Effective_Computation_in_Physics/ch05-functions.ipynb

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  {
   "cells": [
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def sagan():\n",
      "    quote = \"With insufficient data it is easy to go wrong.\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def null():\n",
      "    pass"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# define the function\n",
      "def forty_two():\n",
      "    return 42"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 3
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# call the function\n",
      "forty_two()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 4,
       "text": [
        "42"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# call the function, and print the result\n",
      "print(forty_two())"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "42\n"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# call the function, assign the result \n",
      "# to x, and print x\n",
      "x = forty_two()\n",
      "print(x)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "42\n"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def forty_two_or_bust(x):\n",
      "    if x:\n",
      "        print(42)\n",
      "    else:\n",
      "        print(0)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 7
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# call the function\n",
      "forty_two_or_bust(True)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "42\n"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "bust = False\n",
      "forty_two_or_bust(bust)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "0\n"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def power(base, x):\n",
      "    return base**x"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 10
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from math import sin\n",
      "\n",
      "def sin_inv_x(x):\n",
      "    if x == 0.0:\n",
      "        result = 0.0\n",
      "    else:\n",
      "        result = sin(1.0/x)\n",
      "    return result"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 11
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def power(base, x):\n",
      "    \"\"\"Computes base^x. Both base and x should be integers,\n",
      "    floats, or another numeric type.\n",
      "    \"\"\"\n",
      "    return base**x"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 12
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def line(x, a=1.0, b=0.0):\n",
      "    return a*x + b"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 13
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "line(42)            # no keyword args, returns 1*42 + 0"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 14,
       "text": [
        "42.0"
       ]
      }
     ],
     "prompt_number": 14
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "line(42, 2)         # a=2, returns 84"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 15,
       "text": [
        "84.0"
       ]
      }
     ],
     "prompt_number": 15
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "line(42, b=10)      # b=10, returns 52"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 16,
       "text": [
        "52.0"
       ]
      }
     ],
     "prompt_number": 16
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "line(42, b=10, a=2) # returns 94 "
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 17,
       "text": [
        "94"
       ]
      }
     ],
     "prompt_number": 17
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "line(42, a=2, b=10) # also returns 94 "
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 18,
       "text": [
        "94"
       ]
      }
     ],
     "prompt_number": 18
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Do not do this!\n",
      "def myappend(x, lyst=[]):\n",
      "    lyst.append(x)\n",
      "    return lyst"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 19
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "myappend(6)  # seems right"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 20,
       "text": [
        "[6]"
       ]
      }
     ],
     "prompt_number": 20
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "myappend(42) # hmmm..."
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 21,
       "text": [
        "[6, 42]"
       ]
      }
     ],
     "prompt_number": 21
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "myappend(12, [1, 16])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 22,
       "text": [
        "[1, 16, 12]"
       ]
      }
     ],
     "prompt_number": 22
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "myappend(65) # nope, not right!"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 23,
       "text": [
        "[6, 42, 65]"
       ]
      }
     ],
     "prompt_number": 23
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def myappend(x, lyst=None):\n",
      "    if lyst is None:\n",
      "        lyst = []\n",
      "    lyst.append(x)\n",
      "    return lyst"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 24
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "myappend(6)  "
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 25,
       "text": [
        "[6]"
       ]
      }
     ],
     "prompt_number": 25
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "myappend(42)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 26,
