code/chap07.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Modeling and Simulation in Python\n",
    "\n",
    "Chapter 7\n",
    "\n",
    "Copyright 2017 Allen Downey\n",
    "\n",
    "License: [Creative Commons Attribution 4.0 International](https://creativecommons.org/licenses/by/4.0)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Configure Jupyter so figures appear in the notebook\n",
    "%matplotlib inline\n",
    "\n",
    "# Configure Jupyter to display the assigned value after an assignment\n",
    "%config InteractiveShell.ast_node_interactivity='last_expr_or_assign'\n",
    "\n",
    "# import functions from the modsim.py module\n",
    "from modsim import *\n",
    "\n",
    "from pandas import read_html"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Code from the previous chapter"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "filename = 'data/World_population_estimates.html'\n",
    "tables = read_html(filename, header=0, index_col=0, decimal='M')\n",
    "table2 = tables[2]\n",
    "table2.columns = ['census', 'prb', 'un', 'maddison', \n",
    "                  'hyde', 'tanton', 'biraben', 'mj', \n",
    "                  'thomlinson', 'durand', 'clark']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Year\n",
       "1950    2.525149\n",
       "1951    2.572851\n",
       "1952    2.619292\n",
       "1953    2.665865\n",
       "1954    2.713172\n",
       "Name: un, dtype: float64"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "un = table2.un / 1e9\n",
    "un.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Year\n",
       "1950    2.557629\n",
       "1951    2.594940\n",
       "1952    2.636772\n",
       "1953    2.682053\n",
       "1954    2.730228\n",
       "Name: census, dtype: float64"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "census = table2.census / 1e9\n",
    "census.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_results(census, un, timeseries, title):\n",
    "    \"\"\"Plot the estimates and the model.\n",
    "    \n",
    "    census: TimeSeries of population estimates\n",
    "    un: TimeSeries of population estimates\n",
    "    timeseries: TimeSeries of simulation results\n",
    "    title: string\n",
    "    \"\"\"\n",
    "    plot(census, ':', label='US Census')\n",
    "    plot(un, '--', label='UN DESA')\n",
    "    plot(timeseries, color='gray', label='model')\n",
    "    \n",
    "    decorate(xlabel='Year', \n",
    "             ylabel='World population (billion)',\n",
    "             title=title)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "def run_simulation(system, update_func):\n",
    "    \"\"\"Simulate the system using any update function.\n",
    "    \n",
    "    system: System object\n",
    "    update_func: function that computes the population next year\n",
    "    \n",
    "    returns: TimeSeries\n",
    "    \"\"\"\n",
    "    results = TimeSeries()\n",
    "    results[system.t_0] = system.p_0\n",
    "    \n",
    "    for t in linrange(system.t_0, system.t_end):\n",
    "        results[t+1] = update_func(results[t], t, system)\n",
    "        \n",
    "    return results"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Quadratic growth"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here's the implementation of the quadratic growth model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "def update_func_quad(pop, t, system):\n",
    "    \"\"\"Compute the population next year with a quadratic model.\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": [
    "Here's a `System` object with the parameters `alpha` and `beta`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>values</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>t_0</th>\n",
       "      <td>1950.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>t_end</th>\n",
       "      <td>2016.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>p_0</th>\n",
       "      <td>2.557629</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>alpha</th>\n",
       "      <td>0.025000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>beta</th>\n",
       "      <td>-0.001800</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "t_0      1950.000000\n",
       "t_end    2016.000000\n",
       "p_0         2.557629\n",
       "alpha       0.025000\n",
       "beta       -0.001800\n",
       "dtype: float64"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "t_0 = get_first_label(census)\n",
    "t_end = get_last_label(census)\n",
    "p_0 = census[t_0]\n",
    "\n",
    "system = System(t_0=t_0, \n",
    "                t_end=t_end,\n",
    "                p_0=p_0,\n",
    "                alpha=0.025,\n",
    "                beta=-0.0018)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And here are the results."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Saving figure to file figs/chap03-fig04.pdf\n"
     ]
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "results = run_simulation(system, update_func_quad)\n",
    "plot_results(census, un, results, 'Quadratic model')\n",
    "savefig('figs/chap03-fig04.pdf')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise:**  Can you find values for the parameters that make the model fit better?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Equilibrium\n",
    "\n",
    "To understand the quadratic model better, let's plot net growth as a function of population."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "pop_array = linspace(0, 15, 100)\n",
    "net_growth_array = system.alpha * pop_array + system.beta * pop_array**2\n",
    "None"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here's what it looks like."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Saving figure to file figs/chap03-fig05.pdf\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.set_style('whitegrid')\n",
    "\n",
    "plot(pop_array, net_growth_array)\n",
    "decorate(xlabel='Population (billions)',\n",
    "         ylabel='Net growth (billions)')\n",
    "savefig('figs/chap03-fig05.pdf')\n",
    "\n",
    "sns.set_style('white')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here's what it looks like.  Remember that the x axis is population now, not time."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It looks like the growth rate passes through 0 when the population is a little less than 14 billion.\n",
