{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "0af955cc",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Python Functions and Modules\n",
    "\n",
    "Feng Li\n",
    "\n",
    "School of Statistics and Mathematics\n",
    "\n",
    "Central University of Finance and Economics\n",
    "\n",
    "[feng.li@cufe.edu.cn](mailto:feng.li@cufe.edu.cn)\n",
    "\n",
    "[https://feng.li/python](https://feng.li/python)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "775c1af6",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Build-in Functions\n",
    "\n",
    "- The Python interpreter has a number of functions built into it that are always available. They are listed here in alphabetical order. Use e.g. `help(abs)` to see the function help.\n",
    "\n",
    "\n",
    "```py\n",
    "abs() aiter() all() any() anext() ascii() bin() bool() breakpoint() bytearray() bytes() callable() chr() classmethod() compile() complex() delattr() dict() dir() divmod() enumerate() eval() exec() filter() float() format() frozenset() getattr() globals() hasattr() hash() help() hex() id() input() int() isinstance() issubclass() iter() len() list() locals() map() max() memoryview() min() next() object() oct() open() ord() pow() print() property() range() repr() reversed() round() set() setattr() slice() sorted() staticmethod() str() sum() super() tuple() type() vars() zip() __import__()\n",
    "```\n",
    "\n",
    "- See https://docs.python.org/3/library/functions.html for a complete description of those functions.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f6904adb",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Import modules\n",
    "\n",
    "To import a module (like `math`) that is not in Python's default module, use"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "id": "07f678d3",
   "metadata": {
    "scrolled": true,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "import math"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9be4c800",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Then you can use all the mathematical functions inside `math` module as:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "id": "fd1b30c0",
   "metadata": {
    "scrolled": true,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "math.exp(0)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1ac8d5b9",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "- Alternatively, you can do the following module renaming when importing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "id": "d9920725",
   "metadata": {
    "scrolled": true,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.718281828459045"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import math as mt\n",
    "mt.exp(1)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cef8aea0",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- If you just want to import one or two functions from a module"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "id": "1e31ec02",
   "metadata": {
    "scrolled": false,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "20.085536923187668"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from math import exp\n",
    "exp(3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "id": "546b74b1",
   "metadata": {
    "scrolled": true,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.718281828459045"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from math import exp as myexp\n",
    "myexp(1)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "48e4b9ea",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Install third-party modules\n",
    "\n",
    "### through terminal\n",
    "\n",
    "- Use `pip` in a **terminal** to install a Python module from PyPi (https://pypi.org) on your user directory.\n",
    "```sh\n",
    "pip install numpy --user\n",
    "```\n",
    "- You could also specify a faster mirror close to you\n",
    "```sh\n",
    "pip install numpy --user -i https://pypi.tuna.tsinghua.edu.cn/simple\n",
    "```\n",
    "- Update a Python module\n",
    "```sh\n",
    "pip install pandas -U\n",
    "```\n",
    "- Remove a Python module\n",
    "```sh\n",
    "pip uninstall numpy \n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7a19460e",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### trhough Jupyter notebook\n",
    "\n",
    "You could issue the above commands within the Jupyter notebook. Just place the `!` in front of the command "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "cee4ead2",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Looking in indexes: https://mirrors.163.com/pypi/simple/\n",
      "Requirement already satisfied: pandas in /usr/local/lib/python3.9/dist-packages (1.3.4)\n",
      "Collecting pandas\n",
      "  Using cached https://mirrors.163.com/pypi/packages/48/b4/1081d66b71c4dfc1bc1e19d6f2abbf93ed42f69df7703eb323742d45423e/pandas-1.3.4-cp39-cp39-manylinux_2_17_x86_64.manylinux2014_x86_64.whl (11.5 MB)\n",
      "  Using cached https://mirrors.163.com/pypi/packages/03/ea/98d488a4047b3fd8075b5c1e00469ad42d715e2c1e4fd15fa1ffaef8d635/pandas-1.3.3-cp39-cp39-manylinux_2_17_x86_64.manylinux2014_x86_64.whl (11.5 MB)\n",
      "Requirement already satisfied: python-dateutil>=2.7.3 in /usr/lib/python3/dist-packages (from pandas) (2.8.1)\n",
      "Requirement already satisfied: numpy>=1.17.3 in /usr/local/lib/python3.9/dist-packages (from pandas) (1.21.2)\n",
