From c658a438aca812e4c2e38e6a0931e0c951d5e0e8 Mon Sep 17 00:00:00 2001 From: ChristopherLather Date: Wed, 6 Sep 2017 20:03:15 -0400 Subject: [PATCH 01/10] Adding chap01mine --- code/chap01mine.ipynb | 6925 +++++++++++++++++++++++++++++++++++++++++ 1 file changed, 6925 insertions(+) create mode 100644 code/chap01mine.ipynb diff --git a/code/chap01mine.ipynb b/code/chap01mine.ipynb new file mode 100644 index 00000000..e0780fe9 --- /dev/null +++ b/code/chap01mine.ipynb @@ -0,0 +1,6925 @@ +{ + "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": "code", + "execution_count": 49, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Hello\n" + ] + } + ], + "source": [ + "print('Hello')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This is text." + ] + }, + { + "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": 160, + "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", + "%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 *\n", + "\n", + "print('If this cell runs successfully, it produces no output other than this message.')" + ] + }, + { + "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": 161, + "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": 162, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 162, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "UNITS " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Create a variable named `a` and display its value:" + ] + }, + { + "cell_type": "code", + "execution_count": 163, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "9.8 meter/second2" + ], + "text/latex": [ + "$9.8 \\frac{meter}{second^{2}}$" + ], + "text/plain": [ + "" + ] + }, + "execution_count": 163, + "metadata": {}, + "output_type": "execute_result" + } + ], + "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": 164, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "4 second" + ], + "text/latex": [ + "$4 second$" + ], + "text/plain": [ + "" + ] + }, + "execution_count": 164, + "metadata": {}, + "output_type": "execute_result" + } + ], + "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": 165, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "156.8 meter" + ], + "text/latex": [ + "$156.8 meter$" + ], + "text/plain": [ + "" + ] + }, + "execution_count": 165, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "h = a * t**2\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": 166, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "8.817885349720552 second" + ], + "text/latex": [ + "$8.817885349720552 second$" + ], + "text/plain": [ + "" + ] + }, + "execution_count": 166, + "metadata": {}, + "output_type": "execute_result" + } + ], + "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": 167, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "86.41527642726142 meter/second" + ], + "text/latex": [ + "$86.41527642726142 \\frac{meter}{second}$" + ], + "text/plain": [ + "" + ] + }, + "execution_count": 167, + "metadata": {}, + "output_type": "execute_result" + } + ], + "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": 168, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "mile = UNITS.mile\n", + "hour= UNITS.hour" + ] + }, + { + "cell_type": "code", + "execution_count": 169, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "193.30546802805438 mile/hour" + ], + "text/latex": [ + "$193.30546802805438 \\frac{mile}{hour}$" + ], + "text/plain": [ + "" + ] + }, + "execution_count": 169, + "metadata": {}, + "output_type": "execute_result" + } + ], + "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": 257, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Total time 20.070408163265306\n" + ] + } + ], + "source": [ + "# Solution goes here\n", + "u=0\n", + "v=20\n", + "a=9.8\n", + "s_first=381\n", + "\n", + "t_first=(v-u)/a\n", + "s_second=s_first-t_first*((v+u)/2)\n", + "t_second=s_second/v\n", + "t_sum=t_first+t_second\n", + "print('Total time', t_sum)" + ] + }, + { + "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": 171, + "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": 172, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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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": 175, + "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": [ + "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": 185, + "metadata": {}, + "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": 186, + "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": 187, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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" + ], + "text/plain": [ + "olin 10\n", + "wellesley 2\n", + "dtype: int64" + ] + }, + "execution_count": 188, + "metadata": {}, + "output_type": "execute_result" + } + ], + "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": 189, + "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": 190, + "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": 191, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Saving figure to file chap01_fig01.pdf\n" + ] + } + ], + "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": 192, + "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": 193, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Running move_bike_debug with argument 2\n" + ] + } + ], + "source": [ + "move_bike_debug(2)" + ] + }, + { + "cell_type": "code", + "execution_count": 194, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Running bike_to_olin_debug\n", + "Running move_bike_debug with argument -1\n" + ] + } + ], + "source": [ + "bike_to_olin_debug()" + ] + }, + { + "cell_type": "code", + "execution_count": 195, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Running bike_to_olin_debug\n", + "Running move_bike_debug with argument -1\n" + ] + } + ], + "source": [ + "bike_to_olin_debug()" + ] + }, + { + "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": 196, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "True" + ] + }, + "execution_count": 196, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "flip(1)" + ] + }, + { + "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": 197, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "heads\n" + ] + } + ], + "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": 198, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "heads\n" + ] + } + ], + "source": [ + "if flip(0.7):\n", + " print('heads')\n", + "else:\n", + " print('tails')" + ] + }, + { + "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": 199, + "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": [ + "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": 208, + "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": 209, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "p1 -> 0.5\n", + "p2 -> 0.5\n" + ] + } + ], + "source": [ + "step()\n", + "plot_state()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "If you provide one argument, it overrides the first parameter." + ] + }, + { + "cell_type": "code", + "execution_count": 210, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "p1 -> 0.4\n", + "p2 -> 0.5\n" + ] + } + ], + "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": 211, + "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()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "You can specify the names of the parameters you want to override." + ] + }, + { + "cell_type": "code", + "execution_count": 212, + "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()" + ] + }, + { + "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": 213, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "p1 -> 0.5\n", + "p2 -> 0.2\n" + ] + } + ], + "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": 214, + "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()" + ] + }, + { + "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": 215, + "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", + "\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": 216, + "metadata": {}, + "outputs": [], + "source": [ + "def decorate():\n", + " legend(loc='best')" + ] + }, + { + "cell_type": "code", + "execution_count": 217, + "metadata": {}, + "outputs": [], + "source": [ + "decorate()" + ] + }, + { + "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": 218, + "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": 219, + "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": [ + "bikeshare = System(olin=5, wellesley=5)\n", + "newfig()\n", + "plot_state()" + ] + }, + { + "cell_type": "code", + "execution_count": 254, + "metadata": {}, + "outputs": [], + "source": [ + "run_steps(5,0.4,0.6)" + ] + }, + { + "cell_type": "code", + "execution_count": 235, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "bike_to_olin()" + ] + }, + { + "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 df38863edc8d52c9ffe5d5a15eb696f376291e1e Mon Sep 17 00:00:00 2001 From: Christopher Lather Date: Wed, 13 Sep 2017 21:53:53 -0400 Subject: [PATCH 02/10] Adding chap02mine --- code/chap02mine.ipynb | 8453 +++++++++++++++++++++++++++++++++++++++++ 1 file changed, 8453 insertions(+) create mode 100644 code/chap02mine.ipynb diff --git a/code/chap02mine.ipynb b/code/chap02mine.ipynb new file mode 100644 index 00000000..e75251a2 --- /dev/null +++ b/code/chap02mine.ipynb @@ -0,0 +1,8453 @@ +{ + "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 qt5\n", + "\n", + "from modsim import *" + ] + }, + { + "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():\n", + " \"\"\"Add a legend and label the axes.\n", + " \"\"\"\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": [ + "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": [ + "
\n", + "\n", + "\n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + "
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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 = $('
');\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": "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" + ] + } + ], + "source": [ + "bikeshare = System(olin=10, wellesley=2)\n", + "newfig()\n", + "plot_system(bikeshare)\n", + "decorate()\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": null, + "metadata": {}, + "outputs": [], + "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": 13, + "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": 14, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "True" + ] + }, + "execution_count": 14, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "x < 6" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "You can use `==` in an `if` statement." + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "nah fam\n" + ] + } + ], + "source": [ + "if x == 6:\n", + " print('yes, x is 5')\n", + "else:\n", + " print ('nah fam')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "But if you use `=` in an `if` statement, you get an error." + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": {}, + "outputs": [ + { + "ename": "SyntaxError", + "evalue": "invalid syntax (, 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 if x = 5:\u001b[0m\n\u001b[1;37m ^\u001b[0m\n\u001b[1;31mSyntaxError\u001b[0m\u001b[1;31m:\u001b[0m invalid syntax\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')" + ] + }, + { + "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": 17, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "bikeshare = System(olin=10, wellesley=2, \n", + " olin_empty=0, wellesley_empty=0, clock=0)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Next we need a version of `move_bike` that updates the metrics." + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "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\n", + " \n", + " # system.clock += 1\n", + " # print(system.clock)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now when we run a simulation, it keeps track of unhappy customers." + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "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" + }, + { + "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" + ] + } + ], + "source": [ + "# Solution goes here\n", + "newfig()\n", + "plot_system(bikeshare)\n", + "decorate()\n", + "run_steps(bikeshare, 70, 0.4, 0.2)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "After the simulation, check the final value of `clock`." + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "70\n" + ] + } + ], + "source": [ + "print(bikeshare.clock)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Exercise:** Now suppose we'd like to know how long it takes to run out of bikes at either location. Modify `move_bike` so the first time a student arrives at Olin and doesn't find a bike, it records the value of `clock` in a system variable.\n", + "\n", + "Hint: create a system variable named `t_first_empty` and initialize it to `None`, which is a special value (like `True` and `False`) that can be used to indicate a \"special case\".\n", + "\n", + "Test your code by running a simulation for 60 minutes and checking the metrics." + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Yup, example is None.\n" + ] + } + ], + "source": [ + "example = None\n", + "\n", + "if example == None:\n", + " print('Yup, example is None.')" + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "# Solution goes here\n", + "bikeshare = System(olin=10, wellesley=2, \n", + " olin_empty=0, wellesley_empty=0, clock=0, t_first_empty=-1)\n", + "\n", + "def move_bike(system, n):\n", + " olin_temp = system.olin - n\n", + " if olin_temp < 0:\n", + " system.olin_empty += 1\n", + " if system.t_first_empty == -1:\n", + " system.t_first_empty = system.clock\n", + " return\n", + " \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": "code", + "execution_count": 28, + "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", + "for p1 in p1_array:\n", + " system = run_simulation(p1=p1)\n", + " plot(p1, system.olin_empty, 'rs', label='olin')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "As always, we should decorate the figure. This version of `decorate` takes `xlabel` as a parameter, for reasons you will see soon." + ] + }, + { + "cell_type": "code", + "execution_count": 82, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def decorate(xlabel):\n", + " legend(loc='best')\n", + " label_axes(title='Olin-Wellesley Bikeshare',\n", + " xlabel=xlabel, \n", + " ylabel='Number of unhappy customers')" + ] + }, + { + "cell_type": "code", + "execution_count": 83, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "decorate(xlabel='Arrival rate at Olin (p1 in customers/min)')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Exercise:** Wrap this code in a function named `parameter_sweep` that takes an array called `p1_array` as a parameter. It should create a new figure, run a simulation for each value of `p1` in `p1_array`, and plot the results.\n", + "\n", + "Once you have the function working, modify it so it also plots the number of unhappy customers at Wellesley. Looking at the plot, can you estimate a range of values for `p1` that minimizes the total number of unhappy customers?" + ] + }, + { + "cell_type": "code", + "execution_count": 94, + "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", + "def parameter_sweep2(p2_array):\n", + " for p2 in p2_array:\n", + " system = run_simulation(p2=p2)\n", + " plot(p1, system.olin_empty, 'rs', label='olin')\n", + " plot(p2, system.wellesley_empty, 'bo-', label='wellesley')\n", + " \n", + "parameter_sweep2(p2_array)" + ] + }, + { + "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": 103, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "# Solution goes here\n", + "def run_simulation(num_steps=60, p1=0.4, p2=0.2, plot_flag=False):\n", + " bikeshare = System(olin=10, wellesley=2,olin_empty=0, wellesley_empty=0)\n", + " run_steps(bikeshare, num_steps, p1, p2, plot_flag)\n", + " return bikeshare" + ] + }, + { + "cell_type": "code", + "execution_count": 67, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "# Solution goes here\n" + ] + }, + { + "cell_type": "code", + "execution_count": 68, + "metadata": { + "collapsed": true, + "scrolled": false + }, + "outputs": [], + "source": [ + "# Solution goes here" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": true + }, + "source": [ + "**Exercise:** The code below runs a simulation with the same parameters 10 times and computes the average number of unhappy customers.\n", + "\n", + "1. Wrap this code in a function called `run_simulations` that takes `num_runs` as a parameter.\n", + "\n", + "2. Test `run_simulations`, and increase `num_runs` until the results are reasonably consistent from one run to the next.\n", + "\n", + "3. Generalize `run_simulations` so it also takes the initial value of `olin` as a parameter.\n", + "\n", + "4. Run the generalized version with `olin=12`. How much do the two extra bikes decrease the average number of unhappy customers.\n", + "\n", + "5. Make a plot that shows the average number of unhappy customers as a function of the initial number of bikes at Olin." + ] + }, + { + "cell_type": "code", + "execution_count": 69, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "# Solution goes here" + ] + }, + { + "cell_type": "code", + "execution_count": 70, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "# Solution goes here" + ] + }, + { + "cell_type": "code", + "execution_count": 71, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "# Solution goes here" + ] + }, + { + "cell_type": "code", + "execution_count": 72, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "# Solution goes here" + ] + }, + { + "cell_type": "code", + "execution_count": 73, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "# Solution goes here" + ] + }, + { + "cell_type": "code", + "execution_count": 74, + "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": [] + } + ], + "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 dee1a93f2f8fd3be78e2a70a4d7e95dee4c0b59a Mon Sep 17 00:00:00 2001 From: Christopher Lather Date: Thu, 14 Sep 2017 15:58:44 -0400 Subject: [PATCH 03/10] idk --- code/chap01.ipynb | 159 +++++++++++++++++++++++++++++++++++----------- 1 file changed, 121 insertions(+), 38 deletions(-) diff --git a/code/chap01.ipynb b/code/chap01.ipynb index b0379fbd..67e7fca3 100644 --- a/code/chap01.ipynb +++ b/code/chap01.ipynb @@ -97,7 +97,15 @@ "cell_type": "code", "execution_count": 1, "metadata": {}, - "outputs": [], + "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", @@ -168,7 +176,9 @@ { "cell_type": "code", "execution_count": 3, - "metadata": {}, + "metadata": { + "collapsed": true + }, "outputs": [], "source": [ "a = 9.8 * meter / second**2\n", @@ -187,7 +197,9 @@ { "cell_type": "code", "execution_count": 4, - "metadata": {}, + "metadata": { + "collapsed": true + }, "outputs": [], "source": [ "t = 4 * second\n", @@ -228,7 +240,9 @@ { "cell_type": "code", "execution_count": 6, - "metadata": {}, + "metadata": { + "collapsed": true + }, "outputs": [], "source": [ "h = 381 * meter\n", @@ -248,7 +262,9 @@ { "cell_type": "code", "execution_count": 7, - "metadata": {}, + "metadata": { + "collapsed": true + }, "outputs": [], "source": [ "v = a * t\n", @@ -279,7 +295,9 @@ { "cell_type": "code", "execution_count": 9, - "metadata": {}, + "metadata": { + "collapsed": true + }, "outputs": [], "source": [ "v.to(mile/hour)" @@ -297,7 +315,9 @@ { "cell_type": "code", "execution_count": 10, - "metadata": {}, + "metadata": { + "collapsed": true + }, "outputs": [], "source": [ "# Solution goes here" @@ -338,7 +358,9 @@ { "cell_type": "code", "execution_count": 13, - "metadata": {}, + "metadata": { + "collapsed": true + }, "outputs": [], "source": [ "bikeshare" @@ -354,7 +376,9 @@ { "cell_type": "code", "execution_count": 14, - "metadata": {}, + "metadata": { + "collapsed": true + }, "outputs": [], "source": [ "bikeshare.olin" @@ -364,6 +388,7 @@ "cell_type": "code", "execution_count": 15, "metadata": { + "collapsed": true, "scrolled": true }, "outputs": [], @@ -401,7 +426,9 @@ { "cell_type": "code", "execution_count": 16, - "metadata": {}, + "metadata": { + "collapsed": true + }, "outputs": [], "source": [ "newfig()\n", @@ -419,7 +446,9 @@ { "cell_type": "code", "execution_count": 17, - "metadata": {}, + "metadata": { + "collapsed": true + }, "outputs": [], "source": [ "bikeshare.olin -= 1\n", @@ -456,7 +485,9 @@ { "cell_type": "code", "execution_count": 19, - "metadata": {}, + "metadata": { + "collapsed": true + }, "outputs": [], "source": [ "# Solution goes here" @@ -514,7 +545,9 @@ { "cell_type": "code", "execution_count": 22, - "metadata": {}, + "metadata": { + "collapsed": true + }, "outputs": [], "source": [ "bike_to_wellesley()\n", @@ -534,7 +567,9 @@ { "cell_type": "code", "execution_count": 23, - "metadata": {}, + "metadata": { + "collapsed": true + }, "outputs": [], "source": [ "bike_to_wellesley" @@ -557,7 +592,9 @@ { "cell_type": "code", "execution_count": 24, - "metadata": {}, + "metadata": { + "collapsed": true + }, "outputs": [], "source": [ "# Solution goes here" @@ -580,7 +617,9 @@ { "cell_type": "code", "execution_count": 25, - "metadata": {}, + "metadata": { + "collapsed": true + }, "outputs": [], "source": [ "bikeshare = System(olin=10, wellesley=2)\n", @@ -642,7 +681,9 @@ { "cell_type": "code", "execution_count": 28, - "metadata": {}, + "metadata": { + "collapsed": true + }, "outputs": [], "source": [ "bike_to_wellesley()\n", @@ -660,7 +701,9 @@ { "cell_type": "code", "execution_count": 29, - "metadata": {}, + "metadata": { + "collapsed": true + }, "outputs": [], "source": [ "bike_to_olin()\n", @@ -725,7 +768,9 @@ { "cell_type": "code", "execution_count": 32, - "metadata": {}, + "metadata": { + "collapsed": true + }, "outputs": [], "source": [ "savefig('chap01_fig01.pdf')" @@ -765,7 +810,9 @@ { "cell_type": "code", "execution_count": 34, - "metadata": {}, + "metadata": { + "collapsed": true + }, "outputs": [], "source": [ "# Solution goes here" @@ -774,7 +821,9 @@ { "cell_type": "code", "execution_count": 35, - "metadata": {}, + "metadata": { + "collapsed": true + }, "outputs": [], "source": [ "# Solution goes here" @@ -783,7 +832,9 @@ { "cell_type": "code", "execution_count": 36, - "metadata": {}, + "metadata": { + "collapsed": true + }, "outputs": [], "source": [ "# Solution goes here" @@ -808,7 +859,9 @@ { "cell_type": "code", "execution_count": 37, - "metadata": {}, + "metadata": { + "collapsed": true + }, "outputs": [], "source": [ "flip(0.7)" @@ -845,7 +898,9 @@ { "cell_type": "code", "execution_count": 39, - "metadata": {}, + "metadata": { + "collapsed": true + }, "outputs": [], "source": [ "if flip(0.7):\n", @@ -864,7 +919,9 @@ { "cell_type": "code", "execution_count": 40, - "metadata": {}, + "metadata": { + "collapsed": true + }, "outputs": [], "source": [ "bikeshare = System(olin=10, wellesley=2)\n", @@ -882,7 +939,9 @@ { "cell_type": "code", "execution_count": 41, - "metadata": {}, + "metadata": { + "collapsed": true + }, "outputs": [], "source": [ "if flip(0.7):\n", @@ -903,7 +962,9 @@ { "cell_type": "code", "execution_count": 42, - "metadata": {}, + "metadata": { + "collapsed": true + }, "outputs": [], "source": [ "if flip(0.6):\n", @@ -949,7 +1010,9 @@ { "cell_type": "code", "execution_count": 44, - "metadata": {}, + "metadata": { + "collapsed": true + }, "outputs": [], "source": [ "step()\n", @@ -1021,7 +1084,9 @@ { "cell_type": "code", "execution_count": 47, - "metadata": {}, + "metadata": { + "collapsed": true + }, "outputs": [], "source": [ "bikeshare = System(olin=10, wellesley=2)\n", @@ -1066,7 +1131,9 @@ { "cell_type": "code", "execution_count": 49, - "metadata": {}, + "metadata": { + "collapsed": true + }, "outputs": [], "source": [ "step()\n", @@ -1083,7 +1150,9 @@ { "cell_type": "code", "execution_count": 50, - "metadata": {}, + "metadata": { + "collapsed": true + }, "outputs": [], "source": [ "step(0.4)\n", @@ -1100,7 +1169,9 @@ { "cell_type": "code", "execution_count": 51, - "metadata": {}, + "metadata": { + "collapsed": true + }, "outputs": [], "source": [ "step(0.4, 0.2)\n", @@ -1117,7 +1188,9 @@ { "cell_type": "code", "execution_count": 52, - "metadata": {}, + "metadata": { + "collapsed": true + }, "outputs": [], "source": [ "step(p1=0.4, p2=0.2)\n", @@ -1134,7 +1207,9 @@ { "cell_type": "code", "execution_count": 53, - "metadata": {}, + "metadata": { + "collapsed": true + }, "outputs": [], "source": [ "step(p2=0.2)\n", @@ -1151,7 +1226,9 @@ { "cell_type": "code", "execution_count": 54, - "metadata": {}, + "metadata": { + "collapsed": true + }, "outputs": [], "source": [ "step(0.4, p2=0.2)\n", @@ -1255,7 +1332,9 @@ { "cell_type": "code", "execution_count": 59, - "metadata": {}, + "metadata": { + "collapsed": true + }, "outputs": [], "source": [ "bikeshare = System(olin=10, wellesley=2)\n", @@ -1314,7 +1393,9 @@ { "cell_type": "code", "execution_count": 62, - "metadata": {}, + "metadata": { + "collapsed": true + }, "outputs": [], "source": [ "for i in range(52):\n", @@ -1345,7 +1426,9 @@ { "cell_type": "code", "execution_count": 64, - "metadata": {}, + "metadata": { + "collapsed": true + }, "outputs": [], "source": [ "# Solution goes here" From 4f1da9297d5089f1e0a965afaefffb3222770822 Mon Sep 17 00:00:00 2001 From: Christopher Lather Date: Wed, 20 Sep 2017 17:24:01 -0400 Subject: [PATCH 04/10] adding chapter 3 --- code/chap03mine.ipynb | 3982 +++++++++++++++++++++++++++++++++++++++++ 1 file changed, 3982 insertions(+) create mode 100644 code/chap03mine.ipynb diff --git a/code/chap03mine.ipynb b/code/chap03mine.ipynb new file mode 100644 index 00000000..f050c2cd --- /dev/null +++ b/code/chap03mine.ipynb @@ -0,0 +1,3982 @@ +{ + "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", + "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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censusprbunmaddisonhydetantonbirabenmjthomlinsondurandclark
Year
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\n", + "

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": 20, + "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": 21, + "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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\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": 22, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "un = table2.un / 1e9" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "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": 24, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "1.2862470293832287" + ] + }, + "execution_count": 24, + "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": 25, + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "ename": "NameError", + "evalue": "name 'us' 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[1;32m----> 1\u001b[1;33m \u001b[0mcensus\u001b[0m \u001b[1;33m-\u001b[0m \u001b[0mus\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m", + "\u001b[1;31mNameError\u001b[0m: name 'us' is not defined" + ] + } + ], + "source": [ + "census - us" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "data": { + "text/plain": [ + "Year\n", + "1950 0.032480\n", + "1951 0.022089\n", + "1952 0.017480\n", + "1953 0.016188\n", + "1954 0.017056\n", + "1955 0.020448\n", + "1956 0.023728\n", + "1957 0.028307\n", + "1958 0.032107\n", + "1959 0.030321\n", + "1960 0.016999\n", + "1961 0.001137\n", + "1962 0.000978\n", + "1963 0.008650\n", + "1964 0.017462\n", + "1965 0.021303\n", + "1966 0.023203\n", + "1967 0.021812\n", + "1968 0.020639\n", + "1969 0.021050\n", + "1970 0.021525\n", + "1971 0.023573\n", + "1972 0.023695\n", + "1973 0.022914\n", + "1974 0.021304\n", + "1975 0.018063\n", + "1976 0.014049\n", + "1977 0.011268\n", + "1978 0.008441\n", + "1979 0.007486\n", + " ... \n", + "1986 0.012805\n", + "1987 0.018115\n", + "1988 0.023658\n", + "1989 0.028560\n", + "1990 0.031861\n", + "1991 0.037323\n", + "1992 0.038763\n", + "1993 0.040597\n", + "1994 0.042404\n", + "1995 0.042619\n", + "1996 0.041576\n", + "1997 0.040716\n", + "1998 0.040090\n", + "1999 0.039403\n", + "2000 0.039129\n", + "2001 0.038928\n", + "2002 0.038837\n", + "2003 0.039401\n", + "2004 0.040006\n", + "2005 0.041050\n", + "2006 0.041964\n", + "2007 0.043192\n", + "2008 0.044599\n", + "2009 0.046508\n", + "2010 0.049851\n", + "2011 0.053943\n", + "2012 0.057723\n", + "2013 0.061092\n", + "2014 0.065061\n", + "2015 0.092982\n", + "Length: 66, dtype: float64" + ] + }, + "execution_count": 26, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "abs(census - un)" + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "data": { + "text/plain": [ + "Year\n", + "1950 0.012862\n", + "1951 0.008585\n", + "1952 0.006674\n", + "1953 0.006072\n", + "1954 0.006286\n", + "1955 0.007404\n", + "1956 0.008439\n", + "1957 0.009887\n", + "1958 0.011011\n", + "1959 0.010208\n", + "1960 0.005617\n", + "1961 0.000369\n", + "1962 0.000311\n", + "1963 0.002702\n", + "1964 0.005350\n", + "1965 0.006399\n", + "1966 0.006829\n", + "1967 0.006289\n", + "1968 0.005827\n", + "1969 0.005821\n", + "1970 0.005832\n", + "1971 0.006258\n", + "1972 0.006166\n", + "1973 0.005847\n", + "1974 0.005332\n", + "1975 0.004437\n", + "1976 0.003388\n", + "1977 0.002670\n", + "1978 0.001965\n", + "1979 0.001712\n", + " ... \n", + "1986 0.002585\n", + "1987 0.003591\n", + "1988 0.004604\n", + "1989 0.005461\n", + "1990 0.005988\n", + "1991 0.006900\n", + "1992 0.007054\n", + "1993 0.007277\n", + "1994 0.007490\n", + "1995 0.007423\n", + "1996 0.007142\n", + "1997 0.006903\n", + "1998 0.006709\n", + "1999 0.006511\n", + "2000 0.006386\n", + "2001 0.006274\n", + "2002 0.006183\n", + "2003 0.006197\n", + "2004 0.006216\n", + "2005 0.006302\n", + "2006 0.006365\n", + "2007 0.006473\n", + "2008 0.006604\n", + "2009 0.006805\n", + "2010 0.007208\n", + "2011 0.007708\n", + "2012 0.008153\n", + "2013 0.008530\n", + "2014 0.008982\n", + "2015 0.012652\n", + "Length: 66, dtype: float64" + ] + }, + "execution_count": 27, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "abs(census - un) / un" + ] + }, + { + "cell_type": "code", + "execution_count": 29, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "0.012862470293832286" + ] + }, + "execution_count": 29, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "max (abs(census - un) / un)" + ] + }, + { + "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": 30, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "2.5576286540000002" + ] + }, + "execution_count": 30, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "census[1950]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "And the last element." + ] + }, + { + "cell_type": "code", + "execution_count": 31, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "7.2564900110000004" + ] + }, + "execution_count": 31, + "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": 32, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "(1950, 2015)" + ] + }, + "execution_count": 32, + "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": 33, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "0.07229017472307693" + ] + }, + "execution_count": 33, + "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": 34, + "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": 35, + "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": 35, + "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": 40, + "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": 37, + "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 1970 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": 41, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Saving figure to file chap03-fig02.pdf\n" + ] + }, + { + "data": { + "image/png": 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5ykfs8vLyKj9jIe7HlZwrrI9eT1pBGmhAlabEu7wZVgbu7Pn6Ip1D3HB0rHxO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\n5RQVFUXe3t5UVlamsQyvW39TUxMFBQXRkiVLqLC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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Solution goes here\n", + "first_year = 1970\n", + "last_year = census.index[-1]\n", + "first_year, last_year\n", + "\n", + "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\n", + "\n", + "results = TimeSeries()\n", + "\n", + "results[1970] = census[1970]\n", + "results\n", + "\n", + "for t in linrange(1970, 2015):\n", + " results[t+1] = results[t] + annual_growth\n", + "\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": 42, + "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": 43, + "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": 44, + "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": 45, + "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": 46, + "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": 47, + "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": 48, + "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": 72, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "# Solution goes here\n", + "def run_simulation1b(system):\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.births - system.deathrate * results[t]\n", + " system.results = results" + ] + }, + { + "cell_type": "code", + "execution_count": 73, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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1+Q+Wu7s7Bw4coHXr1pSUlLBs2TJ5BcPAwIC///6b6OhoPvroI7S1tTly5Aj6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\nyckJHh4evX7uLw6k42j6DyjVSYVRkha8vc3BAw9DdYfipVE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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Solution goes here\n", + "system.deathrate = 0.01\n", + "system.births = 0.12\n", + "\n", + "run_simulation1b(system)\n", + "plot_results(system, title='Constant births, proportional death')" + ] + }, + { + "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": 58, + "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": 59, + "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": 60, + "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": 90, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "# Solution goes here\n", + "def run_simulation2b(system):\n", + " results = TimeSeries()\n", + " results[system.t0] = system.p0\n", + " for t in linrange(system.t0, system.t_end):\n", + " growth = results[t] * system.alpha\n", + " results[t+1] = results[t] + growth\n", + " system.results = results" + ] + }, + { + "cell_type": "code", + "execution_count": 101, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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tasWQ9kMY7TKayPBIMjPTcXGpqoxbUlKCUqlUK0TYEtWa/O9eHnD58uWNEozQ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\nxoYKwRCiUPRAZMxHdnU2fiz7Ee3Kdji5mKK9xRw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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Solution goes here\n", + "#system.deathrate = 0.01\n", + "#system.births = 0.12\n", + "\n", + "system.alpha = 0.01685\n", + "\n", + "run_simulation2b(system)\n", + "plot_results(system, title='Alpha')" + ] + }, + { + "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": 108, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def update_func1(pop, t, system):\n", + " print(pop)\n", + " print(t)\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", + " 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": 109, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 109, + "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": 110, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "function" + ] + }, + "execution_count": 110, + "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": 111, + "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": 112, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "2.557628654\n", + "1950.0\n", + "2.60110834112\n", + "1951.0\n", + "2.64532718292\n", + "1952.0\n", + "2.69029774503\n", + "1953.0\n", + "2.73603280669\n", + "1954.0\n", + "2.78254536441\n", + "1955.0\n", + "2.8298486356\n", + "1956.0\n", + "2.87795606241\n", + "1957.0\n", + "2.92688131547\n", + "1958.0\n", + "2.97663829783\n", + "1959.0\n", + "3.02724114889\n", + "1960.0\n", + "3.07870424842\n", + "1961.0\n", + "3.13104222065\n", + "1962.0\n", + "3.1842699384\n", + "1963.0\n", + "3.23840252735\n", + "1964.0\n", + "3.29345537032\n", + "1965.0\n", + "3.34944411161\n", + "1966.0\n", + "3.40638466151\n", + "1967.0\n", + "3.46429320075\n", + "1968.0\n", + "3.52318618517\n", + "1969.0\n", + "3.58308035032\n", + "1970.0\n", + "3.64399271627\n", + "1971.0\n", + "3.70594059245\n", + "1972.0\n", + "3.76894158252\n", + "1973.0\n", + "3.83301358942\n", + "1974.0\n", + "3.89817482044\n", + "1975.0\n", + "3.96444379239\n", + "1976.0\n", + "4.03183933686\n", + "1977.0\n", + "4.10038060559\n", + "1978.0\n", + "4.17008707588\n", + "1979.0\n", + "4.24097855617\n", + "1980.0\n", + "4.31307519163\n", + "1981.0\n", + "4.38639746988\n", + "1982.0\n", + "4.46096622687\n", + "1983.0\n", + "4.53680265273\n", + "1984.0\n", + "4.61392829783\n", + "1985.0\n", + "4.69236507889\n", + "1986.0\n", + "4.77213528523\n", + "1987.0\n", + "4.85326158508\n", + "1988.0\n", + "4.93576703202\n", + "1989.0\n", + "5.01967507157\n", + "1990.0\n", + "5.10500954779\n", + "1991.0\n", + "5.1917947101\n", + "1992.0\n", + "5.28005522017\n", + "1993.0\n", + "5.36981615891\n", + "1994.0\n", + "5.46110303361\n", + "1995.0\n", + "5.55394178519\n", + "1996.0\n", + "5.64835879553\n", + "1997.0\n", + "5.74438089506\n", + "1998.0\n", + "5.84203537027\n", + "1999.0\n", + "5.94134997157\n", + "2000.0\n", + "6.04235292108\n", + "2001.0\n", + "6.14507292074\n", + "2002.0\n", + "6.2495391604\n", + "2003.0\n", + "6.35578132612\n", + "2004.0\n", + "6.46382960867\n", + "2005.0\n", + "6.57371471201\n", + "2006.0\n", + "6.68546786212\n", + "2007.0\n", + "6.79912081577\n", + "2008.0\n", + "6.91470586964\n", + "2009.0\n", + "7.03225586943\n", + "2010.0\n", + "7.15180421921\n", + "2011.0\n", + "7.27338489093\n", + "2012.0\n", + "7.39703243408\n", + "2013.0\n", + "7.52278198546\n", + "2014.0\n", + "7.65066927921\n", + "2015.0\n" + ] + } + ], + "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": 114, + "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\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": 115, + "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": 116, + "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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+ "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": 56, + "metadata": { + "collapsed": true, + "scrolled": false + }, + "outputs": [], + "source": [ + "# Solution goes here\n", + "def update_func1c(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": "code", + "execution_count": 57, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "# Solution goes here\n", + "system.alpha1 = system.birth_rate - system.death_rate\n", + "system.alpha2 = system. birth\n", + "\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": 58, + "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": 59, + "metadata": { + "collapsed": true + }, + "outputs": [], + "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": 60, + "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": 61, + "metadata": { + "collapsed": true + }, + "outputs": [], + "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": 62, + "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": 63, + "metadata": { + "collapsed": true + }, + "outputs": [], + "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": 64, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "# Solution goes here" + ] + }, + { + "cell_type": "code", + "execution_count": 65, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "# Solution goes here" + ] + }, + { + "cell_type": "code", + "execution_count": 66, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "# Solution goes here" + ] + }, + { + "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": 67, + "metadata": { + "collapsed": true + }, + "outputs": [], + "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": 68, + "metadata": { + "collapsed": true + }, + "outputs": [], + "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": 69, + "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": 70, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "table1.columns = ['prb', 'un', 'maddison', 'hyde', 'tanton', \n", + " 'biraben', 'mj', 'thomlinson', 'durand', 'clark']" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This function plots selected estimates." + ] + }, + { + "cell_type": "code", + "execution_count": 71, + "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": 72, + "metadata": { + "collapsed": true, + "scrolled": false + }, + "outputs": [], + "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": 73, + "metadata": { + "collapsed": true + }, + "outputs": [], + "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": 74, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "# Solution goes here" + ] + }, + { + "cell_type": "code", + "execution_count": 75, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "# Solution goes here" + ] + }, + { + "cell_type": "code", + "execution_count": 76, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "# Solution goes here" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": true + }, + "source": [ + "### Disfunctions" + ] + }, + { + "cell_type": "code", + "execution_count": 78, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def carrying_capacity(system):\n", + " K = -system.alpha / system.beta\n", + " return K\n", + " \n", + "sys1 = System(alpha=0.025, beta=-0.0018)\n", + "pop = carrying_capacity(sys1)\n", + "print(pop)" + ] + }, + { + "cell_type": "code", + "execution_count": 80, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def carrying_capacity():\n", + " K = -system.alpha / system.beta\n", + " return K\n", + " \n", + "system = System(alpha=0.025, beta=-0.0018)\n", + "pop = carrying_capacity()\n", + "print(pop)" + ] + }, + { + "cell_type": "code", + "execution_count": 81, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def carrying_capacity(system):\n", + " system = System(alpha=0.025, beta=-0.0018)\n", + " K = -system.alpha / system.beta\n", + " return K\n", + " \n", + "sys1 = System(alpha=0.025, beta=-0.0018)\n", + "pop = carrying_capacity(sys1)\n", + "print(pop)" + ] + }, + { + "cell_type": "code", + "execution_count": 82, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def carrying_capacity(system):\n", + " K = -system.alpha / system.beta\n", + " \n", + "sys1 = System(alpha=0.025, beta=-0.0018)\n", + "pop = carrying_capacity(sys1)\n", + "print(pop)" + ] + }, + { + "cell_type": "code", + "execution_count": 83, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def carrying_capacity(system):\n", + " K = -system.alpha / system.beta\n", + " return K\n", + " \n", + "sys1 = System(alpha=0.025, beta=-0.0018)\n", + "carrying_capacity(sys1)\n", + "print(K)" + ] + }, + { + "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 690310e06cbbdb11f8c713a329066cbde11aa6db Mon Sep 17 00:00:00 2001 From: Christopher Lather Date: Fri, 6 Oct 2017 01:04:48 -0400 Subject: [PATCH 05/10] :) --- code/chap03mine.ipynb | 702 +++++++++++++++++++++++++++++++----------- 1 file changed, 528 insertions(+), 174 deletions(-) diff --git a/code/chap03mine.ipynb b/code/chap03mine.ipynb index f050c2cd..2ffc48a1 100644 --- a/code/chap03mine.ipynb +++ b/code/chap03mine.ipynb @@ -15,7 +15,7 @@ }, { "cell_type": "code", - "execution_count": 1, + "execution_count": 47, "metadata": { "collapsed": true }, @@ -48,7 +48,7 @@ }, { "cell_type": "code", - "execution_count": 2, + "execution_count": 48, "metadata": { "collapsed": true }, @@ -66,7 +66,7 @@ }, { "cell_type": "code", - "execution_count": 3, + "execution_count": 49, "metadata": { "collapsed": true }, @@ -87,7 +87,7 @@ }, { "cell_type": "code", - "execution_count": 4, + "execution_count": 50, "metadata": { "scrolled": true }, @@ -265,7 +265,7 @@ "1954 NaN NaN " ] }, - "execution_count": 4, + "execution_count": 50, "metadata": {}, "output_type": "execute_result" } @@ -284,7 +284,7 @@ }, { "cell_type": "code", - "execution_count": 5, + "execution_count": 51, "metadata": { "scrolled": true }, @@ -462,7 +462,7 @@ "2015 NaN NaN " ] }, - "execution_count": 5, + "execution_count": 51, "metadata": {}, "output_type": "execute_result" } @@ -480,7 +480,7 @@ }, { "cell_type": "code", - "execution_count": 6, + "execution_count": 52, "metadata": { "collapsed": true }, @@ -504,7 +504,7 @@ }, { "cell_type": "code", - "execution_count": 7, + "execution_count": 53, "metadata": {}, "outputs": [ { @@ -1611,7 +1611,7 @@ "[66 rows x 11 columns]" ] }, - "execution_count": 7, + "execution_count": 53, "metadata": {}, "output_type": "execute_result" } @@ -1629,7 +1629,7 @@ }, { "cell_type": "code", - "execution_count": 8, + "execution_count": 54, "metadata": {}, "outputs": [ { @@ -1700,7 +1700,7 @@ "Name: census, Length: 66, dtype: int64" ] }, - "execution_count": 8, + "execution_count": 54, "metadata": {}, "output_type": "execute_result" } @@ -1721,7 +1721,7 @@ }, { "cell_type": "code", - "execution_count": 9, + "execution_count": 55, "metadata": {}, "outputs": [ { @@ -1743,7 +1743,7 @@ " 7256490011], dtype=int64)" ] }, - "execution_count": 9, + "execution_count": 55, "metadata": {}, "output_type": "execute_result" } @@ -1761,7 +1761,7 @@ }, { "cell_type": "code", - "execution_count": 10, + "execution_count": 56, "metadata": {}, "outputs": [ { @@ -1776,7 +1776,7 @@ " dtype='int64', name='Year')" ] }, - "execution_count": 10, + "execution_count": 56, "metadata": {}, "output_type": "execute_result" } @@ -1800,7 +1800,7 @@ }, { "cell_type": "code", - "execution_count": 11, + "execution_count": 57, "metadata": {}, "outputs": [ { @@ -1809,7 +1809,7 @@ "pandas.core.frame.DataFrame" ] }, - "execution_count": 11, + "execution_count": 57, "metadata": {}, "output_type": "execute_result" } @@ -1820,7 +1820,7 @@ }, { "cell_type": "code", - "execution_count": 12, + "execution_count": 58, "metadata": {}, "outputs": [ { @@ -1829,7 +1829,7 @@ "pandas.core.series.Series" ] }, - "execution_count": 12, + "execution_count": 58, "metadata": {}, "output_type": "execute_result" } @@ -1840,7 +1840,7 @@ }, { "cell_type": "code", - "execution_count": 13, + "execution_count": 59, "metadata": {}, "outputs": [ { @@ -1849,7 +1849,7 @@ "pandas.core.indexes.numeric.Int64Index" ] }, - "execution_count": 13, + "execution_count": 59, "metadata": {}, "output_type": "execute_result" } @@ -1860,7 +1860,7 @@ }, { "cell_type": "code", - "execution_count": 14, + "execution_count": 60, "metadata": {}, "outputs": [ { @@ -1869,7 +1869,7 @@ "numpy.ndarray" ] }, - "execution_count": 14, + "execution_count": 60, "metadata": {}, "output_type": "execute_result" } @@ -1889,7 +1889,7 @@ }, { "cell_type": "code", - "execution_count": 20, + "execution_count": 61, "metadata": { "collapsed": true }, @@ -1919,7 +1919,7 @@ }, { "cell_type": "code", - "execution_count": 21, + "execution_count": 62, "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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P8y2LiYlBKcUzzzyT4745rZB13fVjs/5r1qwZ9957L3PmzMnWU+G///3vLftm/ffzzz9n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\n", "text/plain": [ - "" + "" ] }, "metadata": {}, @@ -1957,7 +1957,7 @@ }, { "cell_type": "code", - "execution_count": 22, + "execution_count": 63, "metadata": { "collapsed": true }, @@ -1968,7 +1968,7 @@ }, { "cell_type": "code", - "execution_count": 23, + "execution_count": 64, "metadata": { "collapsed": true }, @@ -1988,7 +1988,7 @@ }, { "cell_type": "code", - "execution_count": 24, + "execution_count": 65, "metadata": {}, "outputs": [ { @@ -1997,7 +1997,7 @@ "1.2862470293832287" ] }, - "execution_count": 24, + "execution_count": 65, "metadata": {}, "output_type": "execute_result" } @@ -2019,7 +2019,7 @@ }, { "cell_type": "code", - "execution_count": 25, + "execution_count": 66, "metadata": { "scrolled": true }, @@ -2031,7 +2031,7 @@ "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[1;32m----> 1\u001b[1;33m \u001b[0mcensus\u001b[0m \u001b[1;33m-\u001b[0m \u001b[0mus\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m", + "\u001b[1;32m\u001b[0m in \u001b[0;36m\u001b[1;34m()\u001b[0m\n\u001b[1;32m----> 1\u001b[1;33m \u001b[0mcensus\u001b[0m \u001b[1;33m-\u001b[0m \u001b[0mus\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m", "\u001b[1;31mNameError\u001b[0m: name 'us' is not defined" ] } @@ -2042,7 +2042,7 @@ }, { "cell_type": "code", - "execution_count": 26, + "execution_count": 67, "metadata": { "scrolled": true }, @@ -2115,7 +2115,7 @@ "Length: 66, dtype: float64" ] }, - "execution_count": 26, + "execution_count": 67, "metadata": {}, "output_type": "execute_result" } @@ -2126,7 +2126,7 @@ }, { "cell_type": "code", - "execution_count": 27, + "execution_count": 68, "metadata": { "scrolled": true }, @@ -2199,7 +2199,7 @@ "Length: 66, dtype: float64" ] }, - "execution_count": 27, + "execution_count": 68, "metadata": {}, "output_type": "execute_result" } @@ -2210,7 +2210,7 @@ }, { "cell_type": "code", - "execution_count": 29, + "execution_count": 69, "metadata": {}, "outputs": [ { @@ -2219,7 +2219,7 @@ "0.012862470293832286" ] }, - "execution_count": 29, + "execution_count": 69, "metadata": {}, "output_type": "execute_result" } @@ -2244,7 +2244,7 @@ }, { "cell_type": "code", - "execution_count": 30, + "execution_count": 70, "metadata": {}, "outputs": [ { @@ -2253,7 +2253,7 @@ "2.5576286540000002" ] }, - "execution_count": 30, + "execution_count": 70, "metadata": {}, "output_type": "execute_result" } @@ -2271,7 +2271,7 @@ }, { "cell_type": "code", - "execution_count": 31, + "execution_count": 71, "metadata": {}, "outputs": [ { @@ -2280,7 +2280,7 @@ "7.2564900110000004" ] }, - "execution_count": 31, + "execution_count": 71, "metadata": {}, "output_type": "execute_result" } @@ -2298,7 +2298,7 @@ }, { "cell_type": "code", - "execution_count": 32, + "execution_count": 72, "metadata": {}, "outputs": [ { @@ -2307,7 +2307,7 @@ "(1950, 2015)" ] }, - "execution_count": 32, + "execution_count": 72, "metadata": {}, "output_type": "execute_result" } @@ -2329,7 +2329,7 @@ }, { "cell_type": "code", - "execution_count": 33, + "execution_count": 73, "metadata": {}, "outputs": [ { @@ -2338,7 +2338,7 @@ "0.07229017472307693" ] }, - "execution_count": 33, + "execution_count": 73, "metadata": {}, "output_type": "execute_result" } @@ -2359,7 +2359,7 @@ }, { "cell_type": "code", - "execution_count": 34, + "execution_count": 74, "metadata": { "collapsed": true }, @@ -2377,7 +2377,7 @@ }, { "cell_type": "code", - "execution_count": 35, + "execution_count": 75, "metadata": {}, "outputs": [ { @@ -2418,7 +2418,7 @@ "dtype: float64" ] }, - "execution_count": 35, + "execution_count": 75, "metadata": {}, "output_type": "execute_result" } @@ -2437,7 +2437,7 @@ }, { "cell_type": "code", - "execution_count": 40, + "execution_count": 76, "metadata": { "collapsed": true }, @@ -2456,7 +2456,7 @@ }, { "cell_type": "code", - "execution_count": 37, + "execution_count": 77, "metadata": {}, "outputs": [ { @@ -2468,9 +2468,9 @@ }, { "data": { - "image/png": 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j6Mrjw9prHCcSf/PTKvk/99xzrFy5koCAAGxtbdXtMpmMiIgIQkJCtLpY9Vqa\nM2bMUHfzdOzYkcjISL766qt7WoP2YXD7EopGRkZIpVKN5yCGhobqbp+kpCT69euncXy3bt3U25KS\nkmjXrp16uC5Aly5d1F+npKRQWVnJK6+8glR6q/evqqpK4/9YELRRVVVFbGws6enpAJRUlpCYk0iR\nbhEyJxnp1wqpLNWhfUU39v+QSnBQG2xt7/6cUGg6dSb/559/Xv21SqUiJSWFwYMHExgYiI2NDUVF\nRZw9exa5XI69vb1WF6ve7/Z1XCUSCR4eHupfmsbk4+NzT10x/v7+NbqCmpKuruZ/h0QiqfOOyNDQ\nsEZb9VA6XV1dJBIJ/16krfrNF25+mgNYvXo1bm5uGvvd/mYgCNqQSqXk5+ejQsWVgitcKbmCzEpG\nlXEVSOCxwJ7k5HekqELKmDHe2NgY3f2kQpOqM/lXVVVpfF/dJ19VVcWNGzcA8PW9+XAmKytLq4t1\n6tQJY2NjjbVaq99YxDj/+vH09OTcuXMabZGRkepthYWF6kXULSwsAIiNjVXv6+bmhp6eHpmZmfTt\n21fdvmbNGhQKBa+88kozvArhYaGjo4OjpyPf/fIdebp5yBzLkOiCga4BIR1DeLTto2R5yJBKJdjZ\niTv++0GdyX/79u2NfjEjIyMmTZrEihUrsLW1xdvbm507d3LlyhVWrVrV6Nd7mE2dOpWnn36apUuX\nEhISQkZGBu+//z79+vXD09MTBwcH1q5dy1tvvUV4eDiZmZkaP2MjIyMmT57M8uXLMTExwc/Pj8OH\nD7N27VoWLlzYgq9MuN+pVCoyMzNxcHBQfzI9kX6C7bHbKTOtIv5SDqZFejwW3J1JXSZha3yzG9HB\nweROpxWaWZ3JPzIykqCg+q+Oc+bMGXXfc21eeeUVjIyMWLRoEbm5uXTo0IHNmzfj4eFR72u1Zt7e\n3qxfv54VK1awfft2LC0tGTFiBK+++ioApqambNu2jQ8++ICQkBDs7e2ZOnWq+oEvwKuvvoqenh4f\nffQROTk5uLq68sEHH4iFfIQ6VRdr5efnExQUpB7w4WTqRImsgrPRN1AqpFjf6M6IYZOxNbZp4YiF\nukhU/+4Y/n+jRo3C09OTmTNnavTR1yU6OpqNGzdy+fJl9u/f36hB3m0VekEQmpZSqSQpKYnk5GSU\nSiUABgYG9O/fX/386EDiATbsO4Rlam9MVLaEhHgzaJDbnU4rNKG75c067/x3797NmjVrGD16NO7u\n7gwdOhR8eoPeAAAgAElEQVR/f39cXFwwMjKiqKiIzMxMIiMjOXbsGKmpqYwfP57ly5c36QsSBKF5\n5eXlER0dTXFxMQBypRyZXEawT7DGIIXh3sN5ZOpANkbEEBLig4eHZUuFLGihzuSvp6fHa6+9Rmho\nKFu3buXbb79l7dq1GqNPVCoVbdq0YdiwYWzYsAEHB4dmCVoQhKb372ItgILyAhJKEiixKsX2RgDe\n3rdGhkklUqytjHnrLVGw9SC46zh/BwcH5syZw5w5c0hJSSE9PZ3i4mKsrKxo06YN7dq1a444BUFo\nRpmZmcTExKinC1GqlKQVpZEkTSLfsJT487mcKlqFleF8unfXLPQUif/BUK+VvDw9PVt9Fa4gPOwu\nX75MTEyM+ntZlYyEsgSum1xHpasiI6kEeakeHhVB7NyZgK+vDebmYtrlB41YxlEQBA1OTk4kJiZS\nWVlJZnkmMcoYys3K4f9v6J/s+SjpB32oKNdl9GhvzMz0WzZgoUFE8hcEQYOBgQHuXu7sP7efZL1k\nVDo3+/v1dPQY22ksfdr24apLMQYGOmLs/gNMJH9BaKVUKhWpqalUVFTQoUMHdXt8djybkzdToFvI\npdQCjIz06OHry5TAKTiZOQHQtq1YT/dBJ5K/ILRCRUVFREVFUVBQgEQiwcHBAWvrm+vkVigqyC7K\nIyY2B5lMTlt5IBOHv4iTmVULRy00JjGDlyC0IkqlkoSEBI4dO0ZBQQFw8xPApUuX1Pt0cezCYK+B\nGElN6Vz6JO6lfThzKrulQhaaiFZ3/hUVFWzYsIEjR44gk8lqzBYJ8PPPPzd6cIIgNJ68vDyioqLU\n62rAzdk4Xdu50tm3s8a+4zqPpYfVQNavTOCpp7x49FHnf59OeMBplfwXLlzIrl276N69O15eXmLK\nX0F4gMjlcuLj49Ur6VWzsLQgRT+Fv679xXSL13F3tlNv09PRw6utE4sW2WFgIHqHH0Za/a/+/PPP\nvPbaa0ybNq2p4xEEoRFlZmYSHR1NeXm5uk1XVxd7N3sOZB4gPS+D1NRCjv+4gE0z3sPb21rjeJH4\nH15a3cJXVlY266ImgiDcu+q1Mm5P/A4ODph4mbD18laulVwj5VIBGddKkKikbNp8Hpms6g5nFB4m\nWiX/Rx99lGPHjjV1LIIgNCKJRIK/vz9SqRQDAwP8Avy4oHeBL+O/pFJxczlQT3dr/FRD8ZE9Rjs3\n61qf5wkPJ60+040aNYq5c+eSn59PYGBgrUsIVq/JKwhCy5DJZBgZGWnMrWNqakq3bt2o1K9kc9Rm\nrhVfU29zNHVkWtA0cj31KSgop08fFzEvTyuiVfJ/6aWXANi7dy979+6tsV0ikYjkLwgtpLpYKyEh\nAR8fnxrzb12RX2H72e3k5Bchl6uwsjKkp0tPQv1CMdA1wFn06LZKWiX/33//vanjEAShAW4v1gJI\nTEzE0dERE5Ob0y7EZ8ez8exGrmWUcCm1EH0dPRaHTeLxTgNbMmzhPqBV8nd2vjXGVyaTUVpaiqWl\nJXp6ek0WmCAIdVMoFOqVtW7vpzcxMUGhUKi/97X1pYNVZ06d/A1DhSUdioaTetQKOrVE1ML9ROtx\nXCdPnmTZsmXExcWpf9n8/f159dVX6dWrV5MFKAiCptzcXKKjo2sUa3l7e+Pp6alRhyORSJjeYwqU\nG3NhtyMebe0YO9anJcIW7jNaJf/Tp0/zwgsv0K5dO15++WVsbGzIysri0KFDTJ06la1bt95x0XZB\nEO5dVVUV8fHxpKWlabTb2Njg7++PiYkJJzNOEtwmGB2pjnq7sZ4xrw2eQrxzLl5eVujqiiJNQcvk\nv3LlSnr16kVERITGaIBZs2Yxbdo0Vq9ezbZt25osSEFo7YqLizlx4kSNYq2OHTvStm1byuXlrD+z\nntNXI9l89U8+GDcLR0fN6ZY7dLBp7rCF+5hWtwCxsbGEhYXVGAYmkUgICwvTWPVHEITGZ2xsjI7O\nrbt5BwcH+vfvj5ubGzdKbrD4r8UcvXiSyLNZ/JlxhIUR31NVpbjDGYXWTqvkb25ujkwmq3VbaWmp\nxi+lIAiNT0dHh4CAAAwMDAgKCiI4OBgjIyOibkSx5K8lZJZkoqsjRS5X4lzRhfIMa+Licls6bOE+\nplXy79mzJ6tXryYzM1OjPTMzk9WrV4sHvoLQiEpLS0lMTKxRbWtjY8OgQYNo0+bmgukHLx5k3el1\nlMtvdgVZmZvw0iPT6aI3hFdfDqZLF/tmj114cGjV5x8eHs7o0aMZNmwYQUFB2NrakpOTQ2RkJKam\nprz55ptNHacgPPSq59VPTExEoVBgZmamTvTVdHR0KJeXs/X8Vs5eP4vk/xfWtTG2YVbwLJzNnJEN\nqsLERKyrK9yZVsnfwcGBvXv3snnzZiIjI0lPT8fc3JzQ0FD+85//YGdnd/eTCIJQp8LCQqKjo9XF\nWgBxcXE4OjpqDN3MkeWw5tQaIi8mceN6KQEBdnRy6MjUoKmY6psCiMQvaEXrcf52dnbMmTOnKWMR\nhFZHoVBw8eJFUlJSNLp5zM3NCQgIqLF2xtbzWzl27gLXr5cCILnsxcujXtYY2ikI2qgz+a9fv55n\nnnkGe3t71q9ff8eTSCQSpk+f3ujBCcLDLDc3l6ioKEpLS9VtdRVrVZsUMInIixfJvF6Ol2wgbiU9\nqChXYmwskr9QP3Um/xUrVvDII49gb2/PihUr7ngSkfwFQXt3K9YyNTWt81g7Ezvee+J1fpZexVLl\nRGhoB/T0ROIX6q/O5J+QkFDr14Ig3JuEhASNxH97sdbttTRFFUWk5l3Gx6ojhoa3/lR9bX3xHu+D\nVCqmXxYaTquhnmvWrKkxzLNaRkYGCxYsaNSgBOFh5u3tjb7+zYeyjo6ODBgwADc3N43Ef7XwKu/9\n9iEzN3/I4vU/1hj2KRK/cK+0Sv5r166tM/mfP3+eb775plGDEoSHhUqlQqlUarQZGBjg7+9Pt27d\n6NatW43FkSKvRbLw6GL++CeR/EIZ+9J3sP/gxeYMW2gF6uz2ee655zh//jxw8xd43LhxdZ7Ez89P\n6wsmJyczYsSIGu1ffvmlmBxOeKiUlpYSHR2Nqalpjb8RJyenGvurVCoOXDzAgYsHQAIODsZcv1KB\nd/kQ9HXF8E2hcdWZ/BcsWMAvv/yCSqVi1apVjB07FkdHR419dHR0MDMzY/DgwVpf8OLFi1hZWbF/\n/36NdktLy3qGLgj3p+qF0y9evIhCoSAnJwdnZ2esra3rPKZCXqEu3KrWvWN7LHQH8ET/LmJSNqHR\n1Zn8PT09mTlzJgBKpZKQkBAcHBzu+YIXL16kffv2ojBMeCgVFhYSFRVFYWGhuk0ikVBQUFBn8s+V\n5fLxkRXkKTLVFbsd7DowNXAqJoNMaj1GEO6VVkVeL774IgD5+flUVVWpHz6pVCpkMhmRkZGEhIRo\ndcGkpCQ8PDwaGK4g3J/qKtaysLAgICAACwuLWo9Lyk3ivQPLiY5Pp42zKe3cLRjQbgBjO41FKhHz\n7gtNR6vkn5iYyBtvvEFycnKt2yUSSb2Sf0VFBWPHjiUjIwMvLy9ef/11/P3FKtLCgyknJ4fo6GiN\nYi0dHR28vb3x8PCotVgLbg7lnPfjEs7H3QAg42opoZ3G82znJ5olbqF10+rW4qOPPqKgoIA5c+bQ\nvXt3Hn30Uf73v//Rr18/JBIJX3zxhVYXKy8v5+rVq5SUlPDWW2/x2WefYW9vz/jx40lJSbmnFyII\nzU2hUBAVFcU///yjkfhtbGzo168f7du3rzPxA5gbmDOldyjW1oboq4wYYDieob79myFyQdDyzv/8\n+fO88847jBkzBiMjI/bv309oaCihoaG8/PLLbN++XauROoaGhpw+fRp9fX31OOclS5YQFxfHzp07\n+d///ndvr0YQmpFUKtVI+np6enTs2BFXV9caCx/VZWC7gRSNKCU32p7xo7tpFHMJQlPS6s6/srIS\nd3d3ANzd3TUqfp955hn1kFBtmJqaqhM/3PwDat++PdevX9f6HIJwP5BIJPj7+yOVSnFycqJ///41\nqnRvl5idxO9/x9c4x9N+o5gS1lMkfqFZaZX827RpQ3p6OnAz+ZeUlJCRkQHcLFi5fWTDncTGxhIY\nGEhsbKy6TaFQkJCQgJeXV31jF4Rmo1KpuHbtWo2CLVNTU/r3719rsdbtfoj+hUnr3+ad3R/xz8kr\nTR2uINyVVsl/8ODBLFu2jF9//RUHBwc8PDxYuXIlKSkpbN26FVdXV60u5uvri7OzM/PmzSMqKoqk\npCTeeecd8vPzmThx4j29EEFoKqWlpfzzzz9ERkZy6dKlGttNTOoejlmlqOKLqC9Y8dsmCovLKdbJ\n4v1dEeTllTVlyIJwV1ol/xdffJEuXbrw7bffAvDOO+/w888/88QTT3D8+HFeeuklrS6mq6vLpk2b\naNeuHTNmzCAkJIScnBx27NiBjY0oYhHuL0qlkuTkZI4cOUJu7s31cBMTEzX6+e8kR5bD0uNLOX7l\nOB4eFhgZ6WKmtGPaoDFYWdX9KUEQmoNWnYxGRkasWbOGyspKAPr06cP+/fuJi4ujU6dOtG3bVusL\nOjg4sHz58oZFKwjNpKCggOjo6BrFWh4eHnfs3qkWnRnNlnNbkFXJANDRkRLabxgj247Bp71YW1do\nefV6wnT7g9q2bdvWK+kLwoNAoVCQmJjIpUuX6lWspT5eqWDxni2cyjuMk9PNefl1pbqM6zyOPm37\naD0KSBCaWp3Jf+jQofX6Rf35558bJSBBaCl1FWv5+Pjg4eFx17+HG/m5zP58EReyEpBKJZiZ6+Nq\n68CMbjNwt3Rv4ugFoX7qTP6BgYHiLkVoNa5fv86ZM2c02mxtbfH397/jA93bnbjxF1fLbhYrKpUq\nqq7ZMveZueqF1QXhflJn8l+yZElzxiEILcre3h5TU1NKSkoaVKwFMNLnCc4ER7Pv6Cke9xzOhxOn\nYKCv14RRC0LDadXnf/bs2bvuExgYeM/BCEJL0dHRwd/fn9TUVDp37qzVQ93CwgosLAxunUOqQ3i/\nFxnlc4Xu7QKaMlxBuGdaJf/Q0NC73gHFx8ffcbsg3A9UKhVXrlwhNzeXrl27avxe29jYaDXkWKVS\nsWnfb3z158+sm/oOvr63jrEysqJ7O6smiV0QGpNWyb+2idtkMhlnzpxh3759rF69utEDE4TGVlJS\nQnR0tHrMvoODA87OzvU6h0Kp4L/b1/ND3I+odGDeti1smfsyJiZipS3hwaJV8u/evXut7f3798fY\n2JjPPvuMDRs2NGpggtBYlEqlemWt26dnuHz5Mm3atNG6Xz9Xlsums5vINE1CV09KVZWSLJNoSsrK\nRfIXHjj3PJNUt27d2LhxY2PEIgiNrqCggKioKIqKitRtEomE9u3b4+XlpXXiP3PtDDuid1BWVYa+\nvg7e3lZYVrXl49A3sDI2b6rwBaHJ3HPyP3z4sNZD4QShucjlci5evFijWMvS0pKAgADMzbVL2Emp\nWXx74RuuKG9NRiiVSJnaO4yhnvWrhRGE+4lWyf/555+v0aZQKLhx4wZXrlxh6tSpjR6YIDRUdnY2\n0dHRyGQydZuOjg6+vr60a9dOq4StUqnYceA4K46to1KvmKBAewwMdLE1tuWFwBfwsBJLkQoPNq2S\nf1VVVY02iUSCp6cnU6ZMYfTo0Y0emCA0VHp6ukbit7W1JSAgAGNjY63PcTY9ik9PL6NMUgVySEou\n4IVhIwj1C8VQV0zKJjz4tEr+27dvb+o4BKHRdOrUiezsbJRKJZ06dcLFxaXe3TOdnHx5JMCLP05e\nwNLMlLnDZ/K4f/+mCVgQWkC9+vyPHj1KZGQkhYWF2Nra0rNnT4KDg5sqNkG4q7KyMnR1ddHTu1VJ\nq6+vT1BQEKamphgYGNzh6LoZ6hryxqDZGOtsI3zQTBzMxEycwsNFq+Sfn5/P1KlTiY2NRV9fH2tr\na3Jzc1m3bh29e/dm7dq1Df4jE4SGUKlUpKWlER8fj7OzM/7+/hrb67M+RHpmLku2f8d/w8LUM3EC\nuFu6s/TJeeKhrvBQ0moxlwULFpCens769euJjo7myJEjxMTEsGbNGmJjY1m2bFlTxykIaiUlJfzz\nzz/ExMQgl8tJS0tTF27V1/d/HeepT2fze9YPvBfxDVVVCo3tIvELDyutkv+xY8eYM2cO/fv312gf\nNGgQ4eHhHDx4sCliEwQNSqWSpKQkjh49qpHsTU1NkUq1+lVWq1RU8nXs1+y5vpkySgA4UXqQqAsZ\njRqzINyvtOr20dHRwczMrNZtdnZ2tY4GEoTGdLdiLR0dHa3PlZqfypbzW8gsycTIUBd3N3Pybih5\nd+QsugWIBYqE1kHrid0+/fRT/Pz8cHBwULeXlJQQERHB+PHjmyxAoXWTy+UkJiaSmpp6T8VaAKlp\nefyU8iMxsuMoVbemeXg88BGe6xSGjamYkE1oPbRK/llZWWRlZTFkyBCCgoKwt7enoKCAs2fPUlpa\nir6+vroQTCKR8Pnnnzdp0ELrUFZWxt9//31PxVoAcrmSL/YdZ/0/m6g0zCcoyAFdXSkGugaM6zSO\nR1wfEX37QqujVfJPS0vD19cXuHkndu3aNQB1m0KhQKFQ1Hm8IDSEoaEhRkZG6uRvZ2eHv79/vYq1\nAE6mnWHV2WVUSOVQCamXCxneozuTu0zG1ti2KUIXhPueKPIS7lsSiYSAgAD+/vtvfH19G1SsBeDv\n0oHOvk5ExlzF2sKYWf0mMrrrCHG3L7Rq9SrySk5O5tSpU5SUlGBlZUVQUBAeHmKOE+HelZWVcenS\nJTp06KAxcsfExIRBgwbVazRPUVEF5ua36k7MDMx4ffA0thvtZc6w2TiaOTZq7ILwINIq+SuVSubN\nm8fu3bs1HrpJJBKefPJJFi9eLO6ihAZRqVRcvnyZhIQE5HI5+vr6eHl5aeyjbeIvK6ti4zd/8UfM\naT5/9yVsbIzU2wKdAuk6uqv4PRWE/6dV8o+IiOD7778nPDyckSNHYmtrS3Z2Nvv372fVqlV4enqK\nmT2FeisuLiY6Opq8vDx1W1JSEm5ubujr129xFIVSwatr1/FX1m8odZSs2O7FB688pZHsReIXhFu0\nSv7fffcdM2bMYMqUKeo2R0dHpk6dSkVFBd99951I/oLWlEolycnJJCUlaaysZWZmhr+/f70Tf3pR\nOtvOb6OoTRKqrJvnO1t1iMrKkRgY3POSFYLwUNLqLyM7O5ugoKBatwUGBhIREdGoQQkPr/z8fKKi\noiguLla3SaVSdbFWffr2FUoFh5IPcTDpIAqlAnMzA9q6mdPe1oN3H58tEr8g3IFWfx2urq6cO3eO\nXr161dh27tw57OzsGj0w4eFSV7GWlZUVAQEBdVaQ1+bGjVLWbj+MzPsEJdJsdbuuVJfXhk1miOcQ\npJL6TfcgCK2NVsl/zJgxfPLJJxgbGzN8+HBsbW3Jycnh4MGDbNiwgenTpzd1nMID7vLly1y6dEn9\nva6uLr6+vri7u9erL/6fk1dZ8PU2UvVOYCzTJbCrPRKJBA8rDyZ1mYSjqRjJIwja0Cr5T5gwgfj4\neJYsWcLSpUvV7SqVilGjRjFz5swmC1B4OHh4eHD16lVKSkqwt7fHz8+v3sVaAOflv5BmcAKVUoVM\nVoWsRMmkHuMY5DFI3O0LQj1oPbHb0qVLmTJlCmfOnKGwsBBzc3OCg4NrDMsTBJVKhUKhQFf31q+X\nVColICAAmUyGs7Nzg0fejO4ykp9ijpKZXczgoEBe7jsNB1OHux8oCIKGej0Rc3JywtXVFQsLC6yt\nrXF1db2ni58/f57Q0FC2bNlCjx497ulcwv1BJpMRExMDQPfu3TWSvLW1NdbW1lqf69y5TPT0pHTu\nfOuZkr2JPa8O/Q9ypZzBnuJuXxAaSusir48//pgdO3Ygl8vVD+yMjIyYOXMm06ZNq/eFZTIZb731\nlpgT6CHx72ItgIyMDFxcXOp9ruLiSnZ8GccPFw5ibmzMlnkvYWx8a5nGgR4DGi1uQWittEr+q1ev\n5osvvmDixIkMGzYMGxsbcnJyOHToEKtWrcLExISwsLB6XXjJkiU4ODiQlpbWoMCF+0dxcTFRUVHk\n5+er2yQSCaWlpQ06X1bZdXZeWUuO4XWkSh12fB/MtNA+jRWuIAjUo8hr1qxZzJ49W93m6upK165d\nMTExYdu2bfVK/kePHuXIkSNs3LiRUaNG1T9q4b5QvbJWcnJyrcVa9eniAVCqlPya8is/JP6AvVcl\nOfFg72iIrvclQCR/QWhMWiX/kpKSGgtkVwsKCmLz5s1aXzAvL4///ve/LFq0CAsLC62PE+4veXl5\nREdH33Oxlkql4saNUqRmpWw5v4XU/FQAbG2N6N6tDaGBYxjiOaRJXoMgtGZaJf/+/fvz9ddf06dP\nzbuvgwcP0rdvX60v+N577zFw4ED69u3LjRs3tI9UuC+oVCri4uK4fPnyPRdr5eaWsW1bLH+mH8Hm\n0RR09G6dz83Sjf/0/w9OZk6NGr8gCDdplfy7devGihUrGDlyJCNGjMDOzo6CggKOHDlCZGQkkydP\nZv369cDNvt66ir727t3LhQsX+OGHHxrvFQjNSiKRUFVVpU78DS3WUqlUfLL+KL/n7qZQ9xpWiQZ0\n7myLrlSXJ7yf4LH2j4mRPILQhLRK/h9++CFw88HeihUramy/vdvnTsl/z549ZGZm8uijjwKoE8jU\nqVN56qmn+OCDD+oXvdAiOnXqRHZ2NhYWFg0u1gIo6/QXRX9fQwKYmurjbObCC4HP42Je/xFCgiDU\nj1bJPyEhoVEutmzZMsrLy9XfZ2dnExYWxoIFC+jdu3ejXENoPCqVimvXrmFvb4+e3q2hlvr6+vTp\n0wdDQ8MGF2tJJBJm9/0PyVmXMTczYGzgkwz3Go6uVEzGJgjNoVn/0hwcNCsxDQwM1O02NjbNGYpw\nF9XFWllZWbi5udV44G9kZFTHkTXl55ezY0ccI0d64u5uqW73tPbktSEv4GHlgZulW6PFLgjC3Ynb\nLEGDSqUiNTWVhIQEdQFeWloazs7ODXqDjovLYc3Gf4iR/ELMti6s++9/0NW91Zc/oJ0o2BKEltCi\nyd/R0ZHExMSWDEG4TVFREVFRURQUFKjbJBIJ7u7uDRqWq1KpSFdd4B/DbVQoyzhRksHpmP706urZ\nmGELgtAA4s5fUBdrJSUlaQzfNDMzIyAgACsrq3qfs7iimJ0xOzl7/Syu7QzIyKjC28ccufU1QCR/\nQWhpIvm3cnl5eURFRVFSUqJuk0qleHl50b59+3qtrCWTVZGbW0au3iV2RO+guOJmAZhTGxN83V14\nIeg/+Nr6NvprEASh/upM/pmZmfU60b8f5gr3v/z8fI4fP67RZm1tjb+/f72KtQDi43OJ2HqaBJ3D\ntAnO0+jX79O2DyGdQjDUNWyUuAVBuHd1Jv9+/frVaxhffHx8owQkNB9LS0v1qmy6urp06NABNze3\neg/frKiQs2TL95xXHaJSJUOWbISvrw2WhpZMCJhAZ/vOTfQKBEFoqDqT/6JFi9RJoLCwkGXLltGr\nVy8ef/xxdYXvH3/8wZEjR3j77bebLWCh4VQqlUZil0gk+Pv7Ex8fT6dOneo1fFODjgKVfySV0TL0\n9KTY2hnT06Un4zqPw1ivYQVggiA0rTqT/zPPPKP+evbs2Tz11FMsWLBAY5+RI0eyYMECfvrpJ8aN\nG9d0UQr3RKVSkZ6eztWrV+nZs6dGP76JiQndunWr9/lufxMx0DXg1UFTeE+2nHZtHJgSPBl/h9on\nAhQE4f6g1dO848eP8/jjj9e6bcCAAZw7d65RgxIaj0wm4+TJk5w/f57c3FxSUlLu6XyXLhWwYNFx\ncnPLNNoDnQIJHzqVxUM/FIlfEB4AWiV/KysroqOja9126tQp8bD3PqRSqbh06RJHjhwhOztb3Z6e\nnq4x9359HD58hbc/+Zbd+atZtuVHjWGhAP3d+2Oib3JPcQuC0Dy0GuoZEhLC2rVrKS8vZ9CgQVhZ\nWZGbm8uhQ4fYvn077777blPHKdRDXcVa7dq1w8fHp17DN6vJqmSckR8g1vggKuC37D1Mz+iPu4uY\nlkMQHkRaJf+ZM2dSXFzM559/TkREhLrdwMCAV155pd5LOApNQ6FQqFfWaqxiLYCoG1F8GfMlheWF\nuLiaUVxcSWAnO6RmpYBI/oLwINIq+UskEubMmcOsWbM4d+4cRUVFWFlZ0bVr1wZP5ys0rrqKtby9\nvfH09Kz33X5KSgFySRl/FfzIqYxT6nZ3N3OCnYN5zu85TPVNGy1+QRCaV70qfM3MzOq1apfQfLKz\nszUSv7W1NQEBAZia1i9Bl5fL2bMnid1//8F1u+N06mqK9P9H9pgbmBPmH0YXxy6NGrsgCM2vzuQ/\ndOjQehX7/Pzzz40SkNAwXl5eXL9+nbKysgYXawHcKMhl47kN3DBOglK4elWFW1tzerj0YFynceKB\nriA8JOpM/oGBgQ1eqENoWhUVFSiVSo2iLKlUSmBgIHp6eg0v1gJMzXWw9CrgRjLY2Bji3daJKd3F\nuH1BeNjUmfyXLFmi/vrgwYP06tULa2vrZglKqF11sVZcXByWlpb06NFD4w3a3Ny8XudTKlVkZclw\ndLx1N29rbMusQeOJMPyCUQFDGN1xtKjSFYSHkFZ9/nPnzmXJkiUMGzasqeMR6iCTyYiKiiInJwe4\n2cefkZGBi0vD1rtNSytk+444LuVfYvX7YzEx0VdvG+QxEE9rDzysPBoldkEQ7j9aJX8HBwfKysru\nvqPQ6KqLtRITE9UrawEYGxtjaNiwWTKVShUfRfzMqfIfKdXJ4fNvnXn5P7dW1JJKpCLxC8JDTqvk\n/9xzz7Fo0SKioqLw9fWtdXjnyJEjGz241u5uxVq6uvVfjqFcXs4PiT+Q5X2QkrgcpFIJ55WHUCr7\nNaj4SxCEB5NW2WPx4sUAfPXVV7Vul0gkIvk3orqKtczNzQkICMDS0vIOR9dUWalAT0/KmWtn2HVh\nF73UposAABwPSURBVIXlhVhbG+Lubk4bB3PGBgwE8WxfEFoVrZL/77//3tRxCP9PLpfz559/Nkqx\nlkKh5I8/rrDr0BlcHksho/ySxvbHAnsS5h+GrbFto8UvCMKDQavk7+zsrP5aJpNRWlqKpaUlenp6\nTRZYa6Wrq4uVlZU6+dvY2ODv71/vYi2AzV+cZ9f5fWQYnMX8tB5+frZIkGBhaEFIxxC6tekmhvMK\nQiuldafxyZMnWbZsGXFxcequCH9/f1599VV69erVZAG2Rh07diQvLw9PT0/atm3b4ASd7XKU9Pgz\nqICqKiUKuYph3oMZ5TNKLKkoCK2cVsn/9OnTvPDCC7Rr146XX34ZGxsbsrKyOHToEFOnTmXr1q31\nXhBEuFmslZiYSIcOHTQ+Renr6zNgwIB7visPC36Go4mn0NGR0LdzAOMDwnAxb9jQUEEQHi5aJf+V\nK1fSq1cvIiIiNBLSrFmzmDZtGqtXr2bbtm1NFuTDRqVScfXqVS5cuEBVVRUqlYqAgACNfeqT+LOy\nSvn8y9M8PaITvt526nY3SzdmDh6Hg4kDPV16ii4eQRDUtHp6GBsbS1hYWI3kIZFICAsLIyYmpkmC\nexiVlpZy4sQJoqKiqKqqAuDKlSsaD3jr48SZNCYvWc6O65+waOdO5HLNhVqe8n2KXq69ROIXBEGD\nVnf+5ubmyGSyWreVlpaio6PTqEE9jO5UrNWQ2TeVKiXHrxzn2+t7uGKQhFKh4nzpUaIuPE2Qf9vG\nDl8QhIeMVsm/Z8+erF69mqCgII0lGzMzM1m9erV44HsXhYWFREVFUVhYqG6TSCR4eHjg4+NTrzdP\nlUrF+Rvn2Ze4j+vF1wFo527BjcxS+nXpiLOH/l3OIAiCoGXyDw8PZ/To0QwbNoygoP9r786jorqy\nPQD/iqFkUmQGFYmAhcqshYyhQWkbhzh12kTFRNt2aHu1+pJFR42y+rVJx3YI4pREOzEah0Rf1IT0\nM52EKDwIIlNKQQZBoVApoUBQFEqo2u8PmqslElGgKGR/a9Va4Z5bh71Tl+2te889ZxxsbW2hVCqR\nnZ0NCwsLxMbG9nScfZJarUZxcTFKS0u7/LAWEeHLs2lIqf4WKtNqrbbRI4Zi7eRZCHbm6/qMsc7p\n9Nw+J0+exCeffILs7Gxcu3YNgwYNwrx587Bo0SLY2dk9uZN+SKFQoKSkRPjZwMAAHh4ecHV1faqH\ntYoVV7DmwAcoqLkEsbEBxkkdYGxkCBMjE/zG/TeIco2C2JDP+Bljnddh8T9//jz8/f2FIYh2dnZ4\n6623dBbY82DIkCGQy+VQKpWwsbGBr68vzM2ffjGUK3cuo/xeMQDgfrMG1ysa8YeJMzF55GReSpEx\n9kw6LP6vvfYaTE1NERAQgNDQUISEhGDkyJG6jK3PaW5u1hqvLxKJ4Ovri+rq6qd6WIuItPad4BqJ\n0a6nkJNfgV+5hWHDnN9jiJV9t8fPGOs/Oiz+u3btQnZ2NrKzs7Flyxao1WrY2toiJCREeD3L5R6F\nQoG///3vOHfuHDQaDV588UWsWbNG60ZyX9PU1IS8vDw0NDQgPDxc65KOmZkZXFxcntiHStWCH9ML\n8dm5LxHgEIr/WhQltIkNxXjrN3+CKkgMqYekR3JgjPUvHRb/qKgoREW1FqDGxkb8/PPPyM7ORmZm\nJv7617+iqakJ7u7uwreCzizsTkRYunQprK2tcfDgQQDAO++8gz/+8Y84ceJEN6WkO48+rAUAJSUl\nkEierkDXNtbii9xT2Pm/J0AgVFQrsUAZAlvbB1Nnezt6AY7dGj5jrB/r1A1fU1NTBAcHC0M6W1pa\nkJmZiS+++AKHDh3CgQMHUFBQ8MR+lEol3Nzc8OabbworUC1cuBB/+tOfUF9fD0tLyy6kolt3796F\nTCZDTU2N1naVSvXE91ZWNsDW1hQNLbdxuuQ0UuWpUGvUsLQUo65ehRrDKziblY+XowN6KnzGWD/X\n6YndVCoVMjIykJ6ejoyMDBQVFUEkEsHb2xuhoaGd6sPOzg7x8fHCzwqFAl988QW8vb37TOEnIpSW\nlqK4uFjrYS1zc3P4+PjA1rbj6ZHPnbuBM2cqUFheAffJN1FplA+15kEfQ4dZwHvoKCz91VxIR3j3\naB6Msf7tF4t/cXExUlNTkZqaiuzsbKhUKgwfPhyhoaFYsWIFgoKCnmmqYaB1XqCkpCRYWloKl4D0\nXUcPa7m5uUEikTzxYa2Ccjm+u3kCNwddQsmlAfDyevAPhZu1G1YHvYRRtqN4rD5jrMd1WPzDw8NR\nXV2NQYMGITAwEOvWrUNoaOgzLxj+qFWrVmH58uXYs2cPFi1ahFOnTun1Td/CwsJ2K2tZWlrC19f3\nsd9aWlo0MDLSHstf45iBqgH5EIlEMDQSgUBwt3bHNMk0jLYdzUWfMaYzHRb/qqoqWFlZ4eWXX0ZI\nSAikUmm3Lt7i4eEBAIiPj0dERAROnjyJ5cuXd1v/3c3AwEAo/IaGhsLKWo8W7Fu3mnD69FXk5Snx\n3/8dAmPjB98GZvu8hPPyHFhYGGOMwyhMk0yDh40HF33GmM51WPz379+P1NRUpKSk4J///CdMTEyE\nMf9hYWFwc3N76l+mVCqRkZGBqVOnCttMTU3h7OyMmzdvPlsGOuLu7o4bN25ALBZ3+LCWRkP4xz/O\no/z2VVSKLyD1p2GI/NUIod3VyhWvSmfAy94LEhsesskY6z0dFv+20T2xsbFQKpVITU1FWloa9u7d\ni/feew+Ojo4ICQlBWFgYQkJCOjVPzY0bN/DGG29g+PDh8PZuvaF5584dXL16FbNmzeq+rLqAiKBQ\nKGBpaQkzswdDLQ0MDBAcHAyxWPzYM3UiQoHyEmpGfYufL8kAAKfzf0TkrxZr7Td79OyeTYAxxjqh\nU6N9bG1tMXPmTMycORMAUFBQgLS0NGRlZWHNmjVQq9XIz89/Yj9eXl6QSqVYv349Nm7cCCMjI2zb\ntg3W1tZC372pqakJFy9ehEKhgJ2dHQIDA7UK/YABA4T/rqtrQkXFHXh62SD7Rjb+XfpvVNRXgKwI\nNjYmGOJkAcMhJdCQBgaizs/jwxhjutDpoZ4AcPv2beTm5iI3NxcXLlxAXl4e1Go1PD09O/V+AwMD\n7Ny5E5s3b8ayZcugUqkQFhaGQ4cOPdOcN92FiCCXy3Hp0iW0tLQAAKqrq3H9+vV2N7hVqhacPFmC\ns/93BVUmBXD7dRVuN9cJ7YYGInh72iNoWBAmuU3iws8Y00u/WPzLysqQm5uLnJwc5Obm4sqVK9Bo\nNHB3d0dQUBDmz5+PwMDApxruaW1tjU2bNnU58O7S0NCACxcutHtYy8XF5bGjjzQGzThVeAr5ZufR\nIlLhbslAvODSOtrH2NAYLw5/Eb92+zWsTa11Ej9jjD2LDot/UFAQ6uvrQUQYMmQIgoKCsGzZMgQF\nBT0XUzhrNBrhYS2N5sHSh+bm5vD19YWNjQ0AQK3WwNDwwdm7oYEhDF2voiVPhYEDxbC0HABzsTki\nX4hE5IhInmWTMdYndFj8AwMDERISguDgYAwf/nwtC1hXVweZTIbbt28L20QiEdzd3TFy5EgYGBig\nsLAG//53GYzN1FixZLywn9hQjDnjp6JF9CXchgzFJLdJCHEO4fn0GWN9SofFPyEhQZdx6My9e/eQ\nmpqq9bDW4MGD4ePjIzysVXatBrG7P8GNATKYaazwu2ov2Nk9GPkzYUQkhg0aCn8nf76mzxjrk57q\nhu/zwMzMDM7OzpDL5TA0NBRW1hKJRFDeU+LM1TNIq0hDzRA57t1SodGgDukXijF9op/Qx8ABAzFu\nyLhezIIxxrrmuS/+jy6MAgBjxoyBWq2GlZUz0tOrIatMRaX4Ai5WXRS+ETg7D4Kp6T24DbfFsDGa\nx3XNGGN91nNb/IkIlZWVuHz5svBwVhtjY2PU3R2EuP2f4MaACxhwtRE+Pto3sT2GDsfy0EgEOwfD\nxMhE1+EzxliPei6Lf2NjI/Ly8qBQKAAAly5dgp+fn9Y++aIkXDFLARHQWA/cu9cMMzNjeNp7YsKI\nCfC08+Q5dxhjz63nqvgTEcrLy1FQUICWlhYQATU1jSgszIe7uwcsLEyFfSePmYj/Sf8eag3B1dkO\nUz0jEfFCBBws9HdmUcYY6y7PTfFvaGiATCZDbW2tsC334nUU11WiiEohzQ1G5IuuQpublRvmT/gN\nRtuOwvih4zHAaMDjumWMsedSny/+Go0GJSUlKCoqBtB6s7a2sRaK+wpcsCzApfpqQAQcTfkekS8u\nE94nEomwdNySXoqaMcZ6V58u/nL5TZw+/RMqK2swwFSEwcPuo7KhEvVm9WiybIKlmRFMq41gb2eK\nEaMbejtcxhjTG326+NfV3UbhlTLcM6xBU0sdrBvEaLJthEbcOjRTLDbC65MnIHJEJLzsvXo5WsYY\n0x99uvhr7O7iutklGDcbo1JTB5W5GJbi1rl2Qp1DEe4SDjvzvj8PEWOMdbc+Xfw97T1h8oIRmlru\nwdXWAiOsXBA5IhIBQwJgbNh9S04yxtjzpk8Xf2NDY/w2MBrV96oR+UIkXK1ceWw+Y4x1Qp8u/gAw\nY9SM3g6BMcb6HJ6SkjHG+qE+ceavVqsBQJiugTHG2C9rq5dt9fNRfaL4V1dXAwDmz5/fy5Ewxljf\nUl1dDRcXl3bbRfTwqiZ6qqmpCXl5ebCzs4OhoWFvh8MYY3pPrVajuroaXl5eMDFpPzNxnyj+jDHG\nuhff8GWMsX6Iiz9jjPVDXPwZY6wf4uLPGGP9EBd/xhjrh/Su+MfFxeHtt9/W2nbq1ClMmzYNfn5+\n+N3vfoe0tDSt9sOHD8PDw0PrNWbMGK19Pv30U0RGRsLX1xeLFi1CWVmZXuVw//59bNq0CaGhofD3\n98fSpUtRUVHRZ3LYuXNnu8+g7bVr1y6d5/Asn0FFRQWWL18OqVSKsLAwrF+/Hrdv39baR58/AwAo\nKyvDkiVLIJVKER4ejh07dqClpUWnOSiVSrz11lsICwuDVCrF4sWLUVxcLLSnpqZixowZ8PHxwUsv\nvYTk5GSt99fU1GDVqlWQSqUIDg7Gli1bdJpDV+Nvc//+fUyfPh1fffVVuzZdHkcdIj2h0Who+/bt\nJJFIaN26dcL2xMRE8vDwoA8//JCuXLlChw4dIm9vbzp37pywT1xcHC1fvpyqqqqEV3V1tdB+7Ngx\n8vf3p9OnT1NhYSEtW7aMJk6cSCqVSm9yWLNmDYWHh9NPP/1ERUVFtGDBApo2bRppNJo+kUNDQ4PW\n//+qqiqKi4uj4OBgUigUOsvhWeNvbm6m6OhoWrFiBZWUlFB2djZFR0fTn//8Z6EPff8M6urqKCQk\nhBYsWED5+fmUmZlJ0dHRtHbtWp3loFar6ZVXXqE5c+aQTCajy5cv08qVKyk4OJhqa2vp8uXL5OXl\nRXv27KGSkhKKj48nT09PKi4uFvqYO3cuzZs3jwoKCujs2bMUFBRE77//vk5y6I74iYju3LlDf/jD\nH0gikdCpU6e02nR1HD2JXhR/uVxOMTExFBgYSBEREVoH/PTp0+nNN9/U2v/tt9+mmJgY4ee5c+dS\nQkJCh/1PmjSJduzYIfzc0NBAfn5+9PXXX+tFDnK5nCQSCf30009Ce2lpKUVERFBZWVmfyOFROTk5\nNGrUKEpOTha29XQOXYm/qKiIJBIJFRYWCu2HDh0if39/ncXf1Rz2799P/v7+dOvWLaE9KyuLJBIJ\nVVRU6CSH/Px8kkgkVFJSImxTqVTk6+tLJ0+epA0bNrQ7ZmJiYmj9+vVE1HrcSCQSksvlQvuJEyfI\n399fKI49mUNX4yciSktLo4kTJ9KsWbMeW/x1cRx1hl5c9snJyYGTkxMSExMxbNgwrbby8nJIpVKt\nbaNHj0Zubq7wVbCkpARubm6P7bumpgZlZWUYP368sM3c3BxeXl7IysrSixxSU1NhbW2N4OBgod3V\n1RVnzpyBi4tLn8jhYUSEd999F5MmTUJ4eDgA3XwOXYnf0tISBgYGOHbsGFQqFWpra/Htt9/Cy8tL\nZ/F3NYfy8nKMHDkSgwcPFtrbLn9mZWXpJAcnJyd89NFHGDFihLCtbZr1+vp6ZGVlaf1+AAgMDBR+\nf1ZWFoYOHQpnZ2ehffz48bh79y4KCgp6PIeuxg8AP/74I2bOnInPP/+8Xf+6Oo46Qy/m9pkxYwZm\nzHj81Mz29vaorKzU2nb9+nU0Nzfj9u3baG5uRn19PVJSUrBz5040NjYiICAAsbGxcHBwECY3cnBw\naNdvd04U15UcysrK4OzsjMTEROzbtw+1tbUYO3Ys1q1bB0dHxz6Rg7W1tbA9KSkJly5dwrZt24Rt\nusihK/E7ODhg/fr12Lp1K44cOQKNRgM3NzccOnRIZ/F3NQd7e3ucOXMGGo0GBgYGQjvQWnR0kYOV\nlRUiIiK0tn322WdoampCWFgYEhISfvH337x5E/b29u3aAaCyshJGRkY9mkNX4weA9evXd9i/ro6j\nztCLM/9fMn36dBw+fBjp6elQq9U4d+4cvvzySwBAc3MzLl++DAAwMjJCfHw83nvvPZSVlWHhwoVo\nampCY2MjAGDAgAFa/YrFYqhUKr3IoaGhAVeuXMH+/fuxdu1aJCQkoKamBq+//jpUKlWfyOFhBw4c\nQHR0tNZkUr2dw5Pi12g0uHr1KoKDg3H06FF8/PHHMDQ0xOrVq6FWq3s9/s7kMHnyZNTU1GDLli1o\nbGyEUqnEO++8AyMjIzQ3N/dKDklJSXj//fexaNEiuLm5oampCWKxuMPf39jY2C4+Y2NjiESiXvlb\neNr4n0QfjqM2enHm/0uWLl2K2tpaLFmyBGq1Gu7u7li8eDG2bduGgQMHIiwsDOnp6Vpnnu7u7ggP\nD0dycjKGDh0KoPXO+8Pu378PU1NTvcjByMgId+7cQUJCgvB1d8eOHQgLC0NycjKGDBmi9zm0USgU\nOH/+PA4cOKD1/raJpXorhyfF//XXXyMxMRFnzpyBmZkZAMDFxQVRUVFITk4Wzj71+TNwcHBAQkIC\n4uLi8Omnn8LMzAwrV65EUVERBg4cqPPP4MSJE9iwYQOmTJmC2NhYAK1F79GThYd/v4mJSbv4mpub\nQUQwMzPTaQ7PEv+T9PbfwcP0/sxfLBYjLi4OOTk5SElJQWJiIkxMTGBrayv8kT5c+IHWr1BWVlao\nrKyEk5MTgAfTQrepqqpq99Wrt3JwcHCAmZmZ1nVOGxsbDB48GNeuXesTObRJSkqCnZ1du+uivZ3D\nk+KXyWRwdXXVysXZ2RlWVlaQy+W9Hn9ncgCACRMmIDU1Fcn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X17O2NQylc3R0RKfTcWaVtoZC1mAusA7w9ttvExYWZnXc6b8MFMUWer2eoqIi\nNDSOFh/laPlRKv0qqXOvAx1cO3g4BUX9KK3Rc+ut0QQEuJ2/UaVVNXXn74z1xK7t9V+dgIbb0X31\nX22t+vUbUAHEA3vAMgKoH/C9jW0omLt5fv/9d6tte/futewrKSmxFFH38fEBYP/+/ZZjw8LCcHJy\nIjc3l1GjRlm2//vf/8ZoNPLwww9fhHehdBQODg4ERwbzv2//x0nHk1QGV6FzBBdHF6b0m8KVPa8k\nL6ISvV5Hly7qjv9S0NQkrzEtfTEpZaUQ4nVgvhAiF/MngDlAJOaRQ4qN7r33Xm655RYWLlzIlClT\nyM7O5rnnnmP06NFERkYSFBTEokWL+Pvf/86jjz5Kbm4ub731luV8Nzc3Zs2axWuvvYaHhwcxMTFs\n2bKFRYsWMX/+/DZ8Z8qlTtM0cnNzCQoKsnwy3ZW1i4/2f0SVZx3J6QV4ljpxbfxlzBw4k0B3czdi\nUJBHU80qF1mjn++FECOa06AQYuR5DpkLvAq8gTn5Xw5cLaWUzbleZxUdHc27777L7t27ufHGG3nq\nqaeYMGECb775JgCenp6sXLkSg8HAlClTeP7557n33nut2vjrX//KHXfcwSuvvMJ1113Hf/7zH55/\n/nn+8Ic/tMVbUtqBsrIyduzYwa+//kpOTo5le4hnCOWVNfyaeJzSEgPOhwdxvf8sS+JXLj26M/uF\nGwghEoBk4EUp5f5zHmR9fDzmh79RUsoW7SgXQoQDR2xdlkBRlJZlMplITU3l8OHDmEwmAFxcXBgz\nZozl+dEGuYH31n+N75EReGiBTJkSzfjxYU01q7SirKwsxo8fD9DrXKsnNNXnPxSYB+ypX9XzU2A3\ncARzv70v5r7/K4HrME/gehuY1nLhK4rS1k6ePEliYiJlZeZ1Hg0mA5WGSuJFvNUghYnRE7ni3nEs\nXZLElCmCiAjftgpZsUFTff51mJdvWAw8AtyLucvm9I8KOuAo8D/gBill9lkNKYrSLp05WQuguLqY\nlPIUyv0qCDwRR3T0qZ5jvU6Pv587f/+7mrDVHpx3nH99Qn8MeEwI0QeIwLywWwGQKaW0bQqtoijt\nRm5uLklJSZblQkyaiczSTFL1qRS5VpC8r5DdpW/h5zqPyy6zHuynEn/7YFclLyllCuZZuYqidFAZ\nGRkkJVmm4lBZV0lKVQo5HjlojhrZqeUYKpyIqBnCmjUp9OkTgLe3Wna5vVFlHBVFsRISEoKUktra\nWnKrc0meTfKYAAAgAElEQVQyJVHtVW3u5AVuGn4lWRsFNdWOTJ4cjZeXc9sGrDSLSv6KolhxcXEh\nPCqcL3//ksNOh9EczP39Tg5OTO0/lZE9R3IstAwXFwc1dr8dU8lfUTopTdM4cuQINTU19O3b17I9\nOT+Z5YeXU+xYQvqRYtzcnBjWpw+zB88mxCsEgJ49VT3d9k4lf0XphEpLS0lISKC4uBidTkdQUBD+\n/uY6uTXGGvJLT5K0v4DKSgM9DYO5a+JDhHj5tXHUSktSK3gpSidiMplISUnhp59+ori4GDB/AkhP\nT7ccMzB4IFdFjcNN78mAipsIrxjJnt35bRWy0kpsLePoCjyFuYavB2f/0tCklBdWyURRlFZ18uRJ\nEhISKC8vt2zT6/X06NWDAX0GWB1724CpDPMbx7tvpnDzzVFceWX3M5tT2jlbu33exFx05UdgP2Bq\nrYAURWlZBoOB5ORkMjIyrLb7+PqQ5pzG9uPbud/nb4R372LZ5+TgRFTPEF56qQsuLqp3uCOy9V/1\nVuBpKeXC1gxGUZSWlZubS2JiItXV1ZZtjo6OdA3ryobcDWSdzObIkRJ2bHqRZQ88S3S0v9X5KvF3\nXLb2+TtjXtdHUZR2QtM00tLSrBJ/UFAQHlEefJDxAcfLj5OWXkz28XJ0mp5ly/dRWVnXRItKR2Jr\n8v8W8+JtiqK0EzqdjtjYWPR6PS4uLsTExXDQ6SCrk1dTazSXA40M9ydGuxpReS29wvzPqv6mdFy2\nfqZbBSwVQgQCO4HKMw9oqMmrKErbqKysxM3NzWptHU9PT4YOHUqtcy3LE5ZzvOxUxdVgz2DuG3If\nhZHOFBdXM3JkqFqXpxOxNfl/Wv91Vv2fM2mASv6K0gYaJmulpKQghCAyMtJq/1HDUT767SMKikox\nGDT8/FwZHjqcaTHTcHF0ofvFK1OtXEJsTf4tXlxdUZQLd/pkLQApJcHBwXh4mJddSM5PZulvSzme\nXU76kRKcHZxYMH0m1/Uf15ZhK5cAm5K/lDKz4bUQwgPwAgrr1/xXFOUiMxqNlspap/fTe3h4YDQa\nLd/3CexDX78B7P7le1yNvvQtnciRrX7Qvy2iVi4lNo/jEkKMARYCQ6hf308IsRt4Rkr5Q6tEpyjK\nWQoLC0lMTDxrslZ0dDSRkZHo9afGceh0Ou4fNhuq3Tn4aTARPbswdaqaj6nYPsN3FOYRPymYq3nl\nAt2AqcBXQojxUsptrRaloijU1dWRnJxMZmam1faAgABiY2Px8PDgl+xfiO8Wj4PewbLf3cmdR66a\nTXL3QqKi/HB0VKu6KLbf+b8AfA9cL6W0fMYUQrwIbMRc63d8i0enKAoAZWVl7Nq166zJWv369aNn\nz55UG6p5d8+7/HpsL8uPbeP52+YQHGy93HLfvgEXO2zlEmbrLcBQYNHpiR+g/vtFQHxLB6Yoyinu\n7u44OJy6mw8KCmLMmDGEhYVxovwEC7YvYOuhX9j7Wx7bsn9k/pLPqaszNtGi0tnZmvyLAM9G9nkB\n6n+ZorQiBwcH4uLicHFxYciQIcTHx+Pm5kbCiQRe3v4yueW5ODroMRhMdK8ZSHW2PwcOFLZ12Mol\nzNbkvxmYJ4SwqtRc//08zF1CiqK0gIqKCqSUZ822DQgIYPz48XTrZv4x3HhoI4t/XUy1wdwV5Oft\nwZ+vuJ+BThP461/iGTiw60WPXWk/bO3zfwrYA6QKIbYDJ4Bg4EqgFHiidcJTlM6jYV19KSVGoxEv\nLy9Lom/g4OBAtaGaD/Z9wG85v6GrL6wb4B7AnPg5dPfqTuX4Ojw8VF1dpWk23flLKbOBQcBiwAe4\nHPDF3N8/SEqZ3sTpiqKcR0lJCdu3b+fgwYOWcfoHDhzAZLJePb2gsoCXt7/Mxt+28ftveRiNJvoE\n9uHpkU8T6m1enkElfsUWNo/zl1KeAB5vxVgUpdMxGo0cOnSItLQ0q24eb29v4uLirMbsA3yw7wN+\n+v0gOTkVAOgyovjLjX+xGtqpKLZoNPkLIZ4GVkgpc+pfN0WTUi5o2dAUpWMrLCwkISGBiooKy7bG\nJms1mBk3k72HDpGbU01U5TjCyodRU23C3V0lf8U+Td35v4j5QW5O/eumaIBK/opig/NN1vL0bGxg\nHXTx6MKzN/yNb/TH8NVCmDatL05OKvEr9ms0+Usp9ed6rSjKhUlJSbFK/KdP1jp9SeXSmlKOnMxA\n+PXD1fXUj2qfwD5EzxDo9Wr5ZaX5bErqQoi5Zw7zPG1fmBDirZYNS1E6rujoaJydzQ9lg4ODGTt2\nLGFhYVaJ/1jJMZ79/gX+tPwFFry76axhnyrxKxfK1ge+zwJfAcfPse9y4D7gLy0VlKJ0FJqmoWma\nVf+9i4sLsbHmRfSDg4PPKqCy9/helu55n593Z1Fba2R90SqGbBTceINakE1pOU098N2OObGDeRXP\nXUI0+p/vV1svKIToBxw4x66RUsrttrajKJe6iooKEhMT8fT0JCYmxmpfSEjIWcdrmsaGQxvYcGgD\n6CAoyJ2cozVEV0/A2VEN31RaVlN3/rOByZgT//PAEiDrjGOMQDHwuR3XjAEK6r+eTs1FVzqEhsLp\nhw4dwmg0UlBQQPfu3fH392/0nBpDjWXiVoPL+vXGx3EsN4wZqBZlU1pcUw98U4D5AEIIB2BZ/WSv\nCzUAOFg/b0BROpSSkhISEhIoKSmxbNPpdBQXFzea/AsrC3n1xzc4acy1zNjt26Uv9w6+F4/xHuc8\nR1EulK2VvJ4DEEIEAM7UF3PB/MDYA3OXzTIbrzkASLYzTkW5pDU2WcvHx4e4uDh8fHzOeV5qYSrP\nbniNxOQsunX3pFe4D2N7jWVq/6nodWqQndJ6bC3mEgOspvHibxpgT/J3FULsAsKB/cDTUsrdNp6v\nKJeUgoICEhMTrSZrOTg4EB0dTURExDkna4F5KOfcTS+z74D5Q3D2sQqm9Z/B7QNuuChxK52brbcW\nrwIBwGPAj8A3wEPAJsyJf4wtjQgh3IAIzOsDPQ7ciHkE0VYhRF874laUNmc0GklISODnn3+2SvwB\nAQGMHj2a3r17N5r4AbxdvJk9Yhr+/q44a26MdZ3B1X3GXITIFcX2oZ6XA49IKZcLISqA6VLKd4B3\nhBD/wzzM87wjdaSUVUIIP6BGSlkDIISYhbku8Bzgz814D4rSJvR6vVXSd3Jyol+/fvTo0eOs4ZuN\nGddrHKXXV1CY2JUZk4daTeZSlNZk6/80FyC1/vUhIO60fSuAd229oJSy9IzvTUKIA0APW9tQlEuB\nTqcjNjaWrVu3EhQUxIABA3B1dW30eJmfSlaqgfFX9LVq45aYG88e+6YorczWbp+jQK/614cAbyFE\nWP331UDjY9hOI4QYIoQoFUIMOW2bAzCQc4/9V5RLgqZpHD9+/Kwllj09PRkzZgxDhw5tMvF/kfgt\nM999kqc+fYWffzna2uEqynnZmvzXAS8LIW6RUh4HUoAX6vvpHwHSbGwnAcgA3hNCDBNC9Mf8ySEQ\neNOuyBXlIqmoqODnn39m7969pKefXbrCw6Px4Zh1xjo+TPiQN75fRklZNWUOeTy3dgknT1a1ZsiK\ncl62Jv/ngF3AvfXfPwLcinmkztWYSzmel5TSAFwHSOBLYDfmimCjpJR5NketKBeByWTi8OHD/Pjj\njxQWmucgSimt+vmbUlBZwMIdC9lxdAcRET64uTniZerCfeNvxc+v8U8JinIx2DrOvxL4gxDCpf77\nb+qHfw4GfpNS2nrn31AVbHpzglWUi6W4uJjExMSzJmtFREQ02b3TIDE3kRW/r6CyrhIABwc900Zf\nw6SetyJ6q9q6Stuza2hBwwid+tdp2N7doyjtgtFoREpJenq6XZO1LOebjCz4bAW7T24hJMS8Lr+j\n3pHbBtzGyJ4jbR4FpCitramF3VIxj+G3hSalVEsOKu1aY5O1hBBEREScN3GfKCrkwfdf4mBeCnq9\nDi9vZ3oEBvHA0AcI9w1v5egVxT5N3fnvwPbkryjtWk5ODnv27LHaFhgYSGxsbJMPdE+368R2jlWZ\nPwybTBp1xwN55g/P4OnceGUuRWkrTS3sNusixqEobapr1654enpSXl7erMlaAJPEDeyJT2T91t1c\nFzmRF+6ajYuzUytGrSjNZ+vaPlec7xgp5c4LD0dR2oaDgwOxsbEcOXLkvJO1GpSU1ODj43KqDb0D\nj45+iBvFUS7rFdfEmYrS9mx94Lud83cBqSrSyiVP0zSOHj1KYWEhgwYNsrqzDwgIICDg/Ovma5rG\nsvXf859t37D43qfo0+fUOX5uflzWy69VYleUlmRr8h97jm2ewEjgTsxFXxTlklZeXk5iYqJlzH5Q\nUBDdu3e3qw2jycg/PnqXLw5sQnOAuStXsOKZv+DhoSptKe2LreP8tzaya6MQohx4BlDr0CqXJJPJ\nZKmsdfryDBkZGXTr1s3mfv3CykKW/baMXM9UHJ301NWZyPNIpLyqWiV/pd1piSUEtwFPtkA7itLi\niouLSUhIoLT01HqCOp2O3r17ExUVZXPi33N8D6sSV1FVV4WzswPR0X741vXk1WmP4efu3VrhK0qr\naYnkPwkoPe9RinIRGQwGDh06dNZkLV9fX+Li4vD2ti1hpx7J45ODH3PUtN+yTa/Tc++I6VwdebWa\ntKW0W7aO9vn2HJsdMC/DHAksbMmgFOVC5Ofnk5iYSGVlpWWbg4MDffr0oVevXjYlbE3TWLVhB2/8\ntJhapzKGDO6Ki4sjge6B3DP4HiL8IlrzLShKq7P1zt+Zs0f7aMBB4BVgeUsGpSgXIisryyrxBwYG\nEhcXh7u7u81t/JaVwOu//pMqXR0YIPVwMfdccz3TYqbh6qgWZVPaP1sf+I5p5TgUpcX079+f/Px8\nTCYT/fv3JzQ01O7umf4hfbgiLorNvxzE18uTZyb+ietix7ROwIrSBuzq8xdCXId5eKcfkAtsllL+\n1BqBKYotqqqqcHR0xMnp1ExaZ2dnhgwZgqenJy4uLk2c3ThXR1ceG/8g7g4reXT8nwjyUitxKh2L\nrX3+AcBXwFCgBsgHugL/V/884BYpZXWrRakoZ9A0jczMTJKTk+nevTuxsbFW+22ZrNUgK7eQlz/6\nH/+YPt2yEidAuG84C2+aqx7qKh2SrcVc3sZcxnGSlNJNStlTSukK3IL5F8LLrRWgopypvLycn3/+\nmaSkJAwGA5mZmZaJW/b6fPsObn79QX7I+4Jnl3xMXZ3Rar9K/EpHZWvyvw54TEq58fSNUsovgKeA\nO1o6MEU5k8lkIjU1la1bt1ole09PT/R6W/8rm9Uaa/nv/v/yWc5yqigHYFfFRhIOZrdozIpyqbK1\nz98AFDeyLwfzaCBFaTXnm6zl4GD70lJHio6wYt8KcstzcXN1JDzMm5MnTDw9aQ5D43q2RviKcsmx\nNfkvBl4SQvxaX8AdACGEN+bZvW+3RnCKYjAYkFJy5MiRC5qsBXAk8yRfpW0iqXIHJu3UMg/XDb6C\nO/pPJ8BTLcimdB62Jv9u9X/ShBDbgeNAADAC8AJqTpsIpkkpr2nxSJVOp6qqip07d17QZC0Ag8HE\nh+t38O7Py6h1LWLIkCAcHfW4OLpwW//buKLHFapvX+l0bE3+vYF9p53T8Nm4YZsDaklnpYW5urri\n5uZmSf5dunQhNjbWrslaAL9k7uGt3/5Jjd4AtXAko4SJwy5j1sBZBLoHtkboinLJs3WS17mWdFaU\nVqXT6YiLi2Pnzp306dOnWZO1AGJD+zKgTwh7k47h7+POnNF3MXnQ9epuX+nU7J3k1Q8YDfhgHuu/\nXUopWyMwpXOpqqoiPT2dvn37Wo3c8fDwYPz48XaN5iktrcHb+9TkLi8XL/521X185LaOJ655kGCv\n4BaNXVHaI1sneemB94A/AqffLmlCiI+Au6WUqti7YjdN08jIyCAlJQWDwYCzszNRUVFWx9ia+Kuq\n6lj68XY2J/3K+0//mYAAN8u+wSGDGTR5kLrbV5R6tt5OPQncVf81FHDC3O//FHA78HirRKd0aGVl\nZezcuZP9+/djMBgASE1Npba21u62jCYjf120mPcO/gvpsJU3PvraanQQqAlbinI6W7t97gHmSylf\nPW1bFvCKEMK1fv8rLR2c0jGZTCYOHz5MamqqVWUtLy8vYmNjcXa2b9pIVmkWK/etpLRbKlqeub3f\n6r6mtnYSLi4tUbJCUToeW38yQoAdjezbifkTgKKcV1FREQkJCZSVlVm26fV6y2Qte/r2jSYjXx/+\nmo2pGzGajHh7udAzzJvegRE8fd2DKvErShNs/elIBy4HfjjHvssxz/JVlEY1NlnLz8+PuLg4vLy8\nbG7rxIkKFn20hcroXZTr8y3bHfWOPHLNLCZETkCvs2+5B0XpbGxN/suABUKICuC/mJdzDsK8ps/T\nwEutE57SUWRkZJCenm753tHRkT59+hAeHm5XX/zPvxzjxf+u5IjTLtwrHRk8qCs6nY4IvwhmDpxJ\nsKcayaMotrA1+b8NDAJeA/552nYdsAqY38JxKR1MREQEx44do7y8nK5duxITE2P3ZC2AfYZvyXTZ\nhWbSqKyso7LcxMxhtzE+Yry621cUO9g6ycsIzBRCvIK5mIs/UAT8JKU80IrxKe2QpmkYjUYcHU/9\n99Lr9cTFxVFZWUn37t2bPfJm8sBJfJW0ldz8Mq4aMpi/jLqPIM+glgpdUToNe5+IHcPc/18E5NW/\nbjYhxHBgO3CVlPLHC2lLuTRUVlaSlJQEwGWXXWaV5P39/fH397e5rd9/z8XJSc+AAV0s27p6dOWv\nV9+NwWTgqkh1t68ozWXPJK9XgIcwj/Fv+ImuEELMl1LaXcxFCOEBfIRaE6hDOHOyFkB2djahoaF2\nt1VWVsuq1Qf44uBGvN3dWTH3z7i7nyrTOC5CrTaiKBfK1tumecDDmPv+R2Be6G0EsBR4XggxpxnX\n/hfmuQJKO1dWVsaOHTusJmvpdDoqKiqa1V5eVQ5rji4iw/Vn9pt+ZNXnu1oyXEVRsG+S1/NSyhdO\n25YO/CyEKAMewbzmv02EEBOB6zFXCEu09Tzl0tJQWevw4cPnnKxlTxcPgEkz8V3ad3whv6BrVC0F\nydA12BXH6HTMj5oURWkptiZ/H2B3I/u2A4/ZekEhRCDwPnA35mcHSjt08uRJEhMTL3iylqZpnDhR\ngd6rghX7VnCk6AgAgYFuXDa0G9MG38qEyAmt8h4UpTOzNflvAB4AvjnHvtuBTXZc8z3gCynl10II\n+zuElTalaRoHDhwgIyPjgidrFRZWsXLlfrZl/UjAlWk4OJ1qL8w3jLvH3E2IV0iLxq8oipmtyf8n\nYL4QIhHzJK8czJW8bgCuBP4lhHi6/lhNSrngXI0IIWZini8Qe0FRK21Gp9NRV1dnSfzNnaylaRr/\nencrPxR+SonjcfykCwMGBOKod+SG6Bu4tve1aiSPorQiW5P/v+u/+gAvnmP/6d0+GnDO5A/Mwrwq\n6AkhBJwaNfSVEGKllPIBG+NR2lD//v3Jz8/Hx8en2ZO1AKr6b6d053F0gKenM929Qrln8B8J9VYf\nCBWltdk6yaulbsFmAG6nfR8MbANmA9+10DWUFqJpGsePH6dr1644OZ0aauns7MzIkSNxdXVt9mQt\nnU7Hg6Pu5nBeBt5eLkwdfBMToybiqFeLsSnKxXBRf9KklNmnfy+EqK5/mS2lzLuYsShNa5islZeX\nR1hYGLGx1j11bm5ujZx5tqKialatOsCkSZGEh/tatkf6R/LIhHuI8IsgzDesxWJXFOX81G2WYkXT\nNI4cOUJKSgpGoxGAzMxMunfvTkBAgN3tHThQwL+X/kyS7luSVg5k8T/uxtHx1AfJsb3UhC1FaQtt\nmvyllFlYl4VU2lBpaSkJCQkUFxdbtul0OsLDw/Hx8bG7PU3TyNIO8rPrSmpMVewqz+bXpDFcPiiy\nJcNWFKUZ1J2/YpmslZqaajV808vLi7i4OPz8/Oxus6ymjDVJa/gt5zd69HIhO7uOaOGNwf84oJK/\norQ1lfw7uZMnT5KQkEB5ebllm16vJyoqit69e9tVWauyso7CwioKndJZlbiKshrzBLCQbh70CQ/l\nniF30yewT4u/B0VR7Ndo8hdCdLOnISnl8QsPR7mYioqK2LHDujqnv78/sbGxdk3WAkhOLmTJB7+S\n4rCFbvEnrfr1R/YcyZT+U3B1dG2RuBVFuXBN3flnYR6zbyu1Omc74+vrS2BgIAUFBTg6OtK3b1/C\nwsLsHr5ZU2Pg5RWfs0/7mlqtksrDbvTpE4Cvqy93xt3JgK4DWukdKIrSXE0l/z9yKvn7Ay9jruH7\nCadm+N6IeZbv31oxRqWFaJpmldh1Oh2xsbEkJyfTv39/u4ZvWnEwosXupTaxEicnPYFd3BkeOpzb\nBtyGu1PzJoApitK6Gk3+UsoPGl4LIdYBH0op7z3jsDVCiDeBqcCSVolQuWCappGVlcWxY8cYPny4\nVT++h4cHQ4cOtbu903+JuDi68Nfxs3m28jV6dQtidvwsYoPUCh6Kcimz9YHv1cDNjezbAJz5S0G5\nRFRWVpKYmEh+fj4AaWlpREVFNbu99PRiVv9nP3MeGEJAwKlPCoNDBvPo1fcS3y0eD2ePC45bUZTW\nZetQjgLgskb2jQGyG9mntBFN00hPT+fHH3+0JH6ArKwsq7X37bFly1Ge/NcnfFr0Nv9csclqWCjA\nmPAxKvErSjth653/UmCuEMIN+ALIB4KAKcBfgL+2TnhKczQ2WatXr14IIewavtmgsq6SPYYN7Hff\niAZ8n/8Z92ePITzU/lm/iqK0PVuT/3zAF3gceOq07dXA/0kpF7V0YIr9jEajpbJWS03WAkg4kcDq\npNWUVJcQ2sOLsrJaBvfvgt6rAvNzf0VR2htbV/XUgMeEEC8AlwN+mLuCdkopm1eoVWlRjU3Wio6O\nJjIy0u67/bS0Ygy6KrYXb2J39qkibuFh3sR3j+eOmDvwdPZssfgVRbm47JrhK6UsAb5upViUC5Cf\nn2+V+P39/YmLi8PT074EXV1t4LPPUvl052Zyuuyg/yBP9PUje7xdvJkeO52BwQNbNHZFUS6+pmb4\npmL7JC9NSilaJiSlOaKiosjJyaGqqqrZk7UAThQXsvT39zjhngoVcOyYRlhPb4aFDuO2/repB7qK\n0kE0dee/A/tm+CoXSU1NDSaTyWpSll6vZ/DgwTg5OTV/shbg6e2Ab1QxJw5DQIAr0T1DmH2ZGrev\nKB1NU5O8ZjW8FkLcDvwgpcxv7Hil9TVM1jpw4AC+vr4MGzbM6u7e29vbrvZMJo28vEqCg0/dzQe6\nBzJn/AyWuH7IjXETmNxvspqlqygdkD1DPWcBn7ZeKEpTKisrSUhIoKCgADD38WdnZxMa2rx6t5mZ\nJXy06gDpRem8/dxUPDycLfvGR4wj0j+CCL+IFoldUZRLj63JPxtQt39toGGylpTSUlkLwN3dHVfX\n5q2SaTJpvLLkG3ZXb6LCoYD3P+nOX+4+VVFLr9OrxK8oHZytyf8d4E0hxHAgASg/8wAp5ZqWDEw5\n/2QtR0f7yzFUG6r5Qn5BXvRGyg8UoNfr2Gf6GpNpdLMmfymK0j7Zmj1er//6p0b2a4BK/i2kscla\n3t7exMXF4evr28TZZ6utNeLkpGfP8T2sPbiWkuoS/P1dCQ/3pluQN1PjxqlimorSydia/Hu1ahSK\nhcFgYNu2bS0yWctoNLF581HWfr2H0GvTyK5Ot9p/7eDhTI+dTqB7YIvFryhK+2DrDN/MhtdCCA/A\nCyiUUta1VmCdlaOjI35+fpbkHxAQQGxsrN2TtQCWf7iPtfvWk+3yG96/OhETE4gOHT6uPkzpN4Wh\n3YY2ay6Aoijtn82dxkKIMcBCYAj1nQRCiN3AM1LKH1oluk6qX79+nDx5ksjISHr27NnsBJ0fupWs\n5D1oQF2dCaNB45roq7hR3KhKKipKJ2dT8hdCjAK+BVKAuUAu0A1zEZevhBDjpZTbWi3KDqqmpgYp\nJX379sXJycmy3dnZmbFjx17wXfn0+D+wVe7GwUHHqAFxzIibTqh384aGKorSsdh65/8C8D1wff0i\nbwAIIV4ENgLzgPEtHl0HpWkax44d4+DBg9TV1aFpGnFxcVbH2JP48/IqeH/1r9xyfX/6RHexbA/z\nDeNPV91GkEcQw0OHqy4eRVEsbH16OBRYdHriB8tqn4uA+JYOrKOqqKhg165dJCQkUFdnfmRy9OhR\nqwe89ti1J5NZL7/Gqpx/8dKaNRgM1oVabu5zM5f3uFwlfkVRrNh6518ENPbE0QswNrJPqdfUZK3m\nrL5p0kzsOLqDT3I+46hLKiajxr6KrSQcvIUhsT1bOnxFUToYW5P/ZmCeEGKblPJ4w0YhRDfMXT7f\nt0JsHUZJSQkJCQmUlJRYtul0OiIiIhBC4ODgYHNbmqax78Q+1sv15JTlANAr3IcTuRWMHtiP7hHO\n52lBURTF9uT/FLAHSBVCbAdOAMHAlUAp8ETrhNe+GY1GDh06RFpa2gVP1tI0jU9/3MFP+V9T42a9\nvl7fXt156rpbuLyH6tdXFMU2to7zzxZCDAIeBUZinvRVhLm//19SyhOtF2L7deLECQ4fPmz5Xq/X\nI4QgIiLCrslah06k8+TKd0guPIizk54hQ4NwcnTA1dGVa3pfw1URV+HsoO74FUWxXVPFXEZjLtNY\nB1Cf4B+/WIF1BN26dePo0aMUFBQQEBBAXFwcHh72F0NJL0sls/IQALV1JrKPVTF7/M1cF3WdKqWo\nKEqzNHXnvwWoEEL8hHmM//dSygMXJ6z2qa6uzmq8vk6nIy4ujvz8fLsma2maZnXsuIix9I34nN8O\nHGN05JX839Q/0s2va4vHryhK59FU8r8Fc5/+SOBVwEEIcQLzw93vMP8ysLu7RwgRinmhuPGYh5p+\nDfzt9AfJ7U11dTX79++nvLycUaNGWXXpuLu7ExYWdt42amoMbP45hY92fUp80Ageufsqyz5nB2ee\nuCyMn20AABLhSURBVOZBaoY7M1REt8p7UBSlc2mqktd6YD2AEMIduBzzL4NR/H97Zx5eVXUt8N/N\nzQAJGAMJyBAZElgIGLC1IihosKCoSGutny3Pp++1pa2ftWpfpd9rrVVbqq991qG+j34dbG1f1U7y\n7IBCVapYh2o1QIYFYQpCgBAMGAKR5N73xz43OYQMF5Lcgbt+33e/JGfvs89aOfuuvc86e68Fy4GB\nIlKOGwhWq2qPid1FJIDbFFYHRALIPwz8ERc2IqnouFkLoLq6mokTT8xA7z+8n6feXsEjf/kDYcLs\nqNvH9ftmkZ/fnkLh7DOmulfshmEYfUC0L3ybgOe9DyKSDlwELAFuBm4FolmvOByoBL6mqtu8th4A\nVohInqq+d6IKxItDhw5RVlZGfX39Mcebm5t7PLe2tpH8/IE0thxkZfVK1taspTXUSm5uJg0HmqkP\nbmHNm+Vcc5ntnTMMo384kcBuA4CLgY/iZu0luDj+b+DeCfSI5ya6ztfmaODzwD+SxfCHw2E2b97M\nxo0bj9mslZOTQ0lJCfn5XYdHfu21Xbz44g6qtu+geMEeatPLaQ21tzFq9CDOHjWJJRd9inPHnd2v\nehiGkdp0a/xFZCpwqfe5EBgAbMYZ+3uAF1X14MlcWERWAItwS0ZLe6ieEHS1WauoqIiJEyf2uFmr\ncnsNq/b8gT2nVVBdkcXUqe0DRdGQIm49fyGT8ifZWn3DMPqd7pZ6vguMwBnnNTjXzqqIu6YPuBNY\nBnwDWC0i56jqzj5qu8+pqqo6LrNWbm4u06ZNIzc397j6LS0h0tOPXctff8br7M0qJxAIEEwPECZM\n8ZBirpx4JWfln2VG3zCMmNHdzH8ksA/4Ke6l7st9mbxFVdcDiMh1wA7gBtxgkJCkpaW1Gf5gMNiW\nWaujwX7vvSOsXLmVDRv2cffds8jIaH8auLpkIW/U/JNBgzKYPHwSV068EhkqZvQNw4g53Rn/j+Lc\nPQuAO4Am35r/VapaeaIXE5HhQKmqPhk5pqpNIrIZGHWi7cWS4uJidu3aRWZmZpebtUKhMPff/wbb\nD26lNnMda/8+mtKL2jNgjs8bz3XnLmLqsKlMHGpLNg3DiB/dLfV8ARfQbalntC8F5uHi/PzAcwut\nxg0Gq1V1fxTXGwM8ISLVqvomgIjkAgL8olea9BHhcJjdu3eTm5tLdnb7Usu0tDRmzpxJZmZmpzP1\ncDhM5b4K6ic9yzsVZQCsLH+B0os+c0y9q8+6un8VMAzDiIJol3ruAR73PojIdNxAMAf4uddORlfn\n+3gTeBn4iYgsAY4C9+HW/cfd+B85coT169eze/duCgoKmDFjxjGGPisrq+33hoYj7NjxPlOmDuWt\nXW/x3Obn2HFgB+G8MEOHDmDkiEEER1YTCodIC0Qfx8cwDCMWRL3UE0BETsdt9poFzMAleUkH3orm\nfFUNicjVwPeBP+FWDz0HXKSqJ5fNpA8Ih8PU1NRQUVFBS0sLAHV1dezcuZPRo49Ne9jc3MLTT1ez\n5uUt7B1QSdG8vRw82tBWHkwLcPaUYZw/+nzmF803w28YRkLS01LPCThDf4H3cxIuJEMFbsPXD4E1\nJ7LcU1X3ATeepLx9TmNjI+vWrTtus9aYMWMYPnz4cfVDaUdZUbWC8uw3aAk0c6h6MGPHuNU+GcEM\nZp85m3lF8xgycEhM5DcMwzgZulvqWQcMAQJADc7YLwNeOBVCOIdCobbNWqFQe+rDnJwcpk2bxtCh\nQwFobQ0RDLbP3oNpQYLjt9KyoZnBgzPJzc0iJzOH0rGllI4rtSibhmEkBT1F9fwr8Lyqbo6RPDGh\noaGBsrIyDh5sf2AJBAIUFxczYcIE0tLSqKqq57nntpGR3cpNnzuvrV5mMJNrz7uClsDvKRo5ivlF\n85lVOMvi6RuGkVR0t9rn2lgKEiuamppYu3btMZu1Tj/9dEpKSto2a217t56vPvozdmWVkR3K45N1\nUykoaF/5M3dcKaNPG8U5I84xn75hGEnJCb3wPRXIzs6msLCQmpoagsFgW2atQCDAvqZ9vLj1RV7Z\n8Qr1I2toeq+Zw2kNvLpuI1ddMr2tjcFZg/nwyKQLQmoYhtHGKW/8OyZGAZg8eTKtra3k5RXy6qt1\nlNWupTZzHev3rm97IigsPI2BA5soOjOf0ZNDnTVtGIaRtJyyxj8cDlNbW8umTZvaNmdFyMjIoOHQ\naXzzsZ+xK2sdWVsPU1JScMz5MupMvnBBKTMLZzIgfUCsxTcMw+hXTknjf/jwYTZs2MDu3W5RUkVF\nBdOnTz+mTnngebZkv0Q4DIcPQFPTUbKzM5gybApzx81lSsEUi7ljGMYpyyll/MPhMNu3b6eyspKW\nlhbCYaivP0xVVTnFxcKgQQPb6i6YfAm/e3U1raEw4wsLuGJKKRePvZjhg45f228YhnGqccoY/8bG\nRsrKyti/vz3E0Nvrd7KxoRYNb+bct2dSOnt8W1lRXhGL517KWfmTOG/UeWSlZ3XWrGEYxilJ0hv/\nUChEdXU1qhtxicVcTtzdH+xmXW4lFQfqIABPvLSa0tmfbzsvEAiw5MOfi5PUhmEY8SWpjX9NzR5W\nrvw7tbX1ZA0McProD6htrOVA9gGO5B4hNzudgXXpDCsYyLiz4hY6yDAMI+FIauPf0HCQqi3baArW\nc6SlgSGNmRzJP0wo0y3NzMxM54YFcykdV8rUYVPjLK1hGEbikNTGP1RwiJ3ZFWQczaA21EBzTia5\nmS7WzgWFFzBnzBwKcgp6bsgwDCPFSGrjP2XYFAaMTedISxPj8wcxLm8MpeNK+cjIj5ARjCa9gGEY\nRmqS1MY/I5jBJ2ZcRl1THaVjSxmfN97W5huGYURBUht/gEWTFsVbBMMwjKTDQlIahmGkIMky8w8C\nbeEaDMMwjO7x2ctgZ+XJYvxHACxevDjechiGYSQbI4DjEnIli/H/BzAbqAVa4yyLYRhGMhDEGf5/\ndFYY8Ge0MgzDMFIDe+FrGIaRgpjxNwzDSEHM+BuGYaQgZvwNwzBSEDP+hmEYKUjCLfUUkeVAuqp+\n1nfsemApMA7YAHxDVVf7ym8CHu3QVKuqpvvq3AbcChQArwA3qeqmBNIhE/gusBjIAV4CblbVrcmg\ng4h8C7iri+buUtV7YqnDSd6DccBDwBzgMPAn4Kuq2uCrk7D3wCuf4OkwC2gEfgrcq6otsdJBRIYD\n/wXMBwYCrwNfUdUNXvl8r1yATcBSVV3pO38Y8EPv/A+Ax4Cvx0qH3srvaycLeAP4nqr+qkNZzPpR\nVyTMzF9EAiJyD/D5Dsc/BfwC+F/gHOBx4BkRudhX7WzgGdya1shnlK+NzwB3A18BZuC+2M96NydR\ndPgRcC3waWAmrtM9IyKBJNHh+xz7/x8BLAf24gxQTHQ4WflFJB34C24fyUzgE8CFwI99bST0PRCR\nPOBlYABQCnwK16d+FCsdRCQNeBqYCCzCDUIHgOdFZKiITMZ9V3/r6fB/wAoRmeJr5vfAGcBFwI3A\nv3ky97sOfSQ/IjLYa6ekk2vEpB/1RELM/EVkPM5ATAVqOhQvBX6tqt/1/t4oItNxs8w13rGpwAuq\n2lX8hzuAB1T1d971Po3bMPYJ4Nfx1sE790bgElV9wWvvi8AqoAioTnQdVLURN9OMtDUTWAJcoao7\nvcP9qkMv+9Ek73OtqlZ67T0C3OdrI6HvAXADkA1co6r7vfY+C6wVkXtVdVsMdJiGGzwn+/6P1wP7\ngSuAC4DXVPU7Xv07ReRC4MvAEq/fXAiM9556y0Tkq8AjInKPqjb3sw69kt+r/1HcgNtA5/R7P4qG\nRJn5zwJ24GbwWzuUTcDNZvy8DczyZmsAU4DKzhr2HiEn0j5Q4BmqN3G7hvuK3ugwH6iLGH5PRlXV\nMapanSQ6tOE9rTwE/F5Vn/WOxUKH3si/HwjhDNAAEcnHzZrfjKH8vdVhAlAeMfy+coA5MdKhBrgS\nUN+xkPczz7vOmg7nrPFdfzaw3e/u9MoHA9NjoENv5QdYiHsqm9Wx8Rj2ox5JiJm/5w/7FYCIdCze\nBRR2ODYWyARO9x6V8oAFnt85B/gbcIeq7gJGe+fs7NBGZ+2eNL3RAdcZtngzgKW0+wFvU9V3SQ4d\n9vmOXwV8COfCitDvOvRGflXdJSJfwvlyb8JNjCpxrgdIjnuwC1goImmqGvKVAwwjNvegHvhzh8O3\n4NyYq4B7e7j+6C7K8eoc9X7vFx36QH5U9cuR3zu5hzHpR9GQEMa/B34J3C4iL+JGyznAZ7yyTNys\nH1ynuA7IB5bhfHQfwj0GAxzp0G4zzjcaC3rS4TScy+ErwG2ebN/F6TCN5NDBz63Ab1W12ncs3jp0\nK7/n650E/BXn6jkN9x7jKRGZR/zlh57vwW+AO4H7ReQu3Gz5YaDFK4+5DiJyFa4vP6CqlSKS3cP1\njytX1aMiEvbqxFSHk5C/JxKhHwHJYfzvw81aVuICFZUD38PdkAOqukpEClS1beYpIuW4kfVyYJt3\nuOPLlCzgUP+K3ka3OuAGrlycr3YrgIhcg/MDXg5s98nsJ5F0AEBERgMXA3M7nH/Y+xkvHXqSfzHu\nSWWMqh4CEJGP4aIhXk777DNh74H39PJJnL/5dtw7mG/iXjoeIMb3QERuxL0wfxLn58aTobvrH1cu\nIhlAwKsTMx1OUv6eiPf3oI1E8fl3iap+oKo342Yxo1S1BGgC9kS+pH7D7/1di3NDFOL8p+CFhfYx\nkuMfvfqFKHTYCRzy+zlVdS9Qj1vSlww6RFiEG7T+1qGJuOoQhfznA1V+XVR1C64fFcdbfk+eaL4L\nf1TVkTj3QgFumWQBbhCLmQ4i8nXv2suBf/W5oXb0cP2uyvHqxESHXsjfE3HvRxES3viLyLdFZKmq\nNvtW83wM539DRG4RkV3e7CByzhhchy/3jOgm2n23iMgg4FzcWvq464B7iZcjImf5zjkD58LanCQ6\nRJgN/M33ZQHaBrO46RCF/O8CE/3L7URkBDAU2BRv+aPRQUQuFJHnRSSoqrWq+oFXfgj4e6x0EJE7\ngG8D31TVL6mqP3TwWv/1PUp9118LjBeRwg7l7wPvxEKHXsrfLYnQjyIkg9tnG/DfIrIeqML5kz8C\nfNEr/zPwHeCnIrIM92V9CFir7ZtfHgC+LyLVuI0xy3Cz0z8kiA4v4QaAJ7wlnoeAB3ErDv6SJDpE\nOAe3Fr0z4qnDNrqX/3Hco/0vReRunG/2B8A7wLMJIH80OlThXrTfLyKPAtOBR4BlqnowFjqISInX\n5s+AH3uTmAjve/K85f2Pn8C52mb4dHgVeA33ruVmILLh6gFvMOtXHfpA/miIdz8CkmDmr6o/wfk1\nfwSswy2Bm6uq6pVvBubhXDxv4DZgrMOtOIm0sRw3QDyA61iZwGW+zhRvHcKevG/iBrNXcD7aeREZ\nE10HHyNwyyY7ayNuOkRxD3binloG4wbiZ4AtwKXq7SxN9HvguT8XenpE3gfcparLfG30tw7X4d5H\n/DvOoPk/t6nqeuDjwDW4gfUqYKF6a+q978LHgT24+/AY8BPgnhjp0Cv5oyHe/SiCJXMxDMNIQRJ+\n5m8YhmH0PWb8DcMwUhAz/oZhGCmIGX/DMIwUxIy/YRhGCmLG3zAMIwUx42+kNCKyXETCInJ5F+VX\neeXfiLVshtGf2Dp/I6URl3GpHAgDU7zY6pGyXKACF/phlqq2xkdKw+h7bOZvpDSq+j4uA9OZuG32\nfr4HDAFuMMNvnGrYzN8wABH5OXA9bob/uojMwcXMv11VH/TV+wIuZd94XBTG5bgE3WFfnS8Cn8Pl\nBwjgnh6+rapPe+WfxcVuWopLwZgGnKsuzaJhxASb+RuG4zZcPJlHRCQT+B9cwL2HIhVE5E7gUVz8\npYW4uDPfwZfnV0RuxyVQ+Q0uD8C/4NIAPuFFCY0wEBcM7AZczJht/aWYYXRGMkT1NIx+R1XfE5Gb\ngKeB1Tg30JWRGb2I5AH/CTysqv/hnbZKRJqA+0TkYS843FjgPlX1Dwg7gNdxOQOe9g6nAd9S1ZX9\nr51hHI8Zf8PwUNUVIvIkLrLjkg6z8Qtwafb+2CFh/TO4dI+lwK9U9RZoGywElwjmEq9ux3SX7/S5\nEoYRJWb8DeNYnsMZ/44z8qHez+e7OG8kgIhMwIVcLsXlZa3CxWwH5//304hhxAkz/oYRHZE8xZ+k\nPS+0n50iEsQl3zkIfBhYp6otXoKQxTGR0jCixIy/YUTHq8BR4AxV/V3koIhcCNwJfA03sy8GvqCq\n//Sdu8D7aQssjITBjL9hRIGq7hGRB3EpEvNw2dbG4vYG1OOWc36AS9B9q4jsxT0BLABu8ZrJibXc\nhtEVNhMxjOhZCnwd58JZiUvy/SdcKsVmb2XQImAv8EvgKVyO3SuAalx6RcNICGyTl2EYRgpiM3/D\nMIwUxIy/YRhGCmLG3zAMIwUx428YhpGCmPE3DMNIQcz4G4ZhpCBm/A3DMFIQM/6GYRgpyP8DqqAN\nBM33y9YAAAAASUVORK5CYII=\n", "text/plain": [ - "" + "" ] }, "metadata": {}, @@ -2505,7 +2505,7 @@ }, { "cell_type": "code", - "execution_count": 41, + "execution_count": 78, "metadata": {}, "outputs": [ { @@ -2517,9 +2517,9 @@ }, { "data": { - "image/png": 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5ykfs8vLyKj9jIe7HlZwrrI9eT1pBGmhAlabEu7wZVgbu7Pn6Ip1D3HB0rHxO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\ngg==\n", 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Pkp2dzbx588jOzuatt96iuLiY2bNnM3LkSNauXcuxY8f4+9//3uR+ixcv5quv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\nha3J/zQwHPiqmbIrgBNtFZDSemazmZ0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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -2535,14 +2535,12 @@ "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\n", "\n", "results = TimeSeries()\n", "\n", - "results[1970] = census[1970]\n", - "results\n", + "results[1950] = census[1950] - 0.5\n", "\n", - "for t in linrange(1970, 2015):\n", + "for t in linrange(1950, 2015):\n", " results[t+1] = results[t] + annual_growth\n", "\n", "newfig()\n", @@ -2568,7 +2566,7 @@ }, { "cell_type": "code", - "execution_count": 42, + "execution_count": 79, "metadata": { "collapsed": true }, @@ -2590,7 +2588,7 @@ }, { "cell_type": "code", - "execution_count": 43, + "execution_count": 80, "metadata": { "collapsed": true }, @@ -2611,7 +2609,7 @@ }, { "cell_type": "code", - "execution_count": 44, + "execution_count": 81, "metadata": { "collapsed": true }, @@ -2640,7 +2638,7 @@ }, { "cell_type": "code", - "execution_count": 45, + "execution_count": 82, "metadata": { "collapsed": true }, @@ -2668,14 +2666,14 @@ }, { "cell_type": "code", - "execution_count": 46, + "execution_count": 83, "metadata": {}, "outputs": [ { "data": { - "image/png": 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MkWSEpqYmNjY2GBgYYKZvxlf+/2U3URgb69CvXxM0NF6uFj1PUqWvsJs3b3L+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\nLf5lZWUwMTHBK6+8gqCgIPj6+nbp5i3Ozs4AgF27dmHs2LE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OBQsWsHTp0gt2LIpyOcgrzeODvR+wP30/TrlOvBW3hG5te1BaWoqvry8ODtoVfnR0zevi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\n3c1/i0gUMAKoMMY09FXGhqqQkBDi4uJagn98fDy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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -2696,7 +2694,7 @@ }, { "cell_type": "code", - "execution_count": 47, + "execution_count": 84, "metadata": {}, "outputs": [ { @@ -2731,7 +2729,7 @@ }, { "cell_type": "code", - "execution_count": 48, + "execution_count": 85, "metadata": { "scrolled": true }, @@ -2753,14 +2751,14 @@ " axes_locator = None\n", " axis_bgcolor = (1.0, 1.0, 1.0, 1.0)\n", " axisbelow = True\n", - " children = [" + "" ] }, "metadata": {}, @@ -2846,7 +2844,7 @@ }, { "cell_type": "code", - "execution_count": 72, + "execution_count": 88, "metadata": { "collapsed": true }, @@ -2857,20 +2855,20 @@ " 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.births - system.deathrate * results[t]\n", + " results[t+1] = results[t] + system.annualbirths - system.deathrate * results[t]\n", " system.results = results" ] }, { "cell_type": "code", - "execution_count": 73, + "execution_count": 99, "metadata": {}, "outputs": [ { "data": { - "image/png": 