{ "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": "markdown", "metadata": {}, "source": [ "# The g-h Filter" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "\n" ], "text/plain": [ "" ] }, "execution_count": 1, "metadata": {}, "output_type": "execute_result" } ], "source": [ "#format the book\n", "%matplotlib inline\n", "from __future__ import division, print_function\n", "from book_format import load_style\n", "load_style()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Before we start, be sure you understand how to use Jupyter Notebooks, and are familiar with the SciPy, NumPy, and Matplotlib packages, as they are used throughout this book. The Preface contains an introduction to these packages." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Building Intuition via Thought Experiments" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Imagine that we live in a world without scales - the devices you stand on to weigh yourself. One day at work a co-worker comes running up to you and announces her invention of a 'scale' to you. After she explains, you eagerly stand on it and announce the results: \"172 lbs\". You are ecstatic - for the first time in your life you know what you weigh. More importantly, dollar signs dance in your eyes as you imagine selling this device to weight loss clinics across the world! This is fantastic!\n", "\n", "Another co-worker hears the commotion and comes over to find out what has you so excited. You explain the invention and once again step onto the scale, and proudly proclaim the result: \"161 lbs.\" And then you hesitate, confused.\n", "\n", "\"It read 172 lbs a few seconds ago\", you complain to your co-worker. \n", "\n", "\"I never said it was accurate,\" she replies.\n", "\n", "Sensors are inaccurate. This is the motivation behind a huge body of work in filtering, and solving this problem is the topic of this book. I could just provide the solutions that have been developed over the last half century, but these solutions were developed by asking very basic, fundamental questions into the nature of what we know and how we know it. Before we attempt the math, let's follow that journey of discovery, and see if it does not inform our intuition about filtering. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Try Another Scale**\n", "\n", "Is there any way we can improve upon this result? The obvious, first thing to try is get a better sensor. Unfortunately, your co-worker informs you that she has built 10 scales, and they all operate with about the same accuracy. You have her bring out another scale, and you weigh yourself on one, and then on the other. The first scale (A) reads \"160 lbs\", and the second (B) reads \"170 lbs\". What can we conclude about your weight?\n", "\n", "Well, what are our choices?\n", "\n", "* We could choose to only believe A, and assign 160lbs to our weight estimate.\n", "* We could choose to only believe B, and assign 170lbs to our weight.\n", "* We could choose a number less than either A or B.\n", "* We could choose a number greater than either A or B.\n", "* We could choose a number between A and B.\n", "\n", "The first two choices are plausible, but we have no reason to favor one scale over the other. Why would we choose to believe A instead of B? We have no reason for such a belief. The third and fourth choices are irrational. The scales are admittedly not very accurate, but there is no reason at all to choose a number outside of the range of what they both measured. The final choice is the only reasonable one. If both scales are inaccurate, and as likely to give a result above my actual weight as below it, more often than not probably the answer is somewhere between A and B. \n", "\n", "In mathematics this concept is formalized as [*expected value*](https://en.wikipedia.org/wiki/Expected_value), and we will cover it in depth later. For now ask yourself what would be the 'usual' thing to happen if we took one million readings. Some of the times both scales will read too low, sometimes both will read too high, and the rest of the time they will straddle the actual weight. If they straddle the actual weight then certainly we should choose a number between A and B. If they don't straddle then we don't know if they are both too high or low, but by choosing a number between A and B we at least mitigate the effect of the worst measurement. For example, suppose our actual weight is 180 lbs. 160 lbs is a big error. But if we choose a weight between 160 lbs and 170 lbs our estimate will be better than 160 lbs. The same argument holds if both scales returned a value greater than the actual weight.\n", "\n", "We will deal with this more formally later, but for now I hope it is clear that our best estimate is the average of A and B. $\\frac{160+170}{2} = 165$.\n", "\n", "We can look at this graphically. I have plotted the measurements of A and B with an assumed error of $\\pm$ 8 lbs. The overlap falls between 160 and 170 so the only weight that makes sense must lie within 160 and 170 pounds. " ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import kf_book.book_plots as book_plots\n", "book_plots.plot_errorbars([(160, 8, 'A'), (170, 8, 'B')], \n", " xlims=(150, 180))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "> A word on how I generated this plot. I import code from the module book_plots in the `kf_book` subdirectory. Generating this plot takes a lot of boilerplate Python that isn't interesting to read. I take this tack often in the book. When the cell is run `plot_errorbars()` gets called and the plot is inserted into the book." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "So 165 lbs looks like a reasonable estimate, but there is more information here that we might be able to take advantage of. The only weights that are possible lie in the intersection between the error bars of A and B. For example, a weight of 161 lbs is impossible because scale B could not give a reading of 170 lbs with a maximum error of 8 pounds. Likewise a weight of 171 lbs is impossible because scale A could not give a reading of 160 lbs with a maximum error of 8 lbs. In this example the only possible weights lie in the range of 162 to 168 lbs.\n", "\n", "That doesn't yet allow us to find a better weight estimate, but let's play 'what if' some more. What if we are now told that A is three times more accurate than B? Consider the 5 options we listed above. It still makes no sense to choose a number outside the range of A and B, so we will not consider those. It perhaps seems more compelling to choose A as our estimate - after all, we know it is more accurate, why not use it instead of B? Can B possibly improve our knowledge over A alone?\n", "\n", "The answer, perhaps counter intuitively, is yes, it can. First, let's look at the same measurements of A=160 and B=170, but with the error of A $\\pm$ 3 lbs and the error of B is 3 times as much, $\\pm$ 9 lbs." