Python_tutorial.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Python tutorial\n",
    "(It is inspired by [this tutorial](https://github.com/kuleshov/cs228-material/blob/master/tutorials/python/cs228-python-tutorial.ipynb) and [this tutorial](https://github.com/oseledets/nla2016/blob/master/lectures/Python_Intro.ipynb))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Basics of Python"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Some facts and references"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- Python developing was started in the late 1980s by [Guido van Rossum](https://gvanrossum.github.io/), who worked at CWI institute, Amsterdam. Now he works at Dropbox.\n",
    "<img src=./fig/van.jpg style=\"width: 150pt; align: center\">\n",
    "- The author called the language in honor of popular British comedy show \"Monty Pythons Flying Circus\"\n",
    "<img src=./fig/MontyPythonsFlyingCircus.png width=\"500\" height=\"400\">\n",
    "- Dynamic type system (PHP, Ruby, Javascript, Erlang, etc) vs. static type system (C/C++, Pascal, Java, etc)\n",
    "- Support multiple programming paradigms\n",
    "    - object-oriented\n",
    "    - imperative \n",
    "    - functional programming \n",
    "    - procedural\n",
    "- Python usage in industry and academia:\n",
    "    - Dropbox was written in Python\n",
    "    - Google: YouTube, YouTube API and others were written in Python\n",
    "    - Facebook\n",
    "    - SciPy stack replaces proprietary tools for scientific computing (MATLAB, Mathemathica)\n",
    "    - scikit-learn is a popular library for machine learning\n",
    "    - Web-development\n",
    "    - Pandas is a popular tool for data processing"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### References\n",
    "\n",
    "* The Hitchhiker’s Guide to Python:\n",
    "http://docs.python-guide.org/en/latest/\n",
    "\n",
    "* Hard way is easier: http://learnpythonthehardway.org\n",
    "\n",
    "* Python crash course from Google:\n",
    "https://developers.google.com/edu/python/\n",
    "\n",
    "* Official tutorial:\n",
    "https://docs.python.org/2/tutorial/\n",
    "\n",
    "* Python Tutor - code visualization (developed by MIT):\n",
    "http://pythontutor.com/\n",
    "\n",
    "* If you feel lost: https://www.codecademy.com/en/tracks/python\n",
    "\n",
    "* Related course in HSE [here](http://math-info.hse.ru/2015-16/%D0%9F%D1%80%D0%BE%D0%B3%D1%80%D0%B0%D0%BC%D0%BC%D0%B8%D1%80%D0%BE%D0%B2%D0%B0%D0%BD%D0%B8%D0%B5_%D0%BD%D0%B0_%D1%8F%D0%B7%D1%8B%D0%BA%D0%B5_Python_%D0%B4%D0%BB%D1%8F_%D1%81%D0%B1%D0%BE%D1%80%D0%B0_%D0%B8_%D0%B0%D0%BD%D0%B0%D0%BB%D0%B8%D0%B7%D0%B0_%D0%B4%D0%B0%D0%BD%D0%BD%D1%8B%D1%85)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Advanced references\n",
    "* Al Sweigart, \"Automate the Boring Stuff with Python\", https://automatetheboringstuff.com\n",
    "* Mark Lutz, \"Python Pocket Reference\" (250 pages)\n",
    "* Mark Lutz, \"Learning Python\" (1600 pages!)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### The Zen of Python, by Tim Peters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 185,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Zen of Python, by Tim Peters\n",
      "\n",
      "Beautiful is better than ugly.\n",
      "Explicit is better than implicit.\n",
      "Simple is better than complex.\n",
      "Complex is better than complicated.\n",
      "Flat is better than nested.\n",
      "Sparse is better than dense.\n",
      "Readability counts.\n",
      "Special cases aren't special enough to break the rules.\n",
      "Although practicality beats purity.\n",
      "Errors should never pass silently.\n",
      "Unless explicitly silenced.\n",
      "In the face of ambiguity, refuse the temptation to guess.\n",
      "There should be one-- and preferably only one --obvious way to do it.\n",
      "Although that way may not be obvious at first unless you're Dutch.\n",
      "Now is better than never.\n",
      "Although never is often better than *right* now.\n",
      "If the implementation is hard to explain, it's a bad idea.\n",
      "If the implementation is easy to explain, it may be a good idea.\n",
      "Namespaces are one honking great idea -- let's do more of those!\n"
     ]
    }
   ],
   "source": [
    "import this"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### How to write code\n",
    "\n",
    "- First of all your code has to be readable!\n",
    "    - Other people can easily understand what your code means and what operations it performs\n",
    "    - Variable, function and class names have to be meaningful\n",
    "    - Style of your code has to be consistent: formatting, spaces, etc\n",
    "\n",
    "- Style giudes:\n",
    "    - [PEP8](http://legacy.python.org/dev/peps/pep-0008/) (PEP = Python Enhancement Proposal)\n",
    "    - [Google Python style guide](https://google.github.io/styleguide/pyguide.html)\n",
    "    - write idiomatic code http://python.net/~goodger/projects/pycon/2007/idiomatic/handout.html"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Python installation\n",
    "\n",
    "- In this course we will use [Python 3.6 from Anaconda distribution](https://www.anaconda.com/download/)\n",
    "- Install it if you didn't do it earlier"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Python 2 vs. Python 3\n",
    "\n",
    "Check your Python version:\n",
    "```bash\n",
    "python --version\n",
    "```\n",
    "This course uses Python 3\n",
    "\n",
    "Main changes in Python 3\n",
    "\n",
    "- Key word ```print``` becomes function\n",
    "- ```xrange()``` is replaced by ```range()```\n",
    "- Integer division\n",
    "- Some methods return iterators, not lists\n",
    "- Support Unicode"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Data types"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- Number\n",
    "- String\n",
    "- Booleans"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Numbers\n",
    "\n",
    "- Float \n",
    "- Complex"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 186,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "15\n",
      "9\n",
      "36\n",
      "531441\n",
      "0.25\n",
      "0\n",
      "2\n"
     ]
    },
    {
     "ename": "NameError",