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1+Q+Wu7s7Bw4coHXr1pSUlLBs2TJ5BcPAwIC///6b6OhoPvroI7S1tTly5Aj6\n+vpiIJrwwpLJZIxxGUNRtgaBh9XR1s1ERSWJ3NxGqKo+aO5UU1PDysoKGxubWuvooqxKg7+ygf9R\nMpmMYcOGVblfYmLic/u1e1E1b96cPXv2sGHDBsaPH09ubi5mZmYMHDhQoSusiooKW7duZfv27ezc\nuZPFixcjk8lwcnJi6dKl9OvXr9I8zMzM2L9/P1u2bGHp0qUkJibSqFEj2rVrx5IlS7C0tAQedCvb\nsWMHq1atYtSoUWhpadG+fXvWrl2rdJPL6tWrWbp0KVOnTiUnJwd7e3s2btwof7xdsGABCxYswMvL\nCxMTE2bNmkVCQoL8Grds2cLy5csZO3YshYWFuLi48N1331X51CEIdSEjP4PjoccZ5TwKDdWH3wlt\ndW3e7TaOn1L/JSkpFDOzB0/YWlpa2NraYmlp+cK855RJj/c1eoKQkBDy8vIqfDHp6elZowV7VExM\nDL179+bUqVNYWFjUWj6CIAhV8U/w5/sb35NVmIVJbktGtRiGi4ulQjdMSZI4c+YMMpkMOzs7zM3N\nle7sUFOqiptKdfUMCAhg1qxZFU4kVDa8+NEBPIIgCK+aopIiDgcf5nTUaQoLS7gfkkdKTgA/BqnS\nsOEwLC0fBliZTEbHjh3R1NSs0b75NUmp4L9kyRJUVFRYtmwZZmZmdf4LJgiC8DzFZcWxzW8bcZlx\naORooJWqDnl6GJSYU1ykxu+/+zFxouIka49233wRKRX8AwMD+frrr+nTp09tl0cQBOGFIUkSZ++e\n5VDAIVQyVGiQ1QCVEhUaazempaUFEWGZWFjo07q1FaWlpaiqqj7vIitNqeDfqFGjl+qiBEEQnlVW\nQRY7/XYSHhGOVpY2KpIMFZkKdo3sMNMzQ01NjZZOLWjXzrlWR+LWFqWC/1tvvcXWrVvp0KHDc++e\nJAiCUNsScxL56txXEAVFmTIycvOwamJES5MWGOoZYmtri5WV1QvTc+dpKBX8Y2NjCQ8Pp0uXLjg4\nOJT7AZDJZHz33Xe1UkBBEIS6ZqRjhJm+GZfSgtHK1US3pDG6Wc1pP6A9zZo1eyVaQpQK/lFRUTg5\nPVxTsmz+FkEQhFdBZmYmmZmZ8i6RKjIV3vF4h4g7S+F6E1TyrMHQHDMzi1ci8IOSwb+y+WIEQRBe\nZqmpqYSFhRF0JwiTBiYYGxvL2+8NtQ3Z+NZKDqqF0KCBBv3726Ci8mJ223wa1ZrSOTw8nCtXrpCd\nnY2hoSEK73aQAAAgAElEQVStW7fG1ta2tsomCIJQ4yRJIiUlhbCwMOIT4wlNDiU1P5XEtAyMb1rQ\nrt3DNS9kMhmjRjk94WwvL6WCf2lpKfPnz+fw4cMKiw/IZDKGDh3KsmXLXtiBDC8LZRdwLxu1N3Dg\nQL755pty+zo6OrJy5UqGDh1ablvZsY/S0tLC2tqaUaNG4e3tLf//eOTIkUqXg4QHC7kMGDAAeDDN\n87p167h8+TLZ2dk0adKEvn37Mn369HKrhsGDSQPPnDnDgQMHKl1cRhBqmiRJJCYmEhYWRlpaGql5\nqYSmhFJYUkRmVgFBWTdJT7OgTRvXV6qGXxmlgv/WrVv56aefmD17NoMHD8bIyIikpCSOHz/OunXr\nsLOzEwuw17ETJ04waNCgpxp7sWnTJlxdXZEkiaysLE6fPs3y5cuJiYlRWMBFVVWVs2fPVniOsrmZ\nkpKS8Pb2pk+fPuzYsYMGDRoQEhLCsmXLCAgI4IcfflA4LikpifPnz2Ntbc3+/ftF8BdqnSRJ3L9/\nn7CwMDIyMiiVSolMiyQ++8Hqe9lqeVxNj6ZxvgvJKbr89dc9+vSp+ymW65pSwf/QoUNMmzaNSZMm\nydPMzMyYPHkyBQUFHDp0SAT/OtasWTMWLFhA27Ztqz1JnoGBAcbGxgCYmJhgZ2eHmpoaK1asYMSI\nETRv3ly+b9l+lfntt9+AB6PAy1hYWKCrq8v48eO5ffu2QmeBn3/+GRMTE8aMGcM333zDp59+WuHT\ngSDUlPv378uXF80uzOZ28m3yivMo1CskXz8fAz0DJjd+lxt/ynB3N6F9+ybPucR1Q6l5GpKSkmjd\nunWF2zw9PYmPr5v1a4WHPv74Y4qKili2bFmNnM/LywsNDQ3+97//Ves4FRUVsrKy8PPzU0hv27Yt\nv/zyS7kpmH/66Sc6dOhA3759ycvL4+eff37msgvCk5iZmaGjo8O9jHtcT7hOmnYamU0zyWuUh0cz\nD+Z3n8/UEf2YNs2NadPcaNCgfiwWpFTNv1mzZly/fp2OHTuW23b9+vUqa4fPy/GQ4/wS+otS+3a1\n6oqPq49C2m7/3Zy7e06p4193eJ3BjoOrXcan1bhxY+bNm8ecOXMYOHAg3bp1e6bz6erqYmFhQWho\naLWOGzRoEN999x3e3t44OzvTvn172rdvT4cOHbC3t1fY99atW4SGhjJ79myaNGmCu7s7Bw8exNvb\n+5nKLgjw4N1kTEwMurq6CosaZRZkciX/CvFSPPdUU4m7m017T0vGuHnT3ry9/D2Xh4fp8yr6c6FU\nzX/kyJFs3ryZnTt3kpiYSGlpKYmJiezYsYMtW7YwfPjw2i6nUIE33niDHj16MH/+/EqXgKyOx5eS\nLCkpwcPDo9x/vXr1ku/TsGFDDh8+zJQpU8jJycHX15epU6fSuXNn9u3bp3D+o0ePoq+vT6dOnYAH\nPxxBQUH4+/s/c9mF+qu0tJS7d+9y+vRpbt68ye3btxU6puio61CgW8DN+3GERKQhSzfCJe0tOlh0\nqNcdVZSq+Y8dO5bg4GCWL1/OihUr5OmSJDFkyBDefffdWitgfVHdBdzLLFy4kEGDBrFy5UoWLVr0\nTGXIzs5WeIpTVVWtcGW2x2d1NTQ0ZPbs2cyePZu4uDguXrzI3r17WbBgAU2bNqV79+4UFhby66+/\n0rt3b/mCMAMGDGDp0qXs379fLM0oVFtpaSn37t0jPDycvLw8eXpqaiopKSnytaLVVdWZ6DGRgIj5\n6ER70KygNfEREoWFJWhovBoDtp6GUsFfVVWVFStWMGnSJK5evUpmZib6+vq0bdu23KP9i2Sw4+Bn\naorxcfUp1xRUW5RdwP1xZmZmzJkzh/nz5zNw4MCnzj8vL4+oqCgGDRqkkF7VwtJbt27FysqK/v37\nA9C0aVNGjhzJkCFDGDBgAGfPnqV79+789ddfpKenc+zYMYV2/tLSUk6cOMG8efPEi19BKSUlJURH\nR5cL+vBgSVkdE51ynSCaGTRjh886dhWEY2SkzbBh9qir19/AD9Uc5GVvb/9CB/uXmbILuFdk1KhR\nnDhxgs8///yp8z948CClpaXV/gHx9/fnf//7H3369FEY9q6hoYG2tra87fXo0aOYmpqyfft2heP9\n/PxYsGABx48f56233nrq8guvvrKgHxYWRn5+vsI2TU1NLKwsuJx9mUsxl7iXncVQjz7o6T18edtA\nswHTprnXiz78yqg0+Pfv35+1a9fi5OREv379qmwbO3nyZI0Xrj5RdgH3yixevJjBg5V7ysnIyCAp\nKQlJksjMzOTvv/9mzZo1TJkyRb6Ob5mkpKQKz6GtrY2enh7vvfce3t7eTJkyhUmTJmFpaUl8fDxH\njx4lIyOD0aNHy/v2v/feezg4OCicx87Ojm3btnHw4EER/IUnCgoK4s6dOwppmpqaNG/enHzdfHbd\n2kVSTjJRkRlciNvK/QAdPprWXSF2icD/UKXB39PTE11dXfm/6/OLkbqg7ALulbGwsGD27Nl8+eWX\nVe776Cjihg0bYmdnx5dfflluVHBJSQldunSp8Bxjxoxh/vz5tGjRgv379/Ptt9/y8ccfk56ejr6+\nPp07d+bHH3/EyMiI77777v+HyY8qdx5VVVXGjRvHsmXLuHXr1hOfcIT6zdramrt37yJJkjzoN7Vo\nys9hP3Mq8BQAmZmFxMXnYFLsSNDNTK5du0/btvWj3351VWsB9+dFLOAuCPVHWZfNpk2bluvoEBgY\niLa2NlZWVsRkxeB73Zf72ffl23U1dGkY3YHYqw1xdzfBx6dlvem3/7inXsA9ISGhWhmZmtavPrKC\nINQsSZKIiYkhNDSU3NxcCgoKyr1jdHZ2pqS0hBNhJzgRdoISqQQZD1olnE2cGec2Dm2ZHv5uSbRp\nYyZaLJ6g0uDfvXv3av3hgoODa6RAgiDUL5IkERsbS2hoKDk5OfL0iIgIrK2tFVbLSs5NZqvfVu6k\n3SE6Oov09ALaeJjj5exFV8uu8pglmnqqVmnwX7p0qfjVFASh1kiSRHx8PKGhoWRlZSls09DQwM7O\nrtyYEh11HdLz0rnpn0RmZiEGxU3pKk2gm1XF088Ilas0+ItRu4Ig1AZJkkhISCAkJITMzEyFberq\n6tjZ2WFjY1PhwEYddR3GuY8jMHw5RontMC/wICZEQhooicpqNVUa/Ddv3qz0SWQyGVOnTq2RAgmC\n8Gq7evVquXeKampq2NraYmtrK2/mkSSJ8NRw7Bsrtvu3MmnFrvHr2b4xDDc3Y/r2tRaB/ylUGvzX\nrFmj9ElE8BcEQVnGxsby4K+qqoqNjQ12dnbyaT8A0vLS2OW/i4DEAHpqezOiW1eFqRga6Rryn/+0\nFf32n0Glwf/27dt1WQ5BEF5BOTk58vFCZSwtLYmKisLU1JTmzZvL18yFB7X9y7GX+THgR9JzsgkL\nTeNKyiaKkw0Y+6aHwnlE4H821ZreQRAEQRlZWVmEhIRw//59unTpojA3laqqKj169Cj3MjezIJM9\n/nu4cf8GAOlp+aSl5WNe5MHfp+Pp0Noae3vDOr2OV5mY3kEQhBqTm5tLSEgIsbGx8mmVb9++TYcO\nHRT2ezzw/xv/L3v895Bd+HByw5Y2lrhkjyTpti69+1hiba1f+xdQj4jpHQRBeGYFBQWEhoZy7969\nclOTq6urU1JSojDxX5mcwhz2BezjauxVJOlhj53u1t0Z0WIE+W0gISEHB4dGdXId9Umlwf/R5QGX\nL19eo5kePHiQ7du3Ex8fT/Pmzfn4448rXCVMqFnXrl1jzJgxSk+TceTIET7//HOCgoLqoHTCy6io\nqIiIiAgiIyMpKSlR2GZiYoKTk1Ola0xHpEaw+dpmUnPSiYhMp7REoqOHHePdx9PSuCUAmgZgYKBZ\n4fHCs1G6zb+0tJTTp0/j5+dHdnY2jRs3pl27dtUO2kePHmXhwoXyxcf37t3L9OnTOX78uJi3RxBe\nEpIkERERQXh4OEVFRQrbGjVqhJOTk8JSihVpqNWQnIJ8/P5NoKCgBLPClrzebQotje1qs+jC/1Mq\n+CcnJzNp0iRu376NhoYGjRo1IiUlhc2bN9OxY0c2bNiAjo5OleeRJIn169czefJkRo4cCcCcOXO4\ndOkS169fF8FfEF4SMpmMlJQUhcCvr6+Pk5MTJiYmSjUTN9ZpjLfbaO5EfIdOWHsaF9sSe6cIOlR5\nqFADlFrDd/ny5SQlJbFt2zb8/f05c+YMt27dYv369QQGBios7fgkkZGRxMbGKiwYoqKiwrFjx5Se\ni/5V5ejoyMGDB3nzzTdxcXFh4MCB3Lhxg71799K9e3c8PT356KOPKCwslB9z7do1fHx88PDwoFOn\nTixevFhhZaPbt2/j4+ODm5sbr7/+OoGBgQp5lpaWsnnzZnr27Im7uzsjRozg7NmzdXbNwsvNyckJ\nAF1dXTw9PenWrRumpqYVBv6C4gICEgPKpXdu1pndE9fS2sKDadPcePNNp1ovt/CAUjX/06dP88UX\nX9C1a1eF9D59+pCamsqqVatYuHBhlecpW4ghMzOTcePGERYWhq2tLbNnz8bT07P6pa9CSEgIoaGh\nSu1rZWVVbh1Zf39/7t69q9TxDg4OODo6VruMj/r6669ZsmQJ1tbWzJ07lylTpuDi4sK2bduIiopi\n9uzZtGnTBm9vb27evMmECRMYO3YsCxcuJCYmhgULFhATE8PmzZvJyMhgwoQJdOjQgcOHD3Pnzh2+\n+OILhfxWr17NH3/8waJFi7C0tOTcuXPMmDGD7du30759+2e6FuHVkZKSQlRUFB4eHgovbQ0MDOjQ\noQONGzcu13vnUWEpYey8sZPknBR6qo9nVP8O8j76MpmMRg30mTu3nehUUseUCv4aGho0aNCgwm1N\nmzZVOrOyNWrnzp3LzJkzsbW15eDBg4wfP56ffvoJO7v63dY3atQoevXqBcDQoUNZtGgRCxYsoFmz\nZjg4OLB9+3bCwsIA8PX1pVWrVsyZMwd4sCLWggULmDJlCmFhYVy9epWioiKWLFmCrq4uzZs3JyEh\nQb7Ie05ODj/88APr16+X/6hbWVlx+/Zttm7dKoK/QGZmJsHBwSQmJgIP2vJtbW0V9jE2Nq70+KKS\nIn66/ROnok6RmVVASEgqflnfYqBizGv9myvsKwJ/3VMq+L/11lusXbsWNzc3jIyM5Om5ubls3boV\nLy8vpTIrm7Nj2rRp8maeli1b4ufnx759+55pDdpXwaNLKGpra6OioqLwHkRLS0ve7BMWFkb37t0V\njm/Tpo18W1hYGDY2NgqjK93d3eX/joiIoLCwkFmzZinU2oqKihT+Hwv1T0V99eHhFMtPquWXuZN+\nhx3Xd8gXWklNzacwR5XmBW04/nMUbVs3xcio6veEQu2pNPi/88478n+Xvdnv06cPnp6eNG7cmMzM\nTP7991+Ki4sxMTFRKrOy/R5dx1Umk2Fra0tMTMzTXkOlHB0dn6kpxtXVtVxTUG16fBZDmUxWaY1I\nS0urXFrZF1VNTQ2ZTMbji7Q9Oi962Twq69evx8rKSmE/Zb7cwqunsLCQ8PBwoqKiFPrqy2QyLCws\ncHR0rPLeKC4t5tfQX/kt/DdKpYfnGODZgeS0lmQWqDBypAONG2vX2nUIyqk0+D/efausTb6oqIj7\n9x/8mpe98Cl7LKyKs7MzOjo6Cmu1lv2wiH7+1WNnZ8f169cV0vz8/OTbMjIy5Iuol/WzDgh4+MLN\nysoKdXV1EhIS6Natmzx9w4YNlJSUMGvWrDq4CuFFUFJSwp07dwgLCyv3vTc1NaVFixaVNvs+Ki4r\nDt/rvtzLuIckgYpMhqaaJl4tvehi2YVE21xUVGQYG4sa/4ug0uC/a9euGs9MW1ub8ePHs2bNGoyM\njHBwcGDv3r3cu3ePdevW1Xh+r7LJkyczbNgwVqxYgZeXF7GxsSxcuJDu3btjZ2eHqakpGzdu5JNP\nPmH27NkkJCQo/I21tbWZMGECq1evRldXFxcXF06fPs3GjRtZsmTJc7wyoS5JksS5c+fKLaZiaGhI\nixYtquyrX+ZSzCV23dxFdl4+oSFp6OmpM6BtO8a7j8dI50EzoqmpbhVnEepSpcHfz8+P1q2rvzrO\ntWvX5G3PFZk1axba2tosXbqUlJQUWrRoga+vb7kXScKTOTg4sHnzZtasWcOuXbto2LAhgwYN4oMP\nPgBAT0+P77//nkWLFuHl5YWJiQmTJ0+Wv/AF+OCDD1BXV2flypUkJyfTrFkzFi1aJBbyqUdkMhnm\n5ubyWXx1dXVp0aIFZmbVW/+2iV4TsnML+PffBEpLVGh0vx2D+k/ASEe5Hw+h7smkxxuG/9+QIUOw\ns7Pj3XffVWijr4y/vz/btm3jzp07HD9+vEYLWdUq9IIgKKegoEBhCmV40Oxz4cIFLC0tsbS0fOp3\nPr+E/MKWY7/RMKozupIRXl4O9O5tVfWBQq2oKm5WWvM/fPgwGzZsYMSIEVhbW9OvXz9cXV2xsLBA\nW1ubzMxMEhIS8PPz4++//yYqKgofHx9Wr15dqxckCEL15efnExISQkxMDN26dVNow1dVVaVr165K\n1/RzCnOIzYrFobFipXCgw0A6Te7Ftq238PJyxNa2YSVnEF4Eldb8yyQkJLBz505++eUXkpKSFG4Q\nSZJo2rQp/fv3Z8KECZiamtZKIUXNXxCeTnFxMREREURERMgnXjM1NaVdu3ZPdb6gpCB23thJflEB\ng/Qm079bq3L7PDo7p/D8PHXNv4ypqSlz5sxhzpw5REREEBMTQ1ZWFoaGhjRt2hQbG5taKbggCE9P\nkiSio6MJCQkhPz+/3LbKpliuTFFJEUeCj/BX1F/k5BQRfDuFq5nrMNRaQLt2igM9ReB/OVRrJS87\nO7t6PwpXEF50SUlJBAUFkZmZqZCur69Py5YtnzgqtyJxWXFs89tGXFYcALFx2RTnqGNb0Jq9e2/j\n5NQYfX0x7fLLRizjKAiviKysLIKCgsqNu9HS0sLJyQkLC4tq1colSeLMnTMcCjpEcWmxPH1ohy7E\n/OpIQb4aI0Y40KCBxhPOIryoRPAXhFeEv78/qamp8s+qqqo0b94cW1vbcqPHq5JVkMX3N7/nVsIt\neZq6qjqjnEfR1bIr0RZZaGqqir77LzER/AXhFdGiRQsuXLiATCajWbNmODo6VjgNSFWCk4Lxve5L\nel4GkVHpaGur097JiUmek2jSoAkAlpZiPd2XnQj+gvCSkSSJpKQkjI2NFZpxylbQMjExqXTpRGUU\nlBSQlJnKrYBkcnOLsSz2ZNzAGTRpYFgTxRdeEGIGL0F4iWRkZPDPP/9w+fJl7t27V267vb39MwV+\nAHczd/rY90JbRY9WOUOxzunKtStJz3RO4cWjVM2/oKCALVu2cObMGXJzc8vNFglw8uTJGi+cIAgP\nFBQUEBISwr179+Tfv5CQEMzNzavdnv+4nMIcdDUU2+5HtxpFe8NebF57mzfesKdLF/NnykN48Sh1\n1yxZsoSDBw/Srl077O3txZS/glBHSktLiYyMJCwsjOLihz1uZDIZTZs2rbAipqzCkkL2B+wnKCmI\nqS0+wtr8YRdQdVV17C2bsHSpMZqaonX4VaTU/9WTJ0/y4YcfMmXKlNoujyAIPGjXT0hIICgoiJyc\nHIVtJiYmtGzZUqlplisTnxXPVr+txGTEEhWVwYUTi9k+7b84ODRS2E8E/leXUv9nCwsL63RRE0Go\nz7KysggMDCQpSbGdXU9PD2dnZ6UXT6rMP9H/sPfWXgpLComITCc+PgcTSYXtvjdYML8rOjrqVZ9E\neOkpFfy7dOnC33//TYcOHWq7PIJQ70VHRysEfnV1dRwcHJReQrEyBcUF/BjwIxejL8rT7KwbYRTX\nmYa5Ttg4NHqmZiTh5aJU8B8yZAiff/45aWlpeHp6Vth3uGxNXkEQno2DgwMxMTEUFhZiZWWFo6Oj\nfNnNp3U/+z5brm2RT9EAYKZnxpTWU0ix0yA9PZ+uXas3Alh4uSkV/N9//30Ajh49ytGjR8ttl8lk\nIvgLwlNISUlBR0cHbe2Ha9qqqanh7u6OlpYW+vrPPpjqauxVdvnvIjktk+JiCUNDLTpYdMDbxRtN\nNU3MRYtuvaRU8D916lRtl0MQ6pW8vDyCgoKIi4vD3NxcvkZ2mWdt1y8TnBTMtn+3ERebTWRUBhqq\n6iwbM57XnHvVyPmFl5dSwd/c/GEf39zcXHJycmjYsCHq6uLFkCBUR0lJibzrZtn8+rGxsVhZWSm9\nXm51OBk50cKwFVcu/4lWSUNaZA4k6qwhONd4VsJLRul+XJcvX2bVqlUEBgbKXwq5urrywQcf0LFj\nx1oroCC8KhISEggMDCzXdbNp06bo6OjUSp4ymYyp7SdBvg5Bh82wtTRm1CjHWslLeLkoFfyvXr3K\nxIkTsbGxYebMmTRu3JjExER+++03Jk+ezM6dO5+4aLsg1Gc5OTkEBASUm2pZX1+fVq1a1ViNX5Ik\nLsdepm3TtqiqPFyoRUddhw/7TCLYPAV7e0PU1MQgTUHJ4L927Vo6duzI1q1bFXoDTJ8+nSlTprB+\n/Xq+//77WiukILyMiouLCQ8PJyIigtLSUnm6uro6Tk5OWFlZ1VjvmryiPHbe2MnVaD98o8+xaPR0\nzMwUp2xo0aLmm5WEl5dSVYCAgADGjBlT7kaVyWSMGTOGW7duVXKkINRfqamphIWFyQO/TCbDysqK\nnj17Ym1tXWOBPz4rnmXnl3E29DJ+/yZyLvYMS7b+RFFRSY2cX3g1KVXz19fXJzc3t8JtOTk51VoL\nVBDqCxMTE0xNTUlISMDQ0JBWrVrRsGHDGs3j5v2b+F73Jb84HzVVFYqLSzEvcCc/oxGBgSm4u9dM\nryHh1aNU8O/QoQPr16+ndevWmJqaytMTEhJYv369eOEr1HvFxcXk5eWVm2/H2dkZMzMzmjVrVqMD\nqCRJ4kTYCX4O+VmeZqivy/udphL+dwPentIKZ2ejGstPePUoFfxnz57NiBEj6N+/P61bt8bIyIjk\n5GT8/PzQ09Pj448/ru1yCsILSZIk7t+/T2BgIDKZjB49eig8Cevq6qKrW7NLHeYX57Pzxk7+jf8X\nGQ9+UBrrNGZ62+mYNzAnt3cRurpiXV3hyZQK/qamphw9ehRfX1/8/PyIiYlBX18fb29v3n77bYyN\njas+iSC8YirqxRMeHo6jY+11pUzOTWbDlQ34hYZxPz4HNzdjnE1bMrn1ZPQ09ABE4BeUonQ/f2Nj\nY+bMmVObZRGEl0JJSQnh4eGEh4cr9OLR1NSs8Vr+43be2Mnf14OIj38wVkB2x56ZQ2YqdO0UBGVU\nGvw3b97M8OHDMTExYfPmzU88iUwmY+rUqTVeOEF40SQmJnLr1i2FDhBlvXicnJxqfdT7eLfx+IWG\nkhCfj31uL6yy21OQX4qOjgj+QvVUGvzXrFlDp06dMDExYc2aNU88iQj+wqsuLy+PwMBA4uPjFdIb\nNmyIq6vrM6+bqyxjXWP++/pHnFSJpqHUBG/vFqiri8AvVF+lwf/27dsV/lsQ6pvS0lLOnTtHQUGB\nPE1dXZ0WLVpgaWlZa9MgZxZkEpV6B0fDlmhpPfyqOhk54eDjiIqKmH5ZeHpKDfLasGEDCQkJFW6L\njY1l8eLFNVooQXiRqKio0Lx5c/nnZs2a0bNnzxodofu46Ixo/vvnl7zr+yXLNp8ot8iKCPzCs1Iq\n+G/cuLHS4H/jxg32799fo4UShOfp0Ze4ZWxsbDA3N6dz5864u7ujqalZa/n7xfmx5Owy/vonhLSM\nXI7F7Ob4r6G1lp9QP1Xa7PPWW29x48YN4EFf5tGjR1d6EhcXF6UzDA8PZ9CgQeXS9+zZIyaHE54r\nSZKIjY0lODiYDh06KAzYkslk5ebcr438fwn9hV9CfwEZmJrqEH+vAIf8vmioie6bQs2qNPgvXryY\n33//HUmSWLduHaNGjcLMzExhH1VVVRo0aECfPn2UzjA0NBRDQ0OOHz+ukF7Tw94FoTqys7Px9/cn\nJSUFAH9/fzp16lRnyxoWFBfIB26VadeyOQZqPXm9h7uYlE2ocZUGfzs7O959913gwWOwl5eXwtQO\nTys0NJTmzZuLgWHCC6GyPvt5eXnk5eXV2jz7j0rJTeGrM2tILUmQj9htYdyCyZ6T0e1du+MGhPpL\nqUFeM2bMACAtLY2ioiL5yydJksjNzcXPzw8vLy+lMgwLC8PW1vYpiysINSc5ORl/f3+FxVVkMhm2\ntrY4ODigpqb0GMinFpYSxn9/WY1/cAxNzfWwsTagp01PRjmPQkUm5t0Xao9Sd3dISAj/+c9/CA8P\nr3C7TCarVvAvKChg1KhRxMbGYm9vz0cffYSrq1hFWqgbhYWFBAUFER0drZBuaGiIq6trjSyarozM\ngkzmn1jOjcD7AMRG5+Dt7MObrV6vk/yF+k2pqsXKlStJT09nzpw5tGvXji5duvDFF1/QvXt3ZDIZ\nP/zwg1KZ5efnEx0dTXZ2Np988gnffvstJiYm+Pj4EBER8UwXIgjKSEhI4PTp0wqBX01NDRcXFzp3\n7lxngR9AX1OfSZ29adRICw1Jm55aPvRz6lFn+Qv1m1I1/xs3bjBv3jxGjhyJtrY2x48fx9vbG29v\nb2bOnMmuXbuU6qmjpaXF1atX0dDQQEPjQe+F5cuXExgYyN69e/niiy+e7WoEoQqampoUFRXJPzdt\n2hRnZ2e0tLSeS3l62fQic1AOKf4m+IxoozCYSxBqk1J3WmFhIdbW1gBYW1srjPgdPnw4//3vf5XO\nUE9PT+Fz2QCax4fNC0JtaNiwIdbW1ty/fx8XF5ca6cSgrJCkMGLCiundqYU8TSaTMcxlCCjfW1oQ\naoRSzT5NmzYlJiYGeBD8s7OziY2NBR7UpDIyMpTKLCAgAE9PTwICAuRpJSUl3L59G3t7++qWXRCe\nKD09nfv375dLd3JyokePHnUa+H/2/53xm+cy7/BK/rl8r87yFYTKKBX8+/Tpw6pVq/jjjz8wNTXF\n1uJTWToAACAASURBVNaWtWvXEhERwc6dO2nWrJlSmTk5OWFubs78+fO5efMmYWFhzJs3j7S0NMaN\nG/dMFyIIZYqLiwkMDOT8+fPcuHFDYU4eeNDGXxc9eQCKSor44eYPrPlzOxlZ+WSpJrLw4FZSU/Pq\nJH9BqIxSwX/GjBm4u7tz4MABAObNm8fJkyd5/fXXuXDhAu+//75SmampqbF9+3ZsbGyYNm0aXl5e\nJCcns3v3bho3FoNYhGeXmJjImTNniIyMRJIkioqKCAoKei5lSc5NZsWFFVy4dwFbWwO0tdVoUGrM\nlN4jMTR8Pu8YBKGMTHp8xqgnKCwslL+ovXfvHoGBgTg7O2NpaVlrBQSIiYmhd+/enDp1CgsLi1rN\nS3g5FRQUEBQUJG+eLGNsbIyrq2udDNZ6lH+CPzuu7yC36OG8//a6bgy2HIljc7GoulD7qoqb1Xr2\nLQv8AJaWlrUe9AWhKmXz8QQGBlJYWChP19DQwNnZGXNz8zqbogGgpLSEZUd2cCX1NE2aPOjcoKai\nxuhWo+lq2bVOyyIIT1Jp8O/Xr1+1btSTJ0/WSIEEQVl5eXn4+/srrKELYGFhQcuWLWt15s2K3E9L\n4b3vlhKUeBsVFRkN9DVoZmTKtDbTsG5oXadlEYSqVBr8PT09RS1FeGFJksSlS5fIzs6Wp2lra+Pq\n6oqJyfNpVrl0/zzReQ8GK5aWShTFGfH58M/lC6sLwouk0uC/fPnyuiyHIFSLTCbDycmJa9euIZPJ\nsLa2xsnJqc568VRksOPrXGvrz7GzV3jNbiBfjpuEpkbtrukrCE9LqW/Kv//+W+U+tT3XuVC/SZJU\n7km0SZMm2NnZYWZmRqNGjeq8TBkZBRgYPGxaUlVRZXb3GQxxvEc7G7c6L48gVIdSwd/b27vKJqDg\n4OAaKZAgPC4zM5ObN2/SokULjIyMFLa1bNmyzssjSRLbj/3JvnMn2TR5Hk5OD7spG2ob0s7GsM7L\nJAjVpVTwr2jittzcXK5du8axY8dYv359jRdMEEpLSwkPDycsLIzS0lJu3rxJ9+7dn2vTTklpCZ/t\n2szPgSeQVGH+9zvY8flMdHXFSlvCy0Wpb1G7du0qTO/Rowc6Ojp8++23bNmypUYLJtRv6enp3Lx5\nk8zMTHlafn4+aWlpz20hoJTcFLb/u50EvTDU1FUoKiolUdef7Lx8EfyFl84zV6HatGnDtm3baqIs\ngkBpaSmhoaGEh4fz6PhDQ0ND3N3dy00MWFeuxV1jt/9u8ory0NBQxcHBkIZFlnzl/R8MdepuGmhB\nqCnPHPxPnz6Nrq5Yak54dunp6dz4v/buOyyqK/8f+HsKVUB6U0CKFGkzFKVJQI2xlzRX0URj12eN\n3/hzY4xhv9+Na0yiQWN0E7PGYEsxUaNxNcWCwSgdFESUjkgbkJE6wMz5/cFydYLEQWGG8nk9D8+z\nnjNz7+ezDJ/cOffcc9LTUVdXx7UJBAK4u7vD0dFRI1OPbxdU4tsb36BY8WAxQj6Pj6WhUZjo3L1n\nYQjpS1Qq/q+99lqnNrlcjvLychQXF2Pp0qU9HhgZPORyOW7duoW8vDylq30zMzP4+vpq5OKCMYZD\nP17Gjkt70KJVB38/S+joCGGub47FfovhZEJbkZL+TaXi//DmFx14PB6cnZ2xZMkSvPDCCz0eGBk8\nmpubUVBQwBV+oVAIDw8PODg4aOzKOvVOBmKStqGJ1wq0Abdza7H4uamY5z0PukJalI30fyoV/4MH\nD/Z2HGQQGzJkCDw8PJCZmQlzc3P4+vqqfSG2P/K0cUeI70icT7gBY0MDbJqyEpN9IjQaEyE9qVtj\n/nFxcUhJSYFUKoW5uTmCgoIQGBjYW7GRAerh1WE7jBgxArq6urC2tu4T4+i6Ql38v/GroS+Ixbrx\nK2FlSCtxkoFFpeJ/7949LF26FJmZmdDW1oapqSmqq6uxZ88ehIaGYvfu3WpfRIv0Px0zeQoKChAW\nFgZDQ0Ouj8fjwcbGRiNx3amoxtaD3+HtqChuJU4AGGE8Au/PjO4T/zEipKeptJnL5s2bcefOHXz6\n6ae4du0aLl68iOvXr+OTTz5BZmYmtm3b1ttxkn5OKpXit99+w+3bt9HW1ob09HR0YyuJXnMi/jJm\nxazGucqT+Pveb9DaKlfqp8JPBiqViv+lS5fw5ptvIiIiQql9/PjxWLduHU6fPt0bsZEBoONq/7ff\nflN6YEsgEDxyIoG6tMhb8HXm1zhW9gWa0L4y6NWG08i4UaqxmAhRJ5WGfQQCgdJX9IdZWFho9I+Y\n9F11dXVIT09HbW0t1yYQCODh4YERI0Zo7Kq64F4B9qfvR0V9BfR0hRjhYISacgU2Tl+FAF/aoIgM\nDiov7BYTEwNvb29YWVlx7fX19di7dy/mz5/fawGS/ocxhvz8fNy8eRMKhYJrNzU1hUgk0thDgQVF\nNTiT9x9cb7wMBXsQ12S/EMz1jIKZAS3IRgYPlYp/ZWUlKisr8eyzz8Lf3x+Wlpaora1FamoqGhoa\noK2tzT0IxuPxsG/fvl4NmvRdjY2NSEtLQ01NDdfG5/Ph7u4OJycnjVztt7UpcOCHy/j0yr/RonsP\n/v5WEAr50BHqYI7nHITYhdDYPhl0VCr+RUVFcHd3BwC0tbXh7t27AMC1yeVyyOXyLt9PBo+Oxdc6\nGBsbQyQSdTlsqA4JRcn4OHUbZPw2oAUoKJRiypjRWChaCHN988cfgJABiB7yIj3K1NQUzs7OyMvL\ng6urK1xcXMDnqzSvoNf4DPeAl7sNUq6XwHSoPlY98wpeEE+lq30yqHXrIa/c3FwkJiaivr4eJiYm\n8Pf3h5MTrXEymDU3N0NXV3m5Azc3N9ja2mLo0KEaien+fRmMjB48d2KoY4g3JizDQb3jePO51bA2\ntNZIXIT0JSoVf4VCgejoaHz//fdKc7N5PB5mzpyJ9957j66iBpnW1lZcv34dVVVVeOaZZ5T+A8Dn\n8zVS+JuaWvH5N/E4fz0J+zb+FWZmelyfn40fxC+I6XNKyH+p9H187969OHHiBNatW4e4uDhkZWXh\n4sWLeOONN3D69Gn8+9//7u04SR9SVVWFixcvorS0FC0tLcjIyND4A1tyhRxrd+/BZzc+Qo4gDjsO\nnu0UExV+Qh5Q6cr/u+++w4oVK7BkyRKuzdraGkuXLoVMJsN3331HyzoPAnK5HNnZ2SgoKFBq19HR\neeQG6+py5/4dxKbH4r7tbbDK9imcqa1n0dIyHTo6mtvykZC+TKW/jKqqKvj7+z+yz8/PD3v37u3R\noEjfI5VKkZaWprTRira2Nnx8fDS2Jo9cIcfZ3LM4ffs05Ao5jAx1YO9gBBdzJ2ycvJoKPyF/QqW/\nDjs7O6SlpSE4OLhTX1pamsb2VCW9jzGG3Nxc3Lp1S+mBLSsrK/j6+mpkQb/y8gbsPngBja5XUc+v\n4tqFfCH+57mFeNb5WfB5mp1hREhfp1Lxf/HFF/HRRx9BX18fU6ZMgbm5OSQSCU6fPo3PPvsMy5cv\n7+04iQY86oEtgUAAT09P2Nvba2SY50pCCTZ/HYsCravQbxTCT2wJHo8HJxMnvCp6FdYGNJOHEFWo\nVPwXLFiA7OxsbN26Fe+//z7XzhjDjBkzsHLlyl4LkGhObW2tUuE3MTGBWCzW6J7N6W0/o0jnKpiC\nobGxFY31Crw6Zg7GO42nq31CukHlhd3ef/99LFmyBMnJyZBKpTAyMkJgYCBGjhzZ2zESDbG1tUVF\nRQVKS0vh6uqKkSNHanzGzAui6ThzPQ4VVXWY4O+HNeHLYGVg9fg3EkKUdOuOmI2NDezs7DB06FCY\nmprCzs7uqU6enp6OefPmYf/+/RgzZsxTHYs8PblcDoFAoNTm5eUFR0dHGBsbqz2etLQKaGnx4eX1\n4J6S5RBLrJ24CG2KNkxwpqt9Qp6Uyg95ffjhhzh06BDa2tq4+dN6enpYuXIlli1b1u0TNzY24m9/\n+xutCdQHKBQK3Lx5ExUVFRg7diyEwgcfCy0tLbUX/rq6Fhw6nIWTN07DSF8f+6P/Cn19La5/nFOk\nWuMhZCBSqfjv2rULBw4cwCuvvILnnnsOZmZmkEgkOHv2LD7++GMMGTIEUVFR3Trx1q1bYWVlhaKi\noicKnPSM+vp6pKamQiqVAgCysrLg6+ur0Zgqm8pwpHg3JLpl4CsEOHQiEMvmjdVoTIQMNCo/5LVq\n1SqsXr2aa7Ozs+Nu/sXGxnar+MfFxeHixYv4/PPPMWPGjO5HTZ4aYwzFxcXIyspS+vbV1NQEhUKh\nkcXYFEyBX/J+wcmck7Ac2QJJNmBprQuhaz4AKv6E9CSVin99fT18fHwe2efv748vvvhC5RPW1NTg\n7bffxpYtWzS28Ndg17EkQ3l5OdfG5/Ph4eEBR0dHtd7UZYyhvLwBfMMG7E/fj4J77U8Pm5vrYXSA\nLeb5vYhnnZ9VWzyEDBYqFf+IiAh8/fXXGDu289XX6dOnER4ervIJ//73v2PcuHEIDw9XKj5EPSQS\nCdLS0tDc3My1GRoaws/PD0ZGRmqNpbq6CbGxmfjtzkWYheVBoPVgLR4HYwcsilgEG0PNPD1MyECn\nUvEPCAjAjh07MH36dEydOhUWFhaora3FxYsXkZKSgoULF+LTTz8F0L54VlcPfR0/fhw3btzAyZMn\ney4DohKFQoGcnBzk5eUpLXjm6OgIDw+PTrN8ehtjDB99Godz1d9DKrwLkxwdeHmZQ8gXYprrNExy\nmUQzeQjpRSoV/3fffRdA+4bcO3bs6NT/8LDPnxX/Y8eOoaKiAmFhYQDAFaGlS5di1qxZ+Mc//tG9\n6InK7ty5g9zcXO7f2traEIlESnsyq1uTZzzu/34XPAAGBtoYZjgci/1ew3Cj4RqLiZDBQqXif/Pm\nzR452bZt25SGG6qqqhAVFYXNmzcjNDS0R85BHs3Ozg6lpaWQSCSwsLCASCTqtAmLOvF4PKwOX4Tc\nykIYGergZb+ZmDJyCoR8WoyNEHVQ61/aH68yOxYFs7KygpmZmTpDGXR4PB7EYjHu3r2r9pu69+41\n49ChLEyf7owRIx48M+Bs6oz/eXYxnEyc4GDsoLZ4CCEqbuZC+pfa2lqkpaV12sxEV1cXTk5Oai38\nWVkSbPy/X/BN/pfYEvs92toUSv2RjpFU+AnRAI1+x7a2tkZOTo4mQxhQGGPIz8/HzZs3oVAooK+v\nDzc3N43Gc4fdwBXdWMgUTbhaX4qk6xEIFjtrLCZCSDsaYB0gZDIZ0tPTUVlZybUVFBTA0dER2tra\nao+nTlaHI9ePILUsFXaOOigtbYWrmxHaTO8CoOJPiKZR8R8AJBIJUlNTIZPJuDZjY2P4+fmptfA3\nNraiuroJ1Vr5OHTtEOpk7bt+2dgOgfuI4Vjsvwju5u5qi4cQ0rUui39FRUW3DqTJKYODFWMMOTk5\nyM3NVRrfd3Z2hru7u1qXaMjOrsbeL5NwU3ABtoE1EAofnHus/Vi85PkSdIWam11ECFHWZfF/5pln\nunVjMDs7u0cCIqppampCWloaqquruTYdHR2IRCJYWlqqNRaZrA1b959AOjuLFtaIxlw9uLubwVjX\nGAt8F8DL0kut8RBCHq/L4r9lyxau+EulUmzbtg3BwcGYPHky94Tv+fPncfHiRWzYsEFtAZP238fV\nq1fR0tLCtZmbm0MsFmtm7r5ADuaTgpZrjdDS4sPcQh9Bw4Mwx2sO9LX01R8PIeSxuiz+zz//PPe/\nV69ejVmzZmHz5s1Kr5k+fTo2b96MM2fOYM6cOb0XJVFiYGAAHR0dtLS0gMfjwc3NDS4uLmqbwskY\nUzqXjlAHa8cvwd8bt8PR1gpLAhfCx+rRCwESQvoGlQaFL1++jMmTJz+yLzIyEmlpaT0aFPlzAoEA\n/v7+MDAwQEhIiFq3V8zPr8XmLZdRXd2k1O5n44d1E5fivYnvUuEnpB9QqfibmJjg2rVrj+xLTEyk\nm729rLa2ttMDW4aGhoiIiICpqana4rhwoRgbPvoW39/bhW37/9MppogRERiirbnN3QkhqlNpqudL\nL72E3bt3o7m5GePHj4eJiQmqq6tx9uxZHDx4EBs3buztOAclhUKBGzduoKCgAL6+vrC3t1fqV+eT\nuo2tjUhu+xGZ+qfBAPxadQzLSyMwYjgty0FIf6RS8V+5ciXq6uqwb98+7N27l2vX0dHB66+/3u0t\nHMnjNTY2IiUlBbW1tQCAzMxMmJiYwNDQUO2xZJRn4PD1w5A2SzHczhB1dS3w87QA37ABABV/Qvoj\nlYo/j8fDm2++iVWrViEtLQ3379+HiYkJxGIx9PVpNkdPKysrQ0ZGBlpbW7k2CwsLtc7kycurRRuv\nCfG1/0FiaSLXPsLBCIHDAjHXey4MtA3UFg8hpGd16wlfQ0PDbu3aRbpHoVAgOzsb+fn5XJu6t1ds\nbm7DsWO38f3v51FmcRmeYgPw/3teIx0jRPlEQWQt6vU4CCG9q8viP3HixG4Vm59++qlHAhqsmpqa\nkJKSgnv37nFt+vr68Pf3h7Gx8Z+8s2eV11bj87TPUK5/G2gASkoYHOyNMGb4GMzxnEM3dAkZILos\n/n5+fmq9oTiYVVRUID09XemhLWtra4hEImhpaak1FgMjAYxH1qI8FzAz04WrvQ2WjKZ5+4QMNF0W\n/61bt3L/+/Tp0wgODlbrtMLBQi6X49q1a1zh5/F4GDVqlFqGeRQKhsrKRlhbP7iaN9c3x6rx87FX\n9wBm+D6LF0a9QE/pEjIAqTTPf9OmTUhKSurtWAYlgUAAsVgMHo8HXV1dhISEqGXDlaIiKba8dwUb\ntx1HQ0OLUt94p3F4f/r/YoHvAir8hAxQKt3wtbKyQlNT0+NfSJ5Ix7o85ubm3NaWvUmhYPhg709I\nbP4PGgQS7Pt2GNYsiuT6+Tw+nEycej0OQojmqFT8586diy1btiAjIwPu7u6PnN45ffr0Hg9uoGGM\nIS8vD8bGxjA3N1fqGzZsmFpiaG5rxsmck6h0PY36LAn4fB7SFWehUDyj1iWgCSGapVLxf++99wAA\nX3311SP7eTweFf/HaG1tRXp6OsrLy6Gjo4Pw8HC1zdtvaZFDS4uP5LvJOHrjKKTNUpia6mLECCPY\nWhnhZd9xAN3bJ2RQUan4nzt3rrfjGNCkUimSk5PR2NgIoH3LxdzcXHh59e4693K5AufPF+Po2WQM\nn5SH0uZ8pf5JfkGI8omCub55F0cghAxUKhX/h4ckGhsb0dDQAGNjY7VPQ+yPSkpKcP36dcjlcq7N\nyckJHh4evX7uLw6k42j6DyjVSYVRkha8vc3BAw9DdYfipVE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//PCDqW1SUhIzZsxg0KBB9OrVi+uvv57XXnut1iilDz/8MEIIDh48aNV3o1AY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\nP5VF2QCkVW6ZAAAAAElFTkSuQmCC\n", "text/plain": [ - "" + "" ] }, "metadata": {}, @@ -2880,7 +2878,7 @@ "source": [ "# Solution goes here\n", "system.deathrate = 0.01\n", - "system.births = 0.12\n", + "system.annualbirths = 0.125\n", "\n", "run_simulation1b(system)\n", "plot_results(system, title='Constant births, proportional death')" @@ -2902,7 +2900,7 @@ }, { "cell_type": "code", - "execution_count": 58, + "execution_count": 101, "metadata": { "collapsed": true }, @@ -2933,7 +2931,7 @@ }, { "cell_type": "code", - "execution_count": 59, + "execution_count": 102, "metadata": { "collapsed": true }, @@ -2952,7 +2950,7 @@ }, { "cell_type": "code", - "execution_count": 60, + "execution_count": 103, "metadata": {}, "outputs": [ { @@ -2964,9 +2962,9 @@ }, { "data": { - "image/png": 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g2fXr13njjTfw8fHB19eXadOmkZyc/AjvliA0ftevX1f5fFhbW9dr4odnPPkfPnyNKVOO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\n62Hp0fuAhBAySAzZ4l9SUoWTP6Tg2vUyKA1bYGCugAoqrl1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nL1LcejRoA/dLRW3grihKc/jr4F/8+MeP5JXlAXAyI49DRWl0KOnP1MHjuOuu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\naH1OAe6AX+0l0fUc7btFRHoDY3Fj6WNeB9xFvHQROSfsOf1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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -2999,7 +2997,7 @@ }, { "cell_type": "code", - "execution_count": 90, + "execution_count": 106, "metadata": { "collapsed": true }, @@ -3010,21 +3008,20 @@ " results = TimeSeries()\n", " results[system.t0] = system.p0\n", " for t in linrange(system.t0, system.t_end):\n", - " growth = results[t] * system.alpha\n", - " results[t+1] = results[t] + growth\n", + " results[t+1] = results[t] + results[t] * system.alpha\n", " system.results = results" ] }, { "cell_type": "code", - "execution_count": 101, + "execution_count": 108, "metadata": {}, "outputs": [ { "data": { - "image/png": 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tasWQ9kMY7TKayPBIMjPTcXGpqoxbUlKCUqlUK0TYEtWa/O9eHnD58uWNEozQ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\nxoYKwRCiUPRAZMxHdnU2fiz7Ee3Kdji5mKK9xRw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SduPGDa49Ly+PSSQSVlNTo5MciouL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\n", 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JSkpKWLNmjW3yhdVqrfE5X2Mw1aXor1IqHvCgmk8MWutV9RjX6e8bDuz/5ZdfCA6WhcBC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\ntZkR6qmjMhpmWflqIpEIGRm7umNOHnzQDSZqjDE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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -3036,7 +3033,7 @@ "#system.deathrate = 0.01\n", "#system.births = 0.12\n", "\n", - "system.alpha = 0.01685\n", + "system.alpha = 0.018\n", "\n", "run_simulation2b(system)\n", "plot_results(system, title='Alpha')" @@ -3058,7 +3055,7 @@ }, { "cell_type": "code", - "execution_count": 108, + "execution_count": 115, "metadata": { "collapsed": true }, @@ -3089,7 +3086,7 @@ }, { "cell_type": "code", - "execution_count": 109, + "execution_count": 116, "metadata": {}, "outputs": [ { @@ -3098,7 +3095,7 @@ "" ] }, - "execution_count": 109, + "execution_count": 116, "metadata": {}, "output_type": "execute_result" } @@ -3116,7 +3113,7 @@ }, { "cell_type": "code", - "execution_count": 110, + "execution_count": 117, "metadata": {}, "outputs": [ { @@ -3125,7 +3122,7 @@ "function" ] }, - "execution_count": 110, + "execution_count": 117, "metadata": {}, "output_type": "execute_result" } @@ -3143,7 +3140,7 @@ }, { "cell_type": "code", - "execution_count": 111, + "execution_count": 118, "metadata": { "collapsed": true }, @@ -3173,7 +3170,7 @@ }, { "cell_type": "code", - "execution_count": 112, + "execution_count": 119, "metadata": {}, "outputs": [ { @@ -3328,14 +3325,14 @@ }, { "cell_type": "code", - "execution_count": 114, + "execution_count": 120, "metadata": {}, "outputs": [ { "data": { - "image/png": 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H/fv355tvviE3NxcfHx+Cg4NVEkRN6qtK//79OXDgALt37+bUqVNVJv9GjRrx448/snTp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\niOjoaFy6dAlnzpxBbGwsDA0NYWNjw31IHy78QMtXKCsrK9y+fRsODg4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v5cUXX2TUqFG89tprzJt3edslcnJyrGz8Dg4OfPfddxXalU/C3rx5c6ZPn870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\nESE3N9eCvjExpL2W/9sc2xO+5iSzZUsFS9/fTMO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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -3369,7 +3366,7 @@ }, { "cell_type": "code", - "execution_count": 115, + "execution_count": 121, "metadata": { "collapsed": true }, @@ -3397,14 +3394,14 @@ }, { "cell_type": "code", - "execution_count": 116, + "execution_count": 122, "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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ne5eWjBjRlpkz+zRKpQGO9zhmAA+YvlcAKWhG7jFow0yH0WwVVWEc8KGUsriK\n5RTA999/z/Dhw7n55purXPbdd9+lS5cuGI1GcnJy2Lx5M6+88gpJSUk2izc5OzuzZcsWu3X4+voC\n2pK0Y8aM4eabb+bDDz/Ex8cHKSXz5s3j4MGDfPLJJzblUlNT2bZtG61bt2b16tXlrkioUDRkSkpK\n2LVrFxcuXLCkBbYMZFvRNg7uP4heb2Da0nd48d4p+Pl5WPLodDomT+5mN3x6Y8JRxfEPYK6U8jWr\ntCTgVSGEh2m7w4pDCBEFtANWOVpGYUtYWBizZ88mNjbW8hB3FF9fXwIDtVg3QUFBtG3bFhcXF+bP\nn88999xDu3btLHnN+crD3POYO3euJS00NBQvLy8mTJhAfHw8HTp0sGz7+uuvCQoKYuzYsbzxxhvM\nnDmzzBroCkVDRq/Xs3PnTtLT0y+n+epZdWEV+fp8Lmbkk5CQgXNBHp9+Fsc/H+1lU76xKw1wfM3x\nFsDv5WzbDrSq4n77oS07W35MYUWFPP300xQXFzNv3rwaqW/UqFG4ubmxYcOGKpVzcnIiJyeH3bt3\n26THxsby7bfflgmD/tVXX9GnTx+GDBlCfn4+X3/99RXLrlDUFUVFRfzxxx8WpVFUUkQCCfyQ+QP5\n+nwAnJ2cCMiJpkfO/Rzcl8nx45kVVdkocbTHcQK4HthkZ9v1QOWr+9jSHThYaa4r5Bv5Dd8mfOtQ\n3n7h/RjXZZxN2vK45Ww9tdWh8rdH3s4IMaLKMlaX5s2b8+yzzzJ9+nSGDRtG//79r6g+Ly8vQkND\nSUhIqFK54cOHs3TpUsaMGUNUVBS9e/emd+/e9OnTh/bt29vkPXDgAAkJCUydOpUWLVrQrVs31qxZ\nw5gxY65IdoWiLigoKGDHjh3k5OQAkJKbQjzx5HjnaKFegYAmAUy9YQI7DMUcOpTGffd1oG3bhhFf\nqiZxVHEsAeYJIS6hDS+lAMHA/cBMNGN5VWgBXKxiGUUp7rzzTjZs2MCsWbP49ttvr3jIp/TytSUl\nJXbXHff39+eXX34BtPDQX3zxBcuWLWPjxo0sW7aMZcuW4e3tzbRp07j//vst5datW0fTpk254YYb\nAE3pvPTSS8TFxVW4LoFC0RAoKCggPz+fwpJCjl48yjmPc2Q4X0KXp8WSGhQxiDvEHbi7uBM2qphR\noyLx9Gyc7raV4ajiWIDWS3gd+K9Vug7NK2quvULlIaUcWZX81wIuLi4YDPaDDhsMBktgtNK88MIL\nDB8+nFfjgepDAAAgAElEQVRffZU5c65sOkxubq6NTcPZ2ZmvvvqqTD4nJ9sRTn9/f6ZOncrUqVM5\nd+4c27dvZ+XKlcyePZuWLVsyYMAAioqK+O677xg8eLBlMahbb72Vl19+mdWrVyvFoWjw+Pn50atX\nL778+UuSPJI4lp7OmaQcQryDee//nkIEXp68d7UqDDOOTgAsASYIIV4F+gP+QAbwm5Sy7OLXDYQR\nYsQVDR+N6zKuzPBVbVH6bd+arKws/Pzsd3dDQkKYPn06s2bNYtiwYdXef35+PidPnmT48OE26eYV\n+8pj0aJFhIeHc8stWsSZli1b8re//Y2RI0dy6623smXLFgYMGMAvv/xCZmYm69evt7FrGAwGvv/+\ne5599lllJFc0eJo3b84Ddz7AmV8v8GvcKVoWdKN15g0kxbkjBte3dHVHlSYAmpREg1UUjZmoqCj2\n7t1bJj0+Pp68vDyio6PLLTt69Gi+//57nnvuuWrvf82aNRgMhiorn7i4ODZs2MDNN99sCa8A4Obm\nhqenJ82bNwe0Yarg4GCWLFliU3737t3Mnj2bb775xmZYS6Gob9LT03F1dUXnrsPH/fKSxe7u7jx2\n40OEX7qBnT8W066dH506Na9HSeuechWHECIB+JuUMk4IcRRtlb/yMEopy86zVzjM+PHjueuuu5g1\naxZjxoyhSZMmJCQk8PrrrzNw4EA6duxYYfmXXnqJESMc611lZWWRmpqK0WgkOzub3377jTfffJOH\nH36YVq1sHeRSU1Pt1uHp6Ym3tzdTpkxhzJgxPPzww0yaNIlWrVpx/vx51q1bR1ZWFvfee69l7saU\nKVOIjLSNxdO2bVsWL17MmjVrlOJQNBiSk5PZ9uc2EjITIAz+2espfLwvz8cI8gpi4h0BRIemEBsb\nclW42FaFinocvwM5Vr8dX5xcUWXatWvHihUreOedd5gwYQJ5eXmEhIQwbNgwpkyZUmn50NBQpk6d\nyosvvlhp3smTJ1t++/n50bZtW1588UXuuOMOm3wlJSXceOONdusYO3Yss2bNomPHjqxevZr33nuP\np59+mszMTJo2bUrfvn1ZtWoVAQEBLF26FJ1Ox+jRo8vU4+zszAMPPMC8efM4cOBAhT0rhaIuOH36\nNBt+38DJjJPoS0pI3pHDQ5sW8vGsJ3B3v/zIdHZ2olev0sG+rw101mEmGipCiNbAyU2bNhEaGlrf\n4igUiquUvw7+xY9//Eh2UTYAZ1OzOZSXTIuCnkzsO4p77+1QSQ0Nh6SkJAYPHgwQIaVMrMm6Kxqq\nalmViqSU565cHIVCoah79CV6Vv26ioPxBzGgeTeWuJbg3daHqO034m0IIj9fj9FovOaGpexR0VBV\nElUbnnKuPItCoVA0LBIzEvlk4yfkpl32ajR4GBhw/QBuE7exigR69AgmKiqgHqVsWFSkOB5E2TUU\nCsVVzLpD69j25zaMOTqys4vw9XXHP9CXibdNJNRPGxYfPz6qnqVseJSrOKSUH9WhHAqFQlGn6PV6\nLiRcoDDdQHZWEaBDV9CCGaMfx8W5SjMVrjkqsnHMrEI9RillzUTbUygUijrA2dmZ2NaxnDhzmgKD\nK655keRdbEVaaiEhIUpxVERFR+elKtRjBJTiUCgUDZa4lDjCmobh7+kPaOHNu3XtRk5+DvEHSsjM\n9GL8+ChCQrzqWdKGT0VDVY1zaSqFQqGwIrswm1UHV7H73G6a6SOYHDOZsLCmgBZ3rf/1/bk+RlvC\n1clJeUw5guqPKRSKqxKj0cj2M9tZe3gtmXk5XEgo4FTWYV459AULZk60KAmdToebm3IKrQoq5IhC\nobjquHDpAsvjliPTJABuWW40v+SOp84fUp3ZsuUMAwdWdf05hRkVckShUFw1lBhK2Hh8I98d/Y7i\nkmIwgkemB75FvngHtiAtCVpGuNOjh5qTcSVUZOP4u9XviXUijaJW2bVrF2PHjsXR0C1ffvklzz33\nHIcPH64D6RSKK+Nkxkk+jfuUM5lJ5Bfo8fJ0pUl6EyJcIghvEY4OJ4zhHtx22wDLmjCK6uGwjUMI\n4QTcDtwI+KKtAvirlPKXWpJNoVAoHCI5N5n5v88nIyOfo8cy0Rl0jGzfg8im7fF209Z5adGiBd27\nd7cJ/6+oHg4pDiFEMPAD0BUoBFKBIODfQohNwF1Syku1JqVCoVBUQIh3CN2CevDeH9/gXORKT6ce\n+GaE4+2vKY2IiAiioqJUnKkawlGX29fR1gm/TUrpKaVsJaX0AO4BemC7nKyiGgghWLNmDffddx/R\n0dEMGzaMffv2sXLlSgYMGECPHj146qmnKCoqspTZtWsX48aNo3v37txwww289NJL5OfnW7bHx8cz\nbtw4unbtyu23386hQ7ZrcBkMBt5//30GDhxIt27duOeee9iyZUudtVmhqC4GY9lllsd2vZ/hUf0Y\nwCACnAPxaqIt3xoVFaWURg3j6FDVCOAxKeWP1olSyq+EEIHAfODRmhbuSpFSkpCQ4FDe8PDwMute\nx8XFcerUKYfKR0ZGIsSVOZb973//Y+7cubRu3ZoZM2bw8MMPEx0dzeLFizl58iRTp04lJiaGMWPG\nsH//fiZOnMj48eN54YUXSEpKYvbs2SQlJfH++++TlZXFxIkT6dOnD1988QWJiYn85z//sdnf66+/\nzk8//cScOXNo1aoVW7du5bHHHmPJkiX07t37itqiUNQGBqOBLYlb2HJqC0/GTsPX6/Jyw95u3gxp\nEcuRzPMEB3vh4eFC9+7dadmySoG+FQ7gqOIoBLLK2ebYk1VRKaNHj2bQoEEA3HHHHcyZM4fZs2cT\nFhZGZGQkS5Ys4ejRowAsW7aMzp07M336dEBbSW/27Nk8/PDDHD16lL/++ovi4mLmzp2Ll5cX7dq1\nIyUlhTlz5gBw6dIlPvnkExYsWEC/fv0ATXnGx8ezaNEipTgUDY4zWWdYHrecExdPciYphzEb5rN8\nxr/x99dW5tPpdMTExFBQsA0nJydiY2Np1qxZPUt9deKo4ngPeFEI8aeUMsWcKITwAmYAi2tDuGsN\n62VbPT09cXJysvF+8vDwsAxVHT16lAEDBtiUj4mJsWw7evQoEREReHldDp/QrVs3y+/jx49TVFTE\nE088gZPT5RHL4uJiAgKUq6Ki4VCoL+SbhG/YdGITBqOBI/HppKcX0MSQyMpVB5jyaKwlr4+PD716\n9cLDw8Pm2lfULBVNANxo9VcHdAJOCCF+R/Oo8gf6Aq5Ag1zESQhxRcNHXbp0KTN8VZu4uNieDp1O\nV+64rIeHR5k082qOLi4u6HQ6Sq/u6OrqavltdkdcsGAB4eHhNvmsFYlCUZ8cSDnAygMruZh/0ZIW\nHuaP99lWhBX2JDszl4ICPR4el++d5s2b14eo1xQV9TjcsJ30t8307QqYX4P3mb7VIGId07ZtW/bu\n3WuTtnv3bsu2rKws1q1bR1ZWFr6+vgAcPHjQkjc8PBxXV1dSUlLo37+/Jf2dd96hpKSEJ554og5a\noVDYJ7Mgk9UHV7Pn/B6bdBEgGDtwLJudUigoSCQoqIDCwkt4ePjWk6TXJhVNALypDuVQVJGHHnqI\nu+66i/nz5zNq1CjOnj3LCy+8wIABA2jbti3BwcEsXLiQZ555hqlTp5KSksLbb79tKe/p6cnEiRN5\n/fXX8fLyIjo6ms2bN7Nw4ULmzp1bjy1TXOv8fvp3Pj/0ORk5ORw7nklEa1+Cm/kzqtMo+oT2ISsr\ni2bNkiks1FFSomfnzp0MHDiwTI9dUXtUNFTVV0r5e1UrFEL0k1JuvTKxFJURGRnJ+++/z5tvvsmn\nn36Kn58fw4cP51//+hcA3t7efPzxx8yZM4dRo0YRFBTEQw89ZDGOA/zrX//C1dWVV199lbS0NMLC\nwpgzZw533313fTVLocCIkTPnLyITMjAYjLQsCWX2Xc/Q1MOH8+fPs3fvXkpKSgBtWLVjx45KadQx\nutLj4GaEEPuBI8BLUsqDdjPZ5o9FM5S3l1LWqGFACNEaOOloqAyFQtF4MRqNPL9xLhs2xdMmdxDN\njGE8+WRPdLp04uPjLfnc3NyIiYlRNo1ySEpKYvDgwQARUsrEmqy7IjUdA8wGdpmi434B7AROApcA\nPzRbx43AbYAAFgBjalJAhUJx9bI/eT9+Hn6E+1120NDpdDw14DFi9Rc4GJfBmDGRpKef5OzZs5Y8\nXl5e9O7dW3lO1RMV2TiK0UKKvAs8CTwEzMLWYK4DTgNrgdullGfLVGQHIcQk4BkgDDgMPK1iXikU\n1w4Z+Rl8dvAz9iXvg2w/HusylS7RwZbtfh5+DLu1KTcPKmL37l1kZGRYtgUEBNCzZ08VqLAeqXRg\n0KQMpgHThBAdgDZoQQ7TgFNSSsemZpsQQkwAFqLNNP8NmAx8LYToXNPdKYVC0bAwGA38cvIXvpZf\nk33pElJmkJl1lpxDn/Fh+8ds3GqNRgPbt/9OXl6eJS08PJzOnTsrl/F6pkoWJSllPBBfacZyEELo\ngBeA+VLKZaa0acAg4AYgsbp1KxSKhk1iZiLL45ZzJusMAE7OOvLyigkpisIzuw0//XSKESPaWvK7\nuLjQqlUr4uPj0el0dOrUiYiICBVzqgFQ164IAggHVpsTpJQGoFu5JRQKRaMmvzifr+K/YsupLTaT\nUsP9wxg2+EE2rbnEzUPCGTo0vEzZdu3akZ+fT0hICEFBQXUptqIC6lpxRJq+/YQQvwCd0XowM6SU\n2+tYFoVCUYsYjUb2nN/DqoOrSL+UQW5uMf5+Hrg6u3J75O3c3OZmnHXO9IvKIzjYi5KSEoqKimxs\nFzqdrk6jNygco64VR1PT98dohvZ4YBLwixCiu5TySB3Lo1Aoaon0/HQW71lMckouJ05kYTAYGX/L\nIP7R6wECmlyOhxYc7EV+fj5//fUXzs7OXH/99cqG0cCp67NTbPqeK6VcKaXcA0wBjtIAw7IrFIrq\nE9AkgCERQzlzJgddkSeRObfhc3igjdIASE9PZ+vWrWRlZXHx4kUOHDhQJs6aomFR1z0Os7vuAXOC\nlNIohDgCRNSxLAqFoga5VHQJLzfbeRUjO4zgwoB8dq1qSqC/LzfeaDuB99SpUzaKQqfT4efnpwzg\nDRxHl471AJ5FW3Pci7I9FaOU0pEwtHvQJg/GArtMdZsj7/7soMwKhaIBUaAvYH38eraf2c4T3abT\npsXlmKeuzq48OnAsu3ySiY4OwN1de+QYDAYOHjxos1Cau7s7PXv2VDPBGwGO9jjeQrNF/AocBMqu\n2+gAUso8IcQbwFwhRApaz2My0BZtGVqFQtGIiEuJY+WBlaTlppOYmM2En19m+eNzCQ+3jVYbExNi\n+V1YWMiuXbu4ePFyqHRfX19iY2Px9PSsM9kV1cdRxfE3YKaUcn4N7HMWkAe8CQShhWYfKqWUNVC3\nQqGoA7ILs/nswGeWsOdHj2Vy4UIezYzN+Xj5fp57th9OTmWHmzIyMti1axcFBQWWtOuuu46uXbvi\n7OxcZ/IrrgxHFYcbWpyqK0ZKaQTmmT4KhaIRYTQa+SPpD9YcWkNe8eUZ3VHtWhJ4pj3NCtrjH+FN\nQYGeJk1cbcqmp6ezY8cODAZtwEKn09GhQwfatm2rbBqNDEcVx0a0QIaba1EWhULRgEnPS+fTuE85\nkmrrNX9D2A38rdPf+MsvHS8vV2JiQuwqAj8/P5o2bUpmZiaurq707NmTwMDAuhJfUYM4qjiWA4uF\nEAHAdrShJhuklCtrUjCFQtFw+OPMH6w8sJKc/HyOHcugRQsvIq8LY1yXcXQM7AjATTdVHKnW2dmZ\nmJgY9u/fT5cuXWjSpEldiK6oBRxVHF+YvieaPqUxAkpxKBRXKT7uPlxIz+bw4XRKSowEZHXhmbun\n4etdvrLIycnB29vbpvfh6elJnz596kJkRS3iqOJQcywUimuYzkGdGdi+H2eO/E7r3IH4lIRwND6H\nmJiyisNoNHLy5EkOHz5Mp06daNOmTT1IrKhNHFIcUkqLs7UQwgvwAdJNa3YoFIqriPM558ktyqV9\n8/Y26RNjxtHN6Va++yaRBx6Ion17/zJl9Xo9+/fv59y5cwAcPnwYX19fNTfjKsPhmeNCiJuA+UBP\ntAWcEELsBJ6TUm6qFekUCkWdYTAa+On4T3wtv0and+eBVv+iV/dWlu0eLh70jr2OmB4tcXEpG60o\nJyeH3bt3k5OTY0nz8/NTtoyrEEdnjvdH86yKR5uHkQK0BEYDG4QQg6WUW2tNSoVCUask5ybz0b6P\nOJFxgrNJuSSeyubotvdZ1XoW/v4elnw6nQ4Xl7IeU2fPniUuLg69Xm9Ja926NVFRUSpg4VWIoz2O\nF9FCggw3zcMAQAjxEvAd2trkg2tcOoVCUasYjAZ+PvEz6+PXozfoMRogOfkSXsWBBOZFs3LlEaZM\n6V5+eYOBw4cPc/LkSUuas7Mz0dHRhIWF1UUTFPWAo4ojBhhtrTTAEqBwIfBZjUumUChqldRLqXy4\n70OOXzxuSXN1cWHK4HH8ubIpYaFNGTmybbnl8/Pz2b17t8164F5eXsTExNC0adNyyykaP44qjgzA\nu5xtPkBJzYijUChqG6PRyNbTW1l7eC25BXm4umihPsJ8w5jYbSKhTUPpE5CGEM1wdrY/zGQ0Gtm1\naxeZmZmWtBYtWtC1a1dcXV3tllFcPTg6+PgLMFsI0dI60fR/NiqyrULRaFi0exGf7l9OwolUdv6Z\nTF6enhFiBM/e+CyhTbWw5506BZSrNECzdURHR+Pk5GRZD7xnz55KaVwjONrjeBYtDPpRIcQ2IBkI\nAW4EsoHptSOeQqGoaToGdmT11k2cP3+JJoZmBMnh3HrPMJyraMT28/OzzABX7rbXFg5dKVLKs0B3\n4F3AF7ge8AMWAt2llCdqTUKFQlGj9GvVj8HRvQjX96RHzv0Ee4SSl1fxlKy0tDRSUlLKpIeFhSml\ncQ3i8DwOKWUy8HQtyqJQKGqYhPQEfNx8aOHTwpKm0+l4dvBT9HVJQq83MmhQK7sh0EGzZSQkJHD0\n6FFcXFzo168fXl4Vx6RSXP2UqziEEDOBD6WU502/K8IopVRh0hWKBoLeoOdr+TU/Hv+R4jQfnur1\nNJ07BVu2O+mcuOmmVhXUAAUFBezZs4f09HQAiouLOXjwIL17965V2RUNn4p6HC+hGb3Pm35XhHmN\nDYVCUc+k5KawdO9SEi6cICHhIhkZScxOWMYnz00rs0ZGeaSmprJ3714KCwstaQEBAXTt2rW2xFY0\nIspVHFJKJ3u/FQpFw8RoNLL9zHZWHVxFUUkROh3k5hbjrw/DO1uwcWMid97ZvsI6DAYDUkqOHTtm\nSdPpdERGRtK+fXu14JICcDzkyCxgiZTynJ1t4cBUKeXjNS2cQqFwjLziPJbHLWf3ud2WtCbu7kwe\nMIG9XzbllqGtuf328ifzAeTl5bFnzx6bCX3u7u706NGDgICAWpNd0fhw1Dj+PLABKKM40DysHgaU\n4lAo6oHjF4+zeM9izmek4uGh3dItfFowqcckQpuGktL1EsHBFRu0k5OT2bdvH8XFl72rAgMD6d69\nO+7u7rUqv6LxUZFxfBuaUgAtGu4OIUR52f+qYbkUCoUD/HjsR9Yc/MJkyyigZ89ghkQOYlTUKNyc\n3QAqVRqgDUeZlYZaC1xRGRX1OCYB96ApjTnAIiCpVJ4SIBP4qlakUygUFZJTlMOBg6lkZxfhYnQn\n4NQgxtwzpsoP/ODgYCIiIkhJSaFHjx74+5dda0OhMFORcTwemAsghHBGs3GcrSvBFApF5dzZ4U7+\njD7A1t/OIS7dQreunSgpMdoNfW7GaDRSUFCAp6enTXqnTp0QQqiwIYpKcXQFwBcAhBDNATdMCzmh\nzTz3AvpJKZfUioQKhQLQQqAXlRTh4XJ5fQwXJxdm3TqN3z0v0DKkKV26BFZYR2FhIfv27SM7O5sB\nAwbg5uZm2ebk5KTWzlA4hKNeVdHACiCqnCxGQCkOhaKWyCrIYsmeJZxJzOPpAf/iuut8LNt83H24\ndahPBaU1Lly4wL59+yxzM+Li4ujZs6eyYyiqjKNeVa8BzYFpwO1AIfANMAy4DbipNoRTKBRwJPUI\n7/25iD2HTpOeXkDGsaUsnfm43eVb7VFSUsKRI0dsFlsC1JKuimrjaL/0euA/Uso3gNWAl5TyPSnl\nCDTDuHLFVShqGIPRwDfyG9768y0yLmWRkVGIDriQlsumTaccqiMrK4utW7faKA13d3f69OlDp06d\nVG9DUS0c7XG4A0dNvxMA67gDHwLv16RQCsW1TnZhNkv3LCU+LR6AJk1ciW5/HcY9sdzd/0YGDao4\nzpTRaOTEiRPEx8djMBgs6SEhIXTp0kXNzVBcEY4qjtNABLAVTXE0FUKESylPAQVAs1qST6G45khI\nT+CDXYvILcqxpHUI6MCDQx7k4iAjERF+FZbPz89n3759pKWlWdKcnZ2JioqiVatWqpehuGIcVRzr\ngFeEEDlSynVCiHjgRSHEPOBJ4HjFxS8jhOgEHLKzqZ+Ucpuj9SgUVxtGo5ENRzfw3uYVnDuXS7fu\nQbi6ODO8/XCGRw7HSeeEb0Tl9aSlpdkoDT8/P7p37463d3mrPysUVcNRxfEC0B54CE2JPGn6Hos2\nCfC+KuwzGkgzfVuTXoU6FIqrjh+P/8j89cu4kJoPQNKJIt4cP4OOgR2rVE9oaCjJycmkpKTQrl07\nIiMjlZutokZxdB5HHnC3EMLd9P9Hk4tuD2CPlNLhHgfQGThsWhhKoVCYGBA+gM9bbuBC6jF89S2J\nuTSKCJ+Ko9kC6PV6XFwu38o6nY4uXbpw6dIlmjVTo8iKmsfhFQABpJSFVr+PU4UhKis6A0eqUU6h\nuKrxdPXk+eFP8b/s9dwYOJS77oys0OVWr9dz+PBhLl68SL9+/XB2drZsc3d3VwZwRa1RUZDDo2gT\n+xzBKKUsNwJiKToDHkKIHUBr4CAwU0q508HyCkWjJ6cwhw37tjJUDMLP7/JM8HC/cN78v39WasBO\nT09n37595OXlARAfH09UVHnzcxWKmqWiHsfvOK44HEII4Qm0AVLR1i8vBB4DtgghekgpVU9EcdVz\n5EI8/1n3Pw6fOMufQRf571NjbRRFRUqjpKQEKSUnTpzAaLx8e+bn52M0GpXHlKJOqCjI4cSa3pmU\nMl8I4Q8Umoe9hBATgZ7AZOCfNb1PhaKhYJ7Q9/ne9Rw+noIR2Jj8Bd//FMPwoR0qLZ+RkcG+ffvI\nzc21pLm6utK5c2euu+46pTQUdYajsapuqCyPlHK7I3VJKbNL/TcIIQ4BYY6UVygaIxfzL7JkzxKO\nXzyOt7croWE+pJzWM6jZ3fTqXvFkPoPBQEJCAseOHbPpZQQGBtK1a9cyUW4VitrGUeP4NioftnKu\nZDtCiJ7AZmCglHK3Kc0Z6AascVAWhaJRsfvcbpbHLSevOM+SNrRHLzpF3cKtN3XCyan8nkJWVhZ7\n9+4lJ+fyZEAXFxc6deqkJvMp6g1HFcdAO2neQD9gPNqCT46wH0gEPhBCTAFygelAAPCWg3UoFI2C\nguICXvrqfX6SW+jSJRAnnQ4nnRMjxUhuaXcLTrrK51akpqbaKI3mzZvTrVs3FaBQUa84Oo9jSzmb\nvhNC5ALPoUXNrawevRDiNuBVtOi6XmhG+P5SyguOiaxQNHySspJ4ePELnLxwDoDTp7Lp0TGCST0m\n0bZZW4fradu2LefPnycnJ4eOHTvSunVr1ctQ1DtVmsdRDluBGY5mNq0iOLYG9qtQNFi83b3x8jOC\n6XXIPb01z/b9N009yw/7UVJSQnFxMR4el91zdTod3bt3R6fT4eVV+drhCkVdUBNxCEYA2ZXmUiiu\nIfw8/Jg5fAqB/j6Mj5rA2pkvVag0Ll68yG+//cbu3bttDOAA3t7eSmkoGhSOelVttJPsjOYJ1RaY\nX5NCKRSNiZISA6t//IOR/WPx9r68FGv3Ft357skl+HiUrzD0ej3x8fEkJiZaFEZiYiIREQ5EM1Qo\n6glHh6rcKOtVZQQOo9krltWkUApFY+HIibNMX/EGx3KOcDrpUWY8bGvqq0hppKamEhcXZ5n9DZrH\nlHXoEIWiIeKocfymWpZDoWh07D63m7f/WMLRnNMArE5YwbDDPejSqWWF5YqKijh8+DBnzpyxSQ8K\nCqJLly5qXoaiwVMl47jJI6of4A+kAL9IKX+rDcEUioZKblEunx34jF3nduHRFIICPUlLL+DWLjcQ\n2a55ueWMRiPnzp3j0KFDFBZa4oXi5uZGVFSUmv2taDQ4auNoDmwAYtDiS6UCQcB/TPaPu6SUBbUm\npULRANDrDfx5ajfrjq8mp/Dy3IqeURHc3eZ+buzQo9yyRqORXbt2kZxsu5pAy5Yt6dy5s4pkq2hU\nONrjWIC2dOwIKeV35kQhxEhgKfAK8K+aF0+haBgcSjjLzJXvcMFNEh0dgA6tZ9C3VV9GdRqFp2vF\nw0s6nc5m0p6HhwfR0dGEhITUqtwKRW3gqOK4DfiXtdIAkFJ+LYR4FpiLUhyKq5TdiQeZtGQOBVyC\nPEhOvkTH1qGM7zqezkGdHa5HCEFycjJBQUF07NjRZvElhaIx4eiVqwcyy9l2Hs3rSqG4KgkLDCIk\nzI3EM5dwdtYR5dud/9w0mSau9sN+6PV6jh07RuvWrW0m87m4uDBgwAClMBSNHkcnAL4LvCyEsHEX\nEUI0RZs1vqCmBVMoGgpBXkE8cct42lwXzMKJ/2He6GnlKo0LFy6wZcsWjh49yqFDh8psV0pDcTXg\n6FXc0vQ5LoTYBpwDmgN9AR+g0GqSoFFKeUuNS6pQ1AG7Dp1k7c9/8NKU+2yWbR3afgj9I/qVqzDy\n8/M5dOgQ58+ft6SdO3eOiIgIte634qrDUcXRDthnVca8gIA5zRkHwqorFA0Vo9HIyys+Y1XcGgyU\nELkunAdH9bVsd9I52VUaRqORkydPIqVEr9db0t3c3OjUqRP+/v51Ir9CUZc4OgHQXlh1heKqICU3\nhU1U4HMAACAASURBVE/jPmXHpb3oKQLgo92fcN/wWJo0Kd98l5GRwYEDB8jKyrJJDwsLo1OnTri5\nKdOf4uqkqhMAOwEDAF+0uRzbpJSyNgRTKGobvUHPxuMb+S7hO/QGPS1aepGWno+vc3Pmjv5nuUqj\nqKiI+Ph4Tp8+bROQ0MfHh+joaJo3L38SoEJxNeDoBEAn4APgQcB6aqtRCPEp8HcpZWUrBCoUDYKS\nEgMrN2zjoPNGMvWplnRnnTNP3j6WOzuNwM2l/N5CZmYmp06dulzO2Zn27dvTtm1bnJxqIuC0QtGw\ncbTHMQN4wPS9Ai3cSAtgDDCHy8EOFYoGzSF5nlmfvc+RvF0EBnrSoYPWOwj3C2d8l/GE+YZVWkdQ\nUBAhISEkJycTHBxM586d1Yp8imsKRxXHP4C5UsrXrNKSgFeFEB6m7UpxKBo8K+VHHM7bBcCF1Hxa\nh8EDvUYzMGKg3aVci4uLycvLw9fX1yY9KiqKsLAwNfNbcU3iaL+6BdoSr/bYzmUvK4WiQTOp330E\nBTbB2VnHoKhevDrsJQa3GVxGaRiNRk6fPs3mzZv566+/bDymAJo0aaKUhuKaxdEexwngemCTnW3X\no80eVygaFEePp+Hl6U7Llj6WtAj/CCYPuY8gzxBuirzBbjTazMxMDh48SEZGhiXt2LFjdOjQoU7k\nVigaOo4qjiXAPCHEJWAVmo0jGLgfmAm8XDviKRRVJzu7kIWrf2StXE3v5jexcMYkGwVxb7d77JYr\nLCwkPj6eM2fO2HhLeXp6lhmqUiiuZaoSHbc78DrwX6t0HbAcLcihQlHvZBdms3TvcpYf/x6Dk5Ft\nF3/g59/6M2SAKLeM4f/bu/Pwqqpz8ePfM2QiJCQnExAgISF5wyCD4oAEFEW9olLtYK3aqr3Wjtep\ntXTSWqfa4Uer1nvtbb0drEPtoKKiMiuoxeKETIsQCIFAIGHMQEKSc35/rJ3kJEA4geTkHPJ+nidP\nwl77rP0uzvCevfZea/n9lJWVsXHjRpqamtq2u91u8vPzGTVqlE4VolSQUAcAtgA3iMjPsQs5+YB9\nwFvGmCMn5FEqzPwBP2+WvcmLG16kobmB7OyBbNtWQ1pGHIlD6o75uKqqKtauXUtNTU2H7VlZWYwd\nO5bExMTeDl2pqNPdr1HbsNc79gG7nb+V6jPV1fWsqSjh7QOvUH6gvG37iBFJTMs7h1svvIlB8Ufv\nZmpubub999/vcJaRmJjIuHHjyMzM7PXYlYpW3RkA+HPgW0AM7YMA60TkQWPMw70Un1JH1djYzIuv\nruN3K55h78D1nHFGFm63fVlmDczi2tOupSi964vZXq8XEWHNmjV4vV4KCgrIy8vTQXxKHUeoZxz3\nArcBvwb+gT3byAI+B9wnIgeNMf/dKxEqdRSb9pTy81UPUO+tgwbYtr2GUSPTmFUwi4vzL8br7vjS\nDgQC7N2794jpQHJycmhsbDxi7Qyl1LF1ZwDgfcaY+4O2bQbeFZEa4A7smh1KhUV+Zg5SkMaH6+tI\nSoplSt7pfPO8m0gfkH7EvtXV1W3XMYqLi0lJSWkrc7vdeputUt0UauIYBLx3jLIVwHd6JhyljlRT\nc5jy8oOMHdueFOK98dx20U08EfsXbrvgy0wYPOGIMRl1dXWsW7eOysrKtm3r1q1jypQpRx2/oZQK\nTaiJ4xXga8AbRym7Bph/IgcXkXOwiWemMWbZidShTl1+f4AlS7by5Pw3OODewXP3/IDk5Li28rOy\nz2TSNROJ9XSckPDw4cOUlJRQVlaG3+9v2+7xeEhLSyMQCGjiUOokhJo43gIeFJHV2AGAO7ErAF4O\nFANzReQHzr4BY8xPj1ehiCQCT6ELQKljqKqtZu7yR9nitTP3P/7XN/j+V2a3lbtcrg5J41jjMQCG\nDRtGUVERCQkJ4QleqVNYqInjN87vQcADRykP7qoKAMdNHMBc7ESJo0KMQfUTLf4WFm1exMsbX2bg\nqBr4BAYkeKlO+wCYfcT+gUCAyspK1q9fT11dxzEbPp+PsWPHdriuoZQ6OaEOAOzR+xNFZBZwGXAp\nsLon61bRqbnZz6ZN+/Bm7uPp1U+zo2YHAKkp8Ywdk87siTP57NijTxXicrnYunVrh6SRmJjI6NGj\nGTx4sHZLKdXDwj6PgoikA08CN2EHEqp+bsOGPfzp2Q9ZeXABQ8+uJjExpq1sWPIw5hRfR15qXpd1\njBkzhrfeeguv10thYSG5ubk6HkOpXtIXE/D8FphnjHldRIb1wfFVBPH7/fzPy/NYWv8KTTEN1G2K\nZcKEDOK98cyW2Vww8oIOU543NjayefNmCgsL8XjaL48lJyczadIkMjIydK1vpXpZWBOHiNyAnSxx\nfDiPqyKXy+UiY+IeWhY14HG7yMhIYELWBL5w2hfwJfja9mtubqa0tJTNmzfT3NxMbGws+fn5HerK\nzs4Od/hK9UvhPuO4ERgGVIoItE9d8pqI/MkY87Uwx6PCrKqqnoyM9mVWXS4XX596E6sr1jE03cdN\nk7/IhMET2sr9fj9bt26lpKSExsbGtu0lJSXk5OTorLVK9YFwv+uuB4LvhxwMLAduBhaGORYVRocO\nNfHSS6W8uPxd5nz1EiaNH9pWljYgjfsvn0NuSi5xXjtOIxAIUFFRgTGG+vr6DnUlJyczevToDl1V\nSqnwOWbiEJGhxyo7GmPMjhD2qeh0jAbnzwpjzO7uHE9Fl+deWM0f33uG3YkbeOj5Sp4u+i6xse0f\n/JJu18sIBALs3r2bDRs2cPDgwQ51JCQkUFRURHZ2tt4ppVQf6uqMYzt2TEao9OufOkIgEGBF+QpW\nJf2NfQO2QDPsTPyArXu2UzAk54j9V61a1WGKEIDY2FhGjRpFbm6unmUoFQG6Shxfpj1x+ICHsWuO\nP0/7yPHZ2NHjd57IwY0x22m/zqFOEc3NftxuFztrd/D0J09TurcUgFEFdhDef4yfRpYv9aiP9fl8\nbYnD4/GQl5dHfn4+MTExR91fKRV+x0wcxpg/tv4tIi8AfzbGfKXTbs+IyCPA1cD/9kqEKqps3ryf\nPzz1MbFjDTviP8QfaJ8ravSIEVx72rWMzRwLQENDwxFTmefm5lJWVkZWVhYFBQXExcWhlIosoV4c\nvxi48hhlrwCdE4rqh1avruL+//0nm+KX0vxBLZMnDyY2xoPH7eHi/IuZVTCLWE8sdXV1bNy4kYqK\nCqZPn05ycnJbHR6PhxkzZujgPaUiWKiJoxo4i6Pf+XQ+UHGU7aqfafSVU5o2n4ZDzXj8LmprD3P2\nqPFcd9p1DEkaQn19PetL1rNt2zYCAdsLaozhzDPP7FCPJg2lIluoieN3wD0ikgDMA6poXwHwVuD2\n3glPRZPTh05k2vixrCoxjC/K5vrTP8+5w8+loaGBTz75hPLy8g7TnIMdp9HS0qIXvZWKIqEmjgeB\nFOAu4PtB2xuAu40xj/d0YCpytbT4Wby4nPqGRq6cLW3bPW4Pt11wMytGreDToz+N1+9l7dq1bN26\n9YiEkZ6eTlFREampR79IrpSKXKHOjhsAviMi9wNTgFRs99U7xpi6Lh+sTik1NYf52dzlvL3vDRo8\n+5l8+i8ZNqz9GkVeah4jU0YeM2H4fD5EhPT0I5d4VUpFh26NHDfGHABe76VYVIQLBAJ8vPc9lsc8\nye7YAwA88eo8Hvjq9R32c7lc1NbWdkgaqampbQlDB+8pFd26GjleQugDAAPGGDn+bipabT+4nWc+\neYbSvaWMyI9n78c1jBiexKizmvH7/Udc0C4sLKSqqoqUlBREhIyMDE0YSp0iujrjeJvujRxXp5jt\n22tY+f42WkatYemWpW1jMgYMiOHS88dytXyWuINxLFu2jPPPP79D8vD5fEydOpXU1FRNGEqdYroa\nAHhj698icg2w2BhTFY6gVN8KBAI8//wGnl+xhE3xb1J4IB5fqp2b0uP2MCN7BnmBPCrXVLZ1R23b\nto2cnI5TiPh8viPqVkpFv1BvmP8dML03A1GRI0CAebv/xLqE+Rx21bF58wECBChIKuDqtKtJ2J7A\nju07OlzDqKrS7xRK9RehXhyvAAYcdy91SnC73Mw8Zxyrd6xhYFIsZ+TnMGNAMXG1cdTU1HTY1+fz\nUVhYqHdJKdWPhJo4/gd4RETOAT4GajvvYIx5picDU+Gxd+8hli7dxlVXFeB2t1+L+PzET/PRtg8p\nco9iiGsInnoPgaBLXunp6RQWFuLz+fQahlL9TKiJ41fO768fozwAaOKIMq+/voVn5r/DJu8K4gZ9\ng8tnntZWNiBmAA9e+hNWvLmCpqamtu2ZmZkUFBTo9Qul+rFQE8fIXo1Chd3BxoMsqvonq+KXEAAe\nW/QUM6bcR2Ji+2y1AxMGkpuby6ZNmxg8eDAFBQUMGjSo74JWSkWEUEeOb239W0QSgSRgjzGm6diP\nUpGo2d/Mki1LeHXjq9QnHyI+3kOGJwnxNfPhmlUUn13cYf+8vDyys7NJSkrqo4iVUpEm5JHjInI+\n8DPgDJzFl0TkPeBHxpjFvRKd6hF79hzi1VdLySuu5bUtL1NdXw1+SKiN57zMArIGZJCfms/+qv3U\n1dWRmJjY9tjY2FhiY2P7MHqlVKQJKXGIyHRgAbABuAfYBQzFLuD0mohcaIxZ3mtRqhO2dGk5//fC\nMjbGvMmg/XXkDU8hviae2NpYEr2J5GXlkRpvJxr0er3U1NR0SBxKKdVZqGcc9wOLgMucCQ8BEJEH\ngFeBe4ELezw6ddLer1vMqvi/E++KIWbXIBJdScR5Y8hJyWFI0hBcuIiPjycvL4+cnBy83m5NX6aU\n6odC/ZSYDFwdnDTAzporIo8Dz/Z4ZKpHXHLmZN78cBkZ/mRSkuPJSRnO8OTheN1eBg4cyKhRo8jO\nztbFk5RSIQs1cewDBh6jLAlo6Zlw1ImqqqrnuX+s5vOfPo3MzPaupnGZ4zjn9CJid3vJTckl3huP\nz+cjPz+frKwsHYOhlOq2UBPHEuBeEVlujNnRulFEhmK7qRb1QmwqRIuWlfCrl/5KhfcDKp+exf23\nfbntDMLlcnHXJd9m5bsrSUhIID8/XxdPUkqdlFATx/eBVUCJiKwAKoHBQDFwEJjTO+GprjQ2N7Jk\nyxL+UfEKzfEHGevJYkf1Wj7+eCOTJhW17RfrjWXq1KnaHaWU6hGhjuOoEJFJwLeBadgBgfuAx4G5\nxpjK3gtRddbY3MjSLUtZvHYxzXub8R1KxD3QS3OznyxfIjuqS5kYkA7dUJo0lFI9pauFnM7DLg3b\nBOAkh7vCFZg60s6q/fz8r09zKHEjiU1ePE0eYogBINOXzMjUXPIG55Gfl9/HkSqlTmVdnXEsBepE\n5C3sGI5Fxpi14QlLdfab+c/yyoo3SHXHkxATQ3K6B4B4bzwjkkcwbuQ48vPzdWlWpVSv6ypxXIW9\nhjEN+AXgEZFK7IXwhdhEol1UYZKY6ifNk4A74KapyQ/NXgoH5zG5aDL5efk6JYhSKmy6WgHwJeAl\nABEZAEzBJpLpwBNAgoisxSaRhcaY13s/3P5h09ZKMlOTSE5uv632M6dfweJ3l5NQk8BpOYVcMvV8\ncnNydToQpVTYhXpxvB5Y7PwgIl7gPOAW4FvA7YAnlLpEZBh2mvYLsSsQvg7cGXybb3/12or3eH7p\nPBoa9nChXMLNX7qyrSw5LpkfXH0bAwMDGaYD9pRSfag7kxzGA+cDM4EZwHjsOhzvYa+BhFKHCztF\nSZVTB8CjwMvYyRP7Hb/fz6rSVSz7aBnbyitpbmzE63Lz0aYPqau7mMTE9oUXxwwb3YeRKqWU1WXi\nEJFxwCXOTzEQD5RiE8V9wFJjzMFuHC8LWA98zxhT5hxjLvCiiKQaY/Z1uwVRpqbmMB98sIvybfvI\nLNrJe2vfo6bWLscaH+fB5QIC4Ipvobr6QIfEoZRSkaCr23G3A0Ow4zWWYbujFrR+4J8I52L6NUHH\nGAZ8Ffh3f0gajY3NfO+H86mJXQdxu8jYG4PH097l5HK5yM8dzkVnzmDKaWfp3VFKqYjU1RnHUKAa\neBJ7AXx5Ty7cJCIvAp/CJqYZx9n9lFDTsp/9WQtwH7IJ4dAhNwMHunG5XYwcMZJLJl/CyCxdbFEp\nFdm6ShwzsV1UlwLfBeqDxnQsMMasP8lj3w08BPwIWCgik4wxFSdZZ0Sorq5n4cKtFBYmc8YZ2W3b\n0xLSSBmSRMP2ehISvAwYFMuEovFcesal+BJ1DW+lVHTo6nbcJdjJDeeISBY2iVyEnbfqV05X1kJs\nIllojNnbnQMbYz4BEJFrgG3ADdhEEtXeeWc7zzy7kqa4MtZsjmHixG/i8dgbzlwuF9fPvJL578xn\nypgpXDjmQuK8cX0bsFJKdVOot+PuAv7s/CAiE7FJZDrwR6eemOPV4ySgGcaY54LqrheRUiD72I+M\nfHV1dZRsLuGjLSupG7SBZg6zoz6O1atLmTSpsG2/s4efzdmfPxu3S2+nVUpFp24t9yYiKdiBgOcC\nZ2MXePIC74dYRQ7wrIhsMsascuocBAjwp+7E0tdaWvy8//5OsrL8mC3rWVe+jl21u2gJtBCT4Mfj\n95CY6KKqsQxoTxyaMJRS0e54t+MWYJPEVOd3EXbQ3jrsYMDfAMu6cUvuKmA58HsRuQVoAh7GjuuI\nmsSxbNkmFi78gIPNZQwccoiWmLoO5cm+GFwpLs4acxZnyVl9FKVSSvWOrm7HrQJ8gAsoxyaKh4Al\nJzpHlTHGLyKfBn4JvIIdF/IGcJ4xpvZE6uwLK8uWU8HHtMQ0UbvfRUaGHWvRlNBESlYKM8bO4Jzh\n5xDr0elAlFKnnuPNjrsIWGyMKe2pAxpjqoEbe6q+3uT3+9m8eSf5+UM7jKkYMSGRT0oP43W58Q5w\ncSi5AckvZGbhTCRNdPyFUuqU1tVdVVeHM5BIUldXz4IFH/PR6g0caKjiO9/8EsOGDW4rv6RoJoty\nlzAoNZ7iomLOyz2PtAFpfRixUkqFT7cujp/KWlpa2LVrF+Xl5ZRuL2Xl2o3sb9oDngDzF/+LW25o\nn3DQl+Djrk/dTn5qPjGe495MppRSp5R+nTgCgQDV1XvZvHkrVXt2ULG/gp21O6lvqicwoJnAgQAB\nV4DyQ2VHPLYovejICpVSqh/ot4mjrGwnr85fwZYd5bQkHCQupRE//rZyb0qApvgGCmU4l42Z0oeR\nKqVUZOm3iWPjvhL+XfE2La4mXIcgI2kArtgAhwcexpXsYnLOZKblTCNnUI5e7FZKqSCndOIIBAJU\nVu5m1SrDtGkTSUlJbivLz8mmMb4eV6OHGvchAkmNjM7PY1r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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -3431,7 +3428,7 @@ }, { "cell_type": "code", - "execution_count": 56, + "execution_count": 128, "metadata": { "collapsed": true, "scrolled": false @@ -3454,15 +3451,26 @@ }, { "cell_type": "code", - "execution_count": 57, + "execution_count": 129, "metadata": { - "collapsed": true + "scrolled": true }, - "outputs": [], + "outputs": [ + { + "data": { + "image/png": 