From d5ff60533944259cb566c9f9d62dbf650a2f96b1 Mon Sep 17 00:00:00 2001 From: Bennett Taylor Date: Thu, 13 Sep 2018 15:55:12 -0400 Subject: [PATCH 01/14] Adding chap 4 notebook --- code/chap04mine.ipynb | 1151 +++++++++++++++++++++++++++++++++++++++++ 1 file changed, 1151 insertions(+) create mode 100644 code/chap04mine.ipynb diff --git a/code/chap04mine.ipynb b/code/chap04mine.ipynb new file mode 100644 index 00000000..817f35e9 --- /dev/null +++ b/code/chap04mine.ipynb @@ -0,0 +1,1151 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Modeling and Simulation in Python\n", + "\n", + "Chapter 4\n", + "\n", + "Copyright 2017 Allen Downey\n", + "\n", + "License: [Creative Commons Attribution 4.0 International](https://creativecommons.org/licenses/by/4.0)\n" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": {}, + "outputs": [], + "source": [ + "# Configure Jupyter so figures appear in the notebook\n", + "%matplotlib inline\n", + "\n", + "# Configure Jupyter to display the assigned value after an assignment\n", + "%config InteractiveShell.ast_node_interactivity='last_expr_or_assign'\n", + "\n", + "# import functions from the modsim library\n", + "from modsim import *" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Returning values" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here's a simple function that returns a value:" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": {}, + "outputs": [], + "source": [ + "def add_five(x):\n", + " return x + 5" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "And here's how we call it." + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "8" + ] + }, + "execution_count": 20, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "y = add_five(3)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "If you run a function on the last line of a cell, Jupyter displays the result:" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "10" + ] + }, + "execution_count": 21, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "add_five(5)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "But that can be a bad habit, because usually if you call a function and don't assign the result in a variable, the result gets discarded.\n", + "\n", + "In the following example, Jupyter shows the second result, but the first result just disappears." + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "10" + ] + }, + "execution_count": 22, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "add_five(3)\n", + "add_five(5)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "When you call a function that returns a variable, it is generally a good idea to assign the result to a variable." + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "8 10\n" + ] + } + ], + "source": [ + "y1 = add_five(3)\n", + "y2 = add_five(5)\n", + "\n", + "print(y1, y2)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Exercise:** Write a function called `make_state` that creates a `State` object with the state variables `olin=10` and `wellesley=2`, and then returns the new `State` object.\n", + "\n", + "Write a line of code that calls `make_state` and assigns the result to a variable named `init`." + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "metadata": {}, + "outputs": [], + "source": [ + "def make_state():\n", + " x =State(olin=10, wellesley=2)\n", + " return x" + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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values
olin10
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" + ], + "text/plain": [ + "olin 10\n", + "wellesley 2\n", + "dtype: int64" + ] + }, + "execution_count": 25, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "init = make_state()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Running simulations" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here's the code from the previous notebook." + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "metadata": {}, + "outputs": [], + "source": [ + "def step(state, p1, p2):\n", + " \"\"\"Simulate one minute of time.\n", + " \n", + " state: bikeshare State object\n", + " p1: probability of an Olin->Wellesley customer arrival\n", + " p2: probability of a Wellesley->Olin customer arrival\n", + " \"\"\"\n", + " if flip(p1):\n", + " bike_to_wellesley(state)\n", + " \n", + " if flip(p2):\n", + " bike_to_olin(state)\n", + " \n", + "def bike_to_wellesley(state):\n", + " \"\"\"Move one bike from Olin to Wellesley.\n", + " \n", + " state: bikeshare State object\n", + " \"\"\"\n", + " if state.olin == 0:\n", + " state.olin_empty += 1\n", + " return\n", + " state.olin -= 1\n", + " state.wellesley += 1\n", + " \n", + "def bike_to_olin(state):\n", + " \"\"\"Move one bike from Wellesley to Olin.\n", + " \n", + " state: bikeshare State object\n", + " \"\"\"\n", + " if state.wellesley == 0:\n", + " state.wellesley_empty += 1\n", + " return\n", + " state.wellesley -= 1\n", + " state.olin += 1\n", + " \n", + "def decorate_bikeshare():\n", + " \"\"\"Add a title and label the axes.\"\"\"\n", + " decorate(title='Olin-Wellesley Bikeshare',\n", + " xlabel='Time step (min)', \n", + " ylabel='Number of bikes')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here's a modified version of `run_simulation` that creates a `State` object, runs the simulation, and returns the `State` object." + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "metadata": {}, + "outputs": [], + "source": [ + "def run_simulation(p1, p2, num_steps):\n", + " \"\"\"Simulate the given number of time steps.\n", + " \n", + " p1: probability of an Olin->Wellesley customer arrival\n", + " p2: probability of a Wellesley->Olin customer arrival\n", + " num_steps: number of time steps\n", + " \"\"\"\n", + " state = State(olin=10, wellesley=2, \n", + " olin_empty=0, wellesley_empty=0)\n", + " \n", + " for i in range(num_steps):\n", + " step(state, p1, p2)\n", + " \n", + " return state" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now `run_simulation` doesn't plot anything:" + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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wellesley11
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wellesley_empty0
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" + ], + "text/plain": [ + "olin 1\n", + "wellesley 11\n", + "olin_empty 2\n", + "wellesley_empty 0\n", + "dtype: int64" + ] + }, + "execution_count": 28, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "state = run_simulation(0.4, 0.2, 60)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "But after the simulation, we can read the metrics from the `State` object." + ] + }, + { + "cell_type": "code", + "execution_count": 29, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "2" + ] + }, + "execution_count": 29, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "state.olin_empty" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now we can run simulations with different values for the parameters. When `p1` is small, we probably don't run out of bikes at Olin." + ] + }, + { + "cell_type": "code", + "execution_count": 30, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "0" + ] + }, + "execution_count": 30, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "state = run_simulation(0.2, 0.2, 60)\n", + "state.olin_empty" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "When `p1` is large, we probably do." + ] + }, + { + "cell_type": "code", + "execution_count": 31, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "11" + ] + }, + "execution_count": 31, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "state = run_simulation(0.6, 0.2, 60)\n", + "state.olin_empty" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## More for loops" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "`linspace` creates a NumPy array of equally spaced numbers." + ] + }, + { + "cell_type": "code", + "execution_count": 32, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([0. , 0.25, 0.5 , 0.75, 1. ])" + ] + }, + "execution_count": 32, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "p1_array = linspace(0, 1, 5)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can use an array in a `for` loop, like this:" + ] + }, + { + "cell_type": "code", + "execution_count": 33, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "0.0\n", + "0.25\n", + "0.5\n", + "0.75\n", + "1.0\n" + ] + } + ], + "source": [ + "for p1 in p1_array:\n", + " print(p1)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This will come in handy in the next section.\n", + "\n", + "`linspace` is defined in `modsim.py`. You can get the documentation using `help`." + ] + }, + { + "cell_type": "code", + "execution_count": 34, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Help on function linspace in module modsim:\n", + "\n", + "linspace(start, stop, num=50, **options)\n", + " Returns an array of evenly-spaced values in the interval [start, stop].\n", + " \n", + " start: first value\n", + " stop: last value\n", + " num: number of values\n", + " \n", + " Also accepts the same keyword arguments as np.linspace. See\n", + " https://docs.scipy.org/doc/numpy/reference/generated/numpy.linspace.html\n", + " \n", + " returns: array or Quantity\n", + "\n" + ] + } + ], + "source": [ + "help(linspace)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "`linspace` is based on a NumPy function with the same name. [Click here](https://docs.scipy.org/doc/numpy/reference/generated/numpy.linspace.html) to read more about how to use it." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Exercise:** \n", + "Use `linspace` to make an array of 10 equally spaced numbers from 1 to 10 (including both)." + ] + }, + { + "cell_type": "code", + "execution_count": 35, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([ 1., 2., 3., 4., 5., 6., 7., 8., 9., 10.])" + ] + }, + "execution_count": 35, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "array = linspace (1,10,10)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Exercise:** The `modsim` library provides a related function called `linrange`. You can view the documentation by running the following cell:" + ] + }, + { + "cell_type": "code", + "execution_count": 36, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Help on function linrange in module modsim:\n", + "\n", + "linrange(start=0, stop=None, step=1, **options)\n", + " Returns an array of evenly-spaced values in the interval [start, stop].\n", + " \n", + " This function works best if the space between start and stop\n", + " is divisible by step; otherwise the results might be surprising.\n", + " \n", + " By default, the last value in the array is `stop-step`\n", + " (at least approximately).\n", + " If you provide the keyword argument `endpoint=True`,\n", + " the last value in the array is `stop`.\n", + " \n", + " start: first value\n", + " stop: last value\n", + " step: space between values\n", + " \n", + " Also accepts the same keyword arguments as np.linspace. See\n", + " https://docs.scipy.org/doc/numpy/reference/generated/numpy.linspace.html\n", + " \n", + " returns: array or Quantity\n", + "\n" + ] + } + ], + "source": [ + "help(linrange)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Use `linrange` to make an array of numbers from 1 to 11 with a step size of 2." + ] + }, + { + "cell_type": "code", + "execution_count": 37, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([1., 3., 5., 7., 9.])" + ] + }, + "execution_count": 37, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "array = linrange (1,11,2)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Sweeping parameters" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "`p1_array` contains a range of values for `p1`." + ] + }, + { + "cell_type": "code", + "execution_count": 38, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([0. , 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1. ])" + ] + }, + "execution_count": 38, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "p2 = 0.2\n", + "num_steps = 60\n", + "p1_array = linspace(0, 1, 11)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The following loop runs a simulation for each value of `p1` in `p1_array`; after each simulation, it prints the number of unhappy customers at the Olin station:" + ] + }, + { + "cell_type": "code", + "execution_count": 39, + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "0.0 0\n", + "0.1 0\n", + "0.2 0\n", + "0.30000000000000004 0\n", + "0.4 5\n", + "0.5 13\n", + "0.6000000000000001 17\n", + "0.7000000000000001 17\n", + "0.8 30\n", + "0.9 30\n", + "1.0 33\n" + ] + } + ], + "source": [ + "for p1 in p1_array:\n", + " state = run_simulation(p1, p2, num_steps)\n", + " print(p1, state.olin_empty)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now we can do the same thing, but storing the results in a `SweepSeries` instead of printing them.\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 40, + "metadata": {}, + "outputs": [], + "source": [ + "sweep = SweepSeries()\n", + "\n", + "for p1 in p1_array:\n", + " state = run_simulation(p1, p2, num_steps)\n", + " sweep[p1] = state.olin_empty\n", + "\n", + " " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "And then we can plot the results." + ] + }, + { + "cell_type": "code", + "execution_count": 41, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Saving figure to file figs/chap02-fig02.pdf\n" + ] + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "plot(sweep, label='Olin')\n", + "\n", + "decorate(title='Olin-Wellesley Bikeshare',\n", + " xlabel='Arrival rate at Olin (p1 in customers/min)', \n", + " ylabel='Number of unhappy customers')\n", + "\n", + "savefig('figs/chap02-fig02.pdf')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Exercises\n", + "\n", + "**Exercise:** Wrap this code in a function named `sweep_p1` that takes an array called `p1_array` as a parameter. It should create a new `SweepSeries`, run a simulation for each value of `p1` in `p1_array`, store the results in the `SweepSeries`, and return the `SweepSeries`.\n", + "\n", + "Use your function to plot the number of unhappy customers at Olin as a function of `p1`. Label the axes." + ] + }, + { + "cell_type": "code", + "execution_count": 42, + "metadata": {}, + "outputs": [], + "source": [ + "def sweep_p1(p1_array):\n", + " sweep = SweepSeries()\n", + " \n", + " for p1 in p1_array:\n", + " state = run_simulation(p1, p2, num_steps)\n", + " sweep[p1] = state.olin_empty\n", + " return sweep\n" + ] + }, + { + "cell_type": "code", + "execution_count": 53, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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" + ], + "text/plain": [ + "0.0 22\n", + "0.1 18\n", + "0.2 13\n", + "0.3 0\n", + "0.4 2\n", + "0.5 2\n", + "0.6 0\n", + "0.7 0\n", + "0.8 0\n", + "0.9 0\n", + "1.0 0\n", + "dtype: int64" + ] + }, + "execution_count": 85, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "p1 = 0.5\n", + "num_steps = 60\n", + "p2_array = linspace(0, 1, 11)\n", + "\n", + "def sweep_p2 (p2_array):\n", + " sweep = SweepSeries ()\n", + "\n", + " for p2 in p2_array:\n", + " state = run_simulation(p1, p2, num_steps)\n", + " sweep[p2] = state.olin_empty\n", + " \n", + " return sweep\n", + " \n", + "sweep_p2(p2_array)" + ] + }, + { + "cell_type": "code", + "execution_count": 86, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "plot(sweep, 'bo', label='Olin')\n", + "\n", + "decorate (title='Olin-Wellesley Bikeshare',\n", + " xlabel='Arrival Rate at Wellesley (p2 in Customers per Minute)',\n", + " ylabel='Number of Unhappy Customers')\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Optional exercises\n", + "\n", + "The following two exercises are a little more challenging. If you are comfortable with what you have learned so far, you should give them a try. If you feel like you have your hands full, you might want to skip them for now.\n", + "\n", + "**Exercise:** Because our simulations are random, the results vary from one run to another, and the results of a parameter sweep tend to be noisy. We can get a clearer picture of the relationship between a parameter and a metric by running multiple simulations with the same parameter and taking the average of the results.\n", + "\n", + "Write a function called `run_multiple_simulations` that takes as parameters `p1`, `p2`, `num_steps`, and `num_runs`.\n", + "\n", + "`num_runs` specifies how many times it should call `run_simulation`.\n", + "\n", + "After each run, it should store the total number of unhappy customers (at Olin or Wellesley) in a `TimeSeries`. At the end, it should return the `TimeSeries`.\n", + "\n", + "Test your function with parameters\n", + "\n", + "```\n", + "p1 = 0.3\n", + "p2 = 0.3\n", + "num_steps = 60\n", + "num_runs = 10\n", + "```\n", + "\n", + "Display the resulting `TimeSeries` and use the `mean` function provided by the `TimeSeries` object to compute the average number of unhappy customers." + ] + }, + { + "cell_type": "code", + "execution_count": 29, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "# Solution goes here" + ] + }, + { + "cell_type": "code", + "execution_count": 30, + "metadata": {}, + "outputs": [], + "source": [ + "# Solution goes here" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Exercise:** Continuting the previous exercise, use `run_multiple_simulations` to run simulations with a range of values for `p1` and\n", + "\n", + "```\n", + "p2 = 0.3\n", + "num_steps = 60\n", + "num_runs = 20\n", + "```\n", + "\n", + "Store the results in a `SweepSeries`, then plot the average number of unhappy customers as a function of `p1`. Label the axes.\n", + "\n", + "What value of `p1` minimizes the average number of unhappy customers?" + ] + }, + { + "cell_type": "code", + "execution_count": 31, + "metadata": { + "scrolled": true + }, + "outputs": [], + "source": [ + "# Solution goes here" + ] + }, + { + "cell_type": "code", + "execution_count": 32, + "metadata": {}, + "outputs": [], + "source": [ + "# Solution goes here" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.6.6" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} From 32fa7b6af3fe93077334635434dffa4635d4fc9f Mon Sep 17 00:00:00 2001 From: Bennett Taylor Date: Sun, 23 Sep 2018 22:21:22 -0400 Subject: [PATCH 02/14] Chapter 8 Notebook --- code/chap08mine.ipynb | 945 ++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 945 insertions(+) create mode 100644 code/chap08mine.ipynb diff --git a/code/chap08mine.ipynb b/code/chap08mine.ipynb new file mode 100644 index 00000000..01ef247c --- /dev/null +++ b/code/chap08mine.ipynb @@ -0,0 +1,945 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Modeling and Simulation in Python\n", + "\n", + "Chapter 8\n", + "\n", + "Copyright 2017 Allen Downey\n", + "\n", + "License: [Creative Commons Attribution 4.0 International](https://creativecommons.org/licenses/by/4.0)\n" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "# Configure Jupyter so figures appear in the notebook\n", + "%matplotlib inline\n", + "\n", + "# Configure Jupyter to display the assigned value after an assignment\n", + "%config InteractiveShell.ast_node_interactivity='last_expr_or_assign'\n", + "\n", + "# import functions from the modsim.py module\n", + "from modsim import *\n", + "\n", + "from pandas import read_html" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Functions from the previous chapter" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "def plot_results(census, un, timeseries, title):\n", + " \"\"\"Plot the estimates and the model.\n", + " \n", + " census: TimeSeries of population estimates\n", + " un: TimeSeries of population estimates\n", + " timeseries: TimeSeries of simulation results\n", + " title: string\n", + " \"\"\"\n", + " plot(census, ':', label='US Census')\n", + " plot(un, '--', label='UN DESA')\n", + " plot(timeseries, color='gray', label='model')\n", + " \n", + " decorate(xlabel='Year', \n", + " ylabel='World population (billion)',\n", + " title=title)" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [], + "source": [ + "def run_simulation(system, update_func):\n", + " \"\"\"Simulate the system using any update function.\n", + " \n", + " system: System object\n", + " update_func: function that computes the population next year\n", + " \n", + " returns: TimeSeries\n", + " \"\"\"\n", + " results = TimeSeries()\n", + " results[system.t_0] = system.p_0\n", + " \n", + " for t in linrange(system.t_0, system.t_end):\n", + " results[t+1] = update_func(results[t], t, system)\n", + " \n", + " return results" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Reading the data" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [], + "source": [ + "filename = 'data/World_population_estimates.html'\n", + "tables = read_html(filename, header=0, index_col=0, decimal='M')\n", + "table2 = tables[2]\n", + "table2.columns = ['census', 'prb', 'un', 'maddison', \n", + " 'hyde', 'tanton', 'biraben', 'mj', \n", + " 'thomlinson', 'durand', 'clark']" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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XLAaXy0UoFCIuLo7nn3+eZ555hhtuuAGPx8ONN97IkiVL2r3W9vaTJCVE9wn5vFSsfoVgTTkAwWAIh8NBzLCJxAyfhM1h3vrPn5xDlMtBbmZ8JMNtU59NUNPGtF/1NntCNrMnZLe5/oLJuVwwObfN9Z+ZMYjPzBh02nENGDCAo0ePMm7cuMZlgUCAo0ePNs4W/KUvfYmLL76Ym266CYCUlBSuvfZatmzZgtb6lGNOnDgRj8fDihUrmD9/frN1jzzyCAUFBTz//PNkZGRw3333cd555zWu37VrF4MHD2bDhg1txlxZWdn4/Mrv9/PRRx/x9a9/nSlTpuBwOJp1sDUMg8rKyg73a/ncSgjRdWwuD47oOALV5ZRX11NQ4yZr2gWMU/nNthuekxShCK05a1V8SqnFSqmaFq+gUurtsxVDT7BgwQKefPJJ9u7dC5jDND388MOkp6czfvx4AC699FKefvpp3nnnHXw+Hz6fjzVr1rBixQouvPDCU47pdru58847ue+++3j33XcJBALU1dXx7LPP8vLLL3PHHXcAcOWVV/Kb3/yGwsJCgsEgv/vd71i8eDH19fXtxlxWVsZXvvIV1q5di8vlIjMzE5vNRmJiInl5efh8Pt544w2CwSDPP/9846C97e0nhOg+NpuNuDFzKK+38WnDIHYlzOS/+xqoq+9do7WctRKU1vovwF9OfFZKTQTeBr53tmLoCe644w4cDgdLliyhtLSUqKgoZsyYwXPPPddYPXf99dfj8Xh46qmnuOuuuzAMg2HDhnHfffcxe/bsVo/7hS98gfj4eJ555hl+8IMfYBgGo0ePZunSpUydOhWAr371qwQCARYvXkxFRQX5+fksXbq0wwFahwwZwv3338+9997L8ePHSU5O5p577mHEiBEA3HPPPTzyyCP86Ec/YtGiRUyaNMnSfkKIMxeqr6Vu30Zi1fTGqjsAR0w8wy6/mXXv7YXqBjxuBzV1/oi3zDsdtkj0EFZKuYBNwG+01r+xsP1gYP+7775LTk7OKet37NjBqFGjujxOcXbJ71EI6wzDoP7QDmp3rsYI+IgeNono4VNwtGiJd+hYNYUltUwamRHRVnqHDx8+UQM0RGt9wMo+kXoGdQfgBZ6K0PmFEKLXCtSUU7P1Q/xlhQA0+ALsW7WCQHUys6Y0r6HIzYzvsY0gOnLWE5RSyo1Zrfc/WuvIDPAkhBC9kBEK4t27kbq9n2KEggDUNwTYWeTncMJEvAfqGDnCS2pidIQj7RqRKEFdAoSA1yNwbiGE6JX85UXUbPmQQE2T0WRsNpJHTaE2KZnaEi92oKi0ThLUGVgELNda97xeYUII0cOE/A3U7VqLt2A7YIAB2MCZmEH8uLk4E1KZM7CelRuPcN452aQkeCIdcpeJRIKaAdwbgfMKIUSv03BY4y3YRihkcLzciy9kY/Tc+XgGjcFmMxs9pCR4WDRnWIQj7XqWEpRSygFMBqYAGUAQKALWaa03nuY5BwNHT3MfIYTolzyDxlB7cCd7tu+lzJHG0YSxpEUNYpCt749U126CUkolA98AbgNSgX1AKeAA0oBBSqlC4GnMJuMVHZ1Qax17pkELIURfZBghDL8Pu/tkNZ3N7iBxwvkQzKagJAZsNnYfKmdQVvv9F/uCNhOUUuoG4CfAu8BXgHe01g0ttkkAzgMWA1uVUndrrZ/vxniFEKJPClSVUrN1BdidxExegNvlaFznSsrgnJnJ7P9gD1NGZ0Z0EsGzqb0S1FRgqta6uK0NtNZVmK3xXldKZQF3A5KghBDCIiPop273eur2byIYCHKsrI6Cw1EsvPpi7PaTgyrHRrtYfMnIfjXQcpuVmFrrr7eXnFrZvlBr/bWuCavvsjLl+xNPPMH48ePZs2dPs21amxzwhJdeeolRo0YxceJEJk6cyIQJE7j00ktZunRpsyk65s2bx/jx4xu3O/H6zGc+07hNQUEBd9xxB1OnTmXixIksXLiQP//5z62e97LLLmPOnDnNBowVQljjKz5I+YfLqdu3ESMUYu+RSsqq/dTW1LLjwKmTk/an5ASn0YpPKZUBjAdcQLOfktb6jS6Oq99raGjgzjvvZPny5bjdbkv75Ofn869//Qswh0HZsGEDd955J1VVVXz7299u3O6xxx47ZdTzE0KhELfeeisLFy7k0UcfxePxsHHjRu644w7cbjef//znG7c9MQhseno6b7/9NgsWLDiDKxai/wg11FGz/WMaCk9+CbXZbCRm5fJx3WB8zjiOldWeMlFqf2OpGYhS6ivAIczBXV8HXmvyerXbouvHZs6cSV1dHY8//nin9rfZbEyaNIkHHniApUuXUlVVZWm/8vJyCgoKWLhwIdHR0dhsNiZOnMhdd911yrYvvPACF110EZ/73Of405/+1Kk4hehPzKnXt1P24QvNk5Mrivhx5zNywRfJzM7isnOHtDvdT39htQT1PeD3wA+01tXdGE+Xqd21jro96y1t68kdRfy45tOlV29ZQf2hU6viWooZPpnY/KmdirHd48bE8PDDD3Pdddcxd+5cpk+f3qnjzJw5E7vdzoYNG1qdEr6l1NRUpk2bxs0338wVV1zRWM135ZVXNtuurKyMd999lzfffJP4+HgefvhhtmzZ0myeKyHESUYoSOXa1/CXFVJT56O4wsugAQlE5+QTN+pc7FHm6A99sT9TZ1ltSJ8L/Kq3JKe+4pxzzmHJkiV8//vft1wCaunE/Es1NTWNy+68887GSQNPvJ588snG9UuXLuXWW29l8+bNfP3rX2fGjBncfvvtFBWdnDb6n//8JzNnziQrK4u4uDiuuOKKNp9TCSHM5uLO+BSOFtdQUFRNhd/N/qRpJJxzYWNyEs1ZLUG9DVwI7O7GWPoFq1O+n3D77bezatUq7r///mbPf6wKBoNUVVWRlZXVuOzRRx9t8xnUiRivu+46rrvuOnw+H+vXr+fxxx/nm9/8Ji+88AKGYbB8+XKOHz/OrFmzAPOZWUNDA3fddRepqf273lyItsTkTyNm9052heI5HjsCT1kUk/zBZk3KxUlWE9Qm4DGl1BXALsDXdKXW+tQHFBEWmz/1jKre4sfNPaXarytYmfK9KYfDwSOPPMKiRYuIiYk57fOtXbsWwzDIz8/veGPM50rLli3jn//8J2Amq5kzZ+JyubjlllsAWL16NRUVFfz73//Gbj9ZCF+yZAnLli1rnMFXiP4qWF9L3a61xKoZzUpHdlcUwxbexLaPDjIyxsXMcVmSnNphtYpvLrAGiAYmEO4jFX613u5ZtMrKlO8t5eXl8cMf/pDly5dbPk8oFGLt2rXce++9LFmyhLi4OEv7zZ07l4MHD/LQQw9RWlqKYRgcOnSIZ599tnG6+RdeeIFLLrmEzMxM0tPTG19XXXUVy5Ytkybnot8yjBDe/Zsp/3AZtQU7WP/v16mpa/Z9HrvTxeWzh3Dh1LxeNbttJFgqQWmtL+juQPoLK1O+t+aaa65hxYoVrF69us1tdu3axcSJEwFwOp1kZ2dzyy23cO211zbb7jvf+Q4Ox6nf2v79738zYMAA/vrXv/LEE0+wcOFCvF4vycnJXHLJJXzjG9+gtLSUd955h+eee+6U/RcuXMhDDz3EW2+9xcKFCy3+RIToG/wVx6jZupJAVQnVtT6OFNcQDJXz8ZodXHzBhGbbtpz1VrTO8pTvSqlM4GvAGMyS1w7g91rrfd0XXuO5ByNTvvd58nsUvVHI30CtXkP9wR2Yc2FAXX2AnccCHE0YR607lWsuzCcz5fSr6PuSzkz5brUf1DTMZ09XASVAMbAQ2KyUkio+IUS/YxgG9Ud2Ub5iGfUHw3M1YbbWSx9/Ls5Ji3AkZ7Fg1pB+n5w6y2ojiV8CfwNuazpNu1LqSeARQKoAhRD9RqC6jJptK/GXFlJR00CU20F0lBN3eh5xY2bjiElgVl4Ah92OyynVeZ1lNUFNAW5pmpzCngCs9YYVQog+IlhTQe2xwxwprqGuPoArJp5Jl1yEJ2to43h5Hnck5oPtW6ym9kLMiQZbGgpI510hRL/iHjAER2ou3oYgxTFD2RR7Lvvqk/rdYK7dzWqK/xPwO6XUt4ATzchmAv8bXhdxhmHIH0cvZrWxjhBnW6CmAsNfjyv5ZD9Fm81G+qTzORydT/H+BibkpzMiNymCUfZNVhPUg8BAYDlmqcsG+DGr+O7untCsczgc+P1+y6N+i57H6/W228xeiLPNCPqp27MB7/5NNNiiCI6/nLyskxMFOmISOOecOIaO8JGS4GnnSKKzrPaD8gG3KqXuBBTgBfZorb3dGZxVSUlJHDt2jOzs7GYjG4iezzAMvF4vR44cITMzM9LhCIFhGPiO7ad2x8f4a6s5Xl5HWWU9laXvk/X5RbicJ/sQOh12SU7dqL0p3y8D/qO19offt5SrlAIiPx9UWloahw8fRmsdyTBEJ7lcLjIzM0lISIh0KKKfC9ZWUrN9Fb7iQ4CZrCprfNS6kjhOKuu2H+Pc8QMjHGX/0V4J6jVgAHA8/L4tBhDRwaTsdjt5eXmRDEEI0Ys1rc4zQsHG5a7oGNKnTGHjfhfZGfGoQcntHEV0tTYTlNba3tp7IYToK5pW5/lqqqj3BYmNNicNj84bTUz+VFJcUXhyqskbEC8Nsc4yaagvhOi3DF891Zveo6yihmNldRghAzUmn5SJc3ElZjRuNyhLqp8job1nUMWcGLujA1rrjI63EkKInsUeFU30sMmUvfcWDYaLY/EjqXOP5ZJEuaX1BO2VoL6HxQQlhBA9nWEYBKtLcSakNVseM3Q82RW1vLo3ipjYGIbnyXOmnqK9Z1DPncU4hBCi25hj563CX1aIb/RlZA/ObVxnszvInTKbizLLGZyV0KwZuYis9qr4LM+Op7U+/bnIhRCim4X8DdTt/gRvwVa89X4KS2opOfwGzs9eR2ZqbLNtR+RKyamnaa+Kr/asRSGEEF3IMAwajmhqd64h5DPHEygur6OuIYg3Jp4PNxzkcxeOlFZ5PVx7VXw3n81AhBCiK/grj1O77SP8FceaLc8ePoJNR9NpcMUzOSuZUMjA4ZAE1ZO1V8X3MHC/1ro2/L4thtb6/3V9aEIIYV3I56VWr6X+0E7qG/zmdBc2sHtiiRs5E3fWMGYfqiAzJYbEuKhIhyssaK+KbyrgavK+LZZb+imlsoDfYk5wWA/8Tmt9r9X9hRCiLdWb3qOusICisloqa3zkDkhkwLhpxAybiM1p3srypYVer9JeFd8Frb0/Q//CnOAwE8gCViildmit/9pFxxdC9FMxI6ZycKemssZHtTuD1Y7xfH7YFGwyo22vZXkkCaVULHAtMAbwAduAF8IjnVvZfzrmBIeztNZ+YL9S6nzMkdGFEMKyUEMdNrcHm+1k8nElZZA7eRbbtlRTYk9j2IAk/IGgTLnei1lKUEqpccAHmIlpM+acUDcDP1FKXaq13mnhMJOBLcCPlVI3YVbxPaW1/mUn4hZC9ENGKIj3wBbqdq/HPnQqiUPH4nCcTEBJo6czNaECt8tBbmZ8BCMVXcFqCer3wMvA/4RLPyilooE/AM8Acy0cIwU4D1iBWZIaCfxbKVUoVXxCiI74Sg5Ts/0jAtVllFbWU7TvLRLnJDNpTG6z7YblyMy2fYXVsu8E4KETyQkgPFnhT4FpFo/RAFRprX+stW7QWm/CTHBXn07AQoj+JeitoerTt6lc+xrBmnIqqhs4VlaHDzebtx2kxuvv+CCiV7JagvoUs/Szq8XyKcB2i8fYCcQopdxNnlvJaOpCiFYZoSDe/Zup27MeIxhoXJ6cHM8ux3AOGANJTYyhviFAXLSrnSOJ3qq9flC3N/m4FnhSKTUFWA0EgfHAbcBDFs/1H6AY+KVS6ruYU8d/JXwMIYRo5Cs5TM22lQRqKjEMA7vd7FAbNXAEcSNnMKnaIKe8jnHD03HYpbNtX9XRaOZNFQGXhF8nlABfBh7o6ERa63ql1FzgCaAQs5HEw1rrf5xWxEKIPq3+yC6zT5PXz9GSWmKjXeQOySNuzCxcKeZ06wM9MDA9LsKRiu7WXj+oIV19Mq31PmBBVx9XCNF3uDMH4zXc7C8sJWhzUmAMJXP0RbhSJCH1N202klBK3Xg6B1JK2ZRSXz7zkIQilizEAAAgAElEQVQQ/YlhNB+Mxu50kzHxPBwZQ9mdOpfKhGFU1UlDiP6ovSq+ieFnRU8D/9RaF7a2kVIqA/gS8FXgna4PUQjRF4V89dTqNRhBP/ETLmw2srhn4AjGXZqHd3sR544fKI0g+qn2qvi+FW4UcR/wuFJqO+boESWADUjHbH6eD7wJ3KS1Xtv9IQshejPDMGg4upvaHf8lUF/H8XIvx4vjmDd/erMklRQfxcXTB0UwUhFp7Tbz1lp/AlyhlBoCXIrZrHw4EMJsNPFr4A2t9cHuDlQI0fsFayup2bYSX8lhQiGDPYcr8AdCVPj2sO/ISOlkK5qx1A9Ja70feKqbYxFC9FFGKIh33yazT1MoCIDdbiMmIZHNwaFUR2WScKRSEpRoRjrKCiG6lb+8iJotHxKoKWuy1Eb04LGMHDyRnSsPMn9kBkqmwhAtSIISQnQLIxSkdsd/8RZso77BT1lVPVlpcbgS04gbNwdXYgYA116sZOp10SpJUEKI7mGzE6yr4nhZLSUVXoI2B/ahoxg767xm02RIchJtkYlShBDdwmazETf2PGxOF1XudHanzmFNWSqBYKQjE73F6UxYOBFzTicXZjPzRlpraUAhRD9mGAa+ov24M/KwOU7eVhzR8Qy/7Do2fVxEhsfF+ZNzZAJBYZnVCQvvxpxaowyobrHaQFr4CdFvBb011Gz9EN/xg5QmjGDYzPNxOR2N690JySw6P47oKKdU54nTYrUEdQtwr9b6we4MRgjRexiGQf2h7dTuXE19XT1Hi2uo3b+GUmcms2aObbZtjEdGghCnz2qCSgWWd2cgQojeI1hXRfWWD/CXHgXA2xCgriFAWfQgjh9qYISqIyMlJsJRit7OaoJ6EVgM/Lj7QhFC9HSGYVB/0Cw1GcGTA7imZmawN3kmx6qjmKwySEn0RDBK0VdYTVBe4AdKqWuA3YCv6Uqt9ee7OjAhRM8SrKumesv7NBQfwTAMHA47YCNm6ARiRkzh3PoQUwNBUhOjIx2q6COsJqgY4K/dGYgQoufyVxyncs2r1NTUcaS4hugoJ4OH5hI/YR6uJLPDbUJshIMUfY7Vsfhu7u5AhBA9lzMhFZ8zhgOFRQAcdecQP/hCUpLSIxyZ6MtOpx/UOOAuYAxmB9+dwK+11h93U2xCiB7CZneQMfViikr+yYbgMEKxaWCXgWhE97LUY04pdSnwKWZrvheBvwPxwAql1MXdF54Q4mwL+bzU7d1wyky3zoRURl91E0Pyh/PFi0cyIlcGdxXdy+pXoAeBB7TW9zddqJS6B7MD79tdHZgQ4uzzFR+ketP7lJVWULC9hHkL5mO3N5np1u1k3pTcCEYo+hOrY46MAv7SyvJlwLiuC0cIEQlGMEDN9o+oXPsGBw4e50hxDfaD69m041CkQxP9mNUEdRCY2MryycDxrgtHCHG2BapKqfjoJbwHtoANPFEOAnY3hxInsuNwHaGQ0fFBhOgGVqv4fgM8rZTKAVaHl80E7gYe7o7AhBDdyzAMvAc2U6fXNs5yC5CdP5Kd5bkMzUhhxtgBzar4hDibrDYz/7VSKh74AZAWXnwU+JHW+snuCk4I0T2C9bXUbH6f0oP7iPW4sNtt2OwOYkefiyd3NFeGTnTEFSJyLLcTDQ8U+6BSKgPwaq1bjmouhOgF/OVFlK15g6NFpVTW+EhN9JAzdDDxEy7EGZcEgMMhpSYReW0mKKXU7cD/aa3rw+9brm98L/NBCdF7OOKSqaoPUlljjli2059N8vD5JMclRjgyIZprrwT1PeAFoD78vi0yH5QQvYjdFcWg2ZdR9sY/2e4YRe6I4aQlyzhFoudpM0FprYe09r4lpZTUBQjRQxmGgb+sEGdyVrPGDu60bEZ/9hYyKhsYMlBKTqJnsjqSxD6lVEorywcCx7o8KiHEGQs11FG+5jV2vP433n939SkjQ8THeiQ5iR6tvWdQVwCzwx8HAz9RStW12Gz46ZxMKfVl4BmgocniO7TWz5/OcYQQ7fMVH6Riw7vs2V+Ezx/CqFnF7iGDyB8+MNKhCWFZe8+gNgHfAk7UC0yk+TxQBlAD3Hga55sE/FJr/f3TCVIIYY0RDFCr1+A9sAUbEOtx4fM3UOHJwVbaQP5pfaUUIrLaewZVAMwDUEo9C3xTa111huebDPzqDI8hhGhFoLqc6o3vEKgubVyWlZXGgeRhjJ0wBpUng7uK3sXyfFBKKadSKhtwhBfbgChgstb6bx0dQynlAMYD1yulHgPqgD8AD2mtZSwVITrJMAzq9m/l8LoPSI5zYQvXebjT84gffwFXuD3YbNKWSfQ+lhKUUmoh8CxwSkMJoBzoMEEB6cAnwPPA1ZgD0P4LqEKaqQvRKaEGL0fXvM2hHTto8AcJBWNIT4kjdtRMPHljJDGJXs3qSBI/x5xS4zHgXeAKYADwv8B3rRxAa10EzG2yaKNS6gngs0iCEqJTjFCAqqOHaPCbY+kdqnYwYN7lRA8YEOHIhDhzVgfbGgH8RGu9HnPiwlit9XLga7TfibeRUmqMUur+FovdmB2BhRCd4IiOZ/Csi/C4HVTEDSXrgi+QlJkZ6bCE6BJWS1BeIBR+vwuYALwJrAfyLR6jAviuUuowsBSzVeA3MJOcEMKChtpq7FExuJyOxmXROfkMX3A9IxPSSIqPimB0QnQtqyWoD4F7lVJJmM+RrlJKuYDzMZ8hdUhrfQSzanBJeJ9/AD/VWr94ukEL0d8YoSAFaz5g3Z+fYs3qrc3W2Ww20rKzJTmJPsdqCeq7wKvAl4GnMftHVWFW0d1t9WRa6/eAKacZoxD9WqCqhML/vsX+3QcAaNjyPkeG55E9QJqNi77NajPzPcAopVS01tqrlJoGXACUaK3XdGuEQvRTRiiId+9Gavd8gidkEB/jorrOD+5oGrwNHR9AiF6uvaGOYjpY/v6Jz1rrlkMgCSHOgL+qlJotHxCoLDYX2GBgRiL7XMOZOuc8YqPdkQ1QiLOgvRJUDeZwRlY4Ot5ECNGRgN/P1pUrCBZsJC8jrnGgMVdSJikT5pEVK4O7iv6jvQR1wVmLQghBfUUJa/75d4zaMgAqa10kJcQQkz+V6CHjsdlkCnbRv7Q3Ft+KsxmIEP2d02En2VlPWfhzSSCWwbM+izNeGkOI/snqUEfraKe6T2s9rcsiEqKfcsanMGjqbGo+fJ/E0TMYOXMWDofUnov+y2oz89da2W8osAD4cVcGJER/UFpWxfbNmnPnTMHRZKbbhPxJTM0ZgSsuKYLRCdEzWG1m3nKIIqBxAsIrgMe7Migh+rINazZQ+ul72IM+NiclM/Gck5M02ewOSU5ChJ3pU9f3gIu6IhAh+rpQQx1VG97Bs/cDnMF67IQ49sl71PsCkQ5NiB7J6jOo1vpEJQL3AIVdGpEQfYxhGNQf2kGtXoPhbyA1MZrKmgYMZxSjZp9LlEueMwnRGqvPoNrqE1UP3Nx14QjRdxiGgd6xn9TSDVBd3LjcZoPhEyeRPH42jqhW+8MLIbCeoFr2iTIAH7BNa13dtSEJ0fuVV9Ty6bvvYC/cRkO8m4HpcQA4YhKIGzsHd1pOhCMUouez2khiBYBSKg5QQNBcrL3dGJsQvVbpun/jKNwJQHl1A8kJ0aSOnkrM8EnYHFa/FwrRv1l9BhWFOevtYswRzAG8SqnfA9/VWge7KT4heqW8STOpPLSXmjo/SQNzyTj/MjzJaZEOS4hexepXuV9jzv30BWAtZuu/6cCjQAPw/7ojOCF6A2+9D1/AIDHu5HxM7tSBDJo8E78rgQGjxmOz2do5ghCiNVYT1OeBy7XWq5ose0kpVQYsRxKU6IeCIYNtG7dR/Mn7BLNGc9HCec0SUdqE8yIYnRC9n9V+UF7A38ryyi6MRYheI1RfS/Hatyj/+F84fFXYD33K/kPFHe8ohLDMagnqB8AflFJLgNVa65BSaizmc6kHm/aTkrmhRF9mhILUF2yjdvc6HAE/yQkeyqrq8TjBXlcOZEQ6RCH6DKsJ6nEgDlgJBJVSIcCFOVvNNOCxJttKr0PR59Q3BKgqLMB58BOCNeWNyzOSo3FkDGHEefNxxyZEMEIh+h6rCerKbo1CiB4qFDLYtrOAQ2veJ8lXxPCcpMbnTI7YJBLHzGaA9GkSolucbj+oaGAE5rOrvdJJV/R1NYUHKFvxAjHBID6grKqetJQEYkZMJnrwOGx2qTAQortY7QflAH4GfJOTVXs+pdRzwNe01jLapeiT4jIGkpGWyLFjZbicdtwDR5Ay/QLsnthIhyZEn2e1iu9B4DrgBmAVZoKahdkP6r7wS4hera7eT0mFl7wBJ58l2V1R5E2dA5s+YfCsi4hOGxjBCIXoX6wmqBuAW7TWbzRZtlwpVQ38DklQohcLBkNs2H6YI+tX4iBIxhe/hCfq5H+NmEGjGTloFDbbmc5OI4Q4HVb/x8UBe1pZvg+Q8VtEr2UYIeoLtlK/+u8k1hwgruYQn36ytdk2NptNkpMQEWD1f9064I5Wln8NWN914Qhx9vhKDlOx8kXqdn5MVpILgCiXgyxKIhyZEAKsV/H9P+ADpdT5wOrwshnAYOCSrg9LiO5RXl1P4eEicup20nDsQOPyhBg3uXlZZE+9gKgBgyMWnxDiJKvNzD9RSk0CvgqMxhz66FXgN1prmVFX9HjBYIhVnx6keOtaUuv2kpCT0DiTrc3hImb4JNKGjJdm40L0IJYnptFa7wLuVEqlAkGtdUX3hSVEF/N7idr2Kmm1VQAcK6sjLzMeT3Y+MWo6Dmk2LkSPY/nJr1LqXqXUUeA4UKqUOqCU+lb3hSZE17FHxZAzJBeA2Ggnmbm5JM28kvgJ8yQ5CdFDWe2o+yBm9d4DNJ8P6h6llEtr/YjVEyqlkoDNwH1a6+dOO2IhOlBYUsuBo5XMHH+yz5LNZmPA5POhtpzUcTPw5IyUOZqE6OGsVvHdAtzYoh/UR0qpPcBvAMsJCngayD6N7YWwJBQy+M+aA5Tu2kSy9zAH0xeTl5XcuN4Zl0T2JTfIcyYhegmrVXxO4FAry/cA8VZPppS6EUgAtljdRwirghWFpBa8w8DqbUQHKtnx0cpTtpHkJETvYTVBPQI8pZTKPbFAKZUC/AJzuKMOKaWGAD8Cvny6QQrRnmB9LVUb36Fi9SsMjPFjt0FirJvxSTUYRijS4QkhOslqFd8XgFHAPqXUISAA5AFuYIZS6hsnNtRanzJjW3iw2T8Dd2qti5RSZxy46N+Ol9exbc9xpiWX4937KUbQnPDZ5bSTPziNBDWF6CETZAQIIXqx05mw8EzcC2it9UtneBwhWLnxCPu27WBA1VaOpEByvKdxXdSAocSOmokj2nLNsxCih7LaUff5MzzPtcBApdTV4c/xmFWG07TWt5/hsUU/k3B0LYPKtwNQXGYnKc6DKz6F2NHn4pbJA4XoMyx31D0TWuuRTT8rpTYCj0szc9EZQ0cMZnPBTqLcDrIyk4gfPQPPoDHSAEKIPuasJCghOqOmzsf6ncc5d3wWLufJ5BM3bDzDD+4gJj2LWDUde1RMBKMUQnSXiCQorfU5kTiv6D227C3hk093kVa+jQ3B2UybOqpxnc3uIGPuNdicrghGKITobtLESfQ4oYAP95GNDD72AfG+45RsWEGt19dsG0lOQvR9bZaglFL/Z/UgWmvp2yTOmGEYNBzdTe3O1aTU11ER5SBkGAxOC+D2VUD0KT0YhBB9WHtVfE3b6bqBy4GdmJMX+oBJwATgr90WnejzgsEQm3aXMCwliLF3Df7yInOFDXO08bQs4seehzNBJm4Wor9pM0Fpra858V4p9TvMVnffabqNUuoBYGTLfYWworCklvfX7MZTtAWb4xg5GXGN6+xR0SRPmEnUwBEyqKsQ/ZTVRhJfxCwxtfQ8sLHrwhH9SaD4AJkH3sZh+KkEUhI8xEa78QwZR8zwydid7kiHKISIIKsJqgiYB+xusXwhUNClEYl+Y8DAdEpi7VTX2chIjiExezBxY2bjjEuKdGhCiB7AaoL6CbBUKTUP+BSwYc4HdRlwTXs7CmEYBnsOV5AU5yE9ObpxuSsxg9xxEwmWHSVp/Hm4MwZJdZ4QopHVoY7+pJQ6DCwBrg8v3gzM0Vqv6a7gRO9XXl3PinUH8BVsJj45iUsWXdQsCaWMn43N7sDmkD7jQojmLN8VtNbvA+93YyyijzEMg+CxfcTpN3EG6wnWudi1bxxqWFbjNnZXVAQjFEL0ZO31g3rY6kG01nd1TTiir/BXHqd2+8cY5UUMiLNRWgkZCQ4y/YeBrA73F0KI9kpQUy0ew+iKQETvZhgG+45UYgt4Sa/aSf3hXZz400hPjiY5NZHUcbOIysmPbKBCiF6jvX5QF5x4r5S6HnhTa11yVqISvUpVrY93Vu/Hf2gLAxv2E5cT1/icyWazEztcmo0LIU6f1WdQvwZmAJKgxCmcDZUk730Dm6+OIFBaWU9aUjTujEHEjToXR2xipEMUQvRCVgeLXQNc1Z2BiN4rOjGJrNRYbEBqooe0rAEkTltI4pRLJTkJITrNagkqBPxMKXUPsB/wNl2ptZ7W1YGJnscfCLFpdzEOG0wcmdm43OZwMWjaXBK2rCJ57Aw8uaOw2WSgfCHEmbGaoNaEX6Kfqqhu4JX3thFbugOP0YAafD0xnpNTXnhy8hkwYLA0GxdCdBmrHXXvP/FeKZUA2LXWFd0WlehRjIAfZ+FWhh9/H19DAwA7Nm5n8owJjdvYbDZskpyEEF3IckddpdRtwA+BgeHPx4Ffaa1/0U2xiQgKhQxshKg/uJ26PZ8S8nkZkOzmaLGfjORoBsRWRjpEIUQfZylBKaXuBO4FHgRWYY7FNwv4vlLKq7X+VfeFKM6miuoGVm85QlztYUY7DxH0Vjeui492M3JUOvEjZ+DOHBy5IIUQ/YLVEtQdwP9orf/WZNlHSqkC4AFAElQfUFHt5bWX3ye9ZheBYC11OYlEuc0/Ebsnltj8qURl50sDCCHEWWE1QaVjzqTb0nogp+vCEZEUh5eRvq3UBP0AVNf5iY6NJXr4JKLzxsiArkKIs8rqHWcr5rQaP2+x/AuY08CLXiYUMqj3BZq1xHPGpzBQjeaI3k5meiKpIycRPXSCjAAhhIgIqwnqPuB1pdRM4L/hZTOBS4CruyMw0T0Mw2D/0Qq2/Hcd0W4bF10+v9n0FxkTziUxPcNMTNIqTwgRQZYeJmit3wYuBBow54P6HFAFTNVav9Z94YmuZISClO3ewt5XniOxaB2OQxs4cKSs2TbO+BRi1TRJTkKIiGtvuo1LgJVa61oArfWHwIdnKzDRdUIBH/UHt+M9sIVQfS0ZsSHKq8BlC9BwcAfkzI50iEIIcYr2qvheBwJKqU+A98Kvj7XWDWclMnHGaqqqqNq9EXfZXgz/yV9bRnI0NqebnHOmkTTinAhGKIQQbWsvQaVh9nWaCcwGvg3YlVKrOZmw1mitg90epTgtteWlbP9oJbUHd+J2GAzPSebEYyZ7VDSJg8eTOWiMNH4QQvRo7c0HVQ68Fn6hlHIAkzAT1kzgy0CaUmql1nrBWYhVWFVZRMOhHRAK4QtBeVU96VmZRA+dgCc7X5qLCyF6Bcs9LsMlpcNAIXAcOBjef2j3hCY6YhgGJRW1lFU1G1yemFxFcoo5zYUtLhXPuHkkz/0C0XmjJTkJIXqNdu9WSqk44HxgPnARMBI4BLwPLAW+pLU+avVkSqmFwM+AIZhJ7mGt9TOdiryfO3ComK0f/5eo0t1EjZnLnLlTGtfZHE5yps8j3ucgZ/gw7HYZ+UEI0fu014pvJTANKAc+wBzO6D2t9Z7OnEgplQW8CFyltX5TKTUJc7ikdVrrTztzzP4oUFNBfcEW7Hu2EVdcCkDtvs2EzpuM3X6yP1Pi4JHIVIFCiN6svRLULMwqvf/DbBDxX621v7Mn0loXKqXStdbVSik7kAoEgOoOdu23jpfXsfNAGcdKa7lifDT1BVvxFR8EINoJLoedYChEhrOWeq+XmNiYCEcshBBdp70ENRSzau9C4DYgVim1CngXM2F9qrU2Tudk4eQUA1SGz/2Q1np3pyLv4/yBIC+/t5O4mkOk1u3nWJWTaE+TX5cNBg/PIyl/IjE50vBBCNH3tNeK7wDwh/ALpdQEYB5mwroX8CulPgDe1Vo/dRrnrAdigfHAG0qp3VrrpZ2Kvg8xDKPZkENOQkzzrqKi2ixgVtVFhxOUDXdGHtGDx+FKzW62jxBC9CWWv3ZrrTcBm5RSvwImAzdjDnt0JWA5QWmtQ4AP+EQp9TtgEWaDi37HMAyOFNewaVcxOZnxTBiR3rjO5nSRPmgoRmAHyfEeYuNiiM4dSfSgsThi5emSEKLv6zBBKaVygOnAjPC/kzCfHX2MORfUB1ZOpJSaCzymtZ7cZHEU0G+njt99qIJ3/7uLZO9hCg67GDfs8mYNHdJHTyQ6WE304LFE5SjpWCuE6Ffaa8X3D8yElIXZkOEj4FXgTmB9J0aQ2AhkK6W+g9kicDrwFeCqTsTdqxmGQaDiGOnFWxhTtp5QMEiw1kVh8RyyM5Mat3OlDCR57rVSjSeE6JfaK0FFAY9jlpA+DVfNdZrWulIpdRnwa+BHmP2pbtFarziT4/YGxeVeNu8pZppKwVm2n/qDOwjUmKOIpyVE4Q8ESU2MJjVwHDiZoCQxCSH6s/YaSSzs6pOF+zv1q6GzV208jN62mxTvQQp2V5CZ1Hwai/TkaFxJGXgGjSVqgAzKIYQQJ0jb5G6WVb6BQPlmAMr9NjIS3dhsNmwOJ1EDhxOdNwZnYnoHRxFCiP5HElQXCIUMDh6rpqi0lhljs5qtyxo6lCK9lZgoJ6mJ0bgS0vDkjSYqe4Q0ehBCiHZIgjpDwWCIv7++HnvpPmL85ZTl3khKYnTjek/2CNSwLKIyB+PJG40zMV2eLQkhhAWSoDopFPDhK9xH/eGd5JfupqrWB4Deppl57slJAO1ON6kXXo/N7ohUqEII0StJgrKopMLLjv0lpNsrGWgcw1e0DyNktrRPjo+itt5PUpyHDHf5KftKchJCiNMnCcqCPbsK2LjqYxLrj1DpCpKa3Xwkh7iYKMZNGUF07kjcGXkRilIIIfoWSVAt+PxB3K7mJZ600HHSvfswDPA2QIMvQJTbiTM+hagchWfgCOxRMpK4EEJ0JUlQYdv2lbL3YAmVRwr47GcvIMbjalwXn6dIiPkAbJCckkTisNFE547EmZAauYCFEKKP6/cJyjBC+EsOU7LuI+JKCkgwguzdM4xxY4c1buOISSB/1vm4kjJxpedgs8kMtUII0d36TYIKBkMcLanlQGEVmSkxDE0KUn9Y01C4h1CDlwGhegoNs9FD7aHd0CRBAcTmT41E2EII0W/1mwS1fX8ZH32yl6T6I7icxSSnNJ9rMSHO7DSblJFBYv7gCEQohBCiqX6ToLICh1Al72LDoMEGoaSUxqkt7FHRxA8cQXp2Po74VOlIK4QQPUC/SVCJmVkkxDhxuxzEx7ixO5xEZQ3Fk52PKy1bnisJIUQP028SlDMpkyHDcrFHxeDJVrizhspYeEII0YP1mwRls9lInvU5bE5XxxsLIYSIuH5VryXJSQgheo9+laCEEEL0HpKghBBC9EiSoIQQQvRIkqCEEEL0SJKghBBC9Ei9pZm5A6CoqCjScQghhOiEJvdvyzO49pYElQWwePHiSMchhBDizGQBe61s2FsS1DrgPKAQCEY4FiGEEKfPgZmc1lndwWYYRsdbCSGEEGeZNJIQQgjRI0mCEkII0SNJghJCCNEjSYISQgjRI0mCEkII0SNJghJCCNEjSYISQgjRI0mCEkII0SP1lpEk2qSUmga8prXOCH9OB34FfAZoAP4P+JHWOhhe/0fg80CgyWHGa633KaXygKXADOA48HWt9Rs9+FrODa8fBRwFfqi1fjG8LmLXcjrXoZR6GriuxSFigbu11j/rhb+Tm4F7gDRgJ/BdrfWq8Lredi1fB74NpAIfA3dorfdF8lqUUhcBvwBGhM/7iNb6GaVUEvAH4CKgBrhHa/1seB8b8FPgq4AbeBb4ntY6EF7/eeBnmKMcrABu0lof74nX0mRfO/APYIXW+vEmyy/A/J0OAzYB12utLQ0r1BP12hKUUsqmlLoFeBvzj+6E54EMzJv2WGAa8JMm6ycBV2qt45q89oXXLQM2Y/6HvBVYppQa2s2X0qlrUUplAa8DTwLxwB3An8M3johcS2euQ2v9P01/F8D3gO3h64rIdXT2WpRS44HHgEVAEvBn4OXwzaS3XcvngQeBm8PxvgL8RynlidS1KKVyMW/KD2D+fL8I/Fwp9Rngt5jDoGXx/9s79xirqisOf4q2zsRoSm2kmiq2xaVIfQSsVmM1mWisgjb4aig+efVhVBq0gQmKqYaXmhoi2hLTllJKsHTGQFOtkVhfrfGBBBz8VZpQaH3hK0oHRAX/WPuGw2HmGsa5955zs75kMnf2PnvP/uXcc9ZZa++zF5wPzDKzM1PTicBo/NofApwMTEt9DsUN7VVJyytJW035HFows8HAcuD7uT4PATqBW1OfHcDDme9f6SjtwPGT8GP8BANgZq3AucBkSW9KegeYDkxIF2kLcAzwYr4zMzsaGAHcLGm7pJX4RTmu9lL2XgtwBfC4pN9J2inpEfwG824DtfRFB5ljvwHMAcZIer+E52QIu66pffCbzNbUtmxaLgIWSPq7pI8l3QtsB9oaqGUwsFhSh6Qdkp4FHgPagIuB6ZK6Jb0ILMANE8CVwC8l/VfSZmAGMCnVjQWWS3pS0jZgKnC6mQ0pohYzOxB4HveOns71ORp4SdIySR9Jmgt8MfVZSspsoO6TNBx4LlNW0fP/TNknwFfwJ4oT8dDeAjPbbGYvmNnIdNxQYKOkbNuXgW/VZPS70xctw4ENZrbEzN4ys1XAIEkf0DgtfdGR5U78prg6/V22c/IwsBZYg9/MZwOXSdpB+fHKlOQAAAXoSURBVLTsm6ur1B9Ng7RIekLSjyp/m9lAdm0ivRP3fnoaz1DcK8/WHZba71YnqRvYRHG1bAOOlTQN+CjXbV4ngKjPd6wmlNZASXq1h7IteBhjjpkNNLMvAzen6hY8FPYE/kR5GB7CWGpmJwAHAt25LruB1too2G3cfdEyEA+tLMJDATOBjuSFNERLH3UAYGbD8Jj77Ezzsp2TA/Abwqn4PNrP8RDfIMqnZRkw0cxGmNn+ZjYBjz600EAtFczsYNxrewb3KLZJyu58nR1PfryVz6091OXb1py90ZK82d7mxxqupb8prYGqwuX40+s6fMKzM5W/J+lvks6W9FxygZcBK4EL8KfFllxfrfgkZaPoVQs+qf2QpBVJy1LgBeB7FE9LNR0VrgE6Jb2RKSuaDqiuZQbwuqRnJH0oaT6wAbiEkmmRtAR/6FmCexTDgEeAd2mwlhRi/CfwBh4O+wA4IBcyzo4nP97KDXtLD3X5tjWlD1qqUcTv2OeiGQ3UV4FJkg6VNAz4H7BOUreZjTKzK3PHfwF3m7uAI9I8VYVj2NNlrie9asHd/i/ljq+syiyalmo6KlzInpPTRdMB1bV8DY/5Z/kYD8WUSktahLNc0jclDQJ+hhup52mgFjP7Lu5pdAIXp3mjV/A5v6N6GU8XYLm61yS9l69Lc3NHUFwt1cjr3Ju2haT0y8x74C5grZlNwb9os9m1ImwAcLeZrcMvtMuA04Dxkjaa2WrgdjObmsovBL5TbwEZqmlZCFxrZmOBxfhT+vHApZI2FUxLNR2V5c5fB57KNpKkgumA6lpW4CGzpXhSth8CxwF/KeA5gepa2oBbzOwM4H08/Pcq8KyknY3QksLXK/BXEOZVyiVtMbMOfBXcOHyJ9QR8ZR7A74EpZvYo7mXMSGXg186TZnYW8A/ca1wl6V8F1VKNDvz7d2n6fD2wA198UUqa0UBNwFe9vIOHXealUAuSOs2sHfgjMAj3QkZK2pjaXgT8Gn8n4S1gnKS1dR5/lmpaVpvZefhNZT6wERgtaVNqWyQtvepIDAY+TCvJ8hRJB1Q/JwvSfMJi/D2oLuC8gp4TqH5e/oBPrq/GowyPAhdk5kYaoeWn+DzyTDObmSm/B1+VNx/4Dx4RuV3SX1P9fcCh+Kq3VuAB0nybpDVmdk065nDco7mkxjqg71p6RdKbZjYKfw/qfuAlYJSk7f09+HoRGXWDIAiCQtKMc1BBEARBExAGKgiCICgkYaCCIAiCQhIGKgiCICgkYaCCIAiCQhIGKgiCICgkYaCCoB9Jm/duTpt/5uvazWxLSpcQBMFnEAYqCPqXG/AX4LMvX2JmRwHt+M4BGxowriAoHWGggqAfkfQ6nlNovJmdkqmah+chm9djwyAI9iB2kgiCfibtRP0UvkXQyfhu+UuBkyR1pWOuxrO6Ho7vJt4u6aFUtx+eonwMnhbmbXx7rimSPjGzRfgea8fie7WNlvRY3QQGQZ0IDyoI+pm0X91EfPPeq4E7gNsyxul8fKPW9nTM/Xgur2+nLqbiKcAvx7P0TgWuA0Zm/s1YfM+1NjxdQxA0Hc24WWwQNBxJa83sLuBXuIc0K1M9DZiVcngBrDezEXhKix/gGXmvkvR4qv+Nmd2EZ0x9MJV1SVpUax1B0EjCQAVB7bgVz6r7C0nZ9NxDgeFmNj1Ttj8pb0/adb/NzObiKdaPx3d8H5A5/t+1HHgQFIEI8QVBjZC0NX3cmqvaD7gRODHzcxyeUwkzuw1PCbFv+n0OkE9lke8zCJqO8KCCoP68DBwpaX2lIHlT24C5wE+AGyQtTHUteELBfXroKwialjBQQVB/5gALzUzASuBs4BZ8/gk8geBIM3saOBgPFR7Enunkg6CpiRBfENQZSQ8Ak4Gb8HmnycAkSX9Kh1yBr95bA/wZWA/8Fhhe98EGQQOJ96CCIAiCQhIeVBAEQVBIwkAFQRAEhSQMVBAEQVBIwkAFQRAEhSQMVBAEQVBIwkAFQRAEhSQMVBAEQVBIwkAFQRAEheRTfmloFmOy4cYAAAAASUVORK5CYII=\n", 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" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "un = table2.un / 1e9\n", + "census = table2.census / 1e9\n", + "plot(census, ':', label='US Census')\n", + "plot(un, '--', label='UN DESA')\n", + " \n", + "decorate(xlabel='Year', \n", + " ylabel='World population (billion)',\n", + " title='Estimated world population')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Running the quadratic model" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here's the update function for the quadratic growth model with parameters `alpha` and `beta`." + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [], + "source": [ + "def update_func_quad(pop, t, system):\n", + " \"\"\"Update population based on a quadratic model.\n", + " \n", + " pop: current population in billions\n", + " t: what year it is\n", + " system: system object with model parameters\n", + " \"\"\"\n", + " net_growth = system.alpha * pop + system.beta * pop**2\n", + " return pop + net_growth" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Extract the starting time and population." + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "2.557628654" + ] + }, + "execution_count": 7, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "t_0 = get_first_label(census)\n", + "t_end = get_last_label(census)\n", + "p_0 = get_first_value(census)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Initialize the system object." + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "data": { + "text/html": [ + "
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values
t_01950.000000
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\n", + "
" + ], + "text/plain": [ + "t_0 1950.000000\n", + "t_end 2016.000000\n", + "p_0 2.557629\n", + "alpha 0.025000\n", + "beta -0.001800\n", + "dtype: float64" + ] + }, + "execution_count": 8, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "system = System(t_0=t_0, \n", + " t_end=t_end,\n", + " p_0=p_0,\n", + " alpha=0.025,\n", + " beta=-0.0018)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Run the model and plot results." + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "results = run_simulation(system, update_func_quad)\n", + "plot_results(census, un, results, 'Quadratic model')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Generating projections" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "To generate projections, all we have to do is change `t_end`" + ] + }, + { + "cell_type": "code", + "execution_count": 30, + "metadata": { + "scrolled": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Saving figure to file figs/chap04-fig01.pdf\n" + ] + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "system.t_end = 2250\n", + "results = run_simulation(system, update_func_quad)\n", + "plot_results(census, un, results, 'World population projection')\n", + "savefig('figs/chap04-fig01.pdf')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The population in the model converges on the equilibrium population, `-alpha/beta`" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "13.856665141368708" + ] + }, + "execution_count": 11, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "results[system.t_end]" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "13.88888888888889" + ] + }, + "execution_count": 12, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "-system.alpha / system.beta" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Help on function linspace in module modsim:\n", + "\n", + "linspace(start, stop, num=50, **options)\n", + " Returns an array of evenly-spaced values in the interval [start, stop].\n", + " \n", + " start: first value\n", + " stop: last value\n", + " num: number of values\n", + " \n", + " Also accepts the same keyword arguments as np.linspace. See\n", + " https://docs.scipy.org/doc/numpy/reference/generated/numpy.linspace.html\n", + " \n", + " returns: array or Quantity\n", + "\n" + ] + } + ], + "source": [ + "help(linspace)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Exercise:** What happens if we start with an initial population above the carrying capacity, like 20 billion? Run the model with initial populations between 1 and 20 billion, and plot the results on the same axes." + ] + }, + { + "cell_type": "code", + "execution_count": 31, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "system = System(t_0=t_0,\n", + " p_0=p_0,\n", + " t_end=t_end,\n", + " alpha=0.025,\n", + " beta=-0.0018,\n", + " )\n", + "poparray=linspace(1,20,20)\n", + "for system.p_0 in poparray:\n", + " results = run_simulation(system, update_func_quad)\n", + " plot(results)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Comparing projections" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can compare the projection from our model with projections produced by people who know what they are doing." + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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United States Census Bureau (2015)[28]Population Reference Bureau (1973-2015)[15]United Nations Department of Economic and Social Affairs (2015)[16]
Year
20167.334772e+09NaN7.432663e+09
20177.412779e+09NaNNaN
20187.490428e+09NaNNaN
20197.567403e+09NaNNaN
20207.643402e+09NaN7.758157e+09
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" + ], + "text/plain": [ + " United States Census Bureau (2015)[28] \\\n", + "Year \n", + "2016 7.334772e+09 \n", + "2017 7.412779e+09 \n", + "2018 7.490428e+09 \n", + "2019 7.567403e+09 \n", + "2020 7.643402e+09 \n", + "\n", + " Population Reference Bureau (1973-2015)[15] \\\n", + "Year \n", + "2016 NaN \n", + "2017 NaN \n", + "2018 NaN \n", + "2019 NaN \n", + "2020 NaN \n", + "\n", + " United Nations Department of Economic and Social Affairs (2015)[16] \n", + "Year \n", + "2016 7.432663e+09 \n", + "2017 NaN \n", + "2018 NaN \n", + "2019 NaN \n", + "2020 7.758157e+09 " + ] + }, + "execution_count": 14, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "table3 = tables[3]\n", + "table3.head()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "`NaN` is a special value that represents missing data, in this case because some agencies did not publish projections for some years." + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": {}, + "outputs": [], + "source": [ + "table3.columns = ['census', 'prb', 'un']" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This function plots projections from the UN DESA and U.S. Census. It uses `dropna` to remove the `NaN` values from each series before plotting it." + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": {}, + "outputs": [], + "source": [ + "def plot_projections(table):\n", + " \"\"\"Plot world population projections.\n", + " \n", + " table: DataFrame with columns 'un' and 'census'\n", + " \"\"\"\n", + " census_proj = table.census / 1e9\n", + " un_proj = table.un / 1e9\n", + " \n", + " plot(census_proj.dropna(), 'b:', label='US Census')\n", + " plot(un_proj.dropna(), 'g--', label='UN DESA')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Run the model until 2100, which is as far as the other projections go." + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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values
t_01950.000000
t_end2100.000000
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\n", + "
" + ], + "text/plain": [ + "t_0 1950.000000\n", + "t_end 2100.000000\n", + "p_0 2.557629\n", + "alpha 0.025000\n", + "beta -0.001800\n", + "dtype: float64" + ] + }, + "execution_count": 17, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "system = System(t_0=t_0, \n", + " t_end=2100,\n", + " p_0=p_0,\n", + " alpha=0.025,\n", + " beta=-0.0018)" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Saving figure to file figs/chap04-fig02.pdf\n" + ] + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "results = run_simulation(system, update_func_quad)\n", + "\n", + "plot_results(census, un, results, 'World population projections')\n", + "plot_projections(table3)\n", + "savefig('figs/chap04-fig02.pdf')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "People who know what they are doing expect the growth rate to decline more sharply than our model projects." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Exercises\n", + "\n", + "**Optional exercise:** The net growth rate of world population has been declining for several decades. That observation suggests one more way to generate projections, by extrapolating observed changes in growth rate.\n", + "\n", + "The `modsim` library provides a function, `compute_rel_diff`, that computes relative differences of the elements in a sequence. It is a wrapper for the NumPy function `ediff1d`:" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": {}, + "outputs": [], + "source": [ + "%psource compute_rel_diff" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here's how we can use it to compute the relative differences in the `census` and `un` estimates:" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "alpha_census = compute_rel_diff(census)\n", + "plot(alpha_census)\n", + "\n", + "alpha_un = compute_rel_diff(un)\n", + "plot(alpha_un)\n", + "\n", + "decorate(xlabel='Year', label='Net growth rate')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Other than a bump around 1990, net growth rate has been declining roughly linearly since 1965. As an exercise, you can use this data to make a projection of world population until 2100.\n", + "\n", + "1. Define a function, `alpha_func`, that takes `t` as a parameter and returns an estimate of the net growth rate at time `t`, based on a linear function `alpha = intercept + slope * t`. Choose values of `slope` and `intercept` to fit the observed net growth rates since 1965.\n", + "\n", + "2. Call your function with a range of `ts` from 1960 to 2020 and plot the results.\n", + "\n", + "3. Create a `System` object that includes `alpha_func` as a system variable.\n", + "\n", + "4. Define an update function that uses `alpha_func` to compute the net growth rate at the given time `t`.\n", + "\n", + "5. Test your update function with `t_0 = 1960` and `p_0 = census[t_0]`.\n", + "\n", + "6. Run a simulation from 1960 to 2100 with your update function, and plot the results.\n", + "\n", + "7. Compare your projections with those from the US Census and UN." + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": {}, + "outputs": [], + "source": [ + "# Solution goes here" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": {}, + "outputs": [], + "source": [ + "# Solution goes here" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "metadata": {}, + "outputs": [], + "source": [ + "# Solution goes here" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "metadata": {}, + "outputs": [], + "source": [ + "# Solution goes here" + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "metadata": {}, + "outputs": [], + "source": [ + "# Solution goes here" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "metadata": {}, + "outputs": [], + "source": [ + "# Solution goes here" + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "metadata": {}, + "outputs": [], + "source": [ + "# Solution goes here" + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "metadata": {}, + "outputs": [], + "source": [ + "# Solution goes here" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Related viewing:** You might be interested in this [video by Hans Rosling about the demographic changes we expect in this century](https://www.youtube.com/watch?v=ezVk1ahRF78)." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.6.6" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} From abc450e31c16e6d9bc010b79c3327d142c2c64e0 Mon Sep 17 00:00:00 2001 From: Bennett Taylor Date: Wed, 26 Sep 2018 21:35:30 -0400 Subject: [PATCH 03/14] Spanish Flu v1.1 --- code/Spanish Flu.ipynb | 401 +++++++++++++++++++++++++++++++++++++++++ 1 file changed, 401 insertions(+) create mode 100644 code/Spanish Flu.ipynb diff --git a/code/Spanish Flu.ipynb b/code/Spanish Flu.ipynb new file mode 100644 index 00000000..9b88bdbf --- /dev/null +++ b/code/Spanish Flu.ipynb @@ -0,0 +1,401 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 305, + "metadata": {}, + "outputs": [], + "source": [ + "# Configure Jupyter so figures appear in the notebook\n", + "%matplotlib inline\n", + "\n", + "# Configure Jupyter to display the assigned value after an assignment\n", + "%config InteractiveShell.ast_node_interactivity='last_expr_or_assign'\n", + "\n", + "# import functions from the modsim library\n", + "from modsim import *\n", + "\n", + "from pandas import read_csv" + ] + }, + { + "cell_type": "code", + "execution_count": 306, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "\"\\nfrom pandas import read_html\\n\\nfilename = 'data/World_population_estimates.html'\\ntables = read_html(filename, header=0, index_col=0, decimal='M')\\ntable2 = tables[2]\\ntable2.columns = ['census', 'prb', 'un', 'maddison', \\n 'hyde', 'tanton', 'biraben', 'mj', \\n 'thomlinson', 'durand', 'clark']\\n\"" + ] + }, + "execution_count": 306, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "\"\"\"\n", + "from pandas import read_html\n", + "\n", + "filename = 'data/World_population_estimates.html'\n", + "tables = read_html(filename, header=0, index_col=0, decimal='M')\n", + "table2 = tables[2]\n", + "table2.columns = ['census', 'prb', 'un', 'maddison', \n", + " 'hyde', 'tanton', 'biraben', 'mj', \n", + " 'thomlinson', 'durand', 'clark']\n", + "\"\"\"" + ] + }, + { + "cell_type": "code", + "execution_count": 307, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "data/Census_Data.csv\n" + ] + } + ], + "source": [ + "filename = 'data/Census_Data.csv'\n", + "print (filename)\n", + "tables = read_csv(filename, header=0, index_col=0, decimal='M')\n", + "tables.columns = ['Population', 'Change', 'Rate']" + ] + }, + { + "cell_type": "code", + "execution_count": 308, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "popData = tables.Population / 1e9\n", + "#change = tables.Change / 1e9\n", + "empty = TimeSeries()\n", + "plot_results(popData, empty, 'US Census Data')" + ] + }, + { + "cell_type": "code", + "execution_count": 309, + "metadata": {}, + "outputs": [], + "source": [ + "def plot_results(census, timeseries, title):\n", + " \"\"\"Plot the estimates and the model.\n", + " \n", + " census: TimeSeries of population estimates\n", + " un: TimeSeries of population estimates\n", + " timeseries: TimeSeries of simulation results\n", + " title: string\n", + " \"\"\"\n", + " plot(census, '--', label='US Census')\n", + " # plot(un, '--', label='UN DESA')\n", + " if len(timeseries):\n", + " plot(timeseries, color='gray', label='model')\n", + " \n", + " decorate(xlabel='Year', \n", + " ylabel='World population (billion)',\n", + " title=title)" + ] + }, + { + "cell_type": "code", + "execution_count": 318, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "0.272690813" + ] + }, + "execution_count": 318, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "init = State(babyboy=2)\n", + "p_0 = get_first_value(popData)" + ] + }, + { + "cell_type": "code", + "execution_count": 319, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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birth_rate0.0555556
death_rate10.0172
death_rate20.028
t_01900
t_end2016
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" + ], + "text/plain": [ + "birth_rate 0.0555556\n", + "death_rate1 0.0172\n", + "death_rate2 0.028\n", + "t_0 1900\n", + "t_end 2016\n", + "init babyboy 2\n", + "dtype: int64\n", + "alpha 0.025\n", + "beta -0.0018\n", + "dtype: object" + ] + }, + "execution_count": 319, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "\n", + "system = System(birth_rate = 1/18,\n", + " #1918 birthrate (does not change, black death did not affect birthrate)\n", + " death_rate1 = .0172,\n", + " #death rate in 1900\n", + " death_rate2 = .028, #code do be duplicated and run alongside curret, replacing .028 with \n", + " t_0 = 1900,\n", + " t_end = 2016,\n", + " init=init,\n", + " alpha=0.025,\n", + " beta=-0.0018)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": 320, + "metadata": {}, + "outputs": [], + "source": [ + "def update_func1(state, t, system):\n", + "\n", + " #print(type(state.babyboy))\n", + " births = system.birth_rate * state.babyboy\n", + " \n", + " #change death rates at start of Spanish Flu\n", + " \n", + " if 1918 < t < 1922:\n", + " deaths = system.death_rate2 * state.babyboy\n", + " babyboy = state.babyboy + births - deaths\n", + " return State(babyboy=babyboy)\n", + " else:\n", + " #deaths = system.death_rate1 * state.babyboy\n", + " net_growth = system.alpha * state.babyboy + system.beta * state.babyboy**2\n", + " net_growth = system.alpha * state.babyboy + system.beta * state.babyboy**2\n", + " return \n", + "\n", + "\n", + " #add rebound pop changes later\n", + " \n", + " #babyboy = state.babyboy + births - deaths\n", + " \n", + " #return State(babyboy=babyboy)\n" + ] + }, + { + "cell_type": "code", + "execution_count": 321, + "metadata": {}, + "outputs": [], + "source": [ + "state = update_func1(init, system.t_0, system)" + ] + }, + { + "cell_type": "code", + "execution_count": 322, + "metadata": {}, + "outputs": [], + "source": [ + "def run_simulation(system, update_func):\n", + " \"\"\"Simulate the system using any update function.\n", + " \n", + " init: initial State object\n", + " system: System object\n", + " update_func: function that computes the population next year\n", + " \n", + " returns: TimeSeries\n", + " \"\"\"\n", + " results = TimeSeries()\n", + " \n", + " state = system.init\n", + " results[system.t_0] = state.babyboy\n", + " \n", + " for t in linrange(system.t_0, system.t_end):\n", + " state = update_func(state, t, system)\n", + " results[t+1] = state.babyboy\n", + " \n", + " return results" + ] + }, + { + "cell_type": "code", + "execution_count": 323, + "metadata": {}, + "outputs": [ + { + "ename": "AttributeError", + "evalue": "'NoneType' object has no attribute 'babyboy'", + "output_type": "error", + "traceback": [ + "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m", + "\u001b[1;31mAttributeError\u001b[0m Traceback (most recent call last)", + "\u001b[1;32m\u001b[0m in \u001b[0;36m\u001b[1;34m()\u001b[0m\n\u001b[1;32m----> 1\u001b[1;33m \u001b[0mresults\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mrun_simulation\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0msystem\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mupdate_func1\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m;\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m", + "\u001b[1;32m\u001b[0m in \u001b[0;36mrun_simulation\u001b[1;34m(system, update_func)\u001b[0m\n\u001b[0;32m 15\u001b[0m \u001b[1;32mfor\u001b[0m \u001b[0mt\u001b[0m \u001b[1;32min\u001b[0m \u001b[0mlinrange\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0msystem\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mt_0\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0msystem\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mt_end\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 16\u001b[0m \u001b[0mstate\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mupdate_func\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mstate\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mt\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0msystem\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m---> 17\u001b[1;33m \u001b[0mresults\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mt\u001b[0m\u001b[1;33m+\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m]\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mstate\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mbabyboy\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 18\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 19\u001b[0m \u001b[1;32mreturn\u001b[0m \u001b[0mresults\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n", + "\u001b[1;31mAttributeError\u001b[0m: 'NoneType' object has no attribute 'babyboy'" + ] + } + ], + "source": [ + "results = run_simulation(system, update_func1);" + ] + }, + { + "cell_type": "code", + "execution_count": 325, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "plot_results(popData, results, 'World population estimates')\n", + "#welp, gotta fix that!" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.6.6" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} From 94684a75faed6c2aa5d73bc11ae3b1f93b63de45 Mon Sep 17 00:00:00 2001 From: Bennett Taylor Date: Sun, 30 Sep 2018 23:51:41 -0400 Subject: [PATCH 04/14] Final Project --- code/Spanish Flu Final.ipynb | 453 +++++++++++++++++++++++++++++++++++ 1 file changed, 453 insertions(+) create mode 100644 code/Spanish Flu Final.ipynb diff --git a/code/Spanish Flu Final.ipynb b/code/Spanish Flu Final.ipynb new file mode 100644 index 00000000..cd072fae --- /dev/null +++ b/code/Spanish Flu Final.ipynb @@ -0,0 +1,453 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# What If The Spanish Flu Had The Same Impact as The Black Death?\n", + "\n", + "\n", + "A Simulation by Anna Letcher Hartman and Bennett Taylor\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Our project posed the question “What would happen if the Spanish Flu held the same effects as the Black Death?” What would the current population look like, and how would the population drop carry through the measured years? The model could demonstrate the effectiveness of the vaccines in reducing infection rates, and put historical information in a more easily understood context. For the model to be feasible we had to make the assumptions listed bellow.\n", + "Assumptions:\n", + "1.\t The biggest effect on birth and death rate around the time of the black plague was the black plague.\n", + "From the research we did this appears to be true, however without going much deeper it is impossible to know for certain.\n", + "2.\tIf 1/3 to 1/2 of the population of America died during the Spanish flu outbreak the rest of the events of the century would progress relatively unchanged\n", + "This assumption is vital to the feasibility of our model. Including it would be at the very least a PHD level problem. However it is blatantly false, the US would not have been able to join WW2 the roaring twenties would likely have changed in character severally if they happened at all. In short it would have completely changed the cores of US history.\n", + "3.\tThe population decline during the epidemic would be relatively linear\n", + "This is a simplification, but a decent assumption since our goal is just to kill a certain percent of the population.\n", + "4.\tThe growth curve accuracy 1900-1918 is unimportant to the models overall accuracy.\n", + " As long as the numeric population value at 1900 and 1918 are accurate, the changes made in the model by the introduced values will still be significant.\n", + "\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Reading and Ploting US Census Data from 1901 to 1990" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "%matplotlib inline\n", + "\n", + "from modsim import *\n", + "from pandas import read_csv\n" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "data/Census_Data.csv\n" + ] + } + ], + "source": [ + "filename = 'data/Census_Data.csv'\n", + "print (filename)\n", + "tables = read_csv(filename, header=0, index_col=0, decimal='M')\n", + "tables.columns = ['Population', 'Change', 'Rate']" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [], + "source": [ + "def plot_results(census, timeseries, title):\n", + " \"\"\"Plot the estimates and the model.\n", + " \n", + " census: TimeSeries of population estimates\n", + " un: TimeSeries of population estimates\n", + " timeseries: TimeSeries of simulation results\n", + " title: string\n", + " \"\"\"\n", + " plot(census, '--', label='US Census')\n", + " # plot(un, '--', label='UN DESA')\n", + " if len(timeseries):\n", + " plot(timeseries, color='gray', label='model')\n", + " \n", + " decorate(xlabel='Year', \n", + " ylabel='US population (billions)',\n", + " title=title)" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "popData = tables.Population / 1e9\n", + "#change = tables.Change / 1e9\n", + "empty = TimeSeries()\n", + "plot_results(popData, empty, 'US Census Data')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Defining Update Function\n", + "\n", + "##### Defing global variabls and system object:\n", + "p_0 and init define the initial population of the simulation, the Alpha and Beta arrays hold a variety of constants that we use to fine tune out quadratick update function.