{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "cell_style": "center",
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "![CDS 411 logo](../../img/cds-411-logo.png)\n",
    "\n",
    "# Class 7: System dynamics models: Growth and decay\n",
    "\n",
    "---\n",
    "\n",
    "![CC BY-SA 4.0 license](../../img/cc-by-sa.png)\n",
    "\n",
    "This notebook is licensed under a [Creative Commons Attribution-ShareAlike 4.0 International License](http://creativecommons.org/licenses/by-sa/4.0/)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "cell_style": "center",
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Load packages"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "cell_style": "center",
    "slideshow": {
     "cell_style": "split",
     "slide_type": "-"
    }
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Growth model for bacterial colony\n",
    "\n",
    "Iteratively solve the difference equation using numerical methods\n",
    "\n",
    "\\begin{equation}\n",
    "P(t)=P(t-\\Delta{}t)-rP(t-\\Delta{}t)\\Delta{}t\n",
    "\\end{equation}\n",
    "\n",
    "Assume the following constants:\n",
    "\n",
    "```python\n",
    "population = 100\n",
    "r = 0.1\n",
    "delta_t = 0.001\n",
    "time_of_simulation = 50.5\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Class-led solution\n",
    "\n",
    "How do I handle this in Python?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Define our constants:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "population = 100\n",
    "r = 0.1\n",
    "delta_t = 0.001\n",
    "time_of_simulation = 50.5"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Define a list to store our simulation history."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "trace = [[0, population]]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Iteratively solve the difference equation using a `for` loop and store the `[time_step, population]` pair in `trace`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "for time_step in range(1, int(time_of_simulation / delta_t) + 1):\n",
    "    population = population + r * population * delta_t\n",
    "    trace.append([time_step, population])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Convert our results into a DataFrame.\n",
    "\n",
    "**How can we extract out the first column and the second column of `trace`?**\n",
    "\n",
    "Remember, these are not `numpy` arrays!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "We use list comprehensions, for example:\n",
    "\n",
    "```\n",
    "[time_step[0] for time_step in trace]\n",
    "```\n",
    "\n",
    "This is equivalent to the following:\n",
    "\n",
    "```python\n",
    "column_one = []\n",
    "for time_step in trace:\n",
    "    column_one.append(time_step[0])\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "With list comprehensions, we can feed each column into `pd.DataFrame` as follows:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "bacteria_df = pd.DataFrame({\n",
    "    \"time_step\": [time_step[0] for time_step in trace],\n",
    "    \"population\": [time_step[1] for time_step in trace]\n",
    "})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "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>time_step</th>\n",
       "      <th>population</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0</td>\n",
       "      <td>100.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>100.010000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2</td>\n",
       "      <td>100.020001</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>3</td>\n",
       "      <td>100.030003</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>4</td>\n",
       "      <td>100.040006</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   time_step  population\n",
       "0          0  100.000000\n",
       "1          1  100.010000\n",
       "2          2  100.020001\n",
       "3          3  100.030003\n",
       "4          4  100.040006"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bacteria_df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "`time_step` is just the iteration index for each step of the simulation. To convert back to \"real\" time, multiply `time_step` by `delta_t`. With our Pandas data frame, this is simple to do:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "bacteria_df[\"time\"] = bacteria_df[\"time_step\"] * delta_t"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Finally, we should visualize the results of our simulation. Here's how to do it in `matplotlib`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()  # Define an \"axis\" object for more control over plot\n",
    "\n",
    "ax.plot(bacteria_df[\"time_step\"], bacteria_df[\"population\"]);\n",
    "\n",
    "# Don't forget to label your plot!\n",
    "ax.set_xlabel(\"time\")\n",
    "ax.set_ylabel(\"population\");"
   ]
  }
 ],
 "metadata": {
  "celltoolbar": "Slideshow",
  "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": "3.6.5"
  },
  "varInspector": {
   "cols": {
    "lenName": 16,
    "lenType": 16,
    "lenVar": 40
   },
   "kernels_config": {
    "python": {
     "delete_cmd_postfix": "",
     "delete_cmd_prefix": "del ",
     "library": "var_list.py",
     "varRefreshCmd": "print(var_dic_list())"
    },
    "r": {
     "delete_cmd_postfix": ") ",
     "delete_cmd_prefix": "rm(",
     "library": "var_list.r",
     "varRefreshCmd": "cat(var_dic_list()) "
    }
   },
   "types_to_exclude": [
    "module",
    "function",
    "builtin_function_or_method",
    "instance",
    "_Feature"
   ],
   "window_display": false
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}