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ne5eWjBjRlpkz+zRKpQGO9zhmAA+YvlcAKWhG7jFow0yH0WwVVWEc8KGUsriK\n5RTA999/z/Dhw7n55purXPbdd9+lS5cuGI1GcnJy2Lx5M6+88gpJSUk2izc5OzuzZcsWu3X4+voC\n2pK0Y8aM4eabb+bDDz/Ex8cHKSXz5s3j4MGDfPLJJzblUlNT2bZtG61bt2b16tXlrkioUDRkSkpK\n2LVrFxcuXLCkBbYMZFvRNg7uP4heb2Da0nd48d4p+Pl5WPLodDomT+5mN3x6Y8JRxfEPYK6U8jWr\ntCTgVSGEh2m7w4pDCBEFtANWOVpGYUtYWBizZ88mNjbW8hB3FF9fXwIDtVg3QUFBtG3bFhcXF+bP\nn88999xDu3btLHnN+crD3POYO3euJS00NBQvLy8mTJhAfHw8HTp0sGz7+uuvCQoKYuzYsbzxxhvM\nnDmzzBroCkVDRq/Xs3PnTtLT0y+n+epZdWEV+fp8Lmbkk5CQgXNBHp9+Fsc/H+1lU76xKw1wfM3x\nFsDv5WzbDrSq4n77oS07W35MYUWFPP300xQXFzNv3rwaqW/UqFG4ubmxYcOGKpVzcnIiJyeH3bt3\n26THxsby7bfflgmD/tVXX9GnTx+GDBlCfn4+X3/99RXLrlDUFUVFRfzxxx8WpVFUUkQCCfyQ+QP5\n+nwAnJ2cCMiJpkfO/Rzcl8nx45kVVdkocbTHcQK4HthkZ9v1QOWr+9jSHThYaa4r5Bv5Dd8mfOtQ\n3n7h/RjXZZxN2vK45Ww9tdWh8rdH3s4IMaLKMlaX5s2b8+yzzzJ9+nSGDRtG//79r6g+Ly8vQkND\nSUhIqFK54cOHs3TpUsaMGUNUVBS9e/emd+/e9OnTh/bt29vkPXDgAAkJCUydOpUWLVrQrVs31qxZ\nw5gxY65IdoWiLigoKGDHjh3k5OQAkJKbQjzx5HjnaKFegYAmAUy9YQI7DMUcOpTGffd1oG3bhhFf\nqiZxVHEsAeYJIS6hDS+lAMHA/cBMNGN5VWgBXKxiGUUp7rzzTjZs2MCsWbP49ttvr3jIp/TytSUl\nJXbXHff39+eXX34BtPDQX3zxBcuWLWPjxo0sW7aMZcuW4e3tzbRp07j//vst5datW0fTpk254YYb\nAE3pvPTSS8TFxVW4LoFC0RAoKCggPz+fwpJCjl48yjmPc2Q4X0KXp8WSGhQxiDvEHbi7uBM2qphR\noyLx9Gyc7raV4ajiWIDWS3gd+K9Vug7NK2quvULlIaUcWZX81wIuLi4YDPaDDhsMBktgtNK88MIL\nDB8+nFfjgepDAAAgAElEQVRffZU5c65sOkxubq6NTcPZ2ZmvvvqqTD4nJ9sRTn9/f6ZOncrUqVM5\nd+4c27dvZ+XKlcyePZuWLVsyYMAAioqK+O677xg8eLBlMahbb72Vl19+mdWrVyvFoWjw+Pn50atX\nL778+UuSPJI4lp7OmaQcQryDee//nkIEXp68d7UqDDOOTgAsASYIIV4F+gP+QAbwm5Sy7OLXDYQR\nYsQVDR+N6zKuzPBVbVH6bd+arKws/Pzsd3dDQkKYPn06s2bNYtiwYdXef35+PidPnmT48OE26eYV\n+8pj0aJFhIeHc8stWsSZli1b8re//Y2RI0dy6623smXLFgYMGMAvv/xCZmYm69evt7FrGAwGvv/+\ne5599lllJFc0eJo3b84Ddz7AmV8v8GvcKVoWdKN15g0kxbkjBte3dHVHlSYAmpREg1UUjZmoqCj2\n7t1bJj0+Pp68vDyio6PLLTt69Gi+//57nnvuuWrvf82aNRgMhiorn7i4ODZs2MDNN99sCa8A4Obm\nhqenJ82bNwe0Yarg4GCWLFliU3737t3Mnj2bb775xmZYS6Gob9LT03F1dUXnrsPH/fKSxe7u7jx2\n40OEX7qBnT8W066dH506Na9HSeuechWHECIB+JuUMk4IcRRtlb/yMEopy86zVzjM+PHjueuuu5g1\naxZjxoyhSZMmJCQk8PrrrzNw4EA6duxYYfmXXnqJESMc611lZWWRmpqK0WgkOzub3377jTfffJOH\nH36YVq1sHeRSU1Pt1uHp6Ym3tzdTpkxhzJgxPPzww0yaNIlWrVpx/vx51q1bR1ZWFvfee69l7saU\nKVOIjLSNxdO2bVsWL17MmjVrlOJQNBiSk5PZ9uc2EjITIAz+2espfLwvz8cI8gpi4h0BRIemEBsb\nclW42FaFinocvwM5Vr8dX5xcUWXatWvHihUreOedd5gwYQJ5eXmEhIQwbNgwpkyZUmn50NBQpk6d\nyosvvlhp3smTJ1t++/n50bZtW1588UXuuOMOm3wlJSXceOONdusYO3Yss2bNomPHjqxevZr33nuP\np59+mszMTJo2bUrfvn1ZtWoVAQEBLF26FJ1Ox+jRo8vU4+zszAMPPMC8efM4cOBAhT0rhaIuOH36\nNBt+38DJjJPoS0pI3pHDQ5sW8vGsJ3B3v/zIdHZ2olev0sG+rw101mEmGipCiNbAyU2bNhEaGlrf\n4igUiquUvw7+xY9//Eh2UTYAZ1OzOZSXTIuCnkzsO4p77+1QSQ0Nh6SkJAYPHgwQIaVMrMm6Kxqq\nalmViqSU565cHIVCoah79CV6Vv26ioPxBzGgeTeWuJbg3daHqO034m0IIj9fj9FovOaGpexR0VBV\nElUbnnKuPItCoVA0LBIzEvlk4yfkpl32ajR4GBhw/QBuE7exigR69AgmKiqgHqVsWFSkOB5E2TUU\nCsVVzLpD69j25zaMOTqys4vw9XXHP9CXibdNJNRPGxYfPz6qnqVseJSrOKSUH9WhHAqFQlGn6PV6\nLiRcoDDdQHZWEaBDV9CCGaMfx8W5SjMVrjkqsnHMrEI9RillzUTbUygUijrA2dmZ2NaxnDhzmgKD\nK655keRdbEVaaiEhIUpxVERFR+elKtRjBJTiUCgUDZa4lDjCmobh7+kPaOHNu3XtRk5+DvEHSsjM\n9GL8+ChCQrzqWdKGT0VDVY1zaSqFQqGwIrswm1UHV7H73G6a6SOYHDOZsLCmgBZ3rf/1/bk+RlvC\n1clJeUw5guqPKRSKqxKj0cj2M9tZe3gtmXk5XEgo4FTWYV459AULZk60KAmdToebm3IKrQoq5IhC\nobjquHDpAsvjliPTJABuWW40v+SOp84fUp3ZsuUMAwdWdf05hRkVckShUFw1lBhK2Hh8I98d/Y7i\nkmIwgkemB75FvngHtiAtCVpGuNOjh5qTcSVUZOP4u9XviXUijaJW2bVrF2PHjsXR0C1ffvklzz33\nHIcPH64D6RSKK+Nkxkk+jfuUM5lJ5Bfo8fJ0pUl6EyJcIghvEY4OJ4zhHtx22wDLmjCK6uGwjUMI\n4QTcDtwI+KKtAvirlPKXWpJNoVAoHCI5N5n5v88nIyOfo8cy0Rl0jGzfg8im7fF209Z5adGiBd27\nd7cJ/6+oHg4pDiFEMPAD0BUoBFKBIODfQohNwF1Syku1JqVCoVBUQIh3CN2CevDeH9/gXORKT6ce\n+GaE4+2vKY2IiAiioqJUnKkawlGX29fR1gm/TUrpKaVsJaX0AO4BemC7nKyiGgghWLNmDffddx/R\n0dEMGzaMffv2sXLlSgYMGECPHj146qmnKCoqspTZtWsX48aNo3v37txwww289NJL5OfnW7bHx8cz\nbtw4unbtyu23386hQ7ZrcBkMBt5//30GDhxIt27duOeee9iyZUudtVmhqC4GY9lllsd2vZ/hUf0Y\nwCACnAPxaqIt3xoVFaWURg3j6FDVCOAxKeWP1olSyq+EEIHAfODRmhbuSpFSkpCQ4FDe8PDwMute\nx8XFcerUKYfKR0ZGIsSVOZb973//Y+7cubRu3ZoZM2bw8MMPEx0dzeLFizl58iRTp04lJiaGMWPG\nsH//fiZOnMj48eN54YUXSEpKYvbs2SQlJfH++++TlZXFxIkT6dOnD1988QWJiYn85z//sdnf66+/\nzk8//cScOXNo1aoVW7du5bHHHmPJkiX07t37itqiUNQGBqOBLYlb2HJqC0/GTsPX6/Jyw95u3gxp\nEcuRzPMEB3vh4eFC9+7dadmySoG+FQ7gqOIoBLLK2ebYk1VRKaNHj2bQoEEA3HHHHcyZM4fZs2cT\nFhZGZGQkS5Ys4ejRowAsW7aMzp07M336dEBbSW/27Nk8/PDDHD16lL/++ovi4mLmzp2Ll5cX7dq1\nIyUlhTlz5gBw6dIlPvnkExYsWEC/fv0ATXnGx8ezaNEipTgUDY4zWWdYHrecExdPciYphzEb5rN8\nxr/x99dW5tPpdMTExFBQsA0nJydiY2Np1qxZPUt9deKo4ngPeFEI8aeUMsWcKITwAmYAi2tDuGsN\n62VbPT09cXJysvF+8vDwsAxVHT16lAEDBtiUj4mJsWw7evQoEREReHldDp/QrVs3y+/jx49TVFTE\nE088gZPT5RHL4uJiAgKUq6Ki4VCoL+SbhG/YdGITBqOBI/HppKcX0MSQyMpVB5jyaKwlr4+PD716\n9cLDw8Pm2lfULBVNANxo9VcHdAJOCCF+R/Oo8gf6Aq5Ag1zESQhxRcNHXbp0KTN8VZu4uNieDp1O\nV+64rIeHR5k082qOLi4u6HQ6Sq/u6OrqavltdkdcsGAB4eHhNvmsFYlCUZ8cSDnAygMruZh/0ZIW\nHuaP99lWhBX2JDszl4ICPR4el++d5s2b14eo1xQV9TjcsJ30t8307QqYX4P3mb7VIGId07ZtW/bu\n3WuTtnv3bsu2rKws1q1bR1ZWFr6+vgAcPHjQkjc8PBxXV1dSUlLo37+/Jf2dd96hpKSEJ554og5a\noVDYJ7Mgk9UHV7Pn/B6bdBEgGDtwLJudUigoSCQoqIDCwkt4ePjWk6TXJhVNALypDuVQVJGHHnqI\nu+66i/nz5zNq1CjOnj3LCy+8wIABA2jbti3BwcEsXLiQZ555hqlTp5KSksLbb79tKe/p6cnEiRN5\n/fXX8fLyIjo6ms2bN7Nw4ULmzp1bjy1TXOv8fvp3Pj/0ORk5ORw7nklEa1+Cm/kzqtMo+oT2ISsr\ni2bNkiks1FFSomfnzp0MHDiwTI9dUXtUNFTVV0r5e1UrFEL0k1JuvTKxFJURGRnJ+++/z5tvvsmn\nn36Kn58fw4cP51//+hcA3t7efPzxx8yZM4dRo0YRFBTEQw89ZDGOA/zrX//C1dWVV199lbS0NMLC\nwpgzZw533313fTVLocCIkTPnLyITMjAYjLQsCWX2Xc/Q1MOH8+fPs3fvXkpKSgBtWLVjx45KadQx\nutLj4GaEEPuBI8BLUsqDdjPZ5o9FM5S3l1LWqGFACNEaOOloqAyFQtF4MRqNPL9xLhs2xdMmdxDN\njGE8+WRPdLp04uPjLfnc3NyIiYlRNo1ySEpKYvDgwQARUsrEmqy7IjUdA8wGdpmi434B7AROApcA\nPzRbx43AbYAAFgBjalJAhUJx9bI/eT9+Hn6E+1120NDpdDw14DFi9Rc4GJfBmDGRpKef5OzZs5Y8\nXl5e9O7dW3lO1RMV2TiK0UKKvAs8CTwEzMLWYK4DTgNrgdullGfLVGQHIcQk4BkgDDgMPK1iXikU\n1w4Z+Rl8dvAz9iXvg2w/HusylS7RwZbtfh5+DLu1KTcPKmL37l1kZGRYtgUEBNCzZ08VqLAeqXRg\n0KQMpgHThBAdgDZoQQ7TgFNSSsemZpsQQkwAFqLNNP8NmAx8LYToXNPdKYVC0bAwGA38cvIXvpZf\nk33pElJmkJl1lpxDn/Fh+8ds3GqNRgPbt/9OXl6eJS08PJzOnTsrl/F6pkoWJSllPBBfacZyEELo\ngBeA+VLKZaa0acAg4AYgsbp1KxSKhk1iZiLL45ZzJusMAE7OOvLyigkpisIzuw0//XSKESPaWvK7\nuLjQqlUr4uPj0el0dOrUiYiICBVzqgFQ164IAggHVpsTpJQGoFu5JRQKRaMmvzifr+K/YsupLTaT\nUsP9wxg2+EE2rbnEzUPCGTo0vEzZdu3akZ+fT0hICEFBQXUptqIC6lpxRJq+/YQQvwCd0XowM6SU\n2+tYFoVCUYsYjUb2nN/DqoOrSL+UQW5uMf5+Hrg6u3J75O3c3OZmnHXO9IvKIzjYi5KSEoqKimxs\nFzqdrk6jNygco64VR1PT98dohvZ4YBLwixCiu5TySB3Lo1Aoaon0/HQW71lMckouJ05kYTAYGX/L\nIP7R6wECmlyOhxYc7EV+fj5//fUXzs7OXH/99cqG0cCp67NTbPqeK6VcKaXcA0wBjtIAw7IrFIrq\nE9AkgCERQzlzJgddkSeRObfhc3igjdIASE9PZ+vWrWRlZXHx4kUOHDhQJs6aomFR1z0Os7vuAXOC\nlNIohDgCRNSxLAqFoga5VHQJLzfbeRUjO4zgwoB8dq1qSqC/LzfeaDuB99SpUzaKQqfT4efnpwzg\nDRxHl471AJ5FW3Pci7I9FaOU0pEwtHvQJg/GArtMdZsj7/7soMwKhaIBUaAvYH38eraf2c4T3abT\npsXlmKeuzq48OnAsu3ySiY4OwN1de+QYDAYOHjxos1Cau7s7PXv2VDPBGwGO9jjeQrNF/AocBMqu\n2+gAUso8IcQbwFwhRApaz2My0BZtGVqFQtGIiEuJY+WBlaTlppOYmM2En19m+eNzCQ+3jVYbExNi\n+V1YWMiuXbu4ePFyqHRfX19iY2Px9PSsM9kV1cdRxfE3YKaUcn4N7HMWkAe8CQShhWYfKqWUNVC3\nQqGoA7ILs/nswGeWsOdHj2Vy4UIezYzN+Xj5fp57th9OTmWHmzIyMti1axcFBQWWtOuuu46uXbvi\n7OxcZ/IrrgxHFYcbWpyqK0ZKaQTmmT4KhaIRYTQa+SPpD9YcWkNe8eUZ3VHtWhJ4pj3NCtrjH+FN\nQYGeJk1cbcqmp6ezY8cODAZtwEKn09GhQwfatm2rbBqNDEcVx0a0QIaba1EWhULRgEnPS+fTuE85\nkmrrNX9D2A38rdPf+MsvHS8vV2JiQuwqAj8/P5o2bUpmZiaurq707NmTwMDAuhJfUYM4qjiWA4uF\nEAHAdrShJhuklCtrUjCFQtFw+OPMH6w8sJKc/HyOHcugRQsvIq8LY1yXcXQM7AjATTdVHKnW2dmZ\nmJgY9u/fT5cuXWjSpEldiK6oBRxVHF+YvieaPqUxAkpxKBRXKT7uPlxIz+bw4XRKSowEZHXhmbun\n4etdvrLIycnB29vbpvfh6elJnz596kJkRS3iqOJQcywUimuYzkGdGdi+H2eO/E7r3IH4lIRwND6H\nmJiyisNoNHLy5EkOHz5Mp06daNOmTT1IrKhNHFIcUkqLs7UQwgvwAdJNa3YoFIqriPM558ktyqV9\n8/Y26RNjxtHN6Va++yaRBx6Ion17/zJl9Xo9+/fv59y5cwAcPnwYX19fNTfjKsPhmeNCiJuA+UBP\ntAWcEELsBJ6TUm6qFekUCkWdYTAa+On4T3wtv0and+eBVv+iV/dWlu0eLh70jr2OmB4tcXEpG60o\nJyeH3bt3k5OTY0nz8/NTtoyrEEdnjvdH86yKR5uHkQK0BEYDG4QQg6WUW2tNSoVCUask5ybz0b6P\nOJFxgrNJuSSeyubotvdZ1XoW/v4elnw6nQ4Xl7IeU2fPniUuLg69Xm9Ja926NVFRUSpg4VWIoz2O\nF9FCggw3zcMAQAjxEvAd2trkg2tcOoVCUasYjAZ+PvEz6+PXozfoMRogOfkSXsWBBOZFs3LlEaZM\n6V5+eYOBw4cPc/LkSUuas7Mz0dHRhIWF1UUTFPWAo4ojBhhtrTTAEqBwIfBZjUumUChqldRLqXy4\n70OOXzxuSXN1cWHK4HH8ubIpYaFNGTmybbnl8/Pz2b17t8164F5eXsTExNC0adNyyykaP44qjgzA\nu5xtPkBJzYijUChqG6PRyNbTW1l7eC25BXm4umihPsJ8w5jYbSKhTUPpE5CGEM1wdrY/zGQ0Gtm1\naxeZmZmWtBYtWtC1a1dcXV3tllFcPTg6+PgLMFsI0dI60fR/NiqyrULRaFi0exGf7l9OwolUdv6Z\nTF6enhFiBM/e+CyhTbWw5506BZSrNECzdURHR+Pk5GRZD7xnz55KaVwjONrjeBYtDPpRIcQ2IBkI\nAW4EsoHptSOeQqGoaToGdmT11k2cP3+JJoZmBMnh3HrPMJyraMT28/OzzABX7rbXFg5dKVLKs0B3\n4F3AF7ge8AMWAt2llCdqTUKFQlGj9GvVj8HRvQjX96RHzv0Ee4SSl1fxlKy0tDRSUlLKpIeFhSml\ncQ3i8DwOKWUy8HQtyqJQKGqYhPQEfNx8aOHTwpKm0+l4dvBT9HVJQq83MmhQK7sh0EGzZSQkJHD0\n6FFcXFzo168fXl4Vx6RSXP2UqziEEDOBD6WU502/K8IopVRh0hWKBoLeoOdr+TU/Hv+R4jQfnur1\nNJ07BVu2O+mcuOmmVhXUAAUFBezZs4f09HQAiouLOXjwIL17965V2RUNn4p6HC+hGb3Pm35XhHmN\nDYVCUc+k5KawdO9SEi6cICHhIhkZScxOWMYnz00rs0ZGeaSmprJ3714KCwstaQEBAXTt2rW2xFY0\nIspVHFJKJ3u/FQpFw8RoNLL9zHZWHVxFUUkROh3k5hbjrw/DO1uwcWMid97ZvsI6DAYDUkqOHTtm\nSdPpdERGRtK+fXu14JICcDzkyCxgiZTynJ1t4cBUKeXjNS2cQqFwjLziPJbHLWf3ud2WtCbu7kwe\nMIG9XzbllqGtuf328ifzAeTl5bFnzx6bCX3u7u706NGDgICAWpNd0fhw1Dj+PLABKKM40DysHgaU\n4lAo6oHjF4+zeM9izmek4uGh3dItfFowqcckQpuGktL1EsHBFRu0k5OT2bdvH8XFl72rAgMD6d69\nO+7u7rUqv6LxUZFxfBuaUgAtGu4OIUR52f+qYbkUCoUD/HjsR9Yc/MJkyyigZ89ghkQOYlTUKNyc\n3QAqVRqgDUeZlYZaC1xRGRX1OCYB96ApjTnAIiCpVJ4SIBP4qlakUygUFZJTlMOBg6lkZxfhYnQn\n4NQgxtwzpsoP/ODgYCIiIkhJSaFHjx74+5dda0OhMFORcTwemAsghHBGs3GcrSvBFApF5dzZ4U7+\njD7A1t/OIS7dQreunSgpMdoNfW7GaDRSUFCAp6enTXqnTp0QQqiwIYpKcXQFwBcAhBDNATdMCzmh\nzTz3AvpJKZfUioQKhQLQQqAXlRTh4XJ5fQwXJxdm3TqN3z0v0DKkKV26BFZYR2FhIfv27SM7O5sB\nAwbg5uZm2ebk5KTWzlA4hKNeVdHACiCqnCxGQCkOhaKWyCrIYsmeJZxJzOPpAf/iuut8LNt83H24\ndahPBaU1Lly4wL59+yxzM+Li4ujZs6eyYyiqjKNeVa8BzYFpwO1AIfANMAy4DbipNoRTKBRwJPUI\n7/25iD2HTpOeXkDGsaUsnfm43eVb7VFSUsKRI0dsFlsC1JKuimrjaL/0euA/Uso3gNWAl5TyPSnl\nCDTDuHLFVShqGIPRwDfyG9768y0yLmWRkVGIDriQlsumTaccqiMrK4utW7faKA13d3f69OlDp06d\nVG9DUS0c7XG4A0dNvxMA67gDHwLv16RQCsW1TnZhNkv3LCU+LR6AJk1ciW5/HcY9sdzd/0YGDao4\nzpTRaOTEiRPEx8djMBgs6SEhIXTp0kXNzVBcEY4qjtNABLAVTXE0FUKESylPAQVAs1qST6G45khI\nT+CDXYvILcqxpHUI6MCDQx7k4iAjERF+FZbPz89n3759pKWlWdKcnZ2JioqiVatWqpehuGIcVRzr\ngFeEEDlSynVCiHjgRSHEPOBJ4HjFxS8jhOgEHLKzqZ+Ucpuj9SgUVxtGo5ENRzfw3uYVnDuXS7fu\nQbi6ODO8/XCGRw7HSeeEb0Tl9aSlpdkoDT8/P7p37463d3mrPysUVcNRxfEC0B54CE2JPGn6Hos2\nCfC+KuwzGkgzfVuTXoU6FIqrjh+P/8j89cu4kJoPQNKJIt4cP4OOgR2rVE9oaCjJycmkpKTQrl07\nIiMjlZutokZxdB5HHnC3EMLd9P9Hk4tuD2CPlNLhHgfQGThsWhhKoVCYGBA+gM9bbuBC6jF89S2J\nuTSKCJ+Ko9kC6PV6XFwu38o6nY4uXbpw6dIlmjVTo8iKmsfhFQABpJSFVr+PU4UhKis6A0eqUU6h\nuKrxdPXk+eFP8b/s9dwYOJS77oys0OVWr9dz+PBhLl68SL9+/XB2drZsc3d3VwZwRa1RUZDDo2gT\n+xzBKKUsNwJiKToDHkKIHUBr4CAwU0q508HyCkWjJ6cwhw37tjJUDMLP7/JM8HC/cN78v39WasBO\nT09n37595OXlARAfH09UVHnzcxWKmqWiHsfvOK44HEII4Qm0AVLR1i8vBB4DtgghekgpVU9EcdVz\n5EI8/1n3Pw6fOMufQRf571NjbRRFRUqjpKQEKSUnTpzAaLx8e+bn52M0GpXHlKJOqCjI4cSa3pmU\nMl8I4Q8Umoe9hBATgZ7AZOCfNb1PhaKhYJ7Q9/ne9Rw+noIR2Jj8Bd//FMPwoR0qLZ+RkcG+ffvI\nzc21pLm6utK5c2euu+46pTQUdYajsapuqCyPlHK7I3VJKbNL/TcIIQ4BYY6UVygaIxfzL7JkzxKO\nXzyOt7croWE+pJzWM6jZ3fTqXvFkPoPBQEJCAseOHbPpZQQGBtK1a9cyUW4VitrGUeP4NioftnKu\nZDtCiJ7AZmCglHK3Kc0Z6AascVAWhaJRsfvcbpbHLSevOM+SNrRHLzpF3cKtN3XCyan8nkJWVhZ7\n9+4lJ+fyZEAXFxc6deqkJvMp6g1HFcdAO2neQD9gPNqCT46wH0gEPhBCTAFygelAAPCWg3UoFI2C\nguICXvrqfX6SW+jSJRAnnQ4nnRMjxUhuaXcLTrrK51akpqbaKI3mzZvTrVs3FaBQUa84Oo9jSzmb\nvhNC5ALPoUXNrawevRDiNuBVtOi6XmhG+P5SyguOiaxQNHySspJ4ePELnLxwDoDTp7Lp0TGCST0m\n0bZZW4fradu2LefPnycnJ4eOHTvSunVr1ctQ1DtVmsdRDluBGY5mNq0iOLYG9qtQNFi83b3x8jOC\n6XXIPb01z/b9N009yw/7UVJSQnFxMR4el91zdTod3bt3R6fT4eVV+drhCkVdUBNxCEYA2ZXmUiiu\nIfw8/Jg5fAqB/j6Mj5rA2pkvVag0Ll68yG+//cbu3bttDOAA3t7eSmkoGhSOelVttJPsjOYJ1RaY\nX5NCKRSNiZISA6t//IOR/WPx9r68FGv3Ft357skl+HiUrzD0ej3x8fEkJiZaFEZiYiIREQ5EM1Qo\n6glHh6rcKOtVZQQOo9krltWkUApFY+HIibNMX/EGx3KOcDrpUWY8bGvqq0hppKamEhcXZ5n9DZrH\nlHXoEIWiIeKocfymWpZDoWh07D63m7f/WMLRnNMArE5YwbDDPejSqWWF5YqKijh8+DBnzpyxSQ8K\nCqJLly5qXoaiwVMl47jJI6of4A+kAL9IKX+rDcEUioZKblEunx34jF3nduHRFIICPUlLL+DWLjcQ\n2a55ueWMRiPnzp3j0KFDFBZa4oXi5uZGVFSUmv2taDQ4auNoDmwAYtDiS6UCQcB/TPaPu6SUBbUm\npULRANDrDfx5ajfrjq8mp/Dy3IqeURHc3eZ+buzQo9yyRqORXbt2kZxsu5pAy5Yt6dy5s4pkq2hU\nONrjWIC2dOwIKeV35kQhxEhgKfAK8K+aF0+haBgcSjjLzJXvcMFNEh0dgA6tZ9C3VV9GdRqFp2vF\nw0s6nc5m0p6HhwfR0dGEhITUqtwKRW3gqOK4DfiXtdIAkFJ+LYR4FpiLUhyKq5TdiQeZtGQOBVyC\nPEhOvkTH1qGM7zqezkGdHa5HCEFycjJBQUF07NjRZvElhaIx4eiVqwcyy9l2Hs3rSqG4KgkLDCIk\nzI3EM5dwdtYR5dud/9w0mSau9sN+6PV6jh07RuvWrW0m87m4uDBgwAClMBSNHkcnAL4LvCyEsHEX\nEUI0RZs1vqCmBVMoGgpBXkE8cct42lwXzMKJ/2He6GnlKo0LFy6wZcsWjh49yqFDh8psV0pDcTXg\n6FXc0vQ5LoTYBpwDmgN9AR+g0GqSoFFKeUuNS6pQ1AG7Dp1k7c9/8NKU+2yWbR3afgj9I/qVqzDy\n8/M5dOgQ58+ft6SdO3eOiIgIte634qrDUcXRDthnVca8gIA5zRkHwqorFA0Vo9HIyys+Y1XcGgyU\nELkunAdH9bVsd9I52VUaRqORkydPIqVEr9db0t3c3OjUqRP+/v51Ir9CUZc4OgHQXlh1heKqICU3\nhU1U4HMAACAASURBVE/jPmXHpb3oKQLgo92fcN/wWJo0Kd98l5GRwYEDB8jKyrJJDwsLo1OnTri5\nKdOf4uqkqhMAOwEDAF+0uRzbpJSyNgRTKGobvUHPxuMb+S7hO/QGPS1aepGWno+vc3Pmjv5nuUqj\nqKiI+Ph4Tp8+bROQ0MfHh+joaJo3L38SoEJxNeDoBEAn4APgQcB6aqtRCPEp8HcpZWUrBCoUDYKS\nEgMrN2zjoPNGMvWplnRnnTNP3j6WOzuNwM2l/N5CZmYmp06dulzO2Zn27dvTtm1bnJxqIuC0QtGw\ncbTHMQN4wPS9Ai3cSAtgDDCHy8EOFYoGzSF5nlmfvc+RvF0EBnrSoYPWOwj3C2d8l/GE+YZVWkdQ\nUBAhISEkJycTHBxM586d1Yp8imsKRxXHP4C5UsrXrNKSgFeFEB6m7UpxKBo8K+VHHM7bBcCF1Hxa\nh8EDvUYzMGKg3aVci4uLycvLw9fX1yY9KiqKsLAwNfNbcU3iaL+6BdoSr/bYzmUvK4WiQTOp330E\nBTbB2VnHoKhevDrsJQa3GVxGaRiNRk6fPs3mzZv566+/bDymAJo0aaKUhuKaxdEexwngemCTnW3X\no80eVygaFEePp+Hl6U7Llj6WtAj/CCYPuY8gzxBuirzBbjTazMxMDh48SEZGhiXt2LFjdOjQoU7k\nVigaOo4qjiXAPCHEJWAVmo0jGLgfmAm8XDviKRRVJzu7kIWrf2StXE3v5jexcMYkGwVxb7d77JYr\nLCwkPj6eM2fO2HhLeXp6lhmqUiiuZaoSHbc78DrwX6t0HbAcLcihQlHvZBdms3TvcpYf/x6Dk5Ft\nF3/g59/6M2SAKLeM4f/bu/Pwqqpz8ePfM2QiJCQnExAgISF5wyCD4oAEFEW9olLtYK3aqr3Wjtep\ntXTSWqfa4Uer1nvtbb0drEPtoKKiMiuoxeKETIsQCIFAIGHMQEKSc35/rJ3kJEA4geTkHPJ+nidP\nwl77rP0uzvCevfZea/n9lJWVsXHjRpqamtq2u91u8vPzGTVqlE4VolSQUAcAtgA3iMjPsQs5+YB9\nwFvGmCMn5FEqzPwBP2+WvcmLG16kobmB7OyBbNtWQ1pGHIlD6o75uKqqKtauXUtNTU2H7VlZWYwd\nO5bExMTeDl2pqNPdr1HbsNc79gG7nb+V6jPV1fWsqSjh7QOvUH6gvG37iBFJTMs7h1svvIlB8Ufv\nZmpubub999/vcJaRmJjIuHHjyMzM7PXYlYpW3RkA+HPgW0AM7YMA60TkQWPMw70Un1JH1djYzIuv\nruN3K55h78D1nHFGFm63fVlmDczi2tOupSi964vZXq8XEWHNmjV4vV4KCgrIy8vTQXxKHUeoZxz3\nArcBvwb+gT3byAI+B9wnIgeNMf/dKxEqdRSb9pTy81UPUO+tgwbYtr2GUSPTmFUwi4vzL8br7vjS\nDgQC7N2794jpQHJycmhsbDxi7Qyl1LF1ZwDgfcaY+4O2bQbeFZEa4A7smh1KhUV+Zg5SkMaH6+tI\nSoplSt7pfPO8m0gfkH7EvtXV1W3XMYqLi0lJSWkrc7vdeputUt0UauIYBLx3jLIVwHd6JhyljlRT\nc5jy8oOMHdueFOK98dx20U08EfsXbrvgy0wYPOGIMRl1dXWsW7eOysrKtm3r1q1jypQpRx2/oZQK\nTaiJ4xXga8AbRym7Bph/IgcXkXOwiWemMWbZidShTl1+f4AlS7by5Pw3OODewXP3/IDk5Li28rOy\nz2TSNROJ9XSckPDw4cOUlJRQVlaG3+9v2+7xeEhLSyMQCGjiUOokhJo43gIeFJHV2AGAO7ErAF4O\nFANzReQHzr4BY8xPj1ehiCQCT6ELQKljqKqtZu7yR9nitTP3P/7XN/j+V2a3lbtcrg5J41jjMQCG\nDRtGUVERCQkJ4QleqVNYqInjN87vQcADRykP7qoKAMdNHMBc7ESJo0KMQfUTLf4WFm1exMsbX2bg\nqBr4BAYkeKlO+wCYfcT+gUCAyspK1q9fT11dxzEbPp+PsWPHdriuoZQ6OaEOAOzR+xNFZBZwGXAp\nsLon61bRqbnZz6ZN+/Bm7uPp1U+zo2YHAKkp8Ywdk87siTP57NijTxXicrnYunVrh6SRmJjI6NGj\nGTx4sHZLKdXDwj6PgoikA08CN2EHEqp+bsOGPfzp2Q9ZeXABQ8+uJjExpq1sWPIw5hRfR15qXpd1\njBkzhrfeeguv10thYSG5ubk6HkOpXtIXE/D8FphnjHldRIb1wfFVBPH7/fzPy/NYWv8KTTEN1G2K\nZcKEDOK98cyW2Vww8oIOU543NjayefNmCgsL8XjaL48lJyczadIkMjIydK1vpXpZWBOHiNyAnSxx\nfDiPqyKXy+UiY+IeWhY14HG7yMhIYELWBL5w2hfwJfja9mtubqa0tJTNmzfT3NxMbGws+fn5HerK\nzs4Od/hK9UvhPuO4ERgGVIoItE9d8pqI/MkY87Uwx6PCrKqqnoyM9mVWXS4XX596E6sr1jE03cdN\nk7/IhMET2sr9fj9bt26lpKSExsbGtu0lJSXk5OTorLVK9YFwv+uuB4LvhxwMLAduBhaGORYVRocO\nNfHSS6W8uPxd5nz1EiaNH9pWljYgjfsvn0NuSi5xXjtOIxAIUFFRgTGG+vr6DnUlJyczevToDl1V\nSqnwOWbiEJGhxyo7GmPMjhD2qeh0jAbnzwpjzO7uHE9Fl+deWM0f33uG3YkbeOj5Sp4u+i6xse0f\n/JJu18sIBALs3r2bDRs2cPDgwQ51JCQkUFRURHZ2tt4ppVQf6uqMYzt2TEao9OufOkIgEGBF+QpW\nJf2NfQO2QDPsTPyArXu2UzAk54j9V61a1WGKEIDY2FhGjRpFbm6unmUoFQG6Shxfpj1x+ICHsWuO\nP0/7yPHZ2NHjd57IwY0x22m/zqFOEc3NftxuFztrd/D0J09TurcUgFEFdhDef4yfRpYv9aiP9fl8\nbYnD4/GQl5dHfn4+MTExR91fKRV+x0wcxpg/tv4tIi8AfzbGfKXTbs+IyCPA1cD/9kqEKqps3ryf\nPzz1MbFjDTviP8QfaJ8ravSIEVx72rWMzRwLQENDwxFTmefm5lJWVkZWVhYFBQXExcWhlIosoV4c\nvxi48hhlrwCdE4rqh1avruL+//0nm+KX0vxBLZMnDyY2xoPH7eHi/IuZVTCLWE8sdXV1bNy4kYqK\nCqZPn05ycnJbHR6PhxkzZujgPaUiWKiJoxo4i6Pf+XQ+UHGU7aqfafSVU5o2n4ZDzXj8LmprD3P2\nqPFcd9p1DEkaQn19PetL1rNt2zYCAdsLaozhzDPP7FCPJg2lIluoieN3wD0ikgDMA6poXwHwVuD2\n3glPRZPTh05k2vixrCoxjC/K5vrTP8+5w8+loaGBTz75hPLy8g7TnIMdp9HS0qIXvZWKIqEmjgeB\nFOAu4PtB2xuAu40xj/d0YCpytbT4Wby4nPqGRq6cLW3bPW4Pt11wMytGreDToz+N1+9l7dq1bN26\n9YiEkZ6eTlFREampR79IrpSKXKHOjhsAviMi9wNTgFRs99U7xpi6Lh+sTik1NYf52dzlvL3vDRo8\n+5l8+i8ZNqz9GkVeah4jU0YeM2H4fD5EhPT0I5d4VUpFh26NHDfGHABe76VYVIQLBAJ8vPc9lsc8\nye7YAwA88eo8Hvjq9R32c7lc1NbWdkgaqampbQlDB+8pFd26GjleQugDAAPGGDn+bipabT+4nWc+\neYbSvaWMyI9n78c1jBiexKizmvH7/Udc0C4sLKSqqoqUlBREhIyMDE0YSp0iujrjeJvujRxXp5jt\n22tY+f42WkatYemWpW1jMgYMiOHS88dytXyWuINxLFu2jPPPP79D8vD5fEydOpXU1FRNGEqdYroa\nAHhj698icg2w2BhTFY6gVN8KBAI8//wGnl+xhE3xb1J4IB5fqp2b0uP2MCN7BnmBPCrXVLZ1R23b\nto2cnI5TiPh8viPqVkpFv1BvmP8dML03A1GRI0CAebv/xLqE+Rx21bF58wECBChIKuDqtKtJ2J7A\nju07OlzDqKrS7xRK9RehXhyvAAYcdy91SnC73Mw8Zxyrd6xhYFIsZ+TnMGNAMXG1cdTU1HTY1+fz\nUVhYqHdJKdWPhJo4/gd4RETOAT4GajvvYIx5picDU+Gxd+8hli7dxlVXFeB2t1+L+PzET/PRtg8p\nco9iiGsInnoPgaBLXunp6RQWFuLz+fQahlL9TKiJ41fO768fozwAaOKIMq+/voVn5r/DJu8K4gZ9\ng8tnntZWNiBmAA9e+hNWvLmCpqamtu2ZmZkUFBTo9Qul+rFQE8fIXo1Chd3BxoMsqvonq+KXEAAe\nW/QUM6bcR2Ji+2y1AxMGkpuby6ZNmxg8eDAFBQUMGjSo74JWSkWEUEeOb239W0QSgSRgjzGm6diP\nUpGo2d/Mki1LeHXjq9QnHyI+3kOGJwnxNfPhmlUUn13cYf+8vDyys7NJSkrqo4iVUpEm5JHjInI+\n8DPgDJzFl0TkPeBHxpjFvRKd6hF79hzi1VdLySuu5bUtL1NdXw1+SKiN57zMArIGZJCfms/+qv3U\n1dWRmJjY9tjY2FhiY2P7MHqlVKQJKXGIyHRgAbABuAfYBQzFLuD0mohcaIxZ3mtRqhO2dGk5//fC\nMjbGvMmg/XXkDU8hviae2NpYEr2J5GXlkRpvJxr0er3U1NR0SBxKKdVZqGcc9wOLgMucCQ8BEJEH\ngFeBe4ELezw6ddLer1vMqvi/E++KIWbXIBJdScR5Y8hJyWFI0hBcuIiPjycvL4+cnBy83m5NX6aU\n6odC/ZSYDFwdnDTAzporIo8Dz/Z4ZKpHXHLmZN78cBkZ/mRSkuPJSRnO8OTheN1eBg4cyKhRo8jO\nztbFk5RSIQs1cewDBh6jLAlo6Zlw1ImqqqrnuX+s5vOfPo3MzPaupnGZ4zjn9CJid3vJTckl3huP\nz+cjPz+frKwsHYOhlOq2UBPHEuBeEVlujNnRulFEhmK7qRb1QmwqRIuWlfCrl/5KhfcDKp+exf23\nfbntDMLlcnHXJd9m5bsrSUhIID8/XxdPUkqdlFATx/eBVUCJiKwAKoHBQDFwEJjTO+GprjQ2N7Jk\nyxL+UfEKzfEHGevJYkf1Wj7+eCOTJhW17RfrjWXq1KnaHaWU6hGhjuOoEJFJwLeBadgBgfuAx4G5\nxpjK3gtRddbY3MjSLUtZvHYxzXub8R1KxD3QS3OznyxfIjuqS5kYkA7dUJo0lFI9pauFnM7DLg3b\nBOAkh7vCFZg60s6q/fz8r09zKHEjiU1ePE0eYogBINOXzMjUXPIG55Gfl9/HkSqlTmVdnXEsBepE\n5C3sGI5Fxpi14QlLdfab+c/yyoo3SHXHkxATQ3K6B4B4bzwjkkcwbuQ48vPzdWlWpVSv6ypxXIW9\nhjEN+AXgEZFK7IXwhdhEol1UYZKY6ifNk4A74KapyQ/NXgoH5zG5aDL5efk6JYhSKmy6WgHwJeAl\nABEZAEzBJpLpwBNAgoisxSaRhcaY13s/3P5h09ZKMlOTSE5uv632M6dfweJ3l5NQk8BpOYVcMvV8\ncnNydToQpVTYhXpxvB5Y7PwgIl7gPOAW4FvA7YAnlLpEZBh2mvYLsSsQvg7cGXybb3/12or3eH7p\nPBoa9nChXMLNX7qyrSw5LpkfXH0bAwMDGaYD9pRSfag7kxzGA+cDM4EZwHjsOhzvYa+BhFKHCztF\nSZVTB8CjwMvYyRP7Hb/fz6rSVSz7aBnbyitpbmzE63Lz0aYPqau7mMTE9oUXxwwb3YeRKqWU1WXi\nEJFxwCXOTzEQD5RiE8V9wFJjzMFuHC8LWA98zxhT5hxjLvCiiKQaY/Z1uwVRpqbmMB98sIvybfvI\nLNrJe2vfo6bWLscaH+fB5QIC4Ipvobr6QIfEoZRSkaCr23G3A0Ow4zWWYbujFrR+4J8I52L6NUHH\nGAZ8Ffh3f0gajY3NfO+H86mJXQdxu8jYG4PH097l5HK5yM8dzkVnzmDKaWfp3VFKqYjU1RnHUKAa\neBJ7AXx5Ty7cJCIvAp/CJqYZx9n9lFDTsp/9WQtwH7IJ4dAhNwMHunG5XYwcMZJLJl/CyCxdbFEp\nFdm6ShwzsV1UlwLfBeqDxnQsMMasP8lj3w08BPwIWCgik4wxFSdZZ0Sorq5n4cKtFBYmc8YZ2W3b\n0xLSSBmSRMP2ehISvAwYFMuEovFcesal+BJ1DW+lVHTo6nbcJdjJDeeISBY2iVyEnbfqV05X1kJs\nIllojNnbnQMbYz4BEJFrgG3ADdhEEtXeeWc7zzy7kqa4MtZsjmHixG/i8dgbzlwuF9fPvJL578xn\nypgpXDjmQuK8cX0bsFJKdVOot+PuAv7s/CAiE7FJZDrwR6eemOPV4ySgGcaY54LqrheRUiD72I+M\nfHV1dZRsLuGjLSupG7SBZg6zoz6O1atLmTSpsG2/s4efzdmfPxu3S2+nVUpFp24t9yYiKdiBgOcC\nZ2MXePIC74dYRQ7wrIhsMsascuocBAjwp+7E0tdaWvy8//5OsrL8mC3rWVe+jl21u2gJtBCT4Mfj\n95CY6KKqsQxoTxyaMJRS0e54t+MWYJPEVOd3EXbQ3jrsYMDfAMu6cUvuKmA58HsRuQVoAh7GjuuI\nmsSxbNkmFi78gIPNZQwccoiWmLoO5cm+GFwpLs4acxZnyVl9FKVSSvWOrm7HrQJ8gAsoxyaKh4Al\nJzpHlTHGLyKfBn4JvIIdF/IGcJ4xpvZE6uwLK8uWU8HHtMQ0UbvfRUaGHWvRlNBESlYKM8bO4Jzh\n5xDr0elAlFKnnuPNjrsIWGyMKe2pAxpjqoEbe6q+3uT3+9m8eSf5+UM7jKkYMSGRT0oP43W58Q5w\ncSi5AckvZGbhTCRNdPyFUuqU1tVdVVeHM5BIUldXz4IFH/PR6g0caKjiO9/8EsOGDW4rv6RoJoty\nlzAoNZ7iomLOyz2PtAFpfRixUkqFT7cujp/KWlpa2LVrF+Xl5ZRuL2Xl2o3sb9oDngDzF/+LW25o\nn3DQl+Djrk/dTn5qPjGe495MppRSp5R+nTgCgQDV1XvZvHkrVXt2ULG/gp21O6lvqicwoJnAgQAB\nV4DyQ2VHPLYovejICpVSqh/ot4mjrGwnr85fwZYd5bQkHCQupRE//rZyb0qApvgGCmU4l42Z0oeR\nKqVUZOm3iWPjvhL+XfE2La4mXIcgI2kArtgAhwcexpXsYnLOZKblTCNnUI5e7FZKqSCndOIIBAJU\nVu5m1SrDtGkTSUlJbivLz8mmMb4eV6OHGvchAkmNjM7PY1rONM7MPpN4b3wfRq6UUpHrlEscgUCA\ngwcPsn37dpYvX8umbRXUBPbSTICrrjivbb+81DzSCgZR01LL9RNmMS2nmKFJQ/swcqWUig6nTOKo\nr6+noqKCiooK9uzfw+663Ziarexx1YALVq5ZxZWXT2/rdnK5XNxzxV34Enx43afMf4NSSvW6qP7E\nrKk5xPLla1m/vowAtaQPg8raSvY22Il63bF+mgIt1HjqiUnZRSAQ6HC9IjMxs69CV0qpqBXViWPn\nzr0senMF9e59NHr3kx4Xh8sFAVeApoQmmhKbSBgClxZeSPGIYtxunWBQKaVOVlQnjsbkvVTGb8DT\n4iEQCFCDH2+aTRqSKZw7/FwmDZ6ka14opVQPiurEUZRRhDfTTWNzA3GZkJyextThU5k6YirpA9L7\nOjyllDolRXXiiPHEMHvGBVTXV1M8opgxGWN0vQullOplUZ04AD4z+jM6QE8ppcIo6r+ea9JQSqnw\nipYzDg9AZeUJrR+llFL9TtDnpaen646WxDEE4LrrruvrOJRSKtoMAXpsMT6InsTxb2AasBNo6eNY\nlFIqGniwSePfPV2xKxAI9HSdSimlTmFRf3FcKaVUeGniUEop1S2aOJRSSnWLJg6llFLdoolDKaVU\nt0Tc7bgi8gTgNcbcHLTti8AcYCSwBviRMWZhUPk3gMc7VdVijPEG7XMHcDuQAbwNfMMYUxJBbYgF\nfgpcByQCbwHfMsZsiYY2iMi9wI+PUd2PjTH3hbMNJ/gcjAQeAaYDh4BXgLuMMfuD9onY58ApL3Da\ncC5QCzwJ3G+MaQ5XG0QkC/g5cDGQAKwEvm2MWeOUX+yUC1ACzDHGvBb0+EzgN87jDwN/AH4Yrjac\nbPxB9cQB7wG/MMb8pVNZ2F5HvSFizjhExCUi9wFf7bT9C8CfgKeBScCfgXkicn7QbqcB87D3LLf+\nZAfV8Z/AT4BvA2djPxRed57YSGnDb4GrgWuBKdgX7DwRcUVJG35Jx///IcATwG7sh1dY2nCi8YuI\nF5iPHSc0BfgMUAz8LqiOiH4ORCQVWA7EAzOAL2BfU78NVxtExA28ABQCn8ImsAPAYhFJE5Ex2Pfq\n35w2vAS8KCJjg6r5BzAYOA+4EbjJibnX29BD8SMiSU49449yjLC8jnpTRJxxiEge9sNlHFDeqXgO\n8Iwx5qfOvzeKyETst9tlzrZxwBJjzLHmJPkuMNcY83fneNdiBxN+Bnimr9vgPPZG4EJjzBKnvq8D\nC4B8YFOkt8EYU4v9htta1xTgFuAyY0yFs7lX23CSr6Mi5+dqY8x6p77HgIeD6ojo5wC4ARgAfNYY\ns9ep72ZghYjcb4wpC0MbJmAT75ig/8cvAnuBy4CpwL+MMQ86+98tIsXAbcAtzuumGMhzzrY/FpG7\ngMdE5D5jTGMvt+Gk4nf2n4lN1vs5ul5/HfW2SDnjOBfYhj1z2NKprAD7LSrYh8C5zrdEgLHA+qNV\n7Jz2FtKeZHA+5FZhR6P3lJNpw8VAVWvScGI0xpgcY8ymKGlDG+cs6RHgH8aY151t4WjDycS/F/Bj\nP7ziRSQd+219VRjjP9k2FABrW5NGUDnA9DC1oRy4HDBB2/zO71TnOMs6PWZZ0PGnAVuDu2id8iRg\nYhjacLLxA1yBPRs8t3PlYXwd9aqIOONw+v/+AiAinYt3AMM7bcsFYoEU5/QuFbjU6WdPBN4EvmuM\n2QEMcx5T0amOo9V7wk6mDdgX0mbnm8cc2vs97zDGbCc62lAdtH02cDq2261Vr7fhZOI3xuwQkf/C\n9l1/A/ulaj22uwSi4znYAVwhIm5jjD+oHCCT8DwHe4BXO22+Fdv1ugC4/zjHH3aMcpx9mpy/e6UN\nPRA/xpjbWv8+ynMYltdRb4uIxHEcTwF3ishSbJaeDvynUxaLPdsA+4K6BkgHHsL2SZ6OPXUHaOhU\nbyO2LzgcjteGZGw3ybeBO5zYfoptwwSiow3Bbgf+ZozZFLStr9vQZfxO33YRsAjbPZWMvW7zVxG5\niL6PH47/HDwP3A38TER+jP2W/ijQ7JSHvQ0iMhv7Wp5rjFkvIgOOc/wjyo0xTSIScPYJaxtOIP7j\niYTX0UmLhsTxMPbb0mvYSbvWAr/APpkHjDELRCTDGNP2jVdE1mIz+iygzNnc+cJTHFDXu6G36bIN\n2KQ3CNs3vQVARD6L7fecBWwNijlYJLUBABEZBpwPXNDp8Yec333VhuPFfx32DCnHGFMHICJXYmcV\nnUX7t96IfQ6cs6bPYfvX78Rec7oHe4H2AGF+DkTkRuzNBc9h+/VxYujq+EeUi0gM4HL2CVsbTjD+\n4+nr90GPiJRrHMdkjDlsjPkW9ttTtjFmPFAP7Gp9gwcnDeffO7FdJ8Ox/cXgTM0eZChHni72ihDa\nUAHUBffrGmN2A3uwt11GQxtafQqb8N7sVEWftiGE+M8BNgS3xRizGfs6GtXX8TvxhPJeeNkYMxTb\nJZKBvZU1A5sAw9YGEfmhc+wngC8FdZ1tO87xj1WOs09Y2nAS8R9Pn7+OekLEJw4ReUBE5hhjGoPu\nmroS29+IiNwqIjucbyWtj8nBvlnWOh/AJbT3VSMiA4HJ2LESfd4G7AXPRBEZHfSYwdhut9IoaUOr\nacCbQW80oC0R9lkbQoh/O1AYfEukiAwB0oCSvo4/lDaISLGILBYRjzFmpzHmsFNeB7wTrjaIyHeB\nB4B7jDH/ZYwJnoJ7RfDxHTOCjr8CyBOR4Z3Ka4CPwtGGk4y/S5HwOuoJ0dBVVQb8PxH5BNiA7T8/\nE/i6U/4q8CDwpIg8hH2jPwKsMO0Do+YCvxSRTdhBUw9hvxX/M0La8BY2eTzr3IZbB/wae2fH/Chp\nQ6tJ2LEGR9OXbSij6/j/jO2OeEpEfoLti/4V8BHwegTEH0obNmBvSviZiDwOTAQeAx4yxhwMRxtE\nZLxT5/8Bv3O+ALWqceJ53/k/fhbbPXh2UBveBf6Fvbb0LaB1MN5cJxH2aht6IP5Q9PXr6KRF/BmH\nMeb32H7c3wKrsbcpXmCMMU55KXARtlvqPezgnNXYO3ta63gCm1zmYl+UscB/BL0Q+7oNASfeVdhE\n+Da2T/qi1hgjvQ1BhmBvbT1aHX3WhhCegwrs2VISNonPAzYDlxhnxHKkPwdOl+0VTjtar3/82Bjz\nUFAdvd2Ga7DXX76M/TAM/rnDGPMJcBXwWWxSng1cYZwxE8574SpgF/Z5+APwe+C+MLXhpOIPRV+/\njnqCLuSklFKqWyL+jEMppVRk0cShlFKqWzRxKKWU6hZNHEoppbpFE4dSSqlu0cShlFKqWzRxqH5N\nRJ4QkYCIzDpG+Wyn/Efhjk2pSKXjOFS/JnaltrVAABjrrI3QWjYIWIedjuRcY0xL30SpVGTRMw7V\nrxljarArt43ATv0Q7BeAD7hBk4ZS7fSMQylARP4IfBF7ZrFSRKZj17y40xjz66D9voZdJjQPO5vp\nE8AvgifCc+Yb+wp2fQ8X9qzlAWPMC075zdi5yOZgl311A5ONXdpVqYinZxxKWXdg50d6TERigf/G\nTj75SOsOInI38Dh2PrErsPMoPUjQuuQicid28aTnset4XI9devRZZ7bdVgnYifFuwM6BVNZbDVOq\np0XD7LhK9TpjzD4R+QbwArAQ23V1eeuZhIikAj8AHjXGfMd52AIRqQceFpFHnYkSc4GHjTHBibd6\nAAAAAWtJREFUyWQbsBK75scLzmY3cK8x5rXeb51SPUsTh1IOY8yLIvIcdobUWzqdBUzFLu35sogE\nv2/mYZeYnQH8xRhzK7QlGsEuAnWhs2/nJXY/6vFGKBUGmjiU6ugNbOLofCaQ5vxefIzHDQUQkQLs\ntOczsOtIb8CuuQD2ekewWpSKQpo4lApN67rqn6N9HftgFSLiwS68dRA4A1htjGl2Fge6LixRKhUG\nmjiUCs27QBMw2Bjz99aNIlIM3A18D3tGMQr4mjHmg6DHXur81ptR1ClBE4dSITDG7BKRX2OXZU3F\nrtKYix37sQd7y+1hYBtwu4jsxp55XArc6lSTGO64leoN+g1IqdDNAX6I7XZ6DXgAeAW7fGujcwfW\np4DdwFPAX7Frgl8GbMIu6apU1NMBgEoppbpFzziUUkp1iyYOpZRS3aKJQymlVLdo4lBKKdUtmjiU\nUkp1iyYOpZRS3aKJQymlVLdo4lBKKdUt/x/ItMUMW82r2gAAAABJRU5ErkJggg==\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], "source": [ "# Solution goes here\n", "system.alpha1 = system.birth_rate - system.death_rate\n", - "system.alpha2 = system. birth\n", + "system.alpha2 = system.births\n", "\n", "run_simulation(system, update_func1c)\n", "plot_results(system, title='Proportional model, combined birth and death')" @@ -3484,7 +3492,7 @@ }, { "cell_type": "code", - "execution_count": 58, + "execution_count": 130, "metadata": { "collapsed": true }, @@ -3512,11 +3520,27 @@ }, { "cell_type": "code", - "execution_count": 59, - "metadata": { - "collapsed": true - }, - "outputs": [], + "execution_count": 132, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Saving figure to file chap03-fig04.pdf\n" + ] + }, + { + "data": { + "image/png": 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39WN8/GomHuFWZs7sfVYmfmjgAu6uIgu4CyGcVVxSzIc/fIjer+kc0I0+3Xoz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\nhVaeXVPMlUvPbTsmKz2La86+JhbVNsaYEyIpk38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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], "source": [ "system.alpha = 0.025\n", "system.beta = -0.0018\n", @@ -3535,7 +3559,7 @@ }, { "cell_type": "code", - "execution_count": 60, + "execution_count": 133, "metadata": { "collapsed": true }, @@ -3556,11 +3580,27 @@ }, { "cell_type": "code", - "execution_count": 61, - "metadata": { - "collapsed": true - }, - "outputs": [], + "execution_count": 134, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Saving figure to file chap03-fig05.pdf\n" + ] + }, + { + "data": { + "image/png": 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WSnbNbd38evspenq1QlKj53K5uGVtCX6/nyOVtivv0OkmPB43G6+dpRXTBBSx+24kFVLI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\nMoRRCoIgCCrDxyOfzAVqkIdQAAAAAElFTkSuQmCC\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], "source": [ "newfig()\n", "sns.set(style='whitegrid', font_scale=1.5)\n", @@ -3580,7 +3620,7 @@ }, { "cell_type": "code", - "execution_count": 62, + "execution_count": 137, "metadata": { "collapsed": true }, @@ -3598,11 +3638,20 @@ }, { "cell_type": "code", - "execution_count": 63, - "metadata": { - "collapsed": true - }, - "outputs": [], + "execution_count": 136, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "13.88888888888889" + ] + }, + "execution_count": 136, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ "-system.alpha / system.beta" ] @@ -3627,35 +3676,55 @@ }, { "cell_type": "code", - "execution_count": 64, + "execution_count": 140, "metadata": { "collapsed": true }, "outputs": [], "source": [ - "# Solution goes here" + "# Solution goes here\n", + "def update_func2b(pop, t, system):\n", + " # net_growth = system.r * pop + system.beta * pop**2\n", + " net_growth = system.r * pop (1 - pop/system.k)\n", + " return pop + net_growth" ] }, { "cell_type": "code", - "execution_count": 65, - "metadata": { - "collapsed": true - }, - "outputs": [], + "execution_count": 141, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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FCoYOHaoepg5orL9QlXufAJYsWaIuc3Z2xtTUlLFjx5KQkKDRWeC7777DwcGB\nsLAwPvzwQ+bOnVtpTWFBeJTKy8uJjo4m7locKXkpuJg3xfScBYGBXdX7NLVqyksvOaGnJ2uw/fZr\nSqtmn6ysLPz9/avc5ufnp/ExSXg03nzzTRQKBcuWLauV84WGhmJgYMAPP/xQo+N0dHQoLCwkKipK\nozwgIIDvv/++0hTM33zzDZ06daJ3796Ulpby3XffPXTsgvCgcnJyOHLsCL/F/0ZiTiIlZeUcS4rm\nz9jKTZbm5gZPTOIHLe/8XVxciI6OpnPnzpW2RUdH3/fusL5EJkby/eXvtdq3W7NuhPuEa5R9GfMl\nv6X+ptXxAz0GEtIqpMYxPihbW1vefvttZs+eTf/+/QkMDHyo85mamuLs7Mzly5drdNyAAQP47LPP\nGDVqFG3atKFjx4507NiRTp064e7urrHvxYsXuXz5MrNmzaJRo0a0a9eOvXv3MmrUqIeKXRBqSpIk\nkpOT+eP8H1zOuYxcKaeiQkVcZgbZCiW6sRmcPXub9u3rbgH1+qbVnf+wYcPYuHEj27dvJzMzE5VK\nRWZmJtu2bWPTpk288MILdR2nUIXnn3+eHj16MH/+/GofrtbEP5eSVCqV+Pr6VvrXs2dP9T5WVlbs\n37+fiRMnUlxczNatW5k0aRJdu3Zl9+7dGuePiIjAwsKCLl26AHffOC5dukRMTMxDxy4I2iovL+fU\n/07x/anvic2MRa6UI+lIlDcqpYXzM/gVhuFg8ORPHa/Vnf/o0aOJj49n+fLlrFixQl0uSRKDBg1i\nypQpdRbg06KmC7jfs3DhQgYMGMD777/PokWLHiqGoqIijU9xurq6Va7M9s9ZXa2trZk1axazZs3i\n5s2bnDp1il27drFgwQIaN25M9+7dkcvlHDx4kF69eqkXhOnXrx9Lly7l66+/FkszCo9ETk4Ov576\nlYs3L1JWUQaA0kCJrImMSf6T8LB8hq+/TmDQIDesrY3qOdq6pVXy19XVZcWKFYwfP54zZ85QUFCA\nhYUFAQEBlT7aNyQhrUIeqikm3Ce8UlNQXdF2Afd/cnJyYvbs2cyfP5/+/fs/cP2lpaVcvXq10hoL\n91beqs7mzZtp1qwZffv2BaBx48YMGzaMQYMG0a9fP44fP0737t359ddfuXPnDt9++61GO79KpeLQ\noUO8/fbb4sGvUKcUSgU/Xv6RC9cvUKFQUVyiwNBForVna8J9wjE3vLtK3NixXvUc6aNRo0Fe7u7u\nDTrZP85ZxPnYAAAgAElEQVS0XcC9KsOHD+fQoUPMmzfvgevfu3cvKpWqxm8gMTEx/PDDDwQHB2vM\n/GpgYICxsbF6fvOIiAgcHR359NNPNY6PiopiwYIFREZG8uKLLz5w/IJwP0pJyaWSS6TL7yDl6JCq\nyGdk6xFMbj+4XtbQrW/VJv++ffvy0Ucf4enpSZ8+fe774vz000+1HtzTRNsF3KuzePFiQkK0+5ST\nn59PVlYWkiRRUFDAiRMnWLNmDRMnTlSv43tPVlZWlecwNjbGzMyMadOmMWrUKCZOnMj48eNp2rQp\nt27dIiIigvz8fEaMGKHu2z9t2rRK6zi4urqyZcsW9u7dK5K/UOsqKirUTaZGekaMazeOV+P/S3GJ\nJe4lw7hywpLy55QYGdXoPviJUO0V+/n5YWpqqv76aXxnfJS0XcC9Os7OzsyaNYv33nvvvvtOnTpV\n/bWVlRWurq689957DB48WGM/pVLJs88+W+U5wsLCmD9/Pq1bt+brr7/mk08+4c033+TOnTtYWFjQ\ntWtXvvrqK+zs7Pjss8+QyWQMHz680nl0dXUZM2YMy5Yt4+LFi//6CUcQtCVJEtGx0eRm5NKtWzcM\nDQ0BcLd1Z82IhezZmIW+gy7jxnk9lYkfariAe30RC7gLgqCt0rJSvvr5KxKvJ9Lc3A0fNy86d+6o\ncQObn1+OubmBxsIrT5oHXsA9IyOjRhU5OjrWPDpBEIRadOnaJfb/up/C0kKKixT871YMiiILAgL8\n0df/a4CWpaVhPUbZMFSb/Lt3716jpp74+PhaCUgQBKGmlCol+07sI/pSNCpJRVlZBQWFcvIUEmcv\nykhNLcLNzbq+w2xQqk3+S5cuFe38giA0eNezr7Pj8A7y8/LVZUameliommKc7ElTF0uMjZ/Odv1/\nU+0rIkbtCoLQkKkkFZHnIjl15hSS8q9Hl2ZWZozuMxorvUb88cdN+vZtjq6uVpMZPFWqTf41WWRd\nJpMxadKkWglIEAThfnJKcthyagu5ibkUFytQKFRYWxnh08aHEd1GoKd7N7X17y8Wm6pOtcl/zZo1\nWp9EJH9BEB4lfV19bstvk5ZTiLHcCFQG9Gnfn2E9utd3aI+NapN/QkLCo4xDEARBaxaGFoS1DePt\n+FUYFTTFpMiftHgz6FvfkT0+REOYIAgNmkpSkZCVQHJyMkqlUl3evnF7to5bTTPDngwa2JpXXvGt\nxygfP2J6B0EQGqzbRbfZfno7WclZNFW1pkfnEtq2vTsDrEwmo6ltYxYudEJPT9zH1pSY3kEQhAZH\nJan4OeVnDp07hOy2HgV5cnLlcRhIxjg7N1FPGAiIxP+Aqk3+f18ecPny5Y8kGKFunT17lrCwMK2n\nyThw4ADz5s3j0qVLjyA6QbjrZuFNtp/bTubVTAyLDSkqlVOhkDBVWZFwWR+l8smeZ/9R0Xrkg0ql\n4ujRo0RFRVFUVIStrS0dOnSocmlHQRCEmlKqlBxOOcyh2EMYZBlgoLi76I+jtQ3WZQ4U5DvTf2Ab\n7OxM6jnSJ4NWyT87O5vx48eTkJCAgYEBNjY25OTksHHjRjp37sz69esxMRE/EEEQHkxaQRrbo7dz\nO/02xnnGyJChgw5NrZoS0CoARwd39PX1aNRILPhTW7RqLFu+fDlZWVls2bKFmJgYjh07xsWLF1m3\nbh1xcXEaSzsKD6ZVq1bs3buXkSNH4u3tTf/+/Tl//jy7du2ie/fu+Pn58frrryOXy9XHnD17lvDw\ncHx9fenSpQuLFy+mtLRUvT0hIYHw8HDatm3LwIEDiYuL06hTpVKxceNGgoKCaNeuHUOHDuX48eOP\n7JoFAeCPG3+w5NgS0hMyKEmSUVigwNzAHP8m/gzsNpD2/u1p2tRKJP5aptWd/9GjR3n33Xfp1q2b\nRnlwcDC5ubmsXLmShQsXal3p3r17+fTTT7l16xZubm68+eabddJ8lJiYyOXLl7Xat1mzZpXWkY2J\niSE1NVWr4z08PGjVqlWNY/y71atXs2TJEpo3b86cOXOYOHEi3t7ebNmyhatXrzJr1izat2/PqFGj\nuHDhAuPGjWP06NEsXLiQtLQ0FixYQFpaGhs3biQ/P59x48bRqVMn9u/fz7Vr13j33Xc16lu1ahU/\n//wzixYtomnTpvz2229Mnz6dTz/9lI4dOz7UtQiCtlpYt6CkpIKC63LMZcYYl9nyjIc/fXp1w9zc\nvL7De2JpdedvYGBQ7Q+hcePGNaowIiKChQsXMmHCBCIjIwkICGDq1KmkpaXV6DxPouHDh9OzZ09a\ntmzJ4MGDyc/PZ8GCBXh4eNC3b19at25NUlISAFu3bsXLy4vZs2fj6upK9+7dWbBgAUePHiUpKYmD\nBw+iUChYsmQJbm5uBAcHM336dHVdxcXFfPHFF8ydO5du3brRrFkzwsPDGTx4MJs3b66vl0B4CjmZ\nOfGi/1CwMMNW7oGR3BUnJ2+R+OuYVnf+L774Ih999BFt27bFzs5OXV5SUsLmzZsJDQ3VqjJJkli3\nbh0TJkxg2LBhAMyePZv//e9/REdHP/ULtfx9CUVjY2N0dHQ0XhMjIyN1s09SUhLdu2sOZW/fvr16\nW1JSEi1atFB31wVo166d+uuUlBTkcjkzZsxAR+evewCFQqHxMxaE2nQ17yoZxRn4O/qjp6en7kLe\nx60PARMC+XLHRUaO9MLR0fQ+ZxIeVrXJ/6WXXlJ/LUkSKSkpBAcH4+fnh62tLQUFBZw7d46Kigoc\nHBy0quzKlSukp6drLBKuo6PDt99++xCXUL1WrVo9VFOMj49PpaagunRvrdF7ZDJZteMrjIwqd3e7\ntyjbvT+qfy7S9vfFLAwM7vakWLduHc2aNdPY7+9vBoJQGxRKBd8mfssvV35BnivDKz+RgX07q9d0\n1pHpYGtjwowZornxUak2+SsUCo3v/fz81OW3b98GwNPTE4DMzEytKrt27RoABQUFjBkzhqSkJFq2\nbMmsWbPU5xe04+rqSnR0tEZZVFSUelt+fr56EXVLS0sAYmNj1fs2a9YMfX19MjIyCAwMVJevX78e\npVLJjBkzHsFVCE+D5NxkPj//ORlFGeQnKTHIM+KS6hLWv5tgZ2eHjY1NfYf4VKo2+e/YsaPWKysq\nKgJgzpw5vPrqq7Rs2ZK9e/cyduxYvvnmG1xdXWu9zifVhAkTGDJkCCtWrCA0NJT09HQWLlxI9+7d\ncXV1xdHRkQ0bNvDWW28xa9YsMjIyWLt2rfp4Y2Njxo0bx6pVqzA1NcXb25ujR4+yYcMGlixZUo9X\nJjwpyivK+SbhG45eOwoKMMsxQ1auRKkyxLKiCVeuFCKXK+5/IqFOVJv8o6Ki8Pf3r/EJz549q257\n/qd7zQ6TJ08mJCQEgGeeeYaoqCh2797NvHnzalzf08rDw4ONGzeyZs0aduzYgZWVFQMGDOC1114D\nwMzMjM8//5xFixYRGhqKg4MDEyZMYNGiRepzvPbaa+jr6/P++++TnZ2Ni4sLixYtEgv5CA/tcs5l\nPj//Odkl2eiV6mGSY4KepEerZi24kQBmFpaEh/fGyUnc9dcXmfTPhuH/N2jQIFxdXZkyZYq6Xe7f\nxMTEsGXLFq5du0ZkZGSV+9ybXmDfvn14e3ury2fMmEF5eXm1C8jcbxV6QRAahvKKciISIjh69SjF\nRQpsFGYYFRphY2SDu607hnqGODk1xc/PSzxbqmP3y5vV3vnv37+f9evXM3ToUJo3b06fPn3w8fHB\n2dkZY2NjCgoKyMjIICoqihMnTnD16lXCw8NZtWpVtcG0adMGExMTLl68qE7+9x4mi2kiBOHx98nZ\nT4jLuMTNa8UYZRqDlQGtXFrhYOqAkZERvr6+ojdZA1Ft8tfX12fmzJmMGjWK7du3s2fPHjZs2KDR\n+0SSJBo3bkzfvn3ZtGkTjo6O/1qZsbExY8eOZc2aNdjZ2eHh4cGuXbu4fv26Rnu0IAiPpwHuA/jl\n/BkMM42xkewwzGmCeTMbHBwcaNeuHYaGhvUdovD/7tvP39HRkdmzZzN79mxSUlJIS0ujsLAQa2tr\nGjduTIsWLWpU4YwZMzA2Nmbp0qXk5OTQunVrtm7dSsuWYq1NQXjcudu6M757KD/tvY1ZEVhbGeLh\n4Unbtp5iWvgGRutZPeFuF8KH7ZFzb71fseavIDy+FEoF3yR8g6uNK36NNLtpP9/6edq/VEh09GWe\nfbYl1tbW9RSl8G9qlPwFQRBS76Sy7fw2bhbeZPeJn+hvPJx+wc9oPFR0djbH2bnmvQWFR0ckf0EQ\ntKJUKTmUdIhDSYcoVyiIv5iHfZkF56T/YWpYwqBB1hrTiQgNm0j+giDc163CW2w7v43UO3dnuTWq\nMKC1rAkmKkdMVDakpeWTlJSkMX+U0LCJ5C8IQrUkSeLotaMciD+AQqkACYzyjXAod6C5hyvxFwto\n0sSMbt3a8swzres7XKEGRPIXBKFKd8rusP38duKz4ikoLMfK2BizHDNaGrfE2fFu+37Xrlb4+/tp\nPbmj0HBolfzLy8vZtGkTx44do6SkpNJskQA//fRTrQcnCEL9UEkqPvj9A24XZJKScgdFtgyXRs74\nu3hjon93yVZ7e3t8fX1F3/3HlFbJf8mSJezdu5cOHTrg7u4uhmULwhNOR6bD857PM3ffSgxyDGkt\nc0U3oxF6zobIZDJat25Ny5YtRd/9x5hWyf+nn35i5syZTJw4sa7jEQShgQhoEsBL3V/g5N4STBVl\n2DkaY25uSocOAVhZWdV3eMJD0ir5y+XyR7qoiSAIj45KUnHw8kG8Hb1pbtVcY9uL7UbQ3jSPhIR4\nnJ2N8fb2rrTokPB40uqn+Oyzz3LixAk6depU1/EIgvAIZZdk89m5z0jJS+Gr3w4T1nQynQMaa4zK\ndXe3xs2ts2jiecJolfwHDRrEvHnzyMvLw8/Pr8olBO/Nzy8IwuPhTPoZvoz5ksLSYi7F5yIr1OH7\nlAOUF/vRv3+wxoNckfifPFol/1deeQWAiIgIIiIiKm2XyWQi+QvCY6K8opyvYr/i1I1TAOjq6uBU\nYUVjWXPMlHZcuZJDTEwMAQEB9RuoUKe0Sv5Hjhyp6zgEQXgErudfZ0vUFjKL7667rSPXwbHAnk6u\nbiTHleLczAx3d3sxy+5TQKvk36RJE/XXJSUlFBcXY2VlpV6WURCEhk2SJH69+iv74/dTUibHUF8X\ng0IDmlc0x9XWFV2ZLjYdLHFxaYKPjw8GBgb1HbJQx7R+bP/nn3+ycuVK4uLi1IO8fHx8eO2118Qq\nXILQgEmSxOaozUTdjCI1tYDbacUENnennXUbHCzujszV1dXFx8eHpk2bivb9p4RWo7XOnDnDyy+/\nTFlZGa+++iqLFi1i+vTplJSUMGHCBM6ePVvXcQqC8IBkMhlNLZuScuUO+WkVtNV1x+xWS2yN7i6n\naGlpSWBgIM2aNROJ/ymi1Z3/Rx99ROfOndm8ebPGL8fUqVOZOHEi69at4/PPP6+zIAVBeDj93Ppx\nvu0lom/n41jhhLmZMSoVeHi44unpKUbtP4W0Sv6xsbGsWbOm0l2BTCYjLCyM119/vU6CEwSh5orl\nxSglJRaGFuoymUzGW91fI8Yqm9jY8zg6yvD19cXe3r4eIxXqk1bJ38LCgpKSkiq3FRcXo6urW6tB\nCYLwYK7ducbmqM3Iyo0Z2XQiHu5W6v76ujq6+Po64uXVE0mSxEPdp5xWyb9Tp06sW7cOf39/HB0d\n1eUZGRmsW7dOPPAVhHomSRLHU4+zJ24PqTfukH61iNu6KkIDu9K7d5DGDZropSeAlsl/1qxZDB06\nlL59++Lv74+dnR3Z2dlERUVhZmbGm2++WddxCoJQjfKKcnbE7OBM+hkqKlQUpStpo+eCqdKICxfS\naNLkEt7e3vUdptDAaJX8HR0diYiIYOvWrURFRZGWloaFhQWjRo3iP//5j2g3FIR6klGUwcazG7lZ\neBNUYJ5vSleHRpSn2WJlZkbLllbo6ekhSZLoySNo0Lqfv729PbNnz67LWARBqIELty+wNXorZRVl\n6JbrYpJjQhOjJrRs1pJ8SzlOTndX2bK1ta3vUIUGqNrkv3HjRl544QUcHBzYuHHjv55EJpMxadKk\nWg9OEITKVJKKyMRIImK/I+nyHbydnLAoM8fdxh0H07uDtry8XPH29hbt+0K1qk3+a9asoUuXLjg4\nOLBmzZp/PYlI/oLw6Pxy5Rd2nTnAlfgCXGS2qG4Y4dOmLeaGZujp6eHt7Y2zs3N9hyk0cNUm/4SE\nhCq/FgShfvVo3oOf4o6TzVVsJFssS1xQlupj29iWdu3aYWJiUt8hCo8BrYb1rV+/noyMjCq3paen\ns3jx4loNShCE6hnoGvB28Ex6+QXjKGuDX7vGdO7cjs6dO4vEL2hNq+S/YcOGapP/+fPn+frrr2s1\nKEEQ7lKqlJxJP4NcXoFKpVKX25nY8fbQ//D664Pp378Xbm5uojePUCPVNvu8+OKLnD9/Hrg7gGTE\niBHVnkT0IRaE2ldYXsims5v4JSoK15z2DO/ZkcDAruokL5PJsLW1rOcohcdVtcl/8eLFHD58GEmS\nWLt2LcOHD8fJyUljH11dXczNzQkODq7zQAXhaXI9/zofn/mYs2euYVNkQaHsKidPm9G4sSPu7u71\nHZ7wBKg2+bu6ujJlyhQAVCoVoaGhGlM7CIJQN/5M+5MdF3agk6tDa/3G5MvKMVM6IFMYcOdOvhiw\nJdQKrQZ5TZ8+HYC8vDwUCoV6MRdJkigpKSEqKorQ0FCtKkxOTmbAgAGVynfu3En79u21jVsQnjgq\nScX+S/v5NfFXTHJM0JXromeqhwMtsDN1YODALjg7O4vEL9QKrZJ/YmIib7zxBsnJyVVul8lkWif/\ny5cvY21tTWRkpEa5lZWVVscLwpOoSF7E2t8/5kZaKuaF5iCBib4Jz9g/g7Ojs+jCKdQ6rZL/+++/\nz507d5g9ezZHjx7FwMCAoKAgTpw4wYkTJ/jiiy+0rvDy5cu4ubmJ+YAE4f9dz7/OkkMfkhVfgK2B\nKViDrbEtrR1a06Z1G1q2bCnu9oVap1VXz/PnzzNjxgzGjRtH//79KS0tZdSoUWzcuJHg4GB27Nih\ndYVJSUm0bNnygQMWhCeJUqVk1fF1XI3JwlRlRFmZEtMKBzq5dqJHYA9cXV1F4hfqhFbJXy6X07x5\ncwCaN2+uMeL3hRdeUHcJ1UZSUhI3b95k+PDhdO3alXHjxhETE1OzqAXhCaGro8srz05C5qRELqlw\noAWdW3ejW7duWFhY3P8EgvCAtEr+jRs3Ji0tDbib/IuKikhPTwfA0NCQ/Px8rSorKyvjxo0bFBUV\n8dZbb/HJJ5/g4OBAeHg4KSkpD3gJgvD4uddpAsDNxo2FL7xGd/cXeGV8GH36dBRr6gp1Tqs2/+Dg\nYFauXImpqSm9e/emZcuWfPTRR0yaNInt27fj4uKiVWVGRkacOXMGAwMD9RJyy5cvJy4ujl27dvHu\nu+8++JUIwmMg7tYljh4+T4fW7gQEtFc36XRy6UincfUbm/B00bqrZ2pqKnv27KF37968/fbbTJ8+\nncjISHR1dVm9erXWFZqZmWl8r6Ojg5ubG7du3apZ5ILwGJEkiZ2/7eXw0WPIFHrI88to0qQxTZo0\nqe/QhKeUVsnf2NiY9evXI5fLAejWrRuRkZHExcXRpk0bmjZtqlVlsbGxjBkzhi+++AIvLy8AlEol\nCQkJ9OvX7wEvQRAatuLyYrb8tIWk+FQkhQwJJfG3L5OY2EYkf6HeaL2SF6BuqgFo2rSp1kn/Hk9P\nT5o0acL8+fP573//i4mJCVu2bCEvL48xY8bU6FyC8DiIux7Hnl/2UFpaiqmZPuVyJRVlBnT37UdQ\nUIf6Dk94ilWb/Pv06VOjLmY//fTT/SvT0+PTTz/l/fffZ/LkyZSWluLn58eXX34plpoTnihKpZJv\nTn7DmbgzqKS/ZuP09vSgt/cLPOPZuB6jE4R/Sf5+fn510r/Y0dGRVatW1fp5BaGhyMjKZNXOzeSX\nZGFpaQiAjq4OQQFB9PGr2U2VINSVapP/8uXLH2UcgvBEuJKdyrufrEJHrgTA0FAXW0dLxvUdRzP7\nZvUcnSD8Ras2/3Pnzt13Hz8/v4cORhAed3cUOdw2zsBBbo0OOihU1rw9cjYGegb3P1gQHiGtkv+o\nUaPu+1E1Pj6+VgIShMeJJEmoVCp0dXUB8GvkR3jQAD7/7kcGPTOE14YPQ0dHNPMIDY9Wyb+qidtK\nSko4e/Ys3377LevWrav1wAShoSsoKOCHn36jTetm6q7LAOG+L9LbNRhna/FQV2i4tEr+HTpU3SWt\nR48emJiY8Mknn7Bp06ZaDUwQGipJkoi5eIldByPJLMogN9efRo0aqXus6evqi8QvNHgPPYFI+/bt\nOX36dG3EIggNXmFhIYePHuaLn3Zzs/gGFTI50dcvceNGVn2HJgg1UqNBXlU5evQopqamtRGLIDRY\nkiSRnJzMyeiTXM6+jI6xEv0SHe7IS8FRQQt35/oOURBqRKvk/9JLL1UqUyqV3L59m+vXrzNhwoRa\nD0wQGorCwkLORJ3h3LVzZBZnAiCTgb6zRC+XnkzpPRIdmZiFU3i8aJX8FQpFpTKZTIarqyvjx49n\n6NChtR6YINQ3SZK4fDmJ7w4f5UZpCkb//wFXaaDE2NmYOZ2m0MK6Rf0GKQgPSKvkX5OVugThSZFf\nWMK6PXsoKL8746yNgREqOwW+bXx50ftFjPSM6jlCQXhwNWrzP378OFFRUeTn52NnZ0enTp0ICAio\nq9gEoV5dLojjok4MzthRKsnJUZTwXq9X8GskBjQKjz+tkn9eXh4TJkwgNjYWAwMDbGxsyMnJ4eOP\nP6Zr165s2LABQ0PDuo5VEOpUQUEB5ubm6gGNAU0C6N+lExG//E5b12dYNvJ1bEys6zlKQagdWiX/\nxYsXk5aWxsaNG+nRo4e6/MiRI7zzzjusXLmSd955p65iFIQ6pVQquXz5MhcvJuDn542bmxtw97nW\nlC7j8Xf2pZdbDzEhm/BE0Sr5nzhxgrlz52okfoBevXqRm5vLhx9+KJK/8FjKyckhOvo8v8fEcD3n\nJiWlFTg5OalXnLMwtCDYPaieoxSE2qdV8tfV1cXc3LzKbfb29lX2BhKEhqyiooL4+Hgup1zmz5QY\nbuVlgwxOJl6ib2Ew/1htVBCeOFpP7Pbhhx/i7e2No6OjuryoqIjNmzcTHh5eZwEKQm3LzMzkwoUL\npOakkpKbgsqgAnQkUuW5mFpVYGCkX98hCkKd0yr5Z2ZmkpmZSe/evfH398fBwYE7d+5w7tw5iouL\nMTAwUA8Ek8lkfPbZZ3UatCA8CLlcTmxsLFevXyUpJ4ncslwAlCYVlDcvpbtJIO8OGy+mXxaeClol\n/9TUVDw9PYG7H5dv3rwJoC5TKpUolco6ClEQHl5BQQHHjp3kdFw8+bq3MDbVQdKRKLUuxdremqW+\n03CzcavvMAXhkRGDvISnwtXb2UScPkYFxchkIFnpUuEgp6d7T573fB4DXXG3LzxdajTIKzk5mdOn\nT1NUVIS1tTX+/v60bNmyrmIThFqTTiJX9VNxlFuRqsjBTd+J+d1ex8PWo75DE4R6oVXyV6lUzJ8/\nn/379yNJkrpcJpMxePBgli1bJvpACw1GYWEhaWlpeHp6qn8v+7r14ajvKY6du0hY0CCm9AjDUE8M\nTBSeXlol/82bN/PNN98wa9YsQkJCsLOzIysri8jISNauXYurq6uY2VOodyqViqSkJKLOxZGTV4iF\nhQVNmjQBQFdHl5lBU5jYpQR3O9G2LwhaJf99+/YxefJkxo8fry5zcnJiwoQJlJeXs2/fPpH8hXqV\nm5vL+fPnOR2dRFJuEkgynE7ZMnRoI3R07k633Ni8MVQ9XEUQnjpaTUKelZWFv79/ldv8/Py4detW\nrQYlCNpSKBTExMRw8veTXEq/RErpJeSyUnJlefyadE00RwpCNbS683dxcSE6OprOnTtX2hYdHY29\nvX2tByYI/0aSJG7dukVsbCzZhdlczrlMiaIEc0t9kksyUZorGf1cC5H8BaEaWiX/YcOGsXr1akxM\nTOjfvz92dnZkZ2dz8OBBNm3axKRJk+o6TkFQKykpISbmIhfjrlCsn8HNwrvjThTGCkqtS+nm0YbJ\nnV+isYVYRF0QqqNV8h89ejTx8fEsX76cFStWqMslSWLQoEFMmTKlzgIUhH86efICv576H7cVqVjY\n6GBookuJTQm65rqMaD2CHs3FDJyCcD9aT+y2YsUKxo8fz9mzZ8nPz8fCwoKAgADc3d3rOkZBUJMk\niW+uHCOvIhU9mS4pd4po1NwAH2dvwrzDsDWxre8QBeGxUKNBXo0aNcLFxQVLS0tsbGxwcXGpq7gE\nAfhr/Wh9/buTrclkMjp2cOHTtPPIVRW4tLDm5Q4v08m5o7jbF4Qa0HqQ1wcffMCXX35JRUWFeqCX\nsbExU6ZMYeLEiXUapPD0ufdA988/o2nRognt2rVTbxvhM4xTKWdp7eTByx1GY24o+m8KQk1plfzX\nrVvHF198wZgxY+jbty+2trZkZ2fz448/snbtWkxNTQkLC6tx5efPn2fUqFFs27aNjh071vh44clU\nUlJCdPQFoqJSSL51g7RbOTRt2hQbGxsAjPSMWDV4MWYGYtJ9QXhQWg/ymjp1KtOmTVOXubi44Ovr\ni6mpKZ9//nmNk39JSQlvvfWWmA1UUFOpVKSkpJCUlMSV61nE3L5EuW4RF9IL6ZPVQ538AZH4BeEh\naTXIq6ioCB8fnyq3+fv7k5mZWeOKly9frrEwjPB0y87O5vjx4yQkJJCWn0aaKh6VYQmZygIuGSeS\nIWXUd4iC8ETRKvn36NGDr776qsptBw8eJDAwsEaVHj9+nGPHjjFv3rwaHSc8ecrLyzl37hynTv1B\n9p1sYjJiSM5NRqGnoKJFGcauMOP54XR0q/rmQxCEB6NVs0/79u1Zs2YNISEhDBgwAHt7e+7cucOx\nYzTU3gcAACAASURBVMeIiopi3LhxbNy4EbjbG+PfBn3l5ubyzjvvsHTpUiwtLWvnKoTHUnFxMT//\nfJT4+CxK9XKQm2ajREmZVRlyczktzBszpu0YXG1c6ztUQXjiaJX833vvPeDuVLlr1qyptH3r1q3q\nr++X/P/73//Ss2dPAgMDuX37dk3jFZ4gRUUSx06lUaifjEJWiompDjRSINOX8ZzbcwxwH4C+rlhP\nVxDqglbJPyEhoVYqi4iI4NKlS3z33Xe1cj7h8SJJkkZffKVxARetj2NdZEaaIhdbmSGdbFozpu0Y\nmlk1q8dIBeHJV6NBXg/rwIEDZGRk8OyzzwKoxwtMmDCB559/nkWLFj3KcIRHRJIkbty4wY0bN+jc\nubN6iuVG5o3o17kj+347jpubNS/6v0A/t37o6TzSX0tBeCo90r+ylStXUlZWpv4+KyuLsLAwFi9e\nTNeuXR9lKMIjkp+fz8WLF0lLyyQrqwR7e3s8PO4unSiTyZjQaRx6hhKhbUJxtnCu52gF4enxSJP/\nP7t2GhoaqsttbcWcLE8SuVxOYmIiqamppKbmk3IjkyKdLKxOm+Pu7q5u/rEysmJm55n1HK0gPH3E\n52uhVt1r4omPj0culyMhkV5yg0y969xW5pN9yZhRqhB0dcU8PIJQn+o1+Ts5OZGY+H/t3XlUU2f+\nP/B3QtgXCTsioCwBFWQRZBVxqWuraBe1aqvjuJSeUU97mKq1nPlObeuv1SJabavTUaxLW39jF9pv\nnbZUcbCKbMWKAQRklRAChJ0AyfP9w+FqitQokgT5vM7JOfI8NzefDwkfb+597vMU6TIE8gjJ5XL8\n9ttvkMvlAIC27rbbi6xYN6G4RQKeOcPY8bfQqeyAhQHdoUuILg1Y/OvqHuyOSrpbd2S7du0abt68\nifb2HpiaGqCypRKVHZXosO5Ar2kvxguFmOAkwurA1TQ1AyF6YMDiP23atAeaIlcsFj+SgMjwJBAY\noby8BaU1EvDsZFA6tkPhpAD4gJGBEZb5L6NFVgjRIwMW/7fffpv7Q21ubsbu3bsRERGBefPmcXf4\n/vzzzzh//jy2bt2qtYCJfiqvZsirKYSMX40qWRP8XG1gxjeEr50vVgWsgp2Zna5DJITcZcDiv2TJ\nEu7fL7/8MuLi4rBz5061bZ566ins3LkT33//PZYuXTp0URK90dHRAbFYDJFIBEvLO/PoC8ZV47pp\nAZrbFbC2NoaZkSlWTFqKqW5T6WifED2k0QXfixcv4sCBA/fsmz59Ok6fPv1IgyL6p7e3F6WlpSgt\nLYVSqUR3dzfCw8O5wj7DYzpiQy6goLoETwSGYdWkVRCaCnUcNSFkIBoVf6FQiKtXr97zRqwrV67Q\nxd7HGGMMt27dglgsRmdnJ1QqhvLyZpSUNmL8+PGwtrYGAPB5fPxl6npUtVQhzIWWVCRE32lU/J99\n9lkcOHAAXV1dmDlzJoRCIRoaGnD27Fl8+umn2L59+1DHSXRALpejoKAAjY2NAICeHhVyfr2Fqu4K\nVPfKsUD6FP5b+wEALlYucLFy0VG0hJAHoVHxf+mll9Da2opPPvkEhw4d4tqNjY2xefPmh1rCkegv\nhUKBwsJCVFVVcfMvAUALa0KBaQ6KumoBPpCS/g3eEq3WXaCEkIemUfHn8Xh47bXXEB8fj7y8PLS0\ntEAoFCIoKAhmZmZDHSPRopqaGly9ehW9vb1cW7eqG2WsDCWCEliLAJN8A7i7WcEvzFiHkRJCBuOB\n7vC1tLR84FW7yPBibm6O3t5edHerUCdtg6W7ClmqLCgMFAAAYyMDzJk6ES8GvoDx9uN1HC0h5GEN\nWPxnz579QBft/v3vfz+SgIhuWVtbo6PDHJl5YuQrr8LKuAMO9re/3fF4PMwYNwOLfBbBWEBH/YQM\nZwMW/+DgYBqx8Rjr6uqCWCyGUCjE2LFjuXbGGLJbr+Os6iwYj6G+lA9bWxO4jhqDFwJewDjhON0F\nTQh5ZAYs/rt27eL+/d133yEiIgI2NjZaCYoMnd+P15dKpXBxcYGh4e3lEnk8HgIm2+LHcj74Bjz4\niuyweHwc5njNoUVWCHmMaPTXvGPHDuzatQtz5swZ6njIEOmbarmoqEhtQR2JpAVVVTXw8BjLtT3r\nvwSZFdkYY+uIFwJXwdnSWQcRE0KGkkbF39HREZ2dnUMdCxki9fX1uH79OlpaWri2zs5elJV1IVdS\nA1OhNzw87mxvLDDG/8x5HUITIZ36I+QxpVHxX758Od5++23k5+fD19f3nsM7n3rqqUceHBmc1tZW\nXL9+HVKpVK3dxMQEjQolvqz/Fi1GEtRfqMHMKB/Y2ppy29iY0ik+Qh5nGhX/d955BwBw6tSpe/bz\neDwq/nqmrq4OWVlZajdpGRgYwG2cG673Xsclxc9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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], "source": [ - "# Solution goes here" + "# Solution goes here\n", + "system.alpha = 0.025\n", + "system.beta = -0.0018\n", + "system.r = system.alpha\n", + "system.k = -system.alpha/system.beta\n", + "\n", + "run_simulation(system, update_func2)\n", + "plot_results(system, title='Quadratic model v2')" ] }, { "cell_type": "code", - "execution_count": 66, + "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ - "# Solution goes here" + "# Solution goes here\n" ] }, { @@ -3674,11 +3743,140 @@ }, { "cell_type": "code", - "execution_count": 67, - "metadata": { - "collapsed": true - }, - "outputs": [], + "execution_count": 149, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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prbunmaddisonhydetantonbirabenmjthomlinsondurandclark
Year
-10000NaNNaNNaNNaNNaNNaN4.0NaNNaNNaN
-9000NaNNaNNaN4.NaNNaNNaNNaNNaNNaN
-80005.0NaNNaN5.NaNNaNNaNNaNNaNNaN
-7000NaNNaNNaN8.NaNNaNNaNNaNNaNNaN
-6000NaNNaNNaN11.NaNNaNNaNNaNNaNNaN
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prbunmaddisonhydetantonbirabenmjthomlinsondurandclark
Year
1913NaNNaN1793.NaNNaNNaNNaNNaNNaNNaN
1920NaN1860.01863.1912.NaNNaNNaNNaNNaN1968.
1925NaNNaNNaNNaNNaNNaN2000.0NaNNaNNaN
1930NaN2070.0NaN2092.NaNNaNNaNNaNNaN2145.
1940NaN2300.02299.2307.NaNNaNNaNNaNNaN2340.
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" + ] + }, + "execution_count": 150, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ "table1.tail()" ] @@ -3711,7 +4046,7 @@ }, { "cell_type": "code", - "execution_count": 69, + "execution_count": 151, "metadata": { "collapsed": true }, @@ -3729,7 +4064,7 @@ }, { "cell_type": "code", - "execution_count": 70, + "execution_count": 152, "metadata": { "collapsed": true }, @@ -3748,7 +4083,7 @@ }, { "cell_type": "code", - "execution_count": 71, + "execution_count": 153, "metadata": { "collapsed": true }, @@ -3776,12 +4111,22 @@ }, { "cell_type": "code", - "execution_count": 72, + "execution_count": 154, "metadata": { - "collapsed": true, "scrolled": false }, - "outputs": [], + "outputs": [ + { + "data": { + "image/png": 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Qhg4dCkBoaCihoaEaxxUKRa4DUkhICJMmTaJ169aMGTMGyAokaWlpavlUKhXG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\ntxl+wTmyC6wuq+HAo8va1ORXSY7sSeXIYznys6Eu7YaRrAbTm5qiC8T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NGzYMgKCgIIKCgjS2KxSKbCepwMBAJk+eTKtWrRg7diyQnlySk5PV6qlUKgwN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\ny3Bz88bDI5xz50LUjzNwwoAEN2MY3dq0JKs4C6O5DB+tN+G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zhRBCNL4mmaRWr17Nzp07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\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], "source": [ "newfig()\n", "plot_prehistory(table1)\n", @@ -3823,35 +4177,35 @@ }, { "cell_type": "code", - "execution_count": 74, + "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ - "# Solution goes here" + "# Solution goes here\n" ] }, { "cell_type": "code", - "execution_count": 75, + "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ - "# Solution goes here" + "# Solution goes here\n" ] }, { "cell_type": "code", - "execution_count": 76, + "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ - "# Solution goes here" + "# Solution goes here\n" ] }, { @@ -3865,7 +4219,7 @@ }, { "cell_type": "code", - "execution_count": 78, + "execution_count": null, "metadata": { "collapsed": true }, @@ -3882,7 +4236,7 @@ }, { "cell_type": "code", - "execution_count": 80, + "execution_count": null, "metadata": { "collapsed": true }, @@ -3899,7 +4253,7 @@ }, { "cell_type": "code", - "execution_count": 81, + "execution_count": null, "metadata": { "collapsed": true }, @@ -3917,7 +4271,7 @@ }, { "cell_type": "code", - "execution_count": 82, + "execution_count": null, "metadata": { "collapsed": true }, @@ -3933,7 +4287,7 @@ }, { "cell_type": "code", - "execution_count": 83, + "execution_count": null, "metadata": { "collapsed": true }, From 56e8bad751a4f6caacec134af7a95eddf0e29063 Mon Sep 17 00:00:00 2001 From: Christopher Lather Date: Wed, 13 Dec 2017 04:17:58 -0500 Subject: [PATCH 06/10] Commiting Notebooks --- code/chap03mine.ipynb | 613 ++++++++----- code/chap04mine.ipynb | 1038 ++++++++++++++++++++++ code/chap05mine.ipynb | 1944 +++++++++++++++++++++++++++++++++++++++++ code/chap06mine.ipynb | 1267 +++++++++++++++++++++++++++ code/chap07mine.ipynb | 1826 ++++++++++++++++++++++++++++++++++++++ 5 files changed, 6467 insertions(+), 221 deletions(-) create mode 100644 code/chap04mine.ipynb create mode 100644 code/chap05mine.ipynb create mode 100644 code/chap06mine.ipynb create mode 100644 code/chap07mine.ipynb diff --git a/code/chap03mine.ipynb b/code/chap03mine.ipynb index 2ffc48a1..455abff7 100644 --- a/code/chap03mine.ipynb +++ b/code/chap03mine.ipynb @@ -15,7 +15,7 @@ }, { "cell_type": "code", - "execution_count": 47, + "execution_count": 1, "metadata": { "collapsed": true }, @@ -48,7 +48,7 @@ }, { "cell_type": "code", - "execution_count": 48, + "execution_count": 2, "metadata": { "collapsed": true }, @@ -66,7 +66,7 @@ }, { "cell_type": "code", - "execution_count": 49, + "execution_count": 47, "metadata": { "collapsed": true }, @@ -87,7 +87,7 @@ }, { "cell_type": "code", - "execution_count": 50, + "execution_count": 48, "metadata": { "scrolled": true }, @@ -265,7 +265,7 @@ "1954 NaN NaN " ] }, - "execution_count": 50, + "execution_count": 48, "metadata": {}, "output_type": "execute_result" } @@ -284,7 +284,7 @@ }, { "cell_type": "code", - "execution_count": 51, + "execution_count": 49, "metadata": { "scrolled": true }, @@ -462,7 +462,7 @@ "2015 NaN NaN " ] }, - "execution_count": 51, + "execution_count": 49, "metadata": {}, "output_type": "execute_result" } @@ -480,7 +480,7 @@ }, { "cell_type": "code", - "execution_count": 52, + "execution_count": 50, "metadata": { "collapsed": true }, @@ -504,7 +504,7 @@ }, { "cell_type": "code", - "execution_count": 53, + "execution_count": 51, "metadata": {}, "outputs": [ { @@ -1611,7 +1611,7 @@ "[66 rows x 11 columns]" ] }, - "execution_count": 53, + "execution_count": 51, "metadata": {}, "output_type": "execute_result" } @@ -1629,7 +1629,7 @@ }, { "cell_type": "code", - "execution_count": 54, + "execution_count": 52, "metadata": {}, "outputs": [ { @@ -1700,7 +1700,7 @@ "Name: census, Length: 66, dtype: int64" ] }, - "execution_count": 54, + "execution_count": 52, "metadata": {}, "output_type": "execute_result" } @@ -1721,7 +1721,7 @@ }, { "cell_type": "code", - "execution_count": 55, + "execution_count": 53, "metadata": {}, "outputs": [ { @@ -1743,7 +1743,7 @@ " 7256490011], dtype=int64)" ] }, - "execution_count": 55, + "execution_count": 53, "metadata": {}, "output_type": "execute_result" } @@ -1761,7 +1761,7 @@ }, { "cell_type": "code", - "execution_count": 56, + "execution_count": 54, "metadata": {}, "outputs": [ { @@ -1776,7 +1776,7 @@ " dtype='int64', name='Year')" ] }, - "execution_count": 56, + "execution_count": 54, "metadata": {}, "output_type": "execute_result" } @@ -1800,7 +1800,7 @@ }, { "cell_type": "code", - "execution_count": 57, + "execution_count": 55, "metadata": {}, "outputs": [ { @@ -1809,7 +1809,7 @@ "pandas.core.frame.DataFrame" ] }, - "execution_count": 57, + "execution_count": 55, "metadata": {}, "output_type": "execute_result" } @@ -1820,7 +1820,7 @@ }, { "cell_type": "code", - "execution_count": 58, + "execution_count": 56, "metadata": {}, "outputs": [ { @@ -1829,7 +1829,7 @@ "pandas.core.series.Series" ] }, - "execution_count": 58, + "execution_count": 56, "metadata": {}, "output_type": "execute_result" } @@ -1840,7 +1840,7 @@ }, { "cell_type": "code", - "execution_count": 59, + "execution_count": 57, "metadata": {}, "outputs": [ { @@ -1849,7 +1849,7 @@ "pandas.core.indexes.numeric.Int64Index" ] }, - "execution_count": 59, + "execution_count": 57, "metadata": {}, "output_type": "execute_result" } @@ -1860,7 +1860,7 @@ }, { "cell_type": "code", - "execution_count": 60, + "execution_count": 58, "metadata": {}, "outputs": [ { @@ -1869,7 +1869,7 @@ "numpy.ndarray" ] }, - "execution_count": 60, + "execution_count": 58, "metadata": {}, "output_type": "execute_result" } @@ -1889,7 +1889,7 @@ }, { "cell_type": "code", - "execution_count": 61, + "execution_count": 59, "metadata": { "collapsed": true }, @@ -1919,7 +1919,7 @@ }, { "cell_type": "code", - "execution_count": 62, + "execution_count": 60, "metadata": { "scrolled": false }, @@ -1933,9 +1933,9 @@ }, { "data": { - "image/png": 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P8y2LiYlBKcUzzzyT4745rZB13fVjs/5r1qwZ9957L3PmzMnWU+G///3vLftm/ffzzz9n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\n", 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D9yF9NMFflZVqKLlr165x9uxZMjIysLGxwdvbW/NUqBBCVDd9Gvfh/O2LZEWkUTe9E0bG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\n", "text/plain": [ - "" + "" ] }, "metadata": {}, @@ -1957,7 +1957,7 @@ }, { "cell_type": "code", - "execution_count": 63, + "execution_count": 61, "metadata": { "collapsed": true }, @@ -1968,7 +1968,7 @@ }, { "cell_type": "code", - "execution_count": 64, + "execution_count": 62, "metadata": { "collapsed": true }, @@ -1988,7 +1988,7 @@ }, { "cell_type": "code", - "execution_count": 65, + "execution_count": 63, "metadata": {}, "outputs": [ { @@ -1997,7 +1997,7 @@ "1.2862470293832287" ] }, - "execution_count": 65, + "execution_count": 63, "metadata": {}, "output_type": "execute_result" } @@ -2019,30 +2019,91 @@ }, { "cell_type": "code", - "execution_count": 66, + "execution_count": 67, "metadata": { "scrolled": true }, "outputs": [ { - "ename": "NameError", - "evalue": "name 'us' 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[1;32m----> 1\u001b[1;33m \u001b[0mcensus\u001b[0m \u001b[1;33m-\u001b[0m \u001b[0mus\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m", - "\u001b[1;31mNameError\u001b[0m: name 'us' is not defined" - ] + "data": { + "text/plain": [ + "Year\n", + "1950 0.032480\n", + "1951 0.022089\n", + "1952 0.017480\n", + "1953 0.016188\n", + "1954 0.017056\n", + "1955 0.020448\n", + "1956 0.023728\n", + "1957 0.028307\n", + "1958 0.032107\n", + "1959 0.030321\n", + "1960 0.016999\n", + "1961 0.001137\n", + "1962 -0.000978\n", + "1963 0.008650\n", + "1964 0.017462\n", + "1965 0.021303\n", + "1966 0.023203\n", + "1967 0.021812\n", + "1968 0.020639\n", + "1969 0.021050\n", + "1970 0.021525\n", + "1971 0.023573\n", + "1972 0.023695\n", + "1973 0.022914\n", + "1974 0.021304\n", + "1975 0.018063\n", + "1976 0.014049\n", + "1977 0.011268\n", + "1978 0.008441\n", + "1979 0.007486\n", + " ... \n", + "1986 -0.012805\n", + "1987 -0.018115\n", + "1988 -0.023658\n", + "1989 -0.028560\n", + "1990 -0.031861\n", + "1991 -0.037323\n", + "1992 -0.038763\n", + "1993 -0.040597\n", + "1994 -0.042404\n", + "1995 -0.042619\n", + "1996 -0.041576\n", + "1997 -0.040716\n", + "1998 -0.040090\n", + "1999 -0.039403\n", + "2000 -0.039129\n", + "2001 -0.038928\n", + "2002 -0.038837\n", + "2003 -0.039401\n", + "2004 -0.040006\n", + "2005 -0.041050\n", + "2006 -0.041964\n", + "2007 -0.043192\n", + "2008 -0.044599\n", + "2009 -0.046508\n", + "2010 -0.049851\n", + "2011 -0.053943\n", + "2012 -0.057723\n", + "2013 -0.061092\n", + "2014 -0.065061\n", + "2015 -0.092982\n", + "Length: 66, dtype: float64" + ] + }, + "execution_count": 67, + "metadata": {}, + "output_type": "execute_result" } ], "source": [ - "census - us" + "census - un" ] }, { "cell_type": "code", - "execution_count": 67, + "execution_count": 68, "metadata": { "scrolled": true }, @@ -2115,7 +2176,7 @@ "Length: 66, dtype: float64" ] }, - "execution_count": 67, + "execution_count": 68, "metadata": {}, "output_type": "execute_result" } @@ -2126,7 +2187,7 @@ }, { "cell_type": "code", - "execution_count": 68, + "execution_count": 69, "metadata": { "scrolled": true }, @@ -2199,7 +2260,7 @@ "Length: 66, dtype: float64" ] }, - "execution_count": 68, + "execution_count": 69, "metadata": {}, "output_type": "execute_result" } @@ -2210,7 +2271,7 @@ }, { "cell_type": "code", - "execution_count": 69, + "execution_count": 70, "metadata": {}, "outputs": [ { @@ -2219,7 +2280,7 @@ "0.012862470293832286" ] }, - "execution_count": 69, + "execution_count": 70, "metadata": {}, "output_type": "execute_result" } @@ -2244,7 +2305,7 @@ }, { "cell_type": "code", - "execution_count": 70, + "execution_count": 71, "metadata": {}, "outputs": [ { @@ -2253,7 +2314,7 @@ "2.5576286540000002" ] }, - "execution_count": 70, + "execution_count": 71, "metadata": {}, "output_type": "execute_result" } @@ -2271,7 +2332,7 @@ }, { "cell_type": "code", - "execution_count": 71, + "execution_count": 72, "metadata": {}, "outputs": [ { @@ -2280,7 +2341,7 @@ "7.2564900110000004" ] }, - "execution_count": 71, + "execution_count": 72, "metadata": {}, "output_type": "execute_result" } @@ -2298,7 +2359,7 @@ }, { "cell_type": "code", - "execution_count": 72, + "execution_count": 73, "metadata": {}, "outputs": [ { @@ -2307,7 +2368,7 @@ "(1950, 2015)" ] }, - "execution_count": 72, + "execution_count": 73, "metadata": {}, "output_type": "execute_result" } @@ -2329,7 +2390,7 @@ }, { "cell_type": "code", - "execution_count": 73, + "execution_count": 74, "metadata": {}, "outputs": [ { @@ -2338,7 +2399,7 @@ "0.07229017472307693" ] }, - "execution_count": 73, + "execution_count": 74, "metadata": {}, "output_type": "execute_result" } @@ -2359,7 +2420,7 @@ }, { "cell_type": "code", - "execution_count": 74, + "execution_count": 75, "metadata": { "collapsed": true }, @@ -2377,7 +2438,7 @@ }, { "cell_type": "code", - "execution_count": 75, + "execution_count": 76, "metadata": {}, "outputs": [ { @@ -2418,7 +2479,7 @@ "dtype: float64" ] }, - "execution_count": 75, + "execution_count": 76, "metadata": {}, "output_type": "execute_result" } @@ -2437,7 +2498,7 @@ }, { "cell_type": "code", - "execution_count": 76, + "execution_count": 77, "metadata": { "collapsed": true }, @@ -2456,7 +2517,7 @@ }, { "cell_type": "code", - "execution_count": 77, + "execution_count": 78, "metadata": {}, "outputs": [ { @@ -2468,9 +2529,9 @@ }, { "data": { - "image/png": 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X17O2NQylc3R0RKfTcWaVtoZC1mAusA7w9ttvExYWZnXc6b8MFMUWer2eoqIi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\nBM33y9YAAAAASUVORK5CYII=\n", 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lly5dQkdHh3bt2iGVSHm+6/Mkp18n56gX5vJ2lMukVFQoMDR8OJY+1+pV1DVfjCAIwoMu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\nk+KXyWRwdXXVysXZ2RlWVlaQy+W9Hn9ncgCACRMmIDU1Fcn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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -2505,7 +2566,7 @@ }, { "cell_type": "code", - "execution_count": 78, + "execution_count": 81, "metadata": {}, "outputs": [ { @@ -2517,9 +2578,9 @@ }, { "data": { - "image/png": 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Pkp2dzbx588jOzuatt96iuLiY2bNnM3LkSNauXcuxY8f4+9//3uR+ixcv5quv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\nhB4drgQmItcBe4CL8OoFREt+fj7l5eXU1NTQu3d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ePZvy8nJteXJyMiNHjiQsLIznn3+ec+fO6dxTrVazYsUKevfuTbt27RgyZAhH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\nf+fwvPjt7Owgk8nU7sjkcjlqa2vh5OTU7/F3J4fU1FS8995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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -2566,7 +2627,7 @@ }, { "cell_type": "code", - "execution_count": 79, + "execution_count": 82, "metadata": { "collapsed": true }, @@ -2588,7 +2649,7 @@ }, { "cell_type": "code", - "execution_count": 80, + "execution_count": 83, "metadata": { "collapsed": true }, @@ -2609,7 +2670,7 @@ }, { "cell_type": "code", - "execution_count": 81, + "execution_count": 84, "metadata": { "collapsed": true }, @@ -2638,7 +2699,7 @@ }, { "cell_type": "code", - "execution_count": 82, + "execution_count": 85, "metadata": { "collapsed": true }, @@ -2666,14 +2727,14 @@ }, { "cell_type": "code", - "execution_count": 83, + "execution_count": 86, "metadata": {}, "outputs": [ { "data": { - "image/png": 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z5s0jKCiI2bNn2x4Yl5WVsWHDBkaOHGkbEObaa6/FaDTy2Wd6Bn9TlIaZzWYS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\nDf5KKTUE/S/ueJcybGcgtAAAAABJRU5ErkJggg==\n", 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MkWSEpqYmNjY2GBgYYKZvxlf+/2U3URgb69CvXxM0NF6uFj1PUqWvsJs3b3L+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\nLf5lZWUwMTHBK6+8gqCgIPj6+nbp5i3Ozs4AgF27dmHs2LE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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -2694,7 +2755,7 @@ }, { "cell_type": "code", - "execution_count": 84, + "execution_count": 87, "metadata": {}, "outputs": [ { @@ -2729,7 +2790,7 @@ }, { "cell_type": "code", - "execution_count": 85, + "execution_count": 88, "metadata": { "scrolled": true }, @@ -2751,14 +2812,14 @@ " axes_locator = None\n", " axis_bgcolor = (1.0, 1.0, 1.0, 1.0)\n", " axisbelow = True\n", - " children = [" + "" ] }, "metadata": {}, @@ -2844,7 +2905,7 @@ }, { "cell_type": "code", - "execution_count": 88, + "execution_count": 89, "metadata": { "collapsed": true }, @@ -2861,14 +2922,14 @@ }, { "cell_type": "code", - "execution_count": 99, + "execution_count": 97, "metadata": {}, "outputs": [ { "data": { - "image/png": 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//PCDqW1SUhIzZsxg0KBB9OrVi+uvv57XXnut1iilDz/8MEIIDh48aNV3o1AY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\nut21vPvuNt5buo09LsPIC/ZTWtn4qCIyIoKcnL6M6TuGc4a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PKHoE/vzzz/n4448ZNmwYw4cPB+DQoUPEx8ezdu3aCgUdT09PWrduzTfffMPDhw+Ry+U8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\nzz8Pf39/vPTSS7h48aJS/4EDB+Dp6an04+XlpfSYb7/9FkOGDIGfnx9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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -2900,7 +2961,7 @@ }, { "cell_type": "code", - "execution_count": 101, + "execution_count": 98, "metadata": { "collapsed": true }, @@ -2931,7 +2992,7 @@ }, { "cell_type": "code", - "execution_count": 102, + "execution_count": 99, "metadata": { "collapsed": true }, @@ -2950,7 +3011,7 @@ }, { "cell_type": "code", - "execution_count": 103, + "execution_count": 100, "metadata": {}, "outputs": [ { @@ -2962,9 +3023,9 @@ }, { "data": { - "image/png": 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nL1LcejRoA/dLRW3grihKc/jr4F/8+MeP5JXlAXAyI49DRWl0KOnP1MHjuOuu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\naH1OAe6AX+0l0fUc7btFRHoDY3Fj6WNeB9xFvHQROSfsOf1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g2fXr13njjTfw8fHB19eXadOmkZyc/AjvliA0ftevX1f5fFhbW9dr4odnPPkfPnyNKVOO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\n62Hp0fuAhBAySAzZ4l9SUoWTP6Tg2vUyKA1bYGCugAoqrl1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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -2997,7 +3058,7 @@ }, { "cell_type": "code", - "execution_count": 106, + "execution_count": 101, "metadata": { "collapsed": true }, @@ -3014,14 +3075,14 @@ }, { "cell_type": "code", - "execution_count": 108, + "execution_count": 102, "metadata": {}, "outputs": [ { "data": { - "image/png": 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my5YtjB07ljFjxvD888+TmprKhAkTSE1N5d133yUrK4uxY8fSt29fvv32Ww4c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\ntZkR6qmjMhpmWflqIpEIGRm7umNOHnzQDSZqjDE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dkURCzYmMjGTkyJFaL5Oxfft2pk+fzsWLF+sgOkGoHTdv3uT8+fPq5Rry8/Mp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\nBfEPtJ3qkEwAAAAASUVORK5CYII=\n", "text/plain": [ - "" + "" ] }, "metadata": {}, @@ -3055,7 +3116,7 @@ }, { "cell_type": "code", - "execution_count": 115, + "execution_count": 103, "metadata": { "collapsed": true }, @@ -3086,7 +3147,7 @@ }, { "cell_type": "code", - "execution_count": 116, + "execution_count": 104, "metadata": {}, "outputs": [ { @@ -3095,7 +3156,7 @@ "" ] }, - "execution_count": 116, + "execution_count": 104, "metadata": {}, "output_type": "execute_result" } @@ -3113,7 +3174,7 @@ }, { "cell_type": "code", - "execution_count": 117, + "execution_count": 105, "metadata": {}, "outputs": [ { @@ -3122,7 +3183,7 @@ "function" ] }, - "execution_count": 117, + "execution_count": 105, "metadata": {}, "output_type": "execute_result" } @@ -3140,7 +3201,7 @@ }, { "cell_type": "code", - "execution_count": 118, + "execution_count": 106, "metadata": { "collapsed": true }, @@ -3170,7 +3231,7 @@ }, { "cell_type": "code", - "execution_count": 119, + "execution_count": 113, "metadata": {}, "outputs": [ { @@ -3325,14 +3386,14 @@ }, { "cell_type": "code", - "execution_count": 120, + "execution_count": 114, "metadata": {}, "outputs": [ { "data": { - "image/png": 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v5cUXX2TUqFG89tprzJt3edslcnJyrGz8Dg4OfPfddxXalU/C3rx5c6ZPn870\n6dM5e/YsO3fuZMWKFcydO5fWrVszZMgQioqK+PHHH7nhhhssCWFuvvlmXnnlFVatWqWUv6LB4+Pj\nQ9++ffn2129JdE3kWFoapxOzCfQI4IN/PY3wu7hBqyEr/VLs3eRVAkwWQrwGDEZL3p4O/C6lrJhM\ntoEwWoy+LFPMxB4TK5iC6gp7E7iXJzAwkJkzZzJnzhxGjhx5ycfPz8/n5MmTjBo1yqq8NPNWZXz8\n8ceEhIRw001adI/WrVvzj3/8gzFjxnDzzTezbds2hgwZwpYtW8jIyGDdunVWdn6j0ciGDRt47rnn\n1MKvosHTsmVL7rv9Pk7/dp7fohJoXdCLthnXkRjlgrjhSktXM2q0ycus6Bussm/M2JvA3Rbjxo1j\nw4YNPP/885d8/NWrV2M0Gmt8A4mKimLjxo3ceOONlq3sAM7Ozri5uVkSyq9du5aAgAAWL15s1X/v\n3r3MnTuX9evXW5mIFIorTVpaGk5OTuhcdHi6XEwf6uLiwqMDHyAk9zp2/1xMhw4+dO3a8gpKemlU\nqvyFEHHAP6SUUUKIo2jZuirDJKWsuKdZYTeTJk3ijjvuYM6cOYwfP55mzZoRFxfHG2+8YZXAvTJe\nfvllRo+27yknMzOTlJQUTCYTWVlZ/P7777z11ls8+OCDtGlj7biVkpJicww3Nzc8PDyYNm0a48eP\n58EHH2Tq1Km0adOGc+fOsXbtWjIzM7n77rstvv3Tpk2jUyfr2CXt27fnk08+YfXq1Ur5KxoMSUlJ\n7PhrB3EZcRAMj/V9Gk+Pi/76/u7+TLnNl+5ByURGBjYY982aUNXM/w8gu8x7+5P9KmpMaQL39957\nj8mTJ5OXl0dgYCAjR45k2rRp1fYPCgpi+vTpvPTSS9W2feSRRyzvfXx8aN++PS+99BK33XabVbuS\nkhIGDhxoc4wJEyYwZ84cunTpwqpVq/jggw945plnyMjIwMvLiwEDBrBy5Up8fX1ZsmQJOp2OcePG\nVRjHwcGB++67jwULFnDo0KEqn3AUivrg1KlTbPxjIyfTT2IoKSFpVzYPbF7E53OewMXlosp0cNDT\nt2/5IMWNhxolcL9SqATuCoWiPvj78N/8/OfPZBVlAXAmJYvovCRaFYQzZcBY7r67czUjNBwuOYG7\nEKJ1TQ4kpTxbY+kUCoWiAWAoMbDyt5Ucjj2M0ZyivMSpBI/2noTtHIiH0Z/8fAMmk6lRmnhsUZXZ\nJ5GamXq4GWjjAAAgAElEQVQcqm+iUCgUDYv49Hi+2PQFOakXve2MrkaGXDuEW8QtrCSOPn0CCAvz\nvYJS1j5VKf/7UXZ+hUJxFbM2ei07/tqBKVtHVlYR3t4uNPfzZsotUwjy0UzMkyaFXWEp64ZKlb+U\n8rN6lEOhUCjqFYPBwPm48xSmGcnKLAJ06ApaMWvc4zg61MgLvlFSlc1/dg3GMUkpayfCmEKhUNQD\nDg4ORLaN5MTpUxQYnXDK60TehTakphQSGNiElT/wcg3GMQFK+SsUigZLVHIUwV7BNHdrDmihlXv1\n7EV2fjaxh0rIyHBn0qQwAgPdr7Ck9UNVZp8rl2JGoVAoaomswixWHl7J3rN7aWEI5ZGIRwgO9gK0\nOFWDrx3MtRFaOkW9/urw5LGHq//ZRqFQNElMJhM7T+9kTcwaMvKyOR9XQEJmDK9Gf8O7s6dYFL1O\np8PZuek5K6rwDgqF4qrjfO55lkUtQ6ZKAJwznWmZ64KbrjmkOLBt22mGDq1pDqqrCxXeQaFQXDWU\nGEvYdHwTPx79keKSYjCBa4Yr3kXeePi1IjURWoe60KfP1eWzfylUZfP/Z5n3U+pFGkWdsmfPHiZM\nmIC9YTK+/fZbnn/+eWJiYupBOoXi8jiZfpIvo77kdEYi+QUG3N2caJbWjFDHUEJahaBDjynElVtu\nGWLJKdGUsdvmL4TQA7cCAwFvtGxev0kpt9SRbAqFQmEXSTlJLPxjIenp+Rw9loHOqGNMxz508uqI\nh7OWJ6JVq1b07t3bKvR4U8Yu5S+ECAB+AnoChUAK4A/8WwixGbhDSplbZ1IqFApFFQR6BNLLvw8f\n/LkehyInwvV98E4PwaO5pvhDQ0MJCwu7auLy1Ab2unO+gZZ39xYppZuUso2U0hW4C+iDdWpHxSUg\nhGD16tXcc889dO/enZEjR3LgwAFWrFjBkCFD6NOnD08//TRFRUWWPnv27GHixIn07t2b6667jpdf\nfpn8/HxLfWxsLBMnTqRnz57ceuutREdb5+ExGo18+OGHDB06lF69enHXXXexbdu2ejtnheJSMZoq\npjyd0PNeRoUNYgjD8HXww72ZlkoxLCxMKX4b2Gv2GQ08KqX8uWyhlPI7IYQfsBB4uLaFu1yklMTF\nxdnVNiQkpEIe2aioKBISEuzq36lTJ4S4PIen//3vf8yfP5+2bdsya9YsHnzwQbp3784nn3zCyZMn\nmT59OhEREYwfP56DBw8yZcoUJk2axIsvvkhiYiJz584lMTGRDz/8kMzMTKZMmUL//v355ptviI+P\n54UXXrA63htvvMEvv/zCvHnzaNOmDdu3b+fRRx9l8eLF9OvX77LORaGoC4wmI9vit7EtYRtPRc7A\n2/1i6k8PZw+Gt4rkSMY5AgLccXV1pHfv3rRuXaMAxU0Ge5V/IZBZSZ192lFRLePGjWPYsGEA3Hbb\nbcybN4+5c+cSHBxMp06dWLx4MUePHgVg6dKldOvWjZkzZwJaRqy5c+fy4IMPcvToUf7++2+Ki4uZ\nP38+7u7udOjQgeTkZEuS99zcXL744gveffddBg0aBGg3wNjYWD7++GOl/BUNjtOZp1kWtYwTF05y\nOjGb8RsXsmzWv2neXMuwpdPpiIiIoKBgB3q9nsjISFq0aHGFpW642Kv8PwBeEkL8JaVMLi0UQrgD\ns4BP6kK4pkbZFIpubm7o9XorrxxXV1eL2efo0aMMGTLEqn9ERISl7ujRo4SGhuLufnGreq9evSzv\njx8/TlFREU888QR6/UXrX3FxMb6+yg1O0XAoNBSyPm49m09sxmgyciQ2jbS0ApoZ41mx8hDTHo60\ntPX09KRv3764urpa/fYVFalqk9emMh91QFfghBDiDzRPn+bAAMAJaJCJXIQQl2WK6dGjRwVTUF3i\n6Gj9deh0ukrtlK6urhXKSrOyOTo6otPpKJ+lzcnJyfK+1NXt3XffJSQkxKpd2ZuBQnElOZR8iBWH\nVnAh/4KlLCS4OR5n2hBcGE5WRg4FBQZcXS/+77Rs2fiSqV8Jqpr5O2O9sWuH+dUJKJ2OHjC/KqNa\nPdO+fXv2799vVbZ3715LXWZmpiWJure3NwCHDx+2tA0JCcHJyYnk5GQGDx5sKX/vvfcoKSnhiSee\nqIezUChsk1GQwarDq9h3bp9VufAVTBg6ga36ZAoK4vH3L6CwMBdXV+8rJGnjpapNXtfXoxyKGvLA\nAw9wxx13sHDhQsaOHcuZM2d48cUXGTJkCO3btycgIIBFixbx7LPPMn36dJKTk3nnnXcs/d3c3Jgy\nZQpvvPEG7u7udO/ena1bt7Jo0SLmz59/Bc9M0dT549QffB39NenZ2Rw7nkFoW28CWjRnbNex9A/q\nT2ZmJi1aJFFYqKOkxMDu3bsZOnRohSdnRdVUZfYZIKX8o6YDCiEGSSm3X55Yiuro1KkTH374IW+9\n9RZffvklPj4+jBo1iieffBIADw8PPv/8c+bNm8fYsWPx9/fngQcesCz4Ajz55JM4OTnx2muvkZqa\nSnBwMPPmzePOO++8UqelUGDCxOlzF5Bx6RiNJlqXBDH3jmfxcvXk3Llz7N+/n5KSEkAzUXbp0kUp\n/ktAV94uXIoQ4iBwBHhZSnnYZiPr9pFoi78dpZS1aigXQrQFTtoblkChUDReTCYT/9k0n42bY2mX\nM4wWpmCeeiocnS6N2NhYSztnZ2ciIiKUjb8SEhMTueGGGwBCpZTx5eurul1GAHOBPeaont8Au4GT\nQC7gg2b7HwjcAgjgXWB87YmvUCiuZg4mHcTH1YcQn4tOBzqdjqeHPEqk4TyHo9IZP74TaWknOXPm\njKWNu7s7/fr1Ux49l0FVNv9itPAN7wNPAQ8Ac7BeBNYBp4A1wK1SyjMVBrKBEGIq8CwQDMQAz6gY\nQQpF0yE9P52vDn/FgaQDkOXDoz2m06N7gKXex9WHkTd7ceOwIvbu3UN6erqlztfXl/DwcBWc7TKp\n1lBmVugzgBlCiM5AO7TAbqlAgpTSvi20ZoQQk4FFaDuCfwceAb4XQnSz9WiiUCiuHowmI1tObuF7\n+T1ZublImU5G5hmyo7/i046PWrlsmkxGdu78g7y8PEtZSEgI3bp1U+7ItUCNVkmklLFAbLUNK0EI\noQNeBBZKKZeay2YAw4DrgPhLHVuhUDRs4jPiWRa1jNOZpwHQO+jIyysmsCgMt6x2/PJLAqNHt7e0\nd3R0pE2bNsTGxqLT6ejatSuhoaEqRk8tUd9L5AIIAVaVFkgpjUCvSnsoFIpGTX5xPt/Ffse2hG1W\nGw9Dmgcz8ob72bw6lxuHhzBiREiFvh06dCA/P5/AwED8/f3rU+yrnvpW/p3Mrz5CiC1AN7QniVlS\nyp31LItCoahDTCYT+87tY+XhlaTlppOTU0xzH1ecHJy4tdOt3NjuRhx0DgwKyyMgwJ2SkhKKioqs\nbPk6na5ed9k3Jepb+XuZXz9HWzyOBaYCW4QQvaWUR+pZHoVCUUek5afxyb5PSErO4cSJTIxGE5Nu\nGsb/9b0P32YX40cFBLiTn5/P33//jYODA9dee62y6dcD9X2Fi82v86WUK6SU+4BpwFEaYEhohUJx\n6fg282V46AhOn85GV+RGp+xb8IwZaqX4AdLS0ti+fTuZmZlcuHCBQ4cOVYhLpah96nvmX+oKeqi0\nQEppEkIcAULrWRaFQlGL5Bbl4u5s7Xc/pvNozg/JZ89KL/yaezNwoPUmzYSEBCtlr9Pp8PHxUYu6\n9YC9aRxdgefQcvi6U/GJwSSltCd85j60DWKRwB7z2KURQ3+1U2aFQtGAKDAUsC52HTtP7+SJXjNp\n1+pinEcnByceHjqBPZ5JdO/ui4uLpnKMRiOHDx+2Spbk4uJCeHi42rFbT9g7838bzTb/G3AYqJhD\nzQ6klHlCiDeB+UKIZLQngEeA9mgpIRUKRSMiKjmKFYdWkJqTRnx8FpN/fYVlj88nJMQ6ymZERKDl\nfWFhIXv27OHChYthmr29vYmMjMTNza3eZG/q2Kv8/wHMllIurIVjzgHygLfQksAfAEZIKWUtjK1Q\nKOqBrMIsvjr0lSXk8tFjGZw/n0cLU0s+X3aQ558bhF5f0XSTnp7Onj17KCgosJRdc8019OzZEwcH\nh3qTX2G/8ndGi+tz2UgpTcAC859CoWhEmEwm/kz8k9XRq8krvrjzNqxDa/xOd6RFQUeah3pQUGCg\nWTMnq75paWns2rULo1EzHOh0Ojp37kz79u2Vjf8KYK/y34QWvG1rHcqiUCgaMGl5aXwZ9SVHUqw9\nsq8Lvo5/dP0Hf/uk4e7uREREoE1l7uPjg5eXFxkZGTg5OREeHo6fn199ia8oh73KfxnwiRDCF9iJ\nZraxQkq5ojYFUygUDYc/T//JikMryM7P59ixdFq1cqfTNcFM7DGRLn5dALj++qojbDo4OBAREcHB\ngwfp0aMHzZo1qw/RFZVgr/L/xvw6xfxXHhOglL9CcZXi6eLJ+bQsYmLSKCkx4ZvZg2fvnIG3R+UK\nPzs7Gw8PD6unADc3N/r3718fIiuqwV7lr3zwFYomTDf/bgztOIjTR/6gbc5QPEsCORqbTUREReVv\nMpk4efIkMTExdO3alXbt2l0BiRXVYZfyl1JanHGFEO6AJ5BmjvmvUCiuIs5lnyOnKIeOLTtalU+J\nmEgv/c38uD6e++4Lo2PH5hX6GgwGDh48yNmzZwGIiYnB29tb+e43QOze4SuEuB5YCISjJXFBCLEb\neF5KublOpFMoFPWG0WTkl+O/8L38Hp3BhfvaPEnf3m0s9a6OrvSLvIaIPq1xdKwYGSY7O5u9e/eS\nnZ1tKfPx8VG2/QaKvTt8B6N5/MSi+eknA62BccBGIcQNKmm7QtF4ScpJ4rMDn3Ei/QRnEnOIT8ji\n6I4PWdl2Ds2bu1ra6XQ6HB0revKcOXOGqKgoDAaDpaxt27aEhYWpIG0NFHtn/i+hhV8YZfbTB0AI\n8TLwI1qu3xtqXTqFQlGnGE1Gfj3xK+ti12EwGjAZISkpF/diP/zyurNixRGmTetdeX+jkZiYGE6e\nPGkpc3BwoHv37gQHB9fHKSguEXuVfwQwrqziB0tQtkXAV7UumUKhqFNSclP49MCnHL9w3FLm5OjI\ntBsm8tcKL4KDvBgzpn2l/fPz89m7d69Vfl13d3ciIiLw8vKqtJ+iYWCv8k8HPCqp8wRKakcchUJR\n15hMJraf2s6amDXkFOTh5KiFVQj2DmZKrykEeQXR3zcVIVrg4GDbZGMymdizZw8ZGRmWslatWtGz\nZ0+cnJxs9lE0LOw1xm0B5gohWpctNH+ei4rIqVA0Gj7e+zFfHlxG3IkUdv+VRF6egdFiNM8NfI4g\nLy3kcteuvpUqftBs/927d0ev11vy64aHhyvF34iwd+b/HFoI5qNCiB1AEhAIDASygJl1I55Coaht\nuvh1YdX2zZw7l0szYwv85ShuvmskDjVcmPXx8bHs1FWunI0Pu75tKeUZoDfwPuANXAv4AIuA3lLK\nE3UmoUKhqFUGtRnEDd37EmIIp0/2vQS4BpGXV/WWndTUVJKTkyuUBwcHK8XfSLHbz19KmQQ8U4ey\nKBSKWiYuLQ5PZ09aebaylOl0Op674WkGOCZiMJgYNqyNzfDLoNn24+LiOHr0KI6OjgwaNAh396pj\n+CgaB5UqfyHEbOBTKeU58/uqMEkpVYhmhaKBYDAa+F5+z8/Hf6Y41ZOn+z5Dt64Blnq9Ts/117ep\nYgQoKChg3759pKWlAVBcXMzhw4fp169fncquqB+qmvm/jLaQe878vipKY/QrFIorTHJOMkv2LyHu\n/Ani4i6Qnp7I3LilfPH8jAox9isjJSWF/fv3U1hYaCnz9fWlZ8+edSW2op6pVPlLKfW23isUioaJ\nyWRi5+mdrDy8kqKSInQ6yMkpprkhGI8swaZN8dx+e8cqxzAajUgpOXbsmKVMp9PRqVMnOnbsqJKu\nXEXYG95hDrBYSnnWRl0IMF1K+XhtC6dQKOwjrziPZVHL2Ht2r6WsmYsLjwyZzP5vvbhpRFtuvbXy\nDVsAeXl57Nu3z2rTlouLC3369MHX17fOZFdcGexd8P0PsBGooPzRPH8eBJTyVyiuAMcvHOeTfZ9w\nLj0FV1ftX7qVZyum9plKkFcQyT1zCQioepE2KSmJAwcOUFx80evHz8+P3r174+LiUqfyK64MVS34\n7kBT7KBF8dwlhKis+d+1LJdCobCDn4/9zOrD35ht+wWEhwcwvNMwxoaNxdnBGaBaxQ+aaadU8avc\nuk2Dqmb+U4G70BT/POBjILFcmxIgA/iuTqRTKBRVkl2UzaHDKWRlFeFocsE3YRjj7xpfY6UdEBBA\naGgoycnJ9OnTh+bNK8bqV1xdVLXgGwvMBxBCOKDZ/M/Ul2AKhaJ6bu98O391P8T2388icm+iV8+u\nlJSYbIZdLsVkMlFQUICbm5tVedeuXRFCqBANTQR7M3m9CCCEaAk4Y07mgrZD2B0YJKVcXCcSKhQK\nQAu/XFRShKvjxfj6jnpH5tw8gz/cztM60IsePfyqHKOwsJADBw6QlZXFkCFDcHZ2ttTp9XoVe78J\nYa+3T3dgORBWSRMToJS/QlFHZBZksnjfYk7H5/HMkCe55hpPS52niyc3j/CsorfG+fPnOXDggMV3\nPyoqivDwcGXXb6LY6+3zOtASmAHcChQC64GRwC3A9XUhnEKhgCMpR/jgr4/ZF32KtLQC0o8tYcns\nx22mUrRFSUkJR44csUq4Aqj0ik0ce5/xrgVekFK+CawC3KWUH0gpR6Mt9io3T4WiljGajKyX63n7\nr7dJz80kPb0QHXA+NYfNmxPsGiMzM5Pt27dbKX4XFxf69+9P165d1ay/CWPvzN8FOGp+HweU3eP9\nKfBhbQqlUDR1sgqzWLJvCbGpsQA0a+ZE947XYNoXyZ2DBzJsWNVxeUwmEydOnCA2Nhaj0WgpDwwM\npEePHsp3X2G38j8FhALb0ZS/lxAiREqZABQALepIPoWiyRGXFsdHez4mpyjbUtbZtzP3D7+fC8NM\nhIb6VNk/Pz+fAwcOkJqaailzcHAgLCyMNm3aqNm+ArBf+a8FXhVCZEsp1wohYoGXhBALgKeA41V3\nv4gQoisQbaNqkJRyh73jKBRXGyaTiY1HN/LB1uWcPZtDr97+ODk6MKrjKEZ1GoVep8c7tPpxUlNT\nrRS/j48PvXv3xsOjskysiqaIvcr/RaAj8ADajeAp8+sEtI1e99TgmN2BVPNrWdJqMIZCcdXx8/Gf\nWbhuKedT8gFIPFHEW5Nm0cWvS43GCQoKIikpieTkZDp06ECnTp2UC6eiAvb6+ecBdwohXMyffza7\nf/YB9kkp7Z75A92AGHNyGIVCYWZIyBC+br2R8ynH8Da0JiJ3LKGeVUfhBDAYDDg6XvxX1ul09OjR\ng9zcXFq0UBZZhW3szuQFIKUsLPP+ODUw95ShG3DkEvopFFc1bk5u/GfU0/wvax0D/UZwx+2dqnTn\nNBgMxMTEcOHCBQYNGoSDg4OlzsXFRS3qKqqkqsBuR9E2b9mDSUpZadS3cnQDXIUQu4C2wGFgtpRy\nt539FYpGT3ZhNhsPbGeEGIaPz8UduyE+Ibz1r8eqXZRNS0vjwIED5OXlARAbG0tYWGV7MBWKilQ1\n8/8D+5W/XQgh3IB2QApaPuBC4FFgmxCij5RSPREornqOnI/lhbX/I+bEGf7yv8B/n55gpeyrUvwl\nJSVIKTlx4gQm08V/z/z8fEwmk/LkUdhNVYHdptT2waSU+UKI5kBhqQlJCDEFCAceAR6r7WMqFA2F\n0k1bX+9fR8zxZEzApqRv2PBLBKNGdK62f3p6OgcOHCAnJ8dS5uTkRLdu3bjmmmuU4lfUCHtj+1xX\nXRsp5U57xpJSZpX7bBRCRAPB9vRXKBojF/IvsHjfYo5fOI6HhxNBwZ4knzIwrMWd9O1d9YYto9FI\nXFwcx44ds5rt+/n50bNnzwrRORUKe7B3wXcH1ZuAHKqpRwgRDmwFhkop95rLHIBewGo7ZVEoGhV7\nz+5lWdQy8orzLGUj+vSla9hN3Hx9V/T6ymfsmZmZ7N+/n+zsixu+HB0d6dq1q9qwpbgs7FX+Q22U\neQCDgEloSV/s4SAQD3wkhJgG5AAzAV/gbTvHUCgaBQXFBbz83Yf8IrfRo4cfep0OvU7PGDGGmzrc\nhF5Xve99SkqKleJv2bIlvXr1UkHZFJeNvX7+2yqp+lEIkQM8jxbts7pxDEKIW4DX0KKCuqMtLA+W\nUp63T2SFouGTmJnIg5+8yMnzWtrrUwlZ9OkSytQ+U2nfoupE6mVp3749586dIzs7my5dutC2bVs1\n21fUCjXy86+E7cAsexubs4FNqIXjKhQNFg8XD9x9TGCe0rikteW5Af/Gy63yEAslJSUUFxfj6nrR\n9VOn09G7d290Oh3u7tXn4lUo7KU29nyPBrKqbaVQNCF8XH2YPWoafs09mRQ2mTWzX65S8V+4cIHf\nf/+dvXv3Wi3qAnh4eCjFr6h17PX22WSj2AHNQ6c9sLA2hVIoGhMlJUZW/fwnYwZH4uFxMS1i71a9\n+fGpxXi6Vq70DQYDsbGxxMfHW5R+fHw8oaF2RHBTKC4De80+zlT09jEBMWj2+6W1KZRC0Vg4cuIM\nM5e/ybHsI5xKfJhZD1ovfVWl+FNSUoiKirLs0gXNk6dsmAaFoq6wd8H3+jqWQ6FodOw9u5d3/lzM\n0exTAKyKW87ImD706Nq6yn5FRUXExMRw+vRpq3J/f3969Oih/PYV9UKNFnzNnjqDgOZAMrBFSvl7\nXQimUDRUcopy+OrQV+w5uwdXL/D3cyM1rYCbe1xHpw4tK+1nMpk4e/Ys0dHRliTqAM7OzoSFhald\nuop6xV6bf0tgIxCBFo8nBfAHXjCvB9whpSyoMykVigaAwWDkr4S9rD2+iuzCi7734WGh3NnuXgZ2\n7lNpX5PJxJ49e0hKso5k3rp1a7p166YicCrqHXtn/u+ipXEcLaX8sbRQCDEGWAK8CjxZ++IpFA2D\n6LgzzF7xHuedJd27+6JDm6EPaDOAsV3H4uZUtalGp9NZbcxydXWle/fuBAYG1qncCkVl2Kv8bwGe\nLKv4AaSU3wshngPmo5S/4iplb/xhpi6eRwG5kAdJSbl0aRvEpJ6T6Obfze5xhBAkJSXh7+9Ply5d\nrBKwKBT1jb2/PgOQUUndOTRvIIXiqiTYz5/AYGfiT+fi4KAjzLs3L1z/CM2cbIdYMBgMHDt2jLZt\n21pt2HJ0dGTIkCFK6SsaBPZu8nofeEUIYeXGIITwQtvd+25tC6ZQNBT83f154qZJtLsmgEVTXmDB\nuBmVKv7z58+zbds2jh49SnR0dIV6pfgVDQV7f4mtzX/HhRA7gLNAS2AA4AkUltkIZpJS3lTrkioU\n9cCe6JOs+fVPXp52j1UKxREdhzM4dFClSj8/P5/o6GjOnTtnKTt79iyhoaEqj66iQWKv8u8AHCjT\npzQAeWmZA3aEdFYoGiomk4lXln/FyqjVGCmh09oQ7h87wFKv1+ltKn6TycTJkyeRUmIwGCzlzs7O\ndO3alebNm9eL/ApFTbF3k5etkM4KxVVBck4yX0Z9ya7c/RgoAuCzvV9wz6hImjWrfDkrPT2dQ4cO\nkZmZaVUeHBxM165dcXZWS2GKhktNN3l1BYYA3mi+/juklLIuBFMo6hqD0cCm45v4Me5HDEYDrVq7\nk5qWj7dDS+aPe6xSxV9UVERsbCynTp2yCsLm6elJ9+7dadmy8o1eCkVDwd5NXnrgI+B+oOwWRJMQ\n4kvgn1LKWk32rlDUFSUlRlZs3MFhh01kGFIs5Q46B566dQK3dx2Ns2Pls/aMjAwSEhIu9nNwoGPH\njrRv3x69vjYC5SoUdY+9M/9ZwH3m1+VooR1aAeOBeVwM8KZQNGii5TnmfPUhR/L24OfnRufO2iw9\nxCeEST0mEexdfSppf39/AgMDSUpKIiAggG7duqnMWopGh73K//+A+VLK18uUJQKvCSFczfVK+Ssa\nPCvkZ8Tk7QHgfEo+bYPhvr7jGBo61GZaxeLiYvLy8vD29rYqDwsLIzg4WO3QVTRa7H1GbYWWbtEW\nO7no/aNQNGimDroHf79mODjoGBbWl9dGvswN7W6ooPhNJhOnTp1i69at/P3331aePADNmjVTil/R\nqLF35n8CuBbYbKPuWrRdvgpFg+Lo8VTc3Vxo3drTUhbaPJRHht+Dv1sg13e6zmYUzYyMDA4fPkx6\nerql7NixY3Tu3Lle5FYo6gN7lf9iYIEQIhdYiWbzDwDuBWYDr9SNeApFzcnKKmTRqp9ZI1fRr+X1\nLJo11UrJ393rLpv9CgsLiY2N5fTp01ZePG5ubhXMPgpFY6cmUT17A28A/y1TrgOWoQV2UyiuOFmF\nWSzZv4xlxzdg1JvYceEnfv19MMOHiEr7GI1G4uPjiYuLo7i42FKu1+tp3749HTp0UGEZFFcd9m7y\nKgEmCyFeQ0vm0gJIB36XUlYMYKJQ1DNGk5Ft8dv4LvY7CgwFXHONB6dPZ9PSzwX3VrmV9ktJSSE6\nOprs7Gyr8oCAAMLCwlTidMVVS02nM6fR7P/pwHnze4XiipGamsfhM0f5I/MHTmWespS3aePJoHb9\nefyGf+LtattkYzAY2Lt3r9Vs393dnW7duuHv71/nsisUV5KabPJ6DXgUcOLiRq9cIcR8KeWrdSSf\nQmGTwkID3/0Ywyc7VnDB4wjh4QHo9drPMsAjgPHdx9PZt+oFWkdHR4QQHD58GEdHRzp27Ei7du3U\nRi1Fk8Demf9c4AngLeAbtFl/ADAWmCeEyJJSvl8nEioUNjiWdpzX9rxMnmMuFMDpxGw6hLZkZMeR\njGg/Ake99U/bZDJx4cKFCqEXQkJCKCwsrBB7X6G42qnJJq95UsqXypSdAP4UQmQDT6HF/Fco6oX2\n/iGIji3ZfyQXT09nrm3Xh2lD/olvM98KbVNTUy12/YEDB+Lj42Op0+v1yoVT0SSxV/l7A7srqdsB\nzBPSiWcAAB0kSURBVKgdcRSKimRnF3HqVBZhYRcVu6ujK08M/ycfOi/jiWH30zOwZwWf/dzcXGJi\nYqySpsfExHDttdfa9O9XKJoS9ir/H4B/AT/bqLsH2HApBxdC9Ee7edwopfztUsZQXL0YjSa2bElg\nyYafydSfZeWc2Xh5uVjq+14TSe97euHsYB2EraioiKNHjxIfH4/RaLSUOzg40LJlS0wmk1L+iiaP\nvcr/d2C+ECIKbZPXObRMXrcCA4H/CSFmm9uapJQLqhtQCOEOfIlKAqOohJScVP63/R1OOmpRwxet\n+pnnHhhjqdfpdFaKvzJ/fYCgoCA6d+6Mm5tb/QivUDRw7FX+75lfvYGXbdSXNfuYgGqVP/A/tOBw\nHeyUQdFEKDGW8OuJX1kftx6PDtlwCJq5OZLach8wpkJ7k8lEUlISR44cITfX2qe/RYsWhIWFWdn5\nFQqF/Zu8atX3TQgxEhgF3AJE1ebYisaJwWDk2LF0HP3TWR61nLPZZwH+v707j6+yuhM//rm5Nxsh\nIQkJOyQkJN8AyqIosgqKMm64jrXVVttxbHU6rlU609rFrXban621/sZO67TWutQuKipadgW1WNxQ\nhC8Q9rAFEMhCQpY7f5wnyU2AcIHkLuT7fr3ySnjOc89zDve53+fc85znHLIyUxg+LIcZo6Zx1fDD\nT8vg8/nYuHFjq8CflpbG0KFD6dOnj3XxGHMYEX9mXURygCeBr+IeFjNd3KpVu3nquQ9Zun8O/cbu\nIi0tsTltQMYAZk68loKsgnbzGDZsGG+99RaBQIDi4mLy8/NtvL4x7YjGhCW/Amap6hsiMiAKxzcx\npLGxkf9+ZRYLq1+lLrGGqrVJjByZS0oghRkyg3MGn9NquuXa2lrWrVtHcXExfn/L7aKMjAxGjx5N\nbm6urZ1rTBgiGvxF5HrcBHEjInlcE7t8Ph+5o3bTMK8Gf4KP3NxURvYeyRdP/SLZqdnN+9XX11Na\nWsq6deuor68nKSmJwsLCVnn1798/0sU3Jm5FuuV/AzAA2C4i0DJNxOsi8pSqfiPC5TERVl5eTW5u\ny5KHPp+Pmyd8leVln9EvJ5uvjvkyI/uMbE5vbGxk48aNrFmzhtra2ubta9asIS8vz2bbNOY4RfqT\ncx0QOtauD7AYuBGYG+GymAg6cKCOl18u5aXF7zLz69MZPaJfc1rPbj25/+KZ5Gfmkxxw4/iDwSBl\nZWWoKtXV1a3yysjIYOjQoa26fYwxx+aIwV9E+h0p7XBUdWsY+5S1OUaN92eZqu48luOZ+PL8i8v5\n3XvPsjNtFQ+9sJ1nSu4hKakleEuOm28/GAyyc+dOVq1axf79+1vlkZqaSklJCf3797cRPMacoPZa\n/ltwY/bDZc0wc4hgMMiSTUtYlv4nPu+2HuphW9oHbNy9haK+eYfsv2zZslbTMQAkJSUxZMgQ8vPz\nrbVvTAdpL/h/jZbgnw08jFvD9wVanvCdgXvK987jObiqbqGl39+cJOrrG0lI8LGtcivPfPIMpXtK\nARhS5B60+qcRk+idnXXY12ZnZzcHf7/fT0FBAYWFhSQmJh52f2PM8Tli8FfV3zX9LSIvAr9X1X9t\ns9uzIvIocDXwP51SQhNX1q3by2+f/pik4crWlA9pDLbMrTN00CC+dOqXGN5rOAA1NTWHTKOcn5/P\nhg0b6N27N0VFRSQnJ2OM6Xjh3vA9H7jsCGmvAm0vCqYLWr68nPv/56+sTVlI/QeVjBnTh6REP/4E\nP+cXns+FRReS5E+iqqqK1atXU1ZWxuTJk8nIyGjOw+/3M3XqVHtAy5hOFm7w3wWcyeFH5EwByg6z\n3XQxtdmbKO05m5oD9fgbfVRWHmTskBFce+q19E3vS3V1NSvXrGTz5s0Eg65HUVU544wzWuVjgd+Y\nzhdu8P818D0RSQVmAeW0rOR1K3B75xTPxJPT+o1i0ojhLFujjCjpz3WnfYHxA8dTU1PDJ598wqZN\nm1pNsQxuHH9DQ4PdyDUmwsIN/g8CmcDdwH+EbK8B7lXVxzu6YCZ2NTQ0Mn/+JqprarlshjRv9yf4\nue2cG1kyZAlXDL2CQGOAFStWsHHjxkOCfk5ODiUlJWRlHf7GrzGmc4U7q2cQ+JaI3A+MA7JwXUHv\nqGpVuy82J5WKioP8+JHFvP3536jx72XMaT9lwICWPvuCrAIGZw4+YtDPzs5GRMjJOXS5RWNM5BzT\nE76qug94o5PKYmJcMBjk4z3vsTjxSXYm7QPgiddm8cDXr2u1n8/no7KyslXgz8rKag769oCWMdHX\n3hO+awj/Ia+gqsrRdzPxasv+LTz7ybOU7illUGEKez6uYNDAdIacWU9jY+MhN2mLi4spLy8nMzMT\nESE3N9eCvjExpL2W/9sc2xO+5iSzZUsFS9/fTMOQT1m4fmHzmP1u3RK5YMpwrparSN6fzKJFi5gy\nZUqrC0B2djYTJkwgKyvLgr4xMai9h7xuaPpbRK4B5qtqeSQKZaIrGAzywgureGHJAtamvEnxvhSy\ns9x8fP4EP1P7T6UgWMD2T7c3d+1s3ryZvLzW0zVkZ2cfkrcxJjaEO6D618DkziyIiR1Bgsza+RSf\npc7moK+Kdev2ESRIUXoRV/e8mtQtqWzdsrVVn355ubULjIkn4d7wLQO6HXUvc1JI8CUw7axTWL71\nU7qnJ3F6YR5Tu00kuTKZioqKVvtmZ2dTXFxso3eMiTPhBv//Bh4VkbOAj4HKtjuo6rMdWTATGXv2\nHGDhws1cfnkRCQktffNfGHUFH23+kJKEIfT19cVf7ScYcgsoJyeH4uJisrOzrU/fmDgUbvD/mff7\n5iOkBwEL/nHmjTfW8+zsd1gbWEJyj1u4eNqpzWndErvx4AU/ZMmbS6irq2ve3qtXL4qKiqw/35g4\nF27wH9yppTARt792P/PK/8qylAUEgcfmPc3UcfeRltYyy2b31O7k5+ezdu1a+vTpQ1FRET169Ihe\noY0xHSbcJ3w3Nv0tImlAOrBbVeuO/CoTi+ob61mwfgGvrX6N6owDpKT4yfWnI9n1fPjpMiaOndhq\n/4KCAvr37096enqUSmyM6QxhP+ErIlOAHwOn4y3AIiLvAd9V1fmdUjrTIXbvPsBrr5VSMLGS19e/\nwq7qXdAIqZUpnN2riN7dcinMKmRv+V6qqqpIS0trfm1SUhJJSUlRLL0xpjOEFfxFZDIwB1gFfA/Y\nAfTDLeLyuoicq6qLO62U5rgtXLiJ/31xEasT36TH3ioKBmaSUpFCUmUSaYE0CnoXkJXiJlcLBAJU\nVFS0Cv7GmJNTuC3/+4F5wEXeJG8AiMgDwGvAD4BzO7x05oS9XzWfZSl/JsWXSOKOHqT50kkOJJKX\nmUff9L748JGSkkJBQQF5eXkEAsc03ZMxJk6F+0kfA1wdGvjBzfYpIo8Dz3V4yUyHmH7GGN78cBG5\njRlkZqSQlzmQgRkDCSQE6N69O0OGDKF///62gIoxXUy4wf9zoPsR0tKBho4pjjle5eXVPP+X5Xzh\nilPp1aul2+aUXqdw1mklJO0MkJ+ZT0oghezsbAoLC+ndu7eN0Temiwo3+C8AfiAii1V1a9NGEemH\n6/KZ1wllM2Gat2gNP3v5j5QFPmD7Mxdy/21fa27J+3w+7p5+F0vfXUpqaiqFhYW2gIoxJuzg/x/A\nMmCNiCwBtgN9gInAfmBm5xTPtKe2vpYF6xfwl7JXqU/Zz3B/b7buWsHHH69m9OiS5v2SAklMmDDB\nunaMMc3CHedfJiKjgbuASbiHvj4HHgceUdXtnVdE01ZtfS0L1y9k/or51O+pJ/tAGgndA9TXN9I7\nO42tu0oZFZRWXToW+I0xodpbzOVs3DKNdQBegL87UgUzh9pWvpf/+uMzHEhbTVpdAH+dn0QSAeiV\nncHgrHwK+hRQWFAY5ZIaY2Jdey3/hUCViLyFG+M/T1VXRKZYpq1fzn6OV5f8jayEFFITE8nI8QOQ\nEkhhUMYgThl8CoWFhbZMojEmLO0F/8txffqTgJ8AfhHZjru5Oxd3MbDunghJy2qkpz+VhGACdXWN\nUB+guE8BY0rGUFhQaNMvGGOOSXsreb0MvAwgIt2AcbiLwWTgCSBVRFbgLgRzVdUWdu8gazdup1dW\nOhkZLUM2rzztEua/u5jUilROzStm+oQp5Ofl29QLxpjjEu4N32pgvveDiASAs4GbgG8CtwP+cPIS\nkQG4KaLPxa0k9gZwZ+gQ0q7q9SXv8cLCWdTU7OZcmc6NX7msOS0jOYP/vPo2uge7M8AeyjLGnKBj\nmdgtBZgCTAOmAiNw8/i/h7snEE4ePtx0EOVeHgC/AF7BTRjX5TQ2NrKsdBmLPlrE5k3bqa+tJeBL\n4KO1H1JVdT5paS0LqA0bMDSKJTXGnEzaDf4icgow3fuZCKQApbhgfx+wUFX3H8PxegMrgW+r6gbv\nGI8AL4lIlqp+fsw1iDMVFQf54IMdbNr8Ob1KtvHeiveoqHRLI6Yk+/H5gCD4UhrYtWtfq+BvjDEd\npb2hnluAvrjx/ItwXTtzmoL28fBuEF8TcowBwNeBf3SFwF9bW8+3vzObiqTPIHkHuXsS8ftbum98\nPh+F+QM574ypjDv1TBu1Y4zpNO21/PsBu4AncTd1F3fk4i0i8hJwKe7iMvUou58UKhr2srf3HBIO\nuKB+4EAC3bsn4EvwMXjQYKaPmc7g3rZomjGm87UX/KfhunsuAO4BqkPG/M9R1ZUneOx7gYeA7wJz\nRWS0qpadYJ4xYdeuaubO3UhxcQann96/eXvP1J5k9k2nZks1qakBuvVIYmTJCC44/QKy02xNXGNM\n5LQ31HMBbkK3mSLSG3chOA83z8/PvG6hubiLwVxV3XMsB1bVTwBE5BpgM3A97mIQ1955ZwvPPreU\nuuQNfLoukVGj/g2/3w2E8vl8XDftMma/M5txw8Zx7rBzSQ4kR7fAxpguKdyhnjuA33s/iMgo3IVg\nMvA7L5/Eo+XjXUSmqurzIXlXi0gp0P/Ir4x9VVVVrFm3ho/WL6WqxyrqOcjW6mSWLy9l9Oji5v3G\nDhzL2C+MJcFnQzWNMdFzTMs2iUgm7mGv8cBY3CIvAeD9MLPIA54TkbWquszLswcgwFPHUpZoa2ho\n5P33t9G7dyO6fiWfbfqMHZU7aAg2kJjaiL/RT1qaj/LaDUBL8Legb4yJBUcb6lmEC/QTvN8luAez\nPsM98PVLYNExDPdcBiwGfiMiNwF1wMO4cf9xE/wXLVrL3LkfsL9+A937HqAhsapVekZ2Ir5MH2cO\nO5Mz5cwoldIYY46svaGe5UA24AM24YL9Q8CC453TR1UbReQK4KfAq7jnBv4GnK2qlceTZzQs3bCY\nMj6mIbGOyr0+cnPdWPy61Doye2cydfhUzhp4Fkl+m3rBGBObjjar5zxgvqqWdtQBVXUXcENH5deZ\nGhsbWbduG4WF/VqNuR80Mo1PSg8S8CUQ6ObjQEYNUljMtOJpSE+x8fnGmJjX3mifqyNZkFhSVVXN\nnDkf89HyVeyrKedb//YVBgzo05w+vWQa8/IX0CMrhYklEzk7/2x6dusZxRIbY8yxOaYbviezhoYG\nduzYwaZNmyjdUsrSFavZW7cb/EFmz/87N13fMsladmo2d196O4VZhST6jzrIyRhjYk6XDv7BYJBd\nu/awbt1GyndvpWxvGdsqt1FdV02wWz3BfUGCviCbDmw45LUlOSWHZmiMMXGiywb/DRu28drsJazf\nuomG1P0kZ9bSSGNzeiAzSF1KDcUykIuGjYtiSY0xpuN12eC/+vM1/KPsbRp8dfgOQG56N3xJQQ52\nP4gvw8eYvDFMyptEXo88u4FrjDnpnNTBPxgMsn37TpYtUyZNGkVmZkZzWmFef2pTqvHV+qlIOEAw\nvZahhQVMypvEGf3PICWQEsWSG2NM5zrpgn8wGGT//v1s2bKFxYtXsHZzGRXBPdQT5PJLzm7eryCr\ngJ5FPahoqOS6kRcyKW8i/dL7RbHkxhgTOSdN8K+urqasrIyysjJ2793NzqqdaMVGdvsqwAdLP13G\nZRdPbu7C8fl8fO+Su8lOzSaQcNL8NxhjTFjiOupVVBxg8eIVrFy5gSCV5AyA7ZXb2VPjJhhNSGqk\nLthAhb+axMwdBIPBVv33vdJ6RavoxhgTVXEd/Ldt28O8N5dQnfA5tYG95CQn4/NB0BekLrWOurQ6\nUvvCBcXnMnHQRFv03BhjPHEd/Gsz9rA9ZRX+Bj/BYJAKGgn0dIFfegnjB45ndJ/RNme+Mca0EdfB\nvyS3hECvBGrra0juBRk5PZkwcAITBk0gp1tOtItnjDExK66Df6I/kRlTz2FX9S4mDprIsNxhNl++\nMcaEIa6DP8CVQ6+0h7CMMeYYxX0z2QK/McYcu3hp+fsBtm8/rjVkjDGmywmJl/7DpcdL8O8LcO21\n10a7HMYYE2/6AocsyBUvwf8fwCRgG9AQ5bIYY0w88OMC/z8Ol+gLBoORLY4xxpioi/sbvsYYY46d\nBX9jjOmCLPgbY0wXZMHfGGO6IAv+xhjTBcXcUE8ReQIIqOqNIdu+DMwEBgOfAt9V1bkh6bcAj7fJ\nqkFVAyH73AHcDuQCbwO3qOqaGKpDEvAj4FogDXgL+Kaqro+HOojID4DvHyG776vqfZGsw3G+B4OB\nR4HJwAHgVeBuVd0bsk/MvgdeepFXh/FAJfAkcL+q1keqDiLSG/gv4HwgFVgK3KWqn3rp53vpAqwB\nZqrq6yGv7wX80nv9QeC3wHciVYcTLX9IPsnAe8BPVPUPbdIidh4dScy0/EXEJyL3AV9vs/2LwFPA\nM8Bo4PfALBGZErLbqcAs3JjWpp/+IXn8C/BD4C5gLO6D/Yb35sRKHX4FXA18CRiHO+lmiYgvTurw\nU1r///cFngB24gJQROpwvOUXkQAwG/ccyTjgSmAi8OuQPGL6PRCRLGAxkAJMBb6IO6d+Fak6iEgC\n8CJQDFyKuwjtA+aLSE8RGYb7rP7Jq8PLwEsiMjwkm78AfYCzgRuAr3pl7vQ6dFD5EZF0L58RhzlG\nRM6jo4mJlr+IFOACxCnApjbJM4FnVfVH3r9Xi8goXCtzkbftFGCBqh5p/od7gEdU9c/e8b6Ee2Ds\nSuDZaNfBe+0NwLmqusDL72ZgDlAIrI31OqhqJa6l2ZTXOOAm4CJVLfM2d2odTvA8KvF+rlbVlV5+\njwEPh+QR0+8BcD3QDbhKVfd4+d0ILBGR+1V1QwTqMBJ38RwW8v/4ZWAPcBEwAfi7qj7o7X+viEwE\nbgNu8s6biUCB9633YxG5G3hMRO5T1dpOrsMJld/bfxrugru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H/fv355tvviE3NxcfHx+Cg4NVEkRN6qtK//79OXDgALt37+bUqVNVJv9GjRrx448/snTp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\niOjoaFy6dAlnzpxBbGwsDA0NYWNjw31IHy78QMtXKCsrK9y+fRsODg4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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -3366,7 +3427,7 @@ }, { "cell_type": "code", - "execution_count": 121, + "execution_count": 115, "metadata": { "collapsed": true }, @@ -3394,14 +3455,14 @@ }, { "cell_type": "code", - "execution_count": 122, + "execution_count": 119, "metadata": {}, "outputs": [ { "data": { - "image/png": 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ne5eWjBjRlpkz+zRKpQGO9zhmAA+YvlcAKWhG7jFow0yH0WwVVWEc8KGUsriK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\n", 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97kG+CgIDA7ly5QqzZ88mIiKC27dv89dff/HBBx/QpUsXWrVqBRTdV/D09CQo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\nB6+//jqysrLg6+vbbRfc6dOn93lwRP/q6lqRlFSGWbO8YWJ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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -3428,9 +3489,8 @@ }, { "cell_type": "code", - "execution_count": 128, + "execution_count": 127, "metadata": { - "collapsed": true, "scrolled": false }, "outputs": [], @@ -3445,22 +3505,25 @@ " \n", " returns: population next year\n", " \"\"\"\n", - " net_growth = system.alpha * pop\n", + " if t > 1980:\n", + " net_growth = system.alpha2 * pop\n", + " else:\n", + " net_growth = system.alpha1 * pop\n", " return pop + net_growth" ] }, { "cell_type": "code", - "execution_count": 129, + "execution_count": 140, "metadata": { "scrolled": true }, "outputs": [ { "data": { - "image/png": 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ne5eWjBjRlpkz+zRKpQGO9zhmAA+YvlcAKWhG7jFow0yH0WwVVWEc8KGUsriK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\n", 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vY2dnp7Sunp5elfc4GjZsSPfu3dm+fTsDBw6kQYMGimUFBQVs2rQJIyMj6tWr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\nHn3OHQAAAABJRU5ErkJggg==\n", "text/plain": [ - "" + "" ] }, "metadata": {}, @@ -3469,8 +3532,8 @@ ], "source": [ "# Solution goes here\n", - "system.alpha1 = system.birth_rate - system.death_rate\n", - "system.alpha2 = system.births\n", + "system.alpha1 = 0.018\n", + "system.alpha2 = 0.015\n", "\n", "run_simulation(system, update_func1c)\n", "plot_results(system, title='Proportional model, combined birth and death')" @@ -3492,7 +3555,7 @@ }, { "cell_type": "code", - "execution_count": 130, + "execution_count": 141, "metadata": { "collapsed": true }, @@ -3520,7 +3583,7 @@ }, { "cell_type": "code", - "execution_count": 132, + "execution_count": 142, "metadata": {}, "outputs": [ { @@ -3532,9 +3595,9 @@ }, { "data": { - "image/png": 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39WN8/GomHuFWZs7sfVYmfmjgAu6uIgu4CyGcVVxSzIc/fIjer+kc0I0+3Xoz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\nhVaeXVPMlUvPbTsmKz2La86+JhbVNsaYEyIpk38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Pnj1Mnz6dnj178vnnn1c6f2hoKCYmJvTo0QO4/8Fx7do1IiMjHzt2QVBXWVkZ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\njAyYmZkhODiY63dycsK5c+fg6Og4JnK4G2MMb775JubOnYv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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -3559,7 +3622,7 @@ }, { "cell_type": "code", - "execution_count": 133, + "execution_count": 143, "metadata": { "collapsed": true }, @@ -3580,7 +3643,7 @@ }, { "cell_type": "code", - "execution_count": 134, + "execution_count": 144, "metadata": {}, "outputs": [ { @@ -3592,9 +3655,9 @@ }, { "data": { - "image/png": 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2zU2Gt5+KipH9wSTaPcWK3lfySIZ7yk3r5si5LgD+8FIjHU1V5GQO3yORDPc1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\nyMyWA4vTQF2Qa9L0Ap+rc+7j03ZjjX1/LgxSuuY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9TRQKBfPmzbNJQML2mppb2XuswLwdGeLNiEh5HCFEZ5ydVNyVOIAd+3IxGo0U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\n6apDrAghRCKRyPmTmppKzM3NSVpamsJ9VDVeLS0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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -3620,7 +3683,7 @@ }, { "cell_type": "code", - "execution_count": 137, + "execution_count": 145, "metadata": { "collapsed": true }, @@ -3638,7 +3701,7 @@ }, { "cell_type": "code", - "execution_count": 136, + "execution_count": 146, "metadata": {}, "outputs": [ { @@ -3647,7 +3710,7 @@ "13.88888888888889" ] }, - "execution_count": 136, + "execution_count": 146, "metadata": {}, "output_type": "execute_result" } @@ -3676,7 +3739,7 @@ }, { "cell_type": "code", - "execution_count": 140, + "execution_count": 148, "metadata": { "collapsed": true }, @@ -3691,14 +3754,14 @@ }, { "cell_type": "code", - "execution_count": 141, + "execution_count": 149, "metadata": {}, "outputs": [ { "data": { "image/png": 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FCoYOHaoepg5orL9QlXufAJYsWaIuc3Z2xtTUlLFjx5KQkKDRWeC7777DwcGB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\nOBlDg+tHA7kAAAAASUVORK5CYII=\n", "text/plain": [ - "" + "" ] }, "metadata": {}, @@ -3718,7 +3781,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 150, "metadata": { "collapsed": true }, @@ -3743,7 +3806,7 @@ }, { "cell_type": "code", - "execution_count": 149, + "execution_count": 151, "metadata": {}, "outputs": [ { @@ -3767,16 +3830,16 @@ " \n", " \n", " \n", - " prb\n", - " un\n", - " maddison\n", - " hyde\n", - " tanton\n", - " biraben\n", - " mj\n", - " thomlinson\n", - " durand\n", - " clark\n", + " Population Reference Bureau (1973–2015)[6]\n", + " United Nations Department of Economic and Social Affairs (2015)[7]\n", + " Maddison (2008)[8]\n", + " HYDE (2010)[citation needed]\n", + " Tanton (1994)[9]\n", + " Biraben (1980)[10]\n", + " McEvedy & Jones (1978)[11]\n", + " Thomlinson (1975)[12]\n", + " Durand (1974)[13]\n", + " Clark (1967)[14]\n", " \n", " \n", " Year\n", @@ -3798,11 +3861,11 @@ " NaN\n", " NaN\n", " NaN\n", - " NaN\n", + " 2M[15]\n", " NaN\n", " NaN\n", " 4.0\n", - " NaN\n", + " 1–10M\n", " NaN\n", " NaN\n", " \n", @@ -3829,7 +3892,7 @@ " NaN\n", " NaN\n", " NaN\n", - " NaN\n", + " 5–10M\n", " NaN\n", " \n", " \n", @@ -3863,16 +3926,48 @@ "
" ], "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" + " 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": 149, + "execution_count": 151, "metadata": {}, "output_type": "execute_result" } @@ -3891,7 +3986,7 @@ }, { "cell_type": "code", - "execution_count": 150, + "execution_count": 152, "metadata": {}, "outputs": [ { @@ -3915,16 +4010,16 @@ " \n", " \n", " \n", - " prb\n", - " un\n", - " maddison\n", - " hyde\n", - " tanton\n", - " biraben\n", - " mj\n", - " thomlinson\n", - " durand\n", - " clark\n", + " Population Reference Bureau (1973–2015)[6]\n", + " United Nations Department of Economic and Social Affairs (2015)[7]\n", + " Maddison (2008)[8]\n", + " HYDE (2010)[citation needed]\n", + " Tanton (1994)[9]\n", + " Biraben (1980)[10]\n", + " McEvedy & Jones (1978)[11]\n", + " Thomlinson (1975)[12]\n", + " Durand (1974)[13]\n", + " Clark (1967)[14]\n", " \n", " \n", " Year\n", @@ -4011,24 +4106,48 @@ "
" ], "text/plain": [ - " prb un maddison hyde tanton biraben mj thomlinson durand \\\n", - "Year \n", - "1913 NaN NaN 1793. NaN NaN NaN NaN NaN NaN \n", - "1920 NaN 1860.0 1863. 1912. NaN NaN NaN NaN NaN \n", - "1925 NaN NaN NaN NaN NaN NaN 2000.0 NaN NaN \n", - "1930 NaN 2070.0 NaN 2092. NaN NaN NaN NaN NaN \n", - "1940 NaN 2300.0 2299. 2307. NaN NaN NaN NaN NaN \n", + " 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", - " clark \n", - "Year \n", - "1913 NaN \n", - "1920 1968. \n", - "1925 NaN \n", - "1930 2145. \n", - "1940 2340. " + " 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": 150, + "execution_count": 152, "metadata": {}, "output_type": "execute_result" } @@ -4046,7 +4165,7 @@ }, { "cell_type": "code", - "execution_count": 151, + "execution_count": 153, "metadata": { "collapsed": true }, @@ -4064,7 +4183,7 @@ }, { "cell_type": "code", - "execution_count": 152, + "execution_count": 154, "metadata": { "collapsed": true }, @@ -4083,7 +4202,7 @@ }, { "cell_type": "code", - "execution_count": 153, + "execution_count": 155, "metadata": { "collapsed": true }, @@ -4111,7 +4230,7 @@ }, { "cell_type": "code", - "execution_count": 154, + "execution_count": 156, "metadata": { "scrolled": false }, @@ -4120,7 +4239,7 @@ "data": { "image/png": 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Qhg4dCkBoaCihoaEaxxUKRa4DUkhICJMmTaJ169aMGTMGyAokaWlpavlUKhXG\nxsZA1lbaKpV6ZE5LS0OSJExMTORA+Wqel8sQBEEQdGPZypKYYM0dCixbFuAsu7CwsDytdNmyZSxY\nsIAePXowceJEeRzJ1tZW3nMp28OHD+UuuDJlynD06FGN45DVTWdrawvAo0eP1Bb8fPjwodgOQRAE\nIZfM3bNm08XtjUN1T4WyrBLLlpZyel7TaQypXLly8k/JkiVRKpXY2Niopetq1apVLFiwgGHDhjFp\n0iS1nUVr165NeHi4Wv5Tp05Rp04d+XhkZCQxL+0pdOrUKUxNTXFycqJUqVLY2dlx+vRp+XhSUhKX\nL1/G/T1aO05fPD09Wbp06WuPRUVF4ejoKE+jf5WjoyO///67PpspCEIhYu5ujt0kOxyWOWA3yU5v\nwQhysWPsqVOn6NSpE3Xq1KFBgwbUrFmTLl268Oeff+pc2bVr15g/fz4dO3akc+fOPHr0SP5JTk6m\nR48enDlzhkWLFnHz5k0WLlzIX3/9Rc+ePQFwdXXFxcUFf39/rly5wtGjR5k9eza+vr7y2FOvXr1Y\ntWoVu3bt4vr164waNQobGxuaNWuWy1/Nf9vu3bs5ePBgQTdDEIQClpAQzu3bU7l+fSC3b08lISH8\nzSe9JZ267MLDw+nTpw+VK1dm2LBhlCpViocPH7J371769evH2rVr5buY19m9ezcZGRls3bqVrVu3\nqh0bPnw4gwYNYvHixcyePZtVq1ZRpUoVli9fLne3KRQKFi9ezOTJk/H29sbU1JROnToxePBguZxu\n3bqRkJDAjBkzSEpKws3NjeDg4EL1UGx4QgJ74uKIUamwVSppZWmJu7n+/up4GxUqVGDy5Mm4u7tT\nokSJgm6OIAgFIL/3Q9IpIC1cuJB69eqxcuVKtS62QYMG0b9/f4KCgli3bt0byxk5cuQbV4Fu1KgR\njRo1yvG4tbU1S5YseW0Zfn5++Pn5vbE9BSE8IYHgl7oco1NT5deFKSiNGTOGgIAAZsyYQWBgYEE3\nRxCEAhAXtyeH9L0Ft0Hf5cuX8fb2VgtGkHXH4u3tzaVLl/K8YR+qPXHaHyjbm0N6QSlVqhTjx48n\nNDQ0T55BEwTh/aNSac6wy0q/p5f6dApI5ubmJL+0SdPLkpKSKFKkSJ426kMWo9L+QNm9HNIL0pdf\nfkmjRo0ICAggMVFzTxRBED5sSqVtDull9VKfTgHp008/JSgoiAcPHqilP3jwgKCgIOrVq6eXxn2I\nbHMYyyqJbQ75AAAgAElEQVSbD2NcRYsWJTMzU+uxzMxMtRXTs02ZMoVnz54xa9YsfTdPEIRCxtKy\nldYtzC0tW+qlPp3GkEaNGkXHjh1p0aIFtWvXxsrKisePH3P27FnMzMzkB1uFN2tlaak2hpStZT5s\ncmhubp7jnU58fDwWFhYa6WXKlGHs2LEEBATQunVrfTdREIRC5B8c2SW1wZb/YcxDHmHNRelzjHBE\nHw/S6BSQSpcuTWhoKGvWrOHs2bNERUVhbm5O9+7d8fX1xdraWg9N+zBlT1zYGxfHPZWKskolLfNp\nlt3HH3/M+fPnNdKvXbtGcnIyNWrU0HIWdO7cmd27dzNx4kR9N1EQhEJkT1wccUrN/ZD2xsXp5TtL\n5x1jra2tGTt2bJ434L/I3dy8QGbU+fj40KFDBwICAujevTsmJiZcv36duXPn0rhxY6pXr05UVJTW\nc7///vu3Wq9QEIT3V36PeecYkJYvX46Xlxc2NjYsX778tYUoFIpCO81aeKFq1ar89NNPLF68mJ49\ne5KcnEyZMmVo3bq12rNc2pQvX55Ro0Yxbdq0fGqtIAgFzVapJFrLwtT6GvNWSJKW/cgBJycnNm/e\nTM2aNXFycnp9IQoFV69e1UsD80tUVBRNmjQhLCyM8uXLF3RzBEEQCtyrz01m62trK/fy5OV3Z453\nSNeuXdP6b0EQBOG/Ib/HvHUeQxIEQRD+e/JzzDvHgNS7d2+dC1EoFKxevTpPGiQIgiAUDgkJ4cTF\n7UGlikGptMXSspVelgzKlmNAenWjPEEQBOG/I78XVoXXBKQNGzbopUJBEASh8IuL28OjNBWRz1NJ\nzszExMCACsWMMNLTwqrwmoD06jJBb5K9q6sgCILw/otKvMO1l9YwTcrM+Pf1bez0VGeOAalhw4Ya\nq3u/zvs+7VsQBEF44UZ6CUBzqbEb6SXw0FOdOQakH374IVcBSRAEQfhwRBStT2XVFq3p+pJjQPLy\n8tJbpYIgCELhZmRWh5sS2Kb+D+PMh6QY2BBj9DkmZm/eHfxtiaWDBEEQBA2tLC0JTtVcWNVLjzsT\n5BiQFixYQP369bGxsWHBggWvLUQEpPeHj48PFStWZPr06RrHevXqhbW1NTdv3iQ+Pp6dO3dibGys\nlmf37t34+/uzbNkyHBwcaNKkidrxYsWKYWdnR+fOnenevbvc7RsSEsL48eNzbNfChQtp2VI/e6wI\ngpB7BbEzgVg6SFBTpEgRfvjhB7766iuCgoL45ptv5GPx8fFMnz6dDh064OnpKa8MvnTpUmrWrIkk\nSTx79ozDhw8TGBhIVFSU2grxRYoU4ejRo1rrLVGihH4vTBCEXMvvnQnE0kEFIL+ffs4tJycn+vXr\nx8qVK2nXrh3Vq1cHYNasWRQtWpQJEyao5S9RooS8J5aNjQ329vYULVqUmTNn0rFjR6pWrSrnFXtn\nCYKQE50CUnx8PEFBQVy4cIFnz55pzbNv3748bdiHqiCefn4bAwcOZP/+/QQEBLB582bOnj3L1q1b\nWbVqFcWLF3/j+Z06dWL+/Pns2bOHoUOH5kOLBUHIa+EnT7Ln2jVi0tOxLVqUVk5OuH/6qd7q0ykg\nTZo0ibCwMD7//HOqVaumt8b8F8TF7ckhXX9PP78NpVLJDz/8QNeuXfntt9/YsGEDnTp14vPPP9fp\nfFNTU8qXL8/169f13FJBEPQh/ORJgi9fll9Hp6fLr/UVlHQKSH/88QcTJ06kW7duemnEf4lKpbm3\nSFb6vXxrw7Zt29i9e7dGempqKl988YX8ulatWvTs2ZPJkydTunTpXO8YbG5uTmLiiwfrMjIycHV1\n1chXsmRJDh06lKuyBUHQrz3XrqE4UZqSf5bCOKEIKeYZPKkXy96i1wo2IJmYmIhN6/KIUmlLamq0\nlvSy+daGpk2bMnLkSI10bQFnxIgR/Pjjj/j5+WFmZparehITE9XGjIoUKcK2bds08hkYGOSqXEEQ\n9C/maCnK7bWRX5vEF8Fkrw33AHrpp06dAlKPHj1YvXo1bm5umJqa6qcl/xGWlq3UxpBepOfflGcz\nMzMqVaqkkV6sWLEc07Qde52UlBRu3bpFmzZt1NK11SsIQuFT+qSV9vRT2tPzgk4Bydvbm9DQUBo2\nbEjlypU1nk1RKBSsW7dOLw380GSPE8XF7UWluodSWRZLy5aFavwoL2zZsoXMzExat25d0E0RBOEt\nlEo1JlZKJE16TiaZGGCAoaIYpZ7nrqckN3Se1HDr1i2qVauW624bQZO5ufsHFYDi4+N59OgRkiSR\nkJDAsWPHWLBgAf3796dixYpqeR89eqS1DGNjY/HeEoRCRLI1gP9LBSnz35RMUKRC2QJ4MPZlhw8f\nZty4cfTq1UtvDRHeX4MGDZL/bWFhgb29PdOmTaN9+/Zq+TIyMvDw0L5OsLe3NwEBAXptpyAIuotp\n8BcmdytQhCLq6Z//BdTUS506BSRTU1McHBz00gAhf71u48W1a9dqTf/nn3+0ppcvXz7HY6/y8vIS\nC/YKwnvk6Wd/8CSlOiUPOWD8tBgpFs954nkdxWdXAR+91KlTQOratSurV6/G1dVVY/xIEARB+PDY\nFrcluskV4ppcUUsvV1x/M651CkixsbFcuHABDw8PqlatqjHTTqFQsHr1ar00UBAEQch/raq2Ivic\n5ozgllX1NyNYp4B048YNPvroI/l1Wlqa3hokCIIgFDz3clkTr/be2Mu9Z/coW7wsLau2lNP1QaeA\n9Lpxh3cREBBARkaG2lYIX331FZcuXVLL99VXX8l5YmNjmTp1KidOnMDQ0BAvLy/8/f0pWvTFpaxd\nu5Z169YRFxeHm5sb3333HXZ2dnq5BkEQhA+Vezl3vQagV+X4iPzZs2ffqsAzZ868MY8kSSxcuJBf\nf/1VI/3GjRvMmTOH48ePyz8v76MzdOhQHj9+zMaNGwkMDCQkJISgoCD5+JYtW1i0aBFjx45l8+bN\nGBkZ0bdvX1Qq1VtdjyAIgpA/cgxIU6ZMwd/fX+fFMS9evMjQoUOZMmXKa/NFRkby9ddfs2nTJsqW\nLatxLCUlBRcXF6ytreWf7OdTzp8/z9mzZwkMDMTJyYmGDRvyzTffsGHDBjngBAcH4+vrS8uWLXF0\ndGTu3LnExsaK1cgFQRAKuRwD0tatW6lYsSIdO3akXbt2BAUFcfToUW7evMm9e/e4du0aR48eZd68\neXz55ZfyTqRbt259bYXnzp3D1taWHTt2aKyPd/36dYoVK0a5cuW0nnvmzBnKlStHhQoV5LS6deuS\nlJTE1atXiY2N5fbt29StW1c+bmpqirOzs053boIgCELByXEMydDQEH9/f7p3787atWvZvHkzS5Ys\nkbekhqwutrJly9KiRQtWrFhB6dKl31hh+/btNR6YzBYREUHx4sUZPXo0p0+fpmTJknh5edGzZ08M\nDAx48OABNjY2audkv46JiZHHkV5th42NDffv339j2wRBEISC88ZJDdnbDowdO5abN28SFRXFs2fP\nKFmyJGXLlqVy5cp51pgbN26QnJyMh4cHfn5+nDt3jlmzZvHs2TOGDRtGSkoKRkZGaucYGhqiUChI\nTU0lJSUFQCOPUqkkNTU1z9opCIIg5L1cbWFub2+Pvb29vtrCzJkzSU5OxvzfPdwdHR159uwZy5cv\nZ+jQoRQrVkxjckJaWhqSJGFiYiKvSP1qHpVKJR7oBcaNG0doaGiOx8uVK5cn+xIdOnQIOzs7qlSp\n8s5lCYLw31GoNqIpWrSoHIyyOTo6kpSUxLNnzyhTpozG4pwPHz4Esu7kbG1tAc0FPB8+fKhTd+KH\nbsKECfLMxS1btgCwdOlSOe2333575zqio6MZOHAgcXFx71yWIAj/LYUqIHXu3Jnvv/9eLe3SpUvY\n2Nhgbm5O7dq1iYyMJCbmxa6rp06dwtTUFCcnJ0qVKoWdnR2nT5+WjyclJXH58mXc3QvP6trh0eFM\nPTqVgTsHMvXoVMKjw/Ol3uLFi8szFy0tLQEoUaKERtq7kCTpncsQBOG/KVdddvrWrFkzFi1ahLOz\nM25ubpw6dYrg4GAmTJgAgKurKy4uLvj7+zNp0iQeP37M7Nmz8fX1RalUAtCrVy9mzZpFpUqVqFat\nGvPmzcPGxoZmzZoV5KXJwqPD1ZbjiE6Ill/n5wNoOYmMjGT27NmcOnWKxMRESpcujY+PD76+vgCM\nHj0aY2NjDA0N2blzJ2lpaTRp0oQpU6ZgZGREkyZNgKzVu7MfaI6KipLLVKlU1K9fn3HjxsmzLBs0\naEDv3r35448/OHXqFGZmZnh7e6utIi4IwoevUN0h9e3bl5EjR7Js2TLatGlDcHAw48ePp1OnTkDW\nmnmLFy+mVKlSeHt78+2339KpUycGDx4sl9GtWzcGDBjAjBkz6NKlC2lpaQQHB8sBq6DtubFHa/re\nG3vzuSWaJEmif//+pKens2HDBnbv3k27du0IDAxUW9U7NDQUAwMDfv31V+bNm8eBAwf46aefKFq0\nqFpX4Pjx40lISKBbt24kJiayZs0a1q1bx9OnT/Hx8SExMVEuc8GCBTRr1oydO3fy9ddfs3DhQi5c\nuJDvvwNBEApOgd4hvbokkUKhwNfXV/5rXBtra2uWLFny2nL9/Pzw8/PLkzbmtZhnMVrT7z27l88t\n0ZSSksJXX31Fu3bt5On0gwcPZvny5URERODo6AhAqVKl+PbbbzEwMKBy5crUq1eP8+fPA6h1BZqZ\nmbF+/XqSkpKYP3++PD64cOFCPD092blzJ127dgWgSZMm8h8e/fv3Z8WKFVy4cAEXF5d8/R0IglBw\ndApIqamprFixgiNHjpCcnKx1nECshKAb2+K2RCdEa6SXLV5WS+78ZWJiQo8ePdi9ezcXL17kzp07\nXLt2DcjaXC9bxYoVMTB4cXNtZmbG06dPtZYZERFB1apV1SarlCpVisqVKxMRESGnvfz4gEKhwMzM\nTCz3JAj/MToFpOnTp7Nlyxbq1q1LtWrV1L6MhNwpiCXddZWYmEi3bt0AaNGiBfXq1aNGjRo0atRI\nLZ+27s+cJjO8+kxYtoyMDLUFcQtLl6ogCAVHp4C0b98+/P396d+/v77b88EriCXddXXs2DEiIiII\nDw+nePHiAPJdjK6z515eyQOgatWqhISEkJCQIN8lxcbGcufOHb7++us8bL0gCO87nQKSSqWiZk39\n7KH+X5TfS7rrqkyZMkiSxPbt22nUqBF37txhxowZgO57YGVv3vjPP/9QtWpV2rdvz4oVKxg5ciQj\nR44kMzOTmTNnYmlpScuWBX9XKAhC4aFT35uHhwfHjh3Td1uEAubm5saoUaNYsWIFrVu3Ztq0aXTo\n0AF3d3eNPapyYmFhQbdu3QgMDCQgIABjY2PWrFlDkSJF8Pb2plevXpQsWZKffvpJvgsTBEEAUEg6\n9MUcOHCAiRMn4unpiZubm7xEz8vatWunlwbml6ioKJo0aUJYWJjGKuSCIAiCdnn53alTl93QoUOB\nrOdPtK2FplAo3vuAJAiCILyQEJ5A3J44VDEqlLZKLFtZYu5u/uYT34FOASksLEyvjRAEQRAKj4Tw\nBGKCXzwzmRqdKr/WZ1DSKSC9vGFecnIySUlJWFhYYGhoqLeGCYIgCAUjbo/2xZHj9sYVfECCrEVM\n58yZw5UrV+QpwDVr1mTEiBHUq1dPbw0UBEEQ8pcqRvtD6ap7+n1YXadZduHh4fTp04fnz58zbNgw\npk6dypAhQ0hOTqZfv35ie3BBEIQPiNJW+4PqyrL6fYBdpzukhQsXUq9ePVauXKn24OOgQYPo378/\nQUFBrFu3Tm+NFARBEPKPZStL/pp+hKfJd8hUpGIgGWFhUolafRvptV6d7pAuX76Mt7e3xlP4CoUC\nb29vnZ9REQRBEAq/v9N+47bHJlRWj8BAQmX1iNsem/g77d038Xwdne6QzM3NSU5O1nosKSmJIkWK\n5GmjBEEQhIJz7cEOIrDhMnbEU4oSxOLMAzIe7ORTeuutXp3ukD799FOCgoJ48OCBWvqDBw8ICgoS\nkxoEQRA+IBE3bTh+oA1PY62QMhU8jbXi+IE2RNy01mu9Ot0hjRo1io4dO9KiRQtq166NlZUVjx8/\n5uzZs5iZmTFmzBi9NlIQBEHIP3+fbaQ1/WoO6XlFpzuk0qVLExoaSrdu3Xj27BkXLlwgISGB7t27\nExoaSoUKFfTaSCFveHp64ujoKP/UqFGDtm3b8ttvL/qFHR0d+f3339+6jpCQED766KO8aK4gCAVE\n8TyHjTFzSs8jOj+HZG1tzdixY/XZFiEf9OvXj549ewJZO8QeP36cgIAArKysaNSoEcePH1fbTE8Q\nhP8eF9fqRIelUybqAWaqTBKVBtwvX5ryHtX1Wm+OAWn58uV4eXlhY2PD