\n" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [], + "source": [ + "p_0 = get_last_value(popData)\n", + "init = State(babyboy=p_0)\n", + "alpha_array_global = linspace(0,0.025,20)\n", + "beta_array = linspace(0,-0.0018,20)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Initializing System Object" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [], + "source": [ + "\n", + "system = System(birth_rate = 0.0292,\n", + " #1918 birthrate (does not change, black death did not affect birthrate)\n", + " death_rate =.0172,\n", + " death_rate1= .0392,\n", + " #death rate in 1900\n", + " death_rate2 = .175, #code do be duplicated and run alongside curret, replacing .028 with \n", + " \n", + " t_0 = 1900,\n", + " t_end = 2018,\n", + " init=init,\n", + " alpha_array= [0.019, 0.01578947, 0.01],\n", + " beta_array= [-1.23157895*10**-3, -1.13684211*10**-3, -1.04210526*10**-3])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "##### Update Function\n", + "We used a set of quadratick equations to model population growth after 1922, during the plage years, between 1918 and 1922, and in the short years before that we uesed a liner model. In this model we used the actual spanish flue updats so we could tweek our model to fit the Data." + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "scrolled": true + }, + "outputs": [], + "source": [ + "def update_func1(state, t, system):\n", + "\n", + " births = system.birth_rate * state.babyboy #constant birthrate throughout, in accordance with historic data\n", + " \n", + " #change death rates at start of Spanish Flu\n", + " \n", + " if 1918 < t < 1922: #area of affect: set to Spanish Flu death rate\n", + " deaths = system.death_rate1 * state.babyboy\n", + " babyboy = state.babyboy + births - deaths\n", + " return State(babyboy=babyboy)\n", + " \n", + " if 1922< t <1950: #model of population before babyboom\n", + " net_growth = system.alpha_array[0] * state.babyboy + system.beta_array[0] * state.babyboy**2\n", + " #net_growth = 0.0022675*t**2+2.6804*t+300.760\n", + " babyboy = state.babyboy + net_growth\n", + " return State(babyboy=babyboy)\n", + " \n", + " if 1966 > t > 1950: #model of population during babyboom\n", + " net_growth = system.alpha_array[1] * state.babyboy + system.beta_array[1] * state.babyboy**2\n", + " babyboy = state.babyboy + net_growth\n", + " return State(babyboy=babyboy)\n", + " \n", + " if t > 1966: #model of population after babyboom\n", + " net_growth = system.alpha_array[2] * state.babyboy + system.beta_array[2] * state.babyboy**2\n", + " babyboy = state.babyboy + net_growth\n", + " return State(babyboy=babyboy)\n", + " \n", + " else: #model of population before SF: linear for numeric accuracy\n", + " deaths = system.death_rate * state.babyboy\n", + " babyboy = state.babyboy + births - deaths\n", + " return State(babyboy=babyboy)" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [], + "source": [ + "state = update_func1(init, system.t_0, system) #sets up recursion variable" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Running the Model" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [], + "source": [ + "def run_simulation(system, update_func):\n", + " \"\"\"Simulate the system using any update function.\n", + " \n", + " init: initial State object\n", + " system: System object\n", + " update_func: function that computes the population next year\n", + " \n", + " returns: TimeSeries\n", + " \"\"\"\n", + " results = TimeSeries()\n", + " \n", + " state = system.init\n", + " results[system.t_0] = state.babyboy\n", + " \n", + " for t in linrange(system.t_0, system.t_end):\n", + " state = update_func(state, t, system)\n", + " results[t+1] = state.babyboy\n", + " \n", + " return results" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "results = run_simulation(system, update_func1); #setting run_simulation result to be saved as \"results\"\n", + "plot_results(popData, results, 'World population estimates')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### New Update Function and Results\n", + "In this version we used the Black Plage death rate." + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [], + "source": [ + "def update_func2(state, t, system):\n", + "\n", + " #print(type(state.babyboy))\n", + " births = system.birth_rate * state.babyboy\n", + " \n", + " #change death rates at start of Spanish Flu\n", + " \n", + " if 1918 < t < 1922:\n", + " deaths = system.death_rate2 * state.babyboy\n", + " babyboy = state.babyboy + births - deaths\n", + " return State(babyboy=babyboy)\n", + " \n", + " if 1922< t <1950:\n", + " net_growth = system.alpha_array[0] * state.babyboy + system.beta_array[0] * state.babyboy**2\n", + " #net_growth = 0.0022675*t**2+2.6804*t+300.760\n", + " babyboy = state.babyboy + net_growth\n", + " return State(babyboy=babyboy)\n", + " \n", + " if 1966 > t > 1950:\n", + " net_growth = system.alpha_array[1] * state.babyboy + system.beta_array[1] * state.babyboy**2\n", + " babyboy = state.babyboy + net_growth\n", + " return State(babyboy=babyboy)\n", + " if t > 1966:\n", + " net_growth = system.alpha_array[2] * state.babyboy + system.beta_array[2] * state.babyboy**2\n", + " babyboy = state.babyboy + net_growth\n", + " return State(babyboy=babyboy)\n", + " else:\n", + " deaths = system.death_rate * state.babyboy\n", + " babyboy = state.babyboy + births - deaths\n", + " return State(babyboy=babyboy)" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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0T21tbfT2Wt1nKysrue2221i3bh3r1q1j8+bNBAQEUFFRAUB4eLhHDIGBgTgcDsLDw3niiScoKytj27ZtbNq0iUcffXTccSLHe5xSE8XhcA77fQsJDuAz5xrWGO2pN1m0iW8cG3JPrNntrLVLhjX7TYT4+HgqKytZsWLFYFl/fz+VlZWDqwV/9rOf5dxzz+Wqq64CICYmhs985jPs378fERl2zpNOOomQkBB27NjBli1bPLbdd999lJWV8cQTTxAXF8edd97J6aefPri9sLCQ1NRUPvzww1FjbmlpGXx+1dfXx5tvvskNN9zAunXr8Pf390iMTqdzcEaIsY4b+txKqYnW22fn37vKWBAVysnLF3tsc2/mUxNPP90Z6sILL+TBBx+kuLgYgObmZn74wx8SGxvLypUrATj//PN55JFHePnll+nt7aW3t5ddu3axY8cOzjnnnGHnDAoK4uabb+bOO+9k+/bt9Pf309nZyeOPP87TTz/NddddB8All1zCQw89RFVVFXa7nV/+8pdcccUVdHd3jxlzY2MjX/ziF3n33XcJDAxk0SKrG+78+fNJTk6mt7eXF198EbvdzhNPPEFHR8e4xyk12bbvPkJpVSvv5ddw6GjT+AeoCaM1qBnquuuuw9/fn6uvvpqGhgaCg4M5+eST+e1vfzv4DOnKK68kJCSEhx9+mFtuuQWn00lGRgZ33nknmzZtGvG8n/70p4mIiODRRx/lv//7v3E6neTk5PDrX/+a9evXA/CVr3yF/v5+rrjiCpqbm8nKyuLXv/41kZGRY8aclpbG3XffzR133EFtbS3R0dHcfvvtZGZmAnD77bdz33338a1vfYutW7eyZs0ar45TarIcrWmjuOLY3I6NLd0w8Q0iahS2udSOb4xJBUq3b99OUlLSsO35+fksW7ZsyuNSE0t/jmoiOBxO/vxyIQ0tXQBkp8SwZUOyj6OaucrLywdabtJE5LA3x2gTn1JKjSD/cONgcgoM8OPkFYvHOUJNNE1QSik1RE+f3WOGiLXZiwgPHXv4hZp4mqCUUspNT5+d53eW0NVjDeMIDw1kdVasj6Oam7SThFJKuXT39PPszhJqmzoHyzatStTu5D4ypQnKGLMKeARYCZQAXxCR3SPs9zHgXiATqAXuE5FHXdvSgSKg0+2QP4nIlyY5fKXULLfjwwqP5HT6qkSWLonyYURz25QlKGNMEPAM8ACwGfgk8C9jTIqItLrttwT4G/B51/5rgZeMMYdF5CVgDfCuiJw8VbErpeaG01YlUN3QQXtXH2euSSI3fYGvQ5rTprIGdSYQKCIPuF7/yRhzPfBp4DG3/VKBP4rIU67Xu40xrwGnAS9hJaw9UxGwUmpuCQ8N5KLT06lv7iIrOdrX4cx5U5mgcoChK+wVACvcC0RkJ7Bz4LUxJgY4Hfi9q2gNMM8YUwiEAy8CN4tI8yTFrZSaJex2B312ByFB1qWvrbOXiLAgj31iIkN0yYxpYioTVDiez41wvQ4b7QBjzHzgWWAXVnMfQBPwFlZTYSjwO+CXwKcmOF6l1CzS1NbNcztLaO3oJS46jIVRIRSUNXHhqWmkLB57FhTlG1PZNaUDK6G4CwPaR9rZGJMFvAPUAJeJiANARD4jIneLSIuIVAO3AhcbY7RH4gT4+c9/zrXXXjvufuXl5RhjaG1tHXdfpXytvauPZ1+3khNAbVMneaWNOBxO/vnOYeqaunwcoRqJVxd1Y8xFwPnAOiAOsAPVwG7geRF52YvT5AE3DSnLxqoBDX2/zVg1pkeAW0XE6SoPA+4C7heRGtfuQUC/KyallPLQ3dPPs68X09bZO+L2BfNDCQ/TQbjT0ZgJyhizDbgTq3nu38BTQAPgDywEVgG/N8a0At8VkWHJxs2rgM0YcxPwIFYvvpWuc7q/ZwbwPHCbiPzcfZuIdLq6oC9wdbCIwuqO/tuBJDZXlJeXc8kll3DjjTcOLkNxww034OfnxyOPPEJvby/XXHMNV111FW+99Rb3338/paWlJCYmct1113HeeecNnue2225j3759pKenk56e7vE+Tz75JL/+9a9pbGxk5cqV3HXXXSxZorNlqpmhqa2bl94po7HVmmnfz2bj3JNTcDicHKluZV5oIOtz4nWc0zQ1aoIyxrwMNAL/CbwxWgIwxtiAc4FrjDFXicjZI+0nIr3GmPOxakXfBg4Dl4hInTHmVuAKEckFrgMigO8bY77vdoqHROSbwP8Bfg5UYtWa/gTc/BG+Z68VFxdTWFg44sKAkyEgIICsrCwyMjK82r+trY0DBw7w6quv8vLLL3PzzTezdetWtm/fzs6dO7nhhhtYsWIFV199NT/4wQ8499xz2b17N9deey2xsbGsXbuWG2+8kZycHB577DFEhC9+8YuDayz961//4mc/+xmPPvoomZmZPP7443z5y1/m+eefn8yPQakJ4XQ6efHNwzS1WcnJZrOxZUMyS5OscU3aS2/6G6sG9U0ReX+8E7gS10tYY5XGXD1ORA4Aw9Z5EJHvAd9zff114OtjnOMwcNF4cU2EkpKSKUtOYC04WFJS4nWCArj22msJCgrilFNOwW63s23bNoKCgjjrrLOw2+385je/YePGjVxwwQUAnHLKKVx00UU89dRTxMXFceDAAX71q18RFBTEihUr2Lp16+DKuE8++STbtm0jNzcXsJbZ+P3vf8+uXbtISUmZ+A9AqQlks9k4c20ST+8oxs8GZ6xJ0qQ0w4xarx0vORljFo5wzHsTEdR0kZ6eTkDA1PW9CAgIGNbENp6oKOtu0N/fH4CIiAgA/PysH213dzcJCQkexyQlJVFVVUVdXR3BwcFER0d7bBtQWVnJww8/PLhy7fr162lra6OysvKjf3NK+UBibDhnnJTIZWdnkZOmg25nGm87ScQCPwJ+DBwAXgA+Zow5DFwoIgWTFaAvZWRkfKTajC/YbLYxt69bt4733vO8bzh69CgLFy5k0aJF9PT00NDQwIIF1h9vTU3N4H5xcXFs27aNz3zmM4NlxcXFJCQk0NDQMIHfhVInxul08n5BLQujQkkd0mV8ecawe2k1Q3j7ZPAhrB53bcB/YM3qcB7wOvCzyQlNTYRNmzbx3nvvDS6l/vbbb/Pcc89x0UUXkZiYyIYNG/jBD35AV1cXBQUF/P3vfx889pJLLuHxxx+nuLgYp9PJc889x9atWz2SmFK+1tndx7M7S3jnQBXbdx+hvavP1yGpCeJt+9XHgM0iUmKM+RHwDxH5tzGmFJ12aFoLCAjg4Ycf5v777+e2225j0aJF3H333YNLvv/kJz/htttu49RTTyUhIYEtW7bQ2NgIWAmqtbWVa6+9ltraWpKTk3nooYdITU2lvLzcl9+WUgCUVrbwyntHB5fG6OrpZ09hLZtWJfo4MjURvE1QNqDTGBMInAN8zVUeDugINx9ISkpCRAZfR0ZGerwGPF6fdtppI55n4cKFPProo6O+z7Zt29i2bdu476/UVOrrt7NzTyV5pceamm02G2tMHBtz430YmZpI3iao14H7gGYgEHjGGLMS+CnwyiTFppRSw1TUtbN995HBWSHAmuT1nPXJLFkU4cPI1ETz9hnU1ViDc9cAnxaRRuBzWM+kbpik2JRSalC/3cHOPRU89VqRR3JamhTFZz5mNDnNQl7VoESkCtg6pOyWSYlIKaWGcDqdPPt6MZX1HYNlwUH+bF6dSFZy9Li9WdXM5G03cxtwCdZaTIFYz6QGabJSSk0mm83GiqULBxNUSnwkZ61bQniozqE3m3n7DOoBrCmI9gJDp6+eVXPgOZ1OvRubwZzOWfXrqNxkLommoq6D2KhQctJi9O90DvA2QV0OfFVEfjWZwfhaYGAgXV1dhIWNukSVmub6+vqmdPYPNTmO1rQRHOhPXIzn3+KZa5JGOULNRt52kggGdkxmINNBXFwcFRUVdHZ26p34DORwOKipqWH+/Pm+DkUdJ4fDyTsHqnh2Zwkv7Sqjt09X0ZnLvL3V/A1wszHmOhGZutlTp1hkpDVFSmVlJX19Ohp9Jpo3bx4LF+rUNjNRe1cf/3qnjMp6aw3TlvYe3t5fxRlaa5qzvE1Q6cAngE8ZY8oAj5W/RGTDRAfmK5GRkYOJSik1NUoqrBkhunuP3f8mxUWwPmeRD6NSvuZtgtrn+qeUUhPGbnewc28lB4rrB8tsNhsbc+NZY+Lw89OOEHOZt+Og7p7sQJRSc0tndx//eOswVQ3HxjaFhwZy7sYUEmLDfRiZmi687u7kWg33ViAXq3NFAfCAiPxpkmJTSs1SdU1dvPBmicfM4xlJUZy1NomQIO2FqSxe9eIzxmwDngb2A9djjYn6AHjcGHPF5IWnlJqNyqpbB5OTzWZj06oEzjs5RZOT8uDtb8N/A18XkYfcyv5gjNkH/BfwhwmPTCk1a63NjqO6oYOq+g7OPTmFlHjtmKSG8zZBpQD/HKH8ZeAnExeOUmo2GjpDi81mY8uGZLp6+omOCPFhZGo683ag7iGsdaCG2gIcmbhwlFKzjZQ18uzOEuwOz8HvIUEBmpzUmLytQf0A+I0xJhd4x1V2CvBl4NrJCEwpNbN19/Sz48NyDh1tBmDXgSpOXZng46jU8XI4HNhstimdA9HbbuZ/dM1o/jWspNQF5AOXi8jzkxifUmoGKqtq5ZX3jtLRfayXXkllC+tz4gkM8LbhRk0HfX19HDhwgMrKShYtWsS6deum7L297jIjIn9AO0MopcbQ1+/grX2V7HcbeAuwLDWG01cnanKaYerr6/nwww/p7u4GoLq6mv7+/imbkHnUdzHG/BC4W0Q6XF+PSteDUkrVNnby8u4jNLZ2D5aFBgdw9rolpCXoBL4zid1up6CggJKSEo/ypUuXTulqAWO903qsxQkHvh6NTvut1BzWb3fw7sFqPiys81gFID1xPmeuSSIsRBcVnEmam5vZs2cPbW1tg2VBQUGsWrWK+Pj4KY1l1AQlImeN9LVSSrnLK23gA6kdfB0Y4MfpqxNZlqqLCs4kDoeDoqIiCgsLPW404uLiWL16NcHBwVMe01hNfDnenkRE8iYmHKXUTJObvpC80kbqm7tIigvnrLVLmB8+9Rczdfza2trYs2cPzc3Ng2UBAQHk5OSQnJzssxuNsZr4DmA1340XmRPwn7CIlFLT2tBBt/5+Ns5et4S6pi5din2GcTqdlJSUUFBQgMPhGCyPiYlh9erVzJs3z4fRjZ2g0qYsCqXUtOd0OjlQ3EBlfTvnbkzxSERx0WHERYeNcbSabjo6OtizZw+NjY2DZX5+fhhjyMjImBY3GmM9gyqbykCUUtNXv93B9t1HBgfdxi+Yx6rMWB9HpY6H0+nk8OHD5OfnY7fbB8vnz5/P6tWrp9WCrWM9g6rDyx56IhI3YREppaaVrp5+Xnyz1GPdpsIjTazIWKgLCs4wnZ2d7Nmzh4aGhsEym81GZmYmmZmZ+PlNr3FqYzXxfQPtQq7UnNbU1s0Lb5TS3N4zWLY8fQGbVidqcppBnE4nZWVl5Ofn09/fP1geERHB6tWriYqK8mF0oxurie+3UxiHUmqaKa1s4d/vHqG3z2oGstlsbFqZwKosbdqbSTo6Oti7d++wWtPSpUvJysqadrUmd2M18b0LfFxEmowxuxmjNiUiGyYjOKXU1HM4nLybV817+TWDZQH+fnxsQzIZSdPzTlsN53Q6KS0tpaCgwONZ03SvNbkbq4nvBWCgXj8hE8IaY1YBjwArgRLgCyKye4T9PgbcC2QCtcB9IvKoa1sU8CvgY0A7cLuIPD4R8Sk117V19vLiW6XUNXUNlkXOC+K8U1K1l94M0tbWxt69e2lqahosmym1JndjNfHdPdLXx8sYEwQ8AzwAbAY+CfzLGJMiIq1u+y0B/gZ83rX/WuAlY8xhEXkJ+AVgBxYDWa5tJSKy40RjVGquCw0OoK//2HiYJYsi+PjGFEKCdSn2mcDhcFBcXExhYaHHuKbIyEhWrVo1I2pN7rz+rTPGnApcA+QCvUAeVs0m38tTnAkEisgDrtd/MsZcD3waeMxtv1TgjyLylOv1bmPMa8BpxpidwGVAroh0AnuMMY8BXwE0QSl1ggL8/ThnXTLPvF7M+pxFnJQVp50hZoiWlhb27t1LS0s31XEeAAAgAElEQVTLYJmfnx9Lly6dlj30vOFVgjLGXA78L/As8BeslXhPxkoQl4nIc16cJgdrDSl3BcAK9wIR2QnsdHvvGOB04PdYNSYn1gq/7ue42JvvQyl1jMPhpLSyZdhzpcUL5/H5C3MI1VrTjGC32yksLKS4uNhjDr2oqChWrVo1rcY1fVTe/gbeC9wkIj93LzTG3AzcB3iToMKBziFlncCoDdvGmPlYSXEXVnPfqUC3iLh32BjzHEqp4Vo7evn3rjKqGjo4d2MKWcnRHts1Oc0M9fX17Nu3j46OY2PU/P39McaQnp4+LWaDOBHe1vkWAy+NUP4ckOLlOTqA0CFlYVgdHYYxxmRhLS9fA1wmIg7XOUJcq/uOew6l1HBF5c38+d8yOPB2xwfltHf2+jgq9VH09vayd+9e3n77bY/ktGDBAs4444xpM1XRifI2Qf0d6/nTUJ8HXvTyHHmAGVKW7Sr3YIzZjFVrehorOQ2sgHYIa/Ja93kCRzyHUsqT3e5gxwfl/PPtw/S4xjb52WycZOJ0zaYZwul0UlFRwWuvvcaRI0cGywMDA1m1ahWnnHKKzyd4nUhjjYN60u3lPOCzxpiPYyUOO1ZX8ZOA//HyvV4FbMaYm4AHsXrxrQSect/JGJOB1a39tqFNiiLSbox5Cvi+MeaLQAbwZeAqL2NQak5q6+zlH28dprbpWCt75Lwgzt2YQvyC2XNBm806OzvZv38/tbW1HuWLFy9m+fLlhISE+CiyyTNWQ3PHkK+fcHvtDxx0/fN2vr5eY8z5WOOgvg0cBi4RkTpjzK3AFSKSC1wHRGAloe+7neIhEfkmcDXwMFAGdAPfFZF/eBODUnNRRV07/3z7MF09x6a4yUiK4qy1SYQE6bOm6c7hcFBaWoqIeAy4DQkJYcWKFVO+yu1Usrn3+pjtjDGpQOn27dtJSkrydThKTbr9xfXs/LACh+vv3M9m47RVCaxcunBWPKOY7Zqamti3bx+trYNDRbHZbKSkpLBs2TICAmbODUZ5eTnnnHMOQJqIHPbmmLGa+B4H7hCRcm9O5Lr4f1tEtnmzv1JqcrV39fHWvsrB5BQWEsh5p6SQsDDcx5Gp8fT19ZGfn8+RI0c8uo5HRkaycuVKoqOjxzh69hgr/T4D7DDGvI/VSeIlEWly38EYEwecAXwO63nU1yYrUKXURxMeGsh5J6fywpulxEaHcv4pqYSHBfk6LDWGgU4QeXl59PQcm0He39+frKws0tPTZ+SA2+M11lRHTxtjXsZ65vM94A/GmGqgHqsnXSwQB5RiPVf6rIh0jHY+pdTUS1kcyYWb0khYGE5gwNy5sM1EbW1tHDhwgPr6eo/yRYsWsXz5csLC5t5wzzEbMEWkHbgfuN8Yk4s1L94iwAFUA++LSMGkR6mUGld7Vx99/XaiIzx7c6XEz9yZBOaC/v5+ioqKKC4u9pg/LzQ0lNzcXOLj4+fs80Kvn7CJyECvPaXUNNPc1sOzO4sBuPSsTMJDdVzTdOd0OqmpqeHAgQN0dR2bPd5ms5GWloYxZkZ1gpgMc/u7V2oWaGjp4pnXS+js7gPghTdLuPzsLJ3kdRrr6OjgwIEDw8Y0xcTEsGLFihk9f95E0gSl1AxW09jJcztL6O61xjgF+Ptxcu5iTU7TlN1u59ChQ8Oa84KCgli2bBlLliyZs815I9EEpdQMVd3QwbM7SwaXZA8K9OcTp6WREKvdyKcbp9NJdXU1Bw8eHNacl5ycTHZ2NkFB2sNyKE1QSs1ANY2dHskpJCiAi09PJy5m7vX0mu7a2to4ePAgdXV1HuVRUVGsWLFixi0iOJW8XQ8qFPgqVi++QKxu5oNE5FMTH5pSaiQ1jZ08+3rxYHIKDQ5g6+YMFkYNXSxA+VJ/fz8iQmlpqcdgW23O8563NahfApcC/wRax9lXKTVJKuvaef7NUo+akyan6cXpdFJeXk5+fr7HYNuBKYqMMdqc5yVvE9R5WANxn5nMYJRSYztY0uCRnC45Q5PTdNLU1MSBAwdobm72KF+wYAHLly/X3nkfkbcJqg8onMxAlFLjO3vdErp6+mlo6ebizeksmK/JaTro6uqioKCA8nLPqUtDQkLIyckhISFBm/OOg7cJ6ifAvcaYL4lI3bh7K6Umhb+/H+efmkZXTz+R87SZyNfsdjvFxcUUFRV5LIXh5+fH0qVLycjImPODbU+Et5/cp7AWF6w2xrQBHutDi0jcRAemlLIG4Q6tJQUG+BEYoMnJl5xOJ5WVleTn53t0GwdrAcGcnJw5OXfeRPM2QT04qVEopYbJL23klfePsjE3nnXLFvk6HOXS1NTEwYMHaWryWNyByMhIli9fzoIFC3wU2ezjVYISkcHVdI0xkYCfiDSPcYhS6gTsL65nxwfW84x3DlQRGhxAbrpe+Hyps7OTgoICKioqPMqDg4MxxpCcnKzPmSaY142jxphrgFuBBNfrWuCnInLvJMWm1Jy0t7COnXuPXQRjo0JJS9DeX77S19dHUVERJSUlHtMT+fn5kZaWRmZmJoGBOjnvZPB2oO7NwB3Ad4E3sAbqngb8lzGmS0R+OnkhKjV37C+q90hOi2LCuOj0dEKC9EH7VHM4HJSVlVFYWEhvr8djd33ONEW8/a2/DviqiPyvW9mbxpgy4B5AE5RSJ+hgSQM7PjzWTXnxgnlcdHo6QYH+Poxq7hmYN6+goID29naPbVFRUeTm5hITE+Oj6OYWbxNULLB7hPL3gaSJC0epuSmvtIFX3z86+Dpek5NPNDU1kZeXR2Njo0d5WFgY2dnZOp5pinmboA4AlwPfH1L+aUBX1FXqBBws8UxOcdFhfGJTmianKdTe3k5BQQFVVVUe5YGBgWRmZpKamoq/v/48ppq3CepO4AVjzCnA266yU7CmQLp0MgJTai7o7O7jjSEdIi7WZ05Tpqenh8LCQsrKyjwmdPXz8yM1NZXMzEydN8+HvO1m/i9jzDnADcCVQBeQD6wXkb2TGJ9Ss1pYSCAXnJrGC2+WEhMZwsWbNTlNhf7+foqLiykuLvaYAQIgISGB7Oxs5s2b56Po1ACv/xJE5HXg9UmMRak5acmiCLZuziA6MliT0yRzOBwcPnyYQ4cODeuZt3DhQpYtW6brM00jo/41GGOeBL4kIq2ur0el60Ep5R2n00l3r53QYM8/vcUL9W59Mg0sgSEiw6YmioyMZNmyZcTGxmoHiGlmrNu1DsDp9rVS6gQ4nU7e2l/FoSNNXHpWpk72OgUGuoyLCG1tbR7bwsLCMMaQmJioiWmaGjVBich/ur38FlAuIg73fYwx/sDqSYpNqVnD4XCy48NyDpY0APD0jiIuOzuTsBCdgWAyOJ1O6uvrKSgoGLY2U3BwMJmZmaSkpODn5+ejCJU3vG3wLgXigaFLbSQDOwEdTq3UKPrtDl5+9whF5cculLFRoQRrN/JJ0djYSEFBAQ0NDR7lAQEBZGRkkJ6erktgzBBjPYP6AvBV10sb8JIxpn/IbvHA4ckJTamZr7unnxfeLKWq4VgreXZKNGevS8bPT5uVJlJzczMiQm1trUe5v78/qampLF26VLuMzzBj3Ub8GWuWCBuwDtgOuM/74XS9/uukRafUDNbS3sNzO0tobu8ZLFuVGcumVTobwURqbW1FRKiurvYot9lsJCcnk5WVRUhIiI+iUydirGdQHcC3AYwxh4E/iUjPaPsrpY6pbezkuTdK6OqxGh1sNhubViawKivWx5HNHm1tbRQWFlJZWelRbrPZSExMxBijk7nOcF6vB2WMOckYkwMMNJzbgGBgrYhcPVkBKjXTlFW38s+3D9PXb/Up8vez8bGNKSxN0vE1E6GtrY1Dhw5RWVnpMfsDWINss7KyiIiI8FF0aiJ5u9zGbcB3sJr05gEtwHzX5hcnJzSlZqayqtbB5BQc5M+Fp6WRsDDcx1HNfO3t7Rw6dIiKiophiSk+Ph5jDJGRum7WbOJtV5argW+IyP3GmHLgZKAf+Bsjz3Ku1Jy1aVUirR29NLR0c9Hp6cRE6vOPEzFWYlq0aBFZWVk6+8Ms5W2CisdKRgB7gFNE5C/GmFuA3+J6VjUeY8wq4BFgJVACfEFERk1wxpgNwPMiEudWFgy0Ae7zlLwlIud6+b0oNan8/Gx8/OQUevsczAvVcU7Ha6ymvLi4OIwxmphmOW8TVB2wAKtLeSGwCvgLUIFrCfjxGGOCgGeAB4DNwCeBfxljUkSkdci+NuCLwI9GONUKoFFE4r2MXalJ43Q6Ka1sJS0h0qNnXmCAP4EBOs7peLS2tnLo0CGqqqpGTExZWVlER0f7KDo1lbxNUM8AvzTGfBF4FXjIGPNvrCRT5uU5zgQCReQB1+s/GWOux1pT6rEh+94NXIi1Wu/tQ7atxarFKeVTTqeT1z+sYH9xPSdlxXHqysXaffwENDc3c+jQoWHdxUET01zlbYK6GfgxsBz4A1Zi2o41R99/eHmOHKwlOtwVYNWIhnpERO40xpw5wrY1QJwxZh+wCGuG9a+JSMUI+yo1Kex2B6+8dxQ50gTAh4W1LIwKwaToUuAfVWNjI4cOHRo2wBb0GdNc5203806OzSoBcJWr9tMtIkNnlxhNONA5pKyTEaZJEpHKoWVuOoA3sZ579QE/A54CNngZh1InpKunn3+8VUpl/bHZITKXRJO5RO/uvTUwV96hQ4eGTUkEsHjxYjIzM5k/f/4IR6u5Yqypji7w5gTGGETEm67mHUDokLIwPGenGJeIfH3I+38dqDPGLBGRo6McptSEaGzt5oU3S2lxmx0iJy2GM9Ys0amLvDAwu3hRUdGwSVxtNhsJCQksXbpUu4srYOwa1PNensPJscG7Y8kDbhpSlg38zsv3AcAY823gf0VkoLlwYHKt7o9yHqU+qrLqVl56p4zePmsFVpvNxikrFnNSlq4jNB6Hw0FlZSVFRUXDlr2w2WwkJSWxdOlSwsN1vJg6ZqypjiZ6HvpXAZsx5ibgQaznWCuxmuc+ipXAOmPMZ12vfwq8ICJDZ1pXasLsL6rn9T3HxuEE+vuxZUMyGTo7xJjsdjtHjhyhuLh42EKBfn5+JCcnk5GRoVMSqRF5O5PEmL89rmdUYxKRXmPM+VjjoL6N1WX9EhGpM8bcClwhIrlehPNFrOdORVjxvwB8xYvjlDouewpreWPvscei4aGBXHhaOrHRQ1us1YDe3l4OHz5MaWnpsKXVAwICSE1NJT09neDgYB9FqGYCb3vxtXNsdd2ReDXgQ0QOAJtGKP8e8L0Ryl8DooaUNQBXePN+Sk2E5PhIQvJr6e7tZ1FMGBeelqYLDY6is7OT0tJSysrKsNvtHtuCgoJIT08nNTWVwED9/NT4vE1QZ41wXAbw/4BvTmhESk0zMZEhfGJTGh8W1rFl/RIdgDuC1tZWiouLR5yOKCwsjPT0dJKTk/H3189Oec/bbuY7RijebowpAu4Dnp7QqJTygX67g7zSBo7WtHPBqakeHR/iF8zj/FPm+TC66Wegq3hxcTF1dcMfAUdGRpKRkUFCQoIura6Oy4mue1yJNQBXqRnL4XCSf7iR3XnVtHf1AXC0po3keO3qPJKBHnnFxcW0trYO275w4UIyMjKIjdXejerEeNtJYqQxUfOxmvj2TmhESk0Rp9NJWXUbb+2rpLHVc5TCwZIGTVBD9PX1UVZWRmlpKd3dnp+XzWZj8eLFZGRk6KwPasJ4W4MaaUxUL9ZSG9dPXDhKTY3Wjl52fFBOWbVnDSAsJJC12XHkpi/wUWTTT0dHByUlJRw9enRYxwd/f3+Sk5NJT0/XruJqwnn7DEobkNWs0NfvYH9RPbvzqumzOwbLgwL9WWPiWJUZS2CA/ro7nU4aGxspKSmhpqZmWMeH4OBg0tLSSElJISgoaJSzKHVivH4GZYzxB7ZgTRhrx5pRfIeIjNX9XKlpo9/u4A//zB98zgRW01RuWgwbcuO16zjWwNrKykpKS0tpaWkZtj0yMpL09HQSExO144OadN4+g0oF/gmkYi2v4QckA/uNMReKSM1kBajURAnw9yM5PoK80kYAFkaFcuaaJOIXaO+87u5uysrKKCsro6enZ9j2uLg40tPTWbhwoXZ8UFPG2xrUo0ApsFlEagGMMfFY8+g9BFw2OeEp9dE5HE7Kqltpbe9lVVasx7Y1ZhHlte2clBVHTvoC/Of4BK9tbW0UFRVRWVmJw+Hw2Obv78+SJUtIS0vTOfKUT3iboE4DNgwkJwARqTbG/D+spS+U8imn00lDSzeFR5ooPNJEe1cfAf5+mJRoQoKP/ZpHRQRz5fnL5nwtoKOjAxEZcTn10NBQUlNTSU5O1udLyqe8TVClWOOd8oaUJ2GNhVJqyjmdThpbuykub6GovHlYV/F+u4P8w42cZOI8yudycnI4HBw6dIhDhw4NS0wxMTGkpaURHx+vz5fUtOBtgnoAeNgYkwW8AfRjrWx7O9ZS8IPjpLxcG0qp41Za2UJxeQsVde20dfaOuE9ocADLUmN0tnE3LS0t7NmzZ9jgWl21Vk1X3iaox1z/3zPCttvdvvZ2bSiljltZVSsFZY3DygP9/UhNmE9WchTJiyLw99daAFi1psLCQoqKijxqTTExMeTk5BAdrSsBq+lJx0GpaWWg2a68pp3y2jaCAv352MYUj32SFkVwoMRaJjwwwI+U+EiWLokiJT5CJ3Idoqmpib1793osEujv7092djZpaWlzurlTTX8faS4+Y8w5QC5WN/N8YLuI9E9GYGpucDqdNLX1cLSmjcq6dirqOujuPfYrFRjgh93u8KgNJcWGc/LyxSTFhRMbHTbne+KNpL+/HxGhtLR0WK1p9erVzJunXevV9OftOKh4rBnL12AtNGgDUoACY8wW9959So3H7nBSXtNGcUUzR6rbPAbODtXX76C6sZPE2GPdnEOCA1i3bNFUhDoj1dXVsW/fPjo7j60jGhAQQHZ2NqmpqVprUjOGtzWon2J1jEgTkQoAY0wC8Efgx8DnJic8NRvZ7Q5efKsUu2PkSUhCgwNIiA1nSVw4SXERREXoqqve6OnpIS8vj/Lyco/y2NhYVq5cqXPlqRnH2wR1HnDWQHICEJFK1ziof09KZGpWcDic2B0Oj2dDQYH+LFkUweEqqzdZcJA/SbFWMkqInUdMZIje5X8ETqeT8vJy8vLyPJZXDwwMJDc3l6SkJP081YzkbYLqZuQl37XXnhpRX7+dA8UN7C+uJ3NJFKesSPDYviw1hujIENIT5rMoJgw/fY50XNrb29m/fz/19fUe5YmJieTm5hIcrLVPNXN5m6D+BfzYGPOZgXn3jDGLgPuBlyYrODXz9PbZ2VdUz57CusHODgdLGlmfE0+AW0eHjKQoHaN0Aux2O0VFRRQVFXlMURQaGsrKlSuJi4sb42ilZgZvE9Q3gFeAMmNMmassBdgHfHYyAlMzi93u4GBpA7vzaujqGd6xs7Glm7gYfQYyEerq6ti/fz8dHR2DZTabjfT0dLKysggIONGFspWaHrwdB1VtjFmJ9SwqB+gC8kXk5ckMTk1/TqeTQ0eb2XWwmpZ2z1mwI+cFscbEkZ0a41F7Usenq6uLvLw8Kis9ZxeLiopi5cqVzJ8/30eRKTU5vL7VEpF+Y8whIBhrPajiSYtKzQhlVa28tb+KhpYuj/KIsCDW5yzCpMToGKUJ4HA4KC0tpbCwkP5+tzFigYEsW7aM5ORk7QShZiVvx0HFAH8BzsRa6t0GBBpjngOuEJGOMQ5Xs1Rdc5dHcgoO8mdd9iJWLF2oNaYJUl9fz/79+2lvb/coT0pKIicnRztBqFnto6wHNR9YIyJ7AYwxa7Dm6Psp8KXJCU9NZ6uzYskrbaCrp5+VS2M5ycQSEqTPPyZCZ2cneXl5VFVVeZRHRESwYsUKFixY4KPIlJo63l5NPg6cMZCcAETkA2PMV7F6+GmCmuXqm7sIDw30WFspwN+P805OJTwsUJdLnyB2u53i4mKKioqw2+2D5QEBARhjSE1N1aUw1JzhbYKqA0a6ZQsC2kYoV7OE3eFkb2Eduw5WkbI4kvNP8ZwqR3vmTQyn00lVVRV5eXl0dXk+00tKSmLZsmWEhIT4KDqlfMPbBHUb1rpPt+O5HtT9WOtE5QzsKCJDFzVUM1RNYyevvn+U+mbrgllS0cLBkgaWZyz0cWSzS3NzMwcPHqSx0XMJkfnz57N8+XJiYmJ8FJlSvuVtgvqj6///4diMEgO30d8Dvut6rTNLzAKNrd3szqumqLzFYybs2OhQEuPCxzhSfRTd3d0UFBRQXl7u8TkHBQWRnZ2tvfPUnOdtgkqb1CjUtNDd088beyuQI80eF8wAfz825MazKjNWu41PgP7+fkpKSoY9Z7LZbKSlpZGVlUVgoD7TU8rbgbpl4++lZrKy6lZe2X2Ujm7PpS/SFkeyaXUi88O1O/OJcjqdHD16FBGhu7vbY1t8fDzLli0jPFxrqEoN0D7BiqbWbp7bWeJRlro4kg058doJYgI4nU7q6urIz8+ntbXVY1tkZCQ5OTnExsb6KDqlpi9NUIroyBBy0mLIK20kNDiAs9ctIS1Bp82ZCC0tLeTl5Q2bbTwkJARjDEuWLNHnTEqNQhPUHOB0OunpdT3rsEFTaw+LF3ou+X3qygTAxsnL43VM0wTo6OhARKioqPAoDwgIICMjg/T0dJ3UValxHNdfiDEmGWgSER0DNY319TuQskb2FdXT2HrsmYefzca2C5YRHhY0WBYSZNWc1Ilpbm6mrKyMo0ePenQ0sdlsJCcnk5WVpeOZlPLSmAnKGHM5cA2wTUTKjTEZwDPAMqDfGPMIcJOIOMY6j9v5VgGPACuBEuALIrJ7jP03AM+LSJxbWRDwIHAZ1qS1PxaR73vz/nNFZ3cf+4vq2V/cMLgmkzuH08n+4gZOWbHYB9HNTrW1tYgIzc3Nw7bFx8eTnZ1NRESEDyJTauYaNUEZYz4F/AH4HdbyGrheLwYuwJpB4jHga8CPx3sjV2J5BngA2Ax8EviXMSZFRFqH7GsDvgj8aIRT3Q0YIANrfsB/GmMqROR348Uw27V19vKh1JJX2ki/3fOewd/PRkCAHw6Hk9DgAMKCtXlpIvT09HDgwIFhS2AALFiwgGXLlhEdHe2DyJSa+ca6St0E3CIiPwEwxqwANgB3ichLrrLbsAbqjpugsGZCDxSRB1yv/2SMuR74NFaic3c3cCFwD3D7kG2fB64SkSagyRjzI+BqrEQ6p0lZE/uKPB/GR84LYtXSWLLTYggO1DHUE8XpdHLkyBHy8/Pp6zvWNd/Pz4+EhARSUlKIjo7WDhBKnYCxEtQK4Eq31+dizRTxrFvZPrwfxJsD5A8pK3C9z1CPiMidxpgz3QuNMVFYNTj36ZRGO8ecszxjAR9ILb19dmKjQlmTHUdGYhR+Orh2QrW0tLBv375hzXm6BIZSE2usBOUA3KdNPgeoFZE9bmVRgLdrQYUDnUPKOoFhA21EZHh7ybFzDBw35jlmu4q6dmIiQwh1a6oLCQpg06oE5oUGkrwoYtS7d7vdTnV1NTU1NYSHh5OZmal3+l7o6+tDRDh8+LBHB4h58+axYsUKHcuk1AQbK0HtBrYC9xljkrAS1G+H7PMF4H0v36sDCB1SFga0j7DvWOdgyHk+6jlmtO6eft7cV0n+4UaWpcZwzvpkj+05aSOvE+R0OmltbeXo0aOUl5d7NEvFxMSwcKFOADsap9NJRUUFeXl59PQcW9bez8+PpUuXsnTpUvz9tflUqYk2VoL6NvAPY8y5WL32uoAfABhj1gNfBbYB53n5XnlYz7XcZfMRnh2JSJMxphqrk8TAAJNsPJv8ZqW+fjsHihv4QGrp6rF65uUfbsSkRJMUN3rvsJ6eHioqKjh69OiwWQwGNDQ0aIIaRUtLCwcOHBg203hsbCzLly/XqYmUmkSjJigR2WGMORX4HPAh8CsRGZgP53JgLXCZiGz38r1eBWzGmJuwuol/Equ7+VMfMebfA98yxuzDavK7GWtV31mpt8/OvqJ69h6qG0xMAzKSooiKGD6mxuFwUFNTQ3l5OTU1NR7NUQMCAgLo77fON1LX6Lmut7eXgoICjhw54vH5hYSEkJuby+LFi7VZVKlJNmZfY9fzpj0jlN8C3PJR3khEeo0x52ONg/o2cBi4RETqjDG3AleISK4Xp7oTax2qg1jPyH7pOues0t3bz75D9ewtqjs2C4RLRFgQm09K9JiOyOl00tLSwtGjR6msrKS3t3fYOf39/Vm8eDFLliwhJCSEV199FbASlNPp1AsuVnIvKytDRIb1zktPTyczM1NngFBqiow1DipnlE19QLOI1H3UNxORA8CmEcq/h9VdfWj5a1gdMdzLuoHrXP9mpdLKFl557+iwGlPkvCDWmDiWpcbg72/1X+ns7KSiooLy8nLa20d+FBcTE0NSUhIJCQmDyzg4nU4CAwPp6+ujt7eXzs5O5s2bN+Lxc0VtbS15eXm0tXlOkBIXF0dubq425yk1xca6FTyA1a186G21E8AYUwXcKyIPTlJsc5bTiUdyigoPZk12HCYlBn8/G319fZSXH6WiooKGhoYRzxEaGkpSUhJJSUkjXlhtNhvR0dHU1tYCVi1qriaotrY28vLyBj+LAfPmzSM3N5e4uDitXSrlA2MlqNHGN/kB0cBpwN3GmHYR+e1EBzaXpSfOJyNxPjWNnZy6MoGlSVE4nQ5qa6opLy+ntrYWh2P47FIBAQEsXryYpKQkFixYMO5FNSoqyiNBJSYmTsr3M1319PQgIsOeMwUEBJCZmUl6ejp+fn5jnEEpNZnG6iQx1iKFpcAHxpgu4EaGdz9XXnA6nRSVNxPg7zdseYsz1iTh72ejtaWJffv2UlVVNdipwZ3NZiM2NpbExETi4+M/0vORqKhjradNTU3H/43MMHa7fXBFW/fPdGBCV2OMDrZVaho40ae9r2PNrac+ouqGDt7cW0lVQwfhoZwuWMkAABGbSURBVIEkxUUQGOCH0+mkqamJiooKqqqqPMbduIuKiiIxMZHExMTjvpi6J6iWlhYcDsesrjGMtaJtbGwsOTk5REZG+ig6pdRQJ5qg/ICRr6BqRPXNXew6WE1pZctgWVtnL7v2lhAT2ktlZSVdXV0jHjtv3rzBpDQRD+yDg4MJCwujs7MTh8NBW1sb8+fPvoUKnU4nNTU15OfnD+tIEhERMbiirT5nUmp6OdEEdRXezyQxp7W097DrYDWFR6ymNKfTiaO/G0dPMzEhPdSX+9E0wpx5ISEhJCQkkJiYyPz58yf8IhoVFUVnpzVzVHNz86xLUA0NDeTn5w9rwgwODiY7O1tXtFVqGhurm/m1o2zyw1rm4lSs6Y/OmYS4Zo2unn7ey69hf3E9drsDR3839q5m+rubiQiBuOgwgobMMh4UFMTixf+/vXsPz7us7zj+TvOkDaFNS85Jm0OTtl9LAR0nmW7KNWFO5doYAjJBBDm5qVMmsEE5qSAFdnGhCMM5hzIuxtAJbpU5Nx0TdDI2RQ6lX5KmadK0OfSQNukph2Z/3L8nfXJolkPz5Pe0n9d19WrzOzz9fZMn9/f53ff9+97lVFRUTGiyw3QsWrRoaKmInTt3Ul1dPWP/Vzp1dXWxfv16OjuHPw2RSCRYtmwZS5cu1fNMIjE33m/ojYfZ3gfsJFSXOMPdXzviV3WU2NzRzXM/28i+vT307+9iYP8uDvYfYEHeXCrL8sideygxJWfgVVRUUFRUlLaxoNRxqKOhosTu3btxd9ra2oZtnzNnDjU1NSxbtkwTIEQyxHiz+Ca6jIaMkJzosG1rK91tb9DXG4bp8nJzKC1ZSF5u+LYnEgnKysqoqKiguLh4ViYoJLsNBwcH6enpoa+vb+hh3kzS09ODu7N169ZRS60vWbIEM+O440bWKhaROFMfxxHS19dPe8c2du7oHDb7rnBBgp3d/ZQW5LEgb+5QUiovL6e4uHjWq2AnEgkWLlw4VO5ox44dlJaWzuo1TUZPTw9vvfUWW7ZsGVVzsKKiAjNTBQiRDKUENQ39/f20t7fzyzcaadjQQu7cLJaUDG8MC/JzKS1aQFlp6azeKY2nsLBwqHtv27ZtGZGguru7qa+vHzMxlZWVsWLFiqNuwofIsUYJapIOHDhAe3s7W7e20bBxM+079tDbF4q59vZlcaBvgHk52cybN4+ysjLKysrSOqY0FYWFhWzYsAFg1LIScbN7927q6+tHdeVBqJlnZsPG1UQkcylBTYK7U19fz+DgIF3dB2jtHP5MTc7ceRSVLObklbUUFBRkzPTl5LUmK6LHcRyqq6uL+vr6UZMfICSmFStWcMIJJ8zClYnITFGCmqDBwUEaGhqGPrUvnD+Pzq599JND3vwCTj25jtNPqmZuTuZ9S3NycsjPz2fXrl2xGocaHBxk+/btNDQ0jJouDlBaWsqKFSt0xyRylMq81nSWZGVlUVNTw+bNm1mwYAGlpaXUWC77B7J5x/LiUc8yZZrCwkJ27QrVLbZv3z6rCWpwcJC2tjYaGhrGnPpeXl7OsmXLlJhEjnJKUJOwatUqVq2ayJqKmaewsJDGxrBg8uGW8JhpAwMDbN68mcbGxlElibKysqioqGD58uUsWHD4Je5F5OihBCUAQxUrkuNQ/f39aau00Nvby6ZNm9i4ceOo4rhz5syhsrKSurq6Y3a9KpFjlRKUAGOPQ5WUlMzo/7lnzx4aGxtpaWlhYGD4svaJRIKamhpqa2tV+UHkGKUEJUNGjkPNRIJKTnxobGyko6Nj1FTx3Nxcamtrqa6uVq08kWOcWgAZkjoO1dnZycqVK4/Yaw8MDNDa2srGjRvZvXv3qP35+fnU1dVRUVER62fGRCR9lKBkyMhxqP3795Obmzut19y3bx9NTU00NzfT29s7an9JSQl1dXUzXrVdRDKPEpQMycnJoaCgYGgWX0dHB1VVVZN+nWQ3XlNTE21tbaO68bKzs1myZAm1tbWqkycih6UEJcOUlpZOOUH19fXR0tLCpk2bRk0TB8jLy6OmpoaqqqrYVaoQkfhRgpJhSkpKWLduHRDGoQ4ePDjumFCyO3DTpk20traOmo0HUFRUxNKlSyktLVU3nohMmBKUDDN//nzy8vLYu3cv/f397Nixg6KiolHH9fX10draSnNz89DMv1SJRILKykqqq6v1YK2ITIkSlAyTlZVFSUkJTU1NQOjmSyao5EKMzc3NbNmyZcy7pfz8fGpqali8eLGmiYvItKgFkVFGJqjKykra29tpaWkZc2wpOzubiooKqqurWbRokbrxROSIUIKSUYqKisjOzmZgYIDu7m6ef/75MY/Lz8+nqqqKJUuWaNKDiBxxSlAySnZ2NoWFhXR0dIzal0gkhu6WFi5cqLslEZkxSlAyptraWjo7OxkcHGTu3LkUFBRQVlZGeXm5xpZEJC3U0siYiouLOeecc+jv7+f444/XnZKIpJ0SlBzWdMsciYhMh6pyiohILClBiYhILClBiYhILKV1DMrM3g48CpwCNAKfcPeXJ3OcmdUCDcDelFOecverZ/jyRUQkjdKWoMxsLvB94EHgPcCHgR+ZWbW7757EcacC/+3uZ6Xr2kVEJP3SeQd1NpDj7g9GXz9lZp8GPgJ8YxLHnQa8MsVryAZoa2ub4ukiIjIVKe1u9kTPSWeCOhF4c8S29cDJkzzuVOB4M3sLmA88B9zg7l0TuIZygEsvvXQSly0iIkdQObBhIgemM0HNZ/i4EdHXeZM8bifwc0IX4HHA48BfAxdP4BpeBn4b2AqMLsUtIiIzJZuQnEbNOzicdCaoPYSEkioPGFkee9zj3P2SlO27zOwW4EUzS7h7/3gX4O4HgBcne+EiInJETOjOKSmd08zXATZi29ui7RM6zszyzOw+MytN2TcX6Ed3RCIiR5V03kH9B5BlZtcDXyPMzjsFeGaix7n7XjM7FyiMJk4sAtYA33L3wTTFISIiaZC2Oyh37wU+QEg4O4DVwPnu3mlmt5jZG//fcdFL/SFQAmwBXgNeBW5IVxwiIpIeWYODuvEQEZH4UakjERGJJSUoERGJJSUoERGJJSUoERGJJa2oC5jZmcBady+Jvi4GvgK8HzgA/C1wh7sPRPsvBr5MeCr6P4Er3L0j2jehiu3pMIW4Pgt8FigEHPi8u78Q7cvYuFLOeyfhQe3l7t4UbcvYuMzsXdH+lYRZrbe4+3ejfVXAN4GzgA7gM+7+XHojOmQKsV0J3AoUEUqdfd7dX4z2zXps0eMua4Dl0TXc7+5fN7NFwN8A5xKKC9zq7o9F52QBXwKuJTy/+RhwY7LAwHjtSszjygMeAP4AmAe8QPiZNE83rmP6DsrMsszsauBHhDdM0rcJU9lXAicBZwJfjM45kfDLcQWhIa8Hnor2JSux/wPhGa27CZXY89MQzpApxnUBcBNwHnAC8FfAWjMrzuS4Us6dTyiLlUjZlrFxmVk58APCs4ILgE8BT0SNN4T35KuE9+g1hKLLtTMfzXBTjO0UDjV4i4AngGfNLNlezWpsZlYJ/CNwV3R9fwTcY2bvJ/zeDBAa4w8Ba8zsvdGp1wIXEOqJLgfOAG6JXvOw7Uq6TCOuNcAyws9xMdDOoTZxWnEd0wkK+ALwx4QfCDD0aeD3gOvdvcPddwC3AddEn4AuA/7Z3V909/3AzcC7zWw5KZXY3b3P3Z8C3iBUYk+nqcRVDnzZ3de5+8Ho09EAoUjv2WRuXEkPAd8b8Xpnk7lxXQ781N2/7e6D7v5vhEZ+p5mtAE4Hbnf3Xnf/CfBPwFXpDQuYWmzLOdQ2ZRHeh/uic+MQWw3wpLs/E/2uvAw8D7wPuBC4zd33uvsrhBUYro3O+zjwoLtvjp7rvBO4Lto3XruSLjVMLa5c4E533+7u+wgfmt5pZonpxnWsJ6hH3f004H9StiW/J3tStg0AxYRPFSeSUp7J3fcCLYSGfKIV22fapONy94fd/eHkDjN7D6Fw7xtkcFwAZnYhUAfcP+L1Mjmu04AmM3vKzLaZ2a+AMnfvJsTV7O6p585GXDC12P4VeJ3wIH4vcC/wEXc/SAxic/cX3P2Tya/NrIBDRagHCXcJY13bsLYj2lcRnT9eu5IWU43L3a9Ndr9Gzgdej7oupxXXMZ2g3H3LGNt6CN0R95lZgZkVArdHu49j/GrrE63YPqOmGNcQMzuJ0O11q7u3k8FxmdliQmK6HDg44vSMjQsoIHRvPUG4+70HeMbM6ohJXDDl2HIJY6BnAccDf07o4isjRrEBmNlCwh3cS8D/AvtHlF1LvbaR1578d2zajqRJxpV63iWEoYLPRJumFdcxnaDG8THCJ7c3CYN6z0bbuxi/2vpEK7bPlvHiAsDMziMMcj7o7vdFmzM1rl2Ecac7kpMiRsjUuLoIEwt+6O5ro+7Jp4FfEsqExT0uGD+2O4E2d3/J3Q+4+yNAE3ARMYot6m78BWHM5UKgG8gd0bWcem0jrz3ZSMeq7ZhCXMmxxtsJY1Xnu/tPo13TiksJamzlwHXuXuruJwGtwJvR7emwautRf3pVtH2iFdtny3hxJWfx/T1wtbvfm3JeRsZFGJR9N/BVM+sCNkXHv2pmHyVD44p+XusJk1lSJSeArAOqzCy1YYhTXDB+bJWE2WCp+oE+YhJb1AX+EiGxXhiNr9QTxsyWHubaRr7f3gZs9bDY6njtStpMJS4zyyG0Gx8Hfsvd/z3luGnFpWnmY3sAeN3MbiB8M+8lDPwBPElYf+ps4L8IXSu/cve3zKyJiVVsny2HjStlKujvuPtLI86baCX62TJmXNE019zkQdFU2Z3AKe7eFM3iy7i4on2PA582s8sI78mLCNd+sbu3mNmvgbvN7GbgXYQZcb+Z7gDGMV5sawndf08TFre7FFgF/CAOsUXdqGuB1e7+UHK7u/eY2TOEmW9XEcY9ryHMYAP4O+AGM/sx4c7izmgbjNOuzHhAkWnE9SDwduAsP1TUO2lacSlBje0awiyVHYQuh4eibgbc/TUz+wTh2ZnFhE8bF0X7es3sA9G+LxK6Jc4f44c2Ww4bF/AXhE+tPzYbdlNxibuvzeC4DiuTf17u/msz+yChYX8EaAYucPeW6NwPE1aa7gC2AVe5++tpvv7xjBfbN6IxkCcJz0GtAz4Yo9g+RZjaf4+Z3ZOy/WHCrLxHCHfr+4G73f1fov2PAqWEFcHzgO8Qjb2N166k0aTjij70fZJwh7txRNuxeLpxqZq5iIjEksagREQklpSgREQklpSgREQklpSgREQklpSgREQklpSgREQklpSgRNIsKvDaGRXjHLlvtZn1mFnNLFyaSKwoQYmk3+cID8mnPgyJmS0FVhOe5G+ahesSiRUlKJE0c/c2wro4V1tY5TfpIeCV6G+RY54qSYjMgqgy9M8Iq8yeAfw+8DTwG+6eLMJ5JWHF1cWE4rer3f2H0b4EYfnwjwIVwHZCwc4b3H3AzJ4gLC+yklA77QJ3fz5tAYocAbqDEpkF0do61xIKvF4J/CVwV0py+hChoOrq6JhvEtZ7OjN6iZsJS3J/jLAC7c3AnwLnpfw3lwFfIayI+osZDknkiFOxWJFZ4u6vm9kDwNcJd0hrUnbfAqyJ1nkCaDCz04E/Ay4hrDZ7Rcq6O4+Z2U2EFUy/H21b5+5PzHQcIjNFCUpkdn2BsGLsl9y9L2X7icBpZnZbyrYconV03P1ZM3ufmd0PrCDcZdUA2SnHb5jJCxeZaeriE5lF7r4v+ue+EbsSwI3AO1L+rCKsfYSZ3UVYrmFO9PfvAiOXnBj5miIZRXdQIvG0Hqh294bkhuhuaj9wP/AnwOfc/fFo33GEhf+yxngtkYykBCUST/cBj5uZAz8BzgXuIIw/QVjo7zwz+zmwkNBVmM/opdJFMpa6+ERiyN2/A1wP3EQYd7oeuM7dvxsdcjlh9t5rwPeABuBbwGlpv1iRGaLnoEREJJZ0ByUiIrGkBCUiIrGkBCUiIrGkBCUiIrGkBCUiIrGkBCUiIrGkBCUiIrGkBCUiIrH0fyibky5A5EuqAAAAAElFTkSuQmCC\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "results = run_simulation(system, update_func2);\n", + "plot_results(popData, results, 'World population estimates')\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Results: Our simulation delivered a model in line with our preconceived ideas. The population dropped significantly between 1918 and 1920, leaving a little under a third of the population dead. The drop in population continued to hold a deficit through the remaining years. According to our model, he 2018 population would be 216.635,000, as opposed to the originally projected 2018 population of 334.7 million, or the currently recorded population of 325.7 million. This is a much higher discrepancy than we theorised. We thought the population would begin to catch up if not return near the actual value. If we were to redo our simulation we would make our data fit better from 1901 to 1918. " + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.6.6" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} From 633b7bdaf2d9949c641e0a8b5acf3131108b8ee5 Mon Sep 17 00:00:00 2001 From: Bennett Taylor Date: Thu, 25 Oct 2018 00:21:05 -0400 Subject: [PATCH 05/14] HIV Model v1 --- code/hiv_model.ipynb | 357 +++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 357 insertions(+) create mode 100644 code/hiv_model.ipynb diff --git a/code/hiv_model.ipynb b/code/hiv_model.ipynb new file mode 100644 index 00000000..70f5d73a --- /dev/null +++ b/code/hiv_model.ipynb @@ -0,0 +1,357 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Keep It Positive (Not Like That)\n", + "Bennett Taylor\n" + ] + } + ], + "source": [ + "print(\"Keep It Positive (Not Like That)\")\n", + "print(\"Bennett Taylor\")" + ] + }, + { + "cell_type": "code", + "execution_count": 30, + "metadata": {}, + "outputs": [], + "source": [ + "# Configure Jupyter so figures appear in the notebook\n", + "%matplotlib inline\n", + "\n", + "# Configure Jupyter to display the assigned value after an assignment\n", + "%config InteractiveShell.ast_node_interactivity='last_expr_or_assign'\n", + "\n", + "# import functions from the modsim.py module\n", + "from modsim import *" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": 31, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "'init = State(R = None, L = None, E = None, V = None)\\nΓ = None\\nτ = None\\nμ = None\\nα = None\\nδ = None\\nσ = None\\nsystem = System(ri_rate=Γ*τ,\\n rl_rate=rl_rate,\\n re_rate=re_rate,\\n ro_rate=μ,\\n le_rate=α,\\n eo_rate=δ,\\n lo_rate=μ,\\n vi_rate=vi_rate,\\n vo_rate=σ)\\nprint(system)'" + ] + }, + "execution_count": 31, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "\"\"\"init = State(R = None, L = None, E = None, V = None)\n", + "Γ = None\n", + "τ = None\n", + "μ = None\n", + "α = None\n", + "δ = None\n", + "σ = None\n", + "system = System(ri_rate=Γ*τ,\n", + " rl_rate=rl_rate,\n", + " re_rate=re_rate,\n", + " ro_rate=μ,\n", + " le_rate=α,\n", + " eo_rate=δ,\n", + " lo_rate=μ,\n", + " vi_rate=vi_rate,\n", + " vo_rate=σ)\n", + "print(system)\"\"\"" + ] + }, + { + "cell_type": "code", + "execution_count": 68, + "metadata": {}, + "outputs": [], + "source": [ + "def make_system(r,tau,mu,alpha,delta,sigma,B,p,pi):\n", + " \"\"\"Make a system object for the SIR model.\n", + " \n", + " beta: contact rate in days\n", + " gamma: recovery rate in days\n", + " \n", + " returns: System object\n", + " \"\"\"\n", + " init = State(R = 1000, L = 0, E = 1, V = 100)\n", + " \n", + " dt= 0.1\n", + " t0=0\n", + " t_end=100\n", + "\n", + " return System(init=init, t0=t0, t_end=t_end,\n", + " r =r ,tau = tau, mu = mu,alpha = alpha,delta = delta,\n", + " sigma = sigma, B=B, p=p, pi=pi, dt=dt)" + ] + }, + { + "cell_type": "code", + "execution_count": 69, + "metadata": {}, + "outputs": [], + "source": [ + "def update_func(state, dt, system):\n", + " unpack(system)\n", + " \n", + " R, L, E, V = state\n", + " \n", + " drdt = r*tau - mu*R - B*R*V\n", + " dldt = p*B*R*V - mu*L - alpha*L\n", + " dedt = (1-p)*B*R*V + alpha*L-delta*E\n", + " dvdt = pi*E - sigma*V\n", + "\n", + " R = drdt\n", + " L = dldt\n", + " E = dedt\n", + " V = dvdt\n", + " \n", + " return State(R=R, L=L, E=E, V=V)" + ] + }, + { + "cell_type": "code", + "execution_count": 70, + "metadata": {}, + "outputs": [ + { + "ename": "SyntaxError", + "evalue": "invalid syntax (, line 2)", + "output_type": "error", + "traceback": [ + "\u001b[1;36m File \u001b[1;32m\"\"\u001b[1;36m, line \u001b[1;32m2\u001b[0m\n\u001b[1;33m \"\"\"Runs a simulation of the system.\u001b[0m\n\u001b[1;37m \n^\u001b[0m\n\u001b[1;31mSyntaxError\u001b[0m\u001b[1;31m:\u001b[0m invalid syntax\n" + ] + } + ], + "source": [ + "\"\"\"def run_simulation(system, update_func):\n", + " \"\"\"Runs a simulation of the system.\n", + " \n", + " system: System object\n", + " update_func: function that updates state\n", + " \n", + " returns: TimeFrame\n", + " \"\"\"\n", + " unpack(system)\n", + " \n", + " frame = TimeFrame(columns=init.index)\n", + " frame.row[t0] = init\n", + " \n", + " timesteps = pd.Series(np.linspace(t0, t_end,int(t_end/dt)))\n", + " \n", + " for t in timesteps.index[:-1]:\n", + " frame.row[timesteps[t+1]] = update_func(frame.row[timesteps[t]], dt, system)\n", + " \n", + " \n", + " return frame\"\"\"" + ] + }, + { + "cell_type": "code", + "execution_count": 71, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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values
initR 1000\n", + "L 0\n", + "E 1\n", + "V 100\n", + "dtype:...