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "book_plots.plot_errorbars([(160, 3, 'A'), (170, 9, 'B')], \n", " xlims=(150, 180))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The overlap of the error bars of A and B are the only possible true weight. This overlap is smaller than the error in A alone. More importantly, in this case we can see that the overlap doesn't include 160 lbs or 165 lbs. If we only used the measurement from A because it is more accurate than B we would give an estimate of 160 lbs. If we average A and B we would get 165 lbs. Neither of those weights are possible given our knowledge of the accuracy of the scales. By including the measurement of B we would give an estimate somewhere between 161 lbs and 163 lbs, the limits of the intersections of the two error bars.\n", "\n", "Let's take this to the extreme limits. Assume we know scale A is accurate to 1 lb. In other words, if we truly weigh 170 lbs, it could report 169, 170, or 171 lbs. We also know that scale B is accurate to 9 lbs. We do a weighing on each scale, and get A=160, and B=170. What should we estimate our weight to be? Let's look at that graphically." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "book_plots.plot_errorbars([(160, 1, 'A'), (170, 9, 'B')],\n", " xlims=(150, 180))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here we can see that the only possible weight is 161 lbs. This is an important result. With two relatively inaccurate sensors we are able to deduce an extremely accurate result.\n", "\n", "So two sensors, even if one is less accurate than the other, is better than one.\n", "\n", "However, we have strayed from our problem. No customer is going to want to buy multiple scales, and besides, we initially started with an assumption that all scales were equally (in)accurate. This insight of using all measurements regardless of accuracy will play a large role later, so don't forget it.\n", "\n", "What if I have one scale, but I weigh myself many times? We concluded that if we had two scales of equal accuracy we should average the results of their measurements. What if I weigh myself 10,000 times with one scale? We have already stated that the scale is equally likely to return a number too large as it is to return one that is too small. It is not that hard to prove that the average of a large number of weights will be very close to the actual weight, but let's write a simulation for now." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Average of measurements is 165.0009\n" ] } ], "source": [ "import numpy as np\n", "measurements = np.random.uniform(160, 170, size=10000)\n", "print('Average of measurements is {:.4f}'.format(\n", " measurements.mean()))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The exact number printed depends on your random number generator, but it should be very close to 165.\n", "\n", "If this is your first time using Jupyter Notebook, the code below is in a *cell*. The text \"In [2]:\" labels this as a cell where you can enter input, and the number in the bracket denotes that this cell was run second. To run the cell, click on it with your mouse so that it has focus, then press CTRL+ENTER on the keyboard. As we continue you will be able to alter the code inside the cells and rerun them. Try changing the values \"160\", \"170\", and \"10000\" to some other value and run the cell. The printed output should change depending on what you entered.\n", "\n", "This code makes one assumption that probably isn't true - that the scale is as likely to read 160 as 165 for a true weight of 165 lbs. This is almost never true. Real sensors are more likely to get readings nearer the true value, and are less and less likely to get readings the further away from the true value it gets. We will cover this in detail in the Gaussian chapter. For now, I will use without further explanation the `numpy.random.normal()` function, which will produce more values nearer 165 lbs, and fewer further away. Take it on faith for now that this will produce noisy measurements very similar to how a real scale would." ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Average of measurements is 164.9544\n" ] } ], "source": [ "measurements = np.random.normal(165, 5, size=10000)\n", "print('Average of measurements is {:.4f}'.format(\n", " measurements.mean()))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The answer again is very close to 165. \n", "\n", "Okay, great, we have an answer to our sensor problem! But it is not a very practical answer. No one has the patience to weigh themselves ten thousand, or even a dozen times. \n", "\n", "So, let's play 'what if' again. What if you measured your weight once a day, and got the readings 170, 161, and then 169. Did you gain weight, lose weight, or is this all just noisy measurements? \n", "\n", "We really can't say. The first measurement was 170, and the last was 169, implying a 1 lb loss. But if the scale is only accurate to 10 lbs, that is explainable by noise. I could have actually gained weight; maybe my weight on day one was 165 lbs, and on day three it was 172. It is possible to get those weight readings with that weight gain. My scale tells me I am losing weight, and I am actually gaining weight! Let's look at that in a chart. I've plotted the measurements along with the error bars, and then some possible weight gain/losses that could be explained by those measurements in dotted green lines." ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "image/png": 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SF6JAkwJCCJFjmjs1Z06nOQBM3DmRzec3K5xR7lOpVHSs0pGtvlsJez+Mdxu+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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "book_plots.plot_hypothesis1()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As we can see there is an extreme range of weight changes that could be explained by these three measurements. Shall we give up? No. Recall that we are talking about measuring a humans' weight. There is no way for a human to weigh 180 lbs on day 1, and 160 lbs on day 3. or to lose 30 lbs in one day only to gain it back the next (we will assume no amputations or other trauma has happened to the person). The behavior of the physical system we are measuring should influence how we interpret the measurements. \n", " \n", "Suppose I take a different scale, and I get the following measurements: 169, 170, 169, 171, 170, 171, 169, 170, 169, 170. What does your intuition tell you? It is possible, for example, that you gained 1 lb each day, and the noisy measurements just happens to look like you stayed the same weight. Equally, you could have lost 1 lb a day and gotten the same readings. But is that likely? How likely is it to flip a coin and get 10 heads in a row? Not very likely. We can't prove it based solely on these readings, but it seems pretty likely that my weight held steady. In the chart below I've plotted the measurements with error bars, and a likely true weight in dashed green. This dashed line is not meant to be the 'correct' answer to this problem, merely one that is reasonable and could be explained by the measurement." ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "book_plots.plot_hypothesis2()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Another what if: what if the readings were 158.0, 164.2, 160.3, 159.9, 162.1, 164.6, 169.6, 167.4, 166.4, 171.0? Let's look at a chart of that and then answer some questions." ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "book_plots.plot_hypothesis3()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Does it 'seem' likely that I lost weight and this is just really noisy data? Not really. Does it seem likely that I held the same weight? Again, no. This data trends upwards over time; not evenly, but definitely upwards. We can't be sure, but that surely looks like a weight gain, and a significant weight gain at that. Let's test this assumption with some more plots. It is often easier to 'eyeball' data in a chart versus a table.\n", "\n", "So let's look at two hypotheses. First, let's assume our weight did not change. To get that number we agreed that we should average the measurements. Let's look at that.\n" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "image/png": 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//RZ/+9vf0K9fPyQkJOCPP/5AZGQk2rZti5s3b2Lt2rVQKpUYNGhQjccuLi7G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\nyRPt379fNTU18vLy0tKlS1VcXEzAGUH/9l5JUkh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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "book_plots.plot_hypothesis4()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "That doesn't look very convincing. In fact, we can see that there is no horizontal line that we could draw that is inside all of the error bars.\n", "\n", "Now, let's assume we gained weight. How much? I don't know, but NumPy does! We want to draw a line through the measurements that looks 'about' right. NumPy has functions that will do this according to a rule called \"least squares fit\". Let's not worry about the details of that computation, or why we are writing our own filter if NumPy provides one, and plot the results." ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "image/png": 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LxMbGok+fPnqlNxMSEiAIAo4fP45x48ZhwIABAIAnnngCM2fOxNChQ9GpU6cW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\nAAAASUVORK5CYII=\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "book_plots.plot_hypothesis5()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This looks much better, at least to my eyes. Notice now the hypothesis lies very close to each measurement, whereas in the previous plot the hypothesis was often quite far from the measurement. It seems far more likely to be true that I gained weight than I didn't gain any weight. Did I actually gain 13 lbs? Who can say? That seems impossible to answer.\n", "\n", "\"But is it impossible?\" pipes up a co-worker.\n", "\n", "Let's try something crazy. Let's assume that I know I am gaining about one lb a day. It doesn't matter how I know that right now, assume I know it is approximately correct. Maybe I am eating a 6000 calorie a day diet, which would result in such a weight gain. Or maybe there is another way to estimate the weight gain. Let's see if we can make use of such information if it was available without worrying about the source of that information yet.\n", "\n", "The first measurement was 158. We have no way of knowing any different, so let's accept that as our estimate. If our weight today is 158, what will it be tomorrow? Well, we think we are gaining weight at 1 lb/day, so our prediction is 159, like so:" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "image/png": 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XOz0mIYQQQvSSy5fNhUVGhvnPwYPg4NrzDnl62gqLtDSYMQN6+ZepQrg71YXG\nqlWr8PLy4ttvv2XJkiX8+7//u3VbTk4OS5cu7dJAHnjgAetqBABbtmxhy5YtgHkVg9DQUAYPHswr\nr7xCWVkZBoOBuLg4fvvb37Jy5UrF5KrrrruOrKwsNm7cyKpVq6ioqCAmJoZFixaxZs0axUoeRqMR\ng8HgcKLVu+++S2BgIHfeeafDMYeEhDg9JiGEEEL0kJoa2LvX1rE4eBAcXMPeIU9PmDzZ1rGYMQOC\ng3titEJohuo5GqLrXG2ORuuVBXr6/ifCNUjOtUdyrj2ayPmlS+bCwjLH4tAh9YWFl5etsEhLg+nT\noZMl6V2VJnIuFPoq5z0+R8OisbGRQ4cOUVVVRXh4OJMmTerSHbdF38nJybEue2m/jrbonyTn2iM5\n155+mfPqavNys5aOxeHDoPb3pN7eMGWKrWMxfTr0kysP+mXORYfcJeddKjReeeUVNm7cyOXLlzGZ\nTOh0OoKDg1m9ejWPPfZYd49RCCGEEFpy8aLiPhYcOdK1wuKGG2wdi2nToNUNNYUQPa9LdwZ//PHH\nmT9/PsuXL2fIkCFcuHCBzZs3s2LFCry9vfntb3/bE2MV3Sw4OBi9Xq/q5oXCvUnOtUdyrj1umfOq\nKtizx9axOHpUfWHh4wNTp9o6FlOnaqawcMuci2viLjlXPUcjPj6eGTNm8Le//a3Ntp///Ofs27fP\neit4oeRqczSEEEKIPlFZaS4sLKtCHTumPoavr7lLYbmPxQ03gL9/Nw9UCNFaj8/ROH/+vGJ52Nbu\nvvtu/v73v6sNKYQQQoj+rLzcVlhkZkJOjvoYfn7mwsLSsbjhBvNjQgiXpbrQGD16NGVlZQ63lZaW\nMmrUqGselBBCCCHcWFmZsmNx/Lj6GP7+5gnblo7FlCnmLoYQwm2oLjTWr1/PI488wqRJkxR3yz56\n9Cjr16/nlVde6dYBCiGEEMLFXbhgm1+RmQk//KA+RkCAubCwdCwmT5bCQgg351ShsWjRIsXf9Xo9\nEyZMIDk52ToZPDc3l+joaP7rv/6LJUuW9MhgRfcqLCy0TiQaMWJEXw9H9ALJufZIzrWnV3JeWmor\nLDIyID9ffYyAAJg509axuP5684RuoZp8zrXHXXLuVKFx9OhRdDqdbScvL4YNG8bly5e5fPkyAMOG\nDQPgWFcmdIk+cfnyZesazEIbJOfaIznXnh7JeUmJsmNx4oT6GIGB5sLC0rG4/nrzErTimsnnXHvc\nJedOFRpFRUU9PAwhhBBCuIxz55Qdi1On1McICoJZs2wdi0mTpLAQQmNUL28rus7VlrfV6/XWGy66\n+jrMontIzrVHcq49Xcr52bOKIcVRAAAgAElEQVS2oiIzE7qyTH1wsLmwsNwgb+JEkPdcr5DPufb0\nVc57fHlb0X/IyUh7JOfaIznXHqdyXlxsKyoyMqCwUP0PCgmB2bNtHYsJE6Sw6CPyOdced8m5U6P0\n8PBQzNHoiE6nQ6/XX9OghBBCCNGNioqUHYuuXBI9YICyY5GaCp6e3TlKIUQ/41ShsWbNGqcLDSGE\nEEL0IZPJ3KFo3bE4c0Z9nLAwZcdi/HgpLIQQqsgcjV7kanM0Ll26hNFoxMPDgwEDBvTJGETvkpxr\nj+RcA0wmOH3a2rEw7t6NR0mJ+jgDB5oLC0vHYtw46KN/n4Q68jnXnr7KuczREE4rLi62Lo0mJyZt\nkJxrj+S8HzKZzKtAte5YtCosnC4NwsPN3QpLxyIlRQoLNyWfc+1xl5w7VWh8+umn/OQnP1EV+Pz5\n8xQWFjJjxowuDUwIIYQQmAuLkyeVcyzOn1cfJyLCVlSkpcHYsVJYCCF6lFOFxoMPPsizzz7LQw89\nxE9+8hNCQkLafe7Bgwd57733+K//+i9efPFFKTRcWHR0NAaDAU+55lYzJOfaIzl3QyaT+U7brTsW\nFy6oDmOMiMBj7lzbDfLGjgWZb9kvyedce9wl507N0aipqWHdunW89dZbGAwGJk6cyKRJkxg0aBB+\nfn5cvHiRgoICsrKyKC0tJSUlhRdeeIGbb765N47BbbjaHA0hhBAuwGSCvDxlx6KsTH2cwYNtRUVa\nGiQmSmEhhOhWar/LqpoMXl1dzV//+le++OILsrKyqK+vt24bOXIkaWlp3HXXXcydO7eLw+/fpNAQ\nQgiByQTHj9uKisxMKC9XH2fIENtlUHPmwJgxUlgIIXpUjxYa9mpqamhoaCA8PBxvb++uhtEMKTSE\nEEKDjEbIzbVdBpWZCZWV6uNERys7FgkJUlgIIXpVr646FRoaSmho6LWEEEIIIfoXoxFycpQdi6oq\n9XFiYpQdi1GjpLAQQrgVWd5Ww44ePWpdGm38+PF9PRzRCyTn2iM57wVGIxw9autY7NkDFy+qjzN0\nKMyda+tYjBzZpcJCcq49knPtcZecS6GhYSaTyfpHaIPkXHsk5z3AYDAXFpaOxZ49UF2tPk5srLJj\nMWJEt3QsJOfaIznXHnfJuRQaGubv74+3tzdeXvI20ArJufZIzruBwQBHjig7FjU16uMMH668j8Xw\n4d06TAvJufZIzrXHXXJ+TZPBhToyGVwIIdyAXm8uLCwdi6+/7lphMXKkrbCYMwfi4rp7pEII0avU\nfpd1iW+4V65cYcWKFdx0001ERkai0+lYt25dm+fde++96HS6Nn8SExPbPPfUqVPcfffdxMbG4u/v\nT3x8PI8++ihVTkzIy8jIcPhzdDodWVlZbZ6/Y8cOpk2bRkBAABEREdx7772Ud2WpQiGEEL1Pr4fv\nv4cXX4Rbb4WBA2HyZHjiCfjsM+eLjPh4uP9++NvfoLgYCgrgvffgF7+QIkMIoUmq+y0jR45k27Zt\npKamttmWk5PDokWLOH36tKqYVVVVvPXWW6SmprJ48WLeeeeddp/r7+/Prl272jzWWkVFBVOnTiUk\nJISNGzcSGxvL4cOHWbt2Lbt37+bgwYNOdRGeffbZNvcESUlJUfw9MzOTH/3oR9x6661s376d8vJy\nnnzySdLT0zlw4AC+vr6d/hwhhBC9qKUFDh2y3SBv716orVUfJyFB2bEYOrSbByqEEO5NdaFRVFRE\nU1OTw22NjY0UFxerHkRcXBzV1dXodDoqKys7LDQ8PDyYOnVqh/G2b99OVVUVn3zyCenp6QDMnTuX\npqYmVq5cSXZ2NhMnTux0XAkJCZ3+rCeeeILRo0ezdetW63VyI0aMYMaMGbz33ns88MADnf4cIYQQ\nPailBQ4csM2x2LsX6urUxxk92lZUzJljXn5WCCFEu7o0g0TXzqoYp0+fJjg4uNvidZXl5oH29/gY\nMGAAAH5+ft3yc0pKSti/fz/PPfecYjLO9OnTGT16NNu2bXPpQuPs2bMYDAY8PT0ZNmxYXw9H9ALJ\nufZoMufNzebCwtKx+PbbrhUWiYnKjkVUVDcPtGdoMucaJznXHnfJuVOFxvvvv8/7779v/fsDDzxA\nSEiI4jkNDQ1kZ2czZ86c7h2hnYaGBoYMGUJFRQVRUVEsXryYDRs2MHDgQOtzFi9eTGxsLI899hhv\nvPEGcXFxHDp0iE2bNrFw4UKSkpKc+lkPPvggd955JwEBAUybNo3Vq1czc+ZM6/acnBwAh+sXjx8/\nnm+++eYaj7ZnXbx40boGsyu/SUX3kZxrjyZy3tQE+/fbOhbffAMNDerjJCUpOxZDhnT3SHuFJnIu\nFCTn2uMuOXeq0Kivr6eiogIwdx8uXbrU5vIpX19ffvrTn7J+/fruH+VVqamppKamWudJZGZm8uqr\nr7Jz5072799PUFAQYO5kZGVlsXTpUsWcimXLlvHBBx90+nNCQ0N5+OGHSUtLIzw8nFOnTvHiiy+S\nlpbG559/zs033wxgnVjeusixGDhwoFMTz3Nzc4mLi1MUbk1NTeTl5QEQFhZGbGysYp+TJ09SX19v\nfU1aq6yspKSkBIDY2FjCwsKs2wwGg7U4ctR5Kiws5PLlywAkJycrujSXLl2yXhYXHR1NZGSkYt+j\nR49iMpnw9/dn9OjRim1nz57l4tWbV40ZM0bRUaqtraWgoACAQYMGEWX3G8Pjx49bP0hjx45VbCst\nLbVOuo+Pj7fmH8yX8eXn5wPmXNh/CE+cOEFDQwM6na5NoVhRUcH58+cB82V9lk4YgF6vJzc3F4CQ\nkBBGjBih2Pf06dPW1RhSUlLw9PS0bquurubMmTMAxMTEEBERodg3OzsbgICAABISEhTbzpw5Q/XV\ndfoTExMVc38uX75MYWEhAIMHD2aI3Zej3Nxc9Hq9w/lC58+ft362R40aRWBgoHVbfX09J0+eBCA8\nPJyhdtef5+fn09jYiKenZ5u5S+Xl5ZSWlgIwfPhwRXexubmZH374ATB/1obbLfFZUFBA7dXr5ceN\nG6eYT1VVVcW5c+cAGDp0KOHh4dZtRqORY8eOARAUFER8fLwiblFRETVXJ/UmJSXh4+Nj3VZTU0NR\nUREAUVFRDBo0SLFvTk4OBoMBPz8/xowZo9h27tw562c9ISGBgIAA67a6ujpOnToFQGRkJNHR0Yp9\n8/LyaGpqwsvLi+TkZMW2CxcuUFZWBpgvx+zqOcKemnPEyJEjFfu6zDmiqck8eTsjg7rPP8c/OxuP\nxkaHx9uRhvh46q67DtLSiLj9dhg82LrtxIkTNJSVueU5wn4xSTXnCPvFVeQcYebq5wij0ajY1lvf\nI1z2HNFKf/0eYZ9z6J3vEfa56YxThcYDDzxgvQRoxIgR/P3vf3c4GbynPfLII4q/z58/n4kTJ3LH\nHXfw9ttvW7dXV1dz2223UV9fz+bNmxk2bBg5OTls3LiRRYsW8fnnn3e47vDEiRMVczhmzZrFkiVL\nGDduHCtWrLAWGhbtXfrlzCVher2+zT8KJpOJlpYW63ZH+1i22zMajdZtjt6EreOOGTMGk8lkHWfr\nuPZjah3XYDA4jGsymayXrbVmMBiuKW57x9o6rv2xtn4NHcW1HKujHDkbtydz01Hcjt4v7b2Ger0e\nDw+PNjnvKDfOxG1paXG4raO4rY9Vbc6dfQ0d7d96TPY6O9bm5maMRqPihO8obldfQ0evkbNxO3u/\npKSkKHLeU+/DnjxH6GtrCczJIeDkSfMk7n374GphEdgmWgdSUqwdi4bJk8m9+gU6IiKCiFZFRutj\ndcdzREJCAj4+PtaxqzlHdHSsco5w3XNEXFwcQUFBDnPuKv9WyfeItnGvJTdRUVEMHDhQ8fN743uE\nWqrnaFgqHlexZMkSAgMDFcvOPv/88xw5coTi4mJrZTtr1iwSExOZN28emzdv5p577lH1cwYMGMCP\nf/xj3nzzTRoaGvD397f+psRR5+LixYsOOx32vLy82rxJdTqd9YPmqCDy8vJy+EEE82R5yzZHb4jW\nce3nqrSOaz+m1nEdnUi9vb0xmUwOx+vp6XlNcVv/t7249sfa+jV0FNdyrI5OEM7G7cncdBS3o/dL\ne6+h5Tn2Oe8oN87EtVwfaq+juK2Ptb241/oadvZ+sdfZsfr4+GAwGDqN25XX0Gg0qv7cqHkf2ue8\np96H3XqOaGyErCzIyCBw504mfv89Hs3NbfbrTEtSEpcmTKDu+uuJuP12glr9ZlzX2Ij3pUvtjted\nzxF+fn6K31aqOUfYk3ME1jG68jnC19dXsQKnK7wP5XtEz54j7HPe+hh78nuEWl2+YV95eTnFxcU0\nOLgOdvbs2V0JCZhbdpGRkaxdu9bhvTTsGY1GgoODWbRoER999BEACxYsID8/v01RVFtbS3BwMI8/\n/jgvvvii6rH9+te/5j//8z9paGjAz8+PkpIShg4dyqZNm3jyyScVz01MTCQ2NpZ//etfirHKDfuE\nEMJOQ4O5S2G5QV5WlnlCtxo6HYwfb7vr9qxZ0OqyGSGEENdO7XdZ1R2N0tJS7r77bnbv3t1mm6U9\n76jt0lO2bt1KfX29Yhna6Ohodu7cSUlJCTGtlh/ct28fQJvrSJ1RXV3NZ599xoQJE6y/IYyJiWHK\nlCl8+OGHPP7449YqMCsri/z8fP7jP/7jWg5NCCH6p/p680pQlsnb33/ftcJiwgTbqlCzZplvtCeE\nEMJlqO5oLF26lIyMDH73u98xfvx4hxNMu7Ly1JdffkldXR1XrlzhvvvuY9myZfzkJz8B4JZbbqGi\nooLly5dz5513MmrUKHQ6HZmZmbz22mvEx8fz3XffWSepHTx4kOnTpxMfH89TTz1lnaPxzDPPoNPp\nyMnJsU6y27BhAxs2bGDnzp3WcS9fvpzY2Fiuv/56IiIiOHnyJC+//DIFBQV8+eWX3HjjjdZxZ2Rk\nMH/+fBYuXMhvfvMbysvLeeqppwgNDW1zwz5X62jU1tZiNBrx8PBQTIAS/ZfkXHtcIud1debCwtKx\n+P57870t1PDwMBcWlo7FzJnQapKqsHGJnIteJTnXnr7KeY93NDIzM3nppZf45S9/2bURtuOBBx5Q\n3Oxvy5YtbNmyBTDPCwkNDWXw4MG88sorlJWVYTAYiIuL47e//S0rV65UrIRx3XXXkZWVxcaNG1m1\nahUVFRXExMSwaNEi1qxZo1jJw2g0YjAYFBNjxo8fzyeffMKbb75JbW0tAwcOZObMmXzwwQdMnjxZ\nMe60tDS++OIL1qxZw8KFCwkICODHP/4xL774osvfFbygoMC6EkNfTO4XvU9yrj19kvPaWvMSs5aO\nxf794GByYoc8PGDSJFvHYuZMaLVyi2iffM61R3KuPe6Sc9UdjcjISD766CPFb/WFc1yto5Gdne0W\nb1LRfSTn2tMrOb9yxVxYWDoWBw50rbC4utQsaWkwYwbY3XRVOEc+59ojOdeevsp5j3c0li1bxmef\nfSaFRj8waNCgdlcEEf2T5Fx7eiTnly/D3r22jsXBg6B2bp6nJ1x/va1jMWMG2N0IVnSNfM61R3Ku\nPe6Sc6c6GocOHbL+/+XLl/m3f/s3fvSjH7Fw4ULFzXAsJk2a1L2j7CdcraMhhBBOqakxFxaWjsXB\ng+Bgff0OeXmZCwtLx2L6dHBw41AhhBCuS+13WacKDQ8PD8Wau5Zd7Nfh7YtVp9yJFBpCCLdw6ZKt\nsMjIgMOHu1ZYTJlivUEe06eDTFIVQgi31iOXTv31r3+99pEJIYRwTdXV8PXXto7F4cOg9hZL3t62\nwiItDaZNg0BV9+0WQgjRz3T5hn1CPeloCCFcwsWLsGePbY5Fdrb6wsLHB264wdaxmDYNAgJ6YrRC\nCCFcRI9PBhf9x/Hjx60rFowdO7avhyN6geRce44fP46xooLQ7GyGFRSYi4ujR7tWWEydautYTJ0K\n/v49MWRxjeRzrj2Sc+1xl5yrLjTuu+++drd5eHgwYMAAJk+ezJIlS/Dx8bmmwYme1dLSQovam2YJ\ntyY514iKCmvHYsT//i/+J0+qj+Hra+5SWDoWN9wghYWbkM+59kjOtcddcq660Ni9ezc1NTVcunQJ\nLy8vwsPDqaqqQq/XM2DAAEwmE6+88gpjxowhIyODwYMH98S4RTfw9vZW/Ff0f5Lzfqq83FxYWOZY\n5ORYNzldGvj52QqLtDTzfAs/v+4fq+hx8jnXHsm59rhLzlXP0Th06BBLlizhhRde4I477sDT0xOD\nwcCWLVt48skn2bJlC3q9nttvv51bb72Vd999t6fG7nZkjoYQoluUlZkLCssci+PH1cfw9zevBGXp\nWEyZYu5iCCGEEO3okeVtW0tLS2Pp0qX8+7//e5ttf/jDH9iyZQt79+7l1Vdf5aWXXqKkpERN+H5N\nCg0hRJdcuGArKjIz4Ycf1McICDDfFM9yg7zJk83zLoQQQggn9fhk8P3797N69WqH21JSUli5ciUA\nEyZMoLKyUm14IYQQ588rOxb5+epjBAaaCwtLx+L666WwEEII0atUFxohISHs3r2b9PT0Ntt27dpF\nSEgIAA0NDQTLXV+FEKJzJSXKjsWJE+pjBAXBzJm2jsV115nvbSGEEEL0EdWFxvLly3n++ecxmUws\nW7aMwYMHU1ZWxieffMLLL7/Mww8/DMDBgwdJSkrq9gGL7lNaWorBYMDT05OoqKi+Ho7oBZJzF3H2\nrLKwOHVKfYzgYHNhYelYTJrksLCQnGuP5Fx7JOfa4y45V11oPPfcc5SWlvLcc8+xadMm6+Mmk4mf\n/exnPPvsswBMmzaNm2++uftGKrpdeXm5dQ1mV36Tiu4jOe8jZ87YCouMDDh9Wn2MkBCYNcvWsZg4\nEbw6P4VLzrVHcq49knPtcZecqy40fHx8+O///m9Wr15NZmYmVVVVhIeHM3v2bMUNQ2688cZuHagQ\nQriN4mJbUZGZCYWF6mOEhMDs2baOxYQJThUWQgghhKtQveqU6DpXW3WqtrYWo9GIh4cHQUFBfTIG\n0bsk5z3AZIKiImXHorhYfZwBA8yFhaVjkZoKnp7XPDzJufZIzrVHcq49fZXzHl/eVnSdqxUaQogu\nMJnMHQpLtyIjw3xplFphYcqOxfjx3VJYCCGEED2lR5a39fT0ZN++fUyZMgUPDw90Ol27z9XpdOj1\nehVDFkIIF2YyQUGBsmNx7pz6OAMHmgsKS8di3DiQXzIIIYTox5wqNNasWcPQoUOt/99RoSGEEG7N\nZDKvAtW6Y9GVG4+Gh9uKirQ0SE6WwkIIIYSmyKVTvcjVLp1qbGzEZDKh0+nw8/PrkzGI3iU5d8Bk\nMt+3onVhUVqqPk5EhO0yqLQ0GDvWJQoLybn2SM61R3KuPX2V8x6/M7joP/Lz861Lo6Wmpvb1cEQv\nkJxjLizy85WrQl24oD7OoEHKjkVSErhgt1dyrj2Sc+2RnGuPu+S8S4VGXl4e69evJyMjg6qqKrKy\nspg0aRLr169n9uzZzJ07t7vHKYQQXWMywQ8/2IqKzEwoK1MfZ/BgZcciMdElCwshhBDCVaguNI4c\nOcKsWbMIDg4mLS2NTz/91LqttraWN998UwoNNzFw4EDrXSWFNmgi5yYTHD+u7FhUVKiPExWl7FiM\nHu2WhYUmci4UJOfaIznXHnfJueo5GgsWLODKlSt89dVX+Pj44OPjw4EDB5g0aRJbtmzhySef5HRX\n7nqrAa42R0OIfsFohNxcZceislJ9nOhoZcciIcEtCwshhBCip/T4HI1vvvmGDz/8kICAAAwGg2Lb\n4MGDudCVa52FEMJZRiPk5Ng6Fnv2QFWV+jgxMbZuRVoaxMdLYSGEEEJ0I9WFhslkwsfHx+G26upq\nfH19r3lQQghhZTTC0aO2jsWePXDxovo4w4YpOxYjR0phIYQQQvQg1dfsjB8/nm3btjnc9r//+79c\nd911qgdx5coVVqxYwU033URkZCQ6nY5169a1ed69996LTqdr8ycxMbHNc0+dOsXdd99NbGws/v7+\nxMfH8+ijj1LlxG8+d+3axX333UdiYiKBgYHExMRw2223cfDgwWsakxDCCQYDHD4Mr74Kt91mXjZ2\n4kR45BH4xz+cLzJiY+Gee+C99+D0aSguhr/9De6/X7oXQgghRC9Q3dF4+OGHWb58OYGBgdx9990A\nnDlzhl27dvHee++xdetW1YOoqqrirbfeIjU1lcWLF/POO++0+1x/f3927drV5rHWKioqmDp1KiEh\nIWzcuJHY2FgOHz7M2rVr2b17NwcPHuxwXsRf/vIXqqqqePjhhxk7diwVFRW8/PLLTJ06lX/+85/M\nmzdP9Zhc0YkTJ9Dr9Xh5eTF69Oi+Ho7oBS6Zc4MBjhxRdixqatTHGT7cdhnUnDnmvwvXzLnoUZJz\n7ZGca4+75Fx1ofHTn/6UgoIC1q1bxx//+EcAli5dipeXF+vXr2fhwoWqBxEXF0d1dTU6nY7KysoO\nCw0PDw+mTp3aYbzt27dTVVXFJ598Qnp6OgBz586lqamJlStXkp2dzcSJE9vd//XXX2fQoEGKxxYs\nWMCoUaN49tln2xQazozJFTU0NFjXYBba4BI51+vNHQvLzfG+/houX1YfZ+RI22VQc+ZAXFx3j7Rf\ncImci14lOdceybn2uEvOu3QfjZUrV/KLX/yCf/7zn5SVlREREcHNN99MXBf/odd18yUMlhc9NDRU\n8fiAAQMAOr2Don2RARAUFMTYsWM5e/ZsN42y77W+1EtoQ5/kXK+HQ4dsHYuvvwa7FSucEh+v7FgM\nG9bNA+2f5HOuPZJz7ZGca4+75LzLdwYfOnQo999/f3eOxSkNDQ0MGTKEiooKoqKiWLx4MRs2bGDg\nwIHW5yxevJjY2Fgee+wx3njjDeLi4jh06BCbNm1i4cKFJCUlqf65NTU1HDp0qE03w9kxuaLx48f3\n9RBEL+uVnLe0wMGDto7F3r1QW6s+TkKCsmMxdGh3j1QT5HOuPZJz7ZGca