8uXLX1uIQqEotFuGF0bh\n4bBnD8TEgK0ttGoF7vm0G4WJiQnW1i/6gbt3705YWBjbtm2jUaNGascEQfhval4pgcsPlaCsAEoo\nCVR4CM4VE4ACWKlhwYIF1K9fHxsbGxYsWPDaQkRA0l14OAS/tGFsdPSL1/kVlF5lbGwsT+l3dHRk\n1qxZtG/fnnHjxvH8+XNiY2P5+++/5bHEefPmsX//fh49eoSZmRmNGzeWt5rI9tNPP7Fs2TKSkpJo\n2LAhAQEBWFpaAhAfH09gYCCHDh1CkiRq1arF+PHjqVKlCgDjxo3DwMAAExMTduzYgUqlwtPTkylT\npmBmZpb/vyBB+I8pcyeO9OoQGQnJSWBiChUqQJm7cRRIQLp27ZrWfwvvZs8e7el79+Z/QJIkiT//\n/JMTJ06wePFirXn27NnDhAkTmDx5Mubm5sycOZPjx48ze/ZsypQpw8WLFxk3bhyOjo706tULyNqe\nfOvWrSxdupT09HQmTZrE+PHjWbFiBZmZmfTv3x8zMzOCg4MxNjZmw4YNdO/enT179lCyZEkAtm/f\nTqdOnfjll1+4e/cuI0aMwN7enkGDBuXXr0cQ/rNUMSqsreHVDhN9Lx2k0xjS4sWL6dSpE6VLl9Y4\nFh0dzY8//sjEiRPzvHEfopgY7en37uVP/UuXLmXVqlVA1k7A6enpNGvWDPccoqG1tbXaVuO1atWi\nTZs21K5dG4Dy5cvz888/c/36dbXzZs+ejb29PQDfffcdPj4+3Llzh+joaC5dusTp06flu50pU6Zw\n8uRJNm/eLN9pW1hYMHHiRIoUKULlypWpX78+Fy5cyNtfhiAIWiltlaRGp2qmF4alg5YsWUKDBg20\nBqQLFy7w66+/ioCkI1vbrG66V5Utmz/1e3t70717dyArIEVERDB79mwGDx4sB6qXvbrhVvv27Tl+\n/DizZs3i9u3b3Lhxg7t376rlK1GihByMAJydnQGIiIjg9u3bZGRk8Pnnn6uVm5qays2bN+XXFStW\nVHvgunjx4hrPwQmCoB+WrSzVtp+Q01ta6rXeHANSt27d5L9IJUmiS5cuORZSo0aNvG/ZB6pVK/Ux\npGwtW+ZP/SVKlKBSpUry62rVqpGens6YMWOIiIjQyP/q7sATJkwgLCyMDh060Lx5c/z9/Zk6dapa\nHgMD9acJsleHNzQ0xNDQEAsLCzZv3qxRl4mJifxvpVLzLzEdNjcWBCEPZG8xEbc3DtU9FcqySixb\nFuAGfd9//z379+9HkiQWLVpE586dKVOmjFqeIkWKULx4cZo2barXRn5IsnvG9u7N6qYrWzYrGBXU\nhAZ48UWfmZn52nxPnjzht99+IygoiObNmwOQnp5OZGQkZV+6xXv69CkxMTHY2toCcO7cORQKBVWr\nVsXQ0JCnT58CyIExIyOD0aNH06xZM1q3bp3n1ycIQu6Zu5vrPQC9KseAZG9vz8CBA4GsL6qcxpCE\n3HN3L7gAlJyczKNHj4Cs/683b94kKCiI6tWr4+Dg8NpzzczMMDMzIywsDCcnJxITE1mxYgUxMTGo\nVC8GOxUKBf7+/kyYMIHk5GSmTp1Ku3btKFeuHGXLlsXFxYURI0YwYcIESpUqxcqVKzl06BCDBw/W\n67ULglC46TSGNGTIECDrL+S0tDT5L2pJkkhOTubs2bN06tRJf60U8syqVavksaIiRYpgaWlJ/fr1\nGTVqlMZq7q8yNDRkwYIFzJw5k7Zt22JpaUmDBg3o3bs3Bw8elPNZW1vTrFkz+vbtS3p6Oq1ateLb\nb78FsoLVkiVLmDlzJoMGDUKlUlG9enVWr15N1apV9XfhgiAUegpJh475f/75h9GjR3Pjxg3thSgU\n/P3333neuPwUFRVFkyZNCAsL0xjIFwRBELTLy+9One6QZs2axdOnTxk7diyHDx9GqVTSuHFjjh07\nxrFjx1i/fv07NUIQBEEQdFpc9cKFCwwfPpxevXrRunVrUlJS6N69O8uXL6dp06Zs2LBB3+0UBEEQ\nPnA6BSSVSoWdnR0AdnZ2ais3eHl5iQcWBUEQhHemU0AqW7YsUVFRQFZASkxMJPrfpzuNjIyIj4/X\nXwsFQRCE/wSdAlLTpk2ZM2cOBw4coHTp0lSpUoWFCxdy8+ZN1q5dK/ZDEgRBEN6ZTgFpyJAhuLi4\nyE/Xjx8/nn379tG2bVtOnDjB0KFD9dpIQRAE4cOn0yw7Y2NjFi9eLD/8+Pnnn7Njxw6uXLnCxx9/\nTMWKFd+q8oCAADIyMpg+fbqclr2S9K1bt6hUqRKjR4+mYcOG8vHY2FimTp3KiRMnMDQ0xMvLC39/\nf4oWfXEpa9euZd26dcTFxeHm5sZ3330nj4EJgiAIhZNOd0jZXl5frGLFirRq1eqtgpEkSSxcuJBf\nf/1VLf3GjRsMHDiQli1bEhoaSpMmTRg8eLDaGmtDhw7l8ePHbNy4kcDAQEJCQggKCpKPb9myhUWL\nFjF27Fg2b96MkZERffv2VVtJQBAEQchBeDhMnQoDB2b9Nzw836rO8Q6pefPmb3xy/2X79u3TKV9k\nZCTffvstERERauufAaxfvx4XFxd5yaIRI0Zw9uxZ1q9fz7Rp0zh//jxnz57l4MGDVKhQAScnJ775\n5humTZvG4MGDUSqVBAcH4+vrS8t/VyudO3cuHh4e7Nu3j3bt2ul8PYIgCP85BbyDaI53SG5ubrn6\n0dW5c+ewtbVlx44dGk/1njlzhrp166qlffLJJ5w5c0Y+Xq5cObVJFHXr1iUpKYmrV68SGxvL7du3\n1cowNTXF2dlZLuO/zNPTE0dHR37++Wetx/v27YujoyO///57rsrT9tO2bdu8bLqa33//HUdHx3cq\n4/Tp03zxxRe4urrSp0+fXG9tcebMGRwdHeXZp4LwQdizh3BLS6Z+/DED69Rh6scfE25pmbUadD7I\n8Q4pMDBQLxW2b9+e9u3baz12//59jQVcbWxsuH//PgAPHjzAxsZG4zhATEyMPI70ujL+6wwNDdm3\nb5+8J1K2p0+fcvLkyVyX169fP3r27KmR/vKYXmGTkJDAoEGD6NmzJ61bt2bMmDFMnz6dRYsWFXTT\nBKFAhaemEvzSXmbRJiZZr2/dIj/Wg9bpW+PcuXNvzJObu6ScPH/+XGMfHKVSSWpq1s6FKSkpGBkZ\nqR03NDREoVCQmppKSkoKgEael8soDBLCE4jbE4cqRoXSVollK/3vM5Lt008/5Y8//iAuLg5Lyxeb\nbR04cIBatWrl+k7SxMQE61f3OS7koqKiePbsGc2aNcPe3p769etz9OjRgm6WIBS4PdWq8TDCgsjL\nFUiON8GkRDIVnCPZW61ovgQknSY1dO/eHW9v79f+5AUjIyPS0tLU0lQqFcbGxkDWZnGvTk7IXn3c\nxMRE3kzu1Twvl1HQEsITiAmOITU6FSlTIjU6lZjgGBLCE/KlfldXV6ysrNRW5wbYs2eP1r2Ijh49\nSqdOnahVqxaenp4Ea9td8DV8fHwYN26cRl21atUiMTERgM2bN9OiRQtq1qxJu3btCA0NVcv/559/\n4uXlRc2aNenSpYtaN9natWupW7eu2v/zpKQkXFxcNK4xW9WqVbGxsWH+/Pn8888/bNu27Z3HF9PT\n01m1ahXNmzenRo0atGvXjt27d8vHg4KC6NOnD0uWLMHDw4OaNWvSv39/ta7CmJgYhg0bhpubG/Xr\n18ff31/t+IULF+jatSsuLi588sknjBkzRt5bShDywl9pLlw77kjSUxMkCZKemnDtuCMX0lzypX6d\nAtL69etZt26d2s+yZcvo06cPVlZWbNq0KU8aY2try8OHD9XSHj58KHfBlSlTRt7L5+XjkNVNl70h\nnLY8hWUvp7g9cdrT92pPz2sKhYLmzZurTUKJi4sjPDycFi1aqOU9f/48AwYM4LPPPmPbtm2MHz+e\nJUuWaN3tNSdffvklBw4cULtD3bFjB02bNsXMzIyff/6Z+fPn4+/vz86dO+nbty/Tp0+Xg9KdO3fo\n378/bm5ubNu2ja5du6pttd6uXTuSkpLU7nD279+PsbGx2uMCL1MqlUycOJEjR47QsWNHevToQf/+\n/XW+Jm0CAwNZvXo1I0eOZPv27bRp04aRI0eq/Z5PnTrFP//8w48//siaNWv4+++/5W7C5ORkfHx8\nMDIy4pdffmH16tWkpaXRs2dPVCoVGRkZDBw4kHr16rFz505WrlzJpUuXmDlz5ju1WxBe9uRqJbCw\ngKKGgCLrvxYWPL1a6Y3n5gWduuxenWiQrVGjRpiYmLBs2TJWrFjxzo2pXbs24a9MMTx16hR16tSR\nj8+ZM0dtN9JTp05hamqKk5MTSqUSOzs7Tp8+LZ+TlJTE5cuX6dq16zu3Ly+oYrRPP1fdy79p6S1b\ntqRXr17Ex8dTokQJ9u/fj5ubG1ZWVmr5NmzYQJ06dRgxYgQAlStX5rvvvqNIkSJynqVLl6oFiGzj\nxo2jS5cutGjRgmnTpnH06FGaN29OfHw8x44dY9myZQAsX76cIUOGyLMiK1asyL1791i+fDkdOnRg\n8+bN2Nra8u2332JgYECVKlWIiIhg9erVAJQqVYoGDRqwfft2mjVrBmRNemjbti2GhoZar//gwYME\nBJp2tR4AACAASURBVATg4ODA9evXqVKlCgCJiYmYmZnl+veZmJjIpk2bCAgIkK9jwIABXLt2jZUr\nV8qBXpIkfvjhB7mO1q1bc+LECQB27dpFSkoKgYGB8u933rx5fPLJJ+zfvx8PDw+ePHmClZUV5cqV\no3z58ixZskSjR0EQ3kXJeFNiiimgmHqPkkW8Sb7U/84jz3Xq1NH6hfQ2evToQceOHVm0aBFt2rRh\n586d/PXXX0yePBnI6m5ycXHB39+fSZMm8fjxY2bPno2vr6889tSrVy9mzZpFpUqVqFatGvPmzcPG\nxkb+sipoSlslqdGa41nKskotufWjdu3alCxZkrCwMLy8vHLsrrt+/ToNGjRQS/vyyy/VXnt7e2tM\nkADk8SkzMzOaNWvGzp07ad68OXv37sXCwoL69esTFxfHgwcPmDlzJnPmzJHPTU9PJyMjA5VKRURE\nBNWrV8fA4MXNvIuLeveBl5cXI0eOJCEhgZSUFE6dOsU333yj9dovX77MsGHDGDVqFH369GHUqFGM\nGzcOOzs7fHx86NmzJ4MGDXrDb1Dd//3f/5Geno6rq6tauru7O4cOHZJfW1lZqQW84sWLywHl77//\nJi4uTv5DKltKSgo3b96kbdu2+Pr6MnXqVIKCgvjss89o3Lixxl2tILyLWpWUSLcgMjWVpMwMTA2K\nUMHICBe7/Pl+eueAdPjwYUxNTfOiLTg6OrJ48WJmz57NqlWrqFKlCsuXL8f+31kfCoWCxYsXM3ny\nZLy9vTE1NaVTp05qW19369aNhIQEZsyYQVJSEm5ubgQHB2tMligolq0siQmO0Uxvaaklt34oFApa\ntGjBvn37aNSoEefOnWP+/Pka+XSZKVeiRAkqVXr97XyHDh0YMGAAiYmJ7Ny5ky+++IIiRYrIdzCT\nJk3SehdetGhRFAoFr+4h+eqdT6NGjTA1NWXfvn3Ex8dTrVo1PvroI61t2bFjB3Z2dvTp0weA6dOn\n0717d3r06EFCQgKenp5az4uJieH58+dUrlxZo42vTqLJlpGRofY71PYezL42Q0NDqlatyuLFizXy\nFC9eHICxY8fi7e3N0aNHOX78OOPHj2fz5s1iPzIhz7RqBfcCYnC8FY1xchopJoY8qVyOloMKUZdd\n7969NdIyMjK4f/8+d+/epV+/fm9VubZ9lBo1akSjRo1yPMfa2polS5a8tlw/Pz/8/Pzeqk36lj2b\nLm5vHKp7KpRllVi2zL9ZdtlatmyJr68v27Zto27dumoz7rLZ29tz+fJltbT58+cTERHB0qVLda7r\n008/pWTJkmzdupUzZ84wadIkIOuLtnTp0kRFRdGpUyc5/6ZNm7h69SpTp07FycmJHTt2kJ6eLn+5\nv9omQ0ND2rZty8GDB4mPj6dDhw45tsXY2JiEhATS0tIwNDSkWLFizJo1izZt2lC+fPkct1GfMWMG\n6enp8nXHx8djYGBAiRIlsLCwwNDQkHPnzuHg4CCfc/bsWZ23Za9WrRpbtmzBwsKCEv/f3p2HN1Xl\nDRz/3jRNV7qvQNkpVSp0BUoRURSpyCIqLiCCCiqMgAuCsry4jKIgqyACiiDjPsCICjPvi4pTFGhL\nBynTAkWBUlK6pG26Jk1y3j9CA7UtBGxDC+fzPHkg59zce06T3F/uuWfx9gasTYEvvPACEyZMoG3b\ntnzwwQe8/PLLto5E3333Hc8++yxFRUX4+/vbdRxJuhhz/l56lpygwuxLjXDB21xG25JfMOdrgX7N\nfny7OjXU1NTUewgh6Nq1K6+++qrtHoNkH694LzrN60T4e+F0mtfJ4cEIrN30vb29effddxtsrgPr\nD5GUlBRWr17NyZMn+ec//8mmTZvqXEVUVlZSUFDQ4KP2179KpWLkyJEsX76cG264oc5J++mnn+aj\njz7i888/59SpU2zfvp2FCxfaupI/+OCDlJSUMH/+fI4fP853333X4A+Z0aNH8/PPP5ORkcGIESMa\nrfe9995LWVkZc+bM4fjx46SkpPDSSy8RHh5OUVERL7zwQoNDBGq7yycnJ9tmuY+Pj8fNzQ1XV1cm\nTpzIsmXL2LlzJydOnGDt2rX861//YuLEiXa9H8OHD8fX15cZM2Zw6NAhjh49yvPPP8/Bgwfp3r07\nvr6+7NixgwULFnD8+HGOHz/Ojh076NChA76+vnYdQ5IuJevvWbh5lxPQNYfQntkEdM3BzbucrC1Z\nl35xE7DrCkmuCHvtUalU3HnnnXz++eeN3l/r2bMnK1euZMWKFaxevZqQkBCeffZZ7rvvPts269at\na/Qe4i+//GK78ho1ahTvv/9+vUHRDz30EEajkQ8++IDXXnuN4OBgpkyZYuv1FhoaykcffcQbb7zB\nPffcQ6dOnZg0aVKde04AN954I506daJdu3YXvVoICwvjww8/5O2332bkyJF4e3uTlJTEjBkzyMjI\n4I033qCkpKRer8wxY8aQk5PD7NmzKS8vp0+fPrzyyiu2/GnTpqFSqXjjjTcoLi6ma9euLFmyhKSk\npEbLciFXV1c2bNjAwoULefTRR1EUhaioKDZu3Girz7p161i0aBFjxozBYrHQp08f1q5dW+f+miT9\nGaY8U8Pp2obTm5oi/thAfxG7d+8mLS2N0tJSAgIC6NevH/EOmN/IEU6fPs3gwYPZtWtXvSmNpJbP\nZDIxaNAg5s+fz5AhQ654P0KIy5rDUZKuJR899hGmM/WDj7qdmgkfTGjwNU157rTrCqm4uJhJkyaR\nkZGBRqPBz8+PoqIiVq9eTWJiIqtWrWr0xq4kNSej0cj333/Pv//9bzQaDbfeeuuf2p8MRtL1LOLe\nCDJWZtRPHx3hkOPbFZBef/11Tp8+zZo1a+p0ONi1axdz5sxh8eLFzJkzp7nKKEmNcnZ25rXXXkOj\n0bBo0aJGxx5JknRp/YZZOy5kbcnCpDWhDlUTMTrClt7c7ApIP/30Ey+//HK93m+DBw9Gp9OxdOlS\nGZCkq0JRFNvgUkmS/rx+w/o5LAD9kV0BycnJyTYW4o8CAwPlaHFJkqRrgF6fgk63A6NRi0YTip9f\nEl5ejusnYPfkqkuXLq23Zkx5eTlr165l3LhxzVI4SZIkyTH0+hS02vUYDLkIYcFgyEWrXY9e3wJW\njL1Qfn4++fn53HHHHcTGxhIUFERJSQkHDhygoqICjUZjGzyrKIptnjFJkiSpddDpdlCQf5ackhIq\nLQJ3lUKYjw8uLjsddpVkV0A6efIkERHWXhYmk4kzZ84A2NLMZjNms7mZiihJkiQ1t9M5/yFLV2x7\nXmER556n06mTY8ogB8ZKkiRJZBcKfj8eQcaBvpQW++PtW0RkzD7UXQsY4KAyXNbkqtnZ2ezfv5/y\n8nJ8fX2JjY21Td0vSZIktV67f72D334+P7C1pCiA5P8dxpmK00xofHrIJmVXQLJYLMyfP5+///3v\ndWZeVhSFkSNH8uabb8oBhZIkSa3Yyf8koK+pwV1djJNiwCxcqDT5cuqg42ausSsgrV27lm3btvH8\n888zfPhwAgICKCgoYPv27axYsYKuXbte8YzfkiRJ0tXnq7RFa9ZRba47xMcHxy2NY1dA+uqrr3jq\nqad44oknbGkhISFMmjQJg8HAV199JQOSJElSK9Y7KhhxAHJKSqgQFjwUFWE+PkRFB1/6xU3ErnFI\nBQUFxMbGNpgXExODVlt/wTlJkiSp9UhKgh6KG4+Uu/BsgROPlLvQQ3Fj6FDHlcGugBQWFkZ6enqD\neenp6ba1ayRJkqTWqQd6hilaAhUDKgSBioFhipYe6B1WBrua7O677z6WLFmCu7s7d911FwEBARQW\nFvLtt9/y/vvvt9jVWSVJkiT76HboCAyEP15f6HbqHLaIqF0B6ZFHHiEzM5OFCxfy1ltv2dKFEIwY\nMYKnn3662QooSZIkNb/TB43knITKSnB3h7AO1uBkPGN0WBnsnlz1rbfe4oknniA1NZXS0lK8vLyI\nj4+ne/fuzV1GSZIkqRmlpMCBkxrcKwwAVFRAVqY1r320xmHluKyBsaGhoYSFheHt7Y2fnx9hYWHN\nVS5JkiTJQXbsgKo2Cl1PFoLJBGo1eHqQk+NGr5daWLdvi8XCokWL2Lx5MyaTyTY41s3NjaeffprJ\nkyc3ayElSZKk5qM9mI8l7yR4CEIrwM1UQ1V5Kb938uUhB90/AjsD0sqVK9m0aRPjx4/nzjvvxN/f\nn8LCQnbu3MmKFSvw8PBg7NixzV1WSZIkqRmEFv+XXFTo3BR0bgDWmXfaq34HOjqsHHYPjJ0yZQpT\np061pYWFhREdHY2HhwcbN26UAUmSJKmVSvLdy3pt/3rpQ332AoMcVg67xiGVl5fTq1evBvNiY2PJ\nz89v0kJJkiRJjhPf28gTEcm09yxGpQjaexbzREQy8VGOXQ3criukQYMG8dlnn3HzzTfXy/v2228Z\nOHBgkxdMkiRJcpCkJHqkbyFQnMRIPhpRhR9lMHS0Q4thV0CKi4tj2bJlDB8+nGHDhhEYGEhJSQk/\n/vgjaWlpTJgwgTVr1gDWGcDlQFlJkqTWQ08PfjX2J4ejVGr0uONGmLE/veiB47o02BmQXnvtNQDK\nyspYtmxZvfwPP/zQ9n8ZkCRJklqHlBRrl2/NlhxEhQueAe1wCyinAsgyn0X54hCJ8YkOK49dASkr\nK6u5yyFJkiQ5UEoKrF9v/X/HkhLMZg0lp0OAPNy8ywE4dfQUiTguINnVqUGSJEm6tuzYARTkQ1oa\nRdXFUF0NZjMVhb62bQrbFDq0TDIgSZIkXYe0B/MhMwsqKvjN0wwWCxgM1FQ42bYx3WxyaJkua+og\nSZIk6doQWvxfqqoUupQI2hjaYBEWjCoLelUllf6VaGO1jL67BfaykyRJkq4tQ8QhjhXdhJcRQIUJ\ncLKA2a0Q/UAzo+8eTXy7eIeWqcU12WVnZ9OjR496j9TUVACSk5MZOXIkvXr1Yvjw4ezevbvO64uK\nipg+fTpxcXEkJCSwaNEiTCbHXnZKkiS1dCFKGzqqy1CrzAC4qgQhzkZ6mwO5J/8ehwcjuMgV0tmz\nZy9rR8HBTbPu+tGjR/H19WX79u110n18fMjOzubpp59mypQpDBkyhO3btzN16lS2bt1qWwbjmWee\nQVEUNm/ezNmzZ5k9ezZqtZpnn322SconSZJ0LTD6dsOVIlxdy+ukWzQ+Dl0D6UKNBqRbbrkFRVHs\n3lFmZmaTFOjo0aN069atwWXRN23aRFRUlG1BwBkzZpCWlsamTZt47bXXSE9PJy0tjf/7v/8jLCyM\niIgIXnzxRV577TWmTp2KRuO4dT0kSZKuutqBRlothIZCUhIpZjM7srLwNbWhUxs3vMpqcKuutm7v\n6orKTUHT9uqcKxsNSG+88YYtIJWWlrJ48WISEhJISkqyzdTw/fff8+OPPzJ79uwmK9CxY8fo0qVL\ng3mpqakkJSXVSevbty/ffvutLb9du3Z11mnq06cPFRUVZGZm0rt37yYrpyRJUot24UAjgNxcUj74\ngPU9e4KbG1WRlfj87oSlyhlcXXE7t5lr1Un8OmiATg4vcqMBafTo870rpk6dyqhRo3j99dfrbDN8\n+HBef/11duzYwQMPPNAkBTp27BgGg4ExY8aQm5tL9+7dee655+jVqxd5eXn1mgaDgoLIy8sDrM2M\nQUFB9fIBtFqtDEiSJF0/duyon+Tra10O1s0NXWcD/725mC77A1DluuNpMuPpryM04je8Tp0A+jm8\nyHb1stuzZw+rVq1qMO/WW2/lyy+/bJLCVFdXk5OTg5+fHy+++CIajYbNmzczbtw4tm7dSnV1db1m\nN41Gg8FgXXa3qqoKFxeXOvnOzs4oimLbRpIk6bqg1dZPcnMj33iCHP0vVFpKcQ9WETY8nBDa8l5u\n7vkNz5Q4sKDn2RWQfH19+fXXX0lMrD+FxP79+5usQ4OrqyspKSloNBpb4Fm4cCGHDx/mk08+wcXF\nhZqautOhG41G3NzcbK83GuvejKupqUEIgbu7e5OUUZIkqUWrvW+UmgpCQIcOcO6evKX6N7LcMsHs\nCkCFUk6WJY1gQzVwwY/5tm2vQsHtDEj3338/q1atorq6msGDB+Pr60tRURE7d+7k448/5uWXX26y\nAnl6etZ5rlKp6NatG1qtltDQ0HprL+Xn59sCYkhISL1u4LXbN1XQlCRJarEuvG/Uvj1kZZFywIkd\n7oPQVvmS5pdFVYwZtw5HwNnZ+jAYwXgYiDm/n6FDr0rx7QpITz/9NGVlZXzwwQesXbvWlu7i4sL0\n6dObbLXYjIwMxo8fz6ZNm4iMjATAbDaTlZXF0KFD8ff3JyUlpc5r9u3bR1xcHGBdLHDx4sW24FWb\n7+HhQURERJOUUZIkqcW68L5RUBAbTw5i5ak7qDRpcFcbKVIpGH/sSUWbUkxO4O5TQvhNB1C8U6FC\nZb0yGjoU4h0/BgnsDEiKojBr1iymTJlCeno6er0eX19foqOjm7QpLCIignbt2jF//nz+53/+B3d3\nd9atW0dxcTHjx4+nsLCQe++9lxUrVjBs2DC++eYbDh48yIIFCwCIjo4mKiqKZ599lnnz5lFYWMii\nRYuYOHGi7PItSdK174L7RhuP9OOlI6OoMmlQW4x4qswUF3pjRuBaVkxI8H+h2I+8/z5Ij3ti4H+e\nuIoFt7qsqYPatGnTrKvDqtVq1q9fz9tvv81TTz1FVVUVMTExbN68GX9/f/z9/Xn33XdZtGgR69at\no0uXLqxZs4auXbsC1sD57rvvsmDBAsaOHYuHhwf3338/U6dObbYyS5IktRihodbu3fkdWXn4VqpM\n1h/iJuFEiVGDGVdMTgZM6nPjjmpnscm+Ok10f9RoQBoyZMhlDYz95z//2SQFCg4O5p133mk0f9Cg\nQQwaNKjR/MDAwEZ7BEqSJF1T/jjwtWNHfvitjDkZd3Ck0hcjKhSVBSe1gkpYqDFqcAbcnY0oKHio\n3QkLiEApD7rkoRyh0YAUExNzWQFJkiRJcqAGBr7+8FsZa/IGcqYqAEVtRmUxYzI5ozibQGVGqCyo\nNQYig/Joq/JG0yEaPIKuVqe6ehoNSAsXLrT9/9tvvyUhIQE/Pz+HFEqSJEm6hAYGvm7P7wo1Nai8\nBK7mSiwWJ1BAWFRYUFBUFtTORnLLQ7C019PeGzRctU519dh1D2nu3LksXLiQO++8s7nLI0mSJF1M\nbTPd55+Dm1udcUbaSh8C9TCmUotzuQaL+SxmkxqzxYlStYrcjsVUhFZSWNid38/4ENj+FFOmBF2t\nTnX12BWQgoODqaqqau6ySJIkSRdzYTOdm5t1GqDMTPRBxehuLKPzb5GEFnSmRl2JxqUavzJnhFCR\nq9bQ0bOMW8+aKS8XFPue5FRncAosbTHBCOwMSA899BBvvPEGBw8eJCIiosGu3sOHD2/ywkmSJEkX\nuLCZLiwMsrLQd6xC2ykD3ANIMJVxQqWgFjX4mZzRaKxTpnU0G3AyWFBQ8KpUY3QV3PAbHFO3rAkD\n7ApIb775JgCffvppg/mKosiAJEmS1FwaaqY7N3G0LmK/tfu2hyfB3p6ouhWi1XrhotOgqEHjVo2q\n2I0qFBRFhbPl/LqsN1W6NXbEq8KugLRr167mLockSZLUkEaa6QAICsLYxRvj2T4YfrmVmuPt8Bbg\n164ci5PA2dQe8KKyyohRqBDCRI2TBZXijMrJgx4BrletWg2xKyC1a9fO9v/KykoqKirw8fHB2dm5\n2QomSZJ03UtJgVmzIC8P3N2hTRtrQALIySGlRw+O5ffDY38UarUzHkHlqE/4YP7NC6dAAaXWTd1D\nNShVUF6upsLTHR9fZ8LCoH1Uy5rBxu6ZGvbt28fixYs5fPgwQggAevXqxYwZM0hISGi2AkqSJLUm\nKXv3siMrC63JRGhlJUlaLfFHj0JxMfj6QkCAdUOVCiyW8/8/t6IrYG2eO3gQTp4EnQ5cXKyBqKIC\nQkKgvJyUgADW9+pF/P9psOgr0Z0NwFitIVAx01Yx4F3jjSHWQI4+B3OhGR+LDz4RPnTr4G0rq9/Q\nljWUx66AlJKSwuOPP07nzp2ZNm0a/v7+5Ofns3PnTiZNmsRHH31km+BUkiTpepWydy/rMzKsT6qq\nyC0tZb1GA8XFxGu18NtvoCjg6moNLOcWF+WGG6zB6Y03rPmBgdZgVFEBZWXWZSRczzWvlZdDTAw7\n+veHmBgqN5STf0qgFpUomCjAlWp1EG2DDXzzwIe2svkd8yM0LZSYqhjad2+P31A/vOK9HPwXuji7\nAtLy5ctJSEhg7dq1dWZvmDJlCpMnT2blypVs3Lix2QopSZLUGuzIyjr/pLzc+q/JxM7wcGtAqm1u\nc3WFo0fB61xAyMqCU6esQUijgb59obLSmufhYd1XbUA6tw/tuTk8tXo33BUzZuX8ekY+Kg2pZ4vr\nlE3XXYeuu45Sr1Lm3TKvaSveRFSX3sS6LMTYsWPrTSWkKApjx47l0KFDzVI4SZKk1kRbO1kpnJ+4\n1GLhjI/P+bTa9NqAU1VlnYuuosKaV1l5vtMCWDsyeHpaH4qCPsaDE+PhZrc1xO39hDYFFXQrLKdD\ncSWeBhPO587T+10aPr2fKTvTlFVuUnZdIXl5eVFZ+8f7g4qKCpycnJq0UJIkSa1RqFpN+jEfcjLC\nqMyLwd1DT1jH/xJcWsqrhVPQVnsSqjpLUlUa8e5664sqKkB97lSsbuSUHBAAMTHo/fLRDlMgAMLS\nQzi5oRsmvZmTJlcCjCaCjAZ07Vw4HhGKwa/hwNO2TQuZuK4BdgWkfv36sXLlSmJjY+usvHr27FlW\nrlwpOzVIkiQBHS2xfJpcG1zMVJS1If2XQXQuKkKYzoDaTC4dWF/aGbr4E1+523pVVHsF5eFhvYdU\nKyICTp9GH+eJrt8xijrnYTreA+XTzlTv7Ila1wZftZGzKlfK1J44KwouTq7ogrx4dEQwP1vql3Fo\ntxYycV0D7ApIzz//PPfeey933nknsbGxBAQEUFhYSFpaGp6ensycObO5yylJktTinTx9Ezf4niWn\npIQKNXjgglLqRblJA+6l1vtDbtZ7QTud7iL+FiAtzXqV5OFh7dwgBJw+bW2eGxiMNg5KXY6gUrlj\n/DWEok23k3c2BM/TvgCEqC04e5RTItyoMYGz3sgTT0B8/I3cmPsEO7N3cqbsDG3btGVot6HEt2tB\ncwX9gd1z2W3dupUPP/yQtLQ0Tp8+jZeXFw8//DATJ04k8NzEfpIkSdczrRYCg4MJvKAl6d/FUAFw\nc7c6255RAe+NqL+MBEBQEPqJ/dH6/kxZWQ7ZX99K4XcD8T/ij8nkgsmjhmpUuAioqVHhbbCgPtcS\nV9VGY5ufLr5dfIsOQH/UaEDav38/0dHRtsGvgYGBzJo1y2EFkyRJam3OLdhah7t73VY4ozEfgyGH\nwMBcvvoqg59+iiQrawLlBS4EWAz4+9ZgCALj4nwCCpPoeuR+2ha54u0EmhoBioJ3qYZSJ3CxDglF\nMZ4/lZtiWtbYosvRaEAaP348bm5uxMfHk5iYSP/+/enevbsjyyZJktSqJCXVvdgxGvPx9y/CbC6l\nqKgAIUCIGpycPAkM/J2//a0rxcVunMppj6KoOVmtoktRFbFHyuhsAa8qJ9QmBVQCZ5NAYwGhgEkF\nrgLyNC74mSyAikpPF7Tt/Rj9eMsaW3Q5Gg1I7777LmlpaaSlpbFo0SLMZjMBAQH079/f9pBNdZIk\nSefVNpXt3AknTuTj5fULQ4YkIzIrKfzuZihyB/9qAu7axY+nIgguVtPlsBfDKs/gabE2v7ljodTF\nCU+jBhdMeFnMVAgnzE5QjQpXYcGkOOGCCudAT/LKYX9gKNEjvBg9lBa1nMTlajQg3X777dx+++0A\nVFVV8Z///Ie0tDRSUlJYsGAB1dXVdOvWzXb1NHDgQIcVWpIkqaWKj7c+TpxYg8GQS8nefGoOxdAh\n7BjmdpWACqdDIfifDKFtsRvGCkFojQkUFR4WI9U44V5jRmUGixOYFQVXIagATE5QZXbCqHJG5aRC\nBLhQGuXHSy97tepAVMuuTg1ubm4kJCTYunebTCZSUlL4/PPP2bx5Mxs3biTzwoFckiRJ1yl9ih7d\nDh35mW1RBfpgzGlP7S0kBRUCa1/s3nkaClwgQNTAuS2chMBVMVOBExrFQrWiYFAJ3M0WUNSoFBUG\ntZo8zzacjAyl7W2t/6roQnZPrmowGNi3bx+//PIL+/bt48iRIyiKwk033URiYmJzllGSJKnFqQ08\nRq0RTagGvyRrZ4Jfl/9Kjj6HkopCXIsE7Y50w7VzHirfclDUIKwzNfgpJgpwxk1Vg+nctD8WlYLT\nucmrhVqAUGFSOVGpUTArzqhNFmo6t2HQrFD6Pdp67xU15qIB6ejRoyQnJ5OcnExaWhoGg4EOHTqQ\nmJjIlClT6NevH56eno4qqyRJUougT9GjXa+1PTfkGtCu11JQUUBWoXU+O5WTB5WmEkpU1Xif8cHD\ntxyVokbl5IVF1ODRvpJuXiaqKzWoys1YLCosahXOFgtuLjXUOAkM7tCm2pkqL0/MnT3pPt7vmgxE\ntRoNSAMHDqSgoAAvLy/69u3Lyy+/TGJiIu3bt3dk+SRJkloc3Q5dw+lpOuho/b+Tyg3UUBFQjos2\ngDZO7qgUF9TO/ri6hOE/siv6n/UYPY1UZVXZ9uEc4oy53IxrB1c8ozxb5KzczaXRgJSfn4+vry/3\n3Xcf/fv3Jy4uTi7IJ0mSBBi1xgbTa0w1dZ47qdww+0NBQAW9e9+L8YwRTVuNLch43OiBbqcORaVg\nKjGh9lFfd0HoQo0GpA0bNpCcnMxPP/3E+vXrcXV1tY1JGjBgAF3PTX0uSZLU0un1Keh0OzAatWg0\nofj5JeHldeU9ATShGgy5hnrphhsM0ECsKhtVRqcnO9VL94r3ui4DT2MaDUi1vepmzpxJYWEhycnJ\n7Nmzh7Vr1/Lmm28SEhJC//79GTBgAP3798endnJASZKkFkSvT0GrPT9a1WDItT2/0qDkl+RXd7DB\n1QAAFQ9JREFU5x5SrS5PduEfR/5BaFoobjo3qvyq0MZqGX336Csr/HXGrl52AQEBjBo1ilGjRgGQ\nmZnJnj17SE1NZfbs2ZjNZg4fPtysBZUkSboSOt2ORtJ3XnFAqr2q0e3U1WmG6xHfA6coJ3bG7iSz\nLJO2bdoyutvoVjWf3NVkd7dvAL1eT3p6Ounp6fz6669kZGRgNpvp2bNnc5VPkqRrVFM3ozXGaKx/\nJWNN/3ML1TXW3NbaJjRtSS4akE6cOEF6ejoHDhwgPT2d3377DYvFQrdu3ejXrx9jx46lb9++suu3\nJEmXpTma0Rqj0YRiMOQ2kN5yF6q7XjUakPr160dpaSlCCNq2bUu/fv148skn6devn5zDTpKkP6U5\nmtEa4+eXxMl/bcHwUyiWAjdUgVW4DNQSOqTlLlR3vWo0IPXt25f+/fuTkJBAhw4dHFkmSZKuktbe\njNagIz1Qvh0GhhwQlVAYiPJtDHTsAbJlrUVpNCAtX77ckeWQJKkRjgoS12ozmm6HDmdNIM6aui07\nup062eW6hVFd7QI0B7PZzDvvvMOAAQOIjo5m2rRpFBYWXu1iSdJlqw0SBkMuQlhsQUKvT2nyY12s\nGa2p+fklYTzkR9mqnpQuiKNsVU+Mh/zw82v6ZrTGBrEazzScLl09l9XLrrVYuXIlW7du5a233sLH\nx4dXXnmFZ555hk8//fRqF+2646hf944+lqPodDswHvKrd/9D59L091qMRm2Dx1J6te5mtMYGsWra\napr2QNKfds0FJKPRyKZNm5g7d65tFvIlS5YwePBgDhw4QExMjN37amg23+a6xHfoiXvvRnRZGzGa\nzqJRB+MX8She/R5t+uM4sAnIkccCx302ylMNVH15flYUy1l3qr7sisLv0KlpjyUyu1P15fk61B5L\n41wG4U17LEc2ozU2iNVvaOtd6vtadc012WVlZVFRUUGfPn1sae3bt6ddu3akpqbavZ/a2XwNuQaE\nRdhm89Wn6Ju8zI5sltHv3Yg2YyEGkxaBBYNJizZjIfq9G5v8WI5sAnLksRz52TD93P2y0v+U/X0b\nTk/p03D6n+DIZjSveC9CnwjFpb0LikrBpb0LoU+EyvtHLdA1d4WUl5cHQHBwcJ30oKAgW549Gp3N\ntxl+wTmyC6wuq+HAo8va1ORXSY7sSeXIYznys6Eu7YaRrAbTm5qiC8T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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -4144,14 +4263,14 @@ }, { "cell_type": "code", - "execution_count": 155, + "execution_count": 157, "metadata": {}, "outputs": [ { "data": { "image/png": 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NGzYMgKCgIIKCgjS2KxSKbCepwMBAJk+eTKtWrRg7diyQnlySk5PV6qlUKgwN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\ny3Bz88bDI5xz50LUjzNwwoAEN2MY3dq0JKs4C6O5DB+tN+G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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -4177,29 +4296,47 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 168, "metadata": { "collapsed": true }, "outputs": [], "source": [ - "# Solution goes here\n" + "# Solution goes here\n", + "p0 = table1.biraben[1]\n", + "prehistory = System(t0 = 1, t_end = 2017, p0 = p0, alpha = 0.0015)\n", + "\n", + "run_simulation(prehistory, update_func1b)" ] }, { "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": true - }, - "outputs": [], + "execution_count": 169, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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jp5hAxVFdHUebA6KtkJoKY7NMYTn+xUjwEEKIAebz+TlU1RR8f0Na+GoF8XfE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\n6Gjq6uq6HKM3i1T1VMaNGzcyYcKEkF+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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], "source": [ - "# Solution goes here\n" + "# Solution goes here\n", + "\n", + "\n", + "newfig()\n", + "plot_prehistory(table1)\n", + "plot(prehistory.results, label='model')" ] }, { "cell_type": "code", - "execution_count": null, + "execution_count": 170, "metadata": { "collapsed": true }, @@ -4219,11 +4356,17 @@ }, { "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": true - }, - "outputs": [], + "execution_count": 171, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "13.8888888889\n" + ] + } + ], "source": [ "def carrying_capacity(system):\n", " K = -system.alpha / system.beta\n", @@ -4236,11 +4379,17 @@ }, { "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": true - }, - "outputs": [], + "execution_count": 172, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "13.8888888889\n" + ] + } + ], "source": [ "def carrying_capacity():\n", " K = -system.alpha / system.beta\n", @@ -4253,11 +4402,17 @@ }, { "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": true - }, - "outputs": [], + "execution_count": 173, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "13.8888888889\n" + ] + } + ], "source": [ "def carrying_capacity(system):\n", " system = System(alpha=0.025, beta=-0.0018)\n", @@ -4271,11 +4426,17 @@ }, { "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": true - }, - "outputs": [], + "execution_count": 174, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "None\n" + ] + } + ], "source": [ "def carrying_capacity(system):\n", " K = -system.alpha / system.beta\n", @@ -4287,11 +4448,21 @@ }, { "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": true - }, - "outputs": [], + "execution_count": 175, + "metadata": {}, + "outputs": [ + { + "ename": "NameError", + "evalue": "name 'K' 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 5\u001b[0m \u001b[0msys1\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mSystem\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0malpha\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;36m0.025\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mbeta\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;33m-\u001b[0m\u001b[1;36m0.0018\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 6\u001b[0m \u001b[0mcarrying_capacity\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0msys1\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m----> 7\u001b[1;33m \u001b[0mprint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mK\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m", + "\u001b[1;31mNameError\u001b[0m: name 'K' is not defined" + ] + } + ], "source": [ "def carrying_capacity(system):\n", " K = -system.alpha / system.beta\n", diff --git a/code/chap04mine.ipynb b/code/chap04mine.ipynb new file mode 100644 index 00000000..955c12cf --- /dev/null +++ b/code/chap04mine.ipynb @@ -0,0 +1,1038 @@ +{ + "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": 35, + "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": 36, + "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": 37, + "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": 38, + "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": 39, + "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": 40, + "metadata": { + "collapsed": true, + "scrolled": true + }, + "outputs": [], + "source": [ + "table2 = tables[2]" + ] + }, + { + "cell_type": "code", + "execution_count": 41, + "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": 42, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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P8y2LiYlBKcUzzzyT4745rZB13fVjs/5r1qwZ9957L3PmzMnWU+G///3vLftm/ffzzz9n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\n/LeLUqof0B9zhbA99h4nyoa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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": 43, + "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": 44, + "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": 57, + "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": 58, + "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": 58, + "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": 59, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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39WN8/GomHuFWZs7sfVYmfmjgAu6uIgu4CyGcVVxSzIc/fIjer+kc0I0+3Xoz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\nhVaeXVPMlUvPbTsmKz2La86+JhbVNsaYEyIpk38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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": 60, + "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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WCgoKwmazlXg34evrS1BQEEFBQQQGBhIUFFRsu9DQUEaNGlWhb/+qamkSUUqVKDc3F6DQ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\nESNGALQzxhyozDHcrRM5C5RWuxMG5JW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Sh4EFpHsGIyPib4WqPZsnaCmujuaq8p2IpBmS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\n", + "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": 61, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "13.856665141368708" + ] + }, + "execution_count": 61, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "system.results[system.t_end]" + ] + }, + { + "cell_type": "code", + "execution_count": 62, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "13.888888888888889" + ] + }, + "execution_count": 62, + "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": 68, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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SV3OaBL22rR0wzdlXwg8w0h9hpH9zd8fHgbLtkClXyZSr5CquwOcqFrmqRbF6\n/x/DdlEU8GgqPl3Dq2t4dBWvrmGqKh69JuyqgoGNahfR7ALYeYRVwKrksCo5bHvzLGT1buoDvDYo\nqCiaB9vWsWyVakWlUlEol6FYhHJJ4DgaQugI9Np6TawfHF0FQ1jooopSLaBWiijlIhTzqHYFXXUb\nKF113IbLFKjmA+mn+7k0Dd3vR/P5UD0eNK8HxfRQ1gVFxSav2OSVKjkqZCmTFmVsTXnwB22BqZv4\ndC8+w4tXN/FoHjy6iVd312v7Ht3EW9vW1d2H5qhaNulchXQu667z5dp+mVyx2rZxOEVR8Hl0/F4d\nr6njNTW8pobH1PHUttfKPbVtj+mK+OPMvhP+xwEhBAXLJl2qki5bZMpV0rWltI2ezr0wNAW/ruE3\ndPyGht/QGuKuueLuqwn72o9bCIFtlaiWM+uWLGVnY4C6B0HVTHTdh2b40DQvmuFFCINyRaVYgGJB\nkMtBLmtRLFi7EgRVVfH6DXw+ox5OQneqKOUCajEH+Qzk0pBNwfrIqGtsczBN8/nQAwH0QADN50ML\nuOKu+/1ofh+a3w8eD2mnQLqUZb6YIlVKs1JMky0v3ONz3l+Q1mI+BU0/fsPnziLXffgNb21GuQ9/\nTew1dW/Dc5fKFivZEquZMiuZEiuZEquZErniFt/vNjF0laDPJOAzCHh1/F4Dn9cVeL/H3V8T+0f1\nDX8vkcK/x1iOIF2usFqsslKqsFqqslqq1GzsD4aiQMDQCJq6u9TFvbbWXXPYvRCOTaWcJpdJUSmn\nqJbSVMsZHOfBf6iKoqIbATTDj2743LVeWxt+VN1LqeiQSRVZWS2SSZXIpEuUiqUHfhZQCxhn1oLG\nmXWR9/oMPAaIbIrK0jLlxRkqk6tUV1MbQ19vA1XX0UMh9GAQPRR01y1LoCXInRCCfLXAci2A31J+\nitXlNJlyrmn08QE+p+ElZAYImoG6wAfNAEHTT8D04zO8G3JB7DWOI0jlyiyuFlhMFVlKuSJfKO3k\n70Yh5DcI+kx37TcJ+g2CPoNQbdtjaHKC2R4ihb+N2I5gtVRhqVhhqVBmpeSabB7kt68qEPYYRDwG\noTWBry0BQ3M9fraJcGzKpVUqxVUqpRSVUopqOcODeIIrqo5hBNDNYG0JYNS2Nd2LUhMgIQT5XIXU\nSoH0apH06gKZdLElreR9n9UUNtofNPEHPARCJoFALWx0LdOYU6lQWligvDhP+c4S6cVFqukH+1yq\nYWBEIhjUVtdMAAAgAElEQVTRCEY47G5H3LXm928pOmvRWhczy7VIrW7E1lL1wRozN0priLAnSMTr\nrsPeEGFPCFNrx9D6znEcwUqmxMJqgcXVIoupIsupIlV7+2+jqqoQDphEAh4iQZNI0EM06CEcNAn7\nZQjwbxsp/DtkzVyzVKiwWCizVCizXKxse3DV1FQiHr0u8u6iEzD1BxL3ZqxqgXJxhXJhmXJhmUpp\nle2KoaoaGJ7whsUV9431sSyblaUCK0t5UssFVpYLVCvbizOkqgqBoIdgLTlMqJYoJhA03fAETQgh\nsLJZCrcnKM7OUZ6fp7y8su3PpXm9mB0dmB0xzFgMs6MDIxZF8/m21aO0HZulwgrzuSV3yS9tPyS3\nohD2BIl5I8R8tcUbIeINYXzL4t5MqWIxv1JgfrnA7HKeueX8tgZXwR0kjYU8dIS9xMLe2tpDJOCR\nJph9jBT+bSKEIFe1mc+VmMuXmM+XKWyzNxvy6MS8Bh1ek5jXpMNn4NN39yorhMCq5CjlFygXligX\nl7Gq2xMkwwxheKOYteVeAr9GtWKxvJRneT7HynKeTKq0LXu8YepuSsiol3DUTzjqJRDcWhSEEFSW\nlt10lbNzlObmNuQu3hwFsyOGJx7H0xXHE49jxGLoft82rm36nHaVudwiM9l55rKLLBaWcZxteJho\nBp1+NzVn3B+jwx8l6o2g77GNfScUSlWmFnJML+aYW8qzki1v698y6DPoivqINy0hvykF/gAihf8e\nFKoWM7kS87kyc/nStoQ+aGrE/R7iPg+dPpOY17iv3X27WNUCpfwCpfwipfwCtnV/QTTMMKYvhumN\nYXojmN4o6jZ6m2s9+uWFHEsLOTKp4n3FwTB1Yh1+op2uwEeiPrw+454NihCCajpDcXqK4qSbn9gu\nb+EtVEfBE+90Bb6rC09XHLOjA9V48F70Wia16ew805k5FnJLjThGW6BrOt2BOF2BjrrQhz2hfWuT\nLlUsZpfyTM5nmV7IsZy5v1kq6DPo6fDTFfPTFfPRFfXh9+6ftxTJ7pDC34QjBAv5MjO5IjPZEqv3\nGbjSVYW436TL7yHuM4n7PXjbmORcODbl4jLF7CzF3BzVSvae5yuKjscXw+PvxOOLY/o60PTtz/nO\nZcsszGZYmM2wspTHuYfdSlEUgiEPsXiAWIefWDxAIGhuS/ycapXi9DT5sXEKE5NYudw9z1dNE29P\nD96+Xry9PXi7u1HNnc9lz1XyTKRmmEhPM5Odv28o7LA3SE+gi55gnJ5gFzFf5KEPrj4IQgiWUiXG\n5zLcnUmzsHrvRltVFOJRH72dfno7A/TFAwTv02BLDjaPvfCXLZvJbJGpTJG5fOme3jaGptDl99Ab\n8NIb9BDzmju2x2+FbZUo5uYoZmcp5Rfu6W2jqgYefxfeQBdefxzDG6kPtm4Hx3ZYXsqzMJtlYTZD\nPrd1T1tRFMJRH/HuIJ1dAWKdfgxz+38+Vi5Hfnyc/N1xitPTCHvrtyfN58PX34+vvw9vbx9mR2xX\nIuQIh8X8MhPpGcZT06wUVu95fswXoT/cS1+oh55gHL/xYOaib4OqZTO1kGNsNsP4bOae7pSaqtDb\nGaC/O0h/V5DumA+jjR0Wyf7nsRT+YtVmIlNgIlNgPl/e0utGVaA74KEv6KM34KHD136hB7CqRQqZ\naQqZScrFrQcuFUXD44/j9XfhDXZjeqMPJPTgzppcms8xO5VifiZD9R7mq1DY6wp9T5DOeOCBhB6g\nkkqTv32b3O07lJeWtjxP1Q18/X34BgbwDfRjdnTsurfpCIe57AK3Vya4m5q8p9dNyBOkP9zLoVAP\nh8I9B0LoASpVm7HZDKNTKSbmslhbeN0oikJX1MdAd5CB7iB98SCGvn/fWCR7z2Mj/IWqzXg6z3i6\nwGJh60lJAVPjUNBHf8hLb8DbNvv8elrFfnnL83QjgC/Yhy/Ui9ffhbKDwULbdliczzI7mWZ+NrOl\ni6Wua3R2B+nuC9HdG8Lnf3BzSjWdJnf7DrnR2/cUe7Ojg8DQIP6hQbw9PfW8vrthu2KvKip9oW4G\no/0MRg4R8YZ3/eyHRbPYj89msLcwx3lMjaHeMMN9YQZ7Qng9j81PXbINHum/hqrtMJktcmc1z2xu\n6x5f3G9yOOxnIOQj4tn9dPWtcOwqhcwUufQ45cJWoqjg8XfiC/bhD/WhmzsbNBRCsLKUZ2p8ldmp\n9JZi7wuY9PaF6e4L09kV2OBOuR2sQpHcrVtkb96ivLi46TmKquHr78M/NERgeAgj3D6xXSqscHPp\nLqMrY1uKvc/wMhjpZzDaT3+491v3lX8QHEcwMZ/l+tgKYzPpLcW+I+xluC/M8KEwvR0B6W0j2ZJH\nTvgdIZjPl7iz6ppyrC1+JD0BD4MRP4fDPgLG3n0NQgjKhUVyqTEKmWmE2EyAFbyBLvyhAfzhQ2j6\n5klUtkMhV2ZqIsXU2AqF/OZvNv6ASd9AlL6BCJHY9vzZ1yNsm8LEJJkbNyiMjW86eKioGv7BwwSP\njhA4MryrAdn1FKslRlfGSC7d2dJm7zO8jHQMMhIboicY39cDspuxnC5yY3yV5PjqljNk41Efxwai\nHB2IEAvt/O9G8njxyAh/oWpzezXHrZUc+S16tz0BD8PRAINhX1u9bzbDquTJpcbIp8e38K9vn9jb\ntsPsVJrJuyssL27uIRMIeugbiNA3ECUcvbfP/r2orKySuX6d7M1bm/rXK6qK//BhgseO4h8eQvN4\ndvSczXCEw0RqhuTSbSbS05s2Ngdd7MtVm5vjq1wfW2FhdfN5GVLsJbvlQAu/EIK5fInkco6pbHHT\nQdqwR2ckGuBINEDwAQcnd1KfUn6e7Mptirk5NhukNTxhgtFhApHBXYk9uL378TsrTNxd2XTWrGFo\nHDocZWA4RrRj6zAE90PYNvm7Y6S/uUpxZmbTc7w9PYROJggeO9pWsQe3d39jaZTri6PkyhuT9Giq\nxpHYICfiRzgU6jlwYg9u7/7K6BLJidVNZ80GvAaJoRgnhzvoCEuxl+yOAyn8VdvhdirPjeUs2fJG\nwTM1lZGon5FYgA7v9nzLd4NjV8ilxsiu3sGqbOxxq5pJIDxIMDqE4Y3uesbu4lyWsdFlFuezG3q9\niqLQ1RNiYDhGz6HwrmKiWPk8mWvXyVy7jpXfKLh6IEDoxAlCpxKY0eiOn7MZQgjm80tcW7jJnZWJ\nTSdV9QS7SMRHGIkNYj7AfIX9gm073J5O883tJWaWNmvQFEb6I5wc6uBwT0ja7CVt40AJf75icWM5\ny63V3Kb+9t0BDyc6ggyG/Q8lMYJVyZNZuUUuNYZwNjZA3kAPodgRfMG+HXnjNGPbDtPjq9y5uUQu\nu3EA0+c3GRzp4PBwB17f7gYuy8vLpL78itytW5s2LIEjRwifPolvYABFbW/v2hEOY6tTfD1/nYXc\nxgFwr+4h0XWURPwo0QPkjdNMuWpz9c4yX99a3NTfvjPs5ezROMcPR6U3jmRPOBB/VSvFCt8sZpjI\nFDaYc0xNZSQW4HgsSPQhTSkvF1fJLN+kkJlivTlHVQ0C0WFCsREMT2jXz6qULcZuLzM2ukRl3duN\noijEe4IMH43T3Rty0+vtECEExekZUpe/ojAxseG45vMROXOa8OnT6MHAjp+zFZZtkVy+w9dz18mW\nN741dQfjnOk+wZHY4L6Mf7MdcoUKX91a4urdZSrrxqFUReHoQIRzR+P0xQNy1qxkT9nXwr+QL3Nl\nMc3MJj3ckEfnVGeIkWhgz3ztm1nzzkkvXqdU2OiyaHgihDuO4Y8cRlV3/7WWilXu3Fxk/PYy9rqJ\nObqhMXikg6GjnQSCu7OnCyHI37nL6hdfbuqK6e3tJXLuLMGRI23xtV9P2arwzUKSb+aTlK3WmcOq\nqnK84whnuk8QD3S0/dkPi9Vsic+vz3NzIoWzrufi9xqcPdrJmSOdBHb5piaRbJd9J/zugG2ZKwtp\n5vMbQwj0BDycjofoD+3MDXEn9SkXFkktXtvU994b6CHceQJvoLst9SkWKtxOLjJxZ2VDVEivz+TI\n8TiDIx0Yxu5EeE3wVz79jMrKyrqjCoEjw8SeOo+3t3dXz9mKslXhyvwNvpm/QcVuNXeYusmZ7hOc\n6T5xYGbRbsZqpsRn1+e5OZnaYDKLhbw8lejixGDssU8DKHn47CvhF0LwycwKt1Y2DnQNRfyc7QrT\n4Xs4g3iuh84C6cVrm8ysVQhEDhPuPIHpbc+gZrFQYfTGApN3VzcIfjjqY+REF4cOR3c9wHcvwVdU\njdDJBNEnz2NG9ybvcckq8838Da7MJ6muE/ygJ8ATPadIxEf2Vbz6B2UlU+LTa/OMTm0U/EPxIE8l\nuhjuC0tzjuRbY18JP9Ai+ooCRyIBznaHiXgenhCUC8usLlzZ0MNXUAlEh4jET6Kb7bFzV8oWozcW\nGBvdGPc9EvNz4nQP3X27D/krhKAwMcnKx59QXm5tyFTdIHLuDJHz5x84fv12qdpVvllIcnn22gbB\nj3jDPNV3hmOdwwfSFXONTL7CpauzJCc2Cv5gb4gLp3rpi7d/fEQieVD2lfArisLZrjATmQI9AS9n\nusKE9tj3vplqOUNq4SqF7HRrvVAJxIaJdCbaJviWZXP31hK3k4sbwinEOgMcP91DV0+wLb3C0vwC\nyx99vMEH/2EIviMckku3+XzmCoVK64SviDfM04fOcrRj6EALfqls8dmNea6MLm0IpzDUG+bC6R56\nO6XgS/YP+0r4AZ7qjfJUb3t9wu+HVS2SXrxGLjVGq5eOQjB2xO3hG/62PEs4gom7K9y8Nk953TT8\naIefxNle4t3tEfxKKs3KJ5+Qu32npfxhCL4Qgrurk3w6/RXpUqblWMQb5plD5xjpGDzQgl+1HL66\ntcgXyYUNXjpDvWGeO9NLT0d7/m4kknay74T/YSIcm8zyTdJLSYRodZUMhA8T6T6DYQbb9ryl+SxX\nL8+QXZcBKRDycPJsH7397bH72uUyq59+RvrKNy0mB0VRCJ85TezZZ9D9eydIS4UVPpz4nLnsQku5\n3/TxzKFzJOJHD7TgCyG4NZniw69nNvjh93YGePFcH4e62vd3I5G0m8dS+IUQFLMzrM5/jVVtHUj2\nBnqIdp/F44u17XmFXJlrX88yN51ufZbP4MTpHg4Pd+zKB38N4ThkbyRZ/uTShjg6waMjdFy8uGeD\ntuCGVvh0+ituLN2mecKFoRk82Xeac90n0bWD/Se3uFrk15enmVlqnWsQDXl44WwfI/0ROWgr2fcc\n7F/hDqiU0qzOf0Up39obNTwRYj1P4Av2tO1ZlmUzen2BOzeXWgZudV3j6MkuRk507SqkQjPF2TmW\n3v9ggy++r6+PzhdfwNvT3ZbnbIbjOFxdvMnn01+3uGYqisKZ7gRPHzqLV29v/J6HTaFU5ZOrc1y7\nu9LyFuXz6Dx/to9Twx0ypILkwPDYCL/jWKQXrpFZuUWzHV/VTKJdZwjGjjxwNqt7MTeT5psvZigV\nW0MjDwzFOHmub9dhFdawCkWWP/qIbPJmS7keDBJ/6UUCI0f2tAc6l1vk12OfsFpsfZsZiPTx4uFn\niPr27g3jYSCE4NrdFT68MkO50rDjq4rC+eNdPHu6B88u51RIJA+bx0L4C9kZVucurwuPrBCKHSXS\ndfqBEpLfj2KhwjdfzjA/0yqE0Q4/Z57sJ9bZpkFiIVyzzocfYZcbE90UTSP21JNEn3oS1dg7F9iy\nVeHS1GWuL95qKQ97Q7xw+GkGI/0H3uSxnC7yzudTzC63mgOHesO8/OQhGRJZcmB5pIXfqhZZnbu8\nwT3T6+8i1vskprd9vVHhCO6OLnHz6jyW1egZmh6dU0/0MTC0u4ThzVRSKRbffY/idKt7ZuDIEeIv\nvYgR3n2MoK0QQnB7ZZyPJj+n2JTtSld1nj50jnM9CbQDGktnDct2+PTaPF8mF1pCLIQDJq8+NcBw\n38EMDieRrPFICr8QgtzqXVILV3Cchs1Z1UxiPecJRAbb2hvNpIp89dkk6dXWAdXBIx2cPNeH2aYI\ni8K2Wf3yMquffYFwGo2LEQoRf/UVAkODbXnOVuTKed4b/4Sp9GxL+WC0n5cGnyXkOfieLJPzWX71\n+SSZpuxlqqrwdKKbZ0/1yPAKkkeCR074rUqe5dnPNwzeBiPDRHvOobVxkNFxBKM3Fhi9Po/TNHEn\nGPbyxDMDdLRxlmZ5aZmFX/6qJYG5oihEzj9Bx4Vn99SsI4QguXSHjyY/b5l16zf9vDT4LMPRgQNv\n1qlaNh98Pcs3t1tna/d1BvjOMwN0Rg5uzCCJZD2PjPC7vfw7rC5caYmNb5ghOvqexhvoauvzMqki\nlz+dJJNq9PJVVeX46W6OnujaUdLyzRC2zeoXX7L62ect3iTe7m66XnsVT1e8Lc/Zilwlz3tj63r5\nisLZ7hM823/+QCUt34qphSy//Ky1l+8xNV48d4jTRzoOfKMmkazngYU/kUj8IaAnk8m/2VT2JvDP\ngARwC/j9ZDL5k7bV8j5s3stXCHeeINp1etdJUJpZ6+XfujbfIsSxzgDnnx0g2Ma0eOXlZRbeXtfL\n1zQ6Lz5H5IlzbU+C0owQglvLd/lw4rMWF82wN8R3jrxAb7C9Dem3QdWy+fDrWa6s6+UfORThO08P\nyDDJkkeWbQt/IpFQgD8A/jbwL5vKTwN/Bvxj4D8Avwv8SSKReDqZTF5tb3VbEUKQT0+wMvflul5+\nmM7+Z/H42hvDPZ8t8+WlCVIrDe8gTVM5caaXkePxtkzCAvdzpb68zMqlTxFN/v/enh66X/9u29Mc\nrqdQKfLe+CdMpJoGxRWFcz0JLhw6f+AnYQHMLef5+aUJ0rmGR5TH1Hj1yX5ODLZvIF4i2Y9s6xec\nSCRGcMX+LLA+PdPvAR8nk8l/Utv/h4lE4uVa+d9qV0XX49gVlme/pJCZbCrdm16+EILJsVWuXZ5p\n8diJdQY4f+EwwVD7xg2sXI75t3/Z4rGjqBodFy8QPf/EnvbyAcZTU7x792NKTUlRwt4g3xl+gd7Q\n3k0Ce1g4juCL5AKXrs61eOzIXr7kcWK7XbcXgUngrwH/bt2xV4A/Wlf2DvBXd1Wze1DKL7I882mL\nX75uBokfeg6Pv729/ErZ4uvPp1rCLaiqwokzvRw90dW2Xj5A7s4dFn75Lk6lIbre7m63lx9rXwiJ\nzbAcm0+mvuDqfOtEsLM9CS70nz/Q8fHXyOQr/OLSeEtic9PQePWpfhKyly95jNiW8CeTyX8N/GuA\nRCKx/vAAML2ubAY4vNvKrUcIh/TiNdJLSZpn3wajR4j1nm9LysNmluazXP50klJTIK5AyMPTFweJ\nxNoX5MypVln64EMy1643lSrEnnmKjmef2ZOUh82sFFO8ffv9ltm3ftPPd4+8QH94bzJwPWxuTqzy\n7hdTlJuiaPZ1Bnjj4hDhwMNJ7iOR7BfaoZR+YH1S3DLQ1mmNViXP4tQnVEqNrFGqZtLZ9wz+cH87\nH4XjCJLfzHE72eoSOnS0k9NPHELT22duKS8uMfezn1NNN0RXDwToeeN1fIcOte05myGE4PriLT6a\n/AK7aV7AUHSA1448f+Dj6wBUqjbvfTnFjfHVepmqKFw43cMzJ3tkfB3JY0k7hL8IrFcID7Axf+IO\nKWSmWZ75rGUyljfQTeehC+htzslaLFT44uMJVpum6ZsenfPPHqbnUPtmbAohyHxzlaUPPmqZjBU8\ndpSu115F8+yt6JatCu+OfcTY6lS9TFM1Xjj8DKe6jj0SZo/ldJGffDRGKts0XhEwefPikEyMInms\naYfwTwJ968oOsdH888AI4ZCav1ILrOaioBLtPkOo80TbxWlhLsvlSxNUyg0Poa7eEE9eOIzH2z4b\nt1OpsPDOe+RGR+tlqm4Qf+UlQicTey66S/kVfn7712TLjdDCHf4or4+8TOyAB1Vb48bYCu98MYVl\nN7yiTg7FePWpAUwZVE3ymNMO4X8feA3XnXON7wLv7eamVrXA0tQnLYnOdSNAfOBi2900hSO4eW2e\n0RsLdd98RVE4caaHYye72yrE5eUV5n76VotpxxOP0/PmG3saKx/ct4wbS6N8MPFZS5joMz0nuDjw\nNPoBj7EDbpyd976c4trdhknQ0FRee2aAk0Pt/buRSA4q7RD+fwF8nkgk/gD4t8BfBy4Cf2enNyxm\n51iauYRjN2ZS+oJ9xPsvoGrtHYgrl6p88ckEywuN3q/Ha/D084N0tjmLUjZ5k4V33kXYDdNO+PQp\n4i+/hKrvrW+8ZVv8evwSt5bv1ssMzeC14ecZ6djbGD8Pi9Vsibc+HmepaTZ1R9jLbzw/JEMuSCRN\n7FptksnklUQi8ZdxZ+7+PnAD+AvJZPL6va/cnMzyLVbnv2oqUYh1n90T087KUp7PPxpvyX0b7wnx\n1HNtNu1YFku/fp/M9Rv1MlXX6XrtVUKJE217zlakShl+Pvpei9dOhz/GG0dfJuJ9NCJNjk6l+OVn\nky25bxODMb7zzACGfvDfZCSSdvLAwp9MJr+zSdmPgB/ttjLCsUktXKnva7qP+MBFvP72xqMRQjBx\nZ4VvvpxuMe0cP93D8ZPdbfXNt3I5Zn/yVktmLDMapec33sTTufemh7HVSX5196OW4Gon4iO8PHjh\nkZiB6ziCT67O8fmN+XqZpiq8+tSAjLMjkWzBvvrlK6qG199NMT+HL9BLZ/+zaHp7k104tsM3X04z\n0WQDNj06T10cpKunvXHsi7OzzP30Zy35b4PHjtH93df2NJomuI3b5zNX+GKmqSFVNV4avMDJrqN7\n+uyHRali8fNPJhify9TLwgGTH7wwTHcb51lIJI8a+0r4AboGX8Kxy20XfIBSscrnH423uGqGoz6e\nfXEYf5sn8aSvXmXp1x/UY+0oikLnSy8SOXd2z3uhFbvKO3c/bHHVDHmCvHHsFeJtntn8bbGSKfHj\nD+6Saoq1M9gb4s2LQ3jNffdnLZHsK/bdL0RRlD0R/dXlPJ992GrP7x+M8cSzA21LeA5uGOXFX7/f\nMgtX83rp/Y038fXv7YQsgHQpw1uj75Fqsuf3h3t5/ejLj8SELIA702l+fmmcqtXwTHrmZDcXz/TJ\nCVkSyTbYd8K/F4zfWebql9P1ZCmKonDqiT6OHI+3tfdtFQrM/fRnlObm6mWeeJzeH/zGnqZDXGMy\nPcPbdz6gYjW8oc71nuTiwFOobUwk/20hhODTa/Ncutb4fg1N5XsXDnP88N7GMpJIHiUeaeEXjuDq\n5RnGmuKtG6bOM88PEm+zPb80v8DcT9/CyjfMSA/Tnv/1/HU+mboMtcFqVVV5degiJ+Ije/rsh0Wl\navPzSxPcbUpiHw6Y/PDFI8Sj0lVTInkQHlnhr1Ysvvh4gsX5bL1sr+z52VujLLz9q6bQCwqdL1wk\n+uT5PbfnW47Ne2OfMNrkn+83/bx57FW6A517+uyHRbZQ4Ucf3G3xzz/cE+I3Lg7hbVM+Y4nkceKR\n/NUUcmUufTBGLtOIHXfocJTzzx5ua4A1IQSrn3/ByqVP62Wq6aH3ze/jH2x7cNINFKslfjb6HvO5\nhqtoT7CLN469gr/NMYy+LeZXCvzog7sUmsZmnjrRzQvnpD1fItkpj5zwryzl+fSDMaqVRrydE2d6\nOX6qvaEXhG2z8Kt3yN5sxBEyIhH6fuuHex56AWC1mOant95pibdzsusYLw0+i/YIhF4AGJ1M8YtP\nJ+rxdlRV4btPH+bUkUfDM0ki+bZ4pIR/anyVrz+bqsehUVWV8xcO0z/Y3lSFVqHI3E/fahnE9fX3\n0/uDN/c8qibAVGaWX4z+upELV1F4fuApzvWcfCQmLAkh+PzGAh9/00jw7jV1fvPFYfrbHEZDInkc\neSSEXwg3fv7ojUb8fNOjc+GlYWJtDr9bWVll9kc/ppptGjs4fYquV17e84QpANcXb/H++Kf1Gce6\nqvO9kZcYjg3s+bMfBrbt8MvPJklONOLnR0MefvulEaJtTHEpkTzOHHjhty2Hy59OMDvV8PYIhb1c\nePlI2wdxC5NTzL31M5zKmrukQvzF54mcf2LPe9qOcLg0dZmv5xrzA/ymnx8ce4144NEwfRRKVX7y\n4RizTRPsBrpD/OAFOSlLImknB/rXVC5VufT+GOnVRu7d7t4wTz8/iN7mmOvpq1dZeu/9ek9b1XV6\n3vg+gSPDbX3OZlTtKr+88yHjqcZM3E5/jB8c/w4B89EITbCSKfHn798hk2/MQTgz0smrTw2gyUFc\niaStHFjhz2VKfPL+XYpNQnHkeBenn+hra5A1IQTLH31M6nIjYqgeCND3w9/E09Xe4HGbka8UeGv0\nXZbyjdhCQ9EBvjfy4iORAB1gejHHjz+8S7niusMqisKL5/p48kTXIzFmIZHsNw6k8C8v5vjswzGq\nTUJx5qlDDB9tcxRP22b+7V+1ZMryxOP0/fA30YN7n7pvtZjmJ7d+Ra7cMH080XuK5waefCRm4gLc\nmlzlF5cmsGuzqg1d5c2LQxw59GhkApNI9iMHTvhnJlNcvjRZ99zRdY2nnx+ku6+9ceXtcpm5n7xF\ncWamXhYYGqLnze/v+UxcgNnsAm+NvlsPv6AoCi8PXeBU1/E9f/bDQAjBlzcX+fDrxvfr9xr89stH\nZGRNiWSPOTDCL4Tgzs0lrjcJhcdrcOGlYaId7RUKK5dj5s9/TGWlYV6JnDlD/JWXUNS972nfWZng\nl3c/aDRums4bR1/hcGTvg7w9DBxH8P5X03w92gil0RH28tsvjxBu84C8RCLZyIEQfuEIrn41w1iT\nUARCHi6+fAR/sL0ufuXlZWb//MctMXc6n79I9KknH4q9+cr8DT6a/KIec8dnePnN4999ZDx3qpbD\nzy+Nc2e64YV1KB7k/2/vvoPjOvIDj39nBhjkRCJngCCaSWASRYFBJLiSGKR1KN8ftrf2ah3q7rwn\n793WlldV50vec9hyUJXP56t1eX0ux7srn6PMhShKzAGEmMTcBIkcBonIwACDmXd/zGBmAAYwzGDw\nHnZXhVQAABiISURBVH6fKpVK/ea9182mfvOmX/evj+wul5k7QiyRZf9/mtfr49qldlxhgWJVdgqv\n7yrHGeE8LZOdnbjqj+Hz+BdG2Ww2cg/ULcn2iIZh0NB5lZuu0PaMGYnpHK6uIz3BGouWpqZnOXq+\nBVfYdM21JZl8ZUcpcRFMjS2EeLZlHfhnpmf54nzrvI1TCksy2byjJKI59AHG7jfRd+JkcOMUe3w8\n+YcOklwS/YVRsz4vp1ou0vyoLViWl5rDwbX7LJNDf2R8mo/PNs/bOGVrdS67agpk5o4QS2zZBv6J\n8Wkaz7YwERYoKqtzWB/hQGEYBsPXrjPYcClYFpeSQsF7R0jIjn52y+nZGY49OI1rLLTquDyrhAOV\nu4mzSM6d3keT/PO5Zqam/fmTbDYbe7cUUlOVE+OaCbEyLcvAP/xoksZzLcyEBYoNWwqpqIrwdE2f\nj4FzFxi5dStY5szKouD9I8SnRX/jlPHpCX7UdHLeblkb86qpLdlumemaLd0jHGtoCyZai3PYeeeN\nUtYURzZ/khDi+S27wN/bM8rVi214A4HC4bCz5Y1SCoojO6/bNztL7/HPmWgJ5bFPKigg/8ihJUm0\nNjg5RH3TKSZnQquOd5ZspSZvvWWGPm4+HODMta7gaudEZxzv76kgP8L5k4QQL2ZZBX6f18eXX3QE\ng368M4439kQ+0ZrX7abnaD3u3t5gWWrVGnIP1GGPi/4fSdeoi08fnMETyK5pt9nZX1FL1eryqN97\nKRiGQcOtHq6EJc1LT3Hy1b2VZKVFfj9lIcSLWVaB32a3+TdKmYbkVP90zZQIZ2T0jI7S/fFRPCOh\n4ZXMzTWs3lW7JE/aTYMtnG5pwGcEvtwc8RyseovC9Pyo33speL0+Tl7p4F5bKLtm3qpk3ttdQXKi\nNVJMCGF2yyvw22zsObCWRwMT5OSnEhcX2Zeb7r4+eo7W452a28LPRvbuWjI310T0Pk9iGAZfuu7Q\n2Hk9WJbsTObI2jpWJVtjvHvG46X+YisdYdtdlhekc/DNMuIj3JdCiJe3rAI/QEJiXMTH8wEm2trp\nPXYc32xgjr7dQd7bB0itWhPxey3kM3xcaL/Mnb7Qbl1ZSRkcrq4j1WmN8e6JKQ//fK6Z/rB9cTdW\nrmbf1mLZIlGIZWbZBf5oGL17j/5Tp0MplZ0JFBw5SFJh9FMgzHpn+bz5/LyUygVpebxb9RYJcdZI\nTzA06ubjBSmV39iYz471eZZ5US2ElVg68BuGwdDlKzz64nKwLC41lcL338O5Kivq93d73Hzy4DR9\n46FUE2tWlbG/otYy++L2DExw9HwL7sAex3abjf3bi9lQEf01EEKIl2PZwG94vfSfPsvovVAKhKVM\nqTw6Pc6P7p9g1B0a767JX8/O4q2WeQpu7hrh00uhOfrxDjuHasspi3CmVCFEZFky8Ps8HlzHjjPZ\n3h4sSy4uJv/Qu9id0R9e6Z8YpL7pFG6P219gs7GrZBub8tZF/d5L5eaDAc5cD83RT0qI4/09leRF\nOFOqECLyLBf4Zycn6Tlaz3R/f7Asrbqa3Lp9S7IZevtwF581n2PWGxj6sNs5ULGbylWlUb/3UvDP\n0Xdx5V5oDURmagJf3VtJRoQzpQohosNSgX9meJiej4/iGQsNr2Rt38aqN3YsyfDKvf6HnG27FHwK\ndsY5ObR2P/mp1shJI3P0hbAGywT+qR4Xrh/V452eS+pmI2ffHjI2boz6vQ3D4Er3Ta523wyWpSak\ncGRtHZlJ1thC8Elz9Mvy0zlUK3P0hTAbSwT+8eZmeo9/juH178Frj4sj7923SSkvj/q9fT4fZ9sa\n0QMPg2Wrk7M4XF1HcnxS1O+/FJ40R39DxWr2b5M5+kKYkekD/8jNW/SfPQ/4h1ccSUkUHDlMYl5u\n1O/t8Xo4/vAsnSM9wbLijALeXrMXp8MaQx8yR18I6zFt4DcMg0cNlxi6FkqBEJ+RQcF7R3BmRn94\nZdIzxSdNpxiYCO3LW51dyVtlO7Evwb68S0Hm6AthTaYM/IbXS9+Jk4w1PQiWJebmkn/kMHHJ0R9e\nGXaPUn//JGPT48GybYWb2F5YY5mn4KaOIT5rbMfr8/+SinfYOVhbTrnM0RfC9EwX+L3T07g+OcZU\nV3ewLKWsjLx338YeH/3hFddYH8cenGF61v8S2WazsadsB+tz1kb93kvBMAyu6j4u3gwNX8kcfSGs\nxVSB3zM6Ss/RemaGQtMJ0zdsIOetPdiWYHjlwWArp1ov4gvsyxtnj+PtNXsozSyK+r2XgtdncPpq\nJ3daBoNlmWkJfHWPzNEXwkpME/jdLhc99cfCUirD6p1vkLkt+ikQDMPgas8trnTdCJYlxidyaO1+\nclOsMd494/HyycVW2sOmaxblpHK4tpzEBNP8NRF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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Solution goes here\n", + " \n", + "newfig()\n", + "\n", + "p0_array = linspace(1, 20, 10)\n", + "\n", + "for system.p0 in p0_array:\n", + " run_simulation(system, update_func2)\n", + " plot(system.results)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Comparing projections" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can compare the projection from our model with projections produced by people who know what they are doing." + ] + }, + { + "cell_type": "code", + "execution_count": 69, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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censusprbun
Year
20167.334772e+09NaN7.432663e+09
20177.412779e+09NaNNaN
20187.490428e+09NaNNaN
20197.567403e+09NaNNaN
20207.643402e+09NaN7.758157e+09
\n", + "
" + ], + "text/plain": [ + " census prb un\n", + "Year \n", + "2016 7.334772e+09 NaN 7.432663e+09\n", + "2017 7.412779e+09 NaN NaN\n", + "2018 7.490428e+09 NaN NaN\n", + "2019 7.567403e+09 NaN NaN\n", + "2020 7.643402e+09 NaN 7.758157e+09" + ] + }, + "execution_count": 69, + "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": 70, + "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": 71, + "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": 72, + "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": 73, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Saving figure to file chap04-fig02.pdf\n" + ] + }, + { + "data": { + "image/png": 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hWI3Jw8vJiwj/iCpPDDqdjnGh44jwj8DXxbfZJA+w/AkkHhgCVFdRNwRItVpE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\nSfRNjT+LSE+gN1CuqjbqXhKVlZXxrwUvU1i5lrp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+ "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": 111, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "# Solution goes here\n", + "p0 = 1000\n", + "alpha = 0.03\n", + "\n", + "t = linrange(11)" + ] + }, + { + "cell_type": "code", + "execution_count": 112, + "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, 1384.23387072])" + ] + }, + "execution_count": 112, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Solution goes here\n", + "geometric = p0 * (1 + alpha) ** t\n", + "geometric" + ] + }, + { + "cell_type": "code", + "execution_count": 113, + "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, 1390.96812846])" + ] + }, + "execution_count": 113, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Solution goes here\n", + "exponential = p0 * exp(alpha * t)\n", + "exponential" + ] + }, + { + "cell_type": "code", + "execution_count": 117, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "0.030454533953516938" + ] + }, + "execution_count": 117, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Solution goes here\n", + "alpha2 = exp(alpha) - 1\n", + "alpha2" + ] + }, + { + "cell_type": "code", + "execution_count": 118, + "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, 1390.96812846])" + ] + }, + "execution_count": 118, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Solution goes here\n", + "geometric = p0 * (1 + alpha2) ** t\n", + "geometric" + ] + }, + { + "cell_type": "code", + "execution_count": 119, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Solution goes here\n", + "newfig()\n", + "plot(t, exponential, '.')\n", + "plot(t, geometric, '-')" + ] + }, + { + "cell_type": "code", + "execution_count": 103, + "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": 143, + "metadata": {}, + "outputs": [], + "source": [ + "# Solution goes here\n", + "p0 = 1000\n", + "years = 1000\n", + "t = linrange(years)\n", + "geometric = p0 * (1 + alpha2) ** t\n", + "exponential = p0 * exp(alpha * t)" + ] + }, + { + "cell_type": "code", + "execution_count": 144, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([ 1000. , 1030.5, 1062. , ..., 528942. , 529970.5, 531000. ])" + ] + }, + "execution_count": 144, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Solution goes here\n", + "b1 = 30\n", + "b2 = 0.5\n", + "polynomial = p0 + b1 * t + b2 * t ** 2\n", + "polynomial" + ] + }, + { + "cell_type": "code", + "execution_count": 145, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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"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 +} diff --git a/code/chap05mine.ipynb b/code/chap05mine.ipynb new file mode 100644 index 00000000..8e227e5f --- /dev/null +++ b/code/chap05mine.ipynb @@ -0,0 +1,1944 @@ +{ + "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": 8, + "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": 11, + "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": 12, + "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": 14, + "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": 15, + "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": 17, + "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": 18, + "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": 18, + "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": 19, + "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": 20, + "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": 20, + "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": 23, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "0.37943042989926101" + ] + }, + "execution_count": 23, + "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", + "end = run_simulation(system, update1)\n", + "\n", + "s0 - end.