      "Requirement already satisfied: pytz>=2017.3 in /usr/lib/python3/dist-packages (from pandas) (2021.3)\n"
     ]
    }
   ],
   "source": [
    "! pip3 install pandas -U"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c46b603d",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Control Flow Tools\n",
    "\n",
    "### The `if` statements\n",
    "Perhaps the most well-known statement type is the if statement. For example:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "c2abe7a9",
   "metadata": {
    "scrolled": true,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Zero\n"
     ]
    }
   ],
   "source": [
    "x = 0\n",
    "\n",
    "if x < 0:\n",
    "    x = 0\n",
    "    print('Negative changed to zero')\n",
    "elif x == 0:\n",
    "    print('Zero')\n",
    "elif x == 1:\n",
    "    print('Single')\n",
    "else:\n",
    "    print('More')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2c6e2c2e",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "**Note** \n",
    "\n",
    "- the comma/colon sign(:) should be right after `if`, `elif` and  `else` statement.\n",
    "- the `indentation` is very important. The first non-blank line after the first line of the string determines the amount of indentation for the entire documentation string."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b20ae42e",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### The `for` Statements"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "id": "f0fab355",
   "metadata": {
    "scrolled": true,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "cat 3\n",
      "window 6\n",
      "defenestrate 12\n"
     ]
    }
   ],
   "source": [
    "words = ['cat', 'window', 'defenestrate']\n",
    "for w in words:\n",
    "    print(w, len(w))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "921cf8d2",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1900 is not a leap year\n",
      "2000 is a leap year\n",
      "2004 is a leap year\n",
      "2011 is not a leap year\n",
      "2022 is not a leap year\n"
     ]
    }
   ],
   "source": [
    "x = [1900, 2000, 2004, 2011, 2022]\n",
    "\n",
    "for year in x:\n",
    "    if (year % 400 == 0) or (year % 100 != 0 and year % 4 == 0):\n",
    "        print(year, \"is a leap year\")\n",
    "    else:\n",
    "        print(year, \"is not a leap year\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "308c1141",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Defining Functions\n",
    "\n",
    "\n",
    "- We can create a function that writes the Fibonacci series to an arbitrary boundary.\n",
    "\n",
    "- The function should also include a proper help with the `docstring`\n",
    "\n",
    "    - The first line should always be a short, concise summary of the object's purpose. \n",
    "\n",
    "    - If there are more lines in the documentation string, the second line should be blank, visually separating the summary from the rest of the description. \n",
    "    \n",
    "    - The following lines should be one or more paragraphs describing the object's calling conventions, its side effects, etc."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "be87e07a",
   "metadata": {
    "scrolled": true,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "# 0, 1, 1, 2, 3, 5,\n",
    "def fib(n):    # write Fibonacci series up to n\n",
    "    \"\"\"Print a Fibonacci series up to n.\n",
    "    \n",
    "    par n: integer\n",
    "    out  : list\n",
    "    \"\"\" # the function help\n",
    "    a, b = 0, 1\n",
    "    while a < n:\n",
    "        print(a, end=' ')\n",
    "        #  better than print(a), why?\n",
    "        a, b = b, a+b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "fff7c7f6",
   "metadata": {
    "scrolled": false,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Help on function fib in module __main__:\n",
      "\n",
      "fib(n)\n",
      "    Print a Fibonacci series up to n.\n",
      "    \n",
      "    par n: integer\n",
      "    out  : list\n",
      "\n"
     ]
    }
   ],
   "source": [
    "help(fib)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "82eddb11",
   "metadata": {
    "scrolled": false,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765 10946 17711 "
     ]
    }
   ],
   "source": [
    "fib(20000)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "212d0198",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "- **Function could also have default values**. The most useful form is to specify a default value for one or more arguments. This creates a function that can be called with fewer arguments than it is defined to allow. For example:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "id": "98a86d98",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "def ask_ok(prompt, retries=4, complaint='Yes or no, please!'):\n",
    "    while True:\n",
    "        ok = input(prompt)\n",
    "        if ok in ('y', 'ye', 'yes'):\n",
    "            return True\n",
    "        if ok in ('n', 'no', 'nop', 'nope'):\n",
    "            return False\n",
    "        retries = retries - 1\n",
    "        if retries < 0:\n",
    "            raise IOError('too many tries')\n",
    "        print(complaint)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "id": "a8eb6a91",
   "metadata": {
    "scrolled": true,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Do you really want to go, dear?a\n",
      "Yes or no, please!\n",