4+75Fx1oTF58mTmz59P\neno6M2fO7NVVplJTU0lNTSUlJQWAzMxMXn31VXbu3Mn+/fsJCgoCzJ2MrKwsli5dan0uwLJly/jg\ngw+69LMffPBB6urqWLVqVZfG1J7c3Fzi4uIICQmxPtbU1EReXh4AYWFhxMbGKvY5efIk9fX11p/f\nWmVlJSUlJQDExsYSFhZm3WYwGMjJyQHMax6PHDlSsW9hYSGXr17CkpycjJeX7e1x6dIliouLAYiO\njiYyMlKx79GjRzGZTPj7+7e5VvDs2bNcvDqBd8yYMYqOUm1tLQUFBYC5kxQVFaXY9/jx49bW4Nix\nYxXbSktLKS8vByA+Pl7xWjc2NpKfnw+Yb2ozzO633ydOnKChoQGdTtfmw1pRUcH58+cB82V9lk4Y\ngF6vJzc3F4CQkBBGjBih2Pf06dPW9aVTUlIUN9Kprq7mzJkzAMTExBAREaHYNzs7G4CAgAASEhIU\n286cOUN1dTUAiYmJis/d5cuXKSwsBMxLTA8ZMkSxb25uLnq9Hl9f3zaLFJw/f56KqzezGzVqFIGB\ngdZt9fX1nDx5EoDw8HCG2n3Rz8/Pp7GxEU+jkZTGRlvHYu9eqKtDtdGjIS2NsqQkKpOT0Q8axLhx\n4xTzqaqqqjh37hxg/mVHeHi4dZvRaOTYsWOAuQMZHx+vCF9UVETN1bkfSUlJitXzampqKCoqAiAq\nKqpNVzMnJweDwYCfnx9jxoxRbDt37px1kYmEhAQCAgKs2+rq6jh16hQAkZGRREdHK/bNy8ujqakJ\nLy8vkpOTFdsuXLhA2dU7mI8YMULOEcg5wm3PEZ6ein+LAcrLyyktLQVg+PDhiisQmpub+eGHHwDz\nv+fD7eZbFRQUUHv1lxdyjpBzhJwjbHrjHKF2PojqQiMqKoo33niDTZs24efnx4wZM7jxxhu58cYb\nu7TilBqPPPKI4u/z589n4sSJ3HHHHbz99tvW7dXV1dx2223U19ezefNmhg0bRk5ODhs3bmTRokV8\n/vnnijd/Z1avXs3mzZv505/+1OYYnR1Te/R6Pfb3TDSZTLS0tFi3O9rHst2e0Wi0bjMajW22OxvX\nfkyt49rfP8US12QyObxW0GAwXFPc9o61dVz7Y239GjqKazlWRy1HZ+O6Sm46O9aWlhb0er3DBRA6\nyk27cZubYf9+Bnz6KX7ffUdQdjY0Njo85o40DB9O87RphC5aZO5YXP3HoTovj4baWnNnxI6zr6Gj\nHLQ+VnudvYbNzc0YjUaHd2Dt0mvYaryWz05X47rK+1DOEW3jukpuev0c0SpuS0uLw20dxbXs21lc\nR+Qc0Tauq7wP5RzRNq6r5OZazhGdUV1o/M///A8Gg4HvvvuOHTt2sHPnTtasWcPKlSsJCwtj3rx5\nfPrpp6oH0lVLliwhMDCQrKws62PPP/88R44cobi42FrZzpo1i8TERObNm8fmzZu55557nIq/fv16\nnnnmGX7/+9/z0EMPdXlM7fHy8mrzJtXpdNYPmqOCyMvLq93JPx4eHtZtjt4Qzsa1H1PruI5OpN7e\n3phMJodxPT09rylu6/+2F9f+WFu/ho7iWo7V0QnC2biukpvOjtVynJ29hu3F1TU343/wIHzwgblj\n8c030NDAYIdH2YGkJEhLQz9zJvmDB6OPiCA0NJRQu99Went7X/Nr2Nmx2uvsNfTx8cFgMHT5NWwv\nrre3N0ajUfXnxhXfh3KOaBvXVXLT0+eIjuIaDAaH2zqKa9m3o7hyjpBzhJq4rf/bXlw5R3TtHNEZ\nnclRmazS999/z5o1a/jXv/6FTqdzWA05q7KyksjISNauXevwXhr2jEYjwcHBLFq0iI8++ggwrxCV\nn59vbQNZ1NbWEhwczOOPP86LL77Yaez169ezbt061q1bx9q1a50+Bkdjsjyu5rbtPa2iosL6j4B9\nC1P0T07lvKkJvvvONsdi3z5oaFD/w5KTbfMrZs+GwapLE9EN5HOuPZJz7ZGca09f5Vztd9kuTQa/\ncOECO3bs4KuvvmLnzj2q9wYAAB9DSURBVJ2UlpYybNgwfvnLX3LjjTd2JWSXbd26lfr6esXystHR\n0ezcuZOSkhJiYmKsj+/btw+gzXWkjmzcuJF169bx9NNPqyoy2huTKzp//rz1ukU5MWmDw5w3NpoL\nC8sci337unQpFOPG2SZvz54N8p5yCfI51x7JufZIzrXHXXKuutAYN24cx48fJywsjLS0NJ5++mnS\n09PbTDpR68svv6Surs5aJR0/ftx6879bbrmFiooKli9fzp133smoUaPQ6XRkZmby2muvkZyczK9+\n9StrrAcffJDNmzczf/58nnrqKescjWeeeYbBgwdz1113WZ+7YcMGNmzYwM6dO5kzZw4AL7/8MmvW\nrGHBggXceuutbS6BshQQxcXFTo9JCFeha2wk8MgR2LbNXFxkZZm7GGqNH6/sWNhNShNCCCGEtqm+\ndMrDwwN/f3/uvvtuFixYwLx58xQrHXTV8OHDrasR2CssLCQ0NJT777+fw4cPU1ZWhsFgIC4ujiVL\nlrBy5co298w4fPgwGzduZP/+/VRUVBATE8O8efNYs2aNYuWAdevWsX79enbv3k1aWhoAaWlpZGZm\ntjtWy0tWXV2takyudunUpUuXMBqNeHh4KFZEEP1Mfb25mMjIQL9jB54HD6JrblYXQ6eD1FRbx2LW\nLGi1motwXfI51x7JufZIzrWnr3Ku9rus6kLj0KFD7Nixgx07drB37170ej3XX3898+fPZ/78+Uyb\nNs3hRBLheoWG6Kfq6+Hbb21zLL77zuEKTh3S6WDCBFvHYtYscPH7wgghhBCiZ/V4odFaU1MTe/fu\n5auvvuKrr77iyJEjBAUFWdehFkpSaIgeUVdnLiwyMsx/9u9XX1h4eMDEibaOxcyZ0GrtdCGEEEKI\nXpkMbnHhwgWKioooLi7m7NmzmEwm6rpyoy4hhPNqa81LzFo6Fvv3g4M1szvk4QGTJtk6FjNngrTb\nhRBCCNGNVBcaf//7362XTp0+fRqTycTo0aP5yU9+Qnp6OvPmzeuJcYoeYLlZoE6nU3UDQ9HLrlwx\nFxaWjsWBA6B2CWlPT7juOoyzZmGcPRtmzMBL5lhognzOtUdyrj2Sc+1xl5x3aTJ4VFQU6enppKen\nc+ONNyqWkBXtc7VLp7Kzs61Lo6WmpvbJGIQDly/D3r22jsXBg10rLK6/3taxmDEDQkIk5xokOdce\nybn2SM61p69y3uOXTuXk5DB27NiujU4I0VZNjbmwsHQsDh0Co1FdDC8vmDzZNsdi+nQIDu6BwQoh\nhBBCOEd1oSFFRv8REhKCXq936ZZbv3TpEnz9te0GeYcPd62wmDLF1rGYPh2CgjrdTXKuPZJz7ZGc\na4/kXHvcJefXtOqUUMfVLp0SvaS62lZYZGTAkSOg9mPn7Q033GDrWEybBoGBPTBYIYQQQgjHenXV\nKSGEAxcvwp49to5Fdrb6wsLHx1xYWDoW06ZBQEBPjFYIIYQQokdIoSHEtaqqshUWGRlw7FjXCotp\n02wdi6lTwd+/BwYrhBBCCNE7pNAQQq2KCmXH4tgx9TF8fc2FhaVjccMNUlgIIYQQol+RQkPDTp8+\nbZ1INHLkyL4ejusqL1d2LHJz1cfw8zNP2LZ0LKZMMT/WyyTn2iM51x7JufZIzrXHXXIuhYaGXbly\nxboGs2ilrMx2D4vMTDh+XH0Mf39zYZGWZv4zebK5i9HHJOfaIznXHsm59kjOtcddci6FhhClpeaC\nwlJc5OWpjxEQYL4pnuVSqMmTzfMuhBBCCCE0Spa37UWutrytodXdpj09PftkDH3i/HllxyI/X32M\nwEBbYZGWBtdd5xaFhWZzrmGSc+2RnGuP5Fx7+irnsrytcJpmTkYlJbaiIiMDTp5UHyMoCGbOtHUs\nrrvOfG8LN6OZnAsrybn2SM61R3KuPe6Scyk0RP9z9qyyY3HqlPoYwcG2wiItDSZNMt+NWwghhBBC\nOEW+OQn3d+aMsmNx+rT6GCEhMGuWbVWoiROlsBBCCCGEuAbyTUrDqqurMRqNeHh4EBYW1tfDcV5R\nkbJjUVioPkZoqLmwsHQsJkwAN2lDXgu3zbnoMsm59kjOtUdyrj3uknMpNDTszJkz1qXRXPZNajKZ\nC4vWHYviYvVxBgyA2bNtcyxSUzVRWNhzi5yLbiU51x7JufZIzrXHXXIuhYZwLSaTuUNhuTleZqb5\n0ii1wsLMBYXlUqhx4zRZWAghhBBC9BUpNDQsJibG2nbrMyYTFBQoOxbnzqmPM3CgraiYM8dcWPTl\ncbkol8i56FWSc+2RnGuP5Fx73CXnch+NXuRq99H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FonPnzuLBBx+U8/3ee+81qa03nsex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\nRU5ErkJggg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "book_plots.plot_estimate_chart_1()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Okay, but what good is this? Sure, we could assume the 1 lb/day is accurate, and predict our weight for the next 10 days, but then why use a scale at all if we don't incorporate its readings? So let's look at the next measurement. We step on the scale again and it displays 164.2 lbs." ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "image/png": 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+Wloajh8/jg0bNti0vuzsbMTGxppdRaurq8Phw4cBSGNau3fvblbn2LFjqK6u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\nLfo1p+64Q95HuQinJ08KO0+E0//CBtVYbbpVVblEHx8fu/4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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "book_plots.plot_estimate_chart_2()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We have a problem. Our prediction doesn't match our measurement. But, that is what we expected, right? If the prediction was always exactly the same as the measurement, it would not be capable of adding any information to the filter. \n", "\n", "> The key insight to this entire book is in the next paragraph. Read it carefully!\n", "\n", "So what do we do? If we only take data from the measurement then the prediction will not affect the result. If we only take data from the prediction then the measurement will be ignored. If this is to work we need to take some kind of *blend of the prediction and measurement* (I've italicized the key point)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Blending two values - this sounds a lot like the two scale problem earlier. Using the same reasoning as before we can see that the only thing that makes sense is to choose a number between the prediction and the measurement. For example, an estimate of 165 makes no sense, nor does 157. Our estimates should lie between 159 (the prediction) and 164.2 (the measurement).\n", "\n", "Should it be half way? Maybe, but in general it seems like we might know that our prediction is more or less accurate compared to the measurements. Probably the accuracy of our prediction differs from the accuracy of the scale. Recall what we did when scale A was much more accurate than scale B - we scaled the answer to be closer to A than B. Let's look at that in a chart." ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "image/png": 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IDg7GypUrMX78eJSVleGZZ56xOX9iYiLOnDmDb775xq7lHT16FNHR0aqrZKWl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\n5aoJbkvLzBTDjwNi5D0LsXiylJaWhtWrV6N9+/Z48cUX8e2331a4rou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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "book_plots.plot_estimate_chart_3()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now let's try a randomly chosen number to scale our estimate: $\\frac{4}{10}$. Our estimate will be four tenths the measurement and the rest will be from the prediction. In other words, we are expressing a belief here, a belief that the prediction is somewhat more likely to be correct than the measurement. We compute that as\n", "\n", "$$\\mathtt{new\\_estimate} = \\mathtt{prediction} + \\frac{4}{10}(\\mathtt{measurement} - \\mathtt{prediction})$$\n", "\n", "The difference between the measurement and prediction is called the *residual*, which is depicted by the black vertical line in the plot above. This will become an important value to use later on, as it is an exact computation of the difference between measurements and the filter's output. Smaller residuals imply better performance.\n", "\n", "Let's code that and see the results when we test it against the series of weights from above. We have to take into account one other factor. Weight gain has units of lbs/time, so to be general we will need to add a time step $t$, which we will set to 1 (day). \n", "\n", "I hand generated the weight data to correspond to a true starting weight of 160 lbs, and a weight gain of 1 lb per day. In other words on the first day (day zero) the true weight is 160lbs, on the second day (day one, the first day of weighing) the true weight is 161 lbs, and so on. \n", "\n", "We need to make a guess for the initial weight. It is too early to talk about initialization strategies, so for now I will assume 160 lbs." ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "scrolled": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "previous: 160.00, prediction: 161.00 estimate 159.80\n", "previous: 159.80, prediction: 160.80 estimate 162.16\n", "previous: 162.16, prediction: 163.16 estimate 162.02\n", "previous: 162.02, prediction: 163.02 estimate 161.77\n", "previous: 161.77, prediction: 162.77 estimate 162.50\n", "previous: 162.50, prediction: 163.50 estimate 163.94\n", "previous: 163.94, prediction: 164.94 estimate 166.80\n", "previous: 166.80, prediction: 167.80 estimate 167.64\n", "previous: 167.64, prediction: 168.64 estimate 167.75\n", "previous: 167.75, prediction: 168.75 estimate 169.65\n", "previous: 169.65, prediction: 170.65 estimate 170.87\n", "previous: 170.87, prediction: 171.87 estimate 172.16\n" ] }, { "data": { "image/png": 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sXbuWDz/8sEz3rCpviqLw0ksv8e9//xubpp0J3nAJM4e7+vqcZDU2TTuTfi6cPsPHsTfO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qOj6d69O+np6Tp133jjDWbOnMmoUaP4/vvvCQoKYuzYsXz44YdlfToVys4TV3hudixTY6/z2a+3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\n4eGF6oWEhKDRaArdGjVqVGS7J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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from kf_book.book_plots import figsize\n", "import kf_book.gh_internal as gh\n", "import matplotlib.pyplot as plt\n", "\n", "weights = [158.0, 164.2, 160.3, 159.9, 162.1, 164.6, \n", " 169.6, 167.4, 166.4, 171.0, 171.2, 172.6]\n", "\n", "time_step = 1.0 # day\n", "scale_factor = 4.0/10\n", "\n", "def predict_using_gain_guess(weight, gain_rate, do_print=True, sim_rate=0): \n", " \"\"\" sim_rate allows for interactive plots in the notebook\"\"\"\n", " \n", " with figsize(y=4):\n", " # store the filtered results\n", " estimates, predictions = [weight], []\n", "\n", " # most filter literature uses 'z' for measurements\n", " for z in weights: \n", " # predict new position\n", " prediction = weight + gain_rate * time_step\n", "\n", " # update filter \n", " weight = prediction + scale_factor * (z - prediction)\n", "\n", " # save\n", " estimates.append(weight)\n", " predictions.append(prediction)\n", " if do_print:\n", " gh.print_results(estimates, prediction, weight)\n", "\n", " # plot results\n", " gh.plot_gh_results(weights, estimates, predictions, sim_rate)\n", "\n", "initial_guess = 160.\n", "predict_using_gain_guess(weight=initial_guess, gain_rate=1) " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "That is pretty good! There is a lot of data here, so let's talk about how to interpret it. The thick blue line shows the estimate from the filter. It starts at day 0 with the initial guess of 160 lbs. The red line shows the prediction that is made from the previous day's weight. So, on day one the previous weight was 160 lbs, the weight gain is 1 lb, and so the first prediction is 161 lbs. The estimate on day one is then part way between the prediction and measurement at 159.8 lbs. Below the chart is a print out of the previous weight, predicted weight, and new estimate for each day. Finally, the thin black line shows the actual weight gain of the person being weighed. \n", "\n", "The estimates are not a straight line, but they are straighter than the measurements and somewhat close to the trend line we created. Also, it seems to get better over time. \n", "\n", "Before I go on, let me show this plot interactively so you get a better feel for how the filter works. First I need to write some boilerplate code to enable plotting interactively. The magic `%matplotlib notebook` enables the interactive plotting module, and the magic `%matplotlib inline` returns us to the non-interactive plotting. Unfortunately `%matplotlib notebook` permanently alters the plot sizes, so I reset it to the book's default with `reset_figsize()`." ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "collapsed": true }, "outputs": [], "source": [ "from contextlib import contextmanager\n", "from kf_book.book_plots import reset_figsize\n", "\n", "@contextmanager\n", "def interactive_plot():\n", " %matplotlib notebook\n", " yield\n", " %matplotlib inline\n", " reset_figsize()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we can run the plot interactively. Put your cursor inside the next cell and press CTRL+Enter to execute the cell. This will cause the plot to be drawn slowly, step by step." ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "scrolled": false }, "outputs": [ { "data": { "application/javascript": [ "/* Put everything inside the global mpl namespace */\n", "window.mpl = {};\n", "\n", "\n", "mpl.get_websocket_type = function() {\n", " if (typeof(WebSocket) !== 'undefined') {\n", " return WebSocket;\n", " } else if (typeof(MozWebSocket) !== 'undefined') {\n", " return MozWebSocket;\n", " } else {\n", " alert('Your browser does not have WebSocket support.' +\n", " 'Please try Chrome, Safari or Firefox ≥ 6. ' +\n", " 'Firefox 4 and 5 are also supported but you ' +\n", " 'have to enable WebSockets in about:config.');\n", " };\n", "}\n", "\n", "mpl.figure = function(figure_id, websocket, ondownload, parent_element) {\n", " this.id = figure_id;\n", "\n", " this.ws = websocket;\n", "\n", " this.supports_binary = (this.ws.binaryType != undefined);\n", "\n", " if (!this.supports_binary) {\n", " var warnings = document.getElementById(\"mpl-warnings\");\n", " if (warnings) {\n", " warnings.style.display = 'block';\n", " warnings.textContent = (\n", " \"This browser does not support binary websocket messages. \" +\n", " \"Performance may be slow.\");\n", " }\n", " }\n", "\n", " this.imageObj = new Image();\n", "\n", " this.context = undefined;\n", " this.message = undefined;\n", " this.canvas = undefined;\n", " this.rubberband_canvas = undefined;\n", " this.rubberband_context = undefined;\n", " this.format_dropdown = undefined;\n", "\n", " this.image_mode = 'full';\n", "\n", " this.root = $('