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": 26, + "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": 27, + "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": 28, + "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": 31, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Saving figure to file chap05-fig01.pdf\n" + ] + }, + { + "data": { + "image/png": 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evJiQkBBSUkr7kW677TaWL1/Oc889R1paGmvWrOHBBx8kLCysZO96byeKOTIy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\nZwG2AG5MvpGggCCiQ6O5pOMlMpFRiHr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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": 33, + "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": 34, + "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": 34, + "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": 35, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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evJiQkBBSUkr7kW677TaWL1/Oc889R1paGmvWrOHBBx8kLCysZO96byeKOTIy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\ne236ks8bQQAAAABJRU5ErkJggg==\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": 45, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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oEGPGjCE3N5chQ4YUPN+Vt+URQpQdi+vkM0+UUnuBd7TW0z3kPQOM0Fp71RSm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\n7HEu0A+fWDwMGJHKLwAmUQ0bPIE/WQ7MCtKKsH7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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", + "model = run_simulation(system, update1)\n", + "\n", + "frame = system.results\n", + "plot_results(frame.S, frame.I, frame.R)\n" + ] + }, + { + "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": 48, + "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": 49, + "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": 56, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "0.043536202687592354" + ] + }, + "execution_count": 56, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Solution goes here\n", + "def fraction_of_students_sick_at_peak(system):\n", + " dataframe = system.results\n", + " return system.results.I.max()\n", + "fraction_of_students_sick_at_peak(system)" + ] + }, + { + "cell_type": "code", + "execution_count": 58, + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "data": { + "text/plain": [ + "30" + ] + }, + "execution_count": 58, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Solution goes here\n", + "def day_of_peak_sick(system):\n", + " dataframe = system.results\n", + " return system.results.I.idxmax()\n", + "day_of_peak_sick(system)" + ] + }, + { + "cell_type": "code", + "execution_count": 68, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "0.00067419431560344738" + ] + }, + "execution_count": 68, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Solution goes here\n", + "def final_fraction_sick(system):\n", + " datafream = system.results\n", + " return system.results.I[system.t_end]\n", + "final_fraction_sick(system)" + ] + }, + { + "cell_type": "code", + "execution_count": 69, + "metadata": { + "collapsed": true, + "scrolled": true + }, + "outputs": [], + "source": [ + "# Solution goes here" + ] + }, + { + "cell_type": "code", + "execution_count": 70, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "# Solution goes here" + ] + }, + { + "cell_type": "code", + "execution_count": 71, + "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": 73, + "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": 74, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "(0.3333333333333333, 0.25)" + ] + }, + "execution_count": 74, + "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": 75, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "0.46832081102878098" + ] + }, + "execution_count": 75, + "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": 76, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "0.30650802853979753" + ] + }, + "execution_count": 76, + "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": 77, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Saving figure to file chap05-fig02.pdf\n" + ] + }, + { + "data": { + "image/png": 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WVR7paWVlhaen500vhtkYmBS5EOIx4D3ga2AYULoK4hdAL2B+XQTXUtlYWzB+YAh2Nto+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\nxRMpXn6tnY3bOljWWMXKpTOZVa29xdThQYOKUoc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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": 78, + "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": 79, + "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": 80, + "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": 81, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Saving figure to file chap05-fig03.pdf\n" + ] + }, + { + "data": { + "image/png": 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T0y3G7zWQAZXr2Lq9kcamCO99aIMsGmPyS8oAIiJDgVpVjfi/O6QarE2qqrYA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\n+9lOYA6k+xmcCjwVDx5++z+o6mFZTWX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+ "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": 85, + "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": 86, + "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": 86, + "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": 94, + "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=200, K=0.3, B=0.01)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here's what it looks like." + ] + }, + { + "cell_type": "code", + "execution_count": 95, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Saving figure to file chap05-fig04.pdf\n" + ] + }, + { + "data": { + "image/png": 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LEjmO09REjkeiqs8Az4hIW6AbsDG+psRpncxftpGZC8NDWgN8SMtxWiFRbSQA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\ncBZJkZTjSEfcspkdzV2PQTTQQLTibUUrNCif9PP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+ "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": 96, + "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": 97, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "(0.3333333333333333, 0.25)" + ] + }, + "execution_count": 97, + "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": 98, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "0.0 0.321413041131 0.425004671528\n", + "100.0 0.306439191196 0.36482277694\n", + "200.0 0.283333333333 0.261513667407\n", + "300.0 0.26022747547 0.161448049009\n", + "400.0 0.245253625536 0.11125062946\n", + "500.0 0.238075920651 0.0926397551038\n", + "600.0 0.23513195433 0.0859833126613\n", + "700.0 0.234002618426 0.0835721609431\n", + "800.0 0.233580595649 0.0826908238415\n", + "900.0 0.233424438453 0.082367394914\n", + "1000.0 0.233366868346 0.0822485213249\n", + "1100.0 0.233345672791 0.0822048050331\n", + "1200.0 0.23333787312 0.0821887247223\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": 99, + "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": 100, + "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": 101, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Saving figure to file chap05-fig05.pdf\n" + ] + }, + { + "data": { + "image/png": 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W7iESifL+ym0cMWlQpsMyxpikgiYsO4AnUvB+C4Aq4ETgAQA/ZMxo4KVmtr8e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\ngCsTVmXrcQkwCvhbbIGqRlT1UP8jzNb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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": 107, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "24" + ] + }, + "execution_count": 107, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "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", + "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": 108, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "0.0 0.988888888889 0.23333787312 0.0821887247223\n", + "1.0 0.977777777778 0.233340817956 0.0767953037589\n", + "2.0 0.966666666667 0.233345672791 0.0718390380331\n", + "3.0 0.955555555556 0.233353676031 0.0672866564782\n", + "4.0 0.944444444444 0.233366868346 0.0631069787275\n", + "5.0 0.933333333333 0.233388611197 0.0592715024582\n", + "6.0 0.922222222222 0.233424438453 0.0557550483336\n", + "7.0 0.911111111111 0.233483451559 0.0525365637898\n", + "8.0 0.9 0.233580595649 0.0496002319759\n", + "9.0 0.888888888889 0.233740347105 0.046937100584\n", + "10.0 0.877777777778 0.234002618426 0.0445475496666\n", + "11.0 0.866666666667 0.234432027596 0.0424450740672\n", + "12.0 0.855555555556 0.23513195433 0.0406620796473\n", + "13.0 0.844444444444 0.236264556408 0.039258674118\n", + "14.0 0.833333333333 0.238075920651 0.0383356602888\n", + "15.0 0.822222222222 0.240919151335 0.0380526432513\n", + "16.0 0.811111111111 0.245253625536 0.0386497996234\n", + "17.0 0.8 0.251575885714 0.0404631151007\n", + "18.0 0.788888888889 0.26022747547 0.0438986900382\n", + "19.0 0.777777777778 0.271087400213 0.0492864920051\n", + "20.0 0.766666666667 0.283333333333 0.0565231196805\n", + "21.0 0.755555555556 0.295579266454 0.0646372366416\n", + "22.0 0.744444444444 0.306439191196 0.0718649121273\n", + "23.0 0.733333333333 0.315090780953 0.0765630182789\n", + "24.0 0.722222222222 0.321413041131 0.078105257597\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": 109, + "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": 110, + "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": 111, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Saving figure to file chap05-fig06.pdf\n" + ] + }, + { + "data": { + "image/png": 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CSlUfxE00PA9YiWuGylPVnw10kCPZ4nNyGD3KdSk1t7Sz8c3yGEdkjBkIu8JW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\nkKXn5YfO1dY388cX94X2GTfxacf+kzQ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+ "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": 112, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "\n", + "# Solution goes here\n", + "def quarantine(system, fraction):\n", + " system.init.I -= fraction" + ] + }, + { + "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 +} diff --git a/code/chap06mine.ipynb b/code/chap06mine.ipynb new file mode 100644 index 00000000..d1eadbb8 --- /dev/null +++ b/code/chap06mine.ipynb @@ -0,0 +1,1267 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Modeling and Simulation in Python\n", + "\n", + "Chapter 6: Analysis\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": [ + "### Code from the previous chapter" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "`make_system`, `plot_results`, and `calc_total_infected` are unchanged." + ] + }, + { + "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 /= np.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": "code", + "execution_count": 6, + "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='Resistant')\n", + " decorate(xlabel='Time (days)',\n", + " ylabel='Fraction of population')" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "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 updated version of `run_simulation` that uses `unpack`." + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "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": 9, + "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", + " \n", + " s, i, r = state\n", + "\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": 10, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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" + ], + "text/plain": [ + " S I R\n", + "0 0.988889 0.011111 0.000000\n", + "1 0.985230 0.011992 0.002778\n", + "2 0.981296 0.012929 0.005776\n", + "3 0.977071 0.013921 0.009008\n", + "4 0.972541 0.014970 0.012488" + ] + }, + "execution_count": 10, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "system = make_system(0.333, 0.25)\n", + "run_simulation(system, update1)\n", + "system.results.head()" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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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": 12, + "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": 13, + "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": 17, + "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": 18, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "infected_sweep = sweep_beta(beta_array, gamma)" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "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": 20, + "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": 20, + "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": 21, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([ 0.1, 0.3, 0.5, 0.7])" + ] + }, + "execution_count": 21, + "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": 22, + "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": 25, + "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": 26, + "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": 26, + "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": 27, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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TwQ1bIQ53RWJohYWLb9y4wYgRI4iPjycgIKCph9Mg5Ofnc/r0aQYNGoRMZlwop1KpiIyM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\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": 28, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "(11, 4)" + ] + }, + "execution_count": 28, + "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": 29, + "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": 31, + "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": 32, + "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": 40, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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4eDjOnj2L0NBQHDt2DLm5uQgICJC6b3FxMXx8fNCrVy+cOXMGM2bMwNq1a3Hj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\n+zs7OyM5OVnsRl1iYiKcnJya9WUbWee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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Solution goes here\n", + "def plot_sweep_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(frac_infected, beta-gamma, 'ro',\n", + " label='Simulation')\n", + " \n", + "plot_sweep_difference(frame)\n", + "\n", + "decorate(xlabel='Fraction infected',\n", + " ylabel='Contact number (beta-gamma)',\n", + " legend=False)" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "# Solution goes here" + ] + }, + { + "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": 41, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "s_inf_array = linspace(0.0001, 0.9999, 101)\n", + "#s_inf_array" + ] + }, + { + "cell_type": "code", + "execution_count": 42, + "metadata": { + "collapsed": true + }, + "outputs": [], + "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": 43, + "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": 44, + "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": 46, + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "data": { + "text/plain": [ + "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" + ] + }, + "execution_count": 46, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Solution goes here\n", + "frac_infected_series" + ] + }, + { + "cell_type": "code", + "execution_count": 47, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "1.158096819542062" + ] + }, + "execution_count": 47, + "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": [] + } + ], + "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 +} diff --git a/code/chap07mine.ipynb b/code/chap07mine.ipynb new file mode 100644 index 00000000..433acc24 --- /dev/null +++ b/code/chap07mine.ipynb @@ -0,0 +1,1826 @@ +{ + "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": 3, + "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": 4, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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+ "outputs": [ + { + "data": { + "image/png": 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sbCxJQnQp3V0scbYz5ZfTOZxLuwxAdW09O4+kk5xRzPBgd8yM5alCdH0aTYFd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\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": 11, + "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": 12, + "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": 13, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "72.299625390403094" + ] + }, + "execution_count": 13, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "coffee = make_system(T_init=90, r=0.01, volume=300, t_end=30)\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": 15, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "7.3790079710980949" + ] + }, + "execution_count": 15, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Solution goes here\n", + "milk = make_system(T_init=5, r=0.01, volume=50, t_end=15)\n", + "run_simulation(milk, update)\n", + "final_temp(milk)" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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LJ89EKGRwLbsCv/x9C4XljaJ2EyMdvBzugqH+9lSvhJCnINccyj///INly5bB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\npUtYs2YNpk2bhmHDhqn7cETMzMzw559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+ "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": 17, + "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": 18, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([ 1.])" + ] + }, + "execution_count": 18, + "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": 19, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([ 2.])" + ] + }, + "execution_count": 19, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "fsolve(func, 1.9)" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([ 3.])" + ] + }, + "execution_count": 20, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "fsolve(func, 2.9)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "But not always." + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([ 3.])" + ] + }, + "execution_count": 21, + "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": 31, + "metadata": {}, + "outputs": [], + "source": [ + "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(T_init=90, r=r, volume=300, t_end=30)\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": 32, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "2.2996253904030937" + ] + }, + "execution_count": 32, + "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": 33, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "0.011543084583973956" + ] + }, + "execution_count": 33, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "solution = fsolve(error_func1, 0.01)\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": 34, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "70.000000000006395" + ] + }, + "execution_count": 34, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "coffee = make_system(T_init=90, r=r_coffee, volume=300, t_end=30)\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": 114, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "19.999999999997765" + ] + }, + "execution_count": 114, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "r_milk = 0.1329607893546\n", + "milk = make_system(T_init=5, t_end=15, r=r_milk, volume=50)\n", + "run_simulation(milk, update)\n", + "final_temp(milk)" + ] + }, + { + "cell_type": "code", + "execution_count": 87, + "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(T_init=5, r=r, volume=50, t_end=15)\n", + " run_simulation(system, update)\n", + " return final_temp(system) - 20" + ] + }, + { + "cell_type": "code", + "execution_count": 88, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "-1.500149245609034" + ] + }, + "execution_count": 88, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Solution goes here\n", + "error_func1(0.1)" + ] + }, + { + "cell_type": "code", + "execution_count": 89, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "0.13296078935466452" + ] + }, + "execution_count": 89, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Solution goes here\n", + "solution = fsolve(error_func1, 0.01)\n", + "r_milk = solution[0]\n", + "r_milk" + ] + }, + { + "cell_type": "code", + "execution_count": 90, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "19.999999999999996" + ] + }, + "execution_count": 90, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Solution goes here\n", + "r_milk = 0.13296078935466452\n", + "milk = make_system(T_init=5, t_end=15, r=r_milk, volume=50)\n", + "run_simulation(milk, update)\n", + "final_temp(milk)" + ] + }, + { + "cell_type": "code", + "execution_count": 115, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "#simulating milk kept in the fridge\n", + "r_milk = 0\n" + ] + }, + { + "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": 116, + "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": 117, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "70.000000000006395" + ] + }, + "execution_count": 117, + "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": 118, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "5.0" + ] + }, + "execution_count": 118, + "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": 119, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Saving figure to file chap07-fig01.pdf\n" + ] + }, + { + "data": { + "image/png": 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6du2Kdu3aISQkRLt0ypPNTfpoFnH09/dHfHx8Vd8GEdUgBtUkvvzyS+Tm5mLC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\nQUREev1/N2Ph9Q1jbRQAAAAASUVORK5CYII=\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": 120, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "60.714285714291194" + ] + }, + "execution_count": 120, + "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": 121, + "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": 122, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "61.42857142857666" + ] + }, + "execution_count": 122, + "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": 123, + "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": 124, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "61.42857142857666" + ] + }, + "execution_count": 124, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "run_and_mix(0)" + ] + }, + { + "cell_type": "code", + "execution_count": 125, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "61.102449020421695" + ] + }, + "execution_count": 125, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "run_and_mix(15)" + ] + }, + { + "cell_type": "code", + "execution_count": 126, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "60.714285714291194" + ] + }, + "execution_count": 126, + "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": 127, + "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": 128, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Saving figure to file chap07-fig02.pdf\n" + ] + }, + { + "data": { + "image/png": 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gMM0Bxu7GdHqMkD5CpBUkCekuBRUF2L9jD98QX6Hmlk3VTYj/Vzyt/UJIH0KFhfQoTRNN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\nx2VxX73sM8nqviotLcWSJUvg5eUFDw8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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": "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": 129, + "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": 130, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "r_coffee2 = 0.011610223142273859" + ] + }, + { + "cell_type": "code", + "execution_count": 131, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "70.0" + ] + }, + "execution_count": 131, + "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": 132, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "70.000000000006395" + ] + }, + "execution_count": 132, + "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": 133, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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" + ], + "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": 2, + "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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\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": 6, + "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": 7, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "I = interpolate(data.insulin)" + ] + }, + { + "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": 8, + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array(68.0)" + ] + }, + "execution_count": 8, + "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": 9, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Saving figure to file chap08-fig02.pdf\n" + ] + }, + { + "data": { + "image/png": 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ma6lYhBDiDiqWxvLee+/x5ptv8vDDD2NqaoqVlRWffvopzZo1IyMjg5YtW2pd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\nMnv2bAYPHsybb74JgKWlJWVlZVrXlZa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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": 10, + "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": 11, + "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": 13, + "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": 14, + "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": 15, + "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": 16, + "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": 22, + "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": 23, + "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": 24, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "(-5.9399999999999995, 0.0)" + ] + }, + "execution_count": 24, + "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": 25, + "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": 26, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "%psource run_odeint" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here's how we run it." + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Wall time: 99.8 ms\n" + ] + } + ], + "source": [ + "%time run_odeint(system2, slope_func)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "And here are the results." + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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8244.3850490.004280
10233.3856890.004877
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
52109.1259280.006436
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14288.3567580.000232
16290.136930-0.000339
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": 28, + "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": 29, + "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": 30, + "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": "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": 31, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "k1 = 0.03\n", + "k2 = 0.02\n", + "k3 = 1e-05\n", + "G0 = 290" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Again, we'll get basal levels from the initial values." + ] + }, + { + "cell_type": "code", + "execution_count": 32, + "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": 33, + "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": 34, + "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": 64, + "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", + " error = system.results.G - data.glucose\n", + " return error.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": 65, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "(290, 0.026456312354216596, 0.010968286681256679, 1.1402632684701284e-05)" + ] + }, + "execution_count": 65, + "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": 66, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "(290, 0.026456312354216596, 0.010968286681256679, 1.1402632684701284e-05)\n" + ] + }, + { + "data": { + "text/plain": [ + "time\n", + "8 8.245142\n", + "10 21.631919\n", + "12 16.344475\n", + "14 12.433851\n", + "16 11.945952\n", + "19 2.592244\n", + "22 10.318723\n", + "27 1.123579\n", + "32 6.514056\n", + "42 -0.240208\n", + "52 1.374451\n", + "62 2.706393\n", + "72 3.041835\n", + "82 5.279407\n", + "92 -2.439177\n", + "102 -2.740593\n", + "122 -4.020714\n", + "142 -2.256353\n", + "162 -2.712115\n", + "182 -4.935796\n", + "dtype: float64" + ] + }, + "execution_count": 66, + "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": 67, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "%psource fit_leastsq" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here's how we call it." + ] + }, + { + "cell_type": "code", + "execution_count": 68, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[ 2.90000000e+02 2.64563124e-02 1.09682867e-02 1.14026327e-05]\n", + "[ 2.90000000e+02 2.64563124e-02 1.09682867e-02 1.14026327e-05]\n", + "[ 2.90000000e+02 2.64563124e-02 1.09682867e-02 1.14026327e-05]\n", + "[ 2.90000004e+02 2.64563124e-02 1.09682867e-02 1.14026327e-05]\n", + "[ 2.90000000e+02 2.64563127e-02 1.09682867e-02 1.14026327e-05]\n", + "[ 2.90000000e+02 2.64563124e-02 1.09682868e-02 1.14026327e-05]\n", + "[ 2.90000000e+02 2.64563124e-02 1.09682867e-02 1.14026329e-05]\n", + "[ 2.69071429e+02 2.53792035e-02 1.23766891e-02 1.14026903e-05]\n", + "[ 2.69071433e+02 2.53792035e-02 1.23766891e-02 1.14026903e-05]\n", + "[ 2.69071429e+02 2.53792039e-02 1.23766891e-02 1.14026903e-05]\n", + "[ 2.69071429e+02 2.53792035e-02 1.23766893e-02 1.14026903e-05]\n", + "[ 2.69071429e+02 2.53792035e-02 1.23766891e-02 1.14026904e-05]\n", + "[ 2.65578352e+02 2.26983296e-02 1.67968354e-02 1.40060563e-05]\n", + "[ 2.65578356e+02 2.26983296e-02 1.67968354e-02 1.40060563e-05]\n", + "[ 2.65578352e+02 2.26983300e-02 1.67968354e-02 1.40060563e-05]\n", + "[ 2.65578352e+02 2.26983296e-02 1.67968356e-02 1.40060563e-05]\n", + "[ 2.65578352e+02 2.26983296e-02 1.67968354e-02 1.40060565e-05]\n", + "[ 2.65733403e+02 2.27223166e-02 1.69002155e-02 1.40772295e-05]\n", + "[ 2.65733403e+02 2.27223166e-02 1.69002155e-02 1.40772295e-05]\n", + "[ 2.65733403e+02 2.27223166e-02 1.69002155e-02 1.40772295e-05]\n", + "[ 2.65733403e+02 2.27223166e-02 1.69002155e-02 1.40772295e-05]\n", + "[ 2.65692401e+02 2.27122853e-02 1.68536398e-02 1.40538113e-05]\n", + "[ 2.65656229e+02 2.27046636e-02 1.68210523e-02 1.40350235e-05]\n", + "[ 2.65624908e+02 2.27001423e-02 1.68057251e-02 1.40217623e-05]\n", + "[ 2.65624912e+02 2.27001423e-02 1.68057251e-02 1.40217623e-05]\n", + "[ 2.65624908e+02 2.27001426e-02 1.68057251e-02 1.40217623e-05]\n", + "[ 2.65624908e+02 2.27001423e-02 1.68057253e-02 1.40217623e-05]\n", + "[ 2.65624908e+02 2.27001423e-02 1.68057251e-02 1.40217625e-05]\n", + "[ 2.65624519e+02 2.27003081e-02 1.68071158e-02 1.40088134e-05]\n", + "[ 2.65624523e+02 2.27003081e-02 1.68071158e-02 1.40088134e-05]\n", + "[ 2.65624519e+02 2.27003084e-02 1.68071158e-02 1.40088134e-05]\n", + "[ 2.65624519e+02 2.27003081e-02 1.68071161e-02 1.40088134e-05]\n", + "[ 2.65624519e+02 2.27003081e-02 1.68071158e-02 1.40088136e-05]\n", + "[ 2.65611212e+02 2.26997713e-02 1.68072219e-02 1.40087110e-05]\n", + "[ 2.65618131e+02 2.27000445e-02 1.68071666e-02 1.40087820e-05]\n", + "[ 2.65621208e+02 2.27001702e-02 1.68071426e-02 1.40088012e-05]\n", + "[ 2.65622842e+02 2.27002379e-02 1.68071295e-02 1.40088083e-05]\n", + "[ 2.65623681e+02 2.27002729e-02 1.68071227e-02 1.40088111e-05]\n", + "[ 2.65624104e+02 2.27002906e-02 1.68071193e-02 1.40088123e-05]\n", + "[ 2.65624336e+02 2.27003004e-02 1.68071174e-02 1.40088129e-05]\n", + "[ 2.65624430e+02 2.27003043e-02 1.68071166e-02 1.40088132e-05]\n", + "[ 2.65624477e+02 2.27003063e-02 1.68071162e-02 1.40088133e-05]\n", + "[ 2.65624500e+02 2.27003073e-02 1.68071160e-02 1.40088133e-05]\n", + "[ 2.65624511e+02 2.27003077e-02 1.68071159e-02 1.40088134e-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": 69, + "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": 70, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Saving figure to file chap08-fig04.pdf\n" + ] + }, + { + "data": { + "image/png": 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dW0Nyenr6HceK2NnZ0a9fP0xMbl1227ZtFBYWEhAQwJUrV7CxsWH27NkEBATw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\nm4TxZHQKu7+7QlZuYV2HKISoA1UmkJS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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": 72, + "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": 73, + "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_G0.022700
S_I0.000834
\n", + "
" + ], + "text/plain": [ + "S_G 0.022700\n", + "S_I 0.000834\n", + "dtype: float64" + ] + }, + "execution_count": 73, + "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": 74, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "I0 = 360\n", + "k = 0.25\n", + "gamma = 0.004\n", + "G_T = 80" + ] + }, + { + "cell_type": "code", + "execution_count": 85, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "# Solution goes here\n", + "def make_system(I0, k, gamma, G_T, 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(I=I0)\n", + " system = System(init=init,\n", + " k=k,\n", + " gamma=gamma, G_T=G_T, \n", + " G=interpolate(data.insulin),\n", + " ts=data.index)\n", + " return system" + ] + }, + { + "cell_type": "code", + "execution_count": 86, + "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": 95, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "# Solution goes here\n", + "def slope_func(state, t, system):\n", + " \n", + " \n", + " \n", + " I = state\n", + " \n", + " unpack(system)\n", + " \n", + " dI = - k * I + gamma * (G(t) - G_T) * t\n", + " \n", + " return dI" + ] + }, + { + "cell_type": "code", + "execution_count": 100, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "I -90.0\n", + "dtype: float64" + ] + }, + "execution_count": 100, + "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": 107, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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QBGFYvhcR0Vh2W5qS5s2bh6NHjyqOHT58GGVlZfL52tpaRX/C4cOHYTabUVJSckvKlGzW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\nHImiodmL+kYPrrnccDR5FJP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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Solution goes here\n", + "run_odeint(system, slop_func)\n", + "plot(system.results)\n", + "plot(data.insulin,'--')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [] + }, + { + "cell_type": "code", + "execution_count": 47, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "# Solution goes here" + ] + }, + { + "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": 111, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "[360, 0.25, 0.004, 80]" + ] + }, + "execution_count": 111, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Solution goes here\n", + "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", + " error = system.results.I - data.insulin\n", + " return error.loc[8:]\n", + "\n", + "params = I0, k, gamma, G_T\n", + "params" + ] + }, + { + "cell_type": "code", + "execution_count": 112, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[360, 0.25, 0.004, 80]\n" + ] + }, + { + "data": { + "text/plain": [ + "time\n", + "8 -2.476273\n", + "10 -21.291152\n", + "12 -30.511971\n", + "14 -35.277852\n", + "16 -35.547314\n", + "19 -37.407039\n", + "22 -42.230439\n", + "27 -45.306835\n", + "32 -52.769572\n", + "42 -55.654399\n", + "52 -62.941706\n", + "62 -75.157612\n", + "72 -84.533744\n", + "82 -96.793755\n", + "92 -108.332070\n", + "102 -120.778722\n", + "122 -143.383598\n", + "142 -167.392637\n", + "162 -190.018810\n", + "182 -214.350539\n", + "dtype: float64" + ] + }, + "execution_count": 112, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Solution goes here\n", + "error_func(params, data)" + ] + }, + { + "cell_type": "code", + "execution_count": 50, + "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": 113, + "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", + "[ 3.69575355e+02 2.78052084e-01 1.54303701e-03 6.67301200e+01]\n", + "[ 3.69575360e+02 2.78052084e-01 1.54303701e-03 6.67301200e+01]\n", + "[ 3.69575355e+02 2.78052088e-01 1.54303701e-03 6.67301200e+01]\n", + "[ 3.69575355e+02 2.78052084e-01 1.54303703e-03 6.67301200e+01]\n", + "[ 3.69575355e+02 2.78052084e-01 1.54303701e-03 6.67301210e+01]\n", + "[ 5.46315703e+02 2.73118946e-01 6.04784316e-04 2.11965290e+01]\n", + "[ 5.46315711e+02 2.73118946e-01 6.04784316e-04 2.11965290e+01]\n", + "[ 5.46315703e+02 2.73118950e-01 6.04784316e-04 2.11965290e+01]\n", + "[ 5.46315703e+02 2.73118946e-01 6.04784325e-04 2.11965290e+01]\n", + "[ 5.46315703e+02 2.73118946e-01 6.04784316e-04 2.11965293e+01]\n", + "[ 5.56446890e+02 2.57358418e-01 3.78698661e-03 -7.74843830e+01]\n", + "[ 5.40204324e+02 2.46771874e-01 4.65517120e-04 1.07723774e+01]\n", + "[ 5.40204332e+02 2.46771874e-01 4.65517120e-04 1.07723774e+01]\n", + "[ 5.40204324e+02 2.46771877e-01 4.65517120e-04 1.07723774e+01]\n", + "[ 5.40204324e+02 2.46771874e-01 4.65517127e-04 1.07723774e+01]\n", + "[ 5.40204324e+02 2.46771874e-01 4.65517120e-04 1.07723776e+01]\n", + "[ 4.85784683e+02 2.32996316e-01 1.49421999e-03 -7.25352594e+00]\n", + "[ 4.85784690e+02 2.32996316e-01 1.49421999e-03 -7.25352594e+00]\n", + "[ 4.85784683e+02 2.32996319e-01 1.49421999e-03 -7.25352594e+00]\n", + "[ 4.85784683e+02 2.32996316e-01 1.49422001e-03 -7.25352594e+00]\n", + "[ 4.85784683e+02 2.32996316e-01 1.49421999e-03 -7.25352583e+00]\n", + "[ 3.99434598e+02 2.14494922e-01 1.44716140e-03 -5.43638204e+00]\n", + "[ 3.99434604e+02 2.14494922e-01 1.44716140e-03 -5.43638204e+00]\n", + "[ 3.99434598e+02 2.14494925e-01 1.44716140e-03 -5.43638204e+00]\n", + "[ 3.99434598e+02 2.14494922e-01 1.44716142e-03 -5.43638204e+00]\n", + "[ 3.99434598e+02 2.14494922e-01 1.44716140e-03 -5.43638196e+00]\n", + "[ 2.25855346e+02 1.67089921e-01 1.52107063e-03 -4.24637539e+00]\n", + "[ 2.25855350e+02 1.67089921e-01 1.52107063e-03 -4.24637539e+00]\n", + "[ 2.25855346e+02 1.67089924e-01 1.52107063e-03 -4.24637539e+00]\n", + "[ 2.25855346e+02 1.67089921e-01 1.52107065e-03 -4.24637539e+00]\n", + "[ 2.25855346e+02 1.67089921e-01 1.52107063e-03 -4.24637533e+00]\n", + "[ 1.69219435e+02 1.25076595e-01 1.44677078e-03 -3.76402412e+00]\n", + "[ 1.69219437e+02 1.25076595e-01 1.44677078e-03 -3.76402412e+00]\n", + "[ 1.69219435e+02 1.25076597e-01 1.44677078e-03 -3.76402412e+00]\n", + "[ 1.69219435e+02 1.25076595e-01 1.44677080e-03 -3.76402412e+00]\n", + "[ 1.69219435e+02 1.25076595e-01 1.44677078e-03 -3.76402407e+00]\n", + "[ 1.56800070e+02 1.16011917e-01 1.39837301e-03 -3.80539493e+00]\n", + "[ 1.56800073e+02 1.16011917e-01 1.39837301e-03 -3.80539493e+00]\n", + "[ 1.56800070e+02 1.16011918e-01 1.39837301e-03 -3.80539493e+00]\n", + "[ 1.56800070e+02 1.16011917e-01 1.39837303e-03 -3.80539493e+00]\n", + "[ 1.56800070e+02 1.16011917e-01 1.39837301e-03 -3.80539488e+00]\n", + "[ 1.47954391e+02 1.16801603e-01 1.43859181e-03 -3.82387975e+00]\n", + "[ 1.47954391e+02 1.16801603e-01 1.43859181e-03 -3.82387975e+00]\n", + "[ 1.52804845e+02 1.17453783e-01 1.42727551e-03 -3.93724647e+00]\n", + "[ 1.55750778e+02 1.16703085e-01 1.41232453e-03 -3.89582049e+00]\n", + "[ 1.56442354e+02 1.16250330e-01 1.40394804e-03 -3.84220323e+00]\n", + "[ 1.56656024e+02 1.16106395e-01 1.40071802e-03 -3.82095133e+00]\n", + "[ 1.56737925e+02 1.16052310e-01 1.39940072e-03 -3.81222595e+00]\n", + "[ 1.56773721e+02 1.16028966e-01 1.39881167e-03 -3.80831323e+00]\n", + "[ 1.56788984e+02 1.16019076e-01 1.39855809e-03 -3.80662671e+00]\n", + "[ 1.56795421e+02 1.16014916e-01 1.39845072e-03 -3.80591219e+00]\n", + "[ 1.56798123e+02 1.16013172e-01 1.39840557e-03 -3.80561168e+00]\n", + "[ 1.56799256e+02 1.16012442e-01 1.39838664e-03 -3.80548565e+00]\n", + "[ 1.56799729e+02 1.16012137e-01 1.39837871e-03 -3.80543291e+00]\n", + "[ 1.56799928e+02 1.16012009e-01 1.39837540e-03 -3.80541084e+00]\n", + "[ 1.56800011e+02 1.16011955e-01 1.39837401e-03 -3.80540158e+00]\n", + "[ 1.56800046e+02 1.16011933e-01 1.39837342e-03 -3.80539766e+00]\n", + "[ 1.56800060e+02 1.16011923e-01 1.39837318e-03 -3.80539610e+00]\n", + "[ 1.56800066e+02 1.16011920e-01 1.39837308e-03 -3.80539544e+00]\n", + "[ 1.56800069e+02 1.16011918e-01 1.39837304e-03 -3.80539513e+00]\n", + "[ 1.56800071e+02 1.16011918e-01 1.39837304e-03 -3.80539513e+00]\n", + "[ 1.56800069e+02 1.16011920e-01 1.39837304e-03 -3.80539513e+00]\n", + "[ 1.56800069e+02 1.16011918e-01 1.39837306e-03 -3.80539513e+00]\n", + "[ 1.56800069e+02 1.16011918e-01 1.39837304e-03 -3.80539508e+00]\n", + "[ 1.56800066e+02 1.16011917e-01 1.39837302e-03 -3.80539518e+00]\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" + ] + }, + { + "ename": "AttributeError", + "evalue": "'numpy.ndarray' object has no attribute 'results'", + "output_type": "error", + "traceback": [ + "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m", + "\u001b[1;31mAttributeError\u001b[0m Traceback (most recent call last)", + "\u001b[1;32m\u001b[0m in \u001b[0;36m\u001b[1;34m()\u001b[0m\n\u001b[0;32m 1\u001b[0m \u001b[1;31m# Solution goes here\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 2\u001b[0m \u001b[0mparameters\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mfit_leastsq\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0merror_func\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mparams\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mdata\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m----> 3\u001b[1;33m \u001b[0mplot\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mparameters\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mresults\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m", + "\u001b[1;31mAttributeError\u001b[0m: 'numpy.ndarray' object has no attribute 'results'" + ] + } + ], + "source": [ + "# Solution goes here\n", + "parameters = fit_leastsq(error_func, params, data)\n", + "plot(parameters.results)" + ] + }, + { + "cell_type": "code", + "execution_count": 118, + "metadata": {}, + "outputs": [], + "source": [ + "# Solution goes here\n", + "system = make_system(*params, data)\n", + "run_odeint(system, slope_func)" + ] + }, + { + "cell_type": "code", + "execution_count": 119, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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QBGFYvhcR0Vh2W5qS5s2bh6NHjyqOHT58GGVlZfL52tpaRX/C4cOHYTabUVJSckvKlGzW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\nYDAQEZECg4GIiBT+f5i5dnHwjWujAAAAAElFTkSuQmCC\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Solution goes here\n", + "plot(system.results)\n", + "plot(data.insulin, '--')" + ] + }, + { + "cell_type": "code", + "execution_count": 54, + "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": 127, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "# Solution goes here\n", + "Imax = data.insulin.max()\n", + "Ib = data.insulin[0]\n", + "G0 = data.glucose.max()\n", + "gb = data.glucose[0]" + ] + }, + { + "cell_type": "code", + "execution_count": 135, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "1.8449612403100775" + ] + }, + "execution_count": 135, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Solution goes here\n", + "phi1 = (Imax - Ib) / (k * (G0 - Gb))\n", + "phi1\n" + ] + }, + { + "cell_type": "code", + "execution_count": 138, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "40.0" + ] + }, + "execution_count": 138, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Solution goes here\n", + "phi2 = gamma * 1e4\n", + "phi2" + ] + }, + { + "cell_type": "code", + "execution_count": 58, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "# Solution goes here" + ] + }, + { + "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 36f0ad0d2ffccb07b74c83a5f6980b761492f64b Mon Sep 17 00:00:00 2001 From: Christopher Lather Date: Wed, 13 Dec 2017 06:33:07 -0500 Subject: [PATCH 08/10] commiting chap09mine --- code/chap09mine.ipynb | 1861 +++++++++++++++++++++++++++++++++++++++++ 1 file changed, 1861 insertions(+) create mode 100644 code/chap09mine.ipynb diff --git a/code/chap09mine.ipynb b/code/chap09mine.ipynb new file mode 100644 index 00000000..f87e7325 --- /dev/null +++ b/code/chap09mine.ipynb @@ -0,0 +1,1861 @@ +{ + "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": 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": { + "collapsed": true + }, + "source": [ + "### Dropping pennies\n", + "\n", + "I'll start by getting the units we'll need from Pint." + ] + }, + { + "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": { + "collapsed": true + }, + "source": [ + "And defining the initial state." + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "data": { + "text/html": [ + "
\n", + "\n", + "\n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + "
value
y381 meter
v0.0 meter / second
\n", + "
" + ], + "text/plain": [ + "y 381 meter\n", + "v 0.0 meter / second\n", + "dtype: object" + ] + }, + "execution_count": 3, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "init = State(y=381 * m, \n", + " v=0 * m/s)\n", + "init" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": true + }, + "source": [ + "Acceleration due to gravity is about 9.8 m / s$^2$." + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "g = 9.8 * m/s**2" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": true + }, + "source": [ + "When we call `odeint`, we need an array of timestamps where we want to compute the solution.\n", + "\n", + "I'll start with a duration of 10 seconds." + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "[ 0. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10.] second" + ], + "text/latex": [ + "$[ 0. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10.] second$" + ], + "text/plain": [ + "" + ] + }, + "execution_count": 5, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "duration = 10 * s\n", + "ts = linspace(0, duration, 11)\n", + "ts" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": true + }, + "source": [ + "Now we make a `System` object." + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "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": 34, + "metadata": {}, + "outputs": [], + "source": [ + "def slope_func(state, t, system):\n", + " \"\"\"Compute derivatives of the state.\n", + " \n", + " state: position, velocity\n", + " t: time\n", + " system: System object containing `g`\n", + " \n", + " returns: derivatives of y and v\n", + " \"\"\"\n", + " y, v = state\n", + " unpack(system) \n", + "\n", + " dydt = v\n", + " dvdt = -g\n", + " \n", + " #print('call')\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": 19, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "call\n", + "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": 20, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "call\n", + "call\n", + "call\n", + "call\n", + "call\n", + "call\n", + "call\n", + "call\n", + "call\n", + "call\n", + "call\n", + "call\n", + "call\n" + ] + } + ], + "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": 21, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
\n", + "\n", + "\n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + "
yv
0.0381.00.0
1.0376.1-9.8
2.0361.4-19.6
3.0336.9-29.4
4.0302.6-39.2
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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" + ] + }, + "execution_count": 21, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "system.results.head()" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
\n", + "\n", + "\n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + "
yv
6.0204.6-58.8
7.0140.9-68.6
8.067.4-78.4
9.0-15.9-88.2
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" + ], + "text/plain": [ + " y v\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": 22, + "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": 23, + "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": 24, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Saving figure to file chap09-fig01.pdf\n" + ] + }, + { + "data": { + "image/png": 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UKnYeKgSs09us/T6bW27ohNZFAqc5alLYAMTGxrJw4UJ71iKEEE1yfrYBjVrN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\n7Nq1yrBxcXHhySefJCMjg50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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plot_position(system.results)\n", + "savefig('chap09-fig01.pdf')" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": true + }, + "source": [ + "**Exercise:** Add a print statement to `slope_func` to print the value of `t` each time it's called. 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": 49, + "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": 50, + "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": 50, + "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": 51, + "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": 52, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array(8.81792826905006)" + ] + }, + "execution_count": 52, + "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": 53, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "8.817885349720552 second" + ], + "text/latex": [ + "$8.817885349720552 second$" + ], + "text/plain": [ + "" + ] + }, + "execution_count": 53, + "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": 54, + "metadata": {}, + "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": 55, + "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": 56, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "-0.003708896250259386 meter" + ], + "text/latex": [ + "$-0.003708896250259386 meter$" + ], + "text/plain": [ + "" + ] + }, + "execution_count": 56, + "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": 57, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "-86.41569703669059 meter/second" + ], + "text/latex": [ + "$-86.41569703669059 \\frac{meter}{second}$" + ], + "text/plain": [ + "" + ] + }, + "execution_count": 57, + "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": 58, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "-311.0965093320861 kilometer/hour" + ], + "text/latex": [ + "$-311.0965093320861 \\frac{kilometer}{hour}$" + ], + "text/plain": [ + "" + ] + }, + "execution_count": 58, + "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": 59, + "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 * s" + ] + }, + { + "cell_type": "code", + "execution_count": 77, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Solution goes here\n", + "v_array = linrange(0,25,1)\n", + "for v_init in v_array:\n", + " system = make_system(10,v_init)\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", + " plot(v_init, T_sidewalk, 'r')" + ] + }, + { + "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": 82, + "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": 83, + "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": 84, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
\n", + "\n", + "\n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + "
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inity 381 meter\n", + "v 0.0 meter / secon...