     "evalue": "name 'sqrt' is not defined",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-186-fff25d409c01>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[1;32m      8\u001b[0m \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mb\u001b[0m \u001b[0;34m//\u001b[0m \u001b[0ma\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      9\u001b[0m \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ma\u001b[0m \u001b[0;34m%\u001b[0m \u001b[0;36m5\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 10\u001b[0;31m \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0msqrt\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m12\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;31mNameError\u001b[0m: name 'sqrt' is not defined"
     ]
    }
   ],
   "source": [
    "a = 12\n",
    "b = 3\n",
    "print(a + b)\n",
    "print(a - b)\n",
    "print(a * b)\n",
    "print(b**a)\n",
    "print(b / a)\n",
    "print(b // a)\n",
    "print(a % 5)\n",
    "print(sqrt(12))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(3+3j)\n",
      "1.4142135623730951\n",
      "4j\n",
      "(-1-1j)\n",
      "(-0.3244472096893367+1.2481068139109326j)\n"
     ]
    }
   ],
   "source": [
    "a = 1 + 1j\n",
    "b = 2 + 2j\n",
    "print(a + b)\n",
    "print(abs(a))\n",
    "print(a * b)\n",
    "print(a - b)\n",
    "print(b**a)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- No unary operaors ++ and --"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(3+3j) (2+2j)\n",
      "(1+1j) (2+2j)\n",
      "4j (2+2j)\n",
      "(1+1j)\n"
     ]
    }
   ],
   "source": [
    "a += b\n",
    "print(a, b)\n",
    "a-= b\n",
    "print(a, b)\n",
    "a *= b\n",
    "print(a, b)\n",
    "a /= b\n",
    "print(a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 192,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.0\n",
      "4.81047738097\n",
      "6.12323399574e-17\n",
      "1.63312393532e+16\n",
      "1.25331413732\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "\n",
    "x = np.pi / 2\n",
    "print(np.sin(x))\n",
    "print(np.exp(x))\n",
    "print(np.cos(x))\n",
    "print(np.tan(x))\n",
    "print(np.sqrt(x))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### String\n",
    "\n",
    "- Immutable type\n",
    "- Sequence of symbols\n",
    "- Indexing and slicing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Moscow State University\n",
      "M\n",
      "ow State University\n",
      "Mosco\n",
      "scow Sta\n",
      "so t\n"
     ]
    }
   ],
   "source": [
    "mystring = \"Moscow State University\"\n",
    "print(mystring)\n",
    "print(mystring[0])\n",
    "print(mystring[4:])\n",
    "print(mystring[:5])\n",
    "print(mystring[2:10])\n",
    "print(mystring[2:10:2])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Moscow State University\n",
      "y\n",
      "rsity\n",
      "Moscow State Universi\n",
      "Univer\n",
      "Uie\n",
      "ytisrevinU etatS wocsoM\n"
     ]
    },
    {
     "ename": "TypeError",
     "evalue": "'str' object does not support item assignment",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mTypeError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-6-03479e704f3e>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[1;32m      6\u001b[0m \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mmystring\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m10\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m4\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[1;32m      7\u001b[0m \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mmystring\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 8\u001b[0;31m \u001b[0mmystring\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\"K\"\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;31mTypeError\u001b[0m: 'str' object does not support item assignment"
     ]
    }
   ],
   "source": [
    "print(mystring)\n",
    "print(mystring[-1])\n",
    "print(mystring[-5:])\n",
    "print(mystring[:-2])\n",
    "print(mystring[-10:-4])\n",
    "print(mystring[-10:-4:2])\n",
    "print(mystring[::-1])\n",
    "mystring[0] = \"K\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- Formatting output"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The most famous university in Russia is Moscow State University\n",
      "The most famous university in Russia is Moscow State University\n",
      "The most famous university in Moscow State University is Russia\n"
     ]
    }
   ],
   "source": [
    "sent = \"The most famous university in Russia is {}\".format(mystring)\n",
    "print(sent)\n",
    "sent = \"The most famous university in {} is {}\".format(\"Russia\", mystring)\n",
    "print(sent)\n",
    "sent = \"The most famous university in {1} is {0}\".format(\"Russia\", mystring)\n",
    "print(sent)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The number pi is 3.1415926536 and the number e is 2.7182818284590450907955983\n",
      "The number e is 2.71828\n"
     ]
    }
   ],
   "source": [
    "print(\"The number pi is {1:.10f} and the number e is {0:.25f}\".format(math.e, math.pi))\n",
    "print(\"The number e is {:.5f}\".format(math.e))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- String methods always return new string, no inplace operations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "moscow is a capital of russia   \n",
      "Moscow is a capital of russia   \n",
      "MOSCOW IS A CAPITAL OF RUSSIA   \n",
      "moscow\n",
      "moscow is a capital of russia\n",
      "mcassccasw is a capital casf russia   \n",
      "32\n",
      "29\n"
     ]
    }
   ],
   "source": [
    "mystring = \"moscow is a capital of russia   \"\n",
    "print(mystring)\n",
    "print(mystring.capitalize())\n",
    "print(mystring.upper())\n",
    "print(\"Moscow\".lower())\n",
    "print(mystring.strip())\n",
    "print(mystring.replace(\"o\", \"cas\"))\n",
    "print(len(mystring))\n",
    "print(len(mystring.strip()))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- Concatenation - always save result in a new string"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "MSU CMC\n"
     ]
    }
   ],
   "source": [
    "w1 = \"MSU\"\n",
    "w2 = \"CMC\"\n",
    "w3 = w1 + \" \" + w2\n",
    "print(w3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Booleans\n",
    "- True\n",
    "- False"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "False\n",
