{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 函数"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 定义函数"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "函数`function`，通常接受输入参数，并有返回值。\n",
    "\n",
    "它负责完成某项特定任务，而且相较于其他代码，具备相对的独立性。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def add(x, y):\n",
    "    \"\"\"Add two numbers\"\"\"\n",
    "    a = x + y\n",
    "    return a"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "函数通常有一下几个特征：\n",
    "- 使用 `def` 关键词来定义一个函数。\n",
    "-  `def` 后面是函数的名称，括号中是函数的参数，不同的参数用 `,` 隔开， `def foo():` 的形式是必须要有的，参数可以为空；\n",
    "- 使用缩进来划分函数的内容；\n",
    "-  `docstring` 用 `\"\"\"` 包含的字符串，用来解释函数的用途，可省略；\n",
    "-  `return` 返回特定的值，如果省略，返回 `None` 。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 使用函数"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "使用函数时，只需要将参数换成特定的值传给函数。\n",
    "\n",
    "**Python**并没有限定参数的类型，因此可以使用不同的参数类型："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "5\n",
      "foobar\n"
     ]
    }
   ],
   "source": [
    "print add(2, 3)\n",
    "print add('foo', 'bar')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "在这个例子中，如果传入的两个参数不可以相加，那么**Python**会将报错："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "ename": "TypeError",
     "evalue": "unsupported operand type(s) for +: 'int' and 'str'",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mTypeError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[1;32m<ipython-input-3-6f8dcf7eb280>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m()\u001b[0m\n\u001b[1;32m----> 1\u001b[1;33m \u001b[1;32mprint\u001b[0m \u001b[0madd\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m2\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;34m\"foo\"\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[1;32m<ipython-input-1-e831943cfaf2>\u001b[0m in \u001b[0;36madd\u001b[1;34m(x, y)\u001b[0m\n\u001b[0;32m      1\u001b[0m \u001b[1;32mdef\u001b[0m \u001b[0madd\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mx\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0my\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      2\u001b[0m     \u001b[1;34m\"\"\"Add two numbers\"\"\"\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m----> 3\u001b[1;33m     \u001b[0ma\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mx\u001b[0m \u001b[1;33m+\u001b[0m \u001b[0my\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m      4\u001b[0m     \u001b[1;32mreturn\u001b[0m \u001b[0ma\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;31mTypeError\u001b[0m: unsupported operand type(s) for +: 'int' and 'str'"
     ]
    }
   ],
   "source": [
    "print add(2, \"foo\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "如果传入的参数数目与实际不符合，也会报错："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "ename": "TypeError",
     "evalue": "add() takes exactly 2 arguments (3 given)",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mTypeError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[1;32m<ipython-input-4-ed7bae31fc7d>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m()\u001b[0m\n\u001b[1;32m----> 1\u001b[1;33m \u001b[1;32mprint\u001b[0m \u001b[0madd\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;36m2\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;36m3\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[1;31mTypeError\u001b[0m: add() takes exactly 2 arguments (3 given)"
     ]
    }
   ],
   "source": [
    "print add(1, 2, 3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "ename": "TypeError",
     "evalue": "add() takes exactly 2 arguments (1 given)",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mTypeError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[1;32m<ipython-input-5-a954233d3b0d>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m()\u001b[0m\n\u001b[1;32m----> 1\u001b[1;33m \u001b[1;32mprint\u001b[0m \u001b[0madd\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[1;31mTypeError\u001b[0m: add() takes exactly 2 arguments (1 given)"
     ]
    }
   ],
   "source": [
    "print add(1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "传入参数时，Python提供了两种选项，第一种是上面使用的按照位置传入参数，另一种则是使用关键词模式，显式地指定参数的值："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "5\n",
      "barfoo\n"
     ]
    }
   ],
   "source": [
    "print add(x=2, y=3)\n",
    "print add(y=\"foo\", x=\"bar\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "可以混合这两种模式："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "5\n"
     ]
    }
   ],
   "source": [
    "print add(2, y=3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 设定参数默认值"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "可以在函数定义的时候给参数设定默认值，例如："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def quad(x, a=1, b=0, c=0):\n",
    "    return a*x**2 + b*x + c"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "可以省略有默认值的参数："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "4.0\n"
     ]
    }
   ],
   "source": [
    "print quad(2.0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "可以修改参数的默认值："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10.0\n"
     ]
    }
   ],
   "source": [
    "print quad(2.0, b=3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "12.0\n"
     ]
    }
   ],
   "source": [
