From 7c7e2c3406810f298bb9ec3fdb69ad70c4fd2bb4 Mon Sep 17 00:00:00 2001 From: Junwon Lee <31522211+junwonlee5@users.noreply.github.com> Date: Tue, 5 Sep 2017 18:37:20 -0400 Subject: [PATCH 01/19] Adding chap01mine --- code/chap01mine.ipynb | 1453 +++++++++++++++++++++++++++++++++++++++++ 1 file changed, 1453 insertions(+) create mode 100644 code/chap01mine.ipynb diff --git a/code/chap01mine.ipynb b/code/chap01mine.ipynb new file mode 100644 index 00000000..5cdb40ba --- /dev/null +++ b/code/chap01mine.ipynb @@ -0,0 +1,1453 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Modeling and Simulation in Python\n", + "\n", + "Chapter 1: Modeling\n", + "\n", + "Copyright 2017 Allen Downey\n", + "\n", + "License: [Creative Commons Attribution 4.0 International](https://creativecommons.org/licenses/by/4.0)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Jupyter\n", + "\n", + "Welcome to Modeling and Simulation, welcome to Python, and welcome to Jupyter.\n", + "\n", + "This is a Jupyter notebook, which is a development environment where you can write and run Python code. Each notebook is divided into cells. Each cell contains either text (like this cell) or Python code (like the cell below this one).\n", + "\n", + "### Selecting and running cells\n", + "\n", + "To select a cell, click in the left margin next to the cell. You should see a blue frame surrounding the selected cell.\n", + "\n", + "To edit a code cell, click inside the cell. You should see a green frame around the selected cell, and you should see a cursor inside the cell.\n", + "\n", + "To edit a text cell, double-click inside the cell. Again, you should see a green frame around the selected cell, and you should see a cursor inside the cell.\n", + "\n", + "To run a cell, hold down SHIFT and press ENTER. If you run a text cell, it will typeset the text and display the result.\n", + "\n", + "If you run a code cell, it runs the Python code in the cell and displays the result, if any.\n", + "\n", + "To try it out, edit this cell, change some of the text, and then press SHIFT-ENTER to run it." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Adding and removing cells\n", + "\n", + "You can add and remove cells from a notebook using the buttons in the toolbar and the items in the menu, both of which you should see at the top of this notebook.\n", + "\n", + "You might want to try the following exercises:\n", + "\n", + "1. From the Insert menu select \"Insert cell below\" to add a cell below this one. By default, you get a code cell, and you can see in the pulldown menu that says \"Code\".\n", + "\n", + "2. In the new cell, add a print statement like `print('Hello')`, and run it.\n", + "\n", + "3. Add another cell, select the new cell, and then click on the pulldown menu that says \"Code\" and select \"Markdown\". This makes the new cell a text cell.\n", + "\n", + "4. In the new cell, type some text, and then run it.\n", + "\n", + "5. Use the arrow buttons in the toolbar to move cells up and down.\n", + "\n", + "6. Use the cut, copy, and paste buttons to delete, add, and move cells.\n", + "\n", + "7. As you make changes, Jupyter saves your notebook automatically, but if you want to make sure, you can press the save button, which looks like a floppy disk from the 1990s.\n", + "\n", + "8. Finally, when you are done with a notebook, selection \"Close and Halt\" from the File menu." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Using the notebooks\n", + "\n", + "The notebooks for each chapter contain the code from the chapter along with addition examples, explanatory text, and exercises. I recommend you read the chapter first to understand the concepts and vocabulary, then run the notebook to review what you learned and see it in action, and then attempt the exercises.\n", + "\n", + "The notebooks contain some explanatory text, but it is probably not enough to make sense if you have not read the book. If you are working through a notebook and you get stuck, you might want to re-read (or read!) the corresponding section of the book.\n", + "\n", + "If you try to work through the notebooks without reading the book, you're gonna have a bad time. If you have previous programming experience, you might get through the first few notebooks, but sooner or later, you will get to the end of your leash, and you won't like it." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Importing modsim\n", + "\n", + "The following cell imports `modsim`, which is a collection of functions we will use throughout the book. Whenever you start the notebook, you will have to run the following cell. It does two things:\n", + "\n", + "1. It uses a Jupyter \"magic command\" to specify whether figures should appear in the notebook, or pop up in a new window.\n", + "\n", + "2. It imports everything defined in `modsim`.\n", + "\n", + "Select the following cell and press SHIFT-ENTER to run it." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# If you want the figures to appear in the notebook, \n", + "# and you want to interact with them, use\n", + "# %matplotlib notebook\n", + "\n", + "# If you want the figures to appear in the notebook, \n", + "# and you don't want to interact with them, use\n", + "# %matplotlib inline\n", + "\n", + "# If you want the figures to appear in separate windows, use\n", + "# %matplotlib qt5\n", + "\n", + "# To switch from one to another, you have to select Kernel->Restart\n", + "\n", + "%matplotlib qt5\n", + "\n", + "from modsim import *\n", + "\n", + "print('If this cell runs successfully, it produces no output other than this message.')\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## The penny myth\n", + "\n", + "The following cells contain code from the beginning of Chapter 1.\n", + "\n", + "`modsim` defines `UNITS`, which contains variables representing pretty much every unit you've ever heard of. The following to lines create new variables named `meter` and `second`." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "meter = UNITS.meter\n", + "second = UNITS.second" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "To find out what units are defined, type `UNITS.` in the next cell and then press TAB. You should see a pop-up menu with a list of units." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "meter = UNITS.meter\n", + "second = UNITS.second" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Create a variable named `a` and display its value:" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "a = 9.8 * meter / second**2\n", + "a" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": true + }, + "source": [ + "Create `t` and display its value:" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "t = 4 * second\n", + "t" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": true + }, + "source": [ + "If you create a variable and don't display the value, you don't get any output:" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "h = a * t**2 * 0.5\n", + "h" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": true + }, + "source": [ + "Add a second line to the previous cell to display the value of `h`.\n", + "\n", + "Now let's solve the falling penny problem. The following lines set `h` to the height of the Empire State Building and compute the time it would take a penny to fall, assuming constant acceleration." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "h = 381 * meter\n", + "t = sqrt(2 * h / a)\n", + "t" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": true + }, + "source": [ + "Given `t`, we can compute the velocity of the penny when it lands." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "v = a * t\n", + "v" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": true + }, + "source": [ + "We can convert from one set of units to another like this:" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "mile = UNITS.mile\n", + "hour= UNITS.hour" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "v.to(mile/hour)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Exercise:** In reality, air resistance prevents the penny from reaching this velocity. At about 20 meters per second, the force of air resistance equals the force of gravity and the penny stops accelerating.\n", + "\n", + "As a simplification, let's assume that the acceleration of the penny is `a` until the penny reaches 20 meters per second, and then 0 afterwards. What is the total time for the penny to fall 381 meters?" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# Solution goes here\n", + "v = 20 * meter / second\n", + "t_1 = v/a\n", + "t_tot = t_1 + (h-(a * t_1**2 * 0.5))/v\n", + "t_tot\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Modeling a bikeshare system" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We'll start with a `System` object that represents the number of bikes at each station." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "bikeshare = System(olin=10, wellesley=2, babson=0)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "If you display the value of a `System` object, it lists the system variables and their values (not necessarily in the order you defined them):" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "bikeshare" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can access the system variables using dot notation." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "bikeshare.olin" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "scrolled": true + }, + "outputs": [], + "source": [ + "bikeshare.wellesley" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Exercise:** What happens if you spell the name of a system variable wrong? Edit the previous cell, change the spelling of `wellesley`, and run the cell again.\n", + "\n", + "The error message uses the word \"attribute\", which is another name for what we are calling a system variable. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Exercise:** Add a third attribute called `babson` with initial value 0, and print the state of `bikeshare` again." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Plotting\n", + "\n", + "`newfig` creates a new figure, which should appear either in the notebook or in a new window, depending on which magic command you ran in the first code cell.\n", + "\n", + "`plot` adds a data point to the figure; in this example, you should see a red square and a blue circle representing the number of bikes at each station." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "newfig()\n", + "plot(bikeshare.olin, 'rs-')\n", + "plot(bikeshare.wellesley, 'bo-')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can use the operators `+=` and `-=` to increase and decrease the system variables. The following lines move a bike from Olin to Wellesley." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "bikeshare.olin -= 1\n", + "bikeshare.wellesley += 1\n", + "bikeshare" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "And the following lines plot the updated state of the system. You should see two new data points with lines connecting them to the old data points." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "plot(bikeshare.olin, 'rs-')\n", + "plot(bikeshare.wellesley, 'bo-')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Exercise:** In the cell below, write a few lines of code to move a bike from Wellesley to Olin and plot the updated state." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "bikeshare.olin, bikeshare.wellesley = bikeshare.wellesley, bikeshare.olin\n", + "bikeshare\n", + "plot(bikeshare.olin, 'rs-')\n", + "plot(bikeshare.wellesley, 'bo-')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Functions\n", + "\n", + "Now we can take the code we've written so far and encapsulate it in functions." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def bike_to_wellesley():\n", + " bikeshare.olin -= 1\n", + " bikeshare.wellesley += 1" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "When you define a function, it doesn't run the statements inside the function, yet." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def plot_state():\n", + " plot(bikeshare.olin, 'rs-', label='Olin')\n", + " plot(bikeshare.wellesley, 'bo-', label='Wellesley')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now when we run the functions, it runs the statements inside." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "bike_to_wellesley()\n", + "plot_state()\n", + "bikeshare" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "You should see two more data points that represent the current state of the system. If the figure is embedded in the notebook, you might have to scroll up to see the change.\n", + "\n", + "One common error is to omit the parentheses, which has the effect of looking up the function, but not running it." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "bike_to_wellesley" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The output indicates that `bike_to_wellesley` is a function defined in a \"namespace\" called `__main__`, but you don't have to understand what that means." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Exercise:** Define a function called `bike_to_olin` that moves a bike from Wellesley to Olin. Run the new function and print or plot the results to confirm that it works." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "def bike_to_olin():\n", + " bikeshare.wellesley -= 1\n", + " bikeshare.olin += 1\n", + "\n", + "bike_to_olin()\n", + "plot_state()\n", + "bikeshare\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Parameters" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Before we go on, let's start with a new state object and a new plot." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "bikeshare = System(olin=10, wellesley=2)\n", + "newfig()\n", + "plot_state()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Since we have two similar functions, we can create a new function, `move_bike` that takes a parameter `n`, which indicates how many bikes are moving, and in which direction." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def move_bike(n):\n", + " bikeshare.olin -= n\n", + " bikeshare.wellesley += n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now we can use `move_bike` to write simpler versions of the other functions." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def bike_to_wellesley():\n", + " move_bike(1)\n", + " \n", + "def bike_to_olin():\n", + " move_bike(-1)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "When we define these functions, we replace the old definitions with the new ones.\n", + "\n", + "Now we can test them and update the figure." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "bike_to_wellesley()\n", + "plot_state()\n", + "bikeshare" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Again, each time you run `plot_state` you should see changes in the figure." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "bike_to_olin()\n", + "plot_state()\n", + "bikeshare" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "At this point, `move_bike` is complicated enough that we should add some documentation. The text in triple-quotation marks is in English, not Python. It doesn't do anything when the program runs, but it helps people understand what this function does and how to use it." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def move_bike(n):\n", + " \"\"\"Move bikes.\n", + " \n", + " n: number of bikes: positive moves from Olin to Wellesley;\n", + " negative moves from Wellesley to Olin\n", + " \"\"\"\n", + " bikeshare.olin -= n\n", + " bikeshare.wellesley += n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Whenever you make a figure, you should put labels on the axes to explain what they mean and what units they are measured in. Here's how:" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "label_axes(title='Olin-Wellesley Bikeshare',\n", + " xlabel='Time step (min)', \n", + " ylabel='Number of bikes')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Again, you might have to scroll up to see the effect.\n", + "\n", + "And you can save figures as files; the suffix of the filename indicates the format you want. This example saves the current figure in a PDF file." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "savefig('chap01_fig01.pdf')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Exercise:** The following function definitions start with print statements so they display messages when they run. Run each of these functions (with appropriate arguments) and confirm that they do what you expect.\n", + "\n", + "Adding print statements like this to functions is a useful debugging technique. Keep it in mind!" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def move_bike_debug(n):\n", + " print('Running move_bike_debug with argument', n)\n", + " bikeshare.olin -= n\n", + " bikeshare.wellesley += n\n", + " \n", + "def bike_to_wellesley_debug():\n", + " print('Running bike_to_wellesley_debug')\n", + " move_bike_debug(1)\n", + " \n", + "def bike_to_olin_debug():\n", + " print('Running bike_to_olin_debug')\n", + " move_bike_debug(-1)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "def bike_to_wellesley_debug():\n", + " print('Running bike_to_wellesley_debug')\n", + " move_bike_debug(1)\n", + " \n", + "move_bike_debug(1)\n", + "bikeshare" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# Solution goes here\n", + "def bike_to_wellesley_debug():\n", + " print('Running bike_to_wellesley_debug')\n", + " move_bike_debug(1)\n", + "\n", + "bike_to_wellesley_debug()\n", + "bikeshare" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# Solution goes here\n", + "def bike_to_olin_debug():\n", + " print('Running bike_to_olin_debug')\n", + " move_bike_debug(-1)\n", + "bike_to_olin_debug()\n", + "bikeshare" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Conditionals" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The function `flip` takes a probability and returns either `True` or `False`, which are special values defined by Python.\n", + "\n", + "In the following example, the probability is 0.7 or 70%. If you run this cell several times, you should get `True` about 70% of the time and `False` about 30%." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "flip(0.6)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Modify the argument in the previous cell and see what effect it has.\n", + "\n", + "In the following example, we use `flip` as part of an if statement. If the result from `flip` is `True`, we print `heads`; otherwise we do nothing." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "if flip(0.7):\n", + " print('heads')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "With an else clause, we can print heads or tails depending on whether `flip` returns `True` or `False`." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "if flip(0.7):\n", + " print('heads')\n", + "else:\n", + " print('tails')\n", + " " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now let's get back to the bikeshare system. Again let's start with a new `System` object and a new plot." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "bikeshare = System(olin=10, wellesley=2)\n", + "newfig()\n", + "plot_state()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Suppose that in any given minute, there is a 70% chance that a student picks up a bike at Olin and rides to Wellesley. We can simulate that like this." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "if flip(0.7):\n", + " bike_to_wellesley()\n", + " print('Moving a bike to Wellesley')\n", + "\n", + "plot_state()\n", + "bikeshare" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "And maybe at the same time, there is also a 60% chance that a student at Wellesley rides to Olin." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "if flip(0.6):\n", + " bike_to_olin()\n", + " print('Moving a bike to Olin')\n", + "\n", + "plot_state()\n", + "bikeshare" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can wrap that code in a function called `step` that simulates one time step. In any given minute, a student might ride from Olin to Wellesley, from Wellesley to Olin, or both, or neither, depending on the results of `flip`." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def step():\n", + " if flip(0.7):\n", + " bike_to_wellesley()\n", + " print('Moving a bike to Wellesley')\n", + " \n", + " if flip(0.6):\n", + " bike_to_olin()\n", + " print('Moving a bike to Olin')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "If you run `step` a few times, it should update the current figure. In each time step, the number of bikes at each location might go up, down, or stay the same." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "step()\n", + "plot_state()\n", + "bikeshare" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The following function labels the axes and adds a legend to the figure." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def decorate(): \n", + " legend(loc='best')\n", + " label_axes(title='Olin-Wellesley Bikeshare',\n", + " xlabel='Time step (min)', \n", + " ylabel='Number of bikes')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "As always, when you define a function, it has no effect until you run it." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "decorate()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Exercise:** Change the argument of `legend` to `'random string'` and run `decorate` again. You should get an error message that lists the valid location where you can put the legend." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Optional parameters" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Again let's start with a new `System` object and a new plot." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "bikeshare = System(olin=10, wellesley=2)\n", + "newfig()\n", + "plot_state()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can make `step` more general by adding parameters. Because these parameters have default values, they are optional." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def step(p1=0.5, p2=0.5):\n", + " print('p1 ->', p1)\n", + " print('p2 ->', p2)\n", + " if flip(p1):\n", + " bike_to_wellesley()\n", + " \n", + " if flip(p2):\n", + " bike_to_olin()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "I added print statements, so each time we run `step` we can see the arguments.\n", + "\n", + "If you provide no arguments, you get the default values:" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "step()\n", + "# Explcitly step(p1=0.7, p2=0.3)\n", + "# Implicitly step(0.7,0.3)\n", + "# Default values: step() = step(0.5, 0.5) = step(p1=0.5, p2=0.5)\n", + "plot_state()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "If you provide one argument, it overrides the first parameter." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "step(0.4)\n", + "plot_state()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "If you provide two arguments, they override both." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "step(0.4, 0.2)\n", + "plot_state()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "You can specify the names of the parameters you want to override." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "step(p1=0.4, p2=0.2)\n", + "plot_state()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Which means you can override the second parameter and use the default for the first." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "step(p2=0.2)\n", + "plot_state()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "You can combine both forms, but it is not very common:" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "step(0.4, p2=0.2)\n", + "plot_state()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "One reason it's not common is that it's error prone. The following example causes an error." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# If you remove the # at the beginning of the next line and run it, you get\n", + "# SyntaxError: positional argument follows keyword argument\n", + "\n", + "step(p1=0.4, 0.2)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "From the error message, you might infer that arguments like `step(0.4, 0.2)` are called \"positional\" and arguments like `step(p1=0.4, p2=0.2)` are called \"keyword arguments\"." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Exercise:** Write a version of `decorate` that takes an optional parameter named `loc` with default value `'best'`. It should pass the value of `loc` along as an argument to `legend.` Test your function with different values of `loc`. [You can see the list of legal values here](https://matplotlib.org/api/pyplot_api.html#matplotlib.pyplot.legend)." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# Solution goes here\n", + "def decorate(loc = 'right'):\n", + " legend(loc = loc)\n", + " label_axes(title='Olin-Wellesley Bikeshare',\n", + " xlabel='Time step (min)', \n", + " ylabel='Number of bikes')\n", + "decorate()\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "# Solution goes here\n", + "def decorate(loc ='best'):\n", + " legend(loc = loc)\n", + " label_axes(title='Olin-Wellesley Bikeshare',\n", + " xlabel='Time step (min)', \n", + " ylabel='Number of bikes')\n", + "decorate('lower right')\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## For loop" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Before we go on, I'll redefine `step` without the print statements." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def step(p1=0.5, p2=0.5):\n", + " if flip(p1):\n", + " bike_to_wellesley()\n", + " \n", + " if flip(p2):\n", + " bike_to_olin()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "And let's start again with a new `System` object and a new figure." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "bikeshare = System(olin=10, wellesley=2)\n", + "newfig()\n", + "plot_state()\n", + "decorate()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can use a for loop to move 4 bikes from Olin to Wellesley." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "for i in range(4):\n", + " bike_to_wellesley()\n", + " plot_state()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Or we can simulate 4 random time steps." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "for i in range(4):\n", + " step()\n", + " plot_state()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "If each step corresponds to a minute, we can simulate the rest of the hour like this." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "for i in range(52):\n", + " step(p1=0.4, p2=0.2)\n", + " plot_state()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Exercise:** Combine the examples from the previous two sections to write a function named `run_steps` that takes three parameters, named `num_steps`, `p1`, and `p2`. It should use a for loop to run `step` the number of times specified by `num_steps`, passing along the specified values of `p1` and `p2`. After each step, it should plot the updated state.\n", + "\n", + "Test your function by creating a new `System` object, creating a new figure, and running `run_steps`." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "# Solution goes here\n", + "def run_steps(num_steps, p1, p2):\n", + " for i in range (num_steps):\n", + " step(p1, p2)\n", + " plot_state()\n", + " \n", + "run_steps(5,0.4,0.7)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "# Solution goes here\n", + "bikeshare = System(olin = 2000, wellesley = 2500)\n", + "run_steps(100, 0.7, 0.35)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "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": "3.6.1" + } + }, + "nbformat": 4, + "nbformat_minor": 1 +} From e05bcb6163648cbbfcb9c89a01ef8ae7493a7ff5 Mon Sep 17 00:00:00 2001 From: Junwon Lee <31522211+junwonlee5@users.noreply.github.com> Date: Tue, 5 Sep 2017 21:41:50 -0400 Subject: [PATCH 02/19] Adding chap01mine --- code/chap01mine.ipynb | 137 +++++++++++++++++++++++++++++++----------- 1 file changed, 103 insertions(+), 34 deletions(-) diff --git a/code/chap01mine.ipynb b/code/chap01mine.ipynb index 5cdb40ba..88f89989 100644 --- a/code/chap01mine.ipynb +++ b/code/chap01mine.ipynb @@ -96,7 +96,9 @@ { "cell_type": "code", "execution_count": null, - "metadata": {}, + "metadata": { + "collapsed": true + }, "outputs": [], "source": [ "# If you want the figures to appear in the notebook, \n", @@ -171,7 +173,9 @@ { "cell_type": "code", "execution_count": null, - "metadata": {}, + "metadata": { + "collapsed": true + }, "outputs": [], "source": [ "a = 9.8 * meter / second**2\n", @@ -190,7 +194,9 @@ { "cell_type": "code", "execution_count": null, - "metadata": {}, + "metadata": { + "collapsed": true + }, "outputs": [], "source": [ "t = 4 * second\n", @@ -209,7 +215,9 @@ { "cell_type": "code", "execution_count": null, - "metadata": {}, + "metadata": { + "collapsed": true + }, "outputs": [], "source": [ "h = a * t**2 * 0.5\n", @@ -230,7 +238,9 @@ { "cell_type": "code", "execution_count": null, - "metadata": {}, + "metadata": { + "collapsed": true + }, "outputs": [], "source": [ "h = 381 * meter\n", @@ -250,7 +260,9 @@ { "cell_type": "code", "execution_count": null, - "metadata": {}, + "metadata": { + "collapsed": true + }, "outputs": [], "source": [ "v = a * t\n", @@ -281,7 +293,9 @@ { "cell_type": "code", "execution_count": null, - "metadata": {}, + "metadata": { + "collapsed": true + }, "outputs": [], "source": [ "v.to(mile/hour)" @@ -299,7 +313,9 @@ { "cell_type": "code", "execution_count": null, - "metadata": {}, + "metadata": { + "collapsed": true + }, "outputs": [], "source": [ "# Solution goes here\n", @@ -345,7 +361,9 @@ { "cell_type": "code", "execution_count": null, - "metadata": {}, + "metadata": { + "collapsed": true + }, "outputs": [], "source": [ "bikeshare" @@ -361,7 +379,9 @@ { "cell_type": "code", "execution_count": null, - "metadata": {}, + "metadata": { + "collapsed": true + }, "outputs": [], "source": [ "bikeshare.olin" @@ -371,6 +391,7 @@ "cell_type": "code", "execution_count": null, "metadata": { + "collapsed": true, "scrolled": true }, "outputs": [], @@ -428,7 +449,9 @@ { "cell_type": "code", "execution_count": null, - "metadata": {}, + "metadata": { + "collapsed": true + }, "outputs": [], "source": [ "bikeshare.olin -= 1\n", @@ -528,7 +551,9 @@ { "cell_type": "code", "execution_count": null, - "metadata": {}, + "metadata": { + "collapsed": true + }, "outputs": [], "source": [ "bike_to_wellesley()\n", @@ -548,7 +573,9 @@ { "cell_type": "code", "execution_count": null, - "metadata": {}, + "metadata": { + "collapsed": true + }, "outputs": [], "source": [ "bike_to_wellesley" @@ -571,7 +598,9 @@ { "cell_type": "code", "execution_count": null, - "metadata": {}, + "metadata": { + "collapsed": true + }, "outputs": [], "source": [ "def bike_to_olin():\n", @@ -665,7 +694,9 @@ { "cell_type": "code", "execution_count": null, - "metadata": {}, + "metadata": { + "collapsed": true + }, "outputs": [], "source": [ "bike_to_wellesley()\n", @@ -683,7 +714,9 @@ { "cell_type": "code", "execution_count": null, - "metadata": {}, + "metadata": { + "collapsed": true + }, "outputs": [], "source": [ "bike_to_olin()\n", @@ -748,7 +781,9 @@ { "cell_type": "code", "execution_count": null, - "metadata": {}, + "metadata": { + "collapsed": true + }, "outputs": [], "source": [ "savefig('chap01_fig01.pdf')" @@ -788,7 +823,9 @@ { "cell_type": "code", "execution_count": null, - "metadata": {}, + "metadata": { + "collapsed": true + }, "outputs": [], "source": [ "def bike_to_wellesley_debug():\n", @@ -802,7 +839,9 @@ { "cell_type": "code", "execution_count": null, - "metadata": {}, + "metadata": { + "collapsed": true + }, "outputs": [], "source": [ "# Solution goes here\n", @@ -817,7 +856,9 @@ { "cell_type": "code", "execution_count": null, - "metadata": {}, + "metadata": { + "collapsed": true + }, "outputs": [], "source": [ "# Solution goes here\n", @@ -847,7 +888,9 @@ { "cell_type": "code", "execution_count": null, - "metadata": {}, + "metadata": { + "collapsed": true + }, "outputs": [], "source": [ "flip(0.6)" @@ -865,7 +908,9 @@ { "cell_type": "code", "execution_count": null, - "metadata": {}, + "metadata": { + "collapsed": true + }, "outputs": [], "source": [ "if flip(0.7):\n", @@ -882,7 +927,9 @@ { "cell_type": "code", "execution_count": null, - "metadata": {}, + "metadata": { + "collapsed": true + }, "outputs": [], "source": [ "if flip(0.7):\n", @@ -922,7 +969,9 @@ { "cell_type": "code", "execution_count": null, - "metadata": {}, + "metadata": { + "collapsed": true + }, "outputs": [], "source": [ "if flip(0.7):\n", @@ -943,7 +992,9 @@ { "cell_type": "code", "execution_count": null, - "metadata": {}, + "metadata": { + "collapsed": true + }, "outputs": [], "source": [ "if flip(0.6):\n", @@ -989,7 +1040,9 @@ { "cell_type": "code", "execution_count": null, - "metadata": {}, + "metadata": { + "collapsed": true + }, "outputs": [], "source": [ "step()\n", @@ -1108,7 +1161,9 @@ { "cell_type": "code", "execution_count": null, - "metadata": {}, + "metadata": { + "collapsed": true + }, "outputs": [], "source": [ "step()\n", @@ -1128,7 +1183,9 @@ { "cell_type": "code", "execution_count": null, - "metadata": {}, + "metadata": { + "collapsed": true + }, "outputs": [], "source": [ "step(0.4)\n", @@ -1145,7 +1202,9 @@ { "cell_type": "code", "execution_count": null, - "metadata": {}, + "metadata": { + "collapsed": true + }, "outputs": [], "source": [ "step(0.4, 0.2)\n", @@ -1162,7 +1221,9 @@ { "cell_type": "code", "execution_count": null, - "metadata": {}, + "metadata": { + "collapsed": true + }, "outputs": [], "source": [ "step(p1=0.4, p2=0.2)\n", @@ -1179,7 +1240,9 @@ { "cell_type": "code", "execution_count": null, - "metadata": {}, + "metadata": { + "collapsed": true + }, "outputs": [], "source": [ "step(p2=0.2)\n", @@ -1196,7 +1259,9 @@ { "cell_type": "code", "execution_count": null, - "metadata": {}, + "metadata": { + "collapsed": true + }, "outputs": [], "source": [ "step(0.4, p2=0.2)\n", @@ -1213,7 +1278,9 @@ { "cell_type": "code", "execution_count": null, - "metadata": {}, + "metadata": { + "collapsed": true + }, "outputs": [], "source": [ "# If you remove the # at the beginning of the next line and run it, you get\n", @@ -1239,7 +1306,9 @@ { "cell_type": "code", "execution_count": null, - "metadata": {}, + "metadata": { + "collapsed": true + }, "outputs": [], "source": [ "# Solution goes here\n", From 2950ed38e69990e0742811445171ac9ef91ce908 Mon Sep 17 00:00:00 2001 From: Junwon Lee <31522211+junwonlee5@users.noreply.github.com> Date: Tue, 5 Sep 2017 21:52:49 -0400 Subject: [PATCH 03/19] Adding chap01mine --- code/chap01mine.ipynb | 1241 ++++++++++++++++++++++++++++++++++------- 1 file changed, 1040 insertions(+), 201 deletions(-) diff --git a/code/chap01mine.ipynb b/code/chap01mine.ipynb index 88f89989..201bfd52 100644 --- a/code/chap01mine.ipynb +++ b/code/chap01mine.ipynb @@ -95,11 +95,17 @@ }, { "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": true - }, - "outputs": [], + "execution_count": 1, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "If this cell runs successfully, it produces no output other than this message.\n" + ] + } + ], "source": [ "# If you want the figures to appear in the notebook, \n", "# and you want to interact with them, use\n", @@ -134,7 +140,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 2, "metadata": { "collapsed": true }, @@ -153,7 +159,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 3, "metadata": { "collapsed": true }, @@ -172,11 +178,26 @@ }, { "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": true - }, - "outputs": [], + "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": [ "a = 9.8 * meter / second**2\n", "a" @@ -193,11 +214,26 @@ }, { "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": true - }, - "outputs": [], + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "4 second" + ], + "text/latex": [ + "$4 second$" + ], + "text/plain": [ + "" + ] + }, + "execution_count": 5, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ "t = 4 * second\n", "t" @@ -214,11 +250,26 @@ }, { "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": true - }, - "outputs": [], + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "78.4 meter" + ], + "text/latex": [ + "$78.4 meter$" + ], + "text/plain": [ + "" + ] + }, + "execution_count": 6, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ "h = a * t**2 * 0.5\n", "h" @@ -237,11 +288,26 @@ }, { "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": true - }, - "outputs": [], + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "8.817885349720552 second" + ], + "text/latex": [ + "$8.817885349720552 second$" + ], + "text/plain": [ + "" + ] + }, + "execution_count": 7, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ "h = 381 * meter\n", "t = sqrt(2 * h / a)\n", @@ -259,11 +325,26 @@ }, { "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": true - }, - "outputs": [], + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "86.41527642726142 meter/second" + ], + "text/latex": [ + "$86.41527642726142 \\frac{meter}{second}$" + ], + "text/plain": [ + "" + ] + }, + "execution_count": 8, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ "v = a * t\n", "v" @@ -280,7 +361,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 9, "metadata": { "collapsed": true }, @@ -292,11 +373,26 @@ }, { "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": true - }, - "outputs": [], + "execution_count": 10, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "193.30546802805438 mile/hour" + ], + "text/latex": [ + "$193.30546802805438 \\frac{mile}{hour}$" + ], + "text/plain": [ + "" + ] + }, + "execution_count": 10, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ "v.to(mile/hour)" ] @@ -312,11 +408,26 @@ }, { "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": true - }, - "outputs": [], + "execution_count": 11, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "20.070408163265306 second" + ], + "text/latex": [ + "$20.070408163265306 second$" + ], + "text/plain": [ + "" + ] + }, + "execution_count": 11, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ "# Solution goes here\n", "v = 20 * meter / second\n", @@ -342,7 +453,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 12, "metadata": { "collapsed": true }, @@ -360,11 +471,62 @@ }, { "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": true - }, - "outputs": [], + "execution_count": 13, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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Falling back on \"best\"; valid locations are\n", + "\tbest\n", + "\tupper right\n", + "\tupper left\n", + "\tlower left\n", + "\tlower right\n", + "\tright\n", + "\tcenter left\n", + "\tcenter right\n", + "\tlower center\n", + "\tupper center\n", + "\tcenter\n", + "\n", + " six.iterkeys(self.codes))))\n" + ] + } + ], "source": [ "decorate()" ] @@ -1113,7 +1903,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 46, "metadata": { "collapsed": true }, @@ -1133,7 +1923,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 47, "metadata": { "collapsed": true }, @@ -1160,11 +1950,18 @@ }, { "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": true - }, - "outputs": [], + "execution_count": 48, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "p1 -> 0.5\n", + "p2 -> 0.5\n" + ] + } + ], "source": [ "step()\n", "# Explcitly step(p1=0.7, p2=0.3)\n", @@ -1182,11 +1979,18 @@ }, { "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": true - }, - "outputs": [], + "execution_count": 49, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "p1 -> 0.4\n", + "p2 -> 0.5\n" + ] + } + ], "source": [ "step(0.4)\n", "plot_state()" @@ -1201,11 +2005,18 @@ }, { "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": true - }, - "outputs": [], + "execution_count": 50, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "p1 -> 0.4\n", + "p2 -> 0.2\n" + ] + } + ], "source": [ "step(0.4, 0.2)\n", "plot_state()" @@ -1220,11 +2031,18 @@ }, { "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": true - }, - "outputs": [], + "execution_count": 51, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "p1 -> 0.4\n", + "p2 -> 0.2\n" + ] + } + ], "source": [ "step(p1=0.4, p2=0.2)\n", "plot_state()" @@ -1239,11 +2057,18 @@ }, { "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": true - }, - "outputs": [], + "execution_count": 52, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "p1 -> 0.5\n", + "p2 -> 0.2\n" + ] + } + ], "source": [ "step(p2=0.2)\n", "plot_state()" @@ -1258,11 +2083,18 @@ }, { "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": true - }, - "outputs": [], + "execution_count": 53, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "p1 -> 0.4\n", + "p2 -> 0.2\n" + ] + } + ], "source": [ "step(0.4, p2=0.2)\n", "plot_state()" @@ -1277,11 +2109,18 @@ }, { "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": true - }, - "outputs": [], + "execution_count": 54, + "metadata": {}, + "outputs": [ + { + "ename": "SyntaxError", + "evalue": "positional argument follows keyword argument (, line 4)", + "output_type": "error", + "traceback": [ + "\u001b[1;36m File \u001b[1;32m\"\"\u001b[1;36m, line \u001b[1;32m4\u001b[0m\n\u001b[1;33m step(p1=0.4, 0.2)\u001b[0m\n\u001b[1;37m ^\u001b[0m\n\u001b[1;31mSyntaxError\u001b[0m\u001b[1;31m:\u001b[0m positional argument follows keyword argument\n" + ] + } + ], "source": [ "# If you remove the # at the beginning of the next line and run it, you get\n", "# SyntaxError: positional argument follows keyword argument\n", @@ -1305,7 +2144,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 55, "metadata": { "collapsed": true }, @@ -1322,7 +2161,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 56, "metadata": { "collapsed": true }, @@ -1354,7 +2193,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 57, "metadata": { "collapsed": true }, @@ -1377,7 +2216,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 58, "metadata": { "collapsed": true }, @@ -1398,7 +2237,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 59, "metadata": { "collapsed": true }, @@ -1418,7 +2257,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 60, "metadata": { "collapsed": true }, @@ -1438,7 +2277,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 64, "metadata": { "collapsed": true }, @@ -1460,7 +2299,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 65, "metadata": { "collapsed": true }, @@ -1477,7 +2316,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 66, "metadata": { "collapsed": true }, From be0667de149bdfbd2731db5b4d8d15ee63cdfbba Mon Sep 17 00:00:00 2001 From: Junwon Lee <31522211+junwonlee5@users.noreply.github.com> Date: Tue, 12 Sep 2017 22:51:33 -0400 Subject: [PATCH 04/19] Adding chap02mine --- code/chap02mine.ipynb | 10305 ++++++++++++++++++++++++++++++++++++++++ 1 file changed, 10305 insertions(+) create mode 100644 code/chap02mine.ipynb diff --git a/code/chap02mine.ipynb b/code/chap02mine.ipynb new file mode 100644 index 00000000..1d1156db --- /dev/null +++ b/code/chap02mine.ipynb @@ -0,0 +1,10305 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Modeling and Simulation in Python\n", + "\n", + "Chapter 2: Simulation\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": "markdown", + "metadata": {}, + "source": [ + "We'll start with the same code we saw last time: the magic command that tells Jupyter where to put the figures, and the import statement that gets the functions defined in the `modsim` module." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "# If you want the figures to appear in the notebook, \n", + "# and you want to interact with them, use\n", + "# %matplotlib notebook\n", + "\n", + "# If you want the figures to appear in the notebook, \n", + "# and you don't want to interact with them, use\n", + "# %matplotlib inline\n", + "\n", + "# If you want the figures to appear in separate windows, use\n", + "# %matplotlib qt5\n", + "\n", + "%matplotlib notebook\n", + "\n", + "from modsim import *\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## More than one System object\n", + "\n", + "Here's the code from the previous chapter, with two changes:\n", + "\n", + "1. I've added DocStrings that explain what each function does, and what parameters it takes.\n", + "\n", + "2. I've added a parameter named `system` to the functions so they work with whatever `System` object we give them, instead of always using `bikeshare`. That will be useful soon when we have more than one `System` object." + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def run_steps(system, num_steps=1, p1=0.5, p2=0.5):\n", + " \"\"\"Simulate the given number of time steps.\n", + " \n", + " system: bikeshare System object\n", + " num_steps: number of time steps\n", + " p1: probability of an Olin->Wellesley customer arrival\n", + " p2: probability of a Wellesley->Olin customer arrival\n", + " \"\"\"\n", + " for i in range(num_steps):\n", + " step(system, p1, p2)\n", + " plot_system(system)\n", + " \n", + "def step(system, p1=0.5, p2=0.5):\n", + " \"\"\"Simulate one minute of time.\n", + " \n", + " system: bikeshare System 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(system)\n", + " \n", + " if flip(p2):\n", + " bike_to_olin(system)\n", + " \n", + "def bike_to_wellesley(system):\n", + " \"\"\"Move one bike from Olin to Wellesley.\n", + " \n", + " system: bikeshare System object\n", + " \"\"\"\n", + " move_bike(system, 1)\n", + " \n", + "def bike_to_olin(system):\n", + " \"\"\"Move one bike from Wellesley to Olin.\n", + " \n", + " system: bikeshare System object\n", + " \"\"\"\n", + " move_bike(system, -1)\n", + " \n", + "def move_bike(system, n):\n", + " \"\"\"Move a bike.\n", + " \n", + " system: bikeshare System object\n", + " n: +1 to move from Olin to Wellesley or\n", + " -1 to move from Wellesley to Olin\n", + " \"\"\"\n", + " system.olin -= n\n", + " system.wellesley += n\n", + " \n", + "def plot_system(system):\n", + " \"\"\"Plot the current system of the bikeshare system.\n", + " \n", + " system: bikeshare System object\n", + " \"\"\"\n", + " plot(system.olin, 'rs-', label='Olin')\n", + " plot(system.wellesley, 'bo-', label='Wellesley')\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": [ + "Now we can create more than one `System` object:" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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" + ], + "text/plain": [ + "olin 10\n", + "wellesley 2\n", + "dtype: int64" + ] + }, + "execution_count": 4, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "bikeshare2 = System(olin=10, wellesley=2)\n", + "bikeshare2" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "And whenever we call a function, we indicate which `System` object to work with:" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "bike_to_olin(bikeshare1)" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "bike_to_wellesley(bikeshare2)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "And you can confirm that the different systems are getting updated independently:" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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" + ], + "text/plain": [ + "olin 11\n", + "wellesley 1\n", + "dtype: int64" + ] + }, + "execution_count": 7, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "bikeshare1" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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" + ], + "text/plain": [ + "olin 9\n", + "wellesley 3\n", + "dtype: int64" + ] + }, + "execution_count": 8, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "bikeshare2" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Negative bikes" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In the code we have so far, the number of bikes at one of the locations can go negative, and the number of bikes at the other location can exceed the actual number of bikes in the system.\n", + "\n", + "If you run this simulation a few times, it happens quite often." + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "data": { + "application/javascript": [ + "/* Put everything inside the global mpl namespace */\n", + "window.mpl = {};\n", + "\n", + "\n", + "mpl.get_websocket_type = function() {\n", + " if (typeof(WebSocket) !== 'undefined') {\n", + " return WebSocket;\n", + " } else if (typeof(MozWebSocket) !== 'undefined') {\n", + " return MozWebSocket;\n", + " } else {\n", + " alert('Your browser does not have WebSocket support.' +\n", + " 'Please try Chrome, Safari or Firefox ≥ 6. ' +\n", + " 'Firefox 4 and 5 are also supported but you ' +\n", + " 'have to enable WebSockets in about:config.');\n", + " };\n", + "}\n", + "\n", + "mpl.figure = function(figure_id, websocket, ondownload, parent_element) {\n", + " this.id = figure_id;\n", + "\n", + " this.ws = websocket;\n", + "\n", + " this.supports_binary = (this.ws.binaryType != undefined);\n", + "\n", + " if (!this.supports_binary) {\n", + " var warnings = document.getElementById(\"mpl-warnings\");\n", + " if (warnings) {\n", + " warnings.style.display = 'block';\n", + " warnings.textContent = (\n", + " \"This browser does not support binary websocket messages. \" +\n", + " \"Performance may be slow.\");\n", + " }\n", + " }\n", + "\n", + " this.imageObj = new Image();\n", + "\n", + " this.context = undefined;\n", + " this.message = undefined;\n", + " this.canvas = undefined;\n", + " this.rubberband_canvas = undefined;\n", + " this.rubberband_context = undefined;\n", + " this.format_dropdown = undefined;\n", + "\n", + " this.image_mode = 'full';\n", + "\n", + " this.root = $('
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');\n", + " var button = $('');\n", + " button.click(function (evt) { fig.handle_close(fig, {}); } );\n", + " button.mouseover('Stop Interaction', toolbar_mouse_event);\n", + " buttongrp.append(button);\n", + " var titlebar = this.root.find($('.ui-dialog-titlebar'));\n", + " titlebar.prepend(buttongrp);\n", + "}\n", + "\n", + "mpl.figure.prototype._root_extra_style = function(el){\n", + " var fig = this\n", + " el.on(\"remove\", function(){\n", + "\tfig.close_ws(fig, {});\n", + " });\n", + "}\n", + "\n", + "mpl.figure.prototype._canvas_extra_style = function(el){\n", + " // this is important to make the div 'focusable\n", + " el.attr('tabindex', 0)\n", + " // reach out to IPython and tell the keyboard manager to turn it's self\n", + " // off when our div gets focus\n", + "\n", + " // location in version 3\n", + " if (IPython.notebook.keyboard_manager) {\n", + " IPython.notebook.keyboard_manager.register_events(el);\n", + " }\n", + " else {\n", + " // location in version 2\n", + " IPython.keyboard_manager.register_events(el);\n", + " }\n", + "\n", + "}\n", + "\n", + "mpl.figure.prototype._key_event_extra = function(event, name) {\n", + " var manager = IPython.notebook.keyboard_manager;\n", + " if (!manager)\n", + " manager = IPython.keyboard_manager;\n", + "\n", + " // Check for shift+enter\n", + " if (event.shiftKey && event.which == 13) {\n", + " this.canvas_div.blur();\n", + " // select the cell after this one\n", + " var index = IPython.notebook.find_cell_index(this.cell_info[0]);\n", + " IPython.notebook.select(index + 1);\n", + " }\n", + "}\n", + "\n", + "mpl.figure.prototype.handle_save = function(fig, msg) {\n", + " fig.ondownload(fig, null);\n", + "}\n", + "\n", + "\n", + "mpl.find_output_cell = function(html_output) {\n", + " // Return the cell and output element which can be found *uniquely* in the notebook.\n", + " // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n", + " // IPython event is triggered only after the cells have been serialised, which for\n", + " // our purposes (turning an active figure into a static one), is too late.\n", + " var cells = IPython.notebook.get_cells();\n", + " var ncells = cells.length;\n", + " for (var i=0; i= 3 moved mimebundle to data attribute of output\n", + " data = data.data;\n", + " }\n", + " if (data['text/html'] == html_output) {\n", + " return [cell, data, j];\n", + " }\n", + " }\n", + " }\n", + " }\n", + "}\n", + "\n", + "// Register the function which deals with the matplotlib target/channel.\n", + "// The kernel may be null if the page has been refreshed.\n", + "if (IPython.notebook.kernel != null) {\n", + " IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);\n", + "}\n" + ], + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "text/html": [ + "" + ], + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "IOPub data rate exceeded.\n", + "The notebook server will temporarily stop sending output\n", + "to the client in order to avoid crashing it.\n", + "To change this limit, set the config variable\n", + "`--NotebookApp.iopub_data_rate_limit`.\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "No Olin Bikes\n" + ] + } + ], + "source": [ + "bikeshare = System(olin=10, wellesley=2)\n", + "newfig()\n", + "plot_system(bikeshare)\n", + "decorate_bikeshare()\n", + "run_steps(bikeshare, 60, 0.4, 0.2)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The variables `olin` and `wellesley` are created inside `move_bike`, so they are local. When the function ends, they go away.\n", + "\n", + "If you try to access a local variable from outside its function, you get an error:" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [ + { + "ename": "NameError", + "evalue": "name 'olin' is not defined", + "output_type": "error", + "traceback": [ + "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m", + "\u001b[1;31mNameError\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 2\u001b[0m \u001b[1;31m# NameError: name 'olin' is not defined\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 3\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m----> 4\u001b[1;33m \u001b[0molin\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m", + "\u001b[1;31mNameError\u001b[0m: name 'olin' is not defined" + ] + } + ], + "source": [ + "# If you remove the # from the last line in this cell and run it, you'll get\n", + "# NameError: name 'olin' is not defined\n", + "\n", + "olin" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Exercise:** Add print statements in `move_bike` so it prints a message each time a customer arrives and doesn't find a bike. Run the simulation again to confirm that it works as you expect. Then you might want to remove the print statements before you go on." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Comparison operators" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The `if` statements in the previous section used the comparison operator `<`. The other comparison operators are listed in the book.\n", + "\n", + "It is easy to confuse the comparison operator `==` with the assignment operator `=`.\n", + "\n", + "Remember that `=` creates a variable or gives an existing variable a new value." + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "x = 5" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Whereas `==` compared two values and returns `True` if they are equal." + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "True" + ] + }, + "execution_count": 19, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "x == 5" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "You can use `==` in an `if` statement." + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "yes, x is 5\n" + ] + } + ], + "source": [ + "if x == 5:\n", + " print('yes, x is 5')\n", + "\n", + " " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "But if you use `=` in an `if` statement, you get an error." + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "yes, x is 5\n" + ] + } + ], + "source": [ + "# If you remove the # from the if statement and run it, you'll get\n", + "# SyntaxError: invalid syntax\n", + "\n", + "if x == 5:\n", + " print('yes, x is 5')\n", + "else:\n", + " print('no, x is not 5')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Exercise:** Add an `else` clause to the `if` statement above, and print an appropriate message.\n", + "\n", + "Replace the `==` operator with one or two of the other comparison operators, and confirm they do what you expect." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Metrics" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now that we have a working simulation, we'll use it to evaluate alternative designs and see how good or bad they are. The metric we'll use is the number of customers who arrive and find no bikes available, which might indicate a design problem." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "First we'll make a new `System` object that creates and initializes the system variables that will keep track of the metrics." + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "bikeshare = System(olin=10, wellesley=2, \n", + " olin_empty=0, wellesley_empty=0)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Next we need a version of `move_bike` that updates the metrics." + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def move_bike(system, n):\n", + " olin_temp = system.olin - n\n", + " if olin_temp < 0:\n", + " system.olin_empty += 1\n", + " return\n", + " \n", + " wellesley_temp = system.wellesley + n\n", + " if wellesley_temp < 0:\n", + " system.wellesley_empty += 1\n", + " return\n", + " \n", + " system.olin = olin_temp\n", + " system.wellesley = wellesley_temp" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now when we run a simulation, it keeps track of unhappy customers." + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "metadata": {}, + "outputs": [ + { + "data": { + "application/javascript": [ + "/* Put everything inside the global mpl namespace */\n", + "window.mpl = {};\n", + "\n", + "\n", + "mpl.get_websocket_type = function() {\n", + " if (typeof(WebSocket) !== 'undefined') {\n", + " return WebSocket;\n", + " } else if (typeof(MozWebSocket) !== 'undefined') {\n", + " return MozWebSocket;\n", + " } else {\n", + " alert('Your browser does not have WebSocket support.' +\n", + " 'Please try Chrome, Safari or Firefox ≥ 6. ' +\n", + " 'Firefox 4 and 5 are also supported but you ' +\n", + " 'have to enable WebSockets in about:config.');\n", + " };\n", + "}\n", + "\n", + "mpl.figure = function(figure_id, websocket, ondownload, parent_element) {\n", + " this.id = figure_id;\n", + "\n", + " this.ws = websocket;\n", + "\n", + " this.supports_binary = (this.ws.binaryType != undefined);\n", + "\n", + " if (!this.supports_binary) {\n", + " var warnings = document.getElementById(\"mpl-warnings\");\n", + " if (warnings) {\n", + " warnings.style.display = 'block';\n", + " warnings.textContent = (\n", + " \"This browser does not support binary websocket messages. \" +\n", + " \"Performance may be slow.\");\n", + " }\n", + " }\n", + "\n", + " this.imageObj = new Image();\n", + "\n", + " this.context = undefined;\n", + " this.message = undefined;\n", + " this.canvas = undefined;\n", + " this.rubberband_canvas = undefined;\n", + " this.rubberband_context = undefined;\n", + " this.format_dropdown = undefined;\n", + "\n", + " this.image_mode = 'full';\n", + "\n", + " this.root = $('
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')\n", + " nav_element.attr('style', 'width: 100%');\n", + " this.root.append(nav_element);\n", + "\n", + " // Define a callback function for later on.\n", + " function toolbar_event(event) {\n", + " return fig.toolbar_button_onclick(event['data']);\n", + " }\n", + " function toolbar_mouse_event(event) {\n", + " return fig.toolbar_button_onmouseover(event['data']);\n", + " }\n", + "\n", + " for(var toolbar_ind in mpl.toolbar_items) {\n", + " var name = mpl.toolbar_items[toolbar_ind][0];\n", + " var tooltip = mpl.toolbar_items[toolbar_ind][1];\n", + " var image = mpl.toolbar_items[toolbar_ind][2];\n", + " var method_name = mpl.toolbar_items[toolbar_ind][3];\n", + "\n", + " if (!name) {\n", + " // put a spacer in here.\n", + " continue;\n", + " }\n", + " var button = $('');\n", + " button.click(method_name, toolbar_event);\n", + " button.mouseover(tooltip, toolbar_mouse_event);\n", + " nav_element.append(button);\n", + " }\n", + "\n", + " // Add the status bar.\n", + " var status_bar = $('');\n", + " nav_element.append(status_bar);\n", + " this.message = status_bar[0];\n", + "\n", + " // Add the close button to the window.\n", + " var buttongrp = $('
');\n", + " var button = $('');\n", + " button.click(function (evt) { fig.handle_close(fig, {}); } );\n", + " button.mouseover('Stop Interaction', toolbar_mouse_event);\n", + " buttongrp.append(button);\n", + " var titlebar = this.root.find($('.ui-dialog-titlebar'));\n", + " titlebar.prepend(buttongrp);\n", + "}\n", + "\n", + "mpl.figure.prototype._root_extra_style = function(el){\n", + " var fig = this\n", + " el.on(\"remove\", function(){\n", + "\tfig.close_ws(fig, {});\n", + " });\n", + "}\n", + "\n", + "mpl.figure.prototype._canvas_extra_style = function(el){\n", + " // this is important to make the div 'focusable\n", + " el.attr('tabindex', 0)\n", + " // reach out to IPython and tell the keyboard manager to turn it's self\n", + " // off when our div gets focus\n", + "\n", + " // location in version 3\n", + " if (IPython.notebook.keyboard_manager) {\n", + " IPython.notebook.keyboard_manager.register_events(el);\n", + " }\n", + " else {\n", + " // location in version 2\n", + " IPython.keyboard_manager.register_events(el);\n", + " }\n", + "\n", + "}\n", + "\n", + "mpl.figure.prototype._key_event_extra = function(event, name) {\n", + " var manager = IPython.notebook.keyboard_manager;\n", + " if (!manager)\n", + " manager = IPython.keyboard_manager;\n", + "\n", + " // Check for shift+enter\n", + " if (event.shiftKey && event.which == 13) {\n", + " this.canvas_div.blur();\n", + " // select the cell after this one\n", + " var index = IPython.notebook.find_cell_index(this.cell_info[0]);\n", + " IPython.notebook.select(index + 1);\n", + " }\n", + "}\n", + "\n", + "mpl.figure.prototype.handle_save = function(fig, msg) {\n", + " fig.ondownload(fig, null);\n", + "}\n", + "\n", + "\n", + "mpl.find_output_cell = function(html_output) {\n", + " // Return the cell and output element which can be found *uniquely* in the notebook.\n", + " // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n", + " // IPython event is triggered only after the cells have been serialised, which for\n", + " // our purposes (turning an active figure into a static one), is too late.\n", + " var cells = IPython.notebook.get_cells();\n", + " var ncells = cells.length;\n", + " for (var i=0; i= 3 moved mimebundle to data attribute of output\n", + " data = data.data;\n", + " }\n", + " if (data['text/html'] == html_output) {\n", + " return [cell, data, j];\n", + " }\n", + " }\n", + " }\n", + " }\n", + "}\n", + "\n", + "// Register the function which deals with the matplotlib target/channel.\n", + "// The kernel may be null if the page has been refreshed.\n", + "if (IPython.notebook.kernel != null) {\n", + " IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);\n", + "}\n" + ], + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "text/html": [ + "" + ], + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "1\n", + "2\n", + "3\n", + "4\n", + "5\n", + "6\n", + "7\n", + "8\n", + "9\n", + "10\n", + "11\n", + "12\n", + "13\n", + "14\n", + "15\n", + "16\n", + "17\n", + "18\n", + "19\n", + "20\n", + "21\n", + "22\n", + "23\n", + "24\n", + "25\n", + "26\n", + "27\n", + "28\n", + "29\n", + "30\n", + "31\n", + "32\n", + "33\n", + "34\n", + "35\n", + "36\n", + "37\n", + "38\n", + "39\n", + "40\n", + "41\n", + "42\n", + "43\n", + "44\n", + "45\n" + ] + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "IOPub data rate exceeded.\n", + "The notebook server will temporarily stop sending output\n", + "to the client in order to avoid crashing it.\n", + "To change this limit, set the config variable\n", + "`--NotebookApp.iopub_data_rate_limit`.\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "52\n", + "53\n", + "54\n", + "55\n", + "56\n", + "57\n", + "58\n", + "59\n", + "60\n" + ] + } + ], + "source": [ + "# Solution goes here\n", + "newfig()\n", + "plot_system(bikeshare)\n", + "decorate_bikeshare()\n", + "run_steps(bikeshare, 60, 0.4, 0.2)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "After the simulation, check the final value of `t_first_empty`." + ] + }, + { + "cell_type": "code", + "execution_count": 36, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "42\n" + ] + } + ], + "source": [ + "print(bikeshare.t_first_empty)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Before we go on, let's put `step` and `move_bike` back the way we found them, so they don't break the examples below." + ] + }, + { + "cell_type": "code", + "execution_count": 37, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def step(system, p1=0.5, p2=0.5):\n", + " if flip(p1):\n", + " bike_to_wellesley(system)\n", + " \n", + " if flip(p2):\n", + " bike_to_olin(system)\n", + "\n", + "def move_bike(system, n):\n", + " olin_temp = system.olin - n\n", + " if olin_temp < 0:\n", + " system.olin_empty += 1\n", + " return\n", + " \n", + " wellesley_temp = system.wellesley + n\n", + " if wellesley_temp < 0:\n", + " system.wellesley_empty += 1\n", + " return\n", + " \n", + " system.olin = olin_temp\n", + " system.wellesley = wellesley_temp" + ] + }, + { + "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": 38, + "metadata": { + "collapsed": true + }, + "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": 39, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "8" + ] + }, + "execution_count": 39, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "y = add_five(3)\n", + "y" + ] + }, + { + "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": 40, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "10" + ] + }, + "execution_count": 40, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "add_five(5)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": true + }, + "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": 41, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "10" + ] + }, + "execution_count": 41, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "add_five(3)\n", + "add_five(5)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": true + }, + "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": 42, + "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_system` that creates a `System` object with the system variables `olin=10` and `wellesley=2`, and then returns the new `System` object.\n", + "\n", + "Write a line of code that calls `make_system` and assigns the result to a variable." + ] + }, + { + "cell_type": "code", + "execution_count": 43, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "# Solution goes here\n", + "def make_system():\n", + " system = System(olin=10, wellesley=2)\n", + " return system" + ] + }, + { + "cell_type": "code", + "execution_count": 44, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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" + ], + "text/plain": [ + "olin 10\n", + "wellesley 2\n", + "dtype: int64" + ] + }, + "execution_count": 44, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Solution goes here\n", + "make_system()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Running simulations" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Before we go on, I want to update `run_steps` so it doesn't always plot the results. The new version takes an additional parameter, `plot_flag`, to indicate whether we want to plot.\n", + "\n", + "\"flag\" is a conventional name for a boolean variable that indicates whether or not a condition is true.\n", + "\n", + "This version of `run_steps` works even if `num_steps` is not an integer. It uses the `int` function to round down. See https://docs.python.org/3/library/functions.html#int" + ] + }, + { + "cell_type": "code", + "execution_count": 45, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def run_steps(system, num_steps=1, p1=0.5, p2=0.5, plot_flag=False):\n", + " \"\"\"Simulate the given number of time steps.\n", + " \n", + " `num_steps` should be an integer; if not, it gets rounded down.\n", + " \n", + " system: bikeshare System object\n", + " num_steps: number of time steps\n", + " p1: probability of an Olin->Wellesley customer arrival\n", + " p2: probability of a Wellesley->Olin customer arrival\n", + " plot_flag: boolean, whether to plot\n", + " \"\"\"\n", + " for i in range(int(num_steps)):\n", + " step(system, p1, p2)\n", + " if plot_flag:\n", + " plot_system(system)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now when we run a simulation, we can choose not to plot the results:" + ] + }, + { + "cell_type": "code", + "execution_count": 46, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "bikeshare = System(olin=10, wellesley=2, \n", + " olin_empty=0, wellesley_empty=0)\n", + "run_steps(bikeshare, 60, 0.4, 0.2, plot_flag=False)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "But after the simulation, we can still read the metrics." + ] + }, + { + "cell_type": "code", + "execution_count": 47, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "8" + ] + }, + "execution_count": 47, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "bikeshare.olin_empty" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's wrap all that in a function." + ] + }, + { + "cell_type": "code", + "execution_count": 48, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def run_simulation():\n", + " system = System(olin=10, wellesley=2, \n", + " olin_empty=0, wellesley_empty=0)\n", + " run_steps(system, 60, 0.4, 0.2, plot_flag=False)\n", + " return system" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "And test it." + ] + }, + { + "cell_type": "code", + "execution_count": 49, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "system = run_simulation()" + ] + }, + { + "cell_type": "code", + "execution_count": 50, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "8 0\n" + ] + } + ], + "source": [ + "print(system.olin_empty, system.wellesley_empty)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "If we generalize `run_simulation` to take `p1` and `p2`, we can use it to run simulations with a range of values for the parameters." + ] + }, + { + "cell_type": "code", + "execution_count": 51, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def run_simulation(p1=0.4, p2=0.2):\n", + " bikeshare = System(olin=10, wellesley=2, \n", + " olin_empty=0, wellesley_empty=0)\n", + " run_steps(bikeshare, 60, p1, p2, plot_flag=False)\n", + " return bikeshare" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "When `p1` is small, we probably don't run out of bikes at Olin." + ] + }, + { + "cell_type": "code", + "execution_count": 52, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "0" + ] + }, + "execution_count": 52, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "system = run_simulation(p1=0.2)\n", + "system.olin_empty" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "When `p1` is large, we probably do." + ] + }, + { + "cell_type": "code", + "execution_count": 53, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "11" + ] + }, + "execution_count": 53, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "system = run_simulation(p1=0.6)\n", + "system.olin_empty" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": true + }, + "source": [ + "**Exercise:** Write a version of `run_simulation` that takes all five model parameters as function parameters." + ] + }, + { + "cell_type": "code", + "execution_count": 54, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "# Solution goes here\n", + "def run_simulation(num_steps, Olin, Wellesley, p1, p2):\n", + " system = System(olin=Olin, wellesley=Wellesley, \n", + " olin_empty=0, wellesley_empty=0)\n", + " run_steps(system, num_steps, p1, p2, plot_flag=False)\n", + " return system" + ] + }, + { + "cell_type": "code", + "execution_count": 55, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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" + ], + "text/plain": [ + "olin 1\n", + "wellesley 11\n", + "olin_empty 3\n", + "wellesley_empty 0\n", + "dtype: int64" + ] + }, + "execution_count": 55, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Solution goes here\n", + "run_simulation(60, 10, 2, 0.4, 0.2)\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": true + }, + "source": [ + "## More for loops" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "`linspace` creates a NumPy array of equally spaced numbers." + ] + }, + { + "cell_type": "code", + "execution_count": 56, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([ 0. , 0.25, 0.5 , 0.75, 1. ])" + ] + }, + "execution_count": 56, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "p1_array = linspace(start=0, stop=1, num=5)\n", + "p1_array" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can use an array in a `for` loop, like this:" + ] + }, + { + "cell_type": "code", + "execution_count": 57, + "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." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Exercise:** The function `linspace` is part of NumPy. [You can read the documentation here](https://docs.scipy.org/doc/numpy/reference/generated/numpy.linspace.html).\n", + "\n", + "Use `linspace` to make an array of 10 equally spaced numbers from 1 to 10 (including both)." + ] + }, + { + "cell_type": "code", + "execution_count": 58, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "1.0\n", + "2.0\n", + "3.0\n", + "4.0\n", + "5.0\n", + "6.0\n", + "7.0\n", + "8.0\n", + "9.0\n", + "10.0\n" + ] + } + ], + "source": [ + "# Solution goes here\n", + "p2_array = linspace(start = 1, stop = 10, num = 10)\n", + "for p2 in p2_array:\n", + " print(p2)" + ] + }, + { + "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": 59, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Help on function linrange in module modsim:\n", + "\n", + "linrange(start=0, stop=None, step=1, **kwargs)\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` (at least approximately).\n", + " If you provide the keyword argument `endpoint=False`, the last value\n", + " in the array is `stop-step`. \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": 60, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "1.0\n", + "3.0\n", + "5.0\n", + "7.0\n", + "9.0\n", + "11.0\n" + ] + } + ], + "source": [ + "# Solution goes here\n", + "p3_array = linrange(start = 1, stop=11, step=2)\n", + "for p3 in p3_array:\n", + " print(p3)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": true + }, + "source": [ + "## Sweeping parameters" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The following example runs simulations with a range of values for `p1`; after each simulation, it prints the number of unhappy customers at the Olin station:" + ] + }, + { + "cell_type": "code", + "execution_count": 61, + "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": 61, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "p1_array = linspace(0, 1, 11)\n", + "p1_array" + ] + }, + { + "cell_type": "code", + "execution_count": 62, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "0.0 0\n", + "0.1 0\n", + "0.2 0\n", + "0.3 0\n", + "0.4 3\n", + "0.5 12\n", + "0.6 13\n", + "0.7 23\n", + "0.8 29\n", + "0.9 30\n", + "1.0 36\n" + ] + } + ], + "source": [ + "for p1 in p1_array:\n", + " system = run_simulation(60, 10, 2, p1, 0.2)\n", + " print(p1, system.olin_empty)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now we can do the same thing, but plotting the results instead of printing them.\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 63, + "metadata": {}, + "outputs": [ + { + "data": { + "application/javascript": [ + "/* Put everything inside the global mpl namespace */\n", + "window.mpl = {};\n", + "\n", + "\n", + "mpl.get_websocket_type = function() {\n", + " if (typeof(WebSocket) !== 'undefined') {\n", + " return WebSocket;\n", + " } else if (typeof(MozWebSocket) !== 'undefined') {\n", + " return MozWebSocket;\n", + " } else {\n", + " alert('Your browser does not have WebSocket support.' +\n", + " 'Please try Chrome, Safari or Firefox ≥ 6. ' +\n", + " 'Firefox 4 and 5 are also supported but you ' +\n", + " 'have to enable WebSockets in about:config.');\n", + " };\n", + "}\n", + "\n", + "mpl.figure = function(figure_id, websocket, ondownload, parent_element) {\n", + " this.id = figure_id;\n", + "\n", + " this.ws = websocket;\n", + "\n", + " this.supports_binary = (this.ws.binaryType != undefined);\n", + "\n", + " if (!this.supports_binary) {\n", + " var warnings = document.getElementById(\"mpl-warnings\");\n", + " if (warnings) {\n", + " warnings.style.display = 'block';\n", + " warnings.textContent = (\n", + " \"This browser does not support binary websocket messages. \" +\n", + " \"Performance may be slow.\");\n", + " }\n", + " }\n", + "\n", + " this.imageObj = new Image();\n", + "\n", + " this.context = undefined;\n", + " this.message = undefined;\n", + " this.canvas = undefined;\n", + " this.rubberband_canvas = undefined;\n", + " this.rubberband_context = undefined;\n", + " this.format_dropdown = undefined;\n", + "\n", + " this.image_mode = 'full';\n", + "\n", + " this.root = $('
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');\n", + "\n", + " canvas_div.attr('style', 'position: relative; clear: both; outline: 0');\n", + "\n", + " function canvas_keyboard_event(event) {\n", + " return fig.key_event(event, event['data']);\n", + " }\n", + "\n", + " canvas_div.keydown('key_press', canvas_keyboard_event);\n", + " canvas_div.keyup('key_release', canvas_keyboard_event);\n", + " this.canvas_div = canvas_div\n", + " this._canvas_extra_style(canvas_div)\n", + " this.root.append(canvas_div);\n", + "\n", + " var canvas = $('');\n", + " canvas.addClass('mpl-canvas');\n", + " canvas.attr('style', \"left: 0; top: 0; z-index: 0; outline: 0\")\n", + "\n", + " this.canvas = canvas[0];\n", + " this.context = canvas[0].getContext(\"2d\");\n", + "\n", + " var backingStore = this.context.backingStorePixelRatio ||\n", + "\tthis.context.webkitBackingStorePixelRatio ||\n", + "\tthis.context.mozBackingStorePixelRatio ||\n", + "\tthis.context.msBackingStorePixelRatio ||\n", + "\tthis.context.oBackingStorePixelRatio ||\n", + "\tthis.context.backingStorePixelRatio || 1;\n", + "\n", + " mpl.ratio = (window.devicePixelRatio || 1) / backingStore;\n", + "\n", + " var rubberband = $('');\n", + " rubberband.attr('style', \"position: absolute; left: 0; top: 0; z-index: 1;\")\n", + "\n", + " var pass_mouse_events = true;\n", + "\n", + " canvas_div.resizable({\n", + " start: function(event, ui) {\n", + " pass_mouse_events = false;\n", + " },\n", + " resize: function(event, ui) {\n", + " fig.request_resize(ui.size.width, ui.size.height);\n", + " },\n", + " stop: function(event, ui) {\n", + " pass_mouse_events = true;\n", + " fig.request_resize(ui.size.width, ui.size.height);\n", + " },\n", + " });\n", + "\n", + " function mouse_event_fn(event) {\n", + " if (pass_mouse_events)\n", + " return fig.mouse_event(event, event['data']);\n", + " }\n", + "\n", + " rubberband.mousedown('button_press', mouse_event_fn);\n", + " rubberband.mouseup('button_release', mouse_event_fn);\n", + " // Throttle sequential mouse events to 1 every 20ms.\n", + " rubberband.mousemove('motion_notify', mouse_event_fn);\n", + "\n", + " rubberband.mouseenter('figure_enter', mouse_event_fn);\n", + " rubberband.mouseleave('figure_leave', mouse_event_fn);\n", + "\n", + " canvas_div.on(\"wheel\", function (event) {\n", + " event = event.originalEvent;\n", + " event['data'] = 'scroll'\n", + " if (event.deltaY < 0) {\n", + " event.step = 1;\n", + " } else {\n", + " event.step = -1;\n", + " }\n", + " mouse_event_fn(event);\n", + " });\n", + "\n", + " canvas_div.append(canvas);\n", + " canvas_div.append(rubberband);\n", + "\n", + " this.rubberband = rubberband;\n", + " this.rubberband_canvas = rubberband[0];\n", + " this.rubberband_context = rubberband[0].getContext(\"2d\");\n", + " this.rubberband_context.strokeStyle = \"#000000\";\n", + "\n", + " this._resize_canvas = function(width, height) {\n", + " // Keep the size of the canvas, canvas container, and rubber band\n", + " // canvas in synch.\n", + " canvas_div.css('width', width)\n", + " canvas_div.css('height', height)\n", + "\n", + " canvas.attr('width', width * mpl.ratio);\n", + " canvas.attr('height', height * mpl.ratio);\n", + " canvas.attr('style', 'width: ' + width + 'px; height: ' + height + 'px;');\n", + "\n", + " rubberband.attr('width', width);\n", + " rubberband.attr('height', height);\n", + " }\n", + "\n", + " // Set the figure to an initial 600x600px, this will subsequently be updated\n", + " // upon first draw.\n", + " this._resize_canvas(600, 600);\n", + "\n", + " // Disable right mouse context menu.\n", + " $(this.rubberband_canvas).bind(\"contextmenu\",function(e){\n", + " return false;\n", + " });\n", + "\n", + " function set_focus () {\n", + " canvas.focus();\n", + " canvas_div.focus();\n", + " }\n", + "\n", + " window.setTimeout(set_focus, 100);\n", + "}\n", + "\n", + "mpl.figure.prototype._init_toolbar = function() {\n", + " var fig = this;\n", + "\n", + " var nav_element = $('
')\n", + " nav_element.attr('style', 'width: 100%');\n", + " this.root.append(nav_element);\n", + "\n", + " // Define a callback function for later on.\n", + " function toolbar_event(event) {\n", + " return fig.toolbar_button_onclick(event['data']);\n", + " }\n", + " function toolbar_mouse_event(event) {\n", + " return fig.toolbar_button_onmouseover(event['data']);\n", + " }\n", + "\n", + " for(var toolbar_ind in mpl.toolbar_items) {\n", + " var name = mpl.toolbar_items[toolbar_ind][0];\n", + " var tooltip = mpl.toolbar_items[toolbar_ind][1];\n", + " var image = mpl.toolbar_items[toolbar_ind][2];\n", + " var method_name = mpl.toolbar_items[toolbar_ind][3];\n", + "\n", + " if (!name) {\n", + " // put a spacer in here.\n", + " continue;\n", + " }\n", + " var button = $('');\n", + " button.click(method_name, toolbar_event);\n", + " button.mouseover(tooltip, toolbar_mouse_event);\n", + " nav_element.append(button);\n", + " }\n", + "\n", + " // Add the status bar.\n", + " var status_bar = $('');\n", + " nav_element.append(status_bar);\n", + " this.message = status_bar[0];\n", + "\n", + " // Add the close button to the window.\n", + " var buttongrp = $('
');\n", + " var button = $('');\n", + " button.click(function (evt) { fig.handle_close(fig, {}); } );\n", + " button.mouseover('Stop Interaction', toolbar_mouse_event);\n", + " buttongrp.append(button);\n", + " var titlebar = this.root.find($('.ui-dialog-titlebar'));\n", + " titlebar.prepend(buttongrp);\n", + "}\n", + "\n", + "mpl.figure.prototype._root_extra_style = function(el){\n", + " var fig = this\n", + " el.on(\"remove\", function(){\n", + "\tfig.close_ws(fig, {});\n", + " });\n", + "}\n", + "\n", + "mpl.figure.prototype._canvas_extra_style = function(el){\n", + " // this is important to make the div 'focusable\n", + " el.attr('tabindex', 0)\n", + " // reach out to IPython and tell the keyboard manager to turn it's self\n", + " // off when our div gets focus\n", + "\n", + " // location in version 3\n", + " if (IPython.notebook.keyboard_manager) {\n", + " IPython.notebook.keyboard_manager.register_events(el);\n", + " }\n", + " else {\n", + " // location in version 2\n", + " IPython.keyboard_manager.register_events(el);\n", + " }\n", + "\n", + "}\n", + "\n", + "mpl.figure.prototype._key_event_extra = function(event, name) {\n", + " var manager = IPython.notebook.keyboard_manager;\n", + " if (!manager)\n", + " manager = IPython.keyboard_manager;\n", + "\n", + " // Check for shift+enter\n", + " if (event.shiftKey && event.which == 13) {\n", + " this.canvas_div.blur();\n", + " // select the cell after this one\n", + " var index = IPython.notebook.find_cell_index(this.cell_info[0]);\n", + " IPython.notebook.select(index + 1);\n", + " }\n", + "}\n", + "\n", + "mpl.figure.prototype.handle_save = function(fig, msg) {\n", + " fig.ondownload(fig, null);\n", + "}\n", + "\n", + "\n", + "mpl.find_output_cell = function(html_output) {\n", + " // Return the cell and output element which can be found *uniquely* in the notebook.\n", + " // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n", + " // IPython event is triggered only after the cells have been serialised, which for\n", + " // our purposes (turning an active figure into a static one), is too late.\n", + " var cells = IPython.notebook.get_cells();\n", + " var ncells = cells.length;\n", + " for (var i=0; i= 3 moved mimebundle to data attribute of output\n", + " data = data.data;\n", + " }\n", + " if (data['text/html'] == html_output) {\n", + " return [cell, data, j];\n", + " }\n", + " }\n", + " }\n", + " }\n", + "}\n", + "\n", + "// Register the function which deals with the matplotlib target/channel.\n", + "// The kernel may be null if the page has been refreshed.\n", + "if (IPython.notebook.kernel != null) {\n", + " IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);\n", + "}\n" + ], + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "text/html": [ + "" + ], + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Solution goes here\n", + "\n", + "def parameter_sweep(p1_array):\n", + " for p1 in p1_array:\n", + " system = run_simulation(60, 10, 2, p1, 0.2)\n", + " plot(p1, system.olin_empty, 'rs', label='olin')\n", + " decorate_bikeshare(xlabel)\n", + "newfig()\n", + "parameter_sweep(p1_array)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [] + }, + { + "cell_type": "code", + "execution_count": 67, + "metadata": {}, + "outputs": [ + { + "data": { + "application/javascript": [ + "/* Put everything inside the global mpl namespace */\n", + "window.mpl = {};\n", + "\n", + "\n", + "mpl.get_websocket_type = function() {\n", + " if (typeof(WebSocket) !== 'undefined') {\n", + " return WebSocket;\n", + " } else if (typeof(MozWebSocket) !== 'undefined') {\n", + " return MozWebSocket;\n", + " } else {\n", + " alert('Your browser does not have WebSocket support.' +\n", + " 'Please try Chrome, Safari or Firefox ≥ 6. ' +\n", + " 'Firefox 4 and 5 are also supported but you ' +\n", + " 'have to enable WebSockets in about:config.');\n", + " };\n", + "}\n", + "\n", + "mpl.figure = function(figure_id, websocket, ondownload, parent_element) {\n", + " this.id = figure_id;\n", + "\n", + " this.ws = websocket;\n", + "\n", + " this.supports_binary = (this.ws.binaryType != undefined);\n", + "\n", + " if (!this.supports_binary) {\n", + " var warnings = document.getElementById(\"mpl-warnings\");\n", + " if (warnings) {\n", + " warnings.style.display = 'block';\n", + " warnings.textContent = (\n", + " \"This browser does not support binary websocket messages. \" +\n", + " \"Performance may be slow.\");\n", + " }\n", + " }\n", + "\n", + " this.imageObj = new Image();\n", + "\n", + " this.context = undefined;\n", + " this.message = undefined;\n", + " this.canvas = undefined;\n", + " this.rubberband_canvas = undefined;\n", + " this.rubberband_context = undefined;\n", + " this.format_dropdown = undefined;\n", + "\n", + " this.image_mode = 'full';\n", + "\n", + " this.root = $('
');\n", + " this._root_extra_style(this.root)\n", + " this.root.attr('style', 'display: inline-block');\n", + "\n", + " $(parent_element).append(this.root);\n", + "\n", + " this._init_header(this);\n", + " this._init_canvas(this);\n", + " this._init_toolbar(this);\n", + "\n", + " var fig = this;\n", + "\n", + " this.waiting = false;\n", + "\n", + " this.ws.onopen = function () {\n", + " fig.send_message(\"supports_binary\", {value: fig.supports_binary});\n", + " fig.send_message(\"send_image_mode\", {});\n", + " if (mpl.ratio != 1) {\n", + " fig.send_message(\"set_dpi_ratio\", {'dpi_ratio': mpl.ratio});\n", + " }\n", + " fig.send_message(\"refresh\", {});\n", + " }\n", + "\n", + " this.imageObj.onload = function() {\n", + " if (fig.image_mode == 'full') {\n", + " // Full images could contain transparency (where diff images\n", + " // almost always do), so we need to clear the canvas so that\n", + " // there is no ghosting.\n", + " fig.context.clearRect(0, 0, fig.canvas.width, fig.canvas.height);\n", + " }\n", + " fig.context.drawImage(fig.imageObj, 0, 0);\n", + " };\n", + "\n", + " this.imageObj.onunload = function() {\n", + " this.ws.close();\n", + " }\n", + "\n", + " this.ws.onmessage = this._make_on_message_function(this);\n", + "\n", + " this.ondownload = ondownload;\n", + "}\n", + "\n", + "mpl.figure.prototype._init_header = function() {\n", + " var titlebar = $(\n", + " '
');\n", + " var titletext = $(\n", + " '
');\n", + " titlebar.append(titletext)\n", + " this.root.append(titlebar);\n", + " this.header = titletext[0];\n", + "}\n", + "\n", + "\n", + "\n", + "mpl.figure.prototype._canvas_extra_style = function(canvas_div) {\n", + "\n", + "}\n", + "\n", + "\n", + "mpl.figure.prototype._root_extra_style = function(canvas_div) {\n", + "\n", + "}\n", + "\n", + "mpl.figure.prototype._init_canvas = function() {\n", + " var fig = this;\n", + "\n", + " var canvas_div = $('
');\n", + "\n", + " canvas_div.attr('style', 'position: relative; clear: both; outline: 0');\n", + "\n", + " function canvas_keyboard_event(event) {\n", + " return fig.key_event(event, event['data']);\n", + " }\n", + "\n", + " canvas_div.keydown('key_press', canvas_keyboard_event);\n", + " canvas_div.keyup('key_release', canvas_keyboard_event);\n", + " this.canvas_div = canvas_div\n", + " this._canvas_extra_style(canvas_div)\n", + " this.root.append(canvas_div);\n", + "\n", + " var canvas = $('');\n", + " canvas.addClass('mpl-canvas');\n", + " canvas.attr('style', \"left: 0; top: 0; z-index: 0; outline: 0\")\n", + "\n", + " this.canvas = canvas[0];\n", + " this.context = canvas[0].getContext(\"2d\");\n", + "\n", + " var backingStore = this.context.backingStorePixelRatio ||\n", + "\tthis.context.webkitBackingStorePixelRatio ||\n", + "\tthis.context.mozBackingStorePixelRatio ||\n", + "\tthis.context.msBackingStorePixelRatio ||\n", + "\tthis.context.oBackingStorePixelRatio ||\n", + "\tthis.context.backingStorePixelRatio || 1;\n", + "\n", + " mpl.ratio = (window.devicePixelRatio || 1) / backingStore;\n", + "\n", + " var rubberband = $('');\n", + " rubberband.attr('style', \"position: absolute; left: 0; top: 0; z-index: 1;\")\n", + "\n", + " var pass_mouse_events = true;\n", + "\n", + " canvas_div.resizable({\n", + " start: function(event, ui) {\n", + " pass_mouse_events = false;\n", + " },\n", + " resize: function(event, ui) {\n", + " fig.request_resize(ui.size.width, ui.size.height);\n", + " },\n", + " stop: function(event, ui) {\n", + " pass_mouse_events = true;\n", + " fig.request_resize(ui.size.width, ui.size.height);\n", + " },\n", + " });\n", + "\n", + " function mouse_event_fn(event) {\n", + " if (pass_mouse_events)\n", + " return fig.mouse_event(event, event['data']);\n", + " }\n", + "\n", + " rubberband.mousedown('button_press', mouse_event_fn);\n", + " rubberband.mouseup('button_release', mouse_event_fn);\n", + " // Throttle sequential mouse events to 1 every 20ms.\n", + " rubberband.mousemove('motion_notify', mouse_event_fn);\n", + "\n", + " rubberband.mouseenter('figure_enter', mouse_event_fn);\n", + " rubberband.mouseleave('figure_leave', mouse_event_fn);\n", + "\n", + " canvas_div.on(\"wheel\", function (event) {\n", + " event = event.originalEvent;\n", + " event['data'] = 'scroll'\n", + " if (event.deltaY < 0) {\n", + " event.step = 1;\n", + " } else {\n", + " event.step = -1;\n", + " }\n", + " mouse_event_fn(event);\n", + " });\n", + "\n", + " canvas_div.append(canvas);\n", + " canvas_div.append(rubberband);\n", + "\n", + " this.rubberband = rubberband;\n", + " this.rubberband_canvas = rubberband[0];\n", + " this.rubberband_context = rubberband[0].getContext(\"2d\");\n", + " this.rubberband_context.strokeStyle = \"#000000\";\n", + "\n", + " this._resize_canvas = function(width, height) {\n", + " // Keep the size of the canvas, canvas container, and rubber band\n", + " // canvas in synch.\n", + " canvas_div.css('width', width)\n", + " canvas_div.css('height', height)\n", + "\n", + " canvas.attr('width', width * mpl.ratio);\n", + " canvas.attr('height', height * mpl.ratio);\n", + " canvas.attr('style', 'width: ' + width + 'px; height: ' + height + 'px;');\n", + "\n", + " rubberband.attr('width', width);\n", + " rubberband.attr('height', height);\n", + " }\n", + "\n", + " // Set the figure to an initial 600x600px, this will subsequently be updated\n", + " // upon first draw.\n", + " this._resize_canvas(600, 600);\n", + "\n", + " // Disable right mouse context menu.\n", + " $(this.rubberband_canvas).bind(\"contextmenu\",function(e){\n", + " return false;\n", + " });\n", + "\n", + " function set_focus () {\n", + " canvas.focus();\n", + " canvas_div.focus();\n", + " }\n", + "\n", + " window.setTimeout(set_focus, 100);\n", + "}\n", + "\n", + "mpl.figure.prototype._init_toolbar = function() {\n", + " var fig = this;\n", + "\n", + " var nav_element = $('
')\n", + " nav_element.attr('style', 'width: 100%');\n", + " this.root.append(nav_element);\n", + "\n", + " // Define a callback function for later on.\n", + " function toolbar_event(event) {\n", + " return fig.toolbar_button_onclick(event['data']);\n", + " }\n", + " function toolbar_mouse_event(event) {\n", + " return fig.toolbar_button_onmouseover(event['data']);\n", + " }\n", + "\n", + " for(var toolbar_ind in mpl.toolbar_items) {\n", + " var name = mpl.toolbar_items[toolbar_ind][0];\n", + " var tooltip = mpl.toolbar_items[toolbar_ind][1];\n", + " var image = mpl.toolbar_items[toolbar_ind][2];\n", + " var method_name = mpl.toolbar_items[toolbar_ind][3];\n", + "\n", + " if (!name) {\n", + " // put a spacer in here.\n", + " continue;\n", + " }\n", + " var button = $('');\n", + " button.click(method_name, toolbar_event);\n", + " button.mouseover(tooltip, toolbar_mouse_event);\n", + " nav_element.append(button);\n", + " }\n", + "\n", + " // Add the status bar.\n", + " var status_bar = $('');\n", + " nav_element.append(status_bar);\n", + " this.message = status_bar[0];\n", + "\n", + " // Add the close button to the window.\n", + " var buttongrp = $('
');\n", + " var button = $('');\n", + " button.click(function (evt) { fig.handle_close(fig, {}); } );\n", + " button.mouseover('Stop Interaction', toolbar_mouse_event);\n", + " buttongrp.append(button);\n", + " var titlebar = this.root.find($('.ui-dialog-titlebar'));\n", + " titlebar.prepend(buttongrp);\n", + "}\n", + "\n", + "mpl.figure.prototype._root_extra_style = function(el){\n", + " var fig = this\n", + " el.on(\"remove\", function(){\n", + "\tfig.close_ws(fig, {});\n", + " });\n", + "}\n", + "\n", + "mpl.figure.prototype._canvas_extra_style = function(el){\n", + " // this is important to make the div 'focusable\n", + " el.attr('tabindex', 0)\n", + " // reach out to IPython and tell the keyboard manager to turn it's self\n", + " // off when our div gets focus\n", + "\n", + " // location in version 3\n", + " if (IPython.notebook.keyboard_manager) {\n", + " IPython.notebook.keyboard_manager.register_events(el);\n", + " }\n", + " else {\n", + " // location in version 2\n", + " IPython.keyboard_manager.register_events(el);\n", + " }\n", + "\n", + "}\n", + "\n", + "mpl.figure.prototype._key_event_extra = function(event, name) {\n", + " var manager = IPython.notebook.keyboard_manager;\n", + " if (!manager)\n", + " manager = IPython.keyboard_manager;\n", + "\n", + " // Check for shift+enter\n", + " if (event.shiftKey && event.which == 13) {\n", + " this.canvas_div.blur();\n", + " // select the cell after this one\n", + " var index = IPython.notebook.find_cell_index(this.cell_info[0]);\n", + " IPython.notebook.select(index + 1);\n", + " }\n", + "}\n", + "\n", + "mpl.figure.prototype.handle_save = function(fig, msg) {\n", + " fig.ondownload(fig, null);\n", + "}\n", + "\n", + "\n", + "mpl.find_output_cell = function(html_output) {\n", + " // Return the cell and output element which can be found *uniquely* in the notebook.\n", + " // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n", + " // IPython event is triggered only after the cells have been serialised, which for\n", + " // our purposes (turning an active figure into a static one), is too late.\n", + " var cells = IPython.notebook.get_cells();\n", + " var ncells = cells.length;\n", + " for (var i=0; i= 3 moved mimebundle to data attribute of output\n", + " data = data.data;\n", + " }\n", + " if (data['text/html'] == html_output) {\n", + " return [cell, data, j];\n", + " }\n", + " }\n", + " }\n", + " }\n", + "}\n", + "\n", + "// Register the function which deals with the matplotlib target/channel.\n", + "// The kernel may be null if the page has been refreshed.\n", + "if (IPython.notebook.kernel != null) {\n", + " IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);\n", + "}\n" + ], + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "text/html": [ + "" + ], + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Solution goes here\n", + "newfig()\n", + "parameter_sweep2()" + ] + }, + { + "cell_type": "code", + "execution_count": 70, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "# Solution goes here\n", + "parameter_sweep2()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Exercise:** Hold `p1=0.4` and `p2=0.2`, and sweep a range of values for `num_steps`.\n", + "\n", + "Hint: You will need a version of `run_simulation` that takes `num_steps` as a parameter.\n", + "\n", + "Hint: Because `num_steps` is supposed to be an integer use `range` rather than `linrange`." + ] + }, + { + "cell_type": "code", + "execution_count": 74, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "# Solution goes here\n", + "def run_simulation(num_steps, p1=0.4, p2=0.2, olin=10, wellesley=2):\n", + " system = System(olin=olin, wellesley=wellesley, \n", + " olin_empty=0, wellesley_empty=0)\n", + " run_steps(system, num_steps, p1, p2, plot_flag=False)\n", + " return system" + ] + }, + { + "cell_type": "code", + "execution_count": 75, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "# Solution goes here\n", + "def parameter_sweep3(p3_array):\n", + " for p3 in p3_array:\n", + " system = run_simulation(num_steps=p3)\n", + " plot(p3, system.olin_empty, 'rs', label='olin')\n", + " plot(p3, system.wellesley_empty, 'bs', label='wellesley')\n", + " decorate_bikeshare(xlabel)" + ] + }, + { + "cell_type": "code", + "execution_count": 76, + "metadata": { + "scrolled": false + }, + "outputs": [ + { + "data": { + "application/javascript": [ + "/* Put everything inside the global mpl namespace */\n", + "window.mpl = {};\n", + "\n", + "\n", + "mpl.get_websocket_type = function() {\n", + " if (typeof(WebSocket) !== 'undefined') {\n", + " return WebSocket;\n", + " } else if (typeof(MozWebSocket) !== 'undefined') {\n", + " return MozWebSocket;\n", + " } else {\n", + " alert('Your browser does not have WebSocket support.' +\n", + " 'Please try Chrome, Safari or Firefox ≥ 6. ' +\n", + " 'Firefox 4 and 5 are also supported but you ' +\n", + " 'have to enable WebSockets in about:config.');\n", + " };\n", + "}\n", + "\n", + "mpl.figure = function(figure_id, websocket, ondownload, parent_element) {\n", + " this.id = figure_id;\n", + "\n", + " this.ws = websocket;\n", + "\n", + " this.supports_binary = (this.ws.binaryType != undefined);\n", + "\n", + " if (!this.supports_binary) {\n", + " var warnings = document.getElementById(\"mpl-warnings\");\n", + " if (warnings) {\n", + " warnings.style.display = 'block';\n", + " warnings.textContent = (\n", + " \"This browser does not support binary websocket messages. \" +\n", + " \"Performance may be slow.\");\n", + " }\n", + " }\n", + "\n", + " this.imageObj = new Image();\n", + "\n", + " this.context = undefined;\n", + " this.message = undefined;\n", + " this.canvas = undefined;\n", + " this.rubberband_canvas = undefined;\n", + " this.rubberband_context = undefined;\n", + " this.format_dropdown = undefined;\n", + "\n", + " this.image_mode = 'full';\n", + "\n", + " this.root = $('
');\n", + " this._root_extra_style(this.root)\n", + " this.root.attr('style', 'display: inline-block');\n", + "\n", + " $(parent_element).append(this.root);\n", + "\n", + " this._init_header(this);\n", + " this._init_canvas(this);\n", + " this._init_toolbar(this);\n", + "\n", + " var fig = this;\n", + "\n", + " this.waiting = false;\n", + "\n", + " this.ws.onopen = function () {\n", + " fig.send_message(\"supports_binary\", {value: fig.supports_binary});\n", + " fig.send_message(\"send_image_mode\", {});\n", + " if (mpl.ratio != 1) {\n", + " fig.send_message(\"set_dpi_ratio\", {'dpi_ratio': mpl.ratio});\n", + " }\n", + " fig.send_message(\"refresh\", {});\n", + " }\n", + "\n", + " this.imageObj.onload = function() {\n", + " if (fig.image_mode == 'full') {\n", + " // Full images could contain transparency (where diff images\n", + " // almost always do), so we need to clear the canvas so that\n", + " // there is no ghosting.\n", + " fig.context.clearRect(0, 0, fig.canvas.width, fig.canvas.height);\n", + " }\n", + " fig.context.drawImage(fig.imageObj, 0, 0);\n", + " };\n", + "\n", + " this.imageObj.onunload = function() {\n", + " this.ws.close();\n", + " }\n", + "\n", + " this.ws.onmessage = this._make_on_message_function(this);\n", + "\n", + " this.ondownload = ondownload;\n", + "}\n", + "\n", + "mpl.figure.prototype._init_header = function() {\n", + " var titlebar = $(\n", + " '
');\n", + " var titletext = $(\n", + " '
');\n", + " titlebar.append(titletext)\n", + " this.root.append(titlebar);\n", + " this.header = titletext[0];\n", + "}\n", + "\n", + "\n", + "\n", + "mpl.figure.prototype._canvas_extra_style = function(canvas_div) {\n", + "\n", + "}\n", + "\n", + "\n", + "mpl.figure.prototype._root_extra_style = function(canvas_div) {\n", + "\n", + "}\n", + "\n", + "mpl.figure.prototype._init_canvas = function() {\n", + " var fig = this;\n", + "\n", + " var canvas_div = $('
');\n", + "\n", + " canvas_div.attr('style', 'position: relative; clear: both; outline: 0');\n", + "\n", + " function canvas_keyboard_event(event) {\n", + " return fig.key_event(event, event['data']);\n", + " }\n", + "\n", + " canvas_div.keydown('key_press', canvas_keyboard_event);\n", + " canvas_div.keyup('key_release', canvas_keyboard_event);\n", + " this.canvas_div = canvas_div\n", + " this._canvas_extra_style(canvas_div)\n", + " this.root.append(canvas_div);\n", + "\n", + " var canvas = $('');\n", + " canvas.addClass('mpl-canvas');\n", + " canvas.attr('style', \"left: 0; top: 0; z-index: 0; outline: 0\")\n", + "\n", + " this.canvas = canvas[0];\n", + " this.context = canvas[0].getContext(\"2d\");\n", + "\n", + " var backingStore = this.context.backingStorePixelRatio ||\n", + "\tthis.context.webkitBackingStorePixelRatio ||\n", + "\tthis.context.mozBackingStorePixelRatio ||\n", + "\tthis.context.msBackingStorePixelRatio ||\n", + "\tthis.context.oBackingStorePixelRatio ||\n", + "\tthis.context.backingStorePixelRatio || 1;\n", + "\n", + " mpl.ratio = (window.devicePixelRatio || 1) / backingStore;\n", + "\n", + " var rubberband = $('');\n", + " rubberband.attr('style', \"position: absolute; left: 0; top: 0; z-index: 1;\")\n", + "\n", + " var pass_mouse_events = true;\n", + "\n", + " canvas_div.resizable({\n", + " start: function(event, ui) {\n", + " pass_mouse_events = false;\n", + " },\n", + " resize: function(event, ui) {\n", + " fig.request_resize(ui.size.width, ui.size.height);\n", + " },\n", + " stop: function(event, ui) {\n", + " pass_mouse_events = true;\n", + " fig.request_resize(ui.size.width, ui.size.height);\n", + " },\n", + " });\n", + "\n", + " function mouse_event_fn(event) {\n", + " if (pass_mouse_events)\n", + " return fig.mouse_event(event, event['data']);\n", + " }\n", + "\n", + " rubberband.mousedown('button_press', mouse_event_fn);\n", + " rubberband.mouseup('button_release', mouse_event_fn);\n", + " // Throttle sequential mouse events to 1 every 20ms.\n", + " rubberband.mousemove('motion_notify', mouse_event_fn);\n", + "\n", + " rubberband.mouseenter('figure_enter', mouse_event_fn);\n", + " rubberband.mouseleave('figure_leave', mouse_event_fn);\n", + "\n", + " canvas_div.on(\"wheel\", function (event) {\n", + " event = event.originalEvent;\n", + " event['data'] = 'scroll'\n", + " if (event.deltaY < 0) {\n", + " event.step = 1;\n", + " } else {\n", + " event.step = -1;\n", + " }\n", + " mouse_event_fn(event);\n", + " });\n", + "\n", + " canvas_div.append(canvas);\n", + " canvas_div.append(rubberband);\n", + "\n", + " this.rubberband = rubberband;\n", + " this.rubberband_canvas = rubberband[0];\n", + " this.rubberband_context = rubberband[0].getContext(\"2d\");\n", + " this.rubberband_context.strokeStyle = \"#000000\";\n", + "\n", + " this._resize_canvas = function(width, height) {\n", + " // Keep the size of the canvas, canvas container, and rubber band\n", + " // canvas in synch.\n", + " canvas_div.css('width', width)\n", + " canvas_div.css('height', height)\n", + "\n", + " canvas.attr('width', width * mpl.ratio);\n", + " canvas.attr('height', height * mpl.ratio);\n", + " canvas.attr('style', 'width: ' + width + 'px; height: ' + height + 'px;');\n", + "\n", + " rubberband.attr('width', width);\n", + " rubberband.attr('height', height);\n", + " }\n", + "\n", + " // Set the figure to an initial 600x600px, this will subsequently be updated\n", + " // upon first draw.\n", + " this._resize_canvas(600, 600);\n", + "\n", + " // Disable right mouse context menu.\n", + " $(this.rubberband_canvas).bind(\"contextmenu\",function(e){\n", + " return false;\n", + " });\n", + "\n", + " function set_focus () {\n", + " canvas.focus();\n", + " canvas_div.focus();\n", + " }\n", + "\n", + " window.setTimeout(set_focus, 100);\n", + "}\n", + "\n", + "mpl.figure.prototype._init_toolbar = function() {\n", + " var fig = this;\n", + "\n", + " var nav_element = $('
')\n", + " nav_element.attr('style', 'width: 100%');\n", + " this.root.append(nav_element);\n", + "\n", + " // Define a callback function for later on.\n", + " function toolbar_event(event) {\n", + " return fig.toolbar_button_onclick(event['data']);\n", + " }\n", + " function toolbar_mouse_event(event) {\n", + " return fig.toolbar_button_onmouseover(event['data']);\n", + " }\n", + "\n", + " for(var toolbar_ind in mpl.toolbar_items) {\n", + " var name = mpl.toolbar_items[toolbar_ind][0];\n", + " var tooltip = mpl.toolbar_items[toolbar_ind][1];\n", + " var image = mpl.toolbar_items[toolbar_ind][2];\n", + " var method_name = mpl.toolbar_items[toolbar_ind][3];\n", + "\n", + " if (!name) {\n", + " // put a spacer in here.\n", + " continue;\n", + " }\n", + " var button = $('');\n", + " button.click(method_name, toolbar_event);\n", + " button.mouseover(tooltip, toolbar_mouse_event);\n", + " nav_element.append(button);\n", + " }\n", + "\n", + " // Add the status bar.\n", + " var status_bar = $('');\n", + " nav_element.append(status_bar);\n", + " this.message = status_bar[0];\n", + "\n", + " // Add the close button to the window.\n", + " var buttongrp = $('
');\n", + " var button = $('');\n", + " button.click(function (evt) { fig.handle_close(fig, {}); } );\n", + " button.mouseover('Stop Interaction', toolbar_mouse_event);\n", + " buttongrp.append(button);\n", + " var titlebar = this.root.find($('.ui-dialog-titlebar'));\n", + " titlebar.prepend(buttongrp);\n", + "}\n", + "\n", + "mpl.figure.prototype._root_extra_style = function(el){\n", + " var fig = this\n", + " el.on(\"remove\", function(){\n", + "\tfig.close_ws(fig, {});\n", + " });\n", + "}\n", + "\n", + "mpl.figure.prototype._canvas_extra_style = function(el){\n", + " // this is important to make the div 'focusable\n", + " el.attr('tabindex', 0)\n", + " // reach out to IPython and tell the keyboard manager to turn it's self\n", + " // off when our div gets focus\n", + "\n", + " // location in version 3\n", + " if (IPython.notebook.keyboard_manager) {\n", + " IPython.notebook.keyboard_manager.register_events(el);\n", + " }\n", + " else {\n", + " // location in version 2\n", + " IPython.keyboard_manager.register_events(el);\n", + " }\n", + "\n", + "}\n", + "\n", + "mpl.figure.prototype._key_event_extra = function(event, name) {\n", + " var manager = IPython.notebook.keyboard_manager;\n", + " if (!manager)\n", + " manager = IPython.keyboard_manager;\n", + "\n", + " // Check for shift+enter\n", + " if (event.shiftKey && event.which == 13) {\n", + " this.canvas_div.blur();\n", + " // select the cell after this one\n", + " var index = IPython.notebook.find_cell_index(this.cell_info[0]);\n", + " IPython.notebook.select(index + 1);\n", + " }\n", + "}\n", + "\n", + "mpl.figure.prototype.handle_save = function(fig, msg) {\n", + " fig.ondownload(fig, null);\n", + "}\n", + "\n", + "\n", + "mpl.find_output_cell = function(html_output) {\n", + " // Return the cell and output element which can be found *uniquely* in the notebook.\n", + " // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n", + " // IPython event is triggered only after the cells have been serialised, which for\n", + " // our purposes (turning an active figure into a static one), is too late.\n", + " var cells = IPython.notebook.get_cells();\n", + " var ncells = cells.length;\n", + " for (var i=0; i= 3 moved mimebundle to data attribute of output\n", + " data = data.data;\n", + " }\n", + " if (data['text/html'] == html_output) {\n", + " return [cell, data, j];\n", + " }\n", + " }\n", + " }\n", + " }\n", + "}\n", + "\n", + "// Register the function which deals with the matplotlib target/channel.\n", + "// The kernel may be null if the page has been refreshed.\n", + "if (IPython.notebook.kernel != null) {\n", + " IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);\n", + "}\n" + ], + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "text/html": [ + "" + ], + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Solution goes here\n", + "\n", + "p4_array = linspace(0, 20, 21)\n", + "\n", + "def parametersweep5(p4_array = p4_array):\n", + " for p4 in p4_array:\n", + " average = run_simulations(500, p4)\n", + " plot(p4, average, 'rs', label='Average # of unhappy customers')\n", + " decorate(title='Average # of unhappy customers vs. # of bikes at Olin',\n", + " xlabel='Number of bikes at Olin', \n", + " ylabel='Average number of unhappy customers')\n", + "newfig() \n", + "parametersweep5()\n", + "\n", + "\n", + " \n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "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": "3.6.1" + } + }, + "nbformat": 4, + "nbformat_minor": 1 +} From 3e6cb5dcccf3bb61f995673c081a33da6b0c351f Mon Sep 17 00:00:00 2001 From: Junwon Lee <31522211+junwonlee5@users.noreply.github.com> Date: Tue, 19 Sep 2017 20:40:23 -0400 Subject: [PATCH 05/19] Adding chap03mine --- code/chap03mine.ipynb | 4270 +++++++++++++++++++++++++++++++++++++++++ 1 file changed, 4270 insertions(+) create mode 100644 code/chap03mine.ipynb diff --git a/code/chap03mine.ipynb b/code/chap03mine.ipynb new file mode 100644 index 00000000..577ab493 --- /dev/null +++ b/code/chap03mine.ipynb @@ -0,0 +1,4270 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Modeling and Simulation in Python\n", + "\n", + "Chapter 3: Explain\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": { + "collapsed": true + }, + "outputs": [], + "source": [ + "# If you want the figures to appear in the notebook, \n", + "# and you want to interact with them, use\n", + "# %matplotlib notebook\n", + "\n", + "# If you want the figures to appear in the notebook, \n", + "# and you don't want to interact with them, use\n", + "# %matplotlib inline\n", + "\n", + "# If you want the figures to appear in separate windows, use\n", + "# %matplotlib qt5\n", + "\n", + "# To switch from one to another, you have to select Kernel->Restart\n", + "\n", + "%matplotlib inline\n", + "\n", + "from modsim import *" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Pandas is a module that provides tools for reading and processing data. The `read_html` reads a web page from a file or the Internet and creates one DataFrame for each table on the page." + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "from pandas import read_html" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The data directory contains a downloaded copy of https://en.wikipedia.org/wiki/World_population_estimates" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "filename = 'data/World_population_estimates.html'\n", + "tables = read_html(filename, header=0, index_col=0, decimal='M')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "`tables` is a sequence of DataFrame objects. We can select the DataFrame we want using the bracket operator. The tables are numbered from 0, so `table2` is actually the third table on the page.\n", + "\n", + "`head` selects the header and the first five rows." + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "data": { + "text/html": [ + "
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" + ], + "text/plain": [ + " United States Census Bureau (2015)[18] \\\n", + "Year \n", + "1950 2557628654 \n", + "1951 2594939877 \n", + "1952 2636772306 \n", + "1953 2682053389 \n", + "1954 2730228104 \n", + "\n", + " Population Reference Bureau (1973–2015)[6] \\\n", + "Year \n", + "1950 2.516000e+09 \n", + "1951 NaN \n", + "1952 NaN \n", + "1953 NaN \n", + "1954 NaN \n", + "\n", + " United Nations Department of Economic and Social Affairs (2015)[7] \\\n", + "Year \n", + "1950 2525149000 \n", + "1951 2572850917 \n", + "1952 2619292068 \n", + "1953 2665865392 \n", + "1954 2713172027 \n", + "\n", + " Maddison (2008)[8] HYDE (2007)[15] Tanton (1994)[9] \\\n", + "Year \n", + "1950 2.544000e+09 2.527960e+09 2.400000e+09 \n", + "1951 2.571663e+09 NaN NaN \n", + "1952 2.617949e+09 NaN NaN \n", + "1953 2.665959e+09 NaN NaN \n", + "1954 2.716927e+09 NaN NaN \n", + "\n", + " Biraben (1980)[10] McEvedy & Jones (1978)[11] Thomlinson (1975)[12] \\\n", + "Year \n", + "1950 2.527000e+09 2.500000e+09 2.400000e+09 \n", + "1951 NaN NaN NaN \n", + "1952 NaN NaN NaN \n", + "1953 NaN NaN NaN \n", + "1954 NaN NaN NaN \n", + "\n", + " Durand (1974)[13] Clark (1967)[14] \n", + "Year \n", + "1950 NaN 2.486000e+09 \n", + "1951 NaN NaN \n", + "1952 NaN NaN \n", + "1953 NaN NaN \n", + "1954 NaN NaN " + ] + }, + "execution_count": 4, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "table2 = tables[2]\n", + "table2.head()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "`tail` selects the last five rows." + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "data": { + "text/html": [ + "
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United States Census Bureau (2015)[18]Population Reference Bureau (1973–2015)[6]United Nations Department of Economic and Social Affairs (2015)[7]Maddison (2008)[8]HYDE (2007)[15]Tanton (1994)[9]Biraben (1980)[10]McEvedy & Jones (1978)[11]Thomlinson (1975)[12]Durand (1974)[13]Clark (1967)[14]
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" + ], + "text/plain": [ + " United States Census Bureau (2015)[18] \\\n", + "Year \n", + "2011 6944055583 \n", + "2012 7022349283 \n", + "2013 7101027895 \n", + "2014 7178722893 \n", + "2015 7256490011 \n", + "\n", + " Population Reference Bureau (1973–2015)[6] \\\n", + "Year \n", + "2011 6.986951e+09 \n", + "2012 7.057075e+09 \n", + "2013 7.136796e+09 \n", + "2014 7.238184e+09 \n", + "2015 7.336435e+09 \n", + "\n", + " United Nations Department of Economic and Social Affairs (2015)[7] \\\n", + "Year \n", + "2011 6997998760 \n", + "2012 7080072417 \n", + "2013 7162119434 \n", + "2014 7243784000 \n", + "2015 7349472000 \n", + "\n", + " Maddison (2008)[8] HYDE (2007)[15] Tanton (1994)[9] \\\n", + "Year \n", + "2011 NaN NaN NaN \n", + "2012 NaN NaN NaN \n", + "2013 NaN NaN NaN \n", + "2014 NaN NaN NaN \n", + "2015 NaN NaN NaN \n", + "\n", + " Biraben (1980)[10] McEvedy & Jones (1978)[11] Thomlinson (1975)[12] \\\n", + "Year \n", + "2011 NaN NaN NaN \n", + "2012 NaN NaN NaN \n", + "2013 NaN NaN NaN \n", + "2014 NaN NaN NaN \n", + "2015 NaN NaN NaN \n", + "\n", + " Durand (1974)[13] Clark (1967)[14] \n", + "Year \n", + "2011 NaN NaN \n", + "2012 NaN NaN \n", + "2013 NaN NaN \n", + "2014 NaN NaN \n", + "2015 NaN NaN " + ] + }, + "execution_count": 5, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "table2.tail()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Long column names are awkard to work with, but we can replace them with abbreviated names." + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "table2.columns = ['census', 'prb', 'un', 'maddison', \n", + " 'hyde', 'tanton', 'biraben', 'mj', \n", + " 'thomlinson', 'durand', 'clark']" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here's what the DataFrame looks like now. \n", + "\n", + "Some of the values use scientific notation; for example, `2.544000e+09` is shorthand for $2.544 \\cdot 10^9$ or 2.544 billion.\n", + "\n", + "`NaN` is a special value that indicates missing data." + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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19754089083233NaN40710204344.070671e+09NaNNaNNaN3.900000e+094.000000e+09NaNNaN
19764160185010NaN41461358504.141445e+09NaNNaNNaNNaNNaNNaNNaN
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19794379013942NaN43715278714.363144e+09NaNNaNNaNNaNNaNNaNNaN
....................................