');\n", " this._root_extra_style(this.root)\n", " this.root.attr('style', 'display: inline-block');\n", "\n", " $(parent_element).append(this.root);\n", "\n", " this._init_header(this);\n", " this._init_canvas(this);\n", " this._init_toolbar(this);\n", "\n", " var fig = this;\n", "\n", " this.waiting = false;\n", "\n", " this.ws.onopen = function () {\n", " fig.send_message(\"supports_binary\", {value: fig.supports_binary});\n", " fig.send_message(\"send_image_mode\", {});\n", " if (mpl.ratio != 1) {\n", " fig.send_message(\"set_dpi_ratio\", {'dpi_ratio': mpl.ratio});\n", " }\n", " fig.send_message(\"refresh\", {});\n", " }\n", "\n", " this.imageObj.onload = function() {\n", " if (fig.image_mode == 'full') {\n", " // Full images could contain transparency (where diff images\n", " // almost always do), so we need to clear the canvas so that\n", " // there is no ghosting.\n", " fig.context.clearRect(0, 0, fig.canvas.width, fig.canvas.height);\n", " }\n", " fig.context.drawImage(fig.imageObj, 0, 0);\n", " };\n", "\n", " this.imageObj.onunload = function() {\n", " fig.ws.close();\n", " }\n", "\n", " this.ws.onmessage = this._make_on_message_function(this);\n", "\n", " this.ondownload = ondownload;\n", "}\n", "\n", "mpl.figure.prototype._init_header = function() {\n", " var titlebar = $(\n", " '
');\n", " var titletext = $(\n", " '
');\n", " titlebar.append(titletext)\n", " this.root.append(titlebar);\n", " this.header = titletext[0];\n", "}\n", "\n", "\n", "\n", "mpl.figure.prototype._canvas_extra_style = function(canvas_div) {\n", "\n", "}\n", "\n", "\n", "mpl.figure.prototype._root_extra_style = function(canvas_div) {\n", "\n", "}\n", "\n", "mpl.figure.prototype._init_canvas = function() {\n", " var fig = this;\n", "\n", " var canvas_div = $('
');\n", "\n", " canvas_div.attr('style', 'position: relative; clear: both; outline: 0');\n", "\n", " function canvas_keyboard_event(event) {\n", " return fig.key_event(event, event['data']);\n", " }\n", "\n", " canvas_div.keydown('key_press', canvas_keyboard_event);\n", " canvas_div.keyup('key_release', canvas_keyboard_event);\n", " this.canvas_div = canvas_div\n", " this._canvas_extra_style(canvas_div)\n", " this.root.append(canvas_div);\n", "\n", " var canvas = $('');\n", " canvas.addClass('mpl-canvas');\n", " canvas.attr('style', \"left: 0; top: 0; z-index: 0; outline: 0\")\n", "\n", " this.canvas = canvas[0];\n", " this.context = canvas[0].getContext(\"2d\");\n", "\n", " var backingStore = this.context.backingStorePixelRatio ||\n", "\tthis.context.webkitBackingStorePixelRatio ||\n", "\tthis.context.mozBackingStorePixelRatio ||\n", "\tthis.context.msBackingStorePixelRatio ||\n", "\tthis.context.oBackingStorePixelRatio ||\n", "\tthis.context.backingStorePixelRatio || 1;\n", "\n", " mpl.ratio = (window.devicePixelRatio || 1) / backingStore;\n", "\n", " var rubberband = $('');\n", " rubberband.attr('style', \"position: absolute; left: 0; top: 0; z-index: 1;\")\n", "\n", " var pass_mouse_events = true;\n", "\n", " canvas_div.resizable({\n", " start: function(event, ui) {\n", " pass_mouse_events = false;\n", " },\n", " resize: function(event, ui) {\n", " fig.request_resize(ui.size.width, ui.size.height);\n", " },\n", " stop: function(event, ui) {\n", " pass_mouse_events = true;\n", " fig.request_resize(ui.size.width, ui.size.height);\n", " },\n", " });\n", "\n", " function mouse_event_fn(event) {\n", " if (pass_mouse_events)\n", " return fig.mouse_event(event, event['data']);\n", " }\n", "\n", " rubberband.mousedown('button_press', mouse_event_fn);\n", " rubberband.mouseup('button_release', mouse_event_fn);\n", " // Throttle sequential mouse events to 1 every 20ms.\n", " rubberband.mousemove('motion_notify', mouse_event_fn);\n", "\n", " rubberband.mouseenter('figure_enter', mouse_event_fn);\n", " rubberband.mouseleave('figure_leave', mouse_event_fn);\n", "\n", " canvas_div.on(\"wheel\", function (event) {\n", " event = event.originalEvent;\n", " event['data'] = 'scroll'\n", " if (event.deltaY < 0) {\n", " event.step = 1;\n", " } else {\n", " event.step = -1;\n", " }\n", " mouse_event_fn(event);\n", " });\n", "\n", " canvas_div.append(canvas);\n", " canvas_div.append(rubberband);\n", "\n", " this.rubberband = rubberband;\n", " this.rubberband_canvas = rubberband[0];\n", " this.rubberband_context = rubberband[0].getContext(\"2d\");\n", " this.rubberband_context.strokeStyle = \"#000000\";\n", "\n", " this._resize_canvas = function(width, height) {\n", " // Keep the size of the canvas, canvas container, and rubber band\n", " // canvas in synch.\n", " canvas_div.css('width', width)\n", " canvas_div.css('height', height)\n", "\n", " canvas.attr('width', width * mpl.ratio);\n", " canvas.attr('height', height * mpl.ratio);\n", " canvas.attr('style', 'width: ' + width + 'px; height: ' + height + 'px;');\n", "\n", " rubberband.attr('width', width);\n", " rubberband.attr('height', height);\n", " }\n", "\n", " // Set the figure to an initial 600x600px, this will subsequently be updated\n", " // upon first draw.\n", " this._resize_canvas(600, 600);\n", "\n", " // Disable right mouse context menu.\n", " $(this.rubberband_canvas).bind(\"contextmenu\",function(e){\n", " return false;\n", " });\n", "\n", " function set_focus () {\n", " canvas.focus();\n", " canvas_div.focus();\n", " }\n", "\n", " window.setTimeout(set_focus, 100);\n", "}\n", "\n", "mpl.figure.prototype._init_toolbar = function() {\n", " var fig = this;\n", "\n", " var nav_element = $('
')\n", " nav_element.attr('style', 'width: 100%');\n", " this.root.append(nav_element);\n", "\n", " // Define a callback function for later on.\n", " function toolbar_event(event) {\n", " return fig.toolbar_button_onclick(event['data']);\n", " }\n", " function toolbar_mouse_event(event) {\n", " return fig.toolbar_button_onmouseover(event['data']);\n", " }\n", "\n", " for(var toolbar_ind in mpl.toolbar_items) {\n", " var name = mpl.toolbar_items[toolbar_ind][0];\n", " var tooltip = mpl.toolbar_items[toolbar_ind][1];\n", " var image = mpl.toolbar_items[toolbar_ind][2];\n", " var method_name = mpl.toolbar_items[toolbar_ind][3];\n", "\n", " if (!name) {\n", " // put a spacer in here.\n", " continue;\n", " }\n", " var button = $('');\n", " button.click(method_name, toolbar_event);\n", " button.mouseover(tooltip, toolbar_mouse_event);\n", " nav_element.append(button);\n", " }\n", "\n", " // Add the status bar.\n", " var status_bar = $('');\n", " nav_element.append(status_bar);\n", " this.message = status_bar[0];\n", "\n", " // Add the close button to the window.\n", " var buttongrp = $('