      "False\n",
      "True\n",
      "True\n"
     ]
    }
   ],
   "source": [
    "t = True\n",
    "f = False\n",
    "print(t and f)\n",
    "print(not t)\n",
    "print(t or f)\n",
    "print(t != f)  # XOR"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10 5\n",
      "5 10\n",
      "False\n",
      "False\n",
      "True\n",
      "False\n"
     ]
    }
   ],
   "source": [
    "a, b = 10, 5\n",
    "print(a, b)\n",
    "a, b = b, a   # Fast swap\n",
    "print(a, b)\n",
    "print(a == b)\n",
    "print(a > b)\n",
    "print(a < b)\n",
    "print(a >= b)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Conditions and loops\n",
    "\n",
    "- if-elif-else\n",
    "- for-loop\n",
    "- while-loop"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### if-elif-else\n",
    "\n",
    "```python\n",
    "if condition1:\n",
    "    pass\n",
    "elif condition2:\n",
    "    pass\n",
    "else:\n",
    "    pass\n",
    "```\n",
    "\n",
    "- Execute body of block that is first true"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0\n"
     ]
    }
   ],
   "source": [
    "# Try different x\n",
    "x = 40\n",
    "if x > 50:\n",
    "    x /= 2\n",
    "elif x > 70:\n",
    "    x += 10\n",
    "else:\n",
    "    x = 0\n",
    "print(x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### for-loop\n",
    "\n",
    "```python\n",
    "for a in sequence:\n",
    "    pass\n",
    "else:\n",
    "    pass\n",
    "```\n",
    "\n",
    "- Iterations over sequential data\n",
    "- May have ```else``` statement in the end to check success iterations over all elements of ```sequence``` without breaks or exceptions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "M\n",
      "S\n",
      "U\n"
     ]
    }
   ],
   "source": [
    "# mystring = \"Moscow\"\n",
    "mystring = \"MSU CMC\"\n",
    "for letter in mystring:\n",
    "    if letter != \" \":\n",
    "        print(letter)\n",
    "    else:\n",
    "        break\n",
    "else:\n",
    "    print(\"Check all letters!\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0\n",
      "2\n",
      "4\n",
      "6\n",
      "8\n"
     ]
    }
   ],
   "source": [
    "# Iteration over  numbers\n",
    "n = 10\n",
    "for i in range(n):\n",
    "    if i % 2 == 0:\n",
    "        print(i)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### while-loop\n",
    "\n",
    "```python\n",
    "while condition:\n",
    "    pass\n",
    "else:\n",
    "    pass\n",
    "```\n",
    "- The same as for-loop but we do not know when this loop will be finished\n",
    "- The same for ```else``` statement"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "9\n",
      "8\n",
      "7\n",
      "6\n",
      "5\n",
      "4\n",
      "3\n",
      "2\n",
      "1\n",
      "0\n",
      "OK!\n"
     ]
    }
   ],
   "source": [
    "n = 10\n",
    "while n > 0:\n",
    "    n -= 1\n",
    "    print(n)\n",
    "else:\n",
    "    print(\"OK!\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "4.0\n",
      "2.0\n",
      "1.0\n"
     ]
    }
   ],
   "source": [
    "m = 8\n",
    "while True:\n",
    "    if m % 2 == 0:\n",
    "        m /= 2\n",
    "    else:\n",
    "        break\n",
    "    print(m)\n",
    "else:\n",
    "    print(\"OK!\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Built-in containers\n",
    "\n",
    "| C++ | Python  |\n",
    "|:--------:|:-----:|\n",
    "|```std::vector```|list|\n",
    "|```std::map```| dict|\n",
    "|```std::set```| set|\n",
    "|```std::tuple```| tuple|"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### List\n",
    "\n",
    "- Mutable type\n",
    "- Store elements of different types\n",
    "- Resizeable\n",
    "- Indexing and slicing are similar to string\n",
    "- Complete docs [here](https://docs.python.org/3/tutorial/datastructures.html)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1, 20, 30, -3]\n",
      "[10, 'Russia', True]\n",
      "1\n",
      "[1000, 20, 30, -3]\n",
      "[1000, 20, 30, -3, 'insert']\n"
     ]
    },
    {
     "ename": "IndexError",
     "evalue": "list assignment index out of range",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mIndexError\u001b[0m                                Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-39-b03444f06b4b>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[1;32m      8\u001b[0m \u001b[0ml1\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0minsert\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m10\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m\"insert\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      9\u001b[0m \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ml1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 10\u001b[0;31m \u001b[0ml1\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m11\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m\"test\"\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;31mIndexError\u001b[0m: list assignment index out of range"
     ]
    }
   ],
   "source": [
    "l1 = [1, 20, 30, -3]\n",
    "print(l1)\n",
    "l2 = [10, \"Russia\", True]\n",
    "print(l2)\n",
    "print(l1[0])\n",
    "l1[0] = 1000\n",
    "print(l1)\n",
    "l1.insert(10, \"insert\")\n",
    "print(l1)\n",
    "l1[11] = \"test\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1000\n",
      "20\n",
      "30\n",
      "-3\n"
     ]
    }
   ],
   "source": [
    "for element in l1:\n",
    "    print(element)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1000, 20, 30, -3, 'False']\n",
      "False [1000, 20, 30, -3]\n",
      "[-3, 30, 20, 1000]\n"
     ]
    }
   ],
   "source": [
    "l1.append(\"False\")\n",
    "print(l1)\n",
    "final_value = l1.pop()\n",
    "print(final_value, l1)\n",
    "l1.reverse()\n",
    "print(l1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-3, 30, 20, 1000, 10, 'Russia', True]\n",
      "[-3, 30, 20, 1000, -3, 30, 20, 1000]\n",
      "[[-3, 30, 20, 1000], [-3, 30, 20, 1000]]\n",
      "[-3, 30, 20, 1000, 10, 'Russia', True]\n"
     ]
    },
    {
     "ename": "TypeError",