    "\n",
    "In the book we found that the net growth is 0 when the population is $-\\alpha/\\beta$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "13.88888888888889"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "-system.alpha / system.beta"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is the equilibrium the population tends toward."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`sns` is a library called Seaborn which provides functions that control the appearance of plots.  In this case I want a grid to make it easier to estimate the population where the growth rate crosses through 0."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Dysfunctions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "When people first learn about functions, there are a few things they often find confusing.  In this section I present and explain some common problems with functions.\n",
    "\n",
    "As an example, suppose you want a function that takes a `System` object, with variables `alpha` and `beta`, as a parameter and computes the carrying capacity, `-alpha/beta`.  Here's a good solution:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "13.88888888888889\n"
     ]
    }
   ],
   "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": "markdown",
   "metadata": {},
   "source": [
    "Now let's see all the ways that can go wrong.\n",
    "\n",
    "**Dysfunction #1:** Not using parameters.  In the following version, the function doesn't take any parameters; when `sys1` appears inside the function, it refers to the object we created outside the function.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "13.88888888888889\n"
     ]
    }
   ],
   "source": [
    "def carrying_capacity():\n",
    "    K = -sys1.alpha / sys1.beta\n",
    "    return K\n",
    "    \n",
    "sys1 = System(alpha=0.025, beta=-0.0018)\n",
    "pop = carrying_capacity()\n",
    "print(pop)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This version actually works, but it is not as versatile as it could be.  If there are several `System` objects, this function can only work with one of them, and only if it is named `system`.\n",
    "\n",
    "**Dysfunction #2:** Clobbering the parameters.  When people first learn about parameters, they often write functions like this:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "13.88888888888889\n"
     ]
    }
   ],
   "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": "markdown",
   "metadata": {},
   "source": [
    "In this example, we have a `System` object named `sys1` that gets passed as an argument to `carrying_capacity`.  But when the function runs, it ignores the argument and immediately replaces it with a new `System` object.  As a result, this function always returns the same value, no matter what argument is passed.\n",
    "\n",
    "When you write a function, you generally don't know what the values of the parameters will be.  Your job is to write a function that works for any valid values.  If you assign your own values to the parameters, you defeat the whole purpose of functions.\n",
    "\n",
    "\n",
    "**Dysfunction #3:** No return value.  Here's a version that computes the value of `K` but doesn't return it."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "None\n"
     ]
    }
   ],
   "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": "markdown",
   "metadata": {},
   "source": [
    "A function that doesn't have a return statement always returns a special value called `None`, so in this example the value of `pop` is `None`.  If you are debugging a program and find that the value of a variable is `None` when it shouldn't be, a function without a return statement is a likely cause.\n",
    "\n",
    "**Dysfunction #4:** Ignoring the return value.  Finally, here's a version where the function is correct, but the way it's used is not."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "13.88888888888889"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def carrying_capacity(system):\n",
    "    K = -system.alpha / system.beta\n",
    "    return K\n",
    "    \n",
    "sys2 = System(alpha=0.025, beta=-0.0018)\n",
    "carrying_capacity(sys2)\n",
    "\n",
    "# print(K)     This line won't work because K only exists inside the function."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this example, `carrying_capacity` runs and returns `K`, but the return value is dropped.\n",
    "\n",
    "When you call a function that returns a value, you should do something with the result.  Often you assign it to a variable, as in the previous examples, but you can also use it as part of an expression.\n",
    "\n",
    "For example, you could eliminate the temporary variable `pop` like this:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "13.88888888888889\n"
     ]
    }
   ],
   "source": [
    "print(carrying_capacity(sys1))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Or if you had more than one system, you could compute the total carrying capacity like this:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "27.77777777777778"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "total = carrying_capacity(sys1) + carrying_capacity(sys2)\n",
    "total"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercises\n",
    "\n",
    "**Exercise:** In the book, I present 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_func` that implements this version of the model.  Test it by computing the values of `r` and `K` that correspond to `alpha=0.025, beta=-0.0018`, and confirm that you get the same results. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "def update_func(pop, t, system):\n",
    "    K = -system.alpha/system.beta\n",
    "    netGrowth = system.alpha * pop * (1-pop/K)\n",
    "    return pop + netGrowth"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Saving figure to file figs/chap03-fig04.pdf\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "results = run_simulation(system, update_func_quad)\n",
    "plot_results(census, un, results, 'Quadratic model')\n",
    "savefig('figs/chap03-fig04.pdf')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Solution goes here"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}