');\n", " var button = $('');\n", " button.click(function (evt) { fig.handle_close(fig, {}); } );\n", " button.mouseover('Stop Interaction', toolbar_mouse_event);\n", " buttongrp.append(button);\n", " var titlebar = this.root.find($('.ui-dialog-titlebar'));\n", " titlebar.prepend(buttongrp);\n", "}\n", "\n", "mpl.figure.prototype._root_extra_style = function(el){\n", " var fig = this\n", " el.on(\"remove\", function(){\n", "\tfig.close_ws(fig, {});\n", " });\n", "}\n", "\n", "mpl.figure.prototype._canvas_extra_style = function(el){\n", " // this is important to make the div 'focusable\n", " el.attr('tabindex', 0)\n", " // reach out to IPython and tell the keyboard manager to turn it's self\n", " // off when our div gets focus\n", "\n", " // location in version 3\n", " if (IPython.notebook.keyboard_manager) {\n", " IPython.notebook.keyboard_manager.register_events(el);\n", " }\n", " else {\n", " // location in version 2\n", " IPython.keyboard_manager.register_events(el);\n", " }\n", "\n", "}\n", "\n", "mpl.figure.prototype._key_event_extra = function(event, name) {\n", " var manager = IPython.notebook.keyboard_manager;\n", " if (!manager)\n", " manager = IPython.keyboard_manager;\n", "\n", " // Check for shift+enter\n", " if (event.shiftKey && event.which == 13) {\n", " this.canvas_div.blur();\n", " event.shiftKey = false;\n", " // Send a \"J\" for go to next cell\n", " event.which = 74;\n", " event.keyCode = 74;\n", " manager.command_mode();\n", " manager.handle_keydown(event);\n", " }\n", "}\n", "\n", "mpl.figure.prototype.handle_save = function(fig, msg) {\n", " fig.ondownload(fig, null);\n", "}\n", "\n", "\n", "mpl.find_output_cell = function(html_output) {\n", " // Return the cell and output element which can be found *uniquely* in the notebook.\n", " // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n", " // IPython event is triggered only after the cells have been serialised, which for\n", " // our purposes (turning an active figure into a static one), is too late.\n", " var cells = IPython.notebook.get_cells();\n", " var ncells = cells.length;\n", " for (var i=0; i= 3 moved mimebundle to data attribute of output\n", " data = data.data;\n", " }\n", " if (data['text/html'] == html_output) {\n", " return [cell, data, j];\n", " }\n", " }\n", " }\n", " }\n", "}\n", "\n", "// Register the function which deals with the matplotlib target/channel.\n", "// The kernel may be null if the page has been refreshed.\n", "if (IPython.notebook.kernel != null) {\n", " IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);\n", "}\n" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import time\n", "with interactive_plot():\n", " for x in range(2, 6):\n", " plt.plot([0, 1], [1, x])\n", " plt.gcf().canvas.draw()\n", " time.sleep(0.5)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Back to filtering. The results of the filter may strike you as quite silly; of course the data will look good if we assume the conclusion, that our weight gain is around 1 lb/day! Let's see what the filter does if our initial guess is bad. Let's predict that there is a weight loss of 1 lb a day:" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "data": { "image/png": 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vZeG20/h7ezClX2Puq1cJpRQVS3kwYdlOY1dmGU9Gdw6he6NicAD8wYPGyJi7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\naKFNr+et8O3hUfDvX1HKiEE/7r/vYyGXbnM3MytXW0p6JpODjrPi0KV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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "predict_using_gain_guess(initial_guess, -1., do_print=False)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "That is not so impressive. Clearly a filter that requires us to correctly guess a rate of change is not very useful. Even if our initial guess was correct, the filter will fail as soon as that rate of change changes. If I stop overeating the filter will have extreme difficulty in adjusting to that change. \n", "\n", "But, 'what if'? What if instead of leaving the weight gain at the initial guess of 1 lb (or whatever), we compute it from the existing measurements and estimates. On day one our estimate for the weight is:\n", "\n", "$$\n", "(160 + 1) + \\frac{4}{10}(158-161) = 159.8\n", "$$\n", "\n", "On the next day we measure 164.2, which implies a weight gain of 4.4 lbs (since 164.2 - 159.8 = 4.4), not 1. Can we use this information somehow? It seems plausible. After all, the weight measurement itself is based on a real world measurement of our weight, so there is useful information. Our estimate of our weight gain may not be perfect, but it is surely better than just guessing our gain is 1 lb. Data is better than a guess, even if it is noisy.\n", "\n", "So, should we set the new gain/day to 4.4 lbs? Yesterday we though the weight gain was 1 lb, today we think it is 4.4 lbs. We have two numbers, and want to combine them somehow. Hmm, sounds like our same problem again. Let's use our same tool, and the only tool we have so far - pick a value part way between the two. This time I will use another arbitrarily chosen number, $\\frac{1}{3}$. The equation is identical as for the weight estimate except we have to incorporate time because this is a rate (gain/day):\n", "\n", "$$\\text{new gain} = \\text{old gain} + \\frac{1}{3}\\frac{\\text{measurement - predicted weight}}{1 \\text{ day}}\n", "$$" ] }, { "cell_type": "code", "execution_count": 20, "metadata": { "scrolled": false }, "outputs": [ { "data": { "application/javascript": [ "/* Put everything inside the global mpl namespace */\n", "window.mpl = {};\n", "\n", "\n", "mpl.get_websocket_type = function() {\n", " if (typeof(WebSocket) !== 'undefined') {\n", " return WebSocket;\n", " } else if (typeof(MozWebSocket) !== 'undefined') {\n", " return MozWebSocket;\n", " } else {\n", " alert('Your browser does not have WebSocket support.' +\n", " 'Please try Chrome, Safari or Firefox ≥ 6. ' +\n", " 'Firefox 4 and 5 are also supported but you ' +\n", " 'have to enable WebSockets in about:config.');\n", " };\n", "}\n", "\n", "mpl.figure = function(figure_id, websocket, ondownload, parent_element) {\n", " this.id = figure_id;\n", "\n", " this.ws = websocket;\n", "\n", " this.supports_binary = (this.ws.binaryType != undefined);\n", "\n", " if (!this.supports_binary) {\n", " var warnings = document.getElementById(\"mpl-warnings\");\n", " if (warnings) {\n", " warnings.style.display = 'block';\n", " warnings.textContent = (\n", " \"This browser does not support binary websocket messages. \" +\n", " \"Performance may be slow.\");\n", " }\n", " }\n", "\n", " this.imageObj = new Image();\n", "\n", " this.context = undefined;\n", " this.message = undefined;\n", " this.canvas = undefined;\n", " this.rubberband_canvas = undefined;\n", " this.rubberband_context = undefined;\n", " this.format_dropdown = undefined;\n", "\n", " this.image_mode = 'full';\n", "\n", " this.root = $('
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