     "evalue": "unsupported operand type(s) for -: 'list' and 'list'",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mTypeError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-21-0d382559b67b>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[1;32m      4\u001b[0m \u001b[0ml1\u001b[0m \u001b[0;34m+=\u001b[0m \u001b[0ml2\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      5\u001b[0m \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ml1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 6\u001b[0;31m \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ml1\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0ml2\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;31mTypeError\u001b[0m: unsupported operand type(s) for -: 'list' and 'list'"
     ]
    }
   ],
   "source": [
    "print(l1 + l2)\n",
    "print(2 * l1)\n",
    "print(2 * [l1])\n",
    "l1 += l2\n",
    "print(l1)\n",
    "print(l1 - l2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- List comprehension"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0, 1, 4, 9, 16]\n",
      "[0, 1, 4, 9, 16]\n",
      "[0, 4, 16]\n"
     ]
    }
   ],
   "source": [
    "nums = [0, 1, 2, 3, 4]\n",
    "squares = []\n",
    "for x in nums:\n",
    "    squares.append(x ** 2)\n",
    "print(squares)\n",
    "# Or\n",
    "squares = [x ** 2 for x in nums]\n",
    "print(squares)\n",
    "# And with if\n",
    "even_squares = [x ** 2 for x in nums if x % 2 == 0]\n",
    "print(even_squares)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[1, 2, 3], [10, 20, 30]]\n",
      "[[123, 2, 3], [10, 20, 30]]\n",
      "[10, 20, 'test']\n"
     ]
    }
   ],
   "source": [
    "l1= [1,2,3]\n",
    "l2 = [10, 20, 30]\n",
    "l = [l1, l2]\n",
    "print(l)\n",
    "l1[0] = 123\n",
    "print(l)\n",
    "l[1][2] = \"test\"\n",
    "print(l2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Tuple\n",
    "\n",
    "- Immutable type as a string\n",
    "- Indexing and slicing work again\n",
    "- Packing and unpacking variables"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(1, 2) Required 40 bytes\n",
      "[1, 2] Required 56 bytes\n"
     ]
    }
   ],
   "source": [
    "t1 = (1, 2)\n",
    "l1 = [1, 2]\n",
    "print(t1, \"Required {} bytes\".format(t1.__sizeof__()))\n",
    "print(l1, \"Required {} bytes\".format(l1.__sizeof__()))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1 2\n"
     ]
    },
    {
     "ename": "IndexError",
     "evalue": "tuple index out of range",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mIndexError\u001b[0m                                Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-24-919c6c456453>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mt1\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mt1\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 2\u001b[0;31m \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mt1\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m3\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;31mIndexError\u001b[0m: tuple index out of range"
     ]
    }
   ],
   "source": [
    "print(t1[0], t1[1])\n",
    "print(t1[3])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(1, 2, 4, 5)\n",
      "(2, 4)\n",
      "(5, 4, 2, 1)\n"
     ]
    },
    {
     "ename": "TypeError",
     "evalue": "'tuple' object does not support item assignment",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mTypeError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-25-d4bf1a581fb5>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[1;32m      3\u001b[0m \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mt3\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;36m3\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      4\u001b[0m \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mt3\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 5\u001b[0;31m \u001b[0mt3\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m3\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;36m4\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;31mTypeError\u001b[0m: 'tuple' object does not support item assignment"
     ]
    }
   ],
   "source": [
    "t3 = t1 + (4, 5)\n",
    "print(t3)\n",
    "print(t3[1:3])\n",
    "print(t3[::-1])\n",
    "t3[3] = 4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "([1, 2], [10, 20])\n",
      "([10, 2], [10, 20])\n"
     ]
    },
    {
     "ename": "TypeError",
     "evalue": "'tuple' object does not support item assignment",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mTypeError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-26-ff1a7fe81bb1>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[1;32m      3\u001b[0m \u001b[0mt4\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;36m10\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      4\u001b[0m \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mt4\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 5\u001b[0;31m \u001b[0mt4\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;36m5\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;31mTypeError\u001b[0m: 'tuple' object does not support item assignment"
     ]
    }
   ],
   "source": [
    "t4 = ([1,2], [10, 20])\n",
    "print(t4)\n",
    "t4[0][0] = 10\n",
    "print(t4)\n",
    "t4[0] = 5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0\n",
      "1\n"
     ]
    }
   ],
   "source": [
    "t5 = ()\n",
    "print(len(t5))\n",
    "t5 = 1,\n",
    "print(len(t5))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "apple blueberry orange\n"
     ]
    }
   ],
   "source": [
    "t6 = (\"apple\", \"blueberry\", \"orange\")\n",
    "apple, bb, orange = t6\n",
    "print(apple, bb, orange)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[(0, 0), (1, 1), (2, 4), (3, 9), (4, 16), (5, 25), (6, 36), (7, 49), (8, 64), (9, 81)]\n"
     ]
    }
   ],
   "source": [
    "l1 = [(i, i**2) for i in range(10)]\n",
    "print(l1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Dict\n",
    "\n",
    "- Store (key, value) pairs\n",
    "- Key has to be immutable type\n",
    "- Values for keys can be changed\n",
    "- Add new pairs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'cat': 12, 'dog': 40}\n",
      "12\n",
      "True\n"
     ]
    }
   ],
   "source": [
    "d = {\"cat\": 12, \"dog\": 40}\n",
    "print(d)\n",
    "print(d[\"cat\"])\n",
    "print(\"cat\" in d)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'cat': 12, 'dog': 40, 'fox': 34}\n"
     ]
    },
    {
     "ename": "TypeError",
