{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<!--NOTEBOOK_HEADER-->\n",
    "*This notebook contains material from [CBE40455-2020](https://jckantor.github.io/CBE40455-2020);\n",
    "content is available [on Github](https://github.com/jckantor/CBE40455-2020.git).*\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<!--NAVIGATION-->\n",
    "< [3.0 Introduction to Discrete Event Simulation](https://jckantor.github.io/CBE40455-2020/03.00-Introduction-to-Discrete-Event-Modeling.html) | [Contents](toc.html) | [3.2 Introduction to Simpy](https://jckantor.github.io/CBE40455-2020/03.02-Introduction-to-Simpy.html) ><p><a href=\"https://colab.research.google.com/github/jckantor/CBE40455-2020/blob/master/docs/03.01-Python-Generators.ipynb\"> <img align=\"left\" src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open in Colab\" title=\"Open in Google Colaboratory\"></a><p><a href=\"https://jckantor.github.io/CBE40455-2020/03.01-Python-Generators.ipynb\"> <img align=\"left\" src=\"https://img.shields.io/badge/Github-Download-blue.svg\" alt=\"Download\" title=\"Download Notebook\"></a>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbpages": {
     "level": 1,
     "link": "[3.1 Python Generators](https://jckantor.github.io/CBE40455-2020/03.01-Python-Generators.html#3.1-Python-Generators)",
     "section": "3.1 Python Generators"
    }
   },
   "source": [
    "# 3.1 Python Generators"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbpages": {
     "level": 2,
     "link": "[3.1.1 A simple simulation model](https://jckantor.github.io/CBE40455-2020/03.01-Python-Generators.html#3.1.1-A-simple-simulation-model)",
     "section": "3.1.1 A simple simulation model"
    }
   },
   "source": [
    "## 3.1.1 A simple simulation model\n",
    "\n",
    "As a simple demonstration, let's consider the task of modeling the progess of a disease in a single person. The person will go through several stages of the disease\n",
    "\n",
    "$$\\text{Uninfected} \\quad \\longrightarrow \\quad \\text{Exposed} \\quad \\longrightarrow \\quad \\text{Infectious} \\quad \\longrightarrow \\quad \\text{Recovered}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbpages": {
     "level": 3,
     "link": "[3.1.1.1 Python generators](https://jckantor.github.io/CBE40455-2020/03.01-Python-Generators.html#3.1.1.1-Python-generators)",
     "section": "3.1.1.1 Python generators"
    }
   },
   "source": [
    "### 3.1.1.1 Python generators\n",
    "\n",
    "Python generators are the basic building block for discrete event simulation in Python. Python generators are similar to functions with three profound differences:\n",
    "\n",
    "1. They return values using the `yield` statement rather than a `return` statement. They don't disappear from memory until all statements have been executed.\n",
    "2. Because they don't disappear, they can start and be restarted with a `next` statement.\n",
    "3. Multiple instances of a generator may be working at the same time."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "nbpages": {
     "level": 3,
     "link": "[3.1.1.1 Python generators](https://jckantor.github.io/CBE40455-2020/03.01-Python-Generators.html#3.1.1.1-Python-generators)",
     "section": "3.1.1.1 Python generators"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def a_function():\n",
    "    return 3\n",
    "\n",
    "a_function()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "nbpages": {
     "level": 3,
     "link": "[3.1.1.1 Python generators](https://jckantor.github.io/CBE40455-2020/03.01-Python-Generators.html#3.1.1.1-Python-generators)",
     "section": "3.1.1.1 Python generators"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<generator object a_generator at 0x7fd645f02450>"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def a_generator():\n",
    "    yield 3\n",
    "    \n",
    "a_generator()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbpages": {
     "level": 3,
     "link": "[3.1.1.1 Python generators](https://jckantor.github.io/CBE40455-2020/03.01-Python-Generators.html#3.1.1.1-Python-generators)",
     "section": "3.1.1.1 Python generators"
    }
   },
   "source": [
    "Using a generator is different from a function because they don't disappear from memory"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "nbpages": {