       "text": [
        "[42]"
       ]
      }
     ],
     "prompt_number": 26
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "myappend(12, [1, 16])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 27,
       "text": [
        "[1, 16, 12]"
       ]
      }
     ],
     "prompt_number": 27
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "myappend(65)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 28,
       "text": [
        "[65]"
       ]
      }
     ],
     "prompt_number": 28
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "max(6, 2)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 29,
       "text": [
        "6"
       ]
      }
     ],
     "prompt_number": 29
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "max(6, 42)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 30,
       "text": [
        "42"
       ]
      }
     ],
     "prompt_number": 30
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "max(1, 16, 12)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 31,
       "text": [
        "16"
       ]
      }
     ],
     "prompt_number": 31
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "max(65, 42, 2, 8)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 32,
       "text": [
        "65"
       ]
      }
     ],
     "prompt_number": 32
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def minimum(*args):\n",
      "    \"\"\"Takes any number of arguments!\"\"\"\n",
      "    m = args[0]\n",
      "    for x in args[1:]:\n",
      "        if x < m:\n",
      "          m = x\n",
      "    return m "
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 33
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "minimum(6, 42)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 34,
       "text": [
        "6"
       ]
      }
     ],
     "prompt_number": 34
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "data = [65, 42, 2, 8]\n",
      "minimum(*data)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 35,
       "text": [
        "2"
       ]
      }
     ],
     "prompt_number": 35
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def blender(*args, **kwargs):\n",
      "    \"\"\"Will it?\"\"\"\n",
      "    print(args, kwargs)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 36
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "blender(\"yes\", 42)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "('yes', 42) {}\n"
       ]
      }
     ],
     "prompt_number": 37
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "blender(z=6, x=42)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "() {'z': 6, 'x': 42}\n"
       ]
      }
     ],
     "prompt_number": 38
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "blender(\"no\", [1], \"yes\", z=6, x=42)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "('no', [1], 'yes') {'z': 6, 'x': 42}\n"
       ]
      }
     ],
     "prompt_number": 39
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "t = (\"no\",)\n",
      "d = {\"mom\": \"ionic\"}\n",
      "blender(\"yes\", kid=\"covalent\", *t, **d)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "('yes', 'no') {'mom': 'ionic', 'kid': 'covalent'}\n"
       ]
      }
     ],
     "prompt_number": 40
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def momentum_energy(m, v):\n",
      "    p = m * v\n",
      "    e = 0.5 * m * v**2\n",
      "    return p, e"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 41
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# returns a tuple\n",
      "p_e = momentum_energy(42.0, 65.0)\n",
      "print(p_e)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "(2730.0, 88725.0)\n"
       ]
      }
     ],
     "prompt_number": 42
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# unpacks the tuple\n",
      "mom, eng = momentum_energy(42.0, 65.0)\n",
      "print(mom)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "2730.0\n"
       ]
      }
     ],
     "prompt_number": 43
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# global scope\n",
      "a = 6\n",
      "b = 42\n",
      "\n",
      "def func(x, y):\n",
      "    # local scope\n",
      "    z = 16\n",
      "    return a*x + b*y + z\n",
      "\n",
      "# global scope\n",
      "c = func(1, 5)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 44
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# global scope\n",
      "a = 6\n",
      "b = 42\n",
      "\n",
      "def outer(m, n):\n",
      "    # outer's scope\n",
      "    p = 10 \n",
      "\n",
      "    def inner(x, y):\n",
      "        # inner's scope\n",
      "        return a*p*x + b*n*y\n",
      "\n",
      "    # outer's scope\n",
      "    return inner(m+1, n+1)\n",
      "\n",
      "# global scope\n",
      "c = outer(1, 5)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 45
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "a = 6\n",
      "\n",
      "def a_global():\n",
      "    print(a)\n",
      "\n",
      "def a_local():\n",
      "    a = 42\n",
      "    print(a)\n",
      "\n",
      "a_global()\n",
      "a_local()\n",
      "print(a)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "6\n",
        "42\n",
        "6\n"
       ]
      }
     ],
     "prompt_number": 46
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "a = \"A\"\n",
      "\n",
      "def func():\n",
      "    # you cannot use the global 'a' because...\n",
      "    print(\"Big \" + a)\n",