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66 rows × 11 columns

\n", + "
" + ], + "text/plain": [ + " census prb un maddison hyde \\\n", + "Year \n", + "1950 2557628654 2.516000e+09 2525149000 2.544000e+09 2.527960e+09 \n", + "1951 2594939877 NaN 2572850917 2.571663e+09 NaN \n", + "1952 2636772306 NaN 2619292068 2.617949e+09 NaN \n", + "1953 2682053389 NaN 2665865392 2.665959e+09 NaN \n", + "1954 2730228104 NaN 2713172027 2.716927e+09 NaN \n", + "1955 2782098943 NaN 2761650981 2.769074e+09 NaN \n", + "1956 2835299673 NaN 2811572031 2.822502e+09 NaN \n", + "1957 2891349717 NaN 2863042795 2.879934e+09 NaN \n", + "1958 2948137248 NaN 2916030167 2.939254e+09 NaN \n", + "1959 3000716593 NaN 2970395814 2.995909e+09 NaN \n", + "1960 3043001508 NaN 3026002942 3.041507e+09 3.042000e+09 \n", + "1961 3083966929 NaN 3082830266 3.082161e+09 NaN \n", + "1962 3140093217 NaN 3141071531 3.135787e+09 NaN \n", + "1963 3209827882 NaN 3201178277 3.201354e+09 NaN \n", + "1964 3281201306 NaN 3263738832 3.266477e+09 NaN \n", + "1965 3350425793 NaN 3329122479 3.333138e+09 NaN \n", + "1966 3420677923 NaN 3397475247 3.402224e+09 NaN \n", + "1967 3490333715 NaN 3468521724 3.471464e+09 NaN \n", + "1968 3562313822 NaN 3541674891 3.543086e+09 NaN \n", + "1969 3637159050 NaN 3616108749 3.615743e+09 NaN \n", + "1970 3712697742 NaN 3691172616 3.691157e+09 3.710000e+09 \n", + "1971 3790326948 NaN 3766754345 3.769818e+09 NaN \n", + "1972 3866568653 NaN 3842873611 3.846499e+09 NaN \n", + "1973 3942096442 NaN 3919182332 3.922793e+09 3.923000e+09 \n", + "1974 4016608813 NaN 3995304922 3.997677e+09 NaN \n", + "1975 4089083233 NaN 4071020434 4.070671e+09 NaN \n", + "1976 4160185010 NaN 4146135850 4.141445e+09 NaN \n", + "1977 4232084578 NaN 4220816737 4.213539e+09 NaN \n", + "1978 4304105753 NaN 4295664825 4.286317e+09 NaN \n", + "1979 4379013942 NaN 4371527871 4.363144e+09 NaN \n", + "... ... ... ... ... ... \n", + "1986 4940571232 NaN 4953376710 4.920968e+09 NaN \n", + "1987 5027200492 NaN 5045315871 5.006672e+09 NaN \n", + "1988 5114557167 NaN 5138214688 5.093306e+09 NaN \n", + "1989 5201440110 NaN 5230000000 5.180540e+09 NaN \n", + "1990 5288955934 NaN 5320816667 5.269029e+09 5.308000e+09 \n", + "1991 5371585922 NaN 5408908724 5.351922e+09 NaN \n", + "1992 5456136278 NaN 5494899570 5.435722e+09 NaN \n", + "1993 5538268316 NaN 5578865109 5.518127e+09 NaN \n", + "1994 5618682132 NaN 5661086346 5.599396e+09 NaN \n", + "1995 5699202985 5.760000e+09 5741822412 5.681575e+09 NaN \n", + "1996 5779440593 NaN 5821016750 5.762212e+09 NaN \n", + "1997 5857972543 5.840000e+09 5898688337 5.842122e+09 NaN \n", + "1998 5935213248 NaN 5975303657 5.921366e+09 NaN \n", + "1999 6012074922 NaN 6051478010 5.999622e+09 NaN \n", + "2000 6088571383 6.067000e+09 6127700428 6.076558e+09 6.145000e+09 \n", + "2001 6165219247 6.137000e+09 6204147026 6.154791e+09 NaN \n", + "2002 6242016348 6.215000e+09 6280853817 6.231704e+09 NaN \n", + "2003 6318590956 6.314000e+09 6357991749 6.308364e+09 NaN \n", + "2004 6395699509 6.396000e+09 6435705595 6.374056e+09 NaN \n", + "2005 6473044732 6.477000e+09 6514094605 6.462987e+09 NaN \n", + "2006 6551263534 6.555000e+09 6593227977 6.540214e+09 NaN \n", + "2007 6629913759 6.625000e+09 6673105937 6.616689e+09 NaN \n", + "2008 6709049780 6.705000e+09 6753649228 6.694832e+09 NaN \n", + "2009 6788214394 6.809972e+09 6834721933 6.764086e+09 NaN \n", + "2010 6866332358 6.892319e+09 6916183482 NaN NaN \n", + "2011 6944055583 6.986951e+09 6997998760 NaN NaN \n", + "2012 7022349283 7.057075e+09 7080072417 NaN NaN \n", + "2013 7101027895 7.136796e+09 7162119434 NaN NaN \n", + "2014 7178722893 7.238184e+09 7243784000 NaN NaN \n", + "2015 7256490011 7.336435e+09 7349472000 NaN NaN \n", + "\n", + " tanton biraben mj thomlinson \\\n", + "Year \n", + "1950 2.400000e+09 2.527000e+09 2.500000e+09 2.400000e+09 \n", + "1951 NaN NaN NaN NaN \n", + "1952 NaN NaN NaN NaN \n", + "1953 NaN NaN NaN NaN \n", + "1954 NaN NaN NaN NaN \n", + "1955 NaN NaN NaN NaN \n", + "1956 NaN NaN NaN NaN \n", + "1957 NaN NaN NaN NaN \n", + "1958 NaN NaN NaN NaN \n", + "1959 NaN NaN NaN NaN \n", + "1960 NaN NaN NaN NaN \n", + "1961 NaN NaN NaN NaN \n", + "1962 NaN NaN NaN NaN \n", + "1963 NaN NaN NaN NaN \n", + "1964 NaN NaN NaN NaN \n", + "1965 NaN NaN NaN NaN \n", + "1966 NaN NaN NaN NaN \n", + "1967 NaN NaN NaN NaN \n", + "1968 NaN NaN NaN NaN \n", + "1969 NaN NaN NaN NaN \n", + "1970 NaN 3.637000e+09 NaN 3.600000e+09 \n", + "1971 NaN NaN NaN NaN \n", + "1972 NaN NaN NaN NaN \n", + "1973 NaN NaN NaN NaN \n", + "1974 NaN NaN NaN NaN \n", + "1975 NaN NaN 3.900000e+09 4.000000e+09 \n", + "1976 NaN NaN NaN NaN \n", + "1977 NaN NaN NaN NaN \n", + "1978 NaN NaN NaN NaN \n", + "1979 NaN NaN NaN NaN \n", + "... ... ... ... ... \n", + "1986 NaN NaN NaN NaN \n", + "1987 NaN NaN NaN NaN \n", + "1988 NaN NaN NaN NaN \n", + "1989 NaN NaN NaN NaN \n", + "1990 NaN NaN NaN NaN \n", + "1991 NaN NaN NaN NaN \n", + "1992 NaN NaN NaN NaN \n", + "1993 NaN NaN NaN NaN \n", + "1994 NaN NaN NaN NaN \n", + "1995 NaN NaN NaN NaN \n", + "1996 NaN NaN NaN NaN \n", + "1997 NaN NaN NaN NaN \n", + "1998 NaN NaN NaN NaN \n", + "1999 NaN NaN NaN NaN \n", + "2000 NaN NaN 5.750000e+09 NaN \n", + "2001 NaN NaN NaN NaN \n", + "2002 NaN NaN NaN NaN \n", + "2003 NaN NaN NaN NaN \n", + "2004 NaN NaN NaN NaN \n", + "2005 NaN NaN NaN NaN \n", + "2006 NaN NaN NaN NaN \n", + "2007 NaN NaN NaN NaN \n", + "2008 NaN NaN NaN NaN \n", + "2009 NaN NaN NaN NaN \n", + "2010 NaN NaN NaN NaN \n", + "2011 NaN NaN NaN NaN \n", + "2012 NaN NaN NaN NaN \n", + "2013 NaN NaN NaN NaN \n", + "2014 NaN NaN NaN NaN \n", + "2015 NaN NaN NaN NaN \n", + "\n", + " durand clark \n", + "Year \n", + "1950 NaN 2.486000e+09 \n", + "1951 NaN NaN \n", + "1952 NaN NaN \n", + "1953 NaN NaN \n", + "1954 NaN NaN \n", + "1955 NaN NaN \n", + "1956 NaN NaN \n", + "1957 NaN NaN \n", + "1958 NaN NaN \n", + "1959 NaN NaN \n", + "1960 NaN NaN \n", + "1961 NaN NaN \n", + "1962 NaN 3.036000e+09 \n", + "1963 NaN NaN \n", + "1964 NaN NaN \n", + "1965 NaN NaN \n", + "1966 NaN 3.288000e+09 \n", + "1967 NaN NaN \n", + "1968 NaN NaN \n", + "1969 NaN NaN \n", + "1970 3,600,000,000– 3,700,000,000 3.632000e+09 \n", + "1971 NaN NaN \n", + "1972 NaN NaN \n", + "1973 NaN 3.860000e+09 \n", + "1974 NaN NaN \n", + "1975 NaN NaN \n", + "1976 NaN NaN \n", + "1977 NaN NaN \n", + "1978 NaN NaN \n", + "1979 NaN NaN \n", + "... ... ... \n", + "1986 NaN NaN \n", + "1987 NaN NaN \n", + "1988 NaN NaN \n", + "1989 NaN NaN \n", + "1990 NaN NaN \n", + "1991 NaN NaN \n", + "1992 NaN NaN \n", + "1993 NaN NaN \n", + "1994 NaN NaN \n", + "1995 NaN NaN \n", + "1996 NaN NaN \n", + "1997 NaN NaN \n", + "1998 NaN NaN \n", + "1999 NaN NaN \n", + "2000 NaN NaN \n", + "2001 NaN NaN \n", + "2002 NaN NaN \n", + "2003 NaN NaN \n", + "2004 NaN NaN \n", + "2005 NaN NaN \n", + "2006 NaN NaN \n", + "2007 NaN NaN \n", + "2008 NaN NaN \n", + "2009 NaN NaN \n", + "2010 NaN NaN \n", + "2011 NaN NaN \n", + "2012 NaN NaN \n", + "2013 NaN NaN \n", + "2014 NaN NaN \n", + "2015 NaN NaN \n", + "\n", + "[66 rows x 11 columns]" + ] + }, + "execution_count": 7, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "table2" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can use dot notatio to select a column from a DataFrame. The result is a Series." + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "Year\n", + "1950 2557628654\n", + "1951 2594939877\n", + "1952 2636772306\n", + "1953 2682053389\n", + "1954 2730228104\n", + "1955 2782098943\n", + "1956 2835299673\n", + "1957 2891349717\n", + "1958 2948137248\n", + "1959 3000716593\n", + "1960 3043001508\n", + "1961 3083966929\n", + "1962 3140093217\n", + "1963 3209827882\n", + "1964 3281201306\n", + "1965 3350425793\n", + "1966 3420677923\n", + "1967 3490333715\n", + "1968 3562313822\n", + "1969 3637159050\n", + "1970 3712697742\n", + "1971 3790326948\n", + "1972 3866568653\n", + "1973 3942096442\n", + "1974 4016608813\n", + "1975 4089083233\n", + "1976 4160185010\n", + "1977 4232084578\n", + "1978 4304105753\n", + "1979 4379013942\n", + " ... \n", + "1986 4940571232\n", + "1987 5027200492\n", + "1988 5114557167\n", + "1989 5201440110\n", + "1990 5288955934\n", + "1991 5371585922\n", + "1992 5456136278\n", + "1993 5538268316\n", + "1994 5618682132\n", + "1995 5699202985\n", + "1996 5779440593\n", + "1997 5857972543\n", + "1998 5935213248\n", + "1999 6012074922\n", + "2000 6088571383\n", + "2001 6165219247\n", + "2002 6242016348\n", + "2003 6318590956\n", + "2004 6395699509\n", + "2005 6473044732\n", + "2006 6551263534\n", + "2007 6629913759\n", + "2008 6709049780\n", + "2009 6788214394\n", + "2010 6866332358\n", + "2011 6944055583\n", + "2012 7022349283\n", + "2013 7101027895\n", + "2014 7178722893\n", + "2015 7256490011\n", + "Name: census, Length: 66, dtype: int64" + ] + }, + "execution_count": 8, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "census = table2.census\n", + "census" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "A Series object has two parts, `values` and `index`.\n", + "\n", + "The `values` part is an array." + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([2557628654, 2594939877, 2636772306, 2682053389, 2730228104,\n", + " 2782098943, 2835299673, 2891349717, 2948137248, 3000716593,\n", + " 3043001508, 3083966929, 3140093217, 3209827882, 3281201306,\n", + " 3350425793, 3420677923, 3490333715, 3562313822, 3637159050,\n", + " 3712697742, 3790326948, 3866568653, 3942096442, 4016608813,\n", + " 4089083233, 4160185010, 4232084578, 4304105753, 4379013942,\n", + " 4451362735, 4534410125, 4614566561, 4695736743, 4774569391,\n", + " 4856462699, 4940571232, 5027200492, 5114557167, 5201440110,\n", + " 5288955934, 5371585922, 5456136278, 5538268316, 5618682132,\n", + " 5699202985, 5779440593, 5857972543, 5935213248, 6012074922,\n", + " 6088571383, 6165219247, 6242016348, 6318590956, 6395699509,\n", + " 6473044732, 6551263534, 6629913759, 6709049780, 6788214394,\n", + " 6866332358, 6944055583, 7022349283, 7101027895, 7178722893,\n", + " 7256490011], dtype=int64)" + ] + }, + "execution_count": 9, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "census.values" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The `index` part is yet another kind of object, an `Int64Index`." + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "Int64Index([1950, 1951, 1952, 1953, 1954, 1955, 1956, 1957, 1958, 1959, 1960,\n", + " 1961, 1962, 1963, 1964, 1965, 1966, 1967, 1968, 1969, 1970, 1971,\n", + " 1972, 1973, 1974, 1975, 1976, 1977, 1978, 1979, 1980, 1981, 1982,\n", + " 1983, 1984, 1985, 1986, 1987, 1988, 1989, 1990, 1991, 1992, 1993,\n", + " 1994, 1995, 1996, 1997, 1998, 1999, 2000, 2001, 2002, 2003, 2004,\n", + " 2005, 2006, 2007, 2008, 2009, 2010, 2011, 2012, 2013, 2014, 2015],\n", + " dtype='int64', name='Year')" + ] + }, + "execution_count": 10, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "census.index" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "If you ever wonder what kind of object a variable refers to, you can use the `type` function.\n", + "\n", + "The result indicates what type the object is, and the module where that type is defined.\n", + "\n", + "DataFrame, Series, and Int64Index are defined by Pandas.\n", + "\n", + "array is defined by NumPy." + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "pandas.core.frame.DataFrame" + ] + }, + "execution_count": 11, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "type(table2)" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "pandas.core.series.Series" + ] + }, + "execution_count": 12, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "type(census)" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "pandas.core.indexes.numeric.Int64Index" + ] + }, + "execution_count": 13, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "type(census.index)" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "numpy.ndarray" + ] + }, + "execution_count": 14, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "type(census.values)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This function plots the estimates generated by the US Censis and UN DESA, and labels the axes.\n", + "\n", + "`1e9` is scientific notation for $1 \\cdot 10^9$ or 1 billion." + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def plot_estimates(table):\n", + " \"\"\"Plot world population estimates.\n", + " \n", + " table: DataFrame with columns 'un' and 'census'\n", + " \"\"\"\n", + " un = table.un / 1e9\n", + " census = table.census / 1e9\n", + " \n", + " plot(census, ':', color='darkblue', label='US Census')\n", + " plot(un, '--', color='green', label='UN DESA')\n", + " \n", + " decorate(xlabel='Year',\n", + " ylabel='World population (billion)')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now we can plot the estimates." + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": { + "scrolled": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Saving figure to file chap03-fig01.pdf\n" + ] + }, + { + "data": { + "image/png": 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sdF2WKMFT+/k7Ojoya9YsZs2axfXr14mJiSE9PR0bGxucnZ1p2LBhRdQphKhE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\n6UIrhCgfWg/slpuby5kzZ/jPf/7DmTN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LSws0Gg0WLFiAxYsXCxfm5MIPjH9dCggIwMDA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\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "newfig()\n", + "plot_estimates(table2)\n", + "savefig('chap03-fig01.pdf')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "From here on, we will work in units of billions." + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "un = table2.un / 1e9" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "census = table2.census / 1e9" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This expression computes the elementwise differences between the series, then divides through by the UN value to produce relative errors, then finds the largest element.\n", + "\n", + "So the largest relative error between the estimates is about 1.3%." + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "1.2862470293832287" + ] + }, + "execution_count": 19, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "max(abs(census - un) / un) * 100" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Exercise:** Break down that expression into smaller steps and display the intermediate results, to make sure you understand how it works.\n", + "\n", + "Where in the series is the largest relative error between the two estimates, near the beginning or the end?\n", + "\n", + "When I computed relative errors, I used `un` as the denominator. But that was an arbitraty choice. What happens if we use `census` instead? How much difference does it make." + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": { + "collapsed": true, + "scrolled": true + }, + "outputs": [], + "source": [ + "# Solution goes here\n", + "difference = abs(census - un)" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "data": { + "text/plain": [ + "0.012862470293832286" + ] + }, + "execution_count": 21, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Solution goes here\n", + "largratio = max(difference / un)\n", + "largratio" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "data": { + "text/plain": [ + "1.2862470293832287" + ] + }, + "execution_count": 22, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Solution goes here\n", + "largerrorpercentage = largratio * 100\n", + "largerrorpercentage" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "1.2813631502151765" + ] + }, + "execution_count": 23, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Solution goes here\n", + "largratio = max(difference / census)\n", + "largerrorpercentage = largratio * 100\n", + "largerrorpercentage\n", + "#difference is minimal" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Constant growth" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can select an element from a series using bracket notation and one of the elements from the index. Here's the first element:" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "2.5576286540000002" + ] + }, + "execution_count": 24, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "census[1950]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "And the last element." + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "7.2564900110000004" + ] + }, + "execution_count": 25, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "census[2015]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "But we can get the first and last years from the index itself:" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "(1950, 2015)" + ] + }, + "execution_count": 26, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "first_year = census.index[0]\n", + "last_year = census.index[-1]\n", + "first_year, last_year" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "And use them to look up the first and last elements.\n", + "\n", + "Then we can compute the average annual growth in billions of people per year." + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "0.07229017472307693" + ] + }, + "execution_count": 27, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "total_growth = census[last_year] - census[first_year]\n", + "elapsed_time = last_year - first_year\n", + "annual_growth = total_growth / elapsed_time\n", + "annual_growth" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now let's create a `TimeSeries` to contain values generated by a linear growth model." + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "results = TimeSeries()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Initially the Series is empty, but we can initialize it so the starting value, in 1950, is the 1950 population estimated by the US Census." + ] + }, + { + "cell_type": "code", + "execution_count": 29, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
\n", + "\n", + "\n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + "
value
19502.557629
\n", + "
" + ], + "text/plain": [ + "1950 2.557629\n", + "dtype: float64" + ] + }, + "execution_count": 29, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "results[1950] = census[1950]\n", + "results" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "After that, the population in the model grows by a constant amount each year." + ] + }, + { + "cell_type": "code", + "execution_count": 30, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "for t in linrange(1950, 2015):\n", + " results[t+1] = results[t] + annual_growth" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here's what the results looks like, compared to the actual data." + ] + }, + { + "cell_type": "code", + "execution_count": 31, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Saving figure to file chap03-fig02.pdf\n" + ] + }, + { + "data": { + "image/png": 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lly5dQkdHh3bt2iGVSHm+6/Mkp18n56gX5vJ2lMukVFQoMDR8OJY+1+pV1DVfjCAIwoMu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\nk+KXyWRwdXXVysXZ2RlWVlaQy+W9Hn9ncgCACRMmIDU1Fcn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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "newfig()\n", + "plot_estimates(table2)\n", + "plot(results, '--', color='gray', label='model')\n", + "decorate(xlabel='Year', ylabel='World population (billion)')\n", + "savefig('chap03-fig02.pdf')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The model fits the data pretty well after 1990, but not so well before." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Exercise:** Try fitting the model using data from 1965 to the present, and see if that does a better job.\n", + "\n", + "Hint: Copy the code from above and make a few changes.\n", + "\n", + "Make sure your model starts in 1950, even though the estimated annual growth is based on later data. You might have to shift the first value in the series up or down to match the data." + ] + }, + { + "cell_type": "code", + "execution_count": 32, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Saving figure to file chap03-fig02.pdf\n" + ] + }, + { + "data": { + "image/png": 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9O3379r2n1yIIteJy49h9aTc5pbkM05nOpNH9VDX6EokECxNT3nyzT7M+XE1N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\n/vvvw8jICE1NTd2SQ1JSEj766CPMnz8fbm5uaGxshFgsbvP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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Solution goes here\n", + "total_growth = census[last_year] - census[1965]\n", + "elapsed_time = last_year - first_year\n", + "annual_growth = total_growth / elapsed_time\n", + "annual_growth\n", + "for t in linrange(1965, 2015):\n", + " results[t+1] = results[t] + annual_growth\n", + "newfig()\n", + "plot_estimates(table2)\n", + "plot(results, '--', color='gray', label='model')\n", + "decorate(xlabel='Year', ylabel='World population (billion)')\n", + "savefig('chap03-fig02.pdf')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Now with system objects" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can rewrite the code from the previous section using system objects." + ] + }, + { + "cell_type": "code", + "execution_count": 33, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "t0 = census.index[0]\n", + "t_end = census.index[-1]\n", + "total_growth = census[t_end] - census[t0]\n", + "elapsed_time = t_end - t0\n", + "annual_growth = total_growth / elapsed_time" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here's the system object." + ] + }, + { + "cell_type": "code", + "execution_count": 34, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "system = System(t0=t0, \n", + " t_end=t_end,\n", + " p0=census[t0],\n", + " annual_growth=annual_growth)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "And we can encapsulate the code tha runs the model in a function that stores the resulting Series as a new system variable." + ] + }, + { + "cell_type": "code", + "execution_count": 35, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def run_simulation1(system):\n", + " \"\"\"Runs the constant growth model.\n", + " \n", + " Adds TimeSeries to `system` as `results`.\n", + " \n", + " system: system object\n", + " \"\"\"\n", + " results = TimeSeries()\n", + " results[system.t0] = system.p0\n", + " for t in linrange(system.t0, system.t_end):\n", + " results[t+1] = results[t] + system.annual_growth\n", + " system.results = results" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can also encapsulate the code that plots the results." + ] + }, + { + "cell_type": "code", + "execution_count": 36, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def plot_results(system, title=None):\n", + " \"\"\"Plot the estimates and the model.\n", + " \n", + " system: System object with `results`\n", + " \"\"\"\n", + " newfig()\n", + " plot_estimates(table2)\n", + " plot(system.results, '--', color='gray', label='model')\n", + " decorate(xlabel='Year', \n", + " ylabel='World population (billion)',\n", + " title=title)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here's how we run it." + ] + }, + { + "cell_type": "code", + "execution_count": 37, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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MkWSEpqYmNjY2GBgYYKZvxlf+/2U3URgb69CvXxM0NF6uFj1PUqWvsJs3b3L+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\nLf5lZWUwMTHBK6+8gqCgIPj6+nbp5i3Ozs4AgF27dmHs2LE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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "run_simulation1(system)\n", + "plot_results(system, title='Constant growth model')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "`plot_results` uses `decorate`, which takes parameters that specify the title of the figure, labels for the $x$ and $y$ axis, and limits for the axes. To read the documentation of `decorate`, run the cells below." + ] + }, + { + "cell_type": "code", + "execution_count": 38, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Help on function decorate in module modsim:\n", + "\n", + "decorate(**kwargs)\n", + " Decorate the current axes.\n", + " \n", + " Call decorate with keyword arguments like\n", + " \n", + " decorate(title='Title',\n", + " xlabel='x',\n", + " ylabel='y')\n", + " \n", + " The keyword arguments can be any of the axis properties\n", + " defined by Matplotlib. To see the list, run plt.getp(plt.gca())\n", + " \n", + " In addition, you can use `legend=False` to suppress the legend.\n", + " \n", + " And you can use `loc` to indicate the location of the legend\n", + " (the default value is 'best')\n", + "\n" + ] + } + ], + "source": [ + "help(decorate)" + ] + }, + { + "cell_type": "code", + "execution_count": 39, + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " adjustable = box\n", + " agg_filter = None\n", + " alpha = None\n", + " anchor = C\n", + " animated = False\n", + " aspect = auto\n", + " autoscale_on = True\n", + " autoscalex_on = True\n", + " autoscaley_on = True\n", + " axes = Axes(0.125,0.125;0.775x0.755)\n", + " axes_locator = None\n", + " axis_bgcolor = (1.0, 1.0, 1.0, 1.0)\n", + " axisbelow = True\n", + " children = [\n", + " label = \n", + " legend = None\n", + " legend_handles_labels = ([], [])\n", + " lines = \n", + " navigate = True\n", + " navigate_mode = None\n", + " path_effects = []\n", + " picker = None\n", + " position = Bbox(x0=0.125, y0=0.125, x1=0.9, y1=0.88)\n", + " rasterization_zorder = None\n", + " rasterized = None\n", + " renderer_cache = None\n", + " shared_x_axes = \n", + " xlabel = \n", + " xlim = (0.0, 1.0)\n", + " xmajorticklabels = \n", + " xminorticklabels = \n", + " xscale = linear\n", + " xticklabels = \n", + " xticklines = \n", + " xticks = [ 0. 0.2 0.4 0.6 0.8 1. ]\n", + " yaxis = YAxis(54.000000,36.000000)\n", + " yaxis_transform = BlendedGenericTransform(BboxTransformTo(Transforme...\n", + " ybound = (0.0, 1.0)\n", + " ygridlines = \n", + " ylabel = \n", + " ylim = (0.0, 1.0)\n", + " ymajorticklabels = \n", + " yminorticklabels = \n", + " yscale = linear\n", + " yticklabels = \n", + " yticklines = \n", + " yticks = [ 0. 0.2 0.4 0.6 0.8 1. ]\n", + " zorder = 0\n" + ] + }, + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.getp(plt.gca())" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Exercise:** The constant growth model doesn't make a lot of sense, because it seems like the number of deaths and births should depend on the size of the population. As a small improvement, let's write a version of `run_simulation1` where the number of deaths is proportional to the size of the population, but the number of births is constant. This model doesn't make a lot of sense, either, but it's a good exercise.\n", + "\n", + "Write a function called `run_simulation1b` that implements a model where the number of births is constant, but the number of deaths is proportional to the current size of the population. Set the death rate to `0.01`, which means that 1% of the population dies each year; then choose the number of annual births to make the model fit the data as well as you can.\n", + "\n", + "Hint: It probably won't fit very well." + ] + }, + { + "cell_type": "code", + "execution_count": 40, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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jdHV1sbOzw8TEBCtjK770/y+hxGBubkD//s3Q0akdd/1QySmdr127xtmzZ8nJ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\nV67cwfnzpcgpLoXblLso18mEXPGgjeEjjOAz3BMrnl6AIGe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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Solution goes here\n", + "def run_simulation1(system, death_prop):\n", + " \"\"\"Runs the constant growth model.\n", + " \n", + " Adds TimeSeries to `system` as `results`.\n", + " \n", + " system: system object\n", + " \"\"\"\n", + " results = TimeSeries()\n", + " results[system.t0] = system.p0\n", + " for t in linrange(system.t0, system.t_end):\n", + " results[t+1] = (1-death_prop) * results[t] + system.annual_growth\n", + " system.results = results\n", + "run_simulation1(system, 0.00001)\n", + "plot_results(system, title='Constant growth model')" + ] + }, + { + "cell_type": "code", + "execution_count": 41, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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Pli1bRosWLZg1a1aV5zt79izz58/n2LFjvPbaa3z//ffo6+s3xGU2CjLpYW9wBKGRSE9P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\nQWtrK+7fv4/W1lbU1tbi0qVL2LVrF5qamhAQEIDVq1fD0tKSW9zI0tK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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Solution goes here\n", + "def run_simulation1b(system, death_prop):\n", + " \"\"\"Runs the constant growth model.\n", + " \n", + " Adds TimeSeries to `system` as `results`.\n", + " \n", + " system: system object\n", + " \"\"\"\n", + " results = TimeSeries()\n", + " results[system.t0] = system.p0\n", + " for t in linrange(system.t0, system.t_end):\n", + " results[t+1] = (1-death_prop) * results[t] + 0.12\n", + " system.results = results\n", + "run_simulation1b(system, 0.01)\n", + "plot_results(system, title='Constant growth model')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Proportional death, proportional birth" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now let's get to a more realistic model where the number of births and deaths is proportional to the current population." + ] + }, + { + "cell_type": "code", + "execution_count": 42, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def run_simulation2(system):\n", + " \"\"\"Runs the constant growth model.\n", + " \n", + " Adds TimeSeries to `system` as `results`.\n", + " \n", + " system: system object\n", + " \"\"\"\n", + " results = TimeSeries()\n", + " results[system.t0] = system.p0\n", + " for t in linrange(system.t0, system.t_end):\n", + " births = system.birth_rate * results[t]\n", + " deaths = system.death_rate * results[t]\n", + " results[t+1] = results[t] + births - deaths\n", + " system.results = results" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "I kept the death rate at 1% and chose the birth rate to fit the data." + ] + }, + { + "cell_type": "code", + "execution_count": 43, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "system.death_rate = 0.01\n", + "system.birth_rate = 0.027" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here's what it looks like." + ] + }, + { + "cell_type": "code", + "execution_count": 44, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Saving figure to file chap03-fig03.pdf\n" + ] + }, + { + "data": { + "image/png": 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ixURERIjVuYRGr7i4mKKiIkrKS4jPiueO3h2yNQuQFVbMvdPXsS8vub2ErpYu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\n62Hp0fuAhBAySAzZ4l9SUoWTP6Tg2vUyKA1bYGCugAoqrl1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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "run_simulation2(system)\n", + "plot_results(system, title='Proportional model')\n", + "savefig('chap03-fig03.pdf')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The model fits the data pretty well for the first 20 years, but not so well after that." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Exercise:** In this implementation, we compute the number of deaths and births separately, but since they are both proportional to the current population, we can combine them.\n", + "\n", + "Write a function called `run_simulation2b` that implements a model with a single parameter, `alpha`, that represents the net growth rate, which is the difference between the birth and death rates. For example, if `alpha=0.01`, the population should grow by 1% per year.\n", + "\n", + "Choose the value of `alpha` that fits the data best." + ] + }, + { + "cell_type": "code", + "execution_count": 45, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "# Solution goes here\n", + "def run_simulation2b(system, alpha):\n", + " results = TimeSeries()\n", + " results[system.t0] = system.p0\n", + " for t in linrange(system.t0, system.t_end):\n", + " change = alpha * results[t]\n", + " results[t+1] = results[t] + change\n", + " system.results = results\n", + " return system.results\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 46, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Saving figure to file chap03-fig03.pdf\n" + ] + }, + { + "data": { + "image/png": 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88cUXZe5j2rRp+Pj4MHz4cCZPnoydnR0xMTGsWbOG+Ph4ZXORr68vO3bsYNq0\naYwbN46CggLmzp1LRkZGiaae0mhpaXHt2jUuXLjAzJkzMTY2JigoCG1tbeUXlrOzM7t376ZVq1YU\nFRWxcOFC5QVG7dq1OXnyJFFRUXzyySfo6emxf/9+DA0Nady48QueaUGoGDKZjOEthiPP0uHiLhM0\nFNro62uTn1+Int7r17xdZvJXN/E/TiaTMWjQoGeul5CQQO3atctdf1XWpEkTduzYwerVqxk1ahQ5\nOTnUq1ePvn37qnSF1dDQYMOGDWzatImtW7cyb948ZDIZTZs2ZcGCBfTs2bPMfdSrV4+ffvqJ9evX\ns2DBAhISEjA2Nsbd3Z358+djaWkJgJmZGVu2bGHp0qV4e3tTo0YN2rRpw4oVK9Ruclm2bBkLFixg\n/PjxZGdnY2dnx5o1a7CysgIePnMwe/ZsvLy8qFu3LlOmTCE+Pl55jOvXr2fRokWMGDGCgoICWrRo\nwebNm5/5q0MQXoX0vHSCbgfh3dwbHc1HfxN62np84DmSw/n30dXVxMPD4pX12y8vmVTcSKuGW7du\nkZubW+qNSVdX15ca2OOio6Pp1q0bR44cwcLCosL2IwiC8Cwh8SFsu7yNzIJM6uY2Z6z7aKytX7+L\n2WflTbW6eoaGhjJlyhRiY2NLLJMkCZlMpvIAjyAIQlUjL5Kz78Y+joUfo0BeRNjtVE6l/El2qBWL\nZ/ZHR0ezskMsF7WS//z589HQ0GDhwoXUq1dP7e56giAIVUFsZiwbgzcSm/nwArioSCI3TZsW2X3I\nSdfn8OH79Ov3ZnVgUSv5X7t2jW+++Ybu3btXdDyCIAivDUmSOBFxgr3X96qMyNnOujWj6nVn9w/h\ndOtmSc+e1pUX5HNSK/kbGxujqflm/aQRBEF4EZn5mXx/5XtC4kMoUkhoasjQ1tTGu7k3HpYPB6K0\ntzanUaNnPzX/OlIr+b/33nts2LCBtm3bVtg4PIIgCK+LhOwEvv7na9Lz04mMzOTBg2z6e7oyse14\n6teqr1zvTU38oGbyj4mJ4c6dO3Ts2BF7e/sSXwAymYzNmzdXSICCIAivmqm+KfVq1uPMpXCSknNp\nmO+MeVg/6nWvV9mhvTRqJf/w8HCaNn00p2Tx+C2CIAhVkYZMg/dd3udOdBxJkfYYF1qTmy2Rn19E\njRqvdA6sCqPWUZQ1XowgCMKbTpIkguOCca3viobsUU9GIz0j1np9zR5uUauWDr16NUZD4/V8YOt5\nlOsr7M7kSqFkAAAgAElEQVSdO5w7d46srCyMjIxo1aoVNjY2FRWbIAhChcrIz2Db5W2EJoTiVKMz\n3i4DMTXVVy6XyWR4ezd9Sg1vLrWSv0KhYNasWezbt4/HHwiWyWQMHDiQhQsXvraPML8punbtypAh\nQ5g4ceJTlxU/tde3b1++/fbbEus6ODiwZMkSBg4cWGJZ8baPq1GjBtbW1nh7e+Pj46N8H/fv38/0\n6dPLjHfFihX07t0beDjM88qVKzl79ixZWVnUr1+fHj16MHHixBKzhsHDQQOPHz/O7t27y5xcRhAq\n2pUHV9gesp203AzCw9P4O3YHUcEGzP+8f5W6wi+LWsl/w4YN/Pzzz/j7+9O/f39MTU1JTEwkKCiI\nlStXYmtrKyZgf8V+/fVX+vXr91zPXqxdu5aWLVsiSRKZmZkcO3aMRYsWER0drTKBi6amJidOnCi1\njuKxmRITE/Hx8aF79+5s2bKFWrVqcevWLRYuXEhoaCjff/+9ynaJiYmcOnUKa2trfvrpJ5H8hVcu\nvzCfPdf38HfE3wDk5siJi8umYb4rSeHaHD0aSffuVpUcZcVTK/nv3buXCRMmMHbsWGVZvXr18PPz\nIz8/n71794rk/4o1atSI2bNn4+bmVu5B8mrXro2ZmRkAdevWxdbWFi0tLRYvXszgwYNp0uTRDEPF\n65Xl999/Bx4+BV7MwsICAwMDRo0axc2bN1U6Cxw8eJC6desyfPhwvv32W2bMmFHqrwNBqAj30+6z\n+eJmErIfTaBuYVqXjq2HcfkvGc7OdWnTpv5Taqg61BqnITExkVatWpW6zNXVlbi4VzN/rfDIZ599\nhlwuZ+HChS+lPi8vL3R0dPjtt9/KtZ2GhgaZmZkEBwerlLu5uXHo0KESQzD//PPPtG3blh49epCb\nm8vBgwdfOHZBeBaFpOCX27+w+NRi4rPjleWu9V2Z1WkW4wf3ZMIEJyZMcKJWreoxWZBaV/6NGjXi\n0qVLtGvXrsSyS5cuPfPqsLIE3Qri0O1Daq3rYeWBb0tflbIfQn5Q/jR8lrft36a/Q/9yx/i8TExM\nmD59OlOnTqVv3754enq+UH0GBgZYWFhw+/btcm3Xr18/Nm/ejI+PD82bN6dNmza0adOGtm3bYmdn\np7Lu1atXuX37Nv7+/tSvXx9nZ2f27NmDj4/PC8UuCE+TnpfOugvruJt6lwcPsnnwIJs2rpYMd/Kh\nTcM2yvtcLi7mlRzpq6XWlf+QIUNYt24dW7duJSEhAYVCQUJCAlu2bGH9+vW8++67FR2nUIp33nmH\nzp07M2vWrDKngCyPJ6eSLCoqwsXFpcS/rl27KtepU6cO+/btY9y4cWRnZxMQEMD48ePp0KEDu3bt\nUqk/MDAQQ0ND2rdvDzz84rh+/TohISEvHLsglEVfW5/cwlxu3UwhLCwNWZopLVLfo61F22rdUUWt\nK/8RI0Zw48YNFi1axOLFi5XlkiQxYMAAPvjggwoLsLoo7wTuxebMmUO/fv1YsmQJc+fOfaEYsrKy\nVH7FaWpqljoz25OjuhoZGeHv74+/vz+xsbGcPn2anTt3Mnv2bBo0aECnTp0oKCjgl19+oVu3bsoJ\nYXr37s2CBQv46aefxNSMQoXR1tRmjMsYQu/OQj/KhUb5rYi7K1FQUPTGDcP8MqmV/DU1NVm8eDFj\nx47l/PnzZGRkYGhoiJubW4mf9q+T/g79X6gpxrelb4mmoIqi7gTuT6pXrx5Tp05l1qxZ9O3b97n3\nn5ubS3h4OP369VMpL555qywbNmzAysqKXr16AdCgQQOGDBnCgAED6N27NydOnKBTp04cPXqUtLQ0\nDhw4oNLOr1Ao+PXXX5k+fbq48Su8FHdT7mJjZKNyVd+odiO2+K5ke/4dTE31GDTIDm3t6pv4oZwP\nednZ2b3Wyf5Npu4E7qXx9vbm119/ZebMmc+9/z179qBQKMr9BRISEsJvv/1G9+7dVUZ+1dHRQU9P\nTzmhfGBgIObm5mzatEll++DgYGbPnk1QUBDvvffec8cvCLnyXH669hP/Rv2LZ52BDHTpTs2aj27e\n1tKtxYQJztWiD786ykz+vXr1YsWKFTRt2pSePXs+s23sjz/+eOnBVSfqTuBelnnz5tG/v3q/ctLT\n00lMTESSJDIyMjh58iTLly9n3Lhxynl8iyUmJpZah56eHjVr1mTSpEn4+Pgwbtw4xo4di6WlJXFx\ncQQGBpKens7QoUOVffsnTZqEvb29Sj22trZs3LiRPXv2iOQvPLdbSbfYenkridlJhN9L55/YDTwI\n1eeTCZ1UcpdI/I+UmfxdXV0xMDBQ/r863xh5FdSdwL0sFhYW+Pv789VXXz1z3cefIq5Tpw62trZ8\n9dVXJZ4KLioqomPHjqXWMXz4cGbNmkWzZs346aef+O677/jss89IS0vD0NCQDh068OOPP2Jqasrm\nzZv//zF57xL1aGpqMnLkSBYuXMjVq1ef+gtHEJ4kL5ITeDOQI/eOAJCRUUBsXDZ1Cx24fiWDCxce\n4OZWPfrtl1e5JnCvLGICd0EQnhSRFkHApQAeZD1QlhnoGFAnqi0x5+vg7FwXX9+3qk2//Sc99wTu\n8fHxZS0qlbl59eojKwhC5ShSFPFr2K/8GvYrRVIRMh62SjSv25yRTiPRk9UkxCmR1q3riRaLpygz\n+Xfq1KlcJ+7GjRsvJSBBEISyJOUksSF4A/dT7xMVlUlaWj6tXRri1dwLD0sPZc4STT3PVmbyX7Bg\ngfjWFAThtaKvrU9abhpXQhLJyCigdmEDPKTReFqVPvyMULYyk794alcQhNeNvrY+I51Hcu3OIkwT\n3GmY70L0LQmpryQuVsupzOS/bt06tSuRyWSMHz/+pQQkCIIAD0cQuJNyBzsT1WeLHOs6sn3UKjat\nCcPJyYwePaxF4n8OZSb/5cuXq12JSP6CILxMqbmpbA/ZTmhCKF30fBjs6aEyFIOxgRGffuom+u2/\ngDKT/82bN19lHIIgCEiSxNmYs/wY+iNp2VmE3U7lXPJaCpNqM2KYi8q6IvG/mKoxDb0gCG+8jPwM\ndoTs4PKDywCkpeaRmppHQ7kLJ4/F0baVNXZ2RpUcZdUhhncQBKHSXYy7yI6QHWQVPBrc8K3GlrTI\nGkLiTQO6dbfE2tqwEiOsesTwDoIgVJrsgmx2he7ifMx5JOlRj51O1p0Y3Gwwea0hPj4be3vjSo60\n6ikz+T8+PeCiRYte6k737NnDpk2biIuLo0mTJnz22WelzhImvFwXLlxg+PDhag+TsX//fmbOnMn1\n69dfQXRCdXM35S7rLqwjJTuNu/fSUBRJtHOxZZTzKN4yewsA3dpQu7ZuJUdaNand5q9QKDh27BjB\nwcFkZWVhYmKCu7t7uZN2YGAgc+bMUU4+vnPnTiZOnEhQUJAYt0cQqpE6NeqQnZ9H8MV48vOLqFfw\nFm97juMtM9vKDq1aUCv5JyUlMXbsWG7evImOjg7GxsYkJyezbt062rVrx+rVq9HX139mPZIksWrV\nKvz8/BgyZAgAU6dO5cyZM1y6dEkkf0GoRkz0TfBxGsr9u5vRD2uDSaENMffl0LayI6se1JrDd9Gi\nRSQmJrJx40ZCQkI4fvw4V69eZdWqVVy7dk1lasenuXfvHjExMSoThmhoaHDgwAG1x6KvqhwcHNiz\nZw/Dhg2jRYsW9O3bl8uXL7Nz5046deqEq6srn3zyCQUFBcptLly4gK+vLy4uLrRv35558+aRm5ur\nXH7z5k18fX1xcnLi7bff5tq1ayr7VCgUrFu3ji5duuDs7MzgwYM5ceLEKztmofrIL8wnNCG0RHmH\nRh34YcwKWlm4MGGCE8OGNa2E6Konta78jx07xpdffomHh4dKeffu3UlJSWHp0qXMmTPnmfXcv38f\ngIyMDEaOHElYWBg2Njb4+/vj6upa/uif4datW9y+fVutda2srErMIxsSEkJERIRa29vb2+Pg4FDu\nGB/3zTffMH/+fKytrZk2bRrjxo2jRYsWbNy4kfDwcPz9/WndujU+Pj5cuXKF0aNHM2LECObMmUN0\ndDSzZ88mOjqadevWkZ6ezujRo2nbti379u3j/v37fPnllyr7W7ZsGYcPH2bu3LlYWlry999/8+GH\nH7Jp0ybatGnzQsciCMXCksPYenkrSdnJdNEehXevtso++jKZDONahkyb5i46lbxiaiV/HR0datWq\nVeqyBg0aqL2z4jlqp02bxuTJk7GxsWHPnj2MGjWKn3/+GVvb6t3W5+3tTdeuXQEYOHAgc+fOZfbs\n2TRq1Ah7e3s2bdpEWFgYAAEBATg6OjJ16lTg4YxYs2fPZty4cYSFhXH+/Hnkcjnz58/HwMCAJk2a\nEB8fr5zkPTs7m++//55Vq1Ypv9StrKy4efMmGzZsEMlfeGHyIjk/3/yZI+FHyMjM59atFIIzv6O2\nhhl9ejVRWVck/ldPreT/3nvvsWLFCpycnDA1NVWW5+TksGHDBry8vNTamba2NgATJkxQNvO89dZb\nBAcHs2vXrheag7YqeHwKRT09PTQ0NFTug9SoUUPZ7BMWFkanTp1Utm/durVyWVhYGI0bN1Z21wVw\ndnZW/v/u3bsUFBQwZcoUNDQetf7J5XKV91gQnsf9tPtsubRFOdFKSkoeBdmaNMlvTdDBcNxaNcDU\n9Nn3CYWKU2byf//995X/lySJu3fv0r17d1xdXTExMSEjI4OLFy9SWFhI3bp11dpZ8XqPz+Mqk8mw\nsbEhOjr6eY+hTA4ODi/UFNOyZcsSTUEVSUtL9e2QyWRlXhHVqFGjRFnxpGxaWlrIZDKenKSt+MsX\nHv6aA1i1ahVWVlYq6z3+ZSAI5VGoKOSX27/w+53fUUgKZXlv17Ykpb5FRr4GQ4bYY2KiV4lRCvCU\n5C+Xy1VeF7fJy+VyHjx4+G3etOnDmzMJCQlq7ax58+bo6+urzNVa/MUi+vmXj62tLZcuXVIpCw4O\nVi5LT09XTqJeu3ZtAEJDH91ws7KyQltbm/j4eDw9PZXlq1evpqioiClTpryCoxCqktjMWAIuBRCZ\nHokkgYZMhq6WLl5vedHRsiMJNjloaMgwMxNX/K+DMpP/9u3bX/rO9PT0GDVqFMuXL8fU1BR7e3t2\n7txJZGQkK1eufOn7q8r8/PwYNGgQixcvxsvLi5iYGObMmUOnTp2wtbXF3NycNWvW8Pnnn+Pv7098\nfLzKOdbT02P06NEsW7YMAwMDWrRowbFjx1izZg3z58+vxCMT3kRnos+w/cp2snLzuH0rlZo1tent\n5s4o51GY6j9sRjQ3N3hGLcKrVGbyDw4OplWr8s+Oc+HCBWXbc2mmTJmCnp4eCxYsIDk5mWbNmhEQ\nEICNjU2591Wd2dvbs27dOpYvX8727dupU6cO/fr14+OPPwagZs2abNu2jblz5+Ll5UXdunXx8/NT\n3vAF+Pjjj9HW1mbJkiUkJSXRqFEj5s6dKybyEcqtfs36ZOXkc/FiPIoiDYwfuNOv12hM9U0qOzSh\nDDLpyYbh/zdgwABsbW354IMPVNroyxISEsLGjRu5f/8+QUFBLzXIZ81CLwhC5Tt06xDrD/xOnfAO\nGEimeHnZ062b1bM3FCrEs/JmmVf++/btY/Xq1QwePBhra2t69uxJy5YtsbCwQE9Pj4yMDOLj4wkO\nDubkyZOEh4fj6+vLsmXLKvSABEGoXNkF2cRkxmBvonpR2Ne+L+39urJxw1W8vBywsalTSREK6ijz\nyr9YfHw8W7du5dChQyQmJqr0PpEkiQYNGtCrVy9Gjx6Nubl5hQQprvwF4fVwPfE6Wy9vJU+eT7+a\nfvTydCyxzuOjcwqV57mv/IuZm5szdepUpk6dyt27d4mOjiYzMxMjIyMaNGhA48aNKyRwQRBeH/Ii\nOftv7Odo+FGys+XcuJnM+YyVGNWYjbu76oOeIvG/Gco1k5etrW21fwpXEKqb2MxYNgZvJDYzFoCY\n2CwKs7WxyW/Fzp03adrUBENDMezym0ZM4ygIQqkkSeL4/ePsvb6XQkWhsnxg245E/+JAfp4Wgwfb\nU6uWTiVGKTwvkfwFQSghMz+TbVe2cTX+qrJMW1Mb7+beeFh6EGWRia6upui7/wYTyV8QBBU3Em8Q\ncCmAtNx07oWnoaenTZumTRnrOpb6teoDYGkp5tN904nkLwiCivyifBIzUrgamkROTiGWha6M7Psh\n9WsZVXZowkskRvASBEGFcz1nutt1RU+jJo7ZA7HO9uDCucTKDkt4ydS68s/Pz2f9+vUcP36cnJyc\nEqNFAvzxxx8vPThBECpedkE2BjqqbfdDHb1pY9SVdStu8s47dnTs2LCSohMqilrJf/78+ezZswd3\nd3fs7OzEkL+CUAUUFBXwU+hPXE+8zvhmn2Dd0Ey5TFtTGzvL+ixYYIaurmgdrorUelf/+OMP/vvf\n/zJu3LiKjkcQhFcgLjOODcEbiE6PITw8nX9+ncemCf/D3t5YZT2R+KsutS7hCwoKXumkJoIgVJx/\no/5lwd8LiM2M5e69NGJis5BJGmwKuExOjvzZFQhVglpf6x07duTkyZO0bdu2ouMRBKGC5Bfm82Po\nj5yOOq0ss7U2xjS2A3VymtLY3rjU+3lC1aRW8h8wYAAzZ84kNTUVV1fXUqcQLJ6TVxCE18+DrAes\nv7BeOUQDQL2a9RjXahzJtjqkpeXh4WEhxuWpRtRK/h999BEAgYGBBAYGllguk8lE8heE19T5mPNs\nD9lOUmoGhYUSRkY1aGvRFp8WPuhq6dJQtOhWS2ol/yNHjlR0HIIgVIAbiTfYeHEjsTFZ3AtPR0dT\nm4XDR9GnedfKDk2oZGol/4YNH/XxzcnJITs7mzp16qCtrV1hgQmC8OKamjalmZEj587+RY2iOjTL\n6Ev4CSNoXtmRCZVN7X5cZ8+eZenSpVy7dk15U6hly5Z8/PHHtGvXrsICFATh+clkMsa3GQt5+lzf\nVw8bSzO8vR0qOyzhNaBW8j9//jxjxoyhcePGTJ48GRMTExISEvj999/x8/Nj69atT520XRCEiidJ\nEmdjzuLWwA1NDU1lub62Pv/tPpYbDZOxszNCS0s8pCmomfxXrFhBu3bt2LBhg0pvgIkTJzJu3DhW\nrVrFtm3bKixIQRCeLleey9bLWzkfFUxA1N/MHTqRevVUh2xo1sykkqITXkdqXQKEhoYyfPjwEt3A\nZDIZw4cP5+rVq2VsKQhCRYvLjGPhqYWcuH2W4IsJ/B1znPkbfkYuL6rs0ITXmFrJ39DQkJycnFKX\nZWdno6mpWeoyQRAq1pUHV1h0ahHxWfFoaWpQWKigYb4zeTHGXLuWXNnhCa8xtZJ/27ZtWbVqFfHx\n8Srl8fHxrFq1StzwFYRXTJIkfrn9C2vPryWvMA8AI0MDPmo/HmftHnw82Q1n57qVHKXwOlOrzd/f\n35/BgwfTq1cvWrVqhampKUlJSQQHB1OzZk0+++yzio5TEIT/l1eYx9bLW7kYdxEZD5tiTfRNmOg2\nkYa1GpLTTY6BgZhXV3g6tZK/ubk5gYGBBAQEEBwcTHR0NIaGhvj4+PCf//wHMzOzZ1ciCMILS8pJ\nYvW51QTfDuNBXDZOTmY0N38Lv1Z+1NSpCSASv6AWtfv5m5mZMXXq1IqMRRCEZ9h6eSsnL10nLi4b\nANl9OyYPmKzStVMQ1FFm8l+3bh3vvvsudevWZd26dU+tRCaTMX78+JcenCAIqkY5jSL49m3i4/Kw\ny+mKVVYb8vMU6OuL5C+UT5nJf/ny5bRv3566deuyfPnyp1Yikr8gvBpmBmb87+1P+EMjijpSfXx8\nmqGtLRK/UH5lJv+bN2+W+n9BEF6NjPwMwlPu42D0FjVqPPpTbWraFHtfBzQ0xPDLwvNTq6vn6tWr\nS3TzLBYTE8O8efNealCCUN1FpUfxv7++4oOAr1i47tcSk6yIxC+8KLWS/5o1a8pM/pcvX+ann356\nqUEJQnUWHBvM/BMLOfrvLVLTczgQ/QNBv9yu7LCEKqbMZp/33nuPy5cvAw8fKBk6dGiZlbRo0ULt\nHd65c4d+/fqVKN+xY4cYHE6o1iRJ4tDtQxy6fQhkYG6uT1xkPvZ5PdDREt03hZerzOQ/b948/vzz\nTyRJYuXKlXh7e1OvXj2VdTQ1NalVqxbdu3dXe4e3b9/GyMiIoKAglfI6deqUM3RBqDryC/OVD24V\nc3+rCbW1uvB2Z2cxKJvw0pWZ/G1tbfnggw8AUCgUeHl5YW5u/sI7vH37Nk2aNBEPhgnC/0vOSebr\n48tJKYpXPrHbzKwZfq5+GHQzeMbWgvB81HrI68MPPwQgNTUVuVyuvPkkSRI5OTkEBwfj5eWl1g7D\nwsKwsbF5znAFoWoJSw7jf4eWEXIjmgYNa9LYujZdGnfBu7k3GjIx7r5QcdRK/rdu3eLTTz/lzp07\npS6XyWTlSv75+fl4e3sTExODnZ0dn3zyCS1bilmkheolIz+DWb8u4vK1BwDERGXj09yXYY5vV3Jk\nQnWg1qXFkiVLSEtLY+rUqbi7u9OxY0e+/PJLOnXqhEwm4/vvv1drZ3l5eURFRZGVlcXnn3/Od999\nR926dfH19eXu3bsvdCCC8KYx1DVkbAcfjI1roCPp0aWGLz2bdq7ssIQ3zJPdgNWl1pX/5cuXmT59\nOkOGDEFPT4+goCB8fHzw8fFh8uTJbN++Xa2eOjVq1OD8+fPo6Oigo/Ow98KiRYu4du0aO3fu5Msv\nv3yugxCEN1XXxl3J6JdNckhdfAe3VnmYSxDKIkkSKSkp3Lt3Dw0NDVq1alXuOtT6pBUUFGBtbQ2A\ntbW1yhO/7777Lv/73//U3mHNmjVVXmtoaNCkSRPi4uLUrkMQ3kS3EsOIDiukW/tmyjKZTMagFgNA\n/d7SQjUXFxfH7du3ycjIAB5+hnJzc9HT0ytXPWo1+zRo0IDo6GjgYfLPysoiJiYGAF1dXdLT09Xa\nWWhoKK6uroSGhirLioqKuHnzJnZ2duUKXBDeJAdD/mTUumlM37eEf89GVnY4whssJydHmfjh4a+A\nhISEctejVvLv3r07S5cu5fDhw5ibm2NjY8OKFSu4e/cuW7dupVGjRmrtrGnTpjRs2JBZs2Zx5coV\nwsLCmD59OqmpqYwcObLcwQvC605eJOf7K9+z/K9NpGfmkamZwJw9G0hJya3s0ITXnCRJKkm+mKWl\nJZqammhqamJlZUXnzp2xsrIqd/1qd/WMiIhg9+7d9OjRg+nTp/Phhx8SFBSEpqYm33zzjXo709Ji\n06ZNLFmyhAkTJpCbm4urqys//PADJibiIRahaknKSWLdhXVEpUdhY1ObtPR8tLKNGNdtCEZGNSo7\nPOE1VVRURGxsLOHh4aSnp+Pp6Unt2rWVy7W1tXFzc6NOnTpoa2s/935kUjluFRcUFChv1EZGRnLt\n2jWaN2+OpaXlcwegjujoaLp168aRI0ewsLCo0H0JwssQEh/ClktbyJHnKMvsDJzobzkEhyZibl2h\npNzcXO7fv09kZCQFBQXKcktLS5ycnMpd37PyZrm6FhQn/uKAKjrpC8KbpkhRxML9WziXcoz69R92\nbtDS0GKo41A8LD2QycRonMIjkiSRnJzM/fv3efDgQYlum5qammhoVMzDfmUm/549e5brg/rHH3+8\nlIAE4U31IDWZSZsXcD3hJhoaMmoZ6tDI1JwJrSdgXce6ssMTXiOFhYVER0dz//59MjMzSyzX19fH\nysoKS0tLlYvul6nM5O/q6iquUgShHM48OEVU7sOHFRUKCXmsKTPfnamcWF0QiuXk5HD16tUS5aam\npjRu3Bhzc/MKz79lJv9FixZV6I4Foarp7/A2F9xCOHDiHH1s+/LVyLHo6jz/DTmhapAkCYVCgabm\no+k2DQ0NMTExITk5GS0tLSwsLLC2tqZWrVqvLC612vwvXrz4zHVcXV1fOBhBeJOkp+dTu7au8rWm\nhib+nT5kgEMk7o3Lf4NOqFry8vKIjIwkIiKCxo0b06RJE5XldnZ21K9fn0aNGqGl9eqf7FZrjz4+\nPs/8CXLjxo2XEpAgvO4kSWLTgb/Y9fcfrPWbTtOmj7opG+kZ4d7YqBKjEypT8bAL9+/fJy4uTnkD\nNyIiAltbW5U8amZmVqlD26uV/EsbuC0nJ4cLFy5w4MABVq1a9dIDE4TXUZGiiC+2r+PgtV+RNGHW\nti1smTkZAwMx01Z1JpfLiY6OJiIiotQbuEVFRWRnZ5cY3qYyqZX83d3dSy3v3Lkz+vr6fPfdd6xf\nv/6lBiYIr5vknGQ2XdxEfM0wtLQ1kMsVJBiEkJWbJ5J/NZWWlkZERAQxMTEUFRWVWG5sbIy1tTX1\n69evsC6bz+uFG5pat27Nxo0bX0YsgvDauhB7gR9CfiBXnouOjib29kbUkVvytc+nGOkbVnZ4QiWQ\nJIng4GBycnJUyotv4FpZWWFo+Pp+Nl44+R87dgwDAzHVnFA1hYUnsPv6T0QqHg1GqCHTwK/DcHra\nlu9ZGOHNVlRUpNJjRyaTYWlpqRzl2NDQEGtraxo2bFgpN3DLS60I33///RJlRUVFPHjwgMjISPz8\n/F56YIJQmSRJ4odD/7D85FoKtDNp5VoXXV0tTPVNGeM6BhsjMRVpdVBUVERcXBwRERHIZDLat2+v\nstzS0pKsrCysra2pU6fOG3UxoFbyl8vlJcpkMhm2traMHTuWwYMHv/TABKEyXYy+wrfnl5Irk0Mh\nhN1JY0yvfvi08KGGlhiUrarLzMwkIiKC6OholfyXlZWlctNWV1cXFxeXygjxhamV/Ldv317RcQjC\na6V5/aa0d7Lj6Nnr1KlVk5l9P6BPy86VHZZQgR6/yk9JSSmxXCaTkZqa+lr12HkR5WqYOnHiBMHB\nwaSnp2Nqakrbtm1xc3OrqNgEodLU0KrBp90moa+5Df9uH2BeS4zEWVWVdZVfrHicnUaNGqGrq1tK\nDW8mtZJ/amoqfn5+hIaGoqOjg7GxMcnJyaxdu5YOHTqwZs2aKnVShOolOj6ZRdv38sXw4cqROAGs\n67u8Y28AACAASURBVFizeOCsN6odVyi/8PBwIiIiVMpkMhn16tXDysoKU1PTKvkZUCv5z5s3j+jo\naNatW0fnzp2V5UeOHOGLL75g6dKlfPHFFxUVoyBUmJ9P/cO8Q6vIVmRSsEGLNTNGo62t2qNDqBok\nSSI3Nxd9fX2VcktLS2XyNzAwwNLSsspd5ZdGreR/8uRJZsyYoZL4Abp160ZKSgrffvutSP7CG6Wg\nqID9N/bza9xhcskC4Ez2L1y53oPWTmKeiqqkoKCAmJgYIiMjycrKomfPniozYNWuXZsmTZpgZmaG\niYlJtfnCVyv5a2pqljnanJmZWantZILwugpPDWfL5S3EZ8WjV0MLaytDUh4omNF/okj8VUTxJCmR\nkZHExcWhUCiUy6Kjo2ncuLHytUwmo1mzZpURZqVSe2C3b7/9lhYtWmBubq4sz8rKYsOGDfj6+lZY\ngILwsoRHpPDb3V+5mvMPCulRMujj2p73mg/HpKYYkO1Nl5ubS1RUFFFRUSWevIWHF7LiYvUhtZJ/\nQkICCQkJ9OjRg1atWlG3bl3S0tK4ePEi2dnZ6OjoKB8Ek8lkbN68uUKDFoTyKCxU8P2Bf1j37yYK\naqTSqpU5Wloa6GrpMrT5UNo3al9tfupXVSkpKYSFhZGYmFhiKkSAOnXqYGlp+cY8ffsqqHUWIiIi\naNq0KfBw+rHY2FgAZVlRUVGpgxoJwuvgbMQFVl5cSr5GIRRA+P10+rZxZ7TzaEz1TSs7POElyM/P\nJyEhQaVMW1sbCwsLLC0tX+sxdiqLeMhLqPJaWjTDsWl9gq9GYVxbn4mdRjLYpZ+42n8DFRQUEBsb\ni6Wlpcoomebm5ujq6lJQUICpqSmWlpaYm5urjMUjqCrX7587d+5w7tw5srKyMDIyolWrVtjYiDFO\nhNdLRkY+hoaPuunV0q3FJ93HsV0vkKm9JlGvVr1KjE4oL0mSSEhIICoqivj4eBQKBTVq1KBevUfv\no4aGBi4uLhgYGJToyimUTq3kr1AomDVrFvv27VNpT5PJZAwcOJCFCxeKqyih0uXmytn40ymOXj3P\n5hkfYWKip1zmWt8Vl8Eu4nP6BsnMzCQqKoro6Gjy8/NVlkVFRakkf6BSZ8V6E6mV/Dds2MDPP/+M\nv78//fv3x9TUlMTERIKCgli5ciW2trZiZE+hUhUpivh4zVpOJfyFQlPB8u12zJ3yjkqyF4n/9Vfc\nrBMVFUVaWlqp6xgZGan0OhSej1rJf+/evUyYMIGxY8cqy+rVq4efnx/5+fns3btXJH+h0kRnRLPt\n8jYyGoQhJTzswnlR/jsFBf3R1RU9O94UCQkJnD9/XqVPfjFdXV0sLCxo1KhRmc8cCeWj1l9GYmLi\n/7V351FNXfsewL8JSZiHTIRRFBQcUAahMkmd6qxV22qdWr1Wbe261tcub6213vda29pWq9ZqW32t\nxaodXFWr9WkHx0odABEnRFERREIG5iEBkv3+4HI0AhoVkmB+n7VYt559OPn9LuHHzj777I2+ffu2\n2BYdHY0NGza0aVCEmMNgNGB/7n7svbIXBqMBHu6O6BTkga6yYCwe8SoVfhvWNHx856cxLy8vk3P4\nfD4UCgUCAwPh7e1Nn9zamFm/HYGBgcjMzER8fHyztszMTBprIxalVFZj3XeHUBN6AlV8NXdcwBfg\nv4bNwFMhT4HPs639UkkjnU6HwsJC3Lx5ExERESYFXyQSQaFQoLa2FoGBgfDz84NIRHsjtxeziv+z\nzz6LTz/9FC4uLhg5ciRkMhk0Gg327t2Lr776CnPnzm3vOAkBABw/WYBlP6TguvAEXGoEiI5q7BEG\ni4PxYuSL8HGjmTy2pmnXv5s3b5o8hFVQUNCstx8VFUXTMy3ErOI/ffp0ZGdnY/ny5fjoo4+444wx\njB07Fq+88kq7BUjInc40/I4bjifAjAw1NfWoqTLixX6TMDh4MPX2bQhjDBqNBoWFhSgqKkJDQ0Oz\nc4qLixEeHm4ynEOF33LMXtjto48+wksvvYT09HSUl5fDw8MDsbGx6NatW3vHSAjnmcgx2HfuCIrV\nlRjSNxrzk+dA4UYzP2yFTqfDtWvXUFhYCJ1O16ydx+NBKpUiICAAvr6+NI5vRQ90R8zX1xeBgYHw\n9PSERCJBYGDgI734mTNnMGXKFGzatAn9+vV7pGuRx09mZjGEQj7Cw2/fU/J29caCoTPRYGzAkBDq\n7dsag8GAq1evNjvu5uaGgIAABAQEwNnZuYXvJJZm9kNen3zyCbZs2YKGhgZuzM7Z2RmvvPIK5syZ\n88AvXFNTg3/961+0JhBpprKyDlu2XsDui3vh4eKCTUv/CReX2+uvDwoeaMXoCADU19ejqKgIcrnc\npJi7urpCLBajtLQUjo6O8PPzQ0BAADw9PamXb2PMKv5r167F5s2b8cILL2DYsGGQSqXQaDTYv38/\nPvvsM7i6umLq1KkP9MLLly+HQqFotn0aIaraImzLXweNUxH4Rgds2RWLOVP6Wzssu2c0GlFcXIzC\nwkJumYXu3bs3G/oNDQ0FYwxyudxk/R1iW8x+yGvevHl49dVXuWOBgYHcWhopKSkPVPyPHDmCw4cP\nY+PGjRg7duyDR00eS0ZmxB9X/8DunN3w7lYHTTbg7eMEQeg1AFT8raFpU5SmG7d3r4V/8+ZNdO3a\n1aRX7+1Nm913BGYV/6qqKvTp06fFtr59++Kbb74x+wVLSkrw9ttv44MPPoCnp6fZ30ceT4wxKJXV\n4LtXY9OZTbheeh0AIJM544kYP0yJfhZPhTxl5SjtC2MM5eXlKCwsxK1bt1q8cQs0bn/o7+8PxhgN\n6XRAZhX/AQMG4IcffkD//s17X3v37kVycrLZL/jvf/8bgwYNQnJyMpRKpfmRkseOVluLlJTz+Ovm\nYUiTrsJBeHvRwCCvIMwcMBO+7r5WjNA+lZeX46+//mqxzcXFBf7+/vD396dlFjo4s4p/TEwMVq9e\njTFjxmDUqFGQy+UoKyvD4cOHkZGRgRkzZuDLL78E0DiVq7WHvnbu3ImLFy9i9+7dbZcB6ZAYY/j0\nyyM4oP0Z5YJbEOc4IjxcBgFfgNGhozG863CayWMBtbW1EAqFJrtbeXp6wsXFhdsGsenGrb+/P7y8\nvKiX/5gwq/i/9957ABqXWF29enWz9juHfe5V/Hfs2IHi4mIkJSUBuL2+x+zZszFu3Di8++67DxY9\n6dBqex1Dxd+3wAPg5iaCv3sAZkX/AwEeAdYO7bGm1+tRVFSEwsJClJSUICIiAp063d64nsfjoVOn\nTqiqqoK/vz/kcjkV/MeQWcX/0qVLbfJiK1asMBk/VKvVmDp1KpYtW4bExMQ2eQ3SMfB4PLyaPBO5\nqjx4uDtiYvTTGNltJAR8WoytPdTV1UGpVOLWrVvQaDQm+3IUFhaaFH8A9PCmHbDob9rda3A7Ojpy\nx6VSqSVDIRZUWqrDli0XMGZMCDp3vr2WS4gkBP/11CwEi4MR5BVkxQgfTw0NDVzBV6vVLS6VzOPx\nwOfz6aatHaJuFmlXFy5o8PnG4zjH+x3nUiKx/u2ZEAhuj+UP7EIPbLWHsrIypKamtljwAUAqlcLP\nzw++vr5cJ4zYF6sWfx8fH+Tk5FgzBNKOGGO4yS7iuFMK9MZanKgqRNq5AYiPCrF2aI8Vg8HA9eCb\nuLu7g8/nmxR/Ly8v+Pv7w9fXl5ZYINTzJ+2jUl+Jbee24XTRaQR2cURhYT1CwzzQILkFgIr/ozIY\nDFCpVLh16xaKi4sRHR1tsqetg4MDfHx8UFFRAX9/f/j5+dHG5sQEFX/SZmpq6qHV1kIrvIYtZ7eg\nUl8JAPD1c0X3zgGY1Xcmusu6WznKjuvOgq9SqUyWSS4qKmq2oXlERAQtr0Ba1WrxLy4ufqAL0YbK\n9i07W4sN36bhksMh+MWWmIzr9+/UH8/1eg5OAicrRtgx3avg36mqqqrZTVsq/OReWi3+Tz755APd\n/c/Ozm6TgEjHo9c3YPmmXTjD9qOO1aAm1xndu0vh5eSF6RHTEe4dbu0QOyS1Wo20tLRWV751c3OD\nn58f/Pz84ObmRrN1yANptfh/8MEH3JupvLwcK1asQHx8PEaMGME94Xvw4EEcPnwYixYtsljAxAY5\nGMD6ZKDubA2EQj5kchfEBcRhUvgkuAhpnNkc9fX1EAgEJgXc09Oz2WydpoLv6+sLd3d3KvjkobVa\n/CdMmMD996uvvopx48Zh2bJlJueMGTMGy5Ytw759+zBp0qT2i5LYlLuHFxwFjlgw+CX8u2Yluvgp\n8FLsDPRRtLwQILmt6cGroqIiaDQaJCQkQCwWc+0ikQhSqRR6vR6+vr7UwydtyqwbvqmpqVi3bl2L\nbQMHDsT27dvbNChiu65dK8PW789j3st9IZXeni4Y7RuNN4bORqxfLFxFrlaM0LbpdDqu4Gu1WpMn\nbYuKikyKPwDExsaarLtDSFsx610lFotx9uzZFpdgOHXqFN3stROHDuXji5/347LTAdRsmogP3phg\n0gsd0HmA9YKzYTU1NVzBLy0tNSn4d593Nyr8pL2Y9c567rnnsG7dOuh0OgwePBhisRharRb79+/H\nd999h8WLF7d3nMTKauprkN7wK8677AUD8Kd6B+YWDkDnAFqW415u3LiBs2fPttouFovh6+sLX19f\nmodPLMqs4v/KK6+gsrISX3/9NTZs2MAdd3R0xGuvvfbAWziSjiVLmYWt57aiXFeOgEB3VFbWIbqX\nHHz3agBU/IHG+yAVFRXNNii6e80qHo8HqVQKX19f+Pj4wMmJpr8S6zCr+PN4PLz55puYN28eMjMz\nUVFRAbFYjKioKOqtPKauXi1DA68Wx8r+D6cKT3HHOwd5INY/FpN7T4abyM2KEVqf0WiEVqtFUVER\nlEol9Ho9Bg8ebPI74ebmBk9PTzg5OcHHxwc+Pj4QiURWjJqQRg80oOju7v5Au3aRjkena8COHVfw\n898HUSRPRa8oN/D/M67v4eiBqX2mItIn0spRWk9DQwNUKhWUSiWKi4ubPXSlVCoRHBxscqx///40\nQ4fYnFaL/9ChQx/oDfvbb7+1SUDEupRlWmzM/ApKlytANVBQwBDUyQP9AvphUq9JdjmTR6fTobi4\nGEqlEhqNptWVMkUiUYs3c6nwE1vUavGPjo6mN60dcvNwgFe3MihzAanUCaGdfPHSE/Y9b//q1au4\ndu1ai20uLi7ccI5EIqHfGdJhtFr8ly9fzv333r17ER8fD4lEYpGgiGUYjQwqVQ18fG735mUuMswb\nPA0bnDZjbMRTeKbnM3bxlC5jDCUlJaisrETnzp1N2nx8fEyKv6enJ1fw6Slb0lGZNea/ZMkSLF++\nHMOGDWvveIiF3LhRju+2XMC10mtY+z8T4ep6+ybk4OBBCJEEI1gcfI8rdHxN4/fFxcUoLi5GfX09\neDwe/P39IRQKufMkEgl8fHwgk8mgUChokgN5LJhV/BUKBWpra9s7FmIhRiPDxxt+wynd/6HaQYOv\nf/LH/Jm3d9Ti8/iPbeGvqanhir1Wq202fs8Yg0qlgr+/P3eMx+MhNjbW0qES0q7MKv6TJ0/GBx98\ngKysLHTv3r3Fns+YMWPaPDjS9nQNOuzO2Q1V6F5UXdCAz+fhjHE/jMYnH+slgHNzc1FYWIiKiopW\nz2majunmZt9TWIl9MKv4f/jhhwCA77//vsV2Ho9Hxd+G1dUZIBTykX4rHdsvbke5rhwSiRM6d/aA\nn8IDEyMGAY/RsHVLm5FXVFS0WPg9PT2hUCigUCjg6elJ4/fEbphV/A8cONDecZB2YDAYcfBgPrbv\nT0fA8Kso1JnOWBkeHYepfaZC5iKzUoRtp7q6GsXFxVCpVHByckJkpOmzCAqFAoWFheDz+dzYvUKh\noL1sid0yq/jfOf5ZU1OD6upqeHl5mdwUI7bnm81nsP3MLyh0PA2PNCF695aBBx48nTzxXM/nEOMX\n02F7ukajESUlJVzBr6qq4tqEQmGz3r+3tzdiYmIgl8tpsTRC8ABP+J48eRIrVqzAhQsXuAdZ+vTp\ngwULFiA+Pr7dAiQPTx1wBDez08EA1NcbYWhgGBY6BGPDxnbILRX1ej03O0etVre6pWF9fT3Ky8vh\n5eXFHRMKhfD19bVUqITYPLOKf1paGmbNmoUuXbpg/vz5kEqlUKlU2L9/P2bPno1vv/0WMTEx7R0r\neUBTYyfgSM4pODjwkBwegWkRUxHgEWDtsB5KQ0MD/vzzz1afrnVwcDAZzqEF0wi5N7OK/5o1axAf\nH48NGzaYfJSeN28e5syZg7Vr1yIlJaXdgiT3plJV4+utaRg/qhe6h8q540FeQXhlyCQoXBWIC4jr\nEEM8dXV1UKvVcHd3h4eHB3dcIBBwS4k3cXFxgbe3NxQKBaRSKRwcHKwRMiEdklnF//z581i9enWz\n4sHj8TB16lS8/vrr7RIcub8T6Tfw7rYU3BCkI3vbYHyz5J8QCG5P2RzXfZwVo7s/xhjKy8uhUqmg\nUqlQVlYGxhhCQkLQs2dPk3N9fHwANN689fb2pi0NCXkEZhV/Dw+PFncZAhpnWVCPy/KMzIjU/FT8\nVLQD+Y5XYDQwnKk+gqyL49G3Tydrh3dPer0earWa+9Lr9c3OUalUzYp/cHBwsxUzCSEPx6ziHxcX\nh7Vr16Jv374mWzYWFxdj7dq1dMPXghhjOKM8g19yfkFRZREAoEtnTyiLq/FkZE/4B9vuWvFlZWU4\nd+4cysvLW93KkMfjwcvLCwqFosX5+oSQtmFW8X/jjTfwzDPPYNiwYejbty9kMhk0Gg0yMjLg5uaG\nhQsXtnecdo8xhp8Pp+Koej/0zmqTth5d/PHWiPGID7SdcX2dTgdHR0eTeIRCIcrKypqd6+joCLlc\nDm9vb8jlctrshBALMHttn507d+Kbb75BRkYGbt68CQ8PD0yZMgUzZ86EXC6//0XIQ7usvIZFKV8g\nW3sRIiEffWMUEAoc4CRwwrCuwzAkeAhEDtYtmAaDASUlJVCr1VCpVKisrMTAgQNNlkpwdXWFq6sr\nampqIBaLuWJPT9YSYnmtFv9Tp04hKiqKe5BLLpfjzTfftFhg5LZrlVdwo+YyAKCu3ojCglq8NHgc\nRnQbYbWtFBljqKqq4sbttVotDAaDyTkqlarZOjl9+/aFi4sLPSBIiJW1WvxfeOEFODs7IzY2FomJ\niUhISEC3bt0sGZvdunuse1DwQPQI3oXTFwrwZEgS3pn4D/iJva0Sm1qtRmFhIdRqNXQ6Xavn8fn8\nFm/k3r3BOSHEOlot/p9//jkyMjKQkZGBTz75BAaDATKZDAkJCdzXwwz3KJVKfPDBBzhx4gSMRiP6\n9++PRYsWmdxItkd6fQMOHr+E7078jFhFIv5r5hCuTeQgwpvDXoU+ToSYsFCLxdTSDVeNRoOCgoIW\nz3dzc4NcLodcLodUKqVlFAixYa3+dg4ZMgRDhjQWoNraWpw5cwYZGRlIS0vDf//3f0On06Fr167c\npwJzNnZnjGHOnDmQSCTYvHkzAGDZsmV45ZVXsGPHjjZKqeMpqS3Bj5m7sPb/doCBoUCtwXRNAmSy\n20tn9/YJB3zaNw7GGCorK6HRaKBWq8EYQ1xcnMk5crkcubm5ABpv4MpkMq7g0yYnhHQcZnXNnJ2d\nER8fz03pbGhoQFpaGn788Uds2bIFKSkpyM7Ovu91NBoNQkJC8MYbbyAgoHGZgRkzZuDVV19FeXm5\n3QwJFBVVQSZzRlVDBfbl7sOx/GMwGA3w9BShrFwPrcM1HE6/gGeHt/8GIjqdDmq1miv4dw7V8Hg8\n1NfXN9vVKiwsDHK5HF5eXnSjlpAOyuzP5Xq9HidPnsTx48dx8uRJ5OTkgMfjoXfv3khMTDTrGnK5\nHKtWreL+rVQq8eOPP6J37952UfhPnLiFQ4cKcOlGAbqOKEaR4AIMxts3Sf0D3NDbvzvmPDkZMV16\nt0sMjDEUFxdDo9FAo9GgsrLynueWlpbC2/v2/QU+n4/QUMsNPRFC2sc9i//ly5dx7NgxHDt2DBkZ\nGdDr9ejUqRMSExMxb948xMXFPfSuR/PmzcOBAwfg6enJDQE97rJv5OP34h0o9riI3IuOCA+/vY5+\niCQEC+LGoLuse7v3ps+ePdvizVgAEIlEkMlk3HAODeUQ8nhqtfgnJydDrVbDw8MD/fr1w+LFi5GY\nmMgN1zyq1157DS+//DLWr1+PmTNnYteuXY/VTd+GBqPJGjsAoPU5CZXjBfB4PDgIeGBg6CrpitGh\no9FD1qNNin7TWjlNPfuAgACTnxmPx4NMJkNhYSGAxp68RCKBXC6HTCajOfeE2IlWi79KpYJYLMaz\nzz6LhIQExMTEtOnc7LCwMADAqlWrMGDAAOzcuRMvv/xym13fWkpLddi37zrOn9fgf/4nAULh7XWP\nJvQZg1P5p+HmJkRPRXeMDh2NMGnYIxXbpvn2Go0GWq0WGo0G9fX1XLtQKGz2B9vf3x/Ozs6QyWSQ\nSCS0NhMhdqjV4r9p0yYcO3YMR48exf/+7//CycmJm/OflJSEkJCQB34xjUaDkydPYtSoUdwxZ2dn\nBAYGori4+OEysCFGI8NHH53CjYrrKBKdxbG/AzDwyS5ce7A4GM/HPI1w73CESh9+3Fyv15uM27c2\nhAMAWq222ZTNpjXvCSH2q9Xi3zS7Z+HChdBoNDh27BhSU1OxYcMGfPjhh/Dx8UFCQgKSkpKQkJBg\nsmtSa27duoXXX38dnTp1Qu/ejTc0Kysrcf36dYwfP77tsrICxhiyNReh7b4fZy5mAQD2XTiIgU/O\nMjlvQo8Jj/xa5eXlyMrKarXdycmJG7eXyWQ0jEMIacas2T4ymQzjxo3DuHGNa8NnZ2cjNTUV6enp\nWLRoEQwGAy5cuHDf64SHhyMmJgZLlizBe++9B4FAgJUrV0IikXDX7ijKynQoKKhEr3ApMm5l4Ler\nv6GgvABMzCCVOsHP1w0OfrkwMiP4PP79L3gHnU7HDeOUlpYiKSnJ5IEpiUQCHo/HrYzZNN9eJpNB\nKpXSOveEkPt6oEcwKyoqkJmZiczMTJw9exbnz5+HwWBAr169zPp+Pp+PtWvX4uOPP8bcuXOh1+uR\nlJSELVu2wNXV9aESsDS9vgE7d+bi8F/XoHLKRshTKlTU316p0oHPQ+9e3ogLiMPQkKFmFX6dTget\nVst93bkZOQCUlpaaPE0tEAjQpUsXrofv4eFBxZ4Q8kDuWfzz8vKQmZmJ06dPIzMzE9euXYPRaETX\nrl0RFxeHqVOnol+/fg803VMikWD58uWPHLi1GPn12HVpFy64nEIDT4/qXHd0Dmp8RkHoIET/Tv3x\nVMhTkDhL7nkdpVIJlUrVYrG/m1arbbaUhrl/cAkhpCWtFv+4uDhu0w0/Pz/ExcVh7ty5iIuLs6sl\nnA0GIxwcbvfeHfgOcAi+jobzeri7i+Dp6QhXkSsGdh6IgV0GtrjKptFoBJ9v+gng5s2bKCoqavE1\n+Xw+xGIxN4wjFovbNilCiN1rtfj369cPCQkJiI+PR6dOtr0tYFtjjCEnpwS//ZYHoYsB82Y/wbWJ\nHESY+MQoNPB+RoifP4aGDEVCYAK3nj5jDLW1tSbDOBKJBFFRUSavIZVKueLfVOylUilkMhm8vLxo\n+iUhpF21WvzXrFljyThsyo3CEixc9w1uOWbBxSjGc+pwyOW3n3Qd1GUgAjz8EeUbBR54qK6uRpG2\nCCUlJdBqtaitrTW5XktbFnp7eyMsLAxSqZSKPSHE4mjN3TtoajQ4dP0QUgtSofXLR02pHrX8Mhw/\nexljB0dy57k7uqOHVw+czjiNkpKSe86zB4C6ujro9Xo4Ojpyx1xdXWmNHEKI1dh18Vcqq3Hw4A04\nddKiSHQW51TnuF56YKAHnJ1rEBIog9i/EgaDwaR3LhQKoVQqW+zVCwQCSCQSSCQSrmd/95g/IYRY\nk90W/4N/5eLTn37GLcezcLxeiz59/nMT2wgI9AKEOSowqmtXeMELZVfKUCYvg1Qq5b5fKBTC3d0d\nFRUVEAqFXKGXSqW0Pg4hxObZbfG/wDuAay5HIWAOcKp0Al8phAtzhEwgg7+7P8ROYuCOTn1JSYlJ\n8QcaH1pr+iNAxZ4Q0pE81sW/ocGIs2fVOHWqCDNnhsPR8Xa6I3oOxl9/pcHT4AJ3VycEOfrD190X\nzgLnZtdxdXVt8Ybs3X8MCCGko3isi//7q/7A6Vup0IuU8N7/IiY8fXvTmRBxCPpHRcCp1Anert7c\nk7g8Hg8eHh7cMI5YLIaTk5O1UiCEkHbxWBR/xhjq6gxgrAFarRZn887i3I1zULEieLjWARAiNeu4\nSfHn8XiY1m8ajh8/DrFYDIlEwv0vbTxOCHncdegqp1ZX4vffs3D58i04u+rg6V+Noqoi6Bp0AABn\nZwFqaurh7CSAl1jfbLqll5cXhg8fTjNxCCF2p0MXf72+Aeln01DjoIWuogzezs7g8W/feOXzeQjr\nGoDwoHD0CerTbNyex+PRjVpCiF3q0MVfK8iHyiUH/HoH8HhAncEIB2cGgasAEZ0jMLD7QPiJ/awd\nJiGE2JwOXfx7ynvC2U+EOoMOzlIHyL3FGBQ8CLF+sRA6tN2Wk4QQ8rjp0MVf6CDEmP6Doa5RY2Dn\ngQgWB9MwDiGEmKFDF38AeLr709YOgRBCOhya5kIIIXaoQ/T8DQYDgMbdrwghhNxfU71sqp936xDF\nX61WAwCmTp1q5UgIIaRjUavVCAoKanacx1pak9jG6HQ6nD9/HnK5nDY9IYQQMxgMBqjVaoSHh7e4\nRE2HKP6EEELaFt3wJYQQO0TFnxBC7BAVf0IIsUNU/AkhxA5R8SeEEDtkc8V/6dKlePvtt02O7dq1\nC6NHj0ZkZCSee+45pKammrRv3boVYWFhJl89e/Y0Oefbb7/FwIEDERERgZkzZyIvL8+mcqirq8Py\n5cuRmJiIqKgozJkzBwUFBR0mh7Vr1zb7GTR9ff755xbP4WF+BgUFBXj55ZcRExODpKQkLFmyGpWy\nGwAADeZJREFUBBUVFSbn2PLPAADy8vIwe/ZsxMTEIDk5GZ999hkaGhosmoNGo8Gbb76JpKQkxMTE\nYNasWbh8+TLXfuzYMTz99NPo06cPxowZgyNHjph8v1arxWuvvYaYmBjEx8fjk08+sWgOjxp/k7q6\nOowdOxa//PJLszZLvo9axWyE0Whkq1evZqGhoWzx4sXc8T179rCwsDD25ZdfsmvXrrEtW7aw3r17\nsxMnTnDnLF26lL388stMpVJxX2q1mmv/6aefWFRUFNu3bx+7dOkSmzt3Lhs8eDDT6/U2k8OiRYtY\ncnIy+/vvv1lOTg6bPn06Gz16NDMajR0ih6qqKpP//1UqFVu6dCmLj49nSqXSYjk8bPz19fVs+PDh\nbN68eSw3N5dlZGSw4cOHs3/+85/cNWz9Z1BWVsYSEhLY9OnT2YULF1haWhobPnw4e+uttyyWg8Fg\nYJMmTWITJ05kWVlZ7MqVK2z+/PksPj6elZSUsCtXrrDw8HC2fv16lpuby1atWsV69erFLl++zF1j\n8uTJbMqUKSw7O5sdPnyYxcXFsU8//dQiObRF/IwxVllZyV566SUWGhrKdu3aZdJmqffR/dhE8c/P\nz2fTpk1j/fr1YwMGDDB5w48dO5a98cYbJue//fbbbNq0ady/J0+ezNasWdPq9YcOHco+++wz7t9V\nVVUsMjKS7d692yZyyM/PZ6Ghoezvv//m2q9evcoGDBjA8vLyOkQOdzt9+jTr3r07O3LkCHesvXN4\nlPhzcnJYaGgou3TpEte+ZcsWFhUVZbH4HzWHTZs2saioKFZaWsq1p6ens9DQUFZQUGCRHC5cuMBC\nQ0NZbm4ud0yv17OIiAi2c+dO9s477zR7z0ybNo0tWbKEMdb4vgkNDWX5+flc+44dO1hUVBRXHNsz\nh0eNnzHGUlNT2eDBg9n48eNbLP6WeB+ZwyaGfU6fPg1fX1/s2bMHAQEBJm03btxATEyMybEePXog\nMzOT+yiYm5uLkJCQFq+t1WqRl5eHJ554gjvm6uqK8PBwpKen20QOx44dg0QiQXx8PNceHByMQ4cO\nISgoqEPkcCfGGN5//30MHToUycnJACzzc3iU+D09PcHn8/HTTz9Br9ejpKQE+/fvR3h4uMXif9Qc\nbty4gW7dusHLy4trbxr+TE9Pt0gOvr6++Oqrr9ClSxfuWNMy6+Xl5Uh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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Solution goes here\n", + "run_simulation2b(system, 0.01)\n", + "plot_results(system, title='Proportional model with birth and death')\n", + "savefig('chap03-fig03.pdf')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Factoring out the update function" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The functions that run the model all look the same except the body of the loop. So we can factor that part out into a function." + ] + }, + { + "cell_type": "code", + "execution_count": 47, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def update_func1(pop, t, system):\n", + " \"\"\"Compute the population next year.\n", + " \n", + " pop: current population\n", + " t: current year\n", + " system: system object containing parameters of the model\n", + " \n", + " returns: population next year\n", + " \"\"\"\n", + " # print(t, pop)\n", + " births = system.birth_rate * pop\n", + " deaths = system.death_rate * pop\n", + " return pop + births - deaths" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now the name `update_func1` refers to a function object." + ] + }, + { + "cell_type": "code", + "execution_count": 48, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 48, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "update_func1" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Which we can confirm by checking its type." + ] + }, + { + "cell_type": "code", + "execution_count": 49, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "function" + ] + }, + "execution_count": 49, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "type(update_func1)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "`run_simulation` takes the update function as a parameter and calls it just like any other function." + ] + }, + { + "cell_type": "code", + "execution_count": 50, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def run_simulation(system, update_func):\n", + " \"\"\"Simulate the system using any update function.\n", + " \n", + " Adds TimeSeries to `system` as `results`.\n", + "\n", + " system: System object\n", + " update_func: function that computes the population next year\n", + " \"\"\"\n", + " results = TimeSeries()\n", + " results[system.t0] = system.p0\n", + " for t in linrange(system.t0, system.t_end):\n", + " results[t+1] = update_func(results[t], t, system)\n", + " system.results = results" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here's how we use it." + ] + }, + { + "cell_type": "code", + "execution_count": 51, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "run_simulation(system, update_func1)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Remember not to put parentheses after `update_func1`. What happens if you try?" + ] + }, + { + "cell_type": "code", + "execution_count": 52, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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H5753pQqCINRlkiQRERHBtWvXcHJywtm58nhhTvWc8Gngww9//k5Buh5OBQPR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\nRPj6668BAOvXr8eSJUtw5MiRJ8ugm1Or1UgtSEXC5QSUFJd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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plot_results(system, title='Proportional model, factored')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Exercise:** When you run `run_simulation`, it runs `update_func1` once for each year between `t0` and `t_end`. To see that for yourself, add a print statement at the beginning of `update_func1` that prints the values of `t` and `pop`, then run `run_simulation` again." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Combining birth and death" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Since births and deaths get added up, we don't have to compute them separately. We can combine the birth and death rates into a single net growth rate." + ] + }, + { + "cell_type": "code", + "execution_count": 53, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def update_func1b(pop, t, system):\n", + " \"\"\"Compute the population next year.\n", + " \n", + " pop: current population\n", + " t: current year\n", + " system: system object containing parameters of the model\n", + " \n", + " returns: population next year\n", + " \"\"\"\n", + " net_growth = system.alpha * pop\n", + " return pop + net_growth" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here's how it works:" + ] + }, + { + "cell_type": "code", + "execution_count": 54, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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97kG+CgIDA7ly5QqzZ88mIiKC27dv89dff/HBBx/QpUsXWrVqBRTdV/D09CQo\nKIidO3cSExPDtWvX2LZtG6tWrWLixIllbmP69OlIksTw4cM5fPgwd+7c4dSpU4wZM4b4+Hhmz54N\nQEBAAOnp6UyfPp1r165x+fJlPvzwQ27dulWieqo0WlpahIeHM3v2bC5dusSdO3fYvn072traymTX\npk0bduzYQUREBOHh4Xz66afKz5mxsTHHjh1THouYmBj27NmDkZERTZs2fcYjLQg159atW4SGhgJF\nY4Y/3pLqSXfS7rDivxXkFeYhIZGeLPFO63fxsvGqrnDLVGbiePPNNyu9MplMRv/+/Z8poFdV8+bN\n2bx5M/fv32fkyJH4+vqyYMECevbsyZIlS5TzaWhosHr1agYNGsSPP/6In58fgwcP5ueff+bLL78s\n9/hbW1uzfft2PDw8+PLLL/H19WX69OnUr1+fnTt30qxZM6CorvWHH34gMTGRQYMGMWbMGOrXr88P\nP/ygdjXRwoULsbGxISgoiL59+/LXX3+xfPlybG1tgaJnSgwNDfH39+f9999n0KBBygFpNDQ0WLVq\nFVCUUP38/IiOjmbdunUVXu0IQm1169YtLl++rHxtYmJS7tWzjZENPrY+5OQWEHOlEK1TXTj7R2GZ\n81cnmVSJEc6vXbtGdnZ2qTdx3dzcnmtgj4uNjaVbt24cOnQIGxubKtuOIAhCVbh586ZKl0AmJiZ4\neXkpq4LLopAUrDi8kXM7jdGRiqq0Jk50xdm54rE4qvJ7U63muGFhYUyePJm7d++WmCZJEjKZrNxL\nLkEQhFfVjRs3CA8PV742NTWlXbt2KkkjKSuJXVd2MdRpqEqLKQ2ZBpO6jWRDXDgnT97ltdcaIZeb\nVmv8pVErccybNw8NDQ3mz5+PtbV1rX2aURAEoTYpLWl4eXkpm9dLksQ/t/9h15Vd5BbkkldQwNDm\nb2NhoXrDfODAFnTq1JBmzUyqNf6yqJU4wsPD+e677+jevXtVxyMIgvBSiI6OVqmJMTMzo127dsqk\nkZydzIZLG7iaUDRPSmoOP/x3kNi6jZg/vR8aGo+a5urr69CsWe1phq5W4jAzM6vVj78LgiDUJpIk\nkZqaqnz9eNKQJInjt4+z68oucgpyAMjLL+Tm5ULsMweQWliXI0du062bbU2FXyG1EsfQoUNZvXo1\nXl5eJR5YqYzTp08zYsSIUqe1a9eODRs2PPW6BUEQaguZTIabmxtnz56lsLAQT09PtLS0SMlOYWPo\nRsIfhKvh18feAAAgAElEQVTM+3rLPryp7cCvB26jp6eNgUHtuboojVqJIy4ujujoaDp16oRcLi/1\nacd169ZVuB5XV1eOHz+uUnbixAlmzJjB2LFjKxG2IAhC7aahoYG7u7vy/xO3T7AjfAc5BTlISMiQ\nYWVgxUiXkdiZ2VEgV1CQp0HPnk0wNHwJEsfNmzdp2bKl8nVxf0SVpaOjg6Xlo2ZkGRkZfPvtt4we\nPRpvb++nWqcgCEJNkySJ+Ph4rKysVLoNKa7ij0yKZMOlDUhI3L37kPv3H/Lhm0PwdxyItmZR6yot\nLQ0GDpTXSPyVpVbiKKv/o2e1YsUKdHR0yn3aWRAEoTaTJInQ0FBu376NXC7H3r5k/3dyczkeDTz4\n6c/fyUqsizzrDbSutUHbpfznOGqrSnWrHh0dzZkzZ8jMzMTU1BR3d3fl08aVlZSUxKZNm5gzZ84z\n3TcRBEGoKQqFgosXLxIXFwcUDYBmbGxc4soDYKjTUJJjNYn61QpNtImISKagQIGW1ov3eINaESsU\nCmbNmkW/fv34/PPP+e677/jkk0+UXVZU4uFzpa1bt2Jubo6fn1+ll30Zde3alRUrVlQ4LTY2Fnt7\nez744INS5y1tZL1ixcs+/ufi4sIbb7zB5s2bVd7HPXv2lJj38b/ff/9dOe/169eZPHkyXl5eODo6\n0qNHD77++usye/sNCgrC3t6eS5cuqXVsBKE2UigUnD9/Xpk0AGxsbLiRd4Mv//mS3IJclfkNdAz4\n2O9tXJ0b0K+fHTNner2QSQPUvOJYvXo1P//8M8HBwfTr1w8LCwsSEhLYv38/S5Yswc7OrtI3t/ft\n28eAAQMqfOReKN2vv/6Kr6/vUz1bs2LFCpydnZEkiYyMDI4cOcJXX31FbGysyuBNmpqaHD16tNR1\nGBsbA0VD0g4bNozu3bvzww8/YGhoyLVr15g/fz5hYWElWsolJCRw/PhxmjRpwvbt28sckVAQarPC\nwkLOnj3LgwcPlGWWDSw5nnecsEthFBQomLpuGV8MnoiJSV3lPDKZjAkT2pTaffqLRK3EsWvXLsaP\nH8+YMWOUZdbW1owdO5bc3Fx27dpVqcQRFRVFTEyMGJjnGTRq1Ig5c+bg6emp/BJXl7GxsbKRQr16\n9bCzs0NLS4sFCxYwcOBAmjdvrpz38cYMpSm+8pg3b56yzMbGBn19fUaOHElERIRKw4p9+/ZRr149\nhg8fzv/93/8xc+bMEmOgC0JtVlBQwJkzZ0hKSnpUZlzAtgfbyC7IJjklm8jIFDRzsti4NZT33m2r\nsvyLnjRAzaqqhIQEZbOyJ7m5uXHvXuXG2z579iyWlpbY2ZU9yJJQvo8++oj8/Hzmz5//XNbn7++P\njo4Ov/32W6WW09DQICMjg3PnzqmUe3p6cuDAgRLdoP/88894eXnRo0cPsrOz2bdv3zPHLgjVJS8v\nj3///VeZNPIK84gkkt9Tfye7IBsATQ0NLDKccMsYStjFVK5fTy1vlS8kta44GjVqxIULF2jfvn2J\naRcuXKjwV+mTrl69ilxe9c3O9l/bz4HIA2rN623rTYBzgErZptBN/BPzj1rLvy5/nX72/Sod49My\nNzdnxowZTJs2jb59++Lj4/NM69PX18fGxobIyMhKLefr68u6desYNmwYDg4OtGvXjnbt2uHl5UWL\nFi1U5r18+TKRkZEEBwdTv3592rRpw86dOxk2bNgzxS4I1SEnJ4dTp06RkZEBQHxmPBFEkGGQAf//\nIsJCz4LgDiM5pcgnPDyRIUNaYmdXO/qXep7UShxvvfUW3333HXp6evTt2xcLCwsSExP55ZdfWLVq\nFUFBQZXa6IMHDypdvSKU9Oabb/Lbb78xe/ZsDhw48MxVPk8OX1tYWFjquOOmpqYcPnwYKOoeevfu\n3axfv56DBw+yfv161q9fj4GBAVOnTmXo0KHK5UJCQjAyMqJDhw5AUdKZO3cuoaGhYlQ/odbLyckh\nOzub3MJcopKjuFv3LimaD5FlFfUl1bVpV96wf4M6WnVo5J+Pv78cXd2X8x6uWokjMDCQq1ev8tVX\nX7FgwQJluSRJ+Pn58e6771ZqoytXrqxclK8ALS2tUsc5gaLWG8Udoz3ps88+w9fXl6+//prPP//8\nmWLIzMxUuXrU1NTk559/LjHfk70jm5qaEhwcTHBwMHfv3uXkyZNs2bKFOXPm0KBBAzp37kxeXh6/\n/PIL3bp1Uw4G1bt3b7788ku2b98uEodQ65mYmNC2bVv2/LWH2LqxRCclcSc2A2sDK74f/yH2lo9q\nUV7WhFFMrcShqanJggULGDNmDP/99x/p6ekYGRnh6elZojqiNuln3++Zqo8CnANKVF9VlSd/7T8u\nLS0NE5PSL3etra2ZNm0as2fPfqZhe7Ozs7l582aJBgvFI/aVZfXq1dja2tKrVy8AGjRowFtvvYWf\nnx+9e/fm6NGjdO7cmcOHD5OamsrevXtV7msoFAp+/fVXZsyYIW6SC7Weubk5I94cwZ2/H/B3aAwN\nctrQJLUDsaF1sO9W09FVn0o9ANiiRYtanSheZA4ODly4cKFEeUREBFlZWTg5OZW57KBBg/j111+Z\nNWvWU29/586dKBSKSief0NBQfvvtN7p3767Sg7KOjg66urqYm5sDRdVUVlZWrF27VmX5c+fOMWfO\nHPbv369SrSUINS0pKQltbW1kdWQY1nk0ZHGdOnWY1Gkstg87cOaPfJo3N6F1a/MajLT6lZk4evXq\nxeLFi2nZsiU9e/assAnZH3/88dyDe5UEBgbSv39/Zs+ezbBhw9DT0yMyMpKFCxfSpUsXWrVqVe7y\nc+fOpV8/9a6u0tLSSEhIQJIk0tPTOXbsGIsWLWLcuHE0btxYZd6EhIRS16Grq4uBgQETJ05k2LBh\njBs3jjFjxtC4cWPu3btHSEgIaWlpDB48WPnsxsSJE0s0irCzs2PNmjXs3LlTJA6h1rh//z7HTx8n\nMjUSGsF7bT/E0ODR8xj19Osx6g0LnGzi8fS0fima2FZGmYnDzc0NfX195f+v2oGpbs2bN2fz5s0s\nW7aMkSNHkpWVhbW1NX379lWrLy8bGxuCg4P54osvKpx3woQJyv9NTEyws7Pjiy++4I033lCZr7Cw\nkE6dOpW6juHDhzN79mxatWrF9u3b+f777/noo49ITU3FyMiIjh07sm3bNiwsLFi3bh0ymYxBgwaV\nWI+mpiYjRoxg/vz5XL58udwrK0GoDrdv3+a3E79xM+UmBYWF3D+VwdhDy/lp9mTq1Hn0lampqUHb\ntvVrMNKaI5Oepr+QalaVg64LgiAU+y/sP/749w/S89IBiEtIJzzrPvVz3BnV0Z/Bg1tWsIbaoyq/\nN8u84oiPj6/UiqysrJ45GEEQhJpQUFjAtr+3ERYRhoKi1o2F2oUY2BnicLITBop6ZGcXIEmSqH2h\nnMTRuXPnSh2gx8fWFQRBeFHcSrnFhoMbyEx81KpRUVdB5/ad6WPfh21E4uZmhYODRQ1GWbuUmTi+\n/PJLkVkFQXiphYSHcPz0caQMGenpeRgb18HU0phRfUZhY1JUvRMY6FDDUdY+ZSaOAQMGVGccgiAI\n1aqgoIAHkQ/ITVKQnpYHyJDl1Gf6oPfR0qzUkwqvnDKPTmWe7pbJZJXudkQQBKEmaWpq4tnEkxt3\nbpOj0EY7S05WcmMSE3KxthaJozxlHp1FixapvRKROARBqO1C40NpZNQIU11ToOh7q41LGzKyM4i4\nXEhqqj6BgQ5YW+vXcKS1X5mJIyIiojrjEARBqBLpuelsC9vGubvnMCtoygSPCTRqZAQU9bvm096H\n9h5FQ7hqaIj7uuoQ12OCILyUJEni5J2T7Lqyi9SsDB5E5hCTdoWvwnezdOYoZZKQyWTo6GhWsDbh\ncaLLEUEQXjoPHj5gU+gmriVeA0AnTQfzh3XQlZlCgiZHj96hS5fGFaxFKIvockQQhJdGoaKQg9cP\n8kvUL+QX5oMEdVPrYpxnjIFlfRJjoUHTOri5iWcynkWZiePxIUm/+uqraglGqFpnz55l+PDhandB\nsGfPHmbNmsWVK1eqITpBeDY3U26yMXQjd1Jjyc4pQF9XG70kPZpqNcW2vi0yNJBs69KnT2flmDDC\n01H7HodCoeDIkSOcO3eOzMxMzM3Nadu2banDyQqCIFSn+5n3WXBiASkp2URFpyJTyPBr4YbcqAUG\nOkXjvNSvXx9XV1eV7v+Fp6NW4khMTGTMmDFERESgo6ODmZkZSUlJrFy5kvbt27Ns2TL09PSqOlZB\nEIRSWRtY06aeG9//ux/NPG3cNdwwTrHFwLQoaTRt2hQHBwdR5f6caFQ8S1FVVUJCAmvWrCE0NJS/\n//6by5cvs3TpUsLDw1WGkxWejr29PTt37mTIkCE4OTnRt29fLl68yJYtW+jcuTNubm58+OGH5OXl\nKZc5e/YsAQEBuLq60qFDB+bOnUt2drZyekREBAEBAbi4uPD6668THh6usk2FQsHKlSvp0qULbdq0\nYeDAgRw9erTa9lkQnpZCKjnM8nCXofg6eNOZrlhoWqKvVzR8q4ODg0gaz5laVxxHjhzhk08+wdvb\nW6W8e/fuJCcn8+233/LZZ59VSYDP4tq1a0RGRqo1r62tbYlxr0NDQ4mJiVFreblcjr29faVjfNx3\n333HvHnzaNKkCdOnT2fcuHE4OTmxZs0abt68SXBwMB4eHgwbNoxLly4xatQoAgMD+eyzz4iNjWXO\nnDnExsaycuVK0tLSGDVqFF5eXuzevZtbt27xySefqGxv4cKF/Pnnn3z++ec0btyYf/75h0mTJrF2\n7VratWv3TPsiCFVBISk4eusoR2OO8oHnVIz1Hw03bKBjQI/6nlxNvYeVlT5162rh6upKgwYNajDi\nl5NaiUNHRwdDQ8NSp4k35fkZNGgQXbt2BeCNN97g888/Z86cOTRq1Ai5XM7atWuJiooCYP369Tg6\nOjJt2jSgaCS9OXPmMG7cOKKiovjvv//Iz89n3rx56Ovr07x5c+Lj4/n8888BePjwIRs2bGDp0qXK\nHwS2trZERESwevVqkTiEWudO2h02hW7iRvJN7sRmMOy3BWya/j9MTYtG5pPJZHh4eJCTcxwNDQ08\nPT0xMzOr4ahfTmoljqFDh7J48WJcXFywsHjUjC0rK4vVq1fj7+9fZQG+Sh4ftlVXVxcNDQ2V1k91\n69ZVVlVFRUXRuXNnleU9PDyU06KiomjatKmySTVAmzZtlP9fv36dvLw8Jk+ejIbGoxrL/Px8lfdY\nEGpabkEu+yP3c+jGIRSSgqsRSSQl5aCnuMWWbZeZ+K6ncl5DQ0Patm1L3bp1VT77wvNVZuJ45513\nlP9LksT169fp3r07bm5umJubk56ezvnz5ykoKKBevXrVEmxl2dvbP1P1kbOzc4nqq6qkpaX6dshk\nsjLrZevWrVuirHgwRy0tLWQyGU8O7qitra38v7g54tKlS7G1tVWZ7/FEIgg16XL8ZbZc3kJydrKy\nzLaRKQZxjWmU6056aiY5OQXUrfvo3DE3N6+JUF8pZSaO/Px8lddubm7K8vv37wPQsmXRMIoPHjyo\nqviEMtjZ2XHhwgWVsnPnzimnpaWlERISQlpaGsbGxgCEhYUp57W1tUVbW5v4+Hh8fHyU5cuWLaOw\nsJDJkydXw14IQulSc1LZHrad8/fOq5TbW9gzvMtwjmjEk5Nzi3r1csjNfUjdusY1FOmrqczEsXHj\nxuqMQ6iksWPH0r9/fxYsWIC/vz9xcXF89tlndO7cGTs7O6ysrFi+fDkff/wxwcHBxMfHs2TJEuXy\nurq6jBo1ioULF6Kvr4+TkxNHjhxh+fLlzJs3rwb3THjVnbh9gh3hO0jJyCD6eipNmxhjZWaKf2t/\nvGy8SEtLw8zsPrm5MgoLCzhz5gxdunQpccUuVJ0yj/S5c+dwd3ev9ArPnj2rrGsXqo5cLmflypUs\nWrSIjRs3YmJigq+vL1OmTAHAwMCAn376ic8//xx/f3/q1avH2LFjlTfHAaZMmYK2tjZff/01iYmJ\nNGrUiM8//1wM4iXUKAmJO/eSuRaZgkIh0aDQhjn9P8aoriH37t3jwoULFBYWAkXVqq1atRJJo5rJ\npCcrwv8/Pz8/7OzsePfdd5HL5RWuKDQ0lDVr1nDr1i3279//XIOMjY2lW7duaneVIQjCi0uSJD49\nOI/fDkXQLLMrZlIjPvjAHZksSWW4Bx0dHTw8PMQ9jTJU5fdmmWl69+7dLFu2jIEDB9KkSRN69uyJ\ns7MzNjY26Orqkp6eTnx8POfOnePYsWPcvHmTgIAAFi5c+FwDFATh5XXp/iVM6ppga/KogYZMJuPD\nzpPwLHhAWGgKw4bJSUq6SVxcnHIefX192rVrJ1pO1ZAyrziKxcfH8+OPP3LgwAESEhJUWvlIkkSD\nBg3o1asXo0aNwsrKSq2N7ty5k7Vr13Lv3j2aN2/ORx99VG6fV+KKQxBeLinZKWwN28rF+xch3YRJ\nzsE4O6l+fxQWKsjLy+PcubOkpKQoyy0sLHB3dxcdFVagRq44illZWTFt2jSmTZvG9evXiY2NJSMj\nA1NTUxo0aEDTpk0rtcGQkBA+++wz5syZg6enJ1u2bGHChAns379fJAVBeMkpJAWHbx5m37V9pD98\nyLVrKaSmxZERvpUfWkxSaVYrSQpOnjxBVlaWsszW1hZHR0fRZLyGVeqOkp2dHXZ2dk+9MUmSWLp0\nKWPHjuWtt94CYNq0aZw6dYoLFy6IxCEIL7FbqbfYFLqJO2l3ANDQlJGVlY91ngO66c34888Y+vV7\n9P2ipaVF48aNiYiIQCaT0bp1a5o2bSr6nKoFqrUpwo0bN4iLi6Nv377KMg0NDfbu3VudYQiCUI2y\n87P5OeJnjsYcVXko1da0EX27vcOhnQ/p3sOWnj1tSyzbvHlzsrOzsba2rrUPGr+KqjVx3Lp1C4D0\n9HRGjBhBVFQUzZo1Izg4WPmAoSAILwdJkjh/7zzbwraR9DCFzMx8TE3qoq2pzevy1+nerDuaMk28\nHbKwstKnsLCQvLw8lXsXMpmsWntvENRTrRWFmZmZAEyfPh1/f3/Wrl1LixYtGDlyJNevX6/OUARB\nqGJJ2UmsOb+GqDv3OHs2nitXkmhmaM+c1+bQu3lvtDSKusaxstInOzubEydO8N9//6FQlOwyXahd\nqjVxFPeVNH78ePr164eDgwOffvopTZo0YevWrdUZiiAIVcxCz4IeTXty504Gsjxd5Bl9MLzSBQs9\n1U40k5KS+Oeff0hLSyM5OZnLly+X6GdNqF2qtaqquI7y8QcKZTIZzZo1IzY2tjpDEQThOXuY9xB9\nHdXnKvxa9uNB52zObjPC0tSYTp1UG8DExMSoJAqZTIaJiYm4AV7LqZU4cnNzWbVqFX///TdZWVml\n/hr4448/KlyPg4MDenp6XL58GScnJ+BRz7ti7HJBeDHlFOSwN2IvJ++cZHKbaTSr/2iMHm1Nbd7t\nMpyzhvdxcrKgTp2irxyFQkFYWJjKQGl16tTB3d1dPAn+AlArccybN4+dO3fStm1bWrRo8dRtqHV1\ndRk5ciSLFi3CwsICuVzOli1buH37tkoHfIIgvBhC40PZcnkLiZlJ3LqVzsi/vmTT+/OwtVXtrdbD\nw1r5f25uLmfPniU5+VFX6cbGxnh6eqKrq1ttsQtPT63E8ccff/DBBx8wbty4Z97g5MmT0dXV5csv\nvyQpKYlWrVqxfv16mjVr9szrFgSheqTnprP18lZlt+dR0ak8eJCFmWTOT5suMWuGNxoaJaubUlJS\nOHv2LDk5Ocqyhg0b4uLigqamZrXFLzwbtRJHXl7ec2sSJ5PJCAoKIigo6LmsTxCE6iNJEv/G/svO\n8J1k5T96otuheQMs77TALKcFpk0NyMkpQE9PW2XZpKQkTp06pWw1JZPJaNmyJXZ2duKexgtGrcTR\nqVMnjh07hpeXV1XHIwhCLZWUlcTG0I1cTbiqUt6hUQfeav0W/5kkoa+vjYeHdamJwMTEBCMjI1JT\nU9HW1sbd3R1LS8vqCl94jtRKHH5+fsyaNYuUlBTc3NxKHba0X79+zz04QRBqh3/v/MuWy1vIyM4m\nOjqF+vX1kTdsRIBzAK0sWwHw2mvl91SrqamJh4cHly5dwtnZGT09veoIXagCaiWO9957DyjqoDAk\nJKTEdJlMJhKHILzEDOsY8iApnStXkigslLBIc+bjAVMxNig7WWRkZGBgYKBy9aGrqytqLl4CaiWO\nQ4cOVXUcgiDUYo71HOnSwps7V0/QJLMLhoXWREVk4OFRMnFIksTNmze5cuUKrVu3Fg1fXkJqJY6G\nDRsq/8/KyuLhw4eYmJgonwQXBOHlcS/jHpl5mbQwb6FSPsojgDYavfll/y1GjHCgRQvTEssWFBRw\n6dIl7t69C8CVK1cwNjYWz2a8ZNR+cvz06dN8++23hIeHKx8AdHZ2ZsqUKeLhPUF4CSgkBX9e/5N9\n1/YhK6jDiMZTaOvaWDm9rlZd2nk2xMOtAVpaJZ/lysjI4Ny5c2RkZCjLTExMxL2Ml5BaieO///5j\n9OjRNG3alPfffx9zc3MePHjA77//ztixY/nxxx/x8PCo6lgFQagi9zPv8+PFH7mRcoO42ExuxaQT\ndXwl25rMxtT0UWMYmUyGllbJFlNxcXGEhoZSUFCgLGvSpAkODg5i0KWXkFqJY/HixbRv357Vq1er\n3OiaMGEC48aNY+nSpfz0009VFqQgCFVDISn468Zf7I3YS4GiAEkB9+8/RD/fEsssJ7ZsucrEia5l\nL69QcOXKFW7evKks09TUxMnJiUaNGlXHLgg1QK3EERYWxqJFi0q0zZbJZAwfPpwPP/ywSoITBKHq\nJDxM4IeLP3A9+dGQBtpaWkzsFsDpLUY0sjHCz6/sET+zs7M5d+6cynjg+vr6eHh4YGRkVKWxCzVL\nrcRhZGSkMu7v4x4+fCi6ChCEF4gkSfxz+x92XdlFZk4W2lpF528j40aMajMKGyMbvCwSsbc3Q1Oz\n9GomSZI4e/YsqampyrL69evj4uIiGs28AtSqfPTy8mLp0qXEx8erlMfHx7N06VJxc1wQXiCrz61m\n46VNRN5I4Mzp+2RlFdDPvh8zOs3Axqio2/PWrS3KTBpQVNvg5OSEhoaGcjxwd3d3kTReEWpdcQQH\nBzNw4EB69eqFu7s7FhYWJCYmcu7cOQwMDPjoo4+qOk5BEJ6TVpat2P7PIe7de4iewox613zpPbAv\nmpW8iW1iYqJ8Alw0t321qPVJsbKyIiQkhKFDh5KRkcHFixdJT09n2LBhhISEiJtggvAC8W7sTTen\nttgWuOOWMRSrujZkZeWXu0xiYmKJGgeARo0aiaTxClL7OQ5LS0umTZtWlbEIgvCcRSZFYqhjSH3D\n+soymUzGjG4f0lErloICia5dG5faBToU3cuIjIwkKioKLS0tvL290dcvv08q4eVXZuJYuXIlAwYM\noF69eqxcubLclRR3lS4IQu1QoChg37V9/HH9D/ITDfmw7Uc4trZSTteQafDaa43LWQPk5ORw/vx5\nkpKSAMjPzycsLIx27dpVaexC7Vdm4li0aBEdOnSgXr16LFq0qNyViMQhCLVHfGY86y6sI/LBDSIj\nk0lJiWVO5Ho2zJpaYoyMsiQkJHDhwgVyc3OVZRYWFri4uFRV2MILpMzEERERUer/giDUTpIkcfLO\nSbaFbSOvMA+ZDDIz8zEtaIRBuj0HD97izTdblLsOhULBtWvXiI6OVpbJZDLkcjktWrQQAy4JgJo3\nx5ctW1bqjTEo6mpg7ty5zzUoQRAqJys/izXn17Dh0gbyCvMA0KtThwmdR+KUNQC/no68/nrZD/NB\nUQemJ0+eVEkaderUwcvLC7lcLpKGoKTWzfHly5fj4+ODlZVViWkXL15k+/btzJo167kHJwhCxa4n\nX2fN+TXcS0mgbt2iU7q+YX3GuI3BxsiGeJeHWFmVf0P7/v37XLx4kfz8R62rLC0tcXV1pU6dOlUa\nv/DiKTNxDB06lIsXLwJFl8CDBw8ucyVOTk7PPzJBECr0R/Qf7Azb/f/vZeTg7m5FD3lX/B380dHU\nAagwaUBRdVRx0hBjgQsVKTNxzJ07l4MHDyJJEkuWLGHQoEFYW1urzKOpqYmhoSHdu3ev8kAFQSgp\nIy+Dy2EJpKfnoSXVwSKmK8MGDqv0F76VlRVNmzYlPj4eNzc3TE1LjrUhCMXKTBx2dna8++67QNEN\nM39//1KrqgRBqDlvtnyT006X+efYXewf9qKNS2sKC6VSuz4vJkkSOTk56OrqqpS3bt0ae3t70W2I\nUCG17nFMmjQJgJSUFPLz85UDOUmSRFZWFufOncPf37/qohQEAYWkIK8wj7paj8bH0NLQYnbvqZzQ\nfUADayOcnS3LXUdubq6y54fOnTujo6OjnKahoSHGzhDUolbiuHbtGlOnTlVpbfE4mUwmEocgVKG0\nnDTWnl/LnVtZfNR5Cg0bGiqnGdYxpHdPw3KWLvLgwQMuXryofDYjNDQUd3d3cR9DqDS1EsfXX39N\namoq06ZN48iRI+jo6NClSxeOHTvGsWPH2LBhQ1XHKQivrKsJV/n+9GrOh98mKSmHlOh1rJv5fqnD\nt5amsLCQq1evqgy2BIghXYWnptYn7+LFi0yePJlRo0bRt29fsrOzGTZsGCtXrqR79+5s3LixquMU\nhFeOQlKw/9p+Fp9eTMrDNFJScpEBDxIzOXQoRq11pKWl8c8//6gkjeJnM1q3bi2uNoSnotYVR15e\nHk2aNAGKxhF+/EnyAQMG8Omnn1ZJcILwqkrPTWfd+XVEJBada3p62ji1aIh03pMBPp3o2rX8fqYk\nSeLGjRtERESgUCiU5dbW1jg7O4tnM4RnolbiaNCgAbGxsXh4eNCkSRMyMzOJi4ujYcOG1KlTh7S0\ntKqOUxBeGZFJkaw6u5rMvAxlWUuLlrzT4x2Su0o0bWpS7vLZ2dlcvHiRxMREZZmmpiYODg40btxY\nXIdTCfUAACAASURBVGUIz0ytxNG9e3e+/fZb9PX16dGjB82aNWPx4sUEBQXx448/Vmo8jujoaHx9\nfUuUb968GQ8PD/UjF4SXjCRJ/Bb1G98f2czdu5m0ca2HtpYmvi188ZX7oiHTwLhpxetJTExUSRom\nJia4urpiYGBQhdELrxK1m+PGxMSwY8cOevTowYwZM5g0aRL79+9HU1OT7777Tu0NRkZGYmpqyv79\n+1XKTUzK/xUlCC+7P67/wYK963mQkA1A7I08FgVOp5Vlq0qtx8bGhvv37xMfH0/z5s2Ry+Wima3w\nXKmVOHR1dVm2bBl5eUWdp3l7e7N//37Cw8OVl7/qioyMpHnz5lhalt/eXBBeNZ1tO7OjwW88SIjG\nuKABHg/9aWpYfm+2AAUFBWhpPTqVZTIZzs7OPHz4EDMzs6oMWXhFqT0CIKDysFDjxo0rlTCKRUVF\n0axZs0ovJwgvO11tXT71/ZDv0vfSybIn/d+Ul9vktqCggCtXrpCcnIy3tzeamprKaXXq1BE3wIUq\nU2bi6NmzZ6Vuov3xxx9qzRcVFUVubi6DBg0iLi6OFi1a8OGHH+Ls7Kz2tgThRZeRm8FvF/+hp31X\nTEwePQlua2LLovHvVXjuJSUlcfHiRbKysoCiMXMcHByqNGZBKFZm4nBzc3vurS9ycnK4c+cOZmZm\nfPzxx+jo6LBp0yYCAgIICQnBzq788QIE4WVw9UEEn4R8x5UbcZyul8y3Hw5XOdfKO+8KCwu5du0a\nN27cUHb9A0UtqSRJEi2mhGpRZuL46quvnvvG6taty3///YeOjo6y2uurr74iPDycLVu28Mknnzz3\nbQpCbVH8QN+OC3u5cj0eCTh4fze//umBb8+WFS6fkpLCxYsXyczMVJZpa2vj6OhIw4YNRdIQqo1a\n9zjOnz9f4Txubm5qbfDJJoEaGho0b96ce/fuqbW8ILyIkrOTWXt+LdeTr2NgoI1NI0PibxfQ1WwA\nbV3Lv1eoUCiIjIwkOjpa5SrD0tISFxeXEr3cCkJVUytxDBtWcf/+V69erXA9YWFhjBgxgg0bNuDo\n6AgUXXpHRETQu3dvdUIRhBfOubvn2BS6iaz8LGVZT7e2tHboRe/XWqOhUfa5lZaWxoULF8jIePQw\noJaWFq1btxYP8wk1Rq3EUVonhllZWZw9e5a9e/eydOlStTbWsmVLGjZsyOzZs/n000/R09NjzZo1\npKSkMGLEiMpFLgi1XE5+DnN/Xsmf147i7GyJhkyGhkwDP3s/ejXvhYas4mcrEhISVJKGubk5bdq0\nER0UCjVKrcTRtm3bUstfe+019PT0+P7771m1alXFG9PSYu3atXz99deMHz+e7Oxs3Nzc2LRpE+bm\n5pWLXBBqsdi0WMat+YybD/5fe3ceFlXZ/w/8PcwwDAwgDLuIIAMDsiirskmYpqZp2mK5lZZbdj3q\nr74+mRrP95dWVhouaaVPmeXSapZZVhJimCEgYSCLoKzKMiAwbAMzc//+4OfRCchBmWHAz+u65rrk\nvs+c+dzOmfnMOedergIASksaETJyBBaHLIZUonsnEKlUimvXrkGhUGDkyJHw8PCgswzS73o1jqM7\nYWFh2Lt3r87bOzk5YevWrXf7soQYNUszS4htGFDd+bdZrQdejl4Pa/Oep/1Qq9Xo6OiASHSzey6P\nx0NwcDB4PB7E4tuvHU6IIdz1PARJSUl0QBPyNzYiG6yb9jwcbK2wwP9pfLVu0z8mjbq6Opw+fRoZ\nGRlaN8CBzg4l9BkjxkSnM45nnnmmS5larUZlZSVKS0uxZMmSPg+MkIFCrdbg85/OYkZsOCwtb86u\nEOwSjOP/57+wEvWcMFQqFfLy8lBcXMwljOLiYowYocNshoT0E50SR0dHR5cyHo8HqVSKxYsX49FH\nH+3zwAgZCHIvV+ClgwkoVOSitPw5rF36kFb9PyWNmpoaXLhwgRv9DXTeB7x16hBCjJFOiYNW+COk\nq4yrGdhx9r+4pCgFAHxecBBTL4ZglN/Qf3xee3s7Ll68iLKyMq1yR0dHjBo1isZlEKPXq5vjycnJ\nyMjIQENDA+zt7REREYHw8HB9xUaIUWpqb8Lhvw4j/Wo6RNaAo4M55LVtmDIqCjKvnnsHMsZw9epV\n5OTkQKlUcuVCoRD+/v40+psMGDoljuvXr2PJkiXIzs6GUCiERCJBbW0tdu/ejejoaOzatYtm4iSD\nnkqlQWpJBr4p+hwK5c2xFaH+I/CI5xzE+PY8ewJjDOnp6aisrNQqHzp0KAICAujzQwYUnRLHpk2b\nUF5ejvfffx9xcXFceWJiItavX48tW7Zg/fr1+oqRkH6XU1CBdYfeRbUwH4GB9uCh88wgeng0Hvd7\nHOam/3x5icfjaQ3aE4lECAwMhLOzs17jJkQfdEocp0+fxrp167SSBgBMmDABdXV1SEhIoMRBBq2M\n4mws/u+raEMz0AJUVjZjpMcwLBi9AAGOATrvx8fHB5WVlXB0dMTIkSO1Fl8iZCDR6cjl8/mwsrLq\nts7BwaHbXleEDBZuDo5wdhOiuKwZfD4P/kOC8UrcCliYdj/th0qlQmFhITw8PLQG8wkEAtx3332U\nMMiAp9MAwLlz5yIhIQFVVVVa5U1NTdizZw/mz5+vl+AIMQaOYkesmrwAnq5O2LXwFbwx+396TBrV\n1dVITk7GpUuXkJOT06WekgYZDHQ6iqurq1FdXY0HHngAoaGhcHR0RH19Pc6fP4/m5mYIhUJukCCP\nx8OHH36o16AJ0Zf0nCv46uRZbHr+Sa1lWyd5P4DYEeN6TBitra3IycnRWh7g6tWrGDFiBK37TQYd\nnRJHSUkJfH07F5pRqVS4erVz4rYbZWq1Gmq1Wk8hEqJ/jDG8fvAwPrvwJTRQQ/aNO555PJqrN+GZ\ndJs0GGO4cuUK8vPzoVKpuHKhUAg/Pz/Y2toaJH5CDIkGAJJ7XlVTFT698Cn+aM6ECu0AgI8zPsGT\n08JhYSHs8XnXr1/HX3/9hYaGBq1yNzc3+Pn5catcEjLY9OqCa2FhIc6dO4empibY2toiNDQUnp6e\n+oqNEL1SaVT4uehnHC84DpVGBZehYshrWzGEb4fXZv+rx6TR3t6OvLw8lJaWak1IaGVlhcDAQFoi\ngAx6OiUOjUaD+Ph4fP3111ofFB6Ph4cffhhvvPEGjXglA4ZarcGhH1OQzf8Z9aoarpzP4+P/PDQP\nM/2mQyjo+Wyhvr4eJSUlN5/H58Pb2xtSqRQmJnc94TQhRk+nxLFnzx4cPXoUL774IqZPnw57e3vU\n1NTg2LFj2LFjB6RSKc2QSwaEnPxriD/8PnJb0uHgYA5f386zA3cbdywYtQBuQ9xuuw9HR0c4Ozuj\nsrISTk5OCAgIoBX5yD1Fp8Tx1VdfYfny5Vi8eDFX5uzsjCVLlkCpVOKrr76ixEEGhEP5H+NiSzoA\noLqmFR5uwFNjZmP8iPHdLuXa0dGBlpYWDBkyRKvc398fbm5uNPKb3JN0Oq+uqalBaGhot3UhISFa\nXRAJMWaLxz0JRwcL8Pk83O8/Bm9N3YQJnhO6JA3GGEpLS5GUlIS0tDStHlMAYGFhQUmD3LN0OuNw\nc3NDZmYmIiMju9RlZmbCwcGhzwMj5G5dKpJDbG6GoUNvznowwnYEVjzwJBzNnREni+r23lx9fT2y\ns7Nx/fp1rqywsJDrfk7IvU6nxPHYY4/hnXfegYWFBaZOnQp7e3vI5XIcP34cH3zwAZYtW6bvOAnR\nWWOjErs+/wlf5X+OsXZx2LV2sVaCeCKo+4XHlEol8vLyUFZWptUJxNzcvMulKkLuZToljgULFiA3\nNxebN2/Gm2++yZUzxjBjxgw899xzeguQkN5oVDbiw8wDOFD0AzQmDCl1J3DydCweuM+nx+doNBoU\nFxejoKBAa941ExMTSKVSeHl50VQhhNxC50kO33zzTSxevBjp6eloaGiAtbU1wsPD4e3tre8YCbkt\nDdMguTgZR/OOok3VBldXS5SVKWDnYAaxS3OPz6upqUFOTg4UCoVWuZOTE/z9/SEWi/UdOiEDTq9+\nRrm4uMDNzQ1DhgyBRCKBm9vtuy4Sok9yeQuyKy7hTMP3KG0o5cqHD7fCOM8IrJywCENE3V9mUqlU\nyMjI0DrLEIvFCAgIgKOjo95jJ2Sg0nkA4Ntvv40DBw5ApVJx13/Nzc3x3HPPYenSpXoNkpC/UypV\nOHr8IvamHEKdZS5CQ51gYtJ5H8PJ0glzA+fC1/6fb2YLBAL4+PggOzsbAoEA3t7e8PT0pEF8hNyG\nTolj586d+OSTT/DUU09h8uTJsLOzg1wux4kTJ7Bjxw6IxWLMmzdP37ESwimsLcJb6ZvQImgG2oCy\ncgW8RthhqvdUTJJOgsBE+9BmjKGurq7LdCDu7u5QKpVd1s4ghPRM5wGAK1aswPPPP8+Vubm5ITg4\nGGKxGPv376fEQQxK6ugOH287ZOY2w8pKiEjPEDx/3yLYW9h32VYul3P3MWJiYmBjY8PVmZiYUDdb\nQnpJp3PypqYmjBo1qtu60NBQVFdX92lQhNxKoWhHTo5cq0wkEGHVA4sQMVqKPYv/g/gp/9MlaTQ3\nNyMtLQ1nz55FY2MjGGO4ePGiVldbQkjv6ZQ44uLi8Nlnn3Vbd/z4ccTGxt7Ri//555/w8/NDamrq\nHT2fDG4aDcPJk8VY+p99WLNvJxoblVr1Y1zD8cGTWxDkEqQ1TqO9vR05OTk4deoUKisruXI+nw87\nOztKHITcJZ0uVYWFhWHbtm2YPn06pk2bBgcHB9TX1+PUqVPIyMjAwoUL8f777wPonDFXlwGBLS0t\n+Pe//00LQJEe1TTJ8c5vO3BFkA8A2PX5T3h5yQyunsfjQci/OYttT+MxAGDYsGHw9fWFubm5YYIn\nZBDTKXFs3LgRAKBQKLBt27Yu9R999BH3b10Tx+bNm+Hk5KQ1PTUhAKDWqHHy8kkcKzgGSy8F8Bdg\nYS6A3O48gBldtmeMobKyErm5uWhu1h6zIZFI4O/vr3VfgxByd3RKHHl5eX36osnJyTh16hT27t2L\nGTO6fhGQe49KpUFh4XUIHK/j4IWDuKroXJ7Y1kYEfz97zAiaiMf8u58qhMfjoaSkRCtpiMVijBw5\nEs7OzrRWDCF9zODzKNTV1WH9+vV4/fXXaf4fAgDIy6vF/sOZSG38GUPHyiEWm3J1w6yH4aWYefC0\n/eeVJv38/HD69GkIBALIZDJ4eHjQeAxC9MTgieM///kP7r//fsTGxmrduCT3Jo1Gg/eOfYeklu/R\nYdqG5kIhRo92gEggwgyfGbh/xP1aU54rlUpcvnwZMpkMfD6fK7e2tkZwcDAcHBxorW9C9MygieOb\nb77BxYsX8d133xnyZYkR4/F4cAiqhfpkG/gmPDg4mGO002jMCZwDibmE206lUqGoqAiXL1+GSqWC\nUCiEVCrV2perq6uhwyfknmTQxHHkyBFUVVUhJiYGALhukUuWLMHMmTPx6quvGjIc0g9qalrg4HBz\nmVUej4fnohfhQsVFDLWXYFHYAox2Hs3VazQalJSU4NKlS1Aqb3bHvXTpEtzd3WnWWkL6gUE/dVu2\nbEFbWxv3d01NDebNm4dNmzYhOjrakKEQA2tt7cC33xbh6G9n8dKyyQgeNZSrs7Oww8aHXoKHjQfM\nBGYAOn9UVFRUID8/Hy0tLVr7sra2xsiRI7UuVRFCDKfHxFFVVdWrHTk5OfV6GzMzM67873MIkcHl\ns28u4ONzh1AtzsPrX1TioO+/IRTe/OL3se9cL4MxhurqauTl5aGxsVFrH+bm5vD19YWrqyv1lCKk\nH/WYOO67775efThzc3P7JCAyuDDGkFKagnSrL3Hd4gqgAq6Jz6OkthzeLu5dtk9PT+/SaUIoFMLL\nywseHh50lkGIEegxcbz++utc4mhoaMCWLVsQGRmJBx98kBs5/uuvv+LUqVNYu3btHb24s7Mz8vPz\n7yxyYrRUKg1MTHi41nQVB/86iKK6IgCAl3fnILwpo8bBSWLb7XMlEgmXOPh8Pjw9PSGVSmFqatrt\n9oQQw+sxcTzyyCPcv59//nnMnDkTmzZt0tpm+vTp2LRpE3788Uc88cQT+ouSDBiXL9dj36dZEPrn\n46ooExqm4epGDh+OuYFz4e/oDwBoa2vrMpW5h4cHiouL4eTkBG9vb+5yJiHEeOh0c/zMmTPYtWtX\nt3Xjx4/Hl19+2adBkYHpwoUabNxzBIWiJKjONyEszBlCUz74JnxMkk7CVO+pEPKFaG5uRkFBASoq\nKhAbGwtra2tuH3w+H+PHj6fBe4QYMZ0Sh62tLS5cuNBtz6dz587pdGOcDH5KSSmK7H5AW6sKfA0P\nTU3tGOs1CvMC58HFygUtLS3IvZSLsrIyrit2fn4+wsPDtfZDSYMQ46ZT4nj88cexa9cutLW1YcKE\nCbC1tUVtbS1OnDiBTz/9FOvWrdN3nGQACBkahHGj/JF+KR+jfF0xP+QJRLlFoa2tDX/99RdKS0uh\n0Wi0nqPRaKBWq+mmNyEDiE6J47nnnoNCocCHH36IPXv2cOVmZmZYtWoVrf53j1GrNUhMLEVLmxIz\nZ/hw5XwTPlbdvxgpXil4ZOQjEGgEyMnJQUlJSZeEYW9vD19fX9jadn+TnBBivHRKHDweDy+99BJW\nrFiBzMxMNDY2wtbWFsHBwbCwsLj9DsigoVC04813fsOZ6z+hjV+PsJAtGDbs5j0KT1tPjLAZ0WPC\nkEgk8PHxgb191yVeCSEDQ69GjltZWd3xan9k4GOMIavuHH4z/RDVwgYAwPvHv8OmZfO1tuPxeGhq\natJKGra2tlzCoMF7hAxsPSaOSZMm9eoD/tNPP/VJQMQ4lTeW49Bfh1BUV4ThUhHqshQY7mYFrzEq\naDSaLje0ZTIZampqYGNjAx8fHzg4OFDCIGSQ6DFxhISE0Af9HlderkBqRhnUXtlIupLEjcmwsDDF\ng3H+mO3zGMwazXDq1CnExcVpJQ+JRILo6GjY2trScUTIINNj4ti8eTP37+PHjyMyMhISiaSnzckg\nwhjDF1/k4YuUX1EoSoasQQSJbeda3XwTPsa7jocn80RldiV3OaqsrAzu7tpTiNDxQsjgpFOH+Q0b\nNiAtLU3fsRAjwcDwXfV+XDT/Ae28Zly+3AAGBm8rb8y2mw3zcnNcLb+qdQ+jpqamHyMmhBiSTjfH\nnZyc0Nraqu9YiJEw4ZlgYkQALlzNhqWVEKFSd4y3iIFZkxkUCoXWthKJBDKZjHpJEXIP0SlxzJkz\nB6+//jqysrLg6+vbbRfc6dOn93lwRP/q6lqRlFSGWbO8YWJ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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "system.alpha = system.birth_rate - system.death_rate\n", + "\n", + "run_simulation(system, update_func1b)\n", + "plot_results(system, title='Proportional model, combined birth and death')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Exercise:** Maybe the reason the proportional model doesn't work very well is that the growth rate, `alpha`, might be changing over time. So let's try a model with different growth rates before and after 1980 (as an arbitrary choice).\n", + "\n", + "Write a function called `update_func1c` that takes `pop`, `t`, and `system` as parameters. The system object, `system`, should contains two parameters: the growth rate before 1980, `alpha1`, and the growth rate after 1980, `alpha2`. It should compute and return the simulated population one year later.\n", + "\n", + "Note: Don't forget the `return` statement." + ] + }, + { + "cell_type": "code", + "execution_count": 55, + "metadata": { + "collapsed": true, + "scrolled": false + }, + "outputs": [], + "source": [ + "# Solution goes here\n", + "def update_func1c(pop, t, system):\n", + " system = System(alpha1 = 0.015, alpha2 = 0.02)\n", + " if t < 1980:\n", + " growth = system.alpha1 * pop\n", + " return pop + growth\n", + " else:\n", + " growth = system.alpha2 * pop\n", + " return pop + growth" + ] + }, + { + "cell_type": "code", + "execution_count": 56, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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/fp3s7GxsbGyAkl5VW7du5bXXXqNz585K6xoaGlZ4j6NBgwb06dOH7777jmHD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\nQQghpFsocRBCCOmW/w9U2+Ivytch0wAAAABJRU5ErkJggg==\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Solution goes here\n", + "run_simulation(system, update_func1c)\n", + "plot_results(system, title='Proportional model, combined birth and death')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Quadratic growth" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here's the implementation of the quadratic growth model." + ] + }, + { + "cell_type": "code", + "execution_count": 57, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def update_func2(pop, t, system):\n", + " \"\"\"Compute the population next year.\n", + " \n", + " pop: current population\n", + " t: current year\n", + " system: system object containing parameters of the model\n", + " \n", + " returns: population next year\n", + " \"\"\"\n", + " net_growth = system.alpha * pop + system.beta * pop**2\n", + " return pop + net_growth" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "And here are the results. Can you find values for the parameters that make the model fit better?" + ] + }, + { + "cell_type": "code", + "execution_count": 58, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Saving figure to file chap03-fig04.pdf\n" + ] + }, + { + "data": { + "image/png": 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Pnj1Mnz6dnj178vnnn1c6f2hoKCYmJvTo0QO4/8Fx7do1IiMjHzt2QVBXWVkZ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\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "system.alpha = 0.025\n", + "system.beta = -0.0018\n", + "\n", + "run_simulation(system, update_func2)\n", + "plot_results(system, title='Quadratic model')\n", + "savefig('chap03-fig04.pdf')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "To understand the quadratic model better, let's plot net growth as a function of population." + ] + }, + { + "cell_type": "code", + "execution_count": 59, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "pop_array = linspace(0.001, 15, 100)\n", + "net_growth_array = system.alpha * pop_array + system.beta * pop_array**2" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here's what it looks like. Remember that the x axis is population now, not time.\n", + "\n", + "The function `sns.set` sets the style for the plots. I added a grid to this one to make it easier to read." + ] + }, + { + "cell_type": "code", + "execution_count": 60, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Saving figure to file chap03-fig05.pdf\n" + ] + }, + { + "data": { + "image/png": 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9TRQKBfPmzbNJQML2mppb2XuswLwdGeLNiEh5HCFEZ5ydVNyVOIAd+3IxGo0U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\n6apDrAghRCKRyPmTmppKzM3NSVpamsJ9VDVeLS0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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "newfig()\n", + "sns.set(style='whitegrid', font_scale=1.5)\n", + "plot(pop_array, net_growth_array, '-')\n", + "decorate(xlabel='Population (billions)',\n", + " ylabel='Net growth (billions)',\n", + " legend=False)\n", + "savefig('chap03-fig05.pdf')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Using `sns.set` to reset the plot style." + ] + }, + { + "cell_type": "code", + "execution_count": 61, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "sns.set(style='white', font_scale=1.5)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In the book we found that the net growth is 0 when the population is $-\\alpha/\\beta$:" + ] + }, + { + "cell_type": "code", + "execution_count": 62, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "13.88888888888889" + ] + }, + "execution_count": 62, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "-system.alpha / system.beta" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This is the equilibrium the population tends toward." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Exercise:** In the book, I presented a different way to parameterize the quadratic model:\n", + "\n", + "$ \\Delta p = r p (1 - p / K) $\n", + "\n", + "where $r=\\alpha$ and $K=\\alpha/\\beta$. Write a version of `update_func2` that implements this version of the model. Test it by computing system variables `r` and `K` equivalent to `alpha` and `beta`, and confirm that you get the same results. " + ] + }, + { + "cell_type": "code", + "execution_count": 63, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "# Solution goes here\n", + "def update_func2(pop, t, system):\n", + " \"\"\"Compute the population next year.\n", + " \n", + " pop: current population\n", + " t: current year\n", + " system: system object containing parameters of the model\n", + " \n", + " returns: population next year\n", + " \"\"\"\n", + " net_growth = r * pop * (1 - pop / K)\n", + " return pop + net_growth" + ] + }, + { + "cell_type": "code", + "execution_count": 64, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Saving figure to file chap03-fig04.pdf\n" + ] + }, + { + "data": { + "image/png": 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Pnj1Mnz6dnj178vnnn1c6f2hoKCYmJvTo0QO4/8Fx7do1IiMjHzt2QVBXWVkZ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\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Solution goes here\n", + "system.alpha = 0.025\n", + "system.beta = -0.0018\n", + "r = system.alpha\n", + "K = -system.alpha / system.beta\n", + "run_simulation(system, update_func2)\n", + "plot_results(system, title='Quadratic model')\n", + "savefig('chap03-fig04.pdf')" + ] + }, + { + "cell_type": "code", + "execution_count": 65, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Saving figure to file chap03-fig05.pdf\n" + ] + }, + { + "data": { + "image/png": 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9TRQKBfPmzbNJQML2mppb2XuswLwdGeLNiEh5HCFEZ5ydVNyVOIAd+3IxGo0U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\n6apDrAghRCKRyPmTmppKzM3NSVpamsJ9VDVeLS0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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Solution goes here\n", + "pop_array = linspace(0.001, 15, 100)\n", + "net_growth_array = r * pop_array * (1 - pop_array / K)\n", + "newfig()\n", + "sns.set(style='whitegrid', font_scale=1.5)\n", + "plot(pop_array, net_growth_array, '-')\n", + "decorate(xlabel='Population (billions)',\n", + " ylabel='Net growth (billions)',\n", + " legend=False)\n", + "savefig('chap03-fig05.pdf')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Exercise:** On the Wikipedia page about world population estimates, the first table contains estimates for prehistoric populations. The following cells process this table and plot some of the results." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Select `table1`, which is the second table on the page." + ] + }, + { + "cell_type": "code", + "execution_count": 66, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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Population Reference Bureau (1973–2015)[6]United Nations Department of Economic and Social Affairs (2015)[7]Maddison (2008)[8]HYDE (2010)[citation needed]Tanton (1994)[9]Biraben (1980)[10]McEvedy & Jones (1978)[11]Thomlinson (1975)[12]Durand (1974)[13]Clark (1967)[14]
Year
-10000NaNNaNNaN2M[15]NaNNaN4.01–10MNaNNaN
-9000NaNNaNNaN4.NaNNaNNaNNaNNaNNaN
-80005.0NaNNaN5.NaNNaNNaNNaN5–10MNaN
-7000NaNNaNNaN8.NaNNaNNaNNaNNaNNaN
-6000NaNNaNNaN11.NaNNaNNaNNaNNaNNaN
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" + ], + "text/plain": [ + " Population Reference Bureau (1973–2015)[6] \\\n", + "Year \n", + "-10000 NaN \n", + "-9000 NaN \n", + "-8000 5.0 \n", + "-7000 NaN \n", + "-6000 NaN \n", + "\n", + " United Nations Department of Economic and Social Affairs (2015)[7] \\\n", + "Year \n", + "-10000 NaN \n", + "-9000 NaN \n", + "-8000 NaN \n", + "-7000 NaN \n", + "-6000 NaN \n", + "\n", + " Maddison (2008)[8] HYDE (2010)[citation needed] Tanton (1994)[9] \\\n", + "Year \n", + "-10000 NaN 2M[15] NaN \n", + "-9000 NaN 4. NaN \n", + "-8000 NaN 5. NaN \n", + "-7000 NaN 8. NaN \n", + "-6000 NaN 11. NaN \n", + "\n", + " Biraben (1980)[10] McEvedy & Jones (1978)[11] Thomlinson (1975)[12] \\\n", + "Year \n", + "-10000 NaN 4.0 1–10M \n", + "-9000 NaN NaN NaN \n", + "-8000 NaN NaN NaN \n", + "-7000 NaN NaN NaN \n", + "-6000 NaN NaN NaN \n", + "\n", + " Durand (1974)[13] Clark (1967)[14] \n", + "Year \n", + "-10000 NaN NaN \n", + "-9000 NaN NaN \n", + "-8000 5–10M NaN \n", + "-7000 NaN NaN \n", + "-6000 NaN NaN " + ] + }, + "execution_count": 66, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "table1 = tables[1]\n", + "table1.head()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Not all agencies and researchers provided estimates for the same dates. Again `NaN` is the special value that indicates missing data." + ] + }, + { + "cell_type": "code", + "execution_count": 67, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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Population Reference Bureau (1973–2015)[6]United Nations Department of Economic and Social Affairs (2015)[7]Maddison (2008)[8]HYDE (2010)[citation needed]Tanton (1994)[9]Biraben (1980)[10]McEvedy & Jones (1978)[11]Thomlinson (1975)[12]Durand (1974)[13]Clark (1967)[14]
Year
1913NaNNaN1793.NaNNaNNaNNaNNaNNaNNaN
1920NaN1860.01863.1912.NaNNaNNaNNaNNaN1968.