     "evalue": "unhashable type: 'list'",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mTypeError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-4-1038b73d315f>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[1;32m      2\u001b[0m \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0md\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      3\u001b[0m \u001b[0md\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m3\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m\"tuple\"\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 4\u001b[0;31m \u001b[0md\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m2\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m3\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m\"list\"\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;31mTypeError\u001b[0m: unhashable type: 'list'"
     ]
    }
   ],
   "source": [
    "d[\"fox\"] = 34\n",
    "print(d)\n",
    "d[(1,2,3)] = \"tuple\"\n",
    "d[[1, 2, 3]] = \"list\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "cat 12\n",
      "dog 40\n",
      "fox 34\n",
      "(1, 2, 3) tuple\n"
     ]
    }
   ],
   "source": [
    "for key in d:\n",
    "    print(key, d[key])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "cat\n",
      "dog\n",
      "fox\n",
      "(1, 2, 3)\n"
     ]
    }
   ],
   "source": [
    "for key in d:\n",
    "    print(key)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "12\n",
      "40\n",
      "34\n",
      "tuple\n"
     ]
    }
   ],
   "source": [
    "for val in d.values():\n",
    "    print(val)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "cat 12\n",
      "dog 40\n",
      "fox 34\n",
      "(1, 2, 3) tuple\n"
     ]
    }
   ],
   "source": [
    "for k, v in d.items():\n",
    "    print(k, v)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- Dict comprehensions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{1: 2, 2: 4, 3: 6}\n"
     ]
    }
   ],
   "source": [
    "d2 = {key: 2*key for key in [1,2,3]}\n",
    "print(d2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Set\n",
    "\n",
    "- Unordered collection with no duplicate elements \n",
    "- Support mathematical operations like union, intersection, difference, and symmetric difference\n",
    "- Complete docs [here](https://docs.python.org/3/tutorial/datastructures.html#sets)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "set()\n",
      "{'r', 'a', 'b', 'c', 'd'} 5\n",
      "{'r', 'a', 'b', 'y', 'c', 'd'} 6\n",
      "{'r', 'b', 'y', 'c', 'd'} 5\n"
     ]
    }
   ],
   "source": [
    "s = set()\n",
    "print(s)\n",
    "string = \"abracadabra\"\n",
    "s = set(string)\n",
    "print(s, len(s))\n",
    "s.add(\"y\")\n",
    "print(s, len(s))\n",
    "s.remove(\"a\")\n",
    "print(s, len(s))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{56, 1, 3}\n",
      "{2}\n",
      "{1, 3, 10, 45, 56}\n",
      "{1, 2, 3, 10, 45, 56}\n"
     ]
    }
   ],
   "source": [
    "s1 = set([1,2,3,2,56])\n",
    "s2 = set([2,45,10])\n",
    "print(s1 - s2)\n",
    "print(s1 & s2)\n",
    "print(s1 ^ s2)\n",
    "print(s1 | s2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Other containers\n",
    "\n",
    "- You can use other containers, which are available in module [collections](https://docs.python.org/3/library/collections.html)\n",
    "- Just import it\n",
    "```python\n",
    "import collections\n",
    "```\n",
    "and you have other containers\n",
    "    - Deque\n",
    "    - OrderedDict\n",
    "    - ..."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Functions\n",
    "\n",
    "```python\n",
    "def function_name(arguments):\n",
    "#     make something\n",
    "    return something\n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "negative\n",
      "zero\n",
      "positive\n"
     ]
    }
   ],
   "source": [
    "def sign(x):\n",
    "    if x > 0:\n",
    "        return 'positive'\n",
    "    elif x < 0:\n",
    "        return 'negative'\n",
    "    else:\n",
    "        return 'zero'\n",
    "\n",
    "for x in [-1, 0, 2]:\n",
    "    print(sign(x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Hello, Ivan!\n",
      "HELLO, GEORGE\n"
     ]
    }
   ],
   "source": [
    "def say_hello(name, loud=False):\n",
    "    if loud:\n",
    "        print('HELLO, {}'.format(name.upper()))\n",
    "    else:\n",
    "        print('Hello, {}!'.format(name))\n",
    "\n",
    "say_hello('Ivan')\n",
    "say_hello('George', loud=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10\n",
      "args elements\n",
      "100\n",
      "string\n",
      "kwargs elements\n",
      "s1 10\n",
      "r2 (1, 67)\n"
     ]
    }
   ],
   "source": [
    "def test_func(x, *args, **kwargs):\n",
    "    print(x)\n",
    "    print(\"args elements\")\n",
    "    for l in args:\n",
    "        print(l)\n",
    "    print(\"kwargs elements\")\n",
    "    for key in kwargs:\n",
    "        print(key, kwargs[key])\n",
    "\n",
    "test_func(10, 100, \"string\", s1=10, r2=(1,67))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Classes\n",
    "\n",
    "- Syntax of class defining is straightforward\n",
    "- No destructors, because of garbage collector works \n",
    "- All methods are virtual and all members are public \n",
    "- But you can make memebers private with special approaches\n",
    "- Complete doc is [here](https://docs.python.org/3/tutorial/classes.html)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Hello, John\n",
      "HELLO, JOHN!\n"
     ]
    }
   ],
   "source": [
    "class Greeter:\n",
    "\n",
    "    # Constructor\n",
    "    def __init__(self, name):\n",
    "        self.name = name  # Create an instance variable\n",
    "\n",
    "    # Instance method\n",
    "    def greet(self, loud=False):\n",
    "        if loud:\n",
    "            print('HELLO, {}!'.format(self.name.upper()))\n",
    "        else:\n",
    "            print('Hello, {}'.format(self.name))\n",
    "\n",
    "g = Greeter('John')  # Construct an instance of the Greeter class\n",
    "g.greet()            # Call an instance method; prints \"Hello, Fred\"\n",
    "g.greet(loud=True)   # Call an instance method; prints \"HELLO, FRED!\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Modules\n",
    "\n",
    "- You can import modules with command \n",