      "    # a local 'a' is eventually defined!\n",
      "    a = \"a\"\n",
      "    print(\"small \" + a)\n",
      "\n",
      "func()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "ename": "UnboundLocalError",
       "evalue": "local variable 'a' referenced before assignment",
       "output_type": "pyerr",
       "traceback": [
        "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m\n\u001b[1;31mUnboundLocalError\u001b[0m                         Traceback (most recent call last)",
        "\u001b[1;32m<ipython-input-47-fe5d3736f26c>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m()\u001b[0m\n\u001b[0;32m      8\u001b[0m     \u001b[0mprint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;34m\"small \"\u001b[0m \u001b[1;33m+\u001b[0m \u001b[0ma\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      9\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m---> 10\u001b[1;33m \u001b[0mfunc\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m",
        "\u001b[1;32m<ipython-input-47-fe5d3736f26c>\u001b[0m in \u001b[0;36mfunc\u001b[1;34m()\u001b[0m\n\u001b[0;32m      3\u001b[0m \u001b[1;32mdef\u001b[0m \u001b[0mfunc\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      4\u001b[0m     \u001b[1;31m# you cannot use the global 'a' because...\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m----> 5\u001b[1;33m     \u001b[0mprint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;34m\"Big \"\u001b[0m \u001b[1;33m+\u001b[0m \u001b[0ma\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m      6\u001b[0m     \u001b[1;31m# a local 'a' is eventually defined!\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      7\u001b[0m     \u001b[0ma\u001b[0m \u001b[1;33m=\u001b[0m \u001b[1;34m\"a\"\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
        "\u001b[1;31mUnboundLocalError\u001b[0m: local variable 'a' referenced before assignment"
       ]
      }
     ],
     "prompt_number": 47
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "a = \"A\"\n",
      "\n",
      "def func():\n",
      "    global a\n",
      "    print(\"Big \" + a)\n",
      "    a = \"a\"\n",
      "    print(\"small \" + a)\n",
      "\n",
      "func()\n",
      "print(\"global \" + a)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Big A\n",
        "small a\n",
        "global a\n"
       ]
      }
     ],
     "prompt_number": 48
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# DO NOT RUN THIS\n",
      "#def func():\n",
      "#    func()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 49
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def fib(n):\n",
      "    if n == 0 or n == 1:\n",
      "        return n\n",
      "    else:\n",
      "        return fib(n - 1) + fib(n - 2)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 50
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import sys\n",
      "sys.getrecursionlimit()      # return the current limit\n",
      "sys.setrecursionlimit(8128)  # change the limit to 8128"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 51
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# a simple lambda\n",
      "lambda x: x**2"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 52,
       "text": [
        "<function __main__.<lambda>>"
       ]
      }
     ],
     "prompt_number": 52
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# a lambda that is called after it is defined\n",
      "(lambda x, y=10: 2*x + y)(42)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 53,
       "text": [
        "94"
       ]
      }
     ],
     "prompt_number": 53
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# just because it is anonymous doesn't mean we can't give it a name!\n",
      "f = lambda: [x**2 for x in range(10)]\n",
      "f()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 54,
       "text": [
        "[0, 1, 4, 9, 16, 25, 36, 49, 64, 81]"
       ]
      }
     ],
     "prompt_number": 54
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# a lambda as a dict value\n",
      "d = {'null': lambda *args, **kwargs: None}"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 55
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# a lambda as a keyword argument f in another function\n",
      "def func(vals, f=lambda x: sum(x)/len(x)):\n",
      "    f(vals)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 56
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# a lambda as a keyword argument in a function call\n",
      "func([6, 28, 496, 8128], lambda data: sum([x**2 for x in data]))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 57
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "nums = [8128, 6, 496, 28]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 58
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "sorted(nums)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 59,
       "text": [
        "[6, 28, 496, 8128]"
       ]
      }
     ],
     "prompt_number": 59
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "sorted(nums, key=lambda x: x%13)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 60,
       "text": [
        "[496, 28, 8128, 6]"
       ]
      }
     ],
     "prompt_number": 60
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def countdown():\n",
      "    yield 3\n",
      "    yield 2\n",
      "    yield 1\n",
      "    yield 'Blast off!'"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 61