1925NaNNaNNaNNaNNaNNaN2000.0NaNNaNNaN
1930NaN2070.0NaN2092.NaNNaNNaNNaNNaN2145.
1940NaN2300.02299.2307.NaNNaNNaNNaNNaN2340.
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" + ], + "text/plain": [ + " Population Reference Bureau (1973–2015)[6] \\\n", + "Year \n", + "1913 NaN \n", + "1920 NaN \n", + "1925 NaN \n", + "1930 NaN \n", + "1940 NaN \n", + "\n", + " United Nations Department of Economic and Social Affairs (2015)[7] \\\n", + "Year \n", + "1913 NaN \n", + "1920 1860.0 \n", + "1925 NaN \n", + "1930 2070.0 \n", + "1940 2300.0 \n", + "\n", + " Maddison (2008)[8] HYDE (2010)[citation needed] Tanton (1994)[9] \\\n", + "Year \n", + "1913 1793. NaN NaN \n", + "1920 1863. 1912. NaN \n", + "1925 NaN NaN NaN \n", + "1930 NaN 2092. NaN \n", + "1940 2299. 2307. NaN \n", + "\n", + " Biraben (1980)[10] McEvedy & Jones (1978)[11] Thomlinson (1975)[12] \\\n", + "Year \n", + "1913 NaN NaN NaN \n", + "1920 NaN NaN NaN \n", + "1925 NaN 2000.0 NaN \n", + "1930 NaN NaN NaN \n", + "1940 NaN NaN NaN \n", + "\n", + " Durand (1974)[13] Clark (1967)[14] \n", + "Year \n", + "1913 NaN NaN \n", + "1920 NaN 1968. \n", + "1925 NaN NaN \n", + "1930 NaN 2145. \n", + "1940 NaN 2340. " + ] + }, + "execution_count": 67, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "table1.tail()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Some of the estimates are in a form we can't read as numbers. We could clean them up by hand, but for simplicity I'll replace any value that has an `M` in it with `NaN`." + ] + }, + { + "cell_type": "code", + "execution_count": 68, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "table1.replace('M', np.nan, regex=True, inplace=True)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Again, we'll replace the long column names with more convenient abbreviations." + ] + }, + { + "cell_type": "code", + "execution_count": 69, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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prbunmaddisonhydetantonbirabenmjthomlinsondurandclark
Year
-10000NaNNaNNaNNaNNaNNaN4.0NaNNaNNaN
-9000NaNNaNNaN4.NaNNaNNaNNaNNaNNaN
-80005.0NaNNaN5.NaNNaNNaNNaNNaNNaN
-7000NaNNaNNaN8.NaNNaNNaNNaNNaNNaN
-6000NaNNaNNaN11.NaNNaNNaNNaNNaNNaN
\n", + "
" + ], + "text/plain": [ + " prb un maddison hyde tanton biraben mj thomlinson durand clark\n", + "Year \n", + "-10000 NaN NaN NaN NaN NaN NaN 4.0 NaN NaN NaN\n", + "-9000 NaN NaN NaN 4. NaN NaN NaN NaN NaN NaN\n", + "-8000 5.0 NaN NaN 5. NaN NaN NaN NaN NaN NaN\n", + "-7000 NaN NaN NaN 8. NaN NaN NaN NaN NaN NaN\n", + "-6000 NaN NaN NaN 11. NaN NaN NaN NaN NaN NaN" + ] + }, + "execution_count": 69, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "table1.columns = ['prb', 'un', 'maddison', 'hyde', 'tanton', \n", + " 'biraben', 'mj', 'thomlinson', 'durand', 'clark']\n", + "table1.head()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This function plots selected estimates." + ] + }, + { + "cell_type": "code", + "execution_count": 70, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def plot_prehistory(table):\n", + " \"\"\"Plots population estimates.\n", + " \n", + " table: DataFrame\n", + " \"\"\"\n", + " plot(table.prb, 'ro', label='PRB')\n", + " plot(table.un, 'co', label='UN')\n", + " plot(table.hyde, 'yo', label='HYDE')\n", + " plot(table.tanton, 'go', label='Tanton')\n", + " plot(table.biraben, 'bo', label='Biraben')\n", + " plot(table.mj, 'mo', label='McEvedy & Jones')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here are the results. Notice that we are working in millions now, not billions." + ] + }, + { + "cell_type": "code", + "execution_count": 71, + "metadata": { + "scrolled": false + }, + "outputs": [ + { + "data": { + "image/png": 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LnjfLeJ8aNbKu0RQaGqo2/XMn+vV5Ef36vBSEfj2o9oDkCNXvzqjnUVhXt8a2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\nUL68B6aFAylf3gPD/gACAhzfjNbUIFbDycbTpcvnonrZtRbLli3jq6+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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "newfig()\n", + "plot_prehistory(table1)\n", + "decorate(xlabel='Year', \n", + " ylabel='World population (millions)',\n", + " title='Prehistorical population estimates')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can use `xlim` to zoom in on everything after Year 0." + ] + }, + { + "cell_type": "code", + "execution_count": 72, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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aGhq5DlKBgYFMmTKFDh068N133wGZwSU1NVUpn0KhQE9PD8hcxlyhUChtT01N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\nuP6u+5DVroUQl9WZpN5//3327t3Lnj172LRpE25ubpY5U0OGDCEsLKw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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "newfig()\n", + "plot_prehistory(table1)\n", + "decorate(xlim=[0, 2000], xlabel='Year', \n", + " ylabel='World population (millions)',\n", + " title='Prehistorical population estimates')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "See if you can find a model that fits these data well from Year -1000 to 1940, or from Year 0 to 1940.\n", + "\n", + "How well does your best model predict actual population growth from 1950 to the present?" + ] + }, + { + "cell_type": "code", + "execution_count": 83, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "# Solution goes here\n", + "p0 = table1.prb[1]\n", + "prehistory = System(t0 = 1, t_end = 2016, p0 = p0, alpha=0.001) " + ] + }, + { + "cell_type": "code", + "execution_count": 84, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "# Solution goes here\n", + "run_simulation(prehistory, update_func1b)" + ] + }, + { + "cell_type": "code", + "execution_count": 85, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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vPYKCggAICgrCwcEBR0dHeX/Dhg1JTk7mxo0bxMTEcO/ePbU8jI2NcXd3l/MQ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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Solution goes here\n", + "newfig()\n", + "plot_prehistory(table1)\n", + "plot(prehistory.results, label='model')\n", + "decorate(xlim=[0, 2000], xlabel='Year', \n", + " ylabel='World population (millions)',\n", + " title='Prehistorical population estimates')" + ] + }, + { + "cell_type": "code", + "execution_count": 86, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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TlStXkpSUhLa2NtWrVycqKooqVapQrVo1qlWrhpqaGrNnz+b+/fuvrEtOTg7z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\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "newfig()\n", + "plot_estimates(table2)\n", + "plot(prehistory.results / 1000, label='model')\n", + "decorate(xlim=[1950, 2016], xlabel='Year', \n", + " ylabel='World population (millions)',\n", + " title='Prehistorical population estimates')" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "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": "3.6.1" + } + }, + "nbformat": 4, + "nbformat_minor": 1 +} From 10344b1c2077ddeb11c0c2db7fc7ffefc01888ff Mon Sep 17 00:00:00 2001 From: Junwon Lee <31522211+junwonlee5@users.noreply.github.com> Date: Tue, 19 Sep 2017 20:52:14 -0400 Subject: [PATCH 06/19] Adding chap03mine --- code/chap03mine.ipynb | 285 +++++++++++++++++++++--------------------- 1 file changed, 142 insertions(+), 143 deletions(-) diff --git a/code/chap03mine.ipynb b/code/chap03mine.ipynb index 577ab493..b733a0c1 100644 --- a/code/chap03mine.ipynb +++ b/code/chap03mine.ipynb @@ -15,7 +15,7 @@ }, { "cell_type": "code", - "execution_count": 1, + "execution_count": 280, "metadata": { "collapsed": true }, @@ -48,7 +48,7 @@ }, { "cell_type": "code", - "execution_count": 2, + "execution_count": 281, "metadata": { "collapsed": true }, @@ -66,7 +66,7 @@ }, { "cell_type": "code", - "execution_count": 3, + "execution_count": 282, "metadata": { "collapsed": true }, @@ -87,7 +87,7 @@ }, { "cell_type": "code", - "execution_count": 4, + "execution_count": 283, "metadata": { "scrolled": true }, @@ -265,7 +265,7 @@ "1954 NaN NaN " ] }, - "execution_count": 4, + "execution_count": 283, "metadata": {}, "output_type": "execute_result" } @@ -284,7 +284,7 @@ }, { "cell_type": "code", - "execution_count": 5, + "execution_count": 284, "metadata": { "scrolled": true }, @@ -462,7 +462,7 @@ "2015 NaN NaN " ] }, - "execution_count": 5, + "execution_count": 284, "metadata": {}, "output_type": "execute_result" } @@ -480,7 +480,7 @@ }, { "cell_type": "code", - "execution_count": 6, + "execution_count": 285, "metadata": { "collapsed": true }, @@ -504,7 +504,7 @@ }, { "cell_type": "code", - "execution_count": 7, + "execution_count": 286, "metadata": {}, "outputs": [ { @@ -1611,7 +1611,7 @@ "[66 rows x 11 columns]" ] }, - "execution_count": 7, + "execution_count": 286, "metadata": {}, "output_type": "execute_result" } @@ -1629,7 +1629,7 @@ }, { "cell_type": "code", - "execution_count": 8, + "execution_count": 287, "metadata": {}, "outputs": [ { @@ -1700,7 +1700,7 @@ "Name: census, Length: 66, dtype: int64" ] }, - "execution_count": 8, + "execution_count": 287, "metadata": {}, "output_type": "execute_result" } @@ -1721,7 +1721,7 @@ }, { "cell_type": "code", - "execution_count": 9, + "execution_count": 288, "metadata": {}, "outputs": [ { @@ -1743,7 +1743,7 @@ " 7256490011], dtype=int64)" ] }, - "execution_count": 9, + "execution_count": 288, "metadata": {}, "output_type": "execute_result" } @@ -1761,7 +1761,7 @@ }, { "cell_type": "code", - "execution_count": 10, + "execution_count": 289, "metadata": {}, "outputs": [ { @@ -1776,7 +1776,7 @@ " dtype='int64', name='Year')" ] }, - "execution_count": 10, + "execution_count": 289, "metadata": {}, "output_type": "execute_result" } @@ -1800,7 +1800,7 @@ }, { "cell_type": "code", - "execution_count": 11, + "execution_count": 290, "metadata": {}, "outputs": [ { @@ -1809,7 +1809,7 @@ "pandas.core.frame.DataFrame" ] }, - "execution_count": 11, + "execution_count": 290, "metadata": {}, "output_type": "execute_result" } @@ -1820,7 +1820,7 @@ }, { "cell_type": "code", - "execution_count": 12, + "execution_count": 291, "metadata": {}, "outputs": [ { @@ -1829,7 +1829,7 @@ "pandas.core.series.Series" ] }, - "execution_count": 12, + "execution_count": 291, "metadata": {}, "output_type": "execute_result" } @@ -1840,7 +1840,7 @@ }, { "cell_type": "code", - "execution_count": 13, + "execution_count": 292, "metadata": {}, "outputs": [ { @@ -1849,7 +1849,7 @@ "pandas.core.indexes.numeric.Int64Index" ] }, - "execution_count": 13, + "execution_count": 292, "metadata": {}, "output_type": "execute_result" } @@ -1860,7 +1860,7 @@ }, { "cell_type": "code", - "execution_count": 14, + "execution_count": 293, "metadata": {}, "outputs": [ { @@ -1869,7 +1869,7 @@ "numpy.ndarray" ] }, - "execution_count": 14, + "execution_count": 293, "metadata": {}, "output_type": "execute_result" } @@ -1889,7 +1889,7 @@ }, { "cell_type": "code", - "execution_count": 15, + "execution_count": 294, "metadata": { "collapsed": true }, @@ -1919,7 +1919,7 @@ }, { "cell_type": "code", - "execution_count": 16, + "execution_count": 295, "metadata": { "scrolled": false }, @@ -1933,9 +1933,9 @@ }, { "data": { - "image/png": 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D9yF9NMFflZVqKLlr165x9uxZMjIysLGxwdvbW/NUqBBCVDd9Gvfh/O2LZEWkUTe9E0bG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\nBRHBx8fHJefT3eS4E1ddF27f8xeLxVAqlejo6EB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1lVgsFvr3l8d2nJ0s4yiEsEvc2Thmb5/NqdRTJJxI5dChc+zL+omm81oxflyh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\nWoG1HBitEEIUT1GjfYaXZSDOJDk5jUd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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -1957,7 +1957,7 @@ }, { "cell_type": "code", - "execution_count": 17, + "execution_count": 296, "metadata": { "collapsed": true }, @@ -1968,7 +1968,7 @@ }, { "cell_type": "code", - "execution_count": 18, + "execution_count": 297, "metadata": { "collapsed": true }, @@ -1988,7 +1988,7 @@ }, { "cell_type": "code", - "execution_count": 19, + "execution_count": 298, "metadata": {}, "outputs": [ { @@ -1997,7 +1997,7 @@ "1.2862470293832287" ] }, - "execution_count": 19, + "execution_count": 298, "metadata": {}, "output_type": "execute_result" } @@ -2019,7 +2019,7 @@ }, { "cell_type": "code", - "execution_count": 20, + "execution_count": 299, "metadata": { "collapsed": true, "scrolled": true @@ -2032,7 +2032,7 @@ }, { "cell_type": "code", - "execution_count": 21, + "execution_count": 300, "metadata": { "scrolled": true }, @@ -2043,7 +2043,7 @@ "0.012862470293832286" ] }, - "execution_count": 21, + "execution_count": 300, "metadata": {}, "output_type": "execute_result" } @@ -2056,7 +2056,7 @@ }, { "cell_type": "code", - "execution_count": 22, + "execution_count": 301, "metadata": { "scrolled": true }, @@ -2067,7 +2067,7 @@ "1.2862470293832287" ] }, - "execution_count": 22, + "execution_count": 301, "metadata": {}, "output_type": "execute_result" } @@ -2080,7 +2080,7 @@ }, { "cell_type": "code", - "execution_count": 23, + "execution_count": 302, "metadata": {}, "outputs": [ { @@ -2089,7 +2089,7 @@ "1.2813631502151765" ] }, - "execution_count": 23, + "execution_count": 302, "metadata": {}, "output_type": "execute_result" } @@ -2118,7 +2118,7 @@ }, { "cell_type": "code", - "execution_count": 24, + "execution_count": 303, "metadata": {}, "outputs": [ { @@ -2127,7 +2127,7 @@ "2.5576286540000002" ] }, - "execution_count": 24, + "execution_count": 303, "metadata": {}, "output_type": "execute_result" } @@ -2145,7 +2145,7 @@ }, { "cell_type": "code", - "execution_count": 25, + "execution_count": 304, "metadata": {}, "outputs": [ { @@ -2154,7 +2154,7 @@ "7.2564900110000004" ] }, - "execution_count": 25, + "execution_count": 304, "metadata": {}, "output_type": "execute_result" } @@ -2172,7 +2172,7 @@ }, { "cell_type": "code", - "execution_count": 26, + "execution_count": 305, "metadata": {}, "outputs": [ { @@ -2181,7 +2181,7 @@ "(1950, 2015)" ] }, - "execution_count": 26, + "execution_count": 305, "metadata": {}, "output_type": "execute_result" } @@ -2203,7 +2203,7 @@ }, { "cell_type": "code", - "execution_count": 27, + "execution_count": 306, "metadata": {}, "outputs": [ { @@ -2212,7 +2212,7 @@ "0.07229017472307693" ] }, - "execution_count": 27, + "execution_count": 306, "metadata": {}, "output_type": "execute_result" } @@ -2233,7 +2233,7 @@ }, { "cell_type": "code", - "execution_count": 28, + "execution_count": 307, "metadata": { "collapsed": true }, @@ -2251,7 +2251,7 @@ }, { "cell_type": "code", - "execution_count": 29, + "execution_count": 308, "metadata": {}, "outputs": [ { @@ -2292,7 +2292,7 @@ "dtype: float64" ] }, - "execution_count": 29, + "execution_count": 308, "metadata": {}, "output_type": "execute_result" } @@ -2311,7 +2311,7 @@ }, { "cell_type": "code", - "execution_count": 30, + "execution_count": 309, "metadata": { "collapsed": true }, @@ -2330,7 +2330,7 @@ }, { "cell_type": "code", - "execution_count": 31, + "execution_count": 310, "metadata": {}, "outputs": [ { @@ -2342,9 +2342,9 @@ }, { "data": { - "image/png": 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lly5dQkdHh3bt2iGVSHm+6/Mkp18n56gX5vJ2lMukVFQoMDR8OJY+1+pV1DVfjCAIwoMu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\nk+KXyWRwdXXVysXZ2RlWVlaQy+W9Hn9ncgCACRMmIDU1Fcn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oqC+gsKGQQm0ZKQVFfLY/m7LjjUy5YFCH5+jta+gO/eEarE3+/wGeFEL8LKUs\nbN0ohHADHgbWWHme1uy6orWbRwhxFzAV0yeHP3d2sK3FXKSU6PV6qwJr787fwcEBrda6nrGIiIgu\n3/m3/keZNGmS+VpycnLQarVcfvnl5tERfn5+eHl5ER8fT0lJCdOnT7e49ujoaFatWoWDgwONjY2M\nGDGCKVOmmNudnZ1Zv349Y8aMoaysjObmZl5++WWLa2xubsbf35/4+HhycnLQaDRWFaboSwUsuqK/\nxw+9ew3Nzc0cPHiQmpoavLy8qGmqQZZIqpyraB7STFW+AXujByPsppOWasfCG0bi7+/a5jzq36F7\ndfZLqLNJXl+d8q0GGAVkCSF2Yxrp4wNMARwAawu55LV8TWndIKU0CiFSgeFWnsNqQoiz6oqJjY1t\n8wuhJ9nbW/5zaDSaDhescnZ2brOtdSidvb09Go2G06u0tRayBlOBdYCXX36Z0NBQi/2s/YWnKK20\nWi3l5eUYMXKs4hjHao5R51NHs2szaODy8ZMpKR9FVaOW666Lws/P5cwnVXpUZ3f+jlhO7NrV8tUB\naB0kfqDlq7VVv34FaoEEYB+YRwCNAr6x8hwKpk8a+/fvt9jW+ls+IiKCyspKcxF1Ly8vAA4ePGje\nNzQ0FAcHBwoLC5k2bZp5+7///W/0ej333HPPObgKZaCws7MjMCKQ/331P8rsy6gLrEdjD072Tswf\nNZ+LQi6iKLwOrVbDoEFt7/iVc6+zSV4zuvvNpJR1Qoh/ASuEEIWYPgHcCURgGjmkWOnWW2/l2muv\nZeXKlcyfP5+8vDwef/xxpk+fTkREBAEBAbzyyiv89a9/5f7776ewsJCXXnrJfLyLiwtLly7l+eef\nx83NjZiYGHbs2MErr7zCihUrevHKlL7OaDRSWFhIQECA+ZPpT7k/8dbBt6h3byY1qwT3KgcuT5jI\nkrFL8Hf1ByAgwK03w1ZO0+HneyHElI7aOiOEmHqGXZYBzwEvYEr+FwCXSillV97vfBUVFcWrr77K\n3r17ufrqq3nkkUe45JJLePHFFwFwd3dnw4YN6HQ65s+fzxNPPMGtt95qcY6//OUv/O53v2PVqlVc\nccUVvPvuuzzxxBP89re/7Y1LUvqB6upqdu/ezS+//EJBQYF5e5B7EDV1jfySnE9VpQ7HI+O40nep\nOfErfY/m9H7hVkKIJCAVeEpKebDdnSz3T8D08DdSStntHeWJiYlGWx/49hfqGnpff48fevYaDAYD\nGRkZHDnhzEf2AAAgAElEQVRyBIPBAICTkxMzZswwPz/aKrfy2pYv8D46BTejP/PnRzF7dmhnp21D\n/Tt0r5ZY2n1w2Fmf/wRgObCvZVXPD4G9wFFM/fbemPr+LwKuwDSB62VgYbdFrihKrysrKyM5OZnq\natM6jzqDjjpdHQkiwWKQwpyoOVx46yzWvJ7C/PmC8HDv3gpZsUJnff7NmJZvWA3cC9yKqcvm1I8K\nGuAY8D/gKillXpsTKYrSL50+WQugoqGCtJo0anxq8T8RR1TUyZ5jrUaLr48rf/3rRFVWsR844zj/\nloT+APCAECIaCMe0sFsJkCOltG4KraIo/UZhYSEpKSnm5UIMRgM5VTlkaDMod64l9UApe6tewsd5\nORMnWg72U4m/f7CpkpeUMg3TrFxFUQao7OxsUlLMU3Goa64jrT6NArcCjPZG8jJq0NU6EN4Yzzvv\npBEd7Yenp1p2ub9RZRwVRbEQFBSElJKmpiYKGwpJMaTQ4NFg6uQFrpl8EbnbBI0N9sybF4WHh2Pv\nBqx0iUr+iqJYcHJyIiwyjE/3f8oRhyMY7Uz9/Q52DiwYvYCpIVM5HlyNk5OdGrvfj6nkryjnKaPR\nyNGjR2lsbGTkyJHm7anFqaw7so4K+0qyjlbg4uLApOhobhl/C0EeQQCEhKh6uv2dSv6Kch6qqqoi\nKSmJiooKNBoNAQEB+Pqa6uQ26hsprioj5WAJdXU6QnTjuWnO3QR5+PRy1Ep3Uit4Kcp5xGAwkJaW\nxvfff09FRQVg+gSQlZVl3mds4FgujpyFi9adMbXXEFY7lX17i3srZKWHWFvG0Rl4BFMNXzfa/tIw\nSinPrpKJoig9qqysjKSkJIu6E1qtlmHDhzEmeozFvtePWcAkn1m8+mIav/lNJBddNPT00yn9nLXd\nPi9iKrryHXAQMPRUQIqidC+dTkdqairZ2dkW2728vch0zGRX/i5u97qPsKEnC6w42DkQGRLE008P\nwslJ9Q4PRNb+q14HPCqlXNmTwSiK0r0KCwtJTk6moaHBvM3e3p7BoYPZWriV3LI8jh6tZPdnT7H2\njr8TFeVrcbxK/AOXtX3+jpjW9VEUpZ8wGo1kZmZaJP6AgADcIt14M/tN8mvyycyqIC+/Bo1Ry9p1\nB6ira+7kjMpAYm3y/wrT4m2KovQTGo2G2NhYtFotTk5OxMTFcNjhMG+nvk2TvgmAiDBfYoyXIuou\nZ3iob5vqb8rAZe1nuo3AGiGEP7AHqDt9h9aavIqi9I6mpiaMRqPF2jru7u5MmDCBJscm1iWtI7/6\nZMXVQPdAbou/jdIIRyoqGpg6NVity3MesTb5f9jydWnLn9MZAZX8FaUXtE7WSk9PZ/DgwURERFi0\nH9Md461f36KkvAqdzoiPjzOTgyezMGYhTvZODD13ZaqVPsTa5N/txdUVRTl7p07WMhgMSCkJDAzE\nzc207EJqcSprfl1Dfl4NWUcrcbRz4JlFS7hi9KxejlzpbVYlfyllTutrIYQb4AGUtqz5ryjKOabX\n682VtU7tp3dzc0Ov15u/j/aPZqTPGPb+/A3Oem9GVs3h6E4fGN0bUSt9idXjuIQQM4CVQDwt6/sJ\nIfYCj0kpv+2R6BRFaaO0tJTk5OQ2k7UCAgKYOnUqWu3JcRwajYbbJ90CDa4c/jCQ8JBBLFig5mMq\n1s/wnYZpxE8apmpehcAQYAHwuRBitpTyhx6LUlEUmpubSU1NJScnx2K7n58fsbGxpKWlsTd/LwlD\nErDT2pnbXR1cuffiW0gdWkpkpA/29mpVF8X6O/8ngW+AK6WU5s+YQoingG2Yav3O7vboFEUBoLq6\nmp9++qnNZK1Ro0YREhJCg66BD3M+pPBYMeuO/8AT199JYKDlcssjR/qd67CVPszaW4AJwCunJn6A\nlu9fARK6OzBFUU5ydXXFzu7k3XxAQAAzZswgNDSUEzUneGbXM/yaf4jEX4v4Ie87Vrz+Mc3N+k7O\nqJzvrE3+5YB7B20egPpfpig9yM7Ojri4OJycnIiPjychIQEXFxeSTiTx7K5nKawpRGunQaczMLRx\nLA15vhw6VNrbYSt9mLXJfzuwXAhhUam55fvlmLqEFEXpBrW1tUgp28y29fPzY/bs2QwZYvox3Ja+\njdW/rKZBZ+oK8nRz5k8X3s5Yh0v4y58TGDt28DmPXek/rO3zfwTYB2QIIXYBJ4BA4CKgCnioZ8JT\nlPNH67r6Ukr0ej0eHh7mRN/Kzs6OBl0Dbx54k18LfkXTUljXz9WPa3yu4YopV1A3uxk3N1VXV+mc\nVXf+Uso8YBywGvACLgC8MfX3j5NSZnVyuKIoZ1BZWcmuXbs4fPiweZz+oUOHMBgsV08vqSvh2V3P\nsu3XH9j/axF6vYFo/2genfooAS4BaDQalfgVq1g9zl9KeQJ4sAdjUZTzjl6vJz09nczMTItuHk9P\nT+Li4izG7AO8eeBNvt9/mIKCWgA02ZH8+eo/WwztVBRrdJj8hRCPAuullAUtrztjlFI+072hKcrA\nVlpaSlJSErW1teZtWq2WqKgoIiIi2iR+gCVxS0hMT6ewoIHIulmE1kyiscGAq6tK/optOrvzfwrT\ng9yCltedMQIq+SuKFc40WcvdvaOBdTDIbRB/v+o+vtQex9sYxMKFI3FwUIlfsV2HyV9KqW3vtaIo\nZyctLc0i8Z86WevUJZWrGqs4WpaN8BmFs/PJH9Vo/2iiFgu0WrX8stJ1ViV1IcSy04d5ntIWKoR4\nqXvDUpSBKyoqCkdH00PZwMBAZs6cSWhoqEXiP155nL9/8yR/XPckz7z6WZthnyrxK2fL2ge+fwc+\nB/LbabsAuA34c3cFpSgDhdFoxGg0WvTfOzk5ERtrWkQ/MDCwTQGVxPxE1ux7gx/35tLUpGdL+Ubi\ntwmuvkotyKZ0n84e+O7ClNjBtIrnT0J0+J/vF2vfUAgxCjjUTtNUKeUua8+jKH1dbW0tycnJuLu7\nExMTY9EWFBTUZn+j0cjW9K1sTd8KGggIcKXgWCNRDZfgaK+Gbyrdq7M7/1uAeZgS/xPA60Duafvo\ngQrgYxveMwYoafl6KjUXXRkQWgunp6eno9frKSkpYejQofj6+nZ4TKOu0Txxq9XEUSPwsp/JVTPG\nqkXZlG7X2QPfNGAFgBDCDljbMtnrbI0BDrfMG1CUAaWyspKkpCQqKyvN2zQaDRUVFR0m/9K6Up77\n7gXK9IXmGbsjB43k1vG34jbbrd1jFOVsWVvJ63EAIYQf4EhLMRdMD4zdMHXZrLXyPccAqTbGqSh9\nWkeTtby8vIiLi8PLy6vd4zJKM/j71udJTs1lyFB3hod5MXP4TBaMXoBWowbZKT1Hc/oogvYIIWKA\nt+m4+JtRSmltYZgM4AjgA4QBB4FHpZR7OzsuMTHxzIEqSi+oqakhLy+PxsZG8zaNRkNAQACDBg1q\n80DXfFxzDU///ALpmVWmY4xabhp3DXPjLmh3f0Xpivj4+Hb/A1o72uc5wA94ALgKaAQ+BeYAVwAz\nrDmJEMIFCAeKMS0V0QjcDewUQoyXUnb6iSA+Pr7NtsTExHa39yfqGnpfV+LX6/UcPHiQqqoqPDw8\n8PDwAEyTteLi4sxF1DujG6xj2QerqSnVMNVlPrddfiVDhnQ8yau7r6GvUdfQvRITEztsszb5XwDc\nK6VcJ4SoBRZJKf8D/EcI8T9MwzzPOFJHSlkvhPABGqWUjQBCiKWY6gLfCfzJyngUpddptVqLpRkc\nHBwYNWoUw4YN6/Bu/3Szhs+i6spaSpMHs3jeBIvJXIrSk6z9n+YEZLS8TgfiTmlbD7xq7RtKKatO\n+94ghDgEDLP2HIrSF2g0GmJjY9m5cycBAQGMGTMGZ2fnDveXxRnkZuiYfeFIi3NcG3N127FvitLD\nrH2idAwY3vI6HfAUQoS2fN8AdDyG7RRCiHghRJUQIv6UbXbAWNof+68ofYLRaCQ/P7/NEsvu7u7M\nmDGDCRMmdJr4P0n+iiWvPswjH67ix5+P9XS4inJG1ib/zcCzQohrpZT5QBrwpBBiJHAvkGnleZKA\nbOA1IcQkIcRoTJ8c/IEXbYpcUc6R2tpafvzxRxITE8nKalu6orO+/WZ9M/9N+i8vfLOWyuoGqu2K\neHzT65SV1fdkyIpyRtYm/8eBn4BbW76/F7gO00idSzGVcjwjKaUO0wNiiemB8V5MFcGmSSmLrI5a\nUc4Bg8HAkSNH+O677ygtNc1BlFJa9PN3pqSuhJW7V7L72G7Cw71wcbHHwzCI22Zfh49Px58SFOVc\nsHacfx3wWyGEU8v3X7YM/xwP/CqltPbOv7Uq2KKuBKso50pFRQXJycltJmuFh4d32r3TKrkwmfX7\n11PXXAeAnZ2WhdMvY27IdYgRqrau0vtsGlrQOkKn5XUm1nf3KEq/oNfrkVKSlZVl02Qt8/EGPc98\ntJ69ZTsICjIN2bTX2nP9mOuZGjLV6lFAitLTOlvYLQNTkRZrGKWUaslBpV8rKSkhOTnZolvHzs4O\nIQTh4eFnTNwnyku5642nOVyUhlarwcPTkWH+Adwx4Q7CvMN6OHpFsU1nd/67sT75K0q/VllZyY8/\n/mixzd/fn9jYWKsmawH8dGIXx+tNH4YNBiPN+f489tvHcHfs2qQtRelJnS3stvQcxqEovcrDwwON\nRkNNTU2XJmsBzBVXsS8hmS0793JFxByevOkWnBwdejBqRek6a9fjufBM+0gp95x9OIrSO7RaLbGx\nsRw9evSMk7VaVVY24uXlZP7eTmvH/dPv5mpxjInD4zo5UlF6n7UPfHdx5i4gVUVa6fOMRiPHjh2j\ntLSUcePGWdzZ+/n54ed35nXzjUYja7d8w7s/fMnqWx8hOvrkMT4uPkwc7tMjsStKd7I2+c9sZ5s7\nMBW4EVPRF0Xp02pqakhOTjaP2Q8ICGDo0KE2nUNv0PO3t17lk0OfYbSDZRvWs/6xP+PmpiptKf2L\nteP8d3bQtE0IUQM8hmm1T0XpcwwGg7my1qnLM2RnZzNkyBCr+/VL60pZ++taCt0zsHfQ0txsoMgt\nmZr6BpX8lX6nO5YQ/AF4uBvOoyjdrqKigqSkJKqqTq4nqNFoGDFiBJGRkVYn/n35+9iYvJH65noc\nHe2IivLBuzmE5xY+gI+rZ0+Fryg9pjuS/1yg6ox7Kco5pNPpSE9PbzNZy9vbm7i4ODw9rUvYGUeL\n+ODw+xwzHDRv02q03DplEZdGXKombSn9lrWjfb5qZ7MdpmWYI4CV3RmUopyN4uJikpOTqaurM2+z\ns7MjOjqa4cOHW5WwjUYjG7fu5oXvV9PkUE38+ME4Odnj7+rPzeNvJtwnvCcvQVF6nLV3/o60He1j\nBA4Dq4B13RmUopyN3Nxci8Tv7+9PXFwcrq6uVp/j19wk/vXLP6jXNIMOMo5UcPNlV7IwZiHO9mpR\nNqX/s/aB74wejkNRus3o0aMpLi7GYDAwevRogoODbe6eGR0UzYVxkWz/+TDeHu48NuePXBE7o2cC\nVpReYFOfvxDiCkzDO32AQmC7lPL7nghMUaxRX1+Pvb09Dg4nZ9I6OjoSHx+Pu7s7Tk5OnRzdMWd7\nZx6YfReudhu4f/YfCfBQK3EqA4u1ff5+wOfABExF14uBwcD/tTwPuFZK2dBjUSrKaYxGIzk5OaSm\npjJ06FBiY2Mt2q2ZrNUqt7CUle9/zotDhHklToAw7zBWXrNMPdRVBiRri7m8jKmM41wppYuUMkRK\n6Qxci+kXwrM9FaCinK6mpoYff/yRlJQUdDodOTk55olbtvp4125+86+7+KVhB39//X2am/UW7Srx\nKwOVtcn/CuABKeW2UzdKKT8BHgF+192BKcrpDAYDGRkZ7Ny50yLZu7u7o9Va+1/ZpEnfxHsH3+Oj\ngnXUUwPAT7XbSDqc160xK0pfZW2fvw6o6KCtANNoIEXpMWearGVnZ/3SUkfLj7L+wHoKawpxcbYn\nLNSTY5kaViz4CxPiQnoifEXpc6xN/quBp4UQv7QUcAdACOGJaXbvyz0RnKLodDqklBw9evSsJmsB\nHM0p4/PMz0ip243BeHKZhyvGX8io2NHMmjCtW2NXlL7M2uQ/pOVPphBiF5AP+AFTAA+g8ZSJYEYp\n5WXdHqly3qmvr2fPnj1nNVkLQKcz8N8tu3n1x7U0OZcTHx+Avb0WJ3snrh99PRcOu5Bff/21py5D\nUfoka5P/CODAKce0fjZu3WaHWtJZ6WbOzs64uLiYk/+gQYOIjY21abIWwM85+3jp13/QqNVBExzN\nrmTOpIksHbsUf1f/nghdUfo8ayd5tbeks6L0KI1GQ1xcHHv27CE6OrpLk7UAYoNHMiY6iMSU4/h6\nuXLn9JuYN+5KNZJHOa/ZOslrFDAd8MI01n+XlFL2RGDK+aW+vp6srCxGjhxpMXLHzc2N2bNn2zSa\np6qqEU/Pk5O7PJw8uO/i23jLZTMPXXYXgR6B3Rq7ovRH1k7y0gKvAX8ATr1dMgoh3gJ+L6VUxd4V\nmxmNRrKzs0lLS0On0+Ho6EhkZKTFPtYm/vr6Zta8v4vtKb/wxqN/ws/Pxdw2Pmg84+aNU3f7itLC\n2tuph4GbWr4GAw6Y+v0fAW4AHuyR6JQBrbq6mj179nDw4EF0Oh0AGRkZNDU12XwuvUHPX15ZzWuH\n/4m028kLb31hMToI1IQtRTmVtd0+NwMrpJTPnbItF1glhHBuaV/V3cEpA5PBYODIkSNkZGRYVNby\n8PAgNjYWR0fbpo3kVuWy4cAGqoZkYCwyne/X5i9oapqLk1N3lKxQlIHH2p+MIGB3B217MH0CUJQz\nKi8vJykpierqavM2rVZrnqxlS9++3qDniyNfsC1jG3qDHk8PJ0JCPRnhH86jV9ylEr+idMLan44s\n4ALg23baLsA0y1dROtTRZC0fHx/i4uLw8PCw+lwnTtTyyls7qIv6iRptsXm7vdaeey9byiURl6DV\n2Lbcg6Kcb6xN/muBZ4QQtcB7mJZzDsC0ps+jwNM9E54yUGRnZ5OVlWX+3t7enujoaMLCwmzqi//x\n5+M89d4Gjjr8hGudPePHDUaj0RDuE86SsUsIdFcjeRTFGtYm/5eBccDzwD9O2a4BNgIrujkuZYAJ\nDw/n+PHj1NTUMHjwYGJiYmyerAVwQPcVOU4/YTQYqatrpq7GwJJJ1zM7fLa621cUG1g7yUsPLBFC\nrMJUzMUXKAe+l1Ie6sH4lH7IaDSi1+uxtz/530ur1RIXF0ddXR1Dhw7t8sibeWPn8nnKTgqLq7k4\nfjx/nnYbAe4B3RW6opw3bH0idhxT/385UNTyusuEEJOBXcDFUsrvzuZcSt9QV1dHSkoKABMnTrRI\n8r6+vvj6+lp9rv37C3Fw0DJmzCDztsFug/nLpb9HZ9BxcYS621eUrrJlktcq4G5MY/xbf6JrhRAr\npJQ2F3MRQrgBb6HWBBoQjEYjR48eNU/WAsjLyyM4ONjmc1VXN7Hx7UN8cngbnq6urF/2J1xdT5Zp\nnBWuVhtRlLNl7W3TcuAeTH3/UzAt9DYFWAM8IYS4swvv/U9McwWUfq66uprMzEyLyVoajYba2tou\nna+ovoB3jr1CtvOPHDR8x8aPf+rOcBVFwbZJXk9IKZ88ZVsW8KMQohq4F9Oa/1YRQswBrsRUISzZ\n2uOUvqW1staRI0eoq6szP8BtnaxlSxcPgMFo4OvMr/lEfsLgyCZKUmFwoDP2UVmYHjUpitJdrE3+\nXsDeDtp2AQ9Y+4ZCCH/gDeD3mJ4dKP1QWVkZycnJZz1Zy2g0cuJELVqPWtYfWM/R8qMA+Pu7MHHC\nEBaOv45LIi7pkWtQlPOZ5vT1T9ojhHgPcJJSXttO2xuAp5RyvjVvKIT4ECiRUt4uhAjG9BB55pke\n+CYmJqqF4/oAo9FIfn5+m4Lprq6uBAcH4+zsbPW5Kiqa2bqtgAMV+/CaLNE6nFzqIcgliKuHXY2/\ns1pvX1HORnx8fLtD66y98/8eWCGESMY0yasAUyWvq4CLgH8KIR5t2dcopXymvZMIIZZgmi8Qa0Ps\nZvHx8W22JSYmtru9P+lv17B//37zKJ7WyVqlpaVMmDDB6nMYjUYee/pLfuQzKv3zaSx1YswYf+y1\n9lwVdRWXj7j8nI7k6W//Bu1R19A39KVrSExM7LDN2uT/75avXsBT7bSf2u1jBNpN/sBSTKuCnhBC\nwMlRQ58LITZIKe+wMh6lF40ePZri4mK8vLzMk7XKyspsPk/96F1U7clHA7i7OzLUI5ibx/+BYE/b\nRwgpimIbayd5ddct2GLA5ZTvA4EfgFuAr7vpPZRu0trFM3jwYBwcTg61dHR0ZOrUqTg7O3d5spZG\no+Guab/nSFE2nh5OLBh/DXMi52CvVYuxKcq5cE5/0qSUead+L4RoaHmZJ6UsOpexKJ1rnaxVVFRE\naGgosbGWPXUuLi4dHNlWeXkDGzceYu7cCMLCvM3bI3wjuPeSmwn3CSfUO7TbYlcU5czUbZZi4dTJ\nWnq9HoCcnByGDh2Kn5+fzec7dKiEf6/5kRTNV6RsGMvqv/0ee/uTHyRnDlcTthSlN/Rq8pdS5mJZ\nFlLpRVVVVSQlJVFRUWHeptFoCAsLw8vLy+bzGY1Gco2H+dF5A42Gen6qyeOXlBlcMC6iO8NWFKUL\n1J2/Yp6slZGRYbHWvoeHB3Fxcfj4+Nh8zurGat5JeYdfC35l2HAn8vKaiRKe6HzzAZX8FaW3qeR/\nnisrKyMpKYmamhrzNq1WS2RkJCNGjLCpslZdXTOlpfWUOmSxMXkj1Y2mCWBBQ9yIDgvm5vjfE+0f\n3e3XoCiK7TpM/kKIIbacSEqZf/bhKOdSeXk5u3dbVuf09fUlNjbWpspaAEeP1rLxg29Js9vBkIQy\ni379qSFTmT96Ps721k8AUxSlZ3V255+Lacy+tdTqnP2Mt7c3/v7+lJSUYG9vz8iRIwkNDbV5+GZj\no443P/+J476/0GSso+6IC9HRfng7e3Nj3I2MGTymh65AUZSu6iz5/4GTyd8XeBZTDd8PODnD92pM\ns3zv68EYlW5iNBotErtGoyE2NpbU1FRGjx5t0/BNC3Z6jLGJNOXV4eCgxX+QK5ODJ3P9mOtxdbC9\nWpeiKD2vw+QvpXyz9bUQYjPwXynlraft9o4Q4kVgAfB6j0SonDWj0Uhubi7Hjx9n8uTJFv34bm5u\nNi3L0Hq+U3+JONk7sTDmat5z+YzhQwK4JWEpsQFdWsFDUZRzxNoHvpcCv+mgbStw+i8FpY+oq6sj\nOTmZ4uJiADIzM4mMjOzy+bKyKnj73YPceUc8fn4nPylEe0Vz/6VDSRiSgJuj21nHrShKz7J2KEcJ\nMLGDthlAXgdtSi8xGo1kZWXx3XffmRM/QG5uLgaDoZMjO7ZjxzEe/ucHfFj+Mv9Y/xmnrwg7I2yG\nSvyK0k9Ye+e/BlgmhHABPgGKgQBgPvBn4C89E57SFR1N1ho+fDhCCJuGb7aqa65jn24rB123YQS+\nKf6I2/NmEBZs+6xfRVF6n7XJfwXgDTwIPHLK9gbg/6SUr3R3YIrt9Hq9ubJWd03WAkg6kcTbKW9T\n2VBJ8DAPqqubGD96EFqPWkzP/RVF6W+sXdXTCDwghHgSuADwwdQVtEdK2bVCrUq36miyVlRUFBER\nETbf7WdmVqDT1LOr4jP25p0s4hYW6knC0AR+F/M73B3duy1+RVHOLZtm+EopK4EveigW5SwUFxdb\nJH5fX1/i4uJwd7ctQTc06Pjooww+3LOdgkG7GT3OHW3LyB5PJ08WxS5ibODYbo1dUZRzr7MZvhlY\nP8nLKKUU3ROS0hWRkZEUFBRQX1/f5claACcqSlmz/zVOuGZALRw/biQ0xJNJwZO4fvT16oGuogwQ\nnd3578a2Gb7KOdLY2IjBYLCYlKXVahk/fjwODg5dn6wFuHva4R1ZwYkj4OfnTFRIELdMVOP2FWWg\n6WyS19LW10KIG4BvpZTFHe2v9LzWyVqHDh3C29ubSZMmWdzde3p62nQ+g8FIUVEdgYEn7+b9Xf25\nc/ZiXnf+L1fHXcK8UfPULF1FGYBsGeq5FPiw50JROlNXV0dSUhIlJSWAqY8/Ly+P4OCu1bvNyank\nrY2HyCrP4uXHF+Dm5mhumx0+iwjfcMJ9wrsldkVR+h5rk38eoG7/ekHrZC0ppbmyFoCrqyvOzl1b\nJdNgMLLq9S/Z2/AZtXYlvPHBUP78+5MVtbQarUr8ijLAWZv8/wO8KISYDCQBNafvIKV8pzsDU848\nWcve3vZyDA26Bj6Rn1AUtY2aQyVotRoOGL7AYJjepclfiqL0T9Zmj3+1fP1jB+1GQCX/btLRZC1P\nT0/i4uLw9vbu5Oi2mpr0ODho2Ze/j02HN1HZUImvrzNhYZ4MCfBkQdwsVUxTUc4z1ib/4T0ahWKm\n0+n44YcfumWyll5vYPv2Y2z6Yh/Bl2eS15Bl0X75+Mksil2Ev6t/t8WvKEr/YO0M35zW10IIN8AD\nKJVSNvdUYOcre3t7fHx8zMnfz8+P2NhYmydrAaz77wE2HdhCntOveP7iQEyMPxo0eDl7MX/UfCYM\nmdCluQCKovR/VncaCyFmACuBeFo6CYQQe4HHpJTf9kh056lRo0ZRVlZGREQEISEhXU7QxcE7yU3d\nhxFobjag1xm5LOpirhZXq5KKinKesyr5CyGmAV8BacAyoBAYgqmIy+dCiNlSyh96LMoBqrGxsc0o\nHgBHR0dmzpx51nflixJ+y065Fzs7DdPGxLE4bhHBnl0bGqooysBi7Z3/k8A3wJUti7wBIIR4CtgG\nLAdmd3t0A5TRaOT48eMcPnyY5ubmdtfXtyXxFxXV8sbbv3DtlaOJjhpk3h7qHcofL76eALcAJgdP\nVl08iqKYWZv8JwALTk38YFrtUwjxCvBut0c2QNXW1pKcnGyerAWmFTlramq61K//074cnnhnAzn2\n+0h9ZzbrHvsT9vYnHwr/JrqjAmyKopzPrE3+5UBHmckD0HfQprTobLJWeHi4zYnfYDSw+9huPij4\niO84EU0AABT4SURBVGNOGRj0Rg7U7iTp8LXEx4Z0d/iKogww1ib/7cByIcQPUsr81o1CiCGYuny+\n6YHYBozKykqSkpKorKw0b9NoNISHhyOE4MCBA1afy2g0cuDEAbbILRRUFwAwPMyLE4W1TB87iqHh\njmc4g6IoivXJ/xFgH5AhhNgFnAACgYuAKuChngmvf9Pr9aSnp5OZmXnWk7WMRuP/t3fu4VVVVwL/\n3YRcSALGEAISgkACLAQELPjgTVCg1FftWD9bx9G2lraOtT5G6UxrrbalOnZo1TpDv7a21U61Dwu1\nDxRUqGKxjrHyDCuEVyIkEMCAIRAIufPHPjc5CXlcSHJzL3f9vu9+Sc7eZ5+1cvZde5919l6LF1a/\nyeuVL1Gb2jS+3gXDBvHv869j8mDz6xuGERmRrvPfLSIXAfcC03Gbvj4AngIWq2pF14kYv1RUVFBS\nUtLwd1JSEiJCXl7eaW3WKq7Yzld/8T8UHdhMMCWJiZMGkNIjmV49ejFv+DyuyLuCYLLN+A3DiJy2\nkrnMxKVpPAHgGfj7oiXY2UBOTg6lpaXs37+frKwsxo8fT3r66SdD2f7hVnbVFANw/EQ9u8uOctvl\nH2f+iPmWStEwjDOirZn/KuCIiLyOW+P/iqpuio5Y8cmJEydISUlp+DsQCDB+/HgqKytPa7NWKBRq\nUnd2XgEX5C3j3U1lzMyfxgM3fJaczP6dLr9hGIlDW8b/OpxPfzrwGJAsIhW4l7srcYPBabt7RCQX\nFyjuciAJlxP4Hv+L5Hjj2LFjbNy4kerqambMmNHEpZOWlsaQIUPabaO2to7X1m7h2bde4OIBU7n7\nM1c0lAWTgyyc96/UXhZkkozsEh0Mw0gs2srk9QfgDwAikgZMxg0GM4AlQKqIbMINBCtVtd3E7iIS\nwG0KqwTCAeSfAP6ICxsRVzTfrAVQUlLCyJGnZ6APHT/E04XP8ORffk+IEGWV+7l5/xT69WtMoXDh\neWPdK3bDMIxOINIXvjXAq94HEekBzAQWAHcAdwHJETQ1ACgCvqqqO722FgPLRCRTVT84XQW6iyNH\njrBu3ToOHDjQ5HhtbW2755aXV9OvXyrVdYdZXrKcpbqUvll9ycgIUnWolgPJ21n9ziau/+jFXSW+\nYRgJzukEdusFzAKuwM3ax+Hi+L+NeyfQLp6b6EZfm7nAF4D/ixfDHwqF2LZtG8XFxU02a6WnpzNu\n3Dj69Ws9PPJbb+1h1aoytuwqY/j8vZT32MTJ+pOcDLl2BuX25sJBo1gw81NMGnZhl+tiGEbi0qbx\nF5GxwDzvMw3oBWzDGfuHgVWqevhMLiwiy4BrcUtGC9qpHhO0tlkrPz+fkSNHkpzc9sNP0a5SVuz9\nPXvP2UzJ5p6MHds4UOT3zeeuy65mVL9RtlbfMIwuJ+DffORHRN4HBuKM82qcwV8Rdtd0FBG5EEgF\nvg5cBlykqrtbq19YWNiyoFGioqKCysrKJpu1UlNTyc3NJTU19ZT6dXX1TWLsADy75XlefPtdAkBG\nRgpDh6aRm57L9AHTGdZ7mBl9wzA6nYkTJ7ZoWNqa+ecA+4Gf4l7qvtGZyVtUdQOAiNwIlAG3AIva\nOmfixFPfCRcWFrZ4vLMpLi5uiL6ZnJzckFmrucH+4INjLF++g40b9/PQQ1NISWl8GsjMy2RP/UP0\n7p3C6AGjuGrkVUiW8O6770ZFh64kWvehq4h3+cF0iBViSYfCwsJWy9oy/lfg3D3zgfuBGt+a/xWq\nWnS6gojIAKBAVZ8PH1PVGhHZBgw63faiyfDhw9mzZw/BYLDVzVr19SEeffRtdh3eQXlwPWv+lkvB\nzMYMmHmZedw46VrG9h/LyCxbsmkYRvfR1lLP13AB3RZ6RnseMAcX5+f7nltoJW4wWKmqByO43hDg\nOREpUdV3AEQkAxDgFx3SpJMIhUJUVFSQkZFBWlrjUsukpCQmT55MMBhs0T0TCoUo2r+ZA6Ne4r3N\n6wBYvuk1CmZ+rkm9T1zwia5VwDAMIwIiXeq5F3jG+yAiE3ADwQzg5147Ka2d7+Md4A3gJyKyADgB\nPIJb99/txv/YsWNs2LCBiooKsrOzufTSS5sY+p49ezb8XlV1jLKyDxkzNovCPYW8vO1lyg6VEcoM\nkZXVi5yBvUnOKaE+VE9SIPI4PoZhGNEg4qWeACJyLm6z1xTgUlySlx5A644lH6paLyKfAL4H/Am3\neuhlYKaqVp+OLJ1JKBSitLSUzZs3U1dXB0BlZSW7d+8mN7dp2sPa2jqWLi1h9Rvb2deriPw5+zh8\noqqhPDkpwIVj+nNZ7mXMzZ9rht8wjJikvaWeI3CGfqr3cxQuJMNm3IavHwKrT2e5p6ruB249Q3k7\nnerqatavX3/KZq0hQ4YwYMCAU+rXJ51g2ZZlbEp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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -2379,7 +2379,7 @@ }, { "cell_type": "code", - "execution_count": 32, + "execution_count": 311, "metadata": {}, "outputs": [ { @@ -2391,9 +2391,9 @@ }, { "data": { - "image/png": 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9O3379r2n1yIIteJy49h9aTc5pbkM05nOpNH9VDX6EokECxNT3nyzT7M+XE1N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\n/vvvw8jICE1NTd2SQ1JSEj766CPMnz8fbm5uaGxshFgsbvP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LY/fu3QghWLlyJREREUyfPp3i4mLc3d2ZP38+K1asYPPmzSQmJlJdXc3s2bMp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\nrVHjx09k8+Z4nnm2jt3JL1O8dzcHjjZ0rI+LjWH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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -2406,7 +2406,8 @@ "elapsed_time = last_year - first_year\n", "annual_growth = total_growth / elapsed_time\n", "annual_growth\n", - "for t in linrange(1965, 2015):\n", + "results[1950] = census[1950]\n", + "for t in linrange(1950, 2015):\n", " results[t+1] = results[t] + annual_growth\n", "newfig()\n", "plot_estimates(table2)\n", @@ -2431,7 +2432,7 @@ }, { "cell_type": "code", - "execution_count": 33, + "execution_count": 312, "metadata": { "collapsed": true }, @@ -2453,7 +2454,7 @@ }, { "cell_type": "code", - "execution_count": 34, + "execution_count": 313, "metadata": { "collapsed": true }, @@ -2474,7 +2475,7 @@ }, { "cell_type": "code", - "execution_count": 35, + "execution_count": 314, "metadata": { "collapsed": true }, @@ -2503,7 +2504,7 @@ }, { "cell_type": "code", - "execution_count": 36, + "execution_count": 315, "metadata": { "collapsed": true }, @@ -2531,14 +2532,14 @@ }, { "cell_type": "code", - "execution_count": 37, + "execution_count": 316, "metadata": {}, "outputs": [ { "data": { - "image/png": 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MkWSEpqYmNjY2GBgYYKZvxlf+/2U3URgb69CvXxM0NF6uFj1PUqWvsJs3b3L+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\nLf5lZWUwMTHBK6+8gqCgIPj6+nbp5i3Ozs4AgF27dmHs2LE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58Hrcavp1GUBZWRl+fn44OWlP+CNG1HwublmtXeb/T6AMeLaV42hXjEYju3fvprKy0rbM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\nMUYGJkuqL6ZOnUpZWRkHDhzo82AtgPLqKh768s+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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -2559,7 +2560,7 @@ }, { "cell_type": "code", - "execution_count": 38, + "execution_count": 317, "metadata": {}, "outputs": [ { @@ -2594,7 +2595,7 @@ }, { "cell_type": "code", - "execution_count": 39, + "execution_count": 318, "metadata": { "scrolled": true }, @@ -2616,14 +2617,14 @@ " axes_locator = None\n", " axis_bgcolor = (1.0, 1.0, 1.0, 1.0)\n", " axisbelow = True\n", - " children = [" + "" ] }, "metadata": {}, @@ -2709,14 +2710,14 @@ }, { "cell_type": "code", - "execution_count": 40, + "execution_count": 319, "metadata": {}, "outputs": [ { "data": { - "image/png": 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jdHV1sbOzw8TEBCtjK770/y+hxGBubkD//s3Q0akdd/1QySmdr127xtmzZ8nJ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\n0KGiogLXrl1DfHy80vM7FpbqqxweF//Jkydx6tQpnD9/HgKBAADg5OS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3PQ5kHcClxIXXVi2lr18/CgoKCAwMxMVFexMYOrTuc3HLau0y/38AlcDzrRxHu2I0Gtm+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\n/OecNAd3YgutcS7SE2NIS0ghLy2PBVMXEBrsy/ICSik1PgV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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -2743,14 +2744,14 @@ }, { "cell_type": "code", - "execution_count": 41, + "execution_count": 320, "metadata": {}, "outputs": [ { "data": { - "image/png": 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Pli1bRosWLZg1a1aV5zt79izz58/n2LFjvPbaa3z//ffo6+s3xGU2CjLpYW9wBKGRSE9P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\nQWtrK+7fv4/W1lbU1tbi0qVL2LVrF5qamhAQEIDVq1fD0tKSW9zI0tK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Jt27dsLe/NPXd2jb/fwIGYHYry9GmsLOzY+fOnVRUVFjK9Ho9q1evZvr06bVek5WVxc8/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\nsombvnZqy7rwkHAuP/VCGoNeIC1xPOekncPCCQt1PH2l1KD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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -2791,7 +2792,7 @@ }, { "cell_type": "code", - "execution_count": 42, + "execution_count": 321, "metadata": { "collapsed": true }, @@ -2822,7 +2823,7 @@ }, { "cell_type": "code", - "execution_count": 43, + "execution_count": 322, "metadata": { "collapsed": true }, @@ -2841,7 +2842,7 @@ }, { "cell_type": "code", - "execution_count": 44, + "execution_count": 323, "metadata": {}, "outputs": [ { @@ -2853,9 +2854,9 @@ }, { "data": { - "image/png": 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ixURERIjVuYRGr7i4mKKiIkrKS4jPiueO3h2yNQuQFVbMvdPXsS8vub2ErpYu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\n62Hp0fuAhBAySAzZ4l9SUoWTP6Tg2vUyKA1bYGCugAoqrl1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xxx0sXryYPXv2NPoNR1HawuHDh9n460YO5R/CUFND1u/F/PXHpXww/0FcXE6n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\nzL24m44HifJ7ICI34G6Y/wbXzo0XQ3evf9x6EUkBfN42USv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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -2888,7 +2889,7 @@ }, { "cell_type": "code", - "execution_count": 45, + "execution_count": 324, "metadata": { "collapsed": true }, @@ -2908,7 +2909,7 @@ }, { "cell_type": "code", - "execution_count": 46, + "execution_count": 325, "metadata": {}, "outputs": [ { @@ -2920,9 +2921,9 @@ }, { "data": { - "image/png": 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88cUXZe5j2rRp+Pj4MHz4cCZPnoydnR0xMTGsWbOG+Ph4ZXORr68vO3bsYNq0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\n", 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QkE2n/AGkRDqyb98lxoyxtJlB08Ja5f8QsFhK+aZJWCywXAjRwhCvlH890rlz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\n43Job+/hlLlF2HM6Mev+gt/vp62tjby8vEHHnc7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BAQUFBTidTvLz84f5/AVBEGJJwhr/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\n8RcEQUhAxPgLgiAkIGL8BUEQEpD/BTAI6Ax8ThsmAAAAAElFTkSuQmCC\n", "text/plain": [ - "" + "" ] }, "metadata": {}, @@ -2952,7 +2953,7 @@ }, { "cell_type": "code", - "execution_count": 47, + "execution_count": 326, "metadata": { "collapsed": true }, @@ -2982,7 +2983,7 @@ }, { "cell_type": "code", - "execution_count": 48, + "execution_count": 327, "metadata": {}, "outputs": [ { @@ -2991,7 +2992,7 @@ "" ] }, - "execution_count": 48, + "execution_count": 327, "metadata": {}, "output_type": "execute_result" } @@ -3009,7 +3010,7 @@ }, { "cell_type": "code", - "execution_count": 49, + "execution_count": 328, "metadata": {}, "outputs": [ { @@ -3018,7 +3019,7 @@ "function" ] }, - "execution_count": 49, + "execution_count": 328, "metadata": {}, "output_type": "execute_result" } @@ -3036,7 +3037,7 @@ }, { "cell_type": "code", - "execution_count": 50, + "execution_count": 329, "metadata": { "collapsed": true }, @@ -3066,7 +3067,7 @@ }, { "cell_type": "code", - "execution_count": 51, + "execution_count": 330, "metadata": { "collapsed": true }, @@ -3084,14 +3085,14 @@ }, { "cell_type": "code", - "execution_count": 52, + "execution_count": 331, "metadata": {}, "outputs": [ { "data": { - "image/png": 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H5753pQqCINRlkiQRERHBtWvXcHJywtm58nhhTvWc8Gngww9//k5Buh5OBQPR\nivFA2/3+/fxrU42GdI6Pj+fUqVPk5eVhbm6Ot7e38q7QmsrIyGDLli3MnTv3ka4jCIIgPC0KhYJz\n585x48YNoHwSJFNT00pnAADDWw8nM0mTuF9t0ESb6OhM5HIFWlpPp+u8WntVKBTMnj2bAQMG8Nln\nn/HVV1/x8ccfK4cHqMFNwkrbt2+nXr16+Pv713jb55G6E7gnJSXh7OzMe++9V+W6Vc2QVaFi27v/\n3N3dGThwIFu3blX5HHfv3l1p3bv/fv/9d+W6ly9fZurUqfj5+eHq6krPnj1ZvHhxtaOUTpgwAWdn\nZ86fP6/WeyMIdZFCoeDMmTPKxA9gZ2fHlZIrfHHsC4rlxSrrG+kY8aH/63i6NWDAAEdmzfJ7aokf\n1DzyX7t2LT///DPBwcEMGDAAS0tL0tLS2LdvH8uXL8fR0bHGF2z37t3Lq6+++sDbm4Wq/frrr/Tv\n3/+h7r345ptvcHNzQ5IkcnNzOXToEAsXLiQpKUllAhdNTU2OHDlSZR2mpqZA+fSQI0aMoEePHnz3\n3XcYGxsTExPDggULiIyMrNSDKy0tjX/++YcmTZqwc+fOamcWE4S6rKysjLCwMFJTU5VlVg2s+Kfk\nHyLPRyKXK5i2YSWfD52MmZmech2ZTMakSR61MiF7TamV/Hft2sXEiRMZO3assszW1pZx48ZRXFzM\nrl27apT84+LiSExMFJNzPAJ7e3vmzp2Lr6+vMhGry9TUVHnh3draGkdHR7S0tFi0aBGDBw+mWbNm\nynXvvkBflYozgPnz5yvL7OzsMDQ0ZPTo0URHR6t0Fti7dy/W1taMHDmSr7/+mlmzZlWaU1gQ6jK5\nXM6pU6fIyMi4U2YqZ0fqDgrlhWRmFRIbm4VmUQGbt0fw9lttVLavC4kf1Gz2SUtLU3ZZupeXlxe3\nbtVs/tqwsDCsrKxwdKx+ohXh/j744ANKS0tZsGDBY6kvICAAHR0dfvvttxptp6GhQW5uLuHh4Srl\nvr6+7N+/v9IQzD///DN+fn707NmTwsJC9u7d+8ixC8KTUlJSwr///qtM/CVlJcQSy++3f6dQXgiA\npoYGlrmt8codTuS521y+fPt+VT41ah3529vbc/bsWdq1a1dp2dmzZx94dHivS5cu4eRU+12a9sXs\nY3/sfrXW7dS4E4FugSplWyK2cCzxmFrbv+z0MgOcB9Q4xodVr149Zs6cyfTp0+nXrx+dO3d+pPoM\nDQ2xs7N+3aONAAAgAElEQVQjNja2Rtv179+fDRs2MGLECFxcXGjbti1t27bFz8+P5s2bq6x74cIF\nYmNjCQ4Opn79+nh4eBASEsKIESMeKXZBeBKKioo4efIkubm5AKTkpRBNNLlGufD/B/OWBpYEtx/N\nSUUpUVHpDBvWAkfHxzcez+OkVvJ/7bXX+OqrrzAwMKBfv35YWlqSnp7OL7/8wpo1a5gwYUKNdpqa\nmlrjpgqhsldeeYXffvuNOXPmsH///kduPrl3KsmysrIq5/E1Nzfn77//BsqHpv3pp5/YuHEjBw4c\nYOPGjWzcuBEjIyOmTZvG8OHDlduFhoZiYmJC+/btgfIfjnnz5hERESFm5xLqvKKiIgoLCykuKyYu\nM46bejfJ0sxHVlA+9k43h24MdB6IrpYu9gGlBAQ4oa9fd69pqpX8g4KCuHTpEgsXLmTRokXKckmS\n8Pf356233qrRTlevXl2zKF8ANZ3AvcKnn35K//79Wbx4MZ999tkjxZCXl6dyFqepqcnPP/9cab17\nR3U1NzcnODiY4OBgbt68yYkTJ9i2bRtz586lQYMGdOnShZKSEn755Re6d++unBCmT58+fPHFF+zc\nuVMkf6HOMzMzo02bNuz+azdJeknEZ2RwPSkXWyMbvp34Ps5Wd1oz6nLSr6BW8tfU1GTRokWMHTuW\n06dPk5OTg4mJCb6+vpVO7euSAc4DHqkpJtAtsFJTUG1RdwL3e9na2jJ9+nTmzJnzSFNoFhYWcvXq\n1UoX4Stm3qrO2rVrady4Mb179wagQYMGvPbaa/j7+9OnTx+OHDlCly5d+Pvvv7l9+zZ79uxRaedX\nKBT8+uuvzJw5U1z4Feq8evXqMeqVUVw/nMrhiEQaFHnQ5HZ7kiJ0ce7+tKOrmRrd5NW8efM6neyf\nZepO4F6VIUOG8OuvvzJ79uyH3n9ISAgKhaLGPyARERH89ttv9OjRQ2XkVx0dHfT19ZUTyoeGhmJj\nY8P69etVtg8PD2fu3Lns27dPpYlIEJ62jIwMtLW1kenKMNa9M32orq4uUzqOo3F+e079UUqzZma0\nalXvKUb6cKpN/r1792bZsmW0aNGCXr16PbB70h9//PHYg3uRBAUFMWjQIObMmcOIESMwMDAgNjaW\nJUuWqEzgXp158+YxYIB6ZznZ2dmkpaUhSRI5OTkcPXqUpUuXMn78eBo1aqSyblpaWpV16OvrY2Rk\nxOTJkxkxYgTjx49n7NixNGrUiFu3bhEaGkp2djZDhw5V9u2fPHlypQv9jo6OrFu3jpCQEJH8hToj\nOTmZf/77h9jbsWAPb7d5H2OjO/31rQ2tGTPQktZ2Kfj62taZ7ps1UW3y9/LywtDQUPn4WXxxz5KK\nCdxXrlzJ6NGjKSgowNbWln79+qk19pGdnR3BwcF8/vnnD1x30qRJysdmZmY4Ojry+eefM3DgQJX1\nysrK6NixY5V1jBw5kjlz5tCyZUt27tzJt99+ywcffMDt27cxMTGhQ4cO7NixA0tLSzZs2IBMJmPI\nkCGV6tHU1GTUqFEsWLCACxcu3PcMRxCehGvXrvHb8d+4mnUVeVkZySdzGXdwFT/MmYqu7p2Uqamp\nQZs29Z9ipI+mRhO4Py1iAndBEJ6E05Gn+ePfP8gpyQHgRloOUQXJ1C/yZkyHAIYObfGAGuqOh57A\nPSUlpUY7srGxqXl0giAIdYC8TM6OwzuIjI5EQXmvuzLtMowcjXE50REjhTWFhXIkSXpuWkGqTf5d\nunSp0Yu8e65KQRCEZ0VCVgKbDmwiL/1ObzuFnoIu7brQ17kvO4jFy8sGFxfLpxjl41dt8v/iiy+e\nm184QRCEqoRGhfLPf/8g5crIySnB1FQXcytTxvQdg51ZeVNJUJDLU46ydlSb/F999dUnGYcgCMIT\nJZfLSY1NpThDQU52CSBDVlSfGUPeQUuzRr3gn0nVvsKa3IUrk8lqPMSDIAjC06SpqYlvE1+uXL9G\nkUIb7QInCjIbkZ5WjK3tC5z8ly5dqnYlIvkLglDXRaREYG9ij7m+OVCetzzcPcgtzCX6Qhm3bxsS\nFOSCra3hU470yag2+UdHRz/JOARBEGpFTnEOOyJ3EH4zHAu5A5N8JmFvbwKUj1PVuV1n2vmUT6eo\nofHiXOd8/s9tBEF4IUmSxInrJ9h1cRe3C3JJjS0iMfsiC6N+YsWsMcpEL5PJ0NHRfEBtzx8xvIMg\nCM+d1PxUtkRsISY9BgCdbB3q5euiLzOHNE2OHLlO166NHlDL800M7yAIwnOjTFHGgcsH+CXuF0rL\nSkECvdt6mJaYYmRVn/QkaOCgi5fX89Vn/2FUm/zvnh5w4cKFTyQYoXaFhYUxcuRItYfJ2L17N7Nn\nz+bixYtPIDpBeDRXs66yOWIz128nUVgkx1BfG4MMAxy0HGhcvzEyNJAa69G3bxflnBIvMrXb/BUK\nBYcOHSI8PJy8vDzq1atHmzZtqpzaURAE4UlKzktm0fFFZGUVEhd/G5lChn9zL5xMmmOkUz5PRP36\n9fH09FQZevxFplbyT09PZ+zYsURHR6Ojo4OFhQUZGRmsXr2adu3asXLlSgwMDGo7VkEQhCrZGtni\nYe3Ft//uQ7NEG28NL0yzGmNkXp74HRwccHFxEc3Xd9F48CrlzT5paWmsW7eOiIgIDh8+zIULF1ix\nYgVRUVEqUzsKD8fZ2ZmQkBCGDRtG69at6devH+fOnWPbtm106dIFLy8v3n//fUpKSpTbhIWFERgY\niKenJ+3bt2fevHkUFhYql0dHRxMYGIi7uzsvv/wyUVFRKvtUKBSsXr2arl274uHhweDBgzly5MgT\ne82C8LAUUuUpT0e6D6e/Sye60A1LTSsMDcqnUnRxcRGJvwpqHfkfOnSIjz/+mE6dOqmU9+jRg8zM\nTL788ks+/fTTWgnwUcTExBAbG6vWuo0bN640j2xERASJiYlqbe/k5ISzs3ONY7zbV199xfz582nS\npAkzZsxg/PjxtG7dmnXr1nH16lWCg4Px8fFhxIgRnD9/njFjxhAUFMSnn35KUlISc+fOJSkpidWr\nV5Odnc2YMWPw8/Pjp59+IiEhgY8//lhlf0uWLOHPP//ks88+o1GjRhw7dowpU6awfv162rZt+0iv\nRRBqg0JScCThCEcSj/Ce7zRMDe9M/WmkY0TP+r5cun0LGxtD9PS08PT0pEGDBk8x4rpLreSvo6OD\nsbFxlcvEG/v4DBkyhG7dugEwcOBAPvvsM+bOnYu9vT1OTk6sX7+euLg4ADZu3IirqyvTp08HymfE\nmjt3LuPHjycuLo7Tp09TWlrK/PnzMTQ0pFmzZqSkpCgnec/Pz2fTpk2sWLFC+aPeuHFjoqOjWbt2\nrUj+Qp1zPfs6WyK2cCXzKteTchnx2yK2zPgIc/PyGbZkMhk+Pj4UFf2DhoYGvr6+WFhYPOWo6y61\nkv/w4cNZtmwZ7u7uWFre6SJVUFDA2rVrCQgIqLUAXyR3T6Gor6+PhoaGSq8cPT09ZbNPXFwcXbp0\nUdnex8dHuSwuLg4HBwdld10ADw8P5ePLly9TUlLC1KlT0dC40/pXWlqq8hkLwtNWLC9mX+w+Dl45\niEJScCk6g4yMIgwUCWzbcYHJb/kq1zU2NqZNmzbo6emp/O8LlVWb/N944w3lY0mSuHz5Mj169MDL\ny4t69eqRk5PDmTNnkMvlWFtbP5Fga8rZ2fmRmmLc3NwqNQXVJi0t1Y9DJpNV206pp6dXqaxiUjYt\nLS1kMhn3TtKmra2tfFzR1W3FihU0btxYZb27fwwE4Wm6kHKBbRe2kVmYqSxrbG+O0Y1G2Bd7k3M7\nj6IiOXp6d7479eo9e5OpPw3VJv/S0lKV515eXsry5ORkAFq0KJ/SLDU1tbbiE6rh6OjI2bNnVcrC\nw8OVy7Kzs5WTqJuamgIQGRmpXLdx48Zoa2uTkpJC586dleUrV66krKyMqVOnPoFXIQhVu110m52R\nOzlz64xKubOlMyO7juSQRgpFRQlYWxdRXJyPnp7pU4r02VVt8t+8efOTjEOooXHjxjFo0CAWLVpE\nQEAAN27c4NNPP6VLly44OjpiY2PDqlWr+PDDDwkODiYlJYXly5crt9fX12fMmDEsWbIEQ0NDWrdu\nzaFDh1i1ahXz589/iq9MeNEdv3acH6N+JCs3l/jLt3FoYoqNhTkBrQLws/MjOzsbC4tkiotllJXJ\nOXXqFF27dq105izcX7XvVnh4ON7e3jWuMCwsTNn2LNQeJycnVq9ezdKlS9m8eTNmZmb079+fd999\nFwAjIyN++OEHPvvsMwICArC2tmbcuHHKC74A7777Ltra2ixevJj09HTs7e357LPPxEQ+wlMlIXH9\nViYxsVkoFBINyuyYO+hDTPSMuXXrFmfPnqWsrAwob6Js2bKlSPwPQSbd2zD8//z9/XF0dOStt97C\nycnpgRVFRESwbt06EhIS2Ldv32MN8kGz0AuC8PyQJIlPDsznt4PRNM3rhoVkz3vveSOTZagMNa+j\no4OPj49o46/Gg/JmtT+XP/30EytXrmTw4ME0adKEXr164ebmhp2dHfr6+uTk5JCSkkJ4eDhHjx7l\n6tWrBAYGsmTJklp9QYIgPD/OJ5/HTM+MxmZ3Oh3IZDLe7zIFX3kqkRFZjBjhREbGVW7cuKFcx9DQ\nkLZt24oePY+g2iP/CikpKXz//ffs37+ftLQ0ld4nkiTRoEEDevfuzZgxY7CxsVFrpyEhIaxfv55b\nt27RrFkzPvjgg/uOESSO/AXh+ZJVmMX2yO2cSz4HOWZMcQvGrbVq/igrU1BSUkJ4eBhZWVnKcktL\nS7y9vcXgbA/w0Ef+FWxsbJg+fTrTp0/n8uXLJCUlkZubi7m5OQ0aNMDBwaFGAYWGhvLpp58yd+5c\nfH192bZtG5MmTWLfvn0isQvCc04hKfj76t/sjdlLTn4+MTFZ3M6+QW7Udr5rPkWly6YkKThx4jgF\nBQXKssaNG+Pq6iq6Iz8GNbpK4ujoiKOj40PvTJIkVqxYwbhx43jttdcAmD59OidPnuTs2bMi+QvC\ncyzhdgJbIrZwPfs6ABqaMgoKSrEtcUE/pyl//pnIgAF38ouWlhaNGjUiOjoamUxGq1atcHBwEGP0\nPCZP9BL5lStXuHHjBv369VOWaWhosGfPnicZhiAIT1BhaSE/R//MkcQjKjceNja3p1/3NzgYkk+P\nno3p1atxpW2bNWtGYWEhtra2dfZm0mfVE03+CQkJAOTk5DBq1Cji4uJo2rQpwcHBypvIBEF4PkiS\nxJlbZ9gRuYOM/Czy8koxN9NDW1Obl51epkfTHmjKNOnkUoCNjSFlZWWUlJSotOXLZLInepf9i+SJ\nNpzl5eUBMGPGDAICAli/fj3Nmzdn9OjRXL58+UmGIghCLcsozGDdmXXEXb9FWFgKFy9m0NTYmbkv\nzaVPsz5oaZQPQ2JjY0hhYSHHjx/n9OnTKBSVh2sWHr8nmvwrxpaZOHEiAwYMwMXFhU8++YQmTZqw\nffv2JxmKIAi1zNLAkp4Ovbh+PRdZiT5OuX0xvtgVSwPVgQMzMjI4duwY2dnZZGZmcuHChUrjUgmP\n3xNt9qlos7v7pjGZTEbTpk1JSkp6kqEIgvCY5ZfkY6ij2u/ev8UAUrsUErbDBCtzUzp2VO3UkZiY\nqJLsZTIZZmZm4qLuE6BW8i8uLmbNmjUcPnyYgoKCKn+V//jjjwfW4+LigoGBARcuXKB169bAnRFD\nxVzAgvBsKpIXsSd6Dyeun2Cqx3Sa1r8zx4e2pjZvdR1JmHEyrVtboqtbnnIUCgWRkZEqkyXp6uri\n7e0t7th9QtRK/vPnzyckJIQ2bdrQvHnzh+5jq6+vz+jRo1m6dCmWlpY4OTmxbds2rl27pjLomCAI\nz4aIlAi2XdhGel4GCQk5jP7rC7a8M5/GjVVH2fTxsVU+Li4uJiwsjMzMO8M0m5qa4uvri76+/hOL\n/UWnVvL/448/eO+99xg/fvwj73Dq1Kno6+vzxRdfkJGRQcuWLdm4cSNNmzZ95LoFQXgycopz2H5h\nu3LI5bj426SmFmAh1eOHLeeZPbMTGhqVm26ysrIICwujqKhIWdawYUPc3d3R1NR8YvELaib/kpKS\nx9bdSiaTMWHCBCZMmPBY6hME4cmRJIl/k/4lJCqEgtI7d966NGuA1fXmWBQ1x9zBiKIiOQYG2irb\nZmRkcPLkSWVvHplMRosWLXB0dBRt/E+BWsm/Y8eOHD16FD8/v9qORxCEOiqjIIPNEZu5lHZJpby9\nfXtea/Uap80yMDTUxsfHtspkbmZmhomJCbdv30ZbWxtvb2+srKyeVPjCPdRK/v7+/syePZusrCy8\nvLyqnEJwwIABjz04QRDqhn+v/8u2C9vILSwkPj6L+vUNcWpoT6BbIC2tWgLw0kv3H2FTU1MTHx8f\nzp8/j5ubGwYGBk8idKEaaiX/t99+GygflC00NLTScplMJpK/IDzHjHWNSc3I4eLFDMrKJCyz3fjw\n1WmYGlWf8HNzczEyMlI5C9DX1xctCHWEWsn/4MGDtR2HIAh1mKu1K12bd+L6peM0yeuKcZktcdG5\n+PhUTv6SJHH16lUuXrxIq1atRGeOOkqt5N+wYUPl44KCAvLz8zEzM1PesSsIwvPjVu4t8kryaF6v\nuUr5GJ9APDT68Mu+BEaNcqF5c/NK28rlcs6fP8/NmzcBuHjxIqampqLvfh2k9h2+//33H19++SVR\nUVHKm7zc3Nx49913xQ1agvAcUEgK/rz8J3tj9iKT6zKq0bu08WykXK6npUdb34b4eDVAS6vyvT65\nubmEh4eTm5urLDMzMxNt+3WUWsn/9OnTvPnmmzg4OPDOO+9Qr149UlNT+f333xk3bhzff/+9mLRd\nEJ5hyXnJfH/ue65kXeFGUh4JiTnE/bOaHU3mYG5+p4OHTCZDS6tyT54bN24QERGBXC5XljVp0gQX\nFxcx8UodpVbyX7ZsGe3atWPt2rUqF28mTZrE+PHjWbFiBT/88EOtBSkIQu1QSAr+uvIXe6L3IFfI\nkRSQnJyPYakVVgWt2bbtEpMne1a/vULBxYsXuXr1qrJMU1OT1q1bY29v/yRegvCQ1Er+kZGRLF26\ntFLfXZlMxsiRI3n//fdrJThBEGpPWn4a3537jsuZd4ZT19bSYnL3QP7bZoK9nQn+/tXP3FdYWEh4\neLjK/LqGhob4+PhgYmJSq7ELj06t5G9iYqIyj+bd8vPzxW3ZgvAMkSSJY9eOseviLvKKCtDWKv/+\n2pvaM8ZjDHYmdvhZpuPsbIGmZtVNNpIkERYWxu3bt5Vl9evXx93dXXQEeUao1Rjn5+fHihUrSElJ\nUSlPSUlhxYoV4oKvIDxD1oavZfP5LcReSePUf8kUFMgZ4DyAmR1nYmdSPuRyq1aW1SZ+KD/rb926\nNRoaGsr5db29vUXif4aodeQfHBzM4MGD6d27N97e3lhaWpKenk54eDhGRkZ88MEHtR2nIAiPSUur\nluw8dpBbt/IxUFhgHdOfPoP7oVnDC7NmZmbKO3VFV85nj1qfto2NDaGhoQwfPpzc3FzOnTtHTk4O\nI0aMIDQ0VFzYEYRnSKdGnejeug2N5d545Q7HRs+OgoLS+26Tnp5e6cwfwN7eXiT+Z5Ta/fytrKyY\nPn16bcYiCMJjFpsRi7GOMfWN6yvLZDIZM7u/TwetJORyiW7dGlU5/DKUt+3HxsYSFxeHlpYWnTp1\nwtDw/mP4CM+GapP/6tWrefXVV7G2tmb16tX3raRimGZBEOoGuULO3pi9/HH5D0rTjXm/zQe4trJR\nLteQafDSS43uUwMUFRVx5swZMjIyACgtLSUyMpK2bdvWauzCk1Ft8l+6dCnt27fH2tqapUuX3rcS\nkfwFoe5IyUthw9kNxKZeITY2k6ysJObGbmTT7GmVxtivTlpaGmfPnqW4uFhZZmlpibu7e22FLTxh\n1Sb/6OjoKh8LglA3SZLEiesn2BG5g5KyEmQyyMsrxVxuj1GOMwcOJPDKK83vW4dCoSAmJob4+Hhl\nmUwmw8nJiebNm4tJV54jal3wXblyZZUXe6D8tu558+Y91qAEQaiZgtIC1p1Zx6bzmygpKwHAQFeX\nSV1G07rgVfx7ufLyy9XfsAXlgzaeOHFCJfHr6uri5+eHk5OTSPzPGbUu+K5atYrOnTtjY2NTadm5\nc+fYuXMns2fPfuzBCYLwYJczL7PuzDpuZaWhp1f+la5vXJ+xXmOxM7EjxT0fG5v7X6RNTk7m3Llz\nlJbe6fVjZWWFp6cnurq6tRq/8HRUm/yHDx/OuXPngPLTyaFDh1ZbSevWrR9/ZIIgPNAf8X8QEvnT\n/7ftF+HtbUNPp24EuASgo6kD8MDED+VNOxWJX8yt+2KoNvnPmzePAwcOIEkSy5cvZ8iQIdja2qqs\no6mpibGxMT169Kj1QAVBqCy3JJcLkWnk5JSgJelimdiNEYNH1Dhp29jY4ODgQEpKCl5eXpibVx6r\nX3i+VJv8HR0deeutt4Dyi0ABAQFVNvsIgvD0vNLiFf5rfYFjR2/inN8bD/dWlJVJVQ67XEGSJIqK\nitDX11cpb9WqFc7OzmKIhheEWm3+U6ZMASArK4vS0lLlZC6SJFFQUEB4eDgBAQG1F6UgCCgkBSVl\nJehp3RlfX0tDizl9pnFcP5UGtia4uVndt47i4mLlHfpdunRBR0dHuUxDQ0OMvf8CUSv5x8TEMG3a\nNJVeAHeTyWQi+QtCLcouymb9mfVcTyjggy7v0rChsXKZsa4xfXoZ32frcqmpqZw7d07Zdz8iIgJv\nb2/Rrv+CUiv5L168mNu3bzN9+nQOHTqEjo4OXbt25ejRoxw9epRNmzbVdpyC8MK6lHaJb/9by5mo\na2RkFJEVv4ENs96pcirFqpSVlXHp0iWVCVcAMb3iC06t/55z584xdepUxowZQ79+/SgsLGTEiBGs\nXr2aHj16sHnz5tqOUxBeOApJwb6YfSz7bxlZ+dlkZRUjA1LT8zh4MFGtOrKzszl27JhK4q/ou9+q\nVStx1P8CU+vIv6SkhCZNmgDl83Lefcfvq6++yieffFIrwQnCiyqnOIcNZzYQnV7+XTMw0KZ184ZI\nZ3x5tXNHunW7/7g8kiRx5coVoqOjUSgUynJbW1vc3NxE331BveTfoEEDkpKS8PHxoUmTJuTl5XHj\nxg0aNmyIrq4u2dnZtR2nILwwYjNiWRO2lrySXGVZC8sWvNHzDTK7STg4mN13+8LCQs6dO0d6erqy\nTFNTExcXFxo1aiSO9gVAzeTfo0cPvvzySwwNDenZsydNmzZl2bJlTJgwge+//75G4/nHx8fTv3//\nSuVbt27Fx8dH/cgF4TkjSRK/xf3Gt4e2cvNmHh6e1mhradK/eX/6O/VHQ6aBqcOD60lPT1dJ/GZm\nZnh6emJkZFSL0QvPGrW7eiYmJvLjjz/Ss2dPZs6cyZQpU9i3bx+ampp89dVXau8wNjYWc3Nz9u3b\np1JuZnb/oxlBeN79cfkPFu3ZSGpaIQBJV0pYGjSDllYta1SPnZ0dycnJpKSk0KxZM5ycnEQXTqES\ntZK/vr4+K1eupKSkfMCoTp06sW/fPqKiopSnkuqKjY2lWbNmWFndvz+yILxoujTuwo8NfiM1LR5T\neQN88gNwML7/KJwAcrkcLa07X2WZTIabmxv5+flYWFjUZsjCM0ztmbwAlRtCGjVqVKOkXyEuLo6m\nTZvWeDtBeN7pa+vzSf/3+SpnDx2tejHoFaf7dueUy+VcvHiRzMxMOnXqhKampnKZrq6uuKgr3Fe1\nyb9Xr141ujD0xx9/qLVeXFwcxcXFDBkyhBs3btC8eXPef/993Nzc1N6XIDzrcotz+e3cMXo5d8PM\n7M4du43NGrN04tsP/O5lZGRw7tw5CgoKgPI5N1xcXGo1ZuH5Um3y9/Lyeuy9AoqKirh+/ToWFhZ8\n+OGH6OjosGXLFgIDAwkNDcXR8f7jjQvC8+BSajQfh37FxSs3+M86ky/fH6nyXbvf966srIyYmBiu\nXLmiHGYFynv4SJIkevIIaqs2+S9cuPCx70xPT4/Tp0+jo6OjbEJauHAhUVFRbNu2jY8//vix71MQ\n6oqKm7Z+PLuHi5dTkIADyT/x658+9O/V4oHbZ2Vlce7cOfLy8pRl2trauLq60rBhQ5H4hRpRq83/\nzJkzD1zHy8tLrR3e291MQ0ODZs2acevWLbW2F4RnUWZhJuvPrOdy5mWMjLSxszcm5Zqcbhav0sbz\n/tfOFAoFsbGxxMfHqxztW1lZ4e7uXml0TkFQh1rJf8SIB48PfunSpQfWExkZyahRo9i0aROurq5A\n+WlsdHQ0ffr0UScUQXjmhN8MZ0vEFgpKC5Rlvbza0MqlN31eaoWGRvXfrezsbM6ePUtu7p0bvrS0\ntGjVqpW4YUt4JGol/6oGbisoKCAsLIw9e/awYsUKtXbWokULGjZsyJw5c/jkk08wMDBg3bp1ZGVl\nMWrUqJpFLgh1XFFpEfN+Xs2fMUdwc7NCQyZDQ6aBv7M/vZv1RkP24L73aWlpKom/Xr16eHh4iEHZ\nhEemVvJv06ZNleUvvfQSBgYGfPvtt6xZs+bBO9PSYv369SxevJiJEydSWFiIl5cXW7ZsoV69ejWL\nXBDqsKTsJMav+5SrqTcBuJaYg1dLB8Z6jcXRQv2ODY6Ojty6dYvc3FxatmxJkyZNxNG+8FjUqJ9/\nVXx8fFi3bp3a69vY2LBkyZJH3a0g1GlGukYYmkmQWv5cN6MJMzt8hIl+9UMslJWVUVpaip7ena6f\nMpkMT09PZDIZhoYPnotXENT1yPd8Hzp0SPxTCsI9zPTMmNV/MlbmxgS5jGbXrHn3TfyZmZkcPXqU\n8PBwlYu6UN5JQnzHhMdNrSP/N954o1JZWVkZycnJXLt2jXHjxj32wAThWVFWpmDnH//i39kXI6M7\nd8F71vfkl/fWY6xXfdKXy+VER0eTkJCgTPoJCQk4OKgxgpsgPAK1kn9paWmlMplMhqOjI2PHjmXw\n4EWq7ygAACAASURBVMGPPTBBeBZcunKD6Vu/Jj73EteS3mLG+JdVlt8v8aelpREREaG8SxfKr4vd\nPUyDINQWtZK/mKlLECoLvxnO8n/XE5d7DYCdsVvpd9ELt1YN7rtdSUkJFy9e5Pr16yrl1tbWuLm5\niX77whNRowu+R44cITw8nOzsbCwtLfHz88PX17e2YhOEOimvJI/tF7YTdjMMPROwttInPaOIPm7t\ncWpWfa81SZK4efMmUVFRyknUoXzARBcXF3GXrvBEqZX8s7KyGDduHJGRkejo6GBhYUFGRgbffPMN\nHTp0YNWqVWIEQeG5J5cr+C8xnNDLO8ktvtP33tvFgVebDqdji+rvcpckibCwMJKTk1XKGzRogKur\nq/j+CE+cWsl/3rx5JCUlsXr1al566SVl+cGDB/noo4/48ssv+eijj2orRkF46qJibzBr20pSdWJo\n3doSGeVH6B0adSCgVQD62vdvqpHJZCo3Zunp6dG6dWtsbW1rNW5BqI5ayf/o0aPMmjVLJfEDdO/e\nnczMTL7++muR/IXnVnhCJGPXf0YR+VAAycn5tGxiR5B7EK7WrmrX4+zsTHJyMtbW1rRs2VJlAhZB\neNLU+u/T1NTE2Ni4ymVWVlZV9gYShOeFvZU1tvY6JFzPR1NThoupJx+/NAkD7aqHWJDL5cTHx9Ok\nSROVG7a0tLTo0qWLSPpCnaDWTV4jRozg66+/JiUlRaU8Ly+PtWvXEhgYWCvBCUJdYG1ozdTeQTRt\naMOqMR+zYMi0ahN/amoqR44cIS4ujqioqErLReIX6gq1/hNTU1NJTU2lZ8+eeHt7Y21tze3btzlz\n5gz5+fno6OgobwSTyWRs2LChVoMWhNoSFnWVXX/9y7zJw1SmUOzVvCedHTpVm/QLCwuJiopSGZr8\n5s2bODg4iHl0hTpJreSfmJhIixblk03I5XJu3iwfrKqirKysjLKysloKURBqnyRJfLF1OzsiQlBQ\nhlNoY94I6KBcriHTqDLxS5LE1atXiYmJQS6XK8t1dHRo1aoV5ubmTyR+QagpcZOX8MJLyUthc8Rm\nTuafRU4JAN+Hb2JYf18MDHSq3S4rK4sLFy6QnZ2tUm5vb0+rVq2Us9UJQl1UowbI+Ph4Tp06RV5e\nHubm5v/X3p2HNXWt+wP/hoQwT2EIqAgSCCigjDJKnY6zOLRH69TqqSN9jvqr11at5dxftda2WkWr\nbfW21tah1dZaqa21ImBxQEDEggyCMogiBATCFEmy7h9ct6ZAjQMB5P08D88De+3svK9JXnfWXnst\n+Pv7w8XFpaNiI6RDKdVKnCw4ieN5x6FUK+HQywSyykZY8K3x3rR/t1v47927h5ycHBQXF2tMwmZm\nZgZvb2+anpx0C1oVf7VajejoaPzwww8ab3Yej4dJkybh/fffpzsTSbehUqlx4NckZPJPolpZwW3n\n8/j4fxNmYfKAiRAK2j9rr66uRlFR0YPH8flwc3ODRCKBnt5TT5RLiE5oVfx37dqFo0ePYsWKFZg4\ncSJsbGxQUVGB2NhYbNu2DRKJhGb2JN1CVu5tRB/8DNkNqbC1NYKHR8tZupOlE+YMnANHC8dHHsPO\nzg729vYoKyuDWCyGl5cXraxFuh2tiv/333+PxYsXY/78+dw2e3t7LFiwAAqFAt9//z0Vf9ItHMj9\nClcbUgEA5RWNcHYEXhk8DcP6DWtzWcXm5mY0NDTAwsJCY7unpyccHR3pDl3SbWn1HbWiogL+/v5t\ntvn5+WkMbyOkK5s/5GXY2RqDz+dhuOdgfDhuPUa4jGhV+BljKC4uRnx8PFJSUjRG8gCAsbExFX7S\nrWl15u/o6Ij09HSEhIS0aktPT4etre0zD4yQp3WtQAYTIwP06vXg7vR+Vv0Q9Y+XYWdkj6HS0Dav\nVVVXVyMzMxN3797ltuXn53NDmwl5HmhV/F966SV8/PHHMDY2xrhx42BjYwOZTIbjx4/j888/x6JF\nizo6TkK0VlurwI7vfsP3ud8hyHoodqyar1Hkp/u0vfiQQqFATk4OSkpKNAY2GBkZter2IaS706r4\nz5kzB9nZ2di4cSM++OADbjtjDJGRkViyZEmHBUjI46hV1OKL9H3YV/AL1HoMSVUncOpMBP7xgnu7\nj1Gr1SgsLEReXp7GPFV6enqQSCRwdXWlaRnIc0frid0++OADzJ8/H6mpqaipqYG5uTkCAwPh5ubW\n0TES8khqpkZiYSKO5hxFk7IJvXuboqREDmtbA5g41Lf7uIqKCmRlZUEul2tsF4vF8PT0pIXTyXPr\nsU5nHBwc4OjoCAsLC4hEIjg6PnpYHCEdSSZrQGbpNZyt+RnFNcXc9r59zTDEJRhLR8yDhWHbXTZK\npRJpaWkaZ/smJibw8vKCnZ1dh8dOSGfS+iavjz76CPv27YNSqeT6Q42MjLBkyRIsXLiwQ4Mk5K8U\nCiWOHr+K3UkHUGWaDX9/MfT0Wvr1xaZizPSeCQ+bv79AKxAI4O7ujszMTAgEAri5ucHFxYVu1CI9\nglbFf/v27fj666/xyiuvYPTo0bC2toZMJsOJEyewbds2mJiYYNasWR0dKyGc/MoCfJi6Hg2CeqAJ\nKLkph2s/a4xzG4dRklEQ6Gm+tRljqKqqajX1gpOTExQKRau59wl53ml9k1dUVBRef/11bpujoyN8\nfX1hYmKCvXv3UvEnOiWxc4K7mzXSs+thZiZEiIsfXn9hHmyMbVrtK5PJuH798PBwWFpacm16eno0\nhJP0SFp9v62rq8PAgQPbbPP390d5efkzDYqQh8nl95CVJdPYZigwxLJ/zEPwIAl2zf8Posf8V6vC\nX19fj5SUFJw/fx61tbVgjOHq1asawzgJ6am0Kv5Dhw7Ft99+22bb8ePHERER8URPfvnyZQwYMADJ\nyclP9HjyfFOrGU6dKsTC/+zByj3bUVur0Ggf3DsQn7+8CT4OPhrj+O/du4esrCwkJCSgrKyM287n\n82FtbU3FnxBo2e0TEBCArVu3YuLEiRg/fjxsbW1RXV2NhIQEpKWlYe7cufjss88AtMz0qc1NXw0N\nDXjzzTdpERjSroo6GT7+YxtuCHIBADu++w2rF0Ry7TweD0L+g9k32xuvDwB9+vSBh4cHjIyMdBM8\nIV2cVsV/3bp1AAC5XI6tW7e2av/yyy+537Ut/hs3boRYLNaYGpcQAFCpVTh1/RRi82Jh6ioH/gSM\njQSQWV8CENlqf8YYysrKkJ2djfp6zTH9IpEInp6eGv38hBAti39OTs4zfdLExEQkJCRg9+7diIxs\n/WEmPY9SqUZ+/l0I7O5i/5X9uCVvWSrUytIQngNsEOkzEi95tj0tA4/HQ1FRkUbhNzExQf/+/WFv\nb09rTRDSBp3fs15VVYW3334bGzZsoPlSCAAgJ6cSew+mI7n2JHoFyWBios+19THvg7fCZ8HF6u9X\njBswYADOnDkDgUAAqVQKZ2dnGq9PyN/QefH/z3/+g+HDhyMiIkLjYhzpmdRqNT6NPYb4hp/RrN+E\n+nwhBg2yhaHAEJHukRjeb7jGdMsKhQLXr1+HVCoFn8/ntpubm8PX1xe2tra0di4hWtBp8f/xxx9x\n9epVHDt2TJdPS7owHo8HW59KqE41ga/Hg62tEQaJB2GG9wyIjETcfkqlEgUFBbh+/TqUSiWEQiEk\nEonGsXr37q3r8AnptnRa/I8cOYI7d+4gPDwcALghdwsWLMDkyZPx7rvv6jIc0gkqKhpga/tgyUMe\nj4clYfNwpfQqetmIMC9gDgbZD+La1Wo1ioqKcO3aNSgUD4Z6Xrt2DU5OTjTbJiFPSKefnE2bNqGp\nqYn7u6KiArNmzcL69esRFhamy1CIjjU2NuOnnwpw9I/zeGvRaPgO7MW1WRtbY92Et+Bs6QwDgQGA\nlhOD0tJS5ObmoqGhQeNY5ubm6N+/v0a3DyHk8bRb/O/cufNYBxKLxY+9j4GBAbf9r3OukOfLtz9e\nwVcXD6DcJAcbDpVhv8ebEAofFG93m5b59hljKC8vR05ODmprazWOYWRkBA8PD/Tu3ZtG8BDylNot\n/i+88MJjfcCys7OfSUDk+cIYQ1JxElLNDuOu8Q1ACdw2uYSiyptwc3BqtX9qamqrgQBCoRCurq5w\ndnams31CnpF2i/+GDRu44l9TU4NNmzYhJCQEY8eO5e7wPX36NBISErBq1aonenJ7e3vk5uY+WeSk\ny1Iq1dDT4+F23S3s/3M/CqoKAACubi03Wo0ZOARikVWbjxWJRFzx5/P5cHFxgUQigb6+fpv7E0Ke\nTLvFf+rUqdzvr7/+OiZPnoz169dr7DNx4kSsX78ev/76K6ZPn95xUZJu4/r1auz5JgNCz1zcMkyH\nmqm5tv59+2Km90x42nkCAJqamlpNo+zs7IzCwkKIxWK4ublxXYOEkGdLqwu+Z8+exY4dO9psGzZs\nGA4fPvxMgyLd05UrFVi36wjyDeOhvFSHgAB7CPX54OvxMUoyCuPcxkHIF6K+vh55eXkoLS1FREQE\nzM3NuWPw+XwMGzaMbtAipINpVfytrKxw5cqVNkfkXLx4UauLveT5pxAVo8D6FzQ1KsFX81BXdw9B\nrgMxy3sWHMwc0NDQgOxr2SgpKeGG+ebm5iIwMFDjOFT4Cel4WhX/f/7zn9ixYweampowYsQIWFlZ\nobKyEidOnMA333yDNWvWdHScpBvw6+WDIQM9kXotFwM9emO233SEOoaiqakJf/75J4qLi6FWqzUe\no1aroVKp6EIuITqmVfFfsmQJ5HI5vvjiC+zatYvbbmBggGXLltEqXj2MSqVGXFwxGpoUmBzpzm3n\n6/GxbPh8JLkmYWr/qRCoBcjKykJRUVGrom9jYwMPDw9YWbV94ZcQ0rG0Kv48Hg9vvfUWoqKikJ6e\njtraWlhZWcHX1xfGxsaPPgB5bsjl9/DBx3/g7N3f0MSvRoDfJvTp86DP3sXKBf0s+7Vb9EUiEdzd\n3WFj03q5RUKI7jzWHb5mZmZPvGoX6f4YY8iouog/9L9AubAGAPDZ8WNYv2i2xn48Hg91dXUahd/K\nyoor+nSDFiGdr93iP2rUqMf6kP7222/PJCDSNd2svYkDfx5AQVUB+koMUZUhR19HM7gOVkKtVre6\nSCuVSlFRUQFLS0u4u7vD1taWij4hXUi7xd/Pz48+rD3czZtyJKeVQOWaifgb8dyYfWNjfYwd6olp\n7i/BoNYACQkJGDp0qMZ/ACKRCGFhYbCysqL3ESFdULvFf+PGjdzvx48fR0hICEQiUXu7k+cIYwyH\nDuXgUNJp5BsmQlpjCJFVy9q3fD0+hvUeBhfmgrLMMq5rp6SkBE5OmtM10PuFkK5LqwHVa9euRUpK\nSkfHQroIBoZj5Xtx1egX3OPV4/r1GjAwuJm5YZr1NBjdNMKtm7c0+vQrKio6MWJCyOPS6oKvWCxG\nY2NjR8dCugg9nh5GBnvhyq1MmJoJ4S9xwjDjcBjUGUAul2vsKxKJIJVKafQOId2MVsV/xowZ2LBh\nAzIyMuDh4dHm8M6JEyc+8+BIx6uqakR8fAmmTHGDnt6DvvnpPlNxuSQdHnqucOA5gN/ABwPj2m1s\nbCCVSiESiahPn5BuSKvi//777wMADh482GY7j8ej4t8NnThxAwd+OYd8QRIMLKIwYaQ312asb4z3\nxv5/JCUmobm5mdtuZ2cHNzc36s8npJvTqvjHxcV1dBxEx2oVtThVcQSphqfBAGw/9Q2GhbwLE5MH\ns2yaGpnC2dkZ+fn5sLe3h5ubGywsLDovaELIM6NV8X94YeyGhgbU19fD0tKS5ljvhpRqJU7fOI3j\necfRYN4IQ0M+bPlmcBcpkZ6ZivCgcI39XVxc0Lt3b5iZmXVSxISQjqD1Hb7JycnYtGkTsrKyuBkZ\nBw4ciOXLlyMkJKTDAiRPr7KyEcePF8AlvA6/3oiFrEEGqAGjOkO8YOcGsbEtJFYSVFdUo76+HiYm\nJtxjhUIhhEJhJ0ZPCOkIWhX/lJQUvPbaa+jXrx+WLl0Ka2trlJeX48SJE1iwYAG++uorBAQEdHSs\n5AnExxfjyx8TkKefCIvqerg4WsJQbghhnRAmAhO4iF1gZdgyuZpAIIBcLtco/oSQ55NWxT8mJgYh\nISHYtWuXxsiOqKgoLFy4ENu3b8fevXs7LEjy5NLq45Bq+D0MefrQv2MBE54ZDAT6cLJ0goOZA3jg\nwdDQEC4uLnBycoJA8FjTPRFCuimtPumZmZnYunVrqyF9PB4Ps2bNwhtvvNEhwZGnNzowAInpCbBV\nm8PS3BBOlo5wNHeEQE8AU1NTuLq6onfv3rSACiE9jFbF39zcHA0NDW221dfX00IcXUBFRQO+/eEK\npk/1hp3dg24bLzsvBPt5QFgugLOlMwwFhhCJRJBIJBCLxTRGn5AeSqviHxwcjO3bt8Pf319jycY7\nd+5g+/btdMG3k51KuIYtP32HUsEllO0fh3XL/sWdyfN4PKwcvQLJ55NhZGQEiURCC6gQQrQr/itW\nrMCLL76I0aNHw9/fHzY2NpDJZEhLS4OpqSlWrlzZ0XGSNiiUCpy+cRo/lP4MpWEtPPli3JJlISMj\nD76+Htx+QoEQYWFh1LVDCOFoPbfPjz/+iC+//BJpaWm4efMmzM3NMXPmTMybNw+2trYdHSd5iEKp\nQPyNeMRlxUFZpYSo0QR6pgIolWqIRSa4JSuAD3PX6NKhwk8IeVi7xf/ixYvw9fXlbuSytbXFW2+9\npbPASGu3K6rx4Xf70WiSB5NmAfjNfOij5fWxE5mjn5UzXOxdIHGRdHKkhJCurt3i/8orr8DIyAiB\ngYEICwtDaGgo3NzcdBkbecgnvxzEz0m/wUrPEEb6+jC3abnIbigwRF/zvvDq5wWJRELLJBJCtNJu\n8f/kk0+QlpaGtLQ0fPTRR1CpVLCxsUFoaCj3Q909umNipYY13wh6TA/NzWpAKYDU3gUBHgGQuEho\n+gVCyGNpt/iPHDkSI0eOBAA0Njbi8uXLSEtLQ0pKCv77v/8bTU1NcHV15b4V0MLuz05+URnsrMxg\nbv5gyOaLfhMRd/4PGMmN4O0kxeiwoXB2cqapFwghT0SrC75GRkYICQnhhnQqlUqkpKTgu+++w759\n+7B3715kZ2dr9YRlZWXYsGEDLly4ALVajSFDhmDVqlUaQ0h7ql+TLuJQ/DE0NVVihPtozH9lMtdm\nbmCONdOWwZSZog/dlEUIeUpa38uvUCiQnJyM8+fPIzk5Gbm5ueDxePD29kZYWJhWx2CMYeHChRCJ\nRPj6668BAOvXr8eSJUtw5MiRJ8ugm1Or1UgtSEXC5QSUFJdBqVBAwNPD5fx01NePgonJg4VzBvTp\n34mREkKeJ39b/PPy8pCUlISkpCSkpaVBoVCgb9++CAsLQ1RUFIKDg2Fqaqr1k8lkMkgkEqxYsQJ9\n+vQBAMydOxevv/46ampqesRc8XL5PVy6dAfFJXdh53EbF7MuQl7XsjSioQEfPB4ABvAMVZDJajSK\nPyGEPCvtFv+IiAhUVFTA3NwcQUFBWLNmDcLCwrii/SRsbW2xZcsW7u+ysjJ899138Pb27hGFX6FQ\nYtXbv0AuvAoY3IFtlT74/AfdNzweDxJnR/wjcBhCvAfTqB1CSIdpt/iXl5fDysoKL730EkJDQxEQ\nEPBMF2+JiopCXFwcLCwsuC6g551cVY1q8UnoNbYU9cZGPZia6oGnx0O/vv0wOmA0+on7dXKUhJCe\noN3iv2fPHiQlJeHMmTP4n//5HxgaGnJj/sPDwyGRPN2NRMuWLcPixYuxc+dOzJs3D0ePHn1uLvrK\nZA34/fciSKXm8Pd/sAqatZE1LB3M0HSzAUZGAhhbCDHIYyDG+o+FyITWxCWE6A6P3V+W62/IZDIk\nJSXh7NmzOHfuHCorK2Fvb4/Q0FCEh4cjNDQUlpaWTxRAY2Mjhg4dinnz5mHx4sVt7nPz5k2MGDEC\ncXFxT9XtpAvnzt3EgYPJaDYohI2VPt5d9brGrKfni8/jl3O/IGRACEYMGAEDgUHnBUsIeW49qm5q\nNdrHxsYGkydPxuTJLUMPs7OzcfbsWaSmpmLVqlVQqVTIysp65HFkMhmSk5Mxfvx4bpuRkREcHR1x\n584dbXPqkurr63Ht+jVcvpGMeoscKHEPtxoMcOVKAXx9pdx+QY5BCJoeBD0eDdUkhHSex1q2qba2\nFunp6UhPT8eVK1eQmZkJlUoFT09PrR5/69YtvPHGG+jbty+8vb0BAHK5HDdu3MCUKVMeP/pOpFKp\nkZZ2G2KxGrk3snG1+Cru1N2Biqmgb6QGX82HiQkPFYpCAA+KPxV9QkhX8LfFv7CwEOnp6bh06RLS\n09Nx/fp1qNVquLq6Ijg4GLNmzUJQUJDWwz29vLwQEBCAtWvXYt26dRAIBNi8eTNEIhH3raI7SEjI\nx++/X0KtshCmDo1Q6ddrtJuL9MGz5GHwgMEY7D64k6IkhJD2tVv8g4ODUVNTA8YYevXqheDgYCxa\ntAjBwcFPPKePnp4etm/fjg8//BCLFi2CQqFAeHg49u3b160WDU8u/AOlyIBKvxl11TzY2raMxW82\naoal2BLDPIch2DEYQj5NvUAI6ZraLf5BQUEIDQ1FSEgI+vbt+8yeUCQSYePGjc/seB1JrVbj+vXb\nkEh6aYy57zvIBH8W3IOApweBMQ+N5k1wl0gxUjoS7tbuND6fENLltVv8Y2JidBlHl1Jf34CTJzNw\n+UoOapoq8F+vv4I+fey59tEeI3HK+TQsrAwR7hGOF5xfgLWxdSdGTAghj+exLvg+z1QqFe7cuYPi\n4mIU3CxAclYeqpsrAT7DL3EXsPDVB9ckREYirJy0HBIrCfT5z+7GN0II0ZUeXfwZY5DJqnD9ehEq\nKm+htLoUt+tuo6G5AcxYCVbDwHgMxY2FrR7rYePR+oCEENJN9NjiX1h4G8d/ScKNW8VQGdXCwFIB\nNdRcu8CSodmwCVJ3R4wfENKJkRJCyLPXY4t/3t1rSCk9CxWvGbxGwNbMGDwhwz3Te+CZ8xDgFIAh\nTkPgZOFEF3AJIc+d57r4M8ZQVlaO1NRcDBniA0tLc65N4tQbCsMG8BR8yPUawcwU6C9xwRCnIQjs\nHQhDgWEnRk4IIR3ruSv+jDHU1tbi5s2b+OOPLOSXlELOqqAEw5SJL3D7uVi5wNrNAnJVHWYPGoch\nTuHoZdarEyMnhBDdeW6Kf0NDA0pLS1FaWorK6kqU15cjV16ESp4c4AHJmamYPCGC68Lh8XiInrgS\nIiMRBHrPzT8DIYRopVtXPbm8EX/8kYXs7EIw1MGmD1BWV4aqpioAgJ5QjWamgpzfAH3LO2CMafTf\n25nYdVbohBDSqbp18b99uwqnEpPQoHcXCkE1bAwMwOMBjMfQbNSMZpNmGDkAY6UjEN43nBY9J4SQ\n/9Oti7/CvAplhjngq/hgjEEONQTWLYXf3c4doY6h8LX3pTnzCSHkL7p18few9YDATg8KZRMM7ABz\nG2uEOYYhrG8YbIxtOjs8Qgjpsrp18dfn6yNy2HDIGmQI7xuOAbYDaL58QgjRQrcu/gDwYv8X6SYs\nQgh5TN3+NJkKPyGEPL5uceavUqkAAGVlZZ0cCSGEdA/36+X9+vlX3aL4V1RUAABmzZrVyZEQQkj3\nUlFRAScnp1bbeYwx1gnxPJampiZkZmbC1tYWfD6/s8MhhJAuT6VSoaKiAl5eXjA0bD1XWbco/oQQ\nQp6tbn/BlxBCyOOj4k8IIT0QFX9CCOmBqPgTQkgPRMWfEEJ6oC5X/KOjo/H2229rbDt69CgmTJgA\nHx8f/POf/8TZs2c12vfv3w93d3eNnwEDBmjs89VXX2HYsGEYNGgQ5s2bh8LCwi6Vw71797Bx40aE\nhYXB19cXCxcuRElJSbfJYfv27a1eg/s/n3zyic5zeJLXoKSkBIsXL0ZAQADCw8Oxdu1a1NbWauzT\nlV8DACgsLMSCBQsQEBCAiIgIbNu2DUqlUqc5yGQyvPXWWwgPD0dAQABee+015OXlce1JSUmYNGkS\nBg4ciIkTJyIxMVHj8ZWVlVi2bBkCAgIQEhKCjz76SKc5PG389927dw+RkZH46aefWrXp8n3ULtZF\nqNVqtnXrViaVStmaNWu47bGxsczd3Z199tln7Pr162zfvn3M29ubXbhwgdsnOjqaLV68mJWXl3M/\nFRUVXPuhQ4eYr68v+/XXX1lOTg5btGgRGzFiBFMoFF0mh1WrVrGIiAh27tw5lpuby+bMmcMmTJjA\n1Gp1t8ihrq5O49+/vLycRUdHs5CQEFZWVqazHJ40/ubmZjZmzBgWFRXF8vPzWVpaGhszZgz797//\nzR2jq78G1dXVLDQ0lM2ZM4dlZWWxlJQUNmbMGLZ69Wqd5aBSqdj06dPZtGnTWEZGBrt27RpbunQp\nCwkJYVVVVezatWvMy8uL7dy5k+Xn57MtW7YwT09PlpeXxx1jxowZbObMmSw7O5slJCSw4OBg9vHH\nH+skh2cRP2OMyeVyNn/+fCaVStnRo0c12nT1PnqULlH8i4uL2ezZs1lQUBAbOnSoxhs+MjKSrVix\nQmP/t99+m82ePZv7e8aMGSwmJqbd448aNYpt27aN+7uuro75+PiwY8eOdYkciouLmVQqZefOnePa\nCwoK2NChQ1lhYWG3yOGvLl26xDw8PFhiYiK3raNzeJr4c3NzmVQqZTk5OVz7vn37mK+vr87if9oc\n9uzZw3x9fdndu3e59tTUVCaVSllJSYlOcsjKymJSqZTl5+dz2xQKBRs0aBD78ccf2TvvvNPqPTN7\n9my2du1axljL+0YqlbLi4mKu/ciRI8zX15crjh2Zw9PGzxhjZ8+eZSNGjGBTpkxps/jr4n2kjS7R\n7XPp0iU4ODggNjYWffr00WgrKipCQECAxrb+/fsjPT2d+yqYn58PiUTS5rErKytRWFiIwYMHc9tM\nTEzg5eWF1NTULpFDUlISRCIRQkJCuHYXFxfEx8fDycmpW+TwMMYY3nvvPYwaNQoREREAdPM6IADr\njQAACrNJREFUPE38FhYW0NPTw6FDh6BQKFBVVYUTJ07Ay8tLZ/E/bQ5FRUVwc3ODpaUl136/+zM1\nNVUnOTg4OODzzz9Hv379uG33J1+sqalBamqqxvMDQFBQEPf8qamp6N27NxwdHbn2wYMHo76+HtnZ\n2R2ew9PGDwCnT5/G5MmT8e2337Y6vq7eR9roEnP7TJo0CZMmTWqzzc7ODrdv39bYVlpaiubmZtTW\n1qK5uRk1NTU4c+YMtm/fjsbGRgQGBmLlypUQi8Xc5EZisbjVcZ/lRHFPk0NhYSEcHR0RGxuL3bt3\no6qqCn5+flizZg3s7e27RQ4ikYjbHhcXh6tXr2Lz5s3cNl3k8DTxi8VirF27Fps2bcKBAwegVqsh\nkUiwb98+ncX/tDnY2dkhPj4earWaW7K0tLQUQEvR0UUOVlZWGDp0qMa2b775Bk1NTQgPD0dMTMzf\nPv+dO3dgZ2fXqh0Abt++DYFA0KE5PG38ALB27dp2j6+r95E2usSZ/9+JjIzE/v37cf78eahUKly4\ncAE//PADAKC5uRnXrl0DAAgEAmzZsgXvv/8+CgsLMXfuXDQ1NaGxsREAYGCguZSjUCiEQqHoEjnU\n1dXh+vXr2LNnD1avXo2YmBhUVlbi1VdfhUKh6BY5PGzv3r0YM2aMxmRSnZ3Do+JXq9W4ceMGQkJC\ncPDgQXzxxRfg8/lYvnw5VCpVp8evTQ5jx45FZWUlPvroIzQ2NkImk2H9+vUQCARobm7ulBzi4uLw\n8ccfY968eZBIJGhqaoJQKGz3+RsbG1vFp6+vDx6P1ymfhceN/1G6wvvovi5x5v93Fi5ciKqqKixY\nsAAqlQqurq547bXXsHnzZpiZmSE8PBznz5/XOPN0dXVFREQEEhMT0bt3bwAtV94fdu/ePRgZGXWJ\nHAQCAeRyOWJiYrivu9u2bUN4eDgSExPRq1evLp/DfWVlZbh48SL27t2r8fj7E0t1Vg6Piv/YsWOI\njY1FfHw8jI2NAQBOTk4YOXIkEhMTubPPrvwaiMVixMTEIDo6Gl999RWMjY2xdOlS5ObmwszMTOev\nwZEjR/DOO+9g3LhxWLlyJYCWovfXk4WHn9/Q0LBVfM3NzWCMwdjYWKc5PEn8j9LZn4OHdfkzf6FQ\niOjoaFy6dAlnzpxBbGwsDA0NYWNjw31IHy78QMtXKCsrK9y+fRsODg4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R4SO4TdzGoQOH6DG+K+PHd8XNrfFcOWvCXuX/Ftps/VXgP+XKdcAKYGFtDiql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\nW5ukn5mZSWFhIRkZ7d/4VUr1rlBH9XSAb4vI/cB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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -3125,7 +3126,7 @@ }, { "cell_type": "code", - "execution_count": 53, + "execution_count": 332, "metadata": { "collapsed": true }, @@ -3153,14 +3154,14 @@ }, { "cell_type": "code", - "execution_count": 54, + "execution_count": 333, "metadata": {}, "outputs": [ { "data": { - "image/png": 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97kG+CgIDA7ly5QqzZ88mIiKC27dv89dff/HBBx/QpUsXWrVqBRTdV/D09CQo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\nB6+//jqysrLg6+vbbRfc6dOn93lwRP/q6lqRlFSGWbO8YWJ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XV8cuXbrEAgIC2O7du1lh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\npFf+H1sFbMS2u8i2AAAAAElFTkSuQmCC\n", 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D8R3H4+5ib6swmUysWHGCsDBPrriidaMojSabOQ5MA+43//8UyEQzco9FG2ZK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\nw7AhwwYxYqWUipw+XRw/nrW2trJz504qKirYuG0jK1avp7Z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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -3187,7 +3188,7 @@ }, { "cell_type": "code", - "execution_count": 55, + "execution_count": 334, "metadata": { "collapsed": true, "scrolled": false @@ -3207,14 +3208,14 @@ }, { "cell_type": "code", - "execution_count": 56, + "execution_count": 335, "metadata": {}, "outputs": [ { "data": { - "image/png": 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/fp3s7GxsbGyAkl5VW7du5bXXXqNz585K6xoaGlZ4j6NBgwb06dOH7777jmHD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yiqn/W80ns57A07NhhFw3uo7DH/ijjGPbgPY1I47GKC+++CJ5eXnMmzevRuob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\niyMrK4usrCwSEhLGVE/u0XYeBmus5x+0DKPFaCrD5s2bw7L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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -3243,7 +3244,7 @@ }, { "cell_type": "code", - "execution_count": 57, + "execution_count": 336, "metadata": { "collapsed": true }, @@ -3271,7 +3272,7 @@ }, { "cell_type": "code", - "execution_count": 58, + "execution_count": 337, "metadata": {}, "outputs": [ { @@ -3283,9 +3284,9 @@ }, { "data": { - "image/png": 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Pnj1Mnz6dnj178vnnn1c6f2hoKCYmJvTo0QO4/8Fx7do1IiMjHzt2QVBXWVkZ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\n", 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zZ1CHTPzQyAXcHUkWcG/b2vs9tPf4Qe6hSklpCZ/++Cn6iKaXT1+G9B3EmDGj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\nvSEcDlNdXU1eXh7B4KGbsbm5uby7bg/lBzaxIaC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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -3310,7 +3311,7 @@ }, { "cell_type": "code", - "execution_count": 59, + "execution_count": 338, "metadata": { "collapsed": true }, @@ -3331,7 +3332,7 @@ }, { "cell_type": "code", - "execution_count": 60, + "execution_count": 339, "metadata": {}, "outputs": [ { @@ -3343,9 +3344,9 @@ }, { "data": { - "image/png": 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9TRQKBfPmzbNJQML2mppb2XuswLwdGeLNiEh5HCFEZ5ydVNyVOIAd+3IxGo0U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\ny8uVtl1SUgIAGDFihNw2Pp/PKq43efJkcLlcZGZm9igpdSU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WSnbNbd38evspenq1QlKj53K5uGVtCX6/nyOVtivv0OkmPB43G6+dpRXTBBSx+24kFVLI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\nyMyWA4vTQF2Qa9L0Ap+rc+7j03ZjjX1/LgxSuuY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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -3371,7 +3372,7 @@ }, { "cell_type": "code", - "execution_count": 61, + "execution_count": 340, "metadata": { "collapsed": true }, @@ -3389,7 +3390,7 @@ }, { "cell_type": "code", - "execution_count": 62, + "execution_count": 341, "metadata": {}, "outputs": [ { @@ -3398,7 +3399,7 @@ "13.88888888888889" ] }, - "execution_count": 62, + "execution_count": 341, "metadata": {}, "output_type": "execute_result" } @@ -3427,7 +3428,7 @@ }, { "cell_type": "code", - "execution_count": 63, + "execution_count": 342, "metadata": { "collapsed": true }, @@ -3449,7 +3450,7 @@ }, { "cell_type": "code", - "execution_count": 64, + "execution_count": 343, "metadata": {}, "outputs": [ { @@ -3463,7 +3464,7 @@ "data": { "image/png": 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Pnj1Mnz6dnj178vnnn1c6f2hoKCYmJvTo0QO4/8Fx7do1IiMjHzt2QVBXWVkZ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\njAyYmZkhODiY63dycsK5c+fg6Og4JnK4G2MMb775JubOnYv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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -3483,7 +3484,7 @@ }, { "cell_type": "code", - "execution_count": 65, + "execution_count": 344, "metadata": {}, "outputs": [ { @@ -3497,7 +3498,7 @@ "data": { "image/png": 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9TRQKBfPmzbNJQML2mppb2XuswLwdGeLNiEh5HCFEZ5ydVNyVOIAd+3IxGo0U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\n6apDrAghRCKRyPmTmppKzM3NSVpamsJ9VDVeLS0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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -3533,7 +3534,7 @@ }, { "cell_type": "code", - "execution_count": 66, + "execution_count": 345, "metadata": {}, "outputs": [ { @@ -3694,7 +3695,7 @@ "-6000 NaN NaN " ] }, - "execution_count": 66, + "execution_count": 345, "metadata": {}, "output_type": "execute_result" } @@ -3713,7 +3714,7 @@ }, { "cell_type": "code", - "execution_count": 67, + "execution_count": 346, "metadata": {}, "outputs": [ { @@ -3874,7 +3875,7 @@ "1940 NaN 2340. " ] }, - "execution_count": 67, + "execution_count": 346, "metadata": {}, "output_type": "execute_result" } @@ -3892,7 +3893,7 @@ }, { "cell_type": "code", - "execution_count": 68, + "execution_count": 347, "metadata": { "collapsed": true }, @@ -3910,7 +3911,7 @@ }, { "cell_type": "code", - "execution_count": 69, + "execution_count": 348, "metadata": {}, "outputs": [ { @@ -4039,7 +4040,7 @@ "-6000 NaN NaN NaN 11. NaN NaN NaN NaN NaN NaN" ] }, - "execution_count": 69, + "execution_count": 348, "metadata": {}, "output_type": "execute_result" } @@ -4059,7 +4060,7 @@ }, { "cell_type": "code", - "execution_count": 70, + "execution_count": 349, "metadata": { "collapsed": true }, @@ -4087,7 +4088,7 @@ }, { "cell_type": "code", - "execution_count": 71, + "execution_count": 350, "metadata": { "scrolled": false }, @@ -4096,7 +4097,7 @@ "data": { "image/png": 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dXV2qVq0q/x/+PXN78xJN48aNuXfvHn/99ZdKmatXrwb44MstDRs2JD09ne3bt6uk//bb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\nUL68B6aFAylf3gPD/gACAhzfjNbUIFbDycbTpcvnonrZtRbLli3jq6+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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -4120,14 +4121,14 @@ }, { "cell_type": "code", - "execution_count": 72, + "execution_count": 351, "metadata": {}, "outputs": [ { "data": { "image/png": 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aGhq5DlKBgYFMmTKFDh068N133wGZwSU1NVUpn0KhQE9PD8hcxlyhUChtT01N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\nUrKjei3D0Lp16wbdhdfZ2ZlNmzbx1ltv8ac//YmysjL69ev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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -4153,7 +4154,7 @@ }, { "cell_type": "code", - "execution_count": 83, + "execution_count": 352, "metadata": { "collapsed": true }, @@ -4166,10 +4167,8 @@ }, { "cell_type": "code", - "execution_count": 84, - "metadata": { - "collapsed": true - }, + "execution_count": 353, + "metadata": {}, "outputs": [], "source": [ "# Solution goes here\n", @@ -4178,14 +4177,14 @@ }, { "cell_type": "code", - "execution_count": 85, + "execution_count": 354, "metadata": {}, "outputs": [ { "data": { "image/png": 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vPYKCggAICgrCwcEBR0dHeX/Dhg1JTk7mxo0bxMTEcO/ePbU8jI2NcXd3l/MQ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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -4204,14 +4203,14 @@ }, { "cell_type": "code", - "execution_count": 86, + "execution_count": 355, "metadata": {}, "outputs": [ { "data": { "image/png": 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TlStXkpSUhLa2NtWrVycqKooqVapQrVo1qlWrhpqaGrNnz+b+/fuvrEtOTg7z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\nhTDG8ODBI9jaGisdbimV38H/Ko5DzmdADfDaY3s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"text/plain": [ - "" + "" ] }, "metadata": {}, From 522bac446914730f88b2aac59cdccb30b8e79c9a Mon Sep 17 00:00:00 2001 From: Junwon Lee <31522211+junwonlee5@users.noreply.github.com> Date: Tue, 26 Sep 2017 21:15:07 -0400 Subject: [PATCH 07/19] Adding chap04mine --- code/chap04mine.ipynb | 1074 +++++++++++++++++++++++++++++++++++++++++ 1 file changed, 1074 insertions(+) create mode 100644 code/chap04mine.ipynb diff --git a/code/chap04mine.ipynb b/code/chap04mine.ipynb new file mode 100644 index 00000000..6256e66c --- /dev/null +++ b/code/chap04mine.ipynb @@ -0,0 +1,1074 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Modeling and Simulation in Python\n", + "\n", + "Chapter 4: Predict\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": 2, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "# If you want the figures to appear in the notebook, \n", + "# and you want to interact with them, use\n", + "# %matplotlib notebook\n", + "\n", + "# If you want the figures to appear in the notebook, \n", + "# and you don't want to interact with them, use\n", + "# %matplotlib inline\n", + "\n", + "# If you want the figures to appear in separate windows, use\n", + "# %matplotlib qt5\n", + "\n", + "# To switch from one to another, you have to select Kernel->Restart\n", + "\n", + "%matplotlib inline\n", + "\n", + "from modsim import *" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Functions from the previous chapter" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def plot_estimates(table):\n", + " \"\"\"Plot world population estimates.\n", + " \n", + " table: DataFrame with columns `un` and `census`\n", + " \"\"\"\n", + " un = table.un / 1e9\n", + " census = table.census / 1e9\n", + " \n", + " plot(census, ':', color='darkblue', label='US Census')\n", + " plot(un, '--', color='green', label='UN DESA')\n", + " \n", + " decorate(xlabel='Year',\n", + " ylabel='World population (billion)')" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def plot_results(system):\n", + " \"\"\"Plot the estimates and the model.\n", + " \n", + " system: System object with `results`\n", + " \"\"\"\n", + " newfig()\n", + " plot_estimates(table2)\n", + " plot(system.results, '--', color='gray', label='model')\n", + " decorate(xlabel='Year', \n", + " ylabel='World population (billion)')" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def run_simulation(system, update_func):\n", + " \"\"\"Run a model.\n", + " \n", + " Adds TimeSeries to `system` as `results`.\n", + "\n", + " system: System object\n", + " update_func: function that computes the population next year\n", + " \"\"\"\n", + " results = Series([])\n", + " results[system.t0] = system.p0\n", + " for t in linrange(system.t0, system.t_end):\n", + " results[t+1] = update_func(results[t], t, system)\n", + " system.results = results" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": true + }, + "source": [ + "### Reading the data" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "# The data directory contains a downloaded copy of\n", + "# https://en.wikipedia.org/wiki/World_population_estimates\n", + "\n", + "from pandas import read_html\n", + "filename = 'data/World_population_estimates.html'\n", + "tables = read_html(filename, header=0, index_col=0, decimal='M')" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "collapsed": true, + "scrolled": true + }, + "outputs": [], + "source": [ + "table2 = tables[2]" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "table2.columns = ['census', 'prb', 'un', 'maddison', \n", + " 'hyde', 'tanton', 'biraben', 'mj', \n", + " 'thomlinson', 'durand', 'clark']" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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sdF2WKMFT+/k7Ojoya9YsZs2axfXr14mJiSE9PR0bGxucnZ1p2LBhRdQphKhE\nLsVd4kr8FV5t+WqRE8JGNo34v+EN+dX6Fv7+LjKtYiVWqpm83NzccHNzK69ahBCVXG5BLjv/2smx\n6GNkZuZz4VABn04dgYnJ4yhRqVT06SMnhZWdTOMohNBKdEo0G0I3EJcRx737Gdy4kUp4wa80/74N\n48a21nV5opQk/IUQf+vRA1t7IvdoxuUxNNDDNtcN9+wehJyPJ2BgNnZ2pjquVJSGhL8QokQPsh+w\nMXQjV5OuatqMDYx5t9dYrqjNiY/PYsKEVhL8VZCEvxDiic7fO8/WS1tJz8lEUSsYGurTyKYR4z3H\n42DugNeoAgwM9GRC9SpKwl8IUczhm4f5Pux7UtNyiYx8gLmZEbMGj2GAxwDNA1vGxhIfVZlW/3u5\nubmsXbuWI0eOkJWV9cSJFg4ePFjmxQkhdMPb2Zudl3Zx6VIMxoWWuCb2w/J+G/SayFl+daFV+P/r\nX/9ix44dtG/fHnd3d/T05BdAiOrMytiKaX6TUMftJi+kNVZmFlhZGeu6LFGGtAr/gwcP8o9//IPJ\nkyeXdz1CiAqWnptORGIE7eq2K9LesnZLlo9rxg6LKPr1a1hs8hVRtWkV/nl5ebRuLf14hahuIhMj\n2RC6gaSMZM7kPGDa8F5FbuAaGuoTGNhMhxWK8qJV+Hfu3Jljx47h6+tb3vUIISqAWlHzc9TP/HL1\nFx4kZxMZmUxIzgaczeox5CUJ+5pAq/APCAhgzpw5JCcn4+XlhYlJ8Y9/j+bkFUJUbqk5qay/sJ6o\npCgAMjLyUXIN8cjuyW8HYvDvVB97ezMdVynKm1bh//rrrwMQHBxMcHBwseUqlUrCX4gqIDwhnA2h\nG0jPTde09WzjQ3aWJ8n3VYwd20KCv4bQKvwPHTpU3nUIIcqRWlGzL2of+67uQ62oUaFCpVLxoseL\n9HfvT1rzPPT0VNKjpwbRKvzr1q2r+T4rK4vMzEysra0xNJThWoWo7NJy09hwYQNX4sO5fj0FPT3w\nal6fCV4TaGrfFABra+nJU9No/YjemTNn+OKLL7hy5YrmIa/WrVvz1ltv4efnV24FCiGeT1puGhHx\nUYSGxpGVVYB1gQsD/abQ1L6xrksTOqTV01rnzp1jwoQJ5OTk8MYbb/DJJ5/w2muvkZWVxaRJkzh/\n/nx51ymEeEYuVi6MahuEuZkR9XM60CpzMHeu5em6LKFjWp35L1u2DD8/P9atW1dk1p7p06czefJk\nVqxYwZbif/BpAAAgAElEQVQtW8qtSCGE9hRFKfJ3CtC5fmc2jXVl67/v0rNnfTp2dNZRdaKy0OrM\nPywsjKCgoGK/UCqViqCgIC5fvlwuxQkhSud++n0WnFhA6NVrxcbgcqtdn//7Pz86dapb7G9Z1Dxa\nhb+VlRVZWVlPXJaZmYm+vn6ZFiWEKL3Q+6HMPz6fY39eYtLaj/nj2I1ir9HTk9AXD2kV/r6+vqxY\nsYK4uLgi7XFxcaxYsUJu+AqhQ2pFza6IXaw5v4br0UlE304nR5XGph9PcP9+hq7LE5WUVtf8Z86c\nydChQ+nTpw/e3t7Y29uTmJhISEgIFhYWvPvuu+VdpxDiCTLzMtkQuoEr8VcAcHY2JyPeENfY3ni5\nN8HUVMbcF0+m1W+Go6MjwcHBbNy4kZCQEGJiYrCysiIwMJBx48bh4OBQ3nUKIf7H3bS7rD63msSs\nRE1ba6dWvD/hVSIuZdC3b0O5zCNKpPVpgYODA7NmzSrPWoQQWgq5F8L68xtJSE7Hzvbh/Ln93PsR\n0CQAPZUejVxq67hCUdmVGP5r1qxhyJAh1K5dmzVr1vztRlQqFVOmTCnz4oQQRSmKwu7I3WwP3U14\neBK5uYW083ThrRem4lnHU9fliSqkxPBfunQpHTt2pHbt2ixduvRvNyLhL0TFUKlUFKoLuXEjlZyc\nQkzV1lhc7EOLITLfhiidEsM/IiLiid8LIXRrcLPBRMXe4teDt2iW348Jgd4YGUl3a1E6WnX1XLly\nZbFuno/cvXuXefPmlWlRQojH/vdhLT2VHm/7v8bqcR/y0Qcv4OXlqKPKRFWmVfivWrWqxPC/ePEi\nP/zwQ5kWJYR4GPq/XP2Ff+5YwF/hCUWWGRsY06ypPbVrm+uoOlHVlXjZZ8SIEVy8eBF4+Ev4yiuv\nlLiRVq1aab3Da9euMWDAgGLt3377LT4+PlpvR4jqLLcgl40XNrHj5B/cv59J1IVCtsx+V4ZeFmWm\nxPCfN28ev/76K4qisHz5coYPH46Tk1OR1+jr62NpaUnPnj213mFUVBQ2Njbs3bu3SLu1tXUpSxei\nekrKSmL1udXcSIomKSkbgPi8GH4KjmT8uDY6rk5UFyWGv5ubG9OmTQNArVYzbNgwHB2f/9piVFQU\njRs3lgfDhHiCiMQI1oWsIzMvEyNDfZo1tSPxvDPDmg8jcEQLXZcnqhGtHvJ67bXXAEhOTiY/P19z\nA0pRFLKysggJCWHYsGFa7fDq1as0atToGcsVonpSFIU/bv7Bzr92olbUAOjr6TOjywTq+7fB1dVS\nRuIUZUqr8I+MjOSdd97h2rVrT1yuUqlKFf65ubkMHz6cu3fv4u7uzttvv03r1tJPWdRM+YX5rD29\nie+OH8TNzRpTEwNqmdRiqs9UGtnIiZIoH1qF/2effUZKSgqzZs3i8OHDGBkZ0a1bN44dO8axY8f4\n+uuvtdpZTk4Od+7cwdbWln/+858YGRmxdetWRo4cSXBwMG5ubs91MEJUNSk5KXz8yxccOv8n+QVq\n8vKSGPRCe2Z0mI61idwHE+VHq66eFy9e5M0332Ts2LH079+f7OxsAgMDWbNmDT179uSbb77Ramcm\nJiacO3eOr7/+Gh8fH1q3bs3ChQtxdXVl27Ztz3UgQlRFJgYmKPoFFKofXkq1TPZgoN14CX5R7rQK\n/7y8PBo0aABAgwYNijzxO2TIEE2XUG1YWFhgZGT0uAA9PRo3bsz9+/e13oYQ1YWJgQmze7xFs8ZO\ntNXvxdrps2nd0unpKwrxnLQKf2dnZ2JiYoCH4Z+RkcHdu3cBMDY2JjU1VaudhYWF4eXlRVhYmKat\nsLCQiIgI3N3dS1u7EFVOfmE+OTkFRdqcLJz4ZswKNvzfDNzdbXVUmahptAr/nj178sUXX/Dbb7/h\n6OhIo0aNWLZsGdevX2fz5s24urpqtbOmTZtSt25d5s6dy59//snVq1d57733SE5OZvTo0c91IEJU\ndjcSoxm+6g2mz99Q7A3A1NAUMzNDHVUmaiKtwv+1116jbdu2bN++HYD33nuPgwcP8uKLL3Ly5Ele\nf/11rXZmYGDA+vXradiwIVOnTmXYsGEkJiaydetW7Ozsnv0ohKjkTt4+SdC/3yEi5jZncvax6pvD\nui5J1HBa9fYxNTVl5cqV5OXlAdClSxf27t3LlStXaNGiBfXq1dN6h46OjixevPjZqhWiiskvzOe7\nsO84efskTnVNSInIQqXokZqfQkGBGgMDrc6/hChzpZrg879v1NarV69UoS9ETROfGc/a82uJSXt4\nv6y2gxmqDCvGtprAwK6e8tCW0KkSw793796l+uU8ePBgmRQkRHWw9Y8DHE/bA/qFmrYOLh0I6heE\nsYGxDisT4qESw9/Ly0vOTIQopZT0TN7ZvIyTd05ia2tCixZ2GOoZ8mrLV+lcr7P8TYlKo8TwX7hw\nYUXWIUS18PmR5Zy8cxKABw9yyEs2Y85Lb1OvllwiFZWLVtf8L1y48NTXeHl5PXcxQlR1YzoO5ezN\nP4mJScfXtR2LB83E1spS12UJUYxW4R8YGPjUj6vh4eFlUpAQVYmiKEX+NjzsPHiz9yiS7qsZ3fVF\nucwjKi2twv9JA7dlZWVx/vx5du/ezYoVK8q8MCEqM0VR2LrvOJf+imXhzJfR13/cZfPFpgOgqQ6L\nE0ILWoV/+/btn9jetWtXzMzM+Pe//83atWvLtDAhKqtCdSGvLVvJ0fu/YaAY47nbncAhnrouS4hS\nee4nTHx8fDh79mxZ1CJEpZeUlcSS00uINjmDgkK+KoftV76noECt69KEKJVSPeT1JIcPH8bc3Lws\nahGi0lIUhbN3z7Lt8jZyCnJwcbEgOTkHdzt3vgh8V57UFVWOVuE/fvz4Ym2FhYXExsZy+/ZtJk2a\nVOaFCVFZ/HX1HkeT93Ix7nGvN32VPu8NGceLTQagp5LgF1WPVuGfn59frE2lUuHm5sbEiRMZOnRo\nmRcmhK6p1QrrfjzE2rPrsXFW497YBgAHcwfGe46XKRZFlaZV+Gs7U5cQ1cmqX7fx73PbUFRw/z7Y\n2poQ0LYnw1sMx8TARNflCfFcSnXN/+jRo4SEhJCamoq9vT2+vr60a9euvGoTQqf8WjVhx2VTEhKy\ncahVixkdptGtqZ+uyxKiTGgV/snJyUyaNImwsDCMjIywtbUlKSmJ1atX06lTJ1atWoWxsQxWJaoX\nn7o+jPDvQ1jkXT59+U1szWx0XZIQZUarO1Xz5s0jJiaGNWvWcOnSJY4cOcLly5dZuXIlYWFhfPHF\nF+VdpxDl6kRoBJ9/dRBFUYq0T/QZy8pRH0rwi2pHq/A/duwYs2bNomvXrkXae/TowcyZM9m3b195\n1CZEuVOr1by3dhNTvvsn2yI3c/j4jSLLDfUNZYgGUS1pFf76+vpYWj55cCoHB4cn9gYSorJLykpi\n6ZmlhOQdRE0hOXppLP/ta9Rq5ekrC1HFaT2w25IlS2jVqhWOjo6a9oyMDNatW8fIkSPLrUAhypqi\nKJy4fYKdf+0kpyCH+vWsSEzIxsW6LvNfGYWenpzpi+pPq/CPj48nPj6eXr164e3tTe3atUlJSeHC\nhQtkZmZiZGSkeRBMpVKxYcOGci1aiGehKAq/Hr9CmMFvRCVFaNr19fWYNXQUQ1sNwkDvuR96F6JK\n0Oo3PTo6mqZNHw5TWFBQwL179wA0bYWFhRQWFpa4vhC6FheXwcdbvuVYwn7q1jehQf1aADhaODKu\n7Tga2jTUcYVCVCx5yEtUe4qisOD3pRxO/A+o4M6dfGo7mDOoVX8CmgRgqG+o6xKFqHCl+ox77do1\nzp49S0ZGBjY2Nnh7e9OokTziLio3lUrFQD8/Tt8KIS0tj1YNGzKn25s0qe2u69KE0Bmtwl+tVjN3\n7lx+/PHHIv2gVSoVL730EgsWLJDucKLSyMkpoLBQjbm5kaate8Pu9G9/DkdjF8Z3ekXO9kWNp1X4\nr1u3jl27djFz5kwGDhyIvb09CQkJ7N27l+XLl+Pm5iYje4pKIfRiLAu2b6VDQ09mTuqhaVepVMzp\n+U8ZgVOI/0+r8N+5cydTp05l4sSJmjYnJycmTZpEbm4uO3fulPAXOnc2PILXvllEun48tyL+ou9f\nrWnR3EGzXIJfiMe0+mtISEjA29v7icu8vLy4f/9+mRYlRGkUqAvYG7mXzTeWY+qUDkCuSQLnYs/o\nuDIhKi+tzvxdXV0JDQ3Fz6/4iIahoaE4ODg8YS0hypdarXA7LZotF7dwL/1h9+NGbtYYGxoxrcer\nBLTop+MKhai8tAr/l19+mS+//BIzMzP69++Pvb09iYmJ7Nu3j7Vr1zJlypTyrlMIjdzcAnbtjWT/\n9X0Yt7gO/zUaQ9Pa7izoPQYnCyfdFShEFaBV+I8aNYrw8HAWLlzIokWLNO2KohAQEMC0adPKrUAh\n/ltBgZq35/3I6ew9ZOml4HHfBicnc4z0jRjUdBDdGnaTa/tCaEGr8NfX12fRokVMnDiR8+fPk5qa\nipWVFe3atcPdXfpKi4qTnp/KDcc9ZN1OAeBBcg5dW3ozqs0o7M3sdVydEFVHqU6R6tSpg6urK/Xq\n1aNRo0a4uro+184vXrxI8+bNOXNGbswJ7diY2jDuhcFYWhrRqlkd/jX8Dd7yfUuCX4hS0vohr88/\n/5ytW7dSUFCgedDL1NSUadOmMXny5FLvOCsri3/+858yJpAo0b17Gezff4PRo1tgaKivaR/c/CXy\nlBwGuA/AxlQmWRHiWWgV/itWrODrr79m9OjR9OnTBzs7OxITEzlw4ADLly/H3NycoKCgUu144cKF\nODo6Eh0d/UyFi+rtwIGbbNn3B9eMjmOy5w2ChnpplhnqGzKytQwjLsTz0Pohr+nTpzNjxgxNm6ur\nK56enpibm7Nly5ZShf/Ro0c5cuQIX331FQEBAaWvWlRrOQU5nEjby0XTgwCsO72Zl/q0wMJC5okW\noqxodc0/IyOD1q1bP3GZt7c38fHxWu/wwYMHfPDBB8ybN49atWppvZ6oGcITwvn4yMfEm4ZRq5Yx\nVlZGNPFVk6uXoevShKhWtDrz79q1K99//z1dunQptmzfvn34+/trvcMPP/yQ7t274+/vT2xsrPaV\nimorMvIB9k4G7I/ew/Ho4wCoUNG8uS3tXLwJah2ElbGVjqsUonrRKvx9fHxYunQpAwcOZMCAATg4\nOJCSksKRI0cICQlh7NixrFmzBng4gFZJD30FBwfz119/sWfPnrI7AlFl5eQUsHNnFHv+c4pMt9O4\nuD++qWtuZM4IrxH4OPvIiLFClAOV8t9jNJfg0YxdWm1QpSI8PPyJy0aNGkVoaCiGhg+H01UUhezs\nbIyNjRk0aBCffPLJE9eLiYmhR48eHDp0CBcXF61rEZVbyJ93eHfTSu4bhQHQsqUdtjameNbxJLBV\noJztC/EcnpabWp35R0REPP1FWvjiiy/IycnR/JyQkEBQUBDz5s2jU6dOZbIPUXUYOiWjdrkB8WBv\nb4qjjQ1jvUfhXcdbzvaFKGcVOlu1o6NjkZ+NjY017XZ2dhVZitCBggI1BgaP+xi0dmzNsE49OBRx\nkl4tO8q1fSEqUIWGv6iZsrLy2bEjkrikVN79R8ciZ/VjvUfRob6PnO0LUcF0Gv5OTk5ERkbqsgRR\nzvLyCvnw0yOEZP9OskE0bQ870Lu7h2a5uZE5Ps4+OqxQiJpJhj8U5ep6ahQ3XHdy3yiMHL10giN2\n6bokIQRy2UeUk5yCHHb+tZPj0cexratgnWKMs7MFbVpaoVbUMuyyEDpWYvjHxcWVakP/ezNX1Dy5\nuQX8/ns0Ll5ZfHflW5KzkwHQ01Ph61WfwFaB0m9fiEqixPB/4YUXSvVHWlLfflEzXLuWzLpN5zmX\n+StGN+7QoMHjoTuk374QlU+J4T9//nxN+KempvLFF1/g5+dHv379NE/4/vHHHxw5coTZs2dXWMGi\ncjoRFcKvuV+Ra5SJ6g7Urm1GbWsbRrQaIT15hKiESgz/IUOGaL6fMWMGgwYNYt68eUVeM3DgQObN\nm8f+/ft55ZVXyq9KUenVb6aPaWgBhZkq3Nys6dLYlxEtR2BpbKnr0oQQT6DVDd+TJ0+yatWqJy7r\n1q0bO3bsKNOiROWWm1tAYaGCmZmhpq1rg670bX+ahOw4xrcbjVcdr7/ZghBC17QKfxsbGy5duvTE\nIRjOnj0rN3trkPDwJNZ/cx7Xhsa8Namrpl2lUvF65ykY6RthYWShuwKFEFrRKvyHDRvGqlWryMnJ\noUePHtjY2JCUlMSBAwf45ptveP/998u7TlEJxMSk8f6qb7luehTjCEu6/tmMtm0ev/HbmtrqsDoh\nRGloFf7Tpk0jPT2dDRs2sG7dOk27sbExb775ZqmncBRVT3J2MrvufUtyw+Pkx+WAcR4n7v9B2zYj\ndF2aEOIZaBX+KpWKWbNmMX36dEJDQ0lLS8PGxgZPT0/MzMzKu0ahQ4qicOL2CXb+tZOcghwaNaqF\nSqXCs2l9unu30XV5QohnVKonfC0tLUs1a5eomhRF4dSpexy/EIGh90WikqI0ywwN9JncazCDmw3G\nxMBEh1UKIZ5HieHfu3fvUvXNPnjwYJkUJHRLURSWLjvHbzd+J9rkNG7GltSp8/AGbm3z2oxuMxp3\nO3cdVymEeF4lhr+Xl5c8mFMDKSiEmm3npsnDJ7bvx2bi7GxJb7feDPQYiKG+4VO2IISoCkoM/4UL\nF2q+37dvH35+ftjaSm+O6k5PpUdAx45cuXcVO1tTOrZsznjvsdSrVU/XpQkhypBWQyvOmTOHc+fO\nlXctooKlpOSwbVs4ubkFRdpfajaQgBe8eWfAeOZ2myPBL0Q1pNUNX0dHR7Kzs8u7FlGBjh+P4Zud\n54nUO0q+wauMGd5Bs8xQ35D/6zpHhl0WohrTKvxHjBjB/Pnz+fPPP2natOkTu3cOHDiwzIsT5aNQ\nXciFlBOcMvqeQlU+G85sJaBXa2xsTDWvkeAXonrTKvwXLFgAwHfffffE5SqVSsK/iohKiuK7y99x\nl7tYWOuRn2+Ac+N00lTx2FBf1+UJISqIVuF/6NCh8q5DlBNFUThz5j51Gurx+919nL17FgAVKpo1\ns8XVui6j2oykvrUEvxA1iVbhX7duXc33WVlZZGZmYm1tjaGhdPurzO7dy+DrrZc4HnOUnHqXadzk\n8fDKxgbGDGk2gB6NemCgJ7N5ClHTaP1Xf+bMGb744guuXLmCoigAtG7dmrfeegs/P79yK1A8u8v3\n/mJ7/CqyTVIgHuwcDbGxNsHH2YeXm7+MjamNrksUQuiIVuF/7tw5JkyYQMOGDXnjjTews7MjPj6e\nAwcOMGnSJDZv3oyPj0951ypKqVFDG6yc8shJABcXSzzq1Gdk20Ca2jfVdWlCCB3TKvyXLVuGn58f\n69atK/LU7/Tp05k8eTIrVqxgy5Yt5VakeLrExCwKCxUcHc01be527gzx60ZY7F+84jmYrg26oq+n\nr8MqhRCVhVbhHxYWxtKlS4sN96BSqQgKCuLtt98ul+LE0xUWqvnl1yjW/LaD+g5OrJo9scj/0xjv\nIPT19GWCFSFEEVqFv5WVFVlZWU9clpmZib6+nE3qglpRs/fSb3x0eD25BlnEPDDl9yNd6dXt8cBr\ntUxq6bBCIURlpVX4+/r6smLFCry9vYtM2RgXF8eKFSvkhm8FUxSFkPsh7IncQ1xGHE71DYiOBiOL\nAhJMwgEZdVMI8fe0Cv+ZM2cydOhQ+vTpg7e3N/b29iQmJhISEoKFhQXvvvtuedcpALVazalrFzgS\ne4A7qXc07a4ultiZ2TC9x0j8XH11WKEQoqrQemyf4OBgNm7cSEhICDExMVhZWREYGMi4ceNwcHAo\n7zprvMOXLvD53k3cz43G29sRfb2Hwy+YGZrRp3EfejTsIcMtCyG0VmL4nz17Fk9PT82DXA4ODsya\nNavCChOPnYk5w8yd88nOeTj65u3b6Xi42dOjYQ/6NO6DmaFMpSmEKJ0Sw3/06NGYmprSrl07OnXq\nRMeOHXF3l2vJutDWqS1NGtbhYvgd9FV6tKnly5zu4+RmrhDimZUY/itXriQkJISQkBA+//xzCgsL\nsbe3p2PHjpqvZ7ncExsby/z58zl9+jRqtZouXbowe/bsIjeSa6qUlBz2Hj9PRrLCtNFdNO3GBsaM\n6zKU4NzzvN43kOYNZBweIcTzUSmPxmr4G9nZ2Vy8eJGQkBDOnTvHpUuXyMnJoXHjxppPBdpM7K4o\nCi+99BK2trbMnj0bgHnz5pGVlcVPP/1U4noxMTH06NGDQ4cO4eLiUorDqzr+uhfFlMXLSdS/iUNB\nY/bMXYS1tUyQLoR4Nk/LTa1u+JqamuLn56fp0llQUMC5c+f44Ycf2Lp1K1u2bCE8PPyp20lMTMTN\nzY2ZM2dqihk7diwzZswgNTWVWrVqxmUMtVpBURT09fW4mXyTn6N+Jiw+jAK7BEiBBINr7DseStBA\n6UIrhCgfWg/slpuby5kzZ/jPf/7DmTN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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "newfig()\n", + "plot_estimates(table2)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": true + }, + "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": 10, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def update_func2(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": [ + "Select the estimates generated by the U.S. Census, and convert to billions." + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "census = table2.census / 1e9" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Extract the starting time and population." + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "t0 = census.index[0]\n", + "p0 = census[t0]\n", + "t_end = census.index[-1]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Initialize the system object." + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "data": { + "text/html": [ + "