t00
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" + ], + "text/plain": [ + "init R 1000\n", + "L 0\n", + "E 1\n", + "V 100\n", + "dtype:...\n", + "t0 0\n", + "t_end 100\n", + "r 1.36\n", + "tau 0.2\n", + "mu 0.00136\n", + "alpha 0.036\n", + "delta 0.33\n", + "sigma 2\n", + "B 0.00027\n", + "p 0.1\n", + "pi 100\n", + "dt 0.1\n", + "dtype: object" + ] + }, + "execution_count": 71, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "system = make_system(1.36, 0.2, 1.36e-3, 3.6e-2, 0.33, 2, 0.00027, 0.1, 100 )\n" + ] + }, + { + "cell_type": "code", + "execution_count": 72, + "metadata": {}, + "outputs": [], + "source": [ + "results, details = run_ode_solver(system, update_func)" + ] + }, + { + "cell_type": "code", + "execution_count": 73, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 73, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "results.plot()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.6.6" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} From 3e5c94fba3ce101be711cc4f82fbe26124c4d15d Mon Sep 17 00:00:00 2001 From: Bennett Taylor Date: Mon, 5 Nov 2018 01:46:35 -0500 Subject: [PATCH 06/14] ModSim Project 2 --- code/BenJerry's Project Final.ipynb | 1054 +++++++++++++++++++++++++++ 1 file changed, 1054 insertions(+) create mode 100644 code/BenJerry's Project Final.ipynb diff --git a/code/BenJerry's Project Final.ipynb b/code/BenJerry's Project Final.ipynb new file mode 100644 index 00000000..660779f4 --- /dev/null +++ b/code/BenJerry's Project Final.ipynb @@ -0,0 +1,1054 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Bang Bang (My Baby Shot Me Downey)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Bennett & Jerry
Section 1" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Question" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### What temperature range of operation is needed from a bang-bang heater to result in a steady ambient temperature of 25 degrees celsius, given heat loss to the environment?" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Model" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "      When deciding on our model, we went through several questions: heat loss in the AC, thermal retention of window glass, even what would happen were the sun to go out. After consulting with the NINJAs and reflecting on what topics we were capable of pursuing, we decided to combind our interest in thermodynamics with the newly discovered topics of bang-bang heaters. Bang-bang heaters are heaters that are either on, and pumping out as much heat as they can muster, or off entirely. The question we decided to pursue was at what temperature would the heater have to turn itself on, and later off, in order to maintain an efficient and stable temperatue, given heat loss from the room it is heating to the environment.
\n", + "\n", + "      In our model, we have simplified the room to a 10 m by 10 m by 5 m box, with all walls but one being perfectly thermally insulated. The final wall, 10 m by 10 m, is constructed out of single pane glass, with a thermal coefficient found via research into building specs of commercial buildings. We assumed that the room is a single thermal object, losing its heat to an unchanging environment at a rate of U*A*deltaT, with U being the thermal coefficient of the surface in contact with the environment, A being the area of said surface, and delta T being the difference between the interior and exterior temperatures. The room was assumed to have constant volume, as dictated by the usage of the equation, which requires this parameter. This would also limit potential errors in our calculations and be relatively accurate under ideal conditions which helps our model significantly. The U value for the glass was assumed to have been 1.05, as found on an encyclopedia of the thermal conductivity of building materials, despite U-values varying for different types of glass.
\n", + "\n", + "      Our data was verified by the use of a secondary model, Build It Solar's Home Heat Loss Calculator. After inputting the various dimensions and thermal conductivity of the room, it delivered a series of values of rates of heat loss and returned the temperature of the room at various points in time. Using Excel to find the line of best fit, we were able to turn the given data points into a polynomial equation, which we graphed using discrete tiemsteps. This became our baseline for the heat loss of the room, and we utilized it in validating the base of our model, the rate of thermal energy loss. The later introduction of the thermal energy input by the bang-bang heater was also in part validated off of this principle, as when searching for a \"break-even\" input rate, it additionally relied on the rate of thermal energy loss to be determined.
" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Importing and Configuration" + ] + }, + { + "cell_type": "code", + "execution_count": 53, + "metadata": {}, + "outputs": [], + "source": [ + "# Configure Jupyter so figures appear in the notebook\n", + "%matplotlib inline\n", + "\n", + "# Configure Jupyter to display the assigned value after an assignment\n", + "%config InteractiveShell.ast_node_interactivity='last_expr_or_assign'\n", + "\n", + "# import functions from the modsim.py module\n", + "from modsim import *" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Creating the System\n", + "**temp_out:** Exterior Temperature, input in Fahrenheit
\n", + "\n", + "**t_oc:** Exterior Temperatur, converted to Celsius
\n", + "* Rate of Thermal Energy Loss equation given in BTU, and takes C in its calculation\n", + "\n", + "**area:** Surface Area of plane exposed to the environment
\n", + "\n", + "**heat_coeff:** Thermal Conductivity of the material of the plane
\n", + "\n", + "**rate_in:** The rate of input of thermal energy by the heater
\n", + "\n", + "**difff:** Variable used to hold shift in range of heater activity
" + ] + }, + { + "cell_type": "code", + "execution_count": 54, + "metadata": {}, + "outputs": [], + "source": [ + "def make_system(temp_out, area, heat_coeff, rate_in, difff): #requested inputs\n", + " \n", + " init = State(temp = 25)\n", + " \n", + " #converted to celcius per BTU\n", + " t_oc = (temp_out-32)*5/9\n", + " \n", + " A = area \n", + " U = heat_coeff\n", + " rate_in = rate_in\n", + " difff = difff\n", + " \n", + " t0 = 0\n", + " t_end = 10000\n", + " \n", + "\n", + " \n", + " return System (init = init, t_oc = t_oc, A = A, U = U, t0 = t0,\n", + " t_end = t_end, rate_in = rate_in, difff = difff) #initialization of system\n", + " \n", + "#currently set up so that there is a single heat_coeff value.\n", + "\n", + "#potentially a need to initialize a system to test each heat_coeff value\n", + "#lack of heat_coeff values, need for a nonlinear array of values" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Slope Function\n" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [], + "source": [ + "def slope_func(state, t, system):\n", + "\n", + " Temp = state\n", + " \n", + " #calculate rate of heat loss\n", + " dHdtJ = system.U * (Temp - system.t_oc) * system.A\n", + " \n", + " # converted from joules to degrees celsius\n", + " dHdt = -dHdtJ / 430800\n", + " \n", + " # return the rate of heat loss\n", + " return dHdt\n", + " " + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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use of linrange\n", + "trendtime = linrange(0, 10000, 1)\n", + "\n", + "#given model rewritten as a graphable equation\n", + " #given model was not transparent, and therefore could not be replicated except through interpretation of its data\n", + "trendline = 2e-7*(trendtime)**2 - 0.0038*(trendtime) + 24.873" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [], + "source": [ + "def plot_results(results, trendline, title):\n", + " \n", + " #plot trendline and modeled temp\n", + " #comparison validates heat loss equation and modeling\n", + " plot(trendline, '--', label='Trendline')\n", + " plot(results['temp'], '.-', label='Modeled Temperature')\n", + " decorate(xlabel='Seconds', \n", + " ylabel='Temperature (degrees C)',\n", + " title=title)" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "data": { + "image/png": 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\n", 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" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "plot_results(results, trendline, 'Calculated Room Temp')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Updating Slope Func, Validation\n" + ] + }, + { + "cell_type": "code", + "execution_count": 55, + "metadata": {}, + "outputs": [], + "source": [ + "def slope_func2(state, t, system):\n", + "\n", + " Temp = state\n", + " \n", + " #calculate rate of heat loss\n", + " dHdtJ = system.U * (Temp - system.t_oc) * system.A\n", + " \n", + " # converted from joules to degrees celsius\n", + " dHdt = -dHdtJ / 430800\n", + " \n", + " # introduce heat input equation- current input is arbitrary, to be swept later \n", + " dIdt = 1000 / 430800\n", + " \n", + " #combination rate: input minus output\n", + " dCdt = dIdt + dHdt\n", + " \n", + " #return heat loss rate if heater is off (when in ideal temp range)\n", + " if (30 < int(Temp) < 21):\n", + " \n", + " return dHdt\n", + " \n", + " #return loss and input if in non ideal temp range (heater on)\n", + " else:\n", + " return dCdt " + ] + }, + { + "cell_type": "code", + "execution_count": 56, + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "data": { + "text/html": [ + "
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" + ], + "text/plain": [ + "sol None\n", + "t_events []\n", + "nfev 38\n", + "njev 0\n", + "nlu 0\n", + "status 0\n", + "message The solver successfully reached the end of the...\n", + "success True\n", + "dtype: object" + ] + }, + "execution_count": 56, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "results2, details = run_ode_solver(system,slope_func2)\n", + "details" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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" + ], + "text/plain": [ + "sol None\n", + "t_events []\n", + "nfev 12008\n", + "njev 0\n", + "nlu 0\n", + "status 0\n", + "message The solver successfully reached the end of the...\n", + "success True\n", + "dtype: object" + ] + }, + "execution_count": 17, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "#heat loss shown to be impacted, room ending at higher temperature\n", + " #heat input equation functional\n", + "#introduce max_step\n", + "results3, details = run_ode_solver(system,slope_func2, max_step=5)\n", + "details" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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Hj+btt9+uey4rK0v2R3VTsrzWBIu7mYXTYxk3NIyLZw9l0GV3EnbBb8Hi1eT51VmJJDz1S4p+/NrFIxWia1x00UW8+OKLZGRkUFNTw4oVK7jqqqsoLy9v8XUDBw5k0qRJPPHEE5SVlXHo0CHee++9Do3l7LPPJjk5mffee4/q6mpSUlK45pprGgQh0X1I0GmGn48HM+MH4u5mfIn8xswi7p7X8Riomn5BZRk5656TzaSiT7jxxhuZOnUqV111FRMnTmTz5s28/PLLDtXn+vvf/05BQQHTpk3jrrvuqstAa6/AwEBWrlzJ2rVrmTp1Kr/4xS+YN29e3X4f0b2YbDan7790KqVUDJC4adMmBg0a5PT3KyiuoHLLqxTt3djsOaZ+gURedIfs6REcPHiQESNGdPUwhOiQpv4fp6amMnfuXIBYrXWSo9eSmY6DbDYb3x3O5vVPDlE45mf0v+oh8PJr+tySfDJef4Cs95918SiFEKJ7k6DjoB+OnOCb79Ox2mx8vjOZooA44u5a1fxyG0aSQdKLt0jFaiGEsJOg4yAVHUSgr5ECWlVjZf3WRIrLqhi09K8ETLu02ddZ87NIWX4ruV+84aqhCiFEt+VQyrRSagSwADgLCMeoj5YJ7AI+ast6Xk/l5enOohmxvLv5CBWVNRSXVbF+ayIXzx5KyJwr8T/zHNLf/is1uU3vNyjYtoaSY3sltVoI0ae1ONNRSk1TSn0GfA9cDpQBe4Harfg3AEeUUhuUUtOdOtJuIMjPi/OnxGC25/9n55Xy+a5kbDYblqBIom9+Hr/x5zX7+uqsRBIe+zn52z901ZCFEKJbaXamo5RagdHF80Xg51rrk82cFwRcCSxXSu3SWju3DnoXi4rwY2b8QL7aa1QpOJaaz84Dnkwe3R+AsAU34jtiGhlr/w6lTXTbtlZzctMqCr77jAE//xOWoI7XxRJCiJ6ipZnOJq31WVrrV5oLOABa6zyt9Yta63HA550/xO5nzJBQxg4NrXu862AWh5Pz6h57x4wm7o6X6TdqZlMvB6AmN03u9Qgh+pxmg47Wus3bebXWb3VsOD3HjHEDGRx5KmV6065kMnNLGpwTcdHvjNRqj37NXqdg2xqSnr9RiocKIfqE1u7pBCulHmnUShql1BNKqceUUoHOHV73ZTabOG9KDMH+Rmkck8lESVnVaed5x4wm7vev4T2s+RLr1qJcMl5/gJwNK5w2XiFE75KSktLVQ2iXZoOOUioS2A7cCAxsdDgPuBbYppQKb/zavsLT4sai6bGE+Htx8eyhDBnUfAzu/7N7W9xQCkavHpn1iK6ilGL06NHk559+L/K8885Dqeb3pLWkfgvqlqSmpqKUorCwsM3v8d577zXZImHdunV1bbfHjh2LUqrucXx8POnp6W1+r+7gtdde46mnnurqYbRLSzOdh4BsYKjWem/9A1rrx4HRQAnwgPOG1/0F+HpyxXxFRLBPq+d6x4wm7q5VDs16pIab6Ar9+vVj48aGJZ6+//57cnJyumhEHXPBBRewb98+9u3bx0svvYSfn1/d43379jFgwICuHmK75OY61sSvO2op6CwA/qi1bvLXDntywTJgoTMG1pM0VUK9sqqG5ura1c16fJqfGZUd2U3Ck1K5WkBVXialR/e6pLLF+eefz0cffdTguQ8++IDzzmu4FWDbtm1ceumljB8/niVLlvDJJ5/UHUtNTeXaa68lPj6eSy+9lOTk5AavfeeddzjvvPOYOHEi119/fbPLREePHmXp0qVMnDiR888/nw8/PLXVID8/n9tuu43x48dz/vnns39/+1cHysvLefTRR5k1axbTp0/ngQceoKysDIDVq1dz8803c++99zJ+/HjmzZvH9u3bue+++5gwYQLnnnsuu3btqjt36dKl3HnnncTHx7NgwQK++uqruvdJT0/nlltuYfLkycybN4/XXnut7tjdd9/NHXfcwTnnnMOCBQuorq5mw4YNXHLJJUyaNIlJkyaxbNkyqqurWb9+PS+//DKff/45l1xyCdXV1SilOHz4cIPrPfHEE81e+/Dhw1x77bVMnDiRBQsWsH79+nZ//dqqpc2hIcDp3csaOoyxWVTUk1dUzodbEhg9JJTxzaw+1ma4Zb3/LCUHtjR9oSqjcnXuV28SsfhWKSDaC5QmfE/pkd3Yak6//9cUa0Up5akabFYwmfEapDB7tj6rrmVys+Az7Cx84sY5dP6CBQu48cYbycrKIiIigqqqKj799FMef/zxuhYER44c4aabbuKJJ55g/vz57Nq1i1tuuYWwsDAmTJjQYjvqTz/9lOeff55///vfDBs2jFdeeYVf//rXpwW6kpKSFltQ33///VRWVvL111+Tm5vLddddh6+vr8Nfl/oef/xxjh07xtq1a7FYLNxzzz089thjPPzwwwB88cUXPPLIIzz66KM8+OCDXHfddTz88MM88MADPP300zz55JOsXr0agG+//ZZ77rmHJ554go0bN3L77bezceNGwsLCuOmmm5g2bRrPPvssqamp3HTTTQQHB7N48WIAduzYwdq1a/Hx8SEjI4M//vGPrFq1ivj4eBITE7niiiuYPXs2CxcuRGtNYmIizz//PNXV1a1+jvWvXV5eznXXXccNN9zAypUr+emnn7jpppvo378/8fHx7foatkVLM51jwNhWXj+W1gNTn5JbUMa7m49QWFLJth/SOZraxF6demoz3Ey+Ic2eYy3IlgKivURZ4vcOBxwAa3kp2KyYPbzBZjMet4GtpoqyxO8dPj8gIIAZM2bw8ccfA7BlyxZGjRrVoGvnxx9/zOTJk1m4cCHu7u5MnTqVJUuWsHbt2lbbUb/zzjtcc801jBo1Cg8PD2688UaKi4vZsWNHg3G01IK6oqKCzZs3c9ttt+Hr60t0dDRXX311m74utaxWK2vWrOEPf/gDISEh+Pv7c9ddd7FmzRqqqox/p4EDB3L55ZdjNpuZMmUKfn5+XHbZZVgsFmbOnElq6qkfgTExMXVjXrx4MUopPvvsM7777jsyMzO555578PDwIC4ujqVLl/LWW6cSfqdMmUJERAR+fn5ERETw8ccfEx8fT1FREfn5+QQGBpKdnd2uz7P+tTdv3kxQUBBLly7FYrEwbtw4Lr744gZjcaaWZjr/Ax5VSn2ttT7tJ6c9c+1RYLWzBtcTBfp6EuLvRfoJI336853J+HpbiAxpPm3aO2Y0sb9dQe4Xb1CwbU2z55Uc2EKC3knw2b8gcMqSTh+7cD7v2HFtmumYvXzAZMZaWQ4mk/G4DUxuFrxjHZvl1LrgggtYsWIF1113HevWrTvtBv3JkydPuxcyaNAgduzY0Wo76vT0dJYvX86KFacyNauqqkhPTyc6OrruuZZaUOfn51NVVUVkZGSD92iPnJwcKisrufbaaxssk5vNZjIzjeXMwMDABs/X7xlkNpuxWq11j6OiGnZ0jYyM5MSJE6Snp1NcXMzkyZPrjlmt1gbBvH47cHd3d1avXs2aNWvw9vZmxIgRVFRUNLtk35rGrcYTEhJO+9qOHdvaHKNztBR0ngEWAT8ppV4CdgMFQBAwEaMETiIgd7zrcXMzs3CaUaMtv7iC6horH29N5LJzhhHg69nia2truGW8+xTV2UlNn1RdwclNq8jfs4GBV94vFQ16GJ+4cQ4vddWqysukKjcdS8gAl/x7z5kzh/vuu48ffviB3bt388QTT5CQkFB3vH///uzevbvBa1JSUggNDW21HXV4eDjXXHMNV1xxRd1zx44dY8CAAQ1ujrfUgjowMBAPDw/S09MJDQ097T3aIjg4GHd3d9auXcvgwYMBqKioIDU1lYEDGyfttq7xONLS0pg6dSrh4eGEh4c3uMdz8uTJBp1W6we9devWsX79etauXUtYWBgAixYtavI9zWZjwap2ZgbGPa/a1zW+dnh4OOPGjeONN05tTM/Kyqq7jrO1tDm0GpgL/AO4CvgA+BJYC1wAPAnM0lqXNHeNvsrL053FM+Lw9jRiellFNR9+k0B5Retrr5agSAb/+m9Ge2yP5n+rra1eLUtuvZ8lKBKfoeNd9guGp6cn8+fP595772X27Nl4ejb8ZWnhwoXs3r2b9evXU1NTw7fffsuHH37IkiVLWm1HfdFFF/HKK69w7NgxbDYbH374IRdeeOFpP6xbakHt4eHB4sWLefbZZykoKCA1NbXBTfm2qF0Ge+qpp8jPz6eiooLHHnus3V1HDx8+zJo1a6iurub9998nKSmJc889l/j4eDw9PVmxYgWVlZXk5uZy88038+KLLzZ5neLiYtzc3LBYLFRWVrJq1SqOHj1aF1g8PDwoKioCjKATHR3NunXrqKqqYseOHXXJDU2ZPXs2x44d4/3336empoaUlBR++ctf1t2XcrYWQ5vWulpr/Vet9VDAH4gG+mmtx2qtn9FaO7443ccE+nmycFosbmbjN4z8ogrWb0uipsbayisNfmNmEff7/7ZYQBTsS25SRFR0siVLlnD06NEm975ER0ezfPlyVq5cyVlnncVDDz3EQw89xIwZM4CW21FfdNFFXHXVVdxyyy2MHz+elStX8uKLLxITE9PgPVprQX3fffcREhLCnDlzuOaaazj77LPb/bn++c9/JiQkhCVLljB9+nRSUlJ46aWX2vWbf1xcHF9//TVTpkzh1VdfZcWKFYSGhuLh4cGKFSvYvXs3M2fOZPHixZxxxhncd999TV7n0ksvZfjw4cydO5ezzz6bPXv2sHDhwroMtblz53LkyBHOOeccAB555BG2bdvGpEmT+M9//tPkv1ut4OBgVq5cybvvvsuUKVP4xS9+wYIFC7jpppva/Pm2h7SrdrKjKfl8sj2p7vGwqCDmTx7cZJp1c6ryMsl8/1mq0o+0eJ7Jy5fQ+dfjN2ZWe4crOpm0q+47Vq9ezZtvvtlgZtdbSLvqHmRoVCDTxp666XokJY8dB9q238ISFEnUrx5vtaKBrbyYnHXPcfxft0u3UiFEtyRBxwXih4cxOu5UlkpeUQVWa9tnmLUVDYxOpc3/09VWsE777/0SfIQQ3YoEHRcwmUzMih/E4Eg/4lU450+Jxmx2fHmtsZA5VxK3bDWeMWNaPK8i+YAkGwjhIpdffnmvXFrrbA61q4a6eye5WusipdQs4BJgp9ZaGsI4wGw2sWh6XF1iQWcYeNWDlCXtJ+vDF7EWNr9prOTAFhIObiNgykWEzLmy095fCCHayqGZjlLqSuAIMEkpNQxYD0wB/qGUuseJ4+tVmgo4NpvNoVTq5njHjCbmtn8aKdYWr+ZPtNZQsG0NCY/9XBrHuVhPT9YRfVtn//91dHltGfA7rfUm4FdAotZ6Ckab6v/r1BH1IVarja/3pfHOpsNN9uJpC78xs4i753Xjfo+5hQmstdoIPk9cKWnWLmCxWOqKRwrRE5WVlWGxWDrteo4GnSHAOvvHi4Ha6nwHgYgmXyFatXl3Mj8eO0FhSSUffZNAZVVNh68ZMudK4u59u9X9PbWVDRKevloqWTtReHg4aWlplJaWyoxH9Cg2m43S0lLS0tIalNHpKEfv6aQCo5VSfhh9dGpnN3OB4502mj5maFQQh5Pzsdps5OSXsX5bEktmxOLm1vH8jrAFNxI45QKyPlpOZfKB5k+sKCVn3XOc+PwVQuf9Svb4dLLaOl3p6ekNypQI0RNYLBYiIiIa1JvrKEeDzt+A94BqYLPWeqtS6l6MRm+/7rTR9DEx/f2ZPWEQm3cb/URSs4vYtDuFcye1bfNocyxBkQy6+mGHNpfaSguN4PPpfwidf50En07k7+/fqd+0QvRkDv1KrbX+J3A2xv2c2vLGO4CztdavOmlsfcLI2BCmjO5f9/hwch7bfszo1Peov7nULajlTom28iJy1j1HwtNXyz0fIUSnc3gdR2u9E/gBmKeU8gGOaq2/ddrI+pAJZ4Q32Dy6T2fz/eHObw/sHTOa6FteaLV/DwAVpcY9H0k4EEJ0IkdTpv2UUh8AhzCqTEcCzyml9imlemaT8W6kdvNo3MCAuue2fJ/G4eQ8p7xfbf+esAt+C96tLPvUJhw8foWkWgshOszRmc7TQAAQA9Tmf94JFAOy3b0TmM0m5k+Opn+9Zm+f70zmeEah097Tb8ws4u42PnqZAAAgAElEQVR8xQg+nq20+q2psu/z+ZkEHyFEuzkadBYDd2mtk2uf0FonArdjZLCJTuDuZmbR9FhC/I1Nnp4ebvh4dV5+fHP8xswi7u5XCbvgt5j6BbV8cu0m079eTs6GFS2fK4QQjTiaveYHNNec3eFSOqJ1Xp7uLJk1hM92HGf2hEEE+bVQZaCT+Y2Zhd+YWQ6V1sFmpWjvRor2forXkHjCzrteupgKIVrl6ExnI3C/UsrN/timlAoBngI+c8rI+jBfbwsXzx7q0oBTX21pnf5XPYR76OBWzrZRfmwvKctv5fg/b6Msab9LxiiE6JkcDTq3A7HACcAH+ARIBkKB3zlnaKKx3IIyijtYLqctvGNGM/imvxN1y4tYBgxr9fyak+lkvP4ACX+7VjLehBBNcmhpTGudAUxRSp0LjLS/7iDwidbasf7LgP31jwPDgGzgKa31v5VSgcBK4FyM5IT7tNavtOkz6eUyTpTw0dYEfL2MWZCXp+tWNWv3+VTlZbZe4QCgvJiTm1ZxcvNr+MWfS9iCG10zUCFEt9fWn1zHAS9gMxDSxoATBawBrgU+ACYAG5VSScBSoAboDwy3P5+gtf6qjePrlcorq/nQXputorKGj7YmcuGsOCzubq2/uBPVr3CQs/Flyo/tA1qoJ1Z332cjlsghhM69Bu+Y0S4brxCi+3Eo6Nhrrr2OkcVmxQgMf7P32FmktU534DIxwBta67X2x7uUUl9iZL9dBozSWpcC3ymlXgJuBCToAF4e7pwdP5DPdhrJg5m5JWzYlsSi6Z1Tp62tLEGRDLhiGQC5X7xBwfYPwNpye4aqzGNkvP4AePkSPP0yAqcsafF8IUTv1JZ9Ov50YJ+O1nqL1vrm2sdKqWBgJpCB8ety/cJgh4CW22L2MSo6mFnxA+seJ2cV8fmu5Ha1ve5MtVWtg+cuBc9+rZ1et/SW8OhlZLz1qLTTFqKP6ZJ9OkqpAIxWCTuAPUC51rr+T89SjIQFUc/YoWFMGnUqLflISj5f7k3pFiXzA6csIe7u1xzMeAOwUWbPekt85leSeCBEH+Fo0Om0fTpKqeHAdiALY1mtCPBSStUvq+yDMYsSjUwcEcG4oWF1j39KPMmW79K6ReCBUxlvccvW2Hv6tP5fzFZWaMx+/iqzHyF6O5fu01FKzcKY3bwPXKa1LsdYVjNhpGTXOgP4ydHr9iUmk4kZZw5gRExw3XM/HD3Btz9mdJvAUytswY3ELVttdDO1eLb+Alu92Y+kXQvRK7lsn45SaghGx9H7tdb31i6naa2LMYqIPqaU8lVKjcPo0fPftnwifYnJZGLOhCiGRQXWPbdXZ5OcWdSFo2peyJwribvnjTYsvYGt7t7PpaT9936Z/QjRSzi6NFakte7oPp1bMZbpHlNKPVbv+ReBm4DlGCnZ5cCjWusNDl63TzKbTcybFE11tZXEjELGq3AGR/p19bBaVLv0Bvast50fQnVlq6+rSD5AyvJbwd0Dv7FzZN+PED2YyZElGaVUInCJ1nqf84fUNva07cRNmzYxaNCgrh6Oy1XXWDmamo8aHNQp3UZdrejHrzn59dvU5LdtJmP2DSJw8oWSei1EF0lNTWXu3LkAsVrrJEdf5+hMx7W7EIXD3N3MnBEd3PqJ3VRtkVFo2+zHWpxnVD3YtAr3sMGEzb9eNp4K0QM4GnTeAD5VSr0BJHBqrw4AWmupcd+NWK02Nu9OIbq/H8OiWmlV0I2EzLmSkDlXUpa0nxObXqMq85hDr6vOSTY2nmLGEhkrlQ+E6MYcDTpXYdxruaSJYzZAgk43UVNj5dMdxzmWVsDh5Dzc3czEDgho/YXdiHfMaKKufxKwz372fAIVJQ680nqq8oHJHe+4sYRKywUhuhVHC35GOXsgonNUVls5WVgBgNVm45Nvk1g4PZboyFbaUndTtbMfgKz3n6XkwDaMMn2tsFXb06/3SgKCEN2Io4kE05o5ZAMqgTStdZfktPb1RIKmFJdV8d4XRygsMe6NuJlNLJoey+AeGngaa+vyWwMSgIToFO1NJGhL9loUxr6eIozNnL40LDH8NfAzrXWO48PuOAk6TSssqeT9r47WBZ7aVthREd07rbqt8rd/SN7297GV5Lf9xWZ3+o2YSsRF0hJKiLZqb9BxdHPocuA7YIzWOkBr7Y+xX2c7RuHPgUAe8Pe2DFo4j38/Dy6cNQQ/Hw/ASK3+eGsiKVndcwNpewVOWULs714mbtkao/KBI0VHa1mrKTmwhYRHLyXhsStIefke6XwqhJM5OtPJxGhhsKfR8/HABq11pFJqNPCV1jrEOUNtdmwxyEynWQXFFaz98mhdx9HeOuNpLGfDCop+/BKqKtrxahNuQREEz/x5XTq3EKIhZ890PICmimf1A7ztH1fQ9qZwwskCfD25ePZQfL0twKkZT1pO766nGrbgRuLueeNU4VF3jza82kZNXiY5654zZkF/u5bcL95w2liF6EscDRKrgf8opX4L7MYIVhMweum8a2/ydh9GMU/RzQT4enLR2UN5/ytjxuPl4VYXhPqCsAU31iUOtGsGVF5MwbY1FGxbA24eeMeMllRsIdrJ0aBzO0aNtA85VZ2gCngZuBtYAIwDrujsAYrOEehnBJ7PdyVz7qTBBPg6UPW5F+pwAKqpPJWKjZTjEaKtHLqnU8s+oxmJEXCOaK27/K603NNpG5vN1iNrtDlb2zahNsPNgnfMGJkFiT7B2bXXUEr1A34BKOCvwHSl1E/1u4mK7q+pgJOSVYTZbGJgmG8XjKh7qL8J9VQadiHgaBF1oKaqwSzI5OWL//jz6q4rhHAw6CilhgFfYJTCGYyx1HY1sFgpdZ7WervzhiicKT2nmPVbE7FBn8hqc0TglCV1y2VVeZlkfbScypRDYHOgEkI9tvr3gkxm3ALDJSNO9HmOznSew2i0djtQaH/ul8A/gaeBGZ0/NOFsVquNzXtSqKoxfpv/6JsEFk6LJbp/76hc0BksQZEMuvrhuse5X7xBwe71UFnWwquaYLPWZcTlrHsOzO5YwqOlOKnocxwNOlOBO7TWNqUUAPaPnwK+d9bghHOZzSYWT4+ry2qrsdr4eFsi50+JIW5gzyoS6ir1l+HqyvFkHQdbddsuZK0+VZwUJAiJPsPRoFOO0ZpaN3p+CKdmPqIHCvTz5JI5w+pK5litRpHQcycP7lFtEbpC/WrY0IFZEJwehEzuuAWGynKc6HUcDTr/A/6hlKqtkhiklFoI/AN40ykjEy7j38+DS2YP5f2vjpFfXIHVZuPTHclYrTZUD24Q52r1Z0FVeZnkbHyZ8sQfwVrV9ovZqhsux+GG2ddf0rNFj+do0LnX/vcWjOoEuzDqy/8b+JMTxiVczNfHg4tnD+WDr49xsrAcm83G57tSqLHaGBnr0spGvYIlKJIBVyyre1zXlrsgp80JCYaaBt1SjTfxwm/M2VIxW/Qobd2n4wMMwwhWR7TWXb60Jvt0OldpeRUffJ1AbsGpJaKzxw9izJDQLhxV79PutOwWmXEPGyStu4VLdPo+nRZ66NQaXS+pYJujbyi6Nx8vCxefPYQPthwjJ88IPOUVbbxJLlpVPy0bjCB0ctsaKCumYceQtrDWa91tJ/2DRDfT0vLaNxj/+02c+i6o/diKUQ7HhrHM1pZqiqKb8/J058JZQ/hwSwJREX5MHCm7652tcRAq+vFrcr94HWvRSTo0E6qupGjvRor2bqx7Sjatiq7UUtCpn7p0MUbfnP8DdmIEmjMx+uysdNroRJfx8nDn4tlDcTNLyZyu4DdmVoOstbKk/eRsfJnq3FSwdWw5rsGmVQDMmLx8JBAJl3C0n85xjK6gOxo9PwH4WGvdZb8Kyz0d16qusfLD0ROcOSwMswSkLpX1/rOUHNzevuw4R3h4E3DWQglEoknOrr3W3E7BfsjSWp9RY7WxcftxEtMLyMwtYf7kaNzdHG3JJDpbxEW/g4tOPa5LTigtameGXCOVZY1mRIDZgkf4YEJkE6toJ0eDzlpO9dPZh3FvZzJGP53/Omlsops5fDyPxPQCABLSCvjom0QWTY/B4u7WyiuFKzS+LwQd7aDaBGsVlfU3sdqZvP0JmnaJ7CESrXI06NwKrAA2cKrbaA3wH4x+OqIPOCMmiJNF5ezT2QCkZhfxwdcJLJ4ei5enNI3tjur3D4JO2LTaDFtZYcM9RIBsaBVNaes+nQBghP3hQa11gVNG1QZyT8e1bDYbew5ls31/Rt1zIf5eXDBrCP36UDfS3qSuhlx2MliraX/KtqPMmH0DJBj1cO29p9Ns0FFKLQOe0Vo7VEjK3m/nLq31w62e3Ikk6HSNH4+e4Kt9qXWPA3w9uWBmXJ/tSNrb1M2IkvZDTaWL3tUEFk+pstBDOCORoALYr5R6G3hPa727qZOUUvEYbQ4ux6jFJvqAMUND8bCY2bQrBavNRkFxBWu+OMriGbGEB/l09fBEBzUu41PrVIfVMowZUWfOimxQVX7aviKDLNX1Fi0urymlooE/ANcAZcBPwAmMRIIwYDRG9tprwBNtiXadRWY6XSsxvYCN249Tbe/JY3E3c8HMIfQP7dfFIxOu0nB5zknp2y2RitxdotOX1+pTSvkB5wATgAiMLdKZwB5gk6NLcM4gQafrpZ8o5uOtiVRU1hDo68klc4bi4yX3d/q6ztzQ2n4mTF79ZOOrEzg16HRnEnS6h9yCMjbvTmH+5Gi5ryNa1KHmd51Olu3aS4KOBJ0uZ7PZMJmkSoFon4bJC1U4P4vOEVIiqDnOrkggRKuaCjhHU/M5nlHI7AlRUsdNtKi55AWo14+o8ARYa3BdQLI2UauuMRNm/1BCZl8p95QcIEFHOE1aTjGf7ThOjdVGSXkVC6ZK9QLRPo0LoNZ3ekXu+oXxXcGGtTCnXpfXpkg6eC0JOsJpEtMLqLEa3/zJmUWs/fIYi6bHyiZS0alaCkhVeZlkfbScypRD9np0rg5ItVpKB2+klxdadTjoKKXOwmhvMByjzODPgQSt9VonjU30cNPHDsDD3Y2dP2UCkJ1Xyrubj7B4RiwhAd5dPDrRF1iCIhl0dfP71U/PsOuqoFRPU4VWm9ETa945FHSUUucB7wFvAaMw9ub4AG8rpW7UWq9y2ghFj2UymZg0KhIfL3e+2peGzWajqLSSNV8cZcHUGKIi/Lp6iKKP844ZzeCb/t7s8ZZLBHV9gGq65l0zzO5YwqMJ7eIK4Y7OdB7BKHHzL6XUzwC01n9RSuVgbB5d5aTxiV5g9JBQ/Hw8+GR7ElXVViqravhwSwJzJkQxIja4q4cnRLO8Y0YTdf2TLZ7TMMmhq1PAW2CtpqpxhXCTG57RIwhf+H9YglzTFs3RoDMS+LSJ5z8Fmv81QQi76P7+XDJ7GB9vTaC4rAqrzcam3ckUlFQweVSkpFqLHqule0r1NWy613iW1EWzJlsNFUn7Sf/fgwz45YMuCTyOBp00IB5IaPT8OUByp45I9FphQd5cds4wPtqayIl8o4jFnkPZxA0IIDxY6rWJ3q1x072mNN16wvkBqqa0gKrc9G4VdB4DViil4gA34Hz7psxbgTva+qZKqUnAR1rrcPtjT6AIqF/OdpvWen5bry26N18fDy6ZPZRPtieRnFnEzDMHSMARwq6lvUqNNV3ZoX0Bys0nAEvIgLYOt10cCjpa61eUUtnAvUA58DhwCLhWa/2uo2+mlDIB1wNPNzo0BjiptXbNoqLoUh4WNxZPjyMhvYChgwK7ejhC9EiO3G+qr66deUkhxn4mwN0D7+jRhJ53ffe6p6OUugd4XWs9o4Pv9xCwCCMx4b56z08AvuvgtUUPYjabmgw4xWVV5BeVMyhcMtuE6ExNtTPvCubWTwFgGeDVCe/3L631BKBxb57xQLhS6gelVJZSarVSamAnvJ/oQaqqrazfmsi6rxP48diJrh6OEMIJHA06HwO3KaWCOvJmWuv0Zg6VAFuBuYDC6N0jm077mG0/pJOdV4rVZuOrval8tTe1rqKBEKJ3cDSRYChwBUbgKcQICnW01h26A6W1vrP+Y6XUnUCOUipKa53SkWuLnmPCiAiyTpaSnVcKwI/HTpBXVMH5U6Px8pCKTUL0Bo5+J//b/scplFIPA29qrQ/an/Kw/13urPcU3Y+vt4WLZw9l8+5kjqTkA5CaXcS7m46waEYsQX6dscIrhOhKjmavvezkcYwFzlJK1Va4ew74WGud4+T3Fd2Mxd3M/MnRBPl7sfOAUbMtv7iCdzcd4bwp0QyO9O/iEQohOsLR7LU3Wjqute5oOdTrgeeBo/YxfQz07frffZjJZGLSyEiC/bz4fFcy1TVWKqpq+OibRKaPHcDYYaFSwUCIHsrR5bWaJl4Xh7G/5vm2vqnW+ksgsN7jXOCqtl5H9G5DowLx9/Vg/dbEutI5W75Pw9PTjTOipWabED2Ro8trVzf1vFLqT8CQTh2REPWEB/lw+dzhrN+WSNbJUgaE9mOYbCgVosdyNGW6OW8Al3fGQIRoTj97gkG8Cuf8qTG4uXX0v60Qoqt09Lt3KUbNNCGcyt3NzPSxA/Dxath11GazkZBWgM0m+3mE6AkcTSTI4PSqcb72P3d19qCEcNSeQ9ls35/BsKhAzjkrCou7W1cPSQjRAkcTCe5r9NiGURF6l9Zad+6QhHBMek4xO+xp1UdS8jlZWMHCaTEE+Hp28ciEEM1xNOhEAH/XWjeoRKCU8ldKPam1vqfzhyZEyyKCfRgVG8z+hFwAcgvKeGfTYeZNHEzsgIAuHp0QoinNBh2lVH+gttTvX4AvlFK5jU6LB24DJOgIl3NzMzN7QhThwT51ddoqKmv4eGsi41U4U0b3x2yW/TxCdCctzXSmAas5dS9na71jNozuQACrOn9YQjhuZGwIIQHebNhm7OcB2KuzycwtZf6UaHy9La1cQQjhKs1mr2mt12AU+lQYAWYqMMz+Z7j9WKTW+joXjFOIFkUE+3DFuYroemVy0k8U8/ZnmpQsSbAUorto8Z6O1joBQCll0Vo3rkpAvWNVTR0TwpW8PN1ZPCOWPYey2XEgE5vNRllFNV/tS+XK+WfIUpsQ3YCjiQTBSqk/AiOB2pxUE+AJjAakJonoFkwmE2eNiCAyxIdPdyRTWVXD+VNiJOAI0U04ujl0BfAzIBGYAxzBaLI9A3jUOUMTov0Ghfvx83nDOX9qDKGB3l09HCGEnaNB5xzgWq31LcAB4D9a6/OAJzESDoTodvp5W4jpf3orhENJJ9l5IBOrdCUVwuUcXV7zxJjdABwEJgB7gP8AXzthXEI4RV5ROV/tS6Wq2kpqdjHzJw/G18ej9RcKITqFozOdw8B0+8cHgcn2j33sf4ToEX44coKqaitgZLe9+ZnmWGp+F49KiL7D0ZnO08AqpZQb8DbwvVLKBkwBtjhrcEJ0tplnDqSft8VYXrMZm0k3fJvE6CGhzBg3AHepYC2EUzn0Haa1fg2YBxy011q7ECNj7VuMrp9C9Ahms5HddvHsofjVW1bbf+wEqz8/TG5BWQuvFkJ0lKNVpj8A/qC1PgSgtd4IbHTmwIRwpv6h/fj5ucP5Yk9q3fJabmE5qzcdYfrYAYweEiItsYVwAkfXEmZgVJUWotfw8nDn/CnRzJkQVbesVl1j5at9qXyxJ6WLRydE7+ToPZ1ngFeVUs8ACUCDNQit9eHOHpgQrmAymRgVF1K3mbR2eW1YVFAXj0yI3snRoPMX+9+1GWy1GxxM9o+lc5bo0UICvPnZ3GFst5fPiYrwa/1FQog2czToDHPqKIToBtzsLbGban19PLMQs8kkwUiIDnIo6GitjwEopYZjVJ3eBIRqrZOdODYhukTjBILS8io+35lMWUU144aFMXVMf0mtFqKdHM1e8wP+ByzBqLk2HPibUioGWKS1TnfaCIXoYt/+mEFZRTUA3x/J4XhmIXPPGkz/0H5dPDIheh5Hf117GggAYjiVRHAnUAw82/nDEqL7mDqmP7H1arjlF1Xw3pdH2fJdWl11AyGEYxwNOouBu+ovp2mtE4HbgbnOGJgQ3YWPl4WF02OZMyEKD4uRM2Oz2fj+SA5vfaZJzynu4hEK0XM4GnT8gNJmjjmajCBEj1WbWv2L+YrBkaeSCQqKjVnP1/tSqapuss+hEKIeR4PORuB+e+01AJtSKgR4CvjMKSMTohvy8/FgyYw45p41GE/LqZ0CPxw9wdovjzWZ+SaEOMXRoHM7EAucwKgq/QmQDIQCv3PO0ITonkwmEyNig/nFeWc0uNdz5vAwKZ0jRCscTZnOAKYopc7FaFntjtHi4BOttdxJFX2Sr7dxr+dwch6p2cUMiwrs6iEJ0e219X5MAsZMpwbYLwFH9HUmkwkVHYyKDj7tWFpOMXsOZXF2/CACfD27YHRCdD+O7tMJBN7ByFSrwSh/Y1ZKrQWu0Vo3l2QgRJ9UXWPliz0p5BdV8OanmkkjIxk3PAw3syy/ib7N0Xs6/8a4fzMJ8MJoXz0VGILs0xHiNGnZxRQUG4XZq2usbPsxnXc+P0xmbkkXj0yIruVo0FkA3KC13qO1ttr/7ARuAi5z3vCE6Jmi+/tz2TnDCAv0rnsut6CMNV8c5cs9KZTbKxwI0dc4GnROAE3VencH5Fc3IZoQEezD5XOHM33sACz2Wm02m439Cbn875ND7D92AqtVUqxF3+JoIsG9wAql1L3AN0A1MB74O/CCvRAoIL11hKjPbDYRr8IZMiiQr/elkpRRCEB5ZTVf7k3lQGIu8yYOJiTAu5UrCdE7OBp03rT//RYNe+kAPA48hvTWEaJZ/v08WDQ9lqSMQrZ8l0ZhiXG/J7+woq60jhB9gfTTEcJFTCYTsQMCiIrwY6/OZu+hbCaMiMDPx6OrhyaEy7Spn44QouPc3cxMGhnJGdHB9PM6/Vtwn84m2N+LwZF+UuFA9DqO7tMZCzwDjMJIl25Aa336zjghRIv8+50+w8krKufbHzOw2ltmzxg3QO73iF7F0eW1VzGy1O4Dyp03HCH6tp0HsrDai4amZBXx1meHGRkbzORRkfh4Wbp4dEJ0nKNBZzgwUWv9kzMHI0RfN/PMAXhazBxIPInNZsNms3EgIZfDyXlMOCOCM4eHSats0aM5+r93K8bSmhDCiXy8LMyeEMUV5w5v0LenqtrK9v0Z/G/DQQ4mnpT9PaLHcnSm82tgq1JqAUbRzwaFPrXWf23LmyqlJgEfaa3D7Y89gH9gVDeoAZ7RWj/WlmsK0ZuEBHhzwcwhHM8sZNv36eQWGqvaxWVVbNqdzL7D2Vx09hBZchM9jqNB589Af2A6EN/omA1wKOgopUzA9cDTjQ49BCiMWm4BwCdKqTSt9WsOjk+IXik60p+ocD9+Ssxlx4FMyuzlcyzuZrw9pWmv6Hkc/V97BXCJ1vqDDr7fQ8Ai4BGMpIRa1wJLtdZ5QJ5S6mmMum4SdESfZzabGD0klOGDg/juSA7fHc5h2tgBp6VTV1XXYHGXjaaie3P0nk4e0Bnlbf6ltZ4A7K59wt42oT9QP0nhEDCmE95PiF7Dw+LGpJGRXLtoJAPDfBscs1ptvLvpCBu+TSK3oKxrBiiEAxyd6fwBeF4pdRdwDKiqf1BrXenIRbTW6U08XfvdU78nTylGszghRCOeTZTN0cfzyC0sJ7ewnGOp+QwdFMjEkRGyx0d0O44Gnb8BIcC+Zo53ZE5fW6W6/neHD1DcgWsK0aecyG84uzmams/R1HyGDApk4ogIQgMl+IjuwdGg80tnDUBrnaeUysRIJEizP30GDZfbhBAtmBk/EBUdxK6fMkm0V7IGOJaaz7HUfIYMDGDiyEgJPqLLOVp7bVPtx0opP6BYa92ZGwX+CzyglPoBY7ntbuC5Try+EL1eeLAPi2bEkX2ylF0Hs0hML6g7diytgGNpBcQNDGDGuIFNluARwhUczrlUSt0J/B4IA4Yrpf4MFAB3a6072gbxfowlvAMYyQ0rgH918JpC9EnhwT4smh5LTl4Zuw5mkpB2KvikZBbhMUEqGoiu42jBz7uA24F7OBUMPgD+CVTan3eY1vpLILDe43LgVvsfIUQnCAvyZuE0I/jsPpjJsbQCRsaF4NVof095ZTUe7m6YzVLRWjifo7/y/Bq4WWv9X+zVCLTW72Psr7nSSWMTQnSCsCBvFkyL5RfzFeNV+GnHt/2Qzv8+OcgPR3OoqrY2cQUhOo+jy2uDMfbONJYESFsDIXqAptKni0srOXQ8D6vVxtf70thxIJNRsSGMGRoqzeWEUzg609kH/Kze49okgptpPo1aCNHN5RVVNNj3U1FZw16dzX/XH2TDt0mknyjGZpPioqLzODrTuRujHtosjCZuDymlzgBGAgucNTghhHNFRfhxzcKRHEzK5bvDORSWGPu8rTZbXbp1eJAPY4eFMmxQIG7SVkF0kEP/g7TW32L01NkHfAwEAV8CI7TWW5w2OiGE01nczYwdGsYvzx/BoumxDAr3a3A8O6+Uz3cm89nO5C4aoehNmp3pKKXuB57WWpcCaK2zaFikUwjRi5jNJmIHBBA7IIDcgjK+P3KCw8l5VNcYyQUqOui019hsttMKjwrRkpZmOg9wqi6aEKIPCQnw5pyzorh20UimjO7PwDBfYvr7NzinpsbKO58fZvv+jLplOSFa09I9Hfn1RYg+ztvTnbNGRHDWiIjTjiWkF5CTX0ZOfhl7DmUzOMKPM2KCiB0QIC21RbNaSyQYpJTyau0iWmtZ7BWijzmaeqrSgc1m43hmIcczC/G0uDE0KpAzooOJDPGR5TfRQGtBZ1crx00Y6dPSOUqIPmb+5GgSowI5kJBLSlZR3fMVVTUcSMjlQEIugb6eqOggRsQE4yv7fgStB505QK4rBiKE6FnczCaGDgpk6KBACoor0Ml5HEo62eD+Tn5xBTsOZOLjZWFUXEgXjlZ0Fy0FHRtwSGud7arBCCF6pgBfTyaNjGTiiAgyTpRw6PhJjqYWUC+1H6AAAA8USURBVFlVg7ubmaFRgQ3Ot1ptHDp+ktgBAXh7Olx3WPQCkkgghOg0JpOJAWG+DAjzZeaZVhLTCygurTqt22lGbgmbd6dgNqUyKNyXIYMCiR3gj4+XpYtGLlylpaDzKiDN1oUQ7WJxNzN88Ol7ewCOpOQDRuWD5KwikrOK+HKvichgH2Ov0EB/gvxazWESPVCzQUdr/StXDkQI0XdEBPmQG9KPjNySuudsNhsZuSVk5Jaw7cd0Av08iRsQgIoOarJYqeiZZDFVCOFyI2KDGREbTHFpJUdT80lIKyQjt6RBcdH8ogr26mz6eVkk6PQiEnSEEF3G18eDM4eHc+bwcErLqzieUURiRgEpmUVU2cvvxAxoWAnBZrOxbksCIQFeDI7wY0CYr2xG7UEk6AghugUfL0vdDKi6xkpKVhHZJ0sJ8PVscN7JwnJSsopIySriu8M5uJlNRIb0Y2CYL/1D+9E/tJ8EoW5Mgo4QottxdzPXFR9trP5GVIAaq420nGLScooBY/9QRLAPA8J8iYrwY2CYlJDsTiToCCF6lFFxIQT5eZGcWcTxrELyiyoaHK+x2kg/UUL6iRIyTpRw8eyhDY7X7h0ym2VXSFeQoCOE6FEs7m5E9/cnur8/MxlIcVkV6TnFxp8TJZwsLK87NyLY57TX7ziQyU+JuYQH+RAe7ENogBehgd4E+XlJIHIBCTpCiB7N19vC8MFBdXuCSsurjJlOTjGDI/1OOz/rZClV1dYGS3JgLMsFB3gRFuhNSIA3oYHehAV642GR0pKdSYKOEKJX8fGy1NWEa8xms1FWUd3k62qsNnLyysjJO7UnftH02NPuK6VkFdHP20JAPw9p390OEnSEEH2GyWTi6gUjKC6tJPNkKSfyy8i19wQqLqs67fxAv4aZc1arjQ+/ScBqNfYT+Xpb8PPxwNfHA/9+xh8/H+M5by93PC1u0tqhEQk6Qog+x9fHg6E+Hg1mQ+UV1Zz4//buPMyquo7j+Hs2lhFEVCANreSRr2GCW7mVW5lamYZoKSEm7qa55orikyK55R4WLj32KOWClJrZY2ZSWtrjCvpVUHMlcRmZYRhmmJn++P4uXC53cEaGM8Pcz+t57jP3nnPPnfM9c+d8z285v9/Hi3m/ZjHv1zTwUW0D666zYtJZuKhxWcIBqFvcFMkqb2SFfMeNHklFRdkK75/z6gf07lURj6r0SM97VVVQVVm+xhJV09IWljQ105ge/ap70a9vtuPdKemIiAB9elcydHB/hg5euR0op7mlhU2G9Kemdgl1i5tWGEFhpc/rVblS9VtNbQP/njP/E/eloryMQQOrGbPn5issn/tWDc+8vGDZ68LU1NLaSnNLK0ubW9h0SH923WboCusff/4dnpv7/rLXXx21MVsPH/yJ+9OZlHRERNppgwF92X/XYUC0AdXVN1Jb30jtoiZq6xtZuGgJtfXxvNiUDfUNxduTCjW3tBZNaIsbljK/jVJVofXXXXnA1KrKFTtFNDa1tOuzOpOSjojIp1BRXsaAfr1XGjFhVQb278P2XxxCY1MzSxqbWZJ+NjYtf54b/qeifPU6KTQ3r5y0qntXsk6fKqqqyuldVdElcxkp6YiIZGTQwL4MGrjqwUtbUxVZsZLOsKED2HC95du30pp7AkB5eRkV5eVUVJQV7eo9avggRg0f9OkD6ARKOiIi3UhZWRmVFcU7ElT3qVrrJ7pTJ3MREcmMko6IiGRGSUdERDKjpCMiIplR0hERkcz0hN5rFQDz53/yXb4iItI58s65HRqGuycknY0Axo4d29X7ISJSijYC5rX3zT0h6TwJfA14F2ju4n0RESkVFUTCebIjG5WtasA6ERGRzqSOBCIikhklHRERyYySjoiIZEZJR0REMqOkIyIimVHSERGRzCjpiIhIZpR0REQkMz1hRIJPzcxGAVOBkcCrwBHu3qG7a7sbM9sLmAJsDrwHXObuN5rZesA0YC+gDjjP3W9J25QBPwOOBnoBtwBnuPvStP5gYDJx9/GjwOHu/l6mgXVQivc54Hx3v7VU4jezjYBfAnsADcCv3H2imfUCrgPGECN3XOnul+RtdyJwJjAAmAkc4+6L0ro9gKuBYcCzwDh3b/ewJ1kysx2BawADFgBT3H1aT4/fzL4C3Ofug9PrNRKvmW0K3ATsSJxfTnT3BzqyryVb0kl/lJnA74D1gIuBh8xs3S7dsdVgZpsAdwMXETEdAlxiZnsTJ6Jm4sT5bWCKme2WNj0aGA1sSySrLwPnpM8cQXzJDgc2AF4BpmcT0WqZCnw273WpxD+TGBJqCHFiGG9mhwIXEifiYUR8483sMID0/TgX2Js4Pn2Aa9O6DYF70/brATOAP5tZtzt3pH2aCVzj7gOI7/916eKyR8ZvZmVmdiTwEHHBlLOm4p1OXMxtABwFTDezzTqyz93iwHWR3YEqd7/K3ZvcfTowG/h+1+7Wavk8cLu7z3D3llRq+xvwdeKKZ6K717v7M8CviZMtwHjgKnd/y90XAJOAY9K6HwJ/dPdZ7t4AnA3sYmabZxVUR5nZeGBd4Pn0upoSiN/MdgA2A05y9wZ3f434nj9CxHixu3/k7q8Dl7M8xvHAze4+293rgLOAQ82sH5GMZ7v73en/5DKgN/Gd6m4GAoOBslR6bQWWAo303PgvBI4jLjTzdXq8ZjYc2J6oPWh0978CfwAmdGSHSznpjABeLFj2ErBVF+xLp3D3x9z92NxrM1uf5YOhthJX6Tn5sY4A5hSs2zhtv8I6d68H3qSbHicz+wJwAXBE3uLhlEb82xGJdpKZvW1m84DvAYuJK9rCGNuKfx5xbhheZB2A0w3jd/cPiCql3wBNxECU5xDf/54a/1R33w54KrcgVSWviXhHAG/kquGKfG67lHLS6QfUFyyrB6q7YF86nZkNIK5C/gX8B2hw9/zRXfNjLTwWuefVRdYVbtttmFkF8FvgdHfPn2CpHyUQP5C7yGgiSjyjgdOB76b1hTEWjT8dpwbWsvhTFVADcCjQlyjlXUAPjt/d3ymyuF/62dnxdsqxKOWks4j4YuarJhqZ12qpGPwE8D+iWqkW6JOqHHLyYy08FrkvUV2RdYXbdicTAXf3ewqWL6I04l8CLHT3Se6+xN2fJTpPjE/rC2MsGn86Tn1Y++IfDezi7tNT1dCjRHtcqcSfkyuJdHa8nXIsSjnpzCEa2vJtwcpFy7WKme1KlG7uBcakdohXgDLgC3lvzY+18FhsAbzr7jWF61L7yKZ0z+P0A2CMmdWYWQ1R7L8BOJHSiP8loDp1ksmpBD4C5rNyjG3FP4w4Xq8UWVe4bXeyCdH+kG8p0YutFOIHwN3X1N97DrCpmfUtsq7dSrnL9CNEg+MpRD3wgUTX6RldulerwcyGAfcB57r7tbnl7l5nZjOInmwTiC/ZUUSPLIDbgNPN7GHiamZSWgZwOzDLzHYHHgcuAZ5295fXeEAd5O5b5L82s2eIDgK3pkbSHh0/8BfiBHuFmZ1GnDwmEA3NrwIXmNlzRDXJ6US3WIhYbzKzu9L7pgD3uPui9L25NHUbnwH8BGghOqh0Nw8Rf+OjiY4i2xJ/5yOBN+j58ee7jU6O190bzexZ4GIzOxvYGdgf2KkjO1ayJR13bwT2JZLNh0QXwgNS76W11QlAf+Ifry7v8XOi50oL8F/gAaJny5/SdlOBO4F/svxq53wAd3+eaJSfCrwPbAkclF1InabHx59KtbsR7TnvAg8Cl7r73UQ8LxA9NJ8kutZPTds9QNynNBN4m7jqPSatew/Yj+i19yFRXbtf+v/pVtx9NlHFdgxQQ1wwnOXuMymB+AusqXgPBL5I3KMzDZjg7i90ZMc0c6iIiGSmZEs6IiKSPSUdERHJjJKOiIhkRklHREQyo6QjIiKZUdIREZHMlPLNoSKrZGaVxE11PyJG8P4YeJgYrXpuF+5aUelmvzp3P7yr90WkLSrpiLRtMnFH+6nE3f3fIW6+/XsayVdEOkglHZG2TQBOdvf70+vX0/Ag7wEHALd21Y6JrK2UdETa1gLsaWZ35Kaudvd6M9uaGOOMNBvjecBQYsDNiXlJCjM7DjglrX8BONXdZ6V13ySGI/kSMcTOdcDl7t5qZocDPwZ+n7avIoa1yZ9WeBwxdP9GxJAvvfJ+b39i2JN9iBGEHyOmFs6fU0gkc6peE2nbFcSgoG+a2U1mNtbMNnT3ue7+cZr29xpinKutgBuBu8xsJwAz+1H6jCnEYLKPAPeb2QZpNPAHgD8C2xCTjU0Ejs/7/SOJ+XG+QVTzjQaOTZ+9B3AzcCUxsGUdMWZWzkXEGGy7p/Ut6f0iXUolHZE2uPsUM3uFGKV5HDHw51Izux44jUgUl6WpzgHmmdl2ad0YIoHc6O43A5jZWel9A4GTgAfdPTfN8MtmNjR95vVpWRVwVJqQbraZPUjMDgqRfO519xvSZ59KlGpyPk/Mo/RaGmX8yLRMpEsp6YisQhqh+e40NcLuwGHEcO/ziRGnd0jDvOdUAblpD0YAv8j7rFbgTAAz25KY5TTfLGBKXieF2oIZUBcC66TnX8rfPlXJPZn33kuA+4EFZvYoMb/SbYh0MVWviRRhZiPN7Lrca3evc/f73P1g4HdEqaKSGAJ+67zHlkQvN4BGoK1h3BcXWZab2TT3f1ls+PyyNp6v8H53f4Io2Uwg2p8mA4+bWZ829kckE0o6IsVVACeY2W5F1i0kTuQvAp9LbTxz0707BwOHpPe9TLSnLGNms83swLRt4eRXOxM94z5qx/49B+xQsGzZ70qlrx3c/XZ3HwfsSLQ7jWzHZ4usMapeEynC3Z82s3uAO83sHKITQH+iUX9s+vkZ4A4ze4mYtXNP4EKi/Qeiam1amsH0CWIGyyHA34F5wFNmdh5RctqWKDXleq990i5eDTyW2nLuI6r9RhHJCKK33LjUlvMu0SFiIcur/kS6hEo6Im07lOiddjLwPNHteB9gH3d/3N1nACcSN4/OAc4Ajs91LEg/zwMuTtvvCuzr7gvc/RmiN9pBRFfqyUT36cnt2bFUfXYQ0avtWaL96I68t/wU+Acx5fCLREL8lrvXfKojIdJJNHOoiIhkRiUdERHJjJKOiIhkRklHREQyo6QjIiKZUdIREZHMKOmIiEhmlHRERCQzSjoiIpKZ/wOTC9mA+HzQswAAAABJRU5ErkJggg==\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "#note the rippling in the temperature readings\n", + "#bang bang heater causing small changes in temperature when the threshold is reached\n", + "#it is this phenomenon that we will focus on\n", + "import matplotlib.pyplot as plt\n", + "plot_results(results3, trendline, 'Calculated Room Temp')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Sweeping Heater Input Rate" + ] + }, + { + "cell_type": "code", + "execution_count": 31, + "metadata": { + "scrolled": true + }, + "outputs": [], + "source": [ + "#sweep possible heat input values\n", + "rate_array = linspace(1000, 3000, 5) \n", + " \n", + "\"\"\"\n", + "for rate_in in rate_array:\n", + " system = make_system(beta, gamma)\n", + " results = run_simulation(system, update_func)\n", + " print(system.beta, calc_total_infected(results))\n", + "\"\"\"\n", + "def slope_func4(state, t, system):\n", + "\n", + " Temp = state\n", + " \n", + " #calculate rate of heat loss\n", + " dHdtJ = system.U * (Temp - system.t_oc) * system.A\n", + " \n", + " # converted from joules to degrees celsius\n", + " dHdt = -dHdtJ / 430800\n", + " \n", + " # introduce heat input equation- current input is arbitrary, to be swept later \n", + " dIdt = system.rate_in / 430800\n", + " \n", + " #combination rate: input minus output\n", + " dCdt = dIdt + dHdt\n", + " \n", + " #return heat loss rate if heater is off (when in ideal temp range)\n", + " if (30 < int(Temp) < 21):\n", + " return dHdt\n", + " \n", + " #return loss and input if in non ideal temp range (heater on)\n", + " else:\n", + " return dCdt" + ] + }, + { + "cell_type": "code", + "execution_count": 37, + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "data": { + "image/png": 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PtxM1cEDj1tmG0WtBPQ48IKVcK4SYC6RJKUcJIa4A3kQ7E6XwMX749je2/S+90ftJykryLOmLPubkd6uwlZRoDzZlxVTFKSBGI+YRwwg8fyiG4CB0i0VtmIyYw8IwBQc3yxL1cgI4kZzs1Tm9jclkIjo6mvbt22M0GptlTL0C1RtY7vh5EvCN4+dkoGOzrETRLDRVlNReUuNQYuOgKdZGHe6no0ePYjAY6NixIwEBARj07psovIbdbsdisXDq1CkyMjLo3r17s4yrV6AygAFCiAhgAHCPo308cKRZVqJoNE0VpfBIlWC1OseXrSBjqXOfxta6XWiuD3x33Fpecl8VFRUhhGi2b+WK5sdgMBAYGEiXLl2QUjbbuHoFaj5aVV0r8KOUcqMQ4h9oRQ3varbVKHSzcV0Km9amUFJsbbhzLbRFUaoaHNCKRMfdjXc/3BdR4uQfNPfvSZdASSnfFELsALoD3zqafwHGSik3N+uKFHWyZ0cGa1cmU5hX5va9RhPEd26ddZEq3WvFxf7rWmvIYnEVG5OZoLj29Lj5JuLGXuKFxSkULYM7qY62CiHygMuFEGuBFCnlUc8tTQFaSPjqZfvIynQ/y5TJbKBXkv/uJ+Xv3UfaBx9SdNRxcNNftKc+sXEVmoBAogcOoPfd0wiOj/fS4hQK/0FvmHkEWn2o3wM2oA8w33E26mop5QmPrbANkptTxDdf7CHtYI7b95pM0KtPnM+LUmlmJqlvvUfe3r1gtfi++NTmRlNio6iHPXv2MGPGDDZv1pxM5eXlPP3006xevRqj0cif/vQnZsyYUdl/0aJFvPPOOxQWFjJ+/Hhmz55NaKhWWHzLli3MmTOHY8eO0bdvX55//vk6AxHc6evr6LWgXgSigAS0khgADwEfAa8ANzb7ytogG386xIbvD7kd7GA0QnwX33LfaWd1llCeXVveMx/BKTq17dX44T6Nwjew2+188cUXPPfcc1XaX3vtNdLS0lizZg2FhYVMnz6djh07MmXKFH7++WcWLFjAwoUL6dy5M//4xz94+umnmTdvHmfOnGHmzJnMnTuXyy67jA8//JBp06ZVCp0r7vT1B/QK1CTgGinlUSEEAFLKNCHE/cAPnlpcWyDt0Gm+W7aX05lF7t1ogM5dW06UfF6AanOzKdFp02TmFJGRdZauHcKJ96B34d///jfr16/nnnvu4c0336xsX7p0Kc8++yxRUVFERUUxbdo0lixZwpQpU1i2bBnXX389SUlJADz88MNMmjSJJ554gjVr1pCUlMTEiRMBmD59OosWLWLz5s2MGTOmytzu9PUH9ApUBFBXXhyVz68RLF+yi13bM9x2bcW0997B2ZQ33+bUjz9BebnH59JFXdFqAQHKvdbG+FVmsfW3TCxWfd6G4lILB9JzsdntGA0G+ia0IzQ4QNe9AWYjI8+LZ6jooKv/1KlT+ctf/sIvv/xS2VZQUEB2djaJiYmVbT179uTgwYMApKSkcMkl5wJeunfvjt1uJz09nZSUFHr3rhpt67y3uui409cf0Csuq4FZQog/OF7bhRCxwAvAGo+srBWye/sxflx5gMJ896LwPBUSXmUfyNL4FEjNQm3i00IJKhW+z66D2brFCaCoxIrNbickyExJmZWiEqtugbJYbew6mK1boDp2rJm7oLhY+34f7JLBIiQkhNLS0srrISEhldec54pKSkpqXHOOU1JSs26sO339Ab0CdT+wFDgNhAKrgK7AIeCPHllZKyE3p4hvPt9D2iH3Ah7MAUZGXdKzWQr6aWHY32ErLmnZMGxXt5sSH0UTGNInzi0LKizEjNFgoKTMitFgICxEv+MnwGxkSJ+4xi4VoFI0ysrOfTktKSmpDIJwFSvQ9rHKy8sJCwurcQ2gtLS08t7q8+jt6w/oPQd1EhglhJgAnOe4LxlYJaVUefZrYfP6VDasOURZiXsHaTt3a9y+Uv7efaS+v5CSo8dq1tLxBtUtIJNJndVReIyhooNui8aJt/agaiMqKoq4uDgOHz5caWGlpaVVuvwSExNJS0ur7H/06FHsdjs9evQgMTGRFStWVBnv8OHDTJ8+vcY87vT1B9zdPzoCBAM/ArFKnGry/df7+eXnNLcMFXdceNnrN5C+eEkdVUE9SPWIN7OJoLg4JUAKvyE+NszrwuTKNddcwxtvvIEQguLiYt577z1uv/12ACZPnszjjz/OxIkT6datG/Pnz2fChAmEhoYyYcIEXnjhBVauXMmECRP46KOPMBqNjBw5ssYc7vT1B9w5B7UYLZpPnYOqRtqh03y3dC+nT+mPxDOaDJx/Qbc6S1dkrdvAkY+9LETVrCBDUBAdxo0l8Z67vTO/QtGK+ctf/sKzzz7LpEmTsNls3HTTTdx8880AjB07lnvuuYd7772X/Px8Ro8ezezZswGIjY1lwYIFzJkzh8cff5ykpCQWLFhAYGAgALNmzeLEiRO8++67Dfb1Nwx2HV/1hRBvAQK4He0c1GC0+LOPgJNSyhY7B+UQybS1a9fStat3S0JsXJfChtUH3Tq3VFsU3qH/vEXWT+u8Ey1XLfxaiZDC10lOTqZfv6bvxSq8Q12/r4yMDMaPHw/QU0qZrmcsdQ6qESxfsotd2zJ093cGPIjyFDKWLqZgayEbbR72jrpaQyoMW6FQ+CHqHJRO0lNOs3LpPk7rzolXQVB5MYk524kvSodkSPfEwgwGbV/IYMAcGUHX66/zi1LOCoVC0RDqHFQDpB06zVeLd1JUWJ/7zaXkts1KbPFxRM42QqzuJ3itE6dFpKLjFApFG0Gdg6qDXduP8f2y/ZTWCBO318z+YLNhtpXRM3c33QsONM8CVJScQqFo4+gVqEIpZZPPQTnufxZIArKAF6SUbwkhegEpVHUjLpFSej14/4cV+9myIY3KLaL6gkhsFUSU5ZB0ZgftSk+5P5nDKlKBCgqFQlETvQK1VwhxnZRyDY106QkhugFfAncAXwPDgNVCiHS0Pa6tUspRjRm7OVj58Va27zgGdh3hmDYrXfIlfc9s0z+BwaCSlSoUCoUb6BUoUzPMlQB8LKVc6ni9TQixDhgDBAC7mmEOt8nPz+eNx5djDYwG6hcnQ0UZvc/8WunGq+HpAyodgkbIiDezYXgUBeEmR5OBULOVCbZUbkYJlEKhUNSHXoH6GPheCPExcBioknlQSvl2QwNIKX8Gfna+FkLEABcDi4D/B4QJIQ4C4cBK4BEpZZ7O9TWadx9fiDWwFwbKsGOixkdit2OsKKNX7q4q+0vVxehYvJmfXcSoNmzYOWstYemBVSw9sKq530qzUU/hceCcMAcaAxiXcCHTR9zs6SUpFIo2iF6BuhUoBa6r5ZodaFCgXBFCRAHLgV/Q3H03AZvQih+GoB0AfhsvFEK0GGMBK8GmVABKK3phJxhsNoKsZ+l9Zicdi9KpAMpBtxj5M3qzNJXbLHx/eAPfH97g0fX4KgaqflYNCbsT13uCjYFcnHAB04ffjKGuciIKRRtFb7LYbs01oRCiD5oo/Qbc6giymOrSJV8I8RjwPyGEWUrp0cynoQEnMRgCMBi0DMAhpgOYi8Loc2o3wdaznA03sOrCCA4lBNe82W4HDPqfTIpWRXUhb0ye+FJbOWsO/8yawz833LmNcl/vWwk8c6Sll+E2cv8B/vXXf/LJys8BsJSXc/34KZgDzj12+w08jzmvPgvAhh/W8+GCDziTk8PAoYN46IlHiI5pB8DhQ6m8/vy/SUs5THznTjz4+MP0OU/UOq87fd3BZDASGRRBTGh0k8fSi95cfKPruGRHMyyOSykzdYxzCZo4LQAek1LahRChwL+A+VJKZyhcIJoHzeNJ6O6f/1deeWQ29goLAbYSLIG5ZCUYSB4UQG54zLnzRxW2c0JU15PIABhNjlsMjq4tWN5CoVB4HbvdzuoVq3jvtaqOpbTUdCIiI1j87ac17jmadoRX573E7JfmkNS3D+//512enTWXZ19/AYvFwuy//YspN13L82/OZ+NPP/PEA/9g4dJFhIZVTX7rTl93qbDbyC3NB/CaSOl18S0GugFGoBDt6RuOy6NaCLEBuFFKmV3bAEKI3sA3wONSytec7VLKYkf4eawQ4j4gGi0UfaGU0itP9wdenMW2XYdYs/QzOlkL6V5QjKHAToypgs5mC6baLCQ9hpPBRFC3vnSYdC8B7eI5dTabD3Z8yr5TB7HY6zYMXUXNoNM8a8w9zTGXQuE3FORAbha06wCRsR6b5r/vfMS2Tb8w9Y+3sGThx5XtKQcO0iup9ooFP65ay8gxo+g/WAue+uM9d3Lj767n+LHjnDpxkgqrlSlTtR2WsRMuZcUXy9nww3qumHxVlXH27tytu29jKbIUE4NvCdR/0PaJ7pBS7gcQQvQF3gM+Az519HkZ+EMdY8xECyefJ4SY59L+BnAt8BpwAs1qWgI84tY7aSIjhiQxuN9D/LDyW7buPEBJWQXtjQX0sp4mKbCIAIOdQKPLDc7zuvUJlb2CsqP7Ofafmdprg5mbo9sTc/FNRAz0/8O3723/hHVpWyi3NVyNt6UEVAl8K+WYhCP7oULnDkB5KWSmV6YFIz4BAmtx29eGyQw9+kM3fW6yq66dxG1338GenburtKfKFPJy87j3DzPIO5PLgCEDufuBe2jfoT1H04+Q1LdPZd/g4GDiOsSRnppGdmYW3RK6Vxmra49upKemUZ2jaUd1920sYQHeK36oV6AeRiursd/ZIKU84LB4vpNSviqEmAWsr2sAKeVDwEP1zNHiCeQCg0K4YvJ1JPbcyvZtO0hON7LVEslmi4ljFT25JOgQYwIPEGTUHsiBRvQJlRO7lYrcTLKXv0r28le1m4LDiDp/IrGX+l9V2WnDb2bacBXB1xQ8LfL+JNbuzEXGQf3iBFDmqCYdEASWMu21XoGqsGrz6RSo2LjarbOgkGDOG9SfW+68FZPZzIKX/sMzf3+KV95/jdLiUoKCg6r2Dw6irLSUkpKSGteCg4MoLS2jOu70dRef3YNC2xMKqqU9DC3qDqDMjfF8FqPRSJ8howiPjqHzri2cyC5k/+EcepDC+rI+rCobWtn3iqBfawqWWzETdig9S/6mL8nf9KXWZDBjakVWlqJ+lMg3THJyMr1jelRpK+53McWHtmOvaFjYAWyYKM3P0WqrmQIIjmiPMUifJWAwBRCaNJzQamtoiNMRmRgNxsq1P/fUvCrX5zz5NBdeeCGhZYHERLYj3Bha5X3aLBX07NCDgHITqbZDVa4F2gOIbhdV43PpGttZd19/QK+gfA68L4T4C7AdbS9qGFpY+BeOgoZPoIWNtwo6J/QhLCKagF9+olP7MI4XBnEkORxcaj+tKhtap2AZTA0d+62DGlYWEBBExMBxxF2pUiEpFAChvQYT2muwW/dYcjOx5JwgILYzAe28X3bm1VdfZdKkSfTure1DWSyauAYFBdUo+V5SUsLJkyfp3bs3QUFBLFy4sMpYhw8fZsqUKTXm6N27t+6+/oA7yWLfAFZwLquEBW0P6hHgSrQihlNrvdtPiYrtwLBLJ5G6bzsXD7mQPwQEsn7nMd5Ztpf8oprf3KoL1pVBvzI27CAhWNCO9jYSSxmFO1dTuHO1o8GAITiMSD91DSoULUFAu/gWESYnUkr27dvH/PnzAZgzZw7jxo0jJiaGSZMmccstt/DLL78wdOhQ5s+fT79+/ejZsyddunTBbrezcOFCbr31Vr7//nuklEyYMKHGHBdccIHuvv6Aroq6ThyW0nlo4nRISlnoqYXppaUq6q7bcYTFy7eReTZAV//h/Tpw54Cz2HYso6LgNNia/3iXISSSdqOvI3pUi2/nKRTNhr9W1P3ll1+YOXMm27dvByA3N5dnnnmG//3vf1RUVDB27FhmzZpFVFQUAKtXr+bll1/m1KlTDB48mLlz59K5c2cADh48yJNPPsmBAwfo2rUrjz32GBdeeCEACxYsYMWKFXz77bcN9vUGzVlRV7dACSHC0DJKCGAuMAL4TUp5VN+yPUNLCVTK3m1kpCZjiO7NF1tLSD9VpOu+Du2Cuf2q8xh7fjcsuZlkr36P0vR9UGGhcUc9GyAgmIiBY5V7UOG3+KtAtVW8XvJdCJEE/ISW7qg7mrvvNmCSEGKilHKmeVDbAAAgAElEQVSLvqW3DrKOp3MsRQtotOceYsa4BNr1GMu7y5PZfiCr/ntzS3lx8U5e+3QXk8f25rapj1e5nrdlBblblmEvLgS7jSaLlqW0mnsQMAYQ2KE7seNvJyRBJa1VKBS+id49qFfRChbeDxQ42v4AvAm8CFzU/EvzXaJiOhAZE0fBGe1McvbxdIoK8nhk6qWERVzIm1/uZuWm9HrHKLPa+GztIT5fe4hh/Tow49pBxMeGET3q9zVcdNnfvU3h3nVgKadZrCybhfLMVE4uftKl0YghOFTtaykUCp9Bl4tPCJELjJJSSiFEITBYSnnYkR1it5Qy3NMLrWdtCbSAi89WUUHK3m0cTzuX4dxkDqDfsIuI66yFc7755W5WbUrXHR7RoV0It1/Vj7Hn15/60CuuwUpMGMMjib5gstrbUrQIysXnX3jdxYfm2msPyGrtvTlnUbUpjCYTfYaMIjImDvnrJmy2CiqsFvb98hPdkwbQ67zzuef6wdxz/WAWrfyNZetTKLfWLyRZuSW8uHgnr3zyK78b1YN7rq89jDagXTydq7kGS9L3cXrtR1iyjroEYDSHcFVgO5vLmbULObN2oUu7EWN4lBIuhULhMfRaUC8AlwN3Az8C44COwOvAUinlwx5cY0NrS6AFLChXCvNy2PfLOkqLzwU1tovrxHkjLiEwKKSybf3OY3z47X6y8/Sd6jZAFfdfY6jqHgTPWlsABse5LRWYoWgelAXlX7SEBfUPx58/o50/3YaWM+8t4DGdY7RaIqJjGX7pJH7b/jNnTmUAkJt9ErlzMwMvvKyy39jzuzH2/G5k5hTx1ld72HEgq165sAPbk7PYnvwDkWEB3Di+D5PHJrq1trgr764hFJWBGEUFNOl8Vq3Yaw/MADCYMEXHqSwZCoVCF+6egwoFktCE7ZCUssXde75gQTmx2+2kH9hN+oHdmM0BDL/s94SERdR7j173nytJ3aL406T+DEyMa+qSK6m5rwWet7ZcUCmeFHWgLCj/wivnoOqpAVUDKeUmvX2bG18SKCc5mRnY7Tbad+recGcH7rr/AIIDjVxzcW9uu+q8xixTFzX3tloiE7fa72rLKIHyL7zl4vsf2tPItbK182cbWsojO5qrr1Fp51orsfG1C2Xm0VRCI6KIbNe+xjV33X8ApeVaqPpnaw/RqX0ot07s22AEoLuEJAyg27Tna7TXHpQBnhEwWx2BGgAGMJoJ6NCd9upcl0LRqqhPoNq5/HwtWqmMe4CtaKI0BK0G1LseW10roiD3NAd2bsRgMNB7wHC69OqLwVAz73l8bBhP3qWlJVm08je+3pBKmaXhfaKTp4t1RQA2F3UJF3g7MMMONguWGue6nBjAZCYgTgmYwjts3LiR+fPnk56eTmxsLNOmTWPq1KkUFBTwxBNPsHHjRkJDQ3nggQe4/vrrAW174JVXXuGzzz7DYrFw3XXX8be//Q2zWXtEr1y5kpdffpns7GxGjBjBs88+S2xs7WU93Onr6+iN4juCVi33l2rtw4BvpZQtloHRF1181bHb7Wz/aQVn889UtsV1SaDv0DGYAxrO5bc3JZsPVuwjJaPArUd9eIiZq0b39KgL0B0K927gzIZPHbkIK1yu+EABP1MAYX1H0XHKAy29EkU1msvFd+psNicKT9E5oiMdw5tv/9aVkydPcvXVV/Pcc88xfvx49u3bx/Tp05k/fz5Lly7FZrMxb9480tPTmTZtGq+88gojR45kyZIlfPTRR7z//vsEBgYyc+ZMxowZw3333UdKSgo33HAD77zzDgMHDuSFF17g4MGDfPTRRzXmd6evp2iJKL6oOtrDUO69BjEYDAwYOY7929ZTmJcDaNknzuadof/IsURE1//tZmBiHC89eCkAX69P4bO1BymoJZt6dc6WWCtdgO0igrj+0kS3owCbk4iBl9QZAFG7eHlRuCosFO3/mcP7f66jgwHMAYT0GED7idNaNCu2AvZkJrP9xB6sOosWFltKOXj6MDZsGDHSp30vQgP0FSw0m8wM7zyIQfENi+Tx48eZNGlSZfbwQYMGMXLkSDZv3szq1av55ptvCAkJoV+/ftxwww18+umnjBw5kmXLlnHHHXcQH6/9vfrzn//Mo48+yn333cfy5cu57LLLGD58OAAPP/wwI0aMID09nYSEhCrzu9PXH9ArUEs5Vw/qV7S9qAvQ6kEt8tDaWhUh4ZEMveRKUvZu40Sadt65pKiAnetXkjToAjolJNXq8qvO5LGayDj3qnbKLGw6nuO5hWW8u3w/7y7f77H9qqZQn3jVvd8F3hMxO1jLKUndybH/7Kynn0oZ5Q32nErWLU4AxZZibNgIMQdTYi2l2FKsW6CsFVb2nErWJVDDhw+vFAeAvLw8tm/fzvDhwzEYDFVEolevXvz444+AZvk460Q5r2VlZZGXl0dKSgoDBpxzTYeEhNCpUycOHjxYQ3Tc6esP6BWomcDbwHdoxQpB24d6H60elEIHJpMZMeRComM7In/dTEWFBZutArlrE7nZJxFDL8QcoM8gdd2r+np9Cl/+dIjcwvIG7tJw7lfNX7yT/r1j+ctNQxt9ENgb1LffBdUT7Lq6Dl3je7yFDXv1Ksl1YQpQe2ONZFDHfm5ZUKEBoRgxUmItxYiR0AB91XRBs6AGdXTfxVhYWMg999zD4MGD6d+/P4GBgVW+hIaEhFBaWgpAcXExISHnDvUHB2viWVpaWuOa83pJSUmNOd3p6w/oEigpZTHwByHETMD5m0qWUuZ7bGWtmI7dehERHcu+resoKsgFIOt4GgW52fQfOa7WKL/6cFpVoOX/+2HrEV3nquzAvtQc7pr7AwEmA4P7xDUpa0VLUVuCXVdqZoivTgvtgVXUF9xRE1Xv6xyD4vvpsmhc8cYelJO0tDTuvfdeEhMTefHFF0lNTaW8vBy73V4pUiUlJYSGakLpKlZA5c+hoaE1rjmvh4XV/HfqTl9/oE6BEkI8DrwkpayUXocg1Vpaw1Ev6mEp5exmX2UrJDQiimFjryZl71ZOpB8EoKykuMnjOvP/OV2Auw5lYa1o+D5Lhb0ya4U/i1VtNCRgUFvkYXVaPpDDXlJQR6h9dRzf0lXKqSp0DI/zuDABbNu2jXvvvZepU6fy0EMPYTAY6NGjB3a7nYyMDLp101zrhw8fJjFR+2LpLPk+bNiwymtxcXFERkbWWw6+Ou709Qfqs6DKgH1CiE+Br6SU22vrJIQYilZ64wa03HwKnZjMZsTQ0UTHdeLgr5vpIQa5bT3VhasL0BkFmJpRoCuxkatYmY3Qs0vzZ67wNWpLCVWdnJ8+Jn/HKigrQRMsV9FqCXdiXTjWUVfKqVpxiJrRhClKZfRoLEePHmXGjBk8+OCD3HbbbZXtYWFhXH755cyfP585c+Zw7NgxPv/8c+bNmwfANddcw/vvv8+FF15ISEgIr732GpMnTwaotxx8ddzp6w/UG2YuhOgBPArcDpQAvwGn0f42xwED0KL4PgKe0xs62Jz4Q5i5HspKigkMDqkRKFFeVlIl4WxTWb/zGItXJXMyx32ftAHo1D6UW3wswMKXqD1llCu+ImLNiUOcDSbM7bsQ97tpzbqn5k+ZJObNm8fChQsrXXdObrnlFu6++26eeuopNm7cSGBgIHfddRe33347ADabjddff53PP/+c0tJSrrjiCv75z38SGKjtSddXDn769Ol07tyZ2bNnN9jXG3i95LsQIgK4DBiGlsXcBmQCO4C1rm5Ab9NaBKo2SooK2f7jCjolJNHrvPMxmkzNOv6ilb/x7cY0ikr1R0O50ik2lFuvUGLVWBreG3PSGkWtOnW7Jf1JoBQtIFC+TGsVKJvNxq8bvqMgV6vaGxHdnvNGXEJoeKRH5muqWPnaoeDWRv2h9rXh3/+uXSka/xf69NBrAbh4IAxGTKGRmCP9M4uCv9ISB3UVXsZWYcUcGFT5ujDvNNt/XEHS4AuI795b15kpd7jtqvMqxaUxYuV6KDjABAmdW/++lTdpKNS+Nk4te4Wi5C1gs1DlwV0nrUHUXN6DvYKKolwqinKbYVyXz89kxhwegym0/koFiqbjVQtKCDEBeBatZEcW8IKU8i0hRDRaTr8JwFngCSnlBzrHTKAVWlCgpUjKSE0mdd927C4uoLjOPRBDRxPgImCewt0zVrWhrCv/Qb/bsTqee464Z0H5I9UDbAyAAUNQCObI9hjNDadD8yX80oISQnQDvgTuAL5G289aLYRIB/6IdvC3E9DH0X5YSrneW+vzRQwGA90SzyO6fUf2b11PSZFWfiv7xBEKzmTTd9hFxHTw7D9c1zNWjSkJAlWtq0CzgUFJrSeEvbWhJyS/LtwXN1+NgvQ21d+3FiFqLyvCkl3kwXnrsaqNJkxh0ZjDoz04f8N408WXAHwspVzqeL1NCLEOGA/8H9DfcSB4lxDiHbTy8m1aoJxERMcy4rLfa2mSnGemSovZvfF7uvY+j179z8dk8vyv0lkSBM5FA2adKaHCjedKufVcCDso66o10RRxc1L3eTTnw7S6qNVGWxU6d6nnc7JZqSg8TUXhaZdGI8bQSAKimucojB50P9WEEMPRSm70AaYANwGHXQSnXqSUP6OVjHeOFwNc7GizA4dcuh8ArtG7traAyRyAGDqa2PhuHPh1I5Yy7bR4RupvtO/UjXZxnby6Hlexch4K3pOaTbnFvYeDq3VlNkJcjO/lCVR4j9rOoyUnJxPUyb2DpjarBWvBaex1nlnTg7LwqmLDVpyH1WDwWuCJLoESQkwEvgKWAP3Rzj6FAp8KIe6WUi50Z1IhRBSwHPgFLVS9VErp+tsvdoyvqEb7Tt0Y2W4yB3ZuJOdUBl179/O6OFXH9VAwnNu3yj9briuRrROr7VyewBcX78RogG4dI5hx7UAVbKFwC6M5gMCY5v93UVFciPXsGagzB2BjhLD6fb6NrawY8CGBAp5BS2O0QAhxI4CU8mkhRDbaQd6FeicUQvRB24P6DbgVLbdfsBDC4CJSoWjBEopaCAwOYeCF4zl17DBxXXrUuG632TAYjbXc6R1c960yc4r495JfSU7PwerOnjtgs8ORzEIee3MTgNq/UrQ4ptAIr0TvWQtyqCgucON8XGOtwvqu144xyHu2g16BOg/4vpb274GX9U4mhLgETZwWAI9JKe1CiENon1RP4LCja180AVPUgcFgIL57TbeHpbyMnRu+I0EMokPXns0eju4u8bFhzJ15UeVrZwh7canV7e+M1fevVDi7orVijoxtsfNbtrISrAU52K3VgqFa4FyZXoE6DgzlnIA4uQw4qmcAIURv4BvgcSnla852KeVZIcRSYJ4QYhrQG7gLLbJP4QZ2ux356yaKC/P4bfsGsk8coc+QUc2aKqmpuJ63asreFYClAg4dy6+0sMxG6BCjUjEpWpa6Sr4fO3aMCRMmVCmHcdVVVzFnzhwAFi1axDvvvENhYSHjx49n9uzZlSmTtmzZUpnDr2/fvjz//PN079691vnd6VsbxqAQAuN848iOXoGaB7wthOgFmIArHOePZgIP6hxjJhCBJkTzXNrfAGYA/wGOAKXAHCnldzrHVTiwlJdSmHeurHz2iSPk5Zyiz+BRdOiS0HILq4Pqe1fOyMDs3BK33YGg7WGdcNnDMhkgMiKI68e1bCVhhW9QmplJyfEThHTpTHC8Zyoinzx5kj//+c81Sr536dKFoqIiBg0axGeffVbjvp9//pkFCxawcOFCOnfuzD/+8Q+efvpp5s2bx5kzZ5g5cyZz587lsssu48MPP2TatGmsXr0aYzVXvjt9/QHdB3WFEFcD/0Bz95nRIu2el1J+4bnl6VpXAq30oG5jsFospO47F47upEPXnvQZPMorh3ubC2ewRUFRORWNEKzaCA40ctnw7txz/eDmGVDhcWo7+Jm3azdntm7HZq0tIW9NrMXFFB6QYLOB0UhEX4E5VN9eitEcQMzI4UQPafjvzPbt21m+fHll4laA++67j6SkJKxWK/n5+VWuOXn44Yfp0qULDz30EABHjhxh0qRJbNmyhW+++YalS5eyZMmSyv5jx45l7ty5jBkzpso4n376qe6+nsLrB3WFEH8DFkspL2qws6JFMQdo4ejtO/dA7txIWalWYyorI4287EztWif/cH+5BlvAuf2rkjKrW9GBrpSW21i5KZ2Vm9IBlJXlp+Tt2q1bnAAqiorBZsMUEkJFSSkVRcW6BcpmtZC3a7cugaqr5PvkyZNZsmQJxcXFTJw4kaKiIsaOHcujjz5KZGQkKSkpXHLJufIm3bt3x263k56eXqMcPEDPnj05ePBgDdFxp68/oNfF9zhaFgiFnxDbsQsjxk8mZe82Mo+mAFrpjr1b1hLfPZGkQSN1l5f3FVz3r6B5LKwKO+QWlPHu8v28u3w/oKIF/YHoIYPdsqBMYaFgNFJRUgpGg/ZaJ0ZzgC5xqo5ryffx48ezcuVKhg4dyh133EFpaSmPPvoo//znP3n11VdrlGo3GAwEBgZSUlKiSr7r4Fvgz0KIp6SUzZF5UeEFAgKD6DfsIuI6d0f+upnyMu0vaebRFGI6dqFjV/8sYuakuoXlTMWUk1/WaAsLakYLAgQGGBiUqETLV4geMtht0fDGHpST6iXfjUYjL798LuA5IiKCBx98kFtuuQWr1VqjVLvdbqe8vJywsLA6y7hXrzkFdZd8r62vP6BXoBKBqWgiVYBWvLASKWVrzuTo97Tv1J2o2I4c3L2FrIw04jr38Mmgiabimt0CzlUSTj9ZgLWiaUchyy01RSvAbGDMoM48fOvweu5U+ArB8fEeFyaoveR7SUkJr732GnfeeSft22upgiwWC2azGZPJVKNU+9GjR7Hb7fTo0YPExERWrFhRZY7Dhw8zffr0GnO709cf0CtQbzn+U/gpAYFB9B8xlrjOPYhu37HG+ShLeZlfBVDoYWBiHC89eGmVtje/3M3abUcpt9iafHbfYrWzbudx1u08Xtmmzma1beoq+R4SEsKmTZvIy8tj1qxZFBQUMH/+fK699loMBgOTJ0/m8ccfZ+LEiXTr1o358+czYcIEQkNDmTBhAi+88AIrV65kwoQJfPTRRxiNRkaOHFljfnf6+gOqYKGCCquVbT9+TWS7OBIHjfCpc1OeZm9KNm8v3cOxU2ex2T2TcMYIhKqkuI3Gnyrq1lfy/eabb+aZZ55hx44dGI1Grr76ah599FGCgrQvhosXL+a9994jPz+f0aNHM2fOHCIjtQKl27ZtY86cORw5coSkpCRmz55N3759AZg1axYnTpzg3XffbbCvN2iJku8f13ddSnmLnsk8gRKoppOybzvHDu0DICAwmKRBI30iC0VL4RotaPeQaIGytvTiTwKlaJl6UBW13NcLGAj8W+cYCh/EbrdXZkYH7bDvb9s3cCojjT5DRhEc0vYCAqpHC4JnRKt6JgzQcn4FqIAMhQLQKVBSyttqaxdCPIaWmkjhpxgMBvoNu4gOXRKQuzZTVqIVSMvJPMbWHzLpPWA4nRP6tFlrykltouW6nwXNI1p2ag/IAAgwGRjcRwmXou3Q1Cp3HwN7gGnNsBZFCxIb35WR46dweP8OjqcdAKDCauHgrs1kZaQhho4mNDyyhVfpW9xz/eAaGSlcz2bZbM3rHrRU1C5c6rCxorXSVIH6I1DYDOtQ+ADmgAD6DBlFh64JHNi5qbLEfN7pTLat/Zpe/c+nW2L/Fl6lb1P9bBY0PSluQ9R22NiJ2QT9EmK5/6ahyupS+B16Ux2dpOaXwXDHfw8396IULUt0+3hGjL+G9AO7OXZoP3a7DZutos27+RpL9aS4TqpbW9D8ARnWCtibmsNdc6taXQbAbIaETipIQ+G76LWgnqj22g6UA9uklLJ5l6TwBUwmM737D9P2pn7dBBjo0tN7oaptgdqsLfBOFKEdsFhrBmk4MQLRkUFcp9yGihZEr0B1BF6WUlbJICGEiBRCPC+l/FvzL03hC0RExzJs7NWUl5fWqNJ7Nv8MZ/Nz6ditl7KumpHaAjKgpnCB50LgbcCZOtyGBsBkgg7tVO0thWepU6CEEJ3Q6jcBPA38JITIqdZtKPBnQAlUK8ZgNBIUXPXgod1uR+7aTMGZbE4eSUEMGUVoRFQLrbBtUJdwVU/p5MRT4mVHcx261t5yxQAYjRAVriwwRdOoz4IaDXzOub/nG12u2TlX0H5h8y9L4etkHkmh4Ew2AHmnT7Ltx+V07zOQ7n0GYDI1NfZG4Q61pXRyUpvVBZ4TL+fYFba6LTBQVphCH/VmknBU0DUCB4ELgdMul+3AWSlllkdX2AAqk0TLUGG1kJa8i4zUZOz2c7UuQsIiSRo0kth49bvwdbwRpNEUnJbYw9d1Y+CA84iOCG7pJenip59+4qWXXiIjI4PY2FimT5/O1KlTKS8v5+mnn66sbvunP/2JGTNmVN7nKyXfm4rXMklIKQ8DCCECpJTVs0ngck1/5TBFq8BkDiBx4Ag6duuF3LWZwlztu0tJUQF7Nv9A+/juJA4aQUhYRAMjKVqKuoI0oG63IXhPxJyWmM1uJzuvlOy80jr7GgwQYDISExlMRFjtdc5yc4o4nVVE+w5htPNQyH1WVhb3338/r7/+OmPHjmX//v3cfPPNDBw4kFWrVpGWlsaaNWsoLCxk+vTpdOzYkSlTpqiS73Wg1xcTI4T4O1q5d5OjzQAEAQOAGA+sTeEHRETHMuySqziefpC0/TuxWssBOJ15lDNZx5Xbz0+pz20IWu2txauSyc4tweqwvpw+f28I2MkjuZxIO0OFVd9slnIrp08WYrfbMRgMxHeNJDIiGKOx4eAes9lI0nkd6S0aDsXv0KEDmzdvJjw8HJvNRl5eHiaTibCwMJYuXcqzzz5LVFQUUVFRTJs2jSVLljBlyhSWLVvG9ddfT1JSEqCVgJ80aRJPPPEEa9asISkpiYkTJwIwffp0Fi1axObNm2tUyXWnrz+g96nxNjAcWAHc5XidCFwE/NUzS1P4Cwajka69+tKhSw8O79/JySOHALDZKjgi9xDXpQfhke1aeJWK5qR67a3q1GeBQdNFLPNonm5xAigvq8ButxMQYMJiqaC42IrBpM/xYzDAb3tP6hIogPDwcEpKShg+fDhWq5W77rqLmJgYsrOzSUw8Z7E6S7EDquR7HegVqMuAa6WUPwohRgPvSyl3CCGeRQummO+xFSr8hsCgEPqeP4ZOCUkc2v0LhXk5dOnVV4lTG6QhCwxq3wNzpT75ie8e7ZYFFRhkwmAwYLFoB84Dg0wN3+TAaDIQFR/BoWN5uvob0DJ4bNqyjaPpqdx9990EB2v7Z84/oWr1W1XyvXb0ClQQcMjxczIwDNgBvA9s8MC6FH5MVEwHho29msyjqcR16VHjen5OFuFRMZjMyu3XlqlvD8zJ3pRsCnIyMBioEoXYqUc7OvVw74vP2fxSCs4UExkTSniU5wIu7GiZ6rPyygmO7saEKyazZduvACSnZeEoqMuhI9kEB4dw6FgeRnMgR06c4UT2WeLahWA2GVXJd/QL1EFgDLAETaAuQHPzhTr+UyiqYDAa6ZSQVKO9rKSY3RvXYA4M1DJVtOG6U4qGGZgYR7LlNIldo+vtV1hUTk5BCVarvU7LKzwq2KPCBLB3907eXfAKr775UWWbxVJOeHgE7WJiOX7sKO3bdwAg49gRuvXoCUD3Hj3JOHaEolIrRScLOXH8GDabDaspmsjYzuxcu7qKBXfwUApXTp5a2eYMEunaLYE1339XZU1toeT7i8BCIYQJ+BTYLYSwA6OAnz21OEXrI3X/dioqLFSUWPht+wYyDieTNHAkkTEqF5yi8USEBdYZvVednPwS8s6WYW/mbPMAvXr3Ied0Nku/+Jhrrr2Jgwf28/2qFTz+r+doFxPLJ4veJaFXIqUlxSz9fDHXXHsTAJdefiX/nj+HMZdcRnynLix89w1GX3QpwSEhXDhmHB+8/To/r/uBCy8ax/KvlmA0GBk4eFjlvHY7lFtt9B86mldfeYn3F31R2ddmg5jOokEXpXY2zUC7iCCfCenXXfJdCHERUCyl3CmEmAjMAHKAf0opMz24xobWlYA6B+U3nEw/ROpvO6oUSQTo2K0XvfoPa5MFEhX105IVdS3WCrJzSyiudtC5PlIOHeDt1+eTnpZK+w4d+cMddzP64kspLy/jvQWvsnHDj9jsdq64egq3/en/VXoQvv36C776/L8UFhQw5PwR3P/IE4SHa8c09u35lbffeImTJzLo3qMnMx/8O7169wHg9VeeJftUJk/Ne6XBvk3BaNCyg7SPDqm3X0uUfP8aeFRKeUDPoN5ECZT/YbVYOCJ3k5GajM12LsTLaDRpYelJ/TGZA1pwhQpfwt9KvucVlpJbWEZFRd3uRn8mJjKI2Ki6RaolSr5fhJa9vFkQQowEvpFSdnC8DkKrK+U6xyYp5e+aa06F72AOCNAq9fYUpO7bTvaJI4AWlp5+YBcn0w/Sq/8wlYRW4ZdERwQ3ykXmSddjc1JUYqlXoJoTvQL1EvChEOIl4DBQJWZRSnlQzyBCCANa9d0Xq10aCJyRUsbrXI+iFRASFsGACy4lNzuTlL1bOZt/BoCy0mLSD+ymQ5cEDCb94cAKhT8TGxXS6Ae/niCR5iIsxHveDb0C9bTjT+dJL+dnYHD8rPcp8hRwNfAMVWtMDQN26RxD0cpoFxfP8HGTyDyayuHfdlJeVkLiwOEYlTgpFLpwJ0ikLopLLeTkl1BmsdXYb3PNUO8t6wn0C1TNeOHGsUBKOUsIMa5a+/lAByHEHrTaUxuAB6SUx5tpXoWP4wxLj+uSQFZGGrHxVbMU2O12jh7aR3z33jVKfygUiqYTGhxAaLBv7f3qyh4opUyVUqaiWUrnAScBi0u7LqSUJ+q4VIRWzmM8INBciEv1jqtoPZgDAujcs0+NvafTJ49yeP8Otnz/FWm//YrVovITKxStHbEEqGEAAB7nSURBVF0WlBAiAvgv8Hu0Ypt9gPmOCLqr6xEeXUgpH6o230NAthCim5TyWFPGVvg/dpuNw/u1oni2CivpcjfH0yUJfYfQOaGPX2ZpVigUDaP3X/aLQBSQwLkAiYeAs8ArTV2EEGK2EMI1LtHpTK07v76i7WAwkDhoJOGR55LmW8pKObR7C1t/WEbW8XT0nudTKBT+g16BmgQ8LKU86myQUqYB96O55ZrKIDSLLFoIEQ28CnwrpcxuhrEVfo7BYCC2YxeGXzqJfsMuJsjlMG9JUQH7t65jx7pvyTl1XAmVQuEmx475rpNKr0BFAMV1XGuOjJ/TgFwgBUhHOw91WzOMq2hFGIxG4rv35oIJ19K7/3DM5nNRS4V5p9mzaQ27/vc99tpSYysUXkAIwaOPPlqj/bbbbmPhwoVuj/f3v/+dOXPm1GhfuHAht93W9EdkcnIyN954Y5PH8RR6xWU1MEsI8QfHa7sQIhZ4AVjj7qRSynVAtMvrHOBWd8dRtE1MJjPd+wygU0ISR+Qejh8+UJmRIjQ8EoPak1K0IMuWLWPcuHFceeWVLb2UBikoKMDiwwFHev8l3w/0BE6jZS9fBRwF2gMPeGZpCkX9BAQGkThwBKN+dz1devbFZA6gR99BNfpZystaYHWKtspNN93Ek08+yalTp2q9XlRUxOzZs7nooosYPXo0f/3rXzlz5kyT5tyxYwc33ngjw4YNY8qUKWzatKnympSSO++8k4suuojBgwdzxx13cOLECXJycrjrrrsoLCxk6NChnDp1irKyMubNm8fYsWMZM2YMs2bNorhYc5599dVXTJ06lalTp3LBBRdw4IDnM9/psqCklCeBUUKICWhh5ma0shurpJTKn6JoUYJCQukzZBS9+g/DHFD1HEd5aQlbvv+K2E5d6dl3CKERUS20SkVzk5a8i/QD+s73d07ogxg6ukqb/HUTJ9IbToKT0HcIPfsN0b2um2++maysLB599FE++OCDGkcmZs2aRVZWFsuWLSM4OJjHHnuMv/71r7z33nu1jvfJJ5+wdGnVUzfl5eUMHjwYgJMnT3LXXXcxe/ZsrrjiCrZs2cL999/PV199Rffu3bn//vu54YYbePfdd/n/7d15eFzVefjx72za981abFm2kY/BgMGsMQTsNJBAKSSE0AIlEBwChQItOAQohvD8sIHGQBJofyTOWvIktNQxLkmapEnAgQQSnBrw+tp4lSVZkrWPthnNTP84d+TRYjyyZWmkeT/Po2c0986dOfdoNO/cc9/7Hr/fz5133snq1at59NFHWb16NXfeeScbNmwA4PHHH2fbtm2sWbOG1NRUHnjgAR5//HFWrlwJwMaNG1m9ejULFy4kM/PEF3Ye7VjIbuw5IgE2a3BSiWRocALYt2MToVCQxgN7+OOvX2Hrhjfo7myfgNapZLJixQp27Ngx7LxTX18fv/zlL1m2bBlFRUVkZWWxfPly3nzzzSMecV133XVs2LBh0M+99x6+MufVV19l4cKFXHHFFXi9Xi688EIuuugi1qxZA8Dq1au5+eabCQaDHDx4kPz8fBobG4e9TiQS4eWXX+b++++nqKiI7Oxs7rvvPtauXUsgYMuk5ufnc9FFF5GVlTUudTLjvQ4qD/gPbMZeCKfyhTFmLfA5ETlSAoVSEyYSidDXG/vWjNBQs4uGmt2UTK+iyiwgM+fDJ8JT6lgUFhayYsUK7rnnHhYtOnzk1t7eTjAYpLy8fGBZcXExKSkp1NfXM23atFG/Vl1dHW+//TZnn332wLJQKMQll1wCwObNm7ntttvo7Oykurqanp4eCgoKhj1PS0sLvb293HLLLYOCj9frpbbWFvUpKSkZdfuOR7xJEt/Enm86F9joLDvbWf414Itj3zSljo/L5eLUcxfT0dLEnm0baWmMXk8eofHAHhoP7KW4YiZVZgFZuaObPlxNvFknj27obShz5qJhw35jacmSJXz6059m2bJlA1OuFxUVkZKSQm1tLcXFdpLOhoYGAoEAhYWFx/Q6JSUlXHrppTzzzDMDyw4cOEBmZiYNDQ0sW7aMH/7whyxcuBCww3h1dcNrK+Tl5eHz+Xj55ZeZPXs2YIcSa2pqqKysZOPGjeM+u0C8Q3yXAV8QkT+LSNj5+RN20sJrTlzzlDp+OQXFLLjgUhZefDkF02LnDIvQVLuXd367js1/fE2TKdSYe+CBBwgGg7z7rj1X5na7ufLKK3n66adpbm7G7/ezYsUKzjzzTGbMmHGUZxvZ5Zdfzvr161m/fj3hcJht27ZxzTXX8Nprr+H3+4lEIqSl2ek/3nrrLdatWzeQuZeSkkIgEKCvrw+Px8OVV17JqlWraG1tJRAI8NRTT3H77bePTWccg3gD1CFgpK+YXmwdPaUSXm5BCQsWfZyzFl8xrBhtV0cbXp0kUY2x9PR0Vq1ahS/m/OiDDz7InDlzuOqqq1i8eDEej4fnn3/+mF+jqqqK5557jueee45zzjmHO+64g1tvvZWrr76aOXPmcPfdd7N06VLOOeccnn32Wa677jp27dpFJBLBGMPJJ5/Meeedh4jw0EMPUVpaylVXXcWiRYvYu3cvq1evxjNBMwvEO6PuXwMrgQeBN4F+bAXyZ4HvAa9EHxvv3FBjRWfUVceqs62Zvdvf41D9fk4+66OUVs4ZtD7Q14svJVUnTZxgk21G3WQ3ETPq/ti5fYnBc0EBPAk8wejnhlJqQmXnFXLa+R/D395K5pD080gkwvt/+DUQoXLuaRSXVeoFwEqNs/GeD0qphDNSgkRb00E62w4BsOVPr5OemUNl9alMq5yNxzMW1b2UUkcT74W6cc/5pNRU0O1vx+32DJRQ6unqQN79A3u2bWT6SadQMcvg9R3fDKZKqQ8X73VQpwPPAPOB1KHrRWR4Ur1Sk1jF7HkUV8zkwK5t1O4W+oM2wy/Q18PuLX9mn7xP+SzD9NnzSMvImuDWKjU1xTtW8QNstt7D6BxNKkmkpKYz+5SFVFafRv2+HdTs3DJw4W+oP0jNzs0c+GAr5sxFlM08aYJbO7VFIhFNVpkExnq6m3gD1FzgHBHZOqavrtQk4PX5mHHSfCpmzaOhZjf7d26m22/LJUUiEfKKRn/1v4qfz+ejp6dn4GJXlbh6enoGpdQfr3gD1O+xw3saoFTScns8lFVVUzrzJJoPHuDArq14fSmkZ2YPelxfTzcNNbspq6rGlzJsRFyNUklJCbW1tVRUVJCenq5HUgkoEonQ09NDbW3tMZVrOpJ4A9StwO+NMZdhC8YOKhIrIivHrEVKJTiXy0VR2QyKymYQDoWGra/dvZ19O95n7/b3KJ15EtNnz9Mq6schJycHsDXnEnnuomTn8/mYNm3awN9rLMQboJYDZcAFwJlD1kWwF/EqlXTcQ66wD/X3U7tH7O+hILW7t1G7exv5xeVUzDYUlc7Q66mOQU5Ozph+8KnJId4A9TfA1SKy7kQ2RqnJzuVyMefUs6j5YCvdnW0Dy1ub6mhtqiM1PZPyqrmUV80lJS19AluqVOKLN0C1AuNawkipycjt8VBeNZeymdW0NtVTu2s7hw7WEC3A0tfTxZ5tG9m7/T2KK2Zizlg04jxWSqn4A9SXgW8YY+4DdgGDBoJFJDDWDVNqMnO5XBSUlFNQUk5Pl5/6vTuo27eDYJ+9SiMSCdPV3orHq1UplDqSeP87ngYKOTwX1FBaf0+pI0jPzGL2/IVUzVtAY+1e6vYI7S2NlM+eNywjraWxDrfbTW7hNM1WU0kv3gD1tye0FUolAbfHQ2nlHEor59DZ1kx65uCT/pFIhF2bNuDvaCEjK5eymdWUzpxDSqqeq1LJKd5afL+J/m6MyQb8IjK2lwwrlUSy84bPntrZ1oy/owWwtQB3bdnA7q3/S1HZDMqq5lJQXKYZgCqpxD0Aboy5F/gSUAzMNcYsB9qBZSLSf4Lap1TS8PpSKK+aS0PNHkIhe5o3EgnTVLePprp9pKZn2iOwGXP0uiqVFOL6OuYkR9wD3A9E58VeB0QnMlRKHaeMrBzMmYu44PJrmbfwAnILSgat7+vpYp+8zx9/vZZNb/92glqp1PiJd7zgVuB2EXkRp4qEiLwC3ARcP9oXNcaca4xpjLmfYoz5ljGmxRjTZIx5cLTPqdRU4fH6KJtZzcKLL+fcv/gUM06aj9c3uGRSRpZetKqmvniH+CqB7SMs3wvEPdWGMcYFLAVWDVn1GGCAOUAu8AtjTK2I/Fu8z63UVJSZk8dJp53D7FMW0txQS0PNLg7V1zBtyPT0AFveWY/Xl0LpjDnkFBRrFqCa9OINUBuBa4GnnPvRBInbOXLq+UgeA/4SeBw7dUfUTcDNItIKtBpjVgG3ARqglMJmABaXV1JcXkkw0DesCG1fTzeNB/YCEer2CKnpmZRUVFEyfRbZeYUarNSkFG+AWoY9qrkIO2HhY8aYecApwGWjeL0XROQRY8zi6AJjTB62zl9spfTtwGmjeF6lksZIFdKb6vdz+HujPV9V88EWaj7YQlpGNiXTqyipqCIrt0CDlZo04k0zf8sYMxe4CwgA+cDrwGdEpCbeFxORuhEWR6cj7Y5Z1g3o5C9KxaliliErJ4+Gmt001u4bmAEYoLe7k/07NrF/xyZ7fVXVXCqr509ga5WKzxEDlDHmEWCViHQDiEgDg4flxkqXcxt7NWIG4D8Br6XUlORyucgrKiWvqJTqBefT2lRP44E9NNXtI9R/uDJZt7+dro7WCWypUvH7sCOoR4EXGHxkM+ZEpNUYcxCbJFHrLJ6HTo6o1DFxu90UTqugcFoF5oyP0NJYS8OBPTTXHyAUClIyfdawbXa8+zYAxeUzyS2ahlsvCFYJ4MMC1HgOVL8IPGqMeR875LcM+Po4vr5SU5Lb46GorJKiskpC/f00Nxwgv7hs0GNC/f3U79tJOByids92vL5UCkunU1w+k4KSMjxerbauJsbRzkFNN8akHe1JRGT/cbbjEWxB2i3Ya7O+hT16U0qNEY/XS0lF1bDlrU11hMOHZwbuD/bRULOLhppduN0e8opKKSytoHDadNL1+is1jo4WoN45ynoXNnVoVNXMReR1IC/mfi9wp/OjlBpHhdOmc8aFn6Cpbj+H6vfT19M1sC4cDtHSWEtLYy07+RPZeYWctfgKzQRU4+JoAWoJ0DweDVFKTQyX201+cRn5xWVUn34unW3NHHKCVVfMrMAAqWmZw4JTj78DXG7SM7NQaix9WICKANtFpPFDHqOUmkJcLhc5+UXk5Bcxe/5Cerv9NDfU0nzwAK2NdRSUVgzbZt+OTdTv20l6Zjb5xeXkl9hgN9L1WkqNRqIkSSilElBaRhYVswwVswyhUH/stcCAncOqpdFe3tjT1UlPl1C3VwAX2XmFFJSUk19cRk5hMR6Pzh6sRufD3jE/AHrGqyFKqcQ2UoAJ9feTmZ1HMNBHOBQ7606EzrZDdLYdYt+O93G7PeQUFGPO+IhOFaLidsQAJSKfH8+GKKUmH6/Px4ILLiEcCtHe0kRrUx2tTfV0tBwi9nArHA7RduggvtTBScGhUD+tjfXkFpbokKAaRo+5lVLHze3xkF9cSn5xKQDBQB9thxpobbQBq9vfTmZO/rAg1Nl6iE1v/wZwkZWbT05BMbkFJeTkF5GelaPZgklOA5RSasz5UlIHqq8D9PV2E+gdfsag7VCD81sEf3sL/vYW6vYIAF5fqk3YKCi2P/lFepSVZDRAKaVOuNS0DFLThtd/TklNJzuviM62ZoZmYPQH+wauwQJbhunU85YMekwkHMalZZmmLA1QSqkJUz5rLuWz5tIfDNLR2kRHi/1pb2kaVJEdICe/eNj2Wze8QUfrIbLzCsjOKyQrr5Ds3AJS0tKHPVZNPhqglFITzuvzUVBSTkFJOWDT13u6Om3Aaj1ER0sTuYUlw7brbGumt7uT3u5Omur2DSxPSU0nMyefzJw8MrPzyMzJIyu3AI9XP/ImE/1rKaUSjsvlIiMrh4ysHEpHmN4ebIp7bFmmWIG+HgJNPbQ2HZ6C7syPfpK8otKB+5FIhPbmRjKycvClpmlCRgLSAKWUmpQ8Xi8fveJ6ujrb8Le10NnWTGd7M/62lkHFb6Myc/IH3Q8Getn4xn87z+UjPTObjKxc0rOySc+0wTE9KxtfigaviaIBSik1abk9HrLzCsnOK6SMasAmTvR0++nqaKOro5WuzjaCfb3DMgB7/J0Dv4f6gwNZhEN5PD4ysnM5e8kVg5b3B4P09wdITU3XRI0TRAOUUmpKcbndA8OD0TT3kUQiYbLziuj2tw+adXioUCg44vqWxlq2/Ol1XC43KWnppKSmk5KWTmpaOilpGaSkptnbtDTS0rNITR+exag+nAYopVRSyisq5ewlVxCJRAgGeunxd9Ltb7e3XR30+Dvo8XcSCgVJy8gctn30/FckEqavp+uI58MACqZNZ8Gijw9aVr9vJ80HD+D1peJLScGbkorPl4rH68Xj9R2+9XhJSUufkGvAIpEI4XAIt8s9IUeJGqCUUknN5XLZo5/U9GGZgpFIhP5gwBbKHSISAV9qGsG+3qO+RuoIae+dbS2DMg8/TGX1qcw59exBy7Zu+B2tjfW43G7cbjcut8cGEo8bt2twMKmcexpFZTOGbP8G3Z3thEP9A4EoHA4TDoWIhMOEwyEikTAwPMFkvGiAUkqpI3C5XPhSUvEx/Oilsno+ldXzCYX6CfT22J++Hvp6ewg4lTOiyzKyhhfI7Q/0DVt2JB6vb9iyYCBAoC++et4jBdGu9lb8HcPPuY0k1D88QI8HDVBKKXUcPB4v6ZnZpGdmj2q7GdXzKSqvJBjooz/QRzAYoD/QRyjUT6i/n1B/cOB2pCockREyFU8Et9szcCQ13jRAKaXUBIhmHx6rU89bQijUTzgUJhJxhuTCYWd47nBAcblcIwbPk8++kHA4fHh40O3G7fY4Q4YeZ7l7QlPsNUAppdQk5PWl4PWlHPP2WbkFY9iaE0OT95VSSiUkDVBKKaUSkgYopZRSCUkDlFJKqYSkAUoppVRCmgpZfB6AgwcPTnQ7lFJKHUHMZ7Qn3m2mQoAqA7jhhhsmuh1KKaWOrgzYFc8Dp0KAegf4KFAPjM+l1UoppUbLgw1O78S7gSsSiZy45iillFLHSJMklFJKJSQNUEoppRKSBiillFIJSQOUUkqphKQBSimlVELSAKWUUiohaYBSSimVkDRAKaWUSkhToZLEcTHGLABeAE4HdgO3iEjcVzonMmPMJcCTQDXQCHxVRL5pjMkDvg1cAviBh0Xke842LuD/AV8EUoDvAV8SkX5n/bXASuwV4euBm0WkcVx37Bg4+/w+8IiIfD/Z+sAYUwb8f2AJ0At8S0SWG2NSgOeBa7CVWJ4RkSditrsL+DKQC6wDbhORLmfdEuDrwBzgPeBGEYmrhM1EMcacD3wDMEAT8KSIfDtZ+sEYcy7wUxEpce6fkP02xlQC3wHOx3723CUiPx9te5P6CMr546wD/h3IA1YAvzLG5Exow8aAMWYGsAZ4HLtv1wFPGGM+gf2gCmE/YP8SeNIYc7Gz6ReBq4GF2MB2DvCQ85ynYN90NwOFwE7gpfHZo+P2AlARcz/Z+mAdthzYNOyHxk3GmOuBx7Af1nOw+3mTMeZzAM575Z+AT2D7KQ14zllXBLzibJ8HrAV+aYxJ2M8Up23rgG+ISC72f+J550vqlO4HY4zLGPMF4FfYL11RJ2q/X8J+ISwEbgVeMsbMHm27E6oTJ8BiwCciXxORoIi8BGwB/npimzUmqoAfichaEQk7R4WvA3+B/ba0XES6ReRdYDX2QxngJuBrInJARJqArwC3Oev+FnhVRN4UkV7gQeACY0z1eO3UsTDG3ATkAJuc+xkkUR8YY84DZgN3i0iviOzBvvdfw+7rChFpFZG9wCoO7+tNwHdFZIuI+IEHgOuNMVnYAL5FRNY4/ztfBVKx769ElQ+UAC7nKDkC9AMBpn4/PAb8HfYLa6wx329jzFzgbOxoRUBEfgv8F7B0tI1O9gB1CrBtyLLtwGkT0JYxJSJviMjt0fvGmAIOF9WNYL/5R8Xu8ynA1iHryp3tB60TkW6ghgTuL2PMLOBR4JaYxXNJoj4AzsIG568YY2qNMbuATwM92G/GQ/f1SP2wC/uZMXeEdQBCAveDiDRjh7N+AASxRUsfwv5PTPV+eEFEzgI2RBc4w9wnYr9PAfZHhwJHeN64JXuAygK6hyzrBjImoC0njDEmF/sN5o/An4FeEYmtEhy7z0P7JPp7xgjrhm6bUIwxHuCHwDIRiZ0wLIsk6QNH9MtJEHskdTWwDLjSWT90X0fsB6e/epmk/eAMP/UC1wPp2KPIR0mCfhCRuhEWZzm3Y73fY9YnyR6gurBv1FgZ2JPmU4JzuP020IAd1uoE0pwhjqjYfR7aJ9E3lX+EdUO3TTTLARGRnwxZ3kXy9AFAH9AhIl8RkT4ReQ+bIHKTs37ovo7YD05/pTF5++Fq4AIReckZllqPPZ+YbP0QFT3CGev9HrM+SfYAtRV7gjDWPIYfuk5KxpiLsEdNrwDXOOdMdgIuYFbMQ2P3eWifzAPqRaRt6DrnXE4lidtffwNcY4xpM8a0YYcY/hW4i+TpA7DDKxlOUlCUF2gFDjJ8X4/UD3Ow/bZzhHVDt01EM7DnSWL1Y7P5kqkfABCRE/X33wpUGmPSR1g3KsmeZv4a9oTpP2LHpj+DTTdfO6GtGgPGmDnAT4F/EpHnostFxG+MWYvN6FuKfdPdis1KA3gRWGaM+Q32m9BXnGUAPwLeNMYsBt4CngA2isiOE75Dx0BE5sXeN8a8i01++L5zonfK94Hjf7Afwk8bY+7DfrAsxZ403w08aox5Hzs0swybOgx2n79jjPlP53FPAj8RkS7nPfTPTsr9WuAeIIxNxElUv8L+zb+ITYpZiP27fwHYT/L0Q6wXGeP9FpGAMeY9YIUx5kFgEXAV8JHRNi6pj6BEJABchg1MLdiUyk85mVuT3Z1ANvYf0h/z8xQ2SycM7AN+js3i+W9nuxeAl4E/cPib0iMAIrIJm2zwAnAImA98dvx2aUwlTR84R84XY88/1QO/AP5ZRNZg92szNnv1HeylCS842/0cez3YOqAW++35NmddI/BX2CzGFuzw8V85/1MJSUS2YIf5bgPasF82HhCRdSRRPwxxovb7M8DJ2Gugvg0sFZHNo22czqirlFIqISX1EZRSSqnEpQFKKaVUQtIApZRSKiFpgFJKKZWQNEAppZRKSBqglFJKJaRkv1BXqVExxnixFzN+Hlsxvh34DbYy+gcT2LQRORdZ+kXk5olui1KjpUdQSo3OSmz1gXuxFRmuwF4Q/TunOrRSaozoEZRSo7MU+AcR+Zlzf69T7qUR+BTw/YlqmFJTjQYopUYnDHzMGPPj6BTwItJtjDkDW+8OZ0bSh4Hp2EKty2MCGsaYvwP+0Vm/GbhXRN501l2KLS9zKraU0vPAKhGJGGNuBv4e+A9nex+2bFHsNNw3YqeQKMOW8kmJed1sbBmbT2KrUr+BnYo7dl4spRKGDvEpNTpPY4vK1hhjvmOMucEYUyQiH4hIuzNN9jewNc5OA74J/Kcx5iMAxpjPO8/xJLYw8WvAz4wxhU71+Z8DrwJnYifTWw7cEfP6p2Pndvo4dqjxauB257mXAN8FnsEWQvVj66VFPY6tx7fYWR92Hq9UQtIjKKVGQUSeNMbsxFYCvxFbOLbfGPMvwH3YoPJVEXnJ2WSXMeYsZ9012GDzTRH5LoAx5gHncfnA3cAvRCQ6LfcOY8x05zn/xVnmA251JmDcYoz5BXbGXLCB6hUR+Vfnue/FHi1FVWHnA9vjVLX/grNMqYSkAUqpUXKqgK9xpuxYDHwOO93AQWx18/OcaQaifEB0Oo5TgGdjnisCfBnAGDMfOwNwrDeBJ2MSMDqHzA7cAWQ6v58au70zLPhOzGOfAH4GNBlj1mPnCXsRpRKUDvEpFSdjzOnGmOej90XELyI/FZFrgX/HHq14sVMQnBHzMx+b7QcQAI40hUDPCMuis/5G/1dHmsbBdYTfBz1eRN7GHjEtxZ4vWwm8ZYxJO0J7lJpQGqCUip8HuNMYc/EI6zqwH/rbgJnOOakPnGujrgWucx63A3v+Z4AxZosx5jPOtkMndVuEzRBsjaN97wPnDVk28FrOUd15IvIjEbkROB97nuz0OJ5bqXGnQ3xKxUlENhpjfgK8bIx5CJvgkI1NWLjBuS0FfmyM2Y6dyfZjwGPY81Vgh/e+7czu+zZ2NtdpwO+AXcAGY8zD2COyhdijsWgW39Ga+HXgDefc00+xQ48LsIELbNbgjc65p3psskcHh4cflUooegSl1Ohcj83S+wdgEzZV+5PAJ0XkLRFZC9yFvZB3K/Al4I5o0oRz+zCwwtn+IuAyEWkSkXexWXmfxaafr8SmnK+Mp2HOEN5nsdl972HPd/045iH3A7/HTtG9DRs8LxeRtmPqCaVOMJ1RVymlVELSIyillFIJSQOUUkqphKQBSimlVELSAKWUUiohaYBSSimVkDRAKaWUSkgaoJRSSiUkDVBKKaUS0v8B6B3+abeT8+QAAAAASUVORK5CYII=\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "#Note: Values of heater input is in J*430800/s\n", + "for rate_in in rate_array:\n", + " system = make_system(40, 100, 1, rate_in, 0)\n", + " results, details = run_ode_solver(system, slope_func4, max_step=5)\n", + " plot(results['temp'], '.-', label=rate_in)\n", + "\n", + "plot(trendline, '--', label='No Heater')\n", + "decorate(xlabel='Seconds', \n", + " ylabel='Temperature (degrees C)',\n", + " title='Swept Heater Input')" + ] + }, + { + "cell_type": "code", + "execution_count": 38, + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "#second sweep, centering in on the semi-horizontal rate around 2000\n", + "rate_array2 = linspace(2000, 2500, 5) \n", + "for rate_in in rate_array2:\n", + " system = make_system(40, 100, 1, rate_in, 0)\n", + " results, details = run_ode_solver(system, slope_func4, max_step=5)\n", + " plot(results['temp'], '.-', label=rate_in)\n", + "\n", + "plot(trendline, '--', label='No Heater')\n", + "decorate(xlabel='Seconds', \n", + " ylabel='Temperature (degrees C)',\n", + " title='Swept Heater Input 2')" + ] + }, + { + "cell_type": "code", + "execution_count": 39, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "#final sweep, centering in on the rate between 2000 and 2125\n", + "rate_array3 = linspace(2000, 2125, 5) \n", + "\n", + "for rate_in in rate_array3:\n", + " system = make_system(40, 100, 1, rate_in, 0)\n", + " results, details = run_ode_solver(system, slope_func4, max_step=5)\n", + " plot(results['temp'], '.-', label=rate_in)\n", + "\n", + "plot(trendline, '--', label='No Heater')\n", + "decorate(xlabel='Seconds', \n", + " ylabel='Temperature (degrees C)',\n", + " title='Swept Heater Input 3')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Sweeping Heater Temperature Range" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "metadata": {}, + "outputs": [], + "source": [ + "#to answer question: sweep possible range values\n", + "diff_array = linspace(0, 24, 5) \n", + "\n", + "def slope_func5(state, t, system):\n", + "\n", + " Temp = state\n", + " \n", + " #calculate rate of heat loss\n", + " dHdtJ = system.U * (Temp - system.t_oc) * system.A\n", + " \n", + " # converted from joules to degrees celsius\n", + " dHdt = -dHdtJ / 430800\n", + " \n", + " # utilize optimal heter input as found in sweep- 0.00464 J/s \n", + " dIdt = 2062.5 / 430800\n", + " \n", + " #combination rate: input minus output\n", + " dCdt = dIdt + dHdt\n", + " \n", + " #each increasing interval of system.difff will decrease the range in which the heater is off\n", + " if ((50-system.difff) > int(Temp) > (0+system.difff)):\n", + " return dHdt\n", + " \n", + " #return loss and input if in non ideal temp range (heater on)\n", + " else:\n", + " return dCdt" + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "for difff in diff_array:\n", + " system = make_system(40, 100, 1, 2111, difff)\n", + " results, details = run_ode_solver(system, slope_func5, max_step=5)\n", + " plot(results['temp'], '.-', label = difff)\n", + "\n", + "plot(trendline, '--', label='No Heater')\n", + "decorate(xlabel='Seconds', \n", + " ylabel='Temperature (degrees C)',\n", + " title='Heater Flucuation Sweep')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Results" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Question**: What temperature range of operation is needed from a bang-bang heater to result in a steady ambient temperature of 25 degrees celsius, given heat loss to the environment?
\n", + "\n", + "**Our Answer**: Through research and our simulation, we found that the heater would need to operate at a range of 24 degrees to 26 degrees to maintain a constant output of 25. While simplistic in hindsight, the dropoffs of the other temperature ranges represent inefficient temperature outputs, demonstrating the definitive need for a one degree leeway. " + ] + }, + { + "cell_type": "code", + "execution_count": 60, + "metadata": { + "scrolled": false + }, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "for difff in diff_array:\n", + " system = make_system(40, 100, 1, 2111, difff)\n", + " results, details = run_ode_solver(system, slope_func5, max_step=5)\n", + " plot(results['temp'], '.-', label = difff)\n", + "\n", + "plot(trendline, '--', label='No Heater')\n", + "decorate(xlabel='Seconds', \n", + " ylabel='Temperature (degrees C)',\n", + " title='Heater Flucuation Sweep')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + " The graph shows how the temperature of the room changes with varying energy inputs of the heater. In comparison to the graphs with a greater range, the energy output of the heater has less variation from 25 degrees with the 2 degree (labeled 24, for the difff value) line. Each consecutive value of greater divide shows a drop in the temperature capable of being maintained at that heat output. The high and low for the 2 degree range is relatively close to 25 and shows that that is the optimal range for the bang bang heater’s function. A smaller range can lead to more effective temperature control. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Main Limitation\n", + "      The main limitation of the model would be the fogginess of its self assessment. It may include an accurate assessment of the rate of thermal energy exiting the room due to the potentially inaccurate value for the heat transfer coefficient, bu thte method by which this was verified was a black box. We were not able to find the equations by which the Home Heat Loss Calculator developed its values, and had to ourselves recreate a modeling equation to fit into our notebook. The fact that a smaller range of bang bang heater operation would require the heater to be on more frequently and consume more energy would make the optimal temperature regulation scenario less preferable as well, given the need for further information into cost and sustainability information, which would drive our model more towards a data question. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Iteration\n", + "      Our iterative process is shown above, as each major change in the code is documented in sequence. Beginning first with a simple model of heat loss, and its subsequent validation, our model grew to include heat output, then varying heat output, than varying operation of a swept heat output. Our major data values were determined in-model, based off of verified assumptions and vaidated date, using sweeps of the heat input rate and fluctuation range.
\n", + "\n", + "      Research was conducted in bulk at the beginning of the project, but more efficient equations were continually discovered. With large portions of unit conversion work being done by hand, the mathematical intricacies of the model were continually shifting. One major step was the conversion of the joule per second energy rates into degree celsius per second area, in opposition to the previously used method of shifting all temperature measurements into joules. This made working with units much simpler, and greatly reduced the effort needed to manage the frequently changing units of our model." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Abstract" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "      We created this model to find what temperature range of operation is needed from a bang-bang heater to maintain 25 degrees celsius in a given area, given heat loss to the environment. With the found optimal temperature of 2062.5/430800 joules/sec output, we determined that a 2 degree range was optimal for maintaining 25 degrees.\n" + ] + }, + { + "attachments": { + "image.png": { + "image/png": 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+ } + }, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "![image.png](attachment:image.png)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "      This graph shows the overall results of our simulation over 2.78 hours, and the varying levels of constant temperature that result from different ranges. The labels, read as \"Range of Deactivation Between 50-x and x Degrees C\", note the various tested values for range. As the graph shows, 24, or a range of deactivation between 26 and 24 degrees C, presents the most direct result of 25 degrees.\n", + "
\n", + "\n", + "      The ideal function of a bang-bang heater, though a mechanically simple device, is helpful in its usage in efficiently maintaining the heat of a building. Were one to compare rates of fluction against cost, given their method of heating and budjet/need, this model could provide the more efficient constraints by which to construct their system." + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.6.6" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} From 71b489927cc3dd203c95e0aab5f7c87427f5858f Mon Sep 17 00:00:00 2001 From: Bennett Taylor Date: Tue, 13 Nov 2018 16:13:53 -0500 Subject: [PATCH 07/14] Earth Falling Simulation --- code/chap20mine.ipynb | 1657 +++++++++++++++++++++++++++++++++++++++++ 1 file changed, 1657 insertions(+) create mode 100644 code/chap20mine.ipynb diff --git a/code/chap20mine.ipynb b/code/chap20mine.ipynb new file mode 100644 index 00000000..e9adb930 --- /dev/null +++ b/code/chap20mine.ipynb @@ -0,0 +1,1657 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Modeling and Simulation in Python\n", + "\n", + "Chapter 20\n", + "\n", + "Copyright 2017 Allen Downey\n", + "\n", + "License: [Creative Commons Attribution 4.0 International](https://creativecommons.org/licenses/by/4.0)\n" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "# Configure Jupyter so figures appear in the notebook\n", + "%matplotlib inline\n", + "\n", + "# Configure Jupyter to display the assigned value after an assignment\n", + "%config InteractiveShell.ast_node_interactivity='last_expr_or_assign'\n", + "\n", + "# import functions from the modsim.py module\n", + "from modsim import *" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Dropping pennies\n", + "\n", + "I'll start by getting the units we need from Pint." + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "second" + ], + "text/latex": [ + "$second$" + ], + "text/plain": [ + "" + ] + }, + "execution_count": 2, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "m = UNITS.meter\n", + "s = UNITS.second" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "And defining the initial state." + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "data": { + "text/html": [ + "
\n", + "\n", + "\n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + "
values
y381 meter
v0.0 meter / second
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" + ], + "text/plain": [ + "y 381 meter\n", + "v 0.0 meter / second\n", + "dtype: object" + ] + }, + "execution_count": 3, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "init = State(y=381 * m, \n", + " v=0 * m/s)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Acceleration due to gravity is about 9.8 m / s$^2$." + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "9.8 meter/second2" + ], + "text/latex": [ + "$9.8 \\frac{meter}{second^{2}}$" + ], + "text/plain": [ + "" + ] + }, + "execution_count": 4, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "g = 9.8 * m/s**2" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "When we call `odeint`, we need an array of timestamps where we want to compute the solution.\n", + "\n", + "I'll start with a duration of 10 seconds." + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "10 second" + ], + "text/latex": [ + "$10 second$" + ], + "text/plain": [ + "" + ] + }, + "execution_count": 5, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "t_end = 10 * s" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now we make a `System` object." + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
\n", + "\n", + "\n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + "
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inity 381 meter\n", + "v 0.0 meter / secon...