     "level": 3,
     "link": "[3.1.1.1 Python generators](https://jckantor.github.io/CBE40455-2020/03.01-Python-Generators.html#3.1.1.1-Python-generators)",
     "section": "3.1.1.1 Python generators"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = a_generator()\n",
    "next(a)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbpages": {
     "level": 3,
     "link": "[3.1.1.1 Python generators](https://jckantor.github.io/CBE40455-2020/03.01-Python-Generators.html#3.1.1.1-Python-generators)",
     "section": "3.1.1.1 Python generators"
    }
   },
   "source": [
    "Let's create a generator that can return multiple values."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "nbpages": {
     "level": 3,
     "link": "[3.1.1.1 Python generators](https://jckantor.github.io/CBE40455-2020/03.01-Python-Generators.html#3.1.1.1-Python-generators)",
     "section": "3.1.1.1 Python generators"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1\n"
     ]
    }
   ],
   "source": [
    "def my_first_generator():\n",
    "    yield 1\n",
    "    yield 2\n",
    "    yield 3\n",
    "    yield 4\n",
    "\n",
    "a = my_first_generator()\n",
    "print(next(a))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbpages": {
     "level": 3,
     "link": "[3.1.1.1 Python generators](https://jckantor.github.io/CBE40455-2020/03.01-Python-Generators.html#3.1.1.1-Python-generators)",
     "section": "3.1.1.1 Python generators"
    }
   },
   "source": [
    "Let's get the next value."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "nbpages": {
     "level": 3,
     "link": "[3.1.1.1 Python generators](https://jckantor.github.io/CBE40455-2020/03.01-Python-Generators.html#3.1.1.1-Python-generators)",
     "section": "3.1.1.1 Python generators"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2\n"
     ]
    }
   ],
   "source": [
    "print(next(a))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbpages": {
     "level": 3,
     "link": "[3.1.1.1 Python generators](https://jckantor.github.io/CBE40455-2020/03.01-Python-Generators.html#3.1.1.1-Python-generators)",
     "section": "3.1.1.1 Python generators"
    }
   },
   "source": [
    "Let's create a second instance of the same generator."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "nbpages": {
     "level": 3,
     "link": "[3.1.1.1 Python generators](https://jckantor.github.io/CBE40455-2020/03.01-Python-Generators.html#3.1.1.1-Python-generators)",
     "section": "3.1.1.1 Python generators"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1\n"
     ]
    }
   ],
   "source": [
    "b = my_first_generator()\n",
    "print(next(b))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbpages": {
     "level": 3,
     "link": "[3.1.1.1 Python generators](https://jckantor.github.io/CBE40455-2020/03.01-Python-Generators.html#3.1.1.1-Python-generators)",
     "section": "3.1.1.1 Python generators"
    }
   },
   "source": [
    "Note how the instances each retain a unique state."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "nbpages": {
     "level": 3,
     "link": "[3.1.1.1 Python generators](https://jckantor.github.io/CBE40455-2020/03.01-Python-Generators.html#3.1.1.1-Python-generators)",
     "section": "3.1.1.1 Python generators"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "4\n",
      "2\n"
     ]
    }
   ],
   "source": [
    "print(next(a))\n",
    "print(next(b))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbpages": {
     "level": 4,
     "link": "[3.1.1.1.1 Exercise](https://jckantor.github.io/CBE40455-2020/03.01-Python-Generators.html#3.1.1.1.1-Exercise)",
     "section": "3.1.1.1.1 Exercise"
    }
   },
   "source": [
    "#### 3.1.1.1.1 Exercise\n",
    "\n",
    "Create a generator that produces a sequence of successive squares."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "nbpages": {
     "level": 4,
     "link": "[3.1.1.1.1 Exercise](https://jckantor.github.io/CBE40455-2020/03.01-Python-Generators.html#3.1.1.1.1-Exercise)",
     "section": "3.1.1.1.1 Exercise"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0\n",
      "1\n",
      "4\n",
      "9\n"
     ]
    }
   ],
   "source": [
    "def succ_sq():\n",
    "    k = 0\n",