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\n", + "
" + ], + "text/plain": [ + "t0 1950.000000\n", + "t_end 2015.000000\n", + "p0 2.557629\n", + "alpha 0.025000\n", + "beta -0.001800\n", + "dtype: float64" + ] + }, + "execution_count": 13, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "system = System(t0=t0, \n", + " t_end=t_end,\n", + " p0=p0,\n", + " alpha=0.025,\n", + " beta=-0.0018)\n", + "\n", + "system" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Run the model and plot results." + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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Pnj1Mnz6dnj178vnnn1c6f2hoKCYmJvTo0QO4/8Fx7do1IiMjHzt2QVBXWVkZ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\njAyYmZkhODiY63dycsK5c+fg6Og4JnK4G2MMb775JubOnYv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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "run_simulation(system, update_func2)\n", + "plot_results(system)\n", + "decorate(title='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": 15, + "metadata": { + "scrolled": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Saving figure to file chap04-fig01.pdf\n" + ] + }, + { + "data": { + "image/png": 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GxsYYPXo0/v77b5w+fRqRkZFSk4iNjQ1CQkKwbds2HD9+HBUVFbCzs8PatWvZRCkve/fu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\nsGEDKioqsH79elRUVCApKQlyuRxBQUFwc3PD4cO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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "system.t_end = 2250\n", + "run_simulation(system, update_func2)\n", + "plot_results(system)\n", + "decorate(title='World population projection')\n", + "savefig('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": 16, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "13.856665141368708" + ] + }, + "execution_count": 16, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "system.results[system.t_end]" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "13.888888888888889" + ] + }, + "execution_count": 17, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "-system.alpha / system.beta" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Exercise:** What happens if we start with an initial population above the carrying capacity, like 20 billion? The the model with initial populations between 1 and 20 billion, and plot the results on the same axes." + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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xB3PghP/JxWc5tXYWbQxKSKSQKCmRQiGFQAm1I6y3vR9PbYft2C6FQNCbC4EU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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Solution goes here\n", + "p0_array = linrange(1, 20)\n", + "newfig()\n", + "for system.p0 in p0_array:\n", + " run_simulation(system, update_func2)\n", + " plot(system.results)\n", + " " + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [] + }, + { + "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": 19, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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United States Census Bureau (2015)[18]Population Reference Bureau (1973-2015)[6]United Nations Department of Economic and Social Affairs (2015)[7]
Year
20167.334772e+09NaN7.432663e+09
20177.412779e+09NaNNaN
20187.490428e+09NaNNaN
20197.567403e+09NaNNaN
20207.643402e+09NaN7.758157e+09
\n", + "
" + ], + "text/plain": [ + " United States Census Bureau (2015)[18] \\\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)[6] \\\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)[7] \n", + "Year \n", + "2016 7.432663e+09 \n", + "2017 NaN \n", + "2018 NaN \n", + "2019 NaN \n", + "2020 7.758157e+09 " + ] + }, + "execution_count": 19, + "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": 20, + "metadata": { + "collapsed": true + }, + "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": 21, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def plot_projections(table):\n", + " \"\"\"Plot world population projections.\n", + " \n", + " table: DataFrame with columns 'un' and 'census'\n", + " \"\"\"\n", + " census = table.census / 1e9\n", + " un = table.un / 1e9\n", + " \n", + " plot(census.dropna(), ':', color='darkblue', label='US Census')\n", + " plot(un.dropna(), '--', color='green', 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": 22, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "system.p0 = census[t0]\n", + "system.t_end = 2100\n", + "run_simulation(system, update_func2)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Plot the results." + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Saving figure to file chap04-fig02.pdf\n" + ] + }, + { + "data": { + "image/png": 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ShEKhqHX3LEEQhCft6tWrxMbGVvvya2hoiJOTEy1btmxSS4w8LmolkCVLlqCh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\nAAAAAElFTkSuQmCC\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plot_results(system)\n", + "plot_projections(table3)\n", + "decorate(title='World population projections')\n", + "savefig('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": [ + "**Exercise:** Suppose there are two banks across the street from each other, The First Geometric Bank (FGB) and Exponential Savings and Loan (ESL). They offer the same interest rate on checking accounts, 3%, but at FGB, they compute and pay interest at the end of each year, and at ESL they compound interest continuously.\n", + "\n", + "If you deposit $p_0$ dollars at FGB at the beginning of Year 0, the balanace of your account at the end of Year $n$ is\n", + "\n", + "$ x_n = p_0 (1 + \\alpha)^n $\n", + "\n", + "where $\\alpha = 0.03$. At ESL, your balance at any time $t$ would be\n", + "\n", + "$ x(t) = p_0 \\exp(\\alpha t) $\n", + "\n", + "If you deposit \\$1000 at each back at the beginning of Year 0, how much would you have in each account after 10 years?\n", + "\n", + "Is there an interest rate FGB could pay so that your balance at the end of each year would be the same at both banks? What is it?\n", + "\n", + "Hint: `modsim` provides a function called `exp`, which is a wrapper for the NumPy function `exp`." + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([ 1000. , 1030. , 1060.9 , 1092.727 ,\n", + " 1125.50881 , 1159.2740743 , 1194.05229653, 1229.87386542,\n", + " 1266.77008139, 1304.77318383, 1343.91637934])" + ] + }, + "execution_count": 24, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Solution goes here\n", + "bank = System(p0 = 1000, a = 0.03)\n", + "\n", + "t_array = linrange(0, 10)\n", + "total_array = bank.p0 * (1+bank.a)**(t_array)\n", + "total_array" + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([ 1000. , 1030.45453395, 1061.83654655, 1094.17428371,\n", + " 1127.49685158, 1161.83424273, 1197.21736312, 1233.67805996,\n", + " 1271.24915032, 1309.96445073, 1349.85880758])" + ] + }, + "execution_count": 25, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Solution goes here\n", + "bank = System(p0 = 1000, a = 0.03)\n", + "\n", + "t_array = linrange(0, 10)\n", + "total_array = bank.p0 * exp(bank.a*(t_array))\n", + "total_array" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([ 1000. , 1030. , 1060.9 , 1092.727 ,\n", + " 1125.50881 , 1159.2740743 , 1194.05229653, 1229.87386542,\n", + " 1266.77008139, 1304.77318383, 1343.91637934])" + ] + }, + "execution_count": 26, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Solution goes here\n", + "a2 = log(1+bank.a)\n", + "total_array = bank.p0 * (1+bank.a)**(t_array)\n", + "total_array\n" + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([ 1000. , 1030. , 1060.9 , 1092.727 ,\n", + " 1125.50881 , 1159.2740743 , 1194.05229653, 1229.87386542,\n", + " 1266.77008139, 1304.77318383, 1343.91637934])" + ] + }, + "execution_count": 27, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Solution goes here\n", + "total_array2 = bank.p0 * exp(a2*(t_array))\n", + "total_array2" + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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lvWNnPBQxEbZd7BTsjhoSw4GI7ijtRAriZ30NISlRrklmZhXrOb/zGI8WmjiGAxHpudvU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\nJYW7M4zExETY2dnhyy+/xJY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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Solution goes here\n", + "plot(t_array, total_array, 'bs-')\n", + "plot(t_array, total_array2, 'rs-')" + ] + }, + { + "cell_type": "code", + "execution_count": 29, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "# Solution goes here" + ] + }, + { + "cell_type": "code", + "execution_count": 30, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "# Solution goes here" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Exercise:** Suppose a new bank opens called the Polynomial Credit Union (PCU). In order to compete with First Geometric Bank and Exponential Savings and Loan, PCU offers a parabolic savings account where the balance is a polynomial function of time:\n", + "\n", + "$ x(t) = p_0 + \\beta_1 t + \\beta_2 t^2 $\n", + "\n", + "As a special deal, they offer an account with $\\beta_1 = 30$ and $\\beta_2 = 0.5$, with those parameters guaranteed for life.\n", + "\n", + "Suppose you deposit \\$1000 at all three banks at the beginning of Year 0. How much would you have in each account at the end of Year 10? How about Year 20? And Year 100?" + ] + }, + { + "cell_type": "code", + "execution_count": 31, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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V+1eSVZFFRUYppv0paK1WBhV05rIT4XhqDXhNupaes9/Ew0t+rUTzJ/8XC3EO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\nHIQQQpxBwkEIIcQZJByEEEKc4f8B08z4L2f5oRQAAAAASUVORK5CYII=\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Solution goes here\n", + "poly = bank.p0 + 30*t_array + 0.5*t_array**2\n", + "\n", + "plot(t_array, total_array, 'bs-')\n", + "plot(t_array, total_array2, 'rs-')\n", + "plot(t_array, poly, 'gs-')" + ] + }, + { + "cell_type": "code", + "execution_count": 32, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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BJv0lXHYZDB0qHVTFmdWscFi3bh1WqzX41BGAy+VCURRWr17Nli1b6NSpE+vW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\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Solution goes here\n", + "t_array = linrange(0, 20)\n", + "total_array = bank.p0 * (1+bank.a)**(t_array)\n", + "total_array2 = bank.p0 * exp(bank.a*(t_array))\n", + "poly = bank.p0 + 30*t_array + 0.5*t_array**2\n", + "plot(t_array, total_array, 'bs-')\n", + "plot(t_array, total_array2, 'rs-')\n", + "plot(t_array, poly, 'gs-')" + ] + }, + { + "cell_type": "code", + "execution_count": 33, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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JDpE3Dr4BQNyMk7SSXDjxQtx67xScJFCEEP3X55/Dxx87NxOmixr9FN40vgrY\na3L9efGTsp9JN1lYRBIRQokQScveQmRvw17OLju7V55fAkUI0f8oZe//fvBg6jbELIMj+jBM0557\n5nbb2/bK2lydy26VvP7p64QTYcLxMG2JNvxuv3NOo/c+QAkUIUT/kO7iUgr27SP09jvOzUjSTbM2\nFMvUsSy7i8sl314dtO/aSlpJQvEQjZHGnBBJ8xt+ppVO67XXlz8SIUT/YZrwwQfQ2AiAsiCivPyP\n+/KcbXu3Xp/p25JurlwKRVOkiaZwE3Gr4+K5GhpDPEMocBega3qv1U9AAkUI0Zeyl59//XV7NFcy\nicIe0BWmgDZXsR0mmr0ul6y2lCvdKklaSf74yR8JJ8KYyiScCOe0Sty6m4DH3hcm/d/eJoEihOh7\n4TCtnzbmLKXSYhbSphWCBZo7tZeJhEmHYb+vHXiNcDxMJBlB0XGeus/wYVkWw/32sjSjCkdx3imZ\nWZ89HSqcTQJFCNG3mpthzx4nTEwTWrUi/ui2twTXdbuLK3splcHWzdXZsN9YMkYoESJuduzW0tEx\ndIMyfxm6rlPiKzlhIZJNAkUIcXJldXM1/voP+OItABjxMGEtQLNWQlx5Qc/MMZF1uWwJK0EoHnK6\ntdozdIOAO0CBUUAwFDzpq7FLoAghTj6lYP9+J0yUAoVGkzacZOpryXAP7iDJbpVs2b+FcMLu1mpf\nGwG7W8vv9uNxZWZ4nsiura5IoAghTq5k0h7J1dQE2CO5YsqgRh/PW8YFgN0q+fO3Bt9IrpyurU/f\ncALkSOxIhxDR0fG7/fjdfqclkh0gcHJCJJsEihDixMveFGvT/6CnZmkb8TDN2jCOaMWYljboRnK1\nL7C/cfANTMseoRVJRLCwOjxG13SKvcUUGAX04pzEXiGBIoQ4OQ4fhr17nTAxTWjWRvBH96WARtKE\ndeOfdMJkMO2yqFAcjh7mcOQwMTPW6X0KjAL8bj+NkUYK3AXO8ZPdrfVFJFCEEL0ve36JUnbxPdEK\n2D1elgUtWglh5QM0XAYU+OGCCzIPy9durvZLokQSkS6L7C7Nhd/tRylFsa8Y6JvaSHdJoAghThzT\nhI8+csLEslJLz+tDSeIGBW6PvchjPms/7DduxgknwjRFmjpdEsXj8hBwB/AaXsCeiNhfQyRbnv8x\nCiH6TCRi72ESCgFgmRDHzR88l5HAY9dLPPBGni6j0j5ElFJEEhHqwnX4DF+H+2toTpHdpQ/MjV0k\nUIQQvSM3gaFNAAAgAElEQVSrm6v+1/8f/vgRQIGCRBLC+GnVikjgcfZ9z/eVghWKtngbR6JHiCQj\nAFgqt9Du1t343f4ORfa+HrF1PCRQhBC9J7XsvD/ebN+0wLSghWIiml1INgy7mysfZa+r9er+Vwkn\nwiStZIe5IxoaBUZBzpIo0L8K7MdDAkUIcfyyWiXBZ1/HHzuMy0pgxMNEND+mctGsD+XP7q8BHeeX\nwMDu5sru1lIoXtv/GuFEmGgy2um6WoZu4HF5KAuUoWkaRb6iAR8i2SRQhBA919REYbQBTVmkv0dj\neDmil6DQ0HS7XpIPizu2r41YyiKaiBJOhp1dENszNIPhBcNxu9wE24JoedrXJ4EihDh+lmXvrHjo\nEJqysCz7UJM2ki3uS0gPCf7z9U/iStWZB2KLpKs92Wtaa5yRWO0ZuuHURmpDtbhd9joy/XnYb09J\noAghjk3WrPeWTX/AZSUAe9Z7G4Uc0UuIKQ+gOTsrugbmoKUO4mY8Z3HG9nNHNDRnXa10gEB+h0g2\nCRQhxLFRCurqoKoKl5VAKXtIsIaLJr0UCx008PkGdhdXulWiULz6iV1gj5mxThdndOtuCtwFFBgF\nTnfWQByl1VMSKEKIo0u3ShIJjvy//8Ewo0BqyXn8tGlFtOFnm3GeM4rrT9cOrPklnW1cFUlEulxT\nS0PD0AxKC0oxZIN7QAJFCNFdzc3w4YcYZtRplejoNOml9pLzKrWw4wDq3ups8mE0GSWcCJNIdeW1\np2s6Jd4SvIaX2lBtTpgMhm6tLyKBIoToKHstLtPk8G/+B08yDEAyYfd6RTQ/RxjJX43zcbnsVsnr\n3+z/rZJOC+zJOMG2IB6j8wkyuqbjN/wUuAuoD9fjc9sz3QdLbaS7JFCEEF1rbYUPP7TDRNmTFE2l\n06IXE8OLUjiF9/6ssxAxLZPPWz/HZ/gwlUlSJfGQGyg+w0eBUZAzkktCpGv9/H8DIcRJk9Uqqfnt\nG/jirXiS9jpc6VZJTPPSohdjoaNp9r4l/T1MspnKdOoicStOwkrgVrnbQhq6gd/w43P70LX+sXHV\nQDGA/lcQQpwUra0URhvQraRdK7HAUhqtWhERrYC/GOflrBD8Wj8tvmeP0tryyRYiyQjRZJRQItTp\n7ofZkw/F8ZFAEWIwy26VPLsVX6INTzKEJx4mqvlRCuKahyN6MRYutH48HLjLUVrJSIcFGdNcmosS\nXwk+w0ewLZgTJtKtdewkUIQQ0Nxst0qUiUotnWK3SoYQ0fw5rZLs4cDQt62SrpZBiSQjXzhKa4hn\nCAXuAupCmaXkpTbScxIoQgw27RZ09CVacScjeFILOqLsLqAGvbRftko6G+obM2PUttV2uQyKjo7P\n7cNv+GmINBDwBAAJkd4mgSLEYJSa7Z5e0NFK9QilayVhNYpt7vPwuO2ie19PUvyiob5ew4tCdbqF\nrozSOrkkUITIdzfl1hZq/99r+OItGFYcM2lnCwqSuGjUR9gjuEi1SvpwUdzOQiRhJqhpq8Hn8mFh\ndTrU16N78Ll9g34ZlL4ggSLEYGGacPAghdEGwB69pSwwcdGqFxGxvGz32K0S3dX3rZK0SDJCW7yN\nSCJizxexkliu3CK7oRm4dTcj/CMG7Pa5+UACRYh81G5OiTsZxZdoQVOWM6dEAWEtQEgrtPcsSdVK\n+uySs1okMTPGa/tfI5qMdl1cR8fQc/cZyQ4T6dY6+SRQhMhnoRD+aBOGFUelZrorBQnNTYtWzJ+N\nr9nLprjtovvJnlOSHSKvf/o60WSUaCJK3Ip3ev/0gozDfMPwGJ6cob5SG+l7EihC5It2o7e8iTY8\nyTC+rNFbFjqt2hCiWgFo4PGe/L1KskNk66db7RBJRjkcPdxhwmGaz+XD5/bhc/kIhjJrbkmI9C8S\nKELkE8uCmhoKI/VoKGf0VnoxxzZtCG8b5+N2g+GGrSdpTkn7EImZMSKJyBeGiMflocAowGf4crbM\nlRDpvyRQhBjI0q0Spaj/zR/xJVrRlYk7HiaC/UVtZi0xr+vgKzjxo7faz1pPh0i6NdIVt+62QyRr\nHS2QUVoDhQSKEAPYG2+AL9FCaet+hoebsRSYyv6LnT16a4fnPDweu05yokZvdTXh8GghYugGBUYB\nlrIY7h/uHJdWyMDTK4FSVVXFZZdd1uH4r371K+bOncubb77JunXr2L9/P+PHj+f73/8+559/vnO/\nxsZGfvzjH/PWW2/hdru56qqrWLVqFYaRubynnnqKX/ziFzQ1NTF79mzWrl3LhAkTeuPyhRhYsvZ0\nn/HpH+0NryxwW3arxEIjjpsGfQRodoh4T9DoreOZtQ52iPgMH5ayKPWXAtAabz0xFylOml4JlI8+\n+oihQ4fy4osv5hwvKSmhqqqKm2++meXLl3PxxRfz4osvsmLFCp5//nmmTJkCwC233IKmaTzzzDPU\n1tZy++23YxgGq1atAmDTpk1s2LCB+++/n4kTJ7J+/XqWLVvG5s2b8Xg63xBHiLzRbmJidsGdJCRS\nExPdQFjzE9IKSVo6u/znnZAVgTsNkWSM2lAmRDqbtZ4OEZ/hw9DtC2uLtznnpTYy8PVaoJx66qmM\nGDGiw7mnn36amTNncvPNNwPwve99j507d/L0009zzz338Le//Y2dO3fy6quvMm7cOKZNm8Ztt93G\nPffcw4oVK/B4PFRUVLB06VIuueQSAB555BEWLFjAK6+8wsKFC3vjLQjR/yUSUF3NkEhdZghwquge\n1XxoyqJVK0LXQSezvHxv6GwRxlgyRl2o7phDJJuESH7plf/l9u3bx6RJkzo9V1lZyde//vWcY+ec\ncw4vv/yyc37MmDGMGzfOOT9//nxCoRB79+5l7NixHDhwgPnz5zvnA4EA06dPp7KyUgJF5KecZeVf\nx5sI4U2GUUqRTGLPSsReWr5VG0ISN82U8M6Q85yCe09aJe2L6m8cfAPLsoiadj0kbtrzRLoKEbfu\nptRf2mmISIE9f/VaoMRiMa699lo+++wzpkyZwr/8y79w9tlnEwwGGTlyZM79y8rKCAaDANTW1lJW\nVtbhPEBNTY1TR/mi5xAiL7Sb3Y6y8CbDDAvVEdX9TtcW2BMT27QhxPHYuybqYCZ7Nnqrq21y00X1\nrmasQyZE0kufBNuCOWEirZDBoceBEo1Gqa6uZtiwYdx22214PB6eeeYZlixZwvPPP080Gu1Q5/B4\nPMRiMQAikQheb27xzu12o2kasViMSCQC0OE+2c8hRF5JJPAm2vAmQqjU5iTprq2kZtDGEGKaF02H\nv/nPy1lW/lhbJZ2FSNJMUtNWQ4G7gKSV7PKxbt3dIUTSS59IV9bg1ONA8fl87NixA4/H4wTHv/3b\nv/H+++/z61//Gq/XSyKR+y+beDxOQUGB8/h4PHeZhUQigVIKv9+PL7W4UPv7ZD+HEANWh9ntITzJ\nMIF4yJnd7gaSGLRphcQ0H5oOLs1ujYwenft0xxsi8WScYCjojLxKWAncVsetcD0uj10TcfnQdZ1E\nW0JCRDh6pcursLAw57au65x66qnU1NRQXl5OXV1dzvm6ujqnC2vUqFFs3bq1w3mwu7nKy8sBqK+v\nZ/z48Tn3mTx5cm9cvhAnT7s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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "\n", + "# Solution goes here\n", + "t_array = linrange(0, 100)\n", + "total_array = bank.p0 * (1+bank.a)**(t_array)\n", + "total_array2 = bank.p0 * exp(bank.a*(t_array))\n", + "poly = bank.p0 + 30*t_array + 0.5*t_array**2\n", + "plot(t_array, total_array, 'bs-')\n", + "plot(t_array, total_array2, 'rs-')\n", + "plot(t_array, poly, 'gs-')" + ] + }, + { + "cell_type": "code", + "execution_count": 34, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "# Solution goes here" + ] + }, + { + "cell_type": "code", + "execution_count": 35, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "# Solution goes here" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "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": "3.6.1" + } + }, + "nbformat": 4, + "nbformat_minor": 1 +} From bc4046fd477042cb748d9f3c49d990d117633bf5 Mon Sep 17 00:00:00 2001 From: Junwon Lee Date: Fri, 6 Oct 2017 00:02:07 -0400 Subject: [PATCH 08/19] Adding chap05mine --- code/chap05mine.ipynb | 1957 +++++++++++++++++++++++++++++++++++++++++ 1 file changed, 1957 insertions(+) create mode 100644 code/chap05mine.ipynb diff --git a/code/chap05mine.ipynb b/code/chap05mine.ipynb new file mode 100644 index 00000000..4e88341d --- /dev/null +++ b/code/chap05mine.ipynb @@ -0,0 +1,1957 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Modeling and Simulation in Python\n", + "\n", + "Chapter 5: Design\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": 2, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "# If you want the figures to appear in the notebook, \n", + "# and you want to interact with them, use\n", + "# %matplotlib notebook\n", + "\n", + "# If you want the figures to appear in the notebook, \n", + "# and you don't want to interact with them, use\n", + "# %matplotlib inline\n", + "\n", + "# If you want the figures to appear in separate windows, use\n", + "# %matplotlib qt5\n", + "\n", + "# To switch from one to another, you have to select Kernel->Restart\n", + "\n", + "%matplotlib inline\n", + "\n", + "from modsim import *" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### SIR implementation\n", + "\n", + "We'll use a `State` object to represent the number or fraction of people in each compartment." + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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" + ], + "text/plain": [ + "S 0.988889\n", + "I 0.011111\n", + "R 0.000000\n", + "dtype: float64" + ] + }, + "execution_count": 4, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "init /= sum(init)\n", + "init" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "`make_system` creates a `System` object with the given parameters." + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def make_system(beta, gamma):\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(S=89, I=1, R=0)\n", + " init /= sum(init)\n", + "\n", + " t0 = 0\n", + " t_end = 7 * 14\n", + "\n", + " return System(init=init, t0=t0, t_end=t_end,\n", + " beta=beta, gamma=gamma)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here's an example with hypothetical values for `beta` and `gamma`." + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "tc = 3 # time between contacts in days \n", + "tr = 4 # recovery time in days\n", + "\n", + "beta = 1 / tc # contact rate in per day\n", + "gamma = 1 / tr # recovery rate in per day\n", + "\n", + "system = make_system(beta, gamma)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The update function takes the state during the current time step and returns the state during the next time step." + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def update1(state, system):\n", + " \"\"\"Update the SIR model.\n", + " \n", + " state: State with variables S, I, R\n", + " system: System with beta and gamma\n", + " \n", + " returns: State object\n", + " \"\"\"\n", + " s, i, r = state\n", + "\n", + " infected = system.beta * i * s \n", + " recovered = system.gamma * i\n", + " \n", + " s -= infected\n", + " i += infected - recovered\n", + " r += recovered\n", + " \n", + " return State(S=s, I=i, R=r)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "To run a single time step, we call it like this:" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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" + ], + "text/plain": [ + "S 0.985226\n", + "I 0.011996\n", + "R 0.002778\n", + "dtype: float64" + ] + }, + "execution_count": 8, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "state = update1(init, system)\n", + "state" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now we can run a simulation by calling the update function for each time step." + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "collapsed": true + }, + "outputs": [], + "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: State object for final state\n", + " \"\"\"\n", + " state = system.init\n", + " for t in linrange(system.t0, system.t_end):\n", + " state = update_func(state, system)\n", + " return state" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The result is the state of the system at `t_end`" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "data": { + "text/html": [ + "
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" + ], + "text/plain": [ + "S 0.520453\n", + "I 0.000615\n", + "R 0.478933\n", + "dtype: float64" + ] + }, + "execution_count": 10, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "run_simulation(system, update1)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Exercise** Suppose the time between contacts is 4 days and the recovery time is 5 days. After 14 weeks, how many students, total, have been infected?\n", + "\n", + "Hint: what is the change in `S` between the beginning and the end of the simulation?" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "0.37943042989926101" + ] + }, + "execution_count": 11, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Solution goes here\n", + "tc = 4 # time between contacts in days \n", + "tr = 5 # recovery time in days\n", + "\n", + "beta = 1 / tc # contact rate in per day\n", + "gamma = 1 / tr # recovery rate in per day\n", + "\n", + "system = make_system(beta, gamma)\n", + "s0 = system.init.S\n", + "fourteen = run_simulation(system, update1)\n", + "s0 - fourteen.S" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Using Series objects" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "If we want to store the state of the system at each time step, we can use one `TimeSeries` object for each state variable." + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def run_simulation(system, update_func):\n", + " \"\"\"Runs a simulation of the system.\n", + " \n", + " Add three Series objects to the System: S, I, R\n", + " \n", + " system: System object\n", + " update_func: function that updates state\n", + " \"\"\"\n", + " S = TimeSeries()\n", + " I = TimeSeries()\n", + " R = TimeSeries()\n", + "\n", + " state = system.init\n", + " t0 = system.t0\n", + " S[t0], I[t0], R[t0] = state\n", + " \n", + " for t in linrange(system.t0, system.t_end):\n", + " state = update_func(state, system)\n", + " S[t+1], I[t+1], R[t+1] = state\n", + " \n", + " system.S = S\n", + " system.I = I\n", + " system.R = R" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here's how we call it." + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "tc = 3 # time between contacts in days \n", + "tr = 4 # recovery time in days\n", + "\n", + "beta = 1 / tc # contact rate in per day\n", + "gamma = 1 / tr # recovery rate in per day\n", + "\n", + "system = make_system(beta, gamma)\n", + "run_simulation(system, update1)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "And then we can plot the results." + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def plot_results(S, I, R):\n", + " \"\"\"Plot the results of a SIR model.\n", + " \n", + " S: TimeSeries\n", + " I: TimeSeries\n", + " R: TimeSeries\n", + " \"\"\"\n", + " plot(S, '--', color='blue', label='Susceptible')\n", + " plot(I, '-', color='red', label='Infected')\n", + " plot(R, ':', color='green', label='Recovered')\n", + " decorate(xlabel='Time (days)',\n", + " ylabel='Fraction of population')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here's what they look like." + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Saving figure to file chap05-fig01.pdf\n" + ] + }, + { + "data": { + "image/png": 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tivt/HYP29vaEh4fTu3dvs3tUqlSJq1evAuCYbyTK7WLOHUatFJhFfLv3Yi0W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\npi/6r1Vhaqr4kNnZCT9qnHvH1lboBhKJdF+Hx8H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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plot_results(system.S, system.I, system.R)\n", + "savefig('chap05-fig01.pdf')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Using a DataFrame" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Instead of making three `TimeSeries` objects, we can use one `DataFrame`.\n", + "\n", + "We have to use `loc` to indicate which row we want to assign the results to. But then Pandas does the right thing, matching up the state variables with the columns of the `DataFrame`." + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def run_simulation(system, update_func):\n", + " \"\"\"Runs a simulation of the system.\n", + " \n", + " Add a DataFrame to the System: results\n", + " \n", + " system: System object\n", + " update_func: function that updates state\n", + " \"\"\"\n", + " frame = DataFrame(columns=system.init.index)\n", + " frame.loc[system.t0] = system.init\n", + " \n", + " for t in linrange(system.t0, system.t_end):\n", + " frame.loc[t+1] = update_func(frame.loc[t], system)\n", + " \n", + " system.results = frame" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here's how we run it, and what the result looks like." + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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SIR
00.9888890.0111110.000000
10.9852260.0119960.002778
20.9812870.0129360.005777
30.9770550.0139340.009011
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\n", + "
" + ], + "text/plain": [ + " S I R\n", + "0 0.988889 0.011111 0.000000\n", + "1 0.985226 0.011996 0.002778\n", + "2 0.981287 0.012936 0.005777\n", + "3 0.977055 0.013934 0.009011\n", + "4 0.972517 0.014988 0.012494" + ] + }, + "execution_count": 17, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "tc = 3 # time between contacts in days \n", + "tr = 4 # recovery time in days\n", + "\n", + "beta = 1 / tc # contact rate in per day\n", + "gamma = 1 / tr # recovery rate in per day\n", + "\n", + "sir = make_system(beta, gamma)\n", + "run_simulation(system, update1)\n", + "system.results.head()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can extract the results and plot them." + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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tivt/HYP29vaEh4fTu3dvs3tUqlSJq1evAuCYbyTK7WLOHUatFJhFfLv3Yi0W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\niQpBEAShM0hUCIIgCJ1BokIQBEHojP8DRPD4ChRIKg0AAAAASUVORK5CYII=\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "frame = system.results\n", + "plot_results(frame.S, frame.I, frame.R)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Exercise** Suppose the time between contacts is 4 days and the recovery time is 5 days. Simulate this scenario for 14 days and plot the results." + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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+/vj7+xMYGMjYsWM5V3iv2P/RFln/In/48a5du9i3bx8LFy7k448/5ptvvrnt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\nMoSXVBYvXgygOgndvn0b9+7dQ1paGgBwq/h5eXnBwsIChw8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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Solution goes here\n", + "tc = 4 # time between contacts in days \n", + "tr = 5 # recovery time in days\n", + "\n", + "beta = 1 / tc # contact rate in per day\n", + "gamma = 1 / tr # recovery rate in per day\n", + "\n", + "system = make_system(beta, gamma)\n", + "run_simulation(system, update1)\n", + "call = system.results\n", + "plot_results(call.S, call.I, call.R)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Metrics" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Given the results, we can compute metrics that quantify whatever we are interested in, like the total number of sick students, for example." + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def calc_total_infected(system):\n", + " \"\"\"Fraction of population infected during the simulation.\n", + " \n", + " system: System object with results.\n", + " \n", + " returns: fraction of population\n", + " \"\"\"\n", + " frame = system.results\n", + " return frame.S[system.t0] - frame.S[system.t_end]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here's an example.|" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "0.333 0.25 0.467162931836\n" + ] + } + ], + "source": [ + "system.beta = 0.333\n", + "system.gamma = 0.25\n", + "run_simulation(system, update1)\n", + "print(system.beta, system.gamma, calc_total_infected(system))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Exercise:** Write functions that take a `System` object as a parameter, extract the `results` object from it, and compute the other metrics mentioned in the book:\n", + "\n", + "1. The fraction of students who are sick at the peak of the outbreak.\n", + "\n", + "2. The day the outbreak peaks.\n", + "\n", + "3. The fraction of students who are sick at the end of the semester.\n", + "\n", + "Hint: If you have a `TimeSeries` called `I`, you can compute the largest value of the series like this:\n", + "\n", + " I.max()\n", + "\n", + "And the index of the largest value like this:\n", + "\n", + " I.idxmax()\n", + "\n", + "You can read about these functions in the `Series` [documentation](https://pandas.pydata.org/pandas-docs/stable/generated/pandas.Series.html)." + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "0.043536202687592354" + ] + }, + "execution_count": 22, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Solution goes here\n", + "def calc_fracsick(system):\n", + " frame = system.results\n", + " return frame.I.max()\n", + "calc_fracsick(system) " + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "data": { + "text/plain": [ + "30" + ] + }, + "execution_count": 23, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Solution goes here\n", + "def calc_daysick(system):\n", + " frame = system.results\n", + " return frame.I.idxmax()\n", + "calc_daysick(system)" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "0.00067419431560344738" + ] + }, + "execution_count": 24, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Solution goes here\n", + "def calc_finsick(system):\n", + " frame = system.results\n", + " return frame.I[system.t_end]\n", + "calc_finsick(system)" + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "metadata": { + "collapsed": true, + "scrolled": true + }, + "outputs": [], + "source": [ + "# Solution goes here" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "# Solution goes here" + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "# Solution goes here" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### What if?" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can use this model to evaluate \"what if\" scenarios. For example, this function models the effect of immunization by moving some fraction of the population from S to R before the simulation starts." + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def add_immunization(system, fraction):\n", + " \"\"\"Immunize a fraction of the population.\n", + " \n", + " Moves the given fraction from S to R.\n", + " \n", + " system: System object\n", + " fraction: number from 0 to 1\n", + " \"\"\"\n", + " system.init.S -= fraction\n", + " system.init.R += fraction" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's start again with the system we used in the previous sections." + ] + }, + { + "cell_type": "code", + "execution_count": 29, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "(0.3333333333333333, 0.25)" + ] + }, + "execution_count": 29, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "tc = 3 # time between contacts in days \n", + "tr = 4 # recovery time in days\n", + "\n", + "beta = 1 / tc # contact rate in per day\n", + "gamma = 1 / tr # recovery rate in per day\n", + "\n", + "system = make_system(beta, gamma)\n", + "system.beta, system.gamma" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "And run the model without immunization." + ] + }, + { + "cell_type": "code", + "execution_count": 30, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "0.46832081102878098" + ] + }, + "execution_count": 30, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "run_simulation(system, update1)\n", + "calc_total_infected(system)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now with 10% immunization." + ] + }, + { + "cell_type": "code", + "execution_count": 31, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "0.30650802853979753" + ] + }, + "execution_count": 31, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "system2 = make_system(beta, gamma)\n", + "add_immunization(system2, 0.1)\n", + "run_simulation(system2, update1)\n", + "calc_total_infected(system2)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "10% immunization leads to a drop in infections of 16 percentage points.\n", + "\n", + "Here's what the time series looks like for S, with and without immunization." + ] + }, + { + "cell_type": "code", + "execution_count": 32, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Saving figure to file chap05-fig02.pdf\n" + ] + }, + { + "data": { + "image/png": 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Pvr6+//jVkrhZuLGg5wJmdJmh1qaSWZhJ+OlwsooavjpQR1uLgd3aoPXA+JXj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\nS5adnc1mzJjhcMyMGTPY0qVLuzur3aL9ei8NKq5QBjzPs8z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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plot(system.results.S, '-', label='No immunization')\n", + "plot(system2.results.S, 'g--', label='10% immunization')\n", + "\n", + "decorate(xlabel='Time (days)',\n", + " ylabel='Fraction susceptible')\n", + "\n", + "savefig('chap05-fig02.pdf')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now we can sweep through a range of values for the fraction of the population who are immunized." + ] + }, + { + "cell_type": "code", + "execution_count": 33, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "0.0 0.468320811029\n", + "0.1 0.30650802854\n", + "0.2 0.161365457006\n", + "0.3 0.0728155898425\n", + "0.4 0.035520216753\n", + "0.5 0.0196887157825\n", + "0.6 0.0116220579983\n", + "0.7 0.00683873780062\n", + "0.8 0.00369649625371\n", + "0.9 0.00148153267227\n", + "1.0 -0.000161212109412\n" + ] + } + ], + "source": [ + "immunize_array = linspace(0, 1, 11)\n", + "for fraction in immunize_array:\n", + " system = make_system(beta, gamma)\n", + " add_immunization(system, fraction)\n", + " run_simulation(system, update1)\n", + " print(fraction, calc_total_infected(system))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This function does the same thing and stores the results in a `Sweep` object." + ] + }, + { + "cell_type": "code", + "execution_count": 34, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def sweep_immunity(immunize_array):\n", + " \"\"\"Sweeps a range of values for immunity.\n", + " \n", + " immunize_array: array of fraction immunized\n", + " \n", + " returns: Sweep object\n", + " \"\"\"\n", + " sweep = SweepSeries()\n", + " for fraction in immunize_array:\n", + " system = make_system(beta, gamma)\n", + " add_immunization(system, fraction)\n", + " run_simulation(system, update1)\n", + " sweep[fraction] = calc_total_infected(system)\n", + " return sweep" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here's how we run it." + ] + }, + { + "cell_type": "code", + "execution_count": 35, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "immunize_array = linspace(0, 1, 21)\n", + "infected_sweep = sweep_immunity(immunize_array)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "And here's what the results look like." + ] + }, + { + "cell_type": "code", + "execution_count": 36, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Saving figure to file chap05-fig03.pdf\n" + ] + }, + { + "data": { + "image/png": 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vbx5gEMDFxYWJEydy+PDhaguwLlGpVHQsNWPhsXPSsVAI0XhZlUDy8/Px9PSs\ncJudnV2FvcgbqrYBbrg4agFTx8JTlzJqOSIhhKgdViWQsLAw1qxZU+G2TZs20b59+yoNqi5Tq1VE\nlJqx8KjMWCiEaKSsSiBTpkxh586dDB06lI8++giVSsWWLVuYMmUK//3vf5k0aVJ1x1mntG/jia2N\n6alLzy4kISmnliMSQoiaZ1UC6datG8uXL0elUrFs2TIUReGTTz7h4sWLLFu2jF69elV3nHWKna2G\n9q1vVukdOSMzFgohGh+rOxJ2796d7777jry8PLKysnBxccHFpfH2xu4Y5E3c2VQUReHy9RxSMwvw\ncpOOhUKIxsOqEshDDz1k7uvh5ORE06ZNzckjLi6OHj16VF+EdZSrk5bAZk3MyzJvuhCisam0BLJx\n40YMBgNgmlL2l19+4cyZM+X227NnD4WFjXO+8E7B3pxNNA3vfvpyBvd18MfJQWYsFEI0DpUmkCNH\njhATEwOY+j8sXry40pOMHTu2ygOrD/w8nfD3dOJaWh5Go0Lc2VTu6+Bf22EJIUSNqDSBvPrqqzz3\n3HMoisKAAQNYunQp7dq1s9hHo9Hg7OyMs7NztQdaV3UM9uba76YJtf44n0aXdj7Y2mhqOSohhKh+\nlSYQrVZLs2bNANiyZQv+/v6kpKTQtGlTADIyMkhISMDPz69mIq2j2jRtgquTluw8HYU6PfGXMugQ\n6HX7A4UQop6zqhHd2dmZMWPGMG7cOPO6uLg4nnnmGZ5//vlyMxU2Jmq15fAmR09Lx0IhRONgVQL5\n17/+RVJSEn/961/N63r37s2XX37JhQsX+OCDD6otwPqgXSsP7GxN1VaZuUVcvJZdyxEJIUT1syqB\n7Nq1i9dee82iw6BaraZ79+5Mnz6drVu3VluA9YHWVkP7NqU6FsotvUKIRsCqBFJQUICDQ8Wd5Fxc\nXMjOlm/cHdt6ob4xUvGVlFyS0/NrOSIhhKheViWQjh078tVXX6HX6y3WG41GVq1aRXh4eLUEV584\nO2pp29zNvCzDmwghGjqrhjKZPHkyY8aM4aGHHuKBBx7Aw8ODjIwMdu3axbVr1/jyyy+rOcz6oVOQ\nN6cTTMO7n72cSY8O/jjfGPpdCCEaGqtKIJ07d2b16tWEhISwYcMGli5dyn//+1/atGnDqlWriIqK\nqu446wUfD0eaepn6xBgVU8dCIYRoqKweTLFDhw78+9//rs5YGoTIEG+upppuazZ1LPRFaysdC4UQ\nDY/VCQRv/4hQAAAgAElEQVRMfT/27NlDSkoK48eP58KFC4SGhuLh4VFd8dU7rfxdcXO2IzO3iKJi\nAycvplv0ExFCiIbCqgRSXFzMzJkz2bhxIzY2NhgMBp566ik+++wzzp07x6pVq2jevHl1x1ovlMyb\nvvNwImCasbBDoBdqteo2RwohRP1iVRvIhx9+yI4dO1iyZAn79+8397SeO3cuDg4Ojb4jYVmhrdyx\n15pyc3aejgtXs2o5IiGEqHpWJZAff/yR6dOnM3DgQLTam3cVtWjRgpdffpl9+/ZVW4D1ka2NhjDp\nWCiEaOCsSiCZmZm0bt26wm3u7u6NeiysynRoe7Pa6lpaHklpebUckRBCVC2rEkjbtm3ZuHFjhdt+\n/fVXAgMDqzSohsDZwZbgUh0Lj0rHQiFEA2NVI/qECROYMmUKOTk59O3bF5VKxZEjR9iwYQNfffUV\n//znP6s7znqpU7AP8ZdudCxMzOK+PB2uTtKxUAjRMFg9J/o///lPDh8+zOzZs1EUhbfffpt169bx\n+uuv8/jjj1d3nPWSl5sDAT6mueMVRSHurJRChBANR6UlkC+++ILHHnsMHx8fAJ588kkGDx7M2bNn\nyczMxMXFhbZt22Jjc0ddSRqdyGBvEpNzADhxIZ2u7f3MQ78LIUR9VmkJ5MMPP+Ty5csAhIeHc+zY\nMVQqFUFBQXTt2pXQ0FBJHlZo4eeCh6s9ALpiAycvpNVyREIIUTUqzQDOzs6sWLGCK1euoNfr2bVr\nFxcvXqz0RIMGDaqO+Oq9ko6F2w+akvHRM6lEtPWWjoVCiHqv0gQyfvx45s+fz5YtW1CpVCxZsqTS\nk6hUKkkgtxDS0p29x69RUKQnJ1/HuSuZBDV3r+2whBDinlSaQMaOHcvQoUPJysqif//+LF26lHbt\n2t3zBQ0GA4sWLWL9+vXk5eXRu3dv3nzzTby8vCrc//vvv+fzzz8nMTGR5s2b8/zzzzNkyJB7jqMm\n2WjUdAj0IvZEEmDqWNg2wA2VSkohQoj665aNGM7Ozjg7O/P2228TFRWFu/u9f2tesmQJ69evZ968\nebi5uTF37lwmT57M6tWry+27efNm/va3v/H3v/+drl27snfvXv7617/i5uZG//797zmWmhQe6MnB\n+OsYjArX0/O5lppHU2/n2g5LCCHumlWt4MOGDSM/P5+dO3dSUFCA0Wgst8+jjz562/PodDpiYmKY\nM2cOPXv2BGDhwoX079+fQ4cO0blzZ4v9MzIyePnll3nqqacAaN68OatWreL333+vdwnE0d6WkJYe\nnLjRiH4wPlkSiBCiXrMqgezZs4eXX36ZvLw880CKpalUKqsSSHx8PHl5eURHR5vXBQQE0KxZMw4c\nOFAugQwfPtz8t16vZ+vWrZw7d44pU6ZYE3adExnizcmL6SiKwqWkbFIzC/Byq3iueSGEqOusSiD/\n+te/aNGiBa+99hp+fn6o1Vb1PywnKcnUBuDr62ux3sfHx7ytIseOHeOZZ57BYDAwdOhQHnjggbu6\nfm1zd7GnTbMmnEvMBODwqWQGdmtZy1EJIcTdsSqBnD17lmXLltG9e/d7ulhBQQFqtRpbW1uL9Vqt\nlqKiokqPCwgIYO3atZw4cYJ//OMfeHl5MW3atHuKpbZ0DvExJ5AzlzPpFu4vw5sIIeolq4oS/v7+\n5Ofn3/PF7O3tMRqN6PV6i/U6nQ4Hh8qrctzd3WnXrh1Dhgxh4sSJfPnllxgMhnuOpzb4ejiahzcx\nKgpHTifXckRCCHF3rEog48ePZ9myZVy/fv2eLubv7w9ASorlmFDJycnlqrUAYmNjOXnypMW6kJAQ\nCgsLycqqv5M0dQ65OcXtiQvp5BcW12I0Qghxd6yqwvrll19ISkqib9+++Pn5YW9vb7FdpVKxYcOG\n254nNDQUJycnYmNjGTx4MACJiYlcuXKFrl27ltv/s88+Q61W88knn5jXxcXF4enpWSW3FNeW5r4u\neLs5kJJZgN5g5NjZVLqF+9d2WEIIcUesSiAuLi5V0nCt1WoZOXIk8+fPx93dHU9PT+bOnUt0dDSd\nOnVCp9ORlZVFkyZN0Gq1PPfcc4wfP57PP/+cAQMGEBsby/Lly5k1a1a97oSnUqnoHOrD5r2XAIg7\nl0rnUB9sbWSQRSFE/WH1XVhVZerUqej1embMmIFerzf3RAc4fPgwY8aMISYmhm7dutGrVy8WL17M\n0qVL+fDDD/H392fOnDkMGzasyuKpLYHN3GjinERWbhFFOgN/nE+jU7BPbYclhBBWUykVdewA0tLS\ncHNzQ6PRkJZ2+xFkPT09b7tPTUlMTKR///78/PPPBAQE1HY4lTp+LpUdhxIB0wyGox9ph0Zzd7dI\nCyHEvbrTz85KSyC9evXi22+/JSIigp49e962yqhsY7e4vdBWHsSeuE5+YTG5BcWcTsikXWuP2g5L\nCCGsUmkC+fvf/07z5s0BePvtt2ssoMbERqMmoq0Xe49fA+Dw6WRCW7nX6/YdIUTjUWkCKd3O0BDa\nHOqq8EBPDp1KRldsID27kIvXsmndtElthyWEELclFe61zF5rQ1ibm+1HB+OTKxxvTAgh6hpJIHVA\nxyBvNDdmKExKy+Naal4tRySEELcnCaQOcHYwDfVe4mC8DG8ihKj7JIHUEZEh3ubG85Kh3oUQoi6T\nBFJHlAz1XuLwKSmFCCHqNqt6ogP88MMP7Nixo8IZCVUqFZ9++mmVB9fYyFDvQoj6xKoE8sEHH/DJ\nJ5/g7++Pr6/vXU8oJW6tZKj3xOQc81DvfSLrbk96IUTjZlUCWbt2LWPGjOH111+v7ngavahQHxKT\ncwDTUO9d2vniaG97m6OEEKLmWVWUyMnJYcCAAdUdiwACfJzxvjFPeslQ70IIURdZlUA6derEkSNH\nqjsWwc2h3kvEnUulWF8/Z18UQjRsVlVhvfTSS0yfPh2j0UhkZGSF089GRERUeXCNlQz1LoSoD6xK\nIKNHjwZg0aJF5Qb6UxQFlUolo/FWIbVaRWSwt3mo9yOnU+gQ6CVDvQsh6hSrEsgXX3xR3XGIMmSo\ndyFEXWdVArnvvvuqOw5Rho1GTccgL34/Zhrq/dApGepdCFG3WF0ncvHiRV555RV69+5NZGQk/fr1\nY8aMGZw/f74642vUwtp4orU1zZOekWMa6l0IIeoKq0ogZ86cYfjw4dja2tK3b1+8vLxISUlhx44d\nbNu2jTVr1hAUFFTdsTY69lobwtuY5gsB0yCLrfxdpRQihKgTrEogCxYsoGXLlsTExODs7Gxen5ub\ny3PPPccHH3zAv//972oLsjHrGOTN0TMpGIyKeaj3pt7Otz9QCCGqmVVVWPv37+cvf/mLRfIAcHZ2\nZsKECRw4cKBaghPg5GBLaCsZ6l0IUfdYlUDs7OwqHf9KrVZTXFxcpUEJS52CZah3IUTdY3VP9OXL\nl6PT6SzWFxUVsXz5cjp37lwtwQkTGepdCFEXWdUGMn36dJ5++mkGDBhA//798fLyIjU1lZ9//pns\n7GxWrlxZ3XE2elFlhnqPDvOjibNdLUclhGjMrCqBBAUFsXr1ajp06MDGjRtZunQpGzduJCIigm++\n+Ybw8PDqjrPR87kx1DuAUVHYfyKpliMSQjR2Vk8oFRoayrJly6ozFnEb0WG+5qHeTyVk0inYBy+3\n8uOSCSFETag0gWzcuJGePXvSpEkTNm7ceNsTPfroo1UamCivqZczrf1duXAtG0VR2Hf8Go/1alPb\nYQkhGqlKE8j06dNZs2YNERERTJ8+/ZYnUalUkkBqSLdwfy4m5aAoCheuZXM1NZemXtIvRAhR8ypN\nIFu2bMHPz8/8t6gbvNwcCG7uxqmEDAB+j7vGU33bSu90IUSNq7QRvUWLFmi1WgCOHj2Kq6srLVq0\nKPfj6OjI9u3bayxgAdFhfqjVpoRxLS2PS0k5tRyREKIxsuourNdee42EhIQKt508eZIFCxZUaVDi\n1po42xHextO8/PuxayiKUosRCSEao0qrsCZOnMiFCxcA06RRU6ZMMZdISktOTqZ58+bVF6GoUJd2\nvpy8mE6x3khaVgGnEzIIaSnzhQghak6lCeSFF17g+++/B+DSpUsEBwfj4WH5AaVWq3F1deVPf/pT\n9UYpynG0t6VTkDf7T14HYN8fSbQNcJNZC4UQNabSBBIVFUVUVBQAer2el19+uUpKGgaDgUWLFrF+\n/Xry8vLo3bs3b775Jl5eXhXuv3HjRj755BMuXbqEt7c3w4YN4/nnn0ej0dxzLPVdpxAfjp1Lo1Cn\nJztPx4kL6XRoW/HzKIQQVc2qr6v/+te/uHTpEu+//755XVxcHOPHj2f//v13dMElS5awfv165s2b\nx8qVK0lKSmLy5MkV7rtz505effVVhg0bxo8//sgrr7zCZ599xscff3xH12yo7Gw1dGnnY17ef/I6\nxXpDLUYkhGhMrEogP/30Ey+88AInTpwwr7O3t6ewsJBx48bx22+/WXUxnU5HTEwM06dPp2fPnoSF\nhbFw4UIOHTrEoUOHyu3/zTff8OCDD/Lss8/SokULHn74YcaOHcu6deusfHgNX3igF84OtgDkFxZz\n9ExqLUckhGgsrEogH330EcOHD+fzzz83rwsODmblypUMHTqURYsWWXWx+Ph48vLyiI6ONq8LCAig\nWbNmFc4p8pe//IWXXnrJMmC1muxsmdq1hI1GTXSYn3n50KlkCov0tRiREKKxsCqBXLp0iYceeqjC\nbQ899BBnz5616mJJSaYBAH19fS3W+/j4mLeVFhERQdu2bc3Lubm5rF69mt69e1t1vcYitKUH7i72\nAOiKDRyU4d6FEDXAqgTi4eHByZMnK9x25swZXF1drbpYQUEBarUaW1tbi/VarZaioqLbHjtp0iSK\niop45ZVXrLpeY6FWq+gefrMUEncmhdx83S2OEEKIe2dVAhk0aBBLlizhu+++IyPDNIRGZmYm69ev\nZ/HixTz++ONWXcze3h6j0Yheb1nFotPpcHCofFTZ9PR0xo0bx4kTJ/jss89o1qyZVddrTNo0a4Kv\nhyMABqNC7InrtRyREKKhs2o49xdffJGzZ8/y17/+lTfffBO1Wo3RaERRFPr168eUKVOsupi/vz8A\nKSkp5r/B1BmxbLVWicTERJ5//nny8vJYuXIloaGhVl2rsVGpVHQP9+e/u84BcPJiOpHB3ri72tdy\nZEKIhsqqBKLValm2bBknT57k4MGDZGZm4uLiQlRU1B1NJhUaGoqTkxOxsbEMHjwYMCWIK1eu0LVr\n13L7p6WlMWbMGDQaDatXr5Ye77fR3NeF5r4uXL5uGq137x9JPHJfq9oOSwjRQFk9oRRAu3btaNeu\nXbn1BQUFt6yCKqHVahk5ciTz58/H3d0dT09P5s6dS3R0NJ06dUKn05GVlUWTJk3QarXMnTuXjIwM\nVqxYgb29PSkpKYDp23ZlHQ8bu/vC/bl83TS44rnETK6n55urtoQQoipZlUCKi4tZtWoV+/fvp7i4\n2Dxwn9FopKCggJMnT3L48GGrLjh16lT0ej0zZsxAr9ebe6IDHD58mDFjxhATE0PHjh3ZunUrRqOR\nYcOGWZxDo9FY9EkRN/l4ONI2wI2zN+ZP33v8GoP7BNZyVEKIhsiqBPL+++/z5ZdfEhgYSEZGBvb2\n9ri5uXHmzBkMBgOTJk2y/oI2NsyaNYtZs2aV29atWzdOnTplXq7szi9xa93C/Th/JQujonD5eg6X\nr+fQ3NeltsMSQjQwVvdEf+6559iwYQOjR48mIiKCdevWsXnzZvz9/VGrZQC/usTdxZ52rW8OfCnD\nvQshqoNVn/ypqak88MADgKkHelxcHABNmzZlwoQJbNiwodoCFHenaztfbG6MzJuckc+5K1m1HJEQ\noqGxKoE4OztTXFwMQKtWrbh27Rp5eXkAtG7dmqtXr1ZfhOKuODtqLUbm3Xv8GkajlEKEEFXHqgQS\nFRXF119/jU6no2XLltjb2/PLL78AcPz4cZycnKo1SHF3okJ8sLM1DXufmVPEyYvptRyREKIhsSqB\nTJo0iX379jF+/HhsbGwYPnw4c+bMYfjw4bz//vs8+OCD1R2nuAv2djZEhpQa7v1EEnqDsRYjEkI0\nJFbdhRUWFsamTZvMd0i99tprODk5cfjwYcaPH89f/vKXag1S3L2OQV7EnU0lv7CY3IJi4s6m0rlU\nUhFCiLtlVQJ59913GTx4MPfffz9g6shXdph1UTfZ2mjo2s6XnYcTATgYf532rT2w195RH1IhhCjH\nqiqsb7/9lszMzOqORVST9q09cHXSAlCkM3DkdEotRySEaAisSiARERFW9zQXdY9Go6Z7+M3BK4+e\nTiG3oLgWIxJCNARW1WN06NCBjz/+mM2bN9OuXTscHS3HVlKpVLz11lvVEqCoGkHN3Th0KpnUzAKK\nDUZ2HrzMoz1bo1Kpajs0IUQ9ZVUC2bBhA56enmRnZ7Nv375y2yWB1H0qlYpeHZvyw07TcO8XrmUT\nfzHDose6EELciUoTyKZNm+jRowdNmjRh586dNRmTqCYBPi5EtDXdlQXw69ErNPNxNrePCCHEnai0\nDeT11183z3X+0EMPER8fX2NBiepzX4emuLnYAab503/enyDjZAkh7kqlJRCtVmse4+rSpUscO3aM\n/Pz8Sk/UuXPnqo9OVDlbGzUDurZg7fazKIrClZRc4s6k0jHYu7ZDE0LUM5UmkKFDh/L555+zevVq\nVCqVec6OshRFQaVSydDr9YifpxNRoT4cOGmaN33Psas093PBQ6a/FULcgUoTyIwZM3jyySfJyMhg\nzJgxvPnmm7Rt27YmYxPVqGs7Xy5dyyYlswCDUWFbbAJD+gWhUctdWUII69zyLqygoCAAJk6cSP/+\n/fH19a2RoET102jUDIhuwZptpzEYFZIz8jkYf53o9n61HZoQop6wqiPh1KlTJXk0QJ5NHOhWqoPh\ngRPXSU6vvJ1LCCFKk6kEG7lOQd409TINx29UFLbtT5ARe4UQVpEE0sip1Sr6d22BrY3ppZCeXcje\n49dqOSohRH0gCUTQxNmOXh2bmZePnE7hSkpuLUYkhKgPJIEIwDRib0s/V/Pyz/sT0BUbajEiIURd\nV+ldWH/729+sPomMhVX/qVQq+nZpzuot8RTpDGTn6dh99Ar9urSo7dCEEHVUpQlk+/btVp9EEkjD\n4OxgywOdA9i89xIAJy6k07ppE1o3bVLLkQkh6qJKE4gMoNg4BTV35/yVLM5cNk0g9suBy4x40BFH\ne9tajkwIUdfccxuIwWCocIh3UX/dHxmA042EUVCkZ+fhKzLgohCiHKvmA0lKSuLvf/87+/fvp7i4\n2PxhYjQa0ev1ADIWVgNib2dDvy7N+d/u8wCcS8zkdIIrIS1l7hAhxE1WlUDeffdd9u7dy+OPP07r\n1q1p3749I0aMoFWrVqhUKpYsWVLdcYoa1tLflbA2nublXYevkJuvq8WIhBB1jVUJZN++fUydOpW3\n3nqLp556CkdHR2bNmsX69euJiopix44d1RymqA29OjY1TzZVVGzg5wOXpSpLCGFmVQLJy8ujXbt2\nALRp04YTJ04AYGNjw6hRo9izZ0/1RShqja2NhgFdW5jnTb98PYfj59JqOSohRF1hVQLx9vYmLc30\nwdGyZUsyMzNJSUkBwN3d3bxNNDxNvZ3pVGqyqd/irpKZU1SLEQkh6gqrEkjv3r1ZsmQJx44dIyAg\nAF9fX2JiYtDpdPz4448yUm8D1y3MD88bk03pDUa27U/AaJSqLCEaO6sSyJQpU7C1tWXBggWAaXj3\n5cuX06lTJ9atW8dzzz1n9QUNBgPvv/8+vXr1IjIykpdffpnU1NTbHpeQkEBkZCRJSUlWX0tUDRuN\nmgHRLVHfqMpKSstj+0FpDxGisbPqNl5PT0/Wr19v/vB+8skn8ff358iRI0RERHDfffdZfcElS5aw\nfv165s2bh5ubG3PnzmXy5MmsXr260mMuXLjACy+8cMs52UX18nZ3IDrMzzxS78mL6QD069Lc3EYi\nhGhcrCqBfPzxx6SkpODvf3PyoW7dujFhwgRatGjBe++9Z9XFdDodMTExTJ8+nZ49exIWFsbChQs5\ndOgQhw4dqvCYFStWMGTIEFxdXSvcLmpOVKgP7Vrd7Aty8mI6v8idWUI0WlYlkA8//LDSqqO4uDi+\n/vprqy4WHx9PXl4e0dHR5nUBAQE0a9aMAwcOVHjMzz//zNtvv83MmTOtuoaoPiqVin5dmtO+dfkk\nIm0iQjQ+lVZhjRo1iqNHjwKgKAojR46scD+DwUBYWJhVFytJQmUb3X18fCpNUDExMQAyXEodoVKp\n6BvVHDANtgimJKIopuostVqqs4RoLCpNIHPnzuWnn35CURSWLVvGk08+iZ+fn8U+arUaV1dXBg4c\naNXFCgoKUKvV2NpaDsyn1WopKpJbQ+uLipJI/KWbbSKSRIRoHCpNIG3btuWll14CTKWMESNG3PPt\nuvb29ubxs2xsbl5ap9Ph4OBwT+cWNetmElFx4oKpH5ApiSj069JCkogQjYBVd2FNnToVgN9++43Y\n2FhycnJwd3enS5cud3QHVkkjfNkG+eTkZOlLUg+ZkkgAQKkkkgEgSUSIRsCqBKLT6XjxxRf59ddf\nsbGxwc3NjYyMDIxGI/fddx8ff/wxWq32tucJDQ3FycmJ2NhYBg8eDEBiYiJXrlyha9eu9/ZIRK0o\nSSIqFfxxXpKIEI2J1XdhHThwgAULFhAXF8fu3buJi4tj/vz5HDlyhGXLlll1Ma1Wy8iRI5k/fz67\ndu3ijz/+YPr06URHR9OpUyd0Oh0pKSnodDLqa32iUql4oHOAxei98Zcy+OWA9FgXoiGzKoFs2LCB\nKVOm8Pjjj6NWmw7RaDQMGjSIl19+mf/9739WX3Dq1KkMGjSIGTNmMGbMGJo2bcqHH34IwOHDh+nV\nqxeHDx++i4cialNlSeRnGfZEiAbLqiqszMxMgoODK9wWHBxsHljRqgva2DBr1ixmzZpVblu3bt04\ndepUhcfdapuoG0qSiAo4fqM661SCqTqrf1epzhKiobGqBNK6dWt2795d4bZff/2VgICAKg1K1F8q\nlYr7OwcQXqokcipBSiJCNERWlUDGjBnDG2+8gdFo5NFHH8Xb25uUlBQ2bNjAypUrKyxNiMarJImA\nZUlEAQZISUSIBsOqBPKnP/2Jixcv8vnnn7NixQrzeo1Gw/PPP8/o0aOrLUBRP5mTiErF8XOm0ZZP\n36jOkiQiRMNgVQIBmDZtGs899xxHjx4lKysLV1dXOnXqhIeHx+0PFo2SSqXi/shmABZJRFFgQHQL\nNJJEhKjXKk0gY8aM4a233iIwMNC8zsPDg759+9ZIYKJhqCiJnLmcQUZOIX2jmuPr4Vib4Qkh7kGl\njeixsbHk5eXVZCyigSpJIuGBXuZ1qZkFfP/LGX49cgVdsaEWoxNC3C2r7sIS4l6VJJGeEU2x0Zhe\ndoqicPRMCl9vjufC1axajlAIcackgYgao1KpiAzxYcSDIbTwdTGvzy0oZsNvF9i89yL5hcW1GKEQ\n4k7cshH9nXfewdnZ+bYnUalUfP7551UWlGjYmjjbMah3G04nZLD76FUKivQAnLmcScL1HHp0aEr7\n1h4yVa4QddwtE4her6e4WL4RiqqnUqkIaelBSz9Xdh+9ap5PpEhnYPvBy5y6lEHfqADcXe1rOVIh\nRGVumUD+9re/ERERUVOxiEbI3s6GAdEtCGnpzo5DiWTlmiYWu5qayzdbT9GlnS+dQ3zQaKS2VYi6\nRt6Vok5o7uvCiAdDiAr1QX2j6spgVNj3RxLfbjvNtVS5I1CIukYSiKgzbDRq7uvQlKcHBFv0D0nP\nLmTt9jPsOJRIkdzyK0SdUWkC+dOf/oS7u3tNxiIEAF5uDgzpG0TvTs2wtbn5Ej1+LpWvf4rnbGIm\niiIDMwpR2yptA3nvvfdqMg4hLKjVKjoGedOmWRN2Hkrk4rVsAPIKi/np94t4uNoT1tqTkJbu2NtZ\nPSKPEKIKyTtP1Gkujloe69mac4lZ7DpyxdxPJD27kF+PXuH349doG9CE9m088fd0klt/hahBkkBE\nnadSqWjb3I0AX2di/0ji5MV0ivVGAPQGI/GXMoi/lCGlEiFqmLzLRL1hr7WhT2QA3cP9OXM5k+Pn\nU0nJKDBvLymV7Dl2lbYBboQFSqlEiOokCUTUO1pbDWFtPAlr40lyej5/XEjjdEKGuVRiMCqcSsjg\nVIKUSoSoTvKOEvWaj4cjPh6O9IxoypnLmfxxPo3kjHzz9nKlkjae+HtJqUSIqiAJRDQId1IqcXex\np1VTVwJ8nGnq5YStjaaWoxeifpIEIhqc25VKMnIKyThVyOFTyajVKvw8HAnwcSHAxxlfD0cZNkUI\nK0kCEQ3W7UolAEajwtXUPK6m5hF7Amw1avy9ncwJxauJg8zfLkQlJIGIRqGkVNKrY1MSk3PNP2lZ\nBRb7FRuMJCTlkJCUA4CdVkOAt7Mpofg64+ZsJ+0nQtwgCUQ0KrY2Glo3bULrpk0AyC8s5kqKKZlc\nvp5Ddp7OYv8inYFzV7I4d8U0Y6Kzgy3NvJ3xcXfEo4k9nk3scbS3rfHHIURdIAlENGqO9rYENXcn\nqLlp3LfsPB2JyTnmEkrZGRJzC4rNjfGlz+HVxB7PJg54utnj6eqAh6udtKWIBk8SiBCluDppad/a\nk/atPVEUhfTsQnMyuZqSW+FowPmFxSQUFpNwPce8Tq1S4eZiZ0oqN0oqXm4OODvYShWYaDAkgQhR\nCZVKdSMBONAxyBujUSEls4Ck1DzSsgtIyyokLasQvcFY7ljjjeSTnl3Imcs319vZavBwtaeJsx2u\nzlpcnbS4Opp+O9rbSoO9qFckgQhhJbVaha+Ho8VcJUajQnaejtSsAtKzCknLKiA1q9A8s2JZRcUG\nrqXlcS2t/ARZarUKV0ctLk6mhOJyI7GU/DjY2UjpRdQpkkCEuAdqtamqys3FDgJuri/WG8wllLQs\nU8DI3l4AABYqSURBVGklNauAIl3lE2IZjQqZuUVkVpJ8bDVqXG4kFmdHWxztbHB0MP12crDF0d4W\nR3sbbKTtRdQQSSBCVANbGw1+nk74eTqZ1ymKQl5BMenZhWTn6cjO05GTrzP/XVCkv+U5iw1Gc7XY\nrdhpNTjdSCaOpX47lVp2sLPBTmuDRqrMxD2QBCJEDVGpVDg7anF21Fa4vVhvqDCxlPzorJzOt0hn\noEhnID379vtqbTXYazXYa22wt7vxW6vB3s7m5nrzdtPftjZqqUoTgCQQIeoMWxuNudG+LEVRKCo2\nJZicPB35hXryCovJLywmv1B/48f0t/EOpvvVFRvQ3TivtTRqFVpbDXa2GrQ3fuxs1aX+1qAtt2xa\nV/K3Rq2SJNQA1HgCMRgMLFq0iPXr15OXl0fv3r1588038fLyqnD/Y8eO8Y9//IOTJ0/i6+vLpEmT\nePLJJ2s4aiFql0qlulEasMHH3bHS/RRFoaBIb04wBeZEY0oweQWm34U6A0XFhruaW95gNF3jdlVu\nt6JWqbC1VWOrMSUaWxu16UejxrbUstZGg42NGm3Jdpub22w0N35s1NhoVNhq1KglMdWoGk8gS5Ys\nYf369cybNw83Nzfmzp3L5MmTWb16dbl909PTGT9+PI8//jj/+Mc/2LNnD2+88QZeXl706tWrpkMX\nos5TqVQ32jls8aJ8SaY0o1FBV2ygQKenSGegoMj0u1Cnp6DIQJFOT6HOcONHT2GRabmi25bvlFFR\nTFVtGKCg+PYHWEmtUt1IKDeTik2ZZGOrUWGjUaO5sU6jUWGjVmNjo0KjNh1n3qZW3dynkuXGnLBq\nNIHodDpiYmKYM2cOPXv2BGDhwoX079+fQ4cO0blzZ4v9v/vuO5ydnXnjjTdQq9UEBgZy4sQJ/vOf\n/0gCEeIeqdUqU7vGHU60pTcYKdKZqr6KblSB6YqNpf4utawvvZ/R/LfReOclH2sYFcUcQ01Rq1Ro\nNDeTj1p9M7mo1aWSklqFWqPGRm3aX60uvU/Jjxq1mhu/b+ynurFNY7m/WmX627ysvrmvutRydfYt\nqtEEEh8fT15eHtHR0eZ1AQEBNGvWjAMHDpRLIAcOHKBr166o1TdvS4yOjmbu3LkoitKoM78QtcVG\no8bGQY2Tw92PAWYwGCnWG9HpjRTrDRTrjaV+DOZter0RXentxQbTeoNpW7HBiN6gmJfvpP2nqhgV\nBaNeoZh7L5lVB5VKhVqFOZmp1SoctBq6hfvTplmTezp3jSaQpKQkAHx9fS3W+/j4mLeV3b99+/bl\n9i0oKCAjIwMPD4/qC1YIUW00N6qQ7O2q9rwG481kojeYforNfyumpKM3ojcaMZRKPgajaZvBaFpX\nsq30crHBiNGoUKw37W+4cVxdpygKBsX03JQkufzCYvYdv1a/EkhBQQFqtRpbW8tvLlqtlqKi8p2n\nCgsL0Wq15fYFU3WYEEKUZqoGMt35VRMURcFoVMyJy2hUzInHYFRuLJf/22AoOc6I0Yh5/5L9TL+N\npv0U5eYxium3wWgqbRkNCoYbMRiNCkaFG+e8uVzRjRJqlYqgFu73/PhrNIHY29tjNBrR6/XY2Ny8\ntE6nw8GhfIOfvb19uURRslzR/kIIUZNUJe0fGlOfmrrIlEhKJyYFjcZ0V9+9qtEE4u/vD0BKSor5\nb4Dk5ORy1VoAfn5+pKSkWKxLTk7G0dERFxeX6g1WCPH/27v/aKjy/w/gTzNFVie/qqW2n8ogZgyh\n1LYRTvujZNOvRSGl2KitE2kr/U5RflVElOpYZ2dld61Oy6ZtrVJUTs4JaQ9id1uxKZGf9/OHr/k2\nUbnDjB/7epwzf8z1vnNfr8t5v2be19wXGQQ4HAVwoADIoL7JtYDo6elBRUUFN2/ehL29PQCgoqIC\nlZWVMDMz6zTe1NQUycnJEhfMc3JyYGJiInFh/XWtre3/gdHVdRVCCCFd65gzO+bQd5FrAVFUVMQX\nX3yBw4cPQ11dHZqamti9ezfMzc1hbGyMpqYm1NbWQlVVFYqKinB0dERsbCx27dqFVatWITs7G6mp\nqYiJiXnrcTo+tTg5OckjLUIIGVSqqqowYcKEd45TYKT5KmoPtLS0IDg4GBcvXkRLS4v4m+gaGhrI\nycnBypUrkZCQAAsLCwDA3bt3sW/fPhQVFWHMmDHw8fHBp59++tZjvHz5EgUFBRg1ahS43P65LkkI\nIf1Na2srqqqqYGhoiGHDhr1zvNwLCCGEkMGBGgcQQgiRChUQQgghUqECQgghRCpUQAghhEiFCggh\nhBCpDLoC0traipCQEMyePRtCoRA+Pj548uTJG8ffu3cPy5cvh0AggJ2dHVJSUuQYbe9jm39aWhrs\n7e1hbGwMW1tbnDp1qttfIuqP2Ob/Kk9PT7i4uMg4Qtljew7+/vtv+Pj4QCgUYubMmQgMDERDQ4Mc\nI+5dbPO/fv06HB0dYWxsDBsbG8TExEjVaKu/2rlzJ7Zv3/7WMVLPg8wgc+zYMWbWrFlMVlYWU1BQ\nwCxZsoRZvnx5l2Orq6sZc3NzZs+ePUxJSQmTkJDAGBgYML/99puco+49bPK/evUqo6+vz5w7d44p\nKytjLl26xEyfPp2JjIyUc9S9h03+r0pMTGR0dXUZZ2dnOUQpW2zOQWNjIzN//nzGxcWFuX//PnP9\n+nXmo48+Ynbv3i3nqHsPm/xLS0sZPp/PREREMOXl5cylS5cYgUDAnD9/Xs5R9762tjYmNDSU0dXV\nZQICAt44rifz4KAqII2NjYxQKGS+++478bZHjx4xurq6TF5eXqfxUVFRjLW1NdPa2ire5u/vz7i5\nuckl3t7GNv9169Yxvr6+EtsiIyMZa2trmccqC2zz71BaWsqYm5szy5YtG/AFhO05EIlEjKmpKfP0\n6VOJbYsXL5ZLvL2Nbf7nzp1jzM3NJbb5+Pgwnp6eMo9VlsrLyxlnZ2fGwsKCmTt37lsLSE/mwUG1\nhPWuhlWve1PDqtu3bw/Ij7Bs81+/fj2+/PJLiW0cDgfPnj2TeayywDZ/oH25w8/PDx4eHtDR0ZFX\nqDLD9hxkZWXB0tISqqr/3xdi8eLFEIlEcom3t7HNX0NDA0+fPkVqaira2tpQXFyM3NxcGBoayjPs\nXnf79m1oa2vjxx9/xAcffPDWsT2ZBwdVAZGmYVVXYzsaVg00bPPn8/mYMmWK+HldXR0SExPx4Ycf\nyjZQGWGbPwBER0cDAFavXi3b4OSE7TkoLS3F2LFjERoaCmtra8ybNw9BQUFd9ucZCNjmb2dnB0dH\nR2zZsgWGhoZYsGABzMzM4OXlJZd4ZcXe3h6HDx/GqFGj3jm2J/PgoCog//WGVWzzf31fLy8vNDY2\nYvPmzbIMU2bY5l9QUID4+HgEBQW99e7OAwnbc1BXVweRSIRHjx4hLCwM27ZtQ1paGnbs2CGvkHsV\n2/yfPXuGyspKeHh4QCQSISgoCNnZ2YiMjJRXyH2uJ/OgXO/GK2v/9YZVbPPvUFNTAy8vL5SUlCAu\nLg5jx46VR7i9jk3+jY2N2Lp1KzZu3Nitu44OFGz/BoYMGQJVVVUcPnwYXC4XRkZGaGlpga+vL7Zt\n2wZ19Z53rZMntvkHBweDy+Viy5YtAAADAwO0tLQgMDAQLi4uAy5/afRkHhwcb7v+z6sNq171X2lY\nxTZ/oL0fy4oVK1BRUYHz58+Dz+fLPE5ZYZN/fn4+Hj58iODgYAiFQgiFQqSkpCA3NxdCoRB//vmn\n3OLuTWz/Bt5//33o6OhI3LW6Y1mzsrJShpHKBtv88/PzO13vEAgEaG5uxl9//SW7QPuRnsyDg6qA\nvNqwqsO7Glbl5uZKXCjqTsOq/opt/tXV1Vi5ciXa2tqQmJgIPT09eYbb69jkz+fz8fPPPyMlJUX8\nsLGxgaGhIVJSUjB69Gh5h98r2P4NTJ8+Hffv30dzc7N4W3FxMbhc7oD8JMo2fy0tLRQVFUlse/Dg\nATgcDsaPHy/zePuDnsyD3MDAwEAZxyc3XC4Xz58/x+nTpzF16lTU1dUhICAAEyZMgJeXF5qamlBT\nU4OhQ4eCy+Vi4sSJiImJQWVlJcaPH4+ffvoJ8fHxCAwMxLhx4/o6HdbY5u/v74+ioiKcPHkS6urq\nqK+vR319PRoaGvDee+/1dTqssclfSUkJampqEo+srCy8ePECbm5uA/INBMD+b2Dy5MlISEhAUVER\npkyZgsLCQuzduxc2Njb47LPP+jod1tjmr6amhsjISHA4HGhpaeH27dvYu3cvFi1aBFtb275Op1dc\nvHgRqqqqmDdvHgD07jzY43847meam5uZgwcPMubm5oyJiQnj6+vLVFdXMwzDMDdu3GB0dXWZGzdu\niMffuXOHWbx4MWNoaMjY2dkxqampfRV6r+hu/g0NDYyenh6jq6vb6aGvr9/HWUiP7e//VQEBAQP+\neyAMw/4cPHjwgHF3d2f4fD4zY8YM5sCBA0xjY2Nfhd9jbPNPT09nHBwcGGNjY8bGxoaJiIhgmpqa\n+ir8Xufs7CzxPZDenAepoRQhhBCpDMzP6YQQQvocFRBCCCFSoQJCCCFEKlRACCGESIUKCCGEEKlQ\nASGDGv2TISGyQwWEyIS/vz94PN4bH9nZ2TKP4c6dO/D09BQ/r6ioAI/Hw/fffy/zYycnJ4PH473x\nLsADhYuLC1xdXeVyLGtr63d2ziP9y6C6mSLpX7S0tBAWFtblz169jbysiEQilJSUiJ+PHj0aSUlJ\ncrlFxdy5c5GUlAQNDQ2ZH0uWdu3aBQUFhb4Og/RTVECIzCgqKsLY2LivwxCTZzwaGhoDvngA8in0\nZOCiJSzSp6ytrXHo0CG4uLiAz+dj9+7dAID79+/D29sbM2bMwLRp0zBnzhzs379foqdDU1OTuBGS\nQCDAggULkJaWBqB9CU0kEqGyshI8Hg/JycldLmE9fPgQXl5emDlzJoRCITw8PFBYWCj+eU5ODng8\nHm7cuAFXV1cIBALMmjULwcHBaG1tfWNery9h+fv7w9PTExcuXICVlRUEAgFWr16NqqoqiEQi2NjY\nQCgUwtXVFRUVFRLn58SJE9i7dy/Mzc1hamqKPXv2oKGhAUFBQbCwsICFhQW2b98uPjcdMb/ege/1\n5Sgej4dvvvkG27Ztg5mZGYRCIXx9fVFdXd3lPh05dfXw9/cX73Pr1i04OTlBIBDAwsICX3/9dacu\nl4WFhXBzc4NQKISVlRV++OGHN55L0n/RJxAiUy0tLZ22cblciWWRc+fOwcPDA2vXroWqqioeP34M\nJycnmJiYICgoCEOHDsW1a9cQHx+P0aNHY82aNQCALVu24Nq1a/Dy8oKRkRHS09Px1VdfQVlZGV5e\nXqitrcW9e/cQGRmJ8ePHo76+XiKOoqIiLF++HFOmTBEXrujoaKxYsQLffvutxLvvzZs3w8nJCevW\nrUNmZiZiYmIwYcIELFmypNvn4tatW6iqqsLOnTtRU1Mj7jmhpKQEf39/vHz5Ejt27MC+ffsQFRUl\n3i82NhZWVlYICwtDVlYWYmNjkZ2dDT09PYSEhODu3buIiIiAjo4O3N3dux0P0N4Pw9bWFqGhoSgr\nK8OhQ4egqKiII0eOdBrbsSz3qvj4eGRkZMDBwUGco5ubGywtLREWFobq6mocO3YMRUVFSExMxJAh\nQ/D48WM4Oztj4sSJOHLkCOrq6hAcHCxRuMjAQAWEyEx5eTmmTZvWaXtgYCBWrFghfj5u3Dhs2rRJ\n/PzatWuYNm0awsLCoKKiAgCwtLTE77//jlu3bmHNmjUoLi7G5cuXsXPnTjg5OQEAZs6cifLycuTk\n5MDKygoaGhoSy1avF5Djx49DWVkZZ8+eFd99eNasWbC1tUV4eDjCw8PFY5ctWyZuczpjxgxkZGTg\n6tWrrArIixcvEBYWJr7DaXp6OjIzM5GRkSHedufOHaSmpkrsp66ujiNHjoDD4cDCwgJJSUlobm5G\ncHAwhgwZgtmzZ+Py5cu4e/dut2PpoKenh4MHD4pzv3fvHjIyMroc+/qyXHp6Oi5fvoyAgABYWFgA\nAEJCQqCjo4OoqCjxHY0NDAzg4OCAtLQ0LFy4EGfOnEFraytiYmLEDZsmTZqEpUuXso6f9C0qIERm\ntLS0umwN+nqfCX19fYnnc+bMwZw5c9Dc3IySkhKUlZWhuLgYNTU1GDlyJAAgLy8PADrdcjs2Nrbb\n8eXm5sLa2lri1vUqKiqwtrbuNImamJh0yq2hoaHbxwIATU1Nidtja2pqQl1dXWKbmpoanj9/LrGf\nkZGReDLmcDhQV1eHvr6+RMc9NTW1TstE3SFtXoWFhdi6dSsWLVqElStXAmhvJ5ufn4+1a9eira0N\nbW1tAICpU6dizJgxyM7OxsKFC5GXlwcTExOJbn8CgQBjxoxhHT/pW1RAiMwoKirCyMjoneNe7z3S\n1taGo0eP4sKFC6ivr4e2tjb4fD6UlJTE3+t4+vQpgPZJWFq1tbXigvQqTU1N1NXVSWwbNmyYxHMO\nhyOeILur49PUq7rTd0Xa/bpDmryqq6uxfv16TJ48Wbz0B7T3F29ra0NUVJTEElyHf/75B0D7ee+q\njfCoUaOkSYH0ISogpN85deoUzpw5gz179sDW1lbcVtPR0VE8pmNbTU2NxMRTXFyMhoYGCASCdx5n\nxIgRePLkSaftVVVVUFNT62kafabj+tLrheDFixcYMWJEj167qakJ3t7eaGxsxPHjx6GkpCT+mYqK\nChQUFODu7o6PP/64074dhVBdXb3L6x0dbwrIwEH/hUX6nby8PPB4PHz++efiQvH48WMUFxeLJ0VT\nU1MAQGZmpsS++/fvx9GjRwFAos93V8zMzJCZmSlxbaS+vh6ZmZni1x+Ihg8fDgASPb1ra2vx8OHD\nHr/2rl27UFBQgPDwcGhpaXU6roGBAUpLS2FkZCR+TJo0CaGhocjPzwfQfg0pLy9Pog93SUkJHj16\n1OP4iHzRJxDS7/D5fJw4cQIxMTEQCAQoKytDdHQ0mpqaxOvz+vr6sLOzw8GDB1FfXw8ej4eMjAzc\nvHkTp0+fBtD+KeXJkyf49ddfO11nAQBvb28sXboUrq6u8PDwANB+DaW+vl58wXwg4vF40NbWRkRE\nhPhdf3R0NJSVlXv0umfOnEFycjLc3d2hrKwscdFeUVERBgYG8PX1xbp16+Dv749PPvkETU1NiImJ\nQXFxMfz8/AAAq1atgkgkgru7OzZs2ICWlhYcO3YMQ4cO7VF8RP6ogJB+x9PTE//++y/Onj2L58+f\nQ1tbG/b29lBQUMCpU6dQV1eH4cOHIyQkBGFhYYiLi0NtbS10dHRw8uRJWFpaAgAcHBxw5coVeHt7\nY+PGjZg/f77EcXg8Hi5cuICjR4/Cz88PHA4H06dPR1JSEng8Xl+k3iu4XC7Cw8Nx4MABbNq0CSNH\njsSqVavwxx9/oLy8XOrX/eWXXwAAcXFxiIuLk/jZ2LFjceXKFXz00UeIjY1FZGQkNmzYACUlJRgZ\nGSEhIQG6uroA2pewEhMTsX//fvj5+UFFRQUeHh7i7/CQgYNa2hJCCJEKXQMhhBAiFSoghBBCpEIF\nhBBCiFSogBBCCJEKFRBCCCFSoQJCCCFEKlRACCGESIUKCCGEEKn8DxDxPWMnMJ36AAAAAElFTkSu\nQmCC\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plot(infected_sweep)\n", + "\n", + "decorate(xlabel='Fraction immunized',\n", + " ylabel='Total fraction infected',\n", + " title='Fraction infected vs. immunization rate',\n", + " legend=False)\n", + "\n", + "savefig('chap05-fig03.pdf')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "If 40% of the population is immunized, less than 4% of the population gets sick." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Logistic function" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "To model the effect of a hand-washing campaign, I'll use a [generalized logistic function](https://en.wikipedia.org/wiki/Generalised_logistic_function), which is a convenient function for modeling curves that have a generally sigmoid shape. The parameters of the GLF correspond to various features of the curve in a way that makes it easy to find a function that has the shape you want, based on data or background information about the scenario." + ] + }, + { + "cell_type": "code", + "execution_count": 37, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def logistic(x, A=0, B=1, C=1, M=0, K=1, Q=1, nu=1):\n", + " \"\"\"Computes the generalize logistic function.\n", + " \n", + " A: controls the lower bound\n", + " B: controls the steepness of the transition \n", + " C: not all that useful, AFAIK\n", + " M: controls the location of the transition\n", + " K: controls the upper bound\n", + " Q: shift the transition left or right\n", + " nu: affects the symmetry of the transition\n", + " \n", + " returns: float or array\n", + " \"\"\"\n", + " exponent = -B * (x - M)\n", + " denom = C + Q * exp(exponent)\n", + " return A + (K-A) / denom ** (1/nu)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The following array represents the range of possible spending." + ] + }, + { + "cell_type": "code", + "execution_count": 38, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([ 0., 60., 120., 180., 240., 300., 360., 420.,\n", + " 480., 540., 600., 660., 720., 780., 840., 900.,\n", + " 960., 1020., 1080., 1140., 1200.])" + ] + }, + "execution_count": 38, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "spending = linspace(0, 1200, 21)\n", + "spending" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "`compute_factor` computes the reduction in `beta` for a given level of campaign spending.\n", + "\n", + "`M` is chosen so the transition happens around \\$500.\n", + "\n", + "`K` is the maximum reduction in `beta`, 20%.\n", + "\n", + "`B` is chosen by trial and error to yield a curve that seems feasible." + ] + }, + { + "cell_type": "code", + "execution_count": 39, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def compute_factor(spending):\n", + " \"\"\"Reduction factor as a function of spending.\n", + " \n", + " spending: dollars from 0 to 1200\n", + " \n", + " returns: fractional reduction in beta\n", + " \"\"\"\n", + " return logistic(spending, M=500, K=0.2, B=0.01)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here's what it looks like." + ] + }, + { + "cell_type": "code", + "execution_count": 40, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Saving figure to file chap05-fig04.pdf\n" + ] + }, + { + "data": { + "image/png": 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Atm7divj4eMTExKB9+/bc1UdsbCzy8vJw69YtjBo1qs7x+/v748yZM9xPdHQ0VqxYge3b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\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "percent_reduction = compute_factor(spending) * 100\n", + "\n", + "plot(spending, percent_reduction)\n", + "\n", + "decorate(xlabel='Hand-washing campaign spending (USD)',\n", + " ylabel='Percent reduction in infection rate',\n", + " title='Effect of hand washing on infection rate',\n", + " legend=False)\n", + "\n", + "savefig('chap05-fig04.pdf')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Exercise:** Modify the parameters `M`, `K`, and `B`, and see what effect they have on the shape of the curve. Read about the [generalized logistic function on Wikipedia](https://en.wikipedia.org/wiki/Generalised_logistic_function). Modify the other parameters and see what effect they have." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Hand washing" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now we can model the effect of a hand-washing campaign by modifying `beta`" + ] + }, + { + "cell_type": "code", + "execution_count": 41, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def add_hand_washing(system, spending):\n", + " \"\"\"Modifies system to model the effect of hand washing.\n", + " \n", + " system: System object\n", + " spending: campaign spending in USD\n", + " \"\"\"\n", + " factor = compute_factor(spending)\n", + " system.beta *= (1 - factor)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's start with the same values of `beta` and `gamma` we've been using." + ] + }, + { + "cell_type": "code", + "execution_count": 42, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "(0.3333333333333333, 0.25)" + ] + }, + "execution_count": 42, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "tc = 3 # time between contacts in days \n", + "tr = 4 # recovery time in days\n", + "\n", + "beta = 1 / tc # contact rate in per day\n", + "gamma = 1 / tr # recovery rate in per day\n", + "\n", + "beta, gamma" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now we can sweep different levels of campaign spending." + ] + }, + { + "cell_type": "code", + "execution_count": 43, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "0.0 0.332887143272 0.466770231236\n", + "100.0 0.332134252669 0.464141650401\n", + "200.0 0.330171608455 0.457217006313\n", + "300.0 0.325386471865 0.439887202912\n", + "400.0 0.315403905242 0.401630646271\n", + "500.0 0.3 0.33703425949\n", + "600.0 0.284596094758 0.267317030568\n", + "700.0 0.274613528135 0.22184699046\n", + "800.0 0.269828391545 0.200791598416\n", + "900.0 0.267865747331 0.192392183393\n", + "1000.0 0.267112856728 0.189213207818\n", + "1100.0 0.26683150821 0.18803175228\n", + "1200.0 0.266727403413 0.187595503995\n" + ] + } + ], + "source": [ + "spending_array = linspace(0, 1200, 13)\n", + "\n", + "for spending in spending_array:\n", + " system = make_system(beta, gamma)\n", + " add_hand_washing(system, spending)\n", + " run_simulation(system, update1)\n", + " print(spending, system.beta, calc_total_infected(system))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here's a function that sweeps a range of spending and stores the results in a `Sweep` object." + ] + }, + { + "cell_type": "code", + "execution_count": 44, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def sweep_hand_washing(spending_array):\n", + " \"\"\"Run simulations with a range of spending.\n", + " \n", + " spending_array: array of dollars from 0 to 1200\n", + " \n", + " returns: Sweep object\n", + " \"\"\"\n", + " sweep = SweepSeries()\n", + " for spending in spending_array:\n", + " system = make_system(beta, gamma)\n", + " add_hand_washing(system, spending)\n", + " run_simulation(system, update1)\n", + " sweep[spending] = calc_total_infected(system)\n", + " return sweep" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here's how we run it." + ] + }, + { + "cell_type": "code", + "execution_count": 45, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "spending_array = linspace(0, 1200, 20)\n", + "infected_sweep = sweep_hand_washing(spending_array)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "And here's what it looks like." + ] + }, + { + "cell_type": "code", + "execution_count": 46, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Saving figure to file chap05-fig05.pdf\n" + ] + }, + { + "data": { + "image/png": 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bt2/Hx8enssOpshKSb/P7wQSj0RDMzdREBHkQ6u+Omdx8KkS1UlafnTJMsfjL\nfD0c6P90IGEB7qj/vMSm1en53/HrrN5+1tAbTggh7iWJRzwSC3M1bUNq0aezPzVd7naJv5GRw887\nzrH76FXytUWnbRBCPLkk8YgyUdPFhj6d/GkbUgvzP+f7URSFI2dTWbX1jNGMqUKIJ5skHlFm1GoV\nYQHu9H86AF8PB0P5rWwN//ffi1y+fusBWwshnhSSeESZc7K3oke7enRpURtry4Ie+3pFYcsfl6Tm\nI4SQxCPKh0qlIrCOKy939TdMMqfTK2zec4lrN7IqOTohRGWSxCPKlb2tJT3bN8DepmBg2Hydnl92\nX5Ieb0I8wSTxiHLnaGdJVPv62FoXJB9Nvo6N/73AjYycSo5MCFEZShwy54MPPijVjkq7vniyuDhY\nE/VUPdbtvECuRkueRseGXRfo1aEBLo7WlR2eEKIClZh4fv/9d6PHaWlpaLVa3N3dqVmzJhkZGVy7\ndg0rKysaNGhQ7oGKqs/NyYYeT9VjQ8wF8vJ15ORp2bDrAi92aICTvQxxJMSTosTEExMTY/h78+bN\nfPzxx8ydO9doeurTp0/z1ltv0bNnz/KNUlQb7i62dG9Xjw27LpCv1ZOVk2+o+djbWlZ2eEKICmBS\nG8+cOXMYN26cUdKBgmkOxowZw1dffVUuwYnqydPNjhci6xluNL2VrWF9zAWyc2R6BSGeBCYlnvT0\n9CITrhWytrYmOzu7TIMS1Z93TXuebVMX9Z8DiWZk5bFh1wXDdAtCiOrLpMTTtGlTvvzyS7KyjO+/\nSE9PZ+HChUUmcRPCFHU8HXmmVV3DAKPpt3LZuKug84EQovoyaSK4iRMnMnDgQDp06EDz5s1xdXUl\nLS2N2NhY7OzsWLBgQXnHKaqpet5OdGlRm99ir6AoCqkZOfyy+xI92tXD0sKsssMTQpQDk2o8jRo1\n4pdffqFXr16kpqYSGxtLeno6gwYNYuPGjfj6+pZ3nKIa86/tQsfwu3N7JKVls2nPJfK1+kqMSghR\nXkye+trLy4tJkyaVZyziCRbk54ZOpxBzOBGAq6lZbPnfJZ5v44eZmdznLER1YvIZrSgKW7ZsYcqU\nKQwfPpz4+Hj+7//+j4sXL5ZnfOIJ0qRBDdqE1DI8vpJ0m1/3xaPTP3GT5ApRrZmUeLKyshgwYABj\nx45l9+7dxMTEkJWVxfr16+nbty+nT58u7zjFE6JZgDstgjwNjy9ezWRb7BX0knyEqDZMSjyzZs3i\nypUrrF2t9V0eAAAgAElEQVS7lt9++w1FKfgQmDt3LnXr1mXu3LnlGqR4skQEeRAW4G54fC7hJr8f\nTDC874QQVZtJiee3335j3LhxBAUFofqz6yuAg4MDw4cP5/Dhw+UWoHjyqFQq2jTxokn9GoayU5fT\n2X30WiVGJYQoKyYlnjt37uDm5lbsMisrK/Ly8so0KCFUKhVPhXnTqK6roezouVTik2QWUyGqOpMS\nT+PGjfnpp5+KXbZlyxaCgoLKNCghoCD5dAz3xa+Wk6Fs58FENPm6SoxKCPGoTEo8o0ePJiYmht69\ne/PFF1+gUqnYunUro0ePZsOGDYwcObK84xRPKLVaRcdwH8MU2rfvaPjf8euVHJUQ4lGYlHhatmzJ\nkiVLUKlULFq0CEVRWLx4MZcvX2bRokVERkaWd5ziCWZrbcFTYd6Gx8cv3OBaqkyfLURVZfINpK1a\ntWL16tVkZ2eTmZmJg4MDDg4O5RmbEAYNfZ05e+Uml68XtPHsOJDAy08HGEa4FkJUHSadtd26dTPc\nq2NnZ0etWrUMSefYsWO0adPG5APqdDrmzJlDZGQkYWFhvP3229y4ccOkbYcNG8agQYOMynJycpgy\nZQotW7akefPmTJ48WUbLroZUKhUdmvkYxm/LyMoj9kRSJUclhPgrSqzxbN68GZ2uoBE3Pj6eHTt2\ncO7cuSLr/fHHH+Tm5pp8wAULFrBu3TpmzpyJs7Mz06ZNY9SoUaxateqB2/3444/s3LmTFi1aGJVP\nnTqVEydOsHjxYrRaLZMmTWLq1KnMmTPH5JhE1WBva0mbJl7sPFQwrM6Rs6k08HHG3dW2kiMTQpRG\niYnnyJEjLF++HCj4tjl//vwSd/Lqq6+adDCNRsPy5cuZPHkybdu2BeDTTz+lc+fOHDp0qMhEc4Xi\n4+P57LPPCAsLMypPSkril19+YdmyZYSGhgIwY8YMoqOjmTBhAh4eHibFJaqOxvXcOJeQwdXULPSK\nwo6DCfTp7I+ZWvXwjYUQj4USE8+7777L4MGDURSFLl26sHDhQho1amS0jpmZGfb29tjb25t0sNOn\nT5OdnW1Ua/Hx8cHb25sDBw4Um3h0Oh0TJ05k6NChXL58mStXrhiWHTp0CLVabbRds2bNMDMz4+DB\ngzz33HMmxSWqjsIu1j/+dgatTs+NjBwOn0mheSP5kiFEVVFiG4+lpSXe3t74+PiwdetW2rdvj0ql\nwtvbG29vb2xtbUlOTjY56UBBDQUoUhNxd3c3LLvf4sWLARgyZEiRZcnJybi6umJhYWEoMzc3x9XV\nlevXpcttdeXsYEXLxnfHc9t/Mon0W6Zf7hVCVC6TOhfY29sTHR3Na6+9Zig7duwY/fr1Y8iQIUVm\nJi1JTk4OarXaKFFAQZIrbvSDuLg4li5dysyZM1Gri4aak5ODlZVVkfKS9ieqj6YNa+LxZ9uOTq+w\n40CCDCQqRBVhUuL55JNPSEpKYsqUKYaydu3asWzZMi5dusRnn31m0sGsra3R6/VotcZTG2s0Gmxs\nbIzK8vLymDBhAmPGjKFOnTol7k+j0RQp12g02NpKg3N1plar6NTcF/WfbTtJadkcP29a70ghROUy\nKfHs2rWLCRMmGN0oqlaradWqFePGjeO3334z6WBeXl4ApKamGpWnpKQUufx29OhRLly4wOzZswkL\nCyMsLIz169dz4MABwsLCuHbtGp6enqSnpxt63wFotVrS09Nxd3dHVG9uTjZGbTt7466TmSU1XSEe\ndyYlnpycnCI1kkIODg7cumXawI2BgYHY2dkRGxtrKEtMTOTq1atEREQYrRsSEsLWrVtZv3694adL\nly4EBwezfv163N3dCQ8PR6vVGo2OffDgQfR6PeHh4SbFJKq28AB33BytAcjX6fn9YKJMnyDEY86k\nxNO0aVO+//77IpfI9Ho9P/zwA8HBwSYdzNLSkldeeYVZs2axa9cuTpw4wbhx42jRogWhoaFoNBpS\nU1PRaDRYW1tTp04dox97e3tDubm5OR4eHjz77LP8/e9/5+DBgxw4cIApU6YQFRUlXamfEGZmajpF\n1DZM15GYcptTl9MrOSohxIOYNGTOqFGjiI6Oplu3bnTo0AFXV1du3rzJrl27uH79OsuWLTP5gGPG\njEGr1TJ+/Hi0Wi3t2rVj6tSpABw+fJjo6GiWL19Oy5YtTdrfjBkzmDFjBm+++Sbm5uZ069aNSZMm\nmRyPqPo8XG0JbViTw2dTANhz9Bq1PR2xt7F4yJZCiMqgUky8LnH8+HG++OILDh06RGZmJvb29oSH\nhzNy5EhCQkLKO84ylZiYSOfOndm+fTs+Pj6VHY4oA/laPf/+7QwZf7bx+NVy4rk2dY0mLhRCPJqy\n+uw0eZDQJk2a8Pnnn//lAwlRnizM1XRs7su6necBuHQtk/OJGTT0dankyIQQ9zM58UDBvTt//PEH\nqampDB06lEuXLhEYGIirq+vDNxainHnXtCe4nhtxF9MA2HX4Kj7uDthYleptLoQoZyadkfn5+Uyc\nOJHNmzdjbm6OTqejV69efP3111y4cIEffvgBX1/f8o5ViIdqE1KLy9dvkZWTT06elt1HrtK1ZfH3\ngQkhKodJvdrmzZvHzp07WbBgAfv37zd0V502bRo2NjYm30AqRHmztDCjQ/jdL0Fn7pnDRwjxeDAp\n8WzcuJFx48bRtWtXLC0tDeW1a9fm7bffZt++feUWoBClVdfLkYDad9t2dh5MQJOve8AWQoiKZFLi\nycjIwM/Pr9hlLi4uJo/VJkRFiQz1NrTtZOXk88exa5UckRCikEmJp0GDBmzevLnYZf/973+pX79+\nmQYlxKOysTLnqTBvw+O4i2lcTZUvSEI8DkzqXDBs2DBGjx7N7du36dixIyqViiNHjrBp0ya+//57\nPv744/KOU4hSa+DjzNlaGVy6lgnAjgMJvNw1AAtzk75vCSHKiUlnYLdu3fj44485fPgw77//Poqi\nMH36dNauXcukSZN44YUXyjtOIUpNpVLRvpkPVhZmAGRm5RF7svh5n4QQFafEGs/SpUt5/vnnDaM8\n9+zZk6ioKM6fP09GRgYODg40aNAAc3O5R0I8vuxtLGjbtBY7DiQAcPRsKsH13HCyLzqPkxCiYpRY\n45k3bx4JCQUna3BwMMePH0elUtGwYUMiIiIIDAyUpCOqhEZ1XalVww4AvaJw4FRyJUckxJOtxMxh\nb2/Pd999x9WrV9FqtezatYvLly+XuKPu3buXR3xCPDKVSkWrYC/W/jmczun4mzQLdMfFwbqSIxPi\nyVRi4hk6dCizZs1i69atqFQqFixYUOJOVCqVJB7xWKtV0x5fDwcSkm+jKAqxJ5Lp1kpGNBCiMpSY\neF599VV69+5NZmYmnTt3ZuHChTRq1KgiYxOiTLVs7ElC8m0Azidm0DzTHTen4ic4FEKUnwc20tjb\n22Nvb8/06dMJDw/HxUVG+hVVl6ebHX5ejly6fuvPWk8Sz7Yp/sZoIUT5Mal3QJ8+fbhz5w4xMTHk\n5OSg1+uLrPPcc8+VeXBClLUWjb249OfYbReuZpJy8w7uLraVHJUQTxaTEs8ff/zB22+/TXZ2drHz\n2atUKkk8okqo6WJDfR9nLiRmABB7IokXIutVclRCPFlMSjyffPIJtWvXZsKECXh6eqJWy53foupq\nEeTBxauZKIrC5eu3SErLxtPNrrLDEuKJYVLiOX/+PIsWLaJVq1blHY8Q5c7NyQZ/X2fOXLkJwN64\nJHq2l/EGhagoJlVdvLy8uHPnTnnHIkSFiQjyRK1SAZCYclsGEBWiApmUeIYOHcqiRYtITpY7vkX1\n4OxgRWDdu70098VdL7b9UghR9ky61LZjxw6SkpLo2LEjnp6eWFsb3/GtUqnYtGlTuQQoRHlp3siT\n0/E30esVrt3IJiH5NrU9HSs7LCGqPZMSj4ODAx06dCjnUISoWI52lgT5uRF34QYA+04k4evhgOrP\nS3BCiPJhcq82Iaqj5o08OHUpDZ1eITn9Dpev38KvllNlhyVEtVZi4klLS8PZ2RkzMzPS0tIeuiM3\nN7cyDUyIimBvY0GTBjU4cjYVKKj11PVylFqPEOWoxMQTGRnJv//9b0JCQmjbtu1DT8RTp06ZdECd\nTsfcuXNZt24d2dnZtGvXjqlTp1KjRo1i1//555/55ptvSExMxNfXlyFDhvDSSy8ZlsfExPDmm28W\n2S4mJgZPT0+TYhJPtmYB7py4kEa+Ts+NjBwuJGbSwNe5ssMSotoqMfH885//xNfXF4Dp06eX2QEX\nLFjAunXrmDlzJs7OzkybNo1Ro0axatWqIuv++uuvfPDBB/zzn/8kIiKCvXv3MmXKFJydnencuTMA\nZ86cISgoiK+++spoW6mBCVPZWlsQ0rAGB0+nABB7Mol63k6o1VLrEaI8lJh4+vTpU+zfj0Kj0bB8\n+XImT55M27ZtAfj000/p3Lkzhw4dolmzZkbr37x5k7fffptevXoB4Ovryw8//MD//vc/Q+I5d+4c\n/v7+1KxZs0xiFE+mMH93jl9IQ5OvI/1WLucSbhJQx7WywxKiWqrQsW9Onz5NdnY2LVq0MJT5+Pjg\n7e3NgQMHiqz/8ssvGy6jabVatmzZwoULFwxJCwoST/36cte5eDTWVuaENrz75SX2ZDI6vdzXI0R5\nqNDEk5SUBICHh4dRubu7u2FZcY4fP05ISAhjxoyhR48ehq7dOp2OixcvEhcXR48ePYiMjGTEiBFc\nvHix3J6DqL6a+tfEytIMgMysPM7Ep1dyREJUTxWaeHJyclCr1VhYWBiVW1pakpeXV+J2Pj4+rFmz\nhg8//JAtW7Ywd+5cAK5cuUJeXh4ajYYZM2Ywd+5cNBoNAwYMMKknnhD3srIwI8zf3fB4/8lkdLqi\nU4AIIR5NhSYea2tr9Ho9Wq3WqFyj0WBjU/JMkC4uLjRq1IiXXnqJ4cOHs2zZMnQ6HX5+fuzbt4/P\nP/+ckJAQmjdvzsKFC9Hr9WzYsKG8n46ohpo2rIGNVUHT5+07Gk5eklqPEGWtQhOPl5cXAKmpqUbl\nKSkpRS6/AcTGxhbpph0QEEBubi6ZmZkAODs7G03TYGNjg6+vL9evXy/r8MUTwMLcjPDAu7WeA6eS\n0UqtR4gyZdLIBQDr169n586dxc5AqlKpinRnLk5gYCB2dnbExsYSFRUFQGJiIlevXiUiIqLI+l9/\n/TVqtZrFixcbyo4dO4abmxsuLi5s27aN8ePHs337dlxdC3ogZWVlcfnyZfr27WvqUxPCSHD9Ghw+\nk0p2bj7ZufnEXbhB6D2X4IQQj8akGs9nn33Ge++9x9GjR8nMzCQ7O9voJyvLtCHlLS0teeWVV5g1\naxa7du3ixIkTjBs3jhYtWhAaGopGoyE1NRWNRgPA4MGDiYmJ4ZtvviE+Pp7Vq1ezZMkSRo0ahUql\nIiIiAnt7e8aPH8/p06c5ceIEo0ePxsXFxZDYhCgtczM1zRvdrYEfPJ1CvlZXiREJUb2YVONZs2YN\n0dHRTJo06ZEPOGbMGLRaLePHj0er1RpGLgA4fPgw0dHRLF++nJYtWxIZGcn8+fNZuHAh8+bNw8vL\ni8mTJxvuK3JycmLZsmV88sknREdHo9Vqadu2Ld999x1WVlaPHKt4cgX5uXLoTAq372jIydNy9NwN\no2QkhPjrVIoJk5A0bdqUr7/+2uj+m6osMTGRzp07s337dnx8fCo7HPGYOnkpjR0HEgCwsjQj+rkg\nrCzMKjkqISpPWX12mnSpLTQ0lCNHjvzlgwhRFQXUccXJvqDmnKfRcfRs6kO2EEKYwqRLbW+99Rbj\nxo1Dr9cTFhZWbNfnkJCQMg9OiMpkplbRIsiD32KvAHDkXCohDWpgbWVynxwhRDFMOoMGDRoEwNy5\nc4uMUq0oCiqVyuTRqYWoShr6unDwdArpt3LR5Os4fDaF1k1qVXZYQlRpJiWepUuXlnccQjyW1GoV\nLYI8+c/eywAcO3eDpg1rYmtt8eANhRAlMinxtG7durzjEOKxVd/HiRrONtzIyCFfp+fg6RTahXpX\ndlhCVFkmj1xw+fJl3nnnHdq1a0dYWBidOnVi/PjxMiCnqPZUKhUtG9+dVPDExTSyc/IrMSIhqjaT\najznzp3j5ZdfxsLCgo4dO1KjRg1SU1PZuXMn27Zt46effqJhw4blHasQlaaulyPuLrak3LyDVqfn\n0Bmp9QjxV5mUeGbPnk2dOnVYvnw59vb2hvKsrCwGDx7MZ599xueff15uQQpR2VQqFRFBHmzacwko\nqPWEB7pLW48Qf4FJl9r279/PiBEjjJIOgL29PcOGDSt2EjchqpvCWg9gqPUIIUrPpMRjZWVlNAK0\n0Q7UavLz5Xq3qP4Kaz2F4i6kcSdX3vtClJbJIxcsWbLEMHhnoby8PJYsWUKzZs3KJTghHjd1vRyp\n6VxwA7VWp+fwGRnNQIjSMqmNZ9y4cfTt25cuXbrQuXNnatSowY0bN9i+fTu3bt1ixYoV5R2nEI8F\nlUpFi8aehrae4xduEBYg9/UIURomJZ6GDRuyatUqFixYwObNm7l16xaOjo5ERETw1ltvERgYWN5x\nCvHYKKz1pGbkFNR6zqbSNkRGMxDCVCYPOhUYGMiiRYvKMxYhqgSVSkXzRh5s+d9lAOLO3yDMX2o9\nQpiqxMSzefNm2rZti5OTE5s3b37ojp577rkyDUyIx1k9b+PRDI6cTaWN1HqEMEmJiWfcuHH89NNP\nhISEMG7cuAfuRKVSSeIRTxSVSkXEPbWegrYed2xk5GohHqrEs2Tr1q14enoa/hZCGKvn7YSbkw1p\nmTnka/UckZGrhTBJid2pa9eujaWlJQBHjx7F0dGR2rVrF/mxtbXl999/r7CAhXhc3H9fz7HzN8jN\n01ZiREJUDSbdxzNhwgSuXLlS7LJTp04xe/bsMg1KiKqivrcTbo7WAORrC3q4CSEerMRLbcOHD+fS\npYJ7FRRFYfTo0YYa0L1SUlLw9fUtvwiFeIypVCqaB3nw69544M+2Hv+aMkupEA9Q4tnxxhtv8PPP\nPwMQHx+Pv78/rq6uRuuo1WocHR158cUXyzdKIR5jDXyc2e+YbJil9Mi5VFoFe1V2WEI8tkpMPOHh\n4YSHhwOg1Wp5++23pWYjRDEK23oKaz3Hzt8gtKHUeoQoiUltPJ988gnx8fHMmTPHUHbs2DGGDh3K\n/v37yy04IaqK+t7OuP7Z1qPJ13H0nLT1CFESkxLPf/7zH9544w1OnjxpKLO2tiY3N5fXXnuNPXv2\nlFuAQlQFanXBaAaFjp6/Qa5GergJURyTEs8XX3zByy+/zDfffGMo8/f3Z8WKFfTu3Zu5c+eWW4BC\nVBUNfJxxcbhb6zl27kYlRyTE48mkxBMfH0+3bt2KXdatWzfOnz9fpkEJURWp1cb39Rw9lyq1HiGK\nYVLicXV15dSpU8UuO3fuHI6OjiYfUKfTMWfOHCIjIwkLC+Ptt9/mxo2Svxn+/PPPPPvsszRp0oTn\nnnuONWvWGC3PyclhypQptGzZkubNmzN58mSys7NNjkeIstTAxxlnBysA8vJ1HDsvtR4h7mdS4une\nvTsLFixg9erV3Lx5E4CMjAzWrVvH/PnzeeGFF0w+4IIFC1i3bh0zZ85kxYoVJCUlMWrUqGLX/fXX\nX/nggw9444032Lx5M6+99hpTpkxh+/bthnWmTp3KwYMHWbx4MV9++SWxsbFMnTrV5HiEKEtqdcEY\nboWOnkslL19XiREJ8RhSTJCXl6eMHDlSCQgIUAIDA5WgoCAlMDBQCQgIUEaMGKHk5eWZshslLy9P\nCQsLU9asWWMoS0hIUPz9/ZWDBw8WWX/VqlXK4sWLjcqioqKU6dOnK4qiKNevX1cCAwOVvXv3Gpbv\n27dPCQgIUJKSkkqMo/CYCQkJJsUtRGnodHrl+80nlQU/HVYW/HRYiT1xvbJDEqJMlNVnp0k3Glha\nWrJo0SJOnTrFwYMHycjIwMHBgfDwcIKDg01OcqdPnyY7O5sWLVoYynx8fPD29ubAgQNFptB++eWX\nDX9rtVp+++03Lly4wOjRowE4dOgQarXaaLtmzZphZmbGwYMHZcRsUSnU6oLRDLbFFgwzdeRcKk0b\n1sTSwqySIxPi8VCqO9waNWpEo0aNipTn5ORgY2Pz0O2TkpIA8PDwMCp3d3c3LCvO8ePH6devHzqd\njt69e9OhQwcAkpOTcXV1xcLi7gRc5ubmuLq6cv36dVOekhDlwt/XhQMnk8nIyiNPU9DWc293ayGe\nZCYlnvz8fH744Qf2799Pfn4+iqIAoNfrycnJ4dSpUxw+fPih+8nJyUGtVhslCiioUeXl5ZW4nY+P\nD2vWrOHkyZP861//okaNGowdO5acnBysrKyKrP+w/QlR3grv69m2v6DWc/hsCiENakitRwhMTDxz\n5sxh2bJl1K9fn5s3b2JtbY2zszPnzp1Dp9MxcuRIkw5mbW2NXq9Hq9Vibn730BqN5oE1JhcXF1xc\nXGjUqBFpaWksWrSIt99+G2trazQaTZH1NRoNtra2JsUkRHnxr+3C/lPJZEqtRwgjJo9cMHjwYDZt\n2sSgQYMICQlh7dq1/Prrr3h5eaFWm7QbvLwKBk5MTTUeTiQlJaXI5TeA2NjYIt24AwICyM3NJTMz\nE09PT9LT09Hp7vYa0mq1pKen4+7ublJMQpQXtVpF88C77+sjZ1PRSA83IUxLPDdu3DC0q/j7+3Ps\n2DEAatWqxbBhw9i0aZNJBwsMDMTOzo7Y2FhDWWJiIlevXiUiIqLI+l9//XWRURGOHTuGm5sbLi4u\nhIeHo9VqjS7zHTx4EL1ebxjgVIjK5F/HBUe7gulEcjVajl+Q+3qEMCnx2Nvbk5+fD0DdunW5fv26\n4SZNPz8/rl27ZtLBLC0teeWVV5g1axa7du3ixIkTjBs3jhYtWhAaGopGoyE1NdVw+Wzw4MHExMTw\nzTffEB8fz+rVq1myZAmjRo1CpVLh4eHBs88+y9///ncOHjzIgQMHmDJlClFRUcXWoISoaGb3jeF2\n+Ewq+Vqp9Ygnm0mJJzw8nJUrV6LRaKhTpw7W1tbs2LEDgLi4OOzs7Ew+4JgxY+jevTvjx48nOjqa\nWrVqMW/ePAAOHz5MZGSkoQYTGRnJ/Pnz2bBhA927d2fJkiVMnjyZ/v37G/Y3Y8YMmjVrxptvvsnf\n/vY3WrVqxQcffGByPEKUt4A6rsa1nvNplRyREJVLpRR2UXuAEydOMHDgQJo0acLy5cuZOXMmK1eu\npFGjRsTFxdG3b98qNVpAYmIinTt3Zvv27fj4+FR2OOIJcOJiGr8fTADAxsqc6OcaYWEuPdxE1VJW\nn50m9Wpr3LgxW7Zs4cyZMwBMmDABOzs7Dh8+zNChQxkxYsRfDkCIJ0FgHRcOnk7mVraGnDwtxy+k\n0SxAOsCIJ5NJiefDDz8kKiqK9u3bAwUzLr711lvlGpgQ1YmZmZrwQA9Drefg6WQa1XXFRmYpFU8g\nk9p4/v3vf5ORkVHesQhRrQXe08MtT6Njb5yMriGeTCYlnpCQEJNGJhBClMzMTE27UG/D45OX0klO\nv1OJEQlROUyq5zdp0oQvv/ySX3/9lUaNGhUZFUClUvGPf/yjXAIUojrxq+WEn5cjl67fQlEUdh1O\npHenhqhUqsoOTYgKY1Li2bRpE25ubty6dYt9+/YVWS6JRwjTRYZ6cyX5Njq9QnL6HU5eSqdxPbfK\nDkuIClNi4tmyZQtt2rTBycmJmJiYioxJiGrNyd6K8EAPYk8WjMj+v+PXqe/thLV0NBBPiBLbeCZN\nmsT58+cB6NatG6dPn66woISo7poFuhvdVCodDcSTpMSvWJaWloYx2OLj4zl+/Dh37pTcEHr/JG5C\niJKZ/9nRYNOeSwCcuJROkJ8b7q4yqrqo/kpMPL179+abb75h1apVqFSqEkcmUBQFlUpVZBRpIcSD\n1fVypI6nI/FJf3Y0OHKVlzo2kI4GotorMfGMHz+enj17cvPmTaKjo5k6dSoNGjSoyNiEqNZUKhXt\nQr1J3FrQ0SApLZvTl2/SyM+1skMTolw9sDWzYcOGAAwfPpzOnTvLiM9ClDFnBytC/d05eDoZgD+O\nX8PP2xFrS+loIKovk24gHTNmjCQdIcpJ80bu2NsUTAefk6cl9kRSJUckRPkybepQIUS5sTA3I/Ke\nEQ2OX0gj9WZOJUYkRPmSxCPEY6C+txO+Hg4AhhENTJixRIgqSRKPEI8BlUrFU2HeqNUFPdqup2Vz\n5srNSo5KiPIhiUeIx4SLgzWhDWsaHv9x7Dp5+TJNtqh+Suw6U5rpo2WsNiHKRkSQB2ev3CQrJ587\nufnEnkgyGtFaiOqgxMTz+++/m7wTSTxClA0LczPaNq3Fr3vjATh+/gZBfq64OdlUcmRClJ0SE48M\nDCpE5Wjg48wJ93QSU26jVxRiDl3lxQ71ZUQDUW08chuPTqcrdqoEIcRfY+ho8GeiuXYji3MJMgOw\nqD5Muj06KSmJf/7zn+zfv5/8/HxDN0+9Xo9WqwWQsdqEKEOujtY0bViTw2dTANhz9Bp1vRyxtDCr\n5MiEeHQm1Xg+/PBD9u7dywsvvICfnx9BQUH079+funXrolKpWLBgQXnHKcQTJyLIAzvrghENsnPz\n2X8yuZIjEqJsmJR49u3bx5gxY/jHP/5Br169sLW15b333mPdunWEh4ezc+fOcg5TiCePpUVBR4NC\nR8+lkn4rtxIjEqJsmJR4srOzadSoEQD16tXj5MmTAJibmzNgwAD++OOP8otQiCdYQ19natWwB0Av\nIxqIasKkxFOzZk3S0tIAqFOnDhkZGaSmpgLg4uJiWGYKnU7HnDlziIyMJCwsjLfffpsbN26UuP7m\nzZuJiooiNDSUrl278tVXX6HT3b2pLiYmhoCAgCI/SUky0KKo+lQqFe2b3e1okJiSxflE6WggqjaT\nEk+7du1YsGABx48fx8fHBw8PD5YvX45Go2Hjxo2lGrl6wYIFrFu3jpkzZ7JixQqSkpIYNWpUsevG\nxK+zOAcAACAASURBVMTw7rvv0qdPHzZu3Mg777zD119/zZdffmlY58yZMwQFBbF7926jH3d3d5Nj\nEuJx5uZkQ5MGNQyP9xy9Rr5WRjQQVZdJiWf06NFYWFgwe/ZsoGCahCVLlhAaGsratWsZPHiwSQfT\naDQsX76ccePG0bZtWxo3bsynn37KoUOHOHToUJH1f/zxR55++mkGDhxI7dq1eeaZZ3j11VdZu3at\nYZ1z587h7+9PzZo1jX7UahkNSFQfLRp7YvtnR4OsHOloIKo2k7pTu7m5sW7dOsPlq549e+Ll5cWR\nI0cICQmhdevWJh3s9OnTZGdn06JFC0OZj48P3t7eHDhwgGbNmhmtP2LECGxtjeegV6vV3Lp1y/D4\n3LlzPPfccyYdX4iqysrCjDYhXmyLvQLAkXOpNPJzxcXBupIjE6L0TKoWfPnll6SmpuLl5WUoa9my\nJcOGDaN27dp89NFHJh2sMHHdf2nO3d292DaZkJAQo+m2s7KyWLVqFe3atQMK2osuXrxIXFwcPXr0\nIDIykhEjRnDx4kWT4hGiKgmo7YKXmx0Aer3CttgraHX6So5KiNIzKfHMmzevxMb6Y8eOsXLlSpMO\nlpOTg1qtxsLCwqjc0tKSvLy8h247cuRI8vLyeOeddwC4cuUKeXl5aDQaZsyYwdy5c9FoNAwYMKBU\nHR6EqAoKOhr4GIbOSU6/w2+xV6SXm6hySrzUNmDAAI4ePQoUTEz1yiuvFLueTqejcePGJh3M2tra\nMNqBufndQ2s0GmxsSh4EMT09nZEjR3L+/Hm+/fZbvL0LRuv18/Nj3759ODo6Gtp0Fi5cSIcOHdiw\nYQOvv/66SXEJUVXUcLYhsmkt/nvkKgAXEjP433FL2oTUesiWQjw+Skw806ZN4z//+Q+KorBo0SJ6\n9uyJp6en0TpqtRpHR0e6du1q0sEKL9Xdf9kuJSWlxJ5xiYmJDBkyhOzsbFasWEFgYKDRcmdnZ6PH\nNjY2+Pr6cv36dZNiEqKqadqwJplZeRw7X3AbwqEzKTjZW9G4nlslRyaEaUpMPA0aNOCtt94CCmo1\n/fv3L1W36eIEBgZiZ2dHbGwsUVFRQEFiuXr1KhEREUXWT0tLIzo6GjMzM1atWoWvr6/R8m3btjF+\n/Hi2b9+Oq6srUNAOdPnyZfr27ftIsQrxOIts6s3tbA2Xrhd0tIk5lIi9rQV1PB0rOTIhHs6kXm1j\nxowBYM+ePcTGxnL79m1cXFxo3ry5yT3aoKAt55VXXmHWrFm4uLjg5ubGtGnTaNGiBaGhoWg0GjIz\nM3FycsLS0pJp06Zx8+ZNvvvuO6ytrQ03rapUKmrUqEFERAT29vaMHz+e8ePHo9Pp+PTTT/+/vfsO\ni+L4/wD+vjs4qiIgiEFEUSmCcBQBBUTEQogGTawRwRZrAE3siuWHFewtoEGNYonmKwajiTFGjQ2U\nohEVlaKIEalSjnLc3fz+wFtZmihwSJzX8/AczO7tzWdv2c/t7NwMNDU1mcRGUf9FXC4Hgx0NcfJS\nMrLzSyElBOein+KL/t3Rvh2du4f6sDUo8YhEIsyePRtXrlyBgoIC2rVrh/z8fEilUvTp0wehoaHg\n8/kNesE5c+ZALBZj/vz5EIvFcHFxwfLlywEACQkJ8PHxwcGDB2FlZYXz589DKpVi1KhRrG3weDzc\nv38fGhoaOHDgAEJCQuDj4wOxWAwnJyf8+OOPUFJSesddQVGti6ICD0OdjHDiwiMUl1ZAVCHBr1dT\nMdLdGOoqim/fAEW1EA5pQJeYkJAQHDlyBEFBQfD09ASXy4VEIsHZs2exYsUKTJgwAXPnzpVHfZtE\nRkYG3N3dceHCBXTq1Kmlq0NRjZJbUIr/XUyGqKJyNAOddir4wq07FBXoFApU02qqc2eDulOfOXMG\nAQEBGDp0KNN7jMfjYdiwYfD398fp06ffuwIURTWOtoYKPBwNmfHcsl+V4o/op5BKaTdr6sPUoMTz\n6tUrGBsb17rM2NiYufdCUVTL6KzXFq42bz6Bpr0oxNU7z+l3fKgPUoMST9euXXH16tVal125coU2\nV1HUB8DcSBu2pm8Gx/0nOQf/PK575HeKaikN6lzg4+ODpUuXQiqVwtPTEzo6OsjOzsaZM2cQERGB\nRYsWNXc9KYpqAEeLjigUivD4WeXUCVf/+Rdt1Pgw0tdo4ZpR1BsNSjwjRozAkydPEB4ejh9//JEp\n5/F4mDJlCiZMmNBsFaQoquE4HA7ce3dGUUkFMnOFIITgj5inGNG/Ozpoqb59AxQlBw1KPAAwd+5c\n+Pr64s6dOygoKEDbtm0hEAiYL25SFPVhUOBx4dm3C37+6zEKhSKIJVKcuZaGkQN6oK1aw772QFHN\nqc57PD4+PkhJSWGVaWlpwc3NDcOHD8eAAQNo0qGoD5SqsiKGuRhBiV/ZpbqkrAK/Xk1FmUjcwjWj\nqHoSz82bNyEUCuVZF4qimpBmG2V81rcreNzKbtZ5hWX4/cZTSOhUClQLo9N0UtR/2Cc66hhg92aM\nw4ysIlxOyKDdrKkWRRMPRf3HmRhqwcH8zcjy99PyEJeU1YI1oj529XYuWL16NdTV1d+6EQ6Hg/Dw\n8CarFEVRTcvOrAMKhSI8eJIHAIhOfIG2anwYd9Zs4ZpRH6N6E49YLEZFRYW86kJRVDPhcDjob9MJ\nRSUVyMgqAgBcuJUOJT6PTqVAyV29iWflypWwtLSUV10oimpGPB4XHn0McfJiMvIKyyCREpy+kgpr\nY104WuiBx6Mt75R80CONoj4iynwFDHU2gprym2kTEh5l4cRfj5FXWNaCNaM+JjTxUNRHpq0aH2MG\nGbOa2HJeleL4n49wNzmH9nijml2diWfEiBHQ1KQ3Hinqv0hVWRFDnbuin7U+FF43sYklUlxOyMCv\nV9NQUkbv7VLNp87Es27dOhgYGNS1mKKoVo7D4cCyuw5GufdgTZf9NLMQR/94iCcvCluwdtR/GW1q\no6iPnLaGCkYN6AGBsQ5TVlouxq9XU3E5PgMVYjrSAdW0aOKhKAo8HhfOVvrw6teN1fHgbkoOTlx4\nhOz80hasHfVfQxMPRVEMgw5tMG6wCbpVmb8nr7AMJ/56hPiHWbTjAdUkaOKhKIpFWUkBHn26YICd\nARRfdzyQSgmu//Mvfvk7FcUlohauIdXa0cRDUVQNHA4HPbtqY8wgE9YEchlZRTh6/iGSM161YO2o\n1o4mHoqi6tSujRK+cOsBO7MO4HAqp1coF0nw+40n+Cs2HRViSctWkGqVaOKhKKpePC4HjhYdMcK1\nG9qovpnB9H5aHo6df4SkJ3kQ0zl+qHdAEw9FUQ3yiY46xgwyZo1oXVBcjj9vpWP/r/dw5fZz5NNh\nd6gGqHeQUIqiqKqU+QoY7GAIQ702uJzwHKKKyqa2cpEEdx5n487jbOjrqMPcSBvd9DXowKNUreR+\nVEgkEmzatAnOzs6wtraGv78/cnJy6lz/7Nmz8PLygkAgwKBBg7Bnzx5IJG/alUtLSxEYGAgHBwfY\n2dlh2bJldMpuimpmJoZa8PYwRd9en6CtGp+17Hl2Mf6IeYoDZ+7j+j//oqC4vIVqSX2o5J54duzY\ngcjISGzYsAERERHIzMyEn59fretevnwZ8+bNw6hRoxAVFYXvvvsOe/fuRWhoKLPO8uXLERcXh7Cw\nMISGhuLmzZtYvny5vMKhqI+WqrIibEx1MeFTM3zuYoRu+hrgvu6AAFSOfhD/MAuHfnuAqL9TkJLx\nClIp/R4QJeemNpFIhIMHD2LZsmVwcnICAGzevBnu7u6Ij4+HjY0Na/1jx45h8ODB8Pb2BgB07twZ\nKSkpOHnyJGbPno3MzEz8+uuvOHDgAAQCAYDKWVN9fHywYMECdOjQQZ7hUdRHicPhoLNeW3TWa4vi\n0grcT8vF/dRcFJe+GWg0/WUR0l8WQV1FET27aqNnVy2oq/Lr2Sr1XybXxJOUlAShUAh7e3umrFOn\nTtDX10dsbGyNxDNz5kyoqqqyyrhcLgoLKwcvjI+PB5fLZT3PxsYGPB4PcXFx8PT0bMZoKIqqTl1F\nEfY99WBn2gFPMwuRmJKL9JdFzIgHxaUVuHk/E7cevESXjm1hYaQNgw5twOVy3rJl6r9EroknMzMT\nAGpciejq6jLLqqo++2lxcTGOHj0KFxcXAMDLly+hpaUFRcU3Y0spKChAS0sLL168aOrqUxTVQFwu\nB10/0UDXTzRQKBThXmouHjzJY6ZbIIQg7d8CpP1bAHUVRejrqENPWw0dtFXRXkOFJqL/OLkmntLS\nUnC5XFaiAAA+n4/y8vpvQJaWlmLWrFkoLy/Hd999x5QpKSnVWLch26MoSj7aqvHRp1dH2PfsgLQX\nlVdBGVlFzPLi0go8TM/Hw/R8AIAijwtdLVXoaatBT7vyUUWJdsD9L5Hru6msrAypVAqxWAwFhTcv\nLRKJoKKiUufz8vLyMGvWLCQnJ2Pfvn3Q19dnticS1Rw3SiQS1WiioyiqZfF4XHTv1A7dO7XDq6Jy\n3EvLxYO0PJSJxKz1KiRSPM8uxvPsYqasnboSk4T0tNWg1VaZXhW1YnJNPB07dgQAZGdnM78DQFZW\nVp0dATIyMjBlyhQIhUJERETA1NSUWaanp4e8vDxIJBLweDwAgFgsRl5eHnR1dZsxEoqiGqNdGyU4\nWX4CR3M9ZL8qxcvcEmTmCfEiR8jqlCDzqrgcr4rLkfS08qqIr8iDrqYq9LRV0VFbDTqaKlBRUmCG\n9aE+bHJNPKamplBTU8PNmzfh5eUFoDKxPH/+HL17966xfm5uLnx8fMDj8XD06NEaM6La2tpCLBYj\nISEBdnZ2AIC4uDhIpVLY2to2f0AURTUKj8dlrmKsUDkRXXGJCJmvE1Fmbgmy8ktqdMMWVUiQkVXE\narJT5HHRRo0PdVVFtFXlQ12Vj7ZqfLRR5aONqiJUlRXpVdIHQq6Jh8/n46uvvkJwcDA0NTWhra2N\nVatWwd7eHgKBACKRCAUFBdDQ0ACfz8eqVauQn5+PH3/8EcrKysjOzgZQ2X2zffv26NChAz799FMs\nXboUa9euBSEEgYGB8PLyol2pKaqVUlflo7sqH90N2gEAxBIpsvNLkZkrRGZeCTJzhBCW1bwqqpBI\nkVdYhrw6hu3hcjlQV1Gskowqf9RVK8vUVBShQEdakAu537GbM2cOxGIx5s+fD7FYDBcXF+YLnwkJ\nCfDx8cHBgwdhZWWF8+fPQyqVYtSoUaxt8Hg83L9/H0Dl93ZWr16NadOmQUFBAUOGDMGSJUvkHRZF\nUc1EgcdFx/Zq6NheDUBlj7iikgpk5grxMrcEL3KFyC8qe+sU3VIpQaFQhEJh3fMJ8bgcKPEVoMzn\nga/Ig5Ii783v/Mq/2Y8KlY98HvgKXNrU10Ac8hFOKZiRkQF3d3dcuHABnTp1aunqUBTVSIQQlIsk\nKCqpQFGJCEVCEYpKXz+WVKBQKKrRiaGpcTgcKCpwocDjQoHHgQKPCx6PAwUuFwoKXChwOeCxlr1Z\nl8fjQvH1+jwuB1wuB1zO68eqv7MeUesyDqcygQIcVD68fnxdx8ZoqnMn7aNIUVSrx+FwoKykAGUl\nBeho1t5DtkL8OjEJRZXJqUSEQmEFil//XlIubtSQPoQQiCokzMCpHyIOpzIxcYDK4Y041R5fl3M4\nQJdPNOBqrd8sV3E08VAU9VFQVOBBqy0PWm2Va11OCIFYQlBeIUG5SPz6UVLzsUZZ5bpva+r7EBBC\nIGvjkqD+JJuYkoOeXbSgq9X0X02hiYeiKAqyprLK5jJ1FcW3P6EaiZSgQiyBREIglkghlkjZv0sJ\nKsR1lEmlEIulEEsIJFICQgikhEAqff1D8PqRsB9ZZW/WkSUYKSGA7PEdtW+nAi2N2pN0Y9HEQ1EU\n1QR4XA54/A/3lCpLRoQQkCp/V09OstZGNeXm+17Uh7uXKIqiqCYju79TeYenZX2UiUc2kVxtA5NS\nFEVRtZOdM6tOxvk+PsrEI/si6vjx41u4JhRFUa1PdnY2DA0N3/v5H+X3eMrKypCYmAgdHR1mjDeK\noiiqfhKJBNnZ2bCwsICy8vt3PPgoEw9FURTVcujARBRFUZRc0cRDURRFyRVNPBRFUZRc0cRDURRF\nyRVNPBRFUZRc0cTzmkQiwaZNm+Ds7Axra2v4+/sjJyenpatVr5ycHCxcuBDOzs6ws7PDlClT8OjR\nI2b51atX4eXlBUtLSwwbNgyXL19mPT83NxcBAQGws7NDnz59EBISArG4eYeOf1e3b99Gz549ERMT\nw5S15rhOnDiBIUOGwNLSEl988QVu3LjBLGutcZWUlCAoKIg5DqdOnYrk5GRmeWuLa/ny5Vi6dCmr\nrCliOHDgANzc3GBlZYVJkybhyZMnzR0KS21xRUREwMPDAwKBAJ6enjhx4gRrebPFRShCCCFbtmwh\nTk5O5OrVqyQxMZGMGjWKjB07tqWrVSeJRELGjBlDRo8eTe7cuUMeP35M/P39SZ8+fUheXh55/Pgx\nsbCwILt37ybJyclky5YtxNzcnDx69IjZxrhx48hXX31FHjx4QC5dukQcHR3J5s2bWzAqNqFQSAYN\nGkSMjY1JdHQ0IYS06rhOnjxJzM3NyYkTJ8iTJ0/I2rVriUAgIM+ePWvVcS1ZsoR4eHiQ2NhYkpyc\nTGbNmkVcXV1JWVlZq4pLKpWSrVu3EmNjY7JkyRKmvCliOH78OLG2tia//fYbSUpKItOnTyfu7u6k\nvLy8xeI6fPgwEQgE5NSpU+Tp06fk+PHjxNzcnERGRjZ7XDTxEELKy8uJtbU1+d///seUPXv2jBgb\nG5O4uLgWrFnd7t27R4yNjUlycjJTVl5eTqysrEhkZCQJDAwk3t7erOd4e3uTZcuWEUIIiY+PJ8bG\nxiQ9PZ1ZfvLkSWJtbS2Xf4aGkMVQNfG01rikUilxc3MjW7duZcokEgn5/PPPSVRUVKuNixBC7O3t\nycGDB5m/Hz9+TIyNjUliYmKriSs9PZ14e3sTBwcH0r9/f9YJuiliGDx4MNm+fTuzvLi4mAgEAhIV\nFdWcYdUb17Bhw0hwcDBr/cWLF5MJEyYQQpo3LtrUBiApKQlCoRD29vZMWadOnaCvr4/Y2NgWrFnd\nOnbsiLCwMHTt2pUpk40kW1BQgNjYWFY8AODg4MDEExsbC319fRgYGDDL7e3tIRQK8eDBAzlEUL/L\nly/j0qVLWLZsGau8tcaVmpqK58+fw9PTkynjcrn45ZdfMGzYsFYbFwBoaWnh7NmzyM3NhUgkws8/\n/wwNDQ0YGBi0mrji4+PRsWNHnD59usbMmo2NITc3F0+ePGFtQ01NDRYWFs1+fqkvrmXLlmHs2LGs\nMi6Xi8LCQgDNGxdNPHgz8F2HDh1Y5bq6uh/sQKKampro378/uNw3b+GhQ4dQVlYGZ2dnZGZm1hvP\ny5cvoaurW2M5ALx48aKZa1+/vLw8LF26FKtXr4aGhgZrWWuNS9buXVhYCB8fH/Tp0wfjx49HfHw8\ngNYbFwAEBQUhMzMTffv2hUAgwPHjx7Fnzx60bdu21cTl5eWF4OBg6Ojo1FjW2Bha8vxSX1z29vas\npPLvv//izJkzcHFxAdC8cdHEA6C0tBRcLheKiuzJn/h8PsrLy1uoVu/mwoUL2Lx5MyZNmoRu3bqh\nrKwMfD6ftU7VeEpLS6GkpMRarqioCA6H0+Ixr1ixAgMGDEC/fv1qLGutcRUXFwMAFi1ahFGjRuGH\nH35Ajx494Ovri5SUlFYbFwA8ffoU7du3x549e3D06FE4OzvD398fmZmZrToumcbGUFpaCgA11vmQ\nzi95eXmYPn062rdvj2nTpgFo3rg+ytGpq1NWVoZUKoVYLIaCwptdIhKJoKJS+/ztH5KTJ08iMDAQ\nnp6emD9/PoDKg6GiooK1XtV4lJWVIRKJWMsrKipACIGqatNPddtQkZGRuH//PqKiompd3lrjkn2o\nmTFjBoYNGwYA6NmzJ+Li4nD06NFWG9ezZ88QGBiII0eOQCAQAAA2bdoET09PHDhwoNXGVVVjY5AN\npll9nQ/l/PLs2TNMnToVZWVliIiIQJs2bQA0b1z0igeV90uAN9MlyGRlZdW4jPzQfP/991i8eDHG\njh2L4OBgpumtY8eOyMrKYq1bNR49Pb1a4wVqXjrL08mTJ/Hy5UumW7uHhwcA4Ouvv8by5ctbbVyy\nJgpjY2OmjMPhwMjICBkZGa02rsTEREgkElhYWDBlioqKMDMzw9OnT1ttXFU1NoYP+fxy7949jBkz\nBlwuF8eOHWM1vTVnXDTxADA1NYWamhpu3rzJlGVkZOD58+fo3bt3C9asfnv37sXWrVvh7++PwMBA\n1jS1tra2uHXrFmv9mJgY2NnZMcufPXvGakePiYmBmpoaTE1N5RNALTZu3IgzZ87g1KlTOHXqFH74\n4QcAwOrVqxEQENBq4zI3N4eqqiru3r3LlBFCkJKSAgMDg1Ybl56eHgDg4cOHTJksri5durTauKpq\nbAza2tro0qUL6/wiFAqRmJjYoueXlJQUTJ48Gfr6+jhy5AiTSGSaNa737qf3HxMSEkL69u1LLl++\nzHyPp3oXyg/JgwcPiJmZGVm8eDHJyspi/QiFQpKUlETMzc3Jtm3bSHJyMtm6dSvp1asX0/1aKpWS\n0aNHkzFjxpDExESmj37VrpEfghcvXrC6U7fmuLZs2UJ69+5Nzp07R9LS0siaNWtIr169SEpKSquN\nSywWk9GjR5OhQ4eSW7dukeTkZBIYGEgEAgHJyMholXF5e3uzuh03RQxHjhwhAoGA/Prrr+Thw4dk\n+vTpZPDgwXLtMl49ri+//JI4OzuT1NRU1vkjNze32eOiiee1iooKsm7dOmJvb09sbGxIQEAA8wZ8\niDZt2kSMjY1r/dm1axchhJCLFy8ST09PYmFhQT7//HNy7do11jaysrLIrFmziJWVFenbty/ZtGkT\nkUgkLRFOnaonHkJab1xSqZSEhoYSV1dXYmFhQUaNGkVu3brFLG+tceXm5pKlS5cSFxcXYmtrS3x9\nfcn9+/eZ5a0truonaEKaJobQ0FDi5OREBAIBmTx5Muv7MfJQNa7U1NQ6zx8DBw5s9rjoRHAURVGU\nXNF7PBRFUZRc0cRDURRFyRVNPBRFUZRc0cRDURRFyRVNPBRFUZRc0cRDURRFyRVNPO9p0aJFGDRo\nUJ3LBwwYUGO2v+Yk79drqJiYGJiYmLx1mHQTExPs3r1bTrVq/d52/H1sduzYgZ49ezJ/T5gwARMn\nTpRrHQIDA7Fr1y4AlUM/mZiY1DlK89KlSzFgwABWWV5eHtauXYuBAwfCwsIC9vb28PX1xfnz51nr\nybZd9adXr14YOHAgVq9ejby8PNb6O3fuxMqVK5su0CZABwmlPgg//fRTjSE7qLrNmjULQqGwpavx\nwVqxYgVrCKnmdvXqVVy9ehW///77ez2/tLQUX331FQBg+vTp6Ny5M4qKinD27Fl88803WLJkCXx9\nfVnP+f7776GlpQVCCEpLS3Hv3j3s3bsXf//9N44dOwYtLS0AwNSpU+Hh4YEbN26gT58+jQu0idDE\nQ30QZCMbUw3TuXPnlq7CB6179+5yey1CCNavX4+JEyfWmCKgoc6dO4e0tDT8+eefrIE6Bw4ciLKy\nMmzfvh3e3t7g8XjMsp49ezJj5QFA37594ezsjNGjR2Pjxo1Yu3YtgMpRpidOnIh169bVOeq7vNGm\nNjkpKSlBSEgIBg8eDAsLC9jY2GDKlClISkpi1lm0aBGmTJmCEydOMOt5eXnhypUrrG0lJSVh0qRJ\nsLa2hpubW4MOprVr18LR0RFVB6qYM2cOTExMkJOTw5Rt2bIFbm5uAACJRIKwsDAMHToUlpaWEAgE\nGDduHGJiYpj1y8rKsHLlSvTr1w8WFhbw8PBAeHh4jddPSUnBpEmTYGlpCScnJ2zevBkSiYRZXrWp\nTdY8Fx0djYkTJ8LKygpOTk7YuHEj6zlFRUVYvHgxHBwcYGtri8DAQGzevLlGE0Z1WVlZWLBgARwd\nHWFjYwNfX1/cu3ePWZ6Xl4cVK1bAzc2NafLw8/PD8+fPmXUmTJiAlStXYseOHXBycoK1tTXmzp2L\n4uJi7NmzBy4uLrC1tYWfnx/y8/NZcR4+fBhz5syBQCCAs7Mztm7dyoqrocdK1aY2kUiE9evXw9nZ\nGQKBAAEBAThw4ABMTExYdV6+fDlCQ0Ph6uqKXr16YezYsayBS2uTmJgIX19f2NrawtraGhMnTsTt\n27dZdZk4cSIOHz4MFxcXWFtbY9q0aUhPT2dt5+HDh/j6669hbW0NW1tbBAQEsJqiGvq+l5eXY926\ndcx+X7x4cY35X6o3tZmYmODYsWNYvHgxevfuDWtrawQEBCA3N5dZhxCCsLAwuLm5wdLSEpMnT8ap\nU6dgYmKCjIyMOvfPpUuXkJKSwppd9l3J/gdrG0hmxowZmDVrVo3pB2pjZmaGIUOGICoqipkvBwA8\nPT3x+PFjXLp06b3r2JRo4mkksVhc6091CxYswKlTpzB9+nTs27cPixcvxsOHDzFv3jzWwXbnzh3s\n378fAQEB2LVrF3g8Hvz9/VFUVASgclZAb29vFBUVISQkBAEBAdi4cSNevnxZbz379++P/Px85uRF\nCGESSNWRd69cuQJXV1cAQHBwMEJDQzFu3Dj88MMPCAoKQn5+PgICApiDeu3atfj777+xaNEihIeH\nw93dHcHBwYiMjGS9/po1a2Bvb4+wsDB4eHggLCwMx48fr7fO3333HfOcoUOHYu/evTh58iSzfObM\nmfjrr78wb948hISEIDk5Gfv37693m0KhEOPGjUNsbCwWLVqEbdu2QSqVYtKkScjMzAQhBFOnTkV0\ndDTmzZuH8PBwfPPNN7h27VqNdvKoqCgkJCRgw4YN8Pf3x9mzZzFy5EhcvXoVq1evxrfffosLFy5g\n586drOdt2bIF5eXl2LZtG8aOHYs9e/YgODiYWd7QY6WqwMBAHD16FFOmTMG2bdsgEomwadOmWJzg\n0gAAD7NJREFUGuudPXsWly5dYpJ0Tk4OAgICIJVKa91ucXExpk6dCk1NTezYsQNbtmxBaWkppk6d\nykxuB1Qmp9DQUMybNw9r1qxBSkoKfHx8UFJSAgBIS0vDuHHjUFBQgJCQEAQFBeHRo0cYP348c2zL\nvO19nz9/Po4fP47p06dj69atKCgowIEDB2qtf1UbN24EAGzduhXz58/HxYsXsX79emb5jh07sG3b\nNgwfPhy7du2Cnp4eAgMD37rd06dPw8bGptZZPhvK2dkZPB4P3t7e2LVrF+7cucPMAWRpaYkpU6Y0\neO6evn37oqKigvWBQldXF9bW1jh9+vR717Ep0aa2RkhPT4e5uflb15PN1hcYGMjML2Nvb4/i4mKs\nX78e+fn5THtsUVERIiMjmcttVVVVeHt7IyYmBgMHDsSBAwcgkUiwd+9eaGpqAgC6du2K0aNH11sH\nOzs7qKqq4saNGzAzM8PDhw+Rn58PMzMz3Lp1C59++ilyc3Nx//59BAQEAKi8Mvj2228xfvx4ZjtK\nSkrw8/PD48ePYWlpiZs3b8LJyYn5tOfg4ABVVVWmbjKTJk3CzJkzAQCOjo64cOECoqOjMW7cuDrr\nPGbMGMyaNYt5zp9//olLly5h1KhRuHHjBm7duoWwsDD079+fWcfd3b3e/RAZGYnnz58jKiqKmRtH\nIBBgxIgRiI+Ph42NDdTU1LBs2TLY2NgwMaWnp+Pnn39mbYsQgu3bt0NdXR3Ozs44efIknj9/jhMn\nTjCTaV25cgUJCQms53Xo0AG7du0Cl8uFq6srhEIhDh06hNmzZ0NJSanBx4pMeno6fvnlFwQGBjLv\nlYuLCz7//HM8fvyYta5EIsEPP/wAdXV1AJWJeOHChXj06FGt0xAkJycjPz8fPj4+zP4wMjLCTz/9\nBKFQyGynqKgI4eHhsLKyAgB069YNXl5eiIyMxPjx47Fz506oqqpi//79UFNTAwD07t0bAwcORERE\nBHNsAPW/748fP8a5c+ewatUqjB07lol12LBhSEtLq++th6mpKdatWwcAcHJywt27d/Hnn38CqLzK\nDA8Ph6+vL3P8u7i4IDs7G3///Xe9242OjoaXl1e967yNqakpNm/ejKCgIGzfvh3bt2+HiooK7Ozs\n8OWXX+LTTz9t8La0tbUBgNWSAQAWFhY4e/Zso+rZVGjiaQQ9Pb0an2Z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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plot(infected_sweep)\n", + "\n", + "decorate(xlabel='Hand-washing campaign spending (USD)',\n", + " ylabel='Total fraction infected',\n", + " title='Effect of hand washing on total infections',\n", + " legend=False)\n", + "\n", + "savefig('chap05-fig05.pdf')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now let's put it all together to make some public health spending decisions." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Optimization" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Suppose we have \\$1200 to spend on any combination of vaccines and a hand-washing campaign." + ] + }, + { + "cell_type": "code", + "execution_count": 47, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "12" + ] + }, + "execution_count": 47, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "num_students = 90\n", + "budget = 1200\n", + "price_per_dose = 100\n", + "max_doses = int(budget / price_per_dose)\n", + "dose_array = linrange(max_doses)\n", + "max_doses" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can sweep through a range of doses from, 0 to `max_doses`, model the effects of immunization and the hand-washing campaign, and run simulations.\n", + "\n", + "For each scenario, we compute the fraction of students who get sick." + ] + }, + { + "cell_type": "code", + "execution_count": 48, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "0.0 0.988888888889 0.266727403413 0.187595503995\n", + "1.0 0.977777777778 0.26683150821 0.174580718826\n", + "2.0 0.966666666667 0.267112856728 0.162909838349\n", + "3.0 0.955555555556 0.267865747331 0.153508349478\n", + "4.0 0.944444444444 0.269828391545 0.148565092315\n", + "5.0 0.933333333333 0.274613528135 0.152945950611\n", + "6.0 0.922222222222 0.284596094758 0.174964415024\n", + "7.0 0.911111111111 0.3 0.217343161684\n", + "8.0 0.9 0.315403905242 0.259071044488\n", + "9.0 0.888888888889 0.325386471865 0.278402884103\n", + "10.0 0.877777777778 0.330171608455 0.277914534623\n", + "11.0 0.866666666667 0.332134252669 0.267357496693\n", + "12.0 0.855555555556 0.332887143272 0.252796945636\n" + ] + } + ], + "source": [ + "for doses in dose_array:\n", + " fraction = doses / num_students\n", + " spending = budget - doses * price_per_dose\n", + " \n", + " system = make_system(beta, gamma)\n", + " add_immunization(system, fraction)\n", + " add_hand_washing(system, spending)\n", + " \n", + " run_simulation(system, update1)\n", + " print(doses, system.init.S, system.beta, calc_total_infected(system))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The following function wraps that loop and stores the results in a `Sweep` object." + ] + }, + { + "cell_type": "code", + "execution_count": 49, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def sweep_doses(dose_array):\n", + " \"\"\"Runs simulations with different doses and campaign spending.\n", + " \n", + " dose_array: range of values for number of vaccinations\n", + " \n", + " return: Sweep object with total number of infections \n", + " \"\"\"\n", + " sweep = SweepSeries()\n", + " for doses in dose_array:\n", + " fraction = doses / num_students\n", + " spending = budget - doses * price_per_dose\n", + " \n", + " system = make_system(beta, gamma)\n", + " add_immunization(system, fraction)\n", + " add_hand_washing(system, spending)\n", + " \n", + " run_simulation(system, update1)\n", + " sweep[doses] = calc_total_infected(system)\n", + "\n", + " return sweep" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now we can compute the number of infected students for each possible allocation of the budget." + ] + }, + { + "cell_type": "code", + "execution_count": 50, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "infected_sweep = sweep_doses(dose_array)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "And plot the results." + ] + }, + { + "cell_type": "code", + "execution_count": 51, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Saving figure to file chap05-fig06.pdf\n" + ] + }, + { + "data": { + "image/png": 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Z2YVdE/ft20d+fj5PP/20cb+9vT1bt241qz5CiMqhKAo79p/n/MWrxrKwNvVM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\nhRBCiEr9P+AKxQwmJbnhAAAAAElFTkSuQmCC\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plot(infected_sweep)\n", + "\n", + "decorate(xlabel='Doses of vaccine',\n", + " ylabel='Total fraction infected',\n", + " title='Total infections vs. doses',\n", + " legend=False)\n", + "\n", + "savefig('chap05-fig06.pdf')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Exercise:** Suppose the price of the vaccine drops to $50 per dose. How does that affect the optimal allocation of the spending?" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Exercise:** Suppose we have the option to quarantine infected students. For example, a student who feels ill might be moved to an infirmary, or a private dorm room, until they are no longer infectious.\n", + "\n", + "How might you incorporate the effect of quarantine in the SIR model?" + ] + }, + { + "cell_type": "code", + "execution_count": 52, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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xb98+eHl59UhwA9HdTynXs8Sob2xWYTSEENJ9OJVeWbFiBSIiIjB+/HiMGTMG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\neDhWrlwJgI6Lx1EPBfXnSIHGsvYNSkpKmnRluwIzMzOdX1x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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Solution goes here\n", + "num_students = 90\n", + "budget = 1200\n", + "price_per_dose = 50\n", + "max_doses = int(budget / price_per_dose)\n", + "dose_array = linrange(max_doses)\n", + "\n", + "\n", + "\n", + "\n", + "infected_sweep = sweep_doses(dose_array)\n", + "\n", + "plot(infected_sweep)\n", + "\n", + "decorate(xlabel='Doses of vaccine',\n", + " ylabel='Total fraction infected',\n", + " title='Total infections vs. doses',\n", + " legend=False)" + ] + }, + { + "cell_type": "code", + "execution_count": 53, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def quarantine(system, fraction):\n", + " quarantine_rate = 0.02\n", + " system.init.I -= quarantine_rate " + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "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": "3.6.1" + } + }, + "nbformat": 4, + "nbformat_minor": 1 +} From b0bec117a6005dfc1d04e5cf44ac1bccf844808a Mon Sep 17 00:00:00 2001 From: Junwon Lee Date: Sat, 7 Oct 2017 12:49:31 -0400 Subject: [PATCH 09/19] Adding chap05mine --- code/chap05mine.ipynb | 163 ++++++++++++++++++++++-------------------- 1 file changed, 86 insertions(+), 77 deletions(-) diff --git a/code/chap05mine.ipynb b/code/chap05mine.ipynb index 4e88341d..4de9e6f0 100644 --- a/code/chap05mine.ipynb +++ b/code/chap05mine.ipynb @@ -15,7 +15,7 @@ }, { "cell_type": "code", - "execution_count": 2, + "execution_count": 1, "metadata": { "collapsed": true }, @@ -50,7 +50,7 @@ }, { "cell_type": "code", - "execution_count": 3, + "execution_count": 2, "metadata": {}, "outputs": [ { @@ -101,7 +101,7 @@ "dtype: int64" ] }, - "execution_count": 3, + "execution_count": 2, "metadata": {}, "output_type": "execute_result" } @@ -120,7 +120,7 @@ }, { "cell_type": "code", - "execution_count": 4, + "execution_count": 3, "metadata": {}, "outputs": [ { @@ -171,7 +171,7 @@ "dtype: float64" ] }, - "execution_count": 4, + "execution_count": 3, "metadata": {}, "output_type": "execute_result" } @@ -190,7 +190,7 @@ }, { "cell_type": "code", - "execution_count": 5, + "execution_count": 4, "metadata": { "collapsed": true }, @@ -223,7 +223,7 @@ }, { "cell_type": "code", - "execution_count": 6, + "execution_count": 5, "metadata": { "collapsed": true }, @@ -247,7 +247,7 @@ }, { "cell_type": "code", - "execution_count": 7, + "execution_count": 6, "metadata": { "collapsed": true }, @@ -282,7 +282,7 @@ }, { "cell_type": "code", - "execution_count": 8, + "execution_count": 7, "metadata": {}, "outputs": [ { @@ -333,7 +333,7 @@ "dtype: float64" ] }, - "execution_count": 8, + "execution_count": 7, "metadata": {}, "output_type": "execute_result" } @@ -352,7 +352,7 @@ }, { "cell_type": "code", - "execution_count": 9, + "execution_count": 8, "metadata": { "collapsed": true }, @@ -381,7 +381,7 @@ }, { "cell_type": "code", - "execution_count": 10, + "execution_count": 9, "metadata": { "scrolled": true }, @@ -434,7 +434,7 @@ "dtype: float64" ] }, - "execution_count": 10, + "execution_count": 9, "metadata": {}, "output_type": "execute_result" } @@ -454,7 +454,7 @@ }, { "cell_type": "code", - "execution_count": 11, + "execution_count": 10, "metadata": {}, "outputs": [ { @@ -463,7 +463,7 @@ "0.37943042989926101" ] }, - "execution_count": 11, + "execution_count": 10, "metadata": {}, "output_type": "execute_result" } @@ -498,7 +498,7 @@ }, { "cell_type": "code", - "execution_count": 12, + "execution_count": 11, "metadata": { "collapsed": true }, @@ -538,7 +538,7 @@ }, { "cell_type": "code", - "execution_count": 13, + "execution_count": 12, "metadata": { "collapsed": true }, @@ -563,7 +563,7 @@ }, { "cell_type": "code", - "execution_count": 14, + "execution_count": 13, "metadata": { "collapsed": true }, @@ -592,7 +592,7 @@ }, { "cell_type": "code", - "execution_count": 15, + "execution_count": 14, "metadata": {}, "outputs": [ { @@ -606,7 +606,7 @@ "data": { "image/png": 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tivt/HYP29vaEh4fTu3dvs3tUqlSJq1evAuCYbyTK7WLOHUatFJhFfLv3Yi0W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\niQpBEAShM0hUCIIgCJ1BokIQBEHojP8DRPD4ChRIKg0AAAAASUVORK5CYII=\n", "text/plain": [ - "" + "" ] }, "metadata": {}, @@ -636,7 +636,7 @@ }, { "cell_type": "code", - "execution_count": 16, + "execution_count": 15, "metadata": { "collapsed": true }, @@ -668,7 +668,7 @@ }, { "cell_type": "code", - "execution_count": 17, + "execution_count": 16, "metadata": {}, "outputs": [ { @@ -741,7 +741,7 @@ "4 0.972517 0.014988 0.012494" ] }, - "execution_count": 17, + "execution_count": 16, "metadata": {}, "output_type": "execute_result" } @@ -767,14 +767,14 @@ }, { "cell_type": "code", - "execution_count": 18, + "execution_count": 17, "metadata": {}, "outputs": [ { "data": { "image/png": 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tivt/HYP29vaEh4fTu3dvs3tUqlSJq1evAuCYbyTK7WLOHUatFJhFfLv3Yi0W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\ndu7ciejoaAQEBCApKQmNjY1q137++eeIi4tDYGAg/P398cw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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -795,14 +795,14 @@ }, { "cell_type": "code", - "execution_count": 19, + "execution_count": 18, "metadata": {}, "outputs": [ { "data": { "image/png": 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+/vj7+xMYGMjYsWM5V3iv2P/RFln/In/48a5du9i3bx8LFy7k448/5ptvvrnt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\nMoSXVBYvXgygOgndvn0b9+7dQ1paGgBwq/h5eXnBwsIChw8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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -839,7 +839,7 @@ }, { "cell_type": "code", - "execution_count": 20, + "execution_count": 19, "metadata": { "collapsed": true }, @@ -865,7 +865,7 @@ }, { "cell_type": "code", - "execution_count": 21, + "execution_count": 20, "metadata": {}, "outputs": [ { @@ -908,7 +908,7 @@ }, { "cell_type": "code", - "execution_count": 22, + "execution_count": 21, "metadata": {}, "outputs": [ { @@ -917,7 +917,7 @@ "0.043536202687592354" ] }, - "execution_count": 22, + "execution_count": 21, "metadata": {}, "output_type": "execute_result" } @@ -932,7 +932,7 @@ }, { "cell_type": "code", - "execution_count": 23, + "execution_count": 22, "metadata": { "scrolled": true }, @@ -943,7 +943,7 @@ "30" ] }, - "execution_count": 23, + "execution_count": 22, "metadata": {}, "output_type": "execute_result" } @@ -958,7 +958,7 @@ }, { "cell_type": "code", - "execution_count": 24, + "execution_count": 23, "metadata": {}, "outputs": [ { @@ -967,7 +967,7 @@ "0.00067419431560344738" ] }, - "execution_count": 24, + "execution_count": 23, "metadata": {}, "output_type": "execute_result" } @@ -982,7 +982,7 @@ }, { "cell_type": "code", - "execution_count": 25, + "execution_count": 24, "metadata": { "collapsed": true, "scrolled": true @@ -994,7 +994,7 @@ }, { "cell_type": "code", - "execution_count": 26, + "execution_count": 25, "metadata": { "collapsed": true }, @@ -1005,7 +1005,7 @@ }, { "cell_type": "code", - "execution_count": 27, + "execution_count": 26, "metadata": { "collapsed": true }, @@ -1030,7 +1030,7 @@ }, { "cell_type": "code", - "execution_count": 28, + "execution_count": 27, "metadata": { "collapsed": true }, @@ -1057,7 +1057,7 @@ }, { "cell_type": "code", - "execution_count": 29, + "execution_count": 28, "metadata": {}, "outputs": [ { @@ -1066,7 +1066,7 @@ "(0.3333333333333333, 0.25)" ] }, - "execution_count": 29, + "execution_count": 28, "metadata": {}, "output_type": "execute_result" } @@ -1091,7 +1091,7 @@ }, { "cell_type": "code", - "execution_count": 30, + "execution_count": 29, "metadata": {}, "outputs": [ { @@ -1100,7 +1100,7 @@ "0.46832081102878098" ] }, - "execution_count": 30, + "execution_count": 29, "metadata": {}, "output_type": "execute_result" } @@ -1119,7 +1119,7 @@ }, { "cell_type": "code", - "execution_count": 31, + "execution_count": 30, "metadata": {}, "outputs": [ { @@ -1128,7 +1128,7 @@ "0.30650802853979753" ] }, - "execution_count": 31, + "execution_count": 30, "metadata": {}, "output_type": "execute_result" } @@ -1151,7 +1151,7 @@ }, { "cell_type": "code", - "execution_count": 32, + "execution_count": 31, "metadata": {}, "outputs": [ { @@ -1165,7 +1165,7 @@ "data": { "image/png": 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Pvr6+//jVkrhZuLGg5wJmdJmh1qaSWZhJ+OlwsooavjpQR1uLgd3aoPXA+JXj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\nVngPADU1NU5VYoC9mkwul0Msvnh7HBkZCQCoqKi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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -1191,7 +1191,7 @@ }, { "cell_type": "code", - "execution_count": 33, + "execution_count": 32, "metadata": {}, "outputs": [ { @@ -1230,7 +1230,7 @@ }, { "cell_type": "code", - "execution_count": 34, + "execution_count": 33, "metadata": { "collapsed": true }, @@ -1261,7 +1261,7 @@ }, { "cell_type": "code", - "execution_count": 35, + "execution_count": 34, "metadata": { "collapsed": true }, @@ -1280,7 +1280,7 @@ }, { "cell_type": "code", - "execution_count": 36, + "execution_count": 35, "metadata": {}, "outputs": [ { @@ -1294,7 +1294,7 @@ "data": { "image/png": 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vbx5gEMDFxYWJEydy+PDhaguwLlGpVHQsNWPhsXPSsVAI0XhZlUDy8/Px9PSs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\nuvb29ubxs2xsbl5ap9Ph4OBwT+cWNet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4Qtljew7+/vtv+Pj4QCgUYubMmQgMDERDQ4Mc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\nQ1tbG/b29lBQUMCpU6dQV1eH4cOHIyQkBGFhYYiLi0NtbS1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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -1335,13 +1335,13 @@ }, { "cell_type": "code", - "execution_count": 37, + "execution_count": 53, "metadata": { "collapsed": true }, "outputs": [], "source": [ - "def logistic(x, A=0, B=1, C=1, M=0, K=1, Q=1, nu=1):\n", + "def logistic(x, A=0, B=100, C=1, M=0, K=1, Q=1, nu=1):\n", " \"\"\"Computes the generalize logistic function.\n", " \n", " A: controls the lower bound\n", @@ -1368,7 +1368,7 @@ }, { "cell_type": "code", - "execution_count": 38, + "execution_count": 54, "metadata": {}, "outputs": [ { @@ -1379,7 +1379,7 @@ " 960., 1020., 1080., 1140., 1200.])" ] }, - "execution_count": 38, + "execution_count": 54, "metadata": {}, "output_type": "execute_result" } @@ -1404,7 +1404,7 @@ }, { "cell_type": "code", - "execution_count": 39, + "execution_count": 55, "metadata": { "collapsed": true }, @@ -1429,7 +1429,7 @@ }, { "cell_type": "code", - "execution_count": 40, + "execution_count": 56, "metadata": {}, "outputs": [ { @@ -1443,7 +1443,7 @@ "data": { "image/png": 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h2sIUro6mMDKg5NFc8R79lxDSPEjK5YhNfIz45CfcYICVGIaBo7URlzwM9ERa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\n", "text/plain": [ - "" + "" ] }, "metadata": {}, @@ -1486,7 +1486,7 @@ }, { "cell_type": "code", - "execution_count": 41, + "execution_count": 57, "metadata": { "collapsed": true }, @@ -1511,7 +1511,7 @@ }, { "cell_type": "code", - "execution_count": 42, + "execution_count": 58, "metadata": {}, "outputs": [ { @@ -1520,7 +1520,7 @@ "(0.3333333333333333, 0.25)" ] }, - "execution_count": 42, + "execution_count": 58, "metadata": {}, "output_type": "execute_result" } @@ -1544,7 +1544,7 @@ }, { "cell_type": "code", - "execution_count": 43, + "execution_count": 59, "metadata": {}, "outputs": [ { @@ -1586,7 +1586,7 @@ }, { "cell_type": "code", - "execution_count": 44, + "execution_count": 60, "metadata": { "collapsed": true }, @@ -1617,7 +1617,7 @@ }, { "cell_type": "code", - "execution_count": 45, + "execution_count": 61, "metadata": { "collapsed": true }, @@ -1636,7 +1636,7 @@ }, { "cell_type": "code", - "execution_count": 46, + "execution_count": 62, "metadata": {}, "outputs": [ { @@ -1650,7 +1650,7 @@ "data": { "image/png": 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bt2/Hx8enssOpshKSb/P7wQSj0RDMzdREBHkQ6u+Omdx8KkS1UlafnTJMsfjL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\n8OWXX+LTTz9t8La0tbUBgNWSAQAWFhY4e/Zso+rZVGjiaQQ9Pb0an2Z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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -1691,7 +1691,7 @@ }, { "cell_type": "code", - "execution_count": 47, + "execution_count": 63, "metadata": {}, "outputs": [ { @@ -1700,7 +1700,7 @@ "12" ] }, - "execution_count": 47, + "execution_count": 63, "metadata": {}, "output_type": "execute_result" } @@ -1725,7 +1725,7 @@ }, { "cell_type": "code", - "execution_count": 48, + "execution_count": 64, "metadata": {}, "outputs": [ { @@ -1770,7 +1770,7 @@ }, { "cell_type": "code", - "execution_count": 49, + "execution_count": 65, "metadata": { "collapsed": true }, @@ -1807,7 +1807,7 @@ }, { "cell_type": "code", - "execution_count": 50, + "execution_count": 66, "metadata": { "collapsed": true }, @@ -1825,7 +1825,7 @@ }, { "cell_type": "code", - "execution_count": 51, + "execution_count": 67, "metadata": {}, "outputs": [ { @@ -1839,7 +1839,7 @@ "data": { "image/png": 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Z2YVdE/ft20d+fj5PP/20cb+9vT1bt241qz5CiMqhKAo79p/n/MWrxrKwNvVM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\nhEIh9+Pq6sr8/PxYRESE0qioemKxmK1cuZL169ePeXh4sBEjRrA9e/Y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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -1875,14 +1875,14 @@ }, { "cell_type": "code", - "execution_count": 52, + "execution_count": 68, "metadata": {}, "outputs": [ { "data": { "image/png": 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xb98+eHl59UhwA9HdTynXs8Sob2xWYTSEENJ9OJVeWbFiBSIiIjB+/HiMGTMG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\nIjkXOXn1A5JX71SgTs0QGujSKU//3LhXwX1xAED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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -1912,7 +1912,7 @@ }, { "cell_type": "code", - "execution_count": 53, + "execution_count": 69, "metadata": { "collapsed": true }, @@ -1923,6 +1923,15 @@ " system.init.I -= quarantine_rate " ] }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [] + }, { "cell_type": "code", "execution_count": null, From 452469e6af508c0d134225cc6df3e4b6b2c9251b Mon Sep 17 00:00:00 2001 From: Junwon Lee <31522211+junwonlee5@users.noreply.github.com> Date: Thu, 12 Oct 2017 20:13:25 -0400 Subject: [PATCH 10/19] Adding chap07mine --- code/chap07mine.ipynb | 1941 +++++++++++++++++++++++++++++++++++++++++ 1 file changed, 1941 insertions(+) create mode 100644 code/chap07mine.ipynb diff --git a/code/chap07mine.ipynb b/code/chap07mine.ipynb new file mode 100644 index 00000000..4cc3e1c3 --- /dev/null +++ b/code/chap07mine.ipynb @@ -0,0 +1,1941 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Modeling and Simulation in Python\n", + "\n", + "Chapter 7: Thermal systems\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": 2, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "# If you want the figures to appear in the notebook, \n", + "# and you want to interact with them, use\n", + "# %matplotlib notebook\n", + "\n", + "# If you want the figures to appear in the notebook, \n", + "# and you don't want to interact with them, use\n", + "# %matplotlib inline\n", + "\n", + "# If you want the figures to appear in separate windows, use\n", + "# %matplotlib qt5\n", + "\n", + "# tempo switch from one to another, you have to select Kernel->Restart\n", + "\n", + "%matplotlib inline\n", + "\n", + "from modsim import *" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### The coffee cooling problem.\n", + "\n", + "I'll use a `State` object to store the initial temperature.\n" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
\n", + "\n", + "\n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + "
value
temp90
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"outputs": [ + { + "data": { + "image/png": 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sbCxJQnQp3V0scbYz5ZfTOZxLuwxAdW09O4+kk5xRzPBgd8yM5alCdH0aTYFd\nunQppqamLFmyhMjISKKjo/n3v//NhAkTUCgUfP75520dpxDtzshAj8gQD/40tAfmJgbq9rTcUr7a\nkcC5tCJUKpUWIxSi7WmUJM6dO8eMGTMYOXIkkZGR5OXlERkZyeuvv86YMWNYuXJlW8cphNZ4OFnw\naIwfAV526raaOiV7YzP5/uAFSitqb/JuITo3jZKEUqnEyckJAE9PT5KTk9XHRo4cecMV2UJ0JQb6\nukT0d2NMhDcWplefKjLzy/hqZwKnkgtpaJCnCtH1aJQkPDw8SElJAaBHjx5UVVWRlpYGNA5eV1RU\ntF2EQnQgrvZmPBrTk36+9urB67r6Bg6ezGbL/hQul1ZrOUIhWpdGSWL06NG89957fP3119jY2ODv\n78+//vUvfv75Z1auXImXl1dbxylEh6Gvp0N4X1ceHuGNjYWRuj23qIL1uxKJPZ+PUp4qRBehUZL4\n61//ypgxYzh8+DAAr776KqdPn2bq1KkkJSXx/PPPt2mQQnRETramPHKfL6G9ndD57alC2aDicHwu\nm/YkUVhcpeUIhbh7Gk2Bzc/P55VXXlH/f2BgILt37yYlJQUvLy8sLKTGjbg36erqEOrvhJebJXuO\nZVJQXAlAYUkVG/ckEeRnz4DeTujpSsVk0Tlp9Df34Ycf5vvvv2/WZm5uTlBQkCQIIQBbS2PGRfow\nJNBFnRAaVCriEgr4elciOZfKtRyhEHdGoyShUCiwtrZu61iE6NR0dBQE+TkwMdoPV3szdXtJWQ2b\n96VwQLZMFZ2QRkni73//O++++y67du0iMzOToqKi6340VVlZycKFCwkPDyckJIRp06apZ04BHDp0\niAcffJDAwEAeeOABKUMuOh0rc0MeGu5FRH+3ZrvdnUm9xLodCeqd8YToDDQak3j//fepqalh5syZ\nLb7m/PnzGn3gW2+9xfHjx1m2bBlWVlYsWbKEadOmsWPHDjIzM5k+fTrPPPMMMTExbN26lb///e9s\n2bIFHx8fza5IiA5AoVAQ4GVHN2cLDhzPIi23FGgsQ77t5zR83K0Z2s9FCgaKDk+jJPHyyy+32gfu\n3r2bZ599luDgYABmz57N6NGjSUlJYf369fTr14/p06cDMGvWLOLi4lizZg0LFy5stRiEaC9mJgaM\nGtKdlKzGLVObypAnZxaTmV9GeD8X/DyspWCg6LA0rgLbWmxsbNi+fTujRo3C3NycTZs2YWlpibu7\nO7GxsYzyvI6TAAAgAElEQVQcObLZ68PCwti2bVurfb4Q7a1pcyN3B3MOncomIb2xDHl1bT27j2aQ\nlFFMRH/3Ziu5hegoNN5yS6VS8eOPP/LLL79QWFjIvHnzOH36NP7+/vTo0UPjD1y4cCHPP/88gwcP\nRldXFyMjIz7//HMsLCzIy8vD0dGx2esdHBzIy8vT/IqE6KCMDPW4L9QTHw9rDhzPUtd8yshrLO0x\n0N+ZPt526OjIU4XoODQauC4vL2fSpEnMnj2bQ4cOceDAAcrLy/n222+ZMGECCQkJGn9geno6dnZ2\nrFq1iq+++orw8HBmzpxJXl4e1dXVGBg0/23KwMCAmpqa27sqITowz98KBvb1+V1pj1PZfLMvmaIr\nsghPdBwaJYl3332XjIwMNm/ezK5du9TlkT/44AO6devGBx98oNGHZWZmsmDBAubPn8/w4cPp27cv\nixcvxtDQkP/85z8YGhpSV1fX7D21tbUYGxvf5mUJ0bHp6+kytF9jaQ/ba0p75F+uZP2uJA7H51Kv\nbNBihEI00ihJ7Nq1izlz5tC7d+9mA2zm5uY8/fTTnDhxQqMPi4+PR6lUEhAQoG7T19enV69epKen\n4+zsTEFBQbP3FBQUXNcFJURX4WRryoT7fAn1d1J3MzWoVMSez+frXYlkF8oiPKFdGiWJyspKbG1t\nb3jM0NBQ4+6gpnLjiYmJ6jaVSkVqairdunUjODiYY8eONXvPkSNHCAkJ0ej8QnRGuro6hPZ2YmK0\nH862pur2krIatuxPYV9cJtW19VqMUNzLNEoS/v7+bNiw4YbHfvjhB3r37q3RhwUGBtKvXz9eeukl\nYmNjSU1N5dVXXyUnJ4fJkyczefJkYmNj+fDDD0lNTWXZsmWcOnWKJ598UvMrEqKTsrEwYuwI7+sW\n4Z29UMS6HYmkZJXITnii3Wk0u+m5555j6tSpjBs3joiICBQKBTt37mTVqlXs3r2bTz75RKMP09XV\nZeXKlSxZsoQ5c+ZQWVlJQEAA69atw9XVFYAVK1bw3nvv8emnn9KjRw8+/vhjKUUu7hnqRXgulvx0\nIosL2Y2rsyur6/jx14t0d7FkeH832V9btBuFSsNfTQ4fPszixYuJj49X/zbj5+fH7NmziYiIaMsY\nbykrK4uoqCj27NmDm5ubVmMRojWl/rYIr6L66oQOA31dBgU4E+BlK4vwxF3R5LtT43USAwcOZOPG\njVRUVHDlyhXMzc0xNzdvtWCFENfzcrPC1cGMw2dyib/QWCOttk7JgRNZjYvwgt2wtZTZf6LtaJwk\nAH7++WdiY2MpLS3F1taWgQMH0r9//7aKTQgBGBnoERHsjq+HNXvjMikpa5wokltUwfrdSfT3cyCk\nl6PsWSHahEZJoqSkhKeffpqTJ0+ip6eHlZUVJSUlLF++nGHDhrF8+fLrFsEJIVqXi70ZE6P9iDuf\nT1xiAQ0NKhoaGqfLpmSWEBHshpuDPN2L1qXRrx5vvvkmaWlprFixgjNnznDo0CFOnz7NsmXLOHny\nJIsXL27rOIUQgJ6uDmEBztdPly2v4dsDqew5lkF1jUyXFa1HoyTx008/8cILL3DfffepB8p0dHSI\niYnhH//4B//73//aNEghRHPXTpc1vGa67PmLl1m7I4HE9MsyXVa0Co13prOysrrhMQcHB2pra1s1\nKCHErTVNl33s/p54u13991lVU8+uoxl8f/ACV8ql7pm4OxoliUcffZQPPviAwsLCZu0VFRWsXr2a\nxx57rE2CE0LcmqmxPn8Y1I3RQ7o3Wz+RmV/GVzsTiUvIR9kgTxXizmg0cH358mXy8vK47777GDBg\nAA4ODpSUlBAXF0dZWRmGhob85S9/ARp/u1m1alWbBi2EuF53F0vcHMw4HJ/H6ZRLqFQq6pUN/Hom\nl6SMEkYEu+F0zTiGEJrQKEmkpKSotw+trKzk4sWLAOqV0FVVUtpYiI6gqbqsn4c1++IyKSxp/LdZ\ndKWKb/al4N/DloEBThgZ3Nbsd3EP0+hvyrp169o6DiFEK3KwMWF8lC8nkws5djaPOmUDKpWK+NRL\nXMi+wtB+Lni7WcmKbXFLt/XrRG1tLWVlZTc81lKVWCGEdujoKOjv54C3mxUHjmeRnlcKNNaB2nE4\nnfNOlxke5IalmaGWIxUdmUZJIjExkXnz5pGQkNDitLrz58+3amBCiNZhYWrAH8O7k5p9hYPX1IFq\n3DY1kdDeTvT1tUdXtk0VN6BRknj11VfJz89n9uzZLU6FFUJ0XAqFAm83K9wdzdV1oJoGtn85k0Ni\n+mVGhLjLwLa4jkZJIiEhgSVLlhAZGdnW8Qgh2pChvi7D+7vh52nN/uNZXGoa2C6tbhzY7m7DwD7O\nMrAt1DRaJ+Hm5qbx7nNCiI7PydaU8VG+DA50Qf+3woAqlYr43zY4SsoolhXbAtAwScyaNYtly5YR\nFxcnq6uF6CJ0fxvYfvT+nnRztlC3V1bXsfNIOt8fvKCuOCvuXRo9U/r4+NDQ0MDkyZOBxh3mfi8+\nPr51IxNCtAsLUwNGD2kc2D50MpvyqsaB7cYV2wkE93Ik2M8BXSlFfk/SKEm8+OKLXLlyhUceeQQ7\nO7u2jkkI0c6aBrY9HM05cvbqim1lg4qjZ/NIyihmeJAb7o5Sivxeo1GSOH/+PO+++y73339/W8cj\nhNAiA/3fVmx7WrM/LouC4koASspq+O6nVPw8rBnS1wUTI9lj+16h0fOjs7MzOjryqCnEvcLB2oRx\nkT4MD3LD4JpS5IkZxazdkUB86iUZ2L5HaPTNP3PmTJYuXcqJEydQKpVtHZMQogPQ0VHQx9uOSff3\nxMfdWt1eU6tk//EsvtmXop5CK7oujbqbVq1aRW5urrok+O+3KlUoFJw8ebL1oxNCaJ2psT73D/Sk\nZzdrfjqRrd6jIq+ogg27kwj0sSO0t1OzJw7RdWiUJCIiIto4DCFER+fpZMGjMWbN99hWqTiZVEhK\nZgnhfV3xcrOUooFdjEZJYtasWW0dhxCiE2jaY9vX05oDx7PJKmgs+FleVcePhy/i4WTOsH5uWJlL\n0cCu4rbW3p8+fZpffvmFwsJCpk2bRlpaGj179sTGxqat4hNCdEDW5kY8OKwHyZklHDqVQ2WzooGN\nayv6+zmgJ2srOj2NkkRdXR0vvvgi27dvR09PD6VSydixY/n0009JTU1l7dq1uLu7t3WsQogORKFQ\n4OthjYeTOUfP5nEmtaj52or0Yob3l7UVnZ1GaX7ZsmXs37+f5cuXc+zYMfXUt9dffx1jY2OWLl3a\npkEKITouIwM9hgW5MT7SBwdrE3V7SXnj2oodhy+qV3GLzkejJPH9998zZ84coqOjm81s8vDwYObM\nmRw5cqTNAhRCdA4ONlfXVhheM9MpObOEdTsSOJnUONgtOheNkkRJSQndu3e/4TFra2vKy8tbNSgh\nROekXlvxh574eVxdW1Fbp+TQqRzW704i55J8X3QmGiUJb29vtm/ffsNjBw8exMvLq1WDEkJ0biZG\n+kSHefLQcC+szY3U7UVXqti8L4U9xzLUg92iY9No4Ppvf/sbzz33HGVlZYwYMUK9eG7btm18+eWX\nvPPOO20dpxCiE3JzMGditC+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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plot(coffee.results.temp, label='coffee')\n", + "decorate(xlabel='Time (minutes)',\n", + " ylabel='Temperature (C)')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "After running the simulation, we can extract the final temperature from the results." + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def final_temp(system):\n", + " \"\"\"Final temperature.\n", + " \n", + " If system has no results, return initial temp.\n", + " \n", + " system: System object.\n", + " \n", + " returns: temperature (degC)\n", + " \"\"\" \n", + " if hasattr(system, 'results'):\n", + " return system.results.temp[system.t_end]\n", + " else:\n", + " return system.init.temp" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "It will be convenient to wrap these steps in a function. `kwargs` is a collection of whatever keyword arguments are provided; they are passed along as arguments to `System`." + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def make_system(T_init=90, r=0.01, volume=300, t_end=30):\n", + " \"\"\"Runs a simulation with the given parameters.\n", + "\n", + " T_init: initial temperature in degC\n", + " r: heat transfer rate, in 1/min\n", + " volume: volume of liquid in mL\n", + " t_end: end time of simulation\n", + " \n", + " returns: System object\n", + " \"\"\"\n", + " init = State(temp=T_init)\n", + " \n", + " system = System(init=init,\n", + " volume=volume,\n", + " r=r,\n", + " T_env=22, \n", + " t0=0,\n", + " t_end=t_end,\n", + " dt=1)\n", + " return system" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here's how we use it:" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "72.299625390403094" + ] + }, + "execution_count": 12, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "coffee = make_system()\n", + "run_simulation(coffee, update)\n", + "final_temp(coffee)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Exercise:** Simulate the temperature of 50 mL of milk with a starting temperature of 5 degC, in a vessel with the same insulation, for 15 minutes, and plot the results." + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "20.001356278974139" + ] + }, + "execution_count": 13, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Solution goes here\n", + "def make_system(T_init=5, r=0.133, volume=50, t_end=15):\n", + " \"\"\"Runs a simulation with the given parameters.\n", + "\n", + " T_init: initial temperature in degC\n", + " r: heat transfer rate, in 1/min\n", + " volume: volume of liquid in mL\n", + " t_end: end time of simulation\n", + " \n", + " returns: System object\n", + " \"\"\"\n", + " init = State(temp=T_init)\n", + " \n", + " system = System(init=init,\n", + " volume=volume,\n", + " r=r,\n", + " T_env=22, \n", + " t0=0,\n", + " t_end=t_end,\n", + " dt=1)\n", + " return system\n", + "milk = make_system()\n", + "run_simulation(milk, update)\n", + "final_temp(milk)" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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MuByMGdgT7o4WOoyMEKIOKmWMFStWoLi4GBwOR/pzP9nk5OTg3Xff1WiQpOtr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\nhxBCiCIo4RBCCFEEJRxCCCGK+A+BfG1w3zM5TgAAAABJRU5ErkJggg==\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plot(milk.results.temp, label='milk')\n", + "decorate(xlabel='Time (minutes)',\n", + " ylabel='Temperature (C)')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Using `fsolve`\n", + "\n", + "As a simple example, let's find the roots of this function; that is, the values of `x` that make the result 0." + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def func(x):\n", + " return (x-1) * (x-2) * (x-3)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "`modsim.py` provides `fsolve`, which does some error-checking and then runs `scipy.optimize.fsolve`. The first argument is the function whose roots we want. The second argument is an initial guess." + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([ 1.])" + ] + }, + "execution_count": 16, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "fsolve(func, x0=0)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Usually the root we get is the one that's closest to the initial guess." + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([ 2.])" + ] + }, + "execution_count": 17, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "fsolve(func, 1.9)" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([ 3.])" + ] + }, + "execution_count": 18, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "fsolve(func, 2.9)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "But not always." + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([ 3.])" + ] + }, + "execution_count": 19, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "fsolve(func, 1.5)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We want to find the value of `r` that makes the final temperature 70, so we define an \"error function\" that takes `r` as a parameter and returns the difference between the final temperature and the goal." + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def make_system(T_init=90, r=0.01, volume=300, t_end=30):\n", + " \"\"\"Runs a simulation with the given parameters.\n", + "\n", + " T_init: initial temperature in degC\n", + " r: heat transfer rate, in 1/min\n", + " volume: volume of liquid in mL\n", + " t_end: end time of simulation\n", + " \n", + " returns: System object\n", + " \"\"\"\n", + " init = State(temp=T_init)\n", + " \n", + " system = System(init=init,\n", + " volume=volume,\n", + " r=r,\n", + " T_env=22, \n", + " t0=0,\n", + " t_end=t_end,\n", + " dt=1)\n", + " return system\n", + "def error_func1(r):\n", + " \"\"\"Runs a simulation and returns the `error`.\n", + " \n", + " r: heat transfer rate, in 1/min\n", + " \n", + " returns: difference between final temp and 70 C\n", + " \"\"\"\n", + " system = make_system(r=r)\n", + " run_simulation(system, update)\n", + " return final_temp(system) - 70" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "With `r=0.01`, we end up a little too warm." + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "2.2996253904030937" + ] + }, + "execution_count": 21, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "error_func1(r=0.01)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The return value from `fsolve` is an array with a single element, the estimated value of `r`." + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "0.011543084583978345" + ] + }, + "execution_count": 22, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "solution = fsolve(error_func1, 0.01, xtol=1e-8)\n", + "r_coffee = solution[0]\n", + "r_coffee" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "If we run the simulation with the estimated value of `r`, the final temperature is 70 C, as expected." + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "70.0" + ] + }, + "execution_count": 23, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "coffee = make_system(r=r_coffee)\n", + "run_simulation(coffee, update)\n", + "final_temp(coffee)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Exercise:** When you call `fsolve`, it calls `error_func1` several times. To see how this works, add a print statement to `error_func1` and run `fsolve` again." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Exercise:** Repeat this process to estimate `r_milk`, given that it starts at 5 C and reaches 20 C after 15 minutes. \n", + "\n", + "Before you use `fsolve`, you might want to try a few values for `r_milk` and see how close you can get by trial and error. Here's an initial guess to get you started:" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "20.001356278974139" + ] + }, + "execution_count": 24, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "r_milk = 0.133\n", + "milk = make_system(T_init=5, t_end=15, r=r_milk)\n", + "run_simulation(milk, update)\n", + "final_temp(milk)" + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "# Solution goes here\n", + "def error_func1(r):\n", + " \"\"\"Runs a simulation and returns the `error`.\n", + " \n", + " r: heat transfer rate, in 1/min\n", + " \n", + " returns: difference between final temp and 70 C\n", + " \"\"\"\n", + " system = make_system(r=r, T_init=5, volume=50, t_end=15)\n", + " run_simulation(system, update)\n", + " print(final_temp(system) - 20)\n", + " return final_temp(system) - 20" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "-12.6209920289\n" + ] + }, + { + "data": { + "text/plain": [ + "-12.620992028901906" + ] + }, + "execution_count": 26, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Solution goes here\n", + "error_func1(r=0.01)" + ] + }, + { + "cell_type": "code", + "execution_count": 52, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "-1.50014924561\n", + "[-1.50014925]\n", + "[-1.50014925]\n", + "[-1.50014925]\n", + "[-1.50014916]\n", + "[-0.26588969]\n", + "[-0.05982148]\n", + "[-0.00336028]\n", + "[ -4.59700669e-05]\n", + "[ -3.60040175e-08]\n", + "[ -3.87245791e-13]\n" + ] + }, + { + "data": { + "text/plain": [ + "0.13296078935465339" + ] + }, + "execution_count": 52, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Solution goes here\n", + "rate = fsolve(error_func1, 0.1)\n", + "coolrate = rate[0]\n", + "coolrate" + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "19.999999999999613" + ] + }, + "execution_count": 28, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Solution goes here\n", + "milk = make_system(T_init=5, t_end=15, r=coolrate)\n", + "run_simulation(milk, update)\n", + "final_temp(milk)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Mixing liquids" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The following function takes `System` objects that represent two liquids, computes the temperature of the mixture, and returns a new `System` object that represents the mixture." + ] + }, + { + "cell_type": "code", + "execution_count": 29, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def mix(s1, s2):\n", + " \"\"\"Simulates the mixture of two liquids.\n", + " \n", + " s1: System representing coffee\n", + " s2: System representing milk\n", + " \n", + " returns: System representing the mixture\n", + " \"\"\"\n", + " assert s1.t_end == s2.t_end\n", + " \n", + " volume = s1.volume + s2.volume\n", + " \n", + " temp = (s1.volume * final_temp(s1) + \n", + " s2.volume * final_temp(s2)) / volume\n", + " \n", + " mixture = make_system(T_init=temp,\n", + " volume=volume,\n", + " r=s1.r)\n", + " \n", + " return mixture" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "First we'll see what happens if we add the milk at the end. We'll simulate the coffee and the milk separately." + ] + }, + { + "cell_type": "code", + "execution_count": 30, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "70.0" + ] + }, + "execution_count": 30, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "coffee = make_system(T_init=90, t_end=30, r=r_coffee, volume=300)\n", + "run_simulation(coffee, update)\n", + "final_temp(coffee)" + ] + }, + { + "cell_type": "code", + "execution_count": 31, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "21.765024898611991" + ] + }, + "execution_count": 31, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "milk = make_system(T_init=5, t_end=30, r=r_milk, volume=50)\n", + "run_simulation(milk, update)\n", + "final_temp(milk)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here's what the results look like." + ] + }, + { + "cell_type": "code", + "execution_count": 32, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Saving figure to file chap07-fig01.pdf\n" + ] + }, + { + "data": { + "image/png": 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GjcOYMWNqHBAhhLibh9VCNDojV+uomDxKVDooHzIiy/SQpiwBnwe5TIzuHcLQNEhmd58q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\nREmCEEKIQ5QkCCGEOERJghBCiEP/D/rzhDHPnHAaAAAAAElFTkSuQmCC\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plot(coffee.results.temp, label='coffee')\n", + "plot(milk.results.temp, '--', label='milk')\n", + "decorate(xlabel='Time (minutes)',\n", + " ylabel='Temperature (C)',\n", + " loc='center left')\n", + "\n", + "savefig('chap07-fig01.pdf')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here's what happens when we mix them." + ] + }, + { + "cell_type": "code", + "execution_count": 33, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "63.109289271230288" + ] + }, + "execution_count": 33, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "mix_last = mix(coffee, milk)\n", + "final_temp(mix_last)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "And here's what we get if we add the milk immediately." + ] + }, + { + "cell_type": "code", + "execution_count": 34, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "coffee = make_system(T_init=90, r=r_coffee, volume=300)\n", + "milk = make_system(T_init=5, r=r_milk, volume=50)" + ] + }, + { + "cell_type": "code", + "execution_count": 35, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "61.428571428571438" + ] + }, + "execution_count": 35, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "mix_first = mix(coffee, milk)\n", + "mix_first.t_end = 30\n", + "run_simulation(mix_first, update)\n", + "final_temp(mix_first)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The following function takes `t_add`, which is the time when the milk is added, and returns the final temperature." + ] + }, + { + "cell_type": "code", + "execution_count": 36, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def run_and_mix(t_add, t_total=30):\n", + " \"\"\"Simulates two liquids and them mixes them at t_add.\n", + " \n", + " t_add: time in minutes\n", + " t_total: total time to simulate, min\n", + " \n", + " returns: final temperature\n", + " \"\"\"\n", + " coffee = make_system(T_init=90, t_end=t_add, \n", + " r=r_coffee, volume=300)\n", + " run_simulation(coffee, update)\n", + "\n", + " milk = make_system(T_init=5, t_end=t_add, \n", + " r=r_milk, volume=50)\n", + " run_simulation(milk, update)\n", + " \n", + " mixture = mix(coffee, milk)\n", + " mixture.t_end = t_total - t_add\n", + " run_simulation(mixture, update)\n", + "\n", + " return final_temp(mixture)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can try it out with a few values." + ] + }, + { + "cell_type": "code", + "execution_count": 37, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "61.428571428571438" + ] + }, + "execution_count": 37, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "run_and_mix(0)" + ] + }, + { + "cell_type": "code", + "execution_count": 38, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "62.90297191448969" + ] + }, + "execution_count": 38, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "run_and_mix(15)" + ] + }, + { + "cell_type": "code", + "execution_count": 39, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "63.109289271230288" + ] + }, + "execution_count": 39, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "run_and_mix(30)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "And then sweep a range of values for `t_add`" + ] + }, + { + "cell_type": "code", + "execution_count": 40, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "sweep = SweepSeries()\n", + "for t_add in linrange(0, 30, 2):\n", + " temp = run_and_mix(t_add)\n", + " sweep[t_add] = temp" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here's what the result looks like." + ] + }, + { + "cell_type": "code", + "execution_count": 41, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Saving figure to file chap07-fig02.pdf\n" + ] + }, + { + "data": { + "image/png": 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PefPmodPp+PDDD2nZsqWhSfbUqVOZPXs23t7eDBgwgM2bN5OXl2dozi3qRmlB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\n7777rqEsMzOT7t27V7n9woULcXR0ZPn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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plot(sweep, color='purple')\n", + "decorate(xlabel='Time added (min)',\n", + " ylabel='Final temperature (C)',\n", + " legend=False)\n", + "\n", + "savefig('chap07-fig02.pdf')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Exercise:** Suppose the coffee shop won't let me take milk in a separate container, but I keep a bottle of milk in the refrigerator at my office. In that case is it better to add the milk at the coffee shop, or wait until I get to the office?\n", + "\n", + "Hint: Think about the simplest way to represent the behavior of a refrigerator in this model. The change you make to test this variation of the problem should be very small!" + ] + }, + { + "cell_type": "code", + "execution_count": 42, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "60.7142857143 61.4285714286\n" + ] + } + ], + "source": [ + "def run_and_mixfridge(t_add, t_total=30):\n", + " \"\"\"Simulates two liquids and them mixes them at t_add.\n", + " \n", + " t_add: time in minutes\n", + " t_total: total time to simulate, min\n", + " \n", + " returns: final temperature\n", + " \"\"\"\n", + " coffee = make_system(T_init=90, t_end=t_add, \n", + " r=r_coffee, volume=300)\n", + " run_simulation(coffee, update)\n", + "\n", + " milk = make_system(T_init=5, t_end=t_add, \n", + " r=0, volume=50)\n", + " run_simulation(milk, update)\n", + " \n", + " mixture = mix(coffee, milk)\n", + " mixture.t_end = t_total - t_add\n", + " run_simulation(mixture, update)\n", + "\n", + " return final_temp(mixture)\n", + "print(run_and_mixfridge(30), run_and_mix(0))" + ] + }, + { + "cell_type": "code", + "execution_count": 43, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "5.0" + ] + }, + "execution_count": 43, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "milk = make_system(T_init=5, t_end=t_add, \n", + " r=0, volume=50)\n", + "run_simulation(milk, update)\n", + "final_temp(milk)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Analysis" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now we can use the analytic result to compute temperature as a function of time. The following function is similar to `run_simulation`." + ] + }, + { + "cell_type": "code", + "execution_count": 44, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def run_analysis(system):\n", + " \"\"\"Computes temperature using the analytic solution.\n", + " \n", + " Adds TimeFrame to `system` as `results`\n", + " \n", + " system: System object\n", + " \"\"\"\n", + " unpack(system)\n", + " \n", + " T_init = init.temp \n", + " ts = linrange(t0, t_end, dt)\n", + " \n", + " temp_array = T_env + (T_init - T_env) * exp(-r * ts)\n", + " temp_series = TimeSeries(temp_array, index=ts)\n", + " \n", + " system.results = TimeFrame(temp_series, columns=['temp'])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here's how we run it. From the analysis, we have the computed value of `r_coffee2`" + ] + }, + { + "cell_type": "code", + "execution_count": 45, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "r_coffee2 = 0.011610223142273859" + ] + }, + { + "cell_type": "code", + "execution_count": 46, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "70.0" + ] + }, + "execution_count": 46, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "init = State(temp=90)\n", + "coffee2 = System(init=init, T_env=22, r=r_coffee2, \n", + " t0=0, t_end=30)\n", + "run_analysis(coffee2)\n", + "final_temp(coffee2)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "And we can compare to the results from simulation." + ] + }, + { + "cell_type": "code", + "execution_count": 47, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "70.0" + ] + }, + "execution_count": 47, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "init = State(temp=90)\n", + "coffee = System(init=init, T_env=22, r=r_coffee, \n", + " t0=0, t_end=30, dt=1)\n", + "run_simulation(coffee, update)\n", + "final_temp(coffee)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "They are identical except for small roundoff errors." + ] + }, + { + "cell_type": "code", + "execution_count": 48, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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frame.S[system.t_end]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here's an updated version of `run_simulation` that uses `unpack`." + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def run_simulation(system, update_func):\n", + " \"\"\"Runs a simulation of the system.\n", + " \n", + " Add a TimeFrame to the System: results\n", + " \n", + " system: System object\n", + " update_func: function that updates state\n", + " \"\"\"\n", + " unpack(system)\n", + " \n", + " frame = TimeFrame(columns=init.index)\n", + " frame.loc[t0] = init\n", + " \n", + " for i in linrange(t0, t_end):\n", + " frame.loc[i+1] = update_func(frame.loc[i], system)\n", + " \n", + " system.results = frame" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Exercise:** Write a version of `update1` that uses `unpack`." + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "# Original\n", + "\n", + "def update1(state, system):\n", + " \"\"\"Update the SIR model.\n", + " \n", + " state: State (s, i, r)\n", + " system: System object\n", + " \n", + " returns: State (sir)\n", + " \"\"\"\n", + " s, i, r = state\n", + "\n", + " infected = system.beta * i * s \n", + " recovered = system.gamma * i\n", + " \n", + " s -= infected\n", + " i += infected - recovered\n", + " r += recovered\n", + " \n", + " return State(S=s, I=i, R=r)" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "# Solution goes here\n", + "def update1(state, system):\n", + " \"\"\"Update the SIR model.\n", + " \n", + " state: State (s, i, r)\n", + " system: System object\n", + " \n", + " returns: State (sir)\n", + " \"\"\"\n", + " unpack(system)\n", + " s, i, r = state\n", + "\n", + " infected = beta * i * s \n", + " recovered = gamma * i\n", + " \n", + " s -= infected\n", + " i += infected - recovered\n", + " r += recovered\n", + " \n", + " return State(S=s, I=i, R=r)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Test the updated code with this example." + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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5hKtXr+Lm5sarr75KUFDQIze7EY8vNRVsbSElRZnHsns3nDsHw4crC1YKUVy0a9eOQYMG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\nAABJRU5ErkJggg==\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "frame = system.results\n", + "plot_results(frame.S, frame.I, frame.R)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Sweeping beta" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Make a range of values for `beta`, with constant `gamma`." + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "beta_array = linspace(0.1, 0.9, 11)\n", + "gamma = 0.25" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Run the simulation once for each value of `beta` and print total infections." + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "0.1 0.00723090166498\n", + "0.18 0.0262722567457\n", + "0.26 0.160575485321\n", + "0.34 0.490862856866\n", + "0.42 0.689867847411\n", + "0.5 0.804506112463\n", + "0.58 0.873610307851\n", + "0.66 0.916554007142\n", + "0.74 0.943729262152\n", + "0.82 0.961060480958\n", + "0.9 0.972099315633\n" + ] + } + ], + "source": [ + "for beta in beta_array:\n", + " system = make_system(beta, gamma)\n", + " run_simulation(system, update1)\n", + " print(system.beta, calc_total_infected(system))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Wrap that loop in a function and return a `SweepSeries` object." + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def sweep_beta(beta_array, gamma):\n", + " \"\"\"SweepSeriess a range of values for beta.\n", + " \n", + " beta_array: array of beta values\n", + " gamma: recovery rate\n", + " \n", + " returns: SweepSeries that maps from beta to total infected\n", + " \"\"\"\n", + " sweep = SweepSeries()\n", + " for beta in beta_array:\n", + " system = make_system(beta, gamma)\n", + " run_simulation(system, update1)\n", + " sweep[system.beta] = calc_total_infected(system)\n", + " return sweep" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "SweepSeries `beta` and plot the results." + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "infected_sweep = sweep_beta(beta_array, gamma)" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Saving figure to file chap06-fig01.pdf\n" + ] + }, + { + "data": { + "image/png": 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ZeJBRrHFrrK2lCfwljpC0sabZ2MSg9J4wlEol1q5diz179qCsrAzBwcFYunQp7O3ta93+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\nYehRzeXdqz1refe8vDyMHTsWKpUKO3f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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "label = 'gamma = ' + str(gamma)\n", + "plot(infected_sweep, label=label)\n", + "decorate(xlabel='Contacts per day (beta)',\n", + " ylabel='Fraction infected')\n", + "\n", + "savefig('chap06-fig01.pdf')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Sweeping gamma" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Using the same array of values for `beta`" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([ 0.1 , 0.18, 0.26, 0.34, 0.42, 0.5 , 0.58, 0.66, 0.74,\n", + " 0.82, 0.9 ])" + ] + }, + "execution_count": 15, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "beta_array = linspace(0.1, 0.9, 11)\n", + "beta_array" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "And now an array of values for `gamma`" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([ 0.1, 0.3, 0.5, 0.7])" + ] + }, + "execution_count": 16, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "gamma_array = linspace(0.1, 0.7, 4)\n", + "gamma_array" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "For each value of `gamma`, SweepSeries `beta` and plot the results." + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Saving figure to file chap06-fig02.pdf\n" + ] + }, + { + "data": { + "image/png": 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27VrWrVvHhg0bTCu9Z86ceU9ja0kYDAbiE9LILzYuRrORSXliYEfs7Wr/qQYO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\nezVUWlXjqxoKrRJatmOTg7ezJ7+CCHL1h0RkHhszIQTgON3TvloFTqn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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "for gamma in gamma_array:\n", + " infected_sweep = sweep_beta(beta_array, gamma)\n", + " label = 'gamma = ' + str(gamma)\n", + " plot(infected_sweep, label=label)\n", + " \n", + "decorate(xlabel='Contacts per day (beta)',\n", + " ylabel='Fraction infected',\n", + " loc='upper left')\n", + "\n", + "savefig('chap06-fig02.pdf')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now wrap that loop in a function and store the results in a `SweepSeriesFrame`" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def sweep_parameters(beta_array, gamma_array):\n", + " \"\"\"SweepSeriess a range of values for beta and gamma.\n", + " \n", + " beta_array: array of infection rates\n", + " gamma_array: array of recovery rates\n", + " \n", + " returns: SweepSeriesFrame with one row for each beta\n", + " and one column for each gamma\n", + " \"\"\"\n", + " frame = SweepFrame(columns=gamma_array)\n", + " for gamma in gamma_array:\n", + " frame[gamma] = sweep_beta(beta_array, gamma)\n", + " return frame" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here's what the results look like." + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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0.10.30.50.7
0.100.0846930.0054440.0027360.001827
0.180.7086230.0159140.0061180.003783
0.260.9007800.0553800.0116390.006427
0.340.9568880.2678640.0221150.010191
0.420.9770450.5245630.0478160.015946
\n", + "
" + ], + "text/plain": [ + " 0.1 0.3 0.5 0.7\n", + "0.10 0.084693 0.005444 0.002736 0.001827\n", + "0.18 0.708623 0.015914 0.006118 0.003783\n", + "0.26 0.900780 0.055380 0.011639 0.006427\n", + "0.34 0.956888 0.267864 0.022115 0.010191\n", + "0.42 0.977045 0.524563 0.047816 0.015946" + ] + }, + "execution_count": 19, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "frame = sweep_parameters(beta_array, gamma_array)\n", + "frame.head()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "And here's how we can plot the results." + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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TwQ1bIQ53RWJohYWLb9y4wYgRI4iPjycgIKCph9Mg5Ofnc/r0aQYNGoRMZlwop1KpiIyM\nZNu2bSbHsKZKx874JApLjNFCzo62PD2iO/Yin5OghWMwGFCV5ZtMTSp1Xp19ZVIZ7Zx8CHT1J9Cl\nHU52ykYcacvhbvdOcddoochkMqKjo4mKimLy5Mmo1Wo+/PBDOnToQFhYGGD8Qf10MtUkFjYyKWMe\n6STEQtBi0Wg13CjOIrXIKBJ3SqmhtHMk0KUdgS7+tHPywUYmvvcPivgEWyguLi588sknxMbGsmXL\nFuRyOREREcTFxSGXG1eF/noxh6vpt2y3w/u2rzdntkDQGBgMBgorikktSie1MIOs0pw6gyUkEgk+\nSi8CXfwJdG2Hm71LqwtrbWqEYLRgBg4cyMCBAy3uS8kq5vi5LNN2WDcvuge6NdbQBIL7RqvXkVGc\nRWpRBmlFGZRUltbZ115uT3tnPwJd/Qlw9hNO6gZGCEYrpKi0kh+Op5iexPy9lDzSs10Tj0ogqJvS\nSjWpRRmkFqWTXpx1x7BXT0d3k6nJy9FDzCIaESEYrYwqrZ7vjl6nUmP8wSkd5Dwe0QFZI6UZFwis\nQW/Qk12ae9PUlE7BHcJe5TI5/s6+RlOTSzsUtsKs2lQIwWhFGAwG9v2aRm5hOQAyqYQnBnZEYd88\nMl0K2jYGg4GsUhUXVJdJLcpAo617HY6LvTOBrsZZhK/SC5m08VPmC2ojBKMVcTo5l0upBabtweEB\n+HqIRWqCpkWn13G1IJUz2RfJVedb7COVSo1hrzdNTc72Thb7CZoWIRithAxVKYd/v5WwL6STBw93\n9mjCEQnaOhVVFZxXJXNelUSZprzWfkdbBe1vCoS/s0+9VoYTNAxCMFoBpeVVfHf0uik/lI+7giHh\n95aPSSCoL/LLCzmbfYnLeddqOa9lUhndPDoR4tUND4WbcFi3MIRgtHB0Oj3fHblGeaUxu6uDnQ2j\nB3ZEJmv+xVgErQeDwUBaUQZnsi+SXpxVa7/C1oGHvbvzkGdX7Ntw8r6WjhCMFs7B39LJzi8DQCox\nOrmVirYZi/7VV1/x0UcfkZmZSXBwMAsXLqRnz5519v/1119ZuXIlFy5cwMnJifHjxxMdHW2xCqDA\nMlW6Ki7nXeNM9iWKKopr7fd0dKeHTzCd3QKF47oVIASjBXP+Wh5nr97Kn/NITz/8vdpmjpwjR47w\n3nvvsWjRIvr27cvmzZt56aWX+P777y1W8EtPT+fll1/m6aefJiYmhhs3bjBv3jy0Wi3vvvtuE7yD\nlkWpRs25nCQuqJJrRztJJHRybU8PnyB8lF7C7NSKEILRQsnOL2N/4q3iRt3auxHWzfoCTK2NTZs2\nMW7cOJ555hkAli5dyrFjx9i5c6fFYk3p6emMGjXKJA6BgYGMGTOGo0ePNuq4WxrZpSrOZF/iWkFq\nrRQdcpmcYK8uPOwdhLNI7tcqEYLRAimrqOK7I9coKS5g31ebuHH1DE5KR9KmTWPHjh289tprPPXU\nU1RWVrJq1Sp++OEHVCoVSqWSYcOGsXjxYhwcHNi9ezfr169n6tSpbNiwgYKCAoYOHcp7773H8uXL\niY+Px8XFhTlz5jBp0iQApk6dSlhYGJmZmcTHx6NUKnnzzTfp3LkzS5cuJSUlhZCQEGJiYkyFnY4f\nP86aNWs4d+4cVVVVdOnShbfffpvBgwdbfH/Dhw8nPT3d4r6tW7cyYMAAsza9Xk9iYiKLFi0ytUml\nUvr160dCQoLF8/Tv399Ugxzg3Llz/PTTTzz++OPW/yHaCHqDnmsFaZzJvkhOaW6t/c72SkK9g+nu\n2RlbEenUqml0wdDpdMTGxrJnzx7UajWDBg1i8eLFeHp6Wux/9OhRPvjgA5KTk/H09OSZZ57h5Zdf\nbpBp7umsCyRknEars1wetCGxkdnQt11Pevo+dMd+er2B74+lUKKuZO+/Y5DJZHy6IQ57uYT333+f\ntLQ0U9+YmBgOHTrEihUr8PX15fTp07zzzjsEBQURFRUFGNMZx8fHs379ejIzM5k1axbHjh1j1qxZ\nvP7668TFxbF48WKGDx+Oi4sLAJ999hlvvfUWc+bMYePGjSxdupROnTqxaNEiHBwciI6OZtWqVcTG\nxpKZmcmMGTOYNm0ay5YtQ61WExsby/z589m/f79Ff8GuXbvqrPddPYaaFBcXU1ZWVqscq7e3N2fO\nnLnj5wnQt29fSkpKCAkJYdasWXft31ao1Gq4oErmXM4l1JqyWvv9nHzo4RNMoGs7pBIRZNEWaHTB\nWLNmDXv27CEmJgZXV1eWLFnC7Nmz+eKLL2r1TUlJ4dVXX2XGjBmsXr2ac+fO8c4776BQKJgyZUq9\nj+109oUmEQsArU7L6ewLdxWMI2cySFeVkn79PDnpV9ny+R4i+oQAsGLFCp588klT37CwMMaOHUuf\nPn0ACAgI4PPPPycpKcnUp6qqisWLF9OxY0e6d+9OcHAwDg4OvPjiiwBMmzaNL7/8kpSUFJMDOTQ0\nlOnTpwPw/PPPs337dqKiokxP7KNHj2bfvn2m80dHRzN9+nSTyEdFRfHiiy+Sl5eHn59frfdoyedw\nJyoqjCmu7ezszNrlcjmVlZV3PFav1xMXF0dRURH/+Mc/eOWVV/j888/btN29sKKYs9kXScq9hlZv\n/nuQSqV0de9IqE8Qnop7+zsJWj6NKhgajYatW7eycOFCHn30UQBWrVrFiBEjSExMpHfv3mb9Dx48\niL29PW+88QYA7du357vvvuPgwYMNIhg9fR5q0hlGT587i0VSagG/JakAyMm4hrOLm0ksALp3746T\n060VshMmTODQoUMsX76c69evk5ycTGpqaq3CKNWmIwCFQmG2v/omXLOcaocOHUyvHRwcap3D3t7e\n1D8wMJCJEyeyZcsWLl26REpKChcuXACocxYxduxYMjIyLO7bsGGDqTjUncYIRrGqHl9dSKVSkxDG\nxMTw9NNPc+rUqVrfxdaOwWAgvSSLM1kXSSuq/dnby+0J8epGiHc3FHKRy6mt0qiCcfHiRdRqtZnt\nOCAgAH9/fxISEmr9SN3d3SksLOTrr79mzJgxJCcnk5CQwHPPPdcg4+vp+9Bdn/CbitzCcn5JuGVu\n8nJTcrelFgsWLCA+Pp5JkyYxatQo5s6da6r7XY1MJkMqNT/R7du3Y2NT+2tT1xN5UlISU6ZMISws\njIEDBzJmzBi0Wq1FR3Q169evR6u1LNq3m50AXF1dUSgU5OTkmLXn5ORY7A+QnJxMdna26cEFjIIL\nkJ2dXefYWhtavY7kvGucyb5oMQGgu8KNHj5BdHHviI0Ii23zNKpgZGUZF/RYsjVX76vJqFGjmDx5\nMn/+85+ZN28eOp2O0aNHtzk7c4VGy3dHr1Ol0wPg6mRH2MgB/O8Xn5Cammp6ur969SolJSUAFBQU\nsGvXLtasWcOoUaMA0Gq1pKWl0a5d46U637FjB35+fmzcuNHUtn37doA6C+H4+9/bKnWJREJ4eDgn\nT55k4sSJgNHUdPLkSZ5++mmLx/zyyy9s3LiRAwcOmGYop0+fBqBr1673dP2WSJmmnHOqJC7kXKZC\ne5vZTiIh0KUdPXyCaefk06bNcwJzGlUwysvLkUqlpopw1dja2lq0NRcXF5vi5ceMGUNSUhL//Oc/\nWbt2LW+++WZjDbtJMRgM/Hg8laJS4+cjtzGWWXV3fojQ0FDmzZvHwoUL0ev1ptmDRCJBqVSiVCqJ\nj48nODiY0tJSPv30UzIzM2uZbhoSX19f0tPTOXz4MB07diQhIYHVq1cDtU1ID0JUVBSvvfYaISEh\nREREsHnzZkpKSpg8ebKpj0qlQqFQ4OjoyMSJE9m4cSPvvfces2bNIisri7/+9a+MGTOGbt261du4\nmhvFFSUkZJzhan4KeoPebJ+NzIYgz86EegfhYu/cRCMUNGcaNbTB3t4evV5fy9yg0Wgs2ppXrlyJ\nTCbjz3/+MyEhIUycOJF58+axfv16CgoKavVvjZw8n01K1q0VtCP6BeLubEytsHbtWlxdXZkyZQqz\nZs1i/PjxSCQS5HI5crmc2NhYzp07x7hx45g1axYuLi5Mnz6ds2fPNtr4X3jhBUaOHMncuXMZP348\n27ZtY8mSJSgUCqsimKxl8ODBLF26lLi4OCZNmkRycjJxcXFmDvTIyEji4uIA8PLyYsuWLeTl5TF5\n8mTmzZvHyJEjiYmJqbcxNScMBgNnsy+x69y3JOddMxMLpZ0jEe17M6XnJB4N7CfEQlAnEkNddoEG\n4PTp0/zxj39k3759ZtExw4cP57nnnmPGjBlm/ceOHctjjz3G3LlzTW2XL19m3Lhx7Nmzh5CQECxx\n48YNRowYQXx8fC0Hb0viWkYR3xy+ZtruHeRtqpyXn5/P6dOnGTRoEDKZ0basUqmIjIxk27ZttRzD\ngrZLcWUp+68dI7PE3Dfjo/Sih08wHd0CRFisALj7vbNRTVLBwcE4Ojpy4sQJJkyYYBpgeno6/fr1\nq9Xf19eXS5cumbVdvnwZqVRqFpXTGikoqeDHE6mm7fY+TkSE3hJZmUxGdHQ0UVFRTJ48GbVazYcf\nfkiHDh0ICwtriiELmhkGg4ELqmSO3Ug0i/xzc3BhUMcB+CrbbmYAwf3RqIJha2vLn/70J5YvX46b\nmxseHh4sWbKE/v3706tXLzQaDUVFRbi4uGBra8sLL7zAzJkzWbduHU8++STJycksW7aMP/3pTyiV\nrTf1gKZKx3dHrqOpMoadOjva8viADkhrlFl1cXHhk08+ITY2li1btiCXy4mIiCAuLq6Wj0jQ9ijV\nqNl/7Zh55liJhF6+IfRp10MkAhTcF3UKRs00C9bwt7/9zap+c+bMQavV8pe//AWtVmta6Q1w6tQp\nXnjhBVP6hyFDhrB27VrWrVvHhg0bTCu9Z86ceU9ja0kYDAbiE9LILzYuRrORSXliYEfs7Wr/qQYO\nHMjAgQMbe4iCZozBYOBS7lWOpv1Kla7K1O5i78ywTgPxVlrOqCAQWEOdgnH48GGz7ZycHLRaLe3a\ntcPLy4vCwkLS0tKwtbUlODjY+gva2PDOO+/wzjvv1No3YMCAWiaoxx57jMcee8zq87d0Tl1SceVG\noWl7aJ8AvN0UTTgiQUtBrSnjwPXj5gvvJBJ6+gTT1z9MrKMQPDB1CsbPP/9ser13715WrlzJmjVr\nzOoLJCcnM2vWLEaPHt2wo2wjpGWXcPRspmm7Z1dPgjuI9AuCO2MwGLicd40jab+apRp3tndiaKeB\nwlchMKOquBhNfj4O/v5I79F8bZUPY/Xq1bz11lu1itF07dqVOXPmsGzZMlPuIcH9UazW8P2xFNNi\nNj8PRx7t2XgL7AQtk7Kqcg5eP0FK4Q2z9lCfIPr5h4k62QITlapcCk6dojT5KmDAsWNH/MY8cU/n\nsEowCgoKcHa2HJstl8spK6udyVJgPVqdnu+OXqNCY4xkcbSX84Qosyq4AwaDgSv5KRxOTaCyxkpt\nJzslQzpF0M7JckoUQdujPCODgsTfKEtNNWvX3UzaeS9YJRi9evXi448/pk+fPmbCkZeXx5o1a2rV\nJxBYj8FgYN+vN1AVlAMglRrLrDo6iCdDgWXKqyo4lHKSawXmN4AQ724MCAgXswoBBoOBspRUChJP\nUWEh7ZKifXu8hgy65/NaJRjz589n6tSpDBs2jN69e+Pu7k5ubi6JiYk4OTmxbt26e76wwMjZK3lc\nTMk3bQ8K88fP07EJRyRozlwrSONgygkqqm49HSrtHBnccQABzrVTxQvaFga9ntIrVylMPEVlXt5t\neyUou3TCrXc4dl7359eySjCCg4P5+uuv+eyzz0hMTCQ1NRU3NzdTXQNXV9f7unhbJzNXzcHfblWW\ne6ijO6FdPJpwRC2br776io8++ojMzEyCg4NZuHBhLb9bTbZt22Yxe+/58+cbeqj3TIW2ksMpJ7mS\nn2LWHuzVlYj2vUWluzaOXqul5NIlChN/o+pmAtJqJFIpTt2749q7F7YPeK+2euGej48P8+fPf6CL\nCW6hLq/iu6PX0d90cnu5OTCkd4DIDHqfHDlyhPfee49FixbRt29fNm/ezEsvvcT3339fZ0GmpKQk\nhg8fbiYazfHzv15wg4MpxymvMatQ2CoY0nEA7V1EYERbRq/RUHTuPIW//Y6uvNxsn9TGBueHQ3AN\n64lNPS1IL+UTAAAgAElEQVR0tlow9Ho93377LYcPH0alUrFw4UJ+++03QkND20Q66PpEp9Pz36PX\nKaswLqyyt7Vh9MBO2Agn932zadMmxo0bxzPPPAPA0qVLOXbsGDt37qyz9sbly5eJiIjA6z6n5w1N\npVbDkdQELuddM2vv7tmZge37YGdTu7ytoG2gLSun6MwZis6cQ68xz/QttbXDtWcoLj17ILO3r9fr\nWnWHKikp4bnnnuMvf/kLJ06c4PDhw6jVavbu3cvTTz/dLKfwzZlDv2eQmacGjE+0j0d0wNnx3n/8\nubm5zJ49m969exMZGcnGjRsZOXIku3fvBqCyspJly5YxbNgwQkNDiYiI4N1336X85pPI7t27eeKJ\nJ9i2bRtDhw4lLCyM6OhosrOzefvtt+nVqxdDhgxhz549pmtOnTqVlStXmvZHRkayc+dOEhISGD9+\nPGFhYTz33HOk1ojIOH78OM8//zzh4eGEhoYyYcIEDhw4UOf7Gj58OEFBQRb/HT9+vFZ/vV5PYmKi\nWWEuqVRKv379SEhIqPM6ycnJdOnSxfoPvBFJLUzny3PfmImFg9yeUV2HMLTTQCEWbZSqkhJUBw+T\n8u//UPBroplY2Dg64vnIQDq++Dzu/fvVu1iAlTOM5cuXk5GRwZ49e+jatSuhoaEAfPjhh7z00kvE\nxsayfv36eh9ca+Ti9XzOXMk1bQ/s4Ud7H6c7HGEZvV7PzJkzkclkbNmyBa1Wy/vvv09a2q2qfDEx\nMRw6dIgVK1bg6+vL6dOneeeddwgKCiIqKgowJn+Mj49n/fr1ZGZmMmvWLI4dO8asWbN4/fXXiYuL\nY/HixQwfPhwXFxcAPvvsM9566y3mzJnDxo0bWbp0KZ06dWLRokU4ODgQHR3NqlWriI2NJTMzkxkz\nZjBt2jSWLVuGWq0mNjaW+fPns3//fmxta9/4du3aVWf51uox1KS4uJiysjKLhbnqSqGenZ1NUVER\nBw4cYM2aNZSXl9OvXz/+8pe/1FmlrzHQ6Ko4mvorl3KvmLV39ejII4F9sbexq+NIQWtGU1BA4anf\nKLmUVKvwmNzFBbfwXjgFdUcia9jV/FYJxo8//sj8+fMJDg42+yErlUpmzJjBggULGmyAjUnhb7+T\nfyIBvbbq7p3vg/JKLdfSi2h/8+/trLTFOceJ5HiQ2shx798X117WZZo9ceIEZ8+e5aeffqJ9+/YA\nrFixgieffNLUJywsjLFjx9KnTx/AWA73888/JykpydSnqqqKxYsX07FjR7p3705wcDAODg6mhZjT\npk3jyy+/JCUlxeRADg0NZfr06QA8//zzbN++naioKNMT/ujRo9m3b5/p/NHR0UyfPt3kH6gOlsjL\nyzNLc19NXT6Huqi4GU9eXTmvGrlcbrEwFxjNUWBMVbN69WoKCgpYtWoVUVFR7NmzB/sGeDq7GzeK\nM9l/7Rhqza11TfZyewZ16E8nt/aNPh5B01ORk0PBr6dQX7sOmAuFnacnruG9UHbpjOQuZZXrC6sE\no6Kios4fsZ2dXaNWcGtICn/7vcHEAiA7v4zqhwM7Wxn+Xkq46WPVa6so/O13qwXj/PnzeHh4mMQC\njDWpnZxuzVYmTJjAoUOHWL58OdevXyc5OZnU1NRaee5rpopXKBRm+6tvwjX/xh06dDC9ri58VfMc\n9vb2pv6BgYFMnDiRLVu2cOnSJVJSUrhw4QJAnbOIsWPHkpGRYXHfhg0batX6sDRGMIqVpcJcYCym\ndPToUbPvddeuXRk8eDD79+/n8ccft3hcQ1Clq+JY2ikuqC6btXdyCySyQz8c5I0vXoKmw2AwUJ6e\nTmHib5TduFFrv4OfH259wnFo377RgzSsEozQ0FC++OILhgwZUmvft99+W2cho5aGa6+wBpthGPQG\nyspvnbe9j5NZunKpjdxqsQBj+Kder79jnwULFhAfH8+kSZMYNWoUc+fOtRhGKr3t6eT27duxsan9\ntanri5uUlMSUKVMICwtj4MCBjBkzBq1WW6cjGmD9+vW1qjJWY8lc5OrqikKhICcnx6w9Jyfnjual\n2x+CvL29cXNzIzMzs44j6p+Mkmz2XTtKaaXa1GZnY0dkh350ce9whyMFrQ2DwYD62nUKE09Rcdt3\nGcCxQwdce4fj4OfbBKMzYpVgREdHM23aNJ566imGDBmCRCLhu+++4+OPP+aXX35h48aNDT3ORsG1\nV9g93bTvhXRVKan7kgFwc7Ln4Sesz/BriaCgIAoKCkhNTTU93V+9epWSmzHYBQUF7Nq1izVr1jBq\n1CgAtFotaWlptGvXeKGYO3bswM/Pz+w7sn37doBatthq/P397+kaEomE8PBwTp48ycSJEwGjj+fk\nyZM8/fTTFo/ZunUr69ev55dffjHVD0lPTyc/P79RanpX6ao4kf4b57KTzNo7uAYwqGN/FHLLMyNB\n68Og01GafIWCxFNoapWeluDUrQuu4eHYeTb9Gi2rBKNfv35s3ryZDz74gE8//RSDwcCmTZt46KGH\n+Pjjj0VNBivIUJWaXrfzevCV3BEREYSGhjJv3jwWLlyIXq83zR4kEglKpRKlUkl8fDzBwcGUlpby\n6aefkpmZ2agmRF9fX9LT0zl8+DAdO3YkISGB1atXA7VNSA9CVFQUr732GiEhIURERLB582ZKSkqY\nPHmyqY9KpUKhUODo6MjQoUNZvXo1CxYsYObMmRQWFvKPf/yDPn368Oijj9bbuCyRVapi37WjFFfc\nWmBla2PLo4F96eresVmuBRHUP3qtluLzFyj6/bSFxXYynIKDcOvdC3kdefyaAqvXYfTr14/t27dT\nUVFBUVERSqUSR0fjjU+v19/VjNHWSVfdMjm0q6fUH2vXrmXJkiVMmTIFJycnXnnlFc6ePYtcLkcu\nlxMbG0tMTAzjxo3D3d2dwYMHM336dH766ad6ub41vPDCC1y5coW5c+ei0+no0qULS5Ys4d133+XM\nmTP1FtY6ePBgli5dyrp164iJiSEkJIS4uDgzs1NkZCRvvPEGs2fPJjAw0PQQ9Mc//hG5XM7w4cMt\n1mmpLwwGA4mZZ/k14wzUmF21d2nH4I4DcLQVdU/aArrKSorPnqPw9Jnai+3kclxCH8alZw9sHJtf\niiCJoS67QA1GjBjBRx99ZLFQ0unTp3nllVc4duxYgwzwfrhbIfPGRqfTs+H/zqLVGX0OUWNDUCoe\nLI4+Pz+f06dPM2jQIGQ3Q+lUKhWRkZFs27atlmNY0PQkZpwlIf1307ZcJueRwD509+gsZhVtAIPB\nQMnFS+QdOYrutug9mb09Lj174NIjFJld04VO3+3eWecM4+uvvzY5HtPT0/nxxx+5ePFirX5Hjx5t\nNVFSDYWqsNwkFs6Otg8sFmB0VkdHRxMVFcXkyZNRq9V8+OGHdOjQgbCwhvHDCO6fs9kXzcSinbMv\nQztFoLRtfk+RgvpHk1+Aav8Bym8LqLBxdMQ1vBfODwXfczGjpqBOwTh37hybN28GjDbxjz76yGI/\niURiiskXWCbDzBxVPzldXFxc+OSTT4iNjWXLli3I5XIiIiKIi4szOXEFzYNLuVc4kvqradvf2Zcn\nug1FJkqmtnr0VVUU/JpI4W+/Y6gR1Sh3csKtbx+cundr8MV29UmdgvHWW28RFRWFwWBg6NChfPzx\nx7XCZ6VSKUqlss5Yd4GR9BoOb3+v+hEMgIEDB4qAg2bO1fxU9l+/lc7ER+nFqK6DhVi0AcpSU1Ht\nP2jm0JZIJLj2CsOtb58WMaO4nToFQy6Xm2LY4+Pj8fb2Jisry7RQLD8/n2vXrplWEQsso9cbTHmj\noH4ipAQtg7SiDH6+etjk4PZQuPFEt6GiwFErR6tWk3v4CKXJ5uld7H198RoyCDuPpg+PvV+sipJy\ncHDg+eefp6CggB9++AGAM2fOMHPmTCIiIlizZo3ZCmPBLXKLytFUGVc0Kx3k95VkUNDyyCrJ4Yfk\nA+gNRjOEi70zY7oPF0kDWzEGvZ7ic+fJO3YcfdWtRbpSWzs8Bg7AOeShFh/cYFUsbExMDCqViiVL\nlpjaBg8ezH/+8x9u3LjBqlWrGmyALZ3MGv4LP09li//CCO5Orjqf7y7vQ6e/+aBg58jYoOEixUcr\nplKVS/ru/0V18JCZWDh170bgn57F5eGQVvHbt0owDh48yLx588zs5RKJhL59+zJ37txGjetvaaTn\n1vRfCHNUa6egvIhvk36mSme8aTjI7RnbfbiIhmql6DUacg8dJu3L/2eWzkPu4kK78ePweWwENorW\n4+O1yiRVWVlZKxNoNY6OjqZ0FAJzDAaDeYRUPTq8Bc2PkspSvkn6mQqtMcbe1saWMd2H42LffFbq\nCuoHY96na+QePIxWfes3LpHKcOsTjmt4L6QWcq61dKx6R2FhYWzdupVBgwaZJZ7T6XT85z//oUeP\nHg02wJZMfnEFFRrjWhYHOxvcnEQtg9ZKmaacb5LiKbuZmtxGZsPobkPxULg18cgE9U1VcQm5Bw+h\nTjGvr+7g74/XkEEPXDe7OWOVYLz55ptMnTqVkSNHMnjwYDw8PMjPz+fgwYOoVCq2bNnS0ONskWTc\nlg6kNdgwBbWp0FbyTVI8xRVG86NUKuXxrkPwUTbP0q+C+8Og01F4+gwFJxPQ18imLHNwwPORgSi7\nd2v1v3GrBKNXr17s2LGDTz75hPj4eAoLC1EqlfTp04d//etfPPzwww09zhZJRm7NhIPCHNXQfPXV\nV3z00UdkZmYSHBzMwoULTUWfbmfNmjWsXbvW4r7Zs2fzxhtvWHVNja6K75J+oaC8CDD69h7rPAh/\n56ZLQS2ofyqyssjZdwBNfr5Zu3PIQ3gMjGjSdB6NidVGtpCQEP71r3815FhaFQaD4baEg0IwGpIj\nR47w3nvvsWjRIvr27cvmzZt56aWX+P777y0W/5o+fTrPPvusWdvatWv58ccf+eMf/2jVNbV6Hd9f\n3o9KnWdskEgY1ukROro1ff4yQf2gq6wk7+gxis9fMGu3dXfHa8jgJq1N0RTck1fm1KlTHD58GJVK\nxcyZM7ly5QohISF4tOCFKA1FUamGsgpjpIydXIaHiwipbEg2bdrEuHHjeOaZZwBYunQpx44dY+fO\nnRaLNTk6OpqyLYPxu71z504+/fRTq2p66/V6frpykMySbFNbZGA/unp0fPA3I2hyDAYDpUmXyT1y\n1CyjrNTGBrd+fXHt2aNFpfSoL6wKq9VoNLz55ps899xzfPrpp+zcuZOCggI2bdrEhAkTSE1NtfqC\nOp2ODz74gMjISMLDw3nzzTfJzc2ts39WVhZvvvkm4eHhDBw4kPfff5/y21ICN0fMzFGejmbV9eqL\n3NxcZs+eTe/evYmMjGTjxo2MHDmS3bt3A8botmXLljFs2DBCQ0OJiIjg3XffNX1+u3fv5oknnmDb\ntm0MHTqUsLAwoqOjyc7O5u2336ZXr14MGTKEPXv2mK45depUVq5cadofGRnJzp07SUhIYPz48YSF\nhfHcc8+ZfSeOHz/O888/T3h4OKGhoUyYMIEDBw7U+b6GDx9OUFCQxX/Hjx+v1V+v15OYmGiqKQ5G\nP0K/fv1ISEi46+doMBj4xz/+wahRoxg8ePBd++sNen65doTUwnRTW/+AcEK8G77wkqDh0RQWkbn3\nG7LjfzYTC8cOHWj/7DO4hfdqk2IBVs4wYmNjOXz4MOvWrePRRx81ZUP9+9//zowZM1i9erWpKM7d\nWLNmDXv27CEmJgZXV1eWLFnC7Nmz+eKLL2r11Wg0TJs2DS8vL7744gsKCwt55513kEqlLF68+B7e\npnVcuaTi8vlstFrLtabvhfScUtSlxvBKVWElX2feOfTYxkZGtxAfugRZ5yjV6/XMnDkTmUzGli1b\n0Gq1vP/++6SlpZn6xMTEcOjQIVasWIGvry+nT5/mnXfeISgoiKioKMCYzjg+Pp7169eTmZnJrFmz\nOHbsGLNmzeL1118nLi6OxYsXM3z4cFxcXAD47LPPeOutt5gzZw4bN25k6dKldOrUiUWLFuHg4EB0\ndDSrVq0iNjaWzMxMZsyYwbRp01i2bBlqtZrY2Fjmz5/P/v37sbWtvfJ5165dddb7rh5DTYqLiykr\nK6s1M/D29ubMmTN3/Szj4+M5f/48H3zwwV37GgwGDqWc5Er+rQiZXn4P08uvdZQpbssYdDoKEk9R\n8OspDPpb3z8bR0c8Bz2KY6dOrd6pfTesEoy9e/fy1ltvMXz4cLMfckBAAG+88Qb//Oc/rbqYRqNh\n69atLFy40FTVbNWqVYwYMYLExER69+5d67oqlYrt27ebbhR1iUt9cDVJVS9iAaCuuBVFobC/+8es\n1eq4mqSyWjBOnDjB2bNn+emnn0z5vVasWMGTTz5p6hMWFsbYsWNN+b4CAgL4/PPPSUq6VRa0qqqK\nxYsX07FjR7p3705wcDAODg68+OKLAEybNo0vv/ySlJQUkwM5NDTUlKH4+eefZ/v27URFRZme8EeP\nHs2+fftM54+Ojmb69OmmH1tUVBQvvvgieXl5+Pn51XpvlnwOd6KiogKg1lohuVxO5W11ByyxZcsW\nnnjiCTp0uHMNbYPBwPEbp7ioSja1PezTnX7+Ip18S6fsRjqq/QeoKiqq0SrBtWco7v37IbXwYNMW\nsUowioqK6vwxubm5UVpaanHf7Vy8eBG1Wm1mOggICMDf35+EhIRagnHo0CEeeeQRs6fKP/zhD/zh\nD3+w6nr3SufuXvUyw9Bo9VTdPIdUKsHB7u4fs42NjM7drQ/DPH/+PB4eHiaxAOjevbtZTq8JEyZw\n6NAhli9fzvXr10lOTiY1NbVWYZTqmuAACoXCbH/1TbhmzZOa34XqTMU1z2Fvb2/qHxgYyMSJE9my\nZQuXLl0iJSWFCxeMDsS6ZhFjx44lIyPD4r4NGzbUKg5laYxgFKu7ZVLOysrixIkTVoWGn8o8x+ms\nW87Pbh6deKR93zb/1NmS0ZaVk3fkKCVJ5rXV7by88B46GDsvERpdE6sEo2vXrnzzzTdERkbW2nfg\nwAGry2xmZWUBWDQdVO+ryfXr14mIiCA2NpavvvoKiUTCqFGjmDNnTp0rzx+ELkFeVj/h34mLKflk\n2BhvIu19nHhycP2UIa2JTCZDXyO/viUWLFhAfHw8kyZNYtSoUcydO9dU97vmeW4vr3u3crs2Flaw\n1nXTTEpKYsqUKYSFhTFw4EDGjBmDVqu16IiuZv369abiXbdjySHt6uqKQqEgp0ZqBoCcnJy7OrDj\n4+Px8vIye4ixxO0FkDq6tWdIpwghFi0Ug8FA8fkL5B09jl5zaxYqlctxH9Afl9CHkYiy07WwSjBe\ne+01Zs+eTVFREcOGDUMikZCYmMhXX33Ftm3bWL58uVUXKy8vRyqV1irwY2tra9F0UFpayq5duxg8\neDAffvgh2dnZ/O1vfyMvL8/qazYFNRfs1Wf