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t_end10 second
\n", + "
" + ], + "text/plain": [ + "init y 381 meter\n", + "v 0.0 meter / secon...\n", + "g 9.8 meter / second ** 2\n", + "t_end 10 second\n", + "dtype: object" + ] + }, + "execution_count": 6, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "system = System(init=init, g=g, t_end=t_end)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "And define the slope function." + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [], + "source": [ + "def slope_func(state, t, system):\n", + " \"\"\"Compute derivatives of the state.\n", + " \n", + " state: position, velocity\n", + " t: time\n", + " system: System object containing `g`\n", + " \n", + " returns: derivatives of y and v\n", + " \"\"\"\n", + " y, v = state\n", + " unpack(system) \n", + "\n", + " dydt = v\n", + " dvdt = -g\n", + " \n", + " return dydt, dvdt" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "It's always a good idea to test the slope function with the initial conditions." + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "0.0 meter / second\n", + "-9.8 meter / second ** 2\n" + ] + } + ], + "source": [ + "dydt, dvdt = slope_func(init, 0, system)\n", + "print(dydt)\n", + "print(dvdt)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now we're ready to call `run_ode_solver`" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "'The solver successfully reached the end of the integration interval.'" + ] + }, + "execution_count": 9, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "results, details = run_ode_solver(system, slope_func, max_step=0.5*s)\n", + "details.message" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here are the results:" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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yv
0.000000381.0000000.000000
0.000102381.000000-0.001000
0.001122380.999994-0.011000
0.011327380.999371-0.111000
0.113367380.937025-1.110997
0.613367379.156526-6.010997
1.113367374.926028-10.910997
1.613367368.245529-15.810997
2.113367359.115031-20.710997
2.613367347.534532-25.610997
3.113367333.504034-30.510997
3.613367317.023535-35.410997
4.113367298.093036-40.310997
4.613367276.712538-45.210997
5.113367252.882039-50.110997
5.613367226.601541-55.010997
6.113367197.871042-59.910997
6.613367166.690544-64.810997
7.113367133.060045-69.710997
7.61336796.979547-74.610997
8.11336758.449048-79.510997
8.61336717.468550-84.410997
9.113367-25.961949-89.310997
9.613367-71.842448-94.210997
10.000000-109.000000-98.000000
\n", + "
" + ], + "text/plain": [ + " y v\n", + "0.000000 381.000000 0.000000\n", + "0.000102 381.000000 -0.001000\n", + "0.001122 380.999994 -0.011000\n", + "0.011327 380.999371 -0.111000\n", + "0.113367 380.937025 -1.110997\n", + "0.613367 379.156526 -6.010997\n", + "1.113367 374.926028 -10.910997\n", + "1.613367 368.245529 -15.810997\n", + "2.113367 359.115031 -20.710997\n", + "2.613367 347.534532 -25.610997\n", + "3.113367 333.504034 -30.510997\n", + "3.613367 317.023535 -35.410997\n", + "4.113367 298.093036 -40.310997\n", + "4.613367 276.712538 -45.210997\n", + "5.113367 252.882039 -50.110997\n", + "5.613367 226.601541 -55.010997\n", + "6.113367 197.871042 -59.910997\n", + "6.613367 166.690544 -64.810997\n", + "7.113367 133.060045 -69.710997\n", + "7.613367 96.979547 -74.610997\n", + "8.113367 58.449048 -79.510997\n", + "8.613367 17.468550 -84.410997\n", + "9.113367 -25.961949 -89.310997\n", + "9.613367 -71.842448 -94.210997\n", + "10.000000 -109.000000 -98.000000" + ] + }, + "execution_count": 10, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "results" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "And here's position as a function of time:" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Saving figure to file figs/chap09-fig01.pdf\n" + ] + }, + { + "data": { + "image/png": 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" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "def plot_position(results):\n", + " plot(results.y, label='y')\n", + " decorate(xlabel='Time (s)',\n", + " ylabel='Position (m)')\n", + "\n", + "plot_position(results)\n", + "savefig('figs/chap09-fig01.pdf')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Onto the sidewalk\n", + "\n", + "To figure out when the penny hit the sidewalk, we can use `crossings`, which finds the times where a `Series` passes through a given value." + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([8.81788535])" + ] + }, + "execution_count": 12, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "t_crossings = crossings(results.y, 0)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "For this example there should be just one crossing, the time when the penny hits the sidewalk." + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "8.817885349720552 second" + ], + "text/latex": [ + "$8.817885349720552 second$" + ], + "text/plain": [ + "" + ] + }, + "execution_count": 13, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "t_sidewalk = t_crossings[0] * s" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can compare that to the exact result. Without air resistance, we have\n", + "\n", + "$v = -g t$\n", + "\n", + "and\n", + "\n", + "$y = 381 - g t^2 / 2$\n", + "\n", + "Setting $y=0$ and solving for $t$ yields\n", + "\n", + "$t = \\sqrt{\\frac{2 y_{init}}{g}}$" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "8.817885349720552 second" + ], + "text/latex": [ + "$8.817885349720552 second$" + ], + "text/plain": [ + "" + ] + }, + "execution_count": 14, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "sqrt(2 * init.y / g)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The estimate is accurate to about 10 decimal places." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Events\n", + "\n", + "Instead of running the simulation until the penny goes through the sidewalk, it would be better to detect the point where the penny hits the sidewalk and stop. `run_ode_solver` provides exactly the tool we need, **event functions**.\n", + "\n", + "Here's an event function that returns the height of the penny above the sidewalk:" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": {}, + "outputs": [], + "source": [ + "def event_func(state, t, system):\n", + " \"\"\"Return the height of the penny above the sidewalk.\n", + " \"\"\"\n", + " y, v = state\n", + " return y" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "And here's how we pass it to `run_ode_solver`. The solver should run until the event function returns 0, and then terminate." + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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0.0011223.810000e+02-0.011000
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1.1337733.747013e+02-11.110971
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" + ], + "text/plain": [ + " y v\n", + "0.000000 3.810000e+02 0.000000\n", + "0.000102 3.810000e+02 -0.001000\n", + "0.001122 3.810000e+02 -0.011000\n", + "0.011327 3.809994e+02 -0.111000\n", + "0.113367 3.809370e+02 -1.110997\n", + "1.133773 3.747013e+02 -11.110971\n", + "8.817885 5.684342e-14 -86.415276" + ] + }, + "execution_count": 17, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "results" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "With the `events` option, the solver returns the actual time steps it computed, which are not necessarily equally spaced. \n", + "\n", + "The last time step is when the event occurred:" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "8.81788534972056 second" + ], + "text/latex": [ + "$8.81788534972056 second$" + ], + "text/plain": [ + "" + ] + }, + "execution_count": 18, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "t_sidewalk = get_last_label(results) * s" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Unfortunately, `run_ode_solver` does not carry the units through the computation, so we have to put them back at the end.\n", + "\n", + "We could also get the time of the event from `details`, but it's a minor nuisance because it comes packed in an array:" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "8.81788534972056 second" + ], + "text/latex": [ + "$8.81788534972056 second$" + ], + "text/plain": [ + "" + ] + }, + "execution_count": 19, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "details.t_events[0][0] * s" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The result is accurate to about 15 decimal places.\n", + "\n", + "We can also check the velocity of the penny when it hits the sidewalk:" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "-86.41527642726152 meter/second" + ], + "text/latex": [ + "$-86.41527642726152 \\frac{meter}{second}$" + ], + "text/plain": [ + "" + ] + }, + "execution_count": 20, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "v_sidewalk = get_last_value(results.v) * m / s" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "And convert to kilometers per hour." + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "-311.0949951381415 kilometer/hour" + ], + "text/latex": [ + "$-311.0949951381415 \\frac{kilometer}{hour}$" + ], + "text/plain": [ + "" + ] + }, + "execution_count": 21, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "km = UNITS.kilometer\n", + "h = UNITS.hour\n", + "v_sidewalk.to(km / h)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "If there were no air resistance, the penny would hit the sidewalk (or someone's head) at more than 300 km/h.\n", + "\n", + "So it's a good thing there is air resistance." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Under the hood\n", + "\n", + "Here is the source code for `crossings` so you can see what's happening under the hood:" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": {}, + "outputs": [], + "source": [ + "%psource crossings" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The [documentation of InterpolatedUnivariateSpline is here](https://docs.scipy.org/doc/scipy/reference/generated/scipy.interpolate.InterpolatedUnivariateSpline.html).\n", + "\n", + "And you can read the [documentation of `scipy.integrate.solve_ivp`](https://docs.scipy.org/doc/scipy/reference/generated/scipy.integrate.solve_ivp.html) to learn more about how `run_ode_solver` works." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Exercises\n", + "\n", + "**Exercise:** Here's a question from the web site [Ask an Astronomer](http://curious.astro.cornell.edu/about-us/39-our-solar-system/the-earth/other-catastrophes/57-how-long-would-it-take-the-earth-to-fall-into-the-sun-intermediate):\n", + "\n", + "\"If the Earth suddenly stopped orbiting the Sun, I know eventually it would be pulled in by the Sun's gravity and hit it. How long would it take the Earth to hit the Sun? I imagine it would go slowly at first and then pick up speed.\"\n", + "\n", + "Use `run_ode_solver` to answer this question.\n", + "\n", + "Here are some suggestions about how to proceed:\n", + "\n", + "1. Look up the Law of Universal Gravitation and any constants you need. I suggest you work entirely in SI units: meters, kilograms, and Newtons.\n", + "\n", + "2. When the distance between the Earth and the Sun gets small, this system behaves badly, so you should use an event function to stop when the surface of Earth reaches the surface of the Sun.\n", + "\n", + "3. Express your answer in days, and plot the results as millions of kilometers versus days.\n", + "\n", + "If you read the reply by Dave Rothstein, you will see other ways to solve the problem, and a good discussion of the modeling decisions behind them.\n", + "\n", + "You might also be interested to know that [it's actually not that easy to get to the Sun](https://www.theatlantic.com/science/archive/2018/08/parker-solar-probe-launch-nasa/567197/)." + ] + }, + { + "cell_type": "code", + "execution_count": 105, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "kilometer" + ], + "text/latex": [ + "$kilometer$" + ], + "text/plain": [ + "" + ] + }, + "execution_count": 105, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "m = UNITS.meter\n", + "s = UNITS.second\n", + "kg = UNITS.kilogram\n", + "AU = UNITS.astronomical_unit\n", + "N = UNITS.newton\n", + "km = UNITS.kilometer" + ] + }, + { + "cell_type": "code", + "execution_count": 106, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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initr 149597870691.0 meter\n", + "v 0.0 meter / s...
G6.67408e-11 meter ** 2 * newton / kilogram ** 2
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m25.972324e+24 kilogram
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t_end1000000000.0 second
r_final701879 kilometer
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" + ], + "text/plain": [ + "init r 149597870691.0 meter\n", + "v 0.0 meter / s...\n", + "G 6.67408e-11 meter ** 2 * newton / kilogram ** 2\n", + "m1 1.989e+30 kilogram\n", + "m2 5.972324e+24 kilogram\n", + "t_0 0 second\n", + "t_end 1000000000.0 second\n", + "r_final 701879 kilometer\n", + "dtype: object" + ] + }, + "execution_count": 120, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "system = System (init = init,\n", + " G = 6.67408e-11*N/kg**2 * m**2,\n", + " m1 = 1.989e30 * kg,\n", + " m2 = 5.972324e24 * kg,\n", + " t_0 = 0 * s,\n", + " t_end = 1e9 * s,\n", + " r_final = 6371 * km + 695508 * km)" + ] + }, + { + "cell_type": "code", + "execution_count": 121, + "metadata": {}, + "outputs": [], + "source": [ + "def universal_gravitation(state, system):\n", + " r, v = state\n", + " unpack(system)\n", + " \n", + " force = G * m1 * m2/ (r**2)\n", + " \n", + " return force" + ] + }, + { + "cell_type": "code", + "execution_count": 122, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "3.5425723405356547e+22 newton" + ], + "text/latex": [ + "$3.5425723405356547e+22 newton$" + ], + "text/plain": [ + "" + ] + }, + "execution_count": 122, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "universal_gravitation(init, system)" + ] + }, + { + "cell_type": "code", + "execution_count": 123, + "metadata": {}, + "outputs": [], + "source": [ + "def event_func(state, t, system):\n", + " \"\"\"Return the height of the penny above the sidewalk.\n", + " \"\"\"\n", + " r, v = state\n", + " return r-system.r_final" + ] + }, + { + "cell_type": "code", + "execution_count": 124, + "metadata": {}, + "outputs": [], + "source": [ + "def slope_func(state, t, system):\n", + " y, v = state\n", + " unpack(system)\n", + " \n", + " force = universal_gravitation(state, system)\n", + " dydt = v\n", + " dvdt = -1 *force / m2\n", + " \n", + " return dydt, dvdt" + ] + }, + { + "cell_type": "code", + "execution_count": 125, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "(,\n", + " )" + ] + }, + "execution_count": 125, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "slope_func(init, 0, system)" + ] + }, + { + "cell_type": "code", + "execution_count": 126, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "3.5425723405356547e+22 newton" + ], + "text/latex": [ + "$3.5425723405356547e+22 newton$" + ], + "text/plain": [ + "" + ] + }, + "execution_count": 126, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "grav = universal_gravitation(init, system)" + ] + }, + { + "cell_type": "code", + "execution_count": 127, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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t_events[[5577256.022519684]]
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njev0
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" + ], + "text/plain": [ + "sol None\n", + "t_events [[5577256.022519684]]\n", + "nfev 33500\n", + "njev 0\n", + "nlu 0\n", + "status 1\n", + "message A termination event occurred.\n", + "success True\n", + "dtype: object" + ] + }, + "execution_count": 127, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "results, details = run_ode_solver(system, slope_func, events = event_func, max_step=1000)\n", + "details" + ] + }, + { + "cell_type": "code", + "execution_count": 128, + "metadata": {}, + "outputs": [], + "source": [ + "# convert seconds to days\n", + "results.index /= 60 * 60 * 24\n", + "# convert meters to millions of km\n", + "results.r /= 1e9" + ] + }, + { + "cell_type": "code", + "execution_count": 130, + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "data": { + "image/png": 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" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "plot(results.r, label='r')\n", + "decorate(xlabel='Time (day)',\n", + " ylabel='Distance from sun (million km)')" + ] + }, + { + "cell_type": "code", + "execution_count": 133, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "64.55157433471857" + ] + }, + "execution_count": 133, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "t_event = get_last_label(results)" + ] + }, + { + "cell_type": "code", + "execution_count": 34, + "metadata": {}, + "outputs": [], + "source": [ + "# Solution goes here" + ] + }, + { + "cell_type": "code", + "execution_count": 35, + "metadata": {}, + "outputs": [], + "source": [ + "# Solution goes here" + ] + }, + { + "cell_type": "code", + "execution_count": 36, + "metadata": {}, + "outputs": [], + "source": [ + "# Solution goes here" + ] + }, + { + "cell_type": "code", + "execution_count": 37, + "metadata": {}, + "outputs": [], + "source": [ + "# Solution goes here" + ] + }, + { + "cell_type": "code", + "execution_count": 38, + "metadata": {}, + "outputs": [], + "source": [ + "# Solution goes here" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.6.6" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} From 583637af596731c5d6094977601490e2e97dfb7a Mon Sep 17 00:00:00 2001 From: Bennett Taylor Date: Thu, 15 Nov 2018 17:17:49 -0500 Subject: [PATCH 08/14] Orbit Model --- code/Orbit Code.ipynb | 1715 +++++++++++++++++++++++++++++++++++++++++ 1 file changed, 1715 insertions(+) create mode 100644 code/Orbit Code.ipynb diff --git a/code/Orbit Code.ipynb b/code/Orbit Code.ipynb new file mode 100644 index 00000000..7050275f --- /dev/null +++ b/code/Orbit Code.ipynb @@ -0,0 +1,1715 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Modeling and Simulation in Python\n", + "\n", + "Chapter 20\n", + "\n", + "Copyright 2017 Allen Downey\n", + "\n", + "License: [Creative Commons Attribution 4.0 International](https://creativecommons.org/licenses/by/4.0)\n" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "# Configure Jupyter so figures appear in the notebook\n", + "%matplotlib inline\n", + "\n", + "# Configure Jupyter to display the assigned value after an assignment\n", + "%config InteractiveShell.ast_node_interactivity='last_expr_or_assign'\n", + "\n", + "# import functions from the modsim.py module\n", + "from modsim import *" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Dropping pennies\n", + "\n", + "I'll start by getting the units we need from Pint." + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "second" + ], + "text/latex": [ + "$second$" + ], + "text/plain": [ + "" + ] + }, + "execution_count": 2, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "m = UNITS.meter\n", + "s = UNITS.second" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "And defining the initial state." + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "data": { + "text/html": [ + "
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" + ], + "text/plain": [ + "y 381 meter\n", + "v 0.0 meter / second\n", + "dtype: object" + ] + }, + "execution_count": 3, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "init = State(y=381 * m, \n", + " v=0 * m/s)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Acceleration due to gravity is about 9.8 m / s$^2$." + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "9.8 meter/second2" + ], + "text/latex": [ + "$9.8 \\frac{meter}{second^{2}}$" + ], + "text/plain": [ + "" + ] + }, + "execution_count": 4, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "g = 9.8 * m/s**2" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "When we call `odeint`, we need an array of timestamps where we want to compute the solution.\n", + "\n", + "I'll start with a duration of 10 seconds." + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "10 second" + ], + "text/latex": [ + "$10 second$" + ], + "text/plain": [ + "" + ] + }, + "execution_count": 5, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "t_end = 10 * s" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now we make a `System` object." + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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" + ], + "text/plain": [ + "init y 381 meter\n", + "v 0.0 meter / secon...\n", + "g 9.8 meter / second ** 2\n", + "t_end 10 second\n", + "dtype: object" + ] + }, + "execution_count": 6, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "system = System(init=init, g=g, t_end=t_end)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "And define the slope function." + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [], + "source": [ + "def slope_func(state, t, system):\n", + " \"\"\"Compute derivatives of the state.\n", + " \n", + " state: position, velocity\n", + " t: time\n", + " system: System object containing `g`\n", + " \n", + " returns: derivatives of y and v\n", + " \"\"\"\n", + " y, v = state\n", + " unpack(system) \n", + "\n", + " dydt = v\n", + " dvdt = -g\n", + " \n", + " return dydt, dvdt" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "It's always a good idea to test the slope function with the initial conditions." + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "0.0 meter / second\n", + "-9.8 meter / second ** 2\n" + ] + } + ], + "source": [ + "dydt, dvdt = slope_func(init, 0, system)\n", + "print(dydt)\n", + "print(dvdt)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now we're ready to call `run_ode_solver`" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "'The solver successfully reached the end of the integration interval.'" + ] + }, + "execution_count": 9, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "results, details = run_ode_solver(system, slope_func, max_step=0.5*s)\n", + "details.message" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here are the results:" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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" + ], + "text/plain": [ + " y v\n", + "0.000000 381.000000 0.000000\n", + "0.000102 381.000000 -0.001000\n", + "0.001122 380.999994 -0.011000\n", + "0.011327 380.999371 -0.111000\n", + "0.113367 380.937025 -1.110997\n", + "0.613367 379.156526 -6.010997\n", + "1.113367 374.926028 -10.910997\n", + "1.613367 368.245529 -15.810997\n", + "2.113367 359.115031 -20.710997\n", + "2.613367 347.534532 -25.610997\n", + "3.113367 333.504034 -30.510997\n", + "3.613367 317.023535 -35.410997\n", + "4.113367 298.093036 -40.310997\n", + "4.613367 276.712538 -45.210997\n", + "5.113367 252.882039 -50.110997\n", + "5.613367 226.601541 -55.010997\n", + "6.113367 197.871042 -59.910997\n", + "6.613367 166.690544 -64.810997\n", + "7.113367 133.060045 -69.710997\n", + "7.613367 96.979547 -74.610997\n", + "8.113367 58.449048 -79.510997\n", + "8.613367 17.468550 -84.410997\n", + "9.113367 -25.961949 -89.310997\n", + "9.613367 -71.842448 -94.210997\n", + "10.000000 -109.000000 -98.000000" + ] + }, + "execution_count": 10, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "results" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "And here's position as a function of time:" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Saving figure to file figs/chap09-fig01.pdf\n" + ] + }, + { + "data": { + "image/png": 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" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "def plot_position(results):\n", + " plot(results.y, label='y')\n", + " decorate(xlabel='Time (s)',\n", + " ylabel='Position (m)')\n", + "\n", + "plot_position(results)\n", + "savefig('figs/chap09-fig01.pdf')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Onto the sidewalk\n", + "\n", + "To figure out when the penny hit the sidewalk, we can use `crossings`, which finds the times where a `Series` passes through a given value." + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([8.81788535])" + ] + }, + "execution_count": 12, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "t_crossings = crossings(results.y, 0)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "For this example there should be just one crossing, the time when the penny hits the sidewalk." + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "8.817885349720552 second" + ], + "text/latex": [ + "$8.817885349720552 second$" + ], + "text/plain": [ + "" + ] + }, + "execution_count": 13, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "t_sidewalk = t_crossings[0] * s" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can compare that to the exact result. Without air resistance, we have\n", + "\n", + "$v = -g t$\n", + "\n", + "and\n", + "\n", + "$y = 381 - g t^2 / 2$\n", + "\n", + "Setting $y=0$ and solving for $t$ yields\n", + "\n", + "$t = \\sqrt{\\frac{2 y_{init}}{g}}$" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "8.817885349720552 second" + ], + "text/latex": [ + "$8.817885349720552 second$" + ], + "text/plain": [ + "" + ] + }, + "execution_count": 14, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "sqrt(2 * init.y / g)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The estimate is accurate to about 10 decimal places." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Events\n", + "\n", + "Instead of running the simulation until the penny goes through the sidewalk, it would be better to detect the point where the penny hits the sidewalk and stop. `run_ode_solver` provides exactly the tool we need, **event functions**.\n", + "\n", + "Here's an event function that returns the height of the penny above the sidewalk:" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": {}, + "outputs": [], + "source": [ + "def event_func(state, t, system):\n", + " \"\"\"Return the height of the penny above the sidewalk.\n", + " \"\"\"\n", + " y, v = state\n", + " return y" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "And here's how we pass it to `run_ode_solver`. The solver should run until the event function returns 0, and then terminate." + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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0.0011223.810000e+02-0.011000
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1.1337733.747013e+02-11.110971
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" + ], + "text/plain": [ + " y v\n", + "0.000000 3.810000e+02 0.000000\n", + "0.000102 3.810000e+02 -0.001000\n", + "0.001122 3.810000e+02 -0.011000\n", + "0.011327 3.809994e+02 -0.111000\n", + "0.113367 3.809370e+02 -1.110997\n", + "1.133773 3.747013e+02 -11.110971\n", + "8.817885 5.684342e-14 -86.415276" + ] + }, + "execution_count": 17, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "results" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "With the `events` option, the solver returns the actual time steps it computed, which are not necessarily equally spaced. \n", + "\n", + "The last time step is when the event occurred:" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "8.81788534972056 second" + ], + "text/latex": [ + "$8.81788534972056 second$" + ], + "text/plain": [ + "" + ] + }, + "execution_count": 18, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "t_sidewalk = get_last_label(results) * s" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Unfortunately, `run_ode_solver` does not carry the units through the computation, so we have to put them back at the end.\n", + "\n", + "We could also get the time of the event from `details`, but it's a minor nuisance because it comes packed in an array:" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "8.81788534972056 second" + ], + "text/latex": [ + "$8.81788534972056 second$" + ], + "text/plain": [ + "" + ] + }, + "execution_count": 19, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "details.t_events[0][0] * s" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The result is accurate to about 15 decimal places.\n", + "\n", + "We can also check the velocity of the penny when it hits the sidewalk:" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "-86.41527642726152 meter/second" + ], + "text/latex": [ + "$-86.41527642726152 \\frac{meter}{second}$" + ], + "text/plain": [ + "" + ] + }, + "execution_count": 20, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "v_sidewalk = get_last_value(results.v) * m / s" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "And convert to kilometers per hour." + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "-311.0949951381415 kilometer/hour" + ], + "text/latex": [ + "$-311.0949951381415 \\frac{kilometer}{hour}$" + ], + "text/plain": [ + "" + ] + }, + "execution_count": 21, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "km = UNITS.kilometer\n", + "h = UNITS.hour\n", + "v_sidewalk.to(km / h)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "If there were no air resistance, the penny would hit the sidewalk (or someone's head) at more than 300 km/h.\n", + "\n", + "So it's a good thing there is air resistance." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Under the hood\n", + "\n", + "Here is the source code for `crossings` so you can see what's happening under the hood:" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": {}, + "outputs": [], + "source": [ + "%psource crossings" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The [documentation of InterpolatedUnivariateSpline is here](https://docs.scipy.org/doc/scipy/reference/generated/scipy.interpolate.InterpolatedUnivariateSpline.html).\n", + "\n", + "And you can read the [documentation of `scipy.integrate.solve_ivp`](https://docs.scipy.org/doc/scipy/reference/generated/scipy.integrate.solve_ivp.html) to learn more about how `run_ode_solver` works." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Exercises\n", + "\n", + "**Exercise:** Here's a question from the web site [Ask an Astronomer](http://curious.astro.cornell.edu/about-us/39-our-solar-system/the-earth/other-catastrophes/57-how-long-would-it-take-the-earth-to-fall-into-the-sun-intermediate):\n", + "\n", + "\"If the Earth suddenly stopped orbiting the Sun, I know eventually it would be pulled in by the Sun's gravity and hit it. How long would it take the Earth to hit the Sun? I imagine it would go slowly at first and then pick up speed.\"\n", + "\n", + "Use `run_ode_solver` to answer this question.\n", + "\n", + "Here are some suggestions about how to proceed:\n", + "\n", + "1. Look up the Law of Universal Gravitation and any constants you need. I suggest you work entirely in SI units: meters, kilograms, and Newtons.\n", + "\n", + "2. When the distance between the Earth and the Sun gets small, this system behaves badly, so you should use an event function to stop when the surface of Earth reaches the surface of the Sun.\n", + "\n", + "3. Express your answer in days, and plot the results as millions of kilometers versus days.\n", + "\n", + "If you read the reply by Dave Rothstein, you will see other ways to solve the problem, and a good discussion of the modeling decisions behind them.\n", + "\n", + "You might also be interested to know that [it's actually not that easy to get to the Sun](https://www.theatlantic.com/science/archive/2018/08/parker-solar-probe-launch-nasa/567197/)." + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "newton" + ], + "text/latex": [ + "$newton$" + ], + "text/plain": [ + "" + ] + }, + "execution_count": 23, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "m = UNITS.meter\n", + "s = UNITS.second\n", + "kg = UNITS.kilogram\n", + "AU = UNITS.astronomical_unit\n", + "N = UNITS.newton" + ] + }, + { + "cell_type": "code", + "execution_count": 36, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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initpx 149597870691.0 meter\n", + "py ...
G6.67408e-11 meter ** 2 * newton / kilogram ** 2
m11.989e+30 kilogram
m25.972324e+24 kilogram
t_00 second
t_end315360000 second
r_final701879000 meter
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" + ], + "text/plain": [ + "init px 149597870691.0 meter\n", + "py ...\n", + "G 6.67408e-11 meter ** 2 * newton / kilogram ** 2\n", + "m1 1.989e+30 kilogram\n", + "m2 5.972324e+24 kilogram\n", + "t_0 0 second\n", + "t_end 315360000 second\n", + "r_final 701879000 meter\n", + "dtype: object" + ] + }, + "execution_count": 37, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "system = System (init = init,\n", + " G = 6.67408e-11*N/kg**2 * m**2,\n", + " m1 = 1.989e30 * kg,\n", + " m2 = 5.972324e24 * kg,\n", + " t_0 = 0 * s,\n", + " #t_end = 31536000 * s,\n", + " t_end = 315360000 * s,\n", + " r_final = 6371000 * m + 695508000 * m)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": 38, + "metadata": {}, + "outputs": [], + "source": [ + "def universal_gravitation(state, system):\n", + " px, py, vx, vy = state\n", + " unpack(system)\n", + " \n", + " position = Vector(px, py)\n", + " P = position.mag\n", + " F_magnitude = G * m1 * m2/ (P**2)\n", + " \n", + " P_direction = position.hat()\n", + " \n", + " F = P_direction * F_magnitude * (-1)\n", + "\n", + " \n", + " return F" + ] + }, + { + "cell_type": "code", + "execution_count": 39, + "metadata": {}, + "outputs": [], + "source": [ + "def event_func(state, t, system):\n", + " \"\"\"Return the height of the penny above the sidewalk.\n", + " \"\"\"\n", + " px, py, vx, vy = state\n", + " position = Vector(px, py)\n", + " \n", + " return position.mag - system.r_final" + ] + }, + { + "cell_type": "code", + "execution_count": 40, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "[-3.54257234e+22 -0.00000000e+00] newton" + ], + "text/latex": [ + "$[-3.54257234e+22 -0.00000000e+00] newton$" + ], + "text/plain": [ + "" + ] + }, + "execution_count": 40, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "universal_gravitation(init, system)" + ] + }, + { + "cell_type": "code", + "execution_count": 67, + "metadata": {}, + "outputs": [], + "source": [ + "def slope_func(state, t, system):\n", + " px, py, vx, vy = state\n", + " unpack(system)\n", + " \n", + " position = Vector(px, py)\n", + " \n", + " F = universal_gravitation(state, system)\n", + " \n", + " Fx = F.x\n", + " Fy = F.y\n", + " \n", + " dpxdt = vx\n", + " \n", + " dpydt = vy\n", + " \n", + " dvxdt = Fx/m2\n", + " \n", + " dvydt = Fy/m2\n", + " \n", + " \n", + " return dpxdt, dpydt, dvxdt, dvydt" + ] + }, + { + "cell_type": "code", + "execution_count": 68, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "(,\n", + " ,\n", + " ,\n", + " )" + ] + }, + "execution_count": 68, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "slope_func(init, 0, system)" + ] + }, + { + "cell_type": "code", + "execution_count": 69, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "[-3.54257234e+22 -0.00000000e+00] newton" + ], + "text/latex": [ + "$[-3.54257234e+22 -0.00000000e+00] newton$" + ], + "text/plain": [ + "" + ] + }, + "execution_count": 69, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "grav = universal_gravitation(init, system)" + ] + }, + { + "cell_type": "code", + "execution_count": 75, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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values
solNone
t_events[[]]
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njev0
nlu0
status0
messageThe solver successfully reached the end of the...
successTrue
\n", + "
" + ], + "text/plain": [ + "sol None\n", + "t_events [[]]\n", + "nfev 890\n", + "njev 0\n", + "nlu 0\n", + "status 0\n", + "message The solver successfully reached the end of the...\n", + "success True\n", + "dtype: object" + ] + }, + "execution_count": 75, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "results, details = run_ode_solver(system, slope_func, events = event_func, method = \"RK23\")\n", + "details" + ] + }, + { + "cell_type": "code", + "execution_count": 76, + "metadata": {}, + "outputs": [], + "source": [ + "# convert seconds to days\n", + "results.index /= 60 * 60 * 24\n", + "# convert meters to millions of km\n", + "results.px /= 1e9\n", + "results.py/= 1e9" + ] + }, + { + "cell_type": "code", + "execution_count": 77, + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 77, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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\n", 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\n", 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" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "plot(results.px, results.py)\n", + "decorate(xlabel='Time (day)',\n", + " ylabel='Distance from sun (million km)')" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# Solution goes here" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# Solution goes here" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# Solution goes here" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# Solution goes here" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# Solution goes here" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.6.6" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} From e2b80ca12e884a9b7034b055f6e76a025fc4e6b7 Mon Sep 17 00:00:00 2001 From: Bennett Taylor Date: Sat, 8 Dec 2018 09:47:20 -0500 Subject: [PATCH 09/14] Asteroid Code v2 --- code/Asteroid v.2.ipynb | 575 ++++++++++++++++++++++++++++++++++++++++ 1 file changed, 575 insertions(+) create mode 100644 code/Asteroid v.2.ipynb diff --git a/code/Asteroid v.2.ipynb b/code/Asteroid v.2.ipynb new file mode 100644 index 00000000..a516bd5a --- /dev/null +++ b/code/Asteroid v.2.ipynb @@ -0,0 +1,575 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "# Configure Jupyter so figures appear in the notebook\n", + "%matplotlib inline\n", + "\n", + "# Configure Jupyter to display the assigned value after an assignment\n", + "%config InteractiveShell.ast_node_interactivity='last_expr_or_assign'\n", + "\n", + "# import functions from the modsim.py module\n", + "from modsim import *\n", + "import math as math" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "%psource crossings" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "newton" + ], + "text/latex": [ + "$newton$" + ], + "text/plain": [ + "" + ] + }, + "execution_count": 3, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "m = UNITS.meter\n", + "s = UNITS.second\n", + "kg = UNITS.kilogram\n", + "AU = UNITS.astronomical_unit\n", + "N = UNITS.newton" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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px300000 meter
py300000 meter
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" + ], + "text/plain": [ + "sol None\n", + "t_events []\n", + "nfev 23444\n", + "njev 0\n", + "nlu 0\n", + "status -1\n", + "message Required step size is less than spacing betwee...\n", + "success False\n", + "dtype: object" + ] + }, + "execution_count": 13, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "ts = linspace(t_0, system.t_end, 500)*s\n", + "results, details = run_ode_solver(system, slope_func, vectorized = True)\n", + "results.px/=1e9\n", + "results.py/=1e9\n", + "details" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", 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G6.67408e-11 meter ** 2 * newton / kilogram ** 2
m16100000000000000.0 kilogram
m25.972324e+24 kilogram
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" + ], + "text/plain": [ + "init px 300000 meter\n", + "py 3...\n", + "G 6.67408e-11 meter ** 2 * newton / kilogram ** 2\n", + "m1 6100000000000000.0 kilogram\n", + "m2 5.972324e+24 kilogram\n", + "t_0 0 second\n", + "t_end 315360000 second\n", + "r_final 6376000 meter\n", + "dtype: object" + ] + }, + "execution_count": 4, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "system = System (init = init,\n", + " G = 6.67408e-11*N/kg**2 * m**2,\n", + " #mass of asteroid that killed dinosaurs\n", + " m1 = 6.1e15* kg,\n", + " #earth mass\n", + " m2 = 5.972324e24* kg,\n", + " t_0 = 0 * s,\n", + " t_end = 315360000* s,\n", + " #radius of earth plus radius of asteroid that killed the dinosaurs\n", + " r_final = (6371000 + 5000)* m)" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [], + "source": [ + "def universal_gravitation(state, system):\n", + " px, py, vx, vy = state\n", + " unpack(system)\n", + " \n", + "\n", + " position = Vector(px, py)\n", + " P = sqrt(px**2 + py**2)\n", + " F_magnitude = G * m1 * m2/ ((P)**2)\n", + " \n", + " P_direction = position/P\n", + " \n", + " F = P_direction * (-1) * F_magnitude\n", + "\n", + " \n", + " return F" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "[-9.55162141e+18 -9.55162141e+18] newton" + ], + "text/latex": [ + "$[-9.55162141e+18 -9.55162141e+18] newton$" + ], + "text/plain": [ + "" + ] + }, + "execution_count": 6, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "universal_gravitation(init, system)" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "metadata": {}, + "outputs": [], + "source": [ + "def event_func(state, t, system):\n", + "\n", + " px, py, vx, vy = state\n", + " \n", + " P = abs(sqrt(px**2 + py**2))\n", + " \n", + " return P - abs(system.r_final - 1)" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "[-9.55162141e+18 -9.55162141e+18] newton" + ], + "text/latex": [ + "$[-9.55162141e+18 -9.55162141e+18] newton$" + ], + "text/plain": [ + "" + ] + }, + "execution_count": 24, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "universal_gravitation(init, system)" + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "metadata": {}, + "outputs": [], + "source": [ + "def slope_func(state, t, system):\n", + " px, py, vx, vy = state\n", + " unpack(system)\n", + " \n", + " position = Vector(px, py)\n", + " \n", + " F = universal_gravitation(state, system)\n", + " \n", + " Fx = F.x\n", + " Fy = F.y\n", + " \n", + " dpxdt = vx\n", + " \n", + " dpydt = vy\n", + " \n", + " dvxdt = Fx/m1\n", + " \n", + " dvydt = Fy/m1\n", + " \n", + " \n", + " return dpxdt, dpydt, dvxdt, dvydt" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "data": { + "text/plain": [ + "(,\n", + " ,\n", + " ,\n", + " )" + ] + }, + "execution_count": 26, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "slope_func(init, 0, system)" + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "[-9.55162141e+18 -9.55162141e+18] newton" + ], + "text/latex": [ + "$[-9.55162141e+18 -9.55162141e+18] newton$" + ], + "text/plain": [ + "" + ] + }, + "execution_count": 27, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "grav = universal_gravitation(init, system)" + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "metadata": { + "scrolled": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Required step size is less than spacing between numbers.\n", + "sol None\n", + "t_events [[]]\n", + "nfev 23444\n", + "njev 0\n", + "nlu 0\n", + "status -1\n", + "message Required step size is less than spacing betwee...\n", + "success False\n", + "dtype: object\n", + "\n" + ] + } + ], + "source": [ + "results, details = run_ode_solver(system, slope_func, vectorized = True, events = event_func)\n", + "results.px/=1e9\n", + "results.py/=1e9\n", + "details\n", + "print(details.message)\n", + "print(details)\n", + "print(results.last)" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "axes = plt.gca()\n", + "axes.set_xlim([0, 0.00005])\n", + "axes.set_ylim([0, 0.00005])\n", + "\n", + "plot(results.px,results.py)" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": {}, + "outputs": [ + { + "ename": "ValueError", + "evalue": "not enough values to unpack (expected 2, got 0)", + "output_type": "error", + "traceback": [ + "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m", + "\u001b[1;31mValueError\u001b[0m Traceback (most recent call last)", + "\u001b[1;32m\u001b[0m in \u001b[0;36m\u001b[1;34m()\u001b[0m\n\u001b[0;32m 1\u001b[0m \u001b[0maxes\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mplt\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mgca\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m----> 2\u001b[1;33m 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\u001b[0;36mset_xlim\u001b[1;34m(self, left, right, emit, auto, **kw)\u001b[0m\n\u001b[0;32m 3134\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 3135\u001b[0m \u001b[1;32mif\u001b[0m \u001b[0mright\u001b[0m \u001b[1;32mis\u001b[0m \u001b[1;32mNone\u001b[0m \u001b[1;32mand\u001b[0m \u001b[0miterable\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mleft\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m-> 3136\u001b[1;33m \u001b[0mleft\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mright\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mleft\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 3137\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 3138\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m_process_unit_info\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mxdata\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mleft\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mright\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n", + "\u001b[1;31mValueError\u001b[0m: not enough values to unpack (expected 2, got 0)" + ] + }, + { + "data": { + "image/png": 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r_final6376000 meter