    "print quad(2.0, 2, c=4)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "这里混合了位置和指定两种参数传入方式，第二个2是传给 `a` 的。\n",
    "\n",
    "注意，在使用混合语法时，要注意不能给同一个值赋值多次，否则会报错，例如："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "ename": "TypeError",
     "evalue": "quad() got multiple values for keyword argument 'a'",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mTypeError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[1;32m<ipython-input-12-101d0c090bbb>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m()\u001b[0m\n\u001b[1;32m----> 1\u001b[1;33m \u001b[1;32mprint\u001b[0m \u001b[0mquad\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m2.0\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;36m2\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0ma\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;36m2\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[1;31mTypeError\u001b[0m: quad() got multiple values for keyword argument 'a'"
     ]
    }
   ],
   "source": [
    "print quad(2.0, 2, a=2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 接收不定参数"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "使用如下方法，可以使函数接受不定数目的参数："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def add(x, *args):\n",
    "    total = x\n",
    "    for arg in args:\n",
    "        total += arg\n",
    "    return total"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "这里，`*args` 表示参数数目不定，可以看成一个元组，把第一个参数后面的参数当作元组中的元素。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10\n",
      "3\n"
     ]
    }
   ],
   "source": [
    "print add(1, 2, 3, 4)\n",
    "print add(1, 2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "这样定义的函数不能使用关键词传入参数，要使用关键词，可以这样："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def add(x, **kwargs):\n",
    "    total = x\n",
    "    for arg, value in kwargs.items():\n",
    "        print \"adding \", arg\n",
    "        total += value\n",
    "    return total"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "这里， `**kwargs` 表示参数数目不定，相当于一个字典，关键词和值对应于键值对。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "adding  y\n",
      "adding  z\n",
      "adding  w\n",
      "46\n"
     ]
    }
   ],
   "source": [
    "print add(10, y=11, z=12, w=13)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "再看这个例子，可以接收任意数目的位置参数和键值对参数："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(2, 3) {'x': 'bar', 'z': 10}\n"
     ]
    }
   ],
   "source": [
    "def foo(*args, **kwargs):\n",
    "    print args, kwargs\n",
    "\n",
    "foo(2, 3, x='bar', z=10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "不过要按顺序传入参数，先传入位置参数 `args` ，在传入关键词参数 `kwargs` 。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 返回多个值"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "函数可以返回多个值："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "5.0 0.927295218002\n"
     ]
    }
   ],
   "source": [
    "from math import atan2\n",
    "\n",
    "def to_polar(x, y):\n",
    "    r = (x**2 + y**2) ** 0.5\n",
    "    theta = atan2(y, x)\n",
    "    return r, theta\n",
    "\n",
    "r, theta = to_polar(3, 4)\n",
    "print r, theta"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "事实上，**Python**将返回的两个值变成了元组："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(5.0, 0.9272952180016122)\n"
     ]
    }
   ],
   "source": [
    "print to_polar(3, 4)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "因为这个元组中有两个值，所以可以使用\n",
    "\n",
    "    r, theta = to_polar(3, 4)\n",
    "\n",
    "给两个值赋值。\n",
    "\n",
    "列表也有相似的功能："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1 2 3\n"
     ]
    }
   ],
   "source": [
    "a, b, c = [1, 2, 3]\n",
    "print a, b, c"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "事实上，不仅仅返回值可以用元组表示，也可以将参数用元组以这种方式传入："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "5\n"
     ]
    }
   ],
   "source": [
    "def add(x, y):\n",
    "    \"\"\"Add two numbers\"\"\"\n",
    "    a = x + y\n",
    "    return a\n",
    "    \n",
    "z = (2, 3)\n",
    "print add(*z)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "这里的`*`必不可少。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "事实上，还可以通过字典传入参数来执行函数："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "5\n"
     ]
    }
   ],
   "source": [
    "def add(x, y):\n",
    "    \"\"\"Add two numbers\"\"\"\n",
    "    a = x + y\n",
    "    return a\n",
    "\n",
    "w = {'x': 2, 'y': 3}\n",
    "print add(**w)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## map 方法生成序列"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "可以通过 `map` 的方式利用函数来生成序列："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 9, 16]\n"
     ]
    }
   ],
   "source": [
    "def sqr(x): \n",
    "    return x ** 2\n",
    "\n",
    "a = [2,3,4]\n",
    "print map(sqr, a)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "其用法为：\n",
    "    \n",
    "    map(aFun, aSeq)\n",
    "\n",
    "将函数 `aFun` 应用到序列 `aSeq` 上的每一个元素上，返回一个列表，不管这个序列原来是什么类型。\n",
    "\n",
    "事实上，根据函数参数的多少，`map` 可以接受多组序列，将其对应的元素作为参数传入函数："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[12, 8, 7]\n"
     ]
    }
   ],
   "source": [
    "def add(x, y): \n",
    "    return x + y\n",
    "\n",
    "a = (2,3,4)\n",
    "b = [10,5,3]\n",
    "print map(add,a,b)"
   ]
  }
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