9i5oEBQVRUFBAamqq6en+6tWrpjQtBQUF7Nq1izVr\n1jBq1CgAtFotaWlptGvXrkHGZIkdO3bg5+fHxo0bTW3bt28HjD9aS/j7+9/TNSQSCeHh4Zw8eZKJ\nEycCRh/PyZMnefrpp+94bEJCAv3797+jSFoqgDSi86NIJeKG0hKpzMtHtf8AFbc9pCq7dsHzkUew\nUYq8X3VhlWCMHDmSFStW8MEHH/Dzzz8D8I9//AN3d3cWL17MmDFjrLqYvb09er0erVZr9pSq0Wgs\nmg5sbGxwcXFh+fLlyGQyevTogVarJTo6mnfffRc3t+aZduH2CKmGICIigtDQUObNm8fChQvR6/Wm\n2YNEIkGpVKJUKomPjyc4OJjS0lI+/fRTMjMzG7Wkrq+vL+np6Rw+fJiOHTuSkJBgCpCoz3FERUXx\n2muvERISQkREBJs3b6akpITJkyeb+qhUKhQKhVk47fnz55k0aVKd5xUFkFoXRefOk3vwUK3qd15D\nBqGoYVYVWKbOR6QNGzaQnX0rxvzJJ59k3759fPvtt3z++efs3buXQ4cO3fUJribVDk6VSmXWXpfp\nwMfHhy5duiCrEcLWtWtXwFhnvDmiLq+isMQ4W5JJJXi7KxrsWmvXrsXV1ZUpU6Ywa9Ysxo8fj0Qi\nQS6XI5fLiY2N5dy5c4wbN45Zs2bh4uLC9OnTOXv2bION6XZeeOEFRo4cydy5cxk/fjzbtm1jyZIl\nKBQKqyKYrGXw4MEsXbqUuLg4Jk2aRHJyMnFxcWYO9MjISOLi4syOU6lUFiOvoHYBJHdRAKnFYtDp\nUB04iGr/AZNYSCQS3HqH0/7Zp4VYWInEUIddoFevXmzatIk+ffrw0EMPsWPHjjrTLFiLRqMhIiKC\nv/71r0yYMAEwhnWOGDGCHTt20KtXL7P+a9euZefOncTHx5vMWN9++y1//vOfOXz4cJ0zjOpzxsfH\n13LwNjSX0wr4/pgx5NLfS8mkoV0b5Dr5+fmcPn2aQYMGmQRVpVIRGRnJtm3bajmGBfdGVkkO3yT9\nbKpp4WLvzPjgkaKmRQtEV1FB1vc/UJ5+K5DCztMT7xHDsfO4t4i81s7d7p11mqSUSiWbN28mNTUV\ng8HAvn37uHr1ap0XqrYd3wlbW1v+9Kc/sXz5ctzc3PDw8GDJkiX079+fXr16odFoKCoqwsXFBVtb\nW5599ln+/e9/M3/+fF5//XWys7NZsWIFEyZMaL7mqNsSDjYUMpmM6OhooqKimDx5Mmq1mg8//JAO\nHTqY1skI7g9RAKn1UJmXT9a335nV1VZ26Yz38GEtsqZ2U1OnYMycOZP/+Z//4aeffkIikbBu3bo6\nTyKRSKwSDIA5c+ag1Wr5y1/+glarZdCgQaZFeKdOneKFF15g69atDBgwAE9PT7Zt28ayZct46qmn\nUCgUjB8/nrfffvse32bjkaFqnISDLi4ufPLJJ8TGxrJlyxbkcjkRERHExcXVCioQWI8ogNR6UF+7\nTvaP8ei1tyrguffvh1uf3iK67T6p0yQFxqim4uJihgwZwieffMJDDz1U54msyb/TWDSVSaqiUsvG\nr4z+AalEwoyJochthHO0pVBSWcr/XfzRVNPC1saWJ4MeEzUtWhgGg4GCXxPJP3HS1Ca1keMzcgSO\nnTo22bhaAvdtkgLjoiwHBweWLVtGWFhYszUDNRcycm+Zo7zdFUIsWhCiAFLrQF9VRc7Pv1B65Zb5\nXO7khO+Y0cJfUQ9YFVY7adIkSktL+fnnnykvL7e4YKxmSoq2SmOE0wrqH1EAqXVQVVxC1n+/p7JG\nMlMH/3b4Pj4Kmb3wP9UHVgnGoUOHePPNNykvL7e42EoikQjBoHEW7AnqF1EAqXVQnpFB1vc/mmWX\ndQkNxfPRgW02s2xDYJVgrFy5kk6dOvHuu+/i4+Nz19QRbZHKKh2qQuOXVSKR4CtmGM0eUQCpdXD7\nYjyJVIrnoEhcHhYZhOsbqwTjypUrrFu3TsT234GsXLVp9uXpYo+dXDzVNGdEAaSWj0GnI/fwUYpq\nLESVOTjg+8QoHCxkQRY8OFYJRrt27azOSNtWEfW7Ww6iAFLLp67FeL6jH0deI2OzoH6xyrY0Y8YM\nPvroozpTTgu4rX63MEc1V0QBpJZPZV4+N778f2ZioezSGf9JE4RYNDBWzTD++9//kp2dzYgRI/Dy\n8rKYKPD777+v98G1FKq0enLyy0zbYobRfLm9AFKItyiA1JIQi/GaFqsEw8vLi8cee6yhx9JiycpT\no7/pv/BwtreqYJKg8UkryqhVAOnRQFEAqSVQ12I878eGo+zcqQlH1raw6s62bNmyhh5HiyazxoI9\nPzG7aJbo9DqzmhaBrv6iAFILQSzGaz7UKRjZ2dl4eHhgY2Njlua8LppTapDGJl0lFuw1d85kX6Ko\nohgAuUzO4I4DRAGkFoBYjNe8qFMwhg4dakppPmTIkLs+iVXXaW5r6HR6soX/olmj1pSRmHmr9kZf\n/54o5Heu9S1oesRivOZHnYLxz3/+k/bt25tei6m7ZbILytDqjAuGXJV2KB1EptjmxvEbp9DqjDXC\n3RxceNirexOPSHA3xGK85kmdglGzbOVTTz3VKINpiZjVv/AS5qjmRmZJDsl5103bjwb2FZkKmjFi\nMV7zRoTzPCCNVf9CcO/oDXoOpyaYtju7d6CdyBHVbBGL8Zo/QjAeAL3eQGZezQV7QjCaE+dzLpNf\nVgCAjdSGiPbhTTwiQV2IyngtAyEYD4CqsJwqrdHG6qSwxdnRtolHJKimvKqChIzTpu3wdg+LqnnN\nFLEYr+UgBOMBEOG0zZeT6b+j0WoAcLZ3oqdP3dUiBU2DWIzX8hCC8QBkCv9FsyRHncfF3Cum7Ufa\n90EmFWGYzQmxGK9lYpVgGAwGdu/ezb59+ygrK6tVREkikbBp06YGGWBzRa83kJEnIqSaGwaDgcMp\nJ+HmdzTQ1Z9AV/8mHpWgJmIxXsvFKsFYtWoVGzZsICAgAF9fX2FXBPKLK6jU6ABQ2MtxVdo18YgE\nAJdyr5oKIkmlUh5p36eJRySoSUVODpnffCcW47VQrBKMPXv2MG3aNObPn9/Q42kx3F6/W4ho01Op\n1XAi/TfTdphvCM72IhyzuVCZl0/m3m/QVVYCYjFeS8QqwSgtLWXYsGENPZYWRbqo393s+DXjNBVV\nFQA42iro5StuRM0FTWERGV/tNYmFzM4O39GP49CuXROPTHAvWLXkNTw8nMTExIYeS4vBYDDctmBP\n+C+amvyyQs7lJJm2B7bvg1wm4vebA9rSUjL3fm0yQ0nlcvyeHCvEogVi1Qzj1Vdf5e2330ar1dK7\nd2/sLTimevfuXe+Da64UllRSXmnMTWRva4O7s3DUNSUGg4HDqQmmYIx2zr50cmvfxKMSAGjLykn/\nv72mBXkSmQy/saOx9/Zu4pEJ7gerBOPFF18EYO3atQBm9nqDwYBEImlT2Wprrr/wE/6LJudKfgqZ\nJcYU/BKJRBRFaiboKivJ3Ps1VUVFgNFn4SfMUM0CrVaHjc29BxlYJRhbt2695xO3ZjJya/ovhDmq\nKWewCfwAACAASURBVKnSVXHsxinTdqhPEG4OLk04IgEY11lkfv0tlXl5N1sk+Ix8DEVgYJOOq61T\nXqbh1PE0CvLUdH3Im6CH7y23mlWC0b9///saXGuklv9C5I9qUk5lnqNMY6xH4iC3p49fjyYekUCv\n1ZL57X+pqFF4zXv4UJRdOjfdoASosks4dTwVzU1zetaNooYRDIArV66wZs0aTpw4QUlJCW5ubvTt\n25dZs2bRtWvXext5C6ZYraG03JjzxlYuw9NVFOJpKgoris1qdA8ICMfWRuTzakoMOh3ZP/xEeXq6\nqc0z8lGcg4OacFRtG4PBQPLFHJLOZZv8fBKJhG4h914l1SrBuHTpEs899xwODg6MGDECDw8PVCoV\nv/zyC7/88gvbt28nKKhtfCFq1r/w9VAglQpbeVNgMBg4mvoreoMx+aO30pNuHiL/UFNi0OvJ+fkX\n1Nevm9o8BvTHtaeY9TUVVVU6fjuRRnZGkanNzl5On4EdcL+P/HdWCcbKlSvp3LkzW7duRaFQmNrL\nysqIiooiNjaWjz/+2KoL6nQ6YmNj2bNnD2q1mkGDBrF48WI8PT3veuzMmTMpKyvj3//+t1XXaghq\nLtgT6y+ajtSidNKKbtZNkEiIDOwnHN1NiMFgQHXgICWXk01tbuHhuPVpO9GTzY3ionJ+PZKCurTS\n1ObuqaR3RCD291kZ1Kp1GAkJCbz66qtmYgGgUCh4+eWXSUhIqOPI2qxZs4Y9e/YQExPDf/7zH7Ky\nspg9e/Zdj9u+fTv79u2z+joNRbrwXzQ5Wr2OI6m/mrYf8uyKp6NIWNdUGAwG8o4eo/j8LfOgS+jD\nuEcI32dTkZ5awOH4ZDOx6Nzdi4ghne9bLMDKGYaDQ912eolEgk6ns+piGo2GrVu3snDhQh599FHA\nmKdqxIgRJCYm1rmWIyUlhdWrVxMe3rQFcErLNBSrjSmzbWRSvN2E/6IpOJ11npJKo3Db2djRLyCs\niUfUtin4NZHC3343bTt1747noEgx42sC9Do9509ncj35VmJHGxsZPfsG0K696wOf36oZRq9evdiw\nYQOVlZVm7RUVFWzcuNHqG/nFixdRq9VmUVcBAQH4+/vXOUvR6XTMnz+fl19+mS5dulh1nYaiZjit\nr4cjMpmoDd3YlFSWcirznGm7n39P7G1E4semovD302b1LBw7dcJ7+FAhFk1ARXkVR/dfNRMLRyc7\nHh3RtV7EAqycYbz99ttMnjyZESNGMHz4cDw9PcnNzeXnn39GrVazbds2qy6WlZUFgI+PuXfe29vb\ntO92Pv30UwBeeuklFi1aZNV1GgqRDqTpOZZ2Cp3eOKP1ULgR7NV2IvSaG8UXLpJ7+IhpWxEQgO+o\nx5BIxYNUY5OnKiXxWCqVFbeqFvr6u9CrX3ts5PWXBdgqwejSpQvbt2/no48+Ij4+nqKiIpydnenX\nrx+vv/463bt3t+pi5eXlSKVS5LfV6LW1ta01ewE4e/YsmzdvZteuXUibwZew5gxDVNhrfG4UZ3Kt\nINW0/WiHfkglTf+9aIuUXE4m55f9pm17X198Rz8uUpQ3MgaDgWuXc7lwOtMsZDa4hy+du3vV+0zP\n6nUYQUFB/Otf/3qgi9nb26PX69FqtdjY3Lq0RqOp5SeprKxk3rx5zJkzhw4dOjzQdeuDsooq8ouN\nmVClUgm+HkIwGhO9Xm/m6O7m0QlfpVcTjqjtok5JJeeneMB4g7Lz9MRv7GikcpHssTHRVun4PeEG\nmTcKTW22djb0HhCIp0/DpPWvUzD27t3LoEGDcHV1Ze/evXc90ZNPPnnXPn5+fgCoVCrTa4CcnJxa\nZqrff/+dK1eusHLlSlauXAkYhUWv1xMeHs4333xDu0bMSVNzduHjpsBG+C8albM5lygsN8aSy2Vy\nBgQ0bQBEW6U8PYOs/9/ee8dHVeX//687Lb33BBIUnPSQEBIIVQggKyAguCoCCvIFqeICCq4FllUX\nBZXy+MiKFfCHKArLUgQWDIoBQkLoKXTSEzLp0+89vz8muZlJcwamJJnzfDzymLnnnjv3PSfJed/z\nPu/yyxH+aVbi5YWg8eMgdKD7SNakvlaJzNN3Ud/4EAsAnt7OSEwJg5Oz5YJX21UYK1aswA8//ABP\nT0+sWLGiww9hGMYohREREQEXFxdkZGRg4sSJAIDCwkIUFRUhKSnJoG9cXByOHj1q0Pbxxx+juLgY\n69evh7+Vs12WVOiXY6XutNZErlYgq/gyf5wYHAtnCfVQszbKMl21PNLoFSl2c0PwhPEQOdPfhTUp\nKazGxXOF0GqbvVN79fZFVN8gCCz8INuuwjh+/Dj8/Pz49+ZAIpFg2rRp+PDDD+Hl5QUfHx+sWbMG\nycnJiI+Ph1qtRk1NDTw8PODo6NjKFOXq6tpmuzUouk83vG3F2cJsaFjdZp6nkwdi/O0jq0BnQlVZ\nieL/HgSn1f0eRC4uCJ44ASJX+r9gLQhHkHulBDfzKvg2oVCA2MQe6BHmZRUZ2lVHISEhkEh0S5tz\n587B2dkZISEhrX4kEgmOHDli9A2XLl2KCRMmYMWKFZg5cyaCg4OxceNGAEB2djaGDBmC7OzsP/kU\n66JUa1FZo1v6MQyDILp/YTVK6ytwvfI2fzwoNLFTOEDYE7pqeQfAqZur5QVPGA+xu7uNJbMfVEoN\nzvx2y0BZOLtIMHhkH6spC8DITe9Vq1Zh9+7d8PJqLVhOTg4++eQTzJ4927gbikRYuXIlVq5c2erc\ngAEDkJeX1+617733nlH3MDcl9xt4m62fpxMkZnRTo7QPRzj8cbfZx/8Rr1D0cA/q4AqKudHW1+tK\nq7aolifxtt4kZe9UVTYg6/RdKBXNLrMBQe6IT+4JscRovyWz0O7d5s2bhxs3dHlhCCFYuHAhv+LQ\np7KyEqHdPMe9Yf0Lun9hLXIrbqJSXgUAEAqEGNiTbnRbE61cjqL//Bfaep05lhEKETT+SVotz0oQ\nQnDnZiVyLhaD45pdZqXRAegT4W+T4Mh2Fcb8+fOxZ88eAMCePXsQGxsLb2/DfD0CgQDu7u6YPHmy\nZaW0MTRgz/ootSqcK2pON5EQFA03B6qsrYWuWt5BvWp5QgT9ZSycgugKzxqwWg6XsgpRdK+KbxNL\nREgYEAr/QMu4zBpDuwojPj4e8fHxAHTpORYsWICePe2vTrJaw6KiSrccZxgGQTRgzyqcK7wIlVZn\nM3dzcEVcYJSNJbIfOLUaJf89yFfLYxgGAWNS4Rxqf///tqChToWsM3dRW63g2zy8nJCY0gvOLrat\n92LU7uEHH3yAW7duYd26dXzbpUuXMGvWLJw5c8ZiwnUGSisbwDXuX/h4OMLRyjZDe+R+gww595vT\nZKf0TIRIQPeNrAGn1aLk8C9Qlpfzbf4jR8D1UVotzxqUFdfi1PHrBsqi5yPeGDSij82VBWCkwjh0\n6BBeeeUV3Lx5k29zcnICx3F4+eWX8dtvv1lMQFtD04FYF0IITt07BzQq6Z4ewQjzDLGxVPYBYVmU\nHTkGRVEx3+Y3dAjcwo1L/UN5cAhHkHelFOf+uA2NRhdfIRAIEJfYA3379+w0iU6NkmLr1q144YUX\n8Pnnn/Ntjz32GL799ls899xzD50ypDNjuH9BbeiW5nrlbZTX67JtChgBUkITaeZTK0A4DmXHf0XD\n3bt8m8/AAfCIjbGhVPaBWqXF2VO3cT2nuQa6k7MEg0b0RuijPjaUrDVGKYx79+5h1KhRbZ4bNWqU\nwcqjO6FlOZTJ5PwxXWFYFrVWjbOFzTE4cYGR8HSkvv6WhhCCipO/of6GXrW8fgnw6ke90ixNtUyO\n3/93HffL6vg2vwA3DB31GDy9nTu40jYYpTB8fHxw9erVNs/l5eXBw8PDrEJ1FspkcrCN7myebg5w\ndqTJ1SxJVsllKDS6AElniTMSgqJtLFH3hxCCyvTTqM3J5ds8YqLhPYBWy7M0925VIv3Xm1DI1Xzb\nY5EBSB7yCCQOnXOv1CipJkyYgC1btsDZ2RmjR4+Gj48PZDIZTpw4gc2bN2PatGmWltMm6JdjpfEX\nlkWmqMaVsuagzYE9EiAWUgVtaaoys1B98RJ/TKvlWR6W5XAluwgFt2V8m1gsRHxyKAKCO/eK2iiF\nsXDhQty6dQtr1qzBP/7xD76dEIIxY8ZgyZIlFhPQlhRX0A1va0AIQfq9LD6aPsgtAL29bZ/SvrtT\nfeEiZOeaK13SanmWR6nQ4Nwfd1BT1WzqdvNwQv+UMLi4df6Mv0YpDLFYjE2bNiE/Px9ZWVmoqamB\nm5sbEhMTERERYWkZbQLLciitpBHe1uB2VQGKa3UVFxmGwSC60W1xaq/l4H76af7YuWdPWi3PwtRU\nyXHujzsGKT5CQr0Ql9gDQlHXGHeTDGVSqbTN6noNDQ1wceleT+AV1QpoWQ4A4O4igasFc8zbMxpW\ng9MFzYWRov2l8HGmeYosSd31GyhPa3aFdwoKQuDYMbRangUpLapB9tl7YBvnFIZhEBUfjF69fbrU\nw5FRCkOtVmPHjh04d+4cNBoNbzrgOA4KhQJ5eXm4cOGCRQW1NobmKLq6sBQXSq+hQa1bnjuKHZEY\nHGdjibo3DXfuGlbL8/ND4JNjabU8C0EIwc28CuRdKeXnTbFYiH4pYfCzUFU8S2KUwli/fj22b98O\nqVQKmUwGBwcHeHt7Iz8/HxqNBosWLbK0nFaniOaPsji1yjpcLL3GHyeHxMNBRFdylkJZVobSI0cN\nquUFj3+SVsuzEBzL4XKLzW1nVwckD+4FV3dHG0r24BhlODty5AhmzZqF/fv3Y/r06YiJicGPP/6I\no0ePIiQkBBzHWVpOq8JxBCV0/8LipBdk8X87fi4+CPel6Scshbq6us1qeUInWi3PEqhVWpz9/baB\nsvD2dcWQkX26rLIAjFQYlZWVGDZsGADdPsbly7pymQEBAZg7dy4OHTpkOQltwP0aBdSN4fmuTmK4\nd4IcLt2Ne9VFuFddpDtgGAwOS+pSttyuhFYuR8l/D4JV6mJchI6OCJownlbLsxD1dSr8ceIGKvWs\nFD3CvDFwWOeNrzAWo6R3c3ODRqPb2Q8LC0NJSQnq6+vh6uqKXr16oaSkxKJCWhv9dCBBvq50IjMz\nLMciXW+jO9znUfi7dK4UCN0FTqNBycHD0NTpIokZoRBB4/4CiWf3DLa1NffL65F1+g406uZ62xGx\nQegd7tct5hGjVhiJiYnYuXMnlEolwsLC4OTkhP/9738AgIsXL8LVtXuZbAwLJtGnMHNzqSwHtUrd\nBCYRSZDcI97GEnVPCMui9JejUFU0lfVkEPjEaDgGBNhUru7KvdsynP3tFq8shEIBElPCbFbsyBIY\npTAWLlyIrKwszJ07FyKRCNOmTcM777yDZ555Bp988gmeeOIJS8tpNQghhh5SdP/CrNSrG5Bd3Jxm\npn9wHJzEXdem21lpyg8lLyjg2/yGD4VLr162E6qbQghBzqViXMos4B0KHBzFSHm8N4J6eNpYOvNi\nlEkqMjIShw4dQn5+PgBg2bJlcHV1xfnz5zF//nzMnTvXokJaE1mtEkq1FgDg5CCCVxeIvuxKnCnI\nhpbTja+3syei/B+zsUTdE1nGOdTmNqda8e6fCI9oWoTK3Gi1LC5kFKC0qIZvc/d0QtLgXnDqhrFb\nRimMtWvXYtKkSRg6dCgAXdDJK6+8YlHBbEXLdCDdZSnZGSioKcYtWXP67MGhSRAwXSPCtStRc/Uq\nqrLO88fuERHwSupvQ4m6Jwq5Guf+uGNQ7CggyB0JA0MhEnXPIEij/lv37NmD2tpaS8vSKSi+rxd/\nQQP2zIZCo0Ta7eZUFL29wxDk5m9DibonDbfvoOLkKf7YOTQUfsOH0gcfM1Mtk+OPEzcMlMWjUj/0\nH9Sr2yoLwEiF0bdvX2RmZv55xy4OIQRFdP/C7BBCcPLOGT51uaPYESmhiTaWqvuhLC1F6dFjMIji\nfmI0TflhZkoKa3A67SafE4phGMQm9kBU32Awgu6tmI0ySUVHR2Pbtm04cuQIIiMj4exsWNiDYRiD\nLLZdlZp6NeRK3R+Bg1gIHw+6GWsOrlVcb465APB4r4FwFtOAMXPSKjDP3R1B456kKT/MSFOaj9zL\nzWEEYokQiQPD4NsF03w8CEYpjCNHjsDf3x9KpRLZ2dmtzneX5W6RQfyFCwTd/GnBGsgU1ThT0GxP\njwkIRyit0W1W+MA8lQoAIHRyQtD4cRA5U6VsLjiWw+XzRSi4033SfDwIRimMEydOWFqOTkHJfVq/\n25xoORYnbqWD5XRPvd7OnkjuQct+mhNOrUbJgUN8YJ5AJELQkzQwz5yoVVpknb5rELnt7euK/oPC\nunzktqm0u4dx+vRpNDQ0tHe6W6IfsEcLJj08GYUXIJNXAQCEAiFGPjoYIgG1p5sLwrIoPXIUqvv3\nAehW+gFjRsMxgDoTmIu20nz07NU90nw8CO0qjNmzZ+PmzZsGbbt370ZVVZXFhbIFtQ1q1DboauuK\nRQL4eXW+AuxdiYKaYlwpa64TPbBnP3g7da8gJltCCEH5rychLyjk2/yGD4NLL1qp0FzcL6/HHyeu\no6FexbdFxAYhrn8PCIT26Q7e7rduilhsgmVZrF69GsXFxRYXyhbou9MG+rhASPcvHpiWLrShniGI\n8qMBeuZEdjYDdY2BtADgndQf7lGRNpSoe3HvVmUbaT56das0Hw+CSWuqlkqkO6EfsEfTmT84LV1o\nncSOGN5roF3/k5mbmitXUXW+2fnEPTICXv2pm7I5IBxB7pUS3Myr4NscHMVIGtwLnt7U6mB/Rrh2\n0M9QS/cvHpxWLrSPpNBcUWak/tZtVPzWHJjnEhYKv+HDqEI2A1oti+yzBSgrto80Hw+C1Q1xLMti\nw4YNGDJkCBISErBkyRLcb9y0a4tDhw5h4sSJiI+Px+jRo/H555+DZdl2+z8IDQoNqhvtlEIBA3/6\nJPFAtHahjUBPj2AbStS9UJSUouzY/9AUmOfo74+AMaPBCOzTnm5OFHI10n+9aaAsAoI9MGhEb6os\n9DD5L+1hn2Q2b96MvXv3Yt26ddi5cydKS0uxePHiNvuePHkSy5cvxzPPPIP9+/dj2bJl2LZtG7Zu\n3fpQMrREf/8iwNsFIjvd0HoYdC60f+i50HrRtOVmRF1VhdJDeoF5Hh4IfPIvNDDPDFTL5Dh13DDN\nR+9wP/RPCevWaT4ehA5NUq+++iokEkPtunDhwlZtgC64789Qq9XYvn073nrrLQwePBgA8PHHHyM1\nNRXnz59Hv379DPp///33GDNmDKZPnw4ACA0Nxc2bN/Hzzz9j4cKFf3o/YzHcv6DmqAdB50JbDUDn\nQptKXWjNhrahASUHDhkE5gWPf5IG5pmBksIaXMi4B5bVlQpmGAax/UIQ+igt6NUW7SqMyZMnt2pr\nOaGbSm5uLhoaGpCcnMy39ejRAyEhIcjMzGz1+fPnz2+VhkQgEJg9EaLB/gXd8DaZe9VFrVxovZxo\n4Jg54NRqg4p5ApEYQeP+ArEHHd+Hgab5eDDaVRgffPCB2W9WWloKQFcLXB9/f3/+nD5xcXEGx/X1\n9di1axefZt0cKFRaVNbqPHoEDINAH7p/YQpyjQJpd87wx9SF1nzwFfP0A/OeGA1HfxqY9zC0lebD\nxdUBSUMegSutf9MhVvWSUigUEAgEELewu0okEqhUqnauar52wYIFUKlUWLZsmdlkKtGL7vb3doaY\n2iyNhhCCk7fPQEldaM2OLjAvDfJCvcC8x4fDJSzUhlJ1fRRyNbLPFkCmt2/p4+eKxBT7S/PxIFh1\nhBwdHcFxHLRaLUSi5lur1Wo4ObVvj5XJZFiwYAFu3LiBr776CiEh5kteZ1j/gu5fmMLV8nwU1DQH\nco54dBB1oTUTsjMZqMu/zh97JyfBPTLChhJ1bQghuHdLhpzLJdBqmr0se/byRmy/ELuN3DYVqyqM\noKAgAEBFRQX/HgDKy8tbmamaKCwsxMsvv4yGhgbs3LkTERHm/acpovsXD4RMXo0zhc0utLGBEejh\nHtTBFRRjqbl8BVV6WaHdoyLhlfhw+4f2TEOdCpeyCg3yQTEMg/CYQPQO96MrYhOwqlqNiIiAi4sL\nMjIy+LbCwkIUFRUhKSmpVf/KykrMnDkTHMdh165dZlcWKg2L+9U6cwrDMAiiKwyj0HIsjt86BY7T\neZb4OHshOYS60JqD+lu3UPH7H/yxS1gY/IbRinkPAuF0G9u/Hcs3UBYubg5Ieby33af5eBCsusKQ\nSCSYNm0aPvzwQ3h5ecHHxwdr1qxBcnIy4uPjoVarUVNTAw8PD0gkEqxZswZVVVX49ttv4ejoiIoK\nXbg+wzDw9fV9aHlK7zfw6U58PRzhIKb7F8ZwtvA8qhS6AKemLLRC6kL70ChKSlB29DgMA/NG0cC8\nB6CuRomLmQWolsn5NoZh0DvcD49FBUBITVAPhNV3eZYuXQqtVosVK1ZAq9Vi6NCheOeddwAA2dnZ\nmDlzJrZv346+ffvi2LFj4DgOzzzzjMFnCIVCXLt27aFloeYo07lXXYSrZc1J71J6JlIXWjOgllWh\n5OAvIBwNzHsYOJbDjbwK3MgpA8c1575z93RC3/494EGzUD8UVlcYIpEIK1euxMqVK1udGzBgAPLy\n8vjjnJwci8pC61+YRksX2jDPHoj062NDiboH2voGFB84CE6tF5g3gVbMM5VqmRwXMwtRV9McsS0Q\nCPBYlD96h/vTCppmwG79yDRaFuV6y1W6f9ExLV1onSVOGN5rALUBPyS6wLxD0NbrVrt8YJ67u40l\n6zqwLIf8q2W4lV9hkFHby8cFcf17wM2OSqhaGrtVGKWVcnCNf1ze7o5wdqRL/464Wp5n4EL7+CMp\ncKQutA8FYVmUHD4CVWUlAJ2NPXAsDcwzhcqKelzKLDQociQUChAeE4hH+viCoasKs2K3CkM/YI/u\nX3SMzoW22c0zLjCSutA+JE2BeYqi5lTwfo8Ph3MoDcwzBq2GRe7lUty5aZjp2tffFXGJPeDsSiO2\nLYHdKowiWv/CKNpyoU0K6Wtjqbo+sjNnaWDeA1JeWofLWYVQyNV8m0gsRGRcEEIf8aZmUgtilwqD\nZTmUVtIVhjG0dKFNpS60D031pcuoyr7AH7tHRdHAPCNQq7S4drEEhXdlBu0BQe6I6RdC61ZYAbtU\nGGVVcrCNLneerg5wdaL7F21xt7rQwIV2UGgiPKkL7QNDCEF9/nXcP5XOt7n06gW/YUPoU/GfUFJY\ngyvZRVApNXybWCJCTEIwgnt60vGzEnapMPTrXwTT+hdtItcocPJ2swttL6+eiPClLrQPirK8HJXp\nZ6AobnYccAwIQMDoVBqY1wEqpQZXsotQUlhj0B7c0xPR8SFwcLTLKcxm2OVo0/oXHUMIQdrt01Bq\ndZ4nzhJnDKMutA+Etr4elWcyUJefb9Au9vBA0JNjaWBeOxBCUHSvGlcvFEOj1vLtDo5ixCaGIDCY\nrnRtgd0pDI4jKNHfv/ClCqMlV8rzUFjTWFiGYTDikRQ4iqjXiSlwajWqzmej+uIlvqwqoHOddY+O\nhndyfwgdqVtyWyjkalzOKkJ5qWGhtJ6PeCMqLghiid1NW50Guxv5imoFNFqdx4+rkxhuzvQJT59K\neRXO6rvQBkQgxD3QhhJ1LQjHoTYnB7KMTLAKhcE5l1694DNoICSenjaSrnPTXgpyJxcJ4hJ7wI9W\nwrM5dqcw9N1pQ/xcqZlFD50L7R+8C62vizd1oTUSQgjkd++h8vQZqKuqDM45+PnBd1AKnEKCbSRd\n56e9FOS9evsgPDYQIlrYrFNgdwqjhO5ftMuZgvOobnShFQlENAutkagq7uN++mmDIDwAELm4wGfg\nALhKH6MPJu1AOIJb1+8j/2opWJbj213cHNC3f0940xipToVdKQyOI4YJB6mHFM/d6kJcK2/hQutI\n8xl1hLa+AbKMDNTm5qMpJTkACMRiePVLgEffOAhEdvUvZhI0BXnXw67+mmW1SqgabaPOjmJ40vQB\nAAC5urULbbhvbxtK1LnhNBpUnb+A6gsXWm9oR0XBK6k/zTTbATQFedfFrhRGy3Qg1EzQ6EJ7h7rQ\nGoNuQzsXsoxzrTe0w8LgkzIQEm8vG0nX+WmoU6GspBYFt2Woq1Xy7TQFedfBrhQGNUe15nJZroEL\n7UjqQtsm8nv3cD/9DNQyw7QUDr6+8Bk0EM49ethIss4L4QhklQ0oL6lFWXEd6uuUrfrQFORdC7tS\nGGV68RchdMMb9+UyZBQ15zTqGxiJYOpCa4DqfiUqT5+GvKDQoJ1uaLeNRsOiorQOZcW1KC+tMwi6\n04emIO+a2JXCcHESo16hgY+7I7zt/IlGy2pxooULbf/gOBtL1XnQbWifQ21uHgw2tEViePaLh2ff\nOBql3UhDvUqnIEpqUVnRYFDESB+hUADfADcEBLkhINiDpvXogtjVb2zCkEdxq7gGoQFudv9UeLrg\nPKoVukha6kLbDKfRoPrCRVRnXwCn1X86ZuAeFQHv5CSInO17U5ZwBFUyOcqKa1FWUov62tampiYc\nncQICHKHf7A7fP1dqedTF8euFIajgwhRj/jYWgybc6eqEDkVzbUYBoX2t3sXWsJxqMvLh+xsBrRy\nucE559BQ+KQMhIOPt42ksz1aDYvy0jrdfkRJ+6YmAPDwckZAsDsCgtzg7ulk9w9n3Qm7UhgUoEEt\nx8k7zS60j3iFItz3URtKZHvkBYWoTD/Nl0ptwsHHBz6DUuDc0z43tOX1KpQ2mppk9xsMXGD1EQoF\n8PV3hX+wOwKC3OFIywV0W6jCsCNYjkXa7dNQNbrQukicMbRXst0+AaoqZahMPw15QYFBu8jZGd4D\nkuEWLrWr1OOmmpr8g3QKwtffFUKR/YyTPUMVRjeGIxzuy6tQVFuC4toylNZXgOUaA80YBiMeHWSX\nLrRauVy3oX0tF4Yb2iJ4JsTDM76v3WxoazUsKsqavZrUqo5MTU68kvDwoqYme4QqjG4EIQRVuZGh\nfAAAHhBJREFUihoU1ZWiqLYUJXXl0LCaNvvGB0Yh2C3AyhLaBq1cAbVMxv/U598Ap9UfFwbuEeHw\nHpAEkUv3js8hhEDeoEZ5o+urrKK+Q1OTj78rAoLcERBMTU0UqjC6NIQQ1KnqGxVEGYrryqDUtG9G\nAAAPR3dIfR9B38AoK0lpPVilslEpVBm8ssr2x8S5Zw/4pKTAwbd7OEMQQqBWsVDI1ZA36H4UDWrI\n5U3vNbwrdVs4OIoREOTGezXRLLEUfajC6GI0qOUoritDUW0piuvKUK9q6LC/i8QZIe6BCHYLQLB7\nAFwlXf8JmlWpWikFtUzWKl1HR0i8veE7aCCcQ0MtKKn5IYRAq2EblYFGpwTkzYpBIddAq2X//IP0\ncPd04lcR1NRE6QiqMDo5Sq0KJXXlvIJoSj/eHg4iB4S4ByDYLRAh7gFwd+i6MSecRmOgEJreaxs6\nVpItEYjEkHh7Nf54Q+LrA6fg4E67oc0rBLka8nqdEtBXDPrFhR4EsUQEL29n+Ae7ISDIHU7OEjNJ\nTunuUIXRydCwGpTWV/AK4r68CmgnchYAREKRbvXgFoAQ90B4O3l2OQXBaTRQV1VBU1UNtUwGVaUM\nmqoqaOrqTPocRiiExEtPMTS+itw6l9JktRzk8kZTkZ4iaFoxdBTjYAwisRDOLhI4OUsaX8VwdpXA\nufFYJKZmJsqDQRWGjWE5FuUNlbyCKK+/D460b2MWCAQIdPXjVxB+zj4QdNIn5SYIy4JVqcGplOBU\nKmhq6wxWDJraOuh7K/0ZjEAIsaeHgVKQeHtD7O5mlVVDk1lIo+GgUbPQaFiDV905tt1z+oWCHgSh\nUAAnF93k7+wsaXwv5pWEWCLsVAqS0n2gCsPKcIRDpbyqcZO6FKV1FdByHTxRMgz8XXz4FUSAqx9E\nNkjhQQgB0WjAKlXgVCqwKiU4lRqsUqcEdG0qcMoW55SqFh5JxsMwDMSengZKQeLtBbGHx0MpBkII\nOI60OaFrNI0TfgfntBqu3XxJ5kAgEMCpUQE0KwQJrxAkDlQhUGyD1RUGy7L49NNPsXfvXjQ0NGDo\n0KF455134Ovr22b/y5cv47333kNOTg4CAgKwYMECTJo0ycpSt4YQApZjoWRVUGs1ULIqqLRq3Y/B\nezVUWlXjqxoKrRJatmOTg7ezJ7+CCHL1h0RkHhszIQTgON3TvloFTqn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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "for gamma in gamma_array:\n", + " label = 'gamma = ' + str(gamma)\n", + " plot(frame[gamma], label=label)\n", + " \n", + "decorate(xlabel='Contacts per day (beta)',\n", + " ylabel='Fraction infected',\n", + " loc='upper left')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "It's often useful to separate the code that generates results from the code that plots the results, so we can run the simulations once, save the results, and then use them for different analysis, visualization, etc." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Contact number" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "After running the SweepSeriess, we have a `SweepSeriesFrame` with one row for each value of `beta` and one column for each value of `gamma`." + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "(11, 4)" + ] + }, + "execution_count": 21, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "frame.shape" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The following loop shows how we can loop through the columns and rows of the `SweepSeriesFrame`. With 11 rows and 4 columns, there are 44 elements.\n", + "\n", + "One implementation note: when we select a column from a `SweepSeriesFrame` we get a `Series` object, rather than a `SweepSeries` object, but they are almost the same." + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "0.1 0.1 0.0846929424381\n", + "0.18 0.1 0.70862278537\n", + "0.26 0.1 0.900780251778\n", + "0.34 0.1 0.956887899544\n", + "0.42 0.1 0.977045257074\n", + "0.5 0.1 0.984595862826\n", + "0.58 0.1 0.987400345318\n", + "0.66 0.1 0.988404249064\n", + "0.74 0.1 0.988743421406\n", + "0.82 0.1 0.988849515052\n", + "0.9 0.1 0.988879570517\n", + "0.1 0.3 0.00544355912239\n", + "0.18 0.3 0.0159140691448\n", + "0.26 0.3 0.0553797621068\n", + "0.34 0.3 0.267864167733\n", + "0.42 0.3 0.524562935844\n", + "0.5 0.3 0.686050483916\n", + "0.58 0.3 0.788378556339\n", + "0.66 0.3 0.85506574641\n", + "0.74 0.3 0.89947913569\n", + "0.82 0.3 0.929469302619\n", + "0.9 0.3 0.949853310327\n", + "0.1 0.5 0.00273576554115\n", + "0.18 0.5 0.00611834135832\n", + "0.26 0.5 0.0116394693217\n", + "0.34 0.5 0.0221147665242\n", + "0.42 0.5 0.0478162266689\n", + "0.5 0.5 0.132438038458\n", + "0.58 0.5 0.303264192648\n", + "0.66 0.5 0.464110227319\n", + "0.74 0.5 0.588476972528\n", + "0.82 0.5 0.682749610978\n", + "0.9 0.5 0.754595298329\n", + "0.1 0.7 0.001826769347\n", + "0.18 0.7 0.00378256160842\n", + "0.26 0.7 0.00642667221076\n", + "0.34 0.7 0.0101905519335\n", + "0.42 0.7 0.0159458265615\n", + "0.5 0.7 0.0257079250464\n", + "0.58 0.7 0.0450077531168\n", + "0.66 0.7 0.0906940688294\n", + "0.74 0.7 0.189795211656\n", + "0.82 0.7 0.318343186735\n", + "0.9 0.7 0.436999374456\n" + ] + } + ], + "source": [ + "for gamma in frame.columns:\n", + " series = frame[gamma]\n", + " for beta in series.index:\n", + " frac_infected = series[beta]\n", + " print(beta, gamma, frac_infected)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now we can wrap that loop in a function and plot the results. For each element of the `SweepSeriesFrame`, we have `beta`, `gamma`, and `frac_infected`, and we plot `beta/gamma` on the x-axis and `frac_infected` on the y-axis." + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def plot_sweep_frame(frame):\n", + " \"\"\"Plots the values from a parameter SweepSeries.\n", + " \n", + " For each (beta, gamma), computes the contact number,\n", + " beta/gamma\n", + " \n", + " frame: SweepFrame with one row per beta, one column per gamma\n", + " \"\"\"\n", + " for gamma in frame.columns:\n", + " series = frame[gamma]\n", + " for beta in series.index:\n", + " frac_infected = series[beta]\n", + " plot(beta/gamma, frac_infected, 'ro',\n", + " label='Simulation')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here's what it looks like:" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Saving figure to file chap06-fig03.pdf\n" + ] + }, + { + "data": { + "image/png": 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LFi1CQEAAfHx8EBUVhRs3bpR7/M6dOxEaGgpvb2906dIFq1evRklJiQEjJiIi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\nTH4J+ubNmyMuLs7g9d6+fRv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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plot_sweep_frame(frame)\n", + "\n", + "decorate(xlabel='Contact number (beta/gamma)',\n", + " ylabel='Fraction infected',\n", + " legend=False)\n", + "\n", + "savefig('chap06-fig03.pdf')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "It turns out that the ratio `beta/gamma`, called the \"contact number\" is sufficient to predict the total number of infections; we don't have to know `beta` and `gamma` separately.\n", + "\n", + "We can see that in the previous plot: when we plot the fraction infected versus the contact number, the results fall close to a curve.\n", + "\n", + "But if we didn't know about the contact number, we might have explored other possibilities, like the difference between `beta` and `gamma`, rather than their ratio." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Exercise:** Write a version of `plot_sweep_frame`, called `plot_sweep_frame_difference`, that plots the fraction infected versus the difference `beta-gamma`.\n", + "\n", + "What do the results look like, and what does that imply? " + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "# Solution goes here\n", + "def plot_sweep_frame_difference(frame):\n", + " \"\"\"Plots the values from a parameter SweepSeries.\n", + " \n", + " For each (beta, gamma), computes the contact number,\n", + " beta/gamma\n", + " \n", + " frame: SweepFrame with one row per beta, one column per gamma\n", + " \"\"\"\n", + " for gamma in frame.columns:\n", + " series = frame[gamma]\n", + " for beta in series.index:\n", + " frac_infected = series[beta]\n", + " plot(beta-gamma, frac_infected, 'ro',\n", + " label='Simulation')" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Saving figure to file chap06-fig03.pdf\n" + ] + }, + { + "data": { + "image/png": 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UwN3dnUuztrZG06ZNkZCQoJT/7Nmz6NixI+rUqcOlDRw4ELGxsYL2RwghRHMENXq3atUK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\nEEIIEeT/AQ7RkL0TPoTXAAAAAElFTkSuQmCC\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Solution goes here\n", + "plot_sweep_frame_difference(frame)\n", + "\n", + "decorate(xlabel='Contact number (beta/gamma)',\n", + " ylabel='Fraction infected',\n", + " legend=False)\n", + "\n", + "savefig('chap06-fig03.pdf')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Analysis" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In the book we figured out the relationship between $c$ and $s_{\\infty}$ analytically. Now we can compute it for a range of values:" + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([ 1.00000000e-04, 1.00980000e-02, 2.00960000e-02,\n", + " 3.00940000e-02, 4.00920000e-02, 5.00900000e-02,\n", + " 6.00880000e-02, 7.00860000e-02, 8.00840000e-02,\n", + " 9.00820000e-02, 1.00080000e-01, 1.10078000e-01,\n", + " 1.20076000e-01, 1.30074000e-01, 1.40072000e-01,\n", + " 1.50070000e-01, 1.60068000e-01, 1.70066000e-01,\n", + " 1.80064000e-01, 1.90062000e-01, 2.00060000e-01,\n", + " 2.10058000e-01, 2.20056000e-01, 2.30054000e-01,\n", + " 2.40052000e-01, 2.50050000e-01, 2.60048000e-01,\n", + " 2.70046000e-01, 2.80044000e-01, 2.90042000e-01,\n", + " 3.00040000e-01, 3.10038000e-01, 3.20036000e-01,\n", + " 3.30034000e-01, 3.40032000e-01, 3.50030000e-01,\n", + " 3.60028000e-01, 3.70026000e-01, 3.80024000e-01,\n", + " 3.90022000e-01, 4.00020000e-01, 4.10018000e-01,\n", + " 4.20016000e-01, 4.30014000e-01, 4.40012000e-01,\n", + " 4.50010000e-01, 4.60008000e-01, 4.70006000e-01,\n", + " 4.80004000e-01, 4.90002000e-01, 5.00000000e-01,\n", + " 5.09998000e-01, 5.19996000e-01, 5.29994000e-01,\n", + " 5.39992000e-01, 5.49990000e-01, 5.59988000e-01,\n", + " 5.69986000e-01, 5.79984000e-01, 5.89982000e-01,\n", + " 5.99980000e-01, 6.09978000e-01, 6.19976000e-01,\n", + " 6.29974000e-01, 6.39972000e-01, 6.49970000e-01,\n", + " 6.59968000e-01, 6.69966000e-01, 6.79964000e-01,\n", + " 6.89962000e-01, 6.99960000e-01, 7.09958000e-01,\n", + " 7.19956000e-01, 7.29954000e-01, 7.39952000e-01,\n", + " 7.49950000e-01, 7.59948000e-01, 7.69946000e-01,\n", + " 7.79944000e-01, 7.89942000e-01, 7.99940000e-01,\n", + " 8.09938000e-01, 8.19936000e-01, 8.29934000e-01,\n", + " 8.39932000e-01, 8.49930000e-01, 8.59928000e-01,\n", + " 8.69926000e-01, 8.79924000e-01, 8.89922000e-01,\n", + " 8.99920000e-01, 9.09918000e-01, 9.19916000e-01,\n", + " 9.29914000e-01, 9.39912000e-01, 9.49910000e-01,\n", + " 9.59908000e-01, 9.69906000e-01, 9.79904000e-01,\n", + " 9.89902000e-01, 9.99900000e-01])" + ] + }, + "execution_count": 27, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "s_inf_array = linspace(0.0001, 0.9999, 101)\n", + "s_inf_array" + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([ 9.2112615 , 4.6422958 , 3.98736457, 3.61213299, 3.3509237 ,\n", + " 3.15180795, 2.99171106, 2.85836348, 2.7444671 , 2.64533168,\n", + " 2.5577667 , 2.47950503, 2.40887895, 2.34462674, 2.28577125,\n", + " 2.23154075, 2.18131534, 2.13458984, 2.09094726, 2.05003956,\n", + " 2.01157331, 1.97529894, 1.94100246, 1.90849906, 1.87762809,\n", + " 1.84824906, 1.82023841, 1.79348694, 1.76789768, 1.74338417,\n", + " 1.71986896, 1.69728247, 1.67556193, 1.65465053, 1.63449675,\n", + " 1.61505364, 1.59627839, 1.5781318 , 1.56057794, 1.54358375,\n", + " 1.52711879, 1.51115495, 1.49566621, 1.48062849, 1.46601941,\n", + " 1.45181817, 1.43800537, 1.42456295, 1.41147401, 1.39872275,\n", + " 1.38629436, 1.37417495, 1.36235148, 1.35081168, 1.339544 ,\n", + " 1.32853755, 1.31778207, 1.30726786, 1.29698574, 1.28692704,\n", + " 1.27708354, 1.26744745, 1.25801137, 1.24876828, 1.2397115 ,\n", + " 1.2308347 , 1.22213183, 1.21359713, 1.20522511, 1.19701055,\n", + " 1.18894843, 1.18103401, 1.1732627 , 1.16563015, 1.15813219,\n", + " 1.15076481, 1.14352419, 1.13640665, 1.12940868, 1.12252689,\n", + " 1.11575804, 1.10909902, 1.10254682, 1.09609857, 1.0897515 ,\n", + " 1.08350294, 1.07735032, 1.07129118, 1.06532312, 1.05944385,\n", + " 1.05365116, 1.04794291, 1.04231704, 1.03677154, 1.03130451,\n", + " 1.02591407, 1.02059843, 1.01535586, 1.01018468, 1.00508325,\n", + " 1.00005 ])" + ] + }, + "execution_count": 28, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "c_array = log(s_inf_array) / (s_inf_array - 1)\n", + "c_array" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "`total_infected` is the change in $s$ from the beginning to the end." + ] + }, + { + "cell_type": "code", + "execution_count": 29, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "frac_infected = 1 - s_inf_array\n", + "frac_infected_series = Series(frac_infected, index=c_array)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now we can plot the analytic results and compare them to the simulations." + ] + }, + { + "cell_type": "code", + "execution_count": 30, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Saving figure to file chap06-fig04.pdf\n" + ] + }, + { + "data": { + "image/png": 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o0i4WQsIZ/Qq1Hk4QO0n6L4QQFiNjNBuwNHd/iHQFwLdXW/B3tXBEQojmTBaF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\nLFiwgOPHj+Pr68uUKVMYOnRo/QRbNq8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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plot_sweep_frame(frame)\n", + "plot(frac_infected_series, label='Analysis')\n", + "\n", + "decorate(xlabel='Contact number (c)',\n", + " ylabel='Fraction infected')\n", + "\n", + "savefig('chap06-fig04.pdf')" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": true + }, + "source": [ + "The agreement is generally good, except for values of `c` less than 1." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Exercise:** Suppose you run a survey at the end of the semester and find that 26% of students had the Freshman Plague at some point. What is your best estimate of `c`?\n", + "\n", + "Hint: if you print `frac_infected_series`, you can read off the answer. " + ] + }, + { + "cell_type": "code", + "execution_count": 31, + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "9.211261 0.999900\n", + "4.642296 0.989902\n", + "3.987365 0.979904\n", + "3.612133 0.969906\n", + "3.350924 0.959908\n", + "3.151808 0.949910\n", + "2.991711 0.939912\n", + "2.858363 0.929914\n", + "2.744467 0.919916\n", + "2.645332 0.909918\n", + "2.557767 0.899920\n", + "2.479505 0.889922\n", + "2.408879 0.879924\n", + "2.344627 0.869926\n", + "2.285771 0.859928\n", + "2.231541 0.849930\n", + "2.181315 0.839932\n", + "2.134590 0.829934\n", + "2.090947 0.819936\n", + "2.050040 0.809938\n", + "2.011573 0.799940\n", + "1.975299 0.789942\n", + "1.941002 0.779944\n", + "1.908499 0.769946\n", + "1.877628 0.759948\n", + "1.848249 0.749950\n", + "1.820238 0.739952\n", + "1.793487 0.729954\n", + "1.767898 0.719956\n", + "1.743384 0.709958\n", + " ... \n", + "1.181034 0.290042\n", + "1.173263 0.280044\n", + "1.165630 0.270046\n", + "1.158132 0.260048\n", + "1.150765 0.250050\n", + "1.143524 0.240052\n", + "1.136407 0.230054\n", + "1.129409 0.220056\n", + "1.122527 0.210058\n", + "1.115758 0.200060\n", + "1.109099 0.190062\n", + "1.102547 0.180064\n", + "1.096099 0.170066\n", + "1.089751 0.160068\n", + "1.083503 0.150070\n", + "1.077350 0.140072\n", + "1.071291 0.130074\n", + "1.065323 0.120076\n", + "1.059444 0.110078\n", + "1.053651 0.100080\n", + "1.047943 0.090082\n", + "1.042317 0.080084\n", + "1.036772 0.070086\n", + "1.031305 0.060088\n", + "1.025914 0.050090\n", + "1.020598 0.040092\n", + "1.015356 0.030094\n", + "1.010185 0.020096\n", + "1.005083 0.010098\n", + "1.000050 0.000100\n", + "Length: 101, dtype: float64\n" + ] + } + ], + "source": [ + "# Solution goes here\n", + "print(frac_infected_series)\n", + "#c = 1.158132" + ] + }, + { + "cell_type": "code", + "execution_count": 32, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "1.158096819542062" + ] + }, + "execution_count": 32, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Alternative solution\n", + "\n", + "\"\"\"We can use `np.interp` to look up `s_inf` and\n", + "estimate the corresponding value of `c`, but it only\n", + "works if the index of the series is sorted in ascending\n", + "order. So we have to use `sort_index` first.\n", + "\"\"\"\n", + "\n", + "frac_infected_series.sort_index(inplace=True)\n", + "np.interp(0.26, frac_infected_series, frac_infected_series.index)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "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": "3.6.1" + } + }, + "nbformat": 4, + "nbformat_minor": 1 +} From 6fa00ad536158df80856728003d383b8c57494c1 Mon Sep 17 00:00:00 2001 From: Junwon Lee <31522211+junwonlee5@users.noreply.github.com> Date: Wed, 25 Oct 2017 18:11:38 -0400 Subject: [PATCH 12/19] Adding chap08mine --- code/chap08mine.ipynb | 2784 +++++++++++++++++++++++++++++++++++++++++ 1 file changed, 2784 insertions(+) create mode 100644 code/chap08mine.ipynb diff --git a/code/chap08mine.ipynb b/code/chap08mine.ipynb new file mode 100644 index 00000000..57c01e4e --- /dev/null +++ b/code/chap08mine.ipynb @@ -0,0 +1,2784 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Modeling and Simulation in Python\n", + "\n", + "Chapter 8: Pharmacokinetics\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": 2, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "# If you want the figures to appear in the notebook, \n", + "# and you want to interact with them, use\n", + "# %matplotlib notebook\n", + "\n", + "# If you want the figures to appear in the notebook, \n", + "# and you don't want to interact with them, use\n", + "# %matplotlib inline\n", + "\n", + "# If you want the figures to appear in separate windows, use\n", + "# %matplotlib qt5\n", + "\n", + "# tempo switch from one to another, you have to select Kernel->Restart\n", + "\n", + "%matplotlib inline\n", + "\n", + "from modsim import *" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Data\n", + "\n", + "We have data from Pacini and Bergman (1986), \"MINMOD: a computer program to calculate insulin sensitivity and pancreatic responsivity from the frequently sampled intravenous glucose tolerance test\", *Computer Methods and Programs in Biomedicine*, 23: 113-122.." + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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glucoseinsulin
time
09211
235026
4287130
625185
824051
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1420541
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1919230
2217230
2716327
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92828
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\n", + "
" + ], + "text/plain": [ + " glucose insulin\n", + "time \n", + "0 92 11\n", + "2 350 26\n", + "4 287 130\n", + "6 251 85\n", + "8 240 51\n", + "10 216 49\n", + "12 211 45\n", + "14 205 41\n", + "16 196 35\n", + "19 192 30\n", + "22 172 30\n", + "27 163 27\n", + "32 142 30\n", + "42 124 22\n", + "52 105 15\n", + "62 92 15\n", + "72 84 11\n", + "82 77 10\n", + "92 82 8\n", + "102 81 11\n", + "122 82 7\n", + "142 82 8\n", + "162 85 8\n", + "182 90 7" + ] + }, + "execution_count": 4, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "data = pd.read_csv('glucose_insulin.csv', index_col='time')\n", + "data" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here's what the glucose time series looks like." + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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GplU33p07dzJgwAASExP585//zPjx4/nxxx/ZsGEDJiYmvPjiiw06+ZEjR1i3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\no4+wv29K1x07duDp6UloaCj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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plot(data.glucose, 'bo', label='glucose')\n", + "decorate(xlabel='Time (min)',\n", + " ylabel='Concentration (mg/dL)')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "And the insulin time series." + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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Ufp+RnyH9nsWFiBozhQrLuXPnsG/fPgDPZt2bmZmhY8eOaN++PR48eIBff/0VoaGhSgmq\nbo6lHKuy/eeUn1lYiKhRU6iwnDlzBoWFhbh58yZu3bqFmzdv4ubNm4iJiUFeXh4AwN/fH2+88Qbs\n7Oxga2sLe3t7jBgxQinhVSmzILPK9nsF9+o5CRGRelH4GouRkRFcXV3h6uoq037//n1poXledM6d\nO4fi4uIGWVgsjC2QkZ8h125pbKmCNERE6qNGhWXZsmVYuHAhTExMqt2mdevWaN26NXr16gUAyM3N\nxdq1azFr1ixxkqoZL3svmWsszw21H6qCNERE6qNGw42tra3h5eWF4OBgXLly5ZXbXr9+HStXrsSI\nESPQtm1budu+NBQeVh6Y4ToD1s2soSXRgnUza8xwncHrK0TU6NXoiOXjjz/GwIEDsWbNGowZMwaW\nlpbo0qULrK2tYWBggIKCAmRlZSEpKQn3799H//798f3336Njx46iBX369CnWrFmD48ePo7i4GC4u\nLliyZAns7e0BAOfPn0dISAju3LmDN954A4sWLUL//v1Fe/2qeFh5sJAQEb2kxtdYOnTogC1btuDm\nzZs4fPgw4uLicOHCBRQUFMDExARWVlYYP348Bg8eDEdHR9GDfvnll0hKSsKGDRvQokULrF27FjNm\nzMDx48eRlpYGPz8/zJo1C4MHD8bhw4fh7++PgwcPwsHBQfQsRERUPYUv3nfo0AELFy5URpZXOnny\nJGbPng03NzcAwCeffILhw4cjJSUFe/fuhYuLi3T1yvnz5yMxMRFRUVFYtWpVvWclImrMNGY9lpYt\nW+I///kPHjx4gNLSUkRHR6N58+awsbFBQkICunfvLrO9p6cnEhISVJSWiKjx0ph1hFetWoV///vf\n6NWrF7S1taGvr4/t27ejWbNmyMrKgpmZmcz2pqamyMrKUlFaIqLGS2OOWO7evYvWrVtj69at+OGH\nH9CnTx/MnTsXWVlZKC4uhq6ursz2urq6KCkpUVFaIqLGSyOOWNLS0rB8+XLs2bMHLi4uAIA1a9Zg\n2LBh2LFjB/T09FBWVibzmNLSUhgYGKgiLhFRo6YRRyyXL19GRUUFOnfuLG3T0dFBp06dcPfuXVhY\nWCAnJ0fmMTk5OXKnx4iISPlqfcRSWFiIoqIiVFZWyvWJ/YFubm4OALhx4wacnJwAAIIg4Pbt2+jX\nrx9at26N+Ph4mcfExcXB3d1d1BxERPR6CheW1NRUfP7550hMTKx2m2vXrtUp1MucnZ2lEyK/+OIL\nmJiY4Pvvv8e9e/cwceJEFBYWYsyYMQgLC8Pw4cNx5MgRXLp0CQEBAaLmICKi11O4sAQGBiIlJQWz\nZ8+Gubk5tLSUfzZNW1sbmzZtwtq1a7FgwQI8ffoUnTt3xp49e2BlZQUACA8PR0hICCIiImBra4vN\nmzfDzs5O6dmIiEiWwoUlISEBq1evrvc7Frds2RKrV6+utn/AgAEYMGBA/QUiIqIqKXy4YWhoiObN\nmysjCxERNQAKF5ZRo0Zh9+7dEARBGXmIiEjD1Wqhr8TERAwZMgTOzs5yc0UkEgkCAwNFC0hERJpF\n4cKyf/9+GBsbo7y8HElJSXL9EolElGBERKSZFC4sp0+fVkYOIiJqIGo9QTIlJQUXLlxAYWEhTExM\n4ObmBltbWzGzERGRBlK4sFRWVmLFihXYv3+/zAV8iUQCb29vfP311zwdRkTUiClcWLZu3YqYmBgs\nXLgQI0eOROvWrZGbm4vDhw8jLCwMdnZ28PX1VUZWIiLSAAoXlujoaHz88ceYMWOGtM3c3By+vr4o\nKSlBdHQ0CwsRUSOm8DyW3Nxc6fLAL3N1dUVmZmadQxERkeZSuLDY2NggOTm5yr7k5GS0adOmzqGI\niEhzKXwqbOzYsVi7di2aNm2KYcOGoXXr1rh//z6OHj2KLVu2YObMmcrISUREGkLhwjJp0iRcu3YN\nQUFBCA4OlrYLgoBRo0bBz89P1IBERKRZFC4s2traCA4OxowZMxAfH4/8/Hw0a9YMHh4ecHBwUEZG\nIiLSILWeIOng4MBCQkREcmpUWJYvX46ZM2fC2toay5cvf+W2vAklEVHjVqPC8ttvv8HHx0f671fh\nrHsiosatRoXlxRtPBgUF4c0334SRkZHcdvn5+a8tPERE1LApPI9lypQp+Pvvv6vsu3r1Kj799NM6\nhyIiIs1VoyOWTz/9VDqjXhAEBAQEVHnE8s8//6B169biJiQiIo1SoyMWLy8vaGtrQ1tbGwCk/37x\nS0dHB25ubjJzW4iIqPGp0RHLgAEDMGDAAADPJkgGBATAzs5OmbmIiEhDKXyNZefOnSorKvv27cOQ\nIUPg7OyM0aNH4/fff5f2nT9/Ht7e3nB2dsbIkSMRGxurkoxERI2dwoXluby8POTk5CA7OxvZ2dnI\nysrC33//jX379omZT+rgwYNYuXIlfH19cfjwYXh4eGDWrFlIT09HSkoK/Pz8MHToUBw8eBCDBg2C\nv78/bt26pZQsRERUPYVn3t+4cQOLFi1CSkpKlf0SiQTjxo2rc7AXCYKAjRs3wtfXF2PHjgXwbEDB\nH3/8geTkZMTHx8PFxUV6n7L58+cjMTERUVFRWLVqlahZiIjo1RQuLN988w0ePXqETz/9FL/++it0\ndXXx1ltv4ezZszh79iyioqJED/n3338jIyMDw4YNk7ZpaWnh0KFDAIBNmzbBy8tL5jGenp44evSo\n6FmIiOjVFD4VdvHiRcybNw9Tp07FsGHDUFRUhAkTJmDz5s14++23sXPnTtFD/vPPPwCeTcCcPHky\nevbsCR8fHyQlJQEAsrKyYGZmJvMYU1NTZGVliZ6FiIheTeHCUlpainbt2gEA2rVrh+vXr0v7Ro8e\njYsXL4oW7rnCwkIAwJIlSzBu3DhERkbCwcEBU6ZMwe3bt1FcXAxdXV2Zx+jq6qKkpET0LERE9GoK\nnwqztLREeno63N3d0a5dOxQWFiIjIwNWVlbQ09PD48ePRQ+po6MDAPj4448xcuRIAMCbb76JxMRE\n/PDDD9DT00NZWZnMY0pLS2FgYCB6FiIiejWFj1jefvtthIaG4sSJEzAzM4OtrS02bNiA27dvY8eO\nHbCxsRE9pKmpKQCgQ4cO0jaJRAJbW1ukp6fDwsICOTk5Mo/JycmROz1GRETKp3BhmT17NlxcXPC/\n//u/AIDPPvsMx48fx4gRI/Dbb79hzpw5ood0cnJC06ZN8ddff0nbBEHA7du3YWNjAzc3N8THx8s8\nJi4uDu7u7qJnISKiV1P4VFhoaChmzpwJR0dHAEDfvn1x5MgRXL58GU5OTmjbtq3oIQ0MDDBlyhSs\nX78erVu3RocOHbBnzx6kpqYiLCwMZWVlGDNmDMLCwjB8+HAcOXIEly5dQkBAgOhZiIjo1RQuLNHR\n0Rg4cKDMxXIbGxulnAJ70bx582BgYICvvvoKDx48QKdOnbB9+3bY2toCAMLDwxESEoKIiAjY2tpi\n8+bNvO0MEZEKKFxYunbtivj4ePTu3VsZeaolkUgwc+ZMzJw5s8r+F+9nRkREqqNwYXFyckJkZCR+\n+eUXdOrUCU2bNpXp59LERESNm8KF5fjx4zA1NUVxcTGSk5Pl+rk0MRFR46ZwYXlxmWIiIqKXKTzc\nOD4+Hk+ePKmyLz8/H8eOHatzKCIi0lwKF5bJkyfj9u3bVfZxzXsiIuKa9yKKz4jHsZRjyCzIhIWx\nBbzsveBh5aHqWERE9Ypr3oskPiMekUmRyMjPQKVQiYz8DEQmRSI+I/71DyYiakC45r1IjqVUfW3p\n55SfedRCRI2KwqPCnq+3UlhYiKKiIlRWVspt0xhv/phZkCnzfc6THKTlp+F86nkIEHhajIgaDYUL\nS1paGj777DMkJiZWu821a9fqFEoTWRhbICM/A8CzonL9wbN1aox0jKSnxQCwuBBRg6dwYVm5ciVS\nUlIwe/ZsmJubQ0tL4YFlDZKXvZe0eKTlp0nbbZr/9x5qPC1GRI2BwoUlISEBq1evxogRI5SRR2M9\nLxg/p/yM86nnYaRjBJvmNmjTtI10m3sF91QVj4io3ihcWAwNDdG8eXNlZNF4HlYe8LDygABBelrs\nRZbGlipIRURUvxQ+jzVq1Cjs3r0bgiAoI0+D4GXvVWX7UPuh9ZyEiKj+KXzEYmRkhMTERAwZMgTO\nzs5y68rz7sayp8XuFdyDpbElhtoP5fUVImoUFC4s+/fvh7GxMcrLy5GUlCTXz7sbP/P8tNhz8Rnx\nCIwN5Kx8ImrweHfjevB8Vv5zHH5MRA1ZrccKZ2VlISYmBlu3bkVubi6uXr2K0tJSMbM1GK+alU9E\n1NAofMQCAMHBwdi5cyfKy8shkUjQu3dvrF27FtnZ2fj+++/RqlUrsXNqtJdn5T/H4cdE1BApfMSy\ndetW7Ny5E4sXL8aJEyeko8Nmz56Nx48fY926daKH1HQWxhZVtnP4MRE1RAoXlr1792LOnDmYPHky\nLC3/+8HYrVs3zJ8/H2fPnhU1YEPA4cdE1JgofCosJycHXbp0qbLPysoKjx49qnOohobDj4moMVG4\nsLRt2xbnzp1Dr1695PoSEhJgY2NTxaPEdfHiRUyYMAHfffcdPD09AQDnz59HSEgI7ty5gzfeeAOL\nFi1C//79lZ6lpjj8mIgaC4ULy5QpU/DFF1+gvLwcAwcOhEQiQVpaGhITE7Ft2zYsWrRIGTmlnj59\nisWLF6OiokLalpKSAj8/P8yaNQuDBw/G4cOH4e/vj4MHD8LBwUGpeWqDw4+JqCFTuLCMHz8eeXl5\n2LRpE3bt2gVBEDB//nzo6Ohg+vTp8PHxUUZOqaCgIJiZmeHu3bvStqioKLi4uMDPzw8AMH/+fCQm\nJiIqKgqrVq1Sap7a4KJgRNSQ1Wq48cyZM+Hj44Pk5GQ8evQIhoaGcHV1RYsWLcTOJyM2NhZnzpxB\nREQERo0aJW1PSEiAl5fsBXJPT08cPXpUqXlqi8OPiaghq9UEyR9++AErVqxA3759MXLkSBgbG2P8\n+PGIiYkRO5/Uw4cPsXTpUqxevVru7spZWVlyq1aampoiKytLaXnqgsOPiaghU7iw7Nq1C4GBgTAy\nMpK2mZubw93dHUuXLsWhQ4dEDfjcF198gYEDB6Jfv35yfcXFxdDV1ZVp09XVRUlJiVKy1BWHHxNR\nQ1arNe9nz54Nf39/aZuNjQ2++uorWFpaIjIyEt7e3qKGPHjwIK5evYqffvqpyn49PT2UlZXJtJWW\nlsrdeVldcPgxETVkCheWrKwsuLq6Vtnn5uaGiIiIOod62YEDB5CdnY0+ffoAgHS2v6+vL959911Y\nWFggJydH5jE5OTlyp8fUycvDj4mIGgqFC4ulpSXi4uLQs2dPub7ExESlfJiHhoaiuLhY+n1ubi58\nfHywevVq9O7dG+vXr0d8fLzMY+Li4uDu7i56FiIiejWFC8u//vUvhISEoLy8HO+88w5atmyJvLw8\nnD59Gtu2bcO8efNED/lysdLT05O2t2rVChMnTsSYMWMQFhaG4cOH48iRI7h06RICAgJEz0JERK+m\ncGGZOnUqsrOzsWPHDmzbtk3arq2tjUmTJmHGjBmiBqwJR0dHhIeHIyQkBBEREbC1tcXmzZthZ2dX\n71lqIz4jHsdSjnEWPhE1CBKhlovXFxQU4OLFi3j06BGMjY3h7OyMli1bip1PqdLT0zFo0CCcOnUK\n1tbWKsnw8iz852a4zmBxISK19LrPzlpNkASeLUHcsWNHVFZWAgDKysqQnZ0NQP7UFVWPs/CJqKFR\nuLCkpqbi888/R2JiYrXbXLt2rU6hGhPOwieihkbhwhIYGIiUlBTMnj0b5ubm0NKq9erGhGez8DPy\nM+TaOQufiDSVwoUlISEBq1evxogRI5SRp9Hxsveq8hoLZ+ETkaZSuLAYGhrK3auLao+z8ImooVG4\nsIwaNQq7d+9Gnz59IJFIlJGp0eEsfCJqSBQuLEZGRkhMTMSQIUPg7Owsdz8uiUSCwMBA0QISEZFm\nUbiw7N+/H8bGxigvL0dSUpJcP49ixFHdpEkxJlNyQiYRKZPCheX06dPKyEEvqG7p4qu5V/H/0v6f\nXDtQ8yWNuSwyESkbxwqroeomTX5/6fsq239O+bnOz63IcxARvUqtZ96npKTgwoULKCwshImJCVxd\nXTXm3lzteKFpAAASjUlEQVTqrrpJk9mF2XBo6SDXrshkSk7IJCJlU7iwVFZWYsWKFdi/fz9evM2Y\nRCKBt7c3vv76a15nqaPqJk2aGVV9qxxFJlNyQiYRKZvCp8K2bt2KmJgYLFy4ELGxsbhy5QrOnDmD\nBQsW4OjRo4iMlJ/sR4qpbuniKV2nVNn+8mTK+Ix4BMYGwu+IHwJjAxGf8d+1argsMhEpm8JHLNHR\n0fj4449lbo9vbm4OX19flJSUIDo6Gr6+vqKGVCVVjKB61aTJN9u8+crJlK+7OM8JmUSkbAoXltzc\nXLi5uVXZ5+rqiq1bt9Y5lLpQ5Qiq6iZNvm4yZU3ulswJmUSkTAqfCrOxsUFycnKVfcnJyWjTpk2d\nQ6kLTRxBxYvzRKRqCheWsWPHYvPmzdixYwdycnJQWVmJnJwcfPfdd9iyZQtGjx6tjJwqoYkf0hbG\nFlW28+I8EdUXhU+FTZo0CdeuXUNQUBCCg4Ol7YIgYNSoUfDz8xM1oCpp4ggq3i2ZiFRN4cIikUgQ\nHBwMX19fxMfH4/HjxzAyMoKnpyccHOTnWGgyTfyQ5sV5IlK1GheW1NRUBAQEoEePHvjoo49gb28P\ne3t7FBYWwtPTEy4uLggJCYGlpfr+Na8oTf2Q5sV5IlKlGhWW7Oxs+Pj4oLy8HN7e3nL9fn5+2LNn\nD/71r3/h4MGDaN26tehBVYUf0tXjzSyJqCo1uni/detW6OrqIiYmRq6wGBkZYfbs2YiOjoYgCA1q\nuDFV7/lQ7Iz8DFQKldKh2C9OxiSixqlGheXcuXPw9fWFmVnVtxQBAEtLS3z44Yc4e/asaOFedP/+\nfXz66afo06cP3N3d8eGHH+LmzZvS/vPnz8Pb2xvOzs4YOXIkYmNjlZKDntHEodhEVD9qVFiys7Nr\ndIPJTp06ISsrq86hXlZZWYnZs2fjn3/+wbfffosff/wRRkZGmDp1KvLy8pCSkgI/Pz8MHToUBw8e\nxKBBg+Dv749bt26JnoWe0cSh2ERUP2pUWExMTJCbm/va7R49eoRmzZrVOdTLrl+/juTkZHz11Vdw\ndnaGvb09QkJC8PTpU8TGxiIqKgouLi7w8/ODnZ0d5s+fj27duiEqKkr0LPQM58sQUXVqVFjc3NwQ\nExPz2u1iYmLg6OhY51Avs7CwwJYtW9C+fXtp2/M7KD9+/BgJCQno3r27zGM8PT2RkJAgehZ6hjez\nJKLq1KiwTJ48Gb/99htCQkJQWloq119aWorQ0FDExsbCx8dH9JAmJiYYMGAAtLT+G3fnzp0oLi5G\nnz59kJWVJXf9x9TUVCmn5egZDysPzHCdAetm1tCSaMG6mTVmuM7gqDAiqtlw465du2Lx4sUIDg5G\nTEwMevToASsrK1RUVODevXuIi4tDXl4e/P39MWDAACVHBk6dOoW1a9di2rRpsLOzQ3FxMXR1dWW2\n0dXVRUlJidKzNGYcik1EVanxBMkpU6agc+fO2LZtG06ePCn90DY0NESfPn0wbdo0uLi4KC3ocwcO\nHMDy5csxbNgw/Pvf/wYA6OnpoaysTGa70tJSGBgYKD0PERHJUuiWLm5ubtJb5j98+BBNmjRRysX6\n6mzatAnr16/HxIkTsWzZMul1FgsLC+Tk5Mhsm5OT88rh0UREpBy1XvO+ZcuWYuZ4rYiICKxfvx5z\n586Fv7+/TJ+bmxvi42Un5sXFxcHd3b0+IxIREWpx23xVuH79OtatW4cxY8Zg/PjxyM3NlX49ffoU\nEydOREJCAsLCwnD79m1s2LABly5dwpQpVS/lS0REylPrI5b69J///AcVFRXYv38/9u/fL9M3b948\nzJo1C+Hh4QgJCUFERARsbW2xefPmGk3qJNUT455jvG8ZkfqQCIIgqDqEqqSnp2PQoEE4deoUrK2t\nVR2nUXp5+efnFBm6LMZzEFHNve6zUyNOhVHDJcY9x3jfMiL1wsJCKiXGPcd43zIi9cLCQiolxj3H\neN8yIvXCwkIqJcY9x3jfMiL1ohGjwqjhEmP5Z01dQpqooWJhqQKHrtYvMe45JtZ9yxrie98QfyZS\nbywsL3l56OrzJXcB8D9jA9cQ3/uG+DOR+mNhecmrhq7yP2LDJuZ7ry5HCfx9JlVgYXkJh642XmK9\n9+p0lMDfZ1IFjgp7CYeuNl5ivffqNGGTv8+kCjxieYmXvVeVtwfh0NWGT6z3Xswjn7qeTuPv86up\nyylLdctSVywsL+HQ1cZLrPfewtgCGfkZcu2KHCWIdTqNv8/VU6dTluqURQwsLFXgkruNlxjvvRhH\nCWJedFe332d1+ctcnQY2qFOW5+ryPrGwEIlMjKOEhnrRXZ3+MlenfaxOWYC6v08sLERKUNejBDFO\np6kjdfrLXJ32sTplAer+PnFUGJEaaqj3P1Onv8zVaR+rUxag7u8Tj1iI1FBDveiuTn+Zq9M+Vqcs\nQN3fJxYWIjWlbhfdxaBuw5/VaR+rU5a6vk+NurBUVFQAALKyslSchKhxsIAFvC29EftPLLKfZMPM\n0Az92/WHhWCB9PR0Vcej//O69+n5Z+bzz9CXNerCkpubCwDw8fFRcRKixisGMaqOQDVQ1fuUm5uL\nN954Q65dIgiCUB+h1FFxcTEuX76MNm3aQFtbW9VxiIg0QkVFBXJzc9G5c2fo6+vL9TfqwkJEROLj\ncGMiIhIVCwsREYmKhYWIiETFwkJERKJiYSEiIlGxsLykoqICa9asQZ8+fdCtWzfMnTsX9+/fV3Us\njZWSkgJHR0e5r4SEBADA+fPn4e3tDWdnZ4wcORKxsbEqTqxZVqxYgaVLl8q0vW6fPnjwAPPmzYO7\nuzt69uyJkJAQlJeX12dsjVHV/h07dqzc7/OL23D/AhBIxrp164TevXsL58+fFy5fviyMGzdOeP/9\n91UdS2MdPXpU8PT0FHJycmS+SktLhVu3bgmdO3cWvv32WyElJUVYt26d4OTkJNy8eVPVsdVeZWWl\nsH79eqFDhw7C559/Lm2vyT794IMPhAkTJgjXrl0Tzpw5I/To0UNYu3atKn4MtVXd/q2srBS6du0q\n/PTTTzK/zwUFBdJtuH8FgYXlBSUlJUK3bt2E/fv3S9vS0tKEDh06CImJiSpMprnWrVsn+Pj4VNm3\nfPlyYeLEiTJtEydOFJYtW1Yf0TRWamqqMHHiRMHT01MYMGCAzAff6/ZpUlKS0KFDByE1NVXaf+DA\nAaFbt25CSUlJ/fwAau5V+/fu3bty++9F3L/P8FTYC65fv44nT56ge/fu0jZra2tYWVlJT92QYm7d\nugVbW9sq+xISEmT2NQB4enpyX79GUlISLCwscPjwYVhbW8v0vW6fJiQkwMrKCjY2NtL+7t2748mT\nJ7h27Zryw2uAV+3fmzdvQl9fH1ZWVlU+lvv3mUZ9r7CXPb+xmpmZmUy7qakpb1RZS7du3UJJSQnG\njx+PjIwMODg4YMGCBXB2dkZWVhb3dS14e3vD29u7yr7X7dPs7GyYmprK9QNAZmYmunbtqoTEmuVV\n+/fWrVswNjbGokWLcOHCBZiYmGD06NGYMmUKtLS0uH//D49YXlBUVAQtLS3o6OjItOvq6qKkpERF\nqTRXcXEx0tLSUFhYiMWLF2PTpk0wNTXFxIkTcfv2bRQXF0NXV1fmMdzXdfO6fVpUVAQ9PT2Zfh0d\nHUgkEu73GkhJScHTp0/Rp08fbNu2DRMmTEBYWBjCw8MBcP8+xyOWF+jr66OyshLl5eVo0uS/u6a0\ntBQGBgYqTKaZ9PX1ER8fD11dXemHXVBQEK5cuYI9e/ZAT08PZWVlMo/hvq6b1+1TfX19lJaWyvSX\nlZVBEAQ0bdq03nJqquDgYDx9+hTNmjUDADg6OqKgoACbN2/GnDlzuH//D49YXmBhYQHgv7fTfy4n\nJ0fu9ALVjJGRkcxf0FpaWrC3t0dmZiYsLCyQk5Mjsz33dd28bp+am5tX+fsNyJ8CJnlNmjSRFpXn\nHB0d8eTJExQUFHD//h8Wlhd07NgRhoaGuHDhgrQtPT0dGRkZ8PBQj5XdNMnly5fh6uqKy5cvS9sq\nKipw/fp1ODg4wM3NDfHx8TKPiYuLg7u7e31HbTBet0/d3NyQlpaGzMxMmX5DQ0N07NixXrNqovHj\nx2P16tUybX/99RdMTU3RrFkz7t//w8LyAl1dXUyYMAHffPMNzp49iytXrmDBggXo3r07XFxcVB1P\n43Ts2BFWVlZYsWIFLl26hFu3buGzzz5DXl4eJk+ejIkTJyIhIQFhYWG4ffs2NmzYgEuXLmHKlCmq\njq6xXrdPu3XrBhcXF3zyySe4cuUKYmNjERISgmnTpsldmyF577zzDvbu3YuYmBikpqZi3759iIyM\nxNy5cwFw/0qperyzuikrKxO+/vproXv37oKrq6swb9484cGDB6qOpbGysrKEBQsWCD169BC6du0q\nTJs2Tbhx44a0/9dffxWGDRsmdO7cWRg1apTw22+/qTCt5pk4caLMPAtBeP0+zcnJEWbNmiV07dpV\n6NWrl7BmzRqhoqKiPmNrjJf3b2VlpbB9+3Zh8ODBQufOnYXBgwcLP/74o8xjuH8FgQt9ERGRqHgq\njIiIRMXCQkREomJhISIiUbGwEBGRqFhYiIhIVCwsREQkKhYWatSWLFlS5QqXL35NmjQJADBp0iRM\nnTpVpXkfPXqEgQMH4u7du7V+jvT0dDg6OuLQoUM1fszjx48xcOBApKWl1fp1qfHgPBZq1FJTU/Hw\n4UPp9ytXroS2tjaWLVsmbTMyMoK9vT1SUlIgkUhgZ2eniqgAgIULF8LMzAyLFy+u9XOUlpbi6tWr\naNu2LVq2bFnjx+3atQvHjx9HVFQUJBJJrV+fGj4WFqIXTJo0Cdra2tixY4eqo8j5888/MWHCBJw9\ne1ahgiCW0tJS9O/fHytXrsTgwYPr/fVJc/BUGFENvXwqzNHREXv37sWiRYvQrVs39OjRA+Hh4Sgs\nLMRnn30GNzc39O7dGyEhIXjx77e8vDwsW7YMPXv2hLOzMz744AMkJia+9vUjIyPRq1cvmaIycOBA\nfPvtt1i1ahW6d+8ONzc3BAYGoqioCMHBwfD09ISnpyeWLl0qXQ/k5VNhBw4cQJcuXZCUlIRx48ah\nS5cueOutt7B9+3aZ19fV1cXgwYOxZcuWuuxGagRYWIjqIDg4GCYmJvj222/x1ltvYePGjRg7diwM\nDAwQHh6Od955B5GRkfjll18AACUlJZg6dSrOnDmDBQsWICwsDM2bN8fUqVPx559/Vvs6T548wenT\np6s8UoiMjMSjR4+wYcMGvP/++9i9ezfee+89ZGZmYs2aNZg0aRKio6Oxe/fuap+/vLwcCxYswMiR\nIxEREQFXV1cEBwfj999/l9lu6NChuHz5Mv7555/a7TBqFLjQF1EdODk5YenSpQCe3c35wIEDaNWq\nFVasWAEA6NGjBw4fPoyLFy9iyJAhOHToEG7cuIF9+/ahS5cuAIB+/fph7NixWLduHb777rsqXych\nIQFlZWVwdnaW6zMxMUFISAi0tLTg6emJvXv3oqysDKGhoWjSpAn69OmD48eP4+LFi9X+HJWVlZgz\nZw7GjBkDAHB1dcWJEyfw66+/omfPntLtOnfuDODZreDbtWun+A6jRoFHLER18OIHvYmJCbS1tWXa\nJBIJmjdvjvz8fADA77//DjMzM3Tq1Anl5eUoLy9HZWUl3nrrLcTHx8utPvhceno6AMDa2lqur0uX\nLtDSevZfWUtLCyYmJnBycpJZBbVFixbSDNVxdXWV/ltXVxctW7ZEUVGRzDbGxsZo1qwZMjIyXvlc\n1LjxiIWoDgwNDeXaXrUE7aNHj5CVlQUnJ6cq+/Py8qpcabCgoAAAqly2WdEM1Xn5ubW0tFBZWVnl\nds/zEFWFhYWoHhkbG8POzg7BwcFV9puYmLyyvaCgQG5p3PqWn59fbU4igKfCiOqVh4cH7t27B1NT\nU3Tp0kX6derUKezcuRM6OjpVPs7S0hIAkJWVVZ9x5Tx+/BhFRUWwsLBQaQ5SbywsRPVo9OjRMDMz\nw7Rp03Do0CH88ccfCAoKwqZNm2BjY1PtxEN3d3fo6+vXaFiyMiUlJQEA+vTpo9IcpN5YWIjqkaGh\nIXbv3o2uXbsiKCgIH330Ec6dO4fly5djzpw51T7OwMAA/fr1w9mzZ+sxrbyzZ8/C2dmZRyz0Spx5\nT6Qh/vzzT3zwwQc4ffp0lRf4la2oqAh9+/ZFUFAQ3n777Xp/fdIcPGIh0hDOzs4YNGiQ3Iz4+rJ3\n717Y29tj0KBBKnl90hw8YiHSIA8fPsTo0aPx/fff44033qi313306BHefffden9d0kwsLEREJCqe\nCiMiIlGxsBARkahYWIiISFQsLEREJCoWFiIiEtX/B0NBll6lrNFiAAAAAElFTkSuQmCC\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plot(data.insulin, 'go', label='insulin')\n", + "decorate(xlabel='Time (min)',\n", + " ylabel='Concentration ($\\mu$U/mL)')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "For the book, I put them in a single figure, using `subplot`" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Saving figure to file chap08-fig01.pdf\n" + ] + }, + { + "data": { + "image/png": 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ycli2bBn9+vUztbds2dL056lTp2IwGEhNTaWwsJA5c+bg7OzMzJkzrboPIiIi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\nxqZNmyCXy5GTk4OGhgZMmzYNiYmJiIiIECliMiS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7zpw5o/fKPC8vD/fv38eePXuwevVq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\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "subplot(2, 1, 1)\n", + "plot(data.glucose, 'bo', label='glucose')\n", + "decorate(ylabel='mg/dL')\n", + "\n", + "subplot(2, 1, 2)\n", + "plot(data.insulin, 'go', label='insulin')\n", + "decorate(xlabel='Time (min)',\n", + " ylabel='$\\mu$U/mL')\n", + "\n", + "savefig('chap08-fig01.pdf')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Interpolation\n", + "\n", + "We have measurements of insulin concentration at discrete points in time, but we need to estimate it at intervening points. We'll use `interpolate`, which is a wrapper for `scipy.interpolate.interp1d`" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "%psource interpolate" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The return value from `interpolate` is a function." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "I = interpolate.interp1d(data.insulin, kind = 'quadratic')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can use the result, `I`, to estimate the insulin level at any point in time." + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array(62.804114412529)" + ] + }, + "execution_count": 6, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "I(7)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "`I` can also take an array of time and return an array of estimates, which we can plot." + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Saving figure to file chap08-fig02.pdf\n" + ] + }, + { + "data": { + "image/png": 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vvMErr7zCvffei7W1NQ4ODnz44Yc0a9aM9PR0WrRoYXC9j48P6enpZnt+1Yql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\nrmzevJkff/xRqQacnZ0ZMGAAzz77LD1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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "ts = linrange(0, 182, 2)\n", + "\n", + "plot(data.insulin, 'go', label='insulin data')\n", + "plot(ts, I(ts), color='green', label='interpolated')\n", + "\n", + "decorate(xlabel='Time (min)',\n", + " ylabel='Concentration ($\\mu$U/mL)')\n", + "\n", + "savefig('chap08-fig02.pdf')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Exercise:** [Read the documentation](https://docs.scipy.org/doc/scipy/reference/generated/scipy.interpolate.interp1d.html) of `scipy.interpolate.interp1d`. Pass a keyword argument to `interpolate` to specify one of the other kinds of interpolation, and run the code again to see what it looks like. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### The glucose minimal model\n", + "\n", + "I'll cheat by starting with parameters that fit the data roughly; then we'll see how to improve them." + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "k1 = 0.03\n", + "k2 = 0.02\n", + "k3 = 1e-05\n", + "G0 = 290" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "To estimate basal levels, we'll use the concentrations at `t=0`." + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "Gb = data.glucose[0]\n", + "Ib = data.insulin[0]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In the initial conditions, `X(0)=0` and `G(0)=G0`, where `G0` is one of the parameters we'll choose." + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "init = State(G=G0, X=0)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here's the system object with all parameters and the interpolation object `I`." + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "system = System(init=init, \n", + " k1=k1, k2=k2, k3=k3,\n", + " I=I, Gb=Gb, Ib=Ib,\n", + " t0=0, t_end=182, dt=2)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "And here's the update function. Using `unpack` to make the system variables accessible without using dot notation, which makes the translation of the differential equations more readable and checkable." + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def update_func(state, t, system):\n", + " \"\"\"Updates the glucose minimal model.\n", + " \n", + " state: State object\n", + " t: time in min\n", + " system: System object\n", + " \n", + " returns: State object\n", + " \"\"\"\n", + " G, X = state\n", + " unpack(system)\n", + " \n", + " dGdt = -k1 * (G - Gb) - X*G\n", + " dXdt = k3 * (I(t) - Ib) - k2 * X\n", + " \n", + " G += dGdt * dt\n", + " X += dXdt * dt\n", + "\n", + " return State(G=G, X=X)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Before running the simulation, it is always a good idea to test the update function using the initial conditions. In this case we can veryify that the results are at least qualitatively correct." + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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"source": [ + "system.results" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The following plot shows the results of the simulation along with the actual glucose data." + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Saving figure to file chap08-fig03.pdf\n" + ] + }, + { + "data": { + "image/png": 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MYdeuXXz++edcuHCB+fPn3/O/2Z1YdJNEVlYWsbGx9O/f35BWp04dmjVrRnp6Oh4eHmRk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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "subplot(2, 1, 1)\n", + "\n", + "plot(system.results.G, 'b-', label='simulation')\n", + "plot(data.glucose, style='bo', label='glucose data')\n", + "decorate(ylabel='mg/dL')\n", + "\n", + "subplot(2, 1, 2)\n", + "\n", + "plot(system.results.X, style='g-', label='remote insulin')\n", + "\n", + "decorate(xlabel='Time (min)', \n", + " ylabel='Arbitrary units')\n", + "\n", + "savefig('chap08-fig03.pdf')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Numerical solution\n", + "\n", + "We can do the same thing using `odeint`. Instead of an update function, we provide a slope function that just evaluates the right-hand side of the differential equations. We don't have to do the update part; `odeint` does it for us." + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def slope_func(state, t, system):\n", + " \"\"\"Computes derivatives of the glucose minimal model.\n", + " \n", + " state: State object\n", + " t: time in min\n", + " system: System object\n", + " \n", + " returns: derivatives of G and X\n", + " \"\"\"\n", + " G, X = state\n", + " unpack(system)\n", + " \n", + " dGdt = -k1 * (G - Gb) - X*G\n", + " dXdt = k3 * (I(t) - Ib) - k2 * X\n", + " \n", + " return dGdt, dXdt" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can test the slope function with the initial conditions." + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "(-5.9399999999999995, 0.0)" + ] + }, + "execution_count": 26, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "slope_func(init, 0, system)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The `System` object we use with `run_odeint` is almost the same as the one we used with `run_simulation`, but instead of providing `t0`, `t_end`, and `dt`, we provide an array of times where we want to evaluate the solution. In this case, we use `data.index`, so the results are evaluated at the same times as the measurements." + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "system2 = System(init=init, \n", + " k1=k1, k2=k2, k3=k3,\n", + " I=I, Gb=Gb, Ib=Ib,\n", + " ts=data.index)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "`run_odeint` is a wrapper for `scipy.integrate.odeint`" + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "%psource run_odeint" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here's how we run it." + ] + }, + { + "cell_type": "code", + "execution_count": 29, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Wall time: 102 ms\n" + ] + } + ], + "source": [ + "%time run_odeint(system2, slope_func)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "And here are the results." + ] + }, + { + "cell_type": "code", + "execution_count": 30, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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12222.8753910.005391
14212.8831040.005807
16203.4326040.006108
19190.3111060.006378
22178.4307230.006560
27161.1412930.006767
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42124.2722570.007043
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14288.3567580.000232
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18291.795663-0.000810
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" + ], + "text/plain": [ + " G X\n", + "time \n", + "0 290.000000 0.000000\n", + "2 278.441946 0.000148\n", + "4 267.246339 0.001463\n", + "6 255.791154 0.003294\n", + "8 244.385049 0.004280\n", + "10 233.385689 0.004877\n", + "12 222.875391 0.005391\n", + "14 212.883104 0.005807\n", + "16 203.432604 0.006108\n", + "19 190.311106 0.006378\n", + "22 178.430723 0.006560\n", + "27 161.141293 0.006767\n", + "32 146.627308 0.006957\n", + "42 124.272257 0.007043\n", + "52 109.125928 0.006436\n", + "62 99.310554 0.005632\n", + "72 93.102455 0.004786\n", + "82 89.434359 0.003872\n", + "92 87.498085 0.002986\n", + "102 86.712650 0.002313\n", + "122 86.844866 0.001199\n", + "142 88.356758 0.000232\n", + "162 90.136930 -0.000339\n", + "182 91.795663 -0.000810" + ] + }, + "execution_count": 30, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "system2.results" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Plotting the results from `run_simulation` and `run_odeint`, we can see that they are not very different." + ] + }, + { + "cell_type": "code", + "execution_count": 31, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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" + ], + "text/plain": [ + " G X\n", + "2 -0.115624 -100.000000\n", + "4 -0.109838 -79.488129\n", + "6 0.197156 -19.008861\n", + "8 0.280333 -5.584132\n", + "10 0.222571 -4.045820\n", + "12 0.146387 -2.574882\n", + "14 0.047791 -1.457351\n", + "16 -0.070980 -0.241936\n", + "22 -0.506705 0.770903\n", + "32 -1.135176 0.739019\n", + "42 -1.553518 1.669890\n", + "52 -1.824149 2.322664\n", + "62 -1.877001 1.900503\n", + "72 -1.764022 2.270604\n", + "82 -1.574539 2.091263\n", + "92 -1.346686 2.279411\n", + "102 -1.093100 0.658312\n", + "122 -0.676648 2.068862\n", + "142 -0.393212 -3.390112\n", + "162 -0.187146 4.346125\n", + "182 -0.077205 1.148839" + ] + }, + "execution_count": 32, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "diff = system.results - system2.results\n", + "percent_diff = diff / system2.results * 100\n", + "percent_diff.dropna()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Exercise:** What happens to these errors if you run the simulation with a smaller value of `dt`?" + ] + }, + { + "cell_type": "code", + "execution_count": 40, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Wall time: 628 ms\n", + "Saving figure to file chap08-fig03.pdf\n" + ] + }, + { + "data": { + "image/png": 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LL8LRo2pshkuX4D//gWHDLJ0rIYQQD6sqDxgSEhKq+iMfSi4u8NJLsHat2t67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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "system = System(init=init, \n", + " k1=k1, k2=k2, k3=k3,\n", + " I=I, Gb=Gb, Ib=Ib,\n", + " t0=0, t_end=182, dt=0.5)\n", + "\n", + "%time run_simulation(system, update_func) \n", + "\n", + "subplot(2, 1, 1)\n", + "plot(system.results.G, 'b-', label='simulation')\n", + "plot(data.glucose, style='bo', label='glucose data')\n", + "decorate(ylabel='mg/dL')\n", + "\n", + "subplot(2, 1, 2)\n", + "\n", + "plot(system.results.X, style='g-', label='remote insulin')\n", + "\n", + "decorate(xlabel='Time (min)', \n", + " ylabel='Arbitrary units')\n", + "\n", + "savefig('chap08-fig03.pdf')\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Optimization" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now let's find the parameters that yield the best fit for the data." + ] + }, + { + "cell_type": "code", + "execution_count": 52, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "k1 = 0.04\n", + "k2 = 0.05\n", + "k3 = 2e-05\n", + "G0 = 280" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Again, we'll get basal levels from the initial values." + ] + }, + { + "cell_type": "code", + "execution_count": 53, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "Gb = data.glucose[0]\n", + "Ib = data.insulin[0]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "And the slope function is the same." + ] + }, + { + "cell_type": "code", + "execution_count": 54, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def slope_func(state, t, system):\n", + " \"\"\"Computes derivatives of the glucose minimal model.\n", + " \n", + " state: State object\n", + " t: time in min\n", + " system: System object\n", + " \n", + " returns: derivatives of G and X\n", + " \"\"\"\n", + " G, X = state\n", + " unpack(system)\n", + " \n", + " dGdt = -k1 * (G - Gb) - X*G\n", + " dXdt = k3 * (I(t) - Ib) - k2 * X\n", + " \n", + " return dGdt, dXdt" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "`make_system` takes the parameters and `DataFrame` and returns a `System` object." + ] + }, + { + "cell_type": "code", + "execution_count": 55, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def make_system(G0, k1, k2, k3, data):\n", + " \"\"\"Makes a System object with the given parameters.\n", + " \n", + " G0: initial blood glucose\n", + " k1: rate parameter\n", + " k2: rate parameter\n", + " k3: rate parameter\n", + " data: DataFrame\n", + " \n", + " returns: System object\n", + " \"\"\"\n", + " init = State(G=G0, X=0)\n", + " system = System(init=init, \n", + " k1=k1, k2=k2, k3=k3,\n", + " Gb=Gb, Ib=Ib, \n", + " I=interpolate(data.insulin),\n", + " ts=data.index)\n", + " return system" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "`error_func` takes the parameters and actual data, makes a `System` object and runs it, then compares the results of the simulation to the data. It returns an array of errors." + ] + }, + { + "cell_type": "code", + "execution_count": 63, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def error_func(params, data):\n", + " \"\"\"Computes an array of errors to be minimized.\n", + " \n", + " params: sequence of parameters\n", + " data: DataFrame of values to be matched\n", + " \n", + " returns: array of errors\n", + " \"\"\"\n", + " print(params)\n", + " \n", + " # make a System with the given parameters\n", + " system = make_system(*params, data)\n", + " \n", + " # solve the ODE\n", + " run_odeint(system, slope_func)\n", + " \n", + " # compute the difference between the model\n", + " # results and actual data\n", + " errors = system.results.G - data.glucose\n", + " return errors.loc[8:]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "When we call `error_func`, we provide a sequence of parameters as a single object." + ] + }, + { + "cell_type": "code", + "execution_count": 64, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "(280, 0.03606407918026959, 0.046899892070931662, 2.0132195591985164e-05)" + ] + }, + "execution_count": 64, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "params = G0, k1, k2, k3\n", + "params" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here's how that works:" + ] + }, + { + "cell_type": "code", + "execution_count": 65, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "(280, 0.03606407918026959, 0.046899892070931662, 2.0132195591985164e-05)\n" + ] + }, + { + "data": { + "text/plain": [ + "time\n", + "8 -13.092776\n", + "10 -2.023568\n", + "12 -9.133973\n", + "14 -14.385897\n", + "16 -15.757971\n", + "19 -25.655911\n", + "22 -17.685069\n", + "27 -25.203599\n", + "32 -17.111782\n", + "42 -17.165104\n", + "52 -8.567942\n", + "62 -0.951820\n", + "72 4.525306\n", + "82 10.809205\n", + "92 6.124838\n", + "102 7.951187\n", + "122 8.616672\n", + "142 10.505829\n", + "162 8.793119\n", + "182 4.621643\n", + "dtype: float64" + ] + }, + "execution_count": 65, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "error_func(params, data)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "`fit_leastsq` is a wrapper for `scipy.optimize.leastsq`" + ] + }, + { + "cell_type": "code", + "execution_count": 66, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "%psource fit_leastsq" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here's how we call it." + ] + }, + { + "cell_type": "code", + "execution_count": 67, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[ 2.80000000e+02 3.60640792e-02 4.68998921e-02 2.01321956e-05]\n", + "[ 2.80000000e+02 3.60640792e-02 4.68998921e-02 2.01321956e-05]\n", + "[ 2.80000000e+02 3.60640792e-02 4.68998921e-02 2.01321956e-05]\n", + "[ 2.80000004e+02 3.60640792e-02 4.68998921e-02 2.01321956e-05]\n", + "[ 2.80000000e+02 3.60640797e-02 4.68998921e-02 2.01321956e-05]\n", + "[ 2.80000000e+02 3.60640792e-02 4.68998928e-02 2.01321956e-05]\n", + "[ 2.80000000e+02 3.60640792e-02 4.68998921e-02 2.01321959e-05]\n", + "[ 2.69518071e+02 3.55313236e-02 -5.40819482e-02 -1.80847289e-05]\n" + ] + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "C:\\ProgramData\\Miniconda3\\lib\\site-packages\\scipy\\integrate\\odepack.py:218: ODEintWarning: Excess work done on this call (perhaps wrong Dfun type). Run with full_output = 1 to get quantitative information.\n", + " warnings.warn(warning_msg, ODEintWarning)\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[ 2.85794533e+02 3.46849299e-02 4.84364485e-02 1.72844074e-05]\n", + "[ 2.85794537e+02 3.46849299e-02 4.84364485e-02 1.72844074e-05]\n", + "[ 2.85794533e+02 3.46849304e-02 4.84364485e-02 1.72844074e-05]\n", + "[ 2.85794533e+02 3.46849299e-02 4.84364492e-02 1.72844074e-05]\n", + "[ 2.85794533e+02 3.46849299e-02 4.84364485e-02 1.72844076e-05]\n", + "[ 2.87973499e+02 3.17682132e-02 2.22962740e-02 1.44216229e-05]\n", + "[ 2.87973503e+02 3.17682132e-02 2.22962740e-02 1.44216229e-05]\n", + "[ 2.87973499e+02 3.17682137e-02 2.22962740e-02 1.44216229e-05]\n", + "[ 2.87973499e+02 3.17682132e-02 2.22962744e-02 1.44216229e-05]\n", + "[ 2.87973499e+02 3.17682132e-02 2.22962740e-02 1.44216231e-05]\n", + "[ 2.88109170e+02 3.17849209e-02 2.22972901e-02 1.44174233e-05]\n", + "[ 2.88109174e+02 3.17849209e-02 2.22972901e-02 1.44174233e-05]\n", + "[ 2.88109170e+02 3.17849214e-02 2.22972901e-02 1.44174233e-05]\n", + "[ 2.88109170e+02 3.17849209e-02 2.22972904e-02 1.44174233e-05]\n", + "[ 2.88109170e+02 3.17849209e-02 2.22972901e-02 1.44174235e-05]\n", + "[ 2.88390829e+02 3.16958561e-02 2.23060359e-02 1.44186802e-05]\n", + "[ 2.88390833e+02 3.16958561e-02 2.23060359e-02 1.44186802e-05]\n", + "[ 2.88390829e+02 3.16958566e-02 2.23060359e-02 1.44186802e-05]\n", + "[ 2.88390829e+02 3.16958561e-02 2.23060362e-02 1.44186802e-05]\n", + "[ 2.88390829e+02 3.16958561e-02 2.23060359e-02 1.44186805e-05]\n", + "[ 2.88620306e+02 3.16870090e-02 2.22689838e-02 1.43686885e-05]\n", + "[ 2.88620310e+02 3.16870090e-02 2.22689838e-02 1.43686885e-05]\n", + "[ 2.88620306e+02 3.16870095e-02 2.22689838e-02 1.43686885e-05]\n", + "[ 2.88620306e+02 3.16870090e-02 2.22689841e-02 1.43686885e-05]\n", + "[ 2.88620306e+02 3.16870090e-02 2.22689838e-02 1.43686887e-05]\n", + "[ 2.89323784e+02 3.16297500e-02 2.22704142e-02 1.43413265e-05]\n", + "[ 2.89323789e+02 3.16297500e-02 2.22704142e-02 1.43413265e-05]\n", + "[ 2.89323784e+02 3.16297505e-02 2.22704142e-02 1.43413265e-05]\n", + "[ 2.89323784e+02 3.16297500e-02 2.22704145e-02 1.43413265e-05]\n", + "[ 2.89323784e+02 3.16297500e-02 2.22704142e-02 1.43413267e-05]\n", + "[ 2.89627042e+02 3.16189563e-02 2.22576393e-02 1.43343146e-05]\n", + "[ 2.89627046e+02 3.16189563e-02 2.22576393e-02 1.43343146e-05]\n", + "[ 2.89627042e+02 3.16189568e-02 2.22576393e-02 1.43343146e-05]\n", + "[ 2.89627042e+02 3.16189563e-02 2.22576396e-02 1.43343146e-05]\n", + "[ 2.89627042e+02 3.16189563e-02 2.22576393e-02 1.43343148e-05]\n", + "[ 2.89653905e+02 3.15871433e-02 2.22576681e-02 1.43320709e-05]\n", + "[ 2.89653909e+02 3.15871433e-02 2.22576681e-02 1.43320709e-05]\n", + "[ 2.89653905e+02 3.15871438e-02 2.22576681e-02 1.43320709e-05]\n", + "[ 2.89653905e+02 3.15871433e-02 2.22576684e-02 1.43320709e-05]\n", + "[ 2.89653905e+02 3.15871433e-02 2.22576681e-02 1.43320712e-05]\n", + "[ 2.89621668e+02 3.15209126e-02 2.22570921e-02 1.43261377e-05]\n", + "[ 2.89621673e+02 3.15209126e-02 2.22570921e-02 1.43261377e-05]\n", + "[ 2.89621668e+02 3.15209131e-02 2.22570921e-02 1.43261377e-05]\n", + "[ 2.89621668e+02 3.15209126e-02 2.22570924e-02 1.43261377e-05]\n", + "[ 2.89621668e+02 3.15209126e-02 2.22570921e-02 1.43261379e-05]\n", + "[ 2.89909749e+02 3.15346207e-02 2.22653410e-02 1.43477093e-05]\n", + "[ 2.89870954e+02 3.15299745e-02 2.22664850e-02 1.43403965e-05]\n", + "[ 2.89776714e+02 3.15156663e-02 2.22683534e-02 1.43270237e-05]\n", + "[ 2.89776718e+02 3.15156663e-02 2.22683534e-02 1.43270237e-05]\n", + "[ 2.89776714e+02 3.15156667e-02 2.22683534e-02 1.43270237e-05]\n", + "[ 2.89776714e+02 3.15156663e-02 2.22683537e-02 1.43270237e-05]\n", + "[ 2.89776714e+02 3.15156663e-02 2.22683534e-02 1.43270239e-05]\n", + "[ 2.89800410e+02 3.15312073e-02 2.22666015e-02 1.43260740e-05]\n", + "[ 2.89775297e+02 3.15240697e-02 2.22677912e-02 1.43268204e-05]\n", + "[ 2.89775617e+02 3.15195084e-02 2.22681084e-02 1.43269451e-05]\n", + "[ 2.89776117e+02 3.15175701e-02 2.22682334e-02 1.43269865e-05]\n", + "[ 2.89776389e+02 3.15166675e-02 2.22682906e-02 1.43270045e-05]\n", + "[ 2.89776545e+02 3.15161776e-02 2.22683214e-02 1.43270140e-05]\n", + "[ 2.89776637e+02 3.15158979e-02 2.22683389e-02 1.43270193e-05]\n", + "[ 2.89776675e+02 3.15157820e-02 2.22683461e-02 1.43270215e-05]\n", + "[ 2.89776694e+02 3.15157240e-02 2.22683498e-02 1.43270226e-05]\n", + "[ 2.89776704e+02 3.15156951e-02 2.22683516e-02 1.43270232e-05]\n", + "[ 2.89776709e+02 3.15156805e-02 2.22683525e-02 1.43270234e-05]\n", + "[ 2.89776711e+02 3.15156733e-02 2.22683529e-02 1.43270236e-05]\n", + "[ 2.89776712e+02 3.15156698e-02 2.22683531e-02 1.43270236e-05]\n", + "[ 2.89776713e+02 3.15156677e-02 2.22683533e-02 1.43270237e-05]\n", + "modsim.py: scipy.optimize.leastsq ran successfully\n", + " and returned the following message:\n", + "The relative error between two consecutive iterates is at most 0.000000\n" + ] + } + ], + "source": [ + "best_params = fit_leastsq(error_func, params, data)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now that we have `best_params`, we can use it to make a `System` object and run it.\n", + "\n", + "We have to use the scatter operator, `*`, to make `best_params` behave like four separate parameters, rather than a single object." + ] + }, + { + "cell_type": "code", + "execution_count": 68, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "system = make_system(*best_params, data)\n", + "run_odeint(system, slope_func)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here are the results, along with the data. The first few points of the model don't fit the data, but we don't expect them to." + ] + }, + { + "cell_type": "code", + "execution_count": 69, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Saving figure to file chap08-fig04.pdf\n" + ] + }, + { + "data": { + "image/png": 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7EhISWLVqVa31R67t9TVz5kxUKhU7duwgIyOD+fPno9FoiIqKMuWt3DS1WkV1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\nEDNZ27QRdZJkqdH9GQgx07PPmi6nuXViL+xiBKJ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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plot(system.results.G, label='simulation')\n", + "plot(data.glucose, style='bo', label='glucose data')\n", + "\n", + "decorate(xlabel='Time (min)',\n", + " ylabel='Concentration (mg/dL)')\n", + "\n", + "savefig('chap08-fig04.pdf')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Exercise:** Since we don't expect the first few points to agree, it's probably better not to make them part of the optimization process. We can ignore them by leaving them out of the `Series` returned by `error_func`. Modify the last line of `error_func` to return `errors.loc[8:]`, which includes only the elements of the `Series` from `t=8` and up.\n", + "\n", + "Does that improve the quality of the fit? Does it change the best parameters by much?\n", + "\n", + "Note: You can read more about this use of `loc` [in the Pandas documentation](https://pandas.pydata.org/pandas-docs/stable/indexing.html#indexing-integer)." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Exercise:** How sensitive are the results to the starting guess for the parameters. If you try different values for the starting guess, do we get the same values for the best parameters?" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Interpreting parameters\n", + "\n", + "Based on the parameters of the model, we can estimate glucose effectiveness and insulin sensitivity." + ] + }, + { + "cell_type": "code", + "execution_count": 70, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def indices(G0, k1, k2, k3):\n", + " \"\"\"Compute glucose effectiveness and insulin sensitivity.\n", + " \n", + " G0: initial blood glucose\n", + " k1: rate parameter\n", + " k2: rate parameter\n", + " k3: rate parameter\n", + " data: DataFrame\n", + " \n", + " returns: State object containing S_G and S_I\n", + " \"\"\"\n", + " return State(S_G=k1, S_I=k3/k2)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here are the results." + ] + }, + { + "cell_type": "code", + "execution_count": 71, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
\n", + "\n", + "\n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + "
value
S_G0.031516
S_I0.000643
\n", + "
" + ], + "text/plain": [ + "S_G 0.031516\n", + "S_I 0.000643\n", + "dtype: float64" + ] + }, + "execution_count": 71, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "indices(*best_params)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### The insulin minimal model\n", + "\n", + "In addition to the glucose minimal mode, Pacini and Bergman present an insulin minimal model, in which the concentration of insulin, $I$, is governed by this differential equation:\n", + "\n", + "$ \\frac{dI}{dt} = -k I(t) + \\gamma (G(t) - G_T) t $" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Exercise:** Write a version of `make_system` that takes the parameters of this model, `I0`, `k`, `gamma`, and `G_T` as parameters, along with a `DataFrame` containing the measurements, and returns a `System` object suitable for use with `run_simulation` or `run_odeint`.\n", + "\n", + "Use it to make a `System` object with the following parameters:" + ] + }, + { + "cell_type": "code", + "execution_count": 183, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "I0 = 360\n", + "k = 0.25\n", + "gamma = 0.004\n", + "G_T = 80\n" + ] + }, + { + "cell_type": "code", + "execution_count": 184, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "# Solution goes here\n", + "def make_system(I0, k, gamma, G_T, data):\n", + " init = State(I=I0)\n", + " system = System(init=init, \n", + " k=k, gamma = gamma, G_T = G_T, \n", + " G=interpolate(data.glucose),\n", + " ts=data.index)\n", + " return system\n", + " " + ] + }, + { + "cell_type": "code", + "execution_count": 185, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "# Solution goes here\n", + "system = make_system(I0, k, gamma, G_T, data)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Exercise:** Write a slope function that takes state, t, system as parameters and returns the derivative of `I` with respect to time. Test your function with the initial condition $I(0)=360$." + ] + }, + { + "cell_type": "code", + "execution_count": 186, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "# Solution goes here\n", + "\n", + "def slope_func(state, t, system):\n", + " I = state\n", + " unpack(system)\n", + " \n", + " dIdt = - k * I + gamma * (G(t) - G_T) * t\n", + " return dIdt" + ] + }, + { + "cell_type": "code", + "execution_count": 187, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "I -90.0\n", + "dtype: float64" + ] + }, + "execution_count": 187, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Solution goes here\n", + "init = State(I=I0)\n", + "slope_func(init, 0, system)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Exercise:** Run `run_odeint` with your `System` object and slope function, and plot the results, along with the measured insulin levels." + ] + }, + { + "cell_type": "code", + "execution_count": 188, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "# Solution goes here\n", + "run_odeint(system, slope_func)\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [] + }, + { + "cell_type": "code", + "execution_count": 189, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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FlRCKJhGOKojEFKhZPZw4wgiNBfH7sWv49Sf6/YfcTitqvGVorKhCQ2UVyh3e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\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Solution goes here\n", + "plot(system.results)\n", + "plot(data.insulin)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Exercise:** Write an error function that takes a sequence of parameters as an argument, along with the `DataFrame` containing the measurements. It should make a `System` object with the given parameters, run it, and compute the difference between the results of the simulation and the measured values. Test your error function by calling it with the parameters from the previous exercise.\n", + "\n", + "Hint: As we did in a previous exercise, you might want to drop the errors for times prior to `t=8`." + ] + }, + { + "cell_type": "code", + "execution_count": 190, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "# Solution goes here\n", + "def error_func(params, data):\n", + " print(params)\n", + " system = make_system(*params, data)\n", + " run_odeint(system, slope_func)\n", + " error = system.results.I - data.insulin\n", + " return error.loc[8:]\n" + ] + }, + { + "cell_type": "code", + "execution_count": 191, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[360, 0.25, 0.004, 80]\n" + ] + }, + { + "data": { + "text/plain": [ + "time\n", + "8 10.636133\n", + "10 -3.234670\n", + "12 -7.946879\n", + "14 -8.010268\n", + "16 -3.593411\n", + "19 1.811071\n", + "22 2.581632\n", + "27 7.014287\n", + "32 3.758216\n", + "42 8.932902\n", + "52 9.554216\n", + "62 0.767804\n", + "72 -3.217947\n", + "82 -10.382598\n", + "92 -7.401702\n", + "102 -9.056569\n", + "122 -3.584244\n", + "142 -3.586427\n", + "162 3.170251\n", + "182 18.702699\n", + "dtype: float64" + ] + }, + "execution_count": 191, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Solution goes here\n", + "params = [I0, k, gamma, G_T]\n", + "params\n", + "error_func(params, data)" + ] + }, + { + "cell_type": "code", + "execution_count": 192, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "# Solution goes here" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Exercise:** Use `fit_leastsq` to find the parameters that best fit the data. Make a `System` object with those parameters, run it, and plot the results along with the measurements." + ] + }, + { + "cell_type": "code", + "execution_count": 193, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[ 3.60000000e+02 2.50000000e-01 4.00000000e-03 8.00000000e+01]\n", + "[ 3.60000000e+02 2.50000000e-01 4.00000000e-03 8.00000000e+01]\n", + "[ 3.60000000e+02 2.50000000e-01 4.00000000e-03 8.00000000e+01]\n", + "[ 3.60000005e+02 2.50000000e-01 4.00000000e-03 8.00000000e+01]\n", + "[ 3.60000000e+02 2.50000004e-01 4.00000000e-03 8.00000000e+01]\n", + "[ 3.60000000e+02 2.50000000e-01 4.00000006e-03 8.00000000e+01]\n", + "[ 3.60000000e+02 2.50000000e-01 4.00000000e-03 8.00000012e+01]\n", + "[ 3.41214716e+02 2.48476650e-01 4.01573092e-03 8.05611945e+01]\n", + "[ 3.41214721e+02 2.48476650e-01 4.01573092e-03 8.05611945e+01]\n", + "[ 3.41214716e+02 2.48476654e-01 4.01573092e-03 8.05611945e+01]\n", + "[ 3.41214716e+02 2.48476650e-01 4.01573098e-03 8.05611945e+01]\n", + "[ 3.41214716e+02 2.48476650e-01 4.01573092e-03 8.05611957e+01]\n", + "[ 3.45910051e+02 2.47820998e-01 3.91185402e-03 8.05803504e+01]\n", + "[ 3.45910056e+02 2.47820998e-01 3.91185402e-03 8.05803504e+01]\n", + "[ 3.45910051e+02 2.47821001e-01 3.91185402e-03 8.05803504e+01]\n", + "[ 3.45910051e+02 2.47820998e-01 3.91185408e-03 8.05803504e+01]\n", + "[ 3.45910051e+02 2.47820998e-01 3.91185402e-03 8.05803516e+01]\n", + "[ 3.45007554e+02 2.48467106e-01 3.84686996e-03 8.04490675e+01]\n", + "[ 3.45007559e+02 2.48467106e-01 3.84686996e-03 8.04490675e+01]\n", + "[ 3.45007554e+02 2.48467109e-01 3.84686996e-03 8.04490675e+01]\n", + "[ 3.45007554e+02 2.48467106e-01 3.84687002e-03 8.04490675e+01]\n", + "[ 3.45007554e+02 2.48467106e-01 3.84686996e-03 8.04490687e+01]\n", + "[ 3.45051065e+02 2.48855798e-01 3.83011719e-03 8.03295605e+01]\n", + "[ 3.45051070e+02 2.48855798e-01 3.83011719e-03 8.03295605e+01]\n", + "[ 3.45051065e+02 2.48855802e-01 3.83011719e-03 8.03295605e+01]\n", + "[ 3.45051065e+02 2.48855798e-01 3.83011724e-03 8.03295605e+01]\n", + "[ 3.45051065e+02 2.48855798e-01 3.83011719e-03 8.03295617e+01]\n", + "[ 3.44987120e+02 2.49050258e-01 3.91079996e-03 8.04365681e+01]\n", + "[ 3.45068248e+02 2.49199738e-01 3.85963688e-03 8.03598764e+01]\n", + "[ 3.45059632e+02 2.49011266e-01 3.84132605e-03 8.03405939e+01]\n", + "[ 3.45054960e+02 2.48925498e-01 3.83491541e-03 8.03342302e+01]\n", + "[ 3.45052537e+02 2.48882019e-01 3.83188685e-03 8.03312744e+01]\n", + "[ 3.45051666e+02 2.48866487e-01 3.83083385e-03 8.03302535e+01]\n", + "[ 3.45051308e+02 2.48860112e-01 3.83040566e-03 8.03298393e+01]\n", + "[ 3.45051163e+02 2.48857532e-01 3.83023303e-03 8.03296724e+01]\n", + "[ 3.45051104e+02 2.48856494e-01 3.83016363e-03 8.03296054e+01]\n", + "[ 3.45051081e+02 2.48856077e-01 3.83013582e-03 8.03295785e+01]\n", + "[ 3.45051071e+02 2.48855910e-01 3.83012466e-03 8.03295677e+01]\n", + "[ 3.45051068e+02 2.48855843e-01 3.83012019e-03 8.03295634e+01]\n", + "[ 3.45051066e+02 2.48855816e-01 3.83011840e-03 8.03295617e+01]\n", + "[ 3.45051066e+02 2.48855806e-01 3.83011768e-03 8.03295610e+01]\n", + "modsim.py: scipy.optimize.leastsq ran successfully\n", + " and returned the following message:\n", + "The relative error between two consecutive iterates is at most 0.000000\n" + ] + } + ], + "source": [ + "# Solution goes here\n", + "best_params = fit_leastsq(error_func, params, data)" + ] + }, + { + "cell_type": "code", + "execution_count": 194, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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K4BExRNGPKAYQEzdhwl5auoZBAB0AADd8CEilqPAFsbxoGcoLAigq8KA44E6d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\nhsNh8cILL4i1a9eKz33uc+I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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Solution goes here\n", + "system = make_system(*best_params, data)\n", + "run_odeint(system, slope_func)\n", + "plot(data.insulin)\n", + "plot(system.results)" + ] + }, + { + "cell_type": "code", + "execution_count": 195, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "# Solution goes here" + ] + }, + { + "cell_type": "code", + "execution_count": 196, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "# Solution goes here" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Exercise:** Using the best parameters, estimate the sensitivity to glucose of the first and second phase pancreatic responsivity:\n", + "\n", + "$ \\phi_1 = \\frac{I_{max} - I_b}{k (G_0 - G_b)} $\n", + "\n", + "$ \\phi_2 = \\gamma \\times 10^4 $" + ] + }, + { + "cell_type": "code", + "execution_count": 203, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "(280, 92)" + ] + }, + "execution_count": 203, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Solution goes here\n", + "I_max = data.insulin.max()\n", + "I_b = data.insulin[0]\n", + "G_b = data.glucose[0]\n" + ] + }, + { + "cell_type": "code", + "execution_count": 205, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "# Solution goes here\n", + "phi1 = (I_max - I_b)/(k * (G0 - G_b))" + ] + }, + { + "cell_type": "code", + "execution_count": 206, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "# Solution goes here\n", + "phi2 = gamma *1e4" + ] + }, + { + "cell_type": "code", + "execution_count": 207, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "(2.5435562602611133, 38.301171870899175)" + ] + }, + "execution_count": 207, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Solution goes here\n", + "phi1, phi2" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "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": "3.6.1" + } + }, + "nbformat": 4, + "nbformat_minor": 1 +} From 874a4c6bb0b668ee221fc30c43de4d4fa997c631 Mon Sep 17 00:00:00 2001 From: Junwon Lee <31522211+junwonlee5@users.noreply.github.com> Date: Wed, 25 Oct 2017 22:21:52 -0400 Subject: [PATCH 13/19] Adding temperature --- code/temperature.ipynb | 335 +++++++++++++++++++++++++++++++++++++++++ 1 file changed, 335 insertions(+) create mode 100644 code/temperature.ipynb diff --git a/code/temperature.ipynb b/code/temperature.ipynb new file mode 100644 index 00000000..e0190a4b --- /dev/null +++ b/code/temperature.ipynb @@ -0,0 +1,335 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 54, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "%matplotlib inline\n", + "\n", + "from modsim import *" + ] + }, + { + "cell_type": "code", + "execution_count": 55, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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k0.23