g9.8 meter / second ** 2
mass0.0025 kilogram
rho1.2 kilogram / meter ** 3
C_d0.4445009981135434 dimensionless
area0.0002835287369864788 meter ** 2
ts[0.0 second, 0.3 second, 0.6 second, 0.8999999...
\n", + "
" + ], + "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": 84, + "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": 85, + "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": 86, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "(, )" + ] + }, + "execution_count": 86, + "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": 87, + "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": 88, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "(,\n", + " )" + ] + }, + "execution_count": 88, + "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": 89, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array(22.439794207078908)" + ] + }, + "execution_count": 89, + "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": 90, + "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": 91, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "(,\n", + " )" + ] + }, + "execution_count": 91, + "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": 92, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Saving figure to file chap09-fig02.pdf\n" + ] + }, + { + "data": { + "image/png": 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EiBBGoCgK0eGeBHo7sedYNoVXawDIL61m4+5Uhkf70S/UXVqhiE7RZoAkJibi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\nhBDiJ9jbWvHA8BDGxQdiZXl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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": 93, + "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": 94, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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cGiDh4eHYu3dvi9dkMtv+63v//v0AAE/PxlP9+vTpg9zcXGzZssWlAkQQBPTq\nEoR/5VwGAJz87QoDhIhcikMDRKlUonv37rf1GteCw9wdd9yBH3744bZeVwq9ugThyK+FMIoiLpVq\nUFimNW24SETk7Fxq0L20tBQJCQn48ssvLdpzcnLQo0cPiapqPR9PJXqaLSzMPlUsYTVERLfG6SbR\nbyQkJASxsbFYtWoVfH19ER4ejm3btuHYsWPYvn271OW1SlyvMJy+0DiZ/vulSpRV1iLYv3kvi4jI\n2bhUDwQA1qxZg+TkZLz00ksYN24cjh49is2bN6Nnz55Sl9Yqwf6e6Gq2zfux0+yFEJFrcOoeSEsr\n0f38/LB8+XIsX77c8QXZSXyvMPx+qfF8kDMXKjDwPzrA38d1FkYSkXtyuR5Ie9Qh2BvRYb4AGk8r\nPH6mROKKiIhujgHiJOJ7hZm+P/l7Gaq0OgmrISK6OQaIk4gO80F40PVden84cUniioiIbowB4iQE\nQUDSnVGmn/MKKpBfxBMLich5MUCcSESIN2I6BZp+/v74RRiMooQVERFZxwBxMneZbapYVlWHnLxS\niSsiImoZA8TJ+HgqMbB3B9PPR34tRE1dg4QVERG1jAHihO7sGYKAq+tA6hsM2H/kAkSRQ1lE5FwY\nIE5ILpfhnrho0zG3+UXVOHaaa0OIyLkwQJxUx3BfxMWEmn7+V85lFJZpJayIiMgSA8SJJfaJMG3v\nbhRFfPnjedTp9BJXRUTUiAHixOQyAaMSO0GllAMAqrQ6fHH4HPQGo7SFERGBAeL0/H08MCK+o+nn\ngmIN9h+5ACPXhxCRxBggLqBHxwAM7hth+jmvoAKHjhXwziwikhQDxEXE9wrDnT2vT6rn/FaG73++\nxBAhIskwQFxE415ZkRZbnfycW4Iv/nWecyJEJAkGiAsRBAEjBnZC96jrJxjmFVRg58E8rlYnIodj\ngLgYuUzA6MFdLIazCsu0+OSrM9y9l4gcigHigmQyAckDopA8IMq0Wl1T24Bdh/Jw8GgBGvQGiSsk\nInfAAHFhd/YMxR+HdIWnx/Wj7X/JK8XHX55Gbn45J9iJyK4YIC6uS4QfHrk3Bl0jr8+LVGl12Pev\n8/j061zkF1UzSIjILhgg7YCXWokxd3fByIROUKuu90aKy2uw61AePvnqDP79+xXerUVEbUpx84eQ\nKxAEAb27BqFrlB+OnS7Gz7mlpsAoqajF11kX8MOJS+gR7Y/u0QGICvWBTCZIXDURuTIGSDujVilw\nV79I9OsFMkLrAAANnUlEQVQegqx/F+HU+XJTkNTp9Mj5rQw5v5XB00OBzh18ER3ui45hvvD2VEpc\nORG5GgZIO+XjpcKw+I4Y3DcCJ89dQU5eKaq0OtP12no9Tp0vx6nz5QAa99wKC/RCeJAnQgO9EOjr\nAS81Q4WIrGOAtHNqDwXiYsIQe0coLpdpcTa/AmcLKpstPKzU1KNSU4/c/HJTm6eHAgE+HvDzVsHP\nWwVfbxW8PZXw8VTCW62Eh0puuo2YiNwPA8RNCIKAyBAfRIb4IOnOKJRU1CK/qBoFxdW4XKqFoYXd\nfWvr9ait1+OylYOsZIIAD5Ucnh4KqFVyeCjlUF39UipkUCnlUMgFKOQyKBQyKOQyyGWC6Z9yuQwy\nQYBM1ri2RSYIkMsEyGQCBEGAIDS+hyAIkAkwtTG0iJwDA8QNyWQCwoO8EB7khYTe4TAYjCitrEPx\nlRoUXanBlao6lFfXoUF/47u2jKJoChlHEwQBAmARKMLV/2n6c+M/BLPntvx6Fj9bXGurqomcV6Cf\nGvfERiPA18Pm5zBACHK5zBQo/a62iaKI6poGVGrqUaXVoUqrg6ZGB22dHppaHWrq9NA1SLfiXRRF\niADM/oeIboOmtgEnfy/D3f0jbX4OA4RaJAiCae7DGoPBiFqdAXX1jWFS32BAvc4And6ABr0RugYj\n9Hoj9Mar/zQYoTeIMBhFGAxGGMVr34sQRRFGUYTR2NgmijC1iSJM/+SiSCL78FDJ0SXC75aewwCh\nVpPLZfDxlMHHwbcAi9fCpPEHGM16IdfaTUFjljcW7S2+brOn3KiIWy3b8um39WyitufpoYBCfmtr\nyxkg5HKuTaZf/QlyKYshcmNuEyAGQ+N4fWFhocSVEBG5jmt/M6/9DTXnNgFSUlICAJgyZYrElRAR\nuZ6SkhJ07tzZok0Q3WRWsq6uDjk5OQgNDYVczkEPIiJbGAwGlJSUoG/fvlCr1RbX3CZAiIiobXE7\ndyIiahUGCBERtQoDhIiIWoUBQkREreLWAWIwGLBmzRokJSUhNjYWc+fORWlpqdRlOYWzZ88iJiam\n2VdWVpbUpUlu2bJlWLx4sUXb999/j3HjxqF///544IEHcPDgQYmqk15Lv5+JEyc2+yw1fUx7VVpa\nioULFyIpKQkJCQl44okncObMGdN1l/7siG5s3bp14pAhQ8Tvv/9ezMnJESdNmiQ+/PDDUpflFD7/\n/HNx0KBBYnFxscWXTqeTujTJGI1Gcf369eIdd9whvvLKK6b23NxcsW/fvuKbb74pnj17Vly3bp3Y\np08f8cyZMxJW63jWfj9Go1G88847xc8++8zis1RdXS1htY5hMBjEP//5z+LkyZPFn3/+WczNzRXn\nzp0r3nXXXeKVK1dc/rPjNgsJm9LpdMjIyMCSJUswZMgQAMDatWsxcuRIHD16FHFxcRJXKK0zZ86g\nR48eCA0NlboUp5Cfn49XXnkFubm5iIy03K00IyMDAwYMwDPPPAMAmDdvHrKzs5GRkYH//M//lKJc\nh7vR7yc/Px+1tbUYMGCA232eTp06hWPHjmHv3r3o3r07ACAlJQWJiYk4ePAgjh496tKfHbcdwjp1\n6hS0Wi0SExNNbdHR0YiKiuIwDYDc3Fx069ZN6jKcxtGjRxEREYHdu3cjOjra4lpWVpbF5wgABg0a\n5Fafoxv9fs6cOQO1Wo2oqCiJqpNOREQE3n77bXTt2tXUdu3smcrKSpf/7LhtD+Ta/i7h4eEW7WFh\nYdwvC40BUl9fj8mTJ+PixYvo2bMn5s+fj/79+0tdmiTGjRuHcePGtXitsLDQ7T9HN/r95ObmwtfX\nFy+++CKOHDmCwMBATJgwAdOmTYNM1r7/GzYwMBDDhg2zaMvMzERdXR2SkpLwxhtvuPRnp33/v3cD\ntbW1kMlkUCottyJXqVSor6+XqCrnUFdXh/z8fGg0Grz00ktITU1FWFgY/vKXvyAvL0/q8pxOXV0d\nVCrLc1P4Obru7NmzqKmpQVJSEtLT0/Hoo49iw4YN2LRpk9SlOdzXX3+NtWvX4vHHH0f37t1d/rPj\ntj0QtVoNo9EIvV4PheL6r0Gn08HT01PCyqSnVqvx008/QaVSmT7cK1euxK+//oqPPvoIS5culbhC\n5+Lh4YGGhgaLNn6Orlu1ahVqamrg59d4WFFMTAyqq6vx1ltvYc6cOW5zxv327duxdOlSjBkzBgsW\nLADg+p8dt+2BREREALi+S+81xcXFzbqU7sjHx8fiv4xkMhl69OiBy5cvS1iVc4qIiEBxcbFFGz9H\n1ykUClN4XBMTEwOtVovq6mqJqnKs1NRUvPzyy3j44YexevVq09Cdq3923DZAevXqBW9vbxw5csTU\nVlBQgIsXL2LgwIESVia9nJwcxMXFIScnx9RmMBhw6tQp9OzZU8LKnFN8fDx++ukni7Yff/wRCQkJ\nElXkXCZPnoz/+q//smj75ZdfEBYW1ixY2qN3330X69evx9y5c7F06VKLHperf3bcNkBUKhUeffRR\nrF69GocOHcKvv/6K+fPnIzExEQMGDJC6PEn16tULUVFRWLZsGX7++Wfk5ubi5ZdfRnl5OR577DGp\ny3M6f/nLX5CVlYUNGzYgLy8Pb7zxBn7++WdMmzZN6tKcwqhRo7B161bs3LkTFy5cwKeffoq0tDTM\nnTtX6tLs7tSpU1i3bh0eeughTJ48GSUlJaavmpoal//suO0cCNB4z7Ver8eCBQug1+uRnJyMZcuW\nSV2W5BQKBdLS0rB69Wo8/fTTqK2tRVxcHD744AMEBwdLXZ7TiYmJwaZNm5CSkoJ3330X3bp1w1tv\nvWW679/dzZw5EwqFAqmpqbh06RIiIyPx8ssvY9KkSVKXZnd79+6FwWDAP/7xD/zjH/+wuPb8889j\n9uzZLv3Z4XkgRETUKm47hEVERLeHAUJERK3CACEiolZhgBARUaswQIiIqFUYIERE1CpuvQ6EqKlF\nixZhx44dN3xMYmIiMjMzMXXqVMjlcrz//vuOKa4FFRUVmDBhAjZv3ozOnTvf9PGbNm1CaWkpli9f\nbv/iqN3jOhAiMxcuXMCVK1dMP7/22muQy+VYsmSJqc3Hxwc9evTA2bNnIQiCpIu+XnjhBYSHh+Ol\nl16y6fF1dXW47777sGLFCtx11112ro7aO/ZAiMx06tQJnTp1Mv3s4+MDuVze4vY2PXr0cGRpzZw4\ncQL79u3DoUOHbH6OWq3G9OnTsWLFCnz22Wd2rI7cAedAiFpp6tSpmD59uunnmJgYbN26FS+++CJi\nY2MxePBgbNq0CRqNBi+//DLi4+MxZMgQpKSkwLzjX15ejiVLluCuu+5C//798cgjjyA7O/um75+W\nloa7774bQUFBpracnBxMmzYN8fHxiI2NxfTp03H8+HGL540ZMwa5ubn49ttvb/t3QO6NAULUhlat\nWoXAwEC8+eabGD58ODZu3IiJEyfC09MTmzZtwqhRo5CWloYvv/wSAFBfX4/p06fj22+/xfz587Fh\nwwb4+/tj+vTpOHHihNX30Wq1OHDgAO69915Tm0ajwcyZMxEYGIiNGzdi3bp1qK2txcyZM6HRaEyP\nCwsLQ2xsLHbv3m2/XwS5BQ5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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": 102, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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i1rthwwbs27cPOTk5ePXVVxXjRKQ+9lbGmDfFCzNHD4Zph2hvW+z3+KXbiigw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\n/bFfTmEREWmxIU7mcLM3RVx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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Solution goes here\n", + "condition.set(v_init = -100 * m/s)\n", + "system = make_system(condition)\n", + "run_odeint(system, slope_func)\n", + "plot_position(system.results)\n", + "plot_velocity(system.results)" + ] + }, + { + "cell_type": "code", + "execution_count": 98, + "metadata": { + "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": 103, + "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": 104, + "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": 105, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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zdu3adcsXmjNnTp8WRkS3x1YmwZwpI3C2oBo/nimHWqOFWqPFwaxSFJY3In68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\nr2LpAAAAAElFTkSuQmCC\n", + "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": 106, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "(,\n", + " )" + ] + }, + "execution_count": 106, + "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": 107, + "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": 108, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "-11.034779626277231 meter" + ], + "text/latex": [ + "$-11.034779626277231 meter$" + ], + "text/plain": [ + "" + ] + }, + "execution_count": 108, + "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": 109, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([ 0.42587017])" + ] + }, + "execution_count": 109, + "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": 110, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "(,\n", + " )" + ] + }, + "execution_count": 110, + "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": [] + } + ], + "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 641b41787427ff5cfd5e94c28193c36292436d16 Mon Sep 17 00:00:00 2001 From: Christopher Lather Date: Wed, 13 Dec 2017 09:11:20 -0500 Subject: [PATCH 09/10] commiting chap10mine --- code/chap10mine.ipynb | 7086 +++++++++++++++++++++++++++++++++++++++++ 1 file changed, 7086 insertions(+) create mode 100644 code/chap10mine.ipynb diff --git a/code/chap10mine.ipynb b/code/chap10mine.ipynb new file mode 100644 index 00000000..15e0add3 --- /dev/null +++ b/code/chap10mine.ipynb @@ -0,0 +1,7086 @@ +{ + "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": 22, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "[ 0. -9.8] meter/second2" + ], + "text/latex": [ + "$[ 0. -9.8] \\frac{meter}{second^{2}}$" + ], + "text/plain": [ + "" + ] + }, + "execution_count": 22, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Solution goes here\n", + "a_grav = Vector(0, -9.8) * m / s**2\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": 28, + "metadata": {}, + "outputs": [], + "source": [ + "# Solution goes here\n", + "\n", + "newton = UNITS.newton\n", + "kg = UNITS.kilogram\n", + "\n", + "angle = 45 * degree\n", + "mag = 0.5 * newton\n", + "force = Vector(x,y)\n", + "mass = 0.3 * kg\n", + "a_force = force / mass" + ] + }, + { + "cell_type": "code", + "execution_count": 31, + "metadata": {}, + "outputs": [ + { + "ename": "NameError", + "evalue": "name 'a_drag' 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 1\u001b[0m \u001b[1;31m# Solution goes here\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m----> 2\u001b[1;33m \u001b[0ma_force\u001b[0m \u001b[1;33m+\u001b[0m \u001b[0ma_drag\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m", + "\u001b[1;31mNameError\u001b[0m: name 'a_drag' is not defined" + ] + } + ], + "source": [ + "# Solution goes here\n", + "a_force + a_drag" + ] + }, + { + "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": 56, + "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 = 20 * 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": 57, + "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": 58, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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initx 0 meter\n", + "y ...
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" + ], + "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": 58, + "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": 59, + "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": 60, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "(,\n", + " ,\n", + " ,\n", + " )" + ] + }, + "execution_count": 60, + "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": 61, + "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": 62, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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" + ], + "text/plain": [ + " x y vx vy\n", + "0.000 0.000000 1.000000 37.587705 13.680806\n", + "0.051 1.906899 1.681354 37.194314 13.040437\n", + "0.102 3.793986 2.330271 36.810668 12.408705\n", + "0.153 5.661746 2.947183 36.436381 11.785274\n", + "0.204 7.510649 3.532505 36.071083 11.169823" + ] + }, + "execution_count": 62, + "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": 63, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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" + ], + "text/plain": [ + " x y vx vy\n", + "4.896 126.687059 -45.944424 17.356104 -27.376544\n", + "4.947 127.568425 -47.347348 17.207340 -27.639546\n", + "4.998 128.442219 -48.763602 17.059203 -27.899243\n", + "5.049 129.308474 -50.193015 16.911701 -28.155647\n", + "5.100 130.167223 -51.635422 16.764840 -28.408769" + ] + }, + "execution_count": 63, + "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": 64, + "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": 65, + "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" + } + ], + "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": 68, + "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": 70, + "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": 71, + "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": 92, + "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: 3.15 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": 93, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "scipy.optimize.optimize.OptimizeResult" + ] + }, + "execution_count": 93, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "type(res)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "With the following variables." + ] + }, + { + "cell_type": "code", + "execution_count": 94, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + " fun: 103.46412613060471\n", + " message: 'Solution found.'\n", + " nfev: 9\n", + " status: 0\n", + " success: True\n", + " x: 41.136412740667161" + ] + }, + "execution_count": 94, + "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": 97, + "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": 98, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "45\n", + "Wall time: 48.1 ms\n" + ] + }, + { + "data": { + "text/plain": [ + "array(102.72237841710975)" + ] + }, + "execution_count": 98, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "%time range_func(45, condition)" + ] + }, + { + "cell_type": "code", + "execution_count": 99, + "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: 469 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": 104, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "# Solution goes here\n", + "def height_func(angle, condition):\n", + " \n", + " print(angle)\n", + " \n", + " condition.set(angle=angle)\n", + " system = make_system(condition)\n", + " run_odeint(system, slope_func)\n", + " \n", + " T = interp_inverse(system.results.x)\n", + " t_wall = T(94.5)\n", + " \n", + " Y = interpolate(system.results.y)\n", + " \n", + " return Y(t_wall)\n", + " \n", + " " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Test your function with a launch angle of 45 degrees:" + ] + }, + { + "cell_type": "code", + "execution_count": 105, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "45\n" + ] + }, + { + "data": { + "text/plain": [ + "array(11.025366370142653)" + ] + }, + "execution_count": 105, + "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": 106, + "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: 702 ms\n" + ] + } + ], + "source": [ + "# Solution goes here\n", + "%time res = max_bounded(range_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": 107, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "41.1364127407\n" + ] + }, + { + "data": { + "text/plain": [ + "array(10.360365286330733)" + ] + }, + "execution_count": 107, + "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": 109, + "metadata": {}, + "outputs": [], + "source": [ + "# Solution goes here\n", + "def best_height(velocity, condition):\n", + " condition.set(velocity = velocity)\n", + " %time res = max_bounded(range_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": 110, + "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: 722 ms\n", + "41.1364127407\n" + ] + }, + { + "data": { + "text/plain": [ + "array(10.360365286330733)" + ] + }, + "execution_count": 110, + "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": 112, + "metadata": {}, + "outputs": [], + "source": [ + "# Solution goes here\n", + "def error_func (velocity, condition):\n", + " height = best_height(velocity, condition)\n", + " return height - 11" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Test your error function like this:" + ] + }, + { + "cell_type": "code", + "execution_count": 113, + "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: 677 ms\n", + "41.1364127407\n" + ] + }, + { + "data": { + "text/plain": [ + "-0.63963471366926683" + ] + }, + "execution_count": 113, + "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": 115, + "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: 675 ms\n", + "41.1364127407\n", + "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: 753 ms\n", + "41.1364127407\n", + "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: 532 ms\n", + "41.1364127407\n", + "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: 638 ms\n", + "41.1364127407\n", + "45.0\n", + "34.3769410125\n", + "55.6230589875\n", + "21.246117975\n", + "41.405185171\n", + "41.2368619719\n", + "41.1390963906\n", + "41.1364126678\n", + "41.1367466113\n", + "41.1360787243\n", + "Wall time: 628 ms\n", + "41.1364127407\n", + "45.0\n", + "34.3769410125\n", + "55.6230589875\n", + "21.246117975\n", + "41.3868594332\n", + "41.2158636745\n", + "41.1177641452\n", + "41.1150266361\n", + "41.1153605792\n", + "41.1146926929\n", + "Wall time: 706 ms\n", + "41.1364127407\n", + "45.0\n", + "34.3769410125\n", + "55.6230589875\n", + "21.246117975\n", + "41.3864739421\n", + "41.2154219413\n", + "41.1173150935\n", + "41.1145776601\n", + "41.1149116032\n", + "41.1142437169\n", + "Wall time: 594 ms\n", + "41.1364127407\n", + "45.0\n", + "34.3769410125\n", + "55.6230589875\n", + "21.246117975\n", + "41.3864710168\n", + "41.2154185892\n", + "41.1173116851\n", + "41.1145742545\n", + "41.1149081977\n", + "41.1142403113\n", + "Wall time: 680 ms\n", + "41.1364127407\n", + "45.0\n", + "34.3769410125\n", + "55.6230589875\n", + "21.246117975\n", + "41.3864710165\n", + "41.2154185889\n", + "41.1173116861\n", + "41.1145742517\n", + "41.1149081948\n", + "41.1142403085\n", + "Wall time: 614 ms\n", + "41.1364127407\n" + ] + }, + { + "data": { + "text/plain": [ + "array([ 40.1820013])" + ] + }, + "execution_count": 115, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Solution goes here\n", + "velocity = fsolve(error_func, 40, condition)\n", + "velocity" + ] + }, + { + "cell_type": "code", + "execution_count": 68, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "# Solution goes here" + ] + }, + { + "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": 117, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "45.0\n", + "34.3769410125\n", + "55.6230589875\n", + "21.246117975\n", + "41.3864710165\n", + "41.2154185889\n", + "41.1173116861\n", + "41.1145742517\n", + "41.1149081948\n", + "41.1142403085\n", + "Wall time: 831 ms\n", + "41.1364127407\n" + ] + }, + { + "data": { + "text/plain": [ + "array(10.99999999999988)" + ] + }, + "execution_count": 117, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "best_height(velocity, condition)" + ] + }, + { + "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 bd22605b1c142a4d582e50fb2f0bc452a735adb7 Mon Sep 17 00:00:00 2001 From: Christopher Lather Date: Wed, 13 Dec 2017 09:39:31 -0500 Subject: [PATCH 10/10] commiting --- code/chap11mine.ipynb | 1971 +++++++++++++++++++++++++++++++++++++++++ 1 file changed, 1971 insertions(+) create mode 100644 code/chap11mine.ipynb diff --git a/code/chap11mine.ipynb b/code/chap11mine.ipynb new file mode 100644 index 00000000..7a50abc2 --- /dev/null +++ b/code/chap11mine.ipynb @@ -0,0 +1,1971 @@ +{ + "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": 5, + "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": 6, + "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": 7, + "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": 8, + "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": 9, + "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": 10, + "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": 11, + "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": 12, + "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": 13, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "(,\n", + " ,\n", + " )" + ] + }, + "execution_count": 13, + "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": 14, + "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": 15, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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thetayr
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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": 15, + "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": 16, + "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": 17, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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3h8GpKVEamTGR1eHLlFX1eyLyU9y5kKHACdz5kIowjqc5C+MJVf0dgIh8CXfo\n626gBgj9bUzBPZ+GM/V7q66EgG2M6TIHSk+yPL+QqprWmJfeyUlcMTWDyRZOabq5Tt21paongTcj\nNBZoPbxVEPA9/SKyAxgLFOJu7gyUGbBfIfCxM/QHvrYxEVdb18jqzcXsPHAsqH1MxkDmz8xmgIVT\nmh6gzQIjIrtx51o6wq+qEobxbMCtNGYB671xJACTcBcYlOKuJHssYJ8FwDve56uBfxeRHFUtDOiv\nBDaFYXzGtMvv97O36AQrNxZRU9d661XflF7MmZ7FBTmDbdVieoz2VjDv0vECExaqWi0iPwaeEJFy\n3ErmHmA8cAPQG8gXkUeA3+Oesnkp7vAZwFpgHfCyiNwLpOFuynzK4mxMpJ2qaWDlxiI+DAmnnDhq\nCLMvzrRwStPjtFlgVPW2LhxHoIdxDzT7D9zjmTcBi1RVAUTkelzReAB3EcA1qroDWg6nXQ/8F7AK\nt3J5AXi0qydheg6/38+O/Ud5d3MJdQ2t4ZQD+rpwyrGZFk5peqaORsXMbafbB1QBH3rnaM6Lqvpx\nGWffa6N/KbC0nf3LgOvPdxzGdMSJqjqW5xdRdCg4nHLyuGFcMS2TlGS7E9/0XB09yb+C1sNlgQeQ\nAw+h+UTkV8CdqtqEMd2Yz+enYM8R1m0tpaGpNZxy0IAUFuRmkz3SwimN6WiBuQ54CRfR/zJQhjt8\ndT3wJdzhqgbcyff9BJ+EN6ZbOeqFU5aFhFNOnziCSyalk9zLYl6MgY4XmG8BP1HVbwW07QJWi0gl\ncIOqzvVuaPxXrMCYbqipyccGPcT6HeU0+VoX78MG9WVhXg5pQ/tFcXTGxJ6OFpjpwLfb6FtNa1TM\nVlxcizHdyqGj1SzLDwmnTEwg76I0cmWkhVMacwYdLTAHgY8Db52h7+O03sSYDoTzzn5joqqh0cf7\n28vYtOsw/oBwyrShLpxy2CALpzSmLR0tMD8EnheRNOBPwGHcOZjrgE8B94rIeNyhsb9GYqDGdLXi\nw1UsX1/I8argcMrLpqQzbYKFUxpzNh0Nu3xBRJpwh8n+v4CufcBtqvprEbnJ+zpcycrGREV9QxNr\ntpSw9cPgxXj2SBdOOWiAhVMa0xGdCbt8EXjRW6mMAIoD4lhQ1ZdwV5oZE7f2l55kxRnCKa+clsmk\nsUMt5sWYTuhU2KWIpOKywmq8r5uDJFHVkrb2MybW1dQ1smpTMbsOBodTjs0cxLyZ2QzoazEvxnRW\nR+/kHw+MJ624AAAYoklEQVT8Avc44rbYLcsm7vj9fnYXHmfVpuLTwinnzshiQraFUxpzrjq6gnkG\nl2j8HaAIFw9jTFyrqmlgZX4h+0qDE44uHD2E2Rdn0SelUwt8Y0yIjv4GzQVuV9XfR3IwxnQFv9/P\n9n1HeXdLCfUh4ZQLcnMYnTGwnb2NMR3V0QJTCRyN5ECM6QounLKQokNVQe1TvHDK3hZOaUzYdLTA\n/Ab4koj8zUs7Niau+Hx+tuw5zLqtZTQGhFMOHpDCwrwcMkcMiOLojOmeOlpgTgBzgF0i8h7ueS1B\nVPXOcA7MmHCpOFHDsvWFlB9t/bFNSEhgxsQRXDI5nV4W82JMRHS0wHwBOO5tf+UZ+m1VY2JOU5OP\n/J2HWL+zHF9AOOXwwX1ZmJvDSAunNCaiOnon/9gztYvIIOBWwFYvJqaUVZxi+fpCKk7WtrQlJSYw\na1I6M2QkSRbzYkzEndN1mCJyCXAXLoesH3AonIMy5lw1NDbx3rYyNu8+EhROmT6sPwvzchg6sE8U\nR2dMz9LhAiMiA4DP4ArLNKAe+DPwK+CNiIzOmE4oLK9keX4hJ0/Vt7QlJyVy2dQMpo4fbuGUxnSx\nsxYYEcnFFZWbgP7ABq/r46r6dgTHZkyH1HnhlNtCwilz0lKZPzPbwimNiZI2C4yI3IErLDOBEuCn\nuEcml+PuiWloa19jusq+khOs3FAUFE6Z0juJ2dOyuHDMEIt5MSaK2lvB/DewBfhHoOX+F+/EfpcQ\nkctwT8z8iKqu8NoWAU8CAuwGHlDVNwL2GYmLtlmEO4z3IrBYVRsx3UZ1bQOrNpWwuzA4nHJ81iDm\nzsimv4VTGhN17RWYP+GeVvkS8FcR+TVdeK5FRPoDvyYgRFNEJgGv4x5stgT4NPCaiMxU1W3eZktw\nl03PA7Jwq65GYHFXjd1Ejt/vZ9fBY6zaVEJtfXA45byZ2UzIHhzF0RljArVZYFT1RhEZijuxfxvu\nhH45rvD4ify9L0/hgjUnBLR9FVinqk94Xz8kIrO99jtF5HJc4vM4Vd0HbBaR+4GnReRRVa3DxK2q\n6npWbChiv4VTGhMX2v2NVNWjwE+An4jIdODzwC1AAvAzEfkd8JKq7grnoETkY8A/4Q7PbQnomgP8\nIWTzFbgLEJr7D3jFJbA/FZgOvBfOcZqu4ff72fZhBWsKSoPCKVP79WZ+bjaj0y2c0phY1OGMDFXd\npKpfBTKBf8ad/3gI2CEi+eEakIgMB34O3A4cC+nOBopD2kqAnLP0E7CNiSPHK+t4dcVeVmwoaiku\nCQkJTJswnJsXiRUXY2JYp48pqGoD7jzHEhFJBz6LO4QWLv8NvK6qb4pIdkhfP6A2pK0O6NNWv6o2\niIg/YBsTB3w+P5t2Heb97SHhlKleOOVwC6c0Jtad10FrVS3DXdH1ZDgGIyKfA2bgbuQ8kxog9KaG\nFNxjnM/YLyLJuEN6pzBx4chxF0556FhrOGViQgIzZCSzJqVZOKUxcSLWzorehjvMVSYi4AoDwBsi\n8j9AIZARsk8mrYfFCoGPnaEfTj90ZmJMU5OPD3aUs2HnIXwBMS8jBvdlYd4oRgzpG8XRGWM6K9YK\nzGeAwHeRdGAV7nzMW8DjuMuPHwvYZgHwjvf5auDfRSRHVQsD+iuBTREctzlPZRWnWLa+kKMh4ZSX\nTE5n+kQLpzQmHsVUgVHVoFWGiDS/2xSr6iEReRrIF5FHgN/jrmi7FLjb224tsA54WUTuBdJwh++e\nUtV6TMxpaGxi3dYytuwJDqfMHN6fBXk5DEm1U2fGxKu4OpitqgXA9cCNuBXJtcA1qrrD6/d7/eW4\nlc+LwAvAo1EZsGlXYXklv/+bsnn34ZbiktwrkXkzsrl+/gQrLsbEuZhawYRS1SJaz8M0ty0Flraz\nTxmuyJgYVVvfyJotJWzfdzSofVR6KvNn5jCwf+8ojcwYE04xXWBM97O36DgrNxZTXRscTjlnehYy\nysIpjelOrMCYLlFd28A7G4vZU3Q8qH189mDmzciiXx8LpzSmu7ECYyLK7/ejB4+xalMxdfWtMS/9\n+iQzb0YW4y2c0phuywqMiZiTp+pZsaGQg2WVQe0XjRnKlRdn0qe3/fgZ053Zb7gJO7/fz9a9Fawp\nKKGhsTXmZWD/3izIzSEnLTWKozPGdBUrMCasjlXWsnx9ISVHWpN5EhISmDZ+OJdNTSe5V1I7extj\nuhMrMCYsmnx+Nu06xPvbymjytd4wOSS1DwvzcsgY3j+KozPGRIMVGHPeDh+rYdn6gxw+XtPSlpiQ\nwMwLR5J3kYVTGtNTWYEx56yxyccH28vZqCHhlEP6sjDXwimN6emswJhzUnrEhVMeq2wNp+yVlMgl\nk9KZPnEEiRZOaUyPZwXGdEp9QxPrtpZSsLciJJxyAAvysi0/zBjTwgqM6bCDZSdZnl9EZXVrMHXv\n5CSumJrB5HHDLObFGBPECow5q9q6RlZvLmHngeBwytHpA1mQm82AfhZOaYw5nRUY064zhVP26d2L\nOdMzmWjhlMaYdliBMWdUXdvAyo3F7A0Jp7wgZzBzpls4pTHm7KzAmCB+v5+d+4+xektwOGX/PsnM\nz81mbOagKI7OGBNPrMCYFidP1bM8v5DC8uBwykljh3HFtAwLpzTGdIq9Yxj8fj8Fe4+wtqDUwimN\nMWFjBaaHO3rShVOWVgSHU158wXAunWzhlMaYc2cFpodq8vnZqIf4YHtwOOXQgS6cMn2YhVMaY85P\nzBUYEUkDngQWAX2B94Cvq+pWr3+R1y/AbuABVX0jYP+RwDPe/vXAi8BiVW3synnEskNHq1mWX8iR\nkHDKvIvSyL1wJEkWTmmMCYOYKjAikgi8CiQA1wFVwHeAt0VkEpAGvA48BiwBPg28JiIzVXWb9zJL\nAD8wD8gCfgk0Aou7bCIxqrHJx/vbyti063BQOGXa0H4szMth2CALpzTGhE9MFRjgYuByYJKq7gAQ\nkVuBo8A/AVcC61T1CW/7h0RkNvBV4E4RuRyYDYxT1X3AZhG5H3haRB5V1bounk/MKDlcxbL1hRyv\nav0n6JWUyCWT05l+gYVTGmPCL9YKzEHg44AGtDVf1jQEmAP8IWSfFcBN3udzgANecQnsTwWm4w63\n9Sj1DU2sLSilYO+RoPasEQNYkJvD4NSUKI3MGNPdxVSBUdUKYGlI81dw52L+hjs0VhzSXwLkeJ9n\nt9GPt02PKjAHSk+yPL+QqprWmJfeyUlcOS2TSWOHWsyLMSaiYqrAhBKRa4HvAU+p6g4R6QfUhmxW\nBzRnxJ/Wr6oNIuIP2Kbbc+GUxew8cCyofWzGQObNtHBKY0zXiNkCIyK3AT8DXgK+6TXXAKHHdFKA\nU231i0gy7qKBU3Rzfr+fPUXHeWdjMTV1rRfN9U3pxZzpWVyQM9hWLcaYLhOTBUZEFgOP4y43/oqq\nNl/yVAhkhGyeSethsULgY2foh9MPnXUrVTUNrNxQxL6SE0HtE0cNYfbFmRZOaYzpcjFXYETkm7ji\n8rCqPhbSvRp3+XFg+wLgnYD+fxeRHFUtDOivBDZFbtTR4/f72bH/KO9uLqGuoTWcckDfZObNtHBK\nY0z0xFSBEZFpwHeBXwA/E5H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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 `y`" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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IVCsu2/Hamtc4cPxAIJaQkMDI9iO5yq6idkrtKGYnUnVUIET8juYd5Z3177Ak\na0lQvG2DtkzqNYn2DdtHJzGRKFGBkBqvyFfEJzs+YdrGaeQWfLsdSVpyGld3uZoR7UfoJrTUSCoQ\nUqNtO7yN19e8zu5vgrdb79+qP9d2v5aGaQ2jlJlI9JVbIMysrFnTZWkboVxEqsyxvGNM3TiVz3Z9\nFhRvXrc51/e4XjOhRaj4DKIW3ozp0ylejVUk5hX5ivh056f8Z+N/ghbWS0lK4fJOl3NZx8tITtSJ\ntQhUUCCccyOrMA+RSrf16628sfaNUpeT+rToww+6/0BzGkRC6KuSVHvf5H7DuxveZXHW4qB40zpN\nua77dfRs3jNKmYnENhUIqbYKigr4ePvHzNg0I2h0UvHlpFEdRpGSlBLFDEVimwqEVEvrDq7jrXVv\nBU12A+jbsi/XdrtWl5NEwqACIdXKwRMH+fe6f7P6wOqgeIu6LZjQY4JGJ4mcARUIqRZyC3KZsWkG\nc7fPpbCoMBBPS05jrI1lZPuRGp0kcob0jpG4VuQr4vPdnzNt47SgpbgTEhIY0mYIV3e5mvqp2hFX\n5GyoQEjc2nxoM2+te6vUsNUOjTowoccE2jVsF6XMRKoHFQiJO9k52UxZP4Uv930ZFG+Y1pBrul3D\ngFYDtBS3SASoQEjcOJl/kg82f8DH2z+moKggEE9JSuG7Hb/LZR0vIzU5NYoZilQvKhAS84qXx3jP\nvcfxU8eD2ga0HsD4ruNpXLtxlLITqb5UICRm+Xw+1h5cy5QNU9h3LHi5rw6NOnBt92vp0KhDlLIT\nqf5UICQm7fpmF1PWT2Fj9sageOPajRnfdTz9W/XXfQaRSqYCITHl65Nf85+N/ym1blJachqjO43m\nO+d9R8tjiFQRFQiJCTn5OczcMpO52+YG3YBOTEhkaNuhXGlXUi+1XhQzFKl5VCAkqgqKCpi/Yz4f\nbP6AE6dOBLX1btGb8V3H06JuiyhlJ1KzqUBIVPh8PpbuWcp/3H84lHMoqK19w/Zc0+0aOmd0jlJ2\nIgJRLhBm9iyQ7Jy7tUTsMuBRwIDNwP3OuQ+jlKJEmM/nY91X65i6YSpZR7OC2pqkN2Fc13H0a9lP\nN6BFYkBUCoSZJQAPAT8BXigR7wZMB34HTAEmAdPM7ALn3Lpo5CqRs+3wNqZumMqmQ5uC4nVr1WVM\n5zEMbzdcC+qJxJAqfzeaWQe8otAD2BXSfC+w2Dn3sP/3B81sqD9+W9VlKZG099hepm2cxqr9q4Li\ntZJqcWlcOyl2AAARdElEQVSHS/nu+d8lLTktStmJSHmi8XVtCLAbuB54M6RtGPB2SGw+MKHy05JI\ny87J5j33Hkv2LMHn8wXiiQmJDGs3jCs6X6GVVkViWJUXCOfcq8CrAGYW2pwJ7AmJ7QXaVH5mEinf\n5H7DB5s/YMGuBUF7M4C3NMaVdiXN6jSLUnYiEq5Yu+CbDuSGxPIAXX+IA8dPHWfWllnM2zGP/ML8\noLYezXpwdZeradNAtV4kXsRagTgJhC7HmQqcKONYiRE5+Tl8tO0jPtr2EXkFeUFt5zc+n6u7XE2n\njE5Ryk5EzlasFYjdQMuQWCtKX3aSGJBbkMvH2z9mztY55OTnBLW1bdCWq7tcTbem3TRkVSROxVqB\nWAiMwBvmWuxi4NPopCNlySvIY/6O+czaOqvU7OeW9VpylV1FnxZ9VBhE4lysFYingOVm9hDwBjAR\nGAjcEdWsBPAKwyc7P2H21tkcyzsW1NasTjOu6HwFA1oPIDEhMUoZikgkxVSBcM6tMbNxeDOp7wc2\nAmOdcxuim1nNVlFhyEjP4IrOVzAoc5AKg0g1E9UC4ZwbWUZsBjCj6rORUBUVhsa1G3N5p8sZ3Gaw\nZj+LVFN6Z0spuQW5zN8xnzlb55Ta4rNR7UZc3ulyhrQZosIgUs3pHS4BOfk5zNs+j7nb55a6+dy4\ndmNGdxqtwiBSg+idLhw/dZyPtn3EvO3zyC0InqeYkZ7B6PNH61KSSA2kd3wNdiT3CLO3zmbBzgWc\nKjwV1Na0TlMu73Q5A1sPJCkxKUoZikg0qUDUQF+d+IpZW2fx+e7Pg7b3BGhRtwWXd7pcw1VFRAWi\nJsk6msXMLTNZtndZ0OqqAJn1MxndaTQXtLxAhUFEABWIas/n87Hl6y3M3DKTtQfXlmrv0KgDozuN\npmeznpr5LCJBVCCqKZ/Px6oDq5i1ZRbbDm8r1d61aVdGnz+azhmdVRhEpEwqENVMfmE+S/YsYfbW\n2Rw4fiCoLSEhgb4t+vK9879Hu4btopShiMQLFYhq4sSpE3y681M+3v4xR/OOBrUlJyYzuM1gRnUY\nRfO6zaOUoYjEGxWIOJedk81H2z5i0e5FpfZiSEtOY0T7EVxy3iU0TGsYpQxFJF6pQMQhn8/HtsPb\nmLNtDiv3ryw1IqlhWkO+0+E7DG83nLRkbcYnImdHBSKOFBYV8uW+L/lo20fsOLKjVHvr+q25rONl\n9G/VX7OeReSc6VMkDpw4dYKFuxYyb8c8Dp88XKq9e7PuXNrhUro26aoRSSISMSoQMWzfsX18vP1j\nPs/6nPzC/KC25MRkLmx9IaM6jqJVvVZRylBEqjMViBjj8/lYc3ANH2//mA1fld4nqV5qPUa0G8GI\n9iOon1o/ChmKSE2hAhEjcvJzWLR7EfO2zyM7J7tUe2b9TL7T4TsMaDWAlKSUKGQoIjWNCkSUZR3N\nYv6O+SzJWlJqRdWEhAT6tOjDxe0v1oxnEalyKhBRUFBUwIp9K5i3Yx5bv95aqj09JZ2hbYcysv1I\nMtIzopChiIgKRJU6lHOIBbsWsHDXwlJ7PIN3Geni8y7mwtYXUiupVhQyFBH5lgpEJSvyFbH24Fo+\n3fkpaw+uLTWpLTEhkX6t+jGi3QjOb3y+LiOJSMxQgagkh08e5rPdn7Fw18Iy5y40qt2IYW2HMazd\nMI1GEpGYpAIRQcVnCwt3LWT1gdWlzhYAujXtxoj2I+jVvJc25hGRmKYCEQGHcg6xcNdCFu1exJHc\nI6Xa66XWY0ibIQxrO4ymdZpGIUMRkTOnAnGW8gvzWbl/JQt3LWRj9sYyj+nSpAvD2g2jT4s+WhtJ\nROKOPrXOgM/nY/fR3Xy26zOW7llKTn5OqWPqpdZjcOZghrYdqr0XRCSuqUCE4VjeMZbuWcqi3YvI\nOppVqj0hIYHuTbsztO1QejXvRVJiUhSyFBGJLBWIchQUFbDmwBo+z/qcNQfWUOQrKnVMRnoGQ9sO\nZXDmYBrVbhSFLEVEKo8KRAk+n48dR3awOGsxX+z9ghOnTpQ6JiUphX4t+zGkzRAtfyEi1ZoKBPDV\nia9YsmcJS7KWcPDEwTKP6di4I0PaDKFfy37UTqldxRmKiFS9mCsQZpYE/B6YDNQDZgJ3OecORPJ1\njuUdY9neZSzds5Rth7eVeUxGegYDWw9kcJvBNKvTLJIvLyIS82KuQAC/BW4CfggcAp4BpgBDz/WJ\ncwtyWbl/JUv3LGXDVxvKvK+QlpxGv1b9GJQ5iE6NO+kSkojUWDFVIMysFnAvcI9zbo4/NgHYbmZD\nnHOLzvQ58wvzWXNwDV/s+YI1B9eU2pkNvPWQejTrwcDMgfRu3lv7LYiIEGMFAuiDd1lpfnHAObfD\nzHYAw4AzKhCLdi/izbVvkleQV2Z7x8YdGdh6IP1a9aNurbpnm7OISLUUawUi0/9zT0h8L9DmTJ9s\nyvoppYpDZv1MLmx9If1b9ddeCyIiFYi1ApEOFDnnQq8D5QFpZ/pkF7S8gE93fkrzus0Z0GoA/Vv1\np2W9lhFJVESkuou1AnESSDSzZOdcQYl4KlB6UsJpTOo1iet7Xk8CCbrZLCJyhmJtvend/p+hX/Nb\nUfqyU1gSExJVHEREzkKsnUGsAo4BI4BXAcysPdAe+LSCxyUB7N+/v3KzExGpRkp8Zpa5gFxCWZva\nRJOZPYI3SW4ycBBvHkSuc25kBY8ZCiyogvRERKqjYc65haHBWDuDAPgfIAXvDCIF/0zq0zzmC7xh\nsPuAwkrNTkSk+kjCu6T/RVmNMXcGISIisSHWblKLiEiMUIEQEZEyqUCIiEiZVCBERKRMKhAiIlKm\nWBzmGhFVtfFQJJlZc+BR4DKgNrAE+IVzbq2//TJ/uwGbgfudcx9GKd3TMrNBwELgUufcfH8sbvpg\nZrcCv8JbKHI98Evn3Mf+trjoh5nVAR4BrsFb6+xzvL+p9f72mO6HmT0LJDvnbi0RqzBnM2sG/BXv\nfXQK+CfwQMjyPVWqnH78FPgp3t/XTuBx59zzJdqj3o/qfAbxW77deGg43kqxU6KZUEXMLBGYCnQG\nrgKGAN8Ac80sw8y6AdOBfwN9gf8A08yse5RSrpD/g+lflJihGU99MLObgKfxPlx7Ap8A082sfTz1\nA3gSuBS4FhgM5AIzzSwtlvthZglm9r/AT0Li4eQ8BWiBtyLDZOBm4KEqSLuUCvpxB97f1u+BXsDj\nwDNmdmOJw6Lej2o5D8K/8VA23sZDL/lj7YHtwEVns/FQZTOzvsCXQDfn3AZ/LBX4GrgDuAiwkjPK\nzWwesNk5d1vVZ1wxM/s7XrEbCVzsnJvvj8V8H8wsAe9v5RXn3G/8sUS8/38exXvDxnw/AMwsG3jI\nOfeU//duwDqgH96HVsz1w8w6AC8APYAcYE7xN+/T/Q2Z2WC8fWM6OOe2+9tvAp4Cmjrnyt4cpur7\nsQqY6Zy7v8TxLwDnOecuiZV+VNcziDI3HgJ24M24jkW7gCsAVyJWvCdqI7y854c8Zj4x2B8zuxwY\nA9wT0hQvfTCgHfBWccA5V+Sc6+Oce5346QfAV8B1ZtbM/8XpR8BhYBux248heAt39sQr1CWdLudh\nwM7iD9US7fXwPheqUkX9uAd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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": "markdown", + "metadata": {}, + "source": [ + "Plotting `r`" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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pOJSynTthxgx48cX0+IknwoQJapQnIgdMxaFUvfGGN8r7/PNkrG1buPpqGDxY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\n", + "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": 20, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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1+Sj6oIitz20NWoo7KSmJ/PPyGX/NeNL7psewQpHEpYCQhHV4+2E2/XlTq2Gr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\niEhYCggREQlLASEiImEpIEREJKz/D0epWC+CCFjhAAAAAElFTkSuQmCC\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": 21, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Saving figure to file chap11-fig01.pdf\n" + ] + }, + { + "data": { + "image/png": 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ZVYypWUB5qcKGIpLcZtog/Az4tDHmMWtt5E8+kXkoGAzh7+ij3h9gf1sv48HI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\ny4QdBj9297+71ud39w1mdgehkuKDwFbg9iup5CgifaCtLVQ0rKkJFQ7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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": 22, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array(125.33333334940457)" + ] + }, + "execution_count": 22, + "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": 23, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array(55.00000000448797)" + ] + }, + "execution_count": 23, + "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": 24, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array(1253.3333334940455)" + ] + }, + "execution_count": 24, + "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": 25, + "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": 26, + "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": 27, + "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": 28, + "metadata": {}, + "outputs": [ + { + 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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
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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": 36, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "system.results.tail()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Extrating the time series" + ] + }, + { + "cell_type": "code", + "execution_count": 37, + "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": 38, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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qi4FNeLvQnwMeD0uDRUSAj/Lbrri6bMY45swYF8YWDZ6wDc45547TOg/SXLYOWNfFPUV4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\nY1MTSB+dwLi0RMalJZKcGKt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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": 39, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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rkqbtef18bf1Bh2hTFckYQRd5/SrRgYgkTGWZ7+k3L8eQXQDDp8LQL2llrmSc\nwPP8zawA2AvIBxo+E2cDvYDDnHO/jH94Ijthx3pYMRPWvwVElaPKyoWhR8Lw47WTlmSsoPP8jwD+\nCgxq4ylbACV/SQ01W6Bstq/BE11bn6zwDJ6TNYNHMl7Qnv//ARuA7wLTgDrgfuB44HvA1IREJxKL\nuu2w6uXWp232neBr62v7RBEgePKfCHzLOfeUmfUFvuucmw3MNrMe+F7/CYkKUqRd9TV+cVbZc802\nSsfX1C/5KvQZl5zYRFJU0OSfDawM/7wQP/bf4AngwXgGJRJIqB7W/QdWzoTqjU2PFQzzPX3V4BFp\nVdDkvxif8N8AHNDLzMw554AcoChB8Ym0FArBxvdhxT9aztXPHwAjToZBB2napkg7gib/R4GbzSzb\nOXeHmb0L/N7MbgOuBD5OWIQiDUIh2Pyx3y+38vOmx3KL/OydIYdDtorVinQk6P8lNwGDgS8CdwDf\nB2YDs4AK4OSgb2hmQ4GbgWOBQuAt4MfaD1jaVbHQJ/2ti5q2ZxfAsON88bUcLTIXCSroIq964LKo\nx++a2Rhgd//QVbR5chQzywaewq8TOAXYClwDzDGzPZ1z69s5XTLR1mV+TH9zsw+XWXlQ/CWf+DVX\nXyRmnf587JzbArwT42n7AocAezrnPgEws3Px00hPAB7qbDzSzVSu9Em/eV39rBwYfJgf4snvm5zY\nRLqBNpO/mdXQZFlku4IWdvsMOBF/07hBQ/H0/gHfS7qzqtW+0uaGd2n6zy8LBh0MI07SAi2ROGiv\n5389wZN/IOFhnVnNmi/Gj/2/GM/3kjSzfR2UPeunbjb/ZzfgAJ/0C4uTEppId9Rm8nfOXZPoNzez\nk4HpwK0Nw0CSYao3+h201r5Jkx20wM/RH3Ey9BqZlNBEurOgtX3O7ug5zrlHY3ljMzsfuAdfLvry\nWM6VbqB6E5Q9D2vfaFZ/B+izh99Bq/fo5MQmkgGC3vD9cxvtIXydn1r8WoBAzOwX+HpBM4CLnXNx\nHV6SFFazBcqfh9X/hFBN02NF42DEKSrFINIFgib/1rpgvYHDgJ8BXwn6hmZ2OT7xX+Wcuy7oeZLm\narb4gmtrXoP6ZruA9h7jh3f67K5SDCJdJOg8/+VtHPrYzPKBP+D/ELTLzPYBbgD+BNxjZtF38LY4\n57YFiUfSSO02n/RXv9qy0mavUT7p991LSV+ki8VjHfyHwI0Bn3smvhbQBeGvaFfiPxFId1C7Dcpf\ngtWvtEy7xo5QAAAP5ElEQVT6hSW+pr6KrokkzU4lfzPLA/4HWN3RcwGcc/8L/O/OvKekuNpKWPUS\nrHoF6rc3PVY43Pf0+++npC+SZEFn+yyk5Zz/HGAI0BP4SZzjknRTW+k3Ulk1p2XSLxgGI06EAZOU\n9EVSRNCe/5u0TP4hfFG3Z51zL8c1KkkftZU+4a96uZWkXxyV9FVeWSSVBL3he36C45B0U7stnPRb\n6+kr6YukuqDDPoe3c7geX51zSdDqnpLGareFh3daGdMvKIbhJ8DAA5T0RVJc0GGf14gM+0QP2kYP\nBdWb2UPAd5xzdXGITVJJzVaf9FubvaOevkjaCZr8T8GXYXgA+AuwCn+z91TgIuAKoAa4DlgW/i7d\nQc0WP3tn9WutJP1hMOIEJX2RNBQ0+f8c+L1z7udRbaXAXDPbApzmnDvczEL4TV+U/NNdTUV4Re4/\nW67ILRzuh3cG7K+kL5Kmgib//YCr2zg2F9/zB/gIKNnZoCSJqjeFk/7rLWvvFA73wzv999eUTZE0\nFzT5N2zC8lIrx04EVoZ/Lga0FWM6qt4YrrI5t2WVzcISP7zTf6KSvkg3ETT53wLcHd58/UlgLX7M\n/xTgDOAHZrYbfrjnhUQEKgmyfZ2vsrnuXxBqdp++1yg/vKMyDCLdTtB5/veaWR1+6OfrUYeWAuc7\n5x42szPDj69o7TUkxVSthvLZsO4tWmyi0mu0H95RwTWRbitwbR/n3P3A/eEe/mBgpXPu86jjj+Nn\nBEkqqyyDsuda2SMX6D3WD+/02UNJX6Sbi6mwm5kVAduAqvDj4Q3HnHNl8Q1N4mrbciibDRv/2/JY\nn9398E7ROCV9kQwRdIXvbvga/F9s52k5cYlI4mvrEr9H7uaPWh7rOwGGHw9Fu3V9XCKSVEF7/jOA\nPYFrgBW0GCSWlBIKwZZSP7xT8WnL4/329cM7vUZ1fWwikhKCJv/DgW855x5LZDCyk0Ih38Mve873\n+JvI8itxh0+FnlqKIZLpgib/LcCGRAYiOyEU8mP5Zc9B5efNDmbDwMk+6RcWt3q6iGSeoMn/z8BF\nZvaic655XX9Jlvo62PCOv5G7fVXTY1m5MOgQGDYFCgYlJz4RSVlBk/9m/AbtpWb2FlDZ/AnOue/E\nMzBpR30NrPu3X5Fb3WxBdVYeDDkchh0L+f2SE5+IpLygyf8CYFP4+V9o5bg+DXSFuh2w9g1fe6dm\nc9Nj2QUw9CgoPhryipITn4ikjaArfEe31m5mfYFzAfX6E6m20tfRX/UK1G1reiynFxR/GYYeCbk9\nkxKeiKSfmBZ5NTCzycCF+Lo+PYE18QxKwmoqwhuovNayln5eXz+0M/gwyOmRlPBEJH0FTv5m1huY\nhk/6+wDVwDPAQ8DshESXqbavg1Uvwto3W1bY7DEIhh3nb+Zm5yUnPhFJex0mfzObhE/4ZwK9gPfD\nh050zs1JYGyZp6rc38Rd/zYt1tEVDPPTNQceqA1URGSntZn8zezb+KS/P1AG3I7fxnE1fs5/TVvn\nSoy2LvNllVuru9NrlC/B0G9f1d0Rkbhpr+d/F/AhMBVonN8fvskrOysUggrnk37FJy2PF5nv6ffZ\nXUlfROKuveT/JH6XrseBF8zsYTS2v/NCIdg0zy/M2ras5fF++/ik33tMl4cmIpmjzeTvnDvdzAbg\nb/Kej7+5uxr/RyGE5vbHpnE17vOwvbzZwSxfgmHYFOg5vNXTRUTiqd0bvs65DcDvgd+b2X7AN4Gz\ngSzgHjN7FHjcOVea8EjTVV01rHsTyl9qZTVuLgw61M/eUQkGEelCsezk9QFwiZn9BDgZ/2ngSuBq\nM/vAOTcpMSGmqdpKPz9/9StQu6XpsewCGHoEDD0a8nULRUS6XsyLvJxzNcDfgb+bWTHwDfwfAgGo\n3uwXZq15Heq3Nz2W29snfK3GFZEk69QK3wbOuVXAzeGvzLZ9LZS/4AuuNV+YlT/Ar8Yd9AXIyU9O\nfCIiUXYq+Quw7XM/XXPDe7S4B14wDIZPgQEHQrZ2uRSR1KHk3xmhEGxZ6JP+5o9bHu812k/X7LeP\n5uiLSEpS8o9FKASbPvRJv8U2iUDfvfzMnaLxSvoiktKU/IPoaI7+gEk+6ffaJSnhiYjESsm/PXU7\nYO1cWPUSVG9seqxxm8RjoWBIcuITEekkJf/W1G6D1a+2vnlKdoHfJrH4aG2TKCJpS8k/2o4Nfo7+\n2jegvrrpsdwin/CHHKE5+iKS9pT8wdfRL38B1r1Fizr6PQZB8bEw+FBtniIi3UZmJ/+tS/xN3E3z\nWh4rLPE3cQceoM1TRKTbybzkHwrB5o98T3/LwpbHi8bBsKnQd09N1xSRbitzkn99HWx41yf9qpUt\nj/ffz/f0VUdfRDJA90/+dTtg3b+g/EWo3tD0WFYODDzIT9csHJac+EREkqD7Jv92p2v2gCGHQfGX\nIb9/cuITEUmiLk/+ZpYD/B++DHQR8DxwkXNudVzeoN3pmg0llY+A3F5xeTsRkXSUjJ7/NcB5+H0A\n1gN34PcH+OJOvWplmR/PX/82LaZr5g+EYceopLKISFiXJn8zywcuAS52zr0UbjsTWGpmhzrn/hXz\ni25Z5JP+pg9bHisc4ffF1XRNEZEmurrnvx9+qOe1hgbn3DIzWwYcBgRP/vU1sOju1pN+0Xg/c6fv\nXpquKSLSiq5O/iXh783nWpYBI2N6pc2ftEz8mq4pIhJIVyf/nkB9eB/gaDuAgpheqdcuvvRC9aao\n6ZrF8YpTRKRb6+rkXwVkm1mucy56o9sewLY2zmldfj/Y5zogS0M7IiIx6uq7oJ+HvzdfUTWclkNB\nHcvKVuIXEemEru75zwO2AEcAfwYws12BXYHX2zkvB2DVqlWJjU5EpJuIypc5rR3PCoVCXRcNYGY3\n4hd4nQ+swc/z3+6cO7Kdc74IvNEF4YmIdDeHOefmNm9MxiKvXwJ5+J5/HuEVvh2c8w5+Kmg5UJfQ\n6EREuocc/BD7O60d7PKev4iIJJ+WvYqIZCAlfxGRDKTkLyKSgZT8RUQykJK/iEgGStudvBK+KUwG\nMrM9gY9bOXSYc26umR0L3AwYsBC4wjk3uytjTGdmdieQ65z7VlRbu9fUzIYAM4BjgWrgfuAXzcqj\nSFgb1/ht4MBmT72v4TmZeo3Tued/DZFNYQ7HVwz9ezID6gb2Btbh5wZHf70V/sMwE/gbMBH4B/C0\nme2VpFjThpllmdm1wIXN2oNc078DxfhV8ecD3wR+1QVhp5V2rnEWsBdwDk3/TV8W9bSMvMZpOc8/\nvCnMOvymMA+E23YFlgJf6NSmMIKZXQcc7pw7opVjdwEWvRLbzF4FFjrnvtN1UaYXMxsD3AdMACqB\nl6J6nO1eUzM7BL/HxRjn3NLw8fOAPwCDnXM7uvSXSVEdXOPdgEVEXcNm52bsNU7Xnn+rm8IAy/Ar\ngaVzJgCftHHsMKKud9hr6Hp35FB8QcO98Z2TaB1d08OA5c2S1mv4f/v7xTnOdNbeNZ6Arya8vI1z\nM/Yap+uYf/w2hZFoE4ACM/sPvtjeR8D/Oufexl9zXe8YOef+TKSIYfPDHV3Tto4Tfs5bcQs0jXVw\njScAm4BHzOwI/L7h9wO3Oef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+ "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": 40, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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H8w4H5L2UIERE6pCwkDDu633fKYPWgVpprQQhIlLHlA1ah4aEAk49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\niFRKCUJERCr1/7vuXTI+B5+IAAAAAElFTkSuQmCC\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": 41, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Saving figure to file chap11-fig02.pdf\n" + ] + }, + { + "data": { + "image/png": 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ImOPp8LG9sp5NO2oprajvc9W9GJeLksI0pk/MYvL4DI3WFxkCIXeOWWs/Ba4y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\nb+20ayj4iwRJ05aBuSPmUltfy76ifew6tYudJ3dysOQgXq/Xf3xNXQ1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MLW4gX9Pzve3b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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": 43, + "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": 44, + "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": 45, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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" + ], + "text/plain": [ + "init theta 0 radian\n", + "omega 0.0 radi...\n", + "k 9.6e-05 meter / radian\n", + "Rmin 0.008 meter\n", + "Rmax 0.016 meter\n", + "mass 0.05 kilogram\n", + "I 3.0625000000000006e-05 kilogram * meter ** 2\n", + "g 9.8 meter / second ** 2\n", + "ts [0.0 second, 0.01 second, 0.02 second, 0.03 se...\n", + "dtype: object" + ] + }, + "execution_count": 45, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "system = make_system(condition)\n", + "system" + ] + }, + { + "cell_type": "code", + "execution_count": 46, + "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": 46, + "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": 51, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "# Solution goes here\n", + "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, v = state\n", + " unpack(system)\n", + " \n", + " if y < 0 * m:\n", + " return 0, 0, 0, 0\n", + " \n", + " r = sqrt(2*k*y + Rmin**2)\n", + " alpha = mass * g * r / (I + mass * r**2)\n", + " a = -r * alpha\n", + " \n", + " \n", + " return omega, alpha, v, a" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Test your slope function with the initial conditions." + ] + }, + { + "cell_type": "code", + "execution_count": 52, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "(,\n", + " ,\n", + " ,\n", + " )" + ] + }, + "execution_count": 52, + "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": 53, + "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": 54, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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\n", + "
" + ], + "text/plain": [ + " theta omega y v\n", + "0.96 67.11465 144.630635 -1.143965e-08 -1.994692\n", + "0.97 67.11465 144.630635 -1.143965e-08 -1.994692\n", + "0.98 67.11465 144.630635 -1.143965e-08 -1.994692\n", + "0.99 67.11465 144.630635 -1.143965e-08 -1.994692\n", + "1.00 67.11465 144.630635 -1.143965e-08 -1.994692" + ] + }, + "execution_count": 54, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "system.results.tail()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Plot the results." + ] + }, + { + "cell_type": "code", + "execution_count": 55, + "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": 56, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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Bh4wxPwGetNY2hTZsEYlFjU0tLFt9wDfzKSUpgesvLyIpUTOfol13PYuNwD5gjrV2axfX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\nM7A/9CyeoG2zpAU4lWtf7ex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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": 57, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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