    "```python\n",
    "import module_name\n",
    "```\n",
    "and use functions from this module as\n",
    "```python\n",
    "module_name.func()\n",
    "```\n",
    "- Other way is to use aliases\n",
    "```python\n",
    "import module_name as mn\n",
    "```\n",
    "and use functions from this module as\n",
    "```python\n",
    "mn.func()\n",
    "```\n",
    "- Other ways of importing are not appropriate"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exerсises\n",
    "\n",
    "1. Implement bubble-sort, merge-sort and quick-sort algorithms as three functions with input argument &mdash; array and output is sorted array. \n",
    "Compare its running time depending on the size of array and also compare running time your functions with built-in method ```sort```. \n",
    "Plot lines time vs. array size for every sorting algorithm. \n",
    "Time has to be computed with [%timeit magic](http://ipython.readthedocs.io/en/stable/interactive/magics.html). \n",
    "How plot lines see further in this notebook.  \n",
    "2. Show convergence of Taylor expansion for functions $\\sin(x)$, $e^x$ and $\\frac{1}{1 - x}$. \n",
    "Plot approximation error vs. number of items in sum. \n",
    "Compare different strategies of ordering items in sum. \n",
    "To compute required functions use ```numpy``` library\n",
    "\n",
    "3. Implement function that tests if given number is prime or not.\n",
    "Input is positive integer, output is ```True``` or ```False```."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Your code is here"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## NumPy, SciPy & Matplotlib\n",
    "\n",
    "- Numpy is the core library for scientific computing in Python \n",
    "- It provides a high-performance multidimensional array object, and tools for working with these arrays\n",
    "- For Matlab users [here](http://scipy.github.io/old-wiki/pages/NumPy_for_Matlab_Users) is great tutorial\n",
    "- SciPy provides tools for working with sparse matrices\n",
    "- Matplotlib is a library to plot your data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "### NumPy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 145,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 0.  0.  0.  0.  0.]\n",
      "[ 1.  1.  1.  1.  1.]\n",
      "[ 0.15578491  0.6744865   0.51882869  0.19480641  0.83091029]\n",
      "[-1.040755    1.393661    0.86498159  0.7941398   1.57691698]\n",
      "[3 1 2 0 2]\n",
      "[[ 1.  0.  0.  0.  0.]\n",
      " [ 0.  1.  0.  0.  0.]\n",
      " [ 0.  0.  1.  0.  0.]\n",
      " [ 0.  0.  0.  1.  0.]\n",
      " [ 0.  0.  0.  0.  1.]]\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "\n",
    "n = 5\n",
    "print(np.zeros(n))\n",
    "print(np.ones(n))\n",
    "print(np.random.rand(n))\n",
    "print(np.random.randn(n))\n",
    "print(np.random.randint(n, size=n))\n",
    "print(np.eye(n))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 136,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0 1 2 3 4] (5,)\n",
      "[ 0.74817055  0.99595381  0.32265908  0.10092179  0.44618531]\n",
      "[ 0.74817055  1.99595381  2.32265908  3.10092179  4.44618531]\n",
      "[-0.74817055  0.00404619  1.67734092  2.89907821  3.55381469]\n",
      "[0 2 4 6 8]\n",
      "[  0.           1.00406263   6.19849292  29.72598856   8.96488504]\n",
      "[ 0  1  4  9 16]\n",
      "[ 0.          1.          1.41421356  1.73205081  2.        ]\n",
      "3.72877857284\n",
      "30.0 30\n"
     ]
    }
   ],
   "source": [
    "x = np.array([i for i in range(n)])\n",
    "print(x, x.shape)\n",
    "y = np.random.rand(n)\n",
    "print(y)\n",
    "print(x + y)\n",
    "print(x - y)\n",
    "print(2 * x)\n",
    "print(x / y)\n",
    "print(np.power(x, 2))\n",
    "print(np.sqrt(x))\n",
    "print(x.dot(y))\n",
    "print(np.linalg.norm(x)**2, x.dot(x))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- Slicing is the same as for lists but slicing for numpy array returns **view** not a copy!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 135,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0 1 2]\n",
      "[1000    1    2    3    4] [1000    1    2]\n",
      "[1000    1    2    3    4] [-1000     1     2]\n"
     ]
    }
   ],
   "source": [
    "x_slice = x[:3]\n",
    "print(x_slice)\n",
    "x_slice[0] = 1000\n",
    "print(x, x_slice)\n",
    "x_copy = x[:3].copy()\n",
    "x_copy[0] = -1000\n",
    "print(x, x_copy)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 143,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 0.34044086  0.70008041  0.43877448  0.2505903   0.46584852]\n",
      " [ 0.58757611  0.03112146  0.54111497  0.10976203  0.93431785]\n",
      " [ 0.94782447  0.80881944  0.33501698  0.21048427  0.01999873]] [0 1 2 3 4]\n",
      "[ 4.19279435  5.17990889  2.19030113]\n",
      "[[ 0.34044086  1.70008041  2.43877448  3.2505903   4.46584852]\n",
      " [ 0.58757611  1.03112146  2.54111497  3.10976203  4.93431785]\n",
      " [ 0.94782447  1.80881944  2.33501698  3.21048427  4.01999873]]\n",
      "[[ 0.          0.70008041  0.87754896  0.7517709   1.86339409]\n",
      " [ 0.          0.03112146  1.08222993  0.32928609  3.73727141]\n",
      " [ 0.          0.80881944  0.67003395  0.63145282  0.07999492]]\n",
      "[[ 0.34044086 -0.29991959 -1.56122552 -2.7494097  -3.53415148]\n",
      " [ 0.58757611 -0.96887854 -1.45888503 -2.89023797 -3.06568215]\n",
      " [ 0.94782447 -0.19118056 -1.66498302 -2.78951573 -3.98000127]]\n",
      "[[        inf  0.70008041  0.21938724  0.0835301   0.11646213]\n",
      " [        inf  0.03112146  0.27055748  0.03658734  0.23357946]\n",
      " [        inf  0.80881944  0.16750849  0.07016142  0.00499968]]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alex/anaconda2/envs/p3/lib/python3.6/site-packages/ipykernel/__main__.py:8: RuntimeWarning: divide by zero encountered in true_divide\n"
     ]
    }
   ],
   "source": [
    "m, n = 3, n\n",
    "X = np.random.rand(m, n)\n",
    "print(X, x)\n",
    "print(X.dot(x))\n",
    "print(X + x)\n",
    "print(X * x)\n",
    "print(X - x)\n",
    "print(X / x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 144,
   "metadata": {},
   "outputs": [
    {
     "ename": "ValueError",