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" + ], + "text/plain": [ + "init px 300000 meter\n", + "py 3...\n", + "G 6.67408e-11 newton / kilogram ** 2 / meter ** 2\n", + "m1 6100000000000000.0 kilogram\n", + "m2 5.972324e+24 kilogram\n", + "t_0 0 second\n", + "t_end 315360000 second\n", + "r_final 6376000 meter\n", + "dtype: object" + ] + }, + "execution_count": 13, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + " #asteroid is starting approximately \"r\" away in the x and y distance\n", + "system = make_system(300000, 300000, 0, -1000)" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": {}, + "outputs": [], + "source": [ + "def universal_gravitation(state, system):\n", + " px, py, vx, vy = state\n", + " unpack(system)\n", + " \n", + "\n", + " position = Vector(px, py)\n", + " P = sqrt(px**2/m**2 + py**2/m**2)\n", + " F_magnitude = G * m1 * m2/ ((P)**2)\n", + " \n", + " P_direction = position/P\n", + " \n", + " F = P_direction * (-1) * F_magnitude * m\n", + "\n", + " \n", + " return F" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "[-9.55162141e+18 -9.55162141e+18] newton" + ], + "text/latex": [ + "$[-9.55162141e+18 -9.55162141e+18] newton$" + ], + "text/plain": [ + "" + ] + }, + "execution_count": 15, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "universal_gravitation(init, system)" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": {}, + "outputs": [], + "source": [ + "def event_func(state, t, system):\n", + "\n", + " px, py, vx, vy = state\n", + " \n", + " P = abs(sqrt(px**2 + py**2))\n", + " \n", + " return P - abs(system.r_final - 1)" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "[-9.55162141e+18 -9.55162141e+18] newton" + ], + "text/latex": [ + "$[-9.55162141e+18 -9.55162141e+18] newton$" + ], + "text/plain": [ + "" + ] + }, + "execution_count": 17, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "universal_gravitation(init, system)" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": {}, + "outputs": [], + "source": [ + "def slope_func(state, t, system):\n", + " px, py, vx, vy = state\n", + " unpack(system)\n", + " \n", + " position = Vector(px, py)\n", + " \n", + " F = universal_gravitation(state, system)\n", + " \n", + " Fx = F.x\n", + " Fy = F.y\n", + " \n", + " dpxdt = vx\n", + " \n", + " dpydt = vy\n", + " \n", + " dvxdt = Fx/m1\n", + " \n", + " dvydt = Fy/m1\n", + " \n", + " \n", + " return dpxdt, dpydt, dvxdt, dvydt" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "data": { + "text/plain": [ + "(,\n", + " ,\n", + " ,\n", + " )" + ] + }, + "execution_count": 19, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "slope_func(init, 0, system)" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "[-9.55162141e+18 -9.55162141e+18] newton" + ], + "text/latex": [ + "$[-9.55162141e+18 -9.55162141e+18] newton$" + ], + "text/plain": [ + "" + ] + }, + "execution_count": 20, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "grav = universal_gravitation(init, system)" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": { + "scrolled": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Required step size is less than spacing between numbers.\n", + "sol None\n", + "t_events [[]]\n", + "nfev 23444\n", + "njev 0\n", + "nlu 0\n", + "status -1\n", + "message Required step size is less than spacing betwee...\n", + "success False\n", + "dtype: object\n", + "\n" + ] + } + ], + "source": [ + "results, details = run_ode_solver(system, slope_func, vectorized = True, events = event_func)\n", + "results.px/=1e9\n", + "results.py/=1e9\n", + "details\n", + "print(details.message)\n", + "print(details)\n", + "print(results.last)" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", 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" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "results.px.plot()\n", + "results.py.plot()\n", + "decorate(ylabel='Distance [billions of km]',\n", + " xlabel='Time [billions of sec]',\n", + " title='Path of Asteroid')" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "axes = plt.gca()\n", + "axes.set_xlim([0, 0.00005])\n", + "axes.set_ylim([0, 0.00005])\n", + "\n", + "plot(results.px,results.py)\n", + "decorate(xlabel='Distance [billions of km]', \n", + " ylabel='Distance [billions of km]',\n", + " title='Path of Asteroid')" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "metadata": {}, + "outputs": [], + "source": [ + "def collision_result(results):\n", + " colvalx = get_last_value(results.px)\n", + " colvaly = get_last_value(results.py)\n", + " print('Final X Value =', colvalx)\n", + " print('Final Y Value =', colvaly)\n", + "\n", + " if -1 < colvalx and colvaly < 1:\n", + " print ('Kaboom! The asteroid hit!')\n", + " else:\n", + " print ('We live to love another day!')" + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Final X Value = 2.401860681452048e-14\n", + "Final Y Value = -7.774799575110358e-14\n", + "Kaboom! The asteroid hit!\n" + ] + } + ], + "source": [ + "collision_result(results)" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "px 300000 meter\n", + "py 300000 meter\n", + "vx 0.0 meter / second\n", + "vy -1000.0 meter / second\n", + "dtype: object\n", + "Final X Value = 2.401860681452048e-05\n", + "Final Y Value = -7.774799575110359e-05\n", + "Kaboom! The asteroid hit!\n", + "px 300000 meter\n", + "py 300000 meter\n", + "vx 0.0 meter / second\n", + "vy -3250.0 meter / second\n", + "dtype: object\n", + "Final X Value = -0.00019528327106418505\n", + "Final Y Value = -5.689207691431667e-05\n", + "Kaboom! The asteroid hit!\n", + "px 300000 meter\n", + "py 300000 meter\n", + "vx 0.0 meter / second\n", + "vy -5500.0 meter / second\n", + "dtype: object\n", + "Final X Value = -0.00022003510963148853\n", + "Final Y Value = 0.0002437331262958202\n", + "Kaboom! The asteroid hit!\n", + "px 300000 meter\n", + "py 300000 meter\n", + "vx 0.0 meter / second\n", + "vy -7750.0 meter / second\n", + "dtype: object\n", + "Final X Value = -0.00042688559468384346\n", + "Final Y Value = 0.00029666007725250536\n", + "Kaboom! The asteroid hit!\n", + "px 300000 meter\n", + "py 300000 meter\n", + "vx 0.0 meter / second\n", + "vy -10000.0 meter / second\n", + "dtype: object\n", + "Final X Value = 0.0004212912287762479\n", + "Final Y Value = 0.00029198178720398925\n", + "Kaboom! The asteroid hit!\n" + ] + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + " vel_array = linspace(1000, 10000, 5) \n", + "for sweep_vel in vel_array:\n", + " system = make_system(300000, 300000, 0, -1*sweep_vel)\n", + " results, details = run_ode_solver(system, slope_func, vectorized = True, events = event_func)\n", + " collision_result(results)\n", + " plot(results.px,results.py)\n", + " decorate(xlabel='Distance [billions of km]', \n", + " ylabel='Distance [billions of km]',\n", + " title='Path of Asteroid')" + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "px 300000 meter\n", + "py 300000 meter\n", + "vx 0.0 meter / second\n", + "vy -10000.0 meter / second\n", + "dtype: object\n", + "Final X Value = 0.0004212912287762479\n", + "Final Y Value = 0.00029198178720398925\n", + "Kaboom! The asteroid hit!\n", + "px 300000 meter\n", + "py 300000 meter\n", + "vx 0.0 meter / second\n", + "vy -32500.0 meter / second\n", + "dtype: object\n", + "Final X Value = -0.0020671600763026167\n", + "Final Y Value = 0.0002242539025830517\n", + "Kaboom! The asteroid hit!\n", + "px 300000 meter\n", + "py 300000 meter\n", + "vx 0.0 meter / second\n", + "vy -55000.0 meter / second\n", + "dtype: object\n", + "Final X Value = -5245427.631310573\n", + "Final Y Value = -3624755.4693640424\n", + "We live to love another day!\n", + "px 300000 meter\n", + "py 300000 meter\n", + "vx 0.0 meter / second\n", + "vy -77500.0 meter / second\n", + "dtype: object\n", + "Final X Value = -2409022.702405719\n", + "Final Y Value = -5903386.559195902\n", + "We live to love another day!\n", + "px 300000 meter\n", + "py 300000 meter\n", + "vx 0.0 meter / second\n", + "vy -100000.0 meter / second\n", + "dtype: object\n", + "Final X Value = -1270004.916780909\n", + "Final Y Value = -6248235.811759452\n", + "We live to love another day!\n" + ] + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + " vel_array2 = linspace(10000, 100000, 5) \n", + "for sweep_vel in vel_array2:\n", + " system = make_system(300000, 300000, 0, -1*sweep_vel)\n", + " results, details = run_ode_solver(system, slope_func, vectorized = True, events = event_func)\n", + " collision_result(results)\n", + " plot(results.px,results.py)\n", + " decorate(xlabel='Distance [billions of km]', \n", + " ylabel='Distance [billions of km]',\n", + " title='Path of Asteroid')" + ] + }, + { + "cell_type": "code", + "execution_count": 29, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "px 300000 meter\n", + "py 300000 meter\n", + "vx 0.0 meter / second\n", + "vy -38125.0 meter / second\n", + "dtype: object\n", + "Final X Value = -0.0017428050717388979\n", + "Final Y Value = 0.002938641321146782\n", + "Kaboom! The asteroid hit!\n", + "px 300000 meter\n", + "py 300000 meter\n", + "vx 0.0 meter / second\n", + "vy -38750.0 meter / second\n", + "dtype: object\n", + "Final X Value = -0.0023891581621569066\n", + "Final Y Value = 0.0022881165665098856\n", + "Kaboom! The asteroid hit!\n", + "px 300000 meter\n", + "py 300000 meter\n", + "vx 0.0 meter / second\n", + "vy -39375.0 meter / second\n", + "dtype: object\n", + "Final X Value = -0.005075074219659456\n", + "Final Y Value = -0.0015658591296571212\n", + "Kaboom! The asteroid hit!\n", + "px 300000 meter\n", + "py 300000 meter\n", + "vx 0.0 meter / second\n", + "vy -40000.0 meter / second\n", + "dtype: object\n", + "Final X Value = -0.004776828468161679\n", + "Final Y Value = -0.0024901375566320073\n", + "Kaboom! The asteroid hit!\n", + "px 300000 meter\n", + "py 300000 meter\n", + "vx 0.0 meter / second\n", + "vy -40625.0 meter / second\n", + "dtype: object\n", + "Final X Value = -0.004541864481159929\n", + "Final Y Value = -0.0029394135776692025\n", + "Kaboom! The asteroid hit!\n", + "px 300000 meter\n", + "py 300000 meter\n", + "vx 0.0 meter / second\n", + "vy -41250.0 meter / second\n", + "dtype: object\n", + "Final X Value = 0.004784932829846704\n", + "Final Y Value = -0.007044018089338927\n", + "Kaboom! The asteroid hit!\n", + "px 300000 meter\n", + "py 300000 meter\n", + "vx 0.0 meter / second\n", + "vy -41875.0 meter / second\n", + "dtype: object\n", + "Final X Value = 0.004818987268221729\n", + "Final Y Value = -0.0070340388361872196\n", + "Kaboom! The asteroid hit!\n", + "px 300000 meter\n", + "py 300000 meter\n", + "vx 0.0 meter / second\n", + "vy -42500.0 meter / second\n", + "dtype: object\n", + "Final X Value = -5216202.023357081\n", + "Final Y Value = 3666687.837753098\n", + "We live to love another day!\n", + "px 300000 meter\n", + "py 300000 meter\n", + "vx 0.0 meter / second\n", + "vy -43125.0 meter / second\n", + "dtype: object\n", + "Final X Value = -5690824.571655385\n", + "Final Y Value = 2875391.9633059264\n", + "We live to love another day!\n", + "px 300000 meter\n", + "py 300000 meter\n", + "vx 0.0 meter / second\n", + "vy -43750.0 meter / second\n", + "dtype: object\n", + "Final X Value = -5975658.614352823\n", + "Final Y Value = 2223705.7747624605\n", + "We live to love another day!\n" + ] + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "#CAN DELETE, JUST NOTE THAT WE JUMPED TO CLOSER RANGE\n", + " vel_array3 = linspace(38125, 43750, 10) \n", + "for sweep_vel in vel_array3:\n", + " system = make_system(300000, 300000, 0, -1*sweep_vel)\n", + " results, details = run_ode_solver(system, slope_func, vectorized = True, events = event_func)\n", + " collision_result(results)\n", + " plot(results.px,results.py)\n", + " decorate(xlabel='Distance [billions of km]', \n", + " ylabel='Distance [billions of km]',\n", + " title='Path of Asteroid')" + ] + }, + { + "cell_type": "code", + "execution_count": 31, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "px 300000 meter\n", + "py 300000 meter\n", + "vx 0.0 meter / second\n", + "vy -42083.0 meter / second\n", + "dtype: object\n", + "Final X Value = -0.005971722393688606\n", + "Final Y Value = 0.006109688285641839\n", + "Kaboom! The asteroid hit!\n", + "px 300000 meter\n", + "py 300000 meter\n", + "vx 0.0 meter / second\n", + "vy -42090.666666666664 meter / second\n", + "dtype: object\n", + "Final X Value = 0.00587532360500044\n", + "Final Y Value = -0.012262102623406948\n", + "Kaboom! The asteroid hit!\n", + "px 300000 meter\n", + "py 300000 meter\n", + "vx 0.0 meter / second\n", + "vy -42098.333333333336 meter / second\n", + "dtype: object\n", + "Final X Value = 0.011949571677247443\n", + "Final Y Value = 0.007136124368947902\n", + "Kaboom! The asteroid hit!\n", + "px 300000 meter\n", + "py 300000 meter\n", + "vx 0.0 meter / second\n", + "vy -42106.0 meter / second\n", + "dtype: object\n", + "Final X Value = -4566115.382494392\n", + "Final Y Value = 4450163.318547882\n", + "We live to love another day!\n", + "px 300000 meter\n", + "py 300000 meter\n", + "vx 0.0 meter / second\n", + "vy -42113.666666666664 meter / second\n", + "dtype: object\n", + "Final X Value = -4591477.724502849\n", + "Final Y Value = 4423990.907924104\n", + "We live to love another day!\n", + "px 300000 meter\n", + "py 300000 meter\n", + "vx 0.0 meter / second\n", + "vy -42121.333333333336 meter / second\n", + "dtype: object\n", + "Final X Value = -4615112.526527914\n", + "Final Y Value = 4399329.450664739\n", + "We live to love another day!\n", + "px 300000 meter\n", + "py 300000 meter\n", + "vx 0.0 meter / second\n", + "vy -42129.0 meter / second\n", + "dtype: object\n", + "Final X Value = -4637322.402593106\n", + "Final Y Value = 4375911.811543864\n", + "We live to love another day!\n", + "px 300000 meter\n", + "py 300000 meter\n", + "vx 0.0 meter / second\n", + "vy -42136.666666666664 meter / second\n", + "dtype: object\n", + "Final X Value = -4658325.222808974\n", + "Final Y Value = 4353546.757132938\n", + "We live to love another day!\n", + "px 300000 meter\n", + "py 300000 meter\n", + "vx 0.0 meter / second\n", + "vy -42144.333333333336 meter / second\n", + "dtype: object\n", + "Final X Value = -4678294.581164022\n", + "Final Y Value = 4332080.684827136\n", + "We live to love another day!\n", + "px 300000 meter\n", + "py 300000 meter\n", + "vx 0.0 meter / second\n", + "vy -42152.0 meter / second\n", + "dtype: object\n", + "Final X Value = -4697366.01959437\n", + "Final Y Value = 4311393.7103866\n", + "We live to love another day!\n" + ] + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "#rempved intermediate sweeps, jumped to more narrowed range\n", + " vel_array4 = linspace(42083.0, 42152, 10) \n", + "for sweep_vel in vel_array4:\n", + " system = make_system(300000, 300000, 0, -1*sweep_vel)\n", + " results, details = run_ode_solver(system, slope_func, vectorized = True, events = event_func)\n", + " collision_result(results)\n", + " plot(results.px,results.py)\n", + " decorate(xlabel='Distance [billions of km]', \n", + " ylabel='Distance [billions of km]',\n", + " title='Path of Asteroid')" + ] + }, + { + "cell_type": "code", + "execution_count": 33, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "px 300000 meter\n", + "py 300000 meter\n", + "vx 0.0 meter / second\n", + "vy -42098.0 meter / second\n", + "dtype: object\n", + "Final X Value = -0.010037090056138108\n", + "Final Y Value = -0.009028403359159429\n", + "Kaboom! The asteroid hit!\n", + "px 300000 meter\n", + "py 300000 meter\n", + "vx 0.0 meter / second\n", + "vy -42099.0 meter / second\n", + "dtype: object\n", + "Final X Value = -0.005490367335749029\n", + "Final Y Value = 0.012047648068709477\n", + "Kaboom! The asteroid hit!\n", + "px 300000 meter\n", + "py 300000 meter\n", + "vx 0.0 meter / second\n", + "vy -42100.0 meter / second\n", + "dtype: object\n", + "Final X Value = -4544786.852473755\n", + "Final Y Value = 4471943.169762189\n", + "We live to love another day!\n", + "px 300000 meter\n", + "py 300000 meter\n", + "vx 0.0 meter / second\n", + "vy -42101.0 meter / second\n", + "dtype: object\n", + "Final X Value = -4548444.578457363\n", + "Final Y Value = 4468222.819500256\n", + "We live to love another day!\n", + "px 300000 meter\n", + "py 300000 meter\n", + "vx 0.0 meter / second\n", + "vy -42102.0 meter / second\n", + "dtype: object\n", + "Final X Value = -4552059.24275189\n", + "Final Y Value = 4464540.278514474\n", + "We live to love another day!\n", + "px 300000 meter\n", + "py 300000 meter\n", + "vx 0.0 meter / second\n", + "vy -42103.0 meter / second\n", + "dtype: object\n", + "Final X Value = -4555632.309621311\n", + "Final Y Value = 4460894.249759279\n", + "We live to love another day!\n", + "px 300000 meter\n", + "py 300000 meter\n", + "vx 0.0 meter / second\n", + "vy -42104.0 meter / second\n", + "dtype: object\n", + "Final X Value = -4559165.161839106\n", + "Final Y Value = 4457283.508491871\n", + "We live to love another day!\n", + "px 300000 meter\n", + "py 300000 meter\n", + "vx 0.0 meter / second\n", + "vy -42105.0 meter / second\n", + "dtype: object\n", + "Final X Value = -4562659.106861685\n", + "Final Y Value = 4453706.896796548\n", + "We live to love another day!\n", + "px 300000 meter\n", + "py 300000 meter\n", + "vx 0.0 meter / second\n", + "vy -42106.0 meter / second\n", + "dtype: object\n", + "Final X Value = -4566115.382494392\n", + "Final Y Value = 4450163.318547882\n", + "We live to love another day!\n" + ] + }, + { + "data": { + "image/png": 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\n", 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" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + " vel_array5 = linspace(42098.0, 42106, 9) \n", + "for sweep_vel in vel_array5:\n", + " system = make_system(300000, 300000, 0, -1*sweep_vel)\n", + " results, details = run_ode_solver(system, slope_func, vectorized = True, events = event_func)\n", + " collision_result(results)\n", + " plot(results.px,results.py)\n", + " decorate(xlabel='Distance [billions of km]', \n", + " ylabel='Distance [billions of km]',\n", + " title='Path of Asteroid')" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.6.6" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} From cfaae469ca12076f840e0f4ebf615335ce3276e4 Mon Sep 17 00:00:00 2001 From: Bennett Taylor Date: Sun, 9 Dec 2018 15:12:59 -0500 Subject: [PATCH 12/14] Asteroid Model: Computational Essay --- code/Asteroid Final.ipynb | 1246 +++++++++++++++++++++++++++++++++++++ 1 file changed, 1246 insertions(+) create mode 100644 code/Asteroid Final.ipynb diff --git a/code/Asteroid Final.ipynb b/code/Asteroid Final.ipynb new file mode 100644 index 00000000..15b2fdeb --- /dev/null +++ b/code/Asteroid Final.ipynb @@ -0,0 +1,1246 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Death by Asteroid\n", + "\n", + "### Olivia Seitelman and Bennett Taylor" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "# Configure Jupyter so figures appear in the notebook\n", + "%matplotlib inline\n", + "\n", + "# Configure Jupyter to display the assigned value after an assignment\n", + "%config InteractiveShell.ast_node_interactivity='last_expr_or_assign'\n", + "\n", + "# import functions from the modsim.py module\n", + "from modsim import *\n", + "import math as math\n", + "\n", + "import numpy as np\n", + "import matplotlib.pyplot as ply\n", + "import scipy, pylab" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Question" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "If an asteroid is passing Earth at a set distance, at what velocity would it enter Earth's orbit or collide with Earth?\n", + "\n", + "This question is important to everyone on Earth, as asteroids pose a threat to human life and their impact can be predicted and prevented." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Model" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We chose to model an asteroid that is approaching the Earth at a varying velocity and will pass tangentially at a set distance. The asteroid starts at `3e8 * m`, which is almost the distance to the moon, and the only force acting on the asteroid is Earth's gravity. Our asteroid is the size of the one that killed the dinosaurs, with a radius of `5000 *m` and a mass of about `6.1e15 * kg`.\n", + "\n", + "To model the asteroid, we created universal gravitation and slope functions to determine the force on the asteroid, and then used the ode solver. We used a sweepseries to sweep velocity values and graphed their different orbits." + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "newton" + ], + "text/latex": [ + "$newton$" + ], + "text/plain": [ + "" + ] + }, + "execution_count": 2, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "m = UNITS.meter\n", + "s = UNITS.second\n", + "kg = UNITS.kilogram\n", + "AU = UNITS.astronomical_unit\n", + "N = UNITS.newton" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "First, we will define our state. The asteroid starts at `(300000 * m, 300000 * m)` with an initial velocity of `-1000 * m/s` in the y direction." + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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" + ], + "text/plain": [ + "px 300000 meter\n", + "py 300000 meter\n", + "vx 0.0 meter / second\n", + "vy -1000.0 meter / second\n", + "dtype: object" + ] + }, + "execution_count": 3, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "#asteroid is starting approximately \"r\" away in the x and y distance\n", + "px_0 = 300000 * m\n", + "py_0 = 300000 * m\n", + "vx_0 = 0 * m/s\n", + "vy_0 = -1000 * m/ s\n", + "init = State(px=px_0,\n", + " py=py_0,\n", + " vx=vx_0,\n", + " vy=vy_0)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Next, we create our system using a make system function from the state variables we have previously defined. We will define the universal gravitation constant, the masses of the bodies, the initial and final times, and the combined radii of the earth and asteroid to help define the event function." + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [], + "source": [ + "def make_system(px_0, py_0, vx_0, vy_0):\n", + " \n", + " init = State(px=px_0 * m,\n", + " py=py_0 * m,\n", + " vx=vx_0 * m/s,\n", + " vy=vy_0 * m/s)\n", + " \n", + " #universal gravitation value\n", + " G = 6.67408e-11*N/(kg**2 * m**2)\n", + " \n", + " #mass of asteroid that killed dinosaurs\n", + " m1 = 6.1e15* kg\n", + " \n", + " #earth mass\n", + " m2 = 5.972324e24* kg\n", + " \n", + " #intial and final time (0s and 1 year in seconds)\n", + " t_0 = 0 * s\n", + " t_end = 315360000 * s\n", + " \n", + " #radius of earth plus radius of asteroid that killed the dinosaurs\n", + " r_final = 6376000 * m\n", + "\n", + " print(init)\n", + " return System(init=init, G=G, m1=m1, m2=m2, t_0=t_0, t_end=t_end, r_final=r_final)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We then made the system with our chosen values of our state variables." + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "px 300000 meter\n", + "py 300000 meter\n", + "vx 0.0 meter / second\n", + "vy -1000.0 meter / second\n", + "dtype: object\n" + ] + }, + { + "data": { + "text/html": [ + "
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" + ], + "text/plain": [ + "init px 300000 meter\n", + "py 3...\n", + "G 6.67408e-11 newton / kilogram ** 2 / meter ** 2\n", + "m1 6100000000000000.0 kilogram\n", + "m2 5.972324e+24 kilogram\n", + "t_0 0 second\n", + "t_end 315360000 second\n", + "r_final 6376000 meter\n", + "dtype: object" + ] + }, + "execution_count": 5, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + " #asteroid is starting approximately \"r\" away in the x and y distance\n", + "system = make_system(300000, 300000, 0, -1000)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We define the universal gravitation function to determine the force on the asteroid caused by the Earth." + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [], + "source": [ + "def universal_gravitation(state, system):\n", + " px, py, vx, vy = state\n", + " unpack(system)\n", + " \n", + "\n", + " position = Vector(px, py)\n", + " P = sqrt(px**2/m**2 + py**2/m**2)\n", + " F_magnitude = G * m1 * m2/ ((P)**2)\n", + " \n", + " P_direction = position/P\n", + " \n", + " F = P_direction * (-1) * F_magnitude * m\n", + "\n", + " \n", + " return F" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "[-9.55162141e+18 -9.55162141e+18] newton" + ], + "text/latex": [ + "$[-9.55162141e+18 -9.55162141e+18] newton$" + ], + "text/plain": [ + "" + ] + }, + "execution_count": 7, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "universal_gravitation(init, system)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We create an event function to stop the ode solver just before the asteroid hits the earth, meaning that the asteroid is at `r_final`, the sum of the radii of the earth and the asteroid. " + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [], + "source": [ + "def event_func(state, t, system):\n", + "\n", + " px, py, vx, vy = state\n", + " \n", + " P = abs(sqrt(px**2 + py**2))\n", + " \n", + " return P - abs(system.r_final - 1)" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "[-9.55162141e+18 -9.55162141e+18] newton" + ], + "text/latex": [ + "$[-9.55162141e+18 -9.55162141e+18] newton$" + ], + "text/plain": [ + "" + ] + }, + "execution_count": 9, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "universal_gravitation(init, system)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The slope function returns derivatives that can be processed by the ode solver." + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [], + "source": [ + "def slope_func(state, t, system):\n", + " px, py, vx, vy = state\n", + " unpack(system)\n", + " \n", + " position = Vector(px, py)\n", + " \n", + " F = universal_gravitation(state, system)\n", + " \n", + " Fx = F.x\n", + " Fy = F.y\n", + " \n", + " dpxdt = vx\n", + " \n", + " dpydt = vy\n", + " \n", + " dvxdt = Fx/m1\n", + " \n", + " dvydt = Fy/m1\n", + " \n", + " \n", + " return dpxdt, dpydt, dvxdt, dvydt" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Calling the slope function should return the x and y velocities we set and the force in the x and y directions, and checking this proves it true" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "data": { + "text/plain": [ + "(,\n", + " ,\n", + " ,\n", + " )" + ] + }, + "execution_count": 11, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "slope_func(init, 0, system)" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "[-9.55162141e+18 -9.55162141e+18] newton" + ], + "text/latex": [ + "$[-9.55162141e+18 -9.55162141e+18] newton$" + ], + "text/plain": [ + "" + ] + }, + "execution_count": 12, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "grav = universal_gravitation(init, system)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The ode solver will return values for x position, y position, x velocity, and y velocity as the asteroid moves through space. X position and y position will then be divided by 1e9 such that they are expresses in millions of kilometers. " + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": { + "scrolled": false + }, + "outputs": [], + "source": [ + "results, details = run_ode_solver(system, slope_func, vectorized = True, events = event_func)\n", + "results.px/=1e6\n", + "results.py/=1e6" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "sol None\n", + "t_events [[]]\n", + "nfev 23444\n", + "njev 0\n", + "nlu 0\n", + "status -1\n", + "message Required step size is less than spacing betwee...\n", + "success False\n", + "dtype: object\n" + ] + }, + { + "data": { + "text/html": [ + "
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" + ], + "text/plain": [ + " px py vx vy\n", + "17.664187 -8.135517e-11 2.326817e-11 6.475701e+08 2.092805e+09\n", + "17.664187 -2.202471e-11 8.062377e-11 2.128075e+09 5.627940e+08\n", + "17.664187 5.772468e-11 6.016299e-11 1.572694e+09 -1.524570e+09\n", + "17.664187 8.081795e-11 -1.841503e-11 -5.172692e+08 -2.125779e+09\n", + "17.664187 2.401861e-11 -7.774800e-11 -2.129400e+09 -5.942638e+08" + ] + }, + "execution_count": 14, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "print(details)\n", + "results.tail()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Plotting x position and y position separately against time produces two nearly identical lines that shown the asteroid getting closer and closer to the earth and then orbiting it in an off center ellipse until it inevitably collides. " + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "results.px.plot()\n", + "results.py.plot()\n", + "decorate(ylabel='Distance to Earth [thousands of km]',\n", + " xlabel='Time [billions of s]',\n", + " title='Path of Asteroid')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can also plot the asteroid on x and y axes to see its motion towards the Earth." + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "plot(results.px,results.py)\n", + "decorate(xlabel='Distance [millions of km]', \n", + " ylabel='Distance [millions of km]',\n", + " title='Path of Asteroid')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can limit the axes to zoom in on its impact with the Earth, which is at the center of the ellipses." + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "axes = plt.gca()\n", + "axes.set_xlim([0, 0.005])\n", + "axes.set_ylim([0, 0.005])\n", + "plot(results.px,results.py)\n", + "decorate(xlabel='Distance [millions of km]', \n", + " ylabel='Distance [millions of km]',\n", + " title='Path of Asteroid')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The event function cannot accurately determine if the asteroid hits the Earth, as the distance between the two gets so small but the event function will never let them collide. Instead of the event function, we can use a function to determine if the last value of the results for x and y are close enough to the Earth such that the asteroid will be guaranteed to hit. " + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": {}, + "outputs": [], + "source": [ + "def collision_result(results):\n", + " colvalx = get_last_value(results.px)\n", + " colvaly = get_last_value(results.py)\n", + " print('Final X Value =', colvalx)\n", + " print('Final Y Value =', colvaly)\n", + "\n", + " if -1 < colvalx and colvaly < 1:\n", + " print ('Kaboom! The asteroid hit!')\n", + " else:\n", + " print ('We live to love another day!')" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Final X Value = 2.401860681452048e-11\n", + "Final Y Value = -7.774799575110359e-11\n", + "Kaboom! The asteroid hit!\n" + ] + } + ], + "source": [ + "collision_result(results)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Results\n", + "\n", + "Sweeping the velocity can show what happens to the asteroid at varying speeds. In this first sweeep, all 5 of the swept speeds result in the asteroid colliding with the Earth. The velocities vary from `1000 * m/s` and `10000 * m/s` in this sweep. We vary the linspace to narrow into the correct velocity or small range in which the asteroid will go into orbit." + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "px 300000 meter\n", + "py 300000 meter\n", + "vx 0.0 meter / second\n", + "vy -1000.0 meter / second\n", + "dtype: object\n", + "Final X Value = 2.401860681452048e-05\n", + "Final Y Value = -7.774799575110359e-05\n", + "Kaboom! The asteroid hit!\n", + "px 300000 meter\n", + "py 300000 meter\n", + "vx 0.0 meter / second\n", + "vy -3250.0 meter / second\n", + "dtype: object\n", + "Final X Value = -0.00019528327106418505\n", + "Final Y Value = -5.689207691431667e-05\n", + "Kaboom! The asteroid hit!\n", + "px 300000 meter\n", + "py 300000 meter\n", + "vx 0.0 meter / second\n", + "vy -5500.0 meter / second\n", + "dtype: object\n", + "Final X Value = -0.00022003510963148853\n", + "Final Y Value = 0.0002437331262958202\n", + "Kaboom! The asteroid hit!\n", + "px 300000 meter\n", + "py 300000 meter\n", + "vx 0.0 meter / second\n", + "vy -7750.0 meter / second\n", + "dtype: object\n", + "Final X Value = -0.00042688559468384346\n", + "Final Y Value = 0.00029666007725250536\n", + "Kaboom! The asteroid hit!\n", + "px 300000 meter\n", + "py 300000 meter\n", + "vx 0.0 meter / second\n", + "vy -10000.0 meter / second\n", + "dtype: object\n", + "Final X Value = 0.0004212912287762479\n", + "Final Y Value = 0.00029198178720398925\n", + "Kaboom! The asteroid hit!\n" + ] + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + " vel_array = linspace(1000, 10000, 5) \n", + "for sweep_vel in vel_array:\n", + " system = make_system(300000, 300000, 0, -1*sweep_vel)\n", + " results, details = run_ode_solver(system, slope_func, vectorized = True, events = event_func)\n", + " collision_result(results)\n", + " results.px/=1e3\n", + " results.py/=1e3\n", + " plot(results.px,results.py)\n", + " decorate(xlabel='Distance [thousands of km]', \n", + " ylabel='Distance [thousands of km]',\n", + " title='Path of Asteroid')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The second sweep takes velocities between 10,000 m/s and 100,000 m/s. The asteroid hits the Earth at 10,000 m/s and 32,500 m/s, but not at 55,000 m/s, 77,500 m/s, or 100,000 m/s." + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "px 300000 meter\n", + "py 300000 meter\n", + "vx 0.0 meter / second\n", + "vy -10000.0 meter / second\n", + "dtype: object\n", + "Final X Value = 4.212912287762479e-10\n", + "Final Y Value = 2.9198178720398924e-10\n", + "Kaboom! The asteroid hit!\n", + "px 300000 meter\n", + "py 300000 meter\n", + "vx 0.0 meter / second\n", + "vy -32500.0 meter / second\n", + "dtype: object\n", + "Final X Value = -2.067160076302617e-09\n", + "Final Y Value = 2.242539025830517e-10\n", + "Kaboom! The asteroid hit!\n", + "px 300000 meter\n", + "py 300000 meter\n", + "vx 0.0 meter / second\n", + "vy -55000.0 meter / second\n", + "dtype: object\n", + "Final X Value = -5.245427631310573\n", + "Final Y Value = -3.6247554693640422\n", + "We live to love another day!\n", + "px 300000 meter\n", + "py 300000 meter\n", + "vx 0.0 meter / second\n", + "vy -77500.0 meter / second\n", + "dtype: object\n", + "Final X Value = -2.409022702405719\n", + "Final Y Value = -5.903386559195902\n", + "We live to love another day!\n", + "px 300000 meter\n", + "py 300000 meter\n", + "vx 0.0 meter / second\n", + "vy -100000.0 meter / second\n", + "dtype: object\n", + "Final X Value = -1.270004916780909\n", + "Final Y Value = -6.248235811759453\n", + "We live to love another day!\n" + ] + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + " vel_array2 = linspace(10000, 100000, 5) \n", + "for sweep_vel in vel_array2:\n", + " system = make_system(300000, 300000, 0, -1*sweep_vel)\n", + " results, details = run_ode_solver(system, slope_func, vectorized = True, events = event_func)\n", + " results.px/=1e6\n", + " results.py/=1e6\n", + " collision_result(results)\n", + " plot(results.px,results.py)\n", + " decorate(xlabel='Distance [millions of km]', \n", + " ylabel='Distance [millions of km]',\n", + " title='Path of Asteroid')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The next sweep takes a much narrower range to determine the exact point at which the asteroid narrowly misses colliding with the Earth. That velocity is shown to be somewhere in between 42098.3 m/s and 42106.0 m/s." + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "px 300000 meter\n", + "py 300000 meter\n", + "vx 0.0 meter / second\n", + "vy -42083.0 meter / second\n", + "dtype: object\n", + "Final X Value = -0.005971722393688606\n", + "Final Y Value = 0.006109688285641839\n", + "Kaboom! The asteroid hit!\n", + "px 300000 meter\n", + "py 300000 meter\n", + "vx 0.0 meter / second\n", + "vy -42090.666666666664 meter / second\n", + "dtype: object\n", + "Final X Value = 0.00587532360500044\n", + "Final Y Value = -0.012262102623406948\n", + "Kaboom! The asteroid hit!\n", + "px 300000 meter\n", + "py 300000 meter\n", + "vx 0.0 meter / second\n", + "vy -42098.333333333336 meter / second\n", + "dtype: object\n", + "Final X Value = 0.011949571677247443\n", + "Final Y Value = 0.007136124368947902\n", + "Kaboom! The asteroid hit!\n", + "px 300000 meter\n", + "py 300000 meter\n", + "vx 0.0 meter / second\n", + "vy -42106.0 meter / second\n", + "dtype: object\n", + "Final X Value = -4566115.382494392\n", + "Final Y Value = 4450163.318547882\n", + "We live to love another day!\n", + "px 300000 meter\n", + "py 300000 meter\n", + "vx 0.0 meter / second\n", + "vy -42113.666666666664 meter / second\n", + "dtype: object\n", + "Final X Value = -4591477.724502849\n", + "Final Y Value = 4423990.907924104\n", + "We live to love another day!\n", + "px 300000 meter\n", + "py 300000 meter\n", + "vx 0.0 meter / second\n", + "vy -42121.333333333336 meter / second\n", + "dtype: object\n", + "Final X Value = -4615112.526527914\n", + "Final Y Value = 4399329.450664739\n", + "We live to love another day!\n", + "px 300000 meter\n", + "py 300000 meter\n", + "vx 0.0 meter / second\n", + "vy -42129.0 meter / second\n", + "dtype: object\n", + "Final X Value = -4637322.402593106\n", + "Final Y Value = 4375911.811543864\n", + "We live to love another day!\n", + "px 300000 meter\n", + "py 300000 meter\n", + "vx 0.0 meter / second\n", + "vy -42136.666666666664 meter / second\n", + "dtype: object\n", + "Final X Value = -4658325.222808974\n", + "Final Y Value = 4353546.757132938\n", + "We live to love another day!\n", + "px 300000 meter\n", + "py 300000 meter\n", + "vx 0.0 meter / second\n", + "vy -42144.333333333336 meter / second\n", + "dtype: object\n", + "Final X Value = -4678294.581164022\n", + "Final Y Value = 4332080.684827136\n", + "We live to love another day!\n", + "px 300000 meter\n", + "py 300000 meter\n", + "vx 0.0 meter / second\n", + "vy -42152.0 meter / second\n", + "dtype: object\n", + "Final X Value = -4697366.01959437\n", + "Final Y Value = 4311393.7103866\n", + "We live to love another day!\n" + ] + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + " vel_array4 = linspace(42083.0, 42152, 10) \n", + "for sweep_vel in vel_array4:\n", + " system = make_system(300000, 300000, 0, -1*sweep_vel)\n", + " results, details = run_ode_solver(system, slope_func, vectorized = True, events = event_func)\n", + " collision_result(results)\n", + " results.px/=1e6\n", + " results.py/=1e6\n", + " plot(results.px,results.py)\n", + " decorate(xlabel='Distance [millions of km]', \n", + " ylabel='Distance [millions of km]',\n", + " title='Path of Asteroid')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Narrowing even further, the asteroid collides when it it travelling between 42099.0 m/s and 42100.0 m/s." + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "px 300000 meter\n", + "py 300000 meter\n", + "vx 0.0 meter / second\n", + "vy -42098.0 meter / second\n", + "dtype: object\n", + "Final X Value = -0.010037090056138108\n", + "Final Y Value = -0.009028403359159429\n", + "Kaboom! The asteroid hit!\n", + "px 300000 meter\n", + "py 300000 meter\n", + "vx 0.0 meter / second\n", + "vy -42099.0 meter / second\n", + "dtype: object\n", + "Final X Value = -0.005490367335749029\n", + "Final Y Value = 0.012047648068709477\n", + "Kaboom! The asteroid hit!\n", + "px 300000 meter\n", + "py 300000 meter\n", + "vx 0.0 meter / second\n", + "vy -42100.0 meter / second\n", + "dtype: object\n", + "Final X Value = -4544786.852473755\n", + "Final Y Value = 4471943.169762189\n", + "We live to love another day!\n", + "px 300000 meter\n", + "py 300000 meter\n", + "vx 0.0 meter / second\n", + "vy -42101.0 meter / second\n", + "dtype: object\n", + "Final X Value = -4548444.578457363\n", + "Final Y Value = 4468222.819500256\n", + "We live to love another day!\n", + "px 300000 meter\n", + "py 300000 meter\n", + "vx 0.0 meter / second\n", + "vy -42102.0 meter / second\n", + "dtype: object\n", + "Final X Value = -4552059.24275189\n", + "Final Y Value = 4464540.278514474\n", + "We live to love another day!\n", + "px 300000 meter\n", + "py 300000 meter\n", + "vx 0.0 meter / second\n", + "vy -42103.0 meter / second\n", + "dtype: object\n", + "Final X Value = -4555632.309621311\n", + "Final Y Value = 4460894.249759279\n", + "We live to love another day!\n", + "px 300000 meter\n", + "py 300000 meter\n", + "vx 0.0 meter / second\n", + "vy -42104.0 meter / second\n", + "dtype: object\n", + "Final X Value = -4559165.161839106\n", + "Final Y Value = 4457283.508491871\n", + "We live to love another day!\n", + "px 300000 meter\n", + "py 300000 meter\n", + "vx 0.0 meter / second\n", + "vy -42105.0 meter / second\n", + "dtype: object\n", + "Final X Value = -4562659.106861685\n", + "Final Y Value = 4453706.896796548\n", + "We live to love another day!\n", + "px 300000 meter\n", + "py 300000 meter\n", + "vx 0.0 meter / second\n", + "vy -42106.0 meter / second\n", + "dtype: object\n", + "Final X Value = -4566115.382494392\n", + "Final Y Value = 4450163.318547882\n", + "We live to love another day!\n" + ] + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + " vel_array5 = linspace(42098.0, 42106, 9) \n", + "for sweep_vel in vel_array5:\n", + " system = make_system(300000, 300000, 0, -1*sweep_vel)\n", + " results, details = run_ode_solver(system, slope_func, vectorized = True, events = event_func)\n", + " collision_result(results)\n", + " results.px/=1e6\n", + " results.py/=1e6\n", + " plot(results.px,results.py)\n", + " decorate(xlabel='Distance [millions of km]', \n", + " ylabel='Distance [millions of km]',\n", + " title='Path of Asteroid')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Interpretation\n", + "\n", + "The asteroid collides with the Earth at velocities of about 42099.0 m/s and below. It slowly converges on the Earth until it eventually hits. \n", + "At a speed somewhere between 42099.0 m/s and 42100.0 m/s, our model predicts that the asteroid goes into orbit.\n", + "At velocity of about 42100.0 m/s and above, the asteroid is travelling fast enough to escape Earth's gravity and does not collide.\n", + "\n", + "Our model did work as expected, although we initially intended to only use the event function and then let the Earth revolve around the sun but we had to redesign our model after the event function did not work. \n", + "\n", + "We found the ideal point at which we all still die because the astroid crashed into the Earth, so if an asteroid is coming at the earth from (300000m, 300000m) slower than \n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.6.6" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} From 7e1dd3ca36a21e9f96b0dd753555a1814d39a75a Mon Sep 17 00:00:00 2001 From: Bennett Taylor Date: Sun, 9 Dec 2018 23:23:24 -0500 Subject: [PATCH 13/14] Asteroid Final Computational Essay --- code/Asteroid Final.ipynb | 95 ++++++++++++++++++++++++++++++++++----- 1 file changed, 83 insertions(+), 12 deletions(-) diff --git a/code/Asteroid Final.ipynb b/code/Asteroid Final.ipynb index 15b2fdeb..d653e682 100644 --- a/code/Asteroid Final.ipynb +++ b/code/Asteroid Final.ipynb @@ -62,6 +62,43 @@ "To model the asteroid, we created universal gravitation and slope functions to determine the force on the asteroid, and then used the ode solver. We used a sweepseries to sweep velocity values and graphed their different orbits." ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Schematic\n", + "![\"Model Schematic\"](schematic.png)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Our model follows a fairly straigh forward phenomenon:the gravitational attraction of the Earth on a passing asteroid." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Differential Equations\n", + "\\begin{align}\n", + "\\frac{dv}{dt} = G \\times \\frac{m_1 \\times m_2}{r^2} \\\\\n", + "\\frac{dy}{dt} = v\n", + "\\end{align}\n", + "\n", + "We used the universal gravitation equation, converting force into the change in velocity over time. For the purposes of using run_ode_solver, we then turned this into a derivative of position, as to have it running a first order differential equation." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Python\n", + "\n", + "Having sketched a schematic and determined our equations, we then went to work writing the model in Python." + ] + }, { "cell_type": "code", "execution_count": 2, @@ -85,6 +122,7 @@ } ], "source": [ + "#the units we will be using throughout\n", "m = UNITS.meter\n", "s = UNITS.second\n", "kg = UNITS.kilogram\n", @@ -313,7 +351,8 @@ } ], "source": [ - " #asteroid is starting approximately \"r\" away in the x and y distance\n", + " #asteroid is starting approximately one moon's distance away in the\n", + " #x and y distance (selected for feasability, asteroids would rarely pass closer)\n", "system = make_system(300000, 300000, 0, -1000)" ] }, @@ -331,16 +370,19 @@ "outputs": [], "source": [ "def universal_gravitation(state, system):\n", + " #position and velocity in x and y directions\n", " px, py, vx, vy = state\n", " unpack(system)\n", " \n", - "\n", + " #divide magnitude of position by vector of position to find direction\n", " position = Vector(px, py)\n", " P = sqrt(px**2/m**2 + py**2/m**2)\n", + " #Calculate magnitude of gravitational force\n", " F_magnitude = G * m1 * m2/ ((P)**2)\n", " \n", " P_direction = position/P\n", " \n", + " #give direction to force magnitude, make it a force vector\n", " F = P_direction * (-1) * F_magnitude * m\n", "\n", " \n", @@ -386,12 +428,16 @@ "metadata": {}, "outputs": [], "source": [ + "#this did not end up functioning as we had desired, but is left in incase of use in future model\n", "def event_func(state, t, system):\n", "\n", " px, py, vx, vy = state\n", " \n", + " #find absolute value of position relative to earth\n", " P = abs(sqrt(px**2 + py**2))\n", " \n", + " #return zero when distance equals distance between the center points of the asteroid and the earth\n", + " #(when they are touching)\n", " return P - abs(system.r_final - 1)" ] }, @@ -438,13 +484,18 @@ " px, py, vx, vy = state\n", " unpack(system)\n", " \n", + " #combind x and y components to make one position value\n", " position = Vector(px, py)\n", " \n", + " #set force using universal ravitation function\n", " F = universal_gravitation(state, system)\n", " \n", + " #seperate force into x and y components\n", " Fx = F.x\n", " Fy = F.y\n", " \n", + " #set chain of differentials, so acceleration (Force divided by mass) is equal to dv/dt\n", + " #and v is equal to dpdt, each in x and y components\n", " dpxdt = vx\n", " \n", " dpydt = vy\n", @@ -486,6 +537,7 @@ } ], "source": [ + "#test slope func\n", "slope_func(init, 0, system)" ] }, @@ -512,6 +564,7 @@ } ], "source": [ + "#test gravity value\n", "grav = universal_gravitation(init, system)" ] }, @@ -530,6 +583,7 @@ }, "outputs": [], "source": [ + "#run ode, with results scaled down to millions\n", "results, details = run_ode_solver(system, slope_func, vectorized = True, events = event_func)\n", "results.px/=1e6\n", "results.py/=1e6" @@ -637,6 +691,9 @@ } ], "source": [ + "#note that success is listed as false\n", + "#the ode solver would not allow the asteroid to hit the earth, no matter how we changed the event function or equations\n", + "#we later impliment an if then statement into the return to work around this\n", "print(details)\n", "results.tail()" ] @@ -667,6 +724,7 @@ } ], "source": [ + "#plot x and y relative to time\n", "results.px.plot()\n", "results.py.plot()\n", "decorate(ylabel='Distance to Earth [thousands of km]',\n", @@ -700,6 +758,7 @@ } ], "source": [ + "#plot x vs y to find full position\n", "plot(results.px,results.py)\n", "decorate(xlabel='Distance [millions of km]', \n", " ylabel='Distance [millions of km]',\n", @@ -755,11 +814,13 @@ "outputs": [], "source": [ "def collision_result(results):\n", + " #store and print final x and y position of asteroid relative to earth\n", " colvalx = get_last_value(results.px)\n", " colvaly = get_last_value(results.py)\n", " print('Final X Value =', colvalx)\n", " print('Final Y Value =', colvaly)\n", "\n", + " #if the asteroid is within 1 meter of the Earth after a year of orbit, it is assumed that it will hit the earth\n", " if -1 < colvalx and colvaly < 1:\n", " print ('Kaboom! The asteroid hit!')\n", " else:\n", @@ -782,6 +843,7 @@ } ], "source": [ + "#test\n", "collision_result(results)" ] }, @@ -860,10 +922,14 @@ ], "source": [ " vel_array = linspace(1000, 10000, 5) \n", + " \n", + " #sweep starting velocities between 1000 and 10000 in the y direction\n", "for sweep_vel in vel_array:\n", " system = make_system(300000, 300000, 0, -1*sweep_vel)\n", " results, details = run_ode_solver(system, slope_func, vectorized = True, events = event_func)\n", " collision_result(results)\n", + " \n", + " #scale results to thousands of km and plot\n", " results.px/=1e3\n", " results.py/=1e3\n", " plot(results.px,results.py)\n", @@ -945,9 +1011,13 @@ ], "source": [ " vel_array2 = linspace(10000, 100000, 5) \n", + " \n", + " #range of sweep altered to 10000 to 100000\n", "for sweep_vel in vel_array2:\n", " system = make_system(300000, 300000, 0, -1*sweep_vel)\n", " results, details = run_ode_solver(system, slope_func, vectorized = True, events = event_func)\n", + " \n", + " #results scaled to millions of km, then plotted\n", " results.px/=1e6\n", " results.py/=1e6\n", " collision_result(results)\n", @@ -1070,10 +1140,14 @@ ], "source": [ " vel_array4 = linspace(42083.0, 42152, 10) \n", + " \n", + " #range narrowed from 42083 to 42152\n", "for sweep_vel in vel_array4:\n", " system = make_system(300000, 300000, 0, -1*sweep_vel)\n", " results, details = run_ode_solver(system, slope_func, vectorized = True, events = event_func)\n", " collision_result(results)\n", + " \n", + " #results scaled to millions of km, then plotted\n", " results.px/=1e6\n", " results.py/=1e6\n", " plot(results.px,results.py)\n", @@ -1187,10 +1261,14 @@ ], "source": [ " vel_array5 = linspace(42098.0, 42106, 9) \n", + " \n", + " #resuts narrowed from 42098 to 42106, all integers tested\n", "for sweep_vel in vel_array5:\n", " system = make_system(300000, 300000, 0, -1*sweep_vel)\n", " results, details = run_ode_solver(system, slope_func, vectorized = True, events = event_func)\n", " collision_result(results)\n", + " \n", + " #results scaled to millions of km, then plotted\n", " results.px/=1e6\n", " results.py/=1e6\n", " plot(results.px,results.py)\n", @@ -1205,21 +1283,14 @@ "source": [ "## Interpretation\n", "\n", - "The asteroid collides with the Earth at velocities of about 42099.0 m/s and below. It slowly converges on the Earth until it eventually hits. \n", + "The asteroid collides with the Earth at velocities of about 42099.0 m/s and below. It slowly converges on the Earth until it eventually hits. Through a sweep of each indicidual starting velocity, we were able to determine to the integer of the velocity at what point an asteroid would be pulled in, given a set starting point.\n", "At a speed somewhere between 42099.0 m/s and 42100.0 m/s, our model predicts that the asteroid goes into orbit.\n", "At velocity of about 42100.0 m/s and above, the asteroid is travelling fast enough to escape Earth's gravity and does not collide.\n", "\n", - "Our model did work as expected, although we initially intended to only use the event function and then let the Earth revolve around the sun but we had to redesign our model after the event function did not work. \n", + "Our model did work as expected, although we initially intended to only use the event function and then let the Earth revolve around the sun but we had to redesign our model using an if then statement and a logical assumption (that an asteroid 1 m away from the surface of the earth will collide with it) after the event function did not work. \n", "\n", - "We found the ideal point at which we all still die because the astroid crashed into the Earth, so if an asteroid is coming at the earth from (300000m, 300000m) slower than \n" + "Our model also has further application, as starting position and velocity can both be altered, with a readable and clear output of both visual and verbal confirmation. To take the model further, we would have introduced the sun and its gravity, placing the earth into orbit to make the model fully accurate to our star system, but the current iteration is sufficient for calculating rough velocities for impact." ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [] } ], "metadata": { From a91704f90892e25e1f5dd8beb279ee8b33432829 Mon Sep 17 00:00:00 2001 From: BennettCTaylor <42953173+BennettCTaylor@users.noreply.github.com> Date: Tue, 21 May 2019 12:41:09 -0400 Subject: [PATCH 14/14] Update Asteroid Final.ipynb --- code/Asteroid Final.ipynb | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/code/Asteroid Final.ipynb b/code/Asteroid Final.ipynb index d653e682..7e6f3209 100644 --- a/code/Asteroid Final.ipynb +++ b/code/Asteroid Final.ipynb @@ -6,7 +6,7 @@ "source": [ "# Death by Asteroid\n", "\n", - "### Olivia Seitelman and Bennett Taylor" + "### Bennett Taylor and Olivia Seitelman" ] }, {