{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Functions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A function in Python is defined using the keyword `def`, followed by a function name, a signature within parentheses `()`, and a colon `:`. The following code, with one additional level of indentation, is the function body."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def func0():   \n",
    "    print(\"test\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "test\n"
     ]
    }
   ],
   "source": [
    "func0()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Optionally, but highly recommended, we can define a so called \"docstring\", which is a description of the functions purpose and behaivor. The docstring should follow directly after the function definition, before the code in the function body."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def func1(s):\n",
    "    \"\"\"\n",
    "    Print a string 's' and tell how many characters it has    \n",
    "    \"\"\"\n",
    "    \n",
    "    print(s + \" has \" + str(len(s)) + \" characters\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Help on function func1 in module __main__:\n",
      "\n",
      "func1(s)\n",
      "    Print a string 's' and tell how many characters it has\n",
      "\n"
     ]
    }
   ],
   "source": [
    "help(func1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "test has 4 characters\n"
     ]
    }
   ],
   "source": [
    "func1(\"test\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Functions that returns a value use the `return` keyword:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def square(x):\n",
    "    \"\"\"\n",
    "    Return the square of x.\n",
    "    \"\"\"\n",
    "    return x ** 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "16"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y = square(4); y"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can return multiple values from a function using tuples (see above):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def powers(x):\n",
    "    \"\"\"\n",
    "    Return a few powers of x.\n",
    "    \"\"\"\n",
    "    return x ** 2, x ** 3, x ** 4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(9, 27, 81)"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "powers(3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "81\n"
     ]
    }
   ],
   "source": [
    "x2, x3, x4 = powers(3)\n",
    "\n",
    "print(x4)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Default argument and keyword arguments"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In a definition of a function, we can give default values to the arguments the function takes:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def myfunc(x, p=2, bug=False):\n",
    "    if bug:\n",
    "        print(\"evaluating myfunc for x = \" + str(x) + \" using exponent p = \" + str(p))\n",
    "    return x**p"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If we don't provide a value of the `debug` argument when calling the the function `myfunc` it defaults to the value provided in the function definition:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "125"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "myfunc(5,p=3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "evaluating myfunc for x = 5 using exponent p = 2\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "25"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "myfunc(5, bug=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If we explicitly list the name of the arguments in the function calls, they do not need to come in the same order as in the function definition. This is called *keyword* arguments, and is often very useful in functions that takes a lot of optional arguments."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "evaluating myfunc for x = 7 using exponent p = 3\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "343"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "myfunc(p=3, debug=True, x=7)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Anonymous/unnamed functions (lambda function)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In Python we can also create unnamed functions, using the `lambda` keyword:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "f1 = lambda x: x**2\n",
    "    \n",
    "# is equivalent to \n",
    "\n",
    "def f2(x):\n",
    "    return x**2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(4, 4)"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f1(2), f2(2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This technique is useful for example when we want to pass a simple function as an argument to another function, like this:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<map at 0x7f8e85f63240>"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# map is a built-in python function\n",
    "map(lambda x: x**2, range(-3,4))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[9, 4, 1, 0, 1, 4, 9]"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# in python 3 we can use `list(...)` to convert the iterator to an explicit list\n",
    "list(map(f2, range(-3,4)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[(11, -3), (3, 1), (1, 2), (5, 10)]"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def key(x):\n",
    "    return x[1]\n",
    "\n",
    "a = [(1, 2), (3, 1), (5, 10), (11, -3)]\n",
    "a.sort(key=key)\n",
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[(11, -3), (3, 1), (1, 2), (5, 10)]"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = [(1, 2), (3, 1), (5, 10), (11, -3)]\n",
    "a.sort(key=lambda x: x[1])\n",
    "a"
   ]
  }
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