    "    while True:\n",
    "        yield k**2\n",
    "        k = k + 1\n",
    "        \n",
    "a = succ_sq()\n",
    "print(next(a))\n",
    "print(next(a))\n",
    "print(next(a))\n",
    "print(next(a))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbpages": {
     "level": 4,
     "link": "[3.1.1.1.2 Exercise](https://jckantor.github.io/CBE40455-2020/03.01-Python-Generators.html#3.1.1.1.2-Exercise)",
     "section": "3.1.1.1.2 Exercise"
    }
   },
   "source": [
    "#### 3.1.1.1.2 Exercise\n",
    "\n",
    "Create generator that creates the Fibonacci sequence\n",
    "\n",
    "$$\\begin{align*}\n",
    "F_0 & = 0 \\\\\n",
    "F_1 & = 1 \\\\\n",
    "F_{n} &= F_{n-1} + F_{n-2}\n",
    "\\end{align*}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "nbpages": {
     "level": 4,
     "link": "[3.1.1.1.2 Exercise](https://jckantor.github.io/CBE40455-2020/03.01-Python-Generators.html#3.1.1.1.2-Exercise)",
     "section": "3.1.1.1.2 Exercise"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0\n",
      "1\n",
      "1\n",
      "2\n",
      "3\n",
      "5\n",
      "8\n",
      "13\n",
      "21\n",
      "34\n",
      "55\n",
      "89\n",
      "144\n",
      "233\n",
      "377\n",
      "610\n",
      "987\n",
      "1597\n",
      "2584\n",
      "4181\n"
     ]
    }
   ],
   "source": [
    "def fib():\n",
    "    a = 0\n",
    "    b = 1\n",
    "    yield a\n",
    "    yield b\n",
    "    while True:\n",
    "        a, b = b, a+b\n",
    "        yield b\n",
    "        \n",
    "f = fib()\n",
    "for k in range(0, 20):\n",
    "    print(next(f))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbpages": {
     "level": 4,
     "link": "[3.1.1.1.3 Exercise](https://jckantor.github.io/CBE40455-2020/03.01-Python-Generators.html#3.1.1.1.3-Exercise)",
     "section": "3.1.1.1.3 Exercise"
    }
   },
   "source": [
    "#### 3.1.1.1.3 Exercise\n",
    "\n",
    "Write a Python generator that simulates the response of a differential equation describing concentration in a stirred tank reactor.\n",
    "\n",
    "$$\\frac{dC}{dt} = -k C + q(t)$$\n",
    "\n",
    "where k = 1.0,  C(0) = 1.0 and q(t) = 0.5. Use Euler's approximation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {
    "nbpages": {
     "level": 4,
     "link": "[3.1.1.1.3 Exercise](https://jckantor.github.io/CBE40455-2020/03.01-Python-Generators.html#3.1.1.1.3-Exercise)",
     "section": "3.1.1.1.3 Exercise"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.0 1.0\n",
      "0.2 0.9\n",
      "0.4 0.82\n",
      "0.6 0.756\n",
      "0.8 0.705\n",
      "1.0 0.664\n",
      "1.2 0.631\n",
      "1.4 0.605\n",
      "1.6 0.584\n",
      "1.8 0.567\n",
      "2.0 0.554\n",
      "2.2 0.543\n",
      "2.4 0.534\n",
      "2.6 0.527\n",
      "2.8 0.522\n",
      "3.0 0.518\n",
      "3.2 0.514\n",
      "3.4 0.511\n",
      "3.6 0.509\n",
      "3.8 0.507\n",
      "4.0 0.506\n",
      "4.2 0.505\n",
      "4.4 0.504\n",
      "4.6 0.503\n",
      "4.8 0.502\n"
     ]
    }
   ],
   "source": [
    "q = 0.5\n",
    "\n",
    "def reactor(dt, k):\n",
    "    C = 1.0\n",
    "    t = 0.0\n",
    "    while t <= 5.0:\n",
    "        yield t, C\n",
    "        t = t + dt\n",
    "        C = C - k*C*dt + q*dt\n",
    "        \n",
    "a = reactor(0.2, 1.0)\n",
    "for t, C in a:\n",
    "    print(round(t, 2), round(C, 3))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<!--NAVIGATION-->\n",
    "< [3.0 Introduction to Discrete Event Simulation](https://jckantor.github.io/CBE40455-2020/03.00-Introduction-to-Discrete-Event-Modeling.html) | [Contents](toc.html) | [3.2 Introduction to Simpy](https://jckantor.github.io/CBE40455-2020/03.02-Introduction-to-Simpy.html) ><p><a href=\"https://colab.research.google.com/github/jckantor/CBE40455-2020/blob/master/docs/03.01-Python-Generators.ipynb\"> <img align=\"left\" src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open in Colab\" title=\"Open in Google Colaboratory\"></a><p><a href=\"https://jckantor.github.io/CBE40455-2020/03.01-Python-Generators.ipynb\"> <img align=\"left\" src=\"https://img.shields.io/badge/Github-Download-blue.svg\" alt=\"Download\" title=\"Download Notebook\"></a>"
   ]
  }
 ],
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