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" + ], + "text/plain": [ + "init temp 150\n", + "dtype: int64\n", + "Area 0.0044\n", + "T_air 25\n", + "k 0.23\n", + "d 0.01\n", + "m 20\n", + "c 3.77\n", + "t0 0\n", + "t_end 1200\n", + "dt 1\n", + "dtype: object" + ] + }, + "execution_count": 55, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "def make_system(T_init = 150, Area = 0.0044, T_air = 25, k = 0.23, d = 0.01, m = 20, c = 3.77, t0 = 0, t_end = 20*60, dt = 1):\n", + " init = State(temp=T_init)\n", + " \n", + " system = System(init = init, Area = Area, T_air = T_air, k = k, d = d, m = m, c = c, t0 = t0, t_end = t_end, dt = dt)\n", + " return system\n", + "\n", + "cheese = make_system()\n", + "\n", + "cheese" + ] + }, + { + "cell_type": "code", + "execution_count": 56, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 56, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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X7KJMEuKjeWp1Jd09brXOB1/czrvOmEZhbkgm7DbGjANDDthU1X8AC4E/4Rr8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\nGVgpaYKknYE98P8PL23kfp2oSyrogPdNKsWeeP/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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "def update(state, system):\n", + " unpack(system)\n", + " T = state.temp\n", + " T += - (k*Area*(T-T_air) * dt / (d * m * c))\n", + " \n", + " return State(temp=T)\n", + "\n", + "def run_simulation_cheese(system, update_func):\n", + " unpack(system)\n", + " \n", + " frame = TimeFrame(columns = init.index)\n", + " frame.loc[t0] = init\n", + " ts = linrange(t0, t_end-dt, dt)\n", + " \n", + " for t in ts:\n", + " frame.loc[t+dt] = update_func(frame.loc[t], system)\n", + " \n", + " system.results = frame\n", + " return system.results\n", + "results = run_simulation_cheese(cheese, update)\n", + "plot(results)\n", + "xlabel('Time (seconds)')\n", + "ylabel('Temperature (Celsius)')\n", + "title('Temperature of Crust vs. Time')" + ] + }, + { + "cell_type": "code", + "execution_count": 57, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "def make_system2(T_init = 150, Area1 = 0.0044, T_air = 25, k = 0.23, d = 0.01, m1 = 5, c1 = 2.87, h = 20, t0 = 0, t_end = 20*60, dt = 1):\n", + " init = State(temp=T_init)\n", + " \n", + " system = System(init = init, Area = Area1, T_air = T_air, h = h, t0 = t0, t_end = t_end, dt = dt, m = m1, c = c1)\n", + " return system\n", + "\n", + "def update2(state, system):\n", + " unpack(system)\n", + " \n", + " T = state.temp\n", + " T += - (h*Area*(T-T_air) * dt)/ (m * c)\n", + " return State(temp=T)\n", + "\n", + "def run_simulation_crust(system, update_func):\n", + " \n", + " frame1 = TimeFrame(columns = init.index)\n", + " frame1.loc[t0] = init\n", + " ts = linrange(t0, t_end-dt, dt)\n", + " \n", + " for t in ts:\n", + " frame1.loc[t+dt] = update_func(frame1.loc[t], system)\n", + " system.results = frame1\n", + " return system.results\n", + "crust = make_system2()\n", + "results2 = run_simulation_crust(crust, update2)\n", + "plot(results2, 'rs', label = 'crust')\n", + "xlabel('time')\n", + "ylabel('temperature')\n", + "title('Temperature vs. Time')\n", + "legend()" + ] + }, + { + "cell_type": "code", + "execution_count": 58, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([ 0.01 , 0.01333333, 0.01666667, 0.02 , 0.02333333,\n", + " 0.02666667, 0.03 , 0.03333333, 0.03666667, 0.04 ])" + ] + }, + "execution_count": 58, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "r_array = 0.01 * linspace(1, 4, 10)\n", + "r_array" + ] + }, + { + "cell_type": "code", + "execution_count": 59, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([ 0.003768 , 0.00530311, 0.00697778, 0.008792 , 0.01074578,\n", + " 0.01283911, 0.015072 , 0.01744444, 0.01995644, 0.022608 ])" + ] + }, + "execution_count": 59, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "Area_array = 2 * 3.14 * r_array**2 + 2 * 3.14 * r_array * 0.05\n", + "Area_array\n" + ] + }, + { + "cell_type": "code", + "execution_count": 60, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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xVZNQ1dst3YvUGPWKdB5pELYboBsGRNMHVotooijinsdP8Yg421y2d/sor3jB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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "for r in r_array:\n", + " cheese = make_system(Area = 2 * 3.14 * r**2 + 2 * 3.14 * r * 0.05, m = 3.14 * pi * r**2 * 0.05 * 473396, d = r)\n", + " results = run_simulation_cheese(cheese, update)\n", + " plot(results)\n", + " xlabel('Time (seconds)')\n", + " ylabel('Temperature (Celsius)')\n", + " title('Temperature of Cheese vs. Time')" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "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": "3.6.1" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} From 876c09217f8c71c763e90d5375dbf082f7235c7e Mon Sep 17 00:00:00 2001 From: Junwon Lee <31522211+junwonlee5@users.noreply.github.com> Date: Fri, 27 Oct 2017 20:22:13 -0400 Subject: [PATCH 14/19] Adding temperature --- code/temperature.ipynb | 87 +++++++++++++++++++++++++----------------- 1 file changed, 52 insertions(+), 35 deletions(-) diff --git a/code/temperature.ipynb b/code/temperature.ipynb index e0190a4b..5a2459e1 100644 --- a/code/temperature.ipynb +++ b/code/temperature.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "code", - "execution_count": 54, + "execution_count": 1, "metadata": { "collapsed": true }, @@ -15,7 +15,7 @@ }, { "cell_type": "code", - "execution_count": 55, + "execution_count": 33, "metadata": {}, "outputs": [ { @@ -103,7 +103,7 @@ "dtype: object" ] }, - "execution_count": 55, + "execution_count": 33, "metadata": {}, "output_type": "execute_result" } @@ -122,24 +122,24 @@ }, { "cell_type": "code", - "execution_count": 56, + "execution_count": 34, "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "" + "" ] }, - "execution_count": 56, + "execution_count": 34, "metadata": {}, "output_type": "execute_result" }, { "data": { - "image/png": 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X7KJMEuKjeWp1Jd09brXOB1/czrvOmEZhbkgm7DbGjANDDthU1X8AC4E/4Rr8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\nGVgpaYKknYE98P8PL23kfp2oSyrogPdNKsWeeP/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2bBkvvPACo0aNIjY2lh9//FGvjuUHOY8mJiba544fP54nn3ySsrIyfvjhB7Kzs/nPf/5T\n7ZpkFhYWrF27lueee45x48YRFBREhw4dyM7OZs+ePdoP7ilTptzztfQ5L927d6dz584sW7aMhIQE\n2rVrx7Vr19iwYQM+Pj707NkTQHtF8t1335GSkqKdE1MZlUrF6NGjWb9+PRYWFgwZMkS7zdzcnMmT\nJ/O///2PWbNm0adPH27cuMGmTZuwtLTUDqPWaDTs2rULJyenKvtB6tPLL7/Mr7/+yosvvshTTz2F\nh4cHJ06c4Oeff2bo0KENMua6IonmIfP4449jZ2fH559/ztq1azE0NMTHx4f169dXuJXzIIKCgrC3\nt2f9+vUoisKAAQN47bXXdDrIX3zxRVxcXPj6669ZuXIl5ubmdOrUiZkzZ9K5c+e7vr6fnx8ff/wx\n//nPf1ixYgVWVlZ4e3vz9ddf8+WXX3Ly5EnKysowNDTk6aefJjQ0lM8++4yLFy/Ss2dPnnnmGfLy\n8ti2bRtLly6lQ4cOrFu3jjVr1uj1/h7kPD7++OPY2try2WefsXr1aoyMjAgICGD58uX3XY/O39+f\nnTt38n//93+EhISwa9cuAHx8fPjwww8ZO3asXq+jz3kxNDTUxn7w4EE2btyInZ0do0ePZs6cOdor\nmQEDBjBs2DAOHDjA0aNHGT58+F2vmMeMGcP69esZPHiwzog8gFdeeQUHBwe2b9/OoUOHMDY2plu3\nbnz66afakWlqtZr58+fTr1+/Bvmh7eDgwObNm1m1ahW7d+/m+vXrtGzZkpkzZ+pV6PNhJkU1RbUU\nFxfj7+/PpEmTePfdd+s7HCFEI9A4bn4KIYRotCTRCCGEqFWSaIQQQtSqJtFHU1RUxPnz53F0dLzn\n8E8hhBDlysrKSE9Px8/PT1vF4340iVFn58+f12vopxBCiIq+++47unfvft/PbxKJxtHRESg/WdWd\nlS2EEE1VSkoKU6ZM0X6G3q8mkWhu3S5r0aKFtuKqEEII/Txol0OTSDRVybxeyMETCdhYmjCouxtm\nJk36dAghRK1o0p+sF2OzSM8pJD2nkDKNwui+batdHkQIIcTdNenhzW1cbLQ/xyXncupS7a5PLoQQ\nTVGTTjRuztZ09XHSPj5xMZX4lNx6jEgIIR4+TTrRADzi50IrJyugfPGiA8cTyC0oucezhBBC6KvJ\nJxoDAxXDe7XGyrx8xcCiklL2HYujtKzmlgoWQoimrMknGgALM2Me7d0GA4PygQBp2Tc4FHatnqMS\nQoiHgySam1o4WNK/s6v28cXYTC7GZtZjREII8XCQRHMHP08HfNzttI+DT18lLevGXZ4hhBDiXiTR\n3EGlUhHYrRUOzcwBKNMo7PszjqLie68zL4QQonKSaP7C2MiQkb3bYGJcXnIht6CE/cfj0Wge+iLX\nQghRKyTRVMLW2pRhPd21jxNS8zh2PrkeIxJCiMZLEk0V2rZsRvf2ztrHYZfTiEzIrseIhBCicZJE\ncxe9Orag7R1lan47lUhatgwOEEKI6pBEcxcqlYphvVpjZ12+slxpmYY9R2K5UaSu58iEEKLxkERz\nDybGhozq2wbTm4MD8gvV7DsWT5lUDhBCCL1IotGDnbUZw3u11i4hkJSRT0h4Uj1HJYQQjYMkGj21\ndrHhEb/by0Cfj8ngwhWpHCCEEPdSr4lm0aJFvPnmm5VuU6vVjB07ltdff12nPTMzk9mzZ9O9e3d6\n9+7N8uXLKS2tmwmVXX2caOdmq30cHHaV5IyCOjm2EEI0VvWSaBRFYdWqVWzevLnKfT799FMuXbpU\noX3mzJlkZGTw7bff8sEHH7Bt2zZWr15dm+FqqVQqBnd3o7lteeUAjUZh77E48m/IsgJCCFGVOk80\niYmJTJ06le+//56WLVtWuk9oaChbt27F29tbpz0sLIzQ0FA++OADfH19GThwIPPnz2fDhg2UlNTN\nh72xkSGj+rTF3LR8FewbRWp2H4lFXVpWJ8cXQojGps4TzenTp3FxcWHXrl20atWqwvaCggIWLFjA\nW2+9hYODg862U6dO4erqipubm7atZ8+eFBQUVHr1U1tsLE3KlxW4OTggPaeQAycSUBQpUyOEEH9V\n54kmKCiIZcuW4ejoWOn2999/n06dOjFq1KgK21JTU3FyctJpu/U4ObluS8S4OloxsOvtRHnl2nWO\nnZMyNUII8VdG9R3AnX799VeCg4P5+eefK91eWFiIqampTpuxsTEqlYri4uK6CFFHRw8HsvOKOBOZ\nDsDpy2nYWZvRvq19nccihBANVYMZ3pyVlcXbb7/Ne++9h62tbaX7mJmZVeiLUavVKIqChYVFXYRZ\nQZ9OLXXK1Px+OpGk9Px6iUUIIRqial3RlJSUkJaWRn5+PnZ2djRv3hxDQ8MaCSQ4OJjMzEzmzp2r\nbSsuLkalUvHLL78QFhZGixYtCA4O1nleWloaAM7OztQHA4PyMjVbf48m83ohGo3CnqNxTBjSjmZW\npvd+ASGEeMjdM9Go1Wq2b9/Orl27CA8PR62+XefL2NiYXr16MWLECIKCgjA2Nr7vQIYNG0bXrl11\n2hYsWICjoyOvvvoqAN26dWPFihUkJyfj4uICwPHjx7G0tMTX1/e+j/2gTIwNGd23LVt+jaSwuJSi\nklJ2H4nlycHttKVrhBCiqbprotm5cycrVqzgxo0bBAYGMnfuXFxdXTE3Nyc3N5eUlBROnz7Nhx9+\nyJo1a5g1axbjxo27r0CsrKywsrLSaTMzM8PS0pLWrVsDEBAQQJcuXZg7dy5vv/02GRkZLF++nGnT\npmFiYnJfx60pNpYmjO7blu1/RFOmUcjKLeKXP+N4rK8HBgaqeo1NCCHqU5WJ5uWXXyYlJYU333yT\nwYMHV/lB/uyzz1JcXMyePXv46quv2L9/P5999lmtBKtSqVizZg1LlixhypQpWFpaMmHCBGbMmFEr\nx6uuFg6WDOnhzv7j8QAkpOQRcuYaAwJctXXShBCiqVEpVUz+2Lp1K08++WS1XkxRFH788UcmTJhQ\nI8HVlKtXrzJkyBB+/fXXSufu1LTj55M5eSlV+7hf55Z08Xa6yzOEEKLhqanPzipHnVU3yUD5FUdD\nSzL1oWfHFjo10Q6HJxF9NaceIxJCiPqj96izpKQkioqK8PDwID8/nzVr1pCcnMyjjz7KyJEjazPG\nRkelUjGkhzsFhWqSbhbdPHA8HkszY1yaW9ZzdEIIUbf0mkcTEhLC8OHD2bJlCwCLFy9mw4YNXLly\nhXnz5rF9+/ZaDbIxMjI0YFSftthalw9xLtMo7D4SS05e3U8sFUKI+qRXovnPf/5Dnz59mD59Orm5\nufzyyy8899xz7Nq1i+eff56vvvqqtuNslMxMjRjTz0NbgLOopJRdh6/IUtBCiCZFr0Rz6dIl/vGP\nf2BjY0NISAhlZWXa22X9+vUjLi6uNmNs1JpZmTK6b1uMDMtP9fX8YvYcjaNUloIWQjQReiUaU1NT\nNJryD8bDhw/j4OCgnSCZkZGBtbV17UX4EGjhYMmIR24vBZ2SWcCB4/FoNFLtWQjx8NMr0QQEBPDV\nV1+xb98+9u3bx9ChQwGIiIjgP//5D926davVIB8GbVs2o1/n2+vvxFy7zpGzSfUYkRBC1A29Es0b\nb7zB1atXmTNnDs7Ozrz88stA+WTNoqIibYkYcXed2znSxfv28gjhUemE36z8LIQQDyu9hje3bt2a\nvXv3kp6ejpOTk/YW0Nq1a+nQoUO9l39pTPr6tySvoISYa9cBCAm/hrmZEd7udvUcmRBC1A69lwkw\nMDDA2dlZp5RKly5dJMlUk0pVXu3ZxeH2fJqDJxJISMmtx6iEEKL26HVF4+/vf89aXeHh4TUSUFNg\nZGigLcCZmVuERlHYeyyOsQO9cLavn3V1hBCituiVaKZNm1Yh0dy4cYPQ0FCSkpKYN29erQT3MDMz\nNWJMfw9+/C2K/EI16lINPx++wrhBXthZm9V3eEIIUWP0SjR3Lkb2V6+88goRERE1FlBTYmVhwuMD\nPNn2ezRFJaUUFpeyK+QK4wa1w8r8/tf2EUKIhuSBl3IeP348P//8c03E0iTZ25jxWL+2GN+c0Jlb\nUMKukCsUlZTWc2RCCFEzHjjRXL16VWfVTVF9LRwsebR3Gwxu3p7MvF7IniNSPUAI8XDQ69bZ+vXr\nK7RpNBqSk5PZuXMnAwYMqPHAmprWLjYM7uHGwRMJACRl5LP/eDyPPtJGVugUQjRqeiWalStXVtpu\nbm5OYGAgb775Zo0G1VT5transKhUWzHgyrXr/B6ayODubrJCpxCi0dIr0Vy4cKFCm0qlwsDgge+8\nib8I8HHiRnEpYZfTALgUl4WJkSH9urSUZCOEaJT0SjSGhoa1HYe4Q59OLhSXlHIxNguA8Oh0jI0N\neMTPpZ4jE0KI6qsy0YwaNYqPP/4YHx8fRo4ceddv0yqVit27d9dKgE2RSqUisKsb6lINUYnlS0Cf\nupSKibEhXX2c6jk6IYSonioTTceOHbGwsND+LLdt6paBgYqhPdwpUWuIv1me5ujZJEyMDPDzbF7P\n0QkhhP6qTDTLly/X/rxixYo6CUboMjQ0YGSfNuwKucK19HwAgsOuYWJsKEU4hRCNht69+YWFhaSn\nl5e0Ly0tZcOGDSxbtowzZ87UWnDidl20WzXQFEXh4IkEYpOu13NkQgihH70SzdmzZwkMDOSbb74B\n4P333+ff//43mzZtYsqUKQQHB9dqkE2dibEhY/p54GBTXgNNoyjsOxZHYmpe/QYmhBB60CvRfPLJ\nJ7Ru3Zrx48dTWFjI9u3b+dvf/sbp06cZO3Ysa9eure04mzwzUyMeH+BJMytTAMo0CnuOxJKUkV/P\nkQkhxN3plWjCw8OZMWMGrVu35ujRoxQVFTF27FgAHnvsMSIjI2s1SFHO0tyYoAGe2oKb6jINu0Ku\nkJJZUM+RCSFE1fTuozEzK79tExISgo2NDZ07dwbKlwu4tU3UPhtLE4IGemJhdjPZlGr4KeQKqVk3\n6jkyIYSonF6JpmPHjmzZsoVz586xd+9eBg4ciEqlIjs7my+//JKOHTvWdpziDnbWZowd6Im5afmg\nwRJ1GT8diiFNko0QogHSK9G8+uqrHD58mAkTJqBSqXjppZcAGD16NFeuXLnrejWidtjblCcbM5Py\nZFOsLmNnSAzp2YX1HJkQQujSeynnAwcOEBkZiY+PD1ZWVgAsWrSIbt264ejoWKtBiso5NDMnaIAn\nOw5FU1xSRnFJGTsPxfBEoCcOzczrOzwhhACq0UdjbW1Nt27dtEkG4NFHH32gJLNo0aIKlZ+//fZb\nHn30Ubp06cKoUaPYsmWLzvbMzExmz55N9+7d6d27N8uXL6e0tOkuEuZoZ05Qf09Mjcvr0RWVlLIj\nOIas3KJ6jkwIIcpVeUVzr/pmd6purTNFUfj000/ZvHkz48eP17Zv3LiRlStXsmTJEgICAjh+/Djv\nvPMOxsbG2lFuM2fORKVS8e2335Kamsrrr7+OkZFRk75952RvweMDPNl5KIYSdRmFxeXJ5omBntjZ\nyEANIUT9umuts9qob5aYmMjChQuJioqiZcuWOts2bdrE5MmTCQoKAsDd3Z2wsDC2bdvG2LFjCQsL\nIzQ0lIMHD+Lm5oavry/z589n6dKlzJgxAxMTkxqPt7Fwtrfg8f4e7DwUg7pUw40iNduDYxg70BN7\nSTZCiHpUZaKprfpmp0+fxsXFhY8++oh58+bpbHvrrbdwcdEthW9gYEBubnlRyVOnTuHq6oqbm5t2\ne8+ePSkoKODSpUvaIddNVQsHS8b082BXyBXUZTeTzR/RjB0ofTZCiPpTrZXLzp49y2effcbSpUtJ\nTk7m6NGjZGVlVeuAQUFBLFu2rNK+nZ49e+okkaSkJHbv3k3//v0BSE1NxclJt0z+rcfJycnViuNh\n1dLRijH9PTA2Kv+vvXUbLSNHRqMJIeqHXolGrVYzb948Jk6cyJo1a9i4cSNZWVmsX7+esWPHkpiY\nWOOBZWVl8eKLL9K8eXNeeOEFoLywp6mpqc5+xsbGqFQqiouLazyGxqqloxWP9/fE5OYAgVvJJi1b\n5tkIIeqeXolm1apV/PHHH6xevZqTJ0+iKAoA77zzDubm5nz88cc1GlRiYiJPPfUUubm5/O9//8Pa\n2hoor06D/DbbAAAgAElEQVRQUlKis69arUZRFO3aOaKcS3NLHu/voTMabeehGKkgIISoc3olmp9+\n+ol58+YxbNgwnQ53d3d3Zs2axfHjx2ssoAsXLjBp0iQMDAzYtGmTzq20Fi1aaJcquCUtLQ0AZ2fn\nGovhYdHCwZKgAZ6YmpQnm1vzbKQ2mhCiLumVaHJycmjbtm2l2+zs7MjPr5kKwjExMfzzn//E1dWV\njRs3VhgY0K1bNxITE3X6Y44fP46lpSW+vr41EsPDxsnegrEDvLQVBErU5clGqj4LIeqKXonGy8uL\nPXv2VLotJCQET0/PGglmwYIFmJiYsGzZMkpLS0lPTyc9PV074CAgIIAuXbowd+5cLly4QHBwMMuX\nL2fatGlNemjzvTjamevURlOXanRW7RRCiNqkVwmaF198kdmzZ5OXl8egQYNQqVScOXOG3bt3s2HD\nBj744IMHDiQ2NpZz584B5RUH7uTu7s6BAwdQqVSsWbOGJUuWMGXKFCwtLZkwYQIzZsx44OM/7Jrb\nmvNEoBc7gmO4UaTWJpuRvdvQ2sWmvsMTQjzEVMqtnv172LFjBytXrtTpI7G1tWXWrFlMnjy51gKs\nCVevXmXIkCH8+uuvtGrVqr7DqVfZuUXsCI6hoEgNgIFKxbBe7rRzs6vnyIQQDU1NfXbqdUUDMHbs\nWIKCgoiOjiYnJwdra2u8vLwwMtL7JUQDYGdjxrhBXuw8FENuQQkaRWH/8QTUpRo6tHWo7/CEEA8h\nvfpoCgrKRympVCratWtHjx49yM/PlyTTSDWzMmVcoBd21uWlaRRF4bdTiZyJTKvnyIQQD6O7Jppz\n587x2GOP8dVXX+m05+Tk8Pe//53hw4cTERFRqwGK2mFlYcITgZ442t4uTXM4PIkTF1LQ826qEELo\npcpEExcXx7Rp01Cr1fj5+elsMzc3Z+nSpQBMmTKlVioDiNpnYWbM2EAvWja31LaduJjC4fAkSTZC\niBpTZaL5/PPPcXFxYevWrQQGBupsMzU1Zfz48WzZsgV7e3s+//zz2o5T1BJTY0PG9PfEvYW1ti08\nKp3fQxPRaCTZCCEeXJWJ5sSJEzz77LM6C539VbNmzZg2bVqNVgYQdc/YyIDRfdri2cpW23YxNotf\njsdTVqapx8iEEA+DKhNNRkZGhfViKuPp6aktAyMaL0NDA0b0ak37NvbatpirOew6fIVidVk9RiaE\naOyqTDTNmzcnKSnpni+QmpqKvb39PfcTDZ+BgYrB3d3o3O72Eg5X0/LZ8Uc0N27OuxFCiOqqMtH0\n7t2bH3744a5PVhSFLVu2VBgsIBovlUpFv84t6d3pdp259JxCfvwtipw8WYpBCFF9VSaaf/zjH1y4\ncIHXXnuN7OzsCtuzs7N5/fXXOX36NM8880ytBinqlkqlopuvM0O6u2Nwcznv3IIStv4eRZosMyCE\nqKYqZ1x6eXnx/vvv8+abb7J//346depEy5YtKSsrIykpiXPnzmFgYMDixYvp3r17XcYs6kj7tvaY\nmRryy5/xlJZpKCwuZXtwNCN7t8G9hdRHE0Lo564TNkePHs2OHTt48sknSUtLY9++ffz222/k5uYy\nZcoUdu/ezcSJE+sqVlEP2rZsxtiBntplBtSlGn4+HEtkQsWrXCGEqMw9a8i0adOGRYsW1UUsooFq\n4WDJuEFe/HQohvxC9c36aPHcKFLTxdupvsMTQjRwVV7RnDlz5r5eMCws7L6DEQ2XvY0Z4we3w8HG\nTNt2ODyJkLBrMrFTCHFXVSaat99+m1dffZWYmBi9XujixYvMmTOHt956q8aCEw2LlYUJTwzSLVkT\nHp3O3mNxqEtlro0QonJV3jrbunUrq1atIigoCC8vL4YPH46/vz+tWrXC3NycvLw8UlJSCA0N5dCh\nQ0RGRjJlyhQ+/PDDuoxf1DEzEyMeH+DJwRMJRF/NASA26Trb/4jhsX5tsTAzrucIhRANzT0XPktK\nSuKrr75iz549ZGZmoro53BXK59E4OzszfPhwpk2bplclgfogC5/VPEVROHoumbDLt6tC2Fia8Fg/\nD+zvuL0mhGi86mzhs5YtW/Lmm2/y5ptvEhkZSWJiInl5edjZ2eHq6oqXl9d9H1w0XiqVir7+LbGx\nNOFQ2DUURSmfa/NbFCP7tKGVk/W9X0QI0SRUa+Uyb29vvL29aysW0Qh18myOjYUJ+/6MQ12qoVhd\nxk8hVxjc3Q3f1lKaSAih5wqbQtxNaxcbxgW2w/Jm/4xGo3DwRAInLsoiakIISTSihjjamTNhiO7w\n5xMXUth/PIFSWWpAiCZNEo2oMVYWJowb3A4359v9M1GJ2Wz/I5qCQqn+LERTJYlG1ChTY0Me6+eB\nn4eDti016wZbfo0kLVsKcgrRFFU70aSmpnLu3DkKCwspLpay8aIiQwMVA7u2YkCAq3Y4fH6hmm2/\nR2vn3gghmg69E01wcDCjR48mMDCQSZMmceXKFV599VUWLVqERiP34IUulUqFv5cjY/q1xdTYEIDS\nMg37jsVxUgYJCNGk6JVogoODmT59Ou7u7rz77rvaxNKjRw+2bdvG+vXrazVI0Xi5t7Bh/OB22FqZ\natuOyyABIZoUvRLNrVI069atY9y4cdr2qVOnMn36dLZt21ZrAYrGz+5mQc47J3HeGiSQL4MEhHjo\n6ZVooqOjGT16dKXbevToQXJyco0GJR4+ZqZGjOlfcZDADwcjSc4oqMfIhBC1Ta9EY2trS3x8fKXb\n4uPjsbOzq9GgxMPpzkECt5aIvlGkZntwNOdjMuo5OiFEbdEr0YwaNYpVq1bx+++/U1ZWXg5epVIR\nHR3NunXrGD58+H0dfNGiRbz55ps6bYcPHyYoKAh/f3/GjBlDcHCwzvbMzExmz55N9+7d6d27N8uX\nL6e0tPS+ji/qnnaQQH8P7aqdGo3CH6ev8ntoImXSbyPEQ0evRDNnzhw6duzI9OnT6datGwD//Oc/\nGTNmDE5OTsyZM6daB1UUhVWrVrF582ad9ujoaKZPn86jjz7K9u3bGTJkCDNmzCAqKkq7z8yZM8nI\nyODbb7/lgw8+YNu2baxevbpaxxf1z83ZmolDvXG0Nde2XbiSyTbptxHioaNXUU0zMzO++uorgoOD\n+fPPP8nJycHa2pqePXsyePBgDAz0n46TmJjIwoULiYqKqrCswDfffEOXLl2YPn06UJ7gQkND+eab\nb1i6dClhYWGEhoZy8OBB3Nzc8PX1Zf78+SxdupQZM2ZgYmJSjbcu6puNpQnjBrXjj9BELidkA7f7\nbUb2boPLHQusCSEaL70SzcyZM5k6dSoDBw5k4MCBD3TA06dP4+LiwkcffcS8efN0tp06dYqRI0fq\ntPXq1Yvdu3drt7u6uuLm5qbd3rNnTwoKCrh06RKdO3d+oNhE3TM2MmBoT3ec7Cw4cjYJjaKU99v8\nEU3/AFf8PBx01kASQjQ+el2KhISEaPtmHlRQUBDLli3D0dGxwraUlBScnZ112pycnEhJSQHKqxI4\nOTlV2A7IyLdGTKVS0dnbkccHeGBuerPfRlEIPn2V304lynwbIRo5vRJNnz592Lt3b40lm6oUFRVV\nuP1lYmKiLXVTWFiIqampznZjY2NUKpWUw3kItHKyZsIQbxztbvfbXIrL4sffosjJk/9fIRorvW6d\n2drasnXrVvbt24eXlxcWFhY621UqFV988cUDB2NqaopardsRXFJSgrl5+QePmZkZJSUlOtvVajWK\nolSISTRONpYmPHmz3yYivrzfJiOnkB9+jWRIdzc8W9nWc4RCiOrS64omLi4Of39/PD09URSFgoIC\nnX/5+fk1EoyLiwtpaWk6bWlpadrbaS1atCA9Pb3CdqDCLTfReBkZGjCkhzuBXVthaFDeP1OiLmPv\nsTgOh1+jTCN10oRoTPS6otm4cWNtxwFAt27dOHnypE7b8ePH6d69u3b7ihUrSE5OxsXFRbvd0tIS\nX1/fOolR1A2VSoWfZ3Oc7CzY92ccuQXlV7JnItNJzbzBiN5tsDI3rucohRD6aFDr0Tz99NOcOnWK\nTz/9lJiYGFatWkV4eDjPPPMMAAEBAXTp0oW5c+dy4cIFgoODWb58OdOmTZOhzQ8pJ3sLJg71pq2L\njbYtObOAzQcuk5iaV4+RCSH0pdcVjb+//z2HmIaHhz9wMD4+PqxZs4bly5ezfv16PDw8+Oyzz/D0\n9ATKv+WuWbOGJUuWMGXKFCwtLZkwYQIzZsx44GOLhsvMxIhRfdsSdjmdY+eTURSFwuJSfgq5Qo8O\nzvRo7yxDoIVowPRKNNOmTavwh3zjxg1CQ0NJSkqqMB9GXxs2bKjQFhgYSGBgYJXPcXR0ZO3atfd1\nPNF4qVQquvo64exgwS9/xnOjqHwQyIkLKSRnFDCspzsWZnIrTYiGSK9EM3fu3Cq3vfLKK0RERNRY\nQELcjaujFZOGerP/eDzX0ssHoSSm5vH9/ssM7elO6xY293gFIURde+A+mvHjx/Pzzz/XRCxC6MXS\n3JigAZ508719y6ywuJRdIVc4cjZJCnMK0cA8cKK5evVqhbkvQtQ2AwMVvTu58Hh/D51bZmGX09j2\nRzTX82WCpxANhV63zipbqlmj0ZCcnMzOnTsZMGBAjQcmhD7cnK352zBvfj2ZSHxKLlBemHPzwUgG\ndWtFOzdZK0mI+qZXolm5cmWl7ebm5gQGBlZYU0aIumRhZsxj/dpyJjKdY+eS0SgKJeoyfvkznsTU\nPPp3ccXYyLC+wxSiydIr0Vy4cKFCm0qlqtbyAELUJpVKRYCPEy0drfjljgmeF2OzSM64wbBe5RWi\nhRB1T69MsWTJEpKTkzE0NNT+u5VkYmNjmTlzZq0GKYS+nO0t+NswH51bZtl5Rfz4WxShEalopHyN\nEHWuyiua1NRU7c9btmxh6NChGBtXnKcQEhJSYbllIeqTibEhw3u54+5szaGwq6jLNGg0CsfOJROf\nnMfQnu7YWEolCSHqSpWJ5u233yYkJAQovy3x0ksvVbqfoij06dOndqIT4j6pVCrat7XHpbklB07E\nk5p1A4CkjHw2HbjMgABXfNztpKKAEHWgykSzdOlSjh49iqIoLFy4kOnTp+Pu7q6zj4GBATY2NvTq\n1avWAxXiftham/LkoHacikjl1MVU7UCBgycSiE/OZWBAK8xM9eqqFELcpyr/wpydnXniiScAKCsr\nY8iQIdjb29dZYELUFAMDFT07tMDd2ZqDJxLIuTnHJioxh+SMAob0cMfN2bqeoxTi4aXXV7kJEyZQ\nUlJCRESEzsJjGo2GwsJCTp06JQMCRIPXwsGSScO8ORyexIUrmQDkF6rZeSiGzu0cecTPBWMjGUkp\nRE3TK9GcOnWKOXPmkJmZWel2c3NzSTSiUTA2MmRQNzfauNjw26lECotLAQiPSic+OZchPdxxaW5Z\nz1EK8XDR6+vbxx9/jKWlJR999BGDBw9m2LBhrF27lokTJ6JSqfjf//5X23EKUaPatmzGU8N9dIpw\n5uQXs+2PaI6cTaJU6qUJUWP0SjQXL15k5syZjBw5ksGDB5OSksLgwYN55513eOKJJ1i3bl1txylE\njbtVUWBwdzdMjMsrByiKQtjlNDYfiCQls6CeIxTi4aBXoikrK6NFixYAtG7dmqioKO22kSNHVlo5\nQIjGQKVS0aGtA08N99EZEJCdV8TW36M5dk6qQQvxoPRKNO7u7kRHRwPg4eFBYWEhsbGxQPmAgIIC\n+eYnGjdrCxMe7+/BoG5u2gEBiqIQGpHGDwcjSbs5D0cIUX16JZrRo0ezfPlyNm3ahL29PR07duT9\n99/nyJEjrFu3TrvUshCNmUqloqOHA08N96WVk5W2PTO3vITNsXPJ0ncjxH3QK9G88MILPPHEE/z5\n558ALF68mLNnz/Lss88SGRnJa6+9VqtBClGXbCxNCBrgycCAVhgblv+JaBSF0IhUNh24TNLNlT2F\nEPrRa3hzamoqb731lvaxv78/Bw8eJDo6Gk9PT2xsZPlc8XBRqVR08mqOewtrfjuVqF02OievfGSa\nn4cDvf1bYmosyw8IcS96XdE8+eST/PTTTzpt1tbWBAQESJIRD7VmVqaMHehJYNdW2pFpAOevZLJx\nXwRXrl2vx+iEaBz0SjQqlQo7O1mpUDRNKpUKP8/mTB7hS9uWzbTtBUVq9hyNZe+xOAoKZTlzIaqi\n162zGTNmsGzZMoqKivD19cXCouICUg4ODjUenBANiZW5MaP6tCHm2nUOhV3jRlF5com5msPVtDz6\n+rekfRt7qQgtxF/olWhWrFhBcXExs2bNqnKfS5cu1VhQQjRUKpUKr1a2tHK04ui5JC7GZgFQXFLG\nb6cSuRyfzcCurbC3MavnSIVoOPRKNAsXLqztOIRoVMxMjRjc3Z12bnb8HpqoXTr6Wnr5ejcB3k50\nb+8sRTqFoBrVm4UQFbk5W/PUcF9OXEwhPDIdjaKg0ZQPhY5KzKZ/F1edfh0hmiK9V3xSFIV9+/Zx\n9OhR0tPTeeONNzh79iwdO3bEw8OjNmMUokEzNjKgr39LfNztCD59leSbNdJyC0rYfSQWD9dm9O/i\nirWFLB8tmia9ruvz8/OZMmUKc+fO5fDhwwQHB5Ofn8+OHTuYOHEiERERtR2nEA1ec1tzxg3yYnB3\nN8xMbn+Hu3LtOhv3RXD6chplGqUeIxSifuiVaJYtW0ZCQgLbtm3jwIEDKEr5H8snn3xCmzZt+OST\nT2o1SCEai1tFOqc86kuHtrdXpFWXaTh6NokfpLKAaIL0SjQHDhxg3rx5dOjQQWfoprW1NS+99BJh\nYWG1FqAQjZH5zcEC4wZ54XDHCLTM3CK2/RHN/uPx5MvcG9FE6JVobty4UeU8GVNTU4qLi2ssoBs3\nbrB06VL69etH9+7dee6557SVowEOHz5MUFAQ/v7+jBkzhuDg4Bo7thA1rWVzKyYO86GPf0udEWiR\nCdl8t+8Spy6lSqFO8dDTK9F07NiRH374odJte/fupUOHDjUW0L///W+OHj3KqlWr2Lx5M6ampjz3\n3HMUFxcTHR3N9OnTefTRR9m+fTtDhgxhxowZOuvjCNHQGBqo6OrjxOQRvrRzs9W2q0s1/Hk+me/3\nXyY26br2lrQQDxu9Es3s2bMJDg5m/PjxrFu3DpVKxf79+5k9ezY7d+7k5ZdfrrGADh48yOTJk+nW\nrRuenp7MnTuX5ORkoqOj+eabb+jSpQvTp0/H09OTOXPmEBAQwDfffFNjxxeitlhbmDDikTY8EeiF\nQzNzbfv1/GJ2H4ll1+ErZOcW1WOEQtQOvRJNr169+PLLL1GpVKxduxZFUfj888+Ji4tj7dq19OvX\nr8YCsre3Z8+ePWRmZlJSUsKPP/5Is2bNcHNz49SpU/Ts2bNCbKdOnaqx4wtR21wdrZg01JuBAa0w\nNbldqDMhJY/v91/mSHgSJeqyeoxQiJql9zyaRx55hC1btlBQUMD169extrbG2tr63k+spqVLl/La\na6/Rp08fDA0NMTMz43//+x82NjakpKTg7Oyss7+TkxMpKSk1HocQtcnAoHwZAi83W46fT+ZCbBaK\noqBRFMIi07ickE2vji1o38YeAwOpnSYaN70TDcCRI0c4deoUubm5ODg48Mgjj9C1a9caDSg+Pp7m\nzZuzZMkSbG1t+e9//8usWbP44YcfKCoqwsREd9KbiYlJjQ5GEKIumZsaEdjNjY4ezQk5c5WkjPLJ\nnjeK1PwemsjZqHT6dG5J6xayHIdovPRKNDk5Obz00kucOXMGIyMjbG1tycnJYfXq1QwYMIDVq1dX\nSAD3IzExkbfffpuNGzfSpUsXAFauXMmoUaP4v//7P0xNTVGrdYeElpSUYG5uXtnLCdFoONqZ80Sg\nF1GJORw9m6Qd+pyZW8SukCu4O1vTt3NLnb4dIRoLvfpo3nvvPWJjY1mzZg3nzp3j8OHDnD17llWr\nVnHmzBlWrlxZI8GcP3+esrIy/Pz8tG3Gxsa0b9+e+Ph4XFxcSEtL03lOWlpahdtpQjRGKpUKb3c7\npjzankf8XHSGQyek5rHpQCS/nUrULk8gRGOhV6I5dOgQ8+fPZ+jQodoJmwYGBgwfPpxXXnmFn3/+\nuUaCadGiBQCXL1/WtimKQkxMDG3atKFbt26cPHlS5znHjx+ne/fuNXJ8IRoCYyMDurd35u8j29PR\nw0H7N6coChdjM9mw9xInL6agLpX5N6Jx0HuFTVtb20q3OTk5UVJSUiPB+Pv706VLF15//XVOnTpF\nTEwMixcvJikpiaeffpqnn36aU6dO8emnnxITE8OqVasIDw/nmWeeqZHjC9GQWJgZM6ibG38b5o17\ni9sDb9SlGo5fSOG7fZe4FJuFRuqniQZOr0Tz1FNP8cknn5Cenq7TXlBQwJdffsnkyZNrJBhDQ0PW\nrVtH586dmTdvHpMmTSIhIYGNGzfi6uqKj48Pa9as4ZdffmHs2LH89ttvfPbZZ3h6etbI8YVoiBya\nmfN4f0/G9PfQKWeTX6jm11MJbDogEz5Fw6bXYICsrCxSUlIYOnQoPXr0wMnJiZycHEJDQ8nLy8PU\n1JTnn38eKL/6+eKLL+47IHt7e957770qtwcGBhIYGHjfry9EY9W6hQ1uTtZcisvi+IUUbV9NVm4R\nu4/E0sLBkt6dXHB1tKrnSIXQpVeiiY6Opl27dkB5LbK4uDgA7ZVEYWFh7UQnhNBhYKCio4cD7dxs\nOROZTlhkmravJiWzgO1/ROPewprefi1xtJMRaqJh0CvRbNy4sbbjEEJUg4mxIT07tsDP04HQiDTO\nx2Ro17pJSMkjIeUy7dzs6NWxBbbWpvUcrWjqqjVhs6SkhLy8vEq3VVXdWQhReyzMjOnfxZXO7Rw5\neTGFiPhsbV9NVGI2MVdz6ODhQPf2zliZG9dztKKp0ivRXL58mTfeeIOIiIgqOxwvXbpUo4EJIfRn\nY2nCkB7udPF25M/zKcQmXQdAoyicj8kgIi6Ljh4OdPN1wsJMEo6oW3olmsWLF5OamsrcuXOrHOYs\nhKh/Ds3MGd23LSmZBRw9m0xSRvlqnqVlGsKj0rlwJZNOns0J8HGUhCPqjF6JJiIigo8++ojBgwfX\ndjxCiBrQwsGSJwI9SUjN4/j5FNKybwDlCScssrxPp5NXcwJ8nDA3rdYddCGqTa/fsFatWknhSiEa\nGZVKResWNrg7WxOXnMuJCymk55SPEFWXaTh9OY1zMRn4ezkS4O2ImSQcUUv0+s2aM2cOK1aswMnJ\niU6dOtVIAU0hRN1QqVS0bdmMNi42xCblcuJiChm3Ek6phtCIVM7FZNClnSP+7ZpjZiIJR9QsvX6j\n2rVrh0aj4emnnwbKZ/D/1fnz52s2MiFEjVKpVHi4NqNtSxtirl3n5IUUMm+u6FmiLuPExRTORKXj\n5+FAF2/pwxE1R69Es2DBAq5fv86kSZNo3rx5bcckhKhFKpUKr1a2eLo2I/pqDicvppJ1R8I5fTmN\ns9EZdGzrQICPI1YWcgdDPBi9Es2lS5dYtmwZI0aMqO14hBB1RKVS0c7NDk9XW6Kv5nDq0u2EU1qm\nITw6nXNXMvBtbU83XyeaWcnET3F/9Eo0Li4uGBjoVX9TCNHIGBiUr4PTzs2WK9eucyoilfTs8j4c\njaZ8aYJLcVm0c7Olm6+TLL4mqk2vRDNr1iw+/vhjmjdvjr+/f6V9NEKIxk2lUuHZyhYP12YkpOYR\neilVu7S0oihEJmQTmZCNp2szuvo642xvUc8Ri8ZCr0TzxRdfkJycrF0O4K+jzlQqFWfOnKn56IQQ\nde7WsOjWLWxISs/n5KVUElNvl56KuXadmGvXcXW0IsDHidYtrLWLswlRGb0SjZTlF6JpauloRZCj\nFalZNzh1KVVb2gbgWno+19LzcbAxo4u3E97uthgayi12UZHe82iEEE2Xs70Fo/u2JfN6Iacj0ohK\nzEFzs+5hZm4Rv55K4PiFZPy9HOno6YCpsdxeF7dVa2bW2bNnOXr0KOnp6Tz33HPExsbi6+uLvb19\nbcUnhGhAHJqZM6xXa3p3cuHMzdppt9bDyS9Uc/RcEqciUunY1oHO7ZrL0GgB6Jlo1Go1CxYsYM+e\nPRgZGVFWVsa4ceNYv349MTExfPfdd7i5udV2rEKIBsLKwoR+nV3p3t6ZC1cyCY/K0K74WaIuIywy\njfCodNq52dK5nSNOMnCgSdPrhuqqVav4448/WL16NSdPntQuFfDOO+9gbm7Oxx9/XKtBCiEaJjMT\nI7r5OvPMqPYM7u6GvY2ZdptGUbickM0Pv0ay9bcoohNz0GgqX2ZEPNz0uqL56aefmDdvHsOGDaOs\nrEzb7u7uzqxZs3j//fdrLUAhRMNnaGhAh7YOtG9jT1xyLmGX07VLFAAkZxaQnFmAlbkx/l6OdGhr\nL0U8mxC9/qdzcnJo27Ztpdvs7OzIz8+vdJsQomm5VcCzbctmpGXdIDwqnairt69kbvXjnLiYgm9r\nO/zbOepcBYmHk163zry8vNizZ0+l20JCQvD09KzRoIQQjZ+TvQXDerXmmVEd6NHeWWfdm9IyDeev\nZLLxlwh2HoohLjm3ytV7ReOn1xXNiy++yOzZs8nLy2PQoEHaCZq7d+9mw4YNfPDBB7UdpxCikbI0\nN6aXnwvd2jsTlZBDeHS6dpkCgMTUPBJT87CxNMHPoznt29rLYmwPGZWi59eIHTt2sHLlStLT07Vt\ntra2zJo1S1sxoKG6evUqQ4YM4ddff6VVq1b1HY4QTZqiKCRlFHA2Kp0rSRWvZAwNyqtL+3k2p4WD\nhVQdqEc19dmp99eGsWPHEhQURHR0NDk5OVhbW+Pl5YWRkXzzEELoT6VS4epohaujFdfzizkXk8Gl\nuCyKS8oHGpVpykerXU7IprmtOZ08m+PtbouxkUwCbayqzBJTp05l8eLFOv0vKpWKdu3a1UlgQoiH\nXzMrU/p1duURPxeiEnI4fyWD1Kwb2u0ZOYX8HprIkbNJ+La2w8+zuQweaISqTDQnTpygoKCgLmMR\nQrgkTRsAABu+SURBVDRRRoYGtG9rT/u29qRl3eD8lQwiE3IoLSuvOlCiLuNsdAZnozNo2dyKjh72\neLayxUhqqzUKct9LCNGgONlbMNjenT7+Lbkcl825Kxnk5BVrtydl5JOUkc+hsGt4u9vRoa0Djnay\nRk5DJolGCNEgmZkY0dnbEf92zbmals/5K5nEXruuLeZZrC7jXEwG52IycLQzp0NbB7zd7aSgZwN0\n10Tz3nvvYWVldc8XUalU/Pe//62xoIQQ4haVSoWbszVuztYUFKqJiM/iYmwW1/NvX+WkZxcSnH2V\nI+FJeLVqRoe2Drg0t5QRaw3EXW9wlpaWolar7/mvpKSkRoPasmULI0aMwN/fn3HjxnHs2DHttsOH\nDxMUFIS/vz9jxowhODi4Ro8thGi4LM2N6ebrzNOP+vJEoBc+7nY6/TSlZRoi4rPZ9kc03/0SwemI\nNPIL1fUYsYB7XNEsWbIEf3//uooFgO3bt/POO++wZMkSevTowcaNG3n55ZfZtWsXRUVFTJ8+nZdf\nfpnhw4eza9cuZsyYwfbt22U0nBBNyJ1DpPuXlBKVkMOF2EydiaA5ecUcPZfEsfPJuDlZ4dvGnrYt\nm2FsJAMI6lqD6qNRFIXVq1fz/PPPM378eAAWLFjAn3/+SVhYGCdPnqRLly5Mnz4dKF+QLTQ0lG++\n+YalS5fWZ+hCiHpiZmJEJ6/m+Hk6kJ5dyMXYTCITcyhRl8/LURSFhNQ8ElLzMDE2xKtVM3xa29NS\nbq3VmQaVaK5cucK1a9cYNWqUts3AwICdO3cCsG7dOkaOHKnznF69erF79+46jVMI0fCoVCqc7C1w\nsregb+eWxFy7TkRcNtfS87XVB0rUZVyMLe/jsbE0wcfdDp/W9tham9Zz9A+3KhPNE088gZ2dXV3G\nQlxcHAC5ublMnTqVqKgoPDw8eOWVV+jatSspKSk4OzvrPMfJyYmUlJQ6jVMI0bAZGxni29oe39b2\n5N0o4XJ8NhHxWTrDpHMLSjh5KZWTl1JxcbDEp7UdXq1sZfmCWlDlGf1//+//1WUcANrlBl5//XVm\nzZqFh4cHW7Zs4ZlnnmHHjh0UFRVhYqK7NKyJiQnFxcWVvZwQQmBtYUL39s5083UiNesGl+OziUzM\n1pa8gdvr5RwKu0brFta0c7ejbUsbKXtTQxpU6jY2NgbgpZdeYsyYMQB06NCB0NBQvv/+e0xNTfn/\n7d15VFTXHQfw7wyyDoLIvgmCDFG2QQEFibgkQknUUxN3LKgkbo20aTQagZhgrQGJRCkhcWlOxD0V\nNVprcyJobFOCGDFEVPYdgUH2YZu5/YPw5IlSkzgOA7/POZzj3Hvnzf0Nnvfj3XffvV1d/BkknZ2d\n0NWlh7UIIQMTCASwMBbBwlgEfw8rFFU14U7JfZRUNXHP5igYQ1FVE4qqmqCpIYS9lQHEY4wwxnwk\nNGgVgl9sUCUaMzMzAIBYLObKBAIBHBwcUF5eDktLS9TU1PDeU1NT0284jRBCBqKhIcQ4m1EYZzMK\nbe1dyCtrwN3S+7x11rrkCuSVNSCvrAHaWhpwtDaEk60RrE31IRTSJIKfY1AlGhcXF+jp6eGHH36A\nm5sbgJ4ZIwUFBfD19YWpqSkyMzN578nIyICXl5cquksIGQL0dDTh4WQKDydTNLZ09CSX0vuQNrVz\nbTo6H0wi0NPRhJPNKDiNGQXz0bSNwZMYVIlGV1cXoaGhSEhIgImJCcRiMY4cOYLS0lLs2bMHXV1d\neOWVV7Bnzx689NJLOHfuHLKzs7Ft2zZVd50QMgQY6mvDa7w5vMabQ9oow93SBuSV3UdT64OH0tva\nu5CdX4vs/Fro62rC0WYUHG0MYWlM06UfZ1AlGgCIiIiArq4uduzYAalUivHjx+PgwYNwcHAAACQm\nJiIuLg779u2Dg4MDkpOTaStpQshTZ2yoC183XUxxtcC9+jbcLb2P/PJGtLU/uE/cIutCdl4tsvNq\nIdLRhIO1IcbZjoKlsYiG1/p44h021RntsEkIeRoUCoaK2hbkld1HYUUT2ju7H9lOV3sEHK0N4Wgz\nSq3v6TzzHTYJIWS4EwofLPAZMJGhsrYFBeUNKKhohKzjQdKRdXQjp1CKnEIpdLRGwMHaEI7WhrA2\n0x+We+hQoiGEkF9Ao0/SmeZpg8q6FhSUN6Kggj+81t7ZjVtFUtwqkkJzhBBjLAzgYGUAO0sD6GgN\nj1Pw8IiSEEKUSCgUwMZsJGzMRuJ5iTWqpa3IL29AYUUjb/Xorm5FzxVQeQOEAgGsTPUx1soAY60M\nYSDSGuAT1BslGkIIeYqEwp4EYmWq/1PSaUNBRQOKKpt4e+goGEN5TTPKa5rxzY0KmIzShYOVIcZa\nGcJklM6QmsFGiYYQQpREIBDA0kQESxMRprpbob6pHUWVTSiqbOQ9HAoAdQ0y1DXI8N2taozU04K9\npQHsLQ2GxH0dSjSEEPIMCAQCGBvqwthQF17jzdEi60JxZSMKKxtRUdMCueLBBODmtk5um+oRGkLY\nmOnDztIAdhYGajnERomGEEJUQF9XE66OJnB1NEFnlxwl1U0oqmxCSVUTOroeLPjZLVeguKoJxVVN\nAIDRBjqw++lqx8JYBA01mDpNiYYQQlRMS1MDTrZGcLI1glzRM226pLonufTd2gAA6pvaUd/Uju/v\n1EBLUwO25iNhb2EAO8uR0NPRVFEEA6NEQwghg0jfadP+HtZobOngks7DQ2ydXXJuFhsAmI7S5d5r\nZSIaNCtOU6IhhJBBzFBfG+7jTOE+zhRd3QqU1zSjpLoZJVVNaG7r5LWtbZChtkGG63dqMEJDCCtT\nEcb8lHhGG6huJhslGkIIUROaI4QY+9MUaMYY6pvauaRTVdfK7asD9NzbKa1uRml1M4Cee0K9Vzs2\nZvrPdJiNEg0hhKihvrPYJjqbobNLjoraFpRWN6PsXjMaWvj3dlpkXcgtrkducT0A/jCbpYlIqVOo\nKdEQQsgQoKWpwV3tAEBTayfK7jWj9F7PQ6F9t64G+MNsGkIBXB1NMNXdSikLgFKiIYSQIchApAUX\nB2O4OBhDoWCoud+Gsns9VzvV0jbeMJtcwZCdVws3RxOMGqn91PtCiYYQQoY4oVAAC2MRLIxF8J5g\nwQ2z9SSeFtxvbof5aD3o6ynnvg0lGkIIGWYeHmaTyxVKnQo9OCZZE0IIURllP28zLK5o5PKem2DV\n1dUq7gkhhKiP3nNm7zn0lxoWiaa2thYAsGzZMhX3hBBC1E9tbS3s7Ox+8fsFjPWZejBEtbe3Iycn\nB6amptDQ0FB1dwghRC3I5XLU1tbC1dUVOjo6v/g4wyLREEIIUR2aDEAIIUSpKNEQQghRKko0hBBC\nlIoSDSGEEKWiREMIIUSphm2ikcvliI+Ph7+/Pzw9PbFhwwbU1dWpulsDqqurw9tvvw1/f394eXlh\n1apVuHv3Lld/9epVzJs3D+7u7pgzZw4uX77Me79UKkVERAS8vLzg6+uLuLg4dHd3P+swBnTjxg1M\nmDABGRkZXJk6x3Xy5EkEBgbC3d0d8+fPx7fffsvVqWtcbW1tiImJ4f4fhoeHIz8/n6tXt7iio6Ox\ndetWXtnTiOGzzz7DjBkz4OHhgRUrVqC4uFjZofA8Kq6UlBQEBQVBIpEgODgYJ0+e5NUrLS42TO3e\nvZtNnTqVXb16leXk5LAFCxawxYsXq7pbjyWXy9miRYvYwoULWXZ2NsvLy2MbNmxgvr6+rL6+nuXl\n5TFXV1eWlJTE8vPz2e7du5mLiwu7e/cud4wlS5awpUuXstzcXJaens6mTJnCPvzwQxVGxdfa2spe\nfPFFJhaL2X//+1/GGFPruE6dOsVcXFzYyZMnWXFxMduxYweTSCSsrKxMreN65513WFBQELt27RrL\nz89n69atYwEBAay9vV2t4lIoFCwhIYGJxWL2zjvvcOVPI4YTJ04wT09PduHCBXb79m22evVqNmvW\nLNbR0aGyuA4fPswkEgk7ffo0KykpYSdOnGAuLi4sNTVV6XENy0TT0dHBPD092d///neurKysjInF\nYpaVlaXCnj3ejz/+yMRiMcvPz+fKOjo6mIeHB0tNTWVRUVEsJCSE956QkBAWGRnJGGPs+vXrTCwW\ns9LSUq7+1KlTzNPT85n8538SvTH0TTTqGpdCoWAzZsxgCQkJXJlcLmdz585lZ8+eVdu4GGPMx8eH\nff7559zrvLw8JhaLWU5OjtrEVVpaykJCQtjkyZPZ9OnTeSfkpxHD7Nmz2Z49e7j6lpYWJpFI2Nmz\nZ5UZ1oBxzZkzh8XGxvLab9myhS1fvpwxpty4huXQ2e3bt9Ha2gofHx+uzMbGBtbW1rh27ZoKe/Z4\nlpaW+OSTTzB27FiurHf/78bGRly7do0XDwBMnjyZi+fatWuwtraGra0tV+/j44PW1lbk5uY+gwgG\ndvnyZaSnpyMyMpJXrq5xFRYWoqKiAsHBwVyZUCjEmTNnMGfOHLWNCwBGjx6Nf/zjH5BKpejs7MQX\nX3wBQ0ND2Nraqk1c169fh6WlJb788kvY2Njw6n5tDFKpFMXFxbxjiEQiuLq6Kv38MlBckZGRWLx4\nMa9MKBSiqakJgHLjGpaJpnehOHNzc165mZnZoF1408jICNOnT4dQ+OBXdujQIbS3t8Pf3x/V1dUD\nxnPv3j2YmZn1qweAqqoqJfd+YPX19di6dSu2b98OQ0NDXp26xtU7bt3U1ITf/e538PX1xbJly3D9\n+nUA6hsXAMTExKC6uhp+fn6QSCQ4ceIEPv30UxgYGKhNXPPmzUNsbCxMTU371f3aGFR5fhkoLh8f\nH14SqaysxPnz5/H8888DUG5cwzLRyGQyCIVCaGryN/nR0tJCR0fHY941uHz99df48MMPsWLFCjg6\nOqK9vR1aWlq8Nn3jkclk0Nbm75ynqakJgUCg8pjfffddzJw5E9OmTetXp65xtbS0AAA2b96MBQsW\nYP/+/XByckJoaCgKCgrUNi4AKCkpgYmJCT799FMcPXoU/v7+2LBhA6qrq9U6rl6/NgaZTAYA/doM\npvNLfX09Vq9eDRMTE7z++usAlBvXsFi9+WE6OjpQKBTo7u7GiBEPvoLOzk7o6uqqsGdP5tSpU4iK\nikJwcDA2btwIoOeX39XVxWvXNx4dHR10dnby6ru6usAYg56e3rPp+COkpqbi1q1bOHv27CPr1TWu\n3j9i1qxZgzlz5gAAJkyYgKysLBw9elRt4yorK0NUVBSOHDkCiUQCAIiPj0dwcDA+++wztY2rr18b\nQ+/ikw+3GSznl7KyMoSHh6O9vR0pKSkYOXIkAOXGNSyvaCwtLQE82D6gV01NTb/LwsHm448/xpYt\nW7B48WLExsZyQ2mWlpaoqanhte0bj4WFxSPjBfpfCj9Lp06dwr1797hp5kFBQQCA1157DdHR0Wob\nV++Qg1gs5soEAgEcHBxQXl6utnHl5ORALpfD1dWVK9PU1MT48eNRUlKitnH19WtjGMznlx9//BGL\nFi2CUCjEsWPHeENpyoxrWCaa5557DiKRCN999x1XVl5ejoqKCnh7e6uwZwPbt28fEhISsGHDBkRF\nRXGTAQBg0qRJyMzM5LXPyMiAl5cXV19WVsYbB8/IyIBIJMJzzz33bAJ4hF27duH8+fM4ffo0Tp8+\njf379wMAtm/fjoiICLWNy8XFBXp6evjhhx+4MsYYCgoKYGtrq7ZxWVhYAADu3LnDlfXGZW9vr7Zx\n9fVrYzA2Noa9vT3v/NLa2oqcnByVnl8KCgqwcuVKWFtb48iRI1zi6KXUuH7xPDo1FxcXx/z8/Njl\ny5e552gentI4mOTm5rLx48ezLVu2sJqaGt5Pa2sru337NnNxcWEfffQRy8/PZwkJCczNzY2bDq1Q\nKNjChQvZokWLWE5ODjdHvu9UxcGgqqqKN71ZnePavXs38/b2ZhcvXmRFRUXsz3/+M3Nzc2MFBQVq\nG1d3dzdbuHAhe/nll1lmZibLz89nUVFRTCKRsPLycrWMKyQkhDcN+GnEcOTIESaRSNi5c+fYnTt3\n2OrVq9ns2bOf6RTuh+N65ZVXmL+/PyssLOSdP6RSqdLjGraJpquri/3lL39hPj4+bOLEiSwiIoL7\nwgej+Ph4JhaLH/nz17/+lTHGWFpaGgsODmaurq5s7ty57N///jfvGDU1NWzdunXMw8OD+fn5sfj4\neCaXy1URzmM9nGgYU9+4FAoFS05OZgEBAczV1ZUtWLCAZWZmcvXqGpdUKmVbt25lzz//PJs0aRIL\nDQ1lt27d4urVLa6HT8iMPZ0YkpOT2dSpU5lEImErV67kPZ/yLPSNq7Cw8LHnjxdeeEHpcdHGZ4QQ\nQpRqWN6jIYQQ8uxQoiGEEKJUlGgIIYQoFSUaQgghSkWJhhBCiFJRoiGEEKJUlGjIoLd582Y4OzsP\n+LN8+XIAwPLlyxEWFqbS/jY0NGDmzJkoKSlRaT+epoyMDDg7Oz/xMvclJSWYNWsWtwQ9Gd6G5aKa\nRL2sW7eOt4/Ge++9Bw0NDd7eNfr6+gB6VoLuuzSPKsTExCAoKAh2dnYq7Ycq2dnZYfbs2di+fTti\nY2NV3R2iYpRoyKA3ZswYjBkzhnutr68PDQ0NbvXgvsaNG/csu9bPzZs3cfHiRVy5ckWl/RgMwsPD\nERAQgNDQULi4uKi6O0SFaOiMDCkPD505Ozvj+PHjeOutt+Dp6YkpU6YgMTERLS0t2LJlCyZNmoSp\nU6ciLi4OfRfJuH//PiIjI+Hr6wt3d3csWbIEWVlZ//fz9+/fDz8/P4wePZory8nJQWhoKCZNmgRP\nT0+EhYXhxo0bvPdlZmZi2bJl8PDwwOTJkxEZGdlv2KmwsBDr16+Ht7c3fHx8sG7dOpSWlnL1DQ0N\niImJwcyZM+Hm5ob58+fjX//6F+8Yzs7OOHbsGLZs2QJvb294enoiIiICUqmU1+7YsWMIDAyEu7s7\nQkJCUFlZyatvb2/Htm3bMG3aNLi6uiIoKAgHDhzgtTE2NsaUKVPwySef/N/vjQxtlGjIkPfBBx/A\nyMgISUlJmDFjBvbu3YtXX30Vurq6SExMxIsvvoj9+/dzJ+WOjg6EhYUhPT0db775Jvbs2QNDQ0OE\nhYXh5s2bj/2c1tZWXLp0CbNnz+bKWlpaEB4eDiMjI+zduxe7d++GTCZDeHg4tzlaZmYmVqxYAZFI\nhI8++gibNm1Ceno6Vq1ahe7ubgA9ux8uWrQIZWVleP/997Fz506Ul5cjLCwMbW1tkMlkWLp0KS5e\nvIi1a9ciMTERDg4OeOONN3D69GleP3ft2gUASEhIwMaNG5G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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -170,19 +170,19 @@ "plot(results)\n", "xlabel('Time (seconds)')\n", "ylabel('Temperature (Celsius)')\n", - "title('Temperature of Crust vs. Time')" + "title('Temperature of Crust vs. Time')\n" ] }, { "cell_type": "code", - "execution_count": 57, + "execution_count": 4, "metadata": {}, "outputs": [ { "data": { - "image/png": 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mDHAHcKG7/zul8khcMa0aUKtGRKpakjGaHsBdCjIdrLGx7ZWdlRggIlUsSaD5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\nGbOI1ScyjA31mQU0mtnArPM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KV1dX9OnTB0uXLsXo0aPh6emJO3fu4LvvvlNqYrkin6OhoaH8uQMGDED//v2Rk5ODvXv3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\n", "text/plain": [ - "" + "" ] }, "metadata": {}, @@ -218,45 +218,46 @@ "plot(results2, 'rs', label = 'crust')\n", "xlabel('time')\n", "ylabel('temperature')\n", - "title('Temperature vs. Time')\n", + "title('Temperature of Crust vs. Time')\n", "legend()" ] }, { "cell_type": "code", - "execution_count": 58, + "execution_count": 60, "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "array([ 0.01 , 0.01333333, 0.01666667, 0.02 , 0.02333333,\n", - " 0.02666667, 0.03 , 0.03333333, 0.03666667, 0.04 ])" + "array([ 0.005 , 0.00578947, 0.00657895, 0.00736842, 0.00815789,\n", + " 0.00894737, 0.00973684, 0.01052632, 0.01131579, 0.01210526,\n", + " 0.01289474, 0.01368421, 0.01447368, 0.01526316, 0.01605263,\n", + " 0.01684211, 0.01763158, 0.01842105, 0.01921053, 0.02 ])" ] }, - "execution_count": 58, + "execution_count": 60, "metadata": {}, "output_type": "execute_result" } ], "source": [ - "r_array = 0.01 * linspace(1, 4, 10)\n", + "r_array = 0.01 * linspace(0.5, 2, 20)\n", "r_array" ] }, { "cell_type": "code", - "execution_count": 59, + "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "array([ 0.003768 , 0.00530311, 0.00697778, 0.008792 , 0.01074578,\n", - " 0.01283911, 0.015072 , 0.01744444, 0.01995644, 0.022608 ])" + "array([ 0.001727 , 0.00322831, 0.00490625, 0.00676081, 0.008792 ])" ] }, - "execution_count": 59, + "execution_count": 9, "metadata": {}, "output_type": "execute_result" } @@ -268,14 +269,14 @@ }, { "cell_type": "code", - "execution_count": 60, + "execution_count": 61, "metadata": {}, "outputs": [ { "data": { - "image/png": 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xVZNQ1dst3YvUGPWKdB5pELYboBsGRNMHVotooijinsdP8Yg421y2d/sor3jB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G/NnYlXK7wWd+yPwa2GIpmSfBd3ujdA0pFprsuAfZp4f1Z2t9ScS8nwlUJ7+/wLM/sY9wWNkrQb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\n", 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GOXiwRWbQa7RhTEwM06dPx9nZGW9vb3bu3MmoUaNISkrigw8+YOnSpRQuXDir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\nr8zd3R3JyclK7V+TZBVn4esWV7jEJYAAE8p7UuI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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -283,23 +284,39 @@ } ], "source": [ + "plan = TimeSeries()\n", "for r in r_array:\n", " cheese = make_system(Area = 2 * 3.14 * r**2 + 2 * 3.14 * r * 0.05, m = 3.14 * pi * r**2 * 0.05 * 473396, d = r)\n", " results = run_simulation_cheese(cheese, update)\n", - " plot(results)\n", - " xlabel('Time (seconds)')\n", - " ylabel('Temperature (Celsius)')\n", - " title('Temperature of Cheese vs. Time')" + " plan[r] = results.loc[t_end].temp\n", + "plot(plan, 'rs')\n", + "xlabel('Radius (m)')\n", + "ylabel('Final Temperature (Celsius)')\n", + "title('Final Temperature of Cheese vs. Different Radius')\n", + "\n", + "I = interpolate(plan, kind = 'quadratic')\n", + "plot(r_array, I(r_array), 'g-')" ] }, { "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [] + "execution_count": 62, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array(63.331725295598176)" + ] + }, + "execution_count": 62, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "I(0.01)\n" + ] }, { "cell_type": "code", From 66ee7c3f3b22714608019ca0a114a83cad67be88 Mon Sep 17 00:00:00 2001 From: Junwon Lee <31522211+junwonlee5@users.noreply.github.com> Date: Wed, 1 Nov 2017 11:17:43 -0400 Subject: [PATCH 15/19] Adding chap09mine --- code/chap09mine.ipynb | 1874 +++++++++++++++++++++++++++++++++++++++++ 1 file changed, 1874 insertions(+) create mode 100644 code/chap09mine.ipynb diff --git a/code/chap09mine.ipynb b/code/chap09mine.ipynb new file mode 100644 index 00000000..e0f70492 --- /dev/null +++ b/code/chap09mine.ipynb @@ -0,0 +1,1874 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Modeling and Simulation in Python\n", + "\n", + "Chapter 9: Projectiles\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": 56, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "# If you want the figures to appear in the notebook, \n", + "# and you want to interact with them, use\n", + "# %matplotlib notebook\n", + "\n", + "# If you want the figures to appear in the notebook, \n", + "# and you don't want to interact with them, use\n", + "# %matplotlib inline\n", + "\n", + "# If you want the figures to appear in separate windows, use\n", + "# %matplotlib qt5\n", + "\n", + "# tempo switch from one to another, you have to select Kernel->Restart\n", + "\n", + "%matplotlib inline\n", + "\n", + "from modsim import *" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": true + }, + "source": [ + "### Dropping pennies\n", + "\n", + "I'll start by getting the units we'll need from Pint." + ] + }, + { + "cell_type": "code", + "execution_count": 57, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "m = UNITS.meter\n", + "s = UNITS.second\n", + "kg = UNITS.kilogram" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": true + }, + "source": [ + "And defining the initial state." + ] + }, + { + "cell_type": "code", + "execution_count": 58, + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "data": { + "text/html": [ + "
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value
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": 58, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "init = State(y=381 * m, \n", + " v=0 * m/s)\n", + "init" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": true + }, + "source": [ + "Acceleration due to gravity is about 9.8 m / s$^2$." + ] + }, + { + "cell_type": "code", + "execution_count": 59, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "g = 9.8 * m/s**2" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": true + }, + "source": [ + "When we call `odeint`, we need an array of timestamps where we want to compute the solution.\n", + "\n", + "I'll start with a duration of 10 seconds." + ] + }, + { + "cell_type": "code", + "execution_count": 60, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "[ 0. 0.5 1. 1.5 2. 2.5 3. 3.5 4. 4.5 5. 5.5 6. 6.5 7. 7.5 8. 8.5 9. 9.5 10. ] second" + ], + "text/latex": [ + "$[ 0. 0.5 1. 1.5 2. 2.5 3. 3.5 4. 4.5 5. 5.5 6. 6.5 7. 7.5 8. 8.5 9. 9.5 10. ] second$" + ], + "text/plain": [ + "" + ] + }, + "execution_count": 60, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "duration = 10 * s\n", + "ts = linspace(0, duration, 21)\n", + "ts" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": true + }, + "source": [ + "Now we make a `System` object." + ] + }, + { + "cell_type": "code", + "execution_count": 61, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "system = System(init=init, g=g, ts=ts)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": true + }, + "source": [ + "And define the slope function." + ] + }, + { + "cell_type": "code", + "execution_count": 62, + "metadata": { + "collapsed": true + }, + "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", + " #print(t)\n", + " return dydt, dvdt" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": true + }, + "source": [ + "It's always a good idea to test the slope function with the initial conditions." + ] + }, + { + "cell_type": "code", + "execution_count": 63, + "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": { + "collapsed": true + }, + "source": [ + "Now we're ready to run `odeint`" + ] + }, + { + "cell_type": "code", + "execution_count": 64, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "run_odeint(system, slope_func)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": true + }, + "source": [ + "Here's what the results look like." + ] + }, + { + "cell_type": "code", + "execution_count": 65, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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" + ], + "text/plain": [ + " y v\n", + "0.0 381.000 0.0\n", + "0.5 379.775 -4.9\n", + "1.0 376.100 -9.8\n", + "1.5 369.975 -14.7\n", + "2.0 361.400 -19.6" + ] + }, + "execution_count": 65, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "system.results.head()" + ] + }, + { + "cell_type": "code", + "execution_count": 66, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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" + ], + "text/plain": [ + " y v\n", + "8.0 67.400 -78.4\n", + "8.5 26.975 -83.3\n", + "9.0 -15.900 -88.2\n", + "9.5 -61.225 -93.1\n", + "10.0 -109.000 -98.0" + ] + }, + "execution_count": 66, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "system.results.tail()" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": true + }, + "source": [ + "The following function plots the results." + ] + }, + { + "cell_type": "code", + "execution_count": 67, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def plot_position(results):\n", + " \"\"\"Plot the results.\n", + " \n", + " results: DataFrame with position, `y`\n", + " \"\"\"\n", + " newfig()\n", + " plot(results.y, label='y')\n", + " \n", + " decorate(xlabel='Time (s)',\n", + " ylabel='Position (m)')" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": true + }, + "source": [ + "Here's what it looks like." + ] + }, + { + "cell_type": "code", + "execution_count": 68, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Saving figure to file chap09-fig01.pdf\n" + ] + }, + { + "data": { + "image/png": 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What can we infer about how `odeint` works, based on the results?" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": true + }, + "source": [ + "**Exercise:** Change the value of `dt` and run the solver again. What effect does it have on the results?" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Onto the sidewalk\n", + "\n", + "Here's the code again to set up the `System` object." + ] + }, + { + "cell_type": "code", + "execution_count": 69, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def make_system(duration, v_init=0):\n", + " \"\"\"Make a system object.\n", + " \n", + " duration: time of simulation in seconds\n", + " v_init: initial velocity, dimensionless\n", + " \n", + " returns: System object\n", + " \"\"\"\n", + " init = State(y=381 * m, v=v_init * m / s)\n", + "\n", + " g = 9.8 * m/s**2\n", + " ts = linspace(0, duration, 11)\n", + " return System(init=init, g=g, ts=ts)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "And run the simulation." + ] + }, + { + "cell_type": "code", + "execution_count": 70, + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "data": { + "text/html": [ + "
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" + ], + "text/plain": [ + " y v\n", + "0.0 381.0 0.0\n", + "1.0 376.1 -9.8\n", + "2.0 361.4 -19.6\n", + "3.0 336.9 -29.4\n", + "4.0 302.6 -39.2\n", + "5.0 258.5 -49.0\n", + "6.0 204.6 -58.8\n", + "7.0 140.9 -68.6\n", + "8.0 67.4 -78.4\n", + "9.0 -15.9 -88.2\n", + "10.0 -109.0 -98.0" + ] + }, + "execution_count": 70, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "system = make_system(10)\n", + "run_odeint(system, slope_func)\n", + "system.results" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": true + }, + "source": [ + "To figure out when the penny hit the sidewalk, we use `interp_inverse`, which return a function that maps from height to time." + ] + }, + { + "cell_type": "code", + "execution_count": 71, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "y = system.results.y\n", + "T = interp_inverse(y, kind='cubic')" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": true + }, + "source": [ + "`T(0)` interpolates the time when the height was 0." + ] + }, + { + "cell_type": "code", + "execution_count": 72, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array(8.81792826905006)" + ] + }, + "execution_count": 72, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "T_sidewalk = T(0)\n", + "T_sidewalk" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": true + }, + "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": 73, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "8.817885349720552 second" + ], + "text/latex": [ + "$8.817885349720552 second$" + ], + "text/plain": [ + "" + ] + }, + "execution_count": 73, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "sqrt(2 * init.y / g)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": true + }, + "source": [ + "The estimate is accurate to 4 decimal places." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": true + }, + "source": [ + "We can double-check by running the simulation for the estimated flight time." + ] + }, + { + "cell_type": "code", + "execution_count": 74, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "system = make_system(duration=T_sidewalk)\n", + "run_odeint(system, slope_func)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": true + }, + "source": [ + "And checking the final state." + ] + }, + { + "cell_type": "code", + "execution_count": 75, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def final_state(results):\n", + " \"\"\"Returns the final position and velocity, with units.\n", + " \n", + " results: TimeFrame with y and v.\n", + " \n", + " returns: y, v at t_end\n", + " \"\"\"\n", + " t_end = results.index[-1]\n", + " y, v = results.loc[t_end]\n", + " return y*m, v*m/s" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": true + }, + "source": [ + "As expected, the final height is close to 0." + ] + }, + { + "cell_type": "code", + "execution_count": 76, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "-0.003708896250259386 meter" + ], + "text/latex": [ + "$-0.003708896250259386 meter$" + ], + "text/plain": [ + "" + ] + }, + "execution_count": 76, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "y_final, v_final = final_state(system.results)\n", + "y_final" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": true + }, + "source": [ + "And we can check the final velocity." + ] + }, + { + "cell_type": "code", + "execution_count": 77, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "-86.41569703669059 meter/second" + ], + "text/latex": [ + "$-86.41569703669059 \\frac{meter}{second}$" + ], + "text/plain": [ + "" + ] + }, + "execution_count": 77, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "v_final" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": true + }, + "source": [ + "And convert to km/h" + ] + }, + { + "cell_type": "code", + "execution_count": 78, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "-311.0965093320861 kilometer/hour" + ], + "text/latex": [ + "$-311.0965093320861 \\frac{kilometer}{hour}$" + ], + "text/plain": [ + "" + ] + }, + "execution_count": 78, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "km = UNITS.kilometer\n", + "h = UNITS.hour\n", + "v_final.to(km / h)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": true + }, + "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": [ + "**Exercise:** Try changing the initial velocity and see what effect it has on the time to hot the sidewalk. Sweep a range of values for the initial velocity, from 0 to 25 m/s, and plot `T_sidewalk` as a function of initial velocity. You might find the following function useful.\n", + "\n", + "Things might go horribly wrong for the larger initial velocities. What's going on?" + ] + }, + { + "cell_type": "code", + "execution_count": 79, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def flight_time(system):\n", + " \"\"\"Simulates the system and computes flight time.\n", + " \n", + " Uses cubic interpolation.\n", + " \n", + " system: System object\n", + " \n", + " returns: flight time in seconds\n", + " \"\"\"\n", + " run_odeint(system, slope_func)\n", + " y = system.results.y\n", + " inverse = Series(y.index, index=y.values)\n", + " T = interpolate(inverse, kind='cubic')\n", + " T_sidewalk = T(0)\n", + " return T_sidewalk" + ] + }, + { + "cell_type": "code", + "execution_count": 80, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Solution goes here\n", + "duration = 10\n", + "v_array = linspace(0, 25, 26)\n", + "for v_init in v_array:\n", + " system = make_system(duration, v_init)\n", + " T = flight_time(system)\n", + " plot(v_init, T, 'b-')\n", + " \n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### With air resistance" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Next we'll add air resistance using the [drag equation](https://en.wikipedia.org/wiki/Drag_equation)\n", + "\n", + "First I'll create a `Condition` object to contain the quantities we'll need." + ] + }, + { + "cell_type": "code", + "execution_count": 81, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "condition = Condition(height = 381 * m,\n", + " v_init = 0 * m / s,\n", + " g = 9.8 * m/s**2,\n", + " mass = 2.5e-3 * kg,\n", + " diameter = 19e-3 * m,\n", + " rho = 1.2 * kg/m**3,\n", + " v_term = 18 * m / s,\n", + " duration = 30 * s)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": true + }, + "source": [ + "Now here's a version of `make_system` that takes a `Condition` object as a parameter.\n", + "\n", + "`make_system` uses the given value of `v_term` to compute the drag coefficient `C_d`." + ] + }, + { + "cell_type": "code", + "execution_count": 82, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def make_system(condition):\n", + " \"\"\"Makes a System object for the given conditions.\n", + " \n", + " condition: Condition with height, g, mass, diameter, \n", + " rho, v_term, and duration\n", + " \n", + " returns: System with init, g, mass, rho, C_d, area, and ts\n", + " \"\"\"\n", + " unpack(condition)\n", + " \n", + " init = State(y=height, v=v_init)\n", + " area = np.pi * (diameter/2)**2\n", + " C_d = 2 * mass * g / (rho * area * v_term**2)\n", + " ts = linspace(0, duration, 101)\n", + " \n", + " return System(init=init, g=g, mass=mass, rho=rho,\n", + " C_d=C_d, area=area, ts=ts)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": true + }, + "source": [ + "Let's make a `System`" + ] + }, + { + "cell_type": "code", + "execution_count": 83, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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inity 381 meter\n", + "v 0.0 meter / secon...
g9.8 meter / second ** 2
mass0.0025 kilogram
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area0.0002835287369864788 meter ** 2
ts[0.0 second, 0.3 second, 0.6 second, 0.8999999...
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" + ], + "text/plain": [ + "init y 381 meter\n", + "v 0.0 meter / secon...\n", + "g 9.8 meter / second ** 2\n", + "mass 0.0025 kilogram\n", + "rho 1.2 kilogram / meter ** 3\n", + "C_d 0.4445009981135434 dimensionless\n", + "area 0.0002835287369864788 meter ** 2\n", + "ts [0.0 second, 0.3 second, 0.6 second, 0.8999999...\n", + "dtype: object" + ] + }, + "execution_count": 83, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "system = make_system(condition)\n", + "system" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": true + }, + "source": [ + "Here's the slope function, including acceleration due to gravity and drag." + ] + }, + { + "cell_type": "code", + "execution_count": 84, + "metadata": { + "collapsed": true + }, + "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, rho,\n", + " C_d, area, and mass\n", + " \n", + " returns: derivatives of y and v\n", + " \"\"\"\n", + " y, v = state\n", + " unpack(system)\n", + " \n", + " f_drag = rho * v**2 * C_d * area / 2\n", + " a_drag = f_drag / mass\n", + " \n", + " dydt = v\n", + " dvdt = -g + a_drag\n", + " \n", + " return dydt, dvdt" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": true + }, + "source": [ + "As always, let's test the slope function with the initial conditions." + ] + }, + { + "cell_type": "code", + "execution_count": 85, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "(, )" + ] + }, + "execution_count": 85, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "slope_func(system.init, 0, system)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": true + }, + "source": [ + "And then run the simulation." + ] + }, + { + "cell_type": "code", + "execution_count": 86, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "run_odeint(system, slope_func)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": true + }, + "source": [ + "First check that the simulation ran long enough for the penny to land." + ] + }, + { + "cell_type": "code", + "execution_count": 87, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "(,\n", + " )" + ] + }, + "execution_count": 87, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "final_state(system.results)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": true + }, + "source": [ + "Then compute the flight time." + ] + }, + { + "cell_type": "code", + "execution_count": 88, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array(22.439794207078908)" + ] + }, + "execution_count": 88, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "y = system.results.y\n", + "inverse = Series(y.index, index=y.values)\n", + "T = interpolate(inverse, kind='cubic')\n", + "T_sidewalk = T(0)\n", + "T_sidewalk" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": true + }, + "source": [ + "Setting the duration to the computed flight time, we can check the final conditions." + ] + }, + { + "cell_type": "code", + "execution_count": 89, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "condition.set(duration=T_sidewalk)\n", + "system = make_system(condition)\n", + "run_odeint(system, slope_func)\n", + "y_final, v_final = final_state(system.results)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": true + }, + "source": [ + "The final height is close to 0, as expected. And the final velocity is close to the given terminal velocity." + ] + }, + { + "cell_type": "code", + "execution_count": 90, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "(,\n", + " )" + ] + }, + "execution_count": 90, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "y_final, v_final" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": true + }, + "source": [ + "Here's the plot of position as a function of time." + ] + }, + { + "cell_type": "code", + "execution_count": 91, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Saving figure to file chap09-fig02.pdf\n" + ] + }, + { + "data": { + "image/png": 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4jhUBU4YgNhEJgIzUBB5fa5g5eax3rK2ji1fePseO/eW0X1MpFHH4m0DagN7H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\nurW2yFp7GNgELDXGLAlsdCI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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plot_position(system.results)\n", + "savefig('chap09-fig02.pdf')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "And velocity as a function of time:" + ] + }, + { + "cell_type": "code", + "execution_count": 92, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def plot_velocity(results):\n", + " \"\"\"Plot the results.\n", + " \n", + " results: DataFrame with velocity, v\n", + " \"\"\"\n", + " newfig()\n", + " plot(results.v, label='v')\n", + " \n", + " decorate(xlabel='Time (s)',\n", + " ylabel='Velocity (m/2)')" + ] + }, + { + "cell_type": "code", + "execution_count": 93, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plot_velocity(system.results)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": true + }, + "source": [ + "From an initial velocity of 0, the penny accelerates downward until it reaches terminal velocity; after that, velocity is constant." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Exercise:** Run the simulation with an initial velocity, downward, that exceeds the penny's terminal velocity. Hint: use `condition.set`.\n", + "\n", + "What do you expect to happen? Plot velocity and position as a function of time, and see if they are consistent with your prediction." + ] + }, + { + "cell_type": "code", + "execution_count": 94, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Solution goes here\n", + "condition.set(v_init = -40 *m/s)\n", + "system = make_system(condition)\n", + "run_odeint(system, slope_func)\n", + "newfig()\n", + "plot_position(system.results)\n", + "newfig()\n", + "plot_velocity(system.results)" + ] + }, + { + "cell_type": "code", + "execution_count": 95, + "metadata": { + "collapsed": true, + "scrolled": false + }, + "outputs": [], + "source": [ + "# Solution goes here" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Dropping quarters" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Suppose we drop a quarter from the Empire State Building and find that its flight time is 19.1 seconds. We can use this measurement to estimate the coefficient of drag.\n", + "\n", + "Here's a `Condition` object with the relevant parameters from\n", + "https://en.wikipedia.org/wiki/Quarter_(United_States_coin)\n" + ] + }, + { + "cell_type": "code", + "execution_count": 96, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "condition = Condition(height = 381 * m,\n", + " v_init = 0 * m / s,\n", + " g = 9.8 * m/s**2,\n", + " mass = 5.67e-3 * kg,\n", + " diameter = 24.26e-3 * m,\n", + " rho = 1.2 * kg/m**3,\n", + " duration = 19.1 * s)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "And here's a modified version of `make_system`" + ] + }, + { + "cell_type": "code", + "execution_count": 97, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def make_system(condition):\n", + " \"\"\"Makes a System object for the given conditions.\n", + " \n", + " condition: Condition with height, v_init, g, mass, diameter, \n", + " rho, C_d, and duration\n", + " \n", + " returns: System with init, g, mass, rho, C_d, area, and ts\n", + " \"\"\"\n", + " unpack(condition)\n", + " \n", + " init = State(y=height, v=v_init)\n", + " area = np.pi * (diameter/2)**2\n", + " ts = linspace(0, duration, 101)\n", + " \n", + " return System(init=init, g=g, mass=mass, rho=rho,\n", + " C_d=C_d, area=area, ts=ts)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can run the simulation with an initial guess of `C_d=0.4`." + ] + }, + { + "cell_type": "code", + "execution_count": 98, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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iYc4NgVVHi2r4rQKrQp6vDaQF6Hmy6H6gylr7gfvPmThPo4vIGOUEVhnyMhN6\nx2rrW3hxSxHHTtfQ3a2bNEORrw3kPeDrxpgNwCPAKwDGmEXAPwC7RqY8EQkUsdGRfPrefJYvyCHC\nnbXe2dXNrqPlvL77HM3u034ldPjaQL4G5OCERl3AOScL4E0gEvjbYa9MRAKOy+Vi7rRUHltdQGpi\nTO94SWUjGwst5yuu+LE6GW0+NRD3GVizgCxr7RxrbaX70jpgls7IEgktyQnRPHrfdBaY9N5nQ3oC\nq7YfLqXjWqefK5TR4PMN3dbabmNMijHmIWACUAvsttZq3ioSghRYJT41EGNMGM6zH3+Ekw3So9sY\n8/8Bf2it1S6aSAjqCaza/n4ZZ8qc+2l6AqsWz85koUknTOdpjUm+7oH8LfAF9+85OPsek4BvABuA\nr49IdSISFKLHRXD/XXmsvmNSb9Z6V3c3+z68yKs7zvae9itji69LWF8CnrHW/shjrAx41hgT7b7+\n7HAXJyLBw+VyMWNyMlmpznlalZeaAaiobeKFQgVWjUW+zkCycG7l7c8enNmIiIgTWLViGotnZfZu\nsPcEVhXuL6atQxvsY4WvDeQcsGSAa0uAi8NTjoiMBWHuwKqHV04jIe561rotucwLhZYK92m/Etx8\nXcL6OfBDY0wzsBGoAjKAzwHfBH4wMuWJSDDLTHECq3YdLefkhTrACaz63Y6zLDTpLJ6twKpg5msD\neQ5YAPwY+GePcRfwK5zAKRGRG0RFhrPqjknkZSaw7f3S3sCqw6eqKKtWYFUw8zUTvRP4ojHmWWAp\nkAxcBnZaaz8awfpEZIyYlptIZkosWw6WUFbtEVhVaLl3/kRm5SuwKth8bAMxxmTgbJKfdTcLNQwR\nGZLxsVE8uMwrsKqzi22HSymudAKrYhRYFTQG3EQ3xowzxvwGJxd9H1BjjHneGKP78ERkyHoCqx69\nr4DkhOuBVefKr7Bxs6WkssGP1cnNGOwurO8CjwH/B/gK8P8CDwI/G4W6RGSMS0uK4dFVBcz1CKxq\nbu1g065z7DqqwKpgMNhc8WHgaWvt93oGjDEfAP9mjIm21raOeHUiMqZFRoSxfGEOeVkJbD1YQkvb\nNQCOna6hrLqJtXdOImVCzMd8FvGXwWYgOcAOr7Hf4zSdySNVkIiEnslZCXxurWFy1vXAqktX3IFV\nRQqsClSDNZAowHuWUev+Xf8kEJFhFRsdyafuyWf5Qq/AqmPlvL5LgVWBaKi3OwzLvXbGmJ8BEdba\nP/YYW4uH1zziAAAQUUlEQVRzrpYBTgNPWWvf8rieDvwrsBZoB34JfMtae204ahIR/3G5XMydmsrE\ntPEU7i+mpt7JXC+pauT5zZZVd+SSnz3Bz1VKj487ymSgeeMtzSeNMS5jzHeBP/UanwVsAl7CeXDx\nNeBVY8xsj5e9jJPDvhx4EvhD4OlbqUdEAktyQjSP3DedhR6BVa3tTmDVNgVWBYyPm4E8Z4zxvKeu\nZ+bxU2NMo8d4t7X2fl++oDFmCvALYA5Q4nX5q8A+a23Pk+3fNsbc6x7/E2PMEuBeYIq19jxwzBjz\ndXed37XWtvlSg4gEvvDwMO6el82kzHi2HLgeWPXRuUuUVzex5s48MhRY5VeDzUB2Ai042R89vyJw\nNtZbvcajBvgc/bkbKAXmAue9ri0FtnuNbXeP91wvdjcPz+vxwPybqEFEgkROejwb1hqm5yb2jtU3\ntfHyu6c5dLKKri5tsPvLgDMQa+2KkfiC1tpf4ZyfhTHG+3IOzoOLniqA3I+5jvs1+4etUBEJGNFR\nEay9M4+8rAR2HimnvaOzN7CqpLKR1Ysn9Tn1V0aHr8e5j5ZYbrzzqw2IHui6O5O92+M1IjIGuVwu\nZuQl8/jqAjJT4nrHK2qb2FhoKSq57MfqQlOgNZAWwPtYznFA80DXjTGROHszzYjImNcbWDU7kzD3\nBnu7O7DqnX3FtLbrhszREmgNpBQn/dBTNteXrQa6DjcubYnIGBUW5mLxrEwe8gqsOl16mRcKixRY\nNUoCrYHsxrk919NKnA39nutTjDG5XtcbgaMjX56IBJKewKqZk5N7xxqvOoFVe49fpFMb7CMq0M5N\nfg44bIx5Gnge+DxwJ/Bl9/W9OCcDv2CM+XOcVMRngZ9Ya9v9UK+I+FlvYFVWAtsO9w2sKq1qZM2d\nk0iK1xbpSAioGYi19jiwHngEZ0bxGWCdtfak+3q3+3oVsAvnKfSf45wcLCIhbFpOIp9bY8hJj+8d\nq758lRcLi/jo3CWdpzUCXKHwl2qMmQyc37p1Kzk5Of4uR0RGUHd3N0eLatjrDqzqkZ89gftuV2DV\nzSgrK2PVqlUA+dbaC97XA2oGIiJyq1wuFwv6Caw6X3GF5zdbihVYNWzUQERkTEpLiuGx1QXMm3Y9\nsOpqawev7zrHriMKrBoOaiAiMmZFhIexbEEO6+6d0mfp6tiZGl7aUsSlKy1+rC74qYGIyJiX5w6s\nyvcMrGpoVWDVLVIDEZGQEBsdyQP35LOin8CqTbvO9Z72K75TAxGRkOFyuZgzNZXHVxeQlng9WLW0\nqpGNmy1ny+r9WF3wUQMRkZCTNEBg1Vt7L/DuIQVW+UoNRERCUk9g1YPLpjA+JrJ3/MT5S7xQWERV\n3VU/Vhcc1EBEJKQpsGro1EBEJOT1BFatXjyJqMhwgN7Aqld3nKGhWUft9UcNRESEvoFVWX0Cq5rZ\nWGixxXV+rC4wqYGIiHiYMH4c61dM406vwKrCAyUKrPKiBiIi4iUszMUd7sCqCeOvh6AqsKovNRAR\nkQE4gVUFzMrvL7Cqgs4QP09LDUREZBCREeHcd/skPrlkMtFRznlaTmBVNS9vO8PlxlY/V+g/aiAi\nIj6YmpPIhrWG3IwbA6s+PFsbkudpqYGIiPhofEwkn1k6hXtvyyY8zNlg7+jsYvv7Zfx+zwWutobW\neVpqICIiN8HlcjG/IJ1HV90YWLWxsCikAqvUQEREhiA1ceDAqp1HykIisEoNRERkiDwDq2Kjr5+n\n9cGZWl7aUkRt/dgOrFIDERG5RXlZCWxYU3BDYNVLW4s4WlQ9ZjfY1UBERIbBQIFVu49VjNnAKjUQ\nEZFh0iewKmnsB1apgYiIDLOkhGgeWTlQYFXJmAmsUgMRERkBPYFVn10+1Suwqm7MBFapgYiIjKCJ\naePdgVVJvWNjJbBKDUREZIQ5gVWTWNNPYNXvtp/hSlObnyscGjUQEZFR4HK5MP0EVl281MwLW4qw\nxXVBd7uvGoiIyCjqCay6a07WDYFVm/eXBFVglRqIiMgoCwtzcfvMDB5aOY1Er8CqjZst5UESWKUG\nIiLiJ5kpcTzuFVjV1NLBq0ESWKUGIiLiR4MFVv1222kuNwRuYJUaiIhIAOgvsKrmcgsvbAncwCo1\nEBGRANETWLX0tom9gVXXegKr3jsfcIFVaiAiIgHE5XJxW0Eaj64qIMUzsOpigxNYdTFwAqvUQERE\nAlBqYgyPri7gtmlpvWNXWzt4fXfgBFapgYiIBKiI8DCWLpjIuqU3Bla9GACBVWogIiIBLi/THViV\nPaF3rM4dWHXE+i+wSg1ERCQIxEZH8sDdk1m5KJdIj8Cq9z6o4LWd/gmsUgMREQkSLpeL2VNSeGxN\nAelJsb3jZdVOYNWZUQ6sUgMREQkySfHRPLxyGotmZPQJrHp77+gGVkWMylcZZsaYcOD7wJNAPPA2\n8BVrbZU/6xIRGS3h4WEsmZvFpMx4CvcX9y5hnThfR3lNM2sWTyLT49TfkRCsM5DvAF8EvgAsA3KA\nl/1ZkIiIP/QXWHWlqY1Xtp3h4InKEQ2sCroGYoyJAr4KfNNaW2itfR/YANxjjLnbv9WJiIy+6KgI\n7r8r74bAqv0fVY5oYFXQNRBgPs6y1faeAWvtBeACsNQvFYmIBACTl8yGNYbs1BsDq06NQGBVMDaQ\nHPfv5V7jFUDuKNciIhJQEuKi+OzyGwOrthwoYfP+4mENrArGBhILdFlrvW96bgOi+3m9iEhI6Qms\nevi+6V6BVfXDGlgVjA2kBQgzxnjfQTYOaPZDPSIiASkjOZbH1xQwe0pK71hPYNWeD249sCoYG0ip\n+/csr/FsblzWEhEJaZER4axclMsDd+f3Cax631bz23dPU3cLgVXB2ECOAY3A8p4BY8xkYDKw0z8l\niYgEtikTJ7BhrWGSZ2BVfQsvbini+BADq4KugVhr24CfAv9sjPmEMWYhsBHYYa3d59/qREQC1/iY\nSNb1E1i14/0ythwouekmEnQNxO3vgF8DvwK2AcXAI36tSEQkCPQEVj22um9glS25TH3jzT0vEpRH\nmVhrrwF/7f4lIiI3KWWCE1i19/hFPjp3iZQJ0STERd3U5wjKBiIiIrcuIjyMpfMncve8bFw4t//e\n1PtHpiwREQkW4TfZOHqESgMJB6isrPR3HSIiQcPjZ2Z4f9dDpYFkATzxxBP+rkNEJBhlAWe9B0Ol\ngRzEOWjxIjA6SSsiIsEvHKd5HOzvostfYewiIhLcgvU5EBER8TM1EBERGRI1EBERGRI1EBERGRI1\nEBERGZJQuY33BsaYcOD7wJM4GetvA1+x1lb5s65gZoyZBXzUz6Wl1trdo11PMDPG/AyIsNb+scfY\nWuBZwACngaestW/5qcSgMsDf5wHgDq+X/sLzNTK4UJ6BfAf4IvAFYBlO1vrL/ixoDJgL1OLcN+75\na78/iwomxhiXMea7wJ96jc8CNgEvAQuA14BXjTGzR7/K4DHI36cLmA08Qd/v1b8a9SKDWEjOQIwx\nUcBXgb+01ha6xzYA540xd1tr9/i1wOA1BzhhrdWZMUNgjJkC/ALn77HE6/JXgX3W2mfcf/62MeZe\n9/ifjF6VweNj/j6nALHAXn2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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "condition.set(C_d=0.4)\n", + "system = make_system(condition)\n", + "run_odeint(system, slope_func)\n", + "plot_position(system.results)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The final height is -11 meters, which means our guess was too low (we need more drag to slow the quarter down)." + ] + }, + { + "cell_type": "code", + "execution_count": 99, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "(,\n", + " )" + ] + }, + "execution_count": 99, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "final_state(system.results)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "`height_func` takes a hypothetical value of `C_d` and returns the height after 19.1 seconds." + ] + }, + { + "cell_type": "code", + "execution_count": 100, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def height_func(C_d, condition):\n", + " \"\"\"Final height as a function of C_d.\n", + " \n", + " C_d: drag coefficient\n", + " condition: Condition object\n", + " \n", + " returns: height in m\n", + " \"\"\"\n", + " condition.set(C_d=C_d)\n", + " system = make_system(condition)\n", + " run_odeint(system, slope_func)\n", + " y, v = final_state(system.results)\n", + " return y" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "If we run it with `C_d=0.4`, we get -11 meters again." + ] + }, + { + "cell_type": "code", + "execution_count": 101, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "-11.034779626277231 meter" + ], + "text/latex": [ + "$-11.034779626277231 meter$" + ], + "text/plain": [ + "" + ] + }, + "execution_count": 101, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "height_func(0.4, condition)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now we can use `fsolve` to find the value of `C_d` that makes the final height 0." + ] + }, + { + "cell_type": "code", + "execution_count": 102, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([ 0.42587017])" + ] + }, + "execution_count": 102, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "solution = fsolve(height_func, 0.4, condition)\n", + "solution" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Plugging in the estimated value, we can run the simulation again to get terminal velocity." + ] + }, + { + "cell_type": "code", + "execution_count": 103, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "(,\n", + " )" + ] + }, + "execution_count": 103, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "condition.set(C_d=solution)\n", + "system = make_system(condition)\n", + "run_odeint(system, slope_func)\n", + "final_state(system.results)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In this example, the terminal velocity of the quarter is higher than that of the penny, but we should not take this result seriously because the measurements we used are not real; I made them up." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "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": "3.6.1" + } + }, + "nbformat": 4, + "nbformat_minor": 1 +} From 0e2f54c76156b766b7cb06c40ed1a7153e51197e Mon Sep 17 00:00:00 2001 From: Junwon Lee <31522211+junwonlee5@users.noreply.github.com> Date: Wed, 8 Nov 2017 20:40:24 -0500 Subject: [PATCH 16/19] Adding chap10mine --- code/chap10mine.ipynb | 7242 +++++++++++++++++++++++++++++++++++++++++ 1 file changed, 7242 insertions(+) create mode 100644 code/chap10mine.ipynb diff --git a/code/chap10mine.ipynb b/code/chap10mine.ipynb new file mode 100644 index 00000000..622bd1fb --- /dev/null +++ b/code/chap10mine.ipynb @@ -0,0 +1,7242 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Modeling and Simulation in Python\n", + "\n", + "Chapter 10: Vectors\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": { + "collapsed": true + }, + "outputs": [], + "source": [ + "# If you want the figures to appear in the notebook, \n", + "# and you want to interact with them, use\n", + "# %matplotlib notebook\n", + "\n", + "# If you want the figures to appear in the notebook, \n", + "# and you don't want to interact with them, use\n", + "# %matplotlib inline\n", + "\n", + "# If you want the figures to appear in separate windows, use\n", + "# %matplotlib qt5\n", + "\n", + "# tempo switch from one to another, you have to select Kernel->Restart\n", + "\n", + "%matplotlib notebook\n", + "\n", + "from modsim import *" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Vectors" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "A `Vector` object is like a combination of a NumPy array and a Pint Quantity.\n", + "\n", + "I'll start by grabbing the units we'll need." + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "m = UNITS.meter\n", + "s = UNITS.second\n", + "kg = UNITS.kilogram" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here's a two dimensional `Vector` in meters." + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "A = Vector(3, 4) * m" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can access the elements by name." + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "3.0 meter" + ], + "text/latex": [ + "$3.0 meter$" + ], + "text/plain": [ + "" + ] + }, + "execution_count": 4, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "A.x" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "4.0 meter" + ], + "text/latex": [ + "$4.0 meter$" + ], + "text/plain": [ + "" + ] + }, + "execution_count": 5, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "A.y" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The magnitude is the length of the vector." + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "5.0 meter" + ], + "text/latex": [ + "$5.0 meter$" + ], + "text/plain": [ + "" + ] + }, + "execution_count": 6, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "A.mag" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The angle is the number of radians between the vector and the positive x axis." + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "0.9272952180016122 radian" + ], + "text/latex": [ + "$0.9272952180016122 radian$" + ], + "text/plain": [ + "" + ] + }, + "execution_count": 7, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "A.angle" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "If we make another `Vector` with the same units," + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "B = Vector(1, 2) * m" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can add `Vector` objects like this" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "[ 4. 6.] meter" + ], + "text/latex": [ + "$[ 4. 6.] meter$" + ], + "text/plain": [ + "" + ] + }, + "execution_count": 9, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "A + B" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "And substract like this:" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "[ 2. 2.] meter" + ], + "text/latex": [ + "$[ 2. 2.] meter$" + ], + "text/plain": [ + "" + ] + }, + "execution_count": 10, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "A - B" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can compute the Euclidean distance between two Vectors." + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "2.8284271247461903 meter" + ], + "text/latex": [ + "$2.8284271247461903 meter$" + ], + "text/plain": [ + "" + ] + }, + "execution_count": 11, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "A.dist(B)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "And the difference in angle" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "-0.17985349979247822 radian" + ], + "text/latex": [ + "$-0.17985349979247822 radian$" + ], + "text/plain": [ + "" + ] + }, + "execution_count": 12, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "A.diff_angle(B)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "If we are given the magnitude and angle of a vector, what we have is the representation of the vector in polar coordinates." + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "mag = A.mag\n", + "angle = A.angle" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can use `pol2cart` to convert from polar to Cartesian coordinates, and then use the Cartesian coordinates to make a `Vector` object.\n", + "\n", + "In this example, the `Vector` we get should have the same components as `A`." + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "[ 3. 4.] meter" + ], + "text/latex": [ + "$[ 3. 4.] meter$" + ], + "text/plain": [ + "" + ] + }, + "execution_count": 14, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "x, y = pol2cart(angle, mag)\n", + "Vector(x, y)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Exercise:** Create a `Vector` named `a_grav` that represents acceleration due to gravity, with x component 0 and y component $-9.8$ meters / second$^2$." + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "[ 0. -9.8] meter/second2" + ], + "text/latex": [ + "$[ 0. -9.8] \\frac{meter}{second^{2}}$" + ], + "text/plain": [ + "" + ] + }, + "execution_count": 15, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Solution goes here\n", + "a_grav = Vector(0, -9.80) *m / s / s\n", + "a_grav" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Degrees and radians\n", + "\n", + "Pint provides units to represent degree and radians." + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "degree = UNITS.degree\n", + "radian = UNITS.radian" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "If you have an angle in degrees," + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "45 degree" + ], + "text/latex": [ + "$45 degree$" + ], + "text/plain": [ + "" + ] + }, + "execution_count": 17, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "angle = 45 * degree\n", + "angle" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "You can convert to radians." + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "0.7853981633974483 radian" + ], + "text/latex": [ + "$0.7853981633974483 radian$" + ], + "text/plain": [ + "" + ] + }, + "execution_count": 18, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "angle_rad = angle.to(radian)\n", + "angle_rad" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "If it's already in radians, `to` does the right thing." + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "0.7853981633974483 radian" + ], + "text/latex": [ + "$0.7853981633974483 radian$" + ], + "text/plain": [ + "" + ] + }, + "execution_count": 19, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "angle_rad.to(radian)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "You can also convert from radians to degrees." + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "45.0 degree" + ], + "text/latex": [ + "$45.0 degree$" + ], + "text/plain": [ + "" + ] + }, + "execution_count": 20, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "angle_rad.to(degree)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "As an alterative, you can use `np.deg2rad`, which works with Pint quantities, but it also works with simple numbers and NumPy arrays:" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "0.7853981633974483 radian" + ], + "text/latex": [ + "$0.7853981633974483 radian$" + ], + "text/plain": [ + "" + ] + }, + "execution_count": 21, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "np.deg2rad(angle)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Exercise:** Create a `Vector` named `a_force` that represents acceleration due to a force of 0.5 Newton applied to an object with mass 0.3 kilograms, in a direction 45 degrees up from the positive x-axis.\n", + "\n", + "Add `a_force` to `a_drag` from the previous exercise. If that addition succeeds, that means that the units are compatible. Confirm that the total acceleration seems to make sense." + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "[ 1.1785113 1.1785113] meter/second2" + ], + "text/latex": [ + "$[ 1.1785113 1.1785113] \\frac{meter}{second^{2}}$" + ], + "text/plain": [ + "" + ] + }, + "execution_count": 22, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Solution goes here\n", + "x, y = pol2cart(angle_rad, 0.5/0.3)\n", + "a_force = Vector(x,y) *m / s/s\n", + "a_force" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "[ 1.1785113 -8.6214887] meter/second2" + ], + "text/latex": [ + "$[ 1.1785113 -8.6214887] \\frac{meter}{second^{2}}$" + ], + "text/plain": [ + "" + ] + }, + "execution_count": 23, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "a_force + a_grav\n", + "# Solution goes here" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Baseball" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here's a `Condition` object that contains the parameters for the Manny Ramirez problem." + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "condition = Condition(x = 0 * m, \n", + " y = 1 * m,\n", + " g = 9.8 * m/s**2,\n", + " mass = 145e-3 * kg,\n", + " diameter = 73e-3 * m,\n", + " rho = 1.2 * kg/m**3,\n", + " C_d = 0.3,\n", + " angle = 45 * degree,\n", + " velocity = 40 * m / s,\n", + " duration = 5.1 * s)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "And here's the function that uses the `Condition` object to make a `System` object." + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def make_system(condition):\n", + " \"\"\"Make a system object.\n", + " \n", + " condition: Condition object with angle, velocity, x, y,\n", + " diameter, duration, g, mass, rho, and C_d\n", + " \n", + " returns: System object\n", + " \"\"\"\n", + " unpack(condition)\n", + " \n", + " # convert angle to degrees\n", + " theta = np.deg2rad(angle)\n", + " \n", + " # compute x and y components of velocity\n", + " vx, vy = pol2cart(theta, velocity)\n", + " \n", + " # make the initial state\n", + " init = State(x=x, y=y, vx=vx, vy=vy)\n", + " \n", + " # compute area from diameter\n", + " area = np.pi * (diameter/2)**2\n", + " \n", + " # compute timestamps\n", + " ts = linspace(0, duration, 101)\n", + " \n", + " return System(init=init, g=g, mass=mass, \n", + " area=area, rho=rho, C_d=C_d, ts=ts)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here's how we use it:" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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value
initx 0 meter\n", + "y ...
g9.8 meter / second ** 2
mass0.145 kilogram
area0.004185386812745002 meter ** 2
rho1.2 kilogram / meter ** 3
C_d0.3
ts[0.0 second, 0.051 second, 0.102 second, 0.153...