      "Do you really want to go, dear?b\n",
      "Yes or no, please!\n",
      "Do you really want to go, dear?c\n"
     ]
    },
    {
     "ename": "OSError",
     "evalue": "too many tries",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mOSError\u001b[0m                                   Traceback (most recent call last)",
      "\u001b[0;32m/tmp/ipykernel_332089/131326152.py\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mask_ok\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"Do you really want to go, dear?\"\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mretries\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;32m/tmp/ipykernel_332089/2101535446.py\u001b[0m in \u001b[0;36mask_ok\u001b[0;34m(prompt, retries, complaint)\u001b[0m\n\u001b[1;32m      8\u001b[0m         \u001b[0mretries\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mretries\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      9\u001b[0m         \u001b[0;32mif\u001b[0m \u001b[0mretries\u001b[0m \u001b[0;34m<\u001b[0m \u001b[0;36m0\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 10\u001b[0;31m             \u001b[0;32mraise\u001b[0m \u001b[0mIOError\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'too many tries'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     11\u001b[0m         \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mcomplaint\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mOSError\u001b[0m: too many tries"
     ]
    }
   ],
   "source": [
    "ask_ok(\"Do you really want to go, dear?\", retries=2)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2419a1e9",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "- **Anonymous functions** Small anonymous functions can be created with the `lambda` keyword. \n",
    "\n",
    "Lambda functions can be used wherever function objects are required. They are syntactically restricted to a single expression. Semantically, they are just syntactic sugar for a normal function definition. Like nested function definitions, lambda functions can reference variables from the containing scope. The example uses a lambda expression to return a function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "ce432d1d",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "def make_incrementor(n):\n",
    "    return lambda x: x + n\n",
    "f = make_incrementor(42)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "id": "e4ec8c01",
   "metadata": {
    "scrolled": true,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "42"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f(0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "id": "15b8ab10",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "43"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f(1)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "aa37d302",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "The anonymous function is very useful in manipulating the `list` and Python DataFrame (`pandas`) "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2daef8c0",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "- If we save the function to a file named `mycollections.py`, we could import the function as follows\n",
    "```python\n",
    ">>> import mycollections\n",
    ">>> mycollections.fib(2000)\n",
    "0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597\n",
    ">>> from mycollections import fib\n",
    ">>> fib(2000)\n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "daffe267",
   "metadata": {},
   "outputs": [],
   "source": [
    "import mycollections"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "ec90694f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<function mycollections.fib(n)>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mycollections.fib"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "77fefda2",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0 1 1 2 3 5 8 13 21 34 55 89 "
     ]
    }
   ],
   "source": [
    "mycollections.fib(100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "40db07d2",
   "metadata": {},
   "outputs": [],
   "source": [
    "from mycollections import fib"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "b0e20576",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0 1 1 2 3 5 8 13 21 34 55 89 144 "
     ]
    }
   ],
   "source": [
    "fib(200)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "e6fe87b6",
   "metadata": {},
   "outputs": [],
   "source": [
    "def fib(n):    # write Fibonacci series up to n\n",
    "    \"\"\"Print a Fibonacci series up to n.\n",
    "\n",
    "        argument\n",
    "            n: numeric number\n",
    "\n",
    "        vaule\n",
    "            return Fibonacci series\n",
    "    \"\"\"\n",
    "    a, b = 0, 1\n",
    "    while a < n:\n",
    "        print(a, end=' ')\n",
    "        #  better than print(a), why?\n",
    "        a, b = b, a+b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "6ab7067f",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0 1 1 2 3 5 8 "
     ]
    }
   ],
   "source": [
    "fib(10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "ecb0a1c0",
   "metadata": {},
   "outputs": [],
   "source": [
    "import feng"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "53d9b21d",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0 1 1 2 3 5 8 13 21 34 55 89 "
     ]
    }
   ],
   "source": [
    "feng.fib(100)"
   ]
  }
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