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# generator\n",
      "g = countdown()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 62
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "next(g)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 63,
       "text": [
        "3"
       ]
      }
     ],
     "prompt_number": 63
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "x = next(g)\n",
      "print(x)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "2\n"
       ]
      }
     ],
     "prompt_number": 64
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "y, z = next(g), next(g)\n",
      "print(z)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Blast off!\n"
       ]
      }
     ],
     "prompt_number": 65
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "next(g)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "ename": "StopIteration",
       "evalue": "",
       "output_type": "pyerr",
       "traceback": [
        "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m\n\u001b[1;31mStopIteration\u001b[0m                             Traceback (most recent call last)",
        "\u001b[1;32m<ipython-input-66-5f315c5de15b>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m()\u001b[0m\n\u001b[1;32m----> 1\u001b[1;33m \u001b[0mnext\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mg\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m",
        "\u001b[1;31mStopIteration\u001b[0m: "
       ]
      }
     ],
     "prompt_number": 66
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "for t in countdown():\n",
      "    if isinstance(t, int):\n",
      "        message = \"T-\" + str(t)\n",
      "    else:\n",
      "        message = t\n",
      "    print(message)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "T-3\n",
        "T-2\n",
        "T-1\n",
        "Blast off!\n"
       ]
      }
     ],
     "prompt_number": 67
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def square_plus_one(n):\n",
      "    for x in range(n):\n",
      "        x2 = x * x\n",
      "        yield x2 + 1"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 68
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "for sp1 in square_plus_one(3):\n",
      "    print(sp1)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "1\n",
        "2\n",
        "5\n"
       ]
      }
     ],
     "prompt_number": 69
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# define a subgenerator\n",
      "def yield_all(x):\n",
      "    for i in x:\n",
      "        yield i\n",
      "\n",
      "# palindrome using yield froms\n",
      "def palindromize(x):\n",
      "    yield from yield_all(x)\n",
      "    yield from yield_all(x[::-1])\n",
      "\n",
      "# the above is equivalent to this full expansion:\n",
      "def palindromize_explicit(x):\n",
      "    for i in x:\n",
      "        yield i\n",
      "    for i in x[::-1]:\n",
      "        yield i"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 70
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def null(f):\n",
      "    \"\"\"Always return None.\"\"\"\n",
      "    return\n",
      "\n",
      "def identity(f):\n",
      "    \"\"\"Return the function.\"\"\"\n",
      "    return f\n",
      "\n",
      "def self_referential(f):\n",
      "    \"\"\"Return the decorator.\"\"\"\n",
      "    return self_referential"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 71
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "@null\n",
      "def nargs(*args, **kwargs):\n",
      "    return len(args) + len(kwargs)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 72
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def nargs(*args, **kwargs):\n",
      "    return len(args) + len(kwargs)\n",
      "nargs = null(nargs)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 73
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def plus1(f):\n",
      "    def wrapper(*args, **kwargs):\n",
      "        return f(*args, **kwargs) + 1\n",
      "    return wrapper"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 74
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "@plus1\n",
      "def power(base, x):\n",
      "    return base**x\n",
      "\n",
      "power(4, 2)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 75,
       "text": [
        "17"
       ]
      }
     ],
     "prompt_number": 75
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "@plus1\n",
      "@identity\n",
      "@plus1\n",
      "@plus1\n",
      "def root(x):\n",
      "    return x**0.5\n",
      "\n",
      "root(4)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 76,
       "text": [
        "5.0"
       ]
      }
     ],
     "prompt_number": 76
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def plus_n(n):\n",
      "    def dec(f):\n",
      "        def wrapper(*args, **kwargs):\n",
      "            return f(*args, **kwargs) + n\n",
      "        return wrapper\n",
      "    return dec"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 77
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "@plus_n(6)\n",
      "def root(x):\n",
      "    return x**0.5\n",
      "\n",
      "root(4)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 78,
       "text": [
        "8.0"
       ]
      }
     ],
     "prompt_number": 78
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "max = plus1(max)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 79
    }
   ],
   "metadata": {}
  }
 ]
}