     "evalue": "shapes (3,4) and (5,) not aligned: 4 (dim 1) != 5 (dim 0)",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mValueError\u001b[0m                                Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-144-6ad24dcb348d>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mrandom\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mrand\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m3\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m4\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdot\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;31mValueError\u001b[0m: shapes (3,4) and (5,) not aligned: 4 (dim 1) != 5 (dim 0)"
     ]
    }
   ],
   "source": [
    "print(np.random.rand(3, 4).dot(x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 161,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 1.00246781  1.36795383  1.56123031]\n",
      " [ 0.97373788  1.89615967  1.08481103]\n",
      " [ 0.47428636  0.58404846  1.02623811]\n",
      " [ 0.80243703  1.16904652  1.41954766]\n",
      " [ 0.88505249  1.60420851  1.2212867 ]]\n"
     ]
    },
    {
     "ename": "ValueError",
     "evalue": "operands could not be broadcast together with shapes (5,5) (5,3) ",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mValueError\u001b[0m                                Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-161-9b6a6b228353>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[1;32m      2\u001b[0m \u001b[0mY\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mrandom\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mrand\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mn\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mm\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      3\u001b[0m \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mX\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdot\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mY\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 4\u001b[0;31m \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mX\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0mY\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;31mValueError\u001b[0m: operands could not be broadcast together with shapes (5,5) (5,3) "
     ]
    }
   ],
   "source": [
    "X = np.random.rand(n, n)\n",
    "Y = np.random.rand(n, m)\n",
    "print(X.dot(Y))\n",
    "print(X + Y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 163,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 0.88929366  0.17644666  0.10875208  0.16778466  0.24410678]\n",
      " [ 0.58166789  0.81937359  0.67989028  0.64453369  0.95157783]\n",
      " [ 0.7824564   0.1528505   0.82226366  0.64670831  0.23811461]]\n",
      "[ 0.88929366  0.58166789  0.7824564 ]\n",
      "[ 0.7824564   0.1528505   0.82226366  0.64670831  0.23811461]\n",
      "[[ 0.88929366  0.17644666  0.10875208  0.16778466  0.24410678]\n",
      " [ 0.7824564   0.1528505   0.82226366  0.64670831  0.23811461]]\n",
      "[[ 0.88929366  0.17644666  0.10875208  0.16778466]\n",
      " [ 0.58166789  0.81937359  0.67989028  0.64453369]\n",
      " [ 0.7824564   0.1528505   0.82226366  0.64670831]]\n",
      "[ 0.81937359  0.1528505 ]\n"
     ]
    }
   ],
   "source": [
    "X = np.random.rand(m, n)\n",
    "print(X)\n",
    "print(X[:, 0])\n",
    "print(X[-1, :])\n",
    "print(X[::2, :])\n",
    "print(X[:3, :-1])\n",
    "print(X[1:, 1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 164,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 0.88929366  0.17644666  0.10875208  0.16778466  0.24410678]\n",
      " [ 0.58166789  0.81937359  0.67989028  0.64453369  0.95157783]\n",
      " [ 0.7824564   0.1528505   0.82226366  0.64670831  0.23811461]]\n",
      "2.34543768133\n",
      "2.53093090622\n",
      "[ 0.88929366  0.81937359  0.82226366]\n",
      "[ 0.88929366  0.17644666  0.10875208  0.16778466  0.24410678  0.58166789\n",
      "  0.81937359  0.67989028  0.64453369  0.95157783  0.7824564   0.1528505\n",
      "  0.82226366  0.64670831  0.23811461]\n",
      "[[ 0.88929366  0.17644666  0.10875208  0.16778466  0.24410678  0.58166789\n",
      "   0.81937359  0.67989028  0.64453369  0.95157783  0.7824564   0.1528505\n",
      "   0.82226366  0.64670831  0.23811461]]\n"
     ]
    }
   ],
   "source": [
    "print(X)\n",
    "print(np.linalg.norm(X))\n",
    "print(np.trace(X))\n",
    "print(np.diag(X))\n",
    "print(X[X > 0.1])\n",
    "print(X.reshape(1, 15))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 165,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.1087520838\n",
      "7.90582058631\n",
      "[ 2.25341794  1.14867074  1.61090602  1.45902666  1.43379922]\n",
      "0.951577826961\n",
      "0.527054705754\n"
     ]
    }
   ],
   "source": [
    "print(X.min())\n",
    "print(X.sum())\n",
    "print(X.sum(axis=0))\n",
    "print(X.max())\n",
    "print(X.mean())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- NumPy includes implementations of almost any mathematical function and applies it element-wise to array\n",
    "- Complete doc is [here](https://docs.scipy.org/doc/numpy-1.13.0/reference/)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 166,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[  0.00000000e+00   1.00000000e+00   1.22464680e-16  -1.00000000e+00\n",
      "  -2.44929360e-16]\n",
      "[  1.00000000e+00   6.12323400e-17  -1.00000000e+00  -1.83697020e-16\n",
      "   1.00000000e+00]\n"
     ]
    }
   ],
   "source": [
    "args = np.arange(0, 2.5*np.pi, 0.5*np.pi)\n",
    "print(np.sin(args))\n",
    "print(np.cos(args))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 168,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "7.73773282507e-14\n"
     ]
    }
   ],
   "source": [
    "n = 100\n",
    "A = np.random.rand(n, n)\n",
    "x_true = np.random.randn(n)\n",
    "b = A.dot(x_true)\n",
    "x = np.linalg.solve(A, b)\n",
    "print(np.linalg.norm(x - x_true))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 167,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Try test numpy functions for your own research routines (optional)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "### SciPy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 171,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import scipy.sparse as spsp\n",
    "\n",
    "main_diagonal = -2 * np.ones(n, )\n",
    "suddiag_values = np.ones(n - 1,)\n",
    "diagonals = [main_diagonal, suddiag_values, suddiag_values]\n",
    "offsets = [0, 1, -1]\n",
    "A = spsp.diags(diagonals, offsets, shape=(n, n), format='csr')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- A lot of stuff for sparse matrices in different formats\n",
    "- Various functions about optimization, approximation, FFT, statistics, special functions and others\n",
    "- Complete doc is [here](https://docs.scipy.org/doc/scipy/reference/)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "### Matplotlib\n",
    "\n",
    "- Library to plot different linea nd figures in 2D and 3D\n",
    "- Tutorial for beginners is [here](https://matplotlib.org/users/pyplot_tutorial.html) and more complete one is [here](https://matplotlib.org/users/beginner.html)\n",
    "- You can tune all parameters of plot: labels, legends, fontsize, colours, ticks, markers, linewidth and many, many others\n",
    "- Label strings support $\\TeX$ notation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 174,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "from mpl_toolkits.mplot3d import Axes3D"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 190,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x7fda0c686f98>"
      ]
     },
     "execution_count": 190,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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40aa9aHRWDEEkNT6auy/owZwNe3hjkY1SMoFBVbnnve8pKfccQgoNsVFIjc2K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\nKwZjjDE1WDEYY4ypwYrBGGNMDf8P+yBEvUQ4xywAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fda0c70ac88>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.linspace(-4, 4)\n",
    "y = np.power(x, 2)\n",
    "plt.plot(x, y)\n",
    "plt.xlabel(\"$x$\", fontsize=12)\n",
    "plt.ylabel(\"$y$\", fontsize=12)\n",
    "plt.title(\"Parabola $y = x^2$\", fontsize=14)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 191,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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uuLu7s2jRItzd3bG1taVGjRppuidTz11m7H4ZUQn/uwwNKk1voGl2nBf0Sam9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\nKdRL3Thcc3sAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fda0c67fe80>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10, 8))\n",
    "plt.scatter(x, y, marker=\"x\", label=\"Parabola, $y = x^2$\", color=\"red\")\n",
    "plt.plot(x, x**3, label=\"Cube, $y = x^3$\", linewidth=6)\n",
    "plt.plot(x, 20 * np.sin(x), color=\"green\", label=\"Sine, $y = 20\\sin(x)$\")\n",
    "plt.legend(loc=\"best\", fontsize=14)\n",
    "plt.xticks(fontsize=20)\n",
    "_ = plt.yticks(fontsize=20)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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QVDalLbEIv2takiRJg6C8CTLmx5JUFk4ZkVQmpa1BrizzZsSVpOEuXMZCUsmUtgYZHEGW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\nJEmqYoIsSZIkVTFBliRJkqr8/x1Cq6r1GQfDAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fda0ae80518>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.linspace(1e-5, 1, 1000)\n",
    "y = 1. / x\n",
    "plt.figure(figsize=(10,4))\n",
    "plt.subplot(1,2,1)\n",
    "plt.plot(x, y)\n",
    "plt.yscale(\"log\")\n",
    "plt.title(\"Log scale\")\n",
    "\n",
    "plt.subplot(1,2,2)\n",
    "plt.plot(x, y)\n",
    "plt.title(\"Linear scale\")\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 187,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x7fda0ae82710>"
      ]
     },
     "execution_count": 187,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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UFBCNRvPywU8urc0G4/Is//tnvs3la/kca6XGZsBmLMY1NcuQw8WYI7P9otEY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+kYMo2+xFIUK3W3TXcB3wj9RrbbCIVCjI6OcurUKc6fP49CoeCWW25h9+7dmM3mpAttvhvfrYY7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RfP3116SnpzN16lQiIyNJSEhg8ODBbb4p1F9vodFoGDduHIqiUFBQwPnz5/H19SUgIMAsCyA7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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fda0ada5390>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "linear_index = np.linspace(0, np.pi, 10, endpoint=True)\n",
    "mesh_x, mesh_y = np.meshgrid(linear_index, linear_index)\n",
    "values_3D = np.sin(mesh_x + mesh_y)\n",
    "\n",
    "fig = plt.figure(figsize=(10,6))\n",
    "ax = fig.gca(projection=\"3d\")\n",
    "\n",
    "surf = ax.plot_surface(mesh_x, mesh_y, values_3D, cmap=\"RdBu\")\n",
    "ax.view_init(azim=-45, elev=30)\n",
    "fig.colorbar(surf)\n",
    "plt.title('The plot of $f(x, y) = \\sin(x+y)$')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### General rules about plots\n",
    "\n",
    "- Legends, labels, titles, ticks must be readable!\n",
    "- If most part of line is near 0, use log-scale for y-axis. The same is true for x-axis if necessary\n",
    "- Plot lines about the same issue in one plot"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "### Exercises\n",
    "\n",
    "1. Generate random low-rank matrix $500 \\times 500$ with rank $r = 10$, perform its SVD and plot how decreases singular values\n",
    "2. Compare running time of square lowrank matrix by vector multiplication in two cases:\n",
    "    - Matrix is given in lowrank format, i.e. product of 2 lowrank matrices\n",
    "    - Matrix is given as it is    \n",
    "Plot graphs time vs. dimension of the matrix for these two cases. Add legend and axis labels.\n",
    "3. Plot density function of normal distribution in 1D and 2D cases for the following parameters:\n",
    "    - $\\mu = 0, \\sigma = 1$\n",
    "    - $\\mu = 1.5, \\sigma = 0.1$\n",
    "    - $\\mu = -0.5, \\sigma = 3$\n",
    "    - $\\mu = (1, 1), \\Sigma = \\begin{bmatrix} \n",
    "    2 & 0\\\\\n",
    "    0 & 1\n",
    "    \\end{bmatrix}$\n",
    "    - $\\mu = (-1, 1), \\Sigma = \\begin{bmatrix} \n",
    "    2 & 0.1\\\\\n",
    "    1 & 1\n",
    "    \\end{bmatrix}$\n",
    "    \n",
    "For 1D case you can plot all lines in the single plot with legend. For 2D case use separate plots, add titles with corresponding parameters and colorbars."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Your code is here"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python [conda env:p3]",
   "language": "python",
   "name": "conda-env-p3-py"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}