\n", + "
" + ], + "text/plain": [ + "init x 0 meter\n", + "y ...\n", + "g 9.8 meter / second ** 2\n", + "mass 0.145 kilogram\n", + "area 0.004185386812745002 meter ** 2\n", + "rho 1.2 kilogram / meter ** 3\n", + "C_d 0.3\n", + "ts [0.0 second, 0.051 second, 0.102 second, 0.153...\n", + "dtype: object" + ] + }, + "execution_count": 26, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "system = make_system(condition)\n", + "system" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here's the slope function that computes acceleration due to gravity and drag." + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def slope_func(state, t, system):\n", + " \"\"\"Computes derivatives of the state variables.\n", + " \n", + " state: State (x, y, x velocity, y velocity)\n", + " t: time\n", + " system: System object with g, rho, C_d, area, mass\n", + " \n", + " returns: sequence (vx, vy, ax, ay)\n", + " \"\"\"\n", + " x, y, vx, vy = state\n", + " unpack(system)\n", + " \n", + " a_grav = Vector(0, -g)\n", + "\n", + " v = Vector(vx, vy)\n", + " \n", + " f_drag = -rho * v.mag * v * C_d * area / 2\n", + " a_drag = f_drag / mass\n", + " \n", + " a = a_grav + a_drag\n", + " \n", + " return vx, vy, a.x, a.y" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Always test the slope function with the initial conditions." + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "(,\n", + " ,\n", + " ,\n", + " )" + ] + }, + "execution_count": 28, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "slope_func(system.init, 0, system)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now we can run `odeint`" + ] + }, + { + "cell_type": "code", + "execution_count": 29, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "run_odeint(system, slope_func)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here are the first few time steps." + ] + }, + { + "cell_type": "code", + "execution_count": 30, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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xyvxvy
0.0000.0000001.00000028.28427128.284271
0.0511.4349292.42222927.98892427.491730
0.1022.8550173.80438927.70222626.712880
0.1534.2606975.14716527.42383625.947141
0.2045.6523846.45121127.15343325.193958
\n", + "
" + ], + "text/plain": [ + " x y vx vy\n", + "0.000 0.000000 1.000000 28.284271 28.284271\n", + "0.051 1.434929 2.422229 27.988924 27.491730\n", + "0.102 2.855017 3.804389 27.702226 26.712880\n", + "0.153 4.260697 5.147165 27.423836 25.947141\n", + "0.204 5.652384 6.451211 27.153433 25.193958" + ] + }, + "execution_count": 30, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "system.results.head()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "And the last few. The last value of `y` is negative, indicating that the ball hit the ground before the end of the simulation." + ] + }, + { + "cell_type": "code", + "execution_count": 31, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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xyvxvy
4.896100.2747613.58038315.135822-21.336469
4.947101.0440112.48328115.030816-21.686507
4.998101.8079021.36842314.925643-22.032810
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5.100103.319572-0.91380014.714856-22.714157
\n", + "
" + ], + "text/plain": [ + " x y vx vy\n", + "4.896 100.274761 3.580383 15.135822 -21.336469\n", + "4.947 101.044011 2.483281 15.030816 -21.686507\n", + "4.998 101.807902 1.368423 14.925643 -22.032810\n", + "5.049 102.566424 0.235998 14.820318 -22.375365\n", + "5.100 103.319572 -0.913800 14.714856 -22.714157" + ] + }, + "execution_count": 31, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "system.results.tail()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Visualizing the results\n", + "\n", + "We can extract the x and y components as `Series` objects." + ] + }, + { + "cell_type": "code", + "execution_count": 32, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "xs = system.results.x\n", + "ys = system.results.y" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The simplest way to visualize the results is to plot x and y as functions of time." + ] + }, + { + "cell_type": "code", + "execution_count": 33, + "metadata": {}, + "outputs": [ + { + "data": { + "application/javascript": [ + "/* Put everything inside the global mpl namespace */\n", + "window.mpl = {};\n", + "\n", + "\n", + "mpl.get_websocket_type = function() {\n", + " if (typeof(WebSocket) !== 'undefined') {\n", + " return WebSocket;\n", + " } else if (typeof(MozWebSocket) !== 'undefined') {\n", + " return MozWebSocket;\n", + " } else {\n", + " alert('Your browser does not have WebSocket support.' +\n", + " 'Please try Chrome, Safari or Firefox ≥ 6. ' +\n", + " 'Firefox 4 and 5 are also supported but you ' +\n", + " 'have to enable WebSockets in about:config.');\n", + " };\n", + "}\n", + "\n", + "mpl.figure = function(figure_id, websocket, ondownload, parent_element) {\n", + " this.id = figure_id;\n", + "\n", + " this.ws = websocket;\n", + "\n", + " this.supports_binary = (this.ws.binaryType != undefined);\n", + "\n", + " if (!this.supports_binary) {\n", + " var warnings = document.getElementById(\"mpl-warnings\");\n", + " if (warnings) {\n", + " warnings.style.display = 'block';\n", + " warnings.textContent = (\n", + " \"This browser does not support binary websocket messages. \" +\n", + " \"Performance may be slow.\");\n", + " }\n", + " }\n", + "\n", + " this.imageObj = new Image();\n", + "\n", + " this.context = undefined;\n", + " this.message = undefined;\n", + " this.canvas = undefined;\n", + " this.rubberband_canvas = undefined;\n", + " this.rubberband_context = undefined;\n", + " this.format_dropdown = undefined;\n", + "\n", + " this.image_mode = 'full';\n", + "\n", + " this.root = $('
');\n", + " this._root_extra_style(this.root)\n", + " this.root.attr('style', 'display: inline-block');\n", + "\n", + " $(parent_element).append(this.root);\n", + "\n", + " this._init_header(this);\n", + " this._init_canvas(this);\n", + " this._init_toolbar(this);\n", + "\n", + " var fig = this;\n", + "\n", + " this.waiting = false;\n", + "\n", + " this.ws.onopen = function () {\n", + " fig.send_message(\"supports_binary\", {value: fig.supports_binary});\n", + " fig.send_message(\"send_image_mode\", {});\n", + " if (mpl.ratio != 1) {\n", + " fig.send_message(\"set_dpi_ratio\", {'dpi_ratio': mpl.ratio});\n", + " }\n", + " fig.send_message(\"refresh\", {});\n", + " }\n", + "\n", + " this.imageObj.onload = function() {\n", + " if (fig.image_mode == 'full') {\n", + " // Full images could contain transparency (where diff images\n", + " // almost always do), so we need to clear the canvas so that\n", + " // there is no ghosting.\n", + " fig.context.clearRect(0, 0, fig.canvas.width, fig.canvas.height);\n", + " }\n", + " fig.context.drawImage(fig.imageObj, 0, 0);\n", + " };\n", + "\n", + " this.imageObj.onunload = function() {\n", + " this.ws.close();\n", + " }\n", + "\n", + " this.ws.onmessage = this._make_on_message_function(this);\n", + "\n", + " this.ondownload = ondownload;\n", + "}\n", + "\n", + "mpl.figure.prototype._init_header = function() {\n", + " var titlebar = $(\n", + " '
');\n", + " var titletext = $(\n", + " '
');\n", + " titlebar.append(titletext)\n", + " this.root.append(titlebar);\n", + " this.header = titletext[0];\n", + "}\n", + "\n", + "\n", + "\n", + "mpl.figure.prototype._canvas_extra_style = function(canvas_div) {\n", + "\n", + "}\n", + "\n", + "\n", + "mpl.figure.prototype._root_extra_style = function(canvas_div) {\n", + "\n", + "}\n", + "\n", + "mpl.figure.prototype._init_canvas = function() {\n", + " var fig = this;\n", + "\n", + " var canvas_div = $('
');\n", + "\n", + " canvas_div.attr('style', 'position: relative; clear: both; outline: 0');\n", + "\n", + " function canvas_keyboard_event(event) {\n", + " return fig.key_event(event, event['data']);\n", + " }\n", + "\n", + " canvas_div.keydown('key_press', canvas_keyboard_event);\n", + " canvas_div.keyup('key_release', canvas_keyboard_event);\n", + " this.canvas_div = canvas_div\n", + " this._canvas_extra_style(canvas_div)\n", + " this.root.append(canvas_div);\n", + "\n", + " var canvas = $('');\n", + " canvas.addClass('mpl-canvas');\n", + " canvas.attr('style', \"left: 0; top: 0; z-index: 0; outline: 0\")\n", + "\n", + " this.canvas = canvas[0];\n", + " this.context = canvas[0].getContext(\"2d\");\n", + "\n", + " var backingStore = this.context.backingStorePixelRatio ||\n", + "\tthis.context.webkitBackingStorePixelRatio ||\n", + "\tthis.context.mozBackingStorePixelRatio ||\n", + "\tthis.context.msBackingStorePixelRatio ||\n", + "\tthis.context.oBackingStorePixelRatio ||\n", + "\tthis.context.backingStorePixelRatio || 1;\n", + "\n", + " mpl.ratio = (window.devicePixelRatio || 1) / backingStore;\n", + "\n", + " var rubberband = $('');\n", + " rubberband.attr('style', \"position: absolute; left: 0; top: 0; z-index: 1;\")\n", + "\n", + " var pass_mouse_events = true;\n", + "\n", + " canvas_div.resizable({\n", + " start: function(event, ui) {\n", + " pass_mouse_events = false;\n", + " },\n", + " resize: function(event, ui) {\n", + " fig.request_resize(ui.size.width, ui.size.height);\n", + " },\n", + " stop: function(event, ui) {\n", + " pass_mouse_events = true;\n", + " fig.request_resize(ui.size.width, ui.size.height);\n", + " },\n", + " });\n", + "\n", + " function mouse_event_fn(event) {\n", + " if (pass_mouse_events)\n", + " return fig.mouse_event(event, event['data']);\n", + " }\n", + "\n", + " rubberband.mousedown('button_press', mouse_event_fn);\n", + " rubberband.mouseup('button_release', mouse_event_fn);\n", + " // Throttle sequential mouse events to 1 every 20ms.\n", + " rubberband.mousemove('motion_notify', mouse_event_fn);\n", + "\n", + " rubberband.mouseenter('figure_enter', mouse_event_fn);\n", + " rubberband.mouseleave('figure_leave', mouse_event_fn);\n", + "\n", + " canvas_div.on(\"wheel\", function (event) {\n", + " event = event.originalEvent;\n", + " event['data'] = 'scroll'\n", + " if (event.deltaY < 0) {\n", + " event.step = 1;\n", + " } else {\n", + " event.step = -1;\n", + " }\n", + " mouse_event_fn(event);\n", + " });\n", + "\n", + " canvas_div.append(canvas);\n", + " canvas_div.append(rubberband);\n", + "\n", + " this.rubberband = rubberband;\n", + " this.rubberband_canvas = rubberband[0];\n", + " this.rubberband_context = rubberband[0].getContext(\"2d\");\n", + " this.rubberband_context.strokeStyle = \"#000000\";\n", + "\n", + " this._resize_canvas = function(width, height) {\n", + " // Keep the size of the canvas, canvas container, and rubber band\n", + " // canvas in synch.\n", + " canvas_div.css('width', width)\n", + " canvas_div.css('height', height)\n", + "\n", + " canvas.attr('width', width * mpl.ratio);\n", + " canvas.attr('height', height * mpl.ratio);\n", + " canvas.attr('style', 'width: ' + width + 'px; height: ' + height + 'px;');\n", + "\n", + " rubberband.attr('width', width);\n", + " rubberband.attr('height', height);\n", + " }\n", + "\n", + " // Set the figure to an initial 600x600px, this will subsequently be updated\n", + " // upon first draw.\n", + " this._resize_canvas(600, 600);\n", + "\n", + " // Disable right mouse context menu.\n", + " $(this.rubberband_canvas).bind(\"contextmenu\",function(e){\n", + " return false;\n", + " });\n", + "\n", + " function set_focus () {\n", + " canvas.focus();\n", + " canvas_div.focus();\n", + " }\n", + "\n", + " window.setTimeout(set_focus, 100);\n", + "}\n", + "\n", + "mpl.figure.prototype._init_toolbar = function() {\n", + " var fig = this;\n", + "\n", + " var nav_element = $('
')\n", + " nav_element.attr('style', 'width: 100%');\n", + " this.root.append(nav_element);\n", + "\n", + " // Define a callback function for later on.\n", + " function toolbar_event(event) {\n", + " return fig.toolbar_button_onclick(event['data']);\n", + " }\n", + " function toolbar_mouse_event(event) {\n", + " return fig.toolbar_button_onmouseover(event['data']);\n", + " }\n", + "\n", + " for(var toolbar_ind in mpl.toolbar_items) {\n", + " var name = mpl.toolbar_items[toolbar_ind][0];\n", + " var tooltip = mpl.toolbar_items[toolbar_ind][1];\n", + " var image = mpl.toolbar_items[toolbar_ind][2];\n", + " var method_name = mpl.toolbar_items[toolbar_ind][3];\n", + "\n", + " if (!name) {\n", + " // put a spacer in here.\n", + " continue;\n", + " }\n", + " var button = $('');\n", + " button.click(method_name, toolbar_event);\n", + " button.mouseover(tooltip, toolbar_mouse_event);\n", + " nav_element.append(button);\n", + " }\n", + "\n", + " // Add the status bar.\n", + " var status_bar = $('');\n", + " nav_element.append(status_bar);\n", + " this.message = status_bar[0];\n", + "\n", + " // Add the close button to the window.\n", + " var buttongrp = $('
');\n", + " var button = $('');\n", + " button.click(function (evt) { fig.handle_close(fig, {}); } );\n", + " button.mouseover('Stop Interaction', toolbar_mouse_event);\n", + " buttongrp.append(button);\n", + " var titlebar = this.root.find($('.ui-dialog-titlebar'));\n", + " titlebar.prepend(buttongrp);\n", + "}\n", + "\n", + "mpl.figure.prototype._root_extra_style = function(el){\n", + " var fig = this\n", + " el.on(\"remove\", function(){\n", + "\tfig.close_ws(fig, {});\n", + " });\n", + "}\n", + "\n", + "mpl.figure.prototype._canvas_extra_style = function(el){\n", + " // this is important to make the div 'focusable\n", + " el.attr('tabindex', 0)\n", + " // reach out to IPython and tell the keyboard manager to turn it's self\n", + " // off when our div gets focus\n", + "\n", + " // location in version 3\n", + " if (IPython.notebook.keyboard_manager) {\n", + " IPython.notebook.keyboard_manager.register_events(el);\n", + " }\n", + " else {\n", + " // location in version 2\n", + " IPython.keyboard_manager.register_events(el);\n", + " }\n", + "\n", + "}\n", + "\n", + "mpl.figure.prototype._key_event_extra = function(event, name) {\n", + " var manager = IPython.notebook.keyboard_manager;\n", + " if (!manager)\n", + " manager = IPython.keyboard_manager;\n", + "\n", + " // Check for shift+enter\n", + " if (event.shiftKey && event.which == 13) {\n", + " this.canvas_div.blur();\n", + " // select the cell after this one\n", + " var index = IPython.notebook.find_cell_index(this.cell_info[0]);\n", + " IPython.notebook.select(index + 1);\n", + " }\n", + "}\n", + "\n", + "mpl.figure.prototype.handle_save = function(fig, msg) {\n", + " fig.ondownload(fig, null);\n", + "}\n", + "\n", + "\n", + "mpl.find_output_cell = function(html_output) {\n", + " // Return the cell and output element which can be found *uniquely* in the notebook.\n", + " // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n", + " // IPython event is triggered only after the cells have been serialised, which for\n", + " // our purposes (turning an active figure into a static one), is too late.\n", + " var cells = IPython.notebook.get_cells();\n", + " var ncells = cells.length;\n", + " for (var i=0; i= 3 moved mimebundle to data attribute of output\n", + " data = data.data;\n", + " }\n", + " if (data['text/html'] == html_output) {\n", + " return [cell, data, j];\n", + " }\n", + " }\n", + " }\n", + " }\n", + "}\n", + "\n", + "// Register the function which deals with the matplotlib target/channel.\n", + "// The kernel may be null if the page has been refreshed.\n", + "if (IPython.notebook.kernel != null) {\n", + " IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);\n", + "}\n" + ], + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "text/html": [ + "" + ], + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "newfig()\n", + "plot(vxs, label='vx')\n", + "plot(vys, label='vy')\n", + "\n", + "decorate(xlabel='Time (s)',\n", + " ylabel='Velocity (m/s)')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Another way to visualize the results is to plot y versus x. The result is the trajectory of the ball through its plane of motion." + ] + }, + { + "cell_type": "code", + "execution_count": 36, + "metadata": {}, + "outputs": [ + { + "data": { + "application/javascript": [ + "/* Put everything inside the global mpl namespace */\n", + "window.mpl = {};\n", + "\n", + "\n", + "mpl.get_websocket_type = function() {\n", + " if (typeof(WebSocket) !== 'undefined') {\n", + " return WebSocket;\n", + " } else if (typeof(MozWebSocket) !== 'undefined') {\n", + " return MozWebSocket;\n", + " } else {\n", + " alert('Your browser does not have WebSocket support.' +\n", + " 'Please try Chrome, Safari or Firefox ≥ 6. ' +\n", + " 'Firefox 4 and 5 are also supported but you ' +\n", + " 'have to enable WebSockets in about:config.');\n", + " };\n", + "}\n", + "\n", + "mpl.figure = function(figure_id, websocket, ondownload, parent_element) {\n", + " this.id = figure_id;\n", + "\n", + " this.ws = websocket;\n", + "\n", + " this.supports_binary = (this.ws.binaryType != undefined);\n", + "\n", + " if (!this.supports_binary) {\n", + " var warnings = document.getElementById(\"mpl-warnings\");\n", + " if (warnings) {\n", + " warnings.style.display = 'block';\n", + " warnings.textContent = (\n", + " \"This browser does not support binary websocket messages. \" +\n", + " \"Performance may be slow.\");\n", + " }\n", + " }\n", + "\n", + " this.imageObj = new Image();\n", + "\n", + " this.context = undefined;\n", + " this.message = undefined;\n", + " this.canvas = undefined;\n", + " this.rubberband_canvas = undefined;\n", + " this.rubberband_context = undefined;\n", + " this.format_dropdown = undefined;\n", + "\n", + " this.image_mode = 'full';\n", + "\n", + " this.root = $('
');\n", + " this._root_extra_style(this.root)\n", + " this.root.attr('style', 'display: inline-block');\n", + "\n", + " $(parent_element).append(this.root);\n", + "\n", + " this._init_header(this);\n", + " this._init_canvas(this);\n", + " this._init_toolbar(this);\n", + "\n", + " var fig = this;\n", + "\n", + " this.waiting = false;\n", + "\n", + " this.ws.onopen = function () {\n", + " fig.send_message(\"supports_binary\", {value: fig.supports_binary});\n", + " fig.send_message(\"send_image_mode\", {});\n", + " if (mpl.ratio != 1) {\n", + " fig.send_message(\"set_dpi_ratio\", {'dpi_ratio': mpl.ratio});\n", + " }\n", + " fig.send_message(\"refresh\", {});\n", + " }\n", + "\n", + " this.imageObj.onload = function() {\n", + " if (fig.image_mode == 'full') {\n", + " // Full images could contain transparency (where diff images\n", + " // almost always do), so we need to clear the canvas so that\n", + " // there is no ghosting.\n", + " fig.context.clearRect(0, 0, fig.canvas.width, fig.canvas.height);\n", + " }\n", + " fig.context.drawImage(fig.imageObj, 0, 0);\n", + " };\n", + "\n", + " this.imageObj.onunload = function() {\n", + " this.ws.close();\n", + " }\n", + "\n", + " this.ws.onmessage = this._make_on_message_function(this);\n", + "\n", + " this.ondownload = ondownload;\n", + "}\n", + "\n", + "mpl.figure.prototype._init_header = function() {\n", + " var titlebar = $(\n", + " '
');\n", + " var titletext = $(\n", + " '
');\n", + " titlebar.append(titletext)\n", + " this.root.append(titlebar);\n", + " this.header = titletext[0];\n", + "}\n", + "\n", + "\n", + "\n", + "mpl.figure.prototype._canvas_extra_style = function(canvas_div) {\n", + "\n", + "}\n", + "\n", + "\n", + "mpl.figure.prototype._root_extra_style = function(canvas_div) {\n", + "\n", + "}\n", + "\n", + "mpl.figure.prototype._init_canvas = function() {\n", + " var fig = this;\n", + "\n", + " var canvas_div = $('
');\n", + "\n", + " canvas_div.attr('style', 'position: relative; clear: both; outline: 0');\n", + "\n", + " function canvas_keyboard_event(event) {\n", + " return fig.key_event(event, event['data']);\n", + " }\n", + "\n", + " canvas_div.keydown('key_press', canvas_keyboard_event);\n", + " canvas_div.keyup('key_release', canvas_keyboard_event);\n", + " this.canvas_div = canvas_div\n", + " this._canvas_extra_style(canvas_div)\n", + " this.root.append(canvas_div);\n", + "\n", + " var canvas = $('');\n", + " canvas.addClass('mpl-canvas');\n", + " canvas.attr('style', \"left: 0; top: 0; z-index: 0; outline: 0\")\n", + "\n", + " this.canvas = canvas[0];\n", + " this.context = canvas[0].getContext(\"2d\");\n", + "\n", + " var backingStore = this.context.backingStorePixelRatio ||\n", + "\tthis.context.webkitBackingStorePixelRatio ||\n", + "\tthis.context.mozBackingStorePixelRatio ||\n", + "\tthis.context.msBackingStorePixelRatio ||\n", + "\tthis.context.oBackingStorePixelRatio ||\n", + "\tthis.context.backingStorePixelRatio || 1;\n", + "\n", + " mpl.ratio = (window.devicePixelRatio || 1) / backingStore;\n", + "\n", + " var rubberband = $('');\n", + " rubberband.attr('style', \"position: absolute; left: 0; top: 0; z-index: 1;\")\n", + "\n", + " var pass_mouse_events = true;\n", + "\n", + " canvas_div.resizable({\n", + " start: function(event, ui) {\n", + " pass_mouse_events = false;\n", + " },\n", + " resize: function(event, ui) {\n", + " fig.request_resize(ui.size.width, ui.size.height);\n", + " },\n", + " stop: function(event, ui) {\n", + " pass_mouse_events = true;\n", + " fig.request_resize(ui.size.width, ui.size.height);\n", + " },\n", + " });\n", + "\n", + " function mouse_event_fn(event) {\n", + " if (pass_mouse_events)\n", + " return fig.mouse_event(event, event['data']);\n", + " }\n", + "\n", + " rubberband.mousedown('button_press', mouse_event_fn);\n", + " rubberband.mouseup('button_release', mouse_event_fn);\n", + " // Throttle sequential mouse events to 1 every 20ms.\n", + " rubberband.mousemove('motion_notify', mouse_event_fn);\n", + "\n", + " rubberband.mouseenter('figure_enter', mouse_event_fn);\n", + " rubberband.mouseleave('figure_leave', mouse_event_fn);\n", + "\n", + " canvas_div.on(\"wheel\", function (event) {\n", + " event = event.originalEvent;\n", + " event['data'] = 'scroll'\n", + " if (event.deltaY < 0) {\n", + " event.step = 1;\n", + " } else {\n", + " event.step = -1;\n", + " }\n", + " mouse_event_fn(event);\n", + " });\n", + "\n", + " canvas_div.append(canvas);\n", + " canvas_div.append(rubberband);\n", + "\n", + " this.rubberband = rubberband;\n", + " this.rubberband_canvas = rubberband[0];\n", + " this.rubberband_context = rubberband[0].getContext(\"2d\");\n", + " this.rubberband_context.strokeStyle = \"#000000\";\n", + "\n", + " this._resize_canvas = function(width, height) {\n", + " // Keep the size of the canvas, canvas container, and rubber band\n", + " // canvas in synch.\n", + " canvas_div.css('width', width)\n", + " canvas_div.css('height', height)\n", + "\n", + " canvas.attr('width', width * mpl.ratio);\n", + " canvas.attr('height', height * mpl.ratio);\n", + " canvas.attr('style', 'width: ' + width + 'px; height: ' + height + 'px;');\n", + "\n", + " rubberband.attr('width', width);\n", + " rubberband.attr('height', height);\n", + " }\n", + "\n", + " // Set the figure to an initial 600x600px, this will subsequently be updated\n", + " // upon first draw.\n", + " this._resize_canvas(600, 600);\n", + "\n", + " // Disable right mouse context menu.\n", + " $(this.rubberband_canvas).bind(\"contextmenu\",function(e){\n", + " return false;\n", + " });\n", + "\n", + " function set_focus () {\n", + " canvas.focus();\n", + " canvas_div.focus();\n", + " }\n", + "\n", + " window.setTimeout(set_focus, 100);\n", + "}\n", + "\n", + "mpl.figure.prototype._init_toolbar = function() {\n", + " var fig = this;\n", + "\n", + " var nav_element = $('
')\n", + " nav_element.attr('style', 'width: 100%');\n", + " this.root.append(nav_element);\n", + "\n", + " // Define a callback function for later on.\n", + " function toolbar_event(event) {\n", + " return fig.toolbar_button_onclick(event['data']);\n", + " }\n", + " function toolbar_mouse_event(event) {\n", + " return fig.toolbar_button_onmouseover(event['data']);\n", + " }\n", + "\n", + " for(var toolbar_ind in mpl.toolbar_items) {\n", + " var name = mpl.toolbar_items[toolbar_ind][0];\n", + " var tooltip = mpl.toolbar_items[toolbar_ind][1];\n", + " var image = mpl.toolbar_items[toolbar_ind][2];\n", + " var method_name = mpl.toolbar_items[toolbar_ind][3];\n", + "\n", + " if (!name) {\n", + " // put a spacer in here.\n", + " continue;\n", + " }\n", + " var button = $('');\n", + " button.click(method_name, toolbar_event);\n", + " button.mouseover(tooltip, toolbar_mouse_event);\n", + " nav_element.append(button);\n", + " }\n", + "\n", + " // Add the status bar.\n", + " var status_bar = $('');\n", + " nav_element.append(status_bar);\n", + " this.message = status_bar[0];\n", + "\n", + " // Add the close button to the window.\n", + " var buttongrp = $('
');\n", + " var button = $('');\n", + " button.click(function (evt) { fig.handle_close(fig, {}); } );\n", + " button.mouseover('Stop Interaction', toolbar_mouse_event);\n", + " buttongrp.append(button);\n", + " var titlebar = this.root.find($('.ui-dialog-titlebar'));\n", + " titlebar.prepend(buttongrp);\n", + "}\n", + "\n", + "mpl.figure.prototype._root_extra_style = function(el){\n", + " var fig = this\n", + " el.on(\"remove\", function(){\n", + "\tfig.close_ws(fig, {});\n", + " });\n", + "}\n", + "\n", + "mpl.figure.prototype._canvas_extra_style = function(el){\n", + " // this is important to make the div 'focusable\n", + " el.attr('tabindex', 0)\n", + " // reach out to IPython and tell the keyboard manager to turn it's self\n", + " // off when our div gets focus\n", + "\n", + " // location in version 3\n", + " if (IPython.notebook.keyboard_manager) {\n", + " IPython.notebook.keyboard_manager.register_events(el);\n", + " }\n", + " else {\n", + " // location in version 2\n", + " IPython.keyboard_manager.register_events(el);\n", + " }\n", + "\n", + "}\n", + "\n", + "mpl.figure.prototype._key_event_extra = function(event, name) {\n", + " var manager = IPython.notebook.keyboard_manager;\n", + " if (!manager)\n", + " manager = IPython.keyboard_manager;\n", + "\n", + " // Check for shift+enter\n", + " if (event.shiftKey && event.which == 13) {\n", + " this.canvas_div.blur();\n", + " // select the cell after this one\n", + " var index = IPython.notebook.find_cell_index(this.cell_info[0]);\n", + " IPython.notebook.select(index + 1);\n", + " }\n", + "}\n", + "\n", + "mpl.figure.prototype.handle_save = function(fig, msg) {\n", + " fig.ondownload(fig, null);\n", + "}\n", + "\n", + "\n", + "mpl.find_output_cell = function(html_output) {\n", + " // Return the cell and output element which can be found *uniquely* in the notebook.\n", + " // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n", + " // IPython event is triggered only after the cells have been serialised, which for\n", + " // our purposes (turning an active figure into a static one), is too late.\n", + " var cells = IPython.notebook.get_cells();\n", + " var ncells = cells.length;\n", + " for (var i=0; i= 3 moved mimebundle to data attribute of output\n", + " data = data.data;\n", + " }\n", + " if (data['text/html'] == html_output) {\n", + " return [cell, data, j];\n", + " }\n", + " }\n", + " }\n", + " }\n", + "}\n", + "\n", + "// Register the function which deals with the matplotlib target/channel.\n", + "// The kernel may be null if the page has been refreshed.\n", + "if (IPython.notebook.kernel != null) {\n", + " IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);\n", + "}\n" + ], + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "text/html": [ + "" + ], + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "newfig()\n", + "decorate(xlabel='x position (m)',\n", + " ylabel='y position (m)',\n", + " xlim=[0, 105],\n", + " ylim=[-5, 35],\n", + " legend=False)\n", + "\n", + "for x, y in zip(xs, ys):\n", + " plot(x, y, 'bo', update=True)\n", + " sleep(0.01)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here's a function that encapsulates that code and runs the animation in (approximately) real time." + ] + }, + { + "cell_type": "code", + "execution_count": 38, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def animate2d(xs, ys, speedup=1):\n", + " \"\"\"Animate the results of a projectile simulation.\n", + " \n", + " xs: x position as a function of time\n", + " ys: y position as a function of time\n", + " \n", + " speedup: how much to divide `dt` by\n", + " \"\"\"\n", + " # get the time intervals between elements\n", + " ts = xs.index\n", + " dts = np.diff(ts)\n", + " dts = np.append(dts, 0)\n", + "\n", + " # decorate the plot\n", + " newfig()\n", + " decorate(xlabel='x position (m)',\n", + " ylabel='y position (m)',\n", + " xlim=[xs.min(), xs.max()],\n", + " ylim=[ys.min(), ys.max()],\n", + " legend=False)\n", + "\n", + " # loop through the values\n", + " for x, y, dt in zip(xs, ys, dts):\n", + " plot(x, y, 'bo', update=True)\n", + " sleep(dt / speedup)" + ] + }, + { + "cell_type": "code", + "execution_count": 39, + "metadata": { + "scrolled": false + }, + "outputs": [ + { + "data": { + "application/javascript": [ + "/* Put everything inside the global mpl namespace */\n", + "window.mpl = {};\n", + "\n", + "\n", + "mpl.get_websocket_type = function() {\n", + " if (typeof(WebSocket) !== 'undefined') {\n", + " return WebSocket;\n", + " } else if (typeof(MozWebSocket) !== 'undefined') {\n", + " return MozWebSocket;\n", + " } else {\n", + " alert('Your browser does not have WebSocket support.' +\n", + " 'Please try Chrome, Safari or Firefox ≥ 6. ' +\n", + " 'Firefox 4 and 5 are also supported but you ' +\n", + " 'have to enable WebSockets in about:config.');\n", + " };\n", + "}\n", + "\n", + "mpl.figure = function(figure_id, websocket, ondownload, parent_element) {\n", + " this.id = figure_id;\n", + "\n", + " this.ws = websocket;\n", + "\n", + " this.supports_binary = (this.ws.binaryType != undefined);\n", + "\n", + " if (!this.supports_binary) {\n", + " var warnings = document.getElementById(\"mpl-warnings\");\n", + " if (warnings) {\n", + " warnings.style.display = 'block';\n", + " warnings.textContent = (\n", + " \"This browser does not support binary websocket messages. \" +\n", + " \"Performance may be slow.\");\n", + " }\n", + " }\n", + "\n", + " this.imageObj = new Image();\n", + "\n", + " this.context = undefined;\n", + " this.message = undefined;\n", + " this.canvas = undefined;\n", + " this.rubberband_canvas = undefined;\n", + " this.rubberband_context = undefined;\n", + " this.format_dropdown = undefined;\n", + "\n", + " this.image_mode = 'full';\n", + "\n", + " this.root = $('
');\n", + " this._root_extra_style(this.root)\n", + " this.root.attr('style', 'display: inline-block');\n", + "\n", + " $(parent_element).append(this.root);\n", + "\n", + " this._init_header(this);\n", + " this._init_canvas(this);\n", + " this._init_toolbar(this);\n", + "\n", + " var fig = this;\n", + "\n", + " this.waiting = false;\n", + "\n", + " this.ws.onopen = function () {\n", + " fig.send_message(\"supports_binary\", {value: fig.supports_binary});\n", + " fig.send_message(\"send_image_mode\", {});\n", + " if (mpl.ratio != 1) {\n", + " fig.send_message(\"set_dpi_ratio\", {'dpi_ratio': mpl.ratio});\n", + " }\n", + " fig.send_message(\"refresh\", {});\n", + " }\n", + "\n", + " this.imageObj.onload = function() {\n", + " if (fig.image_mode == 'full') {\n", + " // Full images could contain transparency (where diff images\n", + " // almost always do), so we need to clear the canvas so that\n", + " // there is no ghosting.\n", + " fig.context.clearRect(0, 0, fig.canvas.width, fig.canvas.height);\n", + " }\n", + " fig.context.drawImage(fig.imageObj, 0, 0);\n", + " };\n", + "\n", + " this.imageObj.onunload = function() {\n", + " this.ws.close();\n", + " }\n", + "\n", + " this.ws.onmessage = this._make_on_message_function(this);\n", + "\n", + " this.ondownload = ondownload;\n", + "}\n", + "\n", + "mpl.figure.prototype._init_header = function() {\n", + " var titlebar = $(\n", + " '
');\n", + " var titletext = $(\n", + " '
');\n", + " titlebar.append(titletext)\n", + " this.root.append(titlebar);\n", + " this.header = titletext[0];\n", + "}\n", + "\n", + "\n", + "\n", + "mpl.figure.prototype._canvas_extra_style = function(canvas_div) {\n", + "\n", + "}\n", + "\n", + "\n", + "mpl.figure.prototype._root_extra_style = function(canvas_div) {\n", + "\n", + "}\n", + "\n", + "mpl.figure.prototype._init_canvas = function() {\n", + " var fig = this;\n", + "\n", + " var canvas_div = $('
');\n", + "\n", + " canvas_div.attr('style', 'position: relative; clear: both; outline: 0');\n", + "\n", + " function canvas_keyboard_event(event) {\n", + " return fig.key_event(event, event['data']);\n", + " }\n", + "\n", + " canvas_div.keydown('key_press', canvas_keyboard_event);\n", + " canvas_div.keyup('key_release', canvas_keyboard_event);\n", + " this.canvas_div = canvas_div\n", + " this._canvas_extra_style(canvas_div)\n", + " this.root.append(canvas_div);\n", + "\n", + " var canvas = $('');\n", + " canvas.addClass('mpl-canvas');\n", + " canvas.attr('style', \"left: 0; top: 0; z-index: 0; outline: 0\")\n", + "\n", + " this.canvas = canvas[0];\n", + " this.context = canvas[0].getContext(\"2d\");\n", + "\n", + " var backingStore = this.context.backingStorePixelRatio ||\n", + "\tthis.context.webkitBackingStorePixelRatio ||\n", + "\tthis.context.mozBackingStorePixelRatio ||\n", + "\tthis.context.msBackingStorePixelRatio ||\n", + "\tthis.context.oBackingStorePixelRatio ||\n", + "\tthis.context.backingStorePixelRatio || 1;\n", + "\n", + " mpl.ratio = (window.devicePixelRatio || 1) / backingStore;\n", + "\n", + " var rubberband = $('');\n", + " rubberband.attr('style', \"position: absolute; left: 0; top: 0; z-index: 1;\")\n", + "\n", + " var pass_mouse_events = true;\n", + "\n", + " canvas_div.resizable({\n", + " start: function(event, ui) {\n", + " pass_mouse_events = false;\n", + " },\n", + " resize: function(event, ui) {\n", + " fig.request_resize(ui.size.width, ui.size.height);\n", + " },\n", + " stop: function(event, ui) {\n", + " pass_mouse_events = true;\n", + " fig.request_resize(ui.size.width, ui.size.height);\n", + " },\n", + " });\n", + "\n", + " function mouse_event_fn(event) {\n", + " if (pass_mouse_events)\n", + " return fig.mouse_event(event, event['data']);\n", + " }\n", + "\n", + " rubberband.mousedown('button_press', mouse_event_fn);\n", + " rubberband.mouseup('button_release', mouse_event_fn);\n", + " // Throttle sequential mouse events to 1 every 20ms.\n", + " rubberband.mousemove('motion_notify', mouse_event_fn);\n", + "\n", + " rubberband.mouseenter('figure_enter', mouse_event_fn);\n", + " rubberband.mouseleave('figure_leave', mouse_event_fn);\n", + "\n", + " canvas_div.on(\"wheel\", function (event) {\n", + " event = event.originalEvent;\n", + " event['data'] = 'scroll'\n", + " if (event.deltaY < 0) {\n", + " event.step = 1;\n", + " } else {\n", + " event.step = -1;\n", + " }\n", + " mouse_event_fn(event);\n", + " });\n", + "\n", + " canvas_div.append(canvas);\n", + " canvas_div.append(rubberband);\n", + "\n", + " this.rubberband = rubberband;\n", + " this.rubberband_canvas = rubberband[0];\n", + " this.rubberband_context = rubberband[0].getContext(\"2d\");\n", + " this.rubberband_context.strokeStyle = \"#000000\";\n", + "\n", + " this._resize_canvas = function(width, height) {\n", + " // Keep the size of the canvas, canvas container, and rubber band\n", + " // canvas in synch.\n", + " canvas_div.css('width', width)\n", + " canvas_div.css('height', height)\n", + "\n", + " canvas.attr('width', width * mpl.ratio);\n", + " canvas.attr('height', height * mpl.ratio);\n", + " canvas.attr('style', 'width: ' + width + 'px; height: ' + height + 'px;');\n", + "\n", + " rubberband.attr('width', width);\n", + " rubberband.attr('height', height);\n", + " }\n", + "\n", + " // Set the figure to an initial 600x600px, this will subsequently be updated\n", + " // upon first draw.\n", + " this._resize_canvas(600, 600);\n", + "\n", + " // Disable right mouse context menu.\n", + " $(this.rubberband_canvas).bind(\"contextmenu\",function(e){\n", + " return false;\n", + " });\n", + "\n", + " function set_focus () {\n", + " canvas.focus();\n", + " canvas_div.focus();\n", + " }\n", + "\n", + " window.setTimeout(set_focus, 100);\n", + "}\n", + "\n", + "mpl.figure.prototype._init_toolbar = function() {\n", + " var fig = this;\n", + "\n", + " var nav_element = $('
')\n", + " nav_element.attr('style', 'width: 100%');\n", + " this.root.append(nav_element);\n", + "\n", + " // Define a callback function for later on.\n", + " function toolbar_event(event) {\n", + " return fig.toolbar_button_onclick(event['data']);\n", + " }\n", + " function toolbar_mouse_event(event) {\n", + " return fig.toolbar_button_onmouseover(event['data']);\n", + " }\n", + "\n", + " for(var toolbar_ind in mpl.toolbar_items) {\n", + " var name = mpl.toolbar_items[toolbar_ind][0];\n", + " var tooltip = mpl.toolbar_items[toolbar_ind][1];\n", + " var image = mpl.toolbar_items[toolbar_ind][2];\n", + " var method_name = mpl.toolbar_items[toolbar_ind][3];\n", + "\n", + " if (!name) {\n", + " // put a spacer in here.\n", + " continue;\n", + " }\n", + " var button = $('');\n", + " button.click(method_name, toolbar_event);\n", + " button.mouseover(tooltip, toolbar_mouse_event);\n", + " nav_element.append(button);\n", + " }\n", + "\n", + " // Add the status bar.\n", + " var status_bar = $('');\n", + " nav_element.append(status_bar);\n", + " this.message = status_bar[0];\n", + "\n", + " // Add the close button to the window.\n", + " var buttongrp = $('
');\n", + " var button = $('');\n", + " button.click(function (evt) { fig.handle_close(fig, {}); } );\n", + " button.mouseover('Stop Interaction', toolbar_mouse_event);\n", + " buttongrp.append(button);\n", + " var titlebar = this.root.find($('.ui-dialog-titlebar'));\n", + " titlebar.prepend(buttongrp);\n", + "}\n", + "\n", + "mpl.figure.prototype._root_extra_style = function(el){\n", + " var fig = this\n", + " el.on(\"remove\", function(){\n", + "\tfig.close_ws(fig, {});\n", + " });\n", + "}\n", + "\n", + "mpl.figure.prototype._canvas_extra_style = function(el){\n", + " // this is important to make the div 'focusable\n", + " el.attr('tabindex', 0)\n", + " // reach out to IPython and tell the keyboard manager to turn it's self\n", + " // off when our div gets focus\n", + "\n", + " // location in version 3\n", + " if (IPython.notebook.keyboard_manager) {\n", + " IPython.notebook.keyboard_manager.register_events(el);\n", + " }\n", + " else {\n", + " // location in version 2\n", + " IPython.keyboard_manager.register_events(el);\n", + " }\n", + "\n", + "}\n", + "\n", + "mpl.figure.prototype._key_event_extra = function(event, name) {\n", + " var manager = IPython.notebook.keyboard_manager;\n", + " if (!manager)\n", + " manager = IPython.keyboard_manager;\n", + "\n", + " // Check for shift+enter\n", + " if (event.shiftKey && event.which == 13) {\n", + " this.canvas_div.blur();\n", + " // select the cell after this one\n", + " var index = IPython.notebook.find_cell_index(this.cell_info[0]);\n", + " IPython.notebook.select(index + 1);\n", + " }\n", + "}\n", + "\n", + "mpl.figure.prototype.handle_save = function(fig, msg) {\n", + " fig.ondownload(fig, null);\n", + "}\n", + "\n", + "\n", + "mpl.find_output_cell = function(html_output) {\n", + " // Return the cell and output element which can be found *uniquely* in the notebook.\n", + " // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n", + " // IPython event is triggered only after the cells have been serialised, which for\n", + " // our purposes (turning an active figure into a static one), is too late.\n", + " var cells = IPython.notebook.get_cells();\n", + " var ncells = cells.length;\n", + " for (var i=0; i= 3 moved mimebundle to data attribute of output\n", + " data = data.data;\n", + " }\n", + " if (data['text/html'] == html_output) {\n", + " return [cell, data, j];\n", + " }\n", + " }\n", + " }\n", + " }\n", + "}\n", + "\n", + "// Register the function which deals with the matplotlib target/channel.\n", + "// The kernel may be null if the page has been refreshed.\n", + "if (IPython.notebook.kernel != null) {\n", + " IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);\n", + "}\n" + ], + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "text/html": [ + "" + ], + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Saving figure to file chap10-fig03.pdf\n" + ] + } + ], + "source": [ + "newfig()\n", + "plot(sweep)\n", + "decorate(xlabel='Launch angle (degree)',\n", + " ylabel='Range (m)',\n", + " legend=False)\n", + "\n", + "savefig('chap10-fig03.pdf')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can use `max_bounded` to search for the peak efficiently." + ] + }, + { + "cell_type": "code", + "execution_count": 49, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "45.0\n", + "34.3769410125\n", + "55.6230589875\n", + "21.246117975\n", + "41.8191039876\n", + "41.6971472537\n", + "41.6051027031\n", + "41.6031028639\n", + "41.6034368143\n", + "41.6027689135\n", + "Wall time: 2.98 s\n" + ] + } + ], + "source": [ + "%time res = max_bounded(range_func, [0, 90], condition)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The result is an `OptimizeResult` object." + ] + }, + { + "cell_type": "code", + "execution_count": 50, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "scipy.optimize.optimize.OptimizeResult" + ] + }, + "execution_count": 50, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "type(res)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "With the following variables." + ] + }, + { + "cell_type": "code", + "execution_count": 51, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + " fun: 109.69517452156008\n", + " message: 'Solution found.'\n", + " nfev: 9\n", + " status: 0\n", + " success: True\n", + " x: 41.603102863878036" + ] + }, + "execution_count": 51, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "res" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "So the optimal angle is about 41 degrees, and the resulting range is 103 meters." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Exercise:** Add a print statement to `range_func` that prints `angle`. Then run `max_bounded` again so you can see how many times it calls `range_func` and what the arguments are." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Turning off units\n", + "\n", + "Each time `range_func` runs, it calls `odeint`, which runs `slope_func` many times. And each time `slop_func` runs, it checks the units for all computations, which takes some time. We can speed up the whole process by removing the units from the computation (now that we are satisfied that they are correct).\n", + "\n", + "Because of the way we organized the code, all units are in the `Condition` object, so we can \"turn off units\" by defining a new `Condition` object with no units:" + ] + }, + { + "cell_type": "code", + "execution_count": 52, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "condition = Condition(g = 9.8,\n", + " mass = 145e-3,\n", + " diameter = 73e-3,\n", + " rho = 1.2,\n", + " C_d = 0.3,\n", + " angle = 45,\n", + " velocity = 40,\n", + " duration = 7)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now `range_func` and `max_bounded` are substantially faster." + ] + }, + { + "cell_type": "code", + "execution_count": 53, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "45\n", + "Wall time: 65.5 ms\n" + ] + }, + { + "data": { + "text/plain": [ + "array(102.72237841710975)" + ] + }, + "execution_count": 53, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "%time range_func(45, condition)" + ] + }, + { + "cell_type": "code", + "execution_count": 54, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "45.0\n", + "34.3769410125\n", + "55.6230589875\n", + "21.246117975\n", + "41.4051852323\n", + "41.2368620421\n", + "41.1390964616\n", + "41.1364127407\n", + "41.1367466842\n", + "41.1360787972\n", + "Wall time: 488 ms\n" + ] + } + ], + "source": [ + "%time res = max_bounded(range_func, [0, 90], condition)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### The Manny Ramirez problem\n", + "\n", + "Finally, let's solve the Manny Ramirez problem:\n", + "\n", + "*What is the minimum effort required to hit a home run in Fenway Park?*\n", + "\n", + "Fenway Park is a baseball stadium in Boston, Massachusetts. One of its most famous features is the \"Green Monster\", which is a wall in left field that is unusually close to home plate, only 310 feet along the left field line. To compensate for the short distance, the wall is unusually high, at 37 feet.\n", + "\n", + "Although the problem asks for a minimum, it is not an optimization problem. Rather, we want to solve for the initial velocity that just barely gets the ball to the top of the wall, given that it launches at the optimal angle.\n", + "\n", + "And we have to be careful about what we mean by \"optimal\". For this problem, we don't want the longest range, we want the maximum height at the point where it reaches the wall.\n", + "\n", + "If you are ready to solve the problem on your own, go ahead. Otherwise I will walk you through the process with an outline and some starter code.\n", + "\n", + "As a first step, write a function called `height_func` that takes a launch angle and a condition as parameters, simulates the flights of a baseball, and returns the height of the baseball when it reaches a point 94.5 meters (310 feet) from home plate." + ] + }, + { + "cell_type": "code", + "execution_count": 55, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "# Solution goes here\n", + "def height_func(angle, condition):\n", + " print(angle)\n", + " condition.set(angle = angle)\n", + " system = make_system(condition)\n", + " run_odeint(system, slope_func)\n", + " T = interp_inverse(system.results.x)\n", + " t_desire = T(94.5)\n", + " \n", + " Y = interpolate(system.results.y)\n", + " return Y(t_desire)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Test your function with a launch angle of 45 degrees:" + ] + }, + { + "cell_type": "code", + "execution_count": 56, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "45\n" + ] + }, + { + "data": { + "text/plain": [ + "array(11.025366370142653)" + ] + }, + "execution_count": 56, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "height_func(45, condition)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now use `max_bounded` to find the optimal angle. Is it higher or lower than the angle that maximizes range?" + ] + }, + { + "cell_type": "code", + "execution_count": 57, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "45.0\n", + "34.3769410125\n", + "55.6230589875\n", + "21.246117975\n", + "40.0964091144\n", + "41.9865507741\n", + "47.1952334237\n", + "44.3729100433\n", + "44.4032473114\n", + "44.7851090803\n", + "44.5491055281\n", + "44.598163681\n", + "44.5182828595\n", + "44.47434319\n", + "44.5178199739\n", + "44.526924287\n", + "44.5215835911\n", + "44.5199261685\n", + "44.5202601622\n", + "44.5195921748\n" + ] + } + ], + "source": [ + "# Solution goes here\n", + "res = max_bounded(height_func, [0, 90], condition)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The following lines compute the height of the ball at the wall, given that it's launched at the optimal angle." + ] + }, + { + "cell_type": "code", + "execution_count": 58, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "44.5199261685\n" + ] + }, + { + "data": { + "text/plain": [ + "array(11.045254540088495)" + ] + }, + "execution_count": 58, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "angle = res.x\n", + "height = height_func(angle, condition)\n", + "height" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Next, we need to find the height of the ball at the wall, for a given velocity, given that it's launched at the optimal angle.\n", + "\n", + "Write a function called `best_height` that takes velocity and a `Condition` object as parameters. It should use `max_bounded` to find the optimal launch angle, then compute and the highest possible height of the ball at the wall, for the given velocity." + ] + }, + { + "cell_type": "code", + "execution_count": 59, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "# Solution goes here\n", + "def best_height(velocity, condition):\n", + " condition.set(velocity = velocity)\n", + " res = max_bounded(height_func, [0,90], condition)\n", + " angle = res.x\n", + " height = height_func(angle, condition)\n", + " return height" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Use this code to test `best_height`" + ] + }, + { + "cell_type": "code", + "execution_count": 60, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "45.0\n", + "34.3769410125\n", + "55.6230589875\n", + "21.246117975\n", + "40.0964091144\n", + "41.9865507741\n", + "47.1952334237\n", + "44.3729100433\n", + "44.4032473114\n", + "44.7851090803\n", + "44.5491055281\n", + "44.598163681\n", + "44.5182828595\n", + "44.47434319\n", + "44.5178199739\n", + "44.526924287\n", + "44.5215835911\n", + "44.5199261685\n", + "44.5202601622\n", + "44.5195921748\n", + "44.5199261685\n" + ] + }, + { + "data": { + "text/plain": [ + "array(11.045254540088495)" + ] + }, + "execution_count": 60, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "best_height(40, condition)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Finally, we want to use `fsolve` to find the initial velocity that makes the height of the ball exactly 11 meters when it reaches the wall.\n", + "\n", + "To use `fsolve`, we need an error function that returns 0 when we have the right velocity. Write a function called `error_func` that takes a velocity and a `Condition` object, uses `best_height` to find the height of the ball at the wall, and returns the difference between the result and the target value (11 meters)." + ] + }, + { + "cell_type": "code", + "execution_count": 61, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "# Solution goes here\n", + "def error_func(velocity, condition):\n", + " condition.set(velocity = velocity)\n", + " bh = best_height(velocity, condition)\n", + " error = abs(bh - 11)\n", + " return error" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Test your error function like this:" + ] + }, + { + "cell_type": "code", + "execution_count": 62, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "45.0\n", + "34.3769410125\n", + "55.6230589875\n", + "21.246117975\n", + "40.0964091144\n", + "41.9865507741\n", + "47.1952334237\n", + "44.3729100433\n", + "44.4032473114\n", + "44.7851090803\n", + "44.5491055281\n", + "44.598163681\n", + "44.5182828595\n", + "44.47434319\n", + "44.5178199739\n", + "44.526924287\n", + "44.5215835911\n", + "44.5199261685\n", + "44.5202601622\n", + "44.5195921748\n", + "44.5199261685\n" + ] + }, + { + "data": { + "text/plain": [ + "0.045254540088494721" + ] + }, + "execution_count": 62, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "error_func(40, condition)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Then use `fsolve` to find the answer to the problem, the minimum velocity that gets the ball out of the park." + ] + }, + { + "cell_type": "code", + "execution_count": 63, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "45.0\n", + "34.3769410125\n", + "55.6230589875\n", + "21.246117975\n", + "40.0964091144\n", + "41.9865507741\n", + "47.1952334237\n", + "44.3729100433\n", + "44.4032473114\n", + "44.7851090803\n", + "44.5491055281\n", + "44.598163681\n", + "44.5182828595\n", + "44.47434319\n", + "44.5178199739\n", + "44.526924287\n", + "44.5215835911\n", + "44.5199261685\n", + "44.5202601622\n", + "44.5195921748\n", + "44.5199261685\n", + "45.0\n", + "34.3769410125\n", + "55.6230589875\n", + "21.246117975\n", + "40.0964091144\n", + "41.9865507741\n", + "47.1952334237\n", + "44.3729100433\n", + "44.4032473114\n", + "44.7851090803\n", + "44.5491055281\n", + "44.598163681\n", + "44.5182828595\n", + "44.47434319\n", + "44.5178199739\n", + "44.526924287\n", + "44.5215835911\n", + "44.5199261685\n", + "44.5202601622\n", + "44.5195921748\n", + "44.5199261685\n", + "45.0\n", + "34.3769410125\n", + "55.6230589875\n", + "21.246117975\n", + "40.0964091144\n", + "41.9865507741\n", + "47.1952334237\n", + "44.3729100433\n", + "44.4032473114\n", + "44.7851090803\n", + "44.5491055281\n", + "44.598163681\n", + "44.5182828595\n", + "44.47434319\n", + "44.5178199739\n", + "44.526924287\n", + "44.5215835911\n", + "44.5199261685\n", + "44.5202601622\n", + "44.5195921748\n", + "44.5199261685\n", + "45.0\n", + "34.3769410125\n", + "55.6230589875\n", + "21.246117975\n", + "40.0964091144\n", + "41.9865507741\n", + "47.1952334237\n", + "44.3729100433\n", + "44.4032473114\n", + "44.7851090803\n", + "44.5491055281\n", + "44.598163681\n", + "44.5182828595\n", + "44.47434319\n", + "44.5178199739\n", + "44.526924287\n", + "44.5215835911\n", + "44.5199261685\n", + "44.5202601622\n", + "44.5195921748\n", + "44.5199261685\n", + "45.0\n", + "34.3769410125\n", + "55.6230589875\n", + "21.246117975\n", + "40.0964101039\n", + "41.9865514818\n", + "47.1952338611\n", + "44.3729107363\n", + "44.4032479885\n", + "44.7851096988\n", + "44.5491061829\n", + "44.5981646707\n", + "44.5182836073\n", + "44.4743439108\n", + "44.5178206755\n", + "44.5269250008\n", + "44.5215843259\n", + "44.5199268969\n", + "44.5202608905\n", + "44.5195929032\n", + "44.5199268969\n", + "45.0\n", + "34.3769410125\n", + "55.6230589875\n", + "21.246117975\n", + "40.0776709524\n", + "41.9731411518\n", + "47.1869458214\n", + "44.3597757581\n", + "44.390414864\n", + "44.7735586919\n", + "44.5367627837\n", + "44.5793338916\n", + "44.504097991\n", + "44.4606749004\n", + "44.5045348687\n", + "44.5135666998\n", + "44.5079847212\n", + "44.506102114\n", + "44.5064361074\n", + "44.5057681205\n", + "44.506102114\n", + "45.0\n", + "34.3769410125\n", + "55.6230589875\n", + "21.246117975\n", + "40.0776675208\n", + "41.9731386943\n", + "47.1869443026\n", + "44.3597733507\n", + "44.3904125118\n", + "44.7735565651\n", + "44.5367605176\n", + "44.5793304962\n", + "44.5040954025\n", + "44.4606724022\n", + "44.5045324311\n", + "44.5135642555\n", + "44.507982281\n", + "44.5060995834\n", + "44.5064335768\n", + "44.5057655899\n", + "44.5060995834\n", + "45.0\n", + "34.3769410125\n", + "55.6230589875\n", + "21.246117975\n", + "40.077674382\n", + "41.9731436079\n", + "47.1869473394\n", + "44.3597781642\n", + "44.3904172148\n", + "44.7735607991\n", + "44.5367650414\n", + "44.579337315\n", + "44.5041005829\n", + "44.4606774002\n", + "44.5045373028\n", + "44.5135691449\n", + "44.5079871595\n", + "44.5061046431\n", + "44.5064386366\n", + "44.5057706497\n", + "44.5061046431\n", + "45.0\n", + "34.3769410125\n", + "55.6230589875\n", + "21.246117975\n", + "40.0776743821\n", + "41.9731436079\n", + "47.1869473394\n", + "44.3597781642\n", + "44.3904172148\n", + "44.7735608007\n", + "44.536765042\n", + "44.579337314\n", + "44.5041005827\n", + "44.4606774001\n", + "44.5045373031\n", + "44.5135691427\n", + "44.5079871588\n", + "44.5061046431\n", + "44.5064386366\n", + "44.5057706497\n", + "44.5061046431\n" + ] + } + ], + "source": [ + "# Solution goes here\n", + "minimum = fsolve(error_func, 40, condition)\n" + ] + }, + { + "cell_type": "code", + "execution_count": 64, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([ 39.98870758])" + ] + }, + "execution_count": 64, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Solution goes here\n", + "minimum" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "And just to check, run `best_height` with the value you found. The result should be 11 meters." + ] + }, + { + "cell_type": "code", + "execution_count": 65, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "45.0\n", + "34.3769410125\n", + "55.6230589875\n", + "21.246117975\n", + "40.0776743821\n", + "41.9731436079\n", + "47.1869473394\n", + "44.3597781642\n", + "44.3904172148\n", + "44.7735608007\n", + "44.536765042\n", + "44.579337314\n", + "44.5041005827\n", + "44.4606774001\n", + "44.5045373031\n", + "44.5135691427\n", + "44.5079871588\n", + "44.5061046431\n", + "44.5064386366\n", + "44.5057706497\n", + "44.5061046431\n" + ] + }, + { + "data": { + "text/plain": [ + "array(11.000000000003942)" + ] + }, + "execution_count": 65, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "best_height(minimum, condition)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "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": "3.6.1" + } + }, + "nbformat": 4, + "nbformat_minor": 1 +} From 74e5dd4ff92f9664cfa464145f44d35dcd78cb77 Mon Sep 17 00:00:00 2001 From: Junwon Lee <31522211+junwonlee5@users.noreply.github.com> Date: Tue, 28 Nov 2017 19:29:10 -0500 Subject: [PATCH 17/19] Add chap11mine --- code/chap11mine.ipynb | 1983 +++++++++++++++++++++++++++++++++++++++++ 1 file changed, 1983 insertions(+) create mode 100644 code/chap11mine.ipynb diff --git a/code/chap11mine.ipynb b/code/chap11mine.ipynb new file mode 100644 index 00000000..fded36b5 --- /dev/null +++ b/code/chap11mine.ipynb @@ -0,0 +1,1983 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Modeling and Simulation in Python\n", + "\n", + "Chapter 11: Rotation\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": { + "collapsed": true + }, + "outputs": [], + "source": [ + "# If you want the figures to appear in the notebook, \n", + "# and you want to interact with them, use\n", + "# %matplotlib notebook\n", + "\n", + "# If you want the figures to appear in the notebook, \n", + "# and you don't want to interact with them, use\n", + "# %matplotlib inline\n", + "\n", + "# If you want the figures to appear in separate windows, use\n", + "# %matplotlib qt5\n", + "\n", + "# tempo switch from one to another, you have to select Kernel->Restart\n", + "\n", + "%matplotlib inline\n", + "\n", + "from modsim import *" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Rolling paper\n", + "\n", + "We'll start by loading the units we need." + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "radian = UNITS.radian\n", + "m = UNITS.meter\n", + "s = UNITS.second" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "And creating a `Condition` object with the system parameters" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "condition = Condition(Rmin = 0.02 * m,\n", + " Rmax = 0.055 * m,\n", + " L = 47 * m,\n", + " duration = 130 * s)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The following function estimates the parameter `k`, which is the increase in the radius of the roll for each radian of rotation. " + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def estimate_k(condition):\n", + " \"\"\"Estimates the parameter `k`.\n", + " \n", + " condition: Condition with Rmin, Rmax, and L\n", + " \n", + " returns: k in meters per radian\n", + " \"\"\"\n", + " unpack(condition)\n", + " \n", + " Ravg = (Rmax + Rmin) / 2\n", + " Cavg = 2 * pi * Ravg\n", + " revs = L / Cavg\n", + " rads = 2 * pi * revs\n", + " k = (Rmax - Rmin) / rads\n", + " return k" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "As usual, `make_system` takes a `Condition` object and returns a `System` object." + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def make_system(condition):\n", + " \"\"\"Make a system object.\n", + " \n", + " condition: Condition with Rmin, Rmax, and L\n", + " \n", + " returns: System with init, k, and ts\n", + " \"\"\"\n", + " unpack(condition)\n", + " \n", + " init = State(theta = 0 * radian,\n", + " y = 0 * m,\n", + " r = Rmin)\n", + " \n", + " k = estimate_k(condition)\n", + " ts = linspace(0, duration, 101)\n", + " \n", + " return System(init=init, k=k, ts=ts)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Testing `make_system`" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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inittheta 0 radian\n", + "y 0 meter\n", + "r ...
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" + ], + "text/plain": [ + "theta 0 radian\n", + "y 0 meter\n", + "r 0.02 meter\n", + "dtype: object" + ] + }, + "execution_count": 7, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "system.init" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now we can write a slope function based on the differential equations\n", + "\n", + "$\\omega = \\frac{d\\theta}{dt} = 10$\n", + "\n", + "$\\frac{dy}{dt} = r \\frac{d\\theta}{dt}$\n", + "\n", + "$\\frac{dr}{dt} = k \\frac{d\\theta}{dt}$\n" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def slope_func(state, t, system):\n", + " \"\"\"Computes the derivatives of the state variables.\n", + " \n", + " state: State object with theta, y, r\n", + " t: time\n", + " system: System object with r, k\n", + " \n", + " returns: sequence of derivatives\n", + " \"\"\"\n", + " theta, y, r = state\n", + " unpack(system)\n", + " \n", + " omega = 10 * radian / s\n", + " dydt = r * omega\n", + " drdt = k * omega\n", + " \n", + " return omega, dydt, drdt" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Testing `slope_func`" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "(,\n", + " ,\n", + " )" + ] + }, + "execution_count": 9, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "slope_func(system.init, 0*s, system)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now we can run the simulation." + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "run_odeint(system, slope_func)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "And look at the results." + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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thetayr
124.81248.046.7070640.054851
126.11261.047.4224870.055214
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\n", + "
" + ], + "text/plain": [ + " theta y r\n", + "124.8 1248.0 46.707064 0.054851\n", + "126.1 1261.0 47.422487 0.055214\n", + "127.4 1274.0 48.142630 0.055577\n", + "128.7 1287.0 48.867493 0.055940\n", + "130.0 1300.0 49.597074 0.056303" + ] + }, + "execution_count": 11, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "system.results.tail()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Extracting one time series per variable (and converting `r` to radians):" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "thetas = system.results.theta\n", + "ys = system.results.y\n", + "rs = system.results.r * 1000" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Plotting `theta`" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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rGEgyinHk+1soUtSy4462FpgS1RcjRIIek3zcGbq8waSkpMDDwwOnTp2Cl5cXZ04ikSA8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\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plot(thetas, label='theta')\n", + "\n", + "decorate(xlabel='Time (s)',\n", + " ylabel='Angle (rad)')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Plotting `y`" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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NzMxaJJwIUQZiqRjH7h3D3xl/yxw1TOszDeYdzF/wakIUS65v+vDwcDx+/BhT\np04FAKirq8vsk5aW1uwPP3PmDH7++WdMnz4ddnZ2EAqFMsuXamlp0fQdpE14UPEAv9/4HQXVBWyN\njhqIMpMrIAIDA1v8g6OiorB06VIEBATgs88+A/B0XieRSMTZr6GhAbq6ui3++YQoSoOkAUfuHsHp\nrNOc5xrsTewxtc9UutZAlJZcAfHxxx+36Idu3rwZERERCAkJwZIlS9jrEJaWliguLubsW1xcLHPa\niRBVca/sHnal7EJx7T//XWtraOOdXu/Av7s/3aFElFqzLiZcv34dly5dQklJCWbNmoXMzEz07t0b\nJiby36O9detWREREYP78+Zg7dy5nm6enJxISEji1+Ph4eHl5NadNQnj3RPQEUXeicOHhBU7dydQJ\nIW4h6KzXmafOCJGfXAHR0NCATz/9FCdPnoSmpibEYjEmTpyI7du3IyMjA3v37pVrFbn09HSsWbMG\n48aNw8SJE1FSUsJu09fXR0hICMaNG4d169YhMDAQR48eRUpKCpYvX/7KAyRE0VKLUrEndQ8qhBVs\nTVdTFxN6T6AlQIlKkeuqWEREBC5duoRNmzYhMTGRPY+6cuVKGBgYYM2aNXJ92PHjxyGRSHDw4EH4\n+flx/uzcuROOjo7YsGEDTpw4gTFjxuDs2bPYsmUL+8wEIcqsqr4KW5O2YuO1jZxw6GPRB8v9l+ON\nrm9QOBCVItcRRExMDBYtWoShQ4dCIpGwdWtra3z88cf47rvv5PqwRYsWYdGiRS/cx9/fX+ZWWEKU\nGcMwuJx7GX/d/gt1ojq2bqBtgPdc3kNfy74UDEQlyb2iXLdu3RrdZmRkhJqamhZtihBVUVxbjN2p\nu3G39C6n7mvji/G9x9N6DUSlyRUQPXv2xLFjx+Dn5yez7cKFC3QKiLQ7YqkYpzJP4ei9oxBLxWy9\ns15nhLiFwMnUicfuCGkZcgVEWFgY5s2bh8rKSgwZMgQCgQDJyck4cuQI9uzZg1WrVrV2n4QojczH\nmdidupvzwJuaQA1v2r6JIMcgWhuatBlyBcTw4cMRHh6O1atX4+zZswCAb7/9FsbGxli2bBmtIkfa\nhTpRHaLvRMvcutqtUzdMcZsCG0MbnjojpHXI/RxEUFAQgoKCkJWVhYqKChgYGMDOzg5qajQ9AGnb\nGIZBYkEi/rz1J6rqq9i6toY2RjuOpmkySJvV7Fn3bG1tOT8nJCTg9OnT+Oqrr1qsKUKURWldKfbe\n3Itbxbf1gCy5AAAaAUlEQVQ4dTdzN0xymUQL+ZA27dWmZX3O7du3ERkZSQFB2hSxVIyTmSdx/P5x\niCT/zA9mqGOISS6T4GHhQbeukjbvtQOCkLbmbuld7Lm5B0U1RWxNIBDAv7s/gh2DoatJk0eS9oEC\ngpD/U1Vfhb9u/4X4vHhOvathV0x2m4zunbrz0xghPKGAIO2elJEi9kEsDqUfglAsZOs6GjoY02sM\nBncfTBehSbtEAUHatazyLOy9uRe5lbmculcXL0xwnoBOOp146owQ/jUZEDNmzJDrDQoKCl6+EyFK\nprq+GtHp0biUc4lTN+9gjvdc3qMnoQnBCwLi3yu7NcXU1BSmpqYt1hAhrUnKSHHh4QUcTj/MmVhP\nU10TAfYBGGE3AhpqdGBNCPCCgNi1a5ci+yCk1WU+zsS+tH0yp5PcLdwx0XkiPdNAyL/Qr0qkzasU\nViLqThSu5l3l1E31TfGu87twNXflqTNClBsFBGmzxFIxzmafxbF7xzh3Jz07nTTcdjg01TV57JAQ\n5UYBQdqkW8W3sP/Wfs7DbgDgYemBCb0n0OkkQuRAAUHalOLaYhy4dQCpRamcukUHC0xymUR3JxHS\nDBQQpE0QioU4du8YzmSfgUT6z7K4Oho6CHIMgn93f7o7iZBmon8xRKVJGSmu5F7BofRDnKm4BQIB\nfG18MabXGHTU7shjh4SoLgoIorLul93H/lv7ZW5btTWyxSSXSejWqfF11Akh8qGAICqntK4UB28f\nRPKjZE69k04njOs9Dv269KOpuAlpARQQRGU8ET3B8fvHcTb7LMRSMVvXVNfEW3ZvYYTdCGhraPPY\nISFtCwUEUXrPpseIuRuDmoYazrZ+Vv0w1mksjHWNeeqOkLaLAoIoLYZhkFachoN3DuJR9SPONlsj\nW0xwngBbI9smXk0IeV0UEEQp5VTm4ODtg0gvTefUjXWNMdZpLLy6eNF1BkJaGQUEUSqPnzzG4fTD\nMvMm6WjoYJT9KAzrMYymxyBEQSggiFKoE9Xh74y/cSbrDOcCtJpADX5d/TDacTQMtA147JCQ9ocC\ngvBKLBXj/IPzOH7/OGobajnb+lj0wVinsbDoYMFTd4S0bxQQhBcMw+Ba/jUcvnsYZXVlnG3dO3XH\nuN7j4GDiwFN3hBCA54BYtmwZJBIJvv32W7YWFxeH8PBwZGdno1u3bvj0008xePBgHrskLYlhGNwq\nuYXoO9HIq8rjbOus1xnvOL0DT0tPugBNiBLgJSAYhsG6deuwf/9+jB8/nq1nZGQgLCwMc+bMwYgR\nIxATE4O5c+ciOjoa9vb2fLRKWlBWeRai70TjXtk9Tr2DVgcEOgRiULdBNKEeIUpE4f8ac3Nz8d//\n/hf3799Hly5dONsiIyPh7u6OsLAwAMDChQuRlJSEyMhIrFixQtGtkhZSUF2AQ+mHkFKYwqlrqWvh\nTds38VbPt6CjocNTd4SQpig8IJKTk2FpaYmff/4ZixYt4mxLTEzEqFGjODUfHx8cO3ZMkS2SFlJa\nV4qYuzGIz48HwzBsXU2ghoHdBuJth7dpplVClJjCAyI4OBjBwcGNbissLIS5uTmnZmZmhsLCQkW0\nRlpIpbASx+8fx8Wci5y1GYCnU2OMdhwNM30znrojhMhLqU74CoVCaGlpcWpaWlqor6/nqSPSHDUN\nNTiRcQLnHpyDSCLibHMxc8GYXmNgY2jDU3eEkOZSqoDQ1taGSMT9YmloaICuri5PHRF51InqcDrr\nNE5nnUa9mBvmPY17YkyvMbA3oZsMCFE1ShUQlpaWKC4u5tSKi4tlTjsR5SAUC3E2+yxOZZ5CnaiO\ns62rYVeM6TUGvU170y2rhKgopQoIT09PJCQkcGrx8fHw8vLiqSPSmHpxPc4/OI8TmSdknn62NLBE\nsGMw3C3cKRgIUXFKFRAhISEYN24c1q1bh8DAQBw9ehQpKSlYvnw5360RPA2G2IexOJl5EtX11Zxt\nZvpmeNvhbfSz6gc1gRpPHRJCWpJSBYSjoyM2bNiA8PBwbN26Fba2ttiyZQvs7Oz4bq1de1EwmOiZ\n4G2Ht9Hfuj8FAyFtDK8BsWvXLpmav78//P39Fd8MkfGiYDDWNUaAfQAG2Aygp58JaaPoXzaRIRQL\ncf7BeZzKPCWzxKeRrhEC7APga+NLwUBIG0f/wgmrTlSHc9nncCb7jMzFZ2NdY4yyH0XBQEg7Qv/S\nCWoaanA66zTOZZ+DUCzkbDPRM8GonqPoVBIh7RD9i2/HKoQVOJl5EhcfXkSDpIGzzVTfFAH2AfCx\n8oG6mjpPHRJC+EQB0Q6V1JbgROYJXMm9wlneEwAsOlggwD6AblclhFBAtCd5VXn4O+NvJBYkcmZX\nBQDrjtYYZT8KfS37UjAQQgBQQLR5DMMg43EG/s74G2nFaTLbbY1sMcp+FFzNXOnJZ0IIBwVEG8Uw\nDFKKUnAi4wSyyrNktjuZOmFUz1FwMHGgYCCENIoCoo0RSUSIz4/HycyTKKop4mwTCATwsPDAyJ4j\n0a1TN546JISoCgqINqK2oRYXHl7A2eyzqKqv4mzTUNPAAJsBGG47HOYdaGZcQoh8KCBUXGldKU5n\nncbl3MsyazHoaOhgcPfBGNpjKDrpdOKpQ0KIqqKAUEEMwyCrPAunsk7hRuENmTuSOul0wjDbYRjU\nbRB0NHR46pIQouooIFSIRCpB8qNknM46jQcVD2S2W3W0wgi7EfDq4kVPPRNCXht9i6iA2oZaxOXE\n4dyDcyh/Ui6z3dnMGW/avgmnzk50RxIhpMVQQCixR9WPcDb7LK7kXYFIwl2rW0NNA95W3hhuNxxd\nDLrw1CEhpC2jgFAyDMPgZvFNnM0+izsld2S2G2gbYHC3wRjcfTA6anfkoUNCSHtBAaEk6kR1uJx7\nGeeyz6G0rlRmu3VHawyzHYZ+XfpBU12Thw4JIe0NBQTP8qrycP7BecTnxcvMqCoQCOBu4Y4h3YfQ\nE8+EEIWjgOCBWCrG9UfXce7BOWQ+zpTZrqepB7+ufvDv7g8TPRMeOiSEEAoIhSqrK8PFnIuIy4mT\nWeMZeHoaaUiPIfC28oaWuhYPHRJCyD8oIFqZlJEirTgNFx5eQFpxmsxDbWoCNXh28cTgboPR07gn\nnUYihCgNCohWUv6kHJdyLyEuJ67RZxeMdI0wsOtADOw2kO5GIoQoJQqIFvTsaCEuJw6pRakyRwsA\n0Nu0NwZ3Hww3czdamIcQotQoIFpAWV0Z4nLicDn3MiqEFTLbDbQN4Gvji4FdB8JU35SHDgkhpPko\nIF6RSCLCjcIbiMuJQ3ppeqP79OrcCwO7DYS7hTvNjUQIUTn0rdUMDMMgtyoXl3Iu4Vr+NdSJ6mT2\nMdA2wADrAfDr6kdrLxBCVBoFhByq66txLf8aLudeRl5Vnsx2gUAAZ1Nn+HX1g5u5G9TV1HnokhBC\nWhYFRBPEUjFuFt3ElbwruFl0E1JGKrOPiZ4J/Lr6YYD1ABjpGvHQJSGEtB4KiOcwDIMHFQ9wNe8q\nEgoSUNtQK7OPpromPC094WvjS9NfEELaNAoIACW1JYjPj0d8XjyKa4sb3cfO2A6+Nr7wtPSErqau\ngjskhBDFU7qAkEgkiIiIQHR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IKxk7dizMzc0xffp0HD58GFevXsUPP/yAzZs3w8bGhrPm\n+PO8vLygo6PDuR22b9++YBgGc+fOxenTp3HlyhUsW7YMNTU1nLudACA5ORl+fn6tOjbSPlBAENJK\nnl036NOnD3744QfMnDkTFy9exNKlSzFv3rwmX6erq4tBgwZxHpIzMTHB9u3bYWBggMWLF2PWrFm4\ndesW1q9fj379+rH7lZSUID09XSY0CHkVNNUGIUooNTUV7733Hs6ePdvoheymbN68GSdOnEB0dHST\nRyiEyIuOIAhRQm5ubhg2bBh+++03uV9TV1eHvXv3YtGiRRQOpEVQQBCipJYvX44TJ07g4cOHcu2/\nfft2DBkyBIMGDWrlzkh7QaeYCCGENIqOIAghhDSKAoIQQkijKCAIIYQ0igKCEEJIoyggCCGENOr/\nA6ef1MpfzGxDAAAAAElFTkSuQmCC\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plot(ys, color='green', label='y')\n", + "\n", + "decorate(xlabel='Time (s)',\n", + " ylabel='Length (m)')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Plotting `r`" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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mPtX7kR5JkhgI8+bJB0Pt2sCECcCkSRwMREak0vcNPsvT0BkZGWjevDneffdd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\nPe44AgICZD/4U1JSEB0djS5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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plot(rs, color='red', label='r')\n", + "\n", + "decorate(xlabel='Time (s)',\n", + " ylabel='Radius (mm)')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can also see the relationship between `y` and `r`, which I derive analytically in the book." + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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V+OGHH2BsbAyFQoEHH3wQH330EfLz8/Hpp592ahW53NxcbNmyBXPmzMGDDz6I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\nUbsYEERE1C4GBBERtYsBQURE7fr/Yjm+Jt2sBpsAAAAASUVORK5CYII=\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plot(rs, ys, color='purple')\n", + "\n", + "decorate(xlabel='Radius (mm)',\n", + " ylabel='Length (m)',\n", + " legend=False)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "And here's the figure from the book." + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Saving figure to file chap11-fig01.pdf\n" + ] + }, + { + "data": { + "image/png": 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QiC5JlwLC6dOnsXz5codjI0eOxJYtWwAAKpXK+mLdHXq9HiUlJQgPD8ejjz4K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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "subplot(3, 1, 1)\n", + "plot(thetas, label='theta')\n", + "decorate(ylabel='Angle (rad)')\n", + "\n", + "subplot(3, 1, 2)\n", + "plot(ys, color='green', label='y')\n", + "decorate(ylabel='Length (m)')\n", + "\n", + "subplot(3, 1, 3)\n", + "plot(rs, color='red', label='r')\n", + "\n", + "decorate(xlabel='Time(s)',\n", + " ylabel='Radius (mm)')\n", + "\n", + "savefig('chap11-fig01.pdf')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can use interpolation to find the time when `y` is 47 meters." + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array(125.33333334940457)" + ] + }, + "execution_count": 18, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "T = interp_inverse(ys, kind='cubic')\n", + "t_end = T(47)\n", + "t_end" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "At that point `r` is 55 mm, which is `Rmax`, as expected." + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array(55.00000000448797)" + ] + }, + "execution_count": 19, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "R = interpolate(rs, kind='cubic')\n", + "R(t_end)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The total amount of rotation is 1253 rad." + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array(1253.3333334940455)" + ] + }, + "execution_count": 20, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "THETA = interpolate(thetas, kind='cubic')\n", + "THETA(t_end)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Unrolling" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "For unrolling the paper, we need more units:" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "kg = UNITS.kilogram\n", + "N = UNITS.newton" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "And a few more parameters in the `Condition` object." + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "condition = Condition(Rmin = 0.02 * m,\n", + " Rmax = 0.055 * m,\n", + " Mcore = 15e-3 * kg,\n", + " Mroll = 215e-3 * kg,\n", + " L = 47 * m,\n", + " tension = 2e-4 * N,\n", + " duration = 180 * s)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "`make_system` computes `rho_h`, which we'll need to compute moment of inertia, and `k`, which we'll use to compute `r`." + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def make_system(condition):\n", + " \"\"\"Make a system object.\n", + " \n", + " condition: Condition with Rmin, Rmax, Mcore, Mroll,\n", + " L, tension, and duration\n", + " \n", + " returns: System with init, k, rho_h, Rmin, Rmax,\n", + " Mcore, Mroll, ts\n", + " \"\"\"\n", + " unpack(condition)\n", + " \n", + " init = State(theta = 0 * radian,\n", + " omega = 0 * radian/s,\n", + " y = L)\n", + " \n", + " area = pi * (Rmax**2 - Rmin**2)\n", + " rho_h = Mroll / area\n", + " k = (Rmax**2 - Rmin**2) / 2 / L / radian \n", + " ts = linspace(0, duration, 101)\n", + " \n", + " return System(init=init, k=k, rho_h=rho_h,\n", + " Rmin=Rmin, Rmax=Rmax,\n", + " Mcore=Mcore, Mroll=Mroll, \n", + " ts=ts)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Testing `make_system`" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "metadata": {}, + "outputs": [ + { + 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" + ], + "text/plain": [ + "theta 0 radian\n", + "omega 0.0 radian / second\n", + "y 47 meter\n", + "dtype: object" + ] + }, + "execution_count": 25, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "system.init" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here's how we compute `I` as a function of `r`:" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def moment_of_inertia(r, system):\n", + " \"\"\"Moment of inertia for a roll of toilet paper.\n", + " \n", + " r: current radius of roll in meters\n", + " system: System object with Mcore, rho, Rmin, Rmax\n", + " \n", + " returns: moment of inertia in kg m**2\n", + " \"\"\"\n", + " unpack(system)\n", + " Icore = Mcore * Rmin**2 \n", + " Iroll = pi * rho_h / 2 * (r**4 - Rmin**4)\n", + " return Icore + Iroll" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "When `r` is `Rmin`, `I` is small." + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "6e-06 kilogram meter2" + ], + "text/latex": [ + "$6e-06 kilogram \\cdot meter^{2}$" + ], + "text/plain": [ + "" + ] + }, + "execution_count": 27, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "moment_of_inertia(system.Rmin, system)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "As `r` increases, so does `I`." + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "0.00037418750000000006 kilogram meter2" + ], + "text/latex": [ + "$0.00037418750000000006 kilogram \\cdot meter^{2}$" + ], + "text/plain": [ + "" + ] + }, + "execution_count": 28, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "moment_of_inertia(system.Rmax, system)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here's the slope function." + ] + }, + { + "cell_type": "code", + "execution_count": 29, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def slope_func(state, t, system):\n", + " \"\"\"Computes the derivatives of the state variables.\n", + " \n", + " state: State object with theta, omega, y\n", + " t: time\n", + " system: System object with Rmin, k, Mcore, rho_h, tension\n", + " \n", + " returns: sequence of derivatives\n", + " \"\"\"\n", + " theta, omega, y = state\n", + " unpack(system)\n", + " \n", + " r = sqrt(2*k*y + Rmin**2)\n", + " I = moment_of_inertia(r, system)\n", + " tau = r * tension\n", + " alpha = tau / I\n", + " dydt = -r * omega\n", + " \n", + " return omega, alpha, dydt " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Testing `slope_func`" + ] + }, + { + "cell_type": "code", + "execution_count": 30, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "(,\n", + " ,\n", + " )" + ] + }, + "execution_count": 30, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "slope_func(system.init, 0*s, system)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now we can run the simulation." + ] + }, + { + "cell_type": "code", + "execution_count": 31, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "run_odeint(system, slope_func)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "And look at the results." + ] + }, + { + "cell_type": "code", + "execution_count": 32, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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thetaomegay
172.8503.3769986.83022222.852269
174.6515.7882196.96058022.346268
176.4528.4371507.09437621.835001
178.2541.3301517.23180221.318468
180.0554.4739407.37306620.796665
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" + ], + "text/plain": [ + " theta omega y\n", + "172.8 503.376998 6.830222 22.852269\n", + "174.6 515.788219 6.960580 22.346268\n", + "176.4 528.437150 7.094376 21.835001\n", + "178.2 541.330151 7.231802 21.318468\n", + "180.0 554.473940 7.373066 20.796665" + ] + }, + "execution_count": 32, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "system.results.tail()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Extrating the time series" + ] + }, + { + "cell_type": "code", + "execution_count": 33, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "thetas = system.results.theta\n", + "omegas = system.results.omega\n", + "ys = system.results.y" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Plotting `theta`" + ] + }, + { + "cell_type": "code", + "execution_count": 34, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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ppZdaOk4hRAdWXa2w98gVTl28tVirp4stE6J6YGUhsw3aqgb9n3n88ccpKChg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\nzVJCQkKU++67T3n33XeVqqqq1gy7Xfn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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plot(thetas, label='theta')\n", + "\n", + "decorate(xlabel='Time (s)',\n", + " ylabel='Angle (rad)')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Plotting `omega`" + ] + }, + { + "cell_type": "code", + "execution_count": 35, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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qkZCQUKxFCWFzbp5Sv9DNuGdfa89m6ty+k7tl6hJllqbw9/X1JTIykqeeeirf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\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plot(omegas, color='orange', label='omega')\n", + "\n", + "decorate(xlabel='Time (s)',\n", + " ylabel='Angular velocity (rad/s)')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Plotting `y`" + ] + }, + { + "cell_type": "code", + "execution_count": 36, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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UFNq0acPChQt59tlnH+p4Qoi652rnymt9X+P9iPe5rb0NwI7YHWiLtYz0GSl9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\nQghRJQkIIYQQVZKAEEIIUaX/D/xvzc1wbORsAAAAAElFTkSuQmCC\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plot(ys, color='green', label='y')\n", + "\n", + "decorate(xlabel='Time (s)',\n", + " ylabel='Length (m)')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here's the figure from the book." + ] + }, + { + "cell_type": "code", + "execution_count": 37, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Saving figure to file chap11-fig02.pdf\n" + ] + }, + { + "data": { + "image/png": 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CHEr+CxcuJCkpiZkzZxIcHIxafe0f8jVr1rBy5Uoef/zxKusB9OzZs8pSwr/9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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "subplot(3, 1, 1)\n", + "plot(thetas, label='theta')\n", + "decorate(ylabel='Angle (rad)')\n", + "\n", + "subplot(3, 1, 2)\n", + "plot(omegas, color='orange', label='omega')\n", + "decorate(ylabel='Angular velocity (rad/s)')\n", + "\n", + "subplot(3, 1, 3)\n", + "plot(ys, color='green', label='y')\n", + "\n", + "decorate(xlabel='Time(s)',\n", + " ylabel='Length (m)')\n", + "\n", + "savefig('chap11-fig02.pdf')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Yo-yo" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Exercise:** Simulate the descent of a yo-yo. How long does it take to reach the end of the string.\n", + "\n", + "I provide a `Condition` object with the system parameters:\n", + "\n", + "* `Rmin` is the radius of the axle. `Rmax` is the radius of the axle plus rolled string.\n", + "\n", + "* `Rout` is the radius of the yo-yo body. `mass` is the total mass of the yo-yo, ignoring the string. \n", + "\n", + "* `L` is the length of the string.\n", + "\n", + "* `g` is the acceleration of gravity." + ] + }, + { + "cell_type": "code", + "execution_count": 38, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "condition = Condition(Rmin = 8e-3 * m,\n", + " Rmax = 16e-3 * m,\n", + " Rout = 35e-3 * m,\n", + " mass = 50e-3 * kg,\n", + " L = 1 * m,\n", + " g = 9.8 * m / s**2,\n", + " duration = 1 * s)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here's a `make_system` function that computes `I` and `k` based on the system parameters.\n", + "\n", + "I estimated `I` by modeling the yo-yo as a solid cylinder with uniform density ([see here](https://en.wikipedia.org/wiki/List_of_moments_of_inertia)). In reality, the distribution of weight in a yo-yo is often designed to achieve desired effects. But we'll keep it simple." + ] + }, + { + "cell_type": "code", + "execution_count": 39, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def make_system(condition):\n", + " \"\"\"Make a system object.\n", + " \n", + " condition: Condition with Rmin, Rmax, Rout, \n", + " mass, L, g, duration\n", + " \n", + " returns: System with init, k, Rmin, Rmax, mass,\n", + " I, g, ts\n", + " \"\"\"\n", + " unpack(condition)\n", + " \n", + " init = State(theta = 0 * radian,\n", + " omega = 0 * radian/s,\n", + " y = L,\n", + " v = 0 * m / s)\n", + " \n", + " I = mass * Rout**2 / 2\n", + " k = (Rmax**2 - Rmin**2) / 2 / L / radian \n", + " ts = linspace(0, duration, 101)\n", + " \n", + " return System(init=init, k=k,\n", + " Rmin=Rmin, Rmax=Rmax,\n", + " mass=mass, I=I, g=g,\n", + " ts=ts)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Testing `make_system`" + ] + }, + { + "cell_type": "code", + "execution_count": 40, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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" + ], + "text/plain": [ + "theta 0 radian\n", + "omega 0.0 radian / second\n", + "y 1 meter\n", + "v 0.0 meter / second\n", + "dtype: object" + ] + }, + "execution_count": 41, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "system.init" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Write a slope function for this system, using these results from the book:\n", + "\n", + "$ r = \\sqrt{2 k y + R_{min}^2} $ \n", + "\n", + "$ T = m g I / I^* $\n", + "\n", + "$ a = -m g r^2 / I^* $\n", + "\n", + "$ \\alpha = m g r / I^* $\n", + "\n", + "where $I^*$ is the augmented moment of inertia, $I + m r^2$.\n", + "\n", + "Hint: If `y` is less than 0, it means you have reached the end of the string, so the equation for `r` is no longer valid. In this case, the simplest thing to do it return the sequence of derivatives `0, 0, 0, 0`" + ] + }, + { + "cell_type": "code", + "execution_count": 49, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "# Solution goes here\n", + "\n", + "def slope_func(state, t, system):\n", + " theta, omega, y, v = state\n", + " unpack(system)\n", + " \n", + " if y < 0*m:\n", + " return 0, 0, 0, 0\n", + " r = sqrt(2*k*y + Rmin**2)\n", + " Is = I + mass*r**2\n", + " alpha = mass*g*r / Is\n", + " a = -(mass*g*r**2)/(Is)\n", + " \n", + " return omega, alpha, v, a\n", + " \n", + " " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Test your slope function with the initial conditions." + ] + }, + { + "cell_type": "code", + "execution_count": 50, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "(,\n", + " ,\n", + " ,\n", + " )" + ] + }, + "execution_count": 50, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "slope_func(system.init, 0*s, system)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Then run the simulation." + ] + }, + { + "cell_type": "code", + "execution_count": 51, + "metadata": { + "collapsed": true, + "scrolled": false + }, + "outputs": [], + "source": [ + "run_odeint(system, slope_func)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Check the final conditions. If things have gone according to plan, the final value of `y` should be close to 0." + ] + }, + { + "cell_type": "code", + "execution_count": 52, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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thetaomegayv
0.9667.11465144.630635-1.582474e-08-1.994692
0.9767.11465144.630635-1.582474e-08-1.994692
0.9867.11465144.630635-1.582474e-08-1.994692
0.9967.11465144.630635-1.582474e-08-1.994692
1.0067.11465144.630635-1.582474e-08-1.994692
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" + ], + "text/plain": [ + " theta omega y v\n", + "0.96 67.11465 144.630635 -1.582474e-08 -1.994692\n", + "0.97 67.11465 144.630635 -1.582474e-08 -1.994692\n", + "0.98 67.11465 144.630635 -1.582474e-08 -1.994692\n", + "0.99 67.11465 144.630635 -1.582474e-08 -1.994692\n", + "1.00 67.11465 144.630635 -1.582474e-08 -1.994692" + ] + }, + "execution_count": 52, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "system.results.tail()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Plot the results." + ] + }, + { + "cell_type": "code", + "execution_count": 53, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "thetas = system.results.theta\n", + "ys = system.results.y" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "`theta` should increase and accelerate." + ] + }, + { + "cell_type": "code", + "execution_count": 54, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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AQF2GSQjRk9/v1SC7QKjcjh7phgBPOz1GRO7T+X2dq6sr/vWvf3W7PzY2FrGxsboLiBBi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\nFoalS5fi+vXrKuc99thjyM/Px/nz5/v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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plot(thetas, label='theta')\n", + "\n", + "decorate(xlabel='Time (s)',\n", + " ylabel='Angle (rad)')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "`y` should decrease and accelerate down." + ] + }, + { + "cell_type": "code", + "execution_count": 55, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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Qovpwt3MnvEs4y48tJ7MgUz8A46tdXqWJcxNzlydqmDIDRKPRsH79eqDkSfMd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\ncmXW1taMGDGCpUuX4uLigpu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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plot(ys, color='green', label='y')\n", + "\n", + "decorate(xlabel='Time (s)',\n", + " ylabel='Length (m)')" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "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": "3.6.1" + } + }, + "nbformat": 4, + "nbformat_minor": 1 +} From 8be3720db06234199ee632fb3c1091d5805a7e33 Mon Sep 17 00:00:00 2001 From: Junwon Lee <31522211+junwonlee5@users.noreply.github.com> Date: Tue, 28 Nov 2017 19:34:40 -0500 Subject: [PATCH 18/19] Adding chap11mine --- code/chap11mine.ipynb | 40 ++++++++++++++++++++-------------------- 1 file changed, 20 insertions(+), 20 deletions(-) diff --git a/code/chap11mine.ipynb b/code/chap11mine.ipynb index fded36b5..a4b06cc9 100644 --- a/code/chap11mine.ipynb +++ b/code/chap11mine.ipynb @@ -498,7 +498,7 @@ "data": { "image/png": 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GF8f6wcOZr+MKSU/U5iGyf/3rX7h48SI+/PBDrF+/HoMGDUJwcDC8vLxgZWWF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\n", 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NzMxaJJwIUQZiqRjH7h3D3xl/yxw1TOszDeYdzF/wakIUS65v+vDwcDx+/BhT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\ngjskhBDFU7qAkEgkiIiIQHR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mPtX7kR5JkhgI8+bJB0Pt2sCECcCkSRwMREak0vcNPsvT0BkZGWjevDneffdd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\nPe44AgICZD/4U1JSEB0djS5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6IwYEEXVXWWoZMj/OhLL15vMGv+l+8Jvpx+cNWtKpgPjPf/6Du+++G6+88gpsbW17uiYi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\nKWqXyWRtbjt1lsRAwnAgIro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QiC5JlwLC6dOnsXz5codjI0eOxJYtWwAAKpXK+mLdHXq9HiUlJQgPD8ejjz4K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\nN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ppZdaOk4hRAdWXa2w98gVTl28tVirp4stE6J6YGUhsw3aqgb9n3n88ccpKChg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\nzVJCQkKU++67T3n33XeVqqqq1gy7Xfn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UFNq0acPChQt59tlnH+p4Qoi652rnymt9X+P9iPe5rb0NwI7YHWiLtYz0GSl9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\nXQBOnjyJi4sLXbp0oaysjLKyMnQ6HYM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CHEr+CxcuJCkpiZkzZxIcHIxafe0f8jVr1rBy5Uoef/zxKusB9OzZs8pSwr/9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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -1682,7 +1682,7 @@ }, { "cell_type": "code", - "execution_count": 49, + "execution_count": 42, "metadata": { "collapsed": true }, @@ -1715,7 +1715,7 @@ }, { "cell_type": "code", - "execution_count": 50, + "execution_count": 43, "metadata": {}, "outputs": [ { @@ -1727,7 +1727,7 @@ " )" ] }, - "execution_count": 50, + "execution_count": 43, "metadata": {}, "output_type": "execute_result" } @@ -1745,7 +1745,7 @@ }, { "cell_type": "code", - "execution_count": 51, + "execution_count": 44, "metadata": { "collapsed": true, "scrolled": false @@ -1764,7 +1764,7 @@ }, { "cell_type": "code", - "execution_count": 52, + "execution_count": 45, "metadata": {}, "outputs": [ { @@ -1843,7 +1843,7 @@ "1.00 67.11465 144.630635 -1.582474e-08 -1.994692" ] }, - "execution_count": 52, + "execution_count": 45, "metadata": {}, "output_type": "execute_result" } @@ -1861,7 +1861,7 @@ }, { "cell_type": "code", - "execution_count": 53, + "execution_count": 46, "metadata": { "collapsed": true }, @@ -1880,14 +1880,14 @@ }, { "cell_type": "code", - "execution_count": 54, + "execution_count": 47, "metadata": {}, "outputs": [ { "data": { "image/png": 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FtSoLF9latRcFpFpPRNvUmmfx6aefwszMDE8//TT279+PEydO4MCBA1iyZAlM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\nFoalS5fi+vXrKuc99thjyM/Px/nz5/v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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -1910,14 +1910,14 @@ }, { "cell_type": "code", - "execution_count": 55, + "execution_count": 48, "metadata": {}, "outputs": [ { "data": { "image/png": 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Qovpwt3MnvEs4y48tJ7MgUz8A46tdXqWJcxNzlydqmDIDRKPRsH79eqDkSfMd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\ncmXW1taMGDGCpUuX4uLigpu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"text/plain": [ - "" + "" ] }, "metadata": {}, From d112d816b04f20cdd7bfed1d49eb26ac8d46c42d Mon Sep 17 00:00:00 2001 From: Junwon Lee <31522211+junwonlee5@users.noreply.github.com> Date: Wed, 29 Nov 2017 20:20:05 -0500 Subject: [PATCH 19/19] Adding galilean cannon --- code/galilean cannon.ipynb | 3571 ++++++++++++++++++++++++++++++++++++ 1 file changed, 3571 insertions(+) create mode 100644 code/galilean cannon.ipynb diff --git a/code/galilean cannon.ipynb b/code/galilean cannon.ipynb new file mode 100644 index 00000000..a208e18c --- /dev/null +++ b/code/galilean cannon.ipynb @@ -0,0 +1,3571 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "58.320859100248526 meter/second" + ], + "text/latex": [ + "$58.320859100248526 \\frac{meter}{second}$" + ], + "text/plain": [ + "" + ] + }, + "execution_count": 3, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "%matplotlib notebook\n", + "from modsim import *\n", + "\n", + "m = UNITS.meter\n", + "s = UNITS.second\n", + "kg = UNITS.kilogram\n", + "condition = Condition(mass_B = 0.625*kg, mass_G = 0.04593*kg, dia_B = 0.2*m, \n", + " dia_G = 0.043*m, a = 9.81*m /s**2, h = 1*m, numB = 1, duration = 20*s, rho = 1.2*kg/m**3, C_d = 0.5)\n", + "\n", + "def make_system(condition):\n", + " 'Using Momentum'\n", + " unpack(condition)\n", + " t_dropB = sqrt(2*(h + (dia_B * numB * 0.5))/a)\n", + " P_dropB = mass_B *numB * a * t_dropB\n", + " t_dropG = sqrt(2*(h + (dia_B * numB)+dia_G/2)/a)\n", + " P_dropG = mass_G * a * t_dropG\n", + " v = (1*P_dropB -P_dropG) / mass_G\n", + " y = (dia_B * numB)+dia_G/2\n", + " area = np.pi * (dia_G/2)**2\n", + " #if v > sqrt(2 * mass_G * a / (rho * area * C_d)):\n", + " # v = sqrt(2 * mass_G * a / (rho * area * C_d))\n", + " init = State(y=y, v=v)\n", + " \n", + " ts = linspace(0, duration, 101)\n", + " return System(init = init, ts = ts, a=-a, rho = rho, C_d = C_d, area = area, mass_G = mass_G)\n", + "system = make_system(condition)\n", + "system.init.v\n", + "\n", + "\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "data": { + "application/javascript": [ + "/* Put everything inside the global mpl namespace */\n", + "window.mpl = {};\n", + "\n", + "\n", + "mpl.get_websocket_type = function() {\n", + " if (typeof(WebSocket) !== 'undefined') {\n", + " return WebSocket;\n", + " } else if (typeof(MozWebSocket) !== 'undefined') {\n", + " return MozWebSocket;\n", + " } else {\n", + " alert('Your browser does not have WebSocket support.' +\n", + " 'Please try Chrome, Safari or Firefox ≥ 6. ' +\n", + " 'Firefox 4 and 5 are also supported but you ' +\n", + " 'have to enable WebSockets in about:config.');\n", + " };\n", + "}\n", + "\n", + "mpl.figure = function(figure_id, websocket, ondownload, parent_element) {\n", + " this.id = figure_id;\n", + "\n", + " this.ws = websocket;\n", + "\n", + " this.supports_binary = (this.ws.binaryType != undefined);\n", + "\n", + " if (!this.supports_binary) {\n", + " var warnings = document.getElementById(\"mpl-warnings\");\n", + " if (warnings) {\n", + " warnings.style.display = 'block';\n", + " warnings.textContent = (\n", + " \"This browser does not support binary websocket messages. \" +\n", + " \"Performance may be slow.\");\n", + " }\n", + " }\n", + "\n", + " this.imageObj = new Image();\n", + "\n", + " this.context = undefined;\n", + " this.message = undefined;\n", + " this.canvas = undefined;\n", + " this.rubberband_canvas = undefined;\n", + " this.rubberband_context = undefined;\n", + " this.format_dropdown = undefined;\n", + "\n", + " this.image_mode = 'full';\n", + "\n", + " this.root = $('
');\n", + " this._root_extra_style(this.root)\n", + " this.root.attr('style', 'display: inline-block');\n", + "\n", + " $(parent_element).append(this.root);\n", + "\n", + " this._init_header(this);\n", + " this._init_canvas(this);\n", + " this._init_toolbar(this);\n", + "\n", + " var fig = this;\n", + "\n", + " this.waiting = false;\n", + "\n", + " this.ws.onopen = function () {\n", + " fig.send_message(\"supports_binary\", {value: fig.supports_binary});\n", + " fig.send_message(\"send_image_mode\", {});\n", + " if (mpl.ratio != 1) {\n", + " fig.send_message(\"set_dpi_ratio\", {'dpi_ratio': mpl.ratio});\n", + " }\n", + " fig.send_message(\"refresh\", {});\n", + " }\n", + "\n", + " this.imageObj.onload = function() {\n", + " if (fig.image_mode == 'full') {\n", + " // Full images could contain transparency (where diff images\n", + " // almost always do), so we need to clear the canvas so that\n", + " // there is no ghosting.\n", + " fig.context.clearRect(0, 0, fig.canvas.width, fig.canvas.height);\n", + " }\n", + " fig.context.drawImage(fig.imageObj, 0, 0);\n", + " };\n", + "\n", + " this.imageObj.onunload = function() {\n", + " this.ws.close();\n", + " }\n", + "\n", + " this.ws.onmessage = this._make_on_message_function(this);\n", + "\n", + " this.ondownload = ondownload;\n", + "}\n", + "\n", + "mpl.figure.prototype._init_header = function() {\n", + " var titlebar = $(\n", + " '
');\n", + " var titletext = $(\n", + " '
');\n", + " titlebar.append(titletext)\n", + " this.root.append(titlebar);\n", + " this.header = titletext[0];\n", + "}\n", + "\n", + "\n", + "\n", + "mpl.figure.prototype._canvas_extra_style = function(canvas_div) {\n", + "\n", + "}\n", + "\n", + "\n", + "mpl.figure.prototype._root_extra_style = function(canvas_div) {\n", + "\n", + "}\n", + "\n", + "mpl.figure.prototype._init_canvas = function() {\n", + " var fig = this;\n", + "\n", + " var canvas_div = $('
');\n", + "\n", + " canvas_div.attr('style', 'position: relative; clear: both; outline: 0');\n", + "\n", + " function canvas_keyboard_event(event) {\n", + " return fig.key_event(event, event['data']);\n", + " }\n", + "\n", + " canvas_div.keydown('key_press', canvas_keyboard_event);\n", + " canvas_div.keyup('key_release', canvas_keyboard_event);\n", + " this.canvas_div = canvas_div\n", + " this._canvas_extra_style(canvas_div)\n", + " this.root.append(canvas_div);\n", + "\n", + " var canvas = $('');\n", + " canvas.addClass('mpl-canvas');\n", + " canvas.attr('style', \"left: 0; top: 0; z-index: 0; outline: 0\")\n", + "\n", + " this.canvas = canvas[0];\n", + " this.context = canvas[0].getContext(\"2d\");\n", + "\n", + " var backingStore = this.context.backingStorePixelRatio ||\n", + "\tthis.context.webkitBackingStorePixelRatio ||\n", + "\tthis.context.mozBackingStorePixelRatio ||\n", + "\tthis.context.msBackingStorePixelRatio ||\n", + "\tthis.context.oBackingStorePixelRatio ||\n", + "\tthis.context.backingStorePixelRatio || 1;\n", + "\n", + " mpl.ratio = (window.devicePixelRatio || 1) / backingStore;\n", + "\n", + " var rubberband = $('');\n", + " rubberband.attr('style', \"position: absolute; left: 0; top: 0; z-index: 1;\")\n", + "\n", + " var pass_mouse_events = true;\n", + "\n", + " canvas_div.resizable({\n", + " start: function(event, ui) {\n", + " pass_mouse_events = false;\n", + " },\n", + " resize: function(event, ui) {\n", + " fig.request_resize(ui.size.width, ui.size.height);\n", + " },\n", + " stop: function(event, ui) {\n", + " pass_mouse_events = true;\n", + " fig.request_resize(ui.size.width, ui.size.height);\n", + " },\n", + " });\n", + "\n", + " function mouse_event_fn(event) {\n", + " if (pass_mouse_events)\n", + " return fig.mouse_event(event, event['data']);\n", + " }\n", + "\n", + " rubberband.mousedown('button_press', mouse_event_fn);\n", + " rubberband.mouseup('button_release', mouse_event_fn);\n", + " // Throttle sequential mouse events to 1 every 20ms.\n", + " rubberband.mousemove('motion_notify', mouse_event_fn);\n", + "\n", + " rubberband.mouseenter('figure_enter', mouse_event_fn);\n", + " rubberband.mouseleave('figure_leave', mouse_event_fn);\n", + "\n", + " canvas_div.on(\"wheel\", function (event) {\n", + " event = event.originalEvent;\n", + " event['data'] = 'scroll'\n", + " if (event.deltaY < 0) {\n", + " event.step = 1;\n", + " } else {\n", + " event.step = -1;\n", + " }\n", + " mouse_event_fn(event);\n", + " });\n", + "\n", + " canvas_div.append(canvas);\n", + " canvas_div.append(rubberband);\n", + "\n", + " this.rubberband = rubberband;\n", + " this.rubberband_canvas = rubberband[0];\n", + " this.rubberband_context = rubberband[0].getContext(\"2d\");\n", + " this.rubberband_context.strokeStyle = \"#000000\";\n", + "\n", + " this._resize_canvas = function(width, height) {\n", + " // Keep the size of the canvas, canvas container, and rubber band\n", + " // canvas in synch.\n", + " canvas_div.css('width', width)\n", + " canvas_div.css('height', height)\n", + "\n", + " canvas.attr('width', width * mpl.ratio);\n", + " canvas.attr('height', height * mpl.ratio);\n", + " canvas.attr('style', 'width: ' + width + 'px; height: ' + height + 'px;');\n", + "\n", + " rubberband.attr('width', width);\n", + " rubberband.attr('height', height);\n", + " }\n", + "\n", + " // Set the figure to an initial 600x600px, this will subsequently be updated\n", + " // upon first draw.\n", + " this._resize_canvas(600, 600);\n", + "\n", + " // Disable right mouse context menu.\n", + " $(this.rubberband_canvas).bind(\"contextmenu\",function(e){\n", + " return false;\n", + " });\n", + "\n", + " function set_focus () {\n", + " canvas.focus();\n", + " canvas_div.focus();\n", + " }\n", + "\n", + " window.setTimeout(set_focus, 100);\n", + "}\n", + "\n", + "mpl.figure.prototype._init_toolbar = function() {\n", + " var fig = this;\n", + "\n", + " var nav_element = $('
')\n", + " nav_element.attr('style', 'width: 100%');\n", + " this.root.append(nav_element);\n", + "\n", + " // Define a callback function for later on.\n", + " function toolbar_event(event) {\n", + " return fig.toolbar_button_onclick(event['data']);\n", + " }\n", + " function toolbar_mouse_event(event) {\n", + " return fig.toolbar_button_onmouseover(event['data']);\n", + " }\n", + "\n", + " for(var toolbar_ind in mpl.toolbar_items) {\n", + " var name = mpl.toolbar_items[toolbar_ind][0];\n", + " var tooltip = mpl.toolbar_items[toolbar_ind][1];\n", + " var image = mpl.toolbar_items[toolbar_ind][2];\n", + " var method_name = mpl.toolbar_items[toolbar_ind][3];\n", + "\n", + " if (!name) {\n", + " // put a spacer in here.\n", + " continue;\n", + " }\n", + " var button = $('');\n", + " button.click(method_name, toolbar_event);\n", + " button.mouseover(tooltip, toolbar_mouse_event);\n", + " nav_element.append(button);\n", + " }\n", + "\n", + " // Add the status bar.\n", + " var status_bar = $('');\n", + " nav_element.append(status_bar);\n", + " this.message = status_bar[0];\n", + "\n", + " // Add the close button to the window.\n", + " var buttongrp = $('
');\n", + " var button = $('');\n", + " button.click(function (evt) { fig.handle_close(fig, {}); } );\n", + " button.mouseover('Stop Interaction', toolbar_mouse_event);\n", + " buttongrp.append(button);\n", + " var titlebar = this.root.find($('.ui-dialog-titlebar'));\n", + " titlebar.prepend(buttongrp);\n", + "}\n", + "\n", + "mpl.figure.prototype._root_extra_style = function(el){\n", + " var fig = this\n", + " el.on(\"remove\", function(){\n", + "\tfig.close_ws(fig, {});\n", + " });\n", + "}\n", + "\n", + "mpl.figure.prototype._canvas_extra_style = function(el){\n", + " // this is important to make the div 'focusable\n", + " el.attr('tabindex', 0)\n", + " // reach out to IPython and tell the keyboard manager to turn it's self\n", + " // off when our div gets focus\n", + "\n", + " // location in version 3\n", + " if (IPython.notebook.keyboard_manager) {\n", + " IPython.notebook.keyboard_manager.register_events(el);\n", + " }\n", + " else {\n", + " // location in version 2\n", + " IPython.keyboard_manager.register_events(el);\n", + " }\n", + "\n", + "}\n", + "\n", + "mpl.figure.prototype._key_event_extra = function(event, name) {\n", + " var manager = IPython.notebook.keyboard_manager;\n", + " if (!manager)\n", + " manager = IPython.keyboard_manager;\n", + "\n", + " // Check for shift+enter\n", + " if (event.shiftKey && event.which == 13) {\n", + " this.canvas_div.blur();\n", + " // select the cell after this one\n", + " var index = IPython.notebook.find_cell_index(this.cell_info[0]);\n", + " IPython.notebook.select(index + 1);\n", + " }\n", + "}\n", + "\n", + "mpl.figure.prototype.handle_save = function(fig, msg) {\n", + " fig.ondownload(fig, null);\n", + "}\n", + "\n", + "\n", + "mpl.find_output_cell = function(html_output) {\n", + " // Return the cell and output element which can be found *uniquely* in the notebook.\n", + " // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n", + " // IPython event is triggered only after the cells have been serialised, which for\n", + " // our purposes (turning an active figure into a static one), is too late.\n", + " var cells = IPython.notebook.get_cells();\n", + " var ncells = cells.length;\n", + " for (var i=0; i= 3 moved mimebundle to data attribute of output\n", + " data = data.data;\n", + " }\n", + " if (data['text/html'] == html_output) {\n", + " return [cell, data, j];\n", + " }\n", + " }\n", + " }\n", + " }\n", + "}\n", + "\n", + "// Register the function which deals with the matplotlib target/channel.\n", + "// The kernel may be null if the page has been refreshed.\n", + "if (IPython.notebook.kernel != null) {\n", + " IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);\n", + "}\n" + ], + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "text/html": [ + "" + ], + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 82, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "def slope_func(state, t, system):\n", + " \n", + " y, v = state\n", + " unpack(system)\n", + " \n", + " a_grav = system.a\n", + " v = v\n", + " f_drag = -np.sign(v)* rho * v * v * C_d * area / 2\n", + " a_drag = f_drag / mass_G\n", + " a = a_grav + a_drag\n", + " return v, a\n", + "slope_func(system.init, 0, system)\n", + "run_odeint(system, slope_func)\n", + "ys = system.results.y\n", + "plot(ys)\n", + "xlabel('Time')\n", + "ylabel('Height')\n", + "title('Height of Golf Ball')" + ] + }, + { + "cell_type": "code", + "execution_count": 84, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "(97.323818198820433, 3.8999999999999999)" + ] + }, + "execution_count": 84, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "def interpolate_range(results):\n", + " ys = results.y\n", + " t_end = ys.index[-1]\n", + " \n", + " if ys[t_end] > 0:\n", + " msg = \"\"\"The final value of y is still positive;\n", + " looks like the simulation didn't run\n", + " long enough.\"\"\"\n", + " raise ValueError(msg)\n", + " \n", + " t_peak = ys.argmax()\n", + " descent = ys.loc[t_peak]\n", + " \n", + " return descent, t_peak\n", + "interpolate_range(system.results)" + ] + }, + { + "cell_type": "code", + "execution_count": 85, + "metadata": {}, + "outputs": [ + { + "data": { + "application/javascript": [ + "/* Put everything inside the global mpl namespace */\n", + "window.mpl = {};\n", + "\n", + "\n", + "mpl.get_websocket_type = function() {\n", + " if (typeof(WebSocket) !== 'undefined') {\n", + " return WebSocket;\n", + " } else if (typeof(MozWebSocket) !== 'undefined') {\n", + " return MozWebSocket;\n", + " } else {\n", + " alert('Your browser does not have WebSocket support.' +\n", + " 'Please try Chrome, Safari or Firefox ≥ 6. ' +\n", + " 'Firefox 4 and 5 are also supported but you ' +\n", + " 'have to enable WebSockets in about:config.');\n", + " };\n", + "}\n", + "\n", + "mpl.figure = function(figure_id, websocket, ondownload, parent_element) {\n", + " this.id = figure_id;\n", + "\n", + " this.ws = websocket;\n", + "\n", + " this.supports_binary = (this.ws.binaryType != undefined);\n", + "\n", + " if (!this.supports_binary) {\n", + " var warnings = document.getElementById(\"mpl-warnings\");\n", + " if (warnings) {\n", + " warnings.style.display = 'block';\n", + " warnings.textContent = (\n", + " \"This browser does not support binary websocket messages. \" +\n", + " \"Performance may be slow.\");\n", + " }\n", + " }\n", + "\n", + " this.imageObj = new Image();\n", + "\n", + " this.context = undefined;\n", + " this.message = undefined;\n", + " this.canvas = undefined;\n", + " this.rubberband_canvas = undefined;\n", + " this.rubberband_context = undefined;\n", + " this.format_dropdown = undefined;\n", + "\n", + " this.image_mode = 'full';\n", + "\n", + " this.root = $('
');\n", + " this._root_extra_style(this.root)\n", + " this.root.attr('style', 'display: inline-block');\n", + "\n", + " $(parent_element).append(this.root);\n", + "\n", + " this._init_header(this);\n", + " this._init_canvas(this);\n", + " this._init_toolbar(this);\n", + "\n", + " var fig = this;\n", + "\n", + " this.waiting = false;\n", + "\n", + " this.ws.onopen = function () {\n", + " fig.send_message(\"supports_binary\", {value: fig.supports_binary});\n", + " fig.send_message(\"send_image_mode\", {});\n", + " if (mpl.ratio != 1) {\n", + " fig.send_message(\"set_dpi_ratio\", {'dpi_ratio': mpl.ratio});\n", + " }\n", + " fig.send_message(\"refresh\", {});\n", + " }\n", + "\n", + " this.imageObj.onload = function() {\n", + " if (fig.image_mode == 'full') {\n", + " // Full images could contain transparency (where diff images\n", + " // almost always do), so we need to clear the canvas so that\n", + " // there is no ghosting.\n", + " fig.context.clearRect(0, 0, fig.canvas.width, fig.canvas.height);\n", + " }\n", + " fig.context.drawImage(fig.imageObj, 0, 0);\n", + " };\n", + "\n", + " this.imageObj.onunload = function() {\n", + " this.ws.close();\n", + " }\n", + "\n", + " this.ws.onmessage = this._make_on_message_function(this);\n", + "\n", + " this.ondownload = ondownload;\n", + "}\n", + "\n", + "mpl.figure.prototype._init_header = function() {\n", + " var titlebar = $(\n", + " '
');\n", + " var titletext = $(\n", + " '
');\n", + " titlebar.append(titletext)\n", + " this.root.append(titlebar);\n", + " this.header = titletext[0];\n", + "}\n", + "\n", + "\n", + "\n", + "mpl.figure.prototype._canvas_extra_style = function(canvas_div) {\n", + "\n", + "}\n", + "\n", + "\n", + "mpl.figure.prototype._root_extra_style = function(canvas_div) {\n", + "\n", + "}\n", + "\n", + "mpl.figure.prototype._init_canvas = function() {\n", + " var fig = this;\n", + "\n", + " var canvas_div = $('
');\n", + "\n", + " canvas_div.attr('style', 'position: relative; clear: both; outline: 0');\n", + "\n", + " function canvas_keyboard_event(event) {\n", + " return fig.key_event(event, event['data']);\n", + " }\n", + "\n", + " canvas_div.keydown('key_press', canvas_keyboard_event);\n", + " canvas_div.keyup('key_release', canvas_keyboard_event);\n", + " this.canvas_div = canvas_div\n", + " this._canvas_extra_style(canvas_div)\n", + " this.root.append(canvas_div);\n", + "\n", + " var canvas = $('');\n", + " canvas.addClass('mpl-canvas');\n", + " canvas.attr('style', \"left: 0; top: 0; z-index: 0; outline: 0\")\n", + "\n", + " this.canvas = canvas[0];\n", + " this.context = canvas[0].getContext(\"2d\");\n", + "\n", + " var backingStore = this.context.backingStorePixelRatio ||\n", + "\tthis.context.webkitBackingStorePixelRatio ||\n", + "\tthis.context.mozBackingStorePixelRatio ||\n", + "\tthis.context.msBackingStorePixelRatio ||\n", + "\tthis.context.oBackingStorePixelRatio ||\n", + "\tthis.context.backingStorePixelRatio || 1;\n", + "\n", + " mpl.ratio = (window.devicePixelRatio || 1) / backingStore;\n", + "\n", + " var rubberband = $('');\n", + " rubberband.attr('style', \"position: absolute; left: 0; top: 0; z-index: 1;\")\n", + "\n", + " var pass_mouse_events = true;\n", + "\n", + " canvas_div.resizable({\n", + " start: function(event, ui) {\n", + " pass_mouse_events = false;\n", + " },\n", + " resize: function(event, ui) {\n", + " fig.request_resize(ui.size.width, ui.size.height);\n", + " },\n", + " stop: function(event, ui) {\n", + " pass_mouse_events = true;\n", + " fig.request_resize(ui.size.width, ui.size.height);\n", + " },\n", + " });\n", + "\n", + " function mouse_event_fn(event) {\n", + " if (pass_mouse_events)\n", + " return fig.mouse_event(event, event['data']);\n", + " }\n", + "\n", + " rubberband.mousedown('button_press', mouse_event_fn);\n", + " rubberband.mouseup('button_release', mouse_event_fn);\n", + " // Throttle sequential mouse events to 1 every 20ms.\n", + " rubberband.mousemove('motion_notify', mouse_event_fn);\n", + "\n", + " rubberband.mouseenter('figure_enter', mouse_event_fn);\n", + " rubberband.mouseleave('figure_leave', mouse_event_fn);\n", + "\n", + " canvas_div.on(\"wheel\", function (event) {\n", + " event = event.originalEvent;\n", + " event['data'] = 'scroll'\n", + " if (event.deltaY < 0) {\n", + " event.step = 1;\n", + " } else {\n", + " event.step = -1;\n", + " }\n", + " mouse_event_fn(event);\n", + " });\n", + "\n", + " canvas_div.append(canvas);\n", + " canvas_div.append(rubberband);\n", + "\n", + " this.rubberband = rubberband;\n", + " this.rubberband_canvas = rubberband[0];\n", + " this.rubberband_context = rubberband[0].getContext(\"2d\");\n", + " this.rubberband_context.strokeStyle = \"#000000\";\n", + "\n", + " this._resize_canvas = function(width, height) {\n", + " // Keep the size of the canvas, canvas container, and rubber band\n", + " // canvas in synch.\n", + " canvas_div.css('width', width)\n", + " canvas_div.css('height', height)\n", + "\n", + " canvas.attr('width', width * mpl.ratio);\n", + " canvas.attr('height', height * mpl.ratio);\n", + " canvas.attr('style', 'width: ' + width + 'px; height: ' + height + 'px;');\n", + "\n", + " rubberband.attr('width', width);\n", + " rubberband.attr('height', height);\n", + " }\n", + "\n", + " // Set the figure to an initial 600x600px, this will subsequently be updated\n", + " // upon first draw.\n", + " this._resize_canvas(600, 600);\n", + "\n", + " // Disable right mouse context menu.\n", + " $(this.rubberband_canvas).bind(\"contextmenu\",function(e){\n", + " return false;\n", + " });\n", + "\n", + " function set_focus () {\n", + " canvas.focus();\n", + " canvas_div.focus();\n", + " }\n", + "\n", + " window.setTimeout(set_focus, 100);\n", + "}\n", + "\n", + "mpl.figure.prototype._init_toolbar = function() {\n", + " var fig = this;\n", + "\n", + " var nav_element = $('
')\n", + " nav_element.attr('style', 'width: 100%');\n", + " this.root.append(nav_element);\n", + "\n", + " // Define a callback function for later on.\n", + " function toolbar_event(event) {\n", + " return fig.toolbar_button_onclick(event['data']);\n", + " }\n", + " function toolbar_mouse_event(event) {\n", + " return fig.toolbar_button_onmouseover(event['data']);\n", + " }\n", + "\n", + " for(var toolbar_ind in mpl.toolbar_items) {\n", + " var name = mpl.toolbar_items[toolbar_ind][0];\n", + " var tooltip = mpl.toolbar_items[toolbar_ind][1];\n", + " var image = mpl.toolbar_items[toolbar_ind][2];\n", + " var method_name = mpl.toolbar_items[toolbar_ind][3];\n", + "\n", + " if (!name) {\n", + " // put a spacer in here.\n", + " continue;\n", + " }\n", + " var button = $('');\n", + " button.click(method_name, toolbar_event);\n", + " button.mouseover(tooltip, toolbar_mouse_event);\n", + " nav_element.append(button);\n", + " }\n", + "\n", + " // Add the status bar.\n", + " var status_bar = $('');\n", + " nav_element.append(status_bar);\n", + " this.message = status_bar[0];\n", + "\n", + " // Add the close button to the window.\n", + " var buttongrp = $('
');\n", + " var button = $('');\n", + " button.click(function (evt) { fig.handle_close(fig, {}); } );\n", + " button.mouseover('Stop Interaction', toolbar_mouse_event);\n", + " buttongrp.append(button);\n", + " var titlebar = this.root.find($('.ui-dialog-titlebar'));\n", + " titlebar.prepend(buttongrp);\n", + "}\n", + "\n", + "mpl.figure.prototype._root_extra_style = function(el){\n", + " var fig = this\n", + " el.on(\"remove\", function(){\n", + "\tfig.close_ws(fig, {});\n", + " });\n", + "}\n", + "\n", + "mpl.figure.prototype._canvas_extra_style = function(el){\n", + " // this is important to make the div 'focusable\n", + " el.attr('tabindex', 0)\n", + " // reach out to IPython and tell the keyboard manager to turn it's self\n", + " // off when our div gets focus\n", + "\n", + " // location in version 3\n", + " if (IPython.notebook.keyboard_manager) {\n", + " IPython.notebook.keyboard_manager.register_events(el);\n", + " }\n", + " else {\n", + " // location in version 2\n", + " IPython.keyboard_manager.register_events(el);\n", + " }\n", + "\n", + "}\n", + "\n", + "mpl.figure.prototype._key_event_extra = function(event, name) {\n", + " var manager = IPython.notebook.keyboard_manager;\n", + " if (!manager)\n", + " manager = IPython.keyboard_manager;\n", + "\n", + " // Check for shift+enter\n", + " if (event.shiftKey && event.which == 13) {\n", + " this.canvas_div.blur();\n", + " // select the cell after this one\n", + " var index = IPython.notebook.find_cell_index(this.cell_info[0]);\n", + " IPython.notebook.select(index + 1);\n", + " }\n", + "}\n", + "\n", + "mpl.figure.prototype.handle_save = function(fig, msg) {\n", + " fig.ondownload(fig, null);\n", + "}\n", + "\n", + "\n", + "mpl.find_output_cell = function(html_output) {\n", + " // Return the cell and output element which can be found *uniquely* in the notebook.\n", + " // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n", + " // IPython event is triggered only after the cells have been serialised, which for\n", + " // our purposes (turning an active figure into a static one), is too late.\n", + " var cells = IPython.notebook.get_cells();\n", + " var ncells = cells.length;\n", + " for (var i=0; i= 3 moved mimebundle to data attribute of output\n", + " data = data.data;\n", + " }\n", + " if (data['text/html'] == html_output) {\n", + " return [cell, data, j];\n", + " }\n", + " }\n", + " }\n", + " }\n", + "}\n", + "\n", + "// Register the function which deals with the matplotlib target/channel.\n", + "// The kernel may be null if the page has been refreshed.\n", + "if (IPython.notebook.kernel != null) {\n", + " IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);\n", + "}\n" + ], + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "text/html": [ + "" + ], + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 87, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "numBs = linspace(1, 25, 25)\n", + "sweep = SweepSeries()\n", + "\n", + "for numB in numBs:\n", + " peak = range_func(numB, condition)\n", + " print(numB, peak)\n", + " sweep[numB] = peak\n", + "newfig()\n", + "plot(sweep, 'bs')\n", + "xlabel('Number of Basketball')\n", + "ylabel('Maximum Height')\n", + "title('Maximum Height vs. Number of Basketball below Golf Ball')" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "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": "3.6.1" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +}