with it. Much of the remainder of this book is devoted to this problem and its various solutions." - ] - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "Summary" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "This information in this chapter takes some time to assimilate. To truly understand this you will probably have to work through this chapter several times. I encourage you to change the various constants and observe the results. Convince yourself that Gaussians are a good representation of a unimodal belief of something like the position of a dog in a hallway. Then convince yourself that multiplying Gaussians truly does compute a new belief from your prior belief and the new measurement. Finally, convince yourself that if you are measuring movement, that adding the Gaussians correctly updates your belief. That is all the Kalman filter does. Even now I alternate between complacency and amazement at the results. \n", - "\n", - "If you understand this, you will be able to understand multidimensional Kalman filters and the various extensions that have been make on them. If you do not fully understand this, I strongly suggest rereading this chapter. Try implementing the filter from scratch, just by looking at the equations and reading the text. Change the constants. Maybe try to implement a different tracking problem, like tracking stock prices. Experimentation will build your intuition and understanding of how these marvelous filters work." - ] - } - ], - "metadata": {} - } - ] -} \ No newline at end of file diff --git a/05_Kalman_Filters/README.md b/05_Kalman_Filters/README.md deleted file mode 100644 index d041551..0000000 --- a/05_Kalman_Filters/README.md +++ /dev/null @@ -1,2 +0,0 @@ -You may read this book online via nbviewer by using this link: -[*Read Online Now*](http://nbviewer.ipython.org/github/rlabbe/Kalman-and-Bayesian-Filters-in-Python/blob/master/table_of_contents.ipynb) diff --git a/05_Kalman_Filters/dog_track.gif b/animations/05_dog_track.gif similarity index 90% rename from 05_Kalman_Filters/dog_track.gif rename to animations/05_dog_track.gif index 775fb4df3a31898fc11cbca5dff5080bb2e1fc95..21ffb48f30aa5aa1192c630c59f7b69320fdb0e3 100644 GIT binary patch delta 16324 zcmciJ)mxNd`|$gF0)}=7VF(H76qS&Y?k)*wQ5q>FWrptV4k-!guAxC%xzNdcP|)FPFMHN&~V4h?9RgC&ffmc&FupD;m*e=sY0wJ 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a/05_Kalman_Filters/Kalman_Filters_Animations.ipynb +++ b/animations/Kalman_Filters_Animations.ipynb @@ -1,7 +1,7 @@ { "metadata": { "name": "", - "signature": "sha256:2864cb6517423288a4854d36160a6a6e45be57d8b3f05f6f01db178492881e70" + "signature": "sha256:42fcc233db58d607109d988acbd2c05f37460792df171ef7155393554328c969" }, "nbformat": 3, "nbformat_minor": 0, @@ -21,7 +21,7 @@ "# use same formatting as rest of book so that the plots are\n", "# consistant with that look and feel.\n", "import book_format\n", - "book_format.load_style()\n", + "book_format.load_style(directory='..')\n", "\n", "\n", "\n", @@ -36,7 +36,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 1 + "prompt_number": 3 }, { "cell_type": "markdown", @@ -103,7 +103,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 2 + "prompt_number": 4 }, { "cell_type": "code", @@ -164,7 +164,7 @@ " plt.tight_layout()\n", " \n", "N=12\n", - "animate('volt_animate.gif', volt_animate, N*3, 350)" + "animate('05_volt_animate.gif', volt_animate, N*3, 350)" ], "language": "python", "metadata": {}, @@ -174,11 +174,11 @@ "output_type": "display_data", "png": 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vL/30t99KVwcRkSNiMDo5tVrqCoiIHAuD0Ul16iR1BUREjonB6KQ++EA/bXjOkYiImsdg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\nnTpVCAkJETw8PITQ0FDh97///+3csQmEQBCFYdZ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"text": [ - "" + "" ] } ], - "prompt_number": 3 + "prompt_number": 5 }, { "cell_type": "markdown", @@ -240,7 +240,7 @@ " plt.tight_layout()\n", "\n", "\n", - "animate('dog_track.gif', dog_animate, N, 200)" + "animate('05_dog_track.gif', dog_animate, N, 200)" ], "language": "python", "metadata": {}, @@ -250,17 +250,17 @@ "output_type": "display_data", "png": 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l3RcRtXsMRqrXrmN/xfX85Drtro5eeG7M50AkgO1tUMjo0fKHLxFRNQYjGSko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\nEZSXl+PTWr34KvldBv6qKwKQzOdNCgBrd8t1xVu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